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Removing DESpecs directory which deserted to git
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Wed, 29 Nov 2017 16:55:37 +0100 |
| parents | 22d6a63640c6 |
| children |
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<?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:KN9XTZRQ.xml</dcterms:identifier> <dcterms:creator identifier="GND:118939297">Gravesande, Willem Jakob</dcterms:creator> <dcterms:title xml:lang="la">Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1721</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language> <dcterms:rights>CC-BY-SA</dcterms:rights> <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> <parameters>despecs=1.1.2</parameters> </metadata> <text xml:lang="la" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/> <figure> <image file="0001-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0001-01"/> </figure> <pb file="0002" n="2"/> <handwritten/> <figure> <image file="0002-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0002-01"/> </figure> <pb file="0003" n="3"/> <pb file="0004" n="4"/> <handwritten/> <handwritten/> <handwritten/> <handwritten/> <pb file="0005" n="5"/> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head1" xml:space="preserve"><emph style="red">PHYSICES</emph> <lb/>ELEMENTA <lb/><emph style="red">MATHEMATICA,</emph> <lb/>EXPERIMENTIS CONFIRMATA. <lb/>Sive <lb/>Introductio ad Philoſophiam <lb/><emph style="red">NEWTONIANAM.</emph> <lb/>Auctore <lb/><emph style="red">GULIELMO JACOBO ’s GRAVESANDE,</emph> <lb/>A. L. M., Fur. Vtr. & Phil. Doctore, Regiæ Societ. Lond. Socio, <lb/>Aſtron. & Math. in Acad. Lugd. Bat. Profeſſore ordinario. <lb/><emph style="red"><emph style="sc">Tomus</emph> <emph style="sc">Primus.</emph></emph> <lb/>Editio Secunda, auctior & emendatior.</head> <figure> <image file="0005-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0005-01"/> </figure> </div> <div xml:id="echoid-div3" type="section" level="1" n="3"> <head xml:id="echoid-head2" xml:space="preserve">LUGDUNI BATAVORUM, <lb/>Apud <emph style="red">PETRUM VANDER As,</emph> <lb/>Typographum Academiæ atque Civitatis.</head> <head xml:id="echoid-head3" xml:space="preserve">MDCC XXV. <lb/>Cum Privilegio Præputent. Ordd. Hollandiæ & Weſt-Friſiæ.</head> <pb file="0006" n="6" rhead="PRIVILEGIE."/> <p style="it"> <s xml:id="echoid-s1" xml:space="preserve">DE Staaten van Holland ende Weſt Vrieſtand, doen <lb/>te weeten, alſoo ons vertoont is by Pieter vander <lb/>Aa, Boekverkooper tot Leyden, hoe dat by Supplt. </s> <s xml:id="echoid-s2" xml:space="preserve">nu al-<lb/>dereerſt nieuw hadde gedrukt, Guilielmi Jacobi <lb/>’s Graveſande Phyſices Elementa Mathematica, <lb/>experimentis confirmata; </s> <s xml:id="echoid-s3" xml:space="preserve">ſive Introductio ad <lb/>Philoſophiam Newtonianam, in Quarto, cum fi-<lb/>guris, het eerſte deel, ſynde het vervolg van het voorſz. <lb/></s> <s xml:id="echoid-s4" xml:space="preserve">werk by den ſupplt. </s> <s xml:id="echoid-s5" xml:space="preserve">meede tegenwoordigh onder de <lb/>Pars, dog alſoo den Supplt beducht was, dat eenige <lb/>nydige, off baetſoekende Menſchen, ’t ſy binnen off <lb/>buytens Iands hem’tvoorn. </s> <s xml:id="echoid-s6" xml:space="preserve">werk ſouden mogen koo-<lb/>men naa te drucken, waar door by van alle ſyne <lb/>groote koſten en arbeyd tot nu toe gedaan en nog te <lb/>doen, ſoude verſteken ſyn, ſoo keerde den Supplt, ſig <lb/>tot Ons, verſoekende Ons Octroy, om het voorn werk <lb/>en vervolg voor den tyd van vyſtien eerſt achter <lb/>een volgende Faren, alleen met ſecluſie van allen an-<lb/>deren hier te Lande te mogen drucken, uyt te geven, <lb/>en te verkoopen in ſodanige taalen en formaten, als den <lb/>Supplt. </s> <s xml:id="echoid-s7" xml:space="preserve">voor ſyn intreſt beſt oirbaar ſoude vinden, <lb/>met expres verbod, waar by aan allen en eenen yge-<lb/>lycken buyten hem Supplt. </s> <s xml:id="echoid-s8" xml:space="preserve">off die ſyn actie off recht <lb/>naarmaels mochten verkrygen, door Ons verboden <lb/>wiert, het voorn. </s> <s xml:id="echoid-s9" xml:space="preserve">werk off vervolg van dienin eeni-<lb/>gerhande taalen te drucken, naa te drucken, tedoen <lb/>naadrucken, uyt te geven, te verkopen, ofte ver-<lb/>handelen, in ’t groot noch klein, in ’t geheel noch ten <lb/>deelen, noch met, noch ſonder Platen, noch onder <lb/>pretext van vermeerdering, verbeteringh, verande-<lb/>ringh van naem, valſche tekens, ofte hoedanigh het <lb/>ook genoemt ſoude mogen werden, ofte in eeniger-<lb/>hande taal off taalen buyten deſen Lande gedrukt <lb/>werdende, deſelve niet te mogen inbrengen, te ver-<lb/>handelen, off te verkopen, alles telkens op verbeurte <lb/>van alle de naagedrukte, ingebrachte, verhandelde off <lb/>verkogte Exemplaren, ſo dikwils en menigmaal als <lb/>deſelve ſouden werden achterhaelt, mitsgaders daar <lb/>en boven een boete van drie duyſent guldens by Ons <lb/>tegens de Contraventeurs te ſtellen. </s> <s xml:id="echoid-s10" xml:space="preserve">SO IST, dat Wy <lb/>de ſaake, en’ verſoeck voorſz. </s> <s xml:id="echoid-s11" xml:space="preserve">overgemerkt hebbende, <lb/>ende genegen weſende ter beede van den Supplt uyt <lb/>Onſe rechte wetenſchap, Souveraine maght, en au-<lb/>thoriteyt den ſelven Supplt. </s> <s xml:id="echoid-s12" xml:space="preserve">geconſenteert, geaccordeert, <lb/>ende geoctroyeert hebben, conſenteeren, accordeeren, <lb/>en octroyeren hem mitsdeſen, dat by geduyrende den <lb/>tyd van vyftien eerſt achter een volgende Faren het <lb/>voorſz. </s> <s xml:id="echoid-s13" xml:space="preserve">werk genaemt Guilielmi Jacobi’s Grave-<lb/>ſande Phyſices Elementa Mathematica, expe-<lb/>rimentis confirmata; </s> <s xml:id="echoid-s14" xml:space="preserve">ſive Introductio ad Phi-<lb/>loſophiam Newtonianam, in Quarto cum figuris <lb/>met het vervolg van dien, binnen den voorſz. </s> <s xml:id="echoid-s15" xml:space="preserve">On-<lb/>ſen Landen alleen ſal mogen drucken, doen drucken, <lb/>uytgeven, en verkoopen, in ſodanige taalen en for-<lb/>maten, als den Supplt. </s> <s xml:id="echoid-s16" xml:space="preserve">voor ſyn intreſt beſt oirbaar <lb/>ſal vinden, verbiedende daerom allen, ende een yge-<lb/>gelyken het ſelve Werk en Vervolg in eenigerhande <lb/>taalen in’t geheel, ofte ten deelen naa te drucken, <lb/>te doen naadrucken, te verhandelen, ofte te verko-<lb/>pen, ofte elders naergedrukt, binnen den ſelven On-<lb/>ſen Lande te brengen, uyt te geven, te verhandelen <lb/>ofte te verkoopen, op verbeurte van alle de naage-<lb/>druckte, ingebragte, verhandelde ofte verkogte Exem-<lb/>plaren, ende een boete van drie duyſent guldens daer <lb/>en boven te verbeuren, te appliceeren een derde part <lb/>voor den Officier, die de Calangie doen ſal, een derde <lb/>part voor den Armen der plaatſe daer de caſus voor-<lb/>vallen ſal, en de reſterende derde part voor den <lb/>Supplt. </s> <s xml:id="echoid-s17" xml:space="preserve">ende dit telkens ſoo menigmael als deſelve ſullen <lb/>werden achterhaelt, alles in dien verſtande, dat Wy <lb/>den Supplt. </s> <s xml:id="echoid-s18" xml:space="preserve">met de ſen Onſen Octroye alleen uillende <lb/>gratificeeren tot verhoedinge van ſyne ſchade door het <lb/>naadrucken van het voorſz. </s> <s xml:id="echoid-s19" xml:space="preserve">Werk of Vervolg, daar <lb/>door in geenen deele verſtaen den inhoude van dien <lb/>te authoriſeeren ofte te advoueeren, ende veel min <lb/>het ſelve onder Onſe protectie ende beſcherminge eenigh <lb/>meerder credit, aanſien ofte reputatie te geven, ne-<lb/>maar den Suppliant in cas daer in iets onbehoorlyks <lb/>ſoude influeeren, alle het ſelve tot ſynen laſte ſal ge-<lb/>houden weſen te verantwoorden, tot dien eynde wel <lb/>expreſſelyck begeerende. </s> <s xml:id="echoid-s20" xml:space="preserve">dat by aldien by deſen On-<lb/>ſen Octroye voor het ſelve Werk ſal willen ſtellen, <lb/>daar van geen geæbbrevieerde oft gecontraheerde men-<lb/>tie ſal mogen maeken, nemaer gehouden ſal weſen <lb/>het ſelve Octroy in’t geheel ende ſonder eenige Omiſſie <lb/>daer voor te drucken, ofte te doen drucken, ende <lb/>dat by gehouden ſal ſyn een Exemplaer van het voorſz. </s> <s xml:id="echoid-s21" xml:space="preserve"><lb/>werk gebonden en wel geconditioneert to brengen in <lb/>de Bibliotheeck van Onſe Univerſiteyt tot Leyden, <lb/>en daer van behoorlyk te doen blycken, alles op pœne <lb/>van het effect van dien te verlieſen, ende ten eynde <lb/>den Supple. </s> <s xml:id="echoid-s22" xml:space="preserve">deſen Onſen Conſente en Octroye moge ge-<lb/>nieten als naer behooren, laſten Wy allen ende <lb/>een ygelycken die’t aangaen mag, dat ſy den Supplt. </s> <s xml:id="echoid-s23" xml:space="preserve"><lb/>van den inhoude van deſen doen laten ende gedogen, <lb/>ruſtelyck, vredelyck ende volkomentlyk genieten ende <lb/>gebruycken, ceſſerende alle beleth ter contrarie. </s> <s xml:id="echoid-s24" xml:space="preserve">Ge-<lb/>daen in den Hage onder Onſen Grooten Zegele hier <lb/>aen doen hangen op den aghſten November in’t Faer <lb/>onſes Heeren en Zalighmakers ſeventien hondert en <lb/>negentien.</s> <s xml:id="echoid-s25" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s26" xml:space="preserve">Was getekent, <lb/>A: </s> <s xml:id="echoid-s27" xml:space="preserve">HEINSIUS, vt <lb/>Ter Ordonnantie van de Staten, <lb/>SIMON <emph style="sc">van</emph> BEAUMONT.</s> <s xml:id="echoid-s28" xml:space="preserve"/> </p> <pb file="0007" n="7" rhead="MONITUM"/> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head4" xml:space="preserve">de hac Secunda Editione.</head> <p style="it"> <s xml:id="echoid-s29" xml:space="preserve">CUm primùm ad hæc Elementa conſcribenda <lb/>animum applicarem, hoc mihi fuit propo-<lb/>ſitum, ut auditores, quæ fuſius explicata au-<lb/>diviſſent, & </s> <s xml:id="echoid-s30" xml:space="preserve">demonſtrata vidiſſent, illa <lb/>facile in memoriam revocare poſſent. </s> <s xml:id="echoid-s31" xml:space="preserve">Etiam, ut le-<lb/>ctoribus, quibus prima tantum Geometriæ elementa <lb/>nota eſſent, ideam darem Philoſophiæ Naturalis Ma-<lb/>thematicâ Methodo tractatæ. </s> <s xml:id="echoid-s32" xml:space="preserve">Cùmque, ut tironibus <lb/>præcipuè liber hicce utilis eſſet, difficiliora omnia in-<lb/>tacta relinquerem, ſæpe propoſitiones indicavi, de <lb/>quibus tantum monui, has à Geometris probari.</s> <s xml:id="echoid-s33" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s34" xml:space="preserve">Ut autem ſecunda hæc editio, & </s> <s xml:id="echoid-s35" xml:space="preserve">lectoribus magis <lb/>in Mathematicis verſatis, uſui eſſet, propoſitiones ta-<lb/>les omnes, in capite quocunque indicatas, Mathema-<lb/>ticè demonſtratas in ſcholiis, capitibus ſubjunctis, adje-<lb/>ci. </s> <s xml:id="echoid-s36" xml:space="preserve">Et ne hæc lectores alios turbarent, ipſa minore <lb/>charactere imprimi curavi. </s> <s xml:id="echoid-s37" xml:space="preserve">Omnia tamen ita diſpo-<lb/>ſui, ut illa ſola, quæ majore charactere edita ſunt, <lb/>ſeparatum quaſi opus conſtituant.</s> <s xml:id="echoid-s38" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s39" xml:space="preserve">In ſcholiis etiam alia quædam tradidi, quæ in ipſo <lb/>opere commode tractari non potuere, quamvis cum <lb/>explicatis relationem habeant, aut ad hæc illuſtranda <lb/>inſerviant.</s> <s xml:id="echoid-s40" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s41" xml:space="preserve">Secunda hæc editio, & </s> <s xml:id="echoid-s42" xml:space="preserve">aliis reſpectibus, eſt au-<lb/>ctior & </s> <s xml:id="echoid-s43" xml:space="preserve">magis accurata.</s> <s xml:id="echoid-s44" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s45" xml:space="preserve">Novæ multæ Machinæ, & </s> <s xml:id="echoid-s46" xml:space="preserve">antiquæ emendatæ in <pb file="0008" n="8" rhead="MONITUM"/> hujus tabulis exhibentur, & </s> <s xml:id="echoid-s47" xml:space="preserve">Experimenta, ipſorum-<lb/>que ſucceſſus, in hac majori cum curâ exponuntur.</s> <s xml:id="echoid-s48" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s49" xml:space="preserve">Novam etiam noſtram Percuſſionis Theoriam, quæ <lb/>LEIBNITZIANAM, quam & </s> <s xml:id="echoid-s50" xml:space="preserve">HUGENIANAM <lb/>dicere auſim, de viribus inſitis doctrinam pro funda-<lb/>mento habet, hîc plenius explicatam, noviſque variis <lb/>experimentis fulcitam, & </s> <s xml:id="echoid-s51" xml:space="preserve">illuſtratam tradimus.</s> <s xml:id="echoid-s52" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s53" xml:space="preserve">Non animus unquam mihi fuit, nec adhucdum eſt, <lb/>cum ullo, utcunque provocatus, in arenam deſcen-<lb/>dere, ut de veritate contendam. </s> <s xml:id="echoid-s54" xml:space="preserve">Quod mihi verum vi-<lb/>detur, hoc, ubi datur occaſio, pro viribus defendo; </s> <s xml:id="echoid-s55" xml:space="preserve">& </s> <s xml:id="echoid-s56" xml:space="preserve">in <lb/>his ut, quantum poſſem, omnem contentionis ſpeciem re-<lb/>moverem, argumenta, quibus memoratæ Theoriæ inniti <lb/>mihi videntur, ita proponere conatus ſum, ut reſpon-<lb/>ſa ad difficultates inde facile deduci queant, paucaſque <lb/>tantum directe ſolvere ſuſcepi: </s> <s xml:id="echoid-s57" xml:space="preserve">lectorique dijudican-<lb/>dum relinquo, an non Virium, Percuſſionum, ut & </s> <s xml:id="echoid-s58" xml:space="preserve"><lb/>Reſiſtentiarum, Retardationumque, corporum in flui-<lb/>dis motorum, Theoriæ cum Phænomenis, & </s> <s xml:id="echoid-s59" xml:space="preserve">inter ſe, <lb/>quàm exactiſſime conveniant.</s> <s xml:id="echoid-s60" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s61" xml:space="preserve">Noſtro labore quiſque pro arbitrio utatur, & </s> <s xml:id="echoid-s62" xml:space="preserve">ne <lb/>nos ad reſpondendum objectionibus, quæ proponi pote-<lb/>runt, devinctos credat. </s> <s xml:id="echoid-s63" xml:space="preserve">Quamdiu illa pro veris habebimus <lb/>quæ ſcripſimus, nos jure ſilere poſſe perſuaſum habe-<lb/>mus.</s> <s xml:id="echoid-s64" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s65" xml:space="preserve">Quamvis in multis, quæ ſpectant memoratas Theori-<lb/>as, à NEWTONIAN Areceſſerim ſententia, non tamen <lb/>titulum Introductionis ad Philoſophiam Newtonia-<lb/>nam ſervare, & </s> <s xml:id="echoid-s66" xml:space="preserve">huic ſecundæ editioni ipſum inſcri- <pb file="0009" n="9" rhead="AD LECTOREM"/> bere, ullo modo dubitavi. </s> <s xml:id="echoid-s67" xml:space="preserve">Varia enim in hiſce illu-<lb/>ſtramus ex iis quæ ab eximio illo Philoſopho fuere tra-<lb/>dita; </s> <s xml:id="echoid-s68" xml:space="preserve">& </s> <s xml:id="echoid-s69" xml:space="preserve">pleraque, quæ hîc explicamus, eo condu-<lb/>cant, ut facilius intelligantur, à ſummis Philoſophis <lb/>in perpetuum celebranda, & </s> <s xml:id="echoid-s70" xml:space="preserve">a nemine unquam ſine <lb/>admiratione legenda, NEWTONI ſcripta Philoſophica.</s> <s xml:id="echoid-s71" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s72" xml:space="preserve">Qui tantum ex Phænomenis, omni fictâ rejectâ <lb/>hypotheſi, in Phyſicis ratiocinatur, &</s> <s xml:id="echoid-s73" xml:space="preserve">, quantum in <lb/>ipſo eſt, caſte hanc methodum ſequitur, ille NEWTO-<lb/>NIveſtigiis inſiſtere conatur, & </s> <s xml:id="echoid-s74" xml:space="preserve">merito NEWTONIA-<lb/>NAM ſe ſectari Philoſophiam profitetur; </s> <s xml:id="echoid-s75" xml:space="preserve">non au-<lb/>tem ille, qui in verba jurat magiſtri.</s> <s xml:id="echoid-s76" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s77" xml:space="preserve">Ut autem augmenta, & </s> <s xml:id="echoid-s78" xml:space="preserve">emendationes, hujus edi-<lb/>tionis, & </s> <s xml:id="echoid-s79" xml:space="preserve">illis, qui primam jam poſſident, inſer-<lb/>virent, ſupplementum ſeparatum edi curavi: <lb/></s> <s xml:id="echoid-s80" xml:space="preserve">in quo, ut primæ editionis poſſeſſoribus utilis eſſem, <lb/>præſtiti quod potui, non autem omne quod voluiſſem. </s> <s xml:id="echoid-s81" xml:space="preserve"><lb/>In ſupplemento dedi omnium machinarum novarum <lb/>deſcriptiones, additamenta omnia, & </s> <s xml:id="echoid-s82" xml:space="preserve">propoſitiones <lb/>mutatas. </s> <s xml:id="echoid-s83" xml:space="preserve">Non autem huic inſerere potui, machina-<lb/>rum correctiones, neque illa, quibus, quæ in prima <lb/>editione continentur, aut illuſtrantur, aut clarius & </s> <s xml:id="echoid-s84" xml:space="preserve"><lb/>magis accurate exprimuntur; </s> <s xml:id="echoid-s85" xml:space="preserve">ſupplementum omnibus <lb/>partibus completum, lectori nimio fuiſſet labori, & </s> <s xml:id="echoid-s86" xml:space="preserve"><lb/>ipſius pretium nimium excreviſſet.</s> <s xml:id="echoid-s87" xml:space="preserve"/> </p> <figure> <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01"/> </figure> <pb file="0010" n="10" rhead="ADDENDA."/> <p style="it"> <s xml:id="echoid-s88" xml:space="preserve">In capite 22. </s> <s xml:id="echoid-s89" xml:space="preserve">lib. </s> <s xml:id="echoid-s90" xml:space="preserve">1. </s> <s xml:id="echoid-s91" xml:space="preserve">prætermiſſa ſunt quæ ſequuntur; </s> <s xml:id="echoid-s92" xml:space="preserve">lecto-<lb/>rem ideo rogo ut hæc velit inſerere ad pag. </s> <s xml:id="echoid-s93" xml:space="preserve">119. </s> <s xml:id="echoid-s94" xml:space="preserve">poſt lin. </s> <s xml:id="echoid-s95" xml:space="preserve">26.</s> <s xml:id="echoid-s96" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">TAB XIX. <lb/>fig. 1</note> <note position="left" xml:space="preserve"><emph style="it">das geht</emph>, aber geht auch <anchor type="note" xlink:label="note-0010-23a" xlink:href="note-0010-23"/>ein anchor?</note> <p> <s xml:id="echoid-s97" xml:space="preserve">Si corpus cujus extremitas conica eſt ut E B F bis, in <lb/>diverſis ſuperficiei argillæ partibus, in hanc incurrat, ve-<lb/>locitatibus quæ ſunt ut unum ad duo, cavitates erunt ut u-<lb/>num ad quatuor, ut ex ante dictis conſtat <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s98" xml:space="preserve">immediatè, <anchor type="note" xlink:label="note-0010-02a" xlink:href="note-0010-02"/> cavitates menſurando, detegitur. </s> <s xml:id="echoid-s99" xml:space="preserve">Tempus autem in quo ef-<lb/>fectus hicce quadruplus editur majus eſt; </s> <s xml:id="echoid-s100" xml:space="preserve">ſed effectum et-<lb/>iam quadruplum eſſe, quamvis minori tempore vim ſuam <lb/>corpus amittat, experimento ſequenti clarum eſt.</s> <s xml:id="echoid-s101" xml:space="preserve"/> </p> <div xml:id="echoid-div4" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0010-02" xlink:href="note-0010-02a" xml:space="preserve">447. 464. <lb/>456.</note> <note symbol="*" position="left" xlink:label="note-0010-23" xlink:href="note-0010-23a" xml:space="preserve"><anchor type="note" xlink:label="note-0010-02a" xlink:href="note-0010-02"/> </note> </div> <note position="left" xml:space="preserve"><p><s xml:id="echoid-s102" xml:space="preserve">TAB XIX. <lb/>fig. 1</s></p></note> </div> <div xml:id="echoid-div6" type="section" level="1" n="5"> <head xml:id="echoid-head5" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s103" xml:space="preserve">Formatur ex ebore, aut ligno duriore, Cylindrus, qui <lb/>ab una parte cono ut E B F terminatur, baſis oppoſita qua-<lb/>tuor conis, omnino huic ſimilibus, obtegitur, qui ſinguli <lb/>æqualiter prominent ita, ut planum, per quatuor vertices <lb/>tranſiens, perpendiculare ſit ad axem cylindri; </s> <s xml:id="echoid-s104" xml:space="preserve">fuſpen-<lb/>ditur hicce ut ille, quo in præcedenti experimento uſi ſu-<lb/>mus, & </s> <s xml:id="echoid-s105" xml:space="preserve">velocitate quacunque perpendiculariter in argillæ <lb/>ſuperficiem incurrit, dum juxta directionem ad axim pa-<lb/>rallelam fertur, cono unico in argillam impingente.</s> <s xml:id="echoid-s106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s107" xml:space="preserve">Converſo nunc Cylindro, mutatoque pyxidis ſitu, ve-<lb/>locitate dupla in argillam incurrat cylindrus, moto iterum <lb/>hoc juxta axis directionem.</s> <s xml:id="echoid-s108" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s109" xml:space="preserve">In priori caſu unica tantum formata fuit cavitas, in hoc <lb/>quatuor formantur, quarum ſingulæ priori quàm exactiſſi-<lb/>mè æquales ſunt.</s> <s xml:id="echoid-s110" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s111" xml:space="preserve">Cum in utroque caſu ad eandem profunditatem in argil-<lb/>lam penetraverit corpus, clarum eſt, minori tempore vim <lb/>integram amiſiſſe, ubi velocitas major fuit.</s> <s xml:id="echoid-s112" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div7" type="section" level="1" n="6"> <head xml:id="echoid-head6" xml:space="preserve">Pag. 310. poſt. lin. 23. adde.</head> <p> <s xml:id="echoid-s113" xml:space="preserve">Hoc tamen difficilius continget, & </s> <s xml:id="echoid-s114" xml:space="preserve">rarius extrahendi e-<lb/>runt emboli, ſi hi ſinguli, in inferiori parte, inter duasla-<lb/>minas æneas orbem contineant ex ſubere ita, ut annulus <lb/>coriaceus intruſo embolo, ſeſe ſuberi non ipſi metallo ap-<lb/>plicet. </s> <s xml:id="echoid-s115" xml:space="preserve">Quod in quibuſdam antliis minoribus Anglicanis <lb/>obſervavi.</s> <s xml:id="echoid-s116" xml:space="preserve"/> </p> <pb file="0011" n="11"/> </div> <div xml:id="echoid-div8" type="section" level="1" n="7"> <head xml:id="echoid-head7" xml:space="preserve">DEDICATIO PRIMÆ EDITIONI PRÆMISSA.</head> <head xml:id="echoid-head8" xml:space="preserve">ILLUSTRIBUS, NOBILISSIMIS, <lb/>& AMPLISSIMIS</head> <head xml:id="echoid-head9" xml:space="preserve">ACADEMIÆ BATAVÆ, <lb/>quæ LEIDÆ eſt,</head> <head xml:id="echoid-head10" xml:space="preserve">CURATORIBUS,</head> <head xml:id="echoid-head11" xml:space="preserve">D. GULIELMO BARONI <lb/><emph style="sc">DE</emph> WASSENAER,</head> <head xml:id="echoid-head12" xml:space="preserve">TOPARCHÆ IN STERRENBERGH, EQUESTRI <lb/>NOBILIUM HOLLANDIÆ ORDINI ADSCRIPTO, <lb/>DELEGATORUM ILLUSTR. ET PRÆPOT. HOLLAN-<lb/>DIÆ ORDINUM PRÆSIDI, ETC. ETC.</head> <head xml:id="echoid-head13" xml:space="preserve">D. HUBERTO ROSEBOOM, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head14" xml:space="preserve">TOPARCHÆ IN ’s GREVELSREGHT, SUPREMÆ <lb/>BATAVORUM CURIÆ PRÆSIDI, ETC. ETC.</head> <head xml:id="echoid-head15" xml:space="preserve">D. HERMANN <emph style="sc">Ovanden</emph> HONERT, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head16" xml:space="preserve">REIPUBLICÆ DORDRACENÆ CONSULI, <lb/>AGGERUM ALBLASSERW AERDENSIUM <lb/>COMITI, ETC. ETC.</head> <pb file="0012" n="12"/> </div> <div xml:id="echoid-div9" type="section" level="1" n="8"> <head xml:id="echoid-head17" xml:space="preserve">EORUMQUE COLLEGIS</head> <head xml:id="echoid-head18" xml:space="preserve">NOBILISSIMIS GRAVISSIMIS QUE <lb/>VIRIS</head> <head xml:id="echoid-head19" xml:space="preserve">REIPUBLICÆ LUGDUNENSIS,</head> <head xml:id="echoid-head20" xml:space="preserve">CONSULIBUS,</head> <head xml:id="echoid-head21" xml:space="preserve">D. JOANNI <emph style="sc">VANDEN</emph> BERGH, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head22" xml:space="preserve">EX FOEDERATA HAC REPUBLICA OLIM, NO-<lb/>MINE IMPERATORIS CAROLI VI., BRABANTIÆ, <lb/>FLANDRIÆ, HANNONIÆ, ETC. EPHORO, ET <lb/>AD RES EARUM ORDINANDAS DELEGATO.</head> <head xml:id="echoid-head23" xml:space="preserve">D. JOHANNI <emph style="sc">VAN</emph> ASSENDELFT, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head24" xml:space="preserve">D. HENRICO <emph style="sc">VAN</emph> WILLIGEN, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head25" xml:space="preserve">D. ABRAHAMO <emph style="sc">VAN</emph> GERWEN, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head26" xml:space="preserve">NEC NON</head> <head xml:id="echoid-head27" xml:space="preserve">VIRO SPECTATISSIMO</head> <head xml:id="echoid-head28" xml:space="preserve">D. PETRO GIJS, <emph style="sc">Jcto</emph>.</head> <head xml:id="echoid-head29" xml:space="preserve">REIPUBLICÆ LUGDUNENSIS SCABINO, <lb/>AMPLISSIMIS CURATORIBUS ET CONSULIBUS <lb/>A SECRETIS,</head> <head xml:id="echoid-head30" xml:space="preserve">Hæc Phyſices Elementa <lb/>D. D. D. <lb/>G. J. ’s GRAVESANDE.</head> <pb file="0013" n="13" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s117" xml:space="preserve">QUi variorum Philoſophorum circa Phyſicam ſcri-<lb/>pta contulerit, ſcientias omnino diverſas hoc <lb/>nomine deſignari, in dubium vocare vix pote-<lb/>rit, dum omnes ſe veram cauſam Phænome-<lb/>nôn naturalium tradituros pollicentur. </s> <s xml:id="echoid-s118" xml:space="preserve">Nil mirum, Ma-<lb/>theſis fallere neſcia non ſemper contentionem omnem a ſe <lb/>removere potuit.</s> <s xml:id="echoid-s119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s120" xml:space="preserve">Sed ne nos ſententiarum varietas averitatis inquiſitione <lb/>abducat, ſtudio & </s> <s xml:id="echoid-s121" xml:space="preserve">labore, quantumvis abſcondita, in lu-<lb/>cem protrahitur veritas, & </s> <s xml:id="echoid-s122" xml:space="preserve">qui flagranti hujus amore ra-<lb/>pitur, ſi errores non omnes, quod minime humanum, <lb/>evitet, difficilius tamen in illos cadit.</s> <s xml:id="echoid-s123" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s124" xml:space="preserve">Caute in Phyſicis procedendum; </s> <s xml:id="echoid-s125" xml:space="preserve">circa Intelligentiæ ſu-<lb/>premæ opera verſatur hæc ſcientia; </s> <s xml:id="echoid-s126" xml:space="preserve">tradit</s> </p> <p style="it"> <s xml:id="echoid-s127" xml:space="preserve">quas, dum primordia rerum <lb/>Pangeret, omniparens Leges violare Creator <lb/>Noluit, æternique operis fundamina fixit:</s> <s xml:id="echoid-s128" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s129" xml:space="preserve">quomodo hiſce Legibus univerſa rerum congeries rega-<lb/>tur, &</s> <s xml:id="echoid-s130" xml:space="preserve">, quomodo ordo, nunquam ſatis mirandus, qui-<lb/>bus omnia peraguntur, iiſdem Legibus in Mundo ſervetur, <lb/>explicat.</s> <s xml:id="echoid-s131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s132" xml:space="preserve">Cavendum ne fictum pro vero admittamus, eoipſoul-<lb/>teriori examini januam claudimus; </s> <s xml:id="echoid-s133" xml:space="preserve">nulla vera Phænome-<lb/>nôn explicatio ex falſo principio deduci poteſt; </s> <s xml:id="echoid-s134" xml:space="preserve">mentiſque <lb/>humanæ figmentum diſcere, aut Intelligentiæ ſapientiſſi-<lb/>mæ opus perpendere quantum intereſt? </s> <s xml:id="echoid-s135" xml:space="preserve">Cumque ſapien-<lb/>tiæ divinæ inveſtigatio, & </s> <s xml:id="echoid-s136" xml:space="preserve">cum hac ſemper conjuncta ve-<lb/>neratio, ſcopus Phyſici eſſe debeat, hîc ex fictis hypo- <pb file="0014" n="14" rhead="PRÆFATIO."/> theſibus ratiocin andum non eſſe ulterius probare inutilefo-<lb/>ret.</s> <s xml:id="echoid-s137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s138" xml:space="preserve">Ipſa ergo Natura indefeſſo labore, animoque attento, <lb/>continuo examinanda eſt. </s> <s xml:id="echoid-s139" xml:space="preserve">Lente quidem progredimur, <lb/>ſed quæ deteguntur certa ſunt; </s> <s xml:id="echoid-s140" xml:space="preserve">&</s> <s xml:id="echoid-s141" xml:space="preserve">, ubi mortalium co-<lb/>gnitionibus limites ponantur, ſæpe determinamus. </s> <s xml:id="echoid-s142" xml:space="preserve">Quod <lb/>fere omnes in errorem duxit, eſt ſciendi immoderata cu-<lb/>pido; </s> <s xml:id="echoid-s143" xml:space="preserve">& </s> <s xml:id="echoid-s144" xml:space="preserve">non fatendæ ignorantiæ, ſæpe ſtudio acquiſitæ, <lb/>a ratione ſuperandus, pudor. </s> <s xml:id="echoid-s145" xml:space="preserve">Sed, ſi in verbis ludere non <lb/>vetitum, docta indoctæ ſcientiæ anteponenda ignorantia <lb/>eſt.</s> <s xml:id="echoid-s146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s147" xml:space="preserve">Phyſica inter partes Matheſeos, cujus objectum eſt <lb/>quantitas in genere, merito refertur. </s> <s xml:id="echoid-s148" xml:space="preserve">Dividitur Mathe-<lb/>fis in puram & </s> <s xml:id="echoid-s149" xml:space="preserve">mixtam. </s> <s xml:id="echoid-s150" xml:space="preserve">In generales figurarum proprie-<lb/>tates inquirit illa, abſtractaſque ideas pro objecto ſuo ha-<lb/>bet. </s> <s xml:id="echoid-s151" xml:space="preserve">In hac res ipſæ examinantur, conſequentiaſque non <lb/>modo legitimas dari requiritur, ſed ut cum rebus ipſis con-<lb/>gruant ideæ circa quas ratiocinamur.</s> <s xml:id="echoid-s152" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s153" xml:space="preserve">Ad Matheſin mixtam pertinet Phyſica; </s> <s xml:id="echoid-s154" xml:space="preserve">ratiociniorum <lb/>Mathematicorum baſes ſunt Corporis Proprietates, & </s> <s xml:id="echoid-s155" xml:space="preserve">Na-<lb/>turæ Leges, quod nemo, qui hujus ſcientiæ ſcopum exa-<lb/>minavit, inficias ire poteſt. </s> <s xml:id="echoid-s156" xml:space="preserve">Quid autem pro Naturæ <lb/>Lege ſit habendum, qua methodo ad has Leges inveſti-<lb/>gandas procedendum, minime inter Philoſophos conve-<lb/>nit. </s> <s xml:id="echoid-s157" xml:space="preserve">Neceſſe ideo duxi in hac Præfatione tueri quam in <lb/>hoc Opere ſecutus ſum philoſophandi Methodum Newto-<lb/>nianam, quæ in primo capite breviter exponitur.</s> <s xml:id="echoid-s158" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s159" xml:space="preserve">Non agitur in Phyſicis de prima rerum formatione; </s> <s xml:id="echoid-s160" xml:space="preserve">ra- <pb file="0015" n="15" rhead="PRÆFATIO."/> tioni non modo conſentaneum eſt, quod Sacræ Litteræ <lb/>tradunt, Mundum a DEO conditum; </s> <s xml:id="echoid-s161" xml:space="preserve">nequidem per mo-<lb/>mentum temporis Naturam examinantem Intelligentiæ ſu-<lb/>premæ veſtigia latent. </s> <s xml:id="echoid-s162" xml:space="preserve">Aſſerere ex quibuſdam generali-<lb/>bus motus Legibus Mundum originem ducere potuiſſe, & </s> <s xml:id="echoid-s163" xml:space="preserve"><lb/>omnino parum referre quid de prima materiæ diviſione <lb/>fingatur. </s> <s xml:id="echoid-s164" xml:space="preserve">Et vix aliquid ſupponi poſſe ex quo non idem <lb/>effectus per eaſdem Naturæ Leges deduci poſſit: </s> <s xml:id="echoid-s165" xml:space="preserve">illudque <lb/>hac de cauſa, quod cum illarum ope materia formas <lb/>omnes quarum eſt capax ſucceſſive aſſumat, ſi formas iſtas <lb/>ordine conſideremus, tandem ad illam, quæ eſt hujus Mun-<lb/>di, nos poſſe devenire: </s> <s xml:id="echoid-s166" xml:space="preserve">adeo ut bîc nibil erroris ex falſa <lb/>ſuppoſitione ſit timendum.</s> <s xml:id="echoid-s167" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s168" xml:space="preserve">Hæc, inquam, aſſerere, & </s> <s xml:id="echoid-s169" xml:space="preserve">notiones maxime claras e-<lb/>vertere, vix differt, ut a plurimis Viris doctis abunde pro-<lb/>batum, & </s> <s xml:id="echoid-s170" xml:space="preserve">ad quod argumenta proferre inutile videbitur <lb/>illi, cui ignotum, ſententiam, adeo a ratione remotam, <lb/>& </s> <s xml:id="echoid-s171" xml:space="preserve">Divino Numini contumelioſam, ab antiquis & </s> <s xml:id="echoid-s172" xml:space="preserve">novis, <lb/>etiam præclaris Philoſophis, & </s> <s xml:id="echoid-s173" xml:space="preserve">ab omni Atheïſmi labe <lb/>remotiſſimis, in medium prolatam.</s> <s xml:id="echoid-s174" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s175" xml:space="preserve">Poſitis ergo omnibus a DEO creatis, explicandum qui-<lb/>bus Legibus omnia regantur; </s> <s xml:id="echoid-s176" xml:space="preserve">& </s> <s xml:id="echoid-s177" xml:space="preserve">ut ſolam Lunam memo-<lb/>rem, dicendum:</s> <s xml:id="echoid-s178" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s179" xml:space="preserve">qua cauſa argentea Phœbe <lb/>Paſſibus haud æquis graditur, cur ſubdita nulli <lb/>Hactenus Aſtronomo numerorum fræna recuſet; <lb/></s> <s xml:id="echoid-s180" xml:space="preserve">Cur remeant nodi, curque auges progrediuntur.</s> </p> <pb file="0016" n="16" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s181" xml:space="preserve">quantis refluum vaga Cynthia Pontum <lb/>Viribus impellit; </s> <s xml:id="echoid-s182" xml:space="preserve">dum fractis fluctibus ulvam <lb/>Deſerit, ac nautis ſuſpectas nudat arenas; <lb/></s> <s xml:id="echoid-s183" xml:space="preserve">Alternisvicibus ſuprema ad littora pulſans.</s> <s xml:id="echoid-s184" xml:space="preserve">De inveſtigiatione autem Naturæ Legum ut dicam, res <lb/>altius petenda eſt.</s> <s xml:id="echoid-s185" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s186" xml:space="preserve">Subſtantiæ quid ſint inter nobis ignota referendum eſt. <lb/></s> <s xml:id="echoid-s187" xml:space="preserve">Quaſdam ex. </s> <s xml:id="echoid-s188" xml:space="preserve">gr. </s> <s xml:id="echoid-s189" xml:space="preserve">materiæ proprietates novimus, ſed in <lb/>quo ſubjecto hæreant hæ nos omnino latet. </s> <s xml:id="echoid-s190" xml:space="preserve">An Corpori <lb/>non multæ aliæ tribuendæ ſint proprietates, de quibus <lb/>nullam habemus ideam, quis aſſerere poteſt? </s> <s xml:id="echoid-s191" xml:space="preserve">Cui etiam <lb/>enotuit an, præter Corporis proprietates quæ a materiæ <lb/>eſſentia pofluunt, non dentur aliæ a DEI libera poteſtate <lb/>pendentes, ſubſtantiamque extenſam & </s> <s xml:id="echoid-s192" xml:space="preserve">ſolidam (hæc e-<lb/>nim a nobis Corpus vocatur) quibuſdam, ſine quibus exi-<lb/>ſtere poſſet, proprietatibus ornari. </s> <s xml:id="echoid-s193" xml:space="preserve">De ignotis nihil af-<lb/>firmandum aut negandum eſt.</s> <s xml:id="echoid-s194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s195" xml:space="preserve">Quantum ab hac regula aberrant illi, qui, quaſi o-<lb/>mnia quæ ad Corpus pertinent pleniſſime perſpecta habe-<lb/>rent, in Phyſicis ratiocinantur, paucaſque Corporis pro-<lb/>prietates notas ipſum Corpus conſtituere aſſerere non <lb/>dubitant.</s> <s xml:id="echoid-s196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s197" xml:space="preserve">Quid obſecro ſibi vult proprietates ſubſtantiæ ipſam <lb/>conſtituere ſubſtantiam? </s> <s xml:id="echoid-s198" xml:space="preserve">An quæ ſeparatim ſubſiſtere non <lb/>poſſunt ſimul juncta ſubſiſtent? </s> <s xml:id="echoid-s199" xml:space="preserve">An extenſum, impenetra-<lb/>bile, mobile eſſe, & </s> <s xml:id="echoid-s200" xml:space="preserve">c. </s> <s xml:id="echoid-s201" xml:space="preserve">concipi poſſunt, ſine ſubjecto cui <lb/>hæ proprietates @mpetant? </s> <s xml:id="echoid-s202" xml:space="preserve">Et an hujus ſubjecti ullam ha-<lb/>bemus ideam?</s> <s xml:id="echoid-s203" xml:space="preserve"/> </p> <pb file="0017" n="17" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s204" xml:space="preserve">In incerto relinquendum quod incertum eſt; </s> <s xml:id="echoid-s205" xml:space="preserve">& </s> <s xml:id="echoid-s206" xml:space="preserve">ne i-<lb/>gnorantiam fateri pudeat: </s> <s xml:id="echoid-s207" xml:space="preserve">neque timendum de ignoto ni-<lb/>mium affirmari, dum ſubjectum omnino ignotum quibuſ-<lb/>dam incognitis proprietatibus forte præditum eſſe aſſeri-<lb/>mus. </s> <s xml:id="echoid-s208" xml:space="preserve">Qui vero cum hoc axiomate ſe nixos dicunt, quod <lb/>de incognitis non ſit ratiocinandum, pro ratiocinii tamen <lb/>fundamento habent, nil circa Corpus ignoti dari, niſi <lb/>forte fortuna errorem non vitabunt.</s> <s xml:id="echoid-s209" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s210" xml:space="preserve">Corporis proprietates a priori detegi nequeunt; </s> <s xml:id="echoid-s211" xml:space="preserve">Cor-<lb/>pus ipſum ideo eſt examinandum, hujuſque proprietates <lb/>exactiſſimè perpendendæ ſunt, ut poſſimus determinare <lb/>quid in rerum Phænomenis ex illis proprietatibus ſequa-<lb/>tur.</s> <s xml:id="echoid-s212" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s213" xml:space="preserve">Corpus majori cum cura examinando, videmus quaſ-<lb/>dam leges dari generales, ſecundum quas corpora moven-<lb/>tur. </s> <s xml:id="echoid-s214" xml:space="preserve">Corpus motum in motu continuare: </s> <s xml:id="echoid-s215" xml:space="preserve">actioni ſemper <lb/>æqualem eſſe & </s> <s xml:id="echoid-s216" xml:space="preserve">contrariam reactionem extra omne du-<lb/>bium eſt. </s> <s xml:id="echoid-s217" xml:space="preserve">Variæque aliæ ſimiles circa Corpus deteguntur <lb/>Leges, quæ minime ex proprietatibus, quæ ipſum Cor-<lb/>pus conſtituere dicuntur, deduci poſſunt; </s> <s xml:id="echoid-s218" xml:space="preserve">cumque hæ <lb/>Leges ſemper, id eſt, in omnibus occaſionibus, & </s> <s xml:id="echoid-s219" xml:space="preserve">ubi-<lb/>que, obtineant, & </s> <s xml:id="echoid-s220" xml:space="preserve">omnia corpora iis ſubjiciantur, pro <lb/>generalibus Naturæ Legibus habendæ ſunt. </s> <s xml:id="echoid-s221" xml:space="preserve">Circa has <lb/>in obſcuro eſt, an ex materiæ eſſentia fluant; </s> <s xml:id="echoid-s222" xml:space="preserve">an dedu-<lb/>cendæ ſint ex proprietatibus corporibus, ex quibus conſtat <lb/>Mundus, a DEO tributis, ſed Corpori minime eſſentialibus; <lb/></s> <s xml:id="echoid-s223" xml:space="preserve">tandem an non pendeant effectus, qui pro Naturæ Legibus <lb/>habentur, a caufis extraneis nobis nequidem ideis attingen-<lb/>dis.</s> <s xml:id="echoid-s224" xml:space="preserve"/> </p> <pb file="0018" n="18" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s225" xml:space="preserve">Quis mortalium de omnibus aut ſingulis Naturæ Legi-<lb/>bus hac in parte aliquid non temere aſſerere audebit? </s> <s xml:id="echoid-s226" xml:space="preserve">Mul-<lb/>tas etiam Leges non eſſe detectas, circa alias varia deſide-<lb/>rari, qui Naturæ Phænomena examinavit, pleniſſime <lb/>perſuaſum habebit.</s> <s xml:id="echoid-s227" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s228" xml:space="preserve">Non tamen, ut ignoto fundamento nixum, contemnen-<lb/>dum Philoſophiæ Naturalis ſtudium. </s> <s xml:id="echoid-s229" xml:space="preserve">Limitibus arctis circum-<lb/>ſcribitur mentis humanæ cognoſcendi capacitas, & </s> <s xml:id="echoid-s230" xml:space="preserve">qui <lb/>niſi evidentiæ aſſenſum dare negat, omnibus momentis in <lb/>dubio hæret, & </s> <s xml:id="echoid-s231" xml:space="preserve">inter incognita refert multa, circa quæ <lb/>vix per momentum temporis dubitandum plerique credunt. <lb/></s> <s xml:id="echoid-s232" xml:space="preserve">Cognita tamen ab ignotis rite ſeparare eſt animæ intelli-<lb/>gentis perfectio, terræ incolam ſuperans, ſed ad quam <lb/>acquirendam, continuo, animo attento, ſeſe applicare <lb/>debet. </s> <s xml:id="echoid-s233" xml:space="preserve">Si in Phyſicis multa latent, quæ in hac ſcientia <lb/>traduntur certa ſunt. </s> <s xml:id="echoid-s234" xml:space="preserve">Ex paucis generalibus principiis in-<lb/>numera Phænomena peculiaria explicantur; </s> <s xml:id="echoid-s235" xml:space="preserve">hæcque ex <lb/>illis Mathematica demonſtratione deducenda ſunt. </s> <s xml:id="echoid-s236" xml:space="preserve">Agi-<lb/>tur ubique de motuum collatione, id eſt, de quantitatum <lb/>comparatione, circa quam qui demonſtrationibus Mathe-<lb/>maticis in ratiociniis non progreditur, ſi non in erro-<lb/>rem, ſaltem in incertas concluſiones incidet.</s> <s xml:id="echoid-s237" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s238" xml:space="preserve">Quæcunque ergo habeat ignota Phyſica, vaſta & </s> <s xml:id="echoid-s239" xml:space="preserve">cer-<lb/>tiſſima eſt nihilominus hæc ſcientia, & </s> <s xml:id="echoid-s240" xml:space="preserve">maxime utilis. <lb/></s> <s xml:id="echoid-s241" xml:space="preserve">Corrigit innumera circa res naturales, & </s> <s xml:id="echoid-s242" xml:space="preserve">divinam ſapien-<lb/>tiam, falſa judicia; </s> <s xml:id="echoid-s243" xml:space="preserve">omnibuſque momentis in DEI ope-<lb/>ribus hanc ſapientiam ante oculos ponit; </s> <s xml:id="echoid-s244" xml:space="preserve">& </s> <s xml:id="echoid-s245" xml:space="preserve">multum dif-<lb/>fert, ſupremi Numinis potentiam, ſapientiamque, argu- <pb file="0019" n="19" rhead="PRÆFATIO."/> mento Metaphyſico noviſſe, & </s> <s xml:id="echoid-s246" xml:space="preserve">has omnibus momentis <lb/>in effectibus ipſis contemplari.</s> <s xml:id="echoid-s247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s248" xml:space="preserve">Satis ergo patet, quinam ſit ſcopus Phyſices, exqui-<lb/>bus Naturæ Legibus Phænomena ſint deducenda; </s> <s xml:id="echoid-s249" xml:space="preserve">& </s> <s xml:id="echoid-s250" xml:space="preserve">qua-<lb/>re, quando ad Leges generales pervenimus, non ulterius <lb/>in cauſarum cognitionem penetrare poſſimus. </s> <s xml:id="echoid-s251" xml:space="preserve">Supereſt, <lb/>ut de ipſarum Legum inveſtigatione dicamus, & </s> <s xml:id="echoid-s252" xml:space="preserve">tres re-<lb/>gulas Newtonianas in primo hujus Operis capite traditas <lb/>ſequendas eſſe probemus.</s> <s xml:id="echoid-s253" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s254" xml:space="preserve">Prima eſt, cauſas rerum naturalium non plures admitti <lb/>debere quam quæ veræ ſint, & </s> <s xml:id="echoid-s255" xml:space="preserve">earum Phænomenis expli-<lb/>candis ſufficiant. </s> <s xml:id="echoid-s256" xml:space="preserve">Pars prior ex ante dictis pleniſſime ſequi-<lb/>tur. </s> <s xml:id="echoid-s257" xml:space="preserve">Altera a nemine, qui ſapientem rerum Conditorem <lb/>non negat, in dubium vocari poteſt; </s> <s xml:id="echoid-s258" xml:space="preserve">ſi cauſa non ſuffi-<lb/>cit, veram non eſſe ſponte ſequitur; </s> <s xml:id="echoid-s259" xml:space="preserve">ſi ſufficit aliam fu-<lb/>peraddere inutile erit. </s> <s xml:id="echoid-s260" xml:space="preserve">Adde effectum ex duplici cauſa <lb/>nunquam exactiſſime eundem eſſe cum effectu ex ſimplici; <lb/></s> <s xml:id="echoid-s261" xml:space="preserve">ergo duabus effectus explicetur, unica non ſufficiet.</s> <s xml:id="echoid-s262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s263" xml:space="preserve">Regulæ duæ ſequentes ut probentur, quædam generalia <lb/>præmittenda ſunt.</s> <s xml:id="echoid-s264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s265" xml:space="preserve">Jam monuimus Demonſtrationes Mathematicas niſi <lb/>circa ideas non verſari, & </s> <s xml:id="echoid-s266" xml:space="preserve">ubi de rebus ipſis agitur ante <lb/>omnia requiri, ut cum rebus ideæ conveniant, quod nul-<lb/>lâ Mathematicâ demonſtratione probari poteſt. </s> <s xml:id="echoid-s267" xml:space="preserve">Cum <lb/>tamen omnibus momentis circa resipſas ratiocinandum <lb/>ſit, & </s> <s xml:id="echoid-s268" xml:space="preserve">nil de rebus in mente dari poſſit præter ha-<lb/>rum ideas, ratiociniaque omnia ideas immediate ſpe-<lb/>ctent, ſequitur a DEO conſtitutas quaſdam regulas, qui- <pb file="0020" n="20" rhead="PRÆFATIO."/> bus de convenientia idearum cum rebus poſſimus judicium <lb/>ferre.</s> <s xml:id="echoid-s269" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s270" xml:space="preserve">Omnia ratiocinia Mathematica idearum tantum com-<lb/>parationem ſpectant; </s> <s xml:id="echoid-s271" xml:space="preserve">unde ſequitur contrarium contradi-<lb/>ctionem involvere. </s> <s xml:id="echoid-s272" xml:space="preserve">Triangulum rectilineum, cujus tres <lb/>anguli duos rectos non æquant, impoſſibile eſt; </s> <s xml:id="echoid-s273" xml:space="preserve">quia idea <lb/>trium angulorum trianguli, ipſa eſt idea duorum angulo-<lb/>rum rectorum. </s> <s xml:id="echoid-s274" xml:space="preserve">Ubi de rebus ipſis agitur, contraria <lb/>propoſitio impoſſibilis non ſemper datur. </s> <s xml:id="echoid-s275" xml:space="preserve">Indubitatum <lb/>eſt, ex. </s> <s xml:id="echoid-s276" xml:space="preserve">gr. </s> <s xml:id="echoid-s277" xml:space="preserve">Petrum vivere, licet certiſſimum ſit, illum heri <lb/>potuiſſe mori. </s> <s xml:id="echoid-s278" xml:space="preserve">Cum autem in innumeris occaſionibus in ca-<lb/>ſu ſimili, cum certitudine, affirmandum aut negandum <lb/>ſit, cumque hoc clare ex rerum conſtitutione, deduca-<lb/>tur: </s> <s xml:id="echoid-s279" xml:space="preserve">ſequitur, in talibus occaſionibus, ratiocinia dari certa, <lb/>a Mathematicis demonſtrationibus neceſſario diverſa, vo-<lb/>luiſſe rerum conditorem. </s> <s xml:id="echoid-s280" xml:space="preserve">Qui enim homines neceſſita-<lb/>te cogit, de veritate aut falſitate propoſitionis pronun-<lb/>ciare, aſſentiendum eſſe, clare indicat, argumentis, qui-<lb/>bus judicium neceſſario nititur; </s> <s xml:id="echoid-s281" xml:space="preserve">& </s> <s xml:id="echoid-s282" xml:space="preserve">non digne de DEO ſen-<lb/>tit qui aliter ratiocinatur.</s> <s xml:id="echoid-s283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s284" xml:space="preserve">Ut ad Phyſicam redeamus, in hac de convenientia re-<lb/>rum cum ideis ſenſibus dijudicandum. </s> <s xml:id="echoid-s285" xml:space="preserve">Extenſio, ex. </s> <s xml:id="echoid-s286" xml:space="preserve">gr. <lb/></s> <s xml:id="echoid-s287" xml:space="preserve">materiæ & </s> <s xml:id="echoid-s288" xml:space="preserve">hujus ſoliditas, quæ hocfundamento affirman-<lb/>tur, extra omne dubium ſunt. </s> <s xml:id="echoid-s289" xml:space="preserve">Non hîc agitur, an ſen-<lb/>ſus quibuſdam in occaſionibus fallant, & </s> <s xml:id="echoid-s290" xml:space="preserve">quomodo error <lb/>vitetur, rem in genere hic examinamus.</s> <s xml:id="echoid-s291" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s292" xml:space="preserve">In Phyſicis de omnibus non poſſumus immediate ſenſi-<lb/>bus judicium ferre; </s> <s xml:id="echoid-s293" xml:space="preserve">datur & </s> <s xml:id="echoid-s294" xml:space="preserve">alia legitima, licet non Ma- <pb file="0021" n="21" rhead="PRÆFATIO."/> thematica, ratiocinandi methodus, hoc axiomate funda-<lb/>ta; </s> <s xml:id="echoid-s295" xml:space="preserve">Pro vero habendum omne quod ſi negetur ſocietas inter <lb/>homines deſtruitur, aut his vivendi ratio adimitur. </s> <s xml:id="echoid-s296" xml:space="preserve">Ex <lb/>qua propoſitione, quæ a nemine in dubium vocari po-<lb/>teſt, regulæ philoſophandi Newtonianæ ſecunda & </s> <s xml:id="echoid-s297" xml:space="preserve">tertia <lb/>evidentiſſime deducuntur.</s> <s xml:id="echoid-s298" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s299" xml:space="preserve">Niſi enim, quæ ubique obtinent ubi Experimenta inſti-<lb/>tuere licet, pro generaliter veris habeantur, effectuſque ſimi-<lb/>les ex cauſa ſimili oriri ponantur, quis per momentum <lb/>temporis tranquille vivere poterit?</s> <s xml:id="echoid-s300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s301" xml:space="preserve">Quotidie, nequidem ad illud attendendo, ſequentia ra-<lb/>tiocinia unuſquiſque pro indubitatis habet, & </s> <s xml:id="echoid-s302" xml:space="preserve">clare videt <lb/>horum concluſiones, ſine præſentis rerum conſtitutionis <lb/>deſtructione, in dubium vocari minime poſſe.</s> <s xml:id="echoid-s303" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s304" xml:space="preserve">Ædificium, hodie in omnibus partibus firmiſſimum, cra-<lb/>ſtino die ſponte non ruet: </s> <s xml:id="echoid-s305" xml:space="preserve">id eſt, partium corporum cohæ-<lb/>ſiohorumque gravitas, quas, niſi interveniente cauſa extra-<lb/>nea, nunquam mutatas vidi, aut audivi, hac nocte non <lb/>mutabuntur; </s> <s xml:id="echoid-s306" xml:space="preserve">quia cauſa cohæſionis & </s> <s xml:id="echoid-s307" xml:space="preserve">gravitatis eadem <lb/>erit craſtino die ac hodie. </s> <s xml:id="echoid-s308" xml:space="preserve">Quod ratiocinium certum eſſe, <lb/>niſi ex memorato principio deduci non poſſe, quis non <lb/>videt?</s> <s xml:id="echoid-s309" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s310" xml:space="preserve">Tigna & </s> <s xml:id="echoid-s311" xml:space="preserve">lapides, quæ in quacunque regione ad ædifi-<lb/>cium conſtruendum apta ſunt, ſepoſita omni mutatione ex <lb/>cauſa extranea, hîc tranſlata inſervire poterunt, & </s> <s xml:id="echoid-s312" xml:space="preserve">de <lb/>ruina non magis ſollicitus ero, ac in prima regione incolæ <lb/>fuiſſent, ſi non tranſlatis tignis & </s> <s xml:id="echoid-s313" xml:space="preserve">lapidibus, ipſi exhis do-<lb/>mum conſtruxiſſent; </s> <s xml:id="echoid-s314" xml:space="preserve">id eſt, vis, qua partes cohærent, &</s> <s xml:id="echoid-s315" xml:space="preserve"> <pb file="0022" n="22" rhead="PRÆFATIO."/> illa, qua corpora gravia ſunt, in variis regionibus non <lb/>differunt.</s> <s xml:id="echoid-s316" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s317" xml:space="preserve">Tali cibo per tot annos uſus ſum, & </s> <s xml:id="echoid-s318" xml:space="preserve">hodie eo ſine timore <lb/>veſcar.</s> <s xml:id="echoid-s319" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s320" xml:space="preserve">Ubi cicutam video, venenum ibi dari concludo, licet de <lb/>hac ipſa quam video nullum experimentum ſumſero.</s> <s xml:id="echoid-s321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s322" xml:space="preserve">Hæc omnia ratiocinia analogiam pro fundamento ha-<lb/>bent, & </s> <s xml:id="echoid-s323" xml:space="preserve">extra omne dubium eſt, nos a rerum Conditore <lb/>neceſſitate cogi per analogiam ratiocinari & </s> <s xml:id="echoid-s324" xml:space="preserve">hanc ideo ra-<lb/>tiociniorum legitimum eſſe fundamentum. </s> <s xml:id="echoid-s325" xml:space="preserve">Analogiæ au-<lb/>tem fundamentum eſt hoc; </s> <s xml:id="echoid-s326" xml:space="preserve">rerum univerſam congeriem <lb/>legibus immutatis regi.</s> <s xml:id="echoid-s327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s328" xml:space="preserve">Quibus ſemel probatis, hac ratiocinandi methodo uti po-<lb/>terimus etiam in illis occaſionibus, in quibus non ſimilis <lb/>ratiocinandi neceſſitas datur. </s> <s xml:id="echoid-s329" xml:space="preserve">Argumento, quod in uno <lb/>caſu procedit, in alio aſſenſum negare non debemus. </s> <s xml:id="echoid-s330" xml:space="preserve">Quis <lb/>enim concipiet, quæ eodem modo probantur non æque <lb/>certa eſſe? </s> <s xml:id="echoid-s331" xml:space="preserve">Adde ex neceſſitate quidem generaliter deduci, <lb/>ratiocinandi methodum eſſe legitimam, ratiocinia vero pe-<lb/>culiaria ab hac neceſſitate non pendere. </s> <s xml:id="echoid-s332" xml:space="preserve">Ex analogia <lb/>concludo, cibum non eſſe veneſicum; </s> <s xml:id="echoid-s333" xml:space="preserve">an argumentum <lb/>non procedit niſi cum eſurio? </s> <s xml:id="echoid-s334" xml:space="preserve">Ex neceſſitate ratiocinandi <lb/>per analogiam, Mundum fixis legibus a rerum conditore <lb/>regi, probamus; </s> <s xml:id="echoid-s335" xml:space="preserve">unde deducimus, & </s> <s xml:id="echoid-s336" xml:space="preserve">ſublatâ neceſſitate, <lb/>ratiocinia hæc extra dubium eſſe poſita.</s> <s xml:id="echoid-s337" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s338" xml:space="preserve">In Phyſicis ergo per Phænomena Naturæ Leges ſunt <lb/>detegendæ; </s> <s xml:id="echoid-s339" xml:space="preserve">per inductionem pro generalibus habendæ; <lb/></s> <s xml:id="echoid-s340" xml:space="preserve">de cetero Mathematice ratiocinandum. </s> <s xml:id="echoid-s341" xml:space="preserve">Qui, quo hæc tra- <pb file="0023" n="23" rhead="PRÆFATIO."/> ctandæ Phyſices methodus fundamento nitatur, ſerio exa-<lb/>minaverit, ſolam hanc eſſe legitimam, hypotheſeſque <lb/>omnes eſſe rejiciendas, facillime percipiet.</s> <s xml:id="echoid-s342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s343" xml:space="preserve">Hæc de philoſophandi Methodo; </s> <s xml:id="echoid-s344" xml:space="preserve">reſtat ut deipſo Opere <lb/>quid dicatur.</s> <s xml:id="echoid-s345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s346" xml:space="preserve">Dividitur totum Opus in quatuor libros. </s> <s xml:id="echoid-s347" xml:space="preserve">Primus agit de <lb/>corpore in genere, & </s> <s xml:id="echoid-s348" xml:space="preserve">corporum ſolidorum motu. </s> <s xml:id="echoid-s349" xml:space="preserve">Secun-<lb/>dus fluida ſpectat. </s> <s xml:id="echoid-s350" xml:space="preserve">Quæ ad lucem pertinent, in tertio tra-<lb/>ctantur. </s> <s xml:id="echoid-s351" xml:space="preserve">In quarto tandem motus corporum cœleſtium, <lb/>& </s> <s xml:id="echoid-s352" xml:space="preserve">quæ in terris ad hos relationem habent, explicantur. <lb/></s> <s xml:id="echoid-s353" xml:space="preserve">Primi duo libri hoc Tomo continentur.</s> <s xml:id="echoid-s354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s355" xml:space="preserve">Ut Phyſices ſtudium quantum fieri poteſt amœnum & </s> <s xml:id="echoid-s356" xml:space="preserve"><lb/>facile reddatur, omnia Experimentis eſſe elucidanda, i-<lb/>pſaſque concluſiones Mathematicas, hac Methodo ſub o-<lb/>culos eſſe ponendas, neceſſarium duxi.</s> <s xml:id="echoid-s357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s358" xml:space="preserve">Qui ſcientiæ elementa conſcribit, non quid novi, quan-<lb/>tum ad materiam, Orbi Litterato pollicetur; </s> <s xml:id="echoid-s359" xml:space="preserve">ideoque <lb/>inutile duxi monere ubi reperiantur quæ hîc traduntur. <lb/></s> <s xml:id="echoid-s360" xml:space="preserve">Pro meo ſumſi quodcunque propoſito meo utile mihi vi-<lb/>ſum eſt, credidique ſatis eſſe de hoc monere ad omnem <lb/>furti ſuſpicionem vitandam. </s> <s xml:id="echoid-s361" xml:space="preserve">Malo gloriam, ſi quam ex <lb/>paucis novis, quæ ſparſim in hoc Tractatu dantur, ſpe-<lb/>rare poſſum amittere, quam alii ſuam detrahere; </s> <s xml:id="echoid-s362" xml:space="preserve">ſumat <lb/>ergo quiſque quod ſuum credit, nihil mihi vindico.</s> <s xml:id="echoid-s363" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s364" xml:space="preserve">Quod Machinas attinet, quibus Experimenta inſtituen-<lb/>da ſunt, varias aliorum Auctorum imitari curavi, multas <lb/>inter has mutavi perfectioreſque reddidi, plures novas ad-<lb/>didi. </s> <s xml:id="echoid-s365" xml:space="preserve">Neque mirum in hanc neceſſitatem illum incidiſſe, <pb file="0024" n="24" rhead="PRÆFATIO."/> qui ad experimentum vocavit multa, de quibus nil ſimile <lb/>nemo antea forte tentavit. </s> <s xml:id="echoid-s366" xml:space="preserve">Mathematicus enim circailla <lb/>quæ Mathematicè demonſtrantur Experimenta ſuperflua <lb/>credit: </s> <s xml:id="echoid-s367" xml:space="preserve">nos autem Mathematicas demonſtrationes, ſem-<lb/>per abſtractas, faciliores reddi, ſi experimentis conclu-<lb/>ſiones ſub oculos ponantur, extra omne dubium habuimus; <lb/></s> <s xml:id="echoid-s368" xml:space="preserve">in hoc imitati Anglos, quorum docendæ Philoſophiæ na-<lb/>turalis Methodus nobis occaſionem dedit cogitandi de hac <lb/>quam in hoc Opere ſecuti ſumus; </s> <s xml:id="echoid-s369" xml:space="preserve">illorum veſtigia tenere <lb/>ſemper gloriabimur, qui, Principe Philoſophorum duce, <lb/>primi in Philoſophicis detegendæ veritatis viam ingreſſi <lb/>ſunt, fictas omnes hypotheſes ex Phyſicis amandantes.</s> <s xml:id="echoid-s370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s371" xml:space="preserve">Circa Machinas ulterius monebo, pleraſque conſtructas <lb/>eſſe ab Artifice in hac urbe ingenioſiſſimo, & </s> <s xml:id="echoid-s372" xml:space="preserve">ſimul Phi-<lb/>loſopho non imperito, Joanne van Muſſchenbroek, cui <lb/>omnes quæ hîc explicantur pleniſſime notæ ſunt; </s> <s xml:id="echoid-s373" xml:space="preserve">quod mo-<lb/>nere non ingratum fore iis credidi, qui fortè quaſdam <lb/>Machinas imitatas deſiderarent.</s> <s xml:id="echoid-s374" xml:space="preserve"/> </p> <figure> <image file="0024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0024-01"/> </figure> <pb file="0025" n="25" rhead="MONITUM"/> </div> <div xml:id="echoid-div10" type="section" level="1" n="9"> <head xml:id="echoid-head31" style="it" xml:space="preserve">De Demonſtrationibus quæ quantitates in-<lb/>finitè exiguas pro fundamento habent.</head> <p> <s xml:id="echoid-s375" xml:space="preserve">IN multis demonſtrationibus, in ſcholiis datis, quantitates conſi-<lb/>deramus infinite exiguas, & </s> <s xml:id="echoid-s376" xml:space="preserve">ita haſce proponimus, ut & </s> <s xml:id="echoid-s377" xml:space="preserve">a le-<lb/>ctoribus intelligi poſſint, quibus illa, quæ de talibus quantitatibus <lb/>a Geometris fuere explicata, ignota ſunt. </s> <s xml:id="echoid-s378" xml:space="preserve">Ne autem ipſis ſcrupulus <lb/>ullus circa demonſtrationes in mente hæreat, & </s> <s xml:id="echoid-s379" xml:space="preserve">ne ſibi de talibus de-<lb/>monſtrationibus non exactam forment ideam, monitum præmittere <lb/>non inutile credidi.</s> <s xml:id="echoid-s380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s381" xml:space="preserve">Sit curva quæcunque ABC; </s> <s xml:id="echoid-s382" xml:space="preserve">quam in B tangit linea DE; </s> <s xml:id="echoid-s383" xml:space="preserve">ſint <lb/> <anchor type="note" xlink:label="note-0025-01a" xlink:href="note-0025-01"/> rectæ duæ quæcunque FB, fG, parallelæ, junctæ lineâ Ff; </s> <s xml:id="echoid-s384" xml:space="preserve">qua-<lb/>rum fG curvam ſecat in b; </s> <s xml:id="echoid-s385" xml:space="preserve">ſit etiam Hb parallela Ff, ſecans tangen-<lb/>tem DE in g. </s> <s xml:id="echoid-s386" xml:space="preserve">Si nunc concipiamus, Ff minui, id eſt lineam, fG <lb/>motu parallelo ferri, dum etiam, per interſectionem hujus lineæ <lb/>cum curva, motu parallelo fertur gbH, clarum eſt rationes inter <lb/>gB, gH, HB, non mutari, donec, coincidentibus fG, FB li-<lb/>neolæ omnes ſimul evaneſcant.</s> <s xml:id="echoid-s387" xml:space="preserve"/> </p> <div xml:id="echoid-div10" type="float" level="2" n="1"> <note position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">TAB. XLVII <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s388" xml:space="preserve">In codem lineæ fG motu, rationes inter bB, bH, HB, con-<lb/>tinuò mutantur, donec ubi evanuere nullæ rationes dentur; </s> <s xml:id="echoid-s389" xml:space="preserve">in ipſo <lb/>autem momento evaneſcentiæ dantur rationes ab omnibus, quæ in <lb/>præcedentibus momentis locum habuere diverſæ.</s> <s xml:id="echoid-s390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s391" xml:space="preserve">Sic corpus quod cadit, & </s> <s xml:id="echoid-s392" xml:space="preserve">libere cadendo continuò celerius move-<lb/>tur, ubi ad punctum quodcunque pervenit, velocitatem habet majo-<lb/>rem omnibus velocitatibus quas antequam ibi perveniret habuit, mi-<lb/>norem autem omnibus illis, quas babebit poſtquam punctum præter-<lb/>greſſum erit, peculiariſque eſt velocitas qua ad punctum appellit, ab <lb/>omnibusaliis, quibus ad puncta alia quæcunque pervenit, diverſa. </s> <s xml:id="echoid-s393" xml:space="preserve">Eodem <lb/>modo non agitur hîc de rationibus, quas habent quantitates ante eva-<lb/>neſcentiam, aut poſtquam evanuere, ſed quas habent dum evaneſcunt.</s> <s xml:id="echoid-s394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s395" xml:space="preserve">In ipſo autem hoc momento evaneſcentiæ, quia curva in puncto <lb/>contactus cum tangente conincidit, confunduntur puncta G, g, b, & </s> <s xml:id="echoid-s396" xml:space="preserve"><lb/>rationes inter bB, bH, HB, non differunt a rationibus gB, gH, <lb/>HB, aut GB, GI, IB.</s> <s xml:id="echoid-s397" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s398" xml:space="preserve">Ubi in demonſtrationibus Bb infinitè exiguam ponimus, hanc <lb/>pro recta habemus, & </s> <s xml:id="echoid-s399" xml:space="preserve">memoratam æqualitatem rationum, etiam <lb/>ponimus: </s> <s xml:id="echoid-s400" xml:space="preserve">Hæc tamen Mathematicè vera non ſunt, niſi in momen-<lb/>to evaneſcentiæ ubi ergo loquimur de quantitatibus infinitè exiguis, <pb file="0026" n="26" rhead="MONITUM"/> intellige evaneſcentes, & </s> <s xml:id="echoid-s401" xml:space="preserve">demonſtrationes nulli Mathematicæ demon-<lb/>ſtrationi firmitate cedent.</s> <s xml:id="echoid-s402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s403" xml:space="preserve">Clarum etiam eſt in momento evaneſcentiæ fb & </s> <s xml:id="echoid-s404" xml:space="preserve">FB confundi <lb/>reveraque æquales eſſe, ergo in demonſtratione quacunque in qua <lb/>portionem curvæ bB infinite exiguam ponimus, quia hanc evane-<lb/>ſcentem intelligimus, tuto lineas ut fb, & </s> <s xml:id="echoid-s405" xml:space="preserve">FB pro æqualibus habemus.</s> <s xml:id="echoid-s406" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s407" xml:space="preserve">Demonſtrationes hæ diſtingui debent a demonſtrationibus in qui-<lb/>bus error, licet inſenſibilis, datur, qualis eſt demonſtratio n. </s> <s xml:id="echoid-s408" xml:space="preserve">1222. <lb/></s> <s xml:id="echoid-s409" xml:space="preserve">ex qua deducimus ſonum, ſive majorem ſive minorem, eâdem ſemper <lb/>velocitate per eundem aërem moveri; </s> <s xml:id="echoid-s410" xml:space="preserve">quod Mathematice verum non <lb/>eſt, ſed differentia velocitatum, quando datur, ita exigua eſt, ut <lb/>nulla arte percipi poſſit, quare differentiam in Phyſicis negligimus; </s> <s xml:id="echoid-s411" xml:space="preserve"><lb/>eodem modo ac in praxi geometriæ, ubi montis altitudinem conſi-<lb/>deramus, hanc non pro mutata habebimus, quamvis arenula adjecta <lb/>ſit. </s> <s xml:id="echoid-s412" xml:space="preserve">In talibus autem demonſtrationibus non agitur de quantitatibus <lb/>infinitè exiguis, ſed de quantitatibus finitis; </s> <s xml:id="echoid-s413" xml:space="preserve">numero enim finito <lb/>non modo exprimi poteſt ratio inter arenulæ diametrum & </s> <s xml:id="echoid-s414" xml:space="preserve">montis <lb/>altitudinem, ſed & </s> <s xml:id="echoid-s415" xml:space="preserve">inter illam diametrum & </s> <s xml:id="echoid-s416" xml:space="preserve">telluris diametrum, aut <lb/>ſi velis diſtantiam ſtellæ fixæ cujuſcunque a Tellure.</s> <s xml:id="echoid-s417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s418" xml:space="preserve">In hiſce demonſtrationibus in quibus pro æqualibus habemus quan-<lb/>titates, quæ tali inſenſibili quantitate differunt, error in demonſtra-<lb/>tione ſenſibilis non erit, & </s> <s xml:id="echoid-s419" xml:space="preserve">ideò, ubi de rebus ipſis agitur, de qui-<lb/>bus ſenſibus dijudicamus, demonſtrationes hæ a Mathematicis jure <lb/>admittuntur; </s> <s xml:id="echoid-s420" xml:space="preserve">ex Matheſi pura removentur, quæ tamen admittit, <lb/>ut demonſtravimus, demonſtrationes quæ infinitè exiguas, aut eva-<lb/>neſcentes, quantitates pro fundamento habent.</s> <s xml:id="echoid-s421" xml:space="preserve"/> </p> <figure> <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/> </figure> <pb file="0027" n="27"/> </div> <div xml:id="echoid-div12" type="section" level="1" n="10"> <head xml:id="echoid-head32" xml:space="preserve">INDEX CAPITUM.</head> <head xml:id="echoid-head33" xml:space="preserve">LIBRII. PARSI.</head> <head xml:id="echoid-head34" xml:space="preserve">De Corpore in Genere.</head> <note position="right" xml:space="preserve"> <lb/>CAP. I. # De Scopo Phyſices, & Regulis Philoſophandi. # Pag. 1 <lb/># II. De Corpore in genere. # 3 <lb/># III. De Extenſione, Soliditate, & Vacuo. # 5 <lb/># IV. De Diviſibilitate corporis in infinitum, & Particularum ſubtilitate. # 6 <lb/><emph style="sc">Schol</emph>. 1. De Materiæ Diviſibilitate. # 8 <lb/># Infinitum Finito contineri. # ibid. <lb/># De Spirali Logarithmica, & hujus Menſura. # 9 <lb/># De Infinitorum Claſſibus. # 10 <lb/># 2. De Partium ſubtilitate. # 12 <lb/>CAP. V. De Cohæſione partium, ubi de Duritie, Mollitie, Fluiditate, & E-<lb/># laſticitate agitur. # 13 <lb/><emph style="sc">Schol</emph>. De Effectu attractionis vitri in aquam. # 19 <lb/># De tubis Capillarihus. # ibid. <lb/># De Aſcenſu aquæ inter plana. # ibid. <lb/># De Motu guttæ inter plana. # 20 <lb/>CAP. VI. De Motu in genere, ubi de loco & Tempore. # 21 <lb/></note> </div> <div xml:id="echoid-div13" type="section" level="1" n="11"> <head xml:id="echoid-head35" xml:space="preserve">LIBRI I. PARS II.</head> <head xml:id="echoid-head36" xml:space="preserve">De Actionibus Potentiarum.</head> <note position="right" xml:space="preserve"> <lb/>CAP. VII. De Actionibus Potentiarum comparandis. # 22 <lb/># VIII. Generalia circa Gravitatem. # 24 <lb/># IX. De Trochlea ſimplici, Libra, & Centro Gravitatis. # 28 <lb/><emph style="sc">Schol</emph>. 1. De Centro Gravitatis. # 33 <lb/># De centri Gravitatis inveſtigatione. # 34 <lb/># 2. Arithmetica Mechanica. # 35 <lb/>CAP. X. De Vecte Machinarum ſimplicium prima. # 36 <lb/># XI. De Axe in Peritrochio, ſecundâ Machinarum ſimplicium, & Rotis <lb/># dentatis. # 39 <lb/># XII. De Trochleâ, Machinarum ſimplicium tertiâ. # 40 <lb/># XIII. De Cuneo & Cochleâ, Machinarum ſimplicium Quartâ & Quintâ. # 43 <lb/><emph style="sc">Schol</emph>. 1. De Ligno findendo. # 46 <lb/># 2. Machinæ cujuſdam Examen. # 47 <pb file="0028" n="28"/> CAP. XIV. De Machinis compoſitis. # 47 <lb/># XV. De Potentiis obliquis. # 49 <lb/></note> </div> <div xml:id="echoid-div14" type="section" level="1" n="12"> <head xml:id="echoid-head37" xml:space="preserve">LIBRI I. PARS III.</head> <head xml:id="echoid-head38" xml:space="preserve">De Motibus, Potentiarum Actionibus, Variatis.</head> <note position="right" xml:space="preserve"> <lb/>CAP. XVI. De Naturæ legibus Newtonianis. # 57 <lb/># XVII. De Acceleratione & Retardatione Gravium. # 59 <lb/># XVIII. De Deſcenſu Gravium ſuper plano inclinato. # 62 <lb/># XIX. De Oſcillatione Pendulorum. # 66 <lb/><emph style="sc">Schol</emph>. 1. De Motu in Cycloïde. # 71 <lb/># 2. De Centro Oſcillationis determinando. # 72 <lb/># 3. De quibusdam Cycloïdis proprietatibus. # 74 <lb/># 4. De Lineâ celerrimi deſcenſus. # 75 <lb/>CAP. XX. De Projectione Gravium. # 77 <lb/># XXI. De Viribus centralibus. # 83 <lb/><emph style="sc">Schol</emph>. 1. Generalia de viribus centralibus. # 98 <lb/># 2. De Motu in circulo. # 99 <lb/># 3. De Motu in Ellipſi. # 101 <lb/># 4. De Motu in Orbitâ agitatâ. # 103 <lb/># 5. De Motu in Ellipſi agitatâ. # 106 <lb/># 6. De Computatione Motuum Apſidum in curvis parum a circulis diffe-<lb/># rentibus. # 108 <lb/></note> </div> <div xml:id="echoid-div15" type="section" level="1" n="13"> <head xml:id="echoid-head39" xml:space="preserve">LIBRI I. PARS IV.</head> <head xml:id="echoid-head40" xml:space="preserve">De Viribus inſitis, & Colliſione corporum.</head> <note position="right" xml:space="preserve"> <lb/>CAP. XXII. De Viribus corporibus motis inſitis. # 109 <lb/># XXIII. De Colliſione Corporum. # 120 <lb/><emph style="sc">Schol</emph>. 1. De viribus amiſſis &c. # 141 <lb/># 2. De Percuſſione Corporum lineis rigidis inter ſe cohærentium, & cir-<lb/># ca centra agitatorum. # 143 <lb/># 3. Examen Experimenti circa corpora in lancem, aut Brachium, libræ <lb/># impingentia. # 146 <lb/># 4. De Centro Oſcillationis, & Percuſſionis. # 150 <lb/>CAP. XXIV. De Congreſſu corporum Elaſticorum. # 151 <lb/><emph style="sc">Schol</emph>. 1 Uberior demonſtratio de æqualitate virium ante & poſt ictum. # 160 <lb/># 2. Illuſtratio circa mutuam Corporum elaſticorum Actionem. # 161 <lb/># 3. Paradoxi explicatio. # 163 <pb file="0029" n="29"/> CAP. XXV. De Motu compoſito. # Pag. 164 <lb/># XXVI. De Percuſſione obliqua. # 168 <lb/># XXVII. De Colliſione compoſita. # 172 <lb/><emph style="sc">Schol</emph>. 1. Demonſtrationes concurſutrium corporum ineadem linea motorum. # 180 <lb/># 2. De concurſu trium Corporum elaſticorum, poſitâ elaſterii relaxatione <lb/># minus ſubitâ. # 182 <lb/># 3. De virium æqualitate in corporibus elaſticis ante & poſt ictum. # 184 <lb/>CAP. XXVIII. De Motu Centri gravitatis. # ibid. <lb/><emph style="sc">Schol</emph>. 1. De Motu abſoluto & relativo variorum corporum ſimul conſiderato-<lb/># rum. # 187 <lb/># 2. De Motu Centri gravitatis trium corporum, in quibuſdam caſibus. # 188 <lb/># 3. Motus determinatio in caſu peculiari. # 189 <lb/>CAP. XXIX. De Legibus Elaſticitatis. # 190 <lb/></note> </div> <div xml:id="echoid-div16" type="section" level="1" n="14"> <head xml:id="echoid-head41" xml:space="preserve">LIBRI II. PARS I.</head> <head xml:id="echoid-head42" xml:space="preserve">De Gravitate & Preſſione Fluidorum.</head> <note position="right" xml:space="preserve"> <lb/>CAP. I. De Gravitate partium Fluidorum, & illius effectu in ipſis Fluidis. # 200 <lb/># II. De Actione Fluidorum in Fundos, Latera, & Opercula vaſorum qui-<lb/># bus continentur. # 204 <lb/># III. De Solidis Fluidis immerſis. # 211 <lb/># IV. De Comparandis Fluidorum Denſitatibus. # 219 <lb/># V. De Hydroſtatica Solidorum Comparatione. # 222 <lb/></note> </div> <div xml:id="echoid-div17" type="section" level="1" n="15"> <head xml:id="echoid-head43" xml:space="preserve">LIBRI II. PARS II.</head> <head xml:id="echoid-head44" xml:space="preserve">De Motu & Reſiſtentia Fluidorum.</head> <note position="right" xml:space="preserve"> <lb/># CAP. VI. De Celeritate Fluidi ex preſſione fluidi ſuperincumbentis. # 226 <lb/># VII. De Fluidis proſilientibus. # 229 <lb/># VIII. De Fluido ex Vaſis profluente, & Irregularitatibus in hoc motu. # 238 <lb/><emph style="sc">Schol</emph>. Computatio de quantitate fluidi ex foramine fluentis. # 246 <lb/>CAP. IX. De Curſu Fluminum. # ibid. <lb/># X. De Motu Undarum. # 252 <lb/># XI. De Reſiſtentia Fluidorum. # 257 <lb/><emph style="sc">Schol</emph>. De Reſiſtentiarum differentiis pro diverſis corporum figuris. # 274 <lb/>CAP. XII. De Retardatione Corporum in Fluidis motorum. # 275 <lb/><emph style="sc">Schol</emph>. 1. De Logarithmica. # 283 <pb file="0030" n="30"/> <emph style="sc">Schol</emph>. 2. De Retardatione in genere. # 284 <lb/># 3. De Retardatione ex prima cauſa. # 285 <lb/># 4. De Retardatione ex ſecunda cauſa. # 286 <lb/># 5. De ambabus Retardationibus conjunctim. # 287 <lb/># 6. De Corporibus in altum projectis. # 290 <lb/># 7. De Corporibus in Fluidis cadentibus. # 291 <lb/># 8. Illuſtratio quorundam quæ ad Retardationem ſpectant. # 292 <lb/></note> </div> <div xml:id="echoid-div18" type="section" level="1" n="16"> <head xml:id="echoid-head45" xml:space="preserve">LIBRI II. PARS III.</head> <head xml:id="echoid-head46" xml:space="preserve">De Aëre & aliis Fluidis Elaſticis.</head> <note position="right" xml:space="preserve"> <lb/>CAP. XIII. Aërem Fluidorum Proprietates habere. # 296 <lb/># XIV. De Aëris Elaſticitate. # 299 <lb/># XV. De quibuſdam aliis Fluidis Elaſticis. # 306 <lb/># XVI. De Antlia Pneumatica. # 309 <lb/># XVII. Experimenta varia circa Aëris gravitatem, & hujus Elaſticita-<lb/># tem. # 313 <lb/># XVIII. Variarum Machinarum, quarum actio ab Aëre pendet, Deſcriptio, <lb/># & harum effectuum Explicatio. # 322 <lb/># XIX. De Aëris motu Undulatorio, ubi de ſone. # 327 <lb/><emph style="sc">Schol</emph>. 1. De Agitatione particularum aërearum, & Soni velocitate. # 342 <lb/># 2. De Soni intenſitate. # 344 <lb/></note> <figure> <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/> </figure> <pb o="1" file="0031" n="31"/> <figure> <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0031-01"/> </figure> </div> <div xml:id="echoid-div19" type="section" level="1" n="17"> <head xml:id="echoid-head47" xml:space="preserve">PHYSICES</head> <head xml:id="echoid-head48" xml:space="preserve">ELEMENTA MATHEMATICA, <lb/>EXPERIMENTIS CONFIRMATA.</head> <head xml:id="echoid-head49" style="it" xml:space="preserve">LIBER I. <lb/>Pars I. de Corpore in genere.</head> <head xml:id="echoid-head50" xml:space="preserve">CAPUT I. <lb/>De Scopo Phyſices & Regulis philoſophandi.</head> <p> <s xml:id="echoid-s422" xml:space="preserve">PHyſica circa res naturales & </s> <s xml:id="echoid-s423" xml:space="preserve">illarum Phænomena ver-<lb/>ſatur.</s> <s xml:id="echoid-s424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div20" type="section" level="1" n="18"> <head xml:id="echoid-head51" xml:space="preserve"><emph style="sc">Definitio</emph> 1. & 2.</head> <p> <s xml:id="echoid-s425" xml:space="preserve">Res naturales ſunt omnia corpora; </s> <s xml:id="echoid-s426" xml:space="preserve">congerieſque illorum <lb/> <anchor type="note" xlink:label="note-0031-01a" xlink:href="note-0031-01"/> omnium univerſum vocatur.</s> <s xml:id="echoid-s427" xml:space="preserve"/> </p> <div xml:id="echoid-div20" type="float" level="2" n="1"> <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">1.</note> </div> </div> <div xml:id="echoid-div22" type="section" level="1" n="19"> <head xml:id="echoid-head52" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s428" xml:space="preserve">Phænomena naturalia, ſunt omnes ſitus & </s> <s xml:id="echoid-s429" xml:space="preserve">omnes mo-<lb/> <anchor type="note" xlink:label="note-0031-02a" xlink:href="note-0031-02"/> tus corporum naturalium, ab actione entis intelligentis imme-<lb/>diate non pendentes, & </s> <s xml:id="echoid-s430" xml:space="preserve">qui a nobis ſenſibus obſervari poſſunt.</s> <s xml:id="echoid-s431" xml:space="preserve"/> </p> <div xml:id="echoid-div22" type="float" level="2" n="1"> <note position="right" xlink:label="note-0031-02" xlink:href="note-0031-02a" xml:space="preserve">2.</note> </div> <p> <s xml:id="echoid-s432" xml:space="preserve">Non excludimus ex numero Phænomenorum natu-<lb/>ralium motus, qui in corpore noſtro ad voluntatem fiunt, <lb/>pendent enim a motu muſculorum, qui etiam motu alio <lb/>agitantur, in hiſce ſolus motus ex actione immediata men-<lb/>tis oriundus, & </s> <s xml:id="echoid-s433" xml:space="preserve">nobis omnino ignotus, non eſt Phænome-<lb/>non naturale.</s> <s xml:id="echoid-s434" xml:space="preserve"/> </p> <pb o="2" file="0032" n="32" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s435" xml:space="preserve">Omnes hi motus regulis certis peraguntur & </s> <s xml:id="echoid-s436" xml:space="preserve">legibus ſem-<lb/>per iisdem adſtricti ſunt.</s> <s xml:id="echoid-s437" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s438" xml:space="preserve">Sol quotidie oritur & </s> <s xml:id="echoid-s439" xml:space="preserve">occidit, tempuſque ortus & </s> <s xml:id="echoid-s440" xml:space="preserve">occa-<lb/>ſus, pro anni tempeſtate & </s> <s xml:id="echoid-s441" xml:space="preserve">loco, ſemper determinatur, ejuſ-<lb/>dem ſpeciei plantæ, iiſdem poſitis circumſtantiis, eodemmo-<lb/>do producuntur & </s> <s xml:id="echoid-s442" xml:space="preserve">creſcunt, & </s> <s xml:id="echoid-s443" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s444" xml:space="preserve">In iis ipſis <lb/>quæ nobis omnino fortuita & </s> <s xml:id="echoid-s445" xml:space="preserve">incerta apparent, certas ob-<lb/>ſervari regulas extra omne dubium eſt.</s> <s xml:id="echoid-s446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s447" xml:space="preserve">Phyſica Phænomena naturalia explicat, id eſt, illorum <lb/> <anchor type="note" xlink:label="note-0032-01a" xlink:href="note-0032-01"/> cauſas tradit.</s> <s xml:id="echoid-s448" xml:space="preserve"/> </p> <div xml:id="echoid-div23" type="float" level="2" n="2"> <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">3.</note> </div> <p> <s xml:id="echoid-s449" xml:space="preserve">Cum in illas cauſas inquirimus, ipſum corpus in genere <lb/>examinandum eſt, deinde quibus regulis rerum conditor <lb/>omnes motus peragi voluerit. </s> <s xml:id="echoid-s450" xml:space="preserve">Hæ regulæ, vocantur leges <lb/>Naturæ.</s> <s xml:id="echoid-s451" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div25" type="section" level="1" n="20"> <head xml:id="echoid-head53" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p style="it"> <s xml:id="echoid-s452" xml:space="preserve">Naturæ lex ergo eſt, Regula & </s> <s xml:id="echoid-s453" xml:space="preserve">norma, ſecundum quam <lb/> <anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/> Deus voluit certos motus ſemper, id eſt, in omnibus occaſio-<lb/>nibus, peragi.</s> <s xml:id="echoid-s454" xml:space="preserve"/> </p> <div xml:id="echoid-div25" type="float" level="2" n="1"> <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">4.</note> </div> <p> <s xml:id="echoid-s455" xml:space="preserve">Eſt ideo noſtri reſpectu lex naturæ, omnis effectus, qui <lb/> <anchor type="note" xlink:label="note-0032-03a" xlink:href="note-0032-03"/> in omnibus occaſionibus idem eſt, cujus cauſa nobis eſt <lb/>ignota, & </s> <s xml:id="echoid-s456" xml:space="preserve">quem videmus exnulla lege, nobis nota, fluere <lb/>poſſe, licet ex ſimpliciori lege, nobis ignota, fluat.</s> <s xml:id="echoid-s457" xml:space="preserve"/> </p> <div xml:id="echoid-div26" type="float" level="2" n="2"> <note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">5.</note> </div> <p> <s xml:id="echoid-s458" xml:space="preserve">Noſtri enim reſpectu non intereſt, utrum quid immedi-<lb/>ate a Dei voluntate pendeat, an vero mediante cauſa, cu-<lb/>jus nullam ideam habemus, producatur.</s> <s xml:id="echoid-s459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s460" xml:space="preserve">Leges naturæ, niſi ex examine Phænomenorum naturali-<lb/>um, non poſſunt elici.</s> <s xml:id="echoid-s461" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s462" xml:space="preserve">Ope legum hac methodo detectarum Phænomena alia ex-<lb/>plicari debent.</s> <s xml:id="echoid-s463" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s464" xml:space="preserve">In inveſtigatione Naturæ legum, ſequentes Regulæ New-<lb/>tonianæ obſervandæ veniunt.</s> <s xml:id="echoid-s465" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div28" type="section" level="1" n="21"> <head xml:id="echoid-head54" xml:space="preserve"><emph style="sc">Regula</emph> 1.</head> <p style="it"> <s xml:id="echoid-s466" xml:space="preserve">Cauſas rerum Naturalium non plures admitti debere <lb/> <anchor type="note" xlink:label="note-0032-04a" xlink:href="note-0032-04"/> quam quæ & </s> <s xml:id="echoid-s467" xml:space="preserve">veræ ſint, & </s> <s xml:id="echoid-s468" xml:space="preserve">earum Phænomenis explicandis <lb/>ſufficiant.</s> <s xml:id="echoid-s469" xml:space="preserve"/> </p> <div xml:id="echoid-div28" type="float" level="2" n="1"> <note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">6.</note> </div> <pb o="3" file="0033" n="33" rhead="MATHEMATICA, LIB. I. CAP. I."/> </div> <div xml:id="echoid-div30" type="section" level="1" n="22"> <head xml:id="echoid-head55" xml:space="preserve"><emph style="sc">Regula</emph> 2.</head> <p style="it"> <s xml:id="echoid-s470" xml:space="preserve">Effectuum Naturalium ejuſdem generis eaſdem eſſe cauſas. <lb/></s> <s xml:id="echoid-s471" xml:space="preserve"> <anchor type="note" xlink:label="note-0033-01a" xlink:href="note-0033-01"/> </s> </p> <div xml:id="echoid-div30" type="float" level="2" n="1"> <note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve">7.</note> </div> </div> <div xml:id="echoid-div32" type="section" level="1" n="23"> <head xml:id="echoid-head56" xml:space="preserve"><emph style="sc">Regula</emph> 3.</head> <p style="it"> <s xml:id="echoid-s472" xml:space="preserve">Qualitates corporum, quæ intendi & </s> <s xml:id="echoid-s473" xml:space="preserve">remitti nequeunt, quæ-<lb/> <anchor type="note" xlink:label="note-0033-02a" xlink:href="note-0033-02"/> que corporibus omnibus competunt, in quibus experimenta in-<lb/>ſtituere licet, pro qualitatibus corporum univer ſorum haben-<lb/>das eſſe.</s> <s xml:id="echoid-s474" xml:space="preserve"/> </p> <div xml:id="echoid-div32" type="float" level="2" n="1"> <note position="right" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">8.</note> </div> </div> <div xml:id="echoid-div34" type="section" level="1" n="24"> <head xml:id="echoid-head57" xml:space="preserve">CAPUT II.</head> <head xml:id="echoid-head58" style="it" xml:space="preserve">De Corpore in genere.</head> <p> <s xml:id="echoid-s475" xml:space="preserve">QUod primum in corpore conſiderandum venit eſt exten-<lb/> <anchor type="note" xlink:label="note-0033-03a" xlink:href="note-0033-03"/> ſio.</s> <s xml:id="echoid-s476" xml:space="preserve"/> </p> <div xml:id="echoid-div34" type="float" level="2" n="1"> <note position="right" xlink:label="note-0033-03" xlink:href="note-0033-03a" xml:space="preserve">9.</note> </div> <p> <s xml:id="echoid-s477" xml:space="preserve">Extenſio quid ſit, nemoignorat, hujus idea fere ſem-<lb/>per menti noſtræ obverſatur, & </s> <s xml:id="echoid-s478" xml:space="preserve">eſt ſimpliciſſima; </s> <s xml:id="echoid-s479" xml:space="preserve">unde, li-<lb/>cet diſtinctiſſima ſit, verbis tamen nullis deſcribi poteſt.</s> <s xml:id="echoid-s480" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s481" xml:space="preserve">Omne corpus eſt extenſum, ſublata corporis extenſione <lb/>integrum tollitur corpus.</s> <s xml:id="echoid-s482" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s483" xml:space="preserve">Omne extenſum non eſt corpus, in quo vero corpus a <lb/>ſpatio differat, non poteſt determinari, niſi prius examinatis <lb/>aliis corporis proprietatibus.</s> <s xml:id="echoid-s484" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s485" xml:space="preserve">Secunda quæ corpus conſideranti ſeſe offert eſt ſoliditas. <lb/></s> <s xml:id="echoid-s486" xml:space="preserve"> <anchor type="note" xlink:label="note-0033-04a" xlink:href="note-0033-04"/> Corpus, omne aliud corpus ex loco a ſe occupato excludit, <lb/>& </s> <s xml:id="echoid-s487" xml:space="preserve">corpora fluidiſſima æque ac maxime dura ea proprietate <lb/>gaudent.</s> <s xml:id="echoid-s488" xml:space="preserve"/> </p> <div xml:id="echoid-div35" type="float" level="2" n="2"> <note position="right" xlink:label="note-0033-04" xlink:href="note-0033-04a" xml:space="preserve">10.</note> </div> <p> <s xml:id="echoid-s489" xml:space="preserve">Tertia corporis proprietas eſt diviſibilitas, eo quod cor-<lb/> <anchor type="note" xlink:label="note-0033-05a" xlink:href="note-0033-05"/> pus eſt extenſum, etiam eſt diviſibile. </s> <s xml:id="echoid-s490" xml:space="preserve">Extenſio enim alia <lb/>extenſione minor ſemper poteſt concipi, unde videmus in <lb/>omni extenſione partes dari, quæ partes in corpore a ſein-<lb/>vicem poſſunt ſeparari; </s> <s xml:id="echoid-s491" xml:space="preserve">quia</s> </p> <div xml:id="echoid-div36" type="float" level="2" n="3"> <note position="right" xlink:label="note-0033-05" xlink:href="note-0033-05a" xml:space="preserve">11.</note> </div> <p> <s xml:id="echoid-s492" xml:space="preserve">Corpus quarta proprietate præditum eſt, quod poſſit de <lb/> <anchor type="note" xlink:label="note-0033-06a" xlink:href="note-0033-06"/> loco in locum transferri, unde corpus mobile dicitur. </s> <s xml:id="echoid-s493" xml:space="preserve">Vi <lb/>autem inſitâ in motu perſeverat.</s> <s xml:id="echoid-s494" xml:space="preserve"/> </p> <div xml:id="echoid-div37" type="float" level="2" n="4"> <note position="right" xlink:label="note-0033-06" xlink:href="note-0033-06a" xml:space="preserve">12.</note> </div> <p> <s xml:id="echoid-s495" xml:space="preserve">Quando nullum datur obſtaculum, corpus ictui minimo <lb/> <anchor type="note" xlink:label="note-0033-07a" xlink:href="note-0033-07"/> cedit, major tamen vis requiritur ad corpus movendum ma-<lb/>jori celeritate quam minori, & </s> <s xml:id="echoid-s496" xml:space="preserve">ad movendum corpus ma-<lb/>jus quam minus, ſi æqualis fuerit velocitas; </s> <s xml:id="echoid-s497" xml:space="preserve">vis etiam ma- <pb o="4" file="0034" n="34" rhead="PHYSICES ELEMENTA"/> jor iisdem in caſibus requiritur, ut corpus in motu ſiſtatur; <lb/></s> <s xml:id="echoid-s498" xml:space="preserve">corpus ergo quieſcens motui & </s> <s xml:id="echoid-s499" xml:space="preserve">corpus motum quieti reſiſtit: </s> <s xml:id="echoid-s500" xml:space="preserve"><lb/>illud oritur ex materiæ Inertia, quæ in omnibus corporibus <lb/>quantitati materiæ proportinalis eſt; </s> <s xml:id="echoid-s501" xml:space="preserve">quia omnibus materiæ <lb/>particulis æqualiter competit.</s> <s xml:id="echoid-s502" xml:space="preserve"/> </p> <div xml:id="echoid-div38" type="float" level="2" n="5"> <note position="right" xlink:label="note-0033-07" xlink:href="note-0033-07a" xml:space="preserve">13.</note> </div> <p> <s xml:id="echoid-s503" xml:space="preserve">Omne corpus figura eſt præditum, & </s> <s xml:id="echoid-s504" xml:space="preserve">Figurabile; </s> <s xml:id="echoid-s505" xml:space="preserve">ſiab omni <lb/> <anchor type="note" xlink:label="note-0034-01a" xlink:href="note-0034-01"/> parte in corpore diviſiones fiant, & </s> <s xml:id="echoid-s506" xml:space="preserve">partes removeantur, <lb/>quod in medio remanet ab omni parte terminatum eſt, & </s> <s xml:id="echoid-s507" xml:space="preserve"><lb/>neceſſario figura præditum; </s> <s xml:id="echoid-s508" xml:space="preserve">Idem corpus varias poteſt in-<lb/>duere figuras, quia in partes poteſt reſolvi, & </s> <s xml:id="echoid-s509" xml:space="preserve">quia hæ, quæ mo-<lb/>biles ſunt, in vario ordine erga ſe invicem diſponi queunt.</s> <s xml:id="echoid-s510" xml:space="preserve"/> </p> <div xml:id="echoid-div39" type="float" level="2" n="6"> <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">14.</note> </div> </div> <div xml:id="echoid-div41" type="section" level="1" n="25"> <head xml:id="echoid-head59" xml:space="preserve">CAPUT III.</head> <head xml:id="echoid-head60" style="it" xml:space="preserve">De Extenſione, Soliditate, & Vacuo.</head> <p> <s xml:id="echoid-s511" xml:space="preserve">HIc conſideranda venit in Scholis decantata quæſtio de Va-<lb/> <anchor type="note" xlink:label="note-0034-02a" xlink:href="note-0034-02"/> cuo; </s> <s xml:id="echoid-s512" xml:space="preserve">fcilicet an detur extenſio omni materia deſtituta, <lb/>hæc enim extenſio vocatur Vacuum, Inane, aut Spatium.</s> <s xml:id="echoid-s513" xml:space="preserve"/> </p> <div xml:id="echoid-div41" type="float" level="2" n="1"> <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">15.</note> </div> <p> <s xml:id="echoid-s514" xml:space="preserve">Vacuum revera dari ex Phænomenis probatur, & </s> <s xml:id="echoid-s515" xml:space="preserve">ideo <lb/>in cap. </s> <s xml:id="echoid-s516" xml:space="preserve"><emph style="sc">XII</emph>. </s> <s xml:id="echoid-s517" xml:space="preserve">lib. </s> <s xml:id="echoid-s518" xml:space="preserve"><emph style="sc">IV</emph>. </s> <s xml:id="echoid-s519" xml:space="preserve">quæſtionem hanc ad examen voca-<lb/>mus.</s> <s xml:id="echoid-s520" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s521" xml:space="preserve">Vacuum poſſibile eſſe ex ſolo examine idearum deduci-<lb/>tur. </s> <s xml:id="echoid-s522" xml:space="preserve">Omne enim quod clare concipimus exiſtere poſſe, poſ-<lb/>ſibile eſt.</s> <s xml:id="echoid-s523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s524" xml:space="preserve">Quæſtio ergo eo redit, an habeamus ideam extenſionis <lb/>non ſolidæ.</s> <s xml:id="echoid-s525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s526" xml:space="preserve">Soliditatis ideam acquirimus contactu; </s> <s xml:id="echoid-s527" xml:space="preserve">corpora quæ-<lb/> <anchor type="note" xlink:label="note-0034-03a" xlink:href="note-0034-03"/> dam nobis reſiſtere ſentimus, & </s> <s xml:id="echoid-s528" xml:space="preserve">quidem omnibus momen-<lb/>tis nobis illa reſiſtunt, quæ deſcenſum verſus inferiora loca <lb/>impediunt; </s> <s xml:id="echoid-s529" xml:space="preserve">ex qua reſiſtentia apparet corpus ex loco a ſe oc-<lb/>cupato omne aliud corpus excludere; </s> <s xml:id="echoid-s530" xml:space="preserve">id eſt, illud ſolidita-<lb/>te præditum eſſe, quam ſoliditatis ideam ad corpora ſubtilio-<lb/>ra, quæ propter partium tenuitatem ſub ſenſus non cadunt, <lb/>transferimus: </s> <s xml:id="echoid-s531" xml:space="preserve">& </s> <s xml:id="echoid-s532" xml:space="preserve">experientia conſtat, hæc ipſa, æque ac <lb/>duriſſima, aliis corporibus reſiſtere.</s> <s xml:id="echoid-s533" xml:space="preserve"/> </p> <div xml:id="echoid-div42" type="float" level="2" n="2"> <note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">16.</note> </div> <pb o="5" file="0035" n="35" rhead="MATHEMATICA, LIB. I. CAP. III."/> </div> <div xml:id="echoid-div44" type="section" level="1" n="26"> <head xml:id="echoid-head61" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s534" xml:space="preserve">Aër in quo vivimus fere ſemper viſum & </s> <s xml:id="echoid-s535" xml:space="preserve">tactum noſtrum <lb/> <anchor type="note" xlink:label="note-0035-01a" xlink:href="note-0035-01"/> fugit, in antlia tamen exacte clauſa embolo reſiſtit, ita ut nul-<lb/>la vi ad antliæ fundum protrudi poſſit.</s> <s xml:id="echoid-s536" xml:space="preserve"/> </p> <div xml:id="echoid-div44" type="float" level="2" n="1"> <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">17.</note> </div> <p> <s xml:id="echoid-s537" xml:space="preserve">In extenſionis autem idea non continetur idea ſolidita-<lb/>tis, hanc non niſi ex contactu, illam vero ſine illo acquiri-<lb/>mus, & </s> <s xml:id="echoid-s538" xml:space="preserve">ſi quis nunquam corpus tetigiſſet, ei ſoliditas omni-<lb/>no ignota eſſet.</s> <s xml:id="echoid-s539" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div46" type="section" level="1" n="27"> <head xml:id="echoid-head62" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s540" xml:space="preserve">Conſpiciat quis idolum inter ſpeculum cavum & </s> <s xml:id="echoid-s541" xml:space="preserve">obje-<lb/> <anchor type="note" xlink:label="note-0035-02a" xlink:href="note-0035-02"/> ctum ſpeculo expoſitum; </s> <s xml:id="echoid-s542" xml:space="preserve">idolum tale non reſiſtit, corpus <lb/>tamen æque denſum ac corpus repræſentatum videtur: </s> <s xml:id="echoid-s543" xml:space="preserve">poſ-<lb/>ſunt enim colores magis vividi in idolo quam ipſius objecti <lb/>colores repræſentari.</s> <s xml:id="echoid-s544" xml:space="preserve"/> </p> <div xml:id="echoid-div46" type="float" level="2" n="1"> <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">18.</note> </div> <p> <s xml:id="echoid-s545" xml:space="preserve">Si homo nihil unquam præter talia idola vidiſſet, & </s> <s xml:id="echoid-s546" xml:space="preserve">ipſi-<lb/>us corpus tali idolo ſimile eſſet, an ullam ſoliditatis haberet <lb/>ideam? </s> <s xml:id="echoid-s547" xml:space="preserve">non videtur; </s> <s xml:id="echoid-s548" xml:space="preserve">extenſionis tamen certiſſime habebit. <lb/></s> <s xml:id="echoid-s549" xml:space="preserve">Hic non agitur de eo quid ſit tale idolum, de ideis diſpu-<lb/>tamus, ſat eſt illud dari.</s> <s xml:id="echoid-s550" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s551" xml:space="preserve">In ſoliditatis privatione non omnis ſita eſt differentia inter <lb/>Spatium & </s> <s xml:id="echoid-s552" xml:space="preserve">Corpus.</s> <s xml:id="echoid-s553" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s554" xml:space="preserve">Spatium eſt infinitum, ac nullis terminari poſſe limitibus, <lb/> <anchor type="note" xlink:label="note-0035-03a" xlink:href="note-0035-03"/> rem attente conſideranti patebit. </s> <s xml:id="echoid-s555" xml:space="preserve">Corpora autem finita <lb/>dantur.</s> <s xml:id="echoid-s556" xml:space="preserve"/> </p> <div xml:id="echoid-div47" type="float" level="2" n="2"> <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">19.</note> </div> <p> <s xml:id="echoid-s557" xml:space="preserve">In ſpatio partes dari clare videmus, a ſe invicem vero <lb/> <anchor type="note" xlink:label="note-0035-04a" xlink:href="note-0035-04"/> ſeparari nequeunt, immobiles ſunt, ut & </s> <s xml:id="echoid-s558" xml:space="preserve">ipſum ſpatium. </s> <s xml:id="echoid-s559" xml:space="preserve">Cor-<lb/>poris vero partes ſeparationem patiuntur.</s> <s xml:id="echoid-s560" xml:space="preserve"/> </p> <div xml:id="echoid-div48" type="float" level="2" n="3"> <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">20.</note> </div> <p> <s xml:id="echoid-s561" xml:space="preserve">Spatii idea ſimpliciſſima eſt; </s> <s xml:id="echoid-s562" xml:space="preserve">corporis magis eſt compo-<lb/>ſita.</s> <s xml:id="echoid-s563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s564" xml:space="preserve">Soliditas a quibuſdam impenetrabilitas vocatur, & </s> <s xml:id="echoid-s565" xml:space="preserve">ex na-<lb/> <anchor type="note" xlink:label="note-0035-05a" xlink:href="note-0035-05"/> tura extenſionis illam deducere conantur; </s> <s xml:id="echoid-s566" xml:space="preserve">pedi cubico ex. <lb/></s> <s xml:id="echoid-s567" xml:space="preserve">gr. </s> <s xml:id="echoid-s568" xml:space="preserve">extenſionis, pes alter cubicus extenſionis addi non poteſt, <lb/>quin habeamus duos pedes cubicos, ſinguli enim habent om-<lb/>nia quæ ad illam magnitudinem conſtituendam requirun-<lb/>tur; </s> <s xml:id="echoid-s569" xml:space="preserve">pars ergo una ſpatii partes omnes alias excludit & </s> <s xml:id="echoid-s570" xml:space="preserve">ipſa <lb/>illas admittere non poteſt.</s> <s xml:id="echoid-s571" xml:space="preserve"/> </p> <div xml:id="echoid-div49" type="float" level="2" n="4"> <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">21.</note> </div> <pb o="6" file="0036" n="36" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s572" xml:space="preserve">Reſp. </s> <s xml:id="echoid-s573" xml:space="preserve">partem ſpatii in alium locum translatam contradi-<lb/>ctionem involvere; </s> <s xml:id="echoid-s574" xml:space="preserve">ex immobilitate ergo partium ſpatii, <lb/>non ex impenetrabilitate, ſeu ſoliditate, ſequitur, duas par-<lb/>tes ſpatii confundi non poſſe.</s> <s xml:id="echoid-s575" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div51" type="section" level="1" n="28"> <head xml:id="echoid-head63" xml:space="preserve">CAPUT IV.</head> <head xml:id="echoid-head64" style="it" xml:space="preserve">De Diviſibilitate Corporis in infinitum, & parti-<lb/>cularum Subtilitate.</head> <p> <s xml:id="echoid-s576" xml:space="preserve">EO quod corpus eſt extenſum etiam eſt diviſibile, ideſt, <lb/>in eo partes conſiderari poſſunt.</s> <s xml:id="echoid-s577" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s578" xml:space="preserve">Differt tamen corporis diviſibilitas, ab extenſionis divi-<lb/>ſibilitate, illius enim partes a ſe invicem ſeparari poſſunt. <lb/></s> <s xml:id="echoid-s579" xml:space="preserve">Hæc vero proprietas cum ab extenſione pendeat, in exten-<lb/>ſione examinari debet: </s> <s xml:id="echoid-s580" xml:space="preserve">demonſtrata deinde facile ad corpus <lb/>transferri poterunt.</s> <s xml:id="echoid-s581" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s582" xml:space="preserve">Corpus eſt diviſibile in infinitum, id eſt, in ejus exten-<lb/> <anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/> ſione nulla pars quantumvis parva poteſt concipi, quin de-<lb/>tur adhuc alia minor.</s> <s xml:id="echoid-s583" xml:space="preserve"/> </p> <div xml:id="echoid-div51" type="float" level="2" n="1"> <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">22.</note> </div> <p> <s xml:id="echoid-s584" xml:space="preserve">Sit linea AD, ad BF, perpendicularis; </s> <s xml:id="echoid-s585" xml:space="preserve">ut & </s> <s xml:id="echoid-s586" xml:space="preserve">GH, ad <lb/> <anchor type="note" xlink:label="note-0036-02a" xlink:href="note-0036-02"/> parvam ab A diſtantiam, ad eandem etiam perpendicula-<lb/>ris; </s> <s xml:id="echoid-s587" xml:space="preserve">centris C,C,C,&</s> <s xml:id="echoid-s588" xml:space="preserve">c. </s> <s xml:id="echoid-s589" xml:space="preserve">& </s> <s xml:id="echoid-s590" xml:space="preserve">radiis CA, CA, &</s> <s xml:id="echoid-s591" xml:space="preserve">c. </s> <s xml:id="echoid-s592" xml:space="preserve">deſcribantur <lb/>circuli ſecantes lineam GH, in punctis e, e &</s> <s xml:id="echoid-s593" xml:space="preserve">c. </s> <s xml:id="echoid-s594" xml:space="preserve">quo major <lb/>eſt radius AC, eo minor eſt pars e G: </s> <s xml:id="echoid-s595" xml:space="preserve">radius poteſt in infi-<lb/>nitum augeri & </s> <s xml:id="echoid-s596" xml:space="preserve">ſic ergo minui pars e G; </s> <s xml:id="echoid-s597" xml:space="preserve">quæ tamen nunquam <lb/>ad nihilum poteſt redigi, quia circulus cum linea recta BF, <lb/>coincidere nunquam poteſt.</s> <s xml:id="echoid-s598" xml:space="preserve"/> </p> <div xml:id="echoid-div52" type="float" level="2" n="2"> <note position="left" xlink:label="note-0036-02" xlink:href="note-0036-02a" xml:space="preserve">TAB. II. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s599" xml:space="preserve">Partes ergo magnitudinis cujuſcunque in infinitumpoſſunt <lb/>minui & </s> <s xml:id="echoid-s600" xml:space="preserve">nullus diviſionis datur finis.</s> <s xml:id="echoid-s601" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s602" xml:space="preserve">Innumeris aliis idem probari poteſt Mathematicis demon-<lb/>ſtrationibus.</s> <s xml:id="echoid-s603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s604" xml:space="preserve">Ex hac diviſibilitate deducimus, data quavis materiæ par-<lb/> <anchor type="note" xlink:label="note-0036-03a" xlink:href="note-0036-03"/> ticula quantumvis exigua, & </s> <s xml:id="echoid-s605" xml:space="preserve">dato ſpatio quovis finito ut-<lb/>cunque amplo, poſſibile eſſe, ut materia iſtius arenulæ per <lb/>totum illud ſpatium diffundatur, atque ipſum ita adimpleat, <pb o="7" file="0037" n="37" rhead="MATHEMATICA, LIB. I. CAP. IV."/> ut nullus ſit in eo porus cujus diameter minimam datam ſu-<lb/>peret lineam. </s> <s xml:id="echoid-s606" xml:space="preserve">Quod ut demonſtremus, ſpatium implendum, <lb/>diviſum concipimus in cellulas cubicas, quarum latera æqua-<lb/>lia aut minora ſint minimâ lineâ datâ: </s> <s xml:id="echoid-s607" xml:space="preserve">numerus cellularum <lb/>finitus erit, & </s> <s xml:id="echoid-s608" xml:space="preserve">in tot partes arenula data dividi poterit, quot <lb/>cellulæ dantur; </s> <s xml:id="echoid-s609" xml:space="preserve">ita ut in ſingulis cellulis particulam unam <lb/>poſitam concipere poſſimus: </s> <s xml:id="echoid-s610" xml:space="preserve">concipiendum ulterius ex ſin-<lb/>gulis hiſce particulis minimis globum cavum formari. </s> <s xml:id="echoid-s611" xml:space="preserve">Pro-<lb/>pter materiæ diviſibilitatem poteſt globus cavus ſemper au-<lb/>geri minuendo materiæ craſſitiem, cum autem in ſingulis <lb/>cellulis globus talis detur, poterunt ſinguli augeri, donec <lb/>vicini ſeſe mutuo tangant, ut omnes ſimul ſpatium impleant.</s> <s xml:id="echoid-s612" xml:space="preserve"/> </p> <div xml:id="echoid-div53" type="float" level="2" n="3"> <note position="left" xlink:label="note-0036-03" xlink:href="note-0036-03a" xml:space="preserve">23.</note> </div> <p> <s xml:id="echoid-s613" xml:space="preserve">Objectiones præcipuæ, contra diviſibilitatem materiæ in <lb/> <anchor type="note" xlink:label="note-0037-01a" xlink:href="note-0037-01"/> infinitum, ſunt, infinitum finito contineri non poſſe; </s> <s xml:id="echoid-s614" xml:space="preserve">ex di-<lb/>viſibilitate in infinitum ſequi, omnia corpora eſſe æqualia, <lb/>aut infinitum alio infinito majus dari.</s> <s xml:id="echoid-s615" xml:space="preserve"/> </p> <div xml:id="echoid-div54" type="float" level="2" n="4"> <note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">24.</note> </div> <p> <s xml:id="echoid-s616" xml:space="preserve">Sed hiſce reſponſio facilis eſt, infinito non tribuendæ ſunt <lb/>proprietates quantitatis finitæ & </s> <s xml:id="echoid-s617" xml:space="preserve">determinatæ. </s> <s xml:id="echoid-s618" xml:space="preserve">Partes infinite <lb/>parvas, numero infinito, in quantitate finita darinon poſle, quis <lb/>unquam probavit; </s> <s xml:id="echoid-s619" xml:space="preserve">ut & </s> <s xml:id="echoid-s620" xml:space="preserve">omnia infinita eſſe æqualia? </s> <s xml:id="echoid-s621" xml:space="preserve">Con-<lb/>trarium in Scholio ſequenti demonſtratur.</s> <s xml:id="echoid-s622" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s623" xml:space="preserve">Si, examinatâ poſſibili materia diviſibilitate, partium ſub-<lb/> <anchor type="note" xlink:label="note-0037-02a" xlink:href="note-0037-02"/> tilitatem in corporibus ad examen revocemus, hanc captum <lb/>noſtrum in immenſumſuperare conſtabit; </s> <s xml:id="echoid-s624" xml:space="preserve">innumeraque in re-<lb/>rum natura dantur exempla talium particularum a ſe invicem <lb/>ſeparatarum.</s> <s xml:id="echoid-s625" xml:space="preserve"/> </p> <div xml:id="echoid-div55" type="float" level="2" n="5"> <note position="right" xlink:label="note-0037-02" xlink:href="note-0037-02a" xml:space="preserve">25.</note> </div> <p> <s xml:id="echoid-s626" xml:space="preserve">Boileus hæc variis probat argumentis.</s> <s xml:id="echoid-s627" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s628" xml:space="preserve">Loquitur de filo ſerico trecentis ulnis Anglicanis longo & </s> <s xml:id="echoid-s629" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0037-03a" xlink:href="note-0037-03"/> ponderis duorum granorum cum ſemiſſe.</s> <s xml:id="echoid-s630" xml:space="preserve"/> </p> <div xml:id="echoid-div56" type="float" level="2" n="6"> <note position="right" xlink:label="note-0037-03" xlink:href="note-0037-03a" xml:space="preserve">26.</note> </div> <p> <s xml:id="echoid-s631" xml:space="preserve">Folia auri menſuravit, & </s> <s xml:id="echoid-s632" xml:space="preserve">ponderavit, & </s> <s xml:id="echoid-s633" xml:space="preserve">reperit quinqua-<lb/> <anchor type="note" xlink:label="note-0037-04a" xlink:href="note-0037-04"/> ginta pollices quadratos unicum tantum ponderare granum; <lb/></s> <s xml:id="echoid-s634" xml:space="preserve">ſi unius pollicis longitudo dividatur in ducentas partes, omnes <lb/>oculo diſtingui poterunt, dantur ergo in pollice quadrato <lb/>partes viſibiles quadraginta millia, & </s> <s xml:id="echoid-s635" xml:space="preserve">in uno auri grano par-<lb/>tium numerus eſt duarum millionum, quas partes viſibiles <lb/>adhuc poſſe dividi nemo negabit.</s> <s xml:id="echoid-s636" xml:space="preserve"/> </p> <div xml:id="echoid-div57" type="float" level="2" n="7"> <note position="right" xlink:label="note-0037-04" xlink:href="note-0037-04a" xml:space="preserve">27.</note> </div> <pb o="8" file="0038" n="38" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s637" xml:space="preserve">Octo granis auri deaurari poteſt integra argenti uncia, <lb/> <anchor type="note" xlink:label="note-0038-01a" xlink:href="note-0038-01"/> quæ deinde porrigitur in filum longitudinis tredecim millium <lb/>pedum.</s> <s xml:id="echoid-s638" xml:space="preserve"/> </p> <div xml:id="echoid-div58" type="float" level="2" n="8"> <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">28.</note> </div> <p> <s xml:id="echoid-s639" xml:space="preserve">In corporibus odoriferis majorem adhuc partium percipi-<lb/> <anchor type="note" xlink:label="note-0038-02a" xlink:href="note-0038-02"/> mus ſubtilitatem & </s> <s xml:id="echoid-s640" xml:space="preserve">quidem a ſe invicem ſeparatarum, plura <lb/>longo tempore fere nihil ſui ponderis amittunt & </s> <s xml:id="echoid-s641" xml:space="preserve">ſpatium <lb/>fatis magnum particulis odoriferis continuo implent, qui <lb/>computum de tali ſubtilitate inire voluerit in illarum nume-<lb/>ro quid portenti facile reperiet.</s> <s xml:id="echoid-s642" xml:space="preserve"/> </p> <div xml:id="echoid-div59" type="float" level="2" n="9"> <note position="left" xlink:label="note-0038-02" xlink:href="note-0038-02a" xml:space="preserve">29.</note> </div> <p> <s xml:id="echoid-s643" xml:space="preserve">Ope microſcopiorum objecta quæ viſum fugiunt magna <lb/> <anchor type="note" xlink:label="note-0038-03a" xlink:href="note-0038-03"/> videntur, dantur animalcula per optima microſcopia vix vi-<lb/>ſibilia, habent tamen partes omnes ad vitam neceſſarias, ſan-<lb/>guinem, & </s> <s xml:id="echoid-s644" xml:space="preserve">alia liquida: </s> <s xml:id="echoid-s645" xml:space="preserve">ſubtilitas partium illa componentium <lb/>quanta ſit quis non videt?</s> <s xml:id="echoid-s646" xml:space="preserve"/> </p> <div xml:id="echoid-div60" type="float" level="2" n="10"> <note position="left" xlink:label="note-0038-03" xlink:href="note-0038-03a" xml:space="preserve">30.</note> </div> </div> <div xml:id="echoid-div62" type="section" level="1" n="29"> <head xml:id="echoid-head65" xml:space="preserve">SCHOLIUM.</head> <head xml:id="echoid-head66" style="it" xml:space="preserve">De Materiæ Diviſibilitate</head> <p> <s xml:id="echoid-s647" xml:space="preserve">In finitum vocant quidam illud, quo non datur majus, & </s> <s xml:id="echoid-s648" xml:space="preserve">negant materiam, <lb/>eſſe diviſibilem in infinitum, quod, hac Infiniti data definitione, libenter <lb/>concedimus. </s> <s xml:id="echoid-s649" xml:space="preserve">Corpus in talem numerum partium, qui ſit omuium maximus, <lb/>non poſſe dividi, nullumque diviſionis dari limitem, defendimus.</s> <s xml:id="echoid-s650" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div63" type="section" level="1" n="30"> <head xml:id="echoid-head67" style="it" xml:space="preserve">Infinitum finito contineri.</head> <p> <s xml:id="echoid-s651" xml:space="preserve">Infinitum eſt quod finitum ſuperat; </s> <s xml:id="echoid-s652" xml:space="preserve">partes autem numero, omnem finitum nu-<lb/> <anchor type="note" xlink:label="note-0038-04a" xlink:href="note-0038-04"/> merum ſuperante, in quantitate finita contineri, ex conſideratione progreſſionis <lb/>geometricæ decreſcentis deducitur.</s> <s xml:id="echoid-s653" xml:space="preserve"/> </p> <div xml:id="echoid-div63" type="float" level="2" n="1"> <note position="left" xlink:label="note-0038-04" xlink:href="note-0038-04a" xml:space="preserve">31.</note> </div> <p> <s xml:id="echoid-s654" xml:space="preserve">Progreſſionem hanc Ex gr. </s> <s xml:id="echoid-s655" xml:space="preserve">{1/2}, {1/4}, {1/8}, {1/16} &</s> <s xml:id="echoid-s656" xml:space="preserve">c. </s> <s xml:id="echoid-s657" xml:space="preserve">in infinitum poſſe continuari, <lb/>nullumque dari continuationis limitem quis non videt? </s> <s xml:id="echoid-s658" xml:space="preserve">Omnium tamen ter-<lb/>minorum ſummam nunquam excedere unitatem; </s> <s xml:id="echoid-s659" xml:space="preserve">imo exacte unitati æquari <lb/>demonſtramus, ſi revera in infinitum continuatam concipiamus progreſſio-<lb/>nem.</s> <s xml:id="echoid-s660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s661" xml:space="preserve">Sit linea AE unitas; </s> <s xml:id="echoid-s662" xml:space="preserve">hujus dimidium AB eſt primus terminus {1/2}; </s> <s xml:id="echoid-s663" xml:space="preserve">BC di-<lb/> <anchor type="note" xlink:label="note-0038-05a" xlink:href="note-0038-05"/> midium reliqui eſt terminus ſecundus {1/4}; </s> <s xml:id="echoid-s664" xml:space="preserve">tertius terminus erit CD {1/8}; </s> <s xml:id="echoid-s665" xml:space="preserve">dividen-<lb/>do DE in duas partes æquales habetur terminus ſequens; </s> <s xml:id="echoid-s666" xml:space="preserve">& </s> <s xml:id="echoid-s667" xml:space="preserve">eodem modo <lb/>in infinitum continuari poteſt ſeries, ſemperque defectus ſummæ termino-<lb/>rum ſeriei AB, BC, CD, &</s> <s xml:id="echoid-s668" xml:space="preserve">c. </s> <s xml:id="echoid-s669" xml:space="preserve">ab integra linea AE ultimo termino ipſius <lb/>ſeriei æqualis erit quantumvis hæc continuetur. </s> <s xml:id="echoid-s670" xml:space="preserve">Quamdiu autem numerus <lb/>terminorum eſt finitus denominator fractionis, ultimum terminum exprimen-<lb/>tis, eſt numerus finitus, & </s> <s xml:id="echoid-s671" xml:space="preserve">ultimus terminus eſt pars finita, qua ſumma ſeriei <lb/>ab integra unitate deficit.</s> <s xml:id="echoid-s672" xml:space="preserve"/> </p> <div xml:id="echoid-div64" type="float" level="2" n="2"> <note position="left" xlink:label="note-0038-05" xlink:href="note-0038-05a" xml:space="preserve">TAB. I. <lb/>fig 1.</note> </div> <p> <s xml:id="echoid-s673" xml:space="preserve">Sivero numerus terminorum lomnem finitum numerum ſuperet, denomi-<lb/>nator ultimi termini omnem numerum finitum ſuperabit, partemque lineæ <lb/>AE exprimet omni parte finita minorem, ideoque differentia ſumman ſeriei <pb o="9" file="0039" n="39" rhead="MATHEMATICA. LIB. I CAP. IV."/> & </s> <s xml:id="echoid-s674" xml:space="preserve">lineam AE inter evaneſcet, id eſt erunt æquales quantitates hæ. </s> <s xml:id="echoid-s675" xml:space="preserve">Q. </s> <s xml:id="echoid-s676" xml:space="preserve">E. </s> <s xml:id="echoid-s677" xml:space="preserve">D.</s> <s xml:id="echoid-s678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s679" xml:space="preserve">Infiniti ideam non habemus; </s> <s xml:id="echoid-s680" xml:space="preserve">ideo ideis non aſſequimur, quæ de infinito de-<lb/>monſtramus; </s> <s xml:id="echoid-s681" xml:space="preserve">quæ tamen ex indubitatis principiis immediate ſequuntur, cer-<lb/>ta ſunt, &</s> <s xml:id="echoid-s682" xml:space="preserve">, quæ ex hiſce deducuntur, etiam in dubium vocari nequeunt.</s> <s xml:id="echoid-s683" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s684" xml:space="preserve">Innumera circa Materiæ diviſibilitatem captum noſtrum ſuperantia eviden-<lb/>tiſſime demonſtrantur, inter hæc notatu maximedigna ſunt, quæ ſpectant cur-<lb/>vam ſpiralem logarithmicam dictam.</s> <s xml:id="echoid-s685" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div66" type="section" level="1" n="31"> <head xml:id="echoid-head68" style="it" xml:space="preserve">De Spirali logaritbmicâ, & bujus menſurâ.</head> <p> <s xml:id="echoid-s686" xml:space="preserve">Hujus curvæ proprietas eſt, quod cum omnibus lineis ad centrum curvæ <lb/> <anchor type="note" xlink:label="note-0039-01a" xlink:href="note-0039-01"/> ductis angulos efficiat inter ſe æquales.</s> <s xml:id="echoid-s687" xml:space="preserve"/> </p> <div xml:id="echoid-div66" type="float" level="2" n="1"> <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">32.</note> </div> <p> <s xml:id="echoid-s688" xml:space="preserve">Sit centrum C: </s> <s xml:id="echoid-s689" xml:space="preserve">in A angulus curvæ, id eſt tangentis ad curvam, cum radio <lb/> <anchor type="note" xlink:label="note-0039-02a" xlink:href="note-0039-02"/> AC, nempe BAC, æqualis eſt angulo EDC, quem tangens, in puncto alio <lb/>quocunque D, cum linea DC efficit.</s> <s xml:id="echoid-s690" xml:space="preserve"/> </p> <div xml:id="echoid-div67" type="float" level="2" n="2"> <note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">TAB. I. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s691" xml:space="preserve">Si angulus hic fuerit rectus, ſpiralis in circulum ſe convertet, ſi autem <lb/>fuerit acutus, ad centrum continuo accederefacile patet: </s> <s xml:id="echoid-s692" xml:space="preserve">non tamen niſi poſt <lb/>infinitos gyros ad hoc pervenire poterit.</s> <s xml:id="echoid-s693" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s694" xml:space="preserve">Ponamus revolutionem primam, poſito curvæ initio in A, terminari in F, <lb/>puncto medio inter A & </s> <s xml:id="echoid-s695" xml:space="preserve">centrum C. </s> <s xml:id="echoid-s696" xml:space="preserve">In hoc caſu angulus BAC paululum <lb/>excedet 80. </s> <s xml:id="echoid-s697" xml:space="preserve">gr. </s> <s xml:id="echoid-s698" xml:space="preserve">57′. </s> <s xml:id="echoid-s699" xml:space="preserve">Secunda revolutio ad FC illam habet relationem, quam <lb/>prima ad AC; </s> <s xml:id="echoid-s700" xml:space="preserve">ideoque terminabitur in G, puncto medio inter F & </s> <s xml:id="echoid-s701" xml:space="preserve">C, quod <lb/>ad gyros ſequentes etiam applicari debet; </s> <s xml:id="echoid-s702" xml:space="preserve">& </s> <s xml:id="echoid-s703" xml:space="preserve">punctum quod in curva movetur <lb/> <anchor type="note" xlink:label="note-0039-03a" xlink:href="note-0039-03"/> in integra revolutione quacunque, accedendo ad centrum, percurrit dimidi-<lb/>um diſtantiæ ſuæ a centro in principio revolutionis. </s> <s xml:id="echoid-s704" xml:space="preserve">Licet ergo ad diſtanti-<lb/>am a centro quantumvis exiguam pervenerit, non unicâ revolutione ad hoc per-<lb/>venire poterit; </s> <s xml:id="echoid-s705" xml:space="preserve">auctoque numero revolutionum, quantum quis voluerit, non-<lb/>dum ultimam attinget; </s> <s xml:id="echoid-s706" xml:space="preserve">& </s> <s xml:id="echoid-s707" xml:space="preserve">numerus revolutionum omnem numer um finitum ſupe-<lb/>rabit.</s> <s xml:id="echoid-s708" xml:space="preserve"/> </p> <div xml:id="echoid-div68" type="float" level="2" n="3"> <note position="right" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">33</note> </div> <p> <s xml:id="echoid-s709" xml:space="preserve">Ad centrum tamen curvam pertingere, ibique terminari, etiam conſtat. </s> <s xml:id="echoid-s710" xml:space="preserve">Sit por-<lb/> <anchor type="note" xlink:label="note-0039-04a" xlink:href="note-0039-04"/> tio curvæ ABEG; </s> <s xml:id="echoid-s711" xml:space="preserve">cujus centrum C; </s> <s xml:id="echoid-s712" xml:space="preserve">quo eodem centro, radio CG, deſcri-<lb/> <anchor type="note" xlink:label="note-0039-05a" xlink:href="note-0039-05"/> batur circuli portio GL, ſecans lineam C A in L.</s> <s xml:id="echoid-s713" xml:space="preserve"/> </p> <div xml:id="echoid-div69" type="float" level="2" n="4"> <note position="right" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">34</note> <note position="right" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">TAB. I. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s714" xml:space="preserve">Concipiamus LA diviſam in partes æquales, ſed exiguas, AD, DI, IL, <lb/>per quarum ſeparationes concipiamus circulorum portiones, centro C de-<lb/>ſcriptas, ſecantes curvam in B & </s> <s xml:id="echoid-s715" xml:space="preserve">E; </s> <s xml:id="echoid-s716" xml:space="preserve">ductiſque radiis BC, EC, formentur <lb/>triangula rectangula ADB, BFE, EHG, in quibus propter exiguas AD, <lb/>DI, IL, hypotenuſæ, licet portiones curvæ, pro rectis haberi poſſunt; </s> <s xml:id="echoid-s717" xml:space="preserve">nume-<lb/>rus enim partium in AL in infinitum poteſt concipi auctus, manentibus, quæ <lb/>huc uſque ſunt expoſita, ut & </s> <s xml:id="echoid-s718" xml:space="preserve">iis, quæ ſequuntur.</s> <s xml:id="echoid-s719" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s720" xml:space="preserve">Triangula memorata ſunt omnia ſimilia inter ſe; </s> <s xml:id="echoid-s721" xml:space="preserve">quia ſunt rectangula, & </s> <s xml:id="echoid-s722" xml:space="preserve"><lb/>præterea ex natura Curvæ angulos habent æquales BAD, EBF, GEH. </s> <s xml:id="echoid-s723" xml:space="preserve">Sunt <lb/>etiam æqualia, propter latera homologa æqualia AD, BF, EH, quod ex æ-<lb/>qualitate partium AD, DI, IL, ſ quitur.</s> <s xml:id="echoid-s724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s725" xml:space="preserve">Ex A ducatur linea A c, cum C A angulum efficiens CA c, æqualem an-<lb/>gulo CAB; </s> <s xml:id="echoid-s726" xml:space="preserve">ad AC in centro C & </s> <s xml:id="echoid-s727" xml:space="preserve">punctis L, I, D, erigantur perpendicu-<lb/>lares C c, L g, I e, D b, ſecantes A c in punctis c, g, e, b; </s> <s xml:id="echoid-s728" xml:space="preserve">ductiſque bf <lb/>& </s> <s xml:id="echoid-s729" xml:space="preserve">eb parallelis ad AC, formantur triangula AD b, bfe, ebg, ſimilia & </s> <s xml:id="echoid-s730" xml:space="preserve">æ-<lb/>qualia inter ſe, ut & </s> <s xml:id="echoid-s731" xml:space="preserve">triangulis ABD, BFE, EHG, ut ex conſtructione li-<lb/>quet.</s> <s xml:id="echoid-s732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s733" xml:space="preserve">Idcirco hypotenuſæ A b, be, eg, æquales ſunt hypotenuſis AB, BE, EG, id <lb/>eſt, linea A g æqualis eſt curvæ portioni AG.</s> <s xml:id="echoid-s734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s735" xml:space="preserve">Hinc patet quomodo portio quæcunque curvæ menſuranda ſit, curvam-<lb/> <anchor type="note" xlink:label="note-0039-06a" xlink:href="note-0039-06"/> <pb o="10" file="0040" n="40" rhead="PHYSICES ELEMENTA"/> que non æquari lineæ A c, niſi ad centrum uſque continuetur, illam autem <lb/>finitæ eſſe longitudinis, licet inſinitos gyros peragat.</s> <s xml:id="echoid-s736" xml:space="preserve"/> </p> <div xml:id="echoid-div70" type="float" level="2" n="5"> <note position="right" xlink:label="note-0039-06" xlink:href="note-0039-06a" xml:space="preserve">35.</note> </div> <p> <s xml:id="echoid-s737" xml:space="preserve">Si nunc concipiamus punctum, quod ex A procedat, & </s> <s xml:id="echoid-s738" xml:space="preserve">velocitate quacun-<lb/>que finita moveatur ita, ut hujus directio ad lineas ad C ductas ſemper æqua-<lb/>liter in clinetur, augulos efficiens æquales angulo c AC, perveniet punctum <lb/> <anchor type="note" xlink:label="note-0040-01a" xlink:href="note-0040-01"/> hoc ad C tempore finito, in co nempe in quo eadem velocitate rectam Ac <lb/>potuiſſet percurrere; </s> <s xml:id="echoid-s739" xml:space="preserve">id eſt finito tempore, velocitate finita, in ſpatio finito, per-<lb/>aget infinitos gyros.</s> <s xml:id="echoid-s740" xml:space="preserve"/> </p> <div xml:id="echoid-div71" type="float" level="2" n="6"> <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">36.</note> </div> </div> <div xml:id="echoid-div73" type="section" level="1" n="32"> <head xml:id="echoid-head69" style="it" xml:space="preserve">De infinitorum Inæqualitate</head> <p> <s xml:id="echoid-s741" xml:space="preserve">Non omnia infinita eſſe æqualia, evidentiſſime patebit, ſi conſideremus lineam, <lb/> <anchor type="note" xlink:label="note-0040-02a" xlink:href="note-0040-02"/> quæ ad partem quamcunque extenditur, in infinitum poſſe produci, talemque <lb/>lineam in finitam eſſe; </s> <s xml:id="echoid-s742" xml:space="preserve">minor tamen erit aliâ lineâ, quam partem utram que ver-<lb/>ſus productam concipimus in infinitum, hanc etiam ambarum ſumma ſupe-<lb/>rabit.</s> <s xml:id="echoid-s743" xml:space="preserve"/> </p> <div xml:id="echoid-div73" type="float" level="2" n="1"> <note position="left" xlink:label="note-0040-02" xlink:href="note-0040-02a" xml:space="preserve">37.</note> </div> <p> <s xml:id="echoid-s744" xml:space="preserve">Infinita linea continet numerum infinitum pedum, duodecuplum numerum <lb/>pollicum.</s> <s xml:id="echoid-s745" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s746" xml:space="preserve">Infinitorum inæqualitatem etiam detegimus, comparando diverſas curvas <lb/>ſpirales logarhthmicas ſtatim indicatas.</s> <s xml:id="echoid-s747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s748" xml:space="preserve">Præter jam memoratam, & </s> <s xml:id="echoid-s749" xml:space="preserve">pro parte hic delineatam, curvam, concipiamus <lb/> <anchor type="note" xlink:label="note-0040-03a" xlink:href="note-0040-03"/> & </s> <s xml:id="echoid-s750" xml:space="preserve">aliam ſpitalem logarithmiam, ex A exeuntem, & </s> <s xml:id="echoid-s751" xml:space="preserve">ad centrum ita tenden-<lb/> <anchor type="note" xlink:label="note-0040-04a" xlink:href="note-0040-04"/> tem, ut duabus revolutionibus pertingat ad F, duabus aliis pertinget ad G; <lb/></s> <s xml:id="echoid-s752" xml:space="preserve">quia duæ requiruntur revolutiones, ut accedendo ad centrum dimidium di-<lb/>ſtantiæ ab hoc percurrat, numerus revolutionum in hac duplus eſt nu-<lb/>meri revolutionum in ſpirali prima, quando æqualiter cum hac prima ADF <lb/>ad centrum accedit; </s> <s xml:id="echoid-s753" xml:space="preserve">duploque numero revolutionum ad centrum pertinget: </s> <s xml:id="echoid-s754" xml:space="preserve"><lb/>utraque tamen curva niſi poſt infinitas revolutiones ad centrum non accedit.</s> <s xml:id="echoid-s755" xml:space="preserve"/> </p> <div xml:id="echoid-div74" type="float" level="2" n="2"> <note position="left" xlink:label="note-0040-03" xlink:href="note-0040-03a" xml:space="preserve">38.</note> <note position="left" xlink:label="note-0040-04" xlink:href="note-0040-04a" xml:space="preserve">TAB. I. <lb/>fig. 4.</note> </div> </div> <div xml:id="echoid-div76" type="section" level="1" n="33"> <head xml:id="echoid-head70" style="it" xml:space="preserve">De infinitorum claſſibus.</head> <p> <s xml:id="echoid-s756" xml:space="preserve">Quæ de infinito omnium maxime paradoxa demonſtrantur, ideaſque no-<lb/>ſtras in immenſum ſuperant, ſunt quæ ſpectant infinitorum claſſes va rias.</s> <s xml:id="echoid-s757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s758" xml:space="preserve">Detur curva ABC parabola, cujus abſciſſa quæqcunque ſit AD ordinata <lb/> <anchor type="note" xlink:label="note-0040-05a" xlink:href="note-0040-05"/> huic reſpondens DC. <lb/></s> <s xml:id="echoid-s759" xml:space="preserve"> <anchor type="note" xlink:label="note-0040-06a" xlink:href="note-0040-06"/> </s> </p> <div xml:id="echoid-div76" type="float" level="2" n="1"> <note position="left" xlink:label="note-0040-05" xlink:href="note-0040-05a" xml:space="preserve">93.</note> <note position="left" xlink:label="note-0040-06" xlink:href="note-0040-06a" xml:space="preserve">TAB. I. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s760" xml:space="preserve">Nota eſt hujus curvæ proprietas, ordinatam mediam eſſe proportionalem <lb/>inter abſciſſam & </s> <s xml:id="echoid-s761" xml:space="preserve">determinatam quandam lineam, quæ parameter dicitur: <lb/></s> <s xml:id="echoid-s762" xml:space="preserve">quare ſi abſciſſa quæcunque dicatur x, ordinata reſpondens y, parameter a, <lb/> <anchor type="note" xlink:label="note-0040-07a" xlink:href="note-0040-07"/> in omnibus parabolæ punctis habemus {.</s> <s xml:id="echoid-s763" xml:space="preserve">./.</s> <s xml:id="echoid-s764" xml:space="preserve">.} x, y, a; </s> <s xml:id="echoid-s765" xml:space="preserve">ideo ax = yy <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s766" xml:space="preserve">quæ ergo æquatio naturam parabolæ exprimit. </s> <s xml:id="echoid-s767" xml:space="preserve">Evaneſcente x evaneſcit y, & </s> <s xml:id="echoid-s768" xml:space="preserve">Parabo-<lb/>la cum AF, per A parallelâ ad abſciſſas, non congruit, daturque tota infra hanc <lb/>lineam, quæ illam tangit, & </s> <s xml:id="echoid-s769" xml:space="preserve">cum qua efficit angulum mixtum FAC.</s> <s xml:id="echoid-s770" xml:space="preserve"/> </p> <div xml:id="echoid-div77" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0040-07" xlink:href="note-0040-07a" xml:space="preserve"> La Hire. <lb/>ſict. cou. <lb/>lib. 3. <lb/>pro. 2.</note> </div> <p> <s xml:id="echoid-s771" xml:space="preserve">Si augeatur a manente x augetur y, & </s> <s xml:id="echoid-s772" xml:space="preserve">ſeſe expandit Parabola, aut potius <lb/>formatur nova, in qua omnes ordinatæ aliûs curvæ ordinatas reſpondentes <lb/>ſuperant; </s> <s xml:id="echoid-s773" xml:space="preserve">ita ut curva prima ſecundâ includatur, quæ inter primam & </s> <s xml:id="echoid-s774" xml:space="preserve">tan-<lb/>gentem AF tranſit, minoremque angulum mixtum cum hac efficit. </s> <s xml:id="echoid-s775" xml:space="preserve">Para-<lb/>meter autem in infinitum poteſt augeri, & </s> <s xml:id="echoid-s776" xml:space="preserve">eo in infinitum minui angulus, <lb/>quem cum tangente efficit Parabola.</s> <s xml:id="echoid-s777" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s778" xml:space="preserve">Servato axe AD & </s> <s xml:id="echoid-s779" xml:space="preserve">vertice A, detur alia curva AEG, cujus ordinatæ di-<lb/> <anchor type="note" xlink:label="note-0040-08a" xlink:href="note-0040-08"/> cantur z, quarum relatio cum reſpondentibus abſciſſis x exprimatur hac æ-<lb/>quatione bbx = z<emph style="super">3</emph>: </s> <s xml:id="echoid-s780" xml:space="preserve">b deſignat lineam conſtantem.</s> <s xml:id="echoid-s781" xml:space="preserve"/> </p> <div xml:id="echoid-div78" type="float" level="2" n="3"> <note position="left" xlink:label="note-0040-08" xlink:href="note-0040-08a" xml:space="preserve">40.</note> </div> <p> <s xml:id="echoid-s782" xml:space="preserve">Augendo b augentur omnes z, & </s> <s xml:id="echoid-s783" xml:space="preserve">mutatur curva in magis apertam, minui-<lb/>turque angulus contactus, qui augendo b in infinitum minui poteſt.</s> <s xml:id="echoid-s784" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s785" xml:space="preserve">Habemus ergo duasclaſſes angulorum decr eſcentium in infinitum; </s> <s xml:id="echoid-s786" xml:space="preserve">barum integra ſe-<lb/> <anchor type="note" xlink:label="note-0040-09a" xlink:href="note-0040-09"/> <pb o="11" file="0041" n="41" rhead="MATHEMATICA. LIB. I. CAP. IV."/> cunda infinite exigua eſt reſpectu primæ, demonſtramus enim angulum quemcun-<lb/>quein ſecunda ſuperari ab angulo quocunque, id eſt, utcumque exiguo, in prima.</s> <s xml:id="echoid-s787" xml:space="preserve"/> </p> <div xml:id="echoid-div79" type="float" level="2" n="4"> <note position="left" xlink:label="note-0040-09" xlink:href="note-0040-09a" xml:space="preserve">41.</note> </div> <p> <s xml:id="echoid-s788" xml:space="preserve">Sit c tertia proportionalis ipſis a & </s> <s xml:id="echoid-s789" xml:space="preserve">b, utcunque ſumtis; </s> <s xml:id="echoid-s790" xml:space="preserve">ergo ac = bb. <lb/></s> <s xml:id="echoid-s791" xml:space="preserve">Multiplicando per c æquationem ax = yy, habemus acx = yyc, id eſt bbx = yyc. </s> <s xml:id="echoid-s792" xml:space="preserve"><lb/>in ſecunda curva bbx valet z<emph style="super">3</emph>; </s> <s xml:id="echoid-s793" xml:space="preserve">ergo z<emph style="super">3</emph> = yyc, ſi abſciſſa x fuerit eademiu <lb/>utraque curva.</s> <s xml:id="echoid-s794" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s795" xml:space="preserve">Ex æquatione hac deducimus z, c:</s> <s xml:id="echoid-s796" xml:space="preserve">:yy, z<emph style="super">2</emph>: </s> <s xml:id="echoid-s797" xml:space="preserve">unde patet yy ſuperari à zz, id <lb/>eſt, y minorem eſſe z, quamdiu hæc ac ſuperatur, unde ſequitur curvam ſe-<lb/>cundam dum ex A profluit, antequam z valeat c, inter tangentem & </s> <s xml:id="echoid-s798" xml:space="preserve">curvam <lb/>primam dari quod univerſaliter obtineri hac demonſtratione conſtat.</s> <s xml:id="echoid-s799" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s800" xml:space="preserve">Ponamus nunc tertiam dari curvam AI, cujus axis etiam eſt AD, & </s> <s xml:id="echoid-s801" xml:space="preserve">cujus æ-<lb/> <anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/> quatio, manentibus iiſdem abſciſſis x, ſit dx = u<emph style="super">4</emph>; </s> <s xml:id="echoid-s802" xml:space="preserve">u eſt ordinata quæ-<lb/>cunque; </s> <s xml:id="echoid-s803" xml:space="preserve">& </s> <s xml:id="echoid-s804" xml:space="preserve">d linea determinata; </s> <s xml:id="echoid-s805" xml:space="preserve">hanc ſi augeamus, mutamus curvam & </s> <s xml:id="echoid-s806" xml:space="preserve">mi-<lb/>nuimus angulum quem curva cum tangente AF efficit; </s> <s xml:id="echoid-s807" xml:space="preserve">formaturque hiſce <lb/>curvis tertia claſſis angulorum, qui in infinitum minui poſſunt, & </s> <s xml:id="echoid-s808" xml:space="preserve">in qua <lb/>nullus datur angulus, qui non ſuperetur ab angulo quocunque in ſecunda.</s> <s xml:id="echoid-s809" xml:space="preserve"/> </p> <div xml:id="echoid-div80" type="float" level="2" n="5"> <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">42.</note> </div> <p> <s xml:id="echoid-s810" xml:space="preserve">Datis b & </s> <s xml:id="echoid-s811" xml:space="preserve">d quibuſcunque, ſit bb ad dd; </s> <s xml:id="echoid-s812" xml:space="preserve">ut dad quartam quam dicamus e; </s> <s xml:id="echoid-s813" xml:space="preserve">erit <lb/>ergo bbe = d<emph style="super">3</emph>, & </s> <s xml:id="echoid-s814" xml:space="preserve">æquatio curvæ bbx = z<emph style="super">3</emph> mutabitur in hanc bbex = d<emph style="super">3</emph> x <lb/> = z<emph style="super">3</emph> e; </s> <s xml:id="echoid-s815" xml:space="preserve">ideoque z<emph style="super">3</emph> e = u<emph style="super">4</emph>, ſi agatur de iiſdem abſciſſis in utraque curva; </s> <s xml:id="echoid-s816" xml:space="preserve">id-<lb/>circo u, e:</s> <s xml:id="echoid-s817" xml:space="preserve">:z<emph style="super">3</emph>, u<emph style="super">3</emph>; </s> <s xml:id="echoid-s818" xml:space="preserve">ergo u ſuperat z, quamdiu e ſuperat u, &</s> <s xml:id="echoid-s819" xml:space="preserve">, exeundo ex A, <lb/>curva, cujus abſciſſæ ſunt u, tranſit inter AF & </s> <s xml:id="echoid-s820" xml:space="preserve">aliam curvam Q. </s> <s xml:id="echoid-s821" xml:space="preserve">D. </s> <s xml:id="echoid-s822" xml:space="preserve">E.</s> <s xml:id="echoid-s823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s824" xml:space="preserve">Curvæ, quarum æquatio eſt f<emph style="super">4</emph> x = t<emph style="super">3</emph> poſita f quantitate determinatâ in ſin-<lb/>gulis curvis, & </s> <s xml:id="echoid-s825" xml:space="preserve">t ordinata quæcunque, dabunt novam claſſem angulorum mino-<lb/> <anchor type="note" xlink:label="note-0041-02a" xlink:href="note-0041-02"/> rum omnibus memoratis, & </s> <s xml:id="echoid-s826" xml:space="preserve">eodem modo claſſes in infinitum formari poſſunt, <lb/>ſemperque omnes anguli in claſſe quacunque ſuperantur ab omnibus angulis in claſ-<lb/>ſe præcedenti, & </s> <s xml:id="echoid-s827" xml:space="preserve">ſuperant omnes angulos in claſſe ſequenti.</s> <s xml:id="echoid-s828" xml:space="preserve"/> </p> <div xml:id="echoid-div81" type="float" level="2" n="6"> <note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">43.</note> </div> <p style="it"> <s xml:id="echoid-s829" xml:space="preserve">Inter duas claſſes quaſcunque datur ſeries infinita claſſium; </s> <s xml:id="echoid-s830" xml:space="preserve">quæ omnes eandem <lb/> <anchor type="note" xlink:label="note-0041-03a" xlink:href="note-0041-03"/> proprietatem babent, ut angulus quicunque unius ſit infinite parvus reſpectu angulo-<lb/>rum claſſis præcedentis, id eſt, ut ab omnibus ſuperetur, & </s> <s xml:id="echoid-s831" xml:space="preserve">infinite magnusre-<lb/>ſpectu claſſis ſequentis, cujus omnes angulos ſuperat.</s> <s xml:id="echoid-s832" xml:space="preserve"/> </p> <div xml:id="echoid-div82" type="float" level="2" n="7"> <note position="right" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">44.</note> </div> <p> <s xml:id="echoid-s833" xml:space="preserve">Curvæ ax = yy & </s> <s xml:id="echoid-s834" xml:space="preserve">bbx = z<emph style="super">3</emph> claſſes formant diverſas; </s> <s xml:id="echoid-s835" xml:space="preserve">quia ordinatarum di-<lb/>menſio z<emph style="super">3</emph> id ſecunda unitate ſuperat dimenſionem y<emph style="super">2</emph> primæ curvæ; </s> <s xml:id="echoid-s836" xml:space="preserve">demon-<lb/>ſtrabimus autem claſſes differre, quantumvis parum hæ dimenſiones differant, <lb/>unde conſtabit propoſitum: </s> <s xml:id="echoid-s837" xml:space="preserve">quia inter hoſce numeros 2 & </s> <s xml:id="echoid-s838" xml:space="preserve">3, & </s> <s xml:id="echoid-s839" xml:space="preserve">alios quoſ-<lb/>cunque, innumeridaripoſſunt, quiinter ſe differunt, quorum nulli, quantumvis <lb/>parum differentes, dari poſſunt, inter quos iterum non alii innumeri dari <lb/>poſſint.</s> <s xml:id="echoid-s840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s841" xml:space="preserve">Sit ax = yy & </s> <s xml:id="echoid-s842" xml:space="preserve">g 1 {1/10} x = s 2 {1/10} id eſt, g {11/10} x = s {21/10}; </s> <s xml:id="echoid-s843" xml:space="preserve">ordinatas deſignat s, & </s> <s xml:id="echoid-s844" xml:space="preserve">g <lb/>conſtantem lineam, quamdiu curva non mutatur. </s> <s xml:id="echoid-s845" xml:space="preserve">Fiat ut a ad g, ita g {1/10} ad <lb/>quartam quantitatem, quæ dicatur b {1/10}; </s> <s xml:id="echoid-s846" xml:space="preserve">ergo g{11/10} = ab{1/10}; </s> <s xml:id="echoid-s847" xml:space="preserve">multiplican-<lb/>do per b {1/10} æquationem ax = yy datur ab {1/10} x = g {11/10} x = y<emph style="super">2</emph> b {1/10} = s {21/10}; <lb/></s> <s xml:id="echoid-s848" xml:space="preserve">under deducimus s {1/10}, b {1/10}:</s> <s xml:id="echoid-s849" xml:space="preserve">: yy. </s> <s xml:id="echoid-s850" xml:space="preserve">ss. </s> <s xml:id="echoid-s851" xml:space="preserve">Idcirco in viciniis puncti A, ubi s <lb/>neceſſario minor eſt determinatâ b, erit etiam y minor s unde liquet quod de <lb/>angulis dictum.</s> <s xml:id="echoid-s852" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s853" xml:space="preserve">Inter duas claſſes quaſcunque, quantitatum, quæ in infinitum differunt, da-<lb/> <anchor type="note" xlink:label="note-0041-04a" xlink:href="note-0041-04"/> ri in infinitum claſſes intermedias ex conſideratione mediarum proportiona-<lb/>lium etiam deducitur.</s> <s xml:id="echoid-s854" xml:space="preserve"/> </p> <div xml:id="echoid-div83" type="float" level="2" n="8"> <note position="right" xlink:label="note-0041-04" xlink:href="note-0041-04a" xml:space="preserve">45.</note> </div> <pb o="12" file="0042" n="42" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s855" xml:space="preserve">Si A ſit infinite magnum reſpectu a, media quæcunque proportionalis b <lb/>inter has quantitates minor eſt A, & </s> <s xml:id="echoid-s856" xml:space="preserve">major a, non tamen finitam habet rationem <lb/>ad A aut a; </s> <s xml:id="echoid-s857" xml:space="preserve">ratio enim A ad a componitur ex rationibus A ad b, & </s> <s xml:id="echoid-s858" xml:space="preserve">b ad a, & </s> <s xml:id="echoid-s859" xml:space="preserve"><lb/>ratio ex duabus finitis rationibus compoſita eſt etiam finita; </s> <s xml:id="echoid-s860" xml:space="preserve">ideo cum A & </s> <s xml:id="echoid-s861" xml:space="preserve">a in <lb/>infinitum differant, ratio inter A & </s> <s xml:id="echoid-s862" xml:space="preserve">b, aut b & </s> <s xml:id="echoid-s863" xml:space="preserve">a, omnem finitam rationem <lb/>ſuperat; </s> <s xml:id="echoid-s864" xml:space="preserve">quare etiam infinita eſt. </s> <s xml:id="echoid-s865" xml:space="preserve">In infinitum mediæ proportionales inter <lb/>duas quantitates dari poſſunt.</s> <s xml:id="echoid-s866" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div85" type="section" level="1" n="34"> <head xml:id="echoid-head71" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head72" style="it" xml:space="preserve">De partium Subtilitate.</head> <p> <s xml:id="echoid-s867" xml:space="preserve">Pondus auri, quo in n°. </s> <s xml:id="echoid-s868" xml:space="preserve">28. </s> <s xml:id="echoid-s869" xml:space="preserve">diximus argentum deaurari, eſt {1/60} ponderis ipſius <lb/> <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/> argenti. </s> <s xml:id="echoid-s870" xml:space="preserve">Volumen auri ſe habet ad volumen argenti, quando pondera <lb/>ſunt æqualia, ut 10 and 19, ergo volumen auri quo argentum obtegitur ad <lb/>volumen ipſius argenti obtecti, ut 1 ad 114. </s> <s xml:id="echoid-s871" xml:space="preserve">nam 10. </s> <s xml:id="echoid-s872" xml:space="preserve">19:</s> <s xml:id="echoid-s873" xml:space="preserve">:60.</s> <s xml:id="echoid-s874" xml:space="preserve">, 114.</s> <s xml:id="echoid-s875" xml:space="preserve"/> </p> <div xml:id="echoid-div85" type="float" level="2" n="1"> <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">46.</note> </div> <p> <s xml:id="echoid-s876" xml:space="preserve">Pes cubicus aquæ ponderat libras 63 {1/2} decies gravius eſt argentum; </s> <s xml:id="echoid-s877" xml:space="preserve">ergo <lb/>pes cubicus argenti libras 635. </s> <s xml:id="echoid-s878" xml:space="preserve">pondo eſt.</s> <s xml:id="echoid-s879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s880" xml:space="preserve">Cubus eſt ad cylindrum, ejuſdem diametri & </s> <s xml:id="echoid-s881" xml:space="preserve">altitudinis, circiter ut 14 ad <lb/>11; </s> <s xml:id="echoid-s882" xml:space="preserve">pondus ergo pedis cylindrici argenti eſt librarum 499. </s> <s xml:id="echoid-s883" xml:space="preserve">aut unciarum 7984.</s> <s xml:id="echoid-s884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s885" xml:space="preserve">Uncia una porrigitur in filum 14000. </s> <s xml:id="echoid-s886" xml:space="preserve">pedum, & </s> <s xml:id="echoid-s887" xml:space="preserve">in pede cylindrico datur <lb/>filum 111776000. </s> <s xml:id="echoid-s888" xml:space="preserve">pedum, id eſt, tot dantur fila unius pedis.</s> <s xml:id="echoid-s889" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s890" xml:space="preserve">Circulorum ſuperficies ſunt ut quadrata diametrorum, ideo quadratum di-<lb/>ametri fili ad quadratum unius pedis, ut 1. </s> <s xml:id="echoid-s891" xml:space="preserve">ad 111776000; </s> <s xml:id="echoid-s892" xml:space="preserve">quorum numero-<lb/>rum radices ſunt 1 & </s> <s xml:id="echoid-s893" xml:space="preserve">10572, in qua ratione ſunt dictæ diametri; </s> <s xml:id="echoid-s894" xml:space="preserve">eſt ergo fili <lb/>diameter {1/10572} pedis, aut {1/881} pollicis. </s> <s xml:id="echoid-s895" xml:space="preserve">Aurum circumponitur & </s> <s xml:id="echoid-s896" xml:space="preserve">volumen <lb/>augetur {1/114}, id eſt ſectio circularis fili ea quantitate augetur, quod fiet ſi <lb/>filo circumponatur lamina, cujus craſſities eſt pars quarta partis {1/114} diame-<lb/>tri, area enim circuli habetur multiplicando circumferentiam per quartam <lb/>diametri partem.</s> <s xml:id="echoid-s897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s898" xml:space="preserve">Eſt ergo auri craſſities {1/456} diametri fili, quæ eſt {1/881} poll. </s> <s xml:id="echoid-s899" xml:space="preserve">ita ut auri <lb/>craſſities ſit {1/401736} pollicis.</s> <s xml:id="echoid-s900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s901" xml:space="preserve">Filahæctenuia deaurata, ut filis ſericis circumvolvantur, plana fiunt, quo ſu-<lb/>perficies ad minimum triplicatur, & </s> <s xml:id="echoid-s902" xml:space="preserve">in eadem ratione craſſities auri minuitur, <lb/>ita ut ſit {1/1205208}.</s> <s xml:id="echoid-s903" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s904" xml:space="preserve">Non æqualiter in omnibus punctis filum deauratur, & </s> <s xml:id="echoid-s905" xml:space="preserve">auri craſſities in qui-<lb/>buſdam locis forte duplo minor eſt, quare nihil a vero remotum ponimus, <lb/>ſi craſſitiem determinemus {1/2000000} pollicis, id eſt milleſima pars pollicis <lb/>in bis mille partes dividitur.</s> <s xml:id="echoid-s906" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s907" xml:space="preserve">Talis actu datur auri diviſio; </s> <s xml:id="echoid-s908" xml:space="preserve">ideoque particulæ, quæ arte ſeparantur, non <lb/>majorem diametrum habent, & </s> <s xml:id="echoid-s909" xml:space="preserve">talium partium in ſphæra aurea unius pollicis <lb/>dantur 8.</s> <s xml:id="echoid-s910" xml:space="preserve">000.</s> <s xml:id="echoid-s911" xml:space="preserve">000.</s> <s xml:id="echoid-s912" xml:space="preserve">000.</s> <s xml:id="echoid-s913" xml:space="preserve">000.</s> <s xml:id="echoid-s914" xml:space="preserve">000.</s> <s xml:id="echoid-s915" xml:space="preserve">000.</s> <s xml:id="echoid-s916" xml:space="preserve">; & </s> <s xml:id="echoid-s917" xml:space="preserve">in arenula minima, cujus nempe <lb/>diameter eſt pars centeſima pollicis, dantur particulæ 8,000.</s> <s xml:id="echoid-s918" xml:space="preserve">000.</s> <s xml:id="echoid-s919" xml:space="preserve">000.</s> <s xml:id="echoid-s920" xml:space="preserve">000: <lb/></s> <s xml:id="echoid-s921" xml:space="preserve">particula itaque ſe habet ad arenulam, ut hæc ad globum, cujus diameter ſu-<lb/>peraret 10. </s> <s xml:id="echoid-s922" xml:space="preserve">pedes, & </s> <s xml:id="echoid-s923" xml:space="preserve">non majorem numerum arenularum contineret globus <lb/>hic, quam particularum continet arenula. </s> <s xml:id="echoid-s924" xml:space="preserve">Globus vero continet 4096. </s> <s xml:id="echoid-s925" xml:space="preserve"><lb/>globosunius pedis.</s> <s xml:id="echoid-s926" xml:space="preserve"/> </p> <pb o="13" file="0043" n="43" rhead="MATHEMATICA. LIB. I. CAP. V."/> </div> <div xml:id="echoid-div87" type="section" level="1" n="35"> <head xml:id="echoid-head73" xml:space="preserve">CAPUT V.</head> <head xml:id="echoid-head74" style="it" xml:space="preserve">De cobæſione partium, ubi de Duritie, Mollitie, Fluidi-<lb/>tate, & Elaſticitate agitur.</head> <p> <s xml:id="echoid-s927" xml:space="preserve">OMne corpus quod in ſenſus noſtros cadit, ex particu-<lb/> <anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/> lis quam minimis conſtat, nulla illarum in ſe eſt in-<lb/>diviſibilis, noſtri reſpectu omnes ſunt, diviſio enim quæ a <lb/>nobis fieri poteſt, eſt particularum ſeparatio.</s> <s xml:id="echoid-s928" xml:space="preserve"/> </p> <div xml:id="echoid-div87" type="float" level="2" n="1"> <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">47.</note> </div> <p> <s xml:id="echoid-s929" xml:space="preserve">Quando magna vis ad illam ſeparationem requiritur, cor-<lb/>pus durum vocatur.</s> <s xml:id="echoid-s930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s931" xml:space="preserve">Si partes facilius cedant & </s> <s xml:id="echoid-s932" xml:space="preserve">cum ſublapſu partium intro-<lb/>cedant molle vocatur.</s> <s xml:id="echoid-s933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s934" xml:space="preserve">Sed hæc in ſignificatione vulgari, vis magna & </s> <s xml:id="echoid-s935" xml:space="preserve">minor ni-<lb/>hil determinati denotant, & </s> <s xml:id="echoid-s936" xml:space="preserve">corpus durum reſpectu unius ho-<lb/>minis, alteri molle videtur.</s> <s xml:id="echoid-s937" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div89" type="section" level="1" n="36"> <head xml:id="echoid-head75" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s938" xml:space="preserve">Philoſophicè corpus durum vocatur, cujus partes inter <lb/> <anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/> ſe cobærent, & </s> <s xml:id="echoid-s939" xml:space="preserve">neutiquam introcedunt, ita ut partes nullo mo-<lb/>tu affici poſſint quin diſrumpatur corpus.</s> <s xml:id="echoid-s940" xml:space="preserve"/> </p> <div xml:id="echoid-div89" type="float" level="2" n="1"> <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">48.</note> </div> <p> <s xml:id="echoid-s941" xml:space="preserve">Corpus tale perfectè durum nullum novimus.</s> <s xml:id="echoid-s942" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div91" type="section" level="1" n="37"> <head xml:id="echoid-head76" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s943" xml:space="preserve">Philoſophice corpus molle vocatur cujus partes introce-<lb/> <anchor type="note" xlink:label="note-0043-03a" xlink:href="note-0043-03"/> dunt & </s> <s xml:id="echoid-s944" xml:space="preserve">ſublabuntur, licet ad illud mallei ictus requirantur.</s> <s xml:id="echoid-s945" xml:space="preserve"/> </p> <div xml:id="echoid-div91" type="float" level="2" n="1"> <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">49.</note> </div> </div> <div xml:id="echoid-div93" type="section" level="1" n="38"> <head xml:id="echoid-head77" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s946" xml:space="preserve">Corpus cujus partes cuicunque impreſſioni cedunt & </s> <s xml:id="echoid-s947" xml:space="preserve">ce-<lb/> <anchor type="note" xlink:label="note-0043-04a" xlink:href="note-0043-04"/> dendo facillime moventur inter ſe vocatur fluidum.</s> <s xml:id="echoid-s948" xml:space="preserve"/> </p> <div xml:id="echoid-div93" type="float" level="2" n="1"> <note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">50.</note> </div> <p> <s xml:id="echoid-s949" xml:space="preserve">Hæc omnia a cohæſione partium pendent, quo arctior <lb/>eſt eo magis ad perfectam duritiem corpus accedit. </s> <s xml:id="echoid-s950" xml:space="preserve">Durities <lb/>vero particularum minimarum ab illarum ſoliditate non dif-<lb/>fert, & </s> <s xml:id="echoid-s951" xml:space="preserve">eſt proprietas eſſentialis corporis, quæ non magis <lb/>explicanda eſt, quam quare corpus ſit extenſum & </s> <s xml:id="echoid-s952" xml:space="preserve">mens <lb/>cogitet.</s> <s xml:id="echoid-s953" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s954" xml:space="preserve">An omnia corpora ex particulis æqualibus & </s> <s xml:id="echoid-s955" xml:space="preserve">ſimilibus con-<lb/>ſtent omnino ignoro, & </s> <s xml:id="echoid-s956" xml:space="preserve">circa cauſam cohæſionis particula-<lb/>rum adhuc multa obſcura ſunt.</s> <s xml:id="echoid-s957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s958" xml:space="preserve">Naturæ leges quæ hic locum habentex Phænomenis dedu-<lb/>cuntur.</s> <s xml:id="echoid-s959" xml:space="preserve"/> </p> <pb o="14" file="0044" n="44" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s960" xml:space="preserve">Cohæſionis lex peculiaris eſt, omnes particulas vi attra-<lb/> <anchor type="note" xlink:label="note-0044-01a" xlink:href="note-0044-01"/> ctiva gaudere, ideſt ſi vicinæ fuerint, ſponte ad ſe mutuo <lb/>tendunt, cujus motus cauſa nos latet, ſed cum hunc ge-<lb/>neraliter locum habere obſervemus, ipſum inter leges natu-<lb/>ræ referimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s961" xml:space="preserve"> <anchor type="note" xlink:label="note-0044-02a" xlink:href="note-0044-02"/> </s> </p> <div xml:id="echoid-div94" type="float" level="2" n="2"> <note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">51</note> <note symbol="*" position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">5.</note> </div> </div> <div xml:id="echoid-div96" type="section" level="1" n="39"> <head xml:id="echoid-head78" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s962" xml:space="preserve">Nomine attractionis intelligo vim quamcunque qua duo <lb/> <anchor type="note" xlink:label="note-0044-03a" xlink:href="note-0044-03"/> corpora ad ſe invicem tendunt; </s> <s xml:id="echoid-s963" xml:space="preserve">licet forte illud per impul-<lb/>ſum fiat.</s> <s xml:id="echoid-s964" xml:space="preserve"/> </p> <div xml:id="echoid-div96" type="float" level="2" n="1"> <note position="left" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve">52.</note> </div> <p style="it"> <s xml:id="echoid-s965" xml:space="preserve">Attractio autem, quæ in cohæſione partium locum habet, <lb/> <anchor type="note" xlink:label="note-0044-04a" xlink:href="note-0044-04"/> hiſce legibus ſubjicitur, ut in ipſo particularum contactu ſit <lb/>perquam magna, & </s> <s xml:id="echoid-s966" xml:space="preserve">ſubito decreſcat, ita ut ad diſtantiam <lb/>quam minimam, quæ ſub ſenſus cadit, non amplius agat, imo <lb/>etiam ad majorem diſtantiam ſeſe mutet in vim repellentem, <lb/>qua particulæ ſeſe mutuo fugiunt.</s> <s xml:id="echoid-s967" xml:space="preserve"/> </p> <div xml:id="echoid-div97" type="float" level="2" n="2"> <note position="left" xlink:label="note-0044-04" xlink:href="note-0044-04a" xml:space="preserve">53.</note> </div> <p> <s xml:id="echoid-s968" xml:space="preserve">Ope hujus legis multa Phænomena facillime explicantur, <lb/>& </s> <s xml:id="echoid-s969" xml:space="preserve">innumeris experimentis chemicis illa attractio & </s> <s xml:id="echoid-s970" xml:space="preserve">repulſio <lb/>pleniſſime probantur, etiam exſequentibus experimentis illas <lb/>dari ſatis patet.</s> <s xml:id="echoid-s971" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div99" type="section" level="1" n="40"> <head xml:id="echoid-head79" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s972" xml:space="preserve">In omnibus corporibus fluidis partes omnes ſeſe mutuo <lb/> <anchor type="note" xlink:label="note-0044-05a" xlink:href="note-0044-05"/> attrahere videmus, ex figura ſphærica quam guttæ ſemper <lb/>habent; </s> <s xml:id="echoid-s973" xml:space="preserve">ex eo etiam quod nullum detur fluidum, cujus par-<lb/>tes non ſint quaſi conglutinatæ, quod in ipſo Mercurio cla-<lb/>re apparet.</s> <s xml:id="echoid-s974" xml:space="preserve"/> </p> <div xml:id="echoid-div99" type="float" level="2" n="1"> <note position="left" xlink:label="note-0044-05" xlink:href="note-0044-05a" xml:space="preserve">54.</note> </div> </div> <div xml:id="echoid-div101" type="section" level="1" n="41"> <head xml:id="echoid-head80" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s975" xml:space="preserve">Sed multo melius hæc mutua particularum attractio pro-<lb/> <anchor type="note" xlink:label="note-0044-06a" xlink:href="note-0044-06"/> batur, ex eo quod in omnibus fluidis duæ guttæ ut A & </s> <s xml:id="echoid-s976" xml:space="preserve">B, <lb/> <anchor type="note" xlink:label="note-0044-07a" xlink:href="note-0044-07"/> ſtatim ac ſe invicem quam minime tangunt, in unam guttam <lb/>majorem F redigantur; </s> <s xml:id="echoid-s977" xml:space="preserve">quæ omnia cum etiam in metallis <lb/>liquefactis locum habeant, ſequitur particulas illa compo-<lb/>nentes & </s> <s xml:id="echoid-s978" xml:space="preserve">tum ſeſe mutuo attrahere, cum motu ignis a jun-<lb/>ctione arcentur.</s> <s xml:id="echoid-s979" xml:space="preserve"/> </p> <div xml:id="echoid-div101" type="float" level="2" n="1"> <note position="left" xlink:label="note-0044-06" xlink:href="note-0044-06a" xml:space="preserve">55.</note> <note position="left" xlink:label="note-0044-07" xlink:href="note-0044-07a" xml:space="preserve">TAB. II. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s980" xml:space="preserve">Hæc non oriuntur ab aëris preſſione, quia & </s> <s xml:id="echoid-s981" xml:space="preserve">in locoaë-<lb/>re vacuo procedunt, neque ab alius materiæ cujuſcunque <lb/>preſſione ab omni parte æquali; </s> <s xml:id="echoid-s982" xml:space="preserve">tali enim preſſione figura, <pb o="15" file="0045" n="45" rhead="MATHEMATICA. LIB. I. CAP. V."/> quæcunque fuerit, minime mutari poteſt, ut in cap. </s> <s xml:id="echoid-s983" xml:space="preserve">3. </s> <s xml:id="echoid-s984" xml:space="preserve">lib. <lb/></s> <s xml:id="echoid-s985" xml:space="preserve">2, ex legibus preſſionis fluidorum deducemus.</s> <s xml:id="echoid-s986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s987" xml:space="preserve">Etiam primo intuitu patet in gutta acbd, preſſiones in ſu-<lb/> <anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/> perficies ad & </s> <s xml:id="echoid-s988" xml:space="preserve">cb minores eſſe preſſionibus in ſuperficies <lb/>ac, db, ſi ab omni parte gutta æqualiter prematur. </s> <s xml:id="echoid-s989" xml:space="preserve">Non <lb/>tamen gutta fiet rotunda, quin preſſiones iſtæ minores, ma-<lb/>jores vincant, quod eſt abſurdum.</s> <s xml:id="echoid-s990" xml:space="preserve"/> </p> <div xml:id="echoid-div102" type="float" level="2" n="2"> <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">TAB. II. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s991" xml:space="preserve">In attractione contra, quo major eſt numerus particula-<lb/>rum ſe mutuo attrahentium inter duas particulas, eo ma-<lb/>jori vi ſe mutuo verſus feruntur; </s> <s xml:id="echoid-s992" xml:space="preserve">unde motus in gutta, donec <lb/>diſtantiæ inter puncta oppoſita in ſuperficie ſint ubique æ-<lb/>quales, quod in ſola figura ſphærica locum habet.</s> <s xml:id="echoid-s993" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s994" xml:space="preserve">Pleraque corpora attractione illa agunt in corpora extra-<lb/>nea. </s> <s xml:id="echoid-s995" xml:space="preserve">Exempla pauca dabo, in quibus effectus attractionis <lb/>illius ſunt maxime notabiles.</s> <s xml:id="echoid-s996" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div104" type="section" level="1" n="42"> <head xml:id="echoid-head81" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s997" xml:space="preserve">Tubuli vitrei exigui ab utraque extremitate aperti aquæ <lb/> <anchor type="note" xlink:label="note-0045-02a" xlink:href="note-0045-02"/> immerguntur, ut in ſchemate repræſentatur. </s> <s xml:id="echoid-s998" xml:space="preserve">Aqua in eos <lb/> <anchor type="note" xlink:label="note-0045-03a" xlink:href="note-0045-03"/> ſponte aſcendit, & </s> <s xml:id="echoid-s999" xml:space="preserve">ad majorem altitudinem quo diameter <lb/>tubuli eſt minor. </s> <s xml:id="echoid-s1000" xml:space="preserve">Tubuli hi dicuntur capillares; </s> <s xml:id="echoid-s1001" xml:space="preserve">ſed <lb/>in majoribus, quorum ex. </s> <s xml:id="echoid-s1002" xml:space="preserve">gr, diametri æquant ſextam pol-<lb/>licis partem, experimentum etiam procedit.</s> <s xml:id="echoid-s1003" xml:space="preserve"/> </p> <div xml:id="echoid-div104" type="float" level="2" n="1"> <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">56.</note> <note position="right" xlink:label="note-0045-03" xlink:href="note-0045-03a" xml:space="preserve">TAB. II. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s1004" xml:space="preserve">Effectum hunc preſſioni aëris tribuendum non eſſe, ſe-<lb/>quenti experimento liquet.</s> <s xml:id="echoid-s1005" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div106" type="section" level="1" n="43"> <head xml:id="echoid-head82" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s1006" xml:space="preserve">Suberiannectuntur tubuli, & </s> <s xml:id="echoid-s1007" xml:space="preserve">filo æneo AB ſuſtinentur, dein-<lb/> <anchor type="note" xlink:label="note-0045-04a" xlink:href="note-0045-04"/> de ope machinæ pneumaticæ aër ex recipiente R, laminæ æ-<lb/> <anchor type="note" xlink:label="note-0045-05a" xlink:href="note-0045-05"/> neæ impoſito, exhauritur, & </s> <s xml:id="echoid-s1008" xml:space="preserve">motu fili AB, aquâin vitro CD <lb/>contentæ immerguntur tubuli, aqua in eo caſu eodem mo-<lb/>do ac in experimento præcedenti in eos aſcendit. </s> <s xml:id="echoid-s1009" xml:space="preserve">Quo-<lb/>modo filum ſine ingreſſu aëris moveri poſſit, in ſequentibus, <lb/>dicetur.</s> <s xml:id="echoid-s1010" xml:space="preserve"/> </p> <div xml:id="echoid-div106" type="float" level="2" n="1"> <note position="right" xlink:label="note-0045-04" xlink:href="note-0045-04a" xml:space="preserve">57.</note> <note position="right" xlink:label="note-0045-05" xlink:href="note-0045-05a" xml:space="preserve">TAB. II. <lb/>fig. 5.</note> </div> </div> <div xml:id="echoid-div108" type="section" level="1" n="44"> <head xml:id="echoid-head83" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s1011" xml:space="preserve">Vitrea duo plana ABCD junguntur in AB, at in CD <lb/> <anchor type="note" xlink:label="note-0045-06a" xlink:href="note-0045-06"/> interpoſitâ laminâ paululum ſeparantur; </s> <s xml:id="echoid-s1012" xml:space="preserve">latera CB aquâ ali-<lb/> <anchor type="note" xlink:label="note-0045-07a" xlink:href="note-0045-07"/> quo colore tinctâ immerguntur tia, ut latera AB & </s> <s xml:id="echoid-s1013" xml:space="preserve">CD <pb o="16" file="0046" n="46" rhead="PHYSICES ELEMENTA"/> ſint verticalia; </s> <s xml:id="echoid-s1014" xml:space="preserve">antea iiſdem planis intus eodem liquore ma-<lb/>defactis.</s> <s xml:id="echoid-s1015" xml:space="preserve"/> </p> <div xml:id="echoid-div108" type="float" level="2" n="1"> <note position="right" xlink:label="note-0045-06" xlink:href="note-0045-06a" xml:space="preserve">58.</note> <note position="right" xlink:label="note-0045-07" xlink:href="note-0045-07a" xml:space="preserve">TAB. II. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s1016" xml:space="preserve">Aqua inter hæc plana, planorum attractione, aſcendit, <lb/>& </s> <s xml:id="echoid-s1017" xml:space="preserve">ad majorem altitudinem aſcendit pro minori inter plana <lb/>diſtantiâ; </s> <s xml:id="echoid-s1018" xml:space="preserve">cum vero continuo à CD, verſus AB, minua-<lb/>tur hæc, aqua ubique ad diverſas altitudines aſcendit, & </s> <s xml:id="echoid-s1019" xml:space="preserve">for-<lb/>mat lineam curvam efg.</s> <s xml:id="echoid-s1020" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div110" type="section" level="1" n="45"> <head xml:id="echoid-head84" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s1021" xml:space="preserve">ABCD ſunt duæ laminæ vitreæ planæ, junctæ in AB, <lb/> <anchor type="note" xlink:label="note-0046-01a" xlink:href="note-0046-01"/> in CD vero paululum ſeparantur, interpoſitâ lami-<lb/>nâ cujuſcunque materiæ. </s> <s xml:id="echoid-s1022" xml:space="preserve">Rectangulo ligneo HILM <lb/>ſuſtinentur; </s> <s xml:id="echoid-s1023" xml:space="preserve">latera ſeparata DC regulæ ligneæ, cum la-<lb/>tere ML rectanguli cohærente, imponuntur; </s> <s xml:id="echoid-s1024" xml:space="preserve">ad horizontem <lb/>utcunque inclinantur laminæ, elevando latera conjuncta <lb/>AB; </s> <s xml:id="echoid-s1025" xml:space="preserve">Cylindro NO laminæ in quocunque ſitu ſuſtinentur; <lb/></s> <s xml:id="echoid-s1026" xml:space="preserve">Cochleâ P cylindrus ad altitudinem quamcunque ſirmatur.</s> <s xml:id="echoid-s1027" xml:space="preserve"/> </p> <div xml:id="echoid-div110" type="float" level="2" n="1"> <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">59.</note> </div> <p> <s xml:id="echoid-s1028" xml:space="preserve">Gutta aquæ aut olei G interponitur, ita ut ambo plana, <lb/>antea eodem liquore madefacta, tangat; </s> <s xml:id="echoid-s1029" xml:space="preserve">ab utroque plano <lb/>attrahitur, ſed attractio majorem in guttam edit effectum; <lb/></s> <s xml:id="echoid-s1030" xml:space="preserve">ubi plana minus diſtant, id eſt, in e quam in f; </s> <s xml:id="echoid-s1031" xml:space="preserve">gutta i-<lb/>deo verſus e movetur, id eſt, aſcendit, & </s> <s xml:id="echoid-s1032" xml:space="preserve">eo celerius quo <lb/>altius aſcendit, ſuperficiebus quibus gutta vitra tangit, cre-<lb/>ſcentibus ubi diſtantia inter plana minuitur. </s> <s xml:id="echoid-s1033" xml:space="preserve">Angulus inclina-<lb/>tionis plani ita poteſt augeri, ut gravitas guttæ æque polleat <lb/>cum effectu attractionis, & </s> <s xml:id="echoid-s1034" xml:space="preserve">tunc gutta quieſcit; </s> <s xml:id="echoid-s1035" xml:space="preserve">& </s> <s xml:id="echoid-s1036" xml:space="preserve">ſi in eo <lb/>caſu magis elevetur planorum pars AB, gutta de-<lb/>ſcendit propter guttæ gravitatem præpollentem.</s> <s xml:id="echoid-s1037" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div112" type="section" level="1" n="46"> <head xml:id="echoid-head85" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s1038" xml:space="preserve">Mercurius Auro & </s> <s xml:id="echoid-s1039" xml:space="preserve">Stanno ſeſe jungit, etiam aqua, & </s> <s xml:id="echoid-s1040" xml:space="preserve">o-<lb/> <anchor type="note" xlink:label="note-0046-02a" xlink:href="note-0046-02"/> leum ligno & </s> <s xml:id="echoid-s1041" xml:space="preserve">vitro nitido adhærent.</s> <s xml:id="echoid-s1042" xml:space="preserve"/> </p> <div xml:id="echoid-div112" type="float" level="2" n="1"> <note position="left" xlink:label="note-0046-02" xlink:href="note-0046-02a" xml:space="preserve">60.</note> </div> <p> <s xml:id="echoid-s1043" xml:space="preserve">Repulſionis exempla habemus inter aquam & </s> <s xml:id="echoid-s1044" xml:space="preserve">oleum, & </s> <s xml:id="echoid-s1045" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0046-03a" xlink:href="note-0046-03"/> in genere inter aquam & </s> <s xml:id="echoid-s1046" xml:space="preserve">omnia corpora pinguia, inter Mer-<lb/>curium & </s> <s xml:id="echoid-s1047" xml:space="preserve">Ferrum, ut & </s> <s xml:id="echoid-s1048" xml:space="preserve">etiam inter particulas pulveris cu-<lb/>juſcunque.</s> <s xml:id="echoid-s1049" xml:space="preserve"/> </p> <div xml:id="echoid-div113" type="float" level="2" n="2"> <note position="left" xlink:label="note-0046-03" xlink:href="note-0046-03a" xml:space="preserve">61.</note> </div> </div> <div xml:id="echoid-div115" type="section" level="1" n="47"> <head xml:id="echoid-head86" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s1050" xml:space="preserve">Si corpus quoddam pingue, quod aqua levius ſit, ſuper-<lb/> <anchor type="note" xlink:label="note-0046-04a" xlink:href="note-0046-04"/> <pb o="17" file="0047" n="47" rhead="MATHEMATICA. LIB. I. CAP. V."/> ficiei aquæ imponatur, aut fruſtum Ferri Mercurio, ſuper-<lb/>ficies liquidorum deprimentur circum corpora immerſa, ut <lb/>circum globum A repræſentantur; </s> <s xml:id="echoid-s1051" xml:space="preserve">& </s> <s xml:id="echoid-s1052" xml:space="preserve">eodem modo ac in <lb/> <anchor type="note" xlink:label="note-0047-01a" xlink:href="note-0047-01"/> caſibus ubi vis attractiva locum habet, ſuperficies fluidi cir-<lb/>cum corpora immerſa altior eſt, ut circum globum B, & </s> <s xml:id="echoid-s1053" xml:space="preserve"><lb/>gravitate ad libellam non defluit; </s> <s xml:id="echoid-s1054" xml:space="preserve">ſic in hiſce ubi vis <lb/>repellens actionem ſuam exerit, fluida pondere ſuo non <lb/>defluunt ad implendas cavitate, quæ circum corpora im-<lb/>merſa formantur.</s> <s xml:id="echoid-s1055" xml:space="preserve"/> </p> <div xml:id="echoid-div115" type="float" level="2" n="1"> <note position="left" xlink:label="note-0046-04" xlink:href="note-0046-04a" xml:space="preserve">62.</note> <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">TAB. II. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s1056" xml:space="preserve">Huc pertinent omnia Phænomena globorum vitreorum le-<lb/> <anchor type="note" xlink:label="note-0047-02a" xlink:href="note-0047-02"/> viſſimorum aquâ innatantium; </s> <s xml:id="echoid-s1057" xml:space="preserve">quando nitidi ſunt aqua ab <lb/>omni parte circa eos aſcendit, ut in B; </s> <s xml:id="echoid-s1058" xml:space="preserve">quando pinguedine <lb/>quadam obteguntur, aqua ab omni parte quaſi excavatur, <lb/>ut in A;</s> <s xml:id="echoid-s1059" xml:space="preserve"/> </p> <div xml:id="echoid-div116" type="float" level="2" n="2"> <note position="right" xlink:label="note-0047-02" xlink:href="note-0047-02a" xml:space="preserve">63.</note> </div> <p> <s xml:id="echoid-s1060" xml:space="preserve">In vaſe vitreo, in quo experimenta fiunt, aqua a lateribus <lb/>vitri ab omni parte etiam ſuſtinetur, & </s> <s xml:id="echoid-s1061" xml:space="preserve">ibi altior eſt, ut in <lb/>C, & </s> <s xml:id="echoid-s1062" xml:space="preserve">D; </s> <s xml:id="echoid-s1063" xml:space="preserve">quando vitrum ita repletur, ut aqua ab omni par-<lb/>te defluat, attractione mutua partium aquæ, altior eſt in <lb/>medio quam ad latera, & </s> <s xml:id="echoid-s1064" xml:space="preserve">ſuperficiem convexam format <lb/> <anchor type="note" xlink:label="note-0047-03a" xlink:href="note-0047-03"/> ABC: </s> <s xml:id="echoid-s1065" xml:space="preserve">ex hiſce ſolis ſequentia Experimenta explicantur.</s> <s xml:id="echoid-s1066" xml:space="preserve"/> </p> <div xml:id="echoid-div117" type="float" level="2" n="3"> <note position="right" xlink:label="note-0047-03" xlink:href="note-0047-03a" xml:space="preserve">TAB. II. <lb/>fig. 9.</note> </div> </div> <div xml:id="echoid-div119" type="section" level="1" n="48"> <head xml:id="echoid-head87" xml:space="preserve"><emph style="sc">Experimentum</emph> 9. 10. 11. 12. 13.</head> <p> <s xml:id="echoid-s1067" xml:space="preserve">Quando vitreum vas non omnino aquâ impletur, globus <lb/> <anchor type="note" xlink:label="note-0047-04a" xlink:href="note-0047-04"/> nitidus ſemper, ſi, ad diſtantiam non admodum magnam <lb/>a latere vaſis, aquâ imponitur, latus verſus fertur & </s> <s xml:id="echoid-s1068" xml:space="preserve">ei ſeſe <lb/>jungit. </s> <s xml:id="echoid-s1069" xml:space="preserve">Globus ab omni parte æqualiter ab aqua premitur, <lb/>quando autem accedit ad latus vaſis, vis, qua ibi aqua ele-<lb/>vatur, tollit pro parte preſſionem illam; </s> <s xml:id="echoid-s1070" xml:space="preserve">& </s> <s xml:id="echoid-s1071" xml:space="preserve">preſſio a parte <lb/>oppoſita præpollet.</s> <s xml:id="echoid-s1072" xml:space="preserve"/> </p> <div xml:id="echoid-div119" type="float" level="2" n="1"> <note position="right" xlink:label="note-0047-04" xlink:href="note-0047-04a" xml:space="preserve">64.</note> </div> <p> <s xml:id="echoid-s1073" xml:space="preserve">Quando vas repletur ita, ut aqua defluat, globus a late-<lb/> <anchor type="note" xlink:label="note-0047-05a" xlink:href="note-0047-05"/> re vitri ſponte medium verſus fertur; </s> <s xml:id="echoid-s1074" xml:space="preserve">vi, qua aqua in medio <lb/>magis elevatur, ab ea parte preſſionem circa globum minuente.</s> <s xml:id="echoid-s1075" xml:space="preserve"/> </p> <div xml:id="echoid-div120" type="float" level="2" n="2"> <note position="right" xlink:label="note-0047-05" xlink:href="note-0047-05a" xml:space="preserve">65.</note> </div> <p> <s xml:id="echoid-s1076" xml:space="preserve">Contrarium in utroque caſu obtinet, quando globus pin-<lb/> <anchor type="note" xlink:label="note-0047-06a" xlink:href="note-0047-06"/> guedine obtegitur, quia vis, qua aqua & </s> <s xml:id="echoid-s1077" xml:space="preserve">globus ſeſe mutuo <lb/>repellunt, major eſt, ubi aqua magis elevata eſt.</s> <s xml:id="echoid-s1078" xml:space="preserve"/> </p> <div xml:id="echoid-div121" type="float" level="2" n="3"> <note position="right" xlink:label="note-0047-06" xlink:href="note-0047-06a" xml:space="preserve">66.</note> </div> <p> <s xml:id="echoid-s1079" xml:space="preserve">Duo globi nitidi, aut pinguedine induti, ſeſe mutuo pe-<lb/> <anchor type="note" xlink:label="note-0047-07a" xlink:href="note-0047-07"/> tunt. </s> <s xml:id="echoid-s1080" xml:space="preserve">Si nitidi fuerint, cauſa eadem eſt ex qua globus ad <pb o="18" file="0048" n="48" rhead="PHYSICES ELEMENTA"/> latus vitri fertur: </s> <s xml:id="echoid-s1081" xml:space="preserve">quando pinguedine obtecti ſunt, cavitas <lb/>circum illos datur, ubi cavitates juguntur preſſio minuitur, <lb/>& </s> <s xml:id="echoid-s1082" xml:space="preserve">verſus illam partem globus uterque fertur.</s> <s xml:id="echoid-s1083" xml:space="preserve"/> </p> <div xml:id="echoid-div122" type="float" level="2" n="4"> <note position="right" xlink:label="note-0047-07" xlink:href="note-0047-07a" xml:space="preserve">67.</note> </div> <p> <s xml:id="echoid-s1084" xml:space="preserve">Si Globus unus ſit nitidus, & </s> <s xml:id="echoid-s1085" xml:space="preserve">alter pinguedine obtectus, <lb/> <anchor type="note" xlink:label="note-0048-01a" xlink:href="note-0048-01"/> ſeſe mutuo fugiunt; </s> <s xml:id="echoid-s1086" xml:space="preserve">eodem modo ac globus pinguedine ob-<lb/>tectus latus vitri fugit.</s> <s xml:id="echoid-s1087" xml:space="preserve"/> </p> <div xml:id="echoid-div123" type="float" level="2" n="5"> <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">68.</note> </div> <p> <s xml:id="echoid-s1088" xml:space="preserve">In cryſtalliſationibus etiam pulcherrima attractionis exem-<lb/> <anchor type="note" xlink:label="note-0048-02a" xlink:href="note-0048-02"/> pla habemus.</s> <s xml:id="echoid-s1089" xml:space="preserve"/> </p> <div xml:id="echoid-div124" type="float" level="2" n="6"> <note position="left" xlink:label="note-0048-02" xlink:href="note-0048-02a" xml:space="preserve">69.</note> </div> </div> <div xml:id="echoid-div126" type="section" level="1" n="49"> <head xml:id="echoid-head88" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s1090" xml:space="preserve">Elaſticitas, vocatur corporum proprietas, qua, ſi figura <lb/> <anchor type="note" xlink:label="note-0048-03a" xlink:href="note-0048-03"/> illorum vi aliqua mutetur, ad priſtinam figuram redeunt; <lb/></s> <s xml:id="echoid-s1091" xml:space="preserve">Si enim corpus quoddam ſit compactum, flectat ſe, & </s> <s xml:id="echoid-s1092" xml:space="preserve">cum <lb/>prematur introcedat ſine ullo partium ſuarum ſublapſu, cor-<lb/>pus revertet ad figuram ſuam vi illa, quæ ex mutua ſuarum <lb/>partium attractione oritur.</s> <s xml:id="echoid-s1093" xml:space="preserve"/> </p> <div xml:id="echoid-div126" type="float" level="2" n="1"> <note position="left" xlink:label="note-0048-03" xlink:href="note-0048-03a" xml:space="preserve">70.</note> </div> <p> <s xml:id="echoid-s1094" xml:space="preserve">Illam vero aëris proprietatem, quæ illius elaſticitas dici-<lb/> <anchor type="note" xlink:label="note-0048-04a" xlink:href="note-0048-04"/> tur, oriri ex vi, qua partes ſeſe mutuo repellunt, ſuo tem-<lb/>pore dicetur.</s> <s xml:id="echoid-s1095" xml:space="preserve"/> </p> <div xml:id="echoid-div127" type="float" level="2" n="2"> <note position="left" xlink:label="note-0048-04" xlink:href="note-0048-04a" xml:space="preserve">71.</note> </div> <p> <s xml:id="echoid-s1096" xml:space="preserve">Et ne quis credat, quia cauſam prædictæ attractionis & </s> <s xml:id="echoid-s1097" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0048-05a" xlink:href="note-0048-05"/> repulſionis non damus, illas inter qualitates occultas eſſe re-<lb/>cenſendas. </s> <s xml:id="echoid-s1098" xml:space="preserve">Cum Newtono reſpondemus, „ nos illa principia <lb/>„ conſiderare, non ut occultas qualitates, quæ ex ſpecificis <lb/>„ rerum formis oriri finguntur; </s> <s xml:id="echoid-s1099" xml:space="preserve">ſed ut univer ſales naturæ <lb/>„ leges, quibus res ipſæ ſunt formatæ; </s> <s xml:id="echoid-s1100" xml:space="preserve">nam principia qui-<lb/>„ dem talia revera exiſtere oſtendunt Phænomena naturæ, <lb/>„ licet, ipſorum cauſæ quæ ſint, nondum fuerit explicatum. <lb/></s> <s xml:id="echoid-s1101" xml:space="preserve">„ Affirmare ſingulas rerum ſpecies ſpecificis præditas eſſe <lb/>„ qualitatibus occultis, per quas eæ vim certam in agendo <lb/>„ habeant, hoc utique eſt nihil dicere. </s> <s xml:id="echoid-s1102" xml:space="preserve">At ex Phænome-<lb/>„ nis naturæ duo vel tria derivare generalia motus princi-<lb/>„ pia, & </s> <s xml:id="echoid-s1103" xml:space="preserve">deinde explicare quemadmodum proprietates, & </s> <s xml:id="echoid-s1104" xml:space="preserve"><lb/>„ actiones rerum omnium, ex principiis iſtis conſequuntur; </s> <s xml:id="echoid-s1105" xml:space="preserve"><lb/>„ id vero magnus eſſet factus in Philoſophia progreſſus, et-<lb/>„ iamſi principiorum iſtorum cauſæ nondum eſſent cognitæ.</s> <s xml:id="echoid-s1106" xml:space="preserve"/> </p> <div xml:id="echoid-div128" type="float" level="2" n="3"> <note position="left" xlink:label="note-0048-05" xlink:href="note-0048-05a" xml:space="preserve">72.</note> </div> <pb o="19" file="0049" n="49" rhead="MATHEMATICA. LIB. I. CAP. V."/> </div> <div xml:id="echoid-div130" type="section" level="1" n="50"> <head xml:id="echoid-head89" xml:space="preserve">SCHOLIUM</head> <head xml:id="echoid-head90" style="it" xml:space="preserve">De efſectu attractionis vitri in aquam.</head> <p> <s xml:id="echoid-s1107" xml:space="preserve">Singulæ particulæ aqueæ ad exiguam a vitro diſtantiam ab hoc attrahuntur, <lb/> <anchor type="note" xlink:label="note-0049-01a" xlink:href="note-0049-01"/> id eſt, per lineas rectas tendunt ad ſingulas vitri particulas, quarum diſtantia <lb/>non ſuperat illam ad quam vitrum & </s> <s xml:id="echoid-s1108" xml:space="preserve">aqua in ſe mutuo agere poſſunt. </s> <s xml:id="echoid-s1109" xml:space="preserve">Sit <lb/> <anchor type="note" xlink:label="note-0049-02a" xlink:href="note-0049-02"/> vitri ſuperficies AB; </s> <s xml:id="echoid-s1110" xml:space="preserve">particula C; </s> <s xml:id="echoid-s1111" xml:space="preserve">hæc ad vitrum tendit per lineam CD, ad <lb/>ſuperficiem perpendicularem; </s> <s xml:id="echoid-s1112" xml:space="preserve">tendit etiam ad punctum e, ſed eodem tem-<lb/>pore æquali vi tendit ad omnia puncta in ſuperficie æqualiter cum e à D di-<lb/>ſtantia, id eſt in cir cumferentia circuli poſita, cujus diameter eſt e f: </s> <s xml:id="echoid-s1113" xml:space="preserve">propter <lb/>harum omnium virium æqualitatem non poterit punctum magis ad punctum u-<lb/>num ferri, quam ad aliud; </s> <s xml:id="echoid-s1114" xml:space="preserve">ideo, omnibus viribus ſimul agentibus, par-<lb/>ticula etiam trahitur per CD. </s> <s xml:id="echoid-s1115" xml:space="preserve">Similem demonſtrationem aliis particulis vitri <lb/>in aquæ particulam agentibus applicando conſtabit, hanc ad vitrum tendere per <lb/> <anchor type="note" xlink:label="note-0049-03a" xlink:href="note-0049-03"/> lineam ad ſuperficiem bujus perpendicularem.</s> <s xml:id="echoid-s1116" xml:space="preserve"/> </p> <div xml:id="echoid-div130" type="float" level="2" n="1"> <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">73.</note> <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">TAB. I. <lb/>fig. 5.</note> <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">74.</note> </div> <p> <s xml:id="echoid-s1117" xml:space="preserve">Detur ſuper plano vitreo AB gutta G. </s> <s xml:id="echoid-s1118" xml:space="preserve">Particulæ ſingulæ parum a vitro <lb/> <anchor type="note" xlink:label="note-0049-04a" xlink:href="note-0049-04"/> diſtantes ad hoc directe tendunt, particulaſque cum quibus cohærent ſecum <lb/>trahunt, unde in gutta oritur motus ſimilis illi, qui in gutta daretur, ſi plano <lb/>CD ad AB parallelo hoc verſus premeretur; </s> <s xml:id="echoid-s1119" xml:space="preserve">qua preſſione gutta ſeſe expan-<lb/>deret quaqua verſum, & </s> <s xml:id="echoid-s1120" xml:space="preserve">expanſio hæc eſt effectus attractionis. <lb/></s> <s xml:id="echoid-s1121" xml:space="preserve"> <anchor type="note" xlink:label="note-0049-05a" xlink:href="note-0049-05"/> </s> </p> <div xml:id="echoid-div131" type="float" level="2" n="2"> <note position="right" xlink:label="note-0049-04" xlink:href="note-0049-04a" xml:space="preserve">TAB. I. <lb/>fig. 6.</note> <note position="right" xlink:label="note-0049-05" xlink:href="note-0049-05a" xml:space="preserve">75.</note> </div> <p> <s xml:id="echoid-s1122" xml:space="preserve">Sit AB aquæ ſuperficies; </s> <s xml:id="echoid-s1123" xml:space="preserve">huic pro parte immergatur perpendiculariter <lb/> <anchor type="note" xlink:label="note-0049-06a" xlink:href="note-0049-06"/> vitreum planum FD, cujus craſſitiem hic repræſentamus. </s> <s xml:id="echoid-s1124" xml:space="preserve">Aqua a plano at <lb/> <anchor type="note" xlink:label="note-0049-07a" xlink:href="note-0049-07"/> trahitur, quo premitur juxta directionem BD <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s1125" xml:space="preserve">conatur quaqua verſum <anchor type="note" xlink:label="note-0049-08a" xlink:href="note-0049-08"/> ſuper plano ſeſe expandere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1126" xml:space="preserve">quo motu non poſſunt agitari niſi particulæ in <anchor type="note" xlink:label="note-0049-09a" xlink:href="note-0049-09"/> D, motibus contrariis infra ſuperficiem ſeſe mutuo deſtruentibus; </s> <s xml:id="echoid-s1127" xml:space="preserve">elevabitur <lb/>ideo aqua, & </s> <s xml:id="echoid-s1128" xml:space="preserve">aſcendentem ſequetur illa, quæ cum ipſa cohæret, ſuſtinebi-<lb/>turque ita aqua a vitro, ut pondus aquæ elevatæ valeat vim qua elevatur.</s> <s xml:id="echoid-s1129" xml:space="preserve"/> </p> <div xml:id="echoid-div132" type="float" level="2" n="3"> <note position="right" xlink:label="note-0049-06" xlink:href="note-0049-06a" xml:space="preserve">76.</note> <note position="right" xlink:label="note-0049-07" xlink:href="note-0049-07a" xml:space="preserve">TAB. I. <lb/>fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0049-08" xlink:href="note-0049-08a" xml:space="preserve">74.</note> <note symbol="*" position="right" xlink:label="note-0049-09" xlink:href="note-0049-09a" xml:space="preserve">75.</note> </div> <p> <s xml:id="echoid-s1130" xml:space="preserve">Sit altitudo hæc, quam juſto majorem repræſentamus, DC; </s> <s xml:id="echoid-s1131" xml:space="preserve">ſuſtinetur autem <lb/>aqua in CDG ſolâ vi qua particulæ in C ſurſum pelluntur: </s> <s xml:id="echoid-s1132" xml:space="preserve">nam ubi aqua <lb/>quieſcit, vires, quibus aqua inter C & </s> <s xml:id="echoid-s1133" xml:space="preserve">D ſeſe quaqua verſum expandere cona-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>, ſeſe mutuo deſtruunt: </s> <s xml:id="echoid-s1134" xml:space="preserve">particula ex. </s> <s xml:id="echoid-s1135" xml:space="preserve">gr. </s> <s xml:id="echoid-s1136" xml:space="preserve">in e æqualiter ſurſum & </s> <s xml:id="echoid-s1137" xml:space="preserve">deor- <anchor type="note" xlink:label="note-0049-10a" xlink:href="note-0049-10"/> ſum pellitur. </s> <s xml:id="echoid-s1138" xml:space="preserve">Vis ergo quæ ſuſtinet aquam, proportionem ſequitur latitudinis <lb/> <anchor type="note" xlink:label="note-0049-11a" xlink:href="note-0049-11"/> ſuperficiei juxta quam aqua adſcendit, menſuratæ, ad altitudinem ad quam aqua <lb/>pertingit, in linea ad ſuperficiem ipſius aquæ parallela: </s> <s xml:id="echoid-s1139" xml:space="preserve">quam eandem rationem <lb/>ſequitur pondus aquæ elevatæ.</s> <s xml:id="echoid-s1140" xml:space="preserve"/> </p> <div xml:id="echoid-div133" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0049-10" xlink:href="note-0049-10a" xml:space="preserve">75.</note> <note position="right" xlink:label="note-0049-11" xlink:href="note-0049-11a" xml:space="preserve">77.</note> </div> </div> <div xml:id="echoid-div135" type="section" level="1" n="51"> <head xml:id="echoid-head91" style="it" xml:space="preserve">De Tubis Capillaribus.</head> <p> <s xml:id="echoid-s1141" xml:space="preserve">Aquam in tubos vitreos minores ſponte adſcendere debere, ex explicatis <lb/>facile deducitur. </s> <s xml:id="echoid-s1142" xml:space="preserve">Quantitas autem aquæ, quæ ſuſtinetur, ſequitur rationem o-<lb/> <anchor type="note" xlink:label="note-0049-12a" xlink:href="note-0049-12"/> ræ aquæ elevatæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1143" xml:space="preserve">& </s> <s xml:id="echoid-s1144" xml:space="preserve">orahæc, ſiagatur detubis cylindricis, perpendiculariter im- <anchor type="note" xlink:label="note-0049-13a" xlink:href="note-0049-13"/> merſis ad inſtar diametri creſcit aut minuitur.</s> <s xml:id="echoid-s1145" xml:space="preserve"/> </p> <div xml:id="echoid-div135" type="float" level="2" n="1"> <note position="right" xlink:label="note-0049-12" xlink:href="note-0049-12a" xml:space="preserve">78.</note> <note symbol="*" position="right" xlink:label="note-0049-13" xlink:href="note-0049-13a" xml:space="preserve">77.</note> </div> <p> <s xml:id="echoid-s1146" xml:space="preserve">Sint duo tubi quorum diametri dicantur D, d; </s> <s xml:id="echoid-s1147" xml:space="preserve">altitudines aquæ A, a; <lb/></s> <s xml:id="echoid-s1148" xml:space="preserve">quantitates aquæ ergo erunt inter ſe ut D<emph style="super">q</emph> x A ad d<emph style="super">q</emph> x a <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1149" xml:space="preserve">ideo D<emph style="super">q</emph> x A, d<emph style="super">q</emph> x a <anchor type="note" xlink:label="note-0049-14a" xlink:href="note-0049-14"/> :</s> <s xml:id="echoid-s1150" xml:space="preserve">: D, d<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1151" xml:space="preserve">dividendo antecedentia per D<emph style="super">q</emph>, & </s> <s xml:id="echoid-s1152" xml:space="preserve">conſequentia per dq habemus, <anchor type="note" xlink:label="note-0049-15a" xlink:href="note-0049-15"/> A, a :</s> <s xml:id="echoid-s1153" xml:space="preserve">: {1/D}, {1/d}, id eſt altitudines ſunt inverſe ut diametri. <lb/></s> <s xml:id="echoid-s1154" xml:space="preserve"> <anchor type="note" xlink:label="note-0049-16a" xlink:href="note-0049-16"/> </s> </p> <div xml:id="echoid-div136" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0049-14" xlink:href="note-0049-14a" xml:space="preserve">2. II. 14. <lb/>El. XII.</note> <note symbol="*" position="right" xlink:label="note-0049-15" xlink:href="note-0049-15a" xml:space="preserve">78.</note> <note position="right" xlink:label="note-0049-16" xlink:href="note-0049-16a" xml:space="preserve">79.</note> </div> </div> <div xml:id="echoid-div138" type="section" level="1" n="52"> <head xml:id="echoid-head92" style="it" xml:space="preserve">De aſcènſu aquæ inter plana, de quo in n. 58.</head> <p> <s xml:id="echoid-s1155" xml:space="preserve">Sint AC, BC, lineæ repræſentantes planorum ſectionem horizontalem a <lb/> <anchor type="note" xlink:label="note-0049-17a" xlink:href="note-0049-17"/> ſuperficie aquæ; </s> <s xml:id="echoid-s1156" xml:space="preserve">ponamus ſpatium, angulo ACB contentum, dividi lineis <lb/> <anchor type="note" xlink:label="note-0049-18a" xlink:href="note-0049-18"/> <pb o="20" file="0050" n="50" rhead="PHYSICES ELEMENTA"/> ut de, fg, hi, l m, &</s> <s xml:id="echoid-s1157" xml:space="preserve">c parum admodum, ſed æqualiter, a ſe mutuo di-<lb/>ſtantibus; </s> <s xml:id="echoid-s1158" xml:space="preserve">manifeſtum eſt æquales aquæ quantitates in ſpatiis dfeg, himl, <lb/>elevari <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1159" xml:space="preserve">ibique ideo dari priſmata æqualia, quorum altitudines ſunt inverſe <anchor type="note" xlink:label="note-0050-01a" xlink:href="note-0050-01"/> ut baſes <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1160" xml:space="preserve">hæ autem, quia pro parallelogrammis haberi poſſunt, & </s> <s xml:id="echoid-s1161" xml:space="preserve">propter la- <anchor type="note" xlink:label="note-0050-02a" xlink:href="note-0050-02"/> titudines df, hl, æquales, ſunt inter ſe ut de ad hi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1162" xml:space="preserve">quæ ſunt ut d C ad h C.</s> <s xml:id="echoid-s1163" xml:space="preserve"> <anchor type="note" xlink:label="note-0050-03a" xlink:href="note-0050-03"/> </s> </p> <div xml:id="echoid-div138" type="float" level="2" n="1"> <note position="right" xlink:label="note-0049-17" xlink:href="note-0049-17a" xml:space="preserve">80.</note> <note position="right" xlink:label="note-0049-18" xlink:href="note-0049-18a" xml:space="preserve">TAB. I. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve">77.</note> <note symbol="*" position="left" xlink:label="note-0050-02" xlink:href="note-0050-02a" xml:space="preserve">34. El. <emph style="sc">XI</emph>.</note> <note symbol="*" position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">1. El. <emph style="sc">VI</emph>.</note> </div> <p> <s xml:id="echoid-s1164" xml:space="preserve">Deducimus ex his curvam efg eſſe Hyperbolam cujus Aſymptoti ſunt lineæ <lb/> <anchor type="note" xlink:label="note-0050-04a" xlink:href="note-0050-04"/> AB, in qua vitra ſeſe mutuo tangunt, & </s> <s xml:id="echoid-s1165" xml:space="preserve">BC, ſuperficies aquæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1166" xml:space="preserve">Propter <anchor type="note" xlink:label="note-0050-05a" xlink:href="note-0050-05"/> angulum rectum ABC Hyperbola eſt æquilatera <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1167" xml:space="preserve">examinavimus enim <anchor type="note" xlink:label="note-0050-06a" xlink:href="note-0050-06"/> caſum in quo linea, in qua vitra ſeſe mutuo tangunt, ad ſuperficiem aquæ <lb/>perpendicularis eſt.</s> <s xml:id="echoid-s1168" xml:space="preserve"/> </p> <div xml:id="echoid-div139" type="float" level="2" n="2"> <note position="left" xlink:label="note-0050-04" xlink:href="note-0050-04a" xml:space="preserve">81.</note> <note position="left" xlink:label="note-0050-05" xlink:href="note-0050-05a" xml:space="preserve">TAB. II. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0050-06" xlink:href="note-0050-06a" xml:space="preserve">La Hire <lb/><emph style="sc">S. C</emph>. l. <emph style="sc">IV</emph>. <lb/>p. 2.</note> </div> <p> <s xml:id="echoid-s1169" xml:space="preserve">Facile etiam confertur altitudo in tubo cum altitudine inter plana.</s> <s xml:id="echoid-s1170" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">ibid. l. <emph style="sc">V</emph>. <lb/>p. 13.</note> <p> <s xml:id="echoid-s1171" xml:space="preserve">Sit tubi cylindrici ſectio M, cujus ſemidiameter æqualis eſt diſtantiæ e d inter <lb/>plana. </s> <s xml:id="echoid-s1172" xml:space="preserve">Clarum eſt vim, quæ ſuſtinet priſma aqueum cujus baſis eſt def pro-<lb/> <anchor type="note" xlink:label="note-0050-08a" xlink:href="note-0050-08"/> portionem ſequi lineæ df; </s> <s xml:id="echoid-s1173" xml:space="preserve">ambabus enim df & </s> <s xml:id="echoid-s1174" xml:space="preserve">eg proportionalis eſt vis quæ pa-<lb/> <anchor type="note" xlink:label="note-0050-09a" xlink:href="note-0050-09"/> rallelopipedum, cujus baſis eſt dfeg, ſuſtinet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1175" xml:space="preserve"> <anchor type="note" xlink:label="note-0050-10a" xlink:href="note-0050-10"/> </s> </p> <div xml:id="echoid-div140" type="float" level="2" n="3"> <note position="left" xlink:label="note-0050-08" xlink:href="note-0050-08a" xml:space="preserve">82.</note> <note position="left" xlink:label="note-0050-09" xlink:href="note-0050-09a" xml:space="preserve">TAB I. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0050-10" xlink:href="note-0050-10a" xml:space="preserve">77.</note> </div> <p> <s xml:id="echoid-s1176" xml:space="preserve">In tubo vis quæ ſuſtinet priſma, cujus baſis eſt nop, proportionalis eſt ipſi np; <lb/></s> <s xml:id="echoid-s1177" xml:space="preserve">quia tota circumferentia proportionalis eſt illi quæ integrum aqueum cylin-<lb/>drum vitro contentum ſuſtinet. </s> <s xml:id="echoid-s1178" xml:space="preserve">Si np & </s> <s xml:id="echoid-s1179" xml:space="preserve">df fuerint æquales; </s> <s xml:id="echoid-s1180" xml:space="preserve">vires quæ pri-<lb/>ſmata ſuſtinent æquales ſunt; </s> <s xml:id="echoid-s1181" xml:space="preserve">ideoque & </s> <s xml:id="echoid-s1182" xml:space="preserve">ipſa priſmata æqualia; </s> <s xml:id="echoid-s1183" xml:space="preserve">ſunt etiam <lb/>in hoc caſu baſes nop, def, æquales, quare priſmatum altitudines non <lb/>difterunt, & </s> <s xml:id="echoid-s1184" xml:space="preserve">aqua in tubum & </s> <s xml:id="echoid-s1185" xml:space="preserve">inter plana ad eandem adſcendit altitudinem.</s> <s xml:id="echoid-s1186" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1187" xml:space="preserve">Variarimultis modis poteſt experimentum de adſcenſu aquæ inter plana.</s> <s xml:id="echoid-s1188" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1189" xml:space="preserve">Nimium longum & </s> <s xml:id="echoid-s1190" xml:space="preserve">ſatis inutile foret, omnia quæ huc ſpectant perpendere; <lb/></s> <s xml:id="echoid-s1191" xml:space="preserve">ſatis eſt caſum præcipuum examinaſſe; </s> <s xml:id="echoid-s1192" xml:space="preserve">Circa duos alios in quibus angulus <lb/> <anchor type="note" xlink:label="note-0050-11a" xlink:href="note-0050-11"/> ABC, quem linea, in qua vitra junguntur, cum ſuperficie aquæ efficit, eſt <lb/> <anchor type="note" xlink:label="note-0050-12a" xlink:href="note-0050-12"/> acutus aut obtuſus, manentibus planis vitreis ad aquæ ſuperficiem perpendi-<lb/>cularibus, notabo, aquam etiam terminari Hyperbolica linea, cujus aſym-<lb/>ptos una eſt aquæ ſuperficies, altera habetur erigendo perpendicularem BF <lb/>ad CB, in puncto B, aſvmptos quæſita erit BE, quæ dividit bifariam FD, <lb/>perpendicularem in puncto quocunque ad BF, & </s> <s xml:id="echoid-s1193" xml:space="preserve">terminatam linea BA.</s> <s xml:id="echoid-s1194" xml:space="preserve"/> </p> <div xml:id="echoid-div141" type="float" level="2" n="4"> <note position="left" xlink:label="note-0050-11" xlink:href="note-0050-11a" xml:space="preserve">83.</note> <note position="left" xlink:label="note-0050-12" xlink:href="note-0050-12a" xml:space="preserve">TAB. I. <lb/>fig. 8. 9.</note> </div> <p> <s xml:id="echoid-s1195" xml:space="preserve">Si DF per punctum D Hyperbolæ tranſect, BF erit ſemidiameter con-<lb/>jugata cum ſemidiametro BD.</s> <s xml:id="echoid-s1196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1197" xml:space="preserve">In Fig. </s> <s xml:id="echoid-s1198" xml:space="preserve">9. </s> <s xml:id="echoid-s1199" xml:space="preserve">ultra F Hyperbola non continuatur; </s> <s xml:id="echoid-s1200" xml:space="preserve">aqua tamen ulterius adſcen-<lb/>dit, ſed aliâ terminatur Curvâ.</s> <s xml:id="echoid-s1201" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1202" xml:space="preserve">In Fig. </s> <s xml:id="echoid-s1203" xml:space="preserve">8. </s> <s xml:id="echoid-s1204" xml:space="preserve">licet Hyperbola vitrorum latera juncta ſecet in D non ibi ad-<lb/>ſcenſus aquæ terminatur, ſed ad certam, & </s> <s xml:id="echoid-s1205" xml:space="preserve">quidem pro diverſo, quem in-<lb/>ter ſe vitra continent, angulo, diverſam ab AB diſtantiam, ab Hyperbola <lb/>deflectitur curva, adſcenſuſque juxta BA continuatur. </s> <s xml:id="echoid-s1206" xml:space="preserve">Ubi enim exigua <lb/> <anchor type="note" xlink:label="note-0050-13a" xlink:href="note-0050-13"/> admodum eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo juvant, quo au-<lb/>getur aquæ adſcenſus. </s> <s xml:id="echoid-s1207" xml:space="preserve">Simile augmentum actionis in n ſequenti memoratur; <lb/></s> <s xml:id="echoid-s1208" xml:space="preserve">in luminis attractione a corporibus etiam locum habet, ut notamus in nume-<lb/>ro ultimo cap. </s> <s xml:id="echoid-s1209" xml:space="preserve">5. </s> <s xml:id="echoid-s1210" xml:space="preserve">lib. </s> <s xml:id="echoid-s1211" xml:space="preserve">3.</s> <s xml:id="echoid-s1212" xml:space="preserve"/> </p> <div xml:id="echoid-div142" type="float" level="2" n="5"> <note position="left" xlink:label="note-0050-13" xlink:href="note-0050-13a" xml:space="preserve">84.</note> </div> </div> <div xml:id="echoid-div144" type="section" level="1" n="53"> <head xml:id="echoid-head93" style="it" xml:space="preserve">De motu guttæ in n. 59,</head> <p> <s xml:id="echoid-s1213" xml:space="preserve">Concipiamus plana, inter quæ gutta movetur, ſecari plano ad plana, & </s> <s xml:id="echoid-s1214" xml:space="preserve">ad <lb/> <anchor type="note" xlink:label="note-0050-14a" xlink:href="note-0050-14"/> lineam in qua junguntur perpendicularem: </s> <s xml:id="echoid-s1215" xml:space="preserve">repræſentatur ſectio hæc; </s> <s xml:id="echoid-s1216" xml:space="preserve">ſed, cum <lb/> <anchor type="note" xlink:label="note-0050-15a" xlink:href="note-0050-15"/> motus ab inclinatione planorum ad ſe invicem pendeat, hanc juſto majorem <lb/>repræſentamus, ut & </s> <s xml:id="echoid-s1217" xml:space="preserve">diſtantiam inter vitra, & </s> <s xml:id="echoid-s1218" xml:space="preserve">diſtantiam ad quam vitrum in <lb/>oleum agit.</s> <s xml:id="echoid-s1219" xml:space="preserve"/> </p> <div xml:id="echoid-div144" type="float" level="2" n="1"> <note position="left" xlink:label="note-0050-14" xlink:href="note-0050-14a" xml:space="preserve">85.</note> <note position="left" xlink:label="note-0050-15" xlink:href="note-0050-15a" xml:space="preserve">TAB. I. <lb/>fig. 10.</note> </div> <p> <s xml:id="echoid-s1220" xml:space="preserve">Sint plana AB, CD; </s> <s xml:id="echoid-s1221" xml:space="preserve">gutta e eff; </s> <s xml:id="echoid-s1222" xml:space="preserve">gh diſtantia ad quam vitrum oleum tra-<lb/>hit: </s> <s xml:id="echoid-s1223" xml:space="preserve">omne ergo oleum inter iehf ad planum trahitur, & </s> <s xml:id="echoid-s1224" xml:space="preserve">conatur ſeſe quaqua <pb o="21" file="0051" n="51" rhead="MATHEMATICA. LIB. I. CAP. V."/> verſum ſuper plano expandere <anchor type="note" xlink:href="" symbol="*"/> non autem poteſt propter cohærentiam par- <anchor type="note" xlink:label="note-0051-01a" xlink:href="note-0051-01"/> tium guttæ, vireſque oppoſitæ in e & </s> <s xml:id="echoid-s1225" xml:space="preserve">f ſeſe mutuo deſtruunt, guttaque, ſi pla-<lb/>na parallela forent non moveretur. </s> <s xml:id="echoid-s1226" xml:space="preserve">Nunc vero, quia actio attractionis per-<lb/>pendiculariter dirigitur ad vitrum, oleum in ſpatio flh a ſuperficie fg attra-<lb/>hitur, ceditque, quia nulla actione contraria deſtruitur hæc, quo motu agi-<lb/>tatur tota gutta cujus partes cohærent inter ſe. </s> <s xml:id="echoid-s1227" xml:space="preserve">Tendit idcirco gutta illam <lb/>partem verſus in qua vitra concurrunt, quamdiu inferius plani inclinatio ad <lb/>horizontem talis eſt, ut vis, qua gravitate ſuper plano conatur deſcendere, <lb/>minor eſt illâ qua ex attractione ſurſum fertur.</s> <s xml:id="echoid-s1228" xml:space="preserve"/> </p> <div xml:id="echoid-div145" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">75.</note> </div> <p> <s xml:id="echoid-s1229" xml:space="preserve">Ubi autem exigua eſt inter vitra diſtantia attractiones oppoſitæ ſeſe mutuo <lb/>juvant’, viſque magis augetur quam ad inſtar diametri guttæ, quod augmen-<lb/>tum in ratione diametri ex ſuperius demonſtratis deduci facile poteſt.</s> <s xml:id="echoid-s1230" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div147" type="section" level="1" n="54"> <head xml:id="echoid-head94" xml:space="preserve">CAPUT VI.</head> <head xml:id="echoid-head95" style="it" xml:space="preserve">De Motu in genere, ubi de Loco & Tempore.</head> <p> <s xml:id="echoid-s1231" xml:space="preserve">MOtus eſt tranſlatio de loco in locum, ſive continua loci <lb/> <anchor type="note" xlink:label="note-0051-02a" xlink:href="note-0051-02"/> mutatio. </s> <s xml:id="echoid-s1232" xml:space="preserve">Unusquiſque illius habet ideam, quæ ſim-<lb/>plex eſt, & </s> <s xml:id="echoid-s1233" xml:space="preserve">verbis explicari nequit.</s> <s xml:id="echoid-s1234" xml:space="preserve"/> </p> <div xml:id="echoid-div147" type="float" level="2" n="1"> <note position="right" xlink:label="note-0051-02" xlink:href="note-0051-02a" xml:space="preserve">86.</note> </div> <p> <s xml:id="echoid-s1235" xml:space="preserve">Locus eſt ſpatium a corpore occupatum, & </s> <s xml:id="echoid-s1236" xml:space="preserve">de eo idem ac <lb/> <anchor type="note" xlink:label="note-0051-03a" xlink:href="note-0051-03"/> de motu dicendum.</s> <s xml:id="echoid-s1237" xml:space="preserve"/> </p> <div xml:id="echoid-div148" type="float" level="2" n="2"> <note position="right" xlink:label="note-0051-03" xlink:href="note-0051-03a" xml:space="preserve">87.</note> </div> <p> <s xml:id="echoid-s1238" xml:space="preserve">Duplex eſt, verus ſeu abſolutus, & </s> <s xml:id="echoid-s1239" xml:space="preserve">relativus.</s> <s xml:id="echoid-s1240" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div150" type="section" level="1" n="55"> <head xml:id="echoid-head96" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s1241" xml:space="preserve">Locus verus eſt pars ſpatii immobilis, quæ a corpore occu-<lb/> <anchor type="note" xlink:label="note-0051-04a" xlink:href="note-0051-04"/> patur.</s> <s xml:id="echoid-s1242" xml:space="preserve"/> </p> <div xml:id="echoid-div150" type="float" level="2" n="1"> <note position="right" xlink:label="note-0051-04" xlink:href="note-0051-04a" xml:space="preserve">88.</note> </div> </div> <div xml:id="echoid-div152" type="section" level="1" n="56"> <head xml:id="echoid-head97" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s1243" xml:space="preserve">Locus relativus, qui ſolus ſenſibus diſtinguitur, eſt ſitus <lb/> <anchor type="note" xlink:label="note-0051-05a" xlink:href="note-0051-05"/> corporis reſpectu aliorum corporum.</s> <s xml:id="echoid-s1244" xml:space="preserve"/> </p> <div xml:id="echoid-div152" type="float" level="2" n="1"> <note position="right" xlink:label="note-0051-05" xlink:href="note-0051-05a" xml:space="preserve">89.</note> </div> <p> <s xml:id="echoid-s1245" xml:space="preserve">Sæpe mutatur locus verus manente relativo, & </s> <s xml:id="echoid-s1246" xml:space="preserve">vice <lb/>verſa.</s> <s xml:id="echoid-s1247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1248" xml:space="preserve">Unde motus alter eſt verus ſeu abſolutus, alter relativus. <lb/></s> <s xml:id="echoid-s1249" xml:space="preserve"> <anchor type="note" xlink:label="note-0051-06a" xlink:href="note-0051-06"/> </s> </p> <div xml:id="echoid-div153" type="float" level="2" n="2"> <note position="right" xlink:label="note-0051-06" xlink:href="note-0051-06a" xml:space="preserve">90.</note> </div> <p> <s xml:id="echoid-s1250" xml:space="preserve">Dum corpus movetur, tempus labitur.</s> <s xml:id="echoid-s1251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1252" xml:space="preserve">Tempus etiam duplex eſt; </s> <s xml:id="echoid-s1253" xml:space="preserve">verum ſeu abſolutum, & </s> <s xml:id="echoid-s1254" xml:space="preserve">re-<lb/> <anchor type="note" xlink:label="note-0051-07a" xlink:href="note-0051-07"/> lativum.</s> <s xml:id="echoid-s1255" xml:space="preserve"/> </p> <div xml:id="echoid-div154" type="float" level="2" n="3"> <note position="right" xlink:label="note-0051-07" xlink:href="note-0051-07a" xml:space="preserve">91.</note> </div> <p> <s xml:id="echoid-s1256" xml:space="preserve">Verum nullam habet relationem ad motum corporum, <lb/> <anchor type="note" xlink:label="note-0051-08a" xlink:href="note-0051-08"/> neque ad ſucceſſionem idearum in Ente intelligenti, ſed ſua <lb/>natura ſemper æqualiter fluit.</s> <s xml:id="echoid-s1257" xml:space="preserve"/> </p> <div xml:id="echoid-div155" type="float" level="2" n="4"> <note position="right" xlink:label="note-0051-08" xlink:href="note-0051-08a" xml:space="preserve">92.</note> </div> </div> <div xml:id="echoid-div157" type="section" level="1" n="57"> <head xml:id="echoid-head98" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s1258" xml:space="preserve">Tempus relativum eſt pars temporis veri per motum cor-<lb/> <anchor type="note" xlink:label="note-0051-09a" xlink:href="note-0051-09"/> porum menſurata, hoc ſolum ſub ſenſus cadit.</s> <s xml:id="echoid-s1259" xml:space="preserve"/> </p> <div xml:id="echoid-div157" type="float" level="2" n="1"> <note position="right" xlink:label="note-0051-09" xlink:href="note-0051-09a" xml:space="preserve">93.</note> </div> <pb o="22" file="0052" n="52" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s1260" xml:space="preserve">Motus omnis poteſt celerior fieri, & </s> <s xml:id="echoid-s1261" xml:space="preserve">etiam corpus tardi-<lb/>us quam ante poteſt moveri; </s> <s xml:id="echoid-s1262" xml:space="preserve">& </s> <s xml:id="echoid-s1263" xml:space="preserve">veriſimillimum eſt nullum <lb/>dari motum corporum omnino æquabilem; </s> <s xml:id="echoid-s1264" xml:space="preserve">unde ſequitur <lb/>tempus relativum a vero differri, hoc enim nunquam ci-<lb/>tius, nunquam tardius fluit.</s> <s xml:id="echoid-s1265" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div159" type="section" level="1" n="58"> <head xml:id="echoid-head99" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p style="it"> <s xml:id="echoid-s1266" xml:space="preserve">Illa motus afſectio, qua in certo tempore certum ſpatium <lb/> <anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/> a corpore moto percurritur, vocatur celeritas aut velocitas; <lb/></s> <s xml:id="echoid-s1267" xml:space="preserve">quæ ergo major aut minor eſt pro magnitudine illius ſpatii, <lb/>& </s> <s xml:id="echoid-s1268" xml:space="preserve">illi ſpatio ſemper proportionalis eſt.</s> <s xml:id="echoid-s1269" xml:space="preserve"/> </p> <div xml:id="echoid-div159" type="float" level="2" n="1"> <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">94.</note> </div> <p style="it"> <s xml:id="echoid-s1270" xml:space="preserve">Spatium percurſum ad inſtar temporis augetur ſi veloci-<lb/> <anchor type="note" xlink:label="note-0052-02a" xlink:href="note-0052-02"/> tas maneat; </s> <s xml:id="echoid-s1271" xml:space="preserve">ideo generaliter ſpatium percurſum ſequitur <lb/>rationem compoſitam temporis & </s> <s xml:id="echoid-s1272" xml:space="preserve">velocitatis.</s> <s xml:id="echoid-s1273" xml:space="preserve"/> </p> <div xml:id="echoid-div160" type="float" level="2" n="2"> <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">95.</note> </div> <p> <s xml:id="echoid-s1274" xml:space="preserve">Datis variis corporibus, ſi pro ſingulis velocitas multi-<lb/>plicetur per tempus, producta erunt ut ſpatia percurſa.</s> <s xml:id="echoid-s1275" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div162" type="section" level="1" n="59"> <head xml:id="echoid-head100" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p style="it"> <s xml:id="echoid-s1276" xml:space="preserve">Motus directio eſt recta, quæ ducta concipitur ver ſus par-<lb/> <anchor type="note" xlink:label="note-0052-03a" xlink:href="note-0052-03"/> tem qua tendit mobile.</s> <s xml:id="echoid-s1277" xml:space="preserve"/> </p> <div xml:id="echoid-div162" type="float" level="2" n="1"> <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">96.</note> </div> </div> <div xml:id="echoid-div164" type="section" level="1" n="60"> <head xml:id="echoid-head101" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s1278" xml:space="preserve">Potentia aut preſſio eſt vis continua in corpus agens ad il-<lb/> <anchor type="note" xlink:label="note-0052-04a" xlink:href="note-0052-04"/> lud ex loco movendum, & </s> <s xml:id="echoid-s1279" xml:space="preserve">quæ actionem in corpus exerere <lb/>poteſt, hoc non moto, aut motu jam impreſſo non mutato. </s> <s xml:id="echoid-s1280" xml:space="preserve">Si <lb/>nempe preſſionis actio contraria preſſione deſtruatur.</s> <s xml:id="echoid-s1281" xml:space="preserve"/> </p> <div xml:id="echoid-div164" type="float" level="2" n="1"> <note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">97.</note> </div> </div> <div xml:id="echoid-div166" type="section" level="1" n="61"> <head xml:id="echoid-head102" style="it" xml:space="preserve">LIBRI I. PARS II.</head> <head xml:id="echoid-head103" xml:space="preserve">De Actionibus Potentiarum.</head> <head xml:id="echoid-head104" xml:space="preserve">CAPUT VII.</head> <head xml:id="echoid-head105" style="it" xml:space="preserve">De Actionibus Potentiarum comparandis.</head> <p style="it"> <s xml:id="echoid-s1282" xml:space="preserve">PReſſiones, id eſt, Potentiarum actiones æquales eſſe has, <lb/> <anchor type="note" xlink:label="note-0052-05a" xlink:href="note-0052-05"/> quæ æqualibus temporibus æquales edunt effectus, pri-<lb/>mo intuitu patet.</s> <s xml:id="echoid-s1283" xml:space="preserve"/> </p> <div xml:id="echoid-div166" type="float" level="2" n="1"> <note position="left" xlink:label="note-0052-05" xlink:href="note-0052-05a" xml:space="preserve">98.</note> </div> <p> <s xml:id="echoid-s1284" xml:space="preserve">Preſſionem contrariam poſſe vincere Preſſionem, in du-<lb/>bium nemo vocabit. </s> <s xml:id="echoid-s1285" xml:space="preserve">Preſſiones æquales ſeſe mutuo deſtrue-<lb/> <anchor type="note" xlink:label="note-0052-06a" xlink:href="note-0052-06"/> <pb file="0053" n="53"/> <anchor type="figure" xlink:label="fig-0053-01a" xlink:href="fig-0053-01"/> <pb file="0053a" n="54"/> <anchor type="figure" xlink:label="fig-0053a-01a" xlink:href="fig-0053a-01"/> <pb file="0054" n="55"/> <pb o="23" file="0055" n="56" rhead="MATHEMATICA. LIB. I CAP. VII."/> re, & </s> <s xml:id="echoid-s1286" xml:space="preserve">has eſſe æquales quæ ſeſe mutuo deſtruunt, ſi pro <lb/>axiomate non habeatur, ex dictis haud difficulter deduci po-<lb/>terit.</s> <s xml:id="echoid-s1287" xml:space="preserve"/> </p> <div xml:id="echoid-div167" type="float" level="2" n="2"> <note position="left" xlink:label="note-0052-06" xlink:href="note-0052-06a" xml:space="preserve">99.</note> <figure xlink:label="fig-0053-01" xlink:href="fig-0053-01a"> <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01"/> </figure> <figure xlink:label="fig-0053a-01" xlink:href="fig-0053a-01a"> <image file="0053a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053a-01"/> </figure> </div> <p> <s xml:id="echoid-s1288" xml:space="preserve">Ex quibus etiam patet, Preſſiones eſſe inter ſe ut effectus <lb/> <anchor type="note" xlink:label="note-0055-01a" xlink:href="note-0055-01"/> æqualibus temporibus editos.</s> <s xml:id="echoid-s1289" xml:space="preserve"/> </p> <div xml:id="echoid-div168" type="float" level="2" n="3"> <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">100.</note> </div> <p> <s xml:id="echoid-s1290" xml:space="preserve">Si prematur obſtaculum & </s> <s xml:id="echoid-s1291" xml:space="preserve">hoc ex loco non recedat, con-<lb/> <anchor type="note" xlink:label="note-0055-02a" xlink:href="note-0055-02"/> trariâ preſſione deſtruitur preſſio; </s> <s xml:id="echoid-s1292" xml:space="preserve">aliter enim hæc nullum <lb/>ederet effectum. </s> <s xml:id="echoid-s1293" xml:space="preserve">Si ergo non deſtruatur, cedit obſtaculum. <lb/></s> <s xml:id="echoid-s1294" xml:space="preserve">Hìc non conſideranda eſt vis quæ in quibuſdam occaſioni-<lb/>bus obſtaculo communicatur & </s> <s xml:id="echoid-s1295" xml:space="preserve">qua in motu perſeverat <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s1296" xml:space="preserve"> <anchor type="note" xlink:label="note-0055-03a" xlink:href="note-0055-03"/> agitur tantum in tota hac parte ſecunda de translatione quæ <lb/> <anchor type="note" xlink:label="note-0055-04a" xlink:href="note-0055-04"/> eſt effectus immediatus preſſionis, & </s> <s xml:id="echoid-s1297" xml:space="preserve">quæ ſemper tantum ſo-<lb/>la locum habet in momento primo infinite exiguo, quando <lb/>actione potentiæ obſtaculum movetur.</s> <s xml:id="echoid-s1298" xml:space="preserve"/> </p> <div xml:id="echoid-div169" type="float" level="2" n="4"> <note position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">101.</note> <note symbol="*" position="right" xlink:label="note-0055-03" xlink:href="note-0055-03a" xml:space="preserve">12.</note> <note position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">102.</note> </div> <p> <s xml:id="echoid-s1299" xml:space="preserve">Cum effectus preſſionis contraria preſſione non deſtructæ <lb/>ſit obſtaculi translatio, ſequitur actiones variarum poten-<lb/> <anchor type="note" xlink:label="note-0055-05a" xlink:href="note-0055-05"/> tiarum tantum inter ſe poſſe differre reſpectu obſtaculorum <lb/>in quæ agunt potentiæ, & </s> <s xml:id="echoid-s1300" xml:space="preserve">reſpectu ſpatiorum ab obſtaculis per-<lb/>cuſſorum.</s> <s xml:id="echoid-s1301" xml:space="preserve"/> </p> <div xml:id="echoid-div170" type="float" level="2" n="5"> <note position="right" xlink:label="note-0055-05" xlink:href="note-0055-05a" xml:space="preserve">103.</note> </div> </div> <div xml:id="echoid-div172" type="section" level="1" n="62"> <head xml:id="echoid-head106" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s1302" xml:space="preserve">Magnitudo preſſionis conſiderata cum relatione ad obſta-<lb/> <anchor type="note" xlink:label="note-0055-06a" xlink:href="note-0055-06"/> culum quod ab illa removetur vocatur Potentiæ intenſitas.</s> <s xml:id="echoid-s1303" xml:space="preserve"/> </p> <div xml:id="echoid-div172" type="float" level="2" n="1"> <note position="right" xlink:label="note-0055-06" xlink:href="note-0055-06a" xml:space="preserve">104.</note> </div> <p style="it"> <s xml:id="echoid-s1304" xml:space="preserve">Sunt igitur potentiarum intenſitates ut obſtacula in quæ <lb/> <anchor type="note" xlink:label="note-0055-07a" xlink:href="note-0055-07"/> illæ agunt.</s> <s xml:id="echoid-s1305" xml:space="preserve"/> </p> <div xml:id="echoid-div173" type="float" level="2" n="2"> <note position="right" xlink:label="note-0055-07" xlink:href="note-0055-07a" xml:space="preserve">105.</note> </div> <p style="it"> <s xml:id="echoid-s1306" xml:space="preserve">Si æqualibus temporibus per ſpatia æqualia obſtacula ce-<lb/> <anchor type="note" xlink:label="note-0055-08a" xlink:href="note-0055-08"/> dunt, actiones Potentiarum ſunt ut harum intenſitates, ideſt, <lb/>ut obſtacula <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1307" xml:space="preserve"> <anchor type="note" xlink:label="note-0055-09a" xlink:href="note-0055-09"/> </s> </p> <div xml:id="echoid-div174" type="float" level="2" n="3"> <note position="right" xlink:label="note-0055-08" xlink:href="note-0055-08a" xml:space="preserve">106.</note> <note symbol="*" position="right" xlink:label="note-0055-09" xlink:href="note-0055-09a" xml:space="preserve">100. <lb/>103. 105.</note> </div> <p style="it"> <s xml:id="echoid-s1308" xml:space="preserve">Si Potentiarum intenſitates fuerint æquales, id eſt, ſi in <lb/> <anchor type="note" xlink:label="note-0055-10a" xlink:href="note-0055-10"/> obſtacula æqualia agant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1309" xml:space="preserve">Potentiarum actiones ſunt ut <anchor type="note" xlink:label="note-0055-11a" xlink:href="note-0055-11"/> ſpatia, æqualibus temporibus, ab obſtaculis percurſa <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1310" xml:space="preserve"> <anchor type="note" xlink:label="note-0055-12a" xlink:href="note-0055-12"/> </s> </p> <div xml:id="echoid-div175" type="float" level="2" n="4"> <note position="right" xlink:label="note-0055-10" xlink:href="note-0055-10a" xml:space="preserve">107.</note> <note symbol="*" position="right" xlink:label="note-0055-11" xlink:href="note-0055-11a" xml:space="preserve">105.</note> <note symbol="*" position="right" xlink:label="note-0055-12" xlink:href="note-0055-12a" xml:space="preserve">100. 102. <lb/>103.</note> </div> <p style="it"> <s xml:id="echoid-s1311" xml:space="preserve">Si autem & </s> <s xml:id="echoid-s1312" xml:space="preserve">obſtacula & </s> <s xml:id="echoid-s1313" xml:space="preserve">viæ ab his æqualibus temporibus <lb/> <anchor type="note" xlink:label="note-0055-13a" xlink:href="note-0055-13"/> percurſæ differant, ſunt potentiarum actiones ut intenſitates, <lb/>aut ut obſtacula, & </s> <s xml:id="echoid-s1314" xml:space="preserve">ut viæ percurſæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1315" xml:space="preserve">id eſt, in harum ra- <anchor type="note" xlink:label="note-0055-14a" xlink:href="note-0055-14"/> tionum ratione compoſita.</s> <s xml:id="echoid-s1316" xml:space="preserve"/> </p> <div xml:id="echoid-div176" type="float" level="2" n="5"> <note position="right" xlink:label="note-0055-13" xlink:href="note-0055-13a" xml:space="preserve">108.</note> <note symbol="*" position="right" xlink:label="note-0055-14" xlink:href="note-0055-14a" xml:space="preserve">106. 107.</note> </div> <p> <s xml:id="echoid-s1317" xml:space="preserve">Ex. </s> <s xml:id="echoid-s1318" xml:space="preserve">Gr. </s> <s xml:id="echoid-s1319" xml:space="preserve">ſi unius potentiæ intenſitas fuerit dupla; </s> <s xml:id="echoid-s1320" xml:space="preserve">id eſt, ſi <lb/>obſtaculum fuerit duplum, & </s> <s xml:id="echoid-s1321" xml:space="preserve">per ſpatium triplum transfera- <pb o="24" file="0056" n="57" rhead="PHYSICES ELEMENTA"/> tur, actio erit bis dupla, aut ter tripla, id eſt, ſextupla. </s> <s xml:id="echoid-s1322" xml:space="preserve">Si, <lb/>datis numeris in ratione intenſitatum, & </s> <s xml:id="echoid-s1323" xml:space="preserve">aliis in ratione ſpa-<lb/>tiorum percurſorum, pro ſingulis potentiis intenſitas per ſpa-<lb/>tium ab obſtaculo percurſum multiplicetur, producta ha-<lb/>bebunt quæſitam compoſitam rationem.</s> <s xml:id="echoid-s1324" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1325" xml:space="preserve">Si numeri dentur, qui actiones potentiarum variarum de-<lb/> <anchor type="note" xlink:label="note-0056-01a" xlink:href="note-0056-01"/> ſignant, erunt hi ut producta obſtaculorum per ſpatia, ergo <lb/>ſi ſinguli ex datis numeris per ſpatium ab obſtaculo ſuo per-<lb/>curſum dividantur, quotientes erunt ut ipſa obſtacula.</s> <s xml:id="echoid-s1326" xml:space="preserve"/> </p> <div xml:id="echoid-div177" type="float" level="2" n="6"> <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">109.</note> </div> <p> <s xml:id="echoid-s1327" xml:space="preserve">Ideo eo majora ſunt obſtacula, quo actiones ſunt majo-<lb/>res, & </s> <s xml:id="echoid-s1328" xml:space="preserve">ſpatia percurſa minora; </s> <s xml:id="echoid-s1329" xml:space="preserve">ideſt, obſtacula ſunt in ratio-<lb/> <anchor type="note" xlink:label="note-0056-02a" xlink:href="note-0056-02"/> ne compoſita directæ actionum, & </s> <s xml:id="echoid-s1330" xml:space="preserve">inverſæ ſpatiorum percur-<lb/>ſorum.</s> <s xml:id="echoid-s1331" xml:space="preserve"/> </p> <div xml:id="echoid-div178" type="float" level="2" n="7"> <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">110.</note> </div> <p> <s xml:id="echoid-s1332" xml:space="preserve">Si numeri qui exprimunt producta obſtaculorum per <lb/>ſpatia, id eſt, qui potentiarum actiones exprimunt, ſinguli <lb/>dividantur per numeros, qui obſtacula deſignant, quotientes <lb/>erunt ut ſpatia, quæ ergo ſunt directe ut actiones, & </s> <s xml:id="echoid-s1333" xml:space="preserve">inver-<lb/> <anchor type="note" xlink:label="note-0056-03a" xlink:href="note-0056-03"/> ſe ut obſtacula.</s> <s xml:id="echoid-s1334" xml:space="preserve"/> </p> <div xml:id="echoid-div179" type="float" level="2" n="8"> <note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">111.</note> </div> <p> <s xml:id="echoid-s1335" xml:space="preserve">Potentiarum actiones ſunt æquales, ſi ſpatia percurſa fue-<lb/> <anchor type="note" xlink:label="note-0056-04a" xlink:href="note-0056-04"/> rint in ratione inverſa obſtaculorum aut intenſit atum poten-<lb/>tiarum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s1336" xml:space="preserve">Quantum enim potentia intenſitate alteram ſupe- <anchor type="note" xlink:label="note-0056-05a" xlink:href="note-0056-05"/> rat, in tantum reſpectu ſpatii percurſi ſuperatur. </s> <s xml:id="echoid-s1337" xml:space="preserve">Ex. </s> <s xml:id="echoid-s1338" xml:space="preserve">Gr. </s> <s xml:id="echoid-s1339" xml:space="preserve">ſi obſta-<lb/>cula fuerint ut octo & </s> <s xml:id="echoid-s1340" xml:space="preserve">ſex, viæ percurſæ ut tria ad quatuor, u-<lb/>traque actio exprimetur per numerum viginti quatuor <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1341" xml:space="preserve"> <anchor type="note" xlink:label="note-0056-06a" xlink:href="note-0056-06"/> </s> </p> <div xml:id="echoid-div180" type="float" level="2" n="9"> <note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">112.</note> <note symbol="*" position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">100.</note> <note symbol="*" position="left" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve">108.</note> </div> </div> <div xml:id="echoid-div182" type="section" level="1" n="63"> <head xml:id="echoid-head107" xml:space="preserve">CAPUT VIII.</head> <head xml:id="echoid-head108" style="it" xml:space="preserve">Generalia circa Gravitatem.</head> <head xml:id="echoid-head109" xml:space="preserve"><emph style="sc">Phænomenon i</emph>.</head> <p style="it"> <s xml:id="echoid-s1342" xml:space="preserve">Omnia Corpora in Terræ viciniis, ſi nullo obſtaculo co-<lb/> <anchor type="note" xlink:label="note-0056-07a" xlink:href="note-0056-07"/> hibeantur, Terram verſum feruntur.</s> <s xml:id="echoid-s1343" xml:space="preserve"/> </p> <div xml:id="echoid-div182" type="float" level="2" n="1"> <note position="left" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve">113.</note> </div> </div> <div xml:id="echoid-div184" type="section" level="1" n="64"> <head xml:id="echoid-head110" xml:space="preserve"><emph style="sc">Definitio</emph>. 1.</head> <p style="it"> <s xml:id="echoid-s1344" xml:space="preserve">Vis qua corpora Tellurem verſus pelluntur, vocatur gravitas. <lb/></s> <s xml:id="echoid-s1345" xml:space="preserve"> <anchor type="note" xlink:label="note-0056-08a" xlink:href="note-0056-08"/> </s> </p> <div xml:id="echoid-div184" type="float" level="2" n="1"> <note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">114.</note> </div> </div> <div xml:id="echoid-div186" type="section" level="1" n="65"> <head xml:id="echoid-head111" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s1346" xml:space="preserve">Vis illa cum relatione ad corpus, quod vi illa propellitur, <lb/> <anchor type="note" xlink:label="note-0056-09a" xlink:href="note-0056-09"/> vocatur corporis pondus.</s> <s xml:id="echoid-s1347" xml:space="preserve"/> </p> <div xml:id="echoid-div186" type="float" level="2" n="1"> <note position="left" xlink:label="note-0056-09" xlink:href="note-0056-09a" xml:space="preserve">115.</note> </div> <pb o="25" file="0057" n="58" rhead="MATHEMATICA. LIB. I. CAP. VIII."/> </div> <div xml:id="echoid-div188" type="section" level="1" n="66"> <head xml:id="echoid-head112" xml:space="preserve"><emph style="sc">Phænomenon</emph> 2.</head> <p style="it"> <s xml:id="echoid-s1348" xml:space="preserve">Vis gravitatis ubique in Terræ viciniis, & </s> <s xml:id="echoid-s1349" xml:space="preserve">omnibus mo-<lb/> <anchor type="note" xlink:label="note-0057-01a" xlink:href="note-0057-01"/> mentis, æqualiter agit.</s> <s xml:id="echoid-s1350" xml:space="preserve"/> </p> <div xml:id="echoid-div188" type="float" level="2" n="1"> <note position="right" xlink:label="note-0057-01" xlink:href="note-0057-01a" xml:space="preserve">116.</note> </div> <p> <s xml:id="echoid-s1351" xml:space="preserve">Parva quidem datur gravitatis differentia in regionibus di-<lb/>verſis, de qua agemus in cap. </s> <s xml:id="echoid-s1352" xml:space="preserve">17. </s> <s xml:id="echoid-s1353" xml:space="preserve">libri IV, nimis tamen <lb/>eſt exigua ut hìc conſideretur, præcipue cum in regionibus, <lb/>quæ inter ſe ſunt vicinæ, omnino ſit inſenſibilis.</s> <s xml:id="echoid-s1354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1355" xml:space="preserve">Quando corporis deſcenſus obſtaculo impeditur, pondere <lb/> <anchor type="note" xlink:label="note-0057-02a" xlink:href="note-0057-02"/> ſuo ſemper æqualiter obſtaculum premit, Terræ centrum <lb/>verſus tendens; </s> <s xml:id="echoid-s1356" xml:space="preserve">poteſt ergo haberi pro potentia in obſtacu-<lb/>lum agenti, & </s> <s xml:id="echoid-s1357" xml:space="preserve">quæ de potentiis in capite præcedenti ſunt <lb/>demonſtrata, hìc etiam locum habent.</s> <s xml:id="echoid-s1358" xml:space="preserve"/> </p> <div xml:id="echoid-div189" type="float" level="2" n="2"> <note position="right" xlink:label="note-0057-02" xlink:href="note-0057-02a" xml:space="preserve">117.</note> </div> </div> <div xml:id="echoid-div191" type="section" level="1" n="67"> <head xml:id="echoid-head113" xml:space="preserve"><emph style="sc">Phænomenon</emph> 3.</head> <p style="it"> <s xml:id="echoid-s1359" xml:space="preserve">Corpora quæ vi gravitatis deſcendunt, ſi omnis tollatur <lb/> <anchor type="note" xlink:label="note-0057-03a" xlink:href="note-0057-03"/> reſiſtentia, ſunt æque velocia.</s> <s xml:id="echoid-s1360" xml:space="preserve"/> </p> <div xml:id="echoid-div191" type="float" level="2" n="1"> <note position="right" xlink:label="note-0057-03" xlink:href="note-0057-03a" xml:space="preserve">118.</note> </div> <p> <s xml:id="echoid-s1361" xml:space="preserve">Phænomenon hoc Experimento ſequenti patet.</s> <s xml:id="echoid-s1362" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div193" type="section" level="1" n="68"> <head xml:id="echoid-head114" xml:space="preserve"><emph style="sc">Machina</emph></head> <p style="it"> <s xml:id="echoid-s1363" xml:space="preserve">Qua duo corpora eodem momento in vacuo dimittuntur.</s> <s xml:id="echoid-s1364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1365" xml:space="preserve">Pneumaticam dicimus machinam illam, cujus ope aër <lb/> <anchor type="note" xlink:label="note-0057-04a" xlink:href="note-0057-04"/> ex vaſe extrahitur, de hac agemus in parte 3<emph style="super">2</emph>. </s> <s xml:id="echoid-s1366" xml:space="preserve">lib. </s> <s xml:id="echoid-s1367" xml:space="preserve">II.</s> <s xml:id="echoid-s1368" xml:space="preserve">, hìc <lb/> <anchor type="note" xlink:label="note-0057-05a" xlink:href="note-0057-05"/> repræſentatur in N.</s> <s xml:id="echoid-s1369" xml:space="preserve"/> </p> <div xml:id="echoid-div193" type="float" level="2" n="1"> <note position="right" xlink:label="note-0057-04" xlink:href="note-0057-04a" xml:space="preserve">119.</note> <note position="right" xlink:label="note-0057-05" xlink:href="note-0057-05a" xml:space="preserve">TAB. I@.. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s1370" xml:space="preserve">Ut magis commode experimentum, quod nunc explican-<lb/>dum eſt, inſtituatur, a pede ſuo tollitur machina pneuma-<lb/>tica, & </s> <s xml:id="echoid-s1371" xml:space="preserve">depreſſo ſuſtentaculo SS ſuperimponitur.</s> <s xml:id="echoid-s1372" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1373" xml:space="preserve">Lamina ænea, cui vitra, ex quibus aër extrahitur, impo-<lb/>nuntur, eſt L.</s> <s xml:id="echoid-s1374" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1375" xml:space="preserve">Ad latera hujus duæ firmantur columnæ ligneæ AE, AE; <lb/></s> <s xml:id="echoid-s1376" xml:space="preserve">harum pedes infra tabulam Machinæ pneumaticæ ſuperiorem <lb/>penetrant, & </s> <s xml:id="echoid-s1377" xml:space="preserve">transverſis lignis, ut t, firmantur.</s> <s xml:id="echoid-s1378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1379" xml:space="preserve">Columnarum altitudo excedit pedes quinque; </s> <s xml:id="echoid-s1380" xml:space="preserve">junguntur <lb/>hæ tabellis ligneis quatuor BB, CC, DD, EE. </s> <s xml:id="echoid-s1381" xml:space="preserve">Diſtantia <lb/>inter L & </s> <s xml:id="echoid-s1382" xml:space="preserve">BB eſt novem aut decem pollicum; </s> <s xml:id="echoid-s1383" xml:space="preserve">BC, CD, DE, <lb/>ſingulæ æquales ſunt octodecim pollicibus.</s> <s xml:id="echoid-s1384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1385" xml:space="preserve">Tabellæ hæ ligneæ latiores ſunt in medio, ut in ſingulis <lb/>apertura, aut foramen rotundum, detur, cujus diameter æ-<lb/>quat pollices quinque cum ſemiſſe.</s> <s xml:id="echoid-s1386" xml:space="preserve"/> </p> <pb o="26" file="0058" n="59" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s1387" xml:space="preserve">Quatuor vitra cylindrica, quorum oræ exactiſſime inter <lb/>ſe conveniunt, (quo pervenimus atterendo oras cum are-<lb/>na madida ſuper plano), ſuperimponuntur Laminæ L, & </s> <s xml:id="echoid-s1388" xml:space="preserve"><lb/>ſibi mutuo.</s> <s xml:id="echoid-s1389" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1390" xml:space="preserve">Cylindrorum ſingulorum diametri interiores ſunt quatuor <lb/>pollicum, & </s> <s xml:id="echoid-s1391" xml:space="preserve">altitudines ſeſquipedis. </s> <s xml:id="echoid-s1392" xml:space="preserve">Transeunt hi cylindri per <lb/>foramina in tabellis ligneis, & </s> <s xml:id="echoid-s1393" xml:space="preserve">firmantur ſinguli, tribus cuneis li-<lb/>gneis x, x, &</s> <s xml:id="echoid-s1394" xml:space="preserve">c, formatis, ut cum vitro & </s> <s xml:id="echoid-s1395" xml:space="preserve">foramine con-<lb/>gruant.</s> <s xml:id="echoid-s1396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1397" xml:space="preserve">Obtegitur cylindrus ſuperior operculo æneo o, quod in <lb/>O ſeparatim repræſentatur.</s> <s xml:id="echoid-s1398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1399" xml:space="preserve">Cum hoc conjungitur pyxis ænea P, aut p, ope cochleæ <lb/>G, quæ intra vitrum per operculum penetrat ita, ut ope <lb/>ejuſdem cum operculo jungatur lamina elaſtica, flexa, in-<lb/>curvata, & </s> <s xml:id="echoid-s1400" xml:space="preserve">perforata in ſuperiori parte, ut repræſentatur in I <lb/>& </s> <s xml:id="echoid-s1401" xml:space="preserve">i.</s> <s xml:id="echoid-s1402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1403" xml:space="preserve">Laminæ extrema r, r, elaſticitate conveniunt, ultimis <lb/>tamen extremitatibus paululum deflexis.</s> <s xml:id="echoid-s1404" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1405" xml:space="preserve">Huic laminæ includitur lamina ænea ovalis H, cujus mi-<lb/>nor diameter intra laminam I contineri poteſt, hujus extre-<lb/>mis non ſeparatis.</s> <s xml:id="echoid-s1406" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1407" xml:space="preserve">Intra eandem laminam I aut i, penetrat filum æneum F <lb/>(f), quod tranſit per pyxidem P (p), & </s> <s xml:id="echoid-s1408" xml:space="preserve">eò etiam per o-<lb/>perculum O (o), ut & </s> <s xml:id="echoid-s1409" xml:space="preserve">per pyxidis operculum Q (q).</s> <s xml:id="echoid-s1410" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1411" xml:space="preserve">Fili F extremum inferius V quadratum eſt & </s> <s xml:id="echoid-s1412" xml:space="preserve">cavum, ut <lb/>cum filo jungatur lamina H, quæ, juncto cum eodem filo <lb/>manubrio M (m), agitari poteſt, & </s> <s xml:id="echoid-s1413" xml:space="preserve">circumvolvi, quo ex-<lb/>trema r, r, laminæ I ſeparantur, longiore diametro ovalis H <lb/>ſuperante diſtantiam inter oppoſitas partes laminæ I, quando <lb/>ipſius extrema elaſticitate junguntur.</s> <s xml:id="echoid-s1414" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1415" xml:space="preserve">Cerâ molli circumpoſitâ cohibetur ne aër inter laminam <lb/>& </s> <s xml:id="echoid-s1416" xml:space="preserve">vitrum transeat, ut & </s> <s xml:id="echoid-s1417" xml:space="preserve">inter operculum o & </s> <s xml:id="echoid-s1418" xml:space="preserve">vitrum; </s> <s xml:id="echoid-s1419" xml:space="preserve">et-<lb/>iam cerâ circumdantur vitra ubi duo junguntur; </s> <s xml:id="echoid-s1420" xml:space="preserve">& </s> <s xml:id="echoid-s1421" xml:space="preserve">cochlea <lb/>G eâdem obducitur, antequam pyxis P (p) cum operculo <lb/>O (o) jungatur.</s> <s xml:id="echoid-s1422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1423" xml:space="preserve">Ne aër juxta filum f (F) vitra intret, pyxis p (P) annulis <pb o="27" file="0059" n="60" rhead="MATHEMATICA. LIB. I. CAP. VIII."/> coreaceis cerâ & </s> <s xml:id="echoid-s1424" xml:space="preserve">oleo imbutis impletur, quæ comprimuntur <lb/>operculo q(Q) ita, ut quam exactiſſime cum filo æneo, quod <lb/>hæc pertranſit, congruant.</s> <s xml:id="echoid-s1425" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div195" type="section" level="1" n="69"> <head xml:id="echoid-head115" xml:space="preserve"><emph style="sc">Experimentum</emph></head> <p> <s xml:id="echoid-s1426" xml:space="preserve">Omnibus ut explicatum dispoſitis, antequam operculum <lb/> <anchor type="note" xlink:label="note-0059-01a" xlink:href="note-0059-01"/> o, cum adjunctis, vitro ſuperiori imponatur, fruſtum au-<lb/>ri cum plumulâ ita diſponenda ſunt, ut hæreant inter ex-<lb/>trema laminæ i, ibique elaſticitate firmiter retineantur.</s> <s xml:id="echoid-s1427" xml:space="preserve"/> </p> <div xml:id="echoid-div195" type="float" level="2" n="1"> <note position="right" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve">120.</note> </div> <p> <s xml:id="echoid-s1428" xml:space="preserve">Impoſito tunc operculo, cerâ aëris ingreſſus inter hoc & </s> <s xml:id="echoid-s1429" xml:space="preserve"><lb/>vitrum, ut ſuperius dictum, cohibeatur; </s> <s xml:id="echoid-s1430" xml:space="preserve">agitatâ antliâ ex-<lb/>hauriatur aër ex vitris.</s> <s xml:id="echoid-s1431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1432" xml:space="preserve">Si nunc manubrium m circumvolvatur; </s> <s xml:id="echoid-s1433" xml:space="preserve">clarum eſt eodem <lb/>momento aurum & </s> <s xml:id="echoid-s1434" xml:space="preserve">plumulam relaxari, & </s> <s xml:id="echoid-s1435" xml:space="preserve">dimitti, exactiſſi-<lb/>me etiam eodem momento ad laminam L pervenient.</s> <s xml:id="echoid-s1436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1437" xml:space="preserve">Corpora cadentia percipiet ſpectator ad talem diſtan-<lb/>tiam poſitus, ut unico intuitu omnia percipiat vitra, ſi ad <lb/>minorem detur diſtantiam oculos dirigat ad ipſam lami-<lb/>nam L.</s> <s xml:id="echoid-s1438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1439" xml:space="preserve">Ex alio etiam Experimento, in ſequentibus memorando, <lb/>idem hocce Phænomenon deducitur.</s> <s xml:id="echoid-s1440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1441" xml:space="preserve">Ex hiſce ſequitur, gravitate obſtacula quæcunque per æqua-<lb/>lia ſpatia æqualibus temporibus transferri, ex actione imme-<lb/>diata gravitatis; </s> <s xml:id="echoid-s1442" xml:space="preserve">patet enim corpora in primo momento eo-<lb/>dem modo moveri, & </s> <s xml:id="echoid-s1443" xml:space="preserve">ſingulis momentis ſequentibus corpus <lb/>utrumque eodem modo accelerari; </s> <s xml:id="echoid-s1444" xml:space="preserve">ſunt ergo actiones gra-<lb/> <anchor type="note" xlink:label="note-0059-02a" xlink:href="note-0059-02"/> vitatis in corpora ut ipſa corpora <anchor type="note" xlink:href="" symbol="*"/>, id eſt pondera ſunt ut <anchor type="note" xlink:label="note-0059-03a" xlink:href="note-0059-03"/> quantitates materiæ; </s> <s xml:id="echoid-s1445" xml:space="preserve">ſingulæque materiæ particulæ æqua-<lb/>les æqualiter ponderant, cujuſcunque corporis particulæ <lb/>fuerint.</s> <s xml:id="echoid-s1446" xml:space="preserve"/> </p> <div xml:id="echoid-div196" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0059-02" xlink:href="note-0059-02a" xml:space="preserve">106.</note> <note position="right" xlink:label="note-0059-03" xlink:href="note-0059-03a" xml:space="preserve">121.</note> </div> <p> <s xml:id="echoid-s1447" xml:space="preserve">Quando pondus conſideratur ut potentia, intenſitas po-<lb/> <anchor type="note" xlink:label="note-0059-04a" xlink:href="note-0059-04"/> tentiæ proportionalis eſt quantitati materiæ in corpore pon-<lb/>deranti, & </s> <s xml:id="echoid-s1448" xml:space="preserve">potentiæ directio eſt verſus Terræ centrum.</s> <s xml:id="echoid-s1449" xml:space="preserve"/> </p> <div xml:id="echoid-div197" type="float" level="2" n="3"> <note position="right" xlink:label="note-0059-04" xlink:href="note-0059-04a" xml:space="preserve">122.</note> </div> <p> <s xml:id="echoid-s1450" xml:space="preserve">Hæc de gravitate notanda erant, quia ponderibus in Ex-<lb/>perimentis circa preſſiones inſtituendis utimur.</s> <s xml:id="echoid-s1451" xml:space="preserve"/> </p> <pb o="28" file="0060" n="61" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div199" type="section" level="1" n="70"> <head xml:id="echoid-head116" xml:space="preserve">CAPUT IX.</head> <p style="it"> <s xml:id="echoid-s1452" xml:space="preserve">De Trochlea ſimplici, Libra, & </s> <s xml:id="echoid-s1453" xml:space="preserve">Centro gravitatis.</s> <s xml:id="echoid-s1454" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div200" type="section" level="1" n="71"> <head xml:id="echoid-head117" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s1455" xml:space="preserve">TRochlea ſimplex, eſt orbiculus circa axem volubilis, <lb/> <anchor type="note" xlink:label="note-0060-01a" xlink:href="note-0060-01"/> cui circumpo ſitus funis ductarius dictus, Trochlea ex-<lb/> <anchor type="note" xlink:label="note-0060-02a" xlink:href="note-0060-02"/> hibetur in A, funis ductarius eſt d c e.</s> <s xml:id="echoid-s1456" xml:space="preserve"/> </p> <div xml:id="echoid-div200" type="float" level="2" n="1"> <note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">123.</note> <note position="left" xlink:label="note-0060-02" xlink:href="note-0060-02a" xml:space="preserve">TAB. II. <lb/>48. 19.</note> </div> <p> <s xml:id="echoid-s1457" xml:space="preserve">Hac Machinâ potentiæ directio mutatur, nec ullîus alîus <lb/>uſus eſt, quando ſuo loco eſt fixa; </s> <s xml:id="echoid-s1458" xml:space="preserve">in hoc enim caſu, vis, <lb/> <anchor type="note" xlink:label="note-0060-03a" xlink:href="note-0060-03"/> ſeu potentia, funi ductario applicata, ut M, æqualis impedi-<lb/>mento P, æquipollet impedimento <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1459" xml:space="preserve">nam potentia moveri <anchor type="note" xlink:label="note-0060-04a" xlink:href="note-0060-04"/> non poteſt, quin impedimentum eodem tempore ſpatium <lb/>æquale percurrat.</s> <s xml:id="echoid-s1460" xml:space="preserve"/> </p> <div xml:id="echoid-div201" type="float" level="2" n="2"> <note position="left" xlink:label="note-0060-03" xlink:href="note-0060-03a" xml:space="preserve">124.</note> <note symbol="*" position="left" xlink:label="note-0060-04" xlink:href="note-0060-04a" xml:space="preserve">100.</note> </div> <p> <s xml:id="echoid-s1461" xml:space="preserve">Pondera explorantur, id eſt, quantitates materiæ in ſin-<lb/>gulis corporibus comparantur <anchor type="note" xlink:href="" symbol="*"/>, adhibitâ librâ aut bilance, <anchor type="note" xlink:label="note-0060-05a" xlink:href="note-0060-05"/> inſtrumento notiſſimo.</s> <s xml:id="echoid-s1462" xml:space="preserve"/> </p> <div xml:id="echoid-div202" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0060-05" xlink:href="note-0060-05a" xml:space="preserve">121.</note> </div> </div> <div xml:id="echoid-div204" type="section" level="1" n="72"> <head xml:id="echoid-head118" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s1463" xml:space="preserve">Axis libræ vocatur linea circa quam libra movetur, aut <lb/> <anchor type="note" xlink:label="note-0060-06a" xlink:href="note-0060-06"/> potius rotatur.</s> <s xml:id="echoid-s1464" xml:space="preserve"/> </p> <div xml:id="echoid-div204" type="float" level="2" n="1"> <note position="left" xlink:label="note-0060-06" xlink:href="note-0060-06a" xml:space="preserve">125.</note> </div> </div> <div xml:id="echoid-div206" type="section" level="1" n="73"> <head xml:id="echoid-head119" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s1465" xml:space="preserve">Quando longitudinem brachiorum ſive jugi conſideramus, <lb/> <anchor type="note" xlink:label="note-0060-07a" xlink:href="note-0060-07"/> axis conſideratur ut punctum, & </s> <s xml:id="echoid-s1466" xml:space="preserve">vocatur centrum libræ.</s> <s xml:id="echoid-s1467" xml:space="preserve"/> </p> <div xml:id="echoid-div206" type="float" level="2" n="1"> <note position="left" xlink:label="note-0060-07" xlink:href="note-0060-07a" xml:space="preserve">126.</note> </div> </div> <div xml:id="echoid-div208" type="section" level="1" n="74"> <head xml:id="echoid-head120" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s1468" xml:space="preserve">Puncta ſuſpenſionis, aut applicationis, vocantur, puncta <lb/> <anchor type="note" xlink:label="note-0060-08a" xlink:href="note-0060-08"/> in quibus vel actu ſunt, vel liberè dependent pondera, aut lan-<lb/>ces, quibus pondera imponuntur.</s> <s xml:id="echoid-s1469" xml:space="preserve"/> </p> <div xml:id="echoid-div208" type="float" level="2" n="1"> <note position="left" xlink:label="note-0060-08" xlink:href="note-0060-08a" xml:space="preserve">127.</note> </div> <p> <s xml:id="echoid-s1470" xml:space="preserve">Circa hanc Machinam ſequentia notanda ſunt.</s> <s xml:id="echoid-s1471" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1472" xml:space="preserve">Pondus æqualiter gravat punctum, ſi liberè ab eo depen-<lb/> <anchor type="note" xlink:label="note-0060-09a" xlink:href="note-0060-09"/> deat, ad quamcunque altitudinem, ac ſi pondus in ipſo poſitum <lb/>intelligeretur.</s> <s xml:id="echoid-s1473" xml:space="preserve"/> </p> <div xml:id="echoid-div209" type="float" level="2" n="2"> <note position="left" xlink:label="note-0060-09" xlink:href="note-0060-09a" xml:space="preserve">128.</note> </div> <p> <s xml:id="echoid-s1474" xml:space="preserve">Pondus enim corporis ad omnes altitudines æqualiter tra-<lb/>hit funem quo ſuſpenditur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1475" xml:space="preserve"> <anchor type="note" xlink:label="note-0060-10a" xlink:href="note-0060-10"/> </s> </p> <div xml:id="echoid-div210" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0060-10" xlink:href="note-0060-10a" xml:space="preserve">115. 116.</note> </div> </div> <div xml:id="echoid-div212" type="section" level="1" n="75"> <head xml:id="echoid-head121" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s1476" xml:space="preserve">In libra AB, pondus P, ope funis BD, ad varias ſuſpen-<lb/> <anchor type="note" xlink:label="note-0060-11a" xlink:href="note-0060-11"/> ditur altitudines; </s> <s xml:id="echoid-s1477" xml:space="preserve">& </s> <s xml:id="echoid-s1478" xml:space="preserve">eo ſitus libræ non mutatur.</s> <s xml:id="echoid-s1479" xml:space="preserve"/> </p> <div xml:id="echoid-div212" type="float" level="2" n="1"> <note position="left" xlink:label="note-0060-11" xlink:href="note-0060-11a" xml:space="preserve">TAB. III. <lb/>fig. 2.</note> </div> <p style="it"> <s xml:id="echoid-s1480" xml:space="preserve">Actio ponderis ad movendam libram eo major eſt, quoma-<lb/> <anchor type="note" xlink:label="note-0060-12a" xlink:href="note-0060-12"/> <pb file="0061" n="62"/> <anchor type="figure" xlink:label="fig-0061-01a" xlink:href="fig-0061-01"/> <pb file="0061a" n="63"/> <anchor type="figure" xlink:label="fig-0061a-01a" xlink:href="fig-0061a-01"/> <pb file="0062" n="64"/> <pb o="29" file="0063" n="65" rhead="MATHEMATICA. LIB. I. CAP. IX."/> gis punctum a pondere gravatum a centro libræ diſtat; </s> <s xml:id="echoid-s1481" xml:space="preserve">& </s> <s xml:id="echoid-s1482" xml:space="preserve"><lb/>actio illa ſequitur proportionem diſtantiæ prædicti punctiab <lb/>illo centro.</s> <s xml:id="echoid-s1483" xml:space="preserve"/> </p> <div xml:id="echoid-div213" type="float" level="2" n="2"> <note position="left" xlink:label="note-0060-12" xlink:href="note-0060-12a" xml:space="preserve">129.</note> <figure xlink:label="fig-0061-01" xlink:href="fig-0061-01a"> <image file="0061-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061-01"/> </figure> <figure xlink:label="fig-0061a-01" xlink:href="fig-0061a-01a"> <image file="0061a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0061a-01"/> </figure> </div> <p> <s xml:id="echoid-s1484" xml:space="preserve">Quando libra rotatur, in eodem libræ motu, punctum <lb/> <anchor type="note" xlink:label="note-0063-01a" xlink:href="note-0063-01"/> B percurrit arcum B b, & </s> <s xml:id="echoid-s1485" xml:space="preserve">punctum A arcum A a, quo-<lb/>rum ultimus maximus eſt; </s> <s xml:id="echoid-s1486" xml:space="preserve">in illo ergo libræ motu actio e-<lb/>juſdem ponderis varia eft, pro puncto cui applicatur, & </s> <s xml:id="echoid-s1487" xml:space="preserve"><lb/>ſequitur proportionem ſpatii ab hoc puncto percurſi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1488" xml:space="preserve">eſt <anchor type="note" xlink:label="note-0063-02a" xlink:href="note-0063-02"/> ergo in A, ut Aa, in B, ut Bb; </s> <s xml:id="echoid-s1489" xml:space="preserve">arcus verò hi ſuntinter <lb/>ſe ut CA, CB.</s> <s xml:id="echoid-s1490" xml:space="preserve"/> </p> <div xml:id="echoid-div214" type="float" level="2" n="3"> <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">TAB. III. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">107. 117.</note> </div> </div> <div xml:id="echoid-div216" type="section" level="1" n="76"> <head xml:id="echoid-head122" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s1491" xml:space="preserve">Libræ AB, cujus jugi longitudo eſt duorum pedum, bra-<lb/> <anchor type="note" xlink:label="note-0063-03a" xlink:href="note-0063-03"/> chia ſingula in partes centum æquales dividuntur, poſito <lb/> <anchor type="note" xlink:label="note-0063-04a" xlink:href="note-0063-04"/> diviſionum initio in ipſo centro libræ.</s> <s xml:id="echoid-s1492" xml:space="preserve"/> </p> <div xml:id="echoid-div216" type="float" level="2" n="1"> <note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">130.</note> <note position="right" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve">TAB. III. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s1493" xml:space="preserve">Actio unciæ unius, applicatæ 60 diviſioni, æqualis eſt <lb/>actioni trium unciarum, 20 diviſioni ſuſpenſarum.</s> <s xml:id="echoid-s1494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1495" xml:space="preserve">Ut hoc Experimentum cum quibusdam ſequentibus com-<lb/>mode inſtituatur, varia dantur pondera ænea unius unciæ, <lb/>ut P, quæ diviſionibus jugi applicari poſſunt, & </s> <s xml:id="echoid-s1496" xml:space="preserve">in inferiori <lb/>parte uncum habent. </s> <s xml:id="echoid-s1497" xml:space="preserve">Dantur etiam lances variæ, ut L, quæ <lb/>ſingulæ cum filis, & </s> <s xml:id="echoid-s1498" xml:space="preserve">unco, cui ſuspenduntur exactiſſime et-<lb/>iam ponderant unciam unam.</s> <s xml:id="echoid-s1499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1500" xml:space="preserve">Ex hiſce ſequitur, actionem ponderis ad movendum li-<lb/> <anchor type="note" xlink:label="note-0063-05a" xlink:href="note-0063-05"/> bram eſſe in ratione compoſita ip ſius ponderis & </s> <s xml:id="echoid-s1501" xml:space="preserve">diſtantiæ a <lb/>centro <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s1502" xml:space="preserve">nam hæc diſtantia eſt ut ſpatium percurſum in mo- <anchor type="note" xlink:label="note-0063-06a" xlink:href="note-0063-06"/> tu libræ. </s> <s xml:id="echoid-s1503" xml:space="preserve">Multiplicando ſingula pondera per ſuas diſtantias <lb/>a centro producta ſunt ut actiones in libram.</s> <s xml:id="echoid-s1504" xml:space="preserve"/> </p> <div xml:id="echoid-div217" type="float" level="2" n="2"> <note position="right" xlink:label="note-0063-05" xlink:href="note-0063-05a" xml:space="preserve">131.</note> <note symbol="*" position="right" xlink:label="note-0063-06" xlink:href="note-0063-06a" xml:space="preserve">10@.</note> </div> </div> <div xml:id="echoid-div219" type="section" level="1" n="77"> <head xml:id="echoid-head123" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s1505" xml:space="preserve">Libra in æquilibrio dicitur, quando actiones ponderum in <lb/> <anchor type="note" xlink:label="note-0063-07a" xlink:href="note-0063-07"/> utrumque brachium ad movendam libram, ſunt æquales; </s> <s xml:id="echoid-s1506" xml:space="preserve">i-<lb/>ta ut ſeſe mutuo deſtruant, ut in præcedenti Experimento.</s> <s xml:id="echoid-s1507" xml:space="preserve"/> </p> <div xml:id="echoid-div219" type="float" level="2" n="1"> <note position="right" xlink:label="note-0063-07" xlink:href="note-0063-07a" xml:space="preserve">132.</note> </div> </div> <div xml:id="echoid-div221" type="section" level="1" n="78"> <head xml:id="echoid-head124" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p> <s xml:id="echoid-s1508" xml:space="preserve">Quando libra eſt in æquilibrio, pondera ab utraque par-<lb/> <anchor type="note" xlink:label="note-0063-08a" xlink:href="note-0063-08"/> te dicuntur æquiponderare.</s> <s xml:id="echoid-s1509" xml:space="preserve"/> </p> <div xml:id="echoid-div221" type="float" level="2" n="1"> <note position="right" xlink:label="note-0063-08" xlink:href="note-0063-08a" xml:space="preserve">133.</note> </div> <p> <s xml:id="echoid-s1510" xml:space="preserve">Pondera inæqualia poſſunt æquiponderare; </s> <s xml:id="echoid-s1511" xml:space="preserve">quando <lb/> <anchor type="note" xlink:label="note-0063-09a" xlink:href="note-0063-09"/> diſtantiæ a centro ſunt reciprocè ut pondera <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1512" xml:space="preserve"> <anchor type="note" xlink:label="note-0063-10a" xlink:href="note-0063-10"/> <pb o="30" file="0064" n="66" rhead="PHYSICES ELEMENTA"/> In hoc caſu, ſi unumquodque pondus per ſuam diſtantiam <lb/>multiplicetur, producta erunt æqualia. </s> <s xml:id="echoid-s1513" xml:space="preserve">Confirmatur hoc <lb/>præcedenti experimento.</s> <s xml:id="echoid-s1514" xml:space="preserve"/> </p> <div xml:id="echoid-div222" type="float" level="2" n="2"> <note position="right" xlink:label="note-0063-09" xlink:href="note-0063-09a" xml:space="preserve">134.</note> <note symbol="*" position="right" xlink:label="note-0063-10" xlink:href="note-0063-10a" xml:space="preserve">132. <gap/></note> </div> <p> <s xml:id="echoid-s1515" xml:space="preserve">Hoc fundamento nititur Statera Romana, qua unico pon-<lb/> <anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/> dere omnia ponderantur.</s> <s xml:id="echoid-s1516" xml:space="preserve"/> </p> <div xml:id="echoid-div223" type="float" level="2" n="3"> <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">135.</note> </div> </div> <div xml:id="echoid-div225" type="section" level="1" n="79"> <head xml:id="echoid-head125" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s1517" xml:space="preserve">Statera Romana A B habet duo brachia admodum inæ-<lb/> <anchor type="note" xlink:label="note-0064-02a" xlink:href="note-0064-02"/> qualia; </s> <s xml:id="echoid-s1518" xml:space="preserve">in breviori lanx ſuſpenditur: </s> <s xml:id="echoid-s1519" xml:space="preserve">longiſſimum in partes æ-<lb/> <anchor type="note" xlink:label="note-0064-03a" xlink:href="note-0064-03"/> quales dividitur, poſito diviſionum initio in centro motus; <lb/></s> <s xml:id="echoid-s1520" xml:space="preserve">diviſiones majores numeris notantur, & </s> <s xml:id="echoid-s1521" xml:space="preserve">ſingula in octo mi-<lb/>nores iterum dividuntur. </s> <s xml:id="echoid-s1522" xml:space="preserve">Pondus tale ei applicatur, ut <lb/>in prima diviſione majori æquiponderet cum ſemiliberâ lan-<lb/>ci impoſitâ: </s> <s xml:id="echoid-s1523" xml:space="preserve">tum corpus ponderandum lanci imponitur, & </s> <s xml:id="echoid-s1524" xml:space="preserve"><lb/>pondus ſtatim memoratum per longitudinem brachii longi-<lb/>oris movetur, donec detur æquilibrium; </s> <s xml:id="echoid-s1525" xml:space="preserve">diviſiones majores <lb/>inter pondus & </s> <s xml:id="echoid-s1526" xml:space="preserve">centrum, ſemi librarum numerum denotant, <lb/>quas corpus ponderat; </s> <s xml:id="echoid-s1527" xml:space="preserve">ſubdiviſiones uncias indicant. </s> <s xml:id="echoid-s1528" xml:space="preserve">Mi-<lb/>nus etiam pondus quodcunque adhiberi poteſt quo minores <lb/>differentiæ inter corporum pondera determinari queunt.</s> <s xml:id="echoid-s1529" xml:space="preserve"/> </p> <div xml:id="echoid-div225" type="float" level="2" n="1"> <note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">136.</note> <note position="left" xlink:label="note-0064-03" xlink:href="note-0064-03a" xml:space="preserve">TAB. VIII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s1530" xml:space="preserve">Eodem etiam nititur fundamento bilanx fallax, cujus nem-<lb/> <anchor type="note" xlink:label="note-0064-04a" xlink:href="note-0064-04"/> pe brachia ſunt inæqualia.</s> <s xml:id="echoid-s1531" xml:space="preserve"/> </p> <div xml:id="echoid-div226" type="float" level="2" n="2"> <note position="left" xlink:label="note-0064-04" xlink:href="note-0064-04a" xml:space="preserve">137.</note> </div> </div> <div xml:id="echoid-div228" type="section" level="1" n="80"> <head xml:id="echoid-head126" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s1532" xml:space="preserve">Libræ ſæpius memoratæ duæ lances, ponderis inæqua-<lb/> <anchor type="note" xlink:label="note-0064-05a" xlink:href="note-0064-05"/> lis, ut detur æquilibrium, applicantur ab una parte cente-<lb/> <anchor type="note" xlink:label="note-0064-06a" xlink:href="note-0064-06"/> fimæad alteram nonageſimæ quintæ diviſioni. </s> <s xml:id="echoid-s1533" xml:space="preserve">Si tunc duo <lb/>pondera dentur quæcumque, quæ ſint inter ſe ut 19 ad <lb/>20, & </s> <s xml:id="echoid-s1534" xml:space="preserve">illud primæ lanci, hoc vero ſecundæ, imponatur æ-<lb/>quiponderabunt.</s> <s xml:id="echoid-s1535" xml:space="preserve"/> </p> <div xml:id="echoid-div228" type="float" level="2" n="1"> <note position="left" xlink:label="note-0064-05" xlink:href="note-0064-05a" xml:space="preserve">138.</note> <note position="left" xlink:label="note-0064-06" xlink:href="note-0064-06a" xml:space="preserve">TAB IV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s1536" xml:space="preserve">Plurima pondera ad varias diſtantias ab una parte, cum <lb/> <anchor type="note" xlink:label="note-0064-07a" xlink:href="note-0064-07"/> unico pondere ad aliam partem, poſſunt æquiponderare. </s> <s xml:id="echoid-s1537" xml:space="preserve">Re-<lb/>quiritur, ut productum hujus ponderis, per ſuam diſtantiam <lb/>a centro, æquale ſit ſummæ productorum omnium aliorum <lb/>ponderum, ſingulatim unumquodque per ſuam diſtantiam a <lb/>centro multiplicatorum.</s> <s xml:id="echoid-s1538" xml:space="preserve"/> </p> <div xml:id="echoid-div229" type="float" level="2" n="2"> <note position="left" xlink:label="note-0064-07" xlink:href="note-0064-07a" xml:space="preserve">139.</note> </div> </div> <div xml:id="echoid-div231" type="section" level="1" n="81"> <head xml:id="echoid-head127" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <note position="left" xml:space="preserve">140.</note> <p> <s xml:id="echoid-s1539" xml:space="preserve">Ad unam partem pondus duarum unciarum 20 diviſioni, <lb/> <anchor type="note" xlink:label="note-0064-09a" xlink:href="note-0064-09"/> <pb o="31" file="0065" n="67" rhead="MATHEMATICA. LIB. I. CAP. IX."/> pondus unius unciæ 30, & </s> <s xml:id="echoid-s1540" xml:space="preserve">tandem pondus trium unciarum <lb/>60 diviſioni applicantur, & </s> <s xml:id="echoid-s1541" xml:space="preserve">æquilibrium datur, ſi pondus <lb/>unicum quinque unciarum 50 diviſioni, alterius brachii, <lb/>ſuſpendatur.</s> <s xml:id="echoid-s1542" xml:space="preserve"/> </p> <div xml:id="echoid-div231" type="float" level="2" n="1"> <note position="left" xlink:label="note-0064-09" xlink:href="note-0064-09a" xml:space="preserve">TAB. III. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s1543" xml:space="preserve">Multiplicando 50 per 5, productum habemus 250. </s> <s xml:id="echoid-s1544" xml:space="preserve">In a-<lb/>lio brachio tria habemus producta, 20 x 2 ideſt 40, 30 x 1, <lb/>ideſt 30, & </s> <s xml:id="echoid-s1545" xml:space="preserve">60 x 3, nempe 180. </s> <s xml:id="echoid-s1546" xml:space="preserve">Colligendo nunc 40, 30, <lb/>180, in unam ſummam etiam habemus 250.</s> <s xml:id="echoid-s1547" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1548" xml:space="preserve">Plurima pondera, numero inæquali, ab utraque parte, <lb/> <anchor type="note" xlink:label="note-0065-01a" xlink:href="note-0065-01"/> poſſunt æquiponderare. </s> <s xml:id="echoid-s1549" xml:space="preserve">In eo caſu, ſi unumquodque mul-<lb/>tiplicetur per ſuam diſtantiam a centro, ſummæ producto-<lb/>rum ab utraque parte erunt æquales: </s> <s xml:id="echoid-s1550" xml:space="preserve">& </s> <s xml:id="echoid-s1551" xml:space="preserve">ſi ſummæ iſtæ ſunt <lb/>æquales, datur æquilibrium.</s> <s xml:id="echoid-s1552" xml:space="preserve"/> </p> <div xml:id="echoid-div232" type="float" level="2" n="2"> <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">141.</note> </div> </div> <div xml:id="echoid-div234" type="section" level="1" n="82"> <head xml:id="echoid-head128" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s1553" xml:space="preserve">Ex inſpectione figuræ Experimentum hoc ſatis patet. <lb/></s> <s xml:id="echoid-s1554" xml:space="preserve"> <anchor type="note" xlink:label="note-0065-02a" xlink:href="note-0065-02"/> Multiplicando ſingula pondera, per ſuas a centro diſtantias, <lb/> <anchor type="note" xlink:label="note-0065-03a" xlink:href="note-0065-03"/> habemus ab una parte producta 15, 40, 110, 80. </s> <s xml:id="echoid-s1555" xml:space="preserve">90. </s> <s xml:id="echoid-s1556" xml:space="preserve">500, <lb/>ad aliam partem 70, 105, 300, 360: </s> <s xml:id="echoid-s1557" xml:space="preserve">quorum ſumma utra-<lb/>que eſt 835.</s> <s xml:id="echoid-s1558" xml:space="preserve"/> </p> <div xml:id="echoid-div234" type="float" level="2" n="1"> <note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">142.</note> <note position="right" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">TAB. III. <lb/>fig. 6.</note> </div> </div> <div xml:id="echoid-div236" type="section" level="1" n="83"> <head xml:id="echoid-head129" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p style="it"> <s xml:id="echoid-s1559" xml:space="preserve">Centrum gravitatis vocatur punctum in corpore, circa <lb/> <anchor type="note" xlink:label="note-0065-04a" xlink:href="note-0065-04"/> quod omnes partes corporis, in quocumque ſitu poſiti, in æ-<lb/>quilibrio ſunt.</s> <s xml:id="echoid-s1560" xml:space="preserve"/> </p> <div xml:id="echoid-div236" type="float" level="2" n="1"> <note position="right" xlink:label="note-0065-04" xlink:href="note-0065-04a" xml:space="preserve">143.</note> </div> <p> <s xml:id="echoid-s1561" xml:space="preserve">Quando duo aut plura corpora junguntur, ſive ſint conti-<lb/> <anchor type="note" xlink:label="note-0065-05a" xlink:href="note-0065-05"/> gua, ſive ſeparata, commune centrum gravitatis habent.</s> <s xml:id="echoid-s1562" xml:space="preserve"/> </p> <div xml:id="echoid-div237" type="float" level="2" n="2"> <note position="right" xlink:label="note-0065-05" xlink:href="note-0065-05a" xml:space="preserve">144.</note> </div> <p style="it"> <s xml:id="echoid-s1563" xml:space="preserve">Quando centrum gravitatis ſuſtinetur, corpus quieſcere <lb/> <anchor type="note" xlink:label="note-0065-06a" xlink:href="note-0065-06"/> poteſt; </s> <s xml:id="echoid-s1564" xml:space="preserve">quia inter partes oppoſitas æquilibrium datur.</s> <s xml:id="echoid-s1565" xml:space="preserve"/> </p> <div xml:id="echoid-div238" type="float" level="2" n="3"> <note position="right" xlink:label="note-0065-06" xlink:href="note-0065-06a" xml:space="preserve">145.</note> </div> </div> <div xml:id="echoid-div240" type="section" level="1" n="84"> <head xml:id="echoid-head130" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s1566" xml:space="preserve">Corpus A ſuſtinetur & </s> <s xml:id="echoid-s1567" xml:space="preserve">quieſcit, quia centrum illius gra-<lb/> <anchor type="note" xlink:label="note-0065-07a" xlink:href="note-0065-07"/> vitatis c, ſuſtinetur a fulcro F.</s> <s xml:id="echoid-s1568" xml:space="preserve"/> </p> <div xml:id="echoid-div240" type="float" level="2" n="1"> <note position="right" xlink:label="note-0065-07" xlink:href="note-0065-07a" xml:space="preserve">146.</note> </div> <note position="right" xml:space="preserve">TAB. IV. <lb/>fig. 2.</note> <p style="it"> <s xml:id="echoid-s1569" xml:space="preserve">Quando centrum gravitatis non ſuſtinetur, corpus movetur <lb/> <anchor type="note" xlink:label="note-0065-09a" xlink:href="note-0065-09"/> donec ſuſtineatur.</s> <s xml:id="echoid-s1570" xml:space="preserve"/> </p> <div xml:id="echoid-div241" type="float" level="2" n="2"> <note position="right" xlink:label="note-0065-09" xlink:href="note-0065-09a" xml:space="preserve">147.</note> </div> </div> <div xml:id="echoid-div243" type="section" level="1" n="85"> <head xml:id="echoid-head131" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <note position="right" xml:space="preserve">148.</note> <p> <s xml:id="echoid-s1571" xml:space="preserve">Corpus A menſæ impoſitum cadet, & </s> <s xml:id="echoid-s1572" xml:space="preserve">corpus B in ſitu, <lb/> <anchor type="note" xlink:label="note-0065-11a" xlink:href="note-0065-11"/> in quo repræſentatur, non manebit, quia horum centra gra-<lb/>vitatis non ſuſtinentur.</s> <s xml:id="echoid-s1573" xml:space="preserve"/> </p> <div xml:id="echoid-div243" type="float" level="2" n="1"> <note position="right" xlink:label="note-0065-11" xlink:href="note-0065-11a" xml:space="preserve">TAB. IV. <lb/>fig. 3.</note> </div> <pb o="32" file="0066" n="68" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s1574" xml:space="preserve">Ex hiſce ratio redditur, quare corpora quædam planis <lb/>inclinatis impoſita, devolvantur, & </s> <s xml:id="echoid-s1575" xml:space="preserve">alia ſimpliciter laban-<lb/>tur.</s> <s xml:id="echoid-s1576" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div245" type="section" level="1" n="86"> <head xml:id="echoid-head132" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s1577" xml:space="preserve">Corpus A labitur, quia centrum gravitatis illius a plano <lb/> <anchor type="note" xlink:label="note-0066-01a" xlink:href="note-0066-01"/> inclinato ſuſtinetur, id eſt, linea verticalis quæ tranſit per <lb/> <anchor type="note" xlink:label="note-0066-02a" xlink:href="note-0066-02"/> centrum illud c, ſecat planum inclinatum intra corpus. </s> <s xml:id="echoid-s1578" xml:space="preserve">Cor-<lb/>pus vero B devolvitur, quia verticalis linea, quæ tranſit per <lb/>centrum gravitatis, ſecat planum inclinatum extra corpus.</s> <s xml:id="echoid-s1579" xml:space="preserve"/> </p> <div xml:id="echoid-div245" type="float" level="2" n="1"> <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">149.</note> <note position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve">TAB. IV. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s1580" xml:space="preserve">Ex prædictis etiam ſequitur, corpus deſcendere quando <lb/> <anchor type="note" xlink:label="note-0066-03a" xlink:href="note-0066-03"/> gravitatis centrum deſcendit, id eſt, Terræ centrum ver-<lb/>ſus movetur.</s> <s xml:id="echoid-s1581" xml:space="preserve"/> </p> <div xml:id="echoid-div246" type="float" level="2" n="2"> <note position="left" xlink:label="note-0066-03" xlink:href="note-0066-03a" xml:space="preserve">150.</note> </div> <p> <s xml:id="echoid-s1582" xml:space="preserve">Aliquando in illo caſu corpus adſcendere videtur, & </s> <s xml:id="echoid-s1583" xml:space="preserve">ſæpe <lb/>etiam revera, ſi integram ipſius maſſam conſideremus, aſcen-<lb/>dit, quando centrum figuræ corporis cum centro gravitatis <lb/>non coincidit.</s> <s xml:id="echoid-s1584" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div248" type="section" level="1" n="87"> <head xml:id="echoid-head133" xml:space="preserve"><emph style="sc">Experimentum</emph> 10.</head> <p> <s xml:id="echoid-s1585" xml:space="preserve">Rota A, cujus axis formatur ex duobus conis quorum ba-<lb/> <anchor type="note" xlink:label="note-0066-04a" xlink:href="note-0066-04"/> ſes rotæ applicantur, ſi ponatur inter duo plana, quorum <lb/> <anchor type="note" xlink:label="note-0066-05a" xlink:href="note-0066-05"/> latera DG, FH, continuata formant angulum FCD, baſin <lb/>apice magis elevatam habentem, ab inferiori parte HG, verſus <lb/>planorum partem maxime elevatam FD, movebitur.</s> <s xml:id="echoid-s1586" xml:space="preserve"/> </p> <div xml:id="echoid-div248" type="float" level="2" n="1"> <note position="left" xlink:label="note-0066-04" xlink:href="note-0066-04a" xml:space="preserve">151.</note> <note position="left" xlink:label="note-0066-05" xlink:href="note-0066-05a" xml:space="preserve">TAB. IV. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s1587" xml:space="preserve">Propter majorem inter plana diſtantiam in FD, rota A, <lb/>cujus axis ab utraque parte eſt conus, magis deſcendit inter <lb/>plana, quando illam partem verſus movetur, & </s> <s xml:id="echoid-s1588" xml:space="preserve">ſic gravita-<lb/>te ſua huc fertur, ſi modo deſcenſus inter plana ſuperet ad-<lb/>ſcenſum ex anguli FCD inclinatione ad horizontem.</s> <s xml:id="echoid-s1589" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div250" type="section" level="1" n="88"> <head xml:id="echoid-head134" xml:space="preserve"><emph style="sc">Experimentum</emph> 11.</head> <p> <s xml:id="echoid-s1590" xml:space="preserve">Cylindrus ligneus A, intus a latere continet cylindrum <lb/> <anchor type="note" xlink:label="note-0066-06a" xlink:href="note-0066-06"/> plumbeum; </s> <s xml:id="echoid-s1591" xml:space="preserve">centrum gravitatis commune illorum eſt in ſe-<lb/> <anchor type="note" xlink:label="note-0066-07a" xlink:href="note-0066-07"/> ctione ad baſin parallela, cylindrum in duas partes æquales <lb/>dividente, & </s> <s xml:id="echoid-s1592" xml:space="preserve">in puncto, reſpondenti, puncto baſis c.</s> <s xml:id="echoid-s1593" xml:space="preserve"/> </p> <div xml:id="echoid-div250" type="float" level="2" n="1"> <note position="left" xlink:label="note-0066-06" xlink:href="note-0066-06a" xml:space="preserve">152.</note> <note position="left" xlink:label="note-0066-07" xlink:href="note-0066-07a" xml:space="preserve">TAB. IV. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s1594" xml:space="preserve">Cylindrus hic utcunque poſitus, movebitur, donec cen-<lb/>trum gravitatis memoratum ſit in infimo ad quem perveni-<lb/>re poteſt loco.</s> <s xml:id="echoid-s1595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1596" xml:space="preserve">Si plano inclinato imponatur, in eo ſitu in quo hic delinea- <pb file="0067" n="69"/> <anchor type="figure" xlink:label="fig-0067-01a" xlink:href="fig-0067-01"/> <pb file="0067a" n="70"/> <anchor type="figure" xlink:label="fig-0067a-01a" xlink:href="fig-0067a-01"/> <pb file="0068" n="71"/> <pb o="33" file="0069" n="72" rhead="MATHEMATICA. LIB. I. CAP. IX."/> tur; </s> <s xml:id="echoid-s1597" xml:space="preserve">deſcendet centrum gravitatis, dum corpus juxta pla-<lb/>num adſcendit, poſita juſta plani inclinatione.</s> <s xml:id="echoid-s1598" xml:space="preserve"/> </p> <div xml:id="echoid-div251" type="float" level="2" n="2"> <figure xlink:label="fig-0067-01" xlink:href="fig-0067-01a"> <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/> </figure> <figure xlink:label="fig-0067a-01" xlink:href="fig-0067a-01a"> <image file="0067a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067a-01"/> </figure> </div> <p> <s xml:id="echoid-s1599" xml:space="preserve">Aſcendit corpus dum rotatur partem plani ſuperiorem <lb/>verſus; </s> <s xml:id="echoid-s1600" xml:space="preserve">ſed dum ſicrotatur cavendum eſt, ne juxta planum <lb/>labatur, ad quod requiritur funis, quo pro parte cylindrus <lb/>circumdatur, cujus extremitas una cylindro in f connecti-<lb/>tur, extremitate alterâ in d plano affixâ manente.</s> <s xml:id="echoid-s1601" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s1602" xml:space="preserve">Ulterius ex iis, quæ de centro gravitatis dicta ſunt, de-<lb/>ducitur; </s> <s xml:id="echoid-s1603" xml:space="preserve">Punctum in quocunque corpore, aut machina, quod <lb/> <anchor type="note" xlink:label="note-0069-01a" xlink:href="note-0069-01"/> ſuſtinet centrum gravitatis alicujus ponderis, totum pondus <lb/>ſuſtinere: </s> <s xml:id="echoid-s1604" xml:space="preserve">totamque vim, qua corpus terram verſus tendit, <lb/>in hoc centro quaſi coactam dari.</s> <s xml:id="echoid-s1605" xml:space="preserve"/> </p> <div xml:id="echoid-div252" type="float" level="2" n="3"> <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">153.</note> </div> </div> <div xml:id="echoid-div254" type="section" level="1" n="89"> <head xml:id="echoid-head135" xml:space="preserve"><emph style="sc">Experimentum</emph> 13.</head> <p> <s xml:id="echoid-s1606" xml:space="preserve">Si corpus A B, cujus centrum gravitatis brachio libræ <lb/> <anchor type="note" xlink:label="note-0069-02a" xlink:href="note-0069-02"/> imponitur, aliquo in ſitu æquiponderat cum pondere P, <lb/> <anchor type="note" xlink:label="note-0069-03a" xlink:href="note-0069-03"/> in omni alio ſitu, ab, ab, manente centro gravitatis C, <lb/>æquiponderabit.</s> <s xml:id="echoid-s1607" xml:space="preserve"/> </p> <div xml:id="echoid-div254" type="float" level="2" n="1"> <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">154.</note> <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">TAB. IV. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s1608" xml:space="preserve">Ad perfectionem libræ requiruntur 1. </s> <s xml:id="echoid-s1609" xml:space="preserve">ut puncta ſuſpen-<lb/> <anchor type="note" xlink:label="note-0069-04a" xlink:href="note-0069-04"/> ſionis lancium, aut ponderum, ſint exactè in eadem linea <lb/>cum centro libræ; </s> <s xml:id="echoid-s1610" xml:space="preserve">2. </s> <s xml:id="echoid-s1611" xml:space="preserve">ut ab utraque parte exactè ab iſto <lb/>centro æqualiter diſtent; </s> <s xml:id="echoid-s1612" xml:space="preserve">3. </s> <s xml:id="echoid-s1613" xml:space="preserve">ut libræ brachia, quantum com-<lb/>modè fieri poteſt, ſint longa; </s> <s xml:id="echoid-s1614" xml:space="preserve">4. </s> <s xml:id="echoid-s1615" xml:space="preserve">ut in motu jugi & </s> <s xml:id="echoid-s1616" xml:space="preserve">lancium, <lb/>quantum fieri poteſt, parvus ſit attritus; </s> <s xml:id="echoid-s1617" xml:space="preserve">5. </s> <s xml:id="echoid-s1618" xml:space="preserve">ut centrum <lb/>gravitatis jugi ponatur paululum infra centrum motus; </s> <s xml:id="echoid-s1619" xml:space="preserve">6. <lb/></s> <s xml:id="echoid-s1620" xml:space="preserve">tandem ut partes axis, quæ jugo ſeparantur, ſint exa-<lb/>ctiſſimè in eadem linea recta, quæ ſitum maximè commo-<lb/>dum habebit, ſi cum jugo angulum efficiat rectum.</s> <s xml:id="echoid-s1621" xml:space="preserve"/> </p> <div xml:id="echoid-div255" type="float" level="2" n="2"> <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">155.</note> </div> </div> <div xml:id="echoid-div257" type="section" level="1" n="90"> <head xml:id="echoid-head136" xml:space="preserve">SCHOLIUM</head> <head xml:id="echoid-head137" style="it" xml:space="preserve">De centro Gravitatis.</head> <p> <s xml:id="echoid-s1622" xml:space="preserve">Centrum gravitatis diximus eſſe punctum in corpore, circa quod omnes <lb/>partes ipſius, in quocunque ſitu poſiti, ſunt in æquilibrio: </s> <s xml:id="echoid-s1623" xml:space="preserve">tale punctum <lb/>in corpore quocunque revera dari, cum pleriſque Mechanicis poſuimus, hoc <lb/>nunc demonſtrabimus.</s> <s xml:id="echoid-s1624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1625" xml:space="preserve">Sint puncta duo gravia A & </s> <s xml:id="echoid-s1626" xml:space="preserve">B, inæqualem quamcunque gravitatem haben-<lb/> <anchor type="note" xlink:label="note-0069-05a" xlink:href="note-0069-05"/> tia; </s> <s xml:id="echoid-s1627" xml:space="preserve">concipiantur hæc juncta, lineâ inflexili, rectâ, ſine pondere; </s> <s xml:id="echoid-s1628" xml:space="preserve">Detur in <lb/> <anchor type="note" xlink:label="note-0069-06a" xlink:href="note-0069-06"/> hac punctum C tale, ut CA ſit ad CB, ut pondus puncti B ad pondus pun-<lb/>cti A. </s> <s xml:id="echoid-s1629" xml:space="preserve">Pondera hæc in æquilibrio erunt circa C, & </s> <s xml:id="echoid-s1630" xml:space="preserve">quidem in ſitu quocun- <pb o="34" file="0070" n="73" rhead="PHYSICES ELEMENTA"/> que, ut ex ante demonſtratis <anchor type="note" xlink:href="" symbol="*"/> deducitur; </s> <s xml:id="echoid-s1631" xml:space="preserve">ideò ſi ſuſtineatur punctum C, ſu- <anchor type="note" xlink:label="note-0070-01a" xlink:href="note-0070-01"/> ſtinentur puncta A & </s> <s xml:id="echoid-s1632" xml:space="preserve">B, & </s> <s xml:id="echoid-s1633" xml:space="preserve">harum actio in puncto C quaſi coacta eſt.</s> <s xml:id="echoid-s1634" xml:space="preserve"/> </p> <div xml:id="echoid-div257" type="float" level="2" n="1"> <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">156.</note> <note position="right" xlink:label="note-0069-06" xlink:href="note-0069-06a" xml:space="preserve">TAB. VIII. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">129.</note> </div> <p> <s xml:id="echoid-s1635" xml:space="preserve">Detur tertium punctum grave D, ponderis cujuſcunque; </s> <s xml:id="echoid-s1636" xml:space="preserve">jungantur D & </s> <s xml:id="echoid-s1637" xml:space="preserve"><lb/>C, etiam rectâ inflexili, ponderis experti; </s> <s xml:id="echoid-s1638" xml:space="preserve">ſitque in hac punctum E, ita de-<lb/>terminatum, ut EC ſe habeat ad ED, ut pondus puncti D ad ſummam pon-<lb/>derum punctorum A & </s> <s xml:id="echoid-s1639" xml:space="preserve">B.</s> <s xml:id="echoid-s1640" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1641" xml:space="preserve">Si A & </s> <s xml:id="echoid-s1642" xml:space="preserve">B juncta darentur in C, circa E daretur æquilibrium, poſitâ li-<lb/>neâ CD in ſitu quocunque <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s1643" xml:space="preserve">ſed A & </s> <s xml:id="echoid-s1644" xml:space="preserve">B, ut demonſtravimus, in ſitu quo- <anchor type="note" xlink:label="note-0070-02a" xlink:href="note-0070-02"/> cunque lineæ AB, agunt quaſi in C juncta eſſent; </s> <s xml:id="echoid-s1645" xml:space="preserve">ergo tria pondera A,B,D, <lb/>lineis inflexilibus conjuncta, in ſitu quocunque, in æquilibrio ſunt circa <lb/>punctum E; </s> <s xml:id="echoid-s1646" xml:space="preserve">quod ergo eſt centrum gravitatis trium punctorum. </s> <s xml:id="echoid-s1647" xml:space="preserve">Puncta <lb/>hæc etiam nullum aliud habere centrum gravitatis, præter punctum E, ex eâ-<lb/>dem demonſtratione conſtat.</s> <s xml:id="echoid-s1648" xml:space="preserve"/> </p> <div xml:id="echoid-div258" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">129</note> </div> <p> <s xml:id="echoid-s1649" xml:space="preserve">Si quartum daretur punctum grave, lineâ inflexili, rectâ, jungendum hoc <lb/>foret cum E, & </s> <s xml:id="echoid-s1650" xml:space="preserve">ſimili demonſtratione conſtaret, quatuor puncta commune <lb/>habere gravitatis centrum, & </s> <s xml:id="echoid-s1651" xml:space="preserve">unicum hoc eſſe.</s> <s xml:id="echoid-s1652" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1653" xml:space="preserve">Cum vero eadem demonſtratio ad numerum quemcunque punctorum re-<lb/>ferri poſſit, applicari poterit omnibus punctis gravibus, ex quibus corpus quod-<lb/> <anchor type="note" xlink:label="note-0070-03a" xlink:href="note-0070-03"/> cunque conſtat: </s> <s xml:id="echoid-s1654" xml:space="preserve">habet ideò corpus centrum gravitatis, & </s> <s xml:id="echoid-s1655" xml:space="preserve">unicum tale habet cen-<lb/>trum.</s> <s xml:id="echoid-s1656" xml:space="preserve"/> </p> <div xml:id="echoid-div259" type="float" level="2" n="3"> <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">157.</note> </div> </div> <div xml:id="echoid-div261" type="section" level="1" n="91"> <head xml:id="echoid-head138" style="it" xml:space="preserve">De Centri gravitatis inveſtigatione.</head> <p> <s xml:id="echoid-s1657" xml:space="preserve">Dentur corpora, numero quocunque, quorum commune gravitatis cen-<lb/> <anchor type="note" xlink:label="note-0070-04a" xlink:href="note-0070-04"/> trum ſit C; </s> <s xml:id="echoid-s1658" xml:space="preserve">per hoc concipiamus planum horizontale, quod ſit planum ipſi-<lb/> <anchor type="note" xlink:label="note-0070-05a" xlink:href="note-0070-05"/> us figuræ. </s> <s xml:id="echoid-s1659" xml:space="preserve">Sint centra gravitatis ipſorum corporum A, B, D, E, F; </s> <s xml:id="echoid-s1660" xml:space="preserve">ſi <lb/>centra hæc ipſo plano horizontali memorato non dentur, ad hoc referenda <lb/>ſunt lineis verticalibus & </s> <s xml:id="echoid-s1661" xml:space="preserve">eodem modo planum corpora gravabunt ac ſi i-<lb/>pſorum centra gravitatis darentur in punctis, in quibus lineæ hæ verticales <lb/> <anchor type="note" xlink:label="note-0070-06a" xlink:href="note-0070-06"/> planum ſecant <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1662" xml:space="preserve"/> </p> <div xml:id="echoid-div261" type="float" level="2" n="1"> <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">158.</note> <note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">TAB. VIII. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">128.</note> </div> <p> <s xml:id="echoid-s1663" xml:space="preserve">Suſtineatur planum linea GH; </s> <s xml:id="echoid-s1664" xml:space="preserve">habentur actiones ponderum ad movendum <lb/>planum circa lineam GH, multiplicando pondus unumquodque per ſuam diſtanti-<lb/> <anchor type="note" xlink:label="note-0070-07a" xlink:href="note-0070-07"/> am a linea GH <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s1665" xml:space="preserve">ſumma productorum dat integram actionem, qua omnia <anchor type="note" xlink:label="note-0070-08a" xlink:href="note-0070-08"/> pondera ſimul planum premunt ad hoc circa GH movendum.</s> <s xml:id="echoid-s1666" xml:space="preserve"/> </p> <div xml:id="echoid-div262" type="float" level="2" n="2"> <note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">159.</note> <note symbol="*" position="left" xlink:label="note-0070-08" xlink:href="note-0070-08a" xml:space="preserve">131.</note> </div> <p> <s xml:id="echoid-s1667" xml:space="preserve">Omnia autem pondera agunt, quaſi eſſent in C <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1668" xml:space="preserve">idcirco habetur etiam i- <anchor type="note" xlink:label="note-0070-09a" xlink:href="note-0070-09"/> pſorum actio, multiplicando ſummam ponderum per diſtantiam puncti C a <lb/>linea GH: </s> <s xml:id="echoid-s1669" xml:space="preserve">Si ergo ſumma memorata productorum, quæ, ut patet, huic ul-<lb/>timo producto æqualis eſt, dividatur per ſummam ponderum, datur in quotiente <lb/>diſtantia centri gravitatis a linea GH.</s> <s xml:id="echoid-s1670" xml:space="preserve"/> </p> <div xml:id="echoid-div263" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0070-09" xlink:href="note-0070-09a" xml:space="preserve">153.</note> </div> <p> <s xml:id="echoid-s1671" xml:space="preserve">Quando agitur de ponderibus, quæ lineis verticalibus ad planum horizon-<lb/>tale referuntur, diſtantiæ punctorum, ad quæ pondera referuntur, à lineâ <lb/>GH, ſunt æquales diſtantiis centrorum gravitatis ipſorum corporum à pla-<lb/>no verticali, per GH tranſeunti.</s> <s xml:id="echoid-s1672" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1673" xml:space="preserve">Cum verò hæc demonſtratio locum habeat in quocunque ſitu corpora den-<lb/>tur, ſi lineis inflexilibus, & </s> <s xml:id="echoid-s1674" xml:space="preserve">ſine pondere, corpora inter ſe coh@reant, nul-<lb/>lum poteſt concipi planum, quod non, ſervato ipſius ſitu reſpectu corporum, <lb/> <anchor type="note" xlink:label="note-0070-10a" xlink:href="note-0070-10"/> poſſit fieri verticale; </s> <s xml:id="echoid-s1675" xml:space="preserve">unde ſequitur datis corporibus & </s> <s xml:id="echoid-s1676" xml:space="preserve">plano quocunque, diſtan-<lb/>tiam centri gravitatis a plano detegi, multiplicando corpus unumquodque per ſui <lb/>centri gravitatis diſtantiam a plano, & </s> <s xml:id="echoid-s1677" xml:space="preserve">dividendo productorum ſummam per ipſo-<lb/>rum corporum ſummam.</s> <s xml:id="echoid-s1678" xml:space="preserve"/> </p> <div xml:id="echoid-div264" type="float" level="2" n="4"> <note position="left" xlink:label="note-0070-10" xlink:href="note-0070-10a" xml:space="preserve">160.</note> </div> <p> <s xml:id="echoid-s1679" xml:space="preserve">Si ſimilem demonſtrationem applicemus plano, quod inter corpora tranſit, <lb/> <anchor type="note" xlink:label="note-0070-11a" xlink:href="note-0070-11"/> differentia inter ſummas productorum ab utraque parte per corporum ſum- <pb file="0071" n="74"/> <anchor type="figure" xlink:label="fig-0071-01a" xlink:href="fig-0071-01"/> <pb file="0071a" n="75"/> <anchor type="figure" xlink:label="fig-0071a-01a" xlink:href="fig-0071a-01"/> <pb file="0072" n="76"/> <pb o="35" file="0073" n="77" rhead="MATHEMATICA. LIB. 1. CAP. IX."/> mam dividenda erit, ad detegendam memoratam diſtantiam centri gravitatis a <lb/>plano.</s> <s xml:id="echoid-s1680" xml:space="preserve"/> </p> <div xml:id="echoid-div265" type="float" level="2" n="5"> <note position="left" xlink:label="note-0070-11" xlink:href="note-0070-11a" xml:space="preserve">161.</note> <figure xlink:label="fig-0071-01" xlink:href="fig-0071-01a"> <image file="0071-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071-01"/> </figure> <figure xlink:label="fig-0071a-01" xlink:href="fig-0071a-01a"> <image file="0071a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0071a-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s1681" xml:space="preserve">Ex hiſce deducimus methodum, qua inveſtigatur centrum gravitatis; </s> <s xml:id="echoid-s1682" xml:space="preserve">quæ-<lb/> <anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/> rendo bujus diſtantiam a tribus planis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s1683" xml:space="preserve">Quæ eadem methodus ad corpus quodcun- <anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/> que peculiare applicari poteſt, referendo adhujus partes, quæ de corporibus ſunt de-<lb/> <anchor type="note" xlink:label="note-0073-03a" xlink:href="note-0073-03"/> monſtrata.</s> <s xml:id="echoid-s1684" xml:space="preserve"/> </p> <div xml:id="echoid-div266" type="float" level="2" n="6"> <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">162.</note> <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">163.</note> <note symbol="*" position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">160</note> </div> <p style="it"> <s xml:id="echoid-s1685" xml:space="preserve">Si Corpora, quorum commune gravitatis centrum quæritur, ſua peculiaria <lb/> <anchor type="note" xlink:label="note-0073-04a" xlink:href="note-0073-04"/> gravitatis centra in eodem plano babeant, determinatur quæſitum centrum, dete-<lb/>gendo bujus diſtantiam â duabus lineis <anchor type="note" xlink:href="" symbol="*"/>, utcunque in eodem hoc plano ductis.</s> <s xml:id="echoid-s1686" xml:space="preserve"> <anchor type="note" xlink:label="note-0073-05a" xlink:href="note-0073-05"/> </s> </p> <div xml:id="echoid-div267" type="float" level="2" n="7"> <note position="right" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve">164.</note> <note symbol="*" position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve">159.</note> </div> <p style="it"> <s xml:id="echoid-s1687" xml:space="preserve">Quando peculiaria gravitatis centra in eâdem lineâ dantur, detegitur commune <lb/> <anchor type="note" xlink:label="note-0073-06a" xlink:href="note-0073-06"/> gravitatis centrum operatione unicâ, qua nempe ipſius diſtantia à puncto quocun-<lb/>que, in eâdem illâ lineâ ſumto, determinatur.</s> <s xml:id="echoid-s1688" xml:space="preserve"/> </p> <div xml:id="echoid-div268" type="float" level="2" n="8"> <note position="right" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve">165.</note> </div> </div> <div xml:id="echoid-div270" type="section" level="1" n="92"> <head xml:id="echoid-head139" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head140" style="it" xml:space="preserve">Arithmetica Mechanica.</head> <p> <s xml:id="echoid-s1689" xml:space="preserve">Regulæ quatuor Arithmeticæ, Additic, Subtractio, Multiplicatio, & </s> <s xml:id="echoid-s1690" xml:space="preserve">Diviſio, ope <lb/>libræ ſuperius memoratæ <anchor type="note" xlink:href="" symbol="*"/>, cujus brachia in partes æquales ſunt diviſa fa- <anchor type="note" xlink:label="note-0073-07a" xlink:href="note-0073-07"/> cile inſtitui poſſunt, operationumque demonſtratio ex ante memoratis quam <lb/>facillimè deducitur; </s> <s xml:id="echoid-s1691" xml:space="preserve">ſatis ideò erit ipſas regulas exemplis illuſtrare.</s> <s xml:id="echoid-s1692" xml:space="preserve"/> </p> <div xml:id="echoid-div270" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve">130.</note> </div> <p> <s xml:id="echoid-s1693" xml:space="preserve">Habeatur pondus quodcunque pro unitate; </s> <s xml:id="echoid-s1694" xml:space="preserve">uncia Ex gr.</s> <s xml:id="echoid-s1695" xml:space="preserve">; decima pars un-<lb/>ciæ eodem modo poſſet adhiberi.</s> <s xml:id="echoid-s1696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1697" xml:space="preserve">Sit numerus 364 libræ applicandus; </s> <s xml:id="echoid-s1698" xml:space="preserve">tres uncias centeſimæ applico divi-<lb/> <anchor type="note" xlink:label="note-0073-08a" xlink:href="note-0073-08"/> ſioni, & </s> <s xml:id="echoid-s1699" xml:space="preserve">unciam unam diviſioni 64<emph style="super">tæ</emph>.</s> <s xml:id="echoid-s1700" xml:space="preserve"/> </p> <div xml:id="echoid-div271" type="float" level="2" n="2"> <note position="right" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">166.</note> </div> <p> <s xml:id="echoid-s1701" xml:space="preserve">Gravetur brachium libræ urcunque; </s> <s xml:id="echoid-s1702" xml:space="preserve">quem numerum valeat actio hæc, de-<lb/> <anchor type="note" xlink:label="note-0073-09a" xlink:href="note-0073-09"/> terminamus, ſuſpendendo in centeſimâ diviſione brachii oppoſiti pondus, <lb/>quod augeatur additâ ſucceſſivè unciâ atque unciâ; </s> <s xml:id="echoid-s1703" xml:space="preserve">ponamus novem uncias <lb/>nondum æquilibrium dare, decem autem excedere; </s> <s xml:id="echoid-s1704" xml:space="preserve">relictis novem mo-<lb/>tu unius juxta brachium quæro æquilibrium, detur hoc ubi pondus ad 47 di-<lb/>viſionem pervenit, actio quæſita valebit 947.</s> <s xml:id="echoid-s1705" xml:space="preserve"/> </p> <div xml:id="echoid-div272" type="float" level="2" n="3"> <note position="right" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve">167.</note> </div> <p> <s xml:id="echoid-s1706" xml:space="preserve">ADDITIO. </s> <s xml:id="echoid-s1707" xml:space="preserve">Sint addenda 34, 54, 268, 407, 45. </s> <s xml:id="echoid-s1708" xml:space="preserve">65. </s> <s xml:id="echoid-s1709" xml:space="preserve">Separatim numeros <lb/> <anchor type="note" xlink:label="note-0073-10a" xlink:href="note-0073-10"/> hos applico eidem brachio libræ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1710" xml:space="preserve">quæro hujus actionis valorem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1711" xml:space="preserve">& </s> <s xml:id="echoid-s1712" xml:space="preserve">dete- <anchor type="note" xlink:label="note-0073-11a" xlink:href="note-0073-11"/> go 873, ſummam quæſitam. <lb/></s> <s xml:id="echoid-s1713" xml:space="preserve"> <anchor type="note" xlink:label="note-0073-12a" xlink:href="note-0073-12"/> </s> </p> <div xml:id="echoid-div273" type="float" level="2" n="4"> <note position="right" xlink:label="note-0073-10" xlink:href="note-0073-10a" xml:space="preserve">168.</note> <note symbol="*" position="right" xlink:label="note-0073-11" xlink:href="note-0073-11a" xml:space="preserve">166.</note> <note symbol="*" position="right" xlink:label="note-0073-12" xlink:href="note-0073-12a" xml:space="preserve">167.</note> </div> <p> <s xml:id="echoid-s1714" xml:space="preserve">SUBTRACTIO. </s> <s xml:id="echoid-s1715" xml:space="preserve">Ex ſumma numerorum 567, 258, ſubtrahenda ſunt 489 <lb/> <anchor type="note" xlink:label="note-0073-13a" xlink:href="note-0073-13"/> & </s> <s xml:id="echoid-s1716" xml:space="preserve">56. </s> <s xml:id="echoid-s1717" xml:space="preserve">Numeros primos uni applico brachio <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1718" xml:space="preserve">ſubtrahendos alteri applico <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0073-14a" xlink:href="note-0073-14"/> & </s> <s xml:id="echoid-s1719" xml:space="preserve">quæro quantum valeat actio, qua actio in brachium unum alteram <lb/> <anchor type="note" xlink:label="note-0073-15a" xlink:href="note-0073-15"/> actionem ſuperat <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s1720" xml:space="preserve">detego differentiam quæſitam 280.</s> <s xml:id="echoid-s1721" xml:space="preserve"> <anchor type="note" xlink:label="note-0073-16a" xlink:href="note-0073-16"/> </s> </p> <div xml:id="echoid-div274" type="float" level="2" n="5"> <note position="right" xlink:label="note-0073-13" xlink:href="note-0073-13a" xml:space="preserve">169.</note> <note symbol="*" position="right" xlink:label="note-0073-14" xlink:href="note-0073-14a" xml:space="preserve">166.</note> <note symbol="*" position="right" xlink:label="note-0073-15" xlink:href="note-0073-15a" xml:space="preserve">166.</note> <note symbol="*" position="right" xlink:label="note-0073-16" xlink:href="note-0073-16a" xml:space="preserve">167.</note> </div> <p> <s xml:id="echoid-s1722" xml:space="preserve">MULTIPLICATIO. </s> <s xml:id="echoid-s1723" xml:space="preserve">Detur numerus 67, multiplicandus per 15. </s> <s xml:id="echoid-s1724" xml:space="preserve">Pon-<lb/> <anchor type="note" xlink:label="note-0073-17a" xlink:href="note-0073-17"/> dus 15. </s> <s xml:id="echoid-s1725" xml:space="preserve">ſuſpendo diviſioni 67 & </s> <s xml:id="echoid-s1726" xml:space="preserve">quæro valorem <anchor type="note" xlink:href="" symbol="*"/>, quo productum quæſitum <anchor type="note" xlink:label="note-0073-18a" xlink:href="note-0073-18"/> detego 1005.</s> <s xml:id="echoid-s1727" xml:space="preserve"/> </p> <div xml:id="echoid-div275" type="float" level="2" n="6"> <note position="right" xlink:label="note-0073-17" xlink:href="note-0073-17a" xml:space="preserve">170.</note> <note symbol="*" position="right" xlink:label="note-0073-18" xlink:href="note-0073-18a" xml:space="preserve">167.</note> </div> <p> <s xml:id="echoid-s1728" xml:space="preserve">DIVISIO. </s> <s xml:id="echoid-s1729" xml:space="preserve">Sit 1005. </s> <s xml:id="echoid-s1730" xml:space="preserve">numerus dividendus per 15, Numerum dividendum <lb/> <anchor type="note" xlink:label="note-0073-19a" xlink:href="note-0073-19"/> applico libræ <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s1731" xml:space="preserve">movendo pondus quindecim juxta brachium, quæro æqui- <anchor type="note" xlink:label="note-0073-20a" xlink:href="note-0073-20"/> librium, quod datur ubi pondus ad 67 diviſionem, quotientem deſignantem, <lb/>pervenit.</s> <s xml:id="echoid-s1732" xml:space="preserve"/> </p> <div xml:id="echoid-div276" type="float" level="2" n="7"> <note position="right" xlink:label="note-0073-19" xlink:href="note-0073-19a" xml:space="preserve">171.</note> <note symbol="*" position="right" xlink:label="note-0073-20" xlink:href="note-0073-20a" xml:space="preserve">166.</note> </div> <p> <s xml:id="echoid-s1733" xml:space="preserve">Præſtat in hiſce duabus ultimis operationibus, minori pondere pro unita-<lb/>te uti.</s> <s xml:id="echoid-s1734" xml:space="preserve"/> </p> <pb o="36" file="0074" n="78" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div278" type="section" level="1" n="93"> <head xml:id="echoid-head141" xml:space="preserve">CAPUT X.</head> <head xml:id="echoid-head142" xml:space="preserve">De Vecte, Machinarum ſimplicium prima.</head> <head xml:id="echoid-head143" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s1735" xml:space="preserve">VEctis à Matbematicis vocatur linearecta inflexilis, pon-<lb/> <anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/> deribus ſuſtinendis, aut elevandis, accommodata, pon-<lb/> <anchor type="note" xlink:label="note-0074-02a" xlink:href="note-0074-02"/> deris vel nullius, vel ſaltem æquabilis.</s> <s xml:id="echoid-s1736" xml:space="preserve"/> </p> <div xml:id="echoid-div278" type="float" level="2" n="1"> <note position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">172.</note> <note position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve">TAB. V. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s1737" xml:space="preserve">Inter Machinas, quæ ſimplices vocantur, primum locum <lb/>occupat, eſt omnium ſimpliciſſima; </s> <s xml:id="echoid-s1738" xml:space="preserve">& </s> <s xml:id="echoid-s1739" xml:space="preserve">uſu venit, quando <lb/>pondera ad parvam altitudinem elevanda ſunt.</s> <s xml:id="echoid-s1740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1741" xml:space="preserve">Quatuor aliæ dantur Machinæ ſimplices, de quibus in tri-<lb/>bus capitibus ſequentibus.</s> <s xml:id="echoid-s1742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1743" xml:space="preserve">Circa Vectem tria conſiderari debent. </s> <s xml:id="echoid-s1744" xml:space="preserve">1. </s> <s xml:id="echoid-s1745" xml:space="preserve">Pondus ſuſti-<lb/> <anchor type="note" xlink:label="note-0074-03a" xlink:href="note-0074-03"/> nendum, aut elevandum, P. </s> <s xml:id="echoid-s1746" xml:space="preserve">2, Potentia, qua ſuſtinetur, aut <lb/>elevatur, quæ hîc pondere M deſignatur, & </s> <s xml:id="echoid-s1747" xml:space="preserve">vulgo eſtactio <lb/>hominis. </s> <s xml:id="echoid-s1748" xml:space="preserve">3. </s> <s xml:id="echoid-s1749" xml:space="preserve">Fulcrum, id eſt, illud quo Vectis ſuſtinetur, <lb/>& </s> <s xml:id="echoid-s1750" xml:space="preserve">ſuper quo movetur, aut potius rotatur, dum ipſum im-<lb/>mobile manet, F.</s> <s xml:id="echoid-s1751" xml:space="preserve"/> </p> <div xml:id="echoid-div279" type="float" level="2" n="2"> <note position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve">173.</note> </div> <p> <s xml:id="echoid-s1752" xml:space="preserve">Vectes triplicis ſunt generis.</s> <s xml:id="echoid-s1753" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">174.</note> <p> <s xml:id="echoid-s1754" xml:space="preserve">1. </s> <s xml:id="echoid-s1755" xml:space="preserve">Aliquando fulerum inter pondus & </s> <s xml:id="echoid-s1756" xml:space="preserve">potentiam ponitur. <lb/></s> <s xml:id="echoid-s1757" xml:space="preserve"> <anchor type="note" xlink:label="note-0074-05a" xlink:href="note-0074-05"/> </s> </p> <div xml:id="echoid-div280" type="float" level="2" n="3"> <note position="left" xlink:label="note-0074-05" xlink:href="note-0074-05a" xml:space="preserve">TAB. V. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s1758" xml:space="preserve">2. </s> <s xml:id="echoid-s1759" xml:space="preserve">Aliquando pondus inter fulcrum & </s> <s xml:id="echoid-s1760" xml:space="preserve">potentiam.</s> <s xml:id="echoid-s1761" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">TAB. V. <lb/>fig. 2.</note> <p> <s xml:id="echoid-s1762" xml:space="preserve">3. </s> <s xml:id="echoid-s1763" xml:space="preserve">Sæpe etiam ipſa potentia agit inter pondus & </s> <s xml:id="echoid-s1764" xml:space="preserve">fulcrum. <lb/></s> <s xml:id="echoid-s1765" xml:space="preserve"> <anchor type="note" xlink:label="note-0074-07a" xlink:href="note-0074-07"/> </s> </p> <div xml:id="echoid-div281" type="float" level="2" n="4"> <note position="left" xlink:label="note-0074-07" xlink:href="note-0074-07a" xml:space="preserve">TAB. V. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s1766" xml:space="preserve">In omnibus caſibus regulæ eædem locum habent, quæ ex <lb/>iis, quæ de libra dicta ſunt <anchor type="note" xlink:href="" symbol="*"/>, ſequuntur, & </s> <s xml:id="echoid-s1767" xml:space="preserve">quæ analogiam in- <anchor type="note" xlink:label="note-0074-08a" xlink:href="note-0074-08"/> ter libram & </s> <s xml:id="echoid-s1768" xml:space="preserve">vectem oſtendunt. </s> <s xml:id="echoid-s1769" xml:space="preserve">Vectis primi generis eſt qua-<lb/>ſi ſtatera Romana ad elevanda pondera accommodata.</s> <s xml:id="echoid-s1770" xml:space="preserve"/> </p> <div xml:id="echoid-div282" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0074-08" xlink:href="note-0074-08a" xml:space="preserve">129.</note> </div> <p style="it"> <s xml:id="echoid-s1771" xml:space="preserve">Actio potentiæ, & </s> <s xml:id="echoid-s1772" xml:space="preserve">ponderis reſiſtentia, creſcunt in ratio-<lb/> <anchor type="note" xlink:label="note-0074-09a" xlink:href="note-0074-09"/> ne diſtantiæ à fulcro <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1773" xml:space="preserve">ideòque, ut potentia valeat ad ſuſti- <anchor type="note" xlink:label="note-0074-10a" xlink:href="note-0074-10"/> nendum pondus, requiritur, ut diſtantia puncti in vecte, <lb/>cui applicatur, ſit ad ponderis diſtantiam, ut pondas ad po-<lb/>tentiæ intenſitatem <anchor type="note" xlink:href="" symbol="*"/>, quæ ſi paululum adaugeatur, pondus <anchor type="note" xlink:label="note-0074-11a" xlink:href="note-0074-11"/> elevabitur.</s> <s xml:id="echoid-s1774" xml:space="preserve"/> </p> <div xml:id="echoid-div283" type="float" level="2" n="6"> <note position="left" xlink:label="note-0074-09" xlink:href="note-0074-09a" xml:space="preserve">175.</note> <note symbol="*" position="left" xlink:label="note-0074-10" xlink:href="note-0074-10a" xml:space="preserve">119.</note> <note symbol="*" position="left" xlink:label="note-0074-11" xlink:href="note-0074-11a" xml:space="preserve">134.</note> </div> </div> <div xml:id="echoid-div285" type="section" level="1" n="94"> <head xml:id="echoid-head144" xml:space="preserve"><emph style="sc">Experimentum</emph> 1. 2. & 3.</head> <p> <s xml:id="echoid-s1775" xml:space="preserve">Hæc regula experimentis confirmatur erga memoratos <lb/> <anchor type="note" xlink:label="note-0074-12a" xlink:href="note-0074-12"/> tres vectes, ut patet ex fig. </s> <s xml:id="echoid-s1776" xml:space="preserve">1. </s> <s xml:id="echoid-s1777" xml:space="preserve">2. </s> <s xml:id="echoid-s1778" xml:space="preserve">& </s> <s xml:id="echoid-s1779" xml:space="preserve">3, Tab. </s> <s xml:id="echoid-s1780" xml:space="preserve">v.</s> <s xml:id="echoid-s1781" xml:space="preserve">; æquilibrium <lb/> <anchor type="note" xlink:label="note-0074-13a" xlink:href="note-0074-13"/> enim datur, quando pondera P, & </s> <s xml:id="echoid-s1782" xml:space="preserve">pondera M quæpoten-<lb/>tias repræſentant, ut & </s> <s xml:id="echoid-s1783" xml:space="preserve">diſtantiæ à fulcro F, proportionem <pb o="37" file="0075" n="79" rhead="MATHEMATICA. LIB. I. CAP. X."/> habent, quæ datur inter numeros in figuris. </s> <s xml:id="echoid-s1784" xml:space="preserve">Conſtructio ma-<lb/>chinarum, quibus hæc experimenta inſtituuntur, ex ſola <lb/>inſpectione Tabulæ ſatis patet, & </s> <s xml:id="echoid-s1785" xml:space="preserve">nulla ulteriori explicatio-<lb/>ne indiget.</s> <s xml:id="echoid-s1786" xml:space="preserve"/> </p> <div xml:id="echoid-div285" type="float" level="2" n="1"> <note position="left" xlink:label="note-0074-12" xlink:href="note-0074-12a" xml:space="preserve">176.</note> <note position="left" xlink:label="note-0074-13" xlink:href="note-0074-13a" xml:space="preserve">TAB. V. <lb/>fig. 1. 2. & 3.</note> </div> <p style="it"> <s xml:id="echoid-s1787" xml:space="preserve">Vectis formatur compoſitus ex variis vectibus junctis. </s> <s xml:id="echoid-s1788" xml:space="preserve">In <lb/> <anchor type="note" xlink:label="note-0075-01a" xlink:href="note-0075-01"/> hoc caſu adhibito ſecundo vecte movetur primus; </s> <s xml:id="echoid-s1789" xml:space="preserve">ſecundus <lb/>tertio poteſt agitari; </s> <s xml:id="echoid-s1790" xml:space="preserve">& </s> <s xml:id="echoid-s1791" xml:space="preserve">ſic ulterius ſi libuerit, ultimo tandem <lb/>applicatur potentia, cujus ratso ad pondus, quando cum pondere <lb/>æquè pollet, componitur ex rationibus potentiarum ad ponde-<lb/>ra in ſingulis vectibus, quando ſeparatim adbibentur.</s> <s xml:id="echoid-s1792" xml:space="preserve"/> </p> <div xml:id="echoid-div286" type="float" level="2" n="2"> <note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">177.</note> </div> </div> <div xml:id="echoid-div288" type="section" level="1" n="95"> <head xml:id="echoid-head145" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s1793" xml:space="preserve">Tres vectes A, B, D, ita diſponuntur, ut potentiâ Mpon-<lb/> <anchor type="note" xlink:label="note-0075-02a" xlink:href="note-0075-02"/> dus P ſuſtineatur. </s> <s xml:id="echoid-s1794" xml:space="preserve">In vecte A, ſi ſolus adhiberetur, po-<lb/> <anchor type="note" xlink:label="note-0075-03a" xlink:href="note-0075-03"/> tentia eſſet ad pondus, ut 1. </s> <s xml:id="echoid-s1795" xml:space="preserve">ad 5.</s> <s xml:id="echoid-s1796" xml:space="preserve">; in vecte B, ut 1. </s> <s xml:id="echoid-s1797" xml:space="preserve">ad 4.</s> <s xml:id="echoid-s1798" xml:space="preserve">; <lb/>& </s> <s xml:id="echoid-s1799" xml:space="preserve">in vecte D, ut 1. </s> <s xml:id="echoid-s1800" xml:space="preserve">ad 6. </s> <s xml:id="echoid-s1801" xml:space="preserve">Ratio, ex his tribus compoſita, <lb/>eſt 1. </s> <s xml:id="echoid-s1802" xml:space="preserve">ad 120; </s> <s xml:id="echoid-s1803" xml:space="preserve">unica etiam uncia M ſuſtinet pondus P cen-<lb/>tum & </s> <s xml:id="echoid-s1804" xml:space="preserve">viginti unciarum. </s> <s xml:id="echoid-s1805" xml:space="preserve">Notandum, in motu hujus machi-<lb/>næ ſpatia à potentia & </s> <s xml:id="echoid-s1806" xml:space="preserve">pondere eodem tempore percurſa eſ-<lb/>ſe ut 120. </s> <s xml:id="echoid-s1807" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s1808" xml:space="preserve">, id eſt, in ratione prædictainverſa, quod <lb/>requiritur ut detur æquilibrium <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1809" xml:space="preserve"> <anchor type="note" xlink:label="note-0075-04a" xlink:href="note-0075-04"/> </s> </p> <div xml:id="echoid-div288" type="float" level="2" n="1"> <note position="right" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">178.</note> <note position="right" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve">TAB. V. <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve">212.</note> </div> <p> <s xml:id="echoid-s1810" xml:space="preserve">Vecte etiam ſæpe utuntur artifices ad pondera vehenda; <lb/></s> <s xml:id="echoid-s1811" xml:space="preserve">& </s> <s xml:id="echoid-s1812" xml:space="preserve">hujus uſus vectis varii dantur caſus, digni quinotentur, & </s> <s xml:id="echoid-s1813" xml:space="preserve"><lb/>quorum demonſtratio ex dictis facile deducitur.</s> <s xml:id="echoid-s1814" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1815" xml:space="preserve">Circa omnes caſus generaliter obſervandum, intenſitatem <lb/> <anchor type="note" xlink:label="note-0075-05a" xlink:href="note-0075-05"/> potentiæ, aut intenſitates potentiarum junctas, quando plu-<lb/>rimæ dantur, æquè pollere debere cumgravitate ponderum ve-<lb/>dorum, aut ſuſtinendorum: </s> <s xml:id="echoid-s1816" xml:space="preserve">in omnibus enim caſibus potentiæ <lb/>& </s> <s xml:id="echoid-s1817" xml:space="preserve">obſtacula æquales vias percurrunt.</s> <s xml:id="echoid-s1818" xml:space="preserve"/> </p> <div xml:id="echoid-div289" type="float" level="2" n="2"> <note position="right" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve">179.</note> </div> <p style="it"> <s xml:id="echoid-s1819" xml:space="preserve">Si duabus potentiis ſuſtineri aut vehi debeat pondus, in-<lb/> <anchor type="note" xlink:label="note-0075-06a" xlink:href="note-0075-06"/> ter potentias collocandum erit, & </s> <s xml:id="echoid-s1820" xml:space="preserve">diſtantiæ potentiarum ab <lb/>utraque parte à pondere debent eſſe in ratione inverſa po-<lb/>téntiarum intenſitatum.</s> <s xml:id="echoid-s1821" xml:space="preserve"/> </p> <div xml:id="echoid-div290" type="float" level="2" n="3"> <note position="right" xlink:label="note-0075-06" xlink:href="note-0075-06a" xml:space="preserve">180.</note> </div> <p> <s xml:id="echoid-s1822" xml:space="preserve">Potentiarum enim actiones ſeſe mutuo turbabunt, niſi in-<lb/>ter has æquilibrium detur circa punctum ſuſpenſionis pon-<lb/>deris; </s> <s xml:id="echoid-s1823" xml:space="preserve">quo æquilibrio poſito, in puncto hoc potentiarum <lb/>actiones ſunt coactæ, & </s> <s xml:id="echoid-s1824" xml:space="preserve">cum pondere contrarie agunt; </s> <s xml:id="echoid-s1825" xml:space="preserve">id- <pb o="38" file="0076" n="80" rhead="PHYSICES ELEMENTA"/> eòque hoc ſuſtinent, propter æqualitatem inter potentias <lb/>& </s> <s xml:id="echoid-s1826" xml:space="preserve">pondus.</s> <s xml:id="echoid-s1827" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div292" type="section" level="1" n="96"> <head xml:id="echoid-head146" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s1828" xml:space="preserve">Confirmatur propſitio hæc Experimento in Fig. </s> <s xml:id="echoid-s1829" xml:space="preserve">4. </s> <s xml:id="echoid-s1830" xml:space="preserve">de-<lb/> <anchor type="note" xlink:label="note-0076-01a" xlink:href="note-0076-01"/> lineato, quod ulteriori explicatione non indiget.</s> <s xml:id="echoid-s1831" xml:space="preserve"/> </p> <div xml:id="echoid-div292" type="float" level="2" n="1"> <note position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">181.</note> </div> <note position="left" xml:space="preserve">TAB V. <lb/>fig. 4.</note> </div> <div xml:id="echoid-div294" type="section" level="1" n="97"> <head xml:id="echoid-head147" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p style="it"> <s xml:id="echoid-s1832" xml:space="preserve">Quando unâ potentiâ duo pondera ſuſtinenda ſunt, potentiam <lb/> <anchor type="note" xlink:label="note-0076-03a" xlink:href="note-0076-03"/> inter pondera poni neceſſe eſt, & </s> <s xml:id="echoid-s1833" xml:space="preserve">tunc quæ ſtatim de duabus <lb/> <anchor type="note" xlink:label="note-0076-04a" xlink:href="note-0076-04"/> potentiis dicta ſunt, ad pondera applicari debent. </s> <s xml:id="echoid-s1834" xml:space="preserve">Ponde-<lb/>ra enim ſuſtineri non poſſunt, niſi horum commune cen-<lb/>trum gravitatis ſuſtineatur<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1835" xml:space="preserve"/> </p> <div xml:id="echoid-div294" type="float" level="2" n="1"> <note position="left" xlink:label="note-0076-03" xlink:href="note-0076-03a" xml:space="preserve">182.</note> <note position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">TAB. VI. <lb/>fig. 1.</note> </div> <note symbol="*" position="left" xml:space="preserve">147.</note> <p> <s xml:id="echoid-s1836" xml:space="preserve">Plurima pondera ſæpe unâ, aut plurimis potentiis, ſuſti-<lb/>nentur aut vehuntur. </s> <s xml:id="echoid-s1837" xml:space="preserve">Circa quod notandum, omnia pon-<lb/> <anchor type="note" xlink:label="note-0076-06a" xlink:href="note-0076-06"/> dera, babere commune centrum gravitatis; </s> <s xml:id="echoid-s1838" xml:space="preserve">quod centrum <lb/>tale eſt, ut ſi ab utraque parte unumquodque pondus mul-<lb/>tiplicetur per ſuam diſtantiam ab iſto puncto, ſumma produ-<lb/>ctorum ab utraque parte ſit eadem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1839" xml:space="preserve"> <anchor type="note" xlink:label="note-0076-07a" xlink:href="note-0076-07"/> </s> </p> <div xml:id="echoid-div295" type="float" level="2" n="2"> <note position="left" xlink:label="note-0076-06" xlink:href="note-0076-06a" xml:space="preserve">183.</note> <note symbol="*" position="left" xlink:label="note-0076-07" xlink:href="note-0076-07a" xml:space="preserve">143. 141.</note> </div> <p> <s xml:id="echoid-s1840" xml:space="preserve">Potentiæ etiam utcunque diſpoſitæ commune babent gravi-<lb/>tatis centrum; </s> <s xml:id="echoid-s1841" xml:space="preserve">poſſunt enim per pondera repræſentari <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0076-08a" xlink:href="note-0076-08"/> & </s> <s xml:id="echoid-s1842" xml:space="preserve">hìc intenſitas uniuſcujuſque potentiæ perſuam diſtantiam à <lb/>centro multiplicari debet, & </s> <s xml:id="echoid-s1843" xml:space="preserve">ſummæ productorum tunc <lb/>erunt ab utraque parte æquales.</s> <s xml:id="echoid-s1844" xml:space="preserve"/> </p> <div xml:id="echoid-div296" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0076-08" xlink:href="note-0076-08a" xml:space="preserve">117.</note> </div> <p> <s xml:id="echoid-s1845" xml:space="preserve">Vt potentiæ ad pondera ſuſtinenda valeant, requiritur po-<lb/>tentiarum & </s> <s xml:id="echoid-s1846" xml:space="preserve">ponderum idem eſſe gravitatis centrum. </s> <s xml:id="echoid-s1847" xml:space="preserve">Tunc <lb/>omnium ponderum, omniumque potentiarum, vires in u-<lb/>num & </s> <s xml:id="echoid-s1848" xml:space="preserve">idem punctum reducuntur, quod viribus æqualibus <lb/>ſurſum & </s> <s xml:id="echoid-s1849" xml:space="preserve">deorſum trahitur, ideoque ſuſtinetur.</s> <s xml:id="echoid-s1850" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div298" type="section" level="1" n="98"> <head xml:id="echoid-head148" xml:space="preserve"><emph style="sc">Experimentum</emph> 7. & 8.</head> <p> <s xml:id="echoid-s1851" xml:space="preserve">Ex dictis explicatio figurarum ſatis patet, in quibus C de-<lb/> <anchor type="note" xlink:label="note-0076-09a" xlink:href="note-0076-09"/> notat centrum gravitatis & </s> <s xml:id="echoid-s1852" xml:space="preserve">ponderum & </s> <s xml:id="echoid-s1853" xml:space="preserve">potentiarum.</s> <s xml:id="echoid-s1854" xml:space="preserve"/> </p> <div xml:id="echoid-div298" type="float" level="2" n="1"> <note position="left" xlink:label="note-0076-09" xlink:href="note-0076-09a" xml:space="preserve">184.</note> </div> <note position="left" xml:space="preserve">TAB. VI. <lb/>fig. 2. & 3.</note> </div> <div xml:id="echoid-div300" type="section" level="1" n="99"> <head xml:id="echoid-head149" xml:space="preserve"><emph style="sc">Experimentum</emph> 9</head> <p> <s xml:id="echoid-s1855" xml:space="preserve">Prædicta etiam locum habent, ſi vectis ab utraque parte <lb/> <anchor type="note" xlink:label="note-0076-11a" xlink:href="note-0076-11"/> à potentiis trahatur; </s> <s xml:id="echoid-s1856" xml:space="preserve">quod videmus in vecte, qui ab utra-<lb/> <anchor type="note" xlink:label="note-0076-12a" xlink:href="note-0076-12"/> que parte horizontaliter trahitur, in quo æquilibrium non <lb/>datur niſi in caſu memoratarum regularum.</s> <s xml:id="echoid-s1857" xml:space="preserve"/> </p> <div xml:id="echoid-div300" type="float" level="2" n="1"> <note position="left" xlink:label="note-0076-11" xlink:href="note-0076-11a" xml:space="preserve">185.</note> <note position="left" xlink:label="note-0076-12" xlink:href="note-0076-12a" xml:space="preserve">TAB. VI. <lb/>fig 4.</note> </div> <p> <s xml:id="echoid-s1858" xml:space="preserve">Circa octo prima hujus cap. </s> <s xml:id="echoid-s1859" xml:space="preserve">Exp. </s> <s xml:id="echoid-s1860" xml:space="preserve">notandum, vectes ipſos <lb/>ſuſtineri debere.</s> <s xml:id="echoid-s1861" xml:space="preserve"/> </p> <pb file="0077" n="81"/> <figure> <image file="0077-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0077-01"/> </figure> <pb file="0077a" n="82"/> <figure> <image file="0077a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0077a-01"/> </figure> <pb file="0078" n="83"/> <pb o="39" file="0079" n="84" rhead="MATHEMATICA. LIB. I. CAP. XI."/> </div> <div xml:id="echoid-div302" type="section" level="1" n="100"> <head xml:id="echoid-head150" xml:space="preserve">CAPUT XI.</head> <p> <s xml:id="echoid-s1862" xml:space="preserve">De Axe in Peritrochio, ſecundâ Machinarum ſimplicium, <lb/>& </s> <s xml:id="echoid-s1863" xml:space="preserve">Rotis dentatis.</s> <s xml:id="echoid-s1864" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1865" xml:space="preserve">VEctis, ut in principio capitis præcedentis dictum, in-<lb/>ſervit ad elevanda pondera ad parvam altitudinem; <lb/></s> <s xml:id="echoid-s1866" xml:space="preserve">quando altitudo major eſt, Axis in Peritrochio uſu venit.</s> <s xml:id="echoid-s1867" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div303" type="section" level="1" n="101"> <head xml:id="echoid-head151" xml:space="preserve"><emph style="sc">Definitio</emph></head> <p> <s xml:id="echoid-s1868" xml:space="preserve">Axis in Peritrochio vocatur rota cum axe volubilis.</s> <s xml:id="echoid-s1869" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">186.</note> <p> <s xml:id="echoid-s1870" xml:space="preserve">Potentia in hac machinâ applicatur peripheriæ rotæ, cu-<lb/> <anchor type="note" xlink:label="note-0079-02a" xlink:href="note-0079-02"/> jus motu funis, cui affixum eſt pondus, axi circumvolvitur, <lb/>quo pondus elevatur.</s> <s xml:id="echoid-s1871" xml:space="preserve"/> </p> <div xml:id="echoid-div303" type="float" level="2" n="1"> <note position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">TAB. VI. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s1872" xml:space="preserve">Sit a b rota; </s> <s xml:id="echoid-s1873" xml:space="preserve">d e axis; </s> <s xml:id="echoid-s1874" xml:space="preserve">p pondus elevandum; </s> <s xml:id="echoid-s1875" xml:space="preserve">m potentia; <lb/></s> <s xml:id="echoid-s1876" xml:space="preserve"> <anchor type="note" xlink:label="note-0079-03a" xlink:href="note-0079-03"/> hujus actione moveatur rota, puncta b & </s> <s xml:id="echoid-s1877" xml:space="preserve">d arcus ſimiles eo <lb/> <anchor type="note" xlink:label="note-0079-04a" xlink:href="note-0079-04"/> motu deſcribunt; </s> <s xml:id="echoid-s1878" xml:space="preserve">arcus illi ſunt viæ percurſæ à potentiâ & </s> <s xml:id="echoid-s1879" xml:space="preserve"><lb/>pondere, & </s> <s xml:id="echoid-s1880" xml:space="preserve">ſunt inter ſe, ut c b ad c d, id eſt ut rotæ dia-<lb/>meter ad axis diametrum, ex quo ſequensregula deducitur.</s> <s xml:id="echoid-s1881" xml:space="preserve"/> </p> <div xml:id="echoid-div304" type="float" level="2" n="2"> <note position="right" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">187.</note> <note position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve">TAB. VI. <lb/>fig. 6.</note> </div> <p style="it"> <s xml:id="echoid-s1882" xml:space="preserve">Potentia eo plus valet, quo major eſt rota, & </s> <s xml:id="echoid-s1883" xml:space="preserve">illius actio <lb/> <anchor type="note" xlink:label="note-0079-05a" xlink:href="note-0079-05"/> creſcit in eâdem ratione cum rotæ diametro. </s> <s xml:id="echoid-s1884" xml:space="preserve">Pondus eo mi-<lb/>nus reſiſtit, quo axis diameter minor eſt, & </s> <s xml:id="echoid-s1885" xml:space="preserve">illius reſiſten-<lb/>tia in eadem ratione cum axis diametro minuitur. </s> <s xml:id="echoid-s1886" xml:space="preserve">Et ut de-<lb/>tur æquilibrium inter potentiam & </s> <s xml:id="echoid-s1887" xml:space="preserve">pondus, requiritur, ut <lb/>rotædiameter ſit ad axis diametrum, in ratione inverſa <lb/>potentiæ ad pondus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1888" xml:space="preserve"> <anchor type="note" xlink:label="note-0079-06a" xlink:href="note-0079-06"/> </s> </p> <div xml:id="echoid-div305" type="float" level="2" n="3"> <note position="right" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve">188.</note> <note symbol="*" position="right" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve">112.</note> </div> <p> <s xml:id="echoid-s1889" xml:space="preserve">Notandum, axis diametro funis diametrum eſſe addendum.</s> <s xml:id="echoid-s1890" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div307" type="section" level="1" n="102"> <head xml:id="echoid-head152" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s1891" xml:space="preserve">Hæc regula diverſimodæ confirmatur ope Machinæ hìc <lb/> <anchor type="note" xlink:label="note-0079-07a" xlink:href="note-0079-07"/> delineatæ, in qua dantur rotæ & </s> <s xml:id="echoid-s1892" xml:space="preserve">axes variæ magnitudinis. <lb/></s> <s xml:id="echoid-s1893" xml:space="preserve"> <anchor type="note" xlink:label="note-0079-08a" xlink:href="note-0079-08"/> Quando axis diameter eſt pars duodecima rotæ diametri, <lb/>ſemilibra ſex libras ſuſtinet, & </s> <s xml:id="echoid-s1894" xml:space="preserve">ſic de cæteris.</s> <s xml:id="echoid-s1895" xml:space="preserve"/> </p> <div xml:id="echoid-div307" type="float" level="2" n="1"> <note position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">189.</note> <note position="right" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve">TAB. VI <lb/>fig. 1</note> </div> <p> <s xml:id="echoid-s1896" xml:space="preserve">Potentia poteſt etiam ſcytalæ applicari, ut in D, & </s> <s xml:id="echoid-s1897" xml:space="preserve">tunc <lb/>diſtantia puncti, cui applicatur, à centro, pro rotæ ſemi-<lb/>diametro habenda eſt.</s> <s xml:id="echoid-s1898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1899" xml:space="preserve">Eodem omnino cum hac Machina nituntur fundamento <lb/>rotæ dentatæ reſpectu axis in peritrochio ſunt, quod <lb/>vectis compoſitus reſpectu vectis ſimplicis.</s> <s xml:id="echoid-s1900" xml:space="preserve"/> </p> <pb o="40" file="0080" n="85" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s1901" xml:space="preserve">Si axis rotæ ſit dentatus, valet ad movendam rotam, cu-<lb/> <anchor type="note" xlink:label="note-0080-01a" xlink:href="note-0080-01"/> jus peripheria dentes habet, & </s> <s xml:id="echoid-s1902" xml:space="preserve">cujus axis tertiæ rotæ motum <lb/>communicare poteſt, & </s> <s xml:id="echoid-s1903" xml:space="preserve">ſic ulterius. </s> <s xml:id="echoid-s1904" xml:space="preserve">In eo caſu</s> </p> <div xml:id="echoid-div308" type="float" level="2" n="2"> <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">TAB. VI. <lb/>fig. 7.</note> </div> <p style="it"> <s xml:id="echoid-s1905" xml:space="preserve">Ratio potentiæ ad pondus ut æquè polleant, eſt ratio compo-<lb/> <anchor type="note" xlink:label="note-0080-02a" xlink:href="note-0080-02"/> ſita ex ratione diametri axis ultimæ rotæ, ad diametrum pri-<lb/>mæ & </s> <s xml:id="echoid-s1906" xml:space="preserve">ratione circumvolutionum ultimæ rotæ, ad circum-<lb/>volutiones primæ, eodem tempore.</s> <s xml:id="echoid-s1907" xml:space="preserve"/> </p> <div xml:id="echoid-div309" type="float" level="2" n="3"> <note position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">190.</note> </div> <p> <s xml:id="echoid-s1908" xml:space="preserve">Cujus regulæ demonſtratio etiam ex comparatione viarum <lb/>percurſarum à pondere & </s> <s xml:id="echoid-s1909" xml:space="preserve">potentia deducitur.</s> <s xml:id="echoid-s1910" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div311" type="section" level="1" n="103"> <head xml:id="echoid-head153" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s1911" xml:space="preserve">Rotæ AB potentia, quæ per pondus M repræſentatur, <lb/> <anchor type="note" xlink:label="note-0080-03a" xlink:href="note-0080-03"/> applicatur, pondus P axi rotæ FG; </s> <s xml:id="echoid-s1912" xml:space="preserve">axis illius diameter eſt <lb/> <anchor type="note" xlink:label="note-0080-04a" xlink:href="note-0080-04"/> octava pars diametri rotæ AB, & </s> <s xml:id="echoid-s1913" xml:space="preserve">hæc rota quinquies cir-<lb/>cumvolvitur, dum rota FG ſemel: </s> <s xml:id="echoid-s1914" xml:space="preserve">ratio ergo potentiæ ad <lb/>pondus componitur ex rationibus 1. </s> <s xml:id="echoid-s1915" xml:space="preserve">ad 8.</s> <s xml:id="echoid-s1916" xml:space="preserve">; & </s> <s xml:id="echoid-s1917" xml:space="preserve">1. </s> <s xml:id="echoid-s1918" xml:space="preserve">ad 5.</s> <s xml:id="echoid-s1919" xml:space="preserve">; eſt <lb/>ergo ratio 1. </s> <s xml:id="echoid-s1920" xml:space="preserve">ad 40.</s> <s xml:id="echoid-s1921" xml:space="preserve">; ſemilibra ſuſtinet in eo caſu viginti li-<lb/>bras.</s> <s xml:id="echoid-s1922" xml:space="preserve"/> </p> <div xml:id="echoid-div311" type="float" level="2" n="1"> <note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">191.</note> <note position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">TAB. VI. <lb/>fig. 7.</note> </div> </div> <div xml:id="echoid-div313" type="section" level="1" n="104"> <head xml:id="echoid-head154" xml:space="preserve">CAPUT XII. <lb/>De Trochlea, Machinarum ſimplicium tertia.</head> <p> <s xml:id="echoid-s1923" xml:space="preserve">MUltis in occaſionibus axis in peritrochio ad elevanda <lb/>pondera inſervire nequit; </s> <s xml:id="echoid-s1924" xml:space="preserve">trochleis in iis caſibus u-<lb/>tendum, & </s> <s xml:id="echoid-s1925" xml:space="preserve">Machina, quæ ex iſtis formatur, eſt admodum <lb/>compendioſa, & </s> <s xml:id="echoid-s1926" xml:space="preserve">facillime de loco in locum transfertur.</s> <s xml:id="echoid-s1927" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1928" xml:space="preserve">Quid ſit Trochlea, jam ante dictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s1929" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">123.</note> <p> <s xml:id="echoid-s1930" xml:space="preserve">Si pondus trochleæ conjunctum ſit ita, ut cum ea traha-<lb/>tur, utraque extremitas funis ductarii ſuſtinet partem dimi-<lb/>diam ponderis. </s> <s xml:id="echoid-s1931" xml:space="preserve">Quando ergo extremitas una, unco alliga-<lb/> <anchor type="note" xlink:label="note-0080-06a" xlink:href="note-0080-06"/> ta, aut aliter fixa eſt, vis movens alteri extremitati appli-<lb/>cata, quæ dimidium ponderis valet, pondus ſuſtinet.</s> <s xml:id="echoid-s1932" xml:space="preserve"/> </p> <div xml:id="echoid-div313" type="float" level="2" n="1"> <note position="left" xlink:label="note-0080-06" xlink:href="note-0080-06a" xml:space="preserve">192.</note> </div> </div> <div xml:id="echoid-div315" type="section" level="1" n="105"> <head xml:id="echoid-head155" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s1933" xml:space="preserve">Pondus P, duarum librarum trochleæ conjungitur, ita ta-<lb/> <anchor type="note" xlink:label="note-0080-07a" xlink:href="note-0080-07"/> men, ut rotatio orbiculi eo non impediatur; </s> <s xml:id="echoid-s1934" xml:space="preserve">unco funis e f <lb/> <anchor type="note" xlink:label="note-0080-08a" xlink:href="note-0080-08"/> alligatur, & </s> <s xml:id="echoid-s1935" xml:space="preserve">altera funis extremitas cd circumit trochleam <lb/>fixam ad directionem mutandam <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s1936" xml:space="preserve">tunc pondus M, unius <anchor type="note" xlink:label="note-0080-09a" xlink:href="note-0080-09"/> <pb file="0081" n="86"/> <anchor type="figure" xlink:label="fig-0081-01a" xlink:href="fig-0081-01"/> <pb file="0081a" n="87"/> <anchor type="figure" xlink:label="fig-0081a-01a" xlink:href="fig-0081a-01"/> <pb file="0082" n="88"/> <pb o="41" file="0083" n="89" rhead="MATHEMATICA. LIB. I. CAP XII."/> libræ, huic extremitati applicatum ſuſtinet pondus P.</s> <s xml:id="echoid-s1937" xml:space="preserve"/> </p> <div xml:id="echoid-div315" type="float" level="2" n="1"> <note position="left" xlink:label="note-0080-07" xlink:href="note-0080-07a" xml:space="preserve">193.</note> <note position="left" xlink:label="note-0080-08" xlink:href="note-0080-08a" xml:space="preserve">TAB. VII. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0080-09" xlink:href="note-0080-09a" xml:space="preserve">124.</note> <figure xlink:label="fig-0081-01" xlink:href="fig-0081-01a"> <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01"/> </figure> <figure xlink:label="fig-0081a-01" xlink:href="fig-0081a-01a"> <image file="0081a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081a-01"/> </figure> </div> <p> <s xml:id="echoid-s1938" xml:space="preserve">Plurimi orbiculi utcunque conjungi poſſunt, & </s> <s xml:id="echoid-s1939" xml:space="preserve">pondus iis <lb/> <anchor type="note" xlink:label="note-0083-01a" xlink:href="note-0083-01"/> annecti; </s> <s xml:id="echoid-s1940" xml:space="preserve">ſi tunc unum extremum funis fixum ſit, & </s> <s xml:id="echoid-s1941" xml:space="preserve">funis <lb/>circumeat omnes orbiculosillos, & </s> <s xml:id="echoid-s1942" xml:space="preserve">fixos æquali numero, par-<lb/>vâ potentiâ magnum pondus elevari poteſt; </s> <s xml:id="echoid-s1943" xml:space="preserve">in hoc caſu quo <lb/>numerus orbiculorum ponderi conjunctorum major eſt, (fi-<lb/>xis enim actio potentiæ non mutatur <anchor type="note" xlink:href="" symbol="*"/>) eo minor potentia <anchor type="note" xlink:label="note-0083-02a" xlink:href="note-0083-02"/> valet ad ſuſtinendum pondus; </s> <s xml:id="echoid-s1944" xml:space="preserve">& </s> <s xml:id="echoid-s1945" xml:space="preserve">potentia, quæ eſt ad pon-<lb/> <anchor type="note" xlink:label="note-0083-03a" xlink:href="note-0083-03"/> dus, ut unitas ad duplum numeri or biculorum, cum pondere æ-<lb/>que pollet.</s> <s xml:id="echoid-s1946" xml:space="preserve"/> </p> <div xml:id="echoid-div316" type="float" level="2" n="2"> <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">194.</note> <note symbol="*" position="right" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">124.</note> <note position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve">195.</note> </div> <p> <s xml:id="echoid-s1947" xml:space="preserve">Hic enim eſt numerus funium, quibus pondus ſuſti-<lb/>netur, & </s> <s xml:id="echoid-s1948" xml:space="preserve">unico funi potentia applicatur.</s> <s xml:id="echoid-s1949" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div318" type="section" level="1" n="106"> <head xml:id="echoid-head156" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s1950" xml:space="preserve">Pondus P ſex librarum regulæ AB annectitur, in quatres <lb/> <anchor type="note" xlink:label="note-0083-04a" xlink:href="note-0083-04"/> orbiculi libere rotantur. </s> <s xml:id="echoid-s1951" xml:space="preserve">Unco extremitas funis alligatur, <lb/> <anchor type="note" xlink:label="note-0083-05a" xlink:href="note-0083-05"/> & </s> <s xml:id="echoid-s1952" xml:space="preserve">funis circumit tres illos orbiculos, & </s> <s xml:id="echoid-s1953" xml:space="preserve">totidem alios fixos; <lb/></s> <s xml:id="echoid-s1954" xml:space="preserve">alteri extremo pondus unius libræ alligatur, & </s> <s xml:id="echoid-s1955" xml:space="preserve">datur æqui-<lb/>librium,</s> </p> <div xml:id="echoid-div318" type="float" level="2" n="1"> <note position="right" xlink:label="note-0083-04" xlink:href="note-0083-04a" xml:space="preserve">196.</note> <note position="right" xlink:label="note-0083-05" xlink:href="note-0083-05a" xml:space="preserve">TAB. VII. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div320" type="section" level="1" n="107"> <head xml:id="echoid-head157" xml:space="preserve"><emph style="sc">Experimentum</emph> 3. & 4</head> <p> <s xml:id="echoid-s1956" xml:space="preserve">Non intereſt quomodocunque orbiculi conjungantur; </s> <s xml:id="echoid-s1957" xml:space="preserve">ad <lb/> <anchor type="note" xlink:label="note-0083-06a" xlink:href="note-0083-06"/> elevanda pondera haud facile præcedens diſpoſitio adhibetur; <lb/></s> <s xml:id="echoid-s1958" xml:space="preserve">artifices ideò inæqualibus orbiculis utuntur diſpoſitis ut in <lb/>fig. </s> <s xml:id="echoid-s1959" xml:space="preserve">3.</s> <s xml:id="echoid-s1960" xml:space="preserve">; magnitudo enim orbiculorum nihil immutat. </s> <s xml:id="echoid-s1961" xml:space="preserve">Sæpe <lb/> <anchor type="note" xlink:label="note-0083-07a" xlink:href="note-0083-07"/> etiam, quæ diſpoſitio eſt omnium maxime compendioſa, <lb/>orbiculi circa eundem axem volubiles ſunt, ut in fig. </s> <s xml:id="echoid-s1962" xml:space="preserve">4.</s> <s xml:id="echoid-s1963" xml:space="preserve">, & </s> <s xml:id="echoid-s1964" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0083-08a" xlink:href="note-0083-08"/> in hiſce duobus caſibus experimentum eodem modo proce-<lb/>dit, ac in 2<emph style="super">do</emph> experimento.</s> <s xml:id="echoid-s1965" xml:space="preserve"/> </p> <div xml:id="echoid-div320" type="float" level="2" n="1"> <note position="right" xlink:label="note-0083-06" xlink:href="note-0083-06a" xml:space="preserve">197.</note> <note position="right" xlink:label="note-0083-07" xlink:href="note-0083-07a" xml:space="preserve">TAB. VII. <lb/>fig. 3.</note> <note position="right" xlink:label="note-0083-08" xlink:href="note-0083-08a" xml:space="preserve">TAB. VII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s1966" xml:space="preserve">Quando extremitas funis ductarii, quæ in experimentis <lb/> <anchor type="note" xlink:label="note-0083-09a" xlink:href="note-0083-09"/> præcedentibus fixa eſt, annectitur ponderi aut orbiculis <lb/> <anchor type="note" xlink:label="note-0083-10a" xlink:href="note-0083-10"/> mobilibus, ratio potentiæ ad pondus non eſt ut 1. </s> <s xml:id="echoid-s1967" xml:space="preserve">ad du-<lb/>plum numeri orbiculorum ponderi affixorum; </s> <s xml:id="echoid-s1968" xml:space="preserve">ſed unitate <lb/>augeri debet numerus hicce duplus; </s> <s xml:id="echoid-s1969" xml:space="preserve">& </s> <s xml:id="echoid-s1970" xml:space="preserve">hîc, ubi duo orbicu-<lb/>li ponderi annectuntur, ratio eſt ut 1 ad 5; </s> <s xml:id="echoid-s1971" xml:space="preserve">tot enim dan-<lb/>tur funes, quibus pondus ſuſtinetur.</s> <s xml:id="echoid-s1972" xml:space="preserve"/> </p> <div xml:id="echoid-div321" type="float" level="2" n="2"> <note position="right" xlink:label="note-0083-09" xlink:href="note-0083-09a" xml:space="preserve">198.</note> <note position="right" xlink:label="note-0083-10" xlink:href="note-0083-10a" xml:space="preserve">TAB. VII. <lb/>fig. 5.</note> </div> </div> <div xml:id="echoid-div323" type="section" level="1" n="108"> <head xml:id="echoid-head158" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <note position="right" xml:space="preserve">199.</note> <p> <s xml:id="echoid-s1973" xml:space="preserve">Plurimi orbiculi ſeparati & </s> <s xml:id="echoid-s1974" xml:space="preserve">mobiles, habentes ſinguli <lb/> <anchor type="note" xlink:label="note-0083-12a" xlink:href="note-0083-12"/> <pb o="42" file="0084" n="90" rhead="PHYSICES ELEMENTA"/> ſuum funem peculiarem, ſi ita diſponantur, ut in hac figura, <lb/>multo magis actionem potentiæ augent. </s> <s xml:id="echoid-s1975" xml:space="preserve">Actio enim du-<lb/>plicatur pro unoquoque orbiculo, ita ut produobus ſit qua-<lb/>drupla, pro tribus octupla, & </s> <s xml:id="echoid-s1976" xml:space="preserve">ſic de cæteris.</s> <s xml:id="echoid-s1977" xml:space="preserve"/> </p> <div xml:id="echoid-div323" type="float" level="2" n="1"> <note position="right" xlink:label="note-0083-12" xlink:href="note-0083-12a" xml:space="preserve">TAB. VIII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s1978" xml:space="preserve">Sæpius memorata regula, ſcilicet ſpatia percurſa à po-<lb/>tentia & </s> <s xml:id="echoid-s1979" xml:space="preserve">pondere, quando æquè pollent, eſſe inter ſe inver-<lb/>ſè, ut potentia ad pondus, in omnibus prædictis locum ha-<lb/>bet.</s> <s xml:id="echoid-s1980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1981" xml:space="preserve">Hic ſemper ſunes paralleli ponuntur; </s> <s xml:id="echoid-s1982" xml:space="preserve">quid ſunium obli-<lb/>quitas diſcriminis adſerat, in ſequentibus videbimus.</s> <s xml:id="echoid-s1983" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div325" type="section" level="1" n="109"> <head xml:id="echoid-head159" xml:space="preserve">CAPUT XIII.</head> <head xml:id="echoid-head160" style="it" xml:space="preserve">De Cuneo & Cocbleâ, Machinarum Simplicium quartâ, & <lb/>quintâ.</head> <p> <s xml:id="echoid-s1984" xml:space="preserve">Ex prædictis ſatis patet, quomodo ope parvæ potentiæ <lb/>pondus magnum ſuſtineri aut elevari poſſit;</s> <s xml:id="echoid-s1985" xml:space="preserve">ad hoſce uſus <lb/>non reſtringitur Ars Mechanica: </s> <s xml:id="echoid-s1986" xml:space="preserve">intenſitates potentiarum <lb/>in omni caſu augeri poſſunt; </s> <s xml:id="echoid-s1987" xml:space="preserve">exemplum pulcherrimum ſup-<lb/>peditat Cuneus, inſtrumentum findendo ligno, pluribuſque <lb/>aliis uſibus, inſerviens.</s> <s xml:id="echoid-s1988" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div326" type="section" level="1" n="110"> <head xml:id="echoid-head161" xml:space="preserve"><emph style="sc">Definitio</emph> I.</head> <p> <s xml:id="echoid-s1989" xml:space="preserve">Cuneus eſt priſma non admodum altum, cujus baſes ſunt <lb/> <anchor type="note" xlink:label="note-0084-01a" xlink:href="note-0084-01"/> <anchor type="note" xlink:label="note-0084-02a" xlink:href="note-0084-02"/> triangula æquicrura; </s> <s xml:id="echoid-s1990" xml:space="preserve">ut A.</s> <s xml:id="echoid-s1991" xml:space="preserve"/> </p> <div xml:id="echoid-div326" type="float" level="2" n="1"> <note position="left" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">200.</note> <note position="left" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve">TAB. VII. <lb/>fig. 6.</note> </div> </div> <div xml:id="echoid-div328" type="section" level="1" n="111"> <head xml:id="echoid-head162" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s1992" xml:space="preserve">Altitudo trianguli eſt cunei altitudo; </s> <s xml:id="echoid-s1993" xml:space="preserve">ut db.</s> <s xml:id="echoid-s1994" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">201.</note> </div> <div xml:id="echoid-div329" type="section" level="1" n="112"> <head xml:id="echoid-head163" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s1995" xml:space="preserve">Trianguli baſis vocatur etiam cunei baſis; </s> <s xml:id="echoid-s1996" xml:space="preserve">ut ce.</s> <s xml:id="echoid-s1997" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">202.</note> </div> <div xml:id="echoid-div330" type="section" level="1" n="113"> <head xml:id="echoid-head164" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s1998" xml:space="preserve">Acies cunei eſt linea recta, quæ conjungit triangulorum <lb/> <anchor type="note" xlink:label="note-0084-05a" xlink:href="note-0084-05"/> vertices, ut bf.</s> <s xml:id="echoid-s1999" xml:space="preserve"/> </p> <div xml:id="echoid-div330" type="float" level="2" n="1"> <note position="left" xlink:label="note-0084-05" xlink:href="note-0084-05a" xml:space="preserve">203.</note> </div> <p> <s xml:id="echoid-s2000" xml:space="preserve">Ligno findendo, aut corporibus ſeparandis, acies cunei <lb/>applicatur, & </s> <s xml:id="echoid-s2001" xml:space="preserve">ictibus mallei, loco preſſionis, cuneus intruditur.</s> <s xml:id="echoid-s2002" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2003" xml:space="preserve">Quando totus cuneus intruditur, ſpatium a puncto d, cui <lb/>ictus mallei applicantur, percurſum, eſt altitudo cunei d b, <lb/>quæ ideo proſpatio à potentia percurſo haberi debet; </s> <s xml:id="echoid-s2004" xml:space="preserve">ſpa- <pb o="43" file="0085" n="91" rhead="MATHEMATICA. LIB. I. CCP. XIII."/> tìum verò, per quod ligni partes, aut corpora, a ſe mutuo <lb/>recedunt, eſt baſis cunei. </s> <s xml:id="echoid-s2005" xml:space="preserve">Unde ſequitur,</s> </p> <p style="it"> <s xml:id="echoid-s2006" xml:space="preserve">‘Potentiam ſe habere ad corporum ſeparandorum reſiſten-<lb/> <anchor type="note" xlink:label="note-0085-01a" xlink:href="note-0085-01"/> tiam, quando cum hac æquè pollet, ut baſis cunei, adillius al-<lb/>titudinem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2007" xml:space="preserve"/> </p> <div xml:id="echoid-div331" type="float" level="2" n="2"> <note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">204.</note> </div> <note symbol="*" position="right" xml:space="preserve">112.</note> <p> <s xml:id="echoid-s2008" xml:space="preserve">Quando agitur de ligno findendo, regula hæclocum non <lb/> <anchor type="note" xlink:label="note-0085-03a" xlink:href="note-0085-03"/> habet; </s> <s xml:id="echoid-s2009" xml:space="preserve">quia non per æqualia ſpatia ſingulæ ligni partes ce-<lb/>dunt, & </s> <s xml:id="echoid-s2010" xml:space="preserve">quia, partibus quam minime ſeparatis, cohæren-<lb/>tia in totum toliitur. </s> <s xml:id="echoid-s2011" xml:space="preserve">Quæ ad lignum findendum ſpectant <lb/>in ſequenti Scholio explicantur.</s> <s xml:id="echoid-s2012" xml:space="preserve"/> </p> <div xml:id="echoid-div332" type="float" level="2" n="3"> <note position="right" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve">205.</note> </div> </div> <div xml:id="echoid-div334" type="section" level="1" n="114"> <head xml:id="echoid-head165" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head166" xml:space="preserve">Qua cunei affectiones demonſtrantur.</head> <p> <s xml:id="echoid-s2013" xml:space="preserve">Tabella T, longitudinis ſex poll.</s> <s xml:id="echoid-s2014" xml:space="preserve">, latitudinis quatuor poll. <lb/></s> <s xml:id="echoid-s2015" xml:space="preserve"> <anchor type="note" xlink:label="note-0085-04a" xlink:href="note-0085-04"/> cum ſemiſſe, in ſitu horizontali firmatur, ad altitudinem <lb/> <anchor type="note" xlink:label="note-0085-05a" xlink:href="note-0085-05"/> circiter trium pedum ſupra menſam M.</s> <s xml:id="echoid-s2016" xml:space="preserve"/> </p> <div xml:id="echoid-div334" type="float" level="2" n="1"> <note position="right" xlink:label="note-0085-04" xlink:href="note-0085-04a" xml:space="preserve">206.</note> <note position="right" xlink:label="note-0085-05" xlink:href="note-0085-05a" xml:space="preserve">TAB. VIII <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s2017" xml:space="preserve">Hoc commodè fit ope columnæ firmæ C, cui in ſuperio-<lb/>ri parte cohæret lignum horizontale B, in cujus extre-<lb/>mo cavum quadratum datur, in quo intruditur cauda li-<lb/>gnèa, quæ cum tabella cohæret, & </s> <s xml:id="echoid-s2018" xml:space="preserve">quæ cum cavo exa-<lb/>cte congruit; </s> <s xml:id="echoid-s2019" xml:space="preserve">quare facile & </s> <s xml:id="echoid-s2020" xml:space="preserve">firmatur, & </s> <s xml:id="echoid-s2021" xml:space="preserve">ex ſitu tollitur, <lb/>tabella T.</s> <s xml:id="echoid-s2022" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2023" xml:space="preserve">Ad quatuor hujus angulos foramina dantur a, a, b, b. <lb/></s> <s xml:id="echoid-s2024" xml:space="preserve">per quæ funes tranſeunt, in ipſis foraminibus fixi; </s> <s xml:id="echoid-s2025" xml:space="preserve">ſunt hi <lb/>æquales inter ſe circiter tres pedes longi.</s> <s xml:id="echoid-s2026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2027" xml:space="preserve">Hiſce funibus ſuſpenduntur lamellæ æneæ quatuor, ut e <lb/>& </s> <s xml:id="echoid-s2028" xml:space="preserve">e; </s> <s xml:id="echoid-s2029" xml:space="preserve">ſed quæ diſtinctius, & </s> <s xml:id="echoid-s2030" xml:space="preserve">juxta veras dimenſiones, repræ-<lb/>ſentantur in E aut E.</s> <s xml:id="echoid-s2031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2032" xml:space="preserve">Ope harum duo ſuſpenduntur cylindri lignei h, h; </s> <s xml:id="echoid-s2033" xml:space="preserve">ſe-<lb/>ctio juxta axem repræſentatur in H; </s> <s xml:id="echoid-s2034" xml:space="preserve">altitudo inter t & </s> <s xml:id="echoid-s2035" xml:space="preserve">t, <lb/>ubi baſes paulum prominent, æqualis eſt diſtantiæ inter fo-<lb/>ramina a & </s> <s xml:id="echoid-s2036" xml:space="preserve">b in tabella T: </s> <s xml:id="echoid-s2037" xml:space="preserve">cylindrorum axes ulterius prominent, <lb/>chalybei ſunt, & </s> <s xml:id="echoid-s2038" xml:space="preserve">tenues, ut tr, tr; </s> <s xml:id="echoid-s2039" xml:space="preserve">hi per lamellarum, ut E, <lb/>foramina majora tranſeunt, cum quibus congruunt; </s> <s xml:id="echoid-s2040" xml:space="preserve">ita ta-<lb/>men ut in his quam liberrimè rotari poſſint.</s> <s xml:id="echoid-s2041" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2042" xml:space="preserve">Cylindrorum diametri ſunt duorum pollicum cum ſemiſ-<lb/>ſe; </s> <s xml:id="echoid-s2043" xml:space="preserve">in medio pars datur tenuior, long tudinis quatuor pol- <pb o="44" file="0086" n="92" rhead="PHYSICES ELEMENTA"/> licum, cujus diameter eſt ſeſquipollicis. </s> <s xml:id="echoid-s2044" xml:space="preserve">Pars hæc tenui-<lb/>or duobus annulis ii, oo, ex ipſo ligno, circumdatur ita, <lb/>ut lamina lignea F, quæ tenuiori huic parti applicatur, an-<lb/>nulos tantum tangat.</s> <s xml:id="echoid-s2045" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2046" xml:space="preserve">In tabella T dantur & </s> <s xml:id="echoid-s2047" xml:space="preserve">duo alia foramina inter a, a, & </s> <s xml:id="echoid-s2048" xml:space="preserve"><lb/>b, b, nempe l, l, per quæ funes tranſeunt, qui in ſuperiori <lb/>parte tabellæ cum paxillis s, s, cohærent. </s> <s xml:id="echoid-s2049" xml:space="preserve">Hiſce funibus <lb/>trochleæ duæ æneæ ſuſtinentur, ut t, aut T, ita ſuſpenſæ <lb/>ut liberrime circa axes ſuos chalybeos, in foraminibus in la-<lb/>mellis æneis rotari poſſint.</s> <s xml:id="echoid-s2050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2051" xml:space="preserve">Trochlea, ut T, cum cylindro uno conjungitur ope la-<lb/>mellæ E, & </s> <s xml:id="echoid-s2052" xml:space="preserve">funium m; </s> <s xml:id="echoid-s2053" xml:space="preserve">cum oppoſitâ lamellâ E funis n n co-<lb/>hæret, qui trochleæ circumponitur & </s> <s xml:id="echoid-s2054" xml:space="preserve">pondere P trahitur. <lb/></s> <s xml:id="echoid-s2055" xml:space="preserve">Simile pondus, ad aliam partem cylindrorum, eodem mo-<lb/>do, ſuſpenditur, quibus duobus ponderibus ad ſe mutuotra-<lb/>huntur cylindri.</s> <s xml:id="echoid-s2056" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2057" xml:space="preserve">Ope paxillorum s, s, elevantur, aut deprimuntur trochleæ, <lb/>donec funes n & </s> <s xml:id="echoid-s2058" xml:space="preserve">m ſint in ſitu horizontali.</s> <s xml:id="echoid-s2059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2060" xml:space="preserve">Cuneus formatur ex duabus laminis ligneis F, F, verti-<lb/>eulis inter ſe conjunctis; </s> <s xml:id="echoid-s2061" xml:space="preserve">quæ angulum quemcunque inter <lb/>ſe efficere poſſunt.</s> <s xml:id="echoid-s2062" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2063" xml:space="preserve">Per haſce ipſas tranſit cochlea, circulariter incurvata, ſu-<lb/>per qua duo fruſta ænea exigua, duæ nempe cochleæ ex-<lb/>teriores, moventur. </s> <s xml:id="echoid-s2064" xml:space="preserve">Hiſce plana F, F ſeparantur, &</s> <s xml:id="echoid-s2065" xml:space="preserve">, ne an-<lb/>gulus, quem efficiunt, minuatur, cohibent.</s> <s xml:id="echoid-s2066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2067" xml:space="preserve">Appenſâ lance, cum pondere Q, cuneus hic inter cylin-<lb/>dros intruditur.</s> <s xml:id="echoid-s2068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2069" xml:space="preserve">Ut ita conſtituatur cuneus, ut ratio inter baſim& </s> <s xml:id="echoid-s2070" xml:space="preserve">altitudi -<lb/>nem determinetur, formantur ex ligno triangula iſocelia mino-<lb/>ra, ad verticem paululum truncata; </s> <s xml:id="echoid-s2071" xml:space="preserve">quibus altitudo, & </s> <s xml:id="echoid-s2072" xml:space="preserve">baſis lon-<lb/>gitudo inſcribuntur, datâ menſurâ quacunque. </s> <s xml:id="echoid-s2073" xml:space="preserve">Commodum <lb/>eſt exprimere altitudinem per numerum 16, ſi integris libris <lb/>cylindri ad ſe mutuo trahantur.</s> <s xml:id="echoid-s2074" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div336" type="section" level="1" n="115"> <head xml:id="echoid-head167" xml:space="preserve"><emph style="sc">Experimentum</emph></head> <p> <s xml:id="echoid-s2075" xml:space="preserve">Rebus, ut in machinæ deſcriptione dictum, diſpoſitis, <lb/> <anchor type="note" xlink:label="note-0086-01a" xlink:href="note-0086-01"/> ſi pondus, quo cuneus inter cylindros intruditur, (id eſt, <pb o="45" file="0087" n="93" rhead="MATHEMATICA. LIB. I. CAP. XIII."/> pondus cunei, cochleæ g g, & </s> <s xml:id="echoid-s2076" xml:space="preserve">lancis cum pondere impoſi-<lb/>to) ſe habet ad ſummam ponderum P,P, ut baſis cunei <lb/>ad ipſius altitudinem, æquilibrium datur, inter vim qua <lb/>cylindri ſeparantur, & </s> <s xml:id="echoid-s2077" xml:space="preserve">illam qua ad ſe mutuo trahuntur. <lb/></s> <s xml:id="echoid-s2078" xml:space="preserve">Hoc exinde elicitur, quia agitatione minimâ cuneus eleva-<lb/>tur aut deprimitur.</s> <s xml:id="echoid-s2079" xml:space="preserve"/> </p> <div xml:id="echoid-div336" type="float" level="2" n="1"> <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">207.</note> </div> <p> <s xml:id="echoid-s2080" xml:space="preserve">Magnam cum cuneo affinitatem habet cochlea. </s> <s xml:id="echoid-s2081" xml:space="preserve">Ex dua-<lb/>bus partibus conſtat.</s> <s xml:id="echoid-s2082" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div338" type="section" level="1" n="116"> <head xml:id="echoid-head168" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s2083" xml:space="preserve">Prima, quæ vocatur cochlea interior, eſt cylindrus ad for-<lb/> <anchor type="note" xlink:label="note-0087-01a" xlink:href="note-0087-01"/> mam belicis ſulcatus, ut AB.</s> <s xml:id="echoid-s2084" xml:space="preserve"/> </p> <div xml:id="echoid-div338" type="float" level="2" n="1"> <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">208.</note> </div> <note position="right" xml:space="preserve">TAB. VII. <lb/>fig. 8.</note> <p> <s xml:id="echoid-s2085" xml:space="preserve">Secunda, quæ vocatur cochlea exterior, & </s> <s xml:id="echoid-s2086" xml:space="preserve">cujus figura <lb/> <anchor type="note" xlink:label="note-0087-03a" xlink:href="note-0087-03"/> differt pro vario uſu Machinæ, eſt ſolidum cylindricè excava-<lb/>tum, cujus ſuperficies concava eodem modo ſulcata eſt, ita ut bu-<lb/>jus eminentiæ alterius cavitatibus congruant, ut DE.</s> <s xml:id="echoid-s2087" xml:space="preserve"/> </p> <div xml:id="echoid-div339" type="float" level="2" n="2"> <note position="right" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">209.</note> </div> <p> <s xml:id="echoid-s2088" xml:space="preserve">Hæ duæ partes in ſe mutuo moveri poſſunt, quod in uſu <lb/>hujus machinæ requiritur. </s> <s xml:id="echoid-s2089" xml:space="preserve">Inſervit præcipuè ad compri-<lb/>menda corpora, quæ jungi & </s> <s xml:id="echoid-s2090" xml:space="preserve">firmiter connecti debent; </s> <s xml:id="echoid-s2091" xml:space="preserve">in <lb/>hac enim Machinâ potentia minima quam arctiſſimé corpo-<lb/>ra comprimit. </s> <s xml:id="echoid-s2092" xml:space="preserve">Poteſt etiam cochlea ad elevanda ponde-<lb/>ra adaptari. </s> <s xml:id="echoid-s2093" xml:space="preserve">In unaquaque revolutione hujus machinæ, quie-<lb/>ſcente parte una, altera protruditur ad diſtantiam æqualem in-<lb/>tervallo duarum proximarum ſpiralium converſionum. </s> <s xml:id="echoid-s2094" xml:space="preserve">Po-<lb/>tentia, quâ cochlea movetur, applicatur manubrio, aut ſcy-<lb/>talæ & </s> <s xml:id="echoid-s2095" xml:space="preserve">potentia eſt ad compreſſionem, quam generat, ut <lb/> <anchor type="note" xlink:label="note-0087-04a" xlink:href="note-0087-04"/> prædicta diſtantia, inter duas proximas ſpiralium converſio-<lb/>nes, ad peripheriam circulià puncto manubrii aut ſcytalæ, <lb/>cui potentia applicatur, percurſi; </s> <s xml:id="echoid-s2096" xml:space="preserve">via enim a puncto aut pla-<lb/>no, quo reſiſtentia ſuperatur, percurſa, illam ad viam po-<lb/>tentiæ rationem habet.</s> <s xml:id="echoid-s2097" xml:space="preserve"/> </p> <div xml:id="echoid-div340" type="float" level="2" n="3"> <note position="right" xlink:label="note-0087-04" xlink:href="note-0087-04a" xml:space="preserve">210.</note> </div> <p> <s xml:id="echoid-s2098" xml:space="preserve">Hic obſervandum eſt, quando potentia cum pondere æquè <lb/>pollet in machinâ quacunque, ſi potentia parte quantumvis <lb/>exiguâ augeatur, illam præpollere, machinâ omnium parti-<lb/>um attritu carente; </s> <s xml:id="echoid-s2099" xml:space="preserve">quando verò attritus datur, potentiâ <lb/>& </s> <s xml:id="echoid-s2100" xml:space="preserve">hic ſuperari debet, & </s> <s xml:id="echoid-s2101" xml:space="preserve">quantum ad illud requiritur ſu-<lb/>peraddi debet, quod ratiocinio mathematico determinari non <pb o="46" file="0088" n="94" rhead="PHYSICES ELEMENTA"/> poteſt. </s> <s xml:id="echoid-s2102" xml:space="preserve">In Cochleis attritus admodum eſt ſenſibilis, & </s> <s xml:id="echoid-s2103" xml:space="preserve">et-<lb/> <anchor type="note" xlink:label="note-0088-01a" xlink:href="note-0088-01"/> iam magni uſus; </s> <s xml:id="echoid-s2104" xml:space="preserve">nam eo machina in ſitu ſuo ſervatur, & </s> <s xml:id="echoid-s2105" xml:space="preserve"><lb/>actione corporum, quæ comprimuntur, aut gravitate pon-<lb/>derum quæ elevantur, ceſſante actione potentiæ, motu con-<lb/>trario non agitatur, & </s> <s xml:id="echoid-s2106" xml:space="preserve">ad priſtinum ſitum non redit.</s> <s xml:id="echoid-s2107" xml:space="preserve"/> </p> <div xml:id="echoid-div341" type="float" level="2" n="4"> <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">211.</note> </div> </div> <div xml:id="echoid-div343" type="section" level="1" n="117"> <head xml:id="echoid-head169" xml:space="preserve">SCHOLIUM I.</head> <head xml:id="echoid-head170" xml:space="preserve">De ligno findendo.</head> <p> <s xml:id="echoid-s2108" xml:space="preserve">Detur lignum, cujus partes jam ſeparatæ efficiant angulum EFL; </s> <s xml:id="echoid-s2109" xml:space="preserve">ſit hoc <lb/> <anchor type="note" xlink:label="note-0088-02a" xlink:href="note-0088-02"/> ulterius findendum ope cunei ACB, cujus baſis eſt AB, & </s> <s xml:id="echoid-s2110" xml:space="preserve">cujus alti-<lb/> <anchor type="note" xlink:label="note-0088-03a" xlink:href="note-0088-03"/> tudinem menſurat CD.</s> <s xml:id="echoid-s2111" xml:space="preserve"/> </p> <div xml:id="echoid-div343" type="float" level="2" n="1"> <note position="left" xlink:label="note-0088-02" xlink:href="note-0088-02a" xml:space="preserve">212.</note> <note position="left" xlink:label="note-0088-03" xlink:href="note-0088-03a" xml:space="preserve">TAB. VIII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s2112" xml:space="preserve">Ubi partes, ut ſuperius monuimus, quantumvis parum ſeparantur, omnis <lb/>tollitur reſiſtentia; </s> <s xml:id="echoid-s2113" xml:space="preserve">antequam autem ſeparentur partes in F, puncta E, L, <lb/>paululum moveri debent, id eſt augendus eſt angulus E F L; </s> <s xml:id="echoid-s2114" xml:space="preserve">de-<lb/>terminaada ideò eſt vis, qua angulus hic augeri poteſt.</s> <s xml:id="echoid-s2115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2116" xml:space="preserve">Ponamus angulum auctum, ut ſit e F l; </s> <s xml:id="echoid-s2117" xml:space="preserve">cuneus intravit, & </s> <s xml:id="echoid-s2118" xml:space="preserve">datur in a c b; <lb/></s> <s xml:id="echoid-s2119" xml:space="preserve">partes ligni E, L, translatæ fuere per E e, L l, ſed quæ minus ab F diſtant <lb/>per minus ſpatium moventur, lineæque EF, LF, motibus ſuis deſeribunt <lb/>areas triangulorum æqualium inter ſe F E, l FL.</s> <s xml:id="echoid-s2120" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2121" xml:space="preserve">Ductis e f & </s> <s xml:id="echoid-s2122" xml:space="preserve">f F, parallelis EF & </s> <s xml:id="echoid-s2123" xml:space="preserve">e E, formetur parallelogrammum e E F f; <lb/></s> <s xml:id="echoid-s2124" xml:space="preserve">ſunt æqualia triangula e F E & </s> <s xml:id="echoid-s2125" xml:space="preserve">f e F <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2126" xml:space="preserve">& </s> <s xml:id="echoid-s2127" xml:space="preserve">parallelogrammum valet ambo tri- <anchor type="note" xlink:label="note-0088-04a" xlink:href="note-0088-04"/> angula e F E & </s> <s xml:id="echoid-s2128" xml:space="preserve">L F l conjuncta: </s> <s xml:id="echoid-s2129" xml:space="preserve">ideò translationes memoratæ linearum <lb/>ambarum EF, LF, conjunctæ, valent translationem ſolius lineæ E F per ſpa-<lb/>tium E e aut F f: </s> <s xml:id="echoid-s2130" xml:space="preserve">quæ lineola ergo diſtantiam repræſentat, qua partes ligni à <lb/>ſe invicem ſeparantur, cum autem de hac ſeparatione hìc agatur, eſt hæci-<lb/>pſa lineola ſpatium, ab obſtaculo quod ſuperandum eſt, percurſum, dum <lb/>ſpatium, quod percurrit potentia, eſt C c, ſpatium nempe per quod cuneus <lb/>fuit tranſlatum.</s> <s xml:id="echoid-s2131" xml:space="preserve"/> </p> <div xml:id="echoid-div344" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0088-04" xlink:href="note-0088-04a" xml:space="preserve">34. El. 1.</note> </div> <p> <s xml:id="echoid-s2132" xml:space="preserve">Vis ergo, qua cuneus intruditur, eſt ad ligni reſiſtentiam, quando æquè pol-<lb/>lent, ut e E ad C c. </s> <s xml:id="echoid-s2133" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/></s> </p> <note symbol="*" position="left" xml:space="preserve">112.</note> <p> <s xml:id="echoid-s2134" xml:space="preserve">Ducatur C g ipſi E e parallela, erunt hæ lineæ æquales <anchor type="note" xlink:href="" symbol="*"/>, quia motu parallelo <anchor type="note" xlink:label="note-0088-06a" xlink:href="note-0088-06"/> latus cunei AG fuit tranſlatum;</s> <s xml:id="echoid-s2135" xml:space="preserve">ratio memorata eſt ergo quæ datur inter g C&</s> <s xml:id="echoid-s2136" xml:space="preserve">Cc.</s> <s xml:id="echoid-s2137" xml:space="preserve"/> </p> <div xml:id="echoid-div345" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">34. El. 1.</note> </div> <p> <s xml:id="echoid-s2138" xml:space="preserve">Lineola E e, ideò etiam g C, perpendicularis eſt ad F E;</s> <s xml:id="echoid-s2139" xml:space="preserve">eſt enim E e arcus cir-<lb/>culi, adeo exiguus ut pro rectâ lineâ haberi poſſit; </s> <s xml:id="echoid-s2140" xml:space="preserve">cujus circuli radius eſt <lb/>F E.</s> <s xml:id="echoid-s2141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2142" xml:space="preserve">Per punctum baseos medium D linea ducatur DH, ad latus AC cunei per-<lb/> <anchor type="note" xlink:label="note-0088-07a" xlink:href="note-0088-07"/> veniens in H & </s> <s xml:id="echoid-s2143" xml:space="preserve">cum FE latere ligni ſeparato, continuato, angulum efficiens re-<lb/>ctum; </s> <s xml:id="echoid-s2144" xml:space="preserve">quare ipſi Cg parallela eſt.</s> <s xml:id="echoid-s2145" xml:space="preserve"/> </p> <div xml:id="echoid-div346" type="float" level="2" n="4"> <note position="left" xlink:label="note-0088-07" xlink:href="note-0088-07a" xml:space="preserve">213.</note> </div> <p> <s xml:id="echoid-s2146" xml:space="preserve">Propter latera c C, CD, in eadem linea, & </s> <s xml:id="echoid-s2147" xml:space="preserve">reliqua parallela, ſunt ſimilia <lb/>triangula C gc, DHC; </s> <s xml:id="echoid-s2148" xml:space="preserve">idcirco DH ſe babet ad DC, id eſt altitudinem cu-<lb/>nei, ut g C ad C c, id eſt, ut vis qua cuneus intruditur ad ligni reſiſtentiam, quan-<lb/>do neutra alteram vincere poteſt, auctâ paulum potentiâ ſeparantur ligni par-<lb/>tes.</s> <s xml:id="echoid-s2149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2150" xml:space="preserve">Quando ligni partes non ſeparantur, niſi quo uſque cuneus intruditur, lineæ AC <lb/> <anchor type="note" xlink:label="note-0088-08a" xlink:href="note-0088-08"/> & </s> <s xml:id="echoid-s2151" xml:space="preserve">EF con veniunt, & </s> <s xml:id="echoid-s2152" xml:space="preserve">angulus DHC eſt rectus, ideoque ſimilia ſunt trian- <pb o="47" file="0089" n="95" rhead="MATHEMATICA. LIB. I. CAP. XIV."/> gula CHD, CAD <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2153" xml:space="preserve">& </s> <s xml:id="echoid-s2154" xml:space="preserve">DH ad DC, ut AD ad AC. </s> <s xml:id="echoid-s2155" xml:space="preserve">In hoc caſu <anchor type="note" xlink:label="note-0089-01a" xlink:href="note-0089-01"/> ergo eſt vis, qua Cuneus intruditur, ad ligni reſiſtentiam, ubi æque pollent, ut ſe-<lb/>mibaſis cunei ad bujus latus.</s> <s xml:id="echoid-s2156" xml:space="preserve"/> </p> <div xml:id="echoid-div347" type="float" level="2" n="5"> <note position="left" xlink:label="note-0088-08" xlink:href="note-0088-08a" xml:space="preserve">214.</note> <note symbol="*" position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">8. El. VI.</note> </div> </div> <div xml:id="echoid-div349" type="section" level="1" n="118"> <head xml:id="echoid-head171" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head172" xml:space="preserve">Machinæ cujuſdam examen.</head> <p> <s xml:id="echoid-s2157" xml:space="preserve">Machinam ad cunei proprietates demonſtrandum, à ſuperius deſcriptâ <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0089-02a" xlink:href="note-0089-02"/> <anchor type="note" xlink:label="note-0089-03a" xlink:href="note-0089-03"/> diverſam, adhibuere alii; </s> <s xml:id="echoid-s2158" xml:space="preserve">ipſe olim talem paululum tantum immuta-<lb/>tam, eodem tamen principio nixam, conſtrui curavi, quæ hìc exhibetur;</s> <s xml:id="echoid-s2159" xml:space="preserve">ſed in <lb/>quo failat breviter dicam.</s> <s xml:id="echoid-s2160" xml:space="preserve"/> </p> <div xml:id="echoid-div349" type="float" level="2" n="1"> <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">215.</note> <note symbol="*" position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">206.</note> </div> <p> <s xml:id="echoid-s2161" xml:space="preserve">In hac cuneus, illi ſimilis cum quo experimenta in noſtra machina inſti-<lb/> <anchor type="note" xlink:label="note-0089-04a" xlink:href="note-0089-04"/> tuuntur, eodem modo ac ubi de noſtra egimus dictum, pondere M inter cy-<lb/>lindros E, E, trahitur; </s> <s xml:id="echoid-s2162" xml:space="preserve">cylindri autem moventur juxta regulas æneas CC, <lb/>CC, ſuper quibus chalybei axes prominentes ponuntur, & </s> <s xml:id="echoid-s2163" xml:space="preserve">quæ cum regulis <lb/>ligneis AA, AA, parallelis inter ſe cohærent. </s> <s xml:id="echoid-s2164" xml:space="preserve">Cylindri trahuntur ponderibus <lb/>P,P, ſuſpenſis funibus, qui cum lamellis æneis cohærent, in quibus forami-<lb/>na dantur per quæ axes chalybei cylindrorum tranſeunt; </s> <s xml:id="echoid-s2165" xml:space="preserve">funes trochleis nt d, d, <lb/>in regulis AA, AA, fixis, & </s> <s xml:id="echoid-s2166" xml:space="preserve">circa axes mobilibus, circumponuntur.</s> <s xml:id="echoid-s2167" xml:space="preserve"/> </p> <div xml:id="echoid-div350" type="float" level="2" n="2"> <note position="right" xlink:label="note-0089-04" xlink:href="note-0089-04a" xml:space="preserve">TAB. VII. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s2168" xml:space="preserve">In hac machina datur æquilibrium, ſi vis, qua cuneus intruditur, ſe ha-<lb/>beat ad ſummam ponderum P,P, ut ſemibaſis cunei ad ipſius altitudinem, quæ <lb/>proportio in cuneo locum non habet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2169" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">204.</note> <p> <s xml:id="echoid-s2170" xml:space="preserve">Machina hæc non repræſentat quæ in actione cunei, quo corpora ſeparan-<lb/>tur, obtinent; </s> <s xml:id="echoid-s2171" xml:space="preserve">pondera enim P,P, non repræſentant vim qua cylindri inter ſe <lb/>cohærent; </s> <s xml:id="echoid-s2172" xml:space="preserve">ſed cylindri ſinguli dimidio ponderum P,P, ad trochleam fixam <lb/>trahuntur; </s> <s xml:id="echoid-s2173" xml:space="preserve">in noſtra autem machina, ponderibus integris P,P, inter ſe co-<lb/>hærent cylindri.</s> <s xml:id="echoid-s2174" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div352" type="section" level="1" n="119"> <head xml:id="echoid-head173" xml:space="preserve">CAPUT XIV.</head> <head xml:id="echoid-head174" xml:space="preserve">De Machinis compoſitis.</head> <p> <s xml:id="echoid-s2175" xml:space="preserve">JAm vidimus, quomodo Machina ex plurimis vectibus <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0089-06a" xlink:href="note-0089-06"/> aut plurimis rotis <anchor type="note" xlink:href="" symbol="*"/>, componi poſſit, & </s> <s xml:id="echoid-s2176" xml:space="preserve">quomodo in iſtis <anchor type="note" xlink:label="note-0089-07a" xlink:href="note-0089-07"/> machinis potentia, ut cum reſiſtentia æquè polleat, ſit adre-<lb/> <anchor type="note" xlink:label="note-0089-08a" xlink:href="note-0089-08"/> ſiſtentiam, in ratione compoſita ex omnibus rationibus, quas in <lb/>ſingulis machinis potentia ad reſiſtentias baberent, ſi ſepa-<lb/>ratim adhiberentur; </s> <s xml:id="echoid-s2177" xml:space="preserve">hæc eadem regula in omnibus aliis <lb/>machinis compoſitis obtinet.</s> <s xml:id="echoid-s2178" xml:space="preserve"/> </p> <div xml:id="echoid-div352" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0089-06" xlink:href="note-0089-06a" xml:space="preserve">177.</note> <note symbol="*" position="right" xlink:label="note-0089-07" xlink:href="note-0089-07a" xml:space="preserve">190.</note> <note position="right" xlink:label="note-0089-08" xlink:href="note-0089-08a" xml:space="preserve">216.</note> </div> <p> <s xml:id="echoid-s2179" xml:space="preserve">Non modo plurimæ machinæ ejuſdem generis poſſunt <lb/>jungi, ex machinis diverſis, variis modis, machina componi <lb/>poteſt; </s> <s xml:id="echoid-s2180" xml:space="preserve">exemplo uno & </s> <s xml:id="echoid-s2181" xml:space="preserve">altero id ſatis patebit.</s> <s xml:id="echoid-s2182" xml:space="preserve"/> </p> <pb o="48" file="0090" n="96" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div354" type="section" level="1" n="120"> <head xml:id="echoid-head175" xml:space="preserve"><emph style="sc">Experimentum</emph> I.</head> <p> <s xml:id="echoid-s2183" xml:space="preserve">Axi in peritrochio funis ductarius trochleæ jungitur, po-<lb/> <anchor type="note" xlink:label="note-0090-01a" xlink:href="note-0090-01"/> tentia rotæ applicatur, & </s> <s xml:id="echoid-s2184" xml:space="preserve">hìc ubi trochleâ quinquies vis au-<lb/> <anchor type="note" xlink:label="note-0090-02a" xlink:href="note-0090-02"/> getur, & </s> <s xml:id="echoid-s2185" xml:space="preserve">ubi diameter axis eſt pars tertia diametri rotæ, <lb/>ratio potentiæ ad pondus componitur ex rationibus 1 ad 5 <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0090-03a" xlink:href="note-0090-03"/> & </s> <s xml:id="echoid-s2186" xml:space="preserve">1 ad 3 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2187" xml:space="preserve">eſt ergo ut 1 ad 15; </s> <s xml:id="echoid-s2188" xml:space="preserve">& </s> <s xml:id="echoid-s2189" xml:space="preserve">ideo unica libra M <anchor type="note" xlink:label="note-0090-04a" xlink:href="note-0090-04"/> ſuſtinet pondus P quindecim librarum.</s> <s xml:id="echoid-s2190" xml:space="preserve"/> </p> <div xml:id="echoid-div354" type="float" level="2" n="1"> <note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">217.</note> <note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">TAB. VIL. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0090-03" xlink:href="note-0090-03a" xml:space="preserve">194.</note> <note symbol="*" position="left" xlink:label="note-0090-04" xlink:href="note-0090-04a" xml:space="preserve">188.</note> </div> <p> <s xml:id="echoid-s2191" xml:space="preserve">Axis in peritrochio moveri poteſt adhibitâ cochleâ ro-<lb/> <anchor type="note" xlink:label="note-0090-05a" xlink:href="note-0090-05"/> ta in hoc caſu dentata requiritur, cujus dentes ſint inclinati, <lb/> <anchor type="note" xlink:label="note-0090-06a" xlink:href="note-0090-06"/> ut cum ſulco cochleæ congruant Talis eſt rota A, quæ <lb/>ope cochleæ BC movetur. </s> <s xml:id="echoid-s2192" xml:space="preserve">Hoc in caſu cochlea perpetua <lb/>dicitur, & </s> <s xml:id="echoid-s2193" xml:space="preserve">mirum admodum hujus ope potentia minima <lb/>exerit effectum; </s> <s xml:id="echoid-s2194" xml:space="preserve">tot enim in ſingul is rotæ revolutionibus, <lb/>revolutiones requiruntur cochleæ, id eſt, manubrii quo <lb/>cochlea movetur, quot dentes rota habet; </s> <s xml:id="echoid-s2195" xml:space="preserve">ſi huic rotæ ul-<lb/>terior rota dentata addatur, potentia eadem majus ob-<lb/>ſtaculum agitare poterit.</s> <s xml:id="echoid-s2196" xml:space="preserve"/> </p> <div xml:id="echoid-div355" type="float" level="2" n="2"> <note position="left" xlink:label="note-0090-05" xlink:href="note-0090-05a" xml:space="preserve">218.</note> <note position="left" xlink:label="note-0090-06" xlink:href="note-0090-06a" xml:space="preserve">TAB. VII. <lb/>fig. 9.</note> </div> </div> <div xml:id="echoid-div357" type="section" level="1" n="121"> <head xml:id="echoid-head176" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s2197" xml:space="preserve">Machina, quam hìc exhibemus, conſtat ex duabus rotis, <lb/> <anchor type="note" xlink:label="note-0090-07a" xlink:href="note-0090-07"/> & </s> <s xml:id="echoid-s2198" xml:space="preserve">cochleâ perpetuâ, quæ manubrio DE movetur. </s> <s xml:id="echoid-s2199" xml:space="preserve">In hac <lb/> <anchor type="note" xlink:label="note-0090-08a" xlink:href="note-0090-08"/> ratio potentiæ ad pondus, quando æquè pollent, componitur <lb/>ex ratione ſemidiametri axis ultimæ rotæ F, ad manubrii <lb/>longitudinem DE, & </s> <s xml:id="echoid-s2200" xml:space="preserve">ratione revolutionum hujus rotæ ad <lb/>manubrii aut cochleæ revolutiones. </s> <s xml:id="echoid-s2201" xml:space="preserve">Prima ratio in hac ma-<lb/>china eſt 1 ad 30; </s> <s xml:id="echoid-s2202" xml:space="preserve">ſecunda ex numero dentium colligitur. <lb/></s> <s xml:id="echoid-s2203" xml:space="preserve">Rota ultima F habet in peripheria dentes 35, axis primæ rotæ <lb/>A continet dentes 7; </s> <s xml:id="echoid-s2204" xml:space="preserve">quinquies ergo prima rota revolvi-<lb/>tur, dum ſecunda ſemel; </s> <s xml:id="echoid-s2205" xml:space="preserve">hæc verò prima continet dentes <lb/>36, totidem igitur revolutiones peragit cochlea, dum hæc <lb/>rota ſemel revolvitur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s2206" xml:space="preserve">ratio ex hiſce duabus compoſita <anchor type="note" xlink:label="note-0090-09a" xlink:href="note-0090-09"/> eſt, 1 ad 180, quæ eſt ſecunda ratio quæſita; </s> <s xml:id="echoid-s2207" xml:space="preserve">& </s> <s xml:id="echoid-s2208" xml:space="preserve">ratio ex <lb/>hac & </s> <s xml:id="echoid-s2209" xml:space="preserve">prima 1 ad 30 compoſita, eſt ratio 1 ad 5400, quæ <lb/>eſt ratio potentiæ ad pondus in caſu æquilibrii; </s> <s xml:id="echoid-s2210" xml:space="preserve">& </s> <s xml:id="echoid-s2211" xml:space="preserve">quan-<lb/>tumvis parum auctâ potentia pondus elevaretur, ſinullus da-<lb/>retur attritus, qui cum in omnibus hiſce machinis non ſit <lb/>contemnendus; </s> <s xml:id="echoid-s2212" xml:space="preserve">ſatis ſenſibiliter potentia, antequam pon- <pb file="0091" n="97"/> <anchor type="figure" xlink:label="fig-0091-01a" xlink:href="fig-0091-01"/> <pb file="0091a" n="98"/> <anchor type="figure" xlink:label="fig-0091a-01a" xlink:href="fig-0091a-01"/> <pb file="0092" n="99"/> <pb o="49" file="0093" n="100" rhead="MATHEMATICA. LIB. I. CAP. XV."/> dus ſuperet, adaugeri debet; </s> <s xml:id="echoid-s2213" xml:space="preserve">pontentiâ tamen minimâ pon-<lb/>dus maximum elevatur. </s> <s xml:id="echoid-s2214" xml:space="preserve">Longitudo ſcytalæ ED duplicari, <lb/>aut etiam ulterius augeri poteſt, quo actio potentiæ dupli-<lb/>catur, aut magis augetur; </s> <s xml:id="echoid-s2215" xml:space="preserve">in hoc caſu capillo tenuiſſimo ho-<lb/>mo fortis ſuperatur.</s> <s xml:id="echoid-s2216" xml:space="preserve"/> </p> <div xml:id="echoid-div357" type="float" level="2" n="1"> <note position="left" xlink:label="note-0090-07" xlink:href="note-0090-07a" xml:space="preserve">219.</note> <note position="left" xlink:label="note-0090-08" xlink:href="note-0090-08a" xml:space="preserve">TAB. VII. <lb/>fig. 9.</note> <note symbol="*" position="left" xlink:label="note-0090-09" xlink:href="note-0090-09a" xml:space="preserve">218.</note> <figure xlink:label="fig-0091-01" xlink:href="fig-0091-01a"> <image file="0091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0091-01"/> </figure> <figure xlink:label="fig-0091a-01" xlink:href="fig-0091a-01a"> <image file="0091a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0091a-01"/> </figure> </div> <p> <s xml:id="echoid-s2217" xml:space="preserve">Innumeræ aliæ Machinæ compoſitæ conſtrui poſſunt, <lb/>quarum vires eodem modo computatione determinantur, <lb/>ope regulæ initio hujus capitis memoratæ, aut etiam compa-<lb/>rando viam percurſam a potentiâ cum viâ à pondere, aut <lb/>alio quocumque impedimento, percurſâ; </s> <s xml:id="echoid-s2218" xml:space="preserve">harum enim ratio <lb/>eſt ratio inverſa potentiæ & </s> <s xml:id="echoid-s2219" xml:space="preserve">ponderis autimpedimenti, quando <lb/>potentiæ actio cum reſiſtentiâ impedimenti æquè pollet.</s> <s xml:id="echoid-s2220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2221" xml:space="preserve">Preſſiones, quæ contrarie agentes æquè pollent, ſemper <lb/>ſunt æquales; </s> <s xml:id="echoid-s2222" xml:space="preserve">ſi ergo potentia intenſitate minor eſt impe-<lb/>dimento, reſpectu viæ percurſæ illud ſuperare debet, & </s> <s xml:id="echoid-s2223" xml:space="preserve"><lb/>quidem toties quoties ab illo intenſitate ſuperatur; </s> <s xml:id="echoid-s2224" xml:space="preserve">nullo e-<lb/>nim alio reſpectu preſſionum effectus differre poſſunt, etiam <lb/>nulla alia compenſatio dari poteſt.</s> <s xml:id="echoid-s2225" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div359" type="section" level="1" n="122"> <head xml:id="echoid-head177" xml:space="preserve">CAPUT XV.</head> <head xml:id="echoid-head178" xml:space="preserve">De Potentiis obliquis.</head> <p> <s xml:id="echoid-s2226" xml:space="preserve">Detur punctum A, quod tribus potentiis filis applicatis <lb/> <anchor type="note" xlink:label="note-0093-01a" xlink:href="note-0093-01"/> per AB, <emph style="sc">A</emph>E, & </s> <s xml:id="echoid-s2227" xml:space="preserve"><emph style="sc">A</emph>D, trabitur, quieſcit, ſi poten-<lb/> <anchor type="note" xlink:label="note-0093-02a" xlink:href="note-0093-02"/> tiæ fuerint inter ſe ut latera trianguli formati lineis juxta <lb/>directiones potentiarum poſitis; </s> <s xml:id="echoid-s2228" xml:space="preserve">id eſt, ſi potentiæ fuerint <lb/>inter ſe ut latera trianguli A Db. </s> <s xml:id="echoid-s2229" xml:space="preserve">In quo caſu poſitis AB, <lb/>AE & </s> <s xml:id="echoid-s2230" xml:space="preserve">AD, reſpectivè ut preſſiones per has lineas agentes, <lb/>ſi duabus ut AD & </s> <s xml:id="echoid-s2231" xml:space="preserve"><emph style="sc">A</emph>E formetur parallelogrammum, pa-<lb/>tet tertiam <emph style="sc">Ba</emph> continuatam fore parallelogrammi diagona-<lb/>lem & </s> <s xml:id="echoid-s2232" xml:space="preserve">AB, Ab, æquales eſſe inter ſe.</s> <s xml:id="echoid-s2233" xml:space="preserve"/> </p> <div xml:id="echoid-div359" type="float" level="2" n="1"> <note position="right" xlink:label="note-0093-01" xlink:href="note-0093-01a" xml:space="preserve">220.</note> <note position="right" xlink:label="note-0093-02" xlink:href="note-0093-02a" xml:space="preserve">TAB. X. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s2234" xml:space="preserve">Punctum autem A in hoc caſu quieſcere ut demonſtremus, <lb/>concipere debemus, ſepoſitâ potentiâ per <emph style="sc">A</emph>B, preſſiones per <lb/>AE & </s> <s xml:id="echoid-s2235" xml:space="preserve">AD deſtrui, punctumque quieſcere, actione quacunque, <lb/>& </s> <s xml:id="echoid-s2236" xml:space="preserve">in hanc actionem inquirendum eſt. </s> <s xml:id="echoid-s2237" xml:space="preserve">Sint lineæ minimæ A d, <lb/>A e, inter ſe ut A D, AE, id eſt, ut preſſiones juxta haſce lineas <lb/>agentes;</s> <s xml:id="echoid-s2238" xml:space="preserve">æquali tempore punctum A per haſce lineas minimas <pb o="50" file="0094" n="101" rhead="PHYSICES ELEMENTA"/> poſſet transferri, ſi ſingulæ ſolæ agerent & </s> <s xml:id="echoid-s2239" xml:space="preserve">non deſtruerentur <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s2240" xml:space="preserve"> <anchor type="note" xlink:label="note-0094-01a" xlink:href="note-0094-01"/> cum punctum quieſcat, integras ſuas actiones ambæ ſimul in <lb/>hoc exerunt, & </s> <s xml:id="echoid-s2241" xml:space="preserve">conatur hoc per ambas ſimul lineas eodem tem-<lb/>pore moveri; </s> <s xml:id="echoid-s2242" xml:space="preserve">ſi autem per ambas ſimul transferatur dabitur in <lb/>b, in diagonali Ab, ductis eb ad Ad, & </s> <s xml:id="echoid-s2243" xml:space="preserve">db ad Ae parallelis; </s> <s xml:id="echoid-s2244" xml:space="preserve">am-<lb/>babus ergo potentiis conatur lineam Ab percurrer@ eo tempo-<lb/>re, quo poſſet percurrere Ae aut Ad; </s> <s xml:id="echoid-s2245" xml:space="preserve">duæ ergo memo-<lb/> <anchor type="note" xlink:label="note-0094-02a" xlink:href="note-0094-02"/> ratæ potentiæ adunicam per Ab agentem reducuntur, & </s> <s xml:id="echoid-s2246" xml:space="preserve">eſt <lb/>hæc potentia ad reliquas duas ut Ab ad Ad & </s> <s xml:id="echoid-s2247" xml:space="preserve">Ae, <lb/>id eſt, ut AB ad AD & </s> <s xml:id="echoid-s2248" xml:space="preserve">AE. </s> <s xml:id="echoid-s2249" xml:space="preserve">Æqualis eſt idcirco <lb/>potentia, qua punctum A trahitur per AB, poten-<lb/>tiæ, ad quam reliquæ duæ reducuntur, & </s> <s xml:id="echoid-s2250" xml:space="preserve">cum hac con-<lb/>trarie agit.</s> <s xml:id="echoid-s2251" xml:space="preserve"/> </p> <div xml:id="echoid-div360" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">107.</note> <note position="left" xlink:label="note-0094-02" xlink:href="note-0094-02a" xml:space="preserve">221.</note> </div> <p> <s xml:id="echoid-s2252" xml:space="preserve">Nota eſt triangulorum proprietas, latera eſſe inter ſe ut <lb/>ſinus angulorum oppoſitorum; </s> <s xml:id="echoid-s2253" xml:space="preserve">ſunt ergo in æquilibrio po-<lb/> <anchor type="note" xlink:label="note-0094-03a" xlink:href="note-0094-03"/> tentiæ tres, quæ ſunt inter ſe ut ſinus angulorum directioni-<lb/>bus potentiarum oppoſitarum formatorum. </s> <s xml:id="echoid-s2254" xml:space="preserve">Id eſt, poten-<lb/>tia quæ per <emph style="sc">A</emph>E agit, eſt ut ſinus anguli BAD, & </s> <s xml:id="echoid-s2255" xml:space="preserve">ſic de <lb/>cæteris.</s> <s xml:id="echoid-s2256" xml:space="preserve"/> </p> <div xml:id="echoid-div361" type="float" level="2" n="3"> <note position="left" xlink:label="note-0094-03" xlink:href="note-0094-03a" xml:space="preserve">222.</note> </div> </div> <div xml:id="echoid-div363" type="section" level="1" n="123"> <head xml:id="echoid-head179" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head180" style="it" xml:space="preserve">Qua demonſtrantur quæ ſpectant punctum quod filis ad <lb/>partes diverſas trabitur.</head> <p> <s xml:id="echoid-s2257" xml:space="preserve">Machina hæc conſtat ex orbe ligneo, diametri circiter o-<lb/> <anchor type="note" xlink:label="note-0094-04a" xlink:href="note-0094-04"/> cto pollicum, horizontalis eſt & </s> <s xml:id="echoid-s2258" xml:space="preserve">pede ſuſtinetur; </s> <s xml:id="echoid-s2259" xml:space="preserve">in medio <lb/> <anchor type="note" xlink:label="note-0094-05a" xlink:href="note-0094-05"/> craſſitiei ſulco circumdatur, quo Trochleæ ad libitum, in <lb/>quocunque circumferentiæ puncto, Machinæ junguntur. <lb/></s> <s xml:id="echoid-s2260" xml:space="preserve">Sulco enim huic inſeritur lamina ænea, cui Trochlea per-<lb/>pendiculariter cohæret, ut in Frepræſentatur.</s> <s xml:id="echoid-s2261" xml:space="preserve"/> </p> <div xml:id="echoid-div363" type="float" level="2" n="1"> <note position="left" xlink:label="note-0094-04" xlink:href="note-0094-04a" xml:space="preserve">223.</note> <note position="left" xlink:label="note-0094-05" xlink:href="note-0094-05a" xml:space="preserve">TAB X <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s2262" xml:space="preserve">Orbis prædictus in ſuperiori parte paululum excavatur, <lb/>ut recipiat orbem minorem <emph style="sc">DFa</emph>, craſſitiei quartæ partis u-<lb/>nius pollicis, & </s> <s xml:id="echoid-s2263" xml:space="preserve">paululum ſupra orbem primum prominen-<lb/>tem; </s> <s xml:id="echoid-s2264" xml:space="preserve">ita ut filum ſuper Trochleâ, ut dictum, Machinæ an-<lb/>nexâ, horizontaliter extenſum ſuperficiem <emph style="sc">Da</emph>F perſtrin-<lb/>gat.</s> <s xml:id="echoid-s2265" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2266" xml:space="preserve">Varii, pro variis Experimentis, tales requiruntur orbes <lb/>minores. </s> <s xml:id="echoid-s2267" xml:space="preserve">Charta ab utraque parte obteguntur, ut com- <pb file="0095" n="102"/> <anchor type="figure" xlink:label="fig-0095-01a" xlink:href="fig-0095-01"/> <pb file="0095a" n="103"/> <anchor type="figure" xlink:label="fig-0095a-01a" xlink:href="fig-0095a-01"/> <pb file="0096" n="104"/> <pb o="51" file="0097" n="105" rhead="MATHEMATICA, LIB. I. CAP. XV."/> mode lineæ, in ſequentibus memorandæ, in iis duci poſ-<lb/>ſint.</s> <s xml:id="echoid-s2268" xml:space="preserve"/> </p> <div xml:id="echoid-div364" type="float" level="2" n="2"> <figure xlink:label="fig-0095-01" xlink:href="fig-0095-01a"> <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0095-01"/> </figure> <figure xlink:label="fig-0095a-01" xlink:href="fig-0095a-01a"> <image file="0095a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0095a-01"/> </figure> </div> </div> <div xml:id="echoid-div366" type="section" level="1" n="124"> <head xml:id="echoid-head181" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s2269" xml:space="preserve">Sit C centrum orbis minoris memorati, & </s> <s xml:id="echoid-s2270" xml:space="preserve">in hoc deli-<lb/> <anchor type="note" xlink:label="note-0097-01a" xlink:href="note-0097-01"/> neatum triangulum <emph style="sc">A</emph>BC, cujus latera ſunt inter ſe ut 2. <lb/></s> <s xml:id="echoid-s2271" xml:space="preserve">3. </s> <s xml:id="echoid-s2272" xml:space="preserve">& </s> <s xml:id="echoid-s2273" xml:space="preserve">4.</s> <s xml:id="echoid-s2274" xml:space="preserve">; Detur linea CE lateri AB trianguli parallela, & </s> <s xml:id="echoid-s2275" xml:space="preserve"><lb/>continuetur latus AC verſus D.</s> <s xml:id="echoid-s2276" xml:space="preserve"/> </p> <div xml:id="echoid-div366" type="float" level="2" n="1"> <note position="right" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">224.</note> </div> <p> <s xml:id="echoid-s2277" xml:space="preserve">Nunc dentur tria fila in C juncta, & </s> <s xml:id="echoid-s2278" xml:space="preserve">juxta lineas CD, <lb/>CE, & </s> <s xml:id="echoid-s2279" xml:space="preserve">CB protenſa ſuper Trochleis majori orbi junctis; <lb/></s> <s xml:id="echoid-s2280" xml:space="preserve">Si filis CD, CE, & </s> <s xml:id="echoid-s2281" xml:space="preserve">CF, appendantur pondera quæ ſint inter <lb/>ſe ut 4. </s> <s xml:id="echoid-s2282" xml:space="preserve">3. </s> <s xml:id="echoid-s2283" xml:space="preserve">& </s> <s xml:id="echoid-s2284" xml:space="preserve">2. </s> <s xml:id="echoid-s2285" xml:space="preserve">fila non moventur, & </s> <s xml:id="echoid-s2286" xml:space="preserve">nodus in C quieſcit; </s> <s xml:id="echoid-s2287" xml:space="preserve"><lb/>ſi ex eo puncto dimoveatur nodus, non quieſcit.</s> <s xml:id="echoid-s2288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2289" xml:space="preserve">In hac propoſitione duæ potentiæ quæcunque cum tertia æ-<lb/>què pollent, id eſt, valent unicam potentiam, quæ in eadem <lb/>directione cum illa tertia, ſed contrarie, agit, & </s> <s xml:id="echoid-s2290" xml:space="preserve">illi ter-<lb/>tiæ æqualis eſt.</s> <s xml:id="echoid-s2291" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2292" xml:space="preserve">Quando quatuor potentiis punctum trahitur, dabitur æ-<lb/> <anchor type="note" xlink:label="note-0097-02a" xlink:href="note-0097-02"/> quilibrium, ſi reductis duabus potentiis ad unicam, hæc <lb/>potentia nova, cum duabus reliquis, ſit in conditione n. <lb/></s> <s xml:id="echoid-s2293" xml:space="preserve">220; </s> <s xml:id="echoid-s2294" xml:space="preserve">id eſt, ſi hiſce reliquis etiam ad unicam reductis, po-<lb/>tentia ex eo orta æqualis ſit, & </s> <s xml:id="echoid-s2295" xml:space="preserve">contrarie agat, cum poten-<lb/>tia nova ſtatim memorata.</s> <s xml:id="echoid-s2296" xml:space="preserve"/> </p> <div xml:id="echoid-div367" type="float" level="2" n="2"> <note position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">225.</note> </div> </div> <div xml:id="echoid-div369" type="section" level="1" n="125"> <head xml:id="echoid-head182" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s2297" xml:space="preserve">Punctum C trahitur quatuor filis, B verſus pondere dua-<lb/> <anchor type="note" xlink:label="note-0097-03a" xlink:href="note-0097-03"/> rum unciarum, F verſus pondere ſex unciarum, E verſus <lb/> <anchor type="note" xlink:label="note-0097-04a" xlink:href="note-0097-04"/> pondere quatuor unciarum & </s> <s xml:id="echoid-s2298" xml:space="preserve">tandem D verſus pondere o-<lb/>cto unciarum, & </s> <s xml:id="echoid-s2299" xml:space="preserve">datur æ quilibrium: </s> <s xml:id="echoid-s2300" xml:space="preserve">formato triangulo <lb/>CFa, aut parallelogrammo CFaE, potentiæ prædictæ per <lb/>CF & </s> <s xml:id="echoid-s2301" xml:space="preserve">CE reducuntur ad unicam agentem per Ca, cum <lb/>vi ponderis octo unciarum, & </s> <s xml:id="echoid-s2302" xml:space="preserve">tunc tres potentiæ per CB, <lb/>CD, Ca exhibent caſum n. </s> <s xml:id="echoid-s2303" xml:space="preserve">220; </s> <s xml:id="echoid-s2304" xml:space="preserve">& </s> <s xml:id="echoid-s2305" xml:space="preserve">ideo ſi potentiæ per <lb/>CB & </s> <s xml:id="echoid-s2306" xml:space="preserve">CD reducantur ad unicam per CA, aget in eadem <lb/>directione ſed contrarie cum potentia per Ca, & </s> <s xml:id="echoid-s2307" xml:space="preserve">huic æ-<lb/>qualis erit.</s> <s xml:id="echoid-s2308" xml:space="preserve"/> </p> <div xml:id="echoid-div369" type="float" level="2" n="1"> <note position="right" xlink:label="note-0097-03" xlink:href="note-0097-03a" xml:space="preserve">226.</note> <note position="right" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">TAB. X. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s2309" xml:space="preserve">Quæ hìc de quatuor potentiis dicuntur, de quinque <lb/> <anchor type="note" xlink:label="note-0097-05a" xlink:href="note-0097-05"/> & </s> <s xml:id="echoid-s2310" xml:space="preserve">pluribus dici potuiſſent; </s> <s xml:id="echoid-s2311" xml:space="preserve">ex quinque enim ſi duæ ad u- <pb o="52" file="0098" n="106" rhead="PHYSICES ELEMENTA"/> nam reducantur, incidimus in exemplum præcedens.</s> <s xml:id="echoid-s2312" xml:space="preserve"/> </p> <div xml:id="echoid-div370" type="float" level="2" n="2"> <note position="right" xlink:label="note-0097-05" xlink:href="note-0097-05a" xml:space="preserve">227.</note> </div> </div> <div xml:id="echoid-div372" type="section" level="1" n="126"> <head xml:id="echoid-head183" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s2313" xml:space="preserve">Punctum C quinque potentiis trahitur, filis CA, CB, <lb/> <anchor type="note" xlink:label="note-0098-01a" xlink:href="note-0098-01"/> CD, CE, & </s> <s xml:id="echoid-s2314" xml:space="preserve">CF; </s> <s xml:id="echoid-s2315" xml:space="preserve">potentiæ ſunt inter ſe ut pondera qui-<lb/> <anchor type="note" xlink:label="note-0098-02a" xlink:href="note-0098-02"/> bus fila trahuntur, & </s> <s xml:id="echoid-s2316" xml:space="preserve">illa habent inter ſe proportionem nu-<lb/>merorum Trochleis in figura adſcriptorum, & </s> <s xml:id="echoid-s2317" xml:space="preserve">æquilibrium <lb/>datur.</s> <s xml:id="echoid-s2318" xml:space="preserve"/> </p> <div xml:id="echoid-div372" type="float" level="2" n="1"> <note position="left" xlink:label="note-0098-01" xlink:href="note-0098-01a" xml:space="preserve">228.</note> <note position="left" xlink:label="note-0098-02" xlink:href="note-0098-02a" xml:space="preserve">TAB. IX. <lb/>fig. 1</note> </div> <p> <s xml:id="echoid-s2319" xml:space="preserve">Potentiæ per CB & </s> <s xml:id="echoid-s2320" xml:space="preserve">CD ad unicam reducuntur per <lb/>CG; </s> <s xml:id="echoid-s2321" xml:space="preserve">potentiæ agentes per CE & </s> <s xml:id="echoid-s2322" xml:space="preserve">CF ad unicam reducun-<lb/>tur per CH, & </s> <s xml:id="echoid-s2323" xml:space="preserve">ita verſamur in caſu n. </s> <s xml:id="echoid-s2324" xml:space="preserve">220; </s> <s xml:id="echoid-s2325" xml:space="preserve">tandem iſtæ <lb/>duæ novæ potentiæ, per CH & </s> <s xml:id="echoid-s2326" xml:space="preserve">CG, ad unicam reducun-<lb/>tur per Ca, quæ quintæ per CA æqualis eſt, & </s> <s xml:id="echoid-s2327" xml:space="preserve">cum hac <lb/>in eadem linea, ſed contrarie, agit.</s> <s xml:id="echoid-s2328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2329" xml:space="preserve">Ex memorata propoſitione n. </s> <s xml:id="echoid-s2330" xml:space="preserve">220. </s> <s xml:id="echoid-s2331" xml:space="preserve">deducimus ulterius, <lb/> <anchor type="note" xlink:label="note-0098-03a" xlink:href="note-0098-03"/> actionem potentiæ cujusvis poſſe reſolvi in actiones <lb/>duarum aliarum potentiarum, & </s> <s xml:id="echoid-s2332" xml:space="preserve">illud quidem innumeris <lb/>modis, propter innumera triangula, quæ formari poſſunt <lb/>ſervato eodem latere. </s> <s xml:id="echoid-s2333" xml:space="preserve">Eo poſſumus in omnibus Machinis <lb/>reducere potentiam oblique agentem ad directam, & </s> <s xml:id="echoid-s2334" xml:space="preserve">pro-<lb/>portionem inter directam & </s> <s xml:id="echoid-s2335" xml:space="preserve">obliquam determinare; </s> <s xml:id="echoid-s2336" xml:space="preserve">quod <lb/>exemplis ſequentibus, Experimentis confirmatis, patebit.</s> <s xml:id="echoid-s2337" xml:space="preserve"/> </p> <div xml:id="echoid-div373" type="float" level="2" n="2"> <note position="left" xlink:label="note-0098-03" xlink:href="note-0098-03a" xml:space="preserve">229.</note> </div> </div> <div xml:id="echoid-div375" type="section" level="1" n="127"> <head xml:id="echoid-head184" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s2338" xml:space="preserve">Vecti <emph style="sc">A</emph>B, cujus brachia ſunt æqualia, applicatur in B <lb/> <anchor type="note" xlink:label="note-0098-04a" xlink:href="note-0098-04"/> pondus P duarum librarum, & </s> <s xml:id="echoid-s2339" xml:space="preserve">in A potentia oblique agens <lb/> <anchor type="note" xlink:label="note-0098-05a" xlink:href="note-0098-05"/> per <emph style="sc">A</emph>D, & </s> <s xml:id="echoid-s2340" xml:space="preserve">quæ repræſentatur per pondus M. </s> <s xml:id="echoid-s2341" xml:space="preserve">Concipia-<lb/>tur linea DE vecti in ſitu horizontali parallela, & </s> <s xml:id="echoid-s2342" xml:space="preserve"><emph style="sc">A</emph>E ad il-<lb/>lam & </s> <s xml:id="echoid-s2343" xml:space="preserve">vectem perpendicularis; </s> <s xml:id="echoid-s2344" xml:space="preserve">nunc ſi <emph style="sc">A</emph>D ſit ad <emph style="sc">A</emph>E, ut <lb/>duo ad tria, & </s> <s xml:id="echoid-s2345" xml:space="preserve">pondus M ſit trium librarum, datur æqui-<lb/>librium.</s> <s xml:id="echoid-s2346" xml:space="preserve"/> </p> <div xml:id="echoid-div375" type="float" level="2" n="1"> <note position="left" xlink:label="note-0098-04" xlink:href="note-0098-04a" xml:space="preserve">230.</note> <note position="left" xlink:label="note-0098-05" xlink:href="note-0098-05a" xml:space="preserve">TAB. IX. <lb/>fig. 2. & 3.</note> </div> <p> <s xml:id="echoid-s2347" xml:space="preserve">Directio motus puncti A ex motu vectis eſt vecti perpen-<lb/> <anchor type="note" xlink:label="note-0098-06a" xlink:href="note-0098-06"/> dicularis, tendit ergo juxta lineam <emph style="sc">Ea</emph> prolongatam; </s> <s xml:id="echoid-s2348" xml:space="preserve">di-<lb/>ſtantia BA cum maneat ſemper eadem, in fig. </s> <s xml:id="echoid-s2349" xml:space="preserve">2 impeditur A ne <lb/>magis accedat ad B, & </s> <s xml:id="echoid-s2350" xml:space="preserve">quaſi repellitur per directionem <lb/>BA; </s> <s xml:id="echoid-s2351" xml:space="preserve">in fig. </s> <s xml:id="echoid-s2352" xml:space="preserve">3 receſſus puncti A à B cohibetur, & </s> <s xml:id="echoid-s2353" xml:space="preserve">ſic A qua-<lb/>ſi trahitur B verſus. </s> <s xml:id="echoid-s2354" xml:space="preserve">Ulterius punctum A pondere M trahitur <lb/>D verſus: </s> <s xml:id="echoid-s2355" xml:space="preserve">tribus ergo punctum hocce trahitur potentiis, qua- <pb o="53" file="0099" n="107" rhead="MATHEMATICA. LIB. I. CAP. XV."/> rum directiones ſunt parallelæ lateribus trianguli AED; </s> <s xml:id="echoid-s2356" xml:space="preserve">& </s> <s xml:id="echoid-s2357" xml:space="preserve"><lb/>quæ ergo, ut detur æquilibrium, ſunt inter ſe ut iſta latera.</s> <s xml:id="echoid-s2358" xml:space="preserve"/> </p> <div xml:id="echoid-div376" type="float" level="2" n="2"> <note position="left" xlink:label="note-0098-06" xlink:href="note-0098-06a" xml:space="preserve">231.</note> </div> <p> <s xml:id="echoid-s2359" xml:space="preserve">Punctum A, ob æqualitatem diſtantiarum punctorum A <lb/>& </s> <s xml:id="echoid-s2360" xml:space="preserve">B a fulcro, juxta <emph style="sc">Ea</emph> continuatam, trahitur eadem vi <lb/>qua pondus P deſcendit, id eſt, pondere duarum librarum; <lb/></s> <s xml:id="echoid-s2361" xml:space="preserve">vis ergo per AD requiritur trium librarum, quia latera AD <lb/>& </s> <s xml:id="echoid-s2362" xml:space="preserve">AE ſunt inter ſe ut tria ad duo. </s> <s xml:id="echoid-s2363" xml:space="preserve">Latus DE exprimit <lb/>quid fulcrum patiatur vi qua punctum A in fig. </s> <s xml:id="echoid-s2364" xml:space="preserve">2. </s> <s xml:id="echoid-s2365" xml:space="preserve">premitur <lb/>B verſus, & </s> <s xml:id="echoid-s2366" xml:space="preserve">in fig. </s> <s xml:id="echoid-s2367" xml:space="preserve">3. </s> <s xml:id="echoid-s2368" xml:space="preserve">à B retrahitur.</s> <s xml:id="echoid-s2369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2370" xml:space="preserve">Idem omnino dicendum de potentia obliqua axi in peri-<lb/>trochio applicata.</s> <s xml:id="echoid-s2371" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div378" type="section" level="1" n="128"> <head xml:id="echoid-head185" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s2372" xml:space="preserve">Pondus P, trochleæ annexum, ſuſtinetur potentiis ab u-<lb/> <anchor type="note" xlink:label="note-0099-01a" xlink:href="note-0099-01"/> traque parte funi ductario applicatis, ſed oblique trahenti-<lb/> <anchor type="note" xlink:label="note-0099-02a" xlink:href="note-0099-02"/> bus per CA & </s> <s xml:id="echoid-s2373" xml:space="preserve">CB; </s> <s xml:id="echoid-s2374" xml:space="preserve">hæ potentiæ ſunt æquales inter ſe, quia <lb/>omnis funis trochleam circumdans non quieſcit, niſi ab u-<lb/>traque parte æqualiter trahatur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2375" xml:space="preserve">ipſum pondus P eſt qua- <anchor type="note" xlink:label="note-0099-03a" xlink:href="note-0099-03"/> ſi tertia potentia, & </s> <s xml:id="echoid-s2376" xml:space="preserve">ita punctum C tribus potentiis trahi-<lb/>tur. </s> <s xml:id="echoid-s2377" xml:space="preserve">Concipiatur linea CE ad horizontem perpendicularis, <lb/>& </s> <s xml:id="echoid-s2378" xml:space="preserve">linea AE parallela lineæ CB: </s> <s xml:id="echoid-s2379" xml:space="preserve">ſi CE ſit ad AE aut AC, <lb/>(hæ enim duæ lineæ ſunt æquales, propter memoratam æ-<lb/>qualitatem potentiarum trahentium per CB, CA <anchor type="note" xlink:href="" symbol="*"/>,) ut <anchor type="note" xlink:label="note-0099-04a" xlink:href="note-0099-04"/> ſex ad quinque, pondus P ſex librarum a ponderibus Q & </s> <s xml:id="echoid-s2380" xml:space="preserve"><lb/>Q quinque librarum ſuſtinetur; </s> <s xml:id="echoid-s2381" xml:space="preserve">cujus ratio patet ex n. </s> <s xml:id="echoid-s2382" xml:space="preserve">220.</s> <s xml:id="echoid-s2383" xml:space="preserve"/> </p> <div xml:id="echoid-div378" type="float" level="2" n="1"> <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">232.</note> <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">TAB. IX. <lb/>fig. 4.</note> <note symbol="*" position="right" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">124.</note> <note symbol="*" position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">220.</note> </div> <p> <s xml:id="echoid-s2384" xml:space="preserve">Si extremitas una funis ductarii annectatur clavo, unico <lb/>pondere ut Q, pondus P ſuſtinetur.</s> <s xml:id="echoid-s2385" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div380" type="section" level="1" n="129"> <head xml:id="echoid-head186" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s2386" xml:space="preserve">Si pondus P Trochleæ non conjungatur, ſed funibus <emph style="sc">Ca</emph> <lb/> <anchor type="note" xlink:label="note-0099-05a" xlink:href="note-0099-05"/> & </s> <s xml:id="echoid-s2387" xml:space="preserve">CB, ei annexis, ſuſtineatur, poterit ſuſtineri poten-<lb/> <anchor type="note" xlink:label="note-0099-06a" xlink:href="note-0099-06"/> tiis duabus inæqualibus; </s> <s xml:id="echoid-s2388" xml:space="preserve">formetur ut in Experimento præ-<lb/>cedenti triangulum <emph style="sc">Ca</emph>E, & </s> <s xml:id="echoid-s2389" xml:space="preserve">ſit AE undecim, <emph style="sc">Ca</emph> duo-<lb/>decim cum ſemiſſe, & </s> <s xml:id="echoid-s2390" xml:space="preserve">CE duodecim; </s> <s xml:id="echoid-s2391" xml:space="preserve">dabitur æquilibri-<lb/>um, ſi pondera Q & </s> <s xml:id="echoid-s2392" xml:space="preserve">Q ſint ad P ut primi numeri ad ulti-<lb/>mum; </s> <s xml:id="echoid-s2393" xml:space="preserve">cujus Experimenti ratio iterum patet ex n. </s> <s xml:id="echoid-s2394" xml:space="preserve">220.</s> <s xml:id="echoid-s2395" xml:space="preserve"/> </p> <div xml:id="echoid-div380" type="float" level="2" n="1"> <note position="right" xlink:label="note-0099-05" xlink:href="note-0099-05a" xml:space="preserve">233.</note> <note position="right" xlink:label="note-0099-06" xlink:href="note-0099-06a" xml:space="preserve">TAB. IX. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s2396" xml:space="preserve">Hic in tranſitu obſervandum, ex datis inclinationibus fi-<lb/> <anchor type="note" xlink:label="note-0099-07a" xlink:href="note-0099-07"/> lorum <emph style="sc">Ca</emph> & </s> <s xml:id="echoid-s2397" xml:space="preserve">CB ad horizontem, proportionem ponderum <pb o="54" file="0100" n="108" rhead="PHYSICES ELEMENTA"/> Q, Q ad pondus P, ex tabulis Trigonometriæ poſſe deter-<lb/>minari. </s> <s xml:id="echoid-s2398" xml:space="preserve">Si in triangulo <emph style="sc">A</emph>CE concipiatur linea <emph style="sc">A</emph>e, per <lb/>punctum <emph style="sc">A</emph> ad horizontem parallela, & </s> <s xml:id="echoid-s2399" xml:space="preserve">illa habeatur pro <lb/>radio circuli, <emph style="sc">Ca</emph> erit ſecans, & </s> <s xml:id="echoid-s2400" xml:space="preserve">eC tangens anguli, quem <lb/>efficit <emph style="sc">Ca</emph> cum horizonte; </s> <s xml:id="echoid-s2401" xml:space="preserve">& </s> <s xml:id="echoid-s2402" xml:space="preserve"><emph style="sc">A</emph>E erit ſecans, & </s> <s xml:id="echoid-s2403" xml:space="preserve">eE tan-<lb/>gens anguli inclinationis fili CB ad horizontem: </s> <s xml:id="echoid-s2404" xml:space="preserve">unde pa-<lb/>tet pondera Q, Q, proportionalia eſſe prædictis ſecantibus, <lb/>& </s> <s xml:id="echoid-s2405" xml:space="preserve">pondus P proportionem ſequi ſummæ memoratarum tan-<lb/>gentium.</s> <s xml:id="echoid-s2406" xml:space="preserve"/> </p> <div xml:id="echoid-div381" type="float" level="2" n="2"> <note position="right" xlink:label="note-0099-07" xlink:href="note-0099-07a" xml:space="preserve">234.</note> </div> <p> <s xml:id="echoid-s2407" xml:space="preserve">In Machina, qua hæc ultima Experimenta peraguntur, <lb/>(cujus conſtructio ex ſola figura, ſi conferatur cum fig. </s> <s xml:id="echoid-s2408" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s2409" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2410" xml:space="preserve">V. </s> <s xml:id="echoid-s2411" xml:space="preserve">abunde liquet) ducantur lineæ, juxta quas fila, <lb/>quæ trochleas circumdant, extendi poſſint; </s> <s xml:id="echoid-s2412" xml:space="preserve">in medio linea-<lb/>rum adſcribantur numeri, deſignantes fecantes angulorum, <lb/>quos illæ lineæ cum horizonte efficiunt; </s> <s xml:id="echoid-s2413" xml:space="preserve">& </s> <s xml:id="echoid-s2414" xml:space="preserve">extremitatibus <lb/>linearum adſcribantur tangentes horum angulorum.</s> <s xml:id="echoid-s2415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2416" xml:space="preserve">Nunc in omni caſu ubi datur æquilibrium, pondera Q & </s> <s xml:id="echoid-s2417" xml:space="preserve"><lb/>Q ſunt ut numeri in medio linearum, juxta quas fila pro-<lb/>tenſa ſunt; </s> <s xml:id="echoid-s2418" xml:space="preserve">& </s> <s xml:id="echoid-s2419" xml:space="preserve">pondus P ut ſumma numerorum extremita-<lb/>tibus ambarum harum linearum adſcriptorum.</s> <s xml:id="echoid-s2420" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2421" xml:space="preserve">Vis qua corpus ſuper plano inclinato deſcendere cona-<lb/>tur, per ea quæ de puncto, quod tribus potentiis trahitur, <lb/>dicta ſunt, determinatur.</s> <s xml:id="echoid-s2422" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div383" type="section" level="1" n="130"> <head xml:id="echoid-head187" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s2423" xml:space="preserve">Planum inclinatum vocatur, quod cum horizonte efficit <lb/> <anchor type="note" xlink:label="note-0100-01a" xlink:href="note-0100-01"/> angulum obliquum.</s> <s xml:id="echoid-s2424" xml:space="preserve"/> </p> <div xml:id="echoid-div383" type="float" level="2" n="1"> <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">235.</note> </div> <p> <s xml:id="echoid-s2425" xml:space="preserve">CB repræſentat lineam horizonti parallelam, <emph style="sc">A</emph>B cum <lb/> <anchor type="note" xlink:label="note-0100-02a" xlink:href="note-0100-02"/> illa efficit angulum obliquum <emph style="sc">A</emph>BC, & </s> <s xml:id="echoid-s2426" xml:space="preserve">planum inclinatum re-<lb/>præſentat. </s> <s xml:id="echoid-s2427" xml:space="preserve"><emph style="sc">A</emph>b extremitate ſuperiori plani dimittitur per-<lb/>pendicularis linea <emph style="sc">A</emph>C ad horizontem.</s> <s xml:id="echoid-s2428" xml:space="preserve"/> </p> <div xml:id="echoid-div384" type="float" level="2" n="2"> <note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">TAB. X. <lb/>fig. 4.</note> </div> </div> <div xml:id="echoid-div386" type="section" level="1" n="131"> <head xml:id="echoid-head188" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s2429" xml:space="preserve">Longitudo AB vocatur Longitudo Plani.</s> <s xml:id="echoid-s2430" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">236.</note> </div> <div xml:id="echoid-div387" type="section" level="1" n="132"> <head xml:id="echoid-head189" xml:space="preserve"><emph style="sc">Definitio</emph> 3</head> <p> <s xml:id="echoid-s2431" xml:space="preserve">Linea AC vocatur Altitudo Plani.</s> <s xml:id="echoid-s2432" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">237.</note> <p> <s xml:id="echoid-s2433" xml:space="preserve">Corpus P plano <emph style="sc">A</emph>B impoſitum juxta directionem <emph style="sc">A</emph>B <lb/>ſuper Plano conatur deſcendere; </s> <s xml:id="echoid-s2434" xml:space="preserve">ponamus filo huic lineæ <pb o="55" file="0101" n="109" rhead="MATHEMATICA. LIB. I. CAP. XV."/> parallelo retineri ut quieſcat, plano ſuſtinetur, id eſt quaſi <lb/>pellitur, juxta directionem dc plano perpendicularem, tan-<lb/>dem gravitate verticaliter per ce conatur deſcendere. </s> <s xml:id="echoid-s2435" xml:space="preserve">Cor-<lb/>pus ergo P tribus quaſi trahitur potentiis, quarum directio-<lb/>nes lateribus trianguli ced parallelæ ſunt, ſed corpus qui-<lb/>eſcit, ſunt idcirco potentiæ inter ſe ut latera hujus triangu-<lb/> <anchor type="note" xlink:label="note-0101-01a" xlink:href="note-0101-01"/> li<anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s2436" xml:space="preserve">Ideo, vis qua corpus ſuper plano conatur deſcendere eſt <anchor type="note" xlink:label="note-0101-02a" xlink:href="note-0101-02"/> ad vim qua verticaliter conatur deſcendere, pondus nempe <lb/>corporis, ut de ad ce aut ut <emph style="sc">A</emph>C ad <emph style="sc">A</emph>B, id eſt, ut alti-<lb/>tudo plani ad hujus longitudinem, ſunt enim ſimilia triangula <lb/>rectangula cde, <emph style="sc">A</emph>BC, habentia angulos æquales ced, CAB <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2437" xml:space="preserve"/> </p> <div xml:id="echoid-div387" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">210.</note> <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">238.</note> </div> <note symbol="*" position="right" xml:space="preserve">29. El. I.</note> </div> <div xml:id="echoid-div389" type="section" level="1" n="133"> <head xml:id="echoid-head190" xml:space="preserve"><emph style="sc">Machina</emph>,</head> <head xml:id="echoid-head191" style="it" xml:space="preserve">Qua plani inclinati affectiones exhibentur.</head> <p> <s xml:id="echoid-s2438" xml:space="preserve">Planum NOQL in ſitu ponitur horizontali; </s> <s xml:id="echoid-s2439" xml:space="preserve">Planum AB <lb/> <anchor type="note" xlink:label="note-0101-04a" xlink:href="note-0101-04"/> IH circa cardines volvitur, & </s> <s xml:id="echoid-s2440" xml:space="preserve">ad inclinationem quam-<lb/> <anchor type="note" xlink:label="note-0101-05a" xlink:href="note-0101-05"/> cunque conſtituitur, ope cochleæ V & </s> <s xml:id="echoid-s2441" xml:space="preserve">quadrantis circu-<lb/>li t.</s> <s xml:id="echoid-s2442" xml:space="preserve"/> </p> <div xml:id="echoid-div389" type="float" level="2" n="1"> <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">239.</note> <note position="right" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">TAB. X. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s2443" xml:space="preserve">Regula lignea EF extremitati uni trochleam connexam <lb/>habet G; </s> <s xml:id="echoid-s2444" xml:space="preserve">circa alteram volvitur; </s> <s xml:id="echoid-s2445" xml:space="preserve">caputque D, in quo mo-<lb/>vetur, ubique in ſciſſura rs, cum plano NOQL connecti-<lb/>tur, auxilio cochleæ infra planum.</s> <s xml:id="echoid-s2446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2447" xml:space="preserve">M eſt cylindrus ligneus, cujus axis eſt chalybeus, & </s> <s xml:id="echoid-s2448" xml:space="preserve">cu-<lb/>jus baſes cylindrum paululum excedunt; </s> <s xml:id="echoid-s2449" xml:space="preserve">ita ut in revolu-<lb/>tione ſuper plano <emph style="sc">A</emph>BIH baſes ſolæ planum tangant.</s> <s xml:id="echoid-s2450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2451" xml:space="preserve">Suſtinetur cylindrus filo tranſeunte ſuper trochlea G; </s> <s xml:id="echoid-s2452" xml:space="preserve">quod <lb/>filum annectitur regulæ tenui æneæ, ita inflexæ, ut per e-<lb/>jus extremitates axis cylindri tranſeat, & </s> <s xml:id="echoid-s2453" xml:space="preserve">rotetur.</s> <s xml:id="echoid-s2454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2455" xml:space="preserve">In Experimentis ita diſponitur trochlea, inclinando re-<lb/>gulam EF, & </s> <s xml:id="echoid-s2456" xml:space="preserve">movendo caput Dper ſciſſuram rs; </s> <s xml:id="echoid-s2457" xml:space="preserve">ut fi-<lb/>lum, quo cylindrus ſuſtinetur, ſit parallelum plano inclina-<lb/>to <emph style="sc">A</emph>BIH.</s> <s xml:id="echoid-s2458" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div391" type="section" level="1" n="134"> <head xml:id="echoid-head192" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s2459" xml:space="preserve">Inclinetur utcumque planum <emph style="sc">A</emph>BIH, pondus corporis <lb/> <anchor type="note" xlink:label="note-0101-06a" xlink:href="note-0101-06"/> Meam habet rationem ad pondus P, quam longitudo plani <lb/><emph style="sc">A</emph>B ad illius altitudinem <emph style="sc">A</emph>C; </s> <s xml:id="echoid-s2460" xml:space="preserve">& </s> <s xml:id="echoid-s2461" xml:space="preserve">pondere P corpus M ſuſti-<lb/>ne tur ſuper plano inclinato, ubicunque ponatur.</s> <s xml:id="echoid-s2462" xml:space="preserve"/> </p> <div xml:id="echoid-div391" type="float" level="2" n="1"> <note position="right" xlink:label="note-0101-06" xlink:href="note-0101-06a" xml:space="preserve">240.</note> </div> <pb o="56" file="0102" n="110" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s2463" xml:space="preserve">Ut exactiſſimè experimenta inſtituantur, minora trian-<lb/>gula rectangula chartacea, aut potius lignea, ſunt adhiben-<lb/>da, & </s> <s xml:id="echoid-s2464" xml:space="preserve">ſuper his planum inclinandum; </s> <s xml:id="echoid-s2465" xml:space="preserve">ut commode & </s> <s xml:id="echoid-s2466" xml:space="preserve">ex-<lb/>acte longitudo plani cum altitudine conferatur.</s> <s xml:id="echoid-s2467" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div393" type="section" level="1" n="135"> <head xml:id="echoid-head193" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s2468" xml:space="preserve">In hoc Experimento eâdem ac in præcedenti utimur Ma-<lb/> <anchor type="note" xlink:label="note-0102-01a" xlink:href="note-0102-01"/> chinâ. </s> <s xml:id="echoid-s2469" xml:space="preserve">Corpus M plano inclinato AB impoſitum, ſuſtinetur <lb/> <anchor type="note" xlink:label="note-0102-02a" xlink:href="note-0102-02"/> potentiâ trahente per MS; </s> <s xml:id="echoid-s2470" xml:space="preserve">concipiantur linea MR, ad ho-<lb/>rizontem perpendicularis, & </s> <s xml:id="echoid-s2471" xml:space="preserve">ASR ad plani ſuperficiem <lb/>normalis: </s> <s xml:id="echoid-s2472" xml:space="preserve">in omni caſu ubi pondus P eſt ad pondus corpo-<lb/>ris M, ut MS ad <emph style="sc">Mr</emph>, corpus quieſcit.</s> <s xml:id="echoid-s2473" xml:space="preserve"/> </p> <div xml:id="echoid-div393" type="float" level="2" n="1"> <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">241.</note> <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">TAB. IX. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s2474" xml:space="preserve">Pondere ſuo corpus M trahitur juxta directionem RM, <lb/>plano inclinato ſuſtinetur directione ad planum perpendicu-<lb/>lari, & </s> <s xml:id="echoid-s2475" xml:space="preserve">Experimentum reducitur ad propoſitionem n. <lb/></s> <s xml:id="echoid-s2476" xml:space="preserve">220.</s> <s xml:id="echoid-s2477" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div395" type="section" level="1" n="136"> <head xml:id="echoid-head194" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s2478" xml:space="preserve">Vectis <emph style="sc">A</emph>CB brachia ſunt æqualia, & </s> <s xml:id="echoid-s2479" xml:space="preserve">angulum formant, <lb/> <anchor type="note" xlink:label="note-0102-03a" xlink:href="note-0102-03"/> ita ut ſi <emph style="sc">A</emph>C continuetur verſus D, & </s> <s xml:id="echoid-s2480" xml:space="preserve">BD ad CD perpen-<lb/> <anchor type="note" xlink:label="note-0102-04a" xlink:href="note-0102-04"/> dicularis ducatur, DC ſit dimidia pars ipſius BC aut CA. <lb/></s> <s xml:id="echoid-s2481" xml:space="preserve">Appenſo in <emph style="sc">A</emph> pondere p unius libræ, & </s> <s xml:id="echoid-s2482" xml:space="preserve">in B pondere P <lb/>duarum librarum, poſitoque brachio <emph style="sc">Ca</emph> in ſitu horizonta-<lb/>li, datur æquilibrium <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2483" xml:space="preserve">quia pondus Pagit quaſi in vecte <anchor type="note" xlink:label="note-0102-05a" xlink:href="note-0102-05"/> recto in puncto D eſſet ſuſpenſum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2484" xml:space="preserve"/> </p> <div xml:id="echoid-div395" type="float" level="2" n="1"> <note position="left" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">242.</note> <note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">TAB. IX. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">175.</note> </div> <note symbol="*" position="left" xml:space="preserve">128.</note> <p> <s xml:id="echoid-s2485" xml:space="preserve">Mutentur pondera, & </s> <s xml:id="echoid-s2486" xml:space="preserve">majus ſuſpendatur in A, minus <lb/> <anchor type="note" xlink:label="note-0102-07a" xlink:href="note-0102-07"/> vero imponatur brachio BC in B; </s> <s xml:id="echoid-s2487" xml:space="preserve">ſi plano verticali illius ca-<lb/>ſus impediatur, dabitur iterum æquilibrium.</s> <s xml:id="echoid-s2488" xml:space="preserve"/> </p> <div xml:id="echoid-div396" type="float" level="2" n="2"> <note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">TAB. IX. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s2489" xml:space="preserve">Brachia vectis ſunt æqualia, & </s> <s xml:id="echoid-s2490" xml:space="preserve">æqualiter motu vectis mo-<lb/>ventur: </s> <s xml:id="echoid-s2491" xml:space="preserve">vi ergo ponderis P pondus p quaſi trahitur verſus <lb/>E in directione ad brachium BC perpendiculari; </s> <s xml:id="echoid-s2492" xml:space="preserve">Ex actio-<lb/>ne plani verticalis premitur corpus illud horizontaliter; </s> <s xml:id="echoid-s2493" xml:space="preserve">& </s> <s xml:id="echoid-s2494" xml:space="preserve"><lb/>tandem vi gravitatis verticaliter pellitur. </s> <s xml:id="echoid-s2495" xml:space="preserve">Tribus igitur po-<lb/>tentiis trahitur pondus p, quæ ſunt inter ſe ut latera trian-<lb/>guli <emph style="sc">BE</emph>D <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2496" xml:space="preserve">Vis ergo tendens terram verſus (pondus p) <anchor type="note" xlink:label="note-0102-08a" xlink:href="note-0102-08"/> ſe habet ad vim trahentem E verſus (pondus P), ut BD ad BE, <lb/>aut DC ad CB <anchor type="note" xlink:href="" symbol="*"/>, ſeu <emph style="sc">Ca</emph>; </s> <s xml:id="echoid-s2497" xml:space="preserve">id eſt, ut unum ad duo; </s> <s xml:id="echoid-s2498" xml:space="preserve">quæ <anchor type="note" xlink:label="note-0102-09a" xlink:href="note-0102-09"/> etiam eſt ratio inter pondera p & </s> <s xml:id="echoid-s2499" xml:space="preserve">P. </s> <s xml:id="echoid-s2500" xml:space="preserve">Et hìc ergo ratio Ex- <pb file="0103" n="111"/> <anchor type="figure" xlink:label="fig-0103-01a" xlink:href="fig-0103-01"/> <pb file="0103a" n="112"/> <anchor type="figure" xlink:label="fig-0103a-01a" xlink:href="fig-0103a-01"/> <pb file="0104" n="113"/> <pb o="57" file="0105" n="114" rhead="MATHEMATICA. LIB. I. CAP. XVI."/> perimenti ex ſæpius memoraton. </s> <s xml:id="echoid-s2501" xml:space="preserve">220. </s> <s xml:id="echoid-s2502" xml:space="preserve">deducitur; </s> <s xml:id="echoid-s2503" xml:space="preserve">ad quem <lb/>omnes alii caſus potentiarum obliquarum, quæ excogitari <lb/>poſſunt, etiam pertient.</s> <s xml:id="echoid-s2504" xml:space="preserve"/> </p> <div xml:id="echoid-div397" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0102-08" xlink:href="note-0102-08a" xml:space="preserve">220.</note> <note symbol="*" position="left" xlink:label="note-0102-09" xlink:href="note-0102-09a" xml:space="preserve">8. El. VI.</note> <figure xlink:label="fig-0103-01" xlink:href="fig-0103-01a"> <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/> </figure> <figure xlink:label="fig-0103a-01" xlink:href="fig-0103a-01a"> <image file="0103a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103a-01"/> </figure> </div> </div> <div xml:id="echoid-div399" type="section" level="1" n="137"> <head xml:id="echoid-head195" style="it" xml:space="preserve">LIBRI I. PARS III.</head> <head xml:id="echoid-head196" xml:space="preserve">De Motibus, Potentiarum actionibus, <lb/>variatis.</head> <head xml:id="echoid-head197" xml:space="preserve">CAPUT XVI.</head> <head xml:id="echoid-head198" style="it" xml:space="preserve">De Naturæ legibus Newtonianis.</head> <p> <s xml:id="echoid-s2505" xml:space="preserve">Preſſiones contrariis preſſionibus deſtructas, & </s> <s xml:id="echoid-s2506" xml:space="preserve">obſtacu-<lb/>la immediatâ potentiæ actione translata, huc uſque <lb/>conſideravimus. </s> <s xml:id="echoid-s2507" xml:space="preserve">Nunc preſſiones in corpora ſibi per-<lb/>miſſa & </s> <s xml:id="echoid-s2508" xml:space="preserve">in motu perſeverantia, agentes examinabimus; <lb/></s> <s xml:id="echoid-s2509" xml:space="preserve">hìc ut in omnibus Phyſicis ex Phænomenis ratiocinandum eſt, <lb/>& </s> <s xml:id="echoid-s2510" xml:space="preserve">ex iis naturæ leges deduci debent.</s> <s xml:id="echoid-s2511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2512" xml:space="preserve">Tres a Newtono traduntur, quibus omnia, quæ ad mo-<lb/>tum pertinent, explicari poſſe credimus.</s> <s xml:id="echoid-s2513" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div400" type="section" level="1" n="138"> <head xml:id="echoid-head199" xml:space="preserve"><emph style="sc">Lex</emph> I.</head> <p style="it"> <s xml:id="echoid-s2514" xml:space="preserve">Corpus omne perſeverat in ſtatu ſuo quieſcendi vel mo-<lb/> <anchor type="note" xlink:label="note-0105-01a" xlink:href="note-0105-01"/> vendi uniformiter in directum, niſi quatenus a viribus im-<lb/>preſſis cogitur ſtatum illum mutare.</s> <s xml:id="echoid-s2515" xml:space="preserve"/> </p> <div xml:id="echoid-div400" type="float" level="2" n="1"> <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">243.</note> </div> <p> <s xml:id="echoid-s2516" xml:space="preserve">Videmus Corpus ſuâ naturâ eſſe iners & </s> <s xml:id="echoid-s2517" xml:space="preserve">incapax ſeſe mo-<lb/>vendi, unde niſi cauſâ extraneâ moveatur, in quiete ſem-<lb/>per neceſſario manet.</s> <s xml:id="echoid-s2518" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2519" xml:space="preserve">Corpus etiam ſemel motum in motu ſecundum eandem <lb/>rectam lineam eadem cum velocitate continuare quotidia-<lb/>nis Experimentis pleniſhme conſtat; </s> <s xml:id="echoid-s2520" xml:space="preserve">nullam enim unquam <lb/>mutationem in motu fieri videmus niſi aliqua ex cauſa.</s> <s xml:id="echoid-s2521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2522" xml:space="preserve">Corpus vi inſitâ transfertur, & </s> <s xml:id="echoid-s2523" xml:space="preserve">vis hæc, ut ex lege hac <lb/> <anchor type="note" xlink:label="note-0105-02a" xlink:href="note-0105-02"/> ſequitur, non mutatur niſi actione cauſæ extraneæ,</s> </p> <div xml:id="echoid-div401" type="float" level="2" n="2"> <note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">244.</note> </div> </div> <div xml:id="echoid-div403" type="section" level="1" n="139"> <head xml:id="echoid-head200" xml:space="preserve"><emph style="sc">Lex</emph> II.</head> <p style="it"> <s xml:id="echoid-s2524" xml:space="preserve">Mutatio motus eſt ſemper proportionalis vi motrici impreſ-<lb/> <anchor type="note" xlink:label="note-0105-03a" xlink:href="note-0105-03"/> <pb o="58" file="0106" n="115" rhead="PHYSICES ELEMENTA"/> ſæ, & </s> <s xml:id="echoid-s2525" xml:space="preserve">fit ſemper ſecundum rectam lineam, qua vis illa im-<lb/>primitur.</s> <s xml:id="echoid-s2526" xml:space="preserve"/> </p> <div xml:id="echoid-div403" type="float" level="2" n="1"> <note position="right" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">245.</note> </div> <p> <s xml:id="echoid-s2527" xml:space="preserve">Quando corpori moto alia ſuperadditur vis, ad illud mo-<lb/>vendum in eadem directione, motus celerior fit.</s> <s xml:id="echoid-s2528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2529" xml:space="preserve">Quando nova impreſſio, motui corporis contraria eſt, <lb/>retardatur motus.</s> <s xml:id="echoid-s2530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2531" xml:space="preserve">Si obliquè agat nova impreſſio, viam ſuam mutat cor-<lb/>pus.</s> <s xml:id="echoid-s2532" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2533" xml:space="preserve">Et in genere omnes mutationes in motu fiunt ſecundum <lb/>directiones & </s> <s xml:id="echoid-s2534" xml:space="preserve">pro magnitudinibus impreſſionum.</s> <s xml:id="echoid-s2535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2536" xml:space="preserve">Sit Corpus in A motum per AE celeritate, quam per <lb/> <anchor type="note" xlink:label="note-0106-01a" xlink:href="note-0106-01"/> hanc ipſam deſignamus lineam, agat in A impreſſio, juxta <lb/>directionem <emph style="sc">A</emph>D, quæ corpori (ut diximus) agitato juxta <lb/>hanc directionem communicat celeritatem <emph style="sc">A</emph>D. </s> <s xml:id="echoid-s2537" xml:space="preserve">Corpus <lb/>duobus nunc agitatur motibus, quibus lineæ <emph style="sc">A</emph>E & </s> <s xml:id="echoid-s2538" xml:space="preserve"><emph style="sc">A</emph>D eo-<lb/>dem tempore percurruntur; </s> <s xml:id="echoid-s2539" xml:space="preserve">hi duo motus ſeſe mutuo non <lb/>turbant, ſed motu ex ambobus compoſito, ſecundum hanc <lb/>legem, quæ ex Phænomenis fuit deducta, corpus fertur.</s> <s xml:id="echoid-s2540" xml:space="preserve"/> </p> <div xml:id="echoid-div404" type="float" level="2" n="2"> <note position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">TAB. X. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s2541" xml:space="preserve">Ut motum hunc compoſitum determinemus, concipiamus <lb/>lineam <emph style="sc">A</emph>D, dum in hac corpus movetur, motu parallelo <lb/>moveri celeritate, qua corpus fertur per <emph style="sc">A</emph>E quam in hoc mo-<lb/>tu punctum A percurrit. </s> <s xml:id="echoid-s2542" xml:space="preserve">Translata jam ſit linea in ad, cor-<lb/>pus erit in b, ita ut <emph style="sc">A</emph>E ſit ad <emph style="sc">A</emph>D, ut A a ad ab; </s> <s xml:id="echoid-s2543" xml:space="preserve">quia & </s> <s xml:id="echoid-s2544" xml:space="preserve"><lb/>motum lineæ, & </s> <s xml:id="echoid-s2545" xml:space="preserve">corporis, in hac æquabilem ponimus. </s> <s xml:id="echoid-s2546" xml:space="preserve">Ab-<lb/>ſoluto parallelogrammo <emph style="sc">A</emph><emph style="sc">DBe</emph>, & </s> <s xml:id="echoid-s2547" xml:space="preserve">ductâ diagonali <emph style="sc">A</emph>B, <lb/>clare patet punctum b in hac diagonali dari,& </s> <s xml:id="echoid-s2548" xml:space="preserve">corpus dari <lb/>in B, ubi linea <emph style="sc">A</emph>D motu ſuo pervenit ad <emph style="sc">E</emph>B: </s> <s xml:id="echoid-s2549" xml:space="preserve">motu ergo <lb/> <anchor type="note" xlink:label="note-0106-02a" xlink:href="note-0106-02"/> compoſito corpus percurrit diagonalem parallelogrammi for-<lb/>mati lineis, ſitu directiones, & </s> <s xml:id="echoid-s2550" xml:space="preserve">longitudinibus celeritates mo-<lb/>tuum deſignantibus; </s> <s xml:id="echoid-s2551" xml:space="preserve">diagonalis autem celeritatem motus com-<lb/>poſiti exprimit.</s> <s xml:id="echoid-s2552" xml:space="preserve"/> </p> <div xml:id="echoid-div405" type="float" level="2" n="3"> <note position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">246.</note> </div> <p> <s xml:id="echoid-s2553" xml:space="preserve">In ſequentibus videbimus & </s> <s xml:id="echoid-s2554" xml:space="preserve">legem reſpectu vis inſitæ lo-<lb/>cum habere, id eſt, vim inſitam corpori, per diagonalem <lb/>AB moto, æqualem eſſe viribus primæ per <emph style="sc">A</emph>E, & </s> <s xml:id="echoid-s2555" xml:space="preserve">ſecun-<lb/>dæ quæ corpori juxta <emph style="sc">A</emph>D communicatur. </s> <s xml:id="echoid-s2556" xml:space="preserve">Si nempe vis <lb/>ſecunda non pro parte cum prima contrarie agat, quod <pb o="59" file="0107" n="116" rhead="MATHEMATICA. LIS. I. CAP. XVI."/> obtinet, quando Angulus <emph style="sc">Ea</emph>D eſt obtuſus.</s> <s xml:id="echoid-s2557" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div407" type="section" level="1" n="140"> <head xml:id="echoid-head201" xml:space="preserve"><emph style="sc">Lex</emph> III.</head> <p style="it"> <s xml:id="echoid-s2558" xml:space="preserve">Actioni contraria ſemper & </s> <s xml:id="echoid-s2559" xml:space="preserve">æqualis eſt reactio; </s> <s xml:id="echoid-s2560" xml:space="preserve">ſive cor-<lb/> <anchor type="note" xlink:label="note-0107-01a" xlink:href="note-0107-01"/> porum duorum actiones in ſe mutuo ſemper ſunt æquales, & </s> <s xml:id="echoid-s2561" xml:space="preserve"><lb/>in partes contrarias diriguntur.</s> <s xml:id="echoid-s2562" xml:space="preserve"/> </p> <div xml:id="echoid-div407" type="float" level="2" n="1"> <note position="right" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s2563" xml:space="preserve">Quomodocunque corpus in aliud agat, ipſum reactionem <lb/>æqualem & </s> <s xml:id="echoid-s2564" xml:space="preserve">contrariam pati ſemper videmus. </s> <s xml:id="echoid-s2565" xml:space="preserve">Digito lapi-<lb/>dem premo, premitur æqualiter digitus a lapide. </s> <s xml:id="echoid-s2566" xml:space="preserve">Currume-<lb/>quus protrahit, à curru æqualiter retrotrahitur; </s> <s xml:id="echoid-s2567" xml:space="preserve">lora enim <lb/>æqualiter verſus utramque partem diſtenduntur.</s> <s xml:id="echoid-s2568" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2569" xml:space="preserve">Corpus in aliud impingitur, quæcumque ſit impreſſio, <lb/>utrumque æqualem patitur; </s> <s xml:id="echoid-s2570" xml:space="preserve">impreſſiones vero contrariæ ſunt: <lb/></s> <s xml:id="echoid-s2571" xml:space="preserve">illud pleniſſime confirmatur Experimentis circa colliſio-<lb/>nes corporum.</s> <s xml:id="echoid-s2572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2573" xml:space="preserve">Magnes ferrum ad ſe trahit, trahitur æqualiter a ferro.</s> <s xml:id="echoid-s2574" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div409" type="section" level="1" n="141"> <head xml:id="echoid-head202" xml:space="preserve"><emph style="sc">Experimentum</emph>.</head> <p> <s xml:id="echoid-s2575" xml:space="preserve">Suſpenditur magnes M, ita ut facillime moveri poſſit, & </s> <s xml:id="echoid-s2576" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0107-02a" xlink:href="note-0107-02"/> ferro admoto ad certam diſtantiam, accedit magnes ad fer-<lb/> <anchor type="note" xlink:label="note-0107-03a" xlink:href="note-0107-03"/> rum; </s> <s xml:id="echoid-s2577" xml:space="preserve">& </s> <s xml:id="echoid-s2578" xml:space="preserve">hoc retrahendo, antequam magnes ad hoc perve-<lb/>nerit, magnes ferrum ſequitur; </s> <s xml:id="echoid-s2579" xml:space="preserve">eodem omnino modo, ac <lb/>ferrum ad magnetem accedit, & </s> <s xml:id="echoid-s2580" xml:space="preserve">hunc ſequitur, quando il-<lb/>lud ſuſpenditur, & </s> <s xml:id="echoid-s2581" xml:space="preserve">magnes admovetur.</s> <s xml:id="echoid-s2582" xml:space="preserve"/> </p> <div xml:id="echoid-div409" type="float" level="2" n="1"> <note position="right" xlink:label="note-0107-02" xlink:href="note-0107-02a" xml:space="preserve">248.</note> <note position="right" xlink:label="note-0107-03" xlink:href="note-0107-03a" xml:space="preserve">TAB. X. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s2583" xml:space="preserve">Sedet quis in cymba, cymbam aliam æqualem, & </s> <s xml:id="echoid-s2584" xml:space="preserve">æqua-<lb/>liter onuſtam, fune trahit; </s> <s xml:id="echoid-s2585" xml:space="preserve">ambæ cymbæ æqualiter moven-<lb/>tur, & </s> <s xml:id="echoid-s2586" xml:space="preserve">in medio diſtantiæ primæ concurrunt: </s> <s xml:id="echoid-s2587" xml:space="preserve">ſi una cym-<lb/>ba altera ſit major, aut magis onuſta, pro diverſis quanti-<lb/>tatibus materiæ in ſingulis celeritates erunt diverſæ.</s> <s xml:id="echoid-s2588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2589" xml:space="preserve">Et hæc eadem lex generaliter in omnibus corporum a-<lb/>ctionibus in alia copora locum habet.</s> <s xml:id="echoid-s2590" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div411" type="section" level="1" n="142"> <head xml:id="echoid-head203" xml:space="preserve">CAPUT XVII.</head> <head xml:id="echoid-head204" style="it" xml:space="preserve">De Acceleratione & Retardatione Gravium.</head> <head xml:id="echoid-head205" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s2591" xml:space="preserve">MOtus acceleratus, eſt cujus celeritas omnibus momentis <lb/> <anchor type="note" xlink:label="note-0107-04a" xlink:href="note-0107-04"/> major fit.</s> <s xml:id="echoid-s2592" xml:space="preserve"/> </p> <div xml:id="echoid-div411" type="float" level="2" n="1"> <note position="right" xlink:label="note-0107-04" xlink:href="note-0107-04a" xml:space="preserve">249.</note> </div> <pb o="60" file="0108" n="117" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div413" type="section" level="1" n="143"> <head xml:id="echoid-head206" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s2593" xml:space="preserve">Motus retardatus, eſt cujus celeritas omnibus momentis mi-<lb/> <anchor type="note" xlink:label="note-0108-01a" xlink:href="note-0108-01"/> nuitur.</s> <s xml:id="echoid-s2594" xml:space="preserve"/> </p> <div xml:id="echoid-div413" type="float" level="2" n="1"> <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">250.</note> </div> <p> <s xml:id="echoid-s2595" xml:space="preserve">Vis gravitatis in omnia corpora pro quantitate materiæ <lb/>continuo agit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2596" xml:space="preserve">quæcunque fuerint, gravitate eodem <anchor type="note" xlink:label="note-0108-02a" xlink:href="note-0108-02"/> modo moventur. </s> <s xml:id="echoid-s2597" xml:space="preserve">Quando corpus liberè cadit, impreſſio <lb/>primi momenti in ſecundo momento non deſtruitur; </s> <s xml:id="echoid-s2598" xml:space="preserve">ergo ei <lb/>ſuperadditur impreſſio ſecundi momenti, & </s> <s xml:id="echoid-s2599" xml:space="preserve">ſic de cæteris; <lb/></s> <s xml:id="echoid-s2600" xml:space="preserve">motus igitur corporis libere cadentis eſt acceleratus, & </s> <s xml:id="echoid-s2601" xml:space="preserve">ex <lb/> <anchor type="note" xlink:label="note-0108-03a" xlink:href="note-0108-03"/> Phænomenis conſtat motum æquabiliter in temporibus æ-<lb/>qualibus accelerari; </s> <s xml:id="echoid-s2602" xml:space="preserve">quod deduci poteſt ex Exp. </s> <s xml:id="echoid-s2603" xml:space="preserve">n. </s> <s xml:id="echoid-s2604" xml:space="preserve">277.</s> <s xml:id="echoid-s2605" xml:space="preserve"/> </p> <div xml:id="echoid-div414" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0108-02" xlink:href="note-0108-02a" xml:space="preserve">124.</note> <note position="left" xlink:label="note-0108-03" xlink:href="note-0108-03a" xml:space="preserve">251.</note> </div> <p> <s xml:id="echoid-s2606" xml:space="preserve">Unde ſequitur gravitatem eodem modo agere in corpus mo-<lb/> <anchor type="note" xlink:label="note-0108-04a" xlink:href="note-0108-04"/> tum ac in corpus quieſcens; </s> <s xml:id="echoid-s2607" xml:space="preserve">ideò celeritates æquales, in mo-<lb/>mentis æqualibus, corpori communicat. </s> <s xml:id="echoid-s2608" xml:space="preserve">Unde celeritas, <lb/> <anchor type="note" xlink:label="note-0108-05a" xlink:href="note-0108-05"/> inter cadendum acquiſita, eſt ut tempus, in quo corpus ce-<lb/>cidit. </s> <s xml:id="echoid-s2609" xml:space="preserve">Velocitas ex. </s> <s xml:id="echoid-s2610" xml:space="preserve">gr. </s> <s xml:id="echoid-s2611" xml:space="preserve">in certo tempore acquiſita erit du-<lb/>pla, ſi tempus fuerit duplum; </s> <s xml:id="echoid-s2612" xml:space="preserve">& </s> <s xml:id="echoid-s2613" xml:space="preserve">tripla, ſi tempus triplum, <lb/>& </s> <s xml:id="echoid-s2614" xml:space="preserve">c.</s> <s xml:id="echoid-s2615" xml:space="preserve"/> </p> <div xml:id="echoid-div415" type="float" level="2" n="3"> <note position="left" xlink:label="note-0108-04" xlink:href="note-0108-04a" xml:space="preserve">252.</note> <note position="left" xlink:label="note-0108-05" xlink:href="note-0108-05a" xml:space="preserve">253.</note> </div> <p> <s xml:id="echoid-s2616" xml:space="preserve">Deſignetur tempus per lineam AB, & </s> <s xml:id="echoid-s2617" xml:space="preserve">initium temporis ſit <lb/> <anchor type="note" xlink:label="note-0108-06a" xlink:href="note-0108-06"/> A. </s> <s xml:id="echoid-s2618" xml:space="preserve">In triangulo ABE, lineæ 1f, 2g, 3h, quæ parallelæ ad <lb/> <anchor type="note" xlink:label="note-0108-07a" xlink:href="note-0108-07"/> baſin, per puncta 1,2,3, ducuntur, ſunt inter ſe ut illarum <lb/>diſtantiæ ab A, A1, A2, A3; </s> <s xml:id="echoid-s2619" xml:space="preserve">id eſt, ut tempora quæ per illas di-<lb/>ſtantias deſignantur; </s> <s xml:id="echoid-s2620" xml:space="preserve">& </s> <s xml:id="echoid-s2621" xml:space="preserve">velocitates corporis libere cadentis <lb/>poſt illa tempora denotant. </s> <s xml:id="echoid-s2622" xml:space="preserve">Si pro lineis Mathematicis aliæ <lb/>adhibeantur cum minima latitudine, unicuique æquali, non <lb/>eo mutatur proportio; </s> <s xml:id="echoid-s2623" xml:space="preserve">& </s> <s xml:id="echoid-s2624" xml:space="preserve">hæ minimæ ſuperficies æque præ-<lb/>dictas velocitates denotant. </s> <s xml:id="echoid-s2625" xml:space="preserve">In tempore minimo velocitas <lb/>pro æquabili haberi poteſt, & </s> <s xml:id="echoid-s2626" xml:space="preserve">ideo ſpatium in eo tempore <lb/>percurſum velocitati proportionale eſt <anchor type="note" xlink:href="" symbol="*"/>, eædemque minimæ <anchor type="note" xlink:label="note-0108-08a" xlink:href="note-0108-08"/> ſuperficies ſpatia minimis, ſed æqualibus, temporibus percur-<lb/>ſa deſignare poterunt: </s> <s xml:id="echoid-s2627" xml:space="preserve">Idcirco in unaquaque minima ſuperfi-<lb/>cie memorata, ſi latitudo ſuperficiei pro tempore habeatur, <lb/>ſuperficies ipſa ſpatium percurſum deſignabit. </s> <s xml:id="echoid-s2628" xml:space="preserve">Totum tem-<lb/>pus AB conſtat ex talibus temporibus minimis; </s> <s xml:id="echoid-s2629" xml:space="preserve">& </s> <s xml:id="echoid-s2630" xml:space="preserve">area tri-<lb/>anguli <emph style="sc">A</emph>BE formatur ex ſumma omnium ſuperficierum mi-<lb/>nimarum hiſce temporibus minimis reſpondentium: </s> <s xml:id="echoid-s2631" xml:space="preserve">area er- <pb o="61" file="0109" n="118" rhead="MATHEMATICA. LIB. I. CAP. XVII."/> go hæc ſpatium tempore <emph style="sc">A</emph>B percurſum deſignat. </s> <s xml:id="echoid-s2632" xml:space="preserve">Eodem <lb/>modo area trianguli A1 f repræſentat ſpatium tempore A1. <lb/></s> <s xml:id="echoid-s2633" xml:space="preserve">percurſum; </s> <s xml:id="echoid-s2634" xml:space="preserve">triangula hæc ſunt ſimilia, & </s> <s xml:id="echoid-s2635" xml:space="preserve">areæ illorum ſunt <lb/>inter ſe ut quadrata laterum <emph style="sc">A</emph>B, A1.</s> <s xml:id="echoid-s2636" xml:space="preserve">, id eſt, ſpatia ab i-<lb/> <anchor type="note" xlink:label="note-0109-01a" xlink:href="note-0109-01"/> nitio caſus percurſa ſunt inter ſe, ut quadrata temporum <lb/>per quæ corpus cecidit; </s> <s xml:id="echoid-s2637" xml:space="preserve">aut ut quadrata velocitatum inter <lb/>cadendum acquiſitarum.</s> <s xml:id="echoid-s2638" xml:space="preserve"/> </p> <div xml:id="echoid-div416" type="float" level="2" n="4"> <note position="left" xlink:label="note-0108-06" xlink:href="note-0108-06a" xml:space="preserve">254.</note> <note position="left" xlink:label="note-0108-07" xlink:href="note-0108-07a" xml:space="preserve">TAB. X. <lb/>fig. 8.</note> <note symbol="*" position="left" xlink:label="note-0108-08" xlink:href="note-0108-08a" xml:space="preserve">94.</note> <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">255.</note> </div> <p> <s xml:id="echoid-s2639" xml:space="preserve">Diviſo tempore <emph style="sc">A</emph>B in partes æquales, A1, 12, 23, <lb/> <anchor type="note" xlink:label="note-0109-02a" xlink:href="note-0109-02"/> 3B; </s> <s xml:id="echoid-s2640" xml:space="preserve">ducantur per diviſiones lineæ ad baſin parallelæ ſpa-<lb/>tia percurſa in illis partibus, id eſt, in primo, ſecundo, <lb/>tertio, & </s> <s xml:id="echoid-s2641" xml:space="preserve">c. </s> <s xml:id="echoid-s2642" xml:space="preserve">momento, poſitis momentis æqualibus, ſunt in-<lb/>ter ſe ut areæ A1f, 1fg2, 2gh3, 3hEB; </s> <s xml:id="echoid-s2643" xml:space="preserve">quæ areæ ut <lb/>ex inſpectione figuræ patet, ſunt inter ſe ut numeri impares <lb/>1. </s> <s xml:id="echoid-s2644" xml:space="preserve">3, 5. </s> <s xml:id="echoid-s2645" xml:space="preserve">7. </s> <s xml:id="echoid-s2646" xml:space="preserve">9.</s> <s xml:id="echoid-s2647" xml:space="preserve"/> </p> <div xml:id="echoid-div417" type="float" level="2" n="5"> <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">256.</note> </div> <p> <s xml:id="echoid-s2648" xml:space="preserve">Si corpus, poſtquam cecidit per tempus <emph style="sc">A</emph>B, non ulte-<lb/>rius acceleretur, ſed celeritate BE, eo caſu acquiſita, u-<lb/>niformiter motum continuet, per tempus BC, æquale tem-<lb/>pori caſus ſpatium eo motu percurſum deſignatur per aream <lb/>BEDC, duplam areæ trianguli ABE; </s> <s xml:id="echoid-s2649" xml:space="preserve">& </s> <s xml:id="echoid-s2650" xml:space="preserve">ideò</s> </p> <p style="it"> <s xml:id="echoid-s2651" xml:space="preserve">Corpus ab altitudine quacunque libere cadens, eacum celeri-<lb/> <anchor type="note" xlink:label="note-0109-03a" xlink:href="note-0109-03"/> tate, quam cadendo acquiſivit in tempore æqualitempori caſus, <lb/>motu æquabili, ſpatium duplum prædictæ altitudinis percurret.</s> <s xml:id="echoid-s2652" xml:space="preserve"/> </p> <div xml:id="echoid-div418" type="float" level="2" n="6"> <note position="right" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">257.</note> </div> <p> <s xml:id="echoid-s2653" xml:space="preserve">Quæ propoſitio in ſequentibus etiam Experimento con-<lb/>firmatur.</s> <s xml:id="echoid-s2654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2655" xml:space="preserve">Motus corporis in altum projecti eodem modo retardatur, <lb/>quo corporis cadentis motus acceleratur, ut ſequitur ex lege <lb/> <anchor type="note" xlink:label="note-0109-04a" xlink:href="note-0109-04"/> 2 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2656" xml:space="preserve">in hoc caſu vis gravitatis cum motu acquiſito conſpi- rat, in illo contrarie agit; </s> <s xml:id="echoid-s2657" xml:space="preserve">cum vero vis gravitatis omnibus <lb/>momentis æqualibus, æquales corpori celeritates commu-<lb/> <anchor type="note" xlink:label="note-0109-05a" xlink:href="note-0109-05"/> nicet <anchor type="note" xlink:href="" symbol="*"/>, celeritas corporis projecti in altum, æqualibus tempo- <anchor type="note" xlink:label="note-0109-06a" xlink:href="note-0109-06"/> ribus, æqualiter minuitur, aut retardatur.</s> <s xml:id="echoid-s2658" xml:space="preserve"/> </p> <div xml:id="echoid-div419" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0109-04" xlink:href="note-0109-04a" xml:space="preserve">245.</note> <note symbol="*" position="right" xlink:label="note-0109-05" xlink:href="note-0109-05a" xml:space="preserve">251.</note> <note position="right" xlink:label="note-0109-06" xlink:href="note-0109-06a" xml:space="preserve">258.</note> </div> <p> <s xml:id="echoid-s2659" xml:space="preserve">Vis eadem gravitatis generat motum in corpore cadente, <lb/>& </s> <s xml:id="echoid-s2660" xml:space="preserve">deſtruit in corpore adſcendente, agitque ſemper in corpus <lb/>motum ut in corpus quieſcens<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2661" xml:space="preserve">æqualibus ergo temporibus <anchor type="note" xlink:label="note-0109-07a" xlink:href="note-0109-07"/> celeritates eædem generantur, & </s> <s xml:id="echoid-s2662" xml:space="preserve">deſtr uuntur. </s> <s xml:id="echoid-s2663" xml:space="preserve">Corpus in <lb/> <anchor type="note" xlink:label="note-0109-08a" xlink:href="note-0109-08"/> altum projectum adſcendit, donec totum motum amiſerit;</s> <s xml:id="echoid-s2664" xml:space="preserve"> <pb o="62" file="0110" n="119" rhead="PHYSICES ELEMENTA"/> ideo adſcendit per tempus, in quo corpus cadendo poteſt ac-<lb/>quirere velocitatem, æqualem velocitati cum qua in altum <lb/>projicitur.</s> <s xml:id="echoid-s2665" xml:space="preserve"/> </p> <div xml:id="echoid-div420" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0109-07" xlink:href="note-0109-07a" xml:space="preserve">252.</note> <note position="right" xlink:label="note-0109-08" xlink:href="note-0109-08a" xml:space="preserve">259.</note> </div> <p> <s xml:id="echoid-s2666" xml:space="preserve">Si <emph style="sc">Ba</emph> repræſentet tempus, in quo corpus adſcendit, & </s> <s xml:id="echoid-s2667" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0110-01a" xlink:href="note-0110-01"/> BE celeritatem, cum qua in altum projicitur; </s> <s xml:id="echoid-s2668" xml:space="preserve">adſcenſus <lb/>ceſſat, ubi celeritas corporis nulla eſt, ideo lineæ paralle-<lb/>læ ad baſin in triangulo <emph style="sc">A</emph>BE repræſentant celeritates in <lb/>momentis temporis, quibus reſpondent <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2669" xml:space="preserve">area triangu- <anchor type="note" xlink:label="note-0110-02a" xlink:href="note-0110-02"/> li <emph style="sc">A</emph>BE ſpatium adſcendendo percurſum deſignat, ut ex de-<lb/>monſtratione, circa corpora cadentia data <anchor type="note" xlink:href="" symbol="*"/> poteſt deduci.</s> <s xml:id="echoid-s2670" xml:space="preserve"> <anchor type="note" xlink:label="note-0110-03a" xlink:href="note-0110-03"/> Cum autem BE ſit velocitas, quam corpus cadendo per <lb/>tempus <emph style="sc">A</emph>B poteſtacquirere<anchor type="note" xlink:href="" symbol="*"/>, triangulum hoc <emph style="sc">A</emph>BE idem eſt, <anchor type="note" xlink:label="note-0110-04a" xlink:href="note-0110-04"/> quod ſpatium cadendo percurſum repræſentat, dum cor-<lb/>pus inter cadendum hanc ipſam celeritatem BE acquirit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2671" xml:space="preserve"> <anchor type="note" xlink:label="note-0110-05a" xlink:href="note-0110-05"/> Unde ſequitur, corpus in altum projectum adſcendere ad <lb/> <anchor type="note" xlink:label="note-0110-06a" xlink:href="note-0110-06"/> eandem altitudinem, à qua cadendo poteſt acquirere veloci-<lb/>tatem, cum qua projicitur. </s> <s xml:id="echoid-s2672" xml:space="preserve">Et altitudines, ad quas corpo-<lb/> <anchor type="note" xlink:label="note-0110-07a" xlink:href="note-0110-07"/> ra cum diverſis velocitatibus projecta poſſunt adſcendere, eſſe <lb/>inter ſe ut quadrata illarum velocitatum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2673" xml:space="preserve"> <anchor type="note" xlink:label="note-0110-08a" xlink:href="note-0110-08"/> </s> </p> <div xml:id="echoid-div421" type="float" level="2" n="9"> <note position="left" xlink:label="note-0110-01" xlink:href="note-0110-01a" xml:space="preserve">260.</note> <note symbol="*" position="left" xlink:label="note-0110-02" xlink:href="note-0110-02a" xml:space="preserve">258.</note> <note symbol="*" position="left" xlink:label="note-0110-03" xlink:href="note-0110-03a" xml:space="preserve">254.</note> <note symbol="*" position="left" xlink:label="note-0110-04" xlink:href="note-0110-04a" xml:space="preserve">259.</note> <note symbol="*" position="left" xlink:label="note-0110-05" xlink:href="note-0110-05a" xml:space="preserve">254.</note> <note position="left" xlink:label="note-0110-06" xlink:href="note-0110-06a" xml:space="preserve">261.</note> <note position="left" xlink:label="note-0110-07" xlink:href="note-0110-07a" xml:space="preserve">262.</note> <note symbol="*" position="left" xlink:label="note-0110-08" xlink:href="note-0110-08a" xml:space="preserve">255.</note> </div> </div> <div xml:id="echoid-div423" type="section" level="1" n="144"> <head xml:id="echoid-head207" xml:space="preserve">CAPUT XVIII.</head> <head xml:id="echoid-head208" style="it" xml:space="preserve">De deſcenſu Gravium ſuper plano inclinato.</head> <p> <s xml:id="echoid-s2674" xml:space="preserve">Vis, qua corpus ſuper plano inclinato deſcendere cona-<lb/>tur, ex gravitate oritur, & </s> <s xml:id="echoid-s2675" xml:space="preserve">ejuſdem eſt naturæ cum <lb/>gravitate; </s> <s xml:id="echoid-s2676" xml:space="preserve">ideo vis illa, omnibus momentis, & </s> <s xml:id="echoid-s2677" xml:space="preserve">in omnibus <lb/>plani partibus, æqualis eſt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2678" xml:space="preserve">agit in corpus motum eo- <anchor type="note" xlink:label="note-0110-09a" xlink:href="note-0110-09"/> dem modo ac in corpus quieſcens <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s2679" xml:space="preserve">eâdem de cauſa motus <anchor type="note" xlink:label="note-0110-10a" xlink:href="note-0110-10"/> corporis, ſuper plano libere devolventis, ejuſdem eſt natur <lb/> <anchor type="note" xlink:label="note-0110-11a" xlink:href="note-0110-11"/> cum motu corporis libere cadentis; </s> <s xml:id="echoid-s2680" xml:space="preserve">& </s> <s xml:id="echoid-s2681" xml:space="preserve">quæ de hoc dicta <lb/>ſunt, de illo etiam affirmari poſſunt. </s> <s xml:id="echoid-s2682" xml:space="preserve">Eſt igitur motus æ-<lb/>quabiliter acceleratus in temporibus æqualibus <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s2683" xml:space="preserve">& </s> <s xml:id="echoid-s2684" xml:space="preserve">propo- <anchor type="note" xlink:label="note-0110-12a" xlink:href="note-0110-12"/> ſitiones num. </s> <s xml:id="echoid-s2685" xml:space="preserve">252. </s> <s xml:id="echoid-s2686" xml:space="preserve">253, 255. </s> <s xml:id="echoid-s2687" xml:space="preserve">256. </s> <s xml:id="echoid-s2688" xml:space="preserve">257. </s> <s xml:id="echoid-s2689" xml:space="preserve">258. </s> <s xml:id="echoid-s2690" xml:space="preserve">259. </s> <s xml:id="echoid-s2691" xml:space="preserve">261. </s> <s xml:id="echoid-s2692" xml:space="preserve">262. </s> <s xml:id="echoid-s2693" xml:space="preserve">ſi <lb/> <anchor type="note" xlink:label="note-0110-13a" xlink:href="note-0110-13"/> pro deſcenſu, & </s> <s xml:id="echoid-s2694" xml:space="preserve">adſcenſu directo, motus ſuper plano in-<lb/>clinato ponatur, hìc etiam locum habent.</s> <s xml:id="echoid-s2695" xml:space="preserve"/> </p> <div xml:id="echoid-div423" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0110-09" xlink:href="note-0110-09a" xml:space="preserve">116.</note> <note symbol="*" position="left" xlink:label="note-0110-10" xlink:href="note-0110-10a" xml:space="preserve">252.</note> <note position="left" xlink:label="note-0110-11" xlink:href="note-0110-11a" xml:space="preserve">263.</note> <note symbol="*" position="left" xlink:label="note-0110-12" xlink:href="note-0110-12a" xml:space="preserve">251.</note> <note position="left" xlink:label="note-0110-13" xlink:href="note-0110-13a" xml:space="preserve">264.</note> </div> <p> <s xml:id="echoid-s2696" xml:space="preserve">Celeritates, quibus corpora duo deſcendunt, quorum u-<lb/> <anchor type="note" xlink:label="note-0110-14a" xlink:href="note-0110-14"/> num libere cadit, & </s> <s xml:id="echoid-s2697" xml:space="preserve">alterum ſuper plano inclinato devolvi- <pb o="63" file="0111" n="120" rhead="MATHEMATICA. LIB. I. CAP XVIII."/> tur, ſi eodem tempore cadere incipiant, ſunt ſemper in ea-<lb/>dem ratione quam in principio caſus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2698" xml:space="preserve">ergo ſpatia eodem <anchor type="note" xlink:label="note-0111-01a" xlink:href="note-0111-01"/> tempore percurrunt, quæ ſunt in ratione longitudinis plani <lb/>ad illius altitudinem. <lb/></s> <s xml:id="echoid-s2699" xml:space="preserve"> <anchor type="note" xlink:label="note-0111-02a" xlink:href="note-0111-02"/> </s> </p> <div xml:id="echoid-div424" type="float" level="2" n="2"> <note position="left" xlink:label="note-0110-14" xlink:href="note-0110-14a" xml:space="preserve">265.</note> <note symbol="*" position="right" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">251. 263.</note> <note symbol="*" position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">237.</note> </div> <p> <s xml:id="echoid-s2700" xml:space="preserve">In plano <emph style="sc">A</emph>B ſpatium a corpore percurſum, dum aliud li-<lb/> <anchor type="note" xlink:label="note-0111-03a" xlink:href="note-0111-03"/> bere cadit per altitudinem plani <emph style="sc">A</emph>C, determinatur, du-<lb/> <anchor type="note" xlink:label="note-0111-04a" xlink:href="note-0111-04"/> cendo ad <emph style="sc">A</emph>B perpendicularem CG: </s> <s xml:id="echoid-s2701" xml:space="preserve">tunc enim longitudo <lb/>plani <emph style="sc">A</emph>B eſt ad illius altitudinem <emph style="sc">A</emph>C, ut <emph style="sc">A</emph>C ad <emph style="sc">A</emph>G<anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s2702" xml:space="preserve">Si <anchor type="note" xlink:label="note-0111-05a" xlink:href="note-0111-05"/> circulus deſcribatur diametro <emph style="sc">A</emph>C, punctum G erit in pe-<lb/>ripheria circuli; </s> <s xml:id="echoid-s2703" xml:space="preserve">quia angulus in ſemicirculo, ut <emph style="sc">A</emph>GC, <lb/>ſemper eſt rectus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2704" xml:space="preserve">& </s> <s xml:id="echoid-s2705" xml:space="preserve">ideo punctum ut G, pro plano ut- <anchor type="note" xlink:label="note-0111-06a" xlink:href="note-0111-06"/> cunque inclinato, ſemper eſt in eadem illa peripheria: </s> <s xml:id="echoid-s2706" xml:space="preserve">un-<lb/>de ſequitur, chordas omnes, ut <emph style="sc">A</emph>G eſſe inter ſe ut vires, <lb/>quibus corpora ſuper his deſcendere conantur; </s> <s xml:id="echoid-s2707" xml:space="preserve">& </s> <s xml:id="echoid-s2708" xml:space="preserve">has per-<lb/>curri a corporibus devolventibus, in tempore in quo cor-<lb/>pus, libere cadendo, poteſt percurrere diametrum <emph style="sc">A</emph>C; <lb/></s> <s xml:id="echoid-s2709" xml:space="preserve">& </s> <s xml:id="echoid-s2710" xml:space="preserve">ita tempora devolutionum per illas chordasſunt æqualia.</s> <s xml:id="echoid-s2711" xml:space="preserve"/> </p> <div xml:id="echoid-div425" type="float" level="2" n="3"> <note position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">266.</note> <note position="right" xlink:label="note-0111-04" xlink:href="note-0111-04a" xml:space="preserve">TAB. X. <lb/>fig. 9.</note> <note symbol="*" position="right" xlink:label="note-0111-05" xlink:href="note-0111-05a" xml:space="preserve">8 El. VI.</note> <note symbol="*" position="right" xlink:label="note-0111-06" xlink:href="note-0111-06a" xml:space="preserve">31 El. III.</note> </div> <p> <s xml:id="echoid-s2712" xml:space="preserve">Per punctum C nulla poteſt duci chorda ut HC, quin de-<lb/>tur per <emph style="sc">A</emph> chorda ut <emph style="sc">A</emph>G ei parallela, id eſt, æqualiter in-<lb/>clinata, & </s> <s xml:id="echoid-s2713" xml:space="preserve">æqualis; </s> <s xml:id="echoid-s2714" xml:space="preserve">igitur in ſemicirculo, ut <emph style="sc">A</emph>HC, Vires <lb/> <anchor type="note" xlink:label="note-0111-07a" xlink:href="note-0111-07"/> quibus corpora juxta chordas, in puncto infimo terminatas <lb/>deſcendere conantur, ſunt inter ſe ut hæ chordæ & </s> <s xml:id="echoid-s2715" xml:space="preserve">quando <lb/> <anchor type="note" xlink:label="note-0111-08a" xlink:href="note-0111-08"/> corpus ſibi permittitur eodem tempore, ad punctum infimum <lb/>ſemicirculi perveniet, ſive libere cadat juxta diametrum, <lb/>ſive deſcendat ſuper chorda HC quacunque.</s> <s xml:id="echoid-s2716" xml:space="preserve"/> </p> <div xml:id="echoid-div426" type="float" level="2" n="4"> <note position="right" xlink:label="note-0111-07" xlink:href="note-0111-07a" xml:space="preserve">267.</note> <note position="right" xlink:label="note-0111-08" xlink:href="note-0111-08a" xml:space="preserve">268.</note> </div> <p> <s xml:id="echoid-s2717" xml:space="preserve">Tempus devolutionis per totum planum <emph style="sc">A</emph>B poteſt confer-<lb/> <anchor type="note" xlink:label="note-0111-09a" xlink:href="note-0111-09"/> ri cum tempore deſcenſus per plani altitudinem <emph style="sc">A</emph>C; </s> <s xml:id="echoid-s2718" xml:space="preserve">nam <lb/>hocce tempus eſt æquale tempori devolutionis per <emph style="sc">A</emph>G; </s> <s xml:id="echoid-s2719" xml:space="preserve">& </s> <s xml:id="echoid-s2720" xml:space="preserve"><lb/>quadrata temporum ſunt inter ſe ut <emph style="sc">A</emph>B ad <emph style="sc">A</emph>G <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2721" xml:space="preserve">ſed <anchor type="note" xlink:label="note-0111-10a" xlink:href="note-0111-10"/> <emph style="sc">A</emph>B eſt ad <emph style="sc">A</emph>C ut <emph style="sc">A</emph>C ad <emph style="sc">A</emph>G: </s> <s xml:id="echoid-s2722" xml:space="preserve">quadrata igitur linearum <emph style="sc">A</emph>B & </s> <s xml:id="echoid-s2723" xml:space="preserve"><lb/><emph style="sc">A</emph>C ſunt inter ſe, ut <emph style="sc">A</emph>B ad <emph style="sc">A</emph>G; </s> <s xml:id="echoid-s2724" xml:space="preserve">& </s> <s xml:id="echoid-s2725" xml:space="preserve">ideo iſtæ lineæ <emph style="sc">A</emph>B <lb/>& </s> <s xml:id="echoid-s2726" xml:space="preserve"><emph style="sc">A</emph>C ſunt inter ſe, ut tempora deſcenſus per <emph style="sc">A</emph>B, & </s> <s xml:id="echoid-s2727" xml:space="preserve"><lb/><emph style="sc">A</emph>G, aut <emph style="sc">A</emph>C, id eſt, tempora, in eo caſu, ſunt ut ſpa-<lb/>tia percurſa.</s> <s xml:id="echoid-s2728" xml:space="preserve"/> </p> <div xml:id="echoid-div427" type="float" level="2" n="5"> <note position="right" xlink:label="note-0111-09" xlink:href="note-0111-09a" xml:space="preserve">269.</note> <note symbol="*" position="right" xlink:label="note-0111-10" xlink:href="note-0111-10a" xml:space="preserve">264 255.</note> </div> <p> <s xml:id="echoid-s2729" xml:space="preserve">In eodem caſu velocitates in fine deſcenſus ſunt æquales; <lb/></s> <s xml:id="echoid-s2730" xml:space="preserve"> <anchor type="note" xlink:label="note-0111-11a" xlink:href="note-0111-11"/> nam poſt tempora æqualia, quando corpora ſunt in G & </s> <s xml:id="echoid-s2731" xml:space="preserve">C, <pb o="64" file="0112" n="121" rhead="PHYSICES ELEMENTA"/> velocitates ſunt in eadem ratione quam in principio caſus <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s2732" xml:space="preserve"> <anchor type="note" xlink:label="note-0112-01a" xlink:href="note-0112-01"/> id eſt, ut AC ad <emph style="sc">A</emph>B <anchor type="note" xlink:href="" symbol="*"/> Quando corpus deſcendit a G ad B, <anchor type="note" xlink:label="note-0112-02a" xlink:href="note-0112-02"/> creſcit velocitas ut tempus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2733" xml:space="preserve">& </s> <s xml:id="echoid-s2734" xml:space="preserve">velocitas in G eſt ad velo- <anchor type="note" xlink:label="note-0112-03a" xlink:href="note-0112-03"/> citatem in B, ut <emph style="sc">A</emph>C ad <emph style="sc">A</emph>B <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s2735" xml:space="preserve">velocitates ergo in B & </s> <s xml:id="echoid-s2736" xml:space="preserve">C <anchor type="note" xlink:label="note-0112-04a" xlink:href="note-0112-04"/> eandem rationem habent ad velocitatem in G, & </s> <s xml:id="echoid-s2737" xml:space="preserve">ſunt æ-<lb/>quales. </s> <s xml:id="echoid-s2738" xml:space="preserve">Ex hiſce deducimus corpus eandem acquirere ve-<lb/> <anchor type="note" xlink:label="note-0112-05a" xlink:href="note-0112-05"/> locitatem, cadendo a certa altitudine, ſive directe cadat, <lb/>ſive per planum inclinatum devolvatur. </s> <s xml:id="echoid-s2739" xml:space="preserve">Et, cum angulus <lb/>inclinationis nullam adferat mutationem, poteſt corpus de-<lb/>volvi per plurima plana varie inclinata, & </s> <s xml:id="echoid-s2740" xml:space="preserve">etiam per cur-<lb/>vam, (quæ ut ex innumeris planis diverſe inclinatis concinna-<lb/>ta conſiderari poteſt) & </s> <s xml:id="echoid-s2741" xml:space="preserve">celeritas ſemper erit eadem, quando al-<lb/>titudo eſt æqualis. </s> <s xml:id="echoid-s2742" xml:space="preserve">Non enim intereſt, utrum Corpus de-<lb/> <anchor type="note" xlink:label="note-0112-06a" xlink:href="note-0112-06"/> ſcendat per <emph style="sc">A</emph>B an per <emph style="sc">Eb</emph>, in Beadem erit celeritas & </s> <s xml:id="echoid-s2743" xml:space="preserve">eo-<lb/>dem modo corpus movebitur per BC; </s> <s xml:id="echoid-s2744" xml:space="preserve">ideoque habebit in <lb/>C velocitatem, quam devolvendo per <emph style="sc">Ec</emph> potuiſſet acqui-<lb/>rere, & </s> <s xml:id="echoid-s2745" xml:space="preserve">in D velocitatem, quam cadendo per GD habuiſ-<lb/>ſet.</s> <s xml:id="echoid-s2746" xml:space="preserve"/> </p> <div xml:id="echoid-div428" type="float" level="2" n="6"> <note position="right" xlink:label="note-0111-11" xlink:href="note-0111-11a" xml:space="preserve">270.</note> <note symbol="*" position="left" xlink:label="note-0112-01" xlink:href="note-0112-01a" xml:space="preserve">251. 263.</note> <note symbol="*" position="left" xlink:label="note-0112-02" xlink:href="note-0112-02a" xml:space="preserve">237.</note> <note symbol="*" position="left" xlink:label="note-0112-03" xlink:href="note-0112-03a" xml:space="preserve">263.</note> <note symbol="*" position="left" xlink:label="note-0112-04" xlink:href="note-0112-04a" xml:space="preserve">269.</note> <note position="left" xlink:label="note-0112-05" xlink:href="note-0112-05a" xml:space="preserve">271</note> <note position="left" xlink:label="note-0112-06" xlink:href="note-0112-06a" xml:space="preserve">TAB. X. <lb/>fig. 10.</note> </div> </div> <div xml:id="echoid-div430" type="section" level="1" n="145"> <head xml:id="echoid-head209" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s2747" xml:space="preserve">In hoc Experimento notandum, corpus filo ſuſpenſum, <lb/> <anchor type="note" xlink:label="note-0112-07a" xlink:href="note-0112-07"/> & </s> <s xml:id="echoid-s2748" xml:space="preserve">cadendo curvam deſcribens, eodem modo cadere ac ſi <lb/>eandem curvam, in plano excavatam, ſine attritu percur-<lb/>reret. </s> <s xml:id="echoid-s2749" xml:space="preserve">Corpus filo ſuſpenſum cadat ab altitudine <emph style="sc">A</emph>C, <lb/> <anchor type="note" xlink:label="note-0112-08a" xlink:href="note-0112-08"/> per curvam DC, & </s> <s xml:id="echoid-s2750" xml:space="preserve">per curvam EC, & </s> <s xml:id="echoid-s2751" xml:space="preserve">per curvam FGHC <lb/>ex portionibus variorum circulorum formatam, & </s> <s xml:id="echoid-s2752" xml:space="preserve">in <lb/>omni caſu, ad eandem altitudinem eandem percurrens curvam <lb/>adſcendet.</s> <s xml:id="echoid-s2753" xml:space="preserve"/> </p> <div xml:id="echoid-div430" type="float" level="2" n="1"> <note position="left" xlink:label="note-0112-07" xlink:href="note-0112-07a" xml:space="preserve">272</note> <note position="left" xlink:label="note-0112-08" xlink:href="note-0112-08a" xml:space="preserve">TAB. XI. <lb/>fig 1.</note> </div> <p style="it"> <s xml:id="echoid-s2754" xml:space="preserve">Corpus ea cum celeritate, quam cadendo per ſuperficiem <lb/> <anchor type="note" xlink:label="note-0112-09a" xlink:href="note-0112-09"/> quamcunque, ſive planam, ſive curvam, acquiſivit, per a-<lb/>liam ſuperficiem ſimilem ad eandem altitudinem, eodem tem-<lb/>pore, adſcendere poteſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2755" xml:space="preserve"> <anchor type="note" xlink:label="note-0112-10a" xlink:href="note-0112-10"/> </s> </p> <div xml:id="echoid-div431" type="float" level="2" n="2"> <note position="left" xlink:label="note-0112-09" xlink:href="note-0112-09a" xml:space="preserve">273.</note> <note symbol="*" position="left" xlink:label="note-0112-10" xlink:href="note-0112-10a" xml:space="preserve">259. 264. 271.</note> </div> <p style="it"> <s xml:id="echoid-s2756" xml:space="preserve">Corpus ea cum celeritate, quam cadendo a certa altitudi-<lb/> <anchor type="note" xlink:label="note-0112-11a" xlink:href="note-0112-11"/> ne acquiſivit, ad eandem altitudinem per curvam quamcun-<lb/>que adſcendere poteſt.</s> <s xml:id="echoid-s2757" xml:space="preserve"/> </p> <div xml:id="echoid-div432" type="float" level="2" n="3"> <note position="left" xlink:label="note-0112-11" xlink:href="note-0112-11a" xml:space="preserve">274.</note> </div> </div> <div xml:id="echoid-div434" type="section" level="1" n="146"> <head xml:id="echoid-head210" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s2758" xml:space="preserve">Corpus P filo ſuſpenſum cadat ab altitudine <emph style="sc">A</emph>C, per <lb/> <anchor type="note" xlink:label="note-0112-12a" xlink:href="note-0112-12"/> <pb file="0113" n="122"/> <anchor type="figure" xlink:label="fig-0113-01a" xlink:href="fig-0113-01"/> <pb file="0113a" n="123"/> <anchor type="figure" xlink:label="fig-0113a-01a" xlink:href="fig-0113a-01"/> <pb file="0114" n="124"/> <pb o="65" file="0115" n="125" rhead="MATHEMATICA. LIB. I. CAP. XVIII."/> curvam quamcunque BC; </s> <s xml:id="echoid-s2759" xml:space="preserve">celeritate eo acquiſita adſcendet <lb/> <anchor type="note" xlink:label="note-0115-01a" xlink:href="note-0115-01"/> ad eandem altitudinem aliam partem verſus per cur-<lb/>vas CD, aut CE, aut C HGF.</s> <s xml:id="echoid-s2760" xml:space="preserve"/> </p> <div xml:id="echoid-div434" type="float" level="2" n="1"> <note position="left" xlink:label="note-0112-12" xlink:href="note-0112-12a" xml:space="preserve">275. <lb/>FAB. VIII. <lb/>fig. 1.</note> <figure xlink:label="fig-0113-01" xlink:href="fig-0113-01a"> <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/> </figure> <figure xlink:label="fig-0113a-01" xlink:href="fig-0113a-01a"> <image file="0113a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113a-01"/> </figure> <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">TAB. XI. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s2761" xml:space="preserve">Ex demonſtratis in hoc capite <anchor type="note" xlink:href="" symbol="*"/>, deducimus methodum <anchor type="note" xlink:label="note-0115-02a" xlink:href="note-0115-02"/> confirmandi experimentis, quæ de velocitate Corporum <lb/>cadentium antea ſunt demonſtrata <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2762" xml:space="preserve"/> </p> <div xml:id="echoid-div435" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0115-02" xlink:href="note-0115-02a" xml:space="preserve">71.</note> </div> <note symbol="*" position="right" xml:space="preserve">2553</note> </div> <div xml:id="echoid-div437" type="section" level="1" n="147"> <head xml:id="echoid-head211" xml:space="preserve"><emph style="sc">Machina</emph>, <lb/>Qua corporum Cadentium velocitates conferuntur.</head> <p> <s xml:id="echoid-s2763" xml:space="preserve">Ex ligno cujus craſſities AB eſt duorum pollicum, & </s> <s xml:id="echoid-s2764" xml:space="preserve">alti-<lb/> <anchor type="note" xlink:label="note-0115-04a" xlink:href="note-0115-04"/> tudo circiter pollicum novem, formatur machina hæc; </s> <s xml:id="echoid-s2765" xml:space="preserve">ex-<lb/> <anchor type="note" xlink:label="note-0115-05a" xlink:href="note-0115-05"/> cavatur lignum juxta portionem cycloïdis à ſuperiori parte <lb/>ligni ad F uſque, ubi curva terminatur in ipſius vertice; <lb/></s> <s xml:id="echoid-s2766" xml:space="preserve">continuaturque lignum ab F ad G, juxta tangentem ad cur-<lb/>vam in vertice F, cujus diſtantia a G eſt unius pedis. </s> <s xml:id="echoid-s2767" xml:space="preserve">Ut <lb/>lignum hoc exactiſſimè ſit elaboratum habeatque ſuperfi-<lb/>ciem admodum politam deſideratur. </s> <s xml:id="echoid-s2768" xml:space="preserve">Formationem autem <lb/>cycloïdis in capite ſequenti explicamus.</s> <s xml:id="echoid-s2769" xml:space="preserve"/> </p> <div xml:id="echoid-div437" type="float" level="2" n="1"> <note position="right" xlink:label="note-0115-04" xlink:href="note-0115-04a" xml:space="preserve">276.</note> <note position="right" xlink:label="note-0115-05" xlink:href="note-0115-05a" xml:space="preserve">TAB. XII, <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s2770" xml:space="preserve">Lignum hoc circumdatur regulis ligneis HH, HI, II; <lb/></s> <s xml:id="echoid-s2771" xml:space="preserve">& </s> <s xml:id="echoid-s2772" xml:space="preserve">ſpatium quod hiſce continetur in duos quaſi canales divi-<lb/>ditur regulâ LL, cujus altitudo eſt quartæ partis unius pol-<lb/>licis.</s> <s xml:id="echoid-s2773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2774" xml:space="preserve">In Canali utroque movetur globus æneus diametri ſemi <lb/>pollicis, in utroque etiam datur obex O, hi ope cochleæ <lb/>lateralis ubi deſideraveris firmantur.</s> <s xml:id="echoid-s2775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2776" xml:space="preserve">Machina tribus ſuſtinetur cochleis æneis, quarum duæ vi-<lb/>dentur in C, C; </s> <s xml:id="echoid-s2777" xml:space="preserve">harum ope ſuperficies FG in ſitu ponitur <lb/>horizontali, cujus ſitus indicium dat perpendiculum NM.</s> <s xml:id="echoid-s2778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2779" xml:space="preserve">Regula LL in ſuperiori parte dividitur, ab F ad G in <lb/>partes æquales, ab F autem ſurſum inæquales ſunt; </s> <s xml:id="echoid-s2780" xml:space="preserve">ſed de-<lb/>monſtrant intervalla æqualia inter altitudines.</s> <s xml:id="echoid-s2781" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2782" xml:space="preserve">Hujus Machinæ hæc eſt proprietas, ut globi ab altitudi-<lb/>nibus, utcunque inæqualibus, dimiſſi, æqualibus tempo-<lb/>ribus ad F perveniant, quod facile patebit ſi obices O, O, <lb/>in F firmentur, & </s> <s xml:id="echoid-s2783" xml:space="preserve">globi eodem momento a diverſis altitu-<lb/>dinibus dimittantur.</s> <s xml:id="echoid-s2784" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2785" xml:space="preserve">Qui hujus proprietatis Geometricam deſiderant demon- <pb o="66" file="0116" n="126" rhead="PHYSICES ELEMENTA"/> ſtrationem caput ſequens adeant; </s> <s xml:id="echoid-s2786" xml:space="preserve">ipſam in machina obſerva-<lb/>re proprietatem in hoc loco ſufficit.</s> <s xml:id="echoid-s2787" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div439" type="section" level="1" n="148"> <head xml:id="echoid-head212" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s2788" xml:space="preserve">Conſtitutâ machinâ, ut dictum, firmentur obices, appli-<lb/> <anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/> cato uno diviſioni quartæ ab F, altero diviſioni ſextæ. </s> <s xml:id="echoid-s2789" xml:space="preserve">Si <lb/>nunc globi dimittantur eodem momento ab altitudinibus, <lb/>quæ ſunt, ut quatuor ad novem, dimiſſo nempe globo illo a mi-<lb/>nori altitudine qui datur in canali, in quo obex minus ab F <lb/>diſtat, eodem etiam momento quàm exactiſſime ad obices <lb/>pervenient.</s> <s xml:id="echoid-s2790" xml:space="preserve"/> </p> <div xml:id="echoid-div439" type="float" level="2" n="1"> <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">277.</note> </div> <p> <s xml:id="echoid-s2791" xml:space="preserve">Globi hi eodem momento in F dantur, æqualibus ergo <lb/>temporibus percurrunt lineas, quæ ſunt ut quatuor ad ſex, <lb/>id eſt, ut duo ad tria, in qua ratione ſunt horum globorum <lb/>velocitates <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2792" xml:space="preserve">horum numerorum quadrata ſunt quatuor &</s> <s xml:id="echoid-s2793" xml:space="preserve"> <anchor type="note" xlink:label="note-0116-02a" xlink:href="note-0116-02"/> novem, id eſt in ratione altitudinum a quibus cadendocor-<lb/>pora acquiſivere velocitates ſuas; </s> <s xml:id="echoid-s2794" xml:space="preserve">quod Experimento confir-<lb/>mandum erat.</s> <s xml:id="echoid-s2795" xml:space="preserve"/> </p> <div xml:id="echoid-div440" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">94.</note> </div> <p> <s xml:id="echoid-s2796" xml:space="preserve">In conſtituendis obicibus ad globorum magnitudinem at-<lb/>tendendum.</s> <s xml:id="echoid-s2797" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div442" type="section" level="1" n="149"> <head xml:id="echoid-head213" xml:space="preserve">CAPUT XIX.</head> <head xml:id="echoid-head214" style="it" xml:space="preserve">De Oſcillatione pendulorum.</head> <head xml:id="echoid-head215" xml:space="preserve"><emph style="sc">Definitio.</emph></head> <p> <s xml:id="echoid-s2798" xml:space="preserve">G Rave, filo tenuiſſimo ſuſpenſium, & </s> <s xml:id="echoid-s2799" xml:space="preserve">cum filo, circa fili <lb/> <anchor type="note" xlink:label="note-0116-03a" xlink:href="note-0116-03"/> punctum fixum, mobile, vocatur Pendulum.</s> <s xml:id="echoid-s2800" xml:space="preserve"/> </p> <div xml:id="echoid-div442" type="float" level="2" n="1"> <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">278.</note> </div> <p> <s xml:id="echoid-s2801" xml:space="preserve">Motus penduli eſt vibratorius, ſeu oſcillatorius.</s> <s xml:id="echoid-s2802" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2803" xml:space="preserve">Quando pondus, filo extenſo, ab una parte elevatur, <lb/>gravitate deſcendit, & </s> <s xml:id="echoid-s2804" xml:space="preserve">celeritate acquiſita ad eandem alti-<lb/>tudinem aliam partem verſus adſcendit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2805" xml:space="preserve">gravitate deinde ite- <anchor type="note" xlink:label="note-0116-04a" xlink:href="note-0116-04"/> rum redit; </s> <s xml:id="echoid-s2806" xml:space="preserve">& </s> <s xml:id="echoid-s2807" xml:space="preserve">vibrationes continuat.</s> <s xml:id="echoid-s2808" xml:space="preserve"/> </p> <div xml:id="echoid-div443" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0116-04" xlink:href="note-0116-04a" xml:space="preserve">273.</note> </div> <p> <s xml:id="echoid-s2809" xml:space="preserve">Rationem circa punctum ſuſpenſionis liberrimam hìc po-<lb/>nimus, & </s> <s xml:id="echoid-s2810" xml:space="preserve">nullam dari aëris reſiſtentiam; </s> <s xml:id="echoid-s2811" xml:space="preserve">quæ in majoribus <lb/>pendulis admodum eſt exigua.</s> <s xml:id="echoid-s2812" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">TAB. XI. <lb/>fig. 2.</note> <p> <s xml:id="echoid-s2813" xml:space="preserve">In motu ſuo corpus P deſcribit portionem circuli PBF; <lb/></s> <s xml:id="echoid-s2814" xml:space="preserve">ſi loco hujus motus corpus deſcendat per chordam PB; </s> <s xml:id="echoid-s2815" xml:space="preserve">& </s> <s xml:id="echoid-s2816" xml:space="preserve">i-<lb/> <anchor type="note" xlink:label="note-0116-06a" xlink:href="note-0116-06"/> terum adſcendat per chordam BF; </s> <s xml:id="echoid-s2817" xml:space="preserve">& </s> <s xml:id="echoid-s2818" xml:space="preserve">vibrationes ſuas per <lb/>chordas peragat; </s> <s xml:id="echoid-s2819" xml:space="preserve">deſcenſus fiet in tempore, in quo corpus ca- <pb o="67" file="0117" n="127" rhead="MATHEMATICA. LIB. I. CAP. XIX."/> dendo poteſt percurrere diametrum AB <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2820" xml:space="preserve">id eſt, longitudi- <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/> nem duplam longitudinis penduli: </s> <s xml:id="echoid-s2821" xml:space="preserve">in tempore æquali, ad-<lb/>ſcendet per chordam BF <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2822" xml:space="preserve">in tempore ergo integræ vibr atio- <anchor type="note" xlink:label="note-0117-02a" xlink:href="note-0117-02"/> nis, corpus cadendo poſſet percurrere quatuor diametros <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2823" xml:space="preserve">id eſt, <anchor type="note" xlink:label="note-0117-03a" xlink:href="note-0117-03"/> longitudinem octuplam longitudinis penduli. </s> <s xml:id="echoid-s2824" xml:space="preserve">Cumque deſcen-<lb/>ſus & </s> <s xml:id="echoid-s2825" xml:space="preserve">adſcenſus per omnes chordas fiat in tempore æquali, o-<lb/>mnes vibrationes per chordas, ſive magnas, ſive exiguas, ſunt æ-<lb/>què diuturnæ. </s> <s xml:id="echoid-s2826" xml:space="preserve">In vibrationibus exiguis harum durationes, dum <lb/>in circulo movetur corpus, cum durationibus vibrationum in <lb/>chordis conſtantem rationem habent, nempe quæ datur inter <lb/>circuli peripheriæ quadrantem & </s> <s xml:id="echoid-s2827" xml:space="preserve">diametrum; </s> <s xml:id="echoid-s2828" xml:space="preserve">idcirco ejuſdem <lb/> <anchor type="note" xlink:label="note-0117-04a" xlink:href="note-0117-04"/> penduli vibrationes exiguæ, licet inæquales, ad ſenſum ſunt <lb/>æque diuturnæ.</s> <s xml:id="echoid-s2829" xml:space="preserve"/> </p> <div xml:id="echoid-div444" type="float" level="2" n="3"> <note position="left" xlink:label="note-0116-06" xlink:href="note-0116-06a" xml:space="preserve">279.</note> <note symbol="*" position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">268.</note> <note symbol="*" position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">273.</note> <note symbol="*" position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">255</note> <note position="right" xlink:label="note-0117-04" xlink:href="note-0117-04a" xml:space="preserve">280.</note> </div> </div> <div xml:id="echoid-div446" type="section" level="1" n="150"> <head xml:id="echoid-head216" xml:space="preserve"><emph style="sc">Experimentum i</emph>.</head> <p> <s xml:id="echoid-s2830" xml:space="preserve">Pendula duo CP & </s> <s xml:id="echoid-s2831" xml:space="preserve">cp æqualia, ſi a punctis P & </s> <s xml:id="echoid-s2832" xml:space="preserve">p eo-<lb/> <anchor type="note" xlink:label="note-0117-05a" xlink:href="note-0117-05"/> dem temporis momento dimittantur, eodem tempore per-<lb/> <anchor type="note" xlink:label="note-0117-06a" xlink:href="note-0117-06"/> venient in B & </s> <s xml:id="echoid-s2833" xml:space="preserve">b, & </s> <s xml:id="echoid-s2834" xml:space="preserve">deinde in F & </s> <s xml:id="echoid-s2835" xml:space="preserve">f; </s> <s xml:id="echoid-s2836" xml:space="preserve">& </s> <s xml:id="echoid-s2837" xml:space="preserve">ſic motum con-<lb/>tinuabunt per arcus PBF & </s> <s xml:id="echoid-s2838" xml:space="preserve">pbf, ſemper eodem tem-<lb/>pore.</s> <s xml:id="echoid-s2839" xml:space="preserve"/> </p> <div xml:id="echoid-div446" type="float" level="2" n="1"> <note position="right" xlink:label="note-0117-05" xlink:href="note-0117-05a" xml:space="preserve">281.</note> <note position="right" xlink:label="note-0117-06" xlink:href="note-0117-06a" xml:space="preserve">TAB. XI. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s2840" xml:space="preserve">Hæc autem æqualitas plenius explicanda eſt, & </s> <s xml:id="echoid-s2841" xml:space="preserve">quare vi-<lb/>brationes in circulo ad vibrationem per chordas quam dixi <lb/>rationem habeant.</s> <s xml:id="echoid-s2842" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2843" xml:space="preserve">Rotetur circulus FEBſuper lineâ AD donec punctum B <lb/> <anchor type="note" xlink:label="note-0117-07a" xlink:href="note-0117-07"/> in A ad lineam hanc perveniat; </s> <s xml:id="echoid-s2844" xml:space="preserve">hoc motu punctum B deſcri-<lb/> <anchor type="note" xlink:label="note-0117-08a" xlink:href="note-0117-08"/> bit curvæ portionem BPA: </s> <s xml:id="echoid-s2845" xml:space="preserve">eodem modo ſimilis curvæ <lb/>portio B| D deſcribitur, totaque curva ABD vocatur Cy-<lb/>cloïs, circulus FEB generator dicitur.</s> <s xml:id="echoid-s2846" xml:space="preserve"/> </p> <div xml:id="echoid-div447" type="float" level="2" n="2"> <note position="right" xlink:label="note-0117-07" xlink:href="note-0117-07a" xml:space="preserve">282.</note> <note position="right" xlink:label="note-0117-08" xlink:href="note-0117-08a" xml:space="preserve">TAB. XI. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s2847" xml:space="preserve">Dividatur in duas partes æquales in B, portioneſque BA <lb/> <anchor type="note" xlink:label="note-0117-09a" xlink:href="note-0117-09"/> & </s> <s xml:id="echoid-s2848" xml:space="preserve">BD diſponantur, ut puncta A & </s> <s xml:id="echoid-s2849" xml:space="preserve">D jungantur in C; </s> <s xml:id="echoid-s2850" xml:space="preserve">pun-<lb/>ctum vero B cum punctis A & </s> <s xml:id="echoid-s2851" xml:space="preserve">D lineæ AD coincidat. <lb/></s> <s xml:id="echoid-s2852" xml:space="preserve">Juxta harum portionum curvaturam laminæ metallicæ in-<lb/>flectantur, ita ut filum penduli in C ſuſpenſi, motu ſuo vi-<lb/>bratorio, ab utraque parte ſeſe laminis iſtis applicet, & </s> <s xml:id="echoid-s2853" xml:space="preserve">ean-<lb/>dem curvaturam cum iſtis adipiſcatur. </s> <s xml:id="echoid-s2854" xml:space="preserve">Nunc poſita longi-<lb/>tudine penduli CB, corpus P in vibrationibus ſuis deſcri-<lb/>bet cycloïdem ABD, ut in ſequenti ſcholio 3° demonſtra- <pb o="68" file="0118" n="128" rhead="PHYSICES ELEMENTA"/> mus, ita ut filum longitudinis BC æquale ſit curvæ <lb/>CA; </s> <s xml:id="echoid-s2855" xml:space="preserve">quare tota curva ABD dupla eſt lineæ CB; </s> <s xml:id="echoid-s2856" xml:space="preserve">& </s> <s xml:id="echoid-s2857" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0118-01a" xlink:href="note-0118-01"/> quadrupla axis FB.</s> <s xml:id="echoid-s2858" xml:space="preserve"/> </p> <div xml:id="echoid-div448" type="float" level="2" n="3"> <note position="right" xlink:label="note-0117-09" xlink:href="note-0117-09a" xml:space="preserve">283.</note> <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">284.</note> </div> <p> <s xml:id="echoid-s2859" xml:space="preserve">In eodem ſcholio demonſtramus. </s> <s xml:id="echoid-s2860" xml:space="preserve">Tangentem ad curvam <lb/> <anchor type="note" xlink:label="note-0118-02a" xlink:href="note-0118-02"/> in puncto, ut P, parallelam eſſe chordæ EB, in circulo <lb/>FBE ductæ ad punctum infimum B ex puncto E, in quo cir-<lb/>culus ſecatur à lineâ PE parrallela ad baſim AD & </s> <s xml:id="echoid-s2861" xml:space="preserve">per <lb/>P tranſeunti: </s> <s xml:id="echoid-s2862" xml:space="preserve">Ut & </s> <s xml:id="echoid-s2863" xml:space="preserve">portionem PB curvæ æqualem eſſe <lb/> <anchor type="note" xlink:label="note-0118-03a" xlink:href="note-0118-03"/> duplæ chordæ EB.</s> <s xml:id="echoid-s2864" xml:space="preserve"/> </p> <div xml:id="echoid-div449" type="float" level="2" n="4"> <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">285.</note> <note position="left" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">286.</note> </div> <p> <s xml:id="echoid-s2865" xml:space="preserve">Cum autem in ſingulis curvæ punctis corpus in curva de-<lb/>ſcendat juxta directionem tangentis ad curvam, ſequi-<lb/>tur corpus in puncto quocunque curvæ conari deſcendere <lb/> <anchor type="note" xlink:label="note-0118-04a" xlink:href="note-0118-04"/> cumvi, quæ proportionalis portioni curvæ inter hoccepun-<lb/>ctum & </s> <s xml:id="echoid-s2866" xml:space="preserve">curvæ punctum infimum B <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s2867" xml:space="preserve">Unde patet, ſi duo <anchor type="note" xlink:label="note-0118-05a" xlink:href="note-0118-05"/> pendula ut CP ab altitudinibus diverſis, eodem momento, <lb/>dimittantur, celeritates, quibus cadere incipiunt, eſſe in-<lb/>ter ſe, ut ſpatia percurrenda, antequam ad B perveniant: <lb/></s> <s xml:id="echoid-s2868" xml:space="preserve">ſi ergo iſtis celeritatibus ſolis, motu non accelerato, agita-<lb/>rentur, eodem temporis momento ad B pervenirent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2869" xml:space="preserve">eo- <anchor type="note" xlink:label="note-0118-06a" xlink:href="note-0118-06"/> dem modo velocitatibus ſecundo momento acquiſitis, et-<lb/>iam ad B eodem momento pertingunt; </s> <s xml:id="echoid-s2870" xml:space="preserve">idemque ratioci-<lb/>nium pro momentis ſequentibus procedit; </s> <s xml:id="echoid-s2871" xml:space="preserve">& </s> <s xml:id="echoid-s2872" xml:space="preserve">ſemi vibra-<lb/>tiones ex omnibus celeritatibus junctis utcunque inæquales, <lb/>ut & </s> <s xml:id="echoid-s2873" xml:space="preserve">vibrationes integræ, iiſdem temporibus peraguntur.</s> <s xml:id="echoid-s2874" xml:space="preserve"/> </p> <div xml:id="echoid-div450" type="float" level="2" n="5"> <note position="left" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">287.</note> <note symbol="*" position="left" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">267 285. <lb/>286.</note> <note symbol="*" position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">94.</note> </div> <p> <s xml:id="echoid-s2875" xml:space="preserve">Ulterius in primo ſcholio demonſtramus. </s> <s xml:id="echoid-s2876" xml:space="preserve">Tempus unius <lb/> <anchor type="note" xlink:label="note-0118-07a" xlink:href="note-0118-07"/> cujuſque vibrationis eſſe ad tempus caſus verticalis, per ſe-<lb/>milongitudinem penduli, ut peripheria circuli, ad diame-<lb/>trum. </s> <s xml:id="echoid-s2877" xml:space="preserve">In hac curva pars infima cum circuli arcu exiguo ad <lb/>ſenſum coincidit; </s> <s xml:id="echoid-s2878" xml:space="preserve">& </s> <s xml:id="echoid-s2879" xml:space="preserve">hæc eſt vera ratio, quare in circulo <lb/>tempora vibrationum exiguarum, utcunque inæqualium, <lb/>ſint æqualia; </s> <s xml:id="echoid-s2880" xml:space="preserve">ideo etiam duratio harum vibrationum ad du-<lb/>rationem vibrationis per chordas, id eſt ad tempus caſus <lb/>verticalis per longitudinem octuplam longitudinis penduli <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0118-08a" xlink:href="note-0118-08"/> aut ſedecuplam ſemi longitudinis penduli, illam habet ra-<lb/>tionem, quæ datur inter peripheriam circuli & </s> <s xml:id="echoid-s2881" xml:space="preserve">quatuor diame-<lb/>tros <anchor type="note" xlink:href="" symbol="*"/>, id eſt circiter ut 785 ad 1000: </s> <s xml:id="echoid-s2882" xml:space="preserve">& </s> <s xml:id="echoid-s2883" xml:space="preserve">celerius per arcum <anchor type="note" xlink:label="note-0118-09a" xlink:href="note-0118-09"/> <pb o="69" file="0119" n="129" rhead="MATHEMATICA. LIB. I. CAP. XIX."/> quam per chordas vibratur corpus.</s> <s xml:id="echoid-s2884" xml:space="preserve"/> </p> <div xml:id="echoid-div451" type="float" level="2" n="6"> <note position="left" xlink:label="note-0118-07" xlink:href="note-0118-07a" xml:space="preserve">288.</note> <note symbol="*" position="left" xlink:label="note-0118-08" xlink:href="note-0118-08a" xml:space="preserve">279.</note> <note symbol="*" position="left" xlink:label="note-0118-09" xlink:href="note-0118-09a" xml:space="preserve">255. <lb/>289.</note> </div> <p> <s xml:id="echoid-s2885" xml:space="preserve">Durationes vibrationum pendulorum inæqualium poſſunt <lb/> <anchor type="note" xlink:label="note-0119-01a" xlink:href="note-0119-01"/> inter ſe comparari. </s> <s xml:id="echoid-s2886" xml:space="preserve">Quando arcus ſunt ſimiles, deviationes re-<lb/>ſpectu chordarum ſunt etiam ſimiles & </s> <s xml:id="echoid-s2887" xml:space="preserve">tempora vibrationum <lb/>per arcus ſunt ut tempora vibrationum per chordas; </s> <s xml:id="echoid-s2888" xml:space="preserve">hæc vero <lb/>ut tempora deſcenſus per longitudines octuplas longitudinum <lb/>pendulorum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2889" xml:space="preserve">& </s> <s xml:id="echoid-s2890" xml:space="preserve">ſic quadrata durationum ſunt ut iſtæ lon- <anchor type="note" xlink:label="note-0119-02a" xlink:href="note-0119-02"/> gitudines octuplæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2891" xml:space="preserve">ſive ut ipſæ longitudines pendulorum.</s> <s xml:id="echoid-s2892" xml:space="preserve"/> </p> <div xml:id="echoid-div452" type="float" level="2" n="7"> <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">290.</note> <note symbol="*" position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">279.</note> </div> <note symbol="*" position="right" xml:space="preserve">225.</note> </div> <div xml:id="echoid-div454" type="section" level="1" n="151"> <head xml:id="echoid-head217" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s2893" xml:space="preserve">Duo pendula CP, cp, quorum longitudines ſunt ut 4. <lb/></s> <s xml:id="echoid-s2894" xml:space="preserve"> <anchor type="note" xlink:label="note-0119-04a" xlink:href="note-0119-04"/> ad 1.</s> <s xml:id="echoid-s2895" xml:space="preserve">, eodem tempore dimittuntur a punctis P & </s> <s xml:id="echoid-s2896" xml:space="preserve">p, ita ut <lb/> <anchor type="note" xlink:label="note-0119-05a" xlink:href="note-0119-05"/> vibrationbius arcus ſimiles deſcribant; </s> <s xml:id="echoid-s2897" xml:space="preserve">pendulum majus ſe-<lb/>mel vibratur, dum minus duas peragit vibrationes; </s> <s xml:id="echoid-s2898" xml:space="preserve">& </s> <s xml:id="echoid-s2899" xml:space="preserve">ita <lb/>quadrata durationum vibrationum ſunt ut 4. </s> <s xml:id="echoid-s2900" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s2901" xml:space="preserve">, nem-<lb/>pe ut longitudines pendulorum.</s> <s xml:id="echoid-s2902" xml:space="preserve"/> </p> <div xml:id="echoid-div454" type="float" level="2" n="1"> <note position="right" xlink:label="note-0119-04" xlink:href="note-0119-04a" xml:space="preserve">291.</note> <note position="right" xlink:label="note-0119-05" xlink:href="note-0119-05a" xml:space="preserve">TAB XI. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s2903" xml:space="preserve">Quando vibrationes ſunt exiguæ, hæc ratio etiam locum <lb/>habet, licèt pendula non vibrentur per arcus ſimiles <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2904" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">280.</note> <p> <s xml:id="echoid-s2905" xml:space="preserve">Velocitates pendulorum in puncto infimo, in vibrationibus <lb/> <anchor type="note" xlink:label="note-0119-07a" xlink:href="note-0119-07"/> inæqualibus, ſunt inter ſe, ut ſubtenſæ arcuum, quos corpus <lb/>deſcendendo deſcribit. </s> <s xml:id="echoid-s2906" xml:space="preserve">Sic velocitas corporis P, cadentis per <lb/> <anchor type="note" xlink:label="note-0119-08a" xlink:href="note-0119-08"/> arcum PB, eſt ad ejus velocitatem quando cadit per DB, <lb/>ut chorda PB ad chordam DB. </s> <s xml:id="echoid-s2907" xml:space="preserve">Nam ductis lineis hori-<lb/> <anchor type="note" xlink:label="note-0119-09a" xlink:href="note-0119-09"/> zonti parallelis P f, D d & </s> <s xml:id="echoid-s2908" xml:space="preserve">junctis P & </s> <s xml:id="echoid-s2909" xml:space="preserve">A, triangula P f B, <lb/>BPA ſunt ſimilia <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s2910" xml:space="preserve">idèo B f, BP, BA ſunt in con- <anchor type="note" xlink:label="note-0119-10a" xlink:href="note-0119-10"/> tinuâ proportione, & </s> <s xml:id="echoid-s2911" xml:space="preserve">quadratum chordæ BP valet produ-<lb/>ctum diametri per B f: </s> <s xml:id="echoid-s2912" xml:space="preserve">eodem modo quadratum chordæ <lb/>B d æquale eſt producto diametri per BD: </s> <s xml:id="echoid-s2913" xml:space="preserve">ergo quadrata <lb/>chordarum ſunt inter ſe ut producta hæc, quæ ſunt ut li-<lb/>neæ f B, dB. </s> <s xml:id="echoid-s2914" xml:space="preserve">Quadrata prædictarum velocitatum ſunt et-<lb/> <anchor type="note" xlink:label="note-0119-11a" xlink:href="note-0119-11"/> iâm ut iſtæ lineæ f B, d B <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2915" xml:space="preserve">ergo velocitates ut chordæ.</s> <s xml:id="echoid-s2916" xml:space="preserve"/> </p> <div xml:id="echoid-div455" type="float" level="2" n="2"> <note position="right" xlink:label="note-0119-07" xlink:href="note-0119-07a" xml:space="preserve">292.</note> <note position="right" xlink:label="note-0119-08" xlink:href="note-0119-08a" xml:space="preserve">TAB. XI. <lb/>fig. 2.</note> <note position="right" xlink:label="note-0119-09" xlink:href="note-0119-09a" xml:space="preserve">293.</note> <note symbol="*" position="right" xlink:label="note-0119-10" xlink:href="note-0119-10a" xml:space="preserve">31-El. III. <lb/>8: El. VI.</note> <note symbol="*" position="right" xlink:label="note-0119-11" xlink:href="note-0119-11a" xml:space="preserve">271. 255. <lb/>253.</note> </div> <p> <s xml:id="echoid-s2917" xml:space="preserve">Circa omnia, quæ hucuſque dependulis dicta ſunt, non in-<lb/>tereſt quantum ponderet corpus quod agitatur, aut an corpora <lb/> <anchor type="note" xlink:label="note-0119-12a" xlink:href="note-0119-12"/> diver ſorum pendulorum inæqualiter ponderent, aut ex diverſa <lb/>dentur materiæ. </s> <s xml:id="echoid-s2918" xml:space="preserve">Cùm vis gravitatis proportionalis ſit quan-<lb/>titati materiæ in omnibus corporibus <anchor type="note" xlink:href="" symbol="*"/>, omnia corpora, in <anchor type="note" xlink:label="note-0119-13a" xlink:href="note-0119-13"/> iiſdem circumſtantiis, gravitate æque celeriter moventur.</s> <s xml:id="echoid-s2919" xml:space="preserve"> <pb o="70" file="0120" n="130" rhead="PHYSICES ELEMENTA"/> Quod etiam ſequenti Experimento confirmatur.</s> <s xml:id="echoid-s2920" xml:space="preserve"/> </p> <div xml:id="echoid-div456" type="float" level="2" n="3"> <note position="right" xlink:label="note-0119-12" xlink:href="note-0119-12a" xml:space="preserve">294.</note> <note symbol="*" position="right" xlink:label="note-0119-13" xlink:href="note-0119-13a" xml:space="preserve">121.</note> </div> </div> <div xml:id="echoid-div458" type="section" level="1" n="152"> <head xml:id="echoid-head218" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s2921" xml:space="preserve">Dentur duo globi æquales, aut inæquales, unus ex plum-<lb/> <anchor type="note" xlink:label="note-0120-01a" xlink:href="note-0120-01"/> bo, alter ex ebore; </s> <s xml:id="echoid-s2922" xml:space="preserve">filis ſuſpendantur, ut forment pendu-<lb/>la æqualia; </s> <s xml:id="echoid-s2923" xml:space="preserve">vibrationes æquales, atque exiguæ utcunque <lb/>inæquales, ſunt æquè diuturnæ.</s> <s xml:id="echoid-s2924" xml:space="preserve"/> </p> <div xml:id="echoid-div458" type="float" level="2" n="1"> <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">295.</note> </div> <p> <s xml:id="echoid-s2925" xml:space="preserve">Sæpe loco fili virga ferrea tenuis ſed rigida adhibetur, & </s> <s xml:id="echoid-s2926" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0120-02a" xlink:href="note-0120-02"/> aliquan-do etiam pondera duo aut plura ei annectuntur, & </s> <s xml:id="echoid-s2927" xml:space="preserve"><lb/>vocatur pendulum compoſitum; </s> <s xml:id="echoid-s2928" xml:space="preserve">in eo caſu regulæ memora-<lb/>tæ locum non habent; </s> <s xml:id="echoid-s2929" xml:space="preserve">ſed iſta pendula ad ſimplicia revocan-<lb/>tur, determinando in iis punctum, in quo ſi pondera forent <lb/>juncta, vibrationes eſſent æquè diuturnæ cum vibrationibus <lb/>penduli compoſiti, Hocce punctum vocatur centrum oſcil-<lb/>lationis. </s> <s xml:id="echoid-s2930" xml:space="preserve">In ſcholio 2°. </s> <s xml:id="echoid-s2931" xml:space="preserve">methodum hujus determinandi ex-<lb/>plicamus.</s> <s xml:id="echoid-s2932" xml:space="preserve"/> </p> <div xml:id="echoid-div459" type="float" level="2" n="2"> <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">296.</note> </div> <p> <s xml:id="echoid-s2933" xml:space="preserve">Corpus cujuſcunque figuræ poteſt ſuſpendi, & </s> <s xml:id="echoid-s2934" xml:space="preserve">circa pun-<lb/>ctum, aut potius axem, vibrari; </s> <s xml:id="echoid-s2935" xml:space="preserve">in eo etiam poteſt deter-<lb/>minari centrum oſcillationis.</s> <s xml:id="echoid-s2936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2937" xml:space="preserve">Quando linea recta, qualis eſt filum ferreum, circa ex-<lb/> <anchor type="note" xlink:label="note-0120-03a" xlink:href="note-0120-03"/> tremitatum alteram vibratur, centrum oſcillationis diſtat a <lb/>puncto ſuſpenſionis duabus partibus tertiis longitudinis fili. <lb/></s> <s xml:id="echoid-s2938" xml:space="preserve">ut in eodem ſcholio demonſtramus.</s> <s xml:id="echoid-s2939" xml:space="preserve"/> </p> <div xml:id="echoid-div460" type="float" level="2" n="3"> <note position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">297.</note> </div> </div> <div xml:id="echoid-div462" type="section" level="1" n="153"> <head xml:id="echoid-head219" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s2940" xml:space="preserve">Lamina ferrea AB ita ſuſpenditur, ut circa extremita-<lb/> <anchor type="note" xlink:label="note-0120-04a" xlink:href="note-0120-04"/> tem A vibretur; </s> <s xml:id="echoid-s2941" xml:space="preserve">pendulum ſimplex CP, cujus longitudo eſt <lb/> <anchor type="note" xlink:label="note-0120-05a" xlink:href="note-0120-05"/> duarum partium tertiarum AB, eodem tempore cum iſta <lb/>lamina dimittitur; </s> <s xml:id="echoid-s2942" xml:space="preserve">& </s> <s xml:id="echoid-s2943" xml:space="preserve">vibrationes penduli, & </s> <s xml:id="echoid-s2944" xml:space="preserve">laminæ, eo-<lb/>dem tempore peraguntur.</s> <s xml:id="echoid-s2945" xml:space="preserve"/> </p> <div xml:id="echoid-div462" type="float" level="2" n="1"> <note position="left" xlink:label="note-0120-04" xlink:href="note-0120-04a" xml:space="preserve">298.</note> <note position="left" xlink:label="note-0120-05" xlink:href="note-0120-05a" xml:space="preserve">TAB. VIII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s2946" xml:space="preserve">Vibrationes pendulorum, ut diximus, licet inæquales, <lb/>ſunt æquè diuturnæ <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2947" xml:space="preserve">hæc pendulorum proprietas ma- <anchor type="note" xlink:label="note-0120-06a" xlink:href="note-0120-06"/> ximi uſus eſt in horologiis, quibus motus æquabilis, pen-<lb/>dulo adjuncto, communicatur.</s> <s xml:id="echoid-s2948" xml:space="preserve"/> </p> <div xml:id="echoid-div463" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0120-06" xlink:href="note-0120-06a" xml:space="preserve">280</note> </div> <p> <s xml:id="echoid-s2949" xml:space="preserve">Horologiis in diverſis locis tranſſatis vim gravitatis non <lb/> <anchor type="note" xlink:label="note-0120-07a" xlink:href="note-0120-07"/> ubique terrarum æqualem eſſe, enotuit ex eo, quod vibra-<lb/>tiones ejuſdem penduli, in diverſis regionibus, reſpectu <lb/>temporis, inæquales repertæ ſunt; </s> <s xml:id="echoid-s2950" xml:space="preserve">& </s> <s xml:id="echoid-s2951" xml:space="preserve">hæc gravitatis diver-<lb/>ſitas per pendula menſuratur.</s> <s xml:id="echoid-s2952" xml:space="preserve"/> </p> <div xml:id="echoid-div464" type="float" level="2" n="3"> <note position="left" xlink:label="note-0120-07" xlink:href="note-0120-07a" xml:space="preserve">299.</note> </div> <pb o="71" file="0121" n="131" rhead="MATHEMATICA. LIB. I. CAP. XIX."/> <p> <s xml:id="echoid-s2953" xml:space="preserve">Dentur duo pendula, CP, cp, quorum longitudines ſint in-<lb/> <anchor type="note" xlink:label="note-0121-01a" xlink:href="note-0121-01"/> terſe, ut vires gravitatis quibus agitantur; </s> <s xml:id="echoid-s2954" xml:space="preserve">ſi arcus ſimiles <lb/> <anchor type="note" xlink:label="note-0121-02a" xlink:href="note-0121-02"/> excurrant, in punctis reſpondentibus gravitates eandem ſem-<lb/>per habebunt rationem inter ſe, propter inclinationes æ-<lb/>quales, & </s> <s xml:id="echoid-s2955" xml:space="preserve">quidem rationem arcuum percurrendorum, (quia <lb/>arcus ſimiles ſunt ut pendulorum longitudines) qui ergo æ-<lb/>qualibus temporibus percurrentur <anchor type="note" xlink:href="" symbol="*"/>, id eſt, vibr ationes e- <anchor type="note" xlink:label="note-0121-03a" xlink:href="note-0121-03"/> runt æ æquè diuturnæ.</s> <s xml:id="echoid-s2956" xml:space="preserve"/> </p> <div xml:id="echoid-div465" type="float" level="2" n="4"> <note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">300.</note> <note position="right" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">TAB. XII. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">94</note> </div> <p> <s xml:id="echoid-s2957" xml:space="preserve">Si ad eandem longitudinem reducantur mutato pendulo <lb/>c p cujus longitudo fiat cq, æqualis CP; </s> <s xml:id="echoid-s2958" xml:space="preserve">quadratum dura-<lb/>tionis vibrationis penduli cq eſt ad quadratum durationisvi-<lb/>brationis penduli cp, aut CP, ut longitudo cq, aut CP, <lb/>ad cp <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s2959" xml:space="preserve">id eſt ut gravitas quæ in pendulum CP agit ad <anchor type="note" xlink:label="note-0121-04a" xlink:href="note-0121-04"/> gravitatem quæ pendulum cq agitat. </s> <s xml:id="echoid-s2960" xml:space="preserve">Id circo ſunt qua-<lb/> <anchor type="note" xlink:label="note-0121-05a" xlink:href="note-0121-05"/> drata durationum vibrationum pendulorum æqualium, inver-<lb/>sè ut gravitates in pendula agentes. </s> <s xml:id="echoid-s2961" xml:space="preserve">Et in genere quadrata <lb/> <anchor type="note" xlink:label="note-0121-06a" xlink:href="note-0121-06"/> durationum vibrationum ſunt directè ut pendulorum longi-<lb/> <anchor type="note" xlink:label="note-0121-07a" xlink:href="note-0121-07"/> tudines <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2962" xml:space="preserve">inversè ut gravitates quibus moventur <anchor type="note" xlink:href="" symbol="*"/>, Et- <anchor type="note" xlink:label="note-0121-08a" xlink:href="note-0121-08"/> iam gravitates hæ ſunt directè ut longitudines <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s2963" xml:space="preserve">inversè <anchor type="note" xlink:label="note-0121-09a" xlink:href="note-0121-09"/> ut quadrata durationum vibrationum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s2964" xml:space="preserve"/> </p> <div xml:id="echoid-div466" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">290.</note> <note position="right" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">301.</note> <note position="right" xlink:label="note-0121-06" xlink:href="note-0121-06a" xml:space="preserve">302.</note> <note symbol="*" position="right" xlink:label="note-0121-07" xlink:href="note-0121-07a" xml:space="preserve">290.</note> <note position="right" xlink:label="note-0121-08" xlink:href="note-0121-08a" xml:space="preserve">303.</note> <note symbol="*" position="right" xlink:label="note-0121-09" xlink:href="note-0121-09a" xml:space="preserve">301. <lb/>* 300.</note> </div> <note symbol="*" position="right" xml:space="preserve">302.</note> </div> <div xml:id="echoid-div468" type="section" level="1" n="154"> <head xml:id="echoid-head220" xml:space="preserve">SCHOLIUM I.</head> <head xml:id="echoid-head221" style="it" xml:space="preserve">De motu in Cycloide.</head> <p> <s xml:id="echoid-s2965" xml:space="preserve">Concipiamus portionem cycloïdis aut integram cycloïdem, in linea recta <lb/>extendi ABD, & </s> <s xml:id="echoid-s2966" xml:space="preserve">corpus in hac linea recta moveri juxta legem penduli o-<lb/> <anchor type="note" xlink:label="note-0121-11a" xlink:href="note-0121-11"/> <anchor type="note" xlink:label="note-0121-12a" xlink:href="note-0121-12"/> ſcillati in cycloïde, id eſt dari preſſionem in corpusagentem, quæ ſequatur ratio-<lb/>nem diſtantiæ corporis a puncto medioB, & </s> <s xml:id="echoid-s2967" xml:space="preserve">quæ in corpus motum agat ut in cor-<lb/>pus quieſcens; </s> <s xml:id="echoid-s2968" xml:space="preserve">centro B, radio BA, deſcribatur Semicirculus ALD, quitempus <lb/>repræſentat, in quo corpus movetur ab A ad D; </s> <s xml:id="echoid-s2969" xml:space="preserve">tempora in quibus portiones <lb/>quæcunque lineæ AD deſcribuntur, erectis ad hanc perpendicularibus, de-<lb/>terminantur, arcus HI tempus in quo FG, & </s> <s xml:id="echoid-s2970" xml:space="preserve">arcus AH tempus in quo AF <lb/>percurruntur, deſignant: </s> <s xml:id="echoid-s2971" xml:space="preserve">celeritates autem in punctis F & </s> <s xml:id="echoid-s2972" xml:space="preserve">G proportionales <lb/>ſunt ipſis perpendicularibus FH, GI.</s> <s xml:id="echoid-s2973" xml:space="preserve"/> </p> <div xml:id="echoid-div468" type="float" level="2" n="1"> <note position="right" xlink:label="note-0121-11" xlink:href="note-0121-11a" xml:space="preserve">304.</note> <note position="right" xlink:label="note-0121-12" xlink:href="note-0121-12a" xml:space="preserve">TAB. XI. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s2974" xml:space="preserve">Quæ ut demonſtrentur, concipiendum eſt corpus, quod in linea AD mo-<lb/> <anchor type="note" xlink:label="note-0121-13a" xlink:href="note-0121-13"/> vetur ita, ut temporibus, quæ ſunt ut arcus AH, HI, percurrat portiones <lb/>AF, FG, & </s> <s xml:id="echoid-s2975" xml:space="preserve">ſic de cæteris: </s> <s xml:id="echoid-s2976" xml:space="preserve">ita ut totum tempus repræſentetur per ſemicircu-<lb/>lum ALD. </s> <s xml:id="echoid-s2977" xml:space="preserve">Concipiamus ulterius ſemicirculum in partes minimas æqua-<lb/>les diviſum, momenta minima æqualia temporis deſignantes, quales ſunt <lb/>H b & </s> <s xml:id="echoid-s2978" xml:space="preserve">I i. </s> <s xml:id="echoid-s2979" xml:space="preserve">Id circo poſitis fh & </s> <s xml:id="echoid-s2980" xml:space="preserve">g i etiam perpendicularibus lineæ AD, tem-<lb/>poribus æqualibus lineæ F f & </s> <s xml:id="echoid-s2981" xml:space="preserve">G g percurruntur, quæ cum exiguæ ſunt percur- <pb o="72" file="0122" n="132" rhead="PHYSICES ELEMENTA"/> runtur motu æquabili, momenta enim temporis adeo exigua coucipipo ſſunt, <lb/>ut acceleratio aut retardatio inſenſibilis ſit; </s> <s xml:id="echoid-s2982" xml:space="preserve">celeritates ergo in punctis F & </s> <s xml:id="echoid-s2983" xml:space="preserve"><lb/>G ſunt, ut F f & </s> <s xml:id="echoid-s2984" xml:space="preserve">G g <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt inter ſe ut FH ad GI; </s> <s xml:id="echoid-s2985" xml:space="preserve">propter triangu- <anchor type="note" xlink:label="note-0122-01a" xlink:href="note-0122-01"/> la ſimilia HBF, A h l, & </s> <s xml:id="echoid-s2986" xml:space="preserve">IGB, I mi, ductis lineis H l & </s> <s xml:id="echoid-s2987" xml:space="preserve">I m parallelis li-<lb/>neæ AD; </s> <s xml:id="echoid-s2988" xml:space="preserve">& </s> <s xml:id="echoid-s2989" xml:space="preserve">propter æquales Hypotenuſas HB, IB, & </s> <s xml:id="echoid-s2990" xml:space="preserve">H b, I i.</s> <s xml:id="echoid-s2991" xml:space="preserve"/> </p> <div xml:id="echoid-div469" type="float" level="2" n="2"> <note position="right" xlink:label="note-0121-13" xlink:href="note-0121-13a" xml:space="preserve">305.</note> <note symbol="*" position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">94.</note> </div> <p> <s xml:id="echoid-s2992" xml:space="preserve">Incrementa celeritatum momentis æqualibus minimis in punctis F & </s> <s xml:id="echoid-s2993" xml:space="preserve">G, ide ſt <lb/> <anchor type="note" xlink:label="note-0122-02a" xlink:href="note-0122-02"/> prefſiones agentes in iſtis punctis <anchor type="note" xlink:href="" symbol="*"/>, ſunt ut l h & </s> <s xml:id="echoid-s2994" xml:space="preserve">m i; </s> <s xml:id="echoid-s2995" xml:space="preserve">ſunt enim differentiæ cele- <anchor type="note" xlink:label="note-0122-03a" xlink:href="note-0122-03"/> ritatum in punctis F, f, & </s> <s xml:id="echoid-s2996" xml:space="preserve">G, g. </s> <s xml:id="echoid-s2997" xml:space="preserve">Sed, propter triangula memorata ſimilia, l h <lb/>& </s> <s xml:id="echoid-s2998" xml:space="preserve">m i ſunt inter ſe, ut FB ad GB; </s> <s xml:id="echoid-s2999" xml:space="preserve">idcirco preſſiones, in punctis F & </s> <s xml:id="echoid-s3000" xml:space="preserve">G in <lb/>corpus agentes ſunt inter ſe ut diſtantiæ a puncto medio B.</s> <s xml:id="echoid-s3001" xml:space="preserve"/> </p> <div xml:id="echoid-div470" type="float" level="2" n="3"> <note position="left" xlink:label="note-0122-02" xlink:href="note-0122-02a" xml:space="preserve">107. 252.</note> <note symbol="*" position="left" xlink:label="note-0122-03" xlink:href="note-0122-03a" xml:space="preserve">107.252.</note> </div> <p> <s xml:id="echoid-s3002" xml:space="preserve">Quæ de incrementis celeritatum demonſtrantur in parte AB Hineæ AD, <lb/>in parte BD de decrementis eodem modo demonſtrantur. </s> <s xml:id="echoid-s3003" xml:space="preserve">Agitatur ergo cor-<lb/>pus juxta legem corporis in cycloïde oſcillati.</s> <s xml:id="echoid-s3004" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3005" xml:space="preserve">Detur corpus motu æquabili ſemicir culum percurrens ALD, in tempore <lb/> <anchor type="note" xlink:label="note-0122-04a" xlink:href="note-0122-04"/> unius vibrationis in cycloide, id eſt in tempore, in quo corpus, in linea <lb/>recta AD ut explicavimus motum, illam percurrit. </s> <s xml:id="echoid-s3006" xml:space="preserve">Ex dictis patet H b, <lb/>F f, & </s> <s xml:id="echoid-s3007" xml:space="preserve">I i, G g, æqualibus temporibus percurri; </s> <s xml:id="echoid-s3008" xml:space="preserve">unde ſequitur, cum dire-<lb/>ctiones ſint parallelæ in L & </s> <s xml:id="echoid-s3009" xml:space="preserve">B, celeritates in hiſce punctis eſſe æquales. </s> <s xml:id="echoid-s3010" xml:space="preserve">Idcirco <lb/>corpus celeritate quam corpus pendulum habet in B, in tempore unius vibrationis <lb/>deſcribit ſemicirculum, cujus diameter eſt arcus cycloidis a corpore percurſus.</s> <s xml:id="echoid-s3011" xml:space="preserve"/> </p> <div xml:id="echoid-div471" type="float" level="2" n="4"> <note position="left" xlink:label="note-0122-04" xlink:href="note-0122-04a" xml:space="preserve">306.</note> </div> <p> <s xml:id="echoid-s3012" xml:space="preserve">Si corpus integram percurrat cycloidem ABD, diameter hæc erit quadru-<lb/> <anchor type="note" xlink:label="note-0122-05a" xlink:href="note-0122-05"/> pla diametri FB <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3013" xml:space="preserve">velocitas in B erit, quam corpus cadendo ab altitudi- <anchor type="note" xlink:label="note-0122-06a" xlink:href="note-0122-06"/> ne FB acquirit <anchor type="note" xlink:href="" symbol="*"/>, qua celeritate motu æquabili corpus in tempore caſus po- <anchor type="note" xlink:label="note-0122-07a" xlink:href="note-0122-07"/> teſt percurrere lineam duplam ipſius FB <anchor type="note" xlink:href="" symbol="*"/> Sed ſpatia æqualibus velocitatibus <anchor type="note" xlink:label="note-0122-08a" xlink:href="note-0122-08"/> percurſa ſunt ut tempora <anchor type="note" xlink:href="" symbol="*"/>, id circo tempus caſus per ſemilongitudinem <anchor type="note" xlink:label="note-0122-09a" xlink:href="note-0122-09"/> penduli eſt ad tempus unius vibrationis per integram cycloidem, aut arcum <lb/> <anchor type="note" xlink:label="note-0122-10a" xlink:href="note-0122-10"/> quemcumque <anchor type="note" xlink:href="" symbol="*"/>, ut dupla FB, ad ſemicircumferentiam circuli, cujus diame- <anchor type="note" xlink:label="note-0122-11a" xlink:href="note-0122-11"/> ter eſt quadrupla lineæ FB, aut ad integram circumferentiam, cujus diame-<lb/>ter eſt etiam dupla FB; </s> <s xml:id="echoid-s3014" xml:space="preserve">ergo in genere ut diameter circuli ad hujus circum-<lb/>ferentiam; </s> <s xml:id="echoid-s3015" xml:space="preserve">ut monuimus in n. </s> <s xml:id="echoid-s3016" xml:space="preserve">288.</s> <s xml:id="echoid-s3017" xml:space="preserve"/> </p> <div xml:id="echoid-div472" type="float" level="2" n="5"> <note position="left" xlink:label="note-0122-05" xlink:href="note-0122-05a" xml:space="preserve">307.</note> <note position="left" xlink:label="note-0122-06" xlink:href="note-0122-06a" xml:space="preserve">TAB. XI. <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0122-07" xlink:href="note-0122-07a" xml:space="preserve">284.</note> <note symbol="*" position="left" xlink:label="note-0122-08" xlink:href="note-0122-08a" xml:space="preserve">271.</note> <note symbol="*" position="left" xlink:label="note-0122-09" xlink:href="note-0122-09a" xml:space="preserve">257.</note> <note symbol="*" position="left" xlink:label="note-0122-10" xlink:href="note-0122-10a" xml:space="preserve">95.</note> <note symbol="*" position="left" xlink:label="note-0122-11" xlink:href="note-0122-11a" xml:space="preserve">280.</note> </div> </div> <div xml:id="echoid-div474" type="section" level="1" n="155"> <head xml:id="echoid-head222" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head223" style="it" xml:space="preserve">De Centro oſcillationis determinando.</head> <p> <s xml:id="echoid-s3018" xml:space="preserve">Sit CA pendulum compoſitum; </s> <s xml:id="echoid-s3019" xml:space="preserve">pondera P & </s> <s xml:id="echoid-s3020" xml:space="preserve">Q; </s> <s xml:id="echoid-s3021" xml:space="preserve">inter bæc datur centrum oſcil-<lb/> <anchor type="note" xlink:label="note-0122-12a" xlink:href="note-0122-12"/> lationis O, cujus hæc eſt proprietas, poſitâ virgâ AC rigidâ & </s> <s xml:id="echoid-s3022" xml:space="preserve">ſine pon-<lb/> <anchor type="note" xlink:label="note-0122-13a" xlink:href="note-0122-13"/> dere, ut pondus Q, multiplicatum per BC, ad pondus P, multiplicatum per <lb/>AC, ita AO ad OQ. </s> <s xml:id="echoid-s3023" xml:space="preserve">Quod ut demonſtremus, conſiderandum eſt pondera Q <lb/>& </s> <s xml:id="echoid-s3024" xml:space="preserve">A moveri directionibus parallelis inter ſe, id eſt æqualiter ad horizontem <lb/>inclinatis; </s> <s xml:id="echoid-s3025" xml:space="preserve">ideo agitari continuo impreſſionibus ex gravitate, quæ, niſi cor-<lb/>pora virgâ rigidâ juncta forent, illis celeritates communicarent æquales <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3026" xml:space="preserve"> <anchor type="note" xlink:label="note-0122-14a" xlink:href="note-0122-14"/> Junctorum autem ponderum celeritates neceſſario ſunt inæquales, & </s> <s xml:id="echoid-s3027" xml:space="preserve">celeri-<lb/>tas corporis P, actione ponderis Q, augetur, dum hocalterius actione retardatur; <lb/></s> <s xml:id="echoid-s3028" xml:space="preserve">quæ actiones contrariæ æquales ſunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3029" xml:space="preserve">Interea punctum intermedium quoddam <anchor type="note" xlink:label="note-0122-15a" xlink:href="note-0122-15"/> O, centrum nempe oſcillationis, movetur celeritate ex actione gravitatis ori-<lb/>unda.</s> <s xml:id="echoid-s3030" xml:space="preserve"/> </p> <div xml:id="echoid-div474" type="float" level="2" n="1"> <note position="left" xlink:label="note-0122-12" xlink:href="note-0122-12a" xml:space="preserve">308.</note> <note position="left" xlink:label="note-0122-13" xlink:href="note-0122-13a" xml:space="preserve">TAB XII. <lb/>fig. 3.</note> <note symbol="*" position="left" xlink:label="note-0122-14" xlink:href="note-0122-14a" xml:space="preserve">118.265.</note> <note symbol="*" position="left" xlink:label="note-0122-15" xlink:href="note-0122-15a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s3031" xml:space="preserve">Sit B b, O o, aut A a (has enim æquales ponimus lineas) ſpatium percur-<lb/>ſum ex actione gravitatis juxta inclinationem quamcunque agentis in tem-<lb/>pore quocunque minimo. </s> <s xml:id="echoid-s3032" xml:space="preserve">Cum punctum O hoc ſpatium percurrit, tantum <lb/>per BE transſertur Q, & </s> <s xml:id="echoid-s3033" xml:space="preserve">potentia quæ in Q agit minuitur quantitate, qua eo <pb file="0123" n="133"/> <anchor type="figure" xlink:label="fig-0123-01a" xlink:href="fig-0123-01"/> <pb file="0123a" n="134"/> <anchor type="figure" xlink:label="fig-0123a-01a" xlink:href="fig-0123a-01"/> <pb file="0124" n="135"/> <pb o="73" file="0125" n="136" rhead="MATHEMATICA. LIB. I. CAP. XIX."/> dem tempore corpus hoc percurreret Eb & </s> <s xml:id="echoid-s3034" xml:space="preserve">quæ exprimitur per Q x E b <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3035" xml:space="preserve"> <anchor type="note" xlink:label="note-0125-01a" xlink:href="note-0125-01"/> Potentia autem, quæ in P agit, augetur quantitate, qua P eodem tempore <lb/>transfertur per aD, & </s> <s xml:id="echoid-s3036" xml:space="preserve">quæ exprimitur per P x a D <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3037" xml:space="preserve">ponimus enim pa- <anchor type="note" xlink:label="note-0125-02a" xlink:href="note-0125-02"/> rallelas Bb, Oo, Aa; </s> <s xml:id="echoid-s3038" xml:space="preserve">potentia ergo quæ retardat motum corporis Q, eſt ad <lb/>potentiam, quæ accelerat motum corporis P, ut Q x E b ad P x a D: </s> <s xml:id="echoid-s3039" xml:space="preserve">Sed po-<lb/>tentiæ hæapplicantur vecti, cujusfulcrum eſt C; </s> <s xml:id="echoid-s3040" xml:space="preserve">idcirco harum actiones, quas <lb/>æquales demonſtravimus, ſunt ut CB x E b x Q ad CA x a D x P <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3041" xml:space="preserve">Ideo CB x Q <anchor type="note" xlink:label="note-0125-03a" xlink:href="note-0125-03"/> ad CA x P, ut aD ad Eb, aut AO ad OB. </s> <s xml:id="echoid-s3042" xml:space="preserve">Q. </s> <s xml:id="echoid-s3043" xml:space="preserve">E. </s> <s xml:id="echoid-s3044" xml:space="preserve">D. </s> <s xml:id="echoid-s3045" xml:space="preserve">Patet etiam in pendu-<lb/>lo tali compoſito producta fore æqualia, ſi unumquodque pondus multipli-<lb/>cetur per ſuas diſtantias a centris ſuſpenſionis & </s> <s xml:id="echoid-s3046" xml:space="preserve">oſcillationis.</s> <s xml:id="echoid-s3047" xml:space="preserve"/> </p> <div xml:id="echoid-div475" type="float" level="2" n="2"> <figure xlink:label="fig-0123-01" xlink:href="fig-0123-01a"> <image file="0123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123-01"/> </figure> <figure xlink:label="fig-0123a-01" xlink:href="fig-0123a-01a"> <image file="0123a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0123a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">108.</note> <note symbol="*" position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">128.</note> <note symbol="*" position="right" xlink:label="note-0125-03" xlink:href="note-0125-03a" xml:space="preserve">175.</note> </div> <p> <s xml:id="echoid-s3048" xml:space="preserve">Si plura pondera dentur & </s> <s xml:id="echoid-s3049" xml:space="preserve">unumquodque per ſuas diſtantias a centris ſuſpenſio-<lb/> <anchor type="note" xlink:label="note-0125-04a" xlink:href="note-0125-04"/> nis & </s> <s xml:id="echoid-s3050" xml:space="preserve">oſcillationis multiplicetur, ſummæ productorum ab utraque parte centri o-<lb/>ſcillationis æquales ſunt. </s> <s xml:id="echoid-s3051" xml:space="preserve">Quod demonſtratione ſimili evincitur.</s> <s xml:id="echoid-s3052" xml:space="preserve"/> </p> <div xml:id="echoid-div476" type="float" level="2" n="3"> <note position="right" xlink:label="note-0125-04" xlink:href="note-0125-04a" xml:space="preserve">309.</note> </div> <p> <s xml:id="echoid-s3053" xml:space="preserve">Unde deducimus Methodum computatione determinandi centrum oſcil-<lb/>lationis.</s> <s xml:id="echoid-s3054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3055" xml:space="preserve">Sint corpora quæcunque A, B, C, D, E, horum diſtantiæ a centro ſuſpen-<lb/> <anchor type="note" xlink:label="note-0125-05a" xlink:href="note-0125-05"/> ſionis reſpectivè litteris a, b, c, d, e, exprimuntur; </s> <s xml:id="echoid-s3056" xml:space="preserve">ſit diſtantia centri oſcilla-<lb/>tionis a centro ſufpenſionis x. </s> <s xml:id="echoid-s3057" xml:space="preserve">Ponamus a, b, c, minores eſſe x, d & </s> <s xml:id="echoid-s3058" xml:space="preserve">e autern <lb/>majores.</s> <s xml:id="echoid-s3059" xml:space="preserve"/> </p> <div xml:id="echoid-div477" type="float" level="2" n="4"> <note position="right" xlink:label="note-0125-05" xlink:href="note-0125-05a" xml:space="preserve">310.</note> </div> <p> <s xml:id="echoid-s3060" xml:space="preserve">Corporum A, B, C, diſtantiæ a centro oſcillationis ſunt x-a, x-b, <lb/>x-c, & </s> <s xml:id="echoid-s3061" xml:space="preserve">corporum reliquorum diſtantiæ ab eodem centro ſunt d-x, <lb/>e-x, multiplicando corpora ſingula per ſuas diſtantias ab utroque cen-<lb/>tro, habemus Aax - Aaa + Bbx - Bbb + Ccx - Ccc = Ddd - Ddx + Eee - Eex <anchor type="note" xlink:href="" symbol="*"/> unde de- <anchor type="note" xlink:label="note-0125-06a" xlink:href="note-0125-06"/> ducimus x = {Aaa + Bbb + Ccc + Ddd + Eee/Aa + Bb + Cc + Dd + Ee}, quam eandem æquationem ha-<lb/>bemus quæcunque ex diſtantiis a, b, c, d, e, ſuperent x; </s> <s xml:id="echoid-s3062" xml:space="preserve">quare generalem hanc <lb/>detegimus regulam.</s> <s xml:id="echoid-s3063" xml:space="preserve"/> </p> <div xml:id="echoid-div478" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0125-06" xlink:href="note-0125-06a" xml:space="preserve">309.</note> </div> <p> <s xml:id="echoid-s3064" xml:space="preserve">Si ſingula corpora multiplicentur per quadrata ſuarum diſtantiarum à centro ſu-<lb/> <anchor type="note" xlink:label="note-0125-07a" xlink:href="note-0125-07"/> ſpenſionis, & </s> <s xml:id="echoid-s3065" xml:space="preserve">ſumma productorum dividatur per ſummam productorum ſingulorum <lb/>corporum raultiplicatorum per ſuas diſtantias ab eodem centro ſuſpenſionis, quotiens <lb/>diviſionis dabit diſtantiam inter centra ſuſpenſionis & </s> <s xml:id="echoid-s3066" xml:space="preserve">oſcillationis.</s> <s xml:id="echoid-s3067" xml:space="preserve"/> </p> <div xml:id="echoid-div479" type="float" level="2" n="6"> <note position="right" xlink:label="note-0125-07" xlink:href="note-0125-07a" xml:space="preserve">311.</note> </div> <p> <s xml:id="echoid-s3068" xml:space="preserve">Si, continuato pendulo ultra centrum ſuſpenſionis, corpora quædam <lb/> <anchor type="note" xlink:label="note-0125-08a" xlink:href="note-0125-08"/> ſupra punctum ſuſpenſionis applicentur, horum diſtantia erit negativa; </s> <s xml:id="echoid-s3069" xml:space="preserve">Si <lb/>Ex. </s> <s xml:id="echoid-s3070" xml:space="preserve">gr. </s> <s xml:id="echoid-s3071" xml:space="preserve">talia forent corpora A&</s> <s xml:id="echoid-s3072" xml:space="preserve">B, pro + a & </s> <s xml:id="echoid-s3073" xml:space="preserve">+ b computatio ineunda foret <lb/>cum -a, -b, quorum quadrata cum etiam ſint + aa & </s> <s xml:id="echoid-s3074" xml:space="preserve">+ bb, diſtantia x in hoc ca-<lb/>ſu erit {Aaa + Bbb + Ccc + Ddd + Eee/-Aa-Bb + Cc + Dd + Ee.</s> <s xml:id="echoid-s3075" xml:space="preserve">}</s> </p> <div xml:id="echoid-div480" type="float" level="2" n="7"> <note position="right" xlink:label="note-0125-08" xlink:href="note-0125-08a" xml:space="preserve">312.</note> </div> <p> <s xml:id="echoid-s3076" xml:space="preserve">Ut memoratam <anchor type="note" xlink:href="" symbol="*"/> regulam applicemus lineæ cujus extremitas eſt ſuſpen- <anchor type="note" xlink:label="note-0125-09a" xlink:href="note-0125-09"/> fionis centrum, ſingula ipſius puncta, aut potius partes minimæ, multipli-<lb/> <anchor type="note" xlink:label="note-0125-10a" xlink:href="note-0125-10"/> candæ ſunt per quadrata diſtantiarum ſuarum ab extremitate, ſumma horum <lb/> <anchor type="note" xlink:label="note-0125-11a" xlink:href="note-0125-11"/> productorum eſt pyramis, cujus baſis eſt lineæ quadratum, & </s> <s xml:id="echoid-s3077" xml:space="preserve">altitudo ipſa <lb/>linea, ſi linea dicatur a, pyramis hæc valet {1/3}a<emph style="super">3</emph> <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3078" xml:space="preserve">Dividenda hæc eſt per ſummam partium minimarum multiplicatarum per ſuas diſtantias ab extre-<lb/> <anchor type="note" xlink:label="note-0125-12a" xlink:href="note-0125-12"/> mitate, quorum productorum ſumma eſt area trianguli cujus baſis eſt a, & </s> <s xml:id="echoid-s3079" xml:space="preserve"><lb/>altitudo etiam a; </s> <s xml:id="echoid-s3080" xml:space="preserve">quæ area valet {1/2}aa <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3081" xml:space="preserve">Dividendo autem {1/3}a<emph style="super">3</emph> per {1/2}a<emph style="super">2</emph> quo- tiens eſt {2/3}a diſtantia centri oſcillationis a centro ſuſpenſionis, ut ſuperius ex-<lb/>perimento confirmavimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3082" xml:space="preserve"/> </p> <div xml:id="echoid-div481" type="float" level="2" n="8"> <note position="right" xlink:label="note-0125-09" xlink:href="note-0125-09a" xml:space="preserve">313.</note> <note symbol="*" position="right" xlink:label="note-0125-10" xlink:href="note-0125-10a" xml:space="preserve">311.</note> <note symbol="*" position="right" xlink:label="note-0125-11" xlink:href="note-0125-11a" xml:space="preserve">7.6. El. XII</note> <note symbol="*" position="right" xlink:label="note-0125-12" xlink:href="note-0125-12a" xml:space="preserve">34. El. I.</note> </div> <note symbol="*" position="right" xml:space="preserve">298.</note> <pb o="74" file="0126" n="137" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div483" type="section" level="1" n="156"> <head xml:id="echoid-head224" xml:space="preserve">SCHOLIUM. 3.</head> <head xml:id="echoid-head225" style="it" xml:space="preserve">In quo quædam in boc capite memoratæ Cycloidis <lb/>proprietates demonſtrantur.</head> <p> <s xml:id="echoid-s3083" xml:space="preserve">Poſitâ cycloidis memoratâ <anchor type="note" xlink:href="" symbol="*"/> formatione; </s> <s xml:id="echoid-s3084" xml:space="preserve">ſit circulus generator BEF. </s> <s xml:id="echoid-s3085" xml:space="preserve">Pona- <anchor type="note" xlink:label="note-0126-01a" xlink:href="note-0126-01"/> mus hunc perveniſſe ad punctum Gbaſeos, punctum F erit in f, poſito arcu Gf <lb/> <anchor type="note" xlink:label="note-0126-02a" xlink:href="note-0126-02"/> lineæ GF æquali; </s> <s xml:id="echoid-s3086" xml:space="preserve">Punctum deſcribens erit in b, & </s> <s xml:id="echoid-s3087" xml:space="preserve">erit hoc punctum Cycloïdis-</s> </p> <div xml:id="echoid-div483" type="float" level="2" n="1"> <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">34.</note> <note symbol="*" position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve"> 282.</note> </div> <note position="left" xml:space="preserve">TAB. XII. <lb/>fig. 4.</note> <p> <s xml:id="echoid-s3088" xml:space="preserve">Ducatur G c H diameter per punctum contactus, erit hæc ad baſin per-<lb/> <anchor type="note" xlink:label="note-0126-04a" xlink:href="note-0126-04"/> pendicularis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3089" xml:space="preserve">parallela diametro BF. </s> <s xml:id="echoid-s3090" xml:space="preserve">Ductâ nunc b L, per punctum Cycloïdis b, baſi parallelâ, ſecante circulum FEB in E, & </s> <s xml:id="echoid-s3091" xml:space="preserve">GH in I; </s> <s xml:id="echoid-s3092" xml:space="preserve">ma-<lb/>nifeſtum eſt, propter æquales GI & </s> <s xml:id="echoid-s3093" xml:space="preserve">FL <anchor type="note" xlink:href="" symbol="*"/>, in circulis æqualibus æquales <anchor type="note" xlink:label="note-0126-05a" xlink:href="note-0126-05"/> eſſe b I, EL; </s> <s xml:id="echoid-s3094" xml:space="preserve">additâ utrimque IE æquales erunt b E, IL, cui æqualis <lb/>GF <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3095" xml:space="preserve"/> </p> <div xml:id="echoid-div484" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">18. El. III.</note> <note symbol="*" position="left" xlink:label="note-0126-05" xlink:href="note-0126-05a" xml:space="preserve">34. El. I.</note> </div> <note symbol="*" position="left" xml:space="preserve">34. El. I.</note> <p> <s xml:id="echoid-s3096" xml:space="preserve">Facile etiam liquet arcus G f, b H, EB, æquales eſſe inter ſe & </s> <s xml:id="echoid-s3097" xml:space="preserve">lineæ <lb/>GF; </s> <s xml:id="echoid-s3098" xml:space="preserve">ideoque lineæ b E.</s> <s xml:id="echoid-s3099" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3100" xml:space="preserve">Ex quibus hanc curvæ deducimus proprietatem, Si ex puncto quocunque Cy-<lb/> <anchor type="note" xlink:label="note-0126-07a" xlink:href="note-0126-07"/> cloidis ad baſin ducatur parallela, quæ ſemicirculum ſecat ſuper axe deſcriptum <lb/>ad partem curvæ, qualis linea hìc eſt b EL, erit hujus portio, inter Cycloi-<lb/>dem & </s> <s xml:id="echoid-s3101" xml:space="preserve">ſemicirculum intercepta, æqualis arcui ſemicir culi inter lineam memora-<lb/>tam & </s> <s xml:id="echoid-s3102" xml:space="preserve">verticem intercepto. </s> <s xml:id="echoid-s3103" xml:space="preserve">id eſt b E arcui EB æqualis eſt.</s> <s xml:id="echoid-s3104" xml:space="preserve"/> </p> <div xml:id="echoid-div485" type="float" level="2" n="3"> <note position="left" xlink:label="note-0126-07" xlink:href="note-0126-07a" xml:space="preserve">315.</note> </div> <p> <s xml:id="echoid-s3105" xml:space="preserve">Sit Cycloïs ADB; </s> <s xml:id="echoid-s3106" xml:space="preserve">vertex B; </s> <s xml:id="echoid-s3107" xml:space="preserve">baſis AF; </s> <s xml:id="echoid-s3108" xml:space="preserve">axis BF, qui diameter eſt ſemi-<lb/> <anchor type="note" xlink:label="note-0126-08a" xlink:href="note-0126-08"/> circuli FMB.</s> <s xml:id="echoid-s3109" xml:space="preserve"/> </p> <div xml:id="echoid-div486" type="float" level="2" n="4"> <note position="left" xlink:label="note-0126-08" xlink:href="note-0126-08a" xml:space="preserve">316.</note> </div> <note position="left" xml:space="preserve">TAB. XII. <lb/>fig. 5.</note> <p> <s xml:id="echoid-s3110" xml:space="preserve">Sumtâ D d portione quacunque infinitè exigua Cycloïdis, poterit hæc <lb/>pro lineâ rectâ haberi, & </s> <s xml:id="echoid-s3111" xml:space="preserve">continuatâ formabit tangentem in puncto D aut d. <lb/></s> <s xml:id="echoid-s3112" xml:space="preserve">Ducantur DL, dl, ad baſin parallelæ ſemicirculum ſecantes in E, e; </s> <s xml:id="echoid-s3113" xml:space="preserve">& </s> <s xml:id="echoid-s3114" xml:space="preserve"><lb/>ductâ B e continuetur hæc donec ſecet in b lineam DL; </s> <s xml:id="echoid-s3115" xml:space="preserve">ſit etiam BO ad ba-<lb/>ſin parallela, circulum tangens in B, & </s> <s xml:id="echoid-s3116" xml:space="preserve">quæ in O ſecatur lineâ eO, con-<lb/>tinuatione lineæ E e.</s> <s xml:id="echoid-s3117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3118" xml:space="preserve">Triangula b Ee & </s> <s xml:id="echoid-s3119" xml:space="preserve">e OB, propter Bo & </s> <s xml:id="echoid-s3120" xml:space="preserve">hE parallelas ſunt ſimilia. </s> <s xml:id="echoid-s3121" xml:space="preserve">La-<lb/>tera autem EO & </s> <s xml:id="echoid-s3122" xml:space="preserve">OB ſunt æqualia <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3123" xml:space="preserve">ergo & </s> <s xml:id="echoid-s3124" xml:space="preserve">æqualia e E, h E; </s> <s xml:id="echoid-s3125" xml:space="preserve">eſt eE ar- <anchor type="note" xlink:label="note-0126-10a" xlink:href="note-0126-10"/> cuum B e BE, aut linearum de, DE, differentia <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3126" xml:space="preserve">quæ eadem differen- <anchor type="note" xlink:label="note-0126-11a" xlink:href="note-0126-11"/> tia eſt ideò etiam h E, quare ſunt æquales parallelæ D h, de; </s> <s xml:id="echoid-s3127" xml:space="preserve">ſuntetiam id-<lb/>circo æquales & </s> <s xml:id="echoid-s3128" xml:space="preserve">parallelæ D d, b e <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3129" xml:space="preserve">id eſt tangens in d parallela chordæ e B, <anchor type="note" xlink:label="note-0126-12a" xlink:href="note-0126-12"/> quam Cycloïdis proprietatem ſuperius indicavimus in n. </s> <s xml:id="echoid-s3130" xml:space="preserve">285.</s> <s xml:id="echoid-s3131" xml:space="preserve"/> </p> <div xml:id="echoid-div487" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0126-10" xlink:href="note-0126-10a" xml:space="preserve">36. El III.</note> <note symbol="*" position="left" xlink:label="note-0126-11" xlink:href="note-0126-11a" xml:space="preserve">315</note> <note symbol="*" position="left" xlink:label="note-0126-12" xlink:href="note-0126-12a" xml:space="preserve">33. El I.</note> </div> <p> <s xml:id="echoid-s3132" xml:space="preserve">Iiſdem poſitis ducatur FE i; </s> <s xml:id="echoid-s3133" xml:space="preserve">erit hæc ad BE aut B b (propter augulum <lb/> <anchor type="note" xlink:label="note-0126-13a" xlink:href="note-0126-13"/> infinite exiguum e BE) perpendicularis <anchor type="note" xlink:href="" symbol="*"/>, dividetque baſin trianguli iſoce- <anchor type="note" xlink:label="note-0126-14a" xlink:href="note-0126-14"/> les b E e in duas partes æquales ita, ut ei ſit dimidium ipſius eb aut d D. <lb/></s> <s xml:id="echoid-s3134" xml:space="preserve">Eſt verò ei differentia inter chordas BE, Be; </s> <s xml:id="echoid-s3135" xml:space="preserve">nam ſi centro B, radio BE, <lb/>circulus deſcribatur coincidet hic cum Ei, quæ infinite exigua eſt; </s> <s xml:id="echoid-s3136" xml:space="preserve">& </s> <s xml:id="echoid-s3137" xml:space="preserve">D d <lb/>eſt differentia arcuum Cycloidis DB, dB.</s> <s xml:id="echoid-s3138" xml:space="preserve"/> </p> <div xml:id="echoid-div488" type="float" level="2" n="6"> <note position="left" xlink:label="note-0126-13" xlink:href="note-0126-13a" xml:space="preserve">317.</note> <note symbol="*" position="left" xlink:label="note-0126-14" xlink:href="note-0126-14a" xml:space="preserve">31. El. III,</note> </div> <p> <s xml:id="echoid-s3139" xml:space="preserve">Concipiamus nunc lineam ad baſim Cycloidis AF parallelam moveri à <lb/>B ad F, aliamque lineam interea circa B ita rotari, ut continuo tranſeat <lb/>per interſectionem primæ cum ſemicirculo. </s> <s xml:id="echoid-s3140" xml:space="preserve">Ubi prima Ex. </s> <s xml:id="echoid-s3141" xml:space="preserve">gr. </s> <s xml:id="echoid-s3142" xml:space="preserve">pervenit <lb/>ad dl erit ſecunda in B e, translatâ primâ ad DL rotatur ſecunda ut ſit in <lb/>BE. </s> <s xml:id="echoid-s3143" xml:space="preserve">In hoc motu, commune initium habent, & </s> <s xml:id="echoid-s3144" xml:space="preserve">continuo augentur, arcus <lb/>Cycloïdis DB & </s> <s xml:id="echoid-s3145" xml:space="preserve">chorda EB; </s> <s xml:id="echoid-s3146" xml:space="preserve">ſed illius augmentum ſemper duplum eſt au-<lb/>gmentihujus, quare & </s> <s xml:id="echoid-s3147" xml:space="preserve">integer arcus qui eſt ſumma augmentorum, erit du-<lb/>plusintegræ chordæ, quæ etiam ſummam valet augmentorum ſuorum. </s> <s xml:id="echoid-s3148" xml:space="preserve">Ha- <pb o="75" file="0127" n="138" rhead="MATHEMATICA. LIB. I. CAP XIX."/> bemus ergo etiam demonſtratam propoſitionem in n, 386. </s> <s xml:id="echoid-s3149" xml:space="preserve">memoratam.</s> <s xml:id="echoid-s3150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3151" xml:space="preserve">Supereſt ut, quæ de evolutione Cycloidis in n. </s> <s xml:id="echoid-s3152" xml:space="preserve">283. </s> <s xml:id="echoid-s3153" xml:space="preserve">dicta ſunt, de mon-<lb/>ſtremus.</s> <s xml:id="echoid-s3154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3155" xml:space="preserve">Detur iterum eadem Cycloïs ADB; </s> <s xml:id="echoid-s3156" xml:space="preserve">baſis AF; </s> <s xml:id="echoid-s3157" xml:space="preserve">axis FB; </s> <s xml:id="echoid-s3158" xml:space="preserve">FEB ſe-<lb/> <anchor type="note" xlink:label="note-0127-01a" xlink:href="note-0127-01"/> micirculus. </s> <s xml:id="echoid-s3159" xml:space="preserve">Producatur BF ad Cita, ut BF & </s> <s xml:id="echoid-s3160" xml:space="preserve">FC ſint æquales; </s> <s xml:id="echoid-s3161" xml:space="preserve">formato-<lb/>que parallelogrammo AfCF; </s> <s xml:id="echoid-s3162" xml:space="preserve">detur ſemicirculus A mf, qui ſemicirculo FEB, <lb/>æqualis erit; </s> <s xml:id="echoid-s3163" xml:space="preserve">ut & </s> <s xml:id="echoid-s3164" xml:space="preserve">ſemi cycloïs A qC, cujus axis eſt A f & </s> <s xml:id="echoid-s3165" xml:space="preserve">quæ æqualis <lb/>eſt ſemi-cycloïdi ADB. </s> <s xml:id="echoid-s3166" xml:space="preserve">Concipiamus etiam filum fixum in C & </s> <s xml:id="echoid-s3167" xml:space="preserve">cycloïdi <lb/>C q A applicatum, evolvi.</s> <s xml:id="echoid-s3168" xml:space="preserve"/> </p> <div xml:id="echoid-div489" type="float" level="2" n="7"> <note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">318.</note> </div> <p> <s xml:id="echoid-s3169" xml:space="preserve">Ponamus filum ad hunc perveniſſe ſitum, ut cum cycloïde tantum con-<lb/>veniat à C ad q, & </s> <s xml:id="echoid-s3170" xml:space="preserve">ulterius protendi juxta tangentem ad curvam in q: </s> <s xml:id="echoid-s3171" xml:space="preserve">ſi <lb/>linea q Q æqualis ſit arcui q A, cui filum, nunc tenſum, fuit applicatum, e-<lb/>rit Q fili extremitas.</s> <s xml:id="echoid-s3172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3173" xml:space="preserve">Ducatur q p ad baſin parallela ſemicirculum A m f ſecans in m, ex quo <lb/>puncto ducatur linea m A ad A, ſunt m A & </s> <s xml:id="echoid-s3174" xml:space="preserve">q N parallelæ <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s3175" xml:space="preserve">æquales;</s> <s xml:id="echoid-s3176" xml:space="preserve"> <anchor type="note" xlink:label="note-0127-02a" xlink:href="note-0127-02"/> ſed q A, ideoque q Q dupla eſt m A aut qN; </s> <s xml:id="echoid-s3177" xml:space="preserve">ſunt ergo æquales N q, NQ; <lb/></s> <s xml:id="echoid-s3178" xml:space="preserve">idcirco ſi per Q ad AF & </s> <s xml:id="echoid-s3179" xml:space="preserve">p q detur parallela QP, erunt æquales PF, A p; </s> <s xml:id="echoid-s3180" xml:space="preserve"><lb/>ergo etiam erunt æquales arcus FM, A m; </s> <s xml:id="echoid-s3181" xml:space="preserve">ut & </s> <s xml:id="echoid-s3182" xml:space="preserve">anguli MFA, m AF <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s3183" xml:space="preserve"> <anchor type="note" xlink:label="note-0127-03a" xlink:href="note-0127-03"/> & </s> <s xml:id="echoid-s3184" xml:space="preserve">eſt FM, parallela A m <anchor type="note" xlink:href="" symbol="*"/>, ut & </s> <s xml:id="echoid-s3185" xml:space="preserve">Q q; </s> <s xml:id="echoid-s3186" xml:space="preserve">unde ſequitur FMQN eſſe paral.</s> <s xml:id="echoid-s3187" xml:space="preserve"> <anchor type="note" xlink:label="note-0127-04a" xlink:href="note-0127-04"/> lelogrammum, & </s> <s xml:id="echoid-s3188" xml:space="preserve">æquales eſie FN, QM; </s> <s xml:id="echoid-s3189" xml:space="preserve">ſunt etiam æquales qm, AN, <lb/>in parallelogrammo m AN q.</s> <s xml:id="echoid-s3190" xml:space="preserve"/> </p> <div xml:id="echoid-div490" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">285 316.</note> <note symbol="*" position="right" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">32 27 <lb/>El. III.</note> <note symbol="*" position="right" xlink:label="note-0127-04" xlink:href="note-0127-04a" xml:space="preserve">27. El. I.</note> </div> <p> <s xml:id="echoid-s3191" xml:space="preserve">Linea mq, aut AN, æqualis eſt arcui A m <anchor type="note" xlink:href="" symbol="*"/>, aut arcui FM; </s> <s xml:id="echoid-s3192" xml:space="preserve">AF, æ- <anchor type="note" xlink:label="note-0127-05a" xlink:href="note-0127-05"/> qualis eſt ſemicirculo FMB <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3193" xml:space="preserve">idcirco NF, aut QM, æqualis eſt arcui <anchor type="note" xlink:label="note-0127-06a" xlink:href="note-0127-06"/> MEB, & </s> <s xml:id="echoid-s3194" xml:space="preserve">punctum Q, ideſt fili extremitas datur in cycloïde ADB <anchor type="note" xlink:href="" symbol="*"/>, quam <anchor type="note" xlink:label="note-0127-07a" xlink:href="note-0127-07"/> integram extremitas hæc percurret dum totum filum evolvitur.</s> <s xml:id="echoid-s3195" xml:space="preserve"/> </p> <div xml:id="echoid-div491" type="float" level="2" n="9"> <note symbol="*" position="right" xlink:label="note-0127-05" xlink:href="note-0127-05a" xml:space="preserve">325.</note> <note symbol="*" position="right" xlink:label="note-0127-06" xlink:href="note-0127-06a" xml:space="preserve">282. 315.</note> <note symbol="*" position="right" xlink:label="note-0127-07" xlink:href="note-0127-07a" xml:space="preserve">315.</note> </div> </div> <div xml:id="echoid-div493" type="section" level="1" n="157"> <head xml:id="echoid-head226" xml:space="preserve">SHOLIUM 4.</head> <head xml:id="echoid-head227" style="it" xml:space="preserve">De linea celerrimi deſcenſus.</head> <p> <s xml:id="echoid-s3196" xml:space="preserve">Monuimus ſuperius <anchor type="note" xlink:href="" symbol="*"/>, quod ex deinde demonſtratis etiam patuit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3197" xml:space="preserve">corpus <anchor type="note" xlink:label="note-0127-08a" xlink:href="note-0127-08"/> per arcus circuli exiguos breviori tempore deſcendere, quàm per ho-<lb/> <anchor type="note" xlink:label="note-0127-09a" xlink:href="note-0127-09"/> rum arcuum chordas. </s> <s xml:id="echoid-s3198" xml:space="preserve">Unde patet corpus quod à puncto ad punctum de-<lb/>ſcendit, quando puncta ambo non in eadem verticali dantur, ut viam ſuam <lb/>breviſſimo tempore peragat, non debere per lineam rectam incedere. </s> <s xml:id="echoid-s3199" xml:space="preserve">Quam-<lb/>nam autem lineam ſequi debeat, lubet hìc demonſtrate; </s> <s xml:id="echoid-s3200" xml:space="preserve">quia ad hoc uſu ve-<lb/>niunt quæ in ſuperiori ſcholio de Cycloïde demonſtrata ſunt.</s> <s xml:id="echoid-s3201" xml:space="preserve"/> </p> <div xml:id="echoid-div493" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0127-08" xlink:href="note-0127-08a" xml:space="preserve">289.</note> <note symbol="*" position="right" xlink:label="note-0127-09" xlink:href="note-0127-09a" xml:space="preserve">307.</note> </div> <p> <s xml:id="echoid-s3202" xml:space="preserve">Sint puncta duo A & </s> <s xml:id="echoid-s3203" xml:space="preserve">B, lineâ CD ſeparata; </s> <s xml:id="echoid-s3204" xml:space="preserve">moveatur punctum & </s> <s xml:id="echoid-s3205" xml:space="preserve">ab A <lb/> <anchor type="note" xlink:label="note-0127-10a" xlink:href="note-0127-10"/> tendat ad B; </s> <s xml:id="echoid-s3206" xml:space="preserve">ſed ea lege, ut antequam ad lineam CD perveniat, feratur velo-<lb/> <anchor type="note" xlink:label="note-0127-11a" xlink:href="note-0127-11"/> citate quam dicimus v, ubi autem tranſivit lineam hanc incedat celeritate <lb/>majori quam vocamus c: </s> <s xml:id="echoid-s3207" xml:space="preserve">Ponamus ulterius punctum velocitatibus ſingulis <lb/>rectas vias percurrere; </s> <s xml:id="echoid-s3208" xml:space="preserve">ideòque moveri per rectam AB, aut lineas AE, EB <lb/>peragrare: </s> <s xml:id="echoid-s3209" xml:space="preserve">determinandum, quomodo motum dirigere debeat, ut tempore <lb/>omnium breviſſimo perveniat ex A in B,</s> </p> <div xml:id="echoid-div494" type="float" level="2" n="2"> <note position="right" xlink:label="note-0127-10" xlink:href="note-0127-10a" xml:space="preserve">319.</note> <note position="right" xlink:label="note-0127-11" xlink:href="note-0127-11a" xml:space="preserve">TAB. XII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s3210" xml:space="preserve">Ponamus tempus quo corpus, velocitate v, lineam quamcunque percur-<lb/>rit ipſâ lineâ percurfâ repræſentari; </s> <s xml:id="echoid-s3211" xml:space="preserve">tempus quo linea percurritur, velocita-<lb/>te aliâ majori, eo brevius eſt, quo velocitas major eſt, & </s> <s xml:id="echoid-s3212" xml:space="preserve">minuitur in ratio-<lb/>ne in qua velocitas augetur; </s> <s xml:id="echoid-s3213" xml:space="preserve">tempus ergo, in quo linea quæcunque, veloci-<lb/>tate c percurritur, repræſentabitur lineâ minore ipſâ percurſâ, & </s> <s xml:id="echoid-s3214" xml:space="preserve">quæ ad percur-<lb/>ſam habet rationem quæ datur inter v & </s> <s xml:id="echoid-s3215" xml:space="preserve">c.</s> <s xml:id="echoid-s3216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3217" xml:space="preserve">Si punctum eat per AE & </s> <s xml:id="echoid-s3218" xml:space="preserve">EB tempus motus per AE; </s> <s xml:id="echoid-s3219" xml:space="preserve">quia velocitate v <pb o="76" file="0128" n="139" rhead="PHYSICES ELEMENTA"/> percurritur linea hæc, hac ipſâ lineâ repræſentatur; </s> <s xml:id="echoid-s3220" xml:space="preserve">tempus quo EB peragratur, <lb/>repræſentatur lineâ EF, quæ ſe habet ad EB, ut v ad c. </s> <s xml:id="echoid-s3221" xml:space="preserve">Punctum ve-<lb/>ro F determinatur ſi ex B ad CD ducatur BD perpendicularis, fiatque c, v:</s> <s xml:id="echoid-s3222" xml:space="preserve">: <lb/>BD, LD & </s> <s xml:id="echoid-s3223" xml:space="preserve">per L ad DC ducatur parallela, ſecabit hæc BE in puncto F: <lb/></s> <s xml:id="echoid-s3224" xml:space="preserve">nam propter parallelas ED, FL, habemus BD, LD :</s> <s xml:id="echoid-s3225" xml:space="preserve">: BE, FE.</s> <s xml:id="echoid-s3226" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3227" xml:space="preserve">Ex hac demoſiſtratione etiam ſequitur, ſi punctum per lineas alias AM, <lb/>MB, progrediatur, quarum ultima ſecat LF in N, tempus motus repræ-<lb/>ſentari lineis AM, MN, ita ut determinandum ſit per quod punctum lineæ <lb/>CD punctum mobile tranſeat, quando ſumma talium linearum tempora repræ-<lb/>ſentantium eſt omnium minima; </s> <s xml:id="echoid-s3228" xml:space="preserve">quod ut fiat ad ſequentia attendendum.</s> <s xml:id="echoid-s3229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3230" xml:space="preserve">Summas ab utraque parte recedendo à puncto quæſito augeri continuo; <lb/></s> <s xml:id="echoid-s3231" xml:space="preserve">ideoque in eo puncto ſolo ſummas vicinas eſſe æquales, idcirco ſi punctum <lb/>hoc ſit E erunt æquales AE + EF & </s> <s xml:id="echoid-s3232" xml:space="preserve">Ae + ef ex qua æqualitate ſitus pun-<lb/> <anchor type="note" xlink:label="note-0128-01a" xlink:href="note-0128-01"/> cti E deducendus eſt.</s> <s xml:id="echoid-s3233" xml:space="preserve"/> </p> <div xml:id="echoid-div495" type="float" level="2" n="3"> <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">TAB XII. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s3234" xml:space="preserve">Centro A, radio A e deſcribatur circuli arcus eb; </s> <s xml:id="echoid-s3235" xml:space="preserve">Centro Bradiis Bf, & </s> <s xml:id="echoid-s3236" xml:space="preserve"><lb/>BE deſcribantur arcus E i, fg, eruntque æquales Ab + Eg & </s> <s xml:id="echoid-s3237" xml:space="preserve">A e + i f ſubtra-<lb/>ctis hiſce quantitatibus æqualibus ex AE + EF = Ae + ef, reſtanth E + gF = ei. <lb/></s> <s xml:id="echoid-s3238" xml:space="preserve">Unde deducimus. </s> <s xml:id="echoid-s3239" xml:space="preserve">hE = ei-gF. </s> <s xml:id="echoid-s3240" xml:space="preserve">Propter triangula ſimilia eiE, fgF, & </s> <s xml:id="echoid-s3241" xml:space="preserve">Bfg, <lb/>Bie ut & </s> <s xml:id="echoid-s3242" xml:space="preserve">BFL, BED,</s> </p> <p> <s xml:id="echoid-s3243" xml:space="preserve">ei, g F :</s> <s xml:id="echoid-s3244" xml:space="preserve">: Ei, fg, :</s> <s xml:id="echoid-s3245" xml:space="preserve">: BE, Bf aut BF (difterentia enim eſt infi nite exigua) <lb/>:</s> <s xml:id="echoid-s3246" xml:space="preserve">: BD, BL. </s> <s xml:id="echoid-s3247" xml:space="preserve">Dividendo</s> </p> <p> <s xml:id="echoid-s3248" xml:space="preserve">ei, ei g F = bE:</s> <s xml:id="echoid-s3249" xml:space="preserve">: BD, BD-BL = LD; </s> <s xml:id="echoid-s3250" xml:space="preserve">id eſt ut velocitas infra lineam ad <lb/>velocitatem ſupra lineam.</s> <s xml:id="echoid-s3251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3252" xml:space="preserve">Triangula eiE, ENO, ſunt ſimilia ut & </s> <s xml:id="echoid-s3253" xml:space="preserve">eb E & </s> <s xml:id="echoid-s3254" xml:space="preserve">e MP; </s> <s xml:id="echoid-s3255" xml:space="preserve">ergo</s> </p> <p> <s xml:id="echoid-s3256" xml:space="preserve">ei, Ee:</s> <s xml:id="echoid-s3257" xml:space="preserve">: EO, EN</s> </p> <p> <s xml:id="echoid-s3258" xml:space="preserve">bE, Ee:</s> <s xml:id="echoid-s3259" xml:space="preserve">: EP, Me = EN nam ſunt radii ejuſdem circuli; </s> <s xml:id="echoid-s3260" xml:space="preserve">E e c-<lb/>nim eſt infinite exigua.</s> <s xml:id="echoid-s3261" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3262" xml:space="preserve">Ex æquo ei, bE:</s> <s xml:id="echoid-s3263" xml:space="preserve">: EO, EP. </s> <s xml:id="echoid-s3264" xml:space="preserve">Sunt autem hæ lineæ coſinus angulorum <lb/> <anchor type="note" xlink:label="note-0128-02a" xlink:href="note-0128-02"/> quos directiones motuum efficiunt cum linea CD quæ ſpatia ſeparat in quibus velo-<lb/>eitates differunt: </s> <s xml:id="echoid-s3265" xml:space="preserve">qui ergo coſinus directionum ſunt inter ut velocitates in ipſis <lb/>iltis directionibus, quando tempus eſt omnium breviſſimum.</s> <s xml:id="echoid-s3266" xml:space="preserve"/> </p> <div xml:id="echoid-div496" type="float" level="2" n="4"> <note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">320.</note> </div> <p> <s xml:id="echoid-s3267" xml:space="preserve">Moveatur iterum corpus ex A & </s> <s xml:id="echoid-s3268" xml:space="preserve">tendat ad B, ea conditioneut dum tranſ-<lb/> <anchor type="note" xlink:label="note-0128-03a" xlink:href="note-0128-03"/> it lineas CD, IL, MN, OP, ſingulis vicibus velocitatem mutet, quæ-<lb/> <anchor type="note" xlink:label="note-0128-04a" xlink:href="note-0128-04"/> ritur qua lege movetur, poſitis hiſce lineis parallelis, ut tempore breviſſimo <lb/>ex A ad B perveniat.</s> <s xml:id="echoid-s3269" xml:space="preserve"/> </p> <div xml:id="echoid-div497" type="float" level="2" n="5"> <note position="left" xlink:label="note-0128-03" xlink:href="note-0128-03a" xml:space="preserve">321.</note> <note position="left" xlink:label="note-0128-04" xlink:href="note-0128-04a" xml:space="preserve">TAB. XII. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s3270" xml:space="preserve">Requiritur ut corpus ex A ad F perveniat tempore breviſſimo poſſibili, <lb/>ut & </s> <s xml:id="echoid-s3271" xml:space="preserve">ex E ad G, ex F ad H, & </s> <s xml:id="echoid-s3272" xml:space="preserve">ex G ad B, aliter enim in toto motu tem-<lb/>pus brevius dari poteſt. </s> <s xml:id="echoid-s3273" xml:space="preserve">Ideò coſinus angulorum quos motus directiones AE, <lb/> <anchor type="note" xlink:label="note-0128-05a" xlink:href="note-0128-05"/> EF, FG, GH, HB, efficiunt cum lineis, parallelis inter ſe, ſeparantibus ſpa-<lb/>tia in quibus diverſa eſt velocitas, ſunt reſpectivè inter ſe ut velocitates quibus ſin-<lb/>gu'a percurruntur.</s> <s xml:id="echoid-s3274" xml:space="preserve"/> </p> <div xml:id="echoid-div498" type="float" level="2" n="6"> <note position="left" xlink:label="note-0128-05" xlink:href="note-0128-05a" xml:space="preserve">322.</note> </div> <p> <s xml:id="echoid-s3275" xml:space="preserve">Conſideremus nunc corpus quod gravitate deſcendit. </s> <s xml:id="echoid-s3276" xml:space="preserve">Celeritas continuo <lb/>deſcendendo augetur, & </s> <s xml:id="echoid-s3277" xml:space="preserve">ad eandem profunditatem ubique eſt eadem <anchor type="note" xlink:href="" symbol="*"/>, innu- <anchor type="note" xlink:label="note-0128-06a" xlink:href="note-0128-06"/> meris ergo, & </s> <s xml:id="echoid-s3278" xml:space="preserve">inter ſe infinitè parum diſtantibus, planis horizontalibus divi-<lb/>duntur ſpatia in quibus celeritas variat: </s> <s xml:id="echoid-s3279" xml:space="preserve">Linea ergo celerrimi deſcenſus inter <lb/> <anchor type="note" xlink:label="note-0128-07a" xlink:href="note-0128-07"/> duo puncta eſt cujus tangens ubique cum borizonte eſſicit angulum, cujus coſinus <lb/>velocitati cadendo acquiſitæ proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>, id eſt radici quadratæ altitu- <anchor type="note" xlink:label="note-0128-08a" xlink:href="note-0128-08"/> dinis per quam corpus cecidit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3280" xml:space="preserve">Hanc autem eſſe Cycloïdis proprietatem de- <anchor type="note" xlink:label="note-0128-09a" xlink:href="note-0128-09"/> monſtramus.</s> <s xml:id="echoid-s3281" xml:space="preserve"/> </p> <div xml:id="echoid-div499" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0128-06" xlink:href="note-0128-06a" xml:space="preserve">271.</note> <note position="left" xlink:label="note-0128-07" xlink:href="note-0128-07a" xml:space="preserve">323.</note> <note symbol="*" position="left" xlink:label="note-0128-08" xlink:href="note-0128-08a" xml:space="preserve">322.</note> <note symbol="*" position="left" xlink:label="note-0128-09" xlink:href="note-0128-09a" xml:space="preserve">255-271.</note> </div> <pb o="77" file="0129" n="140" rhead="MATHEMATICA. LIB. I. CAP. XIX."/> <p> <s xml:id="echoid-s3282" xml:space="preserve">Ponamus Cycloïdem ADB, inverſam, cujus axis ſit verticalis, & </s> <s xml:id="echoid-s3283" xml:space="preserve">corpus <lb/> <anchor type="note" xlink:label="note-0129-01a" xlink:href="note-0129-01"/> ex A deſcendere, demonſtrandum anguliut d DE, aut BEL <anchor type="note" xlink:href="" symbol="*"/>, coſinum pro- <anchor type="note" xlink:label="note-0129-02a" xlink:href="note-0129-02"/> portionalem eſſe radici quadratæ altitudinis FL <anchor type="note" xlink:href="" symbol="*"/>, id eſt proportionem ſe- <anchor type="note" xlink:label="note-0129-03a" xlink:href="note-0129-03"/> qui chordæ FE cujus quadratum ad inſtar altitudinis FL augetur & </s> <s xml:id="echoid-s3284" xml:space="preserve">minui-<lb/> <anchor type="note" xlink:label="note-0129-04a" xlink:href="note-0129-04"/> tur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3285" xml:space="preserve">Angulus BE l æqualis eſt angulo BFE <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3286" xml:space="preserve">cujus coſinus ſi centrum <anchor type="note" xlink:label="note-0129-05a" xlink:href="note-0129-05"/> circuli ſit F, & </s> <s xml:id="echoid-s3287" xml:space="preserve">radius FB, eſt FE; </s> <s xml:id="echoid-s3288" xml:space="preserve">quod in omnibus punctis cycloïdis Io-<lb/> <anchor type="note" xlink:label="note-0129-06a" xlink:href="note-0129-06"/> cum habet, manente eodem radio FB.</s> <s xml:id="echoid-s3289" xml:space="preserve"/> </p> <div xml:id="echoid-div500" type="float" level="2" n="8"> <note position="right" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">324.</note> <note symbol="*" position="right" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">285. 316.</note> <note symbol="*" position="right" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">323.</note> <note position="right" xlink:label="note-0129-04" xlink:href="note-0129-04a" xml:space="preserve">TAB. XII. <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">293.</note> <note position="right" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">8. El. VI.</note> </div> <p style="it"> <s xml:id="echoid-s3290" xml:space="preserve">Linea ergo celerrimi deſcenſus, à puncto ad punctum, eſt Cycloïs inverſa, cu-<lb/> <anchor type="note" xlink:label="note-0129-07a" xlink:href="note-0129-07"/> jus punctum extremum, ut A, cum ſuperiori puncto coincidit & </s> <s xml:id="echoid-s3291" xml:space="preserve">quæ per punctum <lb/>alterum tranſit.</s> <s xml:id="echoid-s3292" xml:space="preserve"/> </p> <div xml:id="echoid-div501" type="float" level="2" n="9"> <note position="right" xlink:label="note-0129-07" xlink:href="note-0129-07a" xml:space="preserve">325.</note> </div> </div> <div xml:id="echoid-div503" type="section" level="1" n="158"> <head xml:id="echoid-head228" xml:space="preserve">CAPUT XX.</head> <head xml:id="echoid-head229" style="it" xml:space="preserve">De Projectione Gravium.</head> <p> <s xml:id="echoid-s3293" xml:space="preserve">SI in corpus motum potentia agat, mutatur motus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3294" xml:space="preserve"> <anchor type="note" xlink:label="note-0129-08a" xlink:href="note-0129-08"/> Corpus projiciatur per AB, in tempore, in quo poteſt <lb/> <anchor type="note" xlink:label="note-0129-09a" xlink:href="note-0129-09"/> percurrere AB, vi gravitatis, fertur terræ centrum verſus <lb/> <anchor type="note" xlink:label="note-0129-10a" xlink:href="note-0129-10"/> per BF, & </s> <s xml:id="echoid-s3295" xml:space="preserve">ita, motu compoſito ex iſtis duobus, movetur <lb/>per AF <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3296" xml:space="preserve">& </s> <s xml:id="echoid-s3297" xml:space="preserve">hoc motu, ſecundo momento, percurreret <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0129-11a" xlink:href="note-0129-11"/> FC, ipſi AF æqualem, niſi ſecundo momento eadem vi <lb/>gravitatis translatum foret per CG, ita ut motus in ſecun-<lb/>do momento ſit per FG; </s> <s xml:id="echoid-s3298" xml:space="preserve">eodem modo, motus tertii mo-<lb/>menti eſt per GH, & </s> <s xml:id="echoid-s3299" xml:space="preserve">quarti momenti per HI; </s> <s xml:id="echoid-s3300" xml:space="preserve">cùm verò <lb/>vis gravitatis continuò agat, illa temporis momenta mini-<lb/>ma ſunt, & </s> <s xml:id="echoid-s3301" xml:space="preserve">ubique dabitur motus aliter compoſitus, id eſt, <lb/>directionis inflexio; </s> <s xml:id="echoid-s3302" xml:space="preserve">in eo caſu ergo corpus movetur in li-<lb/>nea curva.</s> <s xml:id="echoid-s3303" xml:space="preserve"/> </p> <div xml:id="echoid-div503" type="float" level="2" n="1"> <note position="right" xlink:label="note-0129-08" xlink:href="note-0129-08a" xml:space="preserve">326.</note> <note position="right" xlink:label="note-0129-09" xlink:href="note-0129-09a" xml:space="preserve">TAB XIII. <lb/>fig. I.</note> <note symbol="*" position="right" xlink:label="note-0129-10" xlink:href="note-0129-10a" xml:space="preserve">245</note> <note symbol="*" position="right" xlink:label="note-0129-11" xlink:href="note-0129-11a" xml:space="preserve">246.</note> </div> <p> <s xml:id="echoid-s3304" xml:space="preserve">Hic motus corporis ex projectione magis ſimpliciter con-<lb/> <anchor type="note" xlink:label="note-0129-12a" xlink:href="note-0129-12"/> ſiderari poteſt in omnibus projectionibus, quæ a nobis fie-<lb/>ri poſſunt; </s> <s xml:id="echoid-s3305" xml:space="preserve">quia omnes lineæ, quæ ad terræ centrum ten-<lb/>dunt, pro parallelis haberi poſſunt; </s> <s xml:id="echoid-s3306" xml:space="preserve">quare directio motus <lb/>ex gravitate ſemper eſt eadem; </s> <s xml:id="echoid-s3307" xml:space="preserve">unde motus ex projectione <lb/>ex duobus tantum motibus conſtat, primo æquabili per li-<lb/>neam projectionis, ſecundo terram verſus accelerato <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3308" xml:space="preserve"/> </p> <div xml:id="echoid-div504" type="float" level="2" n="2"> <note position="right" xlink:label="note-0129-12" xlink:href="note-0129-12a" xml:space="preserve">327.</note> </div> <note symbol="*" position="right" xml:space="preserve">251.</note> <p> <s xml:id="echoid-s3309" xml:space="preserve">Projiciatur corpus per lineam AE, horizonti parallelam; <lb/></s> <s xml:id="echoid-s3310" xml:space="preserve"> <anchor type="note" xlink:label="note-0129-14a" xlink:href="note-0129-14"/> temporibus æqualibus, hoc motu, percurret partes æquales <lb/>AB, BC, CD, DE: </s> <s xml:id="echoid-s3311" xml:space="preserve">Ex gravitate fertur motu ad horizontem <lb/>perpendiculari, directione BF, CG, DH, aut EI, quæ hìc <lb/>parallelæ ponuntur; </s> <s xml:id="echoid-s3312" xml:space="preserve">motus hic eſt acceleratus, & </s> <s xml:id="echoid-s3313" xml:space="preserve">ideò, ſi <pb o="78" file="0130" n="141" rhead="PHYSICES ELEMENTA"/> poſt primum momentum corpus ſit in F, poſt ſecundum <lb/>erit in G, poſt tertium in H, poſt quartum in I, ita quidem <lb/>ut poſito BF unum, CG ſit quatuor, DH novem, & </s> <s xml:id="echoid-s3314" xml:space="preserve">EI <lb/>ſedecim <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3315" xml:space="preserve">Corpus percurret curvam tranſeuntem per o- <anchor type="note" xlink:label="note-0130-01a" xlink:href="note-0130-01"/> mnia puncta, quæ eodem modo ac F, G, H, I, determinari <lb/>poſſunt, vocaturque Parabola.</s> <s xml:id="echoid-s3316" xml:space="preserve"/> </p> <div xml:id="echoid-div505" type="float" level="2" n="3"> <note position="right" xlink:label="note-0129-14" xlink:href="note-0129-14a" xml:space="preserve">TAB XIII. <lb/>fig. 25</note> <note symbol="*" position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">255.</note> </div> </div> <div xml:id="echoid-div507" type="section" level="1" n="159"> <head xml:id="echoid-head230" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head231" style="it" xml:space="preserve">Qua demonſtrata de corporum projectione confirmantur.</head> <p> <s xml:id="echoid-s3317" xml:space="preserve">Conſtat hæc ex tribus partibus, quarum conſtructio ex <lb/> <anchor type="note" xlink:label="note-0130-02a" xlink:href="note-0130-02"/> figura ſatis patet. </s> <s xml:id="echoid-s3318" xml:space="preserve">Ah eſt altitudinis ſex pollicum; </s> <s xml:id="echoid-s3319" xml:space="preserve">DE eſt <lb/> <anchor type="note" xlink:label="note-0130-03a" xlink:href="note-0130-03"/> exacte ejuſdem altitudinis; </s> <s xml:id="echoid-s3320" xml:space="preserve">longitudo b H eſt duodecim <lb/>pollicum, poſito puncto H, ad diſtantiam unius pollicis ab <lb/>extremitate cavitatis in qua punctum hocce ponitur.</s> <s xml:id="echoid-s3321" xml:space="preserve"/> </p> <div xml:id="echoid-div507" type="float" level="2" n="1"> <note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">328.</note> <note position="left" xlink:label="note-0130-03" xlink:href="note-0130-03a" xml:space="preserve">TAB. XIII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s3322" xml:space="preserve">Circulariter, aut juxta aliam curvam quamcunque, ex-<lb/>cavatur EA; </s> <s xml:id="echoid-s3323" xml:space="preserve">& </s> <s xml:id="echoid-s3324" xml:space="preserve">lamina ferri, ſtanno illiti, & </s> <s xml:id="echoid-s3325" xml:space="preserve">admodum <lb/>politi, obtegitur; </s> <s xml:id="echoid-s3326" xml:space="preserve">ut globus æneus libere juxta illam cur-<lb/>vam devolvi poſſit; </s> <s xml:id="echoid-s3327" xml:space="preserve">in qua devolutione obſervandum, ut <lb/>curvæ directio in A ſit horizontalis.</s> <s xml:id="echoid-s3328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3329" xml:space="preserve">Dividitur A h in novem partes æquales, quarum A f u-<lb/>na eſt, A g quatuor.</s> <s xml:id="echoid-s3330" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3331" xml:space="preserve">Quando huic primæ parti Machinæ conjungitur ſecunda <lb/> <anchor type="note" xlink:label="note-0130-04a" xlink:href="note-0130-04"/> B, pertingit hæc ad g, & </s> <s xml:id="echoid-s3332" xml:space="preserve">g G eſt octo pollicum: </s> <s xml:id="echoid-s3333" xml:space="preserve">ſi huic ſu-<lb/>perimponatur pars tertia C, pertingit hæc ultima ad f, & </s> <s xml:id="echoid-s3334" xml:space="preserve"><lb/>fF eſt quatuor pollicum.</s> <s xml:id="echoid-s3335" xml:space="preserve"/> </p> <div xml:id="echoid-div508" type="float" level="2" n="2"> <note position="left" xlink:label="note-0130-04" xlink:href="note-0130-04a" xml:space="preserve">TAB. XIII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s3336" xml:space="preserve">Suſtinetur Machina hæc tribus cochleis, quarum ope li-<lb/>nea A b ponitur in ſitu verticali, qui ſitus determinatur per-<lb/>pendiculo ad partem machinæ poſticam; </s> <s xml:id="echoid-s3337" xml:space="preserve">eodem omnino <lb/>modo ac hæc in alia Machina exhibentur in fig. </s> <s xml:id="echoid-s3338" xml:space="preserve">I. </s> <s xml:id="echoid-s3339" xml:space="preserve">Tab XII. <lb/></s> <s xml:id="echoid-s3340" xml:space="preserve">& </s> <s xml:id="echoid-s3341" xml:space="preserve">explicantur in n. </s> <s xml:id="echoid-s3342" xml:space="preserve">276.</s> <s xml:id="echoid-s3343" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3344" xml:space="preserve">Diameter globi P, qui in Experimentis dimittitur juxta <lb/>curvam EA, eſt circiter ſemi-pollicis; </s> <s xml:id="echoid-s3345" xml:space="preserve">nec minori globo, <lb/>aut Machinâ, quàm quæ hìc deſcribitur, majori utendum: <lb/></s> <s xml:id="echoid-s3346" xml:space="preserve">quo enim corpora ſunt minora & </s> <s xml:id="echoid-s3347" xml:space="preserve">motus celeriores, eo etiam <lb/>magis, ſervatâ proportione, motus aëris reſiſtentiâ re-<lb/>tardatur; </s> <s xml:id="echoid-s3348" xml:space="preserve">ut ſuo loco dicetur.</s> <s xml:id="echoid-s3349" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3350" xml:space="preserve">Quando globus P ab E dimittitur, devolvendo per cur-<lb/>vam EA certam acquirit velocitatem, quæ in repetitis de- <pb o="78" file="0131" n="142"/> <anchor type="figure" xlink:label="fig-0131-01a" xlink:href="fig-0131-01"/> <pb file="0131a" n="143"/> <anchor type="figure" xlink:label="fig-0131a-01a" xlink:href="fig-0131a-01"/> <pb file="0132" n="144"/> <pb o="79" file="0133" n="145" rhead="MATHEMATICA. LIB. I. CAP. XX."/> volutionibus ſemper eſt eadem; </s> <s xml:id="echoid-s3351" xml:space="preserve">eaque cum celeritate, & </s> <s xml:id="echoid-s3352" xml:space="preserve"><lb/>directione horizontali, motum continuat.</s> <s xml:id="echoid-s3353" xml:space="preserve"/> </p> <div xml:id="echoid-div509" type="float" level="2" n="3"> <figure xlink:label="fig-0131-01" xlink:href="fig-0131-01a"> <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131-01"/> </figure> <figure xlink:label="fig-0131a-01" xlink:href="fig-0131a-01a"> <image file="0131a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131a-01"/> </figure> </div> </div> <div xml:id="echoid-div511" type="section" level="1" n="160"> <head xml:id="echoid-head232" xml:space="preserve"><emph style="sc">Experimentum.</emph></head> <p> <s xml:id="echoid-s3354" xml:space="preserve">Junctis tribus Machinæ partibus; </s> <s xml:id="echoid-s3355" xml:space="preserve">ut in fig. </s> <s xml:id="echoid-s3356" xml:space="preserve">4.</s> <s xml:id="echoid-s3357" xml:space="preserve">, dimittatur <lb/> <anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/> globus P ab E, impinget in F. </s> <s xml:id="echoid-s3358" xml:space="preserve">Sublata parte minori C, ite-<lb/>rum dimittatur globus, impinget in G. </s> <s xml:id="echoid-s3359" xml:space="preserve">Sublata tandem <lb/>parte B, & </s> <s xml:id="echoid-s3360" xml:space="preserve">globo dimiſſo, impingit in H.</s> <s xml:id="echoid-s3361" xml:space="preserve"/> </p> <div xml:id="echoid-div511" type="float" level="2" n="1"> <note position="right" xlink:label="note-0133-01" xlink:href="note-0133-01a" xml:space="preserve">329.</note> </div> <p> <s xml:id="echoid-s3362" xml:space="preserve">Si argilla mollis detur in H & </s> <s xml:id="echoid-s3363" xml:space="preserve">G, punctum impactus exa-<lb/>ctiſſime notatur; </s> <s xml:id="echoid-s3364" xml:space="preserve">in puncto F, propter directionem motus <lb/>nimium obliquam, hæc methodus locum non habet; </s> <s xml:id="echoid-s3365" xml:space="preserve">ſed <lb/>repetitis Experimentis, ſolo viſu, punctum hocce ſatis de-<lb/>terminatur.</s> <s xml:id="echoid-s3366" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3367" xml:space="preserve">Propoſitio n. </s> <s xml:id="echoid-s3368" xml:space="preserve">257, hac Machina Experimento confirma-<lb/> <anchor type="note" xlink:label="note-0133-02a" xlink:href="note-0133-02"/> tur; </s> <s xml:id="echoid-s3369" xml:space="preserve">nam ut ſtatim dictum, globus devolvens per EA im-<lb/> <anchor type="note" xlink:label="note-0133-03a" xlink:href="note-0133-03"/> pingit in H. </s> <s xml:id="echoid-s3370" xml:space="preserve">Devolvendo per EA acquirit celeritatem, <lb/>quam cadendo per ED potuiſſet acquirere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3371" xml:space="preserve">ea cum celeri- <anchor type="note" xlink:label="note-0133-04a" xlink:href="note-0133-04"/> tate, ex puncto A, horizontaliter projicitur, & </s> <s xml:id="echoid-s3372" xml:space="preserve">æquabili-<lb/>ter ſecundum illam directionem movetur per b H, dum ca-<lb/>dendo percurrit A b, ipſi ED æqualem; </s> <s xml:id="echoid-s3373" xml:space="preserve">b H vero eſt i-<lb/>pſius A b aut ED dupla.</s> <s xml:id="echoid-s3374" xml:space="preserve"/> </p> <div xml:id="echoid-div512" type="float" level="2" n="2"> <note position="right" xlink:label="note-0133-02" xlink:href="note-0133-02a" xml:space="preserve">330.</note> <note position="right" xlink:label="note-0133-03" xlink:href="note-0133-03a" xml:space="preserve">TAB XIII. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0133-04" xlink:href="note-0133-04a" xml:space="preserve">271.</note> </div> <p> <s xml:id="echoid-s3375" xml:space="preserve">Quæ de curva a corpore horizontaliter projecto dicta ſunt, <lb/> <anchor type="note" xlink:label="note-0133-05a" xlink:href="note-0133-05"/> etiam pertinent ad projectionem quamcumque.</s> <s xml:id="echoid-s3376" xml:space="preserve"/> </p> <div xml:id="echoid-div513" type="float" level="2" n="3"> <note position="right" xlink:label="note-0133-05" xlink:href="note-0133-05a" xml:space="preserve">331.</note> </div> <p> <s xml:id="echoid-s3377" xml:space="preserve">Projiciatur corpus per AE; </s> <s xml:id="echoid-s3378" xml:space="preserve">& </s> <s xml:id="echoid-s3379" xml:space="preserve">ſint AB, BC, CD, DE, <lb/> <anchor type="note" xlink:label="note-0133-06a" xlink:href="note-0133-06"/> æquales; </s> <s xml:id="echoid-s3380" xml:space="preserve">corpus percurret curvam AFGHI ita, ut ver-<lb/>ticales lineæ BF, CG, DH, EI ſint inter ſe, ut I. </s> <s xml:id="echoid-s3381" xml:space="preserve">4. </s> <s xml:id="echoid-s3382" xml:space="preserve">9. <lb/></s> <s xml:id="echoid-s3383" xml:space="preserve">& </s> <s xml:id="echoid-s3384" xml:space="preserve">16.</s> <s xml:id="echoid-s3385" xml:space="preserve">; in quo caſu etiam curva Parabola vocatur.</s> <s xml:id="echoid-s3386" xml:space="preserve"/> </p> <div xml:id="echoid-div514" type="float" level="2" n="4"> <note position="right" xlink:label="note-0133-06" xlink:href="note-0133-06a" xml:space="preserve">TAB. XIII. <lb/>fig. 506.</note> </div> </div> <div xml:id="echoid-div516" type="section" level="1" n="161"> <head xml:id="echoid-head233" xml:space="preserve"><emph style="sc">Definitio.</emph></head> <p> <s xml:id="echoid-s3387" xml:space="preserve">Sit AI planum quod per A tranſit, ſi curva memorata <lb/> <anchor type="note" xlink:label="note-0133-07a" xlink:href="note-0133-07"/> hoc ſecet in I; </s> <s xml:id="echoid-s3388" xml:space="preserve">AI vocatur amplitudo jactus</s> </p> <div xml:id="echoid-div516" type="float" level="2" n="1"> <note position="right" xlink:label="note-0133-07" xlink:href="note-0133-07a" xml:space="preserve">332.</note> </div> <p> <s xml:id="echoid-s3389" xml:space="preserve">Motus corporum, quæ eadem celeritate projiciuntur, cum <lb/>directionibus diverſe inclinatis, poſſunt inter ſe comparari:</s> <s xml:id="echoid-s3390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3391" xml:space="preserve">Poteſtque corpus celeritate data in plano dato ad diſtantiam <lb/> <anchor type="note" xlink:label="note-0133-08a" xlink:href="note-0133-08"/> quamcunque projici. </s> <s xml:id="echoid-s3392" xml:space="preserve">Sit celeritas data illa, quam corpus acqui-<lb/>rit cadendo ab altitudine LA, quam horizonti AT perpendi-<lb/>cularem concipimus, & </s> <s xml:id="echoid-s3393" xml:space="preserve">corpus in plano AI in I projicien-<lb/>dum ſit. </s> <s xml:id="echoid-s3394" xml:space="preserve">Ductâ LN horizonti parallelâ, erigatur AN nor- <pb o="80" file="0134" n="146" rhead="PHYSICES ELEMENTA"/> malis plano A I, ſecans L N in N; </s> <s xml:id="echoid-s3395" xml:space="preserve">centro puncto medio li-<lb/>neæ <emph style="sc">A</emph>N per <emph style="sc">A</emph> deſcribatur circulus, qui etiam per L tranſ-<lb/>ibit; </s> <s xml:id="echoid-s3396" xml:space="preserve">ſit <emph style="sc">A</emph>R pars quarta lineæ <emph style="sc">A</emph>I; </s> <s xml:id="echoid-s3397" xml:space="preserve">per R ducatur, hori-<lb/>zonti perpendicularis, id eſt parallela lineæ <emph style="sc">A</emph>L, linea R b, <lb/>quæ circulum ſecat in B & </s> <s xml:id="echoid-s3398" xml:space="preserve">b; </s> <s xml:id="echoid-s3399" xml:space="preserve">ſi corpus projiciatur per <emph style="sc">A</emph>B <lb/>aut A b cadet in I. </s> <s xml:id="echoid-s3400" xml:space="preserve">Qua methodo directio jactus determi-<lb/>natur, ſi punctum ſit in linea horizontali per A tranſeunti <lb/>(in quo caſu L & </s> <s xml:id="echoid-s3401" xml:space="preserve">N coincidunt), aut in plano quocunque <lb/>inclinato ſive ſupra ſive infra lineam hanc horizontalem.</s> <s xml:id="echoid-s3402" xml:space="preserve"/> </p> <div xml:id="echoid-div517" type="float" level="2" n="2"> <note position="right" xlink:label="note-0133-08" xlink:href="note-0133-08a" xml:space="preserve">333.</note> </div> <p> <s xml:id="echoid-s3403" xml:space="preserve">Motu æ quabili celeritate, cum qua projectio fit, corpus <lb/> <anchor type="note" xlink:label="note-0134-01a" xlink:href="note-0134-01"/> poteſt percurrere <emph style="sc">A</emph>E, dum cadit per EI Quia corpus pro-<lb/>jicitur velocitate per <emph style="sc">La</emph> cadendo acquiſita, eodem motu <lb/>æ quabili poteſt percurrere duplam <emph style="sc">La</emph> in tempore in quo <lb/>ab altitudine <emph style="sc">La</emph> cadit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3404" xml:space="preserve">Spatia, velocitate eâdem & </s> <s xml:id="echoid-s3405" xml:space="preserve">æ- <anchor type="note" xlink:label="note-0134-02a" xlink:href="note-0134-02"/> quabili percurſa, ſunt ut tempora in quibus percurruntur<anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s3406" xml:space="preserve"> <anchor type="note" xlink:label="note-0134-03a" xlink:href="note-0134-03"/> ergo tempus caſus per <emph style="sc">La</emph> ad tempus caſus per EI, ut <lb/>dupla <emph style="sc">La</emph> ad <emph style="sc">A</emph>E. </s> <s xml:id="echoid-s3407" xml:space="preserve">Ideo 2 <emph style="sc">La</emph><emph style="super">9</emph> ad <emph style="sc">A</emph>E<emph style="super">9</emph> ut, <emph style="sc">La</emph> ad <lb/>EI <anchor type="note" xlink:href="" symbol="*"/>, Quam ergo proportionem ſi demonſtremus dari in <anchor type="note" xlink:label="note-0134-04a" xlink:href="note-0134-04"/> conſtructione præ cedenti, directionem benè fuiſſe determi-<lb/>natam conſtabit.</s> <s xml:id="echoid-s3408" xml:space="preserve"/> </p> <div xml:id="echoid-div518" type="float" level="2" n="3"> <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">334.</note> <note symbol="*" position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">257.</note> <note symbol="*" position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">95.</note> <note symbol="*" position="left" xlink:label="note-0134-04" xlink:href="note-0134-04a" xml:space="preserve">255.</note> </div> <p> <s xml:id="echoid-s3409" xml:space="preserve">Ducatur LB, & </s> <s xml:id="echoid-s3410" xml:space="preserve">habemus angulum <emph style="sc">Ba</emph>R a tangente <emph style="sc">A</emph>R, <lb/>eſt enim perpendicularis radio <emph style="sc">A</emph>O, & </s> <s xml:id="echoid-s3411" xml:space="preserve">a linea circulum ſe-<lb/>cante <emph style="sc">A</emph>B formatum æ qualem angulo <emph style="sc">A</emph>MB in ſegmento <lb/> <anchor type="note" xlink:label="note-0134-05a" xlink:href="note-0134-05"/> oppoſito <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3412" xml:space="preserve">anguli etiam alterni <emph style="sc">RBa</emph>, <emph style="sc">La</emph>B, ſunt æ quales <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s3413" xml:space="preserve"> <anchor type="note" xlink:label="note-0134-06a" xlink:href="note-0134-06"/> ergo ſunt ſimilia triangula <emph style="sc">A</emph>BR, <emph style="sc">A</emph>LB, & </s> <s xml:id="echoid-s3414" xml:space="preserve">lineæ <emph style="sc">La</emph>, <lb/><emph style="sc">A</emph>B, <emph style="sc">Br</emph>, proportionales; </s> <s xml:id="echoid-s3415" xml:space="preserve">ergo <emph style="sc">La</emph><emph style="super">9</emph> ad <emph style="sc">A</emph>B<emph style="super">9</emph> ut <emph style="sc">La</emph> ad <lb/>BR; </s> <s xml:id="echoid-s3416" xml:space="preserve">ideo 2 <emph style="sc">La</emph><emph style="super">9</emph> ad 2 <emph style="sc">A</emph>B<emph style="super">9</emph>, aut <emph style="sc">A</emph>C<emph style="super">9</emph> ut <emph style="sc">La</emph> ad BR: <lb/></s> <s xml:id="echoid-s3417" xml:space="preserve">multiplicando conſequentia per quatuor, habemus 2 <emph style="sc">La</emph><emph style="super">9</emph> <lb/>ad <emph style="sc">A</emph>C<emph style="super">9</emph> multiplicatum per quatuor, id eſt 2 <emph style="sc">A</emph>C<emph style="super">9</emph>, aut <lb/><emph style="sc">A</emph>E<emph style="super">9</emph>, ut <emph style="sc">La</emph> ad 4 BR, aut EI, quod demonſtrandum <lb/>erat.</s> <s xml:id="echoid-s3418" xml:space="preserve"/> </p> <div xml:id="echoid-div519" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0134-05" xlink:href="note-0134-05a" xml:space="preserve">32 EI. III.</note> <note symbol="*" position="left" xlink:label="note-0134-06" xlink:href="note-0134-06a" xml:space="preserve">29. EI. 1.</note> </div> <p> <s xml:id="echoid-s3419" xml:space="preserve">Demonſtratio ſimilis eſt, ſi corpus per A b projiciatur. </s> <s xml:id="echoid-s3420" xml:space="preserve">Un-<lb/> <anchor type="note" xlink:label="note-0134-07a" xlink:href="note-0134-07"/> de ſequitur corpus per duas directiones poſſe projici ut in <lb/>idem punctum cadat, ſi autem diſtantia ſit omnium maxima <lb/>ad quam corpus, data velocitate, in plano dato, poteſt pro-<lb/>jici, unica eſt directio per quam projiciendum eſt corpus, <pb o="81" file="0135" n="147" rhead="MATHEMATICA. LIB. I. CAP. XX."/> punctis B & </s> <s xml:id="echoid-s3421" xml:space="preserve">b coincidentibus in Q, puncto medio arcus <lb/>LQA, a quo puncto ſemper æqualiter diſtant puncta B <lb/>& </s> <s xml:id="echoid-s3422" xml:space="preserve">b.</s> <s xml:id="echoid-s3423" xml:space="preserve"/> </p> <div xml:id="echoid-div520" type="float" level="2" n="5"> <note position="left" xlink:label="note-0134-07" xlink:href="note-0134-07a" xml:space="preserve">335.</note> </div> <p> <s xml:id="echoid-s3424" xml:space="preserve">Si AI ſit horizontalis arcus AQL, eſt ſemicirculus, & </s> <s xml:id="echoid-s3425" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0135-01a" xlink:href="note-0135-01"/> in hoc caſu amplitudo, manente celeritate, cum qua pro-<lb/>jectio fit, eſt omnium maxima, quando directio projectionis <lb/>cum borizonte efficit angulum ſemirectum.</s> <s xml:id="echoid-s3426" xml:space="preserve"/> </p> <div xml:id="echoid-div521" type="float" level="2" n="6"> <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">336.</note> </div> <p> <s xml:id="echoid-s3427" xml:space="preserve">Si celeritas mutetur, & </s> <s xml:id="echoid-s3428" xml:space="preserve">corpus ſecundum eandem dire-<lb/>ctionem projiciatur, amplitudo in eodem plano mutatur in ea-<lb/>dem ratione cum altitudine A L; </s> <s xml:id="echoid-s3429" xml:space="preserve">id eſt, amplitudines, manente <lb/> <anchor type="note" xlink:label="note-0135-02a" xlink:href="note-0135-02"/> eâdem directione, ſunt ut altitudines ad quas corpora, iiſ-<lb/>dem celeritatibus, in altum projecta adſcendere poſſunt; <lb/></s> <s xml:id="echoid-s3430" xml:space="preserve">ſunt ergo ut quadrata celeritatum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3431" xml:space="preserve"/> </p> <div xml:id="echoid-div522" type="float" level="2" n="7"> <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">337.</note> </div> <note symbol="*" position="right" xml:space="preserve">262.</note> <p> <s xml:id="echoid-s3432" xml:space="preserve">Sit iterum <emph style="sc">La</emph> altitudo a qua cadendo corpus acquirit <lb/> <anchor type="note" xlink:label="note-0135-04a" xlink:href="note-0135-04"/> velocitatem cum qua projicitur per <emph style="sc">A</emph>B; </s> <s xml:id="echoid-s3433" xml:space="preserve">punctum altiſſi-<lb/> <anchor type="note" xlink:label="note-0135-05a" xlink:href="note-0135-05"/> mum viæ percurſæ determinatur, ſi deſcripto ſemicirculo <lb/>cujus diameter eſt AL, per punctum B in quo a directio-<lb/>ne projectionis ſecatur ducatur horizontalis linea MBG, <lb/>& </s> <s xml:id="echoid-s3434" xml:space="preserve">fiat BG æqualis BM; </s> <s xml:id="echoid-s3435" xml:space="preserve">punctum quæſitum erit G.</s> <s xml:id="echoid-s3436" xml:space="preserve"/> </p> <div xml:id="echoid-div523" type="float" level="2" n="8"> <note position="right" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">338.</note> <note position="right" xlink:label="note-0135-05" xlink:href="note-0135-05a" xml:space="preserve">TAB XIII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s3437" xml:space="preserve">Hujus patebit demonſtratio ſi ad ſequentia attendamus; <lb/></s> <s xml:id="echoid-s3438" xml:space="preserve"> <anchor type="note" xlink:label="note-0135-06a" xlink:href="note-0135-06"/> ductâ AI horizontali, corpus ut dictum projectum cadet in <lb/>I, poſitâ AI quadrupla MB aut AR <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3439" xml:space="preserve"/> </p> <div xml:id="echoid-div524" type="float" level="2" n="9"> <note position="right" xlink:label="note-0135-06" xlink:href="note-0135-06a" xml:space="preserve">339.</note> </div> <note symbol="*" position="right" xml:space="preserve">134.</note> <p> <s xml:id="echoid-s3440" xml:space="preserve">Dum corpus per AB projicitur motus hicce coincidit <lb/>cum duplici motu horizontali uno & </s> <s xml:id="echoid-s3441" xml:space="preserve">æquabili, altero <lb/>verticali <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3442" xml:space="preserve">Ultimo motu corpus adſcendit & </s> <s xml:id="echoid-s3443" xml:space="preserve">deſcen- <anchor type="note" xlink:label="note-0135-08a" xlink:href="note-0135-08"/> dit, tempuſque adſcenſus æquale eſt tempori deſcenſus; <lb/></s> <s xml:id="echoid-s3444" xml:space="preserve">ideò aſcenſus terminatur ubi corpus motu horizontali dimi-<lb/>dium AI, id eſt MG, percurrit; </s> <s xml:id="echoid-s3445" xml:space="preserve">punctum ergo altiſſimum <lb/>datur in verticali lineâ SC quæ per G tranſit. </s> <s xml:id="echoid-s3446" xml:space="preserve">Dentur IE <lb/>verticalis, AB continuatam ſecans in E, ut & </s> <s xml:id="echoid-s3447" xml:space="preserve">verticalis <lb/>BR; </s> <s xml:id="echoid-s3448" xml:space="preserve">quia MG dupla eſt MB, id eſt <emph style="sc">A</emph>S dupla <emph style="sc">A</emph>R; </s> <s xml:id="echoid-s3449" xml:space="preserve"><lb/>eſt etiam CS dupla BR, id eſt CG æqualis GS: </s> <s xml:id="echoid-s3450" xml:space="preserve">Sed <lb/>AI dupla eſt AS; </s> <s xml:id="echoid-s3451" xml:space="preserve">ergo EI dupla CS, & </s> <s xml:id="echoid-s3452" xml:space="preserve">quadrupla CG; </s> <s xml:id="echoid-s3453" xml:space="preserve"><lb/>etiam AE dupla AC. </s> <s xml:id="echoid-s3454" xml:space="preserve">Dum Corpus motu projectitio per-<lb/>currit <emph style="sc">A</emph>E, cadit per EI; </s> <s xml:id="echoid-s3455" xml:space="preserve">dum percurrit AC, cadendo quar-<lb/>tam partem EI id eſt CG percurrit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3456" xml:space="preserve">tranſit idcirco in <anchor type="note" xlink:label="note-0135-09a" xlink:href="note-0135-09"/> <pb o="82" file="0136" n="148" rhead="PHYSICES ELEMENTA"/> motu ſuo per punctum G, quod eſt punctum altiſſimum <lb/>cùm hoc detur in linea CS.</s> <s xml:id="echoid-s3457" xml:space="preserve"/> </p> <div xml:id="echoid-div525" type="float" level="2" n="10"> <note symbol="*" position="right" xlink:label="note-0135-08" xlink:href="note-0135-08a" xml:space="preserve">246.</note> <note symbol="*" position="right" xlink:label="note-0135-09" xlink:href="note-0135-09a" xml:space="preserve">255.</note> </div> <p> <s xml:id="echoid-s3458" xml:space="preserve">Si detur curvâ à corpore percurſâ, velocitas quam habet <lb/> <anchor type="note" xlink:label="note-0136-01a" xlink:href="note-0136-01"/> corpus in puncto quocunque ut F, illa eſt, quam Corpus po-<lb/>teſt acquirere cadendo à linea horizontali per L ducta ad <lb/>punctum F. </s> <s xml:id="echoid-s3459" xml:space="preserve">Nam Corpus per planum quodcunque ex A, <lb/>velocitate qua projicitur, adſcendere poteſt ad horizontalem <lb/>hanc lineam <anchor type="note" xlink:href="" symbol="*"/>, ſi nunc planum detur ad F uſque cum ipſa <anchor type="note" xlink:label="note-0136-02a" xlink:href="note-0136-02"/> corporis projecti via congruens, in F autem ſurſum defle-<lb/>xum, corpus in F illam habebit velocitatem qua juxta pla-<lb/>num hoc ad horizontalem memoratam pervenire poteſt, <lb/>id eſt quam cadendo ab ipſa horizontali ad F uſque ac-<lb/>quirere poteſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3460" xml:space="preserve"/> </p> <div xml:id="echoid-div526" type="float" level="2" n="11"> <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">340.</note> <note symbol="*" position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">274.</note> </div> <note symbol="*" position="left" xml:space="preserve">274.</note> <p> <s xml:id="echoid-s3461" xml:space="preserve">Sit corpus ex A projiciendum per punctum H in I, poſi-<lb/> <anchor type="note" xlink:label="note-0136-04a" xlink:href="note-0136-04"/> tis tribus hiſce punctis in eodem plano verticali, & </s> <s xml:id="echoid-s3462" xml:space="preserve">puncto <lb/> <anchor type="note" xlink:label="note-0136-05a" xlink:href="note-0136-05"/> medio ſupra lineam quæ reliqua duo jungit. </s> <s xml:id="echoid-s3463" xml:space="preserve">Sit AI ho-<lb/>rizontalis & </s> <s xml:id="echoid-s3464" xml:space="preserve">per tria puncta data ad hanc normales TE, FD, <lb/>AL. </s> <s xml:id="echoid-s3465" xml:space="preserve">Ex I per puncta A & </s> <s xml:id="echoid-s3466" xml:space="preserve">H ducantur lineæ IA, IH, <lb/>quarum ultima ſecat AL in P; </s> <s xml:id="echoid-s3467" xml:space="preserve">fiat GD æqualis <emph style="sc">A</emph>P, & </s> <s xml:id="echoid-s3468" xml:space="preserve"><lb/>habetur <emph style="sc">A</emph>D directio jactus. </s> <s xml:id="echoid-s3469" xml:space="preserve">Celeritas detegitur ſi ſumtâ <lb/><emph style="sc">A</emph>R quartâ parte <emph style="sc">A</emph>I; </s> <s xml:id="echoid-s3470" xml:space="preserve">& </s> <s xml:id="echoid-s3471" xml:space="preserve">ductâ verticali RB, quæ <emph style="sc">A</emph>D <lb/>ſecat in B, ducatur BL ita, ut angulus <emph style="sc">A</emph>BL æqualis ſit <lb/>angulo <emph style="sc">A</emph>RB, velocitas quæſita eſt quam corpus acquirit <lb/>cadendo ex L in A,</s> </p> <div xml:id="echoid-div527" type="float" level="2" n="12"> <note position="left" xlink:label="note-0136-04" xlink:href="note-0136-04a" xml:space="preserve">341.</note> <note position="left" xlink:label="note-0136-05" xlink:href="note-0136-05a" xml:space="preserve">TAB. XIII. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s3472" xml:space="preserve">Corpus projectum æquabili percurrit velocitate <emph style="sc">A</emph>E & </s> <s xml:id="echoid-s3473" xml:space="preserve"><lb/>AD, dum cadit per EI & </s> <s xml:id="echoid-s3474" xml:space="preserve">DH: </s> <s xml:id="echoid-s3475" xml:space="preserve">ut ergo demonſtremus <lb/>corpus per hæc puncta tranſire, demonſtrandum <lb/><emph style="sc">A</emph>E<emph style="super">9</emph> ſe habere ad <emph style="sc">A</emph>D<emph style="super">9</emph>, aut EI<emph style="super">9</emph> ad DG<emph style="super">9</emph>, ut EI ad <lb/>DH <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3476" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">255.</note> <p> <s xml:id="echoid-s3477" xml:space="preserve">In triangulis ſimilibus IHG, <emph style="sc">IPa</emph>, <emph style="sc">A</emph>I ad AG, ut <lb/><emph style="sc">A</emph>P, aut DG, ad DG minus GH, id eſt HD, Sed <lb/>in triangulis ſimilibus <emph style="sc">A</emph>EI, <emph style="sc">A</emph>DG; </s> <s xml:id="echoid-s3478" xml:space="preserve"><emph style="sc">A</emph>I ad <emph style="sc">A</emph>G, ut EI <lb/>ad DG; </s> <s xml:id="echoid-s3479" xml:space="preserve">ergo EI ad DG, ut DG ad HD; </s> <s xml:id="echoid-s3480" xml:space="preserve">idcirco EI<emph style="super">9</emph> <lb/>ad DG<emph style="super">9</emph>, ut EI ad HD. </s> <s xml:id="echoid-s3481" xml:space="preserve">Quod demonſtrandum erat. </s> <s xml:id="echoid-s3482" xml:space="preserve">Ve-<lb/>locitatem autem rite eſſe determinatam conſtabit ex colla-<lb/>tione fig. </s> <s xml:id="echoid-s3483" xml:space="preserve">7. </s> <s xml:id="echoid-s3484" xml:space="preserve">cum 6.</s> <s xml:id="echoid-s3485" xml:space="preserve">; ſi ad puncta B, L, attendamus, quæ <pb o="82" file="0137" n="149"/> <anchor type="figure" xlink:label="fig-0137-01a" xlink:href="fig-0137-01"/> <pb file="0137a" n="150"/> <anchor type="figure" xlink:label="fig-0137a-01a" xlink:href="fig-0137a-01"/> <pb file="0138" n="151"/> <pb o="83" file="0139" n="152" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> in utraque figura iiſdem literis deſignantur.</s> <s xml:id="echoid-s3486" xml:space="preserve"/> </p> <div xml:id="echoid-div528" type="float" level="2" n="13"> <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a"> <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/> </figure> <figure xlink:label="fig-0137a-01" xlink:href="fig-0137a-01a"> <image file="0137a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137a-01"/> </figure> </div> </div> <div xml:id="echoid-div530" type="section" level="1" n="162"> <head xml:id="echoid-head234" xml:space="preserve">CAPUT XXI. <lb/>De Viribus Centralibus.</head> <p> <s xml:id="echoid-s3487" xml:space="preserve">COrpus in motu, motum in linea recta continuat <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s3488" xml:space="preserve"> <anchor type="note" xlink:label="note-0139-01a" xlink:href="note-0139-01"/> ab ea non recedit, niſi impulſu novo agitetur; </s> <s xml:id="echoid-s3489" xml:space="preserve">poſt <lb/>impulſum motus eſt compoſitus, ex duobus naſcitur tertius <lb/>etiam in linea recta <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3490" xml:space="preserve">Si ergo corpus movetur in curva, <anchor type="note" xlink:label="note-0139-02a" xlink:href="note-0139-02"/> omnibus momentis novo impulſu agitatur; </s> <s xml:id="echoid-s3491" xml:space="preserve">curva enim ad <lb/>rectas lineas revocari non poteſt, niſi concipiatur diviſa in <lb/>partes infinite exiguas. </s> <s xml:id="echoid-s3492" xml:space="preserve">Exemplum talis motus habemus in <lb/>projectione gravium <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3493" xml:space="preserve">aliud habemus in omnibus motibus <anchor type="note" xlink:label="note-0139-03a" xlink:href="note-0139-03"/> circa punctum quaſi centrum.</s> <s xml:id="echoid-s3494" xml:space="preserve"/> </p> <div xml:id="echoid-div530" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">140</note> <note symbol="*" position="right" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">148.</note> <note symbol="*" position="right" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">316.</note> </div> <p> <s xml:id="echoid-s3495" xml:space="preserve">Corpus quod continuò centrum aliquod verſus pellitur, ſi <lb/> <anchor type="note" xlink:label="note-0139-04a" xlink:href="note-0139-04"/> projiciatur ſecundum lineam quæ per illud centrum non <lb/>tranſit, curvam deſcrihit: </s> <s xml:id="echoid-s3496" xml:space="preserve">& </s> <s xml:id="echoid-s3497" xml:space="preserve">in omnibus punctis conatur ab <lb/> <anchor type="note" xlink:label="note-0139-05a" xlink:href="note-0139-05"/> illa curva recedere ſecundum directionem curvaturæ, id eſt, <lb/>tangentis ad curvam; </s> <s xml:id="echoid-s3498" xml:space="preserve">ita ut, ſi vis qua ad centrum trahitur, <lb/>ſubito ab actione ceſſaret, corpus in recta linea per tangen-<lb/>tem motum continuaret.</s> <s xml:id="echoid-s3499" xml:space="preserve"/> </p> <div xml:id="echoid-div531" type="float" level="2" n="2"> <note position="right" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">342.</note> <note position="right" xlink:label="note-0139-05" xlink:href="note-0139-05a" xml:space="preserve">343.</note> </div> <p> <s xml:id="echoid-s3500" xml:space="preserve">Lapis fundæ impoſitus, & </s> <s xml:id="echoid-s3501" xml:space="preserve">in gyrum agitatus, curvam <lb/>deſcribit, quia funda manum verſus omnibus momen-<lb/>tis quaſi retrotrahitur; </s> <s xml:id="echoid-s3502" xml:space="preserve">ſi ſibi relinquatur per curvæ tangen-<lb/>tem recedit.</s> <s xml:id="echoid-s3503" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div533" type="section" level="1" n="163"> <head xml:id="echoid-head235" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s3504" xml:space="preserve">Vis qua corpus in caſu prædicto a centro recedere cona-<lb/> <anchor type="note" xlink:label="note-0139-06a" xlink:href="note-0139-06"/> tur, qualis eſt vis qua funda agitata diſtenditur, vocatur vis <lb/>centrifuga.</s> <s xml:id="echoid-s3505" xml:space="preserve"/> </p> <div xml:id="echoid-div533" type="float" level="2" n="1"> <note position="right" xlink:label="note-0139-06" xlink:href="note-0139-06a" xml:space="preserve">344.</note> </div> </div> <div xml:id="echoid-div535" type="section" level="1" n="164"> <head xml:id="echoid-head236" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s3506" xml:space="preserve">Vis autem qua corpus centrum verſus trabitur, aut pelli-<lb/> <anchor type="note" xlink:label="note-0139-07a" xlink:href="note-0139-07"/> tur, vocatur vis centripeta.</s> <s xml:id="echoid-s3507" xml:space="preserve"/> </p> <div xml:id="echoid-div535" type="float" level="2" n="1"> <note position="right" xlink:label="note-0139-07" xlink:href="note-0139-07a" xml:space="preserve">345.</note> </div> </div> <div xml:id="echoid-div537" type="section" level="1" n="165"> <head xml:id="echoid-head237" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s3508" xml:space="preserve">Nomine communi vires hæ vocantur vires centrales.</s> <s xml:id="echoid-s3509" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">346.</note> <p> <s xml:id="echoid-s3510" xml:space="preserve">In omni caſu vis centrifuga & </s> <s xml:id="echoid-s3511" xml:space="preserve">vis centripeta ſunt a qua-<lb/> <anchor type="note" xlink:label="note-0139-09a" xlink:href="note-0139-09"/> les inter ſe; </s> <s xml:id="echoid-s3512" xml:space="preserve">nam agunt contrarie & </s> <s xml:id="echoid-s3513" xml:space="preserve">ſeſe mutuo deſtruunt.</s> <s xml:id="echoid-s3514" xml:space="preserve"> <pb o="84" file="0140" n="153" rhead="PHYSICES ELEMENTA"/> Vicentripetâ corpus retinetur in curvâ, & </s> <s xml:id="echoid-s3515" xml:space="preserve">centrifugâ cona-<lb/>tur ex hac recedere. </s> <s xml:id="echoid-s3516" xml:space="preserve">Funda agitata æqualiter utramque <lb/>partem verſus diſtenditur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3517" xml:space="preserve">lapis eacum vi a manu co- <anchor type="note" xlink:label="note-0140-01a" xlink:href="note-0140-01"/> natur recedere, cum qua retinetur, id eſt, manum verſus <lb/>trahitur.</s> <s xml:id="echoid-s3518" xml:space="preserve"/> </p> <div xml:id="echoid-div537" type="float" level="2" n="1"> <note position="right" xlink:label="note-0139-09" xlink:href="note-0139-09a" xml:space="preserve">347.</note> <note symbol="*" position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s3519" xml:space="preserve">Virium centralium maximus uſus eſt in Philoſophia Na-<lb/>turali; </s> <s xml:id="echoid-s3520" xml:space="preserve">Planetæ omnes in gyros moventur, & </s> <s xml:id="echoid-s3521" xml:space="preserve">plerique, ſi <lb/>non omnes, circa axes rotantur.</s> <s xml:id="echoid-s3522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3523" xml:space="preserve">Propoſitiones præcipuas circa haſce vires ſeligam & </s> <s xml:id="echoid-s3524" xml:space="preserve">ex-<lb/>plicabo, hasque Experimentis confirmabo, & </s> <s xml:id="echoid-s3525" xml:space="preserve">in ſcholiis huic <lb/>capiti adjectis ipſas demonſtrabo.</s> <s xml:id="echoid-s3526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3527" xml:space="preserve">Præmittenda vero eſt Machinarum deſcriptio; </s> <s xml:id="echoid-s3528" xml:space="preserve">quibus hæc <lb/>Experimenta peraguntur.</s> <s xml:id="echoid-s3529" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div539" type="section" level="1" n="166"> <head xml:id="echoid-head238" xml:space="preserve"><emph style="sc">Machina</emph></head> <p style="it"> <s xml:id="echoid-s3530" xml:space="preserve">Qua Experimenta de viribus centralibus inſtituuntur.</s> <s xml:id="echoid-s3531" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3532" xml:space="preserve">A eſt orbis ligneus diametri circiter duorum pedum cum <lb/> <anchor type="note" xlink:label="note-0140-02a" xlink:href="note-0140-02"/> ſemiſſe; </s> <s xml:id="echoid-s3533" xml:space="preserve">hujus fectio verticalis datur in Fig. </s> <s xml:id="echoid-s3534" xml:space="preserve">2.</s> <s xml:id="echoid-s3535" xml:space="preserve">, in qua a a i-<lb/> <anchor type="note" xlink:label="note-0140-03a" xlink:href="note-0140-03"/> pſius orbis ſectionem repræſentat, g h ſectionem ſuſtentacu-<lb/>li tornati, orbi perpendiculariter in centro adjuncti; </s> <s xml:id="echoid-s3536" xml:space="preserve">conſtat <lb/>hoc ex duabus partibus ſeparatis in D, quæ junguntur qua-<lb/>tuor cylindris ferreis tenuibus, quorum extremitates annu-<lb/>lis ex eodem metallo cohærent.</s> <s xml:id="echoid-s3537" xml:space="preserve"/> </p> <div xml:id="echoid-div539" type="float" level="2" n="1"> <note position="left" xlink:label="note-0140-02" xlink:href="note-0140-02a" xml:space="preserve">348.</note> <note position="left" xlink:label="note-0140-03" xlink:href="note-0140-03a" xml:space="preserve">TAB. XIV. <lb/>fig 1. & 2.</note> </div> <p> <s xml:id="echoid-s3538" xml:space="preserve">Pars ſuperior ſuſtentaculi ſulco circumdatur cc; </s> <s xml:id="echoid-s3539" xml:space="preserve">& </s> <s xml:id="echoid-s3540" xml:space="preserve">cylin-<lb/>drice excavatur in f g, cujus foraminis diameter eſt trium <lb/>partium quartarum unius pollicis.</s> <s xml:id="echoid-s3541" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3542" xml:space="preserve">Totius Machinæ pes datur in C, eſt ſolidiſſimus: </s> <s xml:id="echoid-s3543" xml:space="preserve">ab u-<lb/>na parte ei applicatur orbis A, ubi quadrum ſuperius pe-<lb/>dis C excavatur, ut recipiat ſuſtentaculum orbis. </s> <s xml:id="echoid-s3544" xml:space="preserve">Cum hoc <lb/>quadro firmiter connectitur caput ligneum F, (Fig. </s> <s xml:id="echoid-s3545" xml:space="preserve">3.) </s> <s xml:id="echoid-s3546" xml:space="preserve">cu-<lb/>jus angulus G, in g (fig. </s> <s xml:id="echoid-s3547" xml:space="preserve">1.) </s> <s xml:id="echoid-s3548" xml:space="preserve">videri poteſt.</s> <s xml:id="echoid-s3549" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3550" xml:space="preserve">Capiti huic ſuperimponitur lamina ferrea R quæ ipſi li-<lb/>gno inſeritur & </s> <s xml:id="echoid-s3551" xml:space="preserve">cum hoc, ope cochlearum, quales in s, s, <lb/>delineatæ dantur, firmiter connectitur, Cum lamina R <lb/>cohæret alia r circa verticulum mobilem, ita ut laminæ <lb/>ambæ inter ſe recipiant ſuſtentaculum tabulæ dum ipſæ ſul-<lb/>co c c (fig. </s> <s xml:id="echoid-s3552" xml:space="preserve">2.) </s> <s xml:id="echoid-s3553" xml:space="preserve">inſeruntur, in quo caſu cuſpis Z foramina Z, Z, <lb/>trajicit.</s> <s xml:id="echoid-s3554" xml:space="preserve"/> </p> <pb o="85" file="0141" n="154" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> <p> <s xml:id="echoid-s3555" xml:space="preserve">Orbis cum ſuſtentaculo ſuſtinetur ligno ED, in quo da-<lb/>tur lamina ferrea, cui cuſpis æneus b (fig 2.) </s> <s xml:id="echoid-s3556" xml:space="preserve">inſeritur. </s> <s xml:id="echoid-s3557" xml:space="preserve">Ita <lb/>cum pede Machinæ lignum hocce conjungitur, ut altitudo <lb/>ſulci c c cum altitudine laminarum R r congruat.</s> <s xml:id="echoid-s3558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3559" xml:space="preserve">Hiſce ita diſpoſitis, liberrime cirea centrum horizonta-<lb/>liter orbis movetur, & </s> <s xml:id="echoid-s3560" xml:space="preserve">ut commode circumvolvatur, ei ad-<lb/>ditur, inter orbem & </s> <s xml:id="echoid-s3561" xml:space="preserve">ſulcum c e, rota minor, cujus ſectio <lb/>videtur in b b; </s> <s xml:id="echoid-s3562" xml:space="preserve">in eo loco ſuſtentaculum eſt polygonum, & </s> <s xml:id="echoid-s3563" xml:space="preserve"><lb/>congruit cum foramine in ipſa rota, quæ ope cochlearum <lb/>el, el; </s> <s xml:id="echoid-s3564" xml:space="preserve">firmatur. </s> <s xml:id="echoid-s3565" xml:space="preserve">Variæ tales rotæ minores requiruntur, <lb/>quarum peripheriæ, in fundo ſulci quo circumdantur, ſunt <lb/>inter ſe ut duo, tria, quatuor &</s> <s xml:id="echoid-s3566" xml:space="preserve">c; </s> <s xml:id="echoid-s3567" xml:space="preserve">rotæ omnium minimæ <lb/>diameter eſt circiter quinque pollicum.</s> <s xml:id="echoid-s3568" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3569" xml:space="preserve">Orbis B, priori ſimilis, eodem modo, in parte oppoſita <lb/>pedis C circa centrum rotatur. </s> <s xml:id="echoid-s3570" xml:space="preserve">Parva tamen inter ambos <lb/>datur differentia; </s> <s xml:id="echoid-s3571" xml:space="preserve">hujus orbis ſuſtentaculi pars inferior et-<lb/>iam eſt perforata, ut i b (Fig. </s> <s xml:id="echoid-s3572" xml:space="preserve">4.)</s> <s xml:id="echoid-s3573" xml:space="preserve">; </s> <s xml:id="echoid-s3574" xml:space="preserve">commode nihilominus <lb/>circumvolvitur, in h applicatur lamina metallica perforata, <lb/>cui inſeritur tubus inhærens laminæ aliæ M, cujus ſectio <lb/>verticalis videtur in L, & </s> <s xml:id="echoid-s3575" xml:space="preserve">quæ in ligno <emph style="sc">E</emph>D pedis C hæret <lb/>in m. </s> <s xml:id="echoid-s3576" xml:space="preserve">Perforatur etiam lignum ED, in loco reſpondenti <lb/>foramini ſuſtentaculi, ita ut filum a ſuperficie orbis per to-<lb/>tum ſuſtentaculum & </s> <s xml:id="echoid-s3577" xml:space="preserve">lignum ED trajiciatur.</s> <s xml:id="echoid-s3578" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3579" xml:space="preserve">Rota ut b b, quæ huic orbi B additur, cum eo cohæret, <lb/>& </s> <s xml:id="echoid-s3580" xml:space="preserve">eſt æqualis minimæ illarum quæ orbi A ſeparatim anne-<lb/>ctuntur.</s> <s xml:id="echoid-s3581" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3582" xml:space="preserve">Orbes A & </s> <s xml:id="echoid-s3583" xml:space="preserve">B, aut conjunctim, autſeparatim, celeriter <lb/>circumvolvuntur, ope rotæ majoris & </s> <s xml:id="echoid-s3584" xml:space="preserve">verticalis Q, cujus <lb/>pars ſuperior in eodem datur plano horizontali cum rotis <lb/>minoribus ut b b. </s> <s xml:id="echoid-s3585" xml:space="preserve">Cum pede C conjungitur machina quæ <lb/>in fig. </s> <s xml:id="echoid-s3586" xml:space="preserve">5. </s> <s xml:id="echoid-s3587" xml:space="preserve">repræſentatur; </s> <s xml:id="echoid-s3588" xml:space="preserve">conſtat hæc ex plano ligneo, cui <lb/>perpendiculariter inhæret parallelopipedum, in cujus ſuperfi-<lb/>ciei ſuperioris extremitatibus verticaliter inſeruntur tro-<lb/>chleæ v, v, & </s> <s xml:id="echoid-s3589" xml:space="preserve">a latere in extremitate altera datur trochlea <lb/>tertia horizontalis t, cæteris pollice fere magis elevata. </s> <s xml:id="echoid-s3590" xml:space="preserve">Superfi-<lb/>cies ſuperior Machinæ, eſt in eodem plano horizontali cum ſu- <pb o="86" file="0142" n="155" rhead="PHYSICES ELEMENTA"/> perficiebus inferioribus rotarum minorum orbibus con-<lb/>junctarum.</s> <s xml:id="echoid-s3591" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3592" xml:space="preserve">Sit Orbis B ſolus circumvolvendus; </s> <s xml:id="echoid-s3593" xml:space="preserve">Machina Fig. </s> <s xml:id="echoid-s3594" xml:space="preserve">5. </s> <s xml:id="echoid-s3595" xml:space="preserve">pedi C <lb/>connectitur, ope duarum cochlearum tranſeuntium per fora-<lb/>mina ut x, in plano inferiori Machinæ, quæ diſponitur ut illius <lb/>ſuperficies ſuperior, erga rotam minorem Orbi adhærentem, fi-<lb/>tum habeat, qui in Fig. </s> <s xml:id="echoid-s3596" xml:space="preserve">6. </s> <s xml:id="echoid-s3597" xml:space="preserve">videtur, in qua b rotam illam minorem <lb/>deſignat: </s> <s xml:id="echoid-s3598" xml:space="preserve">funis circumit rotam majorem Q, & </s> <s xml:id="echoid-s3599" xml:space="preserve">ab inſeriori hu-<lb/>jus parte tendit a d verſus v, circumponitur rotæ b, & </s> <s xml:id="echoid-s3600" xml:space="preserve">juxta <lb/>t trochleam, c verſus, ad partem ſuperiorem rotæ Q pervenit.</s> <s xml:id="echoid-s3601" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3602" xml:space="preserve">In Fig. </s> <s xml:id="echoid-s3603" xml:space="preserve">7. </s> <s xml:id="echoid-s3604" xml:space="preserve">ſitus Machinæ Fig. </s> <s xml:id="echoid-s3605" xml:space="preserve">5. </s> <s xml:id="echoid-s3606" xml:space="preserve">repræ ſentatur, quando <lb/>ambo Orbes ſimul circumrotandi ſunt; </s> <s xml:id="echoid-s3607" xml:space="preserve">ſunis diſpoſitio ex <lb/>inſpectione figuræ liquet, ab v tendit verſus d, ad rotæ ma-<lb/>joris Q partem inferiorem.</s> <s xml:id="echoid-s3608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3609" xml:space="preserve">In multis Experimentis ulterius requiruntur pyxides oblon-<lb/>gæ P, P, quæ orbibus imponuntur, & </s> <s xml:id="echoid-s3610" xml:space="preserve">cochleis ibi firmantur; <lb/></s> <s xml:id="echoid-s3611" xml:space="preserve">in unaquaque centrum Orbis cum medio pyxidis congruit, & </s> <s xml:id="echoid-s3612" xml:space="preserve"><lb/>ibi datur foramen æquale foramini g f (Fig. </s> <s xml:id="echoid-s3613" xml:space="preserve">2.) </s> <s xml:id="echoid-s3614" xml:space="preserve">& </s> <s xml:id="echoid-s3615" xml:space="preserve">huic reſpon-<lb/>dens, cui inſeritur cylindrus ligneus N (Fig. </s> <s xml:id="echoid-s3616" xml:space="preserve">2.)</s> <s xml:id="echoid-s3617" xml:space="preserve">, ut videtur in L, L: </s> <s xml:id="echoid-s3618" xml:space="preserve"><lb/>hunc trajicit, & </s> <s xml:id="echoid-s3619" xml:space="preserve">in eo hæret tubulus vitreus, diametri circiter <lb/>quartæ partis unius pollicis, cujus extremitates lampadis flam-<lb/>mâ fuſæ anguſtum in medio foramen habent; </s> <s xml:id="echoid-s3620" xml:space="preserve">ita ut per tu-<lb/>bum filum, aut funis tenuis, ſine attritu ſenſibili, moveatur.</s> <s xml:id="echoid-s3621" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3622" xml:space="preserve">In pyxide, ad exiguam ab L diſtantiam, lamina lignea <lb/>ſuſpenditur v, quæ cum pyxidis lateribus angulos efficit re-<lb/>ctos, & </s> <s xml:id="echoid-s3623" xml:space="preserve">in V ſeparatim repræſentatur; </s> <s xml:id="echoid-s3624" xml:space="preserve">circa latus ſuperius <lb/>liberrimè volubilis eſt; </s> <s xml:id="echoid-s3625" xml:space="preserve">in inferiori parte ſciſſura datur, <lb/>ad cujus latus paxillus P laminæ inſeritur, infra quem <lb/>foramen datur, per quod filum trajicit, quod cum paxillo <lb/>cohæret.</s> <s xml:id="echoid-s3626" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3627" xml:space="preserve">Cum latere pyxidis lamina lignea elaſtica s conjungitur <lb/>ope cochlearum q, q; </s> <s xml:id="echoid-s3628" xml:space="preserve">ſeparatim in ſitu inverſo videri po-<lb/>teſt in S; </s> <s xml:id="echoid-s3629" xml:space="preserve">in k cum hac cohæret ſphæræ ſegmentum ex li-<lb/>gno duriori, aut ebore. </s> <s xml:id="echoid-s3630" xml:space="preserve">Cochlearum q, q, figura datur in <lb/>Q. </s> <s xml:id="echoid-s3631" xml:space="preserve">Pars oppoſita pyxidis in partes æquales, recedendo a <lb/>centro, in fundo dividitur.</s> <s xml:id="echoid-s3632" xml:space="preserve"/> </p> <pb o="87" file="0143" n="156" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> <p> <s xml:id="echoid-s3633" xml:space="preserve">Pyxis Globum continet, qui ſeparatim in G (fig. </s> <s xml:id="echoid-s3634" xml:space="preserve">12.) </s> <s xml:id="echoid-s3635" xml:space="preserve">vi-<lb/>detur. </s> <s xml:id="echoid-s3636" xml:space="preserve">Habet hic prominentiam in quo foramen datur ad <lb/>centrum globi tendens, & </s> <s xml:id="echoid-s3637" xml:space="preserve">quod terminatur in foramine <lb/>transverſo; </s> <s xml:id="echoid-s3638" xml:space="preserve">filum foramen primum trajicit, & </s> <s xml:id="echoid-s3639" xml:space="preserve">ex forami-<lb/>ne transverſo exit; </s> <s xml:id="echoid-s3640" xml:space="preserve">hoc cuſpide ligneo c exacte repletur ita, <lb/>ut filum firmiter hæreat. </s> <s xml:id="echoid-s3641" xml:space="preserve">Filum per tubum memoratum im-<lb/>mittitur, & </s> <s xml:id="echoid-s3642" xml:space="preserve">in ſeparatione D ſuſtentaculi Orbis cum ponde-<lb/>re O (Fig. </s> <s xml:id="echoid-s3643" xml:space="preserve">9) connectitur. </s> <s xml:id="echoid-s3644" xml:space="preserve">Pondus parti inferiori ſuſten-<lb/>taculi imponitur, & </s> <s xml:id="echoid-s3645" xml:space="preserve">receſſu Globi a centro elevatur.</s> <s xml:id="echoid-s3646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3647" xml:space="preserve">Pondus hocce eſt Orbis plumbeus, diametri circiter duo-<lb/>rum pollicum; </s> <s xml:id="echoid-s3648" xml:space="preserve">in centro perpendiculariter ei inhæret cy-<lb/>lindrus æneus, cum cujus extremitate ſuperiori filum con-<lb/>jungitur. </s> <s xml:id="echoid-s3649" xml:space="preserve">Ponderat Orbis cum cylindro ſemi-libram, duo <lb/>talia pondera dantur.</s> <s xml:id="echoid-s3650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3651" xml:space="preserve">Dantur varia alia pondera, quædam ſemi-libræ, alia qua-<lb/>drantis, quorum figura datur in P (Fig. </s> <s xml:id="echoid-s3652" xml:space="preserve">9.)</s> <s xml:id="echoid-s3653" xml:space="preserve">, & </s> <s xml:id="echoid-s3654" xml:space="preserve">quæ præ-<lb/>dicto ponderi O ſuperimponuntur, ut ſic ad libitum pondus <lb/>cum Globo conjunctum variari poſſit.</s> <s xml:id="echoid-s3655" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3656" xml:space="preserve">Quando corpus plano impoſitum, cum iſto plano, æquali in <lb/> <anchor type="note" xlink:label="note-0143-01a" xlink:href="note-0143-01"/> tempore, circa commune centrum revolvitur, & </s> <s xml:id="echoid-s3657" xml:space="preserve">circulum <lb/>deſcribit; </s> <s xml:id="echoid-s3658" xml:space="preserve">ſi vis centripeta, qua corpus, omnibus momentis <lb/>centrum verſus trabitur aut pellitur, agere ceſſet, & </s> <s xml:id="echoid-s3659" xml:space="preserve">pla-<lb/>num eadem celeritate movere continuet; </s> <s xml:id="echoid-s3660" xml:space="preserve">corpus a centro re-<lb/>cedere incipit, reſpectu plani, per lineam quæ per centrum <lb/>tranſit.</s> <s xml:id="echoid-s3661" xml:space="preserve"/> </p> <div xml:id="echoid-div540" type="float" level="2" n="2"> <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">349.</note> </div> </div> <div xml:id="echoid-div542" type="section" level="1" n="167"> <head xml:id="echoid-head239" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s3662" xml:space="preserve">Detur Globus funi tenui cohærens, extremitaſque altera <lb/> <anchor type="note" xlink:label="note-0143-02a" xlink:href="note-0143-02"/> fixa ſit in centro Orbis unius <emph style="sc">A</emph> aut B, & </s> <s xml:id="echoid-s3663" xml:space="preserve">ſolus circumvol-<lb/>vatur, donec Globus ei impoſitus eodem tempore cum illo <lb/>circumrotetur; </s> <s xml:id="echoid-s3664" xml:space="preserve">reſpectu Orbis quieſcit Globus, & </s> <s xml:id="echoid-s3665" xml:space="preserve">in eo ſitu, <lb/>ſolo fune centro Orbis alligato, retinetur; </s> <s xml:id="echoid-s3666" xml:space="preserve">nullam ergo im-<lb/>preſſionem in illo plano patitur, nifi qua funis diſtenditur <lb/>id eſt, cujus directio per centrum Orbis tranſit, & </s> <s xml:id="echoid-s3667" xml:space="preserve">ſic, ſi <lb/>ſibi relinquatur, non poteſt in illo plano, in primo momen-<lb/>to, ſecundum aliam directionem moveri.</s> <s xml:id="echoid-s3668" xml:space="preserve"/> </p> <div xml:id="echoid-div542" type="float" level="2" n="1"> <note position="right" xlink:label="note-0143-02" xlink:href="note-0143-02a" xml:space="preserve">350.</note> </div> <p style="it"> <s xml:id="echoid-s3669" xml:space="preserve">Quando corpus circa centrum movetur, ſi inter movendum <lb/> <anchor type="note" xlink:label="note-0143-03a" xlink:href="note-0143-03"/> <pb o="88" file="0144" n="157" rhead="PHYSICES ELEMENTA"/> magis ad centrum accedat, acceleratur illius motus; </s> <s xml:id="echoid-s3670" xml:space="preserve">retar-<lb/>datur contra, ſi a centro recedat.</s> <s xml:id="echoid-s3671" xml:space="preserve"/> </p> <div xml:id="echoid-div543" type="float" level="2" n="2"> <note position="right" xlink:label="note-0143-03" xlink:href="note-0143-03a" xml:space="preserve">351.</note> </div> </div> <div xml:id="echoid-div545" type="section" level="1" n="168"> <head xml:id="echoid-head240" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s3672" xml:space="preserve">Orbi B cohæret pyxis P, per cujus medium Orbi inſeri-<lb/> <anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/> tur cylindrus L, cum ſuo tubo vitreo, ut in deſcriptione <lb/>Machinæ dictum.</s> <s xml:id="echoid-s3673" xml:space="preserve"/> </p> <div xml:id="echoid-div545" type="float" level="2" n="1"> <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">352.</note> </div> <p> <s xml:id="echoid-s3674" xml:space="preserve">Globus t filo alligatus, pyxidi imponitur; </s> <s xml:id="echoid-s3675" xml:space="preserve">filum tranſmit-<lb/>titur per tubum ſtatim memoratum, ut & </s> <s xml:id="echoid-s3676" xml:space="preserve">per integrum <lb/>Orbis ſuſtentaculum, & </s> <s xml:id="echoid-s3677" xml:space="preserve">infra lignum ED pervenit, cui et-<lb/>iam in inferiori parte inſeritur tubus ut N cum tubo vitreo <lb/>quem funis etiam trajicit. </s> <s xml:id="echoid-s3678" xml:space="preserve">Manu extremitas fili retine-<lb/>tur.</s> <s xml:id="echoid-s3679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3680" xml:space="preserve">Orbis circumrotatur; </s> <s xml:id="echoid-s3681" xml:space="preserve">in motu lateri pyxidis Globus ſe <lb/>applicat, & </s> <s xml:id="echoid-s3682" xml:space="preserve">circumfertur ita, ut æquali celeritate cum py-<lb/>xide moveatur. </s> <s xml:id="echoid-s3683" xml:space="preserve">Trahatur filum, ut Globus magis ad centrum <lb/>accedat, ſtatim in latus oppoſitum pyxidis impinget, quia <lb/>celerius quam ipſa pyxis movetur. </s> <s xml:id="echoid-s3684" xml:space="preserve">Nunc ſi manus admo-<lb/>veatur, Globus a centro recedit, & </s> <s xml:id="echoid-s3685" xml:space="preserve">in latus primum py-<lb/>xidis impingit, quia tardius quam pyxis movetur.</s> <s xml:id="echoid-s3686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3687" xml:space="preserve">Hanc accelerationem in acceſſu corporis ad centrum, & </s> <s xml:id="echoid-s3688" xml:space="preserve"><lb/>retardationem ex receſſu, in ſcholio primo ſequenti deter-<lb/>minamus; </s> <s xml:id="echoid-s3689" xml:space="preserve">moveatur ex gr. </s> <s xml:id="echoid-s3690" xml:space="preserve">corpus, quod fertur centrum <lb/> <anchor type="note" xlink:label="note-0144-02a" xlink:href="note-0144-02"/> C verſus, in curva AE, dabitur curva hæc in eodem plano <lb/> <anchor type="note" xlink:label="note-0144-03a" xlink:href="note-0144-03"/> cum centro C; </s> <s xml:id="echoid-s3691" xml:space="preserve">celerius autem movebitur in E, tardius in <lb/>A: </s> <s xml:id="echoid-s3692" xml:space="preserve">ducantur lineæ AC, BC, & </s> <s xml:id="echoid-s3693" xml:space="preserve">EC, DC, ita ut areæ ABC <lb/>& </s> <s xml:id="echoid-s3694" xml:space="preserve">DEC ſint æquales inter ſe, portiones curvæ AB, DE, <lb/>in temporibus æqualibus, a corpore deſcribuntur; </s> <s xml:id="echoid-s3695" xml:space="preserve">& </s> <s xml:id="echoid-s3696" xml:space="preserve">ideo, <lb/>corpus, quod vi verſus centrum tendente in curva retinetur, <lb/> <anchor type="note" xlink:label="note-0144-04a" xlink:href="note-0144-04"/> dicitur deſcribere areas circa illud centrum temporibus pro-<lb/>portionales.</s> <s xml:id="echoid-s3697" xml:space="preserve"/> </p> <div xml:id="echoid-div546" type="float" level="2" n="2"> <note position="left" xlink:label="note-0144-02" xlink:href="note-0144-02a" xml:space="preserve">353.</note> <note position="left" xlink:label="note-0144-03" xlink:href="note-0144-03a" xml:space="preserve">TAB XIV. <lb/>flg. 11.</note> <note position="left" xlink:label="note-0144-04" xlink:href="note-0144-04a" xml:space="preserve">354.</note> </div> <p style="it"> <s xml:id="echoid-s3698" xml:space="preserve">Hujus propoſitionis inverſam etiam demonſtramus, cor-<lb/> <anchor type="note" xlink:label="note-0144-05a" xlink:href="note-0144-05"/> pus, quod movetur in linea aliquâ curvâ in plano, & </s> <s xml:id="echoid-s3699" xml:space="preserve">deſcri-<lb/>bit areas circa punctum quoddam temporibus proportionales, <lb/>à recta linea detorqueri & </s> <s xml:id="echoid-s3700" xml:space="preserve">urgeri vitendente ad idem pun-<lb/>ctum.</s> <s xml:id="echoid-s3701" xml:space="preserve"/> </p> <div xml:id="echoid-div547" type="float" level="2" n="3"> <note position="left" xlink:label="note-0144-05" xlink:href="note-0144-05a" xml:space="preserve">355.</note> </div> <p style="it"> <s xml:id="echoid-s3702" xml:space="preserve">Quo major eſt quantitas materia in corpore, eomajor eſt, <lb/> <anchor type="note" xlink:label="note-0144-06a" xlink:href="note-0144-06"/> <pb o="89" file="0145" n="158" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> cæteris paribus, bujus vis centrifuga; </s> <s xml:id="echoid-s3703" xml:space="preserve">quod oritur exma-<lb/>jori vi inſitâ.</s> <s xml:id="echoid-s3704" xml:space="preserve"/> </p> <div xml:id="echoid-div548" type="float" level="2" n="4"> <note position="left" xlink:label="note-0144-06" xlink:href="note-0144-06a" xml:space="preserve">356.</note> </div> <p> <s xml:id="echoid-s3705" xml:space="preserve">Si ſluida variæ denſitatis in ſpatio determinato includan-<lb/> <anchor type="note" xlink:label="note-0145-01a" xlink:href="note-0145-01"/> tur, ita ut graviora a centro non poſſint recedere, quin le-<lb/>viora ad illud accedant, & </s> <s xml:id="echoid-s3706" xml:space="preserve">diſpoſita ſint, ut pondere ſuo <lb/>graviora ad centrum accedant, in motu circa illud centrum <lb/>leviora verſus hoc feruntur, & </s> <s xml:id="echoid-s3707" xml:space="preserve">graviora centrum fugiunt.</s> <s xml:id="echoid-s3708" xml:space="preserve"/> </p> <div xml:id="echoid-div549" type="float" level="2" n="5"> <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">357.</note> </div> <p> <s xml:id="echoid-s3709" xml:space="preserve">Si ſolidum cum fluido ſpatio determinato includatur, ad <lb/>centrum accedit, ſi fluido levius fuerit; </s> <s xml:id="echoid-s3710" xml:space="preserve">ſi gravius ab eo re-<lb/>cedit. </s> <s xml:id="echoid-s3711" xml:space="preserve">Quæ omnia oriuntur ex majori vi centriſuga in gra-<lb/>viori corpore.</s> <s xml:id="echoid-s3712" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div551" type="section" level="1" n="169"> <head xml:id="echoid-head241" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s3713" xml:space="preserve">Quatuor tubi vitrei, diametri circiter unius pollicis, & </s> <s xml:id="echoid-s3714" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0145-02a" xlink:href="note-0145-02"/> longitudinis unius pedis, plano inclinato firmiter alligantur, <lb/> <anchor type="note" xlink:label="note-0145-03a" xlink:href="note-0145-03"/> hermetice ab utraque parte clauſi. </s> <s xml:id="echoid-s3715" xml:space="preserve">In primo datur mercu-<lb/>rius cum aqua; </s> <s xml:id="echoid-s3716" xml:space="preserve">in ſecundo oleum tartari per deliquium cum <lb/>ſpiritu vini; </s> <s xml:id="echoid-s3717" xml:space="preserve">in tertio aqua cum globo plumbeo; </s> <s xml:id="echoid-s3718" xml:space="preserve">in quarto <lb/>tandem aqua cum fruſto ſuberis, omnes pro dimidia parte <lb/>vacui relinquuntur.</s> <s xml:id="echoid-s3719" xml:space="preserve"/> </p> <div xml:id="echoid-div551" type="float" level="2" n="1"> <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">358.</note> <note position="right" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">TAB. XIV. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s3720" xml:space="preserve">Planum hocce inclinatum Orbi A aut B imponitur ita, <lb/> <anchor type="note" xlink:label="note-0145-04a" xlink:href="note-0145-04"/> ut pars inſerior plani fere ad Orbis centrum pertingat; </s> <s xml:id="echoid-s3721" xml:space="preserve">& </s> <s xml:id="echoid-s3722" xml:space="preserve"><lb/>ope duarum cochlearum, quarum una tranſit per x (Fig. </s> <s xml:id="echoid-s3723" xml:space="preserve">8.)</s> <s xml:id="echoid-s3724" xml:space="preserve">, <lb/>Orbi annectitur. </s> <s xml:id="echoid-s3725" xml:space="preserve">Circumvolvatur Orbis, ſtatim pars infe-<lb/>rior tuborum vacua remanebit, & </s> <s xml:id="echoid-s3726" xml:space="preserve">corpora graviora locum <lb/>a centro maxime remotum occupabunt; </s> <s xml:id="echoid-s3727" xml:space="preserve">ſuber deſcendit <lb/>& </s> <s xml:id="echoid-s3728" xml:space="preserve">hæret in inferiori aquæ parte, dum globus plumbeus ad <lb/>extremitatem uſque tubi adſcendit.</s> <s xml:id="echoid-s3729" xml:space="preserve"/> </p> <div xml:id="echoid-div552" type="float" level="2" n="2"> <note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">TAB. XIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s3730" xml:space="preserve">Vires centrales non modo reſpectu quantitatis materiæ <lb/> <anchor type="note" xlink:label="note-0145-05a" xlink:href="note-0145-05"/> differunt, ſed etiam diſtantia à centro mutationem aſſert, <lb/>ut & </s> <s xml:id="echoid-s3731" xml:space="preserve">celeritas cum qua circumvolvitur corpus; </s> <s xml:id="echoid-s3732" xml:space="preserve">præter hæc <lb/>nihil in iſtis viribus datur ex quo differentia inter illas oriri <lb/>poſht, & </s> <s xml:id="echoid-s3733" xml:space="preserve">in comparandis iſtis viribus hæc ſola conſideran-<lb/>da ſunt.</s> <s xml:id="echoid-s3734" xml:space="preserve"/> </p> <div xml:id="echoid-div553" type="float" level="2" n="3"> <note position="right" xlink:label="note-0145-05" xlink:href="note-0145-05a" xml:space="preserve">359.</note> </div> </div> <div xml:id="echoid-div555" type="section" level="1" n="170"> <head xml:id="echoid-head242" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s3735" xml:space="preserve">Tempus periodicum, eſt tempus in quo corpus circa cen-<lb/> <anchor type="note" xlink:label="note-0145-06a" xlink:href="note-0145-06"/> trum revolvens integram revolutionem peragit; </s> <s xml:id="echoid-s3736" xml:space="preserve">id eſt, ſi <pb o="90" file="0146" n="159" rhead="PHYSICES ELEMENTA"/> curvam deſcribat quæ in ſe redit, tempus elapſum inter re-<lb/>ceſſum a puncto & </s> <s xml:id="echoid-s3737" xml:space="preserve">acceſſum ad idem punctum: </s> <s xml:id="echoid-s3738" xml:space="preserve">ſi curva in <lb/>ſe non redeat, pro puncto linea per centrum tranſiens ſu-<lb/>menda eſt.</s> <s xml:id="echoid-s3739" xml:space="preserve"/> </p> <div xml:id="echoid-div555" type="float" level="2" n="1"> <note position="right" xlink:label="note-0145-06" xlink:href="note-0145-06a" xml:space="preserve">360.</note> </div> <p> <s xml:id="echoid-s3740" xml:space="preserve">Tempus periodicum pendet a corporis celeritate, & </s> <s xml:id="echoid-s3741" xml:space="preserve">ideò <lb/>in comparandis viribus centralibus tempus hocce loco cele-<lb/>ritatis conſiderari poteſt.</s> <s xml:id="echoid-s3742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3743" xml:space="preserve">Quando tempora periodica ſunt aqualia & </s> <s xml:id="echoid-s3744" xml:space="preserve">diſtantia æqua-<lb/> <anchor type="note" xlink:label="note-0146-01a" xlink:href="note-0146-01"/> les a centro, vires centrales ſunt ut quantitates materiæ in <lb/>corporibus quæ revolvuntur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3745" xml:space="preserve">Temporibus enim æquali- <anchor type="note" xlink:label="note-0146-02a" xlink:href="note-0146-02"/> bus eodem modo viribus centralibus moventur.</s> <s xml:id="echoid-s3746" xml:space="preserve"/> </p> <div xml:id="echoid-div556" type="float" level="2" n="2"> <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">361.</note> <note symbol="*" position="left" xlink:label="note-0146-02" xlink:href="note-0146-02a" xml:space="preserve">106.</note> </div> </div> <div xml:id="echoid-div558" type="section" level="1" n="171"> <head xml:id="echoid-head243" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s3747" xml:space="preserve">Applicatur Orbi A, rota omnium minima, ex tribus ro-<lb/> <anchor type="note" xlink:label="note-0146-03a" xlink:href="note-0146-03"/> tis ut b b, de quibus in deſcriptione Machinæ; </s> <s xml:id="echoid-s3748" xml:space="preserve">ita ut ſi am-<lb/> <anchor type="note" xlink:label="note-0146-04a" xlink:href="note-0146-04"/> bo Orbes A & </s> <s xml:id="echoid-s3749" xml:space="preserve">B ſimul agitentur motu rotæ Q in tempore <lb/>æquali circumvolvantur; </s> <s xml:id="echoid-s3750" xml:space="preserve">ſingulis applicantur pyxides oblon-<lb/>gæ P, P; </s> <s xml:id="echoid-s3751" xml:space="preserve">& </s> <s xml:id="echoid-s3752" xml:space="preserve">cylindri cum tubulis vitreis L, L, per <lb/>foramina in medio pyxidum, ſuſtentaculis Orbium inſerun-<lb/>tur.</s> <s xml:id="echoid-s3753" xml:space="preserve"/> </p> <div xml:id="echoid-div558" type="float" level="2" n="1"> <note position="left" xlink:label="note-0146-03" xlink:href="note-0146-03a" xml:space="preserve">362.</note> <note position="left" xlink:label="note-0146-04" xlink:href="note-0146-04a" xml:space="preserve">TAB XIV. <lb/>fig. 1.2.</note> </div> <p> <s xml:id="echoid-s3754" xml:space="preserve">Globus t ponderis ſemi-libræ pyxidi Orbis B imponitur, <lb/>& </s> <s xml:id="echoid-s3755" xml:space="preserve">globus t ponderis unius libræ pyxidi Orbis A; </s> <s xml:id="echoid-s3756" xml:space="preserve">filis per <lb/>tubulos L, L, tranſeuntibus & </s> <s xml:id="echoid-s3757" xml:space="preserve">cum ponderibus, in ſepa-<lb/>rationibus ſuſtentaculorum Orbium poſitis, cohærentibus, <lb/>globi annectuntur ita, ut diſtantiæ globorum a centro, <lb/>quando fila extenduntur, & </s> <s xml:id="echoid-s3758" xml:space="preserve">non elevantur pondera, ſint <lb/>æquales. </s> <s xml:id="echoid-s3759" xml:space="preserve">Inutraque pyxide Elaſterii s extremitas inſeritur ſciſ-<lb/>ſuræ laminæ v (V) & </s> <s xml:id="echoid-s3760" xml:space="preserve">filum paxillo p annexum globo etiam <lb/>conjungitur, dum per idem foramen in prominentiâ globi <lb/>tranſit cum filo primo. </s> <s xml:id="echoid-s3761" xml:space="preserve">Ope paxilli p ita fili ſecundi longitudo <lb/>determinatur, ut ad altitudinem octavæ partis pollicis pondus <lb/>in ſuſtentaculo, receſſu globi a centro, elevari poſſit quieſcente <lb/>lamina v; </s> <s xml:id="echoid-s3762" xml:space="preserve">ſi autem magis a centro recedat globus, trahitur la-<lb/>mina hæc, relaxatur elaſterium, & </s> <s xml:id="echoid-s3763" xml:space="preserve">ſegmentum k in latus pyxidis <lb/>impingit, ſtrepituſque auditur, qui magis erit intenſus ſi la-<lb/>tus pyxidis etiam ſegmento ſphæræ ex ligno duriore aut e-<lb/>bore muniatur.</s> <s xml:id="echoid-s3764" xml:space="preserve"/> </p> <pb o="91" file="0147" n="160" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> <p> <s xml:id="echoid-s3765" xml:space="preserve">Nunc ſit pondus in ſeparatione ſuſtentaculi Orbis A uni-<lb/>us libræ, in ſeparatione ſuſtentaculi Orbis B ſemi-libræ; <lb/></s> <s xml:id="echoid-s3766" xml:space="preserve">aut ſit hoc unius libræ, & </s> <s xml:id="echoid-s3767" xml:space="preserve">illud duarum librarum.</s> <s xml:id="echoid-s3768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3769" xml:space="preserve">Moveatur rota Q celerius atque celerius, donec globo-<lb/>rum vi centrifuga pondera ſtatim memorata eleventur; </s> <s xml:id="echoid-s3770" xml:space="preserve">am-<lb/>bo eodem exactè temporis momento in altum ferentur, <lb/>quod ex ſtrepitu memorato manifeſtum fit. </s> <s xml:id="echoid-s3771" xml:space="preserve">Pondera ergo <lb/>quæ ſunt ut corpora, cæteris paribus, vi centrifuga ſupe-<lb/>rantur.</s> <s xml:id="echoid-s3772" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3773" xml:space="preserve">Quando quantitates materiæ in corporibus circumrotatis <lb/> <anchor type="note" xlink:label="note-0147-01a" xlink:href="note-0147-01"/> ſunt æquales, & </s> <s xml:id="echoid-s3774" xml:space="preserve">tempora periodica æqualia, vires centrales <lb/>ſunt ut diſtantiæ a centro.</s> <s xml:id="echoid-s3775" xml:space="preserve"/> </p> <div xml:id="echoid-div559" type="float" level="2" n="2"> <note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">363.</note> </div> </div> <div xml:id="echoid-div561" type="section" level="1" n="172"> <head xml:id="echoid-head244" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s3776" xml:space="preserve">Hocce Experimentum eodem modo ac præcedens pera <lb/> <anchor type="note" xlink:label="note-0147-02a" xlink:href="note-0147-02"/> gitur; </s> <s xml:id="echoid-s3777" xml:space="preserve">pro globo ſemi-libræ, pyxidi Orbis B globus alteri <lb/> <anchor type="note" xlink:label="note-0147-03a" xlink:href="note-0147-03"/> æqualis, id eſt, unius libræ, imponitur. </s> <s xml:id="echoid-s3778" xml:space="preserve">Diſtantiæ globo-<lb/>rum a centro ſint in quacunque ratione, ſi pondera cum <lb/>quibus globi conjunguntur eandem inter ſe habeant propor-<lb/>tionem, & </s> <s xml:id="echoid-s3779" xml:space="preserve">rota Q motu continuo accelerato circumagatur, <lb/>eodem exacte temporis momento pondera elevantur. </s> <s xml:id="echoid-s3780" xml:space="preserve">Sit <lb/>ex. </s> <s xml:id="echoid-s3781" xml:space="preserve">gr. </s> <s xml:id="echoid-s3782" xml:space="preserve">diſtantia globi Orbis A partium viginti quatuor, & </s> <s xml:id="echoid-s3783" xml:space="preserve"><lb/>pondus ei annexum unius libræ cum ſemiſſe; </s> <s xml:id="echoid-s3784" xml:space="preserve">diſtantia al-<lb/>terius globi ſedecim partium, & </s> <s xml:id="echoid-s3785" xml:space="preserve">pondus annexum unius li-<lb/>bræ; </s> <s xml:id="echoid-s3786" xml:space="preserve">Experimentum procedet.</s> <s xml:id="echoid-s3787" xml:space="preserve"/> </p> <div xml:id="echoid-div561" type="float" level="2" n="1"> <note position="right" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">364.</note> <note position="right" xlink:label="note-0147-03" xlink:href="note-0147-03a" xml:space="preserve">TAB. XIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s3788" xml:space="preserve">Quando tempora periodica ſunt æqualia, ſed diſtantiæ à <lb/> <anchor type="note" xlink:label="note-0147-04a" xlink:href="note-0147-04"/> centro & </s> <s xml:id="echoid-s3789" xml:space="preserve">quantitates materiæ in corporibus revolutis diffe-<lb/>runt, vires centrales ſunt in ratione compoſita, quantitatum <lb/>materiæ, & </s> <s xml:id="echoid-s3790" xml:space="preserve">diſtantiarum; </s> <s xml:id="echoid-s3791" xml:space="preserve">quod ex duabus ultimis propo-<lb/>ſitionibus ſequitur. </s> <s xml:id="echoid-s3792" xml:space="preserve">Ratio hæc compoſita determinatur, ſi <lb/>quantitas materiæ in unoquoque corpore per ſuam diſtan-<lb/>tiam a centro multiplicetur, & </s> <s xml:id="echoid-s3793" xml:space="preserve">producta quæſitam inter ſe <lb/>rationem habent.</s> <s xml:id="echoid-s3794" xml:space="preserve"/> </p> <div xml:id="echoid-div562" type="float" level="2" n="2"> <note position="right" xlink:label="note-0147-04" xlink:href="note-0147-04a" xml:space="preserve">365.</note> </div> </div> <div xml:id="echoid-div564" type="section" level="1" n="173"> <head xml:id="echoid-head245" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s3795" xml:space="preserve">Si in Experimento ultimo globus Orbi B impoſitus mu-<lb/> <anchor type="note" xlink:label="note-0147-05a" xlink:href="note-0147-05"/> tetur, & </s> <s xml:id="echoid-s3796" xml:space="preserve">globus ſemi-libræ ad eandem diſtantiam partium <lb/> <anchor type="note" xlink:label="note-0147-06a" xlink:href="note-0147-06"/> ſedecim a centro pyxidi imponatur, mutetur etiam pondus <pb o="92" file="0148" n="161" rhead="PHYSICES ELEMENTA"/> ei annexum, & </s> <s xml:id="echoid-s3797" xml:space="preserve">pro una libra, ſemi - libra adhibeatur, Ex-<lb/>perimentum procedet, & </s> <s xml:id="echoid-s3798" xml:space="preserve">pondera eodem tempore adſcen-<lb/>dere incipient. </s> <s xml:id="echoid-s3799" xml:space="preserve">Multiplicando globum ſemi-libræ per di-<lb/>ſtantiam a centro ſedecim, productum eſt octo; </s> <s xml:id="echoid-s3800" xml:space="preserve">& </s> <s xml:id="echoid-s3801" xml:space="preserve">mul-<lb/>tiplicando globum unius libræ per diſtantiam viginti quatuor <lb/>a centro, productum eſt viginti quatuor, quæ producta <lb/>ſunt inter ſe ut unum ad tria, id eſt, ut pondera ſemi-libræ, <lb/>& </s> <s xml:id="echoid-s3802" xml:space="preserve">unius libræ cum ſemiſſe, quæ in hoc Experimento ſimul <lb/>elevantur.</s> <s xml:id="echoid-s3803" xml:space="preserve"/> </p> <div xml:id="echoid-div564" type="float" level="2" n="1"> <note position="right" xlink:label="note-0147-05" xlink:href="note-0147-05a" xml:space="preserve">366.</note> <note position="right" xlink:label="note-0147-06" xlink:href="note-0147-06a" xml:space="preserve">TAB. XIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s3804" xml:space="preserve">Differentiæ virium centralium, ex differentiis diſtantia-<lb/>rum a centro & </s> <s xml:id="echoid-s3805" xml:space="preserve">quantitatum materiæ oriundæ, ſeſe mu-<lb/>tuo poſſunt compenſare; </s> <s xml:id="echoid-s3806" xml:space="preserve">nam poſitis quantit atibus materiæ <lb/> <anchor type="note" xlink:label="note-0148-01a" xlink:href="note-0148-01"/> in corporibus circumactis in ratione inverſa diſtantiarum a <lb/>centro, vires centrales erunt æquales; </s> <s xml:id="echoid-s3807" xml:space="preserve">quantum vis una al-<lb/>teri major eſt reſpectu quantitatis materiæ, tantum hæc il-<lb/>lam ſuperat propter majorem diſtantiam.</s> <s xml:id="echoid-s3808" xml:space="preserve"/> </p> <div xml:id="echoid-div565" type="float" level="2" n="2"> <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">367.</note> </div> </div> <div xml:id="echoid-div567" type="section" level="1" n="174"> <head xml:id="echoid-head246" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s3809" xml:space="preserve">Sit globus ſemi libræ ad diſtantiam a centro viginti qua-<lb/> <anchor type="note" xlink:label="note-0148-02a" xlink:href="note-0148-02"/> tuor partium; </s> <s xml:id="echoid-s3810" xml:space="preserve">globus unius libræ ad diſtantiam duodecim <lb/>partium; </s> <s xml:id="echoid-s3811" xml:space="preserve">cæteris manentibus ut in Experimento præceden-<lb/>ti, ſi pondera in ſuſten aculis Orbium fuerint æqualia, eo-<lb/>dem momento adſcendent.</s> <s xml:id="echoid-s3812" xml:space="preserve"/> </p> <div xml:id="echoid-div567" type="float" level="2" n="1"> <note position="left" xlink:label="note-0148-02" xlink:href="note-0148-02a" xml:space="preserve">368.</note> </div> <p> <s xml:id="echoid-s3813" xml:space="preserve">Caſus hujus propoſitionis exſtat, quando duo corpora fi-<lb/> <anchor type="note" xlink:label="note-0148-03a" xlink:href="note-0148-03"/> lo juncta circa commune centrum gravitatis revolvuntur. </s> <s xml:id="echoid-s3814" xml:space="preserve">Di-<lb/>ſtantiæ enim ab illo centro ſu nt in ratione inverſa ponde-<lb/>rum corporum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3815" xml:space="preserve">ergo vires centrales æquales. </s> <s xml:id="echoid-s3816" xml:space="preserve">Viqua <anchor type="note" xlink:label="note-0148-04a" xlink:href="note-0148-04"/> corpus unum a centro conatur recedere, alterum ad cen-<lb/>trum trahitur; </s> <s xml:id="echoid-s3817" xml:space="preserve">& </s> <s xml:id="echoid-s3818" xml:space="preserve">propter virium æqualitatem ſeſe mutuo <lb/>netinent & </s> <s xml:id="echoid-s3819" xml:space="preserve">motum continuant; </s> <s xml:id="echoid-s3820" xml:space="preserve">ſi circa aliud punctum revol-<lb/>vantur, motum non continuant, & </s> <s xml:id="echoid-s3821" xml:space="preserve">corpus, cujus vis <lb/>centrifuga præpollet, a centro recedit, & </s> <s xml:id="echoid-s3822" xml:space="preserve">corpus aliud ſe-<lb/>cum fert.</s> <s xml:id="echoid-s3823" xml:space="preserve"/> </p> <div xml:id="echoid-div568" type="float" level="2" n="2"> <note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">369.</note> <note symbol="*" position="left" xlink:label="note-0148-04" xlink:href="note-0148-04a" xml:space="preserve">143. 134.</note> </div> </div> <div xml:id="echoid-div570" type="section" level="1" n="175"> <head xml:id="echoid-head247" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s3824" xml:space="preserve">Corpora duo inæqualia P & </s> <s xml:id="echoid-s3825" xml:space="preserve">Q, filo junguntur, & </s> <s xml:id="echoid-s3826" xml:space="preserve">in <lb/> <anchor type="note" xlink:label="note-0148-05a" xlink:href="note-0148-05"/> hoc notatur punctum C, centrum commune gravitatis il-<lb/> <anchor type="note" xlink:label="note-0148-06a" xlink:href="note-0148-06"/> lorum corporum quando filum diſtenditur.</s> <s xml:id="echoid-s3827" xml:space="preserve"/> </p> <div xml:id="echoid-div570" type="float" level="2" n="1"> <note position="left" xlink:label="note-0148-05" xlink:href="note-0148-05a" xml:space="preserve">370.</note> <note position="left" xlink:label="note-0148-06" xlink:href="note-0148-06a" xml:space="preserve">TAB. XIV. <lb/>fig. 10.</note> </div> <pb o="93" file="0149" n="162" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> <p> <s xml:id="echoid-s3828" xml:space="preserve">In hoc Experimento unicus adhibetur Orbis, ei imponi-<lb/>tur pyxis oblonga ab utraque parte Orbem excedens, & </s> <s xml:id="echoid-s3829" xml:space="preserve"><lb/>cujus medium cum centro Orbis congruat. </s> <s xml:id="echoid-s3830" xml:space="preserve">Pyxidi huic <lb/>corpora ſtatim memorata imponuntur, & </s> <s xml:id="echoid-s3831" xml:space="preserve">filo quo jungun-<lb/>tur manente extenſo, punctum C puncto medio pyxidis ad-<lb/>movetur. </s> <s xml:id="echoid-s3832" xml:space="preserve">Circumrotatur Orbis, corpora cum pyxide cir-<lb/>cumferuntur, & </s> <s xml:id="echoid-s3833" xml:space="preserve">in hac quieta manent. </s> <s xml:id="echoid-s3834" xml:space="preserve">Removeatur pun-<lb/>ctum C a medio pyxidis, in circumvolutione corpora am-<lb/>bo ferentur ad illam pyxidis extremitatem cui punctum C <lb/>magis acceſlit.</s> <s xml:id="echoid-s3835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3836" xml:space="preserve">Etne in hoc caſu ambo corpora ex pyxidi ejiciantur, cum <lb/>periculo ſpectatorum, pyxidis extremitates obteguntur tabel-<lb/>lis ligneis, ſex poll. </s> <s xml:id="echoid-s3837" xml:space="preserve">longis, infra quas dum corpora in py-<lb/>xidis extrema impingunt ex hac ejici nequeunt.</s> <s xml:id="echoid-s3838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3839" xml:space="preserve">Differentia virium centralium ex differentia temporis pe-<lb/>riodici etiam determinatur.</s> <s xml:id="echoid-s3840" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3841" xml:space="preserve">Quando quantitates materiæ in corporibus circumrotatis, <lb/> <anchor type="note" xlink:label="note-0149-01a" xlink:href="note-0149-01"/> & </s> <s xml:id="echoid-s3842" xml:space="preserve">diſtantiæ a centro ſunt æquales, vires centrales ſunt in <lb/>ratione inverſa quadratorum temporum periodicorum, id eſt, <lb/>directe ut quadrata revolutionum eodem tempore peracta-<lb/>rum.</s> <s xml:id="echoid-s3843" xml:space="preserve"/> </p> <div xml:id="echoid-div571" type="float" level="2" n="2"> <note position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">371.</note> </div> </div> <div xml:id="echoid-div573" type="section" level="1" n="176"> <head xml:id="echoid-head248" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s3844" xml:space="preserve">Orbi A applicatur rota ut b b, (Fig. </s> <s xml:id="echoid-s3845" xml:space="preserve">2.) </s> <s xml:id="echoid-s3846" xml:space="preserve">cujus circumfe-<lb/> <anchor type="note" xlink:label="note-0149-02a" xlink:href="note-0149-02"/> rentia ſe habeat ad circumferentiam rotæ illius quæ cum Orbe <lb/> <anchor type="note" xlink:label="note-0149-03a" xlink:href="note-0149-03"/> B cohæret, ut tria ad duo; </s> <s xml:id="echoid-s3847" xml:space="preserve">ita ut B, quando Orbes ſimul <lb/>moventur, ter revolvatur dum A bis circumagitur, id eſt, <lb/>hujus tempus periodicum eſt alterius tempus periodicum <lb/>feſquiplicatum.</s> <s xml:id="echoid-s3848" xml:space="preserve"/> </p> <div xml:id="echoid-div573" type="float" level="2" n="1"> <note position="right" xlink:label="note-0149-02" xlink:href="note-0149-02a" xml:space="preserve">372.</note> <note position="right" xlink:label="note-0149-03" xlink:href="note-0149-03a" xml:space="preserve">TAB. XIV. <lb/>fig. 1.2.</note> </div> <p> <s xml:id="echoid-s3849" xml:space="preserve">In utraque pyxide P, P, globus unius libræ imponitur, <lb/>ad diſtantias æquales a centro. </s> <s xml:id="echoid-s3850" xml:space="preserve">In Orbe B, conjungitur glo-<lb/>bus cum pondere duarum librarum cum quadrante in ſu-<lb/>ſtentaculo, & </s> <s xml:id="echoid-s3851" xml:space="preserve">alter globus cum pondere unius libræ in ſu-<lb/>ſtentaculo Orbis A. </s> <s xml:id="echoid-s3852" xml:space="preserve">Circumrotantur Orbes, & </s> <s xml:id="echoid-s3853" xml:space="preserve">pondera <lb/>ſimul adſcendunt. </s> <s xml:id="echoid-s3854" xml:space="preserve">Pondera hic ſunt ut 9. </s> <s xml:id="echoid-s3855" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s3856" xml:space="preserve">dum tem-<lb/>pora periodica ut 2. </s> <s xml:id="echoid-s3857" xml:space="preserve">ad 3. </s> <s xml:id="echoid-s3858" xml:space="preserve">quorum quadrata ſunt reciproce <lb/>ut 9. </s> <s xml:id="echoid-s3859" xml:space="preserve">ad 4.</s> <s xml:id="echoid-s3860" xml:space="preserve"/> </p> <pb o="94" file="0150" n="163" rhead="PHYSCES ELEMENTA"/> <p> <s xml:id="echoid-s3861" xml:space="preserve">Quomodocunque inter ſe vires centrales differant, ex <lb/> <anchor type="note" xlink:label="note-0150-01a" xlink:href="note-0150-01"/> jam dictis inter ſe poſſunt comparari; </s> <s xml:id="echoid-s3862" xml:space="preserve">nam ſunt ſemper in <lb/>ratione compoſita, ex ratione quantitatum materiæ in cor-<lb/>poribus revolutis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3863" xml:space="preserve">ratione diſtantiarum a centro <anchor type="note" xlink:href="" symbol="*"/>, ut <anchor type="note" xlink:label="note-0150-02a" xlink:href="note-0150-02"/> & </s> <s xml:id="echoid-s3864" xml:space="preserve">ratione inverſa quadratorum temporum periodicorum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s3865" xml:space="preserve"> <anchor type="note" xlink:label="note-0150-03a" xlink:href="note-0150-03"/> Multiplicando quantitatem materiæ in unoquoque corpore <lb/>per ſuam diſtantiam a centro, & </s> <s xml:id="echoid-s3866" xml:space="preserve">dividendo productum per <lb/>quadratum temporis periodici, quotientes diviſionum erunt <lb/>in dicta ratione compoſita, id eſt, ut vires centrales.</s> <s xml:id="echoid-s3867" xml:space="preserve"/> </p> <div xml:id="echoid-div574" type="float" level="2" n="2"> <note position="left" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">373.</note> <note symbol="*" position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">361. <lb/>363.</note> <note symbol="*" position="left" xlink:label="note-0150-03" xlink:href="note-0150-03a" xml:space="preserve">371.</note> </div> </div> <div xml:id="echoid-div576" type="section" level="1" n="177"> <head xml:id="echoid-head249" xml:space="preserve"><emph style="sc">Experimentum</emph>. 10.</head> <p> <s xml:id="echoid-s3868" xml:space="preserve">Obſervatis iiſdem quæ in Experimento præcedenti, de-<lb/> <anchor type="note" xlink:label="note-0150-04a" xlink:href="note-0150-04"/> tur globus ſemi-libræ, ad diſtantiam ſedecim a centro Or-<lb/>bis B, & </s> <s xml:id="echoid-s3869" xml:space="preserve">cum pondere {3/4} unius libræ in ſuſtentaculo con-<lb/>jungatur; </s> <s xml:id="echoid-s3870" xml:space="preserve">globus alter ſit unius libræ, ad diſtantiam vigin-<lb/>ti quatuor a centro Orbis A, & </s> <s xml:id="echoid-s3871" xml:space="preserve">conjungatur cum pondere <lb/>unius libræ; </s> <s xml:id="echoid-s3872" xml:space="preserve">circumagantur Orbes, eodem momento pon-<lb/>dera elevantur.</s> <s xml:id="echoid-s3873" xml:space="preserve"/> </p> <div xml:id="echoid-div576" type="float" level="2" n="1"> <note position="left" xlink:label="note-0150-04" xlink:href="note-0150-04a" xml:space="preserve">374.</note> </div> <p> <s xml:id="echoid-s3874" xml:space="preserve">Corpora hic ſunt ut {1/2} ad 1.</s> <s xml:id="echoid-s3875" xml:space="preserve">; diſtantiæ ut 16. </s> <s xml:id="echoid-s3876" xml:space="preserve">ad 24.</s> <s xml:id="echoid-s3877" xml:space="preserve">; qua-<lb/>drata temporum periodicorum ut 4. </s> <s xml:id="echoid-s3878" xml:space="preserve">ad 9.</s> <s xml:id="echoid-s3879" xml:space="preserve">; multiplicando <lb/>{1/2} per 16.</s> <s xml:id="echoid-s3880" xml:space="preserve">, & </s> <s xml:id="echoid-s3881" xml:space="preserve">dividendo productum per 4.</s> <s xml:id="echoid-s3882" xml:space="preserve">, quotiens eſt 2. <lb/></s> <s xml:id="echoid-s3883" xml:space="preserve">multiplicando 1. </s> <s xml:id="echoid-s3884" xml:space="preserve">per 24.</s> <s xml:id="echoid-s3885" xml:space="preserve">, & </s> <s xml:id="echoid-s3886" xml:space="preserve">dividendo productum per 9.</s> <s xml:id="echoid-s3887" xml:space="preserve">, <lb/>quotiens diviſionis eſt 2 {2/3}. </s> <s xml:id="echoid-s3888" xml:space="preserve">Vires ergo centrales ſunt inter <lb/>ſe ut 2. </s> <s xml:id="echoid-s3889" xml:space="preserve">ad 2 {2/3}, aut ut 3. </s> <s xml:id="echoid-s3890" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s3891" xml:space="preserve">quam rationem pondera in <lb/>ſuſtentaculis etiam inter ſe habent.</s> <s xml:id="echoid-s3892" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s3893" xml:space="preserve">Quando quantitates materiæ ſunt æquales, diſtantiæ ipſæ <lb/> <anchor type="note" xlink:label="note-0150-05a" xlink:href="note-0150-05"/> per quadrata temporum periodicorum dividuntur ad deter-<lb/>minandam proportionem inter vires centrales.</s> <s xml:id="echoid-s3894" xml:space="preserve"/> </p> <div xml:id="echoid-div577" type="float" level="2" n="2"> <note position="left" xlink:label="note-0150-05" xlink:href="note-0150-05a" xml:space="preserve">375.</note> </div> <p> <s xml:id="echoid-s3895" xml:space="preserve">In hoc caſu ſi quadratatemporum periodicorum fuerint in-<lb/> <anchor type="note" xlink:label="note-0150-06a" xlink:href="note-0150-06"/> ter ſe ut cubi diſtantiarum, quotientes diviſionum erunt in <lb/>ratione inverſa quadratorum diſtantiarum; </s> <s xml:id="echoid-s3896" xml:space="preserve">& </s> <s xml:id="echoid-s3897" xml:space="preserve">in hac ratio-<lb/>ne etiam vires centrales.</s> <s xml:id="echoid-s3898" xml:space="preserve"/> </p> <div xml:id="echoid-div578" type="float" level="2" n="3"> <note position="left" xlink:label="note-0150-06" xlink:href="note-0150-06a" xml:space="preserve">376.</note> </div> </div> <div xml:id="echoid-div580" type="section" level="1" n="178"> <head xml:id="echoid-head250" xml:space="preserve"><emph style="sc">Experimentum</emph> II.</head> <p> <s xml:id="echoid-s3899" xml:space="preserve">Sint tempora periodica Orbis B & </s> <s xml:id="echoid-s3900" xml:space="preserve">A, ut 1. </s> <s xml:id="echoid-s3901" xml:space="preserve">ad 2.</s> <s xml:id="echoid-s3902" xml:space="preserve">; den-<lb/> <anchor type="note" xlink:label="note-0150-07a" xlink:href="note-0150-07"/> tur globi æquales, & </s> <s xml:id="echoid-s3903" xml:space="preserve">diſtantia a centro in orbe B ſit decem <lb/>alterius globi diſtantia a centro ſit ſedecim, pondus primo <lb/>annexum ſit unius libræ cum quadrante, & </s> <s xml:id="echoid-s3904" xml:space="preserve">pondus in ſu- <pb file="0151" n="164"/> <anchor type="figure" xlink:label="fig-0151-01a" xlink:href="fig-0151-01"/> <pb file="0151a" n="165"/> <anchor type="figure" xlink:label="fig-0151a-01a" xlink:href="fig-0151a-01"/> <pb file="0152" n="166"/> <pb o="95" file="0153" n="167" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> ſtentaculo alterius Orbis A ſit ſemi-libræ; </s> <s xml:id="echoid-s3905" xml:space="preserve">in agitatione Or-<lb/>bium pondera eodem momento adſcendunt.</s> <s xml:id="echoid-s3906" xml:space="preserve"/> </p> <div xml:id="echoid-div580" type="float" level="2" n="1"> <note position="left" xlink:label="note-0150-07" xlink:href="note-0150-07a" xml:space="preserve">377.</note> <figure xlink:label="fig-0151-01" xlink:href="fig-0151-01a"> <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151-01"/> </figure> <figure xlink:label="fig-0151a-01" xlink:href="fig-0151a-01a"> <image file="0151a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151a-01"/> </figure> </div> <p> <s xml:id="echoid-s3907" xml:space="preserve">In hocce Experimento vires centrales ſunt ut 5. </s> <s xml:id="echoid-s3908" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s3909" xml:space="preserve">quod <lb/>etiam computatione detegitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s3910" xml:space="preserve">Hæc ratio paululum admo-* <anchor type="note" xlink:label="note-0153-01a" xlink:href="note-0153-01"/> dum differt a ratione inverſa quadratorum diſtantiarum, <lb/>quæ ſunt inter ſe ut 200. </s> <s xml:id="echoid-s3911" xml:space="preserve">ad 512.</s> <s xml:id="echoid-s3912" xml:space="preserve">: cubi etiam diſtantiarum, <lb/>ſunt fere ut quadrata temporum periodicorum; </s> <s xml:id="echoid-s3913" xml:space="preserve">hæc ſunt ut <lb/>1. </s> <s xml:id="echoid-s3914" xml:space="preserve">ad 4.</s> <s xml:id="echoid-s3915" xml:space="preserve">, illi ut 125. </s> <s xml:id="echoid-s3916" xml:space="preserve">ad 512. </s> <s xml:id="echoid-s3917" xml:space="preserve">quæ rationes non admodum dif-<lb/>ferunt. </s> <s xml:id="echoid-s3918" xml:space="preserve">Aliis adhibitis numeris hæ rationes exacte eædem <lb/>erunt, & </s> <s xml:id="echoid-s3919" xml:space="preserve">Experimentum eodem modo procedet; </s> <s xml:id="echoid-s3920" xml:space="preserve">ſed non <lb/>commodètempora periodica, aut pondera, ſecundum quam-<lb/>libet rationem variari poſſunt.</s> <s xml:id="echoid-s3921" xml:space="preserve"/> </p> <div xml:id="echoid-div581" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">375</note> </div> <p style="it"> <s xml:id="echoid-s3922" xml:space="preserve">Si corpora ſint inæqualia, ſed in bæc agant vires centra-<lb/> <anchor type="note" xlink:label="note-0153-02a" xlink:href="note-0153-02"/> les, quæ, ut gravitas, æqualiter in ſingulas materiæ particu-<lb/>las agant, non intereſt quæcunque ſint maſſæ corporum, & </s> <s xml:id="echoid-s3923" xml:space="preserve"><lb/>propoſitio ultima etiam in corporibus inæqualibus obti-<lb/>net.</s> <s xml:id="echoid-s3924" xml:space="preserve"/> </p> <div xml:id="echoid-div582" type="float" level="2" n="3"> <note position="right" xlink:label="note-0153-02" xlink:href="note-0153-02a" xml:space="preserve">378.</note> </div> <p> <s xml:id="echoid-s3925" xml:space="preserve">Ellipſin vocant Geometræ lineam ovalem cujus hæc eſt <lb/> <anchor type="note" xlink:label="note-0153-03a" xlink:href="note-0153-03"/> deſcriptio. </s> <s xml:id="echoid-s3926" xml:space="preserve">Sit A a recta; </s> <s xml:id="echoid-s3927" xml:space="preserve">C punctum hujus medium; </s> <s xml:id="echoid-s3928" xml:space="preserve">F, f, <lb/> <anchor type="note" xlink:label="note-0153-04a" xlink:href="note-0153-04"/> puncta à C æqualiter diſtantia; </s> <s xml:id="echoid-s3929" xml:space="preserve">F G f filum, cujus extremi-<lb/>tates in F & </s> <s xml:id="echoid-s3930" xml:space="preserve">f fixæ ſunt, quod æquale eſt lineæ A a. </s> <s xml:id="echoid-s3931" xml:space="preserve">Ten-<lb/>ſo filo clavo G, in plano in quo datur A a Ellipſis deſcribi-<lb/>tur. </s> <s xml:id="echoid-s3932" xml:space="preserve">Puncta F, f, vocantur foci; </s> <s xml:id="echoid-s3933" xml:space="preserve">C centrum; </s> <s xml:id="echoid-s3934" xml:space="preserve">A a axis major; <lb/></s> <s xml:id="echoid-s3935" xml:space="preserve">minor axis per centrum tranſit, cum majori angulos effici-<lb/>ens rectos, & </s> <s xml:id="echoid-s3936" xml:space="preserve">ab utraque parte curvâ terminatur.</s> <s xml:id="echoid-s3937" xml:space="preserve"/> </p> <div xml:id="echoid-div583" type="float" level="2" n="4"> <note position="right" xlink:label="note-0153-03" xlink:href="note-0153-03a" xml:space="preserve">379.</note> <note position="right" xlink:label="note-0153-04" xlink:href="note-0153-04a" xml:space="preserve">TAB. XV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s3938" xml:space="preserve">Quando vis, qua corpus punctum verſus fertur, non u-<lb/> <anchor type="note" xlink:label="note-0153-05a" xlink:href="note-0153-05"/> bique eſt eadem, ſed cum diſtantia à centro creſcit, aut <lb/>minuitur, ſecundum certam proportionem, variæ inde <lb/>oriuntur curvæ.</s> <s xml:id="echoid-s3939" xml:space="preserve"/> </p> <div xml:id="echoid-div584" type="float" level="2" n="5"> <note position="right" xlink:label="note-0153-05" xlink:href="note-0153-05a" xml:space="preserve">380.</note> </div> <p> <s xml:id="echoid-s3940" xml:space="preserve">Ponamus vim quæ in corpora mota agit ut in quieſcentia, <lb/> <anchor type="note" xlink:label="note-0153-06a" xlink:href="note-0153-06"/> quæ ad diſtantias æquales à centro æqualis ſit, adinæquales de-<lb/>creſcat, in ratione inverſa quadratorum diſtantiarum ab hoc <lb/>puncto, deſcribet corpus Ellipſin cujus focorum alter cum cen-<lb/>tro virium coincidit; </s> <s xml:id="echoid-s3941" xml:space="preserve">ita ut in unaquaque revolutione ſemel ad <lb/>hoc accedat corpus, & </s> <s xml:id="echoid-s3942" xml:space="preserve">iterum ab hoc recedat. </s> <s xml:id="echoid-s3943" xml:space="preserve">In receſſu <lb/>minuitur corporis celeritas <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s3944" xml:space="preserve">quidem ita, ut vis centralis, li- <anchor type="note" xlink:label="note-0153-07a" xlink:href="note-0153-07"/> <pb o="96" file="0154" n="168" rhead="PHYSICES ELEMENTA"/> cet ipſa minuatur, viam corporis flectat, & </s> <s xml:id="echoid-s3945" xml:space="preserve">hoc ad <lb/>centrum accedere cogat: </s> <s xml:id="echoid-s3946" xml:space="preserve">acceſſu augetur velocitas ita, ut, <lb/>licet vis augeatur, corpus iterum a centro recedat.</s> <s xml:id="echoid-s3947" xml:space="preserve"/> </p> <div xml:id="echoid-div585" type="float" level="2" n="6"> <note position="right" xlink:label="note-0153-06" xlink:href="note-0153-06a" xml:space="preserve">381.</note> <note symbol="*" position="right" xlink:label="note-0153-07" xlink:href="note-0153-07a" xml:space="preserve">3526</note> </div> <p> <s xml:id="echoid-s3948" xml:space="preserve">Circulus ad hoc genus curvarum pertinet, & </s> <s xml:id="echoid-s3949" xml:space="preserve">in hoc ca-<lb/> <anchor type="note" xlink:label="note-0154-01a" xlink:href="note-0154-01"/> ſu corpus etiam circulum poteſt deſcribere, qui, ſi bujus <lb/>diameter æqualis ſit aximajori Ellipſeos cujuſcunque, eodem <lb/>tempore cum bac deſcribitur.</s> <s xml:id="echoid-s3950" xml:space="preserve"/> </p> <div xml:id="echoid-div586" type="float" level="2" n="7"> <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">382.</note> </div> <p> <s xml:id="echoid-s3951" xml:space="preserve">Corpus poteſt tali celeritate projici, ut in receſſu a cen-<lb/> <anchor type="note" xlink:label="note-0154-02a" xlink:href="note-0154-02"/> tro vis, quæ auctâ diſtantiâ minuitur, non valeat ad viam <lb/>ita inflectendam, ut corpus redeat; </s> <s xml:id="echoid-s3952" xml:space="preserve">percurrit in hoc caſu <lb/>corpus curvam aliam Parabolam aut Hyperbolam.</s> <s xml:id="echoid-s3953" xml:space="preserve"/> </p> <div xml:id="echoid-div587" type="float" level="2" n="8"> <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">383.</note> </div> <p style="it"> <s xml:id="echoid-s3954" xml:space="preserve">Si vis centralis juxta alvam proportionem quamcunque <lb/> <anchor type="note" xlink:label="note-0154-03a" xlink:href="note-0154-03"/> in receſſu a centro decreſcat, non poterit corpus lineam in <lb/>ſe redeuntem, & </s> <s xml:id="echoid-s3955" xml:space="preserve">a circulo parum aberrantem, deſcribere.</s> <s xml:id="echoid-s3956" xml:space="preserve"/> </p> <div xml:id="echoid-div588" type="float" level="2" n="9"> <note position="left" xlink:label="note-0154-03" xlink:href="note-0154-03a" xml:space="preserve">384.</note> </div> <p> <s xml:id="echoid-s3957" xml:space="preserve">Sed ſi vis decreſcat juxta proportionem parum ab bac ab-<lb/> <anchor type="note" xlink:label="note-0154-04a" xlink:href="note-0154-04"/> errantem, aut curva à circulo non multum differat; </s> <s xml:id="echoid-s3958" xml:space="preserve">poterit <lb/>curva a corpore deſcripta referri ad Ellipſin mobilem, cu-<lb/>jus nempe axis, in plano, in quo corpus revolvitur, mo-<lb/>vetur motu angulari, manente foco in centro virium. </s> <s xml:id="echoid-s3959" xml:space="preserve">Mo-<lb/> <anchor type="note" xlink:label="note-0154-05a" xlink:href="note-0154-05"/> tus autem axeos in eandem partem dirigitur cum motu cor-<lb/>poris, ſi vis celerius decreſcat auctâ diſtantiâ quam prora-<lb/>tione inverſa quadrati diſtantiæ: </s> <s xml:id="echoid-s3960" xml:space="preserve">Si vero vis tardius, id eſt <lb/> <anchor type="note" xlink:label="note-0154-06a" xlink:href="note-0154-06"/> minus, decreſcat in reseſſu a centro, motus Ellipſeos in <lb/>contrariam partem dirigitur.</s> <s xml:id="echoid-s3961" xml:space="preserve"/> </p> <div xml:id="echoid-div589" type="float" level="2" n="10"> <note position="left" xlink:label="note-0154-04" xlink:href="note-0154-04a" xml:space="preserve">385.</note> <note position="left" xlink:label="note-0154-05" xlink:href="note-0154-05a" xml:space="preserve">386.</note> <note position="left" xlink:label="note-0154-06" xlink:href="note-0154-06a" xml:space="preserve">387.</note> </div> <p style="it"> <s xml:id="echoid-s3962" xml:space="preserve">Corpus etiam Ellipſin deſcribit, ſi vis centralis, in re-<lb/> <anchor type="note" xlink:label="note-0154-07a" xlink:href="note-0154-07"/> ceſſu a centro, creſcat, & </s> <s xml:id="echoid-s3963" xml:space="preserve">ſit ubique in ratione diſtantiæ a <lb/>centro, quod in boc caſu cum centro Ellipſeos coincidit.</s> <s xml:id="echoid-s3964" xml:space="preserve"/> </p> <div xml:id="echoid-div590" type="float" level="2" n="11"> <note position="left" xlink:label="note-0154-07" xlink:href="note-0154-07a" xml:space="preserve">388.</note> </div> </div> <div xml:id="echoid-div592" type="section" level="1" n="179"> <head xml:id="echoid-head251" xml:space="preserve"><emph style="sc">Experimentum</emph> 12</head> <p> <s xml:id="echoid-s3965" xml:space="preserve">Longiori filo ſuſpendatur globus plumbeus; </s> <s xml:id="echoid-s3966" xml:space="preserve">ſi a puncto <lb/> <anchor type="note" xlink:label="note-0154-08a" xlink:href="note-0154-08"/> in quo quieſcit retrahatur, gravitate ſua ſemper hoc verſus <lb/>fertur; </s> <s xml:id="echoid-s3967" xml:space="preserve">& </s> <s xml:id="echoid-s3968" xml:space="preserve">ab omni parte, ſi diſtantia fuerit æqualis æqua-<lb/>li cum vi. </s> <s xml:id="echoid-s3969" xml:space="preserve">In motu ſuo a puncto memorato globus circu-<lb/>lum deſcribit, partem quamcunque verſus retrahatur: </s> <s xml:id="echoid-s3970" xml:space="preserve">ſi <lb/>portiones circuli nonfuerint admodum magnæ, cum cycloï-<lb/>de coïncidunt, & </s> <s xml:id="echoid-s3971" xml:space="preserve">vis cum qua globus, in quocumque pun-<lb/>cto, fertur punctum inſimum verſus, eſt ut illius diſtantia <pb o="97" file="0155" n="169" rhead="MATHEMATICA. LIB I. CAP. XXI."/> ab hocce puncto <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s3972" xml:space="preserve">vis ergo illa creſcit in ratione diſtan- <anchor type="note" xlink:label="note-0155-01a" xlink:href="note-0155-01"/> tiæ.</s> <s xml:id="echoid-s3973" xml:space="preserve"/> </p> <div xml:id="echoid-div592" type="float" level="2" n="1"> <note position="left" xlink:label="note-0154-08" xlink:href="note-0154-08a" xml:space="preserve">389.</note> <note symbol="*" position="right" xlink:label="note-0155-01" xlink:href="note-0155-01a" xml:space="preserve">2@7.</note> </div> <p> <s xml:id="echoid-s3974" xml:space="preserve">Retrahatur globus a puncto infimo, & </s> <s xml:id="echoid-s3975" xml:space="preserve">oblique projicia-<lb/>tur, figuram ovalem circa hocce punctum deſcribet, quæ, <lb/>quando globus per ſpatium magnum non excurrit, ab Elli-<lb/>pſi fere nihil differt, propter virium proportionem, & </s> <s xml:id="echoid-s3976" xml:space="preserve">quia <lb/>in eo caſu ad ſenſum in eodem plano movetur globus.</s> <s xml:id="echoid-s3977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3978" xml:space="preserve">Centrum Ellipſis eſt punctum in quo globus quando non <lb/>projicitur quieſcit, in unaquaque revolutione bis ad illud <lb/>globus accedit, & </s> <s xml:id="echoid-s3979" xml:space="preserve">bis ab illo recedit. </s> <s xml:id="echoid-s3980" xml:space="preserve">Si ſupra menſam <lb/>globus ſuſpendatur ita, ut fere menſam quando quieſcit tangat, <lb/>& </s> <s xml:id="echoid-s3981" xml:space="preserve">punctum cui tunc reſpondet in menſa notetur, Experi-<lb/>mentum multo ſit magis ſenſibile; </s> <s xml:id="echoid-s3982" xml:space="preserve">inſequendo globum hujus <lb/>via cum creta in menſa notari poteſt.</s> <s xml:id="echoid-s3983" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3984" xml:space="preserve">Si vis juxta aliam rationem creſcat, curva in ſe non re-<lb/> <anchor type="note" xlink:label="note-0155-02a" xlink:href="note-0155-02"/> dit; </s> <s xml:id="echoid-s3985" xml:space="preserve">Sed poteſt ſæpe ad Ellipſin in plano mobilem referri.</s> <s xml:id="echoid-s3986" xml:space="preserve"/> </p> <div xml:id="echoid-div593" type="float" level="2" n="2"> <note position="right" xlink:label="note-0155-02" xlink:href="note-0155-02a" xml:space="preserve">390.</note> </div> </div> <div xml:id="echoid-div595" type="section" level="1" n="180"> <head xml:id="echoid-head252" xml:space="preserve"><emph style="sc">Experimentum</emph> 13.</head> <p> <s xml:id="echoid-s3987" xml:space="preserve">Iiſdem poſitis quæ in Experimento præcedenti, projiciatur <lb/> <anchor type="note" xlink:label="note-0155-03a" xlink:href="note-0155-03"/> globus ut ad diſtantiam majorem excurrat; </s> <s xml:id="echoid-s3988" xml:space="preserve">curvam deſcri-<lb/>bit quæ ad Ovalem mobilem referri poteſt; </s> <s xml:id="echoid-s3989" xml:space="preserve">bis in unaqua-<lb/>que revolutione quidem accedit ad centrum, & </s> <s xml:id="echoid-s3990" xml:space="preserve">bis ab eo <lb/>recedit; </s> <s xml:id="echoid-s3991" xml:space="preserve">ſed ſitus punctorum, in quibus minime aut maxi-<lb/>me diſtat, in ſingulis revolutionibus mutatur, & </s> <s xml:id="echoid-s3992" xml:space="preserve">ſempere-<lb/>andem partem verſus hæc puncta feruntur, horumque motus <lb/>cum globi motu conſpirat.</s> <s xml:id="echoid-s3993" xml:space="preserve"/> </p> <div xml:id="echoid-div595" type="float" level="2" n="1"> <note position="right" xlink:label="note-0155-03" xlink:href="note-0155-03a" xml:space="preserve">391.</note> </div> <p> <s xml:id="echoid-s3994" xml:space="preserve">Ex hac ultima propoſitione, ſi ad n. </s> <s xml:id="echoid-s3995" xml:space="preserve">384. </s> <s xml:id="echoid-s3996" xml:space="preserve">attendamus, ſe-<lb/> <anchor type="note" xlink:label="note-0155-04a" xlink:href="note-0155-04"/> quitur, nullâ vi centrali, ad æquales diſtantias æqualiter <lb/>agenti, curvam poſſe deſcribi in ſe redeuntem & </s> <s xml:id="echoid-s3997" xml:space="preserve">excentri-<lb/>cam, id eſt cujus centrum cum centro virium non coincidit, <lb/>præter Ellipſin, in cujus focorum altero centrum virium da-<lb/>tur; </s> <s xml:id="echoid-s3998" xml:space="preserve">vimque centralem, in hoc caſu, ſequi rationem in-<lb/>verſam quadrati diſtantiæ</s> </p> <div xml:id="echoid-div596" type="float" level="2" n="2"> <note position="right" xlink:label="note-0155-04" xlink:href="note-0155-04a" xml:space="preserve">392.</note> </div> <note position="right" xml:space="preserve">393.</note> <p> <s xml:id="echoid-s3999" xml:space="preserve">Circulum autem, cujus centrum cum centro virium coin-<lb/>cidit, poſſe deſcribi vi juxta rationem quamcunque creſcen-<lb/>tem aut decreſcentem, ſi modo ad diſtantias æquales æqua-<lb/>liter agat, facile patet.</s> <s xml:id="echoid-s4000" xml:space="preserve"/> </p> <pb o="98" file="0156" n="170" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div598" type="section" level="1" n="181"> <head xml:id="echoid-head253" xml:space="preserve">SCHOLIUM 1.</head> <head xml:id="echoid-head254" style="it" xml:space="preserve">Generalia de viribus centralibus.</head> <p> <s xml:id="echoid-s4001" xml:space="preserve">Concipiamus dari vim, qua corpus, ubicunque detur, pellatur centrum <lb/> <anchor type="note" xlink:label="note-0156-01a" xlink:href="note-0156-01"/> C verſus, non intereſt quomodocunque in punctis diverſis varietur vis <lb/> <anchor type="note" xlink:label="note-0156-02a" xlink:href="note-0156-02"/> hæc; </s> <s xml:id="echoid-s4002" xml:space="preserve">concipiamus vim hanc non eſſe continuam, ſed illam ictibus in cor-<lb/>pus agere, & </s> <s xml:id="echoid-s4003" xml:space="preserve">momenta temporis inter ictus eſſe æqualia. </s> <s xml:id="echoid-s4004" xml:space="preserve">Ponamus etiam cor <lb/>pus projectum per AB hanc percurrere lineam in momento tali; </s> <s xml:id="echoid-s4005" xml:space="preserve">motum <lb/>per BL, æqualem AB, in momento ſequenti continuaret, niſi in B ictu <lb/>in corpus pelleretur hoc ad C; </s> <s xml:id="echoid-s4006" xml:space="preserve">ponamus celeritatem, ex hoc ictu oriundam <lb/>in corpore jam agitato, talem eſſe, ut hac corpus poſſit, in intervallo tem-<lb/>poris inter duos ictus, percurrere lineam LD; </s> <s xml:id="echoid-s4007" xml:space="preserve">ſi LD ſit parallela BC, <lb/>corpus duobus motibus agitatum pecurrit BD <anchor type="note" xlink:href="" symbol="*"/>, daturque in D, in momento in <anchor type="note" xlink:label="note-0156-03a" xlink:href="note-0156-03"/> quo ictu ſequenti iterum ad centrum pellitur. </s> <s xml:id="echoid-s4008" xml:space="preserve">Si ictus hic non daretur, in mo-<lb/>mento ſequenti percurreret DE, poſitis DE & </s> <s xml:id="echoid-s4009" xml:space="preserve">BD æqualibus, ſed eodem <lb/>tempore centrum verſus fertur, id eſt per DC pellitur, ſi juxta hanc dire-<lb/>ctionem percurrat lineam æqualem lineæ EF in tempore in quo percurre-<lb/>ret DE, motu compoſito corpus movetur per DF, poſitis EF & </s> <s xml:id="echoid-s4010" xml:space="preserve">DC pa-<lb/>rallelis. </s> <s xml:id="echoid-s4011" xml:space="preserve">Eodem modo demonſtramus in momento ſequenti corpus percur-<lb/>rere FH, ſi GH ſit æqualis ſpatio in hoc momento, ex ictu C verſus per-<lb/>currendo, poſitiſque FG & </s> <s xml:id="echoid-s4012" xml:space="preserve">DF æqualibus, ut & </s> <s xml:id="echoid-s4013" xml:space="preserve">GH & </s> <s xml:id="echoid-s4014" xml:space="preserve">FC parallelis.</s> <s xml:id="echoid-s4015" xml:space="preserve"/> </p> <div xml:id="echoid-div598" type="float" level="2" n="1"> <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">394.</note> <note position="left" xlink:label="note-0156-02" xlink:href="note-0156-02a" xml:space="preserve">TAB. XV. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">146.</note> </div> <p> <s xml:id="echoid-s4016" xml:space="preserve">Triangula ABC, BLC, habent baſes æquales AB, BL in eadem li-<lb/>nea, & </s> <s xml:id="echoid-s4017" xml:space="preserve">verticem communem C; </s> <s xml:id="echoid-s4018" xml:space="preserve">ſunt ergo æqualia <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4019" xml:space="preserve">Triangula BLC, <anchor type="note" xlink:label="note-0156-04a" xlink:href="note-0156-04"/> BDC baſinhabent communem BC& </s> <s xml:id="echoid-s4020" xml:space="preserve">conſtituuntur inter parallelas BC, LD, <lb/>ſunt ergo æqualia <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4021" xml:space="preserve">Idcirco etiam æqualia ſunt triangula ABC, BDC.</s> <s xml:id="echoid-s4022" xml:space="preserve"> <anchor type="note" xlink:label="note-0156-05a" xlink:href="note-0156-05"/> Eodem modo demonſtramus æqualia triangula BDC, DFC & </s> <s xml:id="echoid-s4023" xml:space="preserve">in gene-<lb/>re æqualia eſſe inter ſe triangula quæcunque ut ABC, BDC, DFC; <lb/></s> <s xml:id="echoid-s4024" xml:space="preserve">FHC, quorum baſes momentis æqualibus a corpore projecto percurrun-<lb/>tur. </s> <s xml:id="echoid-s4025" xml:space="preserve">Ex qua demonſtratione deducitur propoſitio n. </s> <s xml:id="echoid-s4026" xml:space="preserve">351.</s> <s xml:id="echoid-s4027" xml:space="preserve"/> </p> <div xml:id="echoid-div599" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">38. El. 1.</note> <note symbol="*" position="left" xlink:label="note-0156-05" xlink:href="note-0156-05a" xml:space="preserve">37. El. 1.</note> </div> <p style="it"> <s xml:id="echoid-s4028" xml:space="preserve">Etiam patet corpus projectum & </s> <s xml:id="echoid-s4029" xml:space="preserve">vi centrum verſus tendenti agitatum, move-<lb/> <anchor type="note" xlink:label="note-0156-06a" xlink:href="note-0156-06"/> ri in plano, quod tranſit per lineam juxta quam corpus projicitur & </s> <s xml:id="echoid-s4030" xml:space="preserve">per centrum <lb/>virium, ut monuimus in n. </s> <s xml:id="echoid-s4031" xml:space="preserve">353.</s> <s xml:id="echoid-s4032" xml:space="preserve"/> </p> <div xml:id="echoid-div600" type="float" level="2" n="3"> <note position="left" xlink:label="note-0156-06" xlink:href="note-0156-06a" xml:space="preserve">395.</note> </div> <p> <s xml:id="echoid-s4033" xml:space="preserve">Concipiamus nunc momenta inter duos ictus minui, ut & </s> <s xml:id="echoid-s4034" xml:space="preserve">ipſos ictus, ma-<lb/> <anchor type="note" xlink:label="note-0156-07a" xlink:href="note-0156-07"/> nentibus nihilominus illis æqualibus inter ſe, poſitis hiſce utcunque inæ-<lb/>qualibus, demonſtratio eadem locum habebit. </s> <s xml:id="echoid-s4035" xml:space="preserve">Si diminutio ſit in infinitum <lb/>mutantur ictus in preſſionem continuam, & </s> <s xml:id="echoid-s4036" xml:space="preserve">corpus in ſingulis punctis a via <lb/>recta deflectitur; </s> <s xml:id="echoid-s4037" xml:space="preserve">ſubjicitur tamen legi in demonſtratione præcedenti deter-<lb/>minata. </s> <s xml:id="echoid-s4038" xml:space="preserve">Si ergo corpus moveatur in curva ABDE, & </s> <s xml:id="echoid-s4039" xml:space="preserve">tempus concipia-<lb/> <anchor type="note" xlink:label="note-0156-08a" xlink:href="note-0156-08"/> tur diviſum in momenta infinite exigua, & </s> <s xml:id="echoid-s4040" xml:space="preserve">æqualiainter ſe, area trianguli mixti <lb/>ACB continebit tot triangula exigua æqualia inter ſe, quot dantur momen-<lb/>ta in tempore, in quo percurritur AB, & </s> <s xml:id="echoid-s4041" xml:space="preserve">area trianguli mixti DCE eo-<lb/>dem modo continebit tot triangula æqualia inter ſe & </s> <s xml:id="echoid-s4042" xml:space="preserve">prioribus, quot dan-<lb/>tur momenta in tempore in quo percurritur DE; </s> <s xml:id="echoid-s4043" xml:space="preserve">ideoque @empora in quibus <lb/>corpus AB & </s> <s xml:id="echoid-s4044" xml:space="preserve">DE, percurrit, ſunt inter ſe ut numeri triangulorum æqua-<lb/>lium areis ACB, DCE, contentorum, id eſt ut ipſæ areæ. </s> <s xml:id="echoid-s4045" xml:space="preserve">Unde genera-<lb/>lem deducimus propoſitionem in n. </s> <s xml:id="echoid-s4046" xml:space="preserve">354. </s> <s xml:id="echoid-s4047" xml:space="preserve">memoratam</s> </p> <div xml:id="echoid-div601" type="float" level="2" n="4"> <note position="left" xlink:label="note-0156-07" xlink:href="note-0156-07a" xml:space="preserve">396.</note> <note position="left" xlink:label="note-0156-08" xlink:href="note-0156-08a" xml:space="preserve">TAB. XIV-<lb/>fig. 11.</note> </div> <p> <s xml:id="echoid-s4048" xml:space="preserve">Cujus propoſitionis inverſa, quæ continentur in n. </s> <s xml:id="echoid-s4049" xml:space="preserve">355. </s> <s xml:id="echoid-s4050" xml:space="preserve">etiam demonſtratur. <lb/></s> <s xml:id="echoid-s4051" xml:space="preserve"> <anchor type="note" xlink:label="note-0156-09a" xlink:href="note-0156-09"/> Si corpus motum per AB in momento ſequenti, & </s> <s xml:id="echoid-s4052" xml:space="preserve">æquali, percurrat BD, quia <lb/> <anchor type="note" xlink:label="note-0156-10a" xlink:href="note-0156-10"/> <pb o="99" file="0157" n="171" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> motu primo, in momento hoc, per BL æqualem AB motum continuaſſet, <lb/>neceſſario juxta directionem L Da via ſua remotum fuit <anchor type="note" xlink:href="" symbol="*"/>, ſi autem trian- <anchor type="note" xlink:label="note-0157-01a" xlink:href="note-0157-01"/> gula ABC, BDC ſint æqualia, etiam æqualia erunt BDC, BLC; </s> <s xml:id="echoid-s4053" xml:space="preserve">i-<lb/>deoque linea LD parallela BC<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4054" xml:space="preserve">id eſt directio vis quæ corpus a linea re- <anchor type="note" xlink:label="note-0157-02a" xlink:href="note-0157-02"/> cta detorquet centrum C verſus dirigitur.</s> <s xml:id="echoid-s4055" xml:space="preserve"/> </p> <div xml:id="echoid-div602" type="float" level="2" n="5"> <note position="left" xlink:label="note-0156-09" xlink:href="note-0156-09a" xml:space="preserve">397.</note> <note position="left" xlink:label="note-0156-10" xlink:href="note-0156-10a" xml:space="preserve">TAB. XV. <lb/>fig 2.</note> <note symbol="*" position="right" xlink:label="note-0157-01" xlink:href="note-0157-01a" xml:space="preserve">246.</note> <note symbol="*" position="right" xlink:label="note-0157-02" xlink:href="note-0157-02a" xml:space="preserve">39.21.1.</note> </div> <p> <s xml:id="echoid-s4056" xml:space="preserve">Si nunc concipiamus curvam quamcunque dividi, lineis ad centrum viri-<lb/>um ductis, in triangula minima æqualia, horum baſes, temporibus æqua-<lb/>libus a corpore quod in curva vi centrali retinetur, percurruntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4057" xml:space="preserve">ſunt ideo <anchor type="note" xlink:label="note-0157-03a" xlink:href="note-0157-03"/> <anchor type="note" xlink:label="note-0157-04a" xlink:href="note-0157-04"/> corporis velocitates in variis curvæ punctis, ut baſes hæ <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt inversè ut <anchor type="note" xlink:label="note-0157-05a" xlink:href="note-0157-05"/> perpendiculares à centro virium in baſes continuatas <anchor type="note" xlink:href="" symbol="*"/>, id eſt in tangentes adcur- <anchor type="note" xlink:label="note-0157-06a" xlink:href="note-0157-06"/> vam in punctis de quibus agitur.</s> <s xml:id="echoid-s4058" xml:space="preserve"/> </p> <div xml:id="echoid-div603" type="float" level="2" n="6"> <note position="right" xlink:label="note-0157-03" xlink:href="note-0157-03a" xml:space="preserve">398.</note> <note symbol="*" position="right" xlink:label="note-0157-04" xlink:href="note-0157-04a" xml:space="preserve">394.</note> <note symbol="*" position="right" xlink:label="note-0157-05" xlink:href="note-0157-05a" xml:space="preserve">94.</note> <note symbol="*" position="right" xlink:label="note-0157-06" xlink:href="note-0157-06a" xml:space="preserve">1@. El. VI. <lb/>38. El 1.</note> </div> <p> <s xml:id="echoid-s4059" xml:space="preserve">Maxime generalia ſunt huc uſque in ſcholio hoc demonſtrata, quæ nunc <lb/> <anchor type="note" xlink:label="note-0157-07a" xlink:href="note-0157-07"/> addam tantum obtinent, ſi vis in hoc cum gravitate congruat, ut agat in cor-<lb/>poramota ut in quieſcentia, corpora autem ponimus æqualia; </s> <s xml:id="echoid-s4060" xml:space="preserve">ſi verò vis & </s> <s xml:id="echoid-s4061" xml:space="preserve">in <lb/>hoc cum gravitate congruat, ut eodem modo agat in ſingulas materiæ parti-<lb/>culas, non intereſt utrum corpora ſint æqualia nec ne.</s> <s xml:id="echoid-s4062" xml:space="preserve"/> </p> <div xml:id="echoid-div604" type="float" level="2" n="7"> <note position="right" xlink:label="note-0157-07" xlink:href="note-0157-07a" xml:space="preserve">399.</note> </div> <p> <s xml:id="echoid-s4063" xml:space="preserve">Lineæ infinitæ exiguæ, viribus æqualibus, a@cedendo adcentrum, percurſæ ſunt, <lb/> <anchor type="note" xlink:label="note-0157-08a" xlink:href="note-0157-08"/> ut quadrata temporum quibus percurruntur. </s> <s xml:id="echoid-s4064" xml:space="preserve">Vis enim pro uniformi in ſpatio <lb/>infinitè exiguo haberi poteſt, & </s> <s xml:id="echoid-s4065" xml:space="preserve">quæ de corporibus cadentibus demonſtrata <lb/>ſunt <anchor type="note" xlink:href="" symbol="*"/>, hìc referri poſſunt.</s> <s xml:id="echoid-s4066" xml:space="preserve"/> </p> <div xml:id="echoid-div605" type="float" level="2" n="8"> <note position="right" xlink:label="note-0157-08" xlink:href="note-0157-08a" xml:space="preserve">400.</note> </div> <note symbol="*" position="right" xml:space="preserve">235.</note> <p style="it"> <s xml:id="echoid-s4067" xml:space="preserve">Si vires differant, ſed tempora fuerint æqualia, ſpatia percurſa ſunt ut vi-<lb/> <anchor type="note" xlink:label="note-0157-10a" xlink:href="note-0157-10"/> res <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4068" xml:space="preserve"/> </p> <div xml:id="echoid-div606" type="float" level="2" n="9"> <note position="right" xlink:label="note-0157-10" xlink:href="note-0157-10a" xml:space="preserve">401.</note> </div> <note symbol="*" position="right" xml:space="preserve">107</note> <p> <s xml:id="echoid-s4069" xml:space="preserve">Ergo ſpatia infinite exigua, viribus centralibus percurſa, ſunt, ut viresipſæ, & </s> <s xml:id="echoid-s4070" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0157-12a" xlink:href="note-0157-12"/> ut quadrata temporum; </s> <s xml:id="echoid-s4071" xml:space="preserve">in ratione nempe compoſita ex hiſce ambabus ratio-<lb/>nibus.</s> <s xml:id="echoid-s4072" xml:space="preserve"/> </p> <div xml:id="echoid-div607" type="float" level="2" n="10"> <note position="right" xlink:label="note-0157-12" xlink:href="note-0157-12a" xml:space="preserve">402.</note> </div> <p> <s xml:id="echoid-s4073" xml:space="preserve">Ex hiſce deducimus, corpus, quod vi centrali in curva retinetur, in ſingu-<lb/> <anchor type="note" xlink:label="note-0157-13a" xlink:href="note-0157-13"/> lis momentis infinitè exiguis moveri juxta leges explicatas <anchor type="note" xlink:href="" symbol="*"/> de corporibus pro- <anchor type="note" xlink:label="note-0157-14a" xlink:href="note-0157-14"/> jectis. </s> <s xml:id="echoid-s4074" xml:space="preserve">Nam, licet corpus tendat ad centrum, ſi ſpatium percurſum ſit in-<lb/>finitè exiguum reſpectu diſtantiæ a centro, lineæ ad centrum ductæ pro pa-<lb/>rallelis haberi poſſunt.</s> <s xml:id="echoid-s4075" xml:space="preserve"/> </p> <div xml:id="echoid-div608" type="float" level="2" n="11"> <note position="right" xlink:label="note-0157-13" xlink:href="note-0157-13a" xml:space="preserve">403.</note> <note symbol="*" position="right" xlink:label="note-0157-14" xlink:href="note-0157-14a" xml:space="preserve">327. 331.</note> </div> <p> <s xml:id="echoid-s4076" xml:space="preserve">Sit Curva AFGE in qua corpus movetur; </s> <s xml:id="echoid-s4077" xml:space="preserve">C centrum virium; </s> <s xml:id="echoid-s4078" xml:space="preserve">AD <lb/> <anchor type="note" xlink:label="note-0157-15a" xlink:href="note-0157-15"/> tangens ad curvam in puncto A; </s> <s xml:id="echoid-s4079" xml:space="preserve">ponamus AD infinitè exiguam, lineas-<lb/>que BF & </s> <s xml:id="echoid-s4080" xml:space="preserve">DG ad AC dari parallelas, erunt hæ ut quadrata linearum <lb/>AB, AD <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt ut tempora quibus AF, AG percurruntur.</s> <s xml:id="echoid-s4081" xml:space="preserve"/> </p> <div xml:id="echoid-div609" type="float" level="2" n="12"> <note position="right" xlink:label="note-0157-15" xlink:href="note-0157-15a" xml:space="preserve">TAB. XV. <lb/>fig. 3.</note> </div> <note symbol="*" position="right" xml:space="preserve">331. 327.</note> </div> <div xml:id="echoid-div611" type="section" level="1" n="182"> <head xml:id="echoid-head255" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head256" style="it" xml:space="preserve">De Motu in Circulo.</head> <p> <s xml:id="echoid-s4082" xml:space="preserve">Vis quæcunque qua corpus in circulo retinetur, ſi ad circuli centrum dirigatur, <lb/> <anchor type="note" xlink:label="note-0157-17a" xlink:href="note-0157-17"/> agit ſemper perpendiculariter ad motus directionem; </s> <s xml:id="echoid-s4083" xml:space="preserve">tangens enim ad ra-<lb/>dium perpendicularis eſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4084" xml:space="preserve">Idcirco actio hujus vis nunquam cum motu <anchor type="note" xlink:label="note-0157-18a" xlink:href="note-0157-18"/> corporis conſpiràt, aut contrarie agit, quare agit eodem modo ac in corpus qui-<lb/>eſcens ageret; </s> <s xml:id="echoid-s4085" xml:space="preserve">hac de cauſa non intereſt utrum vis in omni caſu eodem modo <lb/>poſſit agere in corpus motum ac in quieſcens ut gravitas, an non.</s> <s xml:id="echoid-s4086" xml:space="preserve"/> </p> <div xml:id="echoid-div611" type="float" level="2" n="1"> <note position="right" xlink:label="note-0157-17" xlink:href="note-0157-17a" xml:space="preserve">404.</note> <note symbol="*" position="right" xlink:label="note-0157-18" xlink:href="note-0157-18a" xml:space="preserve">18. El. 114.</note> </div> <p> <s xml:id="echoid-s4087" xml:space="preserve">Moveatur corpus in circulo cujus Diameter eſt GL; </s> <s xml:id="echoid-s4088" xml:space="preserve">C centrum circuli <lb/> <anchor type="note" xlink:label="note-0157-19a" xlink:href="note-0157-19"/> & </s> <s xml:id="echoid-s4089" xml:space="preserve">virium. </s> <s xml:id="echoid-s4090" xml:space="preserve">Detur corpus æquale per AD projectum, velocitate qua cor-<lb/> <anchor type="note" xlink:label="note-0157-20a" xlink:href="note-0157-20"/> pus in circulo movetur.</s> <s xml:id="echoid-s4091" xml:space="preserve"/> </p> <div xml:id="echoid-div612" type="float" level="2" n="2"> <note position="right" xlink:label="note-0157-19" xlink:href="note-0157-19a" xml:space="preserve">405.</note> <note position="right" xlink:label="note-0157-20" xlink:href="note-0157-20a" xml:space="preserve">TAB XV. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s4092" xml:space="preserve">Corpora hæc æqualibus temporibus percurrunt lineas æquales, infinitè <pb o="100" file="0158" n="172" rhead="PHYSICES ELEMENTA"/> exiguas, AB, GH; </s> <s xml:id="echoid-s4093" xml:space="preserve">æqualibus etiam temporibus percurrunt lineolas BE, <lb/>HI, primum pondere ſuo, ſecundum vi centrali, poſitâ BE verticali, <lb/>& </s> <s xml:id="echoid-s4094" xml:space="preserve">HI ad GC parallelâ; </s> <s xml:id="echoid-s4095" xml:space="preserve">quæ lineolæ ſunt inter ſe, ut corporis pondus ad vim <lb/>centralem quæ corpus in circulo retinet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4096" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">107.</note> <p> <s xml:id="echoid-s4097" xml:space="preserve">Sit DF altitudo à qua cadendo corpus acquirit velocitatem cum qua pro-<lb/>jectio fit, corpus ſpatium hoc cadendo percurrit dum motu uniformi proje-<lb/> <anchor type="note" xlink:label="note-0158-02a" xlink:href="note-0158-02"/> ctitio lineam duplam percurrit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4098" xml:space="preserve">ſi ergo DF ſit verticalis & </s> <s xml:id="echoid-s4099" xml:space="preserve">AD dupla i- <anchor type="note" xlink:label="note-0158-03a" xlink:href="note-0158-03"/> pſius DF corpus projectum per F tranſibit <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s4100" xml:space="preserve">Idcirco AB<emph style="super">q</emph> aut GH<emph style="super">q</emph>, ad <anchor type="note" xlink:label="note-0158-04a" xlink:href="note-0158-04"/> AD<emph style="super">q</emph>, aut 4 x DF<emph style="super">q</emph>, ut BE ad DF<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4101" xml:space="preserve"/> </p> <div xml:id="echoid-div613" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">257.</note> <note symbol="*" position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">327.</note> <note symbol="*" position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">95. 255.</note> </div> <p> <s xml:id="echoid-s4102" xml:space="preserve">In circulo ducta I i parallela GH, id eſt perpendiculari ad diametrum, <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0158-05a" xlink:href="note-0158-05"/> erunt Gi aut <emph style="sc">Hi</emph>, GI aut GH, & </s> <s xml:id="echoid-s4103" xml:space="preserve">GL, in continuâ proportione <anchor type="note" xlink:href="" symbol="*"/>, quare <anchor type="note" xlink:label="note-0158-06a" xlink:href="note-0158-06"/> GH<emph style="super">q</emph> = HI x GL.</s> <s xml:id="echoid-s4104" xml:space="preserve"/> </p> <div xml:id="echoid-div614" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0158-05" xlink:href="note-0158-05a" xml:space="preserve">18. El 111.</note> <note symbol="*" position="left" xlink:label="note-0158-06" xlink:href="note-0158-06a" xml:space="preserve">31. El 111, <lb/>@. 4. El VI.</note> </div> <p> <s xml:id="echoid-s4105" xml:space="preserve">Memorata proportio mutatur ergo in hanc <lb/>HI x GL, 4 x DF<emph style="super">q</emph>:</s> <s xml:id="echoid-s4106" xml:space="preserve">: BE, DF:</s> <s xml:id="echoid-s4107" xml:space="preserve">: BE x GL, DF x GL. </s> <s xml:id="echoid-s4108" xml:space="preserve">Alternando <lb/>HI x GL, BE x GL:</s> <s xml:id="echoid-s4109" xml:space="preserve">: 4 x DF<emph style="super">q</emph>, DF x GL. </s> <s xml:id="echoid-s4110" xml:space="preserve">Unde deducimus <lb/>HI, BE:</s> <s xml:id="echoid-s4111" xml:space="preserve">: DF, {1/4} GL.</s> <s xml:id="echoid-s4112" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4113" xml:space="preserve">Id eſt vis qua corpus in circulo retinetur eſt ad corporis pondus, ut altitudo à <lb/> <anchor type="note" xlink:label="note-0158-07a" xlink:href="note-0158-07"/> qua corpus cadendo acquirit velocitatem cum quæ projectio fit ad quartam partem <lb/>diametri.</s> <s xml:id="echoid-s4114" xml:space="preserve"/> </p> <div xml:id="echoid-div615" type="float" level="2" n="5"> <note position="left" xlink:label="note-0158-07" xlink:href="note-0158-07a" xml:space="preserve">406.</note> </div> <p> <s xml:id="echoid-s4115" xml:space="preserve">Si idem corpus in eodem circulo aliâ velocitate feratur, conſequentia propor-<lb/> <anchor type="note" xlink:label="note-0158-08a" xlink:href="note-0158-08"/> tionis manent; </s> <s xml:id="echoid-s4116" xml:space="preserve">mutantur ideo antecedentia in eadem ratione, id eſt viscen-<lb/>tralis variat, ut altitudo à qua cadendo corpus acquirit velocitatem cum qua <lb/>movetur, quæ altitudo ſequitur proportionem quadrati velociatatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4117" xml:space="preserve"/> </p> <div xml:id="echoid-div616" type="float" level="2" n="6"> <note position="left" xlink:label="note-0158-08" xlink:href="note-0158-08a" xml:space="preserve">407.</note> </div> <note symbol="*" position="left" xml:space="preserve">255.</note> <p> <s xml:id="echoid-s4118" xml:space="preserve">Quamdiu autem de eodem circulo agitur tempus periodicum eo minus eſt, <lb/> <anchor type="note" xlink:label="note-0158-10a" xlink:href="note-0158-10"/> quo velocitas eſt major, & </s> <s xml:id="echoid-s4119" xml:space="preserve">vice verſa, eſtque tempus hoc inverſè ut velo-<lb/>citas, unde patet demonſtratio n. </s> <s xml:id="echoid-s4120" xml:space="preserve">371. </s> <s xml:id="echoid-s4121" xml:space="preserve">vires cæteris paribus eſſe inverſè ut <lb/>quadrata temporum periodicorum.</s> <s xml:id="echoid-s4122" xml:space="preserve"/> </p> <div xml:id="echoid-div617" type="float" level="2" n="7"> <note position="left" xlink:label="note-0158-10" xlink:href="note-0158-10a" xml:space="preserve">408.</note> </div> <p> <s xml:id="echoid-s4123" xml:space="preserve">In n. </s> <s xml:id="echoid-s4124" xml:space="preserve">363. </s> <s xml:id="echoid-s4125" xml:space="preserve">diximus, vires centrales, poſitis corporibus, ut & </s> <s xml:id="echoid-s4126" xml:space="preserve">temporibus <lb/> <anchor type="note" xlink:label="note-0158-11a" xlink:href="note-0158-11"/> periodicis æqualibus, eſſe ut diſtantias a centro, quod ut demonſtremus po-<lb/> <anchor type="note" xlink:label="note-0158-12a" xlink:href="note-0158-12"/> nimus duo corpora æqualia, circulos concentricos BIL, AFM æquali-<lb/>bus temporibus deſcribere; </s> <s xml:id="echoid-s4127" xml:space="preserve">momentis minimis æqualibus arcus ſimiles BI, <lb/>AF percurrunt. </s> <s xml:id="echoid-s4128" xml:space="preserve">Corpora autem momentis iiſdem per tangentes BH, AD, <lb/>moverentur, ſi nulla daretur vis centralis; </s> <s xml:id="echoid-s4129" xml:space="preserve">nam propter arcus exiguos ſunt <lb/>hi tangentibus æquales; </s> <s xml:id="echoid-s4130" xml:space="preserve">Corpora ergo, æqualibus momentis, viribus centra-<lb/>libus, transferuntur per lineas HI, DF, in quorum ratione ſunt vires cen-<lb/>trales; </s> <s xml:id="echoid-s4131" xml:space="preserve">has autem lineas eſſe ut diſtantiæ a centro BC, AC, facile pa-<lb/>tet.</s> <s xml:id="echoid-s4132" xml:space="preserve"/> </p> <div xml:id="echoid-div618" type="float" level="2" n="8"> <note position="left" xlink:label="note-0158-11" xlink:href="note-0158-11a" xml:space="preserve">409.</note> <note position="left" xlink:label="note-0158-12" xlink:href="note-0158-12a" xml:space="preserve">TAB. XV. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s4133" xml:space="preserve">Supereſt circa motum in circulo ut demonſſremus propoſitionem n. <lb/></s> <s xml:id="echoid-s4134" xml:space="preserve"> <anchor type="note" xlink:label="note-0158-13a" xlink:href="note-0158-13"/> ſint diſtantiæ à centro D & </s> <s xml:id="echoid-s4135" xml:space="preserve">d; </s> <s xml:id="echoid-s4136" xml:space="preserve">tempora periodica T, t, vires centrales V, v; <lb/></s> <s xml:id="echoid-s4137" xml:space="preserve">ponamus T<emph style="super">q</emph>, t<emph style="super">q</emph>:</s> <s xml:id="echoid-s4138" xml:space="preserve">: D<emph style="super">c</emph> d<emph style="super">c</emph>; </s> <s xml:id="echoid-s4139" xml:space="preserve">erg<emph style="super">o</emph> {D/T<emph style="super">q</emph>}, {d/t<emph style="super">q</emph>}:</s> <s xml:id="echoid-s4140" xml:space="preserve">: {D/D<emph style="super">c</emph>}, {d/d<emph style="super">c</emph>}:</s> <s xml:id="echoid-s4141" xml:space="preserve">: {1/D<emph style="super">q</emph>}, {1/d<emph style="super">q</emph>}. </s> <s xml:id="echoid-s4142" xml:space="preserve">Sed V, v:</s> <s xml:id="echoid-s4143" xml:space="preserve">: {D/T<emph style="super">q</emph>}, {d<anchor type="note" xlink:href="" symbol="*"/>/t<emph style="super">q</emph>};</s> <s xml:id="echoid-s4144" xml:space="preserve"> ergo V, v:</s> <s xml:id="echoid-s4145" xml:space="preserve">: {1/D<emph style="super">q</emph>}, {1/d<emph style="super">q</emph>}. </s> <s xml:id="echoid-s4146" xml:space="preserve">Q. </s> <s xml:id="echoid-s4147" xml:space="preserve">D, E.</s> <s xml:id="echoid-s4148" xml:space="preserve"/> </p> <div xml:id="echoid-div619" type="float" level="2" n="9"> <note position="right" xlink:label="note-0158-13" xlink:href="note-0158-13a" xml:space="preserve">376.</note> </div> <pb o="101" file="0159" n="173" rhead="MATHEMATICA. LIB. I. CAP XXI"/> </div> <div xml:id="echoid-div621" type="section" level="1" n="183"> <head xml:id="echoid-head257" xml:space="preserve">SHOLIUM 3.</head> <head xml:id="echoid-head258" style="it" xml:space="preserve">De Motu in Ellipſi.</head> <p> <s xml:id="echoid-s4149" xml:space="preserve">In hoc, & </s> <s xml:id="echoid-s4150" xml:space="preserve">ſequentibus ſcholiis, ponimus agi de vi quæ in corpora mota ut <lb/>in quieſcentia agit.</s> <s xml:id="echoid-s4151" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4152" xml:space="preserve">Sit Ellipſis DAE; </s> <s xml:id="echoid-s4153" xml:space="preserve">centrum C; </s> <s xml:id="echoid-s4154" xml:space="preserve">moveatur corpus in Ellipſi, in quare-<lb/>tinetur vi, quæ ad centrum dirigitur; </s> <s xml:id="echoid-s4155" xml:space="preserve">vis hæc determinanda eſt.</s> <s xml:id="echoid-s4156" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">410.</note> <p> <s xml:id="echoid-s4157" xml:space="preserve">Detur Corpus in A, & </s> <s xml:id="echoid-s4158" xml:space="preserve">ſit AI tangens ad Ellipſin; </s> <s xml:id="echoid-s4159" xml:space="preserve">AB diameter; </s> <s xml:id="echoid-s4160" xml:space="preserve">ED <lb/> <anchor type="note" xlink:label="note-0159-02a" xlink:href="note-0159-02"/> diameter ipſi conjugata tangenti parallela <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4161" xml:space="preserve">AL arcus momento exiguo <anchor type="note" xlink:label="note-0159-03a" xlink:href="note-0159-03"/> conſtanti deſcriptus; </s> <s xml:id="echoid-s4162" xml:space="preserve">IL, parallela AC, ſpatium eodem momento vi cen-<lb/>trali percurſum, quod ſpatium ipſius vis centralis rationem ſequitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4163" xml:space="preserve"/> </p> <div xml:id="echoid-div621" type="float" level="2" n="1"> <note position="right" xlink:label="note-0159-02" xlink:href="note-0159-02a" xml:space="preserve">TAB. XV. <lb/>fig. 6.</note> <note symbol="*" position="right" xlink:label="note-0159-03" xlink:href="note-0159-03a" xml:space="preserve">La Hire <lb/>ſect. con. <lb/>Lib. 2. <lb/>pro. 10.</note> </div> <note symbol="*" position="right" xml:space="preserve">401.</note> <p> <s xml:id="echoid-s4164" xml:space="preserve">Ducantur LG parallela IA, & </s> <s xml:id="echoid-s4165" xml:space="preserve">LH ad AC perpendicularis; </s> <s xml:id="echoid-s4166" xml:space="preserve">ut & </s> <s xml:id="echoid-s4167" xml:space="preserve">AF <lb/>ad ED normalis; </s> <s xml:id="echoid-s4168" xml:space="preserve">jungantur etiam C & </s> <s xml:id="echoid-s4169" xml:space="preserve">L.</s> <s xml:id="echoid-s4170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4171" xml:space="preserve">Triangula rectangula LHG, AFC, ſunt ſimilia propter angulos æqua-<lb/>les LGH, ACF <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4172" xml:space="preserve">Ergo LH, LG :</s> <s xml:id="echoid-s4173" xml:space="preserve">: AF, AC; </s> <s xml:id="echoid-s4174" xml:space="preserve">& </s> <s xml:id="echoid-s4175" xml:space="preserve">LH x AC = LG x AF. </s> <s xml:id="echoid-s4176" xml:space="preserve"> <lb/> <anchor type="note" xlink:label="note-0159-05a" xlink:href="note-0159-05"/> </s> </p> <div xml:id="echoid-div622" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0159-05" xlink:href="note-0159-05a" xml:space="preserve">29. El. 1</note> </div> <p> <s xml:id="echoid-s4177" xml:space="preserve">Conſtans autem eſt quantitas LH x AC; </s> <s xml:id="echoid-s4178" xml:space="preserve">eſt enim duplum areæ triangu-<lb/>li ALC <anchor type="note" xlink:href="" symbol="*"/>, quæ momento conſtanti quo AL deſcribitur proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4179" xml:space="preserve"> <anchor type="note" xlink:label="note-0159-06a" xlink:href="note-0159-06"/> </s> </p> <div xml:id="echoid-div623" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0159-06" xlink:href="note-0159-06a" xml:space="preserve">34. El 1.</note> </div> <p> <s xml:id="echoid-s4180" xml:space="preserve">In Ellipſi etiam eſt conſtans quantitas ED x AF <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4181" xml:space="preserve">Ergo ED x AF, <anchor type="note" xlink:label="note-0159-07a" xlink:href="note-0159-07"/> eſt ad LH x AC aut LG x AF, id eſt, ED ad LG, ſemper in eadem <lb/> <anchor type="note" xlink:label="note-0159-08a" xlink:href="note-0159-08"/> ratione ubicunque punctum ut A in Ellipſi ſumatur; </s> <s xml:id="echoid-s4182" xml:space="preserve">conſtans id circo etiam <lb/>eſt ratio inter ED<emph style="super">q</emph> & </s> <s xml:id="echoid-s4183" xml:space="preserve">LG<emph style="super">q</emph>. </s> <s xml:id="echoid-s4184" xml:space="preserve">In Ellipſi autem ED<emph style="super">q</emph>, LG<emph style="super">q</emph>:</s> <s xml:id="echoid-s4185" xml:space="preserve">: AB<emph style="super">q</emph>, AG x <lb/>GB <anchor type="note" xlink:href="" symbol="*"/>, aut LI x AB, propter æquales AG & </s> <s xml:id="echoid-s4186" xml:space="preserve">LI, & </s> <s xml:id="echoid-s4187" xml:space="preserve">differentiam infini- <anchor type="note" xlink:label="note-0159-09a" xlink:href="note-0159-09"/> tè exiguam inter GB & </s> <s xml:id="echoid-s4188" xml:space="preserve">AB; </s> <s xml:id="echoid-s4189" xml:space="preserve">conſtans idcirco etiam eſt ratio inter AB<emph style="super">q</emph> & </s> <s xml:id="echoid-s4190" xml:space="preserve"><lb/>LI x AB, id eſt, inter AB & </s> <s xml:id="echoid-s4191" xml:space="preserve">LI, augetur ideò LI, id eſt, vis centra-<lb/>lis in eadem ratione in qua augetur & </s> <s xml:id="echoid-s4192" xml:space="preserve">minuitur AB, aut ipſius dimidium <lb/>AC, quod æquale eſt diſtantiæ corporis à centro; </s> <s xml:id="echoid-s4193" xml:space="preserve">ut notavimus in n. </s> <s xml:id="echoid-s4194" xml:space="preserve">388.</s> <s xml:id="echoid-s4195" xml:space="preserve"/> </p> <div xml:id="echoid-div624" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0159-07" xlink:href="note-0159-07a" xml:space="preserve">354. 396.</note> <note symbol="*" position="right" xlink:label="note-0159-08" xlink:href="note-0159-08a" xml:space="preserve">La Hire <lb/>ſect. con. <lb/>lib. 5. <lb/>prop. 21.</note> <note symbol="*" position="right" xlink:label="note-0159-09" xlink:href="note-0159-09a" xml:space="preserve">ibid. <lb/>Lib. 3. <lb/>prop 3.</note> </div> <p> <s xml:id="echoid-s4196" xml:space="preserve">Si vero dum corpus in Ellipſi movetur vis ad focum dirigatur, hæc rece-<lb/> <anchor type="note" xlink:label="note-0159-10a" xlink:href="note-0159-10"/> dendo a centro virium decreſcit in ratione inverſa quadrati diſtantiæ, ut <lb/>habetur in n. </s> <s xml:id="echoid-s4197" xml:space="preserve">381. </s> <s xml:id="echoid-s4198" xml:space="preserve">cujus propoſitionis hîc dabimus demonſtrationem.</s> <s xml:id="echoid-s4199" xml:space="preserve"/> </p> <div xml:id="echoid-div625" type="float" level="2" n="5"> <note position="right" xlink:label="note-0159-10" xlink:href="note-0159-10a" xml:space="preserve">411.</note> </div> <p> <s xml:id="echoid-s4200" xml:space="preserve">Sit DAB ſemi Ellipſis; </s> <s xml:id="echoid-s4201" xml:space="preserve">BD axis; </s> <s xml:id="echoid-s4202" xml:space="preserve">C centrum; </s> <s xml:id="echoid-s4203" xml:space="preserve">F focus ad quem vis diſigi-<lb/> <anchor type="note" xlink:label="note-0159-11a" xlink:href="note-0159-11"/> tur; </s> <s xml:id="echoid-s4204" xml:space="preserve">AI tangens ad Ellipſin in puncto quocunque A; </s> <s xml:id="echoid-s4205" xml:space="preserve">AL arcus infinitè <lb/>exiguus.</s> <s xml:id="echoid-s4206" xml:space="preserve"/> </p> <div xml:id="echoid-div626" type="float" level="2" n="6"> <note position="right" xlink:label="note-0159-11" xlink:href="note-0159-11a" xml:space="preserve">TAB XV <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s4207" xml:space="preserve">Ductis AC, AF, ſint LG & </s> <s xml:id="echoid-s4208" xml:space="preserve">CE parallelæ tangenti AI; </s> <s xml:id="echoid-s4209" xml:space="preserve">LI paral-<lb/>lela AC; </s> <s xml:id="echoid-s4210" xml:space="preserve">& </s> <s xml:id="echoid-s4211" xml:space="preserve">L i æqui diſtans AF; </s> <s xml:id="echoid-s4212" xml:space="preserve">erunt æquales LI & </s> <s xml:id="echoid-s4213" xml:space="preserve">AG, ut & </s> <s xml:id="echoid-s4214" xml:space="preserve">L i <lb/>& </s> <s xml:id="echoid-s4215" xml:space="preserve">A g <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4216" xml:space="preserve">AE autem erit æqualis CD ſemi axi majori; </s> <s xml:id="echoid-s4217" xml:space="preserve">ductis enim A f ad <anchor type="note" xlink:label="note-0159-12a" xlink:href="note-0159-12"/> focum alium & </s> <s xml:id="echoid-s4218" xml:space="preserve">f M etiam ad AI parallelam, erunt anguli AMf, AfM <lb/>æquales <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s4219" xml:space="preserve">latera AM, Af, æqualia <anchor type="note" xlink:href="" symbol="*"/>, ſunt etiam æqualia EM, EF <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0159-13a" xlink:href="note-0159-13"/> <anchor type="note" xlink:label="note-0159-14a" xlink:href="note-0159-14"/> <anchor type="note" xlink:label="note-0159-15a" xlink:href="note-0159-15"/> propter æquales CF, Cf<anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s4220" xml:space="preserve">Ergo EM + M Aid eſt EA valet FE + Af, &</s> <s xml:id="echoid-s4221" xml:space="preserve"> <anchor type="note" xlink:label="note-0159-16a" xlink:href="note-0159-16"/> eſt EA dimidium ſummæ linearum FA, Af, quæ ſimul ſumtæ æquales <lb/>ſunt axi BD <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4222" xml:space="preserve"/> </p> <div xml:id="echoid-div627" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0159-12" xlink:href="note-0159-12a" xml:space="preserve">34. El 1.</note> <note symbol="*" position="right" xlink:label="note-0159-13" xlink:href="note-0159-13a" xml:space="preserve">La Hire <lb/>ſect. con. <lb/>Lib. 8. <lb/>prop. 8.</note> <note symbol="*" position="right" xlink:label="note-0159-14" xlink:href="note-0159-14a" xml:space="preserve">5. El. 1.</note> <note symbol="*" position="right" xlink:label="note-0159-15" xlink:href="note-0159-15a" xml:space="preserve">2 El. VI.</note> <note symbol="*" position="right" xlink:label="note-0159-16" xlink:href="note-0159-16a" xml:space="preserve">379.</note> </div> <note symbol="*" position="right" xml:space="preserve">379.</note> <p> <s xml:id="echoid-s4223" xml:space="preserve">Ducantur ulterius LH ad AC normalis, & </s> <s xml:id="echoid-s4224" xml:space="preserve">Lb cum AF angulos effi-<lb/>ciens rectos; </s> <s xml:id="echoid-s4225" xml:space="preserve">junganturque puncta H, b.</s> <s xml:id="echoid-s4226" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4227" xml:space="preserve">Propter angulos rectos ALb, LHA, puncta H, b, ſunt in circumfe-<lb/>rentia ſemi circuli cujus diameter A eſt L <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4228" xml:space="preserve">idcirco anguli bLH, bAH, <anchor type="note" xlink:label="note-0159-18a" xlink:href="note-0159-18"/> ſunt in eodem ſegmento & </s> <s xml:id="echoid-s4229" xml:space="preserve">ideò æquales <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s4230" xml:space="preserve">ſunt etiam in eodem ſegmento, <anchor type="note" xlink:label="note-0159-19a" xlink:href="note-0159-19"/> & </s> <s xml:id="echoid-s4231" xml:space="preserve">æquales anguli LHb & </s> <s xml:id="echoid-s4232" xml:space="preserve">LAb; </s> <s xml:id="echoid-s4233" xml:space="preserve">hic autem quia AL eſt inſinitè exigua <pb o="102" file="0160" n="174" rhead="PHYSICES ELEMENTA"/> cum angulo IAb coincidit & </s> <s xml:id="echoid-s4234" xml:space="preserve">angulo AEC æqualis eſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4235" xml:space="preserve">quare ſimilia <anchor type="note" xlink:label="note-0160-01a" xlink:href="note-0160-01"/> ſunt triangula LbH, AEC, & </s> <s xml:id="echoid-s4236" xml:space="preserve"># <lb/># Lb, LH:</s> <s xml:id="echoid-s4237" xml:space="preserve">: AC, AE aut CD.</s> <s xml:id="echoid-s4238" xml:space="preserve"/> </p> <div xml:id="echoid-div628" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0159-18" xlink:href="note-0159-18a" xml:space="preserve">31 El. 117.</note> <note symbol="*" position="right" xlink:label="note-0159-19" xlink:href="note-0159-19a" xml:space="preserve">21. El. 111.</note> <note symbol="*" position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">29 El 1.</note> </div> <p> <s xml:id="echoid-s4239" xml:space="preserve">Etiam propter triangula ſimilia AgG, AEC, AG eſt ad Ag, aut LI, <lb/>ad Li, ut AC ad AE, aut CD.</s> <s xml:id="echoid-s4240" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4241" xml:space="preserve">Hiſce poſitis concipiamus duo corpora Ellipſin hanc percurrentia, eodem <lb/>tempore, quorum unum retineatur vi, quæ ad centrum Ellipſeos C dirigitur, <lb/>alterum vi ad focorum alterum F tendente.</s> <s xml:id="echoid-s4242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4243" xml:space="preserve">Dum corpora ambo arcum exiguum percurrunt AL, primum vi centrali <lb/>movetur per IL, ſecundum vi centrali percurrit iL, tempora autem quibus <lb/>corpora has lineolas percurrunt, ſuntinter ſe ut areæ LAC, LAF <anchor type="note" xlink:href="" symbol="*"/>, ponimus <anchor type="note" xlink:label="note-0160-02a" xlink:href="note-0160-02"/> enim integram Ellipſin æqualibus temporibus a ſingulis corporibus percurri; <lb/></s> <s xml:id="echoid-s4244" xml:space="preserve">ideoque in utroque caſu idem tempus periodicum per integram aream repræ-<lb/>ſentari. </s> <s xml:id="echoid-s4245" xml:space="preserve">Areæ vero illæ ſunt inter ſe ut harum dupla AC x LH, AF x <lb/>Lb; </s> <s xml:id="echoid-s4246" xml:space="preserve">hæc autem producta quia LH, Lb:</s> <s xml:id="echoid-s4247" xml:space="preserve">: CD, AC, ſunt ut AC x CD ad <lb/>AF x AC, id eſt ut CD, ad AF.</s> <s xml:id="echoid-s4248" xml:space="preserve"/> </p> <div xml:id="echoid-div629" type="float" level="2" n="9"> <note symbol="*" position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">354. 396.</note> </div> <p> <s xml:id="echoid-s4249" xml:space="preserve">Spatia IL, iL, viribus centralibus percurſa, quæ ut vidimus ſunt ad AC ad <lb/>CD, ſunt etiam in ratione compoſita virium, & </s> <s xml:id="echoid-s4250" xml:space="preserve">quadratorum temporum <anchor type="note" xlink:href="" symbol="*"/>, aut li- <anchor type="note" xlink:label="note-0160-03a" xlink:href="note-0160-03"/> nearum CD, AF.</s> <s xml:id="echoid-s4251" xml:space="preserve"/> </p> <div xml:id="echoid-div630" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0160-03" xlink:href="note-0160-03a" xml:space="preserve">402.</note> </div> <p> <s xml:id="echoid-s4252" xml:space="preserve">Vis per AC huic lineæ proportionalis eſt, ut demonſtravimus <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s4253" xml:space="preserve">hac <anchor type="note" xlink:label="note-0160-04a" xlink:href="note-0160-04"/> ipſâ lineâ deſignari poteſt; </s> <s xml:id="echoid-s4254" xml:space="preserve">vim per AF dicimus V: </s> <s xml:id="echoid-s4255" xml:space="preserve">ergo <lb/>AC, CD :</s> <s xml:id="echoid-s4256" xml:space="preserve">: AC x CD<emph style="super">q</emph>, V x AF<emph style="super">q</emph> <lb/>Unde deducimus V = {CD<emph style="super">c</emph>/AF<emph style="super">q</emph>}; </s> <s xml:id="echoid-s4257" xml:space="preserve">patet igitur propter conſtantem CD<emph style="super">c</emph>, mutato <lb/>puncto A, vim V mutari in ratione inverſa quadrati diſtantiæ AF. </s> <s xml:id="echoid-s4258" xml:space="preserve">Q. </s> <s xml:id="echoid-s4259" xml:space="preserve">D. </s> <s xml:id="echoid-s4260" xml:space="preserve">E.</s> <s xml:id="echoid-s4261" xml:space="preserve"/> </p> <div xml:id="echoid-div631" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0160-04" xlink:href="note-0160-04a" xml:space="preserve">410.</note> </div> <note position="left" xml:space="preserve">412.</note> <p> <s xml:id="echoid-s4262" xml:space="preserve">Circa motum in Ellipſi ulterius notavimus <anchor type="note" xlink:href="" symbol="*"/>, quod nunc demonſtrabimus, ſi <anchor type="note" xlink:label="note-0160-06a" xlink:href="note-0160-06"/> vis decreſcat in ratione inverſa quadrati diſtantiæ, circulum cujus diameter <lb/>axi majori Ellipſeos æqualis eſt, eo tempore a corpore percurri in quo hoc <lb/>Ellpiſim ipſam deſcribere poſſet.</s> <s xml:id="echoid-s4263" xml:space="preserve"/> </p> <div xml:id="echoid-div632" type="float" level="2" n="12"> <note position="left" xlink:label="note-0160-06" xlink:href="note-0160-06a" xml:space="preserve">382.</note> </div> <p> <s xml:id="echoid-s4264" xml:space="preserve">Sit ſemi Ellipſis BAD; </s> <s xml:id="echoid-s4265" xml:space="preserve">axis major BD; </s> <s xml:id="echoid-s4266" xml:space="preserve">ſemi axis minor CA; </s> <s xml:id="echoid-s4267" xml:space="preserve">F focus <lb/> <anchor type="note" xlink:label="note-0160-07a" xlink:href="note-0160-07"/> centrum virium. </s> <s xml:id="echoid-s4268" xml:space="preserve">Centro F, & </s> <s xml:id="echoid-s4269" xml:space="preserve">radio FA circulus deſcribatur AP, de-<lb/>monſtrandum tempus periodicum in circulo æquale eſſe tempori periodico <lb/>in Ellipſi; </s> <s xml:id="echoid-s4270" xml:space="preserve">radius enim FA æqualis eſt ſemi axi majori Ellipſeos, ut ex <lb/>hujus deſcriptione ſequitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4271" xml:space="preserve"/> </p> <div xml:id="echoid-div633" type="float" level="2" n="13"> <note position="left" xlink:label="note-0160-07" xlink:href="note-0160-07a" xml:space="preserve">TAB. XV. <lb/>fig. 8.</note> </div> <note symbol="*" position="left" xml:space="preserve">379.</note> <p> <s xml:id="echoid-s4272" xml:space="preserve">Dentur duo corpora in A, quorum unum in circulo, alterum in Ellipſi <lb/>moveatur, ſintque AL, AM arcus minimi codem tempore deſcripti; </s> <s xml:id="echoid-s4273" xml:space="preserve">ſpa-<lb/>tia vicentrali percurſaerunt æqualia; </s> <s xml:id="echoid-s4274" xml:space="preserve">quia ambo corpora ad eandem diſtanti-<lb/>am AF a centro dantur: </s> <s xml:id="echoid-s4275" xml:space="preserve">ſpatia autem hæc ſunt iL, NM, poſitis Ai ad <lb/>Ellipſin & </s> <s xml:id="echoid-s4276" xml:space="preserve">IN ad circulum, tangentibus, ut & </s> <s xml:id="echoid-s4277" xml:space="preserve">NM, & </s> <s xml:id="echoid-s4278" xml:space="preserve">iL, ad AF pa-<lb/>rallelis. </s> <s xml:id="echoid-s4279" xml:space="preserve">Sint etiam IL ad AC, OM ad NA, GL ad AI parallelæ, & </s> <s xml:id="echoid-s4280" xml:space="preserve">du-<lb/>cantur LC, LF, MF.</s> <s xml:id="echoid-s4281" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4282" xml:space="preserve">In circulo OM<emph style="super">q</emph> æquale eſt <emph style="super">2</emph>MN x AF<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4283" xml:space="preserve">nam AF & </s> <s xml:id="echoid-s4284" xml:space="preserve">OF pro æqua- <anchor type="note" xlink:label="note-0160-09a" xlink:href="note-0160-09"/> libus habentur & </s> <s xml:id="echoid-s4285" xml:space="preserve">AO, MN ſunt æquales.</s> <s xml:id="echoid-s4286" xml:space="preserve"/> </p> <div xml:id="echoid-div634" type="float" level="2" n="14"> <note symbol="*" position="left" xlink:label="note-0160-09" xlink:href="note-0160-09a" xml:space="preserve">32. El. 111. <lb/>3. 4 El. VI.</note> </div> <p> <s xml:id="echoid-s4287" xml:space="preserve">In Ellipſi AC<emph style="super">q</emph>, BC<emph style="super">q</emph> aut AF<emph style="super">q</emph>:</s> <s xml:id="echoid-s4288" xml:space="preserve">: <emph style="super">2</emph>IL x AC, GL<emph style="super">q</emph> = {<emph style="super">2</emph>IL x AF<emph style="super">q</emph>/AC} ſunt <lb/> <anchor type="note" xlink:label="note-0160-10a" xlink:href="note-0160-10"/> enim æquales AG, IL, & </s> <s xml:id="echoid-s4289" xml:space="preserve">AC, GC tantum quantitate infinite exigua <lb/>differunt.</s> <s xml:id="echoid-s4290" xml:space="preserve"/> </p> <div xml:id="echoid-div635" type="float" level="2" n="15"> <note symbol="*" position="left" xlink:label="note-0160-10" xlink:href="note-0160-10a" xml:space="preserve">La Hire <lb/>ſect. com. <lb/>lib. 3. <lb/>prop 3.</note> </div> <p> <s xml:id="echoid-s4291" xml:space="preserve">Triangula IiL, ACF, ſunt ſimilia quia latera ſunt reſpectivè parallela; </s> <s xml:id="echoid-s4292" xml:space="preserve">ideò <pb o="103" file="0161" n="175" rhead="MATHEMATICA, LIB I. CAP. XXI."/> FA, AC:</s> <s xml:id="echoid-s4293" xml:space="preserve">: iL, aut MN, IL = {MN x AC/FA}</s> </p> <p> <s xml:id="echoid-s4294" xml:space="preserve">Subſtituendo pro IL valorem in hac æquatione GL<emph style="super">q</emph> = {<emph style="super">2</emph>IL x AF<emph style="super">q</emph>/AC} habe-<lb/>mus GL<emph style="super">q</emph> = <emph style="super">2</emph>MN x AF, cui quantitati etiam æquale eſt OM<emph style="super">q</emph>, ſunt ergo <lb/> <anchor type="note" xlink:label="note-0161-01a" xlink:href="note-0161-01"/> æquales GL & </s> <s xml:id="echoid-s4295" xml:space="preserve">OM, unde patet in Ellipſi corpus in extremitate axeos mino-<lb/>ris eadem velocitate moveri qua aliud fertur in circulo cujus diameter æqualis eſt axi <lb/>Ellipſeos majori, ſi eadem vi centrali quæ ad ſocum Ellipſeos dirigitur, ambo in <lb/>curvis retineantur.</s> <s xml:id="echoid-s4296" xml:space="preserve"/> </p> <div xml:id="echoid-div636" type="float" level="2" n="16"> <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">413.</note> </div> <p> <s xml:id="echoid-s4297" xml:space="preserve">Quia curva in A parallela eſt ipſi Axi BD, ſunt æqualia triangula CAL, <lb/> <anchor type="note" xlink:label="note-0161-02a" xlink:href="note-0161-02"/> FAL <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4298" xml:space="preserve">triangula rectangula CAL, FAM, quorum baſes ſunt æqua- les ſunt inter ſe ut altitudines AC, AF aut CD; </s> <s xml:id="echoid-s4299" xml:space="preserve">In hac eadem ratione <lb/>ſunt inter ſe areæ Ellipſeos, & </s> <s xml:id="echoid-s4300" xml:space="preserve">circuli. </s> <s xml:id="echoid-s4301" xml:space="preserve">Idcirco alternando area trianguli <lb/>CAL, aut FAL, ad aream Ellipſeos, ut area trianguli FAM ad aream <lb/>circuli: </s> <s xml:id="echoid-s4302" xml:space="preserve">ergo tempus in quo corpus movetur per AL ad tempus periodicum <lb/>in Ellipſi, ut tempus in quo percurritur AM ad tempus periodicum in cir-<lb/> <anchor type="note" xlink:label="note-0161-03a" xlink:href="note-0161-03"/> culo <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4303" xml:space="preserve">antecedentia ſunt æqualia ideò & </s> <s xml:id="echoid-s4304" xml:space="preserve">conſequentia Q. </s> <s xml:id="echoid-s4305" xml:space="preserve">D.</s> <s xml:id="echoid-s4306" xml:space="preserve">E.</s> <s xml:id="echoid-s4307" xml:space="preserve"/> </p> <div xml:id="echoid-div637" type="float" level="2" n="17"> <note symbol="*" position="right" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">37. El. 1.</note> <note symbol="*" position="right" xlink:label="note-0161-03" xlink:href="note-0161-03a" xml:space="preserve">354. 396.</note> </div> </div> <div xml:id="echoid-div639" type="section" level="1" n="184"> <head xml:id="echoid-head259" xml:space="preserve">SCHOLIUM 4.</head> <head xml:id="echoid-head260" style="it" xml:space="preserve">De Motu in orbitâ agitatâ</head> <p> <s xml:id="echoid-s4308" xml:space="preserve">Detur curva quæcunque a corpore vi centrali deſcripta, AF; </s> <s xml:id="echoid-s4309" xml:space="preserve">centrum vi-<lb/> <anchor type="note" xlink:label="note-0161-04a" xlink:href="note-0161-04"/> rium C. </s> <s xml:id="echoid-s4310" xml:space="preserve">Dividatur curva hæc ductis radiis ex centro C, CA, CB, <lb/> <anchor type="note" xlink:label="note-0161-05a" xlink:href="note-0161-05"/> CD & </s> <s xml:id="echoid-s4311" xml:space="preserve">c, angulos æquales infinitè exiguos inter ſe continentibus.</s> <s xml:id="echoid-s4312" xml:space="preserve"/> </p> <div xml:id="echoid-div639" type="float" level="2" n="1"> <note position="right" xlink:label="note-0161-04" xlink:href="note-0161-04a" xml:space="preserve">414</note> <note position="right" xlink:label="note-0161-05" xlink:href="note-0161-05a" xml:space="preserve">TAB. XV. <lb/>fig. 9.</note> </div> <p> <s xml:id="echoid-s4313" xml:space="preserve">Concipiamus ſingulos angulos ſervarâ radiorum longitudine æqualiterau-<lb/>geri aut minui, novamque curvam dari a f per radiorum extrema tranſeuntem.</s> <s xml:id="echoid-s4314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4315" xml:space="preserve">Triangula ACB, acb propter baſes æquales CA, ca, ſunt inter ſe utaltitu-<lb/>dines <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt ut anguli ACB, acb; </s> <s xml:id="echoid-s4316" xml:space="preserve">ſinguli autem anguli in unâ cur- <anchor type="note" xlink:label="note-0161-06a" xlink:href="note-0161-06"/> vâ ſunt ad reſpondentes in aliâ in eâdem ratione; </s> <s xml:id="echoid-s4317" xml:space="preserve">in ſingulis enim curvis <lb/>ſunt omnes æquales inter ſe; </s> <s xml:id="echoid-s4318" xml:space="preserve">ideo triangula quæcunque reſpondentia ut <lb/>ACB acb; </s> <s xml:id="echoid-s4319" xml:space="preserve">BCD, bcd, ſunt in eadem ratione, & </s> <s xml:id="echoid-s4320" xml:space="preserve">ſummæ quæcunque <lb/>triangulorum reſpondentium etiam in eadem ratione; </s> <s xml:id="echoid-s4321" xml:space="preserve">idcirco triangula hæc <lb/>mixta ſunt proportionalia ACE, ace:</s> <s xml:id="echoid-s4322" xml:space="preserve">: ECF, ecf; </s> <s xml:id="echoid-s4323" xml:space="preserve">& </s> <s xml:id="echoid-s4324" xml:space="preserve">alternando <lb/>ACE, ECF:</s> <s xml:id="echoid-s4325" xml:space="preserve">: ace, ecf.</s> <s xml:id="echoid-s4326" xml:space="preserve"/> </p> <div xml:id="echoid-div640" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0161-06" xlink:href="note-0161-06a" xml:space="preserve">1. El. VI</note> </div> <p> <s xml:id="echoid-s4327" xml:space="preserve">Ponamus nunc corpus in curva af moveri, dum corpus quod vi centrali <lb/>ad C tendenti curvam AF percurrit; </s> <s xml:id="echoid-s4328" xml:space="preserve">concipiamus ulterius, dum corpus unum <lb/>percurrit AB, alterum per ab transferri, dum primum ad D pertingit, alterum da-<lb/>ri in d, & </s> <s xml:id="echoid-s4329" xml:space="preserve">ſic ulterius; </s> <s xml:id="echoid-s4330" xml:space="preserve">eodem tempore ergo percurruntur AF, ae, & </s> <s xml:id="echoid-s4331" xml:space="preserve">tem-<lb/>pore etiam eodem percurruntur EF & </s> <s xml:id="echoid-s4332" xml:space="preserve">ef. </s> <s xml:id="echoid-s4333" xml:space="preserve">idcirco tempora quibus AE, EF <lb/>percurruntur ſunt ut illa quibus per ae, ef corpus movetur. </s> <s xml:id="echoid-s4334" xml:space="preserve">Tempora autem <lb/>illa ſunt ut areæ ACE; </s> <s xml:id="echoid-s4335" xml:space="preserve">ECF <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4336" xml:space="preserve">quæ ſunt ut areæ ace, ecf; </s> <s xml:id="echoid-s4337" xml:space="preserve">in qua ergo <anchor type="note" xlink:label="note-0161-07a" xlink:href="note-0161-07"/> ratione ſunt tempora quibus per ae, & </s> <s xml:id="echoid-s4338" xml:space="preserve">ef, corpus transfertur; </s> <s xml:id="echoid-s4339" xml:space="preserve">quæ eadem de-<lb/>monſtratio cumlocum habeat, ſumtis arcubus quibuſcunque; </s> <s xml:id="echoid-s4340" xml:space="preserve">ſequitur corpus <lb/>in curva af translatum deſcribere areas lineis ad centrum c ductis tempori-<lb/>bus proportionales, & </s> <s xml:id="echoid-s4341" xml:space="preserve">retineri in curvâ vi centrali ad c tendenti <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4342" xml:space="preserve"/> </p> <div xml:id="echoid-div641" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0161-07" xlink:href="note-0161-07a" xml:space="preserve">354. 396.</note> </div> <note symbol="*" position="right" xml:space="preserve">355. 397.</note> <p> <s xml:id="echoid-s4343" xml:space="preserve">Concipiamus nunc curvam AC circa centrum C moveri ita, ut motus <lb/> <anchor type="note" xlink:label="note-0161-09a" xlink:href="note-0161-09"/> angularis curvæ ſequatur proportionem motus angularis corporis in hac <lb/>curva agitati: </s> <s xml:id="echoid-s4344" xml:space="preserve">dum corpus in curva ab A ad F movetur ipſius motus an-<lb/>gularis eſt ACF, ponamus curvam interea transferri motu angulari, lineam- <pb o="104" file="0162" n="176" rhead="PHYSICES ELEMENTA"/> que a Cad ſitum AC perveniſſe, anguloſque ACF, ACa dum augentur eandem <lb/>ſemper inter ſe rationem habere; </s> <s xml:id="echoid-s4345" xml:space="preserve">quare erunt etiam in ratione conſtanti an-<lb/>guli aCF, ACF.</s> <s xml:id="echoid-s4346" xml:space="preserve"/> </p> <div xml:id="echoid-div642" type="float" level="2" n="4"> <note position="right" xlink:label="note-0161-09" xlink:href="note-0161-09a" xml:space="preserve">TAB. XV. <lb/>fig. 10.</note> </div> <p> <s xml:id="echoid-s4347" xml:space="preserve">Si nunc hæc ratio illa ſit quæ in figura præcedenti datur interangulos acf, <lb/>ACF, & </s> <s xml:id="echoid-s4348" xml:space="preserve">moveatur corpus, retineaturque vi centrali in curva quieſcente <lb/> <anchor type="note" xlink:label="note-0162-01a" xlink:href="note-0162-01"/> AEF, aliudque corpus eodem modo percurrat curvam ſimilem & </s> <s xml:id="echoid-s4349" xml:space="preserve">æqualem, <lb/>ut dictum, agitatam, hoc ultimum, ut facile, patet, revera movebitur in cur-<lb/>vâ aef quieſcente.</s> <s xml:id="echoid-s4350" xml:space="preserve"/> </p> <div xml:id="echoid-div643" type="float" level="2" n="5"> <note position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">Fig. 9.</note> </div> <p style="it"> <s xml:id="echoid-s4351" xml:space="preserve">Hinc deducimus corpus omne quod vi centrali curvam quamcunque deſcribit, <lb/> <anchor type="note" xlink:label="note-0162-02a" xlink:href="note-0162-02"/> eandem curvam, circa centrum virium mobilem, vi aliâ centrali deſcribere <lb/>poſſe.</s> <s xml:id="echoid-s4352" xml:space="preserve"/> </p> <div xml:id="echoid-div644" type="float" level="2" n="6"> <note position="left" xlink:label="note-0162-02" xlink:href="note-0162-02a" xml:space="preserve">415.</note> </div> <p> <s xml:id="echoid-s4353" xml:space="preserve">De differentia inter vires has centrales nunc agendum.</s> <s xml:id="echoid-s4354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4355" xml:space="preserve">Sint A, B, D, tria parum admodum a ſe invicem diſtantia puncta curvæ <lb/> <anchor type="note" xlink:label="note-0162-03a" xlink:href="note-0162-03"/> cujuſcunque a corpore, vicentrali ad C tendenti percurſæ detur GBH tan-<lb/> <anchor type="note" xlink:label="note-0162-04a" xlink:href="note-0162-04"/> gens ad curvam in puncto B; </s> <s xml:id="echoid-s4356" xml:space="preserve">ſintque GD, HA, ad BC parallelæ poni-<lb/>mus GB, BH æquales inter ſe, ideoque AB, BD æqualibus temporibus <lb/>percurri.</s> <s xml:id="echoid-s4357" xml:space="preserve"/> </p> <div xml:id="echoid-div645" type="float" level="2" n="7"> <note position="left" xlink:label="note-0162-03" xlink:href="note-0162-03a" xml:space="preserve">416.</note> <note position="left" xlink:label="note-0162-04" xlink:href="note-0162-04a" xml:space="preserve">TAB. XV. <lb/>fig. 11.</note> </div> <p> <s xml:id="echoid-s4358" xml:space="preserve">Propter diſtantiam inter puncta A, B, D, infinitè exiguam, vis <lb/>centralis in motu per hæc puncta non mutatur, ideò temporibus æqualibus <lb/>quibus AB, BD percurruntur, æqualiter vi centrali a recta deflectitur cor-<lb/>pus, id eſt hujus via æqualiter incurvatur, ex qua æquali deflectione ſequi-<lb/>tur æquales eſſe inter ſe HA, GD.</s> <s xml:id="echoid-s4359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4360" xml:space="preserve">Angulus quem curva quæcunque cum tangenti efficit eſt infinitè exiguus <lb/> <anchor type="note" xlink:label="note-0162-05a" xlink:href="note-0162-05"/> ideoque HA & </s> <s xml:id="echoid-s4361" xml:space="preserve">DG ſunt inſinite exiguæ reſpectu HB, HG; </s> <s xml:id="echoid-s4362" xml:space="preserve">quare cum <lb/>hæ ſint æquales, & </s> <s xml:id="echoid-s4363" xml:space="preserve">infinitè exiguæ, ſunt æquales anguli BCA, BCD.</s> <s xml:id="echoid-s4364" xml:space="preserve"/> </p> <div xml:id="echoid-div646" type="float" level="2" n="8"> <note position="left" xlink:label="note-0162-05" xlink:href="note-0162-05a" xml:space="preserve">417.</note> </div> <p> <s xml:id="echoid-s4365" xml:space="preserve">Sint ulterius anguli ACa, DCd, æquales inter ſe; </s> <s xml:id="echoid-s4366" xml:space="preserve">& </s> <s xml:id="echoid-s4367" xml:space="preserve">centro C deſcri-<lb/>pti arcus circulorum Aa, Dd. </s> <s xml:id="echoid-s4368" xml:space="preserve">Evidentiſſime patet puncta a, B, d, eſſe pun-<lb/>cta curvæ in qua corpus movetur, ſi in curva ABD mobili feratur, poſito mo-<lb/>tu angulari curvæ ad motum angularem corporis, ut angulus aCA ad an-<lb/>gulum ACB <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4369" xml:space="preserve">& </s> <s xml:id="echoid-s4370" xml:space="preserve">in hoc motu corpus ab a ad B fertur eodem tempore, in <anchor type="note" xlink:label="note-0162-06a" xlink:href="note-0162-06"/> quo in curvâ quieſcente ab A ad B pergit.</s> <s xml:id="echoid-s4371" xml:space="preserve"/> </p> <div xml:id="echoid-div647" type="float" level="2" n="9"> <note symbol="*" position="left" xlink:label="note-0162-06" xlink:href="note-0162-06a" xml:space="preserve">434.</note> </div> <p> <s xml:id="echoid-s4372" xml:space="preserve">Ponamus FBI, in puncto B, tangere curvam aBd, & </s> <s xml:id="echoid-s4373" xml:space="preserve">ad BC paralle-<lb/>las dari I a, F d; </s> <s xml:id="echoid-s4374" xml:space="preserve">quia æqualibus temporibus percurruntur a B, Bd, ſuntæ-<lb/>quales IB, BF, quæ iiſdem temporibus ſublatâ vi centrali poſſet percurri; <lb/></s> <s xml:id="echoid-s4375" xml:space="preserve">ſuntque etiam æquales Fd, Ia; </s> <s xml:id="echoid-s4376" xml:space="preserve">quod eâdem demonſtratione evincitur qua <lb/>probavimus æquales HA, GD <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4377" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">416.</note> <p> <s xml:id="echoid-s4378" xml:space="preserve">Jungantur F, G ut & </s> <s xml:id="echoid-s4379" xml:space="preserve">H, I; </s> <s xml:id="echoid-s4380" xml:space="preserve">& </s> <s xml:id="echoid-s4381" xml:space="preserve">ducantur DE parallela FG, & </s> <s xml:id="echoid-s4382" xml:space="preserve">AL paral-<lb/>lela HI; </s> <s xml:id="echoid-s4383" xml:space="preserve">producatur ED ad O ſecans BC in N.</s> <s xml:id="echoid-s4384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4385" xml:space="preserve">Propter æquales BH, BG, & </s> <s xml:id="echoid-s4386" xml:space="preserve">BI, BF, ut & </s> <s xml:id="echoid-s4387" xml:space="preserve">æquales angulos HBI, <lb/>FBG, ſunt æquiangula & </s> <s xml:id="echoid-s4388" xml:space="preserve">congrua triangula FBG, BHI <anchor type="note" xlink:href="" symbol="*"/>, quare ſunt <anchor type="note" xlink:label="note-0162-08a" xlink:href="note-0162-08"/> æquales FG, HI quæ etiam parallelæ ſunt <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s4389" xml:space="preserve">quare etiam æquales & </s> <s xml:id="echoid-s4390" xml:space="preserve">pa- <anchor type="note" xlink:label="note-0162-09a" xlink:href="note-0162-09"/> rallelæ AL, ED <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4391" xml:space="preserve">Sunt quoque æquales La, Ed, cum ſint quantitatum <anchor type="note" xlink:label="note-0162-10a" xlink:href="note-0162-10"/> reſpective æqualium differentiæ A a & </s> <s xml:id="echoid-s4392" xml:space="preserve">D d, angulorum æqualium menſuræ, <lb/>in circulis, quorum radii infinitè parum differunt, ſunt etiam æquales; </s> <s xml:id="echoid-s4393" xml:space="preserve">ideò <lb/>æquiangula ſunt triangula A La, DEd <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s4394" xml:space="preserve">æquales anguli AL a, DE d;</s> <s xml:id="echoid-s4395" xml:space="preserve"> <anchor type="note" xlink:label="note-0162-11a" xlink:href="note-0162-11"/> hic autem æqualis eſt angulo ONC, & </s> <s xml:id="echoid-s4396" xml:space="preserve">ille angulo DNC <anchor type="note" xlink:href="" symbol="*"/>, propter cru- <anchor type="note" xlink:label="note-0162-12a" xlink:href="note-0162-12"/> ta parallela; </s> <s xml:id="echoid-s4397" xml:space="preserve">quare ſunt æquales & </s> <s xml:id="echoid-s4398" xml:space="preserve">recti anguli ONC, DNC.</s> <s xml:id="echoid-s4399" xml:space="preserve"/> </p> <div xml:id="echoid-div648" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0162-08" xlink:href="note-0162-08a" xml:space="preserve">4. El. 1.</note> <note symbol="*" position="left" xlink:label="note-0162-09" xlink:href="note-0162-09a" xml:space="preserve">27. El. 1.</note> <note symbol="*" position="left" xlink:label="note-0162-10" xlink:href="note-0162-10a" xml:space="preserve">30. 34. <lb/>El. 1.</note> <note symbol="*" position="left" xlink:label="note-0162-11" xlink:href="note-0162-11a" xml:space="preserve">8. El. 1.</note> <note symbol="*" position="left" xlink:label="note-0162-12" xlink:href="note-0162-12a" xml:space="preserve">29. El. 1.</note> </div> <p> <s xml:id="echoid-s4400" xml:space="preserve">Eo tempore quo, vi centrali, in curvâ mobili percurritur Fd, in curva <lb/> <anchor type="note" xlink:label="note-0162-13a" xlink:href="note-0162-13"/> quieſcente, vi centrali, percurritur GD, quæ æqualis eſt FE; </s> <s xml:id="echoid-s4401" xml:space="preserve">ideò ſpa-<lb/>tium differentiâ virium eodem tempore percurſum eſt Ed. </s> <s xml:id="echoid-s4402" xml:space="preserve">Punctum au- <pb o="105" file="0163" n="177" rhead="MATHEMATICA. LIB. I. CAP XXI."/> tem E in hac figura determinatur ductâ per D perpendiculari ad BC.</s> <s xml:id="echoid-s4403" xml:space="preserve"/> </p> <div xml:id="echoid-div649" type="float" level="2" n="11"> <note position="left" xlink:label="note-0162-13" xlink:href="note-0162-13a" xml:space="preserve">418.</note> </div> <p> <s xml:id="echoid-s4404" xml:space="preserve">Hiſce poſitis, ſit centrum virium C, & </s> <s xml:id="echoid-s4405" xml:space="preserve">moveatur corpus in curvâ AEG <lb/> <anchor type="note" xlink:label="note-0163-01a" xlink:href="note-0163-01"/> ita circa centruin C agitatâ, ut motus angularis curvæ ſe habeat ad motum an-<lb/> <anchor type="note" xlink:label="note-0163-02a" xlink:href="note-0163-02"/> gularem corporis in curva circa idem centrum C, ut angulus a CA ad an-<lb/>gulum ACE. </s> <s xml:id="echoid-s4406" xml:space="preserve">Sit EG continuatio curvæ AE; </s> <s xml:id="echoid-s4407" xml:space="preserve">centro C radio CG de-<lb/>ſcribatur arcus FG g; </s> <s xml:id="echoid-s4408" xml:space="preserve">ductiſque EC, GC, fiat angulus GCF ad ECG, <lb/>ut angulus a CA ad ACE. </s> <s xml:id="echoid-s4409" xml:space="preserve">Dum corpus percurrit EG in curva AE, mo-<lb/>tu curvæ punctum G ad F transfertur & </s> <s xml:id="echoid-s4410" xml:space="preserve">corpus percurrit EF, tempore quo <lb/>potuiſſet percurrere EG in curva quieſcente Per G ad EC ducatur per-<lb/>pendicularis GH, quæ utrimque continuata ſecat EC in H & </s> <s xml:id="echoid-s4411" xml:space="preserve">CF conti-<lb/>nuatam in f; </s> <s xml:id="echoid-s4412" xml:space="preserve">& </s> <s xml:id="echoid-s4413" xml:space="preserve">erit fF ſpatium differentiâ virium percurſum, poſitis angu-<lb/>lis FCG & </s> <s xml:id="echoid-s4414" xml:space="preserve">GCE infinite exiguis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4415" xml:space="preserve"/> </p> <div xml:id="echoid-div650" type="float" level="2" n="12"> <note position="right" xlink:label="note-0163-01" xlink:href="note-0163-01a" xml:space="preserve">419.</note> <note position="right" xlink:label="note-0163-02" xlink:href="note-0163-02a" xml:space="preserve">TAB XV. <lb/>fig. 12.</note> </div> <note symbol="*" position="right" xml:space="preserve">418.</note> <p> <s xml:id="echoid-s4416" xml:space="preserve">Si, ſumpto puncto E alio quocunque, EG & </s> <s xml:id="echoid-s4417" xml:space="preserve">EF ita determinentur, ut æ-<lb/>quali tempore deſcribantur ubicunque detur punctum E; </s> <s xml:id="echoid-s4418" xml:space="preserve">id eſt, areæ EGC, <lb/>EFC, determinatam habeant magnitudinem <anchor type="note" xlink:href="" symbol="*"/>, lineola f F differentiæ viri- <anchor type="note" xlink:label="note-0163-04a" xlink:href="note-0163-04"/> um proportionalis erit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4419" xml:space="preserve"/> </p> <div xml:id="echoid-div651" type="float" level="2" n="13"> <note symbol="*" position="right" xlink:label="note-0163-04" xlink:href="note-0163-04a" xml:space="preserve">354. 396.</note> </div> <note symbol="*" position="right" xml:space="preserve">401.</note> <p> <s xml:id="echoid-s4420" xml:space="preserve">Area EGC dicatur N; </s> <s xml:id="echoid-s4421" xml:space="preserve">& </s> <s xml:id="echoid-s4422" xml:space="preserve">M area EFC; </s> <s xml:id="echoid-s4423" xml:space="preserve">poſitis N & </s> <s xml:id="echoid-s4424" xml:space="preserve">M quantitatibus <lb/>determinatis. </s> <s xml:id="echoid-s4425" xml:space="preserve">Habemus EC x GH = <emph style="super">2</emph>N & </s> <s xml:id="echoid-s4426" xml:space="preserve">EC x f H = <emph style="super">2</emph>M; </s> <s xml:id="echoid-s4427" xml:space="preserve">unde dedu-<lb/>cimus GH = {<emph style="super">2</emph>N/EC} & </s> <s xml:id="echoid-s4428" xml:space="preserve">fH = {<emph style="super">2</emph>M/EC}; </s> <s xml:id="echoid-s4429" xml:space="preserve">ut & </s> <s xml:id="echoid-s4430" xml:space="preserve">f H + GH, id eſt f g = {<emph style="super">2</emph>M + <emph style="super">2</emph>N/EC}, <lb/>& </s> <s xml:id="echoid-s4431" xml:space="preserve">f H - GH, id eſt f G, = {<emph style="super">2</emph>M - <emph style="super">2</emph>N/EC}. </s> <s xml:id="echoid-s4432" xml:space="preserve">Ex proprietate circuli eſt f G x fg <lb/>= f F x f @ ſumtis FC & </s> <s xml:id="echoid-s4433" xml:space="preserve">CI æqualibus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4434" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">36. El. 213.</note> <p> <s xml:id="echoid-s4435" xml:space="preserve">Æquatio hæc, ſubſtituendo pro f G & </s> <s xml:id="echoid-s4436" xml:space="preserve">fg valores, mutatur in hanc <lb/>{<emph style="super">4</emph>M<emph style="super">q</emph> - <emph style="super">4</emph>N<emph style="super">q</emph>/EC<emph style="super">q</emph>} = fF x fI; </s> <s xml:id="echoid-s4437" xml:space="preserve">ſed, propter f F infinitè exiguam, f I valet <emph style="super">2</emph>FC, <lb/>& </s> <s xml:id="echoid-s4438" xml:space="preserve">quia infinitè parum differunt CF, EC, una pro aliâ uſurpari poteſt: </s> <s xml:id="echoid-s4439" xml:space="preserve">er-<lb/>go iterum mutatur æquatio in hanc {<emph style="super">4</emph>M<emph style="super">q</emph> - <emph style="super">4</emph>N<emph style="super">q</emph>/CF<emph style="super">q</emph>} = <emph style="super">2</emph>f F x CF: </s> <s xml:id="echoid-s4440" xml:space="preserve">idcirco <lb/>f F = {<emph style="super">2</emph>M<emph style="super">q</emph> - <emph style="super">2</emph>N<emph style="super">q</emph>/CF<emph style="super">c</emph>}. </s> <s xml:id="echoid-s4441" xml:space="preserve">Numerator hujus fractionis eſt conſtans quantitas ſe-<lb/>quitur ergo f F, id eſt differentia virium, rationem inverſam denominatoris, <lb/>nempe, cubi diſtantiæ a centro.</s> <s xml:id="echoid-s4442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4443" xml:space="preserve">Vis hæc eſt exceſſus qua vis centralis in curva mobili ſuperat vim in curva <lb/>quieſcente & </s> <s xml:id="echoid-s4444" xml:space="preserve">motus curvæ cum motu corporis conſpirat.</s> <s xml:id="echoid-s4445" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4446" xml:space="preserve">Quando punctum f cadit inter G & </s> <s xml:id="echoid-s4447" xml:space="preserve">H, eadem demonſtratio locum habet, <lb/>ſed vis centralis in curvâ quieſcente excedit aliam, & </s> <s xml:id="echoid-s4448" xml:space="preserve">curvæ motus in con-<lb/>trariam partem dirigitur. </s> <s xml:id="echoid-s4449" xml:space="preserve">Si autem punctum f inter H & </s> <s xml:id="echoid-s4450" xml:space="preserve">g, aut ultra g ca-<lb/>dat, agitur de motu corporis in contrariam partem ex E ad A.</s> <s xml:id="echoid-s4451" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4452" xml:space="preserve">Ex hiſce omnibus deducimus. </s> <s xml:id="echoid-s4453" xml:space="preserve">Si corpus vi centrali quacunque curvam deſcri-<lb/> <anchor type="note" xlink:label="note-0163-07a" xlink:href="note-0163-07"/> bat, ſuperadditâ, aut detractâ, vi quæ ſequatur rationem inverſam cubi diſtan-<lb/>tiæ, eandem curvam, circa centrum virium mobilem, corpus deſcribere. </s> <s xml:id="echoid-s4454" xml:space="preserve">Si vis ſu-<lb/> <anchor type="note" xlink:label="note-0163-08a" xlink:href="note-0163-08"/> peradditur motus curvæ cum motu corporis ad eandem partem tendunt. </s> <s xml:id="echoid-s4455" xml:space="preserve">In con-<lb/> <anchor type="note" xlink:label="note-0163-09a" xlink:href="note-0163-09"/> trarias partes diriguntur ſi vis detrabatur.</s> <s xml:id="echoid-s4456" xml:space="preserve"/> </p> <div xml:id="echoid-div652" type="float" level="2" n="14"> <note position="right" xlink:label="note-0163-07" xlink:href="note-0163-07a" xml:space="preserve">420.</note> <note position="right" xlink:label="note-0163-08" xlink:href="note-0163-08a" xml:space="preserve">421.</note> <note position="right" xlink:label="note-0163-09" xlink:href="note-0163-09a" xml:space="preserve">422.</note> </div> <pb o="106" file="0164" n="178" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div654" type="section" level="1" n="185"> <head xml:id="echoid-head261" xml:space="preserve">SCHOLIUM 5.</head> <head xml:id="echoid-head262" style="it" xml:space="preserve">De Motu in Ellipſi agitatâ.</head> <p> <s xml:id="echoid-s4457" xml:space="preserve">Corpus in Ellipſi retinetur vi centrali ad focum tendente & </s> <s xml:id="echoid-s4458" xml:space="preserve">juxtarationem <lb/> <anchor type="note" xlink:label="note-0164-01a" xlink:href="note-0164-01"/> inverſam quadrati diſtantiæ decreſcente <anchor type="note" xlink:href="" symbol="*"/>, ſi ſuperaddatur vis quæ decre- <anchor type="note" xlink:label="note-0164-02a" xlink:href="note-0164-02"/> ſcat in ratione inverſa cubi diſtantiæ, eandem corpus deſcribit Ellipſim trans-<lb/>latam ita, ut eandem partem verſus motus ipſius cum motu corporis diri-<lb/>gatur <anchor type="note" xlink:href="" symbol="*"/> Vis ultima magis decreſcit, auctâ diſtantiâ, quam prima; </s> <s xml:id="echoid-s4459" xml:space="preserve">idcirco ſum- <anchor type="note" xlink:label="note-0164-03a" xlink:href="note-0164-03"/> ma virium, celerius decreſcit quam juxta rationem inverſam quadrati diſtan-<lb/>tiæ, unde conſtat propoſitio n. </s> <s xml:id="echoid-s4460" xml:space="preserve">386.</s> <s xml:id="echoid-s4461" xml:space="preserve"/> </p> <div xml:id="echoid-div654" type="float" level="2" n="1"> <note position="left" xlink:label="note-0164-01" xlink:href="note-0164-01a" xml:space="preserve">423.</note> <note symbol="*" position="left" xlink:label="note-0164-02" xlink:href="note-0164-02a" xml:space="preserve">381. 411.</note> <note symbol="*" position="left" xlink:label="note-0164-03" xlink:href="note-0164-03a" xml:space="preserve">420. 421.</note> </div> <p> <s xml:id="echoid-s4462" xml:space="preserve">Simili demonſtratione conſtat n. </s> <s xml:id="echoid-s4463" xml:space="preserve">387. </s> <s xml:id="echoid-s4464" xml:space="preserve">nam ſi ex vi quæ ſequitur rationem <lb/> <anchor type="note" xlink:label="note-0164-04a" xlink:href="note-0164-04"/> inverſam quadrati diſtantiæ tollatur vis, quæ ſequatur rationem inverſam cubi <lb/>diſtantiæ, id eſt primâ celerius decreſcens, quæ ſupereſt lentius quàm juxta <lb/>rationem inverſam quadrati diſtantiæ, auctâ hac, minuitur.</s> <s xml:id="echoid-s4465" xml:space="preserve"/> </p> <div xml:id="echoid-div655" type="float" level="2" n="2"> <note position="left" xlink:label="note-0164-04" xlink:href="note-0164-04a" xml:space="preserve">424.</note> </div> <p> <s xml:id="echoid-s4466" xml:space="preserve">In n. </s> <s xml:id="echoid-s4467" xml:space="preserve">385, 386, 387. </s> <s xml:id="echoid-s4468" xml:space="preserve">egimus de viribus, juxta rationem, a ratione dupli-<lb/> <anchor type="note" xlink:label="note-0164-05a" xlink:href="note-0164-05"/> catâ inverſa diſtantiæ parum aberrante, decreſcentibus, aut de curvis circulis fini-<lb/>timis; </s> <s xml:id="echoid-s4469" xml:space="preserve">quia in hiſce caſibus in propoſitionibus error ſenſibilis non datur, licet vires <lb/>ſequantur rationem aliûs poteſtatis cujuſdam diſtantiæ; </s> <s xml:id="echoid-s4470" xml:space="preserve">in quo caſu Mathe-<lb/>maticè loquendo curva non eſt Ellipſis mota juxta leges explicatas, ad quod <lb/>requiritur vis, quæ eſt ſumma aut differentia virium, quarum una ſequitur ra-<lb/>tionem inverſam duplicatam <anchor type="note" xlink:href="" symbol="*"/>, alia inverſam triplicatam, diſtantiæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4471" xml:space="preserve"/> </p> <div xml:id="echoid-div656" type="float" level="2" n="3"> <note position="left" xlink:label="note-0164-05" xlink:href="note-0164-05a" xml:space="preserve">425.</note> </div> <note symbol="*" position="left" xml:space="preserve">331. 411.</note> <note symbol="*" position="left" xml:space="preserve">420.</note> <p> <s xml:id="echoid-s4472" xml:space="preserve">Ut autem ex dato motu angulari Ellipſeos vim addendam aut detrahen-<lb/>dam, & </s> <s xml:id="echoid-s4473" xml:space="preserve">vice verſa ex data hac, motum curvæ determinemus, <lb/> <anchor type="note" xlink:label="note-0164-08a" xlink:href="note-0164-08"/> ſit A extremitas axeos majoris; </s> <s xml:id="echoid-s4474" xml:space="preserve">F focus centrum virium; </s> <s xml:id="echoid-s4475" xml:space="preserve">a A portio circuli <lb/> <anchor type="note" xlink:label="note-0164-09a" xlink:href="note-0164-09"/> centro F, radio F A deſcripti; </s> <s xml:id="echoid-s4476" xml:space="preserve">A L Ellipſeos portio.</s> <s xml:id="echoid-s4477" xml:space="preserve"/> </p> <div xml:id="echoid-div657" type="float" level="2" n="4"> <note position="left" xlink:label="note-0164-08" xlink:href="note-0164-08a" xml:space="preserve">426.</note> <note position="left" xlink:label="note-0164-09" xlink:href="note-0164-09a" xml:space="preserve">TAB. XV. <lb/>fig, 13.</note> </div> <p> <s xml:id="echoid-s4478" xml:space="preserve">Ponamus dum corpus in Ellipſi fertur per AL, ipſam curvam motu an-<lb/>gulari a FA transferri; </s> <s xml:id="echoid-s4479" xml:space="preserve">anguloſque a FL, AFL eſſe inter ſe ut M ad N. <lb/></s> <s xml:id="echoid-s4480" xml:space="preserve">Ponimus etiam angulos hos eſſe infinite exiguos.</s> <s xml:id="echoid-s4481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4482" xml:space="preserve">In a & </s> <s xml:id="echoid-s4483" xml:space="preserve">A ad circulum a A ducantur tangentes a i, EAI, ſibi mutuo oc-<lb/>currentes in E, & </s> <s xml:id="echoid-s4484" xml:space="preserve">quarum ultima etiam Ellipſin tangit in A; </s> <s xml:id="echoid-s4485" xml:space="preserve">ducantur et-<lb/>iam AB, LI, ad a F parallelæ, ultima propter infinite exiguos arcus a A, <lb/>AL, pro parallela haberi poteſt ipſi AF; </s> <s xml:id="echoid-s4486" xml:space="preserve">tandem ſint AC ad a B, & </s> <s xml:id="echoid-s4487" xml:space="preserve">LG ad <lb/>AI parallelæ.</s> <s xml:id="echoid-s4488" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4489" xml:space="preserve">Sunt æquales E a, EA <anchor type="note" xlink:href="" symbol="*"/>, ideoque a E & </s> <s xml:id="echoid-s4490" xml:space="preserve">EB, quæ EA æqualis eſt. </s> <s xml:id="echoid-s4491" xml:space="preserve">Pro- <anchor type="note" xlink:label="note-0164-10a" xlink:href="note-0164-10"/> pter triangula ſimilia EBA, EiI, eſt # <lb/># EB aut {1/2} a B, E i aut a i-{1/2} a B:</s> <s xml:id="echoid-s4492" xml:space="preserve">: BA, i I; <lb/></s> <s xml:id="echoid-s4493" xml:space="preserve">a B autem ſe habet ad a i, ut angulus a F A ad a FL, id eſt, ut M-N ad M: </s> <s xml:id="echoid-s4494" xml:space="preserve"><lb/>ergo <lb/>BA, i I:</s> <s xml:id="echoid-s4495" xml:space="preserve">:{1/2} M-{1/2}N, {1/2}M + {1/2}N:</s> <s xml:id="echoid-s4496" xml:space="preserve">:M-N, M + N.</s> <s xml:id="echoid-s4497" xml:space="preserve"/> </p> <div xml:id="echoid-div658" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0164-10" xlink:href="note-0164-10a" xml:space="preserve">36. El. III.</note> </div> <p> <s xml:id="echoid-s4498" xml:space="preserve">Ex circuli proprietate a C aut BA, a A aut a B, & </s> <s xml:id="echoid-s4499" xml:space="preserve">diameter, ſunt <lb/>in continua proportione <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4500" xml:space="preserve">ergo BA = {a B<emph style="super">q</emph>/2AF}. </s> <s xml:id="echoid-s4501" xml:space="preserve">Ellipſis in extremitate a- <anchor type="note" xlink:label="note-0164-11a" xlink:href="note-0164-11"/> xeos majoris coincidit cum circulo cujus diameter eſt axeos parameter <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4502" xml:space="preserve">id- <anchor type="note" xlink:label="note-0164-12a" xlink:href="note-0164-12"/> <pb o="107" file="0165" n="179" rhead="MATHEMATICA. LIB. I. CAP. XXI."/> eo ſi hæc dicatur 2R, erit IL = {AI<emph style="super">q</emph>/2R} = {Bi<emph style="super">q</emph>/2R}:</s> <s xml:id="echoid-s4503" xml:space="preserve">ſed{aB<emph style="super">q</emph>/2AF} ſe habet ad {Bi<emph style="super">q</emph>/2R}, <lb/>ut {<emph style="ol">M-N</emph><emph style="super">q</emph>/AF} ad{N<emph style="super">q</emph>/R}; </s> <s xml:id="echoid-s4504" xml:space="preserve">idcirco <lb/>IL, AB:</s> <s xml:id="echoid-s4505" xml:space="preserve">: {N<emph style="super">q</emph>/R} {<emph style="ol">M-N</emph><emph style="super">q</emph>/AF}</s> </p> <div xml:id="echoid-div659" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0164-11" xlink:href="note-0164-11a" xml:space="preserve">31. El. 111. <lb/>8. El <emph style="sc">VI.</emph></note> <note symbol="*" position="left" xlink:label="note-0164-12" xlink:href="note-0164-12a" xml:space="preserve">La Hire <lb/>ſect. con. <lb/>lib. 7. cot. <lb/>prop. 6.</note> </div> <p> <s xml:id="echoid-s4506" xml:space="preserve">Sed ut vidimus AB, I i:</s> <s xml:id="echoid-s4507" xml:space="preserve">: M-N, M + N; </s> <s xml:id="echoid-s4508" xml:space="preserve">ergo ex compoſitione rationis <lb/>IL, I i:</s> <s xml:id="echoid-s4509" xml:space="preserve">: {N<emph style="super">q</emph> x <emph style="ol">M-N</emph>/R}, {<emph style="ol">M-N</emph><emph style="super">q</emph> x <emph style="ol">M + N</emph>/AF} = {<emph style="ol">M<emph style="super">q</emph>-N<emph style="super">q</emph></emph> x <emph style="ol">M-N</emph>/AF} :</s> <s xml:id="echoid-s4510" xml:space="preserve">: {N<emph style="super">q</emph>/R}, {M<emph style="super">q</emph>-N<emph style="super">q</emph>/AF} <lb/>Eodem tempore percurruntur IL & </s> <s xml:id="echoid-s4511" xml:space="preserve">i I, prima vi qua corpus retinetur in <lb/>Ellipſi quieſcente, ſecunda difterentiâ vis hujus cum vi qua corpus in El-<lb/>lipſi mobili retinetur, ergo vis in Ellipſi ad differentiam hanc, ut {N<emph style="super">q</emph>/R} <lb/>ad {M<emph style="super">q</emph>-N<emph style="super">q</emph>/AF} <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4512" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">401.</note> <p> <s xml:id="echoid-s4513" xml:space="preserve">Dicatur {N<emph style="super">q</emph>/AF<emph style="super">q</emph>} vis qua corpus in Ellipſi retinetur in puncto A, & </s> <s xml:id="echoid-s4514" xml:space="preserve">fiat <lb/>{N<emph style="super">q</emph>/R}, {M<emph style="super">q</emph>-N<emph style="super">q</emph>/AF} :</s> <s xml:id="echoid-s4515" xml:space="preserve">: {N<emph style="super">q</emph>/AF<emph style="super">q</emph>}, ad differentiam virium {RMM-RNN/AF<emph style="super">c</emph>}</s> </p> <p> <s xml:id="echoid-s4516" xml:space="preserve">Si agatur de diſtantia alia quæcunque quæ dicatur D, vis qua corpus reti-<lb/>netur in Ellipſi hac analogia detegitur <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0165-02a" xlink:href="note-0165-02"/> {I/AF<emph style="super">q</emph>}, {I/D<emph style="super">q</emph>} :</s> <s xml:id="echoid-s4517" xml:space="preserve">: {N<emph style="super">q</emph>/AF<emph style="super">q</emph>} ad vim quæſitam {NN/DD}.</s> <s xml:id="echoid-s4518" xml:space="preserve"/> </p> <div xml:id="echoid-div660" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0165-02" xlink:href="note-0165-02a" xml:space="preserve">381. 411.</note> </div> <p> <s xml:id="echoid-s4519" xml:space="preserve">Difterentia virium detegitur hac regulâ <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0165-03a" xlink:href="note-0165-03"/> {I/AF<emph style="super">c</emph>}, {I/D<emph style="super">c</emph>} :</s> <s xml:id="echoid-s4520" xml:space="preserve">: {RMM-RNN/AF<emph style="super">c</emph>} ad differentiam quæſitam <lb/>{RMM-RNN/D<emph style="super">c</emph>}.</s> <s xml:id="echoid-s4521" xml:space="preserve"/> </p> <div xml:id="echoid-div661" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0165-03" xlink:href="note-0165-03a" xml:space="preserve">410.</note> </div> <p> <s xml:id="echoid-s4522" xml:space="preserve">Idcirco vis integra qua corpus in Ellipſi mobili retinetur ſequitur propor-<lb/> <anchor type="note" xlink:label="note-0165-04a" xlink:href="note-0165-04"/> tionem {NN/D<emph style="super">q</emph>} + {RMM-RNN/D<emph style="super">c</emph>}, quando corpus & </s> <s xml:id="echoid-s4523" xml:space="preserve">Ellipſis ad eandem <lb/>partem tendunt. </s> <s xml:id="echoid-s4524" xml:space="preserve">Si motus hi fuerint contrarii vis proportionalis eſt <lb/>{NN/D<emph style="super">q</emph>}-{RMM - RNN/D<emph style="super">c</emph>}.</s> <s xml:id="echoid-s4525" xml:space="preserve"/> </p> <div xml:id="echoid-div662" type="float" level="2" n="9"> <note position="right" xlink:label="note-0165-04" xlink:href="note-0165-04a" xml:space="preserve">427.</note> </div> <pb o="108" file="0166" n="180" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div664" type="section" level="1" n="186"> <head xml:id="echoid-head263" xml:space="preserve">SCHOLIUM. 6</head> <head xml:id="echoid-head264" xml:space="preserve">De Computatione motuum Apſidum in curvis parum <lb/>cum circulo differentibus.</head> <p> <s xml:id="echoid-s4526" xml:space="preserve">Apſides dicuntur extremitates axeos majoris Ellipſeos in qua movetur cor-<lb/>pus, quod vi ad focum tendente retinetur. </s> <s xml:id="echoid-s4527" xml:space="preserve">Agitur hìc de motus Apſidum <lb/>determinatione, id eſt de motu angulari Ellipſeos, poſitâ vi, quæ ſequatur <lb/>rationem poteſtatis cujuſcunque diſtantiæ, in quo caſu motus ad Elliptin <lb/>mobilem referri non poterit, niſi agatur de curvâ à circulo parum diffe-<lb/>rente <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4528" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">425.</note> <p> <s xml:id="echoid-s4529" xml:space="preserve">Lemmatica autem propoſitio præmittenda eſt. </s> <s xml:id="echoid-s4530" xml:space="preserve">Quadratum hujus quanti-<lb/> <anchor type="note" xlink:label="note-0166-02a" xlink:href="note-0166-02"/> tatis a-b eſt aa-2ab + bb, ut cubus formetur ſingulæ quanti-<lb/>tates hujus quadrati per a-b multiplicari debent, productum duarum prima-<lb/>rum per has eſt a<emph style="super">3</emph> - 3aab + 2abb & </s> <s xml:id="echoid-s4531" xml:space="preserve">in reliqua parte producti adſcendit b <lb/>ad majorem quàm ad primam poteſtatem.</s> <s xml:id="echoid-s4532" xml:space="preserve"/> </p> <div xml:id="echoid-div664" type="float" level="2" n="1"> <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">428.</note> </div> <p> <s xml:id="echoid-s4533" xml:space="preserve">Ut ex cubo formetur quarta poteſtas, ſingulæ cubi quantitates per a-b <lb/>multiplicari debent; </s> <s xml:id="echoid-s4534" xml:space="preserve">multiplicatis duabus primis, habemus a<emph style="super">4</emph> - 4a<emph style="super">3</emph>b + 3aabb <lb/>& </s> <s xml:id="echoid-s4535" xml:space="preserve">in reliquis quantitatibus totius poteſtatis elevatur b ultra primam poteſta-<lb/>tem.</s> <s xml:id="echoid-s4536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4537" xml:space="preserve">Siccontinuando clarè patet: </s> <s xml:id="echoid-s4538" xml:space="preserve">Siagatur de poteſtate quantitatis a-b, cujus index ſit <lb/> <anchor type="note" xlink:label="note-0166-03a" xlink:href="note-0166-03"/> n, primos terminos eſſe a<emph style="super">n</emph> - na<emph style="super">n-1</emph>b, & </s> <s xml:id="echoid-s4539" xml:space="preserve">in reliquis omnibus dabitur b ad poteſta-<lb/>tem magis elevatam.</s> <s xml:id="echoid-s4540" xml:space="preserve"/> </p> <div xml:id="echoid-div665" type="float" level="2" n="2"> <note position="left" xlink:label="note-0166-03" xlink:href="note-0166-03a" xml:space="preserve">429.</note> </div> <p> <s xml:id="echoid-s4541" xml:space="preserve">Poſitis nunc quæ in Scholio præcedenti ſunt demonſtrata; </s> <s xml:id="echoid-s4542" xml:space="preserve">dicatur H di-<lb/> <anchor type="note" xlink:label="note-0166-04a" xlink:href="note-0166-04"/> ſtantia omnium maxima AF; </s> <s xml:id="echoid-s4543" xml:space="preserve">& </s> <s xml:id="echoid-s4544" xml:space="preserve">X difterentia indeterminata inter H & </s> <s xml:id="echoid-s4545" xml:space="preserve">D; <lb/></s> <s xml:id="echoid-s4546" xml:space="preserve">reducendo duas fractiones {NN/D<emph style="super">q</emph>} + {RMM-RNN/D<emph style="super">c</emph>} ad unicam habemus <lb/>{DNN + RMM - RNN/D<emph style="super">c</emph>}, ſubſtituendo in numeratore pro D valorem <lb/>H-X, vis in Ellipſi mobili proportionalis eſt {RMM-RNN - HNN-NNX/D<emph style="super">c</emph>}. </s> <s xml:id="echoid-s4547" xml:space="preserve"><lb/>Detur nunc vis quæ ſequatur rationem cujuſcunque poteſtatis diſtantiæ, cu-<lb/>jus poteſtatis index ſit n-3, id eſt vis eſt ut D<emph style="super">n-3</emph> = {D<emph style="super">n</emph>/D<emph style="super">c</emph>} = {<emph style="ol">H-X</emph><emph style="super">n</emph>/D<emph style="super">c</emph>} = <lb/>{H<emph style="super">n</emph>-nH<emph style="super">n-1</emph>X + &</s> <s xml:id="echoid-s4548" xml:space="preserve">c<anchor type="note" xlink:href="" symbol="*"/>/D<emph style="super">c</emph>} in reliquis terminis numeratoris ultra primam poteſtatem <anchor type="note" xlink:label="note-0166-05a" xlink:href="note-0166-05"/> adſcendit X; </s> <s xml:id="echoid-s4549" xml:space="preserve">ideò hi omnes exigui ſunt reſpectu illorumqui hìc ponuntur, quia X <lb/>exigua eſt reſpectu H: </s> <s xml:id="echoid-s4550" xml:space="preserve">ponimus enim curvam cum circulo parum differrre. <lb/></s> <s xml:id="echoid-s4551" xml:space="preserve">Si nunc motus corporis quod vi hac in curva retinetur referri debeat ad mo-<lb/>tum in Ellipſi mobili, vis hæc analoga ponenda eſt cum vi qua corpus <lb/>in tali Ellipſi revera retinetur, ſunt ergo analogæ quantitates hæ <pb o="109" file="0167" n="181" rhead="MATHEMATICA. LIB. I. CAP XXI."/> {RMM - RNN + HNN - NNX/D<emph style="super">c</emph>} & </s> <s xml:id="echoid-s4552" xml:space="preserve">{H<emph style="super">n</emph>-nH<emph style="super">n-1</emph>X/D<emph style="super">c</emph>} id eſt propter <lb/>communem denominatorem, ſunt analogi numeratores.</s> <s xml:id="echoid-s4553" xml:space="preserve"/> </p> <div xml:id="echoid-div666" type="float" level="2" n="3"> <note position="left" xlink:label="note-0166-04" xlink:href="note-0166-04a" xml:space="preserve">430.</note> <note symbol="*" position="left" xlink:label="note-0166-05" xlink:href="note-0166-05a" xml:space="preserve">429.</note> </div> <p> <s xml:id="echoid-s4554" xml:space="preserve">In Ellipſi a circulo parum differenti, H cum ſemi parametro R vix dif-<lb/>fert, ut ex generatione Ellipſeos <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s4555" xml:space="preserve">parametri definitione ſequitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4556" xml:space="preserve">er- <anchor type="note" xlink:label="note-0167-01a" xlink:href="note-0167-01"/> go -RNN HNN ſeſe mutuo deſtruunt & </s> <s xml:id="echoid-s4557" xml:space="preserve">RMM fit HMM; </s> <s xml:id="echoid-s4558" xml:space="preserve">quanti-<lb/> <anchor type="note" xlink:label="note-0167-02a" xlink:href="note-0167-02"/> tatesque analogæ ſunt HMM-NNX & </s> <s xml:id="echoid-s4559" xml:space="preserve">H<emph style="super">n</emph>-nH<emph style="super">n-1</emph>X, id eſt partes con-<lb/>ſtantes ſunt inter ſe ut indeterminatæ quæ per X multiplicantur; </s> <s xml:id="echoid-s4560" xml:space="preserve">ergo HMM, <lb/>NNX :</s> <s xml:id="echoid-s4561" xml:space="preserve">: H<emph style="super">n</emph>, nH<emph style="super">n-1</emph>X: </s> <s xml:id="echoid-s4562" xml:space="preserve">dividendo antecedentia per H, conſequentia per X, & </s> <s xml:id="echoid-s4563" xml:space="preserve"><lb/>dividendo terminos ſecundæ rationis per H<emph style="super">n-1</emph> habemus <lb/>MM, NN :</s> <s xml:id="echoid-s4564" xml:space="preserve">: I, n. </s> <s xml:id="echoid-s4565" xml:space="preserve">& </s> <s xml:id="echoid-s4566" xml:space="preserve"><lb/>M, N :</s> <s xml:id="echoid-s4567" xml:space="preserve">: I, I n</s> </p> <div xml:id="echoid-div667" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0167-01" xlink:href="note-0167-01a" xml:space="preserve">397.</note> <note symbol="*" position="right" xlink:label="note-0167-02" xlink:href="note-0167-02a" xml:space="preserve">La Hire <lb/>ſect. con. <lb/>det. poſt. <lb/>pro. 3. lib <lb/>3.</note> </div> <p style="it"> <s xml:id="echoid-s4568" xml:space="preserve">Id eſt, motus angularis corporis in Ellipſi translatd ſe habet ad ipſius motum <lb/> <anchor type="note" xlink:label="note-0167-03a" xlink:href="note-0167-03"/> angularem in eadem Ellipſi quieſcente, ut unitas ad radicem quadratam numeri, <lb/>qui tribus excedit indicem poteſtatis, cujus rationem vis ſequitur</s> </p> <div xml:id="echoid-div668" type="float" level="2" n="5"> <note position="right" xlink:label="note-0167-03" xlink:href="note-0167-03a" xml:space="preserve">431.</note> </div> <p> <s xml:id="echoid-s4569" xml:space="preserve">Ex dato igitur motu angulari curvæ, poteſtas quam ſequitur vis detegitur <lb/>& </s> <s xml:id="echoid-s4570" xml:space="preserve">vice verſa ex datâ poteſtate detegitur motus curvæ angularis.</s> <s xml:id="echoid-s4571" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4572" xml:space="preserve">Exemplum unicum dabo, quod uſum ſuum habet in Aſtronomicis Detur cor-<lb/> <anchor type="note" xlink:label="note-0167-04a" xlink:href="note-0167-04"/> pus quod movetur in Ellipſi quæ ſingulis revolutionibus tribus gradibus progre-<lb/>diatur, id eſt motus ipſius in curva translata eſt 363 grad dum m orbe qui-<lb/>eſcente foret 360. </s> <s xml:id="echoid-s4573" xml:space="preserve">grad.</s> <s xml:id="echoid-s4574" xml:space="preserve">; M ergo ad N, ut 363. </s> <s xml:id="echoid-s4575" xml:space="preserve">ad 360. </s> <s xml:id="echoid-s4576" xml:space="preserve">aut ut 121 ad 120; <lb/></s> <s xml:id="echoid-s4577" xml:space="preserve">& </s> <s xml:id="echoid-s4578" xml:space="preserve">MM ad NN ut 14641, ad 14400: </s> <s xml:id="echoid-s4579" xml:space="preserve">ergo n = {14400/14641}, & </s> <s xml:id="echoid-s4580" xml:space="preserve">poteſtas diſtantiæ <lb/>cujus proportionem ſequitur vis eſt {14400/14641} - 3 = -{29523/14641} quare vis eſt reci-<lb/>procè ut D<emph style="super">2</emph>{9523/14641} = D<emph style="super">2</emph>{241/14641} = D<emph style="super">2</emph>{4/243} proximè.</s> <s xml:id="echoid-s4581" xml:space="preserve"/> </p> <div xml:id="echoid-div669" type="float" level="2" n="6"> <note position="right" xlink:label="note-0167-04" xlink:href="note-0167-04a" xml:space="preserve">432.</note> </div> </div> <div xml:id="echoid-div671" type="section" level="1" n="187"> <head xml:id="echoid-head265" xml:space="preserve">LIBRI I. PARS IV.</head> <head xml:id="echoid-head266" xml:space="preserve">De Viribus inſitis, & Colliſione <lb/>corporum.</head> <head xml:id="echoid-head267" xml:space="preserve">CAPUT XXII.</head> <head xml:id="echoid-head268" xml:space="preserve">De Viribus corporibus motis inſitis.</head> <p> <s xml:id="echoid-s4582" xml:space="preserve">Vi inſitâ corpus de loco in locum transferri diximus <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0167-05a" xlink:href="note-0167-05"/> de virium comparatione nunc agendum; </s> <s xml:id="echoid-s4583" xml:space="preserve">quod ut or-<lb/>dine fiat, de harum geneſi quædam præmittenda erunt.</s> <s xml:id="echoid-s4584" xml:space="preserve"/> </p> <div xml:id="echoid-div671" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0167-05" xlink:href="note-0167-05a" xml:space="preserve">12.</note> </div> <p> <s xml:id="echoid-s4585" xml:space="preserve">Vidimus antea corpus ex loco moveri, ſi preſſio, con-<lb/>traria preſſione non deſtructa, in illud agat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4586" xml:space="preserve">quod ergo <anchor type="note" xlink:label="note-0167-06a" xlink:href="note-0167-06"/> obtinebit, ſi corpus nullo obſtaculo retineatur: </s> <s xml:id="echoid-s4587" xml:space="preserve">quacunque <lb/> <anchor type="note" xlink:label="note-0167-07a" xlink:href="note-0167-07"/> celeritate corpus cedit hanc in perpetuum ſervabit quamdiu <pb o="110" file="0168" n="182" rhead="PHYSICES ELEMENTA"/> causâ extraneâ non deſtruitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4588" xml:space="preserve">Si continuetur preſſio in <anchor type="note" xlink:label="note-0168-01a" xlink:href="note-0168-01"/> corpus, augetur celeritas jam acquiſita, illudque quam diu <lb/>corpus premitur.</s> <s xml:id="echoid-s4589" xml:space="preserve"/> </p> <div xml:id="echoid-div672" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0167-06" xlink:href="note-0167-06a" xml:space="preserve">101.</note> <note position="right" xlink:label="note-0167-07" xlink:href="note-0167-07a" xml:space="preserve">433.</note> <note symbol="*" position="left" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">2432</note> </div> <p> <s xml:id="echoid-s4590" xml:space="preserve">Nulla unquam datur preſſio ſine reactione ipſi preſſioni <lb/> <anchor type="note" xlink:label="note-0168-02a" xlink:href="note-0168-02"/> æquali <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4591" xml:space="preserve">uhi non contraria preſſione deſtruitur, ſed ob- <anchor type="note" xlink:label="note-0168-03a" xlink:href="note-0168-03"/> ſtaculum movet preſſio, vimque generat, ex obſtaculi in-<lb/>ertiâ oritur reſiſtentia, aut reactio.</s> <s xml:id="echoid-s4592" xml:space="preserve"/> </p> <div xml:id="echoid-div673" type="float" level="2" n="3"> <note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">434.</note> <note symbol="*" position="left" xlink:label="note-0168-03" xlink:href="note-0168-03a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s4593" xml:space="preserve">Pro parte ſæpe contrariâ preſſione deſtruitur preſſio, quod <lb/>ſupereſt in hoc caſu movet obſtaculum, & </s> <s xml:id="echoid-s4594" xml:space="preserve">vim generat; </s> <s xml:id="echoid-s4595" xml:space="preserve">ſic <lb/>navis quæ fune trahitur, ab aquâ patitur reſiſtentiam, quam-<lb/>diu hæc minor eſt preſſione illâ, qua funis trahitur, auge-<lb/>tur navis celeritas, & </s> <s xml:id="echoid-s4596" xml:space="preserve">reactio, quæ actioni æqualis eſt, cum <lb/>utramque partem verſus funis æqualiter diſtentatur, pro <lb/>parte inertiæ navis tribuenda eſt. </s> <s xml:id="echoid-s4597" xml:space="preserve">Ubi, auctâ celeritate, <lb/>eo uſque reſiſtentia aquæ crevit, ut ſola actionem deſtruat, <lb/>qua navis protrahitur, motu æquabili, viinſitâ, progredi-<lb/>tur hæc; </s> <s xml:id="echoid-s4598" xml:space="preserve">duabus preſſionibus in hanc agentibus ſeſe mutuo <lb/>deſtruentibus.</s> <s xml:id="echoid-s4599" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4600" xml:space="preserve">In omni caſu in quo preſſione obſtaculum movetur, aut hu-<lb/> <anchor type="note" xlink:label="note-0168-04a" xlink:href="note-0168-04"/> jus motus mutatur, non contrariâ preſſione in totum de-<lb/>ſtruitur preſſio, & </s> <s xml:id="echoid-s4601" xml:space="preserve">vis generatur.</s> <s xml:id="echoid-s4602" xml:space="preserve"/> </p> <div xml:id="echoid-div674" type="float" level="2" n="4"> <note position="left" xlink:label="note-0168-04" xlink:href="note-0168-04a" xml:space="preserve">435.</note> </div> <p> <s xml:id="echoid-s4603" xml:space="preserve">Clare etiam patet preſſionem minuere poſſe corporis cele-<lb/> <anchor type="note" xlink:label="note-0168-05a" xlink:href="note-0168-05"/> ritatem, ideoque vim; </s> <s xml:id="echoid-s4604" xml:space="preserve">eodem modo ac auget celeritatem <lb/>& </s> <s xml:id="echoid-s4605" xml:space="preserve">vim.</s> <s xml:id="echoid-s4606" xml:space="preserve"/> </p> <div xml:id="echoid-div675" type="float" level="2" n="5"> <note position="left" xlink:label="note-0168-05" xlink:href="note-0168-05a" xml:space="preserve">436.</note> </div> <p> <s xml:id="echoid-s4607" xml:space="preserve">Videmus, vim eſſe effectum integrum preſſionis, quæ <lb/>per tempus finitum in corpus egit, preſſio autem ipſa, ſingulis <lb/>momentis infinite exiguis deſtruitur. </s> <s xml:id="echoid-s4608" xml:space="preserve">Ergo preſſio omnis <lb/> <anchor type="note" xlink:label="note-0168-06a" xlink:href="note-0168-06"/> reſpectu vis inſitœ eſt infinite exigua. </s> <s xml:id="echoid-s4609" xml:space="preserve">Id circo vis minima <lb/> <anchor type="note" xlink:label="note-0168-07a" xlink:href="note-0168-07"/> maximam poteſt ſuper are preſſionem.</s> <s xml:id="echoid-s4610" xml:space="preserve"/> </p> <div xml:id="echoid-div676" type="float" level="2" n="6"> <note position="left" xlink:label="note-0168-06" xlink:href="note-0168-06a" xml:space="preserve">437.</note> <note position="left" xlink:label="note-0168-07" xlink:href="note-0168-07a" xml:space="preserve">438.</note> </div> <p> <s xml:id="echoid-s4611" xml:space="preserve">Qui conati ſunt experimentis preſſionem cum vi inſitâ <lb/>conferre effectum preſſionis conſiderarunt in quo corpus <lb/>fuit confractum, aut partes intropreſſæ, quod ſine motu <lb/>locali, ideoque geneſi vis inſitæ <anchor type="note" xlink:href="" symbol="*"/>, fieri non potuit, cujus <anchor type="note" xlink:label="note-0168-08a" xlink:href="note-0168-08"/> vis inſitæ effectus, cum effectu alîus vis fuit collatus.</s> <s xml:id="echoid-s4612" xml:space="preserve"/> </p> <div xml:id="echoid-div677" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0168-08" xlink:href="note-0168-08a" xml:space="preserve">435.</note> </div> <p> <s xml:id="echoid-s4613" xml:space="preserve">In his omnibus non agitur de preſſione infinite magna, <lb/>quæ tempore finito vim generat infinite magnam. </s> <s xml:id="echoid-s4614" xml:space="preserve">Quan- <pb file="0169" n="183"/> <anchor type="figure" xlink:label="fig-0169-01a" xlink:href="fig-0169-01"/> <pb file="0169a" n="184"/> <pb file="0170" n="185"/> <pb o="111" file="0171" n="186" rhead="MATHEMATICA. LIB. I. CAP. XXII."/> do preſſio vim generat non in acceleratione æquales gradus <lb/>velocitatis æquali actione communicantur; </s> <s xml:id="echoid-s4615" xml:space="preserve">ut enim æquales <lb/> <anchor type="note" xlink:label="note-0171-01a" xlink:href="note-0171-01"/> gradus velocitatis corporibus æqualibus, quorum unum quie-<lb/>ſcit, alterum movetur, æqualibus actionibus communicentur; <lb/></s> <s xml:id="echoid-s4616" xml:space="preserve">requiritur ut illud quod in corpora agit reſpectu utriuſque <lb/>eandem habeat relationem; </s> <s xml:id="echoid-s4617" xml:space="preserve">id eſt, deſideratur ut cauſa mo-<lb/>vens eadem velocitate cum corpore moto feratur, in quod <lb/>tunc poterit agere ut in corpus quieſcens: </s> <s xml:id="echoid-s4618" xml:space="preserve">actio autem qua <lb/>cauſa movens transfertur ſuper addenda eſt actioni hujus <lb/>ipſius, ut habeamus actionem integram qua corpus move-<lb/>tur. </s> <s xml:id="echoid-s4619" xml:space="preserve">Unde deducimus difficilius corpus acceler ari quam mo-<lb/> <anchor type="note" xlink:label="note-0171-02a" xlink:href="note-0171-02"/> veri.</s> <s xml:id="echoid-s4620" xml:space="preserve"/> </p> <div xml:id="echoid-div678" type="float" level="2" n="8"> <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a"> <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0169-01"/> </figure> <note position="right" xlink:label="note-0171-01" xlink:href="note-0171-01a" xml:space="preserve">439.</note> <note position="right" xlink:label="note-0171-02" xlink:href="note-0171-02a" xml:space="preserve">440.</note> </div> <p> <s xml:id="echoid-s4621" xml:space="preserve">Sint elaſtra infinite parva e, e, e, e, &</s> <s xml:id="echoid-s4622" xml:space="preserve">c, juncta inter ſe, <lb/> <anchor type="note" xlink:label="note-0171-03a" xlink:href="note-0171-03"/> & </s> <s xml:id="echoid-s4623" xml:space="preserve">flexa, quæ, ſi ad priſtinam redeant figuram, illam ac <lb/> <anchor type="note" xlink:label="note-0171-04a" xlink:href="note-0171-04"/> quirant, quæ in E repræſentatur, & </s> <s xml:id="echoid-s4624" xml:space="preserve">per ſpatium infinite <lb/>exiguum ſeſe expandant. </s> <s xml:id="echoid-s4625" xml:space="preserve">Elaſtrorum hæc eſt proprietas, <lb/>ut, ſi, dum ſe expandunt, in corpus ſibi relictum premant, <lb/>huic vim integram, cum qua ſe expandunt, communicent, <lb/>ſi ad partem oppoſitam obſtaculo immobili inſiſtant. </s> <s xml:id="echoid-s4626" xml:space="preserve">Ela-<lb/>ſtrum E communicat corpori P gradum velocitatis infinitè <lb/>exiguum. </s> <s xml:id="echoid-s4627" xml:space="preserve">Ut elaſtrum ſequens corpori æqualem gradum <lb/>velocitatis communicet, requiritur ut elaſtrum, dum ſeſe <lb/>expandit, ea velocitate feratur, quam corpus jam acqui-<lb/>ſivit, aliter non ageret in corpus motum, ut E in corpus <lb/>quieſcens egit; </s> <s xml:id="echoid-s4628" xml:space="preserve">præterea requiritur, ut in hoc motu inſi-<lb/>ſtat Elaſtrum translatum obſtaculo, quod verſus partem op-<lb/>poſitam cedere nequeat; </s> <s xml:id="echoid-s4629" xml:space="preserve">id eſt propellendum eſt ea vi, <lb/>qua hoc propellit corpus; </s> <s xml:id="echoid-s4630" xml:space="preserve">quod obtinebit, ſi elaſtro ſimili <lb/>ſeſe expandente propellatur. </s> <s xml:id="echoid-s4631" xml:space="preserve">Duo ergo elaſtra eodem mo-<lb/>mento ſeſe expandentia requiruntur, ut ſecundus gradus <lb/>celeritatis corpori communicetur, id eſt vis deſidera-<lb/>tur dupla illius, qua primus gradus corpori communicatur. <lb/></s> <s xml:id="echoid-s4632" xml:space="preserve">Simili demonſtratione patebit, tria elaſtra, eodem momen-<lb/>to ſeſe expandentia, aut vim triplam requiri, ut communi-<lb/>cetur tertius velocitatis gradus & </s> <s xml:id="echoid-s4633" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s4634" xml:space="preserve">Poſitis <lb/>nempe gradibus velocitatis infinitè exiguis ne in ſingulis <pb o="112" file="0172" n="187" rhead="PHYSICES ELEMENTA"/> gradibus varii gradus dentur, & </s> <s xml:id="echoid-s4635" xml:space="preserve">poſitis elaſtris ſine inertiâ, <lb/>ne ad hæc transferenda vis quædam conſumatur, quæ ut <lb/>Mathematica ſit demonftratio ponenda ſunt. </s> <s xml:id="echoid-s4636" xml:space="preserve">Patet ergo <lb/>vim, qua gradu infinite exiguo corporis celeritas augetur, <lb/>eo majorem deſiderari, quo corpus majorem jam acquiſivit <lb/>celeritatem, vimque hanc in ratione celeritatis jam acquiſi-<lb/>tæ augeri; </s> <s xml:id="echoid-s4637" xml:space="preserve">unde ſequitur corpus accelerationi reſiſtere in ra-<lb/> <anchor type="note" xlink:label="note-0172-01a" xlink:href="note-0172-01"/> tione velocitatis ſuæ. </s> <s xml:id="echoid-s4638" xml:space="preserve">Eademque actione gradum quemcun-<lb/>que velocitatis tolli qua communicari potuit.</s> <s xml:id="echoid-s4639" xml:space="preserve"/> </p> <div xml:id="echoid-div679" type="float" level="2" n="9"> <note position="right" xlink:label="note-0171-03" xlink:href="note-0171-03a" xml:space="preserve">441.</note> <note position="right" xlink:label="note-0171-04" xlink:href="note-0171-04a" xml:space="preserve"><emph style="sc">TAB. XVI.</emph> <lb/>fig. 1.</note> <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">442.</note> </div> <p> <s xml:id="echoid-s4640" xml:space="preserve">Unde ſequitur difficilius corpus accelerari quam retarda-<lb/> <anchor type="note" xlink:label="note-0172-02a" xlink:href="note-0172-02"/> ri. </s> <s xml:id="echoid-s4641" xml:space="preserve">Si Ex. </s> <s xml:id="echoid-s4642" xml:space="preserve">gr. </s> <s xml:id="echoid-s4643" xml:space="preserve">corpus decem habeat gradus velocitatis, mi-<lb/>nori impetu tollitur decimus, quàm communicatur unde-<lb/>cimus.</s> <s xml:id="echoid-s4644" xml:space="preserve"/> </p> <div xml:id="echoid-div680" type="float" level="2" n="10"> <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">443.</note> </div> <p> <s xml:id="echoid-s4645" xml:space="preserve">Etiam patet, corporis, quod velocitate finita fertur, id <lb/> <anchor type="note" xlink:label="note-0172-03a" xlink:href="note-0172-03"/> eſt quod habet gradus velocitatis infinitè exiguos infinito nu-<lb/>mero, velocitatem gradu infinitè exiguo non poſſe augeri, <lb/>niſi actione in infinitum ſuperante actionem, qua æqualis gra-<lb/>dus infinite exiguus communicari poſſet corpori quieſcen-<lb/>ti <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4646" xml:space="preserve"/> </p> <div xml:id="echoid-div681" type="float" level="2" n="11"> <note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">444.</note> </div> <note symbol="*" position="left" xml:space="preserve">442.</note> <p> <s xml:id="echoid-s4647" xml:space="preserve">Et ne quis objiciat demonftrationem locum non habere, <lb/> <anchor type="note" xlink:label="note-0172-05a" xlink:href="note-0172-05"/> ſi ſucceſſiva non detur, qualem poſuimus, Elaſtrorum re-<lb/>laxatio; </s> <s xml:id="echoid-s4648" xml:space="preserve">ſed velocitatem communicari corpori quieſcenti pro-<lb/>portionalem numero illorum quæ ſimul relaxantur. </s> <s xml:id="echoid-s4649" xml:space="preserve">Reſp. <lb/></s> <s xml:id="echoid-s4650" xml:space="preserve">Talem quidem eſſe velocitatem Elaſterii primi ſepoſitâ, ut <lb/>fecimus, horum inertiâ, & </s> <s xml:id="echoid-s4651" xml:space="preserve">ſepoſitâ omni actione in corpus; </s> <s xml:id="echoid-s4652" xml:space="preserve"><lb/>poſitâ autem hac negamus velocitate tali moveri elaſterium <lb/>primum, quod non corpore celerius moveri poteſt; </s> <s xml:id="echoid-s4653" xml:space="preserve">hujus <lb/>autem celeritatem ex præcedenti demonſtratione deduci de-<lb/>bere liquet, quia relaxatis ſimul elaſteriis, corpus tamen <lb/>ſucceſſivè omnes gradus velocitatis ſuæ acquirit ita, ut de-<lb/>monſtrata de diverſis elaſteriis referri debeant in hoc caſu <lb/>ad ſucceſſivam partium relaxionem in Elaſtris.</s> <s xml:id="echoid-s4654" xml:space="preserve"/> </p> <div xml:id="echoid-div682" type="float" level="2" n="12"> <note position="left" xlink:label="note-0172-05" xlink:href="note-0172-05a" xml:space="preserve">445.</note> </div> <p> <s xml:id="echoid-s4655" xml:space="preserve">Ex præcedenti demonſtratione <anchor type="note" xlink:href="" symbol="*"/> etiam deducimus, juxta <anchor type="note" xlink:label="note-0172-06a" xlink:href="note-0172-06"/> quam rationem, auctâ corporis velocitate, augeatur vis cor-<lb/> <anchor type="note" xlink:label="note-0172-07a" xlink:href="note-0172-07"/> pori inſita. </s> <s xml:id="echoid-s4656" xml:space="preserve">Elaſteria ſeſe expandentia agunt in corpus, cui <lb/>nullum reſiſtit obſtaculum; </s> <s xml:id="echoid-s4657" xml:space="preserve">ideo integram qua ſe expandunt <pb o="113" file="0173" n="188" rhead="MATHEMATICA. LIB. I. CAR. XXII."/> vim corpori communicant; </s> <s xml:id="echoid-s4658" xml:space="preserve">cûm autem elaſteria ſint æqua-<lb/>lia, vires ſunt ut numeri Elaſteriorum, quorum expanſione <lb/>communicantur. </s> <s xml:id="echoid-s4659" xml:space="preserve">Corpus verò expanſione Elaſteriorum non <lb/>poteſt celeritatem acquirere, miſi motu accelerato, ita ut <lb/>per ſingulos gradus minores velocitatis tranſeat. </s> <s xml:id="echoid-s4660" xml:space="preserve">Sit A F <lb/> <anchor type="note" xlink:label="note-0173-01a" xlink:href="note-0173-01"/> celeritas corporis; </s> <s xml:id="echoid-s4661" xml:space="preserve">A b, bc, cd, & </s> <s xml:id="echoid-s4662" xml:space="preserve">c. </s> <s xml:id="echoid-s4663" xml:space="preserve">gradus infinitè exi-<lb/>gui celeritatis, A b primus, bc ſecundus, & </s> <s xml:id="echoid-s4664" xml:space="preserve">c. </s> <s xml:id="echoid-s4665" xml:space="preserve">per quos o-<lb/>mnes tranſit corpus antequam acquirat celeritatem AF. <lb/></s> <s xml:id="echoid-s4666" xml:space="preserve">Parallelogramma A bhe, bcif, cdlg, & </s> <s xml:id="echoid-s4667" xml:space="preserve">c ſunt in-<lb/>ter ſe reſpectivè, ut numeri Elaſteriorum, quibus gradus <lb/>velocitatis primus, ſecundus, tertius, &</s> <s xml:id="echoid-s4668" xml:space="preserve">c. </s> <s xml:id="echoid-s4669" xml:space="preserve">acquiruntur; </s> <s xml:id="echoid-s4670" xml:space="preserve"><lb/>ideoque areæ A dle, AFG e, ſunt inter ſe ut numerie-<lb/>laſteriorum, quibus velocitates A d, AF acquiruntur, id <lb/>eſt ſunt hæ areæ inter ſe ut Vires ejuſdem corporis, aut <lb/> <anchor type="note" xlink:label="note-0173-02a" xlink:href="note-0173-02"/> duorum corporum æqualium, hiſce velocitatibus motorum; <lb/></s> <s xml:id="echoid-s4671" xml:space="preserve">eùm autem lineæ A e, eh, bf, fi, & </s> <s xml:id="echoid-s4672" xml:space="preserve">c. </s> <s xml:id="echoid-s4673" xml:space="preserve">ſint infinitè exi-<lb/>guæ; </s> <s xml:id="echoid-s4674" xml:space="preserve">areæ A dle, AFG e à triangulis ſimilibus adl, afg, <lb/>non differunt, & </s> <s xml:id="echoid-s4675" xml:space="preserve">ſunt inter ſe ut quadrata laterum homolo-<lb/>gorum <anchor type="note" xlink:href="" symbol="*"/>, aut velocitatum A d, AF, quod confirmabimus <anchor type="note" xlink:label="note-0173-03a" xlink:href="note-0173-03"/> experimentis; </s> <s xml:id="echoid-s4676" xml:space="preserve">ſed pauca antea præmittenda ſunt.</s> <s xml:id="echoid-s4677" xml:space="preserve"/> </p> <div xml:id="echoid-div683" type="float" level="2" n="13"> <note position="left" xlink:label="note-0172-06" xlink:href="note-0172-06a" xml:space="preserve">446.</note> <note symbol="*" position="left" xlink:label="note-0172-07" xlink:href="note-0172-07a" xml:space="preserve">441.</note> <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve"><emph style="sc">TAB. XVL.</emph> <lb/>fig. 2.</note> <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">447.</note> <note symbol="*" position="right" xlink:label="note-0173-03" xlink:href="note-0173-03a" xml:space="preserve">19. El. <lb/><emph style="sc">VI</emph>.</note> </div> <p> <s xml:id="echoid-s4678" xml:space="preserve">Vires eſſe inter ſe ut quadrata velocitatum, aliis demon-<lb/>ſtrationibus, quæ ex principiis quæ nil inter ſe, neque cum <lb/>his quæ hìc ponuntur commune habent, deductis, in ſequenti-<lb/>bus etiam demonſtrabo, ubi de viribus obliquis, & </s> <s xml:id="echoid-s4679" xml:space="preserve">de reſiſten-<lb/>tia fluidorum, agam.</s> <s xml:id="echoid-s4680" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4681" xml:space="preserve">Vires, quas corpus cadendo acquirit, ſunt ut altitudines, <lb/> <anchor type="note" xlink:label="note-0173-04a" xlink:href="note-0173-04"/> quas cadendo percurrit, ab initio caſits; </s> <s xml:id="echoid-s4682" xml:space="preserve">ſunt enim hæ ut <lb/>quadrata velocitatum in fine deſcenſus <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4683" xml:space="preserve">Cum propoſitio <anchor type="note" xlink:label="note-0173-05a" xlink:href="note-0173-05"/> hæc ſequentibus Experimentis immediatè demonſtretur, <lb/>patet gravitatem, quæ æqualibus temporibus æquales corpo-<lb/> <anchor type="note" xlink:label="note-0173-06a" xlink:href="note-0173-06"/> ri communicat gradus celeritatis, <anchor type="note" xlink:href="" symbol="*"/> non iidem æquales gradus <anchor type="note" xlink:label="note-0173-07a" xlink:href="note-0173-07"/> vis communicare, <anchor type="note" xlink:href="" symbol="*"/> ſed illud, quo corpus ad Tellurem ten- <anchor type="note" xlink:label="note-0173-08a" xlink:href="note-0173-08"/> dit, cum ipſo corpore moveri <anchor type="note" xlink:href="" symbol="*"/>, dum in corpus motum <anchor type="note" xlink:label="note-0173-09a" xlink:href="note-0173-09"/> agit, ut in quieſcens.</s> <s xml:id="echoid-s4684" xml:space="preserve"/> </p> <div xml:id="echoid-div684" type="float" level="2" n="14"> <note position="right" xlink:label="note-0173-04" xlink:href="note-0173-04a" xml:space="preserve">448.</note> <note symbol="*" position="right" xlink:label="note-0173-05" xlink:href="note-0173-05a" xml:space="preserve">255.</note> <note position="right" xlink:label="note-0173-06" xlink:href="note-0173-06a" xml:space="preserve">419.</note> <note symbol="*" position="right" xlink:label="note-0173-07" xlink:href="note-0173-07a" xml:space="preserve">251.</note> <note symbol="*" position="right" xlink:label="note-0173-08" xlink:href="note-0173-08a" xml:space="preserve">442.</note> <note symbol="*" position="right" xlink:label="note-0173-09" xlink:href="note-0173-09a" xml:space="preserve">439.</note> </div> <p> <s xml:id="echoid-s4685" xml:space="preserve">Si corpora fuerint inæqualia, æqualibus velocitatibus <lb/> <anchor type="note" xlink:label="note-0173-10a" xlink:href="note-0173-10"/> mota, vires inſitæ ſunt inter ſe ut quantitates materiæ in <pb o="114" file="0174" n="189" rhead="PHYSICES ELEMENTA"/> ſingulis; </s> <s xml:id="echoid-s4686" xml:space="preserve">Vis enim corporis eſt ſumma virium omnium par-<lb/>ticularum ex quibus conſtat, & </s> <s xml:id="echoid-s4687" xml:space="preserve">ſingulæ particulæ minimæ <lb/>æquales vires habent æquales, ſivelocitate eâdem ferantur; <lb/></s> <s xml:id="echoid-s4688" xml:space="preserve">idcirco in corporibus æque velocibus ſunt vires, ut nume-<lb/>ri particularum æqualium materiæ in ſingulis.</s> <s xml:id="echoid-s4689" xml:space="preserve"/> </p> <div xml:id="echoid-div685" type="float" level="2" n="15"> <note position="right" xlink:label="note-0173-10" xlink:href="note-0173-10a" xml:space="preserve">450.</note> </div> </div> <div xml:id="echoid-div687" type="section" level="1" n="188"> <head xml:id="echoid-head269" xml:space="preserve"><emph style="sc">Machina.</emph></head> <head xml:id="echoid-head270" xml:space="preserve">Qua corporum motorum vires conferuntur.</head> <p> <s xml:id="echoid-s4690" xml:space="preserve">Aſſeris AB longitudo eſt unius pedis, latitudo decem <lb/> <anchor type="note" xlink:label="note-0174-01a" xlink:href="note-0174-01"/> pollicum, craſſities pollicum duorum. </s> <s xml:id="echoid-s4691" xml:space="preserve">Excavatur hic in <lb/> <anchor type="note" xlink:label="note-0174-02a" xlink:href="note-0174-02"/> a b c d ad profunditatem unius pollicis cum ſemiſſe, & </s> <s xml:id="echoid-s4692" xml:space="preserve"><lb/>cum pedibus EE, EE, quibus ſuſtinetur firmiter conne-<lb/>ctitur.</s> <s xml:id="echoid-s4693" xml:space="preserve"/> </p> <div xml:id="echoid-div687" type="float" level="2" n="1"> <note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">451.</note> <note position="left" xlink:label="note-0174-02" xlink:href="note-0174-02a" xml:space="preserve"><emph style="sc">TAB XVI.</emph> <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s4694" xml:space="preserve">Pedibus hiſce etiam quatuor ſuſtinentur columnæ ligneæ <lb/>CD, CD, CD, CD, ad angulos ipſius aſſeris. </s> <s xml:id="echoid-s4695" xml:space="preserve">Colu-<lb/>mnarum altitudo excedit paululum pedestres. </s> <s xml:id="echoid-s4696" xml:space="preserve">Duæ quæ pede <lb/>eodem, juxta latitudinem aſſeris poſito, inhærent, regulis <lb/>minoribus ee, ee, f, f, g, g, b, b, junguntur ita, ut <lb/>regula RR, tranſiens inter minores reſpondentes, parallela <lb/>ſit ſuperficiei aſſeris.</s> <s xml:id="echoid-s4697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4698" xml:space="preserve">Tres globi (fig. </s> <s xml:id="echoid-s4699" xml:space="preserve">4.) </s> <s xml:id="echoid-s4700" xml:space="preserve">æquales, diametri ſesquipollicis, ex <lb/>ære formantur; </s> <s xml:id="echoid-s4701" xml:space="preserve">ſolidus unus eſt C, reliqui duo cavi; </s> <s xml:id="echoid-s4702" xml:space="preserve">conſtant <lb/>hi ſinguli ex hemiſphæriis duobus A, a, & </s> <s xml:id="echoid-s4703" xml:space="preserve">B, b, quæ co-<lb/>ehleâ junguntur. </s> <s xml:id="echoid-s4704" xml:space="preserve">Globorum pondera ſunt inter ſe ut u-<lb/>num, duo, tria.</s> <s xml:id="echoid-s4705" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4706" xml:space="preserve">Ubi Experimenta inſtituenda ſunt, argillâ molli, & </s> <s xml:id="echoid-s4707" xml:space="preserve">homo-<lb/>geneâ, exacte repletur cavitas a b c d, & </s> <s xml:id="echoid-s4708" xml:space="preserve">cultro ligneo, <lb/>quod ex argillâ prominet, abraditur, ut hujus ſuperficies <lb/>non modo exacte plana ſit, ſed & </s> <s xml:id="echoid-s4709" xml:space="preserve">idem formet planum cum <lb/>illo quod ex aſſeris ſuperficie ſupereſt, cavitatiſque oras <lb/>format.</s> <s xml:id="echoid-s4710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4711" xml:space="preserve">Regula memorata RR inferius paululum juxta longitudi-<lb/>nem, excavata eſt, ut globum quemcunque ex memoratis <lb/>recipiat, qui in G videtur, dum manu M tenetur. </s> <s xml:id="echoid-s4712" xml:space="preserve">In <lb/>hoc ſitu inferius globi punctum ab argillæ ſuperficie diſtat <lb/>pollicibus novem. </s> <s xml:id="echoid-s4713" xml:space="preserve">Diſtantia hæc dupla eſt, ſiregula RR tranſ-<lb/>eat inter regulas f, f, f, f, ſi inter regulas g, g, tripla;</s> <s xml:id="echoid-s4714" xml:space="preserve"> <pb o="115" file="0175" n="190" rhead="MATHEMATICA. LIB. I. CAP. XXII."/> quadrupla verò ſi ponatur RR inter regulas b, b.</s> <s xml:id="echoid-s4715" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div689" type="section" level="1" n="189"> <head xml:id="echoid-head271" xml:space="preserve"><emph style="sc">Experimenta i<emph style="super">2</emph></emph></head> <p> <s xml:id="echoid-s4716" xml:space="preserve">Poſitâ regulâ RR, inter regulas e, e ſucceſſive dimittantur <lb/> <anchor type="note" xlink:label="note-0175-01a" xlink:href="note-0175-01"/> globi ænei tres, hiſce oleo antea illinitis; </s> <s xml:id="echoid-s4717" xml:space="preserve">hi argillâ pro parte <lb/> <anchor type="note" xlink:label="note-0175-02a" xlink:href="note-0175-02"/> immerguntur cavitateſque formant, eo majoresquo globi gra-<lb/>viores ſunt. </s> <s xml:id="echoid-s4718" xml:space="preserve">Cavitates tres A, B, C, repræſentantur in fig. </s> <s xml:id="echoid-s4719" xml:space="preserve">5.</s> <s xml:id="echoid-s4720" xml:space="preserve">; <lb/>punctis notatæ lineæ cavitatum profunditates demonſtrant.</s> <s xml:id="echoid-s4721" xml:space="preserve"/> </p> <div xml:id="echoid-div689" type="float" level="2" n="1"> <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">452.</note> <note position="right" xlink:label="note-0175-02" xlink:href="note-0175-02a" xml:space="preserve"><emph style="sc">TAB. XVI.</emph> <lb/>ſig. 3. 5.</note> </div> <p> <s xml:id="echoid-s4722" xml:space="preserve">Leviori globo cavitas A formata eſt, globum hunc voca-<lb/>mus primum; </s> <s xml:id="echoid-s4723" xml:space="preserve">ſecundum dicimus illum cujus pondus du-<lb/>plum eſt, & </s> <s xml:id="echoid-s4724" xml:space="preserve">qui cavitatem formavit B; </s> <s xml:id="echoid-s4725" xml:space="preserve">tandem tertium vo-<lb/>camus globum ſolidum, cujus pondus eſt primi triplum, & </s> <s xml:id="echoid-s4726" xml:space="preserve"><lb/>qui cadendo ab altitudine novem pollicum cavitatem forma-<lb/>vit C.</s> <s xml:id="echoid-s4727" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4728" xml:space="preserve">Si regula RR poſita ſit inter regulas f, f, & </s> <s xml:id="echoid-s4729" xml:space="preserve">globi dimit-<lb/> <anchor type="note" xlink:label="note-0175-03a" xlink:href="note-0175-03"/> tantur, cavitates formantur, quæ infig. </s> <s xml:id="echoid-s4730" xml:space="preserve">5. </s> <s xml:id="echoid-s4731" xml:space="preserve">notantur litteris B, <lb/>D, E.</s> <s xml:id="echoid-s4732" xml:space="preserve"/> </p> <div xml:id="echoid-div690" type="float" level="2" n="2"> <note position="right" xlink:label="note-0175-03" xlink:href="note-0175-03a" xml:space="preserve">453.</note> </div> <p> <s xml:id="echoid-s4733" xml:space="preserve">Si RR detur inter g, g, & </s> <s xml:id="echoid-s4734" xml:space="preserve">globi primus & </s> <s xml:id="echoid-s4735" xml:space="preserve">ſecundus di-<lb/> <anchor type="note" xlink:label="note-0175-04a" xlink:href="note-0175-04"/> mittantur, cavitates formantur C, E. </s> <s xml:id="echoid-s4736" xml:space="preserve">(fig. </s> <s xml:id="echoid-s4737" xml:space="preserve">5.)</s> <s xml:id="echoid-s4738" xml:space="preserve"/> </p> <div xml:id="echoid-div691" type="float" level="2" n="3"> <note position="right" xlink:label="note-0175-04" xlink:href="note-0175-04a" xml:space="preserve">454.</note> </div> <p> <s xml:id="echoid-s4739" xml:space="preserve">Tandem dimiſſo ab altitudine maximâ, poſitâ RR inter <lb/> <anchor type="note" xlink:label="note-0175-05a" xlink:href="note-0175-05"/> b, b, globo primo cavitas formatur D. </s> <s xml:id="echoid-s4740" xml:space="preserve">(fig. </s> <s xml:id="echoid-s4741" xml:space="preserve">5.)</s> <s xml:id="echoid-s4742" xml:space="preserve"/> </p> <div xml:id="echoid-div692" type="float" level="2" n="4"> <note position="right" xlink:label="note-0175-05" xlink:href="note-0175-05a" xml:space="preserve">455.</note> </div> <p> <s xml:id="echoid-s4743" xml:space="preserve">Ipſæ autem cavitates ſunt ſphæræ ſegmenta quæ ſunt in-<lb/> <anchor type="note" xlink:label="note-0175-06a" xlink:href="note-0175-06"/> ter ſe ut numeri in ipſis poſiti 1. </s> <s xml:id="echoid-s4744" xml:space="preserve">2. </s> <s xml:id="echoid-s4745" xml:space="preserve">3. </s> <s xml:id="echoid-s4746" xml:space="preserve">4. </s> <s xml:id="echoid-s4747" xml:space="preserve">6.</s> <s xml:id="echoid-s4748" xml:space="preserve"/> </p> <div xml:id="echoid-div693" type="float" level="2" n="5"> <note position="right" xlink:label="note-0175-06" xlink:href="note-0175-06a" xml:space="preserve">456.</note> </div> <p> <s xml:id="echoid-s4749" xml:space="preserve">Ut pateat, his Experimentis, quæ de viribus ſunt demon-<lb/>ſtrata, confirmari, conſiderandum, vim inſitam illud eſſe <lb/> <anchor type="note" xlink:label="note-0175-07a" xlink:href="note-0175-07"/> (quodcunque hoc fuerit) quod datur in corpore moto, & </s> <s xml:id="echoid-s4750" xml:space="preserve"><lb/>non datur in corpore quieſcente, id eſt, illud quo corpus <lb/>motum, in obſtaculum incurrens, in hoc agit; </s> <s xml:id="echoid-s4751" xml:space="preserve">Corpus autem <lb/>ipſum dumagit, nullam patitur actionem, exceptâ reactione <lb/>ex obſtaculi reſiſtentiâ, quæ reactio cum actioni æqualis ſit <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0175-08a" xlink:href="note-0175-08"/> ſequitur corpus pati quantum agit; </s> <s xml:id="echoid-s4752" xml:space="preserve">& </s> <s xml:id="echoid-s4753" xml:space="preserve">actionis effectum in <lb/> <anchor type="note" xlink:label="note-0175-09a" xlink:href="note-0175-09"/> obſtaculum ſequi rationem ipſius vis amiſſæ, diminutio <lb/>enim ipſius vis eſt effectus reactionis; </s> <s xml:id="echoid-s4754" xml:space="preserve">unde deducimus, vi-<lb/>res integras proportionales eſſe effectibus quibus conſumun-<lb/>tur, quod etiam aliâ conſideratione evidens eſt.</s> <s xml:id="echoid-s4755" xml:space="preserve"/> </p> <div xml:id="echoid-div694" type="float" level="2" n="6"> <note position="right" xlink:label="note-0175-07" xlink:href="note-0175-07a" xml:space="preserve">457.</note> <note symbol="*" position="right" xlink:label="note-0175-08" xlink:href="note-0175-08a" xml:space="preserve">247.</note> <note position="right" xlink:label="note-0175-09" xlink:href="note-0175-09a" xml:space="preserve">458.</note> </div> <p> <s xml:id="echoid-s4756" xml:space="preserve">Quo major eſt reſiſtentia quam patitur corpus, quo ipſi-<lb/>us actio inſtantanea major eſt, & </s> <s xml:id="echoid-s4757" xml:space="preserve">eo citius integram amittit <pb o="116" file="0176" n="191" rhead="PHYSICES ELEMENTA"/> vim, effectum tamen æqualem edit; </s> <s xml:id="echoid-s4758" xml:space="preserve">nam vis quæ reſiſten-<lb/>tiâ deſtruitur, proportionem ſequitur ipſius reſiſtentiæ, & </s> <s xml:id="echoid-s4759" xml:space="preserve"><lb/>temporis per quod egit, id eſt vis amiſſa ſequitur rationem <lb/>compoſitam reſiſtentiæ & </s> <s xml:id="echoid-s4760" xml:space="preserve">temporis; </s> <s xml:id="echoid-s4761" xml:space="preserve">quam eandem ratio-<lb/>nem ſequitur actio corporis, & </s> <s xml:id="echoid-s4762" xml:space="preserve">effectus quem edit;</s> <s xml:id="echoid-s4763" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4764" xml:space="preserve">Ita ut iterum pateat vim amiſſam effectui, quem edit dum de-<lb/> <anchor type="note" xlink:label="note-0176-01a" xlink:href="note-0176-01"/> ſtruitur, proportionalem eſſe, ſive breviori ſive longiori tem-<lb/>pore deſtruatur.</s> <s xml:id="echoid-s4765" xml:space="preserve"/> </p> <div xml:id="echoid-div695" type="float" level="2" n="7"> <note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">459.</note> </div> <p style="it"> <s xml:id="echoid-s4766" xml:space="preserve">Actio preſſionis eſt indeterminata, & </s> <s xml:id="echoid-s4767" xml:space="preserve">manente intenſitate <lb/> <anchor type="note" xlink:label="note-0176-02a" xlink:href="note-0176-02"/> ſequitur rationem temporis per quodegit. </s> <s xml:id="echoid-s4768" xml:space="preserve">Vis autem corpo-<lb/>ri inſita, datis ipſius maſſâ, & </s> <s xml:id="echoid-s4769" xml:space="preserve">velocitate, determinata eſt, <lb/>& </s> <s xml:id="echoid-s4770" xml:space="preserve">determinatum tantum edere poteſt effectum, quod brevio-<lb/>ri aut longiori præſtatur tempore; </s> <s xml:id="echoid-s4771" xml:space="preserve">pro majori aut minori, quam <lb/>patitur, reſiſtentia <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4772" xml:space="preserve"/> </p> <div xml:id="echoid-div696" type="float" level="2" n="8"> <note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">460.</note> </div> <note symbol="*" position="left" xml:space="preserve">459.</note> <p> <s xml:id="echoid-s4773" xml:space="preserve">Quando corpus cavitatem formando in argillâ, mo-<lb/> <anchor type="note" xlink:label="note-0176-04a" xlink:href="note-0176-04"/> tum cadendo acquiſitum amittit, ſuperat preſſionem qua <lb/>partes argillæ inter ſe cohærent, & </s> <s xml:id="echoid-s4774" xml:space="preserve">reſiſtentiâ, quam hanc <lb/>ſuperando preſſionem patitur, vis ipſa minuitur, & </s> <s xml:id="echoid-s4775" xml:space="preserve">tandem <lb/>in totum deſtruitur; </s> <s xml:id="echoid-s4776" xml:space="preserve">effectus ergo vis, in hoc caſu dum cor-<lb/>pus amittit motum, eſt ſeparatio partium argillæ dum juxta <lb/>ſe invicem hæ moventur, qui effectus proportionem ſequitur <lb/>numeri particularum mot arum, & </s> <s xml:id="echoid-s4777" xml:space="preserve">ſpatiiab his in motu juxta <lb/>ſe invicem percurſi, & </s> <s xml:id="echoid-s4778" xml:space="preserve">ſive hoc lentius ſive celerius fiat, <lb/>cohæſio fuperanda eadem eſt, & </s> <s xml:id="echoid-s4779" xml:space="preserve">evidentiſſimum eſt in du-<lb/>bium minime vocari poſſe, Vires eſſe æquales quæ forman-<lb/> <anchor type="note" xlink:label="note-0176-05a" xlink:href="note-0176-05"/> do in eâdem argillâ cavitates æquales, & </s> <s xml:id="echoid-s4780" xml:space="preserve">ſimiles, conſumun-<lb/>tur.</s> <s xml:id="echoid-s4781" xml:space="preserve"/> </p> <div xml:id="echoid-div697" type="float" level="2" n="9"> <note position="left" xlink:label="note-0176-04" xlink:href="note-0176-04a" xml:space="preserve">461.</note> <note position="left" xlink:label="note-0176-05" xlink:href="note-0176-05a" xml:space="preserve">462.</note> </div> <p> <s xml:id="echoid-s4782" xml:space="preserve">Dimiſſis globis tribus ab altitudine novem pollicum vires <lb/> <anchor type="note" xlink:label="note-0176-06a" xlink:href="note-0176-06"/> <anchor type="note" xlink:label="note-0176-07a" xlink:href="note-0176-07"/> ſunt ut 1. </s> <s xml:id="echoid-s4783" xml:space="preserve">2. </s> <s xml:id="echoid-s4784" xml:space="preserve">3. </s> <s xml:id="echoid-s4785" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> cavitates formantur A, B, C <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4786" xml:space="preserve">cavitates <anchor type="note" xlink:label="note-0176-08a" xlink:href="note-0176-08"/> <anchor type="note" xlink:label="note-0176-09a" xlink:href="note-0176-09"/> hiſce æquales habemus ſi globus primus ſucceſſivè dimitta-<lb/>tur ab altitudinibus novem <anchor type="note" xlink:href="" symbol="*"/>, octodecim <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s4787" xml:space="preserve">viginti ſeptem <anchor type="note" xlink:label="note-0176-10a" xlink:href="note-0176-10"/> <anchor type="note" xlink:label="note-0176-11a" xlink:href="note-0176-11"/> pollicum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4788" xml:space="preserve">in hoc ergo caſu vires ſunt ut altitudines, id eſt <anchor type="note" xlink:label="note-0176-12a" xlink:href="note-0176-12"/> ut quadrata velocitatum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4789" xml:space="preserve"/> </p> <div xml:id="echoid-div698" type="float" level="2" n="10"> <note position="left" xlink:label="note-0176-06" xlink:href="note-0176-06a" xml:space="preserve">463.</note> <note position="left" xlink:label="note-0176-07" xlink:href="note-0176-07a" xml:space="preserve"><emph style="sc">TAB. XVI.</emph> <lb/>ſig. 5.</note> <note symbol="*" position="left" xlink:label="note-0176-08" xlink:href="note-0176-08a" xml:space="preserve">450.</note> <note symbol="*" position="left" xlink:label="note-0176-09" xlink:href="note-0176-09a" xml:space="preserve">452.</note> <note symbol="*" position="left" xlink:label="note-0176-10" xlink:href="note-0176-10a" xml:space="preserve">452.</note> <note symbol="*" position="left" xlink:label="note-0176-11" xlink:href="note-0176-11a" xml:space="preserve">553.</note> <note symbol="*" position="left" xlink:label="note-0176-12" xlink:href="note-0176-12a" xml:space="preserve">454.</note> </div> <note symbol="*" position="left" xml:space="preserve">255.</note> <p> <s xml:id="echoid-s4790" xml:space="preserve">Si globus primus & </s> <s xml:id="echoid-s4791" xml:space="preserve">ſecundus dimittantur ab altitudine <lb/>octodecim pollicum vires ſunt ut 1, 2 <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s4792" xml:space="preserve">cavitates forman- <anchor type="note" xlink:label="note-0176-14a" xlink:href="note-0176-14"/> tur B & </s> <s xml:id="echoid-s4793" xml:space="preserve">D <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4794" xml:space="preserve">hiſce æquales habemus ſi globus primus di- <anchor type="note" xlink:label="note-0176-15a" xlink:href="note-0176-15"/> <pb file="0177" n="192"/> <anchor type="figure" xlink:label="fig-0177-01a" xlink:href="fig-0177-01"/> <pb file="0177a" n="193"/> <pb file="0178" n="194"/> <pb o="117" file="0179" n="195" rhead="MATHEMATICA. LIB. I. CAP. XXII."/> mittatur ſucceſſive ab altitudine octodecim pollicum <anchor type="note" xlink:href="" symbol="*"/> &</s> <s xml:id="echoid-s4795" xml:space="preserve"> <anchor type="note" xlink:label="note-0179-01a" xlink:href="note-0179-01"/> ab altitudine trium pedum <anchor type="note" xlink:href="" symbol="*"/>, ita ut iterum pateat vires eſſe <anchor type="note" xlink:label="note-0179-02a" xlink:href="note-0179-02"/> ut altitudines. </s> <s xml:id="echoid-s4796" xml:space="preserve">Concluſiones ſimiles ex aliis experimentis <lb/>deducuntur.</s> <s xml:id="echoid-s4797" xml:space="preserve"/> </p> <div xml:id="echoid-div699" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0176-14" xlink:href="note-0176-14a" xml:space="preserve">450.</note> <note symbol="*" position="left" xlink:label="note-0176-15" xlink:href="note-0176-15a" xml:space="preserve">453.</note> <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a"> <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">453.</note> <note symbol="*" position="right" xlink:label="note-0179-02" xlink:href="note-0179-02a" xml:space="preserve">455.</note> </div> <p> <s xml:id="echoid-s4798" xml:space="preserve">Dum cavitas formatur ſingula augmenta minora ſunt & </s> <s xml:id="echoid-s4799" xml:space="preserve"><lb/>inter ſe ut numeri particularum quæ cedunt, & </s> <s xml:id="echoid-s4800" xml:space="preserve">ut ſpatia <lb/>per quæ inter alias moventur, id eſt augmenta hæc ſunt ut <lb/>vires quas corpus hæc augmenta formando amittit <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s4801" xml:space="preserve">ideo- <anchor type="note" xlink:label="note-0179-03a" xlink:href="note-0179-03"/> que augmentorum ſumma, id eſt integra cavitas, ſequitur <lb/> <anchor type="note" xlink:label="note-0179-04a" xlink:href="note-0179-04"/> proportionem ſummæ virium amiſſarum, id eſt, vis amiſſæ in <lb/>formatione integræ cavitatis. </s> <s xml:id="echoid-s4802" xml:space="preserve">Quod cum memoratis <lb/>Experimentis congruit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4803" xml:space="preserve"/> </p> <div xml:id="echoid-div700" type="float" level="2" n="12"> <note position="right" xlink:label="note-0179-03" xlink:href="note-0179-03a" xml:space="preserve">* 461.</note> <note position="right" xlink:label="note-0179-04" xlink:href="note-0179-04a" xml:space="preserve">464.</note> </div> <note symbol="*" position="right" xml:space="preserve">456.</note> </div> <div xml:id="echoid-div702" type="section" level="1" n="190"> <head xml:id="echoid-head272" xml:space="preserve"><emph style="sc">Experimenta</emph> 2<emph style="super">R</emph>.</head> <p> <s xml:id="echoid-s4804" xml:space="preserve">Ex Ebore formantur cylindri duo AB, DC, diametri <lb/> <anchor type="note" xlink:label="note-0179-06a" xlink:href="note-0179-06"/> ſeſquipollicis, hemiſphericæ ſunt extremitates A, D, co-<lb/> <anchor type="note" xlink:label="note-0179-07a" xlink:href="note-0179-07"/> nicæ reliquæ B, C. </s> <s xml:id="echoid-s4805" xml:space="preserve">Minoris longitudo eſt fere duorum pol-<lb/>licum cum ſemiſſe; </s> <s xml:id="echoid-s4806" xml:space="preserve">alter duobus pollicibus longior eſt, <lb/>& </s> <s xml:id="echoid-s4807" xml:space="preserve">hujus pondus duplum exacte eſt ponderis alterius. </s> <s xml:id="echoid-s4808" xml:space="preserve">Cum <lb/>his cohærent fila in extremitatibus conicis.</s> <s xml:id="echoid-s4809" xml:space="preserve"/> </p> <div xml:id="echoid-div702" type="float" level="2" n="1"> <note position="right" xlink:label="note-0179-06" xlink:href="note-0179-06a" xml:space="preserve">465.</note> <note position="right" xlink:label="note-0179-07" xlink:href="note-0179-07a" xml:space="preserve"><emph style="sc">TAB. XVL</emph> <lb/>ſig. 6.</note> </div> <p> <s xml:id="echoid-s4810" xml:space="preserve">Deſideratur ut in extremitatibus A & </s> <s xml:id="echoid-s4811" xml:space="preserve">D axium eandem <lb/>habeat ebur elaſticitatem, quod facilius obtinetur quàm <lb/>quis forte crederet; </s> <s xml:id="echoid-s4812" xml:space="preserve">ſi ad illud attendamus ut puncta illa <lb/>coincidant cum axe ipſius dentis, quamvis in hoc pun-<lb/>cto elaſticitas omnium minima ſit, ad quod hîc non atten-<lb/>dimus.</s> <s xml:id="echoid-s4813" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4814" xml:space="preserve">Scrupulus omnis circa æqualitatem hanc elaſticitatis tol-<lb/>li poteſt, ſi duo cylindri conſtruantur æquales, & </s> <s xml:id="echoid-s4815" xml:space="preserve">ſimiles cy-<lb/>lindro DC; </s> <s xml:id="echoid-s4816" xml:space="preserve">dimittantur hi a diverſis, ſed ſemper pro am-<lb/>bobus æqualibus, altitudinibus, quod ut fiat filis ſuis ut C c <lb/>retinentur, quibus relaxatis impingunt cylindrorum partes <lb/>ut D in planum horizontale, quod ex ceruleo marmore <lb/>deſideratur, & </s> <s xml:id="echoid-s4817" xml:space="preserve">probe admodum firmatum, paululum etiam <lb/>madefactum, ut color magis ſit intenſus. </s> <s xml:id="echoid-s4818" xml:space="preserve">In impactu par-<lb/>tes elaſticæ intropremuntur maculamque notabilem admo-<lb/>dum & </s> <s xml:id="echoid-s4819" xml:space="preserve">circinnatam cylindri in marmore, aut potius in hu-<lb/>mido vapore quo obtegitur, relinquunt; </s> <s xml:id="echoid-s4820" xml:space="preserve">ſi amborum cy- <pb o="118" file="0180" n="196" rhead="PHYSICES ELEMENTA."/> lindrorum maculæ, ubi ab æqualibus altitudinibus deſcen-<lb/>dunt, in omni caſu ſint æquales, eandem cylindrosin locis <lb/>ut D elaſticitatem habere extra dubium erit. </s> <s xml:id="echoid-s4821" xml:space="preserve">His expertis <lb/>unus ex cylindris a parte C minuendus eſt, ut magnitudi-<lb/>nem habeat AB, id eſt dimidium ponderis ſui amittat.</s> <s xml:id="echoid-s4822" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4823" xml:space="preserve">Si nunc cylindrus CD dimittatur ab altitudine novem <lb/> <anchor type="note" xlink:label="note-0180-01a" xlink:href="note-0180-01"/> pollicum, & </s> <s xml:id="echoid-s4824" xml:space="preserve">AB ab altitudine octodecim pollicum maculæ <lb/>in marmore erunt quam exactiſſime æquales.</s> <s xml:id="echoid-s4825" xml:space="preserve"/> </p> <div xml:id="echoid-div703" type="float" level="2" n="2"> <note position="left" xlink:label="note-0180-01" xlink:href="note-0180-01a" xml:space="preserve">466</note> </div> <p> <s xml:id="echoid-s4826" xml:space="preserve">Si AB ab altitudine trium pedum, id eſt prioris quadru-<lb/> <anchor type="note" xlink:label="note-0180-02a" xlink:href="note-0180-02"/> plâ, dimittatur, macula major erit & </s> <s xml:id="echoid-s4827" xml:space="preserve">diametri erunt ut 5 ad <lb/>6 proximè,</s> </p> <div xml:id="echoid-div704" type="float" level="2" n="3"> <note position="left" xlink:label="note-0180-02" xlink:href="note-0180-02a" xml:space="preserve">467.</note> </div> <p> <s xml:id="echoid-s4828" xml:space="preserve">Elaſteria æqualia, & </s> <s xml:id="echoid-s4829" xml:space="preserve">ſimilia, viribus æqualibus æqualiter <lb/> <anchor type="note" xlink:label="note-0180-03a" xlink:href="note-0180-03"/> flecti quis in dubium vocavit? </s> <s xml:id="echoid-s4830" xml:space="preserve">dum enim relaxantur vires <lb/>exerunt æquales illis quibus fuere flexa: </s> <s xml:id="echoid-s4831" xml:space="preserve">æqualem autem, dum <lb/>relaxatur elaſterium, ſemper exerit vim, ubi inflexio eſt ea-<lb/>dem, ſive lentius ſive celerius fuerit inflexum, clarum ergo eſt <lb/>vires æquales habuiſſe cylindros AB & </s> <s xml:id="echoid-s4832" xml:space="preserve">CD ubi hoc cecidit <lb/>ab altitudine novem illud ab altitudine octodecim pollicum. <lb/></s> <s xml:id="echoid-s4833" xml:space="preserve">Si ambo ab altitudine cecidiſſent novem pollicum vis cy-<lb/>lindri CD dupla fuiſſet <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4834" xml:space="preserve">duplicata ergo fuit vis cylindri <anchor type="note" xlink:label="note-0180-04a" xlink:href="note-0180-04"/> AB, duplicatâ altitudine, id eſt vis ut altitudo aucta fuit; <lb/></s> <s xml:id="echoid-s4835" xml:space="preserve">id eſt ut quadratum velocitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4836" xml:space="preserve"/> </p> <div xml:id="echoid-div705" type="float" level="2" n="4"> <note position="left" xlink:label="note-0180-03" xlink:href="note-0180-03a" xml:space="preserve">468.</note> <note symbol="*" position="left" xlink:label="note-0180-04" xlink:href="note-0180-04a" xml:space="preserve">450.</note> </div> <note symbol="*" position="left" xml:space="preserve">255.</note> <p> <s xml:id="echoid-s4837" xml:space="preserve">Si autem vis creſceret ut velocitas juxta magis receptam <lb/>ſententiam, duplicanda fuiſſet velocitas ad duplicandam vim, <lb/>hanc autem in hoc caſu magis fuiſſe auctam experimento <lb/>patuit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s4838" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">467.</note> <p> <s xml:id="echoid-s4839" xml:space="preserve">Licet abunde ſatisfactum mihi videatur illis, qui vires <lb/>non ſtatuunt proportionales effectibus quibus conſumuntur, <lb/>hìc experimenta quædam nihilominus addam, quibus con-<lb/>ſtabit æqualibus edendo effectus vires conſumi æquales, licet <lb/>inæqualibus temporibus effectus edantur.</s> <s xml:id="echoid-s4840" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div707" type="section" level="1" n="191"> <head xml:id="echoid-head273" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s4841" xml:space="preserve">Formatur ex ebore (potuiſſet ex ligno duriori & </s> <s xml:id="echoid-s4842" xml:space="preserve">gravio-<lb/> <anchor type="note" xlink:label="note-0180-07a" xlink:href="note-0180-07"/> ri formari) cylindrus cujus ſectio per axem in AB repræſen-<lb/> <anchor type="note" xlink:label="note-0180-08a" xlink:href="note-0180-08"/> tatur, Angulus in hac ſectione CAD eſt 120. </s> <s xml:id="echoid-s4843" xml:space="preserve">gr. </s> <s xml:id="echoid-s4844" xml:space="preserve">angulus <lb/>EBF eſt 54 gr. </s> <s xml:id="echoid-s4845" xml:space="preserve">20′ BG æqualis eſt tribus partibus quar- <pb o="119" file="0181" n="197" rhead="MATHEMATICA. LIB. I. CAP. XXII."/> tis unius pollicis. </s> <s xml:id="echoid-s4846" xml:space="preserve">Ut cylindrus hicce ſuſpendatur, lamel-<lb/>læ æneæ perforatæ dantur H & </s> <s xml:id="echoid-s4847" xml:space="preserve">I, ut & </s> <s xml:id="echoid-s4848" xml:space="preserve">duplicatus uncus <lb/>in medio in L, cui fila connectuntur quæ per lamellarum H, <lb/>I, foramina tranſmittuntur. </s> <s xml:id="echoid-s4849" xml:space="preserve">Lamella H ita ponitur ut di-<lb/>miſſa perpendiculari ad axem, A h ſit trium partium quarta-<lb/>rum unius pollicis.</s> <s xml:id="echoid-s4850" xml:space="preserve"/> </p> <div xml:id="echoid-div707" type="float" level="2" n="1"> <note position="left" xlink:label="note-0180-07" xlink:href="note-0180-07a" xml:space="preserve">469.</note> <note position="left" xlink:label="note-0180-08" xlink:href="note-0180-08a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s4851" xml:space="preserve">Applicatur cylindrus hic machinæ, cujus ope Experi-<lb/>menta circa colliſionem corporum inſtituuntur, & </s> <s xml:id="echoid-s4852" xml:space="preserve">cujus de-<lb/>ſcriptio in capite ſequenti habetur <anchor type="note" xlink:href="" symbol="*"/> dum eidem machinæ <anchor type="note" xlink:label="note-0181-01a" xlink:href="note-0181-01"/> firmiter jungitur pixis, in eâdem deſcriptione memoranda, <lb/>argillam mollem cujus ſuperficies plana eſt, continens.</s> <s xml:id="echoid-s4853" xml:space="preserve"/> </p> <div xml:id="echoid-div708" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">491.</note> </div> <p> <s xml:id="echoid-s4854" xml:space="preserve">In argillam dimittatur cylindrus velocitate quacumque, <lb/>& </s> <s xml:id="echoid-s4855" xml:space="preserve">motum amittat cavitatem formando, extremitate A in <lb/>argillam incurrente. </s> <s xml:id="echoid-s4856" xml:space="preserve">Si, mutato paululum pixidis ſitu, eâ-<lb/>dem velocitate cylindrus in argillam impingat, extremitate <lb/>B in hanc penetrante; </s> <s xml:id="echoid-s4857" xml:space="preserve">quæcunque fuerit velocitas qua cor-<lb/>pus in utroque caſu movetur, ſi in utroque eandem habeat <lb/>velocitatem, id eſt impactione eandem vim amittat; </s> <s xml:id="echoid-s4858" xml:space="preserve">cavita-<lb/>tum diametri erunt ut 2 ad 3.</s> <s xml:id="echoid-s4859" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4860" xml:space="preserve">Cavitatum baſes, quæ ſunt ut quadrata diametrorum <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0181-02a" xlink:href="note-0181-02"/> funt ut 4 ad 9, & </s> <s xml:id="echoid-s4861" xml:space="preserve">cavitatum profunditates ut 9 ad 4, (hoc <lb/>enim ex conorum forma ſequitur) id eſt baſes ſunt inversè <lb/>ut altitudines, quare cavitates ſunt æquales <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4862" xml:space="preserve">ideoque effectus <anchor type="note" xlink:label="note-0181-03a" xlink:href="note-0181-03"/> virium æquales <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4863" xml:space="preserve">inæqualibus tamen temporibus vires <anchor type="note" xlink:label="note-0181-04a" xlink:href="note-0181-04"/> conſumuntur cum ad inæquales profunditates in argillam pe-<lb/>netrent coni.</s> <s xml:id="echoid-s4864" xml:space="preserve"/> </p> <div xml:id="echoid-div709" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">1 El. <emph style="sc">XII</emph></note> <note symbol="*" position="right" xlink:label="note-0181-03" xlink:href="note-0181-03a" xml:space="preserve">15. El, <lb/><emph style="sc">XII</emph>.</note> <note symbol="*" position="right" xlink:label="note-0181-04" xlink:href="note-0181-04a" xml:space="preserve">461.</note> </div> <p> <s xml:id="echoid-s4865" xml:space="preserve">Vires corporibus inſitæ, inter ſe differre non poſſunt niſi <lb/> <anchor type="note" xlink:label="note-0181-05a" xlink:href="note-0181-05"/> reſpectu velocitatis, aut quantitatis materiæ in corporibus: <lb/></s> <s xml:id="echoid-s4866" xml:space="preserve">ergo vires quæeunque, ex dictis <anchor type="note" xlink:href="" symbol="*"/> conferuntur inter ſe, &</s> <s xml:id="echoid-s4867" xml:space="preserve"> <anchor type="note" xlink:label="note-0181-06a" xlink:href="note-0181-06"/> ſunt in ratione compoſita quantitatum materiæ, & </s> <s xml:id="echoid-s4868" xml:space="preserve">quadra-<lb/>torum velocitatum. </s> <s xml:id="echoid-s4869" xml:space="preserve">Si igitur ſingulorum corporum maſſæ <lb/>per quadrata ſuarum velocitatum multiplicentur, producta <lb/>virium rationem exprimunt.</s> <s xml:id="echoid-s4870" xml:space="preserve"/> </p> <div xml:id="echoid-div710" type="float" level="2" n="4"> <note position="right" xlink:label="note-0181-05" xlink:href="note-0181-05a" xml:space="preserve">470.</note> <note symbol="*" position="right" xlink:label="note-0181-06" xlink:href="note-0181-06a" xml:space="preserve">447. 450.</note> </div> <p> <s xml:id="echoid-s4871" xml:space="preserve">Ex his facillime deducimus corpora cadendo vires æqua-<lb/> <anchor type="note" xlink:label="note-0181-07a" xlink:href="note-0181-07"/> les acquirere, ſi altitudines, quas deſcendendo percurrunt, <lb/>ſint inter ſe in ratione inverſa maſſarum. </s> <s xml:id="echoid-s4872" xml:space="preserve">In Experimentis <pb o="120" file="0182" n="198" rhead="PHYSICES ELEMENTA"/> hujus capitis primi cavitates, & </s> <s xml:id="echoid-s4873" xml:space="preserve">in ſecundis partium elaſti-<lb/>carum introceſſiones fuere æquales, ubi corpora cecidere <lb/>ab altitudinibus quæ erant inversè ut maſſæ.</s> <s xml:id="echoid-s4874" xml:space="preserve"/> </p> <div xml:id="echoid-div711" type="float" level="2" n="5"> <note position="right" xlink:label="note-0181-07" xlink:href="note-0181-07a" xml:space="preserve">471.</note> </div> <p> <s xml:id="echoid-s4875" xml:space="preserve">Vires vero ipſas eſſe in hac ratione inverſa maſſarum ſi <lb/> <anchor type="note" xlink:label="note-0182-01a" xlink:href="note-0182-01"/> velocitates fuerint reciprocè ut maſſæ, facile etiam liquet.</s> <s xml:id="echoid-s4876" xml:space="preserve"/> </p> <div xml:id="echoid-div712" type="float" level="2" n="6"> <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">472.</note> </div> <p> <s xml:id="echoid-s4877" xml:space="preserve">Sint maſſa corporis cujuſcunque M & </s> <s xml:id="echoid-s4878" xml:space="preserve">velocitas V; <lb/></s> <s xml:id="echoid-s4879" xml:space="preserve">alterius corporis maſſa m & </s> <s xml:id="echoid-s4880" xml:space="preserve">hujus velocitas v: </s> <s xml:id="echoid-s4881" xml:space="preserve">& </s> <s xml:id="echoid-s4882" xml:space="preserve">po-<lb/>namus m, M:</s> <s xml:id="echoid-s4883" xml:space="preserve">: V, v, id eſt M x V = m x v; </s> <s xml:id="echoid-s4884" xml:space="preserve">hinc deduci-<lb/>mus, V, v:</s> <s xml:id="echoid-s4885" xml:space="preserve">: M x V<emph style="super">q</emph>, m x v<emph style="super">q</emph>, multiplicando V & </s> <s xml:id="echoid-s4886" xml:space="preserve">v per <lb/>æquales quantitates: </s> <s xml:id="echoid-s4887" xml:space="preserve">Sed M x V<emph style="super">q</emph>, m x v<emph style="super">q</emph> ſunt ut vires <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s4888" xml:space="preserve"> <anchor type="note" xlink:label="note-0182-02a" xlink:href="note-0182-02"/> quæ ergo ſunt ut velocitates, id eſt inversè ut maſſæ.</s> <s xml:id="echoid-s4889" xml:space="preserve"/> </p> <div xml:id="echoid-div713" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0182-02" xlink:href="note-0182-02a" xml:space="preserve">470.</note> </div> </div> <div xml:id="echoid-div715" type="section" level="1" n="192"> <head xml:id="echoid-head274" xml:space="preserve">CAPUT XXIII.</head> <head xml:id="echoid-head275" xml:space="preserve">De Colliſione corporum.</head> <head xml:id="echoid-head276" xml:space="preserve"><emph style="sc">Definitio</emph> I.</head> <p style="it"> <s xml:id="echoid-s4890" xml:space="preserve">CEleritas qua duo corpora, ad ſe mutuo accedunt, aut <lb/> <anchor type="note" xlink:label="note-0182-03a" xlink:href="note-0182-03"/> ſeparantur, vocatur celeritas reſpectiva.</s> <s xml:id="echoid-s4891" xml:space="preserve"/> </p> <div xml:id="echoid-div715" type="float" level="2" n="1"> <note position="left" xlink:label="note-0182-03" xlink:href="note-0182-03a" xml:space="preserve">473.</note> </div> <p style="it"> <s xml:id="echoid-s4892" xml:space="preserve">Quando corpora ambo ad eandem partem tendunt, ad ſe <lb/> <anchor type="note" xlink:label="note-0182-04a" xlink:href="note-0182-04"/> invicem accedunt, aut ſeparantur, velocitate, quæ æqualis eſt <lb/>diſſerentiæ velocitatum abſolutarum. </s> <s xml:id="echoid-s4893" xml:space="preserve">Velocitas autem re-<lb/> <anchor type="note" xlink:label="note-0182-05a" xlink:href="note-0182-05"/> ſpectiva eſt ſumma velocitatum abſolutarum, ſi motuum di-<lb/>rectiones ſint contrariæ.</s> <s xml:id="echoid-s4894" xml:space="preserve"/> </p> <div xml:id="echoid-div716" type="float" level="2" n="2"> <note position="left" xlink:label="note-0182-04" xlink:href="note-0182-04a" xml:space="preserve">474.</note> <note position="left" xlink:label="note-0182-05" xlink:href="note-0182-05a" xml:space="preserve">475.</note> </div> </div> <div xml:id="echoid-div718" type="section" level="1" n="193"> <head xml:id="echoid-head277" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s4895" xml:space="preserve">Impactio duorum corporum dicitur directa, ſi directio <lb/> <anchor type="note" xlink:label="note-0182-06a" xlink:href="note-0182-06"/> motus, aut motuum, quando ambo moventur, tranſeat per <lb/>ſingulorum gravitatis centra; </s> <s xml:id="echoid-s4896" xml:space="preserve">ſibæc eadem linea, quœ per <lb/>ambo centra gravitatis tranſit, ſecet partes ſuperficierum quæ <lb/>in ſe mutuo incurrunt; </s> <s xml:id="echoid-s4897" xml:space="preserve">tandem ſi bæ ſuperficies quæ in ſemu-<lb/>tuo incurrunt ad lineam, quæ per centra gravitatis tranſit, <lb/>ſint perpendiculares.</s> <s xml:id="echoid-s4898" xml:space="preserve"/> </p> <div xml:id="echoid-div718" type="float" level="2" n="1"> <note position="left" xlink:label="note-0182-06" xlink:href="note-0182-06a" xml:space="preserve">476.</note> </div> </div> <div xml:id="echoid-div720" type="section" level="1" n="194"> <head xml:id="echoid-head278" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s4899" xml:space="preserve">In omni alio caſu ictus dicitur obliquus.</s> <s xml:id="echoid-s4900" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">477.</note> <p> <s xml:id="echoid-s4901" xml:space="preserve">Quando corpus motum in aliud incurrit, in hoc agit, a-<lb/> <anchor type="note" xlink:label="note-0182-08a" xlink:href="note-0182-08"/> ctioque rationem ſequitur reſiſtentiæ quam patitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4902" xml:space="preserve">&</s> <s xml:id="echoid-s4903" xml:space="preserve"> <anchor type="note" xlink:label="note-0182-09a" xlink:href="note-0182-09"/> quantum agit tantum ex vi inſitâ amittit.</s> <s xml:id="echoid-s4904" xml:space="preserve"/> </p> <div xml:id="echoid-div720" type="float" level="2" n="1"> <note position="left" xlink:label="note-0182-08" xlink:href="note-0182-08a" xml:space="preserve">478.</note> <note symbol="*" position="left" xlink:label="note-0182-09" xlink:href="note-0182-09a" xml:space="preserve">458.</note> </div> <pb o="121" file="0183" n="199" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> <p> <s xml:id="echoid-s4905" xml:space="preserve">Non hic agam de corporibus perfectè duris, talia nulla <lb/> <anchor type="note" xlink:label="note-0183-01a" xlink:href="note-0183-01"/> novimus, & </s> <s xml:id="echoid-s4906" xml:space="preserve">inutile foret in hiſce colliſionum leges deter-<lb/>minare, quod an ſine errore factum eſſet experimentis de-<lb/>terminari non poſſet.</s> <s xml:id="echoid-s4907" xml:space="preserve"/> </p> <div xml:id="echoid-div721" type="float" level="2" n="2"> <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">479.</note> </div> <p> <s xml:id="echoid-s4908" xml:space="preserve">Omnia autem corpora nobis nota conſtant ex partibus in-<lb/> <anchor type="note" xlink:label="note-0183-02a" xlink:href="note-0183-02"/> ter ſe cobærentibus, vi cujus effectum novimus, & </s> <s xml:id="echoid-s4909" xml:space="preserve">cujus <lb/>cauſa nos latet: </s> <s xml:id="echoid-s4910" xml:space="preserve">Sed verâ preſſione partes inter ſe cohærere, <lb/>cuicunque cauſæ hanc tribuamus, in dubium nemo voca-<lb/>bit.</s> <s xml:id="echoid-s4911" xml:space="preserve"/> </p> <div xml:id="echoid-div722" type="float" level="2" n="3"> <note position="right" xlink:label="note-0183-02" xlink:href="note-0183-02a" xml:space="preserve">480.</note> </div> <p> <s xml:id="echoid-s4912" xml:space="preserve">Nulla datur preſſio, quæ minimâ inſitâ vi ſuperari non <lb/>poteſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s4913" xml:space="preserve">ergo nulla datur corporum colliſio ſine quadampar- <anchor type="note" xlink:label="note-0183-03a" xlink:href="note-0183-03"/> <anchor type="note" xlink:label="note-0183-04a" xlink:href="note-0183-04"/> tium introceſſione.</s> <s xml:id="echoid-s4914" xml:space="preserve"/> </p> <div xml:id="echoid-div723" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0183-03" xlink:href="note-0183-03a" xml:space="preserve">438.</note> <note position="right" xlink:label="note-0183-04" xlink:href="note-0183-04a" xml:space="preserve">481.</note> </div> <p> <s xml:id="echoid-s4915" xml:space="preserve">De colliſione corporum in genere hoc capite agam; </s> <s xml:id="echoid-s4916" xml:space="preserve">ex-<lb/>plicandum ideo quid obtineat in corporibus non ebaſticis; <lb/></s> <s xml:id="echoid-s4917" xml:space="preserve"> <anchor type="note" xlink:label="note-0183-05a" xlink:href="note-0183-05"/> nam & </s> <s xml:id="echoid-s4918" xml:space="preserve">hoc ipſum in elaſticis locum babet, in momento in <lb/>quo corpora concurrunt, antequam partes intropreſſæ ad pri-<lb/>ſtinam figuram redeant.</s> <s xml:id="echoid-s4919" xml:space="preserve"/> </p> <div xml:id="echoid-div724" type="float" level="2" n="5"> <note position="right" xlink:label="note-0183-05" xlink:href="note-0183-05a" xml:space="preserve">482.</note> </div> <p> <s xml:id="echoid-s4920" xml:space="preserve">Hac figuræ inſtauratione corpora elaſtica ſeſe mutuo re-<lb/> <anchor type="note" xlink:label="note-0183-06a" xlink:href="note-0183-06"/> pellunt; </s> <s xml:id="echoid-s4921" xml:space="preserve">idcirco poſt ictum ſeparantur. </s> <s xml:id="echoid-s4922" xml:space="preserve">Nulla autem talis <lb/>datur actio ſi omnielaſterio deſtituantur; </s> <s xml:id="echoid-s4923" xml:space="preserve">ergo poſt impactum <lb/> <anchor type="note" xlink:label="note-0183-07a" xlink:href="note-0183-07"/> directum non ſeparantur; </s> <s xml:id="echoid-s4924" xml:space="preserve">nam in impactione hac, directio <lb/>mutari non poteſt, & </s> <s xml:id="echoid-s4925" xml:space="preserve">ideo in eâdem lineâ ambo motum <lb/>contiuuant, in qua ante ictum movebantur, & </s> <s xml:id="echoid-s4926" xml:space="preserve">in qua a ſe <lb/>invicem non repelluntur.</s> <s xml:id="echoid-s4927" xml:space="preserve"/> </p> <div xml:id="echoid-div725" type="float" level="2" n="6"> <note position="right" xlink:label="note-0183-06" xlink:href="note-0183-06a" xml:space="preserve">483.</note> <note position="right" xlink:label="note-0183-07" xlink:href="note-0183-07a" xml:space="preserve">484.</note> </div> <p> <s xml:id="echoid-s4928" xml:space="preserve">Dum partes corporum intropremuntur deſtruitur vis <anchor type="note" xlink:href="" symbol="*"/> quæ <anchor type="note" xlink:label="note-0183-08a" xlink:href="note-0183-08"/> preſſionem qua cohærent <anchor type="note" xlink:href="" symbol="*"/> ſuperat; </s> <s xml:id="echoid-s4929" xml:space="preserve">Ergo corpus in aliud <anchor type="note" xlink:label="note-0183-09a" xlink:href="note-0183-09"/> incurrere non poteſt, aut duo in ſemutuo, ſine diminutione ſum-<lb/> <anchor type="note" xlink:label="note-0183-10a" xlink:href="note-0183-10"/> mæ virium.</s> <s xml:id="echoid-s4930" xml:space="preserve"/> </p> <div xml:id="echoid-div726" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0183-08" xlink:href="note-0183-08a" xml:space="preserve">436.</note> <note symbol="*" position="right" xlink:label="note-0183-09" xlink:href="note-0183-09a" xml:space="preserve">480.</note> <note position="right" xlink:label="note-0183-10" xlink:href="note-0183-10a" xml:space="preserve">485.</note> </div> <p> <s xml:id="echoid-s4931" xml:space="preserve">In corporibus elaſticis partes ictæ ad priſtinam re-<lb/>deunt figuram, & </s> <s xml:id="echoid-s4932" xml:space="preserve">redeuntes premunt in corpus, cujus <lb/>actione introceſſere, hac preſſione nova generatur vis, ſed <lb/>de hac nondum agimus, in ipſis corporibus elaſticis datur, <lb/> <anchor type="note" xlink:label="note-0183-11a" xlink:href="note-0183-11"/> ante figuram inſtauratam, diminutio virium, de qua bic <lb/>agimus.</s> <s xml:id="echoid-s4933" xml:space="preserve"/> </p> <div xml:id="echoid-div727" type="float" level="2" n="8"> <note position="right" xlink:label="note-0183-11" xlink:href="note-0183-11a" xml:space="preserve">486.</note> </div> <p style="it"> <s xml:id="echoid-s4934" xml:space="preserve">Quando corpus, nonictu alius corporis, ſed preſſione movetur, <lb/> <anchor type="note" xlink:label="note-0183-12a" xlink:href="note-0183-12"/> ſi hæc minor ſit illa quapartes cobærent, ſine partium introceſſio-<lb/>ne corporimotus communicatur.</s> <s xml:id="echoid-s4935" xml:space="preserve"/> </p> <div xml:id="echoid-div728" type="float" level="2" n="9"> <note position="right" xlink:label="note-0183-12" xlink:href="note-0183-12a" xml:space="preserve">487.</note> </div> <pb o="122" file="0184" n="200" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s4936" xml:space="preserve">Nulla in corporum colliſione vis deſtruitur, niſi quæ ad <lb/> <anchor type="note" xlink:label="note-0184-01a" xlink:href="note-0184-01"/> partes intro premendas requiritur. </s> <s xml:id="echoid-s4937" xml:space="preserve">Ponamus primo cor-<lb/>pora ad eandem partem tendere, antecedens neceſſario tar-<lb/>dius alio movetur, & </s> <s xml:id="echoid-s4938" xml:space="preserve">ictu acceleratur, conſequens ve-<lb/>ro quia in aliud agit ex vi ſua amittit. </s> <s xml:id="echoid-s4939" xml:space="preserve">Effectus vis a-<lb/>miſſæ eſt augmentum vis in antecedente, & </s> <s xml:id="echoid-s4940" xml:space="preserve">introceſſio <lb/>partium, & </s> <s xml:id="echoid-s4941" xml:space="preserve">effectus hic valet vim amiſſam à con-<lb/>ſequente <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s4942" xml:space="preserve">Sed illa, quam acquiſivit antecedens, non <anchor type="note" xlink:label="note-0184-02a" xlink:href="note-0184-02"/> eſt vis deſtructa, ergo ſola hæc deſtruitur, qua partes in-<lb/>trocedunt. </s> <s xml:id="echoid-s4943" xml:space="preserve">Secundo, tendant corpora in partes contrari-<lb/>as, in hoc caſu corpora ambo ſibi mutuo reſiſtunt, non mo-<lb/>do inertiâ, ſed etiam viribus inſitis, quo vero major eſt re-<lb/>ſiſtentia, eo magis partes comprimuntur, eoque major par-<lb/>tium introceſſio, ita ut vires impropriè dicantur ſeſe mu-<lb/>tuo deſtruere, vi ſua corpus corpori reſiſtit, quâ natâ reſi-<lb/>ſtentiâ vis corporis alîus deſtruitur, ſuperando preſſionem <lb/>qua partes cohærent. </s> <s xml:id="echoid-s4944" xml:space="preserve">Paradoxa hæc propoſitio, vim nun-<lb/> <anchor type="note" xlink:label="note-0184-03a" xlink:href="note-0184-03"/> quam immediate vim deſtruere, experimentis extra dubium <lb/>eſt, quibus conſtat introceſſiones in corporibus ejuſdem ge-<lb/>neris, (nempe quorum partes æqualiter cohærent,) eſſe æ-<lb/>quales, ſi vires æquales ictibus deſtruantur, ſive corpora <lb/>tendant ad eandem partem; </s> <s xml:id="echoid-s4945" xml:space="preserve">ſive directionibus contrariis <lb/>ferantur, viribus æqualibus, aut utcumque inæqualibus; </s> <s xml:id="echoid-s4946" xml:space="preserve">ſive <lb/>in obicem firmum impingat corpus; </s> <s xml:id="echoid-s4947" xml:space="preserve">ut, præmifsâ machinarum <lb/>deſcriptione, exponam.</s> <s xml:id="echoid-s4948" xml:space="preserve"/> </p> <div xml:id="echoid-div729" type="float" level="2" n="10"> <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">488.</note> <note symbol="*" position="left" xlink:label="note-0184-02" xlink:href="note-0184-02a" xml:space="preserve">478</note> <note position="left" xlink:label="note-0184-03" xlink:href="note-0184-03a" xml:space="preserve">489.</note> </div> </div> <div xml:id="echoid-div731" type="section" level="1" n="195"> <head xml:id="echoid-head279" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head280" xml:space="preserve">Qua experimenta circa colliſiones corporum <lb/>inſtituuntur.</head> <p> <s xml:id="echoid-s4949" xml:space="preserve">Tabula lignea ABC, fere triangularis, & </s> <s xml:id="echoid-s4950" xml:space="preserve">verticalis, <lb/> <anchor type="note" xlink:label="note-0184-04a" xlink:href="note-0184-04"/> altitudinis circiter quatuor pedum cum ſemiſſe, & </s> <s xml:id="echoid-s4951" xml:space="preserve">latitudi-<lb/> <anchor type="note" xlink:label="note-0184-05a" xlink:href="note-0184-05"/> nis, circa baſin trianguli, trium pedum, verticaliter diſponitur.</s> <s xml:id="echoid-s4952" xml:space="preserve"/> </p> <div xml:id="echoid-div731" type="float" level="2" n="1"> <note position="left" xlink:label="note-0184-04" xlink:href="note-0184-04a" xml:space="preserve">490.</note> <note position="left" xlink:label="note-0184-05" xlink:href="note-0184-05a" xml:space="preserve"><emph style="sc">TAB. XVII</emph>.</note> </div> <p> <s xml:id="echoid-s4953" xml:space="preserve">In ſuperiori parte datur ad horizontem parallela ſciſſura st, <lb/>in qua duo clavi quadrati, aliquando plures, moventur; </s> <s xml:id="echoid-s4954" xml:space="preserve">qui <lb/>ubique cochleis, ad poſteriorem tabulæ partem applicantis <lb/>firmantur; </s> <s xml:id="echoid-s4955" xml:space="preserve">ut ex figura clavorum in V patet.</s> <s xml:id="echoid-s4956" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4957" xml:space="preserve">Super unoquoque clavo movetur tubulus quadratus X, <pb o="123" file="0185" n="201" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> poteſtque per totam clavi longitudinem firmiter cum eo <lb/>connecti cochlea e in ſuperiori parte. </s> <s xml:id="echoid-s4958" xml:space="preserve">In parte inferiori tubulis <lb/>his unci minimi junguntur; </s> <s xml:id="echoid-s4959" xml:space="preserve">quos fila tenuiſſima (aut potius <lb/>chordæ citharæ) i h, i h trajiciunt, quæ globos veluti P& </s> <s xml:id="echoid-s4960" xml:space="preserve">Q ſu-<lb/>ſtinent. </s> <s xml:id="echoid-s4961" xml:space="preserve">Fila illa annectuntur paxillis l, l; </s> <s xml:id="echoid-s4962" xml:space="preserve">quostorquendo ele-<lb/>vantur, aut deprimuntur, globi.</s> <s xml:id="echoid-s4963" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4964" xml:space="preserve">Clavus, quo globus quicunque ſuſtinetur, ita in ſcif-<lb/>ſura st ſiſtitur, ut illius centri a linea AD, quæ tabulam <lb/>in duas partes æquales verticaliter dividit, diſtantia æqualis ſit <lb/>ſemidiametro globi; </s> <s xml:id="echoid-s4965" xml:space="preserve">illudque pro omnibus globis fit, ductis <lb/>notis in tabulæ ſuperficie.</s> <s xml:id="echoid-s4966" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4967" xml:space="preserve">Tubulus cum unco, quo globus ſuſpenditur, in ea parte <lb/>clavi firmatur, ut fili a tabulæ ſuperficie diſtantia paululum <lb/>excedat ſemidiametrum globi; </s> <s xml:id="echoid-s4968" xml:space="preserve">& </s> <s xml:id="echoid-s4969" xml:space="preserve">dantur in clavis diviſio-<lb/>nes, quibus, pro magnitudine globi, ſitus tubuli determi-<lb/>natur.</s> <s xml:id="echoid-s4970" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4971" xml:space="preserve">Quando duo globi adhibentur, linea AD hos ſeparat; <lb/></s> <s xml:id="echoid-s4972" xml:space="preserve">& </s> <s xml:id="echoid-s4973" xml:space="preserve">in hoc caſu, ut & </s> <s xml:id="echoid-s4974" xml:space="preserve">quando plures adhibentur, ſi diverſæ <lb/>fuerint magnitudinis, globus maximus minoris diſtantiam a <lb/>tabula determinat, & </s> <s xml:id="echoid-s4975" xml:space="preserve">tubuli reſpondentibus clavorum divi-<lb/>ſionibus admoventur, ut globorum omnium centra æque di-<lb/>ſtent a tabula. </s> <s xml:id="echoid-s4976" xml:space="preserve">Centra illa paxillorum l converſione ad ean-<lb/>dem altitudinem reducuntur; </s> <s xml:id="echoid-s4977" xml:space="preserve">quod in omnibus Experimen-<lb/>tis obſervandum.</s> <s xml:id="echoid-s4978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4979" xml:space="preserve">Regulæ duæ æneæ EG, EG, ad horizontem parallelæ diſ-<lb/>ponuntur; </s> <s xml:id="echoid-s4980" xml:space="preserve">ſuperficies tabulæ ad illas recipiendas paululum <lb/>excavatur, ut illarum ſuperficies cum tabulæ ſuperficie con-<lb/>gruat A poſteriori utriuſque regulæ parte datur in tabula <lb/>ſciſſura, longitudinis circiter quinque pollicum, per quam <lb/>tranſit cochlea regulæ cohærens, & </s> <s xml:id="echoid-s4981" xml:space="preserve">cujus ope regula retine-<lb/>tur, & </s> <s xml:id="echoid-s4982" xml:space="preserve">transfertur per longitudinem ſciſſuræ. </s> <s xml:id="echoid-s4983" xml:space="preserve">In Experi-<lb/>mentis diſtantia extremitatis G, utriuſque regulæ, a linea <lb/>AD, æqualis eſt ſemidiametro globi, ad eandem partem <lb/>hujus lineæ ſuſpenſi, quod ut fiat diſtantiæ pro ſingulis glo-<lb/>bis notis indicandæ ſunt.</s> <s xml:id="echoid-s4984" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4985" xml:space="preserve">Diviſiones regularum tales ſunt, ut denotent angulos æ- <pb o="124" file="0186" n="202" rhead="PHYSICES ELEMENTA"/> quales, a filis, quibus globi ſuſpenduntur, percurſos.</s> <s xml:id="echoid-s4986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4987" xml:space="preserve">Uthos angulos in Experimentis menſuremus, dantur <lb/>indices quatuor, duo majores M, M, & </s> <s xml:id="echoid-s4988" xml:space="preserve">duo minores N, <lb/>N.</s> <s xml:id="echoid-s4989" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4990" xml:space="preserve">Moventur indices iſti per ſciſſuras or, or; </s> <s xml:id="echoid-s4991" xml:space="preserve">& </s> <s xml:id="echoid-s4992" xml:space="preserve">cochleis à <lb/>poſteriori parte tabulæ, proarbitrio agentis, conſtituuntur. <lb/></s> <s xml:id="echoid-s4993" xml:space="preserve">Tabulæ ſuperficies juxta ſciſſuras paululum excavatur, ad <lb/>motum indicum dirigendum; </s> <s xml:id="echoid-s4994" xml:space="preserve">majores ad tabulæ extremita-<lb/>tem pertingunt, licet ſciſſuræ extremitas ab ea fere tribus <lb/>pollicibus diſtet.</s> <s xml:id="echoid-s4995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4996" xml:space="preserve">Delineatio majorum indicum datur in figura ſeparata M; <lb/></s> <s xml:id="echoid-s4997" xml:space="preserve">in qua a b eſt lamina, quæ in cavitate in tabulæ ſuperficie <lb/>movetur; </s> <s xml:id="echoid-s4998" xml:space="preserve">c d eſt index, ad illam laminam normalis, & </s> <s xml:id="echoid-s4999" xml:space="preserve">lon-<lb/>gitudinis circiter trium pollicum.</s> <s xml:id="echoid-s5000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5001" xml:space="preserve">Datur etiam in N figura ſeparata indicum minorum; </s> <s xml:id="echoid-s5002" xml:space="preserve">ho-<lb/>rum longitudo æqualis eſt ſemidiametro minimorum globo-<lb/>rum, qui Machinæ applicantur, & </s> <s xml:id="echoid-s5003" xml:space="preserve">quorum diameter commode <lb/>ſtatuitur unius pollicis cum ſemiſſe; </s> <s xml:id="echoid-s5004" xml:space="preserve">indices hi inter majores po-<lb/>nuntur, quia illis motus globorum non impeditur; </s> <s xml:id="echoid-s5005" xml:space="preserve">aliquan-<lb/>do ambo minores in eadem ſciſſura firmantur, quando tres <lb/>anguli ab una parte menſurandi ſunt.</s> <s xml:id="echoid-s5006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5007" xml:space="preserve">In hoc caſu globus ut Q elevatur, aut poſt caſum adſcendit, <lb/>B verſus. </s> <s xml:id="echoid-s5008" xml:space="preserve">Ad diſponendum indicem ut menſuretur angu-<lb/>lus ille, regulæ EG, quæ eſt a parte B, extremitas G con-<lb/>jungi debet cum extremitate G alterius regulæ, poſitæ ut <lb/>ante dictum.</s> <s xml:id="echoid-s5009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5010" xml:space="preserve">Cochleæ tres ferreæ F, F, F, inſerviunt ad tabulam ex-<lb/>acte in ſitu verticali diſponendam ita, ut linea AD ſit ad ho-<lb/>rizontem perpendicularis; </s> <s xml:id="echoid-s5011" xml:space="preserve">quod facillime præſtatur, ſuſpen-<lb/>dendo globo quocunque, & </s> <s xml:id="echoid-s5012" xml:space="preserve">ponendo indice majori ita, ut <lb/>filum tranſiens juxta notam in illo indice ſit parallelum li-<lb/>neæ AD.</s> <s xml:id="echoid-s5013" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5014" xml:space="preserve">In Experimentis circa colliſiones corporum non elaſtico-<lb/>rum, utimur globis, in forma lignea L, ex argilla molli du-<lb/>ctis.</s> <s xml:id="echoid-s5015" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5016" xml:space="preserve">Forma hæc L quinque partibus conſtat; </s> <s xml:id="echoid-s5017" xml:space="preserve">quarum quatuor <pb o="125" file="0187" n="203" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> in H, H, H, H, videntur; </s> <s xml:id="echoid-s5018" xml:space="preserve">hæ junctæ cavitatem ſphæricam <lb/>continent, diametri unius pollicis & </s> <s xml:id="echoid-s5019" xml:space="preserve">ſemiſſis, cum apertura <lb/>in inferiori parte: </s> <s xml:id="echoid-s5020" xml:space="preserve">circumdantur cochlea ita, ut firmiter in-<lb/>ter ſe connectantur ope annuli I, in interiori parte cochleam <lb/>ſimilem continentis.</s> <s xml:id="echoid-s5021" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5022" xml:space="preserve">Partes omnes conjunctæ in L repræſentantur; </s> <s xml:id="echoid-s5023" xml:space="preserve">datur fora-<lb/>men in v, communicationem habens cum cavitate interiori; <lb/></s> <s xml:id="echoid-s5024" xml:space="preserve">per hocce tranſmittitur filum, & </s> <s xml:id="echoid-s5025" xml:space="preserve">cavitas oleo illinitur, & </s> <s xml:id="echoid-s5026" xml:space="preserve">ar-<lb/>gilla impletur; </s> <s xml:id="echoid-s5027" xml:space="preserve">filum memoratum in argillam penetrat, & </s> <s xml:id="echoid-s5028" xml:space="preserve">in <lb/>hac irregulariter diſponitur. </s> <s xml:id="echoid-s5029" xml:space="preserve">Sublato annulo I, quatuor re-<lb/>liquæ partes facillime ſeparantur, & </s> <s xml:id="echoid-s5030" xml:space="preserve">globum in medio relin-<lb/>quunt, qui filo ſtatim memorato alteri filo connectitur, quo <lb/>Machinæ applicatur.</s> <s xml:id="echoid-s5031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5032" xml:space="preserve">Experimenta circa corpora elaſtica inftituuntur adhibitis <lb/>globis eburneis. </s> <s xml:id="echoid-s5033" xml:space="preserve">Sex minores deſiderantur, diametri unius <lb/>pollicis cum femiſſe; </s> <s xml:id="echoid-s5034" xml:space="preserve">præter hos unus ponderis dupli, al-<lb/>ter ponderis tripli, & </s> <s xml:id="echoid-s5035" xml:space="preserve">tandem unus ponderis quadrupli.</s> <s xml:id="echoid-s5036" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5037" xml:space="preserve">In Experimento undecimo capitis ſequentis, ſex memora-<lb/>ti globi æquales Machinæ applicantur; </s> <s xml:id="echoid-s5038" xml:space="preserve">& </s> <s xml:id="echoid-s5039" xml:space="preserve">ita ſuſpenduntur, ut <lb/>ſeſe mutuo tangant. </s> <s xml:id="echoid-s5040" xml:space="preserve">Præſtamus hoc (vide fig. </s> <s xml:id="echoid-s5041" xml:space="preserve">L.) </s> <s xml:id="echoid-s5042" xml:space="preserve">ope laminæ <lb/>m n, quæ cochleis q, q, per ſciſſuram st tranſeuntes, Ma-<lb/>chinæ connectitur. </s> <s xml:id="echoid-s5043" xml:space="preserve">Lamina hæc continet clavos quatuor <lb/>p, p, p, p; </s> <s xml:id="echoid-s5044" xml:space="preserve">in quorum extremitatibus dantur foramina, per quæ <lb/>fila, quibus globi ſuſpenduntur, tranſmittuntur. </s> <s xml:id="echoid-s5045" xml:space="preserve">Paxillis l, l, l, l <lb/>fila illa annectuntur. </s> <s xml:id="echoid-s5046" xml:space="preserve">Globi reliqui duo clavis memoratis V <lb/>ſuſpenduntur.</s> <s xml:id="echoid-s5047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5048" xml:space="preserve">In hac Machina percuſſio globorum in loco infimo ſem-<lb/>per eſt directa: </s> <s xml:id="echoid-s5049" xml:space="preserve">& </s> <s xml:id="echoid-s5050" xml:space="preserve">globi, licet a diverſis altitudinibus, ſive <lb/>ad eandem partem, ſive ad partes contrarias, dimittantur, <lb/>eodem momento ad locum infimum perveniunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5051" xml:space="preserve">& </s> <s xml:id="echoid-s5052" xml:space="preserve">ita, <anchor type="note" xlink:label="note-0187-01a" xlink:href="note-0187-01"/> in eo caſu, percuſſio ſemper eſt directa; </s> <s xml:id="echoid-s5053" xml:space="preserve">celeritates vero <lb/>in loco infimo denotantur diviſionibus regularum EG, <lb/>EG <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5054" xml:space="preserve">nam pro arcubus non majoribus, quam quos glo- <anchor type="note" xlink:label="note-0187-02a" xlink:href="note-0187-02"/> bi in hac Machina excurrunt, ratio inter arcus & </s> <s xml:id="echoid-s5055" xml:space="preserve">chordas <lb/>fenſibiliter non differt. </s> <s xml:id="echoid-s5056" xml:space="preserve">Altitudines, a quibus globi di-<lb/>mittuntur, determinant celeritates ante impactum; </s> <s xml:id="echoid-s5057" xml:space="preserve">& </s> <s xml:id="echoid-s5058" xml:space="preserve">al- <pb o="126" file="0188" n="204" rhead="PHYSICES ELEMENTA"/> titudines, ad quas globi adſcendunt, celeritates poſt impa-<lb/>ctionem.</s> <s xml:id="echoid-s5059" xml:space="preserve"/> </p> <div xml:id="echoid-div732" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">280.</note> <note symbol="*" position="right" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">222.</note> </div> </div> <div xml:id="echoid-div734" type="section" level="1" n="196"> <head xml:id="echoid-head281" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head282" xml:space="preserve">Alia, cujus ope eadem Experimenta circa colliſio-<lb/>nes inſtituuntur.</head> <p> <s xml:id="echoid-s5060" xml:space="preserve">Hîc & </s> <s xml:id="echoid-s5061" xml:space="preserve">aliam, quam eodem fundamento cum præceden-<lb/> <anchor type="note" xlink:label="note-0188-01a" xlink:href="note-0188-01"/> ti nixam conſtrui curavi machinam, etiam exponam. </s> <s xml:id="echoid-s5062" xml:space="preserve">Varia <lb/>huic addidi, quæ & </s> <s xml:id="echoid-s5063" xml:space="preserve">præcedenti applicari poſſunt, ita ut <lb/>omnia experimenta, quibus hæc inſervit, & </s> <s xml:id="echoid-s5064" xml:space="preserve">primâ in-<lb/>ſtitui poſſint, magis tamen commodè adhibitâ hac ſecun-<lb/>da.</s> <s xml:id="echoid-s5065" xml:space="preserve"/> </p> <div xml:id="echoid-div734" type="float" level="2" n="1"> <note position="left" xlink:label="note-0188-01" xlink:href="note-0188-01a" xml:space="preserve">491.</note> </div> <p> <s xml:id="echoid-s5066" xml:space="preserve">Conſtat hæc ex aſſere verticali ABDC, cujus longitu-<lb/> <anchor type="note" xlink:label="note-0188-02a" xlink:href="note-0188-02"/> do BC eſt trium pedum; </s> <s xml:id="echoid-s5067" xml:space="preserve">altitudo AD circiter decem pol-<lb/>licum, craſſities fere ſeſqui pollicis.</s> <s xml:id="echoid-s5068" xml:space="preserve"/> </p> <div xml:id="echoid-div735" type="float" level="2" n="2"> <note position="left" xlink:label="note-0188-02" xlink:href="note-0188-02a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s5069" xml:space="preserve">Huic aſſeri, aut Tabulæ, applicantur, eodem modo ac <lb/>in præcedenti machina, regulæ æneæ diviſæ EG, EG, <lb/>ut & </s> <s xml:id="echoid-s5070" xml:space="preserve">indices majores, M, M, & </s> <s xml:id="echoid-s5071" xml:space="preserve">minores, qui hìc non de-<lb/>lineantur.</s> <s xml:id="echoid-s5072" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5073" xml:space="preserve">Pede ſuſtinetur Tabula ita, ut D ad altitudinem circiter <lb/>duorum pedum cum ſemiſſe elevetur.</s> <s xml:id="echoid-s5074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5075" xml:space="preserve">Columna H pedis poſt tabulam, quæ ipſi applicatur, <lb/>continuatur, & </s> <s xml:id="echoid-s5076" xml:space="preserve">ſuſtinet tenuiorem columnam L, quæ ta-<lb/>men pro parte ipſi tabulæ ſuperimponitur ita, ut ſuperſi-<lb/>cies anterior ligni ſuperioris k ſit in eodem plano cum ſu-<lb/>perficie ABDC.</s> <s xml:id="echoid-s5077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5078" xml:space="preserve">Columna H in ſuperiori parte, ubi huic columna L ſu-<lb/>perimponitur, excavatur, ut recipiat prominentiam in in-<lb/>feriori parte columnæ L, quæ prominentia poligona eſt & </s> <s xml:id="echoid-s5079" xml:space="preserve"><lb/>exacte cum cavitate congruit, in qua firmatur cochleâ. <lb/></s> <s xml:id="echoid-s5080" xml:space="preserve">Cum columnâ L cohæret tabula lignea II, cujus craſſities <lb/>eſt ſemi pollicis & </s> <s xml:id="echoid-s5081" xml:space="preserve">cujus uſus eſt, ut columnam in tali ſitu <lb/>firmet, in quo hujus axis lineæ DA continuatæ, parallelus <lb/>eſt.</s> <s xml:id="echoid-s5082" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5083" xml:space="preserve">Pars columnæ ſuperior ſeparatim in R exhibetur, parti <lb/> <anchor type="note" xlink:label="note-0188-03a" xlink:href="note-0188-03"/> huic applicatur regula ænea quadrata SS, longitudinis cir-<lb/>citer octo pollicum, latitudo & </s> <s xml:id="echoid-s5084" xml:space="preserve">altitudo quartæ parti <pb file="0189" n="205"/> <anchor type="figure" xlink:label="fig-0189-01a" xlink:href="fig-0189-01"/> <pb file="0189a" n="206"/> <pb file="0190" n="207"/> <pb o="127" file="0191" n="208" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> pollicis æquales ſunt. </s> <s xml:id="echoid-s5085" xml:space="preserve">Horizonti regula hæc parallela eſt ut <lb/>& </s> <s xml:id="echoid-s5086" xml:space="preserve">ſuperſiciei ligni R, à quo diſtat tribus partibus quartis <lb/>unius pollicis. </s> <s xml:id="echoid-s5087" xml:space="preserve">Ut firmetur cohæret cum prominentiis t, t <lb/>quæ cochleis ad partem poſticam ligni K retinentur.</s> <s xml:id="echoid-s5088" xml:space="preserve"/> </p> <div xml:id="echoid-div736" type="float" level="2" n="3"> <note position="left" xlink:label="note-0188-03" xlink:href="note-0188-03a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 2.</note> <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a"> <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-01"/> </figure> </div> <p> <s xml:id="echoid-s5089" xml:space="preserve">Regulæ huic unci junguntur quatuor Y, V, V, Y, di-<lb/>ſtantia inter medios V, V, eſt ſeſqui pollicis, hujuſque di-<lb/>ſtantiæ punctum medium datur in plano, quod concipitur per-<lb/>pendiculare ad ſuperficiem K & </s> <s xml:id="echoid-s5090" xml:space="preserve">per axem columnæ l tranſ-<lb/>it; </s> <s xml:id="echoid-s5091" xml:space="preserve">diſtantia Y Y eſt trium pollicum.</s> <s xml:id="echoid-s5092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5093" xml:space="preserve">Juxta regulam hanc SS tubuli duo quadrati moventur, qui <lb/>ad libitum cochleis firmantur, & </s> <s xml:id="echoid-s5094" xml:space="preserve">cum quibus unci exigui, <lb/>ftatim memoratis ſimiles, cohærent. </s> <s xml:id="echoid-s5095" xml:space="preserve">Tand em in medio & </s> <s xml:id="echoid-s5096" xml:space="preserve"><lb/>in extremitatibus regulæ foramina dantur f, f, f, æqualiter a <lb/>ſe in vicem diſtantia, poſitis extremis a ſe mutuo remotis ſe-<lb/>ptem pollicibus cum ſemiſſe,</s> </p> <p> <s xml:id="echoid-s5097" xml:space="preserve">Ut in præcedentis machinæ deſcriptione monui, ſex de <lb/> <anchor type="note" xlink:label="note-0191-01a" xlink:href="note-0191-01"/> ſiderantur globi eburnei diametri ſeſqui pollicis ut A. </s> <s xml:id="echoid-s5098" xml:space="preserve">Loco <lb/>majorum globorum utimur tribus cylindris eburneis quorum <lb/>diametri globorum diametris æquales ſunt. </s> <s xml:id="echoid-s5099" xml:space="preserve">Duorum ſectio <lb/>per axem repræſentatur in C; </s> <s xml:id="echoid-s5100" xml:space="preserve">tertii ſectio datur in B; </s> <s xml:id="echoid-s5101" xml:space="preserve">cy-<lb/>lindri B pondus duplum eſt ponderis globi A ejuſdem dia-<lb/>metri cum cylindro; </s> <s xml:id="echoid-s5102" xml:space="preserve">cylindrorum ſingulorum ut Cpondera <lb/>tripla ſunt ponderum globorum.</s> <s xml:id="echoid-s5103" xml:space="preserve"/> </p> <div xml:id="echoid-div737" type="float" level="2" n="4"> <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s5104" xml:space="preserve">In his cylindris cavendum ut axis dentis eburnei, ex <lb/>quo formantur, perpendiculariter ſecet axem cylindri cir-<lb/>citer in hujus medio. </s> <s xml:id="echoid-s5105" xml:space="preserve">Ubi globus cum cylindro, aut duo <lb/>cylindri, ſimul machinæ applicantur cavendum ut convexi-<lb/>tas unius alterius planam ſuperficiem tangat.</s> <s xml:id="echoid-s5106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5107" xml:space="preserve">Ex ebore, aut ligno duriore & </s> <s xml:id="echoid-s5108" xml:space="preserve">graviore, ulterius quatuor <lb/> <anchor type="note" xlink:label="note-0191-02a" xlink:href="note-0191-02"/> formantur cylindri, quorum duorum minorum ſectiones per <lb/>axem exhibentur in D, reliquorum in E, & </s> <s xml:id="echoid-s5109" xml:space="preserve">F.</s> <s xml:id="echoid-s5110" xml:space="preserve"/> </p> <div xml:id="echoid-div738" type="float" level="2" n="5"> <note position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s5111" xml:space="preserve">Si ex ebore formentur ad ſitum axeos dentis non atten-<lb/>dimus, quia elaſticitate ſua in Experimentis non a-<lb/>gunt</s> </p> <p> <s xml:id="echoid-s5112" xml:space="preserve">Horum cylindrorum diametri ſunt etiam ſeſqui pollicis, <pb o="128" file="0192" n="209" rhead="PHYSICES ELEMENTA"/> in extremo uno ad formam hemiſphærii formantur, ex-<lb/>tremum alterum coni formam habet anguluſque m l n eſt <lb/>centum graduum: </s> <s xml:id="echoid-s5113" xml:space="preserve">angulos centum & </s> <s xml:id="echoid-s5114" xml:space="preserve">viginti graduum, ut <lb/>& </s> <s xml:id="echoid-s5115" xml:space="preserve">nonaginta graduum, in experimentis adhibui, ſed antepo-<lb/>nendum vidi angulum centum graduum.</s> <s xml:id="echoid-s5116" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5117" xml:space="preserve">Pondera cylindrorum ſunt inter ſe ut duo, tria, & </s> <s xml:id="echoid-s5118" xml:space="preserve">quatuor.</s> <s xml:id="echoid-s5119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5120" xml:space="preserve">Cylindri etiam duo cavi formantur ex ligno; </s> <s xml:id="echoid-s5121" xml:space="preserve">quorum <lb/> <anchor type="note" xlink:label="note-0192-01a" xlink:href="note-0192-01"/> diametri externæ ſeſqui pollicis ſunt, minor longitudinis eſt <lb/>trium poll.</s> <s xml:id="echoid-s5122" xml:space="preserve">, major quinque poll.</s> <s xml:id="echoid-s5123" xml:space="preserve">; repræſentatur ille in g, & </s> <s xml:id="echoid-s5124" xml:space="preserve">am-<lb/>borum ſectiones per axem videntur in G & </s> <s xml:id="echoid-s5125" xml:space="preserve">H. </s> <s xml:id="echoid-s5126" xml:space="preserve">Separatio in <lb/>cavitate utriuſque datur ad diſtantiam unius pollicis ab ex-<lb/>tremitate unâ; </s> <s xml:id="echoid-s5127" xml:space="preserve">videntur hæ in a a, a a, & </s> <s xml:id="echoid-s5128" xml:space="preserve">ab eſt unius <lb/>pollicis, craſſities ligni in b eſt octavæ partis pollicis. </s> <s xml:id="echoid-s5129" xml:space="preserve">Majo-<lb/>rem lignum habet craſſitiem in reliqua cylindri parte, ubi <lb/>nempe cavitatem majorem circumdat. </s> <s xml:id="echoid-s5130" xml:space="preserve">Cavitas minor, ubi <lb/>experimenta inſtituenda ſunt, argillâ repletur, & </s> <s xml:id="echoid-s5131" xml:space="preserve">quæ pro-<lb/>minet cultro ligneo abraditur, ut unita ſit ſuperficies in <lb/>quam cylindri, ultimum memorati, in experimentis incur-<lb/>runt; </s> <s xml:id="echoid-s5132" xml:space="preserve">in majorem cavitatem, minori aut majori copiâ ar-<lb/>gilla intruditur pro diverſo pondere cylindro communican-<lb/>do.</s> <s xml:id="echoid-s5133" xml:space="preserve"/> </p> <div xml:id="echoid-div739" type="float" level="2" n="6"> <note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve"><emph style="sc">TAB XVIII</emph>. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s5134" xml:space="preserve">Cylindri omnes eburnei & </s> <s xml:id="echoid-s5135" xml:space="preserve">lignei ſequenti methodo ſu-<lb/>ſpenduntur. </s> <s xml:id="echoid-s5136" xml:space="preserve">Ductâ lineâ in ſuperficie cylindri cujuſcunque ut <lb/>g ad axem parallelâ, in hac duæ tenues lamellæ perforatæ, aut <lb/>exigui annuli, o, o, firmantur ut & </s> <s xml:id="echoid-s5137" xml:space="preserve">duplex uncus v in me-<lb/>dio. </s> <s xml:id="echoid-s5138" xml:space="preserve">Foramina in lamellis o, o, non majora ſunt, niſi ut <lb/>per hæc duplicatæ chordæ citharæ tranſmittantur.</s> <s xml:id="echoid-s5139" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5140" xml:space="preserve">Lamellæ hæ omnes ita ponuntur, ut ductis ad cylindri <lb/>axes perpendicularibus à centris foraminum; </s> <s xml:id="echoid-s5141" xml:space="preserve">quales in <lb/>cylindro D. </s> <s xml:id="echoid-s5142" xml:space="preserve">(fig. </s> <s xml:id="echoid-s5143" xml:space="preserve">4.) </s> <s xml:id="echoid-s5144" xml:space="preserve">o h, o h, perpendiculares hæ axem ſe-<lb/>cent in h, h, ad diſtantiam trium partium quartarum poll. <lb/></s> <s xml:id="echoid-s5145" xml:space="preserve">ab extremitatibus p, l. </s> <s xml:id="echoid-s5146" xml:space="preserve">Notandum tamen reſpectu cylin-<lb/>drorum cavorum, ſatis eſſe ſi hæc tantum obſerventur re-<lb/>ſpectu lamellarum, quæ ad partem cavitatum minorum dan-<lb/>tur.</s> <s xml:id="echoid-s5147" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5148" xml:space="preserve">Cum globis ſingulis, ut A (Fig. </s> <s xml:id="echoid-s5149" xml:space="preserve">3), etiam lamella exi- <pb o="129" file="0193" n="210" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> gua perforata o jungitur in eo loco ubi dentis axis tranſit, & </s> <s xml:id="echoid-s5150" xml:space="preserve"><lb/>uncus exiguus c ad exiguam â lamella diſtantiam ponitur.</s> <s xml:id="echoid-s5151" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5152" xml:space="preserve">Globi & </s> <s xml:id="echoid-s5153" xml:space="preserve">cylindri filis tenuibus, aut chordis citharæ, ſu-<lb/> <anchor type="note" xlink:label="note-0193-01a" xlink:href="note-0193-01"/> ſpenduntur, fila hæc cum paxillis p, p, p, p, cohærent, & </s> <s xml:id="echoid-s5154" xml:space="preserve">tranſ-<lb/>eunt ſuper uncis v, v, z, z; </s> <s xml:id="echoid-s5155" xml:space="preserve">in extremitatibus oppoſitis fila <lb/>duplicantur formato nodo ad diſtantiam aliquot pollicum <lb/>ab extremitate, & </s> <s xml:id="echoid-s5156" xml:space="preserve">per foramina lamellarum exiguarum tranſ-<lb/>mittuntur, & </s> <s xml:id="echoid-s5157" xml:space="preserve">unco duplici connectuntur. </s> <s xml:id="echoid-s5158" xml:space="preserve">Hac methodo cy-<lb/>lindri P & </s> <s xml:id="echoid-s5159" xml:space="preserve">Q ſuſpenduntur, quàm facillimè etiam tollun-<lb/>tur, manentibus filis, quibus cylindri alii annectuntur.</s> <s xml:id="echoid-s5160" xml:space="preserve"/> </p> <div xml:id="echoid-div740" type="float" level="2" n="7"> <note position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s5161" xml:space="preserve">In hac ſuſpenſione diſtantia inter uncum ut z, & </s> <s xml:id="echoid-s5162" xml:space="preserve">vicinum <lb/>v, requiritur, quæ in cylindro datur inter lamellas per quas <lb/>fila transmittuntur, quod admoto cylindro facillime men-<lb/>ſuratur.</s> <s xml:id="echoid-s5163" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5164" xml:space="preserve">Eadem diſtantia deſideratur inter extremitatem G regu-<lb/>læ EG & </s> <s xml:id="echoid-s5165" xml:space="preserve">notam n, quæ ad eandem partem cum regula da-<lb/>tur, & </s> <s xml:id="echoid-s5166" xml:space="preserve">a linea AD diſtat tribus partibus quartis unius polli-<lb/>cis.</s> <s xml:id="echoid-s5167" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5168" xml:space="preserve">Cochleis ferreis F, F, F, ita diſponitur Machina ut cy-<lb/>lindrorum ſeparatio lineæ AD reſpondeat, & </s> <s xml:id="echoid-s5169" xml:space="preserve">ut hi pa-<lb/>rum admodum diſtent a plano ABDC.</s> <s xml:id="echoid-s5170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5171" xml:space="preserve">Quando globus ſuſpenditur, connectitur filo tranſeunti <lb/>ſuper unco v, & </s> <s xml:id="echoid-s5172" xml:space="preserve">extremitas G regulæ EG notæ n admo-<lb/>vetur.</s> <s xml:id="echoid-s5173" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5174" xml:space="preserve">Quando cylindrus cavus ſuſpenditur minor cavitas line-<lb/>am AD verſus datur.</s> <s xml:id="echoid-s5175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5176" xml:space="preserve">Corpora ad eandem altitudinem ſuſpendenda ſunt, & </s> <s xml:id="echoid-s5177" xml:space="preserve">ut <lb/>cylindrorum axes horizonti paralleli ſint cavendum; </s> <s xml:id="echoid-s5178" xml:space="preserve">his in-<lb/>ſervit linea h h horizonti parallela in ſuperficie tabulæ du-<lb/>cta, cui lineæ partes cylindrorum inferiores reſpondere de-<lb/>bent.</s> <s xml:id="echoid-s5179" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5180" xml:space="preserve">Propter filorum amborum, quibus cylindrus quicunque <lb/>ſuſpenditur, paralleliſmum, & </s> <s xml:id="echoid-s5181" xml:space="preserve">æqualitatem, axis in motu <lb/>ſuo paralleliſmum ſervat & </s> <s xml:id="echoid-s5182" xml:space="preserve">ſingula corporis puncta æquali-<lb/>ter deſcendunt, eâdemque velocitate moventur, ubi in <pb o="130" file="0194" n="211" rhead="PHYSICES ELEMENTA"/> loco infimo ad quem pervenire poteſt cylindrus in aliud <lb/>corpus directe incurrit.</s> <s xml:id="echoid-s5183" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5184" xml:space="preserve">Velocitates corporum ante & </s> <s xml:id="echoid-s5185" xml:space="preserve">poſt impactum, ut de præ-<lb/>cedenti machinâ dictum, menſurantur, attendendo ad fila ex-<lb/>terna quamdiu agitur de motu corporum ad illam partem <lb/>lineæ AD ad quam ſuſpenduntur; </s> <s xml:id="echoid-s5186" xml:space="preserve">ſi autem agatur de mo-<lb/>tu corporis ut P ultra AD, verſus C, interius filum adhi-<lb/>bendum, & </s> <s xml:id="echoid-s5187" xml:space="preserve">regulæ EG, qua ad partem C datur, extremitas <lb/>G admovenda eſt notæ n, quæ ad partem B datur.</s> <s xml:id="echoid-s5188" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5189" xml:space="preserve">Lignum N in quibuſdam experimentis applicatur tabulæ <lb/> <anchor type="note" xlink:label="note-0194-01a" xlink:href="note-0194-01"/> ABDC ita ut hujus latus c e cum linea AD congruat, <lb/>firmaturque cochleis per foramina i, i, in tabula, & </s> <s xml:id="echoid-s5190" xml:space="preserve">ſciſſu-<lb/>ras dg, dg, in ligno, tranſeuntibus. </s> <s xml:id="echoid-s5191" xml:space="preserve">Cochleæ hæ in T re-<lb/>præſentantur, horum capita ſuperficiei averſæ tabulæ <lb/>ABDC applicantur, poteſtque lignum hoc ad varias altitu-<lb/>dines firmari.</s> <s xml:id="echoid-s5192" xml:space="preserve"/> </p> <div xml:id="echoid-div741" type="float" level="2" n="8"> <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve"><emph style="sc">TAB. XVIII.</emph> <lb/>fig 6.</note> </div> <p> <s xml:id="echoid-s5193" xml:space="preserve">Excavatur lignum hocce in R ad profunditatem pollicis <lb/>unius, cavitatis hujus altitudo c e eſt quatuor pollicum, la-<lb/>titudo duorum pollicum, lignique craſſities in c e octavæ par-<lb/>tis pollicis tantum eſt.</s> <s xml:id="echoid-s5194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5195" xml:space="preserve">Ubi Experimentis lignum hocce inſervit cavitas argillâ re-<lb/>pletur, cultroque ligneo prominentem argillam abradimus, ut <lb/>ſuperficies unita ſit. </s> <s xml:id="echoid-s5196" xml:space="preserve">In hanc argillam cylindri incurrunt, ubi <lb/>corpora in obicem firmum impingenda ſunt.</s> <s xml:id="echoid-s5197" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div743" type="section" level="1" n="197"> <head xml:id="echoid-head283" xml:space="preserve"><emph style="sc">Experimentumi</emph>.</head> <p> <s xml:id="echoid-s5198" xml:space="preserve">Lignum N (Fig. </s> <s xml:id="echoid-s5199" xml:space="preserve">6.)</s> <s xml:id="echoid-s5200" xml:space="preserve">, repletâ hujus cavitate argillâ molli, <lb/> <anchor type="note" xlink:label="note-0194-02a" xlink:href="note-0194-02"/> applicandum eſt tabulæ ABCD, ibique firmandum, ſub-<lb/> <anchor type="note" xlink:label="note-0194-03a" xlink:href="note-0194-03"/> lato nempe corpore Q, & </s> <s xml:id="echoid-s5201" xml:space="preserve">in loco corporis P cylindrus F <lb/>(Fig. </s> <s xml:id="echoid-s5202" xml:space="preserve">4.) </s> <s xml:id="echoid-s5203" xml:space="preserve">ſuſpendendus eſt ita, ut conus, qui oleo illiniri de-<lb/>bet, argillam verſus dirigatur, & </s> <s xml:id="echoid-s5204" xml:space="preserve">ut inferior ſuperficies <lb/>cylindri lineæ hh reſpondeat.</s> <s xml:id="echoid-s5205" xml:space="preserve"/> </p> <div xml:id="echoid-div743" type="float" level="2" n="1"> <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">492.</note> <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve"><emph style="sc">TAB. XVIII.</emph> <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s5206" xml:space="preserve">Dimittatur cylindrus ab altitudine quinque graduum & </s> <s xml:id="echoid-s5207" xml:space="preserve"><lb/>impingendo in argillam vim ſuam amitter, formando cavi-<lb/>tatem: </s> <s xml:id="echoid-s5208" xml:space="preserve">partes enim argillæ ſolæ cedunt, cùm hujus partes <lb/>multo minus cohæreant, quàm partes eboris aut ligni, & </s> <s xml:id="echoid-s5209" xml:space="preserve">ma-<lb/>jor preſſio minorem vincat.</s> <s xml:id="echoid-s5210" xml:space="preserve"/> </p> <pb o="131" file="0195" n="212" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> <p> <s xml:id="echoid-s5211" xml:space="preserve">Cavitas hæc menſuranda eſt & </s> <s xml:id="echoid-s5212" xml:space="preserve">tollendum lignum N. <lb/></s> <s xml:id="echoid-s5213" xml:space="preserve">Maſſa corporis eſt quatuor, velocitas quinque; </s> <s xml:id="echoid-s5214" xml:space="preserve">ergo vis <lb/>centum <anchor type="note" xlink:href="" symbol="*"/> deſtructa fuit formando cavitatem.</s> <s xml:id="echoid-s5215" xml:space="preserve"> <anchor type="note" xlink:label="note-0195-01a" xlink:href="note-0195-01"/> </s> </p> <div xml:id="echoid-div744" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s5216" xml:space="preserve">Cavitas minor cylindri G (Fig. </s> <s xml:id="echoid-s5217" xml:space="preserve">5.) </s> <s xml:id="echoid-s5218" xml:space="preserve">argillâ replenda eſt, <lb/>ſuperficieſque abradenda cultro ligneo, ut unita ſit; </s> <s xml:id="echoid-s5219" xml:space="preserve">dein-<lb/>de ponderandus eſt cylindrus, tantumque argillæ adjicien-<lb/>dum, ut cum cylindro D (Fig. </s> <s xml:id="echoid-s5220" xml:space="preserve">4.) </s> <s xml:id="echoid-s5221" xml:space="preserve">æqualiter ponderet, quæ ar-<lb/>gilla majori cavitati intrudi debet.</s> <s xml:id="echoid-s5222" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5223" xml:space="preserve">Suſpenſis nunc cylindris ita, ut pars conica cylindri D(Fig. </s> <s xml:id="echoid-s5224" xml:space="preserve">4.)</s> <s xml:id="echoid-s5225" xml:space="preserve">, <lb/>oleo illinita, alium verſus dirigatur; </s> <s xml:id="echoid-s5226" xml:space="preserve">à partibus oppoſitis ſingu-<lb/>li a diviſione quinta dimittendi ſunt, in ſe mutuo incur-<lb/>runt, poſt ictum quieſcunt, & </s> <s xml:id="echoid-s5227" xml:space="preserve">cavitas in argilla formatur. <lb/></s> <s xml:id="echoid-s5228" xml:space="preserve">Menſuranda eſt hæc; </s> <s xml:id="echoid-s5229" xml:space="preserve">ſingulorum corporum maſſæ valent duo, <lb/>velocitates ſunt quinque, ergo ſingulorum vires quinqua-<lb/>ginta <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s5230" xml:space="preserve">vis tota in colliſione deſtructa valet etiam cen- <anchor type="note" xlink:label="note-0195-02a" xlink:href="note-0195-02"/> tum.</s> <s xml:id="echoid-s5231" xml:space="preserve"/> </p> <div xml:id="echoid-div745" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s5232" xml:space="preserve">Iiſdem manentibus, unitâ iterum ſuperficie argillæ in ca-<lb/>vitate minori cylindri, dimittendi ſunt ambo ab eadem par-<lb/>te, unus ab altitudine quinque, alter ab altitudine quindecim; <lb/></s> <s xml:id="echoid-s5233" xml:space="preserve">poſt ictum non ſeparantur & </s> <s xml:id="echoid-s5234" xml:space="preserve">ſimul ad diviſionem decimam <lb/>adſcendunt; </s> <s xml:id="echoid-s5235" xml:space="preserve">ſi enim huic diviſioni index applicetur ad ipſum <lb/>pertingit filum, non autem ad illum pertingit hoc, ſi magis <lb/>index removeatur. </s> <s xml:id="echoid-s5236" xml:space="preserve">Et hìc cavitas formatur, quæ menſuran-<lb/>da eſt. </s> <s xml:id="echoid-s5237" xml:space="preserve">Unius corporis maſſa eſt duo, velocitas quindecim; </s> <s xml:id="echoid-s5238" xml:space="preserve"><lb/>ergo vis quadringenta & </s> <s xml:id="echoid-s5239" xml:space="preserve">quinquaginta, alterius vis eſt quin-<lb/>quaginta, & </s> <s xml:id="echoid-s5240" xml:space="preserve">ſumma virium ante ictum quingenta. </s> <s xml:id="echoid-s5241" xml:space="preserve">Poſt ictum <lb/>maſſa eſt quatuor & </s> <s xml:id="echoid-s5242" xml:space="preserve">velocitas decem; </s> <s xml:id="echoid-s5243" xml:space="preserve">ergo vis quadringen-<lb/>ta: </s> <s xml:id="echoid-s5244" xml:space="preserve">vis ergo ictu deſtructa etiam eſt centum ut in duobus præ-<lb/>cedentibus experimentis.</s> <s xml:id="echoid-s5245" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5246" xml:space="preserve">In tribus hiſce caſibus cavitates quâm exactiſſimè ſunt <lb/>æquales, quod Experimentis confirmandum erat. </s> <s xml:id="echoid-s5247" xml:space="preserve">In primo <lb/>& </s> <s xml:id="echoid-s5248" xml:space="preserve">tertio caſu vires non fuere contrariæ, & </s> <s xml:id="echoid-s5249" xml:space="preserve">niſi ſuperando <lb/>partium cohæſionem potuiſſe vim quandam deſtrui clare <lb/>patet.</s> <s xml:id="echoid-s5250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5251" xml:space="preserve">Experimenta potuiſſent eodem modo inſtitui, partibus <lb/> <anchor type="note" xlink:label="note-0195-03a" xlink:href="note-0195-03"/> cylindrorum hemiſphæricis in argillam incurrentibus, ſed ca- <pb o="132" file="0196" n="213" rhead="PHYSICES ELEMENTA"/> vitates conicæ exactius poſſunt conferri, quod ad Experi-<lb/>menta ſequentia etiam debet referri.</s> <s xml:id="echoid-s5252" xml:space="preserve"/> </p> <div xml:id="echoid-div746" type="float" level="2" n="4"> <note position="right" xlink:label="note-0195-03" xlink:href="note-0195-03a" xml:space="preserve">493.</note> </div> <p> <s xml:id="echoid-s5253" xml:space="preserve">Motu duobus corporibus communi corpora hæc in ſe mu-<lb/>tuo agere non poſſunt; </s> <s xml:id="echoid-s5254" xml:space="preserve">pendet ergo ictus a velocitatereſpe-<lb/> <anchor type="note" xlink:label="note-0196-01a" xlink:href="note-0196-01"/> ctivâ, qua manente, intenſitas impactionis eadem erit, quomo-<lb/>docunque celeritates abſolutæ varient; </s> <s xml:id="echoid-s5255" xml:space="preserve">ab intenſitate hac pen-<lb/>det partium introceſſio, quæ ergo ſemper eadem erit, ſi <lb/> <anchor type="note" xlink:label="note-0196-02a" xlink:href="note-0196-02"/> duo corpora eâdem velocitate reſpectivâ in ſe mutuo incur-<lb/>rant, quibuſcunque velocitatibus moveantur.</s> <s xml:id="echoid-s5256" xml:space="preserve"/> </p> <div xml:id="echoid-div747" type="float" level="2" n="5"> <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">494.</note> <note position="left" xlink:label="note-0196-02" xlink:href="note-0196-02a" xml:space="preserve">495.</note> </div> </div> <div xml:id="echoid-div749" type="section" level="1" n="198"> <head xml:id="echoid-head284" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s5257" xml:space="preserve">Suſpenſo cylindro quocunque ex tribus qui in Fig. </s> <s xml:id="echoid-s5258" xml:space="preserve">4. </s> <s xml:id="echoid-s5259" xml:space="preserve">de-<lb/> <anchor type="note" xlink:label="note-0196-03a" xlink:href="note-0196-03"/> lineantur; </s> <s xml:id="echoid-s5260" xml:space="preserve">& </s> <s xml:id="echoid-s5261" xml:space="preserve">quolibet ex cylindris cavis, Fig. </s> <s xml:id="echoid-s5262" xml:space="preserve">5. <lb/></s> <s xml:id="echoid-s5263" xml:space="preserve"> <anchor type="note" xlink:label="note-0196-04a" xlink:href="note-0196-04"/> </s> </p> <div xml:id="echoid-div749" type="float" level="2" n="1"> <note position="left" xlink:label="note-0196-03" xlink:href="note-0196-03a" xml:space="preserve">496.</note> <note position="left" xlink:label="note-0196-04" xlink:href="note-0196-04a" xml:space="preserve"><emph style="sc">TAB XVIII</emph> <lb/>fig. 4. 5.</note> </div> <p> <s xml:id="echoid-s5264" xml:space="preserve">Hujus minor cavitas argillâ repleatur, ut in deſcriptione <lb/>machinæ & </s> <s xml:id="echoid-s5265" xml:space="preserve">experimento 1°. </s> <s xml:id="echoid-s5266" xml:space="preserve">dictum, & </s> <s xml:id="echoid-s5267" xml:space="preserve">in majorem cavita-<lb/>tem argillæ quantitas quæcunque intrudatur; </s> <s xml:id="echoid-s5268" xml:space="preserve">dimittantur <lb/>hi, unus à decimâ quintâ, alter à quintâ diviſione, ad ean-<lb/>dem partem, & </s> <s xml:id="echoid-s5269" xml:space="preserve">menſuretur cavitatis diameter.</s> <s xml:id="echoid-s5270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5271" xml:space="preserve">Unitâ iterum argillæ ſuperficie incurrat cylindrus unus <lb/>velocitate decem in alium quieſcentem, & </s> <s xml:id="echoid-s5272" xml:space="preserve">iterum menſu-<lb/>retur cavitatis diameter.</s> <s xml:id="echoid-s5273" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5274" xml:space="preserve">Tandem, iterum unitâ argillæ ſuperficie, cylindrus unus <lb/>dimittatur ab altitudine quartæ diviſionis, alter a ſexta di-<lb/>viſione, & </s> <s xml:id="echoid-s5275" xml:space="preserve">in partes contrarias tendant, menſureturque ite-<lb/>rum cavitatis diameter.</s> <s xml:id="echoid-s5276" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5277" xml:space="preserve">In hiſce tribus caſibus velocitates reſpectivæ ſunt æquales <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0196-05a" xlink:href="note-0196-05"/> cavitates etiam minimè differunt.</s> <s xml:id="echoid-s5278" xml:space="preserve"/> </p> <div xml:id="echoid-div750" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0196-05" xlink:href="note-0196-05a" xml:space="preserve">474. 47;.</note> </div> <p> <s xml:id="echoid-s5279" xml:space="preserve">Vires æquales conſumuntur in formandis cavitatibus æ-<lb/>qualibus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5280" xml:space="preserve">nulla vis perit niſi quæ in cavitatibus forman- <anchor type="note" xlink:label="note-0196-06a" xlink:href="note-0196-06"/> dis conſumitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5281" xml:space="preserve">ergo quomodocunque duo corpora movean- <anchor type="note" xlink:label="note-0196-07a" xlink:href="note-0196-07"/> tur, ſi eadem fuerit velocitas reſpectiva, eadem vis ictu <lb/> <anchor type="note" xlink:label="note-0196-08a" xlink:href="note-0196-08"/> deſtructa erit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5282" xml:space="preserve">Hanc idcirco determinabimus in omni <anchor type="note" xlink:label="note-0196-09a" xlink:href="note-0196-09"/> concurſu duorum corporum, manente velocitate reſpectivâ, <lb/>ſi hoc fiat in uno caſu.</s> <s xml:id="echoid-s5283" xml:space="preserve"/> </p> <div xml:id="echoid-div751" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0196-06" xlink:href="note-0196-06a" xml:space="preserve">464</note> <note symbol="*" position="left" xlink:label="note-0196-07" xlink:href="note-0196-07a" xml:space="preserve">488</note> <note position="left" xlink:label="note-0196-08" xlink:href="note-0196-08a" xml:space="preserve">497</note> <note symbol="*" position="left" xlink:label="note-0196-09" xlink:href="note-0196-09a" xml:space="preserve">495</note> </div> <p> <s xml:id="echoid-s5284" xml:space="preserve">Sicorpora duo, ſive æqualia, ſive utcunque inæqualia in con-<lb/> <anchor type="note" xlink:label="note-0196-10a" xlink:href="note-0196-10"/> trarias partes lata, in ſe mutuo incurrant, poteſt, datâ <lb/>velocitate reſpectivâ, ita componi horum motus, ut quod <pb file="0197" n="214"/> <anchor type="figure" xlink:label="fig-0197-01a" xlink:href="fig-0197-01"/> <pb file="0197a" n="215"/> <pb file="0198" n="216"/> <pb o="133" file="0199" n="217" rhead="MATHEMATICA, LIB. I. CAP. XXIII."/> libuerit alium poſt ictum ſecum ferat, unde ſequitur, caſum <lb/>dari, in quo poſt ictum quieſcunt.</s> <s xml:id="echoid-s5285" xml:space="preserve"/> </p> <div xml:id="echoid-div752" type="float" level="2" n="4"> <note position="left" xlink:label="note-0196-10" xlink:href="note-0196-10a" xml:space="preserve">498.</note> <figure xlink:label="fig-0197-01" xlink:href="fig-0197-01a"> <image file="0197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0197-01"/> </figure> </div> <p> <s xml:id="echoid-s5286" xml:space="preserve">In hoc caſu ſumma virium abſolutarum valet vim in <lb/>omni caſu, poſitâ eadem velocitate reſpectivâ, deſtructam <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5287" xml:space="preserve"> <anchor type="note" xlink:label="note-0199-01a" xlink:href="note-0199-01"/> In hoc eodem caſu ſumma hæc eſt, ſervatâ velocitate re-<lb/>ſpectivâ omnium minima: </s> <s xml:id="echoid-s5288" xml:space="preserve">ſi enim ſumma minor daretur, mi-<lb/>nor vis ictu periret, quod impoſſibile <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5289" xml:space="preserve"> <anchor type="note" xlink:label="note-0199-02a" xlink:href="note-0199-02"/> </s> </p> <div xml:id="echoid-div753" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0199-01" xlink:href="note-0199-01a" xml:space="preserve">497.</note> <note symbol="*" position="right" xlink:label="note-0199-02" xlink:href="note-0199-02a" xml:space="preserve">497.</note> </div> <p> <s xml:id="echoid-s5290" xml:space="preserve">Summam autem hanc eſſe omnium minimam, ſi poſitis diro-<lb/> <anchor type="note" xlink:label="note-0199-03a" xlink:href="note-0199-03"/> ctionibus contrariis, celeritates fuerint inverſe ut maſſæ, <lb/>& </s> <s xml:id="echoid-s5291" xml:space="preserve">in hoc caſu ſolo eſſe minimam, in ſcholio ſequenti 1. <lb/></s> <s xml:id="echoid-s5292" xml:space="preserve">demonſtramus.</s> <s xml:id="echoid-s5293" xml:space="preserve"/> </p> <div xml:id="echoid-div754" type="float" level="2" n="6"> <note position="right" xlink:label="note-0199-03" xlink:href="note-0199-03a" xml:space="preserve">499.</note> </div> <p> <s xml:id="echoid-s5294" xml:space="preserve">Unde ergo ſequitur in eo ſolo caſu corpora in contrarias <lb/> <anchor type="note" xlink:label="note-0199-04a" xlink:href="note-0199-04"/> partes lata, & </s> <s xml:id="echoid-s5295" xml:space="preserve">in ſe mutuo incurrentia, poſt ictum quieſce-<lb/>re, ſi velocitates fuerint inverſe ut maſſæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5296" xml:space="preserve"> <anchor type="note" xlink:label="note-0199-05a" xlink:href="note-0199-05"/> </s> </p> <div xml:id="echoid-div755" type="float" level="2" n="7"> <note position="right" xlink:label="note-0199-04" xlink:href="note-0199-04a" xml:space="preserve">500.</note> <note symbol="*" position="right" xlink:label="note-0199-05" xlink:href="note-0199-05a" xml:space="preserve">498:</note> </div> </div> <div xml:id="echoid-div757" type="section" level="1" n="199"> <head xml:id="echoid-head285" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s5297" xml:space="preserve">Suſpenſis cylindris F, (Fig. </s> <s xml:id="echoid-s5298" xml:space="preserve">4. </s> <s xml:id="echoid-s5299" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5300" xml:space="preserve">18.) </s> <s xml:id="echoid-s5301" xml:space="preserve">& </s> <s xml:id="echoid-s5302" xml:space="preserve">G, (Fig. </s> <s xml:id="echoid-s5303" xml:space="preserve">5. </s> <s xml:id="echoid-s5304" xml:space="preserve">Tab 18.) <lb/></s> <s xml:id="echoid-s5305" xml:space="preserve"> <anchor type="note" xlink:label="note-0199-06a" xlink:href="note-0199-06"/> cavendum autem, ut hic, argillâ in poſteriori cavitate in-<lb/> <anchor type="note" xlink:label="note-0199-07a" xlink:href="note-0199-07"/> truſâ, cum cylindro D (Fig. </s> <s xml:id="echoid-s5306" xml:space="preserve">4. </s> <s xml:id="echoid-s5307" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5308" xml:space="preserve">18.) </s> <s xml:id="echoid-s5309" xml:space="preserve">æqualiter ponde-<lb/>ret; </s> <s xml:id="echoid-s5310" xml:space="preserve">maſſæ nunc erunt ut quatuor ad duo, aut ut duo ad unum. <lb/></s> <s xml:id="echoid-s5311" xml:space="preserve">Incurrant hi directionibus contrariis in ſe mutuo, F velo-<lb/>citate quinque, & </s> <s xml:id="echoid-s5312" xml:space="preserve">G velocitate decem, & </s> <s xml:id="echoid-s5313" xml:space="preserve">poſt ictum qui-<lb/> <anchor type="note" xlink:label="note-0199-08a" xlink:href="note-0199-08"/> eſcent. </s> <s xml:id="echoid-s5314" xml:space="preserve">Cavitas in argilla in V repræſentatur.</s> <s xml:id="echoid-s5315" xml:space="preserve"/> </p> <div xml:id="echoid-div757" type="float" level="2" n="1"> <note position="right" xlink:label="note-0199-06" xlink:href="note-0199-06a" xml:space="preserve">501.</note> <note position="right" xlink:label="note-0199-07" xlink:href="note-0199-07a" xml:space="preserve"><emph style="sc">TAB. XIX</emph> <lb/>fig. 2.</note> <note position="right" xlink:label="note-0199-08" xlink:href="note-0199-08a" xml:space="preserve"><emph style="sc">TAB. XIX</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s5316" xml:space="preserve">Vires autem in hoc caſu ſunt inverſè ut velocitates <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5317" xml:space="preserve">er- <anchor type="note" xlink:label="note-0199-09a" xlink:href="note-0199-09"/> go ut corpora inæqualia in contrarias partes lata, poſt ictum <lb/> <anchor type="note" xlink:label="note-0199-10a" xlink:href="note-0199-10"/> quieſcant, vires inſitæ inæquales deſiderantur. </s> <s xml:id="echoid-s5318" xml:space="preserve">Circa quam <lb/>inæqualitatem ſequentia experimenta notatu digniſſima <lb/>ſunt.</s> <s xml:id="echoid-s5319" xml:space="preserve"/> </p> <div xml:id="echoid-div758" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0199-09" xlink:href="note-0199-09a" xml:space="preserve">472.</note> <note position="right" xlink:label="note-0199-10" xlink:href="note-0199-10a" xml:space="preserve">502.</note> </div> </div> <div xml:id="echoid-div760" type="section" level="1" n="200"> <head xml:id="echoid-head286" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s5320" xml:space="preserve">Firmato obice N, (Fig. </s> <s xml:id="echoid-s5321" xml:space="preserve">6. </s> <s xml:id="echoid-s5322" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5323" xml:space="preserve">18.) </s> <s xml:id="echoid-s5324" xml:space="preserve">in argillam incurrat cy-<lb/> <anchor type="note" xlink:label="note-0199-11a" xlink:href="note-0199-11"/> lindrus F ea velocitate, qua in experimento præcedenti mo-<lb/> <anchor type="note" xlink:label="note-0199-12a" xlink:href="note-0199-12"/> tus fuit, cavitatem format S (Fig. </s> <s xml:id="echoid-s5325" xml:space="preserve">3.)</s> <s xml:id="echoid-s5326" xml:space="preserve">. </s> <s xml:id="echoid-s5327" xml:space="preserve">Mutato paululum obi-<lb/> <anchor type="note" xlink:label="note-0199-13a" xlink:href="note-0199-13"/> ce in hunc incurrat cylindrus D (Fig. </s> <s xml:id="echoid-s5328" xml:space="preserve">4. </s> <s xml:id="echoid-s5329" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5330" xml:space="preserve">18.) </s> <s xml:id="echoid-s5331" xml:space="preserve">ea ve-<lb/>locitate qua cylindrus G, qui in præcedenti experimento <lb/>ejuſdem ponderis fuit cum hoc cylindio D, in hoc præce-<lb/>denti experimento fuit agitatus, cavitatem formabit duplam <lb/>præcedentis, quæ in T (fig. </s> <s xml:id="echoid-s5332" xml:space="preserve">3.) </s> <s xml:id="echoid-s5333" xml:space="preserve">repræſentatur, quod <pb o="134" file="0200" n="218" rhead="PHYSICES ELEMENTA"/> manifeſtè virium inæqualitatem indicat.</s> <s xml:id="echoid-s5334" xml:space="preserve"/> </p> <div xml:id="echoid-div760" type="float" level="2" n="1"> <note position="right" xlink:label="note-0199-11" xlink:href="note-0199-11a" xml:space="preserve">503.</note> <note position="right" xlink:label="note-0199-12" xlink:href="note-0199-12a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 4.</note> <note position="right" xlink:label="note-0199-13" xlink:href="note-0199-13a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s5335" xml:space="preserve">Hæ autem duæ cavitates conjunctæ æquales ſunt cavitati <lb/>ſoli quæ in præcedenti experimento fuit formata, & </s> <s xml:id="echoid-s5336" xml:space="preserve">ita an-<lb/>te demonſtrata <anchor type="note" xlink:href="" symbol="*"/> cum Experimentis his exactiſſime congruunt.</s> <s xml:id="echoid-s5337" xml:space="preserve"> <anchor type="note" xlink:label="note-0200-01a" xlink:href="note-0200-01"/> Si enim, adhibito Circino Proportionum conferamus ſoli-<lb/>da ſimilia, quorum latera homologa ſunt diametri trium <lb/>cavitatum, S, T, V, (Fig. </s> <s xml:id="echoid-s5338" xml:space="preserve">3.) </s> <s xml:id="echoid-s5339" xml:space="preserve">in duobus ultimis experimentis <lb/>formatarum, videbimus cavitates has eſſe inter ſe ut unum, <lb/>duo, & </s> <s xml:id="echoid-s5340" xml:space="preserve">tria; </s> <s xml:id="echoid-s5341" xml:space="preserve">id eſt majorem æqualem eſſe duobus mino-<lb/>ribus ſimul ſumtis. </s> <s xml:id="echoid-s5342" xml:space="preserve">Quod etiam ſequenti experimento <lb/>patet.</s> <s xml:id="echoid-s5343" xml:space="preserve"/> </p> <div xml:id="echoid-div761" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0200-01" xlink:href="note-0200-01a" xml:space="preserve">464.</note> </div> </div> <div xml:id="echoid-div763" type="section" level="1" n="201"> <head xml:id="echoid-head287" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s5344" xml:space="preserve">Firmato obice N, in hunc impingat velocitate quinque <lb/> <anchor type="note" xlink:label="note-0200-02a" xlink:href="note-0200-02"/> cylindrus F; </s> <s xml:id="echoid-s5345" xml:space="preserve">ſublato hoc & </s> <s xml:id="echoid-s5346" xml:space="preserve">ſuſpenſo cylindro D, impingat <lb/> <anchor type="note" xlink:label="note-0200-03a" xlink:href="note-0200-03"/> hic velocitate decem in obicem, incurrendo in ipſam cavita-<lb/>tem jam formatamictu cylindri F; </s> <s xml:id="echoid-s5347" xml:space="preserve">cavitatem augebit & </s> <s xml:id="echoid-s5348" xml:space="preserve">hæc <lb/>nunc valebit ambas cavitates in Exper. </s> <s xml:id="echoid-s5349" xml:space="preserve">præcedenti 4<emph style="super">to</emph>. </s> <s xml:id="echoid-s5350" xml:space="preserve">for-<lb/>matas <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s5351" xml:space="preserve">erit æqualis cavitati V (Fig. </s> <s xml:id="echoid-s5352" xml:space="preserve">3.) </s> <s xml:id="echoid-s5353" xml:space="preserve">Exp. </s> <s xml:id="echoid-s5354" xml:space="preserve">penul- <anchor type="note" xlink:label="note-0200-04a" xlink:href="note-0200-04"/> timi.</s> <s xml:id="echoid-s5355" xml:space="preserve"/> </p> <div xml:id="echoid-div763" type="float" level="2" n="1"> <note position="left" xlink:label="note-0200-02" xlink:href="note-0200-02a" xml:space="preserve">504.</note> <note position="left" xlink:label="note-0200-03" xlink:href="note-0200-03a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 6.</note> <note symbol="*" position="left" xlink:label="note-0200-04" xlink:href="note-0200-04a" xml:space="preserve">464.</note> </div> <p> <s xml:id="echoid-s5356" xml:space="preserve">Circa hoc Experimentum 5<emph style="super">tum</emph>. </s> <s xml:id="echoid-s5357" xml:space="preserve">notandum aliquando ictu <lb/> <anchor type="note" xlink:label="note-0200-05a" xlink:href="note-0200-05"/> argillæ ſuperficiem compactiorem fieri & </s> <s xml:id="echoid-s5358" xml:space="preserve">elaſticitatem quan-<lb/>dam acquirere in quo caſu Experimentum non procedit. <lb/></s> <s xml:id="echoid-s5359" xml:space="preserve">Semper autem obſervavi cavitatem, duobus ictibus quibuſ-<lb/>cunque formatam, ſi corpus quod ultimum impingit non <lb/>reſiliat, æqualem eſſe duobus cavitatibus, quæ iiſdem icti-<lb/>bus ſeparatim formari potuiſſent; </s> <s xml:id="echoid-s5360" xml:space="preserve">ſi vero corpus in cavita-<lb/>tem incurrens quantumvis parwm reſiliat indicium habemus <lb/>elaſticitatis argillæ, & </s> <s xml:id="echoid-s5361" xml:space="preserve">in tali caſu cavitatem ex duobus icti-<lb/>bus minorem ſemper detexi ſummâ cavitatum ſeparatarum, <lb/>eoque minorem quo ictu acquiſita elaſticitas major erat, cla-<lb/>re autem patet partes elaſticas argillæ difficilius intropremi <lb/>quam aliæ quæ elaſticitate deſtituuntur. </s> <s xml:id="echoid-s5362" xml:space="preserve">Sequenti etiam <lb/>experimento, quod jam præcedentibus patuit, alio modo <lb/>demonſtramus.</s> <s xml:id="echoid-s5363" xml:space="preserve"/> </p> <div xml:id="echoid-div764" type="float" level="2" n="2"> <note position="left" xlink:label="note-0200-05" xlink:href="note-0200-05a" xml:space="preserve">505.</note> </div> </div> <div xml:id="echoid-div766" type="section" level="1" n="202"> <head xml:id="echoid-head288" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <note position="left" xml:space="preserve">506.</note> <p> <s xml:id="echoid-s5364" xml:space="preserve">Incurrant in ſe mutuo uterque velocitate quinque, cylin-<lb/> <anchor type="note" xlink:label="note-0200-07a" xlink:href="note-0200-07"/> <pb o="135" file="0201" n="219" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> drus ſæpius memoratus F, & </s> <s xml:id="echoid-s5365" xml:space="preserve">cylindrus cavus argillam <lb/>continens H (Fig. </s> <s xml:id="echoid-s5366" xml:space="preserve">5. </s> <s xml:id="echoid-s5367" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5368" xml:space="preserve">18.)</s> <s xml:id="echoid-s5369" xml:space="preserve">, qui cum præcedenti ſit <lb/>ejuſdem ponderis.</s> <s xml:id="echoid-s5370" xml:space="preserve"/> </p> <div xml:id="echoid-div766" type="float" level="2" n="1"> <note position="left" xlink:label="note-0200-07" xlink:href="note-0200-07a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s5371" xml:space="preserve">Sublatis his incurrant in ſe mutuo uterque velocitate de-<lb/> <anchor type="note" xlink:label="note-0201-01a" xlink:href="note-0201-01"/> cem, cylindrus D cum cylindro cavo argillam continenti G, <lb/>qui etiam æqualiter ponderent.</s> <s xml:id="echoid-s5372" xml:space="preserve"/> </p> <div xml:id="echoid-div767" type="float" level="2" n="2"> <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s5373" xml:space="preserve">Tandem ſublato cylindro D, & </s> <s xml:id="echoid-s5374" xml:space="preserve">ſubſtituto cylindro F, <lb/> <anchor type="note" xlink:label="note-0201-02a" xlink:href="note-0201-02"/> unitâque iterum argillâ cylindri G, incurrant hi in ſe invi-<lb/>cem iiſdem velocitatibus, quibus in jam memoratis im-<lb/>pactionibus fuere agitati, id eſt, ut in Exp. </s> <s xml:id="echoid-s5375" xml:space="preserve">3°. </s> <s xml:id="echoid-s5376" xml:space="preserve">hic velocitate <lb/>decem, ille velocitate quinque.</s> <s xml:id="echoid-s5377" xml:space="preserve"/> </p> <div xml:id="echoid-div768" type="float" level="2" n="3"> <note position="right" xlink:label="note-0201-02" xlink:href="note-0201-02a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s5378" xml:space="preserve">In hiſce tribus occaſionibus poſt ictum corpora quieſcunt; <lb/></s> <s xml:id="echoid-s5379" xml:space="preserve">cavitates autem ſunt inæquales. </s> <s xml:id="echoid-s5380" xml:space="preserve">In primo caſu eſt omnium <lb/>minima, repræſentatur in T; </s> <s xml:id="echoid-s5381" xml:space="preserve">in ſecundo eſt omnium maxima, <lb/> <anchor type="note" xlink:label="note-0201-03a" xlink:href="note-0201-03"/> vide X; </s> <s xml:id="echoid-s5382" xml:space="preserve">in tertio media eſt, delineatur in V: </s> <s xml:id="echoid-s5383" xml:space="preserve">& </s> <s xml:id="echoid-s5384" xml:space="preserve">quidem ſunt <lb/>cavitates in proportione arithmetica, ut ipſæ vires ictibus <lb/>deſtructæ. </s> <s xml:id="echoid-s5385" xml:space="preserve">In primo caſu maſſæ ſingulæ valent quatuor <lb/>velocitate quinque corpus utrumque fertur, id eſt utriuſque <lb/>vis eſt centum <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s5386" xml:space="preserve">vis deſtructa valet ducenta.</s> <s xml:id="echoid-s5387" xml:space="preserve"> <anchor type="note" xlink:label="note-0201-04a" xlink:href="note-0201-04"/> </s> </p> <div xml:id="echoid-div769" type="float" level="2" n="4"> <note position="right" xlink:label="note-0201-03" xlink:href="note-0201-03a" xml:space="preserve"><emph style="sc">TAB. XIX</emph> <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0201-04" xlink:href="note-0201-04a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s5388" xml:space="preserve">In Secundo caſu utriuſque corporis maſſa eſt duo, & </s> <s xml:id="echoid-s5389" xml:space="preserve"><lb/>velocitas decem; </s> <s xml:id="echoid-s5390" xml:space="preserve">ergo vis ducenta <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5391" xml:space="preserve">& </s> <s xml:id="echoid-s5392" xml:space="preserve">vis deſtructa <anchor type="note" xlink:label="note-0201-05a" xlink:href="note-0201-05"/> quadringenta, in hoc etiam caſu cavitas dupla eſt cavitatis <lb/>præcedentis.</s> <s xml:id="echoid-s5393" xml:space="preserve"/> </p> <div xml:id="echoid-div770" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0201-05" xlink:href="note-0201-05a" xml:space="preserve">470</note> </div> <p> <s xml:id="echoid-s5394" xml:space="preserve">In tertio caſu unius corporis vis eſt centum, alterius valet <lb/>ducenta & </s> <s xml:id="echoid-s5395" xml:space="preserve">vis quæ deſtructa eſt valet trecenta; </s> <s xml:id="echoid-s5396" xml:space="preserve">cavitasideo <lb/>media eſt inter cavitates præcedentes.</s> <s xml:id="echoid-s5397" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5398" xml:space="preserve">Si in experimento tertio vis minor augeatur, ita tamen <lb/> <anchor type="note" xlink:label="note-0201-06a" xlink:href="note-0201-06"/> ut vim alterius corporis nondum æquet, corpus, cujus vis <lb/>minor erit, corpus majori vi motum regredi coget; </s> <s xml:id="echoid-s5399" xml:space="preserve">directo <lb/>in hoc caſu experimento demonſtramus vim corporis victi, <lb/>alterius vim ſuperare; </s> <s xml:id="echoid-s5400" xml:space="preserve">eodem modo ac in Exp. </s> <s xml:id="echoid-s5401" xml:space="preserve">4. </s> <s xml:id="echoid-s5402" xml:space="preserve">demon-<lb/>ſtravimus vires in Exp. </s> <s xml:id="echoid-s5403" xml:space="preserve">3. </s> <s xml:id="echoid-s5404" xml:space="preserve">fuiſſe inæquales.</s> <s xml:id="echoid-s5405" xml:space="preserve"/> </p> <div xml:id="echoid-div771" type="float" level="2" n="6"> <note position="right" xlink:label="note-0201-06" xlink:href="note-0201-06a" xml:space="preserve">507.</note> </div> <p> <s xml:id="echoid-s5406" xml:space="preserve">Vis corpori inſita alterius vim nunquam immediate de-<lb/> <anchor type="note" xlink:label="note-0201-07a" xlink:href="note-0201-07"/> ſtruit <anchor type="note" xlink:href="" symbol="*"/>, perit hæc actione qua partes intropremuntur <anchor type="note" xlink:href="" symbol="*"/>, ita <anchor type="note" xlink:label="note-0201-08a" xlink:href="note-0201-08"/> <anchor type="note" xlink:label="note-0201-09a" xlink:href="note-0201-09"/> ut corpus eo majorem amittat vim, quo majorem patitur re-<lb/>ſiſtentiam; </s> <s xml:id="echoid-s5407" xml:space="preserve">ſed hæc a materiæ inertiâ & </s> <s xml:id="echoid-s5408" xml:space="preserve">a vi contrariâ ori- <pb o="136" file="0202" n="220" rhead="PHYSICES ELEMENTA"/> poteſt, ita ut corporis vis minuenda ſit, ſi hujus inertia, id <lb/>eſt, materiæ quantitas <anchor type="note" xlink:href="" symbol="*"/> augeatur, ut in utroque <anchor type="note" xlink:href="" symbol="*"/> caſu <anchor type="note" xlink:label="note-0202-01a" xlink:href="note-0202-01"/> æqualiter alii corpori reſiſtat, unde paradoxi explicationem <lb/>deducimus. </s> <s xml:id="echoid-s5409" xml:space="preserve">Nam, ut ex hac obſervatione ſequitur, Quando <lb/> <anchor type="note" xlink:label="note-0202-02a" xlink:href="note-0202-02"/> duo corpora in ſe mutuo incurrunt, duæ dantur actiones, & </s> <s xml:id="echoid-s5410" xml:space="preserve"><lb/>duæ reactiones, utraque actio ſuæ reactioni æqualis eſt; </s> <s xml:id="echoid-s5411" xml:space="preserve">ut <lb/>corpora quieſcant poſt ictum, non requiritur ut ante ictum <lb/>vires contrariæ ſint æquales, ſed ut utrumque corpus <lb/>patiatur reſiſtentiam talem, ut agendo poſſit vim ſuam con-<lb/>ſumere.</s> <s xml:id="echoid-s5412" xml:space="preserve"/> </p> <div xml:id="echoid-div772" type="float" level="2" n="7"> <note position="right" xlink:label="note-0201-07" xlink:href="note-0201-07a" xml:space="preserve">508.</note> <note symbol="*" position="right" xlink:label="note-0201-08" xlink:href="note-0201-08a" xml:space="preserve">489.</note> <note symbol="*" position="right" xlink:label="note-0201-09" xlink:href="note-0201-09a" xml:space="preserve">488.</note> <note symbol="*" position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">13.</note> <note position="left" xlink:label="note-0202-02" xlink:href="note-0202-02a" xml:space="preserve">509.</note> </div> <p> <s xml:id="echoid-s5413" xml:space="preserve">Ex demonſtratis facile deducimus quomodo datis corpo-<lb/> <anchor type="note" xlink:label="note-0202-03a" xlink:href="note-0202-03"/> ribus, & </s> <s xml:id="echoid-s5414" xml:space="preserve">horum velocitate reſpectiva, vis ictu deſtructa de-<lb/>terminetur: </s> <s xml:id="echoid-s5415" xml:space="preserve">determinatâ, nempe ſummâ virium, poſitis, eâ-<lb/>dem velocitate reſpectivâ, motibus contrariis, & </s> <s xml:id="echoid-s5416" xml:space="preserve">velocita-<lb/> <anchor type="note" xlink:label="note-0202-04a" xlink:href="note-0202-04"/> tibus in ratione inverſa maſſarum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5417" xml:space="preserve">Hanc autem ſummam dari in ſcholio 1. </s> <s xml:id="echoid-s5418" xml:space="preserve">ſequenti demonſtramus, Si produ-<lb/>ctum maſſarum per quadratum velocitatis reſpectivæ multi-<lb/>plicetur, & </s> <s xml:id="echoid-s5419" xml:space="preserve">per ſummam maſſarum dividatur.</s> <s xml:id="echoid-s5420" xml:space="preserve"/> </p> <div xml:id="echoid-div773" type="float" level="2" n="8"> <note position="left" xlink:label="note-0202-03" xlink:href="note-0202-03a" xml:space="preserve">510.</note> <note symbol="*" position="left" xlink:label="note-0202-04" xlink:href="note-0202-04a" xml:space="preserve">497. 500.</note> </div> </div> <div xml:id="echoid-div775" type="section" level="1" n="203"> <head xml:id="echoid-head289" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <note position="left" xml:space="preserve">511.</note> <p> <s xml:id="echoid-s5421" xml:space="preserve">Suſpenſis cylindris E (fig. </s> <s xml:id="echoid-s5422" xml:space="preserve">4. </s> <s xml:id="echoid-s5423" xml:space="preserve">Tab 18.) </s> <s xml:id="echoid-s5424" xml:space="preserve">& </s> <s xml:id="echoid-s5425" xml:space="preserve">G, ſæpius memo-<lb/> <anchor type="note" xlink:label="note-0202-06a" xlink:href="note-0202-06"/> rato, redacto hoc ad pondus cylindri D, id eſt ſint maſſæ ut <lb/>tria ad duo; </s> <s xml:id="echoid-s5426" xml:space="preserve">incurrant corpora hæc in ſe mutuo dum am-<lb/>bo in contrarias partes feruntur, majus velocitate ſeptemde-<lb/>cim, minus velocitate tria, in quo caſu velocitas reſpe-<lb/> <anchor type="note" xlink:label="note-0202-07a" xlink:href="note-0202-07"/> ctiva eſt viginti <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5427" xml:space="preserve">Poſt ictum moventur ſimul velocitate novem, id eſt ad nonam uſque diviſionem adſcendunt.</s> <s xml:id="echoid-s5428" xml:space="preserve"/> </p> <div xml:id="echoid-div775" type="float" level="2" n="1"> <note position="left" xlink:label="note-0202-06" xlink:href="note-0202-06a" xml:space="preserve"><emph style="sc">TAB. XXII.</emph> <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0202-07" xlink:href="note-0202-07a" xml:space="preserve">475.</note> </div> <p> <s xml:id="echoid-s5429" xml:space="preserve">Multiplicando maſſas habemus 6. </s> <s xml:id="echoid-s5430" xml:space="preserve">Quadratum velocitatis <lb/>reſpectivæ eſt 400. </s> <s xml:id="echoid-s5431" xml:space="preserve">cujus productum per productum maſſa-<lb/>rum eſt 2400; </s> <s xml:id="echoid-s5432" xml:space="preserve">dividendo numerum hunc per 5. </s> <s xml:id="echoid-s5433" xml:space="preserve">ſummam <lb/>maſſarum habemus, vim amiſſam 480. </s> <s xml:id="echoid-s5434" xml:space="preserve">Hanc autem bene <lb/>determinari demonſtramus.</s> <s xml:id="echoid-s5435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5436" xml:space="preserve">Vis corporis majoris ante ictum habetur multiplicando <lb/>289. </s> <s xml:id="echoid-s5437" xml:space="preserve">per 3 <anchor type="note" xlink:href="" symbol="*"/>, eſt ergo 867. </s> <s xml:id="echoid-s5438" xml:space="preserve">Minoris vis habetur multipli- <anchor type="note" xlink:label="note-0202-08a" xlink:href="note-0202-08"/> cando 9. </s> <s xml:id="echoid-s5439" xml:space="preserve">per 2 <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5440" xml:space="preserve">eſt ideo 18; </s> <s xml:id="echoid-s5441" xml:space="preserve">& </s> <s xml:id="echoid-s5442" xml:space="preserve">ſumma virium eſt 885.</s> <s xml:id="echoid-s5443" xml:space="preserve"> <anchor type="note" xlink:label="note-0202-09a" xlink:href="note-0202-09"/> Poſt ictum maſſa eſt 5 & </s> <s xml:id="echoid-s5444" xml:space="preserve">quadratum velocitatis 81, id circo <lb/>ſupereſt vis 405, quæ ſi ſubducatur ex 885. </s> <s xml:id="echoid-s5445" xml:space="preserve">habemus ut an-<lb/>te vim amiſſam 480.</s> <s xml:id="echoid-s5446" xml:space="preserve"/> </p> <div xml:id="echoid-div776" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0202-08" xlink:href="note-0202-08a" xml:space="preserve">470.</note> <note symbol="*" position="left" xlink:label="note-0202-09" xlink:href="note-0202-09a" xml:space="preserve">470.</note> </div> <pb o="137" file="0203" n="221" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> <p> <s xml:id="echoid-s5447" xml:space="preserve">Si cylindrus F cujus maſſa eſt quatuor, velocitate undecim, <lb/> <anchor type="note" xlink:label="note-0203-01a" xlink:href="note-0203-01"/> demtâ parte vigeſimâ ſecundâ, in obicem firmum incurrat, <lb/>cavitatem formabit æqualem illi, quæ in hoc experimento im-<lb/>pactione corporum fuit formata, vis in hoc caſu amiſſa eſt <lb/>480 {1/121} <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5448" xml:space="preserve">id eſt vix a vi, in impactione memorata amiſſa, <anchor type="note" xlink:label="note-0203-02a" xlink:href="note-0203-02"/> differt; </s> <s xml:id="echoid-s5449" xml:space="preserve">quod ergo <anchor type="note" xlink:href="" symbol="*"/> iterum confirmat, vim ictu deſtructam <anchor type="note" xlink:label="note-0203-03a" xlink:href="note-0203-03"/> regula n. </s> <s xml:id="echoid-s5450" xml:space="preserve">510. </s> <s xml:id="echoid-s5451" xml:space="preserve">bene fuiſſe determinatam.</s> <s xml:id="echoid-s5452" xml:space="preserve"/> </p> <div xml:id="echoid-div777" type="float" level="2" n="3"> <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve"><emph style="sc">TAB. XXII.</emph> <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">470.</note> <note symbol="*" position="right" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">462</note> </div> <p> <s xml:id="echoid-s5453" xml:space="preserve">Ex demonſtratis de corporibus poſt ictum quieſcentibus <lb/>deducimus regulas quibus in omni caſu corporum velocita-<lb/>tes poſt ictum determinantur.</s> <s xml:id="echoid-s5454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5455" xml:space="preserve">Moveantur corpora, aut verſus eandem partem (fig. </s> <s xml:id="echoid-s5456" xml:space="preserve">1.) <lb/></s> <s xml:id="echoid-s5457" xml:space="preserve"> <anchor type="note" xlink:label="note-0203-04a" xlink:href="note-0203-04"/> aut in partes contrarias (fig. </s> <s xml:id="echoid-s5458" xml:space="preserve">2.) </s> <s xml:id="echoid-s5459" xml:space="preserve">& </s> <s xml:id="echoid-s5460" xml:space="preserve">ſint maſſæ ut AB & </s> <s xml:id="echoid-s5461" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0203-05a" xlink:href="note-0203-05"/> BC; </s> <s xml:id="echoid-s5462" xml:space="preserve">ſit hujus velocitas BE; </s> <s xml:id="echoid-s5463" xml:space="preserve">illius BN: </s> <s xml:id="echoid-s5464" xml:space="preserve">velocitas reſpe-<lb/>ctiva erit EN <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5465" xml:space="preserve">Dividatur hæc in I ita, ut IN ſit ad <anchor type="note" xlink:label="note-0203-06a" xlink:href="note-0203-06"/> IE, ut BC ad BA, & </s> <s xml:id="echoid-s5466" xml:space="preserve">erit BI velocitas, qua ambo cor-<lb/>pora poſt ictum feruntur; </s> <s xml:id="echoid-s5467" xml:space="preserve">id eſt mutationes in velocitatibus <lb/>ſunt in ratione inver ſa maſſarum, BC acquirit EI dum AB <lb/>amittit NI. </s> <s xml:id="echoid-s5468" xml:space="preserve">Si enim concipiamus navem translatam velo-<lb/>citate BI, & </s> <s xml:id="echoid-s5469" xml:space="preserve">in hac moveatur corpus BC velocitate IE a <lb/>prora ad puppim, habet velocitatem abſolutam BE; </s> <s xml:id="echoid-s5470" xml:space="preserve">& </s> <s xml:id="echoid-s5471" xml:space="preserve"><lb/>corpus AB feratur a puppi ad proram velocitate IN, ha-<lb/>bebit hoc velocitatem abſolutam BN; </s> <s xml:id="echoid-s5472" xml:space="preserve">hæc corpora, cum <lb/>in nave ferantur directionibus contrariis, & </s> <s xml:id="echoid-s5473" xml:space="preserve">velocitatibus, <lb/>quæ ſunt inverſè ut maſiæ, poſt ictum, in nave quie-<lb/>ſcunt <anchor type="note" xlink:href="" symbol="*"/>, id eſt eadem cum nave velocitate ferun- <anchor type="note" xlink:label="note-0203-07a" xlink:href="note-0203-07"/> tur.</s> <s xml:id="echoid-s5474" xml:space="preserve"/> </p> <div xml:id="echoid-div778" type="float" level="2" n="4"> <note position="right" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">512.</note> <note position="right" xlink:label="note-0203-05" xlink:href="note-0203-05a" xml:space="preserve"><emph style="sc">TAB XX.</emph> <lb/>fig. 1. 2.</note> <note symbol="*" position="right" xlink:label="note-0203-06" xlink:href="note-0203-06a" xml:space="preserve">474. 475.</note> <note symbol="*" position="right" xlink:label="note-0203-07" xlink:href="note-0203-07a" xml:space="preserve">500.</note> </div> <p> <s xml:id="echoid-s5475" xml:space="preserve">Determinatur BI regulâ facili, quam ut detegamus, ſint <lb/>rectangula BM, BF producta maſſarum per ſuas celerita-<lb/>tes, & </s> <s xml:id="echoid-s5476" xml:space="preserve">abſolvantur parallelogramma AO & </s> <s xml:id="echoid-s5477" xml:space="preserve">CD; </s> <s xml:id="echoid-s5478" xml:space="preserve">ductâ <lb/>DO, ſecat hæc BN in I; </s> <s xml:id="echoid-s5479" xml:space="preserve">nam triangula DIE & </s> <s xml:id="echoid-s5480" xml:space="preserve">INQ <lb/>ſunt ſimilia, & </s> <s xml:id="echoid-s5481" xml:space="preserve">IN ad IE, ut NO, aut BC, ad DE, <lb/>aut AB. </s> <s xml:id="echoid-s5482" xml:space="preserve">Per I ducatur HL, parallela AB, & </s> <s xml:id="echoid-s5483" xml:space="preserve">complementa <lb/>IM, IF <anchor type="note" xlink:href="" symbol="*"/>, erunt æqualia; </s> <s xml:id="echoid-s5484" xml:space="preserve">ergo corporibus tendentibus ad ean- <anchor type="note" xlink:label="note-0203-08a" xlink:href="note-0203-08"/> <anchor type="note" xlink:label="note-0203-09a" xlink:href="note-0203-09"/> dem partem, ſi ex ſumma productorum BM, & </s> <s xml:id="echoid-s5485" xml:space="preserve">BF, maſ-<lb/> <anchor type="note" xlink:label="note-0203-10a" xlink:href="note-0203-10"/> ſarum per ſuas velocitates ſubtrahamus MI, & </s> <s xml:id="echoid-s5486" xml:space="preserve">ejus loco ſub- <pb o="138" file="0204" n="222" rhead="PHYSICES ELEMENTA"/> ſtituamus IF, prædicta ſumma æqualis erit rectangulo AL, <lb/>quod ſi dividatur per <emph style="sc">A</emph> C, ſummam maſſarum, quotiens di-<lb/>viſionis dabit <emph style="sc">A</emph> H, aut BI, velocitatem corporibus com-<lb/>munem poſt ictum.</s> <s xml:id="echoid-s5487" xml:space="preserve"/> </p> <div xml:id="echoid-div779" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0203-08" xlink:href="note-0203-08a" xml:space="preserve">43. <emph style="sc">EL</emph>. 1.</note> <note position="right" xlink:label="note-0203-09" xlink:href="note-0203-09a" xml:space="preserve">513.</note> <note position="right" xlink:label="note-0203-10" xlink:href="note-0203-10a" xml:space="preserve">fig. 1.</note> </div> </div> <div xml:id="echoid-div781" type="section" level="1" n="204"> <head xml:id="echoid-head290" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s5488" xml:space="preserve">Globi duo æquales ex argilla molli ſuſpenduntur, ſi hi <lb/> <anchor type="note" xlink:label="note-0204-01a" xlink:href="note-0204-01"/> partem eandem verſus moveantur, P velocitate decem, Q <lb/> <anchor type="note" xlink:label="note-0204-02a" xlink:href="note-0204-02"/> velocitate ſex; </s> <s xml:id="echoid-s5489" xml:space="preserve">poſt ictum motum ſimul continuabunt ve-<lb/>locitate octo.</s> <s xml:id="echoid-s5490" xml:space="preserve"/> </p> <div xml:id="echoid-div781" type="float" level="2" n="1"> <note position="left" xlink:label="note-0204-01" xlink:href="note-0204-01a" xml:space="preserve">514.</note> <note position="left" xlink:label="note-0204-02" xlink:href="note-0204-02a" xml:space="preserve"><emph style="sc">TAB. XXI.</emph> <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s5491" xml:space="preserve">Cum maſſæ ſint æquales unitate deſignari poſſunt, & </s> <s xml:id="echoid-s5492" xml:space="preserve">ſum-<lb/>ma productorum maſſarum per velocitates eſt ſedecim, quæ <lb/>ſi per ſummam maſſarum duo dividatur habemus ut in Ex-<lb/>perimento velocitatem octo,</s> </p> </div> <div xml:id="echoid-div783" type="section" level="1" n="205"> <head xml:id="echoid-head291" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s5493" xml:space="preserve">Suſpenſis cylindris, eburneo E cujus maſſa eſt tria, <lb/> <anchor type="note" xlink:label="note-0204-03a" xlink:href="note-0204-03"/> & </s> <s xml:id="echoid-s5494" xml:space="preserve">ligneo argillam continenti G, cujus maſſa eſt duo, feran-<lb/> <anchor type="note" xlink:label="note-0204-04a" xlink:href="note-0204-04"/> tur hi ad eandem partem, primus velocitate duodecim, ſe-<lb/>cundus velocitate ſeptem, poſt ictum ſimul velocitate de-<lb/>cem moventur.</s> <s xml:id="echoid-s5495" xml:space="preserve"/> </p> <div xml:id="echoid-div783" type="float" level="2" n="1"> <note position="left" xlink:label="note-0204-03" xlink:href="note-0204-03a" xml:space="preserve">515.</note> <note position="left" xlink:label="note-0204-04" xlink:href="note-0204-04a" xml:space="preserve"><emph style="sc">TA. XXII.</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s5496" xml:space="preserve">Multiplicando maſſam 3 per velocitatem 12, habemus <lb/>36, addito 14, producto maſſæ 2 per velocitatem 7, habe-<lb/>mus ſummam productorum 50, quæ ſi dividatur per ſum-<lb/>mam maſſarum 5, habemus velocitatem experimento dete-<lb/>ctam 10.</s> <s xml:id="echoid-s5497" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5498" xml:space="preserve">Si corpora tendant in partes contrarias, & </s> <s xml:id="echoid-s5499" xml:space="preserve">ex producto <lb/> <anchor type="note" xlink:label="note-0204-05a" xlink:href="note-0204-05"/> majori BM ſubtrahamus MI, & </s> <s xml:id="echoid-s5500" xml:space="preserve">ſubſtituamus IF, habe-<lb/> <anchor type="note" xlink:label="note-0204-06a" xlink:href="note-0204-06"/> mus BM æquale gnomoni AHLFEB; </s> <s xml:id="echoid-s5501" xml:space="preserve">ex quo ſi ſub-<lb/>trahamus productum BF, habemus HC diſſerentiam pro-<lb/>ductorum maſſarum per ſuas velocitates; </s> <s xml:id="echoid-s5502" xml:space="preserve">ſi autem hanc di-<lb/>vidamus per ſummam maſſarum AC, quotiens erit veloci-<lb/>tas quæſita BI, quæ dirigitur ad eandem partem cum BN: <lb/></s> <s xml:id="echoid-s5503" xml:space="preserve">id eſt ambo corpora, velocitate detectâ, feruntur verſus <lb/>eandem partem cum corpore, cujus productum maßæ per <lb/>velocitatem alius productum ſimile excedit.</s> <s xml:id="echoid-s5504" xml:space="preserve"/> </p> <div xml:id="echoid-div784" type="float" level="2" n="2"> <note position="left" xlink:label="note-0204-05" xlink:href="note-0204-05a" xml:space="preserve">516.</note> <note position="left" xlink:label="note-0204-06" xlink:href="note-0204-06a" xml:space="preserve"><emph style="sc">TAB. XX.</emph> <lb/>fig. 2.</note> </div> <pb o="139" file="0205" n="223" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> </div> <div xml:id="echoid-div786" type="section" level="1" n="206"> <head xml:id="echoid-head292" xml:space="preserve"><emph style="sc">Experimentum</emph> 10.</head> <p> <s xml:id="echoid-s5505" xml:space="preserve">Suſpenſis globis, ex argilla molli, æqualibus P & </s> <s xml:id="echoid-s5506" xml:space="preserve">Q, ſint <lb/> <anchor type="note" xlink:label="note-0205-01a" xlink:href="note-0205-01"/> hi in contrarias partes moti, P velocitate ſex, Q velocita-<lb/> <anchor type="note" xlink:label="note-0205-02a" xlink:href="note-0205-02"/> te quatuordecim, poſt ictum velocitate quatuor motum con-<lb/>tinuat, Q ſecum ferens P.</s> <s xml:id="echoid-s5507" xml:space="preserve"/> </p> <div xml:id="echoid-div786" type="float" level="2" n="1"> <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">517.</note> <note position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve"><emph style="sc">TAB. XXL.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s5508" xml:space="preserve">Quia propter maſſas æquales hæ unitate deſignari poſſunt, <lb/>producta maſſarum per velocitates ſunt 6. </s> <s xml:id="echoid-s5509" xml:space="preserve">& </s> <s xml:id="echoid-s5510" xml:space="preserve">14.</s> <s xml:id="echoid-s5511" xml:space="preserve">, quorum <lb/>differentia eſt 8.</s> <s xml:id="echoid-s5512" xml:space="preserve">, quæ diviſa per ſummam maſſarum 2, dat <lb/>velocitatem poſt ictum quatuor.</s> <s xml:id="echoid-s5513" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div788" type="section" level="1" n="207"> <head xml:id="echoid-head293" xml:space="preserve"><emph style="sc">Experimentum</emph> 11.</head> <p> <s xml:id="echoid-s5514" xml:space="preserve">Non differt experimentum hoc à colliſione in Experimen-<lb/> <anchor type="note" xlink:label="note-0205-03a" xlink:href="note-0205-03"/> to 7. </s> <s xml:id="echoid-s5515" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> memoratâ, poteſt autem velocitas corporum poſt <anchor type="note" xlink:label="note-0205-04a" xlink:href="note-0205-04"/> ictum ex nunc demonſtratis determinari.</s> <s xml:id="echoid-s5516" xml:space="preserve"/> </p> <div xml:id="echoid-div788" type="float" level="2" n="1"> <note position="right" xlink:label="note-0205-03" xlink:href="note-0205-03a" xml:space="preserve">518.</note> <note position="right" xlink:label="note-0205-04" xlink:href="note-0205-04a" xml:space="preserve"><emph style="sc">TA. XXIL.</emph> <lb/>fig. 1.</note> </div> <note symbol="*" position="right" xml:space="preserve">511.</note> <p> <s xml:id="echoid-s5517" xml:space="preserve">Multiplicando maſſam E per velocitatem 17.</s> <s xml:id="echoid-s5518" xml:space="preserve">, habemus 51; <lb/></s> <s xml:id="echoid-s5519" xml:space="preserve">ſubtractis 6, producto maſſæ 2 per velocitatem 3, reſtat 45; </s> <s xml:id="echoid-s5520" xml:space="preserve"><lb/>quibus diviſis per 5. </s> <s xml:id="echoid-s5521" xml:space="preserve">ſummam maſſarum, habemus velocita-<lb/>tem novem Experimento detectam.</s> <s xml:id="echoid-s5522" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s5523" xml:space="preserve">Si corpus unum quieſcat, ex utrâque regulâ ſequitur cor-<lb/> <anchor type="note" xlink:label="note-0205-06a" xlink:href="note-0205-06"/> poris moti productum velocitatis per maſſam dividi debere <lb/>per maſſarum ſummam.</s> <s xml:id="echoid-s5524" xml:space="preserve"/> </p> <div xml:id="echoid-div789" type="float" level="2" n="2"> <note position="right" xlink:label="note-0205-06" xlink:href="note-0205-06a" xml:space="preserve">519.</note> </div> </div> <div xml:id="echoid-div791" type="section" level="1" n="208"> <head xml:id="echoid-head294" xml:space="preserve"><emph style="sc">Experimentum</emph> 12.</head> <p> <s xml:id="echoid-s5525" xml:space="preserve">Globus P ex argillâ molli in globum æqualem quieſcen-<lb/> <anchor type="note" xlink:label="note-0205-07a" xlink:href="note-0205-07"/> tem Q, velocitate decem, incurrit, poſt ictum ſimul velo-<lb/>citate quinque motum continuant.</s> <s xml:id="echoid-s5526" xml:space="preserve"/> </p> <div xml:id="echoid-div791" type="float" level="2" n="1"> <note position="right" xlink:label="note-0205-07" xlink:href="note-0205-07a" xml:space="preserve"><emph style="sc">TAB XXI.</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s5527" xml:space="preserve">Corpus in motu alii corpori ſine impactione motum com-<lb/> <anchor type="note" xlink:label="note-0205-08a" xlink:href="note-0205-08"/> municare poteſt, in hoc tantum preſſione agendo; </s> <s xml:id="echoid-s5528" xml:space="preserve">in quo ca-<lb/>ſu ſi preſſio qua partes cohærent inter ſe ſuperet preſſionem <lb/>corporum mutuam nulla datur partium introceſſio, & </s> <s xml:id="echoid-s5529" xml:space="preserve">nulla vis <lb/>deſtructa <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s5530" xml:space="preserve">ideoque ſumma virium ante & </s> <s xml:id="echoid-s5531" xml:space="preserve">poſt actionem <anchor type="note" xlink:label="note-0205-09a" xlink:href="note-0205-09"/> eadem eſt.</s> <s xml:id="echoid-s5532" xml:space="preserve"/> </p> <div xml:id="echoid-div792" type="float" level="2" n="2"> <note position="right" xlink:label="note-0205-08" xlink:href="note-0205-08a" xml:space="preserve">520.</note> <note symbol="*" position="right" xlink:label="note-0205-09" xlink:href="note-0205-09a" xml:space="preserve">488;</note> </div> <p> <s xml:id="echoid-s5533" xml:space="preserve">Ut autem demonſtremus quomodo corpora mota, preſſio-<lb/> <anchor type="note" xlink:label="note-0205-10a" xlink:href="note-0205-10"/> ne in alia, ſine impactione, motum communicare poſſint, con-<lb/> <anchor type="note" xlink:label="note-0205-11a" xlink:href="note-0205-11"/> cipiendum eſt corpus Q, quod formatur revolutione figuræ <lb/>a b c d (quæ ſemicirculo & </s> <s xml:id="echoid-s5534" xml:space="preserve">duobus quadrantibus termina-<lb/>tur) circa axem a c.</s> <s xml:id="echoid-s5535" xml:space="preserve"/> </p> <div xml:id="echoid-div793" type="float" level="2" n="3"> <note position="right" xlink:label="note-0205-10" xlink:href="note-0205-10a" xml:space="preserve">521.</note> <note position="right" xlink:label="note-0205-11" xlink:href="note-0205-11a" xml:space="preserve"><emph style="sc">TAB. XXI.</emph> <lb/>fig 4.</note> </div> <pb o="140" file="0206" n="224" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s5536" xml:space="preserve">Quieſcat hoc, quamvis. </s> <s xml:id="echoid-s5537" xml:space="preserve">demonſtratio etiam corpori moto <lb/>applicari poſſit; </s> <s xml:id="echoid-s5538" xml:space="preserve">concipiamus ulterius duo corpora P, P; <lb/></s> <s xml:id="echoid-s5539" xml:space="preserve">duo concipimus ut actio in corpus Q ſit directa; </s> <s xml:id="echoid-s5540" xml:space="preserve">moveantur <lb/>hæc, velocitatibus æqualibus, directionibus parallelis inter ſe, <lb/>& </s> <s xml:id="echoid-s5541" xml:space="preserve">axi corporis Q, moveantur etiam, ut ad Q perveniant ita, ut <lb/>corporis Q ſuperſicies tangat corpora P, P, in punctis in <lb/>quibus hæc ipſa ſuperſicies parallela eſt ipſi directioni mo-<lb/>tus; </s> <s xml:id="echoid-s5542" xml:space="preserve">Corpora ergo P, P, in corpus Q nullam exerunt acti-<lb/>onem, ubiad hoc perveniunt. </s> <s xml:id="echoid-s5543" xml:space="preserve">Dum motum continuant jux-<lb/>ta ſuperſicies excavatas ad, ab, in corpus Q premunt, <lb/>quod cum non retineatur cedit <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s5544" xml:space="preserve">dum preſſio continua- <anchor type="note" xlink:label="note-0206-01a" xlink:href="note-0206-01"/> tur acceleratur Q: </s> <s xml:id="echoid-s5545" xml:space="preserve">donec corpora P, P, hoc deſerant, <lb/>quod ſemper fiet antequam corpora P, P, puncta b & </s> <s xml:id="echoid-s5546" xml:space="preserve">d per-<lb/>veniant.</s> <s xml:id="echoid-s5547" xml:space="preserve"/> </p> <div xml:id="echoid-div794" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve"> 433.</note> </div> <p> <s xml:id="echoid-s5548" xml:space="preserve">Hæc preſſio nullum exſerit effectum præter mo-<lb/>tum quem corpori Q communicat; </s> <s xml:id="echoid-s5549" xml:space="preserve">ideoque corpora P, P, <lb/>ex viribus tantum amittunt, quantum acquirit corpus Q <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5550" xml:space="preserve"> <anchor type="note" xlink:label="note-0206-02a" xlink:href="note-0206-02"/> In hiſce attritum ſeponimus qui ſine quadam partium intro-<lb/>ceſſione dari non poteſt; </s> <s xml:id="echoid-s5551" xml:space="preserve">ideoque ſine virium deſtructione. <lb/></s> <s xml:id="echoid-s5552" xml:space="preserve">In ſcholio autem 3°. </s> <s xml:id="echoid-s5553" xml:space="preserve">Cap, 28. </s> <s xml:id="echoid-s5554" xml:space="preserve">ipſos motus poſt concurſum <lb/>determinamus.</s> <s xml:id="echoid-s5555" xml:space="preserve"/> </p> <div xml:id="echoid-div795" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">458.</note> </div> <p> <s xml:id="echoid-s5556" xml:space="preserve">Si corpus ut P ſimili actione premat in obſtaculum, quod <lb/> <anchor type="note" xlink:label="note-0206-03a" xlink:href="note-0206-03"/> hac preſſione non movetur, & </s> <s xml:id="echoid-s5557" xml:space="preserve">cujus partes ſatis arctè co-<lb/> <anchor type="note" xlink:label="note-0206-04a" xlink:href="note-0206-04"/> hæreant, ut huic actioni non cedant, corpus ex vi ſua non <lb/>amittet; </s> <s xml:id="echoid-s5558" xml:space="preserve">in hoc caſu corporis preſſio in obſtaculum reſi-<lb/>ſtentiâ obſtaculi, quidem deſtruitur, ſed cum nul-<lb/>la detur partium introceſſio, neque vis communicata, nul-<lb/>lam etiam corpus P vim amittit; </s> <s xml:id="echoid-s5559" xml:space="preserve">ſic corpus quod ſuper <lb/>plano inclinato deſcendit eodem modo acceleratur ac cor-<lb/>pus quod libere cadit ſi ad eandem profunditatem ambo <lb/> <anchor type="note" xlink:label="note-0206-05a" xlink:href="note-0206-05"/> deſcendant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5560" xml:space="preserve">licet illud in planum premat. </s> <s xml:id="echoid-s5561" xml:space="preserve">In hiſce occa- ſionibus, illud quod obſtaculum in loco retinet corporis a-<lb/>ctionem deſtruit & </s> <s xml:id="echoid-s5562" xml:space="preserve">corpori vim communicat æqualem illi <lb/>quam actione ſua corpus amittit, quare ipſa corporis vis <lb/>non mutatur.</s> <s xml:id="echoid-s5563" xml:space="preserve"/> </p> <div xml:id="echoid-div796" type="float" level="2" n="6"> <note position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">522.</note> <note position="left" xlink:label="note-0206-04" xlink:href="note-0206-04a" xml:space="preserve"><emph style="sc">TAB. XIX.</emph> <lb/>fig. 9.</note> <note symbol="*" position="left" xlink:label="note-0206-05" xlink:href="note-0206-05a" xml:space="preserve">271.</note> </div> <pb file="0207" n="225"/> <figure> <image file="0207-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0207-01"/> </figure> <pb file="0207a" n="226"/> <pb file="0208" n="227"/> <pb o="141" file="0209" n="228" rhead="MATHEMATICA. LIB. I. CAP XXIII."/> <p> <s xml:id="echoid-s5564" xml:space="preserve">Ex hiſce patet actione corporis hujus vim, ideoque velo-<lb/> <anchor type="note" xlink:label="note-0209-01a" xlink:href="note-0209-01"/> oitatem, non minui ſine ipſius obſtaculi, aut partium hoc <lb/>componentium; </s> <s xml:id="echoid-s5565" xml:space="preserve">translatione ex hac actione oriunda.</s> <s xml:id="echoid-s5566" xml:space="preserve"/> </p> <div xml:id="echoid-div797" type="float" level="2" n="7"> <note position="right" xlink:label="note-0209-01" xlink:href="note-0209-01a" xml:space="preserve">523.</note> </div> </div> <div xml:id="echoid-div799" type="section" level="1" n="209"> <head xml:id="echoid-head295" xml:space="preserve">SCHOLIUM 1.</head> <head xml:id="echoid-head296" xml:space="preserve">Demonſtrationes n. 499. 510</head> <p> <s xml:id="echoid-s5567" xml:space="preserve">Dentur duo corpora A & </s> <s xml:id="echoid-s5568" xml:space="preserve">B; </s> <s xml:id="echoid-s5569" xml:space="preserve">ſit hujus velocitas b; </s> <s xml:id="echoid-s5570" xml:space="preserve">illius celeritas a; </s> <s xml:id="echoid-s5571" xml:space="preserve">velo-<lb/> <anchor type="note" xlink:label="note-0209-02a" xlink:href="note-0209-02"/> citas reſpectiva, ſi in contrarias partes ferantur eſt a + b <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5572" xml:space="preserve">hanc dici- <anchor type="note" xlink:label="note-0209-03a" xlink:href="note-0209-03"/> mus d. </s> <s xml:id="echoid-s5573" xml:space="preserve">Summa virium eſt Aaa + Bbb, quam, manente velocitate reſpecti-<lb/>va, diximus omnium minimam poſitis A, B:</s> <s xml:id="echoid-s5574" xml:space="preserve">: b, a <anchor type="note" xlink:href="" symbol="*"/>, id eſt Aa = Bb.</s> <s xml:id="echoid-s5575" xml:space="preserve"/> </p> <div xml:id="echoid-div799" type="float" level="2" n="1"> <note position="right" xlink:label="note-0209-02" xlink:href="note-0209-02a" xml:space="preserve">524.</note> <note symbol="*" position="right" xlink:label="note-0209-03" xlink:href="note-0209-03a" xml:space="preserve">475.</note> </div> <note symbol="*" position="right" xml:space="preserve">499.</note> <p> <s xml:id="echoid-s5576" xml:space="preserve">Poſitis enim talibus velocitatibus, augeatur a quantitate quacunque e; </s> <s xml:id="echoid-s5577" xml:space="preserve">vis <lb/>corporis A erit nunc Aaa + 2A ae + Aee. </s> <s xml:id="echoid-s5578" xml:space="preserve">Corporis B velocitas, quia <lb/>manet velocitas reſpectiva d = a + b, erit b-e; </s> <s xml:id="echoid-s5579" xml:space="preserve">nam a + e + b - e = a + b; </s> <s xml:id="echoid-s5580" xml:space="preserve">er-<lb/>go vis corporis B erit Bbb - 2Bbe + Bee, & </s> <s xml:id="echoid-s5581" xml:space="preserve">ſumma virium eſt Aaa <lb/>+ Bbb + Aee + Bee + 2Aae - 2Bbe.</s> <s xml:id="echoid-s5582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5583" xml:space="preserve">Sed propter Aa = Bb ſeſe mutuo duo ultimi termini deſtruunt, & </s> <s xml:id="echoid-s5584" xml:space="preserve">ſum-<lb/>ma valet Aaa + Bbb + Aee + Bee, quæ primam excedit. </s> <s xml:id="echoid-s5585" xml:space="preserve">Similis eſt de-<lb/>monſtratio ſi augeatur velocitas b, minutâ, eâdem quantitate, velocitate a; </s> <s xml:id="echoid-s5586" xml:space="preserve">un-<lb/>de patet demonſtratio n. </s> <s xml:id="echoid-s5587" xml:space="preserve">499.</s> <s xml:id="echoid-s5588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5589" xml:space="preserve">Poſuimus A, B:</s> <s xml:id="echoid-s5590" xml:space="preserve">:b, a; </s> <s xml:id="echoid-s5591" xml:space="preserve">componendo A + B, B:</s> <s xml:id="echoid-s5592" xml:space="preserve">:b + a = d, a; </s> <s xml:id="echoid-s5593" xml:space="preserve">ergo <lb/> <anchor type="note" xlink:label="note-0209-05a" xlink:href="note-0209-05"/> a = {Bd/A + B}, ſimiliter b = {Ad/A + B}; </s> <s xml:id="echoid-s5594" xml:space="preserve">idcirco ſumma virium Aaa + Bbb = <lb/>{ABBdd + BAAdd/<emph style="ol">B + A</emph><emph style="super">q</emph>} dividendo numeratorem & </s> <s xml:id="echoid-s5595" xml:space="preserve">denominatorem per <lb/>B + A, quantitas hæc æqualis eſt {ABdd/B + A} ut in n. </s> <s xml:id="echoid-s5596" xml:space="preserve">510. </s> <s xml:id="echoid-s5597" xml:space="preserve">monuimus.</s> <s xml:id="echoid-s5598" xml:space="preserve"/> </p> <div xml:id="echoid-div800" type="float" level="2" n="2"> <note position="right" xlink:label="note-0209-05" xlink:href="note-0209-05a" xml:space="preserve">525.</note> </div> </div> <div xml:id="echoid-div802" type="section" level="1" n="210"> <head xml:id="echoid-head297" style="it" xml:space="preserve">Demonſtrationes Algebraicæ n. 513. 516.</head> <p> <s xml:id="echoid-s5599" xml:space="preserve">Geometrice demonſtravimus regulas n. </s> <s xml:id="echoid-s5600" xml:space="preserve">513. </s> <s xml:id="echoid-s5601" xml:space="preserve">& </s> <s xml:id="echoid-s5602" xml:space="preserve">516. </s> <s xml:id="echoid-s5603" xml:space="preserve">algebraice quam ſa-<lb/>cillime deducuntur ex propoſitione numeri 512.</s> <s xml:id="echoid-s5604" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5605" xml:space="preserve">Sit corpus A motum velocitate a; </s> <s xml:id="echoid-s5606" xml:space="preserve">corpus B agitatum velocitate b: </s> <s xml:id="echoid-s5607" xml:space="preserve">velo-<lb/>citas reſpectiva eſt a - b ſi corpora ad eandem partem tendant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5608" xml:space="preserve">hæc ictu de- <anchor type="note" xlink:label="note-0209-06a" xlink:href="note-0209-06"/> ſtruitur <anchor type="note" xlink:href="" symbol="*"/> quare eſt ſumma mutationum in velocitatibus corporum poſt ictum.</s> <s xml:id="echoid-s5609" xml:space="preserve"> <anchor type="note" xlink:label="note-0209-07a" xlink:href="note-0209-07"/> B eſt ad A ut mutatio velocitatis in A, ad mutationem velocitatis in B <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5610" xml:space="preserve">&</s> <s xml:id="echoid-s5611" xml:space="preserve"> <anchor type="note" xlink:label="note-0209-08a" xlink:href="note-0209-08"/> componendo A + B, A:</s> <s xml:id="echoid-s5612" xml:space="preserve">:a - b, ad mutationem in velocitate corporis B, quæ <lb/> <anchor type="note" xlink:label="note-0209-09a" xlink:href="note-0209-09"/> <pb o="142" file="0210" n="229" rhead="PHYSICES ELEMENTA"/> mutatio ergo eſt {Aa - Ab/A + B}; </s> <s xml:id="echoid-s5613" xml:space="preserve">cum velocitas b minor ſit velocitate a, auge-<lb/>tur illa in percuſſione: </s> <s xml:id="echoid-s5614" xml:space="preserve">ideò velocitas corporis B, id eſt velocitas utriuſ-<lb/>que corporis <anchor type="note" xlink:href="" symbol="*"/> poſt impactionem, eſt b + {Aa - Ab/A + B} = {Bb + Aa/A + B} ut ha- <anchor type="note" xlink:label="note-0210-01a" xlink:href="note-0210-01"/> betur in n. </s> <s xml:id="echoid-s5615" xml:space="preserve">513.</s> <s xml:id="echoid-s5616" xml:space="preserve"/> </p> <div xml:id="echoid-div802" type="float" level="2" n="1"> <note position="right" xlink:label="note-0209-06" xlink:href="note-0209-06a" xml:space="preserve">526.</note> <note symbol="*" position="right" xlink:label="note-0209-07" xlink:href="note-0209-07a" xml:space="preserve">474.</note> <note symbol="*" position="right" xlink:label="note-0209-08" xlink:href="note-0209-08a" xml:space="preserve">484.</note> <note symbol="*" position="right" xlink:label="note-0209-09" xlink:href="note-0209-09a" xml:space="preserve">511.</note> <note symbol="*" position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve"> 484.</note> </div> <p> <s xml:id="echoid-s5617" xml:space="preserve">Poſitâ velocitate reſpectiva a + b, tendentibus nempe corporibus in con-<lb/> <anchor type="note" xlink:label="note-0210-02a" xlink:href="note-0210-02"/> trarias partes <anchor type="note" xlink:href="" symbol="*"/>, ſimili ratiocinio regula n. </s> <s xml:id="echoid-s5618" xml:space="preserve">516. </s> <s xml:id="echoid-s5619" xml:space="preserve">detegitur.</s> <s xml:id="echoid-s5620" xml:space="preserve"> <anchor type="note" xlink:label="note-0210-03a" xlink:href="note-0210-03"/> </s> </p> <div xml:id="echoid-div803" type="float" level="2" n="2"> <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">527.</note> <note symbol="*" position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">475.</note> </div> <p> <s xml:id="echoid-s5621" xml:space="preserve">Haſce ambas regulas de colliſione corporum etiam ex demonſtratis <anchor type="note" xlink:href="" symbol="*"/> cir- <anchor type="note" xlink:label="note-0210-04a" xlink:href="note-0210-04"/> ca quantitatem vis amiſſæ deduci poſſunt, quam demonſtrationem hìc ſub-<lb/>jiciam, ut ſirmitas illorum quæ de viribus inſitis ſuperius demonſtra-<lb/>ta ſunt clarius pateat, dum ex ipſis, per vias omnino diverſas, deducimus <lb/>regulas experimentis conſirmatas.</s> <s xml:id="echoid-s5622" xml:space="preserve"/> </p> <div xml:id="echoid-div804" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0210-04" xlink:href="note-0210-04a" xml:space="preserve">510. 525.</note> </div> <p> <s xml:id="echoid-s5623" xml:space="preserve">Sint iterum corpora A & </s> <s xml:id="echoid-s5624" xml:space="preserve">B; </s> <s xml:id="echoid-s5625" xml:space="preserve">hujus velocitas b illius a; </s> <s xml:id="echoid-s5626" xml:space="preserve">tendant ad eandem <lb/> <anchor type="note" xlink:label="note-0210-05a" xlink:href="note-0210-05"/> partem, & </s> <s xml:id="echoid-s5627" xml:space="preserve">velocitas reſpectiva erit a - b.</s> <s xml:id="echoid-s5628" xml:space="preserve"/> </p> <div xml:id="echoid-div805" type="float" level="2" n="4"> <note position="left" xlink:label="note-0210-05" xlink:href="note-0210-05a" xml:space="preserve">528.</note> </div> <p> <s xml:id="echoid-s5629" xml:space="preserve">Summa virium ante ictum eſt Aaa + Bbb <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5630" xml:space="preserve">vis ictu deſtructa eſt <anchor type="note" xlink:label="note-0210-06a" xlink:href="note-0210-06"/> {ABaa - 2ABab + ABbb/A + B} <anchor type="note" xlink:href="" symbol="*"/>, ſubtrahendo hancex ſumma virium habemus <anchor type="note" xlink:label="note-0210-07a" xlink:href="note-0210-07"/> vim poſt ictum ſuperſtitem {AAaa + 2ABab + BBbb/A + B}; </s> <s xml:id="echoid-s5631" xml:space="preserve">corpora poſt i-<lb/>ctum non ſeparantur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s5632" xml:space="preserve">maſſa eſt A + B, per quam ſi dividamus vim ſuper- <anchor type="note" xlink:label="note-0210-08a" xlink:href="note-0210-08"/> ſtitem poſt ictum, habemus quadratum velocitatis poſt colliſionem; </s> <s xml:id="echoid-s5633" xml:space="preserve">quod <lb/>quadratum ergo eſt {A Aaa + 2A Bab + BBbb/<emph style="ol">A + B</emph><emph style="super">q</emph>} = {<emph style="ol">Aa + Bb</emph><emph style="super">q</emph>/<emph style="ol">A + B</emph><emph style="super">q</emph>}. </s> <s xml:id="echoid-s5634" xml:space="preserve">cujus radix <lb/>{Aa + Bb/A + B} dat velocitatem quæſitam.</s> <s xml:id="echoid-s5635" xml:space="preserve"/> </p> <div xml:id="echoid-div806" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0210-06" xlink:href="note-0210-06a" xml:space="preserve">470.</note> <note symbol="*" position="left" xlink:label="note-0210-07" xlink:href="note-0210-07a" xml:space="preserve">510. 525.</note> <note symbol="*" position="left" xlink:label="note-0210-08" xlink:href="note-0210-08a" xml:space="preserve">484</note> </div> <p> <s xml:id="echoid-s5636" xml:space="preserve">Si adhibita velocitate reſpectiva a + b computatio ineatur regula n. </s> <s xml:id="echoid-s5637" xml:space="preserve">516. <lb/></s> <s xml:id="echoid-s5638" xml:space="preserve"> <anchor type="note" xlink:label="note-0210-09a" xlink:href="note-0210-09"/> detegitur.</s> <s xml:id="echoid-s5639" xml:space="preserve"/> </p> <div xml:id="echoid-div807" type="float" level="2" n="6"> <note position="left" xlink:label="note-0210-09" xlink:href="note-0210-09a" xml:space="preserve">529.</note> </div> <p> <s xml:id="echoid-s5640" xml:space="preserve">Vulgo quantitas motus, quam ipſius vis inſitæ proportionem ſequi ponunt, <lb/> <anchor type="note" xlink:label="note-0210-10a" xlink:href="note-0210-10"/> determinatur multiplicando maſſam non per quadratum velocitatis, ſed per <lb/>ipſam velocitatem, ex hocprincipio deduxere Philoſophiipſas illas regulas n. <lb/></s> <s xml:id="echoid-s5641" xml:space="preserve">513. </s> <s xml:id="echoid-s5642" xml:space="preserve">516. </s> <s xml:id="echoid-s5643" xml:space="preserve">quas nos variis methodis ex principiis noſtris deduximus; </s> <s xml:id="echoid-s5644" xml:space="preserve">mirum <lb/>hìc quid contigit, error erroris ſuit deſtructio, & </s> <s xml:id="echoid-s5645" xml:space="preserve">duplex error ad veritatem <lb/>conduxit; </s> <s xml:id="echoid-s5646" xml:space="preserve">falſum de menſura virium ſecuti ſunt principium, & </s> <s xml:id="echoid-s5647" xml:space="preserve">quod veri-<lb/>tati etiam minime congruum eſt, nullam vim intropremendo partes & </s> <s xml:id="echoid-s5648" xml:space="preserve">ha-<lb/>rum ſuperando cohæſionem corpora amittere poſuere.</s> <s xml:id="echoid-s5649" xml:space="preserve"/> </p> <div xml:id="echoid-div808" type="float" level="2" n="7"> <note position="left" xlink:label="note-0210-10" xlink:href="note-0210-10a" xml:space="preserve">530.</note> </div> <pb o="143" file="0211" n="230" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> </div> <div xml:id="echoid-div810" type="section" level="1" n="211"> <head xml:id="echoid-head298" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head299" xml:space="preserve">De percuſſione corporum lineis rigidis inter ſe cohæ-<lb/>rentium, & circa centra agitatorum.</head> <p style="it"> <s xml:id="echoid-s5650" xml:space="preserve">Sint corpora A & </s> <s xml:id="echoid-s5651" xml:space="preserve">C, lineâ inflexili conjuncta, & </s> <s xml:id="echoid-s5652" xml:space="preserve">circa centrum H agitata; </s> <s xml:id="echoid-s5653" xml:space="preserve">fint <lb/> <anchor type="note" xlink:label="note-0211-01a" xlink:href="note-0211-01"/> etiam corpora alia B & </s> <s xml:id="echoid-s5654" xml:space="preserve">D eodem modo juncta & </s> <s xml:id="echoid-s5655" xml:space="preserve">circa I agitata.</s> <s xml:id="echoid-s5656" xml:space="preserve"/> </p> <div xml:id="echoid-div810" type="float" level="2" n="1"> <note position="right" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">531.</note> </div> <note position="right" xml:space="preserve"><emph style="sc">TAB. XX.</emph> <lb/>fig. 3.</note> <p> <s xml:id="echoid-s5657" xml:space="preserve">Ponamus darihorum corporum percuſſionem directam, quod obtinebit ſi in ſemu-<lb/>tuo impingant, unum ex corporibus adhærentibus uni lineæ, cum corpore quo-<lb/>cunque ex illis quæ cum alia cohærent lineâ, ut A & </s> <s xml:id="echoid-s5658" xml:space="preserve">B. </s> <s xml:id="echoid-s5659" xml:space="preserve">Impactio erit di-<lb/>recta ſi hæc corpora directè in ſe mutuo incurrant, quod fieri non poterit <lb/>niſi in momento incurſus lineæ quibus corpora cohærent ſint parallelæ in-<lb/>ter ſe.</s> <s xml:id="echoid-s5660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5661" xml:space="preserve">Si in momento incurſus in quo in eâdem lineâ ambo moventur corpora, <lb/>motu quodam communi ferantur non hoc motu in ſe mutuo agent; </s> <s xml:id="echoid-s5662" xml:space="preserve">impactio <lb/>ergo pendebit â velocitate reſpectivâ, qua manente eadem datur partium intro-<lb/> <anchor type="note" xlink:label="note-0211-03a" xlink:href="note-0211-03"/> ceſſio <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s5663" xml:space="preserve">eadem vis amiſſa <anchor type="note" xlink:href="" symbol="*"/>, quibuſcunque velocitatibus corpora agi- <anchor type="note" xlink:label="note-0211-04a" xlink:href="note-0211-04"/> tentur.</s> <s xml:id="echoid-s5664" xml:space="preserve"/> </p> <div xml:id="echoid-div811" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0211-03" xlink:href="note-0211-03a" xml:space="preserve">495.</note> <note symbol="*" position="right" xlink:label="note-0211-04" xlink:href="note-0211-04a" xml:space="preserve">497</note> </div> <p> <s xml:id="echoid-s5665" xml:space="preserve">Dari caſum in quo corpora in partes contrarias lata, poſtictum quieſcunt faci-<lb/> <anchor type="note" xlink:label="note-0211-05a" xlink:href="note-0211-05"/> le patet; </s> <s xml:id="echoid-s5666" xml:space="preserve">& </s> <s xml:id="echoid-s5667" xml:space="preserve">in hoc caſu, datâ velocitate reſpectivâ, ſummam virium eſſeomnium <lb/>minimam etiam liquet, tota enim vis deſtruitur & </s> <s xml:id="echoid-s5668" xml:space="preserve">minor quantitas nunquam <lb/>poteſt deſtrui <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5669" xml:space="preserve">quænam autem ſit ratio velocitatum in hoc caſu di- <anchor type="note" xlink:label="note-0211-06a" xlink:href="note-0211-06"/> cam.</s> <s xml:id="echoid-s5670" xml:space="preserve"/> </p> <div xml:id="echoid-div812" type="float" level="2" n="3"> <note position="right" xlink:label="note-0211-05" xlink:href="note-0211-05a" xml:space="preserve">532.</note> <note symbol="*" position="right" xlink:label="note-0211-06" xlink:href="note-0211-06a" xml:space="preserve">531.</note> </div> <p> <s xml:id="echoid-s5671" xml:space="preserve">Sit a diſtantia corporis A â centro H, circa quod rotatur, & </s> <s xml:id="echoid-s5672" xml:space="preserve">c diſtantia <lb/>corporis C ab eodem centro. </s> <s xml:id="echoid-s5673" xml:space="preserve">Eodem modo ſit b diſtantia corporis B, & </s> <s xml:id="echoid-s5674" xml:space="preserve">c <lb/>diſtantia corporis D, â centro I, circa quod hæc corpora agitantur. </s> <s xml:id="echoid-s5675" xml:space="preserve">Sit ulte-<lb/>rius m velocitas corporis A; </s> <s xml:id="echoid-s5676" xml:space="preserve">& </s> <s xml:id="echoid-s5677" xml:space="preserve">n velocitas corporis B.</s> <s xml:id="echoid-s5678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5679" xml:space="preserve">In caſu in quo corpora poſt ictum quieſcunt demonſtramus, poſitis motibus con-<lb/> <anchor type="note" xlink:label="note-0211-07a" xlink:href="note-0211-07"/> trariis m, n:</s> <s xml:id="echoid-s5680" xml:space="preserve">:Bbb + Dddxaa, Aaa + Cccxbb. </s> <s xml:id="echoid-s5681" xml:space="preserve">id eſt, Aaa + Cccx <lb/>bbm = Bbb + Dddxaan.</s> <s xml:id="echoid-s5682" xml:space="preserve"/> </p> <div xml:id="echoid-div813" type="float" level="2" n="4"> <note position="right" xlink:label="note-0211-07" xlink:href="note-0211-07a" xml:space="preserve">533.</note> </div> <p style="it"> <s xml:id="echoid-s5683" xml:space="preserve">In hoc enim caſu ſumma virium, manente velocitate reſpectivâ m + n, eſt o-<lb/> <anchor type="note" xlink:label="note-0211-08a" xlink:href="note-0211-08"/> mnium minima.</s> <s xml:id="echoid-s5684" xml:space="preserve"/> </p> <div xml:id="echoid-div814" type="float" level="2" n="5"> <note position="right" xlink:label="note-0211-08" xlink:href="note-0211-08a" xml:space="preserve">534.</note> </div> <p> <s xml:id="echoid-s5685" xml:space="preserve">Summa virium eſt Amm + {Cccmm/aa} + Bnn + {Dddnn/bb} <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5686" xml:space="preserve">nam a, c:</s> <s xml:id="echoid-s5687" xml:space="preserve">:m, <anchor type="note" xlink:label="note-0211-09a" xlink:href="note-0211-09"/> {mc/a} = velocitati corporis C; </s> <s xml:id="echoid-s5688" xml:space="preserve">& </s> <s xml:id="echoid-s5689" xml:space="preserve">b, d, :</s> <s xml:id="echoid-s5690" xml:space="preserve">:n, {dn/b} = velocitati corporis D.</s> <s xml:id="echoid-s5691" xml:space="preserve"/> </p> <div xml:id="echoid-div815" type="float" level="2" n="6"> <note position="right" xlink:label="note-0211-09" xlink:href="note-0211-09a" xml:space="preserve">535.</note> </div> <note symbol="*" position="right" xml:space="preserve">470.</note> <p> <s xml:id="echoid-s5692" xml:space="preserve">Ponamus nunc velocitatem m augeri quantitate e, & </s> <s xml:id="echoid-s5693" xml:space="preserve">eadern quantitate mi-<lb/>nui velocitatem n, ut velocitas reſpectiva maneat; </s> <s xml:id="echoid-s5694" xml:space="preserve">videbimus ſummam eſſe <lb/>majorem.</s> <s xml:id="echoid-s5695" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5696" xml:space="preserve">Velocitas corporis A nunc eſt m + e; </s> <s xml:id="echoid-s5697" xml:space="preserve">Corporis C eſt {mc + ec/a}; </s> <s xml:id="echoid-s5698" xml:space="preserve">corporis B <pb o="144" file="0212" n="231" rhead="PHYSICES ELEMENTA"/> eſt m - e; </s> <s xml:id="echoid-s5699" xml:space="preserve">& </s> <s xml:id="echoid-s5700" xml:space="preserve">tandem celeritas corporis D eſt {nd - ed/b}. </s> <s xml:id="echoid-s5701" xml:space="preserve">Summa virium nunc <lb/>erit Amm + 2Ame + Acc + {Cccmm + 2Cccme + Cccee/aa} + Bnn - 2Bne <lb/>+ Bee + {Dddnn - 2Dddne + Dddee/bb}. </s> <s xml:id="echoid-s5702" xml:space="preserve">Sed <emph style="ol">Aaa + Ccc</emph> x bbm <lb/>= <emph style="ol">Bbb + Ddd</emph> x aan; </s> <s xml:id="echoid-s5703" xml:space="preserve">ponimus enim de hoc caſu agi; </s> <s xml:id="echoid-s5704" xml:space="preserve">dividendo hanc <lb/>æquationem per aabb, habemus Am + {Cccm/aa} = Bn + {Dddn/bb}; </s> <s xml:id="echoid-s5705" xml:space="preserve">idcirco <lb/>in ultima ſumma ſeſe mutuo deſtruunt + 2Ame + {2Cccme/aa} & </s> <s xml:id="echoid-s5706" xml:space="preserve">- 2Bne -<lb/>{2Dddne/bb} & </s> <s xml:id="echoid-s5707" xml:space="preserve">ſumma ad hanc reducitur Amm + Aee + {Cccmm + Cccee/aa} <lb/>+ Bnn + Bee + {Dddnn + {Dddee/bb} quæ primâ memoratâ ſummâ major <lb/>eſt. </s> <s xml:id="echoid-s5708" xml:space="preserve">Q. </s> <s xml:id="echoid-s5709" xml:space="preserve">D. </s> <s xml:id="echoid-s5710" xml:space="preserve">E.</s> <s xml:id="echoid-s5711" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5712" xml:space="preserve">Nec diverſa eſt demonſtratio ſi augeatur n, imminutâ velocitate m.</s> <s xml:id="echoid-s5713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5714" xml:space="preserve">Vis in colliſione quacunque, datâ velocitate reſpectivâ, deſtructa determi-<lb/> <anchor type="note" xlink:label="note-0212-01a" xlink:href="note-0212-01"/> nari poteſt, nam valet ſummam virium in caſu in quo hæc minima eſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5715" xml:space="preserve">Sit <anchor type="note" xlink:label="note-0212-02a" xlink:href="note-0212-02"/> nunc m + n = r.</s> <s xml:id="echoid-s5716" xml:space="preserve"/> </p> <div xml:id="echoid-div816" type="float" level="2" n="7"> <note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">536.</note> <note symbol="*" position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">531.</note> </div> <p> <s xml:id="echoid-s5717" xml:space="preserve">Datur ratio inter m & </s> <s xml:id="echoid-s5718" xml:space="preserve">n <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s5719" xml:space="preserve">componendo <anchor type="note" xlink:label="note-0212-03a" xlink:href="note-0212-03"/> <emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa, <emph style="ol">Aaa x Ccc</emph> x bb:</s> <s xml:id="echoid-s5720" xml:space="preserve">: <lb/>m + n = r, n; <lb/></s> <s xml:id="echoid-s5721" xml:space="preserve">ergo n = {<emph style="ol">Aaa + Ccc</emph> x bbr/<emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa}. </s> <s xml:id="echoid-s5722" xml:space="preserve">Eodem modo detegi-<lb/>mus m = {<emph style="ol">Bbb + Ddd</emph> x aar/Aaa x Ccc x bb + <emph style="ol">Bbb + Ddd</emph> x aa}. </s> <s xml:id="echoid-s5723" xml:space="preserve">Summa virium eſt <lb/>{<emph style="ol">Aaa + Ccc</emph> x mm/aa} + {<emph style="ol">Bbb + Ddd</emph> x nn/bb} <anchor type="note" xlink:href="" symbol="*"/>, ſubſtituendo pro m & </s> <s xml:id="echoid-s5724" xml:space="preserve">n <anchor type="note" xlink:label="note-0212-04a" xlink:href="note-0212-04"/> valores ſumma hæc erit <lb/>{<emph style="ol">Aaa + Ccc</emph> x <emph style="ol">Bbb + Ddd</emph><emph style="super">q</emph> x aarr + <emph style="ol">Bbb + Ddd</emph> x <emph style="ol">Aaa + Ccc</emph><emph style="super">q</emph> x bbrr/{<emph style="ol">/Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd x aa</emph><emph style="super">q</emph>} <lb/>Dividendo numeratorem & </s> <s xml:id="echoid-s5725" xml:space="preserve">denominatorem per <emph style="ol">Aaa + Ccc</emph> x bb + <pb o="145" file="0213" n="232" rhead="MATHEMATICA. LIB. I. CAP XXIII."/> <emph style="ol">Bbb + Ddd</emph> x aa; </s> <s xml:id="echoid-s5726" xml:space="preserve">habemus {<emph style="ol">Aaa + Ccc</emph> x <emph style="ol">Bbb + Ddd</emph> x rr/<emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + D dd</emph> x aa} vim <lb/> <anchor type="note" xlink:label="note-0213-01a" xlink:href="note-0213-01"/> amiſſam data velocitate reſpectivar.</s> <s xml:id="echoid-s5727" xml:space="preserve"/> </p> <div xml:id="echoid-div817" type="float" level="2" n="8"> <note symbol="*" position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">533.</note> <note symbol="*" position="left" xlink:label="note-0212-04" xlink:href="note-0212-04a" xml:space="preserve">535</note> <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">537.</note> </div> <p> <s xml:id="echoid-s5728" xml:space="preserve">Si Corpora memorata A & </s> <s xml:id="echoid-s5729" xml:space="preserve">B, cum reliquis circa centra I & </s> <s xml:id="echoid-s5730" xml:space="preserve">H agitata, ve-<lb/> <anchor type="note" xlink:label="note-0213-02a" xlink:href="note-0213-02"/> locitatibus quibuſcunque in ſe mutuo incurrant directè, poſt ictum ambo eâ-<lb/>dem velocitate feruntur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s5731" xml:space="preserve">ſeparantur non ex actione corporum, ſed quia <anchor type="note" xlink:label="note-0213-03a" xlink:href="note-0213-03"/> circa centra diverſa H & </s> <s xml:id="echoid-s5732" xml:space="preserve">I moventur.</s> <s xml:id="echoid-s5733" xml:space="preserve"/> </p> <div xml:id="echoid-div818" type="float" level="2" n="9"> <note position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">538.</note> <note symbol="*" position="right" xlink:label="note-0213-03" xlink:href="note-0213-03a" xml:space="preserve">484.</note> </div> <p> <s xml:id="echoid-s5734" xml:space="preserve">Concipiamus dari punctum quod eadem velocitate fertur, qua corpora poſt <lb/>ictum ante ſeparationem ſeruntur, & </s> <s xml:id="echoid-s5735" xml:space="preserve">juxta eandem directionem.</s> <s xml:id="echoid-s5736" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5737" xml:space="preserve">Reſpectu hujus puncti corpora poſt impactionem quieſcunt; </s> <s xml:id="echoid-s5738" xml:space="preserve">ideo reſpectu <lb/>ipſius anteictum contrariis velocitatibus movebantur in ratione <emph style="ol">Bbb + Ddd</emph> <lb/>x aa ad <emph style="ol">Aaa + Ccc</emph> x bb <anchor type="note" xlink:href="" symbol="*"/>, haſque velocitates amittunt, cum reſpectu puncti <anchor type="note" xlink:label="note-0213-04a" xlink:href="note-0213-04"/> poſt ictum quieſcant, quare hæ ipſæ velocitates ſunt mutationes, quæ ex ictu <lb/>in velocitatibus contingunt, quæ ergo mutationes ſunt in memoratà ratione; <lb/></s> <s xml:id="echoid-s5739" xml:space="preserve">& </s> <s xml:id="echoid-s5740" xml:space="preserve">componendo <emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa ad <emph style="ol">Aaa + Ccc</emph> x bb <lb/>ut ſumma mutationum, id eſt velocitas reſpectiva, ad mutationem in veloci-<lb/>tate corporis B.</s> <s xml:id="echoid-s5741" xml:space="preserve"/> </p> <div xml:id="echoid-div819" type="float" level="2" n="10"> <note symbol="*" position="right" xlink:label="note-0213-04" xlink:href="note-0213-04a" xml:space="preserve">533.</note> </div> <p> <s xml:id="echoid-s5742" xml:space="preserve">Si nunc velocitas corporis A dicatur p; </s> <s xml:id="echoid-s5743" xml:space="preserve">& </s> <s xml:id="echoid-s5744" xml:space="preserve">q velocitas corporis B, poſita <lb/>hac minori; </s> <s xml:id="echoid-s5745" xml:space="preserve">velocitas reſpectiva erit p-q ſi motus eandem partem verſus <lb/>dirigantur, & </s> <s xml:id="echoid-s5746" xml:space="preserve">mutatio velocitatis corporis B, detegitur <lb/>{<emph style="ol">Aaa + Ccc</emph> x bbp - <emph style="ol">Aaa + Ccc</emph> x bbq/<emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa} quæ mutatio eſt velocitas <lb/>acquiſita; </s> <s xml:id="echoid-s5747" xml:space="preserve">quia minor velocitas in motibus conſpirantibus augetur: </s> <s xml:id="echoid-s5748" xml:space="preserve">quare ſi <lb/>addatur ipſi velocitati q habemus velocitatem amborum corporum <lb/>poſt ictum; </s> <s xml:id="echoid-s5749" xml:space="preserve">quæ ergo eſt {<emph style="ol">Aaa + Ccc</emph> x bbp + <emph style="ol">Bbb + Ddd</emph> x aaq/<emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa}. <lb/></s> <s xml:id="echoid-s5750" xml:space="preserve"> <anchor type="note" xlink:label="note-0213-05a" xlink:href="note-0213-05"/> </s> </p> <div xml:id="echoid-div820" type="float" level="2" n="11"> <note position="right" xlink:label="note-0213-05" xlink:href="note-0213-05a" xml:space="preserve">539.</note> </div> <p> <s xml:id="echoid-s5751" xml:space="preserve">Si motus in contrariam partem dirigantur velocitas reſpectiva eſt p + q & </s> <s xml:id="echoid-s5752" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0213-06a" xlink:href="note-0213-06"/> velocitas poſt ictum ſimili ratiocinio detegitur <lb/>{<emph style="ol">Aaa + Ccc</emph> x bbp - <emph style="ol">Bbb + Ddd</emph> x aaq/<emph style="ol">Aaa + Ccc</emph> x bb + <emph style="ol">Bbb + Ddd</emph> x aa} ſubtracto nempe in nu-<lb/>meratore producto minore ex majore.</s> <s xml:id="echoid-s5753" xml:space="preserve"/> </p> <div xml:id="echoid-div821" type="float" level="2" n="12"> <note position="right" xlink:label="note-0213-06" xlink:href="note-0213-06a" xml:space="preserve">540.</note> </div> <p> <s xml:id="echoid-s5754" xml:space="preserve">Clarè patet non intereſſe utrum in hac colliſione corpora, quæ eidem lineæ <lb/> <anchor type="note" xlink:label="note-0213-07a" xlink:href="note-0213-07"/> juguntur, ad eandem partem dentur centri circa quod linea movetur, an ad <lb/>partes diverſas, nam eodem niodo corpus movetur, à quacunque parte centri <lb/>detur, ſimodo diſtantia ab hoc ſit eadem, vim etiam centrifugam, qua corpora <lb/>a centro recedere conantur, & </s> <s xml:id="echoid-s5755" xml:space="preserve">actiones quas, dum concurrunt, in retinacu-<lb/>la exerunt, non hîc conſiderari debere, ſatis manifeſtum eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5756" xml:space="preserve"/> </p> <div xml:id="echoid-div822" type="float" level="2" n="13"> <note position="right" xlink:label="note-0213-07" xlink:href="note-0213-07a" xml:space="preserve">541.</note> </div> <note symbol="*" position="right" xml:space="preserve">523.</note> <p> <s xml:id="echoid-s5757" xml:space="preserve">Demonſtrata hæc ad numerum quemcunque corporum poſſunt applicari, & </s> <s xml:id="echoid-s5758" xml:space="preserve">u-<lb/> <anchor type="note" xlink:label="note-0213-09a" xlink:href="note-0213-09"/> niverſales regulæ ex demonſtratis quam facillime illiciuntur.</s> <s xml:id="echoid-s5759" xml:space="preserve"/> </p> <div xml:id="echoid-div823" type="float" level="2" n="14"> <note position="right" xlink:label="note-0213-09" xlink:href="note-0213-09a" xml:space="preserve">542.</note> </div> <p> <s xml:id="echoid-s5760" xml:space="preserve">Videmus etiam quid obtineat, Si corpus in lineâ rectâ motum directè in aliudin-<lb/> <anchor type="note" xlink:label="note-0213-10a" xlink:href="note-0213-10"/> currat quod cum aliis lineæ rectæ, circa centrum mobili, cohæret; </s> <s xml:id="echoid-s5761" xml:space="preserve">Corpus enim il-<lb/>lud in linea recta motum agit quaſi lineæ rectæ, circa punctum quodcunque <lb/>mobili, adhæreret.</s> <s xml:id="echoid-s5762" xml:space="preserve"/> </p> <div xml:id="echoid-div824" type="float" level="2" n="15"> <note position="right" xlink:label="note-0213-10" xlink:href="note-0213-10a" xml:space="preserve">543.</note> </div> <pb o="146" file="0214" n="233" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s5763" xml:space="preserve">Quieſcant corpora A & </s> <s xml:id="echoid-s5764" xml:space="preserve">Cin a & </s> <s xml:id="echoid-s5765" xml:space="preserve">c, dum ut ante mobilia ſunt circa H. </s> <s xml:id="echoid-s5766" xml:space="preserve">Po-<lb/>namus B aut b in linea recta motum, velociate q directè & </s> <s xml:id="echoid-s5767" xml:space="preserve">perpendiculariter <lb/>ad a H incurrere in a; </s> <s xml:id="echoid-s5768" xml:space="preserve">velocitatem poſt ictum detegimus ipſâ formulâ præcedenti. <lb/></s> <s xml:id="echoid-s5769" xml:space="preserve">Pono enim B cum linea cohærere & </s> <s xml:id="echoid-s5770" xml:space="preserve">agitari circa centrum ad diſtantiam quam-<lb/>cunque b; </s> <s xml:id="echoid-s5771" xml:space="preserve">in hac colliſione p & </s> <s xml:id="echoid-s5772" xml:space="preserve">D æquales ſunt nihilo, ideo evaneſcunt quan-<lb/>titates, quæ per has multiplicantur quare memoratâ formula <anchor type="note" xlink:href="" symbol="*"/> in hanc mu- <anchor type="note" xlink:label="note-0214-01a" xlink:href="note-0214-01"/> tatur {Bbbaaq/<emph style="ol">Aaa + Ccc</emph> x bb + Bbbaa} = {Baaq/Aaa + Ccc + Baa}: </s> <s xml:id="echoid-s5773" xml:space="preserve">ex qua <lb/>banc deducimus regulam. </s> <s xml:id="echoid-s5774" xml:space="preserve">Corpus impingens per quadratum diſtantiæ puncti, in <lb/>quod incurrit, âcextro, & </s> <s xml:id="echoid-s5775" xml:space="preserve">per velocitatem ſuam multiplicatur, productumque boc <lb/>dividitur per ſummam omnium corporum, ſingulorum multiplicatorum per quadrata <lb/>ſuarum diſtantiarum à centro.</s> <s xml:id="echoid-s5776" xml:space="preserve"/> </p> <div xml:id="echoid-div825" type="float" level="2" n="16"> <note symbol="*" position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">539.</note> </div> <p> <s xml:id="echoid-s5777" xml:space="preserve">Propoſitiones n. </s> <s xml:id="echoid-s5778" xml:space="preserve">500. </s> <s xml:id="echoid-s5779" xml:space="preserve">510. </s> <s xml:id="echoid-s5780" xml:space="preserve">512. </s> <s xml:id="echoid-s5781" xml:space="preserve">513. </s> <s xml:id="echoid-s5782" xml:space="preserve">516. </s> <s xml:id="echoid-s5783" xml:space="preserve">ſunt caſus peculiares propoſi-<lb/> <anchor type="note" xlink:label="note-0214-02a" xlink:href="note-0214-02"/> tionum in hoc Scholio in n. </s> <s xml:id="echoid-s5784" xml:space="preserve">533. </s> <s xml:id="echoid-s5785" xml:space="preserve">537. </s> <s xml:id="echoid-s5786" xml:space="preserve">538. </s> <s xml:id="echoid-s5787" xml:space="preserve">539. </s> <s xml:id="echoid-s5788" xml:space="preserve">540. </s> <s xml:id="echoid-s5789" xml:space="preserve">demonſtratarum, ut <lb/>patet, ſi ponamus duo corpora quæ cum lineis, circa centra quæcunque mo-<lb/>bilibus, cohærent.</s> <s xml:id="echoid-s5790" xml:space="preserve"/> </p> <div xml:id="echoid-div826" type="float" level="2" n="17"> <note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">544.</note> </div> </div> <div xml:id="echoid-div828" type="section" level="1" n="212"> <head xml:id="echoid-head300" xml:space="preserve">SCHOLIUM 3.</head> <head xml:id="echoid-head301" style="it" xml:space="preserve">Examen Experimenti circa corpora in lancem, aut <lb/>brachium, libræ impingentia.</head> <p> <s xml:id="echoid-s5791" xml:space="preserve">Merſennus, de Lanis, & </s> <s xml:id="echoid-s5792" xml:space="preserve">alii experimentum dedere circa corpora caden-<lb/> <anchor type="note" xlink:label="note-0214-03a" xlink:href="note-0214-03"/> tia inſtitutum, & </s> <s xml:id="echoid-s5793" xml:space="preserve">notarunt corpus in lancem libræ impingens, pondus ma-<lb/>jus, in lance oppoſitâ, paululum elevare; </s> <s xml:id="echoid-s5794" xml:space="preserve">& </s> <s xml:id="echoid-s5795" xml:space="preserve">pondera ſic elevari ad exiguam, ſed <lb/>æqualem (quam tamen circumſtantiam non notat Merſennus) altitudinem, <lb/>ſi corpus quod impingit cadat ab altitudinibus quæ ſunt ut quadrata pon-<lb/>derum quæ elevantur.</s> <s xml:id="echoid-s5796" xml:space="preserve"/> </p> <div xml:id="echoid-div828" type="float" level="2" n="1"> <note position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">545.</note> </div> <p> <s xml:id="echoid-s5797" xml:space="preserve">Merſennus tamen notat in quibuſdam circumſtantiis experimentum non pro-<lb/>ceſſiſſe, quod & </s> <s xml:id="echoid-s5798" xml:space="preserve">mihi contigit, experimentum paululum aliter inſtituenti, quod <lb/>defectui machinæ tribuebam, & </s> <s xml:id="echoid-s5799" xml:space="preserve">in illis ſolis altitudinibus, in quibus regulam <lb/>ſatis exacte obſervari videbam, defectus, qui in machina me non latebant, <lb/>minus noxios credebam. </s> <s xml:id="echoid-s5800" xml:space="preserve">Cum autem attentius rem examinarem me toto <lb/>cælo erraſſe percepi, & </s> <s xml:id="echoid-s5801" xml:space="preserve">ipſis illis principiis Mechanices, de quibus inter omnes <lb/>convenit, adverſari, memoratam dari inter quadrata ponderum elevatorum <lb/>proportionem, quæ datur inter altitudines, a quibus cadit corpus, quod in lancem, <lb/>aut brachium oppoſitum, impingit; </s> <s xml:id="echoid-s5802" xml:space="preserve">& </s> <s xml:id="echoid-s5803" xml:space="preserve">in dubium vocare non potui ipſi defe-<lb/>ctui machinæ tribuendum eſſe, ſi aliquando inter certos limites hæc dete-<lb/>gatur proportio, ut mihi ſemper contigerat. </s> <s xml:id="echoid-s5804" xml:space="preserve">Non ſenſibilis fateor dabitur <lb/>error, ſi corpus cadens, & </s> <s xml:id="echoid-s5805" xml:space="preserve">pondustotius libræ, id eſt, jugi & </s> <s xml:id="echoid-s5806" xml:space="preserve">lancium, admodum <lb/>exigua fuerint reſpectu ponderum elevatorum: </s> <s xml:id="echoid-s5807" xml:space="preserve">ſed in hoc caſu experimen-<lb/>tum inſtitui non poterit; </s> <s xml:id="echoid-s5808" xml:space="preserve">majus enim pondus ſubtiliori libræ imponi non po-<lb/>teſt.</s> <s xml:id="echoid-s5809" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5810" xml:space="preserve">Ut autem, quæ hoc experimentum ſpectant, clarius paterent, Machinam con- <pb o="147" file="0215" n="234" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> ſtrui curavi, qua, quantum poteſt exacte, & </s> <s xml:id="echoid-s5811" xml:space="preserve">omnino ſine ſenſibili errore, ex-<lb/>perimentum inſtituitur: </s> <s xml:id="echoid-s5812" xml:space="preserve">& </s> <s xml:id="echoid-s5813" xml:space="preserve">poſt experimentum inſtitutum circa hoc com-<lb/>putationem inivi.</s> <s xml:id="echoid-s5814" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div830" type="section" level="1" n="213"> <head xml:id="echoid-head302" xml:space="preserve">BILANX</head> <head xml:id="echoid-head303" style="it" xml:space="preserve">Qua altitudines conferuntur, a quibus corpus cadens, pondera <lb/>paululum elevat.</head> <p> <s xml:id="echoid-s5815" xml:space="preserve">Libræ jugum eſt AB; </s> <s xml:id="echoid-s5816" xml:space="preserve">pede ſuſtinetur, dum circa centrum, ut in aliis li-<lb/> <anchor type="note" xlink:label="note-0215-01a" xlink:href="note-0215-01"/> bris, volubile eſt: </s> <s xml:id="echoid-s5817" xml:space="preserve">Lanx L ferrea eſt; </s> <s xml:id="echoid-s5818" xml:space="preserve">oppoſita M eſt lignea & </s> <s xml:id="echoid-s5819" xml:space="preserve">orbicularis, <lb/> <anchor type="note" xlink:label="note-0215-02a" xlink:href="note-0215-02"/> excavata ad profunditatem pollicis. </s> <s xml:id="echoid-s5820" xml:space="preserve">Hæc, ubi experimenta inſtituenda ſunt, <lb/>argillâ molli repletur, quæ cultro ligneo abraditur, ut inæqualitatibus exem-<lb/>ptam, & </s> <s xml:id="echoid-s5821" xml:space="preserve">horizontalem, habeat ſuperficiem; </s> <s xml:id="echoid-s5822" xml:space="preserve">qua de cauſa lanx hæc faciletol-<lb/>li poteſt, iterumque in loco ſuo ſuſpendi. </s> <s xml:id="echoid-s5823" xml:space="preserve">Diſtantia B M excedit pedes tres, <lb/>quare in menſæ extremitate ponenda Machina eſt.</s> <s xml:id="echoid-s5824" xml:space="preserve"/> </p> <div xml:id="echoid-div830" type="float" level="2" n="1"> <note position="right" xlink:label="note-0215-01" xlink:href="note-0215-01a" xml:space="preserve">546.</note> <note position="right" xlink:label="note-0215-02" xlink:href="note-0215-02a" xml:space="preserve">TAB. XX. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s5825" xml:space="preserve">Globus G filo ſuſpenditur, & </s> <s xml:id="echoid-s5826" xml:space="preserve">unco laminæ D cohærenti alligatur.</s> <s xml:id="echoid-s5827" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5828" xml:space="preserve">Pondus Q lanci L imponitur, ut detur æquilibrium. </s> <s xml:id="echoid-s5829" xml:space="preserve">Quibus poſitis, adji-<lb/>citur pondus ictu elevandum P, & </s> <s xml:id="echoid-s5830" xml:space="preserve">ut jugum in ſitu maneat horizontali, bra-<lb/>chium A, quod nunc magis gravatur, gnomone ferreo, cum pede cohæren-<lb/>ti, ſuſtinetur. </s> <s xml:id="echoid-s5831" xml:space="preserve">Facile videmus alio pede, gnomone deſtituto, ſuſtineri debe-<lb/>re machinam ante impoſitum pondus P, ut de æquilibrio conſtet.</s> <s xml:id="echoid-s5832" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5833" xml:space="preserve">Gnomoni in f annectitur lamina elaſtica tenuis fg, quæ extenſa ad i, per-<lb/>tingit, ubi extremitas g retinetur, ope laminæ minimæ i, quæ cum brachio <lb/>A cohæret; </s> <s xml:id="echoid-s5834" xml:space="preserve">paululum elevato brachio laxatur g; </s> <s xml:id="echoid-s5835" xml:space="preserve">unde conſtare poteſt in va-<lb/>riis tentaminibus æqualiter elevati, ſi nempe, paululum tantum imminuto i-<lb/>ctu, quo agitatur libra, elaſterium non relaxetur.</s> <s xml:id="echoid-s5836" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div832" type="section" level="1" n="214"> <head xml:id="echoid-head304" xml:space="preserve"><emph style="sc">Experimentum</emph>.</head> <p> <s xml:id="echoid-s5837" xml:space="preserve">Omnibus ut dictum diſpoſitis, poſitoque pondere P æquali unciis quatuor; <lb/></s> <s xml:id="echoid-s5838" xml:space="preserve"> <anchor type="note" xlink:label="note-0215-03a" xlink:href="note-0215-03"/> globum G ita ſuſpendi, ut ipſius altitudo, diſtantia nempe inter inferiorem <lb/>partem globi & </s> <s xml:id="echoid-s5839" xml:space="preserve">argillæ ſuperficiem, foret pollicum 6 {7/8}, & </s> <s xml:id="echoid-s5840" xml:space="preserve">abſciſſo filo, im-<lb/>pactione globi, laxata eſt lamina fg: </s> <s xml:id="echoid-s5841" xml:space="preserve">repetitoque variis vicibus experimen-<lb/>to eodem modo proceſſit hoc; </s> <s xml:id="echoid-s5842" xml:space="preserve">imminuta autem altitudine, quartâ parte polli-<lb/>cis, aut etiam minus, nunquam elaſterium fuit relaxatum, qua eadem metho-<lb/>do ſequentes altitudines fuere determinatæ.</s> <s xml:id="echoid-s5843" xml:space="preserve"/> </p> <div xml:id="echoid-div832" type="float" level="2" n="1"> <note position="right" xlink:label="note-0215-03" xlink:href="note-0215-03a" xml:space="preserve">547.</note> </div> <p> <s xml:id="echoid-s5844" xml:space="preserve">Duplicato pondere P, altitudo globi fuit pollicum 14 {1/8}</s> </p> <p> <s xml:id="echoid-s5845" xml:space="preserve">Tandem triplicato pondere P, id eſt, poſito hoc duodecim unciarum altitu-<lb/>do fuit 23 {1/2} pollicum.</s> <s xml:id="echoid-s5846" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5847" xml:space="preserve">His omnibus altitudinibus cavitatum ictibus in argillâ formatarum profun-<lb/>ditates addendæ ſunt, & </s> <s xml:id="echoid-s5848" xml:space="preserve">altitudines neglectis exiguis fractionibus erunt <lb/>7. </s> <s xml:id="echoid-s5849" xml:space="preserve">14 {5/16}. </s> <s xml:id="echoid-s5850" xml:space="preserve">23 {3/4}.</s> <s xml:id="echoid-s5851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5852" xml:space="preserve">Si hac eâdem machinâ eadem inſtituantur Experimenta, aliâ adhibitâ argil-<lb/>lâ, altitudines paululum variari poſſunt. </s> <s xml:id="echoid-s5853" xml:space="preserve">Si argilla minus mollis ſit cavitates <lb/>minores erunt, & </s> <s xml:id="echoid-s5854" xml:space="preserve">altitudines ſupra argillæ ſuperficiem planam majores, in-<lb/>tegræ autem altitudines eædem. </s> <s xml:id="echoid-s5855" xml:space="preserve">Sed ſi magis aut minus ponderet argilla, il-<lb/>lud diſcrimen dabit, nam, licet eo non mutetur materia elevanda, materia ta-<lb/>men movenda mutatur, unde diſcrimen neceſſario ſequitur, ut hoc compu-<lb/>tatione ſequenti clarius patebit.</s> <s xml:id="echoid-s5856" xml:space="preserve"/> </p> <pb o="148" file="0216" n="235" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s5857" xml:space="preserve">Jugum Bilancis figuram habet quæ in AB repræſentatur, in ipſis locis A & </s> <s xml:id="echoid-s5858" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0216-01a" xlink:href="note-0216-01"/> B excavatur, ut hoc in fig. </s> <s xml:id="echoid-s5859" xml:space="preserve">4. </s> <s xml:id="echoid-s5860" xml:space="preserve">videri poteſt, de cætero ubique eſt ejuſdem <lb/> <anchor type="note" xlink:label="note-0216-02a" xlink:href="note-0216-02"/> craſſitiei.</s> <s xml:id="echoid-s5861" xml:space="preserve"/> </p> <div xml:id="echoid-div833" type="float" level="2" n="2"> <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">548.</note> <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">TAB. XX. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s5862" xml:space="preserve">Propter figuram irregularem, admodum difficilis foret computatio; </s> <s xml:id="echoid-s5863" xml:space="preserve">ideo, <lb/>ſervato jugi pondere, mutatam concepi figuram; </s> <s xml:id="echoid-s5864" xml:space="preserve">remotis partibus quibuſdam <lb/>à centro, & </s> <s xml:id="echoid-s5865" xml:space="preserve">admotis aliis, poſuique figuram illam eſſe, quæ repræſentatur in <lb/>fig. </s> <s xml:id="echoid-s5866" xml:space="preserve">6.</s> <s xml:id="echoid-s5867" xml:space="preserve">, in qua tota longitudo illa eſt, quæ in Bilance inter puncta ſuſpen-<lb/>ſionis datur; </s> <s xml:id="echoid-s5868" xml:space="preserve">ex qua mutatione exiguus tantum error in computatione dari <lb/>poteſt.</s> <s xml:id="echoid-s5869" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5870" xml:space="preserve">Hujus figuræ ſuperficies, cum jugum ejuſdem ſit craſſitudinis ubique, re-<lb/>præſentare poteſt jugi pondus in omnibus partibus. </s> <s xml:id="echoid-s5871" xml:space="preserve">Figura hæc AB conſt@t <lb/>ex parallelogrammo & </s> <s xml:id="echoid-s5872" xml:space="preserve">duobus triangulis: </s> <s xml:id="echoid-s5873" xml:space="preserve">junctis triangulis, figura reducitur ad <lb/>illam quæ in fig. </s> <s xml:id="echoid-s5874" xml:space="preserve">7. </s> <s xml:id="echoid-s5875" xml:space="preserve">exhibetur, qua adſumtâ computationem inibo.</s> <s xml:id="echoid-s5876" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5877" xml:space="preserve">Hunc uſum computatio hæc habere poterit, quod inde patebit, cum <lb/>demonſtratis circa percuffionem experimenta noſtra congruere. </s> <s xml:id="echoid-s5878" xml:space="preserve">Fundamentum <lb/>autem ipſius computationis habetur in n. </s> <s xml:id="echoid-s5879" xml:space="preserve">543.</s> <s xml:id="echoid-s5880" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5881" xml:space="preserve">Ante omnia ſingula puncta ſuperficiei ADEB, pondus jugi repræſentan-<lb/> <anchor type="note" xlink:label="note-0216-03a" xlink:href="note-0216-03"/> tis, per quadrata diſtantiarum ſuarum a centro motus reſpective multiplicari <lb/>debent. </s> <s xml:id="echoid-s5882" xml:space="preserve">Hoc ſine errore ſenſibili fiet, ſi loco diſtantiarum a centro, di-<lb/>ſtantiæ a lineâ CF uſurpentur, quo computatio facilior evadit.</s> <s xml:id="echoid-s5883" xml:space="preserve"/> </p> <div xml:id="echoid-div834" type="float" level="2" n="3"> <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">TAB. XX. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s5884" xml:space="preserve">Si nunc operatio pro parallelogrammo inſtituatur, ſingulæ lineæ parallelæ & </s> <s xml:id="echoid-s5885" xml:space="preserve"><lb/>æquales lineæ DA, per quadratum ſuæ diſtantiæ à CF multiplicandæ ſunt, <lb/>id eſt, ſingula hæc quadrata per eandem quantitatem AB aut CG multiplica-<lb/>ri debent, id eſt, ſumma quadratorum per CG multiplicanda eſt; </s> <s xml:id="echoid-s5886" xml:space="preserve">ſumma au-<lb/>tem quadratorum eſt pyramis, cujus baſis eſt quadratum AC & </s> <s xml:id="echoid-s5887" xml:space="preserve">altitudo ea-<lb/>dem AC, quæ pyramis valet {1/3} AC<emph style="super">c</emph> <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5888" xml:space="preserve">Multiplicata hac per CG habemus <anchor type="note" xlink:label="note-0216-04a" xlink:href="note-0216-04"/> {1/3} CG x AC x AC<emph style="super">q</emph> ſummam productorum ſingulorum punctorum paralle-<lb/>logrammi DC, multiplicatorum per quadrata diſtantiarum ſuarum a <lb/>CG.</s> <s xml:id="echoid-s5889" xml:space="preserve"/> </p> <div xml:id="echoid-div835" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0216-04" xlink:href="note-0216-04a" xml:space="preserve">7. El. XII.</note> </div> <p> <s xml:id="echoid-s5890" xml:space="preserve">Similis ſumma pro ſingulis punctis trianguli DCG æqualis eſt, {1/12} GF <lb/>x AC x AC<emph style="super">q</emph>. </s> <s xml:id="echoid-s5891" xml:space="preserve">Hoc facile detegent ſubtilioris Geometriæ gnari, & </s> <s xml:id="echoid-s5892" xml:space="preserve">aliis il-<lb/>lud explicare inutiliter laborarem. </s> <s xml:id="echoid-s5893" xml:space="preserve">Duplicando producta hæc habebimus ſi-<lb/>milem ſummam pro integra figura ADFEB; </s> <s xml:id="echoid-s5894" xml:space="preserve">& </s> <s xml:id="echoid-s5895" xml:space="preserve">eſt {2/3} CG x AC x AC<emph style="super">q</emph> <lb/>+ {1/6} GF x AC x AC<emph style="super">q</emph>, = b x AC<emph style="super">q</emph>; </s> <s xml:id="echoid-s5896" xml:space="preserve">ponendo b = {2/3} CG x AC + {1/6} GF x <lb/>AC.</s> <s xml:id="echoid-s5897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5898" xml:space="preserve">His poſitis dicatur a altitudo a qua globus dimittitur, & </s> <s xml:id="echoid-s5899" xml:space="preserve">velocitas ca-<lb/> <anchor type="note" xlink:label="note-0216-05a" xlink:href="note-0216-05"/> dendo acquiſita, qua globus in lancem Mincurrit, & </s> <s xml:id="echoid-s5900" xml:space="preserve">quæ radici quadratæ <lb/>hujus altitudinis proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>, poterit √ a deſignare.</s> <s xml:id="echoid-s5901" xml:space="preserve"/> </p> <div xml:id="echoid-div836" type="float" level="2" n="5"> <note position="left" xlink:label="note-0216-05" xlink:href="note-0216-05a" xml:space="preserve">549.</note> </div> <note symbol="*" position="left" xml:space="preserve">255</note> <p> <s xml:id="echoid-s5902" xml:space="preserve">Multiplicando hanc velocitatem per globum G (fig 4.) </s> <s xml:id="echoid-s5903" xml:space="preserve">& </s> <s xml:id="echoid-s5904" xml:space="preserve">per quadratum di-<lb/>ſtantiæ AC, & </s> <s xml:id="echoid-s5905" xml:space="preserve">dividendo hoc productum per ſummam omnium corporum <lb/>in experimento motorum, reſpectivè multiplicatorum per quadrata diſtantia-<lb/>rum ſuarum a centro motus, habemus velocitatem puncti A poſt ictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5906" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">543.</note> <p> <s xml:id="echoid-s5907" xml:space="preserve">Partem hujus ſummæ jam determinavimus, quoad jugum nempe, quod ſu-<lb/>pereſt habemus multiplicando pondera lancium L & </s> <s xml:id="echoid-s5908" xml:space="preserve">M, ut & </s> <s xml:id="echoid-s5909" xml:space="preserve">P, Q, & </s> <s xml:id="echoid-s5910" xml:space="preserve">G (fig. <lb/></s> <s xml:id="echoid-s5911" xml:space="preserve">4.) </s> <s xml:id="echoid-s5912" xml:space="preserve">per quadratum diſtantiæ AC, nam omnia hæc corpora conſiderari poſſunt <lb/>quaſi darentur in ipſis punctis ſupenſionis A & </s> <s xml:id="echoid-s5913" xml:space="preserve">B<anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5914" xml:space="preserve">Summam ponderum lan- <anchor type="note" xlink:label="note-0216-08a" xlink:href="note-0216-08"/> <pb o="149" file="0217" n="236" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> cium ut & </s> <s xml:id="echoid-s5915" xml:space="preserve">P, Q, & </s> <s xml:id="echoid-s5916" xml:space="preserve">G, dicimus c, & </s> <s xml:id="echoid-s5917" xml:space="preserve">velocitas puncti A poſt ictum erit <lb/>{AC<emph style="super">q</emph> x Gva/b x AC<emph style="super">q</emph> + c x AC<emph style="super">q</emph>} = {Gva <anchor type="note" xlink:href="" symbol="*"/>/b + c}.</s> <s xml:id="echoid-s5918" xml:space="preserve"> <anchor type="note" xlink:label="note-0217-01a" xlink:href="note-0217-01"/> </s> </p> <div xml:id="echoid-div837" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0216-08" xlink:href="note-0216-08a" xml:space="preserve">128.</note> <note symbol="*" position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">543.</note> </div> <p> <s xml:id="echoid-s5919" xml:space="preserve">Ut, data hac velocitate, altitudinem ad quam elevatur punctum A cumal-<lb/>titudine a conferamus, determinandum eſt centrum oſcillationis, quod mo-<lb/>vetur ut corpus in quod gravitas tantum agit <anchor type="note" xlink:href="" symbol="*"/>, diſtantia autem centri oſcil- <anchor type="note" xlink:label="note-0217-02a" xlink:href="note-0217-02"/> lationis a centro motus eſt {b x AC<emph style="super">q</emph> + c x AC<emph style="super">q</emph>/P x AC <anchor type="note" xlink:href="" symbol="*"/>} = {b x AC + c x AC/P}.</s> <s xml:id="echoid-s5920" xml:space="preserve"> <anchor type="note" xlink:label="note-0217-03a" xlink:href="note-0217-03"/> </s> </p> <div xml:id="echoid-div838" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">296.</note> <note symbol="*" position="right" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">3127</note> </div> <p> <s xml:id="echoid-s5921" xml:space="preserve">Diſtantia autem AC ſe habet ad diſtantiam hanc centri oſcillationis, id eſt <lb/>(multiplicando utramque diſtantiam per P, & </s> <s xml:id="echoid-s5922" xml:space="preserve">dividendo per AC) P ad <lb/>b + c, ut velocitas puncti A ad velocitatem centri oſcillationis; </s> <s xml:id="echoid-s5923" xml:space="preserve">& </s> <s xml:id="echoid-s5924" xml:space="preserve">in eadem <lb/>ratione altitudo ad quam adſcendit A, quam dicimus d, ad altitudinem ad <lb/>quam adſcendit centrum oſcillationis; </s> <s xml:id="echoid-s5925" xml:space="preserve">ergo <lb/>P, b + c:</s> <s xml:id="echoid-s5926" xml:space="preserve">: {Gva/b + c}, {Gva/P} = velocitati centri oſcillationis. </s> <s xml:id="echoid-s5927" xml:space="preserve">Et <lb/>P, b + c:</s> <s xml:id="echoid-s5928" xml:space="preserve">: d {db + dc/P} = altitudini, ad quam centrum oſcillationis adſcendit.</s> <s xml:id="echoid-s5929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5930" xml:space="preserve">Altitudo hæc etiam quadrato velocitatis hujus centri exprimitur, cum a ex-<lb/>primat altitudinem ad quam corpus velociate √ a pertingit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s5931" xml:space="preserve"> <anchor type="note" xlink:label="note-0217-04a" xlink:href="note-0217-04"/> Habemus ergo hanc æquationem {G<emph style="super">q</emph> x a/P<emph style="super">q</emph>} = {db + dc/P} id eſt G<emph style="super">q</emph> x a = db <lb/>x P + dc x P: </s> <s xml:id="echoid-s5932" xml:space="preserve">& </s> <s xml:id="echoid-s5933" xml:space="preserve">a = {<emph style="ol">b + c</emph> x d x P/G<emph style="super">q</emph>}</s> </p> <div xml:id="echoid-div839" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0217-04" xlink:href="note-0217-04a" xml:space="preserve">255. 261.</note> </div> <p> <s xml:id="echoid-s5934" xml:space="preserve">Pro litteris ut numeri ſubſtituantur, conſiderandum, b æquale eſſe {2/3} GC <lb/> <anchor type="note" xlink:label="note-0217-05a" xlink:href="note-0217-05"/> x AC + {1/6}-GF x AC, dum ipſa figura ADFHB, id eſt <emph style="super">2</emph>GC x AC + <lb/>GF x AC <anchor type="note" xlink:href="" symbol="*"/>, Jugi pondus repræſentat; </s> <s xml:id="echoid-s5935" xml:space="preserve">quare hoc pondus jugi ad b, ut <anchor type="note" xlink:label="note-0217-06a" xlink:href="note-0217-06"/> <emph style="super">2</emph>GC + GF ad {2/3} GC + {1/6} GF.</s> <s xml:id="echoid-s5936" xml:space="preserve"/> </p> <div xml:id="echoid-div840" type="float" level="2" n="9"> <note position="right" xlink:label="note-0217-05" xlink:href="note-0217-05a" xml:space="preserve">550.</note> <note symbol="*" position="right" xlink:label="note-0217-06" xlink:href="note-0217-06a" xml:space="preserve">34. El. 1.</note> </div> <p> <s xml:id="echoid-s5937" xml:space="preserve">In noſtra machina eſt GC ad GF ut 3 ad 4. </s> <s xml:id="echoid-s5938" xml:space="preserve">& </s> <s xml:id="echoid-s5939" xml:space="preserve">jugi pondus novemdecim <lb/>unciarum cum dragmis duabus & </s> <s xml:id="echoid-s5940" xml:space="preserve">ſcrupulo uno, id eſt ſcrupulorum 463, <lb/>Ergo 15, 4:</s> <s xml:id="echoid-s5941" xml:space="preserve">: 463, b = 123 {1/2}. </s> <s xml:id="echoid-s5942" xml:space="preserve">ſcrup.</s> <s xml:id="echoid-s5943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5944" xml:space="preserve">Pondera lancium additis Q & </s> <s xml:id="echoid-s5945" xml:space="preserve">G id eſt c-P valent 1320. </s> <s xml:id="echoid-s5946" xml:space="preserve">ſcrupula; </s> <s xml:id="echoid-s5947" xml:space="preserve">Globus <lb/>G, ponderat ſcrupula 67; </s> <s xml:id="echoid-s5948" xml:space="preserve">altitudo d æqualis eſto, 21. </s> <s xml:id="echoid-s5949" xml:space="preserve">poll. </s> <s xml:id="echoid-s5950" xml:space="preserve">id eſt, excedit paulu-<lb/>lum quintam pollicis partem.</s> <s xml:id="echoid-s5951" xml:space="preserve"/> </p> <pb o="150" file="0218" n="237" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s5952" xml:space="preserve">Et præcedens æquatio mutatur in hanc <lb/>{a = {<emph style="ol">b + </emph> c x d x P/G<emph style="super">q</emph>} = {<emph style="ol">123 {1/2} + 1320 + P</emph> x 21P/67<emph style="super">q</emph> x 100} = {<emph style="ol">1443 {1/2} + P</emph> x 21P/448900}</s> </p> <p> <s xml:id="echoid-s5953" xml:space="preserve">Subſtituendo ſucceſſive pro P quatuor, octo, & </s> <s xml:id="echoid-s5954" xml:space="preserve">duodecim uncias, id eſt, <lb/>ſcrupula 96, 192, 288 detegimus a = 6, 91. </s> <s xml:id="echoid-s5955" xml:space="preserve">a = 14, 68; </s> <s xml:id="echoid-s5956" xml:space="preserve">& </s> <s xml:id="echoid-s5957" xml:space="preserve">a = 23, 32.</s> <s xml:id="echoid-s5958" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5959" xml:space="preserve">Quæ altitudines parum admodum differunt cum altitudinibus experimento de-<lb/>tectis; </s> <s xml:id="echoid-s5960" xml:space="preserve">differentia autem tribuenda eſt mutationi figuræ jugi in computatione <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0218-01a" xlink:href="note-0218-01"/> </s> </p> <div xml:id="echoid-div841" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">548.</note> </div> </div> <div xml:id="echoid-div843" type="section" level="1" n="215"> <head xml:id="echoid-head305" xml:space="preserve">SCHOLIUM 4.</head> <head xml:id="echoid-head306" style="it" xml:space="preserve">De Centro oſcillationis, & percuſſionis.</head> <p> <s xml:id="echoid-s5961" xml:space="preserve">Superius <anchor type="note" xlink:href="" symbol="*"/>, ex demonſtratis circa preſſionem, deduximus methodum determi- <anchor type="note" xlink:label="note-0218-02a" xlink:href="note-0218-02"/> nandi centrum oſcillationis; </s> <s xml:id="echoid-s5962" xml:space="preserve">eandem ibi traditam regulam quàm facilli-<lb/> <anchor type="note" xlink:label="note-0218-03a" xlink:href="note-0218-03"/> me deducimus ex demonſtratis circa vires.</s> <s xml:id="echoid-s5963" xml:space="preserve"/> </p> <div xml:id="echoid-div843" type="float" level="2" n="1"> <note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">551.</note> <note symbol="*" position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">311. 312.</note> </div> <p> <s xml:id="echoid-s5964" xml:space="preserve">Corpus eandem acquirit velocitatem, ideoque vim, a certa altitudine caden-<lb/>do, quamcunque viam in deſcenſu ſequatur <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s5965" xml:space="preserve">vis acquiſita huic altitudini <anchor type="note" xlink:label="note-0218-04a" xlink:href="note-0218-04"/> proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5966" xml:space="preserve">Dum corpora pendulo compoſito juncta deſcendunt <anchor type="note" xlink:label="note-0218-05a" xlink:href="note-0218-05"/> nulla actione vis deſcendendo acquiſita deſtruitur; </s> <s xml:id="echoid-s5967" xml:space="preserve">nihil etiam datur quoau-<lb/>geri poſſet, ergo ſumma virium æqualis eſt ſummæ virium quas corpora, <lb/>ſeparatim a ſuis altitudinibus cadendo, pot uiſſent acquirere.</s> <s xml:id="echoid-s5968" xml:space="preserve"/> </p> <div xml:id="echoid-div844" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">271.</note> <note symbol="*" position="left" xlink:label="note-0218-05" xlink:href="note-0218-05a" xml:space="preserve">448.</note> </div> <p> <s xml:id="echoid-s5969" xml:space="preserve">Sint corpora A, B, C, D, diſtantiæ a puncto ſuſpenſionis a, b, c, & </s> <s xml:id="echoid-s5970" xml:space="preserve">d. </s> <s xml:id="echoid-s5971" xml:space="preserve">Alti-<lb/>tudines, a quibus corporahæc deſcendunt, ſunt ut a, b, c, & </s> <s xml:id="echoid-s5972" xml:space="preserve">d & </s> <s xml:id="echoid-s5973" xml:space="preserve">in eadem ra-<lb/>tione velocitates. </s> <s xml:id="echoid-s5974" xml:space="preserve">Dicatur diſtantia centri oſcillationis à puncto ſuſpenſio-<lb/>nis x, & </s> <s xml:id="echoid-s5975" xml:space="preserve">velocitas acquiſ@ta deſcendendo ab altitudine a qua centrum hoc deſcen-<lb/>dit √ x; </s> <s xml:id="echoid-s5976" xml:space="preserve">ideò velocitas corporis A, ſi libere cecidiſſet, fuiſſet √ a <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s5977" xml:space="preserve">ipſius <anchor type="note" xlink:label="note-0218-06a" xlink:href="note-0218-06"/> vis A a <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s5978" xml:space="preserve">ſummaque virium ſi ſingula corpora libere cecidiſſent Aa + Bb + <anchor type="note" xlink:label="note-0218-07a" xlink:href="note-0218-07"/> Cc + Dd. </s> <s xml:id="echoid-s5979" xml:space="preserve">Si quædam corpora dentur ad partem oppoſitam puncti ſuſpenſio-<lb/>nis adſcendunt & </s> <s xml:id="echoid-s5980" xml:space="preserve">horum vires negativæ ſunt.</s> <s xml:id="echoid-s5981" xml:space="preserve"/> </p> <div xml:id="echoid-div845" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0218-06" xlink:href="note-0218-06a" xml:space="preserve">255.</note> <note symbol="*" position="left" xlink:label="note-0218-07" xlink:href="note-0218-07a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s5982" xml:space="preserve">In corporibus pendulo junctis velocitas corporis A detegitur hac regulâ <lb/>x, a:</s> <s xml:id="echoid-s5983" xml:space="preserve">: vx, {a/vx}. </s> <s xml:id="echoid-s5984" xml:space="preserve">Cæterorumque corporum velocitates ſunt {b/vx}, {c/vx} & </s> <s xml:id="echoid-s5985" xml:space="preserve"><lb/>{d/vx}; </s> <s xml:id="echoid-s5986" xml:space="preserve">ſummaque virium {Aaa/x} + {Bbb/x} + {Ccc/x} + {Ddd/x} <anchor type="note" xlink:href="" symbol="*"/>, quæ cum memo- <anchor type="note" xlink:label="note-0218-08a" xlink:href="note-0218-08"/> ratæ ſummæ æqualis ſit; </s> <s xml:id="echoid-s5987" xml:space="preserve">detegimus x = {Aaa + Bbb + Ccc + Ddd/Aa + Bb + Cc + Dd} juxtare-<lb/>gulam n. </s> <s xml:id="echoid-s5988" xml:space="preserve">311.</s> <s xml:id="echoid-s5989" xml:space="preserve"/> </p> <div xml:id="echoid-div846" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0218-08" xlink:href="note-0218-08a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s5990" xml:space="preserve">Quando pendulum compoſitum in obicem fixum, ad quamcunque a cen-<lb/> <anchor type="note" xlink:label="note-0218-09a" xlink:href="note-0218-09"/> tro ſuſpenſionis diſtantiam poſitum, impingit, ſæpe in illud quod pendulum <lb/>ſuſtinet premit, integram tamen in obicem vim exerit, ſi preſſio quam in cen- <pb o="151" file="0219" n="238" rhead="MATHEMATICA. LIB. I. CAP. XXIII."/> tro ſuſpenſionis exerit nullum ibi generet motum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s5991" xml:space="preserve">Ita autem obex, in quem <anchor type="note" xlink:label="note-0219-01a" xlink:href="note-0219-01"/> incurrit pendulum, diſponi poteſt ut nullam pendulum in puncto ſuſpenſi-<lb/>onis exerat in retinaculum ſuum preſſionem. </s> <s xml:id="echoid-s5992" xml:space="preserve">Punctum penduli quod in hoc <lb/>caſu in obicem incurrit vocatur centrum percuſſionis. <lb/></s> <s xml:id="echoid-s5993" xml:space="preserve"> <anchor type="note" xlink:label="note-0219-02a" xlink:href="note-0219-02"/> </s> </p> <div xml:id="echoid-div847" type="float" level="2" n="5"> <note position="left" xlink:label="note-0218-09" xlink:href="note-0218-09a" xml:space="preserve">552.</note> <note symbol="*" position="right" xlink:label="note-0219-01" xlink:href="note-0219-01a" xml:space="preserve">523.</note> <note position="right" xlink:label="note-0219-02" xlink:href="note-0219-02a" xml:space="preserve">553.</note> </div> <p style="it"> <s xml:id="echoid-s5994" xml:space="preserve">Centri hujus hæc eſt proprietas, dari æquilibrium inter actiones quibus corpora <lb/>ab utraque parte hujus centri in pendulum agunt.</s> <s xml:id="echoid-s5995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5996" xml:space="preserve">Poſſumus ergo conſiderare pendulum quaſivectem, cujus ſuſtentaculum eſt <lb/>obex, in quem incurrit, poſitus in ipſo centro percuſſionis, & </s> <s xml:id="echoid-s5997" xml:space="preserve">æquilibrium <lb/>dari dum in hunc vectem corpora incurrunt, velocitatibus quibus in pendulo <lb/>moventur.</s> <s xml:id="echoid-s5998" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5999" xml:space="preserve">Penduli A I formati corporibus A & </s> <s xml:id="echoid-s6000" xml:space="preserve">D, junctis lineâ inflexi, ſuſpenſâ in <lb/> <anchor type="note" xlink:label="note-0219-03a" xlink:href="note-0219-03"/> I, centrum percuſſionis erit H, ſi poſitis, vecte cujus ſuſtentaculum eſt H, <lb/> <anchor type="note" xlink:label="note-0219-04a" xlink:href="note-0219-04"/> & </s> <s xml:id="echoid-s6001" xml:space="preserve">in hunc incurrentibus corporibus A & </s> <s xml:id="echoid-s6002" xml:space="preserve">D, in ipſis punctis A & </s> <s xml:id="echoid-s6003" xml:space="preserve">D, velo-<lb/>citatibus quas in pendulo habent, detur inter haſce actiones æquilibrium; </s> <s xml:id="echoid-s6004" xml:space="preserve">tunc <lb/>enim punctum I penduli ullo motu affici non poteſt, aut ſiretineatur, ullam exe-<lb/>rere preſſionem.</s> <s xml:id="echoid-s6005" xml:space="preserve"/> </p> <div xml:id="echoid-div848" type="float" level="2" n="6"> <note position="right" xlink:label="note-0219-03" xlink:href="note-0219-03a" xml:space="preserve">554.</note> <note position="right" xlink:label="note-0219-04" xlink:href="note-0219-04a" xml:space="preserve">TAB. XXIII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s6006" xml:space="preserve">Ut caſum æquilibrii determinemus poſitis variis corporibus, ſingulorum <lb/>actiones determinari debent, id eſt, ſunt hæ actiones conferendæ inter ſe.</s> <s xml:id="echoid-s6007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6008" xml:space="preserve">Relictâ nunc penduli conſideratione, ad ſolum vectem attendendo; </s> <s xml:id="echoid-s6009" xml:space="preserve">ſit Cor-<lb/> <anchor type="note" xlink:label="note-0219-05a" xlink:href="note-0219-05"/> poris A velocitas m, & </s> <s xml:id="echoid-s6010" xml:space="preserve">a diſtantia AH; </s> <s xml:id="echoid-s6011" xml:space="preserve">Corporis D velocitas n, & </s> <s xml:id="echoid-s6012" xml:space="preserve">d diſtantia <lb/>HD. </s> <s xml:id="echoid-s6013" xml:space="preserve">Eodem modo in vectem agit corpus A, utrum in A ad partem M, aut in <lb/>L ad partem N, eadem velocitate in hunc incurrat poſitis HA & </s> <s xml:id="echoid-s6014" xml:space="preserve">HL æqualibus. <lb/></s> <s xml:id="echoid-s6015" xml:space="preserve">Actio etiam erit eadem ſi, ſervatis corporum velocitatibus, concipiamus hæc ro-<lb/>tari circa centrum H & </s> <s xml:id="echoid-s6016" xml:space="preserve">ità agitata in vectem incurrere per e L & </s> <s xml:id="echoid-s6017" xml:space="preserve">f D. </s> <s xml:id="echoid-s6018" xml:space="preserve">Conti-<lb/>nuetur Hfin G, ut HG & </s> <s xml:id="echoid-s6019" xml:space="preserve">He, aut HA, ſint æquales, æquilibrium dabitur, <lb/>ſi velocitas puncti eſe habeat ad velocitatem puncti G, ut Ddd ad Aaa <anchor type="note" xlink:href="" symbol="*"/>, id eſt <anchor type="note" xlink:label="note-0219-06a" xlink:href="note-0219-06"/> Ddd, Aaa:</s> <s xml:id="echoid-s6020" xml:space="preserve">: m, {an/d}, hæc enim eſt velocitas-puncti G; </s> <s xml:id="echoid-s6021" xml:space="preserve">ergo Aam = Ddn; <lb/></s> <s xml:id="echoid-s6022" xml:space="preserve">unde patet actionem ſequi rationem producti maſſæ corporis per velocitatem, & </s> <s xml:id="echoid-s6023" xml:space="preserve">di-<lb/>ſtantiam a fulcro.</s> <s xml:id="echoid-s6024" xml:space="preserve"/> </p> <div xml:id="echoid-div849" type="float" level="2" n="7"> <note position="right" xlink:label="note-0219-05" xlink:href="note-0219-05a" xml:space="preserve">555.</note> <note symbol="*" position="right" xlink:label="note-0219-06" xlink:href="note-0219-06a" xml:space="preserve">533.</note> </div> <p> <s xml:id="echoid-s6025" xml:space="preserve">In pendulo velocitas ſequitur rationem diſtantiæ à puncto ſuſpenſionis; <lb/></s> <s xml:id="echoid-s6026" xml:space="preserve">& </s> <s xml:id="echoid-s6027" xml:space="preserve">diſtantia a fulcro, eſt diſtantia a centro percuſſionis; </s> <s xml:id="echoid-s6028" xml:space="preserve">ergo actio corporis <lb/>ſequitur rationem producti corporis per ſuas diſtantias a centris ſuſpenſionis <lb/>& </s> <s xml:id="echoid-s6029" xml:space="preserve">percuſſionis, daturque æquilibrium inter actiones ab utraque parte centri <lb/>percuſſionis, quando producta hæc ab utraque parte hujus centri ſunt æqualia, <lb/>quam eandem cùm centrum oſcillationis habeat proprietatem <anchor type="note" xlink:href="" symbol="*"/>, ſequitur hoc <anchor type="note" xlink:label="note-0219-07a" xlink:href="note-0219-07"/> cum centro percuſſionis coincidere. <lb/></s> <s xml:id="echoid-s6030" xml:space="preserve"> <anchor type="note" xlink:label="note-0219-08a" xlink:href="note-0219-08"/> </s> </p> <div xml:id="echoid-div850" type="float" level="2" n="8"> <note position="right" xlink:label="note-0219-07" xlink:href="note-0219-07a" xml:space="preserve">556.</note> <note symbol="*" position="right" xlink:label="note-0219-08" xlink:href="note-0219-08a" xml:space="preserve">309.</note> </div> </div> <div xml:id="echoid-div852" type="section" level="1" n="216"> <head xml:id="echoid-head307" xml:space="preserve">CAPUT XXIV.</head> <head xml:id="echoid-head308" style="it" xml:space="preserve">De congreſſu corporum Elaſticorum.</head> <p> <s xml:id="echoid-s6031" xml:space="preserve">Corpora elaſtica, poſt ictum, ut jam notavimus, ſeparan-<lb/>tur, <anchor type="note" xlink:href="" symbol="*"/> ſed vi diverſa in circumſtantiis ſimilibus; </s> <s xml:id="echoid-s6032" xml:space="preserve">nam <anchor type="note" xlink:label="note-0219-09a" xlink:href="note-0219-09"/> in variis corporibus elaſticitas differt.</s> <s xml:id="echoid-s6033" xml:space="preserve"/> </p> <div xml:id="echoid-div852" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0219-09" xlink:href="note-0219-09a" xml:space="preserve">483.</note> </div> <pb o="152" file="0220" n="239" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div854" type="section" level="1" n="217"> <head xml:id="echoid-head309" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p style="it"> <s xml:id="echoid-s6034" xml:space="preserve">Elaſticitas dicitur perfecta, quando partes ictæ ad pri-<lb/> <anchor type="note" xlink:label="note-0220-01a" xlink:href="note-0220-01"/> ſtinum ſitum redeunt, vi æquali illi, cum qua fuere i-<lb/>ctæ.</s> <s xml:id="echoid-s6035" xml:space="preserve"/> </p> <div xml:id="echoid-div854" type="float" level="2" n="1"> <note position="left" xlink:label="note-0220-01" xlink:href="note-0220-01a" xml:space="preserve">557.</note> </div> <p> <s xml:id="echoid-s6036" xml:space="preserve">De perfecta agimus elaſticitate, licetnulla corpora tali e-<lb/>laſticitate prædita nobis nota ſint; </s> <s xml:id="echoid-s6037" xml:space="preserve">regulæ enim generales ni-<lb/>ſi quoad perfectam elaſticitatem tradi non poſſunt; </s> <s xml:id="echoid-s6038" xml:space="preserve">quo ma-<lb/>gis ad hanc corpora accedunt eo magis exacte motus ho-<lb/>rum cum regulis congruunt.</s> <s xml:id="echoid-s6039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6040" xml:space="preserve">Nulla vis in colliſione corporum perit, niſi quæ intro-<lb/>premendo partes conſumitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6041" xml:space="preserve">ideo ſi corpora ſint elaſti- <anchor type="note" xlink:label="note-0220-02a" xlink:href="note-0220-02"/> ca tota impenditur in inflexione partium elaſticarum, ſed <lb/>æquali vi ad priſtinam figuram hæ redeunt; </s> <s xml:id="echoid-s6042" xml:space="preserve">ergo vis de-<lb/>ſtructa iterum inſtauratur; </s> <s xml:id="echoid-s6043" xml:space="preserve">& </s> <s xml:id="echoid-s6044" xml:space="preserve">ſumma virium corporibus inſi-<lb/> <anchor type="note" xlink:label="note-0220-03a" xlink:href="note-0220-03"/> tarum poſt ictum æqualis eſt ſummæ virium ante ictum; <lb/></s> <s xml:id="echoid-s6045" xml:space="preserve">quæ demonſtratio univerſalis maximè eſt, & </s> <s xml:id="echoid-s6046" xml:space="preserve">colliſionibus <lb/>quibuſcunque applicari poteſt.</s> <s xml:id="echoid-s6047" xml:space="preserve"/> </p> <div xml:id="echoid-div855" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0220-02" xlink:href="note-0220-02a" xml:space="preserve">432.</note> <note position="left" xlink:label="note-0220-03" xlink:href="note-0220-03a" xml:space="preserve">558.</note> </div> <p> <s xml:id="echoid-s6048" xml:space="preserve">Hinc ſequitur Corpus elaſticum in obicem firmum elaſticum <lb/> <anchor type="note" xlink:label="note-0220-04a" xlink:href="note-0220-04"/> impingens, eâdem celeritate redire qua acceſſit. </s> <s xml:id="echoid-s6049" xml:space="preserve">Si dire-<lb/>ctio perpendicularis ſit ad obicem etiam in eâdem lineâredi-<lb/>bit, cum non magis unam quàm aliam partem verſus poſ-<lb/>ſit deflecti.</s> <s xml:id="echoid-s6050" xml:space="preserve"/> </p> <div xml:id="echoid-div856" type="float" level="2" n="3"> <note position="left" xlink:label="note-0220-04" xlink:href="note-0220-04a" xml:space="preserve">559.</note> </div> <p> <s xml:id="echoid-s6051" xml:space="preserve">In reliquis de directa impactione tantum in hoc capite <lb/>ago.</s> <s xml:id="echoid-s6052" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6053" xml:space="preserve">Elaſterium flexum, poſitum inter duo corpora quieſcentia, <lb/> <anchor type="note" xlink:label="note-0220-05a" xlink:href="note-0220-05"/> dum ſeſe expandit ambo movet corpora; </s> <s xml:id="echoid-s6054" xml:space="preserve">ſi preſſio qua partes <lb/>corporis cohærent ſuperet preſſiones quas elaſterium in <lb/>corpus hoc exerit, tota elaſterii actio, cum nulla detur <lb/>partium introceſſio, in movendis corporibus conſumitur, <lb/>& </s> <s xml:id="echoid-s6055" xml:space="preserve">ſumma virium corporibus communicatarum valet vim qua <lb/>elaſterium fuit flexum. </s> <s xml:id="echoid-s6056" xml:space="preserve">Sed dum elaſterium hæc movet <lb/>corpora, duas exerit actiones, quæ ſingulæ æquales <lb/>ſunt reactioni quam patiuntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6057" xml:space="preserve">id eſt, utraque actio æ- <anchor type="note" xlink:label="note-0220-06a" xlink:href="note-0220-06"/> qualis eſt reſiſtentiæ quam ad partem oppoſitam patitur. <lb/></s> <s xml:id="echoid-s6058" xml:space="preserve">Reſiſtentiæ hæ ſunt ut quantitates materiæ in corporibus <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s6059" xml:space="preserve"> <anchor type="note" xlink:label="note-0220-07a" xlink:href="note-0220-07"/> <pb o="153" file="0221" n="240" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/> ergo actiones in eadem ratione ad partes oppoſitas; </s> <s xml:id="echoid-s6060" xml:space="preserve">id <lb/> <anchor type="note" xlink:label="note-0221-01a" xlink:href="note-0221-01"/> eſt, ſunt in ratione inverſa corporum motorum, in qua ea-<lb/>dem ratione ſunt velocitates corporibus communicatæ. </s> <s xml:id="echoid-s6061" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0221-02a" xlink:href="note-0221-02"/> </s> </p> <div xml:id="echoid-div857" type="float" level="2" n="4"> <note position="left" xlink:label="note-0220-05" xlink:href="note-0220-05a" xml:space="preserve">560.</note> <note symbol="*" position="left" xlink:label="note-0220-06" xlink:href="note-0220-06a" xml:space="preserve">247.</note> <note symbol="*" position="left" xlink:label="note-0220-07" xlink:href="note-0220-07a" xml:space="preserve">13.</note> <note position="right" xlink:label="note-0221-01" xlink:href="note-0221-01a" xml:space="preserve">561.</note> <note symbol="*" position="right" xlink:label="note-0221-02" xlink:href="note-0221-02a" xml:space="preserve">472.</note> </div> <p> <s xml:id="echoid-s6062" xml:space="preserve">Caſus hic exſtat, ſi duo corpora elaſtica in ſe mutuo incur-<lb/> <anchor type="note" xlink:label="note-0221-03a" xlink:href="note-0221-03"/> rant velocitatibus quæ ſunt inversè ut maſſæ; </s> <s xml:id="echoid-s6063" xml:space="preserve">nam poſitis <lb/>his non elaſticis, poſt ictum quieſcunt; </s> <s xml:id="echoid-s6064" xml:space="preserve">ergo in ipſo mo-<lb/>mento concurſus, ante figuram inſtauratam, datur elaſte-<lb/>rium flexum inter duo corpora quieſcentia. </s> <s xml:id="echoid-s6065" xml:space="preserve">Separantur <lb/>ideo hæc velocitatibus quæ ſunt inversè ut maſſæ <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0221-04a" xlink:href="note-0221-04"/> id eſt, velocitates poſt ictum in eadem ſunt ratione in qua <lb/>ante ictum erant; </s> <s xml:id="echoid-s6066" xml:space="preserve">unde ſequitur corpus utrumque redire <lb/>eâdem velocitate quam ante ictum habuit, nam ſi minuatur <lb/>in uno, non ſervabitur ratio niſi & </s> <s xml:id="echoid-s6067" xml:space="preserve">in altero minuatur, qua-<lb/>re ſumma virium minor erit, quod impoſſibile <anchor type="note" xlink:href="" symbol="*"/>, demon- <anchor type="note" xlink:label="note-0221-05a" xlink:href="note-0221-05"/> ſtratio eadem eſt ſi quis unius corporis auctam velocitatem <lb/>dicat.</s> <s xml:id="echoid-s6068" xml:space="preserve"/> </p> <div xml:id="echoid-div858" type="float" level="2" n="5"> <note position="right" xlink:label="note-0221-03" xlink:href="note-0221-03a" xml:space="preserve">562.</note> <note symbol="*" position="right" xlink:label="note-0221-04" xlink:href="note-0221-04a" xml:space="preserve">561.</note> <note symbol="*" position="right" xlink:label="note-0221-05" xlink:href="note-0221-05a" xml:space="preserve">558.</note> </div> <p> <s xml:id="echoid-s6069" xml:space="preserve">Experimenta de corporibus elaſticis inſtituuntur alteru-<lb/>trâ Machinarum ſuperius <anchor type="note" xlink:href="" symbol="*"/> explicatarum, & </s> <s xml:id="echoid-s6070" xml:space="preserve">adhibitis glo- <anchor type="note" xlink:label="note-0221-06a" xlink:href="note-0221-06"/> bis eburneis aut cylindris in fig. </s> <s xml:id="echoid-s6071" xml:space="preserve">3. </s> <s xml:id="echoid-s6072" xml:space="preserve">Tab. </s> <s xml:id="echoid-s6073" xml:space="preserve">18. </s> <s xml:id="echoid-s6074" xml:space="preserve">delinea-<lb/>tis.</s> <s xml:id="echoid-s6075" xml:space="preserve"/> </p> <div xml:id="echoid-div859" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0221-06" xlink:href="note-0221-06a" xml:space="preserve">490. 491.</note> </div> </div> <div xml:id="echoid-div861" type="section" level="1" n="218"> <head xml:id="echoid-head310" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s6076" xml:space="preserve">Corpora duo P & </s> <s xml:id="echoid-s6077" xml:space="preserve">Q, quorum maſſæ ſunt ut unum ad <lb/> <anchor type="note" xlink:label="note-0221-07a" xlink:href="note-0221-07"/> tria, in ſe mutuo incurrunt, hoc velocitate quinque, illud <lb/> <anchor type="note" xlink:label="note-0221-08a" xlink:href="note-0221-08"/> velocitate quindecim, poſt ictum utrumque ad eandem fe-<lb/>rè à qua cecidit altitudinem redit.</s> <s xml:id="echoid-s6078" xml:space="preserve"/> </p> <div xml:id="echoid-div861" type="float" level="2" n="1"> <note position="right" xlink:label="note-0221-07" xlink:href="note-0221-07a" xml:space="preserve">563.</note> <note position="right" xlink:label="note-0221-08" xlink:href="note-0221-08a" xml:space="preserve">TAB. XXI. <lb/>fig. 9.</note> </div> <p> <s xml:id="echoid-s6079" xml:space="preserve">Defectus elaſticitatis in cauſa eſt quare non exactè ad eaſ-<lb/>dem, à quibus cecidêre, redeant altitudines.</s> <s xml:id="echoid-s6080" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6081" xml:space="preserve">Quæ de elaſterio, inter corpora quieſcentia ſeſe expan-<lb/>dente, demonſtrata ſunt, ad elaſterium inter corpora, eâdem <lb/>cum his velocitate tranſlatum, & </s> <s xml:id="echoid-s6082" xml:space="preserve">reſpectu corporum <lb/>quieſcens, referri debent; </s> <s xml:id="echoid-s6083" xml:space="preserve">ſi ergo in nave duo corpora ela-<lb/> <anchor type="note" xlink:label="note-0221-09a" xlink:href="note-0221-09"/> ſtica velocitatibus, quæ ſunt inverſe ut maſſæ, in ſe mu-<lb/>tuo impingant, velocitatibus iiſdem in nave redibunt.</s> <s xml:id="echoid-s6084" xml:space="preserve"/> </p> <div xml:id="echoid-div862" type="float" level="2" n="2"> <note position="right" xlink:label="note-0221-09" xlink:href="note-0221-09a" xml:space="preserve">564.</note> </div> <p> <s xml:id="echoid-s6085" xml:space="preserve">Poſitis quæ in n. </s> <s xml:id="echoid-s6086" xml:space="preserve">512. </s> <s xml:id="echoid-s6087" xml:space="preserve">dicta ſunt, in nave, quæ velocitate <lb/> <anchor type="note" xlink:label="note-0221-10a" xlink:href="note-0221-10"/> BI fertur, corpora non elaſtica poſt ictum quieſcunt, & </s> <s xml:id="echoid-s6088" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0221-11a" xlink:href="note-0221-11"/> mutationes in velocitatibus ſunt in versè ut maſſæ, deſtru- <pb o="146" file="0222" n="241" rhead="PHYSICES ELEMENTA"/> ctis velocitatibus quibus in nave ad ſe invicem acceſſere; <lb/></s> <s xml:id="echoid-s6089" xml:space="preserve">ſi fuerint elaſtica, in nave a ſe mutuo recedunt iiſdem hiſce <lb/>velocitatibus quibus in nave ad ſe mutuo acceſſere <anchor type="note" xlink:href="" symbol="*"/>, id eſt <anchor type="note" xlink:label="note-0222-01a" xlink:href="note-0222-01"/> ſecunda in velocitatibus datur mutatio æqualis primæ, quare <lb/>utrumque corpus duplam patitur in velocitate mutationem, <lb/>& </s> <s xml:id="echoid-s6090" xml:space="preserve">velocitas reſpectiva poſt ictum æqualis eſt velocitati re-<lb/> <anchor type="note" xlink:label="note-0222-02a" xlink:href="note-0222-02"/> ſpectivæ ante ictum. </s> <s xml:id="echoid-s6091" xml:space="preserve">In fig, 1. </s> <s xml:id="echoid-s6092" xml:space="preserve">corpus motum velocitate <lb/>BN, in nave ante ictum habebat velocitatem IN, hanc <lb/>amiſit, & </s> <s xml:id="echoid-s6093" xml:space="preserve">huic æqualem in contrariam partem acquiſivit <lb/>IG, habet ideo velocitatem BG. </s> <s xml:id="echoid-s6094" xml:space="preserve">Corpus aliud cujus <lb/>velocitas erat BE in nave ante ictum redibat id eſt lentius <lb/>ipſa nave movebatur quantitate IE poſt ictum æquali velo-<lb/>citate in contrariam partem id eſt celerius ipſâ nave fer-<lb/>tur velocitaſque eſt BP, poſitis IE & </s> <s xml:id="echoid-s6095" xml:space="preserve">IP æquali-<lb/>bus.</s> <s xml:id="echoid-s6096" xml:space="preserve"/> </p> <div xml:id="echoid-div863" type="float" level="2" n="3"> <note position="right" xlink:label="note-0221-10" xlink:href="note-0221-10a" xml:space="preserve">565.</note> <note position="right" xlink:label="note-0221-11" xlink:href="note-0221-11a" xml:space="preserve">TAB. XX. <lb/>fig. 1. 2.</note> <note symbol="*" position="left" xlink:label="note-0222-01" xlink:href="note-0222-01a" xml:space="preserve">564.</note> <note position="left" xlink:label="note-0222-02" xlink:href="note-0222-02a" xml:space="preserve">566.</note> </div> <p> <s xml:id="echoid-s6097" xml:space="preserve">Eodem modo in fig. </s> <s xml:id="echoid-s6098" xml:space="preserve">2. </s> <s xml:id="echoid-s6099" xml:space="preserve">Corpus quod habebat velocitatem <lb/>BN, amiſit velocitatem IN, quam in nave habebat, & </s> <s xml:id="echoid-s6100" xml:space="preserve">velocitate, <lb/>huic æquali, IG nunc in nave redit, id eſt velocitate BG poſt <lb/>ictum fertur; </s> <s xml:id="echoid-s6101" xml:space="preserve">corpus aliud cujus velocitas erat BE, in na-<lb/>ve redibat velocitate IE nunc mutato motu velocitate huic <lb/>æquali IP in nave a pupiad proram fertur, & </s> <s xml:id="echoid-s6102" xml:space="preserve">ipſius velocitas <lb/>abſoluta eſt BP.</s> <s xml:id="echoid-s6103" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6104" xml:space="preserve">Ex hiſce deducimus regulas duas quibus corporum ela-<lb/>ſticorum velocitates poſt ictum determinamus.</s> <s xml:id="echoid-s6105" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div865" type="section" level="1" n="219"> <head xml:id="echoid-head311" xml:space="preserve"><emph style="sc">Regula</emph> I.</head> <p style="it"> <s xml:id="echoid-s6106" xml:space="preserve">Si corporis velocitas, poſitis corporibus non elaſticis in ſe <lb/> <anchor type="note" xlink:label="note-0222-03a" xlink:href="note-0222-03"/> mutuo impingentibus, ictu augeatur, augmentum duplica-<lb/>tum priori velocitati eſt addendum, ut celeritas poſt impa-<lb/>ctum determinetur, ſi corpora fuerint elaſtica.</s> <s xml:id="echoid-s6107" xml:space="preserve"/> </p> <div xml:id="echoid-div865" type="float" level="2" n="1"> <note position="left" xlink:label="note-0222-03" xlink:href="note-0222-03a" xml:space="preserve">567.</note> </div> </div> <div xml:id="echoid-div867" type="section" level="1" n="220"> <head xml:id="echoid-head312" xml:space="preserve"><emph style="sc">Regula</emph> II.</head> <p style="it"> <s xml:id="echoid-s6108" xml:space="preserve">Duobus corporibus non elaſticis in ſe mutuo impingenti-<lb/> <anchor type="note" xlink:label="note-0222-04a" xlink:href="note-0222-04"/> bus, ſi corpus ex velocitate amittat, pars amiſſa duplican-<lb/>da eſt, quando elaſtica ſunt corpora; </s> <s xml:id="echoid-s6109" xml:space="preserve">& </s> <s xml:id="echoid-s6110" xml:space="preserve">a priori velocitate <lb/>ſubtrahenda, ad determinandam celeritatem poſt percuſſio-<lb/>nem.</s> <s xml:id="echoid-s6111" xml:space="preserve"/> </p> <div xml:id="echoid-div867" type="float" level="2" n="1"> <note position="left" xlink:label="note-0222-04" xlink:href="note-0222-04a" xml:space="preserve">568.</note> </div> <p> <s xml:id="echoid-s6112" xml:space="preserve">Circa ſecundam regulam obſervandum, corpus quod <lb/> <anchor type="note" xlink:label="note-0222-05a" xlink:href="note-0222-05"/> <pb o="155" file="0223" n="242" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/> redit non modo amittere priſtinam velocitatem, ſed præte-<lb/>rea pro velocitate amiſſa etiam haberi velocitatem, in con-<lb/>trariam partem acquiſitam; </s> <s xml:id="echoid-s6113" xml:space="preserve">& </s> <s xml:id="echoid-s6114" xml:space="preserve">in hoc caſu ſumma ambarum <lb/>harum velocitatum duplicanda eſt & </s> <s xml:id="echoid-s6115" xml:space="preserve">expriori celeritate ſub-<lb/>trahenda. </s> <s xml:id="echoid-s6116" xml:space="preserve">Quando autem major velocitas ex minori ſubdu-<lb/>citur, exceſſus in contrariam partem ſumendus eſt.</s> <s xml:id="echoid-s6117" xml:space="preserve"/> </p> <div xml:id="echoid-div868" type="float" level="2" n="2"> <note position="left" xlink:label="note-0222-05" xlink:href="note-0222-05a" xml:space="preserve">569.</note> </div> </div> <div xml:id="echoid-div870" type="section" level="1" n="221"> <head xml:id="echoid-head313" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s6118" xml:space="preserve">Corpus P, cujus maſſa eſt duo, & </s> <s xml:id="echoid-s6119" xml:space="preserve">celeritas novem, im-<lb/> <anchor type="note" xlink:label="note-0223-01a" xlink:href="note-0223-01"/> pingitur in corpus quieſcens Q, cujus maſſa eſt unum; <lb/></s> <s xml:id="echoid-s6120" xml:space="preserve"> <anchor type="note" xlink:label="note-0223-02a" xlink:href="note-0223-02"/> poſt impactum Q fertur celeritate duodecim, & </s> <s xml:id="echoid-s6121" xml:space="preserve">P mo-<lb/>tum continuat velocitate tria; </s> <s xml:id="echoid-s6122" xml:space="preserve">quod cum prædictis Regu-<lb/>lis congruit: </s> <s xml:id="echoid-s6123" xml:space="preserve">nam ſi corpora non eſſent elaſtica, celeritas <lb/>amborum poſt occurſum eſſet ſex <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6124" xml:space="preserve">corpus ergo Q ac- <anchor type="note" xlink:label="note-0223-03a" xlink:href="note-0223-03"/> quireret ſex gradus velocitatis; </s> <s xml:id="echoid-s6125" xml:space="preserve">ideo per Reg. </s> <s xml:id="echoid-s6126" xml:space="preserve">I. </s> <s xml:id="echoid-s6127" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> acquirit <anchor type="note" xlink:label="note-0223-04a" xlink:href="note-0223-04"/> nunc duodecim gradus. </s> <s xml:id="echoid-s6128" xml:space="preserve">Corpus P quod ſepoſita elaſtici-<lb/>tate amittit tres gradus velocitatis, per Reg. </s> <s xml:id="echoid-s6129" xml:space="preserve">II. </s> <s xml:id="echoid-s6130" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> amittit <anchor type="note" xlink:label="note-0223-05a" xlink:href="note-0223-05"/> ſex, quiſi ſubtrahantur a novem, velocitate priori, reſtant <lb/>tres gradus velocitatis.</s> <s xml:id="echoid-s6131" xml:space="preserve"/> </p> <div xml:id="echoid-div870" type="float" level="2" n="1"> <note position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">570.</note> <note position="right" xlink:label="note-0223-02" xlink:href="note-0223-02a" xml:space="preserve">TAB XXI. <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0223-03" xlink:href="note-0223-03a" xml:space="preserve">519.</note> <note symbol="*" position="right" xlink:label="note-0223-04" xlink:href="note-0223-04a" xml:space="preserve">567.</note> <note symbol="*" position="right" xlink:label="note-0223-05" xlink:href="note-0223-05a" xml:space="preserve">568.</note> </div> </div> <div xml:id="echoid-div872" type="section" level="1" n="222"> <head xml:id="echoid-head314" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s6132" xml:space="preserve">Corpus P, cujus maſſa eſt duo, & </s> <s xml:id="echoid-s6133" xml:space="preserve">velocitas octo, in-<lb/> <anchor type="note" xlink:label="note-0223-06a" xlink:href="note-0223-06"/> currit in corpus Q, cuius maſſa eſt unum, & </s> <s xml:id="echoid-s6134" xml:space="preserve">quod veloci-<lb/> <anchor type="note" xlink:label="note-0223-07a" xlink:href="note-0223-07"/> tate quinque eandem partem verſus fertur; </s> <s xml:id="echoid-s6135" xml:space="preserve">poſt occurſum <lb/>corpus Q movetur velocitate novem, & </s> <s xml:id="echoid-s6136" xml:space="preserve">P velocitate ſex <lb/>fertur. </s> <s xml:id="echoid-s6137" xml:space="preserve">Quod iterum per Regulas præcedentes potuiſſet <lb/>determinari. </s> <s xml:id="echoid-s6138" xml:space="preserve">Si corpora non eſſent elaſtica, ambo celeri-<lb/>tate ſeptem poſt impactum moverentur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6139" xml:space="preserve">corpus Q acqui- <anchor type="note" xlink:label="note-0223-08a" xlink:href="note-0223-08"/> reret duos gradus celeritatis, qui per Reg. </s> <s xml:id="echoid-s6140" xml:space="preserve">I. </s> <s xml:id="echoid-s6141" xml:space="preserve">duplicari de-<lb/>bent, & </s> <s xml:id="echoid-s6142" xml:space="preserve">priori celeritati quinque addi, unde habemus no-<lb/>vem: </s> <s xml:id="echoid-s6143" xml:space="preserve">corpus P amiſit unum gradum velocitatis, per Reg. <lb/></s> <s xml:id="echoid-s6144" xml:space="preserve">II. </s> <s xml:id="echoid-s6145" xml:space="preserve">amittit duos, ei ergo reſtant ſex.</s> <s xml:id="echoid-s6146" xml:space="preserve"/> </p> <div xml:id="echoid-div872" type="float" level="2" n="1"> <note position="right" xlink:label="note-0223-06" xlink:href="note-0223-06a" xml:space="preserve">571.</note> <note position="right" xlink:label="note-0223-07" xlink:href="note-0223-07a" xml:space="preserve">TAB. XXI. <lb/>fig. 6.</note> <note symbol="*" position="right" xlink:label="note-0223-08" xlink:href="note-0223-08a" xml:space="preserve">513.</note> </div> </div> <div xml:id="echoid-div874" type="section" level="1" n="223"> <head xml:id="echoid-head315" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s6147" xml:space="preserve">Corpus P in aliud Q, quieſcens & </s> <s xml:id="echoid-s6148" xml:space="preserve">triplum, velocitate <lb/> <anchor type="note" xlink:label="note-0223-09a" xlink:href="note-0223-09"/> duodecim impingitur, & </s> <s xml:id="echoid-s6149" xml:space="preserve">velocitate ſex regreditur. </s> <s xml:id="echoid-s6150" xml:space="preserve">In hoc <lb/> <anchor type="note" xlink:label="note-0223-10a" xlink:href="note-0223-10"/> caſu corpora non elaſtica moverentur celeritate tria; </s> <s xml:id="echoid-s6151" xml:space="preserve">cor-<lb/>pus ergo Pamiſiſſet novem gradus velocitatis, amittit ergo per <lb/>Reg. </s> <s xml:id="echoid-s6152" xml:space="preserve">II. </s> <s xml:id="echoid-s6153" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> octodecim gradus; </s> <s xml:id="echoid-s6154" xml:space="preserve">qui ſi ſubtrahantur a priori ve- <anchor type="note" xlink:label="note-0223-11a" xlink:href="note-0223-11"/> <pb o="156" file="0224" n="243" rhead="PHYSICES ELEMENTA"/> locitate duodecim, dantur ſex grad. </s> <s xml:id="echoid-s6155" xml:space="preserve">in contrariam partem <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s6156" xml:space="preserve"> <anchor type="note" xlink:label="note-0224-01a" xlink:href="note-0224-01"/> eodem modo ſequentibus Experimentis confirmatur quod <lb/>per Regulas detegitur.</s> <s xml:id="echoid-s6157" xml:space="preserve"/> </p> <div xml:id="echoid-div874" type="float" level="2" n="1"> <note position="right" xlink:label="note-0223-09" xlink:href="note-0223-09a" xml:space="preserve">572.</note> <note position="right" xlink:label="note-0223-10" xlink:href="note-0223-10a" xml:space="preserve">TAB. XXI. <lb/>fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0223-11" xlink:href="note-0223-11a" xml:space="preserve">568.</note> <note symbol="*" position="left" xlink:label="note-0224-01" xlink:href="note-0224-01a" xml:space="preserve">569.</note> </div> </div> <div xml:id="echoid-div876" type="section" level="1" n="224"> <head xml:id="echoid-head316" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s6158" xml:space="preserve">Corpus P velocitate novendecim fertur eandem partem <lb/> <anchor type="note" xlink:label="note-0224-02a" xlink:href="note-0224-02"/> verſus cum corpore triplo Q, moto celeritate tria; </s> <s xml:id="echoid-s6159" xml:space="preserve">poſt im-<lb/> <anchor type="note" xlink:label="note-0224-03a" xlink:href="note-0224-03"/> pactum corpus P regreditur velocitate quinque.</s> <s xml:id="echoid-s6160" xml:space="preserve"/> </p> <div xml:id="echoid-div876" type="float" level="2" n="1"> <note position="left" xlink:label="note-0224-02" xlink:href="note-0224-02a" xml:space="preserve">573.</note> <note position="left" xlink:label="note-0224-03" xlink:href="note-0224-03a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig 8.</note> </div> </div> <div xml:id="echoid-div878" type="section" level="1" n="225"> <head xml:id="echoid-head317" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s6161" xml:space="preserve">Corpus P celeritate quinque, & </s> <s xml:id="echoid-s6162" xml:space="preserve">corpus Q triplum ce-<lb/> <anchor type="note" xlink:label="note-0224-04a" xlink:href="note-0224-04"/> leritate undecim, in partes contrarias feruntur; </s> <s xml:id="echoid-s6163" xml:space="preserve">poſt occur-<lb/> <anchor type="note" xlink:label="note-0224-05a" xlink:href="note-0224-05"/> ſum, Q motum continuat celeritate tria, & </s> <s xml:id="echoid-s6164" xml:space="preserve">P regreditur <lb/>velocitate novemdecim.</s> <s xml:id="echoid-s6165" xml:space="preserve"/> </p> <div xml:id="echoid-div878" type="float" level="2" n="1"> <note position="left" xlink:label="note-0224-04" xlink:href="note-0224-04a" xml:space="preserve">574.</note> <note position="left" xlink:label="note-0224-05" xlink:href="note-0224-05a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig. 10.</note> </div> </div> <div xml:id="echoid-div880" type="section" level="1" n="226"> <head xml:id="echoid-head318" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s6166" xml:space="preserve">Eadem corpora P & </s> <s xml:id="echoid-s6167" xml:space="preserve">Q in contrarias partes feruntur, P <lb/> <anchor type="note" xlink:label="note-0224-06a" xlink:href="note-0224-06"/> celeritate ſedecim, & </s> <s xml:id="echoid-s6168" xml:space="preserve">Q velocitate octo; </s> <s xml:id="echoid-s6169" xml:space="preserve">ambo poſt impa-<lb/> <anchor type="note" xlink:label="note-0224-07a" xlink:href="note-0224-07"/> ctum regrediuntur, P cum viginti & </s> <s xml:id="echoid-s6170" xml:space="preserve">Q cum quatuor gradi-<lb/>bus velocitatis.</s> <s xml:id="echoid-s6171" xml:space="preserve"/> </p> <div xml:id="echoid-div880" type="float" level="2" n="1"> <note position="left" xlink:label="note-0224-06" xlink:href="note-0224-06a" xml:space="preserve">575.</note> <note position="left" xlink:label="note-0224-07" xlink:href="note-0224-07a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig. 11.</note> </div> <p> <s xml:id="echoid-s6172" xml:space="preserve">Omnes caſus percuſſionum corporum elaſticorum Regu-<lb/>lis memoratis determinantur; </s> <s xml:id="echoid-s6173" xml:space="preserve">ſequentem etiam ex illis de-<lb/>ducimus propoſitionem.</s> <s xml:id="echoid-s6174" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s6175" xml:space="preserve">Quando corpora ſunt æqualia, & </s> <s xml:id="echoid-s6176" xml:space="preserve">eandem partem ver ſivs <lb/> <anchor type="note" xlink:label="note-0224-08a" xlink:href="note-0224-08"/> feruntur, permutatis velocitatibus motum continuant; </s> <s xml:id="echoid-s6177" xml:space="preserve">ſi in <lb/>contrarias partes ferantur, permutatis velocitatibus regre-<lb/>diuntur.</s> <s xml:id="echoid-s6178" xml:space="preserve"/> </p> <div xml:id="echoid-div881" type="float" level="2" n="2"> <note position="left" xlink:label="note-0224-08" xlink:href="note-0224-08a" xml:space="preserve">576.</note> </div> <p> <s xml:id="echoid-s6179" xml:space="preserve">Cas. </s> <s xml:id="echoid-s6180" xml:space="preserve">I. </s> <s xml:id="echoid-s6181" xml:space="preserve">Tendant corpora ad eandem plagam, & </s> <s xml:id="echoid-s6182" xml:space="preserve">ſit A B <lb/> <anchor type="note" xlink:label="note-0224-09a" xlink:href="note-0224-09"/> velocitas unius corporis, B C velocitas alterius corporis; <lb/></s> <s xml:id="echoid-s6183" xml:space="preserve"> <anchor type="note" xlink:label="note-0224-10a" xlink:href="note-0224-10"/> propter maſſas æquales, ſunt velocitates ut producta maſſa-<lb/>rum per velocitates. </s> <s xml:id="echoid-s6184" xml:space="preserve">Dividatur linea A C in duas partes <lb/>æquales in D, & </s> <s xml:id="echoid-s6185" xml:space="preserve">ſit D b æqualis DB; </s> <s xml:id="echoid-s6186" xml:space="preserve">AD aut DC de-<lb/>notat celeritatem utriuſque corporis poſt occurſum, ſi non <lb/>ſint elaſtica <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6187" xml:space="preserve">& </s> <s xml:id="echoid-s6188" xml:space="preserve">celeritas BC augetur quantitate DB, du- <anchor type="note" xlink:label="note-0224-11a" xlink:href="note-0224-11"/> plici quantitate tali augeri debet propter elaſticitatem <anchor type="note" xlink:href="" symbol="*"/>, id <anchor type="note" xlink:label="note-0224-12a" xlink:href="note-0224-12"/> eſt, fiet b C: </s> <s xml:id="echoid-s6189" xml:space="preserve">celeritas AB; </s> <s xml:id="echoid-s6190" xml:space="preserve">in corporibus non elaſticis, <lb/>minuitur quantitate DB; </s> <s xml:id="echoid-s6191" xml:space="preserve">duplici illa quantitate minui de-<lb/>bet, ex prædicta ratione <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6192" xml:space="preserve">& </s> <s xml:id="echoid-s6193" xml:space="preserve">fiet a b. </s> <s xml:id="echoid-s6194" xml:space="preserve">Velocitates igi- <anchor type="note" xlink:label="note-0224-13a" xlink:href="note-0224-13"/> tur AB & </s> <s xml:id="echoid-s6195" xml:space="preserve">BC mutantur in velocitates A b & </s> <s xml:id="echoid-s6196" xml:space="preserve">b C; </s> <s xml:id="echoid-s6197" xml:space="preserve">A <pb o="157" file="0225" n="244" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/> B vero & </s> <s xml:id="echoid-s6198" xml:space="preserve">b C, ut & </s> <s xml:id="echoid-s6199" xml:space="preserve">BC & </s> <s xml:id="echoid-s6200" xml:space="preserve">A b, ſunt æquales inter <lb/>ſe.</s> <s xml:id="echoid-s6201" xml:space="preserve"/> </p> <div xml:id="echoid-div882" type="float" level="2" n="3"> <note position="left" xlink:label="note-0224-09" xlink:href="note-0224-09a" xml:space="preserve">577.</note> <note position="left" xlink:label="note-0224-10" xlink:href="note-0224-10a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0224-11" xlink:href="note-0224-11a" xml:space="preserve">513.</note> <note symbol="*" position="left" xlink:label="note-0224-12" xlink:href="note-0224-12a" xml:space="preserve">567.</note> <note symbol="*" position="left" xlink:label="note-0224-13" xlink:href="note-0224-13a" xml:space="preserve">568</note> </div> </div> <div xml:id="echoid-div884" type="section" level="1" n="227"> <head xml:id="echoid-head319" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s6202" xml:space="preserve">Corpora duo æqualia &</s> <s xml:id="echoid-s6203" xml:space="preserve">, primum velocitate decem, alte-<lb/> <anchor type="note" xlink:label="note-0225-01a" xlink:href="note-0225-01"/> rum velocitate quinque, eandem partem verſus feruntur; <lb/></s> <s xml:id="echoid-s6204" xml:space="preserve">mutatis velocitatibus poſt impactum motum continuant: </s> <s xml:id="echoid-s6205" xml:space="preserve"><lb/>quod etiam detegitur computatione ex præcedentibus Re-<lb/>gulis.</s> <s xml:id="echoid-s6206" xml:space="preserve"/> </p> <div xml:id="echoid-div884" type="float" level="2" n="1"> <note position="right" xlink:label="note-0225-01" xlink:href="note-0225-01a" xml:space="preserve">578.</note> </div> <p> <s xml:id="echoid-s6207" xml:space="preserve">Cas. </s> <s xml:id="echoid-s6208" xml:space="preserve">2. </s> <s xml:id="echoid-s6209" xml:space="preserve">Sit AB celeritas unius corporis, CB celeritas <lb/> <anchor type="note" xlink:label="note-0225-02a" xlink:href="note-0225-02"/> alterius; </s> <s xml:id="echoid-s6210" xml:space="preserve">differentia AC dividatur in duas partes æqua-<lb/> <anchor type="note" xlink:label="note-0225-03a" xlink:href="note-0225-03"/> les, & </s> <s xml:id="echoid-s6211" xml:space="preserve">fiat A b æqualis CB. </s> <s xml:id="echoid-s6212" xml:space="preserve">Quando corpora non ſunt <lb/>elaſtica, velocitas utriuſque poſt occurſum, verſus ean-<lb/>dem partem, eſt AD <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6213" xml:space="preserve">corpus ergo primum amiſit ve- <anchor type="note" xlink:label="note-0225-04a" xlink:href="note-0225-04"/> locitatem DB, corpus alterum amiſit totam velocitatem CB <lb/>& </s> <s xml:id="echoid-s6214" xml:space="preserve">in contrariam partem acquiſivit DC; </s> <s xml:id="echoid-s6215" xml:space="preserve">tota ergo quan-<lb/> <anchor type="note" xlink:label="note-0225-05a" xlink:href="note-0225-05"/> titas amiſſa etiam eſt DB <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6216" xml:space="preserve">hæc quantitas ſi duplicetur, erit b B quantitas celeritatis ab utroque corpore amiſſa <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s6217" xml:space="preserve"> <anchor type="note" xlink:label="note-0225-06a" xlink:href="note-0225-06"/> quæ ſubtracta ex velocitate utriuſque corporis, dat in u-<lb/>troque caſu velocitatem in contrariam partem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6218" xml:space="preserve">differen- <anchor type="note" xlink:label="note-0225-07a" xlink:href="note-0225-07"/> tia hæc reſpectu motus AB eſt b A, pro motu CB eſt <lb/>C b; </s> <s xml:id="echoid-s6219" xml:space="preserve">C b vero & </s> <s xml:id="echoid-s6220" xml:space="preserve">AB, ut & </s> <s xml:id="echoid-s6221" xml:space="preserve">b A & </s> <s xml:id="echoid-s6222" xml:space="preserve">CB, ſunt æquales <lb/>inter ſe.</s> <s xml:id="echoid-s6223" xml:space="preserve"/> </p> <div xml:id="echoid-div885" type="float" level="2" n="2"> <note position="right" xlink:label="note-0225-02" xlink:href="note-0225-02a" xml:space="preserve">579.</note> <note position="right" xlink:label="note-0225-03" xlink:href="note-0225-03a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0225-04" xlink:href="note-0225-04a" xml:space="preserve">516.</note> <note symbol="*" position="right" xlink:label="note-0225-05" xlink:href="note-0225-05a" xml:space="preserve">569.</note> <note symbol="*" position="right" xlink:label="note-0225-06" xlink:href="note-0225-06a" xml:space="preserve">568.</note> <note symbol="*" position="right" xlink:label="note-0225-07" xlink:href="note-0225-07a" xml:space="preserve">569.</note> </div> </div> <div xml:id="echoid-div887" type="section" level="1" n="228"> <head xml:id="echoid-head320" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s6224" xml:space="preserve">Si corpora æqualia, unum celeritate decem, alte-<lb/> <anchor type="note" xlink:label="note-0225-08a" xlink:href="note-0225-08"/> rum velocitate quinque, in contrarias partes ferantur, per-<lb/>mutatis velocitatibus ambo regrediuntur poſt percuſſio-<lb/>nem.</s> <s xml:id="echoid-s6225" xml:space="preserve"/> </p> <div xml:id="echoid-div887" type="float" level="2" n="1"> <note position="right" xlink:label="note-0225-08" xlink:href="note-0225-08a" xml:space="preserve">580.</note> </div> <p style="it"> <s xml:id="echoid-s6226" xml:space="preserve">Corpus impingitur in alind æquale quieſcens, ſi velocitates <lb/> <anchor type="note" xlink:label="note-0225-09a" xlink:href="note-0225-09"/> permutentur, corpus primum poſt impactum quieſcet, alte-<lb/>rum vero cum velocitate prioris movebitur.</s> <s xml:id="echoid-s6227" xml:space="preserve"/> </p> <div xml:id="echoid-div888" type="float" level="2" n="2"> <note position="right" xlink:label="note-0225-09" xlink:href="note-0225-09a" xml:space="preserve">581.</note> </div> </div> <div xml:id="echoid-div890" type="section" level="1" n="229"> <head xml:id="echoid-head321" xml:space="preserve"><emph style="sc">Experimentum</emph> 10.</head> <p> <s xml:id="echoid-s6228" xml:space="preserve">Corpus velocitate decem impingat in corpus æquale quie-<lb/> <anchor type="note" xlink:label="note-0225-10a" xlink:href="note-0225-10"/> tum, primum poſt occurſum quieſcet, & </s> <s xml:id="echoid-s6229" xml:space="preserve">aliud celeritate de-<lb/>cem movetur.</s> <s xml:id="echoid-s6230" xml:space="preserve"/> </p> <div xml:id="echoid-div890" type="float" level="2" n="1"> <note position="right" xlink:label="note-0225-10" xlink:href="note-0225-10a" xml:space="preserve">582.</note> </div> <p> <s xml:id="echoid-s6231" xml:space="preserve">In omnibus hiſce experimentis notandum, hæc hìc tra-<lb/>di ut obtinerent ſi perfecta foret elaſticitas, ad cujus defe-<lb/>ctum ſemper attendere debemus.</s> <s xml:id="echoid-s6232" xml:space="preserve"/> </p> <pb o="158" file="0226" n="245" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s6233" xml:space="preserve">In corporibus elaſticis ſubita admodum eſt elaterii actio. <lb/></s> <s xml:id="echoid-s6234" xml:space="preserve"> <anchor type="note" xlink:label="note-0226-01a" xlink:href="note-0226-01"/> Ideo ſi varia corpora elaſtica ſint contigua, & </s> <s xml:id="echoid-s6235" xml:space="preserve">extremum <lb/>percutiatur, omnia ſequentia agitantur quaſi eſſent ſe-<lb/>parata; </s> <s xml:id="echoid-s6236" xml:space="preserve">etiam ſi ex variis contiguis, eâdem velocitate <lb/>motis, antecedens in corpus quodcumque incurrat, agit <lb/>ut à reliquis ſeparatum ageret; </s> <s xml:id="echoid-s6237" xml:space="preserve">Unde ſequitur corpus move-<lb/> <anchor type="note" xlink:label="note-0226-02a" xlink:href="note-0226-02"/> ri ſola actione corporis vicini, & </s> <s xml:id="echoid-s6238" xml:space="preserve">in vicinum corpus tantum <lb/>agere, partibus elaſticis ad figuram redeuntibus, antequam <lb/>actio corpori ſequenti communicari poſſit.</s> <s xml:id="echoid-s6239" xml:space="preserve"/> </p> <div xml:id="echoid-div891" type="float" level="2" n="2"> <note position="left" xlink:label="note-0226-01" xlink:href="note-0226-01a" xml:space="preserve">583.</note> <note position="left" xlink:label="note-0226-02" xlink:href="note-0226-02a" xml:space="preserve">584.</note> </div> </div> <div xml:id="echoid-div893" type="section" level="1" n="230"> <head xml:id="echoid-head322" xml:space="preserve"><emph style="sc">Experimentum</emph> 11.</head> <p> <s xml:id="echoid-s6240" xml:space="preserve">I. </s> <s xml:id="echoid-s6241" xml:space="preserve">Sint corpora plurima æqualia P, Q, R, S, T, V, <lb/> <anchor type="note" xlink:label="note-0226-03a" xlink:href="note-0226-03"/> in eadem linea diſpoſita, & </s> <s xml:id="echoid-s6242" xml:space="preserve">ſeſe mutuo tangentia; </s> <s xml:id="echoid-s6243" xml:space="preserve">corpus <lb/> <anchor type="note" xlink:label="note-0226-04a" xlink:href="note-0226-04"/> P impingatur in Q. </s> <s xml:id="echoid-s6244" xml:space="preserve">quacunque velocitate, poſt occur-<lb/>ſum P,Q,R,S, & </s> <s xml:id="echoid-s6245" xml:space="preserve">T quieta manent, & </s> <s xml:id="echoid-s6246" xml:space="preserve">V ſolum movetur.</s> <s xml:id="echoid-s6247" xml:space="preserve"/> </p> <div xml:id="echoid-div893" type="float" level="2" n="1"> <note position="left" xlink:label="note-0226-03" xlink:href="note-0226-03a" xml:space="preserve">585.</note> <note position="left" xlink:label="note-0226-04" xlink:href="note-0226-04a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s6248" xml:space="preserve">2. </s> <s xml:id="echoid-s6249" xml:space="preserve">Moveantur æqualibus velocitatibus P & </s> <s xml:id="echoid-s6250" xml:space="preserve">Q, ita ut Q im-<lb/> <anchor type="note" xlink:label="note-0226-05a" xlink:href="note-0226-05"/> pingatur in R, poſt impactum P,Q,R, & </s> <s xml:id="echoid-s6251" xml:space="preserve">S quieſcunt, T <lb/>& </s> <s xml:id="echoid-s6252" xml:space="preserve">V vero ſimul moventur.</s> <s xml:id="echoid-s6253" xml:space="preserve"/> </p> <div xml:id="echoid-div894" type="float" level="2" n="2"> <note position="left" xlink:label="note-0226-05" xlink:href="note-0226-05a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s6254" xml:space="preserve">3. </s> <s xml:id="echoid-s6255" xml:space="preserve">Eodem modo ſi tria moventur, poſt occurſum tria etiam <lb/> <anchor type="note" xlink:label="note-0226-06a" xlink:href="note-0226-06"/> moventur.</s> <s xml:id="echoid-s6256" xml:space="preserve"/> </p> <div xml:id="echoid-div895" type="float" level="2" n="3"> <note position="left" xlink:label="note-0226-06" xlink:href="note-0226-06a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s6257" xml:space="preserve">4. </s> <s xml:id="echoid-s6258" xml:space="preserve">Tandem ſi, P,Q,R, S & </s> <s xml:id="echoid-s6259" xml:space="preserve">ſimul moveantur, & </s> <s xml:id="echoid-s6260" xml:space="preserve">S per-<lb/> <anchor type="note" xlink:label="note-0226-07a" xlink:href="note-0226-07"/> cutiat T, poſt percuſſionem P & </s> <s xml:id="echoid-s6261" xml:space="preserve">Q quieſcunt, R, S, T, <lb/>& </s> <s xml:id="echoid-s6262" xml:space="preserve">V ſimul moventur. </s> <s xml:id="echoid-s6263" xml:space="preserve">Generaliter quicunque ſit globorum <lb/>numerus, quot moventur ante occurſum, tot etiam poſt il-<lb/>lum moventur.</s> <s xml:id="echoid-s6264" xml:space="preserve"/> </p> <div xml:id="echoid-div896" type="float" level="2" n="4"> <note position="left" xlink:label="note-0226-07" xlink:href="note-0226-07a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 9.</note> </div> <p> <s xml:id="echoid-s6265" xml:space="preserve">Agunt hæc corpora quaſi eſſent ſeparata <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6266" xml:space="preserve">In primo cafu P <anchor type="note" xlink:label="note-0226-08a" xlink:href="note-0226-08"/> impingitur in Q & </s> <s xml:id="echoid-s6267" xml:space="preserve">quieſcit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6268" xml:space="preserve">Q ictu agitatum impingitur in <anchor type="note" xlink:label="note-0226-09a" xlink:href="note-0226-09"/> R & </s> <s xml:id="echoid-s6269" xml:space="preserve">etiam quieſcit, & </s> <s xml:id="echoid-s6270" xml:space="preserve">ſic de cæteris, donec tandem T per-<lb/> <anchor type="note" xlink:label="note-0226-10a" xlink:href="note-0226-10"/> cutiat V, quod, cùm nullo obſtaculo retineatur, ſolum in <lb/>motu continuat.</s> <s xml:id="echoid-s6271" xml:space="preserve"/> </p> <div xml:id="echoid-div897" type="float" level="2" n="5"> <note position="left" xlink:label="note-0226-08" xlink:href="note-0226-08a" xml:space="preserve"><emph style="sc">TA. XXII</emph> <lb/>fig. 6.</note> <note symbol="*" position="left" xlink:label="note-0226-09" xlink:href="note-0226-09a" xml:space="preserve">583.</note> <note symbol="*" position="left" xlink:label="note-0226-10" xlink:href="note-0226-10a" xml:space="preserve">501.</note> </div> <p> <s xml:id="echoid-s6272" xml:space="preserve">In ſecundo caſu, corpus Q eodem modo corpus V <lb/> <anchor type="note" xlink:label="note-0226-11a" xlink:href="note-0226-11"/> propellit; </s> <s xml:id="echoid-s6273" xml:space="preserve">inſequitur immediate P impingens in Q, <lb/>quod jam ex priori impactu quieſcit, motus ille etiam <lb/>eodem modo communicatur corpori T, quod non pot-<lb/>eſt percutere V jam in motu; </s> <s xml:id="echoid-s6274" xml:space="preserve">& </s> <s xml:id="echoid-s6275" xml:space="preserve">cum motus corporum <lb/>P & </s> <s xml:id="echoid-s6276" xml:space="preserve">Q æque veloces ſint, & </s> <s xml:id="echoid-s6277" xml:space="preserve">illa corpora quam proxi-<lb/>me ſeſe inſequantur, ſenſibile tempus inter illas duas mo- <pb o="159" file="0227" n="246" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/> tus communicationes non datur, unde etiam corpora V & </s> <s xml:id="echoid-s6278" xml:space="preserve"><lb/>T æque velociter moventur & </s> <s xml:id="echoid-s6279" xml:space="preserve">non ſeparantur.</s> <s xml:id="echoid-s6280" xml:space="preserve"/> </p> <div xml:id="echoid-div898" type="float" level="2" n="6"> <note position="left" xlink:label="note-0226-11" xlink:href="note-0226-11a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s6281" xml:space="preserve">A lio experimento conſtat, ita ſubitam eſſe elaſterii actio-<lb/>nem ut vix concipiatur.</s> <s xml:id="echoid-s6282" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div900" type="section" level="1" n="231"> <head xml:id="echoid-head323" xml:space="preserve"><emph style="sc">Experimentum</emph> 12.</head> <p> <s xml:id="echoid-s6283" xml:space="preserve">Globus eburneus cavus, diametri circiter@ duorum pol-<lb/> <anchor type="note" xlink:label="note-0227-01a" xlink:href="note-0227-01"/> licum, ex duobus conſtat hemiſphæriis A & </s> <s xml:id="echoid-s6284" xml:space="preserve">B, quæ cochleâ <lb/> <anchor type="note" xlink:label="note-0227-02a" xlink:href="note-0227-02"/> quàm arctiſſimè inter ſe conjungi poſſunt.</s> <s xml:id="echoid-s6285" xml:space="preserve"/> </p> <div xml:id="echoid-div900" type="float" level="2" n="1"> <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">586.</note> <note position="right" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve"><emph style="sc">TA. XXII</emph>. <lb/>fig. 10.</note> </div> <p> <s xml:id="echoid-s6286" xml:space="preserve">Hemiſphærium B dimittitur ita, ab altitudine quacunque, <lb/>ex. </s> <s xml:id="echoid-s6287" xml:space="preserve">gr. </s> <s xml:id="echoid-s6288" xml:space="preserve">octodecim pollicum, ut plano marmoreo cœru-<lb/>leo, paululum madefacto, impingat; </s> <s xml:id="echoid-s6289" xml:space="preserve">& </s> <s xml:id="echoid-s6290" xml:space="preserve">quidem ut pun-<lb/>ctum medium ſuperficiei in planum incurrat. </s> <s xml:id="echoid-s6291" xml:space="preserve">Hoc haud <lb/>difficulter obtineri poteſt, ſi in eo loco majorem ha-<lb/>beat craſſitiem hemiſphærium quâm extrema verſus. </s> <s xml:id="echoid-s6292" xml:space="preserve">Men-<lb/>furetur macula quam in marmore corpus impactu impri-<lb/>mit.</s> <s xml:id="echoid-s6293" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6294" xml:space="preserve">Conjungatur hemiſphærium A, & </s> <s xml:id="echoid-s6295" xml:space="preserve">dimittatur ab eadem <lb/>altitudine globus ita, ut idem punctum ſuperficiei hemi-<lb/>ſphærii B in planum marmoreum incurrat, quod facile fiet ſi <lb/>hemiſphærium A alio levius fuerit: </s> <s xml:id="echoid-s6296" xml:space="preserve">Macula priori quam ex-<lb/>actiſſime æqualis erit, & </s> <s xml:id="echoid-s6297" xml:space="preserve">globus multo minus reſiliet.</s> <s xml:id="echoid-s6298" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6299" xml:space="preserve">Tandem in globi cavitatem inſeratur plumbi fruſtum P, <lb/>ejuſdem ponderis cum ipſo globo, ibique firmetur; </s> <s xml:id="echoid-s6300" xml:space="preserve">dimiſſo <lb/>eodem modo globo, & </s> <s xml:id="echoid-s6301" xml:space="preserve">in hoc tertio caſu macula eadem <lb/>erit, & </s> <s xml:id="echoid-s6302" xml:space="preserve">globus vix reſiliet.</s> <s xml:id="echoid-s6303" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6304" xml:space="preserve">Dimiſſo autem ab eadem altitudine globo ſolido ex ebo-<lb/>re, globo memorato æquali, macula major eſt, & </s> <s xml:id="echoid-s6305" xml:space="preserve">fere ad il-<lb/>lam à qua cecidit altitudinem globus redit.</s> <s xml:id="echoid-s6306" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6307" xml:space="preserve">In hoc experimento videmus, partes ictas hemiſphærii <lb/>B ad figuram rediiſſe, antequam huic hemiſphærio actio <lb/>hemiſphærii A, aut plumbi inſerti, communicari potuerit, <lb/>licet ſatis arcte hæc corpora cohæreant.</s> <s xml:id="echoid-s6308" xml:space="preserve"/> </p> <pb o="160" file="0228" n="247" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div902" type="section" level="1" n="232"> <head xml:id="echoid-head324" xml:space="preserve">SCHOLIUM I.</head> <head xml:id="echoid-head325" xml:space="preserve">Uberior demonſtratio n. 558.</head> <p> <s xml:id="echoid-s6309" xml:space="preserve">Demonſtravimus in congreſſu corporum elaſticorum ſummam virium ante <lb/> <anchor type="note" xlink:label="note-0228-01a" xlink:href="note-0228-01"/> & </s> <s xml:id="echoid-s6310" xml:space="preserve">poſt ictum eſſe eandem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6311" xml:space="preserve">unde ſequitur, poſitis explicatis in n. </s> <s xml:id="echoid-s6312" xml:space="preserve">565. </s> <s xml:id="echoid-s6313" xml:space="preserve">566.</s> <s xml:id="echoid-s6314" xml:space="preserve"> AB x BN<emph style="super">q</emph> + BC x BE<emph style="super">q</emph> = AB x BG<emph style="super">q</emph> + BC x BP<emph style="super">q</emph>; </s> <s xml:id="echoid-s6315" xml:space="preserve">cujus & </s> <s xml:id="echoid-s6316" xml:space="preserve">hìc geometri-<lb/> <anchor type="note" xlink:label="note-0228-02a" xlink:href="note-0228-02"/> cam dabimus demonſtrationem.</s> <s xml:id="echoid-s6317" xml:space="preserve"/> </p> <div xml:id="echoid-div902" type="float" level="2" n="1"> <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve"><emph style="sc">TAB. XX</emph>. <lb/>fig. 12.</note> <note symbol="*" position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s6318" xml:space="preserve">Primo tendant corpora eandem partem verſus. </s> <s xml:id="echoid-s6319" xml:space="preserve">Formentur quadrata li-<lb/> <anchor type="note" xlink:label="note-0228-03a" xlink:href="note-0228-03"/> nearum BE, BG, BN, & </s> <s xml:id="echoid-s6320" xml:space="preserve">BP; </s> <s xml:id="echoid-s6321" xml:space="preserve">ducatur omnium diagonalis BV. </s> <s xml:id="echoid-s6322" xml:space="preserve">Du-<lb/> <anchor type="note" xlink:label="note-0228-04a" xlink:href="note-0228-04"/> catur IS parallela ad PV; </s> <s xml:id="echoid-s6323" xml:space="preserve">& </s> <s xml:id="echoid-s6324" xml:space="preserve">per S, punctum, in quo diagonalem ſecat, <lb/>ducatur XSK, parallela PB; </s> <s xml:id="echoid-s6325" xml:space="preserve">continuentur GR & </s> <s xml:id="echoid-s6326" xml:space="preserve">EQ in Z & </s> <s xml:id="echoid-s6327" xml:space="preserve">K; </s> <s xml:id="echoid-s6328" xml:space="preserve">quia <lb/>IN & </s> <s xml:id="echoid-s6329" xml:space="preserve">IG ſunt æquales, ut & </s> <s xml:id="echoid-s6330" xml:space="preserve">IP & </s> <s xml:id="echoid-s6331" xml:space="preserve">IE, triangula YST, RSZ ſunt æ-<lb/>qualia, etiam triangula SXV, SKQ. </s> <s xml:id="echoid-s6332" xml:space="preserve">Idcirca Trapezium GRTN æ-<lb/>quale eſt rectangulo GZYN, & </s> <s xml:id="echoid-s6333" xml:space="preserve">trapezium EQVP æquale rectangulo <lb/>EKXP.</s> <s xml:id="echoid-s6334" xml:space="preserve"/> </p> <div xml:id="echoid-div903" type="float" level="2" n="2"> <note position="left" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">587.</note> <note position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve"><emph style="sc">TAB. XX</emph>. <lb/>fig. 18.</note> </div> <p> <s xml:id="echoid-s6335" xml:space="preserve">Semidifferentia quadratorum linearum BN, BG eſt trapezium GRTN, <lb/>id eſt rectangulum GZYN. </s> <s xml:id="echoid-s6336" xml:space="preserve">Eodem modo ſemidifterentia quadratorum linea-<lb/>rum BP, BE eſt rectangulum EKXP; </s> <s xml:id="echoid-s6337" xml:space="preserve">Sed rectangula hæc, propter communem <lb/>altitudinem IS, ſunt ut baſes <anchor type="note" xlink:href="" symbol="*"/>, aut ut baſium ſemiſſes IN, IE; </s> <s xml:id="echoid-s6338" xml:space="preserve">etiam ut <anchor type="note" xlink:label="note-0228-05a" xlink:href="note-0228-05"/> ſunt ſemidifferentiæ quadratorum ita integræ differentiæ: </s> <s xml:id="echoid-s6339" xml:space="preserve">ergo</s> </p> <div xml:id="echoid-div904" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0228-05" xlink:href="note-0228-05a" xml:space="preserve">1. El. VI.</note> </div> <p> <s xml:id="echoid-s6340" xml:space="preserve">BN<emph style="super">q</emph> - BG<emph style="super">q</emph>, BP<emph style="super">q</emph> - BE<emph style="super">q</emph>:</s> <s xml:id="echoid-s6341" xml:space="preserve">:IN, IE, id eſt ut BC ad AB ex conſtructione. <lb/></s> <s xml:id="echoid-s6342" xml:space="preserve">Idcirco AB x BN<emph style="super">q</emph> - AB x BG<emph style="super">q</emph> = BC x BP<emph style="super">q</emph> - BC x BE<emph style="super">q</emph>; </s> <s xml:id="echoid-s6343" xml:space="preserve">ideo AB x BN<emph style="super">q</emph> <lb/>+ BC x BE<emph style="super">q</emph> = AB x BG<emph style="super">q</emph> + BC x BP<emph style="super">q</emph>. </s> <s xml:id="echoid-s6344" xml:space="preserve">quod demonſtrandum erat.</s> <s xml:id="echoid-s6345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6346" xml:space="preserve">Tendant nunc corpora in partes contrarias. </s> <s xml:id="echoid-s6347" xml:space="preserve">Formentur iterum quadrata <lb/> <anchor type="note" xlink:label="note-0228-06a" xlink:href="note-0228-06"/> linearum BP, BN, BE aut B e, & </s> <s xml:id="echoid-s6348" xml:space="preserve">BG aut B g. </s> <s xml:id="echoid-s6349" xml:space="preserve">Propter æquales IN, <lb/> <anchor type="note" xlink:label="note-0228-07a" xlink:href="note-0228-07"/> IG, & </s> <s xml:id="echoid-s6350" xml:space="preserve">IP, IE, æquales ſunt NP, EG, aut e g; </s> <s xml:id="echoid-s6351" xml:space="preserve">addamus utrim-<lb/>que e N, erunt æquales e P, g N. </s> <s xml:id="echoid-s6352" xml:space="preserve">Differentia quadratorum BV & </s> <s xml:id="echoid-s6353" xml:space="preserve">BQ, <lb/>id eſt quadratorum linearum BP, BE, eſt rectangulum, cujus baſis eſt PV, <lb/>& </s> <s xml:id="echoid-s6354" xml:space="preserve">e Q, id eſt PE, & </s> <s xml:id="echoid-s6355" xml:space="preserve">altitudo e P; </s> <s xml:id="echoid-s6356" xml:space="preserve">differentia quadratorum BT, BR, <lb/>id eſt quadratorum linearum BN, B g aut BG, eſt rectangulum, cujus ba-<lb/>ſis eſt NT, & </s> <s xml:id="echoid-s6357" xml:space="preserve">g R, id eſt NG, & </s> <s xml:id="echoid-s6358" xml:space="preserve">altitudo g N; </s> <s xml:id="echoid-s6359" xml:space="preserve">propter æquales alti-<lb/>tudines rectangula hæc ſunt ut baſes PE, NG, aut ut harum ſemiſſes IE, <lb/>IN, quæ ſuntut AB, BC; </s> <s xml:id="echoid-s6360" xml:space="preserve">ergo <lb/>BP<emph style="super">q</emph> - BE<emph style="super">q</emph>, BN<emph style="super">q</emph> - BG<emph style="super">q</emph>:</s> <s xml:id="echoid-s6361" xml:space="preserve">: AB, BC</s> </p> <div xml:id="echoid-div905" type="float" level="2" n="4"> <note position="left" xlink:label="note-0228-06" xlink:href="note-0228-06a" xml:space="preserve">588.</note> <note position="left" xlink:label="note-0228-07" xlink:href="note-0228-07a" xml:space="preserve"><emph style="sc">TAB. XX</emph>. <lb/>fig. 29.</note> </div> <p> <s xml:id="echoid-s6362" xml:space="preserve">Idcirco AB x BN<emph style="super">q</emph> - AB x BG<emph style="super">q</emph> = BC x BP<emph style="super">q</emph> - BC x B<emph style="super">Eq</emph>; </s> <s xml:id="echoid-s6363" xml:space="preserve">unde <lb/>deducimus AB x BN<emph style="super">q</emph> + BC x BE<emph style="super">q</emph> = AB x BG<emph style="super">q</emph> + BC x BP<emph style="super">q</emph>. </s> <s xml:id="echoid-s6364" xml:space="preserve">Quod <lb/>demonſtrandum erat.</s> <s xml:id="echoid-s6365" xml:space="preserve"/> </p> <pb file="0229" n="248"/> <pb file="0229a" n="249"/> <figure> <image file="0229a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0229a-01"/> </figure> <pb file="0230" n="250"/> <pb o="161" file="0231" n="251" rhead="MATHEMATICA. LIB. I. CAP XXIV."/> </div> <div xml:id="echoid-div907" type="section" level="1" n="233"> <head xml:id="echoid-head326" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head327" style="it" xml:space="preserve">Illuſtratio circa mutuam corporum elaſticorum <lb/>actionem.</head> <p> <s xml:id="echoid-s6366" xml:space="preserve">Licet circa ſummæ virium æqualitatem ante & </s> <s xml:id="echoid-s6367" xml:space="preserve">poſt ictum dubium ſapereſſe <lb/> <anchor type="note" xlink:label="note-0231-01a" xlink:href="note-0231-01"/> nullum poſſit, cum hæc ex ipſa perſecta claſticitate ſequatur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6368" xml:space="preserve">etiam, <anchor type="note" xlink:label="note-0231-02a" xlink:href="note-0231-02"/> utin præcedenti ſcholio fecimus, ex regulis computationis deducatur, obſcurum <lb/>quid nihilominus in hiſce dari non diffiteor; </s> <s xml:id="echoid-s6369" xml:space="preserve">cum ex demonſtratis non pa-<lb/>teat, quomodo elaſterium, quod dum ſe inter corpora expandit, & </s> <s xml:id="echoid-s6370" xml:space="preserve">ad partes <lb/>oppoſitas vires, quæ ſuntinverſè ut maſſæ, communicat <anchor type="note" xlink:href="" symbol="*"/>, poſſit ſæpe unico <anchor type="note" xlink:label="note-0231-03a" xlink:href="note-0231-03"/> corpori integram non modo, qua ſe expandit, imprimere vim; </s> <s xml:id="echoid-s6371" xml:space="preserve">ſed præter-<lb/>ea quantum ex vi aliûs corporis tollit. </s> <s xml:id="echoid-s6372" xml:space="preserve">Si Ex. </s> <s xml:id="echoid-s6373" xml:space="preserve">C. </s> <s xml:id="echoid-s6374" xml:space="preserve">corpus A duobus gradi-<lb/> <anchor type="note" xlink:label="note-0231-04a" xlink:href="note-0231-04"/> bus velocitatis, id eſt, cum quatuor grad. </s> <s xml:id="echoid-s6375" xml:space="preserve">vis <anchor type="note" xlink:href="" symbol="*"/>, incurrat in corpus B æquale quieſcens, poſt ictum, ſepoſita elaſticitate, ambo unico gradu velocitatis gau-<lb/> <anchor type="note" xlink:label="note-0231-05a" xlink:href="note-0231-05"/> dent <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s6376" xml:space="preserve">ſingula unicum gradum vis habent <anchor type="note" xlink:href="" symbol="*"/>, id eſt, amborum vis valet duo, <anchor type="note" xlink:label="note-0231-06a" xlink:href="note-0231-06"/> & </s> <s xml:id="echoid-s6377" xml:space="preserve">duobus reliquis gradibus vis partes fuere compreſſæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6378" xml:space="preserve">id eſt, ſi corpora <anchor type="note" xlink:label="note-0231-07a" xlink:href="note-0231-07"/> ſint elaſtica, hac ipſa vielaſterium fuit flexum, & </s> <s xml:id="echoid-s6379" xml:space="preserve">eadem vi ſeſe expandit <anchor type="note" xlink:href="" symbol="*"/>:</s> <s xml:id="echoid-s6380" xml:space="preserve"> <anchor type="note" xlink:label="note-0231-08a" xlink:href="note-0231-08"/> Poſt ictum verò corpus B duos habet gradus velocitatis <anchor type="note" xlink:href="" symbol="*"/>, id eſt vim qua- <anchor type="note" xlink:label="note-0231-09a" xlink:href="note-0231-09"/> tuor <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6381" xml:space="preserve">quieſcit A; </s> <s xml:id="echoid-s6382" xml:space="preserve">Elaſterium ergo ipſi B tres gradus vis communicavit, <anchor type="note" xlink:label="note-0231-10a" xlink:href="note-0231-10"/> & </s> <s xml:id="echoid-s6383" xml:space="preserve">gradum unum ex A ſuſtulit; </s> <s xml:id="echoid-s6384" xml:space="preserve">quamvis duobus tantum gradibus vis fuerit <lb/>flexum; </s> <s xml:id="echoid-s6385" xml:space="preserve">& </s> <s xml:id="echoid-s6386" xml:space="preserve">licet propter corpora æqualia, æquales impreſſiones ab utraque <lb/>parte exeruerit.</s> <s xml:id="echoid-s6387" xml:space="preserve"/> </p> <div xml:id="echoid-div907" type="float" level="2" n="1"> <note position="right" xlink:label="note-0231-01" xlink:href="note-0231-01a" xml:space="preserve">589.</note> <note symbol="*" position="right" xlink:label="note-0231-02" xlink:href="note-0231-02a" xml:space="preserve">557.</note> <note symbol="*" position="right" xlink:label="note-0231-03" xlink:href="note-0231-03a" xml:space="preserve">561.</note> <note symbol="*" position="right" xlink:label="note-0231-04" xlink:href="note-0231-04a" xml:space="preserve">470.</note> <note symbol="*" position="right" xlink:label="note-0231-05" xlink:href="note-0231-05a" xml:space="preserve">519.</note> <note symbol="*" position="right" xlink:label="note-0231-06" xlink:href="note-0231-06a" xml:space="preserve">470.</note> <note symbol="*" position="right" xlink:label="note-0231-07" xlink:href="note-0231-07a" xml:space="preserve">488.</note> <note symbol="*" position="right" xlink:label="note-0231-08" xlink:href="note-0231-08a" xml:space="preserve">557.</note> <note symbol="*" position="right" xlink:label="note-0231-09" xlink:href="note-0231-09a" xml:space="preserve">576.</note> <note symbol="*" position="right" xlink:label="note-0231-10" xlink:href="note-0231-10a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s6388" xml:space="preserve">Ut hæc tollatur difficultas, inter vim abſolutam & </s> <s xml:id="echoid-s6389" xml:space="preserve">relativam diſtinguen-<lb/> <anchor type="note" xlink:label="note-0231-11a" xlink:href="note-0231-11"/> dum. </s> <s xml:id="echoid-s6390" xml:space="preserve">Elaſterium inter corpora poſitum vires ipſis communicat, quæ ſuut inverſè <lb/>ut maſſæ, ſi inter corpora quieſcat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6391" xml:space="preserve">id eſt, ſi, translatis corporibus, eodem <anchor type="note" xlink:label="note-0231-12a" xlink:href="note-0231-12"/> motu cum hiſce feratur; </s> <s xml:id="echoid-s6392" xml:space="preserve">quales ideò motus corporibus communicantur in <lb/>nave quæ eadem velocitate cum corporibus fertur, & </s> <s xml:id="echoid-s6393" xml:space="preserve">in qua idcirco hæc cum e-<lb/>laſterio quieſcunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6394" xml:space="preserve">ſed propoſitio hæc ad motus abſolutos referrinon debet, quo- <anchor type="note" xlink:label="note-0231-13a" xlink:href="note-0231-13"/> rum unus acceleratur, alter retardatur, translato jam ipſo elaſterio ante hu-<lb/>jus actionem, ad caſum ita conſideratum demonſtratio propoſitionis appli-<lb/>cari nequit.</s> <s xml:id="echoid-s6395" xml:space="preserve"/> </p> <div xml:id="echoid-div908" type="float" level="2" n="2"> <note position="right" xlink:label="note-0231-11" xlink:href="note-0231-11a" xml:space="preserve">590.</note> <note symbol="*" position="right" xlink:label="note-0231-12" xlink:href="note-0231-12a" xml:space="preserve">561.</note> <note symbol="*" position="right" xlink:label="note-0231-13" xlink:href="note-0231-13a" xml:space="preserve">564.</note> </div> <p> <s xml:id="echoid-s6396" xml:space="preserve">Circa vires abſolutas notandum, has corpori ſæpe communicari, cauſâ mo-<lb/>venti quæ ipſa transfertur, in quo caſu non ſola cauſa movens in corpus agit, <lb/> <anchor type="note" xlink:label="note-0231-14a" xlink:href="note-0231-14"/> ſed & </s> <s xml:id="echoid-s6397" xml:space="preserve">in corpus datur actio illa quæ ipſam transfert canſam moventem, corporique <lb/>communicatur vis, quæ valet ſummam barum actionem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6398" xml:space="preserve">nam vis hæc eſt ef- <anchor type="note" xlink:label="note-0231-15a" xlink:href="note-0231-15"/> fectus ambarum actionum conjunctarum; </s> <s xml:id="echoid-s6399" xml:space="preserve">agitur enim de caſu in quo hæ a-<lb/>lium nullum effectum edunt. </s> <s xml:id="echoid-s6400" xml:space="preserve">Hæc jam alia occaſione notavimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6401" xml:space="preserve"/> </p> <div xml:id="echoid-div909" type="float" level="2" n="3"> <note position="right" xlink:label="note-0231-14" xlink:href="note-0231-14a" xml:space="preserve">591.</note> <note symbol="*" position="right" xlink:label="note-0231-15" xlink:href="note-0231-15a" xml:space="preserve">249.</note> </div> <note symbol="*" position="right" xml:space="preserve">446.</note> <p> <s xml:id="echoid-s6402" xml:space="preserve">Quando elaſterium obſtaculo inſiſtit quod ad partem oppoſitam non cedit, <lb/>totam vim qua fuit infiexum corpori quod ab obſtaculo repellit communicat, <lb/>ut hoc antea notavimus <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6403" xml:space="preserve">ſequitur ex demonſtrationen. </s> <s xml:id="echoid-s6404" xml:space="preserve">561. </s> <s xml:id="echoid-s6405" xml:space="preserve">& </s> <s xml:id="echoid-s6406" xml:space="preserve">confirmatur <anchor type="note" xlink:label="note-0231-17a" xlink:href="note-0231-17"/> experimentis memoratis <anchor type="note" xlink:href="" symbol="*"/> addita propoſitione n. </s> <s xml:id="echoid-s6407" xml:space="preserve">559; </s> <s xml:id="echoid-s6408" xml:space="preserve">quæ, poſitâ perfectâ ela- <anchor type="note" xlink:label="note-0231-18a" xlink:href="note-0231-18"/> ſticitate, in dubium a nemine vocatur, neque vocari poteſt.</s> <s xml:id="echoid-s6409" xml:space="preserve"/> </p> <div xml:id="echoid-div910" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0231-17" xlink:href="note-0231-17a" xml:space="preserve">441.</note> <note symbol="*" position="right" xlink:label="note-0231-18" xlink:href="note-0231-18a" xml:space="preserve">492.</note> </div> <p> <s xml:id="echoid-s6410" xml:space="preserve">Si autem elaſterium quod ab una parte inſiſtit obſtaculo quod non cedit <lb/>totam ſuam ad oppoſitam partem vim exerat, multo magis Elaſterium quod <lb/> <anchor type="note" xlink:label="note-0231-19a" xlink:href="note-0231-19"/> ad illam transſertur partem ad quam agit, integram vim, quarelaxatur, corpori com-<lb/>municabit, cui etiam imprimet vim quæ valet actionem, quæ ipſum transfert ela-<lb/>ſterium dum relaxatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6411" xml:space="preserve"/> </p> <div xml:id="echoid-div911" type="float" level="2" n="5"> <note position="right" xlink:label="note-0231-19" xlink:href="note-0231-19a" xml:space="preserve">592.</note> </div> <note symbol="*" position="right" xml:space="preserve">591.</note> <pb o="162" file="0232" n="252" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s6412" xml:space="preserve">Ex quibus quoque ſequitur, quando obſtaculo non omnino immobili inſi ſtit E-<lb/> <anchor type="note" xlink:label="note-0232-01a" xlink:href="note-0232-01"/> laſterium hoc ad partem oppoſitam exerere vim ſuam totam, demtâ illâ, quâ obſtacu-<lb/>lum poteſt movere.</s> <s xml:id="echoid-s6413" xml:space="preserve"/> </p> <div xml:id="echoid-div912" type="float" level="2" n="6"> <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">593.</note> </div> <p> <s xml:id="echoid-s6414" xml:space="preserve">Si hæc applicemus ad caſum memoratum, facile videmus corpori B com-<lb/> <anchor type="note" xlink:label="note-0232-02a" xlink:href="note-0232-02"/> municari duos gradus vis, quibus partes elaſticæ fuere flexæ, & </s> <s xml:id="echoid-s6415" xml:space="preserve">prætereaim-<lb/>preſſionem qua elaſterium fuit translatum, durante expanſione <anchor type="note" xlink:href="" symbol="*"/>, quæ impreſ- <anchor type="note" xlink:label="note-0232-03a" xlink:href="note-0232-03"/> ſio eſt actio corporis A in Elaſterium, & </s> <s xml:id="echoid-s6416" xml:space="preserve">valet vim a corpore A in hac a-<lb/>ctione amiſſam <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6417" xml:space="preserve">Amiſit autem A unum gradum vis, qui ergo ipſi B, præ- <anchor type="note" xlink:label="note-0232-04a" xlink:href="note-0232-04"/> ter duos memoratos, fuit communicatus; </s> <s xml:id="echoid-s6418" xml:space="preserve">accepit ergo B tres gradus vis, qui <lb/>additi uni gradui, quem ante elaſterii actionem habebat, dant quatuor gra-<lb/>dus vis. </s> <s xml:id="echoid-s6419" xml:space="preserve">Quod explicandum erat.</s> <s xml:id="echoid-s6420" xml:space="preserve"/> </p> <div xml:id="echoid-div913" type="float" level="2" n="7"> <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">594.</note> <note symbol="*" position="left" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">591.</note> <note symbol="*" position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">478.</note> </div> <p> <s xml:id="echoid-s6421" xml:space="preserve">Ratiocinium omnino ſimile eſt in aliis caſibus, in quibus poſt ſeparatio-<lb/> <anchor type="note" xlink:label="note-0232-05a" xlink:href="note-0232-05"/> nem ad eandem partem corpora tendunt, aut unum quieſcit; </s> <s xml:id="echoid-s6422" xml:space="preserve">ſi autem ad <lb/>partes propoſitas poſt ictum moveantur ex iiſdem principiis difficultas tolli-<lb/>tur, uthoc patebit exemplo.</s> <s xml:id="echoid-s6423" xml:space="preserve"/> </p> <div xml:id="echoid-div914" type="float" level="2" n="8"> <note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">595.</note> </div> <p> <s xml:id="echoid-s6424" xml:space="preserve">Sit corpus A cujus maſſa eſt I. </s> <s xml:id="echoid-s6425" xml:space="preserve">quod velocitate 6.</s> <s xml:id="echoid-s6426" xml:space="preserve">, id eſt, cum vi 36. </s> <s xml:id="echoid-s6427" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, in- <anchor type="note" xlink:label="note-0232-06a" xlink:href="note-0232-06"/> currit in corpus duplum quieſcens B; </s> <s xml:id="echoid-s6428" xml:space="preserve">ponimus corpora perfecte elaſtica. <lb/></s> <s xml:id="echoid-s6429" xml:space="preserve"> <anchor type="note" xlink:label="note-0232-07a" xlink:href="note-0232-07"/> Poſt ictum B habebit velocitatem 4, id eſt, vim 32. </s> <s xml:id="echoid-s6430" xml:space="preserve">& </s> <s xml:id="echoid-s6431" xml:space="preserve">A redibit velocitate 2, <lb/> <anchor type="note" xlink:label="note-0232-08a" xlink:href="note-0232-08"/> habebitque vim. </s> <s xml:id="echoid-s6432" xml:space="preserve">4 <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6433" xml:space="preserve">Hoc, jam ante demonſtratum, nunc eſt illuſtrandum.</s> <s xml:id="echoid-s6434" xml:space="preserve"/> </p> <div xml:id="echoid-div915" type="float" level="2" n="9"> <note position="left" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">596.</note> <note symbol="*" position="left" xlink:label="note-0232-07" xlink:href="note-0232-07a" xml:space="preserve">470.</note> <note symbol="*" position="left" xlink:label="note-0232-08" xlink:href="note-0232-08a" xml:space="preserve">519. 567. <lb/>568.</note> </div> <p> <s xml:id="echoid-s6435" xml:space="preserve">Ante inſtauratam figuram, corpora ambo cum duobus gradibus velocita-<lb/>tis moventur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6436" xml:space="preserve">Elaſtrum fuit flexum vi 24. </s> <s xml:id="echoid-s6437" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6438" xml:space="preserve">Si navem concipiamus in <anchor type="note" xlink:label="note-0232-09a" xlink:href="note-0232-09"/> qua corpora poſt ictum, ante ſeparationem quieſcunt, id eſt cujus velocitas <lb/> <anchor type="note" xlink:label="note-0232-10a" xlink:href="note-0232-10"/> etiam eſt duo; </s> <s xml:id="echoid-s6439" xml:space="preserve">corpora in hac ſeparantur viribus & </s> <s xml:id="echoid-s6440" xml:space="preserve">velocitatibus, quæ ſunt in-<lb/>verſe ut maſſæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6441" xml:space="preserve">B velocitate 2.</s> <s xml:id="echoid-s6442" xml:space="preserve">, & </s> <s xml:id="echoid-s6443" xml:space="preserve">A celeritate 4.</s> <s xml:id="echoid-s6444" xml:space="preserve">, ſi Elaſtrum minus fuiſ- <anchor type="note" xlink:label="note-0232-11a" xlink:href="note-0232-11"/> ſet flexum, etiam vires fuiſſent inverſè ut maſſæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6445" xml:space="preserve">ergo, pro parte relaxato <anchor type="note" xlink:label="note-0232-12a" xlink:href="note-0232-12"/> Elaſterio, in hac ratione ſunt vires, ideoque velocitates <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6446" xml:space="preserve">idcirco ubi B ha- <anchor type="note" xlink:label="note-0232-13a" xlink:href="note-0232-13"/> bet unum gradum velocitatis in nave, A duos habet, & </s> <s xml:id="echoid-s6447" xml:space="preserve">actio elaſtri valet 6. <lb/></s> <s xml:id="echoid-s6448" xml:space="preserve">gradus vis.</s> <s xml:id="echoid-s6449" xml:space="preserve"/> </p> <div xml:id="echoid-div916" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0232-09" xlink:href="note-0232-09a" xml:space="preserve">519.</note> <note symbol="*" position="left" xlink:label="note-0232-10" xlink:href="note-0232-10a" xml:space="preserve">510.</note> <note symbol="*" position="left" xlink:label="note-0232-11" xlink:href="note-0232-11a" xml:space="preserve">472 561.</note> <note symbol="*" position="left" xlink:label="note-0232-12" xlink:href="note-0232-12a" xml:space="preserve">564.</note> <note symbol="*" position="left" xlink:label="note-0232-13" xlink:href="note-0232-13a" xml:space="preserve">472.</note> </div> <p> <s xml:id="echoid-s6450" xml:space="preserve">Tum, motus abſolutos conſiderando, B habet velocitatem 3, & </s> <s xml:id="echoid-s6451" xml:space="preserve">A quieſcit; <lb/></s> <s xml:id="echoid-s6452" xml:space="preserve">Elaſtrum verò vim 18. </s> <s xml:id="echoid-s6453" xml:space="preserve">ſuperſtitem exerit, dum corpori B ſecundum gradum <lb/>velocitatis in nave & </s> <s xml:id="echoid-s6454" xml:space="preserve">corpori A tertium & </s> <s xml:id="echoid-s6455" xml:space="preserve">quartum in ipſa communicat. </s> <s xml:id="echoid-s6456" xml:space="preserve">Ha-<lb/>bet nunc B, ſepoſita nave, velocitatem 4. </s> <s xml:id="echoid-s6457" xml:space="preserve">& </s> <s xml:id="echoid-s6458" xml:space="preserve">redit A velocìtate 2.</s> <s xml:id="echoid-s6459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6460" xml:space="preserve">Corpus B ante elaſtrum relaxatum vim habet 8 <anchor type="note" xlink:href="" symbol="*"/>, dum Elaſtrum primos <anchor type="note" xlink:label="note-0232-14a" xlink:href="note-0232-14"/> 6. </s> <s xml:id="echoid-s6461" xml:space="preserve">gradus vis exerit nondum redit A, verſamurque in caſu n. </s> <s xml:id="echoid-s6462" xml:space="preserve">595. </s> <s xml:id="echoid-s6463" xml:space="preserve">ideo ſex <lb/>hi gradus corpori B communicantur, & </s> <s xml:id="echoid-s6464" xml:space="preserve">præterea quantum amittit A ut hoc <lb/>in n. </s> <s xml:id="echoid-s6465" xml:space="preserve">594. </s> <s xml:id="echoid-s6466" xml:space="preserve">explicavimus, id eſt 4; </s> <s xml:id="echoid-s6467" xml:space="preserve">habetque B vim 18. </s> <s xml:id="echoid-s6468" xml:space="preserve">quæ reſpondet velo-<lb/>citati 3 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6469" xml:space="preserve">maſſa enim eſt duo.</s> <s xml:id="echoid-s6470" xml:space="preserve"/> </p> <div xml:id="echoid-div917" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0232-14" xlink:href="note-0232-14a" xml:space="preserve">470.</note> </div> <note symbol="*" position="left" xml:space="preserve">470.</note> <p> <s xml:id="echoid-s6471" xml:space="preserve">Elaſtrum nunc ab una parte inſiſtit corpori quieſcenti, ad alteram corpo-<lb/>ri agitato, ipſumque huc uſque totum fuit translatum, nunc autem pro par-<lb/>te tantum transfertur & </s> <s xml:id="echoid-s6472" xml:space="preserve">poteſt repellere corpus A vi 4, ideoque reliquam tan-<lb/>tum vim 14 poterit ipſi B imprimere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6473" xml:space="preserve">hi additi ad 18, dant gradus 32. </s> <s xml:id="echoid-s6474" xml:space="preserve">quos <anchor type="note" xlink:label="note-0232-16a" xlink:href="note-0232-16"/> ut ex aute demonſtratis liquet revera habet.</s> <s xml:id="echoid-s6475" xml:space="preserve"/> </p> <div xml:id="echoid-div918" type="float" level="2" n="12"> <note symbol="*" position="left" xlink:label="note-0232-16" xlink:href="note-0232-16a" xml:space="preserve">593.</note> </div> <pb file="0233" n="253"/> <pb file="0233a" n="254"/> <figure> <image file="0233a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0233a-01"/> </figure> <pb file="0234" n="255"/> <pb o="163" file="0235" n="256" rhead="MATHEMATICA. LIB. I. CAP. XXIV."/> </div> <div xml:id="echoid-div920" type="section" level="1" n="234"> <head xml:id="echoid-head328" xml:space="preserve">SCHOLIUM 3.</head> <head xml:id="echoid-head329" style="it" xml:space="preserve">Paradoxi explicatio.</head> <p> <s xml:id="echoid-s6476" xml:space="preserve">Ex corporum elafticorum proprietate in n. </s> <s xml:id="echoid-s6477" xml:space="preserve">584. </s> <s xml:id="echoid-s6478" xml:space="preserve">memorata deducitur para-<lb/> <anchor type="note" xlink:label="note-0235-01a" xlink:href="note-0235-01"/> doxi, quod non minus notabile eſt quàm vulgare, explicatio.</s> <s xml:id="echoid-s6479" xml:space="preserve"/> </p> <div xml:id="echoid-div920" type="float" level="2" n="1"> <note position="right" xlink:label="note-0235-01" xlink:href="note-0235-01a" xml:space="preserve">597.</note> </div> <p> <s xml:id="echoid-s6480" xml:space="preserve">Fabri argentarii, qui domus cujuſcunque partem ſuperiorem occupant, <lb/>incudem pulvino ſuperimponunt, quo magis ictibus mallei incus reſiſtit, & </s> <s xml:id="echoid-s6481" xml:space="preserve"><lb/>minus tremit domus.</s> <s xml:id="echoid-s6482" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6483" xml:space="preserve">Ponamus, ſublato pulvino, trabi incudem imponi, incus corpus eſt elaſti-<lb/>cum, & </s> <s xml:id="echoid-s6484" xml:space="preserve">trabs, quæ in extremitatibus fixa eſt, etiam corpus eſt elaſticum. <lb/></s> <s xml:id="echoid-s6485" xml:space="preserve">Ponamus malleo incudem percuti.</s> <s xml:id="echoid-s6486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6487" xml:space="preserve">Dicatur mallei maſſa M; </s> <s xml:id="echoid-s6488" xml:space="preserve">incudis maſſa I; </s> <s xml:id="echoid-s6489" xml:space="preserve">& </s> <s xml:id="echoid-s6490" xml:space="preserve">maſſa trabis cum corporibus <lb/>cohærentibus & </s> <s xml:id="echoid-s6491" xml:space="preserve">quæ cum ipſa agitantur T; </s> <s xml:id="echoid-s6492" xml:space="preserve">ſit etiam velocitas mallei v. <lb/></s> <s xml:id="echoid-s6493" xml:space="preserve">Multiplicando M per v, & </s> <s xml:id="echoid-s6494" xml:space="preserve">dividendo productum per ſummam Maſſarum <lb/>mallei & </s> <s xml:id="echoid-s6495" xml:space="preserve">incudis & </s> <s xml:id="echoid-s6496" xml:space="preserve">habemus dimidium velocitatis incudi communicatæ <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0235-02a" xlink:href="note-0235-02"/> nam licet trabi impoſita ſit incus agitatur quaſi ſola eſſet <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6497" xml:space="preserve">ipſius velocitas <anchor type="note" xlink:label="note-0235-03a" xlink:href="note-0235-03"/> eſt {2Mxv/M + I}, qua velocitate incus percutit trabem & </s> <s xml:id="echoid-s6498" xml:space="preserve">corpora cum hac conjun-<lb/>cta; </s> <s xml:id="echoid-s6499" xml:space="preserve">multiplicando velocitatem incudis per maſſam habemus {2MxIxv/M + I} divi-<lb/>dendo duplum hujus producti per ſummam maſſarum habemus {4MxIxv/M + Ix1 + T} <lb/>trabis velocitatem <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6500" xml:space="preserve">Denominator hujus fractionis MxI + IxI + TxM <anchor type="note" xlink:label="note-0235-04a" xlink:href="note-0235-04"/> + TxI, propter M exiguum reſpectu 1 & </s> <s xml:id="echoid-s6501" xml:space="preserve">T, vix ab hoc alio differt M x I <lb/>+ IxI + TxI, quo poſito, velocitas detecta mutatur in hanc {4Mxv/M + I + T}.</s> <s xml:id="echoid-s6502" xml:space="preserve"/> </p> <div xml:id="echoid-div921" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0235-02" xlink:href="note-0235-02a" xml:space="preserve">519 567.</note> <note symbol="*" position="right" xlink:label="note-0235-03" xlink:href="note-0235-03a" xml:space="preserve">585.</note> <note symbol="*" position="right" xlink:label="note-0235-04" xlink:href="note-0235-04a" xml:space="preserve">519. 585.</note> </div> <p> <s xml:id="echoid-s6503" xml:space="preserve">Interpoſito corpore molli, pulvino nempe, inter trabem & </s> <s xml:id="echoid-s6504" xml:space="preserve">incudem, cor-<lb/>pora hæc unicam quaſi formant maſſam, ideoque cum nunc malleus majus <lb/>percutiat corpus majorem patitur refiſtentiam, & </s> <s xml:id="echoid-s6505" xml:space="preserve">velocitas trabi communicata <lb/>habetur dividendo 2 Mxv per ſummam maſſarum M + I + T <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6506" xml:space="preserve">velocitas eſt <anchor type="note" xlink:label="note-0235-05a" xlink:href="note-0235-05"/> {2Mxv/M + I + T} dimidium velocitatis ſublato pulvino; </s> <s xml:id="echoid-s6507" xml:space="preserve">& </s> <s xml:id="echoid-s6508" xml:space="preserve">agitatio, ſublato hoc i-<lb/>pſo, quadruplum poteſt edere effectum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6509" xml:space="preserve"/> </p> <div xml:id="echoid-div922" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0235-05" xlink:href="note-0235-05a" xml:space="preserve">519. 567.</note> </div> <note symbol="*" position="right" xml:space="preserve">447. 459.</note> <pb o="164" file="0236" n="257" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div924" type="section" level="1" n="235"> <head xml:id="echoid-head330" xml:space="preserve">CAPUT XXV.</head> <head xml:id="echoid-head331" style="it" xml:space="preserve">De motu compoſito.</head> <p style="it"> <s xml:id="echoid-s6510" xml:space="preserve">SI corpus moveatur, & </s> <s xml:id="echoid-s6511" xml:space="preserve">hujus celeritas augenda aut minu-<lb/> <anchor type="note" xlink:label="note-0236-01a" xlink:href="note-0236-01"/> enda ſit, manente directione, evidens eſt, impre ſſionem <lb/>requiri, quæ proportionalis ſit differentiæ quadratorum ve-<lb/>locitatis quam corpus ante actionem habuit, & </s> <s xml:id="echoid-s6512" xml:space="preserve">illius quam <lb/>poſt actionem habet, huic enim differentiæ vis communicata <lb/>aut ſublata proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6513" xml:space="preserve"> <anchor type="note" xlink:label="note-0236-02a" xlink:href="note-0236-02"/> </s> </p> <div xml:id="echoid-div924" type="float" level="2" n="1"> <note position="left" xlink:label="note-0236-01" xlink:href="note-0236-01a" xml:space="preserve">598.</note> <note position="right" xlink:label="note-0236-02" xlink:href="note-0236-02a" xml:space="preserve">447.</note> </div> <p> <s xml:id="echoid-s6514" xml:space="preserve">Ponamus duas actiones eodem tempore in corpus juxta e an-<lb/> <anchor type="note" xlink:label="note-0236-03a" xlink:href="note-0236-03"/> dem directionem agere. </s> <s xml:id="echoid-s6515" xml:space="preserve">Dum augetur velocitas; </s> <s xml:id="echoid-s6516" xml:space="preserve">creſcit in <lb/>ratione duplicata vis corpori inſita <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6517" xml:space="preserve">id eſt hujus augmen- <anchor type="note" xlink:label="note-0236-04a" xlink:href="note-0236-04"/> tum ſequitur proportionem augmenti trianguli quod dum <lb/>augetur eidem ſimile manet, & </s> <s xml:id="echoid-s6518" xml:space="preserve">cujus latus unum velocitatem <lb/> <anchor type="note" xlink:label="note-0236-05a" xlink:href="note-0236-05"/> repræſentat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6519" xml:space="preserve">vis dum velocitas eſt A g, eſt ad vim ubi <anchor type="note" xlink:label="note-0236-06a" xlink:href="note-0236-06"/> velocitas eſt A l, ut area A g r ad A l s.</s> <s xml:id="echoid-s6520" xml:space="preserve"/> </p> <div xml:id="echoid-div925" type="float" level="2" n="2"> <note position="left" xlink:label="note-0236-03" xlink:href="note-0236-03a" xml:space="preserve">599.</note> <note position="left" xlink:label="note-0236-04" xlink:href="note-0236-04a" xml:space="preserve">447.</note> <note position="left" xlink:label="note-0236-05" xlink:href="note-0236-05a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0236-06" xlink:href="note-0236-06a" xml:space="preserve">19. El. vi.</note> </div> <p> <s xml:id="echoid-s6521" xml:space="preserve">Concipiamus, actiones alternatim in corpus agere per in-<lb/>tervalla temporis æqualia; </s> <s xml:id="echoid-s6522" xml:space="preserve">actione primâ communicari vim <lb/>A d o, ſecundâ vim d o p e; </s> <s xml:id="echoid-s6523" xml:space="preserve">iterum actione prima commu-<lb/>nicari vim p e f q, & </s> <s xml:id="echoid-s6524" xml:space="preserve">ſecundâ f q r g & </s> <s xml:id="echoid-s6525" xml:space="preserve">ſic ulterius; </s> <s xml:id="echoid-s6526" xml:space="preserve">ſumma <lb/>arearum albarum repræſentat vim integram prima actione <lb/>communicatam, & </s> <s xml:id="echoid-s6527" xml:space="preserve">ſumma nigrarum deſignat vim integram <lb/>ſecundâ actione corpori impreſſam. </s> <s xml:id="echoid-s6528" xml:space="preserve">Cum per tempora æ-<lb/>qualia actiones egerint, vires hæ, id eſt, ſummæ arearum, <lb/>ſunt ut ipſæ actiones, in qua etiam ratione eſt area. </s> <s xml:id="echoid-s6529" xml:space="preserve">quæcun-<lb/>que alba ad ſuam vicinam nigram: </s> <s xml:id="echoid-s6530" xml:space="preserve">ſi momenta temporum <lb/>fuerint inſinitè exigua, ut ſunt quando actiones ſimul agunt, <lb/>areæ hæ pro parallelogrammis haberi poſſunt, & </s> <s xml:id="echoid-s6531" xml:space="preserve">parallelogram-<lb/>ma vicina eandem habebunt altitudinem; </s> <s xml:id="echoid-s6532" xml:space="preserve">ideoque erunt in-<lb/>ter ſe ut baſes <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6533" xml:space="preserve">ergo baſis albi ad baſim vicini nigri, ut <anchor type="note" xlink:label="note-0236-07a" xlink:href="note-0236-07"/> actio prima ad ſecundam, & </s> <s xml:id="echoid-s6534" xml:space="preserve">in eadem ratione ſumma ba-<lb/>ſium parallelogrammorum alborum ad ſummam baſium ni-<lb/>grorum; </s> <s xml:id="echoid-s6535" xml:space="preserve">id eſt, ita ſe habet velocit as quam communicavit <lb/>actio prima ad velocitatem ex ſecundâ oriundam. </s> <s xml:id="echoid-s6536" xml:space="preserve">Quæ ea- <pb o="165" file="0237" n="258" rhead="MATHEMATICA. LIB. I. CAP XXV."/> dem demonſtratio in acceleratione quacunque corporis ex <lb/>duabus actionibus locum habet.</s> <s xml:id="echoid-s6537" xml:space="preserve"/> </p> <div xml:id="echoid-div926" type="float" level="2" n="3"> <note position="left" xlink:label="note-0236-07" xlink:href="note-0236-07a" xml:space="preserve">I. El. VI.</note> </div> <p> <s xml:id="echoid-s6538" xml:space="preserve">Si in corpus motum, actio detur juxta directionem di-<lb/>verſam a directione motus primi, mutationem in directione <lb/>dari ſuperius vidimus <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6539" xml:space="preserve">quæ velocitates in hiſce caſibus <anchor type="note" xlink:label="note-0237-01a" xlink:href="note-0237-01"/> fpectant examinavimus <anchor type="note" xlink:href="" symbol="*"/>, de viribus nunc agendum. </s> <s xml:id="echoid-s6540" xml:space="preserve">Movea- <anchor type="note" xlink:label="note-0237-02a" xlink:href="note-0237-02"/> tur corpus per AD, celeritate, quam hac lineâ deſigna-<lb/>mus, & </s> <s xml:id="echoid-s6541" xml:space="preserve">vis nova hoc pellat per AE, celeritate, quam hac <lb/> <anchor type="note" xlink:label="note-0237-03a" xlink:href="note-0237-03"/> linea deſignamus; </s> <s xml:id="echoid-s6542" xml:space="preserve">corpus duabus celeritatibus latum, mo-<lb/>vetur per AB <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6543" xml:space="preserve">Non tamen in ſingulis hiſce caſibus im- <anchor type="note" xlink:label="note-0237-04a" xlink:href="note-0237-04"/> preſſione æ quali æ qualis communicatur velocitas lateralis; <lb/></s> <s xml:id="echoid-s6544" xml:space="preserve"> <anchor type="note" xlink:label="note-0237-05a" xlink:href="note-0237-05"/> ponimus AB & </s> <s xml:id="echoid-s6545" xml:space="preserve">AE in tribus figuris reſpectivè æquales. <lb/></s> <s xml:id="echoid-s6546" xml:space="preserve">In fig. </s> <s xml:id="echoid-s6547" xml:space="preserve">4. </s> <s xml:id="echoid-s6548" xml:space="preserve">motus ſecundus, pro parte cum motu primo con-<lb/>ſpirat, ita ut in hoc motu contineatur acceleratio motus <lb/>per AD. </s> <s xml:id="echoid-s6549" xml:space="preserve">Eodem modo retardatio velocitatis per AD con-<lb/>tinetur in motu per AE in fig. </s> <s xml:id="echoid-s6550" xml:space="preserve">5. </s> <s xml:id="echoid-s6551" xml:space="preserve">Idcirco impreſſiones, qui-<lb/>bus corpora per AE pelluntur, ut velocitatem hac lineâ <lb/>deſignatam corporibus ſingulis communicent, non ſunt æ-<lb/>quales inter ſe <anchor type="note" xlink:href="" symbol="*"/>, neque impreſſioni, qua corpori quieſcenti <anchor type="note" xlink:label="note-0237-06a" xlink:href="note-0237-06"/> hæc poſſet communicari velocitas <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6552" xml:space="preserve"/> </p> <div xml:id="echoid-div927" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">245.</note> <note position="right" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">246.</note> <note position="right" xlink:label="note-0237-03" xlink:href="note-0237-03a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 314. 5.</note> <note position="right" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">600.</note> <note position="right" xlink:label="note-0237-05" xlink:href="note-0237-05a" xml:space="preserve">246.</note> <note symbol="*" position="right" xlink:label="note-0237-06" xlink:href="note-0237-06a" xml:space="preserve">443.</note> </div> <note position="right" xml:space="preserve">440.</note> <p> <s xml:id="echoid-s6553" xml:space="preserve">In ſolo caſu fig. </s> <s xml:id="echoid-s6554" xml:space="preserve">3, in quo angulus EAD eſt rectus, motus <lb/> <anchor type="note" xlink:label="note-0237-08a" xlink:href="note-0237-08"/> lateralis neque conſpirat neque contrarie agit cum motu per <lb/>AD, & </s> <s xml:id="echoid-s6555" xml:space="preserve">impreſſio, qua corpus movetur, in corpus agit quaſi <lb/>quieſceret; </s> <s xml:id="echoid-s6556" xml:space="preserve">idcirco in hoc caſu vis corpori communicata pro-<lb/>portionalis eſt quadrato ſuæ velocitatis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6557" xml:space="preserve">cùm impreſſio non poſſit vim per AE minuere, corporis vis integra pro-<lb/> <anchor type="note" xlink:label="note-0237-09a" xlink:href="note-0237-09"/> portionalis eſt ambobus quadratis linearum AD & </s> <s xml:id="echoid-s6558" xml:space="preserve">AE, quod <lb/>congruit cum demonſtratis: </s> <s xml:id="echoid-s6559" xml:space="preserve">nam fertur corpus celeritate AB,<anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0237-10a" xlink:href="note-0237-10"/> cujus quadratum valet memorata duo quadrata <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6560" xml:space="preserve"/> </p> <div xml:id="echoid-div928" type="float" level="2" n="5"> <note position="right" xlink:label="note-0237-08" xlink:href="note-0237-08a" xml:space="preserve">601.</note> <note symbol="*" position="right" xlink:label="note-0237-09" xlink:href="note-0237-09a" xml:space="preserve">447.</note> <note symbol="*" position="right" xlink:label="note-0237-10" xlink:href="note-0237-10a" xml:space="preserve">246.</note> </div> <note position="right" xml:space="preserve">[47. El I.</note> <p> <s xml:id="echoid-s6561" xml:space="preserve">Ex his virium menſura ſi hæc ignota eſſet, detegi poſſet. </s> <s xml:id="echoid-s6562" xml:space="preserve">Cor-<lb/> <anchor type="note" xlink:label="note-0237-12a" xlink:href="note-0237-12"/> pori, quod habet vim quæ reſpondet celeritati AD, communi-<lb/>catur vis quæ velocitati AE reſpondet, quæ cum corpori com-<lb/>municetur quaſi quieſceret, vim primam mutare non poteſt; </s> <s xml:id="echoid-s6563" xml:space="preserve">va-<lb/>let ideò corporis vis integra ſummam harum virium, dum <lb/>ipſius velocitas eſt AB; </s> <s xml:id="echoid-s6564" xml:space="preserve">ergo vis quæ huic reſpondet velocitati, <lb/>memoratæ ſummæ æqualis eſt. </s> <s xml:id="echoid-s6565" xml:space="preserve">Quod ſieri non poterit in omni <pb o="166" file="0238" n="259" rhead="PHYSICES ELEMENTA"/> caſu niſi quadratis velocitatis vires proportionales ſint <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6566" xml:space="preserve"/> </p> <div xml:id="echoid-div929" type="float" level="2" n="6"> <note position="right" xlink:label="note-0237-12" xlink:href="note-0237-12a" xml:space="preserve">601.</note> </div> <note symbol="*" position="left" xml:space="preserve">47. El. v.</note> <p> <s xml:id="echoid-s6567" xml:space="preserve">Deducimus ex his non intereſſe neque reſpectu impreſ-<lb/> <anchor type="note" xlink:label="note-0238-02a" xlink:href="note-0238-02"/> ſionum, quibus corpus agitatur, neque reſpectu virium, ne-<lb/>que velocitatum, utrum corpus per AB feratur celeritate <lb/>AB, an per AD & </s> <s xml:id="echoid-s6568" xml:space="preserve">AE celeritatibus hiſce lineis proportio-<lb/>nalibus, quæ inter ſe angulum rectum continent. </s> <s xml:id="echoid-s6569" xml:space="preserve">Quare <lb/>motus per AB, juxta directionem ut AD, nil continet præ-<lb/> <anchor type="note" xlink:label="note-0238-03a" xlink:href="note-0238-03"/> ter motum velocitate AD.</s> <s xml:id="echoid-s6570" xml:space="preserve"/> </p> <div xml:id="echoid-div930" type="float" level="2" n="7"> <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 3.</note> <note position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">603.</note> </div> <p style="it"> <s xml:id="echoid-s6571" xml:space="preserve">Deducimus etiam motum corporis reſolvi poſſe in duos <lb/> <anchor type="note" xlink:label="note-0238-04a" xlink:href="note-0238-04"/> alios innumeris modis, quod fiet, ſi linea, in directione motus da-<lb/>ti poſita, & </s> <s xml:id="echoid-s6572" xml:space="preserve">longitudine celeritatem deſignans, ſit hypotenu-<lb/>ſa trianguli rectanguli; </s> <s xml:id="echoid-s6573" xml:space="preserve">nam hujus reliqua duo latera ſitu <lb/>motuum quæ ſitorum directiones dabunt, & </s> <s xml:id="echoid-s6574" xml:space="preserve">longitudinibus ſuis <lb/>reſpective velocitates horum expriment: </s> <s xml:id="echoid-s6575" xml:space="preserve">eruntque vires juxta <lb/>has directiones quadratis velocitatum proportionales.</s> <s xml:id="echoid-s6576" xml:space="preserve"/> </p> <div xml:id="echoid-div931" type="float" level="2" n="8"> <note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">604.</note> </div> <p> <s xml:id="echoid-s6577" xml:space="preserve">Ut nunc determinemus, qua vi corpus per AE ſit agitandum, <lb/> <anchor type="note" xlink:label="note-0238-05a" xlink:href="note-0238-05"/> ut ei communicetur celeritas AE, in caſu in quo motus hic cum <lb/> <anchor type="note" xlink:label="note-0238-06a" xlink:href="note-0238-06"/> primo motu pro parte conſpirat; </s> <s xml:id="echoid-s6578" xml:space="preserve">motum per A Ein duos reſol-<lb/> <anchor type="note" xlink:label="note-0238-07a" xlink:href="note-0238-07"/> vo <anchor type="note" xlink:href="" symbol="*"/> per A f & </s> <s xml:id="echoid-s6579" xml:space="preserve">A g, ângulum rectum continentes, & </s> <s xml:id="echoid-s6580" xml:space="preserve">ducitur E g parallelâ A f. </s> <s xml:id="echoid-s6581" xml:space="preserve">Per A f tantum corpori vis communicanda eſt, <lb/>qua corpus ſi quieſceret hac celeritate poſſet ferri, & </s> <s xml:id="echoid-s6582" xml:space="preserve">quæ <lb/>proportionalis eſt quadrato A f <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6583" xml:space="preserve">per A g autem vis com- <anchor type="note" xlink:label="note-0238-08a" xlink:href="note-0238-08"/> municanda eſt, qua celeritas AD quantitate A g augeatur, <lb/>id eſt fiat A h, quæ vis proportionalis eſt differentiæ qua-<lb/> <anchor type="note" xlink:label="note-0238-09a" xlink:href="note-0238-09"/> dratorum A h, AD <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6584" xml:space="preserve">Hæ vires ſimul communicandæ e- runt juxta AE ut corpus hac celeritate poſſit ferri; </s> <s xml:id="echoid-s6585" xml:space="preserve">& </s> <s xml:id="echoid-s6586" xml:space="preserve">vis <lb/>integra corporis proportionalis eſt quadrato lineæ AD, dif-<lb/>ferentiæ quadratorum linearum A h & </s> <s xml:id="echoid-s6587" xml:space="preserve">AD, & </s> <s xml:id="echoid-s6588" xml:space="preserve">quadrato <lb/>A f; </s> <s xml:id="echoid-s6589" xml:space="preserve">primis duobus ex hiſce tribus quantitatibus in unam <lb/>ſummam collectis, habemus quadratum lineæ A h, cui ſi <lb/>addatur quadratum lineæ A f, aut h B, habemus quadra-<lb/>tum lineæ AB; </s> <s xml:id="echoid-s6590" xml:space="preserve">cui proportionalem eſſe vim corpori inſi-<lb/> <anchor type="note" xlink:label="note-0238-10a" xlink:href="note-0238-10"/> tam ex ante demonſtratis ſequitur <anchor type="note" xlink:href="" symbol="*"/>, cum conſtet corpus <anchor type="note" xlink:label="note-0238-11a" xlink:href="note-0238-11"/> celeritate AB ferri <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6591" xml:space="preserve"> <anchor type="note" xlink:label="note-0238-12a" xlink:href="note-0238-12"/> </s> </p> <div xml:id="echoid-div932" type="float" level="2" n="9"> <note position="left" xlink:label="note-0238-05" xlink:href="note-0238-05a" xml:space="preserve">605.</note> <note position="left" xlink:label="note-0238-06" xlink:href="note-0238-06a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0238-07" xlink:href="note-0238-07a" xml:space="preserve">246.</note> <note symbol="*" position="left" xlink:label="note-0238-08" xlink:href="note-0238-08a" xml:space="preserve">601. 447.</note> <note symbol="*" position="left" xlink:label="note-0238-09" xlink:href="note-0238-09a" xml:space="preserve">591.</note> <note symbol="*" position="left" xlink:label="note-0238-10" xlink:href="note-0238-10a" xml:space="preserve">447. <lb/>*246.</note> <note position="left" xlink:label="note-0238-11" xlink:href="note-0238-11a" xml:space="preserve">606.</note> <note position="left" xlink:label="note-0238-12" xlink:href="note-0238-12a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s6592" xml:space="preserve">Simotum per AE eodem modo in duos reſolvamus per A f & </s> <s xml:id="echoid-s6593" xml:space="preserve"><lb/>A g <anchor type="note" xlink:href="" symbol="*"/>, motu hoc ſecundo retardatur motus per AD; </s> <s xml:id="echoid-s6594" xml:space="preserve">unde ſequi- <anchor type="note" xlink:label="note-0238-13a" xlink:href="note-0238-13"/> tur, ut corpus per AE, celeritate hac lineâ deſignatâ feratur, illi <pb o="167" file="0239" n="260" rhead="MATHEMATICA. LIB. I. CAP. XXV."/> communicandam eſſe vim, quæ proportionalis ſit quadrato <lb/>A f, & </s> <s xml:id="echoid-s6595" xml:space="preserve">impreſſionem, qua agitatur, ulterius tantum valere <lb/>debere, ut quantitate A g poſſit minuere velocitatem AD, <lb/>in hoc caſu corpus juxta directionem AD tantum ſuperſti-<lb/>tem habebit vim proportionalem quadrato A b <anchor type="note" xlink:href="" symbol="*"/>, cui ſi ad- <anchor type="note" xlink:label="note-0239-01a" xlink:href="note-0239-01"/> datur vis proportionalis quadrato A f<anchor type="note" xlink:href="" symbol="*"/>, habemus vim propor- <anchor type="note" xlink:label="note-0239-02a" xlink:href="note-0239-02"/> tionalem quadrato AB; </s> <s xml:id="echoid-s6596" xml:space="preserve">quod iterum cum ante demonſtra-<lb/>tis congruit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6597" xml:space="preserve"/> </p> <div xml:id="echoid-div933" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0238-13" xlink:href="note-0238-13a" xml:space="preserve">604.</note> <note symbol="*" position="right" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">598.</note> <note symbol="*" position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">601.</note> </div> <note symbol="*" position="right" xml:space="preserve">246 447.</note> <p> <s xml:id="echoid-s6598" xml:space="preserve">Propoſitionem hanc, vim ſequi proportionem quadrati <lb/> <anchor type="note" xlink:label="note-0239-04a" xlink:href="note-0239-04"/> velocitatis, non poſſe referri ad illam cum qua alia in ea-<lb/>dem linea agit, facile ex ante demonſtratis ſequitur <anchor type="note" xlink:href="" symbol="*"/>, hac <anchor type="note" xlink:label="note-0239-05a" xlink:href="note-0239-05"/> de causâ ubi vim in duas reſolvimus, hæ quadratis veloci-<lb/>tatum proportionales non erunt, niſi ambarum directiones <lb/>angulum rectum contineant ne aliter pro parte conſpirent <lb/>aut contrarie agant <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6599" xml:space="preserve">Ex quibus deducimus vim reſolu- <anchor type="note" xlink:label="note-0239-06a" xlink:href="note-0239-06"/> tam non iterum poſſe reſolvi. </s> <s xml:id="echoid-s6600" xml:space="preserve">Motus per AB reſolvitur <lb/>in duos motus ejuſdem corporis per AD & </s> <s xml:id="echoid-s6601" xml:space="preserve">AE, & </s> <s xml:id="echoid-s6602" xml:space="preserve">vires <lb/> <anchor type="note" xlink:label="note-0239-07a" xlink:href="note-0239-07"/> quadratis velociratum ſunt proportionales; </s> <s xml:id="echoid-s6603" xml:space="preserve">ſed ſi motus per <lb/>AE iterum in duos per AF & </s> <s xml:id="echoid-s6604" xml:space="preserve">AG angulum rectum con-<lb/>tinentes ſeparetur, non erunt hæ ultimæ quadratis veloci-<lb/>tatum proportionales, & </s> <s xml:id="echoid-s6605" xml:space="preserve">non poterit hîc applicari n. </s> <s xml:id="echoid-s6606" xml:space="preserve">604, <lb/>in quo agitur de viribus, quæ non modo inter ſe non con-<lb/>fpirant, neque contrarie agunt, ſed quæ cum tertiâ nil <lb/>commune habent. </s> <s xml:id="echoid-s6607" xml:space="preserve">Hîc autem ipſe motus corporis per <lb/>AB in tres motus reſolvitur per AD, AF & </s> <s xml:id="echoid-s6608" xml:space="preserve">AG, in qui-<lb/>bus AF & </s> <s xml:id="echoid-s6609" xml:space="preserve">AD pro parte conſpirant, AD & </s> <s xml:id="echoid-s6610" xml:space="preserve">AG partim <lb/>contrariè agunt; </s> <s xml:id="echoid-s6611" xml:space="preserve">& </s> <s xml:id="echoid-s6612" xml:space="preserve">reſolutio quæ ad velocitates poteſtappli-<lb/>cari, cùm demonſtratio n. </s> <s xml:id="echoid-s6613" xml:space="preserve">246. </s> <s xml:id="echoid-s6614" xml:space="preserve">eadem ſit, ſive motus in re-<lb/>folutione conſpirent, ſive contrarie agunt, ad vires non poſſe <lb/>referri ex ante demonſtratis clarum eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6615" xml:space="preserve"> <anchor type="note" xlink:label="note-0239-08a" xlink:href="note-0239-08"/> </s> </p> <div xml:id="echoid-div934" type="float" level="2" n="11"> <note position="right" xlink:label="note-0239-04" xlink:href="note-0239-04a" xml:space="preserve">607.</note> <note symbol="*" position="right" xlink:label="note-0239-05" xlink:href="note-0239-05a" xml:space="preserve">598. 599</note> <note symbol="*" position="right" xlink:label="note-0239-06" xlink:href="note-0239-06a" xml:space="preserve">601.</note> <note position="right" xlink:label="note-0239-07" xlink:href="note-0239-07a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig 54.</note> <note position="right" xlink:label="note-0239-08" xlink:href="note-0239-08a" xml:space="preserve">440. 443.</note> </div> <p> <s xml:id="echoid-s6616" xml:space="preserve">In n. </s> <s xml:id="echoid-s6617" xml:space="preserve">605. </s> <s xml:id="echoid-s6618" xml:space="preserve">606. </s> <s xml:id="echoid-s6619" xml:space="preserve">motum per AB compoſitum habemus ex <lb/> <anchor type="note" xlink:label="note-0239-09a" xlink:href="note-0239-09"/> duobus, quorum unum in alios reſolvimus, ſed ita, ut poſt <lb/> <anchor type="note" xlink:label="note-0239-10a" xlink:href="note-0239-10"/> reſolutionem omnes motus darentur in duabus lineis, angu-<lb/>lum rectum continentibus: </s> <s xml:id="echoid-s6620" xml:space="preserve">quare motus in ſingulis lineis, <lb/>ſeparatim conſiderari potuere, quod nunquam fieri poteſt <lb/>ubi motus varii in pluribus quàm duabus lineis dantur, tunce- <pb o="168" file="0240" n="261" rhead="PHYSICES ELEMENTA"/> nim quidam neceſſario motuspro parte conſpirant, aut con-<lb/>trarie agunt; </s> <s xml:id="echoid-s6621" xml:space="preserve">de his nihil demonſtravimus, ex eadem tamen <lb/>theoria virium deduci poſſunt.</s> <s xml:id="echoid-s6622" xml:space="preserve"/> </p> <div xml:id="echoid-div935" type="float" level="2" n="12"> <note position="right" xlink:label="note-0239-09" xlink:href="note-0239-09a" xml:space="preserve">608.</note> <note position="right" xlink:label="note-0239-10" xlink:href="note-0239-10a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 4. 5.</note> </div> </div> <div xml:id="echoid-div937" type="section" level="1" n="236"> <head xml:id="echoid-head332" xml:space="preserve">CAPUT XXVI.</head> <head xml:id="echoid-head333" style="it" xml:space="preserve">De Percuſſione obliqua.</head> <head xml:id="echoid-head334" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s6623" xml:space="preserve">ANgulus incidentiæ vocatur angulus quem directio motus <lb/> <anchor type="note" xlink:label="note-0240-01a" xlink:href="note-0240-01"/> corporis, ad aliud accedentis, efficit cum perpendicula-<lb/>ri ad ſuperficiem hujus in puncto, in quo percutitur.</s> <s xml:id="echoid-s6624" xml:space="preserve"/> </p> <div xml:id="echoid-div937" type="float" level="2" n="1"> <note position="left" xlink:label="note-0240-01" xlink:href="note-0240-01a" xml:space="preserve">609.</note> </div> </div> <div xml:id="echoid-div939" type="section" level="1" n="237"> <head xml:id="echoid-head335" xml:space="preserve"><emph style="sc">Definitio</emph>. 2.</head> <p style="it"> <s xml:id="echoid-s6625" xml:space="preserve">Angulus reflexionis eſt angulus, quem cum eadem per-<lb/> <anchor type="note" xlink:label="note-0240-02a" xlink:href="note-0240-02"/> pendiculari efficit directio motus corporis poſt percuſſio-<lb/>nem.</s> <s xml:id="echoid-s6626" xml:space="preserve"/> </p> <div xml:id="echoid-div939" type="float" level="2" n="1"> <note position="left" xlink:label="note-0240-02" xlink:href="note-0240-02a" xml:space="preserve">610.</note> </div> <p> <s xml:id="echoid-s6627" xml:space="preserve">Si Corpus elaſticum P in obicem firmum elaſticum FG in-<lb/> <anchor type="note" xlink:label="note-0240-03a" xlink:href="note-0240-03"/> currat, obliquè juxta directionem P a, redibit per a p, i-<lb/> <anchor type="note" xlink:label="note-0240-04a" xlink:href="note-0240-04"/> ta, ut angulus incidentiæ P a B æqualis ſit angulo reflexio-<lb/>nis B a p. </s> <s xml:id="echoid-s6628" xml:space="preserve">Motus per P a, quam longitudine celeritatem <lb/>corporis deſignare ponimus, poteſt reſolvi in duos, quorum <lb/>unius directio parallela ſit lineæ B a, alterius huic perpen-<lb/>dicularis; </s> <s xml:id="echoid-s6629" xml:space="preserve">& </s> <s xml:id="echoid-s6630" xml:space="preserve">corpus in obicem incurret in a, quaſi celeritati-<lb/>bus C a, B a, & </s> <s xml:id="echoid-s6631" xml:space="preserve">juxta haſce directiones, ad hunc accederet *. <lb/></s> <s xml:id="echoid-s6632" xml:space="preserve"> <anchor type="note" xlink:label="note-0240-05a" xlink:href="note-0240-05"/> Motus per C a ictu non mutatur & </s> <s xml:id="echoid-s6633" xml:space="preserve">celeritate a E corpus <lb/>motum continuat, poſitis C a, a E æqualibus; </s> <s xml:id="echoid-s6634" xml:space="preserve">motu per <lb/>B a directè in obſtaculum incurrit, & </s> <s xml:id="echoid-s6635" xml:space="preserve">per eandem lineam, <lb/>ea qua acceſſit celeritate redit <anchor type="note" xlink:href="" symbol="*"/>, id eſt per a B; </s> <s xml:id="echoid-s6636" xml:space="preserve">hiſce au- <anchor type="note" xlink:label="note-0240-06a" xlink:href="note-0240-06"/> tem duobus motibus agitatum corpus redit per a p, diago-<lb/>nalem rectanguli lineis a E, a B, formati <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6637" xml:space="preserve">Triangula ve- <anchor type="note" xlink:label="note-0240-07a" xlink:href="note-0240-07"/> rò BP a, B a p eſſe æqualia liquet, unde conſtat propoſi-<lb/>tum. </s> <s xml:id="echoid-s6638" xml:space="preserve">Simili methodo detegimus motus corporum oblique <lb/>in ſe mutuo impingentium.</s> <s xml:id="echoid-s6639" xml:space="preserve"/> </p> <div xml:id="echoid-div940" type="float" level="2" n="2"> <note position="left" xlink:label="note-0240-03" xlink:href="note-0240-03a" xml:space="preserve">611.</note> <note position="left" xlink:label="note-0240-04" xlink:href="note-0240-04a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 6.</note> <note symbol="*" position="left" xlink:label="note-0240-05" xlink:href="note-0240-05a" xml:space="preserve">604.</note> <note symbol="*" position="left" xlink:label="note-0240-06" xlink:href="note-0240-06a" xml:space="preserve">559.</note> <note symbol="*" position="left" xlink:label="note-0240-07" xlink:href="note-0240-07a" xml:space="preserve">246.</note> </div> <p> <s xml:id="echoid-s6640" xml:space="preserve">Corpus Q quieſcit, corpus P, directione & </s> <s xml:id="echoid-s6641" xml:space="preserve">celeritate <lb/> <anchor type="note" xlink:label="note-0240-08a" xlink:href="note-0240-08"/> PA, in illud impingitur. </s> <s xml:id="echoid-s6642" xml:space="preserve">Per centra amborum corporum, <lb/>cum P in A pervenerit, ducatur linea DB, & </s> <s xml:id="echoid-s6643" xml:space="preserve">ad illam <pb o="169" file="0241" n="262" rhead="MATHEMATICA. LIB. I. CAP. XXVI."/> perpendicularis PB, & </s> <s xml:id="echoid-s6644" xml:space="preserve">abſolvatur parallelogrammum ABPC; <lb/></s> <s xml:id="echoid-s6645" xml:space="preserve">motus per PA reſolvitur in duos alios per PB & </s> <s xml:id="echoid-s6646" xml:space="preserve">PC, aut <lb/>BA, CA <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6647" xml:space="preserve">motu per CA corpus P non agit in corpus Q;</s> <s xml:id="echoid-s6648" xml:space="preserve"> <anchor type="note" xlink:label="note-0241-01a" xlink:href="note-0241-01"/> actio ergo oritur ex ſolo motu per BA, id eſt, corpus P, <lb/> <anchor type="note" xlink:label="note-0241-02a" xlink:href="note-0241-02"/> impactu obliquo per PA, celeritate PA, in corpus 2 agit, <lb/>eodem modo ac ſi directe in illud incurreret per BA, cele-<lb/>ritate BA. </s> <s xml:id="echoid-s6649" xml:space="preserve">Quare motus corporis Q ex illa actione, ſive <lb/>corpora ſint elaſtica, ſive non, determinatur ex iis quæ de <lb/>impactu directo dicta ſunt.</s> <s xml:id="echoid-s6650" xml:space="preserve"/> </p> <div xml:id="echoid-div941" type="float" level="2" n="3"> <note position="left" xlink:label="note-0240-08" xlink:href="note-0240-08a" xml:space="preserve"><emph style="sc">TAB XXII</emph>. <lb/>fig. 11. & 12.</note> <note symbol="*" position="right" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">604.</note> <note position="right" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">612</note> </div> <p> <s xml:id="echoid-s6651" xml:space="preserve">Motus corporis P poft impactum ex iiſdem principiis de-<lb/> <anchor type="note" xlink:label="note-0241-03a" xlink:href="note-0241-03"/> ducitur Motus per C A non mutatur; </s> <s xml:id="echoid-s6652" xml:space="preserve">ergo motu illo <lb/>æquali celeritate corpus P fertur, directione AE; </s> <s xml:id="echoid-s6653" xml:space="preserve">ſit ideo <lb/>AE æqualis CA. </s> <s xml:id="echoid-s6654" xml:space="preserve">Mutatio in motu BA determinatur re-<lb/>ſpectu corporis P, eodem modo ac motus corporis Q, ex <lb/>iis quæ de colliſione directâ explicata ſunt. </s> <s xml:id="echoid-s6655" xml:space="preserve">Sit celeritas poſt <lb/>impactum AD, in ſig. </s> <s xml:id="echoid-s6656" xml:space="preserve">11.</s> <s xml:id="echoid-s6657" xml:space="preserve">, quando corpus progreditur, & </s> <s xml:id="echoid-s6658" xml:space="preserve"><lb/>in fig. </s> <s xml:id="echoid-s6659" xml:space="preserve">12.</s> <s xml:id="echoid-s6660" xml:space="preserve">, quando regreditur; </s> <s xml:id="echoid-s6661" xml:space="preserve">ex iſto motu & </s> <s xml:id="echoid-s6662" xml:space="preserve">motu per <lb/>AE oritur motus compoſitus per diagonalem A p, quæ ſitu <lb/>& </s> <s xml:id="echoid-s6663" xml:space="preserve">longitudine directionem & </s> <s xml:id="echoid-s6664" xml:space="preserve">celeritatem corporis P poſt im-<lb/>pactum denotat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6665" xml:space="preserve"/> </p> <div xml:id="echoid-div942" type="float" level="2" n="4"> <note position="right" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">613</note> </div> <note symbol="*" position="right" xml:space="preserve">246.</note> <p> <s xml:id="echoid-s6666" xml:space="preserve">Quando corpora ſunt æqualia & </s> <s xml:id="echoid-s6667" xml:space="preserve">elaſtica, totus motus per <lb/> <anchor type="note" xlink:label="note-0241-05a" xlink:href="note-0241-05"/> BA ex percuſſione deſtruitur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6668" xml:space="preserve">ſolus motus per C A ſu- <anchor type="note" xlink:label="note-0241-06a" xlink:href="note-0241-06"/> pereſt, qua directione tunc etiam fertur corpus P. </s> <s xml:id="echoid-s6669" xml:space="preserve">In hoc <lb/>caſu ſemper poſt impulſum corpora ambo, quocunque modo <lb/>corpus P ad aliud accedat, ſeparantur directionibus angulum <lb/>rectum continentibus.</s> <s xml:id="echoid-s6670" xml:space="preserve"/> </p> <div xml:id="echoid-div943" type="float" level="2" n="5"> <note position="right" xlink:label="note-0241-05" xlink:href="note-0241-05a" xml:space="preserve">614.</note> <note symbol="*" position="right" xlink:label="note-0241-06" xlink:href="note-0241-06a" xml:space="preserve">581.</note> </div> </div> <div xml:id="echoid-div945" type="section" level="1" n="238"> <head xml:id="echoid-head336" xml:space="preserve"><emph style="sc">Machina</emph>.</head> <p style="it"> <s xml:id="echoid-s6671" xml:space="preserve">Qua Experimenta quæ dam de Colliſione obliqua, & </s> <s xml:id="echoid-s6672" xml:space="preserve"><lb/>compoſita, inſtituuntur.</s> <s xml:id="echoid-s6673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6674" xml:space="preserve">Duo plana lignea CDE, CDE, ad formam trianguli rectan-<lb/> <anchor type="note" xlink:label="note-0241-07a" xlink:href="note-0241-07"/> guli, cujus latus CD eſt longitudinis circiter trium pedum <lb/> <anchor type="note" xlink:label="note-0241-08a" xlink:href="note-0241-08"/> cum ſemiſſe, latus DE unius pedis cum ſemiſſe, laborata, <lb/>verticaliter poſita, circa cardines A & </s> <s xml:id="echoid-s6675" xml:space="preserve">B convertuntur.</s> <s xml:id="echoid-s6676" xml:space="preserve"/> </p> <div xml:id="echoid-div945" type="float" level="2" n="1"> <note position="right" xlink:label="note-0241-07" xlink:href="note-0241-07a" xml:space="preserve">615</note> <note position="right" xlink:label="note-0241-08" xlink:href="note-0241-08a" xml:space="preserve"><emph style="sc">TAB XXIV</emph>. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s6677" xml:space="preserve">Experimenta in hac Machina adhibitis globis eburneis in-<lb/>ſtituuntur diametri unius pollicis cum ſemiſſe.</s> <s xml:id="echoid-s6678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6679" xml:space="preserve">Plana ita conjunguntur, ut ſi hiſce alia parallela, ad diſtan- <pb o="170" file="0242" n="263" rhead="PHYSICES ELEMENTA"/> tiam quæ paululum ſemidiametrum globorum excedit, <lb/>concipiantur, horum interſectio ſit ipſe axis circumvolutio-<lb/>nis: </s> <s xml:id="echoid-s6680" xml:space="preserve">quod præſtatur ſi cardines adhibeantur ut G (fig. </s> <s xml:id="echoid-s6681" xml:space="preserve">2.) <lb/></s> <s xml:id="echoid-s6682" xml:space="preserve">quorum partes b, b, ad majorem firmitatem, ligno inſerun-<lb/>tur.</s> <s xml:id="echoid-s6683" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6684" xml:space="preserve">In centro cardinis ſuperioris A, datur cylindrus parvus a, <lb/>(fig. </s> <s xml:id="echoid-s6685" xml:space="preserve">2.) </s> <s xml:id="echoid-s6686" xml:space="preserve">in cujus baſi foramen datur, quod cum alio a latere <lb/>conjungitur, ita ut per illa immittatur filum i h, quo glo-<lb/>bus P ſuſpenditur, & </s> <s xml:id="echoid-s6687" xml:space="preserve">quod paxillo annectitur.</s> <s xml:id="echoid-s6688" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6689" xml:space="preserve">Ope cochlearum F, F, F, F, F, Machina in ſitu ver-<lb/>ticali diſponitur, ita ut filum h i cum axe Machinæ coinci-<lb/>dat.</s> <s xml:id="echoid-s6690" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6691" xml:space="preserve">In m, m, clavi duo planis memoratis inſeruntur, his glo-<lb/>bi Q, Q, ſuſpenduntur, ad talem diſtantiam a planis ut unum-<lb/>quodque illud, cui applicatur, fere tangat; </s> <s xml:id="echoid-s6692" xml:space="preserve">id eſt, ut linea, <lb/>quæ concipitur per centra globorum P & </s> <s xml:id="echoid-s6693" xml:space="preserve">Q, huic plano ſit <lb/>parallela; </s> <s xml:id="echoid-s6694" xml:space="preserve">requiritur ulterius, ut hi globi, ad eandem altitudi-<lb/>nem poſiti, ſeſe mutuo tangant.</s> <s xml:id="echoid-s6695" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6696" xml:space="preserve">Fila, quibus globi Q & </s> <s xml:id="echoid-s6697" xml:space="preserve">Q ſuſpenduntur, trajiciunt fora-<lb/>mina in prædictis clavis, & </s> <s xml:id="echoid-s6698" xml:space="preserve">paxillis l, l annectuntur, ut <lb/>commode elevari, deprimique, & </s> <s xml:id="echoid-s6699" xml:space="preserve">omnium globorum cen-<lb/>tra in eodem plano, ad horizontem parallelo, diſponi poſ-<lb/>ſint. </s> <s xml:id="echoid-s6700" xml:space="preserve">Regula ænea R, ita inflexa ut juxta illam globus Pin <lb/>ſuo motu adſcendat, convertitur circa extremitatum alte-<lb/>ram, & </s> <s xml:id="echoid-s6701" xml:space="preserve">centrum motus cum axe Machinæ coïncidit. </s> <s xml:id="echoid-s6702" xml:space="preserve">In-<lb/>ſervit ad notandam viam globi P, & </s> <s xml:id="echoid-s6703" xml:space="preserve">altitudinem ad quam <lb/>adſcendit.</s> <s xml:id="echoid-s6704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6705" xml:space="preserve">Globus uterque Q juxta planum cui applicatur dimittitur, <lb/>& </s> <s xml:id="echoid-s6706" xml:space="preserve">altitudo a qua dimittitur notatur indice plano infixo, ad <lb/>quod in utroque plano foramina quatuor dantur, angulos <lb/>æquales, reſpectu motus filorum, continentia.</s> <s xml:id="echoid-s6707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6708" xml:space="preserve">Quando globus Q a certa altitudine dimittitur, in glo-<lb/>bum P impingit, illumque ſecundum eandem directionem <lb/>propellit.</s> <s xml:id="echoid-s6709" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div947" type="section" level="1" n="239"> <head xml:id="echoid-head337" xml:space="preserve"><emph style="sc">Experimentum</emph>. I.</head> <note position="left" xml:space="preserve">616</note> <p> <s xml:id="echoid-s6710" xml:space="preserve">Exhibetur hic horizontalis ſectio hujus Machinæ, cui <lb/> <anchor type="note" xlink:label="note-0242-02a" xlink:href="note-0242-02"/> <pb file="0243" n="264"/> <pb file="0243a" n="265"/> <anchor type="figure" xlink:label="fig-0243a-01a" xlink:href="fig-0243a-01"/> <pb file="0244" n="266"/> <pb o="171" file="0245" n="267" rhead="MATHEMATICA. LIB. I. CAP. XXVI."/> ſuſpenduntur globus P, & </s> <s xml:id="echoid-s6711" xml:space="preserve">unus ex globis Q. </s> <s xml:id="echoid-s6712" xml:space="preserve">Planis ad angulum <lb/>rectum diſpoſitis, quacunque directione, & </s> <s xml:id="echoid-s6713" xml:space="preserve">à quacunque <lb/>altitudine cadendo, corpus P impingatur in corpus Q, poſt <lb/>impactum corpora directiones planorum ſequuntur.</s> <s xml:id="echoid-s6714" xml:space="preserve"/> </p> <div xml:id="echoid-div947" type="float" level="2" n="1"> <note position="left" xlink:label="note-0242-02" xlink:href="note-0242-02a" xml:space="preserve"><emph style="sc">TAB. XXIV</emph>. <lb/>fig. 3.</note> <figure xlink:label="fig-0243a-01" xlink:href="fig-0243a-01a"> <image file="0243a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0243a-01"/> </figure> </div> <p> <s xml:id="echoid-s6715" xml:space="preserve">Ex iiſdem principiis etiam deducitur motus duorum cor-<lb/> <anchor type="note" xlink:label="note-0245-01a" xlink:href="note-0245-01"/> porum poſt percuſſionem, quando ambo moventur, quo-<lb/>modocunque in ſe mutuo ferantur. </s> <s xml:id="echoid-s6716" xml:space="preserve">Caſus præcipui repræ-<lb/>ſentantur in Tab. </s> <s xml:id="echoid-s6717" xml:space="preserve">XXIII, & </s> <s xml:id="echoid-s6718" xml:space="preserve">omnes eodem modo reſolvun-<lb/>tur.</s> <s xml:id="echoid-s6719" xml:space="preserve"/> </p> <div xml:id="echoid-div948" type="float" level="2" n="2"> <note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">617</note> </div> <p> <s xml:id="echoid-s6720" xml:space="preserve">Corpus P moveatur directione & </s> <s xml:id="echoid-s6721" xml:space="preserve">celeritate P A; </s> <s xml:id="echoid-s6722" xml:space="preserve">corpus <lb/> <anchor type="note" xlink:label="note-0245-02a" xlink:href="note-0245-02"/> Q directione & </s> <s xml:id="echoid-s6723" xml:space="preserve">celeritate Q a; </s> <s xml:id="echoid-s6724" xml:space="preserve">ducatur linea B b, tranſiens <lb/>per amborum corporum centra ubiſeſe mutuo tangunt; </s> <s xml:id="echoid-s6725" xml:space="preserve">ad <lb/>illam ſint CA & </s> <s xml:id="echoid-s6726" xml:space="preserve">c a perpendiculares, & </s> <s xml:id="echoid-s6727" xml:space="preserve">abſolvantur pa-<lb/>rallelogramma PBAC & </s> <s xml:id="echoid-s6728" xml:space="preserve">Q b a c. </s> <s xml:id="echoid-s6729" xml:space="preserve">Motus corporis P re-<lb/>ſolvitur in duos alios, quorum celeritates & </s> <s xml:id="echoid-s6730" xml:space="preserve">directiones <lb/>deſignant CA, BA. </s> <s xml:id="echoid-s6731" xml:space="preserve">Motus, in quos reſolvitur motus cor-<lb/>poris Q, deſignantur per c a, b a <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6732" xml:space="preserve">Motibus per CA & </s> <s xml:id="echoid-s6733" xml:space="preserve">c a <anchor type="note" xlink:label="note-0245-03a" xlink:href="note-0245-03"/> corpora non agunt in ſe mutuo, non mutantur ergo hi mo-<lb/>tus, & </s> <s xml:id="echoid-s6734" xml:space="preserve">poſt occurſum deſignantur per A E & </s> <s xml:id="echoid-s6735" xml:space="preserve">a e, ipſis AC <lb/>& </s> <s xml:id="echoid-s6736" xml:space="preserve">a c æquales; </s> <s xml:id="echoid-s6737" xml:space="preserve">percuſſio ex motibus per lineas B A, b a eſt <lb/>directa, & </s> <s xml:id="echoid-s6738" xml:space="preserve">determinatur in capitibus <emph style="sc">XXIII. XXIV.</emph>: </s> <s xml:id="echoid-s6739" xml:space="preserve">ſit mo-<lb/>tus corporis P verſus D, & </s> <s xml:id="echoid-s6740" xml:space="preserve">ejus celeritas AD; </s> <s xml:id="echoid-s6741" xml:space="preserve">corporis Q <lb/>motus verſus d, & </s> <s xml:id="echoid-s6742" xml:space="preserve">ejus celeritas a d. </s> <s xml:id="echoid-s6743" xml:space="preserve">Poſt occurſum ergo <lb/>motus corporis P componitur ex motibus per AE & </s> <s xml:id="echoid-s6744" xml:space="preserve">AD, <lb/>& </s> <s xml:id="echoid-s6745" xml:space="preserve">movetur per diagonalem A p Corporis Q motus poſt <lb/>impactum componitur ex motibus per a e & </s> <s xml:id="echoid-s6746" xml:space="preserve">a d, unde cor-<lb/>pus illud fertur per diagonalem a q; </s> <s xml:id="echoid-s6747" xml:space="preserve">& </s> <s xml:id="echoid-s6748" xml:space="preserve">longitudines illarum <lb/>diagonalium celeritates corporum poſt occurſum denotant <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6749" xml:space="preserve"> <anchor type="note" xlink:label="note-0245-04a" xlink:href="note-0245-04"/> In Fig. </s> <s xml:id="echoid-s6750" xml:space="preserve">7. </s> <s xml:id="echoid-s6751" xml:space="preserve">8. </s> <s xml:id="echoid-s6752" xml:space="preserve">& </s> <s xml:id="echoid-s6753" xml:space="preserve">9. </s> <s xml:id="echoid-s6754" xml:space="preserve">corpora non elaſtica ponuntur. </s> <s xml:id="echoid-s6755" xml:space="preserve">Fig. </s> <s xml:id="echoid-s6756" xml:space="preserve">10. <lb/></s> <s xml:id="echoid-s6757" xml:space="preserve">11. </s> <s xml:id="echoid-s6758" xml:space="preserve">& </s> <s xml:id="echoid-s6759" xml:space="preserve">12. </s> <s xml:id="echoid-s6760" xml:space="preserve">eoſdem caſus datis corporibus elaſticis repræſen-<lb/>tant. </s> <s xml:id="echoid-s6761" xml:space="preserve">In fig. </s> <s xml:id="echoid-s6762" xml:space="preserve">7. </s> <s xml:id="echoid-s6763" xml:space="preserve">litteræ quædam deſunt, quia puncta ipſis <lb/>deſignata cum aliis coincidunt.</s> <s xml:id="echoid-s6764" xml:space="preserve"/> </p> <div xml:id="echoid-div949" type="float" level="2" n="3"> <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve"><emph style="sc">TAB. XXIII.</emph> <lb/>fig 7. 8. 9. <lb/>10. 11. & <lb/>12.</note> <note symbol="*" position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">604</note> <note symbol="*" position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">246.</note> </div> <pb o="172" file="0246" n="268" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div951" type="section" level="1" n="240"> <head xml:id="echoid-head338" xml:space="preserve">CAPUT XXVII.</head> <head xml:id="echoid-head339" xml:space="preserve">De Colliſione compoſita.</head> <head xml:id="echoid-head340" xml:space="preserve"><emph style="sc">Definitio.</emph></head> <p> <s xml:id="echoid-s6765" xml:space="preserve">COmpoſitam dicimus colliſionem ubi plura dantur quam <lb/> <anchor type="note" xlink:label="note-0246-01a" xlink:href="note-0246-01"/> duo corpor a concurrentia, aut ubi corpus unum in plu-<lb/>ra plana eodem tempore incurrit.</s> <s xml:id="echoid-s6766" xml:space="preserve"/> </p> <div xml:id="echoid-div951" type="float" level="2" n="1"> <note position="left" xlink:label="note-0246-01" xlink:href="note-0246-01a" xml:space="preserve">618</note> </div> <p> <s xml:id="echoid-s6767" xml:space="preserve">In hoc capite quædam examinabo circa colliſionem tri-<lb/>um corporum, & </s> <s xml:id="echoid-s6768" xml:space="preserve">impactionem corporis in duo pla-<lb/>na.</s> <s xml:id="echoid-s6769" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6770" xml:space="preserve">Corpus P, velocitate AP, incurrit in angulum GCF, juxta <lb/> <anchor type="note" xlink:label="note-0246-02a" xlink:href="note-0246-02"/> directionem AP; </s> <s xml:id="echoid-s6771" xml:space="preserve">determinandum qua actione in utrumque <lb/> <anchor type="note" xlink:label="note-0246-03a" xlink:href="note-0246-03"/> planum GC & </s> <s xml:id="echoid-s6772" xml:space="preserve">FC incurrit.</s> <s xml:id="echoid-s6773" xml:space="preserve"/> </p> <div xml:id="echoid-div952" type="float" level="2" n="2"> <note position="left" xlink:label="note-0246-02" xlink:href="note-0246-02a" xml:space="preserve">619</note> <note position="left" xlink:label="note-0246-03" xlink:href="note-0246-03a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig 1. 2.</note> </div> <p> <s xml:id="echoid-s6774" xml:space="preserve">Notandum corpus, integram ſuam amittere vim; </s> <s xml:id="echoid-s6775" xml:space="preserve">ponimus <lb/>enim obſtaculum fixum.</s> <s xml:id="echoid-s6776" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6777" xml:space="preserve">Ductis AB & </s> <s xml:id="echoid-s6778" xml:space="preserve">AD, quæ cum CG & </s> <s xml:id="echoid-s6779" xml:space="preserve">CF angulos effi-<lb/>ciunt rectos, ſint PE & </s> <s xml:id="echoid-s6780" xml:space="preserve">PH ad has reſpectivè parallelæ.</s> <s xml:id="echoid-s6781" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6782" xml:space="preserve">Si nunc concipiamus Corpus P, eodem tempore ferri per <lb/>AE & </s> <s xml:id="echoid-s6783" xml:space="preserve">AH, velocitatibus hiſce lineis proportionalibus, revera <lb/> <anchor type="note" xlink:label="note-0246-04a" xlink:href="note-0246-04"/> movebitur per AP velocitate AP <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6784" xml:space="preserve">ideò poſſumus conſi- derare corpus, dum pertingit ad P, agitari velocitatibus <lb/>HP & </s> <s xml:id="echoid-s6785" xml:space="preserve">EP, & </s> <s xml:id="echoid-s6786" xml:space="preserve">juxta haſce directiones in plana CG, CF <lb/>incurrere directè ita ut quæſtio eo reducatur, quibus viribus <lb/>corpus eodem tempore per AE & </s> <s xml:id="echoid-s6787" xml:space="preserve">AH ferri poſſit.</s> <s xml:id="echoid-s6788" xml:space="preserve"/> </p> <div xml:id="echoid-div953" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0246-04" xlink:href="note-0246-04a" xml:space="preserve">246.</note> </div> <p> <s xml:id="echoid-s6789" xml:space="preserve">Si angulus FCG eſſet rectus, & </s> <s xml:id="echoid-s6790" xml:space="preserve">rectus eſſet angulus <lb/>EAH; </s> <s xml:id="echoid-s6791" xml:space="preserve">idcirco motus hi neque contrarie agerent, neque <lb/>ad eandem partem tenderent, & </s> <s xml:id="echoid-s6792" xml:space="preserve">quadratis velocitatum AE <lb/>& </s> <s xml:id="echoid-s6793" xml:space="preserve">AH actiones proportionales eſſent <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6794" xml:space="preserve"> <anchor type="note" xlink:label="note-0246-05a" xlink:href="note-0246-05"/> </s> </p> <div xml:id="echoid-div954" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0246-05" xlink:href="note-0246-05a" xml:space="preserve">604.</note> </div> <p> <s xml:id="echoid-s6795" xml:space="preserve">Ubi autem angulus, quem plana continent, eſt acutus, aut <lb/>obtuſus; </s> <s xml:id="echoid-s6796" xml:space="preserve">ut in hiſce figuris, ducendæ ſunt ad AP perpen-<lb/>diculares EL, HI. </s> <s xml:id="echoid-s6797" xml:space="preserve">In motu per AE continetur motus <lb/>per AP velocitate AL; </s> <s xml:id="echoid-s6798" xml:space="preserve">in motu per AH continetur motus <lb/>per AP velocitate AI, & </s> <s xml:id="echoid-s6799" xml:space="preserve">nil præterea ex motu per A P <lb/>in his motibus continetur, propter angulum rectum AIH <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0246-06a" xlink:href="note-0246-06"/> Ita ut non interſit, quantum ad motum corporis, utrum eo- <pb file="0247" n="269"/> <pb file="0247a" n="270"/> <anchor type="figure" xlink:label="fig-0247a-01a" xlink:href="fig-0247a-01"/> <pb file="0248" n="271"/> <pb o="173" file="0249" n="272" rhead="MATHEMATICA. LIB. I. CAP. XXVII."/> dem tempore moveatur corpus per AH & </s> <s xml:id="echoid-s6800" xml:space="preserve">AE, velocitatibus <lb/>hiſce lineis proportionalibus; </s> <s xml:id="echoid-s6801" xml:space="preserve">an in linea AP moveatur eo-<lb/>dem tempore velocitatibus AI & </s> <s xml:id="echoid-s6802" xml:space="preserve">AL. </s> <s xml:id="echoid-s6803" xml:space="preserve">In utroque caſu <lb/>revera movetur corpus per AP, velocitate AP; </s> <s xml:id="echoid-s6804" xml:space="preserve">quæ ergo <lb/>valet ambas velocitates AL, AI, quod & </s> <s xml:id="echoid-s6805" xml:space="preserve">aliunde conſtat: <lb/></s> <s xml:id="echoid-s6806" xml:space="preserve">Nam AL & </s> <s xml:id="echoid-s6807" xml:space="preserve">IP ſunt æquales propter triangula ſimilia & </s> <s xml:id="echoid-s6808" xml:space="preserve"><lb/>æqualia AEL, HIP habentia latera reſpectivè parallela, <lb/>quorum AE & </s> <s xml:id="echoid-s6809" xml:space="preserve">HP ſunt æqualia <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6810" xml:space="preserve"> <anchor type="note" xlink:label="note-0249-01a" xlink:href="note-0249-01"/> </s> </p> <div xml:id="echoid-div955" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0246-06" xlink:href="note-0246-06a" xml:space="preserve">603.</note> <figure xlink:label="fig-0247a-01" xlink:href="fig-0247a-01a"> <image file="0247a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0247a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0249-01" xlink:href="note-0249-01a" xml:space="preserve">34. El 17</note> </div> <p> <s xml:id="echoid-s6811" xml:space="preserve">Jam cum motus per A L contineatur in motu per AE <lb/>quo agit in planum GC, & </s> <s xml:id="echoid-s6812" xml:space="preserve">motus per AI contineatur in <lb/>motu per AH, quo in aliud planum corpus agit; </s> <s xml:id="echoid-s6813" xml:space="preserve">ſequitur <lb/>actiones in plana eſſe vires quibus corpus eodem tempore <lb/>fertur velocitatibus AL & </s> <s xml:id="echoid-s6814" xml:space="preserve">AI: </s> <s xml:id="echoid-s6815" xml:space="preserve">vires verò hæ ſunt ut ipſæ <lb/>velocitates <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6816" xml:space="preserve">integra vis corporis, quæ quadrato veloci- <anchor type="note" xlink:label="note-0249-02a" xlink:href="note-0249-02"/> tatis AP proportionalis eſt <anchor type="note" xlink:href="" symbol="*"/>, ſecari debet in duas partes <anchor type="note" xlink:label="note-0249-03a" xlink:href="note-0249-03"/> quæ ſint inter ſe ut AL & </s> <s xml:id="echoid-s6817" xml:space="preserve">AI; </s> <s xml:id="echoid-s6818" xml:space="preserve">partes hæ ſunt rectangula <lb/>AP per AL, & </s> <s xml:id="echoid-s6819" xml:space="preserve">AP per AI.</s> <s xml:id="echoid-s6820" xml:space="preserve"/> </p> <div xml:id="echoid-div956" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0249-02" xlink:href="note-0249-02a" xml:space="preserve">599.</note> <note symbol="*" position="right" xlink:label="note-0249-03" xlink:href="note-0249-03a" xml:space="preserve">447.</note> </div> <p> <s xml:id="echoid-s6821" xml:space="preserve">Si, poſito angulo GCF obtuſo, directio motus AP cum <lb/> <anchor type="note" xlink:label="note-0249-04a" xlink:href="note-0249-04"/> crure uno, ut CF, angulum etiam efficiat obtuſum, in <lb/> <anchor type="note" xlink:label="note-0249-05a" xlink:href="note-0249-05"/> hoc ultimum planum tantum actionem exerit corpus, pro-<lb/>portionalem quadrato lineæ AD, perpendiculari ad FC, <lb/>& </s> <s xml:id="echoid-s6822" xml:space="preserve">ictu non integram amittit vim, ſed per CF motum <lb/>poſt impactionem continuat, velocitate linea DC proportio-<lb/>nali.</s> <s xml:id="echoid-s6823" xml:space="preserve"/> </p> <div xml:id="echoid-div957" type="float" level="2" n="7"> <note position="right" xlink:label="note-0249-04" xlink:href="note-0249-04a" xml:space="preserve">620</note> <note position="right" xlink:label="note-0249-05" xlink:href="note-0249-05a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s6824" xml:space="preserve">Hæc ex reſolutione motus <anchor type="note" xlink:href="" symbol="*"/> ſequuntur. </s> <s xml:id="echoid-s6825" xml:space="preserve">Nam aliundè <anchor type="note" xlink:label="note-0249-06a" xlink:href="note-0249-06"/> demonſtrabimus nullam in planum GC dari actionem.</s> <s xml:id="echoid-s6826" xml:space="preserve"/> </p> <div xml:id="echoid-div958" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0249-06" xlink:href="note-0249-06a" xml:space="preserve">604</note> </div> <p> <s xml:id="echoid-s6827" xml:space="preserve">In caſu fig. </s> <s xml:id="echoid-s6828" xml:space="preserve">2. </s> <s xml:id="echoid-s6829" xml:space="preserve">ubi angulus; </s> <s xml:id="echoid-s6830" xml:space="preserve">quem AP cum CF efficit, eſt <lb/>acutus, actio in planum GC minuitur, aucto angulo hoc, <lb/>ſi hic rectus ſit, ut in fig 3. </s> <s xml:id="echoid-s6831" xml:space="preserve">datâ corporis directione a P, <lb/>parallelogrammi AEPH diagonalis AP coincidit cum latere <lb/>AH, & </s> <s xml:id="echoid-s6832" xml:space="preserve">latus aliud AE, ideoque AL, evaneſcunt, & </s> <s xml:id="echoid-s6833" xml:space="preserve">cum <lb/>hiſce actio in planum GC etiam tollitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6834" xml:space="preserve">quæ ergo auctâ <anchor type="note" xlink:label="note-0249-07a" xlink:href="note-0249-07"/> inclinatione viæ corporis ad planum hoc etiam nulla e-<lb/>rit.</s> <s xml:id="echoid-s6835" xml:space="preserve"/> </p> <div xml:id="echoid-div959" type="float" level="2" n="9"> <note symbol="*" position="right" xlink:label="note-0249-07" xlink:href="note-0249-07a" xml:space="preserve">619.</note> </div> <p> <s xml:id="echoid-s6836" xml:space="preserve">In determinandis quæſpectant directam colliſionem trium <lb/>corporum, illi ſimili utimur methodo quam circa duorum cor- <pb o="174" file="0250" n="273" rhead="PHYSICES ELEMENTA"/> porum colliſionem in cap. </s> <s xml:id="echoid-s6837" xml:space="preserve"><emph style="sc">XXIII.</emph> adhibuimus. </s> <s xml:id="echoid-s6838" xml:space="preserve">Vbitria dantur <lb/> <anchor type="note" xlink:label="note-0250-01a" xlink:href="note-0250-01"/> corpora duæ dantur velocitates reſpectivæ à quibus pendent <lb/>actiones corporum in ſe mutuo <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6839" xml:space="preserve">partium introceſſio- <anchor type="note" xlink:label="note-0250-02a" xlink:href="note-0250-02"/> nes, quæ manentibus corporibus, & </s> <s xml:id="echoid-s6840" xml:space="preserve">hiſce duabus velocita-<lb/>tibus, eadem ſemper eſt, ideoque & </s> <s xml:id="echoid-s6841" xml:space="preserve">vis ictu deſtructa <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6842" xml:space="preserve">Quan- <anchor type="note" xlink:label="note-0250-03a" xlink:href="note-0250-03"/> do corpora poſt ictum quieſcunt ſumma virium eſt, datis ve-<lb/> <anchor type="note" xlink:label="note-0250-04a" xlink:href="note-0250-04"/> locitatibus reſpectivis, omnium minima; </s> <s xml:id="echoid-s6843" xml:space="preserve">ſi enim ſumma mi-<lb/>nor daretur minor vis ictu deſtruetur, quod fieri non pot-<lb/>eſt.</s> <s xml:id="echoid-s6844" xml:space="preserve"/> </p> <div xml:id="echoid-div960" type="float" level="2" n="10"> <note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">621.</note> <note symbol="*" position="left" xlink:label="note-0250-02" xlink:href="note-0250-02a" xml:space="preserve">494.</note> <note position="left" xlink:label="note-0250-03" xlink:href="note-0250-03a" xml:space="preserve">622</note> <note symbol="*" position="left" xlink:label="note-0250-04" xlink:href="note-0250-04a" xml:space="preserve">488.</note> </div> <p> <s xml:id="echoid-s6845" xml:space="preserve">Demonſtramus autem in Scholio 1. </s> <s xml:id="echoid-s6846" xml:space="preserve">hujus cap. </s> <s xml:id="echoid-s6847" xml:space="preserve">vim, datis ve-<lb/> <anchor type="note" xlink:label="note-0250-05a" xlink:href="note-0250-05"/> locitatibus reſpectivis, eſſe omnium minimam, ſi motis duobus <lb/>corporibus unam partem verſus, aliud in contrariam partem <lb/>ita feratur, ut bujus maſſæ productum per ſuam velocitatem <lb/>valeat ſummam productorum maſſarum reliquorum duo-<lb/>rum, ſingularum multiplicatarum per ſuas velocita-<lb/>tes.</s> <s xml:id="echoid-s6848" xml:space="preserve"/> </p> <div xml:id="echoid-div961" type="float" level="2" n="11"> <note position="left" xlink:label="note-0250-05" xlink:href="note-0250-05a" xml:space="preserve">623</note> </div> <p> <s xml:id="echoid-s6849" xml:space="preserve">In hoc autem caſu corpora poſt ictum quieſcere, & </s> <s xml:id="echoid-s6850" xml:space="preserve">ideo <lb/>ſummam virium eſſe omnium minimam etiam deducimus ex <lb/>demonſtratis circa colliſionem corporum duorum, ad quam <lb/>trium corporum colliſionem referimus.</s> <s xml:id="echoid-s6851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6852" xml:space="preserve">Sint corpora tria A, B, C; </s> <s xml:id="echoid-s6853" xml:space="preserve">velocitas primi f b; </s> <s xml:id="echoid-s6854" xml:space="preserve">ſecundi <lb/> <anchor type="note" xlink:label="note-0250-06a" xlink:href="note-0250-06"/> g i; </s> <s xml:id="echoid-s6855" xml:space="preserve">tertii l i. </s> <s xml:id="echoid-s6856" xml:space="preserve">Ponimus producta A per f b & </s> <s xml:id="echoid-s6857" xml:space="preserve">B per g i, <lb/> <anchor type="note" xlink:label="note-0250-07a" xlink:href="note-0250-07"/> ſimul ſumta, valere productum C per l i.</s> <s xml:id="echoid-s6858" xml:space="preserve"/> </p> <div xml:id="echoid-div962" type="float" level="2" n="12"> <note position="left" xlink:label="note-0250-06" xlink:href="note-0250-06a" xml:space="preserve">624</note> <note position="left" xlink:label="note-0250-07" xlink:href="note-0250-07a" xml:space="preserve"><emph style="sc">TAB XXV.</emph> <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s6859" xml:space="preserve">Concipiamus corpus C in duas partes reſolvi D & </s> <s xml:id="echoid-s6860" xml:space="preserve">E ita, <lb/> <anchor type="note" xlink:label="note-0250-08a" xlink:href="note-0250-08"/> ut D per l i valeat A per f b, & </s> <s xml:id="echoid-s6861" xml:space="preserve">E per l i æquale ſit B per <lb/>g i; </s> <s xml:id="echoid-s6862" xml:space="preserve">id eſt ſit D ad E, ut A per f b ad B per g i. </s> <s xml:id="echoid-s6863" xml:space="preserve">In hoc <lb/>caſu A ad D, ut l i ad f b, & </s> <s xml:id="echoid-s6864" xml:space="preserve">corpora hæc concurrentia poſt <lb/> <anchor type="note" xlink:label="note-0250-09a" xlink:href="note-0250-09"/> ictum quieſcunt <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s6865" xml:space="preserve">quieſcunt etiam B & </s> <s xml:id="echoid-s6866" xml:space="preserve">E <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6867" xml:space="preserve">quia B ad E, <anchor type="note" xlink:label="note-0250-10a" xlink:href="note-0250-10"/> ut l i ad g i. </s> <s xml:id="echoid-s6868" xml:space="preserve">Hæc autem quatuor corpora à tribus da-<lb/>tis, memoratis velocitatibus agitatis, non differunt.</s> <s xml:id="echoid-s6869" xml:space="preserve"/> </p> <div xml:id="echoid-div963" type="float" level="2" n="13"> <note position="left" xlink:label="note-0250-08" xlink:href="note-0250-08a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0250-09" xlink:href="note-0250-09a" xml:space="preserve">500.</note> <note symbol="*" position="left" xlink:label="note-0250-10" xlink:href="note-0250-10a" xml:space="preserve">500.</note> </div> <p> <s xml:id="echoid-s6870" xml:space="preserve">Vis in ictu quocunque amiſſa datis velocitatibus reſpectivis <lb/>valet ſummam virium in caſu in quo corpora quieſcunt <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s6871" xml:space="preserve"> <anchor type="note" xlink:label="note-0250-11a" xlink:href="note-0250-11"/> hæc autem ſumma ſolis datis velocitatibus reſpectivis exprimi <lb/>poteſt &</s> <s xml:id="echoid-s6872" xml:space="preserve">, ut in Scholio 1. </s> <s xml:id="echoid-s6873" xml:space="preserve">demonſtramus. </s> <s xml:id="echoid-s6874" xml:space="preserve">In omni concurſu <lb/> <anchor type="note" xlink:label="note-0250-12a" xlink:href="note-0250-12"/> directo trium corporum, vis amiſſa proportionem ſequitur <lb/>ſummætrium productorum, quæ formantur multiplicatis dua- <pb o="175" file="0251" n="274" rhead="MATHEMATICA. LIB. I. CAP XXVII."/> bus maſſis in ſe mutuo, & </s> <s xml:id="echoid-s6875" xml:space="preserve">per quadratum velocitatis reſpe-<lb/>ctivæ barum ipſarum, diviſâ ſummâ bacper ſummam trium <lb/>maſſarum.</s> <s xml:id="echoid-s6876" xml:space="preserve"/> </p> <div xml:id="echoid-div964" type="float" level="2" n="14"> <note symbol="*" position="left" xlink:label="note-0250-11" xlink:href="note-0250-11a" xml:space="preserve">622.</note> <note position="left" xlink:label="note-0250-12" xlink:href="note-0250-12a" xml:space="preserve">625.</note> </div> <p> <s xml:id="echoid-s6877" xml:space="preserve">Datis corporibus A, B, & </s> <s xml:id="echoid-s6878" xml:space="preserve">C; </s> <s xml:id="echoid-s6879" xml:space="preserve">1. </s> <s xml:id="echoid-s6880" xml:space="preserve">multiplicari debet maſſa <lb/>A per maſſam B & </s> <s xml:id="echoid-s6881" xml:space="preserve">productum hoc per quadratum velocita-<lb/>tis reſpectivæ A & </s> <s xml:id="echoid-s6882" xml:space="preserve">B; </s> <s xml:id="echoid-s6883" xml:space="preserve">2. </s> <s xml:id="echoid-s6884" xml:space="preserve">productum maſſæ A per maſſam C <lb/>multiplicandum eſt per quadratum velocitatis reſpectivæ ho-<lb/>rum corporum; </s> <s xml:id="echoid-s6885" xml:space="preserve">3. </s> <s xml:id="echoid-s6886" xml:space="preserve">tandem ductis maſſis B & </s> <s xml:id="echoid-s6887" xml:space="preserve">C in ſe invi-<lb/>cem, productum multiplicari debet per quadratum velocita-<lb/>tis reſpectivæ horum corporum; </s> <s xml:id="echoid-s6888" xml:space="preserve">ſumma verò trium horum <lb/>productorum dividenda eſt per ſummam maſſarum, & </s> <s xml:id="echoid-s6889" xml:space="preserve">habe-<lb/>bimus vim ictu amiſſam.</s> <s xml:id="echoid-s6890" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6891" xml:space="preserve">Si non fuerint elaſtica tria corpora, de talibus enim agi-<lb/> <anchor type="note" xlink:label="note-0251-01a" xlink:href="note-0251-01"/> mus, poſt ictum eadem velocitate feruntur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6892" xml:space="preserve">hæc eſt ve- <anchor type="note" xlink:label="note-0251-02a" xlink:href="note-0251-02"/> locitas quam navis haberet, in qua corpora juxta legem in <lb/>n. </s> <s xml:id="echoid-s6893" xml:space="preserve">610. </s> <s xml:id="echoid-s6894" xml:space="preserve">indicatam agitata forent; </s> <s xml:id="echoid-s6895" xml:space="preserve">quia poſt ictum in nave <lb/>corpora quieſcerent, translatis ipſis eadem cum nave ve-<lb/>locitate. </s> <s xml:id="echoid-s6896" xml:space="preserve">Navis velocitatem in Scholio 1. </s> <s xml:id="echoid-s6897" xml:space="preserve">detegimus, & </s> <s xml:id="echoid-s6898" xml:space="preserve">ha-<lb/>betur, multiplicando ſingulorum corporum maſſas per ſuas <lb/>velocitates & </s> <s xml:id="echoid-s6899" xml:space="preserve">dividendo per ſummam maſſarum ſummam <lb/>productorum, ſi tria corpora ad eandem partem tendant; </s> <s xml:id="echoid-s6900" xml:space="preserve">ſin <lb/>minus, motuum contrariorum producta à ſe invicem ſub-<lb/>trabi debent.</s> <s xml:id="echoid-s6901" xml:space="preserve"/> </p> <div xml:id="echoid-div965" type="float" level="2" n="15"> <note position="right" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">626</note> <note symbol="*" position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">484.</note> </div> <p> <s xml:id="echoid-s6902" xml:space="preserve">Videmus quæ ſpectant trium corporum colliſionem, in <lb/>multis cum iis quæ de duobus corporibus demonſtrata ſunt <lb/>convenire, quod etiam referri poteſt ad demonſtrata de mu-<lb/>tationibus velocitatum in ratione inverſa maſſarum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s6903" xml:space="preserve">Nam <anchor type="note" xlink:label="note-0251-03a" xlink:href="note-0251-03"/> ut in Scholio 1. </s> <s xml:id="echoid-s6904" xml:space="preserve">demonſtramus; </s> <s xml:id="echoid-s6905" xml:space="preserve">Mutationes in velocitatibus <lb/> <anchor type="note" xlink:label="note-0251-04a" xlink:href="note-0251-04"/> duorum corporum, oriundæ ex actione mutua borum corporum <lb/>in colliſione, ſunt inverſe ut corporum maſſæ, licet & </s> <s xml:id="echoid-s6906" xml:space="preserve">aliâ a-<lb/>ctione eodem tempore unius motus mutetur.</s> <s xml:id="echoid-s6907" xml:space="preserve"/> </p> <div xml:id="echoid-div966" type="float" level="2" n="16"> <note symbol="*" position="right" xlink:label="note-0251-03" xlink:href="note-0251-03a" xml:space="preserve">512.</note> <note position="right" xlink:label="note-0251-04" xlink:href="note-0251-04a" xml:space="preserve">627</note> </div> <p> <s xml:id="echoid-s6908" xml:space="preserve">Si nunc concipiamus corpora perfectè elaſtica, hæc in <lb/> <anchor type="note" xlink:label="note-0251-05a" xlink:href="note-0251-05"/> nave memoratâ, ſolâ elaſterii actione moventur, & </s> <s xml:id="echoid-s6909" xml:space="preserve">à ſe in-<lb/>vicem recedunt iiſdem celeritatibus, & </s> <s xml:id="echoid-s6910" xml:space="preserve">viribus, quibus ad <lb/>ſe invicem acceſſere; </s> <s xml:id="echoid-s6911" xml:space="preserve">in hoc enim caſu ſingula elaſteria, <lb/>quæ, dum relaxantur, vires generant æquales illis, quibus, <pb o="176" file="0252" n="275" rhead="PHYSICES ELEMENTA"/> fuere flexa <anchor type="note" xlink:href="" symbol="*"/>, deſideratam, ut hunc præſtent effectum, pati- <anchor type="note" xlink:label="note-0252-01a" xlink:href="note-0252-01"/> untur reſiſtentiam, æqualem nempe illi, quam in inflexione <lb/>paſſa ſunt, nam eodem modo corpus reſiſtit, dum certam a-<lb/>mittit vim & </s> <s xml:id="echoid-s6912" xml:space="preserve">dum eandem acquirit.</s> <s xml:id="echoid-s6913" xml:space="preserve"/> </p> <div xml:id="echoid-div967" type="float" level="2" n="17"> <note position="right" xlink:label="note-0251-05" xlink:href="note-0251-05a" xml:space="preserve">628</note> <note symbol="*" position="left" xlink:label="note-0252-01" xlink:href="note-0252-01a" xml:space="preserve">557.</note> </div> <p> <s xml:id="echoid-s6914" xml:space="preserve">Unde generalem hanc deducimus concluſionem, mutationem <lb/> <anchor type="note" xlink:label="note-0252-02a" xlink:href="note-0252-02"/> in velocitate, in impactione corporum elaſticorum quorumcun-<lb/>que, reſpectu ſingulorum duplam eſſe illius quæ in eodem in-<lb/>curſu, datis corporibus non elaſticis, locum baberet: </s> <s xml:id="echoid-s6915" xml:space="preserve">ideo <lb/>regulæ n 567. </s> <s xml:id="echoid-s6916" xml:space="preserve">568. </s> <s xml:id="echoid-s6917" xml:space="preserve">& </s> <s xml:id="echoid-s6918" xml:space="preserve">hìc applicari poſſunt.</s> <s xml:id="echoid-s6919" xml:space="preserve"/> </p> <div xml:id="echoid-div968" type="float" level="2" n="18"> <note position="left" xlink:label="note-0252-02" xlink:href="note-0252-02a" xml:space="preserve">629</note> </div> <p> <s xml:id="echoid-s6920" xml:space="preserve">In demonſtratione hac ponimus actione mutua duorum <lb/> <anchor type="note" xlink:label="note-0252-03a" xlink:href="note-0252-03"/> corporum ut A & </s> <s xml:id="echoid-s6921" xml:space="preserve">Belaſticas horum corporum partes tantum <lb/> <anchor type="note" xlink:label="note-0252-04a" xlink:href="note-0252-04"/> intropremi, id eſt, illud tantum flecti elaſterium quod da-<lb/>tur inter hæc corpora ubi in a, b, concurrunt nullamque <lb/>hujus actionis partem transferri ad inflectendas partes elaſti-<lb/>cas inter b & </s> <s xml:id="echoid-s6922" xml:space="preserve">c.</s> <s xml:id="echoid-s6923" xml:space="preserve"/> </p> <div xml:id="echoid-div969" type="float" level="2" n="19"> <note position="left" xlink:label="note-0252-03" xlink:href="note-0252-03a" xml:space="preserve">630</note> <note position="left" xlink:label="note-0252-04" xlink:href="note-0252-04a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig 4.</note> </div> <p> <s xml:id="echoid-s6924" xml:space="preserve">Hæc ſic ſeſe revera haberi ſequi videtur ex ſubitâ admo-<lb/>dum partium elaſticarum inflexione & </s> <s xml:id="echoid-s6925" xml:space="preserve">inſtauratione, quam <lb/>ſuperius demonſtravimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6926" xml:space="preserve"> <anchor type="note" xlink:label="note-0252-05a" xlink:href="note-0252-05"/> </s> </p> <div xml:id="echoid-div970" type="float" level="2" n="20"> <note symbol="*" position="left" xlink:label="note-0252-05" xlink:href="note-0252-05a" xml:space="preserve">583. 584.</note> </div> <p> <s xml:id="echoid-s6927" xml:space="preserve">Si autem concipiamus partes lentius intropremi, ut in-<lb/>tropremuntur partes corporum mollium non ſeparantur cor-<lb/>pora elaſtica, ut ad ſe mutuo acceſſere, & </s> <s xml:id="echoid-s6928" xml:space="preserve">difficilior eſt mo-<lb/>tus determinatio.</s> <s xml:id="echoid-s6929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6930" xml:space="preserve">In concurſu trium Corporum mollium A, B, & </s> <s xml:id="echoid-s6931" xml:space="preserve">C, eodemmo-<lb/> <anchor type="note" xlink:label="note-0252-06a" xlink:href="note-0252-06"/> mento ad ſe mutuo accedentium, introceſſiones ſunt æquales <lb/>inter a & </s> <s xml:id="echoid-s6932" xml:space="preserve">b & </s> <s xml:id="echoid-s6933" xml:space="preserve">inter b & </s> <s xml:id="echoid-s6934" xml:space="preserve">c, licet actiones ſint inæquales; </s> <s xml:id="echoid-s6935" xml:space="preserve">nam <lb/>dum, Cagit in B, ſi hæc actio, actionem ſuperet quam A in B <lb/>ad partem oppoſitam exerit non modo c intropremit partes <lb/>inter b & </s> <s xml:id="echoid-s6936" xml:space="preserve">c; </s> <s xml:id="echoid-s6937" xml:space="preserve">ſed & </s> <s xml:id="echoid-s6938" xml:space="preserve">premit, in b ita ut augeatur actio in-<lb/>ter b & </s> <s xml:id="echoid-s6939" xml:space="preserve">a; </s> <s xml:id="echoid-s6940" xml:space="preserve">quareactione mutua corporum c & </s> <s xml:id="echoid-s6941" xml:space="preserve">b, non modo <lb/>partes inter hæc corpora intropremuntur, ſed & </s> <s xml:id="echoid-s6942" xml:space="preserve">augetur <lb/>introceſſio partium inter a & </s> <s xml:id="echoid-s6943" xml:space="preserve">c, & </s> <s xml:id="echoid-s6944" xml:space="preserve">hæc actio diſpergitur ita, <lb/>ut b, quod inter a & </s> <s xml:id="echoid-s6945" xml:space="preserve">c quieſcit, æqualiter ab utraque par-<lb/>te prematur; </s> <s xml:id="echoid-s6946" xml:space="preserve">quare ab utraque parte, introceſſiones ſi æque <lb/>facile partes introcedant, æquales ſunt; </s> <s xml:id="echoid-s6947" xml:space="preserve">ſumma vero cavi-<lb/>tatum ambarum ſequitur proportionem vis deſtructæ in his <lb/>formandis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6948" xml:space="preserve"> <anchor type="note" xlink:label="note-0252-07a" xlink:href="note-0252-07"/> </s> </p> <div xml:id="echoid-div971" type="float" level="2" n="21"> <note position="left" xlink:label="note-0252-06" xlink:href="note-0252-06a" xml:space="preserve">631</note> <note symbol="*" position="left" xlink:label="note-0252-07" xlink:href="note-0252-07a" xml:space="preserve">464. 488.</note> </div> <pb o="177" file="0253" n="276" rhead="MATHEMATICA. LIB. I. CAP. XXVII."/> </div> <div xml:id="echoid-div973" type="section" level="1" n="241"> <head xml:id="echoid-head341" xml:space="preserve"><emph style="sc">Experimentum</emph>. 1</head> <p> <s xml:id="echoid-s6949" xml:space="preserve">Suſpendatur Globus ex argillâ molli ita, ut reſpondeat me-<lb/>dio Machinæ n. </s> <s xml:id="echoid-s6950" xml:space="preserve">491. </s> <s xml:id="echoid-s6951" xml:space="preserve">tranſmiſſo filo per foramen medium f <lb/>(Tab. </s> <s xml:id="echoid-s6952" xml:space="preserve">18. </s> <s xml:id="echoid-s6953" xml:space="preserve">fig. </s> <s xml:id="echoid-s6954" xml:space="preserve">2.) </s> <s xml:id="echoid-s6955" xml:space="preserve">ad latera hujus duo ſuſpendantur cylin-<lb/>dri D & </s> <s xml:id="echoid-s6956" xml:space="preserve">F, (Tab. </s> <s xml:id="echoid-s6957" xml:space="preserve">18. </s> <s xml:id="echoid-s6958" xml:space="preserve">fig. </s> <s xml:id="echoid-s6959" xml:space="preserve">4.) </s> <s xml:id="echoid-s6960" xml:space="preserve">adhibitis uncis YY, loco <lb/>uncorum V, V, (fig. </s> <s xml:id="echoid-s6961" xml:space="preserve">2.) </s> <s xml:id="echoid-s6962" xml:space="preserve">Quieſcente globo, in hunc di-<lb/>mittantur, eodem momento, cylindri, major ve-<lb/>locitate quinque, & </s> <s xml:id="echoid-s6963" xml:space="preserve">alter velocitate decem, quæ <lb/>velocitates ſunt inversè ut maſſæ, in qua ratione et-<lb/>iam ſunt vires <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s6964" xml:space="preserve">poſt ictum tria corpora quieſcunt & </s> <s xml:id="echoid-s6965" xml:space="preserve">ca- vitates ab utraque parte ſunt æquales. </s> <s xml:id="echoid-s6966" xml:space="preserve">Inæquales eſſe ca-<lb/>vitates ſi corpora hæc ipſa eodem modo mota impingant in <lb/> <anchor type="note" xlink:label="note-0253-01a" xlink:href="note-0253-01"/> obicem fixum ſuperius vidimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s6967" xml:space="preserve"/> </p> <div xml:id="echoid-div973" type="float" level="2" n="1"> <note position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>503.</note> </div> <p> <s xml:id="echoid-s6968" xml:space="preserve">In hoc experimento vis majoris cylindri habetur multi-<lb/>plicando maſſam quatuor per quadratum velocitatis viginti <lb/>quinque <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s6969" xml:space="preserve">eſt 100; </s> <s xml:id="echoid-s6970" xml:space="preserve">eodem modo vis alîus cylindri de- <anchor type="note" xlink:label="note-0253-02a" xlink:href="note-0253-02"/> tegitur 200.</s> <s xml:id="echoid-s6971" xml:space="preserve">, & </s> <s xml:id="echoid-s6972" xml:space="preserve">ſumma virium 300; </s> <s xml:id="echoid-s6973" xml:space="preserve">vis hæc ictu perit, & </s> <s xml:id="echoid-s6974" xml:space="preserve"><lb/>cum cavitates ſint æquales in utraque formanda conſu-<lb/>mitur vis 150. </s> <s xml:id="echoid-s6975" xml:space="preserve">quod experimento ſequenti confirma-<lb/>tur.</s> <s xml:id="echoid-s6976" xml:space="preserve"/> </p> <div xml:id="echoid-div974" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0253-02" xlink:href="note-0253-02a" xml:space="preserve">470.</note> </div> </div> <div xml:id="echoid-div976" type="section" level="1" n="242"> <head xml:id="echoid-head342" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s6977" xml:space="preserve">Iiſdem poſitis quæ in experimento primo, tollatur cy-<lb/> <anchor type="note" xlink:label="note-0253-03a" xlink:href="note-0253-03"/> lindrus major & </s> <s xml:id="echoid-s6978" xml:space="preserve">in ipſius locum ſuſpendatur cylindrus minori <lb/>ſimilis & </s> <s xml:id="echoid-s6979" xml:space="preserve">æqualis. </s> <s xml:id="echoid-s6980" xml:space="preserve">Si globus paululum convertatur & </s> <s xml:id="echoid-s6981" xml:space="preserve">in <lb/>hunc cylindri ambo dimittantur velocitate 8 {2/3}, poſt ictum <lb/>corpora quieſcunt, & </s> <s xml:id="echoid-s6982" xml:space="preserve">cavitates erunt æquales inter ſe, & </s> <s xml:id="echoid-s6983" xml:space="preserve"><lb/>illis quæ in primo experimento formatæ ſunt. </s> <s xml:id="echoid-s6984" xml:space="preserve">Cum vires <lb/>ſint æquales & </s> <s xml:id="echoid-s6985" xml:space="preserve">cavitates æquales, corpus utrumque ſuam <lb/>format cavitatem, vis autem quæ conſumitur habetur multi-<lb/>plicando maſſam duo per quadratum velocitatis 75 {1/9}, & </s> <s xml:id="echoid-s6986" xml:space="preserve">eſt <lb/>150 {2/9}.</s> <s xml:id="echoid-s6987" xml:space="preserve"/> </p> <div xml:id="echoid-div976" type="float" level="2" n="1"> <note position="right" xlink:label="note-0253-03" xlink:href="note-0253-03a" xml:space="preserve">632.</note> </div> <p> <s xml:id="echoid-s6988" xml:space="preserve">Si nunc concipiamus partes elaſticas flecti, ut memo-<lb/> <anchor type="note" xlink:label="note-0253-04a" xlink:href="note-0253-04"/> ratorum corporum mollium partes introcedunt, inflexio in-<lb/> <anchor type="note" xlink:label="note-0253-05a" xlink:href="note-0253-05"/> ter a & </s> <s xml:id="echoid-s6989" xml:space="preserve">b æqualis erit illi quæ datur inter b & </s> <s xml:id="echoid-s6990" xml:space="preserve">c; </s> <s xml:id="echoid-s6991" xml:space="preserve">& </s> <s xml:id="echoid-s6992" xml:space="preserve">con-<lb/>ſideranda ſunt corpora quaſi ſeparata actione elaſterio-<lb/>rum duorum æquè potentium inter hæc poſitorum. </s> <s xml:id="echoid-s6993" xml:space="preserve">Quo- <pb o="178" file="0254" n="277" rhead="PHYSICES ELEMENTA"/> modo in hoc caſu ſeparatio determinetur in Scholio 2. <lb/></s> <s xml:id="echoid-s6994" xml:space="preserve">videbimus.</s> <s xml:id="echoid-s6995" xml:space="preserve"/> </p> <div xml:id="echoid-div977" type="float" level="2" n="2"> <note position="right" xlink:label="note-0253-04" xlink:href="note-0253-04a" xml:space="preserve">633.</note> <note position="right" xlink:label="note-0253-05" xlink:href="note-0253-05a" xml:space="preserve"><emph style="sc">TA. XXV.</emph> <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s6996" xml:space="preserve">Quomodo duo corpora, directionibus diverſis mota, in <lb/>tertium eodem momento directè incurrentia hoc agitent, <lb/>etiam explicabimus.</s> <s xml:id="echoid-s6997" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6998" xml:space="preserve">Dentur corporaA,B, directè eodem momento, velocitatibus <lb/> <anchor type="note" xlink:label="note-0254-01a" xlink:href="note-0254-01"/> quibuſcunque, incurrentia in corpus quieſcens C, directio-<lb/> <anchor type="note" xlink:label="note-0254-02a" xlink:href="note-0254-02"/> nibus AK, BK. </s> <s xml:id="echoid-s6999" xml:space="preserve">Productis hiſce directionibus, ſint KD velo-<lb/>citas corporis A, & </s> <s xml:id="echoid-s7000" xml:space="preserve">KE corporis B celeritas; </s> <s xml:id="echoid-s7001" xml:space="preserve">erigantur <lb/>D Fad K D normalis, & </s> <s xml:id="echoid-s7002" xml:space="preserve">EG cum K E angulum rectum <lb/>efficiens; </s> <s xml:id="echoid-s7003" xml:space="preserve">dividatur KD in H ita, ut KH ſe habeat ad <lb/>HD, ut maſſa corporis A ad maſſam C; </s> <s xml:id="echoid-s7004" xml:space="preserve">eodem modo di-<lb/>videnda eſt KE in L, ut KL ſit LE; </s> <s xml:id="echoid-s7005" xml:space="preserve">ut maſſa B ad maſ-<lb/>ſam C. </s> <s xml:id="echoid-s7006" xml:space="preserve">Ductis nunc F H, GL, ſeſe mutuo interſecanti-<lb/>bus in N, linea K N ſitu directionem, & </s> <s xml:id="echoid-s7007" xml:space="preserve">longitudine velo-<lb/>citatem, demonſtrabit corporis C poſt ictum.</s> <s xml:id="echoid-s7008" xml:space="preserve"/> </p> <div xml:id="echoid-div978" type="float" level="2" n="3"> <note position="left" xlink:label="note-0254-01" xlink:href="note-0254-01a" xml:space="preserve">634.</note> <note position="left" xlink:label="note-0254-02" xlink:href="note-0254-02a" xml:space="preserve"><emph style="sc">TA. XXV.</emph> <lb/>fig 6.7.</note> </div> <p> <s xml:id="echoid-s7009" xml:space="preserve">Corpora autem A & </s> <s xml:id="echoid-s7010" xml:space="preserve">B in lineis K D, K E, motum con-<lb/>tinuant, cum nullâ actione horum directio mutari poſſit. <lb/></s> <s xml:id="echoid-s7011" xml:space="preserve">Velocitates verò determinantur dimiſſis ex N ad KD & </s> <s xml:id="echoid-s7012" xml:space="preserve">KE <lb/>perpendicularibus NI, NM; </s> <s xml:id="echoid-s7013" xml:space="preserve">eſtque KI corporis A, & </s> <s xml:id="echoid-s7014" xml:space="preserve"><lb/>K M corporis B velocitas poſt ictum.</s> <s xml:id="echoid-s7015" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7016" xml:space="preserve">Nulla datur actio qua corpora A & </s> <s xml:id="echoid-s7017" xml:space="preserve">Cin ictu directo, cum <lb/> <anchor type="note" xlink:label="note-0254-03a" xlink:href="note-0254-03"/> non ſint elaſtica, ſeparari poſſint <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7018" xml:space="preserve">& </s> <s xml:id="echoid-s7019" xml:space="preserve">licet actione corpo- <anchor type="note" xlink:label="note-0254-04a" xlink:href="note-0254-04"/> ris B moveatur corpus C, eo quidem minuitur actio corpo-<lb/>ris A, ſed non C ab A juxta directionem KD ſeparat; </s> <s xml:id="echoid-s7020" xml:space="preserve">tunc <lb/>enim C ab actione ipſius A ſubduceret; </s> <s xml:id="echoid-s7021" xml:space="preserve">ergo poſt ictum A <lb/>& </s> <s xml:id="echoid-s7022" xml:space="preserve">C eadem velocitate moventur juxta directionem K D; <lb/></s> <s xml:id="echoid-s7023" xml:space="preserve">idcirco ſi C percurrit AN, velocitate quam hac lineâ ex-<lb/>primimus, movebitur A velocitate KI; </s> <s xml:id="echoid-s7024" xml:space="preserve">motus enim per KN, <lb/>juxta directionem K D, nil continet præter velocitatem <lb/>KI <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7025" xml:space="preserve">& </s> <s xml:id="echoid-s7026" xml:space="preserve">corpus A amittet velocitatem DI.</s> <s xml:id="echoid-s7027" xml:space="preserve"/> </p> <div xml:id="echoid-div979" type="float" level="2" n="4"> <note position="left" xlink:label="note-0254-03" xlink:href="note-0254-03a" xml:space="preserve">635.</note> <note symbol="*" position="left" xlink:label="note-0254-04" xlink:href="note-0254-04a" xml:space="preserve">484.</note> </div> <note symbol="*" position="left" xml:space="preserve">603.</note> <p> <s xml:id="echoid-s7028" xml:space="preserve">Ulterius ad hoc debemus attendere, ductis lineis <lb/>NO, NP, parallelis KE & </s> <s xml:id="echoid-s7029" xml:space="preserve">KD, corpus C impactucor-<lb/>porum A & </s> <s xml:id="echoid-s7030" xml:space="preserve">B eodem tempore juxta directiones K O & </s> <s xml:id="echoid-s7031" xml:space="preserve"><lb/>KP propelli, & </s> <s xml:id="echoid-s7032" xml:space="preserve">quidem velocitatibus hiſce lineis propor- <pb o="179" file="0255" n="278" rhead="MATHEMATICA. LIB. I. CAP XXVII."/> tionalibus, ſi per KN, velocitate KN moveatur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7033" xml:space="preserve">mu- <anchor type="note" xlink:label="note-0255-01a" xlink:href="note-0255-01"/> tatio in velocitate corporis quieſcentis C, ex actione cor-<lb/>poris <emph style="sc">A</emph> erit KO; </s> <s xml:id="echoid-s7034" xml:space="preserve">ergo KO ad ID, ſi N ritè ſit determi-<lb/>natum, ut maſſa <emph style="sc">A</emph> ad maſſam C <anchor type="note" xlink:href="" symbol="*"/>, id eſt ut KH ad HD, <anchor type="note" xlink:label="note-0255-02a" xlink:href="note-0255-02"/> quod tantum obtinet ſi punctum N detur in FH; </s> <s xml:id="echoid-s7035" xml:space="preserve">produ-<lb/>cta enim PN donec ſecet FD in Q, habemus PN ad NQ, <lb/>ut KH ad HD, ſed PN æqualis eſt KO, & </s> <s xml:id="echoid-s7036" xml:space="preserve">NQ ipſi ID <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7037" xml:space="preserve"> <anchor type="note" xlink:label="note-0255-03a" xlink:href="note-0255-03"/> Eodem modo demonſtramus quæſitum punctum N dari in <lb/>linea GL; </s> <s xml:id="echoid-s7038" xml:space="preserve">ideoque in interſectione hujus lineæ cum linea <lb/>FH. </s> <s xml:id="echoid-s7039" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s7040" xml:space="preserve"/> </p> <div xml:id="echoid-div980" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0255-01" xlink:href="note-0255-01a" xml:space="preserve">246.</note> <note symbol="*" position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">6271.</note> <note symbol="*" position="right" xlink:label="note-0255-03" xlink:href="note-0255-03a" xml:space="preserve">34. El. 1.</note> </div> <p> <s xml:id="echoid-s7041" xml:space="preserve">Si corpora ſint elaſtica, mutationes velocitatum duplæ <lb/> <anchor type="note" xlink:label="note-0255-04a" xlink:href="note-0255-04"/> ſunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7042" xml:space="preserve">ergo ſi producatur & </s> <s xml:id="echoid-s7043" xml:space="preserve">duplicetur KN, habebimus <anchor type="note" xlink:label="note-0255-05a" xlink:href="note-0255-05"/> motum corporis C per K n, velocitate K n; </s> <s xml:id="echoid-s7044" xml:space="preserve">& </s> <s xml:id="echoid-s7045" xml:space="preserve">ſumtis, I i <lb/>ipſi l D, & </s> <s xml:id="echoid-s7046" xml:space="preserve">M m lineæ ME, æqualibus, habebimus K i & </s> <s xml:id="echoid-s7047" xml:space="preserve"><lb/>K m corporum A & </s> <s xml:id="echoid-s7048" xml:space="preserve">B velocitates. </s> <s xml:id="echoid-s7049" xml:space="preserve">In hoc caſu ſummæ viri-<lb/> <anchor type="note" xlink:label="note-0255-06a" xlink:href="note-0255-06"/> um ante & </s> <s xml:id="echoid-s7050" xml:space="preserve">poſt ictum ſunt æquales <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7051" xml:space="preserve">quod etiam ex hac ve- <anchor type="note" xlink:label="note-0255-07a" xlink:href="note-0255-07"/> locitatum determinatione ſequi in Scholio 3. </s> <s xml:id="echoid-s7052" xml:space="preserve">demonſtrabi-<lb/>mus.</s> <s xml:id="echoid-s7053" xml:space="preserve"/> </p> <div xml:id="echoid-div981" type="float" level="2" n="6"> <note position="right" xlink:label="note-0255-04" xlink:href="note-0255-04a" xml:space="preserve">636.</note> <note symbol="*" position="right" xlink:label="note-0255-05" xlink:href="note-0255-05a" xml:space="preserve">629.</note> <note position="right" xlink:label="note-0255-06" xlink:href="note-0255-06a" xml:space="preserve">637.</note> <note symbol="*" position="right" xlink:label="note-0255-07" xlink:href="note-0255-07a" xml:space="preserve">558.</note> </div> <p> <s xml:id="echoid-s7054" xml:space="preserve">Quando angulus EKG eſt obtuſus cum corporum A & </s> <s xml:id="echoid-s7055" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0255-08a" xlink:href="note-0255-08"/> B motus pro parte contrarii ſint & </s> <s xml:id="echoid-s7056" xml:space="preserve">hîc referri debent quæ <lb/>in n. </s> <s xml:id="echoid-s7057" xml:space="preserve">630. </s> <s xml:id="echoid-s7058" xml:space="preserve">notata fuere.</s> <s xml:id="echoid-s7059" xml:space="preserve"/> </p> <div xml:id="echoid-div982" type="float" level="2" n="7"> <note position="right" xlink:label="note-0255-08" xlink:href="note-0255-08a" xml:space="preserve">638.</note> </div> <p> <s xml:id="echoid-s7060" xml:space="preserve">Difficile admodum eſt demonſtrata hæc experimentis con-<lb/> <anchor type="note" xlink:label="note-0255-09a" xlink:href="note-0255-09"/> firmare. </s> <s xml:id="echoid-s7061" xml:space="preserve">Experimenta circa corpora non elaſtica inſtitui non <lb/>poſſunt, quia globi ex argillâ ſi omni elaſterio deſtituantur, quod <lb/>in experimentis deſideratur, poſtictum cohærent inter ſe; </s> <s xml:id="echoid-s7062" xml:space="preserve">& </s> <s xml:id="echoid-s7063" xml:space="preserve"><lb/>præterea quod etiam in corporibus elaſticis locum habet <lb/>nunquam certi ſumus an exactiſſimè eodem momento ambo <lb/>corpora incurrant, de quo, ubi agitur de deferentiâ mini-<lb/>mâ, niſi ex viâ quam ſequitur corpus C judicium ferre non <lb/>poſſumus, quæ ergo experimento determinari nequit. </s> <s xml:id="echoid-s7064" xml:space="preserve">In eo <lb/>ſolo caſu in quo corpora A & </s> <s xml:id="echoid-s7065" xml:space="preserve">B ſunt æqualia, & </s> <s xml:id="echoid-s7066" xml:space="preserve">æqualibus <lb/>velocitatibus mota, primo intuitu patet corpora hæc eodem <lb/>momento in C impegiſſe, ſi hujus via angulum DKE in duas <lb/>partes æquales dividat: </s> <s xml:id="echoid-s7067" xml:space="preserve">de hoc caſu ſequens inſtitui poteſt <lb/>experimentum.</s> <s xml:id="echoid-s7068" xml:space="preserve"/> </p> <div xml:id="echoid-div983" type="float" level="2" n="8"> <note position="right" xlink:label="note-0255-09" xlink:href="note-0255-09a" xml:space="preserve">639.</note> </div> <pb o="180" file="0256" n="279" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div985" type="section" level="1" n="243"> <head xml:id="echoid-head343" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s7069" xml:space="preserve">Sectio horizontalis Machinæ, in n. </s> <s xml:id="echoid-s7070" xml:space="preserve">615 deſcriptæ, hîc re-<lb/> <anchor type="note" xlink:label="note-0256-01a" xlink:href="note-0256-01"/> præſentatur, applicatis huic Machinæ tribus globis ebur-<lb/> <anchor type="note" xlink:label="note-0256-02a" xlink:href="note-0256-02"/> neis in deſcriptione memoratis. </s> <s xml:id="echoid-s7071" xml:space="preserve">Si corpora Q, Q, eodem <lb/>momento dimittantur ab æqualibus altitudinibus, & </s> <s xml:id="echoid-s7072" xml:space="preserve">forme-<lb/>tur parallelogrammum abcf cujus latera ab, ac, ſunt dire-<lb/>ctiones corporum Q, Q, continuatæ, & </s> <s xml:id="echoid-s7073" xml:space="preserve">æqualia ſubtenſis <lb/>arcuum per quos corpora Q, Q, deſcendunt; </s> <s xml:id="echoid-s7074" xml:space="preserve">corpus P, <lb/>ſi angulus QPQ ſit acutus minori adſcendit velocitate, quàm <lb/>qua adſcendendo poſſet percurrere arcum cujus ſubtenſa me-<lb/>morati parallelogrammi foret diagonalis.</s> <s xml:id="echoid-s7075" xml:space="preserve"/> </p> <div xml:id="echoid-div985" type="float" level="2" n="1"> <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">640.</note> <note position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve"><emph style="sc">TA XXIV.</emph> <lb/>fig. 4.5.</note> </div> <p> <s xml:id="echoid-s7076" xml:space="preserve">Poſito autem angulo obtuſo ad majorem adſcendit alti-<lb/>tudinem quam quæ diagonali parallelogrammi determina-<lb/>tur.</s> <s xml:id="echoid-s7077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7078" xml:space="preserve">Quæ cum explicatis in n. </s> <s xml:id="echoid-s7079" xml:space="preserve">634. </s> <s xml:id="echoid-s7080" xml:space="preserve">636. </s> <s xml:id="echoid-s7081" xml:space="preserve">conveniunt.</s> <s xml:id="echoid-s7082" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div987" type="section" level="1" n="244"> <head xml:id="echoid-head344" xml:space="preserve">SCHOLIUM 1.</head> <head xml:id="echoid-head345" xml:space="preserve">Demonſtrationes n. 623. 625. 626. 627.</head> <p> <s xml:id="echoid-s7083" xml:space="preserve">Dentur tria corpora A, B, C, directè in ſe mutuo impingentia, poſitâ pri-<lb/> <anchor type="note" xlink:label="note-0256-03a" xlink:href="note-0256-03"/> mi velocitate a, ſecundi b, tertii c, ſumma virium eſt A a a - B b b -<lb/>C c c <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7084" xml:space="preserve">ſi A & </s> <s xml:id="echoid-s7085" xml:space="preserve">B ad eandem partem & </s> <s xml:id="echoid-s7086" xml:space="preserve">C in contrariam tendant, ciximus in <anchor type="note" xlink:label="note-0256-04a" xlink:href="note-0256-04"/> n. </s> <s xml:id="echoid-s7087" xml:space="preserve">623. </s> <s xml:id="echoid-s7088" xml:space="preserve">ſummam hanc fore, datis velocitatibus reſpectivis omnium mini-<lb/>mam, ſi A a - B b = C c; </s> <s xml:id="echoid-s7089" xml:space="preserve">Quod ex quiete corporum poſt ictum, in n. </s> <s xml:id="echoid-s7090" xml:space="preserve">624. <lb/></s> <s xml:id="echoid-s7091" xml:space="preserve">demonſtrato, quidem ſequitur, ſed directè etiam probatur, ſi velocitatem <lb/>quamcunque concipiamus auctam aut diminutam quantitate quacunque ut x, <lb/>& </s> <s xml:id="echoid-s7092" xml:space="preserve">computatio ineatur de ſumma virium.</s> <s xml:id="echoid-s7093" xml:space="preserve"/> </p> <div xml:id="echoid-div987" type="float" level="2" n="1"> <note position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">641.</note> <note symbol="*" position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">470.</note> </div> <p> <s xml:id="echoid-s7094" xml:space="preserve">Sit Ex. </s> <s xml:id="echoid-s7095" xml:space="preserve">Gr. </s> <s xml:id="echoid-s7096" xml:space="preserve">Corporis A velocitas a - x; </s> <s xml:id="echoid-s7097" xml:space="preserve">ut ſerventur velocitates reſpecti-<lb/>væ movetur B velocitate b - x; </s> <s xml:id="echoid-s7098" xml:space="preserve">& </s> <s xml:id="echoid-s7099" xml:space="preserve">corporis C velocitas erit c - x. </s> <s xml:id="echoid-s7100" xml:space="preserve">ſumma <lb/>virium eſt A aa + 2A a x + A xx + B bb + 2B bx + B xx + C cc - 2C cx <lb/>+ C x x, quæ excedit primam quantitate A x x + B x x + C x x ſublatis 2A a x + <lb/>2 B b x - C c x quæ ſeſe mutuo deſtruunt; </s> <s xml:id="echoid-s7101" xml:space="preserve">cum autem exceſſus detur quo-<lb/>modocunque velocitates mutatas ſervatis velocitatibus reſpectivis, conci-<lb/>piamus, ſequitur ſummam in caſu memorato fuiſſe minimam.</s> <s xml:id="echoid-s7102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7103" xml:space="preserve">liſdem poſitis, velocitas reſpectiva corporum A & </s> <s xml:id="echoid-s7104" xml:space="preserve">B eſt a-b <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7105" xml:space="preserve">corporum <anchor type="note" xlink:label="note-0256-05a" xlink:href="note-0256-05"/> <anchor type="note" xlink:label="note-0256-06a" xlink:href="note-0256-06"/> A & </s> <s xml:id="echoid-s7106" xml:space="preserve">C eſt a + c <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7107" xml:space="preserve">& </s> <s xml:id="echoid-s7108" xml:space="preserve">tandem velocitas reſpectiva corporum B & </s> <s xml:id="echoid-s7109" xml:space="preserve">C valet <anchor type="note" xlink:label="note-0256-07a" xlink:href="note-0256-07"/> b + c <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7110" xml:space="preserve">Vis amiſſa datis hiſce velocitatibus reſpectivis valet ſummam vi- <anchor type="note" xlink:label="note-0256-08a" xlink:href="note-0256-08"/> rium in hoc caſu, in quo ſumma hæc eſt minima <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7111" xml:space="preserve">in quo A a + B b = C c.</s> <s xml:id="echoid-s7112" xml:space="preserve"> <anchor type="note" xlink:label="note-0256-09a" xlink:href="note-0256-09"/> Vim hanc amiſſam diximus æqualem eſſe <pb file="0257" n="280"/> <anchor type="figure" xlink:label="fig-0257-01a" xlink:href="fig-0257-01"/> <pb file="0257a" n="281"/> <pb file="0258" n="282"/> <pb o="181" file="0259" n="283" rhead="MATHEMATICA. LIB. I. CAP. XXVII."/> {ABx <emph style="ol">a-b</emph><emph style="super">2</emph> + ACx<emph style="ol">a + c</emph><emph style="super">2</emph> + BCx<emph style="ol">b + c</emph><emph style="super">2</emph>/A + B + C} <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7113" xml:space="preserve">Quod ut demonſtremus pto- <anchor type="note" xlink:label="note-0259-01a" xlink:href="note-0259-01"/> bandum quantitatem hanc æqualem eſſe A a a + B bb + C cc. </s> <s xml:id="echoid-s7114" xml:space="preserve">aut <lb/>{ABx<emph style="ol">a-b</emph><emph style="super">2</emph>/x A + B + C. </s> <s xml:id="echoid-s7115" xml:space="preserve">+ ACx<emph style="ol">a + c</emph><emph style="super">2</emph> + BCx<emph style="ol">b + c</emph><emph style="super">2</emph> = Aaa + Bbb + Ccc}</s> </p> <div xml:id="echoid-div988" type="float" level="2" n="2"> <note position="left" xlink:label="note-0256-05" xlink:href="note-0256-05a" xml:space="preserve">642.</note> <note symbol="*" position="left" xlink:label="note-0256-06" xlink:href="note-0256-06a" xml:space="preserve">474.</note> <note symbol="*" position="left" xlink:label="note-0256-07" xlink:href="note-0256-07a" xml:space="preserve">475.</note> <note symbol="*" position="left" xlink:label="note-0256-08" xlink:href="note-0256-08a" xml:space="preserve">475.</note> <note symbol="*" position="left" xlink:label="note-0256-09" xlink:href="note-0256-09a" xml:space="preserve">621.</note> <figure xlink:label="fig-0257-01" xlink:href="fig-0257-01a"> <image file="0257-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0257-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">625.</note> </div> <p> <s xml:id="echoid-s7116" xml:space="preserve">Quia A a + B b = C c etiam AA aa + 2AB ab + BB bb = CC cc = AC ac <lb/>+ BC bc unde deducimus AA aa + BB bb + CC cc = 2AC ac + 2BC bc <lb/>-2AB ab. </s> <s xml:id="echoid-s7117" xml:space="preserve">Sed multiplicatis A aa + B bb + C cc per A + B + C habemus <lb/>AA aa + BA aa + CA aa + AB bb + BB bb + CB bb + AC cc <lb/>BC cc + CC cc, & </s> <s xml:id="echoid-s7118" xml:space="preserve">ſubſtituendo pro AA aa + BB bb + CC cc <lb/>valorem detectum, habemus A aa + B bb + C cc x A + B + C = AB aa <lb/>-2AB ab + AB bb + AC aa + 2AC ac + AC cc + BC bb + <lb/>2BC bc + BC cc + ABx<emph style="ol">a-b</emph><emph style="super">2</emph> + ACx<emph style="ol">a + c</emph><emph style="super">2</emph> + BC<emph style="ol">b + c</emph><emph style="super">2</emph>. </s> <s xml:id="echoid-s7119" xml:space="preserve">Quod <lb/>demonſtrandum erat.</s> <s xml:id="echoid-s7120" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7121" xml:space="preserve">Sint iterum tria corpora A, B, C; </s> <s xml:id="echoid-s7122" xml:space="preserve">velocitas primi m; </s> <s xml:id="echoid-s7123" xml:space="preserve">ſecundi n; </s> <s xml:id="echoid-s7124" xml:space="preserve">& </s> <s xml:id="echoid-s7125" xml:space="preserve">tertii p. <lb/></s> <s xml:id="echoid-s7126" xml:space="preserve"> <anchor type="note" xlink:label="note-0259-02a" xlink:href="note-0259-02"/> Ut regulam n. </s> <s xml:id="echoid-s7127" xml:space="preserve">626. </s> <s xml:id="echoid-s7128" xml:space="preserve">demonſtremus, dicimus x velocitatem navis ibi <lb/>memoratæ & </s> <s xml:id="echoid-s7129" xml:space="preserve">velocitates corporum A & </s> <s xml:id="echoid-s7130" xml:space="preserve">B in nave, ſi concipiamus hæc i-<lb/>pſâ nave celerius ferri, erunt m-x & </s> <s xml:id="echoid-s7131" xml:space="preserve">n-x; </s> <s xml:id="echoid-s7132" xml:space="preserve">C vero, ſi hoc nave lentius mo-<lb/>veatur, in hac in contrariam partem fertur velocitate x-p. </s> <s xml:id="echoid-s7133" xml:space="preserve">Cum agatur de <lb/>caſu in quo poſt ictum corpora quieſcunt habemus A m-A x + B n-B x <lb/>= C x-C p <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7134" xml:space="preserve"/> </p> <div xml:id="echoid-div989" type="float" level="2" n="3"> <note position="right" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">643.</note> </div> <note symbol="*" position="right" xml:space="preserve">622. 615. <lb/>641.</note> <p> <s xml:id="echoid-s7135" xml:space="preserve">Unde deducimus x = {Am + Bn + Cp/A + B + C}. </s> <s xml:id="echoid-s7136" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s7137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7138" xml:space="preserve">Si non omnia corpora ad eandem partem tendant illorum quæ in con-<lb/>trariam partem feruntur velocitates ſunt negativæ & </s> <s xml:id="echoid-s7139" xml:space="preserve">producta in numeratore <lb/>negativa.</s> <s xml:id="echoid-s7140" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7141" xml:space="preserve">Ponamus ut in præcedentibus demonſtrationibus corpora A, B, & </s> <s xml:id="echoid-s7142" xml:space="preserve">C, & </s> <s xml:id="echoid-s7143" xml:space="preserve">con-<lb/> <anchor type="note" xlink:label="note-0259-04a" xlink:href="note-0259-04"/> cipiamus hæc ad eandem partem ferri ita, ut in nave, quæ movetur ea velo-<lb/> <anchor type="note" xlink:label="note-0259-05a" xlink:href="note-0259-05"/> citate qua corpora poſt ictum agitantur, velocitates corporum A & </s> <s xml:id="echoid-s7144" xml:space="preserve">B à pup-<lb/>pi ad proram ſint f h, g i, corporis C velocitas à prorâ ad puppim l i. </s> <s xml:id="echoid-s7145" xml:space="preserve">In <lb/>hoc caſu corpus ſolum C lentius nave movetur, & </s> <s xml:id="echoid-s7146" xml:space="preserve">actione amborum alio-<lb/>rum acceleratur. </s> <s xml:id="echoid-s7147" xml:space="preserve">Cum in nave corpora poſt ictum quieſcant ſumma pro <lb/>ductorum A per f b, & </s> <s xml:id="echoid-s7148" xml:space="preserve">B per g i, valet C per l i <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7149" xml:space="preserve"/> </p> <div xml:id="echoid-div990" type="float" level="2" n="4"> <note position="right" xlink:label="note-0259-04" xlink:href="note-0259-04a" xml:space="preserve">644.</note> <note position="right" xlink:label="note-0259-05" xlink:href="note-0259-05a" xml:space="preserve"><emph style="sc">TAB. XXV</emph> <lb/>fig. 4.</note> </div> <note symbol="*" position="right" xml:space="preserve">622. 623.</note> <note position="right" xml:space="preserve">641.</note> <p> <s xml:id="echoid-s7150" xml:space="preserve">Diviſo C in duas partes D & </s> <s xml:id="echoid-s7151" xml:space="preserve">E, ut ſupra <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7152" xml:space="preserve">quæ ſint inter ſe ut A per fh <anchor type="note" xlink:label="note-0259-08a" xlink:href="note-0259-08"/> <anchor type="note" xlink:label="note-0259-09a" xlink:href="note-0259-09"/> ad B per g i, ſi A agat in D, & </s> <s xml:id="echoid-s7153" xml:space="preserve">B in E, etiam corpora in nave quieſcunt <anchor type="note" xlink:href="" symbol="*"/>, id eſt; </s> <s xml:id="echoid-s7154" xml:space="preserve">conſiderando motus abſolutos, non attendendo ad navem, agitatis <lb/> <anchor type="note" xlink:label="note-0259-10a" xlink:href="note-0259-10"/> D & </s> <s xml:id="echoid-s7155" xml:space="preserve">E ante ictum æqualibus velocitatibus, & </s> <s xml:id="echoid-s7156" xml:space="preserve">æqualiter accelerantur hæc <lb/>actionibus corporum A & </s> <s xml:id="echoid-s7157" xml:space="preserve">B, quantitate nempe i l & </s> <s xml:id="echoid-s7158" xml:space="preserve">vires iis communican-<lb/>tur quæ ſunt inter ſe ut maſſæ D & </s> <s xml:id="echoid-s7159" xml:space="preserve">E <anchor type="note" xlink:href="" symbol="*"/>, id eſt, ut producta A per f b & </s> <s xml:id="echoid-s7160" xml:space="preserve">B <anchor type="note" xlink:label="note-0259-11a" xlink:href="note-0259-11"/> per g i. </s> <s xml:id="echoid-s7161" xml:space="preserve">Unde ſequitur, in colliſione trium horum corporum, actiones cor-<lb/> <anchor type="note" xlink:label="note-0259-12a" xlink:href="note-0259-12"/> porum A & </s> <s xml:id="echoid-s7162" xml:space="preserve">B in C, dum ſimul accelerant motum hujus corporis, eſſe in-<lb/>ter ſe ut A per f b & </s> <s xml:id="echoid-s7163" xml:space="preserve">B per g i, in qua ratione ſunt etiam velocitates, quæ <lb/>hiſce actionibus corpori C communicantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7164" xml:space="preserve"/> </p> <div xml:id="echoid-div991" type="float" level="2" n="5"> <note position="right" xlink:label="note-0259-08" xlink:href="note-0259-08a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0259-09" xlink:href="note-0259-09a" xml:space="preserve">624.</note> <note symbol="*" position="right" xlink:label="note-0259-10" xlink:href="note-0259-10a" xml:space="preserve">624.</note> <note symbol="*" position="right" xlink:label="note-0259-11" xlink:href="note-0259-11a" xml:space="preserve">450.</note> <note position="right" xlink:label="note-0259-12" xlink:href="note-0259-12a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig. 4.</note> </div> <note symbol="*" position="right" xml:space="preserve">199.</note> <p> <s xml:id="echoid-s7165" xml:space="preserve">Diviſâ integrâ velocitate communicatâ i l in duas partes i m, m l, quæ ſint <pb o="182" file="0260" n="284" rhead="PHYSICES ELEMENTA"/> inter ſeut A per f b ad B per g i, erit i m velocitas communicata actione cor-<lb/>poris A.</s> <s xml:id="echoid-s7166" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7167" xml:space="preserve">Multiplicando i m & </s> <s xml:id="echoid-s7168" xml:space="preserve">m l per C, quo ratio non mutatur, habemus i m per <lb/>C ad m l per C, ut A per f b ad B per g i; </s> <s xml:id="echoid-s7169" xml:space="preserve">unde deducimus i m per C plus <lb/>m l per C, id eſt C per i l, ad i m per C, ut A per f b plus B per g i ad Aper <lb/>f b: </s> <s xml:id="echoid-s7170" xml:space="preserve">antecedentia autem ſunt æqualia ergo & </s> <s xml:id="echoid-s7171" xml:space="preserve">conſequentia.</s> <s xml:id="echoid-s7172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7173" xml:space="preserve">Idcirco A ad C. </s> <s xml:id="echoid-s7174" xml:space="preserve">ut i m mutatio velocitatis in corpore C ex actione cor-<lb/>poris A, ad f b mutationem in velocitate corporis A. </s> <s xml:id="echoid-s7175" xml:space="preserve">Id eſt, mutationes <lb/>in velocitatibus horum corporum oriundæ ex actione mutua in colliſione. <lb/></s> <s xml:id="echoid-s7176" xml:space="preserve">ſunt inverſè ut maſſæ, ut hoc notavimus in num. </s> <s xml:id="echoid-s7177" xml:space="preserve">627.</s> <s xml:id="echoid-s7178" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div993" type="section" level="1" n="245"> <head xml:id="echoid-head346" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head347" xml:space="preserve">Inveſtigatio motus memorati in n. 633.</head> <p> <s xml:id="echoid-s7179" xml:space="preserve">Concipiamus tria corpora A, B, C, perfecte elaſtica; </s> <s xml:id="echoid-s7180" xml:space="preserve">ſit primi velocitas m, <lb/> <anchor type="note" xlink:label="note-0260-01a" xlink:href="note-0260-01"/> ſecundi n; </s> <s xml:id="echoid-s7181" xml:space="preserve">tertii p; </s> <s xml:id="echoid-s7182" xml:space="preserve">tendant hæc ad eandem partem: </s> <s xml:id="echoid-s7183" xml:space="preserve">Poſt ictum ante in-<lb/>ſtauratam figuram velocitas eſt {Am + Bn + Cp/A + B + C} <anchor type="note" xlink:href="" symbol="*"/>, dicatur hæc v.</s> <s xml:id="echoid-s7184" xml:space="preserve"/> </p> <div xml:id="echoid-div993" type="float" level="2" n="1"> <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">645.</note> </div> <note symbol="*" position="left" xml:space="preserve">626. 643.</note> <p> <s xml:id="echoid-s7185" xml:space="preserve">Vis ictu deſtructa eſt {ABx<emph style="ol">m-n</emph><emph style="super">2</emph> + ACx<emph style="ol">m-p</emph><emph style="super">2</emph> + BCx<emph style="ol">n-p</emph><emph style="super">2</emph>/A + B + C} <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0260-03a" xlink:href="note-0260-03"/> Sit hæc æqualis 2Aff + 2Bff + 2Cff.</s> <s xml:id="echoid-s7186" xml:space="preserve"/> </p> <div xml:id="echoid-div994" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0260-03" xlink:href="note-0260-03a" xml:space="preserve">625. 641.</note> </div> <p> <s xml:id="echoid-s7187" xml:space="preserve">Si non omnia corpora ad eandem partem tenderent velocitas poſt ictum, <lb/>& </s> <s xml:id="echoid-s7188" xml:space="preserve">vis deſtructa, iiſdem regulis determinari poſſent,</s> </p> <p> <s xml:id="echoid-s7189" xml:space="preserve">Sepoſito elaſterio poſt ictum corpora in nave, velocitate v motâ, quie-<lb/>ſcerent, ſolo ergo elaſterio in hac poſt ictum moventur & </s> <s xml:id="echoid-s7190" xml:space="preserve">iiſdem velocitati-<lb/>bus in nave moventur, quibus iiſdem elaſteriis corpora ſi revera quieſce-<lb/>rent, agitarentur; </s> <s xml:id="echoid-s7191" xml:space="preserve">determinatis ergo motibus in hoc ultimo caſu habebimus <lb/>motus in nave, unde motus abſoluti facile deducuntur.</s> <s xml:id="echoid-s7192" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7193" xml:space="preserve">Ponimus igitur corpora quieſcentia A, B, C, & </s> <s xml:id="echoid-s7194" xml:space="preserve">inter hæc elaſteria flexa <lb/> <anchor type="note" xlink:label="note-0260-04a" xlink:href="note-0260-04"/> viribus quibus in ictu partes fuere compreſſæ, quæ valent 2 A ff + 2 B ff + <lb/>2C ff. </s> <s xml:id="echoid-s7195" xml:space="preserve">Cum agatur de caſu in quo inter A & </s> <s xml:id="echoid-s7196" xml:space="preserve">B, & </s> <s xml:id="echoid-s7197" xml:space="preserve">inter B & </s> <s xml:id="echoid-s7198" xml:space="preserve">C, partes <lb/>æqualiter inflectuntur, vis qua elaſterium utrumque comprimitur eſt A ff <lb/>+ B ff + C ff talemque vim dum elaſterium ſeſe expandit corporibus com-<lb/>municat <anchor type="note" xlink:href="" symbol="*"/>,</s> </p> <div xml:id="echoid-div995" type="float" level="2" n="3"> <note position="left" xlink:label="note-0260-04" xlink:href="note-0260-04a" xml:space="preserve">646.</note> </div> <note symbol="*" position="left" xml:space="preserve">560.</note> <p> <s xml:id="echoid-s7199" xml:space="preserve">Elaſterium inter A & </s> <s xml:id="echoid-s7200" xml:space="preserve">B ſeſe expandens Corpori A communicat vim B ff <lb/>+ C ff, & </s> <s xml:id="echoid-s7201" xml:space="preserve">in corpus B actionem exerit, quæ valet vim A ff <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7202" xml:space="preserve">Eodem mo- <anchor type="note" xlink:label="note-0260-06a" xlink:href="note-0260-06"/> do elaſterium aliud corpori C communicat vim A ff + B ff & </s> <s xml:id="echoid-s7203" xml:space="preserve">in Bexerit a-<lb/>ctionem quæ valet vim C ff <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7204" xml:space="preserve"/> </p> <div xml:id="echoid-div996" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0260-06" xlink:href="note-0260-06a" xml:space="preserve">561.</note> </div> <note symbol="*" position="left" xml:space="preserve">561.</note> <p> <s xml:id="echoid-s7205" xml:space="preserve">Corpus B premitur ergo duabus actionibus in partes oppoſitas, ſi A ſuperet <lb/>C, magis hoc corpus verſus premitur corpus B, actione quæ valet differen-<lb/>tiam actionum A ff & </s> <s xml:id="echoid-s7206" xml:space="preserve">C ff, de cætero actiones in utramque partem ſunt æ-<lb/>quales inter ſe & </s> <s xml:id="echoid-s7207" xml:space="preserve">valent C ff.</s> <s xml:id="echoid-s7208" xml:space="preserve"/> </p> <pb o="183" file="0261" n="285" rhead="MATHEMATICA. Lib. I. Cap. XXVII."/> <p> <s xml:id="echoid-s7209" xml:space="preserve">Dum elaſteria actionibus æqualibus in ſe mutuo premunt, utrumque agit <lb/>quaſi obſtaculo immobili inſiſteret; </s> <s xml:id="echoid-s7210" xml:space="preserve">& </s> <s xml:id="echoid-s7211" xml:space="preserve">integram ſuam vim in partem oppoſitam <lb/>exerit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7212" xml:space="preserve">id eſt elaſteria agunt in corpora A & </s> <s xml:id="echoid-s7213" xml:space="preserve">C ita, ut ſingulis, præter me- <anchor type="note" xlink:label="note-0261-01a" xlink:href="note-0261-01"/> moratas vires, communicent vim C ff; </s> <s xml:id="echoid-s7214" xml:space="preserve">quare vis corpori A communicata va-<lb/>let B ff + 2C ff, & </s> <s xml:id="echoid-s7215" xml:space="preserve">C movetur vi A ff + B ff + Cff, dum B ad par-<lb/>tem Cpellitur actione quæ valet A ff-C ff.</s> <s xml:id="echoid-s7216" xml:space="preserve"/> </p> <div xml:id="echoid-div997" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0261-01" xlink:href="note-0261-01a" xml:space="preserve">561.</note> </div> <p> <s xml:id="echoid-s7217" xml:space="preserve">Sed B non poteſt moveri, quin eâdem velocitate propellatur elaſterium <lb/>inter B & </s> <s xml:id="echoid-s7218" xml:space="preserve">C, & </s> <s xml:id="echoid-s7219" xml:space="preserve">ab elaſterio ita agitato accipit corpus C vim ftatim memo-<lb/>ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-<lb/>re neſcio inſiſteret, actione elaſterii moveretur; </s> <s xml:id="echoid-s7220" xml:space="preserve">id eſt velocitas qua <lb/>corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-<lb/>ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7221" xml:space="preserve">Si corporis B ve- <anchor type="note" xlink:label="note-0261-02a" xlink:href="note-0261-02"/> locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. </s> <s xml:id="echoid-s7222" xml:space="preserve">Summa viri-<lb/>um horum corporum eſt A ff + B ff + C ff & </s> <s xml:id="echoid-s7223" xml:space="preserve">præterea A ff-C ff, ideſt <lb/>valet ſumma hæc 2 A ff + B ff; </s> <s xml:id="echoid-s7224" xml:space="preserve">Unde deducimus {B xx + C xx + <lb/>2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s7225" xml:space="preserve"> <anchor type="note" xlink:label="note-0261-03a" xlink:href="note-0261-03"/> aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; </s> <s xml:id="echoid-s7226" xml:space="preserve">& </s> <s xml:id="echoid-s7227" xml:space="preserve"><lb/>{x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: </s> <s xml:id="echoid-s7228" xml:space="preserve">additâ velocitate <lb/>f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem <lb/>{fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}</s> </p> <div xml:id="echoid-div998" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">470.</note> <note symbol="*" position="right" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">479.</note> </div> <p> <s xml:id="echoid-s7229" xml:space="preserve">Corporis autem A velocitas ex ipſius vi ante determinata detegitur eſtque <lb/>velocitas hæc {f√AB + 2AC\x{0020}/A}.</s> <s xml:id="echoid-s7230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7231" xml:space="preserve">Velocitates hæ ex velocitate v ſunt ſubtrahendæ, aut ipſi ſunt addendæ, <lb/> <anchor type="note" xlink:label="note-0261-04a" xlink:href="note-0261-04"/> pro ut cum motu navis conſpirant aut contrariæ agunt.</s> <s xml:id="echoid-s7232" xml:space="preserve"/> </p> <div xml:id="echoid-div999" type="float" level="2" n="7"> <note position="right" xlink:label="note-0261-04" xlink:href="note-0261-04a" xml:space="preserve">647.</note> </div> <p> <s xml:id="echoid-s7233" xml:space="preserve">Si in primo motu A celerius B feratur, id eſt m ſuperet n, velocitas cor-<lb/>poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; </s> <s xml:id="echoid-s7234" xml:space="preserve">reliquæ velocitates detectæ <lb/>corporum B & </s> <s xml:id="echoid-s7235" xml:space="preserve">C ipſi v addendæ ſunt.</s> <s xml:id="echoid-s7236" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7237" xml:space="preserve">In ſcholio 2. </s> <s xml:id="echoid-s7238" xml:space="preserve">Capitis ſequentis demonſtrabimus ſummam virium poſt ictum <lb/> <anchor type="note" xlink:label="note-0261-05a" xlink:href="note-0261-05"/> æqualem eſſe A mm + B nn + C pp; </s> <s xml:id="echoid-s7239" xml:space="preserve">quod cum ante demonſtratis congruit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7240" xml:space="preserve"/> </p> <div xml:id="echoid-div1000" type="float" level="2" n="8"> <note position="right" xlink:label="note-0261-05" xlink:href="note-0261-05a" xml:space="preserve">648.</note> </div> <note symbol="*" position="right" xml:space="preserve">558.</note> <pb o="184" file="0262" n="286" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1002" type="section" level="1" n="246"> <head xml:id="echoid-head348" xml:space="preserve">SCHOLIUM 3.</head> <head xml:id="echoid-head349" xml:space="preserve">Demonſtratio n. 637.</head> <p> <s xml:id="echoid-s7241" xml:space="preserve">Diximus ſummam virium poſt ictum æqualem eſſe ſummæ virium ante i-<lb/>ctum in colliſione in n. </s> <s xml:id="echoid-s7242" xml:space="preserve">636. </s> <s xml:id="echoid-s7243" xml:space="preserve">explicata; </s> <s xml:id="echoid-s7244" xml:space="preserve">Poſitâ igitur velocitatum determi-<lb/> <anchor type="note" xlink:label="note-0262-01a" xlink:href="note-0262-01"/> natione ibi traditâ demonſtrandum Corpus C tantum virium acquirere quan-<lb/>tum amittunt A & </s> <s xml:id="echoid-s7245" xml:space="preserve">B.</s> <s xml:id="echoid-s7246" xml:space="preserve"/> </p> <div xml:id="echoid-div1002" type="float" level="2" n="1"> <note position="left" xlink:label="note-0262-01" xlink:href="note-0262-01a" xml:space="preserve"><emph style="sc">TAB. XXV.</emph> <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s7247" xml:space="preserve">Quadratum lineæ KN æquale eſt quadratis linearum KO & </s> <s xml:id="echoid-s7248" xml:space="preserve">ON, aut <lb/> <anchor type="note" xlink:label="note-0262-02a" xlink:href="note-0262-02"/> KP, & </s> <s xml:id="echoid-s7249" xml:space="preserve">bis rectangulo IOK <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7250" xml:space="preserve">etiam æquale eſt idem quadratum quadratis <anchor type="note" xlink:label="note-0262-03a" xlink:href="note-0262-03"/> KO & </s> <s xml:id="echoid-s7251" xml:space="preserve">KP & </s> <s xml:id="echoid-s7252" xml:space="preserve">bis rectangulo MPK <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7253" xml:space="preserve">unde ſequitur æqualia eſſe rectangula hæc, <anchor type="note" xlink:label="note-0262-04a" xlink:href="note-0262-04"/> & </s> <s xml:id="echoid-s7254" xml:space="preserve">quadratum KN valere quadratum KO, & </s> <s xml:id="echoid-s7255" xml:space="preserve">rectangulum IOK, ut & </s> <s xml:id="echoid-s7256" xml:space="preserve"><lb/>quadratum KP cum rectangulo MPK; </s> <s xml:id="echoid-s7257" xml:space="preserve">ergo quadratum KN æquale eſt <lb/>rectangulis IKO & </s> <s xml:id="echoid-s7258" xml:space="preserve">MKP; </s> <s xml:id="echoid-s7259" xml:space="preserve">& </s> <s xml:id="echoid-s7260" xml:space="preserve">quadratum K n, duplæ ipſius KN, quod <lb/>quadruplum eſt quadrati KN, valebit quater ſummam rectangulorum IKO <lb/>& </s> <s xml:id="echoid-s7261" xml:space="preserve">MKP. </s> <s xml:id="echoid-s7262" xml:space="preserve">Multiplicatis his per C, habemus vim corporis C, ictu acquiſi-<lb/>tam, æqualem 4CxKOxKl + 4CxKPxKM <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7263" xml:space="preserve"/> </p> <div xml:id="echoid-div1003" type="float" level="2" n="2"> <note position="left" xlink:label="note-0262-02" xlink:href="note-0262-02a" xml:space="preserve">649.</note> <note symbol="*" position="left" xlink:label="note-0262-03" xlink:href="note-0262-03a" xml:space="preserve">12. El. 11.</note> <note symbol="*" position="left" xlink:label="note-0262-04" xlink:href="note-0262-04a" xml:space="preserve">12. El. 11.</note> </div> <p> <s xml:id="echoid-s7264" xml:space="preserve">Vis, quam ictu amiſit corpus A, habetur multiplicando A per difterenti-<lb/> <anchor type="note" xlink:label="note-0262-05a" xlink:href="note-0262-05"/> am quadratorum KD, K i, velocitatum ante & </s> <s xml:id="echoid-s7265" xml:space="preserve">poſt ictum <anchor type="note" xlink:href="" symbol="*"/>, Differentia <anchor type="note" xlink:label="note-0262-06a" xlink:href="note-0262-06"/> autem hæc propter æquales DI, I i, valet quater rectangulum KID <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7266" xml:space="preserve">& </s> <s xml:id="echoid-s7267" xml:space="preserve">vis a- <anchor type="note" xlink:label="note-0262-07a" xlink:href="note-0262-07"/> miſſa eſt 4AxIDxKI: </s> <s xml:id="echoid-s7268" xml:space="preserve">Sed in n, 635 vidimus A, C:</s> <s xml:id="echoid-s7269" xml:space="preserve">:KO, ID; </s> <s xml:id="echoid-s7270" xml:space="preserve">ergo <lb/>AxID = CxKO, & </s> <s xml:id="echoid-s7271" xml:space="preserve">vis quam amittit A eſt 4CxKOxKI.</s> <s xml:id="echoid-s7272" xml:space="preserve"/> </p> <div xml:id="echoid-div1004" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0262-05" xlink:href="note-0262-05a" xml:space="preserve">470.</note> <note symbol="*" position="left" xlink:label="note-0262-06" xlink:href="note-0262-06a" xml:space="preserve">598.</note> <note symbol="*" position="left" xlink:label="note-0262-07" xlink:href="note-0262-07a" xml:space="preserve">8. El. 11.</note> </div> <p> <s xml:id="echoid-s7273" xml:space="preserve">Eodem modo demonſtramus vim quam amittit B æqualem eſſe 4CxKP <lb/>xKM, ideoque ſummam virium amiſſarum valere vim quam C acquiſivit <lb/>Q. </s> <s xml:id="echoid-s7274" xml:space="preserve">D. </s> <s xml:id="echoid-s7275" xml:space="preserve">E.</s> <s xml:id="echoid-s7276" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7277" xml:space="preserve">Vix differt demonſtratio quando agitur de caſu fig. </s> <s xml:id="echoid-s7278" xml:space="preserve">7.</s> <s xml:id="echoid-s7279" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1006" type="section" level="1" n="247"> <head xml:id="echoid-head350" xml:space="preserve">CAPUT XXVIII.</head> <head xml:id="echoid-head351" xml:space="preserve">De Motu Centri gravitatis.</head> <p> <s xml:id="echoid-s7280" xml:space="preserve">IN colliſione corporum, motus reſpectivos, a motibus ab-<lb/>ſolutis diſtingui, in variis occaſionibus jam notavimus; <lb/></s> <s xml:id="echoid-s7281" xml:space="preserve">his nunc ulterius addendum, corporum ipſorum motus ab-<lb/>ſolutos, cum motu abſoluto omnium corporum ſimul conſi-<lb/>deratorum non debere confundi.</s> <s xml:id="echoid-s7282" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1007" type="section" level="1" n="248"> <head xml:id="echoid-head352" xml:space="preserve"><emph style="sc">Definitio.</emph></head> <p style="it"> <s xml:id="echoid-s7283" xml:space="preserve">Motum abſolutum corporum quorumcumque ſimul conſider a-<lb/> <anchor type="note" xlink:label="note-0262-08a" xlink:href="note-0262-08"/> torum vocamus motum centri gravitatis communis.</s> <s xml:id="echoid-s7284" xml:space="preserve"/> </p> <div xml:id="echoid-div1007" type="float" level="2" n="1"> <note position="left" xlink:label="note-0262-08" xlink:href="note-0262-08a" xml:space="preserve">650.</note> </div> <p> <s xml:id="echoid-s7285" xml:space="preserve">Ut in ſingulis corporibus de motu dijudicamus ex motu <lb/>centri gravitatis, & </s> <s xml:id="echoid-s7286" xml:space="preserve">hoc ad plura ſimul conſiderata applica-<lb/>ri poſſe clarum eſt.</s> <s xml:id="echoid-s7287" xml:space="preserve"/> </p> <pb o="185" file="0263" n="287" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/> <p> <s xml:id="echoid-s7288" xml:space="preserve">Circa motum hunc abſolutum plurimorum corporum nota-<lb/> <anchor type="note" xlink:label="note-0263-01a" xlink:href="note-0263-01"/> mus, ipſum, actione reſpectivâ, qualis eſt omnis colliſio, non <lb/>mutari; </s> <s xml:id="echoid-s7289" xml:space="preserve">ideoque Centrum gravitatis commune variorum <lb/> <anchor type="note" xlink:label="note-0263-02a" xlink:href="note-0263-02"/> corporum in eâdem lineâ, eâdem velocitate, ante & </s> <s xml:id="echoid-s7290" xml:space="preserve">poſt i-<lb/>ctum moveri. </s> <s xml:id="echoid-s7291" xml:space="preserve">Quod in omnibus colliſionibus ante explica-<lb/>tis obtineri demonſtrabimus.</s> <s xml:id="echoid-s7292" xml:space="preserve"/> </p> <div xml:id="echoid-div1008" type="float" level="2" n="2"> <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">650.</note> <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">651.</note> </div> <p> <s xml:id="echoid-s7293" xml:space="preserve">Sint A & </s> <s xml:id="echoid-s7294" xml:space="preserve">B centra gravitatis duorum corporum, ſi ad C, <lb/> <anchor type="note" xlink:label="note-0263-03a" xlink:href="note-0263-03"/> centrum gravit atis commune, accedant ambo corpora, veloci-<lb/> <anchor type="note" xlink:label="note-0263-04a" xlink:href="note-0263-04"/> tatibus quæ ſunt inter ſe ut diſtantiæ ſuæ à centro, nempeut <lb/>AC ad BC, id eſt, inverſe ut maſſæ ipſorum corporum <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0263-05a" xlink:href="note-0263-05"/> quieſcit in hoc motu centrum gravitatis; </s> <s xml:id="echoid-s7295" xml:space="preserve">nam dum eodem <lb/>tempore percurrunt A a, B b, quæ ſunt ut AC, BC, <lb/>reſtant a C, b C in eâdem ratione inverſa maſſarum, qua-<lb/>re & </s> <s xml:id="echoid-s7296" xml:space="preserve">in hoc ſitu C eſt commune gravitatis centrum <anchor type="note" xlink:href="" symbol="*"/>, quod <anchor type="note" xlink:label="note-0263-06a" xlink:href="note-0263-06"/> in motu hoc non fuit tranſlatum.</s> <s xml:id="echoid-s7297" xml:space="preserve"/> </p> <div xml:id="echoid-div1009" type="float" level="2" n="3"> <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve"><emph style="sc">TA. XXV.</emph> <lb/>fig. 8.</note> <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">652.</note> <note symbol="*" position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">134. 143.</note> <note symbol="*" position="right" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">134.</note> </div> <p style="it"> <s xml:id="echoid-s7298" xml:space="preserve">Eadem demonſtratio poteſt applicari ad motum corpo-<lb/> <anchor type="note" xlink:label="note-0263-07a" xlink:href="note-0263-07"/> rum à commune gravitatis centro recedentium, velocitati-<lb/>bus quæ ſunt inverſe ut maſſæ, in quo caſu ergo etiam cen-<lb/>trum hoc quieſcit.</s> <s xml:id="echoid-s7299" xml:space="preserve"/> </p> <div xml:id="echoid-div1010" type="float" level="2" n="4"> <note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">653.</note> </div> <p> <s xml:id="echoid-s7300" xml:space="preserve">Si varia dentur corpora, ut A, B, D, & </s> <s xml:id="echoid-s7301" xml:space="preserve">hæc in eâdem <lb/> <anchor type="note" xlink:label="note-0263-08a" xlink:href="note-0263-08"/> lineâ mota, accedant omnia ad C commune gravitatis centrum, <lb/> <anchor type="note" xlink:label="note-0263-09a" xlink:href="note-0263-09"/> aut recedant ab hoc, velocitatibus quæ in ſingulis corpori-<lb/>bus ſunt ut diſtantiæ ab hoc centro quieſcit etiam hoc ipſum. <lb/></s> <s xml:id="echoid-s7302" xml:space="preserve">Nam cum in ſitu A, B, D ſumma productorum maſſarum <lb/>per diſtantias a C ab una parte hujus puncti æqualis ſit ſimi-<lb/>li ſummæ ad aliam partem <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7303" xml:space="preserve">hoc locum habebit muta- <anchor type="note" xlink:label="note-0263-10a" xlink:href="note-0263-10"/> tis omnibus diſtantiis, ut hîc fit, in eadem ratione, quare <lb/>C manet centrum commune gravitatis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7304" xml:space="preserve">quod ergo quie- <anchor type="note" xlink:label="note-0263-11a" xlink:href="note-0263-11"/> ſcit.</s> <s xml:id="echoid-s7305" xml:space="preserve"/> </p> <div xml:id="echoid-div1011" type="float" level="2" n="5"> <note position="right" xlink:label="note-0263-08" xlink:href="note-0263-08a" xml:space="preserve">654.</note> <note position="right" xlink:label="note-0263-09" xlink:href="note-0263-09a" xml:space="preserve"><emph style="sc">TA. XXV.</emph> <lb/>fig. 9.</note> <note symbol="*" position="right" xlink:label="note-0263-10" xlink:href="note-0263-10a" xml:space="preserve">141. 143.</note> <note symbol="*" position="right" xlink:label="note-0263-11" xlink:href="note-0263-11a" xml:space="preserve">141.</note> </div> <p style="it"> <s xml:id="echoid-s7306" xml:space="preserve">In hoc caſu, multiplicatis ſingulis maſſis per ſuas veloci-<lb/>tates, ſumma productorum ab una parte centri gravitatis, <lb/>æqualis eſt ſimili ſummæ ad aliam partem; </s> <s xml:id="echoid-s7307" xml:space="preserve">ponimus enim <lb/>velocitates ut diſtantias à centro hoc.</s> <s xml:id="echoid-s7308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7309" xml:space="preserve">Ex hiſce ſequentes deducimus concluſiones.</s> <s xml:id="echoid-s7310" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7311" xml:space="preserve">Corporum duorum, aut trium, in ſe mutuo directè incur-<lb/> <anchor type="note" xlink:label="note-0263-12a" xlink:href="note-0263-12"/> rentium ita, ut poſt ictum, ſi non ſint elaſtica, quieſcant, an- <pb o="186" file="0264" n="288" rhead="PHYSICES ELEMENTA"/> te ictum quieſcit centrum gravitatis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7312" xml:space="preserve">In hoc eodem con- <anchor type="note" xlink:label="note-0264-01a" xlink:href="note-0264-01"/> <anchor type="note" xlink:label="note-0264-02a" xlink:href="note-0264-02"/> curſu, etiam quieſcit centrum hoc ſi @orpora ſint elaſtica <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7313" xml:space="preserve"> <anchor type="note" xlink:label="note-0264-03a" xlink:href="note-0264-03"/> </s> </p> <div xml:id="echoid-div1012" type="float" level="2" n="6"> <note position="right" xlink:label="note-0263-12" xlink:href="note-0263-12a" xml:space="preserve">655.</note> <note position="left" xlink:label="note-0264-01" xlink:href="note-0264-01a" xml:space="preserve">656</note> <note symbol="*" position="left" xlink:label="note-0264-02" xlink:href="note-0264-02a" xml:space="preserve">500. 652. <lb/>622. 623. <lb/>654.</note> <note symbol="*" position="left" xlink:label="note-0264-03" xlink:href="note-0264-03a" xml:space="preserve">562 629. <lb/>653. 654.</note> </div> <p> <s xml:id="echoid-s7314" xml:space="preserve">Si corpora duo aut tria directe in ſ<unsure/>e mutuo incurrant & </s> <s xml:id="echoid-s7315" xml:space="preserve"><lb/>navis concipiatur ita agitata, ut corpora, poſitis his non e-<lb/>laſticis, in hac poſt ictum quieſcant, in hac ipſa anteictum <lb/> <anchor type="note" xlink:label="note-0264-04a" xlink:href="note-0264-04"/> quieſcit centrum gravitatis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7316" xml:space="preserve">in tali conflictu poſt ictum <anchor type="note" xlink:label="note-0264-05a" xlink:href="note-0264-05"/> etiam quieſcit idem hoc centrum, ſi corpora ſint elaſtica <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0264-06a" xlink:href="note-0264-06"/> unde ſequitur navem hanc moveri ea velocitate, qua an-<lb/>te & </s> <s xml:id="echoid-s7317" xml:space="preserve">poſt ictum, commune corporum gravitatis centrum <lb/>fertur, cujus ergo centri motus non mutatur.</s> <s xml:id="echoid-s7318" xml:space="preserve"/> </p> <div xml:id="echoid-div1013" type="float" level="2" n="7"> <note position="left" xlink:label="note-0264-04" xlink:href="note-0264-04a" xml:space="preserve">657.</note> <note symbol="*" position="left" xlink:label="note-0264-05" xlink:href="note-0264-05a" xml:space="preserve">655.</note> <note symbol="*" position="left" xlink:label="note-0264-06" xlink:href="note-0264-06a" xml:space="preserve">656.</note> </div> <p> <s xml:id="echoid-s7319" xml:space="preserve">Hoc quoque locum habere in motibus memoratis in n. <lb/></s> <s xml:id="echoid-s7320" xml:space="preserve"> <anchor type="note" xlink:label="note-0264-07a" xlink:href="note-0264-07"/> 633. </s> <s xml:id="echoid-s7321" xml:space="preserve">634. </s> <s xml:id="echoid-s7322" xml:space="preserve">636. </s> <s xml:id="echoid-s7323" xml:space="preserve">demonſtrabimus in ſcholio ſequenti 2.</s> <s xml:id="echoid-s7324" xml:space="preserve"/> </p> <div xml:id="echoid-div1014" type="float" level="2" n="8"> <note position="left" xlink:label="note-0264-07" xlink:href="note-0264-07a" xml:space="preserve">658.</note> </div> <p> <s xml:id="echoid-s7325" xml:space="preserve">In concurſu obliquo duorum corporum duos conſideravi-<lb/> <anchor type="note" xlink:label="note-0264-08a" xlink:href="note-0264-08"/> mus motus, unum quo directe in ſe mutuo incurrunt, al-<lb/>terum lateralem <anchor type="note" xlink:href="" symbol="*"/>, qui in impactu non mutatur; </s> <s xml:id="echoid-s7326" xml:space="preserve">quare ne- <anchor type="note" xlink:label="note-0264-09a" xlink:href="note-0264-09"/> que mutatur centri gravitatis motus lateralis; </s> <s xml:id="echoid-s7327" xml:space="preserve">ſed neque <lb/>juxta aliam directionem centri gravitatis motus mutari po-<lb/>teſt, quia impactu directo non mutatur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7328" xml:space="preserve">Idcirco nullo <anchor type="note" xlink:label="note-0264-10a" xlink:href="note-0264-10"/> reſpectu motus hic variat & </s> <s xml:id="echoid-s7329" xml:space="preserve">velocitatem directionemque ſuam <lb/>ſervat commune corporum gravitatis centrum.</s> <s xml:id="echoid-s7330" xml:space="preserve"/> </p> <div xml:id="echoid-div1015" type="float" level="2" n="9"> <note position="left" xlink:label="note-0264-08" xlink:href="note-0264-08a" xml:space="preserve">659.</note> <note symbol="*" position="left" xlink:label="note-0264-09" xlink:href="note-0264-09a" xml:space="preserve">617.</note> <note symbol="*" position="left" xlink:label="note-0264-10" xlink:href="note-0264-10a" xml:space="preserve">657.</note> </div> <p> <s xml:id="echoid-s7331" xml:space="preserve">Unicum circa motum centri gravitatis notandum ſuper <lb/>eſt quod in Scholio ſequenti 1. </s> <s xml:id="echoid-s7332" xml:space="preserve">demonſtramus; </s> <s xml:id="echoid-s7333" xml:space="preserve">ſummam <lb/> <anchor type="note" xlink:label="note-0264-11a" xlink:href="note-0264-11"/> virium corporum quorumcumque concurrentium, æqualem <lb/>eſſe ſummæ vis quam haberent omnia corpora, ſimul agita-<lb/>ta ea velocitate, qua fertur cummune gravitatis centrum, <lb/>& </s> <s xml:id="echoid-s7334" xml:space="preserve">omnium virium quibus corpora reſpectu centri bujus mo-<lb/>ventur. </s> <s xml:id="echoid-s7335" xml:space="preserve">Id eſt ſi ſumma maſſarum per quadratum veloci-<lb/>tatis centri gravitatis multiplicetur, & </s> <s xml:id="echoid-s7336" xml:space="preserve">ſingulæ maſſæ mul-<lb/>tiplicentur per quadrata velocitatum, quibus ad gravitatis <lb/> <anchor type="note" xlink:label="note-0264-12a" xlink:href="note-0264-12"/> centrum tendunt, id eſt, quibus in nave, in qua centrum <lb/>gravitatis quieſceret agitata forent, ſumma omnium produ-<lb/>ctorum æqualis erit ſummæ productorum ſingularum maſ-<lb/>ſarum ductarum in quadrata velocitatum ſuarum. </s> <s xml:id="echoid-s7337" xml:space="preserve">Id circo <lb/>ſi mutatis motibus, ſuma virium in hac nave non mutetur, <lb/>neque mutabitur ſumma virium abſolutarum.</s> <s xml:id="echoid-s7338" xml:space="preserve"/> </p> <div xml:id="echoid-div1016" type="float" level="2" n="10"> <note position="left" xlink:label="note-0264-11" xlink:href="note-0264-11a" xml:space="preserve">660.</note> <note position="left" xlink:label="note-0264-12" xlink:href="note-0264-12a" xml:space="preserve">661.</note> </div> <p> <s xml:id="echoid-s7339" xml:space="preserve">Propoſitio hæc univerſalis eſt; </s> <s xml:id="echoid-s7340" xml:space="preserve">ſed cum in hiſce omnibus <pb o="187" file="0265" n="289" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/> de colliſione agatur, corpora tantum concurrentia conſide-<lb/>ramus.</s> <s xml:id="echoid-s7341" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1018" type="section" level="1" n="249"> <head xml:id="echoid-head353" xml:space="preserve">SCHOLIUM 1.</head> <head xml:id="echoid-head354" style="it" xml:space="preserve">Demonſtratio n. 660.</head> <p> <s xml:id="echoid-s7342" xml:space="preserve">QUamdiu corpora moventur in eâdem lineâ propoſitio ultimum memo-<lb/> <anchor type="note" xlink:label="note-0265-01a" xlink:href="note-0265-01"/> rata ſimplici algebraica computatione patet.</s> <s xml:id="echoid-s7343" xml:space="preserve"/> </p> <div xml:id="echoid-div1018" type="float" level="2" n="1"> <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">662.</note> </div> <p> <s xml:id="echoid-s7344" xml:space="preserve">Sint corpora A, B, C, primi velocitas m; </s> <s xml:id="echoid-s7345" xml:space="preserve">ſecundi n, tertii p; </s> <s xml:id="echoid-s7346" xml:space="preserve">centri gravi-<lb/>tatis velocitas d. </s> <s xml:id="echoid-s7347" xml:space="preserve">Tendant corpora ad eandem partem; </s> <s xml:id="echoid-s7348" xml:space="preserve">& </s> <s xml:id="echoid-s7349" xml:space="preserve">ſint m & </s> <s xml:id="echoid-s7350" xml:space="preserve">n majores <lb/>ipſa d; </s> <s xml:id="echoid-s7351" xml:space="preserve">p verò minor: </s> <s xml:id="echoid-s7352" xml:space="preserve">Ergo velocitates, quibus corpora ad centrum gravitatis <lb/>tendunt ſunt m - d, n - d, d - p; </s> <s xml:id="echoid-s7353" xml:space="preserve">& </s> <s xml:id="echoid-s7354" xml:space="preserve">A x <emph style="ol">m - d</emph> + B x <emph style="ol">n - d</emph> = C x <emph style="ol">d - p<anchor type="note" xlink:href="" symbol="*"/></emph>; </s> <s xml:id="echoid-s7355" xml:space="preserve">quare <anchor type="note" xlink:label="note-0265-02a" xlink:href="note-0265-02"/> 2 A md - 2A dd + 2B nd - 2 B dd = 2 C dd - 2C dp, multiplicando inte-<lb/>gram æquationem per 2d. </s> <s xml:id="echoid-s7356" xml:space="preserve">Demonſtrandum A mm + B nn + C pp = <emph style="ol">A + B + C</emph> <lb/>x dd + A x <emph style="ol">m - d</emph><emph style="super">2</emph> + B x <emph style="ol">n - d</emph><emph style="super">2</emph> + C x <emph style="ol">d - p</emph><emph style="super">2</emph>. </s> <s xml:id="echoid-s7357" xml:space="preserve">Ultima hæc quantitas ſic pot-<lb/>eſt exprimi A mm-2 A md + 2 A dd + B nn - 2B nd + 2 B dd + C pp <lb/>- 2 C pd + 2C dd. </s> <s xml:id="echoid-s7358" xml:space="preserve">Sed - 2A md + 2A dd - 2B nd + 2B dd & </s> <s xml:id="echoid-s7359" xml:space="preserve">- 2C pd <lb/>+ 2 C dd ſeſe mutuo deſtruunt & </s> <s xml:id="echoid-s7360" xml:space="preserve">quantitas hæc tantum valet A mm + B nn <lb/>+ C pp. </s> <s xml:id="echoid-s7361" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s7362" xml:space="preserve"/> </p> <div xml:id="echoid-div1019" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0265-02" xlink:href="note-0265-02a" xml:space="preserve">654.</note> </div> <p> <s xml:id="echoid-s7363" xml:space="preserve">Sint iterum tria corpora A, B, C, quorum tantum gravitatis centra conſi-<lb/> <anchor type="note" xlink:label="note-0265-03a" xlink:href="note-0265-03"/> deramus; </s> <s xml:id="echoid-s7364" xml:space="preserve">ſit commune gravitatis centrum D; </s> <s xml:id="echoid-s7365" xml:space="preserve">ponamus corpora moveri per <lb/> <anchor type="note" xlink:label="note-0265-04a" xlink:href="note-0265-04"/> AE, BE, CF, velocitatibus hiſce lineis proportionalibus. </s> <s xml:id="echoid-s7366" xml:space="preserve">Directio & </s> <s xml:id="echoid-s7367" xml:space="preserve">ce-<lb/>leritas centri gravitatis D eſt DE. </s> <s xml:id="echoid-s7368" xml:space="preserve">Velocitates, quibus corpora ad centrum <lb/>commune gravitatis tendunt, ſunt AD, BD, CD, hæ enim eſſent corpo-<lb/>rum velocitates in nave, in qua centrum gravitatis quieſceret. </s> <s xml:id="echoid-s7369" xml:space="preserve">Idcirco de-<lb/>monſtrandum A x AE<emph style="super">q</emph> + B x BE<emph style="super">q</emph> + C x CE<emph style="super">q</emph> = A + B + C x DE<emph style="super">q</emph> + A x AD<emph style="super">q</emph> <lb/>+ B x BD<emph style="super">q</emph> + C x CD<emph style="super">q</emph>.</s> <s xml:id="echoid-s7370" xml:space="preserve"/> </p> <div xml:id="echoid-div1020" type="float" level="2" n="3"> <note position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">663.</note> <note position="right" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve"><emph style="sc">TA. XXV.</emph> <lb/>fig. 10.</note> </div> <p> <s xml:id="echoid-s7371" xml:space="preserve">Ad DE ducantur perpendieulares AF, BG, CH, LDL. </s> <s xml:id="echoid-s7372" xml:space="preserve">Diſtantiæ <lb/>corporum A, B, C à linea LDL ſunt FD, GD, HD; </s> <s xml:id="echoid-s7373" xml:space="preserve">ergo, quia D eſt <lb/>centrum commune gravitatis A x FD + B x GD = C x D <anchor type="note" xlink:href="" symbol="*"/> unde patet D <anchor type="note" xlink:label="note-0265-05a" xlink:href="note-0265-05"/> eorum corporum eſſe commune gravitatis centrum poſitis his in F, G <lb/>& </s> <s xml:id="echoid-s7374" xml:space="preserve">H <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7375" xml:space="preserve">Si in hoc ſitu concipiamus corpora moveri A velocitate FE, B <anchor type="note" xlink:label="note-0265-06a" xlink:href="note-0265-06"/> velocitate GE, & </s> <s xml:id="echoid-s7376" xml:space="preserve">tandem C velocitate HE; </s> <s xml:id="echoid-s7377" xml:space="preserve">centri gravitatis velocitas <lb/>erit DE; </s> <s xml:id="echoid-s7378" xml:space="preserve">Ergo A x FE<emph style="super">q</emph> + B x GE<emph style="super">q</emph> + C x HE<emph style="super">q</emph> = <emph style="ol">A + B + C</emph> x DE<emph style="super">q</emph> <lb/>+ A x FD<emph style="super">q</emph> + B x GD<emph style="super">q</emph> + C x HD<emph style="super">q</emph> <anchor type="note" xlink:href="" symbol="*"/> addendo utrimque A x AF<emph style="super">q</emph> + <anchor type="note" xlink:label="note-0265-07a" xlink:href="note-0265-07"/> B x BG<emph style="super">q</emph> + C x CH<emph style="super">q</emph> & </s> <s xml:id="echoid-s7379" xml:space="preserve">ſubſtituendo triangulorum rectangulorum AFD, <lb/>BGD, CHD, AFE, BGE, CHE, quadrata Hypotenuſarum pro <lb/>quadratis laterum <anchor type="note" xlink:href="" symbol="*"/>, habebimus propoſitum.</s> <s xml:id="echoid-s7380" xml:space="preserve"> <anchor type="note" xlink:label="note-0265-08a" xlink:href="note-0265-08"/> </s> </p> <div xml:id="echoid-div1021" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">141. 159</note> <note symbol="*" position="right" xlink:label="note-0265-06" xlink:href="note-0265-06a" xml:space="preserve">141.</note> <note symbol="*" position="right" xlink:label="note-0265-07" xlink:href="note-0265-07a" xml:space="preserve">661.</note> <note symbol="*" position="right" xlink:label="note-0265-08" xlink:href="note-0265-08a" xml:space="preserve">47. <emph style="sc">EL</emph> @</note> </div> <pb o="188" file="0266" n="290" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1023" type="section" level="1" n="250"> <head xml:id="echoid-head355" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head356" style="it" xml:space="preserve">Demonſtrationes n. 658. ut & 648.</head> <p> <s xml:id="echoid-s7381" xml:space="preserve">DIximus <anchor type="note" xlink:href="" symbol="*"/> in caſu n. </s> <s xml:id="echoid-s7382" xml:space="preserve">633. </s> <s xml:id="echoid-s7383" xml:space="preserve">quem in n. </s> <s xml:id="echoid-s7384" xml:space="preserve">645. </s> <s xml:id="echoid-s7385" xml:space="preserve">peculiarius explicavimus etiam <anchor type="note" xlink:label="note-0266-01a" xlink:href="note-0266-01"/> motum centri gravitatis non mutari, quod ut demonſtrctur, probandum <lb/>corpora ita à ſe invicem ſeparari, ut conſideratis ſolis motibus quibus ſepa-<lb/>rantur, quieſcat centrum gravitatis; </s> <s xml:id="echoid-s7386" xml:space="preserve">tunc enim ſi concipiamus corpora ſe-<lb/>parari in nave, ea velocitate mota qua corpora conjunctim ante ſeparationem <lb/>moventur, velocitate qua navis fertur commune gravitatis centrum motum <lb/>continuabit.</s> <s xml:id="echoid-s7387" xml:space="preserve"/> </p> <div xml:id="echoid-div1023" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">658.</note> </div> <p> <s xml:id="echoid-s7388" xml:space="preserve">Poſitis quæ in n. </s> <s xml:id="echoid-s7389" xml:space="preserve">645. </s> <s xml:id="echoid-s7390" xml:space="preserve">fuere expllcata demonſtrandum A multiplicatum <lb/> <anchor type="note" xlink:label="note-0266-02a" xlink:href="note-0266-02"/> per velocitatem ibi determinatam quod productum eſt@ f √AB + 2AC\x{0020}, <lb/>valere ſummam productorum corporum B & </s> <s xml:id="echoid-s7391" xml:space="preserve">C, ſingulorum multiplicato-<lb/>rum per velocitates ibi detectas <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7392" xml:space="preserve">Producta hæc ſunt <anchor type="note" xlink:label="note-0266-03a" xlink:href="note-0266-03"/> {fB√AB + 2AC\x{0020} - fB√AC + BC + CC\x{0020}/B + C} & </s> <s xml:id="echoid-s7393" xml:space="preserve"><lb/>{fC√AB + 2AC\x{0020} + fB√AC + BC + CC\x{0020}/B + C} quorum ſumma eſt <lb/>{fB√AB + 2AC\x{0020} + fC√AB + 2AC\x{0020}/B + C}, id eſt f√AB + 2AC\x{0020}. <lb/></s> <s xml:id="echoid-s7394" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s7395" xml:space="preserve"/> </p> <div xml:id="echoid-div1024" type="float" level="2" n="2"> <note position="left" xlink:label="note-0266-02" xlink:href="note-0266-02a" xml:space="preserve">664.</note> <note symbol="*" position="left" xlink:label="note-0266-03" xlink:href="note-0266-03a" xml:space="preserve">654.</note> </div> <p> <s xml:id="echoid-s7396" xml:space="preserve">Hiſce demonſtratis facile patent, quæ in n. </s> <s xml:id="echoid-s7397" xml:space="preserve">648. </s> <s xml:id="echoid-s7398" xml:space="preserve">fuere memorata, ſummam <lb/>virium ante & </s> <s xml:id="echoid-s7399" xml:space="preserve">poſt ictum, in motu in n. </s> <s xml:id="echoid-s7400" xml:space="preserve">645. </s> <s xml:id="echoid-s7401" xml:space="preserve">& </s> <s xml:id="echoid-s7402" xml:space="preserve">ſeq. </s> <s xml:id="echoid-s7403" xml:space="preserve">memorato eſſe æqualem. <lb/></s> <s xml:id="echoid-s7404" xml:space="preserve"> <anchor type="note" xlink:label="note-0266-04a" xlink:href="note-0266-04"/> Vires quibus partes elaſticas inflexas poſuimus, ſunt vires quibus ad centrum <lb/>commune gravitatis acceſſere corpora <anchor type="note" xlink:href="" symbol="*"/>, ſervatâ eâdem virium ſummâ à ſe- invicem, uti ex computatione ipſa ſequitur, fuere ſeparata, id eſt, illa ipſa <lb/> <anchor type="note" xlink:label="note-0266-05a" xlink:href="note-0266-05"/> fuit ſumma virium quibus à centro gravitatis receſſere, cum hujus centri ve-<lb/>locitas ictu non fuerit mutatâ <anchor type="note" xlink:href="" symbol="*"/>, unde ſequitur ſummam virium abſoluta- rum etiam eandem eſſe ante & </s> <s xml:id="echoid-s7405" xml:space="preserve">poſt ictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7406" xml:space="preserve"/> </p> <div xml:id="echoid-div1025" type="float" level="2" n="3"> <note position="left" xlink:label="note-0266-04" xlink:href="note-0266-04a" xml:space="preserve">665.</note> <note symbol="*" position="left" xlink:label="note-0266-05" xlink:href="note-0266-05a" xml:space="preserve">642. 654.</note> </div> <note symbol="*" position="left" xml:space="preserve">664.</note> <p> <s xml:id="echoid-s7407" xml:space="preserve">In n. </s> <s xml:id="echoid-s7408" xml:space="preserve">658. </s> <s xml:id="echoid-s7409" xml:space="preserve">diximus etiam centrum commune gravitatis corporum in col-<lb/> <anchor type="note" xlink:label="note-0266-07a" xlink:href="note-0266-07"/> liſionibus compoſitis in n. </s> <s xml:id="echoid-s7410" xml:space="preserve">634. </s> <s xml:id="echoid-s7411" xml:space="preserve">636 memoratis, eadem directione & </s> <s xml:id="echoid-s7412" xml:space="preserve">veloci-<lb/> <anchor type="note" xlink:label="note-0266-08a" xlink:href="note-0266-08"/> tate motum poſt corporum concurſum continuare.</s> <s xml:id="echoid-s7413" xml:space="preserve"/> </p> <div xml:id="echoid-div1026" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0266-07" xlink:href="note-0266-07a" xml:space="preserve">661</note> <note position="left" xlink:label="note-0266-08" xlink:href="note-0266-08a" xml:space="preserve">666.</note> </div> <p> <s xml:id="echoid-s7414" xml:space="preserve">Si concipiamus corpora A & </s> <s xml:id="echoid-s7415" xml:space="preserve">B ultra K eadem velocitate, qua anteictum <lb/>movebantur, motum continuare quieſcente eodem modo corpore C, neque <lb/> <anchor type="note" xlink:label="note-0266-09a" xlink:href="note-0266-09"/> directio neque velocitas centri gravitatis communis mutata erit; </s> <s xml:id="echoid-s7416" xml:space="preserve">conſtabit <lb/>ergo propoſitum ſi demonſtremus in eodem puncto verſari centrum gravita-<lb/>tis, poſitis corporibus, C in K, A in D, & </s> <s xml:id="echoid-s7417" xml:space="preserve">B in E; </s> <s xml:id="echoid-s7418" xml:space="preserve">aut poſitis his, C in N, <lb/>A in I, & </s> <s xml:id="echoid-s7419" xml:space="preserve">B in M; </s> <s xml:id="echoid-s7420" xml:space="preserve">aut tandem poſitis, C in n, A in i, & </s> <s xml:id="echoid-s7421" xml:space="preserve">B in m. </s> <s xml:id="echoid-s7422" xml:space="preserve">Patebit <lb/>autem in hiſce tribus occaſionibus idem eſſe gravitatis centrum ſi demonſtre-<lb/>mus hujus diſtantias à lineis KF & </s> <s xml:id="echoid-s7423" xml:space="preserve">KG non mutari.</s> <s xml:id="echoid-s7424" xml:space="preserve"/> </p> <div xml:id="echoid-div1027" type="float" level="2" n="5"> <note position="left" xlink:label="note-0266-09" xlink:href="note-0266-09a" xml:space="preserve"><emph style="sc">TA. XXV</emph> <lb/>fig. 6. 7.</note> </div> <p> <s xml:id="echoid-s7425" xml:space="preserve">Reſpectu lineæ utriusque demonſtratio eadem eſt, quare de KF tantum a-<lb/>gam.</s> <s xml:id="echoid-s7426" xml:space="preserve"/> </p> <pb o="189" file="0267" n="291" rhead="MATHEMATICA. LIB. I. CAP. XXVIII."/> <p> <s xml:id="echoid-s7427" xml:space="preserve">Diſtantia puncti N ab hac linea eſt NM; </s> <s xml:id="echoid-s7428" xml:space="preserve">puncti n eſt 2NM; </s> <s xml:id="echoid-s7429" xml:space="preserve">puncto-<lb/>rum D, I, & </s> <s xml:id="echoid-s7430" xml:space="preserve">i diſtantiæ ab cadem KF deteguntur hiſce proportionibus <lb/>PN, NM:</s> <s xml:id="echoid-s7431" xml:space="preserve">: { KD, {NM x KD/PN} \\ KI, {NM x KI/PN} \\ Ki, {NM x Ki/PN} <lb/>Quibus detectis, diſtantiæ centri gravitatis communis corporum, à memo-<lb/>ratâ lineâ KF, in tribus memoratis corporum diſpoſitionibus, deteguntur <lb/>{NM x KD x A/PN x A + B + C}, {NM x C/A + B + C} + {NM x KI x A/PN x A + B + C}, & </s> <s xml:id="echoid-s7432" xml:space="preserve">{2 NM x C/A + B + C} <lb/>+ {NM x Ki + A/PN x A + B + C} <anchor type="note" xlink:href="" symbol="*"/> quas æquales demonſtramus.</s> <s xml:id="echoid-s7433" xml:space="preserve"> <anchor type="note" xlink:label="note-0267-01a" xlink:href="note-0267-01"/> </s> </p> <div xml:id="echoid-div1028" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0267-01" xlink:href="note-0267-01a" xml:space="preserve">159.</note> </div> <p> <s xml:id="echoid-s7434" xml:space="preserve">Ex conſtructione ſequitur PN ſe habere ad NQ, & </s> <s xml:id="echoid-s7435" xml:space="preserve">etiam 2 PN ad <lb/>2 NQ, ut A ad C; </s> <s xml:id="echoid-s7436" xml:space="preserve">NQ æqualis eſt ID, & </s> <s xml:id="echoid-s7437" xml:space="preserve">valet KD-KI ergo PN x C <lb/>= KD x A - KI x A, & </s> <s xml:id="echoid-s7438" xml:space="preserve">PN x C + KI x A = KD x A.</s> <s xml:id="echoid-s7439" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7440" xml:space="preserve">Eodem modo 2NQ valet 2ID, id eſt iD, & </s> <s xml:id="echoid-s7441" xml:space="preserve">æqualis eſt KD - Ki; <lb/></s> <s xml:id="echoid-s7442" xml:space="preserve">unde deducimus 2PN x C + Ki x A = KD x A.</s> <s xml:id="echoid-s7443" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7444" xml:space="preserve">Multiplicatis hiſce tribus quantitatibus æqualibus KD x A, PN x C + <lb/>KI x A, & </s> <s xml:id="echoid-s7445" xml:space="preserve">2PN x C + Ki x A, per NM & </s> <s xml:id="echoid-s7446" xml:space="preserve">diviſis productis per <lb/>PN x <emph style="ol">A + B + C</emph>, habebimus quotientes æquales, à diſtantiis detectis non di-<lb/>verſos. </s> <s xml:id="echoid-s7447" xml:space="preserve">Q. </s> <s xml:id="echoid-s7448" xml:space="preserve">D. </s> <s xml:id="echoid-s7449" xml:space="preserve">E.</s> <s xml:id="echoid-s7450" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1030" type="section" level="1" n="251"> <head xml:id="echoid-head357" xml:space="preserve">SCHOLIUM 3.</head> <p> <s xml:id="echoid-s7451" xml:space="preserve">SI demonſtratam in hoc capite propoſitionem, ante & </s> <s xml:id="echoid-s7452" xml:space="preserve">poſt colliſionem <lb/> <anchor type="note" xlink:label="note-0267-02a" xlink:href="note-0267-02"/> centrum gravitatis eâdem velocitate ferri, applicemus ad colliſionem in n. <lb/></s> <s xml:id="echoid-s7453" xml:space="preserve">521. </s> <s xml:id="echoid-s7454" xml:space="preserve">memoratam, corporum poſt colliſionem velocitates determinare poſſu-<lb/>mus.</s> <s xml:id="echoid-s7455" xml:space="preserve"/> </p> <div xml:id="echoid-div1030" type="float" level="2" n="1"> <note position="right" xlink:label="note-0267-02" xlink:href="note-0267-02a" xml:space="preserve">667.</note> </div> <p> <s xml:id="echoid-s7456" xml:space="preserve">Tria corpora poſt ictum, juxta directionem primi motus feruntur veloci-<lb/>tate, qua ante ictum centrum gravitatis fertur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7457" xml:space="preserve">nam nulla datur actio qua <anchor type="note" xlink:label="note-0267-03a" xlink:href="note-0267-03"/> directe ſeparari poſſint; </s> <s xml:id="echoid-s7458" xml:space="preserve">velocitas hæc detegitur regulâ in n. </s> <s xml:id="echoid-s7459" xml:space="preserve">519. </s> <s xml:id="echoid-s7460" xml:space="preserve">traditâ. <lb/></s> <s xml:id="echoid-s7461" xml:space="preserve">itaque moventur ut corpora mollia poſt impactionem directam, ſed quæ in <lb/>hac corporum mollium impactione deſtruitur, corpora impingentia vim ſer-<lb/>vant in caſu quem examinamus; </s> <s xml:id="echoid-s7462" xml:space="preserve">& </s> <s xml:id="echoid-s7463" xml:space="preserve">hac idcirco lateraliter feruntur <anchor type="note" xlink:href="" symbol="*"/> quæ vis <anchor type="note" xlink:label="note-0267-04a" xlink:href="note-0267-04"/> datur <anchor type="note" xlink:href="" symbol="*"/> quare lateralis velocitas, quæ nempe cum prima directione angulumeffi- <anchor type="note" xlink:label="note-0267-05a" xlink:href="note-0267-05"/> cit rectum, detegi poteſt: </s> <s xml:id="echoid-s7464" xml:space="preserve">ideoque directiones & </s> <s xml:id="echoid-s7465" xml:space="preserve">velocitates abſolutas qui-<lb/>bus corpora impingentia poſt ictum moventur facile determinantur.</s> <s xml:id="echoid-s7466" xml:space="preserve"/> </p> <div xml:id="echoid-div1031" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0267-03" xlink:href="note-0267-03a" xml:space="preserve">652.</note> <note symbol="*" position="right" xlink:label="note-0267-04" xlink:href="note-0267-04a" xml:space="preserve">601.</note> <note symbol="*" position="right" xlink:label="note-0267-05" xlink:href="note-0267-05a" xml:space="preserve">510. 525.</note> </div> <p> <s xml:id="echoid-s7467" xml:space="preserve">Dicatur Q maſſa corporis quieſcentis; </s> <s xml:id="echoid-s7468" xml:space="preserve">ſint aliorum maſſæ P, P; </s> <s xml:id="echoid-s7469" xml:space="preserve">& </s> <s xml:id="echoid-s7470" xml:space="preserve">horum <lb/> <anchor type="note" xlink:label="note-0267-06a" xlink:href="note-0267-06"/> volocitas v.</s> <s xml:id="echoid-s7471" xml:space="preserve"/> </p> <div xml:id="echoid-div1032" type="float" level="2" n="3"> <note position="right" xlink:label="note-0267-06" xlink:href="note-0267-06a" xml:space="preserve"><emph style="sc">TAB XXI.</emph> <lb/>fig. 4</note> </div> <pb o="190" file="0268" n="292" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s7472" xml:space="preserve">Poſt ictum corpus Q movetur velocitate {2Pv/2P + Q} <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7473" xml:space="preserve">eâdem velocitate, jux- <anchor type="note" xlink:label="note-0268-01a" xlink:href="note-0268-01"/> ta eandem directionem, feruntur corpora P, P, ſed hæc præterea laterali-<lb/>ter feruntur viribus quæ valent {2PQvv/2P + Q} <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7474" xml:space="preserve">quare utriuſque lateralis ve- <anchor type="note" xlink:label="note-0268-02a" xlink:href="note-0268-02"/> locitas eſt {v√Q\x{0020}/√2P + Q\x{0020}} <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7475" xml:space="preserve">velocitas abſoluta {v √4PP + 2PQ + QQ\x{0020}/2P + Q} <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7476" xml:space="preserve"> <anchor type="note" xlink:label="note-0268-03a" xlink:href="note-0268-03"/> <anchor type="note" xlink:label="note-0268-04a" xlink:href="note-0268-04"/> </s> </p> <div xml:id="echoid-div1033" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0268-01" xlink:href="note-0268-01a" xml:space="preserve">519.</note> <note symbol="*" position="left" xlink:label="note-0268-02" xlink:href="note-0268-02a" xml:space="preserve">510. 525.</note> <note symbol="*" position="left" xlink:label="note-0268-03" xlink:href="note-0268-03a" xml:space="preserve">470.</note> <note symbol="*" position="left" xlink:label="note-0268-04" xlink:href="note-0268-04a" xml:space="preserve">610.</note> </div> </div> <div xml:id="echoid-div1035" type="section" level="1" n="252"> <head xml:id="echoid-head358" xml:space="preserve">CAPUT XXIX.</head> <head xml:id="echoid-head359" style="it" xml:space="preserve">De Legibus Elaſticitatis.</head> <p> <s xml:id="echoid-s7477" xml:space="preserve">QUid ſit Elaſticitas, & </s> <s xml:id="echoid-s7478" xml:space="preserve">unde oriatur, jam vidimus <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s7479" xml:space="preserve"> <anchor type="note" xlink:label="note-0268-05a" xlink:href="note-0268-05"/> etiam quid ex eo in congreſſu corporum, ſive dire-<lb/>cte, ſive oblique, in ſe mutuo impingentium eve-<lb/>niat; </s> <s xml:id="echoid-s7480" xml:space="preserve">ſupereſt ut ipſius Elaſticitatis leges examinemus, il-<lb/>ludque ex Phænomenis.</s> <s xml:id="echoid-s7481" xml:space="preserve"/> </p> <div xml:id="echoid-div1035" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0268-05" xlink:href="note-0268-05a" xml:space="preserve">701.</note> </div> <p> <s xml:id="echoid-s7482" xml:space="preserve">Omnia corpora, in quibus Elaſticitatem obſervamus, <lb/>conſtant ex filamentis tenuibus, aut ſaltem quaſi ex talibus <lb/>conſtantia conſiderari poſſunt, corpus enim in fila diviſum <lb/>concipi poteſt; </s> <s xml:id="echoid-s7483" xml:space="preserve">illaque fila, ad ſe mutuo appoſita, corpus <lb/>formare; </s> <s xml:id="echoid-s7484" xml:space="preserve">ut ergo in caſu omnium minime compoſito E-<lb/>laſticitas examinetur, chordæ conſiderandæ ſunt, & </s> <s xml:id="echoid-s7485" xml:space="preserve">qui-<lb/>dem metallicæ; </s> <s xml:id="echoid-s7486" xml:space="preserve">chordæ enim exinteſtinis ovium ſpiram for-<lb/>mant, & </s> <s xml:id="echoid-s7487" xml:space="preserve">non ut fibræ, ex quibus corpora formantur, con-<lb/>ſiderari queunt.</s> <s xml:id="echoid-s7488" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7489" xml:space="preserve">Fibrarum Elaſticitas in eo ſita eſt, quod extendi poſſint, <lb/> <anchor type="note" xlink:label="note-0268-06a" xlink:href="note-0268-06"/> & </s> <s xml:id="echoid-s7490" xml:space="preserve">ſublata vi qua producuntur, iterum ad priſtinam longi-<lb/>tudinem redeant.</s> <s xml:id="echoid-s7491" xml:space="preserve"/> </p> <div xml:id="echoid-div1036" type="float" level="2" n="2"> <note position="left" xlink:label="note-0268-06" xlink:href="note-0268-06a" xml:space="preserve">668.</note> </div> <p> <s xml:id="echoid-s7492" xml:space="preserve">Fibræ nullam habent Elaſticitatem, niſi certâ vi ten-<lb/> <anchor type="note" xlink:label="note-0268-07a" xlink:href="note-0268-07"/> ſæ ſint; </s> <s xml:id="echoid-s7493" xml:space="preserve">ut patet ex chordis parum tenſis, & </s> <s xml:id="echoid-s7494" xml:space="preserve">quarum ex-<lb/>tremitates fixæ ſunt; </s> <s xml:id="echoid-s7495" xml:space="preserve">quæ ſi a ſitu paululum removeantur, <lb/>ad illum ſponte non redeunt: </s> <s xml:id="echoid-s7496" xml:space="preserve">quiſnam vero ſit gradus ten-<lb/>ſionis, in quo Elaſticitas inchoetur, Experimentis nondum <lb/>fuit determinatum.</s> <s xml:id="echoid-s7497" xml:space="preserve"/> </p> <div xml:id="echoid-div1037" type="float" level="2" n="3"> <note position="left" xlink:label="note-0268-07" xlink:href="note-0268-07a" xml:space="preserve">669.</note> </div> <p> <s xml:id="echoid-s7498" xml:space="preserve">Quando nimia vi fibra tenditur, Elaſticitatem amittit; <lb/></s> <s xml:id="echoid-s7499" xml:space="preserve"> <anchor type="note" xlink:label="note-0268-08a" xlink:href="note-0268-08"/> <pb file="0269" n="293"/> <pb file="0269a" n="294"/> <anchor type="figure" xlink:label="fig-0269a-01a" xlink:href="fig-0269a-01"/> <pb file="0270" n="295"/> <pb o="191" file="0271" n="296" rhead="MATHEMATICA. LIB. I. CAP XXIX."/> & </s> <s xml:id="echoid-s7500" xml:space="preserve">neque gradus hicce tenſionis notus eſt; </s> <s xml:id="echoid-s7501" xml:space="preserve">illud conſtat, <lb/>tenſionem fibrarum, quæ Elaſticitatem conſtituit, certis <lb/>limitibus terminari.</s> <s xml:id="echoid-s7502" xml:space="preserve"/> </p> <div xml:id="echoid-div1038" type="float" level="2" n="4"> <note position="left" xlink:label="note-0268-08" xlink:href="note-0268-08a" xml:space="preserve">670.</note> <figure xlink:label="fig-0269a-01" xlink:href="fig-0269a-01a"> <image file="0269a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0269a-01"/> </figure> </div> <p> <s xml:id="echoid-s7503" xml:space="preserve">Ex hiſce patet differentia corporum elaſticorum & </s> <s xml:id="echoid-s7504" xml:space="preserve">non <lb/> <anchor type="note" xlink:label="note-0271-01a" xlink:href="note-0271-01"/> elaſticorum; </s> <s xml:id="echoid-s7505" xml:space="preserve">quare corpus elaſticum Elaſticitatem amit tit, <lb/>& </s> <s xml:id="echoid-s7506" xml:space="preserve">quomodo Elaſticitate deſtitutum proprietatem hanc acqui-<lb/>rit. </s> <s xml:id="echoid-s7507" xml:space="preserve">Lamina metallica, repetitis mallei ictibus, quibus fibræ <lb/>tenduntur, fit elaſtica, calefacta vim hanc amittit, dum vi <lb/>ignis ſitus partium turbatur.</s> <s xml:id="echoid-s7508" xml:space="preserve"/> </p> <div xml:id="echoid-div1039" type="float" level="2" n="5"> <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">671.</note> </div> <p> <s xml:id="echoid-s7509" xml:space="preserve">Inter limites tenſionis, quibus elaſticitas terminatur, pro <lb/>vario tenſionis gradu, vis diverſa requiritur, ad chordam <lb/>certa quantítate producendam; </s> <s xml:id="echoid-s7510" xml:space="preserve">quænam hic proportio lo-<lb/>cum habeat Experimentis determinari debet, quæ, ut jam <lb/>dictum, cum chordis metallicis inſtituenda ſunt. </s> <s xml:id="echoid-s7511" xml:space="preserve">Cum ve-<lb/>ro hæ chordæ vix ſenſibiliter producantur, directe produ-<lb/>ctionum proportiones menſurari nequeunt; </s> <s xml:id="echoid-s7512" xml:space="preserve">alia methodo <lb/>hæ determinantur.</s> <s xml:id="echoid-s7513" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7514" xml:space="preserve">Sit chorda horizontalis AB, certa vi tenſa; </s> <s xml:id="echoid-s7515" xml:space="preserve">cujus extre <lb/> <anchor type="note" xlink:label="note-0271-02a" xlink:href="note-0271-02"/> mitates in A & </s> <s xml:id="echoid-s7516" xml:space="preserve">B fixæ ſunt; </s> <s xml:id="echoid-s7517" xml:space="preserve">pondere in medio chordæ ap-<lb/>penſo inflectatur chorda, ut ſitum ACB acquirat.</s> <s xml:id="echoid-s7518" xml:space="preserve"/> </p> <div xml:id="echoid-div1040" type="float" level="2" n="6"> <note position="right" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve"><emph style="sc">TA XXVI</emph> <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div1042" type="section" level="1" n="253"> <head xml:id="echoid-head360" xml:space="preserve"><emph style="sc">Definitio.</emph></head> <p style="it"> <s xml:id="echoid-s7519" xml:space="preserve">Linea ut C c a puncto medio chordæ poſt inflexionem, ad <lb/> <anchor type="note" xlink:label="note-0271-03a" xlink:href="note-0271-03"/> punctum medium in ſitu naturali, vocatur chordæ ſagit-<lb/>ta.</s> <s xml:id="echoid-s7520" xml:space="preserve"/> </p> <div xml:id="echoid-div1042" type="float" level="2" n="1"> <note position="right" xlink:label="note-0271-03" xlink:href="note-0271-03a" xml:space="preserve">672.</note> </div> <p> <s xml:id="echoid-s7521" xml:space="preserve">Sit c e circuli portio, centro B, & </s> <s xml:id="echoid-s7522" xml:space="preserve">radio B c, deſcripti. <lb/></s> <s xml:id="echoid-s7523" xml:space="preserve">Inflexione dimidia pars chordæ producta fuit quantita-<lb/>te C e, quæ quantitas cum ſagitta C c certam relationem <lb/>habet.</s> <s xml:id="echoid-s7524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7525" xml:space="preserve">Pondus etiam, quo chorda inflectitur, certam cum vi, <lb/>qua fibra producitur, id eſt, per BC trahitur, relationem <lb/>habet; </s> <s xml:id="echoid-s7526" xml:space="preserve">& </s> <s xml:id="echoid-s7527" xml:space="preserve">ita in variis Experimentis ex comparationibus ſa-<lb/>gittarum, & </s> <s xml:id="echoid-s7528" xml:space="preserve">ponderum quibus chordæ inflectuntur, pro-<lb/>ductionum proportiones determinari poſſunt, ut ſequentibus <lb/>Experimentis patebit.</s> <s xml:id="echoid-s7529" xml:space="preserve"/> </p> <pb o="192" file="0272" n="297" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1044" type="section" level="1" n="254"> <head xml:id="echoid-head361" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head362" style="it" xml:space="preserve">Qua Experimenta de Elaſticitate inſtituuntur.</head> <p> <s xml:id="echoid-s7530" xml:space="preserve">Machinæ hujus pars præcipua eſt tabula lignea verti-<lb/> <anchor type="note" xlink:label="note-0272-01a" xlink:href="note-0272-01"/> calis, longitudinis circiter trium pedum, altitudinis unius <lb/> <anchor type="note" xlink:label="note-0272-02a" xlink:href="note-0272-02"/> pedis.</s> <s xml:id="echoid-s7531" xml:space="preserve"/> </p> <div xml:id="echoid-div1044" type="float" level="2" n="1"> <note position="left" xlink:label="note-0272-01" xlink:href="note-0272-01a" xml:space="preserve">673.</note> <note position="left" xlink:label="note-0272-02" xlink:href="note-0272-02a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s7532" xml:space="preserve">Regulæ ligneæ mn, mn, tabulæ cohærent, & </s> <s xml:id="echoid-s7533" xml:space="preserve">iis ſuſti-<lb/>nentur duo Priſmata H, H, ad formam cunei, quæ juxta illas <lb/>regulas moventur, & </s> <s xml:id="echoid-s7534" xml:space="preserve">ubique ope cochlearum tranſeuntium <lb/>per ſcisſuras in tabula firmantur.</s> <s xml:id="echoid-s7535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7536" xml:space="preserve">Dantur inter A & </s> <s xml:id="echoid-s7537" xml:space="preserve">B diviſiones æquales, a medio tabulæ <lb/>partem utramque verſus, ad ſitum Priſmatum determinan-<lb/>dum.</s> <s xml:id="echoid-s7538" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7539" xml:space="preserve">In O datur ſulcus, quo Machinæ a latere connectitur tro-<lb/>chlea T, cujus figura datur in F, fig. </s> <s xml:id="echoid-s7540" xml:space="preserve">2. </s> <s xml:id="echoid-s7541" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7542" xml:space="preserve">X.</s> <s xml:id="echoid-s7543" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7544" xml:space="preserve">Chorda, cum qua Experimenta fiunt, ab una parte an-<lb/>nectitur extremitati regulæ m n, & </s> <s xml:id="echoid-s7545" xml:space="preserve">ad aliam partem circumit <lb/>trochleam T, pondere P illam tendente, & </s> <s xml:id="echoid-s7546" xml:space="preserve">Priſmatibus H. <lb/></s> <s xml:id="echoid-s7547" xml:space="preserve">H, in punctis, quæ a medio Machinæ æque diſtant, illam <lb/>ſuſtinentibus.</s> <s xml:id="echoid-s7548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7549" xml:space="preserve">Medio Tabulæ inſeritur lamina ænea d e, in partes mini-<lb/>mas diviſa, juxta quas diviſiones movetur lamina ænea fg, <lb/>quæ chordæ appenditur, & </s> <s xml:id="echoid-s7550" xml:space="preserve">in qua foramen datur per quod <lb/>hæc immittitur; </s> <s xml:id="echoid-s7551" xml:space="preserve">huic laminæ conjuncta eſt lanx L, quæ unâ <lb/>cum lamina f g exacte eſt ponderis unius unciæ.</s> <s xml:id="echoid-s7552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7553" xml:space="preserve">Longitudo chordæ in Experimentis æqualis eſt di-<lb/>ſtantiæ inter apices Priſmatum H, H; </s> <s xml:id="echoid-s7554" xml:space="preserve">nam in inflexionibus <lb/>minimis, circa quas ſolas Experimenta fiunt; </s> <s xml:id="echoid-s7555" xml:space="preserve">ponderibus in <lb/>C appenſis, chorda ſuper Priſmatibus non movetur, pondus <lb/>P non elevatur, & </s> <s xml:id="echoid-s7556" xml:space="preserve">pars, ut AB, ſola inflexionibus iſtis <lb/>producitur.</s> <s xml:id="echoid-s7557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7558" xml:space="preserve">In chordæ inflexionibus ſagittæ menſurantur diviſioni-<lb/>bus laminæ e d, nam extremitas g laminæ g c æqualiter ſemper <lb/>cum puncto C, in chordæ inflexione, deſcendit.</s> <s xml:id="echoid-s7559" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1046" type="section" level="1" n="255"> <head xml:id="echoid-head363" xml:space="preserve"><emph style="sc">Experimentum. i.</emph></head> <p> <s xml:id="echoid-s7560" xml:space="preserve">Sit pondus P duarum librarum, & </s> <s xml:id="echoid-s7561" xml:space="preserve">inflectatur chorda in <lb/> <anchor type="note" xlink:label="note-0272-03a" xlink:href="note-0272-03"/> C pondere unius unciæ, id eſt, pondere lancis & </s> <s xml:id="echoid-s7562" xml:space="preserve">laminæ <pb o="193" file="0273" n="298" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/> f g, noteturque diviſio in lamina de ad quam extremitas <lb/>g laminæ f g deſcendit. </s> <s xml:id="echoid-s7563" xml:space="preserve">Mutetur pondus P, & </s> <s xml:id="echoid-s7564" xml:space="preserve">ſit quatuor <lb/>librarum, duplicandum etiam eſt pondus, quo chorda infle-<lb/>ctitur, ut deſcendat g ad eandem diviſionem, & </s> <s xml:id="echoid-s7565" xml:space="preserve">pondus hoc <lb/>eſt duarum unciarum; </s> <s xml:id="echoid-s7566" xml:space="preserve">tres unciæ ad eandem inflexionem <lb/>requiruntur, quando pondus P eſt ſex librarum.</s> <s xml:id="echoid-s7567" xml:space="preserve"/> </p> <div xml:id="echoid-div1046" type="float" level="2" n="1"> <note position="left" xlink:label="note-0272-03" xlink:href="note-0272-03a" xml:space="preserve">674.</note> </div> <p> <s xml:id="echoid-s7568" xml:space="preserve">Ex hoc Experimento ſequitur, pondus, quo certa quan-<lb/> <anchor type="note" xlink:label="note-0273-01a" xlink:href="note-0273-01"/> titate producitur fibra, in variis gradibus tenſionis fibræ, <lb/>eandem cum tenſione rationem ſequi: </s> <s xml:id="echoid-s7569" xml:space="preserve">ſi dentur ex. </s> <s xml:id="echoid-s7570" xml:space="preserve">gr. </s> <s xml:id="echoid-s7571" xml:space="preserve">tres <lb/>fibræ ejuſdem generis, longitudinis, & </s> <s xml:id="echoid-s7572" xml:space="preserve">craſſitiei, quarum <lb/>tenſiones ſunt ut 1. </s> <s xml:id="echoid-s7573" xml:space="preserve">2. </s> <s xml:id="echoid-s7574" xml:space="preserve">& </s> <s xml:id="echoid-s7575" xml:space="preserve">3.</s> <s xml:id="echoid-s7576" xml:space="preserve">; pondera quæcunque in eadem <lb/>proportione æqualiter producunt illas fibras.</s> <s xml:id="echoid-s7577" xml:space="preserve"/> </p> <div xml:id="echoid-div1047" type="float" level="2" n="2"> <note position="right" xlink:label="note-0273-01" xlink:href="note-0273-01a" xml:space="preserve">675.</note> </div> <p> <s xml:id="echoid-s7578" xml:space="preserve">Ejuſdem fibræ productiones minimæ ſunt inter ſe quam <lb/> <anchor type="note" xlink:label="note-0273-02a" xlink:href="note-0273-02"/> proxime ut vires quibus fibræ producuntur. </s> <s xml:id="echoid-s7579" xml:space="preserve">Detur ex. <lb/></s> <s xml:id="echoid-s7580" xml:space="preserve">gr. </s> <s xml:id="echoid-s7581" xml:space="preserve">fibra tenſa pondere centum unciarum, ſi ſeparatim <lb/>producatur viribus unius unciæ, duarum unciarum, & </s> <s xml:id="echoid-s7582" xml:space="preserve">tri-<lb/>um unciarum, productiones erunt quam proxime ut unum, <lb/>duo, & </s> <s xml:id="echoid-s7583" xml:space="preserve">tria <anchor type="note" xlink:href="" symbol="*"/>, id eſt, unaquæque uncia ſuperaddita fere <anchor type="note" xlink:label="note-0273-03a" xlink:href="note-0273-03"/> æqualiter producit fibram: </s> <s xml:id="echoid-s7584" xml:space="preserve">nam tenſiones ponderibus 100. <lb/></s> <s xml:id="echoid-s7585" xml:space="preserve">101. </s> <s xml:id="echoid-s7586" xml:space="preserve">& </s> <s xml:id="echoid-s7587" xml:space="preserve">102. </s> <s xml:id="echoid-s7588" xml:space="preserve">unciarum, quibus in ſingulis caſibus, quando <lb/>uncia ſuperadditur, tenditur fibra, parum inter ſe diffe-<lb/>runt.</s> <s xml:id="echoid-s7589" xml:space="preserve"/> </p> <div xml:id="echoid-div1048" type="float" level="2" n="3"> <note position="right" xlink:label="note-0273-02" xlink:href="note-0273-02a" xml:space="preserve">676.</note> <note symbol="*" position="right" xlink:label="note-0273-03" xlink:href="note-0273-03a" xml:space="preserve">673.</note> </div> <p> <s xml:id="echoid-s7590" xml:space="preserve">Hæc fibrarum proprietas ad inflexionem ipſarum appli-<lb/> <anchor type="note" xlink:label="note-0273-04a" xlink:href="note-0273-04"/> cari poteſt, & </s> <s xml:id="echoid-s7591" xml:space="preserve">magni uſus eſt. </s> <s xml:id="echoid-s7592" xml:space="preserve">Inflectatur chorda AB, ita ut <lb/> <anchor type="note" xlink:label="note-0273-05a" xlink:href="note-0273-05"/> ſitus A c B, A c B, & </s> <s xml:id="echoid-s7593" xml:space="preserve">ACB acquirat, ita tamen ut in maxima <lb/>inflexione ſagitta non ſit quartæ partis unius pollicis, po-<lb/>ſitâ chordæ longitudine duorum pedum cum ſemiſſe; </s> <s xml:id="echoid-s7594" xml:space="preserve">in <lb/>iſtis caſibus productiones chordæ ſunt admodum parvæ, er-<lb/>go in ratione virium, a quibus oriuntur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7595" xml:space="preserve">iſtas vires de- <anchor type="note" xlink:label="note-0273-06a" xlink:href="note-0273-06"/> ſignant; </s> <s xml:id="echoid-s7596" xml:space="preserve">denotet c D vim qua chorda non inflexa tenditur, <lb/>& </s> <s xml:id="echoid-s7597" xml:space="preserve">centro B deſcribatur circulus Dd; </s> <s xml:id="echoid-s7598" xml:space="preserve">lineæ dc, dc, dC, quæ <lb/>ſingulæ ſuperant lineam cD, quantitate, qua in ſingulis inflexio-<lb/>nibus fibra fuit producta, exprimunt vires integras, quibus in <lb/>ſingulis caſibus fibra tenditur. </s> <s xml:id="echoid-s7599" xml:space="preserve">Sed hic arcus D d vix eſt unius <lb/>gradus, & </s> <s xml:id="echoid-s7600" xml:space="preserve">D ſemper a puncto c ſatis diſtat, quare D d pro linea <lb/>recta ipſic C parallela haberi poteſt, & </s> <s xml:id="echoid-s7601" xml:space="preserve">lineæ cd, cd, C d <pb o="194" file="0274" n="299" rhead="PHYSICES ELEMENTA"/> in eadem ſunt ratione cum lineis cB, cB, CB. </s> <s xml:id="echoid-s7602" xml:space="preserve">Punctum <lb/>ideo C verſus B & </s> <s xml:id="echoid-s7603" xml:space="preserve">A ſemper trahitur, viribus lineæ CB <lb/>aut CA proportionalibus; </s> <s xml:id="echoid-s7604" xml:space="preserve">& </s> <s xml:id="echoid-s7605" xml:space="preserve">vis qua chorda inflectitur, cu-<lb/>jus directio eſt per c C, duplicatæ ſagittæ rationem ſequi-<lb/> <anchor type="note" xlink:label="note-0274-01a" xlink:href="note-0274-01"/> tur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7606" xml:space="preserve">eſt ut ipſa ſagitta. </s> <s xml:id="echoid-s7607" xml:space="preserve">In omnibus ergo chordæ cu- <anchor type="note" xlink:label="note-0274-02a" xlink:href="note-0274-02"/> juſcunque inflexionibus minimis, ſagitta creſcit & </s> <s xml:id="echoid-s7608" xml:space="preserve">minuitur <lb/>in eadem ratione cum vi qua chorda inflectitur.</s> <s xml:id="echoid-s7609" xml:space="preserve"/> </p> <div xml:id="echoid-div1049" type="float" level="2" n="4"> <note position="right" xlink:label="note-0273-04" xlink:href="note-0273-04a" xml:space="preserve">677.</note> <note position="right" xlink:label="note-0273-05" xlink:href="note-0273-05a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0273-06" xlink:href="note-0273-06a" xml:space="preserve">676.</note> <note symbol="*" position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">220, 231.</note> <note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">678.</note> </div> </div> <div xml:id="echoid-div1051" type="section" level="1" n="256"> <head xml:id="echoid-head364" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s7610" xml:space="preserve">Chorda AB, pondere quocunque tenſa, inflectitur pon-<lb/> <anchor type="note" xlink:label="note-0274-03a" xlink:href="note-0274-03"/> deribus unius unciæ, duarum, & </s> <s xml:id="echoid-s7611" xml:space="preserve">trium unciarum, deſcen-<lb/> <anchor type="note" xlink:label="note-0274-04a" xlink:href="note-0274-04"/> ſus puncti g, id eſt, ipſæ ſagittæ, ſunt inter ſe ut unum, <lb/>duo, & </s> <s xml:id="echoid-s7612" xml:space="preserve">tria.</s> <s xml:id="echoid-s7613" xml:space="preserve"/> </p> <div xml:id="echoid-div1051" type="float" level="2" n="1"> <note position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">679.</note> <note position="left" xlink:label="note-0274-04" xlink:href="note-0274-04a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s7614" xml:space="preserve">In chordis ejuſdem generis, craſſitiei, & </s> <s xml:id="echoid-s7615" xml:space="preserve">æqualiter tenſis, <lb/> <anchor type="note" xlink:label="note-0274-05a" xlink:href="note-0274-05"/> ſed diverſæ longitudinis, productiones, quæ ex ſuperadditis <lb/>æqualibus ponderibus oriuntur, ſunt inter ſe ut chor darum <lb/>longitudines. </s> <s xml:id="echoid-s7616" xml:space="preserve">Ex eo hoc patet, quod chorda in omnibus <lb/>punctis ſit æque tenſa; </s> <s xml:id="echoid-s7617" xml:space="preserve">productio ergo integræ chordæ eſt <lb/>dupla productionis dimidiæ partis, aut chordæ dimidiæ lon-<lb/>gitudinis.</s> <s xml:id="echoid-s7618" xml:space="preserve"/> </p> <div xml:id="echoid-div1052" type="float" level="2" n="2"> <note position="left" xlink:label="note-0274-05" xlink:href="note-0274-05a" xml:space="preserve">680.</note> </div> <p> <s xml:id="echoid-s7619" xml:space="preserve">Quod ad inflexionem harum chordarum attinet, ſint <lb/> <anchor type="note" xlink:label="note-0274-06a" xlink:href="note-0274-06"/> AB, ab, chordæ ejuſdem generis & </s> <s xml:id="echoid-s7620" xml:space="preserve">craſſitiei, ſed diverſæ <lb/> <anchor type="note" xlink:label="note-0274-07a" xlink:href="note-0274-07"/> longitudinis, æque tenſæ & </s> <s xml:id="echoid-s7621" xml:space="preserve">ita inflexæ, ut ACB ſit ſitus <lb/>illius; </s> <s xml:id="echoid-s7622" xml:space="preserve">adb hujus inflexio; </s> <s xml:id="echoid-s7623" xml:space="preserve">& </s> <s xml:id="echoid-s7624" xml:space="preserve">ſint triangula BCc & </s> <s xml:id="echoid-s7625" xml:space="preserve">bDd ſi-<lb/>milia: </s> <s xml:id="echoid-s7626" xml:space="preserve">cB eſt ad Db, id eſt, ſunt chordarum longitudines, <lb/>ut CB ad db; </s> <s xml:id="echoid-s7627" xml:space="preserve">chordæ ergo proportionaliter ad longitudi-<lb/>nes producuntur, & </s> <s xml:id="echoid-s7628" xml:space="preserve">ideo viribus æqualibus, juxta directio-<lb/>nes bd, ad, BC, AC trahuntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7629" xml:space="preserve">propter ſimilitudinem <anchor type="note" xlink:label="note-0274-08a" xlink:href="note-0274-08"/> autem triangulorum ſtatim memoratorum vires etiam juxta <lb/>cC & </s> <s xml:id="echoid-s7630" xml:space="preserve">Dd agentes ſunt æquales inter ſe <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7631" xml:space="preserve">ſagittæ cC, <anchor type="note" xlink:label="note-0274-09a" xlink:href="note-0274-09"/> Dd ſunt ut chordarum longitudines; </s> <s xml:id="echoid-s7632" xml:space="preserve">quod igitur, cæteris <lb/> <anchor type="note" xlink:label="note-0274-10a" xlink:href="note-0274-10"/> paribus, in chordis inæqualibus & </s> <s xml:id="echoid-s7633" xml:space="preserve">inflexis ſemper obti-<lb/>net.</s> <s xml:id="echoid-s7634" xml:space="preserve"/> </p> <div xml:id="echoid-div1053" type="float" level="2" n="3"> <note position="left" xlink:label="note-0274-06" xlink:href="note-0274-06a" xml:space="preserve">681.</note> <note position="left" xlink:label="note-0274-07" xlink:href="note-0274-07a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0274-08" xlink:href="note-0274-08a" xml:space="preserve">680.</note> <note position="left" xlink:label="note-0274-09" xlink:href="note-0274-09a" xml:space="preserve">682.</note> <note symbol="*" position="left" xlink:label="note-0274-10" xlink:href="note-0274-10a" xml:space="preserve">200. 232.</note> </div> </div> <div xml:id="echoid-div1055" type="section" level="1" n="257"> <head xml:id="echoid-head365" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s7635" xml:space="preserve">Chorda A B pondere quocunque tenditur, applicatis <lb/> <anchor type="note" xlink:label="note-0274-11a" xlink:href="note-0274-11"/> Priſmatibus H, H, ab utraque parte ad ſextam diviſionem; <lb/></s> <s xml:id="echoid-s7636" xml:space="preserve"> <anchor type="note" xlink:label="note-0274-12a" xlink:href="note-0274-12"/> inflectatur pondere quocunque, ita ut ſagitta ſit ſex divi- <pb o="195" file="0275" n="300" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/> ſionum laminæ ed. </s> <s xml:id="echoid-s7637" xml:space="preserve">Mutentur Priſmata & </s> <s xml:id="echoid-s7638" xml:space="preserve">ad quartam ta-<lb/>bulæ diviſionem ab utraque parte ponantur, ſagitta erit qua-<lb/>tuor diviſionum laminæ, & </s> <s xml:id="echoid-s7639" xml:space="preserve">ſic pro quocunque ſitu Priſma-<lb/>tum.</s> <s xml:id="echoid-s7640" xml:space="preserve"/> </p> <div xml:id="echoid-div1055" type="float" level="2" n="1"> <note position="left" xlink:label="note-0274-11" xlink:href="note-0274-11a" xml:space="preserve">683.</note> <note position="left" xlink:label="note-0274-12" xlink:href="note-0274-12a" xml:space="preserve"><emph style="sc">TA. XXVI</emph> <lb/>fig. a.</note> </div> <p> <s xml:id="echoid-s7641" xml:space="preserve">Fibræ ejuſdem generis, ſed diverſæ craſſitiei, ſi inter ſe <lb/>comparantur, poſſunt conſiderari quaſi formatæ ex multis <lb/>fibris tenuiſſimis ejuſdem craſſitiei, quarum numerus in fi-<lb/>bris memoratis erit in ratione ſoliditatis harum fibrarum, <lb/>id eſt, ut quadrata diametrorum, aut ut pondera quando <lb/> <anchor type="note" xlink:label="note-0275-01a" xlink:href="note-0275-01"/> fibræ ſunt æquales. </s> <s xml:id="echoid-s7642" xml:space="preserve">Viribus ergo in eadem ratione quadra-<lb/>torum diametrorum, hæ fibræ æqualiter tenduntur; </s> <s xml:id="echoid-s7643" xml:space="preserve">quæ <lb/>etiam ratio inter vires, quibus chordæ inflectuntur, requi-<lb/>ritur, ut ſagittæ datis fibris æqualibus ſint æquales. </s> <s xml:id="echoid-s7644" xml:space="preserve">Sed <lb/>minuendo in eadem ratione vim, qua fibra tenditur, cum <lb/>vi, qua inflectitur, ſagitta non mutatur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7645" xml:space="preserve">poſitis igitur vi- <anchor type="note" xlink:label="note-0275-02a" xlink:href="note-0275-02"/> ribus, quibus fibræ tenduntur, æqualibus, ſi æqualibus vi-<lb/>ribus inflectantur, etiam in eo caſu ſagittæ erunt æquales, <lb/>quæcunque fuerit craſſitiei diverſitas.</s> <s xml:id="echoid-s7646" xml:space="preserve"/> </p> <div xml:id="echoid-div1056" type="float" level="2" n="2"> <note position="right" xlink:label="note-0275-01" xlink:href="note-0275-01a" xml:space="preserve">684.</note> <note symbol="*" position="right" xlink:label="note-0275-02" xlink:href="note-0275-02a" xml:space="preserve">673.</note> </div> </div> <div xml:id="echoid-div1058" type="section" level="1" n="258"> <head xml:id="echoid-head366" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s7647" xml:space="preserve">Dentur chordæ quæcunque ejuſdem generis, & </s> <s xml:id="echoid-s7648" xml:space="preserve">inæqua-<lb/> <anchor type="note" xlink:label="note-0275-03a" xlink:href="note-0275-03"/> lis craſſitiei; </s> <s xml:id="echoid-s7649" xml:space="preserve">ſeparatim applicentur Machinæ, relictis Priſma-<lb/> <anchor type="note" xlink:label="note-0275-04a" xlink:href="note-0275-04"/> tìbus H, H, ſi eodem pondere Ptendantur, & </s> <s xml:id="echoid-s7650" xml:space="preserve">etiam eodem <lb/>pondere Linflectantur, ſagittæ erunt æquales.</s> <s xml:id="echoid-s7651" xml:space="preserve"/> </p> <div xml:id="echoid-div1058" type="float" level="2" n="1"> <note position="right" xlink:label="note-0275-03" xlink:href="note-0275-03a" xml:space="preserve">685.</note> <note position="right" xlink:label="note-0275-04" xlink:href="note-0275-04a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s7652" xml:space="preserve">Sichordautcunque tenſa AB inflectatur, ut figuram ACB <lb/> <anchor type="note" xlink:label="note-0275-05a" xlink:href="note-0275-05"/> acquirat, & </s> <s xml:id="echoid-s7653" xml:space="preserve">ſibirelinquatur, ex elaſticitate ad primam figuram <lb/> <anchor type="note" xlink:label="note-0275-06a" xlink:href="note-0275-06"/> redit, & </s> <s xml:id="echoid-s7654" xml:space="preserve">in eo caſu motus puncti C eſt acceleratus; </s> <s xml:id="echoid-s7655" xml:space="preserve">nam in ſitu <lb/>ACB chordæ, punctum Cmovetur, nam trahitur vi qua in illo <lb/>ſitu retineri poteſt; </s> <s xml:id="echoid-s7656" xml:space="preserve">motus hicce non deſtruitur, & </s> <s xml:id="echoid-s7657" xml:space="preserve">ei ſuperad-<lb/>ditur, in ſingulis punctis ſagittæ, motus oriundus ex vi qua pun-<lb/>ctum C in ipſis retineri poſſet; </s> <s xml:id="echoid-s7658" xml:space="preserve">celeritas omnium maxima eſt <lb/>in c, & </s> <s xml:id="echoid-s7659" xml:space="preserve">eâ punctum C ulterius fertur, deinde redit, variaſ-<lb/>que vibrationes peragit, in quibus punctum C niſi parva ſpa-<lb/>tia non excurrit; </s> <s xml:id="echoid-s7660" xml:space="preserve">qua de cauſa vis, qua, in omnibus diſtan-<lb/>tiis a c, agitatur punctum C, eſt ut hæc diſtantia <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7661" xml:space="preserve">Congruit <anchor type="note" xlink:label="note-0275-07a" xlink:href="note-0275-07"/> ergo motus hicce cum motu corporis in cycloïde vibrati, <lb/>& </s> <s xml:id="echoid-s7662" xml:space="preserve">vibrationes licet inæquales ſunt æque diuturnæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7663" xml:space="preserve"> <anchor type="note" xlink:label="note-0275-08a" xlink:href="note-0275-08"/> </s> </p> <div xml:id="echoid-div1059" type="float" level="2" n="2"> <note position="right" xlink:label="note-0275-05" xlink:href="note-0275-05a" xml:space="preserve">686.</note> <note position="right" xlink:label="note-0275-06" xlink:href="note-0275-06a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0275-07" xlink:href="note-0275-07a" xml:space="preserve">678.</note> <note symbol="*" position="right" xlink:label="note-0275-08" xlink:href="note-0275-08a" xml:space="preserve">380. 387</note> </div> <pb o="196" file="0276" n="301" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s7664" xml:space="preserve">Nam cum cauſa movens ſit chordæ Elaſticitas transfertur <lb/> <anchor type="note" xlink:label="note-0276-01a" xlink:href="note-0276-01"/> cauſa hæc cum ipſa fibra, quæ reſpectu ipſius quieſcit, quare in <lb/>hanc, licet agitatam, premit quaſi quieſceret hæc, ita ut <lb/>hìc vis movens ſit ejuſdem generis cum gravitate <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7665" xml:space="preserve"/> </p> <div xml:id="echoid-div1060" type="float" level="2" n="3"> <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">687.</note> </div> <note symbol="*" position="left" xml:space="preserve">252.</note> <p> <s xml:id="echoid-s7666" xml:space="preserve">Poſitis duabus chordis ſimilibus & </s> <s xml:id="echoid-s7667" xml:space="preserve">æqualibus, ſed inæ-<lb/> <anchor type="note" xlink:label="note-0276-03a" xlink:href="note-0276-03"/> qualiter tenſis, vires inæquales requiruntur ut æqualiter <lb/>inflectantur; </s> <s xml:id="echoid-s7668" xml:space="preserve">ergo vibrationes temporibus inæqualibus pera-<lb/>gunt.</s> <s xml:id="echoid-s7669" xml:space="preserve"/> </p> <div xml:id="echoid-div1061" type="float" level="2" n="4"> <note position="left" xlink:label="note-0276-03" xlink:href="note-0276-03a" xml:space="preserve">688.</note> </div> <p> <s xml:id="echoid-s7670" xml:space="preserve">Motus illarum conferri poſſunt cum motibus pendulo-<lb/>rum in cycloïdibus vibratorum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7671" xml:space="preserve">æquales cycloïdes, viri- <anchor type="note" xlink:label="note-0276-04a" xlink:href="note-0276-04"/> bus diverſis, deſcribentium; </s> <s xml:id="echoid-s7672" xml:space="preserve">quæ vires ſunt inverſe ut qua-<lb/>drata temporum vibrationum <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s7673" xml:space="preserve">in chordis ergo etiam qua- <anchor type="note" xlink:label="note-0276-05a" xlink:href="note-0276-05"/> drata temporum vibrationum ſunt inter ſe inverſe, ut vires <lb/>quibus æqualiter inflectuntur; </s> <s xml:id="echoid-s7674" xml:space="preserve">quæ ſunt ut pondera quibus <lb/>chordæ tenduntur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7675" xml:space="preserve"> <anchor type="note" xlink:label="note-0276-06a" xlink:href="note-0276-06"/> </s> </p> <div xml:id="echoid-div1062" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0276-04" xlink:href="note-0276-04a" xml:space="preserve">685.</note> <note symbol="*" position="left" xlink:label="note-0276-05" xlink:href="note-0276-05a" xml:space="preserve">301.</note> <note symbol="*" position="left" xlink:label="note-0276-06" xlink:href="note-0276-06a" xml:space="preserve">674.</note> </div> <p> <s xml:id="echoid-s7676" xml:space="preserve">Quando chordæ ſunt ſimiles, æque tenſæ, ſed diverſæ <lb/> <anchor type="note" xlink:label="note-0276-07a" xlink:href="note-0276-07"/> longitudinis, motus harum cum motu pendulorum etiam <lb/> <anchor type="note" xlink:label="note-0276-08a" xlink:href="note-0276-08"/> confertur. </s> <s xml:id="echoid-s7677" xml:space="preserve">Non intereſt quantum ad actionem gravitatis <lb/>in corpus, & </s> <s xml:id="echoid-s7678" xml:space="preserve">ideo quantum ad motum corporis ex gravi-<lb/>tate, utrum manente materiâ, ipſa vis gravitatis minuatur <lb/>in certa ratione, an vero manente hac vi materia in ea-<lb/>dem ratione augeatur <anchor type="note" xlink:href="" symbol="*"/>, quod ergo ad motum chordæ et- <anchor type="note" xlink:label="note-0276-09a" xlink:href="note-0276-09"/> iam applicari poteſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7679" xml:space="preserve">Ergo chordæ, ACB, adb, quæ <anchor type="note" xlink:label="note-0276-10a" xlink:href="note-0276-10"/> ponderibus æqualibus inflectuntur, agitantur ut corpora in <lb/>quibus gravitates agerent, quæ forent inter ſe ut ab, ad <lb/>AB; </s> <s xml:id="echoid-s7680" xml:space="preserve">in hac enim ratione inverſa ſunt quantitates materiæ <lb/>in chordis. </s> <s xml:id="echoid-s7681" xml:space="preserve">Chordæ etiam hæ moventur ut pendula, quo-<lb/>rum longitudines ſunt ut cB ad Db, aut AB ad ab; </s> <s xml:id="echoid-s7682" xml:space="preserve">ergo <lb/>quadrata durationum vibrationum, quæ ſunt inversè ut vi-<lb/>res, & </s> <s xml:id="echoid-s7683" xml:space="preserve">directè ut longitudines pendulorum <anchor type="note" xlink:href="" symbol="*"/>, ſunt in ra- <anchor type="note" xlink:label="note-0276-11a" xlink:href="note-0276-11"/> tione compoſita ex inverſa ratione ab ad AB, id eſt, AB <lb/>ad ab, & </s> <s xml:id="echoid-s7684" xml:space="preserve">directa ipſius AB ad ab; </s> <s xml:id="echoid-s7685" xml:space="preserve">quæ ratio compoſita <lb/>eſt ratio quadratorum longitudinum; </s> <s xml:id="echoid-s7686" xml:space="preserve">chordarum igitur lon-<lb/>gitudines ſunt ut vibrationum tempora.</s> <s xml:id="echoid-s7687" xml:space="preserve"/> </p> <div xml:id="echoid-div1063" type="float" level="2" n="6"> <note position="left" xlink:label="note-0276-07" xlink:href="note-0276-07a" xml:space="preserve">689.</note> <note position="left" xlink:label="note-0276-08" xlink:href="note-0276-08a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0276-09" xlink:href="note-0276-09a" xml:space="preserve">111.</note> <note symbol="*" position="left" xlink:label="note-0276-10" xlink:href="note-0276-10a" xml:space="preserve">687.</note> <note symbol="*" position="left" xlink:label="note-0276-11" xlink:href="note-0276-11a" xml:space="preserve">3@2.</note> </div> <p> <s xml:id="echoid-s7688" xml:space="preserve">Eodem modo comparantur tempora vibrationum chorda-<lb/> <anchor type="note" xlink:label="note-0276-12a" xlink:href="note-0276-12"/> rum diverſæ craſſitiei, poſitis chordis æqualibus, & </s> <s xml:id="echoid-s7689" xml:space="preserve">aqua- <pb o="197" file="0277" n="302" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/> libus ponderibus tenſis; </s> <s xml:id="echoid-s7690" xml:space="preserve">hæ æqualibus ponderibus æqualiter <lb/>inflectuntur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7691" xml:space="preserve">ideò agitantur ut pendula æqualia, in quæ <anchor type="note" xlink:label="note-0277-01a" xlink:href="note-0277-01"/> agunt gravitates, quæ ſunt inversè ut quantitates materiæ <lb/>in chordis <anchor type="note" xlink:href="" symbol="*"/>, id eſt, ut quadrata diametrorum; </s> <s xml:id="echoid-s7692" xml:space="preserve">quæ ratio <anchor type="note" xlink:label="note-0277-02a" xlink:href="note-0277-02"/> iterum invertenda eſt ad habendam proportionem quadra-<lb/>torum durationum vibrationum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7693" xml:space="preserve">Ideo diametri ipſæ ſunt <anchor type="note" xlink:label="note-0277-03a" xlink:href="note-0277-03"/> ut durationes.</s> <s xml:id="echoid-s7694" xml:space="preserve"/> </p> <div xml:id="echoid-div1064" type="float" level="2" n="7"> <note position="left" xlink:label="note-0276-12" xlink:href="note-0276-12a" xml:space="preserve">690.</note> <note symbol="*" position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">684</note> <note symbol="*" position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">112.</note> <note symbol="*" position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">301.</note> </div> <p> <s xml:id="echoid-s7695" xml:space="preserve">Datis chordis ejuſdem generis quibuſcunque, vibratio <lb/> <anchor type="note" xlink:label="note-0277-04a" xlink:href="note-0277-04"/> num durationes ſunt in ratione compoſita, ex ratione inver-<lb/>ſa radicum quadratarum ponderum, quibus chordæ tendun-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>, ratione longitudinum chordarum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7696" xml:space="preserve">ratione dia- <anchor type="note" xlink:label="note-0277-05a" xlink:href="note-0277-05"/> metrorum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7697" xml:space="preserve">Multiplicando diametrum per longitudinem, <anchor type="note" xlink:label="note-0277-06a" xlink:href="note-0277-06"/> dividendo productum per radicem quadratam ponderis, <lb/> <anchor type="note" xlink:label="note-0277-07a" xlink:href="note-0277-07"/> quo chorda tenditur, ſi pro variis chordis eadem operatio <lb/>inſtituatur, quotientes diviſionum erunt inter ſe ut vibra-<lb/>tionum tempora.</s> <s xml:id="echoid-s7698" xml:space="preserve"/> </p> <div xml:id="echoid-div1065" type="float" level="2" n="8"> <note position="right" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">691.</note> <note symbol="*" position="right" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">868.</note> <note symbol="*" position="right" xlink:label="note-0277-06" xlink:href="note-0277-06a" xml:space="preserve">689.</note> <note symbol="*" position="right" xlink:label="note-0277-07" xlink:href="note-0277-07a" xml:space="preserve">690.</note> </div> <p> <s xml:id="echoid-s7699" xml:space="preserve">Lamina elaſtica pro congerie chordarum haberi poteſt: <lb/></s> <s xml:id="echoid-s7700" xml:space="preserve"> <anchor type="note" xlink:label="note-0277-08a" xlink:href="note-0277-08"/> quando lamina inflectitur, fibræ quædam producuntur, & </s> <s xml:id="echoid-s7701" xml:space="preserve"><lb/>productiones inæquales ſunt in diverſis laminæ punctis, & </s> <s xml:id="echoid-s7702" xml:space="preserve"><lb/>ex iis, quæ de chordis dicta ſunt, curva, quæ a lamina in-<lb/>flexa formatur, detegitur.</s> <s xml:id="echoid-s7703" xml:space="preserve"/> </p> <div xml:id="echoid-div1066" type="float" level="2" n="9"> <note position="right" xlink:label="note-0277-08" xlink:href="note-0277-08a" xml:space="preserve">692.</note> </div> <p> <s xml:id="echoid-s7704" xml:space="preserve">Comparando inter ſe varias ejuſdem laminæ inflexiones, <lb/> <anchor type="note" xlink:label="note-0277-09a" xlink:href="note-0277-09"/> hæ proportionales ſunt viribus quibus lamina flectitur. </s> <s xml:id="echoid-s7705" xml:space="preserve">Sit <lb/> <anchor type="note" xlink:label="note-0277-10a" xlink:href="note-0277-10"/> lamina AB, cujus extremitas A fixa eſt, duabus inflecta-<lb/>tur viribus, quibus perveniat ad ab & </s> <s xml:id="echoid-s7706" xml:space="preserve">ab; </s> <s xml:id="echoid-s7707" xml:space="preserve">ſi una fuerit <lb/>alterius dupla, bb & </s> <s xml:id="echoid-s7708" xml:space="preserve">bB erunt æquales; </s> <s xml:id="echoid-s7709" xml:space="preserve">& </s> <s xml:id="echoid-s7710" xml:space="preserve">ideo in vi-<lb/>brationibus motus laminæ eodem modo acceleratur ac <lb/> <anchor type="note" xlink:label="note-0277-11a" xlink:href="note-0277-11"/> motus chordæ <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7711" xml:space="preserve">hæ vibrationes ſunt æque diutur- <anchor type="note" xlink:label="note-0277-12a" xlink:href="note-0277-12"/> næ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7712" xml:space="preserve"> <anchor type="note" xlink:label="note-0277-13a" xlink:href="note-0277-13"/> </s> </p> <div xml:id="echoid-div1067" type="float" level="2" n="10"> <note position="right" xlink:label="note-0277-09" xlink:href="note-0277-09a" xml:space="preserve">693.</note> <note position="right" xlink:label="note-0277-10" xlink:href="note-0277-10a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 5.</note> <note position="right" xlink:label="note-0277-11" xlink:href="note-0277-11a" xml:space="preserve">694.</note> <note symbol="*" position="right" xlink:label="note-0277-12" xlink:href="note-0277-12a" xml:space="preserve">678.</note> <note symbol="*" position="right" xlink:label="note-0277-13" xlink:href="note-0277-13a" xml:space="preserve">686.</note> </div> </div> <div xml:id="echoid-div1069" type="section" level="1" n="259"> <head xml:id="echoid-head367" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s7713" xml:space="preserve">Lamina A ex variis laminis elaſticis junctis conſtat, The-<lb/> <anchor type="note" xlink:label="note-0277-14a" xlink:href="note-0277-14"/> cæ B inſeritur, ibique ad latus utrumque movetur inter re-<lb/> <anchor type="note" xlink:label="note-0277-15a" xlink:href="note-0277-15"/> gulas cd, cd; </s> <s xml:id="echoid-s7714" xml:space="preserve">fila duo ſupremæ parti laminæ annectuntur, <lb/>& </s> <s xml:id="echoid-s7715" xml:space="preserve">per foramina e, e, in fundo Thecæ, immittuntur. </s> <s xml:id="echoid-s7716" xml:space="preserve">Pon-<lb/>dus ſemi-libræ filis appenditur, & </s> <s xml:id="echoid-s7717" xml:space="preserve">deſcendit hoc per ſpatium <lb/>ſemi-pollicis; </s> <s xml:id="echoid-s7718" xml:space="preserve">ſuperaddito æquali pondere, deſcenſus iterum <pb o="198" file="0278" n="303" rhead="PHYSICES ELEMENTA"/> eſt ſemi-pollicis, & </s> <s xml:id="echoid-s7719" xml:space="preserve">ſic ulterius donec non amplius compri-<lb/>mi poſſit lamina.</s> <s xml:id="echoid-s7720" xml:space="preserve"/> </p> <div xml:id="echoid-div1069" type="float" level="2" n="1"> <note position="right" xlink:label="note-0277-14" xlink:href="note-0277-14a" xml:space="preserve">695.</note> <note position="right" xlink:label="note-0277-15" xlink:href="note-0277-15a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s7721" xml:space="preserve">Unaquæque lamina minor proportionaliter ad pondus in-<lb/>flectitur, & </s> <s xml:id="echoid-s7722" xml:space="preserve">motus ponderis, ex omnibus inflexionibus jun-<lb/>ctis, eandem proportionem ſequitur. </s> <s xml:id="echoid-s7723" xml:space="preserve">Cum pluribus laminis <lb/>junctis Experimentum inſtituitur, quia in variis inflexioni-<lb/>bus directio actionis ponderis in laminas ſenſibiliter non <lb/>mutatur.</s> <s xml:id="echoid-s7724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7725" xml:space="preserve">Quæ de inflexione laminarum dicta ſunt, ad laminam <lb/> <anchor type="note" xlink:label="note-0278-01a" xlink:href="note-0278-01"/> curvam ACB transferri poſſunt; </s> <s xml:id="echoid-s7726" xml:space="preserve">ſi illa duobus ponderibus <lb/> <anchor type="note" xlink:label="note-0278-02a" xlink:href="note-0278-02"/> gravetur ut ſitus acb, acb acquirat, & </s> <s xml:id="echoid-s7727" xml:space="preserve">pondera ſint inter ſe <lb/>ut unum ad duo, diſtantiæ cc & </s> <s xml:id="echoid-s7728" xml:space="preserve">cC erunt æquales <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7729" xml:space="preserve">in- <anchor type="note" xlink:label="note-0278-03a" xlink:href="note-0278-03"/> troceſſiones igitur puncti C ſunt ut pondera quibus lamina <lb/>gravatur: </s> <s xml:id="echoid-s7730" xml:space="preserve">quod etiam referri poteſt ad introceſſiones pluri-<lb/>marum laminarum junctarum.</s> <s xml:id="echoid-s7731" xml:space="preserve"/> </p> <div xml:id="echoid-div1070" type="float" level="2" n="2"> <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">696.</note> <note position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">693.</note> </div> <p> <s xml:id="echoid-s7732" xml:space="preserve">Non tamen in Globo ACB, ex materia elaſtica, qui quaſi <lb/> <anchor type="note" xlink:label="note-0278-04a" xlink:href="note-0278-04"/> ex variis laminis conſtans conſiderari poteſt; </s> <s xml:id="echoid-s7733" xml:space="preserve">introceſſiones <lb/> <anchor type="note" xlink:label="note-0278-05a" xlink:href="note-0278-05"/> puncti ut C erunt proportionales viribus, quibus corpus <lb/>comprimitur. </s> <s xml:id="echoid-s7734" xml:space="preserve">Nam ſi introceſſio duplicetur, dupla vis qui-<lb/>dem requiritur propter duplam laminarum inflexionem, ſed <lb/>augenda ulterius eſt vis propter majorem numerum lamina-<lb/>rum inflexarum, & </s> <s xml:id="echoid-s7735" xml:space="preserve">experimentis conſtat, hac de cauſa <lb/>vim duplicandam eſſe, ita ut vis quadiupla requiratur: </s> <s xml:id="echoid-s7736" xml:space="preserve">et-<lb/>iam in genere experimentis conſtat, quadratum introceſſio-<lb/>nis ſequi eandem proportionem cum vi, qua globus com-<lb/>primitur, id eſt, ſi ipſe globus in obicem firmum incurrat, <lb/>ſunt introceſſiones ut velocitates, quibus in hunc impingi-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7737" xml:space="preserve"> <anchor type="note" xlink:label="note-0278-06a" xlink:href="note-0278-06"/> </s> </p> <div xml:id="echoid-div1071" type="float" level="2" n="3"> <note position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">697.</note> <note position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 8.</note> <note symbol="*" position="left" xlink:label="note-0278-06" xlink:href="note-0278-06a" xml:space="preserve">447.</note> </div> <p> <s xml:id="echoid-s7738" xml:space="preserve">Impingat, variis vicibus, punctum C globi ACBE in <lb/> <anchor type="note" xlink:label="note-0278-07a" xlink:href="note-0278-07"/> planum quodcunque, & </s> <s xml:id="echoid-s7739" xml:space="preserve">punctum C introcedat ad d, d, & </s> <s xml:id="echoid-s7740" xml:space="preserve">D, <lb/> <anchor type="note" xlink:label="note-0278-08a" xlink:href="note-0278-08"/> velocitates in ictibus erunt inter ſe ut lineæ Cd, Cd, CD; </s> <s xml:id="echoid-s7741" xml:space="preserve">in <lb/>primo ictu pars aCb plana fit, in ſecundo pars aCb, in tertio <lb/>pars ACB: </s> <s xml:id="echoid-s7742" xml:space="preserve">cum hìc ſemper agatur de arcubus minimis, arcus, <lb/>id eſt, diametri ſuperficierum planarum ex ictibus, ſunt in-<lb/>ter ſe ad ſenſum ut chordæ Ca, Ca & </s> <s xml:id="echoid-s7743" xml:space="preserve">CA; </s> <s xml:id="echoid-s7744" xml:space="preserve">ergo ipſæ <lb/>ſuperficies ut quadrata illarum chordarum, in qua etiam <pb o="199" file="0279" n="304" rhead="MATHEMATICA. LIB. I. CAP. XXIX."/> ratione, ſunt lineæ Cd, Cd, & </s> <s xml:id="echoid-s7745" xml:space="preserve">CD <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt inter <anchor type="note" xlink:label="note-0279-01a" xlink:href="note-0279-01"/> ſe ut velocitates <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7746" xml:space="preserve">In Sphæra igitur elaſtica ſuperficies pla- <anchor type="note" xlink:label="note-0279-02a" xlink:href="note-0279-02"/> næ ex ictibus eandem cum velocitatibus, quibus in obicem <lb/> <anchor type="note" xlink:label="note-0279-03a" xlink:href="note-0279-03"/> incurrit, proportionem ſequuntur.</s> <s xml:id="echoid-s7747" xml:space="preserve"/> </p> <div xml:id="echoid-div1072" type="float" level="2" n="4"> <note position="left" xlink:label="note-0278-07" xlink:href="note-0278-07a" xml:space="preserve">698.</note> <note position="left" xlink:label="note-0278-08" xlink:href="note-0278-08a" xml:space="preserve"><emph style="sc">TA. XXVI.</emph> <lb/>fig. 9.</note> <note symbol="*" position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">293.</note> <note symbol="*" position="right" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">698.</note> <note position="right" xlink:label="note-0279-03" xlink:href="note-0279-03a" xml:space="preserve">699.</note> </div> </div> <div xml:id="echoid-div1074" type="section" level="1" n="260"> <head xml:id="echoid-head368" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s7748" xml:space="preserve">Detur planum marmoreum, cæruleum, horizontaliter <lb/> <anchor type="note" xlink:label="note-0279-04a" xlink:href="note-0279-04"/> aliquo in loco firmatum, & </s> <s xml:id="echoid-s7749" xml:space="preserve">paululum madefactum, quan-<lb/> <anchor type="note" xlink:label="note-0279-05a" xlink:href="note-0279-05"/> tum neceſſe eſt, ut color magis ſit intenſus; </s> <s xml:id="echoid-s7750" xml:space="preserve">ſi in illud glo-<lb/>bus eburneus cadendo impingat, pars globi, quæ plana <lb/>facta ſeſe lapidi applicat, maculam circinnatam in hujus ſu-<lb/>perficie relinquit. </s> <s xml:id="echoid-s7751" xml:space="preserve">Cadat globus ab altitudine novem pol-<lb/>licum, & </s> <s xml:id="echoid-s7752" xml:space="preserve">ſit macula illa E; </s> <s xml:id="echoid-s7753" xml:space="preserve">cadat ab altitudine trium pe-<lb/>dum prioris quadrupla, & </s> <s xml:id="echoid-s7754" xml:space="preserve">ſit macula F; </s> <s xml:id="echoid-s7755" xml:space="preserve">tandem cadat ab <lb/>altitudine ſex pedum & </s> <s xml:id="echoid-s7756" xml:space="preserve">novem pollicum noncupla prioris, <lb/>& </s> <s xml:id="echoid-s7757" xml:space="preserve">ſit macula G. </s> <s xml:id="echoid-s7758" xml:space="preserve">In hoc Experimento velocitates corporis <lb/>ſunt inter ſe, ut unum, duo, & </s> <s xml:id="echoid-s7759" xml:space="preserve">tria <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7760" xml:space="preserve">in qua etiam ratio- <anchor type="note" xlink:label="note-0279-06a" xlink:href="note-0279-06"/> ne ſunt maculæ E, F, & </s> <s xml:id="echoid-s7761" xml:space="preserve">G; </s> <s xml:id="echoid-s7762" xml:space="preserve">nam formando triangula re-<lb/>ctangula DAB, DBC, in quibus latera DA, AB, BC <lb/>ſunt æqualia inter ſe & </s> <s xml:id="echoid-s7763" xml:space="preserve">diametro maculæ E, linea BC ex-<lb/>actiſſime æqualis erit diametro maculæ F, & </s> <s xml:id="echoid-s7764" xml:space="preserve">linea CD dia-<lb/>metro maculæ G, unde conſtat propoſitum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7765" xml:space="preserve"> <anchor type="note" xlink:label="note-0279-07a" xlink:href="note-0279-07"/> </s> </p> <div xml:id="echoid-div1074" type="float" level="2" n="1"> <note position="right" xlink:label="note-0279-04" xlink:href="note-0279-04a" xml:space="preserve">700.</note> <note position="right" xlink:label="note-0279-05" xlink:href="note-0279-05a" xml:space="preserve"><emph style="sc">TA XXVI.</emph> <lb/>fig. 10.</note> <note symbol="*" position="right" xlink:label="note-0279-06" xlink:href="note-0279-06a" xml:space="preserve">255.</note> <note symbol="*" position="right" xlink:label="note-0279-07" xlink:href="note-0279-07a" xml:space="preserve">47. El. 7. <lb/>2, El, XI@.</note> </div> </div> <div xml:id="echoid-div1076" type="section" level="1" n="261"> <head xml:id="echoid-head369" xml:space="preserve">SCHOLIUM.</head> <p> <s xml:id="echoid-s7766" xml:space="preserve">IN comparandis motibus chordarum, ipſarum inflexionem tantum conſide-<lb/> <anchor type="note" xlink:label="note-0279-08a" xlink:href="note-0279-08"/> ravimus in puncto medio, non attendendo ad curvaturam ipſius fibræ dum <lb/>agitatur, quo demonſtrationes de comparandis variarum fibrarum vibratio-<lb/>nibus non mutatur, fi autem tempus ipſum vibrationis cujuſcunque detegen-<lb/>dum eſſet, quod fit determinando longitudinem penduli eodem tempore vi-<lb/>brationes peragentis cum fibra, curvatura hæc conſideranda foret; </s> <s xml:id="echoid-s7767" xml:space="preserve">ſed de hoc <lb/>tempore hìc non agam, neque de curvâ elaſticâ in n. </s> <s xml:id="echoid-s7768" xml:space="preserve">691. </s> <s xml:id="echoid-s7769" xml:space="preserve">memoratâ; </s> <s xml:id="echoid-s7770" xml:space="preserve">quia <lb/>in hiſce uſus Methodorum fluxionum directæ & </s> <s xml:id="echoid-s7771" xml:space="preserve">inverſæ deſideratur, quod ad <lb/>ipſa Elementa Phyſices ſpectare mihi non videtur.</s> <s xml:id="echoid-s7772" xml:space="preserve"/> </p> <div xml:id="echoid-div1076" type="float" level="2" n="1"> <note position="right" xlink:label="note-0279-08" xlink:href="note-0279-08a" xml:space="preserve">701.</note> </div> </div> <div xml:id="echoid-div1078" type="section" level="1" n="262"> <head xml:id="echoid-head370" xml:space="preserve">FINIS LIBRI PRIMI.</head> <pb o="200" file="0280" n="305"/> </div> <div xml:id="echoid-div1079" type="section" level="1" n="263"> <head xml:id="echoid-head371" xml:space="preserve">PHYSICES</head> <head xml:id="echoid-head372" xml:space="preserve">ELEMENTA MATHEMATICA</head> <head xml:id="echoid-head373" xml:space="preserve">EXPERIMENTIS CONFIRMATA.</head> <head xml:id="echoid-head374" style="it" xml:space="preserve">LIBER II. <lb/>Pars I. de Gravitate, & Preſſione Fluidorum.</head> <head xml:id="echoid-head375" xml:space="preserve">CAPUT I. <lb/>De Gravitate partium Fluidorum, & illius Effectu in <lb/>ipſis Fluidis.</head> <p> <s xml:id="echoid-s7773" xml:space="preserve">FLuidum vocatur corpus, cujus partes impreſſioni <lb/>cuicunque cedunt, & </s> <s xml:id="echoid-s7774" xml:space="preserve">cedendo facillime mo-<lb/>ventur inter ſe <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7775" xml:space="preserve">Unde ſequitur fluiditatem ex <anchor type="note" xlink:label="note-0280-01a" xlink:href="note-0280-01"/> eo oriri, quod partes non arcte inter ſe cohære-<lb/> <anchor type="note" xlink:label="note-0280-02a" xlink:href="note-0280-02"/> ant, & </s> <s xml:id="echoid-s7776" xml:space="preserve">quod motus non impediatur inæqualita-<lb/>tibus in Partium ſuperficiebus, ut fit in pulveribus.</s> <s xml:id="echoid-s7777" xml:space="preserve"/> </p> <div xml:id="echoid-div1079" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0280-01" xlink:href="note-0280-01a" xml:space="preserve">50.</note> <note position="left" xlink:label="note-0280-02" xlink:href="note-0280-02a" xml:space="preserve">702.</note> </div> <p> <s xml:id="echoid-s7778" xml:space="preserve">Particulæ autem, ex quibus fluida conſtant, non diffe-<lb/> <anchor type="note" xlink:label="note-0280-03a" xlink:href="note-0280-03"/> runt ab aliorum corporum particulis, & </s> <s xml:id="echoid-s7779" xml:space="preserve">cum his eaſdem pro-<lb/>prietates habent; </s> <s xml:id="echoid-s7780" xml:space="preserve">fluida enim ſæpe in ſolida convertuntur, <lb/>quando magis arcta inter partes cohæſio datur, ut glacies: <lb/></s> <s xml:id="echoid-s7781" xml:space="preserve">metalla contra liquefacta exemplum ſolidi in fluidum mu-<lb/>tati præbent.</s> <s xml:id="echoid-s7782" xml:space="preserve"/> </p> <div xml:id="echoid-div1080" type="float" level="2" n="2"> <note position="left" xlink:label="note-0280-03" xlink:href="note-0280-03a" xml:space="preserve">703.</note> </div> <p> <s xml:id="echoid-s7783" xml:space="preserve">Fluida & </s> <s xml:id="echoid-s7784" xml:space="preserve">eo cum corporibus ſolidis congruunt, quod con-<lb/> <anchor type="note" xlink:label="note-0280-04a" xlink:href="note-0280-04"/> ſtent ex particulis gravibus, gravitatem materiæ quanti-<lb/>tati proportionalem, ubicunque poſitæ, habentibus. </s> <s xml:id="echoid-s7785" xml:space="preserve">Si in <lb/>ipſo fluido gravitas ſenſibilis non ſit, ex eo hoc oritur, <lb/>quod partes inferiores ſuperiores ſuſtineant, haſque deſcen- <pb file="0281" n="306"/> <pb file="0281a" n="307"/> <anchor type="figure" xlink:label="fig-0281a-01a" xlink:href="fig-0281a-01"/> <pb file="0282" n="308"/> <pb o="201" file="0283" n="309" rhead="MATHEMATICA. LIB. II. CAP. I."/> ſu arceant; </s> <s xml:id="echoid-s7786" xml:space="preserve">ipſam vero gravitatem eo non deſtrui liquet, <lb/>cum vaſe contentum fluidum pro ſua quantitate gravet li-<lb/>bram, cui vas appenditur; </s> <s xml:id="echoid-s7787" xml:space="preserve">etiam ſequenti Experimento <lb/>ubique in fluido particulas gravitatem ſervare probatur.</s> <s xml:id="echoid-s7788" xml:space="preserve"/> </p> <div xml:id="echoid-div1081" type="float" level="2" n="3"> <note position="left" xlink:label="note-0280-04" xlink:href="note-0280-04a" xml:space="preserve">704.</note> <figure xlink:label="fig-0281a-01" xlink:href="fig-0281a-01a"> <image file="0281a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0281a-01"/> </figure> </div> </div> <div xml:id="echoid-div1083" type="section" level="1" n="264"> <head xml:id="echoid-head376" xml:space="preserve"><emph style="sc">Bilanx</emph> <emph style="sc">Hydrostatica</emph>.</head> <p> <s xml:id="echoid-s7789" xml:space="preserve">In hoc, ut & </s> <s xml:id="echoid-s7790" xml:space="preserve">in aliis multis Experimentis Hydroſtaticis, <lb/> <anchor type="note" xlink:label="note-0283-01a" xlink:href="note-0283-01"/> id eſt, circa gravitatem fluidorum, utimur bilance, quan-<lb/> <anchor type="note" xlink:label="note-0283-02a" xlink:href="note-0283-02"/> tum fieri poteſt, exacta, jugi longitudo eſt circiter octo pol-<lb/>licum; </s> <s xml:id="echoid-s7791" xml:space="preserve">in medio inferiorum ſuperficierum lancium unci <lb/>junguntur, quibus corpora fluidis immergenda ſuſpendun-<lb/>tur; </s> <s xml:id="echoid-s7792" xml:space="preserve">cum lancibus etiam ſingulis cohærent pedes tres mino-<lb/>res, longitudinis circiter ſemi pollicis, quibus ſuſtinentur <lb/>quando lances, ſuſpensâ bilance, tabellæ T imponuntur.</s> <s xml:id="echoid-s7793" xml:space="preserve"/> </p> <div xml:id="echoid-div1083" type="float" level="2" n="1"> <note position="right" xlink:label="note-0283-01" xlink:href="note-0283-01a" xml:space="preserve">705.</note> <note position="right" xlink:label="note-0283-02" xlink:href="note-0283-02a" xml:space="preserve"><emph style="sc">TAB. XXVII,</emph> <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s7794" xml:space="preserve">Suſpenditur autem bilanx duobus funibus, qui ſinguli <lb/>duobus trochleis cum columna C cohærentibus, ut A & </s> <s xml:id="echoid-s7795" xml:space="preserve">B, <lb/>circumponuntur ita, ut moto pondere P, bilanx elevetur, <lb/>& </s> <s xml:id="echoid-s7796" xml:space="preserve">deprimatur, donec lances ipſi tabellæ T imponantur.</s> <s xml:id="echoid-s7797" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7798" xml:space="preserve">In tabella hac foramina duo, diametri trium partium <lb/>quartarum pollicis, dantur, quæ uncis lancium reſpondent, <lb/>& </s> <s xml:id="echoid-s7799" xml:space="preserve">per quæ tranſeunt fila ænea, aut capilli equini, quibus <lb/>corpora libræ applicanda uncis junguntur.</s> <s xml:id="echoid-s7800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7801" xml:space="preserve">Duplicem adhibemus funem, ut bilancis circumvolutio-<lb/>nem cohibeamus, ipſius autem nimiam agitationem vita-<lb/>mus, imponendo lances tabellæ T, & </s> <s xml:id="echoid-s7802" xml:space="preserve">haſce dein lente <lb/>paululum tantum elevando.</s> <s xml:id="echoid-s7803" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1085" type="section" level="1" n="265"> <head xml:id="echoid-head377" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s7804" xml:space="preserve">Phiala D clauſa, libræ memoratæ capillo equino juncta, <lb/> <anchor type="note" xlink:label="note-0283-03a" xlink:href="note-0283-03"/> aquâ immergitur, & </s> <s xml:id="echoid-s7805" xml:space="preserve">pondere lanci E impoſito datur æqui-<lb/>librium; </s> <s xml:id="echoid-s7806" xml:space="preserve">ſi phiala, manente immerſâ, aperiatur & </s> <s xml:id="echoid-s7807" xml:space="preserve">aquâ im-<lb/>pleatur, aqua in phiala gravabit libram, licet cum aqua ex-<lb/>teriori communicationem habeat; </s> <s xml:id="echoid-s7808" xml:space="preserve">ſi novo pondere æquili-<lb/>brium inſtauretur, ſervabitur ad quamcumque altitudinem <lb/>phiala aquâ immergatur.</s> <s xml:id="echoid-s7809" xml:space="preserve"/> </p> <div xml:id="echoid-div1085" type="float" level="2" n="1"> <note position="right" xlink:label="note-0283-03" xlink:href="note-0283-03a" xml:space="preserve">706.</note> </div> <p> <s xml:id="echoid-s7810" xml:space="preserve">Ex hac gravitate ſequitur, ſuperficiem fluidi, vaſe in-<lb/> <anchor type="note" xlink:label="note-0283-04a" xlink:href="note-0283-04"/> cluſi ne effluat, ſi ſuperne illud non prematur, aut æqualiter <lb/>prematur, quo gravitatis actio non mutatur, planam fieri, <pb o="202" file="0284" n="310" rhead="PHYSICES ELEMENTA"/> & </s> <s xml:id="echoid-s7811" xml:space="preserve">borizonti parallelam. </s> <s xml:id="echoid-s7812" xml:space="preserve">Cum enim impreſſioni cuicunque <lb/>particulæ cedant, tam diu gravitate moventur, donec de-<lb/>ſcenſui locus non amplius detur.</s> <s xml:id="echoid-s7813" xml:space="preserve"/> </p> <div xml:id="echoid-div1086" type="float" level="2" n="2"> <note position="right" xlink:label="note-0283-04" xlink:href="note-0283-04a" xml:space="preserve">707.</note> </div> <p> <s xml:id="echoid-s7814" xml:space="preserve">Particulæ inſeriores ſuperiores ſuſtinent, & </s> <s xml:id="echoid-s7815" xml:space="preserve">hiſce premun-<lb/> <anchor type="note" xlink:label="note-0284-01a" xlink:href="note-0284-01"/> tur, preſſioque bæc ſequitur proportionem materiæ incum-<lb/>bentis, id eſt, altitudinis fluidi ſupra particulam preſſam; <lb/></s> <s xml:id="echoid-s7816" xml:space="preserve">cum vero ſuperficies ſuprema fluidi ſit ad horizontem paral-<lb/>lela <anchor type="note" xlink:href="" symbol="*"/>, omnia puncta ſuperficiei cujuſcunque, quæ con- <anchor type="note" xlink:label="note-0284-02a" xlink:href="note-0284-02"/> cipitur in fluido ad horizontem parallela, æqualiter pre-<lb/>muntur.</s> <s xml:id="echoid-s7817" xml:space="preserve"/> </p> <div xml:id="echoid-div1087" type="float" level="2" n="3"> <note position="left" xlink:label="note-0284-01" xlink:href="note-0284-01a" xml:space="preserve">708.</note> <note symbol="*" position="left" xlink:label="note-0284-02" xlink:href="note-0284-02a" xml:space="preserve">707.</note> </div> <p> <s xml:id="echoid-s7818" xml:space="preserve">Si ergo in aliquo loco talis ſuperficiei preſſio detur minor <lb/> <anchor type="note" xlink:label="note-0284-03a" xlink:href="note-0284-03"/> quàm in cæteris punctis, fluidum, quod impreſſioni cui-<lb/>cunque cedit, ibi movebitur, id eſt, adſcendet, donec preſ-<lb/>ſio fuerit æqualis.</s> <s xml:id="echoid-s7819" xml:space="preserve"/> </p> <div xml:id="echoid-div1088" type="float" level="2" n="4"> <note position="left" xlink:label="note-0284-03" xlink:href="note-0284-03a" xml:space="preserve">709.</note> </div> </div> <div xml:id="echoid-div1090" type="section" level="1" n="266"> <head xml:id="echoid-head378" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s7820" xml:space="preserve">Tubi vitrei C ab utraque parte aperti, cujus extremitas <lb/> <anchor type="note" xlink:label="note-0284-04a" xlink:href="note-0284-04"/> una digito clauditur, extremitas altera aquâ immergitur; <lb/></s> <s xml:id="echoid-s7821" xml:space="preserve"> <anchor type="note" xlink:label="note-0284-05a" xlink:href="note-0284-05"/> cum tubus aëre repleatur, aqua in hunc ad parvam admo-<lb/>dum altitudinem adſcendit; </s> <s xml:id="echoid-s7822" xml:space="preserve">ſi digitus tollatur ut aër preſ-<lb/>ſus exeat, ſuperficies, quæ in aqua concipitur horizonti <lb/>parallela juxta partem inferiorem tubi, minus in parte re-<lb/>ſpondenti aperturæ tubi premitur, aqua etiam in tubum <lb/>tunc adſcendit, donec in eo habeat altitudinem æqualem <lb/>cum aqua exteriori.</s> <s xml:id="echoid-s7823" xml:space="preserve"/> </p> <div xml:id="echoid-div1090" type="float" level="2" n="1"> <note position="left" xlink:label="note-0284-04" xlink:href="note-0284-04a" xml:space="preserve">710.</note> <note position="left" xlink:label="note-0284-05" xlink:href="note-0284-05a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s7824" xml:space="preserve">Preſſio in particulas inferiores, quæ oritur ex gravitate <lb/> <anchor type="note" xlink:label="note-0284-06a" xlink:href="note-0284-06"/> fluidi ſuperioris, actionem ſuam exerit verſus omnes par-<lb/>tes, & </s> <s xml:id="echoid-s7825" xml:space="preserve">quidem æqualiter. </s> <s xml:id="echoid-s7826" xml:space="preserve">Quod ex natura fluidi ſequitur; <lb/></s> <s xml:id="echoid-s7827" xml:space="preserve">nam hujus partes impreſſioni cuicunque cedunt, & </s> <s xml:id="echoid-s7828" xml:space="preserve">facil-<lb/>lime moventur; </s> <s xml:id="echoid-s7829" xml:space="preserve">gutta ergo quæcunque locum quem occu-<lb/>pat non ſervabit, ſi, dum à fluido ſuperiori premitur, ab <lb/>omni parte non æqualiter prematur; </s> <s xml:id="echoid-s7830" xml:space="preserve">moveri autem non poteſt <lb/>propter guttas vicinas, quæ eodem modo & </s> <s xml:id="echoid-s7831" xml:space="preserve">eadem cum vi <lb/>à fluido ſupereminenti premuntur; </s> <s xml:id="echoid-s7832" xml:space="preserve">quieſcit idcirco gutta pri-<lb/>ma, & </s> <s xml:id="echoid-s7833" xml:space="preserve">æqualiter ab omni parte, id eſt, juxta directionem <lb/>quamcunque, premitur.</s> <s xml:id="echoid-s7834" xml:space="preserve"/> </p> <div xml:id="echoid-div1091" type="float" level="2" n="2"> <note position="left" xlink:label="note-0284-06" xlink:href="note-0284-06a" xml:space="preserve">711.</note> </div> <pb o="203" file="0285" n="311" rhead="MATHEMATICA. LIB. II. CAP. I."/> </div> <div xml:id="echoid-div1093" type="section" level="1" n="267"> <head xml:id="echoid-head379" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s7835" xml:space="preserve">Tubi vitrei A, B, D, eodem modo, ac de tubo A in <lb/> <anchor type="note" xlink:label="note-0285-01a" xlink:href="note-0285-01"/> præcedenti Experimento dictum, aquâ immerguntur, & </s> <s xml:id="echoid-s7836" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0285-02a" xlink:href="note-0285-02"/> aqua in omnes, ſublato digito, ad eandem altitudinem ad-<lb/>ſcendit, quàm in tubo C; </s> <s xml:id="echoid-s7837" xml:space="preserve">in hoc preſſio ſurſum dirigitur; <lb/></s> <s xml:id="echoid-s7838" xml:space="preserve">in tubo B deorſum; </s> <s xml:id="echoid-s7839" xml:space="preserve">in tubo A eſt lateralis; </s> <s xml:id="echoid-s7840" xml:space="preserve">in tubo D ob-<lb/>liqua; </s> <s xml:id="echoid-s7841" xml:space="preserve">in unoquoque tamen preſſio æqualis eſt; </s> <s xml:id="echoid-s7842" xml:space="preserve">ſi major <lb/>fluidi quantitas vaſe infundatur, æqualiter etiam aqua in ſin-<lb/>gulis tubis elevatur.</s> <s xml:id="echoid-s7843" xml:space="preserve"/> </p> <div xml:id="echoid-div1093" type="float" level="2" n="1"> <note position="right" xlink:label="note-0285-01" xlink:href="note-0285-01a" xml:space="preserve">712.</note> <note position="right" xlink:label="note-0285-02" xlink:href="note-0285-02a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s7844" xml:space="preserve">Ex hiſce ſequitur fluidorum particulas ſingulas ab omni <lb/> <anchor type="note" xlink:label="note-0285-03a" xlink:href="note-0285-03"/> parte æqualiter premi, & </s> <s xml:id="echoid-s7845" xml:space="preserve">ideo quieſcere; </s> <s xml:id="echoid-s7846" xml:space="preserve">illaſque non con-<lb/>tinuo inter ſe moveri, ut a multis ſtatuitur.</s> <s xml:id="echoid-s7847" xml:space="preserve"/> </p> <div xml:id="echoid-div1094" type="float" level="2" n="2"> <note position="right" xlink:label="note-0285-03" xlink:href="note-0285-03a" xml:space="preserve">713.</note> </div> <p> <s xml:id="echoid-s7848" xml:space="preserve">In tubis communicantibus, ſive æqualibus, ſive inæqua-<lb/> <anchor type="note" xlink:label="note-0285-04a" xlink:href="note-0285-04"/> libus, ſive rectis, ſive obliquis, fluidum eandem adipiſcitur <lb/>altitudinem; </s> <s xml:id="echoid-s7849" xml:space="preserve">id eſt, omnes ſuperficies ſupremæ ſunt in eo-<lb/>dem plano horizonti parallelo; </s> <s xml:id="echoid-s7850" xml:space="preserve">quod facile ex dictis dedu-<lb/>citur.</s> <s xml:id="echoid-s7851" xml:space="preserve"/> </p> <div xml:id="echoid-div1095" type="float" level="2" n="3"> <note position="right" xlink:label="note-0285-04" xlink:href="note-0285-04a" xml:space="preserve">714.</note> </div> <p> <s xml:id="echoid-s7852" xml:space="preserve">Sit vas A, tubus verticalis B, & </s> <s xml:id="echoid-s7853" xml:space="preserve">tubus inclinatus D; </s> <s xml:id="echoid-s7854" xml:space="preserve">com-<lb/> <anchor type="note" xlink:label="note-0285-05a" xlink:href="note-0285-05"/> municationem habeant ope tubi CE; </s> <s xml:id="echoid-s7855" xml:space="preserve">detur in his fluidum, <lb/> <anchor type="note" xlink:label="note-0285-06a" xlink:href="note-0285-06"/> & </s> <s xml:id="echoid-s7856" xml:space="preserve">concipiatur ſuperficies horizonti parallela fgb; </s> <s xml:id="echoid-s7857" xml:space="preserve">ſi alti-<lb/>tudines fi & </s> <s xml:id="echoid-s7858" xml:space="preserve">gl ſuerint inæquales, aqua adſcendet ubi mi-<lb/>nor eſt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s7859" xml:space="preserve">Ex eadem ratione niſi preſſiones in g & </s> <s xml:id="echoid-s7860" xml:space="preserve">b fue- <anchor type="note" xlink:label="note-0285-07a" xlink:href="note-0285-07"/> rint æquales, aqua non quieſcet; </s> <s xml:id="echoid-s7861" xml:space="preserve">ſunt vero æquales, quan-<lb/>do l & </s> <s xml:id="echoid-s7862" xml:space="preserve">n ſunt in eodem plano horizontali; </s> <s xml:id="echoid-s7863" xml:space="preserve">nam cum preſ-<lb/>ſio oriatur ex gravitate partium, quæ tendit ad terræ cen-<lb/>trum, altitudo fluidi prementis juxta hanc directionem <lb/>menſurari debet, id eſt, erit bm; </s> <s xml:id="echoid-s7864" xml:space="preserve">obliquitas vero colu-<lb/>mnæ bn nullam mutationem adfert; </s> <s xml:id="echoid-s7865" xml:space="preserve">quia ad eandem pro-<lb/>funditatem ubique preſſio verſus omnes partes æqualis da-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s7866" xml:space="preserve"> <anchor type="note" xlink:label="note-0285-08a" xlink:href="note-0285-08"/> </s> </p> <div xml:id="echoid-div1096" type="float" level="2" n="4"> <note position="right" xlink:label="note-0285-05" xlink:href="note-0285-05a" xml:space="preserve">715.</note> <note position="right" xlink:label="note-0285-06" xlink:href="note-0285-06a" xml:space="preserve"><emph style="sc">TAB XXVII</emph>. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0285-07" xlink:href="note-0285-07a" xml:space="preserve">709.</note> <note symbol="*" position="right" xlink:label="note-0285-08" xlink:href="note-0285-08a" xml:space="preserve">711.</note> </div> </div> <div xml:id="echoid-div1098" type="section" level="1" n="268"> <head xml:id="echoid-head380" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s7867" xml:space="preserve">Machinæ hic delineatæ aqua infunditur; </s> <s xml:id="echoid-s7868" xml:space="preserve">poſt agitatio-<lb/> <anchor type="note" xlink:label="note-0285-09a" xlink:href="note-0285-09"/> nem quamcunque non quieſcit, niſi omnes ſuperficies <lb/> <anchor type="note" xlink:label="note-0285-10a" xlink:href="note-0285-10"/> ſint in eodem plano horizonti parallelo. </s> <s xml:id="echoid-s7869" xml:space="preserve">Vas vitreum A <lb/>cum tubis vitreis B & </s> <s xml:id="echoid-s7870" xml:space="preserve">D, ope tubi ænei CE, conjungi-<lb/>tur.</s> <s xml:id="echoid-s7871" xml:space="preserve"/> </p> <div xml:id="echoid-div1098" type="float" level="2" n="1"> <note position="right" xlink:label="note-0285-09" xlink:href="note-0285-09a" xml:space="preserve">716.</note> <note position="right" xlink:label="note-0285-10" xlink:href="note-0285-10a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig. 4.</note> </div> <pb o="204" file="0286" n="312" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s7872" xml:space="preserve">Non omnia fluida ſunt æque gravia, id eſt, non eandem <lb/>materiæ quantitatem in eodem ſpatio continent, in ſingu-<lb/>lis tamen prædicta locum habent.</s> <s xml:id="echoid-s7873" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s7874" xml:space="preserve">Quando fluida diver ſæ gravitatis eodem vaſe continentur, <lb/> <anchor type="note" xlink:label="note-0286-01a" xlink:href="note-0286-01"/> gravius locum infimum occupat, & </s> <s xml:id="echoid-s7875" xml:space="preserve">premitur a leviori, illud-<lb/>que pro altitudine bujus.</s> <s xml:id="echoid-s7876" xml:space="preserve"/> </p> <div xml:id="echoid-div1099" type="float" level="2" n="2"> <note position="left" xlink:label="note-0286-01" xlink:href="note-0286-01a" xml:space="preserve">717.</note> </div> </div> <div xml:id="echoid-div1101" type="section" level="1" n="269"> <head xml:id="echoid-head381" xml:space="preserve"><emph style="sc">Experimentum</emph>. 5.</head> <p> <s xml:id="echoid-s7877" xml:space="preserve">Detur aqua, aliquo colore tincta, in vaſe vitreo A, ad al-<lb/> <anchor type="note" xlink:label="note-0286-02a" xlink:href="note-0286-02"/> titudinem bc; </s> <s xml:id="echoid-s7878" xml:space="preserve">ei immergatur tubus vitreus de; </s> <s xml:id="echoid-s7879" xml:space="preserve">aquain hunc <lb/> <anchor type="note" xlink:label="note-0286-03a" xlink:href="note-0286-03"/> adſcendit ad altitudinem bc <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s7880" xml:space="preserve">nunc infundatur oleum te- rebinthinæ, quod fluidum eſt aquâ levius, ſtatim aqua in <lb/>tubo adſcendet; </s> <s xml:id="echoid-s7881" xml:space="preserve">& </s> <s xml:id="echoid-s7882" xml:space="preserve">eo magis quo ad majorem altitudinem <lb/>oleum infunditur; </s> <s xml:id="echoid-s7883" xml:space="preserve">non tamen aqua in tubo ad eandem per-<lb/>tingit altitudinem cum oleo in vaſe; </s> <s xml:id="echoid-s7884" xml:space="preserve">quia cum aqua gravi-<lb/>or ſit, non eadem quam olei altitudo requiritur, ut preſſio-<lb/>nes ſint æquales.</s> <s xml:id="echoid-s7885" xml:space="preserve"/> </p> <div xml:id="echoid-div1101" type="float" level="2" n="1"> <note position="left" xlink:label="note-0286-02" xlink:href="note-0286-02a" xml:space="preserve">718.</note> <note position="left" xlink:label="note-0286-03" xlink:href="note-0286-03a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s7886" xml:space="preserve">Qui hocce Experimentum cum Mercurio & </s> <s xml:id="echoid-s7887" xml:space="preserve">aqua inſti-<lb/>tuere voluerit, majorem inter altitudines reperiet differen-<lb/>tiam, propter majus inter gravitates diſcrimen.</s> <s xml:id="echoid-s7888" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1103" type="section" level="1" n="270"> <head xml:id="echoid-head382" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s7889" xml:space="preserve">Immergatur tubi extremitas aquâ; </s> <s xml:id="echoid-s7890" xml:space="preserve">oleumque tubo infun-<lb/> <anchor type="note" xlink:label="note-0286-04a" xlink:href="note-0286-04"/> datur; </s> <s xml:id="echoid-s7891" xml:space="preserve">aqua in tubo deprimitur ad d; </s> <s xml:id="echoid-s7892" xml:space="preserve">altitudo tamen olei <lb/> <anchor type="note" xlink:label="note-0286-05a" xlink:href="note-0286-05"/> de major eſt altitudine aquæ in vaſe; </s> <s xml:id="echoid-s7893" xml:space="preserve">ſi profundius im-<lb/>mergatur tubus, aqua majori quantitate hunc ingreditur; <lb/></s> <s xml:id="echoid-s7894" xml:space="preserve">ſi elevetur, aqua iterum exit, ipſumque oleum inſequitur, <lb/>ſi ad illam tollatur altitudinem ut olei preſſio aquæ preſſio-<lb/>nem, in parte inferiori tubi, ſuperet.</s> <s xml:id="echoid-s7895" xml:space="preserve"/> </p> <div xml:id="echoid-div1103" type="float" level="2" n="1"> <note position="left" xlink:label="note-0286-04" xlink:href="note-0286-04a" xml:space="preserve">719.</note> <note position="left" xlink:label="note-0286-05" xlink:href="note-0286-05a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig. 6.</note> </div> </div> <div xml:id="echoid-div1105" type="section" level="1" n="271"> <head xml:id="echoid-head383" xml:space="preserve">CAPUT II.</head> <head xml:id="echoid-head384" style="it" xml:space="preserve">De Actione Fluidorum in Fundos, Latera, & Opercula, <lb/>vaſorum quibus continentur.</head> <p> <s xml:id="echoid-s7896" xml:space="preserve">FVndus & </s> <s xml:id="echoid-s7897" xml:space="preserve">latera vaſis, quo fluidum continetur, ut & </s> <s xml:id="echoid-s7898" xml:space="preserve">o-<lb/> <anchor type="note" xlink:label="note-0286-06a" xlink:href="note-0286-06"/> perculum, quando ſupra hoc in tubo fluidum elevatur, <lb/>a partibus fluidi illa immediate tangentibus premuntur, &</s> <s xml:id="echoid-s7899" xml:space="preserve"> <pb o="205" file="0287" n="313" rhead="MATHEMATICA. LIB. II. CAP. II."/> propter actioni æqualem reactionem <anchor type="note" xlink:href="" symbol="*"/>, æqualem etiam <anchor type="note" xlink:label="note-0287-01a" xlink:href="note-0287-01"/> particulæ iſtæ preſſionem ſuſtinent. </s> <s xml:id="echoid-s7900" xml:space="preserve">Cum vero preſſio in <lb/>fluidis omnes partes verſus ſit æqualis, fundus & </s> <s xml:id="echoid-s7901" xml:space="preserve">latera æ-<lb/>que premuntur ac partes fluidi vicinæ actio ergo hæc ad <lb/>inſtar altitudinis fluidi’ creſcit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s7902" xml:space="preserve">ubique ad eandem <anchor type="note" xlink:label="note-0287-02a" xlink:href="note-0287-02"/> profunditatem eſt æqualis, pendetque ab illa altitudine, & </s> <s xml:id="echoid-s7903" xml:space="preserve"><lb/>nullo modo a fluidi quantitate. </s> <s xml:id="echoid-s7904" xml:space="preserve">Manente igitur fluidi altitu-<lb/>dine, & </s> <s xml:id="echoid-s7905" xml:space="preserve">fundi magnitudine, æqualis ſemper erit actio in <lb/>fundum, utcunque mutetur vaſis figura. </s> <s xml:id="echoid-s7906" xml:space="preserve">In omni caſu preſ-<lb/> <anchor type="note" xlink:label="note-0287-03a" xlink:href="note-0287-03"/> ſio, quam patitur ſuperficies quæcunque, valet pondus co-<lb/>lumnæ ex fluido, cujus baſis eſt ipſa ſuperficies, & </s> <s xml:id="echoid-s7907" xml:space="preserve">altitudo, <lb/>in ſingulis punctis, diſtantia verticalis ſupremæ ſuperficiei <lb/>fluidi ab his punctis.</s> <s xml:id="echoid-s7908" xml:space="preserve"/> </p> <div xml:id="echoid-div1105" type="float" level="2" n="1"> <note position="left" xlink:label="note-0286-06" xlink:href="note-0286-06a" xml:space="preserve">720.</note> <note symbol="*" position="right" xlink:label="note-0287-01" xlink:href="note-0287-01a" xml:space="preserve"> 2471</note> <note symbol="*" position="right" xlink:label="note-0287-02" xlink:href="note-0287-02a" xml:space="preserve">711. 708.</note> <note position="right" xlink:label="note-0287-03" xlink:href="note-0287-03a" xml:space="preserve">721.</note> </div> <p> <s xml:id="echoid-s7909" xml:space="preserve">Talem eſſe in vaſe priſmatico verticali preſſionem in fun-<lb/>dum non facile in dubium quis vocabit; </s> <s xml:id="echoid-s7910" xml:space="preserve">nam totum fluidi <lb/>pondus, & </s> <s xml:id="echoid-s7911" xml:space="preserve">nil præterea, ſuſtinet fundus: </s> <s xml:id="echoid-s7912" xml:space="preserve">ſervatâ autem alti-<lb/>tudine fluidi, & </s> <s xml:id="echoid-s7913" xml:space="preserve">baſi vaſeos, non mutatur preſſio in fun-<lb/>dum, licet, mutatâ figurâ, vas majorem aut minorem flui-<lb/>di copiam contineat; </s> <s xml:id="echoid-s7914" xml:space="preserve">quod cum experimentis congruit, & </s> <s xml:id="echoid-s7915" xml:space="preserve"><lb/>ex natura fluiditatis deducitur, ut, poſt expoſita experi-<lb/>menta, dicam.</s> <s xml:id="echoid-s7916" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1107" type="section" level="1" n="272"> <head xml:id="echoid-head385" xml:space="preserve"><emph style="sc">Machina</emph></head> <p style="it"> <s xml:id="echoid-s7917" xml:space="preserve">Qua Experimenta de Fluidorum Preſſione inſtituun-<lb/>tur.</s> <s xml:id="echoid-s7918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7919" xml:space="preserve">Cylindrus cavus A, ab utraque parte apertus, ab inte-<lb/> <anchor type="note" xlink:label="note-0287-04a" xlink:href="note-0287-04"/> riori parte exactiſſime politur; </s> <s xml:id="echoid-s7920" xml:space="preserve">hujus diameter ut & </s> <s xml:id="echoid-s7921" xml:space="preserve">altitu-<lb/> <anchor type="note" xlink:label="note-0287-05a" xlink:href="note-0287-05"/> do parum excedunt tres pollices cum ſemiſſe, & </s> <s xml:id="echoid-s7922" xml:space="preserve">aqua in hoc <lb/>cylindro ad altitudinem trium pollicum ponderat libram u-<lb/>nam, ope cochleæ ei additur annulus E, ut a tripode ſu-<lb/>ſtineatur. </s> <s xml:id="echoid-s7923" xml:space="preserve">Pedes autem cochleis annulo junguntur, ut, ubi <lb/>neceſſe hoc eſt, tollantur.</s> <s xml:id="echoid-s7924" xml:space="preserve"/> </p> <div xml:id="echoid-div1107" type="float" level="2" n="1"> <note position="right" xlink:label="note-0287-04" xlink:href="note-0287-04a" xml:space="preserve">722.</note> <note position="right" xlink:label="note-0287-05" xlink:href="note-0287-05a" xml:space="preserve"><emph style="sc">TAB. XXVII</emph>. <lb/>fig 7. 8.</note> </div> <p> <s xml:id="echoid-s7925" xml:space="preserve">In cylindro datur ſundus æneus mobilis F, cum quo an-<lb/>nulus G, etiam æneus, ab interiori parte cochleam conti-<lb/>nens, conjungitur; </s> <s xml:id="echoid-s7926" xml:space="preserve">hoc annulo retinetur & </s> <s xml:id="echoid-s7927" xml:space="preserve">firmatur an-<lb/>nulus coriaceus ab omni parte fundum quantitate ſemi-pol-<lb/>licis excedens; </s> <s xml:id="echoid-s7928" xml:space="preserve">obtegit hic annuli ænei ſuperficiem exterio- <pb o="206" file="0288" n="314" rhead="PHYSICES ELEMENTA"/> rem, quando fundus cylindro intruditur, impeditque ne <lb/>aqua dum fundus movetur effluat. </s> <s xml:id="echoid-s7929" xml:space="preserve">Corium hocce oleo im-<lb/>mergitur, poſt aliquot dies extrahitur, ut per æquale tem-<lb/>pus in aqua maceretur; </s> <s xml:id="echoid-s7930" xml:space="preserve">qua adhibita præparatione, co-<lb/>rium probe oleo & </s> <s xml:id="echoid-s7931" xml:space="preserve">aqua illinitur, moveturque fundus va-<lb/>riis vicibus per cylindrum, & </s> <s xml:id="echoid-s7932" xml:space="preserve">per biduum aut triduum <lb/>in hoc relinquitur. </s> <s xml:id="echoid-s7933" xml:space="preserve">Ita præparatum corium per multos an-<lb/>nos experimentis inſervire poteſt, ſi, ubi hæc inſtituenda <lb/>ſunt, corium cum fundo jungatur, oleo & </s> <s xml:id="echoid-s7934" xml:space="preserve">aquâ illiniatur, tunc-<lb/>que per aliquot horas, aut integrum diem in cylindro relin-<lb/>quatur, antequam Experimenta inſtituantur. </s> <s xml:id="echoid-s7935" xml:space="preserve">Immediate <lb/>etiam ante Experimenta iterum oleo & </s> <s xml:id="echoid-s7936" xml:space="preserve">aquâ illiniri debet, & </s> <s xml:id="echoid-s7937" xml:space="preserve"><lb/>facile tunc fundus movetur, & </s> <s xml:id="echoid-s7938" xml:space="preserve">exacte aquam retinet. </s> <s xml:id="echoid-s7939" xml:space="preserve">Co-<lb/>rium neque nimis tenue neque nimis craſſum adhibendum; <lb/></s> <s xml:id="echoid-s7940" xml:space="preserve">quod judicio artificis relinquitur.</s> <s xml:id="echoid-s7941" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7942" xml:space="preserve">In centro fundi cum hoc cohæret cylindrus æneus tenuis <lb/>hi, quo motus fundi dirigitur, tranſit enim hicce cylin-<lb/>drus per forameo m in lamina B, quæ cylindro majori A <lb/>ſuperimponitur, & </s> <s xml:id="echoid-s7943" xml:space="preserve">in ejus ora in inciſione hæret. </s> <s xml:id="echoid-s7944" xml:space="preserve">In ſuperio-<lb/>ri parte cylindri hi foramen datur, ut cum fundo, ope unci <lb/>n, jungatur catena ænea pn, quæ per tubum ſtatim memo-<lb/>randum D immittitur, ut ope hujus catenæ fundus cum bra-<lb/>chio libræ conjungatur.</s> <s xml:id="echoid-s7945" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7946" xml:space="preserve">Cylindrus A operculo C tegitur, & </s> <s xml:id="echoid-s7947" xml:space="preserve">ne aqua effluere poſ-<lb/>ſit obtegenda eſt ora cylindri annulo coriaceo, qui ope co-<lb/>chleæ, qua operculum jungitur cum cylindro, inter oram <lb/>& </s> <s xml:id="echoid-s7948" xml:space="preserve">ipſum operculum arcte comprimitur; </s> <s xml:id="echoid-s7949" xml:space="preserve">operculo ut & </s> <s xml:id="echoid-s7950" xml:space="preserve">ipſi <lb/>cylindro adduntur anſæ, ut magis commode aperiatur & </s> <s xml:id="echoid-s7951" xml:space="preserve">clau-<lb/>datur cylindrus. </s> <s xml:id="echoid-s7952" xml:space="preserve">In medio perforatur operculum, & </s> <s xml:id="echoid-s7953" xml:space="preserve">cylin-<lb/>drus cavus l, ab exteriori parte cochleâ circumdatus, cum <lb/>illo cohæret, ut tubus D cum machina conjungatur; </s> <s xml:id="echoid-s7954" xml:space="preserve">etiam <lb/>hîc adhibito corio aquæ effluxus cohibetur.</s> <s xml:id="echoid-s7955" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1109" type="section" level="1" n="273"> <head xml:id="echoid-head386" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s7956" xml:space="preserve">Partibus machinæ, ut dictum, junctis, catena, quæ cum <lb/> <anchor type="note" xlink:label="note-0288-01a" xlink:href="note-0288-01"/> fundo mobili cohæret, brachio libræ annectatur, ita ut ju-<lb/>gum libræ ſit in fitu horizontali, quando fundus ab opercu- <pb file="0289" n="315"/> <pb file="0289a" n="316"/> <anchor type="figure" xlink:label="fig-0289a-01a" xlink:href="fig-0289a-01"/> <pb file="0290" n="317"/> <pb o="207" file="0291" n="318" rhead="MATHEMATICA. LIB. II. CAP. II."/> lo diſtat duobus pollicibus; </s> <s xml:id="echoid-s7957" xml:space="preserve">lanci, brachio oppoſito ſuſpen-<lb/>ſæ, pondus imponitur, ut detur æquilibrium cum ponde-<lb/>re ſolius fundi & </s> <s xml:id="echoid-s7958" xml:space="preserve">catenæ; </s> <s xml:id="echoid-s7959" xml:space="preserve">quantum ponderis ad hoc requi-<lb/>ritur antea explorandum. </s> <s xml:id="echoid-s7960" xml:space="preserve">Cum tubo D, cujus longitudo eſt <lb/>pollicum triginta duorum in ſuperiori parte, ope cochleæ in-<lb/>fundibulum conjungitur cylindricum cujus diameter eſt cir-<lb/>citer novem pollicum, & </s> <s xml:id="echoid-s7961" xml:space="preserve">in hac figura non exhibetur.</s> <s xml:id="echoid-s7962" xml:space="preserve"/> </p> <div xml:id="echoid-div1109" type="float" level="2" n="1"> <note position="left" xlink:label="note-0288-01" xlink:href="note-0288-01a" xml:space="preserve">723.</note> <figure xlink:label="fig-0289a-01" xlink:href="fig-0289a-01a"> <image file="0289a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0289a-01"/> </figure> </div> <p> <s xml:id="echoid-s7963" xml:space="preserve">Jugo libræ horizontaliter diſpoſito infundatur aqua tubo <lb/>D, ut ad altitudinem duorum pollicum in infundibulo per-<lb/>tingat: </s> <s xml:id="echoid-s7964" xml:space="preserve">pondere duodecim librarum lanci impoſito æquili-<lb/>brium datur; </s> <s xml:id="echoid-s7965" xml:space="preserve">diminuto, aut aucto, pondere, adſcendit, aut <lb/>deſcendit, fundus. </s> <s xml:id="echoid-s7966" xml:space="preserve">Quantitate tamen non admodum exi-<lb/>gua, exempli gratia unius libræ, augendum aut minuendum <lb/>eſt pondus, propter attritum fundi, ſæpe major differentia <lb/>deſideratur, quod ab attritu pendet.</s> <s xml:id="echoid-s7967" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7968" xml:space="preserve">Altitudo ſupremæ ſuperficiei aquæ ſupra fundum, in hoc <lb/>Experimento, eſt trium pedum, columnæ aqueæ, cujus <lb/>hæc eſt altitudo, & </s> <s xml:id="echoid-s7969" xml:space="preserve">quæ baſin æqualem fundo cylindri ha-<lb/>bet, pondus eſt duodecim librarum, & </s> <s xml:id="echoid-s7970" xml:space="preserve">tantum etiam valet <lb/>preſſio aquæ in fundum, licet exigua tantum aquæ copia <lb/>in fundum premat.</s> <s xml:id="echoid-s7971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7972" xml:space="preserve">Cum de ſolo motu fundi agatur, machina firmanda eſt <lb/>ne tota elevetur, quod fit impoſitis ponderibus, qualia re-<lb/>præſentantur in P, P, fig. </s> <s xml:id="echoid-s7973" xml:space="preserve">1. </s> <s xml:id="echoid-s7974" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7975" xml:space="preserve">XXIX.</s> <s xml:id="echoid-s7976" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1111" type="section" level="1" n="274"> <head xml:id="echoid-head387" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s7977" xml:space="preserve">Sublato operculo cum tubo, cylindrus A conjungatur <lb/> <anchor type="note" xlink:label="note-0291-01a" xlink:href="note-0291-01"/> cum cono truncato inverſo DE, cui in inferiori parte co-<lb/> <anchor type="note" xlink:label="note-0291-02a" xlink:href="note-0291-02"/> hæret annulus cochleam continens; </s> <s xml:id="echoid-s7978" xml:space="preserve">aqua huic machinæ in-<lb/>funditur ad eandem altitudinem ſupra fundum ac in præ-<lb/>cedenti Experimento; </s> <s xml:id="echoid-s7979" xml:space="preserve">Experimentum de cætero eodem <lb/>modo peragitur, & </s> <s xml:id="echoid-s7980" xml:space="preserve">eodem modo procedit; </s> <s xml:id="echoid-s7981" xml:space="preserve">preſſioque, <lb/>ſervata aquæ altitudine, ex mutato vaſe & </s> <s xml:id="echoid-s7982" xml:space="preserve">aquæ quantitate; <lb/></s> <s xml:id="echoid-s7983" xml:space="preserve">non mutatur.</s> <s xml:id="echoid-s7984" xml:space="preserve"/> </p> <div xml:id="echoid-div1111" type="float" level="2" n="1"> <note position="right" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">724.</note> <note position="right" xlink:label="note-0291-02" xlink:href="note-0291-02a" xml:space="preserve"><emph style="sc">TAB. XXVIII</emph>. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div1113" type="section" level="1" n="275"> <head xml:id="echoid-head388" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s7985" xml:space="preserve">Vas cylindricum A libræ ſuſpenditur, pro parte hocce <lb/> <anchor type="note" xlink:label="note-0291-03a" xlink:href="note-0291-03"/> repletur cylindro ligneo D e, quod cum ligno B c, quomo-<lb/> <anchor type="note" xlink:label="note-0291-04a" xlink:href="note-0291-04"/> <pb o="208" file="0292" n="319" rhead="PHYSICES ELEMENTA"/> docunque firmato, cohæret, & </s> <s xml:id="echoid-s7986" xml:space="preserve">neque latera neque fun-<lb/>dum vaſis memorati tangit; </s> <s xml:id="echoid-s7987" xml:space="preserve">ſi vaſi aqua ad quamcunque al-<lb/>titudinem infundatur, & </s> <s xml:id="echoid-s7988" xml:space="preserve">pondere lanci oppoſitæ impoſito <lb/>æquilibrium detur; </s> <s xml:id="echoid-s7989" xml:space="preserve">hocce pondus erit pondus totius aquæ <lb/>quæ in vaſe, ſublato cylindro, continetur, poſita hac ad ean-<lb/>dem altitudinem quam in Experimento; </s> <s xml:id="echoid-s7990" xml:space="preserve">& </s> <s xml:id="echoid-s7991" xml:space="preserve">parva aquæ <lb/>quantitas, cujus ſuprema ſuperficies elevatur, qua preſſio in <lb/>fundum augetur, magnum pondus ſuſtinet.</s> <s xml:id="echoid-s7992" xml:space="preserve"/> </p> <div xml:id="echoid-div1113" type="float" level="2" n="1"> <note position="right" xlink:label="note-0291-03" xlink:href="note-0291-03a" xml:space="preserve">725.</note> <note position="right" xlink:label="note-0291-04" xlink:href="note-0291-04a" xml:space="preserve"><emph style="sc">TAB. XXVIII</emph>. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s7993" xml:space="preserve">Preſſionem lateralem verticali æquari, adhibita ſequenti <lb/>machina, ad oculum patebit.</s> <s xml:id="echoid-s7994" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1115" type="section" level="1" n="276"> <head xml:id="echoid-head389" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head390" style="it" xml:space="preserve">Qua demonſtratur Preſſio Fluidorum <lb/>lateralis.</head> <p> <s xml:id="echoid-s7995" xml:space="preserve">Vas DB eſt parallelopipedum ligneum altitudinis circi-<lb/> <anchor type="note" xlink:label="note-0292-01a" xlink:href="note-0292-01"/> ter viginti pollicum; </s> <s xml:id="echoid-s7996" xml:space="preserve">a latere fundum verſus datur foramen, <lb/> <anchor type="note" xlink:label="note-0292-02a" xlink:href="note-0292-02"/> in quo hæret annulus æneus cochleam continens, ut cylin-<lb/>drus A, quem ſupra memoravimus <anchor type="note" xlink:href="" symbol="*"/>, ibi firmetur, ſubla- <anchor type="note" xlink:label="note-0292-03a" xlink:href="note-0292-03"/> tis pedibus, qui cochleis annulo inferiori annectuntur. </s> <s xml:id="echoid-s7997" xml:space="preserve">Mo-<lb/>tus fundi in cylindro in hoc caſu eſt horizontalis. </s> <s xml:id="echoid-s7998" xml:space="preserve">Ad la-<lb/>tera machinæ huic junguntur duæ regulæ ligneæ, quarum <lb/>una videtur in GH, ſuper his horizontaliter movetur <lb/>regula CC, quæ in medio F latior eſt, ut hujus motu in-<lb/>trudatur cylindri fundus, quem regula premit paululum <lb/>infra centrum. </s> <s xml:id="echoid-s7999" xml:space="preserve">In C & </s> <s xml:id="echoid-s8000" xml:space="preserve">C funes ut CE huic regulæ alli-<lb/>gantur, qui juxta regulas ut GH protenduntur, tranſeun-<lb/>tes ſuper trochleis in harum regularum extremitatibus ut T, <lb/>& </s> <s xml:id="echoid-s8001" xml:space="preserve">iis appenduntur pondera ut P.</s> <s xml:id="echoid-s8002" xml:space="preserve"/> </p> <div xml:id="echoid-div1115" type="float" level="2" n="1"> <note position="left" xlink:label="note-0292-01" xlink:href="note-0292-01a" xml:space="preserve">726.</note> <note position="left" xlink:label="note-0292-02" xlink:href="note-0292-02a" xml:space="preserve"><emph style="sc">TAB XXVIII</emph>. <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0292-03" xlink:href="note-0292-03a" xml:space="preserve">722.</note> </div> </div> <div xml:id="echoid-div1117" type="section" level="1" n="277"> <head xml:id="echoid-head391" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s8003" xml:space="preserve">Infundatur aqua vaſi BD, ita ut aquæ ſuperficies altior ſit <lb/> <anchor type="note" xlink:label="note-0292-04a" xlink:href="note-0292-04"/> regula CC quindecim pollicibus, ſint pondera ut P duarum <lb/>librarum cum ſemiſſe, ita ut ſimul ſumta valeant quinque <lb/>libras, preſſio aquæ hocce pondus ſuſtinebit, & </s> <s xml:id="echoid-s8004" xml:space="preserve">fundus in <lb/>hoc caſu æque facile intruditur ac extrahitur</s> </p> <div xml:id="echoid-div1117" type="float" level="2" n="1"> <note position="left" xlink:label="note-0292-04" xlink:href="note-0292-04a" xml:space="preserve">727.</note> </div> <p> <s xml:id="echoid-s8005" xml:space="preserve">Vim, qua aqua ſurſum premit, æqualem eſſe illi qua deor-<lb/>ſum & </s> <s xml:id="echoid-s8006" xml:space="preserve">ad latera premit, ſequenti Experimento probatur.</s> <s xml:id="echoid-s8007" xml:space="preserve"/> </p> <pb o="209" file="0293" n="320" rhead="MATHEMATICA. LIB. II. CAP. II."/> </div> <div xml:id="echoid-div1119" type="section" level="1" n="278"> <head xml:id="echoid-head392" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s8008" xml:space="preserve">Inmedio ſuperficiei ſuperioris ſuſtentaculi B, datur cy-<lb/> <anchor type="note" xlink:label="note-0293-01a" xlink:href="note-0293-01"/> lindrus diametri circiter duorum pollicum, cui imponitur <lb/> <anchor type="note" xlink:label="note-0293-02a" xlink:href="note-0293-02"/> fundus mobilis cylindri ſæpius memorati A <anchor type="note" xlink:href="" symbol="*"/>, ita ut ma- <anchor type="note" xlink:label="note-0293-03a" xlink:href="note-0293-03"/> nente fundo ipſe cylindrus moveri poſſit; </s> <s xml:id="echoid-s8009" xml:space="preserve">hic operculo ſuo <lb/>obtegitur, & </s> <s xml:id="echoid-s8010" xml:space="preserve">cum eo conjungitur tubus D longitudinis tri-<lb/>um pedum cum ſemiſſe, cui in ſuperiori extremitate additur <lb/>infundibulum cujus diameter eſt trium aut quatuor poll. <lb/></s> <s xml:id="echoid-s8011" xml:space="preserve">Infunditur aqua, qua, manente fundo, machina elevatur; </s> <s xml:id="echoid-s8012" xml:space="preserve"><lb/>imponuntur operculo pondera P, P, P, quæ ſimul valent <lb/>libras novem, hæc, cum pondere totius machinæ, ab aqua in <lb/>tubo ſuſtinentur; </s> <s xml:id="echoid-s8013" xml:space="preserve">pondus vero machinæ cum tubis & </s> <s xml:id="echoid-s8014" xml:space="preserve">infun-<lb/>dibulo excedit quatuor libras cum ſemiſſe.</s> <s xml:id="echoid-s8015" xml:space="preserve"/> </p> <div xml:id="echoid-div1119" type="float" level="2" n="1"> <note position="right" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">728.</note> <note position="right" xlink:label="note-0293-02" xlink:href="note-0293-02a" xml:space="preserve"><emph style="sc">TAB. XXIX</emph>. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0293-03" xlink:href="note-0293-03a" xml:space="preserve">722.</note> </div> <p> <s xml:id="echoid-s8016" xml:space="preserve">Vis, quæ in operculum agit, valet pondus columnæ aqueæ, <lb/>cujus baſis eſt operculum, demto foramine cui reſpondet tu-<lb/>bus, & </s> <s xml:id="echoid-s8017" xml:space="preserve">cujus altitudo eſt, aquæ elevatio in tubo ſupra ſu-<lb/>perficiem interiorem operculi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8018" xml:space="preserve">quod cum hoc Experimen- <anchor type="note" xlink:label="note-0293-04a" xlink:href="note-0293-04"/> to congruit.</s> <s xml:id="echoid-s8019" xml:space="preserve"/> </p> <div xml:id="echoid-div1120" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0293-04" xlink:href="note-0293-04a" xml:space="preserve">723</note> </div> <p> <s xml:id="echoid-s8020" xml:space="preserve">Manente tubo ſi machina major detur, actio in operculum <lb/>in eadem ratione cum operculo creſcet, ita ut minima aquæ <lb/>quantitate pondus maximum ſuſtineatur, ac etiam elevetur.</s> <s xml:id="echoid-s8021" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1122" type="section" level="1" n="279"> <head xml:id="echoid-head393" xml:space="preserve"><emph style="sc">Follis hydrostaticus</emph>.</head> <p> <s xml:id="echoid-s8022" xml:space="preserve">Duo orbes lignei AB, AB, diametri quindecim pollicum, <lb/> <anchor type="note" xlink:label="note-0293-05a" xlink:href="note-0293-05"/> corio circumdantur & </s> <s xml:id="echoid-s8023" xml:space="preserve">junguntur ita, ut formetur vas cylin-<lb/> <anchor type="note" xlink:label="note-0293-06a" xlink:href="note-0293-06"/> dricum folli aliquomodo ſimile, quod aquam continere poteſt.</s> <s xml:id="echoid-s8024" xml:space="preserve"/> </p> <div xml:id="echoid-div1122" type="float" level="2" n="1"> <note position="right" xlink:label="note-0293-05" xlink:href="note-0293-05a" xml:space="preserve">729.</note> <note position="right" xlink:label="note-0293-06" xlink:href="note-0293-06a" xml:space="preserve"><emph style="sc">TAB. XXIX</emph>. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s8025" xml:space="preserve">In orbe ſuperiori datur foramen in l, cui reſpondet cy-<lb/>lindrus æneus, cum orbe cohærens, & </s> <s xml:id="echoid-s8026" xml:space="preserve">cochlea circumdatus, <lb/>quo tubus D, ejusdem longitudinis cum tubo in præceden-<lb/>ti Experimento, machinæ jungitur.</s> <s xml:id="echoid-s8027" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1124" type="section" level="1" n="280"> <head xml:id="echoid-head394" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s8028" xml:space="preserve">Aqua machinæ per tubum infundatur, & </s> <s xml:id="echoid-s8029" xml:space="preserve">aqua in tubo <lb/> <anchor type="note" xlink:label="note-0293-07a" xlink:href="note-0293-07"/> ſuſtinebit pondera P,P,P,P,P,P, ſimul excedentia ducentas <lb/>& </s> <s xml:id="echoid-s8030" xml:space="preserve">quinquagintâ libras. </s> <s xml:id="echoid-s8031" xml:space="preserve">Pondera hæc infundendo aquam in <lb/>tubum etiam elevari poterunt.</s> <s xml:id="echoid-s8032" xml:space="preserve"/> </p> <div xml:id="echoid-div1124" type="float" level="2" n="1"> <note position="right" xlink:label="note-0293-07" xlink:href="note-0293-07a" xml:space="preserve">730.</note> </div> <p> <s xml:id="echoid-s8033" xml:space="preserve">Hæc omnia quantumvis paradoxa ex natura fluiditatis ſe-<lb/> <anchor type="note" xlink:label="note-0293-08a" xlink:href="note-0293-08"/> quuntur; </s> <s xml:id="echoid-s8034" xml:space="preserve">gutta quæcunque quæ quieſcit, omnes partes <pb o="210" file="0294" n="321" rhead="PHYSICES ELEMENTA"/> verſus æquali cum vi conatur recedere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8035" xml:space="preserve">ſi ergo ab una <anchor type="note" xlink:label="note-0294-01a" xlink:href="note-0294-01"/> parte prematur, illam partem verſus, propter æqualem a-<lb/>ctioni reactionem, ipſa premet, & </s> <s xml:id="echoid-s8036" xml:space="preserve">hac eadem vi omnes par-<lb/>tes verſus recedere conabitur. </s> <s xml:id="echoid-s8037" xml:space="preserve">In primo Experimento, a-<lb/>qua, quæ fundum tangit, & </s> <s xml:id="echoid-s8038" xml:space="preserve">tubo reſpondet, ſuſtinet pon-<lb/>dus columnæ aqueæ in tubo contentæ, & </s> <s xml:id="echoid-s8039" xml:space="preserve">adfundum uſque <lb/>continuatæ, & </s> <s xml:id="echoid-s8040" xml:space="preserve">tali cum vi fundum premit, ut & </s> <s xml:id="echoid-s8041" xml:space="preserve">aquam <lb/>vicinam, quæ cum effluere non poſſit in fundum, & </s> <s xml:id="echoid-s8042" xml:space="preserve">aquam <lb/>vicinam, hac eadem vi agit; </s> <s xml:id="echoid-s8043" xml:space="preserve">quod & </s> <s xml:id="echoid-s8044" xml:space="preserve">ad aquam huic vici-<lb/>nam applicari poteſt, quare in omnibus fundi punctis datur <lb/>preſſio æqualis preſſioni in loco in quem aqua in tubo gra-<lb/>vat; </s> <s xml:id="echoid-s8045" xml:space="preserve">& </s> <s xml:id="echoid-s8046" xml:space="preserve">ideo fundus hic gravatur eodem modo ac ſi aquæ <lb/>columna, ejuſdem altitudinis cum aqua in tubo, & </s> <s xml:id="echoid-s8047" xml:space="preserve">cu us <lb/>baſis eſſet ipſe fundus, huic imponeretur.</s> <s xml:id="echoid-s8048" xml:space="preserve"/> </p> <div xml:id="echoid-div1125" type="float" level="2" n="2"> <note position="right" xlink:label="note-0293-08" xlink:href="note-0293-08a" xml:space="preserve">731.</note> <note symbol="*" position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">711.</note> </div> <p> <s xml:id="echoid-s8049" xml:space="preserve">Simili ratiocinio dilucidantur Experimenta 5. </s> <s xml:id="echoid-s8050" xml:space="preserve">& </s> <s xml:id="echoid-s8051" xml:space="preserve">6. </s> <s xml:id="echoid-s8052" xml:space="preserve">Pa-<lb/>tet enim ſingula operculi puncta ſurſum premi ab a-<lb/>qua ea vi, qua aqua quæ in apertura operculi hæret à ſuperiori <lb/>quæ in tubo hæret, deorſum premitur.</s> <s xml:id="echoid-s8053" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8054" xml:space="preserve">In ſecundo Experimento concipiatur, cylindrum A con-<lb/>tinuari ita, ut ad aquæ ſuperficiem perveniat; </s> <s xml:id="echoid-s8055" xml:space="preserve">eo aqua ex-<lb/>terior ab aqua hoc cylindro contenta ſeparatur, hæcque <lb/>ſola in fundum premit, funduſque hanc totam ſuſtinet. </s> <s xml:id="echoid-s8056" xml:space="preserve">Aqua <lb/>in cylindro premit in latera cylindri, aqua exterior premit <lb/>in ſuperficiem exteriorem cylindri, & </s> <s xml:id="echoid-s8057" xml:space="preserve">ſuperficies exterior <lb/>eodem modo premitur ac interior, preſſioneſque in puncta <lb/>oppoſita ſunt æquales; </s> <s xml:id="echoid-s8058" xml:space="preserve">ita ut, ſi ſuperficies tolleretur, preſ-<lb/>ſiones hæ ſeſe mutuo deſtruerent; </s> <s xml:id="echoid-s8059" xml:space="preserve">non intereſt igitur utrum <lb/>talis ſuperficies detur an non, & </s> <s xml:id="echoid-s8060" xml:space="preserve">ea ſublata, id eſt, ſub-<lb/>lata cylindri continuatione, non mutatur actio in fun-<lb/>dum.</s> <s xml:id="echoid-s8061" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8062" xml:space="preserve">In Experimento tertio pondus lanci impoſitum non mo-<lb/>do ſuſtinetur ab aqua in vaſe, ſed etiam ab actione ſuperfi-<lb/>ciei inferioris cylindri D e in aquam, quæ actio æqualis eſt <lb/>actioni aquæ in hanc ſuperficiem, in quam eodem modo pre-<lb/>mit aqua ac in Exp. </s> <s xml:id="echoid-s8063" xml:space="preserve">5. </s> <s xml:id="echoid-s8064" xml:space="preserve">in operculum agit.</s> <s xml:id="echoid-s8065" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8066" xml:space="preserve">Preſſionem lateralem, qualem in Exp. </s> <s xml:id="echoid-s8067" xml:space="preserve">4. </s> <s xml:id="echoid-s8068" xml:space="preserve">demonſtravi- <pb o="211" file="0295" n="322" rhead="MATHEMATICA. LIB. II. CAP II."/> mus, æqualem eſſe illi, quæ ſurſum aut deorſum dirigitur, <lb/>ex æqualitate actionis fluidi omnes partes verſus facile de-<lb/>ducitur.</s> <s xml:id="echoid-s8069" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8070" xml:space="preserve">Quamvis hæc omnia a gravitate fluidorum pendeant, <lb/> <anchor type="note" xlink:label="note-0295-01a" xlink:href="note-0295-01"/> horum actiones ab ipſorum pondere diſtingui debent, quod <lb/>ſemper quantitati materiæ eſt proportionale <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8071" xml:space="preserve"/> </p> <div xml:id="echoid-div1126" type="float" level="2" n="3"> <note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">732.</note> </div> <note symbol="*" position="right" xml:space="preserve">704.</note> </div> <div xml:id="echoid-div1128" type="section" level="1" n="281"> <head xml:id="echoid-head395" xml:space="preserve">CAPUT III. <lb/>De Solidis fluidis immerſis.</head> <p> <s xml:id="echoid-s8072" xml:space="preserve">DIverſa corporum, ſive ſolidorum, ſive fluidorum, pon-<lb/>dera a diverſâ materiæ quantitate, quam continent, <lb/>pendere, non a ſpatio quod hæc occupat, vidimus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8073" xml:space="preserve">vo- lumen enim, manente pondere, mutatis poris, variari <lb/>poteſt.</s> <s xml:id="echoid-s8074" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1129" type="section" level="1" n="282"> <head xml:id="echoid-head396" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s8075" xml:space="preserve">Materiæ quantitas in corpore, conſiderata cum relatione <lb/> <anchor type="note" xlink:label="note-0295-03a" xlink:href="note-0295-03"/> ad volumen corporis, id eſt, ad ſpatium ab hoc occupatum, <lb/>vocatur corporis Denſitas.</s> <s xml:id="echoid-s8076" xml:space="preserve"/> </p> <div xml:id="echoid-div1129" type="float" level="2" n="1"> <note position="right" xlink:label="note-0295-03" xlink:href="note-0295-03a" xml:space="preserve">733.</note> </div> <p> <s xml:id="echoid-s8077" xml:space="preserve">Corpus dicitur habere denſitatem duplam, aut triplam, <lb/>&</s> <s xml:id="echoid-s8078" xml:space="preserve">c. </s> <s xml:id="echoid-s8079" xml:space="preserve">denſitatis alterius corporis, quando, poſitis volumini-<lb/>bus æqualibus, materiæ quantitas dupla, aut tripla &</s> <s xml:id="echoid-s8080" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s8081" xml:space="preserve">eſt.</s> <s xml:id="echoid-s8082" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1131" type="section" level="1" n="283"> <head xml:id="echoid-head397" xml:space="preserve"><emph style="sc">Definitio.</emph> 2.</head> <p style="it"> <s xml:id="echoid-s8083" xml:space="preserve">Corpus homogeneum dicitur, quod in omnibus partibus eſt <lb/> <anchor type="note" xlink:label="note-0295-04a" xlink:href="note-0295-04"/> ejuſdem denſitatis.</s> <s xml:id="echoid-s8084" xml:space="preserve"/> </p> <div xml:id="echoid-div1131" type="float" level="2" n="1"> <note position="right" xlink:label="note-0295-04" xlink:href="note-0295-04a" xml:space="preserve">734.</note> </div> </div> <div xml:id="echoid-div1133" type="section" level="1" n="284"> <head xml:id="echoid-head398" xml:space="preserve"><emph style="sc">Definitio.</emph> 3.</head> <p style="it"> <s xml:id="echoid-s8085" xml:space="preserve">Heterogeneum cujus non omnes partes æqualem denſi-<lb/> <anchor type="note" xlink:label="note-0295-05a" xlink:href="note-0295-05"/> tatem habent.</s> <s xml:id="echoid-s8086" xml:space="preserve"/> </p> <div xml:id="echoid-div1133" type="float" level="2" n="1"> <note position="right" xlink:label="note-0295-05" xlink:href="note-0295-05a" xml:space="preserve">735.</note> </div> </div> <div xml:id="echoid-div1135" type="section" level="1" n="285"> <head xml:id="echoid-head399" xml:space="preserve"><emph style="sc">Definitio.</emph> 4.</head> <p style="it"> <s xml:id="echoid-s8087" xml:space="preserve">Pondus corporis conſideratum cum relatione ad volumen <lb/> <anchor type="note" xlink:label="note-0295-06a" xlink:href="note-0295-06"/> vocatur corporis Gravitas ſpecifica.</s> <s xml:id="echoid-s8088" xml:space="preserve"/> </p> <div xml:id="echoid-div1135" type="float" level="2" n="1"> <note position="right" xlink:label="note-0295-06" xlink:href="note-0295-06a" xml:space="preserve">736.</note> </div> <p> <s xml:id="echoid-s8089" xml:space="preserve">Gravitas ſpecifica dicitur dupla, quando manente volu-<lb/>mine pondus eſt duplum.</s> <s xml:id="echoid-s8090" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8091" xml:space="preserve">Gravitates ergo ſpecificæ & </s> <s xml:id="echoid-s8092" xml:space="preserve">denſitates corporum, in cor-<lb/> <anchor type="note" xlink:label="note-0295-07a" xlink:href="note-0295-07"/> <pb o="212" file="0296" n="323" rhead="PHYSICES ELEMENTA"/> poribus homogeneis, in eadem ſunt ratione; </s> <s xml:id="echoid-s8093" xml:space="preserve">& </s> <s xml:id="echoid-s8094" xml:space="preserve">ſunt inter ſe <lb/>ut pondera corporum æqualium quantum ad volumen.</s> <s xml:id="echoid-s8095" xml:space="preserve"/> </p> <div xml:id="echoid-div1136" type="float" level="2" n="2"> <note position="right" xlink:label="note-0295-07" xlink:href="note-0295-07a" xml:space="preserve">737.</note> </div> <p> <s xml:id="echoid-s8096" xml:space="preserve">Si corpora homogenea fuerint ejuſdem ponderis, vo-<lb/> <anchor type="note" xlink:label="note-0296-01a" xlink:href="note-0296-01"/> lumina eo ſunt minora quo denſitates ſunt majores, & </s> <s xml:id="echoid-s8097" xml:space="preserve">ma-<lb/>nente pondere, minuitur volumen in eadem ratione, in <lb/>qua denſitas augetur; </s> <s xml:id="echoid-s8098" xml:space="preserve">ſunt ideo in hoc cafu volumina inver-<lb/>ſe ut denſitates.</s> <s xml:id="echoid-s8099" xml:space="preserve"/> </p> <div xml:id="echoid-div1137" type="float" level="2" n="3"> <note position="left" xlink:label="note-0296-01" xlink:href="note-0296-01a" xml:space="preserve">438.</note> </div> <p> <s xml:id="echoid-s8100" xml:space="preserve">In homogeneis corporibus, ſi duæ dentur ex tribus ra-<lb/>tionibus, ponderum, voluminum, & </s> <s xml:id="echoid-s8101" xml:space="preserve">denſitatum, tertia <lb/>detegitur.</s> <s xml:id="echoid-s8102" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s8103" xml:space="preserve">Pondera enim ſunt in ratione compoſita voluminum & </s> <s xml:id="echoid-s8104" xml:space="preserve">denſi-<lb/> <anchor type="note" xlink:label="note-0296-02a" xlink:href="note-0296-02"/> tatum.</s> <s xml:id="echoid-s8105" xml:space="preserve"/> </p> <div xml:id="echoid-div1138" type="float" level="2" n="4"> <note position="left" xlink:label="note-0296-02" xlink:href="note-0296-02a" xml:space="preserve">739.</note> </div> <p style="it"> <s xml:id="echoid-s8106" xml:space="preserve">Volumina idcirco ſunt directè ut pondera, & </s> <s xml:id="echoid-s8107" xml:space="preserve">inverſe ut <lb/> <anchor type="note" xlink:label="note-0296-03a" xlink:href="note-0296-03"/> denſitates.</s> <s xml:id="echoid-s8108" xml:space="preserve"/> </p> <div xml:id="echoid-div1139" type="float" level="2" n="5"> <note position="left" xlink:label="note-0296-03" xlink:href="note-0296-03a" xml:space="preserve">740.</note> </div> <p style="it"> <s xml:id="echoid-s8109" xml:space="preserve">Tandem denſitates ſunt directè ut pondera, & </s> <s xml:id="echoid-s8110" xml:space="preserve">inverſè ut <lb/> <anchor type="note" xlink:label="note-0296-04a" xlink:href="note-0296-04"/> volumina.</s> <s xml:id="echoid-s8111" xml:space="preserve"/> </p> <div xml:id="echoid-div1140" type="float" level="2" n="6"> <note position="left" xlink:label="note-0296-04" xlink:href="note-0296-04a" xml:space="preserve">741.</note> </div> <p style="it"> <s xml:id="echoid-s8112" xml:space="preserve">Quando ſolidum fluido immergitur, a fluido ab omni par-<lb/> <anchor type="note" xlink:label="note-0296-05a" xlink:href="note-0296-05"/> te premitur, preſſioque hæc in ratione altitudinis fluidi ſu-<lb/>pra ſolidum creſcit. </s> <s xml:id="echoid-s8113" xml:space="preserve">Ut hoc ex dictis in capite præcedenti <lb/>ſequitur, ac etiam directo Experimento probatur.</s> <s xml:id="echoid-s8114" xml:space="preserve"/> </p> <div xml:id="echoid-div1141" type="float" level="2" n="7"> <note position="left" xlink:label="note-0296-05" xlink:href="note-0296-05a" xml:space="preserve">742.</note> </div> </div> <div xml:id="echoid-div1143" type="section" level="1" n="286"> <head xml:id="echoid-head400" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s8115" xml:space="preserve">Extremitati tubi vitrei B m alligatur ſaccus coriaceus S, <lb/> <anchor type="note" xlink:label="note-0296-06a" xlink:href="note-0296-06"/> mercurio plenus, veſica etiam poteſt adhiberi; </s> <s xml:id="echoid-s8116" xml:space="preserve">immergitur <lb/> <anchor type="note" xlink:label="note-0296-07a" xlink:href="note-0296-07"/> ſaccus hic aquâ, ita, ut extremitas B tubi ſupra aquam <lb/>perveniat.</s> <s xml:id="echoid-s8117" xml:space="preserve">. Preſſione aquæ in ſuperficiem ſacci. </s> <s xml:id="echoid-s8118" xml:space="preserve">adſcendit <lb/>mercurius in tubum, ut perveniat ad m; </s> <s xml:id="echoid-s8119" xml:space="preserve">adſcenſusque mer-<lb/>curii ſequitur proportionem altitudinis aquæ ſupra ſaccum.</s> <s xml:id="echoid-s8120" xml:space="preserve"/> </p> <div xml:id="echoid-div1143" type="float" level="2" n="1"> <note position="left" xlink:label="note-0296-06" xlink:href="note-0296-06a" xml:space="preserve">743.</note> <note position="left" xlink:label="note-0296-07" xlink:href="note-0296-07a" xml:space="preserve">TAB. XXIX. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s8121" xml:space="preserve">Quando ſolidum ad magnam profunditatem fluido im-<lb/>mergitur, preſſio in ſuperiorem partem a preſſione in in-<lb/>feriorem vix differt; </s> <s xml:id="echoid-s8122" xml:space="preserve">unde corpora altè immerſa ab omni <lb/> <anchor type="note" xlink:label="note-0296-08a" xlink:href="note-0296-08"/> parte quaſi æqualiter premuntur; </s> <s xml:id="echoid-s8123" xml:space="preserve">quæ preſſio a corporibus <lb/>mollibus ſine figuræ mutatione, & </s> <s xml:id="echoid-s8124" xml:space="preserve">ab admodum fragilibus <lb/>fine diſruptione, ſuſtineri poteſt.</s> <s xml:id="echoid-s8125" xml:space="preserve"/> </p> <div xml:id="echoid-div1144" type="float" level="2" n="2"> <note position="left" xlink:label="note-0296-08" xlink:href="note-0296-08a" xml:space="preserve">744.</note> </div> </div> <div xml:id="echoid-div1146" type="section" level="1" n="287"> <head xml:id="echoid-head401" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s8126" xml:space="preserve">Fruſtum ceræ mollis, figuræ irregularis, & </s> <s xml:id="echoid-s8127" xml:space="preserve">ovum, ve-<lb/> <anchor type="note" xlink:label="note-0296-09a" xlink:href="note-0296-09"/> ſicæ aquâ repletæ includuntur, veſica exacte clauſa pyxidi <lb/> <anchor type="note" xlink:label="note-0296-10a" xlink:href="note-0296-10"/> <pb o="213" file="0297" n="324" rhead="MATHEMATICA. LIB. II. CAP. III."/> æneæ A inſeritur; </s> <s xml:id="echoid-s8128" xml:space="preserve">operculo ligneo O hæc obtegitur, ita <lb/>ut a veſica ſuſtineatur; </s> <s xml:id="echoid-s8129" xml:space="preserve">pondus P centum, aut centum & </s> <s xml:id="echoid-s8130" xml:space="preserve"><lb/>quinquaginta librarum, etiam majus abhiberi poteſt, ſuper-<lb/>imponitur, quo neque ovum frangitur, neque ceræ figura <lb/>ullo modo mutatur.</s> <s xml:id="echoid-s8131" xml:space="preserve"/> </p> <div xml:id="echoid-div1146" type="float" level="2" n="1"> <note position="left" xlink:label="note-0296-09" xlink:href="note-0296-09a" xml:space="preserve">745.</note> <note position="left" xlink:label="note-0296-10" xlink:href="note-0296-10a" xml:space="preserve">TAB. XXVIII. <lb/>fig 5.</note> </div> <p> <s xml:id="echoid-s8132" xml:space="preserve">Ne quidem guttæ cujuſcunque fluidi figura, preſſione alte-<lb/> <anchor type="note" xlink:label="note-0297-01a" xlink:href="note-0297-01"/> rius fluidi ab omni parte æquali, mutari poteſt. </s> <s xml:id="echoid-s8133" xml:space="preserve">Sit gutta fi-<lb/> <anchor type="note" xlink:label="note-0297-02a" xlink:href="note-0297-02"/> guræ irregularis A, quæ alio fluido ab omni parte æquali-<lb/>ter prematur. </s> <s xml:id="echoid-s8134" xml:space="preserve">Directio preſſionis in omnibus punctis eſt <lb/> <anchor type="note" xlink:label="note-0297-03a" xlink:href="note-0297-03"/> perpendicularis ad ſuperficiem; </s> <s xml:id="echoid-s8135" xml:space="preserve">quod ſi negetur, reſolven-<lb/>da erit preſſio in duas <anchor type="note" xlink:href="" symbol="*"/>, quarum una perpendiculariter a- <anchor type="note" xlink:label="note-0297-04a" xlink:href="note-0297-04"/> gat ad ſuperficiem, alia juxta directionem ſuperficiei paral-<lb/>lelam, quæ ſecunda cum in ſuperficiem non agat, premitur <lb/>gutta illâ ſolâ, cujus directio perpendicularis eſt ad ſuperfi-<lb/>ciem. </s> <s xml:id="echoid-s8136" xml:space="preserve">Prematur punctum B, guttula preſſa quaquaverſum <lb/>æquali cum vi premit, & </s> <s xml:id="echoid-s8137" xml:space="preserve">guttæ minores ſingulæ preſſæ eo-<lb/>dem modo premunt, ita ut preſſio ſtatim per integram gut-<lb/>tam datam diſpergatur, quare particula ut D, quæ in gut-<lb/>ta ab omni parte æqualiter premitur, conatur cedere per <lb/>DE, cum vi qua premitur, id eſt, cum vi qua externe <lb/>premitur particula B, ſed æquali vi ponimus per ED pre-<lb/>mi particulam D; </s> <s xml:id="echoid-s8138" xml:space="preserve">non poterit ergo hæc moveri; </s> <s xml:id="echoid-s8139" xml:space="preserve">eadem <lb/>demonſtratio poterit applicari puncto F, ut alii puncto cui-<lb/>cunque ſuperficiei, ita ut nullibi gutta moveri poſ-<lb/>ſit.</s> <s xml:id="echoid-s8140" xml:space="preserve"/> </p> <div xml:id="echoid-div1147" type="float" level="2" n="2"> <note position="right" xlink:label="note-0297-01" xlink:href="note-0297-01a" xml:space="preserve">746.</note> <note position="right" xlink:label="note-0297-02" xlink:href="note-0297-02a" xml:space="preserve">TAB. XXVIII. <lb/>fig. 6.</note> <note position="right" xlink:label="note-0297-03" xlink:href="note-0297-03a" xml:space="preserve">747.</note> <note symbol="*" position="right" xlink:label="note-0297-04" xlink:href="note-0297-04a" xml:space="preserve">229.</note> </div> <p> <s xml:id="echoid-s8141" xml:space="preserve">Solidum fluido ſpecifice gravius, ad quamcunque alti. <lb/></s> <s xml:id="echoid-s8142" xml:space="preserve"> <anchor type="note" xlink:label="note-0297-05a" xlink:href="note-0297-05"/> tudinem fluido immerſum, deorſum pellitur preſſione, quæ <lb/>valet pondus columnæ quæ formatur ex ipſo corpore & </s> <s xml:id="echoid-s8143" xml:space="preserve">flui-<lb/>do ſuperincumbenti. </s> <s xml:id="echoid-s8144" xml:space="preserve">Pondus columoæ ſimilis, ſed quæ <lb/>tota ex fluido conſtat, eſt vis cum qua corpus a fluido ſur-<lb/>ſum premitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8145" xml:space="preserve">Cum vero ſolidum ponatur fluido ſpeci- <anchor type="note" xlink:label="note-0297-06a" xlink:href="note-0297-06"/> fice gravius, vis hæc minor eſt illâ, & </s> <s xml:id="echoid-s8146" xml:space="preserve">ab eadem ſuperatur, <lb/>& </s> <s xml:id="echoid-s8147" xml:space="preserve">corpus deſcendit.</s> <s xml:id="echoid-s8148" xml:space="preserve"/> </p> <div xml:id="echoid-div1148" type="float" level="2" n="3"> <note position="right" xlink:label="note-0297-05" xlink:href="note-0297-05a" xml:space="preserve">748.</note> <note symbol="*" position="right" xlink:label="note-0297-06" xlink:href="note-0297-06a" xml:space="preserve">742. 711.</note> </div> <p> <s xml:id="echoid-s8149" xml:space="preserve">Simili ratiocinio, ſolidum fluido ſpecifice levius immer ſum, <lb/> <anchor type="note" xlink:label="note-0297-07a" xlink:href="note-0297-07"/> ad ſupremam fluidi ſuperficiem adſcendere debere, proba-<lb/>tur.</s> <s xml:id="echoid-s8150" xml:space="preserve"/> </p> <div xml:id="echoid-div1149" type="float" level="2" n="4"> <note position="right" xlink:label="note-0297-07" xlink:href="note-0297-07a" xml:space="preserve">749.</note> </div> <pb o="214" file="0298" n="325" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s8151" xml:space="preserve">Poſita verò eadem ſolidi cum fluido gravitate ſpecifica, <lb/> <anchor type="note" xlink:label="note-0298-01a" xlink:href="note-0298-01"/> neque adſcendet, neque deſcendet, ſed ad quamcunque al-<lb/>titudinem in fluido ſuſpenſum manebit, & </s> <s xml:id="echoid-s8152" xml:space="preserve">fluidum inte-<lb/>grum corpus ſuſtinebit; </s> <s xml:id="echoid-s8153" xml:space="preserve">in quo caſu, propter æqualitatem <lb/>gravitatum ſpecificarum, fluidum ſuſtinet pondus æquale <lb/>ponderi fluidi, quod impleret ſpatium a corpore occupa-<lb/>tum. </s> <s xml:id="echoid-s8154" xml:space="preserve">Fluidum autem eodem modo agit in omnia ſolida <lb/>æqualia ad eandem profunditatem immerſa, & </s> <s xml:id="echoid-s8155" xml:space="preserve">æqualiter <lb/>hæc ſuſtinet; </s> <s xml:id="echoid-s8156" xml:space="preserve">amittit ergo Corpus omne immerſum partem <lb/> <anchor type="note" xlink:label="note-0298-02a" xlink:href="note-0298-02"/> ponderis, æqualem ponderi fluidi quod æquale ſpatium cum <lb/>corpore occupat.</s> <s xml:id="echoid-s8157" xml:space="preserve"/> </p> <div xml:id="echoid-div1150" type="float" level="2" n="5"> <note position="left" xlink:label="note-0298-01" xlink:href="note-0298-01a" xml:space="preserve">750.</note> <note position="left" xlink:label="note-0298-02" xlink:href="note-0298-02a" xml:space="preserve">751.</note> </div> <p> <s xml:id="echoid-s8158" xml:space="preserve">Proprie loquendo non quidem amittit corpus partem pon-<lb/>deris quæ a fluido ſuſtinetur; </s> <s xml:id="echoid-s8159" xml:space="preserve">ſed deſcendit in fluido aut <lb/>trahit funem quo ſuſtinetur, quaſi revera pondus imminutum <lb/>foret.</s> <s xml:id="echoid-s8160" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1152" type="section" level="1" n="288"> <head xml:id="echoid-head402" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s8161" xml:space="preserve">Ex unco lancis libræ ſuperius memoratæ <anchor type="note" xlink:href="" symbol="*"/> ſuſpendatur <anchor type="note" xlink:label="note-0298-03a" xlink:href="note-0298-03"/> cylindrus æneus cavus E; </s> <s xml:id="echoid-s8162" xml:space="preserve">unco, fundo hujus cohærenti, <lb/> <anchor type="note" xlink:label="note-0298-04a" xlink:href="note-0298-04"/> ope capilli equini, ſuſpenditur cylindrus ſolidus C, ex eo-<lb/> <anchor type="note" xlink:label="note-0298-05a" xlink:href="note-0298-05"/> dem metallo, qui ſi alteri E inſeratur, hunc exacte implet <lb/>ita, ut in E, quando aquâ repletur, contineatur aquæ <lb/>quantitas, quæ poteſt implere locum a Coccupatum. </s> <s xml:id="echoid-s8163" xml:space="preserve">Lan-<lb/>ci oppoſitæ pondus imponatur ut detur æquilibrium; </s> <s xml:id="echoid-s8164" xml:space="preserve">de-<lb/>ſcendat bilanx, ut cylindrus C aquâ, vaſe D contentâ, im-<lb/>mergatur; </s> <s xml:id="echoid-s8165" xml:space="preserve">eo æquilibrium deſtruitur, quia C pro parte ab <lb/>aqua ſuſtinetur; </s> <s xml:id="echoid-s8166" xml:space="preserve">ad hoc verò redit libra, ſi vas E aquâ im-<lb/>pleatur.</s> <s xml:id="echoid-s8167" xml:space="preserve"/> </p> <div xml:id="echoid-div1152" type="float" level="2" n="1"> <note position="left" xlink:label="note-0298-03" xlink:href="note-0298-03a" xml:space="preserve">752.</note> <note position="left" xlink:label="note-0298-04" xlink:href="note-0298-04a" xml:space="preserve">TAB. XXX. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0298-05" xlink:href="note-0298-05a" xml:space="preserve">705.</note> </div> </div> <div xml:id="echoid-div1154" type="section" level="1" n="289"> <head xml:id="echoid-head403" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p style="it"> <s xml:id="echoid-s8168" xml:space="preserve">Pondus, quod corpus fluido immer ſum ſervat, vocatur il-<lb/> <anchor type="note" xlink:label="note-0298-06a" xlink:href="note-0298-06"/> lius gravitas reſpectiva.</s> <s xml:id="echoid-s8169" xml:space="preserve"/> </p> <div xml:id="echoid-div1154" type="float" level="2" n="1"> <note position="left" xlink:label="note-0298-06" xlink:href="note-0298-06a" xml:space="preserve">753.</note> </div> <p style="it"> <s xml:id="echoid-s8170" xml:space="preserve">Hæcque gravitas reſpectiva eſt exceſſus gravitatis ſpeci-<lb/> <anchor type="note" xlink:label="note-0298-07a" xlink:href="note-0298-07"/> ficæ ſolidi ſuper gravitatem ſpecificam fluidi;</s> <s xml:id="echoid-s8171" xml:space="preserve"/> </p> <div xml:id="echoid-div1155" type="float" level="2" n="2"> <note position="left" xlink:label="note-0298-07" xlink:href="note-0298-07a" xml:space="preserve">754.</note> </div> <p> <s xml:id="echoid-s8172" xml:space="preserve">Ex hiſce ſequitur, omnia ſolida æqualia, licet diver ſæ <lb/> <anchor type="note" xlink:label="note-0298-08a" xlink:href="note-0298-08"/> gravitatis ſpecificæ, quando eodem fluido immerguntur, pon-<lb/>dus æquale amittere <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8173" xml:space="preserve">Experimentum ultimum eodem mo- <anchor type="note" xlink:label="note-0298-09a" xlink:href="note-0298-09"/> do procedit cum cylindro ex quocunque alio metallo & </s> <s xml:id="echoid-s8174" xml:space="preserve">af- <pb file="0299" n="326"/> <pb file="0299a" n="327"/> <anchor type="figure" xlink:label="fig-0299a-01a" xlink:href="fig-0299a-01"/> <pb file="0300" n="328"/> <pb o="215" file="0301" n="329" rhead="MATHEMATICA. LIB. II. CAP. III."/> fuſâ eâdem aquæ quantitate, quæ nempe implet vas E, æ-<lb/>quilibrium ſemper inſtauratur.</s> <s xml:id="echoid-s8175" xml:space="preserve"/> </p> <div xml:id="echoid-div1156" type="float" level="2" n="3"> <note position="left" xlink:label="note-0298-08" xlink:href="note-0298-08a" xml:space="preserve">755.</note> <note symbol="*" position="left" xlink:label="note-0298-09" xlink:href="note-0298-09a" xml:space="preserve">751.</note> <figure xlink:label="fig-0299a-01" xlink:href="fig-0299a-01a"> <image file="0299a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0299a-01"/> </figure> </div> <p> <s xml:id="echoid-s8176" xml:space="preserve">Ex dictis ulterius ſequitur quomodocunque inter ſe diffe-<lb/> <anchor type="note" xlink:label="note-0301-01a" xlink:href="note-0301-01"/> rant denſitates corporum inæqualium, ſi eodem fluido im-<lb/>mergantur, pondera ab iis amiſſa eſſe in ratione volu-<lb/>minum. </s> <s xml:id="echoid-s8177" xml:space="preserve">In ea enim ratione ſunt ſpatia ab iis in fluido occu-<lb/>pata.</s> <s xml:id="echoid-s8178" xml:space="preserve"/> </p> <div xml:id="echoid-div1157" type="float" level="2" n="4"> <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">756.</note> </div> <p> <s xml:id="echoid-s8179" xml:space="preserve">Idcirco corpora ejuſdem ponderis, ſed diverſæ denſi-<lb/>tatis, partes inæquales ponderis amittunt, quando eo-<lb/>dem fluido immerguntur, propter voluminum inæqualita-<lb/>tem.</s> <s xml:id="echoid-s8180" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1159" type="section" level="1" n="290"> <head xml:id="echoid-head404" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s8181" xml:space="preserve">Fruſta ejuſdem ponderis, unum auri, alterum plumbi, <lb/> <anchor type="note" xlink:label="note-0301-02a" xlink:href="note-0301-02"/> g, g, capillis equinis, uncis bilancis ſæpius memoratæ <anchor type="note" xlink:href="" symbol="*"/> ſuſ- <anchor type="note" xlink:label="note-0301-03a" xlink:href="note-0301-03"/> penduntur, æquilibrium datur; </s> <s xml:id="echoid-s8182" xml:space="preserve">deſcendat bilanx, & </s> <s xml:id="echoid-s8183" xml:space="preserve">corpo-<lb/> <anchor type="note" xlink:label="note-0301-04a" xlink:href="note-0301-04"/> ra g, g, aquâ, vaſis F, F contentâ, immergantur, æquilibri-<lb/>um deſtruetur.</s> <s xml:id="echoid-s8184" xml:space="preserve"/> </p> <div xml:id="echoid-div1159" type="float" level="2" n="1"> <note position="right" xlink:label="note-0301-02" xlink:href="note-0301-02a" xml:space="preserve">757.</note> <note position="right" xlink:label="note-0301-03" xlink:href="note-0301-03a" xml:space="preserve">TAB. XXIX. <lb/>fig. 4.</note> <note symbol="*" position="right" xlink:label="note-0301-04" xlink:href="note-0301-04a" xml:space="preserve">701.</note> </div> <p> <s xml:id="echoid-s8185" xml:space="preserve">Quando ſolidum, fluido ſpecifice gravius, in fluido <lb/>ſuſpenditur, fluidum, ab omni parte, in illud ſolidum, <lb/>pro altitudine ſua, agit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8186" xml:space="preserve">ſolidum æqualiter in illud rea- <anchor type="note" xlink:label="note-0301-05a" xlink:href="note-0301-05"/> git; </s> <s xml:id="echoid-s8187" xml:space="preserve">actiones illæ ſunt igitur eædem, ac ſi ſpatium, a ſolido <lb/>occupatum, ipſo fluido impleretur; </s> <s xml:id="echoid-s8188" xml:space="preserve">& </s> <s xml:id="echoid-s8189" xml:space="preserve">ita non intereſt, quo <lb/> <anchor type="note" xlink:label="note-0301-06a" xlink:href="note-0301-06"/> ad pondus totius fluidi, utrum in eo ſolidum ſpecifice gravius <lb/>ſuſpendatur, an affundatur ejuſdem fluidi quantitas, quæ <lb/>æquale ſpatium cum ſolido occupat.</s> <s xml:id="echoid-s8190" xml:space="preserve"/> </p> <div xml:id="echoid-div1160" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0301-05" xlink:href="note-0301-05a" xml:space="preserve">742.</note> <note position="right" xlink:label="note-0301-06" xlink:href="note-0301-06a" xml:space="preserve">758.</note> </div> </div> <div xml:id="echoid-div1162" type="section" level="1" n="291"> <head xml:id="echoid-head405" xml:space="preserve"><emph style="sc">Experimentum.</emph> 5.</head> <p> <s xml:id="echoid-s8191" xml:space="preserve">Vas A, aquam continens, brachio libræ ſuſpenditur, ei-<lb/> <anchor type="note" xlink:label="note-0301-07a" xlink:href="note-0301-07"/> que immergitur cylindrus æneus C, qui capillo equino ſuſti-<lb/> <anchor type="note" xlink:label="note-0301-08a" xlink:href="note-0301-08"/> netur, ne fundum vaſis tangat; </s> <s xml:id="echoid-s8192" xml:space="preserve">pondere lanci oppoſitæ <lb/>impoſito, datur æquilibrium. </s> <s xml:id="echoid-s8193" xml:space="preserve">Extracto cylindro C deſtrui-<lb/>tur æquilibrium, & </s> <s xml:id="echoid-s8194" xml:space="preserve">inſtauratur infundendo aquam, quæ cy-<lb/>lindro cavo E contineri poteſt, in quo ſi inſeratur cylindrus <lb/>ſolidus C, exacte ab hoc repletur.</s> <s xml:id="echoid-s8195" xml:space="preserve"/> </p> <div xml:id="echoid-div1162" type="float" level="2" n="1"> <note position="right" xlink:label="note-0301-07" xlink:href="note-0301-07a" xml:space="preserve">759.</note> <note position="right" xlink:label="note-0301-08" xlink:href="note-0301-08a" xml:space="preserve">TAB. XXX. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s8196" xml:space="preserve">Ex collatione n. </s> <s xml:id="echoid-s8197" xml:space="preserve">751. </s> <s xml:id="echoid-s8198" xml:space="preserve">& </s> <s xml:id="echoid-s8199" xml:space="preserve">758.</s> <s xml:id="echoid-s8200" xml:space="preserve">, ut & </s> <s xml:id="echoid-s8201" xml:space="preserve">Experimentorum 3. </s> <s xml:id="echoid-s8202" xml:space="preserve">& </s> <s xml:id="echoid-s8203" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0301-09a" xlink:href="note-0301-09"/> 5. </s> <s xml:id="echoid-s8204" xml:space="preserve">quibus illi confirmantur, patet, fluidum acquirere pondus <lb/>quod ſolidum immerſum amittit. </s> <s xml:id="echoid-s8205" xml:space="preserve">Vis gravitatis ſemper pro- <pb o="216" file="0302" n="330" rhead="PHYSICES ELEMENTA"/> portionalis eſt quantitati materiæ, & </s> <s xml:id="echoid-s8206" xml:space="preserve">non mutatur immerſio-<lb/>ne ſolidi in fluidum; </s> <s xml:id="echoid-s8207" xml:space="preserve">quare ſumma ponderum ſolidi & </s> <s xml:id="echoid-s8208" xml:space="preserve">flui-<lb/>di, & </s> <s xml:id="echoid-s8209" xml:space="preserve">ante & </s> <s xml:id="echoid-s8210" xml:space="preserve">poſt immerſionem, non differt.</s> <s xml:id="echoid-s8211" xml:space="preserve"/> </p> <div xml:id="echoid-div1163" type="float" level="2" n="2"> <note position="right" xlink:label="note-0301-09" xlink:href="note-0301-09a" xml:space="preserve">760.</note> </div> </div> <div xml:id="echoid-div1165" type="section" level="1" n="292"> <head xml:id="echoid-head406" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s8212" xml:space="preserve">Unco Vlancis A libræ appendatur ſolidum C, & </s> <s xml:id="echoid-s8213" xml:space="preserve">detur æqui-<lb/> <anchor type="note" xlink:label="note-0302-01a" xlink:href="note-0302-01"/> librium, lanci B impoſitis ponderibus P & </s> <s xml:id="echoid-s8214" xml:space="preserve">p, quorum p va-<lb/> <anchor type="note" xlink:label="note-0302-02a" xlink:href="note-0302-02"/> let pondus quod corpus C in aqua amittit. </s> <s xml:id="echoid-s8215" xml:space="preserve">Detur etiam <lb/>vas D aquam continens, & </s> <s xml:id="echoid-s8216" xml:space="preserve">libræ EF, quæ pede ſuſtine-<lb/>tur, appenſum; </s> <s xml:id="echoid-s8217" xml:space="preserve">pondere lanci oppoſitæ impoſito, detur <lb/>& </s> <s xml:id="echoid-s8218" xml:space="preserve">hìc æquilibrium; </s> <s xml:id="echoid-s8219" xml:space="preserve">deſcendat bilanx cum corpore C, ut <lb/>hoc aquâ, in vaſe D, contentâ immergatur, deſtruitur <lb/>æquilibrium in ambabus libris, quæ ambæ ad ipſum rede-<lb/>unt, transferendo pondus p ex lance B in lancem bra-<lb/>chii F.</s> <s xml:id="echoid-s8220" xml:space="preserve"/> </p> <div xml:id="echoid-div1165" type="float" level="2" n="1"> <note position="left" xlink:label="note-0302-01" xlink:href="note-0302-01a" xml:space="preserve">761.</note> <note position="left" xlink:label="note-0302-02" xlink:href="note-0302-02a" xml:space="preserve">TAB. XXIX. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s8221" xml:space="preserve">Corpus, fluido ſpecifice gravius, & </s> <s xml:id="echoid-s8222" xml:space="preserve">quod in hoc de-<lb/> <anchor type="note" xlink:label="note-0302-03a" xlink:href="note-0302-03"/> ſcendit, majori vi deorſum fertur quam ſurſum premitur, <lb/>ut antea explicatum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8223" xml:space="preserve">quarum virium differentia eſt cor- <anchor type="note" xlink:label="note-0302-04a" xlink:href="note-0302-04"/> poris gravitas reſpectiva. </s> <s xml:id="echoid-s8224" xml:space="preserve">Vis prima pro parte conſtat ex <lb/>pondere fluidi corpori ſuperincumbentis; </s> <s xml:id="echoid-s8225" xml:space="preserve">& </s> <s xml:id="echoid-s8226" xml:space="preserve">corpus ad ta-<lb/>lem poteſt immergi profunditatem, ut hocce pondus æqua-<lb/>le ſit memoratæ gravitati reſpectivæ; </s> <s xml:id="echoid-s8227" xml:space="preserve">ſi in hoc caſu fluidum <lb/>hoc ſuperincumbens tollatur, ſuſtinebitur corpus a preſſione <lb/>fluidi inferioris. </s> <s xml:id="echoid-s8228" xml:space="preserve">Si ad majorem profunditatem corpus im-<lb/> <anchor type="note" xlink:label="note-0302-05a" xlink:href="note-0302-05"/> mergatur, & </s> <s xml:id="echoid-s8229" xml:space="preserve">etiam fluidum cohibeatur ne in ſuperficiem <lb/>corporis ſupremam premat, (cum preſſio, qua corpus ſur-<lb/>ſum pellitur, cum profunditate ad quam immergitur cre-<lb/>ſcat <anchor type="note" xlink:href="" symbol="*"/>) majori vi in altum feretur corpus quam gravi- <anchor type="note" xlink:label="note-0302-06a" xlink:href="note-0302-06"/> tate deſcendet, quare, ſi libere moveri poſſit, adſcen-<lb/>det.</s> <s xml:id="echoid-s8230" xml:space="preserve"/> </p> <div xml:id="echoid-div1166" type="float" level="2" n="2"> <note position="left" xlink:label="note-0302-03" xlink:href="note-0302-03a" xml:space="preserve">662.</note> <note symbol="*" position="left" xlink:label="note-0302-04" xlink:href="note-0302-04a" xml:space="preserve">748.</note> <note position="left" xlink:label="note-0302-05" xlink:href="note-0302-05a" xml:space="preserve">763.</note> <note symbol="*" position="left" xlink:label="note-0302-06" xlink:href="note-0302-06a" xml:space="preserve">742.</note> </div> </div> <div xml:id="echoid-div1168" type="section" level="1" n="293"> <head xml:id="echoid-head407" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s8231" xml:space="preserve">Cylindro C, ab utraque parte aperto, applicetur ab in-<lb/> <anchor type="note" xlink:label="note-0302-07a" xlink:href="note-0302-07"/> feriori parte lamina plumbea F, craſſitiei quartæ partis <lb/> <anchor type="note" xlink:label="note-0302-08a" xlink:href="note-0302-08"/> unius pollicis; </s> <s xml:id="echoid-s8232" xml:space="preserve">ſi ita exacte cum cylindro congruat, ut aquam <lb/>excludat, laminaque filo, unco V in centro laminæ alligato, <lb/>ſuſtineatur, donec ad profunditatem circiter trium pollicum <lb/>aquâ immergatur, ab aqua ſuſtinebitur, quod relicto filo pate- <pb o="217" file="0303" n="331" rhead="MATHEMATICA. LIB. II. CAP. III."/> bit. </s> <s xml:id="echoid-s8233" xml:space="preserve">Ad majorem profunditatem magis arcte cum cylindro <lb/>cohærebit, ad minorem cadet.</s> <s xml:id="echoid-s8234" xml:space="preserve"/> </p> <div xml:id="echoid-div1168" type="float" level="2" n="1"> <note position="left" xlink:label="note-0302-07" xlink:href="note-0302-07a" xml:space="preserve">764.</note> <note position="left" xlink:label="note-0302-08" xlink:href="note-0302-08a" xml:space="preserve">TAB. XXX. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s8235" xml:space="preserve">Si cum lamina aurea hocce Experimentum inſtitueretur, <lb/>ad majorem profunditatem immergenda eſſet; </s> <s xml:id="echoid-s8236" xml:space="preserve">auri enim <lb/>gravitas ſpecifica eſt ad aquæ gravitatem ſpecificam ut 19. <lb/></s> <s xml:id="echoid-s8237" xml:space="preserve">ad 1; </s> <s xml:id="echoid-s8238" xml:space="preserve">quare illius gravitas reſpectiva eſt ad aquæ gravita-<lb/>tem ſpecificam ut 18. </s> <s xml:id="echoid-s8239" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s8240" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8241" xml:space="preserve">Columna idcirco aquea de- <anchor type="note" xlink:label="note-0303-01a" xlink:href="note-0303-01"/> cies & </s> <s xml:id="echoid-s8242" xml:space="preserve">octies, altitudine ſua, craſſitiem laminæ aureæ ſupe-<lb/>rare debet, ut valeat hujus gravitatem reſpectivam; </s> <s xml:id="echoid-s8243" xml:space="preserve">requi-<lb/>ritur ergo ut aquæ altitudo, ſupra ſuperficiem ſuperiorem <lb/>laminæ aureæ, toties ad minimum valeat ipſius laminæ craſ-<lb/>ſitiem.</s> <s xml:id="echoid-s8244" xml:space="preserve"/> </p> <div xml:id="echoid-div1169" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0303-01" xlink:href="note-0303-01a" xml:space="preserve">714.</note> </div> </div> <div xml:id="echoid-div1171" type="section" level="1" n="294"> <head xml:id="echoid-head408" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s8245" xml:space="preserve">Cylindrus A cum fundo mobili operculo obtectus & </s> <s xml:id="echoid-s8246" xml:space="preserve">cum <lb/> <anchor type="note" xlink:label="note-0303-02a" xlink:href="note-0303-02"/> tubo D conjunctus, ut ante expoſitum <anchor type="note" xlink:href="" symbol="*"/>, aquâ immergitur, <anchor type="note" xlink:label="note-0303-03a" xlink:href="note-0303-03"/> funduſque, quando ad profunditatem unius pedis infra aquæ <lb/> <anchor type="note" xlink:label="note-0303-04a" xlink:href="note-0303-04"/> ſuperficiem pervenit, adſcendit, licet ponderet integram <lb/>libram cum quadrante, & </s> <s xml:id="echoid-s8247" xml:space="preserve">licet, ope cochleæ, in centro <lb/>fundi ab inferiori parte cohærentis, conjungatur cum pon-<lb/>dere P unius libræ, & </s> <s xml:id="echoid-s8248" xml:space="preserve">præter pondera quæ elevantur ſupe-<lb/>ratur attritus.</s> <s xml:id="echoid-s8249" xml:space="preserve"/> </p> <div xml:id="echoid-div1171" type="float" level="2" n="1"> <note position="right" xlink:label="note-0303-02" xlink:href="note-0303-02a" xml:space="preserve">765.</note> <note position="right" xlink:label="note-0303-03" xlink:href="note-0303-03a" xml:space="preserve">TAB. XXX. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0303-04" xlink:href="note-0303-04a" xml:space="preserve">722.</note> </div> <p> <s xml:id="echoid-s8250" xml:space="preserve">Idem ſolidum, quod fluidis diverſæ denſitatis immergi-<lb/> <anchor type="note" xlink:label="note-0303-05a" xlink:href="note-0303-05"/> tur, diverſam ponderis ſui partem amittit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8251" xml:space="preserve">ideò quan- <anchor type="note" xlink:label="note-0303-06a" xlink:href="note-0303-06"/> do duo corpora, ejuſdem denſitatis & </s> <s xml:id="echoid-s8252" xml:space="preserve">ponderis, fluidis di-<lb/>verſæ denſitatis immerguntur, deſtruitur inter illa æquili-<lb/>brium.</s> <s xml:id="echoid-s8253" xml:space="preserve"/> </p> <div xml:id="echoid-div1172" type="float" level="2" n="2"> <note position="right" xlink:label="note-0303-05" xlink:href="note-0303-05a" xml:space="preserve">766.</note> <note symbol="*" position="right" xlink:label="note-0303-06" xlink:href="note-0303-06a" xml:space="preserve">751.</note> </div> </div> <div xml:id="echoid-div1174" type="section" level="1" n="295"> <head xml:id="echoid-head409" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s8254" xml:space="preserve">Duæ laminæ g, g ejuſdem metalli & </s> <s xml:id="echoid-s8255" xml:space="preserve">æ quales, uncislan-<lb/> <anchor type="note" xlink:label="note-0303-07a" xlink:href="note-0303-07"/> cium A & </s> <s xml:id="echoid-s8256" xml:space="preserve">B ſuſpenduntur; </s> <s xml:id="echoid-s8257" xml:space="preserve">deſcenſu libræ fluidis, vaſis F, F <lb/> <anchor type="note" xlink:label="note-0303-08a" xlink:href="note-0303-08"/> contentis, immerguntur; </s> <s xml:id="echoid-s8258" xml:space="preserve">una in aquam, altera in oleum <lb/>terebinthinæ, æquilibrium deſtruitur, & </s> <s xml:id="echoid-s8259" xml:space="preserve">illa hac levior <lb/>fit.</s> <s xml:id="echoid-s8260" xml:space="preserve"/> </p> <div xml:id="echoid-div1174" type="float" level="2" n="1"> <note position="right" xlink:label="note-0303-07" xlink:href="note-0303-07a" xml:space="preserve">767.</note> <note position="right" xlink:label="note-0303-08" xlink:href="note-0303-08a" xml:space="preserve">TAB. XXIX <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s8261" xml:space="preserve">Solidum fluido levius, & </s> <s xml:id="echoid-s8262" xml:space="preserve">hoc immerſum, adſcendit, & </s> <s xml:id="echoid-s8263" xml:space="preserve">in <lb/> <anchor type="note" xlink:label="note-0303-09a" xlink:href="note-0303-09"/> ſuprema fluidi ſuperficie hæret <anchor type="note" xlink:href="" symbol="*"/>, ita ut pro parte tantum <anchor type="note" xlink:label="note-0303-10a" xlink:href="note-0303-10"/> immergatur; </s> <s xml:id="echoid-s8264" xml:space="preserve">pro majori tamen gravitate ſpecifica in fluido <lb/>magis deſcendit, & </s> <s xml:id="echoid-s8265" xml:space="preserve">corpus non quieſcit, niſi pars immerſa <pb o="218" file="0304" n="332" rhead="PHYSICES ELEMENTA"/> tale ſpatium in fluido occupet, ut fluidum, quod idem hocce <lb/>ſpatium impleret, ejuſdem ponderis cum toto corpore ſit. <lb/></s> <s xml:id="echoid-s8266" xml:space="preserve">In alio enim caſu ſolidum non eadem cum vi in partes vi-<lb/>cinas fluidi agit, cum qua fluidum ageret, ſi corporis locum <lb/>occuparet, in hoc tamen caſu ſolo quies fluidi <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s8267" xml:space="preserve">ipſius <anchor type="note" xlink:label="note-0304-01a" xlink:href="note-0304-01"/> corporis dari poteſt.</s> <s xml:id="echoid-s8268" xml:space="preserve"/> </p> <div xml:id="echoid-div1175" type="float" level="2" n="2"> <note position="right" xlink:label="note-0303-09" xlink:href="note-0303-09a" xml:space="preserve">768.</note> <note symbol="*" position="right" xlink:label="note-0303-10" xlink:href="note-0303-10a" xml:space="preserve">749.</note> <note symbol="*" position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">713.</note> </div> <p> <s xml:id="echoid-s8269" xml:space="preserve">Sequitur ex hac propoſitione, corporum, in ſuperficie <lb/> <anchor type="note" xlink:label="note-0304-02a" xlink:href="note-0304-02"/> ejuſdem fluidi natantium, partes immerſas eſſe inter ſe <lb/>ut corporum pondera. </s> <s xml:id="echoid-s8270" xml:space="preserve">Idcirco ſi, ſuperaddito pondere, <lb/>corporis gravitas mutetur, in eâdem ratione augetur pars <lb/>immerſa; </s> <s xml:id="echoid-s8271" xml:space="preserve">& </s> <s xml:id="echoid-s8272" xml:space="preserve">partes, quæ variis ponderibus in fluidum de-<lb/> <anchor type="note" xlink:label="note-0304-03a" xlink:href="note-0304-03"/> ſcendunt, ſunt inter ſe ut hæc pondera.</s> <s xml:id="echoid-s8273" xml:space="preserve"/> </p> <div xml:id="echoid-div1176" type="float" level="2" n="3"> <note position="left" xlink:label="note-0304-02" xlink:href="note-0304-02a" xml:space="preserve">769.</note> <note position="left" xlink:label="note-0304-03" xlink:href="note-0304-03a" xml:space="preserve">770.</note> </div> </div> <div xml:id="echoid-div1178" type="section" level="1" n="296"> <head xml:id="echoid-head410" xml:space="preserve"><emph style="sc">Experimentum</emph>. 10.</head> <p> <s xml:id="echoid-s8274" xml:space="preserve">Detur vas aquam continens A; </s> <s xml:id="echoid-s8275" xml:space="preserve">detur cylindrus cavus ex <lb/> <anchor type="note" xlink:label="note-0304-04a" xlink:href="note-0304-04"/> <anchor type="note" xlink:label="note-0304-05a" xlink:href="note-0304-05"/> quocunque metallo C; </s> <s xml:id="echoid-s8276" xml:space="preserve">huic imponatur pondus p, ut parte <lb/>b d in aquam deſcendat; </s> <s xml:id="echoid-s8277" xml:space="preserve">ſuperaddito pondere ſemi libræ, <lb/>menſuretur quantum deſcendat; </s> <s xml:id="echoid-s8278" xml:space="preserve">addatur iterum atque ite-<lb/>rum pondus æquale, & </s> <s xml:id="echoid-s8279" xml:space="preserve">ſingulis vicibus æqualiter deſcen-<lb/>dit.</s> <s xml:id="echoid-s8280" xml:space="preserve"/> </p> <div xml:id="echoid-div1178" type="float" level="2" n="1"> <note position="left" xlink:label="note-0304-04" xlink:href="note-0304-04a" xml:space="preserve">771.</note> <note position="left" xlink:label="note-0304-05" xlink:href="note-0304-05a" xml:space="preserve">TAB. XXXI <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s8281" xml:space="preserve">In n. </s> <s xml:id="echoid-s8282" xml:space="preserve">762. </s> <s xml:id="echoid-s8283" xml:space="preserve">& </s> <s xml:id="echoid-s8284" xml:space="preserve">763.</s> <s xml:id="echoid-s8285" xml:space="preserve">, Experimentis 7. </s> <s xml:id="echoid-s8286" xml:space="preserve">& </s> <s xml:id="echoid-s8287" xml:space="preserve">8. </s> <s xml:id="echoid-s8288" xml:space="preserve">confirmatis, vi-<lb/> <anchor type="note" xlink:label="note-0304-06a" xlink:href="note-0304-06"/> dimus, quomodo corpus fluido gravius ab hoc ſuſtineatur <lb/>& </s> <s xml:id="echoid-s8289" xml:space="preserve">quaſi natet; </s> <s xml:id="echoid-s8290" xml:space="preserve">ſimili methodo corpus fluido levius in fundo <lb/>retineri poteſt; </s> <s xml:id="echoid-s8291" xml:space="preserve">in illo caſu preſſio fluidi ſuperincumbentis <lb/>tollitur, hìc tollenda eſt preſſio fluidi inferioris qua corpus <lb/>ſurſum pellitur.</s> <s xml:id="echoid-s8292" xml:space="preserve"/> </p> <div xml:id="echoid-div1179" type="float" level="2" n="2"> <note position="left" xlink:label="note-0304-06" xlink:href="note-0304-06a" xml:space="preserve">772.</note> </div> </div> <div xml:id="echoid-div1181" type="section" level="1" n="297"> <head xml:id="echoid-head411" xml:space="preserve"><emph style="sc">Experimentum</emph> 11.</head> <p> <s xml:id="echoid-s8293" xml:space="preserve">Lamina ænea b c, exacte plana, ſuſtentaculo D impoſi-<lb/> <anchor type="note" xlink:label="note-0304-07a" xlink:href="note-0304-07"/> <anchor type="note" xlink:label="note-0304-08a" xlink:href="note-0304-08"/> ta, in fundo vaſis A hæret; </s> <s xml:id="echoid-s8294" xml:space="preserve">lamina ſimilis b c cum fruſto <lb/>ſuberis E conjungitur, ita ut cum hoc conſtituat corpus <lb/>aqua levius; </s> <s xml:id="echoid-s8295" xml:space="preserve">congruant hæ laminæ, & </s> <s xml:id="echoid-s8296" xml:space="preserve">baculo ſuber retinea-<lb/>tur dum aqua affunditur; </s> <s xml:id="echoid-s8297" xml:space="preserve">relicto ſubere non adſcendet, <lb/>donec, hoc è loco moto, laminæ ſeparentur, ut aqua in <lb/>laminam cum ſubere conjunctam preſſionem ſuam exerere <lb/>poſſit, illamque cum ſubere in altum ferre.</s> <s xml:id="echoid-s8298" xml:space="preserve"/> </p> <div xml:id="echoid-div1181" type="float" level="2" n="1"> <note position="left" xlink:label="note-0304-07" xlink:href="note-0304-07a" xml:space="preserve">773.</note> <note position="left" xlink:label="note-0304-08" xlink:href="note-0304-08a" xml:space="preserve">TAB. XXXI <lb/>fig. 2.</note> </div> <pb file="0305" n="333"/> <pb file="0305a" n="334"/> <figure> <image file="0305a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0305a-01"/> </figure> <pb file="0306" n="335"/> <pb o="219" file="0307" n="336" rhead="MATHEMATICA. LIB. II. CAP. IV."/> </div> <div xml:id="echoid-div1183" type="section" level="1" n="298"> <head xml:id="echoid-head412" xml:space="preserve">CAPUT IV.</head> <head xml:id="echoid-head413" xml:space="preserve">De comparandis Fluidorum Denſitatibus.</head> <p> <s xml:id="echoid-s8299" xml:space="preserve">CUm corporis denſitas ſequatur proportionem ponderis <lb/>ipſius, dato volumine, comparando corporum æqua-<lb/> <anchor type="note" xlink:label="note-0307-01a" xlink:href="note-0307-01"/> lium pondera, detegimus ipſorum denſitates <anchor type="note" xlink:href="" symbol="*"/>, Si ergo vas <anchor type="note" xlink:label="note-0307-02a" xlink:href="note-0307-02"/> quodcunque exacte fluido repleatur, & </s> <s xml:id="echoid-s8300" xml:space="preserve">fluidum hoc ponde-<lb/>retur, idemque alio fluido repleatur, quod etiam ponderetur, <lb/>pondera erunt ut denſitates. </s> <s xml:id="echoid-s8301" xml:space="preserve">Sed cum hæc methodus in <lb/>praxi variis obnoxia ſit difficultatibus, in hac explicanda <lb/>non inhæremus.</s> <s xml:id="echoid-s8302" xml:space="preserve"/> </p> <div xml:id="echoid-div1183" type="float" level="2" n="1"> <note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">774.</note> <note symbol="*" position="right" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">288.</note> </div> <p> <s xml:id="echoid-s8303" xml:space="preserve">Quando duorum fluidorum preſſiones ſunt æquales, mate-<lb/> <anchor type="note" xlink:label="note-0307-03a" xlink:href="note-0307-03"/> riæ quantitates, id eſt, pondera, in columnis, æquales ba-<lb/>ſes habentibus, non differunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8304" xml:space="preserve">quare volumina, quæ ſunt <anchor type="note" xlink:label="note-0307-04a" xlink:href="note-0307-04"/> ut columnarum altitudines, ſunt inverſè ut denſitates <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s8305" xml:space="preserve"> <anchor type="note" xlink:label="note-0307-05a" xlink:href="note-0307-05"/> ex quo deducitur methodus haſce comparandi in tubis com-<lb/>municantibus; </s> <s xml:id="echoid-s8306" xml:space="preserve">in quibus tamen non deſiderantur baſes co-<lb/>lumnarum æquales, id eſt, non intereſt an tubi ſint inæqua-<lb/>les nec ne, quod altitudinem non mutat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8307" xml:space="preserve"/> </p> <div xml:id="echoid-div1184" type="float" level="2" n="2"> <note position="right" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">775.</note> <note symbol="*" position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">708.</note> <note symbol="*" position="right" xlink:label="note-0307-05" xlink:href="note-0307-05a" xml:space="preserve">738.</note> </div> <note symbol="*" position="right" xml:space="preserve">714.</note> </div> <div xml:id="echoid-div1186" type="section" level="1" n="299"> <head xml:id="echoid-head414" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s8308" xml:space="preserve">Tubo vitreo curvo A infundatur mercurius, quo pars <lb/> <anchor type="note" xlink:label="note-0307-07a" xlink:href="note-0307-07"/> inferior tubi a b ad c impletur; </s> <s xml:id="echoid-s8309" xml:space="preserve">infundatur aqua ab una par-<lb/> <anchor type="note" xlink:label="note-0307-08a" xlink:href="note-0307-08"/> te à b ad e; </s> <s xml:id="echoid-s8310" xml:space="preserve">in crus oppoſitum infundatur oleum terebinthi-<lb/>næ, donec ambæ ſuperficies b, c, mercurii ſint in eadem li-<lb/>nea horizontali, ſitque altitudo olei c d; </s> <s xml:id="echoid-s8311" xml:space="preserve">erunt hæ altitudi-<lb/>nes ut 87. </s> <s xml:id="echoid-s8312" xml:space="preserve">ad 100. </s> <s xml:id="echoid-s8313" xml:space="preserve">in qua ratione inverſa eſt denſitas aquæ <lb/>ad olei terebinthinæ denſitatem, ſunt ergo hæ ut {1/87} ad {1/100}, <lb/>aut ut 100. </s> <s xml:id="echoid-s8314" xml:space="preserve">ad 87.</s> <s xml:id="echoid-s8315" xml:space="preserve"/> </p> <div xml:id="echoid-div1186" type="float" level="2" n="1"> <note position="right" xlink:label="note-0307-07" xlink:href="note-0307-07a" xml:space="preserve">776.</note> <note position="right" xlink:label="note-0307-08" xlink:href="note-0307-08a" xml:space="preserve">TAB. XXXI. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s8316" xml:space="preserve">Mercurius infunditur, ne fluida in fundo tubi miſcean-<lb/>tur.</s> <s xml:id="echoid-s8317" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8318" xml:space="preserve">Adhibito ſolido immerſo etiam comparantur fluidorum <lb/>denſitates, ſi enim ſolidum, fluidis comparandis levius, va-<lb/> <anchor type="note" xlink:label="note-0307-09a" xlink:href="note-0307-09"/> riis fluidis immergatur, partes immerſæ erunt inversè ut <lb/>fluidorum denſitates; </s> <s xml:id="echoid-s8319" xml:space="preserve">nam, quia idem ſolidum adhibetur, <lb/>portiones variorum fluidorum, quæ ſingulis caſibus ſpatium <pb o="220" file="0308" n="337" rhead="PHYSICES ELEMENTA"/> a parte immerſa occupatum poſſent implere, ſunt ejuſdem <lb/>ponderis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8320" xml:space="preserve">ergo volumina illarum portionum immerſarum, <anchor type="note" xlink:label="note-0308-01a" xlink:href="note-0308-01"/> ſunt inverſè ut denſitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8321" xml:space="preserve"/> </p> <div xml:id="echoid-div1187" type="float" level="2" n="2"> <note position="right" xlink:label="note-0307-09" xlink:href="note-0307-09a" xml:space="preserve">777.</note> <note symbol="*" position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">768.</note> </div> <note symbol="*" position="left" xml:space="preserve">738.</note> </div> <div xml:id="echoid-div1189" type="section" level="1" n="300"> <head xml:id="echoid-head415" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head416" xml:space="preserve">Qua Fluidorum denſitates conferuntur.</head> <note position="left" xml:space="preserve">778.</note> <p> <s xml:id="echoid-s8322" xml:space="preserve">Machina hæc A vitrea eſt, conſtat ex globo cavo, cum <lb/> <anchor type="note" xlink:label="note-0308-04a" xlink:href="note-0308-04"/> tubo cylindrico in partes æquales diviſo Infra globum al-<lb/>ter minor additur, qui pro parte mercurio aut globulis exi-<lb/>guis plumbeis impletur, ut eo pondere tubus verticaliter <lb/>in fluida deſcendat, & </s> <s xml:id="echoid-s8323" xml:space="preserve">in hoc ſitu retineatur; </s> <s xml:id="echoid-s8324" xml:space="preserve">ne nimium <lb/>ponderis in minori globo detur cavendum; </s> <s xml:id="echoid-s8325" xml:space="preserve">nam ut machi-<lb/>na fluidis comparandis levior ſit requiritur. </s> <s xml:id="echoid-s8326" xml:space="preserve">In variis flui-<lb/>dis ad varias profunditates deſcendit machina, & </s> <s xml:id="echoid-s8327" xml:space="preserve">denſitates <lb/>horum, ſunt inversè ut partes immerſæ, quæ ergo inter ſe <lb/>comparandæ ſunt.</s> <s xml:id="echoid-s8328" xml:space="preserve"/> </p> <div xml:id="echoid-div1189" type="float" level="2" n="1"> <note position="left" xlink:label="note-0308-04" xlink:href="note-0308-04a" xml:space="preserve">TAB XXXI <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s8329" xml:space="preserve">Filum machinæ alligatur, & </s> <s xml:id="echoid-s8330" xml:space="preserve">machina cum filo annexo <lb/>exacte ponderatur, pondus noſtræ fuit gr. </s> <s xml:id="echoid-s8331" xml:space="preserve">550.</s> <s xml:id="echoid-s8332" xml:space="preserve">; machina <lb/>aquâ immerſa ad b deſcendit; </s> <s xml:id="echoid-s8333" xml:space="preserve">pondus ergo aquæ ejuſdem <lb/>voluminis cum parte machinæ immerſa valet gr. </s> <s xml:id="echoid-s8334" xml:space="preserve">550 <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s8335" xml:space="preserve"> <anchor type="note" xlink:label="note-0308-05a" xlink:href="note-0308-05"/> hocce volumen hoc numero poteſt exprimi. </s> <s xml:id="echoid-s8336" xml:space="preserve">Filum memo-<lb/>ratum unco lancis bilancis hydroſtaticæ <anchor type="note" xlink:href="" symbol="*"/> annectitur; </s> <s xml:id="echoid-s8337" xml:space="preserve">ma- <anchor type="note" xlink:label="note-0308-06a" xlink:href="note-0308-06"/> chinâ manente immerſâ, lanci oppoſitæ pondus viginti gr. <lb/></s> <s xml:id="echoid-s8338" xml:space="preserve">imponitur, & </s> <s xml:id="echoid-s8339" xml:space="preserve">lente bilanx elevatur, (quo tubus pro parte <lb/>aqua extrahitur,) donec detur æquilibrium, ſuperficieſque <lb/>aquæ tunc pertingit ad punctum d. </s> <s xml:id="echoid-s8340" xml:space="preserve">Aqua ſuſtinet pondus <lb/>totius machinæ, demtis granis viginti, id eſt, ſuſtinet gr. </s> <s xml:id="echoid-s8341" xml:space="preserve"><lb/>530.</s> <s xml:id="echoid-s8342" xml:space="preserve">, & </s> <s xml:id="echoid-s8343" xml:space="preserve">pondus aquæ ejuſdem voluminis cum parte nunc <lb/>immerſâ tot grana valet, & </s> <s xml:id="echoid-s8344" xml:space="preserve">hoc numero exprimitur, volu-<lb/>menque partis d b tubi erit 20. </s> <s xml:id="echoid-s8345" xml:space="preserve">Si fpatium d b dividatur <lb/>in partes æquales 10. </s> <s xml:id="echoid-s8346" xml:space="preserve">& </s> <s xml:id="echoid-s8347" xml:space="preserve">diviſiones continuentur adſcenden-<lb/>do ultra b, & </s> <s xml:id="echoid-s8348" xml:space="preserve">deſcendendo infra d, ſingulæ valebunt 2; </s> <s xml:id="echoid-s8349" xml:space="preserve">& </s> <s xml:id="echoid-s8350" xml:space="preserve"><lb/>ex nota diviſione, ad quam mazhina in fluidum deſcendit, <lb/>dabitur volumen partis immerſæ, Ex. </s> <s xml:id="echoid-s8351" xml:space="preserve">gr. </s> <s xml:id="echoid-s8352" xml:space="preserve">ſi totus tubus ex-<lb/>tra aquam hæreat, volumen immerſum erit 526. </s> <s xml:id="echoid-s8353" xml:space="preserve">ſi ad ſu-<lb/>premam hìc notatam diviſionem deſcendat, volumen im-<lb/>merſum erit 556; </s> <s xml:id="echoid-s8354" xml:space="preserve">& </s> <s xml:id="echoid-s8355" xml:space="preserve">denſitates fluidorum, in quibus hoc <pb file="0309" n="338"/> <pb file="0309a" n="339"/> <anchor type="figure" xlink:label="fig-0309a-01a" xlink:href="fig-0309a-01"/> <pb file="0310" n="340"/> <pb o="221" file="0311" n="341" rhead="MATHEMATICA. LIB. II. CAP. IV."/> contingit, ſunt inverſè ut illi numeri, id eſt, ut 556. </s> <s xml:id="echoid-s8356" xml:space="preserve">ad <lb/>526. </s> <s xml:id="echoid-s8357" xml:space="preserve">& </s> <s xml:id="echoid-s8358" xml:space="preserve">ſolæ denſitates intermediæ ope hujus machinæ <lb/>comparari poſſunt. </s> <s xml:id="echoid-s8359" xml:space="preserve">Si globus minorem ad tubum rationem <lb/>haberet, fluida, quorum denſitates magis inter ſe differ-<lb/>rent, comparari poſſent.</s> <s xml:id="echoid-s8360" xml:space="preserve"/> </p> <div xml:id="echoid-div1190" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0308-05" xlink:href="note-0308-05a" xml:space="preserve">768.</note> <note symbol="*" position="left" xlink:label="note-0308-06" xlink:href="note-0308-06a" xml:space="preserve">705.</note> <figure xlink:label="fig-0309a-01" xlink:href="fig-0309a-01a"> <image file="0309a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0309a-01"/> </figure> </div> <p> <s xml:id="echoid-s8361" xml:space="preserve">Quando fluida varia comparantur, numeri, volumina <lb/>partium immerſarum deſignantes, habentur pro denomina-<lb/>toribus fractionum, unitatem in numeratore habentium, <lb/>deſignantque hæ fractiones rationem denſitatum; </s> <s xml:id="echoid-s8362" xml:space="preserve">ſunt enim <lb/>inter ſe inverſè ut denominatores.</s> <s xml:id="echoid-s8363" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1192" type="section" level="1" n="301"> <head xml:id="echoid-head417" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s8364" xml:space="preserve">Sint comparandæ denſitates aquarum diverſas ſalis quan-<lb/> <anchor type="note" xlink:label="note-0311-01a" xlink:href="note-0311-01"/> titates continentium, in unam deſcendit machina ad divi-<lb/>ſionem a; </s> <s xml:id="echoid-s8365" xml:space="preserve">alterà ſi immergatur, deſcendit tantum ad divi-<lb/>ſionem c; </s> <s xml:id="echoid-s8366" xml:space="preserve">denſitates harum erunt inter ſe ut {1/546} ad {1/542}.</s> <s xml:id="echoid-s8367" xml:space="preserve"/> </p> <div xml:id="echoid-div1192" type="float" level="2" n="1"> <note position="right" xlink:label="note-0311-01" xlink:href="note-0311-01a" xml:space="preserve">779.</note> </div> <p> <s xml:id="echoid-s8368" xml:space="preserve">Non poſſunt hac methodo inter ſe conferri fluidorum <lb/>denſitates niſi quæ parum differunt, uſumque machinæ <lb/>hæ habent ubi vina, aut cereviſiæ conferri debent.</s> <s xml:id="echoid-s8369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8370" xml:space="preserve">Methodus omnium optima eſt, adhibito ſolido fluidis <lb/>graviore. </s> <s xml:id="echoid-s8371" xml:space="preserve">Quando idem corpus variis fluidis immergitur, <lb/> <anchor type="note" xlink:label="note-0311-02a" xlink:href="note-0311-02"/> pondera ab illo, in his amiſſa, ſunt inter ſe ut horum den-<lb/> <anchor type="note" xlink:label="note-0311-03a" xlink:href="note-0311-03"/> ſitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8372" xml:space="preserve"/> </p> <div xml:id="echoid-div1193" type="float" level="2" n="2"> <note position="right" xlink:label="note-0311-02" xlink:href="note-0311-02a" xml:space="preserve">780.</note> <note symbol="*" position="right" xlink:label="note-0311-03" xlink:href="note-0311-03a" xml:space="preserve">751. 737.</note> </div> </div> <div xml:id="echoid-div1195" type="section" level="1" n="302"> <head xml:id="echoid-head418" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head419" xml:space="preserve">Alia qua Fluidorum Denſitates conferuntur.</head> <note position="right" xml:space="preserve">781.</note> <p> <s xml:id="echoid-s8373" xml:space="preserve">Utendum hìc bilance hydroſtatica <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8374" xml:space="preserve">vitri fruſto ſolido <anchor type="note" xlink:label="note-0311-05a" xlink:href="note-0311-05"/> cujuscunque figuræ ut C; </s> <s xml:id="echoid-s8375" xml:space="preserve">hoc, capillo equino, unco lan-<lb/> <anchor type="note" xlink:label="note-0311-06a" xlink:href="note-0311-06"/> cis A ſuſpenditur. </s> <s xml:id="echoid-s8376" xml:space="preserve">Deſideratur & </s> <s xml:id="echoid-s8377" xml:space="preserve">pondus æneum P, cujus no-<lb/>ta eſt differentia cum pondere ipſius vitri C: </s> <s xml:id="echoid-s8378" xml:space="preserve">quæ differen-<lb/>tia in noſtrâ machinâ eſt 700. </s> <s xml:id="echoid-s8379" xml:space="preserve">gr. </s> <s xml:id="echoid-s8380" xml:space="preserve">& </s> <s xml:id="echoid-s8381" xml:space="preserve">ipſi ponderi inſcripta; <lb/></s> <s xml:id="echoid-s8382" xml:space="preserve">pondus hoc alii lanci B annectitur.</s> <s xml:id="echoid-s8383" xml:space="preserve"/> </p> <div xml:id="echoid-div1195" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0311-05" xlink:href="note-0311-05a" xml:space="preserve">705.</note> <note position="right" xlink:label="note-0311-06" xlink:href="note-0311-06a" xml:space="preserve">TAB. XXX. <lb/>fig. 4. 5. 6.</note> </div> <p> <s xml:id="echoid-s8384" xml:space="preserve">Si nunc vitrum C in fluido quocunque ſuſpendatur, & </s> <s xml:id="echoid-s8385" xml:space="preserve"><lb/>æquilibrium detur, impoſito pondere lancium uni aut alteri, <lb/>denſitas fluidi detegitur. </s> <s xml:id="echoid-s8386" xml:space="preserve">Si lanci A, addatur numerus gr. <lb/></s> <s xml:id="echoid-s8387" xml:space="preserve">impoſitorum differentiæ memoratæ gr. </s> <s xml:id="echoid-s8388" xml:space="preserve">700.</s> <s xml:id="echoid-s8389" xml:space="preserve">; ſi lanci B, <lb/>ſubtrahatur numerus ille ex iiſdem 700. </s> <s xml:id="echoid-s8390" xml:space="preserve">& </s> <s xml:id="echoid-s8391" xml:space="preserve">in utroque caſu, <pb o="222" file="0312" n="342" rhead="PHYSICES ELEMENTA"/> ut patet, determinatur pondus a corpore amiſſum, id eſt, <lb/>pondus denſitatem fluidi exprimens.</s> <s xml:id="echoid-s8392" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1197" type="section" level="1" n="303"> <head xml:id="echoid-head420" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <note position="left" xml:space="preserve">782.</note> <p> <s xml:id="echoid-s8393" xml:space="preserve">Oleo Terebinthinæ immergatur vitrum C, lanci A ſuſ-<lb/>penſum, dum pondus P lanci B adhæret; </s> <s xml:id="echoid-s8394" xml:space="preserve">lanci B impoſi-<lb/>tis gr. </s> <s xml:id="echoid-s8395" xml:space="preserve">100. </s> <s xml:id="echoid-s8396" xml:space="preserve">æquilibrium datur. </s> <s xml:id="echoid-s8397" xml:space="preserve">Si aquâ idem vitrum im-<lb/>mergatur 11. </s> <s xml:id="echoid-s8398" xml:space="preserve">gr. </s> <s xml:id="echoid-s8399" xml:space="preserve">in eadem lance deſiderantur ut bilanx ſit <lb/>in æquilibrio. </s> <s xml:id="echoid-s8400" xml:space="preserve">Si verò de lacte agatur 10. </s> <s xml:id="echoid-s8401" xml:space="preserve">gr. </s> <s xml:id="echoid-s8402" xml:space="preserve">lanci A impo-<lb/>nenda ſunt. </s> <s xml:id="echoid-s8403" xml:space="preserve">Subtractis numero primo & </s> <s xml:id="echoid-s8404" xml:space="preserve">ſecundo ex ſe-<lb/>ptingentis, & </s> <s xml:id="echoid-s8405" xml:space="preserve">hiſce addito numero tertio, habemus 600, <lb/>689, 710, denſitates memoratorum fluidorum.</s> <s xml:id="echoid-s8406" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8407" xml:space="preserve">Sit nunc aliunde notum pedem cubicum aquæ ponde-<lb/> <anchor type="note" xlink:label="note-0312-02a" xlink:href="note-0312-02"/> rarelibras 63. </s> <s xml:id="echoid-s8408" xml:space="preserve">cum unciis 7. </s> <s xml:id="echoid-s8409" xml:space="preserve">drachmis 2. </s> <s xml:id="echoid-s8410" xml:space="preserve">& </s> <s xml:id="echoid-s8411" xml:space="preserve">ſcrup. </s> <s xml:id="echoid-s8412" xml:space="preserve">2.</s> <s xml:id="echoid-s8413" xml:space="preserve">: quod de-<lb/>tegimus determinando pondus in aqua amiſſum a corpore cu-<lb/>jus capacitas nota eſt. </s> <s xml:id="echoid-s8414" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> Uſus ego ſum cylindro cupreo cavo cu- <anchor type="note" xlink:label="note-0312-03a" xlink:href="note-0312-03"/> jus latera exacte erant ſex poll. </s> <s xml:id="echoid-s8415" xml:space="preserve">Rhenolandicorum. </s> <s xml:id="echoid-s8416" xml:space="preserve">Pondus hoc <lb/>valet gr. </s> <s xml:id="echoid-s8417" xml:space="preserve">487360. </s> <s xml:id="echoid-s8418" xml:space="preserve">dum volumen aquæ æquale vitro noſtro C <lb/>ponderat grana 689; </s> <s xml:id="echoid-s8419" xml:space="preserve">unde conſtat volumen hoc debere <lb/>multiplicari per 707 {1/3} ut habeamus pedem cubicum; </s> <s xml:id="echoid-s8420" xml:space="preserve">& </s> <s xml:id="echoid-s8421" xml:space="preserve"><lb/>multiplicatis per hunc numerum 710. </s> <s xml:id="echoid-s8422" xml:space="preserve">habebimus grana in <lb/>pede cubico lactis; </s> <s xml:id="echoid-s8423" xml:space="preserve">& </s> <s xml:id="echoid-s8424" xml:space="preserve">hac methodo pondus pedis cubi-<lb/>ci fluidi cujuſcunque detegitur.</s> <s xml:id="echoid-s8425" xml:space="preserve"/> </p> <div xml:id="echoid-div1197" type="float" level="2" n="1"> <note position="left" xlink:label="note-0312-02" xlink:href="note-0312-02a" xml:space="preserve">783.</note> <note symbol="*" position="left" xlink:label="note-0312-03" xlink:href="note-0312-03a" xml:space="preserve">751.</note> </div> </div> <div xml:id="echoid-div1199" type="section" level="1" n="304"> <head xml:id="echoid-head421" xml:space="preserve">CAPUT V.</head> <head xml:id="echoid-head422" xml:space="preserve">De hydroſtatica Solidorum Comparatione.</head> <p> <s xml:id="echoid-s8426" xml:space="preserve">IN omnibus corporibus homogeneis, denſitates ſunt in ra-<lb/>tione compoſita, ex directa ponderum & </s> <s xml:id="echoid-s8427" xml:space="preserve">inverſa vo-<lb/>luminum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8428" xml:space="preserve">ideò dividendo pondera per volumina dantur <anchor type="note" xlink:label="note-0312-04a" xlink:href="note-0312-04"/> denſitates, id eſt, dantur numeri, qui ſunt inter ſe ut hæ <lb/> <anchor type="note" xlink:label="note-0312-05a" xlink:href="note-0312-05"/> denſitates.</s> <s xml:id="echoid-s8429" xml:space="preserve"/> </p> <div xml:id="echoid-div1199" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0312-04" xlink:href="note-0312-04a" xml:space="preserve">741.</note> <note position="left" xlink:label="note-0312-05" xlink:href="note-0312-05a" xml:space="preserve">784.</note> </div> <p> <s xml:id="echoid-s8430" xml:space="preserve">In omnibus corporibus, adhibita libra, pondera compa-<lb/> <anchor type="note" xlink:label="note-0312-06a" xlink:href="note-0312-06"/> rantur; </s> <s xml:id="echoid-s8431" xml:space="preserve">volumina deteguntur immergendo corpora eodem <lb/>fluido; </s> <s xml:id="echoid-s8432" xml:space="preserve">pondera enim ab iis amiſſa ſunt ut ipſorum volumi-<lb/>na <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8433" xml:space="preserve"/> </p> <div xml:id="echoid-div1200" type="float" level="2" n="2"> <note position="left" xlink:label="note-0312-06" xlink:href="note-0312-06a" xml:space="preserve">785.</note> </div> <note symbol="*" position="left" xml:space="preserve">756.</note> <pb o="223" file="0313" n="343" rhead="MATHEMATICA. LIB. II. CAP IV."/> </div> <div xml:id="echoid-div1202" type="section" level="1" n="305"> <head xml:id="echoid-head423" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head424" xml:space="preserve">Qua ſolidorum Corporum Denſitates conferuntur.</head> <p> <s xml:id="echoid-s8434" xml:space="preserve">Hìc iterum bilanx hydroſtatica uſu venit <anchor type="note" xlink:href="" symbol="*"/>, ut & </s> <s xml:id="echoid-s8435" xml:space="preserve">vas vi- <anchor type="note" xlink:label="note-0313-01a" xlink:href="note-0313-01"/> treum ut D, cui corpora comparanda imponi poſſunt; </s> <s xml:id="echoid-s8436" xml:space="preserve">re-<lb/> <anchor type="note" xlink:label="note-0313-02a" xlink:href="note-0313-02"/> quiritur etiam pondus ut P (fig.</s> <s xml:id="echoid-s8437" xml:space="preserve">6.) </s> <s xml:id="echoid-s8438" xml:space="preserve">quod cum hoc vaſe in <lb/> <anchor type="note" xlink:label="note-0313-03a" xlink:href="note-0313-03"/> aqua ſuſpenſum æquiponderet.</s> <s xml:id="echoid-s8439" xml:space="preserve"/> </p> <div xml:id="echoid-div1202" type="float" level="2" n="1"> <note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">786.</note> <note position="right" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">TAB XXXI <lb/>fig 7.</note> <note symbol="*" position="right" xlink:label="note-0313-03" xlink:href="note-0313-03a" xml:space="preserve">705.</note> </div> <p> <s xml:id="echoid-s8440" xml:space="preserve">Annectitur, ope capilli equini, vas D, loco corporis C <lb/>(vide fig. </s> <s xml:id="echoid-s8441" xml:space="preserve">4.) </s> <s xml:id="echoid-s8442" xml:space="preserve">lanci A, & </s> <s xml:id="echoid-s8443" xml:space="preserve">aquâ immergitur, pondere P <lb/>lanci B appenſo, datur æquilibrium. </s> <s xml:id="echoid-s8444" xml:space="preserve">Corpus, cujus den-<lb/>ſitas quæritur lanci A imponitur, & </s> <s xml:id="echoid-s8445" xml:space="preserve">ponderatur: </s> <s xml:id="echoid-s8446" xml:space="preserve">Idem hoc <lb/>corpus, reliquis manentibus in vas D, aquâ ut dictum immer-<lb/>ſum, transfertur, lancique A imponitur quantum ponderis <lb/>requiritur ut æquilibrium detur; </s> <s xml:id="echoid-s8447" xml:space="preserve">hocque eft pondus a cor-<lb/>pore in aquâ amiſſum, per hoc ergo ipſius corporis pondus <lb/>dividendum eſt, ut habeamus denſitatem <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s8448" xml:space="preserve">id eſt dividi- <anchor type="note" xlink:label="note-0313-04a" xlink:href="note-0313-04"/> mus pondus in lance B per pondus in lance A.</s> <s xml:id="echoid-s8449" xml:space="preserve"/> </p> <div xml:id="echoid-div1203" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">784.</note> </div> </div> <div xml:id="echoid-div1205" type="section" level="1" n="306"> <head xml:id="echoid-head425" xml:space="preserve"><emph style="sc">Experimentum</emph></head> <p> <s xml:id="echoid-s8450" xml:space="preserve">In ſubjecta tabella habemus quorundam corporum pon-<lb/> <anchor type="note" xlink:label="note-0313-05a" xlink:href="note-0313-05"/> dera, & </s> <s xml:id="echoid-s8451" xml:space="preserve">pondera in aqua amiſſa, indeque deductas denſitates.</s> <s xml:id="echoid-s8452" xml:space="preserve"/> </p> <div xml:id="echoid-div1205" type="float" level="2" n="1"> <note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">787.</note> </div> <note position="right" xml:space="preserve"> <lb/># Pondera \\ corporum. # Pondera in \\ aqua amiſſa. # Denſitates. <lb/>Plumbum # 582 {1/2} gr. # 51 {1/2} gr. # 11, 31. <lb/>Argentum # 439 {1/2} gr. # 42 {1/2} gr. # 10, 34. <lb/>Cuprum # 474. gr. # 54. gr. # 8, 78. <lb/>Æs calamin. # 356. gr. # 43. gr. # 8, 28. <lb/>Ferrum # 329. gr. # 43 {1/4} gr. # 7, 60. <lb/>Stannum # 534 {1/4} gr. # 71 {2/2} gr. # 7, 47. <lb/>### Aquæ denſitas cum reliquis collata. # 1, 00. <lb/></note> <p> <s xml:id="echoid-s8453" xml:space="preserve">Talis enim detegitur denſitas corporis, quod cum aqua <lb/>eandem gravitatem fpecificam habet.</s> <s xml:id="echoid-s8454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8455" xml:space="preserve">Hac methodo denſitates etiam corporum aquâ ſpecificè <lb/>leviorum deteguntur, ſi ita cum vaſe jungantur ut hujus <lb/>pondere in aquam trahantur.</s> <s xml:id="echoid-s8456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8457" xml:space="preserve">Annectendo corpus cujus denſitas quæritur, & </s> <s xml:id="echoid-s8458" xml:space="preserve">quod flui-<lb/>do gravius eſt, corpori fluido leviori, etiam denſitas dete-<lb/>gitur.</s> <s xml:id="echoid-s8459" xml:space="preserve"/> </p> <pb o="224" file="0314" n="344" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1207" type="section" level="1" n="307"> <head xml:id="echoid-head426" xml:space="preserve"><emph style="sc">Machina</emph>2.</head> <head xml:id="echoid-head427" style="it" xml:space="preserve">Qua Corporum ſolidorum Denſitates conferuntur.</head> <p> <s xml:id="echoid-s8460" xml:space="preserve">Sit machina A, ſimilis machinæ in capite præcedenti de-<lb/> <anchor type="note" xlink:label="note-0314-01a" xlink:href="note-0314-01"/> ſcriptæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8461" xml:space="preserve">in inferiori parte cum hac cohæret annulus DE;</s> <s xml:id="echoid-s8462" xml:space="preserve"> <anchor type="note" xlink:label="note-0314-02a" xlink:href="note-0314-02"/> proprio pondere globus pro parte tantum aquâ immergitur. <lb/></s> <s xml:id="echoid-s8463" xml:space="preserve"> <anchor type="note" xlink:label="note-0314-03a" xlink:href="note-0314-03"/> Uſui hæc Machina adaptari nequit, niſi, quantum ponde-<lb/>ris corpus quodcunque in aqua amittat, alia quacunque me-<lb/>thodo conſtet; </s> <s xml:id="echoid-s8464" xml:space="preserve">notumque ideo ponimus 109 {7/10} gr. </s> <s xml:id="echoid-s8465" xml:space="preserve">plumbi <lb/>in aqua ponderare 100 gr.</s> <s xml:id="echoid-s8466" xml:space="preserve">; imponantur ideo tot gr. </s> <s xml:id="echoid-s8467" xml:space="preserve">an-<lb/>nulo DE, quo machina, in aquam immiſſa, deſcendit ad <lb/>a; </s> <s xml:id="echoid-s8468" xml:space="preserve">adjiciatur aliud pondus ad libitum quod Ex. </s> <s xml:id="echoid-s8469" xml:space="preserve">gr. </s> <s xml:id="echoid-s8470" xml:space="preserve">in aqua <lb/>valet grana octo, & </s> <s xml:id="echoid-s8471" xml:space="preserve">machina deſcendet ad c; </s> <s xml:id="echoid-s8472" xml:space="preserve">ſpatium a c divi-<lb/>datur in partes octo, diviſionesque ſurſum & </s> <s xml:id="echoid-s8473" xml:space="preserve">deorſum conti-<lb/>nuentur, diviſioque a pro centeſima habeatur, diviſio c e-<lb/>rit centeſima octava, omnium infima in hac figura erit nona-<lb/>geſima ſeptima. </s> <s xml:id="echoid-s8474" xml:space="preserve">Clare patet, ſi n. </s> <s xml:id="echoid-s8475" xml:space="preserve">770 conferatur cum <lb/>præparatione memorata, diviſionem, ad quam machina in <lb/>aquam deſcendit, indicare pondus granorum, quo machi-<lb/>na gravatur; </s> <s xml:id="echoid-s8476" xml:space="preserve">impoſito ideò corpore annulo DE, illius <lb/>pondus in aquâ determinatur; </s> <s xml:id="echoid-s8477" xml:space="preserve">ſubtrahendo hocce pondus <lb/>ab illius pondere extra aquam, datur pondus in aqua amiſ-<lb/>ſum; </s> <s xml:id="echoid-s8478" xml:space="preserve">per quod, ſi pondus extra aquam dividatur, denſitas, <lb/>ut in principio hujus capitis dictum, detegitur.</s> <s xml:id="echoid-s8479" xml:space="preserve"/> </p> <div xml:id="echoid-div1207" type="float" level="2" n="1"> <note position="left" xlink:label="note-0314-01" xlink:href="note-0314-01a" xml:space="preserve">788.</note> <note position="left" xlink:label="note-0314-02" xlink:href="note-0314-02a" xml:space="preserve">TAB. XXXI. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0314-03" xlink:href="note-0314-03a" xml:space="preserve">778</note> </div> <p> <s xml:id="echoid-s8480" xml:space="preserve">Cum vero præcedens methodus & </s> <s xml:id="echoid-s8481" xml:space="preserve">magis compendioſa, <lb/> <anchor type="note" xlink:label="note-0314-04a" xlink:href="note-0314-04"/> quia & </s> <s xml:id="echoid-s8482" xml:space="preserve">in hoc librâ indigemus, & </s> <s xml:id="echoid-s8483" xml:space="preserve">magis accurata ſit hæc <lb/>negligi poſſet, & </s> <s xml:id="echoid-s8484" xml:space="preserve">machinam ipſam non indicaſſem, niſi uſu <lb/>veniret, ubi determinandum generaliter utrum corpora æ-<lb/>qualiter ponderantia denſitate differant, quod, ubi monetæ ex-<lb/>plorandæ ſunt, plerumque quæritur: </s> <s xml:id="echoid-s8485" xml:space="preserve">Machina autem hæc, <lb/>neglecta omni prævia præparatione hoc indicat, ſi ſucceſ-<lb/>ſive impoſitis corporibus annulo, machina ad profundi-<lb/>tates diverſas immergatur.</s> <s xml:id="echoid-s8486" xml:space="preserve"/> </p> <div xml:id="echoid-div1208" type="float" level="2" n="2"> <note position="left" xlink:label="note-0314-04" xlink:href="note-0314-04a" xml:space="preserve">789.</note> </div> <p> <s xml:id="echoid-s8487" xml:space="preserve">Si pondus pedis cubici aquæ <anchor type="note" xlink:href="" symbol="*"/> multiplicemus per <anchor type="note" xlink:label="note-0314-05a" xlink:href="note-0314-05"/> numerum, qui corporis denſitatem exprimit, habemus <lb/> <anchor type="note" xlink:label="note-0314-06a" xlink:href="note-0314-06"/> pondus pedis cubici ipſius corporis, quæ ponderis deter-<lb/>minatio in multis occaſionibus uſum magnum habet.</s> <s xml:id="echoid-s8488" xml:space="preserve"/> </p> <div xml:id="echoid-div1209" type="float" level="2" n="3"> <note position="left" xlink:label="note-0314-05" xlink:href="note-0314-05a" xml:space="preserve">790.</note> <note symbol="*" position="left" xlink:label="note-0314-06" xlink:href="note-0314-06a" xml:space="preserve">783.</note> </div> <pb file="0315" n="345"/> <pb file="0315a" n="346"/> <figure> <image file="0315a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0315a-01"/> </figure> <pb file="0316" n="347"/> <pb o="225" file="0317" n="348" rhead="MATHEMATICA. LIB. II. CAP. V."/> <p> <s xml:id="echoid-s8489" xml:space="preserve">Præter hunc & </s> <s xml:id="echoid-s8490" xml:space="preserve">alium uſum collationis denſitatum indi-<lb/>cabo.</s> <s xml:id="echoid-s8491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8492" xml:space="preserve">Si ex metallis duobus notis mixtum detur, poterit deter-<lb/> <anchor type="note" xlink:label="note-0317-01a" xlink:href="note-0317-01"/> minari quantum utriuſque contineat, ſi metallorum & </s> <s xml:id="echoid-s8493" xml:space="preserve">mixti <lb/>denſitates dentur.</s> <s xml:id="echoid-s8494" xml:space="preserve"/> </p> <div xml:id="echoid-div1210" type="float" level="2" n="4"> <note position="right" xlink:label="note-0317-01" xlink:href="note-0317-01a" xml:space="preserve">791.</note> </div> <p> <s xml:id="echoid-s8495" xml:space="preserve">Sint metallorum denſitates AB, AD; </s> <s xml:id="echoid-s8496" xml:space="preserve">mixti denſitas AC. <lb/></s> <s xml:id="echoid-s8497" xml:space="preserve"> <anchor type="note" xlink:label="note-0317-02a" xlink:href="note-0317-02"/> Sint etiam AL & </s> <s xml:id="echoid-s8498" xml:space="preserve">LI, ut volumina metallorum primi & </s> <s xml:id="echoid-s8499" xml:space="preserve">ſe-<lb/>cundi in mixto. </s> <s xml:id="echoid-s8500" xml:space="preserve">Ponamus formatum rectangulum ABEI, <lb/>ductaſque lineas CG, DH, FL, lateribus parallelas.</s> <s xml:id="echoid-s8501" xml:space="preserve"/> </p> <div xml:id="echoid-div1211" type="float" level="2" n="5"> <note position="right" xlink:label="note-0317-02" xlink:href="note-0317-02a" xml:space="preserve">TAB. XXXI. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s8502" xml:space="preserve">Pondus primi metalli in mixtura rectangulo AF repræ-<lb/>ſentari poteſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8503" xml:space="preserve">repræſentatque in hoc caſu rectangulum <anchor type="note" xlink:label="note-0317-03a" xlink:href="note-0317-03"/> LH pondus metalli ſecundi, eſtque gnomon ABFMHIA <lb/>pondus integri mixti; </s> <s xml:id="echoid-s8504" xml:space="preserve">hoc etiam rectangulo ACGI exhi-<lb/>betur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8505" xml:space="preserve">quod idcirco gnomoni memorato æquale eſt.</s> <s xml:id="echoid-s8506" xml:space="preserve"/> </p> <div xml:id="echoid-div1212" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0317-03" xlink:href="note-0317-03a" xml:space="preserve">739.</note> </div> <note symbol="*" position="right" xml:space="preserve">739</note> <p> <s xml:id="echoid-s8507" xml:space="preserve">Subtracto utrimque gnomone communi CNMHI, re-<lb/>ſtant æqualia rectangula BN, NH, ductaque DE tranſibit <lb/>hæc per punctum N <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8508" xml:space="preserve">Ergo DH, aut AI, ad NG, <anchor type="note" xlink:label="note-0317-05a" xlink:href="note-0317-05"/> aut LI, ut HE ad GE; </s> <s xml:id="echoid-s8509" xml:space="preserve">id eſt volumen mixti ad volu-<lb/> <anchor type="note" xlink:label="note-0317-06a" xlink:href="note-0317-06"/> men ſecundi metalli in mixto, ut differentia denſitatum me-<lb/>tallorum primi & </s> <s xml:id="echoid-s8510" xml:space="preserve">ſecundi ad differentiam denſitatum metal-<lb/>li primi & </s> <s xml:id="echoid-s8511" xml:space="preserve">mixti.</s> <s xml:id="echoid-s8512" xml:space="preserve"/> </p> <div xml:id="echoid-div1213" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0317-05" xlink:href="note-0317-05a" xml:space="preserve">43. El. Id</note> <note position="right" xlink:label="note-0317-06" xlink:href="note-0317-06a" xml:space="preserve">792.</note> </div> <p> <s xml:id="echoid-s8513" xml:space="preserve">Pondus autem totius mixturæ eſt ad pondus metalli ſe-<lb/> <anchor type="note" xlink:label="note-0317-07a" xlink:href="note-0317-07"/> cundi in mixto, in ratione compoſita denſitatum mixti & </s> <s xml:id="echoid-s8514" xml:space="preserve"><lb/>ſecundi metalli, & </s> <s xml:id="echoid-s8515" xml:space="preserve">ratione voluminis mixti & </s> <s xml:id="echoid-s8516" xml:space="preserve">voluminis <lb/>ſecundi metalli in mixto <anchor type="note" xlink:href="" symbol="*"/>, id eſt ut productum denſitatis <anchor type="note" xlink:label="note-0317-08a" xlink:href="note-0317-08"/> mixti per differentiam denſitatum metallorum ad denſita-<lb/>tem ſecundi metalli ductamin differentiam denſitatum primi <lb/>metalli & </s> <s xml:id="echoid-s8517" xml:space="preserve">mixti.</s> <s xml:id="echoid-s8518" xml:space="preserve"/> </p> <div xml:id="echoid-div1214" type="float" level="2" n="8"> <note position="right" xlink:label="note-0317-07" xlink:href="note-0317-07a" xml:space="preserve">793.</note> <note symbol="*" position="right" xlink:label="note-0317-08" xlink:href="note-0317-08a" xml:space="preserve">739.</note> </div> <pb o="226" file="0318" n="349" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1216" type="section" level="1" n="308"> <head xml:id="echoid-head428" style="it" xml:space="preserve">LIBRI II. Pars II.</head> <head xml:id="echoid-head429" xml:space="preserve">De Motu & Reſiſtentiâ Fluidorum.</head> <head xml:id="echoid-head430" xml:space="preserve">CAPUT VI.</head> <head xml:id="echoid-head431" style="it" xml:space="preserve">De celeritate fluidi, ex preſſione fluidi ſuperincum-<lb/>bentis.</head> <p> <s xml:id="echoid-s8519" xml:space="preserve">FLuidum inferius a ſuperiori premitur, & </s> <s xml:id="echoid-s8520" xml:space="preserve">quidem <lb/>æqualiter omnes partes verſus hæc preſſio dirigitur, & </s> <s xml:id="echoid-s8521" xml:space="preserve"><lb/>æqualiter omnes partes verſus fluidum conatur recedere; <lb/></s> <s xml:id="echoid-s8522" xml:space="preserve">idcirco ſi preſſio ab una parte tollatur, ad illam partem <lb/> <anchor type="note" xlink:label="note-0318-01a" xlink:href="note-0318-01"/> movetur fluidum; </s> <s xml:id="echoid-s8523" xml:space="preserve">& </s> <s xml:id="echoid-s8524" xml:space="preserve">non intereſt a quacunque parte preſſio <lb/>tollatur, eadem celeritate movetur; </s> <s xml:id="echoid-s8525" xml:space="preserve">quod Experimentis <lb/>in capite de fluidis proſilientibus memorandis confirma-<lb/>tur.</s> <s xml:id="echoid-s8526" xml:space="preserve"/> </p> <div xml:id="echoid-div1216" type="float" level="2" n="1"> <note position="left" xlink:label="note-0318-01" xlink:href="note-0318-01a" xml:space="preserve">794.</note> </div> <p> <s xml:id="echoid-s8527" xml:space="preserve">Ad eandem profunditatem celeritas eſt etiam ubique ea-<lb/>dem, propter preſſionis æqualitatem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8528" xml:space="preserve">mutata vero pro- <anchor type="note" xlink:label="note-0318-02a" xlink:href="note-0318-02"/> funditate mutatur celeritas.</s> <s xml:id="echoid-s8529" xml:space="preserve"/> </p> <div xml:id="echoid-div1217" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0318-02" xlink:href="note-0318-02a" xml:space="preserve">707. 708.</note> </div> <p> <s xml:id="echoid-s8530" xml:space="preserve">Hanc dicimus preſſione communicari velocitatem, non <lb/> <anchor type="note" xlink:label="note-0318-03a" xlink:href="note-0318-03"/> autem particulas hanc cadendo acquirere: </s> <s xml:id="echoid-s8531" xml:space="preserve">primæ enim par-<lb/>ticulæ quæ exeunt, non lentius illis, quæ ſequuntur, moven-<lb/>tur. </s> <s xml:id="echoid-s8532" xml:space="preserve">Præterea non tantum exeunt quæ deſcendunt, ſed & </s> <s xml:id="echoid-s8533" xml:space="preserve"><lb/>quæ lateraliter adfluunt; </s> <s xml:id="echoid-s8534" xml:space="preserve">moveturque particula preſſione <lb/>omnium particularum circumambientium exceptis illis quæ <lb/>in motu præcedunt, & </s> <s xml:id="echoid-s8535" xml:space="preserve">ita particula, quæ deſcendit, non <lb/>tam a ſuperincumbentibus a quibus ſtatim ſeparatur, cum <lb/>ipſis velocius debeat agitari, ſed præcipue lateralium preſ-<lb/>ſione velocitatem acquirit, duratque preſſio hæc, donec <lb/>particula a reliquis ſeparatur, & </s> <s xml:id="echoid-s8536" xml:space="preserve">aliæ locum quem occupabat <lb/>impleverint, & </s> <s xml:id="echoid-s8537" xml:space="preserve">non ulterius; </s> <s xml:id="echoid-s8538" xml:space="preserve">ab inſequentibus enim, eàdem <lb/>velocitate agitatis, accelerari non poteſt. </s> <s xml:id="echoid-s8539" xml:space="preserve">Unde ſequitur a- <pb o="227" file="0319" n="350" rhead="MATHEMATICA. LIB. II. CAP. VI."/> ctionem fluidi in particulam, qua actione velocitas particulæ <lb/>communicatur, pendere a tali deſcenſu particularum quo <lb/>locus a particula occupatus impletur. </s> <s xml:id="echoid-s8540" xml:space="preserve">Deſcenſus autem hic-<lb/> <anchor type="note" xlink:label="note-0319-01a" xlink:href="note-0319-01"/> ce, ſi A ſit particula mota, cujus diameter ſit d e, quo-<lb/>modocunque concipiatur, valet deſcenſum totius colu-<lb/>mnæ BC ad profunditatem d e, poſitâ C in ſuperficie fluidi; <lb/></s> <s xml:id="echoid-s8541" xml:space="preserve">& </s> <s xml:id="echoid-s8542" xml:space="preserve">vis in hoc deſcenſu acquiſita tota impenditur actione <lb/>in particulam motam, cui ergo vis communicatur æqualis <lb/>illi quam columna hæc BD in deſcenſu hoc per d e acquirit, <lb/>eſtque hæc æqualis illi quam particula acquireret cadendo <lb/>ab altitudine CB <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8543" xml:space="preserve"/> </p> <div xml:id="echoid-div1218" type="float" level="2" n="3"> <note position="left" xlink:label="note-0318-03" xlink:href="note-0318-03a" xml:space="preserve">795.</note> <note position="right" xlink:label="note-0319-01" xlink:href="note-0319-01a" xml:space="preserve">TAB XXXIII. <lb/>fig. 1.</note> </div> <note symbol="*" position="right" xml:space="preserve">471.</note> <p> <s xml:id="echoid-s8544" xml:space="preserve">Hinc ſequitur fluidum preſſione fluidi ſuperincumbentis, <lb/> <anchor type="note" xlink:label="note-0319-03a" xlink:href="note-0319-03"/> (ab hac enim pendet etiam preſſio lateralis) ex foramine <lb/>ea proſilire velocitate, quam corpus acquirit cadendo à ſupre-<lb/>ma fluidi ſuperficie ad for amen uſque; </s> <s xml:id="echoid-s8545" xml:space="preserve">ſepoſitâ nempe, ut <lb/>in hac demonſtratione, partium cobæſione, quæ licet exi-<lb/>gua ſit, in fluidis plerisque tamen obſervatur; </s> <s xml:id="echoid-s8546" xml:space="preserve">qua cohæ-<lb/>ſione particulæ exeuntes retinentur; </s> <s xml:id="echoid-s8547" xml:space="preserve">ideoque retardantur. <lb/></s> <s xml:id="echoid-s8548" xml:space="preserve">Sed & </s> <s xml:id="echoid-s8549" xml:space="preserve">præter hanc retardationem, quæ ab ipſo fluido pen-<lb/>det, ex variis aliis cauſis extraneis velocitas fluidi minuitur, <lb/>de quibus in capite ſequenti agam.</s> <s xml:id="echoid-s8550" xml:space="preserve"/> </p> <div xml:id="echoid-div1219" type="float" level="2" n="4"> <note position="right" xlink:label="note-0319-03" xlink:href="note-0319-03a" xml:space="preserve">796.</note> </div> </div> <div xml:id="echoid-div1221" type="section" level="1" n="309"> <head xml:id="echoid-head432" xml:space="preserve"><emph style="sc">Machina</emph></head> <head xml:id="echoid-head433" style="it" xml:space="preserve">Qua Experimenta de Fluidis proſilientibus inſti-<lb/>tuuntur.</head> <p> <s xml:id="echoid-s8551" xml:space="preserve">Parallelopipedum ligneum AB, longitudinis & </s> <s xml:id="echoid-s8552" xml:space="preserve">latitudi-<lb/> <anchor type="note" xlink:label="note-0319-04a" xlink:href="note-0319-04"/> nis quindecim pollicum, & </s> <s xml:id="echoid-s8553" xml:space="preserve">altitudinis duorum pedum, a-<lb/> <anchor type="note" xlink:label="note-0319-05a" xlink:href="note-0319-05"/> quâ impletur; </s> <s xml:id="echoid-s8554" xml:space="preserve">ita diſponitur ut fundus ejus elevetur circi-<lb/>ter decem pollicibus ſupra fundum horizontalem arcæ li-<lb/>gneæ CD, cujus longitudo eſt fere quatuor pedum, latitu-<lb/>do unius pedis cum ſemiſſe, profunditas quinque aut ſex <lb/>pollicum.</s> <s xml:id="echoid-s8555" xml:space="preserve"/> </p> <div xml:id="echoid-div1221" type="float" level="2" n="1"> <note position="right" xlink:label="note-0319-04" xlink:href="note-0319-04a" xml:space="preserve">797.</note> <note position="right" xlink:label="note-0319-05" xlink:href="note-0319-05a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s8556" xml:space="preserve">In F, ad altitudinem circiter ſedecim pollicum ſupra fun-<lb/>dum arcæ CD, hæret tubus æneus horizontalis, cujus ca-<lb/>vitatis diameter excedit ſemipollicem; </s> <s xml:id="echoid-s8557" xml:space="preserve">pars anterior lami-<lb/>nâ clauditur, in cujus medio foramen datur diametri par-<lb/>tis duodecimæ unius pollicis: </s> <s xml:id="echoid-s8558" xml:space="preserve">foramen hocce clauditur o- <pb o="228" file="0320" n="351" rhead="PHYSICES ELEMENTA"/> perculo, quo pars tubi anterior obtegitur, & </s> <s xml:id="echoid-s8559" xml:space="preserve">quod cum <lb/>hoc ope cochleæ jungitur: </s> <s xml:id="echoid-s8560" xml:space="preserve">duo tubi ſimiles aptantur in E <lb/>circa fundum vaſis AB, & </s> <s xml:id="echoid-s8561" xml:space="preserve">in G, hicque ſupra F elevatur <lb/>quantum ille infra F deprimitur.</s> <s xml:id="echoid-s8562" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8563" xml:space="preserve">Circa fundum etiam ejuſdem machinæ firmatur epiſto-<lb/>mium N, cochleâ inſtructum ut ipſi tubus jungatur.</s> <s xml:id="echoid-s8564" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1223" type="section" level="1" n="310"> <head xml:id="echoid-head434" xml:space="preserve"><emph style="sc">Experimentum</emph>1.</head> <p> <s xml:id="echoid-s8565" xml:space="preserve">Vas AB aqua impletur ita, ut altitudo ſuperficiei ſu-<lb/> <anchor type="note" xlink:label="note-0320-01a" xlink:href="note-0320-01"/> premæ aquæ ſupra fundum vaſis CD foramine in F in duas <lb/>partes æquales dividatur, quæ ſingulæ in noſtra machina <lb/>ſunt 15 {3/4}. </s> <s xml:id="echoid-s8566" xml:space="preserve">pol. </s> <s xml:id="echoid-s8567" xml:space="preserve">Aqua ex hoc foramine ad M proſilit, ita <lb/>ut diſtantia horizontalis puncti M à foramine ſit 29 {1/2}. </s> <s xml:id="echoid-s8568" xml:space="preserve">poll. </s> <s xml:id="echoid-s8569" xml:space="preserve">duo-<lb/>bus poll. </s> <s xml:id="echoid-s8570" xml:space="preserve">deficiens ab altitudine aquæ ſupra fundum va-<lb/>ſis CD; </s> <s xml:id="echoid-s8571" xml:space="preserve">ſi ad diſtantiam 31 {1/2} poll. </s> <s xml:id="echoid-s8572" xml:space="preserve">pertingeret, percurret <lb/>aqua, motu æquabili, celeritate cum qua exit, in tempore <lb/>in quo corpus cadere poteſt ab F ad fundum arcæ CD, <lb/>fpatium, duplum hujus altitudinis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8573" xml:space="preserve">ideo agitaretur ce- <anchor type="note" xlink:label="note-0320-02a" xlink:href="note-0320-02"/> leritate quam corpus ab hac altitudine cadendo poteſt ac-<lb/>quirere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8574" xml:space="preserve">hæc autem altitudo æqualis eſt altitudini ſuper- <anchor type="note" xlink:label="note-0320-03a" xlink:href="note-0320-03"/> ficiei aquæ ſupra foramen. </s> <s xml:id="echoid-s8575" xml:space="preserve">Cum vero tantum pertingat ad <lb/>diſtantiam 29 {1/2} poll. </s> <s xml:id="echoid-s8576" xml:space="preserve">deficit vera aquæ velocitas a velocita-<lb/>te memorata decima ſexta circiter parte.</s> <s xml:id="echoid-s8577" xml:space="preserve"/> </p> <div xml:id="echoid-div1223" type="float" level="2" n="1"> <note position="left" xlink:label="note-0320-01" xlink:href="note-0320-01a" xml:space="preserve">798.</note> <note symbol="*" position="left" xlink:label="note-0320-02" xlink:href="note-0320-02a" xml:space="preserve">327.</note> <note symbol="*" position="left" xlink:label="note-0320-03" xlink:href="note-0320-03a" xml:space="preserve">257.</note> </div> <p> <s xml:id="echoid-s8578" xml:space="preserve">Sepoſitis retardationibus, quadrata velocitatum, quibus <lb/> <anchor type="note" xlink:label="note-0320-04a" xlink:href="note-0320-04"/> fluidum ex variis foraminibus exit, ſunt inter ſe ut altitu-<lb/>dines fluidi ſupra foramina <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8579" xml:space="preserve">Experimentis etiam conſtat <anchor type="note" xlink:label="note-0320-05a" xlink:href="note-0320-05"/> retardationes parum admodum hanc proportionem turba-<lb/>re quamdiu altitudines non excedunt pedes 30. </s> <s xml:id="echoid-s8580" xml:space="preserve">aut 35. <lb/></s> <s xml:id="echoid-s8581" xml:space="preserve">In minoribus altitudinibus proportionem hanc ſequenti Ex-<lb/>perimento ante oculos ponimus.</s> <s xml:id="echoid-s8582" xml:space="preserve"/> </p> <div xml:id="echoid-div1224" type="float" level="2" n="2"> <note position="left" xlink:label="note-0320-04" xlink:href="note-0320-04a" xml:space="preserve">799.</note> <note symbol="*" position="left" xlink:label="note-0320-05" xlink:href="note-0320-05a" xml:space="preserve">796. 255.</note> </div> </div> <div xml:id="echoid-div1226" type="section" level="1" n="311"> <head xml:id="echoid-head435" xml:space="preserve"><emph style="sc">Experimentum</emph>2.</head> <p> <s xml:id="echoid-s8583" xml:space="preserve">Uſu hîc venit Machina ſuperius memorata <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8584" xml:space="preserve">& </s> <s xml:id="echoid-s8585" xml:space="preserve">circa <anchor type="note" xlink:label="note-0320-06a" xlink:href="note-0320-06"/> exp. </s> <s xml:id="echoid-s8586" xml:space="preserve">hoc notamus, diſtantias, ad quas proſilit aqua in fundo <lb/> <anchor type="note" xlink:label="note-0320-07a" xlink:href="note-0320-07"/> <anchor type="note" xlink:label="note-0320-08a" xlink:href="note-0320-08"/> arcæ CD, dum horizontaliter exit ex foramine ut E, po-<lb/>fitis diverſis ſuperficiei aquæ altitudinibus, eſſe ſpatia hori-<lb/>zontaliter motu æquabili percurſa, in tempore in quo cor-<lb/>pus cadendo poteſt percurrere IL æqualem altitudini fora- <pb o="229" file="0321" n="352" rhead="MATHEMATICA. LIB. II. CAP. VII."/> minis ſupra fundum arcæ <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s8587" xml:space="preserve">hasque idcirco diſtantias eſſe <anchor type="note" xlink:label="note-0321-01a" xlink:href="note-0321-01"/> ut velocitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8588" xml:space="preserve"/> </p> <div xml:id="echoid-div1226" type="float" level="2" n="1"> <note position="left" xlink:label="note-0320-06" xlink:href="note-0320-06a" xml:space="preserve">800.</note> <note position="left" xlink:label="note-0320-07" xlink:href="note-0320-07a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0320-08" xlink:href="note-0320-08a" xml:space="preserve">797.</note> <note symbol="*" position="right" xlink:label="note-0321-01" xlink:href="note-0321-01a" xml:space="preserve">327.</note> </div> <note symbol="*" position="right" xml:space="preserve">94.</note> <p> <s xml:id="echoid-s8589" xml:space="preserve">Si nunc detur aqua in vaſe AB, ad altitudinem octo <lb/>pollicum ſupra foramen in E, & </s> <s xml:id="echoid-s8590" xml:space="preserve">menſuretur diſtantia ad <lb/>quam proſilit; </s> <s xml:id="echoid-s8591" xml:space="preserve">& </s> <s xml:id="echoid-s8592" xml:space="preserve">infuſâ ulterius aquâ, donec altitudo ſit octo-<lb/>decim pollicum, iterum menſuretur diſtantia; </s> <s xml:id="echoid-s8593" xml:space="preserve">erunt hæ <lb/>ut 2. </s> <s xml:id="echoid-s8594" xml:space="preserve">ad 3. </s> <s xml:id="echoid-s8595" xml:space="preserve">Quadrata diſtantiarum ſunt hîc ut aquæ alti-<lb/>tudines, in qua ratione quadrata celeritatum.</s> <s xml:id="echoid-s8596" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1228" type="section" level="1" n="312"> <head xml:id="echoid-head436" xml:space="preserve">CAPUT VII.</head> <head xml:id="echoid-head437" style="it" xml:space="preserve">De Fluidis proſilientibus.</head> <p> <s xml:id="echoid-s8597" xml:space="preserve">FLuidum verticaliter ex foramine proſiliens, ea velocita-<lb/> <anchor type="note" xlink:label="note-0321-03a" xlink:href="note-0321-03"/> te in altum adſcendit, qua ad altitudinem ſupre-<lb/>mæ ſuperficiei fluidi pervenire poteſt, nunquam tamen ad <lb/>hanc altitudinem pertingit, variis ex cauſis, præter par-<lb/>tium cohæſionem ſupra memoratam <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8598" xml:space="preserve"/> </p> <div xml:id="echoid-div1228" type="float" level="2" n="1"> <note position="right" xlink:label="note-0321-03" xlink:href="note-0321-03a" xml:space="preserve">801.</note> </div> <note symbol="*" position="right" xml:space="preserve">796.</note> <p> <s xml:id="echoid-s8599" xml:space="preserve">1. </s> <s xml:id="echoid-s8600" xml:space="preserve">Celeritas, qua fluidum in altum adſcendit, omnibus <lb/> <anchor type="note" xlink:label="note-0321-05a" xlink:href="note-0321-05"/> momentis minuitur, & </s> <s xml:id="echoid-s8601" xml:space="preserve">columna fluidi proſilientis conſtat <lb/>ex partibus, ad varias altitudines, celeritate diverſa motis: <lb/></s> <s xml:id="echoid-s8602" xml:space="preserve">columnæ ubique ejuſdem craſſitiei partes omnes neceſſario <lb/>eadem celeritate moventur; </s> <s xml:id="echoid-s8603" xml:space="preserve">prædicta columna fit ergo la-<lb/>tior omnibus momentis, dum fluidi celeritas minuitur; </s> <s xml:id="echoid-s8604" xml:space="preserve"><lb/>quod ex impetu fluidi inſequentis oritur, & </s> <s xml:id="echoid-s8605" xml:space="preserve">ex natura flui-<lb/>di impreſſioni cuicunque cedentis, & </s> <s xml:id="echoid-s8606" xml:space="preserve">facile verſus omnes <lb/>partes moti; </s> <s xml:id="echoid-s8607" xml:space="preserve">ex hoc impetu motus ubique retardatur.</s> <s xml:id="echoid-s8608" xml:space="preserve"/> </p> <div xml:id="echoid-div1229" type="float" level="2" n="2"> <note position="right" xlink:label="note-0321-05" xlink:href="note-0321-05a" xml:space="preserve">802.</note> </div> <p> <s xml:id="echoid-s8609" xml:space="preserve">2. </s> <s xml:id="echoid-s8610" xml:space="preserve">Minuitur & </s> <s xml:id="echoid-s8611" xml:space="preserve">hicce motus ex fluido, quod, cum totum <lb/>motum amiſit, hæret in ſuperiori parte columnæ, & </s> <s xml:id="echoid-s8612" xml:space="preserve">flui-<lb/>do inſequenti ſuſtinetur per momentum temporis, ante-<lb/>quam ad latera defluat, quo fluidum hoc in ſequens retar-<lb/>datur, quæ retardatio toti columnæ communicatur.</s> <s xml:id="echoid-s8613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8614" xml:space="preserve">3. </s> <s xml:id="echoid-s8615" xml:space="preserve">Attritu juxta latera foraminis minor eſt fluidi proſili-<lb/>entis celeritas; </s> <s xml:id="echoid-s8616" xml:space="preserve">qui attritus augetur, quando per tubos & </s> <s xml:id="echoid-s8617" xml:space="preserve"><lb/>epiſtomia fluidum deducitur.</s> <s xml:id="echoid-s8618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8619" xml:space="preserve">4. </s> <s xml:id="echoid-s8620" xml:space="preserve">Tandem aëris reſiſtentia motui fluidorum remoram facit.</s> <s xml:id="echoid-s8621" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8622" xml:space="preserve">Cauſam primam retardationis memoratam corrigi mini-<lb/>me poſſe nemo eſt qui non videt.</s> <s xml:id="echoid-s8623" xml:space="preserve"/> </p> <pb o="230" file="0322" n="353" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s8624" xml:space="preserve">Secunda corrigitur paululum inclinando fluidi directio-<lb/>nem, ut per ſe patet; </s> <s xml:id="echoid-s8625" xml:space="preserve">hac de cauſa, fluidum, directione paululum <lb/> <anchor type="note" xlink:label="note-0322-01a" xlink:href="note-0322-01"/> ad horizontem inclinata, altius quâm verticaliter adſcendit.</s> <s xml:id="echoid-s8626" xml:space="preserve"/> </p> <div xml:id="echoid-div1230" type="float" level="2" n="3"> <note position="left" xlink:label="note-0322-01" xlink:href="note-0322-01a" xml:space="preserve">803.</note> </div> </div> <div xml:id="echoid-div1232" type="section" level="1" n="313"> <head xml:id="echoid-head438" xml:space="preserve"><emph style="sc">Experimentum i</emph>.</head> <p> <s xml:id="echoid-s8627" xml:space="preserve">Machinæ ſuperius deſcriptæ <anchor type="note" xlink:href="" symbol="*"/>, ope cochleæ in N jun- <anchor type="note" xlink:label="note-0322-02a" xlink:href="note-0322-02"/> gitur tubus curvus NO, ex quo aqua per foramen exiguum <lb/> <anchor type="note" xlink:label="note-0322-03a" xlink:href="note-0322-03"/> in altum proſilit verticaliter; </s> <s xml:id="echoid-s8628" xml:space="preserve">convertendo paululum tubum, <lb/> <anchor type="note" xlink:label="note-0322-04a" xlink:href="note-0322-04"/> quod facile fit propter cochleam in N, inclinatur directio <lb/>motus aquæ, & </s> <s xml:id="echoid-s8629" xml:space="preserve">altius hæc adſcendit. </s> <s xml:id="echoid-s8630" xml:space="preserve">Hac autem inclina-<lb/>tione ſpectaculi amœnitas deſtruitur.</s> <s xml:id="echoid-s8631" xml:space="preserve"/> </p> <div xml:id="echoid-div1232" type="float" level="2" n="1"> <note position="left" xlink:label="note-0322-02" xlink:href="note-0322-02a" xml:space="preserve">804.</note> <note position="left" xlink:label="note-0322-03" xlink:href="note-0322-03a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0322-04" xlink:href="note-0322-04a" xml:space="preserve">797.</note> </div> <p> <s xml:id="echoid-s8632" xml:space="preserve">Circa tertiam cauſam retardationis notandum, eo majo-<lb/>rem, ſervata proportione, dari attritum quo foramen mi-<lb/>nus eſt; </s> <s xml:id="echoid-s8633" xml:space="preserve">circumferentia enim, in qua attritus datur, creſcit <lb/>ut diameter, & </s> <s xml:id="echoid-s8634" xml:space="preserve">ipſum foramen augetur ut quadratum dia-<lb/>metri <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8635" xml:space="preserve">augeturque magis fluidi proſilientis quantitas quàm <anchor type="note" xlink:label="note-0322-05a" xlink:href="note-0322-05"/> attritus. </s> <s xml:id="echoid-s8636" xml:space="preserve">Etiam auctâ celeritate attritum augeri clarum eſt, <lb/>quare foramina cum altitudine aquæ proſilientis ſunt augenda, <lb/> <anchor type="note" xlink:label="note-0322-06a" xlink:href="note-0322-06"/> ut dum ex una cauſa attritus augetur, ex alia minua-<lb/>tur.</s> <s xml:id="echoid-s8637" xml:space="preserve"/> </p> <div xml:id="echoid-div1233" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0322-05" xlink:href="note-0322-05a" xml:space="preserve">El. XII.</note> <note position="left" xlink:label="note-0322-06" xlink:href="note-0322-06a" xml:space="preserve">805.</note> </div> <p> <s xml:id="echoid-s8638" xml:space="preserve">Extremitates tuborum, ex quibus aqua proſilit, vulgo <lb/> <anchor type="note" xlink:label="note-0322-07a" xlink:href="note-0322-07"/> figuram coni truncati habent, ut in P repræſentatur; </s> <s xml:id="echoid-s8639" xml:space="preserve">in <lb/>qua extremitate magnum aqua attritum patitur & </s> <s xml:id="echoid-s8640" xml:space="preserve">irregula-<lb/>riter movetur, motuque irregulari in altum exit. </s> <s xml:id="echoid-s8641" xml:space="preserve">Corri-<lb/>guntur hæc obtegendo extremitatem tubi laminâ planâ & </s> <s xml:id="echoid-s8642" xml:space="preserve">po-<lb/> <anchor type="note" xlink:label="note-0322-08a" xlink:href="note-0322-08"/> litâ, in qua foramen datur, cujus latera admodum polita <lb/>etiam deſiderantur; </s> <s xml:id="echoid-s8643" xml:space="preserve">altius tunc aqua proſilit; </s> <s xml:id="echoid-s8644" xml:space="preserve">&</s> <s xml:id="echoid-s8645" xml:space="preserve">, quia <lb/>motu omnino regulari adſcendit, perfecte eſt transluci-<lb/>da.</s> <s xml:id="echoid-s8646" xml:space="preserve"/> </p> <div xml:id="echoid-div1234" type="float" level="2" n="3"> <note position="left" xlink:label="note-0322-07" xlink:href="note-0322-07a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 3.</note> <note position="left" xlink:label="note-0322-08" xlink:href="note-0322-08a" xml:space="preserve">806.</note> </div> </div> <div xml:id="echoid-div1236" type="section" level="1" n="314"> <head xml:id="echoid-head439" xml:space="preserve"><emph style="sc">Experimentum</emph>2.</head> <p> <s xml:id="echoid-s8647" xml:space="preserve">Detur tubus memoratus P, ut & </s> <s xml:id="echoid-s8648" xml:space="preserve">cylindrus Q, ab una <lb/> <anchor type="note" xlink:label="note-0322-09a" xlink:href="note-0322-09"/> parte, laminâ perforatâ, clauſus; </s> <s xml:id="echoid-s8649" xml:space="preserve">hi ſeparatim ope cochleæ <lb/> <anchor type="note" xlink:label="note-0322-10a" xlink:href="note-0322-10"/> jungantur extremitati O tubi NO (fig. </s> <s xml:id="echoid-s8650" xml:space="preserve">2.)</s> <s xml:id="echoid-s8651" xml:space="preserve">; </s> <s xml:id="echoid-s8652" xml:space="preserve">manente aqua <lb/>ad eandem altitudinem in vaſe AB, ſi proſiliat ex tubo P, <lb/>& </s> <s xml:id="echoid-s8653" xml:space="preserve">ex cylindro Q, duorum pollicum ad minimum in hac <lb/>exigua altitudine differentia dabitur.</s> <s xml:id="echoid-s8654" xml:space="preserve"/> </p> <div xml:id="echoid-div1236" type="float" level="2" n="1"> <note position="left" xlink:label="note-0322-09" xlink:href="note-0322-09a" xml:space="preserve">807.</note> <note position="left" xlink:label="note-0322-10" xlink:href="note-0322-10a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s8655" xml:space="preserve">Tubi, per quos aqua ex receptaculo deducitur, latiſſi-<lb/> <anchor type="note" xlink:label="note-0322-11a" xlink:href="note-0322-11"/> <pb o="231" file="0323" n="354" rhead="MATHEMATICA. LIB. II. CAP. VII."/> mi, reſpectu foraminis, requiruntur; </s> <s xml:id="echoid-s8656" xml:space="preserve">ut lente aqua in hiſ-<lb/>ce tubis moveatur, & </s> <s xml:id="echoid-s8657" xml:space="preserve">ſenſibilis attritus non detur. </s> <s xml:id="echoid-s8658" xml:space="preserve">Etiam <lb/>epiſtomiorum aperturæ latiſſimæ deſiderantur, ut attritus mi-<lb/>nuatur.</s> <s xml:id="echoid-s8659" xml:space="preserve"/> </p> <div xml:id="echoid-div1237" type="float" level="2" n="2"> <note position="left" xlink:label="note-0322-11" xlink:href="note-0322-11a" xml:space="preserve">808.</note> </div> </div> <div xml:id="echoid-div1239" type="section" level="1" n="315"> <head xml:id="echoid-head440" xml:space="preserve"><emph style="sc">Experimentum</emph>3.</head> <p> <s xml:id="echoid-s8660" xml:space="preserve">Vaſi AB, ad eandem altitudinem cum tubo F, inſeri-<lb/> <anchor type="note" xlink:label="note-0323-01a" xlink:href="note-0323-01"/> tur epiſtomium H; </s> <s xml:id="echoid-s8661" xml:space="preserve">tubus, in quo epiſtomium datur, lami-<lb/> <anchor type="note" xlink:label="note-0323-02a" xlink:href="note-0323-02"/> nâ clauditur eodem modo ac tubus F, & </s> <s xml:id="echoid-s8662" xml:space="preserve">ſimiliter hæc la-<lb/>mina perforatur; </s> <s xml:id="echoid-s8663" xml:space="preserve">ipſius epiſtomii apertura eſt quartæ partis <lb/>unius pollicis. </s> <s xml:id="echoid-s8664" xml:space="preserve">Aqua, quæ per hoc epiſtomium tranſit, in <lb/>ſpatium magis anguſtum redigitur quàm quæ per tubum F <lb/>movetur; </s> <s xml:id="echoid-s8665" xml:space="preserve">hæc magis eſt tranſiucida, & </s> <s xml:id="echoid-s8666" xml:space="preserve">ad majorem diſtan-<lb/>tiam proſilit.</s> <s xml:id="echoid-s8667" xml:space="preserve"/> </p> <div xml:id="echoid-div1239" type="float" level="2" n="1"> <note position="right" xlink:label="note-0323-01" xlink:href="note-0323-01a" xml:space="preserve">809.</note> <note position="right" xlink:label="note-0323-02" xlink:href="note-0323-02a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s8668" xml:space="preserve">Reſiſtentia aëris ſenſibilem in motu fluidorum exerit effe-<lb/> <anchor type="note" xlink:label="note-0323-03a" xlink:href="note-0323-03"/> ctum. </s> <s xml:id="echoid-s8669" xml:space="preserve">Ut corpora omnia motui reſiſtit, daturque fluidi <lb/>proſilientis in particulas aëreas actio, & </s> <s xml:id="echoid-s8670" xml:space="preserve">harum reactione <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0323-04a" xlink:href="note-0323-04"/> minuitur fluidi motus.</s> <s xml:id="echoid-s8671" xml:space="preserve"/> </p> <div xml:id="echoid-div1240" type="float" level="2" n="2"> <note position="right" xlink:label="note-0323-03" xlink:href="note-0323-03a" xml:space="preserve">810.</note> <note symbol="*" position="right" xlink:label="note-0323-04" xlink:href="note-0323-04a" xml:space="preserve">478.</note> </div> <p> <s xml:id="echoid-s8672" xml:space="preserve">Præter hanc reſiſtentiam, datur & </s> <s xml:id="echoid-s8673" xml:space="preserve">alia minime conte-<lb/>mnenda aëris actio in fluidum proſiliens. </s> <s xml:id="echoid-s8674" xml:space="preserve">Fluidorum proprie-<lb/>tates aërem habere, in Parte ſequenti videbimus. </s> <s xml:id="echoid-s8675" xml:space="preserve">Circumdat <lb/>fluidum hoc totam columnam fluidi ſalientis, motuique hu-<lb/>jus, quo ad latera ſeſe expandit dum latior fit, reſiſtit, & </s> <s xml:id="echoid-s8676" xml:space="preserve"><lb/>major vis fluidi inſequentis requiritur, quàm ſi reſiſtentia <lb/>hæc ſublata eſſet; </s> <s xml:id="echoid-s8677" xml:space="preserve">reſiſtit ergo aër etiam preſſione laterali.</s> <s xml:id="echoid-s8678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8679" xml:space="preserve">Reſiſtentia ex fluidi ictu in aërem creſcit cum ſuperficie im-<lb/>pingenti, id eſt, ſi maneat celeritas, augetur cum forami-<lb/>ne, in qua etiam ratione creſcit quantitas materiæ motæ, <lb/>& </s> <s xml:id="echoid-s8680" xml:space="preserve">hujus reſpectu non intereſt cujuſcunque magnitudinis <lb/>fuerit foramen.</s> <s xml:id="echoid-s8681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8682" xml:space="preserve">Preſſio lateralis ſequitur proportionem ſuperficiei colu-<lb/>mnæ; </s> <s xml:id="echoid-s8683" xml:space="preserve">materia mota, quæ manente celeritate ſequitur ra-<lb/>tionem ipſius vis inſitæ <anchor type="note" xlink:href="" symbol="*"/>, ad inſtar totius columnæ, id eſt, <anchor type="note" xlink:label="note-0323-05a" xlink:href="note-0323-05"/> quadrati ſuperficiei hujus mutatur: </s> <s xml:id="echoid-s8684" xml:space="preserve">magis ergo, ſi foramen <lb/>augeatur, creſcit vis fluidi quàm ipſa cauſa retardans; <lb/></s> <s xml:id="echoid-s8685" xml:space="preserve">in majoribus ideo fluidorum proſilientium altitudinibus, ut <lb/> <anchor type="note" xlink:label="note-0323-06a" xlink:href="note-0323-06"/> preſlio lateralis, quæ, cum diutius agat majorem actionem <pb o="232" file="0324" n="355" rhead="PHYSICES ELEMENTA"/> exerit, melius ſuperari poſſit, major a deſiderantur foramina, <lb/>quod & </s> <s xml:id="echoid-s8686" xml:space="preserve">in eodem caſu ex alia cauſa requiri antea diximus <anchor type="note" xlink:href="" symbol="*"/>:</s> <s xml:id="echoid-s8687" xml:space="preserve"> <anchor type="note" xlink:label="note-0324-01a" xlink:href="note-0324-01"/> in quo loco ut & </s> <s xml:id="echoid-s8688" xml:space="preserve">hìc majora foramina in majoribus tantum <lb/>altitudinibus neceſſaria ponimus, licet demonſtrationes pro-<lb/>bent hæc foramina, in majoribus altitudinibus maxime ne-<lb/>ceſſaria, in genere eſſe anteponenda.</s> <s xml:id="echoid-s8689" xml:space="preserve"/> </p> <div xml:id="echoid-div1241" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0323-05" xlink:href="note-0323-05a" xml:space="preserve">450.</note> <note position="right" xlink:label="note-0323-06" xlink:href="note-0323-06a" xml:space="preserve">811.</note> <note symbol="*" position="left" xlink:label="note-0324-01" xlink:href="note-0324-01a" xml:space="preserve">205.</note> </div> <p> <s xml:id="echoid-s8690" xml:space="preserve">Magna foramina etiam motui obſtant; </s> <s xml:id="echoid-s8691" xml:space="preserve">nam 1. </s> <s xml:id="echoid-s8692" xml:space="preserve">Major da-<lb/> <anchor type="note" xlink:label="note-0324-02a" xlink:href="note-0324-02"/> tur ſuperficies, cui incumbit fluidum altiſſimum, quod to-<lb/>tum motum amiſit, ibique diutius hæret antequam ad late-<lb/>ra defluat. </s> <s xml:id="echoid-s8693" xml:space="preserve">2. </s> <s xml:id="echoid-s8694" xml:space="preserve">Fluidum non tantum illud ex foramine exit, <lb/>quod huic reſpondet, ſed, ut fluxus continuus detur, flui-<lb/>dum vicinum continuo adfluit, quod oblique movetur, & </s> <s xml:id="echoid-s8695" xml:space="preserve"><lb/>dum proſilit motu compoſito agitatur, quo motus fluidi <lb/>proſilientis turbatur; </s> <s xml:id="echoid-s8696" xml:space="preserve">& </s> <s xml:id="echoid-s8697" xml:space="preserve">in majoribus foraminibus major eſt <lb/>perturbatio ex hac cauſa oriunda.</s> <s xml:id="echoid-s8698" xml:space="preserve"/> </p> <div xml:id="echoid-div1242" type="float" level="2" n="4"> <note position="left" xlink:label="note-0324-02" xlink:href="note-0324-02a" xml:space="preserve">812.</note> </div> <p> <s xml:id="echoid-s8699" xml:space="preserve">In minoribus foraminibus prævalent retardationes, quæ, <lb/>aucto foramine, corriguntur; </s> <s xml:id="echoid-s8700" xml:space="preserve">ita tamen poteſt augeri fora-<lb/>men, ut hæ prævaleant tardationes, quæ aucto foramine <lb/>creſcunt. </s> <s xml:id="echoid-s8701" xml:space="preserve">Quare datur in omnibus altitudinibus certa fora-<lb/> <anchor type="note" xlink:label="note-0324-03a" xlink:href="note-0324-03"/> minis menſura, per quod fluidum ad maximam quam poteſt <lb/>adſcendit altitudinem. </s> <s xml:id="echoid-s8702" xml:space="preserve">Regulæ tamen de determinando fora-<lb/>mine dari nequeunt, quia latitudo tuborum, per quos aqua <lb/>deducitur, horumque inflexiones illud mutant, ita ut va-<lb/>riatio in infinitum detur.</s> <s xml:id="echoid-s8703" xml:space="preserve"/> </p> <div xml:id="echoid-div1243" type="float" level="2" n="5"> <note position="left" xlink:label="note-0324-03" xlink:href="note-0324-03a" xml:space="preserve">813.</note> </div> <p style="it"> <s xml:id="echoid-s8704" xml:space="preserve">Notandum autem altitudinem, ad quam fluidum adſcen-<lb/> <anchor type="note" xlink:label="note-0324-04a" xlink:href="note-0324-04"/> dere poteſt, ut & </s> <s xml:id="echoid-s8705" xml:space="preserve">for aminis magnitudinem, limites habere, <lb/>quos excedere vetitum.</s> <s xml:id="echoid-s8706" xml:space="preserve"/> </p> <div xml:id="echoid-div1244" type="float" level="2" n="6"> <note position="left" xlink:label="note-0324-04" xlink:href="note-0324-04a" xml:space="preserve">814.</note> </div> <p> <s xml:id="echoid-s8707" xml:space="preserve">Nam aucta nimium fluidi celeritate, tanta vi in aërem <lb/>impingit, ut in guttas diſpergatur; </s> <s xml:id="echoid-s8708" xml:space="preserve">in quo caſu minuendo <lb/>celeritatem altitudo ad quam adſcendit fluidum augetur, <lb/>& </s> <s xml:id="echoid-s8709" xml:space="preserve">altitudo omnium maxima ad quam fluidum adſcendere <lb/>poteſt in diverſis fluidis differt; </s> <s xml:id="echoid-s8710" xml:space="preserve">hæcque in aqua proſilien-<lb/>ti, vix centum pedes ſuperat. </s> <s xml:id="echoid-s8711" xml:space="preserve">Diameter foraminis, quod <lb/>huic maximæ altitudini reſpondet, vix excedit pollicem cum <lb/>quarta parte.</s> <s xml:id="echoid-s8712" xml:space="preserve"/> </p> <pb o="233" file="0325" n="356" rhead="MATHEMATICA. LIB. II. CAP. VII."/> <p> <s xml:id="echoid-s8713" xml:space="preserve">Fluida, quæ oblique proſiliunt, non ex tot cauſis, neque <lb/> <anchor type="note" xlink:label="note-0325-01a" xlink:href="note-0325-01"/> tantum, quàm verticaliter proſilientiaretardantur. </s> <s xml:id="echoid-s8714" xml:space="preserve">Secun-<lb/>da retardationis cauſa antea memorata <anchor type="note" xlink:href="" symbol="*"/> hîc locum non ha- <anchor type="note" xlink:label="note-0325-02a" xlink:href="note-0325-02"/> bet, & </s> <s xml:id="echoid-s8715" xml:space="preserve">effectus primæ minor eſt. </s> <s xml:id="echoid-s8716" xml:space="preserve">De cætero in his locum <lb/>habent, quæ de ſolidis oblique projectis dicta ſunt in capite <lb/>20. </s> <s xml:id="echoid-s8717" xml:space="preserve">libri primi, & </s> <s xml:id="echoid-s8718" xml:space="preserve">fluidum ut innumera ſolida ſeſe mutuo <lb/> <anchor type="note" xlink:label="note-0325-03a" xlink:href="note-0325-03"/> inſequentia, & </s> <s xml:id="echoid-s8719" xml:space="preserve">eandem viam percurrentia, conſiderari <lb/>poteſt. </s> <s xml:id="echoid-s8720" xml:space="preserve">In motu fluidi via percurſa ſenſibilis eſt, & </s> <s xml:id="echoid-s8721" xml:space="preserve">quæ <lb/>de ſolidis oblique projectis dicta ſunt ope fluidorum ad <lb/>Experimentum vocantur; </s> <s xml:id="echoid-s8722" xml:space="preserve">ad quod hydrargyro utendum, <lb/>propter hujus fluidi, præ cæteris, gravitatem ſpecificam. <lb/></s> <s xml:id="echoid-s8723" xml:space="preserve">Hæc autem Machinâ peculiari inſtituenda ſunt Experimen-<lb/>ta.</s> <s xml:id="echoid-s8724" xml:space="preserve"/> </p> <div xml:id="echoid-div1245" type="float" level="2" n="7"> <note position="right" xlink:label="note-0325-01" xlink:href="note-0325-01a" xml:space="preserve">815.</note> <note symbol="*" position="right" xlink:label="note-0325-02" xlink:href="note-0325-02a" xml:space="preserve">802.</note> <note position="right" xlink:label="note-0325-03" xlink:href="note-0325-03a" xml:space="preserve">816.</note> </div> </div> <div xml:id="echoid-div1247" type="section" level="1" n="316"> <head xml:id="echoid-head441" xml:space="preserve"><emph style="sc">Machina</emph>,</head> <head xml:id="echoid-head442" style="it" xml:space="preserve">Qua inſtituuntur Experimenta de Fluidis oblique <lb/>proſilientibus.</head> <p> <s xml:id="echoid-s8725" xml:space="preserve">Arca lignea ABCDEFH longitudinis eſt quatuor pe-<lb/> <anchor type="note" xlink:label="note-0325-04a" xlink:href="note-0325-04"/> dum cum ſemiſſe, latitudinis octo aut decem pollicum, alti-<lb/> <anchor type="note" xlink:label="note-0325-05a" xlink:href="note-0325-05"/> tudinis ſex aut ſeptem pollicum. </s> <s xml:id="echoid-s8726" xml:space="preserve">Fundus conſtat ex tabula <lb/>lignea excavata ad profunditatem ſemi-pollicis, ut melius mer-<lb/>curium contineat.</s> <s xml:id="echoid-s8727" xml:space="preserve"/> </p> <div xml:id="echoid-div1247" type="float" level="2" n="1"> <note position="right" xlink:label="note-0325-04" xlink:href="note-0325-04a" xml:space="preserve">817.</note> <note position="right" xlink:label="note-0325-05" xlink:href="note-0325-05a" xml:space="preserve">TAB. XXXII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s8728" xml:space="preserve">In extremitate H, lateris EFH, datur aſſer, aut tabula, <lb/>HI, latitudinis ſex pollicum, altitudinis duorum pedum, <lb/>in qua datur ſciſſura o t. </s> <s xml:id="echoid-s8729" xml:space="preserve">Hujus ope parallelopipedum li-<lb/>gneum s, cuia poſteriori parte cochlea cohæret, ad altitu-<lb/>dinem quamcunque firmatur.</s> <s xml:id="echoid-s8730" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8731" xml:space="preserve">Parallelopipedum hoc videtur in S (fig. </s> <s xml:id="echoid-s8732" xml:space="preserve">2.) </s> <s xml:id="echoid-s8733" xml:space="preserve">huic additur <lb/>pyxis buxea cylindrica P, quæ ſulco circumdatur, cui in-<lb/>ſeruntur laminæ duæ æneæ, quarum una videtur in fe, ha-<lb/>rum extremitates junguntur cochleâ g, qua pyxis immobilis <lb/>redditur, hæc vero circa axem eſt volubilis, quando relaxa-<lb/>tur paululum cochlea.</s> <s xml:id="echoid-s8734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8735" xml:space="preserve">In fundo hujus pyxidis datur cavitas cylindrica ab, diame-<lb/>tri quartæ partis unius pollicis. </s> <s xml:id="echoid-s8736" xml:space="preserve">Habet hæc communicatio-<lb/>nem cum ſimili cavitate b c, quæ terminatur in medio cavi-<lb/>tatis majoris c d, cujus diameter ſemi-pollicem excedit, &</s> <s xml:id="echoid-s8737" xml:space="preserve"> <pb o="234" file="0326" n="357" rhead="PHYSICES ELEMENTA"/> cui inſeritur conus truncatus H (fig. </s> <s xml:id="echoid-s8738" xml:space="preserve">3.) </s> <s xml:id="echoid-s8739" xml:space="preserve">buxeus, cujus exte-<lb/>rior ſuperficies, cum interiori cavitatis ſuperficie congruit <lb/>ita, ut conus circa axem in hac cavitate rotari poſſit, dum <lb/>firmiter retinetur cochleâ R, laminam æneam QO trajici-<lb/>ente.</s> <s xml:id="echoid-s8740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8741" xml:space="preserve">Ad angulos rectos cohæret conus truncatus H cum <lb/>cylindro IL, conumque cum cylindro flexa trajicit <lb/>cavitas b i l, ejuſdem diametri cum cavitate b c, & </s> <s xml:id="echoid-s8742" xml:space="preserve">huic <lb/>reſpondens. </s> <s xml:id="echoid-s8743" xml:space="preserve">Latior autem illa eſt in L, ut ipſi inſeratur tu-<lb/>bus vitreus NM.</s> <s xml:id="echoid-s8744" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8745" xml:space="preserve">Tubilongitudo eſt ſeſqui pedis, extremitas altera videtur <lb/>in NM, (fig. </s> <s xml:id="echoid-s8746" xml:space="preserve">5.) </s> <s xml:id="echoid-s8747" xml:space="preserve">quæ inſeritur cylindro buxeo LI ad for-<lb/>mam gnomonis excavati in l i b; </s> <s xml:id="echoid-s8748" xml:space="preserve">in b c datur cavitas ma-<lb/>jor, cui inſeritur conus truncatus ED, quo hæc exacte re-<lb/>pletur, & </s> <s xml:id="echoid-s8749" xml:space="preserve">qui in hac circa axem convertitur, ope manu-<lb/>brii EA.</s> <s xml:id="echoid-s8750" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8751" xml:space="preserve">Cavitas b i reſpondet cavitati d e, quæ communicatur cum <lb/>f g; </s> <s xml:id="echoid-s8752" xml:space="preserve">pars hæc buxi annulo ferreo BQ circumdatur, in quo <lb/>exiguum admodum datur foramen g, quod, partibus ma-<lb/>chinæ junctis, cum cavitate pyxidis P (fig. </s> <s xml:id="echoid-s8753" xml:space="preserve">2.) </s> <s xml:id="echoid-s8754" xml:space="preserve">communica-<lb/>tionem habet.</s> <s xml:id="echoid-s8755" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8756" xml:space="preserve">Ne tubus frangatur, extremitates L, L, cylindrorum bu-<lb/>xeorum (fig. </s> <s xml:id="echoid-s8757" xml:space="preserve">3. </s> <s xml:id="echoid-s8758" xml:space="preserve">& </s> <s xml:id="echoid-s8759" xml:space="preserve">5.) </s> <s xml:id="echoid-s8760" xml:space="preserve">cum tubo applicantur regulæ ligneæ <lb/>m n (fig. </s> <s xml:id="echoid-s8761" xml:space="preserve">1.)</s> <s xml:id="echoid-s8762" xml:space="preserve">. </s> <s xml:id="echoid-s8763" xml:space="preserve">Cum hujus extremitate inferiori m jungitur <lb/>lamina ferrea, (ut videtur in fig. </s> <s xml:id="echoid-s8764" xml:space="preserve">6.) </s> <s xml:id="echoid-s8765" xml:space="preserve">cujus extremitas LPBQ <lb/>gnomonis duplicati ſpeciem fert: </s> <s xml:id="echoid-s8766" xml:space="preserve">cum extremitas L (fig. <lb/></s> <s xml:id="echoid-s8767" xml:space="preserve">5.) </s> <s xml:id="echoid-s8768" xml:space="preserve">cylindri buxei applicetur extremitati regulæ MN, I <lb/>fig. </s> <s xml:id="echoid-s8769" xml:space="preserve">5. </s> <s xml:id="echoid-s8770" xml:space="preserve">cum I fig. </s> <s xml:id="echoid-s8771" xml:space="preserve">6. </s> <s xml:id="echoid-s8772" xml:space="preserve">congruit, & </s> <s xml:id="echoid-s8773" xml:space="preserve">cochlea Q in o comprimit <lb/>cylindrum BD fig. </s> <s xml:id="echoid-s8774" xml:space="preserve">5.</s> <s xml:id="echoid-s8775" xml:space="preserve">, huncque firmiter cum cylindro LI <lb/>conjungit.</s> <s xml:id="echoid-s8776" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8777" xml:space="preserve">Machinæ omnes partes conjunctæ videntur in fig. </s> <s xml:id="echoid-s8778" xml:space="preserve">1.</s> <s xml:id="echoid-s8779" xml:space="preserve">; hy-<lb/>drargyrum pyxidi p infunditur, & </s> <s xml:id="echoid-s8780" xml:space="preserve">ex foramine g fig. </s> <s xml:id="echoid-s8781" xml:space="preserve">5. <lb/></s> <s xml:id="echoid-s8782" xml:space="preserve">proſilit. </s> <s xml:id="echoid-s8783" xml:space="preserve">Manente mercurio ad eandem altitudinem in pyxi-<lb/>de, & </s> <s xml:id="echoid-s8784" xml:space="preserve">non variata regulæ n m inclinatione, eadem cum ce-<lb/>leritate, juxta directionem quamcunque, proſilit hydrargy-<lb/>rum; </s> <s xml:id="echoid-s8785" xml:space="preserve">variatur autem inclinatio directionis, motu manubrii <pb o="235" file="0327" n="358" rhead="MATHEMATICA. LIB. II. CAP. VII."/> e a (EA in fig. </s> <s xml:id="echoid-s8786" xml:space="preserve">5.) </s> <s xml:id="echoid-s8787" xml:space="preserve">Angulus a directione, juxta quam mer-<lb/>curius ex foramine exit, cum horizonte formatus menſura-<lb/>tur ope quadrantis circuli diviſi q, juxta quem movetur in-<lb/>dex f b, qui pondere ſuo ſemper in ſitu verticali retinetur. <lb/></s> <s xml:id="echoid-s8788" xml:space="preserve">Quadrans hicce videtur in fig. </s> <s xml:id="echoid-s8789" xml:space="preserve">7. </s> <s xml:id="echoid-s8790" xml:space="preserve">index eſt FH. </s> <s xml:id="echoid-s8791" xml:space="preserve">A poſteriori <lb/>parte duo dantur annuli, per quos tranſit manubrium EA <lb/>fig. </s> <s xml:id="echoid-s8792" xml:space="preserve">5.</s> <s xml:id="echoid-s8793" xml:space="preserve">; quando manubrium hocce eſt in ſitu verticali, index <lb/>cum diviſione anguli 45. </s> <s xml:id="echoid-s8794" xml:space="preserve">gr. </s> <s xml:id="echoid-s8795" xml:space="preserve">congruit, & </s> <s xml:id="echoid-s8796" xml:space="preserve">directio motus mer-<lb/>curii exeuntis in eo caſu angulum ſemi-rectum cum hori-<lb/>zonte efficit.</s> <s xml:id="echoid-s8797" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8798" xml:space="preserve">In fig. </s> <s xml:id="echoid-s8799" xml:space="preserve">1. </s> <s xml:id="echoid-s8800" xml:space="preserve">proſilitiones mercurii juxta varias directiones re-<lb/>præſentantur: </s> <s xml:id="echoid-s8801" xml:space="preserve">ſenſibiles hæ redduntur ope tabulæ ligneæ G, <lb/>nigro colore tinctæ, quam mercurius in motu ſuo fere ra-<lb/>dit; </s> <s xml:id="echoid-s8802" xml:space="preserve">in hac, quod hìc repræſentari non potuit, ſecundum di-<lb/>cta in n. </s> <s xml:id="echoid-s8803" xml:space="preserve">331.</s> <s xml:id="echoid-s8804" xml:space="preserve">, delineantur viæ a corpore, eadem celeritate, <lb/>juxta directiones varios angulos cum horizonte ſormantes, <lb/>percurſæ; </s> <s xml:id="echoid-s8805" xml:space="preserve">ſemi-circulus etiam AL fig. </s> <s xml:id="echoid-s8806" xml:space="preserve">5. </s> <s xml:id="echoid-s8807" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8808" xml:space="preserve">XIII. </s> <s xml:id="echoid-s8809" xml:space="preserve">in <lb/>hac tabula deſcribitur.</s> <s xml:id="echoid-s8810" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8811" xml:space="preserve">Variæ tales tabulæ dantur, in quibus hæc eadem pro <lb/>diverſis celeritatibus repræſentantur.</s> <s xml:id="echoid-s8812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8813" xml:space="preserve">Tabula fere in medio arcæ erigitur, & </s> <s xml:id="echoid-s8814" xml:space="preserve">cohæret cum la-<lb/>tere EFH, ita ut juxta longitudinem pyxidis moveri poſ-<lb/>ſit.</s> <s xml:id="echoid-s8815" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8816" xml:space="preserve">Celeritas mercurii proſilientis variatur mutando inclina-<lb/>tionem regulæ n m, & </s> <s xml:id="echoid-s8817" xml:space="preserve">deſcenſu pyxidis p; </s> <s xml:id="echoid-s8818" xml:space="preserve">apertura, ex qua <lb/>proſilit hydrargyrum, ad altitudinem delineationi in tabula <lb/>congruentem diſponitur.</s> <s xml:id="echoid-s8819" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8820" xml:space="preserve">Siſtitur hydrargyri proſilitio obturando cavitatem a b (fig. <lb/></s> <s xml:id="echoid-s8821" xml:space="preserve">2.) </s> <s xml:id="echoid-s8822" xml:space="preserve">paxillo DE (fig. </s> <s xml:id="echoid-s8823" xml:space="preserve">4.)</s> <s xml:id="echoid-s8824" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1249" type="section" level="1" n="317"> <head xml:id="echoid-head443" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s8825" xml:space="preserve">Partibus Machinæ conjunctis, & </s> <s xml:id="echoid-s8826" xml:space="preserve">diſpoſitis, ut in deſcri-<lb/> <anchor type="note" xlink:label="note-0327-01a" xlink:href="note-0327-01"/> ptione dictum, inclinetur regula n m, donec altitudo, ad quam <lb/> <anchor type="note" xlink:label="note-0327-02a" xlink:href="note-0327-02"/> proſilit mercurius, quando directione, quæ a verticali pau-<lb/>lulum admodum divergit, in altum adſcendit, fere æquet <lb/>diametrum ſemi-circuli in tabula G delineati. </s> <s xml:id="echoid-s8827" xml:space="preserve">Ad talem <lb/>altitudinem pyxis p conſtituatur, & </s> <s xml:id="echoid-s8828" xml:space="preserve">tabula G diſponatur, <pb o="236" file="0328" n="359" rhead="PHYSICES ELEMENTA"/> ut axis circumvolutionis cylindri BD (fig. </s> <s xml:id="echoid-s8829" xml:space="preserve">5.) </s> <s xml:id="echoid-s8830" xml:space="preserve">reſpondeat <lb/>puncto infimo ſemi-circuli memorati. </s> <s xml:id="echoid-s8831" xml:space="preserve">Quomodocunque in-<lb/>clinetur jactus directio, hujus amplitudo ſemper erit fere <lb/>quadruplum lineæ BM in ſemi-circulo ABL (Tab. </s> <s xml:id="echoid-s8832" xml:space="preserve">XIII. <lb/></s> <s xml:id="echoid-s8833" xml:space="preserve">fig. </s> <s xml:id="echoid-s8834" xml:space="preserve">5.) </s> <s xml:id="echoid-s8835" xml:space="preserve">Exigua quædam datur differentia, quæ præcipue <lb/>ex aëris reſiſtentia oritur.</s> <s xml:id="echoid-s8836" xml:space="preserve"/> </p> <div xml:id="echoid-div1249" type="float" level="2" n="1"> <note position="right" xlink:label="note-0327-01" xlink:href="note-0327-01a" xml:space="preserve">818.</note> <note position="right" xlink:label="note-0327-02" xlink:href="note-0327-02a" xml:space="preserve">TAB. XXXII. <lb/>fig. 1.</note> </div> </div> <div xml:id="echoid-div1251" type="section" level="1" n="318"> <head xml:id="echoid-head444" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s8837" xml:space="preserve">Machinâ, ut in præcedenti Experimento, diſpoſitâ, ſi pro-<lb/> <anchor type="note" xlink:label="note-0328-01a" xlink:href="note-0328-01"/> ſiliat hydrargyrum per duas directiones, quarum unius incli-<lb/>natio angulum ſemi-rectum excedit, quantum alterius incli-<lb/>natio ab hoc deficit, mercurius in punctis, parum diſtanti-<lb/>bus ſecabit lineam horizontalem, quæ per ſemi-circuli, in <lb/>tabula G delineati, punctum infimum tranſit.</s> <s xml:id="echoid-s8838" xml:space="preserve"/> </p> <div xml:id="echoid-div1251" type="float" level="2" n="1"> <note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">819.</note> </div> </div> <div xml:id="echoid-div1253" type="section" level="1" n="319"> <head xml:id="echoid-head445" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s8839" xml:space="preserve">Manente Machinæ diſpoſitione, ſi via pro quacunque mo-<lb/> <anchor type="note" xlink:label="note-0328-02a" xlink:href="note-0328-02"/> tus directione in tabula, ut in Machinæ deſcriptione dictum, <lb/>delineata ſit, & </s> <s xml:id="echoid-s8840" xml:space="preserve">index f b cum diviſione quadrantis, hanc <lb/>denotans inclinationem, congruat, hydrargyrum in motu <lb/>ſuo a via delineata parum aberrabit. </s> <s xml:id="echoid-s8841" xml:space="preserve">Si pro variis angulis viæ <lb/>delineantur, motu manubrii a e ſucceſſive hoc idem in di-<lb/>verſis hiſce viis obſervari poterit.</s> <s xml:id="echoid-s8842" xml:space="preserve"/> </p> <div xml:id="echoid-div1253" type="float" level="2" n="1"> <note position="left" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">820.</note> </div> </div> <div xml:id="echoid-div1255" type="section" level="1" n="320"> <head xml:id="echoid-head446" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s8843" xml:space="preserve">Si alia tabula ut G adhibeatur, in qua prædicta pro alia <lb/> <anchor type="note" xlink:label="note-0328-03a" xlink:href="note-0328-03"/> mercurii celeritate ſunt delineata, Experimenta eodem mo-<lb/>do procedunt.</s> <s xml:id="echoid-s8844" xml:space="preserve"/> </p> <div xml:id="echoid-div1255" type="float" level="2" n="1"> <note position="left" xlink:label="note-0328-03" xlink:href="note-0328-03a" xml:space="preserve">821.</note> </div> <p> <s xml:id="echoid-s8845" xml:space="preserve">Simili methodo, qua per ſemi-circulum determinatur di-<lb/>ſtantia, ad quam corpora oblique projecta cadunt, detegitur <lb/>diſtantia, ad quam fluidum ex foramine in latere vaſis pro-<lb/>ſilit, quando vas plano horizontali imponitur: </s> <s xml:id="echoid-s8846" xml:space="preserve">diverſa eſt hæc <lb/>diſtantia pro varia foraminis altitudine, manente ſuperficie <lb/>ſuperiori fluidi.</s> <s xml:id="echoid-s8847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8848" xml:space="preserve">Sit AB vaſis fluido repleti altitudo; </s> <s xml:id="echoid-s8849" xml:space="preserve">ſecetur hæc in duas <lb/> <anchor type="note" xlink:label="note-0328-04a" xlink:href="note-0328-04"/> partes æquales in C; </s> <s xml:id="echoid-s8850" xml:space="preserve">centro C & </s> <s xml:id="echoid-s8851" xml:space="preserve">radio EA ſemi-circu-<lb/> <anchor type="note" xlink:label="note-0328-05a" xlink:href="note-0328-05"/> lus deſcribatur; </s> <s xml:id="echoid-s8852" xml:space="preserve">detur foramen in E; </s> <s xml:id="echoid-s8853" xml:space="preserve">tandem ducatur ad <lb/>AB perpendicularis ED in ſemi circuli circumferentia ter-<lb/>minata in D. </s> <s xml:id="echoid-s8854" xml:space="preserve">Proſiliat fluidum ex E ad F in plano borizon- <pb file="0329" n="360"/> <pb file="0329a" n="361"/> <anchor type="figure" xlink:label="fig-0329a-01a" xlink:href="fig-0329a-01"/> <pb file="0330" n="362"/> <pb o="237" file="0331" n="363" rhead="MATHEMATICA. LIB. II. CAP. VII."/> tali, diſtantia BF, ſepoſitis omnibus retardationibus, du-<lb/>pla erit ipſius perpendicularis ED.</s> <s xml:id="echoid-s8855" xml:space="preserve"/> </p> <div xml:id="echoid-div1256" type="float" level="2" n="2"> <note position="left" xlink:label="note-0328-04" xlink:href="note-0328-04a" xml:space="preserve">822.</note> <note position="left" xlink:label="note-0328-05" xlink:href="note-0328-05a" xml:space="preserve">TAB. XXXII. <lb/>fig. 4.</note> <figure xlink:label="fig-0329a-01" xlink:href="fig-0329a-01a"> <image file="0329a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0329a-01"/> </figure> </div> <p> <s xml:id="echoid-s8856" xml:space="preserve">Quod ut demonſtretur, conſiderandum fluidum, mo-<lb/>tu æquabili, celeritate qua ex foramine exit, in tempore <lb/>in quo corpus cadere poteſt ab E ad B, percurrere ſpatium <lb/>BF <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8857" xml:space="preserve">In omni motu, ſpatium percurſum ſequitur rationem compoſitam celeritatis & </s> <s xml:id="echoid-s8858" xml:space="preserve">temporis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8859" xml:space="preserve">& </s> <s xml:id="echoid-s8860" xml:space="preserve">hoc per illam mul- <anchor type="note" xlink:label="note-0331-01a" xlink:href="note-0331-01"/> tiplicando datur ſpatium percurſum; </s> <s xml:id="echoid-s8861" xml:space="preserve">id eſt, ſi pro variis <lb/>motibus hæc inſtituatur operatio, dantur quantitates, quæ <lb/>ſpatiorum percurſorum proportionem exprimunt. </s> <s xml:id="echoid-s8862" xml:space="preserve">Si cum <lb/>quadratis celeritatum & </s> <s xml:id="echoid-s8863" xml:space="preserve">temporum computatio ineatur, da-<lb/>bitur ratio quadratorum ſpatiorum percurſorum. </s> <s xml:id="echoid-s8864" xml:space="preserve">AE hìc de-<lb/>ſignat quadratum celeritatis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8865" xml:space="preserve">EB autem quadratum tem- poris <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s8866" xml:space="preserve">harum linearum productum exprimit ergo qua- <anchor type="note" xlink:label="note-0331-02a" xlink:href="note-0331-02"/> dratum ſpatii percurſi BF. </s> <s xml:id="echoid-s8867" xml:space="preserve">Hocce autem productum eſt <lb/> <anchor type="note" xlink:label="note-0331-03a" xlink:href="note-0331-03"/> quadratum lineæ ED; </s> <s xml:id="echoid-s8868" xml:space="preserve">quæ idcirco, mutato foramine, <lb/>creſcit & </s> <s xml:id="echoid-s8869" xml:space="preserve">minuitur in eadem ratione cum diſtantia BF. </s> <s xml:id="echoid-s8870" xml:space="preserve">Po-<lb/>ſito foramine in centro C, diſtantia BG, ad quam flui-<lb/>dum proſilit, ſepoſitis omnibus retardationibus, ipſi BA <lb/>æqualis eſt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8871" xml:space="preserve">eſt dupla perpendicularis, quæ in C ad <anchor type="note" xlink:label="note-0331-04a" xlink:href="note-0331-04"/> AB in ſemi-circulo duci poteſt; </s> <s xml:id="echoid-s8872" xml:space="preserve">quod ergo in omni-<lb/>bus foraminibus obtinet, & </s> <s xml:id="echoid-s8873" xml:space="preserve">ED erit dimidium ipſius <lb/>BF.</s> <s xml:id="echoid-s8874" xml:space="preserve"/> </p> <div xml:id="echoid-div1257" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">95.</note> <note symbol="*" position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">799.</note> <note symbol="*" position="right" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">255.</note> <note symbol="*" position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">796. 798.</note> </div> <p style="it"> <s xml:id="echoid-s8875" xml:space="preserve">Ex hiſce ſequitur fluidum ex foramine in centro C ad <lb/> <anchor type="note" xlink:label="note-0331-05a" xlink:href="note-0331-05"/> diſtantiam omnium maximam proſilire.</s> <s xml:id="echoid-s8876" xml:space="preserve"/> </p> <div xml:id="echoid-div1258" type="float" level="2" n="4"> <note position="right" xlink:label="note-0331-05" xlink:href="note-0331-05a" xml:space="preserve">823.</note> </div> </div> <div xml:id="echoid-div1260" type="section" level="1" n="321"> <head xml:id="echoid-head447" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s8877" xml:space="preserve">Utendum hìc machina in capite præcedenti deſcri-<lb/> <anchor type="note" xlink:label="note-0331-06a" xlink:href="note-0331-06"/> pta <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8878" xml:space="preserve">Proſiliat aqua ex foramine F, ut in Expe- <anchor type="note" xlink:label="note-0331-07a" xlink:href="note-0331-07"/> rimento 1. </s> <s xml:id="echoid-s8879" xml:space="preserve">Capitis VI. </s> <s xml:id="echoid-s8880" xml:space="preserve">proſiliat eodem tempore <lb/> <anchor type="note" xlink:label="note-0331-08a" xlink:href="note-0331-08"/> ex E, ut & </s> <s xml:id="echoid-s8881" xml:space="preserve">ex G; </s> <s xml:id="echoid-s8882" xml:space="preserve">foramen G minus quam F, fo-<lb/>ramen F, vero magis a ſuperficie aquæ diſtat, ex <lb/>neutro pervenit aqua ad diſtantiam ad quam ex F pro-<lb/>ſilit.</s> <s xml:id="echoid-s8883" xml:space="preserve"/> </p> <div xml:id="echoid-div1260" type="float" level="2" n="1"> <note position="right" xlink:label="note-0331-06" xlink:href="note-0331-06a" xml:space="preserve">824.</note> <note position="right" xlink:label="note-0331-07" xlink:href="note-0331-07a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0331-08" xlink:href="note-0331-08a" xml:space="preserve">797.</note> </div> <p style="it"> <s xml:id="echoid-s8884" xml:space="preserve">Ex dictis ulterius ſequitur ex foraminibus E & </s> <s xml:id="echoid-s8885" xml:space="preserve">e æque <lb/> <anchor type="note" xlink:label="note-0331-09a" xlink:href="note-0331-09"/> diſtantibus a centro C fluidum ad eandem proſilire diſtan-<lb/> <anchor type="note" xlink:label="note-0331-10a" xlink:href="note-0331-10"/> <pb o="238" file="0332" n="364" rhead="PHYSICES ELEMENTA"/> tiam, quia in eo caſu perpendiculares ED, ed ſunt æ-<lb/>quales.</s> <s xml:id="echoid-s8886" xml:space="preserve"/> </p> <div xml:id="echoid-div1261" type="float" level="2" n="2"> <note position="right" xlink:label="note-0331-09" xlink:href="note-0331-09a" xml:space="preserve">825.</note> <note position="right" xlink:label="note-0331-10" xlink:href="note-0331-10a" xml:space="preserve">TAB. XXXIII. <lb/>fig 4.</note> </div> </div> <div xml:id="echoid-div1263" type="section" level="1" n="322"> <head xml:id="echoid-head448" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s8887" xml:space="preserve">Per F concipiatur linea horizontalis, quæ tranſit per H; <lb/></s> <s xml:id="echoid-s8888" xml:space="preserve"> <anchor type="note" xlink:label="note-0332-01a" xlink:href="note-0332-01"/> HG & </s> <s xml:id="echoid-s8889" xml:space="preserve">HE ſunt æquales, & </s> <s xml:id="echoid-s8890" xml:space="preserve">ex utroque foramine G <lb/> <anchor type="note" xlink:label="note-0332-02a" xlink:href="note-0332-02"/> & </s> <s xml:id="echoid-s8891" xml:space="preserve">E aqua proſilit ad L.</s> <s xml:id="echoid-s8892" xml:space="preserve"/> </p> <div xml:id="echoid-div1263" type="float" level="2" n="1"> <note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">826.</note> <note position="left" xlink:label="note-0332-02" xlink:href="note-0332-02a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 1.</note> </div> </div> <div xml:id="echoid-div1265" type="section" level="1" n="323"> <head xml:id="echoid-head449" xml:space="preserve">CAPUT VIII.</head> <head xml:id="echoid-head450" style="it" xml:space="preserve">De Fluido ex vaſis profluente, & Irregularitatibus <lb/>in boc motu.</head> <p> <s xml:id="echoid-s8893" xml:space="preserve">FLuidi quantitas, quæ in dato tempore, ex dato forami-<lb/> <anchor type="note" xlink:label="note-0332-03a" xlink:href="note-0332-03"/> ne, fluit, ad inſtar fluidi exeuntis velocitatis creſcit: <lb/></s> <s xml:id="echoid-s8894" xml:space="preserve">pendet hæc ab altitudine fluidi ſupra foramen, & </s> <s xml:id="echoid-s8895" xml:space="preserve">non in-<lb/>tereſt quamcunque partem verſus motus fluidi dirigatur <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s8896" xml:space="preserve"> <anchor type="note" xlink:label="note-0332-04a" xlink:href="note-0332-04"/> & </s> <s xml:id="echoid-s8897" xml:space="preserve">ſepoſitis retardationibus, quadrata quantitatum effluen-<lb/>tium ſunt in ratione altitudinum fluidi ſupra foramina <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8898" xml:space="preserve"/> </p> <div xml:id="echoid-div1265" type="float" level="2" n="1"> <note position="left" xlink:label="note-0332-03" xlink:href="note-0332-03a" xml:space="preserve">827.</note> <note symbol="*" position="left" xlink:label="note-0332-04" xlink:href="note-0332-04a" xml:space="preserve">794</note> </div> <note symbol="*" position="left" xml:space="preserve">799</note> <p> <s xml:id="echoid-s8899" xml:space="preserve">In tempore in quo corpus libere cadendo percurrit alti-<lb/> <anchor type="note" xlink:label="note-0332-06a" xlink:href="note-0332-06"/> tudinem fluidi ſupra foramen, exit ex foramine, ſepoſitis <lb/>retardationibus, fluidi columna longitudine duplum altitu-<lb/>dinis hujus æquans <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s8900" xml:space="preserve">Foramen ipſum eſt baſis columnæ, <anchor type="note" xlink:label="note-0332-07a" xlink:href="note-0332-07"/> & </s> <s xml:id="echoid-s8901" xml:space="preserve">datur: </s> <s xml:id="echoid-s8902" xml:space="preserve">ſi altitudo fluidi ſupra foramen nota ſit, datur <lb/>tota columna; </s> <s xml:id="echoid-s8903" xml:space="preserve">tempus etiam facile Experimentis determi-<lb/>natur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s8904" xml:space="preserve">detecta autem quantitate, quæ in tempore <anchor type="note" xlink:label="note-0332-08a" xlink:href="note-0332-08"/> noto exit, quid, in tempore quocunque dato effluat, <lb/>non latet.</s> <s xml:id="echoid-s8905" xml:space="preserve"/> </p> <div xml:id="echoid-div1266" type="float" level="2" n="2"> <note position="left" xlink:label="note-0332-06" xlink:href="note-0332-06a" xml:space="preserve">828.</note> <note symbol="*" position="left" xlink:label="note-0332-07" xlink:href="note-0332-07a" xml:space="preserve">796. 257.</note> <note symbol="*" position="left" xlink:label="note-0332-08" xlink:href="note-0332-08a" xml:space="preserve">288.</note> </div> <p> <s xml:id="echoid-s8906" xml:space="preserve">Quantitas autem fluidi, quæ hac computatione detegi-<lb/> <anchor type="note" xlink:label="note-0332-09a" xlink:href="note-0332-09"/> tur ſenſibiliter admodum excedit illam, quæ revera exit: </s> <s xml:id="echoid-s8907" xml:space="preserve">& </s> <s xml:id="echoid-s8908" xml:space="preserve"><lb/>quod maxime notabile eſt, Experimenta quæ circa has ve-<lb/> <anchor type="note" xlink:label="note-0332-10a" xlink:href="note-0332-10"/> locitates, & </s> <s xml:id="echoid-s8909" xml:space="preserve">illa, quæ de quantitatibus fluidorum, certo tem-<lb/>pore ex foraminibus fluentium, inſtituuntur, minime reci-<lb/>porcantur; </s> <s xml:id="echoid-s8910" xml:space="preserve">& </s> <s xml:id="echoid-s8911" xml:space="preserve">non poteſt quantitas hæc ex nota velocitate <lb/>determinari.</s> <s xml:id="echoid-s8912" xml:space="preserve"/> </p> <div xml:id="echoid-div1267" type="float" level="2" n="3"> <note position="left" xlink:label="note-0332-09" xlink:href="note-0332-09a" xml:space="preserve">829.</note> <note position="left" xlink:label="note-0332-10" xlink:href="note-0332-10a" xml:space="preserve">830.</note> </div> <p> <s xml:id="echoid-s8913" xml:space="preserve">Fluidum quod juxta foraminis latera exit, attritum patitur & </s> <s xml:id="echoid-s8914" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0332-11a" xlink:href="note-0332-11"/> <pb o="239" file="0333" n="365" rhead="MATHEMATICA. LIB. II. CAP. VIII."/> retardatur, quam retardationem non patitur fluidum illud <lb/>quod ex foraminis centro irrumpit; </s> <s xml:id="echoid-s8915" xml:space="preserve">retardatur quidem hoc <lb/>a fluido laterali cum quo cohæret; </s> <s xml:id="echoid-s8916" xml:space="preserve">ſed fluidi partes facile <lb/>moventur inter ſe, & </s> <s xml:id="echoid-s8917" xml:space="preserve">retardatio hæc exigua eſt reſpectu <lb/>alterius, idcirco parum etiam acceleratur fluidum laterale a <lb/>medio, & </s> <s xml:id="echoid-s8918" xml:space="preserve">hoc continuo celerius illo movetur; </s> <s xml:id="echoid-s8919" xml:space="preserve">non tamen <lb/>a medio fluido ſeparatur laterale, nam quamvis facile juxta <lb/>ſe invicem fluidorum partes moventur, difficilius à ſe invi-<lb/>cem divelluntur; </s> <s xml:id="echoid-s8920" xml:space="preserve">fluidum ergo medium, fluxu ſuo conti-<lb/>nuo, ſecum fert laterale, quod licet lentius motum, ad e-<lb/>andem diſtantiam aut altitudinem cum medio pertingit.</s> <s xml:id="echoid-s8921" xml:space="preserve"/> </p> <div xml:id="echoid-div1268" type="float" level="2" n="4"> <note position="left" xlink:label="note-0332-11" xlink:href="note-0332-11a" xml:space="preserve">831.</note> </div> <p> <s xml:id="echoid-s8922" xml:space="preserve">Judicium autem de velocitate, niſi ex diſtantia aut alti-<lb/>tudine fertur; </s> <s xml:id="echoid-s8923" xml:space="preserve">velocitas verò quæ ſic determinatur, pau-<lb/>lulum deficit a velocitate qua fluidum ex medio foraminis <lb/>exit, quia hoc in toto motu ſuo a laterali fluido, & </s> <s xml:id="echoid-s8924" xml:space="preserve">aliis cau-<lb/>ſis, retardatur. </s> <s xml:id="echoid-s8925" xml:space="preserve">Sed multo magis excedit velocitas hæc <lb/>lateralis fluidi velocitatem, ut ex nunc explicatis ſequitur; <lb/></s> <s xml:id="echoid-s8926" xml:space="preserve">ſi quis ergo toti fluido exeunti menſuratam tribuat veloci-<lb/>tatem, quantitatem fluidi, certo tempore exeuntis, deter-<lb/>minabit veram excedentem; </s> <s xml:id="echoid-s8927" xml:space="preserve">minus tamen veram excedet <lb/>quam ſi in determinanda velocitate omnes retardationes <lb/>ſeponat, & </s> <s xml:id="echoid-s8928" xml:space="preserve">juxta regulam, in n. </s> <s xml:id="echoid-s8929" xml:space="preserve">828. </s> <s xml:id="echoid-s8930" xml:space="preserve">indicatam, compu-<lb/>tationem ineat.</s> <s xml:id="echoid-s8931" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8932" xml:space="preserve">Experimentis autem conſtat quantitates aquæ ex æquali-<lb/> <anchor type="note" xlink:label="note-0333-01a" xlink:href="note-0333-01"/> bus foraminibus, determinato tempore, exeuntes; </s> <s xml:id="echoid-s8933" xml:space="preserve">ſi per <lb/>latiores tubos aqua deducatur, & </s> <s xml:id="echoid-s8934" xml:space="preserve">per foramen in lamina <lb/>exeat, rationem ſequi a ſubduplicata altitudinis aquæ ſupra <lb/>foramen parum differentem; </s> <s xml:id="echoid-s8935" xml:space="preserve">cum verò hæc ratio non ſit ex-<lb/>acta, ſi nimium differant altitudines, regula locum non ha-<lb/>bet.</s> <s xml:id="echoid-s8936" xml:space="preserve"/> </p> <div xml:id="echoid-div1269" type="float" level="2" n="5"> <note position="right" xlink:label="note-0333-01" xlink:href="note-0333-01a" xml:space="preserve">832.</note> </div> <p> <s xml:id="echoid-s8937" xml:space="preserve">Ubi Computationes ineundæ erunt de aquæ quantitate, <lb/>quæ effluit ex foramine dato, manente altitudine aquæ ſu-<lb/>pra foramen, ſubjecta tabella uſu venire poterit, quæ ad al-<lb/>titudines majores aut minores non producenda eſt. </s> <s xml:id="echoid-s8938" xml:space="preserve">Quo <lb/>Experimento nitatur hæc & </s> <s xml:id="echoid-s8939" xml:space="preserve">quæ in computatione hu-<lb/>jus obſervanda fuere in ſcholio huic capiti ſubjecto dicam.</s> <s xml:id="echoid-s8940" xml:space="preserve"/> </p> <pb o="240" file="0334" n="366" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s8941" xml:space="preserve">Pono aquam fluere ex foramine circulari, cujus diameter <lb/>eſt ſemi pollicis Rhenolandici; </s> <s xml:id="echoid-s8942" xml:space="preserve">agitur ulterius hìc de pe-<lb/>dibus Rhenolandicis.</s> <s xml:id="echoid-s8943" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">833.</note> <note position="right" xml:space="preserve"> <lb/>Altitudo \\ Aquæ # Tempus in quo \\ pes cylindricus aquæ effluit. <lb/> 4 pedes # 52, 16. Min. S. 5 # 46, 60. 6 # 42, 59, 7 # 39, 43. 8 # 36, 89. 9 # 34, 78. 10 # 32, 99. 11 # 31, 55. 12 # 30, 12. </note> <note position="right" xml:space="preserve"> <lb/>Altitudo \\ Aquæ. # Tempus in quo \\ pes cylindricus Aquæ effluit. <lb/>13 pedes # 28, 94. Min. S. <lb/>14 # 27. 88. <lb/>15 # 26, 94. <lb/>16 # 26, 08. <lb/>17 # 25, 30 <lb/>18 # 24, 59 <lb/>19 # 23, 93. <lb/>20 # 23, 33. <lb/>21 # 22, 71. <lb/></note> <p> <s xml:id="echoid-s8944" xml:space="preserve">Si foramina differant & </s> <s xml:id="echoid-s8945" xml:space="preserve">altitudo maneat, quantitas <lb/> <anchor type="note" xlink:label="note-0334-04a" xlink:href="note-0334-04"/> fluidi quæ determinato tempore exit, ipſius foraminis ra-<lb/>tionem ſequitur, ſi in omnibus punctis foraminis æquali <lb/>velocitate fluidum feratur; </s> <s xml:id="echoid-s8946" xml:space="preserve">quod quamvis non obtineat, <lb/>parum tamen a memorata ratione aberrare quantitates, quæ <lb/>revera exeunt, experimentis cum aqua inſtitutis con-<lb/>ſtat.</s> <s xml:id="echoid-s8947" xml:space="preserve"/> </p> <div xml:id="echoid-div1270" type="float" level="2" n="6"> <note position="left" xlink:label="note-0334-04" xlink:href="note-0334-04a" xml:space="preserve">834.</note> </div> <p> <s xml:id="echoid-s8948" xml:space="preserve">Cæteris paribus, quantitates quæ effluunt, eſſe ut tempora <lb/> <anchor type="note" xlink:label="note-0334-05a" xlink:href="note-0334-05"/> clarum eſt: </s> <s xml:id="echoid-s8949" xml:space="preserve">ſunt ergo quantitates hæ generaliter in ratio-<lb/>ne compoſita temporis, foraminum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s8950" xml:space="preserve">radicum quadr atarum <anchor type="note" xlink:label="note-0334-06a" xlink:href="note-0334-06"/> altitudinum fluidi ſupra foramina <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s8951" xml:space="preserve"/> </p> <div xml:id="echoid-div1271" type="float" level="2" n="7"> <note position="left" xlink:label="note-0334-05" xlink:href="note-0334-05a" xml:space="preserve">835.</note> <note symbol="*" position="left" xlink:label="note-0334-06" xlink:href="note-0334-06a" xml:space="preserve">834.</note> </div> <note symbol="*" position="left" xml:space="preserve">832.</note> <p> <s xml:id="echoid-s8952" xml:space="preserve">In vaſis, in quibus fluidi adfluxus non datur, hujus ce-<lb/> <anchor type="note" xlink:label="note-0334-08a" xlink:href="note-0334-08"/> leritas dum effluit continuo mutatur, ad quod attenden-<lb/>dum in comparatione temporum in quibus vaſa diverſa e-<lb/>vacuantur.</s> <s xml:id="echoid-s8953" xml:space="preserve"/> </p> <div xml:id="echoid-div1272" type="float" level="2" n="8"> <note position="left" xlink:label="note-0334-08" xlink:href="note-0334-08a" xml:space="preserve">836.</note> </div> <p> <s xml:id="echoid-s8954" xml:space="preserve">Vaſa cylindricâ hìc conſideramus, & </s> <s xml:id="echoid-s8955" xml:space="preserve">dicta, ad vaſa quæ-<lb/>cunque eandem juxta integram altitudinem capacitatem <lb/>ſervantia, referri poterunt; </s> <s xml:id="echoid-s8956" xml:space="preserve">ponimus fluidum per foramen <lb/>in fundo effluere.</s> <s xml:id="echoid-s8957" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s8958" xml:space="preserve">Tempora, in quibus vaſa cylindrica, ejuſdem diametri <lb/> <anchor type="note" xlink:label="note-0334-09a" xlink:href="note-0334-09"/> & </s> <s xml:id="echoid-s8959" xml:space="preserve">altitudinis, evacuantur, fluido ex foraminibus in-<lb/>æqualibus fluente, ſunt inter ſe inverſe ut bæc fo-<lb/>ramina.</s> <s xml:id="echoid-s8960" xml:space="preserve"/> </p> <div xml:id="echoid-div1273" type="float" level="2" n="9"> <note position="left" xlink:label="note-0334-09" xlink:href="note-0334-09a" xml:space="preserve">837.</note> </div> <pb o="241" file="0335" n="367" rhead="MATHEMATICA. LIB. II. CAP VIII."/> <p> <s xml:id="echoid-s8961" xml:space="preserve">Vaſa hæc, planis ad baſin parallelis, concipiantur diviſa <lb/>in partes æquales minimas; </s> <s xml:id="echoid-s8962" xml:space="preserve">& </s> <s xml:id="echoid-s8963" xml:space="preserve">diviſiones utriuſque vaſis <lb/>non differant inter ſe; </s> <s xml:id="echoid-s8964" xml:space="preserve">cum agatur de partibus minimis, <lb/>concipi poteſt celeritatem in evacuatione unius partis non <lb/>mutari. </s> <s xml:id="echoid-s8965" xml:space="preserve">Fluidi quantitas, quæ ex foramine fluit, ſi alti-<lb/>tudo non mutetur, creſcit cum foramine & </s> <s xml:id="echoid-s8966" xml:space="preserve">eo breviori <lb/>tempore evacuatur determinata fluidi quantitas, quo fora-<lb/>men majus eſt; </s> <s xml:id="echoid-s8967" xml:space="preserve">& </s> <s xml:id="echoid-s8968" xml:space="preserve">minuitur tempus hoc in ratione qua fo-<lb/>ramen augetur. </s> <s xml:id="echoid-s8969" xml:space="preserve">Dum partes reſpondentes in vaſis e-<lb/>vacuantur altitudines ſunt æquales; </s> <s xml:id="echoid-s8970" xml:space="preserve">partes etiam i-<lb/>pſæ, & </s> <s xml:id="echoid-s8971" xml:space="preserve">ideo quantitates fluidi quæ effluunt, ſunt æ-<lb/>quales, ergo tempora in inverſa ratione foraminum; <lb/></s> <s xml:id="echoid-s8972" xml:space="preserve">quod cùm in ſingulis partibus reſpondentibus locum ha-<lb/>beat, ad tempora evacuationum integrorum vaſorum etiam <lb/>referri debet.</s> <s xml:id="echoid-s8973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8974" xml:space="preserve">Quando vaſa cylindrica ſunt inæqualia & </s> <s xml:id="echoid-s8975" xml:space="preserve">æque alta, per <lb/> <anchor type="note" xlink:label="note-0335-01a" xlink:href="note-0335-01"/> foramina æqualia, in temporibus, quæ ſunt ut cylindrorum <lb/>baſes, evacuantur. </s> <s xml:id="echoid-s8976" xml:space="preserve">Vaſa iterum in partes minimas, & </s> <s xml:id="echoid-s8977" xml:space="preserve">nu-<lb/>mero æquali in utroque vaſe, diviſa concipiantur: </s> <s xml:id="echoid-s8978" xml:space="preserve">ex par-<lb/>tibus reſpondentibus per foramina æqualia, liquidum fluit, <lb/>elevato hoc ad eandem altitudinem in utroque vaſe; </s> <s xml:id="echoid-s8979" xml:space="preserve">quan-<lb/>titates ergo quæ effluunt ſunt ut tempora; </s> <s xml:id="echoid-s8980" xml:space="preserve">& </s> <s xml:id="echoid-s8981" xml:space="preserve">ideò in hac <lb/>temporum ratione ſunt ipſæ partes reſpondentes, quæ ſunt <lb/>ut cylindrorum baſes: </s> <s xml:id="echoid-s8982" xml:space="preserve">tempora autem integrarum evacua-<lb/>tionum ſunt ut tempora in quibus partes reſpondentes e-<lb/>vacuantur.</s> <s xml:id="echoid-s8983" xml:space="preserve"/> </p> <div xml:id="echoid-div1274" type="float" level="2" n="10"> <note position="right" xlink:label="note-0335-01" xlink:href="note-0335-01a" xml:space="preserve">838.</note> </div> <p> <s xml:id="echoid-s8984" xml:space="preserve">Dentur tandem duo vaſa cylindrica EI, AD, quorum <lb/> <anchor type="note" xlink:label="note-0335-02a" xlink:href="note-0335-02"/> baſes ſunt æquales, altitudines vero diverſæ, ex. </s> <s xml:id="echoid-s8985" xml:space="preserve">gr. </s> <s xml:id="echoid-s8986" xml:space="preserve">ut 1. <lb/></s> <s xml:id="echoid-s8987" xml:space="preserve"> <anchor type="note" xlink:label="note-0335-03a" xlink:href="note-0335-03"/> ad 4. </s> <s xml:id="echoid-s8988" xml:space="preserve">& </s> <s xml:id="echoid-s8989" xml:space="preserve">evacuentur bæc per foramina æqualia: </s> <s xml:id="echoid-s8990" xml:space="preserve">concipiantur <lb/>etiam hæc vaſa planis ad baſin parallelis in partes minimas <lb/>diviſa, quales ſunt Hi, Cd; </s> <s xml:id="echoid-s8991" xml:space="preserve">ſitqueidem numerus partium in u-<lb/>troque vaſe, & </s> <s xml:id="echoid-s8992" xml:space="preserve">ſint partes inter ſe ut ipſa vaſa, id eſt, ut <lb/>1. </s> <s xml:id="echoid-s8993" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s8994" xml:space="preserve">Partes ſingulæ motu æquabili evacuantur, quia de <lb/>minimis agitur: </s> <s xml:id="echoid-s8995" xml:space="preserve">celeritates in partibus reſpondentibus ſunt <lb/>ubique ut 1. </s> <s xml:id="echoid-s8996" xml:space="preserve">ad 2. </s> <s xml:id="echoid-s8997" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, quia altitudines harum partium ſu- <anchor type="note" xlink:label="note-0335-04a" xlink:href="note-0335-04"/> pra baſes ſunt ut vaſorum altitudines, quæ ſunt ut horum <pb o="242" file="0336" n="368" rhead="PHYSICES ELEMENTA"/> numerorum quadrata. </s> <s xml:id="echoid-s8998" xml:space="preserve">Unde ſequitur tempora, in qui-<lb/>bus partes reſpondentes evacuantur, etiam eſſe inter ſe ut <lb/>unum ad duo; </s> <s xml:id="echoid-s8999" xml:space="preserve">quia in tempore duplo, celeritate dupla, <lb/>quantitas quadrupla evacuatur. </s> <s xml:id="echoid-s9000" xml:space="preserve">Cum autem tempora ſint <lb/>in eadem ratione pro ſingulis partibus reſpondentibus, tem-<lb/>pora, in quibus integra vaſa evacuantur, ſunt etiam ut <lb/>unum ad duo. </s> <s xml:id="echoid-s9001" xml:space="preserve">Si vaſa ſint ut 1 ad 9. </s> <s xml:id="echoid-s9002" xml:space="preserve">tempora, ut de-<lb/>monſtratione ſimili evincitur, erunt ut 1. </s> <s xml:id="echoid-s9003" xml:space="preserve">ad 3; </s> <s xml:id="echoid-s9004" xml:space="preserve">& </s> <s xml:id="echoid-s9005" xml:space="preserve">in gene-<lb/>re tempora ſunt ut celeritates, quibus partes reſpondentes <lb/>evacuantur, quarum celeritatum quadrata ſunt ut vaſorum <lb/>altitudines, <anchor type="note" xlink:href="" symbol="*"/> in qua ratione ergo etiam ſunt quadratatem- <anchor type="note" xlink:label="note-0336-01a" xlink:href="note-0336-01"/> porum.</s> <s xml:id="echoid-s9006" xml:space="preserve"/> </p> <div xml:id="echoid-div1275" type="float" level="2" n="11"> <note position="right" xlink:label="note-0335-02" xlink:href="note-0335-02a" xml:space="preserve">839.</note> <note position="right" xlink:label="note-0335-03" xlink:href="note-0335-03a" xml:space="preserve">TAB. XXXIII. <lb/>fig. 5. 6.</note> <note symbol="*" position="right" xlink:label="note-0335-04" xlink:href="note-0335-04a" xml:space="preserve">799.</note> <note symbol="*" position="left" xlink:label="note-0336-01" xlink:href="note-0336-01a" xml:space="preserve">799.</note> </div> </div> <div xml:id="echoid-div1277" type="section" level="1" n="324"> <head xml:id="echoid-head451" xml:space="preserve"><emph style="sc">Experimentum i.</emph></head> <p> <s xml:id="echoid-s9007" xml:space="preserve">Dentur ex metallo tenui tria vaſa cylindrica A, C, B, <lb/> <anchor type="note" xlink:label="note-0336-02a" xlink:href="note-0336-02"/> diametros æquales habentia, & </s> <s xml:id="echoid-s9008" xml:space="preserve">quorum altitudines ſunt ut <lb/> <anchor type="note" xlink:label="note-0336-03a" xlink:href="note-0336-03"/> unum, tria, & </s> <s xml:id="echoid-s9009" xml:space="preserve">quatuor; </s> <s xml:id="echoid-s9010" xml:space="preserve">unumquodque inciſionem in ora ha-<lb/>beat, qua effluit aqua certam ſuperans altitudinem, quæ pro <lb/>vaſis altitudine habetur; </s> <s xml:id="echoid-s9011" xml:space="preserve">in fundis vaſorum A & </s> <s xml:id="echoid-s9012" xml:space="preserve">B, quæ <lb/>ſunt ut unum & </s> <s xml:id="echoid-s9013" xml:space="preserve">quatuor, foramina æqualia dentur, & </s> <s xml:id="echoid-s9014" xml:space="preserve">a-<lb/>quà impleantur; </s> <s xml:id="echoid-s9015" xml:space="preserve">eodem momento foramina aperiantur; </s> <s xml:id="echoid-s9016" xml:space="preserve">ſi <lb/>aqua ex B fluens vaſe C recipiatur, impletur hoc in tem-<lb/>pore in quo A evacuatur: </s> <s xml:id="echoid-s9017" xml:space="preserve">C continet tres partes quartas <lb/>vaſis B; </s> <s xml:id="echoid-s9018" xml:space="preserve">partem quartam, quæ ſupereſt, æquali etiamtem-<lb/>pore cum vaſe A evacuari, a nemine in dubium vocari po-<lb/>teſt; </s> <s xml:id="echoid-s9019" xml:space="preserve">bis ergo evacuatur A, dum B ſemel.</s> <s xml:id="echoid-s9020" xml:space="preserve"/> </p> <div xml:id="echoid-div1277" type="float" level="2" n="1"> <note position="left" xlink:label="note-0336-02" xlink:href="note-0336-02a" xml:space="preserve">840.</note> <note position="left" xlink:label="note-0336-03" xlink:href="note-0336-03a" xml:space="preserve">TAB. XXXIII. <lb/>fig 7.</note> </div> <p style="it"> <s xml:id="echoid-s9021" xml:space="preserve">Tempora, in quibus vaſa cylindrica quæcunque evacuan-<lb/> <anchor type="note" xlink:label="note-0336-04a" xlink:href="note-0336-04"/> tur, ſunt in ratione compoſita baſium <anchor type="note" xlink:href="" symbol="*"/>, inverſa forami- <anchor type="note" xlink:label="note-0336-05a" xlink:href="note-0336-05"/> num <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s9022" xml:space="preserve">radicum quadratarum altitudinum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9023" xml:space="preserve"/> </p> <div xml:id="echoid-div1278" type="float" level="2" n="2"> <note position="left" xlink:label="note-0336-04" xlink:href="note-0336-04a" xml:space="preserve">841.</note> <note symbol="*" position="left" xlink:label="note-0336-05" xlink:href="note-0336-05a" xml:space="preserve">838.</note> </div> <note symbol="*" position="left" xml:space="preserve">837.</note> <note symbol="*" position="left" xml:space="preserve">839.</note> <p> <s xml:id="echoid-s9024" xml:space="preserve">Dividi ita poteſt, vas cylindricum, ut partes inter diviſio-<lb/> <anchor type="note" xlink:label="note-0336-08a" xlink:href="note-0336-08"/> nes interceptæ æqualibus temporibus evacuentur, quod <lb/> <anchor type="note" xlink:label="note-0336-09a" xlink:href="note-0336-09"/> fiet, ſi diviſionum a baſi diſtantiæ fuerint ut numerorum na-<lb/>turalium quadrata; </s> <s xml:id="echoid-s9025" xml:space="preserve">tempora enim evacuationum vaſorum, <lb/>quorum altitudines hanc ſequuntur proportionem, ſunt <lb/>ut numeri naturales <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s9026" xml:space="preserve">temporum differentiæ æqua- <anchor type="note" xlink:label="note-0336-10a" xlink:href="note-0336-10"/> les.</s> <s xml:id="echoid-s9027" xml:space="preserve"/> </p> <div xml:id="echoid-div1279" type="float" level="2" n="3"> <note position="left" xlink:label="note-0336-08" xlink:href="note-0336-08a" xml:space="preserve">842.</note> <note position="left" xlink:label="note-0336-09" xlink:href="note-0336-09a" xml:space="preserve">TAB. XXXIII. <lb/>fig 6.</note> <note symbol="*" position="left" xlink:label="note-0336-10" xlink:href="note-0336-10a" xml:space="preserve">839.</note> </div> <p> <s xml:id="echoid-s9028" xml:space="preserve">Tempus in quo vas cylindricum evacuatur eſt ut celeri- <pb o="243" file="0337" n="369" rhead="MATHEMATICA. LIB. II. CAP. VIII."/> tas cum qua fluidum effluere inchoat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9029" xml:space="preserve">celeritas ergo, <anchor type="note" xlink:label="note-0337-01a" xlink:href="note-0337-01"/> dum fluidum in vaſe deſcendit, in eadem ratione minui-<lb/>tur, cum tempore evacuationis fluidi in vaſe ſuperſtitis; </s> <s xml:id="echoid-s9030" xml:space="preserve">& </s> <s xml:id="echoid-s9031" xml:space="preserve"><lb/>motus fluidi, ex vaſe cylindrico fluentis, eſt retardatus æqua-<lb/> <anchor type="note" xlink:label="note-0337-02a" xlink:href="note-0337-02"/> liter in temporibus æqualibus.</s> <s xml:id="echoid-s9032" xml:space="preserve"/> </p> <div xml:id="echoid-div1280" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0337-01" xlink:href="note-0337-01a" xml:space="preserve">839. 792.</note> <note position="right" xlink:label="note-0337-02" xlink:href="note-0337-02a" xml:space="preserve">843.</note> </div> <p> <s xml:id="echoid-s9033" xml:space="preserve">Si ex cylindro, & </s> <s xml:id="echoid-s9034" xml:space="preserve">alio vaſe ejuſdem altitudinis, & </s> <s xml:id="echoid-s9035" xml:space="preserve">flui-<lb/> <anchor type="note" xlink:label="note-0337-03a" xlink:href="note-0337-03"/> dum ſemper ad eandem altitudinem continenti, per for amina <lb/>æqualia fluat fluidum, in tempore in quo evacuatur cylin-<lb/>drus, ex vaſe memorato fluit dupla fluidi quantitas quàm ex <lb/>cylindro. </s> <s xml:id="echoid-s9036" xml:space="preserve">Nam, propter altitudines vaſorum æquales, ce-<lb/>leritates in principio ſunt æquales; </s> <s xml:id="echoid-s9037" xml:space="preserve">fluidi, quod ex vaſe ſem-<lb/>per repleto exit, celeritas eſt æquabilis; </s> <s xml:id="echoid-s9038" xml:space="preserve">celeritas fluidi, ex <lb/>cylindro fluentis, eſt æquabiliter retardata <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9039" xml:space="preserve">Idcirco ex <anchor type="note" xlink:label="note-0337-04a" xlink:href="note-0337-04"/> iſto vaſe, dum cylindrus evacuatur, fluet dupla aquæ <lb/>quantitas quàm ex cylindro. </s> <s xml:id="echoid-s9040" xml:space="preserve">Si enim duo corpora eadem <lb/>celeritate propellantur, & </s> <s xml:id="echoid-s9041" xml:space="preserve">primum motu æquabili progre-<lb/>diatur, ſecundum autem motu æquabiliter retardato, & </s> <s xml:id="echoid-s9042" xml:space="preserve"><lb/>moveantur donec hoc totum motum amiſerit, primum in eo <lb/>tempore percurret ſpatium duplum ſpatii a ſecundo percur-<lb/>ſi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9043" xml:space="preserve">hìc fluidum, quod effluit, pro ſpatio percurſo haberi <anchor type="note" xlink:label="note-0337-05a" xlink:href="note-0337-05"/> poteſt, quia foramina ſunt æqualia.</s> <s xml:id="echoid-s9044" xml:space="preserve"/> </p> <div xml:id="echoid-div1281" type="float" level="2" n="5"> <note position="right" xlink:label="note-0337-03" xlink:href="note-0337-03a" xml:space="preserve">844.</note> <note symbol="*" position="right" xlink:label="note-0337-04" xlink:href="note-0337-04a" xml:space="preserve">843.</note> <note symbol="*" position="right" xlink:label="note-0337-05" xlink:href="note-0337-05a" xml:space="preserve">258. 259. <lb/>257.</note> </div> <p> <s xml:id="echoid-s9045" xml:space="preserve">Notavimus ſupra partium cohæſionem motum fluidorum <lb/> <anchor type="note" xlink:label="note-0337-06a" xlink:href="note-0337-06"/> retardare, contrarium etiam in multis occaſionibus obſer-<lb/>vamus; </s> <s xml:id="echoid-s9046" xml:space="preserve">& </s> <s xml:id="echoid-s9047" xml:space="preserve">licet velocitas ex preſſione oriunda, quaſcunque <lb/>partes verſus eadem ſit, omnium tamen celerrime movetur <lb/>fluidum, dum verticaliter deſcendit; </s> <s xml:id="echoid-s9048" xml:space="preserve">hoc in motu ſuo ca-<lb/>dendo continuo acceleratur, cum inſequenti cohæret & </s> <s xml:id="echoid-s9049" xml:space="preserve">ſe-<lb/>cum quaſi trahit, velocitatemque fluidi ex vaſe profluentis <lb/>auget.</s> <s xml:id="echoid-s9050" xml:space="preserve"/> </p> <div xml:id="echoid-div1282" type="float" level="2" n="6"> <note position="right" xlink:label="note-0337-06" xlink:href="note-0337-06a" xml:space="preserve">845.</note> </div> <p> <s xml:id="echoid-s9051" xml:space="preserve">Circa aquam quædam obſervabo, quia cum hac experi-<lb/>menta fuere ſumta, quamvis hæc ipſa etiam ad alia fluida <lb/>applicari poſſint, magiſque in fluidis glutinoſis hæc ſenſi-<lb/>bilia forent de quibus tamen hìc non agitur.</s> <s xml:id="echoid-s9052" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9053" xml:space="preserve">Motus ex vaſe, cum quo in inferiori parte tubus con-<lb/> <anchor type="note" xlink:label="note-0337-07a" xlink:href="note-0337-07"/> jungitur, etiam acceleratur. </s> <s xml:id="echoid-s9054" xml:space="preserve">Sit vas tale E æquale & </s> <s xml:id="echoid-s9055" xml:space="preserve">ſi-<lb/> <anchor type="note" xlink:label="note-0337-08a" xlink:href="note-0337-08"/> mile vaſi A, & </s> <s xml:id="echoid-s9056" xml:space="preserve">quod cum tubo altitudinem habeat vaſis B;</s> <s xml:id="echoid-s9057" xml:space="preserve"> <pb o="244" file="0338" n="370" rhead="PHYSICES ELEMENTA"/> habeat tubus aperturas ambas æquales foraminibus in fundis <lb/>vaſorum A & </s> <s xml:id="echoid-s9058" xml:space="preserve">B; </s> <s xml:id="echoid-s9059" xml:space="preserve">impleantur aquâ vaſa <emph style="sc">A</emph>, E, & </s> <s xml:id="echoid-s9060" xml:space="preserve">B. </s> <s xml:id="echoid-s9061" xml:space="preserve">In <lb/>principio motus, ex vaſis A & </s> <s xml:id="echoid-s9062" xml:space="preserve">E æquali celeritate aqua <lb/>fluit, quia ex tubo non major fluere poteſt aquæ quantitas, <lb/>quam quæ tubum per aperturam ſuperiorem intrat, quem <lb/>major aquæ quantitas ingredi nequit, quam quæ ex vaſe A <lb/>fluere poteſt. </s> <s xml:id="echoid-s9063" xml:space="preserve">Sed aqua quæ per tubum deſcendit accele-<lb/>ratur, & </s> <s xml:id="echoid-s9064" xml:space="preserve">cum integram tubi capacitatem repleat; </s> <s xml:id="echoid-s9065" xml:space="preserve">magis a-<lb/>quam inſequentem ſecum trahit quàm ſublato tubo, tunc <lb/>enim tenuior fit continuò columna aquæ effluentis. </s> <s xml:id="echoid-s9066" xml:space="preserve">Aqua <lb/>autem quæ per tubum fluit, dum inſequentem accelerat, ab <lb/>hac retardatur; </s> <s xml:id="echoid-s9067" xml:space="preserve">quare aquæ quantitas, quæ certo tempore ex <lb/>vaſe E effluit, eſt media inter aquæ quantitates, quæ ex vaſis <lb/><emph style="sc">A</emph> & </s> <s xml:id="echoid-s9068" xml:space="preserve">B, eodem tempore fluere poſſunt.</s> <s xml:id="echoid-s9069" xml:space="preserve"/> </p> <div xml:id="echoid-div1283" type="float" level="2" n="7"> <note position="right" xlink:label="note-0337-07" xlink:href="note-0337-07a" xml:space="preserve">846.</note> <note position="right" xlink:label="note-0337-08" xlink:href="note-0337-08a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 7.</note> </div> </div> <div xml:id="echoid-div1285" type="section" level="1" n="325"> <head xml:id="echoid-head452" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s9070" xml:space="preserve">Vaſis A, E, & </s> <s xml:id="echoid-s9071" xml:space="preserve">B, ſecundum proportiones memoratas, ex <lb/> <anchor type="note" xlink:label="note-0338-01a" xlink:href="note-0338-01"/> metallo tenui conſtructis; </s> <s xml:id="echoid-s9072" xml:space="preserve">aquâ impleantur A & </s> <s xml:id="echoid-s9073" xml:space="preserve">E; </s> <s xml:id="echoid-s9074" xml:space="preserve">eodem <lb/>momento apertis foraminibus, celerius deſcendet aquæ ſu-<lb/>perficies in E quàm in A: </s> <s xml:id="echoid-s9075" xml:space="preserve">contra adhibitis vaſis E & </s> <s xml:id="echoid-s9076" xml:space="preserve">B, ce-<lb/>lerius deſcendit in hoc quàm in illo.</s> <s xml:id="echoid-s9077" xml:space="preserve"/> </p> <div xml:id="echoid-div1285" type="float" level="2" n="1"> <note position="left" xlink:label="note-0338-01" xlink:href="note-0338-01a" xml:space="preserve">847.</note> </div> <p> <s xml:id="echoid-s9078" xml:space="preserve">Maneat apertura ſuperior tubi, qua cum vaſe tubus com-<lb/> <anchor type="note" xlink:label="note-0338-02a" xlink:href="note-0338-02"/> municationem babet; </s> <s xml:id="echoid-s9079" xml:space="preserve">augeatur apertura inferior; </s> <s xml:id="echoid-s9080" xml:space="preserve">major a-<lb/>quæ quantitas effluet, & </s> <s xml:id="echoid-s9081" xml:space="preserve">magis accelerabitur aqua, quæ tu-<lb/>bum intrat; </s> <s xml:id="echoid-s9082" xml:space="preserve">ſatiſque poteſt augeri hæc apertura, non mu-<lb/>tata tubi longitudine, ut ex ipſa major aquæ quantitas fluat <lb/>quam ex vaſe B. </s> <s xml:id="echoid-s9083" xml:space="preserve">In hoc caſu, per aperturam tubi ſupe-<lb/>riorem ad parvam infra aquæ ſuperficiem profunditatem, <lb/>major fluit aquæ quantitas quàm ex apertura æquali ad <lb/>profunditatem quadruplam. </s> <s xml:id="echoid-s9084" xml:space="preserve">Adhibito longiori tubo, 1-<lb/>dem præſtari poterit, licet non augeatur tubi apertura in-<lb/>ferior.</s> <s xml:id="echoid-s9085" xml:space="preserve"/> </p> <div xml:id="echoid-div1286" type="float" level="2" n="2"> <note position="left" xlink:label="note-0338-02" xlink:href="note-0338-02a" xml:space="preserve">848.</note> </div> </div> <div xml:id="echoid-div1288" type="section" level="1" n="326"> <head xml:id="echoid-head453" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s9086" xml:space="preserve">Sit vas F, a vaſe E in eo ſolo differens, quod apertura <lb/> <anchor type="note" xlink:label="note-0338-03a" xlink:href="note-0338-03"/> tubi inferior in illo major ſit; </s> <s xml:id="echoid-s9087" xml:space="preserve">ſit etiam vas antea memoratum <lb/> <anchor type="note" xlink:label="note-0338-04a" xlink:href="note-0338-04"/> B. </s> <s xml:id="echoid-s9088" xml:space="preserve">Diametri foraminis in hujus fundo, & </s> <s xml:id="echoid-s9089" xml:space="preserve">aperturæ ſuperio-<lb/>ris tubi cum vaſe P conjuncti, ſunt 4. </s> <s xml:id="echoid-s9090" xml:space="preserve">lin.</s> <s xml:id="echoid-s9091" xml:space="preserve">; apertura inferior <pb o="245" file="0339" n="371" rhead="MATHEMATICA. LIB. II. CAP. VIII."/> hujus tubi eſt 5. </s> <s xml:id="echoid-s9092" xml:space="preserve">lin. </s> <s xml:id="echoid-s9093" xml:space="preserve">Aquâ vaſa impleantur; </s> <s xml:id="echoid-s9094" xml:space="preserve">& </s> <s xml:id="echoid-s9095" xml:space="preserve">eodem mo-<lb/>mento fluat ex utroque; </s> <s xml:id="echoid-s9096" xml:space="preserve">citius aquæ ſuperficies in vaſe F <lb/>quàm in B deſcendet. </s> <s xml:id="echoid-s9097" xml:space="preserve">Altitudo vaſis B eſt circiter ſede-<lb/>cim pollicum.</s> <s xml:id="echoid-s9098" xml:space="preserve"/> </p> <div xml:id="echoid-div1288" type="float" level="2" n="1"> <note position="left" xlink:label="note-0338-03" xlink:href="note-0338-03a" xml:space="preserve">849.</note> <note position="left" xlink:label="note-0338-04" xlink:href="note-0338-04a" xml:space="preserve">TAB. XXXIII. <lb/>fig 2.</note> </div> <p> <s xml:id="echoid-s9099" xml:space="preserve">His Experimentis duo alia notabilia admodum circa par-<lb/>tium cohæ ſionem ſubjungam, quibus effectus hujus cohæ-<lb/>ſionis dilucidantur.</s> <s xml:id="echoid-s9100" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1290" type="section" level="1" n="327"> <head xml:id="echoid-head454" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s9101" xml:space="preserve">Antliæ, duæ æquales A, B, junguntur fruſto æneo G; </s> <s xml:id="echoid-s9102" xml:space="preserve">huic <lb/> <anchor type="note" xlink:label="note-0339-01a" xlink:href="note-0339-01"/> tubi duo E da, F db inſeruntur, quorum hic cum antlia <lb/> <anchor type="note" xlink:label="note-0339-02a" xlink:href="note-0339-02"/> B, ille cum A communicatur. </s> <s xml:id="echoid-s9103" xml:space="preserve">Tuborum horum axes in eo-<lb/>dem plano dantur, & </s> <s xml:id="echoid-s9104" xml:space="preserve">ſeſe mutuo ad angulos rectos ſecant, <lb/>confundunturque tubi in d.</s> <s xml:id="echoid-s9105" xml:space="preserve"/> </p> <div xml:id="echoid-div1290" type="float" level="2" n="1"> <note position="right" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">850.</note> <note position="right" xlink:label="note-0339-02" xlink:href="note-0339-02a" xml:space="preserve">TAB. XXXV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s9106" xml:space="preserve">Antlia A repletur aquâ rubro, aut alio colore, tinctâ, B <lb/>repletur aquâ purâ; </s> <s xml:id="echoid-s9107" xml:space="preserve">emboli junguntur laminâ L, quæ con-<lb/>chleis firmatur & </s> <s xml:id="echoid-s9108" xml:space="preserve">ſimul intruduntur. </s> <s xml:id="echoid-s9109" xml:space="preserve">Tincta aqua viam ſe-<lb/>quitur E db, alia viam F da, & </s> <s xml:id="echoid-s9110" xml:space="preserve">vix ſenſibilis aquarum per <lb/>mixtio datur, dum in d juxta ſe invicem tranſeunt, & </s> <s xml:id="echoid-s9111" xml:space="preserve">vias <lb/>flectunt.</s> <s xml:id="echoid-s9112" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1292" type="section" level="1" n="328"> <head xml:id="echoid-head455" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s9113" xml:space="preserve">Differt Experimentum hoc a præcedenti in unicâ circum-<lb/> <anchor type="note" xlink:label="note-0339-03a" xlink:href="note-0339-03"/> ſtantia, effectus tamen diverſus omnino eſt. </s> <s xml:id="echoid-s9114" xml:space="preserve">Tuborum <lb/> <anchor type="note" xlink:label="note-0339-04a" xlink:href="note-0339-04"/> E da, F db, axes non in eodem dantur plano, ſed unius axis <lb/>alterius cavitatem quaſi tangit ita, ut pro parte tantum tu-<lb/>bi confundantur in d. </s> <s xml:id="echoid-s9115" xml:space="preserve">Intruſis nunc embolis, colorata a-<lb/>qua, quæ pro parte libere tranſit per E da omnem aliam <lb/>coloratam ſecum trahit; </s> <s xml:id="echoid-s9116" xml:space="preserve">dum eodem modo aqua pura per <lb/>F db fertur; </s> <s xml:id="echoid-s9117" xml:space="preserve">his vix ſenſibiliter permixtis quamvis juxta ſe <lb/>invicem aquæ in d tranſeant.</s> <s xml:id="echoid-s9118" xml:space="preserve"/> </p> <div xml:id="echoid-div1292" type="float" level="2" n="1"> <note position="right" xlink:label="note-0339-03" xlink:href="note-0339-03a" xml:space="preserve">851.</note> <note position="right" xlink:label="note-0339-04" xlink:href="note-0339-04a" xml:space="preserve">TAB. XXXV. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s9119" xml:space="preserve">Experimentum hoc celebrem auctorem in errorem indu-<lb/>xit, qui hoc ipſum inſtituit experimentum, cum in animum <lb/>haberet præcedens tentare, concluſionemque deduxit am-<lb/>bobus experimentis contrariam; </s> <s xml:id="echoid-s9120" xml:space="preserve">fluidi particulas liberrime <lb/>ſine confuſione inter alîus fluidi particulas viam continuare, <lb/>agitato licet hoc fluido juxta aliam directionem.</s> <s xml:id="echoid-s9121" xml:space="preserve"/> </p> <pb o="246" file="0340" n="372" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1294" type="section" level="1" n="329"> <head xml:id="echoid-head456" xml:space="preserve">SCHOLIUM.</head> <p> <s xml:id="echoid-s9122" xml:space="preserve">DIxi me in hoc ſcholio explicaturum, ex quo experimento, & </s> <s xml:id="echoid-s9123" xml:space="preserve">quomodo, <lb/>computatio tabulæ n. </s> <s xml:id="echoid-s9124" xml:space="preserve">833. </s> <s xml:id="echoid-s9125" xml:space="preserve">fuerit inita.</s> <s xml:id="echoid-s9126" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9127" xml:space="preserve">Mariotte Experimento, variis vicibus repetito, obſervatisque cautelis ne-<lb/> <anchor type="note" xlink:label="note-0340-01a" xlink:href="note-0340-01"/> ceſſariis, determinavit ex foramine, cujus diameter erat {1/4} poll.</s> <s xml:id="echoid-s9128" xml:space="preserve">, ſervatâ aquæ <lb/>altitudine ſupra hoc 13. </s> <s xml:id="echoid-s9129" xml:space="preserve">ped.</s> <s xml:id="echoid-s9130" xml:space="preserve">, ſingulis vicibus effluxiſſe, in uno minuto pri-<lb/>mo, pintas 28.</s> <s xml:id="echoid-s9131" xml:space="preserve">, quarum pes cubicus continet 70. </s> <s xml:id="echoid-s9132" xml:space="preserve">Agitur hîc de pede regio <lb/>Gallico, qui ad pedem Rhenolandicum ſe habet ut 144. </s> <s xml:id="echoid-s9133" xml:space="preserve">ad 139.</s> <s xml:id="echoid-s9134" xml:space="preserve"/> </p> <div xml:id="echoid-div1294" type="float" level="2" n="1"> <note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">852.</note> </div> <p> <s xml:id="echoid-s9135" xml:space="preserve">Dato hoc experimento detegendum in quo tempore pes cylindricus eva-<lb/>cuari poteſt, per foramen cujus diameter eſt ſemi poll.</s> <s xml:id="echoid-s9136" xml:space="preserve">, poſitâ etiam aquæ <lb/>altitudine ſupra hoc 13. </s> <s xml:id="echoid-s9137" xml:space="preserve">pedum, # dum # menſura # Rhenolandica ad-<lb/>hibetur.</s> <s xml:id="echoid-s9138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9139" xml:space="preserve">Tempus quo certa aquæ quantitas evacuatur, eo brevius eſt quo major <lb/> <anchor type="note" xlink:label="note-0340-02a" xlink:href="note-0340-02"/> quantitas determinato tempore exit; </s> <s xml:id="echoid-s9140" xml:space="preserve">tempora ergo ſunt inverſe ut hæ quanti-<lb/>tates, quæ cæteris paribus ſunt in ratione ſubduplicata altitudinum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9141" xml:space="preserve"/> </p> <div xml:id="echoid-div1295" type="float" level="2" n="2"> <note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">853.</note> </div> <note symbol="*" position="left" xml:space="preserve">832.</note> <p> <s xml:id="echoid-s9142" xml:space="preserve">Tempora etiam ſunt eo minora quo foramina majora, id eſt, cæteris pa-<lb/>ribus ſunt in ratione inverſa quadratorum diametrorum foraminum.</s> <s xml:id="echoid-s9143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9144" xml:space="preserve">Tandem, cæteris paribus, tempora ſunt directe ut quantitates quæ effiuunt.</s> <s xml:id="echoid-s9145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9146" xml:space="preserve">In experimento à Mariotte inſtituto, altitudo tredecim pedum Gallicorum <lb/>eſt ad altitudinem totidem pedum Rhenolandicorum in caſu de quo agitur, <lb/>ut 144. </s> <s xml:id="echoid-s9147" xml:space="preserve">ad. </s> <s xml:id="echoid-s9148" xml:space="preserve">139.</s> <s xml:id="echoid-s9149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9150" xml:space="preserve">Quadrata diametrorum foraminum ſunt ut 1. </s> <s xml:id="echoid-s9151" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s9152" xml:space="preserve">& </s> <s xml:id="echoid-s9153" xml:space="preserve">ut <emph style="ol">144.</emph><emph style="super">q</emph> ad <emph style="ol">132.</emph><emph style="super">q</emph></s> </p> <p> <s xml:id="echoid-s9154" xml:space="preserve">Quantitates aquæ ſunt, ut pintæ 28. </s> <s xml:id="echoid-s9155" xml:space="preserve">ad pedem cylindricum Rhenolandi-<lb/>cum; </s> <s xml:id="echoid-s9156" xml:space="preserve">quæ quantitates ſunt in ratione compoſita, rationis 28. </s> <s xml:id="echoid-s9157" xml:space="preserve">ad 70. </s> <s xml:id="echoid-s9158" xml:space="preserve">aut 14. <lb/></s> <s xml:id="echoid-s9159" xml:space="preserve">ad 35, id eſt, quantitatis quæ effluxit ad pedem cubicum Gallicum, rationis pe-<lb/>dis cubici Gallici ad pedem cubicum Rhenolandicum, & </s> <s xml:id="echoid-s9160" xml:space="preserve">rationis pedis cu-<lb/>bici ad pedem cylindricum, aut 452. </s> <s xml:id="echoid-s9161" xml:space="preserve">ad 355.</s> <s xml:id="echoid-s9162" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9163" xml:space="preserve">Idcirco tempus unius minuti primi, aut 60. </s> <s xml:id="echoid-s9164" xml:space="preserve">m. </s> <s xml:id="echoid-s9165" xml:space="preserve">ſ.</s> <s xml:id="echoid-s9166" xml:space="preserve">, ad tempus quæſi-<lb/>tum, in ratione compoſita ex hiſce ſex rationibus, √139.</s> <s xml:id="echoid-s9167" xml:space="preserve">\x{0020} ad √144\x{0020}, 4. </s> <s xml:id="echoid-s9168" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s9169" xml:space="preserve">, <lb/><emph style="ol">139.</emph><emph style="super">q</emph> ad <emph style="ol">144.</emph><emph style="super">q</emph>, 14. </s> <s xml:id="echoid-s9170" xml:space="preserve">ad 35.</s> <s xml:id="echoid-s9171" xml:space="preserve">, <emph style="ol">144.</emph><emph style="super">c</emph> ad <emph style="ol">139.</emph><emph style="super">c</emph>, & </s> <s xml:id="echoid-s9172" xml:space="preserve">452. </s> <s xml:id="echoid-s9173" xml:space="preserve">ad. </s> <s xml:id="echoid-s9174" xml:space="preserve">355.</s> <s xml:id="echoid-s9175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9176" xml:space="preserve">Rationes prima, tertia, & </s> <s xml:id="echoid-s9177" xml:space="preserve">quinta, reducuntur ad rationem, √144.</s> <s xml:id="echoid-s9178" xml:space="preserve">\x{0020} ad <lb/>√139\x{0020}; </s> <s xml:id="echoid-s9179" xml:space="preserve">& </s> <s xml:id="echoid-s9180" xml:space="preserve">ſunt 60. </s> <s xml:id="echoid-s9181" xml:space="preserve">m. </s> <s xml:id="echoid-s9182" xml:space="preserve">ſ. </s> <s xml:id="echoid-s9183" xml:space="preserve">ad tempus quæſitum, ut 4 x 14 x 452 x 12. </s> <s xml:id="echoid-s9184" xml:space="preserve">ad <lb/> <anchor type="note" xlink:label="note-0340-04a" xlink:href="note-0340-04"/> 1 x 35 x 355 x √139.</s> <s xml:id="echoid-s9185" xml:space="preserve">\x{0020} quod tempus detegitur 28, 94. </s> <s xml:id="echoid-s9186" xml:space="preserve">m. </s> <s xml:id="echoid-s9187" xml:space="preserve">ſ. </s> <s xml:id="echoid-s9188" xml:space="preserve">Quo tempore dato <lb/>reliqua quæ notantur in tabella n. </s> <s xml:id="echoid-s9189" xml:space="preserve">833. </s> <s xml:id="echoid-s9190" xml:space="preserve">deteguntur quærendo numeros in ra-<lb/>tione inverſa ſubduplicata altitudinum.</s> <s xml:id="echoid-s9191" xml:space="preserve"/> </p> <div xml:id="echoid-div1296" type="float" level="2" n="3"> <note position="left" xlink:label="note-0340-04" xlink:href="note-0340-04a" xml:space="preserve">854.</note> </div> </div> <div xml:id="echoid-div1298" type="section" level="1" n="330"> <head xml:id="echoid-head457" xml:space="preserve">CAPUT IX.</head> <head xml:id="echoid-head458" style="it" xml:space="preserve">De Curſu Fluminum.</head> <head xml:id="echoid-head459" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s9192" xml:space="preserve">FLumen vocamus aquam, in canali ſuperius aperto, pro-<lb/> <anchor type="note" xlink:label="note-0340-05a" xlink:href="note-0340-05"/> pria gravitate fluentem, ut A E. <lb/></s> <s xml:id="echoid-s9193" xml:space="preserve"> <anchor type="note" xlink:label="note-0340-06a" xlink:href="note-0340-06"/> </s> </p> <div xml:id="echoid-div1298" type="float" level="2" n="1"> <note position="left" xlink:label="note-0340-05" xlink:href="note-0340-05a" xml:space="preserve">855.</note> <note position="left" xlink:label="note-0340-06" xlink:href="note-0340-06a" xml:space="preserve">TAB XXXIV. <lb/>fig. 1.</note> </div> <pb file="0341" n="373"/> <pb file="0341a" n="374"/> <figure> <image file="0341a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0341a-01"/> </figure> <pb file="0342" n="375"/> <pb o="247" file="0343" n="376" rhead="MATHEMATICA. LIB. II. CAP. IX."/> </div> <div xml:id="echoid-div1300" type="section" level="1" n="331"> <head xml:id="echoid-head460" xml:space="preserve"><emph style="sc">Definitio.</emph> 2.</head> <p style="it"> <s xml:id="echoid-s9194" xml:space="preserve">Flumen in eodem ſtatu manere, aut in ſtatu manente, <lb/> <anchor type="note" xlink:label="note-0343-01a" xlink:href="note-0343-01"/> dicitur, quando aqua uniformiter fluit, ita ut in eodem lo-<lb/>co ſemper ſit ad eandem altitudinem.</s> <s xml:id="echoid-s9195" xml:space="preserve"/> </p> <div xml:id="echoid-div1300" type="float" level="2" n="1"> <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">856.</note> </div> </div> <div xml:id="echoid-div1302" type="section" level="1" n="332"> <head xml:id="echoid-head461" xml:space="preserve"><emph style="sc">Definitio.</emph> 3.</head> <p style="it"> <s xml:id="echoid-s9196" xml:space="preserve">Sectio Fluminis vocatur planum Flumen ſecans perpen-<lb/> <anchor type="note" xlink:label="note-0343-02a" xlink:href="note-0343-02"/> diculariter ad fundum, & </s> <s xml:id="echoid-s9197" xml:space="preserve">ad quæ directionem in medio, ut <lb/>ponq.</s> <s xml:id="echoid-s9198" xml:space="preserve"/> </p> <div xml:id="echoid-div1302" type="float" level="2" n="1"> <note position="right" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">857.</note> </div> <p> <s xml:id="echoid-s9199" xml:space="preserve">Quando Flumen a lateribus terminatur, planis inter ſe pa-<lb/>rallelis, & </s> <s xml:id="echoid-s9200" xml:space="preserve">ad horizontem normalibus, & </s> <s xml:id="echoid-s9201" xml:space="preserve">fundus etiam eſt <lb/>planum, ſive horizontale, ſive inclinatum, ſectio Fluminis <lb/>cum tribus hiſce planis angulos rectos efficit, & </s> <s xml:id="echoid-s9202" xml:space="preserve">eſt paralle-<lb/>logrammum.</s> <s xml:id="echoid-s9203" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9204" xml:space="preserve">In omni Flumine in ſtatu manente, eadem aquæ quantitas <lb/> <anchor type="note" xlink:label="note-0343-03a" xlink:href="note-0343-03"/> per ſingulas ſectiones eodem tempore fluit. </s> <s xml:id="echoid-s9205" xml:space="preserve">Niſi enim in lo-<lb/>co quocunque eadem aquæ quantitas adfluat, quæ ex eo <lb/>defluit, in eodem ſtatu Flumen non manebit; </s> <s xml:id="echoid-s9206" xml:space="preserve">& </s> <s xml:id="echoid-s9207" xml:space="preserve">demon-<lb/>ſtratio hæc locum habet, quæcunque fuerit alvei irregula-<lb/>ritas, ex qua, alio reſpectu, multæ in Fluminis motu mu-<lb/>tationes oriuntur; </s> <s xml:id="echoid-s9208" xml:space="preserve">attritus ex. </s> <s xml:id="echoid-s9209" xml:space="preserve">gr. </s> <s xml:id="echoid-s9210" xml:space="preserve">major eſt pro majore al-<lb/>vei inæqualitate.</s> <s xml:id="echoid-s9211" xml:space="preserve"/> </p> <div xml:id="echoid-div1303" type="float" level="2" n="2"> <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">858.</note> </div> <p> <s xml:id="echoid-s9212" xml:space="preserve">Irregularitates in Fluminis motu in infinitum variari <lb/>poſſunt, & </s> <s xml:id="echoid-s9213" xml:space="preserve">regulæ circa illas tradi nequeunt; </s> <s xml:id="echoid-s9214" xml:space="preserve">ſepoſitis <lb/>ergo irregularitatibus omnibus Fluminum curſus exami-<lb/>nandus eſt; </s> <s xml:id="echoid-s9215" xml:space="preserve">niſi enim in hoc caſu motus leges notæ fue-<lb/>rint, de nullo judicium, vero fundamento nixum, ferri <lb/>poterit.</s> <s xml:id="echoid-s9216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9217" xml:space="preserve">Ponimus ergo aquam fluere per canalem regularem, ſi-<lb/> <anchor type="note" xlink:label="note-0343-04a" xlink:href="note-0343-04"/> ne ſenſibili attritu; </s> <s xml:id="echoid-s9218" xml:space="preserve">canalem terminari ad latera planis pa-<lb/>rallelis inter ſe & </s> <s xml:id="echoid-s9219" xml:space="preserve">verticalibus; </s> <s xml:id="echoid-s9220" xml:space="preserve">fundumque etiam planum <lb/>eſſe & </s> <s xml:id="echoid-s9221" xml:space="preserve">ad horizontem inclinari.</s> <s xml:id="echoid-s9222" xml:space="preserve"/> </p> <div xml:id="echoid-div1304" type="float" level="2" n="3"> <note position="right" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">859.</note> </div> <p> <s xml:id="echoid-s9223" xml:space="preserve">Sit canalis A E; </s> <s xml:id="echoid-s9224" xml:space="preserve">ex receptaculo majori aqua in illum <lb/>fluat, maneatque in receptaculo ſemper ad eandem altitu-<lb/>dinem, ut Flumen ſit in ſtatu manenti. </s> <s xml:id="echoid-s9225" xml:space="preserve">Aqua juxta pla-<lb/>num inclinatum deſcendit & </s> <s xml:id="echoid-s9226" xml:space="preserve">acceleratur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9227" xml:space="preserve">quo, propter <anchor type="note" xlink:label="note-0343-05a" xlink:href="note-0343-05"/> æqualem aquæ quantitatem per ſingulas ſectiones fluen- <pb o="248" file="0344" n="377" rhead="PHYSICES ELEMENTA"/> tem <anchor type="note" xlink:href="" symbol="*"/>, altitudo aquæ, recedendo a Fluminis initio.</s> <s xml:id="echoid-s9228" xml:space="preserve">, con- <anchor type="note" xlink:label="note-0344-01a" xlink:href="note-0344-01"/> tinuo minuitur, & </s> <s xml:id="echoid-s9229" xml:space="preserve">aquæ ſuperſicies adipiſcitur figuram iqs.</s> <s xml:id="echoid-s9230" xml:space="preserve"/> </p> <div xml:id="echoid-div1305" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0343-05" xlink:href="note-0343-05a" xml:space="preserve">263.</note> <note symbol="*" position="left" xlink:label="note-0344-01" xlink:href="note-0344-01a" xml:space="preserve">858.</note> </div> <note position="left" xml:space="preserve">860.</note> <p> <s xml:id="echoid-s9231" xml:space="preserve">Ad determinandam aquæ in variis locis velocitatem, con-<lb/> <anchor type="note" xlink:label="note-0344-03a" xlink:href="note-0344-03"/> cipiamus canalis aperturam ADCB plano claudi; </s> <s xml:id="echoid-s9232" xml:space="preserve">ſi perfo-<lb/>retur planum, eo celerius ex foramine proſiliet aqua, quo <lb/>magis hoc diſtabit a ſuperficie aquæ bi; </s> <s xml:id="echoid-s9233" xml:space="preserve">eandemque habe-<lb/>bit aqua celeritatem, quam corpus, cadendo a ſuperficie <lb/>aquæ ad profunditatem foraminis infra illam, acquirit <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s9234" xml:space="preserve"> <anchor type="note" xlink:label="note-0344-04a" xlink:href="note-0344-04"/> quod ex preſſione aquæ ſuperincumbentis oritur. </s> <s xml:id="echoid-s9235" xml:space="preserve">Datur <lb/>eadem preſſio, id eſt, eadem vis motrix, quando impedi-<lb/>mentum in AC tollitur; </s> <s xml:id="echoid-s9236" xml:space="preserve">ponimus enim capax adeo rece-<lb/>ptaculum, ut & </s> <s xml:id="echoid-s9237" xml:space="preserve">in hoc caſu preſſio lateralis agat in aquam <lb/>quæ canalem intrat.</s> <s xml:id="echoid-s9238" xml:space="preserve"/> </p> <div xml:id="echoid-div1306" type="float" level="2" n="5"> <note position="left" xlink:label="note-0344-03" xlink:href="note-0344-03a" xml:space="preserve">861.</note> <note symbol="*" position="left" xlink:label="note-0344-04" xlink:href="note-0344-04a" xml:space="preserve">796.</note> </div> <p> <s xml:id="echoid-s9239" xml:space="preserve">Hunc nunc ingreditur unaquæque particula aquæ ea <lb/>celeritate, quam corpus acquirit, cadendo ab aquæ ſuperfi-<lb/>cie ad particulæ profunditatem. </s> <s xml:id="echoid-s9240" xml:space="preserve">Particula hæc, juxta pla-<lb/>num inclinatum, in canale movetur, & </s> <s xml:id="echoid-s9241" xml:space="preserve">hujus motus acce-<lb/>leratur; </s> <s xml:id="echoid-s9242" xml:space="preserve">& </s> <s xml:id="echoid-s9243" xml:space="preserve">quidem eodem modo ac ſi verticaliter cadendo <lb/>motum continuaſſet ad eandem profunditatem infra ſuper-<lb/>ficiem aquæ in origine Fluminis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9244" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">271.</note> <p> <s xml:id="echoid-s9245" xml:space="preserve">Si ducatur horizontalis linea it, particula in r habebit <lb/>celeritatem quam corpus cadendo per i C & </s> <s xml:id="echoid-s9246" xml:space="preserve">devolvendo <lb/>per Cr poteſt acquirere; </s> <s xml:id="echoid-s9247" xml:space="preserve">quæ eſt celeritas, caſu per tr, a <lb/>corpore acquiſita. </s> <s xml:id="echoid-s9248" xml:space="preserve">Vbique ergo menſuratur particulæ cele-<lb/> <anchor type="note" xlink:label="note-0344-06a" xlink:href="note-0344-06"/> ritas, ducendo ab hac perpendicularem ad planum horizon-<lb/>tale, quod per ſuperficiem aquæ in origine Fluminis concipi-<lb/>tur, & </s> <s xml:id="echoid-s9249" xml:space="preserve">velocitas, quam corpus per hanc perpendicularem ca-<lb/>dendo acquirit, erit particulæ celeritas, quæ major eſt pro <lb/>majori perpendicularis longitudine, & </s> <s xml:id="echoid-s9250" xml:space="preserve">non augetur preſſione <lb/> <anchor type="note" xlink:label="note-0344-07a" xlink:href="note-0344-07"/> aquæ ſuper incumbentis, quæ non poteſt augere celeritatem <lb/>aquæ, quæ aliunde majorem habet quam quæ ex hac preſ-<lb/>ſione oriri poteſt: </s> <s xml:id="echoid-s9251" xml:space="preserve">eodem modo ac corpus inſequens in an-<lb/>tecedens celerius motum agere non poteſt.</s> <s xml:id="echoid-s9252" xml:space="preserve"/> </p> <div xml:id="echoid-div1307" type="float" level="2" n="6"> <note position="left" xlink:label="note-0344-06" xlink:href="note-0344-06a" xml:space="preserve">862.</note> <note position="left" xlink:label="note-0344-07" xlink:href="note-0344-07a" xml:space="preserve">863.</note> </div> <p> <s xml:id="echoid-s9253" xml:space="preserve">In puncto quocunque r ad Fluminis fundum ducatur per-<lb/>pendicularis rs, Fluminis altitudinem menſurans; </s> <s xml:id="echoid-s9254" xml:space="preserve">cum non <lb/>horizontalis ſit rs, ſi a variis hujus lineæ punctis ad it per- <pb o="249" file="0345" n="378" rhead="MATHEMATICA. LIB. II. CAP. IX."/> pendiculares ducantur, eo hæ breviores erunt, quo magis <lb/>ab r diſtabunt, omniumque breviſſima erit sv; </s> <s xml:id="echoid-s9255" xml:space="preserve">ideoque <lb/>particularum, in linea rs, celeritates eo minores ſunt, quo <lb/>magis hæ ad ſuperficiem Fluminis accedunt, & </s> <s xml:id="echoid-s9256" xml:space="preserve">aqua infe-<lb/> <anchor type="note" xlink:label="note-0345-01a" xlink:href="note-0345-01"/> rior celerius ſuperiori movetur.</s> <s xml:id="echoid-s9257" xml:space="preserve"/> </p> <div xml:id="echoid-div1308" type="float" level="2" n="7"> <note position="right" xlink:label="note-0345-01" xlink:href="note-0345-01a" xml:space="preserve">864.</note> </div> <p> <s xml:id="echoid-s9258" xml:space="preserve">Harum tamen aquarum in progreſſu fluminis ad æqualita-<lb/> <anchor type="note" xlink:label="note-0345-02a" xlink:href="note-0345-02"/> tem continuo magis accedunt celeritates. </s> <s xml:id="echoid-s9259" xml:space="preserve">Nam celeritatum <lb/>harum quadrata ſunt ut rt ad sv, quarum linearum dif-<lb/>ferentia, recedendo a fluminis origine, continuo minuitur, <lb/>propter imminutam altitudinem rs<anchor type="note" xlink:href="" symbol="*"/>, dum lineæ ipſæ au- <anchor type="note" xlink:label="note-0345-03a" xlink:href="note-0345-03"/> gentur. </s> <s xml:id="echoid-s9260" xml:space="preserve">Quod cum in quadratis obtineat, multo magis in <lb/>ipſis celeritatibus locum habet, quarum differentia ergo et-<lb/>iam minuitur, dum ipſæ creſcunt.</s> <s xml:id="echoid-s9261" xml:space="preserve"/> </p> <div xml:id="echoid-div1309" type="float" level="2" n="8"> <note position="right" xlink:label="note-0345-02" xlink:href="note-0345-02a" xml:space="preserve">865.</note> <note symbol="*" position="right" xlink:label="note-0345-03" xlink:href="note-0345-03a" xml:space="preserve">860.</note> </div> <p> <s xml:id="echoid-s9262" xml:space="preserve">Si fundi inclinatio in principio fluminis mutetur ut ſit <lb/> <anchor type="note" xlink:label="note-0345-04a" xlink:href="note-0345-04"/> yZ, & </s> <s xml:id="echoid-s9263" xml:space="preserve">major aquæ quantitas in canalem fluat, altior erit <lb/>ubique in flumine, ſed non mutatur celeritas aquæ in loco quo-<lb/>cunque. </s> <s xml:id="echoid-s9264" xml:space="preserve">Hæc enim celeritas non ab altitudine aquæ in flu-<lb/>mine pendet, ſed, ut demonſtratum, a diſtantia inter par-<lb/>riculam motam & </s> <s xml:id="echoid-s9265" xml:space="preserve">planum horizontale per aquæ ſu-<lb/>perficiem in origine fluminis tranſiens; </s> <s xml:id="echoid-s9266" xml:space="preserve">quæ diſtantia per-<lb/>pendiculari ut rt aut sv menſuratur; </s> <s xml:id="echoid-s9267" xml:space="preserve">hæ autem adfluxu a-<lb/>quæ non variantur, ſi modo maneat aquæ ſuperficies in re-<lb/>ceptaculo.</s> <s xml:id="echoid-s9268" xml:space="preserve"/> </p> <div xml:id="echoid-div1310" type="float" level="2" n="9"> <note position="right" xlink:label="note-0345-04" xlink:href="note-0345-04a" xml:space="preserve">866.</note> </div> <p> <s xml:id="echoid-s9269" xml:space="preserve">Claudatur canalis pars ſuperior obſtaculo ut X, quod quan-<lb/> <anchor type="note" xlink:label="note-0345-05a" xlink:href="note-0345-05"/> tumvis parum infra aquæ ſuperficiem deſcendat; </s> <s xml:id="echoid-s9270" xml:space="preserve">aqua o-<lb/>mnis quæ adfluit perfluere non poterit, adſcendet idcirco; <lb/></s> <s xml:id="echoid-s9271" xml:space="preserve">ſed eo celeritas aquæ infra cataractam non augetur <anchor type="note" xlink:href="" symbol="*"/>, con- <anchor type="note" xlink:label="note-0345-06a" xlink:href="note-0345-06"/> tinuoque accumulatur aqua adfluens; </s> <s xml:id="echoid-s9272" xml:space="preserve">quæ ergo ita <lb/>adſcendit ut ſupra impedimentum aut ripas fluminis de-<lb/>fluat. </s> <s xml:id="echoid-s9273" xml:space="preserve">Si vero ripæ eleventur & </s> <s xml:id="echoid-s9274" xml:space="preserve">impedimentum continue-<lb/>tur, ſupra lineam it aquæ altitudo excreſcet, antea enim <lb/>hujus celeritas augeri nequit: </s> <s xml:id="echoid-s9275" xml:space="preserve">in quo caſu totius aquæ in <lb/>receptaculo altitudo augebitur; </s> <s xml:id="echoid-s9276" xml:space="preserve">cum enim ponamus <lb/>flumen in ſtatu manenti neceſſe eſt ut aliunde continuo in <lb/>receptaculum tantum aquæ adfluat, quantum ex illo in flu-<lb/>men defluit; </s> <s xml:id="echoid-s9277" xml:space="preserve">imminuta verò aquæ defluentis quantitate, <pb o="250" file="0346" n="379" rhead="PHYSICES ELEMENTA"/> neceſſario altitudo in receptaculo augetur, donec celeritas <lb/>aquæ infra obſtaculum fluentis ita augeatur, ut eadem <lb/>aquæ quantitas infra hocce obſtaculum tranſeat, quæ <lb/>ante poſitam cataractam per hanc fluminis ſectionem flu-<lb/>xit.</s> <s xml:id="echoid-s9278" xml:space="preserve"/> </p> <div xml:id="echoid-div1311" type="float" level="2" n="10"> <note position="right" xlink:label="note-0345-05" xlink:href="note-0345-05a" xml:space="preserve">867.</note> <note symbol="*" position="right" xlink:label="note-0345-06" xlink:href="note-0345-06a" xml:space="preserve">866.</note> </div> <p> <s xml:id="echoid-s9279" xml:space="preserve">Hæc omnia, ut jam monuimus, ſepoſitis irregularitati-<lb/>bus omnibus, vera ſunt, & </s> <s xml:id="echoid-s9280" xml:space="preserve">quo irregularitates ſunt mino-<lb/>res, eo magis cum dictis motus veri congruunt; </s> <s xml:id="echoid-s9281" xml:space="preserve">de qui-<lb/>bus ut judicium feratur, neceſſe eſt ut Experimentis velo-<lb/>citates aquarum poſſimus comparare, & </s> <s xml:id="echoid-s9282" xml:space="preserve">ipſas velocitates i-<lb/>ta determinare, ut ſpatia in certo tempore percurſa dete-<lb/>gantur; </s> <s xml:id="echoid-s9283" xml:space="preserve">hæc autem detegere poterimus ſi in ſubſidium vo-<lb/>cemus, quæ in Capite <emph style="sc">XI</emph>. </s> <s xml:id="echoid-s9284" xml:space="preserve">de fluidorum actionibus demon-<lb/>ſtrantur.</s> <s xml:id="echoid-s9285" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9286" xml:space="preserve">Sit circuli quadrans ACB in gradus diviſus; </s> <s xml:id="echoid-s9287" xml:space="preserve">in centro <lb/> <anchor type="note" xlink:label="note-0346-01a" xlink:href="note-0346-01"/> ei annectitur filum, cujus extremitas altera cum globo P, <lb/> <anchor type="note" xlink:label="note-0346-02a" xlink:href="note-0346-02"/> aquâ graviori, cohæret.</s> <s xml:id="echoid-s9288" xml:space="preserve"/> </p> <div xml:id="echoid-div1312" type="float" level="2" n="11"> <note position="left" xlink:label="note-0346-01" xlink:href="note-0346-01a" xml:space="preserve">868.</note> <note position="left" xlink:label="note-0346-02" xlink:href="note-0346-02a" xml:space="preserve">TAB. XXXIV. <lb/>fig 2.</note> </div> <p> <s xml:id="echoid-s9289" xml:space="preserve">Aquâ fluenti globus immergitur, ſervato latere CA qua-<lb/> <anchor type="note" xlink:label="note-0346-03a" xlink:href="note-0346-03"/> drantis in ſitu verticali; </s> <s xml:id="echoid-s9290" xml:space="preserve">globus actione aquæ ita ſuſtinetur, <lb/>ut filum PC cum latere CA angulum PCA conſtituat, <lb/>cujus ope aquæ in globum impingentis celeritas detegi-<lb/>tur.</s> <s xml:id="echoid-s9291" xml:space="preserve"/> </p> <div xml:id="echoid-div1313" type="float" level="2" n="12"> <note position="left" xlink:label="note-0346-03" xlink:href="note-0346-03a" xml:space="preserve">869.</note> </div> <p> <s xml:id="echoid-s9292" xml:space="preserve">Globus in aqua quieſcens tribus potentiis trahitur; </s> <s xml:id="echoid-s9293" xml:space="preserve">gra-<lb/>vitate ſua verticaliter deſcendere conatur; </s> <s xml:id="echoid-s9294" xml:space="preserve">ex fluidi actio-<lb/>ne juxta motus aquæ directionem fertur; </s> <s xml:id="echoid-s9295" xml:space="preserve">& </s> <s xml:id="echoid-s9296" xml:space="preserve">tandem filo per <lb/>PC trahitur, Formetur triangulum EFG, in quo EF <lb/>lineam verticalem deſignat, cum hac conſtituat linea FG <lb/>angulum EFG, æqualem angulo a directione motus flu-<lb/>minis cum linea verticali formato, tandem ſit angulus GEF <lb/>æqualis angulo PCA. </s> <s xml:id="echoid-s9297" xml:space="preserve">Trianguli EFG latera parallela <lb/>ſunt directionibus trium memoratarum potentiarum, po-<lb/>tentiæ ipſæ idcirco ſunt ut hæc latera <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9298" xml:space="preserve">ſi ergo EF globi <anchor type="note" xlink:label="note-0346-04a" xlink:href="note-0346-04"/> gravitatem reſpectivam deſignat, FG exprimet actionem <lb/>aquæ in globum. </s> <s xml:id="echoid-s9299" xml:space="preserve">Si pro variis Experimentis, eodem adhi-<lb/>bito globo, variis in locis inſtitutis, talia triangula deline-<lb/>antur, latere EF manente, (gravitatem globi reſpectivam, <pb o="251" file="0347" n="380" rhead="MATHEMATICA. LIB. II. CAP. IX."/> quæ non mutatur, deſignante) latera ut FG inter ſe pro-<lb/>portionem actionum aquæ in globum ſervabunt. </s> <s xml:id="echoid-s9300" xml:space="preserve">Hæ au-<lb/>tem ſunt ut quadrata velocitatum aquarum in locis <lb/>in quibus Experimenta inſtituta ſunt ut in cap. </s> <s xml:id="echoid-s9301" xml:space="preserve"><emph style="sc">XI</emph>. </s> <s xml:id="echoid-s9302" xml:space="preserve">videbi-<lb/>mus.</s> <s xml:id="echoid-s9303" xml:space="preserve"/> </p> <div xml:id="echoid-div1314" type="float" level="2" n="13"> <note symbol="*" position="left" xlink:label="note-0346-04" xlink:href="note-0346-04a" xml:space="preserve">210</note> </div> <p> <s xml:id="echoid-s9304" xml:space="preserve">Actio aquæ in globum cum pondere conferri poteſt, eſt <lb/> <anchor type="note" xlink:label="note-0347-01a" xlink:href="note-0347-01"/> enim ad globi pondus reſpectivum ut FG ad EF.</s> <s xml:id="echoid-s9305" xml:space="preserve"/> </p> <div xml:id="echoid-div1315" type="float" level="2" n="14"> <note position="right" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">870.</note> </div> <p> <s xml:id="echoid-s9306" xml:space="preserve">Pondusque hac proportione detectum eſt pondus cy-<lb/>lindri aquei, cujusbaſeos diameter eſt globi diameter, & </s> <s xml:id="echoid-s9307" xml:space="preserve">cujus <lb/>altitudo illa eſt, a qua cadendo in vacuo corpus acquirit ve-<lb/>locitatem qua aqua in globum incurrit; </s> <s xml:id="echoid-s9308" xml:space="preserve">ut hoc etiam in cap. <lb/></s> <s xml:id="echoid-s9309" xml:space="preserve"><emph style="sc">XI</emph>. </s> <s xml:id="echoid-s9310" xml:space="preserve">demonſtramus. </s> <s xml:id="echoid-s9311" xml:space="preserve">Data nunc hac altitudine, dabitur (ſi du-<lb/>ratio vibrationis penduli cujuſcunque, cujus longitudo no-<lb/>ta eſt, determinata fuerit) ſpatium, quod ab aqua in tem-<lb/>pore noto poteſt percurri<anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s9312" xml:space="preserve">ſicetiam aquæ quantitas quæ <anchor type="note" xlink:label="note-0347-02a" xlink:href="note-0347-02"/> per locum magnitudine datum, in fluminis ſectione, in <lb/>dato tempore, fluit.</s> <s xml:id="echoid-s9313" xml:space="preserve"/> </p> <div xml:id="echoid-div1316" type="float" level="2" n="15"> <note symbol="*" position="right" xlink:label="note-0347-02" xlink:href="note-0347-02a" xml:space="preserve">288. 255. 257.</note> </div> <p> <s xml:id="echoid-s9314" xml:space="preserve">Notandum hanc velocitatis aquæ determinationem non <lb/>bene procedere in aquæ ſuperficie; </s> <s xml:id="echoid-s9315" xml:space="preserve">quia actio aquæ <lb/>in globum ibi irregularis eſt. </s> <s xml:id="echoid-s9316" xml:space="preserve">Poteſt hæc celeri-<lb/> <anchor type="note" xlink:label="note-0347-03a" xlink:href="note-0347-03"/> tas detegi immergendo aquâ corpus, aquâ paululum levius, <lb/>quod verſus ſuperficiem hæreat, & </s> <s xml:id="echoid-s9317" xml:space="preserve">non ſatis hanc excedat <lb/>ut motu venti affici poſſit; </s> <s xml:id="echoid-s9318" xml:space="preserve">cum gravitates ſpecificæ aquæ <lb/>& </s> <s xml:id="echoid-s9319" xml:space="preserve">corporis vix differant, & </s> <s xml:id="echoid-s9320" xml:space="preserve">hoc pro toto immerſo haberi <lb/>poſſit, eadem celeritate cum aqua movebitur, & </s> <s xml:id="echoid-s9321" xml:space="preserve">menſura-<lb/>ri tempus, ope penduli, poterit, dum corpus ſpatium an-<lb/>te menſuratum percurrit. </s> <s xml:id="echoid-s9322" xml:space="preserve">Quando vento aquæ ſuperfi-<lb/>cies agitatur, non bene Experimentum procedet, pro-<lb/>pter motum undarum, quo in corporis motu irregularitas <lb/>datur.</s> <s xml:id="echoid-s9323" xml:space="preserve"/> </p> <div xml:id="echoid-div1317" type="float" level="2" n="16"> <note position="right" xlink:label="note-0347-03" xlink:href="note-0347-03a" xml:space="preserve">871.</note> </div> <pb o="252" file="0348" n="381" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1319" type="section" level="1" n="333"> <head xml:id="echoid-head462" xml:space="preserve">CAPUT X.</head> <head xml:id="echoid-head463" style="it" xml:space="preserve">De Motu Undarum.</head> <p> <s xml:id="echoid-s9324" xml:space="preserve">AQuæ quieſcentis ſuperficies plana eſt & </s> <s xml:id="echoid-s9325" xml:space="preserve">ad horizontem <lb/> <anchor type="note" xlink:label="note-0348-01a" xlink:href="note-0348-01"/> parallela <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9326" xml:space="preserve">ſi aliqua ex cauſa hæc cava fiat in A, cir- <anchor type="note" xlink:label="note-0348-02a" xlink:href="note-0348-02"/> cumdatur hæc cavitas elevatione BB; </s> <s xml:id="echoid-s9327" xml:space="preserve">elevata hæc aqua <lb/> <anchor type="note" xlink:label="note-0348-03a" xlink:href="note-0348-03"/> gravitate deſcendit, & </s> <s xml:id="echoid-s9328" xml:space="preserve">celeritate deſcendendo acquiſita ca-<lb/>vitatem novam format, quo motu aqua ad latera hujus ca-<lb/>vitatis adſcendit, & </s> <s xml:id="echoid-s9329" xml:space="preserve">implet cavitatem A, dum nova ele-<lb/>vatio C verſus formatur; </s> <s xml:id="echoid-s9330" xml:space="preserve">hæc dum deprimitur de novo a-<lb/>qua eandem partem verſus adſcendit; </s> <s xml:id="echoid-s9331" xml:space="preserve">unde motus in aquæ <lb/>ſuperficie oritur, & </s> <s xml:id="echoid-s9332" xml:space="preserve">cavitas, præ ſe elevationem ferens, <lb/>ab A ad C movetur.</s> <s xml:id="echoid-s9333" xml:space="preserve"/> </p> <div xml:id="echoid-div1319" type="float" level="2" n="1"> <note position="left" xlink:label="note-0348-01" xlink:href="note-0348-01a" xml:space="preserve">872.</note> <note position="left" xlink:label="note-0348-02" xlink:href="note-0348-02a" xml:space="preserve">TAB XXXIV. <lb/>fig. 3.</note> <note symbol="*" position="left" xlink:label="note-0348-03" xlink:href="note-0348-03a" xml:space="preserve">707.</note> </div> </div> <div xml:id="echoid-div1321" type="section" level="1" n="334"> <head xml:id="echoid-head464" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s9334" xml:space="preserve">Cavitas hæc cum conjuncta elevatione vocatur unda</s> </p> <note position="left" xml:space="preserve">873.</note> </div> <div xml:id="echoid-div1322" type="section" level="1" n="335"> <head xml:id="echoid-head465" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s9335" xml:space="preserve">Latitudo undæ eſt ſpatium ab unda in ſuperficie aquæ <lb/> <anchor type="note" xlink:label="note-0348-05a" xlink:href="note-0348-05"/> occupatum & </s> <s xml:id="echoid-s9336" xml:space="preserve">menſuratum juxta motus undæ directionem.</s> <s xml:id="echoid-s9337" xml:space="preserve"/> </p> <div xml:id="echoid-div1322" type="float" level="2" n="1"> <note position="left" xlink:label="note-0348-05" xlink:href="note-0348-05a" xml:space="preserve">874.</note> </div> <p> <s xml:id="echoid-s9338" xml:space="preserve">Cavitas ut A ab omni parte elevatione circumdatur, & </s> <s xml:id="echoid-s9339" xml:space="preserve"><lb/>motus memoratus omnes partes verſus ſeſe expandit; </s> <s xml:id="echoid-s9340" xml:space="preserve">un-<lb/> <anchor type="note" xlink:label="note-0348-06a" xlink:href="note-0348-06"/> dæ ideo per circulum moventur.</s> <s xml:id="echoid-s9341" xml:space="preserve"/> </p> <div xml:id="echoid-div1323" type="float" level="2" n="2"> <note position="left" xlink:label="note-0348-06" xlink:href="note-0348-06a" xml:space="preserve">875.</note> </div> <p> <s xml:id="echoid-s9342" xml:space="preserve">Detur obſtaculum AB, in quod unda, cujus origo eſt <lb/> <anchor type="note" xlink:label="note-0348-07a" xlink:href="note-0348-07"/> in C, incurrat; </s> <s xml:id="echoid-s9343" xml:space="preserve">examinandum quam in puncto quocunque <lb/> <anchor type="note" xlink:label="note-0348-08a" xlink:href="note-0348-08"/> ut E mutationem patiatur unda, quando in hoc puncto ad <lb/>obſtaculum pervenit. </s> <s xml:id="echoid-s9344" xml:space="preserve">In omnibus locis, per quæ unda tranſ-<lb/>it, dum hæc latitudinem ſuam percurrit, aqua elevatur, <lb/>cavitas deinde formatur, quæ iterum impletur; </s> <s xml:id="echoid-s9345" xml:space="preserve">quam mu-<lb/>tationem dum ſuperficies aquæ ſubit, hujus particulæ per <lb/>parvum ſpatium eunt & </s> <s xml:id="echoid-s9346" xml:space="preserve">redeunt. </s> <s xml:id="echoid-s9347" xml:space="preserve">Directio hujus motus <lb/>eſt per CE, celeritaſque per hanc lineam repræſentari po-<lb/>teſt; </s> <s xml:id="echoid-s9348" xml:space="preserve">concipiatur hicce motus in duos alios reſolutus per <lb/>GE & </s> <s xml:id="echoid-s9349" xml:space="preserve">DE, quorum celeritates per haſce lineas reſpecti-<lb/>ve repræſentantur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9350" xml:space="preserve">Motu per DE particulæ in obſtacu- <anchor type="note" xlink:label="note-0348-09a" xlink:href="note-0348-09"/> lum non agunt, & </s> <s xml:id="echoid-s9351" xml:space="preserve">eadem celeritate, poſt impactum, jux-<lb/>ta hanc directionem motum continuant; </s> <s xml:id="echoid-s9352" xml:space="preserve">motuſque hic re- <pb o="253" file="0349" n="382" rhead="MATHEMATICA. LIB. II. CAP. X."/> præſentatur per EF, poſit is EF & </s> <s xml:id="echoid-s9353" xml:space="preserve">ED inter ſe æqualibus. </s> <s xml:id="echoid-s9354" xml:space="preserve">Mo-<lb/>tu per GE particulæ directe ad obſtaculum accedunt, & </s> <s xml:id="echoid-s9355" xml:space="preserve">aqua, <lb/>quæ ultra obſtaculum progredi nequit, & </s> <s xml:id="echoid-s9356" xml:space="preserve">ab inſequenti <lb/>propellitur, cedit illam partem verſus in qua minima reſi-<lb/>ſtentia datur, id eſt, adſcendit; </s> <s xml:id="echoid-s9357" xml:space="preserve">hæcque major quam in <lb/>cæteris locis elevatio ex motu per GE oritur; </s> <s xml:id="echoid-s9358" xml:space="preserve">quia hoc <lb/>motu ſolo ad obſtaculum particulæ accedunt. </s> <s xml:id="echoid-s9359" xml:space="preserve">Deſcenſu a-<lb/>qua eam acquirit velocitatem cum qua fuit elevata, & </s> <s xml:id="echoid-s9360" xml:space="preserve">ea-<lb/>dem cum vi particulæ aqueæ ab obſtaculo juxta directio-<lb/>nem EG repelluntur cum qua ad obſtaculum acceſſere. <lb/></s> <s xml:id="echoid-s9361" xml:space="preserve">Ex hoc motu & </s> <s xml:id="echoid-s9362" xml:space="preserve">motu memorato per EF oritur motus <lb/>per EH, cujus celeritas per lineam EH, æqualem <lb/>lineæ CE, deſignatur, & </s> <s xml:id="echoid-s9363" xml:space="preserve">reflexione celeritas undæ non <lb/>mutatur; </s> <s xml:id="echoid-s9364" xml:space="preserve">reditque hæc per EH, eodem modo ac ſublato <lb/>obſtaculo per Eb motum continuaſſet. </s> <s xml:id="echoid-s9365" xml:space="preserve">Si a C perpendi-<lb/>cularis CD ducatur ad obſtaculum, & </s> <s xml:id="echoid-s9366" xml:space="preserve">hæc producatur, <lb/>fiatque Dc æqualis CD, linea HE continuata tranſibit per <lb/>c; </s> <s xml:id="echoid-s9367" xml:space="preserve">& </s> <s xml:id="echoid-s9368" xml:space="preserve">cum hæc demonſtratio in omnibus punctis obſtaculi <lb/>procedat, ſequitur undam reflexam eandem habere figuram <lb/> <anchor type="note" xlink:label="note-0349-01a" xlink:href="note-0349-01"/> ab hac parte obſtaculi, quam, ſublato obſtaculo, ultra hoc <lb/>habuiſſet. </s> <s xml:id="echoid-s9369" xml:space="preserve">Si obſtaculum ad horizontem inclinetur, aqua <lb/> <anchor type="note" xlink:label="note-0349-02a" xlink:href="note-0349-02"/> ſuper illo adſcendit & </s> <s xml:id="echoid-s9370" xml:space="preserve">deſcendit, & </s> <s xml:id="echoid-s9371" xml:space="preserve">attritum patitur, quo <lb/>undæ reflexio turbatur, & </s> <s xml:id="echoid-s9372" xml:space="preserve">ſæpiſſime in totum deſtruitur. <lb/></s> <s xml:id="echoid-s9373" xml:space="preserve">Hæc eſt ratio quare plerumque fluminum ripæ undas non <lb/>reflectant.</s> <s xml:id="echoid-s9374" xml:space="preserve"/> </p> <div xml:id="echoid-div1324" type="float" level="2" n="3"> <note position="left" xlink:label="note-0348-07" xlink:href="note-0348-07a" xml:space="preserve">876.</note> <note position="left" xlink:label="note-0348-08" xlink:href="note-0348-08a" xml:space="preserve">TAB. XXXIV. <lb/>fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0348-09" xlink:href="note-0348-09a" xml:space="preserve">604.</note> <note position="right" xlink:label="note-0349-01" xlink:href="note-0349-01a" xml:space="preserve">877.</note> <note position="right" xlink:label="note-0349-02" xlink:href="note-0349-02a" xml:space="preserve">878.</note> </div> <p> <s xml:id="echoid-s9375" xml:space="preserve">Quando in obſtaculo ut BL foramen datur ut I, pars un-<lb/> <anchor type="note" xlink:label="note-0349-03a" xlink:href="note-0349-03"/> dæ, quæ per hoc tranſit, motum directe continuat, & </s> <s xml:id="echoid-s9376" xml:space="preserve"><lb/>QQ verſus ſeſe expandit, & </s> <s xml:id="echoid-s9377" xml:space="preserve">nova unda formatur, quæ <lb/>per ſemicirculum movetur, cujus centrum eſt ipſum fora-<lb/>men. </s> <s xml:id="echoid-s9378" xml:space="preserve">Nam pars undæ elevata, quæ primo transgreditur <lb/>foramen, ſtatim paululumad latera defluit, & </s> <s xml:id="echoid-s9379" xml:space="preserve">deinde deſcen-<lb/>dendo cavitatem format, quæ ab omni parte ultra ſoramen <lb/>elevatione circumdatur, quæ ad omnes partes, eodem mo-<lb/>do, ac de geneſi primæ undæ dictum <anchor type="note" xlink:href="" symbol="*"/>, ſeſe expandit.</s> <s xml:id="echoid-s9380" xml:space="preserve"/> </p> <div xml:id="echoid-div1325" type="float" level="2" n="4"> <note position="right" xlink:label="note-0349-03" xlink:href="note-0349-03a" xml:space="preserve">879.</note> </div> <note symbol="*" position="right" xml:space="preserve">872.</note> <p> <s xml:id="echoid-s9381" xml:space="preserve">Unda, cui opponitur obſtaculum ut AO, inter <lb/> <anchor type="note" xlink:label="note-0349-05a" xlink:href="note-0349-05"/> O & </s> <s xml:id="echoid-s9382" xml:space="preserve">N motum continuat; </s> <s xml:id="echoid-s9383" xml:space="preserve">ſed R verſus per portio- <pb o="254" file="0350" n="383" rhead="PHYSICES ELEMENTA"/> nem circuli, cujus centrum non multum ab O diſtat, ſeſe <lb/>expandit.</s> <s xml:id="echoid-s9384" xml:space="preserve"/> </p> <div xml:id="echoid-div1326" type="float" level="2" n="5"> <note position="right" xlink:label="note-0349-05" xlink:href="note-0349-05a" xml:space="preserve">880.</note> </div> <p> <s xml:id="echoid-s9385" xml:space="preserve">Ex hiſce ſacile deducitur motus undæ ponè obſtaculum <lb/> <anchor type="note" xlink:label="note-0350-01a" xlink:href="note-0350-01"/> ut MN.</s> <s xml:id="echoid-s9386" xml:space="preserve"/> </p> <div xml:id="echoid-div1327" type="float" level="2" n="6"> <note position="left" xlink:label="note-0350-01" xlink:href="note-0350-01a" xml:space="preserve">881.</note> </div> <p> <s xml:id="echoid-s9387" xml:space="preserve">Undæ ſæpe producuntur ex motu corporis tremulo, quæ <lb/> <anchor type="note" xlink:label="note-0350-02a" xlink:href="note-0350-02"/> etiam per circulum ſeſe expandunt, licet per lineam rectam <lb/>corpus eat & </s> <s xml:id="echoid-s9388" xml:space="preserve">redeat; </s> <s xml:id="echoid-s9389" xml:space="preserve">aqua enim agitatione elevata deſcen-<lb/>dendo cavitatem format, quæ ab omni parte elevatione cir-<lb/>cumdatur.</s> <s xml:id="echoid-s9390" xml:space="preserve"/> </p> <div xml:id="echoid-div1328" type="float" level="2" n="7"> <note position="left" xlink:label="note-0350-02" xlink:href="note-0350-02a" xml:space="preserve">882.</note> </div> <p> <s xml:id="echoid-s9391" xml:space="preserve">Undæ variæ ſeſe mutuo non perturbant, dum juxta va-<lb/> <anchor type="note" xlink:label="note-0350-03a" xlink:href="note-0350-03"/> rias directiones moventur. </s> <s xml:id="echoid-s9392" xml:space="preserve">Cujus effectus ratio hæc eſt; <lb/></s> <s xml:id="echoid-s9393" xml:space="preserve">quamcunque ex motu undæ figuram adepta fuerit aquæ ſu-<lb/>perficies, in hac elevatio & </s> <s xml:id="echoid-s9394" xml:space="preserve">depreſſio dari poſſunt, ut & </s> <s xml:id="echoid-s9395" xml:space="preserve"><lb/>motus qualis in undæ motu requiritur.</s> <s xml:id="echoid-s9396" xml:space="preserve"/> </p> <div xml:id="echoid-div1329" type="float" level="2" n="8"> <note position="left" xlink:label="note-0350-03" xlink:href="note-0350-03a" xml:space="preserve">883.</note> </div> <p> <s xml:id="echoid-s9397" xml:space="preserve">Qui unquam undarum motum attente conſideravit, hæc <lb/>omnia cum Experimentis congruere vidit.</s> <s xml:id="echoid-s9398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9399" xml:space="preserve">Celeritas undarum ut determinetur, motus alius cum ha-<lb/>rum motu analogus examinandus eſt. </s> <s xml:id="echoid-s9400" xml:space="preserve">Detur fluidum in <lb/> <anchor type="note" xlink:label="note-0350-04a" xlink:href="note-0350-04"/> tubo cylindrico curvo EH, ſuperetque altitudo fluidi in <lb/> <anchor type="note" xlink:label="note-0350-05a" xlink:href="note-0350-05"/> crure EF altitudinem in alio crure quantitate lE, quæ <lb/>differentia in duas partes æquales ſecanda eſt in i. </s> <s xml:id="echoid-s9401" xml:space="preserve">Gravi-<lb/>tate ſua deſcendit fluidum in crure EH, dum æqualiter in <lb/>tubo EH adſcendit, & </s> <s xml:id="echoid-s9402" xml:space="preserve">ita quando ſuperficies fluidi perve-<lb/>nit ad i, ad eandem in utroque crure datur altitudinem, & </s> <s xml:id="echoid-s9403" xml:space="preserve"><lb/>in hoc ſitu ſolo fluidum poteſt quieſcere: </s> <s xml:id="echoid-s9404" xml:space="preserve">ſed celeritate de-<lb/>ſcendendo acquiſita motum continuat, magisque adſcendit <lb/>in tubo GH, & </s> <s xml:id="echoid-s9405" xml:space="preserve">in EF deprimitur ad l uſque, niſi qua-<lb/>tenus ab attritu tubi motus minuitur. </s> <s xml:id="echoid-s9406" xml:space="preserve">Fluidum in tubo <lb/>GH magis elevatum etiam gravitate deſcendit, & </s> <s xml:id="echoid-s9407" xml:space="preserve">fluidum <lb/>in tubo it & </s> <s xml:id="echoid-s9408" xml:space="preserve">redit, donec ex attritu totum motum amiſe-<lb/>rit.</s> <s xml:id="echoid-s9409" xml:space="preserve"/> </p> <div xml:id="echoid-div1330" type="float" level="2" n="9"> <note position="left" xlink:label="note-0350-04" xlink:href="note-0350-04a" xml:space="preserve">884.</note> <note position="left" xlink:label="note-0350-05" xlink:href="note-0350-05a" xml:space="preserve">TAB. XXXIV. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s9410" xml:space="preserve">Quantitas materiæ movendæ eſt totum fluidum in tubo; <lb/></s> <s xml:id="echoid-s9411" xml:space="preserve">vis motrix eſt pondus columnæ lE; </s> <s xml:id="echoid-s9412" xml:space="preserve">hoc fluidum premens <lb/>eodem motu cum reliquo fluido in tubo agitatur & </s> <s xml:id="echoid-s9413" xml:space="preserve">reſpe-<lb/>ctu hujus quieſcit; </s> <s xml:id="echoid-s9414" xml:space="preserve">agit ergo in fluidum motum ut in quie-<lb/>ſcens & </s> <s xml:id="echoid-s9415" xml:space="preserve">toto ſuo pondere premit in inferius fluidum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9416" xml:space="preserve">Al- <anchor type="note" xlink:label="note-0350-06a" xlink:href="note-0350-06"/> <pb o="255" file="0351" n="384" rhead="MATHEMATIC A. LIB. II. CAP. X."/> titudo autem hujus fluidi prementis ſemper eſt duplum di-<lb/>ſtantiæ Ei, quæ ergo diſtantia cum hac vi motrice in ea-<lb/>dem ratione creſcit & </s> <s xml:id="echoid-s9417" xml:space="preserve">minuitur. </s> <s xml:id="echoid-s9418" xml:space="preserve">Diſtantia autem Ei eſt <lb/>ſpatium a fluido percurrendum, ut a ſitu EH perveniat <lb/>ad ſitum quietis; </s> <s xml:id="echoid-s9419" xml:space="preserve">quod ergo ſpatium ſemper eſt ut vis quæ <lb/>continuo in fluidum agit: </s> <s xml:id="echoid-s9420" xml:space="preserve">ſed tali ex cauſa demonſtravi-<lb/>mus penduli in cycloide oſcillati vibrationes omnes eſſe æ-<lb/>que diuturnas <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9421" xml:space="preserve">ideo & </s> <s xml:id="echoid-s9422" xml:space="preserve">hîc quæcunque fuerit agitationum <anchor type="note" xlink:label="note-0351-01a" xlink:href="note-0351-01"/> inæqualitas, æquali ſemper tempore fluidum it aut redit.</s> <s xml:id="echoid-s9423" xml:space="preserve"/> </p> <div xml:id="echoid-div1331" type="float" level="2" n="10"> <note symbol="*" position="left" xlink:label="note-0350-06" xlink:href="note-0350-06a" xml:space="preserve">252.</note> <note symbol="*" position="right" xlink:label="note-0351-01" xlink:href="note-0351-01a" xml:space="preserve">287.</note> </div> <p> <s xml:id="echoid-s9424" xml:space="preserve">Tempus in quo fluidum ſic agitatum adſcendit aut de-<lb/> <anchor type="note" xlink:label="note-0351-02a" xlink:href="note-0351-02"/> ſcendit, eſt tempus in quo vibratur pendulum, cujus longi-<lb/>tudo, id eſt, diſtantia inter centra oſcillationis & </s> <s xml:id="echoid-s9425" xml:space="preserve">ſuſpen-<lb/>ſionis, æqualis eſt ſemi-longitudini fluidi in tubo, ſive ſe-<lb/>mi-ſummæ linearum EE, FG, & </s> <s xml:id="echoid-s9426" xml:space="preserve">GH: </s> <s xml:id="echoid-s9427" xml:space="preserve">longitudo hæc <lb/>in axe tubi menſuranda eſt.</s> <s xml:id="echoid-s9428" xml:space="preserve"/> </p> <div xml:id="echoid-div1332" type="float" level="2" n="11"> <note position="right" xlink:label="note-0351-02" xlink:href="note-0351-02a" xml:space="preserve">885.</note> </div> <p> <s xml:id="echoid-s9429" xml:space="preserve">Vibretur hocce pendulum in cycloïde methodo ſuperius <lb/> <anchor type="note" xlink:label="note-0351-03a" xlink:href="note-0351-03"/> explicata <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9430" xml:space="preserve">Pendulum PC & </s> <s xml:id="echoid-s9431" xml:space="preserve">arcus AD ejuſdem ſunt <anchor type="note" xlink:label="note-0351-04a" xlink:href="note-0351-04"/> longitudinis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9432" xml:space="preserve">in puncto A directio curvæ ad horizontem <anchor type="note" xlink:label="note-0351-05a" xlink:href="note-0351-05"/> <anchor type="note" xlink:label="note-0351-06a" xlink:href="note-0351-06"/> perpendicularis eſt, & </s> <s xml:id="echoid-s9433" xml:space="preserve">corpus toto ſuo pondere juxta cur-<lb/>vam deſcendere conatur: </s> <s xml:id="echoid-s9434" xml:space="preserve">hoc autem pondus eſt ad vim in <lb/>corpus agens, poſito hoc in P, ut AD, aut PC ad PD<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9435" xml:space="preserve"> <anchor type="note" xlink:label="note-0351-07a" xlink:href="note-0351-07"/> Sit nunc fluidum in eo ſitu, ut iE (fig. </s> <s xml:id="echoid-s9436" xml:space="preserve">5.) </s> <s xml:id="echoid-s9437" xml:space="preserve">æqualis ſit PD; <lb/></s> <s xml:id="echoid-s9438" xml:space="preserve">pondus totius materiæ movendæ, id eſt, totius fluidi, eſt <lb/>ad pondus lE, quod eſt vis in hoc ſitu in fluidum agens <lb/>ut longitudo fluidi in tubo ad lineam lE, in qua ratione <lb/>etiam ſunt harum quantitatum ſemiſſes, id eſt PC ad PD <lb/>(fig. </s> <s xml:id="echoid-s9439" xml:space="preserve">6.)</s> <s xml:id="echoid-s9440" xml:space="preserve">. </s> <s xml:id="echoid-s9441" xml:space="preserve">In pendulo ergo pondus materiæ movendæ eſt <lb/>ad vim in hanc agentem in P, ut in tubo pondus materiæ mo-<lb/>vendæ ad vim in hanc agentem in ſitu EH. </s> <s xml:id="echoid-s9442" xml:space="preserve">Æqualibus viribus <lb/>ideo corpus pendulum & </s> <s xml:id="echoid-s9443" xml:space="preserve">fluidum in hac occaſione propel-<lb/>luntur, & </s> <s xml:id="echoid-s9444" xml:space="preserve">hoc ubique obtinet ubi ſpatia, a fluido in agi-<lb/>tatione & </s> <s xml:id="echoid-s9445" xml:space="preserve">a corpore in vibratione percurſa, ſunt æqualia; </s> <s xml:id="echoid-s9446" xml:space="preserve"><lb/>idcirco in hoc caſu agitatio & </s> <s xml:id="echoid-s9447" xml:space="preserve">vibratio eodem tempore per-<lb/>aguntur, & </s> <s xml:id="echoid-s9448" xml:space="preserve">non modo in hoc caſu, ſed ſemper <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9449" xml:space="preserve">Cum <anchor type="note" xlink:label="note-0351-08a" xlink:href="note-0351-08"/> vero vibrationes exiguæ in circulo a vibrationibus in cy- <pb o="256" file="0352" n="385" rhead="PHYSICES ELEMENTA"/> cloïde non differant, etiam ad illas demonſtratio referri <lb/>debet.</s> <s xml:id="echoid-s9450" xml:space="preserve"/> </p> <div xml:id="echoid-div1333" type="float" level="2" n="12"> <note position="right" xlink:label="note-0351-03" xlink:href="note-0351-03a" xml:space="preserve">886.</note> <note position="right" xlink:label="note-0351-04" xlink:href="note-0351-04a" xml:space="preserve">TAB. XXXIV. <lb/>fig 6.</note> <note symbol="*" position="right" xlink:label="note-0351-05" xlink:href="note-0351-05a" xml:space="preserve">283.</note> <note symbol="*" position="right" xlink:label="note-0351-06" xlink:href="note-0351-06a" xml:space="preserve">284.</note> <note symbol="*" position="right" xlink:label="note-0351-07" xlink:href="note-0351-07a" xml:space="preserve">287.</note> <note symbol="*" position="right" xlink:label="note-0351-08" xlink:href="note-0351-08a" xml:space="preserve">884.</note> </div> </div> <div xml:id="echoid-div1335" type="section" level="1" n="336"> <head xml:id="echoid-head466" xml:space="preserve"><emph style="sc">Experimentum</emph>.</head> <p> <s xml:id="echoid-s9451" xml:space="preserve">Detur tubus vitreus cylindricus curvus ut EFGH; </s> <s xml:id="echoid-s9452" xml:space="preserve">ſit <lb/> <anchor type="note" xlink:label="note-0352-01a" xlink:href="note-0352-01"/> crurum longitudo unius pedis, & </s> <s xml:id="echoid-s9453" xml:space="preserve">cylindri diameter ſemi-<lb/>pollicis; </s> <s xml:id="echoid-s9454" xml:space="preserve">tubo mercurius infundatur, & </s> <s xml:id="echoid-s9455" xml:space="preserve">conſtitato pendu-<lb/>lo, cujus longitudo æquet dimidium longitudinis cylindri <lb/>mercurii in tubo, ſi mercurius in tubo agitetur, iiſdem <lb/>temporibus adſcendit & </s> <s xml:id="echoid-s9456" xml:space="preserve">deſcendit hic, in quibus pendu-<lb/>lum oſcillando it & </s> <s xml:id="echoid-s9457" xml:space="preserve">redit.</s> <s xml:id="echoid-s9458" xml:space="preserve"/> </p> <div xml:id="echoid-div1335" type="float" level="2" n="1"> <note position="left" xlink:label="note-0352-01" xlink:href="note-0352-01a" xml:space="preserve">887.</note> </div> <p> <s xml:id="echoid-s9459" xml:space="preserve">Ut ex dictis determinemus undarum celeritatem, variæ <lb/> <anchor type="note" xlink:label="note-0352-02a" xlink:href="note-0352-02"/> undæ æquales & </s> <s xml:id="echoid-s9460" xml:space="preserve">ſeſe mutuo immediate inſequentes con-<lb/> <anchor type="note" xlink:label="note-0352-03a" xlink:href="note-0352-03"/> ſiderandæ ſunt ut AB, CD, EF, quæ ab A ad F <lb/>moventur. </s> <s xml:id="echoid-s9461" xml:space="preserve">Unda AB percurrit latitudinem ſuam, quan-<lb/>do cavitas A pervenit ad C; </s> <s xml:id="echoid-s9462" xml:space="preserve">quod fieri non poteſt, niſi a-<lb/>qua in C ad altitudinem undarum culminum adſcendat, i-<lb/>terumque ad profunditatem C deſcendat; </s> <s xml:id="echoid-s9463" xml:space="preserve">in quo motu aqua <lb/>infra lineam hi ſenſibiliter non agitatur: </s> <s xml:id="echoid-s9464" xml:space="preserve">congruit ergo hic-<lb/>ce motus cum motu memorato in tubo, & </s> <s xml:id="echoid-s9465" xml:space="preserve">aqua adſcendit <lb/>& </s> <s xml:id="echoid-s9466" xml:space="preserve">deſcendit, id eſt, unda latitudinem ſuam percurrit, dum <lb/>pendulum longitudinis dimidii BC duas peragit oſcillatio-<lb/>nes <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9467" xml:space="preserve">aut dum pendulum longitudinis BCD, prioris qua- <anchor type="note" xlink:label="note-0352-04a" xlink:href="note-0352-04"/> druplæ, ſemel vibratur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9468" xml:space="preserve"/> </p> <div xml:id="echoid-div1336" type="float" level="2" n="2"> <note position="left" xlink:label="note-0352-02" xlink:href="note-0352-02a" xml:space="preserve">888.</note> <note position="left" xlink:label="note-0352-03" xlink:href="note-0352-03a" xml:space="preserve">TAB. XXXIV. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0352-04" xlink:href="note-0352-04a" xml:space="preserve">885.</note> </div> <note symbol="*" position="left" xml:space="preserve">290.</note> <p> <s xml:id="echoid-s9469" xml:space="preserve">Pendet igitur celeritas undæ à longitudine lineæ BCD, <lb/>quæ pro majori undarum latitudine, & </s> <s xml:id="echoid-s9470" xml:space="preserve">pro majori profun-<lb/>ditate ad quam in motu undarum aqua deſcendit, major <lb/>eſt.</s> <s xml:id="echoid-s9471" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9472" xml:space="preserve">In undis latioribus, quæ non alte elevantur, linea ut <lb/>BCD a latitudine undæ vix differt, & </s> <s xml:id="echoid-s9473" xml:space="preserve">in eo caſu unda <lb/> <anchor type="note" xlink:label="note-0352-06a" xlink:href="note-0352-06"/> latitudinem ſuam percurrit, dum pendulum huic latitudi-<lb/>ni æquale ſemel oſcillatur. </s> <s xml:id="echoid-s9474" xml:space="preserve">In omni motu æquabili mul-<lb/>tiplicando tempus per celeritatem datur ſpatium percur-<lb/>ſum <anchor type="note" xlink:href="" symbol="*"/>, unde ſequitur celeritates undarum eſſe ut radices <anchor type="note" xlink:label="note-0352-07a" xlink:href="note-0352-07"/> <anchor type="note" xlink:label="note-0352-08a" xlink:href="note-0352-08"/> quadratas latitudinum: </s> <s xml:id="echoid-s9475" xml:space="preserve">nam cum in hac ratione ſint tem-<lb/>pora quibus latitudines ſuas percurrunt <anchor type="note" xlink:href="" symbol="*"/>, eadem in harum <anchor type="note" xlink:label="note-0352-09a" xlink:href="note-0352-09"/> <pb file="0353" n="386"/> <pb file="0353a" n="387"/> <anchor type="figure" xlink:label="fig-0353a-01a" xlink:href="fig-0353a-01"/> <pb file="0354" n="388"/> <pb o="257" file="0355" n="389" rhead="MATHEMATICA. LIB. II. CAP. XI."/> celeritatibus ratio requiritur, ut producta temporum per <lb/>celeritates ſint ut undarum latitudines, quæ ſunt ſpatia <lb/>percurſa.</s> <s xml:id="echoid-s9476" xml:space="preserve"/> </p> <div xml:id="echoid-div1337" type="float" level="2" n="3"> <note position="left" xlink:label="note-0352-06" xlink:href="note-0352-06a" xml:space="preserve">889.</note> <note symbol="*" position="left" xlink:label="note-0352-07" xlink:href="note-0352-07a" xml:space="preserve">95.</note> <note position="left" xlink:label="note-0352-08" xlink:href="note-0352-08a" xml:space="preserve">890.</note> <note symbol="*" position="left" xlink:label="note-0352-09" xlink:href="note-0352-09a" xml:space="preserve">290. 889.</note> <figure xlink:label="fig-0353a-01" xlink:href="fig-0353a-01a"> <image file="0353a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0353a-01"/> </figure> </div> <p> <s xml:id="echoid-s9477" xml:space="preserve">Hæc omnia tantum pro quamproxime veris habenda <lb/>ſunt, quia undarum motus a motu in tubo paululum dif-<lb/>fert; </s> <s xml:id="echoid-s9478" xml:space="preserve">qui error pro parte tamen compenſatur ex eo quod <lb/>penduli longitudo menſuretur juxta lineas inclinatas BC & </s> <s xml:id="echoid-s9479" xml:space="preserve"><lb/>CD.</s> <s xml:id="echoid-s9480" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1339" type="section" level="1" n="337"> <head xml:id="echoid-head467" xml:space="preserve">CAPUT XI.</head> <head xml:id="echoid-head468" style="it" xml:space="preserve">De Reſiſtentia Fluidorum.</head> <p> <s xml:id="echoid-s9481" xml:space="preserve">OMne corpus quod in fluido movetur reſiſtentiam patitur, <lb/> <anchor type="note" xlink:label="note-0355-01a" xlink:href="note-0355-01"/> & </s> <s xml:id="echoid-s9482" xml:space="preserve">quidem ex duplici cauſa.</s> <s xml:id="echoid-s9483" xml:space="preserve"/> </p> <div xml:id="echoid-div1339" type="float" level="2" n="1"> <note position="right" xlink:label="note-0355-01" xlink:href="note-0355-01a" xml:space="preserve">891.</note> </div> <p> <s xml:id="echoid-s9484" xml:space="preserve">Quamvis fluidorum partes parum admodum cohæreant <lb/>illas tamen vi quadam cohærere extra dubium eſt <anchor type="note" xlink:href="" symbol="*"/>, hanc <anchor type="note" xlink:label="note-0355-02a" xlink:href="note-0355-02"/> autem, dum corpus in motu ſuo ſeparat fluidorum particu-<lb/> <anchor type="note" xlink:label="note-0355-03a" xlink:href="note-0355-03"/> las, ſuperare debet cobæſionem; </s> <s xml:id="echoid-s9485" xml:space="preserve">bæcque eſt prima reſiſten-<lb/>tiæ cauſa.</s> <s xml:id="echoid-s9486" xml:space="preserve"/> </p> <div xml:id="echoid-div1340" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0355-02" xlink:href="note-0355-02a" xml:space="preserve">54. 55.</note> <note position="right" xlink:label="note-0355-03" xlink:href="note-0355-03a" xml:space="preserve">892.</note> </div> <p> <s xml:id="echoid-s9487" xml:space="preserve">Actio bæc ſimilis eſt illi qua corporum mollium partes ſe-<lb/> <anchor type="note" xlink:label="note-0355-04a" xlink:href="note-0355-04"/> parantur, dum in ipſis cavitas formatur, quam formari vi-<lb/>dimus actione, quæ ſequitur proportionem ipſius cavitatis <lb/> <anchor type="note" xlink:label="note-0355-05a" xlink:href="note-0355-05"/> formatæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9488" xml:space="preserve">quam demonſtrationem ad corpus in fluido mo- tum etiam poſſumus applicare; </s> <s xml:id="echoid-s9489" xml:space="preserve">in hoc autem motu corpus <lb/>cavitatem format proportionalem ſpatio percurſo, quamvis <lb/>cavitas hæc ſingulis momentis affluxu fluidi iterum implea-<lb/>tur. </s> <s xml:id="echoid-s9490" xml:space="preserve">Unde deducimus corpus ex hac prima cauſa, reſi-<lb/> <anchor type="note" xlink:label="note-0355-06a" xlink:href="note-0355-06"/> ſtentiam pati proportionalem huic ſpatio percurſo; </s> <s xml:id="echoid-s9491" xml:space="preserve">quæid-<lb/>circo ad inſtar velocitatis augetur & </s> <s xml:id="echoid-s9492" xml:space="preserve">minuitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9493" xml:space="preserve"/> </p> <div xml:id="echoid-div1341" type="float" level="2" n="3"> <note position="right" xlink:label="note-0355-04" xlink:href="note-0355-04a" xml:space="preserve">893.</note> <note symbol="*" position="right" xlink:label="note-0355-05" xlink:href="note-0355-05a" xml:space="preserve">464.</note> <note position="right" xlink:label="note-0355-06" xlink:href="note-0355-06a" xml:space="preserve">894.</note> </div> <note symbol="*" position="right" xml:space="preserve">94</note> <p> <s xml:id="echoid-s9494" xml:space="preserve">Dum corpus in corpore molli cavitatem format, partes <lb/> <anchor type="note" xlink:label="note-0355-08a" xlink:href="note-0355-08"/> immediata tantum actione corporum in ſe mutuo transfe-<lb/>runtur, qua ceſſante actione ceſſat particularum <lb/>motus; </s> <s xml:id="echoid-s9495" xml:space="preserve">hac de cauſa in formanda cavitate tantum <lb/>conſumitur vis qua partium cohæſio ſuperatur, poſ- <pb o="258" file="0356" n="390" rhead="PHYSICES ELEMENTA"/> ſuntque corpora integras in formandis cavitatibus vires in-<lb/>ſitas amittere.</s> <s xml:id="echoid-s9496" xml:space="preserve"/> </p> <div xml:id="echoid-div1342" type="float" level="2" n="4"> <note position="right" xlink:label="note-0355-08" xlink:href="note-0355-08a" xml:space="preserve">895.</note> </div> <p> <s xml:id="echoid-s9497" xml:space="preserve">Corpus autem in motu per fluidum non tantum trans-<lb/>fert particulas actione immediata, dum ſibi viam in-<lb/>ter has aperit, in qua translatione immediata cohæſionem <lb/>ſuperat; </s> <s xml:id="echoid-s9498" xml:space="preserve">ſed & </s> <s xml:id="echoid-s9499" xml:space="preserve">præterea ipſis particulis vim communicat, <lb/>qua poſt ceſlatam corporis actionem inter ſe moventur: <lb/></s> <s xml:id="echoid-s9500" xml:space="preserve">reactio verò particularum, dum ipſis motus hicce impri-<lb/> <anchor type="note" xlink:label="note-0356-01a" xlink:href="note-0356-01"/> mitur, ex harum inertia oriunda, eſt ſecunda cauſa reſi-<lb/>ſtentiæ.</s> <s xml:id="echoid-s9501" xml:space="preserve"/> </p> <div xml:id="echoid-div1343" type="float" level="2" n="5"> <note position="left" xlink:label="note-0356-01" xlink:href="note-0356-01a" xml:space="preserve">896.</note> </div> <p> <s xml:id="echoid-s9502" xml:space="preserve">Ut clarius concipiamus quæ reſiſtentias has ſpectant, ad <lb/>hoc attendere debemus. </s> <s xml:id="echoid-s9503" xml:space="preserve">Mutuam actionem corporis & </s> <s xml:id="echoid-s9504" xml:space="preserve">fluidi <lb/> <anchor type="note" xlink:label="note-0356-02a" xlink:href="note-0356-02"/> eandem eſſe, ſive corpus certa velocitate in fluido quieſcente <lb/>moveatur, ſive, quieſcente corpore, eâdem velocitate flui-<lb/>dum in hoc incurrat. </s> <s xml:id="echoid-s9505" xml:space="preserve">Actio enim hæc a motu reſpectivo <lb/>pendet, qui in hiſce caſibus non variat.</s> <s xml:id="echoid-s9506" xml:space="preserve"/> </p> <div xml:id="echoid-div1344" type="float" level="2" n="6"> <note position="left" xlink:label="note-0356-02" xlink:href="note-0356-02a" xml:space="preserve">897.</note> </div> <p> <s xml:id="echoid-s9507" xml:space="preserve">Si nunc ſepoſitâ partium cohæſione ad motum fluidi at-<lb/>tendamus, & </s> <s xml:id="echoid-s9508" xml:space="preserve">hoc conſideremus dum in corpus quieſcens <lb/>incurrit, facile videbimus fluidi actionem eſſe preſſionem, <lb/> <anchor type="note" xlink:label="note-0356-03a" xlink:href="note-0356-03"/> particulaſque non impingere in corpus ſed juxta hoc, aut <lb/>juxta particulas fluidi, quæ corpus tangunt, moveri & </s> <s xml:id="echoid-s9509" xml:space="preserve">inter-<lb/>ea illas premere corpus, eodem modo ac corpus premit <lb/>planum ſuper quo movetur, quales preſſiones ex viribus <lb/>oriundas ſuperius <anchor type="note" xlink:href="" symbol="*"/> indicavimus.</s> <s xml:id="echoid-s9510" xml:space="preserve"/> </p> <div xml:id="echoid-div1345" type="float" level="2" n="7"> <note position="left" xlink:label="note-0356-03" xlink:href="note-0356-03a" xml:space="preserve">898.</note> </div> <note symbol="*" position="left" xml:space="preserve">120. 321. 522.</note> <p> <s xml:id="echoid-s9511" xml:space="preserve">Preſſio hæc a vi inſitâ particularum oriunda, eſt ut hæc <lb/> <anchor type="note" xlink:label="note-0356-05a" xlink:href="note-0356-05"/> vis, id eſt ut quadratum velocitatis <anchor type="note" xlink:href="" symbol="*"/>, augetur etiam ut nu- <anchor type="note" xlink:label="note-0356-06a" xlink:href="note-0356-06"/> merus particularum determinato tempore incurrentium, <lb/>qui numerus velocitatis ſequitur proportionem: </s> <s xml:id="echoid-s9512" xml:space="preserve">tandem <lb/>preſſio de qua agimus ſequitur rationem temporis per quod <lb/>ſingulæ particulæ in determinatam partem ſuperficiei pre-<lb/>munt, quod tempus eo minus eſt quo velocitas eſt major, <lb/>ſequiturque rationem inverſam velocitatis; </s> <s xml:id="echoid-s9513" xml:space="preserve">quare ultimæ duæ <lb/>rationes ſeſe mutuo deſtruunt ſuperſtitemque habemus ſo-<lb/> <anchor type="note" xlink:label="note-0356-07a" xlink:href="note-0356-07"/> lam rationem quadrati velocitatis; </s> <s xml:id="echoid-s9514" xml:space="preserve">quam idcirco ſequitur <lb/>reſiſtentia ex ſecunda cauſa.</s> <s xml:id="echoid-s9515" xml:space="preserve"/> </p> <div xml:id="echoid-div1346" type="float" level="2" n="8"> <note position="left" xlink:label="note-0356-05" xlink:href="note-0356-05a" xml:space="preserve">899.</note> <note symbol="*" position="left" xlink:label="note-0356-06" xlink:href="note-0356-06a" xml:space="preserve">477.</note> <note position="left" xlink:label="note-0356-07" xlink:href="note-0356-07a" xml:space="preserve">900.</note> </div> <p> <s xml:id="echoid-s9516" xml:space="preserve">Quomodo autem ambæ reſiſtentiæ cauſæ ſimul agant <lb/> <anchor type="note" xlink:label="note-0356-08a" xlink:href="note-0356-08"/> <pb o="259" file="0357" n="391" rhead="MATHEMATICA. LIB. II. CAP. XI."/> concipimus, ſi ad hoc attendamus, particulas quæ in cor-<lb/> <anchor type="note" xlink:label="note-0357-01a" xlink:href="note-0357-01"/> pus, ut A agunt, ad latera defluere in B & </s> <s xml:id="echoid-s9517" xml:space="preserve">D, ibique, <lb/>ſepoſitâ cohæſione, nullam exerere actionem, poſitâ autem <lb/>cohæſione hac, particulæ hæ laterales ſecum trahunt, & </s> <s xml:id="echoid-s9518" xml:space="preserve"><lb/>actione ſua inſequentes ſeparant, quæ deſideratur ſeparatio <lb/>ut fluidum ab omni parte defluat: </s> <s xml:id="echoid-s9519" xml:space="preserve">cohæſio autem ſuperari <lb/>minime poterit niſi corpus reſiſtat, & </s> <s xml:id="echoid-s9520" xml:space="preserve">actio in hoc detur <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s9521" xml:space="preserve"> <anchor type="note" xlink:label="note-0357-02a" xlink:href="note-0357-02"/> quæ actioni ex inertia oriundæ ſuperaddenda eſt.</s> <s xml:id="echoid-s9522" xml:space="preserve"/> </p> <div xml:id="echoid-div1347" type="float" level="2" n="9"> <note position="left" xlink:label="note-0356-08" xlink:href="note-0356-08a" xml:space="preserve">901.</note> <note position="right" xlink:label="note-0357-01" xlink:href="note-0357-01a" xml:space="preserve">TAB. XXXVI. <lb/>fg. 5.</note> <note symbol="*" position="right" xlink:label="note-0357-02" xlink:href="note-0357-02a" xml:space="preserve">247.</note> </div> </div> <div xml:id="echoid-div1349" type="section" level="1" n="338"> <head xml:id="echoid-head469" xml:space="preserve"><emph style="sc">Machina,</emph></head> <p style="it"> <s xml:id="echoid-s9523" xml:space="preserve">Qua Experimenta de Fluidorum Reſiſtentiis inſtituuntur.</s> <s xml:id="echoid-s9524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9525" xml:space="preserve">Arca lignea AB longitudinem habet quinque pedum, <lb/> <anchor type="note" xlink:label="note-0357-03a" xlink:href="note-0357-03"/> latitudinem duorum pedum cum ſemiſſe, altitudinem o-<lb/> <anchor type="note" xlink:label="note-0357-04a" xlink:href="note-0357-04"/> cto aut decem pollicum.</s> <s xml:id="echoid-s9526" xml:space="preserve"/> </p> <div xml:id="echoid-div1349" type="float" level="2" n="1"> <note position="right" xlink:label="note-0357-03" xlink:href="note-0357-03a" xml:space="preserve">902.</note> <note position="right" xlink:label="note-0357-04" xlink:href="note-0357-04a" xml:space="preserve">TAB. XXXV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s9527" xml:space="preserve">Quatuor hæc ſuſtinetur columnis ligneis, altitudinis quin-<lb/>que pedum, qui minori arcæ CD imponuntur, quæ ipſa <lb/>pedibus gaudet quatuor, altitudinis circiter decem pollicum; <lb/></s> <s xml:id="echoid-s9528" xml:space="preserve">non autem minorem hiſce pedibus tribuimus altitudinem, <lb/>ut ex epiſtomio Eaqua in ſitulam, fere hujus altitudinis, re-<lb/>cipiatur.</s> <s xml:id="echoid-s9529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9530" xml:space="preserve">Parallelopipedum cavum ligneum F longitudinem ha-<lb/>bet trium pedum cum ſemiſſe à g ad b; </s> <s xml:id="echoid-s9531" xml:space="preserve">hujus cavitatis ba-<lb/>ſis eſt quadratum quinque pollicum. </s> <s xml:id="echoid-s9532" xml:space="preserve">In figura repræſenta-<lb/>tur quomodo verticaliter regulis ligneis firmetur Parallelo-<lb/>pipedum. </s> <s xml:id="echoid-s9533" xml:space="preserve">Diſtantia inter hujus ſuperficiem ſuperiorem & </s> <s xml:id="echoid-s9534" xml:space="preserve"><lb/>arcæ AB fundum eſt quindecim pollicum.</s> <s xml:id="echoid-s9535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9536" xml:space="preserve">In hoc ipſo fundo, in medio reſpectu longitudinis, fora-<lb/>men datur rotundum, diametri circiter quatuor pollicum <lb/>cum ſemiſſe, quod paulo minus diſtat ab uno latere quàm <lb/>ab alio, ut magis commode experimenta inſtituantur.</s> <s xml:id="echoid-s9537" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9538" xml:space="preserve">Huic foramini reſpondet foramen, quod parum cum <lb/>præcedenti differt, ſed tamen minus eſt, in medio ligni ſu-<lb/>perioris parallelopipedi F.</s> <s xml:id="echoid-s9539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9540" xml:space="preserve">In hiſce foraminibus tubus plumbeus T verticaliter fir-<lb/>matur, quo communicatio datur inter arcam AB & </s> <s xml:id="echoid-s9541" xml:space="preserve">pa-<lb/>rallelopipedum F. </s> <s xml:id="echoid-s9542" xml:space="preserve">Tubi longitudo eſt octodecim polli- <pb o="260" file="0358" n="392" rhead="PHYSICES ELEMENTA"/> cum; </s> <s xml:id="echoid-s9543" xml:space="preserve">ipſius cavitas eſt cylindrica, bene lævigata, diametrum-<lb/>que habet quatuor pollicum.</s> <s xml:id="echoid-s9544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9545" xml:space="preserve">Probe firmatur tubus, & </s> <s xml:id="echoid-s9546" xml:space="preserve">aquæ effluxus, inter hunc & </s> <s xml:id="echoid-s9547" xml:space="preserve">li-<lb/>gnum, interpoſitis lini filamentis, cohibetur.</s> <s xml:id="echoid-s9548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9549" xml:space="preserve">Et tubi anguſtiores ſæpe adhibentur, in quo caſu annu-<lb/>lis ligneis extremitates circumdantur, ut eodem modo fir-<lb/>mentur in foraminibus memoratis.</s> <s xml:id="echoid-s9550" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9551" xml:space="preserve">In inferiori parte Parallelopipedi F epiſtomia dantur qua-<lb/>tuor I, L, M, N. </s> <s xml:id="echoid-s9552" xml:space="preserve">Horum aperturæ in laminis dantur <lb/>horizontalibus, quæ omnes in eodem poſitæ ſunt plano ho-<lb/>rizontali; </s> <s xml:id="echoid-s9553" xml:space="preserve">ſuntque hæ aperturæ ipſis epiſtomiorum capaci-<lb/>tatibus multo minores, ut aqua ſine ſenſibili attritu effluat. <lb/></s> <s xml:id="echoid-s9554" xml:space="preserve">Minorum duorum epiſtomiorum, quæ æqualia ſunt, aper-<lb/>turæ æquales ſunt, alîus dupla eſt, & </s> <s xml:id="echoid-s9555" xml:space="preserve">maximi tripla. </s> <s xml:id="echoid-s9556" xml:space="preserve">Dia-<lb/>meter aperturæ mediæ ſemi poll. </s> <s xml:id="echoid-s9557" xml:space="preserve">æqualis eſt.</s> <s xml:id="echoid-s9558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9559" xml:space="preserve">Quantumvis exacte hæ menſurentur aperturæ, non o-<lb/>mnis error vitari poteſt, qui quomodo corrigatur, ſtatim di-<lb/>cam.</s> <s xml:id="echoid-s9560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9561" xml:space="preserve">Oris arcæ AB in medio imponitur tabula P, cujus lon-<lb/>gitudo arcæ latitudinem paululum excedit & </s> <s xml:id="echoid-s9562" xml:space="preserve">cujus latitu-<lb/>do ſedecim aut octodecim eſt poll. </s> <s xml:id="echoid-s9563" xml:space="preserve">Hæc, ne impoſita <lb/>caſu in aquam cadat, oris, ſemipollicem altis, circumdatur. <lb/></s> <s xml:id="echoid-s9564" xml:space="preserve">Firmatur tabula regulis ligneis quatuor, quarum duæ viden-<lb/>tur in o & </s> <s xml:id="echoid-s9565" xml:space="preserve">q, cum ipſa cohærentibus, & </s> <s xml:id="echoid-s9566" xml:space="preserve">inter quas promi-<lb/>nentia lignea r, cum arca cohærens, recipitur.</s> <s xml:id="echoid-s9567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9568" xml:space="preserve">Tabulæ huic ſuperimponitur crux lignea S, infra tabu-<lb/>lam penetrans, ut cochleâ firmetur. </s> <s xml:id="echoid-s9569" xml:space="preserve">Cruci appenditur bi-<lb/>lanx V, quâ in aliis experimentis utimur, & </s> <s xml:id="echoid-s9570" xml:space="preserve">de qua antea <lb/>egimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9571" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">703</note> <p> <s xml:id="echoid-s9572" xml:space="preserve">Ita ſuſpenditur hæc, ut, quando eſt in æquilibrio, lan-<lb/>cium pedes ſupra tabulam ad altitudinem, quæ paululum <lb/>excedit quartam partem pollicis, tantum eleventur.</s> <s xml:id="echoid-s9573" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9574" xml:space="preserve">Uncus autem lancis k reſpondet foramini in tabula, quod <lb/>diametrum habet trium partium quartarum pollicis, & </s> <s xml:id="echoid-s9575" xml:space="preserve">cu-<lb/>jus centrum datur in axe continuato tubi T.</s> <s xml:id="echoid-s9576" xml:space="preserve"/> </p> <pb o="261" file="0359" n="393" rhead="MATHEMATICA. LIB. II. CAP. XI."/> <p> <s xml:id="echoid-s9577" xml:space="preserve">Uſu veniunt in experimentis, quæ hac Machinâ inſtituun-<lb/>tur, globi, cylindri, & </s> <s xml:id="echoid-s9578" xml:space="preserve">coni varii, qui ſinguli capillis equi-<lb/>nis ſuſpenduntur; </s> <s xml:id="echoid-s9579" xml:space="preserve">in qua ſuſpenſione reſpectu cylindrorum <lb/>& </s> <s xml:id="echoid-s9580" xml:space="preserve">conorum attendendum, ut axem habeant verticalem, & </s> <s xml:id="echoid-s9581" xml:space="preserve"><lb/>conorum vertices ſurſum dirigantur.</s> <s xml:id="echoid-s9582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9583" xml:space="preserve">An aperturæ epiſtomiorum eſſent exactæ, ut explorarem, <lb/>& </s> <s xml:id="echoid-s9584" xml:space="preserve">errores corrigerem, methodo uſus ſum, quam nunc <lb/>exponam.</s> <s xml:id="echoid-s9585" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9586" xml:space="preserve">Rebus ut explicavi diſpoſitis, in T applicato tubo, cujus <lb/> <anchor type="note" xlink:label="note-0359-01a" xlink:href="note-0359-01"/> diameter erat hypotenuſa trianguli rectanguli iſoſceles, cu-<lb/>jus latera ſuntduorum pollicum, arcam AB aquâ replevi ita, <lb/>ut oræ arcæ duobus tantum pollicibus aquam ſuperarent, <lb/>quo etiam F & </s> <s xml:id="echoid-s9587" xml:space="preserve">T repleta fuere.</s> <s xml:id="echoid-s9588" xml:space="preserve"/> </p> <div xml:id="echoid-div1350" type="float" level="2" n="2"> <note position="right" xlink:label="note-0359-01" xlink:href="note-0359-01a" xml:space="preserve">903.</note> </div> <p> <s xml:id="echoid-s9589" xml:space="preserve">In tubo T, capillo equino cylindrum ſuſpendi æneum, cujus <lb/>diameter pollicem fere quartâ parte excedit, & </s> <s xml:id="echoid-s9590" xml:space="preserve">cujus altitudo <lb/>eſt ſeſqui pollicis, ſuprema ſuperficies paululum convexa eſt, <lb/>& </s> <s xml:id="echoid-s9591" xml:space="preserve">cavus ipſe eſt, ut minusgravet libram, & </s> <s xml:id="echoid-s9592" xml:space="preserve">exacte clauſus, <lb/>ne aqua in ipſum penetrare poſſit: </s> <s xml:id="echoid-s9593" xml:space="preserve">capillus equinus cum unco k <lb/>lancis libræ V cohærebat, & </s> <s xml:id="echoid-s9594" xml:space="preserve">pondere lanci oppoſitæ <lb/>impoſito dabatur æquilibrium.</s> <s xml:id="echoid-s9595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9596" xml:space="preserve">Quæſivi quodnam pondus adjiciendum eſſet, ut æqui-<lb/>librium daretur, aperto uno ex epiſtomiis minoribus; </s> <s xml:id="echoid-s9597" xml:space="preserve">de-<lb/>tegitur pondus hoc tentando; </s> <s xml:id="echoid-s9598" xml:space="preserve">Primo pondus ad libitum <lb/>imponitur, libraque manu in ſitu æquilibrii retinetur, &</s> <s xml:id="echoid-s9599" xml:space="preserve">, <lb/>poſt apertum epiſtomium, relinquitur; </s> <s xml:id="echoid-s9600" xml:space="preserve">ſi libra moveatur, <lb/>pro diverſo motu augetur, aut minuitur, pondus, & </s> <s xml:id="echoid-s9601" xml:space="preserve">eadem <lb/>operatio repetitur, donec, relictâ bilance, hæc in æqui-<lb/>librio maneat, habemuſque tunc pondus quod valet actio-<lb/>nem quam aqua, dum per tubum movetur, in corpus exerit.</s> <s xml:id="echoid-s9602" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9603" xml:space="preserve">Hac methodo detexi, apertis ſucceſſive epiſtomiis mino-<lb/>ribus, parum actiones differre; </s> <s xml:id="echoid-s9604" xml:space="preserve">ideoque non exactiſſime æ-<lb/>quales eſſe aquæ quantitates per ſingula effluentes, qui er-<lb/>ror facillime paululum admodum aucto foramine uno cor-<lb/>rectus fuit.</s> <s xml:id="echoid-s9605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9606" xml:space="preserve">Apertis tunc ambobus his epiſtomiis I, L, ſimul, ut a- <pb o="262" file="0360" n="394" rhead="PHYSICES ELEMENTA"/> quæ quantitas dupla efflueret, quæſivi aquæ actionem in cy-<lb/>lindrum, curavique ut actio eadem foret aperto unico epi-<lb/>ſtomio M.</s> <s xml:id="echoid-s9607" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9608" xml:space="preserve">Tandem eâdem methodo eo reduxi epiſtomium N, ut <lb/>ex hoc ea flueret aquæ quantitas, quæ ex epiſtomio M & </s> <s xml:id="echoid-s9609" xml:space="preserve"><lb/>uno ex epiſtomiis I, aut L, ſimul, æquali tempore, <lb/>fluit.</s> <s xml:id="echoid-s9610" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9611" xml:space="preserve">In his omnibus obſervavi, & </s> <s xml:id="echoid-s9612" xml:space="preserve">hoc in omnibus experi-<lb/>mentis, quæ hac machinâ inſtituuntur, obſervandum, ut <lb/>aqua in arca ſervetur ad eandem altitudinem, quare, ubi <lb/>uno pollice depreſſa eſt ſuperficies, de novo aqua infundenda <lb/>eſt.</s> <s xml:id="echoid-s9613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9614" xml:space="preserve">Poteſt nunc machina experimentis inſervire. </s> <s xml:id="echoid-s9615" xml:space="preserve">Aperto e-<lb/> <anchor type="note" xlink:label="note-0360-01a" xlink:href="note-0360-01"/> piſtomio I, aut L, certa aquæ quantitas effluit, determi-<lb/>natâque velocitate movetur aqua in tubo T, & </s> <s xml:id="echoid-s9616" xml:space="preserve">uniformem <lb/>velocitatem habet in toto tubo; </s> <s xml:id="echoid-s9617" xml:space="preserve">in hunc enim continuo in-<lb/>trat & </s> <s xml:id="echoid-s9618" xml:space="preserve">eodem tempore exit aquæ quantitas, æqualis illi, quæ <lb/>ex epiſtomio deſluit. </s> <s xml:id="echoid-s9619" xml:space="preserve">Dupla eſt aquæ velocitas in tubo, ſi <lb/>dupla aquæ quantitas defluat, id eſt, ſi ambo epiſtomia I & </s> <s xml:id="echoid-s9620" xml:space="preserve"><lb/>L, aut ſolum M, aperiantur. </s> <s xml:id="echoid-s9621" xml:space="preserve">Tripla eſtaperto M & </s> <s xml:id="echoid-s9622" xml:space="preserve">I vel <lb/>L ſimul, aut N ſolo. </s> <s xml:id="echoid-s9623" xml:space="preserve">Quadrupla eſt velocitas apertis tri-<lb/>bus epiſtomiis I, L, & </s> <s xml:id="echoid-s9624" xml:space="preserve">M, aut N & </s> <s xml:id="echoid-s9625" xml:space="preserve">uno ex I & </s> <s xml:id="echoid-s9626" xml:space="preserve">L. </s> <s xml:id="echoid-s9627" xml:space="preserve">Quin-<lb/>tupla eſt apertis ſimul M & </s> <s xml:id="echoid-s9628" xml:space="preserve">N. </s> <s xml:id="echoid-s9629" xml:space="preserve">Sextupla apertis N, M, <lb/>& </s> <s xml:id="echoid-s9630" xml:space="preserve">uno ex I & </s> <s xml:id="echoid-s9631" xml:space="preserve">L. </s> <s xml:id="echoid-s9632" xml:space="preserve">Septupla tandem apertis omnibus ſi-<lb/>mul.</s> <s xml:id="echoid-s9633" xml:space="preserve"/> </p> <div xml:id="echoid-div1351" type="float" level="2" n="3"> <note position="left" xlink:label="note-0360-01" xlink:href="note-0360-01a" xml:space="preserve">904.</note> </div> <p> <s xml:id="echoid-s9634" xml:space="preserve">In his omnibus motibus nunquam acceleratio aquæ in <lb/>tubo T dari poteſt ex cohæſione oriunda, qualem alio lo-<lb/>co <anchor type="note" xlink:href="" symbol="*"/> memoravimus; </s> <s xml:id="echoid-s9635" xml:space="preserve">quæ ſi daretur non hæc procederet <anchor type="note" xlink:label="note-0360-02a" xlink:href="note-0360-02"/> concluſio, æqualem certo tempore per epiſtomium fluere <lb/>aquæ quantitatem; </s> <s xml:id="echoid-s9636" xml:space="preserve">ſive ſolum, ſive cum aliis aperiatur, quod <lb/>hìc extra dubium eſt; </s> <s xml:id="echoid-s9637" xml:space="preserve">quia ex ſola preſſione aquæ ſupra ori-<lb/>ficium tubi incumbentis dari poteſt velocitas quæ variis <lb/>vicibus maximam ſuperat quâ in hiſce aqua in tubo gau-<lb/>det.</s> <s xml:id="echoid-s9638" xml:space="preserve"/> </p> <div xml:id="echoid-div1352" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0360-02" xlink:href="note-0360-02a" xml:space="preserve">246.</note> </div> <pb o="263" file="0361" n="395" rhead="MATHEMATICA. LIB. II. CAP. XI."/> </div> <div xml:id="echoid-div1354" type="section" level="1" n="339"> <head xml:id="echoid-head470" xml:space="preserve"><emph style="sc">Experimentum 1.</emph></head> <p> <s xml:id="echoid-s9639" xml:space="preserve">Rebus, ut in machinæ deſcriptione expoſitum, diſpo-<lb/> <anchor type="note" xlink:label="note-0361-01a" xlink:href="note-0361-01"/> ſitis, adhibitoque tubo T, ſuperius memorato, cujus dia-<lb/> <anchor type="note" xlink:label="note-0361-02a" xlink:href="note-0361-02"/> meter eſt hypotenuſa trianguli rectanguli iſoſceles, cujus <lb/>ſingula latera ſunt duorum pollicum, globus æneus G, cujus <lb/>diameter eſt ſemi poll.</s> <s xml:id="echoid-s9640" xml:space="preserve">, ſuſpenditur ad profunditatem, non <lb/>intereſt quamcunque, ſex, octo, aut decem pollicum, in tu-<lb/>bo, in cujus axe datur globus; </s> <s xml:id="echoid-s9641" xml:space="preserve">quia capillus equinus, cui <lb/>cohæret, cum unco lancis E conjungitur.</s> <s xml:id="echoid-s9642" xml:space="preserve"/> </p> <div xml:id="echoid-div1354" type="float" level="2" n="1"> <note position="right" xlink:label="note-0361-01" xlink:href="note-0361-01a" xml:space="preserve">905.</note> <note position="right" xlink:label="note-0361-02" xlink:href="note-0361-02a" xml:space="preserve">TAB. XXXV. <lb/>fig. 1.2.</note> </div> <p> <s xml:id="echoid-s9643" xml:space="preserve">Methodo in n. </s> <s xml:id="echoid-s9644" xml:space="preserve">903. </s> <s xml:id="echoid-s9645" xml:space="preserve">tradita quæruntur actiones aquæ in <lb/>globum, dum ſucceſſive, diverſis velocitatibus, aqua per tu-<lb/>bum tranſit, quæ actiones valent reſiſtentias corporis, quan-<lb/>do hoc, quieſcente aquâ, iisdem velocitatibus, in hac movetur.</s> <s xml:id="echoid-s9646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9647" xml:space="preserve">Pondera minima quibus utor in his actionibus determi-<lb/>nandis, quartam partem grani valent; </s> <s xml:id="echoid-s9648" xml:space="preserve">ſuntque actiones quæ <lb/>ſquuntur.</s> <s xml:id="echoid-s9649" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">906.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ <lb/> 1. # gr. {3/4}. 2. # gr. 1 {1/2}. 3. # gr. 3. 4. # gr. 4 {3/4}. 5. # gr. 7 {3/4}. 6. # gr. 10 {1/2}. 7. # gr. 14. </note> <p> <s xml:id="echoid-s9650" xml:space="preserve">In tribus primis velocitatibus deficiebant paululum a-<lb/>ctiones a ponderibus notatis.</s> <s xml:id="echoid-s9651" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9652" xml:space="preserve">Experimenta hæc, adhibitâ admodum exactâ bilance, fue-<lb/> <anchor type="note" xlink:label="note-0361-05a" xlink:href="note-0361-05"/> re inſtituta, maximâ cum curâ, non tamen nullum omni-<lb/>no errorem quantumvis exiguum dari aſlerere non auſim.</s> <s xml:id="echoid-s9653" xml:space="preserve"/> </p> <div xml:id="echoid-div1355" type="float" level="2" n="2"> <note position="right" xlink:label="note-0361-05" xlink:href="note-0361-05a" xml:space="preserve">907</note> </div> <p> <s xml:id="echoid-s9654" xml:space="preserve">Fateor potius exiguos, quarta parte grani minores, vitari <lb/>non potuiſſe, & </s> <s xml:id="echoid-s9655" xml:space="preserve">non credo ab experimento recedi, quando <lb/>tale quid ſuppletur, ubi regularis ſeries hoc poſtulat,</s> </p> <p> <s xml:id="echoid-s9656" xml:space="preserve">Errorem talem dari in prima actione, hîc determinatâ, <lb/>quæ parum deficit a {3/4} gr.</s> <s xml:id="echoid-s9657" xml:space="preserve">, & </s> <s xml:id="echoid-s9658" xml:space="preserve">qui reſpectu hujus ponderis ſen- <pb o="264" file="0362" n="396" rhead="PHYSICES ELEMENTA"/> ſiblis eſt, non tantum indicat regularis ſeries ex reliquis ex-<lb/>perimentis deducenda, ſed & </s> <s xml:id="echoid-s9659" xml:space="preserve">hoc confirmat Experimen-<lb/>tum ſequens.</s> <s xml:id="echoid-s9660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9661" xml:space="preserve">Experimenta hìc traduntur, ut ante initam ullam compu-<lb/>tationem a me fuere inſtituta.</s> <s xml:id="echoid-s9662" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9663" xml:space="preserve">Diviſo nunc grano in centum partes, patet in ſequenti <lb/>ſerie reſiſtentiam pro parte ſequi rationem velocitatis, pro <lb/>parte rationem quadrati velocitatis.</s> <s xml:id="echoid-s9664" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">908.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ \\ ex primacauſa. # Reſiſtentiæ \\ exſecunda cauſa. # Summæ \\ ambarum. # Reſiſtentiæ \\ In Exp. <lb/> 1. # 1 X 20 = 20. # 1 X 26 = 26. # 46. # 75. 2. # 2 X 20 = 40, # 4 X 26 = 104. # 144. # 150. 3. # 3 X 20 = 60, # 9 X 26 = 234. # 294. # 300. 4. # 4 X 20 = 80, # 16 X 26 = 416. # 496. # 475. 5. # 5 X 20 = 100, # 25 X 26 = 650. # 750. # 775. 6. # 6 X 20 = 120, # 36 X 26 = 936. # 1056. # 1050. 7. # 7 X 20 = 140, # 49 X 26 = 1274. # 1414. # 1400. </note> <p> <s xml:id="echoid-s9665" xml:space="preserve">Quando corpora ſimilia, ſimiliter, & </s> <s xml:id="echoid-s9666" xml:space="preserve">velocitatibus æqua-<lb/> <anchor type="note" xlink:label="note-0362-03a" xlink:href="note-0362-03"/> libus, per idem fluidum, moventur, deducitur ex ante de-<lb/> <anchor type="note" xlink:label="note-0362-04a" xlink:href="note-0362-04"/> monſtratis <anchor type="note" xlink:href="" symbol="*"/>, reſiſtentiam utramque augeri & </s> <s xml:id="echoid-s9667" xml:space="preserve">minui, ut au- getur & </s> <s xml:id="echoid-s9668" xml:space="preserve">minuitur numerus particularum fluidi ex loco mota-<lb/>rum eodem tempore, id eſt, ſequitur reſiſtentia integra ra-<lb/> <anchor type="note" xlink:label="note-0362-05a" xlink:href="note-0362-05"/> tionem quadratorum laterum homologorum <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s9669" xml:space="preserve">, ſi de glo- bis, cylindris, aut conis, agatur, rationem quadratorum dia-<lb/>metrorum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9670" xml:space="preserve"/> </p> <div xml:id="echoid-div1356" type="float" level="2" n="3"> <note position="left" xlink:label="note-0362-03" xlink:href="note-0362-03a" xml:space="preserve">909.</note> <note symbol="*" position="left" xlink:label="note-0362-04" xlink:href="note-0362-04a" xml:space="preserve">893. 899.</note> <note symbol="*" position="left" xlink:label="note-0362-05" xlink:href="note-0362-05a" xml:space="preserve">20. El. VI.</note> </div> <note symbol="*" position="left" xml:space="preserve">2 El. XII.</note> </div> <div xml:id="echoid-div1358" type="section" level="1" n="340"> <head xml:id="echoid-head471" xml:space="preserve"><emph style="sc">Experimentum 2.</emph></head> <p> <s xml:id="echoid-s9671" xml:space="preserve">Differt hoc cum præcedenti tantum reſpectu magnitudi-<lb/> <anchor type="note" xlink:label="note-0362-07a" xlink:href="note-0362-07"/> nis globi, qui in tubo T ſuſpenditur. </s> <s xml:id="echoid-s9672" xml:space="preserve">In hoc adhibemus <lb/> <anchor type="note" xlink:label="note-0362-08a" xlink:href="note-0362-08"/> globum H, cujus diameter eſt hypotenuſa trianguli rectan-<lb/>guli iſoſceles, cujus latera ſunt ſemipoll.</s> <s xml:id="echoid-s9673" xml:space="preserve">, æqualia nempe <lb/>diametro globi Gin experimento I. </s> <s xml:id="echoid-s9674" xml:space="preserve">adhibito; </s> <s xml:id="echoid-s9675" xml:space="preserve">quare qua-<lb/>drata diametrorum ſunt ut unum ad duo <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9676" xml:space="preserve">in qua ratione <anchor type="note" xlink:label="note-0362-09a" xlink:href="note-0362-09"/> etiam detectæ fuere reſiſtentiæ, ut ſequenti tabella patet, in <lb/>qua + denotat exceſlum, & </s> <s xml:id="echoid-s9677" xml:space="preserve">- defectum exprimit.</s> <s xml:id="echoid-s9678" xml:space="preserve"/> </p> <div xml:id="echoid-div1358" type="float" level="2" n="1"> <note position="left" xlink:label="note-0362-07" xlink:href="note-0362-07a" xml:space="preserve">910.</note> <note position="left" xlink:label="note-0362-08" xlink:href="note-0362-08a" xml:space="preserve">TAB. XXXV. <lb/>fig. 1.2.</note> <note symbol="*" position="left" xlink:label="note-0362-09" xlink:href="note-0362-09a" xml:space="preserve">47. El. I.</note> </div> <pb o="265" file="0363" n="397" rhead="MATHEMATICA. LIB. II. CAP. XI."/> <note position="right" xml:space="preserve">911.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ globi H. # Reſiſtentiæ globi G in exp. I. <lb/> 1 # {3/4} + # {3/4} - 2 # 2 {3/4} # 1 {1/2} - 3 # 6 -- # 3 -- 4 # 9 {3/4} + # 4 {3/4} 5 # 15 {1/4} # 7 {3/4} 6 # 21 # 10 {1/2} 7 # 28 # 14. </note> <p> <s xml:id="echoid-s9679" xml:space="preserve">Reſiſtentiæ in minori velocitate ſolæ ſunt quæ cum propo-<lb/>ſitione non congruunt; </s> <s xml:id="echoid-s9680" xml:space="preserve">ſed jam in experimento præcedenti <lb/>vidimus illam corrigendam eſſe, quæ in illo experimento <lb/>fuit detecta; </s> <s xml:id="echoid-s9681" xml:space="preserve">reſiſtentia verò ibi in regulari ſerie poſita, <lb/>dimidium eſt illius, quæ, in eadem velocitate, in hoc ulti-<lb/>mo experimento, fuit determinata.</s> <s xml:id="echoid-s9682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9683" xml:space="preserve">Reſiſtentia ex prima cauſa non mutatur pro diverſa cor-<lb/> <anchor type="note" xlink:label="note-0363-03a" xlink:href="note-0363-03"/> poris figura, ſi modo cavitas formata in motu eadem ſit <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s9684" xml:space="preserve"> <anchor type="note" xlink:label="note-0363-04a" xlink:href="note-0363-04"/> quare in cono & </s> <s xml:id="echoid-s9685" xml:space="preserve">cylindro juxta axeos directionem motis, <lb/>ut & </s> <s xml:id="echoid-s9686" xml:space="preserve">in globo, ſi horum corporum diametri fuerint æqua-<lb/>les, & </s> <s xml:id="echoid-s9687" xml:space="preserve">agatur de eodem fluido, & </s> <s xml:id="echoid-s9688" xml:space="preserve">eadem velocitate, re-<lb/>ſiſtentia eadem eſt.</s> <s xml:id="echoid-s9689" xml:space="preserve"/> </p> <div xml:id="echoid-div1359" type="float" level="2" n="2"> <note position="right" xlink:label="note-0363-03" xlink:href="note-0363-03a" xml:space="preserve">912.</note> <note symbol="*" position="right" xlink:label="note-0363-04" xlink:href="note-0363-04a" xml:space="preserve">893 464.</note> </div> <p> <s xml:id="echoid-s9690" xml:space="preserve">Reſiſtentia autem ex ſecunda cauſa variat pro diverſa <lb/> <anchor type="note" xlink:label="note-0363-05a" xlink:href="note-0363-05"/> corporis figura; </s> <s xml:id="echoid-s9691" xml:space="preserve">nam licet ſluidum quieſcens quaqua ver ſum æ-<lb/>quali vi premat, hoc ad preſſionem ex motu oriundam non <lb/>debere referri facile patet, quæ juxta unicam tantum dire-<lb/>ctionem agit, & </s> <s xml:id="echoid-s9692" xml:space="preserve">non tota ſuſtinetur niſi a plano ad hanc di-<lb/>ctionem perpendiculari.</s> <s xml:id="echoid-s9693" xml:space="preserve"/> </p> <div xml:id="echoid-div1360" type="float" level="2" n="3"> <note position="right" xlink:label="note-0363-05" xlink:href="note-0363-05a" xml:space="preserve">913.</note> </div> <p> <s xml:id="echoid-s9694" xml:space="preserve">Demonſtramus in ſcholio ſequenti reſiſtentiam cylindri <lb/> <anchor type="note" xlink:label="note-0363-06a" xlink:href="note-0363-06"/> ſe babere ad coni reſiſtentiam, ſi ambo fuerint recti, & </s> <s xml:id="echoid-s9695" xml:space="preserve">eâ-<lb/>dem velocitate, juxta axium directiones, in eodem fluido, mo-<lb/>ti, ut linea in coni ſuperficie, à vertice ad punctum quod-<lb/>cunque baſeos ducta, ad ſemidiametrum baſeos.</s> <s xml:id="echoid-s9696" xml:space="preserve"/> </p> <div xml:id="echoid-div1361" type="float" level="2" n="4"> <note position="right" xlink:label="note-0363-06" xlink:href="note-0363-06a" xml:space="preserve">914.</note> </div> <p style="it"> <s xml:id="echoid-s9697" xml:space="preserve">Cylindri autem recti & </s> <s xml:id="echoid-s9698" xml:space="preserve">globi reſiſtentias eſſe inter ſe ut <lb/> <anchor type="note" xlink:label="note-0363-07a" xlink:href="note-0363-07"/> tria ad duo, ſi diametri fuerint æquales, & </s> <s xml:id="echoid-s9699" xml:space="preserve">ille juxta a- <pb o="266" file="0364" n="398" rhead="PHYSICES ELEMENTA"/> xeos directionem feratur, in eodem ſcholio demonſtra-<lb/>mus.</s> <s xml:id="echoid-s9700" xml:space="preserve"/> </p> <div xml:id="echoid-div1362" type="float" level="2" n="5"> <note position="right" xlink:label="note-0363-07" xlink:href="note-0363-07a" xml:space="preserve">915.</note> </div> <p style="it"> <s xml:id="echoid-s9701" xml:space="preserve">Unde ſequitur reſiſtentiam globi ſe babere ad reſiſtentiam <lb/> <anchor type="note" xlink:label="note-0364-01a" xlink:href="note-0364-01"/> conirecti, juxta axeos directionem moti, & </s> <s xml:id="echoid-s9702" xml:space="preserve">cujus baſeos dia-<lb/>meter æqualis eſt diametro globi, ut duæ tertiæ partes li-<lb/>neæ, in ſuperficie coni ad punctum baſeos ductæ, ſe babent ad <lb/>ſemidiametrum baſeos.</s> <s xml:id="echoid-s9703" xml:space="preserve"/> </p> <div xml:id="echoid-div1363" type="float" level="2" n="6"> <note position="left" xlink:label="note-0364-01" xlink:href="note-0364-01a" xml:space="preserve">916.</note> </div> <p> <s xml:id="echoid-s9704" xml:space="preserve">Obſervandum coni verticem in motibus hiſce præcede-<lb/>re; </s> <s xml:id="echoid-s9705" xml:space="preserve">ſienim baſis reſiſtentiam pateretur, clarum eſſet hanc a <lb/>reſiſtentia cylindri ejuſdem diametri non differre.</s> <s xml:id="echoid-s9706" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1365" type="section" level="1" n="341"> <head xml:id="echoid-head472" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s9707" xml:space="preserve">Experimentum hoc ut præcedentia inſtituitur, differt <lb/> <anchor type="note" xlink:label="note-0364-02a" xlink:href="note-0364-02"/> tantum corpus in quod aqua agit. </s> <s xml:id="echoid-s9708" xml:space="preserve">Uſus ſum cono in O <lb/> <anchor type="note" xlink:label="note-0364-03a" xlink:href="note-0364-03"/> delineato, baſis diameter eſt ſemipollicis, altitudo ſemipol-<lb/>licis a vertice v ad centrum circuli qui figuram conicam <lb/>terminat, infra quam figuram conicam cylindricum erat <lb/>corpus, eratque partis cylindricæ altitudo circiter octavæ <lb/>partis pollicis. </s> <s xml:id="echoid-s9709" xml:space="preserve">Hæc vero inferior pars corporis conſide-<lb/>randa non eſt, quia in hanc aqua, juxta axeos corporis dire-<lb/>ctionem mota, incurrere non poteſt.</s> <s xml:id="echoid-s9710" xml:space="preserve"/> </p> <div xml:id="echoid-div1365" type="float" level="2" n="1"> <note position="left" xlink:label="note-0364-02" xlink:href="note-0364-02a" xml:space="preserve">917</note> <note position="left" xlink:label="note-0364-03" xlink:href="note-0364-03a" xml:space="preserve">TAB. XXXV. <lb/>fig. 1. 3.</note> </div> <p> <s xml:id="echoid-s9711" xml:space="preserve">Actiones aquæ in corpus tabellâ ſequenti continen-<lb/>tur.</s> <s xml:id="echoid-s9712" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">918.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ <lb/> 1. # gr. {1/2}. - 2. # gr. 1 {1/4} + 3. # gr. 2 {1/2} - 4. # gr. 4. 5. # gr. 6. - 6. # gr. 8 {1/2} 7. # gr. 11. </note> <p> <s xml:id="echoid-s9713" xml:space="preserve">Diviſo grano in centum partes, in tabella ſequentiſe-<lb/>paramus reſiſtentias ex utraque cauſa.</s> <s xml:id="echoid-s9714" xml:space="preserve"/> </p> <pb o="267" file="0365" n="399" rhead="MATHEMATICA. LIB. II. CAP XI."/> <note position="left" xml:space="preserve">919.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates. # Reſiſtentiæ # Reſiſtentiæ # Summæ # Reſiſtentiæ <lb/> exprimâcauſâ. # ex 2<emph style="super">2</emph>. cauſâ # ambarum. # in Exp. 1. # 1 x 20 = 20. # 1 x 20 = 20 # 40 # 50 - 2. # 2 x 20 = 40. # 4 x 20 = 80 # 120 # 125 + 3. # 3 x 20 = 60. # 9 x 20 = 180 # 240 # 250 - 4. # 4 x 20 = 80. # 16 x 20 = 320 # 400 # 400 5. # 5 x 20 = 100. # 25 x 20 = 500 # 600 # 600 - 6. # 6 x 20 = 120. # 36 x 20 = 720 # 840 # 850 7. # 7 x 20 = 140. # 49 x 20 = 980 # 1120 # 1100 </note> <p> <s xml:id="echoid-s9715" xml:space="preserve">Qui tabellam hanc examinaverit, vix quicquam magis ac-<lb/>curatum in talibus experimentis poſſe ſperari, facile vide-<lb/>bit.</s> <s xml:id="echoid-s9716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9717" xml:space="preserve">Conferendo hoc Experimentum cum primo <anchor type="note" xlink:href="" symbol="*"/>, confirma- <anchor type="note" xlink:label="note-0365-03a" xlink:href="note-0365-03"/> tur n. </s> <s xml:id="echoid-s9718" xml:space="preserve">912.</s> <s xml:id="echoid-s9719" xml:space="preserve"/> </p> <div xml:id="echoid-div1366" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0365-03" xlink:href="note-0365-03a" xml:space="preserve">908. 919.</note> </div> <p> <s xml:id="echoid-s9720" xml:space="preserve">Liquet etiam quoad reſiſtentiam ex ſecunda cauſa, hanc <lb/>in hoc caſu ſe habere ad reſiſtentiam globiejuſdem diame-<lb/>tri ut 26. </s> <s xml:id="echoid-s9721" xml:space="preserve">ad 20 <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9722" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">908. 919.</note> <p> <s xml:id="echoid-s9723" xml:space="preserve">Ut nunc computationem ineamus de hiſce reſiſtentiis; </s> <s xml:id="echoid-s9724" xml:space="preserve">ſunt <lb/> <anchor type="note" xlink:label="note-0365-05a" xlink:href="note-0365-05"/> hæ inter ſe ut {2/3} v b ad ſemidiametrum baſis <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s9725" xml:space="preserve">ſi hæc ſemidi <anchor type="note" xlink:label="note-0365-06a" xlink:href="note-0365-06"/> ameter dicatur 1.</s> <s xml:id="echoid-s9726" xml:space="preserve">, erit coni altitudo 2.</s> <s xml:id="echoid-s9727" xml:space="preserve">; & </s> <s xml:id="echoid-s9728" xml:space="preserve">valebit vb radicem <lb/>quadratam numeri 5 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9729" xml:space="preserve">ſunt ergo reſiſtentiæ ut {2/3}√5. </s> <s xml:id="echoid-s9730" xml:space="preserve">ad I.</s> <s xml:id="echoid-s9731" xml:space="preserve"> <anchor type="note" xlink:label="note-0365-07a" xlink:href="note-0365-07"/> Sed in ſuperiori parte, ut in vertice conus ſuſpendi poſſit, <lb/>figura conica non ſervatur, quare reſiſtentia augenda <lb/>eſt.</s> <s xml:id="echoid-s9732" xml:space="preserve"/> </p> <div xml:id="echoid-div1367" type="float" level="2" n="3"> <note position="right" xlink:label="note-0365-05" xlink:href="note-0365-05a" xml:space="preserve">920.</note> <note symbol="*" position="right" xlink:label="note-0365-06" xlink:href="note-0365-06a" xml:space="preserve">916.</note> <note symbol="*" position="right" xlink:label="note-0365-07" xlink:href="note-0365-07a" xml:space="preserve">47. El. 1.</note> </div> <p> <s xml:id="echoid-s9733" xml:space="preserve">Ad latera foraminis per quod filum transmittitur, duæ <lb/>exiguæ dantur ſuperficies planæ, quæ ſimul circiter valent <lb/>{1/25} ſuperficiei circuli cujus diameter eſt bd, quare vigeſi-<lb/>ma quinta pars reſiſtentiæ coni augenda in ratione reſiſten-<lb/>tiæ coni hujus ad reſiſtentiam cylindri, id eſt, in ratione I <lb/>ad √5 <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9734" xml:space="preserve">Sunt ergo reſiſtentiæ quæſitæ ut {25 x 2/3} √5. </s> <s xml:id="echoid-s9735" xml:space="preserve">ad <anchor type="note" xlink:label="note-0365-08a" xlink:href="note-0365-08"/> <pb o="268" file="0366" n="400" rhead="PHYSICES ELEMENTA"/> 24 + √ 5. </s> <s xml:id="echoid-s9736" xml:space="preserve">quæ ratio vix differt a ratione 26. </s> <s xml:id="echoid-s9737" xml:space="preserve">ad 19. </s> <s xml:id="echoid-s9738" xml:space="preserve">In <lb/>qua computatione negleximus conſiderationem figuræ i-<lb/>pſius verticis cui filum fuit alligatum.</s> <s xml:id="echoid-s9739" xml:space="preserve"/> </p> <div xml:id="echoid-div1368" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0365-08" xlink:href="note-0365-08a" xml:space="preserve">915.</note> </div> <p> <s xml:id="echoid-s9740" xml:space="preserve">Differt hæc reſiſtentia ex computatione a reſiſtentia in <lb/>exp. </s> <s xml:id="echoid-s9741" xml:space="preserve">vigeſima parte, quomodocunque mutetur velocitas, <lb/>unde patet differentiam hanc figuræ ipſi tribuendam eſſe.</s> <s xml:id="echoid-s9742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9743" xml:space="preserve">Cum autem non admodum magna ſit hæc differentia, & </s> <s xml:id="echoid-s9744" xml:space="preserve"><lb/>cum non commode ad computum potuerit revocari pars <lb/>quædam figuræ, facile patet experimento hoc propoſitionem <lb/>n. </s> <s xml:id="echoid-s9745" xml:space="preserve">916. </s> <s xml:id="echoid-s9746" xml:space="preserve">confirmari.</s> <s xml:id="echoid-s9747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9748" xml:space="preserve">Experimentis cum cylindris inſtitutis non uſus ſum ad <lb/> <anchor type="note" xlink:label="note-0366-01a" xlink:href="note-0366-01"/> demonſtrata confirmanda; </s> <s xml:id="echoid-s9749" xml:space="preserve">difficultas horum experimento-<lb/>rum in cauſa eſt; </s> <s xml:id="echoid-s9750" xml:space="preserve">vix enim poteſt ſuſpendi cylindrus quin <lb/>agitetur, dum aqua juxta hunc movetur; </s> <s xml:id="echoid-s9751" xml:space="preserve">unde irregularis <lb/>eſt ſeries reſiſtentiarum, & </s> <s xml:id="echoid-s9752" xml:space="preserve">in majoribus velocitatibus ad-<lb/>modum incerta.</s> <s xml:id="echoid-s9753" xml:space="preserve"/> </p> <div xml:id="echoid-div1369" type="float" level="2" n="5"> <note position="left" xlink:label="note-0366-01" xlink:href="note-0366-01a" xml:space="preserve">921.</note> </div> <p> <s xml:id="echoid-s9754" xml:space="preserve">Diverſaſque detexi reſiſtentias cylindrorum, quorum dia-<lb/>metri erant æquales, ſed altitudines diverſæ; </s> <s xml:id="echoid-s9755" xml:space="preserve">quod clarum <lb/>eſt indicium agitationis cujuſdam, cum extra dubium ſit, <lb/>reſiſtentiam cylindri juxta axeos directionem moti ab ipſius <lb/>altitudine non pendere. </s> <s xml:id="echoid-s9756" xml:space="preserve">Cum vero facile ſphæræ coni ita <lb/>fuſpendantur, ut agitatio nulla timenda ſit, hæc corpora ad-<lb/>hibenda credidi.</s> <s xml:id="echoid-s9757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9758" xml:space="preserve">Hoc tamen de experimentis cum cylindris inſtitutis addam.</s> <s xml:id="echoid-s9759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9760" xml:space="preserve">Inter quatuor cylindros cum quibus experimenta tentavi <lb/>unum datur, cujus diameter eſt ſemipollicis, & </s> <s xml:id="echoid-s9761" xml:space="preserve">altitudo <lb/>{2/3} poll.</s> <s xml:id="echoid-s9762" xml:space="preserve">, cujus reſiſtentiæ dant ſeriem regularem, quæ cum <lb/>ante demonſtratis exacte ſatis congruit; </s> <s xml:id="echoid-s9763" xml:space="preserve">ſi illam excipiamus <lb/>reſiſtentiam, quæ reſpondet velocitati ſex, quæ 1 {1/4} gr. </s> <s xml:id="echoid-s9764" xml:space="preserve">id <lb/>eſt circiter duodecima parte in exp. </s> <s xml:id="echoid-s9765" xml:space="preserve">deſicit ab illa quæ <lb/>in ſerie deſideratur, quæ differentia certè notabilis eſt.</s> <s xml:id="echoid-s9766" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1371" type="section" level="1" n="342"> <head xml:id="echoid-head473" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s9767" xml:space="preserve">Hoc ut præcedentia fuit inſtitutum, ſuſpenſo cylindro <lb/> <anchor type="note" xlink:label="note-0366-02a" xlink:href="note-0366-02"/> K, cujus diameter erat ſemi pollicis; </s> <s xml:id="echoid-s9768" xml:space="preserve">motus aquæ e-<lb/> <anchor type="note" xlink:label="note-0366-03a" xlink:href="note-0366-03"/> <pb file="0367" n="401"/> <pb file="0367a" n="402"/> <anchor type="figure" xlink:label="fig-0367a-01a" xlink:href="fig-0367a-01"/> <pb file="0368" n="403"/> <pb o="269" file="0369" n="404" rhead="MATHEMATICA. LIB. II. CAP. XI."/> rat juxta directionem axeos cylindri. <lb/></s> <s xml:id="echoid-s9769" xml:space="preserve"> <anchor type="note" xlink:label="note-0369-01a" xlink:href="note-0369-01"/> </s> </p> <div xml:id="echoid-div1371" type="float" level="2" n="1"> <note position="left" xlink:label="note-0366-02" xlink:href="note-0366-02a" xml:space="preserve">922.</note> <note position="left" xlink:label="note-0366-03" xlink:href="note-0366-03a" xml:space="preserve">TAB. XXXV <lb/>fig 1. 4.</note> <figure xlink:label="fig-0367a-01" xlink:href="fig-0367a-01a"> <image file="0367a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0367a-01"/> </figure> <note position="right" xlink:label="note-0369-01" xlink:href="note-0369-01a" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ <lb/>1. # gr. {3/4}. <lb/>2. # gr. 2. <lb/>3. # gr. 4. <lb/>4. # gr. 7 {1/2}. <lb/>5. # gr. 11. <lb/>6. # gr. 14. <lb/>7. # gr. 20 {1/2}. <lb/></note> </div> <p> <s xml:id="echoid-s9770" xml:space="preserve">Diviſo grano in centum partes ſeparantur reſiſtentiæ ex <lb/>duabus cauſis.</s> <s xml:id="echoid-s9771" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">923.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates # Reſiſtentiæ # Reſiſtentiæ # Summæ # Reſiſtentiæ <lb/>ex 1<emph style="super">2</emph> cauſa # ex 2<emph style="super">2</emph>. cauſa # ambarum # in exper. <lb/> 1. # 1 x 20 = 20. # 1 x 39 = 39. # 59. # 75. 2. # 2 x 20 = 40. # 4 x 39 = 156. # 196. # 200. 3. # 3 x 20 = 60. # 9 x 39 = 351. # 411. # 400. 4. # 4 x 20 = 80. # 16 x 39 = 624. # 704. # 750. 5. # 5 x 20 = 100. # 25 x 39 = 975. # 1075. # 1100. 6. # 6 x 20 = 120. # 36 x 39 = 1404. # 1524. # 1400. 7. # 7 x 20 = 140. # 49 x 39 = 1911. # 2051. # 2050. </note> <p> <s xml:id="echoid-s9772" xml:space="preserve">Unde patet reſiſtentiam ex prima cauſa in hoc caſu illam <lb/>eſſe, quæ obſervata fuit, in experimentis cum globo & </s> <s xml:id="echoid-s9773" xml:space="preserve">co-<lb/>no inſtitutis ejuſdem diametri cum hoc cylindro, juxta <lb/>demonſtrata in n. </s> <s xml:id="echoid-s9774" xml:space="preserve">912. </s> <s xml:id="echoid-s9775" xml:space="preserve">Patet etiam reſiſtentiam ex ſe-<lb/>cunda cauſa in hoc experimento ſe habere ad reſiſtentiam <lb/>globi ut 39 ad 26. </s> <s xml:id="echoid-s9776" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, id eſt ut 3. </s> <s xml:id="echoid-s9777" xml:space="preserve">ad 2, ut monui in n.</s> <s xml:id="echoid-s9778" xml:space="preserve"> <anchor type="note" xlink:label="note-0369-04a" xlink:href="note-0369-04"/> 915.</s> <s xml:id="echoid-s9779" xml:space="preserve"/> </p> <div xml:id="echoid-div1372" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0369-04" xlink:href="note-0369-04a" xml:space="preserve">923. 908.</note> </div> <p> <s xml:id="echoid-s9780" xml:space="preserve">Reſiſtentia ex prima cauſa in variis fluidis differt, hanc-<lb/> <anchor type="note" xlink:label="note-0369-05a" xlink:href="note-0369-05"/> que differentiam niſi experimentis determinari non poſſe <lb/>facile etiam patet.</s> <s xml:id="echoid-s9781" xml:space="preserve"/> </p> <div xml:id="echoid-div1373" type="float" level="2" n="3"> <note position="right" xlink:label="note-0369-05" xlink:href="note-0369-05a" xml:space="preserve">924.</note> </div> <p> <s xml:id="echoid-s9782" xml:space="preserve">In motibus velocioribus, ſi fluida glutinoſa excipiamus <lb/> <anchor type="note" xlink:label="note-0369-06a" xlink:href="note-0369-06"/> exigua eſt reſiſtentia ex cobæſione partium, collata cum re, <lb/>ſiſtentia ex ſecunda cauſa; </s> <s xml:id="echoid-s9783" xml:space="preserve">quod ex diverſis rationibus, ſe-<lb/>cundum quas augentur, ſequitur. </s> <s xml:id="echoid-s9784" xml:space="preserve">Centies ex gr. </s> <s xml:id="echoid-s9785" xml:space="preserve">auctâ ve- <pb o="270" file="0370" n="405" rhead="PHYSICES ELEMENTA"/> locitate in qua æquales ſunt reſiſtentiæ hæ, prima erit ad <lb/>ſecundam ut unum ad centum.</s> <s xml:id="echoid-s9786" xml:space="preserve"/> </p> <div xml:id="echoid-div1374" type="float" level="2" n="4"> <note position="right" xlink:label="note-0369-06" xlink:href="note-0369-06a" xml:space="preserve">925.</note> </div> <p> <s xml:id="echoid-s9787" xml:space="preserve">Reſiſtentia autem ex ſecundâ caujâ in variis fluidis ſe-<lb/> <anchor type="note" xlink:label="note-0370-01a" xlink:href="note-0370-01"/> quitur rationem particularum ex loco motarum; </s> <s xml:id="echoid-s9788" xml:space="preserve">pendete-<lb/>nim a materiæ inertia, quæ materiæ quantitatis rationem <lb/>ſequitur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s9789" xml:space="preserve">eſt ergo reſiſtentia hæc ceteris paribus ut fluidi <anchor type="note" xlink:label="note-0370-02a" xlink:href="note-0370-02"/> denſitas.</s> <s xml:id="echoid-s9790" xml:space="preserve"/> </p> <div xml:id="echoid-div1375" type="float" level="2" n="5"> <note position="left" xlink:label="note-0370-01" xlink:href="note-0370-01a" xml:space="preserve">926.</note> <note symbol="*" position="left" xlink:label="note-0370-02" xlink:href="note-0370-02a" xml:space="preserve">13.</note> </div> <p> <s xml:id="echoid-s9791" xml:space="preserve">Computatio de reſiſtentia ex ſecunda cauſâ iniri poteſt, <lb/>nullo inſtituto experimento, determinando pondus quod <lb/>hanc reſiſtentiam valet.</s> <s xml:id="echoid-s9792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9793" xml:space="preserve">Sit corpus cujus ſuperficies AB reſiſtentiam patitur, dum <lb/> <anchor type="note" xlink:label="note-0370-03a" xlink:href="note-0370-03"/> motus directio ad hanc ſuperſiciem perpendicularis eſt; </s> <s xml:id="echoid-s9794" xml:space="preserve">po-<lb/> <anchor type="note" xlink:label="note-0370-04a" xlink:href="note-0370-04"/> nimus autem ut ſuperius, corpus quieſcere, dum fluidum <lb/>movetur, quo actio fluidi in corpus non mutatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9795" xml:space="preserve"/> </p> <div xml:id="echoid-div1376" type="float" level="2" n="6"> <note position="left" xlink:label="note-0370-03" xlink:href="note-0370-03a" xml:space="preserve">927.</note> <note position="left" xlink:label="note-0370-04" xlink:href="note-0370-04a" xml:space="preserve">TAB. XXXVI. <lb/>fig. 4.</note> </div> <note symbol="*" position="left" xml:space="preserve">897.</note> <p> <s xml:id="echoid-s9796" xml:space="preserve">Sit ſuperficiei AB æqualis ſuperficies CD in fundo vaſis, <lb/>continentis ſimile fluidum ad altitudinem EF; </s> <s xml:id="echoid-s9797" xml:space="preserve">ponamus præ-<lb/>terea preſſionem quam patitur pars CD fundi, æqualem eſſe <lb/>actioni, quam patitur AB, ſepoſita partium cohæſio-<lb/>ne.</s> <s xml:id="echoid-s9798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9799" xml:space="preserve">Plana hæc duo æqualia, cohibent ſingula motum fluidi; <lb/></s> <s xml:id="echoid-s9800" xml:space="preserve">& </s> <s xml:id="echoid-s9801" xml:space="preserve">propter actionum ſuarum æqualitatem, æquales motus <lb/>cohibent. </s> <s xml:id="echoid-s9802" xml:space="preserve">Ideoque ſublatis ipſis planis, fluidum in locis in <lb/>quibus plana agebant eâdem velocitate fertur, id eſt, flui-<lb/>dum, quod in fuperficiem AB agit, movetur velocitate qua <lb/>fluidum per foramen in CD exire poteſt, id eſt veloci-<lb/>tate, quam corpus acquirit in vacuo cadendo ab altitudine <lb/>EC <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9803" xml:space="preserve">ſeponimus enim cohæſionem partium & </s> <s xml:id="echoid-s9804" xml:space="preserve">omnem at- <anchor type="note" xlink:label="note-0370-06a" xlink:href="note-0370-06"/> tritum. </s> <s xml:id="echoid-s9805" xml:space="preserve">Ergo actio, quam patitur ſuperficies AB, dum <lb/>fluidum in hancagit, valet pondus columnæ fluidi, cujus ba-<lb/>ſis eſt CD, aut AB, & </s> <s xml:id="echoid-s9806" xml:space="preserve">altitudo EF; </s> <s xml:id="echoid-s9807" xml:space="preserve">hæc eſt enim preſſio <lb/>quam patitur CD <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9808" xml:space="preserve"/> </p> <div xml:id="echoid-div1377" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0370-06" xlink:href="note-0370-06a" xml:space="preserve">796.</note> </div> <note symbol="*" position="left" xml:space="preserve">721.</note> <p style="it"> <s xml:id="echoid-s9809" xml:space="preserve">Unde patet Priſmatis recti, juxta directionem ad baſim <lb/> <anchor type="note" xlink:label="note-0370-08a" xlink:href="note-0370-08"/> perpendicularem, in fluido moti, reſiſtentiam valere pondus <lb/>columnæ ejuſdem fluidi, cujus baſis æqualis eſt baſi priſma-<lb/>tis, & </s> <s xml:id="echoid-s9810" xml:space="preserve">cujus altitudo illa eſt, à qua corpus in vacuo ca- <pb o="271" file="0371" n="406" rhead="MATHEMATICA. LIB. II. CAP. XI."/> dendo acquirit velocitatem qua priſma in fluido fer-<lb/>tur.</s> <s xml:id="echoid-s9811" xml:space="preserve"/> </p> <div xml:id="echoid-div1378" type="float" level="2" n="8"> <note position="left" xlink:label="note-0370-08" xlink:href="note-0370-08a" xml:space="preserve">928.</note> </div> <p> <s xml:id="echoid-s9812" xml:space="preserve">Demonſtratio hæc tantum locum habet ubi ſuperficies, <lb/> <anchor type="note" xlink:label="note-0371-01a" xlink:href="note-0371-01"/> quæ reſiſtentiam patitur, ad motus directionem perpendicu-<lb/>laris eſt <anchor type="note" xlink:href="" symbol="*"/>, ubi de aliis ſuperficiebus agitur ad demonſtrata <anchor type="note" xlink:label="note-0371-02a" xlink:href="note-0371-02"/> de his <anchor type="note" xlink:href="" symbol="*"/> attendendum eſt.</s> <s xml:id="echoid-s9813" xml:space="preserve"/> </p> <div xml:id="echoid-div1379" type="float" level="2" n="9"> <note position="right" xlink:label="note-0371-01" xlink:href="note-0371-01a" xml:space="preserve">929.</note> <note symbol="*" position="right" xlink:label="note-0371-02" xlink:href="note-0371-02a" xml:space="preserve">913.</note> </div> <note symbol="*" position="right" xml:space="preserve">214. 915.</note> <p> <s xml:id="echoid-s9814" xml:space="preserve">Quare ſi de globo agatur, reſiſtentia valebit duas tertias <lb/>partes ponderis cylindri ex fluido cujus diameter æqualis <lb/>eſt diametro globi, & </s> <s xml:id="echoid-s9815" xml:space="preserve">cujus altitudo illa eſt a qua caden-<lb/>do in vacuo corpus acquirit velocitatem, cum qua in fluido <lb/>movetur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9816" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">928. 915.</note> <p style="it"> <s xml:id="echoid-s9817" xml:space="preserve">Altitudo a qua corpus cadendo acquirit velocitatem, qua <lb/> <anchor type="note" xlink:label="note-0371-05a" xlink:href="note-0371-05"/> ſi in fluido feratur, reſiſtentia ex ſecunda cauſa ponderi i-<lb/>pſius corporis æqualis ſit, ex his facile detegitur. </s> <s xml:id="echoid-s9818" xml:space="preserve">Si de pri-<lb/>ſmate agatur, denſitas fluidi ſe babebit ad priſmatis denſi-<lb/>tatem, ut bujus altitudo ad altitudinem quæſitam <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9819" xml:space="preserve"/> </p> <div xml:id="echoid-div1380" type="float" level="2" n="10"> <note position="right" xlink:label="note-0371-05" xlink:href="note-0371-05a" xml:space="preserve">930.</note> </div> <note symbol="*" position="right" xml:space="preserve">928. 732.</note> <p> <s xml:id="echoid-s9820" xml:space="preserve">Si de globo agatur denſitas fluidi ſe babebit ad globi den-<lb/> <anchor type="note" xlink:label="note-0371-07a" xlink:href="note-0371-07"/> ſitatem, ut altitudo cylindri ejuſdem ponderis cum globo <lb/>& </s> <s xml:id="echoid-s9821" xml:space="preserve">diametrum æqualem globi diametro habentis, quæ alti-<lb/>tudo valet duas tertias partes diametri, ad duas tertias par-<lb/>tes altitudinis quæſitæ <anchor type="note" xlink:href="" symbol="*"/>, id eſt ut diameter ad altitudinem <anchor type="note" xlink:label="note-0371-08a" xlink:href="note-0371-08"/> quæſitam.</s> <s xml:id="echoid-s9822" xml:space="preserve"/> </p> <div xml:id="echoid-div1381" type="float" level="2" n="11"> <note position="right" xlink:label="note-0371-07" xlink:href="note-0371-07a" xml:space="preserve">931.</note> <note symbol="*" position="right" xlink:label="note-0371-08" xlink:href="note-0371-08a" xml:space="preserve">928. 915. <lb/>738.</note> </div> <p> <s xml:id="echoid-s9823" xml:space="preserve">Pondus quod reſiſtentiam valet, ideoque ipſa reſiſten-<lb/> <anchor type="note" xlink:label="note-0371-09a" xlink:href="note-0371-09"/> tia ex ſecunda cauſa, ſequitur rationem baſeos priſmatis, <lb/>denſitatis fluidi & </s> <s xml:id="echoid-s9824" xml:space="preserve">quadrati velocitatis corporis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9825" xml:space="preserve">Quod <anchor type="note" xlink:label="note-0371-10a" xlink:href="note-0371-10"/> cum ante demonſtratis <anchor type="note" xlink:href="" symbol="*"/> congruit.</s> <s xml:id="echoid-s9826" xml:space="preserve"/> </p> <div xml:id="echoid-div1382" type="float" level="2" n="12"> <note position="right" xlink:label="note-0371-09" xlink:href="note-0371-09a" xml:space="preserve">932.</note> <note symbol="*" position="right" xlink:label="note-0371-10" xlink:href="note-0371-10a" xml:space="preserve">928 255.</note> </div> <note symbol="*" position="right" xml:space="preserve">908. 926. <lb/>900.</note> <p> <s xml:id="echoid-s9827" xml:space="preserve">Quæ de pondere reſiſtentiam valenti dicta ſunt <anchor type="note" xlink:href="" symbol="*"/> etiam cum <anchor type="note" xlink:label="note-0371-12a" xlink:href="note-0371-12"/> experimentis congruunt, ut patebit ſi computatio ineatur <lb/> <anchor type="note" xlink:label="note-0371-13a" xlink:href="note-0371-13"/> de pondere quod valet reſiſtentiam, data velocitate qua-<lb/>cunque ex illis quas in experimentis aqua habuit.</s> <s xml:id="echoid-s9828" xml:space="preserve"/> </p> <div xml:id="echoid-div1383" type="float" level="2" n="13"> <note position="right" xlink:label="note-0371-12" xlink:href="note-0371-12a" xml:space="preserve">933.</note> <note symbol="*" position="right" xlink:label="note-0371-13" xlink:href="note-0371-13a" xml:space="preserve">928.</note> </div> <p> <s xml:id="echoid-s9829" xml:space="preserve">Velocitatem aquæ diximus 2. </s> <s xml:id="echoid-s9830" xml:space="preserve">aperto epiſtomio cujus a-<lb/> <anchor type="note" xlink:label="note-0371-14a" xlink:href="note-0371-14"/> pertura erat circulus diametri ſemi pollicis, & </s> <s xml:id="echoid-s9831" xml:space="preserve">ſupra quod <lb/>foramen aquæ altitudo erat quinque pedum; </s> <s xml:id="echoid-s9832" xml:space="preserve">ita ut pes cy-<lb/>lindricus aquæ effluere potuerit in tempore 46, 66. </s> <s xml:id="echoid-s9833" xml:space="preserve">minu-<lb/>torum ſecundorum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9834" xml:space="preserve">Pes cylindricus in tubo, in quo ex- <anchor type="note" xlink:label="note-0371-15a" xlink:href="note-0371-15"/> <pb o="272" file="0372" n="407" rhead="PHYSICES ELEMENTA"/> perimenta fuere inſtituta, ſi hicce continuatus foret occu-<lb/>paret pedes 18 <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9835" xml:space="preserve">Ergo aqua per tubum tranſivit velocita- <anchor type="note" xlink:label="note-0372-01a" xlink:href="note-0372-01"/> te qua pédes 18, percurruntur, in tempore minutorum <lb/>ſecundorum 46, 66. </s> <s xml:id="echoid-s9836" xml:space="preserve">& </s> <s xml:id="echoid-s9837" xml:space="preserve">ubi velocitas in Exp. </s> <s xml:id="echoid-s9838" xml:space="preserve">fuit 6.</s> <s xml:id="echoid-s9839" xml:space="preserve">, hoc <lb/>idem ſpatium 18. </s> <s xml:id="echoid-s9840" xml:space="preserve">pedum potuit percurri in min. </s> <s xml:id="echoid-s9841" xml:space="preserve">ſec. </s> <s xml:id="echoid-s9842" xml:space="preserve">15, <lb/>55. </s> <s xml:id="echoid-s9843" xml:space="preserve">Experimentis cum pendulis inſtitutis, & </s> <s xml:id="echoid-s9844" xml:space="preserve">computatio-<lb/>ne, juxta regulam ante memoratam <anchor type="note" xlink:href="" symbol="*"/>, initâ, conſtat, cor- <anchor type="note" xlink:label="note-0372-02a" xlink:href="note-0372-02"/> pus in uno minuto ſecundo cadere ab altitudine 15, 626. <lb/></s> <s xml:id="echoid-s9845" xml:space="preserve">pedum Rhenolandicorum, quales ubique in menſuris noſtris <lb/>adhibemus; </s> <s xml:id="echoid-s9846" xml:space="preserve">& </s> <s xml:id="echoid-s9847" xml:space="preserve">velocitate ab hac altitudine cadendo acqui-<lb/>ſita corpus in uno minuto ſecundo percurrit pedes 31, 252. </s> <s xml:id="echoid-s9848" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s9849" xml:space="preserve"> & </s> <s xml:id="echoid-s9850" xml:space="preserve">in minutis ſec. </s> <s xml:id="echoid-s9851" xml:space="preserve">15, 55. </s> <s xml:id="echoid-s9852" xml:space="preserve">percurret pedes 486, 06.</s> <s xml:id="echoid-s9853" xml:space="preserve">; ergo ve-<lb/>locitas 6. </s> <s xml:id="echoid-s9854" xml:space="preserve">in exp. </s> <s xml:id="echoid-s9855" xml:space="preserve">ad velocitatem acquiſitam cadendo ab al-<lb/>titudine 15, 626. </s> <s xml:id="echoid-s9856" xml:space="preserve">pedum, ut 18. </s> <s xml:id="echoid-s9857" xml:space="preserve">ad 486, 06. </s> <s xml:id="echoid-s9858" xml:space="preserve">Idcirco acqui-<lb/>rit corpus velocitatem hanc exp.</s> <s xml:id="echoid-s9859" xml:space="preserve">, cadendo in vacuo ab alti-<lb/>tudine o, 257. </s> <s xml:id="echoid-s9860" xml:space="preserve">poll. </s> <s xml:id="echoid-s9861" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, quæ vix excedit quartam pollicis par- <anchor type="note" xlink:label="note-0372-03a" xlink:href="note-0372-03"/> tem.</s> <s xml:id="echoid-s9862" xml:space="preserve"/> </p> <div xml:id="echoid-div1384" type="float" level="2" n="14"> <note position="right" xlink:label="note-0371-14" xlink:href="note-0371-14a" xml:space="preserve">934.</note> <note symbol="*" position="right" xlink:label="note-0371-15" xlink:href="note-0371-15a" xml:space="preserve">833.</note> <note position="left" xlink:label="note-0372-01" xlink:href="note-0372-01a" xml:space="preserve">15 El. XII.</note> <note symbol="*" position="left" xlink:label="note-0372-02" xlink:href="note-0372-02a" xml:space="preserve">288.</note> <note symbol="*" position="left" xlink:label="note-0372-03" xlink:href="note-0372-03a" xml:space="preserve">255.</note> </div> <p> <s xml:id="echoid-s9863" xml:space="preserve">Pes cubicus aquæ ponderat grana 487360 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9864" xml:space="preserve">& </s> <s xml:id="echoid-s9865" xml:space="preserve">pondus <anchor type="note" xlink:label="note-0372-04a" xlink:href="note-0372-04"/> pedis cylindrici eſt gran. </s> <s xml:id="echoid-s9866" xml:space="preserve">382772. </s> <s xml:id="echoid-s9867" xml:space="preserve">& </s> <s xml:id="echoid-s9868" xml:space="preserve">poll. </s> <s xml:id="echoid-s9869" xml:space="preserve">cylindrici <lb/>gran. </s> <s xml:id="echoid-s9870" xml:space="preserve">221 {1/2}.</s> <s xml:id="echoid-s9871" xml:space="preserve"/> </p> <div xml:id="echoid-div1385" type="float" level="2" n="15"> <note symbol="*" position="left" xlink:label="note-0372-04" xlink:href="note-0372-04a" xml:space="preserve">783.</note> </div> <p> <s xml:id="echoid-s9872" xml:space="preserve">Reſiſtentia cylindri cujus diameter eſt ſemi poll. </s> <s xml:id="echoid-s9873" xml:space="preserve">& </s> <s xml:id="echoid-s9874" xml:space="preserve">ve-<lb/>locitas illa quæ in experimentis dicitur 6. </s> <s xml:id="echoid-s9875" xml:space="preserve">eſt pondus cylin-<lb/>dri aquei cujus diameter eſt ſemi poll. </s> <s xml:id="echoid-s9876" xml:space="preserve">& </s> <s xml:id="echoid-s9877" xml:space="preserve">altitudo æqualis <lb/>o, 257. </s> <s xml:id="echoid-s9878" xml:space="preserve">poll. </s> <s xml:id="echoid-s9879" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, valet ergo gr. </s> <s xml:id="echoid-s9880" xml:space="preserve">14, 23.</s> <s xml:id="echoid-s9881" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">928.</note> <p> <s xml:id="echoid-s9882" xml:space="preserve">Ponendo nunc reſiſtentiam hanc in ratione duplicata ve-<lb/>locitatum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9883" xml:space="preserve">& </s> <s xml:id="echoid-s9884" xml:space="preserve">globi reſiſtentiam duas tertias partes reſi- <anchor type="note" xlink:label="note-0372-06a" xlink:href="note-0372-06"/> ſtentiæ cylindri <anchor type="note" xlink:href="" symbol="*"/>, tabellam ſequentem formamus, in qua <anchor type="note" xlink:label="note-0372-07a" xlink:href="note-0372-07"/> partes, centeſimâ grani parte minores, negliguntur.</s> <s xml:id="echoid-s9885" xml:space="preserve"/> </p> <div xml:id="echoid-div1386" type="float" level="2" n="16"> <note symbol="*" position="left" xlink:label="note-0372-06" xlink:href="note-0372-06a" xml:space="preserve">932.</note> <note symbol="*" position="left" xlink:label="note-0372-07" xlink:href="note-0372-07a" xml:space="preserve">915</note> </div> <pb o="273" file="0373" n="408" rhead="MATHEMATICA. LIB. II. CAP. XI."/> <note position="right" xml:space="preserve">935.</note> <note symbol="*" position="right" xml:space="preserve">923.</note> <note symbol="*" position="right" xml:space="preserve">908.</note> <note position="right" xml:space="preserve"> <lb/>Velocitates. # # Reſiſtentiæ # ex # ſecundâ # cauſâ. <lb/> # # Cylindri ## Globi # comp. # Exp.<anchor type="note" xlink:href="" symbol="*"/> # comp. # Exp.<anchor type="note" xlink:href="" symbol="*"/> 1. # 39. # 39. # 26. # 26. 2. # 158. # 156. # 105. # 104. 3. # 356. # 351. # 237. # 234. 4. # 632. # 624. # 421. # 416. 5. # 988. # 975. # 659. # 650. 6. # 1423. # 1404. # 949. # 936. 7. # 1937. # 1911. # 1291. # 1274. </note> <p> <s xml:id="echoid-s9886" xml:space="preserve">Exiguam dari differentiam inter has reſiſtentias, compu-<lb/> <anchor type="note" xlink:label="note-0373-05a" xlink:href="note-0373-05"/> tatione detectas, & </s> <s xml:id="echoid-s9887" xml:space="preserve">illas, quæ experimentis deteguntur, non <lb/>mirum; </s> <s xml:id="echoid-s9888" xml:space="preserve">cum pendeat collatio hæc, 1. </s> <s xml:id="echoid-s9889" xml:space="preserve">à menſura aquæ ef-<lb/>fluentis certo tempore, 2. </s> <s xml:id="echoid-s9890" xml:space="preserve">à menſura ſpatii percurſi certo <lb/>tempore a corpore cadente, 3. </s> <s xml:id="echoid-s9891" xml:space="preserve">à menſura ponderis pedis <lb/>cubici aquæ, & </s> <s xml:id="echoid-s9892" xml:space="preserve">4. </s> <s xml:id="echoid-s9893" xml:space="preserve">tandem à menſura ipſarum reſiſtentiarum. <lb/></s> <s xml:id="echoid-s9894" xml:space="preserve">In ſingulis harum quatuor menſurarum errores exigui vitari <lb/>minime poſſunt; </s> <s xml:id="echoid-s9895" xml:space="preserve">non tamen tales ſunt ut ſcrupulus ullus <lb/>circa experimenta ſupereſſe poſſit.</s> <s xml:id="echoid-s9896" xml:space="preserve"/> </p> <div xml:id="echoid-div1387" type="float" level="2" n="17"> <note position="right" xlink:label="note-0373-05" xlink:href="note-0373-05a" xml:space="preserve">936.</note> </div> <p> <s xml:id="echoid-s9897" xml:space="preserve">In cap. </s> <s xml:id="echoid-s9898" xml:space="preserve">22. </s> <s xml:id="echoid-s9899" xml:space="preserve">lib. </s> <s xml:id="echoid-s9900" xml:space="preserve">1. </s> <s xml:id="echoid-s9901" xml:space="preserve">diximus, nos in hoc capite tradituros de-<lb/> <anchor type="note" xlink:label="note-0373-06a" xlink:href="note-0373-06"/> monſtrationem ab illa diverſam, quæ in n. </s> <s xml:id="echoid-s9902" xml:space="preserve">446. </s> <s xml:id="echoid-s9903" xml:space="preserve">datur, de <lb/>virium menſura, quas in eodem corpore quadratis veloci-<lb/>tatum ſtatuimus proportionales <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s9904" xml:space="preserve">Hac ergo caput hoc <anchor type="note" xlink:label="note-0373-07a" xlink:href="note-0373-07"/> terminabo.</s> <s xml:id="echoid-s9905" xml:space="preserve"/> </p> <div xml:id="echoid-div1388" type="float" level="2" n="18"> <note position="right" xlink:label="note-0373-06" xlink:href="note-0373-06a" xml:space="preserve">937.</note> <note symbol="*" position="right" xlink:label="note-0373-07" xlink:href="note-0373-07a" xml:space="preserve">447.</note> </div> <p> <s xml:id="echoid-s9906" xml:space="preserve">A nemine in dubium vocatur fluidi velocitatem, ex preſ-<lb/>ſione fluidi ſuperincumbentis oriundam, ſequi rationem ſub-<lb/>duplicatam altitudinis fluidi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9907" xml:space="preserve">demonſtravimus in hoc ca- <anchor type="note" xlink:label="note-0373-08a" xlink:href="note-0373-08"/> pite <anchor type="note" xlink:href="" symbol="*"/>, reſiſtentiam ex ſecunda cauſa ſequi hujus altitudinis <anchor type="note" xlink:label="note-0373-09a" xlink:href="note-0373-09"/> rationem; </s> <s xml:id="echoid-s9908" xml:space="preserve">ideoque rationem duplicatam velocitatis; </s> <s xml:id="echoid-s9909" xml:space="preserve">ſed <lb/>etiam vidimus reſiſtentiam eandem ſequi rationem cum vi in-<lb/>ſita particulis ſingulis fluidi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9910" xml:space="preserve">quare vis hæc etiam eſt ut <anchor type="note" xlink:label="note-0373-10a" xlink:href="note-0373-10"/> quadratum velocitatis. </s> <s xml:id="echoid-s9911" xml:space="preserve">Q. </s> <s xml:id="echoid-s9912" xml:space="preserve">D. </s> <s xml:id="echoid-s9913" xml:space="preserve">E.</s> <s xml:id="echoid-s9914" xml:space="preserve"/> </p> <div xml:id="echoid-div1389" type="float" level="2" n="19"> <note symbol="*" position="right" xlink:label="note-0373-08" xlink:href="note-0373-08a" xml:space="preserve">799.</note> <note symbol="*" position="right" xlink:label="note-0373-09" xlink:href="note-0373-09a" xml:space="preserve">928.</note> <note symbol="*" position="right" xlink:label="note-0373-10" xlink:href="note-0373-10a" xml:space="preserve">899.</note> </div> <pb o="274" file="0374" n="409" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1391" type="section" level="1" n="343"> <head xml:id="echoid-head474" xml:space="preserve">SCHOLIUM, <lb/>Demonſtrationes n. 914. & 915.</head> <p> <s xml:id="echoid-s9915" xml:space="preserve">Sint ABCD, EFG, ſectiones per axes cylindri & </s> <s xml:id="echoid-s9916" xml:space="preserve">coni, quorum ba-<lb/> <anchor type="note" xlink:label="note-0374-01a" xlink:href="note-0374-01"/> ſium diametri ſunt æquales; </s> <s xml:id="echoid-s9917" xml:space="preserve">moveatur fluidum juxta directiones axium. <lb/></s> <s xml:id="echoid-s9918" xml:space="preserve"> <anchor type="note" xlink:label="note-0374-02a" xlink:href="note-0374-02"/> Planum AB integram fluidi actionem ſuſtinet, dum hoc juxta hanc ſuperfi-<lb/>ciem ab omni parte continuo defluit. </s> <s xml:id="echoid-s9919" xml:space="preserve">Superficies autem FE minorem ſuſti-<lb/>net preſſionem & </s> <s xml:id="echoid-s9920" xml:space="preserve">eo minorem quo ipſius obliquitas ad motus directionem <lb/>major eſt <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s9921" xml:space="preserve">revocaturque preſſio, in punctum quodcunque M, ad preſſio- <anchor type="note" xlink:label="note-0374-03a" xlink:href="note-0374-03"/> nem perpendicularem ad ſuperficiem, ſi poſita IM, juxta motus directio-<lb/>nem, ipſi FE æqualem, detur in M perpendicularis ML ad FE, & </s> <s xml:id="echoid-s9922" xml:space="preserve">duca-<lb/>tur huic parallela IL. </s> <s xml:id="echoid-s9923" xml:space="preserve">Tunc preſſio ex motu oriunda ſe habet ad preſſionem <lb/>quam ſuperficies patitur ut IM ad ML <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9924" xml:space="preserve">talemque preſſionem ſuperficies FE <anchor type="note" xlink:label="note-0374-04a" xlink:href="note-0374-04"/> in omnibus punctis patitur, fluidum enim, quod in omnibus punctis tangit <lb/>ſuperficiem, a continuo accedente fluido talem patitur actionem. </s> <s xml:id="echoid-s9925" xml:space="preserve">Ita res ſe-<lb/>ſe non haberet, ſi de motu corporum ſeparatorum ageretur; </s> <s xml:id="echoid-s9926" xml:space="preserve">tuncenim nu-<lb/>merus corporum in ſuperficiem EF incurrentium, æqualis eſſet numero cor-<lb/>porum, quæ, ſublata ſuperficie EF, in ſuperficiem EH impingi poſſent.</s> <s xml:id="echoid-s9927" xml:space="preserve"/> </p> <div xml:id="echoid-div1391" type="float" level="2" n="1"> <note position="left" xlink:label="note-0374-01" xlink:href="note-0374-01a" xml:space="preserve">938.</note> <note position="left" xlink:label="note-0374-02" xlink:href="note-0374-02a" xml:space="preserve">TAB. XXXVI. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0374-03" xlink:href="note-0374-03a" xml:space="preserve">913.</note> <note symbol="*" position="left" xlink:label="note-0374-04" xlink:href="note-0374-04a" xml:space="preserve">229.</note> </div> <p> <s xml:id="echoid-s9928" xml:space="preserve">Si preſſio per LM in duas ſolvatur ducta LN perpendiculari ad IM, deſi-<lb/>gnabit NM actionem qua corpus juxta directionem motus fluidi propellitur.</s> <s xml:id="echoid-s9929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9930" xml:space="preserve">Actio nunc tota in conumad actionem in cylindrum, ut coni ſuperficies <lb/>convexa ad cylindri baſin; </s> <s xml:id="echoid-s9931" xml:space="preserve">tales enim ſunt ſuperficies in quas preſſiones a-<lb/>gunt; </s> <s xml:id="echoid-s9932" xml:space="preserve">id eſt ut EF ad EH: </s> <s xml:id="echoid-s9933" xml:space="preserve">& </s> <s xml:id="echoid-s9934" xml:space="preserve">ut actio, quæ in ſingulis punctis in conum agit, <lb/>juxta directionem motus fluidi, ad actionem, quæ in ſingulis punctis cylindrum <lb/>propellit, id eſt, ut NM ad IM. </s> <s xml:id="echoid-s9935" xml:space="preserve">Ratio ex his compoſita eſt ratio pro-<lb/>ducti EF per NM ad productum EH per IM.</s> <s xml:id="echoid-s9936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9937" xml:space="preserve">Quæ producta propter æquales EF, IM, ſunt ut NM ad EH, aut <lb/>ML; </s> <s xml:id="echoid-s9938" xml:space="preserve">ſunt enim æquales hæ lineæ; </s> <s xml:id="echoid-s9939" xml:space="preserve">propter æqualia & </s> <s xml:id="echoid-s9940" xml:space="preserve">ſimilia trian-<lb/>gula IML, EFH. </s> <s xml:id="echoid-s9941" xml:space="preserve">Sunt etiam ſimilia triangula LMN, LMI <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9942" xml:space="preserve">qua- <anchor type="note" xlink:label="note-0374-05a" xlink:href="note-0374-05"/> re MN ad ML, ut ML ad MI, aut ut EH ad EF. </s> <s xml:id="echoid-s9943" xml:space="preserve">Ergo reſiſtentia <lb/>coni ſe habet ad cylindri reſiſtentiam, poſitis ambobus rectis, habentibus ba-<lb/>ſes æquales, & </s> <s xml:id="echoid-s9944" xml:space="preserve">velocitatibus æqualibus, juxta axium directiones, in eodem <lb/>fluido, agitatis, ut ſemidiameter baſis ad rectam in coni ſuperficie a ver-<lb/>tice ad punctum baſeos ducta, ut diximus in n. </s> <s xml:id="echoid-s9945" xml:space="preserve">914.</s> <s xml:id="echoid-s9946" xml:space="preserve"/> </p> <div xml:id="echoid-div1392" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0374-05" xlink:href="note-0374-05a" xml:space="preserve">8. El. VI.</note> </div> <p> <s xml:id="echoid-s9947" xml:space="preserve">Ponamus nunc cylindrum cum ſphæra, diametros æquales habentes, eâ-<lb/> <anchor type="note" xlink:label="note-0374-06a" xlink:href="note-0374-06"/> dem velocitate, in eodem fluido, moveri, cylindrumque juxta axcos dire-<lb/>ctionem transferri.</s> <s xml:id="echoid-s9948" xml:space="preserve"/> </p> <div xml:id="echoid-div1393" type="float" level="2" n="3"> <note position="left" xlink:label="note-0374-06" xlink:href="note-0374-06a" xml:space="preserve">939.</note> </div> <p> <s xml:id="echoid-s9949" xml:space="preserve">Sit hic ABLM, dum ſphæra repræſentatur per DFEG; </s> <s xml:id="echoid-s9950" xml:space="preserve">eſtque C cen-<lb/> <anchor type="note" xlink:label="note-0374-07a" xlink:href="note-0374-07"/> trum. </s> <s xml:id="echoid-s9951" xml:space="preserve">Reſiſtentia quam patitur pars baſeos cylindri, infinitè exigua, I i, ſe <lb/>habet ad reſiſtentiam quam patitur pars reſpondens F f ſuperficiei ſphæræ <lb/>ductis IH, ih, ad axem cylindri, ideoque ad directionem motus, paralle-<lb/>lis, ut F f ad F g, quæ ad AB parallela ducitur; </s> <s xml:id="echoid-s9952" xml:space="preserve">quod patet hìc applicando <lb/>demonſtrationem datam in numero præcedenti. </s> <s xml:id="echoid-s9953" xml:space="preserve">Triangula F fg, FHC, <lb/>ambo rectangula, & </s> <s xml:id="echoid-s9954" xml:space="preserve">habentia angulos æquales f F g, CFH, quorum ſin-<lb/>gulorum defectus ab angulo recto eſt angulus g FC, ſunt ſimilia: </s> <s xml:id="echoid-s9955" xml:space="preserve">ergo</s> </p> <div xml:id="echoid-div1394" type="float" level="2" n="4"> <note position="left" xlink:label="note-0374-07" xlink:href="note-0374-07a" xml:space="preserve">TAB. XXXVI. <lb/>fig. 6.</note> </div> </div> <div xml:id="echoid-div1396" type="section" level="1" n="344"> <head xml:id="echoid-head475" xml:space="preserve">F f, F g :: FC aut IH, FH</head> <p> <s xml:id="echoid-s9956" xml:space="preserve">Idcirco ſi IH repræſentat reſiſtentiam quam patitur pars ſuperficiei I i, <lb/>FH ipſam repræſentabit quam patitur pars reſpondens F f ſuperficiei globi.</s> <s xml:id="echoid-s9957" xml:space="preserve"> <pb o="275" file="0375" n="410" rhead="MATHEMATICA. LIB. II. CAP. XII."/> Et cum hæc demonſtratio ad ſingula ſuperficiei hemiſphærii DFE puncta <lb/>poſſit applicari; </s> <s xml:id="echoid-s9958" xml:space="preserve">ſequitur, cylindrum ADEB, hemiſphærio circumſcriptum, <lb/>ſe habere ad ipſum hemiſphærium, ut integra reſiſtentia cylindri ad inte-<lb/>gram ſpheræ reſiſtentiam; </s> <s xml:id="echoid-s9959" xml:space="preserve">quæ ergo reſiſtentiæ ſunt ut tria ad duo, ut monui <lb/>in n. </s> <s xml:id="echoid-s9960" xml:space="preserve">115.</s> <s xml:id="echoid-s9961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9962" xml:space="preserve">Ex iiſdem hiſce principiis quæ corporum quorumcunque reſiſtentias ſpe-<lb/> <anchor type="note" xlink:label="note-0375-01a" xlink:href="note-0375-01"/> ctant deducuntur. </s> <s xml:id="echoid-s9963" xml:space="preserve">Ex. </s> <s xml:id="echoid-s9964" xml:space="preserve">gr. </s> <s xml:id="echoid-s9965" xml:space="preserve">facile ex his probatur, cylindri recti, cujus altitudo <lb/> <anchor type="note" xlink:label="note-0375-02a" xlink:href="note-0375-02"/> diametro æqualis eſt, reſiſtentiam ex ſecunda cauſa eandem eſſe, ſi velocitas ea-<lb/>dem fuerit, juxta quamcunque directionem feratur.</s> <s xml:id="echoid-s9966" xml:space="preserve"/> </p> <div xml:id="echoid-div1396" type="float" level="2" n="1"> <note position="right" xlink:label="note-0375-01" xlink:href="note-0375-01a" xml:space="preserve">940.</note> <note position="right" xlink:label="note-0375-02" xlink:href="note-0375-02a" xml:space="preserve">941.</note> </div> </div> <div xml:id="echoid-div1398" type="section" level="1" n="345"> <head xml:id="echoid-head476" xml:space="preserve">CAPUT XII. <lb/>De Retardatione Corporum in Fluidis motorum.</head> <p> <s xml:id="echoid-s9967" xml:space="preserve">VIdimus ſuperius corpus in fluido motum reſiſtentiam pa-<lb/> <anchor type="note" xlink:label="note-0375-03a" xlink:href="note-0375-03"/> ti <anchor type="note" xlink:href="" symbol="*"/>, darique preſſionem motui contrariam, qua corpus <anchor type="note" xlink:label="note-0375-04a" xlink:href="note-0375-04"/> retardari manifeſtum eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9968" xml:space="preserve"/> </p> <div xml:id="echoid-div1398" type="float" level="2" n="1"> <note position="right" xlink:label="note-0375-03" xlink:href="note-0375-03a" xml:space="preserve">942.</note> <note symbol="*" position="right" xlink:label="note-0375-04" xlink:href="note-0375-04a" xml:space="preserve">891.</note> </div> <note symbol="*" position="right" xml:space="preserve">436.</note> <p> <s xml:id="echoid-s9969" xml:space="preserve">Cum duplex detur reſiſtentia, corpus etiam ex duplici <lb/>cauſa a motu ſuo amittit.</s> <s xml:id="echoid-s9970" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9971" xml:space="preserve">Natura utriuſque reſiſtentiæ cum diverſa ſit, generant hæ <lb/> <anchor type="note" xlink:label="note-0375-06a" xlink:href="note-0375-06"/> retardationes diverſas, in ipſis illis caſibus, in quibus preſſio-<lb/>nes, quas in corpus exerunt, ſunt æquales, ſed preſſiones <lb/>non ſunt ejuſdem generis.</s> <s xml:id="echoid-s9972" xml:space="preserve"/> </p> <div xml:id="echoid-div1399" type="float" level="2" n="2"> <note position="right" xlink:label="note-0375-06" xlink:href="note-0375-06a" xml:space="preserve">943.</note> </div> <p style="it"> <s xml:id="echoid-s9973" xml:space="preserve">In caſu in quo corpus quieſcit dum fluidum movetur cau-<lb/> <anchor type="note" xlink:label="note-0375-07a" xlink:href="note-0375-07"/> ſæ quæ, moto corpore, hoc retardant, nunc ipſi motum <lb/>communicant & </s> <s xml:id="echoid-s9974" xml:space="preserve">eſt hæc velocitas acquiſita, æqualis ipſi re-<lb/>tardationi, quam patitur corpus quando, quieſcentefluido, corpus <lb/>movetur, ea velocitate, quam in caſu primo fluidum babuit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9975" xml:space="preserve"/> </p> <div xml:id="echoid-div1400" type="float" level="2" n="3"> <note position="right" xlink:label="note-0375-07" xlink:href="note-0375-07a" xml:space="preserve">944.</note> </div> <note symbol="*" position="right" xml:space="preserve">897.</note> <p> <s xml:id="echoid-s9976" xml:space="preserve">In caſu autem hoc in quo fluidum movetur, cobæſio par-<lb/> <anchor type="note" xlink:label="note-0375-09a" xlink:href="note-0375-09"/> tium immediate nunquam motum corporipoteſt communicare, <lb/>ſed tantum mediante motu aliarum particularum, ut ex-<lb/>plicavimus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9977" xml:space="preserve">quod non itidem ad ſecundam cauſam reſi- <anchor type="note" xlink:label="note-0375-10a" xlink:href="note-0375-10"/> ſtentiæ applicari poteſt, quæ immediate corpori motum com-<lb/>municat: </s> <s xml:id="echoid-s9978" xml:space="preserve">quare ex principiis omnino diverſis, quæ retarda-<lb/> <anchor type="note" xlink:label="note-0375-11a" xlink:href="note-0375-11"/> tiones ex hiſce diverſis reſiſtentiis oriundas ſpectant, dedu-<lb/>cenda ſunt.</s> <s xml:id="echoid-s9979" xml:space="preserve"/> </p> <div xml:id="echoid-div1401" type="float" level="2" n="4"> <note position="right" xlink:label="note-0375-09" xlink:href="note-0375-09a" xml:space="preserve">945.</note> <note symbol="*" position="right" xlink:label="note-0375-10" xlink:href="note-0375-10a" xml:space="preserve">901.</note> <note position="right" xlink:label="note-0375-11" xlink:href="note-0375-11a" xml:space="preserve">946.</note> </div> <p> <s xml:id="echoid-s9980" xml:space="preserve">Quando corpus quieſcit, & </s> <s xml:id="echoid-s9981" xml:space="preserve">fluidum movetur, particulæ <lb/> <anchor type="note" xlink:label="note-0375-12a" xlink:href="note-0375-12"/> quæ ad latera defluunt cohæſionem ſuperant, & </s> <s xml:id="echoid-s9982" xml:space="preserve">hæ ex vi ſua <pb o="276" file="0376" n="411" rhead="PHYSICES ELEMENTA"/> amittunt, quæ actio conſideranda foret ad determinandam <lb/>velocitatem ex hac corpori communicatam, & </s> <s xml:id="echoid-s9983" xml:space="preserve">difficilior eſt <lb/>hujus celeritatis determinatio, quam tamen in ſcholio hujus <lb/>cap. </s> <s xml:id="echoid-s9984" xml:space="preserve">ultimo explicabo. </s> <s xml:id="echoid-s9985" xml:space="preserve">In quo etiam ſcrupulos quof-<lb/>dam tollam.</s> <s xml:id="echoid-s9986" xml:space="preserve"/> </p> <div xml:id="echoid-div1402" type="float" level="2" n="5"> <note position="right" xlink:label="note-0375-12" xlink:href="note-0375-12a" xml:space="preserve">947.</note> </div> <p> <s xml:id="echoid-s9987" xml:space="preserve">Præſtabit hic retardationem determinare quam patitur <lb/>corpus in caſu, in quo hoc movetur, & </s> <s xml:id="echoid-s9988" xml:space="preserve">fluidum quieſcit.</s> <s xml:id="echoid-s9989" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9990" xml:space="preserve">Vidimus reſiſtentiam ex prima cauſa ejuſdem eſſe naturæ <lb/> <anchor type="note" xlink:label="note-0376-01a" xlink:href="note-0376-01"/> cum reſiſtentia corporum mollium, dum in his cavitas for-<lb/>matur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s9991" xml:space="preserve"/> </p> <div xml:id="echoid-div1403" type="float" level="2" n="6"> <note position="left" xlink:label="note-0376-01" xlink:href="note-0376-01a" xml:space="preserve">948.</note> </div> <note symbol="*" position="left" xml:space="preserve">893.</note> <p> <s xml:id="echoid-s9992" xml:space="preserve">Vidimus etiam cavitatem hanc proportionem ſequi ipſi-<lb/>us vis amiſſæ in hac formanda <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9993" xml:space="preserve">cavitas autem quam cor- <anchor type="note" xlink:label="note-0376-03a" xlink:href="note-0376-03"/> pus in fluido format, dum per hoc movetur, ſpatio per-<lb/> <anchor type="note" xlink:label="note-0376-04a" xlink:href="note-0376-04"/> curſo proportionalis eſt: </s> <s xml:id="echoid-s9994" xml:space="preserve">ergo & </s> <s xml:id="echoid-s9995" xml:space="preserve">huic ſpatio vis, ex hac re-<lb/>ſiſtentia ex primâ cauſâ amiſſa, proportionalis eſt.</s> <s xml:id="echoid-s9996" xml:space="preserve"/> </p> <div xml:id="echoid-div1404" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0376-03" xlink:href="note-0376-03a" xml:space="preserve">464.</note> <note position="left" xlink:label="note-0376-04" xlink:href="note-0376-04a" xml:space="preserve">949.</note> </div> <p> <s xml:id="echoid-s9997" xml:space="preserve">Corpus quod in vacuo verticaliter in altum projicitur, in <lb/>adſcenſu ſuo amittit continuo vim proportionalem ſpatio <lb/>percurſo <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s9998" xml:space="preserve">ſequitur igitur retardatio in hoc adſcenſu ean- <anchor type="note" xlink:label="note-0376-05a" xlink:href="note-0376-05"/> dem rationem quam ſequitur retardatio corporis oriunda ex <lb/> <anchor type="note" xlink:label="note-0376-06a" xlink:href="note-0376-06"/> reſiſtentia de qua agimus; </s> <s xml:id="echoid-s9999" xml:space="preserve">ſed retardatio corporis adſcen-<lb/>dentis eſt æquabilis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10000" xml:space="preserve">ergo & </s> <s xml:id="echoid-s10001" xml:space="preserve">talis eſt retardatio quam <anchor type="note" xlink:label="note-0376-07a" xlink:href="note-0376-07"/> examinamus.</s> <s xml:id="echoid-s10002" xml:space="preserve"/> </p> <div xml:id="echoid-div1405" type="float" level="2" n="8"> <note symbol="*" position="left" xlink:label="note-0376-05" xlink:href="note-0376-05a" xml:space="preserve">448, 261.</note> <note position="left" xlink:label="note-0376-06" xlink:href="note-0376-06a" xml:space="preserve">950.</note> <note symbol="*" position="left" xlink:label="note-0376-07" xlink:href="note-0376-07a" xml:space="preserve">258.</note> </div> <p> <s xml:id="echoid-s10003" xml:space="preserve">Quamdiu ergo idem corpus, eodem modo, per idem flui-<lb/> <anchor type="note" xlink:label="note-0376-08a" xlink:href="note-0376-08"/> dum movetur, quacunque velocitate feratur, ſepoſit â reſi-<lb/>ſtentiâ ex ſecundâ cauſâ, æqualibus temporibus, æquales <lb/>gradus velocitatis amittit; </s> <s xml:id="echoid-s10004" xml:space="preserve">& </s> <s xml:id="echoid-s10005" xml:space="preserve">percurrendo ſpatium deter-<lb/>minatum <anchor type="note" xlink:href="" symbol="*"/>, quod quadrato velocitatis initio proportionale <anchor type="note" xlink:label="note-0376-09a" xlink:href="note-0376-09"/> erit <anchor type="note" xlink:href="" symbol="*"/>, in tempore ipſi velocitati huic proportionale <anchor type="note" xlink:href="" symbol="*"/>, in- <anchor type="note" xlink:label="note-0376-10a" xlink:href="note-0376-10"/> tegrum amittet motum.</s> <s xml:id="echoid-s10006" xml:space="preserve"/> </p> <div xml:id="echoid-div1406" type="float" level="2" n="9"> <note position="left" xlink:label="note-0376-08" xlink:href="note-0376-08a" xml:space="preserve">951.</note> <note symbol="*" position="left" xlink:label="note-0376-09" xlink:href="note-0376-09a" xml:space="preserve">949.</note> <note symbol="*" position="left" xlink:label="note-0376-10" xlink:href="note-0376-10a" xml:space="preserve">950. 258. <lb/>262.</note> </div> <note symbol="*" position="left" xml:space="preserve">950. 258. <lb/>259 255.</note> <p> <s xml:id="echoid-s10007" xml:space="preserve">Hinc videmus corpora in fluido mota tandem quieſcere, <lb/> <anchor type="note" xlink:label="note-0376-12a" xlink:href="note-0376-12"/> quod communi admiſſà opinione, de viribus ipſis velocitati-<lb/>bus proportionalibus, difficulter admodum explicari poterit, <lb/>ſi queat; </s> <s xml:id="echoid-s10008" xml:space="preserve">nam niſi tempore infinito tota velocitas conſumi <lb/>poſſet.</s> <s xml:id="echoid-s10009" xml:space="preserve"/> </p> <div xml:id="echoid-div1407" type="float" level="2" n="10"> <note position="left" xlink:label="note-0376-12" xlink:href="note-0376-12a" xml:space="preserve">952.</note> </div> <p> <s xml:id="echoid-s10010" xml:space="preserve">Retardatio ex ſecunda cauſa determinatur, ponendo cor-<lb/>pus quieſcens, & </s> <s xml:id="echoid-s10011" xml:space="preserve">fluidum in hoc incurrens; </s> <s xml:id="echoid-s10012" xml:space="preserve">quia facilius de- <pb o="277" file="0377" n="412" rhead="MATHEMATICA. LIB. II. CAP. XII."/> terminatur velocitas, quæ corpori quieſcenti a fluido com-<lb/>municatur, quàm retardatio quam corpus patitur; </s> <s xml:id="echoid-s10013" xml:space="preserve">præſtabit <lb/>ergo velocitatem hanc conſiderare, quæ ab ipſa retardatione, <lb/>corporis agitati per fluidum quieſcens, non differt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10014" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">944.</note> <p> <s xml:id="echoid-s10015" xml:space="preserve">Preſſio, quam in corpus quieſcens exerit fluidum, im-<lb/> <anchor type="note" xlink:label="note-0377-02a" xlink:href="note-0377-02"/> mediate corpus poteſt transferre, ſequitur igitur velocitatem <lb/>infinite exiguam, momento infinite exiguo conſtanti, com-<lb/>municari, proportionalem ipſi ſpatio, per quod corpus hoc <lb/>quieſcens actione fluidi immediate transfertur, quod ſpa-<lb/>tium ipſi preſſioni proportionale eſt <anchor type="note" xlink:href="" symbol="*"/>, quæ ipſa rationem <anchor type="note" xlink:label="note-0377-03a" xlink:href="note-0377-03"/> ſequitur quadrati velocitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10016" xml:space="preserve"/> </p> <div xml:id="echoid-div1408" type="float" level="2" n="11"> <note position="right" xlink:label="note-0377-02" xlink:href="note-0377-02a" xml:space="preserve">953.</note> <note symbol="*" position="right" xlink:label="note-0377-03" xlink:href="note-0377-03a" xml:space="preserve">107.</note> </div> <note symbol="*" position="right" xml:space="preserve">500.</note> <p style="it"> <s xml:id="echoid-s10017" xml:space="preserve">Diminutiones idcirco velocitatis, quas corpus in fluido mo-<lb/> <anchor type="note" xlink:label="note-0377-05a" xlink:href="note-0377-05"/> tum, momentis infinite exiguis, æqualibus, ex reſiſtentiâ <lb/>ex ſecundâ cauſâ, patitur, ſunt ut quadrata velocitatum <lb/>ipſius corporis.</s> <s xml:id="echoid-s10018" xml:space="preserve"/> </p> <div xml:id="echoid-div1409" type="float" level="2" n="12"> <note position="right" xlink:label="note-0377-05" xlink:href="note-0377-05a" xml:space="preserve">954.</note> </div> <p style="it"> <s xml:id="echoid-s10019" xml:space="preserve">Ex qua demonſtratione ſequitur nunquam corpus ex ſolâ <lb/> <anchor type="note" xlink:label="note-0377-06a" xlink:href="note-0377-06"/> reſiſtentiâ ex ſecundâ cauſâ integram poſſe amittere veloci-<lb/>tatem.</s> <s xml:id="echoid-s10020" xml:space="preserve"/> </p> <div xml:id="echoid-div1410" type="float" level="2" n="13"> <note position="right" xlink:label="note-0377-06" xlink:href="note-0377-06a" xml:space="preserve">955.</note> </div> <p> <s xml:id="echoid-s10021" xml:space="preserve">Patet etiam in omni caſu retardationem, ex bacreſiſten-<lb/> <anchor type="note" xlink:label="note-0377-07a" xlink:href="note-0377-07"/> tia, eandem cum ipſa rationem ſequi, quamdiu corpus mo-<lb/>tum eandem materiæ quantitatem continet, ubi autem hæc <lb/>eſt diverſa, retardatio eſt cæteris paribus, inverſe ut hæc <lb/> <anchor type="note" xlink:label="note-0377-08a" xlink:href="note-0377-08"/> materiæ quantitas <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10022" xml:space="preserve">Ex quibus facile videmus, quomodo <anchor type="note" xlink:label="note-0377-09a" xlink:href="note-0377-09"/> poſitis demonſtratis in capite præcedenti retardationes pro <lb/>variis corporibus, & </s> <s xml:id="echoid-s10023" xml:space="preserve">variis fluidis, inter ſe conferri poſ-<lb/>ſint.</s> <s xml:id="echoid-s10024" xml:space="preserve"/> </p> <div xml:id="echoid-div1411" type="float" level="2" n="14"> <note position="right" xlink:label="note-0377-07" xlink:href="note-0377-07a" xml:space="preserve">956.</note> <note position="right" xlink:label="note-0377-08" xlink:href="note-0377-08a" xml:space="preserve">957.</note> <note symbol="*" position="right" xlink:label="note-0377-09" xlink:href="note-0377-09a" xml:space="preserve">112.</note> </div> <p> <s xml:id="echoid-s10025" xml:space="preserve">Si de ſphæris, cylindris, aut conis ſimilibus, Ex. </s> <s xml:id="echoid-s10026" xml:space="preserve">gr. </s> <s xml:id="echoid-s10027" xml:space="preserve">a-<lb/> <anchor type="note" xlink:label="note-0377-10a" xlink:href="note-0377-10"/> gatur, poſitis cylindris, & </s> <s xml:id="echoid-s10028" xml:space="preserve">conis, juxta axium directiones <lb/>motis, erunt retardationes ex ſecunda cauſa directè ut qua-<lb/> <anchor type="note" xlink:label="note-0377-11a" xlink:href="note-0377-11"/> drata diametrorum <anchor type="note" xlink:href="" symbol="*"/>, ut quadrata velocitatum <anchor type="note" xlink:href="" symbol="*"/>, ut denſi- <anchor type="note" xlink:label="note-0377-12a" xlink:href="note-0377-12"/> tates fluidorum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10029" xml:space="preserve">& </s> <s xml:id="echoid-s10030" xml:space="preserve">inverſe ut denſitates corporum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10031" xml:space="preserve">cu- <anchor type="note" xlink:label="note-0377-13a" xlink:href="note-0377-13"/> <anchor type="note" xlink:label="note-0377-14a" xlink:href="note-0377-14"/> bi diametrorum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10032" xml:space="preserve">ſed ratio directa quadratorum, & </s> <s xml:id="echoid-s10033" xml:space="preserve">inver- <anchor type="note" xlink:label="note-0377-15a" xlink:href="note-0377-15"/> ſa cuborum diametrorum, ad inverſam ipſarum diametro-<lb/>rum reducitur; </s> <s xml:id="echoid-s10034" xml:space="preserve">Idcirco, junctis rationibus ultimâ & </s> <s xml:id="echoid-s10035" xml:space="preserve">primâ, <lb/>ſunt retardationes inverſe ut diametri.</s> <s xml:id="echoid-s10036" xml:space="preserve"/> </p> <div xml:id="echoid-div1412" type="float" level="2" n="15"> <note position="right" xlink:label="note-0377-10" xlink:href="note-0377-10a" xml:space="preserve">958.</note> <note symbol="*" position="right" xlink:label="note-0377-11" xlink:href="note-0377-11a" xml:space="preserve">956. 909.</note> <note symbol="*" position="right" xlink:label="note-0377-12" xlink:href="note-0377-12a" xml:space="preserve">954.</note> <note symbol="*" position="right" xlink:label="note-0377-13" xlink:href="note-0377-13a" xml:space="preserve">956 926.</note> <note symbol="*" position="right" xlink:label="note-0377-14" xlink:href="note-0377-14a" xml:space="preserve">957.</note> <note symbol="*" position="right" xlink:label="note-0377-15" xlink:href="note-0377-15a" xml:space="preserve">957.</note> </div> <p> <s xml:id="echoid-s10037" xml:space="preserve">Numeri in harum rationum ratione compoſita detegun-<lb/> <anchor type="note" xlink:label="note-0377-16a" xlink:href="note-0377-16"/> <pb o="278" file="0378" n="413" rhead="PHYSICES ELEMENTA"/> tur, multiplicando pro ſingulis corporibus fluidi denſitatem <lb/>per quadratum velocitatis corporis, & </s> <s xml:id="echoid-s10038" xml:space="preserve">dividendo pro-<lb/>ductum hoc per diametrum ductam in denſitatem corporis, <lb/>diviſionumque quotientes exprimunt retardationum rela-<lb/>tiones.</s> <s xml:id="echoid-s10039" xml:space="preserve"/> </p> <div xml:id="echoid-div1413" type="float" level="2" n="16"> <note position="right" xlink:label="note-0377-16" xlink:href="note-0377-16a" xml:space="preserve">959.</note> </div> <p> <s xml:id="echoid-s10040" xml:space="preserve">Hæ etiam deteguntur ſi pro ſingulis corporibus pondus, <lb/> <anchor type="note" xlink:label="note-0378-01a" xlink:href="note-0378-01"/> quod valet reſiſtentiam <anchor type="note" xlink:href="" symbol="*"/>, dividatur per corporis pondus;</s> <s xml:id="echoid-s10041" xml:space="preserve"> <anchor type="note" xlink:label="note-0378-02a" xlink:href="note-0378-02"/> quotientes enim ſunt ut retardationes <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10042" xml:space="preserve"/> </p> <div xml:id="echoid-div1414" type="float" level="2" n="17"> <note position="left" xlink:label="note-0378-01" xlink:href="note-0378-01a" xml:space="preserve">960.</note> <note symbol="*" position="left" xlink:label="note-0378-02" xlink:href="note-0378-02a" xml:space="preserve">928.</note> </div> <note symbol="*" position="left" xml:space="preserve">956 957. <lb/>121.</note> <p> <s xml:id="echoid-s10043" xml:space="preserve">Dum corpus in fluido retardatur, ſingulis momentis, cum <lb/>mutata velocitate, mutatur retardatio, unde varia circa mo-<lb/>tum corporis, in fluido continuatum, deducuntur, quorum <lb/>quædam in ſcholiis, huic capiti ſubjunctis, demonſtramus; <lb/></s> <s xml:id="echoid-s10044" xml:space="preserve">horum pauca hîc indicabo.</s> <s xml:id="echoid-s10045" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10046" xml:space="preserve">Sepoſitâ, ut in ultimis propoſitionibus, reſiſtentiâ ex <lb/> <anchor type="note" xlink:label="note-0378-04a" xlink:href="note-0378-04"/> partium cobæſione, moveatur corpus per ſluidum, percur-<lb/>ret boc ſpatia æqualia, temporibus inæqualibus, quæ erunt <lb/>in progreſſione geometrica; </s> <s xml:id="echoid-s10047" xml:space="preserve">in qua eadem progreſſione, ſed <lb/>inverſâ, ſunt velocitates in initiis borum momento-<lb/>rum.</s> <s xml:id="echoid-s10048" xml:space="preserve"/> </p> <div xml:id="echoid-div1415" type="float" level="2" n="18"> <note position="left" xlink:label="note-0378-04" xlink:href="note-0378-04a" xml:space="preserve">961.</note> </div> <p style="it"> <s xml:id="echoid-s10049" xml:space="preserve">Si globus aut cylindrus rectus, juxta axeos directionem <lb/> <anchor type="note" xlink:label="note-0378-05a" xlink:href="note-0378-05"/> moveantur per fluidum, cylindri longitudo, & </s> <s xml:id="echoid-s10050" xml:space="preserve">globi diame-<lb/>ter, ſe babebunt ad ſpatia, quibus percurrendo corpora hæc <lb/>reſpectivè dimidium velocitatis amittunt, in ratione compo-<lb/>ſita denſitatis fluidi ad denſitatem corporis, & </s> <s xml:id="echoid-s10051" xml:space="preserve">numeri 10000. <lb/></s> <s xml:id="echoid-s10052" xml:space="preserve">ad 13863.</s> <s xml:id="echoid-s10053" xml:space="preserve"/> </p> <div xml:id="echoid-div1416" type="float" level="2" n="19"> <note position="left" xlink:label="note-0378-05" xlink:href="note-0378-05a" xml:space="preserve">962.</note> </div> <p style="it"> <s xml:id="echoid-s10054" xml:space="preserve">Corporis autem, quod in fluido movetur, retardatio ab <lb/> <anchor type="note" xlink:label="note-0378-06a" xlink:href="note-0378-06"/> utraque cauſa reſiſtentiæ pendet, & </s> <s xml:id="echoid-s10055" xml:space="preserve">eſt pro parte æquabi-<lb/>lis <anchor type="note" xlink:href="" symbol="*"/>, pro parte ut quadratum velocitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10056" xml:space="preserve"/> </p> <div xml:id="echoid-div1417" type="float" level="2" n="20"> <note position="left" xlink:label="note-0378-06" xlink:href="note-0378-06a" xml:space="preserve">963.</note> </div> <note symbol="*" position="left" xml:space="preserve">950.</note> <note symbol="*" position="left" xml:space="preserve">954.</note> <p> <s xml:id="echoid-s10057" xml:space="preserve">Quod etiam ad corpora adſcendentia & </s> <s xml:id="echoid-s10058" xml:space="preserve">deſcendentia ap-<lb/>plicari poteſt.</s> <s xml:id="echoid-s10059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10060" xml:space="preserve">Corpus fluido ſpecificè gravius, quod adſcendit, aut fluido <lb/> <anchor type="note" xlink:label="note-0378-09a" xlink:href="note-0378-09"/> ſpecificè levius quod deſcendit, præter retardationem ex in-<lb/>ertia fluidi oriundam <anchor type="note" xlink:href="" symbol="*"/>, aliam æquabilem patitur, non modo ex <anchor type="note" xlink:label="note-0378-10a" xlink:href="note-0378-10"/> cohæſione <anchor type="note" xlink:href="" symbol="*"/>, ſed eſt præterea, in primo caſu, ex gravitate <anchor type="note" xlink:label="note-0378-11a" xlink:href="note-0378-11"/> reſpectiva <anchor type="note" xlink:href="" symbol="*"/>, in ſecundo, ex vi qua in fluido ſurſum pelli- <anchor type="note" xlink:label="note-0378-12a" xlink:href="note-0378-12"/> tur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10061" xml:space="preserve"/> </p> <div xml:id="echoid-div1418" type="float" level="2" n="21"> <note position="left" xlink:label="note-0378-09" xlink:href="note-0378-09a" xml:space="preserve">964.</note> <note symbol="*" position="left" xlink:label="note-0378-10" xlink:href="note-0378-10a" xml:space="preserve">954.</note> <note symbol="*" position="left" xlink:label="note-0378-11" xlink:href="note-0378-11a" xml:space="preserve">951</note> <note symbol="*" position="left" xlink:label="note-0378-12" xlink:href="note-0378-12a" xml:space="preserve">251.</note> </div> <note symbol="*" position="left" xml:space="preserve">749.</note> <pb o="279" file="0379" n="414" rhead="MATHEMATICA. LIB. II. CAP. XII."/> <p> <s xml:id="echoid-s10062" xml:space="preserve">E contra Si corpus, ſpecifice fluido quo immergitur gra-<lb/> <anchor type="note" xlink:label="note-0379-01a" xlink:href="note-0379-01"/> vius, deſcendat, aut fluido levius adſcendat, continuo ac-<lb/>celeratur vi quæ valet differentiam gravitatum ſpecificarum <lb/>corporis & </s> <s xml:id="echoid-s10063" xml:space="preserve">fluidi <anchor type="note" xlink:href="" symbol="*"/>, quæ acceleratio, à gravitate oriunda, <anchor type="note" xlink:label="note-0379-02a" xlink:href="note-0379-02"/> æquabilis eſt <anchor type="note" xlink:href="" symbol="*"/>, minuitur hæc retardatione a cohæſione o- <anchor type="note" xlink:label="note-0379-03a" xlink:href="note-0379-03"/> riundà, ſed æquabiliter <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10064" xml:space="preserve">eſt adhucdum æquabilis ac- <anchor type="note" xlink:label="note-0379-04a" xlink:href="note-0379-04"/> celeratio. </s> <s xml:id="echoid-s10065" xml:space="preserve">Cum autem retardatio ex ſecundâ caufâ cum <lb/>velocitate creſcat, minuitur continuò acceleratio; </s> <s xml:id="echoid-s10066" xml:space="preserve">& </s> <s xml:id="echoid-s10067" xml:space="preserve">cor-<lb/> <anchor type="note" xlink:label="note-0379-05a" xlink:href="note-0379-05"/> pus magis ac magis accedit ad velocitatem quandam maxi-<lb/>mam determinatam, ad quam tamen nunquam pertingere po-<lb/>teſt.</s> <s xml:id="echoid-s10068" xml:space="preserve"/> </p> <div xml:id="echoid-div1419" type="float" level="2" n="22"> <note position="right" xlink:label="note-0379-01" xlink:href="note-0379-01a" xml:space="preserve">965.</note> <note symbol="*" position="right" xlink:label="note-0379-02" xlink:href="note-0379-02a" xml:space="preserve">751.</note> <note symbol="*" position="right" xlink:label="note-0379-03" xlink:href="note-0379-03a" xml:space="preserve">251.</note> <note symbol="*" position="right" xlink:label="note-0379-04" xlink:href="note-0379-04a" xml:space="preserve">951.</note> <note position="right" xlink:label="note-0379-05" xlink:href="note-0379-05a" xml:space="preserve">966.</note> </div> <p> <s xml:id="echoid-s10069" xml:space="preserve">Illa verò eſt velocitas maxima in qua retardatio accele-<lb/> <anchor type="note" xlink:label="note-0379-06a" xlink:href="note-0379-06"/> rationi æqualis eſt; </s> <s xml:id="echoid-s10070" xml:space="preserve">ſi enim ad hanc pertingeret corpus, <lb/>æquabiliter motum continuaret, preſſionibus oppoſitis ſeſe <lb/>mutuo deſtruentibus.</s> <s xml:id="echoid-s10071" xml:space="preserve"/> </p> <div xml:id="echoid-div1420" type="float" level="2" n="23"> <note position="right" xlink:label="note-0379-06" xlink:href="note-0379-06a" xml:space="preserve">967.</note> </div> <p style="it"> <s xml:id="echoid-s10072" xml:space="preserve">Corpus cylindricum banc acquirit velocitatem maximam <lb/> <anchor type="note" xlink:label="note-0379-07a" xlink:href="note-0379-07"/> in vacuo cadendo ab altitudine quæ ſe babet ad cylindri lon-<lb/>gitudinem, ſi bic juxta axeos directionem in fluido deſcendat, <lb/>aut ſi de globo agatur, ad hujus diametrum, ut differentia <lb/>denſitatis corporis in fluido moti cum fluidi denſitate ad hanc <lb/>fluidi denſitatem <anchor type="note" xlink:href="" symbol="*"/>, ſinempe ſeponamus retardationem ex par- <anchor type="note" xlink:label="note-0379-08a" xlink:href="note-0379-08"/> tium cobæſione oriundam, qua autem poſita minor erit al-<lb/>titudo aqua in vacuo cadendo corpus acquirit velocitatem <lb/>de qua agimus maximam.</s> <s xml:id="echoid-s10073" xml:space="preserve"/> </p> <div xml:id="echoid-div1421" type="float" level="2" n="24"> <note position="right" xlink:label="note-0379-07" xlink:href="note-0379-07a" xml:space="preserve">968.</note> <note symbol="*" position="right" xlink:label="note-0379-08" xlink:href="note-0379-08a" xml:space="preserve">928.</note> </div> <p> <s xml:id="echoid-s10074" xml:space="preserve">Relictis nunc motibus, in lineis rectis pauca etiam ad-<lb/>dam de motu pendulorum.</s> <s xml:id="echoid-s10075" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10076" xml:space="preserve">Sit ABD arcus cycloidis in quo pendulum vibratur; </s> <s xml:id="echoid-s10077" xml:space="preserve">B pun-<lb/> <anchor type="note" xlink:label="note-0379-09a" xlink:href="note-0379-09"/> ctum infimum. </s> <s xml:id="echoid-s10078" xml:space="preserve">Acceleratio ex gravitate in puncto quocunque <lb/> <anchor type="note" xlink:label="note-0379-10a" xlink:href="note-0379-10"/> ut E eſt ut EB <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10079" xml:space="preserve">ſed hæc a cohæſione minuiter æquabili- <anchor type="note" xlink:label="note-0379-11a" xlink:href="note-0379-11"/> ter <anchor type="note" xlink:href="" symbol="*"/>, ſit hæc diminutio ut BF, acceleratio erit nunc ut <anchor type="note" xlink:label="note-0379-12a" xlink:href="note-0379-12"/> EF, & </s> <s xml:id="echoid-s10080" xml:space="preserve">in A erit ut AF. </s> <s xml:id="echoid-s10081" xml:space="preserve">Adſcenſu corporis, retardatio in <lb/>G a gravitate oriunda, erit ut GB, a cohæſione erit ut BF <lb/>& </s> <s xml:id="echoid-s10082" xml:space="preserve">ex his cauſis conjunctis eſt ut GF; </s> <s xml:id="echoid-s10083" xml:space="preserve">& </s> <s xml:id="echoid-s10084" xml:space="preserve">in tota vibratio-<lb/>ne ſepoſitâ aliâ reſiſtentiâ, corpus reſpectu puncti F move-<lb/>tur ut in vacuo agitatur reſpectu B.</s> <s xml:id="echoid-s10085" xml:space="preserve"/> </p> <div xml:id="echoid-div1422" type="float" level="2" n="25"> <note position="right" xlink:label="note-0379-09" xlink:href="note-0379-09a" xml:space="preserve">969.</note> <note position="right" xlink:label="note-0379-10" xlink:href="note-0379-10a" xml:space="preserve">TAB. XXXVI. <lb/>fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0379-11" xlink:href="note-0379-11a" xml:space="preserve">287.</note> <note symbol="*" position="right" xlink:label="note-0379-12" xlink:href="note-0379-12a" xml:space="preserve">951.</note> </div> <p> <s xml:id="echoid-s10086" xml:space="preserve">Vocabimus ideo deſcenſum motum penduli uſque ad F, <pb o="280" file="0380" n="415" rhead="PHYSICES ELEMENTA"/> & </s> <s xml:id="echoid-s10087" xml:space="preserve">adſcenſum motum ultra punctum hoc; </s> <s xml:id="echoid-s10088" xml:space="preserve">agam enim depen-<lb/>dulis a parte A deſcendentibus.</s> <s xml:id="echoid-s10089" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10090" xml:space="preserve">Ut autem demonſtremus quæ obtinent, quando pendulum <lb/> <anchor type="note" xlink:label="note-0380-01a" xlink:href="note-0380-01"/> etiam reſiſtentiâ ex ſecunda cauſa retardatur, fingam re-<lb/>ſiſtentiam quæ retardationem generat in ratione velocitatis, <lb/>quaſdamque, hac poſitâ, propoſitiones demonſtrabo, qui-<lb/>bus expoſitis facilius patebunt quæ locum habent quando <lb/>retardatio eſt ut quadratum velocitatis.</s> <s xml:id="echoid-s10091" xml:space="preserve"/> </p> <div xml:id="echoid-div1423" type="float" level="2" n="26"> <note position="left" xlink:label="note-0380-01" xlink:href="note-0380-01a" xml:space="preserve">970.</note> </div> <p> <s xml:id="echoid-s10092" xml:space="preserve">Poſitâ nunc retardatione in ratione ipſius velocitatis, & </s> <s xml:id="echoid-s10093" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0380-02a" xlink:href="note-0380-02"/> pendula duo, omnino ſimilia, in cycloide oſcillata, inæquales <lb/>peragant vibrationes, eodemque momento cadere incipiant; <lb/></s> <s xml:id="echoid-s10094" xml:space="preserve">moveri inchoant velocitatibus quæ ſunt ut arcus deſcenſu <lb/>deſcribendi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10095" xml:space="preserve">ſi hæ impreſſiones primi momenti ſolæ con- <anchor type="note" xlink:label="note-0380-03a" xlink:href="note-0380-03"/> ſiderantur, poſt tempus quodcunque celeritates erunt in <lb/>eadem ratione ac in principio; </s> <s xml:id="echoid-s10096" xml:space="preserve">nam retardationes, quæ <lb/>ſunt ut ipſæ velocitates, harum proportionem immutare <lb/>nequeunt; </s> <s xml:id="echoid-s10097" xml:space="preserve">ratio enim inter quantitates non mutatur, addi-<lb/>tione, aut ſubtractione, quantitatum in eadem ratione. </s> <s xml:id="echoid-s10098" xml:space="preserve">Tem-<lb/>poribus igitur æqualibus, utcunque inter movendum ex <lb/>reſiſtentia mutetur corporis celeritas, ſpatia percurruntur <lb/>quæ ſunt ut velocitates in principio <anchor type="note" xlink:href="" symbol="*"/>, id eſt, ut arcus de- <anchor type="note" xlink:label="note-0380-04a" xlink:href="note-0380-04"/> ſcenſu deſcribendi; </s> <s xml:id="echoid-s10099" xml:space="preserve">idcirco poſt tempus quodcunque cor-<lb/>pora ſunt in horum arcuum punctis reſpondentibus. </s> <s xml:id="echoid-s10100" xml:space="preserve">In <lb/>hiſce autem punctis accelerationes ſunt in eadem ratione <lb/>quàm in principio <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10101" xml:space="preserve">& </s> <s xml:id="echoid-s10102" xml:space="preserve">ratio inter celeritates, quæ ex <anchor type="note" xlink:label="note-0380-05a" xlink:href="note-0380-05"/> reſiſtentia non variatur, ex acceleratione etiam nullam muta-<lb/>tionem patitur. </s> <s xml:id="echoid-s10103" xml:space="preserve">In adſcenſu motus corporum retardatur, ſed in <lb/>punctis reſpondentibus retardationes ſunt in eadem ratione in <lb/>qua ſunt in deſcenſu accelerationes. </s> <s xml:id="echoid-s10104" xml:space="preserve">Ubique ergo in punctis re-<lb/>ſpondentibus celeritates ſunt in eadem ratione. </s> <s xml:id="echoid-s10105" xml:space="preserve">Cum autem <lb/>iiſdem momentis corpora ſint in hiſce punctis reſpon-<lb/>dentibus, ſequitur motum amborum eodem momento de-<lb/>ſtrui, id eſt, iiſdem temporibus vibrationes abſolvi. </s> <s xml:id="echoid-s10106" xml:space="preserve">Spa-<lb/>tia in integris vibrationibus percurſa, cum æqualibus tem-<lb/>poribus percurrantur, & </s> <s xml:id="echoid-s10107" xml:space="preserve">cum in ſingulis momentis veloci-<lb/>tates ſint inter ſe eadem ratione, ſunt quoque in hac ra- <pb o="281" file="0381" n="416" rhead="MATHEMATICA. LIB. II. CAP. XII."/> tione; </s> <s xml:id="echoid-s10108" xml:space="preserve">id eſt, arcus integrarum vibrationum ſunt ut arcus <lb/> <anchor type="note" xlink:label="note-0381-01a" xlink:href="note-0381-01"/> deſcenſu deſcripti, quorum dupla ſunt arcus in vacuo de-<lb/>ſcribendi. </s> <s xml:id="echoid-s10109" xml:space="preserve">Ergo Defectus arcuum in fluido deſcriptorum <lb/> <anchor type="note" xlink:label="note-0381-02a" xlink:href="note-0381-02"/> ab arcubus in vacuo deſcribendorum ſunt differentiæ quan-<lb/>titatum in eadem ratione, & </s> <s xml:id="echoid-s10110" xml:space="preserve">ſunt ut arcus deſcenſu deſcri-<lb/>pti.</s> <s xml:id="echoid-s10111" xml:space="preserve"/> </p> <div xml:id="echoid-div1424" type="float" level="2" n="27"> <note position="left" xlink:label="note-0380-02" xlink:href="note-0380-02a" xml:space="preserve">971.</note> <note symbol="*" position="left" xlink:label="note-0380-03" xlink:href="note-0380-03a" xml:space="preserve">287.</note> <note symbol="*" position="left" xlink:label="note-0380-04" xlink:href="note-0380-04a" xml:space="preserve">94.</note> <note symbol="*" position="left" xlink:label="note-0380-05" xlink:href="note-0380-05a" xml:space="preserve">287.</note> <note position="right" xlink:label="note-0381-01" xlink:href="note-0381-01a" xml:space="preserve">972.</note> <note position="right" xlink:label="note-0381-02" xlink:href="note-0381-02a" xml:space="preserve">973.</note> </div> <p style="it"> <s xml:id="echoid-s10112" xml:space="preserve">Creſcat nunc retardatio in ratione duplicata velocitatis, <lb/> <anchor type="note" xlink:label="note-0381-03a" xlink:href="note-0381-03"/> & </s> <s xml:id="echoid-s10113" xml:space="preserve">vibrationes inæquales peragat corpus pendulum; </s> <s xml:id="echoid-s10114" xml:space="preserve">majores <lb/>erunt magis diuturnæ, propter reſiſtentiam magis creſcen-<lb/>tem quàm in caſu n. </s> <s xml:id="echoid-s10115" xml:space="preserve">971.</s> <s xml:id="echoid-s10116" xml:space="preserve"/> </p> <div xml:id="echoid-div1425" type="float" level="2" n="28"> <note position="right" xlink:label="note-0381-03" xlink:href="note-0381-03a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s10117" xml:space="preserve">Celeritates tamen, poſitis arcubus non admodum inæqua-<lb/> <anchor type="note" xlink:label="note-0381-04a" xlink:href="note-0381-04"/> libus, in arcuum deſcriptorum punctis reſpondentibus, ſunt <lb/>ubique quam proximè in eadem ratione, & </s> <s xml:id="echoid-s10118" xml:space="preserve">quidem ratione <lb/>arcuum deſcenſu deſcriptorum. </s> <s xml:id="echoid-s10119" xml:space="preserve">Si retardatio eſſet in ratio-<lb/>ne celeritatis, hæc proportio obtineret, nunc vero turba-<lb/>tur propter majorem reſiſtentiam in majori vibratione, qua <lb/>motus in hac magis minuitur. </s> <s xml:id="echoid-s10120" xml:space="preserve">Sed duplici ex cauſa magis <lb/>acceleratur. </s> <s xml:id="echoid-s10121" xml:space="preserve">1. </s> <s xml:id="echoid-s10122" xml:space="preserve">Vibratio hæc major diutius durat <anchor type="note" xlink:href="" symbol="*"/>, cor- <anchor type="note" xlink:label="note-0381-05a" xlink:href="note-0381-05"/> puſque diutius hæret in certo ſpatio quàm in ſpatio reſpon-<lb/>denti in vibratione minori, & </s> <s xml:id="echoid-s10123" xml:space="preserve">per longius tempus accele-<lb/>ratur. </s> <s xml:id="echoid-s10124" xml:space="preserve">2. </s> <s xml:id="echoid-s10125" xml:space="preserve">Defectus arcus deſcripti, ab arcu in vacuo deſcri-<lb/>bendo, major eſt, ſervata proportione, in vibratione ma-<lb/>jori; </s> <s xml:id="echoid-s10126" xml:space="preserve">quia in hac retardatio magis differt a retardatione in mi-<lb/>nori vibratione, quam in n. </s> <s xml:id="echoid-s10127" xml:space="preserve">973. </s> <s xml:id="echoid-s10128" xml:space="preserve">Puncta ergo reſponden-<lb/>tia, ſervata proportione, magis a puncto F in arcu majori <lb/>quam in minori diſtant, quamdiu in hoc corpus deſcendit; <lb/></s> <s xml:id="echoid-s10129" xml:space="preserve">major ideo, ſervata proportione, in illo datur acceleratio, <lb/>quia acceleratio eſt ut corporis diſtantia a puncto F. </s> <s xml:id="echoid-s10130" xml:space="preserve">Datur er-<lb/>go compenſatio, & </s> <s xml:id="echoid-s10131" xml:space="preserve">memorata proportio inſtauratur. </s> <s xml:id="echoid-s10132" xml:space="preserve">In <lb/>adſcenſu corporis, duratio retardationis concurrit cum ipſa <lb/>retardatione ad hanc turbandam proportionem, ſed nunc mi-<lb/>nus in majori arcu puncta reſpondentia, ſervata proportio-<lb/>ne, a puncto F diſtant, quàm in minori, & </s> <s xml:id="echoid-s10133" xml:space="preserve">ex gravitate <lb/>minor, ſervata proportione, retardatio datur; </s> <s xml:id="echoid-s10134" xml:space="preserve">& </s> <s xml:id="echoid-s10135" xml:space="preserve">ita jam, <lb/>ſervatâ proportione, crevit differentia diſtantiæ punctorum <pb o="282" file="0382" n="417" rhead="PHYSICES ELEMENTA"/> reſpondentium a puncto infimo, ut ex hoc ſolo facile com-<lb/>penſatio detur,</s> </p> <div xml:id="echoid-div1426" type="float" level="2" n="29"> <note position="right" xlink:label="note-0381-04" xlink:href="note-0381-04a" xml:space="preserve">975.</note> <note symbol="*" position="right" xlink:label="note-0381-05" xlink:href="note-0381-05a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s10136" xml:space="preserve">Retardationes quæ ſunt ut quadrata celeritatum, ſunt <lb/>igitur ubique in punctis reſpondentibus, ut quadrata ar-<lb/>cuum deſcenſu deſcriptorum; </s> <s xml:id="echoid-s10137" xml:space="preserve">cùm harum ſingulæ in punctis <lb/>reſpondentibus eandem ſervent rationem, in ea etiam e-<lb/>runt ratione ſummæ omnium, id eſt, retardationes integræ, <lb/>quæ ſunt differentiæ inter arcus deſcenſu & </s> <s xml:id="echoid-s10138" xml:space="preserve">adſcenſu pro-<lb/> <anchor type="note" xlink:label="note-0382-01a" xlink:href="note-0382-01"/> ximo deſcriptos. </s> <s xml:id="echoid-s10139" xml:space="preserve">Hæ ergo differentiæ, ſi vibrationes non <lb/>fuerint admodum inæquales, ſunt quam proxime ut quadra-<lb/>ta arcuum deſcenſu deſcriptorum. </s> <s xml:id="echoid-s10140" xml:space="preserve">Hoc etiam cum Expe-<lb/>rimentis ſatis exacte congruit.</s> <s xml:id="echoid-s10141" xml:space="preserve"/> </p> <div xml:id="echoid-div1427" type="float" level="2" n="30"> <note position="left" xlink:label="note-0382-01" xlink:href="note-0382-01a" xml:space="preserve">976.</note> </div> </div> <div xml:id="echoid-div1429" type="section" level="1" n="346"> <head xml:id="echoid-head477" xml:space="preserve"><emph style="sc">Machina</emph>, <lb/>Qua Experimenta de Pendulorum Retardationibus <lb/>inſtituuntur.</head> <p> <s xml:id="echoid-s10142" xml:space="preserve">Arca ABFCD, longitudinis trium pedum, latitudinis <lb/> <anchor type="note" xlink:label="note-0382-02a" xlink:href="note-0382-02"/> & </s> <s xml:id="echoid-s10143" xml:space="preserve">altitudinis unius pedis, aquâ impletur; </s> <s xml:id="echoid-s10144" xml:space="preserve">unco V, medio <lb/> <anchor type="note" xlink:label="note-0382-03a" xlink:href="note-0382-03"/> Arcæ reſpondenti, pendulum V p ſuſpenditur; </s> <s xml:id="echoid-s10145" xml:space="preserve">conſtat <lb/>hoc ex filo æneo longitudinis ſeptem aut octo pedum, & </s> <s xml:id="echoid-s10146" xml:space="preserve"><lb/>ex globo plumbeo p diametri unius pollicis cum ſemiſſe; <lb/></s> <s xml:id="echoid-s10147" xml:space="preserve">quando pendulum quieſcit, diſtat globus ab Arcæ fundo <lb/>tribus pollicibus In P globus major plumbeus, diametri <lb/>trium pollicum, cum memorato filo jungitur, ut globus p <lb/>in aqua minus retardetur.</s> <s xml:id="echoid-s10148" xml:space="preserve"/> </p> <div xml:id="echoid-div1429" type="float" level="2" n="1"> <note position="left" xlink:label="note-0382-02" xlink:href="note-0382-02a" xml:space="preserve">977.</note> <note position="left" xlink:label="note-0382-03" xlink:href="note-0382-03a" xml:space="preserve">TAB. XXXI. <lb/>fig. 7.</note> </div> <p> <s xml:id="echoid-s10149" xml:space="preserve">Juxta latitudinem Arcæ, ſuper hujus ora, moveri po-<lb/>teſt tabula lignea altitudinis circiter quinque pollicum, cui <lb/>applicantur regulæ diviſæ æneæ, EG, EG, & </s> <s xml:id="echoid-s10150" xml:space="preserve">indices <lb/>MM, ad angulos, a pendulo deſcenſu & </s> <s xml:id="echoid-s10151" xml:space="preserve">adſcenſu deſcriptos, <lb/>menſurandos, methodo in n. </s> <s xml:id="echoid-s10152" xml:space="preserve">490. </s> <s xml:id="echoid-s10153" xml:space="preserve">p. </s> <s xml:id="echoid-s10154" xml:space="preserve">123. </s> <s xml:id="echoid-s10155" xml:space="preserve">& </s> <s xml:id="echoid-s10156" xml:space="preserve">124. </s> <s xml:id="echoid-s10157" xml:space="preserve">tradita.</s> <s xml:id="echoid-s10158" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1431" type="section" level="1" n="347"> <head xml:id="echoid-head478" xml:space="preserve"><emph style="sc">Experimentum</emph>.</head> <p> <s xml:id="echoid-s10159" xml:space="preserve">Regulæ EG, EG, ita diſponantur, ut extremitates G, G <lb/> <anchor type="note" xlink:label="note-0382-04a" xlink:href="note-0382-04"/> pendulo reſpondeant quando hoc quieſcit, & </s> <s xml:id="echoid-s10160" xml:space="preserve">ut inter il-<lb/>las extremitates diſtantia detur æqualis diametro fili ænei <lb/>cui corpora P, p, cohærent. </s> <s xml:id="echoid-s10161" xml:space="preserve">Dimittatur pendulum ſucceſſi-<lb/>vè a variis altitudinibus quæ in ſingulis occaſionibus indi- <pb o="283" file="0383" n="418" rhead="MATHEMATICA. LIB. II. CAP XII."/> ce notantur, deteguntur altitudines ad quas pendulum ad-<lb/>ſcendit, ſi variis vicibus ab eadem altitudine dimittatur, <lb/>& </s> <s xml:id="echoid-s10162" xml:space="preserve">index alter mutetur, donec ad hunc pendulum in adſcen-<lb/>ſu appellat, ſed remoto indice ad ipſum non pertingat.</s> <s xml:id="echoid-s10163" xml:space="preserve"/> </p> <div xml:id="echoid-div1431" type="float" level="2" n="1"> <note position="left" xlink:label="note-0382-04" xlink:href="note-0382-04a" xml:space="preserve">978.</note> </div> <p> <s xml:id="echoid-s10164" xml:space="preserve">Differentiæ arcuum adſcenſu & </s> <s xml:id="echoid-s10165" xml:space="preserve">deſcenſu deſcriptorum <lb/>erunt proxime inter ſe ut quadrata arcuum deſcenſu de-<lb/>ſcriptorum, ſi ad hoc attendamus æqualiter vibrationes ſin-<lb/>gulas eſſe minuendas, propter reſiſtentiam ex partium <lb/>cohæſione.</s> <s xml:id="echoid-s10166" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10167" xml:space="preserve">Notandum autem pendulum non eſſe dimittendum niſi <lb/>quieſcente aquæ ſuperficie.</s> <s xml:id="echoid-s10168" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1433" type="section" level="1" n="348"> <head xml:id="echoid-head479" xml:space="preserve">SCHOLIUM 1. <lb/>De Logarithmica.</head> <p> <s xml:id="echoid-s10169" xml:space="preserve">QUæ in ſcholiis ſequentibus de retardationibus corporum, in fluidis mo-<lb/>torum, demonſtrantur, lineæ logarithmicæ proprietates profundamen-<lb/>to habent. </s> <s xml:id="echoid-s10170" xml:space="preserve">Formationem ideò hujus curvæ, proprietatesque quibus in ſe-<lb/>quentibus indigemus, in hocſcholio exponam.</s> <s xml:id="echoid-s10171" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10172" xml:space="preserve">Sit AB recta, & </s> <s xml:id="echoid-s10173" xml:space="preserve">in hac partes infinite exiguæ AD, DF, FH, &</s> <s xml:id="echoid-s10174" xml:space="preserve">c. </s> <s xml:id="echoid-s10175" xml:space="preserve">æ-<lb/> <anchor type="note" xlink:label="note-0383-01a" xlink:href="note-0383-01"/> quales inter ſe. </s> <s xml:id="echoid-s10176" xml:space="preserve">Sint præterea ad AB, perpendiculares AC, DE, FG, <lb/> <anchor type="note" xlink:label="note-0383-02a" xlink:href="note-0383-02"/> HI, &</s> <s xml:id="echoid-s10177" xml:space="preserve">c. </s> <s xml:id="echoid-s10178" xml:space="preserve">infinite parum differentes, & </s> <s xml:id="echoid-s10179" xml:space="preserve">quæ ſint progreſſione continua ge-<lb/>ometrica. </s> <s xml:id="echoid-s10180" xml:space="preserve">Si nunc curva tranſeat per extremitates C, E, G, I, &</s> <s xml:id="echoid-s10181" xml:space="preserve">c. </s> <s xml:id="echoid-s10182" xml:space="preserve">erit hæc <lb/>logarithmica, cujus Aſymtotos erit AB, ad quam continuo curva acce-<lb/>dit, & </s> <s xml:id="echoid-s10183" xml:space="preserve">ad quam nunquam pertingere poteſt.</s> <s xml:id="echoid-s10184" xml:space="preserve"/> </p> <div xml:id="echoid-div1433" type="float" level="2" n="1"> <note position="right" xlink:label="note-0383-01" xlink:href="note-0383-01a" xml:space="preserve">979.</note> <note position="right" xlink:label="note-0383-02" xlink:href="note-0383-02a" xml:space="preserve">TAB, XXXVII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s10185" xml:space="preserve">Eadem datur ratio inter ordinatas duas quaſcunque, ſi inter ipſas eadem detur <lb/> <anchor type="note" xlink:label="note-0383-03a" xlink:href="note-0383-03"/> diſtantia. </s> <s xml:id="echoid-s10186" xml:space="preserve">AB ſe habet HI, ut LM ad RS, ſi diſtantia AH diſtantiæ LR <lb/>fuerit æqualis. </s> <s xml:id="echoid-s10187" xml:space="preserve">Ratio enim quæ datur inter AC & </s> <s xml:id="echoid-s10188" xml:space="preserve">HI componitur ex ra-<lb/>tionibus AC ad DE, DE ad FG, & </s> <s xml:id="echoid-s10189" xml:space="preserve">FG ad HI; </s> <s xml:id="echoid-s10190" xml:space="preserve">ratio LM ad RS, <lb/>componitur ex rationibus LM ad NO, NO ad PQ, & </s> <s xml:id="echoid-s10191" xml:space="preserve">PQ ad RS: </s> <s xml:id="echoid-s10192" xml:space="preserve">ra-<lb/>tiones componentes ſingulæ ſunt æquales inter ſe <anchor type="note" xlink:href="" symbol="*"/>, numeruſquerationum <anchor type="note" xlink:label="note-0383-04a" xlink:href="note-0383-04"/> componentium in utroque caſu idem eſt, propter æquales diſtantias AH, <lb/>LR; </s> <s xml:id="echoid-s10193" xml:space="preserve">ergo & </s> <s xml:id="echoid-s10194" xml:space="preserve">æquales ſunt rationes compoſitæ. </s> <s xml:id="echoid-s10195" xml:space="preserve">Q. </s> <s xml:id="echoid-s10196" xml:space="preserve">D. </s> <s xml:id="echoid-s10197" xml:space="preserve">E.</s> <s xml:id="echoid-s10198" xml:space="preserve"/> </p> <div xml:id="echoid-div1434" type="float" level="2" n="2"> <note position="right" xlink:label="note-0383-03" xlink:href="note-0383-03a" xml:space="preserve">983.</note> <note symbol="*" position="right" xlink:label="note-0383-04" xlink:href="note-0383-04a" xml:space="preserve">979.</note> </div> </div> <div xml:id="echoid-div1436" type="section" level="1" n="349"> <head xml:id="echoid-head480" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s10199" xml:space="preserve">Logarithmus ordinatæ cujuſcunque dicitur abſciſſa ipſi reſpondens, ubicunque ini-<lb/> <anchor type="note" xlink:label="note-0383-05a" xlink:href="note-0383-05"/> tium abſciſſarum ponatur.</s> <s xml:id="echoid-s10200" xml:space="preserve"/> </p> <div xml:id="echoid-div1436" type="float" level="2" n="1"> <note position="right" xlink:label="note-0383-05" xlink:href="note-0383-05a" xml:space="preserve">981.</note> </div> </div> <div xml:id="echoid-div1438" type="section" level="1" n="350"> <head xml:id="echoid-head481" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s10201" xml:space="preserve">Diſtantia inter duas ordinatas vocatur logarithmus rationis quæ inter ipſas da-<lb/> <anchor type="note" xlink:label="note-0383-06a" xlink:href="note-0383-06"/> tur. </s> <s xml:id="echoid-s10202" xml:space="preserve">Eſtque differentia logarithmorum ipſarum ordinatarum.</s> <s xml:id="echoid-s10203" xml:space="preserve"/> </p> <div xml:id="echoid-div1438" type="float" level="2" n="1"> <note position="right" xlink:label="note-0383-06" xlink:href="note-0383-06a" xml:space="preserve">982.</note> </div> <p> <s xml:id="echoid-s10204" xml:space="preserve">Poſitis iterum AH & </s> <s xml:id="echoid-s10205" xml:space="preserve">LR æqualibus habemus</s> </p> </div> <div xml:id="echoid-div1440" type="section" level="1" n="351"> <head xml:id="echoid-head482" xml:space="preserve">AC, HI :: LM, RS <anchor type="note" xlink:href="" symbol="*"/>; & dividendo</head> <note symbol="*" position="right" xml:space="preserve">982.</note> <p> <s xml:id="echoid-s10206" xml:space="preserve">AC - HI = TC, AC :</s> <s xml:id="echoid-s10207" xml:space="preserve">: LM - RS = VM, LM. </s> <s xml:id="echoid-s10208" xml:space="preserve">Quare eſt</s> </p> <pb o="284" file="0384" n="419" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1441" type="section" level="1" n="352"> <head xml:id="echoid-head483" xml:space="preserve">TC, VM:: AC, LM.</head> <p> <s xml:id="echoid-s10209" xml:space="preserve">Id eſt ordinatæ ſunt inter ſe, ut harum ſingularum differentiæ cum aliis or dina-<lb/> <anchor type="note" xlink:label="note-0384-01a" xlink:href="note-0384-01"/> tis æqualiter ab his diſtantibus.</s> <s xml:id="echoid-s10210" xml:space="preserve"/> </p> <div xml:id="echoid-div1441" type="float" level="2" n="1"> <note position="left" xlink:label="note-0384-01" xlink:href="note-0384-01a" xml:space="preserve">983.</note> </div> <p> <s xml:id="echoid-s10211" xml:space="preserve">In puncto quocunque C logarithmicæ CM, ductâ tangente CT, quæ a-<lb/> <anchor type="note" xlink:label="note-0384-02a" xlink:href="note-0384-02"/> ſymtoton ſecat in T, habetur ſubtangens AT; </s> <s xml:id="echoid-s10212" xml:space="preserve">& </s> <s xml:id="echoid-s10213" xml:space="preserve">eſt hæc conſtans in omnibus <lb/>curvæ punctis, ductâque in M tangente MV, erunt æquales AT, LV. <lb/></s> <s xml:id="echoid-s10214" xml:space="preserve"> <anchor type="note" xlink:label="note-0384-03a" xlink:href="note-0384-03"/> Ut hoc pateat ſint AD, LN infinitæ exiguæ & </s> <s xml:id="echoid-s10215" xml:space="preserve">æquales, ductiſque ordina-<lb/>tis DE, NO, ſint E c, O m, ipſi AB parallelæ. </s> <s xml:id="echoid-s10216" xml:space="preserve">Triangula C c E, CAT, <lb/>ſunt ſimilia, ut & </s> <s xml:id="echoid-s10217" xml:space="preserve">M m O & </s> <s xml:id="echoid-s10218" xml:space="preserve">MLV; </s> <s xml:id="echoid-s10219" xml:space="preserve">ergo</s> </p> <div xml:id="echoid-div1442" type="float" level="2" n="2"> <note position="left" xlink:label="note-0384-02" xlink:href="note-0384-02a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 2.</note> <note position="left" xlink:label="note-0384-03" xlink:href="note-0384-03a" xml:space="preserve">984.</note> </div> </div> <div xml:id="echoid-div1444" type="section" level="1" n="353"> <head xml:id="echoid-head484" xml:space="preserve">C c, c E:: CA, AT, & <lb/>M m, m O :: ML, LV.</head> <p> <s xml:id="echoid-s10220" xml:space="preserve">Sunt autem proportionalia antecedentia, in hiſce proportionibus <lb/>Cc, M m :</s> <s xml:id="echoid-s10221" xml:space="preserve">: CA, ML <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10222" xml:space="preserve">ergo & </s> <s xml:id="echoid-s10223" xml:space="preserve">conſequentia c E, m O :</s> <s xml:id="echoid-s10224" xml:space="preserve">: AT, LV:</s> <s xml:id="echoid-s10225" xml:space="preserve"> <anchor type="note" xlink:label="note-0384-04a" xlink:href="note-0384-04"/> ſed ſunt æquales c E, m O; </s> <s xml:id="echoid-s10226" xml:space="preserve">idcirco & </s> <s xml:id="echoid-s10227" xml:space="preserve">AT, LV.</s> <s xml:id="echoid-s10228" xml:space="preserve"/> </p> <div xml:id="echoid-div1444" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0384-04" xlink:href="note-0384-04a" xml:space="preserve">983.</note> </div> <p> <s xml:id="echoid-s10229" xml:space="preserve">Si ſervatis ordinatis AC, DE, FG, HI &</s> <s xml:id="echoid-s10230" xml:space="preserve">c. </s> <s xml:id="echoid-s10231" xml:space="preserve">ſervataque æqualitate di-<lb/> <anchor type="note" xlink:label="note-0384-05a" xlink:href="note-0384-05"/> ſtantiarum AD, DF, FH, &</s> <s xml:id="echoid-s10232" xml:space="preserve">c. </s> <s xml:id="echoid-s10233" xml:space="preserve">diſtantiæ hæ augeantur, aut minuantur, <lb/> <anchor type="note" xlink:label="note-0384-06a" xlink:href="note-0384-06"/> manifeſtum eſt logarithmicam mutari, ſubtangentemque etiam mutari in <lb/>eadem ratione in qua diſtantiæ hæ mutantur; </s> <s xml:id="echoid-s10234" xml:space="preserve">nam in triangulo C c E, ſervato <lb/> <anchor type="note" xlink:label="note-0384-07a" xlink:href="note-0384-07"/> latere C c, ſi mutetur c E, in triangulo ſimili CAT, cujus latus CA ſerva-<lb/>tur, in eadem ratione cum c E mutabitur AT.</s> <s xml:id="echoid-s10235" xml:space="preserve"/> </p> <div xml:id="echoid-div1445" type="float" level="2" n="2"> <note position="left" xlink:label="note-0384-05" xlink:href="note-0384-05a" xml:space="preserve">985.</note> <note position="left" xlink:label="note-0384-06" xlink:href="note-0384-06a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 1.</note> <note position="left" xlink:label="note-0384-07" xlink:href="note-0384-07a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s10236" xml:space="preserve">Etiam in eadem ratione in qua ſingulæ diſtantiæ minores mutantur, mu-<lb/> <anchor type="note" xlink:label="note-0384-08a" xlink:href="note-0384-08"/> tantur ſummæ diſtantiarum quatumcunque: </s> <s xml:id="echoid-s10237" xml:space="preserve">id eſt ut mutatur AD ſic & </s> <s xml:id="echoid-s10238" xml:space="preserve"><lb/>mutatur AH, log. </s> <s xml:id="echoid-s10239" xml:space="preserve">rationis AC ad HI; </s> <s xml:id="echoid-s10240" xml:space="preserve">unde ſequitur, in diverſis logari-<lb/> <anchor type="note" xlink:label="note-0384-09a" xlink:href="note-0384-09"/> tbmicis ſubtangentes eſſe inter ſe, ut ſunt logarithmi ear undem rationum.</s> <s xml:id="echoid-s10241" xml:space="preserve"/> </p> <div xml:id="echoid-div1446" type="float" level="2" n="3"> <note position="left" xlink:label="note-0384-08" xlink:href="note-0384-08a" xml:space="preserve">TAB. XXXVII. <lb/>fig 2.</note> <note position="left" xlink:label="note-0384-09" xlink:href="note-0384-09a" xml:space="preserve">986.</note> </div> <p> <s xml:id="echoid-s10242" xml:space="preserve">In Tabulis logarithmorum quas editas habemus, logarithmus rationis u-<lb/> <anchor type="note" xlink:label="note-0384-10a" xlink:href="note-0384-10"/> nius ad decem eſt ipſa unitas, & </s> <s xml:id="echoid-s10243" xml:space="preserve">logarithmi rationum intermediarum per <lb/>fractiones decimales exprimuntur, eſtque ſubtangens logarithmicæ tabularum <lb/>o, 43429. </s> <s xml:id="echoid-s10244" xml:space="preserve">44819.</s> <s xml:id="echoid-s10245" xml:space="preserve"/> </p> <div xml:id="echoid-div1447" type="float" level="2" n="4"> <note position="left" xlink:label="note-0384-10" xlink:href="note-0384-10a" xml:space="preserve">987.</note> </div> </div> <div xml:id="echoid-div1449" type="section" level="1" n="354"> <head xml:id="echoid-head485" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head486" style="it" xml:space="preserve">De Retardatione in genere.</head> <p> <s xml:id="echoid-s10246" xml:space="preserve">REtardatio, & </s> <s xml:id="echoid-s10247" xml:space="preserve">acceleratio, menſuratur, poſitis momentis infinitè exiguis æqua-<lb/> <anchor type="note" xlink:label="note-0384-11a" xlink:href="note-0384-11"/> libus; </s> <s xml:id="echoid-s10248" xml:space="preserve">retardatio quæ a prima cauſa pendet æquabilis dicitur, quia di-<lb/>minutiones velocitatis æqualibus temporibus ſunt æquales <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10249" xml:space="preserve">Retardatio ex <anchor type="note" xlink:label="note-0384-12a" xlink:href="note-0384-12"/> ſecunda cauſa dicitur ut quadratum velocitatis, quia diminutiones, in mo-<lb/>mentis infinitè exiguis æqualibus, ſunt ut hæc quadrata. </s> <s xml:id="echoid-s10250" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/></s> </p> <div xml:id="echoid-div1449" type="float" level="2" n="1"> <note position="left" xlink:label="note-0384-11" xlink:href="note-0384-11a" xml:space="preserve">988.</note> <note symbol="*" position="left" xlink:label="note-0384-12" xlink:href="note-0384-12a" xml:space="preserve">951.</note> </div> <note symbol="*" position="left" xml:space="preserve">954.</note> <p> <s xml:id="echoid-s10251" xml:space="preserve">In ſingulis autem momentis infinitè exiguis retardationes, & </s> <s xml:id="echoid-s10252" xml:space="preserve">accelerationes, ſunt <lb/> <anchor type="note" xlink:label="note-0384-14a" xlink:href="note-0384-14"/> æquabiles, nam in tali momento mutatio in actione reſpectiva pro nulla ha-<lb/>beri poteſt; </s> <s xml:id="echoid-s10253" xml:space="preserve">&</s> <s xml:id="echoid-s10254" xml:space="preserve">, durante integro momento eodem modo variat motus relativus <lb/>fluidi & </s> <s xml:id="echoid-s10255" xml:space="preserve">corporis: </s> <s xml:id="echoid-s10256" xml:space="preserve">ergo ſi momenta differant erunt retardationes, & </s> <s xml:id="echoid-s10257" xml:space="preserve">accelerationes <lb/> <anchor type="note" xlink:label="note-0384-15a" xlink:href="note-0384-15"/> ut ipſa momenta; </s> <s xml:id="echoid-s10258" xml:space="preserve">id eſt ſunt hæ in momentis infinitè exiguis inæqualibus, in <lb/>ratione compoſita rationis retar dationum, & </s> <s xml:id="echoid-s10259" xml:space="preserve">accelerationum, poſitis momentis æ-<lb/> <anchor type="note" xlink:label="note-0384-16a" xlink:href="note-0384-16"/> qualibus <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10260" xml:space="preserve">rationis ipſorum momentorum inæqualium <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10261" xml:space="preserve"/> </p> <div xml:id="echoid-div1450" type="float" level="2" n="2"> <note position="left" xlink:label="note-0384-14" xlink:href="note-0384-14a" xml:space="preserve">989.</note> <note position="left" xlink:label="note-0384-15" xlink:href="note-0384-15a" xml:space="preserve">990.</note> <note symbol="*" position="left" xlink:label="note-0384-16" xlink:href="note-0384-16a" xml:space="preserve">988.</note> </div> <note symbol="*" position="left" xml:space="preserve">989.</note> <p> <s xml:id="echoid-s10262" xml:space="preserve">Quando ſpatiola infinite exigua ſunt æqualia, momenta quibus ſingula <lb/> <anchor type="note" xlink:label="note-0384-18a" xlink:href="note-0384-18"/> ſpatiola percurruntur ſunt inverſè ut velocitates <anchor type="note" xlink:href="" symbol="*"/>, ergo retardationes, & </s> <s xml:id="echoid-s10263" xml:space="preserve">acce- <anchor type="note" xlink:label="note-0384-19a" xlink:href="note-0384-19"/> <pb o="285" file="0385" n="420" rhead="MATHEMATICA. LIB. II. CAP. XII."/> lerationes, quas corpus patitur, percurrendo ſingula talia ſpatiola æqualia, ſunt di-<lb/>rectè ut retardationes, poſitis momentis æqualibus, & </s> <s xml:id="echoid-s10264" xml:space="preserve">inverſè ut velocita-<lb/>tes <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10265" xml:space="preserve"/> </p> <div xml:id="echoid-div1451" type="float" level="2" n="3"> <note position="left" xlink:label="note-0384-18" xlink:href="note-0384-18a" xml:space="preserve">991.</note> <note symbol="*" position="left" xlink:label="note-0384-19" xlink:href="note-0384-19a" xml:space="preserve">95.</note> </div> <note symbol="*" position="right" xml:space="preserve">990.</note> <p> <s xml:id="echoid-s10266" xml:space="preserve">Ideo in retardatione ex prima cauſa, ſi ſpatiola infinitè exigua fuerint æqualia, <lb/> <anchor type="note" xlink:label="note-0385-02a" xlink:href="note-0385-02"/> ſunt velocitatis diminutiones inverſè ut velocitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10267" xml:space="preserve"/> </p> <div xml:id="echoid-div1452" type="float" level="2" n="4"> <note position="right" xlink:label="note-0385-02" xlink:href="note-0385-02a" xml:space="preserve">992.</note> </div> <note symbol="*" position="right" xml:space="preserve">951.</note> <p> <s xml:id="echoid-s10268" xml:space="preserve">In retardatione ex ſecunda cauſa, ſunt velocitatis diminutiones, in ſpatiolis æqua-<lb/> <anchor type="note" xlink:label="note-0385-04a" xlink:href="note-0385-04"/> libus, directè ut quadrata velocitatum, & </s> <s xml:id="echoid-s10269" xml:space="preserve">inverſè ut ipſæ velocitates <anchor type="note" xlink:href="" symbol="*"/>, id eſt <anchor type="note" xlink:label="note-0385-05a" xlink:href="note-0385-05"/> directe ut velocitates.</s> <s xml:id="echoid-s10270" xml:space="preserve"/> </p> <div xml:id="echoid-div1453" type="float" level="2" n="5"> <note position="right" xlink:label="note-0385-04" xlink:href="note-0385-04a" xml:space="preserve">993.</note> <note symbol="*" position="right" xlink:label="note-0385-05" xlink:href="note-0385-05a" xml:space="preserve">954. 990.</note> </div> </div> <div xml:id="echoid-div1455" type="section" level="1" n="355"> <head xml:id="echoid-head487" xml:space="preserve">SCHOLIUM 3.</head> <head xml:id="echoid-head488" style="it" xml:space="preserve">De Retardatione ex prima Cauſa.</head> <p> <s xml:id="echoid-s10271" xml:space="preserve">SIt AC ſpatium, in quo corpus totam amittit velocitatem, quando ex pri-<lb/> <anchor type="note" xlink:label="note-0385-06a" xlink:href="note-0385-06"/> ma cauſa ſola retardatur, dum velocitas in initio repræſentatur lineâ <lb/> <anchor type="note" xlink:label="note-0385-07a" xlink:href="note-0385-07"/> AD.</s> <s xml:id="echoid-s10272" xml:space="preserve"/> </p> <div xml:id="echoid-div1455" type="float" level="2" n="1"> <note position="right" xlink:label="note-0385-06" xlink:href="note-0385-06a" xml:space="preserve">994.</note> <note position="right" xlink:label="note-0385-07" xlink:href="note-0385-07a" xml:space="preserve">TAB. XXXVI. <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s10273" xml:space="preserve">Dum ſpatium hoc AC a corpore percurritur, patitur hoc eaſdem muta-<lb/>tiones, quibus ſubjicitur corpus adſcendens, quod ſola retardaretur gravitate, <lb/>& </s> <s xml:id="echoid-s10274" xml:space="preserve">quod ad altitudinem AC adſcendendo totam amitteret velocitatem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10275" xml:space="preserve"> <anchor type="note" xlink:label="note-0385-08a" xlink:href="note-0385-08"/> Quadratum igitur velocitatis in A, ſe habet ad quadratum velocitatis in alio <lb/> <anchor type="note" xlink:label="note-0385-09a" xlink:href="note-0385-09"/> puncto quocunque B, ut AC ad BC <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10276" xml:space="preserve">Si ergo fuerit AD ad BE, in ra- <anchor type="note" xlink:label="note-0385-10a" xlink:href="note-0385-10"/> tione ſubduplicata AC ad BC, repræſentabit BE velocitatem in B. </s> <s xml:id="echoid-s10277" xml:space="preserve">Datur <lb/>autem ratio hæc inter ordinatas parabolæ quæ tranſit per C & </s> <s xml:id="echoid-s10278" xml:space="preserve">D, poſita <lb/>C extremitate diametri AC †.</s> <s xml:id="echoid-s10279" xml:space="preserve"/> </p> <div xml:id="echoid-div1456" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0385-08" xlink:href="note-0385-08a" xml:space="preserve">258. 951.</note> <note symbol="*" position="right" xlink:label="note-0385-09" xlink:href="note-0385-09a" xml:space="preserve">261. 255.</note> <note position="right" xlink:label="note-0385-10" xlink:href="note-0385-10a" xml:space="preserve">† la Hire <lb/>fect. con. <lb/>lib. 3. <lb/>prop. 2.</note> </div> <p> <s xml:id="echoid-s10280" xml:space="preserve">Idcirco ſi parabolæ diameter repræſentat ſpatium percurſum, ordinatæ ad dia-<lb/> <anchor type="note" xlink:label="note-0385-11a" xlink:href="note-0385-11"/> metrum velocitates, in punctis quibuſcunque, deſignabunt, ſi corpus ex ſola prima <lb/>cauſa retardetur, aut aliam quamcunque retardationem æquabilem patiatur.</s> <s xml:id="echoid-s10281" xml:space="preserve"/> </p> <div xml:id="echoid-div1457" type="float" level="2" n="3"> <note position="right" xlink:label="note-0385-11" xlink:href="note-0385-11a" xml:space="preserve">995.</note> </div> <p> <s xml:id="echoid-s10282" xml:space="preserve">Si ſpatiola A a & </s> <s xml:id="echoid-s10283" xml:space="preserve">B b, infinitè exigua, fuerint æqualia, diminutiones velo-<lb/>citatum DF, GE, erunt inverſè ut ipſæ velocitates AD, BE <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10284" xml:space="preserve">Si A a aut <anchor type="note" xlink:label="note-0385-12a" xlink:href="note-0385-12"/> B b mutetur, mutatur in eadem ratione DF aut GE; </s> <s xml:id="echoid-s10285" xml:space="preserve">ergo in Parabola, <lb/> <anchor type="note" xlink:label="note-0385-13a" xlink:href="note-0385-13"/> differentiæ infinitè exiguæ or dinatarum vicinarum ſunt directe ut differentiæ ab-<lb/>ſciſſarum reſpondentium, & </s> <s xml:id="echoid-s10286" xml:space="preserve">inverſe ut ipſæ ordinatæ. </s> <s xml:id="echoid-s10287" xml:space="preserve">Quod etiam ex ſola con-<lb/>ſideratione parabolæ deduci potuiſſet.</s> <s xml:id="echoid-s10288" xml:space="preserve"/> </p> <div xml:id="echoid-div1458" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0385-12" xlink:href="note-0385-12a" xml:space="preserve">992.</note> <note position="right" xlink:label="note-0385-13" xlink:href="note-0385-13a" xml:space="preserve">996.</note> </div> <p> <s xml:id="echoid-s10289" xml:space="preserve">Si duo dentur corpora, æqualibus velocitatibus mota, quæ diverſas patiuntur re-<lb/> <anchor type="note" xlink:label="note-0385-14a" xlink:href="note-0385-14"/> tardationes ex prima cauſa, aut in genere retardationes diverſas æquabiles, ſunt <lb/>ſpatia, quibus percurrendo integræ velocitates tolluntur, inverſè ut retardationes <lb/>in momentis æqualibus, ut hoc facile deducitur ex demonſtratis de adſcenſu <lb/>ſuper planis inclinatis. </s> <s xml:id="echoid-s10290" xml:space="preserve">Nam velocitatibus æqualibus corpora ad eandem ad-<lb/>ſcendunt altitudinem ſuper planis diverſis <anchor type="note" xlink:href="" symbol="*"/>, id eſt ſpatia, quibus percurren- do integras amittunt velocitates, ſunt ut planorum longitudines, poſitis alti-<lb/> <anchor type="note" xlink:label="note-0385-15a" xlink:href="note-0385-15"/> dinibus æqualibus: </s> <s xml:id="echoid-s10291" xml:space="preserve">ſed in hoc caſu ſunt preſſiones, quibus corpora ſuper his <lb/>planis deſcendere conantur, quæ ſunt ut velocitates eodem tempore com-<lb/>municatæ, aut ſublatæ, in ratione inverſâ longitudinum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10292" xml:space="preserve">Q. </s> <s xml:id="echoid-s10293" xml:space="preserve">D, E.</s> <s xml:id="echoid-s10294" xml:space="preserve"/> </p> <div xml:id="echoid-div1459" type="float" level="2" n="5"> <note position="right" xlink:label="note-0385-14" xlink:href="note-0385-14a" xml:space="preserve">997.</note> <note symbol="*" position="right" xlink:label="note-0385-15" xlink:href="note-0385-15a" xml:space="preserve">274.</note> </div> <note symbol="*" position="right" xml:space="preserve">238.</note> <pb o="286" file="0386" n="421" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1461" type="section" level="1" n="356"> <head xml:id="echoid-head489" xml:space="preserve">SCHOLIUM 4.</head> <head xml:id="echoid-head490" style="it" xml:space="preserve">De Retardatione ex ſecunda Cauſâ.</head> <p> <s xml:id="echoid-s10295" xml:space="preserve">SIAB, logarithmicæ aſymtotos, ſpatium a corpore in fluido percurſum repræſentat, <lb/> <anchor type="note" xlink:label="note-0386-01a" xlink:href="note-0386-01"/> poterunt velocitates in ſingulis punctis ordinatis repræſentari; </s> <s xml:id="echoid-s10296" xml:space="preserve">ſunt enim velo-<lb/> <anchor type="note" xlink:label="note-0386-02a" xlink:href="note-0386-02"/> citatum decrementa, in ſpatiis infinite exiguis æqualibus, AD, DF, <lb/>FH, &</s> <s xml:id="echoid-s10297" xml:space="preserve">c. </s> <s xml:id="echoid-s10298" xml:space="preserve">ut ipſæ velocitates <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10299" xml:space="preserve">decrementa ordinatarum AC, DE, <anchor type="note" xlink:label="note-0386-03a" xlink:href="note-0386-03"/> FG, &</s> <s xml:id="echoid-s10300" xml:space="preserve">c. </s> <s xml:id="echoid-s10301" xml:space="preserve">ut ipſæ ordinatæ<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10302" xml:space="preserve"/> </p> <div xml:id="echoid-div1461" type="float" level="2" n="1"> <note position="left" xlink:label="note-0386-01" xlink:href="note-0386-01a" xml:space="preserve">998.</note> <note position="left" xlink:label="note-0386-02" xlink:href="note-0386-02a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0386-03" xlink:href="note-0386-03a" xml:space="preserve">993.</note> </div> <note symbol="*" position="left" xml:space="preserve">983.</note> <p> <s xml:id="echoid-s10303" xml:space="preserve">Unde ſequitur ſi ſpatia fuerint æqualia, ut AL, LX, XB, velocitates <lb/> <anchor type="note" xlink:label="note-0386-05a" xlink:href="note-0386-05"/> in punctis A, L, X, B, quæ deſignantur ordinatis AC, LM, XZ, BK, <lb/>eſſe in progreſſione geometrica <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10304" xml:space="preserve">ut notavimus in n. </s> <s xml:id="echoid-s10305" xml:space="preserve">961.</s> <s xml:id="echoid-s10306" xml:space="preserve"/> </p> <div xml:id="echoid-div1462" type="float" level="2" n="2"> <note position="left" xlink:label="note-0386-05" xlink:href="note-0386-05a" xml:space="preserve">999.</note> </div> <note symbol="*" position="left" xml:space="preserve">980.</note> <p> <s xml:id="echoid-s10307" xml:space="preserve">Sit A T logarithmicæ aſymtos; </s> <s xml:id="echoid-s10308" xml:space="preserve">BY logarithmica; </s> <s xml:id="echoid-s10309" xml:space="preserve">BM ejuſdem conti-<lb/> <anchor type="note" xlink:label="note-0386-07a" xlink:href="note-0386-07"/> nuatio in ſitu contrario poſita.</s> <s xml:id="echoid-s10310" xml:space="preserve"/> </p> <div xml:id="echoid-div1463" type="float" level="2" n="3"> <note position="left" xlink:label="note-0386-07" xlink:href="note-0386-07a" xml:space="preserve">1000.</note> </div> <note position="left" xml:space="preserve">TAB. XXXVII. <lb/>fig. 3.</note> <p> <s xml:id="echoid-s10311" xml:space="preserve">Si nunc ſumamus ordinatam quamcunque ut TYM; </s> <s xml:id="echoid-s10312" xml:space="preserve">Logarithmus ra-<lb/>tionis TM ad AB eſt AT<anchor type="note" xlink:href="" symbol="*"/>, qui etiam eſt logarithmus rationis AB ad TY;</s> <s xml:id="echoid-s10313" xml:space="preserve"> <anchor type="note" xlink:label="note-0386-09a" xlink:href="note-0386-09"/> ſunt ergo in continua proportione TM, AB, TY <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s10314" xml:space="preserve">& </s> <s xml:id="echoid-s10315" xml:space="preserve">quadratum AB <anchor type="note" xlink:label="note-0386-10a" xlink:href="note-0386-10"/> valet TM x TY: </s> <s xml:id="echoid-s10316" xml:space="preserve">ſuntque æqualia eidem quadrato AB, ideoque inter ſe, <lb/>rectangula omnia ut TM x TY, SX x SL; </s> <s xml:id="echoid-s10317" xml:space="preserve">PE x PG, &</s> <s xml:id="echoid-s10318" xml:space="preserve">c.</s> <s xml:id="echoid-s10319" xml:space="preserve"/> </p> <div xml:id="echoid-div1464" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0386-09" xlink:href="note-0386-09a" xml:space="preserve">982.</note> <note symbol="*" position="left" xlink:label="note-0386-10" xlink:href="note-0386-10a" xml:space="preserve">980.</note> </div> <p> <s xml:id="echoid-s10320" xml:space="preserve">Idcirco creſcunt ordinatæ, quæ curvâ BM terminantur, ut minuuntur <lb/> <anchor type="note" xlink:label="note-0386-11a" xlink:href="note-0386-11"/> reſpondentes, quæ curva BY terminantur, ſuntque primæ inverſè ut ſe-<lb/>cundæ.</s> <s xml:id="echoid-s10321" xml:space="preserve"/> </p> <div xml:id="echoid-div1465" type="float" level="2" n="5"> <note position="left" xlink:label="note-0386-11" xlink:href="note-0386-11a" xml:space="preserve">1001.</note> </div> <p> <s xml:id="echoid-s10322" xml:space="preserve">Spatiola infinite exigua velocitate æquabili ſingula percurruntur; </s> <s xml:id="echoid-s10323" xml:space="preserve">ſunt ergo <lb/> <anchor type="note" xlink:label="note-0386-12a" xlink:href="note-0386-12"/> momenta quibus talia ſpatiola æqualia AC, CP, PQ, &</s> <s xml:id="echoid-s10324" xml:space="preserve">c. </s> <s xml:id="echoid-s10325" xml:space="preserve">percurruntur <lb/>inverſè ut velocitates quibus percurruntur <anchor type="note" xlink:href="" symbol="*"/>, id eſt inverſè ut AB, CD, <anchor type="note" xlink:label="note-0386-13a" xlink:href="note-0386-13"/> PE, & </s> <s xml:id="echoid-s10326" xml:space="preserve">c <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10327" xml:space="preserve">aut directe ut AB, CF, PG &</s> <s xml:id="echoid-s10328" xml:space="preserve">c <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10329" xml:space="preserve">quæ ſunt ut differentiæ, <anchor type="note" xlink:label="note-0386-14a" xlink:href="note-0386-14"/> B b, F f. </s> <s xml:id="echoid-s10330" xml:space="preserve">G g &</s> <s xml:id="echoid-s10331" xml:space="preserve">c <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10332" xml:space="preserve"/> </p> <div xml:id="echoid-div1466" type="float" level="2" n="6"> <note position="left" xlink:label="note-0386-12" xlink:href="note-0386-12a" xml:space="preserve">1002.</note> <note symbol="*" position="left" xlink:label="note-0386-13" xlink:href="note-0386-13a" xml:space="preserve">95.</note> <note symbol="*" position="left" xlink:label="note-0386-14" xlink:href="note-0386-14a" xml:space="preserve">998.</note> </div> <note symbol="*" position="left" xml:space="preserve">1001.</note> <p> <s xml:id="echoid-s10333" xml:space="preserve">Totum igitur tempus quo linea ut AQ percurritur, omnibus hiſce diffe-<lb/> <anchor type="note" xlink:label="note-0386-16a" xlink:href="note-0386-16"/> rentiis conjunctim repræſentatur, id eſt, lineâ NH; </s> <s xml:id="echoid-s10334" xml:space="preserve">eodem modo OM <lb/>repræſentat tempus quo QT percurritur: </s> <s xml:id="echoid-s10335" xml:space="preserve">ſi vero ſpatia AQ, QT, fue-<lb/> <anchor type="note" xlink:label="note-0386-17a" xlink:href="note-0386-17"/> rint æqualia, erit NH ad OM, ut QH ad TM <anchor type="note" xlink:href="" symbol="*"/>, id eſt inverſè ut QK <anchor type="note" xlink:label="note-0386-18a" xlink:href="note-0386-18"/> ad TY <anchor type="note" xlink:href="" symbol="*"/>, aut AB ad QK <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10336" xml:space="preserve"/> </p> <div xml:id="echoid-div1467" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0386-16" xlink:href="note-0386-16a" xml:space="preserve">983.</note> <note symbol="*" position="left" xlink:label="note-0386-17" xlink:href="note-0386-17a" xml:space="preserve">983.</note> <note symbol="*" position="left" xlink:label="note-0386-18" xlink:href="note-0386-18a" xml:space="preserve">1001.</note> </div> <note symbol="*" position="left" xml:space="preserve">980.</note> <p> <s xml:id="echoid-s10337" xml:space="preserve">Tempora ergo, quibus ſpatia æqualia ſucceſſivè percurruntur, ſunt inverſè <lb/> <anchor type="note" xlink:label="note-0386-20a" xlink:href="note-0386-20"/> ut velocitates in fine, aut inverſè ut velocitates in initiis ſpatiorum; </s> <s xml:id="echoid-s10338" xml:space="preserve">ut mo-<lb/>nuimus in n. </s> <s xml:id="echoid-s10339" xml:space="preserve">961.</s> <s xml:id="echoid-s10340" xml:space="preserve"/> </p> <div xml:id="echoid-div1468" type="float" level="2" n="8"> <note position="left" xlink:label="note-0386-20" xlink:href="note-0386-20a" xml:space="preserve">1003.</note> </div> <p> <s xml:id="echoid-s10341" xml:space="preserve">Ponamus iterum corpus quod in linea AB movetur, & </s> <s xml:id="echoid-s10342" xml:space="preserve">ex ſecunda cauſa <lb/> <anchor type="note" xlink:label="note-0386-21a" xlink:href="note-0386-21"/> ſola retardatur, ſit AC velocitas in A, & </s> <s xml:id="echoid-s10343" xml:space="preserve">CM logarithmica, quæ in aliis pun-<lb/> <anchor type="note" xlink:label="note-0386-22a" xlink:href="note-0386-22"/> ctis velocitates determinat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10344" xml:space="preserve">ut hac curvâ, & </s> <s xml:id="echoid-s10345" xml:space="preserve">tabulis utamur in computa- tionibus neceſſe eſt, ut determinemus magnitudinem ſubtangentis logarithmi-<lb/> <anchor type="note" xlink:label="note-0386-23a" xlink:href="note-0386-23"/> cæ, quæ uſu venire poteſt in caſu quocunque propoſito, aut quod idem eſt, <lb/>debemus determinare, in figura data quacunque, quodnam ſpatium ſubtan-<lb/>gente repræſentatur.</s> <s xml:id="echoid-s10346" xml:space="preserve"/> </p> <div xml:id="echoid-div1469" type="float" level="2" n="9"> <note position="left" xlink:label="note-0386-21" xlink:href="note-0386-21a" xml:space="preserve">1004.</note> <note position="left" xlink:label="note-0386-22" xlink:href="note-0386-22a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0386-23" xlink:href="note-0386-23a" xml:space="preserve">998.</note> </div> <p> <s xml:id="echoid-s10347" xml:space="preserve">Ponamus AC eſſe velocitatem, qua ſi corpus in fluido feratur, reſiſtentia <lb/>ex ſecunda cauſa ipſi ponderi corporis æqualis ſit.</s> <s xml:id="echoid-s10348" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10349" xml:space="preserve">Ergo Corporis pondus, id eſt, preſſio ex gravitate quæ corpus adſcendens retar-<lb/> <anchor type="note" xlink:label="note-0386-24a" xlink:href="note-0386-24"/> dat, æqualis eſt preſſioni quam corpus de quo agimus ex reſiſtentia ex ſecunda <lb/>cauſa patitur. </s> <s xml:id="echoid-s10350" xml:space="preserve">Preſſiones hæ ambæ immediate corpus transferunt, quando in <pb file="0387" n="422"/> <pb file="0387a" n="423"/> <anchor type="figure" xlink:label="fig-0387a-01a" xlink:href="fig-0387a-01"/> <pb file="0388" n="424"/> <pb o="287" file="0389" n="425" rhead="MATHEMATICA. LIB. II. CAP. XII."/> hoc agunt: </s> <s xml:id="echoid-s10351" xml:space="preserve">ergo æqualiter eundem motum ejuſdem corporis mutare poſſunt; </s> <s xml:id="echoid-s10352" xml:space="preserve">eſt-<lb/>que retardatio, quam corpus in fluido patitur in primo momento, æqualis <lb/>velocitati, quam in momento æquali corpus adſcendens, & </s> <s xml:id="echoid-s10353" xml:space="preserve">quod gravitas <lb/>retardat, amittit.</s> <s xml:id="echoid-s10354" xml:space="preserve"/> </p> <div xml:id="echoid-div1470" type="float" level="2" n="10"> <note position="left" xlink:label="note-0386-24" xlink:href="note-0386-24a" xml:space="preserve">1005.</note> <figure xlink:label="fig-0387a-01" xlink:href="fig-0387a-01a"> <image file="0387a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0387a-01"/> </figure> </div> <p> <s xml:id="echoid-s10355" xml:space="preserve">Sit nunc C c retardatio quam corpus patitur percurrendo AD, erit C c <lb/>velocitas quam corpus amittit, adſcendendo ad altitudinem AD, quando gra-<lb/>vitate retardatur. </s> <s xml:id="echoid-s10356" xml:space="preserve">Concipiamus nunc parabolam deſcriptam, cujus axis ſit <lb/>AB, & </s> <s xml:id="echoid-s10357" xml:space="preserve">quæ per puncta C & </s> <s xml:id="echoid-s10358" xml:space="preserve">E tranſeat, id eſt eandem habeat tangentem <lb/>AT cum logarithmica, quæ per C & </s> <s xml:id="echoid-s10359" xml:space="preserve">E tranſit, & </s> <s xml:id="echoid-s10360" xml:space="preserve">cujus Aſymtos eſt <lb/>AB.</s> <s xml:id="echoid-s10361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10362" xml:space="preserve">Ordinatæ logarithmicæ hujus deſignabunt velocitates corporis in fluido mo-<lb/>ti, cujus velocitas in A eſt AC<anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s10363" xml:space="preserve">& </s> <s xml:id="echoid-s10364" xml:space="preserve">AX axis parabolæ, cujus vertex eſt X, <anchor type="note" xlink:label="note-0389-01a" xlink:href="note-0389-01"/> demonſtrabit altitudinem ad quam corpus, velocitate AC in altum proje-<lb/> <anchor type="note" xlink:label="note-0389-02a" xlink:href="note-0389-02"/> ctum, & </s> <s xml:id="echoid-s10365" xml:space="preserve">ſola gravitate retardatum, poteſt adſcendere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10366" xml:space="preserve">igitur XA, dimi- <anchor type="note" xlink:label="note-0389-03a" xlink:href="note-0389-03"/> dium ſubtangentis AT<anchor type="note" xlink:href="" symbol="*"/>, deſignat altitudinem a qua corpus in vacuo cadendo ac- <anchor type="note" xlink:label="note-0389-04a" xlink:href="note-0389-04"/> quirit velocitatem, qua ſi corpus per fluidum moveatur, reſiſtentiam patitur pon-<lb/>deri ipſius corporis æqualem, quæ altitudo datur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10367" xml:space="preserve"/> </p> <div xml:id="echoid-div1471" type="float" level="2" n="11"> <note symbol="*" position="right" xlink:label="note-0389-01" xlink:href="note-0389-01a" xml:space="preserve">998.</note> <note symbol="*" position="right" xlink:label="note-0389-02" xlink:href="note-0389-02a" xml:space="preserve">995.</note> <note position="right" xlink:label="note-0389-03" xlink:href="note-0389-03a" xml:space="preserve">1006.</note> <note symbol="*" position="right" xlink:label="note-0389-04" xlink:href="note-0389-04a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 2. <lb/>prop 20.</note> </div> <note symbol="*" position="right" xml:space="preserve">930.</note> <p> <s xml:id="echoid-s10368" xml:space="preserve">Hiſce poſitis ſequentia ſponte ſequuntur.</s> <s xml:id="echoid-s10369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10370" xml:space="preserve">Ut altitudo, à qua corpus in vacuo cadendo, acquirit velocitatem, quæ dat re-<lb/> <anchor type="note" xlink:label="note-0389-06a" xlink:href="note-0389-06"/> ſiſtentiam pondericorporis æqualem, ad ſpatium à corpore in fluido percurſum, ita <lb/>dimidium ſubtangentis tabularum, 0, 21714. </s> <s xml:id="echoid-s10371" xml:space="preserve">72409. </s> <s xml:id="echoid-s10372" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, ad logarihtmum rationis in- <anchor type="note" xlink:label="note-0389-07a" xlink:href="note-0389-07"/> ter velocitates in initio & </s> <s xml:id="echoid-s10373" xml:space="preserve">in fine ſpatii <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10374" xml:space="preserve"/> </p> <div xml:id="echoid-div1472" type="float" level="2" n="12"> <note position="right" xlink:label="note-0389-06" xlink:href="note-0389-06a" xml:space="preserve">1007.</note> <note symbol="*" position="right" xlink:label="note-0389-07" xlink:href="note-0389-07a" xml:space="preserve">987.</note> </div> <note symbol="*" position="right" xml:space="preserve">938.</note> <p> <s xml:id="echoid-s10375" xml:space="preserve">Numeri quicunque in tabulis, quorum logarihtmorum differentia eſt lo-<lb/> <anchor type="note" xlink:label="note-0389-09a" xlink:href="note-0389-09"/> garithmus rationis detectus, ſunt inter ſe ut hæ velocitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10376" xml:space="preserve"/> </p> <div xml:id="echoid-div1473" type="float" level="2" n="13"> <note position="right" xlink:label="note-0389-09" xlink:href="note-0389-09a" xml:space="preserve">1008.</note> </div> <note symbol="*" position="right" xml:space="preserve">982. 980.</note> <p> <s xml:id="echoid-s10377" xml:space="preserve">Eâdem hac regulâ, data ratione inter velocitates in initio & </s> <s xml:id="echoid-s10378" xml:space="preserve">fine ſpatii per-<lb/> <anchor type="note" xlink:label="note-0389-11a" xlink:href="note-0389-11"/> curſi, detegitur ſpatium hoc.</s> <s xml:id="echoid-s10379" xml:space="preserve"/> </p> <div xml:id="echoid-div1474" type="float" level="2" n="14"> <note position="right" xlink:label="note-0389-11" xlink:href="note-0389-11a" xml:space="preserve">1009.</note> </div> <p> <s xml:id="echoid-s10380" xml:space="preserve">Logarihtmus rationis 2. </s> <s xml:id="echoid-s10381" xml:space="preserve">ad I. </s> <s xml:id="echoid-s10382" xml:space="preserve">habetur, ſubtrahendo ex log. </s> <s xml:id="echoid-s10383" xml:space="preserve">numeri duo <lb/> <anchor type="note" xlink:label="note-0389-12a" xlink:href="note-0389-12"/> 0, 30102. </s> <s xml:id="echoid-s10384" xml:space="preserve">99957. </s> <s xml:id="echoid-s10385" xml:space="preserve">log. </s> <s xml:id="echoid-s10386" xml:space="preserve">o. </s> <s xml:id="echoid-s10387" xml:space="preserve">unitatis, ergo ut o, 21714. </s> <s xml:id="echoid-s10388" xml:space="preserve">72409, ad 0, 30102. </s> <s xml:id="echoid-s10389" xml:space="preserve">99957, <lb/>id eſt, ut 10000000000. </s> <s xml:id="echoid-s10390" xml:space="preserve">ad 13862945972.</s> <s xml:id="echoid-s10391" xml:space="preserve">, ita altitudo, a qua in vacuo caden-<lb/>do corpus acquirit velocitatem, quæ dat reſiſtentiam ponderi æqualem, ad <lb/>ſpatium in quo corpus dimidium velocitatis amittit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10392" xml:space="preserve">Congruit hoc cum <anchor type="note" xlink:label="note-0389-13a" xlink:href="note-0389-13"/> indicatis in n. </s> <s xml:id="echoid-s10393" xml:space="preserve">962.</s> <s xml:id="echoid-s10394" xml:space="preserve"/> </p> <div xml:id="echoid-div1475" type="float" level="2" n="15"> <note position="right" xlink:label="note-0389-12" xlink:href="note-0389-12a" xml:space="preserve">1010.</note> <note symbol="*" position="right" xlink:label="note-0389-13" xlink:href="note-0389-13a" xml:space="preserve">1007.</note> </div> <p> <s xml:id="echoid-s10395" xml:space="preserve">Si in puncto quocunque retardatio ex ſecunda cauſa fiat æquabilis, ſpatium <lb/> <anchor type="note" xlink:label="note-0389-14a" xlink:href="note-0389-14"/> in quo tota deſtruitur velocitas dimidiata ſubtangente repræſentatur, ut ſequi-<lb/>tur ex demonſtratione n. </s> <s xml:id="echoid-s10396" xml:space="preserve">1005, quæ & </s> <s xml:id="echoid-s10397" xml:space="preserve">hîc applicari poteſt; </s> <s xml:id="echoid-s10398" xml:space="preserve">cum autem ſub-<lb/>tangens conſtans ſit <anchor type="note" xlink:href="" symbol="*"/>, ſequitur etiam in fluido homogeneo, quale in his ubi- <anchor type="note" xlink:label="note-0389-15a" xlink:href="note-0389-15"/> que ponimus, ſpatium illud non mutari, quomodocunque varietur veloci-<lb/>tas, & </s> <s xml:id="echoid-s10399" xml:space="preserve">æquari altitudini a qua in vacuo cadendo corpus acquirit velocitatem, qua <lb/>poſitâ, reſiſtentia ponderi æqualis eſt<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10400" xml:space="preserve"/> </p> <div xml:id="echoid-div1476" type="float" level="2" n="16"> <note position="right" xlink:label="note-0389-14" xlink:href="note-0389-14a" xml:space="preserve">1011.</note> <note symbol="*" position="right" xlink:label="note-0389-15" xlink:href="note-0389-15a" xml:space="preserve">984.</note> </div> <note symbol="*" position="right" xml:space="preserve">1006.</note> </div> <div xml:id="echoid-div1478" type="section" level="1" n="357"> <head xml:id="echoid-head491" xml:space="preserve">SCHOLIUM 5.</head> <head xml:id="echoid-head492" style="it" xml:space="preserve">De ambabus Retardationibus conjunctim.</head> <p> <s xml:id="echoid-s10401" xml:space="preserve">Sit A M linea, quam corpus in fluido percurrit; </s> <s xml:id="echoid-s10402" xml:space="preserve">ſit hæc Aſymtos loga-<lb/> <anchor type="note" xlink:label="note-0389-17a" xlink:href="note-0389-17"/> rithmicæ ISP; </s> <s xml:id="echoid-s10403" xml:space="preserve">cujus AI eſt ordinata; </s> <s xml:id="echoid-s10404" xml:space="preserve">ſit præterea GFB parabola cu-<lb/> <anchor type="note" xlink:label="note-0389-18a" xlink:href="note-0389-18"/> jus axis eſt IB; </s> <s xml:id="echoid-s10405" xml:space="preserve">vertex B; </s> <s xml:id="echoid-s10406" xml:space="preserve">ordinata GI, parallela AM; </s> <s xml:id="echoid-s10407" xml:space="preserve">Parameter BI: </s> <s xml:id="echoid-s10408" xml:space="preserve">Si <lb/>AB fuerit ad BI, ut retardatio ex prima cauſa ad retardationem ex ſecun- <pb o="288" file="0390" n="426" rhead="PHYSICES ELEMENTA"/> da in puncto A, poterit velocitas in puncto quocunque, ut C, determina-<lb/>ri. </s> <s xml:id="echoid-s10409" xml:space="preserve">Nam ſi in hoc puncto detur CD, ad AM perpendicularis, ordinata <lb/>logarithmicæ, & </s> <s xml:id="echoid-s10410" xml:space="preserve">per D ducta ſit DF ad IG & </s> <s xml:id="echoid-s10411" xml:space="preserve">AM parallela, erunt GI <lb/>& </s> <s xml:id="echoid-s10412" xml:space="preserve">FE, ut velocitates in punctis A & </s> <s xml:id="echoid-s10413" xml:space="preserve">C.</s> <s xml:id="echoid-s10414" xml:space="preserve"/> </p> <div xml:id="echoid-div1478" type="float" level="2" n="1"> <note position="right" xlink:label="note-0389-17" xlink:href="note-0389-17a" xml:space="preserve">1012.</note> <note position="right" xlink:label="note-0389-18" xlink:href="note-0389-18a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s10415" xml:space="preserve">Ut hoc demonſtremus ponimus A a & </s> <s xml:id="echoid-s10416" xml:space="preserve">C c infinite exiguas, & </s> <s xml:id="echoid-s10417" xml:space="preserve">æquales; <lb/></s> <s xml:id="echoid-s10418" xml:space="preserve"> <anchor type="note" xlink:label="note-0390-01a" xlink:href="note-0390-01"/> velocitates in punctis a & </s> <s xml:id="echoid-s10419" xml:space="preserve">c, ſi ut in puncto C determinentur, erunt KH & </s> <s xml:id="echoid-s10420" xml:space="preserve"><lb/>e f; </s> <s xml:id="echoid-s10421" xml:space="preserve">decrementa ergo velocitatum, dum ſpatia æqualia A a, C c percurrun-<lb/>tur, ſunt G g & </s> <s xml:id="echoid-s10422" xml:space="preserve">FL; </s> <s xml:id="echoid-s10423" xml:space="preserve">demonſtrandum, ſi G g reſolvatur in duas partes quæ <lb/>ſint ut AB ad BI, FL poſſe reſolvi in duas ita, ut partes primæ utriuſque <lb/>decrementi ſint inverſè ut GI ad FE <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10424" xml:space="preserve">& </s> <s xml:id="echoid-s10425" xml:space="preserve">ſecundæ directe in eadem ra- <anchor type="note" xlink:label="note-0390-02a" xlink:href="note-0390-02"/> tione GI aut BI, (quia hæc eſt parabolæ parameter †) ad FE <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s10426" xml:space="preserve">id eſt <anchor type="note" xlink:label="note-0390-03a" xlink:href="note-0390-03"/> debemus probare G g ſe habere ad FL, ut {AB/GI} + {BI/GI} ad {AB/FE} + {FE/GI}. <lb/></s> <s xml:id="echoid-s10427" xml:space="preserve"> <anchor type="note" xlink:label="note-0390-04a" xlink:href="note-0390-04"/> Hæc eſt autem demonſtratio; </s> <s xml:id="echoid-s10428" xml:space="preserve">G g, FL :</s> <s xml:id="echoid-s10429" xml:space="preserve">:{IK/GI}, {Ee/FE} <anchor type="note" xlink:href="" symbol="*"/> :</s> <s xml:id="echoid-s10430" xml:space="preserve">: {AI/GI} = {AB/GI} + {BI/GI}, <anchor type="note" xlink:label="note-0390-05a" xlink:href="note-0390-05"/> {AE/FE} = {AB/FE} + {BE/FE} <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10431" xml:space="preserve"/> </p> <div xml:id="echoid-div1479" type="float" level="2" n="2"> <note position="left" xlink:label="note-0390-01" xlink:href="note-0390-01a" xml:space="preserve">1013.</note> <note symbol="*" position="left" xlink:label="note-0390-02" xlink:href="note-0390-02a" xml:space="preserve">992</note> <note position="left" xlink:label="note-0390-03" xlink:href="note-0390-03a" xml:space="preserve">4 la Hire ſect con. lib 3. prop. 2.</note> <note symbol="*" position="left" xlink:label="note-0390-04" xlink:href="note-0390-04a" xml:space="preserve">993.</note> <note symbol="*" position="left" xlink:label="note-0390-05" xlink:href="note-0390-05a" xml:space="preserve">996.</note> </div> <note symbol="*" position="left" xml:space="preserve">983.</note> <p> <s xml:id="echoid-s10432" xml:space="preserve">Sed {BE/FE} = {BE x FE/FE x FE} = {BE x FE/BE x BI} <anchor type="note" xlink:href="" symbol="*"/> = {FE/BI} = {FE/GI} propter æquales BI, <anchor type="note" xlink:label="note-0390-07a" xlink:href="note-0390-07"/> GI: </s> <s xml:id="echoid-s10433" xml:space="preserve">Ergo G g, FL :</s> <s xml:id="echoid-s10434" xml:space="preserve">: {AB/GI} + {BI/GI}, {AB/FE} + {FE/GI}. </s> <s xml:id="echoid-s10435" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s10436" xml:space="preserve"/> </p> <div xml:id="echoid-div1480" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0390-07" xlink:href="note-0390-07a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 3. <lb/>prop. 2.</note> </div> <p> <s xml:id="echoid-s10437" xml:space="preserve">Spatium in quo corpus totam amittit velocitatem eſt BP, aut AQ; </s> <s xml:id="echoid-s10438" xml:space="preserve">in <lb/>puncto enim Q velocitas nulla eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10439" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">1012.</note> <p> <s xml:id="echoid-s10440" xml:space="preserve">Ut nunc hæc figura computationi inſerviat, ſpatium, datâ lineâ repræ-<lb/> <anchor type="note" xlink:label="note-0390-09a" xlink:href="note-0390-09"/> ſentatum, determinandum eſt, ut & </s> <s xml:id="echoid-s10441" xml:space="preserve">ratio quæ datur inter IB & </s> <s xml:id="echoid-s10442" xml:space="preserve">BA, ad quæ <lb/>ſine experimentis, circa ipſas retardationes inſtitutis, pervenire non poſſu-<lb/>mus.</s> <s xml:id="echoid-s10443" xml:space="preserve"/> </p> <div xml:id="echoid-div1481" type="float" level="2" n="4"> <note position="left" xlink:label="note-0390-09" xlink:href="note-0390-09a" xml:space="preserve">1014.</note> </div> <p> <s xml:id="echoid-s10444" xml:space="preserve">Ponimus ergo experimento detectum fuiſſe ſpatium AQ, in quo corpus <lb/>totam amittit velocitatem, quo ſpatio dato, ratio inter AB & </s> <s xml:id="echoid-s10445" xml:space="preserve">BI, quæ eſt <lb/>ratio retardationum in puncto A, detegi poteſt.</s> <s xml:id="echoid-s10446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10447" xml:space="preserve">Velocitas in A lineâ GI, aut BI ipſi æquali, repræſentatur, & </s> <s xml:id="echoid-s10448" xml:space="preserve">retarda-<lb/>tio dum ſpatium A a percurritur eſt G g, ut vidimus, quæ (propter ſubtan-<lb/>gentem duplam abſciſſæ BI <anchor type="note" xlink:href="" symbol="*"/>, ideoque duplam GI) dimidium eſt ipſius <anchor type="note" xlink:label="note-0390-10a" xlink:href="note-0390-10"/> g H, aut i k.</s> <s xml:id="echoid-s10449" xml:space="preserve"/> </p> <div xml:id="echoid-div1482" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0390-10" xlink:href="note-0390-10a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 2. <lb/>prop. 20.</note> </div> <p> <s xml:id="echoid-s10450" xml:space="preserve">Logarithmicam ISP tangit linea I k O; </s> <s xml:id="echoid-s10451" xml:space="preserve">ſumtâ AM duplà AO, ductâ-<lb/>que IM, quæ ſecat k i in m, erit k i dupla m i, quæ ergo G g æqualis eſt, <lb/>retardationemque repræſentat.</s> <s xml:id="echoid-s10452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10453" xml:space="preserve">Sit ad A I parallela MT; </s> <s xml:id="echoid-s10454" xml:space="preserve">quam in N ſecat BP producta; </s> <s xml:id="echoid-s10455" xml:space="preserve">ita ut æqua-<lb/>les ſint AB, MN, ut & </s> <s xml:id="echoid-s10456" xml:space="preserve">BI, NT; </s> <s xml:id="echoid-s10457" xml:space="preserve">ductâ ergo IN, quæ m i ſecat in n <lb/>erit AB, ad BI, id eſt prima retardatio ad ſecundam in puncto A, ut m n, <lb/>ad n i; </s> <s xml:id="echoid-s10458" xml:space="preserve">repræſentant idcirco hæ ſeparatim utramque retardationem; </s> <s xml:id="echoid-s10459" xml:space="preserve">nam <lb/>ſumma retardationes conjunctim deſignat.</s> <s xml:id="echoid-s10460" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10461" xml:space="preserve">Eſt nunc n i retardatio, quam corpus dum BI, quæ GI æqualis eſt, veloci- <pb o="289" file="0391" n="427" rhead="MATHEMATICA. LIB. II. CAP. XII."/> tatem in A exprimit ex ſecunda cauſa ſola patitur. </s> <s xml:id="echoid-s10462" xml:space="preserve">Si igitur concipia-<lb/>mus logarithmicam IR cujus aſymtos ſit BN, & </s> <s xml:id="echoid-s10463" xml:space="preserve">quæ tranſeat per I & </s> <s xml:id="echoid-s10464" xml:space="preserve">n, <lb/>deſignabit PR velocitatem quam corpus, ſi ex ſola ſecunda cauſa retarda-<lb/>retur ſuperſtitem haberet, percurrendo ſpatium experimento detectum AQ, <lb/> <anchor type="note" xlink:label="note-0391-01a" xlink:href="note-0391-01"/> aut BP <anchor type="note" xlink:href="" symbol="*"/>, poteſtque ratio inter BI & </s> <s xml:id="echoid-s10465" xml:space="preserve">PR detegi <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10466" xml:space="preserve"/> </p> <div xml:id="echoid-div1483" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0391-01" xlink:href="note-0391-01a" xml:space="preserve">998.</note> </div> <note symbol="*" position="right" xml:space="preserve">1007.</note> <p> <s xml:id="echoid-s10467" xml:space="preserve">Subtangens logarithmicæ IR eſt BN, aut AM dupla AO, quæ eſt ſub-<lb/>tangens logarithmicæ IP.</s> <s xml:id="echoid-s10468" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10469" xml:space="preserve">Si ergo AQ, æqualis BP, logarithmo rationis BI ad PR, in duas partes <lb/>æquales dividatur in V, & </s> <s xml:id="echoid-s10470" xml:space="preserve">VS detur perpendicularis ad AQ, erit BI ad PR, <lb/> <anchor type="note" xlink:label="note-0391-03a" xlink:href="note-0391-03"/> ut AI ad VS <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10471" xml:space="preserve">Sunt autem in continuâ proportione AI, VS, QP <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10472" xml:space="preserve">er- <anchor type="note" xlink:label="note-0391-04a" xlink:href="note-0391-04"/> go A I<emph style="super">q</emph> ad V S<emph style="super">q</emph>, id eſt B I<emph style="super">q</emph> ad P R<emph style="super">q</emph>, ut AI ad QP, aut AB; </s> <s xml:id="echoid-s10473" xml:space="preserve">& </s> <s xml:id="echoid-s10474" xml:space="preserve">divi-<lb/>dendo</s> </p> <div xml:id="echoid-div1484" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0391-03" xlink:href="note-0391-03a" xml:space="preserve">986.</note> <note symbol="*" position="right" xlink:label="note-0391-04" xlink:href="note-0391-04a" xml:space="preserve">980.</note> </div> </div> <div xml:id="echoid-div1486" type="section" level="1" n="358"> <head xml:id="echoid-head493" xml:space="preserve">B I<emph style="super">q</emph> - PR<emph style="super">q</emph>, PR<emph style="super">q</emph> :: AI-AB = BI, AB.</head> <p> <s xml:id="echoid-s10475" xml:space="preserve">Quod ſic enuntiari poteſt: </s> <s xml:id="echoid-s10476" xml:space="preserve">Quadratum velocitatis corporis ininitio minus qua-<lb/> <anchor type="note" xlink:label="note-0391-05a" xlink:href="note-0391-05"/> drato velocitatis, quam, ſi corpus ex ſola ſecunda cauſa retardaretur, ſuperſtitem ha-<lb/>beret, poſt percurſum ſpatium, in quo, dum ex ambabus cauſis retardatur, totum <lb/>motum amittit, ad hoc ultimum quadrarum, ita retardatio ex ſecunda ad retar-<lb/>dationem ex prima, in primo momento motus.</s> <s xml:id="echoid-s10477" xml:space="preserve"/> </p> <div xml:id="echoid-div1486" type="float" level="2" n="1"> <note position="right" xlink:label="note-0391-05" xlink:href="note-0391-05a" xml:space="preserve">1015.</note> </div> <p> <s xml:id="echoid-s10478" xml:space="preserve">His præmiſſis, computatione detegimus velocitatem in puncto quocunque <lb/> <anchor type="note" xlink:label="note-0391-06a" xlink:href="note-0391-06"/> dato lineæ AQ, ut C.</s> <s xml:id="echoid-s10479" xml:space="preserve"/> </p> <div xml:id="echoid-div1487" type="float" level="2" n="2"> <note position="right" xlink:label="note-0391-06" xlink:href="note-0391-06a" xml:space="preserve">1016.</note> </div> <p> <s xml:id="echoid-s10480" xml:space="preserve">Quærimus in numeris tabularum logarithmum rationis BI ad PR <anchor type="note" xlink:href="" symbol="*"/>, qui <anchor type="note" xlink:label="note-0391-07a" xlink:href="note-0391-07"/> eſt logarithmus rationis AI ad VS; </s> <s xml:id="echoid-s10481" xml:space="preserve">ſi hic duplicetur habemus numerum <lb/>qui repræſentat AQ, ſi ponamus ISP eſſe logarithmicam tabularum; <lb/></s> <s xml:id="echoid-s10482" xml:space="preserve">demonſtrata enim ad logarithmicam quamcunque applicari poſſunt; </s> <s xml:id="echoid-s10483" xml:space="preserve">Dica-<lb/>tur hic numerus L.</s> <s xml:id="echoid-s10484" xml:space="preserve"/> </p> <div xml:id="echoid-div1488" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0391-07" xlink:href="note-0391-07a" xml:space="preserve">1007.</note> </div> <p> <s xml:id="echoid-s10485" xml:space="preserve">Ut ſpatium AQ, in quo corpus totum motum amittit, ad ſpatium da-<lb/>tum AC, id eſt AQ ad AC, ita L ad logarithmum rationis AI ad CD aut <lb/>AI ad AE: </s> <s xml:id="echoid-s10486" xml:space="preserve">qui ergo datur, poteſtque deſignari littera M.</s> <s xml:id="echoid-s10487" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10488" xml:space="preserve">Sumto nunc ad libitum numero qui deſignat AI, Log. </s> <s xml:id="echoid-s10489" xml:space="preserve">AI - M erit <lb/>log. </s> <s xml:id="echoid-s10490" xml:space="preserve">numeri qui deſignat CD <anchor type="note" xlink:href="" symbol="*"/>, aut AE. </s> <s xml:id="echoid-s10491" xml:space="preserve">Log. </s> <s xml:id="echoid-s10492" xml:space="preserve">A I - L eſt log.</s> <s xml:id="echoid-s10493" xml:space="preserve"> <anchor type="note" xlink:label="note-0391-08a" xlink:href="note-0391-08"/> numeri qui deſignat QP, aut AB: </s> <s xml:id="echoid-s10494" xml:space="preserve">quos numeros determinamus: <lb/></s> <s xml:id="echoid-s10495" xml:space="preserve"> <anchor type="note" xlink:label="note-0391-09a" xlink:href="note-0391-09"/> dantur ergo tres numeri, qui ſunt inter ſe ut AI, AE, AB; </s> <s xml:id="echoid-s10496" xml:space="preserve">quare ex <lb/> <anchor type="note" xlink:label="note-0391-10a" xlink:href="note-0391-10"/> primis duobus ſubtracto ultimo, reſtant numeri, qui ſunt ut BI <lb/>ad BE, ut id eſt quadrata velocitatum in A & </s> <s xml:id="echoid-s10497" xml:space="preserve">C <anchor type="note" xlink:href="" symbol="*"/>, in initio & </s> <s xml:id="echoid-s10498" xml:space="preserve">puncto dato.</s> <s xml:id="echoid-s10499" xml:space="preserve"/> </p> <div xml:id="echoid-div1489" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0391-08" xlink:href="note-0391-08a" xml:space="preserve">982.</note> <note symbol="*" position="right" xlink:label="note-0391-09" xlink:href="note-0391-09a" xml:space="preserve">1012.</note> <note position="right" xlink:label="note-0391-10" xlink:href="note-0391-10a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 3.</note> </div> <p> <s xml:id="echoid-s10500" xml:space="preserve">Operatione contraria, datis velocitatibus GI & </s> <s xml:id="echoid-s10501" xml:space="preserve">FE, & </s> <s xml:id="echoid-s10502" xml:space="preserve">ſpa-<lb/>tio AQ, in quo corpus totam amittit velocitatem, detegi-<lb/> <anchor type="note" xlink:label="note-0391-11a" xlink:href="note-0391-11"/> tur punctum C. </s> <s xml:id="echoid-s10503" xml:space="preserve">Nam data AQ detegitur ratio inter BI & </s> <s xml:id="echoid-s10504" xml:space="preserve">BA <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10505" xml:space="preserve">ſumto- <anchor type="note" xlink:label="note-0391-12a" xlink:href="note-0391-12"/> que numero qui velocitatem GI, æqualem BI, exprimit datur BA; <lb/></s> <s xml:id="echoid-s10506" xml:space="preserve">ſed ut GI<emph style="super">q</emph> ad FE<emph style="super">q</emph> ita BI ad BE, datur ergo numerus qui lineam hanc ex-<lb/>primit; </s> <s xml:id="echoid-s10507" xml:space="preserve">ideoque numeros determinamus, qui ſunt inter ſe ut AB, AE, <lb/>AI. </s> <s xml:id="echoid-s10508" xml:space="preserve">Ex demonſtratis autem conſtat <anchor type="note" xlink:href="" symbol="*"/> differentiam log. </s> <s xml:id="echoid-s10509" xml:space="preserve">AI, AB, ad dif- <anchor type="note" xlink:label="note-0391-13a" xlink:href="note-0391-13"/> ferentiam log. </s> <s xml:id="echoid-s10510" xml:space="preserve">AI, AE, ita AQ ad AC, ſpatium percurſum, quod ergo <lb/>detegitur.</s> <s xml:id="echoid-s10511" xml:space="preserve"/> </p> <div xml:id="echoid-div1490" type="float" level="2" n="5"> <note position="right" xlink:label="note-0391-11" xlink:href="note-0391-11a" xml:space="preserve">1017.</note> <note symbol="*" position="right" xlink:label="note-0391-12" xlink:href="note-0391-12a" xml:space="preserve">1015.</note> <note symbol="*" position="right" xlink:label="note-0391-13" xlink:href="note-0391-13a" xml:space="preserve">1013.</note> </div> <p> <s xml:id="echoid-s10512" xml:space="preserve">Determinatur etiam CQ ſpatium in quo corpus amittit totum motum da-<lb/> <anchor type="note" xlink:label="note-0391-14a" xlink:href="note-0391-14"/> ta velocitate FE in initio, ſubtrahendo nempe AC ex AQ.</s> <s xml:id="echoid-s10513" xml:space="preserve"/> </p> <div xml:id="echoid-div1491" type="float" level="2" n="6"> <note position="right" xlink:label="note-0391-14" xlink:href="note-0391-14a" xml:space="preserve">1018.</note> </div> <p> <s xml:id="echoid-s10514" xml:space="preserve">Si nunc concipiamus, datâ velocitate GI, ſolam locum habere retarda- <pb o="290" file="0392" n="428" rhead="PHYSICES ELEMENTA"/> tionem ex ſecunda cauſâ hancque æquabilem fieri, datur ſpatium in quo tota <lb/> <anchor type="note" xlink:label="note-0392-01a" xlink:href="note-0392-01"/> deſtruitur velocitas <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10515" xml:space="preserve">hoc autem ſpatium ſe habet ad ſpatium in quo, ſolâ reſi- <anchor type="note" xlink:label="note-0392-02a" xlink:href="note-0392-02"/> ſtentiâ ex primâ cauſâ, tota velocitas deſtruitur, ut AB ad BI <anchor type="note" xlink:href="" symbol="*"/>, quæ ratio <anchor type="note" xlink:label="note-0392-03a" xlink:href="note-0392-03"/> cum detur <anchor type="note" xlink:href="" symbol="*"/>, etiam determinamus ſpatium hoc. </s> <s xml:id="echoid-s10516" xml:space="preserve">Spatia autem hæc, in diverſis <anchor type="note" xlink:label="note-0392-04a" xlink:href="note-0392-04"/> fluidis, ſunt inverſe ut partium cohæſiones.</s> <s xml:id="echoid-s10517" xml:space="preserve"/> </p> <div xml:id="echoid-div1492" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0392-01" xlink:href="note-0392-01a" xml:space="preserve">1011.</note> <note position="left" xlink:label="note-0392-02" xlink:href="note-0392-02a" xml:space="preserve">1019.</note> <note symbol="*" position="left" xlink:label="note-0392-03" xlink:href="note-0392-03a" xml:space="preserve">997.</note> <note symbol="*" position="left" xlink:label="note-0392-04" xlink:href="note-0392-04a" xml:space="preserve">1015.</note> </div> <note position="left" xml:space="preserve">1020.</note> </div> <div xml:id="echoid-div1494" type="section" level="1" n="359"> <head xml:id="echoid-head494" xml:space="preserve">SCHOLIUM. 6</head> <head xml:id="echoid-head495" style="it" xml:space="preserve">De Corporibus in altum projectis.</head> <p> <s xml:id="echoid-s10518" xml:space="preserve">Corpus, fluido ſpecificè gravius, quod in boc in altum projicitur, tribus ex cau <lb/> <anchor type="note" xlink:label="note-0392-06a" xlink:href="note-0392-06"/> ſis retardatur, ex gravitate & </s> <s xml:id="echoid-s10519" xml:space="preserve">ambabus cauſis in hoc capite explicatis. <lb/></s> <s xml:id="echoid-s10520" xml:space="preserve">Retardatio ex gravitate & </s> <s xml:id="echoid-s10521" xml:space="preserve">ex prima cauſa ſunt ambæ æquabiles <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10522" xml:space="preserve">conjun- <anchor type="note" xlink:label="note-0392-07a" xlink:href="note-0392-07"/> ctæ æquabilem tantum efficiunt retardationem; </s> <s xml:id="echoid-s10523" xml:space="preserve">quare & </s> <s xml:id="echoid-s10524" xml:space="preserve">hîc applicari poſ-<lb/>ſunt quæ in ſuperiori ſcholio demonſtrata ſunt.</s> <s xml:id="echoid-s10525" xml:space="preserve"/> </p> <div xml:id="echoid-div1494" type="float" level="2" n="1"> <note position="left" xlink:label="note-0392-06" xlink:href="note-0392-06a" xml:space="preserve">1021.</note> <note symbol="*" position="left" xlink:label="note-0392-07" xlink:href="note-0392-07a" xml:space="preserve">258. 950.</note> </div> <p> <s xml:id="echoid-s10526" xml:space="preserve">Si ergo unico experimento conſtet ad quam altitudinem corpus in fluido, datâ ve-<lb/> <anchor type="note" xlink:label="note-0392-08a" xlink:href="note-0392-08"/> locitate, adſcendit, ſequentia problemata ſolvuntur.</s> <s xml:id="echoid-s10527" xml:space="preserve"/> </p> <div xml:id="echoid-div1495" type="float" level="2" n="2"> <note position="left" xlink:label="note-0392-08" xlink:href="note-0392-08a" xml:space="preserve">1022.</note> </div> <p> <s xml:id="echoid-s10528" xml:space="preserve">1. </s> <s xml:id="echoid-s10529" xml:space="preserve">Detegitur altitudo ad quam, datâ aliâ velocitate quacunque, corpus adſcendere <lb/>poteſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10530" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">1018.</note> <p> <s xml:id="echoid-s10531" xml:space="preserve">2. </s> <s xml:id="echoid-s10532" xml:space="preserve">Datâ velocitate in initio, detegitur velocitas in puncto dato <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10533" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1023.</note> <p> <s xml:id="echoid-s10534" xml:space="preserve">3. </s> <s xml:id="echoid-s10535" xml:space="preserve">Detegitur data velocitate, ſpatium in quo, ſepoſitâ reſiſtentiâ ex ſecundâ <lb/> <anchor type="note" xlink:label="note-0392-11a" xlink:href="note-0392-11"/> cauſâ, id eſt gravitate reſpectivâ & </s> <s xml:id="echoid-s10536" xml:space="preserve">cobæſione conjunctim, corpus motum ſuum <lb/> <anchor type="note" xlink:label="note-0392-12a" xlink:href="note-0392-12"/> amitteret <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10537" xml:space="preserve"/> </p> <div xml:id="echoid-div1496" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0392-11" xlink:href="note-0392-11a" xml:space="preserve">1016.</note> <note position="left" xlink:label="note-0392-12" xlink:href="note-0392-12a" xml:space="preserve">1024.</note> </div> <note symbol="*" position="left" xml:space="preserve">1019.</note> <p> <s xml:id="echoid-s10538" xml:space="preserve">4. </s> <s xml:id="echoid-s10539" xml:space="preserve">Detegitur ſpatium in quo corpus, data velocitate motum, ex ſola cobæſione mo-<lb/> <anchor type="note" xlink:label="note-0392-14a" xlink:href="note-0392-14"/> tum amitteret.</s> <s xml:id="echoid-s10540" xml:space="preserve"/> </p> <div xml:id="echoid-div1497" type="float" level="2" n="4"> <note position="left" xlink:label="note-0392-14" xlink:href="note-0392-14a" xml:space="preserve">1025.</note> </div> <p> <s xml:id="echoid-s10541" xml:space="preserve">Cum velocitas detur, datur altitudo ad quam corpus in vacuo adſcendere <lb/>poteſt; </s> <s xml:id="echoid-s10542" xml:space="preserve">eſt hæc ad altitudinem ad quam in fluido corpus, dum ſolâ gravi-<lb/>tate reſpectiva retardatur, adſcendit, ut gravitas hæc reſpectiva eſt ad pon-<lb/>dus integrum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10543" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">997.</note> <p> <s xml:id="echoid-s10544" xml:space="preserve">Eſt vero altitudo hæc ultima, ad altitudinem ad quam adſcendit corpus <lb/>dum gravitate reſpectiva & </s> <s xml:id="echoid-s10545" xml:space="preserve">cohæſione retardatur, quæ altitudo etiam datur <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0392-16a" xlink:href="note-0392-16"/> ut retardatio ex his ambabus cauſis ad retardationem ex ſola gravitate reſpe-<lb/>ctiva <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10546" xml:space="preserve"/> </p> <div xml:id="echoid-div1498" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0392-16" xlink:href="note-0392-16a" xml:space="preserve">1024.</note> </div> <note symbol="*" position="left" xml:space="preserve">997.</note> <p> <s xml:id="echoid-s10547" xml:space="preserve">Idcirco dividendo; </s> <s xml:id="echoid-s10548" xml:space="preserve">ut differentia barum altitudinum ad ultimam, ita retar-<lb/> <anchor type="note" xlink:label="note-0392-18a" xlink:href="note-0392-18"/> datio ex cohæſione ad retar dationem ex gravitate reſpectiva & </s> <s xml:id="echoid-s10549" xml:space="preserve">in eadem ratione <lb/>altitudo dum ſola gravitas reſpectiva retardat ad ſpatium in quo ſola cohæ-<lb/>ſione motus perit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10550" xml:space="preserve"/> </p> <div xml:id="echoid-div1499" type="float" level="2" n="6"> <note position="left" xlink:label="note-0392-18" xlink:href="note-0392-18a" xml:space="preserve">1026.</note> </div> <note symbol="*" position="left" xml:space="preserve">997.</note> <p> <s xml:id="echoid-s10551" xml:space="preserve">5. </s> <s xml:id="echoid-s10552" xml:space="preserve">Tandem, data velocitate, detegimus ſpatium, in quo corpus in motu bori-<lb/> <anchor type="note" xlink:label="note-0392-20a" xlink:href="note-0392-20"/> zontali, dum cohæſione & </s> <s xml:id="echoid-s10553" xml:space="preserve">inertiâ retardatur, motum amitteret.</s> <s xml:id="echoid-s10554" xml:space="preserve"/> </p> <div xml:id="echoid-div1500" type="float" level="2" n="7"> <note position="left" xlink:label="note-0392-20" xlink:href="note-0392-20a" xml:space="preserve">1027.</note> </div> <p> <s xml:id="echoid-s10555" xml:space="preserve">Datur in præcedenti computatione ratio inter retardationem ex cohæſio-<lb/>ne & </s> <s xml:id="echoid-s10556" xml:space="preserve">retardationem ex gravitate reſpectiva <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10557" xml:space="preserve">Datur altitudo a qua caden- <anchor type="note" xlink:label="note-0392-21a" xlink:href="note-0392-21"/> do corpus acquirit velocitatem, qua ſi agitaretur, retardatio ex inertia æqua-<lb/>lis eſſet retardationi ex pondere reſpectivo <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10558" xml:space="preserve">Altitudo autem hæc ſe habet <anchor type="note" xlink:label="note-0392-22a" xlink:href="note-0392-22"/> ad altitudinem, à qua cadendo corpus acquirit velocitatem de qua agitur, <lb/>ut retardatio ex inertia, quando retardationi ex pondere reſpectivo æqua-<lb/>lis eſt, ad retardationem ex inertia in velocitate data quam examinamus, <lb/>id eſt altitudines ſunt ut retardationes; </s> <s xml:id="echoid-s10559" xml:space="preserve">nam hæ & </s> <s xml:id="echoid-s10560" xml:space="preserve">illæ ſunt ut quadrata ve-<lb/>locitatum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10561" xml:space="preserve"/> </p> <div xml:id="echoid-div1501" type="float" level="2" n="8"> <note symbol="*" position="left" xlink:label="note-0392-21" xlink:href="note-0392-21a" xml:space="preserve">1026.</note> <note symbol="*" position="left" xlink:label="note-0392-22" xlink:href="note-0392-22a" xml:space="preserve">928. 1005.</note> </div> <note symbol="*" position="left" xml:space="preserve">255. 954.</note> <pb o="291" file="0393" n="429" rhead="MATHEMATICA. LIB. II. CAP. XII."/> <p> <s xml:id="echoid-s10562" xml:space="preserve">Ratio retardationis ex cohæſione, quæ æquabilis eſt <anchor type="note" xlink:href="" symbol="*"/>, ad retardationem ex <anchor type="note" xlink:label="note-0393-01a" xlink:href="note-0393-01"/> inertia, in velocitate data, eſt compoſita ex ratione retardationis primæ ad <lb/>retardationem ex pondere reſpectivo, & </s> <s xml:id="echoid-s10563" xml:space="preserve">ratione retardationis hujus ad ſe-<lb/>cundam. </s> <s xml:id="echoid-s10564" xml:space="preserve">Vidimus rationes componentes dari, datur ergo & </s> <s xml:id="echoid-s10565" xml:space="preserve">compoſita, id <lb/> <anchor type="note" xlink:label="note-0393-02a" xlink:href="note-0393-02"/> eſt ſi hoc applicemus ad demonſtrata in ſcholio præcedenti <anchor type="note" xlink:href="" symbol="*"/>, datur ratio AB ad BI; </s> <s xml:id="echoid-s10566" xml:space="preserve">unde deducitur ratio BI ad PR <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10567" xml:space="preserve">qua data detegitur BP <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0393-03a" xlink:href="note-0393-03"/> ſpatium quæſitum.</s> <s xml:id="echoid-s10568" xml:space="preserve"/> </p> <div xml:id="echoid-div1502" type="float" level="2" n="9"> <note symbol="*" position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">950.</note> <note position="right" xlink:label="note-0393-02" xlink:href="note-0393-02a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 4.</note> <note symbol="*" position="right" xlink:label="note-0393-03" xlink:href="note-0393-03a" xml:space="preserve"> 1013. 1014.</note> </div> <note symbol="*" position="right" xml:space="preserve">1015. 1014.</note> <p> <s xml:id="echoid-s10569" xml:space="preserve">Corpus fluido ſpecifice levius, eodem modo in hoc ſurſum fertur, acgra-<lb/> <anchor type="note" xlink:label="note-0393-05a" xlink:href="note-0393-05"/> vius fundum petit; </s> <s xml:id="echoid-s10570" xml:space="preserve">quare demonſtrata in hoc ſcholio, ad corpora fluidis ſpe-<lb/> <anchor type="note" xlink:label="note-0393-06a" xlink:href="note-0393-06"/> cifice leviora, & </s> <s xml:id="echoid-s10571" xml:space="preserve">in his motu impreſſo deſcendentia referri debent.</s> <s xml:id="echoid-s10572" xml:space="preserve"/> </p> <div xml:id="echoid-div1503" type="float" level="2" n="10"> <note symbol="*" position="right" xlink:label="note-0393-05" xlink:href="note-0393-05a" xml:space="preserve">1009.</note> <note position="right" xlink:label="note-0393-06" xlink:href="note-0393-06a" xml:space="preserve">1028.</note> </div> </div> <div xml:id="echoid-div1505" type="section" level="1" n="360"> <head xml:id="echoid-head496" xml:space="preserve">SCHOLIUM. 7.</head> <head xml:id="echoid-head497" style="it" xml:space="preserve">De Corporibus in Fluidis cadentibus.</head> <p> <s xml:id="echoid-s10573" xml:space="preserve">COrpus quod in fluido ſponte cadit, continuo æquabiliter acceleratur <anchor type="note" xlink:href="" symbol="*"/>, dum re- <anchor type="note" xlink:label="note-0393-07a" xlink:href="note-0393-07"/> ſiſtentiam patitur, quæ eſt ut quadratum velocitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10574" xml:space="preserve"/> </p> <div xml:id="echoid-div1505" type="float" level="2" n="1"> <note position="right" xlink:label="note-0393-07" xlink:href="note-0393-07a" xml:space="preserve">1029.</note> </div> <note symbol="*" position="right" xml:space="preserve">251. 950.</note> <p> <s xml:id="echoid-s10575" xml:space="preserve">Quæ motum hunc ſpectant etiam parabolâ, & </s> <s xml:id="echoid-s10576" xml:space="preserve">logarithmicâ exhiben-<lb/> <anchor type="note" xlink:label="note-0393-09a" xlink:href="note-0393-09"/> tur.</s> <s xml:id="echoid-s10577" xml:space="preserve"/> </p> <div xml:id="echoid-div1506" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0393-09" xlink:href="note-0393-09a" xml:space="preserve">954.</note> </div> <p> <s xml:id="echoid-s10578" xml:space="preserve">Sit QAR logarithmicæ BDH aſymtos; </s> <s xml:id="echoid-s10579" xml:space="preserve">ordinata hujus curvæ ad Aſymto-<lb/> <anchor type="note" xlink:label="note-0393-10a" xlink:href="note-0393-10"/> ton perpendicularis AB; </s> <s xml:id="echoid-s10580" xml:space="preserve">quæ etiam eſt axis parabolæ BFQ, cujus para-<lb/> <anchor type="note" xlink:label="note-0393-11a" xlink:href="note-0393-11"/> metrum ponimus AB.</s> <s xml:id="echoid-s10581" xml:space="preserve"/> </p> <div xml:id="echoid-div1507" type="float" level="2" n="3"> <note position="right" xlink:label="note-0393-10" xlink:href="note-0393-10a" xml:space="preserve">1030.</note> <note position="right" xlink:label="note-0393-11" xlink:href="note-0393-11a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s10582" xml:space="preserve">Si AR repræſentat ſpatium cadendo percurſum, poſito in A puncto ex <lb/>quo corpus dimittitur, determinatur velocitas in puncto quocunque ut C, <lb/>ductâ CD ad AB parallelâ, &</s> <s xml:id="echoid-s10583" xml:space="preserve">per D ad RAQ parallelâ DEF, velocitatem <lb/>quæſitam deſignabit parabolæ ordinata EF, dum AQ velocitatem maxi-<lb/>mam exprimit, ad quam corpus non pertingit, niſi poſt percurſum ſpatium <lb/>AR in infinitum productum.</s> <s xml:id="echoid-s10584" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10585" xml:space="preserve">Hæc patebunt ſi, ſumtis ad libitum ſpatiolis æqualibus infinite exiguis, <lb/>C c, G g demonſtremus augmenta velocitatum, quæ hìc f L & </s> <s xml:id="echoid-s10586" xml:space="preserve">k M expri-<lb/>munt, eſſe inter ſe inverſè ut lineæ FE & </s> <s xml:id="echoid-s10587" xml:space="preserve">KI, quas velocitates exprimere <lb/>dicimus, ſublatis partibus quæ ſunt ut ipſæ hæ lineæ FE & </s> <s xml:id="echoid-s10588" xml:space="preserve">KI <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10589" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">991. 993. <lb/>1029.</note> </div> <div xml:id="echoid-div1509" type="section" level="1" n="361"> <head xml:id="echoid-head498" xml:space="preserve">f L, k M :: {E e/FE}, {Ii/KI}<anchor type="note" xlink:href="" symbol="*"/> :: {CD/FE} = {BA/FE} -{BE/FE}, {GH/KI} = {BA/KI} - {BI/KI}<anchor type="note" xlink:href="" symbol="*"/></head> <note symbol="*" position="right" xml:space="preserve">995.</note> <note symbol="*" position="right" xml:space="preserve">983.</note> <p> <s xml:id="echoid-s10590" xml:space="preserve">Sed BE x BA = FE x FE<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10591" xml:space="preserve">ergo {BE/FE} = {FE/BA}. </s> <s xml:id="echoid-s10592" xml:space="preserve">Eodem modo {BI/KI} <anchor type="note" xlink:label="note-0393-15a" xlink:href="note-0393-15"/> = KI/BA}. </s> <s xml:id="echoid-s10593" xml:space="preserve">Idcirco</s> </p> <div xml:id="echoid-div1509" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0393-15" xlink:href="note-0393-15a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 3. <lb/>prop. 2.</note> </div> </div> <div xml:id="echoid-div1511" type="section" level="1" n="362"> <head xml:id="echoid-head499" xml:space="preserve">fL, kM :: {BA/FE}-{FE/BA}, {BA/KI} = {KI/BA}</head> <p> <s xml:id="echoid-s10594" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s10595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10596" xml:space="preserve">Ut figurâ hac in computatione utamur, velocitas maxima ad quam corpus <lb/> <anchor type="note" xlink:label="note-0393-16a" xlink:href="note-0393-16"/> pertingere poteſt, & </s> <s xml:id="echoid-s10597" xml:space="preserve">quæ QA repræſentatur, determinanda eſt:</s> <s xml:id="echoid-s10598" xml:space="preserve"/> </p> <div xml:id="echoid-div1511" type="float" level="2" n="1"> <note position="right" xlink:label="note-0393-16" xlink:href="note-0393-16a" xml:space="preserve">1031.</note> </div> <p> <s xml:id="echoid-s10599" xml:space="preserve">Quærimus igitur velocitatem, qua conceſſa, retardatio ex ſecunda cauſa <pb o="292" file="0394" n="430" rhead="PHYSICES ELEMENTA"/> accelerationi, ex pondere reſpectivo, demta retardatione ex prima cauſa, <lb/>æqualis eſt; </s> <s xml:id="echoid-s10600" xml:space="preserve">hæc enim eſt uniformis acceleratio quæ retardatione ex ſecuu-<lb/>da cauſa deſtruenda eſt, ut acceleratio ceſſet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10601" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">967.</note> <p> <s xml:id="echoid-s10602" xml:space="preserve">Hic iterum experimento indigemus; </s> <s xml:id="echoid-s10603" xml:space="preserve">detur idcirco altitudo, ad quam in flui-<lb/>do corpus data velocitate quacunque adſcendit; </s> <s xml:id="echoid-s10604" xml:space="preserve">ex hac notâ, elicimus ratio-<lb/>nem inter accelerationem ex pondere reſpectivo & </s> <s xml:id="echoid-s10605" xml:space="preserve">retardationem ex cohæſio-<lb/> <anchor type="note" xlink:label="note-0394-02a" xlink:href="note-0394-02"/> ne <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10606" xml:space="preserve">ideoque rationem accelerationis hujus ad hanc ipſam, demtâ retardatione ex cohæſione: </s> <s xml:id="echoid-s10607" xml:space="preserve">eſt quæ hæc ratio ipſa quæ datur inter altitudinem, a qua cor-<lb/>pus in vacuo cadendo acquirit velocitatem, quæ dat reſiſtentiam ponderi <lb/>reſpectivo æqualem, quæ altitudo datur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10608" xml:space="preserve">altitudinem a qua corpus in va- <anchor type="note" xlink:label="note-0394-03a" xlink:href="note-0394-03"/> cuo cadendo acquirit velocitatem quæſitam QA <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10609" xml:space="preserve"/> </p> <div xml:id="echoid-div1512" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0394-02" xlink:href="note-0394-02a" xml:space="preserve">1026.</note> <note symbol="*" position="left" xlink:label="note-0394-03" xlink:href="note-0394-03a" xml:space="preserve">928. 929.</note> </div> <note symbol="*" position="left" xml:space="preserve">255. 954.</note> <p> <s xml:id="echoid-s10610" xml:space="preserve">Hac autem detecta altitudine, detegimus etiam aliam a qua nempe corpus <lb/> <anchor type="note" xlink:label="note-0394-05a" xlink:href="note-0394-05"/> in fluido cadendo, ſepoſitâ reſiſtentiâ ex ſecunda cauſa, hanc eandem velo-<lb/>citatem QA acquireret; </s> <s xml:id="echoid-s10611" xml:space="preserve">eſt enim altitudo in vacuo ad altitudinem in fluido, <lb/>ut retardatio ex pondere reſpectivo, dempta retardatione ex cohæſione par-<lb/>tium, ad retardationem ex integro pondere <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10612" xml:space="preserve">Concipiamus hanc altitudinem re- <anchor type="note" xlink:label="note-0394-06a" xlink:href="note-0394-06"/> præſentari lineâ BA, b O deſignabit velocitatem, eodem modo cadendo ab <lb/>altitudine B b acquiſitam <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10613" xml:space="preserve"/> </p> <div xml:id="echoid-div1513" type="float" level="2" n="3"> <note position="left" xlink:label="note-0394-05" xlink:href="note-0394-05a" xml:space="preserve">1032.</note> <note symbol="*" position="left" xlink:label="note-0394-06" xlink:href="note-0394-06a" xml:space="preserve">997</note> </div> <note symbol="*" position="left" xml:space="preserve">995</note> <p> <s xml:id="echoid-s10614" xml:space="preserve">Præterea debemus determinare ſpatium, notâ quâdam portione rectæ AR, <lb/> <anchor type="note" xlink:label="note-0394-08a" xlink:href="note-0394-08"/> deſiguatum; </s> <s xml:id="echoid-s10615" xml:space="preserve">quod fiet ſi ad hoc attendamus; </s> <s xml:id="echoid-s10616" xml:space="preserve">in principio caſus corpus ac-<lb/>celerari pondere reſpectivo demta retardatione ex prima cauſa, quia hæc ac-<lb/>celeratio æquabilis eſt, non autem retardari ex ſecunda cauſa quia velocitas <lb/>nulla eſt; </s> <s xml:id="echoid-s10617" xml:space="preserve">ideoque velocitatem bO, in primo momento infinito exiguo, cadendo <lb/>ab altitudine quæ Aa repræſentatur, acquiri ut in motu indicato, cadendo per <lb/>Bb; </s> <s xml:id="echoid-s10618" xml:space="preserve">repræſentantqueidcirco Bb & </s> <s xml:id="echoid-s10619" xml:space="preserve">Aa, in his lineis diverſis, ſpatia æqua-<lb/>lia: </s> <s xml:id="echoid-s10620" xml:space="preserve">ſed eſt Bb ad Aa, aut bN, ut BA ad AP, logarihtmicæ ſubtan-<lb/>gentem; </s> <s xml:id="echoid-s10621" xml:space="preserve">deſignant ergo etiam BA & </s> <s xml:id="echoid-s10622" xml:space="preserve">AP ſpatia æqualia; </s> <s xml:id="echoid-s10623" xml:space="preserve">ſpatiumque ſub-<lb/>tangente repræſentatum eſt altitudo à qua corpus in fluido cadendo, ſepoſita <lb/> <anchor type="note" xlink:label="note-0394-09a" xlink:href="note-0394-09"/> reſiſtentià ex inertia, velocitatem maximam acquirere poteſt.</s> <s xml:id="echoid-s10624" xml:space="preserve"/> </p> <div xml:id="echoid-div1514" type="float" level="2" n="4"> <note position="left" xlink:label="note-0394-08" xlink:href="note-0394-08a" xml:space="preserve">1033.</note> <note position="left" xlink:label="note-0394-09" xlink:href="note-0394-09a" xml:space="preserve">1034</note> </div> <p> <s xml:id="echoid-s10625" xml:space="preserve">Ubi nunc tabulis utendum eſt, patet, altitudinem hanc ſe habere ad altitudinem <lb/>quamcunque datam, AG, ut ſubtangens tabularum, 0, 43429, 54819. </s> <s xml:id="echoid-s10626" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> ad numerum in <anchor type="note" xlink:label="note-0394-10a" xlink:href="note-0394-10"/> tabulis qui altitudinem datam exprimit. </s> <s xml:id="echoid-s10627" xml:space="preserve">Numerus bicce eſt logaritbmus rationis <lb/> <anchor type="note" xlink:label="note-0394-11a" xlink:href="note-0394-11"/> BA & </s> <s xml:id="echoid-s10628" xml:space="preserve">GH, quæ ergo ratio datur; </s> <s xml:id="echoid-s10629" xml:space="preserve">quare etiam datur ratio AB & </s> <s xml:id="echoid-s10630" xml:space="preserve">BI, qu æ <lb/>eſt ratio quadratorum velocitatum AQ & </s> <s xml:id="echoid-s10631" xml:space="preserve">IK <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10632" xml:space="preserve">id eſt velocitatis maximæ, &</s> <s xml:id="echoid-s10633" xml:space="preserve"> <anchor type="note" xlink:label="note-0394-12a" xlink:href="note-0394-12"/> velocitatis, quam corpus in fluido revera acquirit, cadendo ab altitudine data AG <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10634" xml:space="preserve"/> </p> <div xml:id="echoid-div1515" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0394-10" xlink:href="note-0394-10a" xml:space="preserve">987</note> <note position="left" xlink:label="note-0394-11" xlink:href="note-0394-11a" xml:space="preserve">1035</note> <note symbol="*" position="left" xlink:label="note-0394-12" xlink:href="note-0394-12a" xml:space="preserve">la Hire <lb/>ſect. con. <lb/>lib. 3. <lb/>piop. 1.</note> </div> </div> <div xml:id="echoid-div1517" type="section" level="1" n="363"> <head xml:id="echoid-head500" xml:space="preserve">SCHOLIUM 8. <lb/>Illuſtratio quorundam quæ ad retardationem ſpectant.</head> <p> <s xml:id="echoid-s10635" xml:space="preserve">VAria circa retardationes illuſtranda ſunt, quæ dum ex ante demonſtratis <lb/>ſequuntur, non tamen bene inter ſe, aut cum ante demonſtratis, con-<lb/>venire videntur, ſaltem primo intuitu; </s> <s xml:id="echoid-s10636" xml:space="preserve">quos ut removeam ſcrupulos, <lb/>& </s> <s xml:id="echoid-s10637" xml:space="preserve">ipſis ſublatis, magis, mutuâ omnium partium convenientiâ, confirmen-<lb/>tur & </s> <s xml:id="echoid-s10638" xml:space="preserve">virium & </s> <s xml:id="echoid-s10639" xml:space="preserve">retardationum Theoriæ, ſcholium hoc reliquis addere ne-<lb/>ceſſarium duxi.</s> <s xml:id="echoid-s10640" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10641" xml:space="preserve">Scrupulus primus ſpectat quod diximus in n. </s> <s xml:id="echoid-s10642" xml:space="preserve">989. </s> <s xml:id="echoid-s10643" xml:space="preserve">Retardationem & </s> <s xml:id="echoid-s10644" xml:space="preserve">Ac-<lb/>celerationem in ſingulis momentis infinite exiguis eſſe æquabiles; </s> <s xml:id="echoid-s10645" xml:space="preserve">difficultas <pb o="293" file="0395" n="431" rhead="MATHEMATICA. LIB. II. CAP. XII."/> autem datur reſpectu accelerationis, & </s> <s xml:id="echoid-s10646" xml:space="preserve">ſpectat convenientiam hujus propoſi-<lb/>tionis cum demonſtratis de viribus inſitis.</s> <s xml:id="echoid-s10647" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10648" xml:space="preserve">Concipiamus corpus quieſcens in fluido agitato; </s> <s xml:id="echoid-s10649" xml:space="preserve">hoc illi in momento <lb/> <anchor type="note" xlink:label="note-0395-01a" xlink:href="note-0395-01"/> primo infinite exiguo velocitatem infinite exiguam communicat: </s> <s xml:id="echoid-s10650" xml:space="preserve">Dividatur <lb/>momentum in duas partes æquales, in ſingulis partibus æqualis communi-<lb/>catur velocitas, propter accelerationem æquabilem; </s> <s xml:id="echoid-s10651" xml:space="preserve">id eſt in prima parte u-<lb/>nicus gradus infinite exiguus vis, & </s> <s xml:id="echoid-s10652" xml:space="preserve">in ſecunda tres ſimiles gradus com-<lb/>municantur corpori <anchor type="note" xlink:href="" symbol="*"/>, licet actio reſpectiva non aucta fuerit, quod im- <anchor type="note" xlink:label="note-0395-02a" xlink:href="note-0395-02"/> poſſibile videtur.</s> <s xml:id="echoid-s10653" xml:space="preserve"/> </p> <div xml:id="echoid-div1517" type="float" level="2" n="1"> <note position="right" xlink:label="note-0395-01" xlink:href="note-0395-01a" xml:space="preserve">1036.</note> <note symbol="*" position="right" xlink:label="note-0395-02" xlink:href="note-0395-02a" xml:space="preserve">447.</note> </div> <p> <s xml:id="echoid-s10654" xml:space="preserve">Ut hunc tollamus ſcrupulum diſtinguendum dicimus inter actiones abſo-<lb/> <anchor type="note" xlink:label="note-0395-03a" xlink:href="note-0395-03"/> lutas & </s> <s xml:id="echoid-s10655" xml:space="preserve">actiones reſpectivas. </s> <s xml:id="echoid-s10656" xml:space="preserve">Dum has conſideramus in caſu de quo agitur, <lb/>æquales ſunt gradus velocitatis, qui in partibus æqualibus momenti infini-<lb/>te exigui, communicantur, propter non ſenſibiliter mutatam actionem reſpecti-<lb/>vam; </s> <s xml:id="echoid-s10657" xml:space="preserve">etiam, ad motus reſpectivos attendendo, non major vis in ſecunda parte <lb/>quàm in prima ipſius momenti, corpori imprimitur: </s> <s xml:id="echoid-s10658" xml:space="preserve">corpus cui ſuperadditur <lb/>gradus unus velocitatis, unicum gradum vis acquirit in nave, in qua corpus <lb/>quieſcebat, quacunque velocitate hæc feratur.</s> <s xml:id="echoid-s10659" xml:space="preserve"/> </p> <div xml:id="echoid-div1518" type="float" level="2" n="2"> <note position="right" xlink:label="note-0395-03" xlink:href="note-0395-03a" xml:space="preserve">1037.</note> </div> <p> <s xml:id="echoid-s10660" xml:space="preserve">In examine autem actionum abſolutarum non tantum actiones <lb/> <anchor type="note" xlink:label="note-0395-04a" xlink:href="note-0395-04"/> reſpectivæ, ſed & </s> <s xml:id="echoid-s10661" xml:space="preserve">abſolutæ conſiderandæ veniunt, & </s> <s xml:id="echoid-s10662" xml:space="preserve">ex ante demonſtra-<lb/>tis de colliſionibus evidentiſſime ſequitur: </s> <s xml:id="echoid-s10663" xml:space="preserve">corpus quodcunque A, veloci-<lb/>tate a motum, in corpus B incurrens, majorem huic communicare vim, ſi B <lb/>ad eandem partem cum A feratur, quàm ſi quieſceret; </s> <s xml:id="echoid-s10664" xml:space="preserve">licet velocitas reſpecti-<lb/>va in illo caſu minor ſit, ſi modo velocitas corporis B certum limitem non <lb/>excedat. </s> <s xml:id="echoid-s10665" xml:space="preserve">Diverſa enim eſt actio in corpus pro diverſa vi qua jam gaudet, & </s> <s xml:id="echoid-s10666" xml:space="preserve"><lb/>impoſſibile ſi videatur, corpus idem, eodem modo motum, in idem corpus <lb/>incurrens, majorem huic communicare vim in certo caſu in quo velocitas <lb/>reſpectiva eſt minor, ad non bene intellectam virium theoriam illud refe-<lb/>rendum eſt; </s> <s xml:id="echoid-s10667" xml:space="preserve">quod enim experimentis immediatè probatur, ad impoſſibilia <lb/>minime referri poſſe clarum eſt.</s> <s xml:id="echoid-s10668" xml:space="preserve"/> </p> <div xml:id="echoid-div1519" type="float" level="2" n="3"> <note position="right" xlink:label="note-0395-04" xlink:href="note-0395-04a" xml:space="preserve">1038.</note> </div> <p> <s xml:id="echoid-s10669" xml:space="preserve">Sit corpus A, quod, velocitate 6.</s> <s xml:id="echoid-s10670" xml:space="preserve">, in corpus æquale B, quieſcens, di-<lb/>rectè incurrit, pono corpora non elaſtica, acquirit B velocitatem tria <anchor type="note" xlink:href="" symbol="*"/>, id eſt <anchor type="note" xlink:label="note-0395-05a" xlink:href="note-0395-05"/> vim quæ formando in argilla cavitates deſtrui poteſt; </s> <s xml:id="echoid-s10671" xml:space="preserve">ponamus hanc con-<lb/>ſumi formando cavitates novem.</s> <s xml:id="echoid-s10672" xml:space="preserve"/> </p> <div xml:id="echoid-div1520" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0395-05" xlink:href="note-0395-05a" xml:space="preserve">519.</note> </div> <p> <s xml:id="echoid-s10673" xml:space="preserve">Incurrat iterum corpus hoc idem A, velocitate 6. </s> <s xml:id="echoid-s10674" xml:space="preserve">motum, in idem cor-<lb/>pus B, ad eandem partem velocitate 2. </s> <s xml:id="echoid-s10675" xml:space="preserve">translatum, habebit B poſt ictum ve-<lb/>locitatem 4. </s> <s xml:id="echoid-s10676" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10677" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">513</note> <p> <s xml:id="echoid-s10678" xml:space="preserve">Ante ictum corpus B habuit capacitatem formandi quatuor cavitates, qua-<lb/>les memoravimus, poſt ictum habet vim qua ſedecim tales cavitates poteſt <lb/>formare; </s> <s xml:id="echoid-s10679" xml:space="preserve">ictu ergo, poſitâ velocitate reſpectivâ 4.</s> <s xml:id="echoid-s10680" xml:space="preserve">, acquiſivit vim, qua po-<lb/>teſt formare cavitates duodecim, dum in primo caſu, poſitâ velocitate re-<lb/>ſpectivâ 6, tantum acquiſiverit facultatem formandi cavitates tales novem.</s> <s xml:id="echoid-s10681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10682" xml:space="preserve">Hæc immediate conſtare experimentis in dubium nemo vocabit qui ad il-<lb/>la, quæ de viribus & </s> <s xml:id="echoid-s10683" xml:space="preserve">colliſione in libro primo ſunt memorata, attendit, <lb/>non neglecto experimento 4. </s> <s xml:id="echoid-s10684" xml:space="preserve">cap. </s> <s xml:id="echoid-s10685" xml:space="preserve">22. </s> <s xml:id="echoid-s10686" xml:space="preserve">quod in ipſo illo capite fuit præter-<lb/>miſlum, ſed in fine Moniti de hac ſecunda editione memoratum.</s> <s xml:id="echoid-s10687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10688" xml:space="preserve">In primo caſu, ubi velocitas reſpectiva fuit 6, actio corporis A majoreſt <lb/> <anchor type="note" xlink:label="note-0395-07a" xlink:href="note-0395-07"/> quàm in ſecundo caſu, ubi tantum fuit 4.</s> <s xml:id="echoid-s10689" xml:space="preserve">: ſunt autem actiones hæ ut 27. <lb/></s> <s xml:id="echoid-s10690" xml:space="preserve">ad 20.</s> <s xml:id="echoid-s10691" xml:space="preserve">; ſed vires commuicatæ corpori B non ſunt effectus integri harum a-<lb/>ctionum.</s> <s xml:id="echoid-s10692" xml:space="preserve"/> </p> <div xml:id="echoid-div1521" type="float" level="2" n="5"> <note position="right" xlink:label="note-0395-07" xlink:href="note-0395-07a" xml:space="preserve">1039.</note> </div> <pb o="294" file="0396" n="432" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s10693" xml:space="preserve">Corpus A ante actionem habet vim qua triginta ſex cavitates, memoratis <lb/>æquales, formari poſſunt; </s> <s xml:id="echoid-s10694" xml:space="preserve">ſi incurrat in B quod quieſcit, cavitates tales for-<lb/>mabit octodecim, & </s> <s xml:id="echoid-s10695" xml:space="preserve">ipſi B communicabit vim, qua novem formari poſſunt, <lb/>æqualemque vim ipſum ſuperſtitem habebit.</s> <s xml:id="echoid-s10696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10697" xml:space="preserve">In ſecundo caſu, in incurſu tantum formabit cavitates octo, communi-<lb/>cabit vim qua duodecim formari poſſunt, habebitque ſuperſtitem facultatem <lb/>formandi cavitates ſedecim. </s> <s xml:id="echoid-s10698" xml:space="preserve">Effectus totales, non partiales, cauſis propor-<lb/>tionales ſunt.</s> <s xml:id="echoid-s10699" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10700" xml:space="preserve">Si agatur de corporibus quæ preſſione tantum agunt in alia, ſine partium <lb/> <anchor type="note" xlink:label="note-0396-01a" xlink:href="note-0396-01"/> introceſſione, ad hoc attendendum generaliter: </s> <s xml:id="echoid-s10701" xml:space="preserve">motus corporis directionem <lb/>non poſſe mutari, niſi deſtructo primo motu, generatoque novo, quantum <lb/>nempe motus differunt; </s> <s xml:id="echoid-s10702" xml:space="preserve">nam motus, per diverſas directiones, non proeo-<lb/>dem motu haberi poſſunt, niſi quantum conſpirant.</s> <s xml:id="echoid-s10703" xml:space="preserve"/> </p> <div xml:id="echoid-div1522" type="float" level="2" n="6"> <note position="left" xlink:label="note-0396-01" xlink:href="note-0396-01a" xml:space="preserve">1040.</note> </div> <p> <s xml:id="echoid-s10704" xml:space="preserve">Quando corpus directionem ſuam mutat, ut in n. </s> <s xml:id="echoid-s10705" xml:space="preserve">522. </s> <s xml:id="echoid-s10706" xml:space="preserve">corpus premit <lb/>in obſtaculum veramque in hoc exerit actionem, & </s> <s xml:id="echoid-s10707" xml:space="preserve">quidem vi inſitâ agit; <lb/></s> <s xml:id="echoid-s10708" xml:space="preserve">quare hæc in ſingulis momentis infinite exiguis minuitur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s10709" xml:space="preserve">Sed obſtaculum <anchor type="note" xlink:label="note-0396-02a" xlink:href="note-0396-02"/> reagit, & </s> <s xml:id="echoid-s10710" xml:space="preserve">cum hoc non cedat, neque vim accipiat, totâ ſuâ reſiſtentiâ novam <lb/> <anchor type="note" xlink:label="note-0396-03a" xlink:href="note-0396-03"/> corpori obſtaculum communicat vim, quæ ipſi amiſſæ æquatis eſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10711" xml:space="preserve">qua- re ſingulis momentis vis deſtructa inſtauratur, ſervatque corpus velocitatem.</s> <s xml:id="echoid-s10712" xml:space="preserve"/> </p> <div xml:id="echoid-div1523" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0396-02" xlink:href="note-0396-02a" xml:space="preserve">458.</note> <note symbol="*" position="left" xlink:label="note-0396-03" xlink:href="note-0396-03a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s10713" xml:space="preserve">In caſu n. </s> <s xml:id="echoid-s10714" xml:space="preserve">521 corpora impingentia duos edunt effectus, corpori in quod <lb/>incurrunt motum communicant & </s> <s xml:id="echoid-s10715" xml:space="preserve">viam flectunt, vimque quam in impa-<lb/>ctu, intropremendo partes, conſumerent, nunc etiam in actione ſua con-<lb/>ſumunt, licet aliam ipſi æqualem lateralem accipiant.</s> <s xml:id="echoid-s10716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10717" xml:space="preserve">Ratiocinium ſimile ad fluida poſſe applicari, quæ etiam lateralem motum <lb/>acquirunt, clarum eſt; </s> <s xml:id="echoid-s10718" xml:space="preserve">& </s> <s xml:id="echoid-s10719" xml:space="preserve">ſolam conſiderandam non eſſe actionem reſpecti-<lb/>vam ubi de actione abſoluta agitur: </s> <s xml:id="echoid-s10720" xml:space="preserve">integroſque effectus eſſe comparandos <lb/>ut inter hos cauſarum proportionem detegamus.</s> <s xml:id="echoid-s10721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10722" xml:space="preserve">Scrupulus ſecundus, in hoc ſcholio removendus, ſpectat retardationem <lb/> <anchor type="note" xlink:label="note-0396-04a" xlink:href="note-0396-04"/> ex prima cauſa, quam æquabilem eſſedemonſtravimus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10723" xml:space="preserve">unde ſequitur ex a- <anchor type="note" xlink:label="note-0396-05a" xlink:href="note-0396-05"/> ctione, a cohæſione partium oriunda, quam ſuperius <anchor type="note" xlink:href="" symbol="*"/> explicavimus, æqua- <anchor type="note" xlink:label="note-0396-06a" xlink:href="note-0396-06"/> li tempori, æqualem corpori quieſcenti communicari velocitatem, quacun-<lb/>que velocitate fluidum in hoc incurrat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10724" xml:space="preserve"/> </p> <div xml:id="echoid-div1524" type="float" level="2" n="8"> <note position="left" xlink:label="note-0396-04" xlink:href="note-0396-04a" xml:space="preserve">1041.</note> <note symbol="*" position="left" xlink:label="note-0396-05" xlink:href="note-0396-05a" xml:space="preserve">950.</note> <note symbol="*" position="left" xlink:label="note-0396-06" xlink:href="note-0396-06a" xml:space="preserve">901.</note> </div> <p> <s xml:id="echoid-s10725" xml:space="preserve">Hæc autem convenire non videntur cum ante demonſtratis: </s> <s xml:id="echoid-s10726" xml:space="preserve">vidimus e-<lb/>nim corpus, ex actione a partium cohæſione oriunda, quando in loco re-<lb/>tinetur, pati preſſionem, quæ ad inſtar velocitatis augetur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s10727" xml:space="preserve">circa preſſionem <anchor type="note" xlink:label="note-0396-07a" xlink:href="note-0396-07"/> in genere demonſtravimus, hanc corpori quieſcenti, in momento determi-<lb/>nato, infinite exiguo, communicare velocitatem, quæ ipſius preſſionis ra-<lb/>tionem ſequitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10728" xml:space="preserve"/> </p> <div xml:id="echoid-div1525" type="float" level="2" n="9"> <note symbol="*" position="left" xlink:label="note-0396-07" xlink:href="note-0396-07a" xml:space="preserve">894. 908.</note> </div> <note symbol="*" position="left" xml:space="preserve">107. 243.</note> <p> <s xml:id="echoid-s10729" xml:space="preserve">Fundamentum ratiocinii, quo hanc tolli credimus difficultatem ſupetius <lb/> <anchor type="note" xlink:label="note-0396-09a" xlink:href="note-0396-09"/> indicavimus <anchor type="note" xlink:href="" symbol="*"/>, ipſum nunc ratiocinium clarius explicandum.</s> <s xml:id="echoid-s10730" xml:space="preserve"/> </p> <div xml:id="echoid-div1526" type="float" level="2" n="10"> <note position="left" xlink:label="note-0396-09" xlink:href="note-0396-09a" xml:space="preserve">1042.</note> </div> <note symbol="*" position="left" xml:space="preserve">945.</note> <p> <s xml:id="echoid-s10731" xml:space="preserve">Diximus diſtinguendum inter preſſionem quæ immediate corpus transfert <lb/>& </s> <s xml:id="echoid-s10732" xml:space="preserve">preſſionem quæ non immediate corpus transfert De prima agitur in n. <lb/></s> <s xml:id="echoid-s10733" xml:space="preserve">107. </s> <s xml:id="echoid-s10734" xml:space="preserve">& </s> <s xml:id="echoid-s10735" xml:space="preserve">ipſius demonſtratio non poteſt applicari ad caſum, in quo preſſio <lb/>quæ ſeparat particulas, ita agit, ut & </s> <s xml:id="echoid-s10736" xml:space="preserve">eodem tempore obſtaculum transferre <lb/>debeat.</s> <s xml:id="echoid-s10737" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10738" xml:space="preserve">Hæc actiones toto cœlo diſtinctas exerit, pro ut in obſtacula immobilia <lb/>aut mobilia, majora, aut minora, agit. </s> <s xml:id="echoid-s10739" xml:space="preserve">Ut autem quæ hoc genus preſ-<lb/>fionum ſpectant determinemus, quæ ſequuntur conſideranda erunt.</s> <s xml:id="echoid-s10740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10741" xml:space="preserve">Actio fluidi in corpus, ex cohæſione partium oriunda, analoga & </s> <s xml:id="echoid-s10742" xml:space="preserve">ſimilis <pb o="295" file="0397" n="433" rhead="MATHEMATICA. LIB. II. CAP. XII."/> eſt actioni, quam corpora ut A, B, filo juncta, in corpus C exerunt, dum <lb/> <anchor type="note" xlink:label="note-0397-01a" xlink:href="note-0397-01"/> ad latera hujus tranſeunt, filumque, actione ſua in C, frangunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10743" xml:space="preserve"/> </p> <div xml:id="echoid-div1527" type="float" level="2" n="11"> <note position="right" xlink:label="note-0397-01" xlink:href="note-0397-01a" xml:space="preserve">TAB. XXXVII. <lb/>fig. 6.</note> </div> <note symbol="*" position="right" xml:space="preserve">901.</note> <p> <s xml:id="echoid-s10744" xml:space="preserve">Corpora A & </s> <s xml:id="echoid-s10745" xml:space="preserve">B, quamdiu partes fili cohærent, premunt in C, filo fracto ceſſat <lb/>preſſio, ſed ſi ſtatim, eodem modo, alia duo ſimilia D & </s> <s xml:id="echoid-s10746" xml:space="preserve">F, premant, & </s> <s xml:id="echoid-s10747" xml:space="preserve">poſt hæc <lb/>G & </s> <s xml:id="echoid-s10748" xml:space="preserve">H, &</s> <s xml:id="echoid-s10749" xml:space="preserve">c. </s> <s xml:id="echoid-s10750" xml:space="preserve">dabitur preſſio, quæ a preſſione fluidi ex cohæſione oriun-<lb/>da non differt, ſatis ergo erit demonſtrare, motis hiſce corporibus, æqua-<lb/>li tempore, æqualem corpori C communicari velocitatem, quacunque ve-<lb/>locitate ferantur corpora A, B, D, E, F, G, &</s> <s xml:id="echoid-s10751" xml:space="preserve">c, quæ æqualia ponimus, & </s> <s xml:id="echoid-s10752" xml:space="preserve">æ-<lb/>quali velocitate mota. </s> <s xml:id="echoid-s10753" xml:space="preserve">Ipſa autem in obſtaculum immobile exerere preſſio-<lb/>nem quæ ſequitur rationem velocitatis qua feruntur.</s> <s xml:id="echoid-s10754" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10755" xml:space="preserve">Corpus omne quod quieſcit aut cujus velocitas datur, eo magis reſiſtit <lb/> <anchor type="note" xlink:label="note-0397-03a" xlink:href="note-0397-03"/> quo celerius acceleratur; </s> <s xml:id="echoid-s10756" xml:space="preserve">dum enim determinatum gradum velocitatis ac-<lb/>quirit determinatus gradus, vis ipſi communicatur propter primam datam <lb/>velocitatem; </s> <s xml:id="echoid-s10757" xml:space="preserve">dum autem gradum determinatum vis acquirit determinatam <lb/>exerit reſiſtentiam <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s10758" xml:space="preserve">hæc idcirco eadem eſt ſive lentius ſive velocius gradus <anchor type="note" xlink:label="note-0397-04a" xlink:href="note-0397-04"/> hicce vis communicetur, conſiderando nempe totalem reſiſtentiam. </s> <s xml:id="echoid-s10759" xml:space="preserve">Eâdem <lb/>de cauſa, reſiſtentia inſtantanea eo major eſt, quo celerius corpus accelera-<lb/>tur, totalis enim reſiſtentia ſequitur proportionem reſiſtentiæ inſtantaneæ, <lb/>& </s> <s xml:id="echoid-s10760" xml:space="preserve">temporis per quod duravit, ſi ergo hoc minuatur illa augenda erit, ut <lb/>totalis reſiſtentia ſervetur: </s> <s xml:id="echoid-s10761" xml:space="preserve">tempus vero minuitur in ratione in qua ipſa <lb/>acceleratio augetur, creſcitque cum ipſa acceleratione inſtantanea reſiſten-<lb/>tia, ſi totalis reſiſtentia determinata ſit.</s> <s xml:id="echoid-s10762" xml:space="preserve"/> </p> <div xml:id="echoid-div1528" type="float" level="2" n="12"> <note position="right" xlink:label="note-0397-03" xlink:href="note-0397-03a" xml:space="preserve">1043.</note> <note symbol="*" position="right" xlink:label="note-0397-04" xlink:href="note-0397-04a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s10763" xml:space="preserve">Quando acceleratio æquabilis eſt, reſiſtit corpus in ratione velocitatis <lb/>quam habet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10764" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve"><unsure/></note> <p> <s xml:id="echoid-s10765" xml:space="preserve">Generaliter ergo corporis, quod acceleratur, inſtantanea reſiſtentia eſtin ratione <lb/> <anchor type="note" xlink:label="note-0397-06a" xlink:href="note-0397-06"/> compoſita velocitatis quam babet, & </s> <s xml:id="echoid-s10766" xml:space="preserve">ipſius accelerationis.</s> <s xml:id="echoid-s10767" xml:space="preserve"/> </p> <div xml:id="echoid-div1529" type="float" level="2" n="13"> <note position="right" xlink:label="note-0397-06" xlink:href="note-0397-06a" xml:space="preserve">1044.</note> </div> <p style="it"> <s xml:id="echoid-s10768" xml:space="preserve">Si ergo detur reſiſtentia inſtantanea, velocitas corporis eſt inverſè, ut accelera-<lb/> <anchor type="note" xlink:label="note-0397-07a" xlink:href="note-0397-07"/> tio.</s> <s xml:id="echoid-s10769" xml:space="preserve"/> </p> <div xml:id="echoid-div1530" type="float" level="2" n="14"> <note position="right" xlink:label="note-0397-07" xlink:href="note-0397-07a" xml:space="preserve">1045.</note> </div> <p> <s xml:id="echoid-s10770" xml:space="preserve">Propoſitio hæc ad caſum de quo agitur applicanda nunc eſt.</s> <s xml:id="echoid-s10771" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10772" xml:space="preserve">Corpora A & </s> <s xml:id="echoid-s10773" xml:space="preserve">B in corpus C agunt, donec hujus inſtantanea reſiſtentia, <lb/> <anchor type="note" xlink:label="note-0397-08a" xlink:href="note-0397-08"/> quæ ſola cum preſſione contrariè agere poteſt, æqualis ſit ipſi preſſioni qua <lb/>fili partes cohærent; </s> <s xml:id="echoid-s10774" xml:space="preserve">acceleratio eo uſque durat; </s> <s xml:id="echoid-s10775" xml:space="preserve">ſed ubi hæc datur æquali-<lb/>tas, ceſſat actio, & </s> <s xml:id="echoid-s10776" xml:space="preserve">filum frangitur; </s> <s xml:id="echoid-s10777" xml:space="preserve">&</s> <s xml:id="echoid-s10778" xml:space="preserve">, ſive celerius ſive lentius moveantur <lb/>corpora A & </s> <s xml:id="echoid-s10779" xml:space="preserve">B, conſtans in corpore C inſtantanea reſiſtentia deſideratur, <lb/>ut filum frangatur. </s> <s xml:id="echoid-s10780" xml:space="preserve">Sed quo velocius A & </s> <s xml:id="echoid-s10781" xml:space="preserve">B moventur, eo major eſt ac-<lb/>celeratio, dum hæc protrahunt corpus C; </s> <s xml:id="echoid-s10782" xml:space="preserve">eo ergo minor velocitas ipſi C <lb/>communicata eſt, dum frangitur filum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10783" xml:space="preserve">Si ex. </s> <s xml:id="echoid-s10784" xml:space="preserve">gr. </s> <s xml:id="echoid-s10785" xml:space="preserve">tripla ſit velocitas cor- <anchor type="note" xlink:label="note-0397-09a" xlink:href="note-0397-09"/> porum A & </s> <s xml:id="echoid-s10786" xml:space="preserve">Bin uno caſu quàm in alio, dum in utroque C quieſcit, quia in <lb/>caſu primo tripla eſt acceleratio, tertia pars velocitatis tantum corpori C com-<lb/>municatur, dum durat actio corporum in C. </s> <s xml:id="echoid-s10787" xml:space="preserve">Si hic gradus velocitatis fuerit exi-<lb/>guus, ut actio reſpectiva ſequentium corporum D & </s> <s xml:id="echoid-s10788" xml:space="preserve">E non ſenſibiliter difterat, <lb/>hæc æqualem gradum velocitatis communicabunt, & </s> <s xml:id="echoid-s10789" xml:space="preserve">niſi poſt tria fila con-<lb/>fracta habebit C velocitatem, quam habet, dum unicum diſrumpitur filum in <lb/>ſecundo caſu. </s> <s xml:id="echoid-s10790" xml:space="preserve">Sed dum in ſecundo caſu ſola corpora A & </s> <s xml:id="echoid-s10791" xml:space="preserve">B juxta C tranſ-<lb/>eunt, in primo tranſeunt, A, B, & </s> <s xml:id="echoid-s10792" xml:space="preserve">D, E, ut & </s> <s xml:id="echoid-s10793" xml:space="preserve">F, G; </s> <s xml:id="echoid-s10794" xml:space="preserve">id eſt tria fila in <lb/>primo caſu franguntur, dum unicum in ſecundo dilaceratur, & </s> <s xml:id="echoid-s10795" xml:space="preserve">æqualibus <lb/>temporibus memoratæ æquales communicantur velocitates, Q.</s> <s xml:id="echoid-s10796" xml:space="preserve">D.</s> <s xml:id="echoid-s10797" xml:space="preserve">E.</s> <s xml:id="echoid-s10798" xml:space="preserve"/> </p> <div xml:id="echoid-div1531" type="float" level="2" n="15"> <note position="right" xlink:label="note-0397-08" xlink:href="note-0397-08a" xml:space="preserve">1046.</note> <note symbol="*" position="right" xlink:label="note-0397-09" xlink:href="note-0397-09a" xml:space="preserve">1045.</note> </div> <p> <s xml:id="echoid-s10799" xml:space="preserve">Res vulgo nota eſt corpori, quod filo protrahitur, eo minorem communicari <lb/> <anchor type="note" xlink:label="note-0397-10a" xlink:href="note-0397-10"/> velocitatem, dum filum frangitur, quo celerius hoc trahitur; </s> <s xml:id="echoid-s10800" xml:space="preserve">hac de cauſa <pb o="296" file="0398" n="434" rhead="PHYSICES ELEMENTA"/> ſi lente corpus acceleretur, ipſi magna poterit communicari velocitas; </s> <s xml:id="echoid-s10801" xml:space="preserve">licet <lb/>tenui filo trahatur.</s> <s xml:id="echoid-s10802" xml:space="preserve"/> </p> <div xml:id="echoid-div1532" type="float" level="2" n="16"> <note position="right" xlink:label="note-0397-10" xlink:href="note-0397-10a" xml:space="preserve">1047.</note> </div> <p> <s xml:id="echoid-s10803" xml:space="preserve">Quando corpora A & </s> <s xml:id="echoid-s10804" xml:space="preserve">B, frangendo filum, vim communicant corpori C, <lb/> <anchor type="note" xlink:label="note-0398-01a" xlink:href="note-0398-01"/> ex viribus amittunt, quantum communicant, & </s> <s xml:id="echoid-s10805" xml:space="preserve">quantum deſideratur, ad fi-<lb/>lum dilacerandum; </s> <s xml:id="echoid-s10806" xml:space="preserve">eo ergo minus ex vi amittunt quo celerius moven-<lb/>tur.</s> <s xml:id="echoid-s10807" xml:space="preserve"/> </p> <div xml:id="echoid-div1533" type="float" level="2" n="17"> <note position="left" xlink:label="note-0398-01" xlink:href="note-0398-01a" xml:space="preserve">1048.</note> </div> <p> <s xml:id="echoid-s10808" xml:space="preserve">Si ex loco cedere nequeat obſtaculum C, unicus eſt eſtectus actionis cor-<lb/>porum A & </s> <s xml:id="echoid-s10809" xml:space="preserve">B, & </s> <s xml:id="echoid-s10810" xml:space="preserve">ex vi tantum amittunt, quantum deſideratur ad filum fran-<lb/>gendum, actioque, quam patitur illud quod retinet C in loco, eadem eſt pro <lb/>ſingulis filis quæ franguntur. </s> <s xml:id="echoid-s10811" xml:space="preserve">In præcedenti caſu, quo lentius moventur <lb/>corpora A & </s> <s xml:id="echoid-s10812" xml:space="preserve">B, eo diutius agunt antequam C reſiſtat quantum requiritur, <lb/>ut filum dilaceretur; </s> <s xml:id="echoid-s10813" xml:space="preserve">in hoc autem caſu ubi filum accedit hæc datur reſi-<lb/>ſtentia: </s> <s xml:id="echoid-s10814" xml:space="preserve">Quare in hoc caſu actio quam patitur C ſequitur rationem filorum <lb/>determinato tempore fractorum, id eſt velocitatis corporum. </s> <s xml:id="echoid-s10815" xml:space="preserve">Quod etiam <lb/>demonſtrandum crat.</s> <s xml:id="echoid-s10816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10817" xml:space="preserve">Quid analogum cum iis quæ ſuperius <anchor type="note" xlink:href="" symbol="*"/> explicavimus, obſervamus in col- <anchor type="note" xlink:label="note-0398-02a" xlink:href="note-0398-02"/> liſione corporum; </s> <s xml:id="echoid-s10818" xml:space="preserve">corpora duo inæqualia corporibus duobus æqualibus qui-<lb/> <anchor type="note" xlink:label="note-0398-03a" xlink:href="note-0398-03"/> eſcentibus, in colliſione directa, communicant velocitates, quæ ſunt inverſè <lb/>ut velocitates corporum impingentium, ſi introceſſiones partium fuerint æ-<lb/>quales, ponendo partes æquè facile in utraque colliſione cedere.</s> <s xml:id="echoid-s10819" xml:space="preserve"/> </p> <div xml:id="echoid-div1534" type="float" level="2" n="18"> <note position="left" xlink:label="note-0398-02" xlink:href="note-0398-02a" xml:space="preserve">1049.</note> <note symbol="*" position="left" xlink:label="note-0398-03" xlink:href="note-0398-03a" xml:space="preserve">1046.</note> </div> <p> <s xml:id="echoid-s10820" xml:space="preserve">Introceſſiones autem partium ſunt ut ipſæ velocitates corporum impingen-<lb/>tium, ſi hæc æquales communicent corporibus quieſcentibus velocitates.</s> <s xml:id="echoid-s10821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10822" xml:space="preserve">Ut hæc ſequuntur ex ante demonſtratis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10823" xml:space="preserve">& </s> <s xml:id="echoid-s10824" xml:space="preserve">directis experimentis poſ- <anchor type="note" xlink:label="note-0398-04a" xlink:href="note-0398-04"/> ſunt evinci.</s> <s xml:id="echoid-s10825" xml:space="preserve"/> </p> <div xml:id="echoid-div1535" type="float" level="2" n="19"> <note symbol="*" position="left" xlink:label="note-0398-04" xlink:href="note-0398-04a" xml:space="preserve">520. 462. <lb/>519.</note> </div> </div> <div xml:id="echoid-div1537" type="section" level="1" n="364"> <head xml:id="echoid-head501" style="it" xml:space="preserve">LIBRI II. Pars III. <lb/>De Aëre, & aliis Fluidis Elaſticis.</head> <head xml:id="echoid-head502" xml:space="preserve">CAPUT XIII. <lb/>Aërem Fluidorum proprietates habere.</head> <p> <s xml:id="echoid-s10826" xml:space="preserve">DE Aëre ſæpius locuti ſumus, cum in hoc vivamus & </s> <s xml:id="echoid-s10827" xml:space="preserve"><lb/>hoc ſemper circumdemur, in multis Experimentis, ut <lb/>monuimus, ad illius effectum attendendum eſt; </s> <s xml:id="echoid-s10828" xml:space="preserve">nunc autem <lb/>ipſius proprietates ſingulatim examinandæ veniunt.</s> <s xml:id="echoid-s10829" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10830" xml:space="preserve">Aërem vocamus fluidum, quod Telluris ſuperficiem <lb/> <anchor type="note" xlink:label="note-0398-05a" xlink:href="note-0398-05"/> obtegit, ipſamque tellurem ab omni parte cingit.</s> <s xml:id="echoid-s10831" xml:space="preserve"/> </p> <div xml:id="echoid-div1537" type="float" level="2" n="1"> <note position="left" xlink:label="note-0398-05" xlink:href="note-0398-05a" xml:space="preserve">1050.</note> </div> <p> <s xml:id="echoid-s10832" xml:space="preserve">Fluido autem Tellurem circumdari conſtat; </s> <s xml:id="echoid-s10833" xml:space="preserve">obſervamus <pb file="0399" n="435"/> <pb file="0399a" n="436"/> <anchor type="figure" xlink:label="fig-0399a-01a" xlink:href="fig-0399a-01"/> <pb file="0400" n="437"/> <pb o="297" file="0401" n="438" rhead="MATHEMATICA. LIB. II. CAP XIII."/> enim corpore hanc obtegi quod grave eſt, cujus partes im-<lb/>preſſioni cuicunque cedunt, & </s> <s xml:id="echoid-s10834" xml:space="preserve">facillime moventur inter <lb/>ſe, quod premit pro altitudine ſua, & </s> <s xml:id="echoid-s10835" xml:space="preserve">cujus preſſio omnes <lb/>partes verſus eſt æqualis.</s> <s xml:id="echoid-s10836" xml:space="preserve"/> </p> <div xml:id="echoid-div1538" type="float" level="2" n="2"> <figure xlink:label="fig-0399a-01" xlink:href="fig-0399a-01a"> <image file="0399a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0399a-01"/> </figure> </div> </div> <div xml:id="echoid-div1540" type="section" level="1" n="365"> <head xml:id="echoid-head503" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s10837" xml:space="preserve">Omnis aër, quo Terra circumdatur, ſimul conſideratus, <lb/> <anchor type="note" xlink:label="note-0401-01a" xlink:href="note-0401-01"/> vocatur Telluris Atmoſphæra, aut ſimpliciter Atmoſphæra.</s> <s xml:id="echoid-s10838" xml:space="preserve"/> </p> <div xml:id="echoid-div1540" type="float" level="2" n="1"> <note position="right" xlink:label="note-0401-01" xlink:href="note-0401-01a" xml:space="preserve">1051</note> </div> </div> <div xml:id="echoid-div1542" type="section" level="1" n="366"> <head xml:id="echoid-head504" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s10839" xml:space="preserve">Aëris altitudo ſupra Terræ ſuperficiem vocatur Atmoſphæ-<lb/> <anchor type="note" xlink:label="note-0401-02a" xlink:href="note-0401-02"/> ræ altitudo.</s> <s xml:id="echoid-s10840" xml:space="preserve"/> </p> <div xml:id="echoid-div1542" type="float" level="2" n="1"> <note position="right" xlink:label="note-0401-02" xlink:href="note-0401-02a" xml:space="preserve">1052.</note> </div> <p> <s xml:id="echoid-s10841" xml:space="preserve">Ubique in Telluris ſuperficie corpus dari, quamvis ipſius <lb/> <anchor type="note" xlink:label="note-0401-03a" xlink:href="note-0401-03"/> partes plerumque viſum fugiant, experimento con <lb/>ſtat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s10842" xml:space="preserve"/> </p> <div xml:id="echoid-div1543" type="float" level="2" n="2"> <note position="right" xlink:label="note-0401-03" xlink:href="note-0401-03a" xml:space="preserve">1053.</note> </div> <note symbol="*" position="right" xml:space="preserve">27</note> <p> <s xml:id="echoid-s10843" xml:space="preserve">Hoc impreſſioni cuicunque cedere, & </s> <s xml:id="echoid-s10844" xml:space="preserve">ipſius partes facile <lb/> <anchor type="note" xlink:label="note-0401-05a" xlink:href="note-0401-05"/> moveri, a nemine in dubium vocari poteſt.</s> <s xml:id="echoid-s10845" xml:space="preserve"/> </p> <div xml:id="echoid-div1544" type="float" level="2" n="3"> <note position="right" xlink:label="note-0401-05" xlink:href="note-0401-05a" xml:space="preserve">1054.</note> </div> <p> <s xml:id="echoid-s10846" xml:space="preserve">Grave eſſe probatur, quia in ceterorum fluidorum ſu-<lb/> <anchor type="note" xlink:label="note-0401-06a" xlink:href="note-0401-06"/> perficies premit, hæcque in tubis ſuſtinet.</s> <s xml:id="echoid-s10847" xml:space="preserve"/> </p> <div xml:id="echoid-div1545" type="float" level="2" n="4"> <note position="right" xlink:label="note-0401-06" xlink:href="note-0401-06a" xml:space="preserve">1055.</note> </div> </div> <div xml:id="echoid-div1547" type="section" level="1" n="367"> <head xml:id="echoid-head505" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s10848" xml:space="preserve">Detur tubus vitreus AB, longitudinis circiter trium <lb/> <anchor type="note" xlink:label="note-0401-07a" xlink:href="note-0401-07"/> pedum, & </s> <s xml:id="echoid-s10849" xml:space="preserve">cujus cavitatis diameter ſit quartæ partis unius <lb/> <anchor type="note" xlink:label="note-0401-08a" xlink:href="note-0401-08"/> pollicis; </s> <s xml:id="echoid-s10850" xml:space="preserve">ſi extremitas A obturetur, & </s> <s xml:id="echoid-s10851" xml:space="preserve">tubus mercurio re-<lb/>pleatur, alteraque extremitas vaſe V mercurium continenti <lb/>immergatur, mercurius ſuſtinebitur ad altitudinem circi-<lb/>ter viginti novem pollicum. </s> <s xml:id="echoid-s10852" xml:space="preserve">Oritur hoc ex aëris preſſio-<lb/>ne in ſuperficiem mercurii in vaſe, quæ ubique æqualiter <lb/>premi non poteſt, niſi in tubo, cui aër nullus ineſt, mercu-<lb/>rii columna detur, quæ æqualiter cum aëre exteriori pre-<lb/>mat <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10853" xml:space="preserve">Tubus hic Torricellianus dicitur; </s> <s xml:id="echoid-s10854" xml:space="preserve">a primo qui hoc <anchor type="note" xlink:label="note-0401-09a" xlink:href="note-0401-09"/> exp. </s> <s xml:id="echoid-s10855" xml:space="preserve">demonſtravit Torricelli.</s> <s xml:id="echoid-s10856" xml:space="preserve"/> </p> <div xml:id="echoid-div1547" type="float" level="2" n="1"> <note position="right" xlink:label="note-0401-07" xlink:href="note-0401-07a" xml:space="preserve">1056.</note> <note position="right" xlink:label="note-0401-08" xlink:href="note-0401-08a" xml:space="preserve">TAB XXXVIII. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0401-09" xlink:href="note-0401-09a" xml:space="preserve">709.</note> </div> </div> <div xml:id="echoid-div1549" type="section" level="1" n="368"> <head xml:id="echoid-head506" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s10857" xml:space="preserve">Ne mutetur hæc preſſio, quando tubus inclinatur, re-<lb/> <anchor type="note" xlink:label="note-0401-10a" xlink:href="note-0401-10"/> quiritur, ut eandem mercurius ſervet altitudinem vertica-<lb/> <anchor type="note" xlink:label="note-0401-11a" xlink:href="note-0401-11"/> lem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10858" xml:space="preserve">ideò ſi dentur duo vaſa, hydrargyrum continentia, <anchor type="note" xlink:label="note-0401-12a" xlink:href="note-0401-12"/> in quibus tubi, ut dictum, immerguntur, quorum ED <lb/>ad horizontem inclinatur, ſuſtinetur mercurius ad alti- <pb o="298" file="0402" n="439" rhead="PHYSICES ELEMENTA"/> tudines hf, & </s> <s xml:id="echoid-s10859" xml:space="preserve">ig, ita ut f & </s> <s xml:id="echoid-s10860" xml:space="preserve">g ſint in eadem linea ho-<lb/>rizontali, poſitis ſuperficiebus mercurii in vaſis in eodem <lb/>plano.</s> <s xml:id="echoid-s10861" xml:space="preserve"/> </p> <div xml:id="echoid-div1549" type="float" level="2" n="1"> <note position="right" xlink:label="note-0401-10" xlink:href="note-0401-10a" xml:space="preserve">1057.</note> <note position="right" xlink:label="note-0401-11" xlink:href="note-0401-11a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0401-12" xlink:href="note-0401-12a" xml:space="preserve">715.</note> </div> </div> <div xml:id="echoid-div1551" type="section" level="1" n="369"> <head xml:id="echoid-head507" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s10862" xml:space="preserve">Hæc eadem aëris preſſio ſuſtinet aquam in vitro V, quod <lb/> <anchor type="note" xlink:label="note-0402-01a" xlink:href="note-0402-01"/> aquâ immergitur & </s> <s xml:id="echoid-s10863" xml:space="preserve">hac repletur, deinde extrahitur, orifi-<lb/> <anchor type="note" xlink:label="note-0402-02a" xlink:href="note-0402-02"/> cio manente immerſo.</s> <s xml:id="echoid-s10864" xml:space="preserve"/> </p> <div xml:id="echoid-div1551" type="float" level="2" n="1"> <note position="left" xlink:label="note-0402-01" xlink:href="note-0402-01a" xml:space="preserve">1058.</note> <note position="left" xlink:label="note-0402-02" xlink:href="note-0402-02a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s10865" xml:space="preserve">Eodem modo aqua ſuſtineretur, licet vitri altitudo tri-<lb/> <anchor type="note" xlink:label="note-0402-03a" xlink:href="note-0402-03"/> ginta & </s> <s xml:id="echoid-s10866" xml:space="preserve">duos pedes æquaret. </s> <s xml:id="echoid-s10867" xml:space="preserve">Hydrargyrum enim gravita-<lb/>te ſua ſpecifica fere decies & </s> <s xml:id="echoid-s10868" xml:space="preserve">quater ſuperat aquæ gravita-<lb/>tem ſpecificam, & </s> <s xml:id="echoid-s10869" xml:space="preserve">columna aquea, triginta & </s> <s xml:id="echoid-s10870" xml:space="preserve">duos pedes <lb/>excedens, æqualiter cum mercurii columna viginti novem <lb/>pollicum premit, quæ preſſio Atmoſphæræ preſſioni æqui-<lb/>pollet.</s> <s xml:id="echoid-s10871" xml:space="preserve"/> </p> <div xml:id="echoid-div1552" type="float" level="2" n="2"> <note position="left" xlink:label="note-0402-03" xlink:href="note-0402-03a" xml:space="preserve">1059.</note> </div> <p> <s xml:id="echoid-s10872" xml:space="preserve">Preſſionem aëris ab hujus altitudine pendere, ex dictis <lb/> <anchor type="note" xlink:label="note-0402-04a" xlink:href="note-0402-04"/> facillimè deduci poteſt; </s> <s xml:id="echoid-s10873" xml:space="preserve">ſed immediatè probatur, transfe-<lb/>rendo tubum cum mercurio memoratum in locum <lb/>elevatum, nam circiter octavâ parte unius pollicis deſcen-<lb/>dit mercurius pro altitudine centum pedum, ad quam Ma-<lb/>china elevatur.</s> <s xml:id="echoid-s10874" xml:space="preserve"/> </p> <div xml:id="echoid-div1553" type="float" level="2" n="3"> <note position="left" xlink:label="note-0402-04" xlink:href="note-0402-04a" xml:space="preserve">1060.</note> </div> <p> <s xml:id="echoid-s10875" xml:space="preserve">Aërem omnes partes verſus æqualiter premere ex eo patet, <lb/> <anchor type="note" xlink:label="note-0402-05a" xlink:href="note-0402-05"/> quod a corporibus mollibus hujus preſſio ſine figuræ muta-<lb/>tione, & </s> <s xml:id="echoid-s10876" xml:space="preserve">à fragilibus ſine diſruptione, ſuſtineatur; </s> <s xml:id="echoid-s10877" xml:space="preserve">quamvis hæc <lb/>valeat preſſionem mercurii ad altitudinem viginti novem pol-<lb/>licum, aut aquæ ad altitudinem triginta duorum pedum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10878" xml:space="preserve">nil, <anchor type="note" xlink:label="note-0402-06a" xlink:href="note-0402-06"/> præter preſſionem æqualem ab omni parte, memorata corpo-<lb/>ra intacta ſervare poſſe, quis non videt; </s> <s xml:id="echoid-s10879" xml:space="preserve">hanc autem preſſio-<lb/>nem illud præſtare conſtat <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10880" xml:space="preserve">Sublato aëre ab una parte, <anchor type="note" xlink:label="note-0402-07a" xlink:href="note-0402-07"/> preſſio in partem oppoſitam ſenſibilis eſt.</s> <s xml:id="echoid-s10881" xml:space="preserve"/> </p> <div xml:id="echoid-div1554" type="float" level="2" n="4"> <note position="left" xlink:label="note-0402-05" xlink:href="note-0402-05a" xml:space="preserve">1061.</note> <note symbol="*" position="left" xlink:label="note-0402-06" xlink:href="note-0402-06a" xml:space="preserve">1059.</note> <note symbol="*" position="left" xlink:label="note-0402-07" xlink:href="note-0402-07a" xml:space="preserve">745. 746.</note> </div> </div> <div xml:id="echoid-div1556" type="section" level="1" n="370"> <head xml:id="echoid-head508" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s10882" xml:space="preserve">Suſpendatur lanci uni, bilancis AB, tubus vitreus, <lb/> <anchor type="note" xlink:label="note-0402-08a" xlink:href="note-0402-08"/> clauſus in D, longitudinis circiter trium pedum; </s> <s xml:id="echoid-s10883" xml:space="preserve">impleatur <lb/> <anchor type="note" xlink:label="note-0402-09a" xlink:href="note-0402-09"/> hic mercurio, & </s> <s xml:id="echoid-s10884" xml:space="preserve">extremitas E mercurio vaſe V, contento, <lb/>immergatur. </s> <s xml:id="echoid-s10885" xml:space="preserve">Hydrargyrum ex aëris preſſione ſuſtinetur ad <lb/>altitudinem f, & </s> <s xml:id="echoid-s10886" xml:space="preserve">pars ſuperior tubi f D aëre vacua relinqui- <pb o="299" file="0403" n="440" rhead="MATHEMATICA. LIB. II. CAP. XIII."/> tur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s10887" xml:space="preserve">ut æquilibrium detur, lanci oppoſitæ imponitur pon- <anchor type="note" xlink:label="note-0403-01a" xlink:href="note-0403-01"/> dus, æquale ponderi tubi, & </s> <s xml:id="echoid-s10888" xml:space="preserve">mercurii in hoc contenti.</s> <s xml:id="echoid-s10889" xml:space="preserve"/> </p> <div xml:id="echoid-div1556" type="float" level="2" n="1"> <note position="left" xlink:label="note-0402-08" xlink:href="note-0402-08a" xml:space="preserve">1062.</note> <note position="left" xlink:label="note-0402-09" xlink:href="note-0402-09a" xml:space="preserve">TAB. XXXVIII. <lb/>fig 3.</note> <note symbol="*" position="right" xlink:label="note-0403-01" xlink:href="note-0403-01a" xml:space="preserve">1056.</note> </div> <p> <s xml:id="echoid-s10890" xml:space="preserve">Mercurius in tubo libram gravare nequit; </s> <s xml:id="echoid-s10891" xml:space="preserve">illius enim a-<lb/>ctio in latera tubi, horizontalis eſt: </s> <s xml:id="echoid-s10892" xml:space="preserve">ſed aër agit in ſupe-<lb/>riorem partem tubi, & </s> <s xml:id="echoid-s10893" xml:space="preserve">columna quæ a tubo ſuſtinetur æ-<lb/>quiponderat cum columna mercurii in tubo contenta. </s> <s xml:id="echoid-s10894" xml:space="preserve">Si <lb/>ſublato mercurio aër intromittatur, ſolus tubus libram gra-<lb/>vat; </s> <s xml:id="echoid-s10895" xml:space="preserve">quod probat, actionem aëris, in ſuperficiem inferiorem <lb/>partis ſuperioris tubi, deſtruere actionem in ſuperficiem ex-<lb/>teriorem ejuſdem partis tubi, aëremque ſurſum & </s> <s xml:id="echoid-s10896" xml:space="preserve">deorſum <lb/>æqualiter premere.</s> <s xml:id="echoid-s10897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10898" xml:space="preserve">Hoc etiam Experimento, quæ de aëris gravitate dicta <lb/>funt, confirmantur.</s> <s xml:id="echoid-s10899" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1558" type="section" level="1" n="371"> <head xml:id="echoid-head509" xml:space="preserve">CAPUT XIV. <lb/>De Aëris Elaſticitate.</head> <p> <s xml:id="echoid-s10900" xml:space="preserve">CEterorum fluidorum proprietates aërem habere vidi-<lb/> <anchor type="note" xlink:label="note-0403-02a" xlink:href="note-0403-02"/> mus; </s> <s xml:id="echoid-s10901" xml:space="preserve">præter has peculiarem habet, poteſtque locum <lb/>majorem aut minorem occupare, prout vi diverſa compri-<lb/>mitur; </s> <s xml:id="echoid-s10902" xml:space="preserve">& </s> <s xml:id="echoid-s10903" xml:space="preserve">ſtatim ac vis hæc minuitur, ſeſe expandit. </s> <s xml:id="echoid-s10904" xml:space="preserve">Pro-<lb/>pter analogiam hujus effectus cum corporum elaſticitate, <lb/>hæc aëris proprietas hujus Elaſticitas dicitur.</s> <s xml:id="echoid-s10905" xml:space="preserve"/> </p> <div xml:id="echoid-div1558" type="float" level="2" n="1"> <note position="right" xlink:label="note-0403-02" xlink:href="note-0403-02a" xml:space="preserve">1063.</note> </div> <p> <s xml:id="echoid-s10906" xml:space="preserve">Aërem poſſe comprimi Experimento jam memorato con-<lb/> <anchor type="note" xlink:label="note-0403-03a" xlink:href="note-0403-03"/> ſtat <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s10907" xml:space="preserve">Et illum poſſe dilatari ſequenti probatur.</s> <s xml:id="echoid-s10908" xml:space="preserve"/> </p> <div xml:id="echoid-div1559" type="float" level="2" n="2"> <note position="right" xlink:label="note-0403-03" xlink:href="note-0403-03a" xml:space="preserve">1064.</note> </div> <note symbol="*" position="right" xml:space="preserve">17.</note> </div> <div xml:id="echoid-div1561" type="section" level="1" n="372"> <head xml:id="echoid-head510" xml:space="preserve"><emph style="sc">Experimentum.</emph> 1.</head> <p> <s xml:id="echoid-s10909" xml:space="preserve">Detur tubus AB clauſus in A, inſundatur mercurius <lb/> <anchor type="note" xlink:label="note-0403-05a" xlink:href="note-0403-05"/> ita, ut in tubo aër relinquatur, qui in ſtatu aëris exterioris <lb/> <anchor type="note" xlink:label="note-0403-06a" xlink:href="note-0403-06"/> occupet ſpatium Al; </s> <s xml:id="echoid-s10910" xml:space="preserve">ſi tubi extremitas B mercurio im-<lb/>mergatur, deſcendet mercurius ad g, ibique hærebit. </s> <s xml:id="echoid-s10911" xml:space="preserve">Al-<lb/>titudo ig multum diſſert ab altitudine mercurii in Expe-<lb/>rimento 1. </s> <s xml:id="echoid-s10912" xml:space="preserve">capitis præcedentis.</s> <s xml:id="echoid-s10913" xml:space="preserve"/> </p> <div xml:id="echoid-div1561" type="float" level="2" n="1"> <note position="right" xlink:label="note-0403-05" xlink:href="note-0403-05a" xml:space="preserve">1065.</note> <note position="right" xlink:label="note-0403-06" xlink:href="note-0403-06a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s10914" xml:space="preserve">Hoc ex pondere aëris in tubo non oritur; </s> <s xml:id="echoid-s10915" xml:space="preserve">ni-<lb/>mium exiguum eſt hocce pondus, ut ſenſibilem diffe- <pb o="300" file="0404" n="441" rhead="PHYSICES ELEMENTA"/> rentiam in altitudine mercurii producat: </s> <s xml:id="echoid-s10916" xml:space="preserve">aëris ergo expanſio <lb/>hujus effectus cauſa eſt.</s> <s xml:id="echoid-s10917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10918" xml:space="preserve">Experimento detegimus, aërem ſeſe ita dilatare, ut <lb/> <anchor type="note" xlink:label="note-0404-01a" xlink:href="note-0404-01"/> ſpatium ab hoc occupatum ſit inverſè ut vis qua comprimi-<lb/>tur.</s> <s xml:id="echoid-s10919" xml:space="preserve"/> </p> <div xml:id="echoid-div1562" type="float" level="2" n="2"> <note position="left" xlink:label="note-0404-01" xlink:href="note-0404-01a" xml:space="preserve">1069.</note> </div> </div> <div xml:id="echoid-div1564" type="section" level="1" n="373"> <head xml:id="echoid-head511" xml:space="preserve"><emph style="sc">Machina,</emph> <lb/>Qua Aëris Dilatationes, ut & Vires comprimentes, <lb/>conferuntur inter ſe.</head> <p> <s xml:id="echoid-s10920" xml:space="preserve">Machina hæc ex variis conſtat partibus. </s> <s xml:id="echoid-s10921" xml:space="preserve">Pars prima eſt tu-<lb/> <anchor type="note" xlink:label="note-0404-02a" xlink:href="note-0404-02"/> bus vitreus AB, cujus cavitatis diameter eſt ſemipoll.</s> <s xml:id="echoid-s10922" xml:space="preserve">, lon-<lb/> <anchor type="note" xlink:label="note-0404-03a" xlink:href="note-0404-03"/> gitudo circiter trium pedum; </s> <s xml:id="echoid-s10923" xml:space="preserve">hujus extremitas clau-<lb/>ſa, inferior A, cylindro cupreo, ab inferiori parte laminâ <lb/>ejusdem metalli clauſo, circumdatur, qui cylindrus intritâ cum <lb/>tubo jungitur; </s> <s xml:id="echoid-s10924" xml:space="preserve">cautela hæc obſervanda eſt, ne hæc tubi <lb/>extremitas frangatur.</s> <s xml:id="echoid-s10925" xml:space="preserve"/> </p> <div xml:id="echoid-div1564" type="float" level="2" n="1"> <note position="left" xlink:label="note-0404-02" xlink:href="note-0404-02a" xml:space="preserve">1067.</note> <note position="left" xlink:label="note-0404-03" xlink:href="note-0404-03a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s10926" xml:space="preserve">Tubo huic jungitur pyxis buxea cylindrica F, cujus dia-<lb/>meter eſt circiter quatuor poll.</s> <s xml:id="echoid-s10927" xml:space="preserve">, eſtque altitudo diametro <lb/>proxime æqualis; </s> <s xml:id="echoid-s10928" xml:space="preserve">jungitur tubus pyxidi dum cylindro li-<lb/>gneo G, cum fundo pyxidis cohærenti, intruditur; </s> <s xml:id="echoid-s10929" xml:space="preserve">da-<lb/>turque in fundo pyxidis foramen, quo hæc cum tubo com-<lb/>municationem habet.</s> <s xml:id="echoid-s10930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10931" xml:space="preserve">Pyxis cum tubo regulæ ligneæ CD, quæ ſulcata eſt, ap-<lb/>plicantur, & </s> <s xml:id="echoid-s10932" xml:space="preserve">firmantur transmittendo regulam per foramen <lb/>menſæ, quæ regulæ extremum latius D ſuſtinet.</s> <s xml:id="echoid-s10933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10934" xml:space="preserve">Hoc ipſo regulæ extremo D, pyxis F fulcitur, dum tubi <lb/>extremitas A prominentiæ ligneæ e inſiſtit.</s> <s xml:id="echoid-s10935" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10936" xml:space="preserve">Pars ſecunda Machinæ eſt tubus vitreus HI, qui facile <lb/>in tubum AB intruditur; </s> <s xml:id="echoid-s10937" xml:space="preserve">clauſus eſt in I habetque ibidem <lb/>indicem transverſum.</s> <s xml:id="echoid-s10938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10939" xml:space="preserve">Tandem pars tertia conſtat ex duabus regulis LM, <lb/>NO, juxta ſe invicem mobilibus, & </s> <s xml:id="echoid-s10940" xml:space="preserve">longæ circiter duos <lb/>pedes cum ſemiſſe ſingulæ; </s> <s xml:id="echoid-s10941" xml:space="preserve">diviſæ ſunt ambæ, initiaque <lb/>diviſionum ſunt in inferioribus extremitatibus regularum.</s> <s xml:id="echoid-s10942" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10943" xml:space="preserve">Poſterior regula diviſa eſt in pollices & </s> <s xml:id="echoid-s10944" xml:space="preserve">minores partes æ-<lb/>quales. </s> <s xml:id="echoid-s10945" xml:space="preserve">Anterior ſulcata eſt, ut tubum HI recipiat, ſuntque <pb o="301" file="0405" n="442" rhead="MATHEMATICA. LIB. II. CAP. XIV."/> hujus diviſiones inæquales, indicantes æquales partes cavi-<lb/>tatis tubi HI.</s> <s xml:id="echoid-s10946" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10947" xml:space="preserve">Si tubus hic exacte cylindricus foret, æquales hæ forent <lb/>diviſiones, cumque raro admodum hoc contingat, dicam <lb/>quomodo diviſiones regulæ LM notentur.</s> <s xml:id="echoid-s10948" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10949" xml:space="preserve">Invertitur tubus HI, ipſique regulæ applicatur ita, <lb/>ut index in I extremitati regulæ reſpondeat. </s> <s xml:id="echoid-s10950" xml:space="preserve">In-<lb/>funditur mercurius exiguâ copià, cujus ex. </s> <s xml:id="echoid-s10951" xml:space="preserve">gr. </s> <s xml:id="echoid-s10952" xml:space="preserve">altitu-<lb/>do in tubo quartam aut tertiam partem poll. </s> <s xml:id="echoid-s10953" xml:space="preserve">valeat, nota-<lb/>turque in regula altitudo ad quam pertingit; </s> <s xml:id="echoid-s10954" xml:space="preserve">æqualis quan-<lb/>titas mercurii iterum ſuperinfunditur, ſecundaque diviſio <lb/>notatur; </s> <s xml:id="echoid-s10955" xml:space="preserve">ſicque continuando regula tota dividi poteſt. </s> <s xml:id="echoid-s10956" xml:space="preserve">Æ-<lb/>quales mercurii quantitates ipſas ponderando determinan-<lb/>tur.</s> <s xml:id="echoid-s10957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10958" xml:space="preserve">Sed longum & </s> <s xml:id="echoid-s10959" xml:space="preserve">difficile eſt, tot portiunculas mercurii ſepa-<lb/>rare ita, ut exacte æqualiter ponderent; </s> <s xml:id="echoid-s10960" xml:space="preserve">ideò, ſi tubus re-<lb/>gularis ſit, id eſt, ſi ſit portio coni truncanti, ut contin-<lb/>git plerumque, ſi etiam parum a cylindro differat, <lb/>quod facile habetur, alia methodo uti poſſumus; </s> <s xml:id="echoid-s10961" xml:space="preserve">quia in <lb/>hoc caſu diviſiones a progreſſione arithmetica non ſenſibi-<lb/>liter aberrant.</s> <s xml:id="echoid-s10962" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10963" xml:space="preserve">Primæ quatuor aut quinque diviſiones, methodo indica-<lb/>tâ, notandæ ſunt, quia dum hermeticè clauditur tubus <lb/>non regularem ſervat figuram; </s> <s xml:id="echoid-s10964" xml:space="preserve">deinde decupla aut duo-<lb/>decupla mercurii quantitas infundenda tubo erit, & </s> <s xml:id="echoid-s10965" xml:space="preserve">diviſio <lb/>notanda erit, quæ ab ultima notata diſtabit, partibus de-<lb/>cem aut duodecim partibus minoribus, & </s> <s xml:id="echoid-s10966" xml:space="preserve">continuando re-<lb/>liquum regulæ, eodem modo in partes tales majores, æ-<lb/>quales portiones capacitatis tubi deſignantes, dividendum <lb/>erit; </s> <s xml:id="echoid-s10967" xml:space="preserve">quæ dein geometrice ſubdividi debent ita, ut omnes <lb/>minores continuam forment arithmeticam progreſſionem.</s> <s xml:id="echoid-s10968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10969" xml:space="preserve">Examinandum autem an majores notatæ diviſiones in a-<lb/>rithmetica ſint progreſſione, ſin minus geometrica divi-<lb/>ſio, propter tubi irregularitatem, locum habere nequit.</s> <s xml:id="echoid-s10970" xml:space="preserve"/> </p> <pb o="302" file="0406" n="443" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1566" type="section" level="1" n="374"> <head xml:id="echoid-head512" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s10971" xml:space="preserve">Menſurandum ante omnia exactè, ad quam altitudinem <lb/> <anchor type="note" xlink:label="note-0406-01a" xlink:href="note-0406-01"/> mercurius ſuſtineatur in tubo Torricelliano <anchor type="note" xlink:href="" symbol="*"/>, cujus ſupe- <anchor type="note" xlink:label="note-0406-02a" xlink:href="note-0406-02"/> rior extremitas bene aëre vacua eſt.</s> <s xml:id="echoid-s10972" xml:space="preserve"/> </p> <div xml:id="echoid-div1566" type="float" level="2" n="1"> <note position="left" xlink:label="note-0406-01" xlink:href="note-0406-01a" xml:space="preserve">1068.</note> <note symbol="*" position="left" xlink:label="note-0406-02" xlink:href="note-0406-02a" xml:space="preserve">1056.</note> </div> <p> <s xml:id="echoid-s10973" xml:space="preserve">Tubus AB mercurio repletur ita, ut hic in ipſa pyxide <lb/>F detur ad altitudinem ſemi, aut ſi velis, integri pollicis. </s> <s xml:id="echoid-s10974" xml:space="preserve">Tu-<lb/>bus HI pro parte mercurio repletur; </s> <s xml:id="echoid-s10975" xml:space="preserve">aërque in hoc ipſo <lb/>occupat longitudinem duorum, trium, aut quatuor polli-<lb/>cum, vel etiam majorem.</s> <s xml:id="echoid-s10976" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10977" xml:space="preserve">Extremitas aperta digito clauditur & </s> <s xml:id="echoid-s10978" xml:space="preserve">mercurio, pyxide <lb/>F contento, immergitur, tubusque in tubum BH intruditur, <lb/>deprimiturque donec ſuperficies mercurii in tubo HI, & </s> <s xml:id="echoid-s10979" xml:space="preserve"><lb/>in pyxide, ſint in eodem plano.</s> <s xml:id="echoid-s10980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10981" xml:space="preserve">Regula LM tubo applicatur ita, ut extremitas L mer-<lb/>curii ſuperficiem tangat, index tunc I, indicat diviſionem <lb/>regulæ, quæ ſpatium, ab aëre in tubo occupatum, de-<lb/>monſtrat.</s> <s xml:id="echoid-s10982" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10983" xml:space="preserve">Aër hic cum externo aëre æqualiter comprimitur <anchor type="note" xlink:href="" symbol="*"/>, viſ- <anchor type="note" xlink:label="note-0406-03a" xlink:href="note-0406-03"/> que comprimens ipſa eſt quæ mercurium ſuſtinet in tubo <lb/>Torricelliano.</s> <s xml:id="echoid-s10984" xml:space="preserve"/> </p> <div xml:id="echoid-div1567" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0406-03" xlink:href="note-0406-03a" xml:space="preserve">709.</note> </div> <p> <s xml:id="echoid-s10985" xml:space="preserve">Regula LM juxta poſteriorem nunc movetur ita, ut parsre-<lb/>gulæ NO, quæ infra alîus regulæ extremitatem deſcendit, æ-<lb/>qualis ſit ſemi altitudini mercurii in tubo Torricelliano, ſi <lb/>tunc regulæ retineantur verticaliter, extremitasque inferior <lb/>regulæ NO ſuperficiem Mercurii in pyxide tangat, & </s> <s xml:id="echoid-s10986" xml:space="preserve">ele-<lb/>vetur tubus HI, donec mercurius in tubo ad extremita-<lb/>tem L regulæ LM pertingat, capacitas tubi vacua LI, quæ <lb/>diviſionibus regulæ LM menſuratur, dupla erit illius, quam <lb/>aër occupavit in ſtatu aëris externi.</s> <s xml:id="echoid-s10987" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10988" xml:space="preserve">Atmoſphæra, (cujus preſſione Mercurius in tubo Tor-<lb/> <anchor type="note" xlink:label="note-0406-04a" xlink:href="note-0406-04"/> ricelliano ſuſtinetur) dum in ſuperficiem mercurii in pyxide <lb/>premit, duos exerit effectus, ſuſtinet mercurium ad L uſque, <lb/>& </s> <s xml:id="echoid-s10989" xml:space="preserve">aërem in LI comprimit. </s> <s xml:id="echoid-s10990" xml:space="preserve">Dimidio totius actionis mer-<lb/>curium ſuſtinet, & </s> <s xml:id="echoid-s10991" xml:space="preserve">idcirco dimidio actionis comprimit aë-<lb/>rem; </s> <s xml:id="echoid-s10992" xml:space="preserve">id eſt reducta preſſione ad ſemiſſem aër duplum oc-<lb/>cupat ſpatium.</s> <s xml:id="echoid-s10993" xml:space="preserve"/> </p> <div xml:id="echoid-div1568" type="float" level="2" n="3"> <note position="left" xlink:label="note-0406-04" xlink:href="note-0406-04a" xml:space="preserve">1069.</note> </div> <pb o="303" file="0407" n="444" rhead="MATHEMATICA. LIB. II. CAP. XIV."/> <p> <s xml:id="echoid-s10994" xml:space="preserve">Quando altitudo Mercurii FL valet duas tertias partes <lb/>altitudinis Mercurii in tubo Torricelliano, preſſio, quæ aë-<lb/>rem in LI comprimit, eſt pars tertia totius actionis, quæ <lb/>in aërem tubo incluſum egit, ubi in ſtatu fuit aëris externi; <lb/></s> <s xml:id="echoid-s10995" xml:space="preserve">occupabit tunc etiam aër ſpatium triplum illius quod in <lb/>hoc ſtatu occupavit.</s> <s xml:id="echoid-s10996" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10997" xml:space="preserve">Poteſtque innumeris modis hac Machina variari experi-<lb/>mentum, & </s> <s xml:id="echoid-s10998" xml:space="preserve">ſemper, altitudo mercurii iu tubo Torricellia-<lb/>no ad differentiam altitudinis hujus cum altitudine aut e-<lb/>levatione ipſius in tubo HI ſupra mercurium in pyxide; </s> <s xml:id="echoid-s10999" xml:space="preserve">id <lb/>eſt vis quæ aërem premit, ubi in ſtatu eſt aëris externi, ad <lb/>vim quæ illum comprimit in experimento quocunque, ita <lb/>ſe habet capacitas tubi, in hoc caſu aëre repleta, ad ſpa-<lb/>tium quod in illo caſu occupat.</s> <s xml:id="echoid-s11000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11001" xml:space="preserve">Hæc eadem regula in aëre compreſſo obtinet.</s> <s xml:id="echoid-s11002" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1570" type="section" level="1" n="375"> <head xml:id="echoid-head513" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s11003" xml:space="preserve">Detur tubus curvus ABCD, apertus in A, clauſus in <lb/> <anchor type="note" xlink:label="note-0407-01a" xlink:href="note-0407-01"/> D, pars BC mercurio impleatur ita, ut pars CD aërem <lb/> <anchor type="note" xlink:label="note-0407-02a" xlink:href="note-0407-02"/> contineat in eodem ſtatu cum aëre exteriori; </s> <s xml:id="echoid-s11004" xml:space="preserve">vis ergo <lb/>comprimens eſt columna mercurii, cujus altitudo eſt hf <lb/>(Fig. </s> <s xml:id="echoid-s11005" xml:space="preserve">1.)</s> <s xml:id="echoid-s11006" xml:space="preserve">, & </s> <s xml:id="echoid-s11007" xml:space="preserve">hæc altitudo vim illam deſignat; </s> <s xml:id="echoid-s11008" xml:space="preserve">ſpatium au-<lb/>tem ab aëre occupatum eſt CD. </s> <s xml:id="echoid-s11009" xml:space="preserve">Tubo AB mercurius <lb/>infundatur ut ad g pertingat, aër reducetur in ſpatium e D: <lb/></s> <s xml:id="echoid-s11010" xml:space="preserve">vis comprimens nunc valet columnam mercurii altitudinis <lb/>fg, ut & </s> <s xml:id="echoid-s11011" xml:space="preserve">preſſionem aëris exterioris in ſuperficiem g mercurii; </s> <s xml:id="echoid-s11012" xml:space="preserve"><lb/>vis hæc deſignatur per ſummam altitudinum fg in hac figu-<lb/>ra & </s> <s xml:id="echoid-s11013" xml:space="preserve">hf in fig. </s> <s xml:id="echoid-s11014" xml:space="preserve">1. </s> <s xml:id="echoid-s11015" xml:space="preserve">Hæc ſumma eſt ſemper ad hf (fig. </s> <s xml:id="echoid-s11016" xml:space="preserve">1.) </s> <s xml:id="echoid-s11017" xml:space="preserve">ut <lb/>CD ad eD; </s> <s xml:id="echoid-s11018" xml:space="preserve">iterumque vires ſunt inverſe ut ſpatia.</s> <s xml:id="echoid-s11019" xml:space="preserve"/> </p> <div xml:id="echoid-div1570" type="float" level="2" n="1"> <note position="right" xlink:label="note-0407-01" xlink:href="note-0407-01a" xml:space="preserve">1070.</note> <note position="right" xlink:label="note-0407-02" xlink:href="note-0407-02a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s11020" xml:space="preserve">Aëris elaſticitas eſt ut hujus denſitas; </s> <s xml:id="echoid-s11021" xml:space="preserve">hæc enim eſt in-<lb/> <anchor type="note" xlink:label="note-0407-03a" xlink:href="note-0407-03"/> verſè ut ſpatium ab aëre occupatum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11022" xml:space="preserve">ideò ut vis aë- <anchor type="note" xlink:label="note-0407-04a" xlink:href="note-0407-04"/> rem comprimens <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s11023" xml:space="preserve">quæ æqualis illi qua aër conatur ſeſe <anchor type="note" xlink:label="note-0407-05a" xlink:href="note-0407-05"/> expandere <anchor type="note" xlink:href="" symbol="*"/>, hæc autem eſt hujus elaſticiras.</s> <s xml:id="echoid-s11024" xml:space="preserve"/> </p> <div xml:id="echoid-div1571" type="float" level="2" n="2"> <note position="right" xlink:label="note-0407-03" xlink:href="note-0407-03a" xml:space="preserve">1071.</note> <note symbol="*" position="right" xlink:label="note-0407-04" xlink:href="note-0407-04a" xml:space="preserve">738</note> <note symbol="*" position="right" xlink:label="note-0407-05" xlink:href="note-0407-05a" xml:space="preserve">1066.</note> </div> <note symbol="*" position="right" xml:space="preserve">247.</note> <p> <s xml:id="echoid-s11025" xml:space="preserve">Ex hiſce ſequitur, aërem in quo vivimus, ad illam quam <lb/>in terræ viciniis habet denſitatem reduci ex preſſione aëris <lb/>ſuperincumbentis, illumque magis aut minus comprimi pro <pb o="304" file="0408" n="445" rhead="PHYSICES ELEMENTA"/> majore aut minore Atmoſphæræ pondere; </s> <s xml:id="echoid-s11026" xml:space="preserve">ex qua etiam <lb/>ratione in apice montis minus denſus eſt aer quàm in valle; <lb/></s> <s xml:id="echoid-s11027" xml:space="preserve">minori enim pondere comprimitur.</s> <s xml:id="echoid-s11028" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11029" xml:space="preserve">Vis, qua particulæ aëreæ ſeſe mutuo repellunt, creſcit <lb/> <anchor type="note" xlink:label="note-0408-01a" xlink:href="note-0408-01"/> in ratione in qua diſtantia inter centra particularum mi-<lb/> <anchor type="note" xlink:label="note-0408-02a" xlink:href="note-0408-02"/> nuitur, id eſt, vis illa eſt inverſè ut hæc diſtantia. </s> <s xml:id="echoid-s11030" xml:space="preserve">Quod <lb/>ut demonſtretur, conſiderentur duo cubi æquales A & </s> <s xml:id="echoid-s11031" xml:space="preserve">B, <lb/>inæquales aëris quantitates continentes; </s> <s xml:id="echoid-s11032" xml:space="preserve">ſint diſtantiæ inter <lb/>centra particularum ut duo ad unum; </s> <s xml:id="echoid-s11033" xml:space="preserve">in eadem ratione, ſed <lb/>inverſa, erunt numeri particularum in lineis de & </s> <s xml:id="echoid-s11034" xml:space="preserve">hi: </s> <s xml:id="echoid-s11035" xml:space="preserve">nu-<lb/>meri particularum agentium in ſuperſicies dg & </s> <s xml:id="echoid-s11036" xml:space="preserve">hm ſunt <lb/>ut unum ad quatuor, nempe ut quadrata numerorum parti-<lb/>cularum in lineis æqualibus; </s> <s xml:id="echoid-s11037" xml:space="preserve">& </s> <s xml:id="echoid-s11038" xml:space="preserve">ut horum numerorum cubi, <lb/>ſcilicet ut unum ad octo, ſunt aëris quantitates in cubis <lb/>contentæ; </s> <s xml:id="echoid-s11039" xml:space="preserve">in qua etiam ratione ſunt vires comprimentes <lb/>aërem in cubis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11040" xml:space="preserve">Vires agentes in ſuperficies æquales dg <anchor type="note" xlink:label="note-0408-03a" xlink:href="note-0408-03"/> & </s> <s xml:id="echoid-s11041" xml:space="preserve">bm ſunt ut vires, quibus aër comprimitur <anchor type="note" xlink:href="" symbol="*"/>, ſunt etiam <anchor type="note" xlink:label="note-0408-04a" xlink:href="note-0408-04"/> in ratione compoſita numerorum particularum agentium, & </s> <s xml:id="echoid-s11042" xml:space="preserve"><lb/>actionum ſingularum particularum; </s> <s xml:id="echoid-s11043" xml:space="preserve">hæc ergo ratio compo-<lb/>ſita eſt ratio unius ad octo: </s> <s xml:id="echoid-s11044" xml:space="preserve">rationum componentium prima, <lb/>ut dictum, eſt unius ad quatuor, quare neceſſario ſecunda <lb/>eſt unius ad duo, quæ eſt ratio inverſa diſtantiæ inter par-<lb/>ticulas. </s> <s xml:id="echoid-s11045" xml:space="preserve">Hæcque demonſtratio generalis eſt, nam unum & </s> <s xml:id="echoid-s11046" xml:space="preserve"><lb/>octo cubos quo@cunque, unum & </s> <s xml:id="echoid-s11047" xml:space="preserve">quatuor quadrata radicum <lb/>cuborum, & </s> <s xml:id="echoid-s11048" xml:space="preserve">tandem unum & </s> <s xml:id="echoid-s11049" xml:space="preserve">duo ipſas radices, in genere <lb/>deſignare poſſunt.</s> <s xml:id="echoid-s11050" xml:space="preserve"/> </p> <div xml:id="echoid-div1572" type="float" level="2" n="3"> <note position="left" xlink:label="note-0408-01" xlink:href="note-0408-01a" xml:space="preserve">1072.</note> <note position="left" xlink:label="note-0408-02" xlink:href="note-0408-02a" xml:space="preserve">TAB. XXXVIII. <lb/>fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0408-03" xlink:href="note-0408-03a" xml:space="preserve">1071. 247.</note> <note symbol="*" position="left" xlink:label="note-0408-04" xlink:href="note-0408-04a" xml:space="preserve">247.</note> </div> <p> <s xml:id="echoid-s11051" xml:space="preserve">Hæc demonſtratio probat actionem, quam particulæ con-<lb/>tinuò ab omni parte patiuntur, augeri in ratione in qua <lb/>diſtantia inter centra particularum minuitur, ſive hæc actio ad <lb/>particulas tantum vicinas, ſive etiam ad magis diſtantes, <lb/>referri debeat: </s> <s xml:id="echoid-s11052" xml:space="preserve">videbimus enim in capite ſequenti particulas <lb/>aëreas ſeſe mutuo repellere, quamvis ſeſe invicem non im-<lb/>mediate tangant. </s> <s xml:id="echoid-s11053" xml:space="preserve">In primo caſu vis ipſa repellens, qua ſingu-<lb/>læ particulæ gaudent, eſt ut actio memorata, id eſt, in-<lb/>verſè ut diſtantia inter particularum centra.</s> <s xml:id="echoid-s11054" xml:space="preserve"/> </p> <pb o="305" file="0409" n="446" rhead="MATHEMATICA. LIB. II. CAP. XIV."/> <p> <s xml:id="echoid-s11055" xml:space="preserve">In ſecundo caſu vis repellens ad omnes diſtantias eſt æqua-<lb/>lis; </s> <s xml:id="echoid-s11056" xml:space="preserve">tunc enim pendet actio in ſingulas particulas ab harum <lb/>numero in eadem linea, qui numerus eſt inverſè ut di-<lb/>ſtantia inter particularum centra. </s> <s xml:id="echoid-s11057" xml:space="preserve">Tunc etiam, poſitâ eâ-<lb/>dem aëris denſitate, ibi major erit elaſticitas, ubi major <lb/>aëris quantitas, quod cum experimentis non congruit, <lb/>primum idcirco caſum locum habere videmus.</s> <s xml:id="echoid-s11058" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11059" xml:space="preserve">Effectus elaſticitatis aëris ſimiles ſunt effectibus gravi-<lb/> <anchor type="note" xlink:label="note-0409-01a" xlink:href="note-0409-01"/> tatis; </s> <s xml:id="echoid-s11060" xml:space="preserve">aerque incluſus elaſticitate eodem modo quàm non <lb/>incluſus pondere ſuo agit.</s> <s xml:id="echoid-s11061" xml:space="preserve"/> </p> <div xml:id="echoid-div1573" type="float" level="2" n="4"> <note position="right" xlink:label="note-0409-01" xlink:href="note-0409-01a" xml:space="preserve">1073.</note> </div> <p> <s xml:id="echoid-s11062" xml:space="preserve">Aër, a totius Atmoſphæræ pondere gravatus, omnes <lb/>partes verſus premit ex ipſa natura fluiditatis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11063" xml:space="preserve">vim <anchor type="note" xlink:label="note-0409-02a" xlink:href="note-0409-02"/> quam exerit ab elaſticitate nullo modo pendere liquet; </s> <s xml:id="echoid-s11064" xml:space="preserve">quia, <lb/>hac poſitâ aut ſublatâ, vis illa, quæ a pondere Atmoſphæ-<lb/>ræ oritur, & </s> <s xml:id="echoid-s11065" xml:space="preserve">huic æqualis eſt, minime mutari poteſt. </s> <s xml:id="echoid-s11066" xml:space="preserve">Cum <lb/>vero aër ſit elaſticus, pondere Atmoſphæræ in tale ſpatium <lb/>redigitur, ut elaſticitas, qua renititur in pondus compri-<lb/>mens, hocce pondus æquet <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11067" xml:space="preserve">Elaſticitas autem creſcit <anchor type="note" xlink:label="note-0409-03a" xlink:href="note-0409-03"/> & </s> <s xml:id="echoid-s11068" xml:space="preserve">minuitur cum diminuta aut aucta diſtantia particularum <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0409-04a" xlink:href="note-0409-04"/> & </s> <s xml:id="echoid-s11069" xml:space="preserve">non intereſt an pondere Atmoſphæræ an quocunque alio <lb/>modo aër in certo ſpatio retineatur, in utroque caſu ea-<lb/>dem cum vi ſeſe expandere conatur, & </s> <s xml:id="echoid-s11070" xml:space="preserve">omnes partes ver-<lb/>ſus premit. </s> <s xml:id="echoid-s11071" xml:space="preserve">Idcirco ſi in terræ viciniis aër, ſervata hujus <lb/>denſitate, includatur, incluſi preſſio valebit totius Atmoſphæ-<lb/>ræ pondus.</s> <s xml:id="echoid-s11072" xml:space="preserve"/> </p> <div xml:id="echoid-div1574" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0409-02" xlink:href="note-0409-02a" xml:space="preserve">711.</note> <note symbol="*" position="right" xlink:label="note-0409-03" xlink:href="note-0409-03a" xml:space="preserve">247.</note> <note symbol="*" position="right" xlink:label="note-0409-04" xlink:href="note-0409-04a" xml:space="preserve">1071.</note> </div> </div> <div xml:id="echoid-div1576" type="section" level="1" n="376"> <head xml:id="echoid-head514" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s11073" xml:space="preserve">Tubus, Torricellianus vitro DC includitur, ita <lb/> <anchor type="note" xlink:label="note-0409-05a" xlink:href="note-0409-05"/> ut aër, in ſuperſiciem mercurii vaſe V contenti pre-<lb/> <anchor type="note" xlink:label="note-0409-06a" xlink:href="note-0409-06"/> mens, nullam cum aëre exteriori communicationem ha-<lb/>beat; </s> <s xml:id="echoid-s11074" xml:space="preserve">aëris elaſticitate ad eandem, ac in aëre aperto, ſu-<lb/>ſtinetur altitudinem mercurius in tubo.</s> <s xml:id="echoid-s11075" xml:space="preserve"/> </p> <div xml:id="echoid-div1576" type="float" level="2" n="1"> <note position="right" xlink:label="note-0409-05" xlink:href="note-0409-05a" xml:space="preserve">1074.</note> <note position="right" xlink:label="note-0409-06" xlink:href="note-0409-06a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s11076" xml:space="preserve">Manente eadem aëris conſtitutione, prædicta ſemper lo-<lb/> <anchor type="note" xlink:label="note-0409-07a" xlink:href="note-0409-07"/> cum habent; </s> <s xml:id="echoid-s11077" xml:space="preserve">ſed non immutabilis eſt hæc conſtitutio; </s> <s xml:id="echoid-s11078" xml:space="preserve">au-<lb/>getur ſæpe aut minuitur vis repellens particularum, licet <pb o="306" file="0410" n="447" rhead="PHYSICES ELEMENTA"/> diſtantia inter harum centranon mutetur; </s> <s xml:id="echoid-s11079" xml:space="preserve">de hac mutatione <lb/>quædam in capite ſequenti dicam, in libro ſequenti etiam <lb/>videbimus calore augeri elaſticitatem, frigore minui.</s> <s xml:id="echoid-s11080" xml:space="preserve"/> </p> <div xml:id="echoid-div1577" type="float" level="2" n="2"> <note position="right" xlink:label="note-0409-07" xlink:href="note-0409-07a" xml:space="preserve">1075.</note> </div> <p> <s xml:id="echoid-s11081" xml:space="preserve">Alia quædam, circa aëris elaſticitatem, memorabo expe-<lb/>rimenta in cap. </s> <s xml:id="echoid-s11082" xml:space="preserve">XVII.</s> <s xml:id="echoid-s11083" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1579" type="section" level="1" n="377"> <head xml:id="echoid-head515" xml:space="preserve">CAPUT XV.</head> <head xml:id="echoid-head516" style="it" xml:space="preserve">De quibuſdam aliis Fluidis Elaſticis.</head> <p> <s xml:id="echoid-s11084" xml:space="preserve">VAria dantur Fluida, in quibus circa aërem memoratam <lb/> <anchor type="note" xlink:label="note-0410-01a" xlink:href="note-0410-01"/> detegimus proprietatem, Elaſticitatem. <lb/></s> <s xml:id="echoid-s11085" xml:space="preserve">Inter hæc vapor notabilem occupat locum, de hoc agi-<lb/>mus in libro 3. </s> <s xml:id="echoid-s11086" xml:space="preserve">capite 4.</s> <s xml:id="echoid-s11087" xml:space="preserve"/> </p> <div xml:id="echoid-div1579" type="float" level="2" n="1"> <note position="left" xlink:label="note-0410-01" xlink:href="note-0410-01a" xml:space="preserve">1076.</note> </div> <p> <s xml:id="echoid-s11088" xml:space="preserve">Fermentationibus, & </s> <s xml:id="echoid-s11089" xml:space="preserve">efferveſcentiis, ex corporibus flui-<lb/> <anchor type="note" xlink:label="note-0410-02a" xlink:href="note-0410-02"/> da exeunt elaſtica, diverſa pro corporum differentia.</s> <s xml:id="echoid-s11090" xml:space="preserve"/> </p> <div xml:id="echoid-div1580" type="float" level="2" n="2"> <note position="left" xlink:label="note-0410-02" xlink:href="note-0410-02a" xml:space="preserve">1077.</note> </div> <p style="it"> <s xml:id="echoid-s11091" xml:space="preserve">Ex innumeris corporibus tale exit fluidum ubi preſſio <lb/> <anchor type="note" xlink:label="note-0410-03a" xlink:href="note-0410-03"/> aëris externi minuitur aut tollitur.</s> <s xml:id="echoid-s11092" xml:space="preserve"/> </p> <div xml:id="echoid-div1581" type="float" level="2" n="3"> <note position="left" xlink:label="note-0410-03" xlink:href="note-0410-03a" xml:space="preserve">1078.</note> </div> <p style="it"> <s xml:id="echoid-s11093" xml:space="preserve">Quod etiam in quibuſdam obſervatur, ubi tantum made-<lb/> <anchor type="note" xlink:label="note-0410-04a" xlink:href="note-0410-04"/> facta ſunt.</s> <s xml:id="echoid-s11094" xml:space="preserve"/> </p> <div xml:id="echoid-div1582" type="float" level="2" n="4"> <note position="left" xlink:label="note-0410-04" xlink:href="note-0410-04a" xml:space="preserve">1079.</note> </div> <p> <s xml:id="echoid-s11095" xml:space="preserve">Fluida hæc omnia quantumvis diverſa inter ſe, eodem <lb/>nomine aëris, ſi forte vaporem excipiamus, deſignantur <lb/>plerumque. </s> <s xml:id="echoid-s11096" xml:space="preserve">Cum vero aër ſit fluidum hoc, quo Telluris <lb/> <anchor type="note" xlink:label="note-0410-05a" xlink:href="note-0410-05"/> tota ſuperficies obtegitur, hic proprie loquendo eſt mixtum <lb/>ex variis fluidis elaſticis, in quo natant corpuſcula inumera <lb/>varii generis.</s> <s xml:id="echoid-s11097" xml:space="preserve"/> </p> <div xml:id="echoid-div1583" type="float" level="2" n="5"> <note position="left" xlink:label="note-0410-05" xlink:href="note-0410-05a" xml:space="preserve">1080.</note> </div> <p> <s xml:id="echoid-s11098" xml:space="preserve">Corpuſcula hæc pro diverſa gravitate ſpeciſica ad varias <lb/>adſcendunt altitudines <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11099" xml:space="preserve">etiam diverſorum corporum <anchor type="note" xlink:label="note-0410-06a" xlink:href="note-0410-06"/> exhalationes quæ fluida ſunt elaſtica ad diverſas elevantur <lb/>altitudines: </s> <s xml:id="echoid-s11100" xml:space="preserve">Unde deducimus, aërem in loco elevato non <lb/> <anchor type="note" xlink:label="note-0410-07a" xlink:href="note-0410-07"/> tantum denſitate differre cum aëre inferiori.</s> <s xml:id="echoid-s11101" xml:space="preserve"/> </p> <div xml:id="echoid-div1584" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0410-06" xlink:href="note-0410-06a" xml:space="preserve">749. 750</note> <note position="left" xlink:label="note-0410-07" xlink:href="note-0410-07a" xml:space="preserve">1081.</note> </div> <p> <s xml:id="echoid-s11102" xml:space="preserve">Fluida elaſtica diverſa diverſas proprietates habere, in <lb/> <anchor type="note" xlink:label="note-0410-08a" xlink:href="note-0410-08"/> dubium non facile vocari poteſt, quod etiam experimen-<lb/>tis conſtat; </s> <s xml:id="echoid-s11103" xml:space="preserve">effectus enim diverſarum exhalationum diffe-<lb/>runt inter ſe.</s> <s xml:id="echoid-s11104" xml:space="preserve"/> </p> <div xml:id="echoid-div1585" type="float" level="2" n="7"> <note position="left" xlink:label="note-0410-08" xlink:href="note-0410-08a" xml:space="preserve">1082.</note> </div> <pb o="307" file="0411" n="448" rhead="MATHEMATICA. LIB. II. CAP. XV."/> <p> <s xml:id="echoid-s11105" xml:space="preserve">Dum ſluida elaſtica in corporibus hærent, ad fluida ela-<lb/> <anchor type="note" xlink:label="note-0411-01a" xlink:href="note-0411-01"/> ſtica non magis referri poſſunt, quàm aqua, antequam in <lb/>vaporem convertatur, pro vapore haberi poteſt,</s> </p> <div xml:id="echoid-div1586" type="float" level="2" n="8"> <note position="right" xlink:label="note-0411-01" xlink:href="note-0411-01a" xml:space="preserve">1083.</note> </div> <p> <s xml:id="echoid-s11106" xml:space="preserve">Spatium autem occupatum, a materia elaſtica, dum in <lb/>ipſis corporibus hæret, exiguum admodum eſt collatum <lb/>cum ſpatio quod occupat, dum elaſticitatem exerit, præ-<lb/>cipue ſi parum comprimatur.</s> <s xml:id="echoid-s11107" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11108" xml:space="preserve">Aqua, dum ſe in vaporem convertit, licet hic a ponde-<lb/> <anchor type="note" xlink:label="note-0411-02a" xlink:href="note-0411-02"/> re totius atmoſphæræ comprimatur, ad mi imum decies & </s> <s xml:id="echoid-s11109" xml:space="preserve"><lb/>quater millies ſeſe expandit, inipſis illis locis ex quibus aë-<lb/>rem excludit; </s> <s xml:id="echoid-s11110" xml:space="preserve">hanc autem expanſionem in immenſum poſ-<lb/>ſe augeri, ſublata atmoſphæræ preſſione, quis non vi-<lb/>det?</s> <s xml:id="echoid-s11111" xml:space="preserve"/> </p> <div xml:id="echoid-div1587" type="float" level="2" n="9"> <note position="right" xlink:label="note-0411-02" xlink:href="note-0411-02a" xml:space="preserve">1084.</note> </div> <p> <s xml:id="echoid-s11112" xml:space="preserve">Aqua fluidum continet Elaſticum, quod calore, frigore, <lb/> <anchor type="note" xlink:label="note-0411-03a" xlink:href="note-0411-03"/> aut ſublata aëris preſſione ex hac ſeparatur, hancque ad-<lb/>modum ſubitaneam obſervamus ſeparationem, ſi ſubito o-<lb/>mnis preſſio tollatur.</s> <s xml:id="echoid-s11113" xml:space="preserve"/> </p> <div xml:id="echoid-div1588" type="float" level="2" n="10"> <note position="right" xlink:label="note-0411-03" xlink:href="note-0411-03a" xml:space="preserve">1085.</note> </div> </div> <div xml:id="echoid-div1590" type="section" level="1" n="378"> <head xml:id="echoid-head517" xml:space="preserve"><emph style="sc">Experimentum</emph> I.</head> <p> <s xml:id="echoid-s11114" xml:space="preserve">Vas vitreum AB exactiſſimè aqua repletur; </s> <s xml:id="echoid-s11115" xml:space="preserve">in extremi-<lb/> <anchor type="note" xlink:label="note-0411-04a" xlink:href="note-0411-04"/> tate B cum ipſo cohæret cylindrus æneus, ut, ope cochleæ, <lb/> <anchor type="note" xlink:label="note-0411-05a" xlink:href="note-0411-05"/> ipſi jungatur antlia, quæ in fig. </s> <s xml:id="echoid-s11116" xml:space="preserve">6, Tab 42. </s> <s xml:id="echoid-s11117" xml:space="preserve">exhibetur.</s> <s xml:id="echoid-s11118" xml:space="preserve"/> </p> <div xml:id="echoid-div1590" type="float" level="2" n="1"> <note position="right" xlink:label="note-0411-04" xlink:href="note-0411-04a" xml:space="preserve">1086.</note> <note position="right" xlink:label="note-0411-05" xlink:href="note-0411-05a" xml:space="preserve">TAB XXXVIII <lb/>fig. 8.</note> </div> <p> <s xml:id="echoid-s11119" xml:space="preserve">Dum antliæ embolus extrahitur, aqua gravitate in an-<lb/>tliam deſcendit, locuſque in ſuperiori vaſis parte aquâ & </s> <s xml:id="echoid-s11120" xml:space="preserve"><lb/>aëre vacuus datur. </s> <s xml:id="echoid-s11121" xml:space="preserve">Statim etiam ubique in aquâ innume-<lb/>ræ bullæ fluidi elaſtici, eodem momento, ſeſe demonſtrant, <lb/>totaque aqua hiſce bullis albeſcit.</s> <s xml:id="echoid-s11122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11123" xml:space="preserve">Fluidum hoc elaſticum ab aëre, quo Telluris ſuperficies <lb/> <anchor type="note" xlink:label="note-0411-06a" xlink:href="note-0411-06"/> obtegitur, differt, licet magnâ copiâ in aëre detur.</s> <s xml:id="echoid-s11124" xml:space="preserve"/> </p> <div xml:id="echoid-div1591" type="float" level="2" n="2"> <note position="right" xlink:label="note-0411-06" xlink:href="note-0411-06a" xml:space="preserve">1087.</note> </div> </div> <div xml:id="echoid-div1593" type="section" level="1" n="379"> <head xml:id="echoid-head518" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s11125" xml:space="preserve">Si phiala repleatur aquâ, ex qua igne, aut aliter, omne flui-<lb/> <anchor type="note" xlink:label="note-0411-07a" xlink:href="note-0411-07"/> dum elaſticum fuit expulſum, &</s> <s xml:id="echoid-s11126" xml:space="preserve">, relictâ exiguâ aëris bullâ, <lb/>invertatur phiala, aperturaque immergatur aquâ, vaſe quo-<lb/>cunque contentâ, bulla hæc aërea, in tempore aliquot die-<lb/>rum, tota intrabit in aquam, & </s> <s xml:id="echoid-s11127" xml:space="preserve">ſucceſſive eodem modo va-<lb/>riæ bullæ aquam intrant. </s> <s xml:id="echoid-s11128" xml:space="preserve">Sed reſpectu ſingularum hoc <pb o="308" file="0412" n="449" rhead="PHYSICES ELEMENTA"/> obſervandum, primo die partem multo majorem bullæ quam <lb/>diebus ſequentibus intrare.</s> <s xml:id="echoid-s11129" xml:space="preserve"/> </p> <div xml:id="echoid-div1593" type="float" level="2" n="1"> <note position="right" xlink:label="note-0411-07" xlink:href="note-0411-07a" xml:space="preserve">1088.</note> </div> <p> <s xml:id="echoid-s11130" xml:space="preserve">Ex hoc Experimento ſequitur dari partem aëris, quæ <lb/> <anchor type="note" xlink:label="note-0412-01a" xlink:href="note-0412-01"/> facilius in aquam intrat, ibique hæret, quàm reliquum <lb/>aëris.</s> <s xml:id="echoid-s11131" xml:space="preserve"/> </p> <div xml:id="echoid-div1594" type="float" level="2" n="2"> <note position="left" xlink:label="note-0412-01" xlink:href="note-0412-01a" xml:space="preserve">1089.</note> </div> <p> <s xml:id="echoid-s11132" xml:space="preserve">Unde ſequitur, dum aqua aëri aperto expoſita eſt, in ipſam <lb/>majori copia penetrare illius materiæ, quæ facilius intrat, & </s> <s xml:id="echoid-s11133" xml:space="preserve"><lb/>aërem, quiintravit, ab ipſo aëre externo differre, obſervamus <lb/>etiam ſæpe magis hocce fluidum imminuta preſſione ſeſe <lb/>dilatare quàm juxta regulam n. </s> <s xml:id="echoid-s11134" xml:space="preserve">1066. </s> <s xml:id="echoid-s11135" xml:space="preserve">Hujus autem fluidi ex-<lb/>panſio immenſa eſt.</s> <s xml:id="echoid-s11136" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11137" xml:space="preserve">Memorat Mariotte experimentum de dilatatione hujus <lb/> <anchor type="note" xlink:label="note-0412-02a" xlink:href="note-0412-02"/> materiæ elaſticæ, qua conſtat, materiam hanc, quæ alore ex <lb/>aqua fuerat expulſa, ubi refrigerata erat, & </s> <s xml:id="echoid-s11138" xml:space="preserve">pon@ustoti us at-<lb/>moſphæræ ſuſtinebat, occupaſſe ſpatium decuplum ſpatii ab <lb/>ipſa aqua, qua contenta fuerat, occupati.</s> <s xml:id="echoid-s11139" xml:space="preserve"/> </p> <div xml:id="echoid-div1595" type="float" level="2" n="3"> <note position="left" xlink:label="note-0412-02" xlink:href="note-0412-02a" xml:space="preserve">1090.</note> </div> <p> <s xml:id="echoid-s11140" xml:space="preserve">Conſtat etiam nunquam experimentis diminutionem vo-<lb/>luminis aquæ, dum materia elaſtica ex hac exit obſervari <lb/>potuiſſe.</s> <s xml:id="echoid-s11141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11142" xml:space="preserve">Tandem aliud memorat Mariotte experimentum, in quo <lb/>materia elaſtica, quæ aqua fuerat contenta, quatuor millies, <lb/>ſublata preſſione, magis expanſa fuit, quàm ubi preſſionem <lb/>atmoſphæræ ſuſtinuit.</s> <s xml:id="echoid-s11143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11144" xml:space="preserve">Collatis hiſce quis non videt, ſpatium ab hac materia, in <lb/> <anchor type="note" xlink:label="note-0412-03a" xlink:href="note-0412-03"/> ultimùm memorato experimento, occupatum, ad minimum, <lb/>variis vicibus, centum millies ſuperaſſe ſpatium, quod ipſa <lb/>in aqua occupabat.</s> <s xml:id="echoid-s11145" xml:space="preserve"/> </p> <div xml:id="echoid-div1596" type="float" level="2" n="4"> <note position="left" xlink:label="note-0412-03" xlink:href="note-0412-03a" xml:space="preserve">1091.</note> </div> <p> <s xml:id="echoid-s11146" xml:space="preserve">Ex quibus deducimus, fluidorum elaſticorum particulas <lb/> <anchor type="note" xlink:label="note-0412-04a" xlink:href="note-0412-04"/> non eſſe ejuſdem naturæ cum cæteris corporibus elaſticis, <lb/>nam non poſſunt particulæ ſingulæ centum millies, & </s> <s xml:id="echoid-s11147" xml:space="preserve">quod <lb/>excedit, ſeſe expandere ſervata ſuperficie, omni inæquali-<lb/>tate, aut angulo, experta; </s> <s xml:id="echoid-s11148" xml:space="preserve">in omni enim expanſione partes <lb/>facile moventur inter ſe: </s> <s xml:id="echoid-s11149" xml:space="preserve">unde ſequitur particulas ſeſe mu-<lb/>tuo non tangere, quamvis ſeſe invicem repellant, qualem par-<lb/>ticularum proprietatem ſuperius jam memoravimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11150" xml:space="preserve"/> </p> <div xml:id="echoid-div1597" type="float" level="2" n="5"> <note position="left" xlink:label="note-0412-04" xlink:href="note-0412-04a" xml:space="preserve">1092.</note> </div> <note symbol="*" position="left" xml:space="preserve">61.</note> <pb file="0413" n="450"/> <pb file="0413a" n="451"/> <figure> <image file="0413a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0413a-01"/> </figure> <pb file="0414" n="452"/> <pb o="309" file="0415" n="453" rhead="MATHEMATICA. LIB. II. CAP. XVI."/> </div> <div xml:id="echoid-div1599" type="section" level="1" n="380"> <head xml:id="echoid-head519" xml:space="preserve">CAPUT XVI.</head> <head xml:id="echoid-head520" style="it" xml:space="preserve">De Antlia Pneumatica.</head> <p> <s xml:id="echoid-s11151" xml:space="preserve">AEris elaſticitas fundamentum eſt conſtructionis Machi-<lb/> <anchor type="note" xlink:label="note-0415-01a" xlink:href="note-0415-01"/> næ, qua aër ex vaſe exhauritur. </s> <s xml:id="echoid-s11152" xml:space="preserve">Antlia Pneumati-<lb/>ca vocatur, quæ variis modis conſtruitur.</s> <s xml:id="echoid-s11153" xml:space="preserve"/> </p> <div xml:id="echoid-div1599" type="float" level="2" n="1"> <note position="right" xlink:label="note-0415-01" xlink:href="note-0415-01a" xml:space="preserve">1093.</note> </div> <p> <s xml:id="echoid-s11154" xml:space="preserve">In omnibus pars præcipua eſt cylindrus metallicus cavus, ab <lb/>interiori parte politus; </s> <s xml:id="echoid-s11155" xml:space="preserve">in hoc movetur embolus, exactiſſime <lb/>cum cylindri ſuperficie interiori congruens; </s> <s xml:id="echoid-s11156" xml:space="preserve">ne aëri tranſitus <lb/>ad latera detur. </s> <s xml:id="echoid-s11157" xml:space="preserve">Fundo cylindri embolus applicatur, deinde <lb/>elevatur, quo ex cylindri cavitate aër omnis excluditur. </s> <s xml:id="echoid-s11158" xml:space="preserve">Si <lb/>cum vaſe quocunque, per tubum in fundo cylindri, cavi-<lb/>tas hæc communicationem habeat, aër in vaſe ſeſe expan-<lb/>det, & </s> <s xml:id="echoid-s11159" xml:space="preserve">pro parte cylindrum intrabit, donec in cylindro & </s> <s xml:id="echoid-s11160" xml:space="preserve"><lb/>vaſe eandem habeat denſitatem. </s> <s xml:id="echoid-s11161" xml:space="preserve">Claudatur communicatio <lb/>inter vas & </s> <s xml:id="echoid-s11162" xml:space="preserve">cylindrum, aërque ex cylindro ejiciatur, & </s> <s xml:id="echoid-s11163" xml:space="preserve"><lb/>embolus fundo applicetur. </s> <s xml:id="echoid-s11164" xml:space="preserve">Si ſecunda vice embolus ele-<lb/>vetur, reſeratâ communicatione inter cylindrum & </s> <s xml:id="echoid-s11165" xml:space="preserve">vas me-<lb/>moratum, iterum aëris denſitas in vaſe minuetur; </s> <s xml:id="echoid-s11166" xml:space="preserve">& </s> <s xml:id="echoid-s11167" xml:space="preserve">repe-<lb/>tito emboli motu tandem aër in vaſe ad denſitatem mini-<lb/>mam reducetur. </s> <s xml:id="echoid-s11168" xml:space="preserve">aër tamen omnis hac methodo nunquam <lb/>exhauriri poteſt; </s> <s xml:id="echoid-s11169" xml:space="preserve">ſingulis enim vicibus aër ſeſe ita expandit, <lb/>ut eandem in cylindro denſitatem habeat ac in vaſe, in quo <lb/>ideò ſemper aër quidam ſupereſt.</s> <s xml:id="echoid-s11170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11171" xml:space="preserve">Antliæ omnes prædicta communia habent, in multis ta-<lb/> <anchor type="note" xlink:label="note-0415-02a" xlink:href="note-0415-02"/> men differunt. </s> <s xml:id="echoid-s11172" xml:space="preserve">1. </s> <s xml:id="echoid-s11173" xml:space="preserve">Variis modis clauditur & </s> <s xml:id="echoid-s11174" xml:space="preserve">reſeratur com-<lb/>municatio inter vas exhauriendum & </s> <s xml:id="echoid-s11175" xml:space="preserve">cylindrum. </s> <s xml:id="echoid-s11176" xml:space="preserve">2. </s> <s xml:id="echoid-s11177" xml:space="preserve">Variæ <lb/>dantur methodi, quibus aër ex cylindro expellitur, quan-<lb/>do embolus fundo admovetur. </s> <s xml:id="echoid-s11178" xml:space="preserve">3. </s> <s xml:id="echoid-s11179" xml:space="preserve">Emboli in variis antliis <lb/>differunt. </s> <s xml:id="echoid-s11180" xml:space="preserve">4. </s> <s xml:id="echoid-s11181" xml:space="preserve">Situs cylindri non in omnibus eſt idem. </s> <s xml:id="echoid-s11182" xml:space="preserve">5. </s> <s xml:id="echoid-s11183" xml:space="preserve">Di-<lb/>verſæ adhibentur machinæ, quibus embolus agitatur. <lb/></s> <s xml:id="echoid-s11184" xml:space="preserve">6. </s> <s xml:id="echoid-s11185" xml:space="preserve">Tandem duo ſæpe junguntur cylindri, in quorum uno <lb/>embolus elevatur, dum in alio deprimitur.</s> <s xml:id="echoid-s11186" xml:space="preserve"/> </p> <div xml:id="echoid-div1600" type="float" level="2" n="2"> <note position="right" xlink:label="note-0415-02" xlink:href="note-0415-02a" xml:space="preserve">1094.</note> </div> <p> <s xml:id="echoid-s11187" xml:space="preserve">Antlia noſtra hic delineatur; </s> <s xml:id="echoid-s11188" xml:space="preserve">pars oppoſita thecæ, non <lb/> <anchor type="note" xlink:label="note-0415-03a" xlink:href="note-0415-03"/> <pb o="310" file="0416" n="454" rhead="PHYSICES ELEMENTA"/> apertâ januâ, quæ ad illam partem datur, videtur in fig. </s> <s xml:id="echoid-s11189" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s11190" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11191" xml:space="preserve">43. </s> <s xml:id="echoid-s11192" xml:space="preserve">Antliæ hujus deſcriptionem non dabo, ge-<lb/>neralia tantum quædam notabo, peculiarem omnium par-<lb/>tium explicationem alia occaſione daturus.</s> <s xml:id="echoid-s11193" xml:space="preserve"/> </p> <div xml:id="echoid-div1601" type="float" level="2" n="3"> <note position="right" xlink:label="note-0415-03" xlink:href="note-0415-03a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 1.</note> </div> </div> <div xml:id="echoid-div1603" type="section" level="1" n="381"> <head xml:id="echoid-head521" xml:space="preserve"><emph style="sc">Machina</emph> <emph style="sc">Pneumatica</emph>.</head> <p> <s xml:id="echoid-s11194" xml:space="preserve">In fig. </s> <s xml:id="echoid-s11195" xml:space="preserve">1. </s> <s xml:id="echoid-s11196" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11197" xml:space="preserve">39. </s> <s xml:id="echoid-s11198" xml:space="preserve">antlia repræſentatur a parte antica, <lb/> <anchor type="note" xlink:label="note-0416-01a" xlink:href="note-0416-01"/> ſublatis nempe thecæ, cui includitur, januis.</s> <s xml:id="echoid-s11199" xml:space="preserve"/> </p> <div xml:id="echoid-div1603" type="float" level="2" n="1"> <note position="left" xlink:label="note-0416-01" xlink:href="note-0416-01a" xml:space="preserve">1095.</note> </div> <p> <s xml:id="echoid-s11200" xml:space="preserve">Antlia eadem, ex theca extracta, a parte poſtica, deli-<lb/>neatur in fig. </s> <s xml:id="echoid-s11201" xml:space="preserve">1. </s> <s xml:id="echoid-s11202" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11203" xml:space="preserve">40. </s> <s xml:id="echoid-s11204" xml:space="preserve">liſdem litteris eædem partes in <lb/>utraque figura notantur.</s> <s xml:id="echoid-s11205" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11206" xml:space="preserve">Conſtat antlia duobus cylindris, A, B; </s> <s xml:id="echoid-s11207" xml:space="preserve">in utroque mo-<lb/>vetur embolus, cujus partes ſeparatæ exhibentur in C, D, E, F, <lb/>(fig. </s> <s xml:id="echoid-s11208" xml:space="preserve">2. </s> <s xml:id="echoid-s11209" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11210" xml:space="preserve">40.)</s> <s xml:id="echoid-s11211" xml:space="preserve">.</s> <s xml:id="echoid-s11212" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11213" xml:space="preserve">Partes E, F, cochleâ junguntur, & </s> <s xml:id="echoid-s11214" xml:space="preserve">inter ipſas firmatur <lb/> <anchor type="note" xlink:label="note-0416-02a" xlink:href="note-0416-02"/> annulus coriaceus, qui ab omni parte prominet, & </s> <s xml:id="echoid-s11215" xml:space="preserve">qui, <lb/>dum embolus cylindro intruditur, ſeſe ſuperficiei e e ap-<lb/>plicat. </s> <s xml:id="echoid-s11216" xml:space="preserve">Methodus hæc in Anglia in uſu eſt. </s> <s xml:id="echoid-s11217" xml:space="preserve">Corium hoc-<lb/>ce in oleo & </s> <s xml:id="echoid-s11218" xml:space="preserve">aqua macerari debet, ut monuimus in n. </s> <s xml:id="echoid-s11219" xml:space="preserve">722.</s> <s xml:id="echoid-s11220" xml:space="preserve"/> </p> <div xml:id="echoid-div1604" type="float" level="2" n="2"> <note position="left" xlink:label="note-0416-02" xlink:href="note-0416-02a" xml:space="preserve">TAB. XL. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s11221" xml:space="preserve">Embolis, quando antliis intruduntur, aqua ſuperinfunditur, <lb/>cujus aliquando, exſiccatis paululum coriis, pars quædam in <lb/>antlias deſcendit, quod tamen experimenta turbare non po-<lb/>teſt; </s> <s xml:id="echoid-s11222" xml:space="preserve">in quo caſu emboli extrahendi ſunt & </s> <s xml:id="echoid-s11223" xml:space="preserve">per aliquotho-<lb/>ras in aqua relinquendi, oleoque probe eliniri debent.</s> <s xml:id="echoid-s11224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11225" xml:space="preserve">Cauda C emboli, ut fere in omnibus antliis, dentata eſt; <lb/></s> <s xml:id="echoid-s11226" xml:space="preserve">hujus extremitas inferior cc cylindrica eſt, & </s> <s xml:id="echoid-s11227" xml:space="preserve">cochleâ ter-<lb/>minatur. </s> <s xml:id="echoid-s11228" xml:space="preserve">Transmittitur cylindrica pars hæc per cavitatem <lb/>cylindricam in prominentia f emboli; </s> <s xml:id="echoid-s11229" xml:space="preserve">cujus cavitatis dia-<lb/>meter parum tantum ſuperat cylindri c c diametrum. </s> <s xml:id="echoid-s11230" xml:space="preserve">Cum <lb/>hoc conjungitur nunc conus truncatus D, qui cochleam <lb/>fæminam continet, & </s> <s xml:id="echoid-s11231" xml:space="preserve">firmatur hic transverſâ cochleâ g: </s> <s xml:id="echoid-s11232" xml:space="preserve"><lb/>poteſtque cauda C elevari & </s> <s xml:id="echoid-s11233" xml:space="preserve">deprimi per ſpatium trium <lb/>partium quartarum pollicis, ipſo embolo immoto manente.</s> <s xml:id="echoid-s11234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11235" xml:space="preserve">Emboli ambo moventur agitatione rotæ R, cujus motus, <lb/> <anchor type="note" xlink:label="note-0416-03a" xlink:href="note-0416-03"/> dum it & </s> <s xml:id="echoid-s11236" xml:space="preserve">redit, parum deficit à tertiâ circuli parte.</s> <s xml:id="echoid-s11237" xml:space="preserve"/> </p> <div xml:id="echoid-div1605" type="float" level="2" n="3"> <note position="left" xlink:label="note-0416-03" xlink:href="note-0416-03a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 1.</note> </div> <note position="left" xml:space="preserve">TAB. XL. <lb/>fig. 1.</note> <p> <s xml:id="echoid-s11238" xml:space="preserve">Vaſa exhaurienda laminæ L L imponuntur, & </s> <s xml:id="echoid-s11239" xml:space="preserve">hæc per <pb o="311" file="0417" n="455" rhead="MATHEMATICA. LIB. II. CAP. XVI."/> tubum D communicationem habent cum antliis. </s> <s xml:id="echoid-s11240" xml:space="preserve">Da-<lb/>tur enim infra laminam L L, cavitas quæ tubo E E reſpon-<lb/>det, in quo duo dantur epiſtomia, inter quæ cum tubo <lb/>hoc conjungitur tubus OO, qui infra laminam, cui antliæ <lb/>imponuntur, cum his communicatur.</s> <s xml:id="echoid-s11241" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11242" xml:space="preserve">Antliæ ſingulæ epiſtomium infra fundum ſuum habent, <lb/>horum caudæ videntur in G, G, quæ regulis æneis ad ſe <lb/>invicem applicatis junguntur ita, ut motu harum regularum <lb/>epiſtomia ambo eodem tempore moveantur. </s> <s xml:id="echoid-s11243" xml:space="preserve">Inter regulas, <lb/>in medio longitudinis, rotula ænea datur T. </s> <s xml:id="echoid-s11244" xml:space="preserve">Cum a-<lb/>xe rotæ R a poſtica parte jungitur crux ferrea HKNM, <lb/>qua epiſtomia hæc agitantur.</s> <s xml:id="echoid-s11245" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11246" xml:space="preserve">In ſitu in quo partes machinæ in his figuris repræſentan-<lb/>tur, antlia B cum vaſe exhauriendo communicationem ha-<lb/>bet, antlia A cum aëre externo; </s> <s xml:id="echoid-s11247" xml:space="preserve">& </s> <s xml:id="echoid-s11248" xml:space="preserve">deprimendo hujus an-<lb/>tliæ embolum omnis aër ex hac ejicitur, & </s> <s xml:id="echoid-s11249" xml:space="preserve">interea magis <lb/>elevatur embolus alter.</s> <s xml:id="echoid-s11250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11251" xml:space="preserve">Ubi verò embolus fundo antliæ A applicatur, extremi-<lb/>tas N crucis ad n pertingit, in quo motu ſuper rotulâ <lb/>T tranſit, hancque in motu radit; </s> <s xml:id="echoid-s11252" xml:space="preserve">Eo autem momento <lb/>quo N tranſit ſuper T, clavus, aut cylindrus, ferreus K, <lb/>ad vectem CF, ferreum, incurvatum, circa P mobilem, <lb/>in b accedit; </s> <s xml:id="echoid-s11253" xml:space="preserve">huncque premit in motu puncti N à T ad n.</s> <s xml:id="echoid-s11254" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11255" xml:space="preserve">Rotatur interea vectis circa centrum P, & </s> <s xml:id="echoid-s11256" xml:space="preserve">extremitas F <lb/>in rotulam T premit, hancque elevat; </s> <s xml:id="echoid-s11257" xml:space="preserve">quo ſitus epiſto-<lb/>miorum paululum quidem mutatur, non tamen me-<lb/>moratæ communicationes antliæ B cum vaſe exhauriendo, <lb/>& </s> <s xml:id="echoid-s11258" xml:space="preserve">A cum aëre externo, obturantur.</s> <s xml:id="echoid-s11259" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11260" xml:space="preserve">Motus rotæ nunc in contrariam partem dirigendus eſt. <lb/></s> <s xml:id="echoid-s11261" xml:space="preserve">Ubi in reditu punctum N ab n ad T pervenit, quia rotula <lb/>elevata fuit, in hanc incurrit crucis extremum, trochleam-<lb/>que propellit, donec converſione epiſtomiorum G, G, ita <lb/>deprimatur, ut ſuper hac tranſeat N.</s> <s xml:id="echoid-s11262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11263" xml:space="preserve">In hac epiſtomiorum converſione, G, G, arcus deſcri-<lb/>bunt, qui paululum tantum excedunt gradus nonaginta;</s> <s xml:id="echoid-s11264" xml:space="preserve"> <pb o="312" file="0418" n="456" rhead="PHYSICES ELEMENTA"/> clauditurque communicatio antliæ B cum vaſe, & </s> <s xml:id="echoid-s11265" xml:space="preserve">nova <lb/>cum aëre externo reſeratur; </s> <s xml:id="echoid-s11266" xml:space="preserve">contrarium reſpectu antliæ A <lb/>locum habet.</s> <s xml:id="echoid-s11267" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11268" xml:space="preserve">Durante hac epiſtomiorum agitatione, elevatur quidem <lb/>Q, ſed embolusipſe fundo antliæ A applicatus manet; </s> <s xml:id="echoid-s11269" xml:space="preserve">quod <lb/>deſideratur ne aër externus iterum in antliam intret, & </s> <s xml:id="echoid-s11270" xml:space="preserve"><lb/>quod quomodo fiat in deſcriptione embolorum dixi-<lb/>mus.</s> <s xml:id="echoid-s11271" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11272" xml:space="preserve">Si nunc motus rotæ continuetur, elevatur embolus an-<lb/>tliæ A, quæ cum vaſe exhauriendo communicationem ha-<lb/>bet, & </s> <s xml:id="echoid-s11273" xml:space="preserve">ex antlia B aër ejicitur, extremitasque M crucis ſu-<lb/>per rotula T tranſit, clavuſque K in vectem Spremit, & </s> <s xml:id="echoid-s11274" xml:space="preserve"><lb/>quæ in motu contrario fuere explicata, in hoc caſu eodem <lb/>modo, obtinent.</s> <s xml:id="echoid-s11275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11276" xml:space="preserve">Rota agitatur manubrio MM, cujus longitudo eſt cir-<lb/> <anchor type="note" xlink:label="note-0418-01a" xlink:href="note-0418-01"/> citer duorum pedum, & </s> <s xml:id="echoid-s11277" xml:space="preserve">quod in ſitu datur horizontali, dum <lb/>pars HK crucis eſt verticalis.</s> <s xml:id="echoid-s11278" xml:space="preserve"/> </p> <div xml:id="echoid-div1606" type="float" level="2" n="4"> <note position="left" xlink:label="note-0418-01" xlink:href="note-0418-01a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s11279" xml:space="preserve">Quando in hac agitatione contingit, majorem dari reſi-<lb/>ſtentiam, ubi epiſtomia moventur, quàm in reliquo motu, <lb/>indicium hoc eſt, oleo & </s> <s xml:id="echoid-s11280" xml:space="preserve">cerâ eliniri debere epiſtomia; </s> <s xml:id="echoid-s11281" xml:space="preserve">quod <lb/>in tempeſtate calidiori repeti debet, ubi per tres aut qua-<lb/>tuor horas machina in continuo fuit motu.</s> <s xml:id="echoid-s11282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11283" xml:space="preserve">Quod ſpectat epiſtomia E, E, ſuperius memorata, uno, <lb/>communicatio, exhauſtio aëre, clauditur inter vas exhau-<lb/>ſtum & </s> <s xml:id="echoid-s11284" xml:space="preserve">cylindros; </s> <s xml:id="echoid-s11285" xml:space="preserve">altero, aër de novo vaſe intromittitur, <lb/>& </s> <s xml:id="echoid-s11286" xml:space="preserve">cummunicatio impeditur cum indice mercuriali.</s> <s xml:id="echoid-s11287" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11288" xml:space="preserve">Index hicce mercurialis in hac figura commode repræ-<lb/>ſentari non potuit; </s> <s xml:id="echoid-s11289" xml:space="preserve">hujus uſus eſt determinatio quantitatis <lb/>aëris ex vaſe exhauſti, ut & </s> <s xml:id="echoid-s11290" xml:space="preserve">quantitatis in hoc ſuperſtitis; <lb/></s> <s xml:id="echoid-s11291" xml:space="preserve">eo etiam vaſorum exhauriendorum capacitates menſurantur; </s> <s xml:id="echoid-s11292" xml:space="preserve"><lb/>quæ ut exacte notæ ſint in variis Experimetis deſideratur; </s> <s xml:id="echoid-s11293" xml:space="preserve"><lb/>index noſter a vulgaribus differt.</s> <s xml:id="echoid-s11294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11295" xml:space="preserve">In D ſæpe ope cochleæ orbi jungitur cylindrus parvus, <lb/>cochlea circumdatus, quo globus exhauriendus, aut vas ali-<lb/>ud, machinæ applicari poteſt,</s> </p> <pb file="0419" n="457"/> <pb file="0419a" n="458"/> <figure> <image file="0419a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0419a-01"/> </figure> <pb file="0420" n="459"/> <pb o="313" file="0421" n="460" rhead="MATHEMATICA. LIB. II. CAP. XVI."/> <p> <s xml:id="echoid-s11296" xml:space="preserve">In medio Orbis LL foramen datur, quod cochleâ clau-<lb/>ditur, ſed quo machinæ variæ cum orbe jungi queunt,</s> </p> <p> <s xml:id="echoid-s11297" xml:space="preserve">Sæpe hac methodo orbi adaptatur pyxis cylindrica, or-<lb/> <anchor type="note" xlink:label="note-0421-01a" xlink:href="note-0421-01"/> bibus coriaceis, cerâ imbutis, repleta, per quorum centra <lb/>tranſmittitur filum æneum, quod ope manubrii agitari po-<lb/>teſt, quæ agitatio communicatur in loco aëre vacuo; </s> <s xml:id="echoid-s11298" xml:space="preserve">co-<lb/>chleâ circumdatur, & </s> <s xml:id="echoid-s11299" xml:space="preserve">pyxidem intrat hujus operculum, quo <lb/>coria comprimuntur, ut exactius tranſitum aëris impe-<lb/>diant.</s> <s xml:id="echoid-s11300" xml:space="preserve"/> </p> <div xml:id="echoid-div1607" type="float" level="2" n="5"> <note position="right" xlink:label="note-0421-01" xlink:href="note-0421-01a" xml:space="preserve">1096.</note> </div> <p> <s xml:id="echoid-s11301" xml:space="preserve">Pyxis ſimilis ſæpe jungitur operculo, quod vaſis exhau-<lb/>riendis ſuperimponitur, ut videtur in fig. </s> <s xml:id="echoid-s11302" xml:space="preserve">3. </s> <s xml:id="echoid-s11303" xml:space="preserve">Tab 41. </s> <s xml:id="echoid-s11304" xml:space="preserve">& </s> <s xml:id="echoid-s11305" xml:space="preserve"><lb/>in fig. </s> <s xml:id="echoid-s11306" xml:space="preserve">2. </s> <s xml:id="echoid-s11307" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11308" xml:space="preserve">47.</s> <s xml:id="echoid-s11309" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11310" xml:space="preserve">Quando vaſa orbi LL imponuntur; </s> <s xml:id="echoid-s11311" xml:space="preserve">aut quando operculis <lb/> <anchor type="note" xlink:label="note-0421-02a" xlink:href="note-0421-02"/> vaſa obteguntur, aut quando cochleis machinæ junguntur, <lb/>& </s> <s xml:id="echoid-s11312" xml:space="preserve">in genere quando aëris ingreſſus cohibendus eſt, utimur <lb/>mixto ex quatuor partibus ceræ albæ, duabus reſinæ, & </s> <s xml:id="echoid-s11313" xml:space="preserve"><lb/>una olei olivarum, æſtate minor, hieme major olei copia de-<lb/>ſideratur. </s> <s xml:id="echoid-s11314" xml:space="preserve">In multis experimentis ſatis eſt, ſi vaſa corio <lb/>madido ſuperimponantur.</s> <s xml:id="echoid-s11315" xml:space="preserve"/> </p> <div xml:id="echoid-div1608" type="float" level="2" n="6"> <note position="right" xlink:label="note-0421-02" xlink:href="note-0421-02a" xml:space="preserve">1097.</note> </div> </div> <div xml:id="echoid-div1610" type="section" level="1" n="382"> <head xml:id="echoid-head522" xml:space="preserve">CAPUT XVII.</head> <head xml:id="echoid-head523" style="it" xml:space="preserve">Experimenta varia circa Aëris Gravitatem & <lb/>hujus Elaſticitatem.</head> <p> <s xml:id="echoid-s11316" xml:space="preserve">AErem gravem eſſe vidimus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s11317" xml:space="preserve">poteſt ut cetera corpo- <anchor type="note" xlink:label="note-0421-03a" xlink:href="note-0421-03"/> ra ponderari, & </s> <s xml:id="echoid-s11318" xml:space="preserve">hujus denſitas cum ceterorum cor-<lb/> <anchor type="note" xlink:label="note-0421-04a" xlink:href="note-0421-04"/> porum denſitate conferri <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11319" xml:space="preserve">Si vas idem aërem continens, <anchor type="note" xlink:label="note-0421-05a" xlink:href="note-0421-05"/> ut & </s> <s xml:id="echoid-s11320" xml:space="preserve">exhauſto aëre, ponderetur, ponderum differentia e-<lb/>rit aëris pondus; </s> <s xml:id="echoid-s11321" xml:space="preserve">quæ methodus hoc incommodi habet, <lb/>quod ſæpe bilance, etiam exactiſſimâ, pondere magno gra-<lb/>vatâ, ponderum differentiæ minores exactè non detegan-<lb/>tur; </s> <s xml:id="echoid-s11322" xml:space="preserve">ſequenti in hoc caſu methodo utendum.</s> <s xml:id="echoid-s11323" xml:space="preserve"/> </p> <div xml:id="echoid-div1610" type="float" level="2" n="1"> <note position="right" xlink:label="note-0421-03" xlink:href="note-0421-03a" xml:space="preserve">1098.</note> <note symbol="*" position="right" xlink:label="note-0421-04" xlink:href="note-0421-04a" xml:space="preserve">1055.</note> <note symbol="*" position="right" xlink:label="note-0421-05" xlink:href="note-0421-05a" xml:space="preserve">737.</note> </div> </div> <div xml:id="echoid-div1612" type="section" level="1" n="383"> <head xml:id="echoid-head524" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <note position="right" xml:space="preserve">1099.</note> <p> <s xml:id="echoid-s11324" xml:space="preserve">Exhauſto aëre ex globo vitreo, cujus capacitas eſt 283. <lb/></s> <s xml:id="echoid-s11325" xml:space="preserve"> <anchor type="note" xlink:label="note-0421-07a" xlink:href="note-0421-07"/> <pb o="314" file="0422" n="461" rhead="PHYSICES ELEMENTA"/> pollicum cubicorum, & </s> <s xml:id="echoid-s11326" xml:space="preserve">pondere tali huic adjuncto, ut gra-<lb/>vitate ſpecifica aquæ gravitatem ſpecificam fere æquet, <lb/>aquâ vaſe DE contentâ globus immergatur, filo jungatur <lb/>unco adhærenti lanci libræ AB, de qua ſuperius <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11327" xml:space="preserve">Ele- <anchor type="note" xlink:label="note-0422-01a" xlink:href="note-0422-01"/> vetur bilanx, donec pondere minimo æquilibrium detur; <lb/></s> <s xml:id="echoid-s11328" xml:space="preserve">ſi, aperto epiſtomio, aër globum intret, in lance oppoſita, <lb/>ut æquilibrium inſtauretur, requiritur pondus P circiter <lb/>centum granorum, aliquando majus, ſæpe minus, pro di-<lb/>verſa aëris conftitutione, quæ pondere Atmoſphæræ muta-<lb/>to, & </s> <s xml:id="echoid-s11329" xml:space="preserve">aliis de cauſis, variationem ſubit.</s> <s xml:id="echoid-s11330" xml:space="preserve"/> </p> <div xml:id="echoid-div1612" type="float" level="2" n="1"> <note position="right" xlink:label="note-0421-07" xlink:href="note-0421-07a" xml:space="preserve">TAB XLII. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0422-01" xlink:href="note-0422-01a" xml:space="preserve">705.</note> </div> <p> <s xml:id="echoid-s11331" xml:space="preserve">Cùm autem nactus ſim bilancem, quæ, quamvis ponde-<lb/>re aliquot librarum gravata, minimam differentiam indicat, <lb/>immerſionem in aquam negligo, ubi aëris pondus deter-<lb/>minare ſuſcipio.</s> <s xml:id="echoid-s11332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11333" xml:space="preserve">Corpora fluidis immerſa ab iis ſuſtinentur, magiſque aut <lb/>minus pro volumine corporis majori aut minori <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11334" xml:space="preserve">pon- <anchor type="note" xlink:label="note-0422-02a" xlink:href="note-0422-02"/> dus amiſſum ex nota fluidi denſitate determinatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11335" xml:space="preserve">Præ- <anchor type="note" xlink:label="note-0422-03a" xlink:href="note-0422-03"/> cedenti Experimento cognoſcitur ergo, quantum corpora in <lb/>aëre minus quam in vacuo gravitent.</s> <s xml:id="echoid-s11336" xml:space="preserve"/> </p> <div xml:id="echoid-div1613" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0422-02" xlink:href="note-0422-02a" xml:space="preserve">756.</note> <note symbol="*" position="left" xlink:label="note-0422-03" xlink:href="note-0422-03a" xml:space="preserve">751.</note> </div> <p style="it"> <s xml:id="echoid-s11337" xml:space="preserve">Ex his etiam deducimus, corpora in æquilibrio in aëre, <lb/> <anchor type="note" xlink:label="note-0422-04a" xlink:href="note-0422-04"/> ſi horum volumina fuerint inæqualia, in loco aëre vacuo <lb/>non æque ponder are, quod confirmatur ſequenti Experi-<lb/>mento.</s> <s xml:id="echoid-s11338" xml:space="preserve"/> </p> <div xml:id="echoid-div1614" type="float" level="2" n="3"> <note position="left" xlink:label="note-0422-04" xlink:href="note-0422-04a" xml:space="preserve">1100.</note> </div> </div> <div xml:id="echoid-div1616" type="section" level="1" n="384"> <head xml:id="echoid-head525" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s11339" xml:space="preserve">Lancibus bilancis a b imponuntur fruſtum ceræ c & </s> <s xml:id="echoid-s11340" xml:space="preserve">pon-<lb/> <anchor type="note" xlink:label="note-0422-05a" xlink:href="note-0422-05"/> dus metallicum p, & </s> <s xml:id="echoid-s11341" xml:space="preserve">datur æquilibrium. </s> <s xml:id="echoid-s11342" xml:space="preserve">Bilanx in reci-<lb/>piente vitreo ſuſpenditur, & </s> <s xml:id="echoid-s11343" xml:space="preserve">aere exhauſto præponderat ce-<lb/>ra, cujus volumen ſuperat volumen corporis p, & </s> <s xml:id="echoid-s11344" xml:space="preserve">magis ab <lb/>aëre ſuſtinetur, quando hic in recipiente admittitur, quo <lb/>æquilibrium inſtauratur.</s> <s xml:id="echoid-s11345" xml:space="preserve"/> </p> <div xml:id="echoid-div1616" type="float" level="2" n="1"> <note position="left" xlink:label="note-0422-05" xlink:href="note-0422-05a" xml:space="preserve">TAB. XLI. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s11346" xml:space="preserve">Aëris elaſticitas, in capite 14. </s> <s xml:id="echoid-s11347" xml:space="preserve">probata, magis fit ſenſi-<lb/>bilis Experimento ſequenti.</s> <s xml:id="echoid-s11348" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1618" type="section" level="1" n="385"> <head xml:id="echoid-head526" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s11349" xml:space="preserve">Veſica exacte clauſa parvam admodum aëris quantitatem-<lb/> <anchor type="note" xlink:label="note-0422-06a" xlink:href="note-0422-06"/> contineat, vitro tegatur, & </s> <s xml:id="echoid-s11350" xml:space="preserve">exhauriatur aër, quo preſſio <pb file="0423" n="462"/> <pb file="0423a" n="463"/> <anchor type="figure" xlink:label="fig-0423a-01a" xlink:href="fig-0423a-01"/> <pb file="0424" n="464"/> <pb o="315" file="0425" n="465" rhead="MATHEMATICA. LIB. II. CAP. XVII."/> in veſicæ ſuperficiem exteriorem minuitur; </s> <s xml:id="echoid-s11351" xml:space="preserve">eodem <lb/>tempore aë veſicæ incluſus ſeſe expandet, & </s> <s xml:id="echoid-s11352" xml:space="preserve">hæc inflabi-<lb/>tur.</s> <s xml:id="echoid-s11353" xml:space="preserve"/> </p> <div xml:id="echoid-div1618" type="float" level="2" n="1"> <note position="left" xlink:label="note-0422-06" xlink:href="note-0422-06a" xml:space="preserve">1101.</note> <figure xlink:label="fig-0423a-01" xlink:href="fig-0423a-01a"> <image file="0423a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0423a-01"/> </figure> </div> <p> <s xml:id="echoid-s11354" xml:space="preserve">Elaſticitatis vim totius Atmoſphæræ ponderi æquari vi-<lb/>dimus; </s> <s xml:id="echoid-s11355" xml:space="preserve">effectus hujus vis ſub oculos ſequenti Experimento <lb/>ponitur.</s> <s xml:id="echoid-s11356" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1620" type="section" level="1" n="386"> <head xml:id="echoid-head527" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s11357" xml:space="preserve">Veſica exacte clauſa, & </s> <s xml:id="echoid-s11358" xml:space="preserve">aëre pro parte tantum repleta, <lb/> <anchor type="note" xlink:label="note-0425-01a" xlink:href="note-0425-01"/> pyxidi æneæ A, cujus diameter eſt trium pollicum cum ſe-<lb/> <anchor type="note" xlink:label="note-0425-02a" xlink:href="note-0425-02"/> miſſe, includitur, obtegiturque hæc operculo ligneo, aut <lb/>plumbeo, quod in ipſam pyxidem penetrat ita, ut quamvis e-<lb/>levetur non decidat.</s> <s xml:id="echoid-s11359" xml:space="preserve"/> </p> <div xml:id="echoid-div1620" type="float" level="2" n="1"> <note position="right" xlink:label="note-0425-01" xlink:href="note-0425-01a" xml:space="preserve">1102.</note> <note position="right" xlink:label="note-0425-02" xlink:href="note-0425-02a" xml:space="preserve">TAB. XLI. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s11360" xml:space="preserve">Operculo pondera plumbea P, P, imponuntur, habent hæc <lb/>foramen in medio, & </s> <s xml:id="echoid-s11361" xml:space="preserve">trajiciuntur cylindro E, cum oper-<lb/>culo cohærenti. </s> <s xml:id="echoid-s11362" xml:space="preserve">Exhauſto aëre veſica, ut in præcedenti Ex-<lb/>perimento, inflatur, quo pondera elevantur. </s> <s xml:id="echoid-s11363" xml:space="preserve">Plura pro vitri <lb/>magnitudine adhibentur pondera, & </s> <s xml:id="echoid-s11364" xml:space="preserve">licet borum ſumma ſe-<lb/>xaginta aut ſeptuaginta libras ſuperet, facillime elevantur.</s> <s xml:id="echoid-s11365" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11366" xml:space="preserve">Aëris gravitas, hujus preſſio quæ ex gravitate oritur, ut <lb/>& </s> <s xml:id="echoid-s11367" xml:space="preserve">elaſticitas, effectus varios notabiles edunt; </s> <s xml:id="echoid-s11368" xml:space="preserve">quoſdam ſe-<lb/>ligam, & </s> <s xml:id="echoid-s11369" xml:space="preserve">Experimentis confirmabo.</s> <s xml:id="echoid-s11370" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1622" type="section" level="1" n="387"> <head xml:id="echoid-head528" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s11371" xml:space="preserve">Foramini in medio orbis LL antliæ pneumaticæ, in in-<lb/> <anchor type="note" xlink:label="note-0425-03a" xlink:href="note-0425-03"/> feriori parte, ope cochleæ, jungitur cylindrus æneus per-<lb/> <anchor type="note" xlink:label="note-0425-04a" xlink:href="note-0425-04"/> foratus, cohærens cum tubo vitreo AB, ab utraque parte <lb/>aperto, cujus extremitas B mercurio immergitur. </s> <s xml:id="echoid-s11372" xml:space="preserve">In tu-<lb/>bo e g, clauſo in e, & </s> <s xml:id="echoid-s11373" xml:space="preserve">aëre vacuo, mercurius ſuſtinetur, ut <lb/>antea dictum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11374" xml:space="preserve">Vas V cum tubo orbi L L imponitur &</s> <s xml:id="echoid-s11375" xml:space="preserve"> <anchor type="note" xlink:label="note-0425-05a" xlink:href="note-0425-05"/> vitro D C obtegitur, quo omnis communicatio tollitur in-<lb/>ter aërem exteriorem & </s> <s xml:id="echoid-s11376" xml:space="preserve">vas V, quod cum cavitate tubi AB <lb/>communicatur. </s> <s xml:id="echoid-s11377" xml:space="preserve">Aër in hoc tubo elaſticitate ſua impedit, <lb/>ne mercurius preſſione aëris externi, in tubum adſcendat; <lb/></s> <s xml:id="echoid-s11378" xml:space="preserve">aër etiam recipienti DC incluſus elaſticitate ſuſtinet mer-<lb/>curium in tubo g e <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11379" xml:space="preserve">Ex vaſe DC aër exhauriatur; </s> <s xml:id="echoid-s11380" xml:space="preserve">dum <anchor type="note" xlink:label="note-0425-06a" xlink:href="note-0425-06"/> denſitas minuitur, elaſticitas etiam decreſcit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11381" xml:space="preserve">minor <anchor type="note" xlink:label="note-0425-07a" xlink:href="note-0425-07"/> <pb o="316" file="0426" n="466" rhead="PHYSICES ELEMENTA"/> eſt vis cum qua mercurius in tubo g e ſuſtinetur, deſcendit <lb/>ergo hydrargyrum. </s> <s xml:id="echoid-s11382" xml:space="preserve">Eodem tempore reſiſtentiam in tubo <lb/>AB vincit preſſio aëris externi, & </s> <s xml:id="echoid-s11383" xml:space="preserve">in tubum mercurius ad-<lb/>ſcendit. </s> <s xml:id="echoid-s11384" xml:space="preserve">Diminutio elaſticitatis in tubo AB, & </s> <s xml:id="echoid-s11385" xml:space="preserve">in vaſe <lb/>BC, eadem eſt, & </s> <s xml:id="echoid-s11386" xml:space="preserve">effectus diminutionis in utroque caſu <lb/>idem: </s> <s xml:id="echoid-s11387" xml:space="preserve">idcirco tantum in tubo e g deſcendit mercurius, <lb/>quantum adſcendit in tubum AB, quod cum Experimen-<lb/>to congruit. </s> <s xml:id="echoid-s11388" xml:space="preserve">Elevatur hac methodo mercurius ad f, dum <lb/>tubus g e fere omnino vacuus remanet; </s> <s xml:id="echoid-s11389" xml:space="preserve">admiſſo iterum <lb/>aëre, mercurius in tubum g e adſcendit, dum in tubo AB <lb/>deprimitur.</s> <s xml:id="echoid-s11390" xml:space="preserve"/> </p> <div xml:id="echoid-div1622" type="float" level="2" n="1"> <note position="right" xlink:label="note-0425-03" xlink:href="note-0425-03a" xml:space="preserve">1103.</note> <note position="right" xlink:label="note-0425-04" xlink:href="note-0425-04a" xml:space="preserve">TAB. XXXIX. <lb/>fig. 3.</note> <note position="right" xlink:label="note-0425-05" xlink:href="note-0425-05a" xml:space="preserve">* 1056.</note> <note position="right" xlink:label="note-0425-06" xlink:href="note-0425-06a" xml:space="preserve">* 1073.</note> <note position="right" xlink:label="note-0425-07" xlink:href="note-0425-07a" xml:space="preserve">* 1071.</note> </div> </div> <div xml:id="echoid-div1624" type="section" level="1" n="388"> <head xml:id="echoid-head529" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s11391" xml:space="preserve">Detur antlia A, cujus embolus fundo applicetur, tubus <lb/> <anchor type="note" xlink:label="note-0426-01a" xlink:href="note-0426-01"/> cum antlia cohærens aquâ immergatur; </s> <s xml:id="echoid-s11392" xml:space="preserve">elevetur embolus, <lb/> <anchor type="note" xlink:label="note-0426-02a" xlink:href="note-0426-02"/> inſequetur illum aqua; </s> <s xml:id="echoid-s11393" xml:space="preserve">hæcque cavum inter antliæ fundum <lb/>& </s> <s xml:id="echoid-s11394" xml:space="preserve">embolum implebit, quod ex preſſione aëris exterioris o-<lb/>ritur.</s> <s xml:id="echoid-s11395" xml:space="preserve"/> </p> <div xml:id="echoid-div1624" type="float" level="2" n="1"> <note position="left" xlink:label="note-0426-01" xlink:href="note-0426-01a" xml:space="preserve">1104.</note> <note position="left" xlink:label="note-0426-02" xlink:href="note-0426-02a" xml:space="preserve">TAB. XLII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s11396" xml:space="preserve">In loco aëre vacuo non adſcendit aqua in antliam, cum <lb/>hæc deficiat preſſio.</s> <s xml:id="echoid-s11397" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1626" type="section" level="1" n="389"> <head xml:id="echoid-head530" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s11398" xml:space="preserve">Cum antlia A, quæ cum operculo, quo vitrum exhau-<lb/> <anchor type="note" xlink:label="note-0426-03a" xlink:href="note-0426-03"/> riendum obtegitur, cohæret, conjungatur tubus vitreus b c, <lb/> <anchor type="note" xlink:label="note-0426-04a" xlink:href="note-0426-04"/> cujus extremitas c infra aquæ, vaſe V contentæ, ſuperfici-<lb/>em deſcendit; </s> <s xml:id="echoid-s11399" xml:space="preserve">fundo antliæ embolus applicetur, & </s> <s xml:id="echoid-s11400" xml:space="preserve">ex re-<lb/>cipiente aër exhauriatur. </s> <s xml:id="echoid-s11401" xml:space="preserve">Si embolus elevetur, non adſcen-<lb/>det aqua.</s> <s xml:id="echoid-s11402" xml:space="preserve"/> </p> <div xml:id="echoid-div1626" type="float" level="2" n="1"> <note position="left" xlink:label="note-0426-03" xlink:href="note-0426-03a" xml:space="preserve">1105.</note> <note position="left" xlink:label="note-0426-04" xlink:href="note-0426-04a" xml:space="preserve">TAB. XLII. <lb/>fig. 5.</note> </div> </div> <div xml:id="echoid-div1628" type="section" level="1" n="390"> <head xml:id="echoid-head531" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s11403" xml:space="preserve">Vis, qua aër in corpora premit, hæc ſæpe diſrumpit, <lb/> <anchor type="note" xlink:label="note-0426-05a" xlink:href="note-0426-05"/> quando preſſio ab omni parte non eſt æqualis. </s> <s xml:id="echoid-s11404" xml:space="preserve">Cylindrus <lb/> <anchor type="note" xlink:label="note-0426-06a" xlink:href="note-0426-06"/> æneus, aut conus truncatus, A laminâ vitreâ planâ obtegitur, <lb/>ſi ex cylindro aër extrahatur, preſſione aëris externi con-<lb/>fringitur lamina vitrea, & </s> <s xml:id="echoid-s11405" xml:space="preserve">in fruſta exigua quaſi in pulverem <lb/>redigitur, ſi non nimium tenuis ſit; </s> <s xml:id="echoid-s11406" xml:space="preserve">nimis craſſa preſſionem <lb/>ſuſtinet, & </s> <s xml:id="echoid-s11407" xml:space="preserve">non disrumpitur.</s> <s xml:id="echoid-s11408" xml:space="preserve"/> </p> <div xml:id="echoid-div1628" type="float" level="2" n="1"> <note position="left" xlink:label="note-0426-05" xlink:href="note-0426-05a" xml:space="preserve">1106.</note> <note position="left" xlink:label="note-0426-06" xlink:href="note-0426-06a" xml:space="preserve">TAB. XLI. <lb/>fig. 6.</note> </div> <pb o="317" file="0427" n="467" rhead="MATHEMATICA. LIB. II. CAP. XVII."/> </div> <div xml:id="echoid-div1630" type="section" level="1" n="391"> <head xml:id="echoid-head532" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s11409" xml:space="preserve">Detur antlia A diametri trium partium quartarum unius <lb/> <anchor type="note" xlink:label="note-0427-01a" xlink:href="note-0427-01"/> pollicis; </s> <s xml:id="echoid-s11410" xml:space="preserve">applicetur embolus fundo antliæ, & </s> <s xml:id="echoid-s11411" xml:space="preserve">apertura in <lb/> <anchor type="note" xlink:label="note-0427-02a" xlink:href="note-0427-02"/> fundo antliæ claudatur; </s> <s xml:id="echoid-s11412" xml:space="preserve">ſi pondus ſex librarum P cum an-<lb/>tlia conjungatur, & </s> <s xml:id="echoid-s11413" xml:space="preserve">manubrium B emboli ſuſtineatur, non <lb/>deſcendit antlia; </s> <s xml:id="echoid-s11414" xml:space="preserve">deſcendere enim non poteſt, niſi pondus <lb/>ſuperet aëris preſſionem, & </s> <s xml:id="echoid-s11415" xml:space="preserve">emboli attritum; </s> <s xml:id="echoid-s11416" xml:space="preserve">illa vero <lb/>preſſio ſola ſex libras excedit.</s> <s xml:id="echoid-s11417" xml:space="preserve"/> </p> <div xml:id="echoid-div1630" type="float" level="2" n="1"> <note position="right" xlink:label="note-0427-01" xlink:href="note-0427-01a" xml:space="preserve">1107.</note> <note position="right" xlink:label="note-0427-02" xlink:href="note-0427-02a" xml:space="preserve">TAB. XLII. <lb/>fig. 1.</note> </div> </div> <div xml:id="echoid-div1632" type="section" level="1" n="392"> <head xml:id="echoid-head533" xml:space="preserve"><emph style="sc">Experimentum.</emph> 10.</head> <p> <s xml:id="echoid-s11418" xml:space="preserve">In loco aëre vacuo ſolo pondere p, quo attritus emboli <lb/> <anchor type="note" xlink:label="note-0427-03a" xlink:href="note-0427-03"/> ſuperatur, deſcendit antlia.</s> <s xml:id="echoid-s11419" xml:space="preserve"/> </p> <div xml:id="echoid-div1632" type="float" level="2" n="1"> <note position="right" xlink:label="note-0427-03" xlink:href="note-0427-03a" xml:space="preserve">1108.</note> </div> <note position="right" xml:space="preserve">TAB. XLII. <lb/>fig 1.</note> </div> <div xml:id="echoid-div1634" type="section" level="1" n="393"> <head xml:id="echoid-head534" xml:space="preserve"><emph style="sc">Experimentum</emph> 11.</head> <p> <s xml:id="echoid-s11420" xml:space="preserve">Magis ſenſibilem videmus effectum compreſſionis aëris, <lb/> <anchor type="note" xlink:label="note-0427-05a" xlink:href="note-0427-05"/> quando duo ſphæræ ſegmenta H & </s> <s xml:id="echoid-s11421" xml:space="preserve">I junguntur. </s> <s xml:id="echoid-s11422" xml:space="preserve">Sit utri-<lb/> <anchor type="note" xlink:label="note-0427-06a" xlink:href="note-0427-06"/> uſque ora polita, & </s> <s xml:id="echoid-s11423" xml:space="preserve">congruant hæ inter ſe, cerâque cir-<lb/>cumpoſitâ aër excludatur. </s> <s xml:id="echoid-s11424" xml:space="preserve">In ſegmento H epiſtomium da-<lb/>tur, quo ſegmenta conjuncta antliæ pneumaticæ applican-<lb/>tur, & </s> <s xml:id="echoid-s11425" xml:space="preserve">quod exhauſto aëre clauditur. </s> <s xml:id="echoid-s11426" xml:space="preserve">Annulo A ſegmen-<lb/>ta ſuſpenduntur, & </s> <s xml:id="echoid-s11427" xml:space="preserve">ope annuli Q his pondera appendun-<lb/>tur, quæ tabulæ T imponuntur. </s> <s xml:id="echoid-s11428" xml:space="preserve">Poſito ſegmentorum dia-<lb/>metro trium pollicum cum ſemiſſe, pondus centum & </s> <s xml:id="echoid-s11429" xml:space="preserve">cir-<lb/>citer quadraginta librarum requiritur ut ſegmenta ſeparentur.</s> <s xml:id="echoid-s11430" xml:space="preserve"/> </p> <div xml:id="echoid-div1634" type="float" level="2" n="1"> <note position="right" xlink:label="note-0427-05" xlink:href="note-0427-05a" xml:space="preserve">1109.</note> <note position="right" xlink:label="note-0427-06" xlink:href="note-0427-06a" xml:space="preserve">TAB. XLII. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div1636" type="section" level="1" n="394"> <head xml:id="echoid-head535" xml:space="preserve"><emph style="sc">Experimentum</emph> 12.</head> <p> <s xml:id="echoid-s11431" xml:space="preserve">Ut in Experimento præcedenti ſegmenta ſphæræ jungan-<lb/>tur, & </s> <s xml:id="echoid-s11432" xml:space="preserve">aër exhauriatur; </s> <s xml:id="echoid-s11433" xml:space="preserve">ſi in loco aëre vacuo ſuſpenſa fue-<lb/> <anchor type="note" xlink:label="note-0427-07a" xlink:href="note-0427-07"/> rint pondere exiguo P, quo ceræ cohæſio ſuperatur, ſe-<lb/> <anchor type="note" xlink:label="note-0427-08a" xlink:href="note-0427-08"/> parantur. </s> <s xml:id="echoid-s11434" xml:space="preserve">In hoc Experimento cum orbe L L conjungitur <lb/>pyxis cum coriis <anchor type="note" xlink:href="" symbol="*"/>, quam filum æneum EF, cui pondus ap- penditur, trajicit. </s> <s xml:id="echoid-s11435" xml:space="preserve">Ne, caſu ſegmenti inferioris, vitrum, <lb/> <anchor type="note" xlink:label="note-0427-09a" xlink:href="note-0427-09"/> in quo Experimentum fit, frangatur, cylindro ligneo cavo <lb/>M hoc ſegmentum recipitur.</s> <s xml:id="echoid-s11436" xml:space="preserve"/> </p> <div xml:id="echoid-div1636" type="float" level="2" n="1"> <note position="right" xlink:label="note-0427-07" xlink:href="note-0427-07a" xml:space="preserve">1110.</note> <note position="right" xlink:label="note-0427-08" xlink:href="note-0427-08a" xml:space="preserve">TAB. XLIII. <lb/>fig. 1.</note> <note position="right" xlink:label="note-0427-09" xlink:href="note-0427-09a" xml:space="preserve">* 1096.</note> </div> <p> <s xml:id="echoid-s11437" xml:space="preserve">Vi eâdem, quæ in Experimento 11. </s> <s xml:id="echoid-s11438" xml:space="preserve">deſideratur, ad ſe-<lb/>gmenta memorata ſeparanda, hæc a ſe mutuo divellun-<lb/>tur, quando, vaſe incluſa, relicto inter ſegmenta aëre <lb/>in ſtatu aëris externi, & </s> <s xml:id="echoid-s11439" xml:space="preserve">clauſo epiſtomio, in vaſe aër ad <pb o="318" file="0428" n="468" rhead="PHYSICES ELEMENTA"/> denſitatem duplam redigitur.</s> <s xml:id="echoid-s11440" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1638" type="section" level="1" n="395"> <head xml:id="echoid-head536" xml:space="preserve"><emph style="sc">Machina</emph>,</head> <head xml:id="echoid-head537" style="it" xml:space="preserve">Qua in Aëre compreſſo Experimenta inſtituuntur.</head> <p> <s xml:id="echoid-s11441" xml:space="preserve">Tabulæ ligneæ a a, longitudinis circiter quindecim & </s> <s xml:id="echoid-s11442" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0428-01a" xlink:href="note-0428-01"/> latitudinis decem pollicum, imponitur orbis æneus N, dia-<lb/> <anchor type="note" xlink:label="note-0428-02a" xlink:href="note-0428-02"/> metri quinque aut ſex pollicum, cujus figura ſeparata da-<lb/>tur in N Tab. </s> <s xml:id="echoid-s11443" xml:space="preserve">42. </s> <s xml:id="echoid-s11444" xml:space="preserve">fig. </s> <s xml:id="echoid-s11445" xml:space="preserve">4.</s> <s xml:id="echoid-s11446" xml:space="preserve">; cum hoc, ab inferiori parte, co-<lb/>hæret cauda, aut prominentia, cylindrica P, quæ non <lb/>perforatur, & </s> <s xml:id="echoid-s11447" xml:space="preserve">tabulam a a trajicit. </s> <s xml:id="echoid-s11448" xml:space="preserve">Huic orbi imponitur, & </s> <s xml:id="echoid-s11449" xml:space="preserve"><lb/>cum ipſo cochleis jungitur vas æneum VV, altitudinis cir-<lb/>citer decem pollicum.</s> <s xml:id="echoid-s11450" xml:space="preserve"/> </p> <div xml:id="echoid-div1638" type="float" level="2" n="1"> <note position="left" xlink:label="note-0428-01" xlink:href="note-0428-01a" xml:space="preserve">1111.</note> <note position="left" xlink:label="note-0428-02" xlink:href="note-0428-02a" xml:space="preserve">TAB. XLIV. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s11451" xml:space="preserve">Obtegitur vas operculo D. </s> <s xml:id="echoid-s11452" xml:space="preserve">Columnæ CS, CS, cum ta-<lb/>bula a a cohærent, trajiciuntque lignum d e, quo opercu-<lb/>lum D arcte cum vaſe conjungitur, ope cochlearum f f. </s> <s xml:id="echoid-s11453" xml:space="preserve">Ta-<lb/>lis arcta compreſſio maxime eſt neceſſaria, ingreſſuſque aë-<lb/>ris interpoſitis coriis, oleo imbutis, cohibetur.</s> <s xml:id="echoid-s11454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11455" xml:space="preserve">Operculi ſeparata Figura datur in D, Tab. </s> <s xml:id="echoid-s11456" xml:space="preserve">42. </s> <s xml:id="echoid-s11457" xml:space="preserve">fig. </s> <s xml:id="echoid-s11458" xml:space="preserve">4.</s> <s xml:id="echoid-s11459" xml:space="preserve">; <lb/>cum hoc cohæret pyxis cum coriis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11460" xml:space="preserve">ne ſuperficiei ni- <anchor type="note" xlink:label="note-0428-03a" xlink:href="note-0428-03"/> mis parvæ applicetur lignum d e, circumdatur pyxis annulo, <lb/>qui cum operculo cohæret & </s> <s xml:id="echoid-s11461" xml:space="preserve">diametrum habet diametro <lb/>operculi fere æqualem.</s> <s xml:id="echoid-s11462" xml:space="preserve"/> </p> <div xml:id="echoid-div1639" type="float" level="2" n="2"> <note position="left" xlink:label="note-0428-03" xlink:href="note-0428-03a" xml:space="preserve">* 1096.</note> </div> <p> <s xml:id="echoid-s11463" xml:space="preserve">Trajicit pyxidem cum coriis filum æneum perforatum C, <lb/>cum quo cohæret epiſtomium B.</s> <s xml:id="echoid-s11464" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11465" xml:space="preserve">Comprimitur aër in vaſe, jungendo epiſtomio poſtremo <lb/> <anchor type="note" xlink:label="note-0428-04a" xlink:href="note-0428-04"/> memorato antliam AB: </s> <s xml:id="echoid-s11466" xml:space="preserve">cum hac conjunctum datur epiſto-<lb/> <anchor type="note" xlink:label="note-0428-05a" xlink:href="note-0428-05"/> mium, in quo, præter foramen ſolitum, aliud obliquum <lb/>datur, quod ad f pervenit, & </s> <s xml:id="echoid-s11467" xml:space="preserve">quo, clauſa communicatione <lb/>inter vas & </s> <s xml:id="echoid-s11468" xml:space="preserve">antliam, hæc cum aëre exteriori communicatur, <lb/>& </s> <s xml:id="echoid-s11469" xml:space="preserve">aëre impletur elevando embolum. </s> <s xml:id="echoid-s11470" xml:space="preserve">Aperta communica-<lb/>tione inter vas & </s> <s xml:id="echoid-s11471" xml:space="preserve">antliam, deſcenſu emboli aër in antlia con-<lb/>tentus vaſe intruditur; </s> <s xml:id="echoid-s11472" xml:space="preserve">hacque ſæpius repetita operatione <lb/>tandem ad propoſitam denſitatem redigitur.</s> <s xml:id="echoid-s11473" xml:space="preserve"/> </p> <div xml:id="echoid-div1640" type="float" level="2" n="3"> <note position="left" xlink:label="note-0428-04" xlink:href="note-0428-04a" xml:space="preserve">1112.</note> <note position="left" xlink:label="note-0428-05" xlink:href="note-0428-05a" xml:space="preserve">TAB. XLII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s11474" xml:space="preserve">Indice mercuriali denſitas aëris determinatur. </s> <s xml:id="echoid-s11475" xml:space="preserve">Eſt index hic <lb/>tubus vitreus, admodum anguſtus, qui cohæret cum fruſto <lb/>æneo, quod cochleis inter epiſtomia Machinæ & </s> <s xml:id="echoid-s11476" xml:space="preserve">Antliæ <lb/>aptatur. </s> <s xml:id="echoid-s11477" xml:space="preserve">Dum aër in Machina comprimitur, mercurius in <pb file="0429" n="469"/> <pb file="0429a" n="470"/> <anchor type="figure" xlink:label="fig-0429a-01a" xlink:href="fig-0429a-01"/> <pb file="0430" n="471"/> <pb o="319" file="0431" n="472" rhead="MATHEMATICA. LIB. II. CAP. XVII."/> tubo comprimit aërem in poſtica tubi parte, & </s> <s xml:id="echoid-s11478" xml:space="preserve">hæc <lb/>compreſſio, quæ æqualis eſt compreſſioni in vaſe, facile men-<lb/>ſuratur.</s> <s xml:id="echoid-s11479" xml:space="preserve"/> </p> <div xml:id="echoid-div1641" type="float" level="2" n="4"> <figure xlink:label="fig-0429a-01" xlink:href="fig-0429a-01a"> <image file="0429a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0429a-01"/> </figure> </div> </div> <div xml:id="echoid-div1643" type="section" level="1" n="396"> <head xml:id="echoid-head538" xml:space="preserve"><emph style="sc">Experimentum</emph> 13.</head> <p> <s xml:id="echoid-s11480" xml:space="preserve">Ut nunc in aëre compreſſo ſegmenta ſphærica ſeparen-<lb/> <anchor type="note" xlink:label="note-0431-01a" xlink:href="note-0431-01"/> tur, ſuſtentaculo ML ſegmentum I cum orbe N conjun-<lb/> <anchor type="note" xlink:label="note-0431-02a" xlink:href="note-0431-02"/> gitur, ope cochlearum in M & </s> <s xml:id="echoid-s11481" xml:space="preserve">L. </s> <s xml:id="echoid-s11482" xml:space="preserve">Eodem modo, co-<lb/>chleis in F & </s> <s xml:id="echoid-s11483" xml:space="preserve">E, ſegmentum H cum filo C cohæret. </s> <s xml:id="echoid-s11484" xml:space="preserve">Se-<lb/>gmenta ſibi mutu o applicantur, & </s> <s xml:id="echoid-s11485" xml:space="preserve">cerâ circumdantur. </s> <s xml:id="echoid-s11486" xml:space="preserve">De ce-<lb/>tero, quæ in deſcriptione machinæ dicta ſunt, obſervantur, aër-<lb/>que in vaſe comprimitur, ut habeat denſitatem duplam illius <lb/>quâm ex Atmoſphæræ compreſſione acquirit. </s> <s xml:id="echoid-s11487" xml:space="preserve">In Pannulus Q <lb/>orbi N annectitur, ut & </s> <s xml:id="echoid-s11488" xml:space="preserve">annulus A epiſtomio B. </s> <s xml:id="echoid-s11489" xml:space="preserve">Invertitur ma-<lb/> <anchor type="note" xlink:label="note-0431-03a" xlink:href="note-0431-03"/> china, & </s> <s xml:id="echoid-s11490" xml:space="preserve">annulo Q ſuſpenditur; </s> <s xml:id="echoid-s11491" xml:space="preserve">tabula T, cui pondera im-<lb/>ponuntur, annulo A appenditur; </s> <s xml:id="echoid-s11492" xml:space="preserve">& </s> <s xml:id="echoid-s11493" xml:space="preserve">ni pondera centum & </s> <s xml:id="echoid-s11494" xml:space="preserve"><lb/>quadraginta libras circiter valeant, non ſeparantur ſegmen-<lb/>ta. </s> <s xml:id="echoid-s11495" xml:space="preserve">Ne nimium, in ſegmentorum ſeparatione, deſcendat <lb/>tabula T, cavetur, quia cochleâ elevatur, & </s> <s xml:id="echoid-s11496" xml:space="preserve">deprimitur un-<lb/>cus, cui appenditur annulus Q, quod commode fit, ſi cylin-<lb/>drus ferreus cochleâ circumdatus, & </s> <s xml:id="echoid-s11497" xml:space="preserve">circa quem cochlea <lb/>exterior movetur, trajiciat lignum, quod tripode ſuſtinetur.</s> <s xml:id="echoid-s11498" xml:space="preserve"/> </p> <div xml:id="echoid-div1643" type="float" level="2" n="1"> <note position="right" xlink:label="note-0431-01" xlink:href="note-0431-01a" xml:space="preserve">1113.</note> <note position="right" xlink:label="note-0431-02" xlink:href="note-0431-02a" xml:space="preserve">TAB. XLII. <lb/>fig. 4.</note> <note position="right" xlink:label="note-0431-03" xlink:href="note-0431-03a" xml:space="preserve">TAB. XLII. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s11499" xml:space="preserve">Quæ hìc repræſentatur Machina, vitrea eſt, ſed cùm mi-<lb/>hi bis contigerit, in experimentis confractum fuiſſe tale vi-<lb/>trum, cupreâ machinâ nunc utor.</s> <s xml:id="echoid-s11500" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1645" type="section" level="1" n="397"> <head xml:id="echoid-head539" xml:space="preserve"><emph style="sc">Experimentum</emph> 14.</head> <p> <s xml:id="echoid-s11501" xml:space="preserve">Orbi LL machinæ pneumaticæ adaptetur tubus AB, <lb/> <anchor type="note" xlink:label="note-0431-04a" xlink:href="note-0431-04"/> epiſtomium in ſuperiori parte connexum habens, & </s> <s xml:id="echoid-s11502" xml:space="preserve">jun-<lb/> <anchor type="note" xlink:label="note-0431-05a" xlink:href="note-0431-05"/> ctus cum tubo minori ſupra orbem prominenti. </s> <s xml:id="echoid-s11503" xml:space="preserve">Huic im-<lb/>ponitur recipiens vitreus R, quo tubus prominens obtegi-<lb/>tur. </s> <s xml:id="echoid-s11504" xml:space="preserve">Extremitas B tubi A B, aquâ vaſe V contentâ, immer-<lb/>gitur, & </s> <s xml:id="echoid-s11505" xml:space="preserve">evacuato recipiente R, epiſtomium aperitur; </s> <s xml:id="echoid-s11506" xml:space="preserve">ma-<lb/>gna cum vi in recipientem proſilit aqua, eadem preſſione, <lb/>qua, in tubo aëre vacuo, ad altitudinem triginta duorum <lb/> <anchor type="note" xlink:label="note-0431-06a" xlink:href="note-0431-06"/> pedum ſuſtineri poteſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11507" xml:space="preserve"/> </p> <div xml:id="echoid-div1645" type="float" level="2" n="1"> <note position="right" xlink:label="note-0431-04" xlink:href="note-0431-04a" xml:space="preserve">1114.</note> <note position="right" xlink:label="note-0431-05" xlink:href="note-0431-05a" xml:space="preserve">TAB. XLIII. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0431-06" xlink:href="note-0431-06a" xml:space="preserve">1059.</note> </div> </div> <div xml:id="echoid-div1647" type="section" level="1" n="398"> <note position="right" xml:space="preserve">1115.</note> <head xml:id="echoid-head540" xml:space="preserve"><emph style="sc">Experimentum</emph> 15. <lb/> </head> <p> <s xml:id="echoid-s11508" xml:space="preserve">Aëris elaſticitas eundem edit effectum. </s> <s xml:id="echoid-s11509" xml:space="preserve">Detur vas æ-<lb/> <anchor type="note" xlink:label="note-0431-08a" xlink:href="note-0431-08"/> <pb o="320" file="0432" n="473" rhead="PHYSICES ELEMENTA"/> neum cylindricum V, exactiſſime clauſum; </s> <s xml:id="echoid-s11510" xml:space="preserve">in fundo aper-<lb/>tura datur, per quam aqua infunditur, & </s> <s xml:id="echoid-s11511" xml:space="preserve">quæ cochleâ clau-<lb/>ditur. </s> <s xml:id="echoid-s11512" xml:space="preserve">Superiori vaſis parti adferruminatur tubus ad fun-<lb/>dum vaſis fere pertingens, & </s> <s xml:id="echoid-s11513" xml:space="preserve">cui in extremitate extra vas <lb/>prominenti epiſtomium jungitur (vide fig.</s> <s xml:id="echoid-s11514" xml:space="preserve">4.)</s> <s xml:id="echoid-s11515" xml:space="preserve">. </s> <s xml:id="echoid-s11516" xml:space="preserve">Open co-<lb/>chleæ adaptatur vas hocce inferiori parti orbis LL antliæ <lb/>pueumaticæ, datur & </s> <s xml:id="echoid-s11517" xml:space="preserve">hic tubus prominens, qui recipienti <lb/>R obtegitur. </s> <s xml:id="echoid-s11518" xml:space="preserve">Si ex hoc aër exhauriatur, & </s> <s xml:id="echoid-s11519" xml:space="preserve">vas V circiter <lb/>duabus partibus tertiis aquâ impletum ſit, aperto epiſtomio <lb/>violenter in recipientem aqua proſiliet, exelaſticitate aëris, <lb/>in ſuperiori parte vaſis V contenti. </s> <s xml:id="echoid-s11520" xml:space="preserve">Aër hic in aquæ ſuper-<lb/>ficiem premit, in tubo autem, aperto epiſtomio, preſſio mi-<lb/>nor datur; </s> <s xml:id="echoid-s11521" xml:space="preserve">tubum ideo aqua intrat.</s> <s xml:id="echoid-s11522" xml:space="preserve"/> </p> <div xml:id="echoid-div1647" type="float" level="2" n="1"> <note position="right" xlink:label="note-0431-08" xlink:href="note-0431-08a" xml:space="preserve">TAB. XLIII. <lb/>. 3.</note> </div> </div> <div xml:id="echoid-div1649" type="section" level="1" n="399"> <head xml:id="echoid-head541" xml:space="preserve"><emph style="sc">Experimentum</emph> 16.</head> <p> <s xml:id="echoid-s11523" xml:space="preserve">In ipſo aëre aperto violentiſſime proſiliet aqua ex vaſe V, <lb/> <anchor type="note" xlink:label="note-0432-01a" xlink:href="note-0432-01"/> ſi, hoc duabus partibus tertiis aqua repleto, aër in ſuperio-<lb/> <anchor type="note" xlink:label="note-0432-02a" xlink:href="note-0432-02"/> rem partem intrudatur, adhibitâ antliâ antea memora-<lb/>tâ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11524" xml:space="preserve"/> </p> <div xml:id="echoid-div1649" type="float" level="2" n="1"> <note position="left" xlink:label="note-0432-01" xlink:href="note-0432-01a" xml:space="preserve">1116.</note> <note position="left" xlink:label="note-0432-02" xlink:href="note-0432-02a" xml:space="preserve">TAB. XLIII. <lb/>fig. 4.</note> </div> <note symbol="*" position="left" xml:space="preserve">1112.</note> </div> <div xml:id="echoid-div1651" type="section" level="1" n="400"> <head xml:id="echoid-head542" xml:space="preserve"><emph style="sc">Experimentum</emph> 17.</head> <p> <s xml:id="echoid-s11525" xml:space="preserve">Vitrum R everſum aquâ vaſe V contentâ immergitur, <lb/> <anchor type="note" xlink:label="note-0432-04a" xlink:href="note-0432-04"/> aër aquam excludit, ad quamcunque profunditatem im-<lb/> <anchor type="note" xlink:label="note-0432-05a" xlink:href="note-0432-05"/> mergatur; </s> <s xml:id="echoid-s11526" xml:space="preserve">quo tamen vitrum profundius deſcendit, eo <lb/>etiam in minus ſpatium aër in hoc reducitur.</s> <s xml:id="echoid-s11527" xml:space="preserve"/> </p> <div xml:id="echoid-div1651" type="float" level="2" n="1"> <note position="left" xlink:label="note-0432-04" xlink:href="note-0432-04a" xml:space="preserve">1117.</note> <note position="left" xlink:label="note-0432-05" xlink:href="note-0432-05a" xml:space="preserve">TAB. XLIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s11528" xml:space="preserve">Hoc fundamento nituntur machinæ, quibus urinatores in <lb/> <anchor type="note" xlink:label="note-0432-06a" xlink:href="note-0432-06"/> mare deſcendunt. </s> <s xml:id="echoid-s11529" xml:space="preserve">Campanæ ſpeciem referunt hæ, & </s> <s xml:id="echoid-s11530" xml:space="preserve">gravitate <lb/>ſua deſcendunt; </s> <s xml:id="echoid-s11531" xml:space="preserve">aqua ad ipſum urinatorem non pertingit; </s> <s xml:id="echoid-s11532" xml:space="preserve">no-<lb/>vus aër continuo huic mittitur, contentus in veſicis, funi al-<lb/>ligatis, quas ad ſe trahit. </s> <s xml:id="echoid-s11533" xml:space="preserve">Aër inſpiratione calefactus ad ſu-<lb/>periorem partem machinæ adſcendit, & </s> <s xml:id="echoid-s11534" xml:space="preserve">per epiſtomium in <lb/>eo loco expellitur, preſſione aquæ, quæ in inferiori par-<lb/>te in aërem campana contentum premit, quæ preſſio <lb/>vim ſuperat, qua aqua per epiſtomium deſcendere co-<lb/>natur; </s> <s xml:id="echoid-s11535" xml:space="preserve">preſſio enim fluidorum cum profunditate auge-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11536" xml:space="preserve"/> </p> <div xml:id="echoid-div1652" type="float" level="2" n="2"> <note position="left" xlink:label="note-0432-06" xlink:href="note-0432-06a" xml:space="preserve">1118.</note> </div> <note position="left" xml:space="preserve">* 743.</note> <pb file="0433" n="474"/> <pb file="0433a" n="475"/> <figure> <image file="0433a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0433a-01"/> </figure> <pb file="0434" n="476"/> <pb o="321" file="0435" n="477" rhead="MATHEMATICA. LIB. H. CAP. XVII."/> </div> <div xml:id="echoid-div1654" type="section" level="1" n="401"> <head xml:id="echoid-head543" xml:space="preserve"><emph style="sc">Experimentum</emph> 18.</head> <p> <s xml:id="echoid-s11537" xml:space="preserve">Ex vitro conflantur homuli altitudinis circiter unius pol-<lb/> <anchor type="note" xlink:label="note-0435-01a" xlink:href="note-0435-01"/> licis cum ſemiſſe; </s> <s xml:id="echoid-s11538" xml:space="preserve">cavi hi ſunt, & </s> <s xml:id="echoid-s11539" xml:space="preserve">aëre replentur, foramen-<lb/> <anchor type="note" xlink:label="note-0435-02a" xlink:href="note-0435-02"/> que exiguum in pedum altero datur. </s> <s xml:id="echoid-s11540" xml:space="preserve">Ut aquâ paululum le-<lb/>viores ſint etiam requiritur. </s> <s xml:id="echoid-s11541" xml:space="preserve">Aquâ vaſe <emph style="sc">A</emph>B contentâ im-<lb/>merguntur. </s> <s xml:id="echoid-s11542" xml:space="preserve">Vas hoc altitudinem habet unius pedis, aut <lb/>quindecim pollicum, & </s> <s xml:id="echoid-s11543" xml:space="preserve">veſicâ obtegitur, quæ ſuperiori <lb/>vaſis parti firmiter alligatur, relictâ aëris bullâ inter veſi-<lb/>cam & </s> <s xml:id="echoid-s11544" xml:space="preserve">aquæ ſuperficiem. </s> <s xml:id="echoid-s11545" xml:space="preserve">Si digito veſica comprimatur, <lb/>in minus ſpatium aër memoratus redigitur, & </s> <s xml:id="echoid-s11546" xml:space="preserve">aquæ ſuper-<lb/>ficies magis comprimitur; </s> <s xml:id="echoid-s11547" xml:space="preserve">aqua magis compreſſa homun-<lb/>culos intrat per foramina in illorum pedibus, & </s> <s xml:id="echoid-s11548" xml:space="preserve">aërem <lb/>in ipſis magis comprimit. </s> <s xml:id="echoid-s11549" xml:space="preserve">Graviores homuli facti fundum <lb/>vafis petunt, citius aut lentius pro foraminis magnitudine, <lb/>etiam pro gravitate ſpecifica homuncionum magis aut <lb/>minus cum aquæ gravitate ſpecifica congruente. </s> <s xml:id="echoid-s11550" xml:space="preserve">Subla-<lb/>to digito minus in homulis compreſſus aër ſeſe expandit, <lb/>& </s> <s xml:id="echoid-s11551" xml:space="preserve">aquam expellit, iterumque ad aquæ ſuperficiem adſcen-<lb/>dunt.</s> <s xml:id="echoid-s11552" xml:space="preserve"/> </p> <div xml:id="echoid-div1654" type="float" level="2" n="1"> <note position="right" xlink:label="note-0435-01" xlink:href="note-0435-01a" xml:space="preserve">1119.</note> <note position="right" xlink:label="note-0435-02" xlink:href="note-0435-02a" xml:space="preserve">TAB. XLIV. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div1656" type="section" level="1" n="402"> <head xml:id="echoid-head544" xml:space="preserve"><emph style="sc">Experimentum</emph> 19.</head> <p> <s xml:id="echoid-s11553" xml:space="preserve">Animalia ad vivendum aëre indigent. </s> <s xml:id="echoid-s11554" xml:space="preserve">Si animal quod-<lb/> <anchor type="note" xlink:label="note-0435-03a" xlink:href="note-0435-03"/> cunque vitro V includudatur, & </s> <s xml:id="echoid-s11555" xml:space="preserve">aër exhauriatur, ſtatim vio-<lb/> <anchor type="note" xlink:label="note-0435-04a" xlink:href="note-0435-04"/> lento motu agitatur, & </s> <s xml:id="echoid-s11556" xml:space="preserve">ni ſubito aër iterum admittatur, <lb/>vitæ expers cadit. </s> <s xml:id="echoid-s11557" xml:space="preserve">Dantur quædam animalia quæ diutius <lb/>in loco evacuato vivnt. </s> <s xml:id="echoid-s11558" xml:space="preserve">Inflantur animalium corpora, <lb/>dum, ſublatâ externâ preſſione, aër, aut fluidum quod-<lb/>cunque elaſticum, in vaſis ſeſe expandit.</s> <s xml:id="echoid-s11559" xml:space="preserve"/> </p> <div xml:id="echoid-div1656" type="float" level="2" n="1"> <note position="right" xlink:label="note-0435-03" xlink:href="note-0435-03a" xml:space="preserve">1120.</note> <note position="right" xlink:label="note-0435-04" xlink:href="note-0435-04a" xml:space="preserve">TAB. XLIV. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div1658" type="section" level="1" n="403"> <head xml:id="echoid-head545" xml:space="preserve"><emph style="sc">Experimentum</emph> 20.</head> <p> <s xml:id="echoid-s11560" xml:space="preserve">Quidam etiam piſces ſine aëre vivere nequeunt; </s> <s xml:id="echoid-s11561" xml:space="preserve">in aliis <lb/> <anchor type="note" xlink:label="note-0435-05a" xlink:href="note-0435-05"/> nulla fere obſervatur mutatio, niſi quod oculi inflentur. </s> <s xml:id="echoid-s11562" xml:space="preserve">Ex-<lb/> <anchor type="note" xlink:label="note-0435-06a" xlink:href="note-0435-06"/> perimenta circa piſces inſtituenda ſunt in vitro V, quod <lb/>orbi antliæ pneumaticæ imponitur, & </s> <s xml:id="echoid-s11563" xml:space="preserve">foramini, per quod <lb/>aër exhauritur, jungitur tubus ad vitri partem ſuperiorem <lb/>fere pertingens; </s> <s xml:id="echoid-s11564" xml:space="preserve">aqua infunditur; </s> <s xml:id="echoid-s11565" xml:space="preserve">piſces in hanc injiciun-<lb/>tur; </s> <s xml:id="echoid-s11566" xml:space="preserve">operculo vitrum clauditur; </s> <s xml:id="echoid-s11567" xml:space="preserve">& </s> <s xml:id="echoid-s11568" xml:space="preserve">pars vitri ſuperior eva- <pb o="322" file="0436" n="478" rhead="PHYSICES ELEMENTA"/> cuatur. </s> <s xml:id="echoid-s11569" xml:space="preserve">Sublata aëris preſſione in aquæ ſuperficiem ſeſe aër <lb/>in piſcis corpore expandit, quo hic levior factus in aquam <lb/>deſcendere nequit.</s> <s xml:id="echoid-s11570" xml:space="preserve"/> </p> <div xml:id="echoid-div1658" type="float" level="2" n="1"> <note position="right" xlink:label="note-0435-05" xlink:href="note-0435-05a" xml:space="preserve">1121.</note> <note position="right" xlink:label="note-0435-06" xlink:href="note-0435-06a" xml:space="preserve">TAB. XLIV <lb/>fig. 44</note> </div> </div> <div xml:id="echoid-div1660" type="section" level="1" n="404"> <head xml:id="echoid-head546" xml:space="preserve"><emph style="sc">Experimentum</emph> 21.</head> <p> <s xml:id="echoid-s11571" xml:space="preserve">In aëre compreſſo Experimenta circa animalia inſtituun-<lb/> <anchor type="note" xlink:label="note-0436-01a" xlink:href="note-0436-01"/> tur, ope machinæ ſuperius deſcriptæ <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11572" xml:space="preserve">In hoc caſu non <anchor type="note" xlink:label="note-0436-02a" xlink:href="note-0436-02"/> ſubito animalia moriuntur, quia compreſſione aëris va-<lb/> <anchor type="note" xlink:label="note-0436-03a" xlink:href="note-0436-03"/> ſa in corpore non franguntur, ſi tamen diutius in tali aëre <lb/>degant, noxius illis eſt, & </s> <s xml:id="echoid-s11573" xml:space="preserve">etiam in compreſſione majori, <lb/>brevi tempore pereunt.</s> <s xml:id="echoid-s11574" xml:space="preserve"/> </p> <div xml:id="echoid-div1660" type="float" level="2" n="1"> <note position="left" xlink:label="note-0436-01" xlink:href="note-0436-01a" xml:space="preserve">1122.</note> <note position="left" xlink:label="note-0436-02" xlink:href="note-0436-02a" xml:space="preserve">TAB. XLIV. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0436-03" xlink:href="note-0436-03a" xml:space="preserve">1111.</note> </div> </div> <div xml:id="echoid-div1662" type="section" level="1" n="405"> <head xml:id="echoid-head547" xml:space="preserve"><emph style="sc">Experimentum</emph> 22.</head> <p> <s xml:id="echoid-s11575" xml:space="preserve">Fluida pleraque aërem, aut aliud fluidum elaſticum con-<lb/> <anchor type="note" xlink:label="note-0436-04a" xlink:href="note-0436-04"/> tinent; </s> <s xml:id="echoid-s11576" xml:space="preserve">quando vitro obteguntur, & </s> <s xml:id="echoid-s11577" xml:space="preserve">aër ex hoc extrahitur <lb/>fluidum elaſticum ſeſe ſeparat, dilatat & </s> <s xml:id="echoid-s11578" xml:space="preserve">exit. </s> <s xml:id="echoid-s11579" xml:space="preserve">In hoc caſu <lb/>ſæpiſſime fluidi violentiſſimam obſervamus ebullitionem.</s> <s xml:id="echoid-s11580" xml:space="preserve"/> </p> <div xml:id="echoid-div1662" type="float" level="2" n="1"> <note position="left" xlink:label="note-0436-04" xlink:href="note-0436-04a" xml:space="preserve">1123.</note> </div> </div> <div xml:id="echoid-div1664" type="section" level="1" n="406"> <head xml:id="echoid-head548" xml:space="preserve">CAPUT XVIII.</head> <head xml:id="echoid-head549" xml:space="preserve">Variarum Machinarum, quarum Actio ab Aëre <lb/>pendet, Deſcriptio, & harum Effectuum <lb/>Explicatio.</head> <head xml:id="echoid-head550" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s11581" xml:space="preserve">TUbi incurvi a S b extremitas a aquâ immergitur, dum <lb/> <anchor type="note" xlink:label="note-0436-05a" xlink:href="note-0436-05"/> extremitas b infra aquæ ſuperficiem deſcendit. </s> <s xml:id="echoid-s11582" xml:space="preserve">Siſu-<lb/> <anchor type="note" xlink:label="note-0436-06a" xlink:href="note-0436-06"/> gendo, aut quocunque alio modo, aëre evacuetur tubus, <lb/>fluet aqua per b. </s> <s xml:id="echoid-s11583" xml:space="preserve">Hæc machina ſipho vocatur.</s> <s xml:id="echoid-s11584" xml:space="preserve"/> </p> <div xml:id="echoid-div1664" type="float" level="2" n="1"> <note position="left" xlink:label="note-0436-05" xlink:href="note-0436-05a" xml:space="preserve">1124.</note> <note position="left" xlink:label="note-0436-06" xlink:href="note-0436-06a" xml:space="preserve">TAB. XLV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s11585" xml:space="preserve">Hujus effectus a preſſione aëris pendet; </s> <s xml:id="echoid-s11586" xml:space="preserve">qui aquam in <lb/> <anchor type="note" xlink:label="note-0436-07a" xlink:href="note-0436-07"/> ſiphonem pellit, premens in ſuperficiem aquæ vaſe contentæ; <lb/></s> <s xml:id="echoid-s11587" xml:space="preserve">premit etiam aër in aquam ex orificio b exeuntem, illam-<lb/>que ſuſtinet; </s> <s xml:id="echoid-s11588" xml:space="preserve">preſſiones hæ ſunt æquales, & </s> <s xml:id="echoid-s11589" xml:space="preserve">in ſuperiori <lb/>parte ſiphonis contrarie agunt, ibique valent Atmoſphæræ <lb/>pondus, demto pondere columnarum aquearum, quæ a <lb/>preſſionibus ſuſtinentur. </s> <s xml:id="echoid-s11590" xml:space="preserve">Columna aquea in crure S b al-<lb/>titudine oppoſitam columnam ſuperat; </s> <s xml:id="echoid-s11591" xml:space="preserve">ergo a parte b S ma- <pb file="0437" n="479"/> <pb file="0437a" n="480"/> <anchor type="figure" xlink:label="fig-0437a-01a" xlink:href="fig-0437a-01"/> <pb file="0438" n="481"/> <pb o="323" file="0439" n="482" rhead="MATHEMATICA. LIB. II. CAP. XVIII."/> gis aëris preſſio minuitur, & </s> <s xml:id="echoid-s11592" xml:space="preserve">preſſio oppoſita hanc vincit, <lb/>fluitque aqua b verſus.</s> <s xml:id="echoid-s11593" xml:space="preserve"/> </p> <div xml:id="echoid-div1665" type="float" level="2" n="2"> <note position="left" xlink:label="note-0436-07" xlink:href="note-0436-07a" xml:space="preserve">1125.</note> <figure xlink:label="fig-0437a-01" xlink:href="fig-0437a-01a"> <image file="0437a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0437a-01"/> </figure> </div> </div> <div xml:id="echoid-div1667" type="section" level="1" n="407"> <head xml:id="echoid-head551" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s11594" xml:space="preserve">Sipho memoratus hoc incommodi habet, quod, ab effe-<lb/> <anchor type="note" xlink:label="note-0439-01a" xlink:href="note-0439-01"/> ctu ſi ceſſaverit, non iterum aqua fluat, niſi aëre tubus de <lb/>novo evacuetur. </s> <s xml:id="echoid-s11595" xml:space="preserve">Corrigitur defectus hic, conſtruendo ſipho-<lb/> <anchor type="note" xlink:label="note-0439-02a" xlink:href="note-0439-02"/> nem figuræ a S b, cujus cruraſunt æqualia & </s> <s xml:id="echoid-s11596" xml:space="preserve">incurvata; </s> <s xml:id="echoid-s11597" xml:space="preserve">ſi e-<lb/>nim aquâ impleatur ſipho, & </s> <s xml:id="echoid-s11598" xml:space="preserve">crus unum aquâ immergatur, ut <lb/>aqua orificium ſuperet, ex ratione, in explicatione præce-<lb/>dentis Experimenti data, fluet aqua per crus alterum. <lb/></s> <s xml:id="echoid-s11599" xml:space="preserve">Crura cùm incurvata ſint, non evacuatur ſipho, quando flu-<lb/>xus aquæ ceſſat, & </s> <s xml:id="echoid-s11600" xml:space="preserve">ſemel impleto ſiphone, ſemper ad effe-<lb/>ctum ſuum producendum paratus eſt. </s> <s xml:id="echoid-s11601" xml:space="preserve">Aqua per illum <lb/>fluit & </s> <s xml:id="echoid-s11602" xml:space="preserve">refluit pro majori altitudine ab una aut alia parte.</s> <s xml:id="echoid-s11603" xml:space="preserve"/> </p> <div xml:id="echoid-div1667" type="float" level="2" n="1"> <note position="right" xlink:label="note-0439-01" xlink:href="note-0439-01a" xml:space="preserve">1126.</note> <note position="right" xlink:label="note-0439-02" xlink:href="note-0439-02a" xml:space="preserve">TAB. XLIV. <lb/>fig. 6.</note> </div> </div> <div xml:id="echoid-div1669" type="section" level="1" n="408"> <head xml:id="echoid-head552" xml:space="preserve"><emph style="sc">Sipho</emph>,</head> <head xml:id="echoid-head553" xml:space="preserve">Quo aqua elevatur.</head> <p> <s xml:id="echoid-s11604" xml:space="preserve">Eodem, cum machinis præcedentibus, nititur fundamen-<lb/> <anchor type="note" xlink:label="note-0439-03a" xlink:href="note-0439-03"/> to ſipho ad aquam in receptaculum evehendam adaptatus. <lb/></s> <s xml:id="echoid-s11605" xml:space="preserve"> <anchor type="note" xlink:label="note-0439-04a" xlink:href="note-0439-04"/> Effectus hujus ſiphonis ſenſibilis redditur ope machinæ, con-<lb/>ſtantis ex duobus globis vitreis H & </s> <s xml:id="echoid-s11606" xml:space="preserve">I, qui junguntur tubo <lb/>CDE. </s> <s xml:id="echoid-s11607" xml:space="preserve">Globus I cum aqua evehenda communicationem <lb/>habet tubo AB, qui ad globi ſummitatem fere pertingit. <lb/></s> <s xml:id="echoid-s11608" xml:space="preserve">In inferiori parte jungitur globo H tubus FG, longitudi-<lb/>ne tubum integrum AB æquans.</s> <s xml:id="echoid-s11609" xml:space="preserve"/> </p> <div xml:id="echoid-div1669" type="float" level="2" n="1"> <note position="right" xlink:label="note-0439-03" xlink:href="note-0439-03a" xml:space="preserve">1127.</note> <note position="right" xlink:label="note-0439-04" xlink:href="note-0439-04a" xml:space="preserve">TAB. XLV. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s11610" xml:space="preserve">Globus H aquâ impletur ope infundibuli, & </s> <s xml:id="echoid-s11611" xml:space="preserve">hoc obtu-<lb/>ratur.</s> <s xml:id="echoid-s11612" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11613" xml:space="preserve">In machinis quæ ad uſum applicantur ex receptaculo, <lb/>aquam evehendam continenti, quocunque modo, hæc in <lb/>vas H deducitur, & </s> <s xml:id="echoid-s11614" xml:space="preserve">epiſtomio inter vas & </s> <s xml:id="echoid-s11615" xml:space="preserve">receptaculum <lb/>clauditur communicatio.</s> <s xml:id="echoid-s11616" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1671" type="section" level="1" n="409"> <head xml:id="echoid-head554" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s11617" xml:space="preserve">Aperto epiſtomio G fluet aqua, & </s> <s xml:id="echoid-s11618" xml:space="preserve">per tubum AB in <lb/> <anchor type="note" xlink:label="note-0439-05a" xlink:href="note-0439-05"/> vas I adſcendet; </s> <s xml:id="echoid-s11619" xml:space="preserve">quo repleto deducitur aqua in locum quem-<lb/>cunque, & </s> <s xml:id="echoid-s11620" xml:space="preserve">repetita machinæ operatione continuatur aquæ <lb/>elevatio.</s> <s xml:id="echoid-s11621" xml:space="preserve"/> </p> <div xml:id="echoid-div1671" type="float" level="2" n="1"> <note position="right" xlink:label="note-0439-05" xlink:href="note-0439-05a" xml:space="preserve">1128.</note> </div> <pb o="324" file="0440" n="483" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s11622" xml:space="preserve">Aperto epiſtomio G, premit aër in aquam ex tubo FG <lb/> <anchor type="note" xlink:label="note-0440-01a" xlink:href="note-0440-01"/> exeuntem; </s> <s xml:id="echoid-s11623" xml:space="preserve">premit etiam aër in ſuperficiem aquæ in rece-<lb/>ptaculo, qua preſſione in tubo AB ſuſtinetur. </s> <s xml:id="echoid-s11624" xml:space="preserve">Preſſio-<lb/>nes hæ ſunt æquales, & </s> <s xml:id="echoid-s11625" xml:space="preserve">ab hiſce demtis aquæ columnis <lb/>quas ſuſtinent, dantur vires quibus agunt in aërem, in <lb/>yaſorum partibus ſuperioribus, & </s> <s xml:id="echoid-s11626" xml:space="preserve">tubo CDE, con-<lb/>tentum. </s> <s xml:id="echoid-s11627" xml:space="preserve">Columna FG, quia ei ſuperadditur aquæ <lb/>altitudo in vaſe H, ſemper ſuperat columnam in tubo <lb/>AB; </s> <s xml:id="echoid-s11628" xml:space="preserve">preſſio ergo in G alia magis minuitur & </s> <s xml:id="echoid-s11629" xml:space="preserve">ab ipſa ſu-<lb/>peratur, adſcenditque aqua per tubum AB, deſcendit ve-<lb/>ro per FG.</s> <s xml:id="echoid-s11630" xml:space="preserve"/> </p> <div xml:id="echoid-div1672" type="float" level="2" n="2"> <note position="left" xlink:label="note-0440-01" xlink:href="note-0440-01a" xml:space="preserve">1129.</note> </div> </div> <div xml:id="echoid-div1674" type="section" level="1" n="410"> <head xml:id="echoid-head555" xml:space="preserve"><emph style="sc">Antliæ</emph> <emph style="sc">Vulgares</emph>.</head> <p> <s xml:id="echoid-s11631" xml:space="preserve">Ut antliarum vulgarium actio & </s> <s xml:id="echoid-s11632" xml:space="preserve">effectus ante oculos po-<lb/> <anchor type="note" xlink:label="note-0440-02a" xlink:href="note-0440-02"/> natur, conſtruitur antlia parva ex vitro. </s> <s xml:id="echoid-s11633" xml:space="preserve">Sit AB cylin-<lb/> <anchor type="note" xlink:label="note-0440-03a" xlink:href="note-0440-03"/> drus vitreus longitudinis ſex aut ſeptem pollicum, & </s> <s xml:id="echoid-s11634" xml:space="preserve">cujus <lb/>diameter ſit unius pollicis cum ſemiſſe. </s> <s xml:id="echoid-s11635" xml:space="preserve">In ſundo ei jungi-<lb/>tur tubus cujuſcunque longitudinis CD. </s> <s xml:id="echoid-s11636" xml:space="preserve">Hujus apertura <lb/>ſuperior clauditur globo plumbeo ita, ut aqua ex cylindro <lb/>AB defcendere nequeat, in hunc autem adſcendere facile poſ-<lb/>ſit elevando globum, quo loco valvulæ utimur. </s> <s xml:id="echoid-s11637" xml:space="preserve">Embolus in cy-<lb/>lindro AB movetur, qui corio circumdatus hujus capacita-<lb/>tem exactè implet: </s> <s xml:id="echoid-s11638" xml:space="preserve">datur in embolo foramen, quod etiam, loco <lb/>valvulæ, globo obturatur, ita ut per embolum aqua ad-<lb/>ſcendere, deſcendere non verò poſſit.</s> <s xml:id="echoid-s11639" xml:space="preserve"/> </p> <div xml:id="echoid-div1674" type="float" level="2" n="1"> <note position="left" xlink:label="note-0440-02" xlink:href="note-0440-02a" xml:space="preserve">1130.</note> <note position="left" xlink:label="note-0440-03" xlink:href="note-0440-03a" xml:space="preserve">TAB. XLV. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div1676" type="section" level="1" n="411"> <head xml:id="echoid-head556" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s11640" xml:space="preserve">Fundo cylindri admoveatur embolus, huic ſuperinfun-<lb/> <anchor type="note" xlink:label="note-0440-04a" xlink:href="note-0440-04"/> datur aqua, ut aëris tranſitus cohibeatur, ſi aquâ immer-<lb/>gatur extremitas D tubi CD, & </s> <s xml:id="echoid-s11641" xml:space="preserve">elevetur embolus, adſcen-<lb/>det aqua in cylindrum AB <anchor type="note" xlink:href="" symbol="*"/>, ex quo deſcendere nequit;</s> <s xml:id="echoid-s11642" xml:space="preserve"> <anchor type="note" xlink:label="note-0440-05a" xlink:href="note-0440-05"/> quare per embolum tranſit, quando hic deſcendit. </s> <s xml:id="echoid-s11643" xml:space="preserve">Elevato <lb/>iterum embolo novâ aquâ cylindrus repletur; </s> <s xml:id="echoid-s11644" xml:space="preserve">& </s> <s xml:id="echoid-s11645" xml:space="preserve">prima in <lb/>vas ligneum F cum cylindro vitreo cohærens elevatur, ex <lb/>quo per tubum G fluit.</s> <s xml:id="echoid-s11646" xml:space="preserve"/> </p> <div xml:id="echoid-div1676" type="float" level="2" n="1"> <note position="left" xlink:label="note-0440-04" xlink:href="note-0440-04a" xml:space="preserve">1131.</note> <note symbol="*" position="left" xlink:label="note-0440-05" xlink:href="note-0440-05a" xml:space="preserve">1104.</note> </div> <p> <s xml:id="echoid-s11647" xml:space="preserve">Cum omnium machinarum in hoc capite deſcriptarum <lb/> <anchor type="note" xlink:label="note-0440-06a" xlink:href="note-0440-06"/> effectus ab Atmoſphæræ preſſione pendeant, non multum <pb file="0441" n="484"/> <pb file="0441a" n="485"/> <anchor type="figure" xlink:label="fig-0441a-01a" xlink:href="fig-0441a-01"/> <pb file="0442" n="486"/> <pb o="325" file="0443" n="487" rhead="MATHEMATICA. LIB. H. CAP. XVIII."/> ultra triginta duos pedes in hiſce machinis aqua adſcen-<lb/>dit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11648" xml:space="preserve"/> </p> <div xml:id="echoid-div1677" type="float" level="2" n="2"> <note position="left" xlink:label="note-0440-06" xlink:href="note-0440-06a" xml:space="preserve">1132.</note> <figure xlink:label="fig-0441a-01" xlink:href="fig-0441a-01a"> <image file="0441a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0441a-01"/> </figure> </div> <note symbol="*" position="right" xml:space="preserve">1059.</note> </div> <div xml:id="echoid-div1679" type="section" level="1" n="412"> <head xml:id="echoid-head557" xml:space="preserve"><emph style="sc">Fonticulus</emph> <emph style="sc">Heronis</emph>.</head> <p> <s xml:id="echoid-s11649" xml:space="preserve">Fonticuli varii dantur Heronis dicti; </s> <s xml:id="echoid-s11650" xml:space="preserve">unius conſtructio-<lb/> <anchor type="note" xlink:label="note-0443-02a" xlink:href="note-0443-02"/> nem explicabo.</s> <s xml:id="echoid-s11651" xml:space="preserve"/> </p> <div xml:id="echoid-div1679" type="float" level="2" n="1"> <note position="right" xlink:label="note-0443-02" xlink:href="note-0443-02a" xml:space="preserve">1133.</note> </div> <note position="right" xml:space="preserve">TAB. XLV. <lb/>fig. 4.</note> <p> <s xml:id="echoid-s11652" xml:space="preserve">Vaſa elliptica duo æqualia AB & </s> <s xml:id="echoid-s11653" xml:space="preserve">CD, ab omni parte <lb/>exacte clauſa, ex ære conſtruuntur.</s> <s xml:id="echoid-s11654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11655" xml:space="preserve">In utroque datur ſeparatio per centrum ellipſeos tranſiens <lb/>& </s> <s xml:id="echoid-s11656" xml:space="preserve">vas integrum in duas partes æquales ſecans.</s> <s xml:id="echoid-s11657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11658" xml:space="preserve">Separatio l m n i in vaſe DC ad ellipſis axim perpendi-<lb/>cularis eſt, ſeparatio c f g h alterius vaſis ad hunc axim in-<lb/>clinatur.</s> <s xml:id="echoid-s11659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11660" xml:space="preserve">Orâ elevatâ lamina ſuperior vaſis AB circumdatur.</s> <s xml:id="echoid-s11661" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11662" xml:space="preserve">Quatuor tubis vaſa junguntur. </s> <s xml:id="echoid-s11663" xml:space="preserve">Primus o p cavitatem B <lb/>vaſis AB trajicit, & </s> <s xml:id="echoid-s11664" xml:space="preserve">nullam cum hac communicationem <lb/>habet, & </s> <s xml:id="echoid-s11665" xml:space="preserve">ad fundum uſque cavitatis D fere deſcendit. </s> <s xml:id="echoid-s11666" xml:space="preserve">Se-<lb/>cundus s t ſuperiori parti cavitatis D adferruminatur, & </s> <s xml:id="echoid-s11667" xml:space="preserve"><lb/>ad ſupremam partem cavitatis B adſcendit, non vero lami-<lb/>nam ſupremam tangit. </s> <s xml:id="echoid-s11668" xml:space="preserve">Tertius q r ab inferiori parte ca-<lb/>vitatis B fere ad fundum cavitatis C pervenit. </s> <s xml:id="echoid-s11669" xml:space="preserve">Quartus <lb/>x v ſuperiori parti cavitatis cohæret, & </s> <s xml:id="echoid-s11670" xml:space="preserve">ad ſuperiorem par-<lb/>tem cavitatis A fere pertingit.</s> <s xml:id="echoid-s11671" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11672" xml:space="preserve">Datur tandem tubus z y, qui dum laminam ſupremam <lb/>vaſis AB trajicit, & </s> <s xml:id="echoid-s11673" xml:space="preserve">illi adferruminatur, in cavitatem A <lb/>deſcendit, ita ut extremitas z a fundo non multum di-<lb/>ſtet.</s> <s xml:id="echoid-s11674" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11675" xml:space="preserve">Cavitatibus ſingulis junguntur epiſtomia; </s> <s xml:id="echoid-s11676" xml:space="preserve">aut in illis aliæ <lb/>aperturæ dantur, quæ cochleis, & </s> <s xml:id="echoid-s11677" xml:space="preserve">interpoſito corio, ob-<lb/>turantur; </s> <s xml:id="echoid-s11678" xml:space="preserve">harum præcipuus uſus eſt, ut exactè cavitates <lb/>evacuentur, ne ab interiori parte æruginem contrahant.</s> <s xml:id="echoid-s11679" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1681" type="section" level="1" n="413"> <head xml:id="echoid-head558" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s11680" xml:space="preserve">Tubo o p aqua infundatur, qua cavitas D impletur; </s> <s xml:id="echoid-s11681" xml:space="preserve">ad-<lb/> <anchor type="note" xlink:label="note-0443-04a" xlink:href="note-0443-04"/> ſcenditque aqua, ſi infuſio continuetur, per tubum s t, & </s> <s xml:id="echoid-s11682" xml:space="preserve"><lb/>per q r in cavitatem C deſcendit, quæ etiam impletur, aë-<lb/>re adſcendente per x v & </s> <s xml:id="echoid-s11683" xml:space="preserve">exunte per z y. </s> <s xml:id="echoid-s11684" xml:space="preserve">Evertatur ma- <pb o="326" file="0444" n="488" rhead="PHYSICES ELEMENTA"/> china, apertis epiſtomiis cavitatum C & </s> <s xml:id="echoid-s11685" xml:space="preserve">D, deſcendet a-<lb/>qua in cavitates B & </s> <s xml:id="echoid-s11686" xml:space="preserve">A. </s> <s xml:id="echoid-s11687" xml:space="preserve">Clauſis iterum epiſtomiis, ut & </s> <s xml:id="echoid-s11688" xml:space="preserve">a-<lb/>pertura y tubi z y erigatur machina, & </s> <s xml:id="echoid-s11689" xml:space="preserve">infundatur aqua <lb/>de novo tubo o p, donec ſuperficies ſuprema machinæ aqua <lb/>obtegatur. </s> <s xml:id="echoid-s11690" xml:space="preserve">Si nunc apertura y reſeratur, aqua in altum <lb/>proſiliet fere ad altitudinem duplam totius machinæ, & </s> <s xml:id="echoid-s11691" xml:space="preserve"><lb/>durabit aquæ motus donec cavitas C evacuata fuerit. </s> <s xml:id="echoid-s11692" xml:space="preserve">Mi-<lb/>nuetur continuo aquæ proſilientis altitudo, & </s> <s xml:id="echoid-s11693" xml:space="preserve">in fine non <lb/>erit dupla diſtantiæ inter vaſa.</s> <s xml:id="echoid-s11694" xml:space="preserve"/> </p> <div xml:id="echoid-div1681" type="float" level="2" n="1"> <note position="right" xlink:label="note-0443-04" xlink:href="note-0443-04a" xml:space="preserve">1134.</note> </div> <p> <s xml:id="echoid-s11695" xml:space="preserve">Hujus machinæ effectus tribuendus eſt compreſſioni aëris <lb/> <anchor type="note" xlink:label="note-0444-01a" xlink:href="note-0444-01"/> in vaſis. </s> <s xml:id="echoid-s11696" xml:space="preserve">Preſſio Atmoſphæræ in o & </s> <s xml:id="echoid-s11697" xml:space="preserve">in y, ut & </s> <s xml:id="echoid-s11698" xml:space="preserve">preſſiones inde <lb/>oriundæ in ipſis vaſis ſunt æquales, & </s> <s xml:id="echoid-s11699" xml:space="preserve">hæ preſſiones ſeſe mutuo <lb/>deſtruunt, quare in examine machinæ non conſiderantur. <lb/></s> <s xml:id="echoid-s11700" xml:space="preserve">Quando ultimo loco aqua tubo op infunditur, in hoc ſuſtinetur <lb/>preſſione aëris in cavitate D contenti, & </s> <s xml:id="echoid-s11701" xml:space="preserve">in ſuperficiem aquæ, <lb/>quæ ad parvam in hac cavitate altitudinem datur, agentis; </s> <s xml:id="echoid-s11702" xml:space="preserve">qui <lb/>ergo aër comprimitur pondere aquæ ad altitudinem po: </s> <s xml:id="echoid-s11703" xml:space="preserve">a-<lb/>gitur de preſſione qua preſſio Atmoſphæræ ſuperatur. </s> <s xml:id="echoid-s11704" xml:space="preserve">Aër, <lb/>in ſuperiori parte cavitatis B contentus, per tubum s t, cum <lb/>aëre memorato communicationem habet, & </s> <s xml:id="echoid-s11705" xml:space="preserve">æqualiter com-<lb/>primitur, eademque cum vi agit in ſuperficiem aquæ in hac <lb/>cavitate. </s> <s xml:id="echoid-s11706" xml:space="preserve">Hæc preſſio ſuperaddenda eſt preſſioni ex aquæ <lb/>altitudine, ut habeamus vim qua aër, qui continetur in <lb/>cavitate C, comprimitur, ut & </s> <s xml:id="echoid-s11707" xml:space="preserve">ille qui inſuperiori parte <lb/>cavitatis A hæret, propter communicationem per tubum <lb/>x v. </s> <s xml:id="echoid-s11708" xml:space="preserve">Preſſio ergo quæ in ſuperficiem aquæ, in hac cavitate A, <lb/>datur, valet columnam aqueam, cujus altitudo eſt fere du-<lb/>plum altitudinis totius machinæ; </s> <s xml:id="echoid-s11709" xml:space="preserve">& </s> <s xml:id="echoid-s11710" xml:space="preserve">ideò proſilit, quaſi a <lb/>tali columna premeretur; </s> <s xml:id="echoid-s11711" xml:space="preserve">id eſt, ad altitudinem non <lb/>multum ab altitudine hujus columnæ differentem adſcen-<lb/>dit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11712" xml:space="preserve"/> </p> <div xml:id="echoid-div1682" type="float" level="2" n="2"> <note position="left" xlink:label="note-0444-01" xlink:href="note-0444-01a" xml:space="preserve">1135.</note> </div> <note symbol="*" position="left" xml:space="preserve">301.</note> <p> <s xml:id="echoid-s11713" xml:space="preserve">Minuitur continuo altitudo hæc; </s> <s xml:id="echoid-s11714" xml:space="preserve">columnæ enim aqueæ, <lb/>quæ aërem comprimunt, continuo minuuntur; </s> <s xml:id="echoid-s11715" xml:space="preserve">quia aqua <lb/>in cavitatibus C & </s> <s xml:id="echoid-s11716" xml:space="preserve">D elevatur, & </s> <s xml:id="echoid-s11717" xml:space="preserve">hujus altitudo minuitur <lb/>in cavitate B. </s> <s xml:id="echoid-s11718" xml:space="preserve">Eodem tempore etiam continuò evacuatur <pb file="0445" n="489"/> <pb file="0445a" n="490"/> <anchor type="figure" xlink:label="fig-0445a-01a" xlink:href="fig-0445a-01"/> <pb file="0446" n="491"/> <pb o="327" file="0447" n="492" rhead="MATHEMATICA. LIB. II. CAP XIX."/> cavitas A, & </s> <s xml:id="echoid-s11719" xml:space="preserve">per majus ſpatium adſcendit aqua antequam <lb/>ad y perveniat; </s> <s xml:id="echoid-s11720" xml:space="preserve">ideoque ad minorem ſupra y altitudinem <lb/>propellitur.</s> <s xml:id="echoid-s11721" xml:space="preserve"/> </p> <div xml:id="echoid-div1683" type="float" level="2" n="3"> <figure xlink:label="fig-0445a-01" xlink:href="fig-0445a-01a"> <image file="0445a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0445a-01"/> </figure> </div> </div> <div xml:id="echoid-div1685" type="section" level="1" n="414"> <head xml:id="echoid-head559" xml:space="preserve">CAPUT XIX.</head> <head xml:id="echoid-head560" xml:space="preserve">De Aëris motu undulatorio, ubi de Sono.</head> <p> <s xml:id="echoid-s11722" xml:space="preserve">S l aër quocunque modo agitetur, particulæ motæ e loco <lb/> <anchor type="note" xlink:label="note-0447-01a" xlink:href="note-0447-01"/> recedunt, vicinaſque in minus ſpatium reducunt; </s> <s xml:id="echoid-s11723" xml:space="preserve">& </s> <s xml:id="echoid-s11724" xml:space="preserve"><lb/>aër dum in uno loco dilatatur in vicino comprimitur Aër <lb/>compreſſus, dum inſtauratur elater, ad priſtinum non mo-<lb/>do ſtatum redit, ſed ipſe dilatatur a particulis, motu ac-<lb/>quiſito, ultra priſtinum ſtatum, a ſe invicem receden-<lb/>tibus.</s> <s xml:id="echoid-s11725" xml:space="preserve"/> </p> <div xml:id="echoid-div1685" type="float" level="2" n="1"> <note position="right" xlink:label="note-0447-01" xlink:href="note-0447-01a" xml:space="preserve">1136.</note> </div> <p> <s xml:id="echoid-s11726" xml:space="preserve">Hoc motu, aër primo dilatatus, ad primum ſtatum redit, <lb/>aërque alias partes verſus comprimitur. </s> <s xml:id="echoid-s11727" xml:space="preserve">Hoc iterum obti-<lb/>net dum aër ultimo compreſſus ſeſe expandit, quo de no-<lb/>vo aër comprimitur. </s> <s xml:id="echoid-s11728" xml:space="preserve">Oritur ergo ex agitatione quacunque <lb/>motus analogus cum motu undæ in aquæ ſuperficie <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s11729" xml:space="preserve">eodem <anchor type="note" xlink:label="note-0447-02a" xlink:href="note-0447-02"/> nomine datur, & </s> <s xml:id="echoid-s11730" xml:space="preserve">vocatur aëris unda aër compreſſus cum <lb/>inſequenti dilatato <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11731" xml:space="preserve"/> </p> <div xml:id="echoid-div1686" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0447-02" xlink:href="note-0447-02a" xml:space="preserve">872.</note> </div> <note symbol="*" position="right" xml:space="preserve">873.</note> <p> <s xml:id="echoid-s11732" xml:space="preserve">Aër compreſſus omnes partes verſus dilatatur, & </s> <s xml:id="echoid-s11733" xml:space="preserve">motus <lb/> <anchor type="note" xlink:label="note-0447-04a" xlink:href="note-0447-04"/> undarum eſt motus ſphæræ ſeſe expandentis, eodem <lb/>modo ac in ſuperficie aquæ undæ per circulum moven-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11734" xml:space="preserve"/> </p> <div xml:id="echoid-div1687" type="float" level="2" n="3"> <note position="right" xlink:label="note-0447-04" xlink:href="note-0447-04a" xml:space="preserve">1137.</note> </div> <note symbol="*" position="right" xml:space="preserve">875.</note> <p style="it"> <s xml:id="echoid-s11735" xml:space="preserve">Dum unda in aëre movetur ubicunque tranſit, particulæ <lb/> <anchor type="note" xlink:label="note-0447-06a" xlink:href="note-0447-06"/> e loco removentur & </s> <s xml:id="echoid-s11736" xml:space="preserve">ad hunc redeunt, ſpatiumque breviſſi-<lb/>mum itu & </s> <s xml:id="echoid-s11737" xml:space="preserve">reditu percurrunt.</s> <s xml:id="echoid-s11738" xml:space="preserve"/> </p> <div xml:id="echoid-div1688" type="float" level="2" n="4"> <note position="right" xlink:label="note-0447-06" xlink:href="note-0447-06a" xml:space="preserve">1138.</note> </div> <p> <s xml:id="echoid-s11739" xml:space="preserve">Ut hujus motus leges pateant, concipiamus particulas aë-<lb/> <anchor type="note" xlink:label="note-0447-07a" xlink:href="note-0447-07"/> reas ad diſtantias æquales in linearecta eſſe diſpoſitas a, b, c, d, <lb/>& </s> <s xml:id="echoid-s11740" xml:space="preserve">c. </s> <s xml:id="echoid-s11741" xml:space="preserve">f; </s> <s xml:id="echoid-s11742" xml:space="preserve">moveatur unda per hanc lineam; </s> <s xml:id="echoid-s11743" xml:space="preserve">ponamus autem il-<lb/>lam perveniſſe inter b & </s> <s xml:id="echoid-s11744" xml:space="preserve">p; </s> <s xml:id="echoid-s11745" xml:space="preserve">aërem dilatari inter b & </s> <s xml:id="echoid-s11746" xml:space="preserve">h, <lb/>comprimi vero inter h & </s> <s xml:id="echoid-s11747" xml:space="preserve">p; </s> <s xml:id="echoid-s11748" xml:space="preserve">ut hæc omnia in linea 1. </s> <s xml:id="echoid-s11749" xml:space="preserve">re-<lb/>præſentantur.</s> <s xml:id="echoid-s11750" xml:space="preserve"/> </p> <div xml:id="echoid-div1689" type="float" level="2" n="5"> <note position="right" xlink:label="note-0447-07" xlink:href="note-0447-07a" xml:space="preserve">TAB. XLVI. <lb/>fig 1.</note> </div> <pb o="328" file="0448" n="493" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s11751" xml:space="preserve">Denſitas maxima datur in m, loco medio inter h & </s> <s xml:id="echoid-s11752" xml:space="preserve">p, & </s> <s xml:id="echoid-s11753" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0448-01a" xlink:href="note-0448-01"/> maxima dilatatio inter b & </s> <s xml:id="echoid-s11754" xml:space="preserve">h in medio e.</s> <s xml:id="echoid-s11755" xml:space="preserve"/> </p> <div xml:id="echoid-div1690" type="float" level="2" n="6"> <note position="left" xlink:label="note-0448-01" xlink:href="note-0448-01a" xml:space="preserve">1139.</note> </div> <p> <s xml:id="echoid-s11756" xml:space="preserve">Vbicunque particulæ vicinæ non æquè diſtant, actio ex e-<lb/> <anchor type="note" xlink:label="note-0448-02a" xlink:href="note-0448-02"/> laſticitate datur, qua particulæ minus diſtantes magis di-<lb/>ſtantes verſus premuntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s11757" xml:space="preserve">hæcque preſſio, ſepoſito omni <anchor type="note" xlink:label="note-0448-03a" xlink:href="note-0448-03"/> motu acquiſito, examinanda eſt.</s> <s xml:id="echoid-s11758" xml:space="preserve"/> </p> <div xml:id="echoid-div1691" type="float" level="2" n="7"> <note position="left" xlink:label="note-0448-02" xlink:href="note-0448-02a" xml:space="preserve">1140.</note> <note symbol="*" position="left" xlink:label="note-0448-03" xlink:href="note-0448-03a" xml:space="preserve">1072.</note> </div> <p style="it"> <s xml:id="echoid-s11759" xml:space="preserve">Inter b & </s> <s xml:id="echoid-s11760" xml:space="preserve">e datur preſſio a b verſus e, id eſt, cum motu <lb/> <anchor type="note" xlink:label="note-0448-04a" xlink:href="note-0448-04"/> undæ conſpirans; </s> <s xml:id="echoid-s11761" xml:space="preserve">quæ etiam datur inter m & </s> <s xml:id="echoid-s11762" xml:space="preserve">p.</s> <s xml:id="echoid-s11763" xml:space="preserve"/> </p> <div xml:id="echoid-div1692" type="float" level="2" n="8"> <note position="left" xlink:label="note-0448-04" xlink:href="note-0448-04a" xml:space="preserve">1141.</note> </div> <p> <s xml:id="echoid-s11764" xml:space="preserve">Preſſio autem contraria eſt inter e & </s> <s xml:id="echoid-s11765" xml:space="preserve">m, & </s> <s xml:id="echoid-s11766" xml:space="preserve">ab m verſus <lb/> <anchor type="note" xlink:label="note-0448-05a" xlink:href="note-0448-05"/> e dirigitur.</s> <s xml:id="echoid-s11767" xml:space="preserve"/> </p> <div xml:id="echoid-div1693" type="float" level="2" n="9"> <note position="left" xlink:label="note-0448-05" xlink:href="note-0448-05a" xml:space="preserve">1142.</note> </div> <p> <s xml:id="echoid-s11768" xml:space="preserve">In m & </s> <s xml:id="echoid-s11769" xml:space="preserve">e, ubi motus directiones mutantur, nulla ex e-<lb/> <anchor type="note" xlink:label="note-0448-06a" xlink:href="note-0448-06"/> laſticitate datur actio, quia particulæ vicinæ ad diſtantias <lb/>æquales inter ſe poſitæ ſunt.</s> <s xml:id="echoid-s11770" xml:space="preserve"/> </p> <div xml:id="echoid-div1694" type="float" level="2" n="10"> <note position="left" xlink:label="note-0448-06" xlink:href="note-0448-06a" xml:space="preserve">1143.</note> </div> <p> <s xml:id="echoid-s11771" xml:space="preserve">In locis b, h, & </s> <s xml:id="echoid-s11772" xml:space="preserve">p omnium maxima eſt diſtantiarum parti-<lb/> <anchor type="note" xlink:label="note-0448-07a" xlink:href="note-0448-07"/> cularum vicinarum differentia; </s> <s xml:id="echoid-s11773" xml:space="preserve">ideoque omnium maxima <lb/>elaſticitatis actio.</s> <s xml:id="echoid-s11774" xml:space="preserve"/> </p> <div xml:id="echoid-div1695" type="float" level="2" n="11"> <note position="left" xlink:label="note-0448-07" xlink:href="note-0448-07a" xml:space="preserve">1144.</note> </div> <p> <s xml:id="echoid-s11775" xml:space="preserve">Deducimus ex his particulam, pro vario in unda ſitu, va-<lb/>riam ab elaſticitate actionem pati, qua illius motus genera-<lb/>tur, acceleratur, minuitur, aut deſtruitur; </s> <s xml:id="echoid-s11776" xml:space="preserve">idcirco dire-<lb/>ctio motus particulæ, ex ſola directione memoratæ actio-<lb/>nis, determinari nequit, & </s> <s xml:id="echoid-s11777" xml:space="preserve">cum hac directione non ſemper <lb/>congruit illa, ſingularumque particularum motus omnibus <lb/>momentis mutatur.</s> <s xml:id="echoid-s11778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11779" xml:space="preserve">Particulæ omnes inter b & </s> <s xml:id="echoid-s11780" xml:space="preserve">p tranſlatæ ſunt, juxta ordi-<lb/>nem litterarum. </s> <s xml:id="echoid-s11781" xml:space="preserve">Particulæ inter h & </s> <s xml:id="echoid-s11782" xml:space="preserve">p juxta hanc dire-<lb/>ctionem motum continuant, ceteræ inter h & </s> <s xml:id="echoid-s11783" xml:space="preserve">b verſus b <lb/>redeunt, ut in ſequentibus dicetur.</s> <s xml:id="echoid-s11784" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11785" xml:space="preserve">Perſeverant hæ in motu quo redeunt, donec ex actione <lb/>elateris, cujus directio in puncto e mutatur, motus acqui-<lb/>ſitus altera vice deſtruatur; </s> <s xml:id="echoid-s11786" xml:space="preserve">in quo caſu particula ut b ad <lb/>quietem & </s> <s xml:id="echoid-s11787" xml:space="preserve">priſtinum ſitum redit. </s> <s xml:id="echoid-s11788" xml:space="preserve">In momento ſequenti <lb/>particula c in ſitu priſtino quieſcit, p vero ad q accedit, ut <lb/>in linea 2; </s> <s xml:id="echoid-s11789" xml:space="preserve">& </s> <s xml:id="echoid-s11790" xml:space="preserve">ſucceſſive, in momentis æqualibus, adipiſci-<lb/>tur unda omnes ſitus, qui hîc in lineis 1. </s> <s xml:id="echoid-s11791" xml:space="preserve">2. </s> <s xml:id="echoid-s11792" xml:space="preserve">3. </s> <s xml:id="echoid-s11793" xml:space="preserve">&</s> <s xml:id="echoid-s11794" xml:space="preserve">c. </s> <s xml:id="echoid-s11795" xml:space="preserve">13. </s> <s xml:id="echoid-s11796" xml:space="preserve">viden-<lb/>tur; </s> <s xml:id="echoid-s11797" xml:space="preserve">& </s> <s xml:id="echoid-s11798" xml:space="preserve">dum unda a ſitu in linea 1. </s> <s xml:id="echoid-s11799" xml:space="preserve">ad ſitum in linea 13. </s> <s xml:id="echoid-s11800" xml:space="preserve">per-<lb/> <anchor type="note" xlink:label="note-0448-08a" xlink:href="note-0448-08"/> <pb o="329" file="0449" n="494" rhead="MATHEMATICA. LIB. II. CAP XIX."/> venit, totam percurrit latitudinem ſuam. </s> <s xml:id="echoid-s11801" xml:space="preserve">Particula p in <lb/>hoc motu it & </s> <s xml:id="echoid-s11802" xml:space="preserve">redit, hujuſque motus in hac figura ſenſi-<lb/>bilis eſt, &</s> <s xml:id="echoid-s11803" xml:space="preserve">, ut clare patet, particula hæc ſucceſſivè per <lb/>omnes ſitus particularum in unda tranſit. </s> <s xml:id="echoid-s11804" xml:space="preserve">Singulæ particu-<lb/>læ ſucceſſivè ſimili motu agitantur: </s> <s xml:id="echoid-s11805" xml:space="preserve">& </s> <s xml:id="echoid-s11806" xml:space="preserve">diviſo tempore, in <lb/> <anchor type="note" xlink:label="note-0449-01a" xlink:href="note-0449-01"/> quo unda latitudinem percurrit, in tot partes quot <lb/>particulæ dantur in ipſa latitudine, particula unaquæque <lb/>in eo ſitu datur, in quo momento præcedenti fuit particula <lb/>ſequens, quæ per unum momentum tale diutius fuit in mo-<lb/>tu.</s> <s xml:id="echoid-s11807" xml:space="preserve"/> </p> <div xml:id="echoid-div1696" type="float" level="2" n="12"> <note position="left" xlink:label="note-0448-08" xlink:href="note-0448-08a" xml:space="preserve">1145.</note> <note position="right" xlink:label="note-0449-01" xlink:href="note-0449-01a" xml:space="preserve">1146.</note> </div> <p> <s xml:id="echoid-s11808" xml:space="preserve">Motus cujuſcunque particulæ, ut p, in itu & </s> <s xml:id="echoid-s11809" xml:space="preserve">reditu ſuo, <lb/> <anchor type="note" xlink:label="note-0449-02a" xlink:href="note-0449-02"/> analogus eſt cum motu penduli vibratorio, dum duas peragit <lb/>oſcillationes; </s> <s xml:id="echoid-s11810" xml:space="preserve">id eſt, ſemel it & </s> <s xml:id="echoid-s11811" xml:space="preserve">redit. </s> <s xml:id="echoid-s11812" xml:space="preserve">Pendulum in o-<lb/>ſcillatione deſcendit, motuſque acquiſitus cum gravitatis a-<lb/>ctione conſpirat & </s> <s xml:id="echoid-s11813" xml:space="preserve">hac acceleratur, donec ad punctum ar-<lb/>cus deſcribendi infimum, id eſt medium viæ percurrendæ, <lb/>pervenerit; </s> <s xml:id="echoid-s11814" xml:space="preserve">pergit motu acquiſito, qui actione gravitatis, <lb/>cujus directio in hoc puncto mutatur, deſtruitur, dum cor-<lb/>pus per alteram arcus deſcribendi partem adſcendit: </s> <s xml:id="echoid-s11815" xml:space="preserve">corpus <lb/>hoc iisdem legibus redit.</s> <s xml:id="echoid-s11816" xml:space="preserve"/> </p> <div xml:id="echoid-div1697" type="float" level="2" n="13"> <note position="right" xlink:label="note-0449-02" xlink:href="note-0449-02a" xml:space="preserve">1147.</note> </div> <p> <s xml:id="echoid-s11817" xml:space="preserve">Particula p ex elaſticitate movetur, motuſque accelera-<lb/>tur ex elaſticitatis actione, donec ipſa ad ſitum particulæ <lb/>m in linea 1. </s> <s xml:id="echoid-s11818" xml:space="preserve">pervenerit <anchor type="note" xlink:href="" symbol="*"/>, qui ſitus in linea 4. </s> <s xml:id="echoid-s11819" xml:space="preserve">vide- <anchor type="note" xlink:label="note-0449-03a" xlink:href="note-0449-03"/> tur, in qua particula p occupat punctum medium <lb/>ſpatii itu & </s> <s xml:id="echoid-s11820" xml:space="preserve">reditu percurrendi. </s> <s xml:id="echoid-s11821" xml:space="preserve">Motu acquiſito, <lb/>quamvis elaſticitas contrarie agat <anchor type="note" xlink:href="" symbol="*"/>, in motu perſeverat, <anchor type="note" xlink:label="note-0449-04a" xlink:href="note-0449-04"/> donec hac actione totus motus ſit deſtructus; </s> <s xml:id="echoid-s11822" xml:space="preserve">quod fit per-<lb/>currendo ſpatium æquale illi in quo fuit generatus; </s> <s xml:id="echoid-s11823" xml:space="preserve">datur <lb/>tunc particula p in ſitu, in quo videtur in linea 7.</s> <s xml:id="echoid-s11824" xml:space="preserve">, qui re-<lb/>ſpondet cum ſitu particulæ h in linea 1. </s> <s xml:id="echoid-s11825" xml:space="preserve">Ex elaſticitate <lb/>tunc particula redit & </s> <s xml:id="echoid-s11826" xml:space="preserve">acceleratur, donec ſitum particulæ <lb/>e in linea 1. </s> <s xml:id="echoid-s11827" xml:space="preserve">adepta ſit <anchor type="note" xlink:href="" symbol="*"/>, ut in linea 10.</s> <s xml:id="echoid-s11828" xml:space="preserve">; id eſt, donec ite- <anchor type="note" xlink:label="note-0449-05a" xlink:href="note-0449-05"/> rum, ut in linea 4, verſetur in puncto medio viæ percurren-<lb/>dæ. </s> <s xml:id="echoid-s11829" xml:space="preserve">In reditu ſuo continuat particula donec ex actione e-<lb/>lateris, cujus directio iterum mutatur <anchor type="note" xlink:href="" symbol="*"/>, totus motus de- <anchor type="note" xlink:label="note-0449-06a" xlink:href="note-0449-06"/> <pb o="330" file="0450" n="495" rhead="PHYSICES ELEMENTA"/> ſtruatur; </s> <s xml:id="echoid-s11830" xml:space="preserve">tuncque particula ad priſtinum ſitum, ut in linea <lb/>13.</s> <s xml:id="echoid-s11831" xml:space="preserve">, redit, & </s> <s xml:id="echoid-s11832" xml:space="preserve">ibi, cùm nova actione non agitetur, quieſcit. <lb/></s> <s xml:id="echoid-s11833" xml:space="preserve">Quæ omnia ex demonſtratis in ſcholio 1. </s> <s xml:id="echoid-s11834" xml:space="preserve">ſequenti profluunt. </s> <s xml:id="echoid-s11835" xml:space="preserve"><lb/>Idcirco ceſſante motu corporis tremulo, quo aër agitatur, <lb/> <anchor type="note" xlink:label="note-0450-01a" xlink:href="note-0450-01"/> novæ undæ non generantur, numeruſque undarum a nume-<lb/>ro agitationum ipſius corporis non differt.</s> <s xml:id="echoid-s11836" xml:space="preserve"/> </p> <div xml:id="echoid-div1698" type="float" level="2" n="14"> <note symbol="*" position="right" xlink:label="note-0449-03" xlink:href="note-0449-03a" xml:space="preserve">1141.</note> <note symbol="*" position="right" xlink:label="note-0449-04" xlink:href="note-0449-04a" xml:space="preserve">1142.</note> <note symbol="*" position="right" xlink:label="note-0449-05" xlink:href="note-0449-05a" xml:space="preserve">1142.</note> <note symbol="*" position="right" xlink:label="note-0449-06" xlink:href="note-0449-06a" xml:space="preserve">1143.</note> <note position="left" xlink:label="note-0450-01" xlink:href="note-0450-01a" xml:space="preserve">1148.</note> </div> <p> <s xml:id="echoid-s11837" xml:space="preserve">Si in pendulo poſt duas vibrationes gravitatis actio ceſſa-<lb/> <anchor type="note" xlink:label="note-0450-02a" xlink:href="note-0450-02"/> ret, ut in aëre, poſt itum & </s> <s xml:id="echoid-s11838" xml:space="preserve">reditum particulæ, elaſticita-<lb/>tis actio in hanc particulam ceſſat, in omnibus motus par-<lb/>ticulæ aëreæ cum motu corporis penduli congrueret. </s> <s xml:id="echoid-s11839" xml:space="preserve">In <lb/>puncto medio arcus oſcillatione percurrendi nulla datur gra-<lb/>vitatis actio, hujuſque directio mutatur; </s> <s xml:id="echoid-s11840" xml:space="preserve">in puncto medio <lb/>ſpatii a particula p, itu & </s> <s xml:id="echoid-s11841" xml:space="preserve">reditu, percurrendi, in quo datur <lb/>in linea 4. </s> <s xml:id="echoid-s11842" xml:space="preserve">& </s> <s xml:id="echoid-s11843" xml:space="preserve">10.</s> <s xml:id="echoid-s11844" xml:space="preserve">, congruit hujus particulæ ſitus cum ſitu <lb/>particularum m & </s> <s xml:id="echoid-s11845" xml:space="preserve">e in linea 1.</s> <s xml:id="echoid-s11846" xml:space="preserve">, in quibus punctis nulla ela-<lb/>ſticitatis actio datur, & </s> <s xml:id="echoid-s11847" xml:space="preserve">hujus directio mutatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11848" xml:space="preserve">In pen- <anchor type="note" xlink:label="note-0450-03a" xlink:href="note-0450-03"/> dulo quo magis corpus oſcillatum a puncto infimo, aut me-<lb/>dio, arcus deſcribendi diſtat, eo magis vis gravitatis in il-<lb/>lud agit; </s> <s xml:id="echoid-s11849" xml:space="preserve">quo magis etiam particula p a puncto medio ſpatii <lb/>percurrendi diſtat, eo major in illam eſt elaſticitatis actio, <lb/>& </s> <s xml:id="echoid-s11850" xml:space="preserve">in lineis 1. </s> <s xml:id="echoid-s11851" xml:space="preserve">7. </s> <s xml:id="echoid-s11852" xml:space="preserve">& </s> <s xml:id="echoid-s11853" xml:space="preserve">13.</s> <s xml:id="echoid-s11854" xml:space="preserve">, in quibus maximè à puncto memo-<lb/>rato diſtat particula, ſitus hujus congruit cum punctis b, h, <lb/>& </s> <s xml:id="echoid-s11855" xml:space="preserve">p, in linea 1.</s> <s xml:id="echoid-s11856" xml:space="preserve">, in quibus elaſticitatis actio eſt omnium <lb/>maxima <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11857" xml:space="preserve"/> </p> <div xml:id="echoid-div1699" type="float" level="2" n="15"> <note position="left" xlink:label="note-0450-02" xlink:href="note-0450-02a" xml:space="preserve">1149.</note> <note symbol="*" position="left" xlink:label="note-0450-03" xlink:href="note-0450-03a" xml:space="preserve">1143</note> </div> <note symbol="*" position="left" xml:space="preserve">1144.</note> <p> <s xml:id="echoid-s11858" xml:space="preserve">Qua lege hæc elaſticitatis actio, cum aucta a ſæpius me-<lb/> <anchor type="note" xlink:label="note-0450-05a" xlink:href="note-0450-05"/> morato puncto medio diſtantia creſcat, determinatur ex le-<lb/>ge ipſa elaſticitatis aëris, cujus particulæ ſeſe mutuo fugiunt <lb/>cum vi quæ eſt inverſè ut diſtantia inter particularum cen-<lb/>tra <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s11859" xml:space="preserve">& </s> <s xml:id="echoid-s11860" xml:space="preserve">demonſtramus in ſcholio 1. </s> <s xml:id="echoid-s11861" xml:space="preserve">huic capiti ſubjuncto ela- <anchor type="note" xlink:label="note-0450-06a" xlink:href="note-0450-06"/> ſticitatis actionem, in particulam up p, ad inſtar diſtantiæ a <lb/>puncto ſpatii percurrendi medio augeri aut minui.</s> <s xml:id="echoid-s11862" xml:space="preserve"/> </p> <div xml:id="echoid-div1700" type="float" level="2" n="16"> <note position="left" xlink:label="note-0450-05" xlink:href="note-0450-05a" xml:space="preserve">1150.</note> <note symbol="*" position="left" xlink:label="note-0450-06" xlink:href="note-0450-06a" xml:space="preserve">1072.</note> </div> <p> <s xml:id="echoid-s11863" xml:space="preserve">Qua de cauſa particulæ ſingulæ, in motu ſuo, eunt, & </s> <s xml:id="echoid-s11864" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0450-07a" xlink:href="note-0450-07"/> redeunt, juxta legem corporis in cycloïde oſcillati <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11865" xml:space="preserve"/> </p> <div xml:id="echoid-div1701" type="float" level="2" n="17"> <note position="left" xlink:label="note-0450-07" xlink:href="note-0450-07a" xml:space="preserve">1151.</note> </div> <note symbol="*" position="left" xml:space="preserve">287.</note> <p> <s xml:id="echoid-s11866" xml:space="preserve">In eodem ſcholio demonſtramus, undæ velocitatem æqua-<lb/> <anchor type="note" xlink:label="note-0450-09a" xlink:href="note-0450-09"/> lem eſſe illi, quam corpus acquirit cadendo a ſemialtitudi- <pb o="331" file="0451" n="496" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> ne, quam Atmoſphæra haberet, ſi manente aëris quantita-<lb/>te, ubique illam haberet denſitatem, quam habet in loco, <lb/>in quo unda movetur. </s> <s xml:id="echoid-s11867" xml:space="preserve">Et demonſtratio locum habet <lb/>quæcunque fuerit undæ latitudo, & </s> <s xml:id="echoid-s11868" xml:space="preserve">ſive per majus aut mi-<lb/>nus ſpatium particulæ in itu & </s> <s xml:id="echoid-s11869" xml:space="preserve">reditu excurrant; </s> <s xml:id="echoid-s11870" xml:space="preserve">unde con-<lb/>ſtat, Vndas omnes æquali celeritate moveri.</s> <s xml:id="echoid-s11871" xml:space="preserve"/> </p> <div xml:id="echoid-div1702" type="float" level="2" n="18"> <note position="left" xlink:label="note-0450-09" xlink:href="note-0450-09a" xml:space="preserve">1152.</note> </div> <note position="right" xml:space="preserve">1153.</note> <p> <s xml:id="echoid-s11872" xml:space="preserve">Locum hoc habebit quamdiu altitudo Atmoſphæræ, po-<lb/>ſitâ hac ubique ejuſdem denſitatis, non mutatur, mutata <lb/>autem hac, celeritas undarum mutatur; </s> <s xml:id="echoid-s11873" xml:space="preserve">& </s> <s xml:id="echoid-s11874" xml:space="preserve">ſequuntur qua-<lb/> <anchor type="note" xlink:label="note-0451-02a" xlink:href="note-0451-02"/> drata celeritatum rationem altitudinum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11875" xml:space="preserve">Mutatur autem <anchor type="note" xlink:label="note-0451-03a" xlink:href="note-0451-03"/> ſæpe altitudo hæc, nam manente elaſticitate aëris denſitas <lb/> <anchor type="note" xlink:label="note-0451-04a" xlink:href="note-0451-04"/> ſæpe variat: </s> <s xml:id="echoid-s11876" xml:space="preserve">& </s> <s xml:id="echoid-s11877" xml:space="preserve">mutari poteſt elaſticitas denſitate manente: <lb/></s> <s xml:id="echoid-s11878" xml:space="preserve">tandem ambæ ſimul mutationi ſæpiſſime obnoxiæ ſunt.</s> <s xml:id="echoid-s11879" xml:space="preserve"/> </p> <div xml:id="echoid-div1703" type="float" level="2" n="19"> <note position="right" xlink:label="note-0451-02" xlink:href="note-0451-02a" xml:space="preserve">1154.</note> <note symbol="*" position="right" xlink:label="note-0451-03" xlink:href="note-0451-03a" xml:space="preserve">1152 255.</note> <note position="right" xlink:label="note-0451-04" xlink:href="note-0451-04a" xml:space="preserve">1155.</note> </div> <p> <s xml:id="echoid-s11880" xml:space="preserve">In primo caſu, manente nempe elaſticitate, dum denſitas <lb/>variat, poſitâ Atmoſphærâ ubique ejuſdem denſitatis, alti-<lb/>tudo mutatur, quantitas verò aëris comprimentis non vari-<lb/>at: </s> <s xml:id="echoid-s11881" xml:space="preserve">quia hujus pondus æquale eſt elaſticitati; </s> <s xml:id="echoid-s11882" xml:space="preserve">& </s> <s xml:id="echoid-s11883" xml:space="preserve">eſt altitu-<lb/>do ut ſpatium ab aere occupatum; </s> <s xml:id="echoid-s11884" xml:space="preserve">ideo inverſè ut denſitas <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0451-05a" xlink:href="note-0451-05"/> quare undarum celeritatum quadrata ſunt inverſè ut denſita-<lb/>tes <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11885" xml:space="preserve"/> </p> <div xml:id="echoid-div1704" type="float" level="2" n="20"> <note symbol="*" position="right" xlink:label="note-0451-05" xlink:href="note-0451-05a" xml:space="preserve">738.</note> </div> <note symbol="*" position="right" xml:space="preserve">1154.</note> <p> <s xml:id="echoid-s11886" xml:space="preserve">Quando denſitas manet, ſed mutatur elaſticitas, altitu-<lb/> <anchor type="note" xlink:label="note-0451-07a" xlink:href="note-0451-07"/> do Atmoſphæræ mutatur, ut pondus comprimens, id eſt, <lb/>ut elaſticitas <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11887" xml:space="preserve">Ergo quadrata celeritatum undarum ſunt ut <anchor type="note" xlink:label="note-0451-08a" xlink:href="note-0451-08"/> elaſticitatis gradus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11888" xml:space="preserve"/> </p> <div xml:id="echoid-div1705" type="float" level="2" n="21"> <note position="right" xlink:label="note-0451-07" xlink:href="note-0451-07a" xml:space="preserve">1156.</note> <note symbol="*" position="right" xlink:label="note-0451-08" xlink:href="note-0451-08a" xml:space="preserve">247.</note> </div> <note symbol="*" position="right" xml:space="preserve">1154.</note> <p style="it"> <s xml:id="echoid-s11889" xml:space="preserve">Si & </s> <s xml:id="echoid-s11890" xml:space="preserve">elaſticitas & </s> <s xml:id="echoid-s11891" xml:space="preserve">denſitas differant, quadrata velocita-<lb/> <anchor type="note" xlink:label="note-0451-10a" xlink:href="note-0451-10"/> tum undarum erunt in ratione compoſita directæ elaſticita-<lb/>tis <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11892" xml:space="preserve">inverſæ denſitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11893" xml:space="preserve"/> </p> <div xml:id="echoid-div1706" type="float" level="2" n="22"> <note position="right" xlink:label="note-0451-10" xlink:href="note-0451-10a" xml:space="preserve">1157.</note> </div> <note symbol="*" position="right" xml:space="preserve">1156.</note> <note symbol="*" position="right" xml:space="preserve">1155.</note> <p> <s xml:id="echoid-s11894" xml:space="preserve">Si denſitas & </s> <s xml:id="echoid-s11895" xml:space="preserve">elaſticitas creſcant, aut minuantur, in eadem <lb/> <anchor type="note" xlink:label="note-0451-13a" xlink:href="note-0451-13"/> ratione, inverſa ratio denſitatis directam elaſticitatis deſtru-<lb/>et, & </s> <s xml:id="echoid-s11896" xml:space="preserve">non mutabitur undarum celeritas.</s> <s xml:id="echoid-s11897" xml:space="preserve"/> </p> <div xml:id="echoid-div1707" type="float" level="2" n="23"> <note position="right" xlink:label="note-0451-13" xlink:href="note-0451-13a" xml:space="preserve">1158.</note> </div> <p> <s xml:id="echoid-s11898" xml:space="preserve">Ultimus hic caſus exſtat in aëris compreſſione ex aëre ad-<lb/>fluente <anchor type="note" xlink:href="" symbol="*"/>, quo etiam, ſi de cetero maneat aëris conſtitutio, <anchor type="note" xlink:label="note-0451-14a" xlink:href="note-0451-14"/> altitudo Atmoſphæræ, poſitâ hac ubique ejuſdem denſita-<lb/>tis, non mutatur; </s> <s xml:id="echoid-s11899" xml:space="preserve">nam pro ratione ponderis ſuperadditi in <lb/>minus ſpatium redigitur. </s> <s xml:id="echoid-s11900" xml:space="preserve">Idcirco ex mutata altitudine co-<lb/> <anchor type="note" xlink:label="note-0451-15a" xlink:href="note-0451-15"/> <pb o="332" file="0452" n="497" rhead="PHYSICES ELEMENTA"/> lumnæ mercurii, quæ ex Atmoſphæræ preſſione in tubo aëre <lb/>vacuo ſuſtinetur <anchor type="note" xlink:href="" symbol="*"/>, quod pondus, quo aër in terræ viciniis <anchor type="note" xlink:label="note-0452-01a" xlink:href="note-0452-01"/> comprimitur, mutatum indicat, non debemus undarum ce-<lb/>leritatem mutatam dijudicare. </s> <s xml:id="echoid-s11901" xml:space="preserve">Eadem de cauſa undæ æqua-<lb/> <anchor type="note" xlink:label="note-0452-02a" xlink:href="note-0452-02"/> li celeritate in apice montis & </s> <s xml:id="echoid-s11902" xml:space="preserve">in valle moverentur; </s> <s xml:id="echoid-s11903" xml:space="preserve">niſiaë-<lb/>ris conſtitutio differret pro majori elevatione <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11904" xml:space="preserve"/> </p> <div xml:id="echoid-div1708" type="float" level="2" n="24"> <note symbol="*" position="right" xlink:label="note-0451-14" xlink:href="note-0451-14a" xml:space="preserve">1071.</note> <note position="right" xlink:label="note-0451-15" xlink:href="note-0451-15a" xml:space="preserve">1159.</note> <note symbol="*" position="left" xlink:label="note-0452-01" xlink:href="note-0452-01a" xml:space="preserve">1056.</note> <note position="left" xlink:label="note-0452-02" xlink:href="note-0452-02a" xml:space="preserve">1160.</note> </div> <note symbol="*" position="left" xml:space="preserve">1081.</note> <p> <s xml:id="echoid-s11905" xml:space="preserve">Vndas æſtate celerius quam hieme moveri ex aëris elaſti-<lb/> <anchor type="note" xlink:label="note-0452-04a" xlink:href="note-0452-04"/> citate calore aucta <anchor type="note" xlink:href="" symbol="*"/> deducitur.</s> <s xml:id="echoid-s11906" xml:space="preserve"/> </p> <div xml:id="echoid-div1709" type="float" level="2" n="25"> <note position="left" xlink:label="note-0452-04" xlink:href="note-0452-04a" xml:space="preserve">1161.</note> </div> <note symbol="*" position="left" xml:space="preserve">1075.</note> <p> <s xml:id="echoid-s11907" xml:space="preserve">Altitudo Atmoſphæræ, poſitâ hac ubique ejuſdem den-<lb/> <anchor type="note" xlink:label="note-0452-06a" xlink:href="note-0452-06"/> ſitatis, detegitur, ſi menſuretur altitudo columnæ Mercurii, <lb/>quæ in tubo Torricelliano cum preſſione Atmoſphæræ æ-<lb/>quiponderat <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s11908" xml:space="preserve">comparando aëris denſitatem cum den- <anchor type="note" xlink:label="note-0452-07a" xlink:href="note-0452-07"/> ſitate mercurii; </s> <s xml:id="echoid-s11909" xml:space="preserve">quod ponderando aërem <anchor type="note" xlink:href="" symbol="*"/> fieri poteſt. </s> <s xml:id="echoid-s11910" xml:space="preserve">De- <anchor type="note" xlink:label="note-0452-08a" xlink:href="note-0452-08"/> tectâ verò Atmoſphæræ altitudine, celeritas, quam corpus <lb/>a dimidia hac altitudine cadendo acquirit, per experimen-<lb/>ta pendulorum determinatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s11911" xml:space="preserve"/> </p> <div xml:id="echoid-div1710" type="float" level="2" n="26"> <note position="left" xlink:label="note-0452-06" xlink:href="note-0452-06a" xml:space="preserve">1162.</note> <note symbol="*" position="left" xlink:label="note-0452-07" xlink:href="note-0452-07a" xml:space="preserve">1055.</note> <note symbol="*" position="left" xlink:label="note-0452-08" xlink:href="note-0452-08a" xml:space="preserve">1099.</note> </div> <note symbol="*" position="left" xml:space="preserve">288. 290.</note> <p> <s xml:id="echoid-s11912" xml:space="preserve">Aëris motus, de quo in hac computatione agitur, <lb/>a ſola elaſticitate pendet, & </s> <s xml:id="echoid-s11913" xml:space="preserve">exacta eſſet computatio, <lb/>ſi particulæ ipſæ ad interſtitia inter has ſenſibilem ra-<lb/>tionem non haberent; </s> <s xml:id="echoid-s11914" xml:space="preserve">ſi verò ponamus dari hìc ratio-<lb/>nem ſenſibilem, velocior erit undarum motus; </s> <s xml:id="echoid-s11915" xml:space="preserve">propa-<lb/>gatur enim per corpora ſolida in inſtanti, quod etiam <lb/>referri debet ad corpuſcula heterogenea in aëre natan-<lb/>tia.</s> <s xml:id="echoid-s11916" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s11917" xml:space="preserve">Conſideravimus autem particulas aëreas, quaſi eſſent <lb/> <anchor type="note" xlink:label="note-0452-10a" xlink:href="note-0452-10"/> puncta, & </s> <s xml:id="echoid-s11918" xml:space="preserve">celeritates, quæ in hac bypotheſi deteguntur, au-<lb/>gendæ ſunt pro ratione quam habet materia ad interſtitia, <lb/>ut veræ detegantur velocitates.</s> <s xml:id="echoid-s11919" xml:space="preserve"/> </p> <div xml:id="echoid-div1711" type="float" level="2" n="27"> <note position="left" xlink:label="note-0452-10" xlink:href="note-0452-10a" xml:space="preserve">1163.</note> </div> <p style="it"> <s xml:id="echoid-s11920" xml:space="preserve">Quare quamdiu idem aër ſuam ſervat denſitatem, ean-<lb/> <anchor type="note" xlink:label="note-0452-11a" xlink:href="note-0452-11"/> dem cum ipſa velocitate rationem ſequitur hujus angmentum.</s> <s xml:id="echoid-s11921" xml:space="preserve"/> </p> <div xml:id="echoid-div1712" type="float" level="2" n="28"> <note position="left" xlink:label="note-0452-11" xlink:href="note-0452-11a" xml:space="preserve">1164.</note> </div> <p> <s xml:id="echoid-s11922" xml:space="preserve">Si vero denſitas mutetur, augmentum non modo ſequitur <lb/> <anchor type="note" xlink:label="note-0452-12a" xlink:href="note-0452-12"/> rationem velocitatis, ſed & </s> <s xml:id="echoid-s11923" xml:space="preserve">rationem, materiæ ad materi-<lb/>am in eadem linea, quæ eſt ratio radicis cubicæ denſita-<lb/>tis.</s> <s xml:id="echoid-s11924" xml:space="preserve"/> </p> <div xml:id="echoid-div1713" type="float" level="2" n="29"> <note position="left" xlink:label="note-0452-12" xlink:href="note-0452-12a" xml:space="preserve">1165.</note> </div> <p> <s xml:id="echoid-s11925" xml:space="preserve">Si de diverſo aëre agatur, hæc regula non procedit, nam <lb/> <anchor type="note" xlink:label="note-0452-13a" xlink:href="note-0452-13"/> <pb o="333" file="0453" n="498" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> ipſæ particulæ, ſervata aëris denſitate, diverſam denſita-<lb/>tatem habere poſſunt, & </s> <s xml:id="echoid-s11926" xml:space="preserve">mutabitur ratio diametrorum par-<lb/>ticularum ad interſtitia.</s> <s xml:id="echoid-s11927" xml:space="preserve"/> </p> <div xml:id="echoid-div1714" type="float" level="2" n="30"> <note position="left" xlink:label="note-0452-13" xlink:href="note-0452-13a" xml:space="preserve">1166.</note> </div> <p> <s xml:id="echoid-s11928" xml:space="preserve">Vndarum in aëre motus ſonum producit; </s> <s xml:id="echoid-s11929" xml:space="preserve">de quo ante-<lb/> <anchor type="note" xlink:label="note-0453-01a" xlink:href="note-0453-01"/> quam agamus, pauca de ſenſationibus in genere præmitten-<lb/>da ſunt.</s> <s xml:id="echoid-s11930" xml:space="preserve"/> </p> <div xml:id="echoid-div1715" type="float" level="2" n="31"> <note position="right" xlink:label="note-0453-01" xlink:href="note-0453-01a" xml:space="preserve">1167.</note> </div> <p> <s xml:id="echoid-s11931" xml:space="preserve">Adeo arctum eſt mentis & </s> <s xml:id="echoid-s11932" xml:space="preserve">corporis vinculum, ut qui-<lb/> <anchor type="note" xlink:label="note-0453-02a" xlink:href="note-0453-02"/> dam motus in hoc cum certis in illa ideis quaſi cohæreant, <lb/>& </s> <s xml:id="echoid-s11933" xml:space="preserve">ſeparari nequeant. </s> <s xml:id="echoid-s11934" xml:space="preserve">Ex corporis motu omnibus momen-<lb/>tis ideæ novæ in mente excitantur, taleſque ſunt rerum <lb/>omnium ſenſibilium ideæ; </s> <s xml:id="echoid-s11935" xml:space="preserve">nihil tamen commune in-<lb/>ter motum in corpore & </s> <s xml:id="echoid-s11936" xml:space="preserve">ideam in mente percipimus. <lb/></s> <s xml:id="echoid-s11937" xml:space="preserve">Nexus qui hic datur perſpicientiam noſtram fugit, ne-<lb/>que ullum poſſibilem eſſe concipimus. </s> <s xml:id="echoid-s11938" xml:space="preserve">Innumera in <lb/>rerum univerſitate latent, quæ ne quidem ideis attingi-<lb/>mus.</s> <s xml:id="echoid-s11939" xml:space="preserve"/> </p> <div xml:id="echoid-div1716" type="float" level="2" n="32"> <note position="right" xlink:label="note-0453-02" xlink:href="note-0453-02a" xml:space="preserve">1168.</note> </div> <p> <s xml:id="echoid-s11940" xml:space="preserve">Aëris motus undulatorius agitat tympanum auris, quo <lb/> <anchor type="note" xlink:label="note-0453-03a" xlink:href="note-0453-03"/> aëri, hoc organo contento, motus communicatur, qui ubi <lb/>in nervum auditorium eſt tranſlatus, ſoni idea in mente <lb/>excitatur.</s> <s xml:id="echoid-s11941" xml:space="preserve"/> </p> <div xml:id="echoid-div1717" type="float" level="2" n="33"> <note position="right" xlink:label="note-0453-03" xlink:href="note-0453-03a" xml:space="preserve">1169.</note> </div> <p> <s xml:id="echoid-s11942" xml:space="preserve">Auris ſtructura mirabilis eſt, & </s> <s xml:id="echoid-s11943" xml:space="preserve">interna, & </s> <s xml:id="echoid-s11944" xml:space="preserve">externa; </s> <s xml:id="echoid-s11945" xml:space="preserve">ſed <lb/>de motu aëris agimus; </s> <s xml:id="echoid-s11946" xml:space="preserve">hunc eſſe vehiculum ſoni Experi-<lb/> <anchor type="note" xlink:label="note-0453-04a" xlink:href="note-0453-04"/> mento probatur,</s> </p> <div xml:id="echoid-div1718" type="float" level="2" n="34"> <note position="right" xlink:label="note-0453-04" xlink:href="note-0453-04a" xml:space="preserve">1170.</note> </div> </div> <div xml:id="echoid-div1720" type="section" level="1" n="415"> <head xml:id="echoid-head561" xml:space="preserve"><emph style="sc">Experimentum i</emph>.</head> <p> <s xml:id="echoid-s11947" xml:space="preserve">Orbi plumbeo O adhærent cylindri ex eodem metallo <lb/> <anchor type="note" xlink:label="note-0453-05a" xlink:href="note-0453-05"/> C, C, campana minor A filo æneo b d jungitur; </s> <s xml:id="echoid-s11948" xml:space="preserve">ligulis alli-<lb/> <anchor type="note" xlink:label="note-0453-06a" xlink:href="note-0453-06"/> gatur illa cylindris C, C. </s> <s xml:id="echoid-s11949" xml:space="preserve">Orbis O laminæ æneæ Machinæ <lb/>Pneumaticæ, interpoſito pulvillo ex bombyce xyli, impo-<lb/>nitur; </s> <s xml:id="echoid-s11950" xml:space="preserve">campana A, cum orbe & </s> <s xml:id="echoid-s11951" xml:space="preserve">cylindris, vitro obtegun-<lb/>tur. </s> <s xml:id="echoid-s11952" xml:space="preserve">Clauditur hoc operculo cum pyxide, quam filum æ-<lb/>neum mobile DE trajicit <anchor type="note" xlink:href="" symbol="*"/>, cohærente, filo jungitur lami- <anchor type="note" xlink:label="note-0453-07a" xlink:href="note-0453-07"/> na e f, ita. </s> <s xml:id="echoid-s11953" xml:space="preserve">ut circumvolutione fili campana A agitetur: </s> <s xml:id="echoid-s11954" xml:space="preserve">Aër <lb/>ſi exhauriatur ex vitro memorato, &</s> <s xml:id="echoid-s11955" xml:space="preserve">, ut dictum, agitetur cam-<lb/>pana, ſonus non auditur. </s> <s xml:id="echoid-s11956" xml:space="preserve">Unica circumvolutione fili DE <lb/>campana variis vicibus in motuſuo it & </s> <s xml:id="echoid-s11957" xml:space="preserve">redit, & </s> <s xml:id="echoid-s11958" xml:space="preserve">de hoc <pb o="334" file="0454" n="499" rhead="PHYSICES ELEMENTA"/> motu agitur, in quo lamina ef non tangit filum bd. </s> <s xml:id="echoid-s11959" xml:space="preserve">Ad-<lb/>miſſo aëre ſonus ut ante auditur.</s> <s xml:id="echoid-s11960" xml:space="preserve"/> </p> <div xml:id="echoid-div1720" type="float" level="2" n="1"> <note position="right" xlink:label="note-0453-05" xlink:href="note-0453-05a" xml:space="preserve">1171.</note> <note position="right" xlink:label="note-0453-06" xlink:href="note-0453-06a" xml:space="preserve">TAB. XLVI. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0453-07" xlink:href="note-0453-07a" xml:space="preserve">1096.</note> </div> <p> <s xml:id="echoid-s11961" xml:space="preserve">Ex eo ſolo quod aër ſit vehiculum ſoni, & </s> <s xml:id="echoid-s11962" xml:space="preserve">quod ſine <lb/>aëris tranilatione ſonus per illum moveatur, clare ſequitur <lb/>in ſono motum aëris undulatorium dari, & </s> <s xml:id="echoid-s11963" xml:space="preserve">ſonum ex motu <lb/> <anchor type="note" xlink:label="note-0454-01a" xlink:href="note-0454-01"/> corporum tremulo oriri. </s> <s xml:id="echoid-s11964" xml:space="preserve">Hoc etiam extra omne dubium <lb/>eſt, in chordis aut nervis tenſis, ex quibus agitatione tre-<lb/>mula ſonus elicitur. </s> <s xml:id="echoid-s11965" xml:space="preserve">In campanis majoribus & </s> <s xml:id="echoid-s11966" xml:space="preserve">in multis <lb/>aliis corporibus motus hicce tremulus admodum ſenſibilis <lb/>eſt; </s> <s xml:id="echoid-s11967" xml:space="preserve">in campana vitrea ſonum edente, Experimento ſequen-<lb/>ti, viſibilis fit.</s> <s xml:id="echoid-s11968" xml:space="preserve"/> </p> <div xml:id="echoid-div1721" type="float" level="2" n="2"> <note position="left" xlink:label="note-0454-01" xlink:href="note-0454-01a" xml:space="preserve">1172.</note> </div> </div> <div xml:id="echoid-div1723" type="section" level="1" n="416"> <head xml:id="echoid-head562" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s11969" xml:space="preserve">Campana vitrea CC gypſo, aut arenato, coagmentatur <lb/> <anchor type="note" xlink:label="note-0454-02a" xlink:href="note-0454-02"/> cochleæ ligneæ, cujus ope campana firmiter cum ligno AB <lb/> <anchor type="note" xlink:label="note-0454-03a" xlink:href="note-0454-03"/> conjungitur; </s> <s xml:id="echoid-s11970" xml:space="preserve">ſuſtinetur hoc duabus columnis S, S, & </s> <s xml:id="echoid-s11971" xml:space="preserve">co-<lb/>chleis firmatur. </s> <s xml:id="echoid-s11972" xml:space="preserve">Harum columnarum alteram, ad altitudi-<lb/>nem oræ campanæ, trajicit clavus cochlea circumdatus, <lb/>ita ut hunc circumvolvendo extremitas ad quamcumque di-<lb/>ſtantiam a campanæ ora firmetur. </s> <s xml:id="echoid-s11973" xml:space="preserve">Poſitâ diſtantiâ hac exi-<lb/>guâ, ſi pulſetur campana, motu ſuo tremulo in clavi extre-<lb/>mitatem variis vicibus impinget.</s> <s xml:id="echoid-s11974" xml:space="preserve"/> </p> <div xml:id="echoid-div1723" type="float" level="2" n="1"> <note position="left" xlink:label="note-0454-02" xlink:href="note-0454-02a" xml:space="preserve">1173.</note> <note position="left" xlink:label="note-0454-03" xlink:href="note-0454-03a" xml:space="preserve">TAB. XLVI. <lb/>fig. 3.</note> </div> <p style="it"> <s xml:id="echoid-s11975" xml:space="preserve">Non tamen immediate ab hoc motu viſibili pendet ſonus, <lb/> <anchor type="note" xlink:label="note-0454-04a" xlink:href="note-0454-04"/> ſed ab alio motu tremulo, quo, in motu memorato, particu-<lb/>læ minores afficiuntur.</s> <s xml:id="echoid-s11976" xml:space="preserve"/> </p> <div xml:id="echoid-div1724" type="float" level="2" n="2"> <note position="left" xlink:label="note-0454-04" xlink:href="note-0454-04a" xml:space="preserve">1174.</note> </div> </div> <div xml:id="echoid-div1726" type="section" level="1" n="417"> <head xml:id="echoid-head563" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s11977" xml:space="preserve">Lamina ferrea elaſtica ACB, motu tremulo viſibili affi-<lb/> <anchor type="note" xlink:label="note-0454-05a" xlink:href="note-0454-05"/> citur, ſi ad ſe invicem applicatis extremitatibus <emph style="sc">A</emph> & </s> <s xml:id="echoid-s11978" xml:space="preserve">B, <lb/> <anchor type="note" xlink:label="note-0454-06a" xlink:href="note-0454-06"/> hæ ſubito relaxentur, non tamen ſonus auditur; </s> <s xml:id="echoid-s11979" xml:space="preserve">ſi autem <lb/>alio ferro lateraliter percutiatur, quo non motu viſibili tre-<lb/>mulo agitatur, ex ipſa ſonus elicitur.</s> <s xml:id="echoid-s11980" xml:space="preserve"/> </p> <div xml:id="echoid-div1726" type="float" level="2" n="1"> <note position="left" xlink:label="note-0454-05" xlink:href="note-0454-05a" xml:space="preserve">1175.</note> <note position="left" xlink:label="note-0454-06" xlink:href="note-0454-06a" xml:space="preserve">TAB. XLVII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s11981" xml:space="preserve">Corpus percuſſum per aliquod tempus poſt ictum ſonum e-<lb/> <anchor type="note" xlink:label="note-0454-07a" xlink:href="note-0454-07"/> dit; </s> <s xml:id="echoid-s11982" xml:space="preserve">nam fibra agitata per aliquod tempus ex elaſticitate vi-<lb/>brationes continuat <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s11983" xml:space="preserve">Sonus etiam, ſubſiſtente motu tre- <anchor type="note" xlink:label="note-0454-08a" xlink:href="note-0454-08"/> mulo, ceſſat.</s> <s xml:id="echoid-s11984" xml:space="preserve"/> </p> <div xml:id="echoid-div1727" type="float" level="2" n="2"> <note position="left" xlink:label="note-0454-07" xlink:href="note-0454-07a" xml:space="preserve">1176.</note> <note symbol="*" position="left" xlink:label="note-0454-08" xlink:href="note-0454-08a" xml:space="preserve">686.</note> </div> <p> <s xml:id="echoid-s11985" xml:space="preserve">Sæpiſſime videmus, ut in Experimento 1.</s> <s xml:id="echoid-s11986" xml:space="preserve">, corpus ſo- <pb o="335" file="0455" n="500" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> num edere, licet aër ab eo agitatus nullam cum aëre ex-<lb/>teriori communicationem habeat; </s> <s xml:id="echoid-s11987" xml:space="preserve">ex quo ſequitur aëris a-<lb/> <anchor type="note" xlink:label="note-0455-01a" xlink:href="note-0455-01"/> gitatione fibras, ex quibus corpora conſtant, moveri; </s> <s xml:id="echoid-s11988" xml:space="preserve">qui <lb/>motus in aërem exteriorem transfertur.</s> <s xml:id="echoid-s11989" xml:space="preserve"/> </p> <div xml:id="echoid-div1728" type="float" level="2" n="3"> <note position="right" xlink:label="note-0455-01" xlink:href="note-0455-01a" xml:space="preserve">1177.</note> </div> <p> <s xml:id="echoid-s11990" xml:space="preserve">Hæc ſoni tranſſatio ex fibrarum motu tremulo maxime <lb/>notabilis eſt; </s> <s xml:id="echoid-s11991" xml:space="preserve">& </s> <s xml:id="echoid-s11992" xml:space="preserve">quouſque hujus motus communicatio ſeſe <lb/>extendat, unico Experimento patebit.</s> <s xml:id="echoid-s11993" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1730" type="section" level="1" n="418"> <head xml:id="echoid-head564" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s11994" xml:space="preserve">Differt hoc cum Experimento 1. </s> <s xml:id="echoid-s11995" xml:space="preserve">in hoc ſolo, loco <lb/> <anchor type="note" xlink:label="note-0455-02a" xlink:href="note-0455-02"/> machinæ plumbeæ COC campana funibus alligatur extre-<lb/> <anchor type="note" xlink:label="note-0455-03a" xlink:href="note-0455-03"/> mitatibus laminæ æneæ ad inſtar gnomonis duplicis inflexæ, <lb/>quæ cum orbe Antliæ Pneumaticæ ope cochleæ cohæret. <lb/></s> <s xml:id="echoid-s11996" xml:space="preserve">De cetero, evacuato aëre, campana eodem modo ac in 1. </s> <s xml:id="echoid-s11997" xml:space="preserve"><lb/>Experimento agitatur; </s> <s xml:id="echoid-s11998" xml:space="preserve">& </s> <s xml:id="echoid-s11999" xml:space="preserve">parva tantum inter ſonos, admiſſo <lb/>aut exhauſto aëre, percipitur differentia.</s> <s xml:id="echoid-s12000" xml:space="preserve"/> </p> <div xml:id="echoid-div1730" type="float" level="2" n="1"> <note position="right" xlink:label="note-0455-02" xlink:href="note-0455-02a" xml:space="preserve">1178.</note> <note position="right" xlink:label="note-0455-03" xlink:href="note-0455-03a" xml:space="preserve">TAB. XLVI. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s12001" xml:space="preserve">Motus tremulus partium campanæ communicatur filo <lb/> <anchor type="note" xlink:label="note-0455-04a" xlink:href="note-0455-04"/> æneo bd, quo funes, quibus campana ſuſpenditur, moven-<lb/>tur, motuſque transfertur in laminam æneam inflexam; <lb/></s> <s xml:id="echoid-s12002" xml:space="preserve">cochlea, qua hæc cum orbe æneo Machinæ Pneumaticæ <lb/>conjungitur, orbem hunc tangit, & </s> <s xml:id="echoid-s12003" xml:space="preserve">huic motum tremu-<lb/>lum communicat, quo aër agitatur, & </s> <s xml:id="echoid-s12004" xml:space="preserve">ſonus campanæ au-<lb/>ditur.</s> <s xml:id="echoid-s12005" xml:space="preserve"/> </p> <div xml:id="echoid-div1731" type="float" level="2" n="2"> <note position="right" xlink:label="note-0455-04" xlink:href="note-0455-04a" xml:space="preserve">1179.</note> </div> <p> <s xml:id="echoid-s12006" xml:space="preserve">Ut per ſolida corpora, ſic & </s> <s xml:id="echoid-s12007" xml:space="preserve">per fluida propagatur ſonus, <lb/> <anchor type="note" xlink:label="note-0455-05a" xlink:href="note-0455-05"/> in quo tamen caſu admodum debilitatur.</s> <s xml:id="echoid-s12008" xml:space="preserve"/> </p> <div xml:id="echoid-div1732" type="float" level="2" n="3"> <note position="right" xlink:label="note-0455-05" xlink:href="note-0455-05a" xml:space="preserve">1180.</note> </div> </div> <div xml:id="echoid-div1734" type="section" level="1" n="419"> <head xml:id="echoid-head565" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s12009" xml:space="preserve">Vitro A includitur companula C quæ malleis m, m, motu ro-<lb/> <anchor type="note" xlink:label="note-0455-06a" xlink:href="note-0455-06"/> tulæ agitatis, percutitur; </s> <s xml:id="echoid-s12010" xml:space="preserve">rotæque motus elafterio, illis ſimili, <lb/> <anchor type="note" xlink:label="note-0455-07a" xlink:href="note-0455-07"/> quæ in horologiis portatilibus uſu veniunt, per duo aut tria <lb/>minuta prima continuatur, vitrum operculo ligneo O obtegi-<lb/>tur, & </s> <s xml:id="echoid-s12011" xml:space="preserve">cerâ molli ingreſſus aquæ cohibetur. </s> <s xml:id="echoid-s12012" xml:space="preserve">Vitrum hoc-<lb/>ce vitro majori B, cujus fundus, ad altitudinem unius aut <lb/>duorum pollicum, mercurio obtegitur, immittitur, & </s> <s xml:id="echoid-s12013" xml:space="preserve"><lb/>vitrum B aquâ repletur. </s> <s xml:id="echoid-s12014" xml:space="preserve">Sonus auditur debilitatus tamen.</s> <s xml:id="echoid-s12015" xml:space="preserve"/> </p> <div xml:id="echoid-div1734" type="float" level="2" n="1"> <note position="right" xlink:label="note-0455-06" xlink:href="note-0455-06a" xml:space="preserve">1181.</note> <note position="right" xlink:label="note-0455-07" xlink:href="note-0455-07a" xml:space="preserve">TAB. XLVII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s12016" xml:space="preserve">Nulla autem inter campanam & </s> <s xml:id="echoid-s12017" xml:space="preserve">aërem externum, niſi <lb/>per fluida, aquam aut mercurium, communicatio datur.</s> <s xml:id="echoid-s12018" xml:space="preserve"/> </p> <pb o="336" file="0456" n="501" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s12019" xml:space="preserve">Celeritas ſoni eadem eſt cum celeritate undarum, quæ au-<lb/> <anchor type="note" xlink:label="note-0456-01a" xlink:href="note-0456-01"/> rem percutiunt, & </s> <s xml:id="echoid-s12020" xml:space="preserve">quæ de harum celeritate dicta ſunt <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0456-02a" xlink:href="note-0456-02"/> huc referri debent. </s> <s xml:id="echoid-s12021" xml:space="preserve">Circa n. </s> <s xml:id="echoid-s12022" xml:space="preserve">1152. </s> <s xml:id="echoid-s12023" xml:space="preserve">notandum ſoni celeri-<lb/>tatem computatione minime poſſe determinari <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12024" xml:space="preserve">ignota <anchor type="note" xlink:label="note-0456-03a" xlink:href="note-0456-03"/> enim eſt proportio inter diametros particularum & </s> <s xml:id="echoid-s12025" xml:space="preserve">interſtitia <lb/>inter has; </s> <s xml:id="echoid-s12026" xml:space="preserve">ut &</s> <s xml:id="echoid-s12027" xml:space="preserve">, quantum ſpatium particulæ hetorogeneæ <lb/>in aëre occupant, non conſtat. </s> <s xml:id="echoid-s12028" xml:space="preserve">Immediatè Experimento <lb/>detegitur ſoni celeritas.</s> <s xml:id="echoid-s12029" xml:space="preserve"/> </p> <div xml:id="echoid-div1735" type="float" level="2" n="2"> <note position="left" xlink:label="note-0456-01" xlink:href="note-0456-01a" xml:space="preserve">1182.</note> <note symbol="*" position="left" xlink:label="note-0456-02" xlink:href="note-0456-02a" xml:space="preserve">1152. 1153. <lb/>1155. 1156. <lb/>1157. 1158. <lb/>1159. 1160. <lb/>1161. 1163. <lb/>1164. 1165. <lb/>1166.</note> <note symbol="*" position="left" xlink:label="note-0456-03" xlink:href="note-0456-03a" xml:space="preserve">1162.</note> </div> <p> <s xml:id="echoid-s12030" xml:space="preserve">Nocte accendatur ignis cum ſtrepitu conjunctus, ad <lb/> <anchor type="note" xlink:label="note-0456-04a" xlink:href="note-0456-04"/> quamcunque ab hoc igne antea menſuratam diſtantiam de-<lb/>tur ſpectator, qui breviori pendulo menſuret tempus inter <lb/>lumen viſum & </s> <s xml:id="echoid-s12031" xml:space="preserve">ſonum auditum, quo datur ſoni celeritas; <lb/></s> <s xml:id="echoid-s12032" xml:space="preserve">luminis enim motus, ſaltem in ſpatio in quo hoc Experi-<lb/>mentum inſtitui poteſt, eſt momentaneus.</s> <s xml:id="echoid-s12033" xml:space="preserve"/> </p> <div xml:id="echoid-div1736" type="float" level="2" n="3"> <note position="left" xlink:label="note-0456-04" xlink:href="note-0456-04a" xml:space="preserve">1183.</note> </div> <p> <s xml:id="echoid-s12034" xml:space="preserve">Tali Experimento in Gallia enotuit ſonum percurrere pe-<lb/> <anchor type="note" xlink:label="note-0456-05a" xlink:href="note-0456-05"/> des Gallicos mille & </s> <s xml:id="echoid-s12035" xml:space="preserve">octoginta, id eſt, Rhenolandicos mille-<lb/>centum & </s> <s xml:id="echoid-s12036" xml:space="preserve">ſeptemdecim, in ſpatio temporis unius minuti <lb/>ſecundi: </s> <s xml:id="echoid-s12037" xml:space="preserve">ſed non conſtans eſt hæc celeritas <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12038" xml:space="preserve"/> </p> <div xml:id="echoid-div1737" type="float" level="2" n="4"> <note position="left" xlink:label="note-0456-05" xlink:href="note-0456-05a" xml:space="preserve">1184.</note> </div> <note symbol="*" position="left" xml:space="preserve">1161.</note> <p> <s xml:id="echoid-s12039" xml:space="preserve">Si eodem tempore, in quo hac methodo determinatur <lb/> <anchor type="note" xlink:label="note-0456-07a" xlink:href="note-0456-07"/> ſoni velocitas, detegatur ſpatium percurſum ex elaſticitate <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0456-08a" xlink:href="note-0456-08"/> dabitur ſoni acceleratio ex craſſitie particularum & </s> <s xml:id="echoid-s12040" xml:space="preserve">mate-<lb/>ria heterogenea.</s> <s xml:id="echoid-s12041" xml:space="preserve"/> </p> <div xml:id="echoid-div1738" type="float" level="2" n="5"> <note position="left" xlink:label="note-0456-07" xlink:href="note-0456-07a" xml:space="preserve">1185.</note> <note symbol="*" position="left" xlink:label="note-0456-08" xlink:href="note-0456-08a" xml:space="preserve">1152. 1162.</note> </div> <p style="it"> <s xml:id="echoid-s12042" xml:space="preserve">Soni celeritas eſt æquabilis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12043" xml:space="preserve">in majori nihilominus ſpa- <anchor type="note" xlink:label="note-0456-09a" xlink:href="note-0456-09"/> tio aliquando acceler atur aut retardatur <anchor type="note" xlink:href="" symbol="*"/>, ex diverſo ela- <anchor type="note" xlink:label="note-0456-10a" xlink:href="note-0456-10"/> <anchor type="note" xlink:label="note-0456-11a" xlink:href="note-0456-11"/> ſticitatis gradu, qui in variis locis, ſæpe datur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12044" xml:space="preserve"/> </p> <div xml:id="echoid-div1739" type="float" level="2" n="6"> <note position="left" xlink:label="note-0456-09" xlink:href="note-0456-09a" xml:space="preserve">1186.</note> <note symbol="*" position="left" xlink:label="note-0456-10" xlink:href="note-0456-10a" xml:space="preserve">1153.</note> <note symbol="*" position="left" xlink:label="note-0456-11" xlink:href="note-0456-11a" xml:space="preserve">1156.</note> </div> <note symbol="*" position="left" xml:space="preserve">1075.</note> <p> <s xml:id="echoid-s12045" xml:space="preserve">Soni celeritas parum variat ex vento cum illius motu con-<lb/> <anchor type="note" xlink:label="note-0456-13a" xlink:href="note-0456-13"/> ſpirante, aut in contrarium flante. </s> <s xml:id="echoid-s12046" xml:space="preserve">Vento certa aëris quanti-<lb/>tas de loco in locum transfertur; </s> <s xml:id="echoid-s12047" xml:space="preserve">acceleratur ſonus, quam-<lb/>diu per illam aëris partem movetur, ſi ſoni directio cum <lb/>venti directione eadem fuerit; </s> <s xml:id="echoid-s12048" xml:space="preserve">cum autem ſonus celerrime <lb/>moveatur, in tempore breviſſimo percurrit aërem a vento <lb/>agitatum, & </s> <s xml:id="echoid-s12049" xml:space="preserve">non diu acceleratio durat; </s> <s xml:id="echoid-s12050" xml:space="preserve">quæ de cetero <lb/>non admodum eſt magna: </s> <s xml:id="echoid-s12051" xml:space="preserve">venti enim violentiſſimi, quo <lb/>arbores eradicantur, & </s> <s xml:id="echoid-s12052" xml:space="preserve">ædificia ſubvertuntur, celeritas ſe <lb/>habet ad ſoni velocitatem, circiter ut unum ad triginta tria.</s> <s xml:id="echoid-s12053" xml:space="preserve"> <pb o="337" file="0457" n="502" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> Eodem argumento exiguam ex vento dari in ſoni motu re-<lb/>tardationem probatur.</s> <s xml:id="echoid-s12054" xml:space="preserve"/> </p> <div xml:id="echoid-div1740" type="float" level="2" n="7"> <note position="left" xlink:label="note-0456-13" xlink:href="note-0456-13a" xml:space="preserve">1187.</note> </div> <p> <s xml:id="echoid-s12055" xml:space="preserve">Spatium a particulis itu & </s> <s xml:id="echoid-s12056" xml:space="preserve">reditu percurſum a vento au-<lb/>geri aut minui poteſt; </s> <s xml:id="echoid-s12057" xml:space="preserve">idcirco ad majorem aut minorem di-<lb/> <anchor type="note" xlink:label="note-0457-01a" xlink:href="note-0457-01"/> ſtantiam ſonus auditur pro venti directione.</s> <s xml:id="echoid-s12058" xml:space="preserve"/> </p> <div xml:id="echoid-div1741" type="float" level="2" n="8"> <note position="right" xlink:label="note-0457-01" xlink:href="note-0457-01a" xml:space="preserve">1188.</note> </div> <p> <s xml:id="echoid-s12059" xml:space="preserve">Intenſitas ſoni pendet ab ictibus aëris in nervum audito-<lb/> <anchor type="note" xlink:label="note-0457-02a" xlink:href="note-0457-02"/> rium; </s> <s xml:id="echoid-s12060" xml:space="preserve">& </s> <s xml:id="echoid-s12061" xml:space="preserve">ſunt hi ut vires particulis percutientibus inſi-<lb/>tæ.</s> <s xml:id="echoid-s12062" xml:space="preserve"/> </p> <div xml:id="echoid-div1742" type="float" level="2" n="9"> <note position="right" xlink:label="note-0457-02" xlink:href="note-0457-02a" xml:space="preserve">1189.</note> </div> <p> <s xml:id="echoid-s12063" xml:space="preserve">Vires hæ ſunt ut numeri particularum eodem tempore in <lb/>tympanum incurrentium, & </s> <s xml:id="echoid-s12064" xml:space="preserve">ut quadrata celeritatum qui-<lb/>bus incurrunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12065" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">476.</note> <p style="it"> <s xml:id="echoid-s12066" xml:space="preserve">In determinanda ſoni intenſitate, conſideranda ergo ſunt, <lb/> <anchor type="note" xlink:label="note-0457-04a" xlink:href="note-0457-04"/> aëris denſitas, ſoni velocitas, ſpatium itu & </s> <s xml:id="echoid-s12067" xml:space="preserve">reditu a par-<lb/>ticulis percur ſum, & </s> <s xml:id="echoid-s12068" xml:space="preserve">numerus undarum certo tempore in au-<lb/>rem incurrentium.</s> <s xml:id="echoid-s12069" xml:space="preserve"/> </p> <div xml:id="echoid-div1743" type="float" level="2" n="10"> <note position="right" xlink:label="note-0457-04" xlink:href="note-0457-04a" xml:space="preserve">1190.</note> </div> <p> <s xml:id="echoid-s12070" xml:space="preserve">Cæteris manentibus ſi mutetur tantum pondus quo aër com-<lb/> <anchor type="note" xlink:label="note-0457-05a" xlink:href="note-0457-05"/> primitur, non eo mutabitur ſpatium itu & </s> <s xml:id="echoid-s12071" xml:space="preserve">reditu a par-<lb/>ticulis percurſum, quod tantum aucta, aut imminuta, agi-<lb/>tatione tremula partium corporis variat; </s> <s xml:id="echoid-s12072" xml:space="preserve">neque numerus <lb/>undarum, hæ etiam a corpore tremulo pendent; </s> <s xml:id="echoid-s12073" xml:space="preserve">non etiam <lb/>mutatur ſoni velocitas <anchor type="note" xlink:href="" symbol="*"/>, ſepoſita acceleratione de qua in <anchor type="note" xlink:label="note-0457-06a" xlink:href="note-0457-06"/> n. </s> <s xml:id="echoid-s12074" xml:space="preserve">1163. </s> <s xml:id="echoid-s12075" xml:space="preserve">locuti ſumus, quæ hîc non conſideranda eſt, quia <lb/>agitur de velocitatè qua ſingulæ particulæ feruntur; </s> <s xml:id="echoid-s12076" xml:space="preserve">ſola <lb/>ergo variat denſitas, id eſt, ſolus mutatur numerus par-<lb/> <anchor type="note" xlink:label="note-0457-07a" xlink:href="note-0457-07"/> ticularum certo tempore incurrentium, & </s> <s xml:id="echoid-s12077" xml:space="preserve">in hac ratio-<lb/>ne mutatur ſoni intenſitas <anchor type="note" xlink:href="" symbol="*"/>, id eſt, in ratione ipſius <anchor type="note" xlink:label="note-0457-08a" xlink:href="note-0457-08"/> denſitatis, quæ ponderis comprimentis rationem ſequi-<lb/>tur.</s> <s xml:id="echoid-s12078" xml:space="preserve"/> </p> <div xml:id="echoid-div1744" type="float" level="2" n="11"> <note position="right" xlink:label="note-0457-05" xlink:href="note-0457-05a" xml:space="preserve">1191.</note> <note symbol="*" position="right" xlink:label="note-0457-06" xlink:href="note-0457-06a" xml:space="preserve">1153.</note> <note symbol="*" position="right" xlink:label="note-0457-07" xlink:href="note-0457-07a" xml:space="preserve">1189.</note> <note symbol="*" position="right" xlink:label="note-0457-08" xlink:href="note-0457-08a" xml:space="preserve">1066.</note> </div> <p> <s xml:id="echoid-s12079" xml:space="preserve">Augeri intenſitatem experimento conſtat.</s> <s xml:id="echoid-s12080" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1746" type="section" level="1" n="420"> <head xml:id="echoid-head566" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s12081" xml:space="preserve">Agitetur campana A, in aëre compreſſo <anchor type="note" xlink:href="" symbol="*"/>, eodem modo <anchor type="note" xlink:label="note-0457-09a" xlink:href="note-0457-09"/> <anchor type="note" xlink:label="note-0457-10a" xlink:href="note-0457-10"/> ac in vacuo agitatur in Experimento 1.</s> <s xml:id="echoid-s12082" xml:space="preserve">, augebitur ſonus; <lb/></s> <s xml:id="echoid-s12083" xml:space="preserve"> <anchor type="note" xlink:label="note-0457-11a" xlink:href="note-0457-11"/> qui iterum minuetur, ſi aperto epiſtomio aër in ſtatum pri-<lb/>ſtinum inſtauretur.</s> <s xml:id="echoid-s12084" xml:space="preserve"/> </p> <div xml:id="echoid-div1746" type="float" level="2" n="1"> <note position="right" xlink:label="note-0457-09" xlink:href="note-0457-09a" xml:space="preserve">1192.</note> <note symbol="*" position="right" xlink:label="note-0457-10" xlink:href="note-0457-10a" xml:space="preserve">1111.</note> <note position="right" xlink:label="note-0457-11" xlink:href="note-0457-11a" xml:space="preserve">TAB. XLVI. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12085" xml:space="preserve">Cum in aëre compreſſo incluſo ſoni intenſitas major ſit, <pb o="338" file="0458" n="503" rhead="PHYSICES ELEMENTA"/> etiam magis fibræ ex quibus vas VV conſtat agitantur, ma-<lb/>jorque agitatio aëri exteriori communicatur.</s> <s xml:id="echoid-s12086" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12087" xml:space="preserve">Si cetera maneant, elaſticitas autem augeatur, in ea-<lb/> <anchor type="note" xlink:label="note-0458-01a" xlink:href="note-0458-01"/> dem ratione cum aucta elaſticitate minuitur quidem den-<lb/>ſitas <anchor type="note" xlink:href="" symbol="*"/>, ſed demonſtramus in ſcholio, huic capiti ſubjun- <anchor type="note" xlink:label="note-0458-02a" xlink:href="note-0458-02"/> cto, ſoni intenſitatem augeri in ratione quam ſequitur <lb/>radix quadrata elaſticitatis. </s> <s xml:id="echoid-s12088" xml:space="preserve">Unde ſequitur Æſtate, <lb/> <anchor type="note" xlink:label="note-0458-03a" xlink:href="note-0458-03"/> cæteris paribus, ſoni intenſitatem majorem eſſe quàm Hie-<lb/>me.</s> <s xml:id="echoid-s12089" xml:space="preserve"/> </p> <div xml:id="echoid-div1747" type="float" level="2" n="2"> <note position="left" xlink:label="note-0458-01" xlink:href="note-0458-01a" xml:space="preserve">1193.</note> <note symbol="*" position="left" xlink:label="note-0458-02" xlink:href="note-0458-02a" xml:space="preserve">1071</note> <note position="left" xlink:label="note-0458-03" xlink:href="note-0458-03a" xml:space="preserve">1194.</note> </div> </div> <div xml:id="echoid-div1749" type="section" level="1" n="421"> <head xml:id="echoid-head567" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s12090" xml:space="preserve">Campana A in vitro ſuſpendatur, habeatque, aperto e-<lb/> <anchor type="note" xlink:label="note-0458-04a" xlink:href="note-0458-04"/> piſtomio, aër in vitro communicationem cum aëre exterio-<lb/> <anchor type="note" xlink:label="note-0458-05a" xlink:href="note-0458-05"/> ri. </s> <s xml:id="echoid-s12091" xml:space="preserve">Agitetur vitrum, & </s> <s xml:id="echoid-s12092" xml:space="preserve">determinetur diſtantia ad quam ſo-<lb/>nus audiri poteſt, Calefacto vitro cum aëre interno, & </s> <s xml:id="echoid-s12093" xml:space="preserve"><lb/>Experimento repetito, ad majorem diſtantiam audietur ſo-<lb/>nus.</s> <s xml:id="echoid-s12094" xml:space="preserve"/> </p> <div xml:id="echoid-div1749" type="float" level="2" n="1"> <note position="left" xlink:label="note-0458-04" xlink:href="note-0458-04a" xml:space="preserve">1195.</note> <note position="left" xlink:label="note-0458-05" xlink:href="note-0458-05a" xml:space="preserve">TAB. XLVI. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s12095" xml:space="preserve">Datur etiam differentia in ſono ex numero vibrationum <lb/> <anchor type="note" xlink:label="note-0458-06a" xlink:href="note-0458-06"/> fibrarum corporis ſonum edentis, id eſt, ex numero unda-<lb/>rum certo tempore in aëre productarum; </s> <s xml:id="echoid-s12096" xml:space="preserve">pro diverſo enim <lb/>numero percuſſionum in aurem, ſenſatio diverſa in mente <lb/>datur.</s> <s xml:id="echoid-s12097" xml:space="preserve"/> </p> <div xml:id="echoid-div1750" type="float" level="2" n="2"> <note position="left" xlink:label="note-0458-06" xlink:href="note-0458-06a" xml:space="preserve">1196.</note> </div> <p style="it"> <s xml:id="echoid-s12098" xml:space="preserve">Ab hoc vibrationum numero pendet tonus muſicus, qui <lb/> <anchor type="note" xlink:label="note-0458-07a" xlink:href="note-0458-07"/> eo magis acutus dicitur, quo magis crebri ſunt recurſus <lb/>in aëre; </s> <s xml:id="echoid-s12099" xml:space="preserve">eo vero gravior, quo minor eſt undarum nume-<lb/>rus.</s> <s xml:id="echoid-s12100" xml:space="preserve"/> </p> <div xml:id="echoid-div1751" type="float" level="2" n="3"> <note position="left" xlink:label="note-0458-07" xlink:href="note-0458-07a" xml:space="preserve">1197.</note> </div> <p style="it"> <s xml:id="echoid-s12101" xml:space="preserve">Gradusque acuminis diver ſorum ſonorum ſunt inter ſe ut <lb/> <anchor type="note" xlink:label="note-0458-08a" xlink:href="note-0458-08"/> undarum numeri, quæ eodem tempore in aëre dantur.</s> <s xml:id="echoid-s12102" xml:space="preserve"/> </p> <div xml:id="echoid-div1752" type="float" level="2" n="4"> <note position="left" xlink:label="note-0458-08" xlink:href="note-0458-08a" xml:space="preserve">1198.</note> </div> <p style="it"> <s xml:id="echoid-s12103" xml:space="preserve">Tonus ab intenſitate ſoni non pendet, & </s> <s xml:id="echoid-s12104" xml:space="preserve">chorda agitata <lb/> <anchor type="note" xlink:label="note-0458-09a" xlink:href="note-0458-09"/> eundem edit ſonum, ſive per majus ſive per minus ſpatium <lb/>eat, & </s> <s xml:id="echoid-s12105" xml:space="preserve">redeat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12106" xml:space="preserve"/> </p> <div xml:id="echoid-div1753" type="float" level="2" n="5"> <note position="left" xlink:label="note-0458-09" xlink:href="note-0458-09a" xml:space="preserve">1199.</note> </div> <note symbol="*" position="left" xml:space="preserve">686. 1197.</note> <p style="it"> <s xml:id="echoid-s12107" xml:space="preserve">Conſonantiæ oriuntur ex convenientia inter varios mo-<lb/> <anchor type="note" xlink:label="note-0458-11a" xlink:href="note-0458-11"/> tus in aëre, qui eodem tempore nervum auditorium affi-<lb/>ciunt.</s> <s xml:id="echoid-s12108" xml:space="preserve"/> </p> <div xml:id="echoid-div1754" type="float" level="2" n="6"> <note position="left" xlink:label="note-0458-11" xlink:href="note-0458-11a" xml:space="preserve">1200.</note> </div> <p style="it"> <s xml:id="echoid-s12109" xml:space="preserve">Si duo corpora tremula, temporibus æqualibus, vibratio-<lb/> <anchor type="note" xlink:label="note-0458-12a" xlink:href="note-0458-12"/> nes peragant, nulla inter tonos datur differentia, & </s> <s xml:id="echoid-s12110" xml:space="preserve">con- <pb file="0459" n="504"/> <pb file="0459a" n="505"/> <anchor type="figure" xlink:label="fig-0459a-01a" xlink:href="fig-0459a-01"/> <pb file="0460" n="506"/> <pb o="339" file="0461" n="507" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> ſonantia hæc omnium perfectiſſima Vniſonus dicitur.</s> <s xml:id="echoid-s12111" xml:space="preserve"/> </p> <div xml:id="echoid-div1755" type="float" level="2" n="7"> <note position="left" xlink:label="note-0458-12" xlink:href="note-0458-12a" xml:space="preserve">1201.</note> <figure xlink:label="fig-0459a-01" xlink:href="fig-0459a-01a"> <image file="0459a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0459a-01"/> </figure> </div> <p style="it"> <s xml:id="echoid-s12112" xml:space="preserve">Si vibrationes fuerint ut unum ad duo, conſonantia vo-<lb/> <anchor type="note" xlink:label="note-0461-01a" xlink:href="note-0461-01"/> catur Octava, aut Diapaſon.</s> <s xml:id="echoid-s12113" xml:space="preserve"/> </p> <div xml:id="echoid-div1756" type="float" level="2" n="8"> <note position="right" xlink:label="note-0461-01" xlink:href="note-0461-01a" xml:space="preserve">1202.</note> </div> <p> <s xml:id="echoid-s12114" xml:space="preserve">Poſitis vibrationibus ut duo ad tria, id eſt, ſi unius cor-<lb/> <anchor type="note" xlink:label="note-0461-02a" xlink:href="note-0461-02"/> poris vibratio ſecunda cum tertia alterius ſemper concur-<lb/>rat, conſonantia dicitur Quinta, aut Diapente.</s> <s xml:id="echoid-s12115" xml:space="preserve"/> </p> <div xml:id="echoid-div1757" type="float" level="2" n="9"> <note position="right" xlink:label="note-0461-02" xlink:href="note-0461-02a" xml:space="preserve">1203.</note> </div> <p style="it"> <s xml:id="echoid-s12116" xml:space="preserve">Vibrationes, quæ ſunt ut tria ad quatuor, dant conſo-<lb/> <anchor type="note" xlink:label="note-0461-03a" xlink:href="note-0461-03"/> nantiam, quæ vocatur Quarta, aut Diate{ſS}aron.</s> <s xml:id="echoid-s12117" xml:space="preserve"/> </p> <div xml:id="echoid-div1758" type="float" level="2" n="10"> <note position="right" xlink:label="note-0461-03" xlink:href="note-0461-03a" xml:space="preserve">1204.</note> </div> <p style="it"> <s xml:id="echoid-s12118" xml:space="preserve">Ditonus nominatur, ſi aëris recurſus fuerint ut quatuor <lb/> <anchor type="note" xlink:label="note-0461-04a" xlink:href="note-0461-04"/> ad quinque.</s> <s xml:id="echoid-s12119" xml:space="preserve"/> </p> <div xml:id="echoid-div1759" type="float" level="2" n="11"> <note position="right" xlink:label="note-0461-04" xlink:href="note-0461-04a" xml:space="preserve">1205.</note> </div> <p style="it"> <s xml:id="echoid-s12120" xml:space="preserve">Et Seſquiditonus dicitur conſonantia ex concur ſu quintæ <lb/> <anchor type="note" xlink:label="note-0461-05a" xlink:href="note-0461-05"/> vibrationis unius corporis cum ſexta alterius.</s> <s xml:id="echoid-s12121" xml:space="preserve"/> </p> <div xml:id="echoid-div1760" type="float" level="2" n="12"> <note position="right" xlink:label="note-0461-05" xlink:href="note-0461-05a" xml:space="preserve">1206.</note> </div> <p> <s xml:id="echoid-s12122" xml:space="preserve">Conſonantiæ ex agitatione chordarum, ſi hæ fuerint e-<lb/>juſdem generis, ex notis harum dimenſionibus ut & </s> <s xml:id="echoid-s12123" xml:space="preserve">tenſio-<lb/>ne, facile determinantur; </s> <s xml:id="echoid-s12124" xml:space="preserve">minimarum enim partium agita-<lb/>tiones ab in integrarum chordarum agitationibus pen-<lb/>dent.</s> <s xml:id="echoid-s12125" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s12126" xml:space="preserve">Ceteris paribus, ſi duarum chordarum longitudines fue-<lb/> <anchor type="note" xlink:label="note-0461-06a" xlink:href="note-0461-06"/> rint ut numeri recur ſuum in conſonantia, datur hæc inter <lb/>ſonos quos chordæ edunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12127" xml:space="preserve"/> </p> <div xml:id="echoid-div1761" type="float" level="2" n="13"> <note position="right" xlink:label="note-0461-06" xlink:href="note-0461-06a" xml:space="preserve">1207.</note> </div> <note symbol="*" position="right" xml:space="preserve">689.</note> <p style="it"> <s xml:id="echoid-s12128" xml:space="preserve">Idem obtinet, ſi ceteris paribus diametri prædictam pro-<lb/> <anchor type="note" xlink:label="note-0461-08a" xlink:href="note-0461-08"/> portionem habent <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12129" xml:space="preserve"/> </p> <div xml:id="echoid-div1762" type="float" level="2" n="14"> <note position="right" xlink:label="note-0461-08" xlink:href="note-0461-08a" xml:space="preserve">1208.</note> </div> <note symbol="*" position="right" xml:space="preserve">690.</note> <p style="it"> <s xml:id="echoid-s12130" xml:space="preserve">Etiam ſi ceteris paribus proportio vibrationum in conſo-<lb/> <anchor type="note" xlink:label="note-0461-10a" xlink:href="note-0461-10"/> nantia detur inter radices quadratas tenſionum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12131" xml:space="preserve"/> </p> <div xml:id="echoid-div1763" type="float" level="2" n="15"> <note position="right" xlink:label="note-0461-10" xlink:href="note-0461-10a" xml:space="preserve">1209.</note> </div> <note symbol="*" position="right" xml:space="preserve">688.</note> <p style="it"> <s xml:id="echoid-s12132" xml:space="preserve">Et generaliter, poſitis chordis ejuſdem generis quibus-<lb/> <anchor type="note" xlink:label="note-0461-12a" xlink:href="note-0461-12"/> cunque, ſi ratio compoſita ex directa longitudinum, & </s> <s xml:id="echoid-s12133" xml:space="preserve">dia-<lb/>metrorum, & </s> <s xml:id="echoid-s12134" xml:space="preserve">inverſa radicum quadratarum tenſionum, ſit <lb/>ratio inter numeros vibrationum eodem tempore peractarum <lb/>in conſonantia quacunque, datur hæc ex agitatione chor-<lb/>darum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12135" xml:space="preserve"/> </p> <div xml:id="echoid-div1764" type="float" level="2" n="16"> <note position="right" xlink:label="note-0461-12" xlink:href="note-0461-12a" xml:space="preserve">1210.</note> </div> <note symbol="*" position="right" xml:space="preserve">691.</note> <p> <s xml:id="echoid-s12136" xml:space="preserve">Hæc omnia a Muſicis fuere Experimentis confir-<lb/>mata.</s> <s xml:id="echoid-s12137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12138" xml:space="preserve">Notarunt hi circa haſce chordas Phænomenon admodum <lb/>notabile, cujus caſus varii digni ſunt qui explicentur.</s> <s xml:id="echoid-s12139" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12140" xml:space="preserve">Dentur chordæ quæcunquæ tenſæ, vibrationes ſuas æqua-<lb/> <anchor type="note" xlink:label="note-0461-14a" xlink:href="note-0461-14"/> <pb o="340" file="0462" n="508" rhead="PHYSICES ELEMENTA"/> libus temporibus peragentes; </s> <s xml:id="echoid-s12141" xml:space="preserve">agitetur una, movebitur & </s> <s xml:id="echoid-s12142" xml:space="preserve"><lb/>altera. </s> <s xml:id="echoid-s12143" xml:space="preserve">Singulæ aëris undæ ex illius chordæ motu tremu-<lb/>lo impingunt in hanc, motumque minimum huic communi-<lb/>cant; </s> <s xml:id="echoid-s12144" xml:space="preserve">ex motu quantumvis exiguo variis vicibus it & </s> <s xml:id="echoid-s12145" xml:space="preserve">re-<lb/>dit chorda <anchor type="note" xlink:href="" symbol="*"/>, moveturque ex prioris undæ ictu, dum ſe- <anchor type="note" xlink:label="note-0462-01a" xlink:href="note-0462-01"/> cunda accedit, cujus motus cum chordæ motu conſpirat <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0462-02a" xlink:href="note-0462-02"/> & </s> <s xml:id="echoid-s12146" xml:space="preserve">hunc accelerat. </s> <s xml:id="echoid-s12147" xml:space="preserve">Quæ de ſecunda unda dicuntur, etiam <lb/>ad ſequentes referri debent, & </s> <s xml:id="echoid-s12148" xml:space="preserve">acceleratio dabitur donec <lb/>ambarum chordarum motus fuerint fere æquales.</s> <s xml:id="echoid-s12149" xml:space="preserve"/> </p> <div xml:id="echoid-div1765" type="float" level="2" n="17"> <note position="right" xlink:label="note-0461-14" xlink:href="note-0461-14a" xml:space="preserve">1211.</note> <note symbol="*" position="left" xlink:label="note-0462-01" xlink:href="note-0462-01a" xml:space="preserve">686.</note> <note symbol="*" position="left" xlink:label="note-0462-02" xlink:href="note-0462-02a" xml:space="preserve">686.</note> </div> <p style="it"> <s xml:id="echoid-s12150" xml:space="preserve">Ex eadem demonſtratione ſequitur chordam agitatam mo-<lb/> <anchor type="note" xlink:label="note-0462-03a" xlink:href="note-0462-03"/> tum communicare alteri, quæ duas aut tres peragit vibra-<lb/>tiones dum prior ſemel vibratur.</s> <s xml:id="echoid-s12151" xml:space="preserve"/> </p> <div xml:id="echoid-div1766" type="float" level="2" n="18"> <note position="left" xlink:label="note-0462-03" xlink:href="note-0462-03a" xml:space="preserve">1212.</note> </div> <p> <s xml:id="echoid-s12152" xml:space="preserve">Si autem chorda agitata varias peragit vibrationes dum <lb/> <anchor type="note" xlink:label="note-0462-04a" xlink:href="note-0462-04"/> chorda ex aëre movenda unicam peragere poteſt, ex præ-<lb/>cedenti demonſtratione ſequetur motum peculiarem huic <lb/>communicatum iri. </s> <s xml:id="echoid-s12153" xml:space="preserve">Qui ut detegatur, notandum, dura-<lb/>tionem vibrationis & </s> <s xml:id="echoid-s12154" xml:space="preserve">chordæ longitudinem reciprocari ita, <lb/>ut, ceteris manentibus, determinata longitudo ab immi-<lb/>nuta duratione vibrationis ſeparari neutiquam poſſit. <lb/></s> <s xml:id="echoid-s12155" xml:space="preserve">Si ergo chorda quæcumque variis ictibus percutiatur, quibus <lb/>huic motus communicatur, & </s> <s xml:id="echoid-s12156" xml:space="preserve">ictus magis crebri ſint, quam <lb/>qui longitudini chordæ conveniunt, hujus pars, cujus longitu-<lb/>do cum duratione communicatarum vibrationum reſpondet, <lb/>tantum agitabitur, & </s> <s xml:id="echoid-s12157" xml:space="preserve">motus quaſi undulatorius chordæ com-<lb/>municabitur; </s> <s xml:id="echoid-s12158" xml:space="preserve">& </s> <s xml:id="echoid-s12159" xml:space="preserve">longitudo undarum in chorda pendebit a du-<lb/>ratione vibrationis communicatæ, id eſt, a tempore inter ictus.</s> <s xml:id="echoid-s12160" xml:space="preserve"/> </p> <div xml:id="echoid-div1767" type="float" level="2" n="19"> <note position="left" xlink:label="note-0462-04" xlink:href="note-0462-04a" xml:space="preserve">1213.</note> </div> <p> <s xml:id="echoid-s12161" xml:space="preserve">Dentur duæ chordæ, quarum una bis vibratur dum al-<lb/> <anchor type="note" xlink:label="note-0462-05a" xlink:href="note-0462-05"/> tera ſemel, & </s> <s xml:id="echoid-s12162" xml:space="preserve">illa agitetur, duratio vibrationum, quæ ex <lb/>aëris motu huic chordæ communicantur, competit chordæ <lb/>ſemilongitudinis hujus <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s12163" xml:space="preserve">talis eſt longitudo undarum in <anchor type="note" xlink:label="note-0462-06a" xlink:href="note-0462-06"/> hac ipſa. </s> <s xml:id="echoid-s12164" xml:space="preserve">Idcirco ex motu communicato dividitur chorda in <lb/>duas partes æquales, punctumque medium quieſcit. </s> <s xml:id="echoid-s12165" xml:space="preserve">Expe-<lb/>rimento hoc confirmatur jungendo chartæ fruſtum chordæ, <lb/>cui motus communicatur, quod ſi in puncto medio pona-<lb/>tur quieſcit, in omni alio loco motu tremulo afficitur.</s> <s xml:id="echoid-s12166" xml:space="preserve"/> </p> <div xml:id="echoid-div1768" type="float" level="2" n="20"> <note position="left" xlink:label="note-0462-05" xlink:href="note-0462-05a" xml:space="preserve">1214.</note> <note symbol="*" position="left" xlink:label="note-0462-06" xlink:href="note-0462-06a" xml:space="preserve">689.</note> </div> <pb o="341" file="0463" n="509" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> <p> <s xml:id="echoid-s12167" xml:space="preserve">Si chorda agitata, ut ex hujus motu altera moveatur, <lb/> <anchor type="note" xlink:label="note-0463-01a" xlink:href="note-0463-01"/> tres peragat vibrationes dum chorda movenda ſemel vibratur, <lb/>ex motu communicato dividetur hæc in tres partes, & </s> <s xml:id="echoid-s12168" xml:space="preserve">duo <lb/>dabuntur puncta quietis, quod eodem modo Experimento <lb/>confirmatur. </s> <s xml:id="echoid-s12169" xml:space="preserve">Alii caſus motus communicati, qui a Muſicis <lb/>obſervantur, facile ex prædictis deducuntur.</s> <s xml:id="echoid-s12170" xml:space="preserve"/> </p> <div xml:id="echoid-div1769" type="float" level="2" n="21"> <note position="right" xlink:label="note-0463-01" xlink:href="note-0463-01a" xml:space="preserve">1215.</note> </div> <p> <s xml:id="echoid-s12171" xml:space="preserve">Quæ de reflexione & </s> <s xml:id="echoid-s12172" xml:space="preserve">inflexione undarum in aqua dicta <lb/> <anchor type="note" xlink:label="note-0463-02a" xlink:href="note-0463-02"/> ſunt <anchor type="note" xlink:href="" symbol="*"/>, ad harum reflexionem in aëre referri poſſunt, ela- <anchor type="note" xlink:label="note-0463-03a" xlink:href="note-0463-03"/> ſticitate in hoc caſu eundem effectum cum preſſione aquæ <lb/>elevatæ in illo exerente.</s> <s xml:id="echoid-s12173" xml:space="preserve"/> </p> <div xml:id="echoid-div1770" type="float" level="2" n="22"> <note position="right" xlink:label="note-0463-02" xlink:href="note-0463-02a" xml:space="preserve">1216.</note> <note symbol="*" position="right" xlink:label="note-0463-03" xlink:href="note-0463-03a" xml:space="preserve">877. 879. <lb/>880. 883.</note> </div> <p> <s xml:id="echoid-s12174" xml:space="preserve">Ex ſoni reflexione ſæpiſſime oritur ſoni repetitio, quæ <lb/> <anchor type="note" xlink:label="note-0463-04a" xlink:href="note-0463-04"/> Echo vocatur. </s> <s xml:id="echoid-s12175" xml:space="preserve">Si ejuſdem undæ, per ſphæram ſeſe expan-<lb/>dentis <anchor type="note" xlink:href="" symbol="*"/>, partes variæ in varias ſuperficies impingant ita, <anchor type="note" xlink:label="note-0463-05a" xlink:href="note-0463-05"/> ut reflexæ concurrant, fortior ibi eſt aëris motus, & </s> <s xml:id="echoid-s12176" xml:space="preserve">ſonus <lb/>auditur. </s> <s xml:id="echoid-s12177" xml:space="preserve">Variis vicibus ſæpe idem ſonus repetitur, ex va-<lb/> <anchor type="note" xlink:label="note-0463-06a" xlink:href="note-0463-06"/> riis ejuſdem undæ partibus ad varias diſtantias reflexis, & </s> <s xml:id="echoid-s12178" xml:space="preserve"><lb/>quarum quædam ſucceſſive in eodem loco concurrunt. </s> <s xml:id="echoid-s12179" xml:space="preserve">Ta-<lb/>lis repetitio etiam aliquando datur ex repetita reflexione.</s> <s xml:id="echoid-s12180" xml:space="preserve"/> </p> <div xml:id="echoid-div1771" type="float" level="2" n="23"> <note position="right" xlink:label="note-0463-04" xlink:href="note-0463-04a" xml:space="preserve">1217.</note> <note symbol="*" position="right" xlink:label="note-0463-05" xlink:href="note-0463-05a" xml:space="preserve">1137.</note> <note position="right" xlink:label="note-0463-06" xlink:href="note-0463-06a" xml:space="preserve">1218.</note> </div> <p> <s xml:id="echoid-s12181" xml:space="preserve">In tubo per reflexionem augetur ſonus; </s> <s xml:id="echoid-s12182" xml:space="preserve">ut in tubis ften-<lb/> <anchor type="note" xlink:label="note-0463-07a" xlink:href="note-0463-07"/> toreis obſervatur. </s> <s xml:id="echoid-s12183" xml:space="preserve">Figura omnium perfectiſſima, quæ ta-<lb/>li tubæ dari poteſt, eſt parabolæ, circa lineam axi ad di-<lb/>ſtantiam quartæ partis pollicis parallelam, rotantis. </s> <s xml:id="echoid-s12184" xml:space="preserve">Si e-<lb/>nim quis in tali tuba loquatur, ponendo os in axe machinæ <lb/>& </s> <s xml:id="echoid-s12185" xml:space="preserve">in foco parabolæ, undæ ita reflectuntur, ut ſingulæ harum <lb/>partes motum, axi machinæ parallelum, acquirant; </s> <s xml:id="echoid-s12186" xml:space="preserve">quo un-<lb/>dæ vis & </s> <s xml:id="echoid-s12187" xml:space="preserve">etiam ſonus multum augetur. </s> <s xml:id="echoid-s12188" xml:space="preserve">Tubi extremitas, <lb/>major ex qua ſonus exit, ad formam labiorum inflectitur, <lb/>ut facilius unda quaquaverſum ſeſe diſpergat.</s> <s xml:id="echoid-s12189" xml:space="preserve"/> </p> <div xml:id="echoid-div1772" type="float" level="2" n="24"> <note position="right" xlink:label="note-0463-07" xlink:href="note-0463-07a" xml:space="preserve">1219.</note> </div> </div> <div xml:id="echoid-div1774" type="section" level="1" n="422"> <head xml:id="echoid-head568" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s12190" xml:space="preserve">Loquatur quis ſubmiſſa voce, dum os aperturæ minori <lb/> <anchor type="note" xlink:label="note-0463-08a" xlink:href="note-0463-08"/> Tubæ memoratæ applicat, ſi hæc longitudinem habeat qua-<lb/> <anchor type="note" xlink:label="note-0463-09a" xlink:href="note-0463-09"/> tuor pedum, ſonus ad magnam diſtantiam, & </s> <s xml:id="echoid-s12191" xml:space="preserve">in vicimis ad-<lb/>modum auctum, audietur.</s> <s xml:id="echoid-s12192" xml:space="preserve"/> </p> <div xml:id="echoid-div1774" type="float" level="2" n="1"> <note position="right" xlink:label="note-0463-08" xlink:href="note-0463-08a" xml:space="preserve">1220.</note> <note position="right" xlink:label="note-0463-09" xlink:href="note-0463-09a" xml:space="preserve">TAB. XLVII. <lb/>fig. 3.</note> </div> <pb o="342" file="0464" n="510" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1776" type="section" level="1" n="423"> <head xml:id="echoid-head569" xml:space="preserve">SCHOLIUM. 1.</head> <head xml:id="echoid-head570" xml:space="preserve">Demonſtrationes n. 1150. 1152.</head> <p> <s xml:id="echoid-s12193" xml:space="preserve">UT, quæ de lege, cui particulæ, in motu undulatorio, in itu & </s> <s xml:id="echoid-s12194" xml:space="preserve">reditu, ſub-<lb/> <anchor type="note" xlink:label="note-0464-01a" xlink:href="note-0464-01"/> jiciuntur, dicta ſunt, pateant, conſiderandum; </s> <s xml:id="echoid-s12195" xml:space="preserve">legem elaſticitatis deter-<lb/>minare aëris motum, & </s> <s xml:id="echoid-s12196" xml:space="preserve">vice verſa, ex motu dato, poſſe determinari legem <lb/>elaſticitatis.</s> <s xml:id="echoid-s12197" xml:space="preserve"/> </p> <div xml:id="echoid-div1776" type="float" level="2" n="1"> <note position="left" xlink:label="note-0464-01" xlink:href="note-0464-01a" xml:space="preserve">1221.</note> </div> <p> <s xml:id="echoid-s12198" xml:space="preserve">Hac utar ſecundâ methodo, & </s> <s xml:id="echoid-s12199" xml:space="preserve">ponendo, ſingulas particulas, in itu & </s> <s xml:id="echoid-s12200" xml:space="preserve">re-<lb/>ditu, agitari, ut corpus quod in cycloïde vibratur, id eſt, ipſas premi vi <lb/>quæ cum diſtantia a puncto medio ſpatii, itu & </s> <s xml:id="echoid-s12201" xml:space="preserve">reditu percurſi, augetur & </s> <s xml:id="echoid-s12202" xml:space="preserve"><lb/>minuitur <anchor type="note" xlink:href="" symbol="*"/>, demonſtrabo ad hoc requiri illam ipſam legem elaſticitatis, quam <anchor type="note" xlink:label="note-0464-02a" xlink:href="note-0464-02"/> in aëre locum habere ante vidimus <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s12203" xml:space="preserve">unde conſtabit, particulas aëreas re- <anchor type="note" xlink:label="note-0464-03a" xlink:href="note-0464-03"/> vera moveri juxta legem corporis penduli in cycloïde oſcillati.</s> <s xml:id="echoid-s12204" xml:space="preserve"/> </p> <div xml:id="echoid-div1777" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0464-02" xlink:href="note-0464-02a" xml:space="preserve">287.</note> <note symbol="*" position="left" xlink:label="note-0464-03" xlink:href="note-0464-03a" xml:space="preserve">1072.</note> </div> <p> <s xml:id="echoid-s12205" xml:space="preserve">Detur circulus AFB, cujus circumferentia æqualis ſit latitudini undæ <lb/> <anchor type="note" xlink:label="note-0464-04a" xlink:href="note-0464-04"/> ſit circulus minor, priori concentricus, GIOL, cujus diameter æqualis <lb/> <anchor type="note" xlink:label="note-0464-05a" xlink:href="note-0464-05"/> ſit ſpatio itu & </s> <s xml:id="echoid-s12206" xml:space="preserve">reditu percurſo a particulis, quod cum exiguum ſit, circulus <lb/>hic reſpectu alterius ſenſibilem non habet magnitudinem.</s> <s xml:id="echoid-s12207" xml:space="preserve"/> </p> <div xml:id="echoid-div1778" type="float" level="2" n="3"> <note position="left" xlink:label="note-0464-04" xlink:href="note-0464-04a" xml:space="preserve">1222.</note> <note position="left" xlink:label="note-0464-05" xlink:href="note-0464-05a" xml:space="preserve">T. XLVII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12208" xml:space="preserve">Ponamus circumferentiam circuli minoris repræſentare tempus, in quo <lb/>unda latitudinem ſuam percurrit, id eſt tempus, in quo particula it & </s> <s xml:id="echoid-s12209" xml:space="preserve">re-<lb/>dit <anchor type="note" xlink:href="" symbol="*"/>, ideoque bis lineam GO percurrit, juxta legem corporis gravitate in <anchor type="note" xlink:label="note-0464-06a" xlink:href="note-0464-06"/> cycloïde moti: </s> <s xml:id="echoid-s12210" xml:space="preserve">ſemicirculus ergo repræſentat tempus, in quo ſemel linea <lb/>hæc percurritur.</s> <s xml:id="echoid-s12211" xml:space="preserve"/> </p> <div xml:id="echoid-div1779" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0464-06" xlink:href="note-0464-06a" xml:space="preserve">1145.</note> </div> <p> <s xml:id="echoid-s12212" xml:space="preserve">Sit, in majori circulo, EF diſtantia inter centra duarum particularum vi-<lb/>cinarum quieſcentium; </s> <s xml:id="echoid-s12213" xml:space="preserve">ductis ex E & </s> <s xml:id="echoid-s12214" xml:space="preserve">F lineis ad centrum, arcus I i, in <lb/>minori circulo, repræſentabit momentum ex his, de quibus n. </s> <s xml:id="echoid-s12215" xml:space="preserve">1146. </s> <s xml:id="echoid-s12216" xml:space="preserve">majo-<lb/>rem enim circumferentiam latitudini undæ æqualem poſuimus.</s> <s xml:id="echoid-s12217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12218" xml:space="preserve">Idcirco, ſi particula translata ſit per GH, ſequens particula, quæ per mo-<lb/>mentum unum diutius fuit agitata, translata erit per G b <anchor type="note" xlink:href="" symbol="*"/>, ductis <anchor type="note" xlink:label="note-0464-07a" xlink:href="note-0464-07"/> IH, ih, perpendicularibus ad GO; </s> <s xml:id="echoid-s12219" xml:space="preserve">& </s> <s xml:id="echoid-s12220" xml:space="preserve">differentia translationum erit Hb; <lb/></s> <s xml:id="echoid-s12221" xml:space="preserve">differentia autem translationum particularum vicinarum, eſt augmentum, aut <lb/>diminutio, diſtantiæ inter has: </s> <s xml:id="echoid-s12222" xml:space="preserve">in hoc caſu, in quo antecedens particula <lb/>per minus ſpatium fuit translata, H b, aut I m, quam huic parallelam po-<lb/>nimus, eſt diminutio diſtantiæ, quæ ergo eſt EF minus I m.</s> <s xml:id="echoid-s12223" xml:space="preserve"/> </p> <div xml:id="echoid-div1780" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0464-07" xlink:href="note-0464-07a" xml:space="preserve">304.</note> </div> <p> <s xml:id="echoid-s12224" xml:space="preserve">Ratio quæ datur inter I m & </s> <s xml:id="echoid-s12225" xml:space="preserve">EF eſt compoſita, ex ratione I m ad I i, <lb/>& </s> <s xml:id="echoid-s12226" xml:space="preserve">I i ad EF. </s> <s xml:id="echoid-s12227" xml:space="preserve">Prima ratio eſt quæ datur inter IH & </s> <s xml:id="echoid-s12228" xml:space="preserve">IC; </s> <s xml:id="echoid-s12229" xml:space="preserve">propter ſimilia <lb/>rectangula triangula I m i, IHC. </s> <s xml:id="echoid-s12230" xml:space="preserve">Secunda ratio eſt eadem quæ datur in-<lb/>ter IC & </s> <s xml:id="echoid-s12231" xml:space="preserve">CE, ut patet. </s> <s xml:id="echoid-s12232" xml:space="preserve">Ratio ex his compoſita eſt IH ad EC, aut <lb/>AC.</s> <s xml:id="echoid-s12233" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12234" xml:space="preserve">Idcirco ſi ſemidiametro majoris circuli diſtantiam inter particulas, antea-<lb/>gitationem, deſignemus, HI repræſentabit diminutionem diſtantiæ, dum <lb/>arcus GI tempus agitationis repræſentat <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s12235" xml:space="preserve">ſimili demonſtratione conſtat, in <anchor type="note" xlink:label="note-0464-08a" xlink:href="note-0464-08"/> reditu particularum, HL repræſentare augmentum diſtantiæ, ſi arcus OL <lb/>tempus reditus repræſentat, id eſt, arcus GIOL tempus agitationis.</s> <s xml:id="echoid-s12236" xml:space="preserve"/> </p> <div xml:id="echoid-div1781" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0464-08" xlink:href="note-0464-08a" xml:space="preserve">304.</note> </div> <p> <s xml:id="echoid-s12237" xml:space="preserve">Si nunc concipiamus lineam PQ, parallelam GO, & </s> <s xml:id="echoid-s12238" xml:space="preserve">quæ in P circulum <lb/>majorem tangat; </s> <s xml:id="echoid-s12239" xml:space="preserve">& </s> <s xml:id="echoid-s12240" xml:space="preserve">continuetur HI in R; </s> <s xml:id="echoid-s12241" xml:space="preserve">erit HR æqualis AC, ſubtractâ <lb/>HI reſtat IR, quæ diſtantiam particulæ cum vicina deſignat, poſito tem-<lb/>pore agitationis GI; </s> <s xml:id="echoid-s12242" xml:space="preserve">ſi foret hoc GIOL diſtantia inter particulas eſlet <pb o="343" file="0465" n="511" rhead="MATHEMATICA. LIB. II. CAP. XIX."/> RL, & </s> <s xml:id="echoid-s12243" xml:space="preserve">diſtantiæ in momentis quibuſcunque deſignantur lineis parallelis <lb/>lineæ PC, ab una parte lineâ QP & </s> <s xml:id="echoid-s12244" xml:space="preserve">ad aliam ſemicirculo GIO in itu, & </s> <s xml:id="echoid-s12245" xml:space="preserve"><lb/>OLG in reditu, terminatis.</s> <s xml:id="echoid-s12246" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12247" xml:space="preserve">Differentia inter duas diſtantias vicinas eſt im aut nl, ſi Ii, aut L l, ut <lb/>ante deſignat momentum, de quo in n. </s> <s xml:id="echoid-s12248" xml:space="preserve">1146. </s> <s xml:id="echoid-s12249" xml:space="preserve">in quo caſu hæ lineolæ conſtan-<lb/>tes ſunt: </s> <s xml:id="echoid-s12250" xml:space="preserve">ſed cum ponamus particulas agitari, in itu & </s> <s xml:id="echoid-s12251" xml:space="preserve">reditu, juxta legem <lb/>corporis penduli, gravitate in cycloïde oſcillati, lineolæ ut im aut nl, ſi <lb/>I i aut L l fuerint conſtantes, deſignant vim accelerantem motum, dum <lb/>tempus agitationis deſignatur per GI, aut GIOL <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s12252" xml:space="preserve">Ergo vis accelerans, <anchor type="note" xlink:label="note-0465-01a" xlink:href="note-0465-01"/> quæ in particulas ſingulas, in motu quem finximus, omnibus momentis agit, pro. <lb/></s> <s xml:id="echoid-s12253" xml:space="preserve"> <anchor type="note" xlink:label="note-0465-02a" xlink:href="note-0465-02"/> portionalis eſt differentiæ inter diſtantias vicinas particularum; </s> <s xml:id="echoid-s12254" xml:space="preserve">ſi nempe vis hæc <lb/>accelerans in eo cum gravitate conveniat, ut agat in particulam motam, ut <lb/>in quieſcentem ageret <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12255" xml:space="preserve">quod obtinebit, ſi vis accelerans ab aëris elaſtici- <anchor type="note" xlink:label="note-0465-03a" xlink:href="note-0465-03"/> tate pendeat, tunc enim cauſa movens cum ipſis particulis transfertur.</s> <s xml:id="echoid-s12256" xml:space="preserve"/> </p> <div xml:id="echoid-div1782" type="float" level="2" n="7"> <note position="right" xlink:label="note-0465-01" xlink:href="note-0465-01a" xml:space="preserve">1223.</note> <note symbol="*" position="right" xlink:label="note-0465-02" xlink:href="note-0465-02a" xml:space="preserve">305.</note> <note symbol="*" position="right" xlink:label="note-0465-03" xlink:href="note-0465-03a" xml:space="preserve">252.</note> </div> <p> <s xml:id="echoid-s12257" xml:space="preserve">Ipſam autem hanc vim accelerantem revera in aëre locum habere demon-<lb/> <anchor type="note" xlink:label="note-0465-04a" xlink:href="note-0465-04"/> ſtramus. </s> <s xml:id="echoid-s12258" xml:space="preserve">Vis, qua particulæ, quarum diſtantia deſignatur per IR, ſeſemu-<lb/>tuo repellunt, eſt ad vim qua a ſe invicem repelluntur particulæ, quarum <lb/>diſtantia exprimitur per ir, ut {I/RI} ad {I/ri} <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12259" xml:space="preserve">& </s> <s xml:id="echoid-s12260" xml:space="preserve">harum virium differentia eſt <anchor type="note" xlink:label="note-0465-05a" xlink:href="note-0465-05"/> vls, qua particula media agitatur, quæ vis exprimitur per <lb/>{I/ri} - {I/RI} <unsure/> {RI - ri/RI x ri <unsure/> {mi/RI x ri}; </s> <s xml:id="echoid-s12261" xml:space="preserve">dum vis, qua particulæ quieſcentes ſeſe mu-<lb/>tuo fugiunt, quarum diſtantiam deſignat GQ, eſt {I/GQ}.</s> <s xml:id="echoid-s12262" xml:space="preserve"/> </p> <div xml:id="echoid-div1783" type="float" level="2" n="8"> <note position="right" xlink:label="note-0465-04" xlink:href="note-0465-04a" xml:space="preserve">1224.</note> <note symbol="*" position="right" xlink:label="note-0465-05" xlink:href="note-0465-05a" xml:space="preserve">1272.</note> </div> <p> <s xml:id="echoid-s12263" xml:space="preserve">Sunt ergo vires hæ ut {mi/RI x ri} ad {I/GQ}, ſive ut mi x GQ ad RI x ri; </s> <s xml:id="echoid-s12264" xml:space="preserve">aut <lb/>ad GQ<emph style="super">q</emph>; </s> <s xml:id="echoid-s12265" xml:space="preserve">quia cùm circulus minor, reſpectu majoris, ſenſibilem magnitu-<lb/>dinem non habeat, QG, RI, ri, pro æqualibus ſine errore ſenſibili ha-<lb/>beri poſſunt. </s> <s xml:id="echoid-s12266" xml:space="preserve">Ultima ergo memorata ratio eſt, quæ datur inter mi & </s> <s xml:id="echoid-s12267" xml:space="preserve">GQ; <lb/></s> <s xml:id="echoid-s12268" xml:space="preserve">dividendo nempe utramque quantitatem per GQ, quo ratio inter has non mu-<lb/>tatur. </s> <s xml:id="echoid-s12269" xml:space="preserve">Si ergo per GQ deſignemus vim, qua particulæ quieſcentes ſeſe <lb/>mutuo fugiunt, im, id eſt differentia diſtantiarum vicinarum, vimacceleran-<lb/>tem exprimet, quæ eſt ipſa quæ requiritur, ut ſingulæ particulæ juxta legem <lb/> <anchor type="note" xlink:label="note-0465-06a" xlink:href="note-0465-06"/> corporis in cycloide oſcillati agitentur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12270" xml:space="preserve">Quod demonſtrandum erat.</s> <s xml:id="echoid-s12271" xml:space="preserve"/> </p> <div xml:id="echoid-div1784" type="float" level="2" n="9"> <note symbol="*" position="right" xlink:label="note-0465-06" xlink:href="note-0465-06a" xml:space="preserve">1223.</note> </div> <p> <s xml:id="echoid-s12272" xml:space="preserve">Vis accelerans, quæ in aëris particulas agit, cum gravitate poteſt conferri, <lb/> <anchor type="note" xlink:label="note-0465-07a" xlink:href="note-0465-07"/> & </s> <s xml:id="echoid-s12273" xml:space="preserve">celeritas undæ cum celeritate corporis cadentis, ut diximus in n. </s> <s xml:id="echoid-s12274" xml:space="preserve">1152.</s> <s xml:id="echoid-s12275" xml:space="preserve"/> </p> <div xml:id="echoid-div1785" type="float" level="2" n="10"> <note position="right" xlink:label="note-0465-07" xlink:href="note-0465-07a" xml:space="preserve">1225.</note> </div> <p> <s xml:id="echoid-s12276" xml:space="preserve">Quando corpus in cycloïde oſcillatum, hanc integram percurrit curvam, <lb/>in punctis, a puncto medio viæ percurrendæ maximè remotis, toto ſuo pre-<lb/>mitur pondere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12277" xml:space="preserve">Idcirco, ut cum gravitate conferamus vim accelerantem <anchor type="note" xlink:label="note-0465-08a" xlink:href="note-0465-08"/> motum particulæ, dum per GO it & </s> <s xml:id="echoid-s12278" xml:space="preserve">redit, debemus cum pondere particu-<lb/>læ conferre vim, quæ in hanc agit in G, aut O, & </s> <s xml:id="echoid-s12279" xml:space="preserve">hanc C verſus, premit.</s> <s xml:id="echoid-s12280" xml:space="preserve"/> </p> <div xml:id="echoid-div1786" type="float" level="2" n="11"> <note symbol="*" position="right" xlink:label="note-0465-08" xlink:href="note-0465-08a" xml:space="preserve">285. 316.</note> </div> <p> <s xml:id="echoid-s12281" xml:space="preserve">Lineæ ut I i & </s> <s xml:id="echoid-s12282" xml:space="preserve">im in puncto G confunduntur; </s> <s xml:id="echoid-s12283" xml:space="preserve">ideo poſitis AD & </s> <s xml:id="echoid-s12284" xml:space="preserve">EF <lb/>æqualibus, id eſt, poſitâ AD æquali diſtantiæ inter centra particularum <lb/>quieſcentium, & </s> <s xml:id="echoid-s12285" xml:space="preserve">ductâ DC ad centrum, G g, quæ æqualis eſt I i, expri- <pb o="344" file="0466" n="512" rhead="PHYSICES ELEMENTA"/> met vim quæ in G particulam C verſus premit, dum GQ vim exprimit, <lb/>qua particulæ quieſcentes ſeſe mutuo repellunt.</s> <s xml:id="echoid-s12286" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12287" xml:space="preserve">Ponamus Atmoſphæram, non mutatâ aëris quantitate, ubique ſupra lo-<lb/>cum, in quo unda movetur, eſſe ejuſdem denſitatis cum aëre in hoc loco, <lb/>& </s> <s xml:id="echoid-s12288" xml:space="preserve">ſit in hoc caſu altitudo Atmoſphæræ SV; </s> <s xml:id="echoid-s12289" xml:space="preserve">ſit S s; </s> <s xml:id="echoid-s12290" xml:space="preserve">æqualis AD, diſtan-<lb/>tiæ inter centra duarum particularum vicinarum; </s> <s xml:id="echoid-s12291" xml:space="preserve">Ss eſt ad SV, ut unitas <lb/>ad numerum particularum in s V; </s> <s xml:id="echoid-s12292" xml:space="preserve">id eſt Ss ad SV, ut pondus unius par-<lb/>ticulæ ad pondus quo particulæ S, s, ad ſe mutuo pelluntur, quodpondus va-<lb/>let vim qua elaſticitate particulæ hæ a ſe mutuo recedere conantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12293" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">247.</note> <p> <s xml:id="echoid-s12294" xml:space="preserve">Pondus autem unius particulæ eſt ad vim in G, de qua ſtatim locuti ſu-<lb/>mus, in ratione compoſita ponderis unius particulæ ad vim elaſticam aë-<lb/>ris quieſcentis; </s> <s xml:id="echoid-s12295" xml:space="preserve">& </s> <s xml:id="echoid-s12296" xml:space="preserve">hujus vis elaſticæ ad vim in G, id eſt in ratione compo-<lb/>ſita Ss ad SV, & </s> <s xml:id="echoid-s12297" xml:space="preserve">QG ad Gg. </s> <s xml:id="echoid-s12298" xml:space="preserve">Ultima hæc ratio componitur <lb/>ex ratione QG, aut AC, ad GC, & </s> <s xml:id="echoid-s12299" xml:space="preserve">GC ad Gg, quæ eadem eſt cum ra-<lb/>tione AC ad AD aut Ss. </s> <s xml:id="echoid-s12300" xml:space="preserve">Idcirco ratio compoſita ex rationibus Ss ad SV, <lb/>& </s> <s xml:id="echoid-s12301" xml:space="preserve">QG ad Gg, etiam componitur ex rationibus, Ss ad SV, AC ad <lb/>GC, & </s> <s xml:id="echoid-s12302" xml:space="preserve">AC ad Ss; </s> <s xml:id="echoid-s12303" xml:space="preserve">quæ eſt ratio Ss X AC X AC ad SV X GC X Ss, <lb/>aut AC<emph style="super">q</emph>, ad SV X GC; </s> <s xml:id="echoid-s12304" xml:space="preserve">ſunt ergo in hac ratione, vis gravitatis cum vi <lb/>qua particulæ in motu undulatorio agitantur; </s> <s xml:id="echoid-s12305" xml:space="preserve">& </s> <s xml:id="echoid-s12306" xml:space="preserve">qua vi, ſi pendulum longi-<lb/>tudinis CG loco gravitatis agitaretur, aduas perageret vibrationes, in tem-<lb/>pore in quo unda latitudinem ſuam percurrit; </s> <s xml:id="echoid-s12307" xml:space="preserve">in hoc enim tempore parti-<lb/>cula it & </s> <s xml:id="echoid-s12308" xml:space="preserve">redit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12309" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">1145.</note> <p> <s xml:id="echoid-s12310" xml:space="preserve">Ergo ſi aliud detur pendulum vi gravitatis agitatum & </s> <s xml:id="echoid-s12311" xml:space="preserve">longitudinis SV, <lb/>quadratum temporis in quo hoc duas peragit vibrationes, eſt ad quadratum <lb/>temporis in quo unda latitudinem ſuam percurrit, in ratione compoſita di-<lb/>rectæ SV ad GC, & </s> <s xml:id="echoid-s12312" xml:space="preserve">inverſæ AC<emph style="super">q</emph> ad SV X GC <anchor type="note" xlink:href="" symbol="*"/>, ex quibus componitur <anchor type="note" xlink:label="note-0466-03a" xlink:href="note-0466-03"/> ratio SV<emph style="super">q</emph> ad AC<emph style="super">q</emph>. </s> <s xml:id="echoid-s12313" xml:space="preserve">Idcirco ipſa tempora ſunt ut SV ad AC. </s> <s xml:id="echoid-s12314" xml:space="preserve">Tempus <lb/>autem, in quo pendulum, cujus longitudo eſt SV, duas peragit vibratio-<lb/>nes, eſt æquale tempori, in quo corpus, celeritate, cadendo a ſemialtitu-<lb/>ne SV acquiſitâ, poteſt percurrere circumferentiam circuli, cujus ſemidia-<lb/>meter eſt SV <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12315" xml:space="preserve">quod tempus cum ſit ad tempus, in quo unda latitudinem <anchor type="note" xlink:label="note-0466-04a" xlink:href="note-0466-04"/> ſuam, id eſt, circumferentiam circuli, cujus ſemidiameter AC percurrit, <lb/>ut SV eſt ad AC, in qua ratione ſunt ipſæ circumferentiæ, ſpatia percur-<lb/>ſa ſunt tempora; </s> <s xml:id="echoid-s12316" xml:space="preserve">ideo velocitates æquales <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s12317" xml:space="preserve">conſtat propoſitio in n.</s> <s xml:id="echoid-s12318" xml:space="preserve"> <anchor type="note" xlink:label="note-0466-05a" xlink:href="note-0466-05"/> 1152. </s> <s xml:id="echoid-s12319" xml:space="preserve">tradita.</s> <s xml:id="echoid-s12320" xml:space="preserve"/> </p> <div xml:id="echoid-div1787" type="float" level="2" n="12"> <note symbol="*" position="left" xlink:label="note-0466-03" xlink:href="note-0466-03a" xml:space="preserve">302.</note> <note symbol="*" position="left" xlink:label="note-0466-04" xlink:href="note-0466-04a" xml:space="preserve">257. 288. 307.</note> <note symbol="*" position="left" xlink:label="note-0466-05" xlink:href="note-0466-05a" xml:space="preserve">95.</note> </div> </div> <div xml:id="echoid-div1789" type="section" level="1" n="424"> <head xml:id="echoid-head571" xml:space="preserve">SCHOLIUM 2.</head> <head xml:id="echoid-head572" style="it" xml:space="preserve">De Soni intenſitate.</head> <p> <s xml:id="echoid-s12321" xml:space="preserve">VIdimus ſoni intenſitatem ſequi rationem compoſitam, ex ratione nume-<lb/> <anchor type="note" xlink:label="note-0466-06a" xlink:href="note-0466-06"/> ri particularum, certo tempore, in aurem incurrentium & </s> <s xml:id="echoid-s12322" xml:space="preserve">ratione qua-<lb/> <anchor type="note" xlink:label="note-0466-07a" xlink:href="note-0466-07"/> drati velocitatis qua incurrunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12323" xml:space="preserve">Rationes hæ nunc determinandæ ſunt.</s> <s xml:id="echoid-s12324" xml:space="preserve"/> </p> <div xml:id="echoid-div1789" type="float" level="2" n="1"> <note position="left" xlink:label="note-0466-06" xlink:href="note-0466-06a" xml:space="preserve">1226.</note> <note symbol="*" position="left" xlink:label="note-0466-07" xlink:href="note-0466-07a" xml:space="preserve">1198.</note> </div> <p> <s xml:id="echoid-s12325" xml:space="preserve">Numerus particularum ſequitur rationem denſitatis aëris. </s> <s xml:id="echoid-s12326" xml:space="preserve">Ut & </s> <s xml:id="echoid-s12327" xml:space="preserve">ratio-<lb/>nem velocitatis undæ; </s> <s xml:id="echoid-s12328" xml:space="preserve">quo enim hæc velocior eſt, eo idem numerus particu-<lb/>larum breviori tempore in aurem agit, & </s> <s xml:id="echoid-s12329" xml:space="preserve">eo major eſt numerus particula- <pb file="0467" n="513"/> <pb file="0467a" n="514"/> <anchor type="figure" xlink:label="fig-0467a-01a" xlink:href="fig-0467a-01"/> <pb file="0468" n="515"/> <pb o="345" file="0469" n="516" rhead="MATHEMATICA. LIB. II. CAP XIX."/> rum eodem tempore agentium. </s> <s xml:id="echoid-s12330" xml:space="preserve">Etiam rationem ſpatii itu & </s> <s xml:id="echoid-s12331" xml:space="preserve">reditu a par-<lb/>ticulis percurſi; </s> <s xml:id="echoid-s12332" xml:space="preserve">quo enim hoc ſpatium majus eſt, eo particulæ à tym-<lb/>pano magis remotæ in hoc incurrunt. </s> <s xml:id="echoid-s12333" xml:space="preserve">Tandem rationem inverſam latitu-<lb/>dinis undæ.</s> <s xml:id="echoid-s12334" xml:space="preserve"/> </p> <div xml:id="echoid-div1790" type="float" level="2" n="2"> <figure xlink:label="fig-0467a-01" xlink:href="fig-0467a-01a"> <image file="0467a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0467a-01"/> </figure> </div> <p> <s xml:id="echoid-s12335" xml:space="preserve">Quadratum velocitatis quo ſingulæ particulæ agunt, ſequitur rationem <lb/>quadrati velocitatis undæ. </s> <s xml:id="echoid-s12336" xml:space="preserve">Quadrati ſpatii itu & </s> <s xml:id="echoid-s12337" xml:space="preserve">reditu percurſi. </s> <s xml:id="echoid-s12338" xml:space="preserve">Tandem <lb/>rationem inverſam quadrati latitudinis undæ,</s> </p> <p> <s xml:id="echoid-s12339" xml:space="preserve">Quando velocitas undæ non mutatur ratio inverſa latitudinis undæ eſt ratio di-<lb/> <anchor type="note" xlink:label="note-0469-01a" xlink:href="note-0469-01"/> recta numeri undarum determinato tempore in aurem incurrentium; </s> <s xml:id="echoid-s12340" xml:space="preserve">poſitis un-<lb/>dis æqualibus ſeſe mutuo inſequentibus, quales ſunt undæ, quæ ex continua-<lb/>ta fibræ agitatione generantur.</s> <s xml:id="echoid-s12341" xml:space="preserve"/> </p> <div xml:id="echoid-div1791" type="float" level="2" n="3"> <note position="right" xlink:label="note-0469-01" xlink:href="note-0469-01a" xml:space="preserve">1227.</note> </div> <p> <s xml:id="echoid-s12342" xml:space="preserve">Ratio compoſita ex memoratis omnibus eſt ratio compoſita ex ratione <lb/>denſitatis, ratione cubi velocitatis, ratione cubi ſpatii itu & </s> <s xml:id="echoid-s12343" xml:space="preserve">reditu percurſi, <lb/>& </s> <s xml:id="echoid-s12344" xml:space="preserve">ratione inverſa cubi latitudinis undæ.</s> <s xml:id="echoid-s12345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12346" xml:space="preserve">Si ſeponamus accelerationem in n. </s> <s xml:id="echoid-s12347" xml:space="preserve">1163. </s> <s xml:id="echoid-s12348" xml:space="preserve">memoratam, (quæ non mutat <lb/>velocitatem qua ſingulæ particulæ moventur, de qua in hiſce tantum agitur;) <lb/></s> <s xml:id="echoid-s12349" xml:space="preserve">cubus velocitatis ſequitur rationem ſeſquiplicatam directam Elaſticitatis <lb/>& </s> <s xml:id="echoid-s12350" xml:space="preserve">ſeſquiplicatam inverſam denſitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12351" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">1157.</note> <p> <s xml:id="echoid-s12352" xml:space="preserve">Duæ ergo primæ rationes memoratæ reducuntur ad rationem ſeſquiplica-<lb/>tam elaſticitatis & </s> <s xml:id="echoid-s12353" xml:space="preserve">rationem inverſam ſubduplicatam denſitatis. </s> <s xml:id="echoid-s12354" xml:space="preserve">Elaſticitas <lb/>autem eſt ut pondus comprimens <anchor type="note" xlink:href="" symbol="*"/>, quod ſequitur rationem altitudinis Mer- <anchor type="note" xlink:label="note-0469-03a" xlink:href="note-0469-03"/> curii in Tubo Torricelliano.</s> <s xml:id="echoid-s12355" xml:space="preserve"/> </p> <div xml:id="echoid-div1792" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0469-03" xlink:href="note-0469-03a" xml:space="preserve">247.</note> </div> <p style="it"> <s xml:id="echoid-s12356" xml:space="preserve">Generaliter ergo, eſt ſoni intenſitas directe ut radix quadrata cubi altitudinis <lb/> <anchor type="note" xlink:label="note-0469-04a" xlink:href="note-0469-04"/> Mercurii in tubo Torricelliano, ut cubus ſpatii itu & </s> <s xml:id="echoid-s12357" xml:space="preserve">reditupercurſi, & </s> <s xml:id="echoid-s12358" xml:space="preserve">inverſè ut <lb/>subus latitudinis undæ, & </s> <s xml:id="echoid-s12359" xml:space="preserve">ut radix quadrata denſitatis.</s> <s xml:id="echoid-s12360" xml:space="preserve"/> </p> <div xml:id="echoid-div1793" type="float" level="2" n="5"> <note position="right" xlink:label="note-0469-04" xlink:href="note-0469-04a" xml:space="preserve">1228.</note> </div> </div> <div xml:id="echoid-div1795" type="section" level="1" n="425"> <head xml:id="echoid-head573" xml:space="preserve">FINIS.</head> <head xml:id="echoid-head574" xml:space="preserve">CORRIGENDA.</head> <note position="right" xml:space="preserve"> <lb/>Pag. # lin. # dele # lege <lb/>10. # 5. # augulos # angulos <lb/>10. # 18. # logarhthmicas # logarithmicas <lb/>69. # 18. # pendulorum # penduli <lb/>72. # 4. # Abl # Hbl <lb/>72. # 36. # OQ # BQ <lb/>72. # 37. # A # P <lb/>77. # 5. # BEl # BEL <lb/>80. # 23. # AMB # ALB <lb/>98. # penult. # continentur # continetur <lb/>100. # 35. # quorum # quarum <lb/>101. # 4. a fine # ALb # AbL <lb/>101. # 3. a fine # A eſt L # eſt AL <lb/>102. # 4. # LI, # LI <lb/></note> <pb file="0470" n="517"/> <note position="right" xml:space="preserve"> <lb/>pag. # lin. # dele # lege <lb/>102. # 17. # ad # ut <lb/>110. # 21. # generatur. # generatur, aut deſtrui- \\ tur. <lb/>117. # 5. # & # <lb/>120. # 1. # primi # primis <lb/>128. # 1. # formantur # terminantur <lb/>140. # 13. # antequam corpora \\ P, P, puncta # ubi corpora P, P, ad \\ puncta <lb/>140. # 14. # veniant # veniant <lb/>143. # 22. # e # d <lb/>144. # 1. # m # n <lb/>144. # 15. # Aaa X Ccc # Aaa + Ccc <lb/>161. # 34. # actionem # actionum <lb/>167. # 5. # Ab # Ab <lb/>175. # 16. # n. 610. # n. 623. <lb/>178. # 13. # LE # ad LE <lb/>179. # 19. # EKG # EKD <lb/>186. # 3. a fine # ſuma # ſumma <lb/>187. # 28. # C X D # C X HD <lb/>189. # 3. a fine. # determinatur # determinamus <lb/>199. # 4. a fine # n. 691. # n. 692. <lb/>207. # 7. # & in hac figura non # ut in hac figura <lb/>222. # 15. # cylindro # cubo <lb/>259. # 15. # qui # quæ <lb/>262. # 20. # aperto # apertis <lb/>263. # 6. a fine # non <lb/>282. # 25. # AB # AC <lb/>308. # 13. # qua # quo <lb/></note> </div> <div xml:id="echoid-div1796" type="section" level="1" n="426"> <head xml:id="echoid-head575" xml:space="preserve">IN MARGINE</head> <note position="right" xml:space="preserve"> <lb/>61. # 4. # TAB. VIII. # 19. El. VI. <lb/>64. # ult. # fig 1. <lb/>70. # 25. # TAB. VIII. # TAB XL. <lb/>109. # 4. # 397. # 379. <lb/>116. # 5. a fine # 353. # 453. <lb/>127. # 29. # TAB. XXIII. # TAB. XVIII. <lb/>163. # 15. # 585. # 584. <lb/>163. # 20. # 584. # 567. <lb/>166. # 25. # 59. # 598. <lb/>177. # 10. # # * 472. <lb/>245. # 9. & 21. # TAB. XXXV. # TAB. XXXVI. <lb/>343. # 18. # 1272. # 1172. <lb/>444. # 5. # 1198. # 1189. <lb/></note> </div> <div xml:id="echoid-div1797" type="section" level="1" n="427"> <head xml:id="echoid-head576" xml:space="preserve">FINIS.</head> <pb file="0471" n="518" rhead="CATALOGUE"/> </div> <div xml:id="echoid-div1798" type="section" level="1" n="428"> <head xml:id="echoid-head577" xml:space="preserve">De quelques Livres nouveaux & autres, que PIERRE VANDER Aa a LEIDE a <lb/>imprimé oureçu de divers endroits, & quiſe trouvent dans ſa Boutique.</head> <note position="right" xml:space="preserve"> <lb/>Academie univerſelle des Feux, 12°. 2 voll. <lb/>Atlas des plus celebres Itineraires, fol. 2 voll. <lb/># de 103. Nouv. Cartes Geographiques. fol. <lb/># Item de 203. Cartes Geogr. fol. 2 voll. <lb/># Item avec les Villes Capitales, fol. 3 voll. <lb/>Boerhaave de comparando certo in Phyſicis, 4°. <lb/># de Chemia ſuos errores expurgante. 4°. <lb/># de Vita & Obitu Prof. Bernardi Albini, 4°. <lb/># Index Plantarum Horti Academici L. Bat. 8°. <lb/># Alter Index Plant. ejuſd. Horti, 4°. 2 voll. <lb/># & Ruyſch de Glandulis, 4°. <lb/>Bartholini Anatomie, 4°. <lb/>Livre de Gueux, par Blommert, 4°. <lb/>Beſchryving van Morea, fol. # China, door Nieuhof, fol. <lb/>Brief over de Oudheid van’t Hof van Holland, 8°. & fol. <lb/>Cabinet de 42. grandes Villes d’ Europe, chacun de 4. ſeuilles, fol <lb/>Les cing Sens, fol. magno. <lb/>Comedies de Plaute, par Gedeville, 12°. 10 voll. <lb/>Colloques d’ Eraſine, par Gedeville, 12°. 6 voll. <lb/>Côtes de France & d’ Eſpagne, fol. 2 voll. <lb/>Catalogus Bibliothecæ publicæ Acad. Lug. Bat. fol. <lb/># publ. Acad. Franekeranæ, fol. <lb/># J. G. Grævii, 12°. <lb/>Creenii Muſæum Philologicum, 8°. 2 voll. <lb/># Helvici Elenchus Judaicus, 8°. <lb/># Faſciculus Exerc. Phil. tom. Primus 8°. <lb/># Analecta Critico-Sacra, 8°. 2 voll. <lb/># Faſcis Exercitat. tomi aliquot. 8°. <lb/>Conſultatien en Advyſen van Holland. 4°. 6 deelen. <lb/>Delices d’ Eſpagne & Portugal, 12°. 6 voll. <lb/># d’ Italie, 12°. 6 voll. <lb/># de Rome ancienne & moderne, 12°. 10 voll, <lb/>Delices de Suiſſe, 12°. 4 voll. --- de France, 12°. 2 voll. <lb/># & Galanteries del’ Ile de France, 12°. <lb/># de la Ville de Leide, 8°. <lb/>Devoirs des Maitres par Fleury, 12°. <lb/>Divers Ouvrages de belles figures par Caratz, G. Reni & c. ſol. <lb/>Habits des Paiſans & c. d’ Hollande, fol. <lb/>Effigies Veter. Illuſtr. Virorum ac Fœminar. fol. 4 voll. <lb/># Profeſſorum Leydenſium, fol. 2 voll. <lb/>Eraſmi Epiſtolæ omnes fol. 2. voll. <lb/># Nov. Teſt. Gr. Lat. fol. <lb/># Paraphraſis N. Teſtam. fol. <lb/># Opera Omnia, fol. XI. voll. <lb/>Lettres d’ Oſſat, 12°. 5 voll. <lb/>Forces del’ Europe, nouv. edition augmentée, fol 20. voll. <lb/>Livre des toutes ſortes des Oyſeaux, fol. <lb/>Grand Theatre Hiſtorique, par Imhof, fol. 5 voll. gr. pap. <lb/># Supplement, fol. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Graveſande Phyſices Elementa Mathem. 4°. 2. voll. Auctior. <lb/># Supplementum ad 1. part. prim. editionis, 4°. <lb/># Inſtitutiones Philoſophiæ Newtonianæ, 12°. <lb/>Gronovii marmorea baſis Coloſſi Tiberio Cæſ. erectæ, 8°. <lb/>Gereformeerd Gezangboek, door Halma, 8°. & 12°. <lb/>Gottfried Ooſt en Weſt-Indiſe Voyagien, fol. 8. deelen. <lb/>La Haye, avec ſes Edifues, Vues, & c. fol. <lb/>Habillemens de pluſieurs Nations 4°. <lb/>Hiſtoria del Teſtam. Vecchio, di Raſael Urb. fol. <lb/>Hermanni Paradiſus Batavus, 4°. <lb/>Honslaardyk avec ſes Vues, & c. fol. <lb/>Icones Arborum, Fruticum & Herb, exoticarum. 4°. <lb/>Voyagien van Robert Harcourt, 8°. <lb/>Imagines Principum & Eruditorum Virorum, fol. <lb/># XIX. Clar. Theolog. & Philolog. fol. <lb/># XX. Celeb. Medicorum. & c. fol. <lb/># XLI. Viror. Celeb. in Politicis &c. fol. <lb/>Kippingii Antiquitates Romanæ, 8°. <lb/>Nouvelle Carte d’ Allemagne, avec les Poſtes, 9. feuilles. <lb/># d’ Eſpagne & du Portugal, 9. feuilles. <lb/># de la France, 6. ſeuilles. # d’ Italie, 6. ſeuilles. <lb/>Nouvelle Carte des XVII. Provinces, 9. feuilles. <lb/># des Provinces Unies, 5 {1/2}. ſeuilles. <lb/>La Maiſon d’ Autriche, Portraits des Empereurs, fol. <lb/># Majeſté de Veniſe, fol. 2. voll. <lb/>Le Monde, en tailles douces, per Allard, fol. <lb/># Nouveau grand Theatre du Monde. fol. Atlanti. <lb/>La Ville de Leide, avec ſes Ediſices, & c. <lb/>Les Indes Orientales & Occid. par Romein de Hooge, fol. <lb/>Les principales Fortereſſes de France, d’ Eſpagne &c, fol. <lb/># Villes de l’ Europe, grand folio & petit. <lb/>Portraits des premiers Evêques du Pais bas, fol. <lb/>Livre de toutes ſortes des Fleurs, par Viſſcher, ſol. <lb/>Theatre des Martyrs Mennonites, par Luyke 4°. <lb/>Magniſicence d’ Amſterdam, avec ſes Ediſices & c. fol. <lb/>Morale de Tacite, par Amelot, 12°. <lb/>Magnol Hortus Regius Botanic. Monſpelienſis, 8°. <lb/>Maimonides de Siclis, Hebr. & Lat. cum notis 4°. <lb/>Marckii Diſſertationes Phil. V. Teſtamenti, 4°. <lb/>Nouveau Atlas portatif du Voyageur en general, 8°. <lb/># d’ Allemagne, 8°. <lb/># d’ Eſpagne & du Portugal, 8°. <lb/># de la France & Suiſſe, 8°. <lb/># de la Grand Bretagne & Irlande, 8°. <lb/># d’ Italie, Naples Sicile & c 8°. <lb/># des XVII. Provinces, 8°. Deux differens Sortes. <lb/># de Suede & Danemarc, 8°. <lb/># d’ Aſie, Afrique & Amerique, 8°. <lb/>Noodt Opera Varia. 4°. <lb/></note> <pb file="0472" n="519" rhead="CATALOGUE"/> <note position="right" xml:space="preserve"> <lb/>Loo, avec ſes Vues, &c. fol. <lb/>Oeuvres de Coquillage, Corail, &c. par Rumphius, fol. <lb/># de Mariotte, 4°. 2 voll. <lb/># de Perrault en Phyſique & Mathem. 4°. 2 voll. <lb/># d’ Architecture, par Poſt fol. <lb/># par Scamozzi, fol. <lb/># par Vingboons, fol. <lb/>XXV. Differens Plans des Villes, par Mortier, fol. <lb/>Portraits des Dieux Payens, Heros, Rois, Reines, anciens <lb/>Philoſaphes, Medicins, Poetes, Hiſtoriens, & c. fol. 8 voll. <lb/># XLVIII. de quelques Papes, Empereurs, & c. fol. <lb/># des Hommes Illuſtres en forme de medailles, fol. <lb/># XLI. des Grands Ducs & c. fol. <lb/># des Princes & Princeſſes de ce tems, fol. <lb/># XLVIII. des Comtes, Barons &c. fol. <lb/># XXV. des Hommes’ Celebres, fol. <lb/># des premiers Reformateurs, fol. <lb/>Paris, avec ſes principaux Edifices &c. fol. <lb/>Les Tuilleries, en grand. # Fontame bleau, en grand. <lb/>Verſailles avec ſes Battimens. Vues, & c. fol. <lb/>Perizonii Stemmata Illuſtrium Familiar. fol. <lb/># Tabulæ Chronologicæ, fol. plano. <lb/>Recueil de belles tailles douces en maniere noire, fol. <lb/># de pluſieurs nouv. Machines, par Perrault, 4°. <lb/>Reftexions, Penſées & bons mots anecdotes, 12°. <lb/>Vignole regles d’ Architecture, 8°. <lb/>Ruſes & ſtratagemes de la Guerre, 12°. <lb/>Rumphii Theſaurus Conchyliorum, &c. ſol. <lb/>Rotterdam avec ſes Edifices, Vues, &c. fol. <lb/>Sardaigne paranymphe de la Paix. <lb/>Scheuchzeri Herbarium Diluvianum, duplo auctior. fol. <lb/># Itinera Alpina, novem, 4°. 4 voll. <lb/>Ughellii Italia Sacra, fol. 10. voll. <lb/>Spanhemii Hiſtoria Jobi, 8°. <lb/>Villes & Habits du Monde, par Allard, fol. <lb/>Portraits de cinquante Saints & Saintes, fol. <lb/>Theatre de la Fontaine, 12°. <lb/># des Villes du Monde, par de Wit, grand fol. 4 voll. <lb/>Portraits des Comtes d’ Hollande, par Soutman, fol. <lb/>Vaillant de ſtructura Florum, 4°. <lb/># Botanicon Pariſienſe, 8°. <lb/>Vie de Charles V. en tres belles figures, fol. <lb/>Les Villes de Friſe, par Allard, fol. <lb/>Voyages aux Indes Orientales, par Bontekoe, 12°. <lb/>Voyages en Moſcovie, Tartarie &c. par Olearius & Mandelslo, fol. <lb/>4 voll beaucoup augmenté & avec tresbelles figures. <lb/>Vuës des Villes, Edifices &c. d’ Ejpagne & Portugal, 4°. <lb/># de France, fol. 2 voll. <lb/># de la Grande Bretagne & Irlande, 4°. 6. voll. <lb/>Vuës des Villes, Edifices & e. d’ Eſeoſſe & d’ Irlande 4°. 2 voll. <lb/># de l’ Italie, de Naples & c. 4°. <lb/># de la Ville de Cambridge, fol. <lb/># de Londres, Canterbury, &c. ſol. 2. voll. <lb/></note> <note position="right" xml:space="preserve"> <lb/># d’ Oxford. fol. <lb/># de Yorck, Lancaſter, & c. fol. <lb/>Verſameling van Ooſt en Weſt-Indiſe Voyagien, 8°. 29. deelen. <lb/>Vignole van de 5 orders der Architecture, 8°. <lb/>Vingboons Architectuur Werken, fol. 3. voll. <lb/>Wilſon principia Trigonometriæ 8°. <lb/>Ambaſſade des Hollandois au Fapon, 12°. 2 voll. <lb/>Arrianus Gr. Lat Gronovii, fol. <lb/>Catalogus Libror. Theſauri Italiæ, &c. 12°. <lb/>Arriani ars Tactica, Gr. Lat. cum notis, 8°. <lb/>Authores de Cruce, 12°. 4 voll. <lb/>Begeri Bellum Trojanum, 4°. <lb/>Beughem la France Savante, 12°. <lb/>Boſſe ordres del’ Archicecture, fol. <lb/>Chambrai Paralelle de l’ Architecture, fol. <lb/>Pautre Oeuvres d’ Architecture, fol. <lb/>Broekhuyſen Oeconomia Animalis. 4°. <lb/># Rationes Philoſophico-Medicæ, 4°. <lb/>Commelini Flora Malebarica, 8°. <lb/>Deſcription de France, par Fig. de la Force, 12°. 6 voll. <lb/>Harpocrationis Lexicon, Gronovii, 4°. <lb/>Dictionaire Geographique de Baudrand, fol. <lb/>Emmii Reſpublica Græciæ, 24°. 2 voll. <lb/>Epiſtolæ Præſtantium Virorum, fol. <lb/>Ferratii Selectæ Queſtiones, 8°. <lb/>Fleetwood Inſcriptiones, 8°. <lb/>Gronovii variæ Lectiones in Srephanum de Urbibus, fol. <lb/># Emendationes Pandectarum, 8°. <lb/># Indices in Theſaur. Antiq. Græcar. fol. <lb/>Guericke Experimenta de vacuo ſpatio, fol. <lb/>Heidani Corpus Theologiæ, 4°. 2 voll. <lb/>Diſputationes Theol. Philol. Profeſſor. Leidens. 4°. <lb/>Hiſtoriæ rei Nummariæ Scriptores, 4°. 2 voll. <lb/>Jocoſeriæ Diſſertationes, 12°. <lb/>Lipſii Opera Omnia, 8°. 4 voll. <lb/># Opuſcula, 4°. z voll. <lb/>Hifloria del Gianſeniſino, per l’ Abb. Tozzi, 12°. 3 voll. <lb/>Loix Civiles dans leur ordre Naturel, fol. 2. voll. <lb/>Lubinietzkii Theatrum Cometicum, fol. 2 voll. <lb/>Cavacii Hiſtoria Cœnobii D. Juſtinæ, 4°. <lb/>Marmi Eruditi di Sert. Orſato, 4 <lb/>Lydius de re Militari 4. <lb/>Vita & res geſtæ Franciſci Mauroceni, 4°. <lb/>Mobachius de triumpho Romano, 8°. <lb/>Muntingii vera Herba Brittannica, 4°. <lb/>Newton Optica, 4°. <lb/>{ictet Morale Chrêtienne, 12. 8 voll. <lb/>Plumier Art de Tourner, fol. <lb/>Przipcovii Opera, fol. <lb/>Rozzi Memorie Breſciane, 4°. <lb/>Iſtoria Fiorentina di B. Varchi, fol. <lb/>Stockmans Opera J uridica, 4°. <lb/>Teyler Architectura militaris, 4°. <lb/></note> <pb file="0473" n="520" rhead="DES LIVRES."/> <note position="right" xml:space="preserve"> <lb/>Theſaurus Theologiælocupletiſſimus, fol. <lb/>Biblia Græca LXX. Interpretum, per Bos; 4°. <lb/>Bocharti Opera Omnia, fol. 2 voll. <lb/>Ennii Fragmenta Columnæ, 4°. <lb/>Rocchi Pirri Sicilia Sacra, fol. 2 voll. <lb/>Hildeberti & Marbodæi Opera, fol. <lb/>Lydii Agoniſtica Sacra, 12°. <lb/>Smidt Miſcellanea Sacra, 8°. 2 voll. <lb/># de VII. Aſiæ Eccleſiis, 8°. 2 voll. <lb/>Tentamen de Variolis, 12°. <lb/>Chauvini Lexicon Philoſophicum, fol. <lb/>Bible de Martin, fol. & 4°. <lb/># par Sacy, 4°. 2 voll. <lb/># Idem avec figures 4°. 2 voll. <lb/>Entretiens de Charles V. & Francois. I. 12°. <lb/>Hiſtoire des Martyrs du tems de la Reſormation, 12°. <lb/>Vies des Electeurs de Brandenbourg, fol. <lb/># des Saints, par Ribadeneira, fol. 2 voll. <lb/>Beſchryving van Arabien, Archipel, Japan, fol. <lb/>Galilæi Opera Mathematica 4°. <lb/>Grævii & Burmanni Theſaurus Antiq. & Hiſtor. Italiæ, <lb/>Magnæ Græciæ, Neapolis &c. fol 30 voll. <lb/># Theſaur. Antiq. & Hiſtor. Siciliæ, fol. 15. voll. <lb/>Hauteroche Oeuvres, 12°. <lb/>Ruſes de la Guerre, 12°. <lb/>Semaine de Montalban, 12°. <lb/>Boccalini Raguagli di Parnaſſo, 12°. 2 voll. <lb/>Bois Hiſtoria Eccleſ. Pariſienſis, fol. 2 voll. <lb/>Fontenelle Oeuvres, 8°. <lb/>Herbelot Bibliotheque Orientale, fol. <lb/>Herodote, pardu Ryer, 12°. 3 voll. <lb/>Hiſtoire du Wiclefianiſme, 12. <lb/># de Floride, par la Vega, 12°. 2 voll. <lb/>Leydecker de Republica Hebræorum, fol. <lb/>Hiſtoire de Bretagne, par Lobineau, ſol 2 voll. <lb/>Plaidoyez de le Maitre, 4°. # de Patru. 4°, <lb/>Geometrie de Mallet 8°. 4 voll. <lb/>Opere di Moliere, 12°. 4 voll. <lb/>Cabinet de S. Genevieve, par Molinet, fol. <lb/>Morale du Janſeniſme, 8°. <lb/>Dictionaire Mathematique par Ozanam, 4°. <lb/>Hiſtoire Univerſelle, par Petau, 12°. 5. voll. <lb/># des Drogues, par Pomet, fol. <lb/>Renaudot Hiſtoria Patriarcharum, 4°. <lb/>Sanſon l’ Univers, 4°. <lb/>Seguini Numiſmata, 4°. 2 voll. <lb/>Vaillant de Coloniis, fol. 2 voll. <lb/>Virgile Oeuvres par Martignac, 12°. 3 voll. <lb/>Ocuvres de le Noble, 12°. 19 voll. <lb/>Barrelierius de Plantis, fol. <lb/>Veteris Orbis Tabulæ Geographicæ ad Melam, 4°. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Architecture Francoiſe, par Savot, 8°. <lb/>Authores in uſum Delphini, 4°. <lb/># Apulejus, A. Gellius, Catullus, Tib. Prop. Ciceroni <lb/>Epiſt. C. Nepos, Horatius, Juvenalis & Perſius, Plau-<lb/>tus, & Ovidius. <lb/>Hilarii Opera, fol. <lb/>Ediſices antiques de Rome, par Desgodets, fol. <lb/>Themiſti Orationes, Gr. Lat. fol. <lb/>Hiſtoriæ Byzantinæ poſt Theophanem, Gr. Lat. fol. <lb/>Nicephorus Gregoras, Gr. Lat. fol. 2 voll. <lb/>Chronicon Orientale, Gr. Lat. fol. <lb/># Paſchale, Gr. Lat. fol. <lb/>Cinnamus, Gr. Lat. fol. <lb/>Zonaras, Gr. Lat fol. 2 voll. <lb/>Notitia Dignitatum Imperii, 12°. <lb/>Hommes Illuſtres, par Colombiere, fol. <lb/>Hippocrates & Galenus, Gr. Lat. fol. 13 voll. <lb/>Montfaucon Palæographia, fol. <lb/>Reyneau Analyſe demontrée, 4°. 2 voll. <lb/># Science du Calcul, 4°. <lb/>Defenſe des Ss. Peres accuſez de Platoniſme, par Baltus, 4°. <lb/>Cabaſſutii Notitia Eccl. Conciliorum, fol. <lb/>Chryſogoni Mundus Marianus, fol. <lb/>Auguſtini Operum Appendix, Clerici, fol. <lb/>Proſperi Aquitanici Opera, fol. <lb/>Bnrnet Theſaurus Medicinæ Practicæ, 4°. <lb/>Jacob Bril-Werken, 4°. <lb/>Collegium Argentoratenſe, per Biceium, 4°. <lb/>Begeri Numiſmata Imperatorum Romanorum, fol. <lb/>Geometrie Francoiſe par Beaulieu, 8°. <lb/>Hiſtoire du V. & N. Teſtament, par Baſnage, 12° 4 voll. <lb/>Bayeri Oryctographia Norica, 4°. <lb/>Aſtorius in antiquum Alcmanis Monumentum, fol. <lb/>Admiranda rerum memorabilium encomia, 12°. <lb/>Admonitio de morte corporali, 4° <lb/>Fables d’ Eſope, en quatrains 12°. <lb/>Animadverſiones in Salmaſii Specimen, 8°. <lb/>Antonini Iter Brittannicum, Gale, 4°. <lb/>Antoninus Liberalis, Gr Lat Berkeli, 12. <lb/>Secrets concernant les Arts & Metiers, 12°. <lb/>Cant Impetus primi Anatomici, fol. <lb/>Petri Cunaei, Eloquentiae & Juris Romani quondam in <lb/>Academia Batava Profeſſoris, & Doctorum Virorum ad <lb/>eumdem Epiſtolae. Quibus accedit Oratio in obitum Bo-<lb/>naventurae Vulcanii. Nunc primum editae. Cura Petri Bur-<lb/>manni. 8°. <lb/>Catalogus Rariſſimorum & Praeſtantiſſimorum Libro-<lb/>rum qui in Theſauris Romano Graeco Italico & Siculo <lb/>continentur. Secundum Nomina Auctorem per Alpha-<lb/>beti Ordinem Digeſtus, cum Praefatione Petri Burman-<lb/>ni. 8°. <lb/></note> </div> <div xml:id="echoid-div1799" type="section" level="1" n="429"> <head xml:id="echoid-head578" xml:space="preserve">ET AUTRES</head> <pb file="0474" n="521"/> <pb file="0475" n="522"/> </div> <div xml:id="echoid-div1800" type="section" level="1" n="430"> <head xml:id="echoid-head579" xml:space="preserve">PHYSICES ELEMENTA</head> </div> <div xml:id="echoid-div1801" type="section" level="1" n="431"> <head xml:id="echoid-head580" xml:space="preserve">MATHEMATICA, EXPERIMENTIS CONFIRMATA. Sive Introductio ad Philoſophiam</head> </div> <div xml:id="echoid-div1802" type="section" level="1" n="432"> <head xml:id="echoid-head581" xml:space="preserve">NEWTONIANAM.</head> <head xml:id="echoid-head582" style="it" xml:space="preserve">Auctore</head> <head xml:id="echoid-head583" xml:space="preserve">GULIELMO JACOB ’s GRAVESANDE,</head> <head xml:id="echoid-head584" xml:space="preserve">A. L. M. Jur. Vtr. & Phil. Doctore, Regiæ Societ. Lond. Socio, <lb/>Aſtron. & Math. in Acad. Lugd. Bat. Profeſſore ordinario.</head> <head xml:id="echoid-head585" xml:space="preserve"><emph style="sc">Tomus</emph> <emph style="sc">Secundus</emph>.</head> <figure> <image file="0475-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0475-01"/> </figure> </div> <div xml:id="echoid-div1803" type="section" level="1" n="433"> <head xml:id="echoid-head586" xml:space="preserve">LUGDUNI BATAVORUM, <lb/>Apud{<emph style="red">PETRUM VANDER Aa,</emph>\\ Typographum Academiæ atque Civitatis,\\-&\\<emph style="red">B.</emph> & <emph style="red">P. JANSSONIOS VANDER Aa.</emph>}Bibliop.</head> <head xml:id="echoid-head587" xml:space="preserve">MDCC XXI. <lb/>Cum Privilegio Præpotent. Ordd. Hollandiæ & Weſt-Friſiæ.</head> <pb file="0476" n="523"/> <pb file="0477" n="524"/> </div> <div xml:id="echoid-div1804" type="section" level="1" n="434"> <head xml:id="echoid-head588" xml:space="preserve">PRIVILEGIE.</head> <p style="it"> <s xml:id="echoid-s12361" xml:space="preserve">DE Staaten van Holland ende Weſt-Vrieſland, doen <lb/>te weeten, alſoo ons vertoont is by Pieter vander <lb/>Aa, Boekverkooper tot Leyden, hoe dat by Supplt<unsure/>, nu al-<lb/>dereerſt nizuw hadde gedrukt Gulielmi Jacobi’s Gra-<lb/>veſande Phyſices Elementa Mathematica, experimen-<lb/>tis confirmata. </s> <s xml:id="echoid-s12362" xml:space="preserve">Sive Introductio ad Philoſophiam New-<lb/>tonianam, in Quarto, cum figuris, het eerſte deel, ſyn-<lb/>de het vervolgh van het voorſz. </s> <s xml:id="echoid-s12363" xml:space="preserve">werk by den ſupplt. <lb/></s> <s xml:id="echoid-s12364" xml:space="preserve">meede tegenwoordigh onder de Pars, dogh alſoo den <lb/>Supplt<unsure/>. </s> <s xml:id="echoid-s12365" xml:space="preserve">beducht was, dat eenige nydige, off baetſoeken-<lb/>de Menſchen, ’t ſy binnen off buytens Lands, hem’t <lb/>voorn. </s> <s xml:id="echoid-s12366" xml:space="preserve">werk ſouden mogen koomen naate drucken, waar <lb/>door by van alle ſyne groote koſten en arbeyd tot nu toe <lb/>gedaan en nog te doen, ſoude verſteken ſyn, ſoo keerde <lb/>den Supplt<unsure/>. </s> <s xml:id="echoid-s12367" xml:space="preserve">ſig tot Ons verſoekende Ons Octroy, om <lb/>het voorn. </s> <s xml:id="echoid-s12368" xml:space="preserve">werk en vervolg voor den tyd van vyftien <lb/>cerſt achter een volgende Jaren, alleen met ſecluſie van <lb/>allen anderen hier te Lande te mogen drucken, uyt te ge-<lb/>ven, en te verkopen in ſodanige taalen en formaten, als <lb/>den Supplt<unsure/>. </s> <s xml:id="echoid-s12369" xml:space="preserve">voor ſyn intereſt beſt oirbaar joude vinden, <lb/>met expres verbod, waar by aan allen en eenen ygelyc-<lb/>ken buyten hem Supplt<unsure/>. </s> <s xml:id="echoid-s12370" xml:space="preserve">off die ſyn actie off recht naer-<lb/>maels mochten verkrygen, door Ons verboden wiert, <lb/>het voorn. </s> <s xml:id="echoid-s12371" xml:space="preserve">werck off vervolg van dien in enigerhande <lb/>taalen te drucken, naate drucken, te doen naadrucken, <lb/>uyt te geven, te verkopen, ofte verhandelen, in’t groot <lb/>noch klein, in’t geheel noch ten deelen, noch met, noch <lb/>ſonder Platen, noch onder pretext van vermeerdering, <lb/>verbeteringh, veranderingh van naem, valſche tekens, <lb/>ofte hoedanigh het ook genoemt ſoude mogen werden, <lb/>ofte in eenigerhande taal off taalen buyten deſen Lande <lb/>gedrukt werdende, deſelve niet te mogen inbrengen, te <lb/>verhandelen, off te verkopen, alles telckens op verbeurte <lb/>van alle de naagedruckte, ingebrachte, verhandelde off <lb/>verkogte Exemplaren, ſoo dikwils en menigmaal als <lb/>deſelve ſouden werden achterhaelt, mitsgaders daar <lb/>en boven een boete van drie duyſent guldens by Ons te-<lb/>gens de Contraventeurs te ſiellen. </s> <s xml:id="echoid-s12372" xml:space="preserve">SOO IS’T, dat Wy <lb/>de ſaake, en’t vorſoek voorſz. </s> <s xml:id="echoid-s12373" xml:space="preserve">overgemerkt hebbende, <lb/>ende genegen weſende ter beede van den Supplt<unsure/>. </s> <s xml:id="echoid-s12374" xml:space="preserve">uyt Onſe <lb/>rechte wetenſchap, Souveraine magt, en authoriteyt <lb/>den ſelven Supplt<unsure/>. </s> <s xml:id="echoid-s12375" xml:space="preserve">geconſenteert, geaccordeert, ende geo-<lb/>ctroyeert hebben, conſenteeren, accordeeren, en octro-<lb/>yeeren hem mitsdeſen, dat by geduyrende den tyd van <lb/>vyftien eerſt achter een volgende Jaren het voorſz werk <lb/>genaemt Gulielmi Jacobi’s Graveſande Phyſices Ele-<lb/>menta Mathematica, experimentis confirmata, ſive In-<lb/>troductio ad Philoſophiam Newtonianam, in Quarto <lb/>cum figuris met het vervolg van dien, binnen den <lb/>voorſz. </s> <s xml:id="echoid-s12376" xml:space="preserve">Onſen Lande alleen ſal mogen drucken, doen <lb/>drucken, uytgeven, en verkoopen, in ſodanige taa-<lb/>len en formaten, als den Supplt<unsure/>. </s> <s xml:id="echoid-s12377" xml:space="preserve">voor ſynintereſt beſt <lb/>oirbaar ſal vinden, verbiedende daerom allen, ende een <lb/>ygelycken het ſelve Werk en Vervolg in eenigerhan-<lb/>de taalen in ’t geheel, ofte ten deelen naa te druc-<lb/>ken, te doen naa drucken, te verhandelen, ofte te ver-<lb/>kopen, ofte elders naergedruckt, binnen den ſelven <lb/>Onſen Lande te brengen, uvt te geven, te verhan-<lb/>delen ofte te verkoopen, op verbeurte van alle de <lb/>naagedruckte, ingebragte, verhandelde ofte verkog-<lb/>te Exemplaren, ende een boete van drie duyſent guldens <lb/>daer en boven te verbeuren, te appliceren een derde part <lb/>voor den Officier, die de Calangie doen ſal, een derde <lb/>part voor den Armen der plaatſe daer het caſus voor-<lb/>vallen ſal, en het reſterende derde part voor den Supplt<unsure/>. </s> <s xml:id="echoid-s12378" xml:space="preserve"><lb/>ende dit telkens ſoo menigmael als deſelve ſullen wer-<lb/>den achterhaelt, alles in dien verſtande, dat W, den <lb/>Supplt<unsure/>. </s> <s xml:id="echoid-s12379" xml:space="preserve">met deſen Onſen Octroye alleen willlende gratifi-<lb/>ceren totver hoedinge van ſyne ſchade door het naadruc-<lb/>ken van het voorſz Werk of Vervolg, daar door in geni-<lb/>gen deele verſtaen den inhoude van den te authoriſee-<lb/>ren ofte te advoueren, ende veel min het ſelve onder <lb/>Onſe protectie ende beſcherminge enigh meerder credit, <lb/>aanſien ofte reputatie te geven, nemaar den Suppliant in <lb/>cas daer in iets onbehoorlykx ſoude influeeren, alle het ſel-<lb/>ve tot ſynen laſte ſal gehouden weſen te verantwoorden, <lb/>tot dien eynde wel expreſſelyck begeerende, dat by aldien <lb/>hy deſen Onſen Octroye voor het ſelveWerk ſalwillen ſtel-<lb/>len, daar van geen geabrevieer de ofte gecontrabeerde <lb/>mentie ſal mogen maecken, nemaer gehouden ſal weſen, <lb/>het ſelve Octroy in ’t geheel ende ſonder eenige Omiſſie <lb/>daer voor te drucken, ofte te doen drucken, ende dat by <lb/>gehouden ſal ſyn een Exemplaer van het voorſz werk <lb/>gebonden ende wel geconditioneert te brengen in de Bi-<lb/>bliotbeeck van Onſe Univerſiteyt tot Leyden, en daer <lb/>van behoorlyck te doen blycken, a les op pæne van het <lb/>effect van dien te verlieſen; </s> <s xml:id="echoid-s12380" xml:space="preserve">ende ten eynde den Supplt<unsure/>. </s> <s xml:id="echoid-s12381" xml:space="preserve">de-<lb/>ſen Onſen Conſente en Octroye moge genieten als naer be-<lb/>horen, laſtenWy allen ende een ygelycken die ’t aangaen <lb/>mag, dat ſy den Supplt<unsure/>. </s> <s xml:id="echoid-s12382" xml:space="preserve">van den inhoude van deſen <lb/>doen laten ende gedogen, ruſtelyck, vredelyck ende <lb/>volkomentlyk genieten ende gebruycken, ceſſeerende alle <lb/>beleth ter contrarie. </s> <s xml:id="echoid-s12383" xml:space="preserve">Gedaen in den Hage onder Onſen <lb/>Grooten Zegele bier aen doen hangen op den aghtſten <lb/>November in’t Jaer onſes Heeren en Zaligmdakers ſe-<lb/>venthien hondert en negentien.</s> <s xml:id="echoid-s12384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12385" xml:space="preserve">Was getekent,</s> </p> <p> <s xml:id="echoid-s12386" xml:space="preserve">A: </s> <s xml:id="echoid-s12387" xml:space="preserve">HEINSIUS, vt</s> </p> <p style="it"> <s xml:id="echoid-s12388" xml:space="preserve">Ter Ordonnantie van de Staten,</s> </p> <p> <s xml:id="echoid-s12389" xml:space="preserve">SIMON <emph style="sc">VAN</emph> BEAUMONT.</s> <s xml:id="echoid-s12390" xml:space="preserve"/> </p> <pb file="0478" n="525"/> <pb file="0479" n="526" rhead="LECTORI S."/> <p> <s xml:id="echoid-s12391" xml:space="preserve">DE Methodo Philoſophandi, in Capite primo <lb/><emph style="sc">Tomi</emph> <emph style="sc">Primi</emph>, egi. </s> <s xml:id="echoid-s12392" xml:space="preserve">Quam ſecutus ſum, eam <lb/>conatus ſum in Præfatione vindicare. </s> <s xml:id="echoid-s12393" xml:space="preserve">Præ-<lb/>ſtantiæ hujus Methodi exempla præclara hoc <lb/><emph style="sc">Tomo</emph> continentur; </s> <s xml:id="echoid-s12394" xml:space="preserve">quibus patet, quantum <lb/>ingenio cæteros anteceſſit Philoſophos <lb/>Newtonus.</s> <s xml:id="echoid-s12395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12396" xml:space="preserve">Ante illum innumera, quæ lumen & </s> <s xml:id="echoid-s12397" xml:space="preserve">præcipuè colores <lb/>ſpectant, Phyſicos latuere. </s> <s xml:id="echoid-s12398" xml:space="preserve">Quis, ut unicum memorem, <lb/>unquam ſuſpicatus eſt, corporis opacitatem ab interſtitiis <lb/>pendere; </s> <s xml:id="echoid-s12399" xml:space="preserve">ita ut, his repletis medio ejuſdem denſitatis cum <lb/>particulis ipſius corporis, tranſlucidum fiat hoc.</s> <s xml:id="echoid-s12400" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12401" xml:space="preserve">Non minus digna eſt quæ in perpetuum celebretur <lb/>totius Syſtematis Planetarii, & </s> <s xml:id="echoid-s12402" xml:space="preserve">præcipuè motus Lunæ, ex-<lb/>plicatio Phyſica. </s> <s xml:id="echoid-s12403" xml:space="preserve">Hac poterit Aſtronomia proferriultra limi-<lb/>tes, quibus attentus Obſervator artem ſuam circumſcribi <lb/>imaginatur. </s> <s xml:id="echoid-s12404" xml:space="preserve">Quem enim non latent, quibus Syſtema re-<lb/>gitur, leges, exactiùs, ex præviis obſervationibus, motus <lb/>cœleſtes computatione determinabit, quàm ſi obſervatio-<lb/>nes unicum computationis fundamentum forent.</s> <s xml:id="echoid-s12405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12406" xml:space="preserve">Propoſitum noſtrum, in libris duobus, hoc <emph style="sc">Tomo</emph> conten-<lb/>tis, fuit, ideam generalem tradere præcipuorum inven-<lb/>torum Newtoni in Phyſicis; </s> <s xml:id="echoid-s12407" xml:space="preserve">ut lectorem, qui primis tantum <lb/>principiis Geometriæ præmunitus ad hæc Elementa legenda <lb/>aptus erit, excitemus ad ſubtiliora Matheſeos ſtudia; </s> <s xml:id="echoid-s12408" xml:space="preserve">quibus <lb/>in fonte ipſo, id eſt in noſtri Philoſophi ſcriptis, poterit ea <lb/>haurirè, ad quæ ne quidem præſtantiſſmi Philoſophi po-<lb/>tuere attingere, & </s> <s xml:id="echoid-s12409" xml:space="preserve">quæ, niſi cum Mathematicis diligen-<lb/>tioribus, non communicavit Newtonus.</s> <s xml:id="echoid-s12410" xml:space="preserve"/> </p> <pb file="0480" n="527" rhead="LECTORI."/> <p> <s xml:id="echoid-s12411" xml:space="preserve">Supereſt ut lectorem Anglicum de verſionibus hujus ope-<lb/>ris Anglicis ſequentia moneam.</s> <s xml:id="echoid-s12412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12413" xml:space="preserve">Auctorum querelas lectori faſtidii multum adferre ple-<lb/>niſſimè perſuaſum habeo; </s> <s xml:id="echoid-s12414" xml:space="preserve">has tamen vetitas quis aſſeret, <lb/>ubi, à lectoris intereſſe, injuria, quam ſibi illatam con-<lb/>tendit auctor, ſeparari nequit.</s> <s xml:id="echoid-s12415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12416" xml:space="preserve">In Anglicum ſermonem tranſlatus <emph style="sc">Tomus</emph> primus ho-<lb/>rum Elementorum, brevi poſtquam publici juris factus eſt, <lb/>editus fuit Londini, cum inſcriptione nominis Celeberrimi <lb/>Profeſſoris; </s> <s xml:id="echoid-s12417" xml:space="preserve">quaſi Mathematicus Doctiff. </s> <s xml:id="echoid-s12418" xml:space="preserve">& </s> <s xml:id="echoid-s12419" xml:space="preserve">ſcriptis ſuis Cla-<lb/>rus interpretationem emendaſſet: </s> <s xml:id="echoid-s12420" xml:space="preserve">de abuſu autem Cl. </s> <s xml:id="echoid-s12421" xml:space="preserve">No-<lb/>minis nemo dubitabit, qui vel unicam paginam, ferè ad li-<lb/>bitum electam, ad examen revocabit; </s> <s xml:id="echoid-s12422" xml:space="preserve">ubique enim, Ma-<lb/>theſeos aut Phyſices principia interpreti non ſatis <lb/>fuiſſe nota clarè patet. </s> <s xml:id="echoid-s12423" xml:space="preserve">Silentio prætereo negligentiam <lb/>reſpectu corrigendorum, ad calcem Libri adjectorum, <lb/>ad quæ non attendit; </s> <s xml:id="echoid-s12424" xml:space="preserve">reſpectu numerorum in margine; <lb/></s> <s xml:id="echoid-s12425" xml:space="preserve">ut & </s> <s xml:id="echoid-s12426" xml:space="preserve">reſpectu diſtinctionum Propoſitionum.</s> <s xml:id="echoid-s12427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12428" xml:space="preserve">Ante ſuſceptam illam, & </s> <s xml:id="echoid-s12429" xml:space="preserve">aliam ejuſdem libri interpre-<lb/>tationem Anglicam inchoaverat Philoſophus ingenioſus <lb/>Job. </s> <s xml:id="echoid-s12430" xml:space="preserve">Theoph. </s> <s xml:id="echoid-s12431" xml:space="preserve">Deſaguliers, cujus peritia in inſtituendis Ex-<lb/>perimentis nota eſt. </s> <s xml:id="echoid-s12432" xml:space="preserve">Hic tamen, occaſione præcedentis <lb/>verſionis, nimis opus maturans, non omnes potuit feſti-<lb/>nationis ſcopulos effugere. </s> <s xml:id="echoid-s12433" xml:space="preserve">Mihi etiam inopinatum ac-<lb/>cidit, hanc publicari quaſi me rogante ſuſceptam, quod me <lb/>inſcio factum, interpretis ad me datæ litteræ teſtantur. </s> <s xml:id="echoid-s12434" xml:space="preserve">Hic <lb/>querelis meis reſpondit, ſe inſcio & </s> <s xml:id="echoid-s12435" xml:space="preserve">abſente, hoc à Biblio-<lb/>polâ Monito interpretis fuiſſe inſertum. </s> <s xml:id="echoid-s12436" xml:space="preserve">Ut errores Typo-<lb/>graphicos condonet Lector, & </s> <s xml:id="echoid-s12437" xml:space="preserve">ad corrigenda, in fine utrius-<lb/>que Tomi adjecta, velit attendere, rogatur.</s> <s xml:id="echoid-s12438" xml:space="preserve"/> </p> <pb file="0481" n="528"/> </div> <div xml:id="echoid-div1805" type="section" level="1" n="435"> <head xml:id="echoid-head589" xml:space="preserve">INDEX <lb/>CAPITUM.</head> <head xml:id="echoid-head590" xml:space="preserve">LIBER TERTIUS.</head> <head xml:id="echoid-head591" xml:space="preserve"><emph style="sc">Pars</emph> <emph style="sc">Prima</emph>. De Igne.</head> <note style="it" position="right" xml:space="preserve"> <lb/><emph style="sc">Cap</emph>. I. De Ignis proprietatibus in genere. # Pag. 1 <lb/># II. Ignem corporibus adhærere, & hiſce contineri. Ubi de Electricitate. # 2 <lb/># III. De motu Ignis. Ubi de Calore & Lumine. # 10 <lb/># IV. De Dilatatione ex Calore. # 13 <lb/></note> </div> <div xml:id="echoid-div1806" type="section" level="1" n="436"> <head xml:id="echoid-head592" xml:space="preserve"><emph style="sc">Pars</emph> <emph style="sc">Secunda</emph>. De Inflectione, Refractione, <lb/>& Reflectione Luminis.</head> <note style="it" position="right" xml:space="preserve"> <lb/><emph style="sc">Cap</emph>. V. De Inflectione Radiorum Luminis. # 17 <lb/># VI. De Luminis Refractione, & bujus legibus. # 19 <lb/># VII. De Luminis Refractione quando Media ſuperficie planâ ſeparantur. # 28 <lb/># VIII. De Refractione Luminis, poſitis Mediis ſuperficie ſphæricâ ſepara-<lb/># tis. # 31 <lb/># IX. De motu Luminis trans Medium denſius. Ubi de Lentium affectioni-<lb/># bus. # 38 <lb/># X. De Viſu. Ubi de Oculi conſtructione. # 42 <lb/># XI. De viſione trans Vitra, & corrigendis quibuſdam Oculorum vitiis. # 49 <lb/># XII. De Microſcopiis & Teleſcopiis. # 54 <lb/># XIII. De Reflectione Luminis. # 59 <lb/># XIV. De Speculis planis. # 64 <lb/># XV. De Speculis ſphæricis. # ibid. <lb/># XVI. De Lucernâ Magicâ. # 72 <lb/></note> </div> <div xml:id="echoid-div1807" type="section" level="1" n="437"> <head xml:id="echoid-head593" xml:space="preserve"><emph style="sc">Pars</emph> <emph style="sc">Tertia</emph>. De Opaco & Coloribus.</head> <head xml:id="echoid-head594" xml:space="preserve"><emph style="sc">Cap</emph>. XVII. De corporum opacitate. # 75</head> <note style="it" position="right" xml:space="preserve"> <lb/># XVIII. De diverſâ Radiorum Solarium refrangibilitate. # 78 <lb/># XIX. De Radiorum Coloribus & horum immutabilitate. # 84 <lb/># XX. De Colorum permixtione. Ubi de Albore. # 89 <lb/># XXI. De Iride. # 92 <lb/># XXII. De tenuium Laminarum Coloribus. # 98 <lb/># XXIII. De corporum naturalium Coloribus. # 103 <lb/></note> <pb file="0482" n="529"/> </div> <div xml:id="echoid-div1808" type="section" level="1" n="438"> <head xml:id="echoid-head595" xml:space="preserve">INDEX CAPITUM. <lb/>LIBER QUARTUS. <lb/><emph style="sc">Pars</emph> <emph style="sc">Prima</emph>. De Mundi Syſtemate.</head> <note style="it" position="right" xml:space="preserve"> <lb/><emph style="sc">Cap</emph>. I. Idea generalis Syſtematis Planetarii. # Pag.107 <lb/># II.De Motu Apparenti. # 114 <lb/># III.De Phænomenis Solis ex motu Telluris in Orbitâ. # 117 <lb/># IV.De Phænomenis Planetarum Inferiorum, ex horum & Telluris moti-<lb/># bus in Orbitis ſuis. # 119 <lb/># V.De Phænomenis Planetarum Superiorum ex horum & Telluris motibus in <lb/># Orbitis ſuis. # 122 <lb/># VI.De Phænomenis Satellitum ex motu horum in Orbitis. Ubi de Eclipſibus <lb/># Solis & Lunæ. # 123 <lb/># VII.De Phænomenis ex motu Solis, Planetarum & Lunæ circa Axes. # 128 <lb/># VIII.De Phænomenis Telluris ſuperficiem & peculiares bujus partes ſpectan-<lb/># tibus. # 132 <lb/># IX.De Phænomenis ex motu Axeos Telluris. # 143 <lb/># X.De Stellis fixis. # 144 <lb/></note> </div> <div xml:id="echoid-div1809" type="section" level="1" n="439"> <head xml:id="echoid-head596" xml:space="preserve"><emph style="sc">Pars</emph> <emph style="sc">Secunda</emph>. Motuum Cœleſtium caulæ <lb/>Phyſicæ.</head> <note style="it" position="right" xml:space="preserve"> <lb/><emph style="sc">Cap</emph>. XI.De Univerſali Gravitate. # 146 <lb/># XII.De Materiâ Cœleſti. # Ubi vacuum dari probatur. # 153 <lb/># XIII.De Motu Telluris. # 157 <lb/># XIV.De Denſitate Planetarum. # 160 <lb/># XV.Totius Syſtematis Planetarii Explicatio Phyſica. # 165 <lb/># XVI.Motus Lunæ Explicatio Phyſica. # 170 <lb/># XVII.De Planetarum Figuris. # 185 <lb/># XVIII.Motus Axeos Telluris Explicatio Phyſica. # 189 <lb/># XIX.De Æſtu Maris. # 191 <lb/># XX.De Lunæ Denſitate & Figurâ. # 197 <lb/></note> <figure> <image file="0482-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0482-01"/> </figure> <pb o="(1)" file="0483" n="530"/> </div> <div xml:id="echoid-div1810" type="section" level="1" n="440"> <head xml:id="echoid-head597" xml:space="preserve">PHYSICES <lb/>ELEMENTA MATHEMATICA, <lb/>EXPERIMENTIS CONFIRMATA.</head> <head xml:id="echoid-head598" xml:space="preserve">LIBER III. <lb/>Pars I. De Igne. <lb/>CAPUT I. <lb/>De Ignis proprietatibus in genere.</head> <p> <s xml:id="echoid-s12439" xml:space="preserve">VArias Ignis proprietates novimus, multa tamen <lb/>circa hunc nos latent.</s> <s xml:id="echoid-s12440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12441" xml:space="preserve">Hypotheſes non fingam, ex Experimentis ratio-<lb/>cinaturus ſum & </s> <s xml:id="echoid-s12442" xml:space="preserve">quod nondum pleniſſime no-<lb/>tum eſt intactum relinquam.</s> <s xml:id="echoid-s12443" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12444" xml:space="preserve">Ignis omnia corpora quantumvis denſa & </s> <s xml:id="echoid-s12445" xml:space="preserve">dura facillime <lb/> <anchor type="note" xlink:label="note-0483-01a" xlink:href="note-0483-01"/> penetrat. </s> <s xml:id="echoid-s12446" xml:space="preserve">Nullum enim novimus corpus quod admoto <lb/>igne non in omnibus punctis calefiat.</s> <s xml:id="echoid-s12447" xml:space="preserve"/> </p> <div xml:id="echoid-div1810" type="float" level="2" n="1"> <note position="right" xlink:label="note-0483-01" xlink:href="note-0483-01a" xml:space="preserve">544.</note> </div> <p> <s xml:id="echoid-s12448" xml:space="preserve">Ignis celerrime movetur; </s> <s xml:id="echoid-s12449" xml:space="preserve">conſtat hoc ex obſervationibus <lb/> <anchor type="note" xlink:label="note-0483-02a" xlink:href="note-0483-02"/> Aſtronomicis.</s> <s xml:id="echoid-s12450" xml:space="preserve"/> </p> <div xml:id="echoid-div1811" type="float" level="2" n="2"> <note position="right" xlink:label="note-0483-02" xlink:href="note-0483-02a" xml:space="preserve">545.</note> </div> <p> <s xml:id="echoid-s12451" xml:space="preserve">Ignis ſeſe corporibus jungit; </s> <s xml:id="echoid-s12452" xml:space="preserve">nam quando igni admoven-<lb/> <anchor type="note" xlink:label="note-0483-03a" xlink:href="note-0483-03"/> tur, ut jam dictum, incaleſcunt; </s> <s xml:id="echoid-s12453" xml:space="preserve">in hoc etiam caſu expan-<lb/> <anchor type="note" xlink:label="note-0483-04a" xlink:href="note-0483-04"/> duntur: </s> <s xml:id="echoid-s12454" xml:space="preserve">Quæ expanſio etiam obſervatur in corporibus cu-<lb/>jus partes non cohærent, in quo caſu elaſticitatem, ſæ-<lb/> <anchor type="note" xlink:label="note-0483-05a" xlink:href="note-0483-05"/> pe perquam magnam, acquirunt, ut illud obſervatur in aëre <lb/>& </s> <s xml:id="echoid-s12455" xml:space="preserve">vaporibus.</s> <s xml:id="echoid-s12456" xml:space="preserve"/> </p> <div xml:id="echoid-div1812" type="float" level="2" n="3"> <note position="right" xlink:label="note-0483-03" xlink:href="note-0483-03a" xml:space="preserve">546.</note> <note position="right" xlink:label="note-0483-04" xlink:href="note-0483-04a" xml:space="preserve">547.</note> <note position="right" xlink:label="note-0483-05" xlink:href="note-0483-05a" xml:space="preserve">548.</note> </div> <p> <s xml:id="echoid-s12457" xml:space="preserve">Ignem a corporibus ad certam ab his diſtantiam attrahi, <lb/> <anchor type="note" xlink:label="note-0483-06a" xlink:href="note-0483-06"/> in parte ſequenti patebit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12458" xml:space="preserve"/> </p> <div xml:id="echoid-div1813" type="float" level="2" n="4"> <note position="right" xlink:label="note-0483-06" xlink:href="note-0483-06a" xml:space="preserve">549.</note> </div> <note symbol="*" position="right" xml:space="preserve">611.</note> <p> <s xml:id="echoid-s12459" xml:space="preserve">Si corpora quæcunque juxta ſe mutuo violento motu agi-<lb/>tentur ex attritu incaleſcunt, & </s> <s xml:id="echoid-s12460" xml:space="preserve">quidem magnopere, quod <lb/>ignis præſentiam indicat, id eſt, omnia corpora ignem conti-<lb/> <anchor type="note" xlink:label="note-0483-08a" xlink:href="note-0483-08"/> nere: </s> <s xml:id="echoid-s12461" xml:space="preserve">ex attritu enim ignis quidem moveri, a corpore ſepa-<lb/>rari, minime vero generari poteſt.</s> <s xml:id="echoid-s12462" xml:space="preserve"/> </p> <div xml:id="echoid-div1814" type="float" level="2" n="5"> <note position="right" xlink:label="note-0483-08" xlink:href="note-0483-08a" xml:space="preserve">550.</note> </div> <pb o="(2)" file="0484" n="531" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s12463" xml:space="preserve">Quibus in genere expoſitis pleraque peculiarius ſunt exa-<lb/>minanda.</s> <s xml:id="echoid-s12464" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1816" type="section" level="1" n="441"> <head xml:id="echoid-head599" xml:space="preserve">CAPUT II.</head> <p> <s xml:id="echoid-s12465" xml:space="preserve">Ignem corporibus adbærere & </s> <s xml:id="echoid-s12466" xml:space="preserve">in hiſce contineri, <lb/># ubi de electricitate.</s> <s xml:id="echoid-s12467" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12468" xml:space="preserve">IGnem omnibus corporibus contineri ex eo probari <lb/> <anchor type="note" xlink:label="note-0484-01a" xlink:href="note-0484-01"/> diximus, quod nulla dentur corpora quæ ex attritu non ca-<lb/>lefiant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12469" xml:space="preserve">illumque arcte cum corporum partibus cohærere in fumo & </s> <s xml:id="echoid-s12470" xml:space="preserve">vaporibus patet: </s> <s xml:id="echoid-s12471" xml:space="preserve">conſtant enim fumus & </s> <s xml:id="echoid-s12472" xml:space="preserve">vapor ex <lb/>partibus a corporibus ſeparatis & </s> <s xml:id="echoid-s12473" xml:space="preserve">ab igne cum illis conjuncto <lb/>agitatis, ſæpe violentiſſime.</s> <s xml:id="echoid-s12474" xml:space="preserve"/> </p> <div xml:id="echoid-div1816" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0484-01" xlink:href="note-0484-01a" xml:space="preserve">550.</note> </div> <p> <s xml:id="echoid-s12475" xml:space="preserve">Varia de cætero dantur notabilia phœnomena ex igne <lb/>corporibus contento oriunda, quorum quædam hic ſunt <lb/>memoranda: </s> <s xml:id="echoid-s12476" xml:space="preserve">inter hæc dantur, quæ cum electricitate con-<lb/>nexionem notabilem habent, qua de cauſa de his ipſis ele-<lb/>ctricitatis phœnomenis agendum etiam erit.</s> <s xml:id="echoid-s12477" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1818" type="section" level="1" n="442"> <head xml:id="echoid-head600" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p style="it"> <s xml:id="echoid-s12478" xml:space="preserve">Electricitas eſt hæc corporum proprietas qua, ſi attritu ca-<lb/> <anchor type="note" xlink:label="note-0484-02a" xlink:href="note-0484-02"/> lefiant, trahunt, & </s> <s xml:id="echoid-s12479" xml:space="preserve">repellunt, corpora leviora ad diſtantiam <lb/>ſenſibilem.</s> <s xml:id="echoid-s12480" xml:space="preserve"/> </p> <div xml:id="echoid-div1818" type="float" level="2" n="1"> <note position="left" xlink:label="note-0484-02" xlink:href="note-0484-02a" xml:space="preserve">551.</note> </div> </div> <div xml:id="echoid-div1820" type="section" level="1" n="443"> <head xml:id="echoid-head601" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s12481" xml:space="preserve">Dentur duo fruſta cryſtalli montanæ, agitentur juxta ſe mu-<lb/> <anchor type="note" xlink:label="note-0484-03a" xlink:href="note-0484-03"/> tuo, ſtatim lucida in totum fiunt, licet ex attritu calorem <lb/>ſenſibilem non acquirant. </s> <s xml:id="echoid-s12482" xml:space="preserve">Lumen æque ac calor ignem da-<lb/>ri indicat; </s> <s xml:id="echoid-s12483" xml:space="preserve">lumen autem major datur in punctis in quibus <lb/>ambo fruſta ſeſe mutuo tangunt.</s> <s xml:id="echoid-s12484" xml:space="preserve"/> </p> <div xml:id="echoid-div1820" type="float" level="2" n="1"> <note position="left" xlink:label="note-0484-03" xlink:href="note-0484-03a" xml:space="preserve">552.</note> </div> </div> <div xml:id="echoid-div1822" type="section" level="1" n="444"> <head xml:id="echoid-head602" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s12485" xml:space="preserve">Tubus vitreus longitudinis circiter quindecim aut octode-<lb/> <anchor type="note" xlink:label="note-0484-04a" xlink:href="note-0484-04"/> cim pollicum & </s> <s xml:id="echoid-s12486" xml:space="preserve">diametri unius pollicis, ſi linteo aut panno <lb/>quocunque in loco obſcuro atteratur, lumen emittit.</s> <s xml:id="echoid-s12487" xml:space="preserve"/> </p> <div xml:id="echoid-div1822" type="float" level="2" n="1"> <note position="left" xlink:label="note-0484-04" xlink:href="note-0484-04a" xml:space="preserve">553.</note> </div> </div> <div xml:id="echoid-div1824" type="section" level="1" n="445"> <head xml:id="echoid-head603" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s12488" xml:space="preserve">Idem hicce tubus attritu calefactus electricitatem ſenſibi-<lb/> <anchor type="note" xlink:label="note-0484-05a" xlink:href="note-0484-05"/> lem admodum habet; </s> <s xml:id="echoid-s12489" xml:space="preserve">ſi enim corpora levia, ut fruſta folii <lb/> <anchor type="note" xlink:label="note-0484-06a" xlink:href="note-0484-06"/> aurei tenuiſſimi & </s> <s xml:id="echoid-s12490" xml:space="preserve">fuligo, plano imponantur, & </s> <s xml:id="echoid-s12491" xml:space="preserve">admovea-<lb/>tur tubus, agitantur hæc corpora; </s> <s xml:id="echoid-s12492" xml:space="preserve">a tubo attrahuntur & </s> <s xml:id="echoid-s12493" xml:space="preserve">re- <pb o="(3)" file="0485" n="532" rhead="MATHEMATICA. LIB. III. CAP. II."/> pelluntur variiſque motibus afficiuntur. </s> <s xml:id="echoid-s12494" xml:space="preserve">Et exerit tubus <lb/>hunc ſuum effectum ad varias diſtantias pro varia aëris con-<lb/>ſtitutione, aliquando ad diſtantiam unius pedis; </s> <s xml:id="echoid-s12495" xml:space="preserve">vapores in <lb/>aëre effectum minuunt.</s> <s xml:id="echoid-s12496" xml:space="preserve"/> </p> <div xml:id="echoid-div1824" type="float" level="2" n="1"> <note position="left" xlink:label="note-0484-05" xlink:href="note-0484-05a" xml:space="preserve">554.</note> <note position="left" xlink:label="note-0484-06" xlink:href="note-0484-06a" xml:space="preserve">TAB. I. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s12497" xml:space="preserve">Circa hoc experimentum notatu dignum, & </s> <s xml:id="echoid-s12498" xml:space="preserve">explicatu dif-<lb/> <anchor type="note" xlink:label="note-0485-01a" xlink:href="note-0485-01"/> ficillimum, eſt quod ſpectat directionem attritus; </s> <s xml:id="echoid-s12499" xml:space="preserve">manu ex-<lb/>tremitas tubi tenetur dum manu altera atteritur, quod ſi fiat <lb/>recedendo a manu tenente, effectus ſenſibilis non eſt; </s> <s xml:id="echoid-s12500" xml:space="preserve">con-<lb/>trarium obſervatur ſi attritus ab extremitate tubi libera diri-<lb/>gatur verſus illam quæ manu tenetur. </s> <s xml:id="echoid-s12501" xml:space="preserve">Hæcque indeſcrimi-<lb/>natim obtinent, quando cum tubo ab una parte clauſo ab al-<lb/>tera aperto experimentum inſtituitur, ſive tubi extremitas <lb/>clauſa, ſive altera extremitas manu teneatur.</s> <s xml:id="echoid-s12502" xml:space="preserve"/> </p> <div xml:id="echoid-div1825" type="float" level="2" n="2"> <note position="right" xlink:label="note-0485-01" xlink:href="note-0485-01a" xml:space="preserve">555.</note> </div> <p> <s xml:id="echoid-s12503" xml:space="preserve">In Experimentis ſequentibus globi vitrei celerrime circum-<lb/> <anchor type="note" xlink:label="note-0485-02a" xlink:href="note-0485-02"/> rotantur; </s> <s xml:id="echoid-s12504" xml:space="preserve">quod ut fiat requiritur ut in duobus locis oppoſi-<lb/> <anchor type="note" xlink:label="note-0485-03a" xlink:href="note-0485-03"/> tis cylindrice terminentur globi, unus tantum ex hiſce <lb/>cylindris apertus eſt, ambo cylindris cupreis circumdantur; <lb/></s> <s xml:id="echoid-s12505" xml:space="preserve">talis globus videtur in G : </s> <s xml:id="echoid-s12506" xml:space="preserve">ad partem globi apertam cum cy-<lb/>lindro aeneo jungitur epiſtomium E, & </s> <s xml:id="echoid-s12507" xml:space="preserve">cum cylindro aeneo <lb/>oppoſito jungitur rota minor r diametri circiter unius pol-<lb/>licis cum ſemiſſe; </s> <s xml:id="echoid-s12508" xml:space="preserve">cum rota hac in centro cohæret & </s> <s xml:id="echoid-s12509" xml:space="preserve">pro-<lb/>minet cylindrus aeneus exiguus; </s> <s xml:id="echoid-s12510" xml:space="preserve">ſimilis ad partem oppoſitam <lb/>datur qui jungitur cum epiſtomio E, ope cochleæ, ut <lb/>quando neceſſe eſt tolli poſſit. </s> <s xml:id="echoid-s12511" xml:space="preserve">Cylindri hi ad profundita-<lb/>tem quartæ partis unius pollicis intrant foramina in ſuſten-<lb/>taculis S, S, quibus globus ſuſtinetur, & </s> <s xml:id="echoid-s12512" xml:space="preserve">ſuper his cylindris <lb/>movetur globus & </s> <s xml:id="echoid-s12513" xml:space="preserve">circa axem revolvitur.</s> <s xml:id="echoid-s12514" xml:space="preserve"/> </p> <div xml:id="echoid-div1826" type="float" level="2" n="3"> <note position="right" xlink:label="note-0485-02" xlink:href="note-0485-02a" xml:space="preserve">556.</note> <note position="right" xlink:label="note-0485-03" xlink:href="note-0485-03a" xml:space="preserve">TAB. I. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s12515" xml:space="preserve">Imponuntur ſuſtentacula S, S, tabulæ ligneæ firmiſſimæ <lb/>craſſitiei ad minimum ſeſqui pollicis quæ tribus aliis tabulis <lb/>ut in figura videtur ſuſtinetur: </s> <s xml:id="echoid-s12516" xml:space="preserve">in harum anteriori datur fo-<lb/>ramen f ut ſuſtentaculum S ope cochleæ firmari poſſit, eo-<lb/>dem modo ope cochleæ in inferiori parte tabulæ ſuperioris <lb/>firmatur ſuſtentaculum alterum S, quod in ſciſſura movetur: <lb/></s> <s xml:id="echoid-s12517" xml:space="preserve">neceſſe eſt enim hicce motus ad globos in hoc ſitu firmandos <lb/>aut tollendos, & </s> <s xml:id="echoid-s12518" xml:space="preserve">ut ſeiſſura longitudinem quatuor aut quin-<lb/>que pollicum habeat deſideratur, quia globis majoribus & </s> <s xml:id="echoid-s12519" xml:space="preserve">mi-<lb/>noribus pro variis experimentis utendum eſt.</s> <s xml:id="echoid-s12520" xml:space="preserve"/> </p> <pb o="(4)" file="0486" n="533" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s12521" xml:space="preserve">Rota major R manubrio M agitatur, & </s> <s xml:id="echoid-s12522" xml:space="preserve">illius ope globus <lb/>G celerrime circumvolvitur.</s> <s xml:id="echoid-s12523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12524" xml:space="preserve">Ad latus tabulæ ſuperioris hujus machinæ datur ſciſſu-<lb/>ra, per quam movetur trochlea t; </s> <s xml:id="echoid-s12525" xml:space="preserve">cohæret hæc cum co-<lb/>chlea c, cujus ope per ſciſſuram movetur, quo tenditur fu-<lb/>nis rotas R & </s> <s xml:id="echoid-s12526" xml:space="preserve">r circumdans.</s> <s xml:id="echoid-s12527" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1828" type="section" level="1" n="446"> <head xml:id="echoid-head604" xml:space="preserve"><emph style="sc">Experimentum</emph> 4. & 5.</head> <p> <s xml:id="echoid-s12528" xml:space="preserve">Globus vitreus diametri circiter octo aut novem pollicum, <lb/> <anchor type="note" xlink:label="note-0486-01a" xlink:href="note-0486-01"/> machinæ memoratæ conjungatur, & </s> <s xml:id="echoid-s12529" xml:space="preserve">celerrime in loco ob-<lb/> <anchor type="note" xlink:label="note-0486-02a" xlink:href="note-0486-02"/> ſcuro agitetur, dum manu globo applicata attritus datur.</s> <s xml:id="echoid-s12530" xml:space="preserve"/> </p> <div xml:id="echoid-div1828" type="float" level="2" n="1"> <note position="left" xlink:label="note-0486-01" xlink:href="note-0486-01a" xml:space="preserve">557.</note> <note position="left" xlink:label="note-0486-02" xlink:href="note-0486-02a" xml:space="preserve">TAB. II. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s12531" xml:space="preserve">Si globus aëre ſit vacuus, totus quaſi lucidus fit ab inte-<lb/>riori parte, lumenque majus eſt in locis in quibus manus vi-<lb/>trum tangit.</s> <s xml:id="echoid-s12532" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12533" xml:space="preserve">Si autem glòbus aërem contineat, & </s> <s xml:id="echoid-s12534" xml:space="preserve">eodem modo agite-<lb/> <anchor type="note" xlink:label="note-0486-03a" xlink:href="note-0486-03"/> tur, & </s> <s xml:id="echoid-s12535" xml:space="preserve">manus applicetur, nullum in interiori aut exteriori <lb/>globi ſuperficie lumen apparet; </s> <s xml:id="echoid-s12536" xml:space="preserve">corpora vero ad exiguam a <lb/>globo diſtantiam ex. </s> <s xml:id="echoid-s12537" xml:space="preserve">gr. </s> <s xml:id="echoid-s12538" xml:space="preserve">quartæ partis unius pollicis aut mi-<lb/>norem lucida fiunt, ſicque ſolæ partes manus applicatæ, <lb/>quæ terminant aut potius circumdant partes immediate tan-<lb/>gentes globum, lucidæ ſunt.</s> <s xml:id="echoid-s12539" xml:space="preserve"/> </p> <div xml:id="echoid-div1829" type="float" level="2" n="2"> <note position="left" xlink:label="note-0486-03" xlink:href="note-0486-03a" xml:space="preserve">558.</note> </div> </div> <div xml:id="echoid-div1831" type="section" level="1" n="447"> <head xml:id="echoid-head605" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s12540" xml:space="preserve">Eodem globo quo uſi ſumus in experimentis præcedenti-<lb/> <anchor type="note" xlink:label="note-0486-04a" xlink:href="note-0486-04"/> bus & </s> <s xml:id="echoid-s12541" xml:space="preserve">hic utimur, eodem modo machinæ ut circumvolvi <lb/> <anchor type="note" xlink:label="note-0486-05a" xlink:href="note-0486-05"/> poſſit applicatur; </s> <s xml:id="echoid-s12542" xml:space="preserve">circumdatur globi pars ſuperior, ad diſtan-<lb/>tiam a globo circiter quatuor pollicum, filo æneo a b c, in <lb/>ſuperiori parte circulariter inflexo, cui fila tenuia annectun-<lb/>turquæ verſus centrum globi protenſa ad diſtantiam quartæ <lb/>partis unius pollicis a globo pertingunt.</s> <s xml:id="echoid-s12543" xml:space="preserve"/> </p> <div xml:id="echoid-div1831" type="float" level="2" n="1"> <note position="left" xlink:label="note-0486-04" xlink:href="note-0486-04a" xml:space="preserve">559.</note> <note position="left" xlink:label="note-0486-05" xlink:href="note-0486-05a" xml:space="preserve">TAB. I. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s12544" xml:space="preserve">Agitetur globus & </s> <s xml:id="echoid-s12545" xml:space="preserve">manus applicetur, ſtatim ex aëris agi-<lb/>tatione fila irregulariter agitantur; </s> <s xml:id="echoid-s12546" xml:space="preserve">calefacto vero ex attritu <lb/>vitro, fila omnia, ut in fig. </s> <s xml:id="echoid-s12547" xml:space="preserve">videtur, verſus globi centrum di-<lb/>riguntur, ſi manus globo paululum ad latus applicetur verſus <lb/>punctum in axe ad latus etiam diriguntur fila.</s> <s xml:id="echoid-s12548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12549" xml:space="preserve">Si globo aër extrahatur effectus totus hicce ceſſat.</s> <s xml:id="echoid-s12550" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">560.</note> </div> <div xml:id="echoid-div1833" type="section" level="1" n="448"> <head xml:id="echoid-head606" xml:space="preserve"><emph style="sc">Experimentum</emph>. 7.</head> <p> <s xml:id="echoid-s12551" xml:space="preserve">Detur globus in eo ſolo cum eo quo præcedentia experi-<lb/> <anchor type="note" xlink:label="note-0486-07a" xlink:href="note-0486-07"/> menta inſtituuntur differens, quod in hoc experimento a-<lb/> <anchor type="note" xlink:label="note-0486-08a" xlink:href="note-0486-08"/> <pb o="(5)" file="0487" n="534" rhead="MATHEMATICA. LIB. III. CAP. II."/> pertura globi G major requiratur, ut in hoc circellus ligneus <lb/>o cum filo aut cylindro æneo conjunctus, intrudatur. </s> <s xml:id="echoid-s12552" xml:space="preserve">Co-<lb/>hæret cylindrus hic, ut in medio globi firmetur circellus, <lb/>cum operculo quod in h. </s> <s xml:id="echoid-s12553" xml:space="preserve">aperturæ globi, ad hanc obturan-<lb/>dam, applicatur & </s> <s xml:id="echoid-s12554" xml:space="preserve">cochleis firmatur; </s> <s xml:id="echoid-s12555" xml:space="preserve">epiſtomium E in cen-<lb/>tro operculi huic conjungitur.</s> <s xml:id="echoid-s12556" xml:space="preserve"/> </p> <div xml:id="echoid-div1833" type="float" level="2" n="1"> <note position="left" xlink:label="note-0486-07" xlink:href="note-0486-07a" xml:space="preserve">561.</note> <note position="left" xlink:label="note-0486-08" xlink:href="note-0486-08a" xml:space="preserve">TAB. I. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s12557" xml:space="preserve">Circumferentiæ circelli o junguntur fila tenuia quæ pro-<lb/>tenſa ad globi ſuperficiem fere pertingunt.</s> <s xml:id="echoid-s12558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12559" xml:space="preserve">Machinæ antea memoratæ globus applicatur & </s> <s xml:id="echoid-s12560" xml:space="preserve">agitatur, <lb/>attrituſque ut in experimentis præcedentibus datur, calefacto <lb/>attritu globo, ſi ceſſet agitatio manuſque tollatur, ſtatim fi-<lb/>la eriguntur & </s> <s xml:id="echoid-s12561" xml:space="preserve">ut radii circuli verſus globi ſuperficiem diri-<lb/>guntur, vix tamen per momentum temporis quieſcunt, & </s> <s xml:id="echoid-s12562" xml:space="preserve"><lb/>agitatione aëris exterioris, licet globus ab omni parte exacte <lb/>ſit clauſus, agitantur fila hæc, ut patet flando verſus globum <lb/>licet os ab hoc duos pedes & </s> <s xml:id="echoid-s12563" xml:space="preserve">ultra diſtet. </s> <s xml:id="echoid-s12564" xml:space="preserve">Si digitus glo-<lb/>bo admoveatur, licet ille hunc non tangat, fila vicina a di-<lb/>gito attrahuntur & </s> <s xml:id="echoid-s12565" xml:space="preserve">verſus digitum diriguntur, aliquando <lb/>etiam hunc fugiunt. </s> <s xml:id="echoid-s12566" xml:space="preserve">Si manus globo applicetur, violenter <lb/>& </s> <s xml:id="echoid-s12567" xml:space="preserve">irregulariter fila agitantur.</s> <s xml:id="echoid-s12568" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12569" xml:space="preserve">Extracto aëre etiam ut in experimento præcedenti totus <lb/> <anchor type="note" xlink:label="note-0487-01a" xlink:href="note-0487-01"/> effectus ceſſat & </s> <s xml:id="echoid-s12570" xml:space="preserve">filorum ſitus, poſt æque ac ante attritum, <lb/>a gravitate pendet.</s> <s xml:id="echoid-s12571" xml:space="preserve"/> </p> <div xml:id="echoid-div1834" type="float" level="2" n="2"> <note position="right" xlink:label="note-0487-01" xlink:href="note-0487-01a" xml:space="preserve">562.</note> </div> <p> <s xml:id="echoid-s12572" xml:space="preserve">Si ad omnia præcedentia attendamus experimenta, ſe-<lb/>quentes concluſiones ex illis deduci poſſe videntur, quas <lb/>non ut certas tradimus, ſed ut valde probabiles; </s> <s xml:id="echoid-s12573" xml:space="preserve">certum <lb/>a probabile rite ſemper diſtinguendum.</s> <s xml:id="echoid-s12574" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12575" xml:space="preserve">Vitrum in ſe continere, hujuſque ſuperficiem circumdari at-<lb/> <anchor type="note" xlink:label="note-0487-02a" xlink:href="note-0487-02"/> moſphærâ quadam quæ attritu excitatur <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s12576" xml:space="preserve">motu vibratorio <anchor type="note" xlink:label="note-0487-03a" xlink:href="note-0487-03"/> agitatur, trahit enim & </s> <s xml:id="echoid-s12577" xml:space="preserve">repellit corpora levia <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12578" xml:space="preserve">partes mi- <anchor type="note" xlink:label="note-0487-04a" xlink:href="note-0487-04"/> nimæ vitri ex atritu agitantur & </s> <s xml:id="echoid-s12579" xml:space="preserve">propter harum elaſticitatem <lb/>motus hicce eſt vibratorius, qui at moſphæræ memoratæ com-<lb/>municatur, ideoque atmoſphæra eo ad majorem diſtantiam <lb/>actionem exerit quo ex majori attritu partes vitri magis agi-<lb/>tantur.</s> <s xml:id="echoid-s12580" xml:space="preserve"/> </p> <div xml:id="echoid-div1835" type="float" level="2" n="3"> <note position="right" xlink:label="note-0487-02" xlink:href="note-0487-02a" xml:space="preserve">563.</note> <note symbol="*" position="right" xlink:label="note-0487-03" xlink:href="note-0487-03a" xml:space="preserve">554. 559. 561.</note> <note symbol="*" position="right" xlink:label="note-0487-04" xlink:href="note-0487-04a" xml:space="preserve">554.</note> </div> <p> <s xml:id="echoid-s12581" xml:space="preserve">Ignis vitro contentus ex actione hujus atmoſphæræ expel-<lb/> <anchor type="note" xlink:label="note-0487-05a" xlink:href="note-0487-05"/> litur, ſaltem cum hac atmoſphæra movetur; </s> <s xml:id="echoid-s12582" xml:space="preserve">dum enim cor- <pb o="(6)" file="0488" n="535" rhead="PHYSICES ELEMENTA"/> pora levia ad diſtantiam a vitro agitantur, corpora etiam <lb/>ad diſtantiam lucida fiunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s12583" xml:space="preserve"/> </p> <div xml:id="echoid-div1836" type="float" level="2" n="4"> <note position="right" xlink:label="note-0487-05" xlink:href="note-0487-05a" xml:space="preserve">564.</note> </div> <note symbol="*" position="left" xml:space="preserve">559. 558.</note> <p> <s xml:id="echoid-s12584" xml:space="preserve">Atmoſphæram & </s> <s xml:id="echoid-s12585" xml:space="preserve">ignem facilius moveri in vacuo etiam pa-<lb/> <anchor type="note" xlink:label="note-0488-02a" xlink:href="note-0488-02"/> tet: </s> <s xml:id="echoid-s12586" xml:space="preserve">ſi enim globo aër extrahatur nullum lumen, neque ele-<lb/>ctricitatis actio ab exteriori parte obſervari poſſunt <anchor type="note" xlink:href="" symbol="*"/>, pars <anchor type="note" xlink:label="note-0488-03a" xlink:href="note-0488-03"/> vero globi interior maxime lucida apparet, igniſque majori <lb/>copia in hoc experimento quam in ſtatim memorato <anchor type="note" xlink:href="" symbol="*"/> ſenſi- <anchor type="note" xlink:label="note-0488-04a" xlink:href="note-0488-04"/> bilis eſt.</s> <s xml:id="echoid-s12587" xml:space="preserve"/> </p> <div xml:id="echoid-div1837" type="float" level="2" n="5"> <note position="left" xlink:label="note-0488-02" xlink:href="note-0488-02a" xml:space="preserve">565.</note> <note symbol="*" position="left" xlink:label="note-0488-03" xlink:href="note-0488-03a" xml:space="preserve">557. 560.</note> <note symbol="*" position="left" xlink:label="note-0488-04" xlink:href="note-0488-04a" xml:space="preserve">558.</note> </div> <p> <s xml:id="echoid-s12588" xml:space="preserve">Electricitatis autem actio extracto aëre etiam ab interiori <lb/>parte ceſſat <anchor type="note" xlink:href="" symbol="*"/>, quo everti videtur quod de faciliori motu <anchor type="note" xlink:label="note-0488-05a" xlink:href="note-0488-05"/> atmoſphæræ in vacuo dictum. </s> <s xml:id="echoid-s12589" xml:space="preserve">Minime tamen probabile <lb/>eſt atmoſphæram ſæpius memoratam in hoc caſu nullibi mo-<lb/>veri. </s> <s xml:id="echoid-s12590" xml:space="preserve">Videtur e contra illam eandem cum igne viam ſequi <lb/>& </s> <s xml:id="echoid-s12591" xml:space="preserve">verſus illam partem moveri ad quam minor datur reſiſten-<lb/>tia; </s> <s xml:id="echoid-s12592" xml:space="preserve">& </s> <s xml:id="echoid-s12593" xml:space="preserve">ceſſationem actionis electricitatis tribuendam eſſe <lb/>ipſi privationi aëris, quo mediante ab atmoſphæra fila mo-<lb/> <anchor type="note" xlink:label="note-0488-06a" xlink:href="note-0488-06"/> ventur; </s> <s xml:id="echoid-s12594" xml:space="preserve">eodem modo ut in ſequentibus videbimus <anchor type="note" xlink:href="" symbol="*"/>, ac <anchor type="note" xlink:label="note-0488-07a" xlink:href="note-0488-07"/> ignis, qui liberrime omnia corpora penetrat, mediante aëre <lb/>aut vapore violenter in illa agit.</s> <s xml:id="echoid-s12595" xml:space="preserve"/> </p> <div xml:id="echoid-div1838" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0488-05" xlink:href="note-0488-05a" xml:space="preserve">561.</note> <note position="left" xlink:label="note-0488-06" xlink:href="note-0488-06a" xml:space="preserve">566.</note> <note symbol="*" position="left" xlink:label="note-0488-07" xlink:href="note-0488-07a" xml:space="preserve">605. 607.</note> </div> <p> <s xml:id="echoid-s12596" xml:space="preserve">Miſſis conjecturis, nixis licet multis experimentis, ad cæte-<lb/>ra quæ ignem ſpectant redeamus. </s> <s xml:id="echoid-s12597" xml:space="preserve">Varia autem experimen-<lb/>ta in vacuo peragenda ſunt, in quibus attritus requiritur, <lb/>quæ ſequenti Machinâ inſtituenda ſunt.</s> <s xml:id="echoid-s12598" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12599" xml:space="preserve">Sit M Machina Pneumatica de qua antea actum <anchor type="note" xlink:href="" symbol="*"/>, LL lami- <anchor type="note" xlink:label="note-0488-08a" xlink:href="note-0488-08"/> na ænea cui vitrea vaſa ſuper imponuntur; </s> <s xml:id="echoid-s12600" xml:space="preserve">ad latera lami-<lb/> <anchor type="note" xlink:label="note-0488-09a" xlink:href="note-0488-09"/> næ dantur columnæ ligneæ duæ AD, AD, harum baſes <lb/> <anchor type="note" xlink:label="note-0488-10a" xlink:href="note-0488-10"/> imponuntur tabulæ ſupremæ Machinæ Pneumaticæ, pro <lb/>parte tamen infra hanc tabulam per foramina penetrant ut <lb/>columnæ, lignis transverſis, facile firmentur & </s> <s xml:id="echoid-s12601" xml:space="preserve">finitis expe-<lb/>rimentis tollantur.</s> <s xml:id="echoid-s12602" xml:space="preserve"/> </p> <div xml:id="echoid-div1839" type="float" level="2" n="7"> <note position="left" xlink:label="note-0488-08" xlink:href="note-0488-08a" xml:space="preserve">567.</note> <note position="left" xlink:label="note-0488-09" xlink:href="note-0488-09a" xml:space="preserve">TAB. II. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0488-10" xlink:href="note-0488-10a" xml:space="preserve">437.</note> </div> <p> <s xml:id="echoid-s12603" xml:space="preserve">Vas vitreum in quo experimenta inſtituuntur, cujus al-<lb/>titudo eſt circiter novem poll. </s> <s xml:id="echoid-s12604" xml:space="preserve">& </s> <s xml:id="echoid-s12605" xml:space="preserve">diameter ſex poll.</s> <s xml:id="echoid-s12606" xml:space="preserve">. o-<lb/>perculo obtegitur, cum quo cohæret pixis cum coriis <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0488-11a" xlink:href="note-0488-11"/> hanc pertranſit axis æneus, & </s> <s xml:id="echoid-s12607" xml:space="preserve">ne, dum axis circumrotatur <lb/>operculum moveri poſſit datur pars pixidis quadrata, quæ <lb/>exacte congruit cum foramine quadrato in tabella lignea EE, <lb/>quæ ab operculo ſuſtinetur, & </s> <s xml:id="echoid-s12608" xml:space="preserve">quæ firmatur hanc cochleis <pb o="(7)" file="0489" n="536" rhead="MATHEMATICA. LIB. III. CAP. II."/> B, Bad latera deprimendo, non autem ab ipſis columnis ſu-<lb/>ſtinetur.</s> <s xml:id="echoid-s12609" xml:space="preserve"/> </p> <div xml:id="echoid-div1840" type="float" level="2" n="8"> <note symbol="*" position="left" xlink:label="note-0488-11" xlink:href="note-0488-11a" xml:space="preserve">440.</note> </div> <p> <s xml:id="echoid-s12610" xml:space="preserve">Verſus ſuperioreḿ columnarum partem ab his ſuſtinetur <lb/>tabella minor FF, quæ ope cochlearum etiam firmatur, <lb/>cum hac lamella in inferiori parte in medio cohæret fruſtum <lb/>æneum g, in quo cavitas datur, in qua movetur extremitas ſu-<lb/>perior axis memorati, cujus maxima pars vitro contenta, in <lb/>formam helicis ſulco circumdata cochleam format, circa <lb/>quam cochleæ exteriores duæ d, d, moventur ad varia cor-<lb/>pora cum axe firmanda inſervientes.</s> <s xml:id="echoid-s12611" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12612" xml:space="preserve">Inferior axis extremitas in cavitate c movetur. </s> <s xml:id="echoid-s12613" xml:space="preserve">Lami-<lb/>na ænea inflexa elaſtica ff cum fruſto æneo c cohæret, & </s> <s xml:id="echoid-s12614" xml:space="preserve"><lb/>ope cochleæ cum lamina LL connectitur in foramine, per <lb/>quod aër extrahitur, ſervato tamen in c minori foramine ut <lb/>aëri tranſitus detur & </s> <s xml:id="echoid-s12615" xml:space="preserve">vas exhauriri poſſit.</s> <s xml:id="echoid-s12616" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12617" xml:space="preserve">Evacuato vaſe vitreo, axis memoratus, propter coria in <lb/>pixide P, circumrotatur nullo admiſſo aëre, ſed ut celeri-<lb/>ter circumvolvatur datur rota ænea minor r diametri circi-<lb/>ter duorum pollicum, pinnulis armata in fundo ſulci in quo <lb/>funis applicatur.</s> <s xml:id="echoid-s12618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12619" xml:space="preserve">Rota major R diametri circiter trium pedum in ſitu ver-<lb/>ticali, cum ſuſtentaculo, ad latus Machinæ Pneumaticæ diſ-<lb/>ponitur, & </s> <s xml:id="echoid-s12620" xml:space="preserve">cum hujus pede rotæ ſuſtentaculum ope cochle-<lb/>arum jungitur.</s> <s xml:id="echoid-s12621" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12622" xml:space="preserve">Funis, minorem rotam r circumdans, ſuper trochleis <lb/>oblique poſitis in ſuperiori parte columnarum C, C, dedu-<lb/>citur, & </s> <s xml:id="echoid-s12623" xml:space="preserve">ibi inflexus ad majorem rotam pervenit quam cir-<lb/>cumdat, ita ut agitatione rotæ verticalis R, axis ſæpius me-<lb/>moratus celerrime circumrotetur, quo in vacuo datur motus <lb/>ad varia experimenta inſtituenda.</s> <s xml:id="echoid-s12624" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1842" type="section" level="1" n="449"> <head xml:id="echoid-head607" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s12625" xml:space="preserve">Detur globus vitreus diametri trium pollicum, aut duo-<lb/> <anchor type="note" xlink:label="note-0489-01a" xlink:href="note-0489-01"/> rum pollicum cum ſemiſſe, perforatus ab utraque parte, etiam <lb/>poteſt ad foramina cylindrice terminari. </s> <s xml:id="echoid-s12626" xml:space="preserve">Per hæc forami-<lb/>na, ut globus circumagatur, tranſmittitur axis ſtatim me-<lb/>moratus; </s> <s xml:id="echoid-s12627" xml:space="preserve">ſubere ab utraque parte globi ora obteguntur & </s> <s xml:id="echoid-s12628" xml:space="preserve">fir-<lb/>mantur hic ope cochlearum d, d, eodem modo ac in figura, <pb o="(8)" file="0490" n="537" rhead="PHYSICES ELEMENTA"/> harum ope firmantur orbiculi per quos axis tranſit.</s> <s xml:id="echoid-s12629" xml:space="preserve"/> </p> <div xml:id="echoid-div1842" type="float" level="2" n="1"> <note position="right" xlink:label="note-0489-01" xlink:href="note-0489-01a" xml:space="preserve">568.</note> </div> <p> <s xml:id="echoid-s12630" xml:space="preserve">Globus, ſic firmatus, cum axe in vacuo motu rotæ R celer-<lb/>rime movetur: </s> <s xml:id="echoid-s12631" xml:space="preserve">ut attritus detur, pannus applicatur ab utra-<lb/>que parte laminæ f, f, quæ elaſticitate ab utraque parte <lb/>globum premit.</s> <s xml:id="echoid-s12632" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12633" xml:space="preserve">Si in loco obſcuro experimentum inſtituatur globus luci-<lb/>dus apparebit, continuato motu ut globus attritu incaleſcat, <lb/>lumen quidem augetur, ſed fixum tunc datur in locis ubi at-<lb/>tritus datur.</s> <s xml:id="echoid-s12634" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12635" xml:space="preserve">Sequitur ex hoc experimento Ignem vitro contentum ut <lb/> <anchor type="note" xlink:label="note-0490-01a" xlink:href="note-0490-01"/> appareat aëre non indigere, incaleſcit enim & </s> <s xml:id="echoid-s12636" xml:space="preserve">lucet ſublato <lb/>aëre & </s> <s xml:id="echoid-s12637" xml:space="preserve">interno & </s> <s xml:id="echoid-s12638" xml:space="preserve">externo.</s> <s xml:id="echoid-s12639" xml:space="preserve"/> </p> <div xml:id="echoid-div1843" type="float" level="2" n="2"> <note position="left" xlink:label="note-0490-01" xlink:href="note-0490-01a" xml:space="preserve">569.</note> </div> </div> <div xml:id="echoid-div1845" type="section" level="1" n="450"> <head xml:id="echoid-head608" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s12640" xml:space="preserve">Detur orbis ligneus diametri circiter duorum pollicum <lb/> <anchor type="note" xlink:label="note-0490-02a" xlink:href="note-0490-02"/> aut duorum pollicum cum ſemiſſe, & </s> <s xml:id="echoid-s12641" xml:space="preserve">cujus craſſities ſit ſemi-<lb/>pollicis, ad latus circumdetur orbis cavitatibus ut globulis <lb/>gypſeis circumdari poſſit, qui ſi in cavitatibus applicentur, <lb/>firmiter orbi alligari poterunt ope fili ſingulos globos per <lb/>medium trajicientis. </s> <s xml:id="echoid-s12642" xml:space="preserve">Si per centrum hujus orbis tranſeat <lb/>axis in experimento præcedenti, memoratus & </s> <s xml:id="echoid-s12643" xml:space="preserve">orbis firme-<lb/>tur ut de globo ibi dictum, & </s> <s xml:id="echoid-s12644" xml:space="preserve">detur attritus ut in illo experi-<lb/>mento, evacuato vaſe, in loco obſcuro lumen apparebit.</s> <s xml:id="echoid-s12645" xml:space="preserve"/> </p> <div xml:id="echoid-div1845" type="float" level="2" n="1"> <note position="left" xlink:label="note-0490-02" xlink:href="note-0490-02a" xml:space="preserve">570.</note> </div> </div> <div xml:id="echoid-div1847" type="section" level="1" n="451"> <head xml:id="echoid-head609" xml:space="preserve"><emph style="sc">Experimentum</emph> 10.</head> <p> <s xml:id="echoid-s12646" xml:space="preserve">Mercurium ignem continere experimentis in vacuo inſti-<lb/> <anchor type="note" xlink:label="note-0490-03a" xlink:href="note-0490-03"/> tutis patet. </s> <s xml:id="echoid-s12647" xml:space="preserve">Si enim mercurius probe depurgatus in vitro <lb/>aëre vacuo agitetur lucidus apparet.</s> <s xml:id="echoid-s12648" xml:space="preserve"/> </p> <div xml:id="echoid-div1847" type="float" level="2" n="1"> <note position="left" xlink:label="note-0490-03" xlink:href="note-0490-03a" xml:space="preserve">571.</note> </div> <p> <s xml:id="echoid-s12649" xml:space="preserve">Si Globo vitreo contineatur Mercurius, poterit ille cir-<lb/> <anchor type="note" xlink:label="note-0490-04a" xlink:href="note-0490-04"/> cumrotari ut in aliis experimentis dictum, & </s> <s xml:id="echoid-s12650" xml:space="preserve">amœnum da-<lb/>bitur ſpectaculum ſi lente moveatur globus. </s> <s xml:id="echoid-s12651" xml:space="preserve">Ope aceti fer-<lb/>vidiſſimi & </s> <s xml:id="echoid-s12652" xml:space="preserve">calidi depurgatur mercurius niſi ſtannum con-<lb/>tineat.</s> <s xml:id="echoid-s12653" xml:space="preserve"/> </p> <div xml:id="echoid-div1848" type="float" level="2" n="2"> <note position="left" xlink:label="note-0490-04" xlink:href="note-0490-04a" xml:space="preserve">572.</note> </div> <p> <s xml:id="echoid-s12654" xml:space="preserve">Evacuatur aëre globus mercurium continens, jungendo <lb/> <anchor type="note" xlink:label="note-0490-05a" xlink:href="note-0490-05"/> cum globo tubum longitudinis circiter duorum pedum, & </s> <s xml:id="echoid-s12655" xml:space="preserve"><lb/>jungendo aliam tubi extremitatem ab inferiori parte cum <lb/>foramine in medio laminæ Machinæ Pneumaticæ.</s> <s xml:id="echoid-s12656" xml:space="preserve"/> </p> <div xml:id="echoid-div1849" type="float" level="2" n="3"> <note position="left" xlink:label="note-0490-05" xlink:href="note-0490-05a" xml:space="preserve">573.</note> </div> <p> <s xml:id="echoid-s12657" xml:space="preserve">Si tunc foramen hoc, ut & </s> <s xml:id="echoid-s12658" xml:space="preserve">illud per quod aër extrahitur, <lb/>tegantur vaſe laminæ memoratæ ſuper impoſito, aër facile ex <lb/>globo deducitur.</s> <s xml:id="echoid-s12659" xml:space="preserve"/> </p> <pb o="(9)" file="0491" n="538" rhead="MATHEMATICA. LIB. III. CAP. II."/> </div> <div xml:id="echoid-div1851" type="section" level="1" n="452"> <head xml:id="echoid-head610" xml:space="preserve"><emph style="sc">Experimentum</emph>. 10.</head> <p> <s xml:id="echoid-s12660" xml:space="preserve">Sit orbis O; </s> <s xml:id="echoid-s12661" xml:space="preserve">jungatur hic, adhibito tubo EE, ope co-<lb/> <anchor type="note" xlink:label="note-0491-01a" xlink:href="note-0491-01"/> chleæ cum foramine in lamina Machinæ pneumaticæ ita ut <lb/> <anchor type="note" xlink:label="note-0491-02a" xlink:href="note-0491-02"/> aër ex vaſe R, orbi O ſuperimpoſito, extrahi poſſit. </s> <s xml:id="echoid-s12662" xml:space="preserve">Tubus <lb/>autem per quod aër extrahitur prominet in vaſe ad altitudi-<lb/>nem quatuor aut quinque pollicum, inflectitur & </s> <s xml:id="echoid-s12663" xml:space="preserve">parvam <lb/>habet aperturam; </s> <s xml:id="echoid-s12664" xml:space="preserve">quæ omnia obſervanda ſunt, ne quam mi-<lb/>nime Mercurius ad Machinam pneumaticam pervenire poſſit.</s> <s xml:id="echoid-s12665" xml:space="preserve"/> </p> <div xml:id="echoid-div1851" type="float" level="2" n="1"> <note position="right" xlink:label="note-0491-01" xlink:href="note-0491-01a" xml:space="preserve">574.</note> <note position="right" xlink:label="note-0491-02" xlink:href="note-0491-02a" xml:space="preserve">TAB. I. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12666" xml:space="preserve">Cum orbe in medio jungitur tubus æneus B; </s> <s xml:id="echoid-s12667" xml:space="preserve">inferior pars <lb/>clauſa pertingit fere ad fundum vaſis V, Mercurium depur-<lb/>gatum continentis; </s> <s xml:id="echoid-s12668" xml:space="preserve">ad latus foramen datur, quod clavo A <lb/>exacte obturatur, ſuperior tubi B extremitas in vaſe R datur <lb/>& </s> <s xml:id="echoid-s12669" xml:space="preserve">aperturam habet exiguam.</s> <s xml:id="echoid-s12670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12671" xml:space="preserve">Altitudo vaſis R eſt circiter ſedecim pollicum, diameter <lb/>quatuor pollicum; </s> <s xml:id="echoid-s12672" xml:space="preserve">ſi ex hoc aër evacuetur & </s> <s xml:id="echoid-s12673" xml:space="preserve">foramen ad <lb/>latus tubi B aperiatur, preſſione aëris exterioris violentiſſi-<lb/>me Mercurius tubum intrabit, & </s> <s xml:id="echoid-s12674" xml:space="preserve">proſiliet magno impetu in <lb/>ſuperiorem partem vaſis R impingens.</s> <s xml:id="echoid-s12675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12676" xml:space="preserve">In loco obſcuro inſtituendum Experimentum eſt, & </s> <s xml:id="echoid-s12677" xml:space="preserve">Mer-<lb/>curius lucidus apparebit.</s> <s xml:id="echoid-s12678" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1853" type="section" level="1" n="453"> <head xml:id="echoid-head611" xml:space="preserve"><emph style="sc">Experimentum</emph>. 11.</head> <p> <s xml:id="echoid-s12679" xml:space="preserve">Notiſſima datur chemica præparatio ex urina, Phoſphorus <lb/> <anchor type="note" xlink:label="note-0491-03a" xlink:href="note-0491-03"/> Vrinæ dicta, in aqua ſervatur; </s> <s xml:id="echoid-s12680" xml:space="preserve">ſi ex illo ſtilus formetur & </s> <s xml:id="echoid-s12681" xml:space="preserve"><lb/>litteræ ſuper charta ſcribantur, in loco obſcuro, igneæ appa-<lb/>rebunt. </s> <s xml:id="echoid-s12682" xml:space="preserve">Phoſphorus ipſe aqua extractus ſtatim incaleſcit & </s> <s xml:id="echoid-s12683" xml:space="preserve"><lb/>fumum emittit; </s> <s xml:id="echoid-s12684" xml:space="preserve">quæ omnia ignem magnâ copiâ Phoſphoro <lb/>contineri probant.</s> <s xml:id="echoid-s12685" xml:space="preserve"/> </p> <div xml:id="echoid-div1853" type="float" level="2" n="1"> <note position="right" xlink:label="note-0491-03" xlink:href="note-0491-03a" xml:space="preserve">575.</note> </div> <p> <s xml:id="echoid-s12686" xml:space="preserve">In hoc Experimento ſenſibilem obſervamus aquæ actionem <lb/> <anchor type="note" xlink:label="note-0491-04a" xlink:href="note-0491-04"/> in ignem Phoſphoro contentum; </s> <s xml:id="echoid-s12687" xml:space="preserve">illa enim hunc retinet ita, ut <lb/>minimè ex Phoſphoro, quamdiu aquâ circumdatur, exire <lb/>poſſit; </s> <s xml:id="echoid-s12688" xml:space="preserve">ſublatâ autem aquâ calor & </s> <s xml:id="echoid-s12689" xml:space="preserve">fumus ſtatim indicant <lb/>ignem a Phoſphoro recedentem.</s> <s xml:id="echoid-s12690" xml:space="preserve"/> </p> <div xml:id="echoid-div1854" type="float" level="2" n="2"> <note position="right" xlink:label="note-0491-04" xlink:href="note-0491-04a" xml:space="preserve">576.</note> </div> <p> <s xml:id="echoid-s12691" xml:space="preserve">Aër etiam ignem aquâ calidâ contentum quodammodo in <lb/> <anchor type="note" xlink:label="note-0491-05a" xlink:href="note-0491-05"/> hac retinet, id eſt cohibet ne eadem celeritate ac in vacuo <lb/>exeat.</s> <s xml:id="echoid-s12692" xml:space="preserve"/> </p> <div xml:id="echoid-div1855" type="float" level="2" n="3"> <note position="right" xlink:label="note-0491-05" xlink:href="note-0491-05a" xml:space="preserve">577.</note> </div> </div> <div xml:id="echoid-div1857" type="section" level="1" n="454"> <head xml:id="echoid-head612" xml:space="preserve"><emph style="sc">Experimentum</emph>. 12.</head> <p> <s xml:id="echoid-s12693" xml:space="preserve">Dentur duo vaſa quæcunque æqualia & </s> <s xml:id="echoid-s12694" xml:space="preserve">ſimilia, infunda- <pb o="(10)" file="0492" n="539" rhead="PHYSICES ELEMENTA"/> tur aqua ebulliens, æquali quantitate in utroque; </s> <s xml:id="echoid-s12695" xml:space="preserve">impona-<lb/>tur unum laminæ Machinæ Pneumaticæ & </s> <s xml:id="echoid-s12696" xml:space="preserve">ſuperimpoſito <lb/>vaſe aër ex hoc extrahatur; </s> <s xml:id="echoid-s12697" xml:space="preserve">dum aër extrahitur ebullit aqua <lb/>violenter ex actione ignis exeuntis; </s> <s xml:id="echoid-s12698" xml:space="preserve">ſtatim enim hæc tepida <lb/>fit, dum aqua, quæ in vaſe alio aëri remanſit expoſita, vix <lb/>ex calore quid amiſit.</s> <s xml:id="echoid-s12699" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12700" xml:space="preserve">Quid ſimile obſervamus reſpectu ligni lucidi; </s> <s xml:id="echoid-s12701" xml:space="preserve">lignum enim <lb/> <anchor type="note" xlink:label="note-0492-01a" xlink:href="note-0492-01"/> datur, quod in terra putrefactum, ſi terrâ extrahatur, lucet; <lb/></s> <s xml:id="echoid-s12702" xml:space="preserve">terra quæ lignum circundat retinet ignem, ſublatâ hac i-<lb/>gnis exit & </s> <s xml:id="echoid-s12703" xml:space="preserve">per aliquot dies lucidum manet. </s> <s xml:id="echoid-s12704" xml:space="preserve">In vacuo cito <lb/>perit lumen & </s> <s xml:id="echoid-s12705" xml:space="preserve">admiſſo aëre non reſtituitur.</s> <s xml:id="echoid-s12706" xml:space="preserve"/> </p> <div xml:id="echoid-div1857" type="float" level="2" n="1"> <note position="left" xlink:label="note-0492-01" xlink:href="note-0492-01a" xml:space="preserve">578.</note> </div> <p> <s xml:id="echoid-s12707" xml:space="preserve">Quomodo autem ignis in corpore retineatur a corporibus <lb/>circundantibus & </s> <s xml:id="echoid-s12708" xml:space="preserve">cuinam actioni effectus hic tribuendus ſit, <lb/>non facile determinari poterit; </s> <s xml:id="echoid-s12709" xml:space="preserve">minimè probabile eſt preſ-<lb/>fionem hìc eſſe conſiderandam, cùm ignis omnia corpora <lb/>ſubtilitate ſua facile penetret.</s> <s xml:id="echoid-s12710" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1859" type="section" level="1" n="455"> <head xml:id="echoid-head613" xml:space="preserve">CAPUT III.</head> <head xml:id="echoid-head614" style="it" xml:space="preserve">De motu Ignis, ubi de Calore & Lumine.</head> <p> <s xml:id="echoid-s12711" xml:space="preserve">IGnem celerrime moveri diximus <anchor type="note" xlink:href="" symbol="*"/>, motus hicce pro variis <anchor type="note" xlink:label="note-0492-02a" xlink:href="note-0492-02"/> circumſtantiis diverſos edit effectus. </s> <s xml:id="echoid-s12712" xml:space="preserve">Calor & </s> <s xml:id="echoid-s12713" xml:space="preserve">lumen di-<lb/>verſitati motus ignis adſcribenda ſunt.</s> <s xml:id="echoid-s12714" xml:space="preserve"/> </p> <div xml:id="echoid-div1859" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0492-02" xlink:href="note-0492-02a" xml:space="preserve">545.</note> </div> <p> <s xml:id="echoid-s12715" xml:space="preserve">Calor in corpore calido eſt agitatio partium corporis & </s> <s xml:id="echoid-s12716" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0492-03a" xlink:href="note-0492-03"/> ignis in hoc contenti, qua agitatione motus in corpore no-<lb/>ſtro datur, qui ideam caloris in mente noſtra excitat;</s> <s xml:id="echoid-s12717" xml:space="preserve"/> </p> <div xml:id="echoid-div1860" type="float" level="2" n="2"> <note position="left" xlink:label="note-0492-03" xlink:href="note-0492-03a" xml:space="preserve">579.</note> </div> <p style="it"> <s xml:id="echoid-s12718" xml:space="preserve">Calor noſtri reſpectu nibil eſt præter illam ideam, & </s> <s xml:id="echoid-s12719" xml:space="preserve">in <lb/> <anchor type="note" xlink:label="note-0492-04a" xlink:href="note-0492-04"/> corpore calido nil datur præter motum.</s> <s xml:id="echoid-s12720" xml:space="preserve"/> </p> <div xml:id="echoid-div1861" type="float" level="2" n="3"> <note position="left" xlink:label="note-0492-04" xlink:href="note-0492-04a" xml:space="preserve">580.</note> </div> <p> <s xml:id="echoid-s12721" xml:space="preserve">Hic in memoriam revocare debemus, quæ no. </s> <s xml:id="echoid-s12722" xml:space="preserve">502. </s> <s xml:id="echoid-s12723" xml:space="preserve">de <lb/>ſenſationibus in genere dicta ſunt, quæ etiam ad lumen re-<lb/>ſerri debent.</s> <s xml:id="echoid-s12724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12725" xml:space="preserve">Quando ignis per lineas rectas oculos noſtros intrat, ex <lb/> <anchor type="note" xlink:label="note-0492-05a" xlink:href="note-0492-05"/> motu quem fibris in fundo oculi communicat, ideam luminis <lb/>excitat; </s> <s xml:id="echoid-s12726" xml:space="preserve">de quo fibrarum motu in ſequentibus peculiarius <lb/>erit agendum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12727" xml:space="preserve">Motum per lineas rectas in lumine dari ex <anchor type="note" xlink:label="note-0492-06a" xlink:href="note-0492-06"/> obſtaculo quo lumen intercipitur facile probatur. </s> <s xml:id="echoid-s12728" xml:space="preserve">Contra <lb/> <anchor type="note" xlink:label="note-0492-07a" xlink:href="note-0492-07"/> autem talem motum in calore non requiri, motumque irre- <pb file="0493" n="540"/> <pb file="0493a" n="541"/> <anchor type="figure" xlink:label="fig-0493a-01a" xlink:href="fig-0493a-01"/> <pb file="0494" n="542"/> <pb o="11" file="0495" n="543" rhead="MATHEMATIC A LIB. III. CAP. III."/> gularem magis aptum eſſe ex eo probatur, quòd radii ſola-<lb/>res directe a Sole ad apicem montis pervenientes, ſenſibilem <lb/>quantum ad calorem non edant effectum; </s> <s xml:id="echoid-s12729" xml:space="preserve">dum in valle in <lb/>quo motu irregulari variis reflexionibus agitantur radii, ca-<lb/>lor ſæpe detur maxime intenſus.</s> <s xml:id="echoid-s12730" xml:space="preserve"/> </p> <div xml:id="echoid-div1862" type="float" level="2" n="4"> <note position="left" xlink:label="note-0492-05" xlink:href="note-0492-05a" xml:space="preserve">581.</note> <note position="left" xlink:label="note-0492-06" xlink:href="note-0492-06a" xml:space="preserve">582.</note> <note symbol="*" position="left" xlink:label="note-0492-07" xlink:href="note-0492-07a" xml:space="preserve">716.</note> <figure xlink:label="fig-0493a-01" xlink:href="fig-0493a-01a"> <image file="0493a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0493a-01"/> </figure> </div> </div> <div xml:id="echoid-div1864" type="section" level="1" n="456"> <head xml:id="echoid-head615" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s12731" xml:space="preserve">Corpus vocatur lucidum, quod lumen emittit, id eſt, i-<lb/>gnem per lineas rectas agitat.</s> <s xml:id="echoid-s12732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12733" xml:space="preserve">Lumen non ubique dari ubi datur ignis, extra omne du-<lb/> <anchor type="note" xlink:label="note-0495-01a" xlink:href="note-0495-01"/> bium eſt; </s> <s xml:id="echoid-s12734" xml:space="preserve">corpora calida non ſemper lucere quotidie vide-<lb/>mus.</s> <s xml:id="echoid-s12735" xml:space="preserve"/> </p> <div xml:id="echoid-div1864" type="float" level="2" n="1"> <note position="right" xlink:label="note-0495-01" xlink:href="note-0495-01a" xml:space="preserve">583.</note> </div> <p> <s xml:id="echoid-s12736" xml:space="preserve">An autem corpus detur lucidum ſine calore determinari <lb/> <anchor type="note" xlink:label="note-0495-02a" xlink:href="note-0495-02"/> non poteſt. </s> <s xml:id="echoid-s12737" xml:space="preserve">Calor in corporibus eſt motus qui in infinitum <lb/>minui poteſt; </s> <s xml:id="echoid-s12738" xml:space="preserve">& </s> <s xml:id="echoid-s12739" xml:space="preserve">motus ille dari poteſt licet nobis non ſit <lb/>ſenſibilis, de quo calore ſæpe nihil inveſtigare poſſumus; <lb/></s> <s xml:id="echoid-s12740" xml:space="preserve">Verùm enim verò certiſſime conſtat multa dari corpora lu-<lb/>cida ſine calore nobis ſenſibili <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12741" xml:space="preserve">Circa quod notandum, <anchor type="note" xlink:label="note-0495-03a" xlink:href="note-0495-03"/> nullum dari calorem nobis ſenſibilem, niſi corpus quod in <lb/>organa noſtra agit habeat calorem ſuperantem calorem ipſo-<lb/>rum organorum. </s> <s xml:id="echoid-s12742" xml:space="preserve">Unde videmus judicium circa calorem, <lb/>quod ſenſibus fertur, omnino eſſe incertum.</s> <s xml:id="echoid-s12743" xml:space="preserve"/> </p> <div xml:id="echoid-div1865" type="float" level="2" n="2"> <note position="right" xlink:label="note-0495-02" xlink:href="note-0495-02a" xml:space="preserve">584.</note> <note symbol="*" position="right" xlink:label="note-0495-03" xlink:href="note-0495-03a" xml:space="preserve">571.</note> </div> <p> <s xml:id="echoid-s12744" xml:space="preserve">Quando partes minimæ ex quibus corpus quodcunque con-<lb/>ſtat, attritu, aut actione ignis extranei, aut alio quocunque mo-<lb/>do agitantur, ignis ab his ſeparatur & </s> <s xml:id="echoid-s12745" xml:space="preserve">in corpore agitatur, tunc-<lb/>que ignis & </s> <s xml:id="echoid-s12746" xml:space="preserve">particulæ corporis attractione in ſe mutuo agunt, <lb/>ut illud, experimentis in ſequentibus memorandis <anchor type="note" xlink:href="" symbol="*"/>, probatur.</s> <s xml:id="echoid-s12747" xml:space="preserve"> <anchor type="note" xlink:label="note-0495-04a" xlink:href="note-0495-04"/> Qua actione particulæ quædam a corpore ſeparantur & </s> <s xml:id="echoid-s12748" xml:space="preserve">mo-<lb/>tu ignis a corpore auferuntur. </s> <s xml:id="echoid-s12749" xml:space="preserve">Hæc autem eſt cauſa quare <lb/>corpora duriora violento attritu ſæpe combur antur.</s> <s xml:id="echoid-s12750" xml:space="preserve"/> </p> <div xml:id="echoid-div1866" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0495-04" xlink:href="note-0495-04a" xml:space="preserve">611.</note> </div> <note position="right" xml:space="preserve">585.</note> <p style="it"> <s xml:id="echoid-s12751" xml:space="preserve">Deducimus ex hiſce combuſtionem corporum eſſe partium <lb/> <anchor type="note" xlink:label="note-0495-06a" xlink:href="note-0495-06"/> ſeparationem ex actione mutua in ſe invicem partium cor-<lb/>poris & </s> <s xml:id="echoid-s12752" xml:space="preserve">ignis; </s> <s xml:id="echoid-s12753" xml:space="preserve">harum partium quædam motu ignis ablatæ <lb/> <anchor type="note" xlink:label="note-0495-07a" xlink:href="note-0495-07"/> flammam & </s> <s xml:id="echoid-s12754" xml:space="preserve">fumum formant.</s> <s xml:id="echoid-s12755" xml:space="preserve"/> </p> <div xml:id="echoid-div1867" type="float" level="2" n="4"> <note position="right" xlink:label="note-0495-06" xlink:href="note-0495-06a" xml:space="preserve">586.</note> <note position="right" xlink:label="note-0495-07" xlink:href="note-0495-07a" xml:space="preserve">587.</note> </div> <p> <s xml:id="echoid-s12756" xml:space="preserve">Videmus ulterius, corpus, quod admoto igne comburi-<lb/>tur, non modo diſſolvi ex actione ignis extranei, ſed etiam <lb/>ex actione ignis in ipſo corpore contenti; </s> <s xml:id="echoid-s12757" xml:space="preserve">caloremque auge-<lb/>ri & </s> <s xml:id="echoid-s12758" xml:space="preserve">ex novo igne accedente, & </s> <s xml:id="echoid-s12759" xml:space="preserve">ex aucta agitatione ignis <pb o="12" file="0496" n="544" rhead="PHYSICES ELEMENTA"/> quem corpus ipſum continet, & </s> <s xml:id="echoid-s12760" xml:space="preserve">ita calorem non ſequi pro-<lb/> <anchor type="note" xlink:label="note-0496-01a" xlink:href="note-0496-01"/> portionem quantitatis ignis.</s> <s xml:id="echoid-s12761" xml:space="preserve"/> </p> <div xml:id="echoid-div1868" type="float" level="2" n="5"> <note position="left" xlink:label="note-0496-01" xlink:href="note-0496-01a" xml:space="preserve">588.</note> </div> <p> <s xml:id="echoid-s12762" xml:space="preserve">Circa motum luminis conſtat, ut diximus <anchor type="note" xlink:href="" symbol="*"/>, hoc moveri <anchor type="note" xlink:label="note-0496-02a" xlink:href="note-0496-02"/> per lineas rectas; </s> <s xml:id="echoid-s12763" xml:space="preserve">ſed utrum ſit ſucceſſivus, an momenta-<lb/>neus luminis motus, diſputatur, id eſt, utrum eodem quo <lb/>corpus lucere inchoat momento, lumen ad diſtantiam quam-<lb/>cunque ſenſibile ſit, an vero ſucceſſive lumen ad loca magis <lb/>ac magis diſtantia perveniat.</s> <s xml:id="echoid-s12764" xml:space="preserve"/> </p> <div xml:id="echoid-div1869" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0496-02" xlink:href="note-0496-02a" xml:space="preserve">581.</note> </div> <p> <s xml:id="echoid-s12765" xml:space="preserve">Ex obſervationibus variis aſtronomicis clare ſequi videtur, <lb/> <anchor type="note" xlink:label="note-0496-03a" xlink:href="note-0496-03"/> motum hunc eſſe ſucceſſivum & </s> <s xml:id="echoid-s12766" xml:space="preserve">diu de eo non dubitarunt <lb/>Philoſophi; </s> <s xml:id="echoid-s12767" xml:space="preserve">quibuſdam tamen recentioribus obſervationibus <lb/>concluſiones ex primis deductæ labefactantur, & </s> <s xml:id="echoid-s12768" xml:space="preserve">quid igno-<lb/>tum circa motum luminis dari fateri cogimur.</s> <s xml:id="echoid-s12769" xml:space="preserve"/> </p> <div xml:id="echoid-div1870" type="float" level="2" n="7"> <note position="left" xlink:label="note-0496-03" xlink:href="note-0496-03a" xml:space="preserve">589.</note> </div> <p> <s xml:id="echoid-s12770" xml:space="preserve">Motus de loco in locum non ſucceſſivus contradictionem <lb/>involvit, & </s> <s xml:id="echoid-s12771" xml:space="preserve">lumini motum de loco in locum eſſe tribuendum <lb/> <anchor type="note" xlink:label="note-0496-04a" xlink:href="note-0496-04"/> vix in dubium vocari poteſt.</s> <s xml:id="echoid-s12772" xml:space="preserve"/> </p> <div xml:id="echoid-div1871" type="float" level="2" n="8"> <note position="left" xlink:label="note-0496-04" xlink:href="note-0496-04a" xml:space="preserve">590.</note> </div> <p> <s xml:id="echoid-s12773" xml:space="preserve">Obſervamus enim tranſlationem ignis in vaporibus & </s> <s xml:id="echoid-s12774" xml:space="preserve">in <lb/>fumo; </s> <s xml:id="echoid-s12775" xml:space="preserve">in quibus caſibus ignis ſecum fert corpora quibus ad-<lb/>hæret & </s> <s xml:id="echoid-s12776" xml:space="preserve">ſæpe tamen celeriter movetur: </s> <s xml:id="echoid-s12777" xml:space="preserve">ſi ignis ſubtilitas <lb/>confideretur, facile patebit illum in immenſum retardari a <lb/>corporibus quibus adhæret, & </s> <s xml:id="echoid-s12778" xml:space="preserve">liberatum velocitate maxima <lb/>debere transferri.</s> <s xml:id="echoid-s12779" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12780" xml:space="preserve">Circa calorem & </s> <s xml:id="echoid-s12781" xml:space="preserve">lumen varia præterea obſervanda ſunt, <lb/>maxime digna quæ notentur, ſed quorum multa explicatu <lb/>ſunt difficillima. </s> <s xml:id="echoid-s12782" xml:space="preserve">In Phyſicis ubi cauſæ latent, effectus ſal-<lb/>tem ſunt memorandi.</s> <s xml:id="echoid-s12783" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12784" xml:space="preserve">Corpora calefacta videmus multa, quorum ſi calor augea-<lb/> <anchor type="note" xlink:label="note-0496-05a" xlink:href="note-0496-05"/> tur lucida fiunt; </s> <s xml:id="echoid-s12785" xml:space="preserve">talia ſunt metalla: </s> <s xml:id="echoid-s12786" xml:space="preserve">Partium agitatione ignem <lb/>emittunt, ſed non per lineas rectas; </s> <s xml:id="echoid-s12787" xml:space="preserve">aucto verò partium <lb/>motu, per lineas rectas pro parte movetur ignis & </s> <s xml:id="echoid-s12788" xml:space="preserve">cor-<lb/>pus lucet.</s> <s xml:id="echoid-s12789" xml:space="preserve"/> </p> <div xml:id="echoid-div1872" type="float" level="2" n="9"> <note position="left" xlink:label="note-0496-05" xlink:href="note-0496-05a" xml:space="preserve">591.</note> </div> <p> <s xml:id="echoid-s12790" xml:space="preserve">Eodem plane modo fumus, ſi admotâ flammâ magis in-<lb/> <anchor type="note" xlink:label="note-0496-06a" xlink:href="note-0496-06"/> caleſcat, ipſe in flammam convertitur; </s> <s xml:id="echoid-s12791" xml:space="preserve">id eſt in corpus lu-<lb/>cidum mutatur.</s> <s xml:id="echoid-s12792" xml:space="preserve"/> </p> <div xml:id="echoid-div1873" type="float" level="2" n="10"> <note position="left" xlink:label="note-0496-06" xlink:href="note-0496-06a" xml:space="preserve">592.</note> </div> </div> <div xml:id="echoid-div1875" type="section" level="1" n="457"> <head xml:id="echoid-head616" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s12793" xml:space="preserve">Sit candela C, flatu extincta, quæ fumum emittit F; <lb/></s> <s xml:id="echoid-s12794" xml:space="preserve"> <anchor type="note" xlink:label="note-0496-07a" xlink:href="note-0496-07"/> admoveatur candela alia A; </s> <s xml:id="echoid-s12795" xml:space="preserve">fumus ſeſe convertet in flam- <pb o="13" file="0497" n="545" rhead="MATHEMATIC A. LIB. III. CAP. IV."/> mam, & </s> <s xml:id="echoid-s12796" xml:space="preserve">quidem ſucceſſive ad candelam C uſque, quæ ta-<lb/>li modo accenditur ope candelæ A, quæ a prima diſtat <lb/>pollices ſex aut octo.</s> <s xml:id="echoid-s12797" xml:space="preserve"/> </p> <div xml:id="echoid-div1875" type="float" level="2" n="1"> <note position="left" xlink:label="note-0496-07" xlink:href="note-0496-07a" xml:space="preserve">TAB II. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s12798" xml:space="preserve">Aërem in ignem agere diximus <anchor type="note" xlink:href="" symbol="*"/>, illius actio in hunc in <anchor type="note" xlink:label="note-0497-01a" xlink:href="note-0497-01"/> multis occaſionibus minime contemnenda datur reſpectu lu-<lb/>minis. </s> <s xml:id="echoid-s12799" xml:space="preserve">Sæpe ut lumen detur, aut ut ignis ſervetur, aëris <lb/> <anchor type="note" xlink:label="note-0497-02a" xlink:href="note-0497-02"/> præſentia neceſſaria eſt, quod in combuſtione omnium cor-<lb/>porum obſervatur, quæ abſente aëre extinguuntur.</s> <s xml:id="echoid-s12800" xml:space="preserve"/> </p> <div xml:id="echoid-div1876" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0497-01" xlink:href="note-0497-01a" xml:space="preserve">577.</note> <note position="right" xlink:label="note-0497-02" xlink:href="note-0497-02a" xml:space="preserve">593.</note> </div> </div> <div xml:id="echoid-div1878" type="section" level="1" n="458"> <head xml:id="echoid-head617" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s12801" xml:space="preserve">Si candela lucens, laminæ Machinæ Pneumaticæ impoſi-<lb/>ta, vitro obtegatur, & </s> <s xml:id="echoid-s12802" xml:space="preserve">aër extrahatur, ſtatim extinguitur.</s> <s xml:id="echoid-s12803" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1879" type="section" level="1" n="459"> <head xml:id="echoid-head618" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s12804" xml:space="preserve">Detur orbis chalibeus diametri circiter trium pollicum, <lb/> <anchor type="note" xlink:label="note-0497-03a" xlink:href="note-0497-03"/> perforetur in medio, ut per orbem tranſeat axis in vacuo <lb/>mobilis <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s12805" xml:space="preserve">firmetur ille inter duos orbes ligneos ope co- <anchor type="note" xlink:label="note-0497-04a" xlink:href="note-0497-04"/> chlearum d, d; </s> <s xml:id="echoid-s12806" xml:space="preserve">laminæ elaſticæ f f annectantur fruſta Pyritæ, <lb/>ita ut motu axeos attritus detur inter peripheriam orbis cha-<lb/>libei & </s> <s xml:id="echoid-s12807" xml:space="preserve">Pyritas. </s> <s xml:id="echoid-s12808" xml:space="preserve">Quamdiu aër datur in vitro, lumen ex attri-<lb/>tu dari obſervatur; </s> <s xml:id="echoid-s12809" xml:space="preserve">extracto vero aëre, licet attritus conti-<lb/>nuetur, lumen non apparet; </s> <s xml:id="echoid-s12810" xml:space="preserve">admiſſo aëre iterum ſenſibile <lb/>eſt.</s> <s xml:id="echoid-s12811" xml:space="preserve"/> </p> <div xml:id="echoid-div1879" type="float" level="2" n="1"> <note position="right" xlink:label="note-0497-03" xlink:href="note-0497-03a" xml:space="preserve">TAB. II. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0497-04" xlink:href="note-0497-04a" xml:space="preserve">567.</note> </div> <p> <s xml:id="echoid-s12812" xml:space="preserve">Contra etiam obſervamus aëris abſentiam ſæpiſſime requi-<lb/> <anchor type="note" xlink:label="note-0497-05a" xlink:href="note-0497-05"/> ri in lumine, ut illud in experimentis ante memoratis obſer-<lb/> <anchor type="note" xlink:label="note-0497-06a" xlink:href="note-0497-06"/> vari potuit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12813" xml:space="preserve">Tandem ſublato aëre augetur aliquando lu- <anchor type="note" xlink:label="note-0497-07a" xlink:href="note-0497-07"/> men, quod & </s> <s xml:id="echoid-s12814" xml:space="preserve">in aëre videri poteſt.</s> <s xml:id="echoid-s12815" xml:space="preserve"/> </p> <div xml:id="echoid-div1880" type="float" level="2" n="2"> <note position="right" xlink:label="note-0497-05" xlink:href="note-0497-05a" xml:space="preserve">594.</note> <note symbol="*" position="right" xlink:label="note-0497-06" xlink:href="note-0497-06a" xml:space="preserve">557. 571.</note> <note position="right" xlink:label="note-0497-07" xlink:href="note-0497-07a" xml:space="preserve">595.</note> </div> </div> <div xml:id="echoid-div1882" type="section" level="1" n="460"> <head xml:id="echoid-head619" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s12816" xml:space="preserve">Phoſphoro urinæ, de quo antea <anchor type="note" xlink:href="" symbol="*"/>, litteræ inſcribantur <anchor type="note" xlink:label="note-0497-08a" xlink:href="note-0497-08"/> aut figuræ delineentur in charta; </s> <s xml:id="echoid-s12817" xml:space="preserve">in loco obſcuro ut dictum <lb/>lucidæ erunt; </s> <s xml:id="echoid-s12818" xml:space="preserve">detur hæc charta in loco vacuo, magis lit-<lb/>teræ eluceſcent.</s> <s xml:id="echoid-s12819" xml:space="preserve"/> </p> <div xml:id="echoid-div1882" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0497-08" xlink:href="note-0497-08a" xml:space="preserve">575.</note> </div> </div> <div xml:id="echoid-div1884" type="section" level="1" n="461"> <head xml:id="echoid-head620" xml:space="preserve">CAPUT IV.</head> <head xml:id="echoid-head621" style="it" xml:space="preserve">De dilatatione ex calore.</head> <p> <s xml:id="echoid-s12820" xml:space="preserve">OMnia corpora ex ignis actione dilatantur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s12821" xml:space="preserve">hanc autem <anchor type="note" xlink:label="note-0497-09a" xlink:href="note-0497-09"/> dilat at ionem, cum mutato calore immutari obſervamus; <lb/></s> <s xml:id="echoid-s12822" xml:space="preserve"> <anchor type="note" xlink:label="note-0497-10a" xlink:href="note-0497-10"/> ita ut a motu ignis non verò ab hujus quantitate pendere vi- <pb o="14" file="0498" n="546" rhead="PHYSICES ELEMENTA"/> deatur; </s> <s xml:id="echoid-s12823" xml:space="preserve">corpora enim ſive attritu ſive admoto igne extraneo <lb/>calefiant ſeſe expandunt.</s> <s xml:id="echoid-s12824" xml:space="preserve"/> </p> <div xml:id="echoid-div1884" type="float" level="2" n="1"> <note position="right" xlink:label="note-0497-09" xlink:href="note-0497-09a" xml:space="preserve">596.</note> <note symbol="*" position="right" xlink:label="note-0497-10" xlink:href="note-0497-10a" xml:space="preserve">547.</note> </div> </div> <div xml:id="echoid-div1886" type="section" level="1" n="462"> <head xml:id="echoid-head622" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s12825" xml:space="preserve">Detur lamina ferrea L, longa circiter tres pedes, ſit hæc <lb/> <anchor type="note" xlink:label="note-0498-01a" xlink:href="note-0498-01"/> quadrata & </s> <s xml:id="echoid-s12826" xml:space="preserve">craſſitiei quartæ partis unius pollicis; </s> <s xml:id="echoid-s12827" xml:space="preserve">ſuper ta-<lb/>bula ponitur inter duo obſtacula firma O, O; </s> <s xml:id="echoid-s12828" xml:space="preserve">inter obſtacu-<lb/>lum unum & </s> <s xml:id="echoid-s12829" xml:space="preserve">laminæ extremitatem datur regula ferrea R r, <lb/>longitudinis circiter quatuor aut quinque pollicum; </s> <s xml:id="echoid-s12830" xml:space="preserve">latior eſt <lb/>hæc regula in R quam in r quantitate quartæ partis unius <lb/>pollicis, & </s> <s xml:id="echoid-s12831" xml:space="preserve">paululum eſt obliqua extremitas laminæ L ut cum <lb/>regulæ latere congruat, quæ in partes æquales exiguas divi-<lb/>ditur, & </s> <s xml:id="echoid-s12832" xml:space="preserve">quantum poteſt intruditur inter obſtaculum & </s> <s xml:id="echoid-s12833" xml:space="preserve">re-<lb/>gulæ extremitatem, & </s> <s xml:id="echoid-s12834" xml:space="preserve">notatur diviſio quæ cum latere la-<lb/>minæ congruit.</s> <s xml:id="echoid-s12835" xml:space="preserve"/> </p> <div xml:id="echoid-div1886" type="float" level="2" n="1"> <note position="left" xlink:label="note-0498-01" xlink:href="note-0498-01a" xml:space="preserve">TAB. III. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s12836" xml:space="preserve">Calefiat deinde lamina ſive attritu, ſive admoto igne, ite-<lb/>rumque inter obſtacula ponatur & </s> <s xml:id="echoid-s12837" xml:space="preserve">intrudatur regula R r, <lb/>non ad eandem diviſionem quam antea poterit intrudi quod <lb/>dilatatam laminam clariſſimè indicat.</s> <s xml:id="echoid-s12838" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1888" type="section" level="1" n="463"> <head xml:id="echoid-head623" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s12839" xml:space="preserve">Liquida eodem modo ac ſolida ex calore dilatari hac me-<lb/> <anchor type="note" xlink:label="note-0498-02a" xlink:href="note-0498-02"/> thodo probatur. </s> <s xml:id="echoid-s12840" xml:space="preserve">Sit Globus vitreus G, cui annectitur tu-<lb/> <anchor type="note" xlink:label="note-0498-03a" xlink:href="note-0498-03"/> bus exiguus E D, ſi globus liquido quocunque impleatur ita, ut <lb/>ad altitudinem quamcunque in tubo pertingat, calefacto <lb/>globo aſcendet liquidum in tubo; </s> <s xml:id="echoid-s12841" xml:space="preserve">ad quod calor exiguus <lb/>ſufficit, etiamſi de Mercurio liquidorum denſiſſimo agatur. <lb/></s> <s xml:id="echoid-s12842" xml:space="preserve">Experimentum eodem modo, ſed melius, procedit ſi loco glo-<lb/>bi detur cylindrus cavus C cum annexo tubo B A; </s> <s xml:id="echoid-s12843" xml:space="preserve">citius e-<lb/>nim calor toto liquido communicatur in cylindro quam in <lb/>globo.</s> <s xml:id="echoid-s12844" xml:space="preserve"/> </p> <div xml:id="echoid-div1888" type="float" level="2" n="1"> <note position="left" xlink:label="note-0498-02" xlink:href="note-0498-02a" xml:space="preserve">597.</note> <note position="left" xlink:label="note-0498-03" xlink:href="note-0498-03a" xml:space="preserve">TAB. II. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12845" xml:space="preserve">Si tubus, E D aut B A in partes aquales dividatur; </s> <s xml:id="echoid-s12846" xml:space="preserve">aut <lb/> <anchor type="note" xlink:label="note-0498-04a" xlink:href="note-0498-04"/> tubus, cum globo aut cylindro, tabulæ applicetur ita, ut di-<lb/>viſiones æquales in tabula cum tubo congruant, poterit tali <lb/>Machinâ calor quodammodo menſurari: </s> <s xml:id="echoid-s12847" xml:space="preserve">aſcendit enim & </s> <s xml:id="echoid-s12848" xml:space="preserve"><lb/>deſcendit liquidum in tubo dum creſcit aut minuitur calor <lb/>corporum circumdantium. </s> <s xml:id="echoid-s12849" xml:space="preserve">Thermometra vocantur hæ Ma-<lb/> <anchor type="note" xlink:label="note-0498-05a" xlink:href="note-0498-05"/> chinæ & </s> <s xml:id="echoid-s12850" xml:space="preserve">vulgares admodum ſunt. </s> <s xml:id="echoid-s12851" xml:space="preserve">Indicant quidem hæ <lb/>mutationem in calore, ſed an caloris gradum monſtrent in- <pb o="15" file="0499" n="547" rhead="MATHEMATICA LIB. III. CAP. IV."/> certum eſt, id eſt ignotum eſt quænam relatio detur inter <lb/>mutationem in expanſione & </s> <s xml:id="echoid-s12852" xml:space="preserve">mutationem in calore; </s> <s xml:id="echoid-s12853" xml:space="preserve">ut ex <lb/>comparatis dilatationibus gradus caloris poſſint conferri in-<lb/>ter ſe.</s> <s xml:id="echoid-s12854" xml:space="preserve"/> </p> <div xml:id="echoid-div1889" type="float" level="2" n="2"> <note position="left" xlink:label="note-0498-04" xlink:href="note-0498-04a" xml:space="preserve">598.</note> <note position="left" xlink:label="note-0498-05" xlink:href="note-0498-05a" xml:space="preserve">599.</note> </div> <p> <s xml:id="echoid-s12855" xml:space="preserve">Si ſubito incaleſcat globus G aut cylindrus C, ſtatim li-<lb/> <anchor type="note" xlink:label="note-0499-01a" xlink:href="note-0499-01"/> quidum in tubo deſcendit, ſed immediate poſt aſcendit. <lb/></s> <s xml:id="echoid-s12856" xml:space="preserve">Ex calore ſubito citius vitrum ipſum incaleſcit quam liqui-<lb/>dum in vitro contentum; </s> <s xml:id="echoid-s12857" xml:space="preserve">ideo dilatato ex calore vitro, & </s> <s xml:id="echoid-s12858" xml:space="preserve"><lb/>eo auctâ hujus capacitate, deſcendit liquidum, ſed imme-<lb/>diate poſt calor liquido communicatur, quod ideo aſcendit.</s> <s xml:id="echoid-s12859" xml:space="preserve"/> </p> <div xml:id="echoid-div1890" type="float" level="2" n="3"> <note position="right" xlink:label="note-0499-01" xlink:href="note-0499-01a" xml:space="preserve">600.</note> </div> <p> <s xml:id="echoid-s12860" xml:space="preserve">Ex corporum expanſione patet particulas, ex quibus cor-<lb/> <anchor type="note" xlink:label="note-0499-02a" xlink:href="note-0499-02"/> pora conſtant, ex actione ignis acquirere vim repellentem <lb/>qua a ſe mutuo recedere conantur, & </s> <s xml:id="echoid-s12861" xml:space="preserve">quæ cum vi qua par-<lb/>ticulæ ſe ſe mutuo petunt <anchor type="note" xlink:href="" symbol="*"/> contrarie agit. </s> <s xml:id="echoid-s12862" xml:space="preserve">Quamdiu hæc vis <anchor type="note" xlink:label="note-0499-03a" xlink:href="note-0499-03"/> illam ſuperat particulæ cohœrent minus aut magis pro di-<lb/>verſo caloris gradu. </s> <s xml:id="echoid-s12863" xml:space="preserve">Quando vis repellens fere adæquat vim <lb/>attrahentem, particulæ antea intimè junctæ vix cohœrent, & </s> <s xml:id="echoid-s12864" xml:space="preserve"><lb/>inpreſſioni cuicunque cedunt & </s> <s xml:id="echoid-s12865" xml:space="preserve">facile moventur inter ſe; <lb/></s> <s xml:id="echoid-s12866" xml:space="preserve">unde videmus corpus ſolidum calore in liquidum mutari, <lb/> <anchor type="note" xlink:label="note-0499-04a" xlink:href="note-0499-04"/> quod in omnibus corporibus quæ calore liquefiunt obſerva-<lb/>tur, imminuto vero calore ad priſtinum ſtatum redeunt. <lb/></s> <s xml:id="echoid-s12867" xml:space="preserve">Quæritur an non fluiditas omnis a calore pendeat? </s> <s xml:id="echoid-s12868" xml:space="preserve">quod de-<lb/> <anchor type="note" xlink:label="note-0499-05a" xlink:href="note-0499-05"/> terminari non poteſt, quia corpus omnino igne deſtitutum <lb/>nullum novimus; </s> <s xml:id="echoid-s12869" xml:space="preserve">illud certum eſt calorem non modo cauſam <lb/>eſſe fluiditatis in metallis, cerâ & </s> <s xml:id="echoid-s12870" xml:space="preserve">ſimilibus corporibus lique-<lb/>factis, ſed multa corpora, quæ vulgo inter fluida referuntur, a <lb/>calore ſolo fluere; </s> <s xml:id="echoid-s12871" xml:space="preserve">ſic aqua eſt glacies liquefacta, ſublato <lb/> <anchor type="note" xlink:label="note-0499-06a" xlink:href="note-0499-06"/> enim proparte aquæ calore coaleſcit.</s> <s xml:id="echoid-s12872" xml:space="preserve"/> </p> <div xml:id="echoid-div1891" type="float" level="2" n="4"> <note position="right" xlink:label="note-0499-02" xlink:href="note-0499-02a" xml:space="preserve">601.</note> <note symbol="*" position="right" xlink:label="note-0499-03" xlink:href="note-0499-03a" xml:space="preserve">31.</note> <note position="right" xlink:label="note-0499-04" xlink:href="note-0499-04a" xml:space="preserve">602.</note> <note position="right" xlink:label="note-0499-05" xlink:href="note-0499-05a" xml:space="preserve">603.</note> <note position="right" xlink:label="note-0499-06" xlink:href="note-0499-06a" xml:space="preserve">604.</note> </div> <p> <s xml:id="echoid-s12873" xml:space="preserve">Calor ita poteſt adaugeri, ut in quibuſdam corporibus tota <lb/> <anchor type="note" xlink:label="note-0499-07a" xlink:href="note-0499-07"/> vis attrahens ſuperetur a vi repellente, in quo caſu particu-<lb/>læ ſeſe mutuo fugiunt; </s> <s xml:id="echoid-s12874" xml:space="preserve">id eſt vim elaſticam acquirunt, quæ <lb/>ſimilis eſt illi qua particulæ aëris gaudent <anchor type="note" xlink:href="" symbol="*"/>, quæ etiam in <anchor type="note" xlink:label="note-0499-08a" xlink:href="note-0499-08"/> aëre calore augetur; </s> <s xml:id="echoid-s12875" xml:space="preserve">effectum hunc obſervamus in fumo & </s> <s xml:id="echoid-s12876" xml:space="preserve"><lb/>vaporibus.</s> <s xml:id="echoid-s12877" xml:space="preserve"/> </p> <div xml:id="echoid-div1892" type="float" level="2" n="5"> <note position="right" xlink:label="note-0499-07" xlink:href="note-0499-07a" xml:space="preserve">605.</note> <note symbol="*" position="right" xlink:label="note-0499-08" xlink:href="note-0499-08a" xml:space="preserve">431.</note> </div> </div> <div xml:id="echoid-div1894" type="section" level="1" n="464"> <head xml:id="echoid-head624" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s12878" xml:space="preserve">Detur globus cavus æneus E, diametri circiter quatuor <lb/> <anchor type="note" xlink:label="note-0499-09a" xlink:href="note-0499-09"/> pollicum, cum manubrio M; </s> <s xml:id="echoid-s12879" xml:space="preserve">cum globo jungitur tubus T <pb o="16" file="0500" n="548" rhead="PHYSICES ELEMENTA"/> cujus apertura vigeſimam pollicis partem vix æquat. </s> <s xml:id="echoid-s12880" xml:space="preserve">Cale-<lb/>fiat globus, aër in globo ſeſe expandet <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s12881" xml:space="preserve">per tubum exi- <anchor type="note" xlink:label="note-0500-01a" xlink:href="note-0500-01"/> bit; </s> <s xml:id="echoid-s12882" xml:space="preserve">aquâ frigidâ immergatur globus, frigore aër iterum con-<lb/>denſabitur &</s> <s xml:id="echoid-s12883" xml:space="preserve">, preſſione atmoſphæræ in aquæ ſuperficiem, <lb/>aqua intrabit globum.</s> <s xml:id="echoid-s12884" xml:space="preserve"/> </p> <div xml:id="echoid-div1894" type="float" level="2" n="1"> <note position="right" xlink:label="note-0499-09" xlink:href="note-0499-09a" xml:space="preserve">TAB. III. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0500-01" xlink:href="note-0500-01a" xml:space="preserve">597.</note> </div> <p> <s xml:id="echoid-s12885" xml:space="preserve">Globo tali modo pro parte aquâ impleto ſuper igne pona-<lb/>tur, eo momento quo aqua in vapores mutabitur exibunt va-<lb/>pores per T; </s> <s xml:id="echoid-s12886" xml:space="preserve">ſi autem calor augeatur ita ut violenter ebul-<lb/>liat aqua, vapores compreſſi in ſuperiore parte globi ab omni <lb/>parte elaſticitate ſua recedere conantur & </s> <s xml:id="echoid-s12887" xml:space="preserve">violento motu per <lb/>tubum exeunt. </s> <s xml:id="echoid-s12888" xml:space="preserve">Æoli Pila vocatur hæc Machina.</s> <s xml:id="echoid-s12889" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">606.</note> </div> <div xml:id="echoid-div1896" type="section" level="1" n="465"> <head xml:id="echoid-head625" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s12890" xml:space="preserve">Magis ſenſibilem effectum vis elaſticæ vaporum in Expe-<lb/> <anchor type="note" xlink:label="note-0500-03a" xlink:href="note-0500-03"/> rimento ſequenti habemus.</s> <s xml:id="echoid-s12891" xml:space="preserve"/> </p> <div xml:id="echoid-div1896" type="float" level="2" n="1"> <note position="left" xlink:label="note-0500-03" xlink:href="note-0500-03a" xml:space="preserve">607.</note> </div> <p> <s xml:id="echoid-s12892" xml:space="preserve">Globus E cujus diameter eſt etiam quatuor pollicum, ſed <lb/> <anchor type="note" xlink:label="note-0500-04a" xlink:href="note-0500-04"/> qui ex craſſiori metallo conſtruitur quam globus quo in præ-<lb/>cedenti experimento uſi ſumus, rhedæ exiguæ & </s> <s xml:id="echoid-s12893" xml:space="preserve">levi impo-<lb/>nitur ut in figura videtur. </s> <s xml:id="echoid-s12894" xml:space="preserve">In ſuperiori parte tubus T qua-<lb/>dratus cum globo jungitur. </s> <s xml:id="echoid-s12895" xml:space="preserve">In medio tubi ſeparatio datur & </s> <s xml:id="echoid-s12896" xml:space="preserve"><lb/>cavitas poſterior communicationem cum globo habet; </s> <s xml:id="echoid-s12897" xml:space="preserve">fora-<lb/>men, cujus diameter eſt circiter pars octava pollicis, datur <lb/>in medio ſeparationis in tubo, qui ab anteriori parte apertus <lb/>eſt. </s> <s xml:id="echoid-s12898" xml:space="preserve">Clauditur foramen laminâ quæ per duo tranſit forami-<lb/>na in lateribus tubi & </s> <s xml:id="echoid-s12899" xml:space="preserve">ſeparationi in tubo applicatur; </s> <s xml:id="echoid-s12900" xml:space="preserve">cùm la-<lb/>mina paululum ſit obliqua, ſi ictu mallei intrudatur exacte <lb/>claudet foramen.</s> <s xml:id="echoid-s12901" xml:space="preserve"/> </p> <div xml:id="echoid-div1897" type="float" level="2" n="2"> <note position="left" xlink:label="note-0500-04" xlink:href="note-0500-04a" xml:space="preserve">TAB. III. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s12902" xml:space="preserve">Globus a rheda ſeparatur & </s> <s xml:id="echoid-s12903" xml:space="preserve">foramen reſeratur, calefacto <lb/>globo ſi hic aquâ immergatur, pro parte impletur aqua ut <lb/>in experimento præcedenti. </s> <s xml:id="echoid-s12904" xml:space="preserve">Clauſo foramine iterum glo-<lb/>bus igni inponatur donec aqua violenter ebulliat; </s> <s xml:id="echoid-s12905" xml:space="preserve">ſi tunc <lb/>globus cum rheda jungatur & </s> <s xml:id="echoid-s12906" xml:space="preserve">foramen aperiatur, exibit <lb/>vapor violenter verſus unam partem dum rheda verſus par-<lb/>tem oppoſitam feretur.</s> <s xml:id="echoid-s12907" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12908" xml:space="preserve">Vapor violenter compreſſus conatur verſus omnes partes <lb/> <anchor type="note" xlink:label="note-0500-05a" xlink:href="note-0500-05"/> recedere & </s> <s xml:id="echoid-s12909" xml:space="preserve">quidem æqualiter, ideoque preſſiones oppoſitæ <lb/>ſeſe mutuo deſtruunt, aperto vero foramine vapor qui exit <lb/>non premit; </s> <s xml:id="echoid-s12910" xml:space="preserve">tollitur ergo preſſio quædam ab una parte & </s> <s xml:id="echoid-s12911" xml:space="preserve"><lb/>contraria prævalet, rheda movetur.</s> <s xml:id="echoid-s12912" xml:space="preserve"/> </p> <div xml:id="echoid-div1898" type="float" level="2" n="3"> <note position="left" xlink:label="note-0500-05" xlink:href="note-0500-05a" xml:space="preserve">608.</note> </div> <pb file="0501" n="549"/> <pb file="0501a" n="550"/> <figure> <image file="0501a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0501a-01"/> </figure> <pb file="0502" n="551"/> <pb o="17" file="0503" n="552" rhead="MATHEMATIC A. LIB. III. CAP. V."/> <p> <s xml:id="echoid-s12913" xml:space="preserve">Tubuli pulvere nitrato farti accenſi in altum feruntur, quia <lb/> <anchor type="note" xlink:label="note-0503-01a" xlink:href="note-0503-01"/> pulvis accenſus elaſticitatem acquirit, & </s> <s xml:id="echoid-s12914" xml:space="preserve">hujus partes quaqua-<lb/>verſum conantur recedere: </s> <s xml:id="echoid-s12915" xml:space="preserve">cùm ab una parte tubus ſit aper-<lb/>tus, preſſio in tubum minor datur verſus illam partem & </s> <s xml:id="echoid-s12916" xml:space="preserve">con-<lb/>traria ideo prævalet.</s> <s xml:id="echoid-s12917" xml:space="preserve"/> </p> <div xml:id="echoid-div1899" type="float" level="2" n="4"> <note position="right" xlink:label="note-0503-01" xlink:href="note-0503-01a" xml:space="preserve">609.</note> </div> </div> <div xml:id="echoid-div1901" type="section" level="1" n="466"> <head xml:id="echoid-head626" style="it" xml:space="preserve">LIBRI III. Pars II.</head> <p> <s xml:id="echoid-s12918" xml:space="preserve">De Inflexione, Refractione, & </s> <s xml:id="echoid-s12919" xml:space="preserve">Reflexione luminis.</s> <s xml:id="echoid-s12920" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1902" type="section" level="1" n="467"> <head xml:id="echoid-head627" xml:space="preserve">CAPUT V.</head> <head xml:id="echoid-head628" style="it" xml:space="preserve">De Inflexione radiorum luminis.</head> <p> <s xml:id="echoid-s12921" xml:space="preserve">PRæmiſſis, in parte præcedenti, quæ ignem in genere ſpe-<lb/>ctant, luminis proprietates & </s> <s xml:id="echoid-s12922" xml:space="preserve">phœnomena ex iis oriunda <lb/>ad examen revocanda ſunt.</s> <s xml:id="echoid-s12923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12924" xml:space="preserve">Mira admodum ſunt quæ circa lumen obſervantur, pau-<lb/>cis tamen naturæ legibus pleraque explicantur.</s> <s xml:id="echoid-s12925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12926" xml:space="preserve">Lumen movetur per lineas rectas <anchor type="note" xlink:href="" symbol="*"/>, obſtaculo poteſt in- <anchor type="note" xlink:label="note-0503-02a" xlink:href="note-0503-02"/> tercipi, quod totum illud & </s> <s xml:id="echoid-s12927" xml:space="preserve">quidem ſolum intercipit quod <lb/>ad obſtaculum accedit.</s> <s xml:id="echoid-s12928" xml:space="preserve"/> </p> <div xml:id="echoid-div1902" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0503-02" xlink:href="note-0503-02a" xml:space="preserve">581.</note> </div> </div> <div xml:id="echoid-div1904" type="section" level="1" n="468"> <head xml:id="echoid-head629" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s12929" xml:space="preserve">Lumen quodcunque conſideratum juxta directionem mo-<lb/> <anchor type="note" xlink:label="note-0503-03a" xlink:href="note-0503-03"/> tus ſui, ſi totum juxta eandem directionem feratur, vocatur <lb/>Radius luminis.</s> <s xml:id="echoid-s12930" xml:space="preserve"/> </p> <div xml:id="echoid-div1904" type="float" level="2" n="1"> <note position="right" xlink:label="note-0503-03" xlink:href="note-0503-03a" xml:space="preserve">610.</note> </div> <p> <s xml:id="echoid-s12931" xml:space="preserve">Tale eſt lumen quod a Sole procedens per foramen tranſit.</s> <s xml:id="echoid-s12932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12933" xml:space="preserve">Ignis, ut antea dictum, a corporibus attrahitur <anchor type="note" xlink:href="" symbol="*"/>, cujus <anchor type="note" xlink:label="note-0503-04a" xlink:href="note-0503-04"/> attractionis effectus notabiles in combuſtione corporum ob-<lb/>ſervamus; </s> <s xml:id="echoid-s12934" xml:space="preserve">in lumine etiam ſenſibiles ſunt; </s> <s xml:id="echoid-s12935" xml:space="preserve">deflectitur enim <lb/>a via recta lumen quando juxta corpora tranſit; </s> <s xml:id="echoid-s12936" xml:space="preserve">quod ut di-<lb/> <anchor type="note" xlink:label="note-0503-05a" xlink:href="note-0503-05"/> ſtinctè obſervetur ſequens inſtituendum experimentum.</s> <s xml:id="echoid-s12937" xml:space="preserve"/> </p> <div xml:id="echoid-div1905" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0503-04" xlink:href="note-0503-04a" xml:space="preserve">549.</note> <note position="right" xlink:label="note-0503-05" xlink:href="note-0503-05a" xml:space="preserve">611.</note> </div> </div> <div xml:id="echoid-div1907" type="section" level="1" n="469"> <head xml:id="echoid-head630" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s12938" xml:space="preserve">Detur tabella T longitudinis & </s> <s xml:id="echoid-s12939" xml:space="preserve">altitudinis circiter ſex pol-<lb/> <anchor type="note" xlink:label="note-0503-06a" xlink:href="note-0503-06"/> licum; </s> <s xml:id="echoid-s12940" xml:space="preserve">in ſuperficie tabellæ datur cavitas c c, in qua moven-<lb/>tur fruſta duo chalibea; </s> <s xml:id="echoid-s12941" xml:space="preserve">utriuſque acies ſimilis eſt aciei cul-<lb/>tri; </s> <s xml:id="echoid-s12942" xml:space="preserve">concurrunt amborum acies in medio tabellæ, & </s> <s xml:id="echoid-s12943" xml:space="preserve">exactè <pb o="(18)" file="0504" n="553" rhead="PHYSICES ELEMENTA"/> junguntur. </s> <s xml:id="echoid-s12944" xml:space="preserve">Datur ubi concurrunt foramen quadratum in ta-<lb/>bella, cujus latus fere pollicem æquat, ut ad memoratas acies <lb/>radius luminis in cubiculum tenebroſum per foramen, cujus <lb/>diameter æquat quartam pollicis partem, penetrans perveni-<lb/>re poſſit.</s> <s xml:id="echoid-s12945" xml:space="preserve"/> </p> <div xml:id="echoid-div1907" type="float" level="2" n="1"> <note position="right" xlink:label="note-0503-06" xlink:href="note-0503-06a" xml:space="preserve">TAB. III. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12946" xml:space="preserve">Si inter acies memoratas detur diſtantia circiter decimæ <lb/>partis unius pollicis, & </s> <s xml:id="echoid-s12947" xml:space="preserve">lumen inter has tranſeat, poſita tabel-<lb/>la T ad diſtantiam trium pedum a feneſtra, ſi lumen cadat <lb/>ſuper charta A, ad diſtantiam quinque pedum a tabella, ad <lb/>latera luminis apparebit, ab utraque parte, lumen ſimile caudæ <lb/>cometæ, quod probat lumen inftecti dum juxta acies tranſit, <lb/>ut ex figura ſatis patet.</s> <s xml:id="echoid-s12948" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12949" xml:space="preserve">Si magis ad ſe mutuo accedant acies, ut ex. </s> <s xml:id="echoid-s12950" xml:space="preserve">gr. </s> <s xml:id="echoid-s12951" xml:space="preserve">diſtantia in-<lb/>ter has ſit centeſimæ partis unius pollicis, loco luminis memo-<lb/>rati ab utraque parte apparent fimbriæ coloratæ tres, in ſitu pa-<lb/>rallelo ad acies, quæ & </s> <s xml:id="echoid-s12952" xml:space="preserve">magis diſtinctæ apparent, ſi foramen in <lb/>feneſtra minuitur. </s> <s xml:id="echoid-s12953" xml:space="preserve">Unde autem colores hi oriantur in ſequen-<lb/>tibus dicam. </s> <s xml:id="echoid-s12954" xml:space="preserve">Nunc ſatis erit ex hoc experimento deducere, <lb/>lumen attrabi a corporibus a quibus radii inflectuntur; </s> <s xml:id="echoid-s12955" xml:space="preserve">niſi e-<lb/>nim daretur motus verſus corpus, per rectam radius motum <lb/>continuaret.</s> <s xml:id="echoid-s12956" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12957" xml:space="preserve">Actio vero corporum, quâ in lumen agunt ad hoc attraben-<lb/> <anchor type="note" xlink:label="note-0504-01a" xlink:href="note-0504-01"/> dum, ſeſe exerit ad diſtantiam ſenſibilem; </s> <s xml:id="echoid-s12958" xml:space="preserve">ut experimento <lb/>conſtat.</s> <s xml:id="echoid-s12959" xml:space="preserve"/> </p> <div xml:id="echoid-div1908" type="float" level="2" n="2"> <note position="left" xlink:label="note-0504-01" xlink:href="note-0504-01a" xml:space="preserve">612.</note> </div> </div> <div xml:id="echoid-div1910" type="section" level="1" n="470"> <head xml:id="echoid-head631" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s12960" xml:space="preserve">Poſitis quæ in experimento præcedenti, ſi diſtantia inter <lb/> <anchor type="note" xlink:label="note-0504-02a" xlink:href="note-0504-02"/> acies detur circiter quadringenteſimæ partis pollicis, nullum <lb/>lumen inter ſimbrias memoratas ſuper charta apparebit, ita <lb/>ut, in hoc caſu, totum lumen quod inter acies tranſit verſus <lb/>utramque partem inflectatur & </s> <s xml:id="echoid-s12961" xml:space="preserve">formet fimbrias memoratas. <lb/></s> <s xml:id="echoid-s12962" xml:space="preserve">Quod clarè indicat chalibem ad minimum ad diſtantiam o-<lb/>ctingenteſimæ partis pollicis in lumen agere.</s> <s xml:id="echoid-s12963" xml:space="preserve"/> </p> <div xml:id="echoid-div1910" type="float" level="2" n="1"> <note position="left" xlink:label="note-0504-02" xlink:href="note-0504-02a" xml:space="preserve">TAB. III. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12964" xml:space="preserve">Actionem illam cum imminutâ diſtantiâ augeri, etiam pro-<lb/> <anchor type="note" xlink:label="note-0504-03a" xlink:href="note-0504-03"/> batur.</s> <s xml:id="echoid-s12965" xml:space="preserve"/> </p> <div xml:id="echoid-div1911" type="float" level="2" n="2"> <note position="left" xlink:label="note-0504-03" xlink:href="note-0504-03a" xml:space="preserve">613.</note> </div> </div> <div xml:id="echoid-div1913" type="section" level="1" n="471"> <head xml:id="echoid-head632" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s12966" xml:space="preserve">Poſitis quæin præcedenti experimento, minuatur diſtantia <lb/> <anchor type="note" xlink:label="note-0504-04a" xlink:href="note-0504-04"/> inter acies; </s> <s xml:id="echoid-s12967" xml:space="preserve">fimbriæ ſucceſſivè evaneſcunt, donec junctis a- <pb o="(19)" file="0505" n="554" rhead="MATHEMATICA LIB. III. CAP. VI."/> ciebus lumen nullum inter has tranſeat. </s> <s xml:id="echoid-s12968" xml:space="preserve">Primæ autem fim-<lb/>briæ quæ evaneſcunt, ſunt quæ radiis minimè inflexis for-<lb/>mantur, ultimæ quæ a radiis maximè inflexis; </s> <s xml:id="echoid-s12969" xml:space="preserve">id eſt, dum <lb/>accedunt ad ſe mutuo acies, umbra inter fimbrias ab utra-<lb/>que acie formatas continuò augetur, donec tandem totum <lb/>lumen ab utraque parte evaneſcat. </s> <s xml:id="echoid-s12970" xml:space="preserve">Unde clarè ſequitur, eo <lb/>magis inflecti radios, quo ad minorem diſtantiam ab aeiebus <lb/>tranſeunt, id eſt attractionem cum imminutâ diſtantiâ au-<lb/>geri.</s> <s xml:id="echoid-s12971" xml:space="preserve"/> </p> <div xml:id="echoid-div1913" type="float" level="2" n="1"> <note position="left" xlink:label="note-0504-04" xlink:href="note-0504-04a" xml:space="preserve">TAB. III. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s12972" xml:space="preserve">Hæc autem attractio, quid peculiare habet, nam attractio <lb/> <anchor type="note" xlink:label="note-0505-01a" xlink:href="note-0505-01"/> unius aciei admotâ aliâ augetur. </s> <s xml:id="echoid-s12973" xml:space="preserve">Quod in hoc ultimo expe-<lb/>rimento clare patet, nam in acceſſu acierum ad ſe mutuo <lb/>inflexio radiorum continuò major eſt.</s> <s xml:id="echoid-s12974" xml:space="preserve"/> </p> <div xml:id="echoid-div1914" type="float" level="2" n="2"> <note position="right" xlink:label="note-0505-01" xlink:href="note-0505-01a" xml:space="preserve">614.</note> </div> </div> <div xml:id="echoid-div1916" type="section" level="1" n="472"> <head xml:id="echoid-head633" xml:space="preserve">CAPUT VI.</head> <head xml:id="echoid-head634" style="it" xml:space="preserve">De Luminis Refractione & hujus legibus.</head> <head xml:id="echoid-head635" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s12975" xml:space="preserve">OMne quod lumini tranſitum dat, vocatur Medium.</s> <s xml:id="echoid-s12976" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">615.</note> <p> <s xml:id="echoid-s12977" xml:space="preserve">Vitrum, Aqua, ipſum Vacuum ſunt media.</s> <s xml:id="echoid-s12978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12979" xml:space="preserve">Dum radius ex uno medio in aliud penetrat, ſæpe a <lb/>linea recta deflectitur.</s> <s xml:id="echoid-s12980" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1917" type="section" level="1" n="473"> <head xml:id="echoid-head636" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s12981" xml:space="preserve">Inflectio hæc Refractio dicitur.</s> <s xml:id="echoid-s12982" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">616.</note> <p style="it"> <s xml:id="echoid-s12983" xml:space="preserve">Vt detur refractio requiritur, ut media denſitate differant, <lb/> <anchor type="note" xlink:label="note-0505-04a" xlink:href="note-0505-04"/> & </s> <s xml:id="echoid-s12984" xml:space="preserve">ut radius cum ſuperficie media dirimente angulum obli-<lb/>quum formet.</s> <s xml:id="echoid-s12985" xml:space="preserve"/> </p> <div xml:id="echoid-div1917" type="float" level="2" n="1"> <note position="right" xlink:label="note-0505-04" xlink:href="note-0505-04a" xml:space="preserve">617.</note> </div> <p> <s xml:id="echoid-s12986" xml:space="preserve">Oritur refractio ex eo, quòd radii a denſiori medio magis <lb/> <anchor type="note" xlink:label="note-0505-05a" xlink:href="note-0505-05"/> quam a rariori attrahantur, a qua attractione, quæ in capi-<lb/>te præcedenti probatur, omnia quæ refractionem ſpectant <lb/>deducuntur.</s> <s xml:id="echoid-s12987" xml:space="preserve"/> </p> <div xml:id="echoid-div1918" type="float" level="2" n="2"> <note position="right" xlink:label="note-0505-05" xlink:href="note-0505-05a" xml:space="preserve">618.</note> </div> <p> <s xml:id="echoid-s12988" xml:space="preserve">Sit EF mediorum ſeparatio, ſit verſus X medium den-<lb/> <anchor type="note" xlink:label="note-0505-06a" xlink:href="note-0505-06"/> ſius, verſus Z medium rarius. </s> <s xml:id="echoid-s12989" xml:space="preserve">Singulæ materiæ particulæ <lb/> <anchor type="note" xlink:label="note-0505-07a" xlink:href="note-0505-07"/> vi attractivâ gaudent <anchor type="note" xlink:href="" symbol="*"/>, hæcque vis reſpectu luminis locum <anchor type="note" xlink:label="note-0505-08a" xlink:href="note-0505-08"/> habet <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12990" xml:space="preserve">Sit diſtantia, ad quam actionem ſuam particulæ exe- <anchor type="note" xlink:label="note-0505-09a" xlink:href="note-0505-09"/> runt, illa, quæ datur inter lineas EF & </s> <s xml:id="echoid-s12991" xml:space="preserve">GH. </s> <s xml:id="echoid-s12992" xml:space="preserve">Lumen er-<lb/>go quod inter has lineas datur a medio X attrahitur.</s> <s xml:id="echoid-s12993" xml:space="preserve"/> </p> <div xml:id="echoid-div1919" type="float" level="2" n="3"> <note position="right" xlink:label="note-0505-06" xlink:href="note-0505-06a" xml:space="preserve">619.</note> <note position="right" xlink:label="note-0505-07" xlink:href="note-0505-07a" xml:space="preserve">TAB. IV. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0505-08" xlink:href="note-0505-08a" xml:space="preserve">31.</note> <note symbol="*" position="right" xlink:label="note-0505-09" xlink:href="note-0505-09a" xml:space="preserve">611.</note> </div> <pb o="(20)" file="0506" n="555" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s12994" xml:space="preserve">Ad diſtantiam ad quam datur linea GH, ſolæ particulæ <lb/>extremæ medii X in lumen agunt; </s> <s xml:id="echoid-s12995" xml:space="preserve">in diſtantia minore cum <lb/>his & </s> <s xml:id="echoid-s12996" xml:space="preserve">aliæ agunt ita, ut vis attrahens creſcat, quando diſtantia <lb/>minuitur, ut ante jam obſervatum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s12997" xml:space="preserve">Detur in medio den- <anchor type="note" xlink:label="note-0506-01a" xlink:href="note-0506-01"/> ſiori X, linea IL ad eandem ab EF diſtantiam, ad quam in me-<lb/>dio Z datur GH. </s> <s xml:id="echoid-s12998" xml:space="preserve">Intret lumen medium X, ab omni par-<lb/>te attrahetur a particulis medii, quarum diſtantiæ a lumine <lb/>minores ſunt diſtantiâ inter EF & </s> <s xml:id="echoid-s12999" xml:space="preserve">GH; </s> <s xml:id="echoid-s13000" xml:space="preserve">ad hanc enim <lb/>diſtantiam lumen a particulis medii X attrahi ponitur.</s> <s xml:id="echoid-s13001" xml:space="preserve"/> </p> <div xml:id="echoid-div1920" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0506-01" xlink:href="note-0506-01a" xml:space="preserve">613.</note> </div> <p> <s xml:id="echoid-s13002" xml:space="preserve">Quamdiu lumen verſatur inter lineas EF & </s> <s xml:id="echoid-s13003" xml:space="preserve">IL, vis <lb/>attrahens verſus JL prævalet, quia majori numero par-<lb/>ticulæ verſus hanc partem trahunt; </s> <s xml:id="echoid-s13004" xml:space="preserve">creſſente autem numero <lb/>particularum in contrariam partem agentium, id eſt, creſ-<lb/>ſente diſtantia ab EF minuitur vis verſus IL, donec in <lb/>ipſa linea IL verſus omnes partes æqualiter attrahatur lu-<lb/>men, quod ubique in Medio X ultra IL etiam obtinet.</s> <s xml:id="echoid-s13005" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13006" xml:space="preserve">Accedat radius luminis A a & </s> <s xml:id="echoid-s13007" xml:space="preserve">obliquè incidat in ſuperficiem <lb/>dirimentem media, aut potius in ſuperficiem GH, ubi da-<lb/>tur initium actionis, qua lumen verſus Medium X pellitur; <lb/></s> <s xml:id="echoid-s13008" xml:space="preserve">Quando radius pervenit ad a detorquetur a linea recta per <lb/>vim, qua a medio X attrahitur; </s> <s xml:id="echoid-s13009" xml:space="preserve">id eſt, qua juxta directio-<lb/>nem ad hujus medii ſuperficiem perpendicularem verſus hoc <lb/>pellitur. </s> <s xml:id="echoid-s13010" xml:space="preserve">Et quidem in omnibus punctis deflectitur radius a <lb/>linea recta, quamdiu datur inter lineas GH & </s> <s xml:id="echoid-s13011" xml:space="preserve">IL, inter <lb/>quas memorata attractio agit; </s> <s xml:id="echoid-s13012" xml:space="preserve">ideoque inter has lineas Ra-<lb/>dius curvam a b deſcribit, eodem modo ac de gravibus pro-<lb/>jectis dictum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13013" xml:space="preserve">Ultra lineam IL ceſſat actio Radium de- <anchor type="note" xlink:label="note-0506-02a" xlink:href="note-0506-02"/> flectens; </s> <s xml:id="echoid-s13014" xml:space="preserve">rectâ ergo pergit per b B, juxta directionem curvæ <lb/>in puncto b.</s> <s xml:id="echoid-s13015" xml:space="preserve"/> </p> <div xml:id="echoid-div1921" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0506-02" xlink:href="note-0506-02a" xml:space="preserve">208.</note> </div> <p> <s xml:id="echoid-s13016" xml:space="preserve">Diſtantia inter lineas GH & </s> <s xml:id="echoid-s13017" xml:space="preserve">IL admodum eſt exigua, <lb/>quare in conſideratione refractionis ad partem incurvatam <lb/>radii non attendimus, radiuſque conſideratur quaſi con-<lb/>ſtans ex duabus lineis rectis AC, CB concurrentibus in G, <lb/>nempe in ſuperficie media dirimente.</s> <s xml:id="echoid-s13018" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13019" xml:space="preserve">Per C ad ſuperficiem EF detur perpendicularis NCM.</s> <s xml:id="echoid-s13020" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1923" type="section" level="1" n="474"> <head xml:id="echoid-head637" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s13021" xml:space="preserve">Pars A C Radii memorati vocatur Radius incidens.</s> <s xml:id="echoid-s13022" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">620.</note> <pb file="0507" n="556"/> <pb file="0507a" n="557"/> <figure> <image file="0507a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0507a-01"/> </figure> <pb file="0508" n="558"/> <pb o="(21)" file="0509" n="559" rhead="MATHEMATICA LIB. III. CAP. VI."/> </div> <div xml:id="echoid-div1924" type="section" level="1" n="475"> <head xml:id="echoid-head638" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s13023" xml:space="preserve">Angulus A C N vocatur Angulus incidentiæ.</s> <s xml:id="echoid-s13024" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">621.</note> </div> <div xml:id="echoid-div1925" type="section" level="1" n="476"> <head xml:id="echoid-head639" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s13025" xml:space="preserve">Pars CB radii dicitur Radius refractus.</s> <s xml:id="echoid-s13026" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">622.</note> </div> <div xml:id="echoid-div1926" type="section" level="1" n="477"> <head xml:id="echoid-head640" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p> <s xml:id="echoid-s13027" xml:space="preserve">Angulus BCM vocatur Angulus refractionis.</s> <s xml:id="echoid-s13028" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">623.</note> <p> <s xml:id="echoid-s13029" xml:space="preserve">In hoc caſu, ubi lumen e medio rariori in denſius penetrat, <lb/> <anchor type="note" xlink:label="note-0509-04a" xlink:href="note-0509-04"/> Angulus refractionis minor eſt Angulo incidentiæ, ex infle-<lb/>xione radii; </s> <s xml:id="echoid-s13030" xml:space="preserve">æquales enim forent hi anguli, ſi radius AC <lb/>per CD rectâ viâ motum continuaret. </s> <s xml:id="echoid-s13031" xml:space="preserve">Accedit autem Ra-<lb/>dius CB magis ad perpendicularem CM; </s> <s xml:id="echoid-s13032" xml:space="preserve">quare refractio <lb/>dicitur fieri verſus perpendicularem.</s> <s xml:id="echoid-s13033" xml:space="preserve"/> </p> <div xml:id="echoid-div1926" type="float" level="2" n="1"> <note position="right" xlink:label="note-0509-04" xlink:href="note-0509-04a" xml:space="preserve">624.</note> </div> <p> <s xml:id="echoid-s13034" xml:space="preserve">Contra, ſi radius e medio denſiori in rarius tranſeat, rece-<lb/> <anchor type="note" xlink:label="note-0509-05a" xlink:href="note-0509-05"/> det a perpendiculari, quia attractio medii denſioris in ra-<lb/>dium eadem eſt, ſive radius ex rariori in denſius, ſive e den-<lb/>ſiori in rarius penetret. </s> <s xml:id="echoid-s13035" xml:space="preserve">Idcirco ſi BC ſit radius inciden-<lb/>tiæ, CA erit radius refractus, id eſt, per eaſdem lineas <lb/> <anchor type="note" xlink:label="note-0509-06a" xlink:href="note-0509-06"/> movetur radius a quacunque parte procedat. </s> <s xml:id="echoid-s13036" xml:space="preserve">Ideoque, ſi duo <lb/> <anchor type="note" xlink:label="note-0509-07a" xlink:href="note-0509-07"/> radii, unus e medio denſiori in rarius, alter e rariori in denſius, <lb/>penetrent, anguluſque refractionis bujus æqualis ſit angulo in-<lb/>cidentiæ illius, reliqui duo anguli incidentiæ & </s> <s xml:id="echoid-s13037" xml:space="preserve">refractionis <lb/>erunt æquales inter ſe.</s> <s xml:id="echoid-s13038" xml:space="preserve"/> </p> <div xml:id="echoid-div1927" type="float" level="2" n="2"> <note position="right" xlink:label="note-0509-05" xlink:href="note-0509-05a" xml:space="preserve">625.</note> <note position="right" xlink:label="note-0509-06" xlink:href="note-0509-06a" xml:space="preserve">626.</note> <note position="right" xlink:label="note-0509-07" xlink:href="note-0509-07a" xml:space="preserve">627.</note> </div> <p> <s xml:id="echoid-s13039" xml:space="preserve">Exquibus ſequitur, directionemradii non mutari, ſi movea-<lb/> <anchor type="note" xlink:label="note-0509-08a" xlink:href="note-0509-08"/> tur trans medium terminatum duabus ſuperficiebus parallelis <lb/>inter ſe, quantum enim in ingreſſu verſus aliquam partem <lb/>deflectitur, in tantum exactiſſime dum exit verſus partem <lb/>oppoſitam inflectitur.</s> <s xml:id="echoid-s13040" xml:space="preserve"/> </p> <div xml:id="echoid-div1928" type="float" level="2" n="3"> <note position="right" xlink:label="note-0509-08" xlink:href="note-0509-08a" xml:space="preserve">628.</note> </div> <p> <s xml:id="echoid-s13041" xml:space="preserve">Si radius perpendiculariter cadat in ſuperficiem qua duo <lb/> <anchor type="note" xlink:label="note-0509-09a" xlink:href="note-0509-09"/> media ſeparantur, a recta via non deflectetur attractione me-<lb/>dii denſioris; </s> <s xml:id="echoid-s13042" xml:space="preserve">actione hac cum radii motu in eadem dire-<lb/>ctione in hoc caſu agente.</s> <s xml:id="echoid-s13043" xml:space="preserve"/> </p> <div xml:id="echoid-div1929" type="float" level="2" n="4"> <note position="right" xlink:label="note-0509-09" xlink:href="note-0509-09a" xml:space="preserve">629.</note> </div> <p> <s xml:id="echoid-s13044" xml:space="preserve">Ut dicta Experimentis confirmentur, datur pixis P, lon-<lb/> <anchor type="note" xlink:label="note-0509-10a" xlink:href="note-0509-10"/> gitudinis circiter unius pedis, latitudinis & </s> <s xml:id="echoid-s13045" xml:space="preserve">altitudinis qua-<lb/> <anchor type="note" xlink:label="note-0509-11a" xlink:href="note-0509-11"/> tuor pollicum. </s> <s xml:id="echoid-s13046" xml:space="preserve">Latera duo majora a b c d, a b c d, ſunt <lb/>plana vitrea parallela inter ſe, pixis hæc aquam continet ad <lb/>altitudinem circiter duorum pollicum cum ſemiſſe.</s> <s xml:id="echoid-s13047" xml:space="preserve"/> </p> <div xml:id="echoid-div1930" type="float" level="2" n="5"> <note position="right" xlink:label="note-0509-10" xlink:href="note-0509-10a" xml:space="preserve">630.</note> <note position="right" xlink:label="note-0509-11" xlink:href="note-0509-11a" xml:space="preserve">TAB. IV. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s13048" xml:space="preserve">In loco obſcuro inſtituuntur experimenta; </s> <s xml:id="echoid-s13049" xml:space="preserve">lumen intromit- <pb o="(22)" file="0510" n="560" rhead="PHYSICES ELEMENTA"/> titur per ſciſſuram in orbe mobili O, qui in feneſtra datur, <lb/>& </s> <s xml:id="echoid-s13050" xml:space="preserve">rotatur ut ſciſſura ad libitum poſſit inclinari; </s> <s xml:id="echoid-s13051" xml:space="preserve">ſciſſuræ lon-<lb/>gitudo eſt quatuor pollicum, latitudo octavæ pollicis partis.</s> <s xml:id="echoid-s13052" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13053" xml:space="preserve">Lumen intromiſſum in ſpeculum Simpingit; </s> <s xml:id="echoid-s13054" xml:space="preserve">ita ſciſſura in-<lb/>clinatur & </s> <s xml:id="echoid-s13055" xml:space="preserve">ſpeculum diſponitur, ut radius per ſciſſuram in-<lb/>tromiſſus a ſpeculo horizontaliter reflectatur, manente ra-<lb/>dio in ſitu verticali, ut tranſeat per ſciſſuram verticalem in <lb/>tabella T, ſimilem illi quæ datur in orbe O. </s> <s xml:id="echoid-s13056" xml:space="preserve">Tabella hæc <lb/>cum fciſſura adhibetur ad minuendam radii intromſſi latitu-<lb/>dinem, quæ continuo creſcit propter lumen a lateribus Solis <lb/>proveniens.</s> <s xml:id="echoid-s13057" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1932" type="section" level="1" n="478"> <head xml:id="echoid-head641" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s13058" xml:space="preserve">Poſitis, quæ in explicatione Machinæ dicta, incidat ra-<lb/>dius perpendiculariter in ſuperficiem a b c d; </s> <s xml:id="echoid-s13059" xml:space="preserve">rectâ tranſi-<lb/>bit per aquam ut per ſuperiorem pixidis partem, & </s> <s xml:id="echoid-s13060" xml:space="preserve">neque <lb/>in ingreſſu, neque in exitu deflectetur a via: </s> <s xml:id="echoid-s13061" xml:space="preserve">quo confirma-<lb/>tur n. </s> <s xml:id="echoid-s13062" xml:space="preserve">629.</s> <s xml:id="echoid-s13063" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1933" type="section" level="1" n="479"> <head xml:id="echoid-head642" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s13064" xml:space="preserve">Iiſdem poſitis, incidat oblique radius in ſuperficiem a b <lb/>c d in f g; </s> <s xml:id="echoid-s13065" xml:space="preserve">pars radii ſuperior motum ſuum per h rectâ viâ <lb/>continuabit; </s> <s xml:id="echoid-s13066" xml:space="preserve">pars verò inferior in aqua, inflectetur ver-<lb/>ſus i, accedendo ad perpendicularem: </s> <s xml:id="echoid-s13067" xml:space="preserve">quod confirmat <lb/>n. </s> <s xml:id="echoid-s13068" xml:space="preserve">624.</s> <s xml:id="echoid-s13069" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1934" type="section" level="1" n="480"> <head xml:id="echoid-head643" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s13070" xml:space="preserve">Manentibus quæ in Experimentis præcedentibus, radius <lb/>qui in i, ex aqua in aërem tranſit, deflectitur a via ſua rece-<lb/>dendo a perpendiculari, & </s> <s xml:id="echoid-s13071" xml:space="preserve">quidem ita, ut ſequatur eandem <lb/>directionem cum radio in aquam incidente in g; </s> <s xml:id="echoid-s13072" xml:space="preserve">ille enim <lb/>motu parallelo fertur cum radio f h continuato: </s> <s xml:id="echoid-s13073" xml:space="preserve">quod con-<lb/>firmat n. </s> <s xml:id="echoid-s13074" xml:space="preserve">625. </s> <s xml:id="echoid-s13075" xml:space="preserve">626. </s> <s xml:id="echoid-s13076" xml:space="preserve">& </s> <s xml:id="echoid-s13077" xml:space="preserve">628.</s> <s xml:id="echoid-s13078" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13079" xml:space="preserve">In dictis huc uſque, tantum conſideravimus attractionem <lb/>medii denſioris quia hæc prævalet, non tamen contemnen-<lb/>da eſt actio medii rarioris, quia hæc minuit actionem medii <lb/>denſioris, quæ eo minor erit in lumen, quo media inter ſe <lb/>minus denſitate differunt. </s> <s xml:id="echoid-s13080" xml:space="preserve">Idcirco nulla datur refractio <lb/> <anchor type="note" xlink:label="note-0510-01a" xlink:href="note-0510-01"/> ubi denſitates mediorum ſunt æquales, & </s> <s xml:id="echoid-s13081" xml:space="preserve">eomajor eſt, quo hæ <lb/>denſitates magis inter ſe differunt.</s> <s xml:id="echoid-s13082" xml:space="preserve"/> </p> <div xml:id="echoid-div1934" type="float" level="2" n="1"> <note position="left" xlink:label="note-0510-01" xlink:href="note-0510-01a" xml:space="preserve">631.</note> </div> <pb o="(23)" file="0511" n="561" rhead="MATHEMATICA LIB. III. CAP. VI."/> <p> <s xml:id="echoid-s13083" xml:space="preserve">Refractionis leges ex acceleratione quam generat attractio <lb/>deducuntur; </s> <s xml:id="echoid-s13084" xml:space="preserve">examinanda ideo eſt hæc acceleratio.</s> <s xml:id="echoid-s13085" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div1936" type="section" level="1" n="481"> <head xml:id="echoid-head644" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p> <s xml:id="echoid-s13086" xml:space="preserve">Spatium planis GH & </s> <s xml:id="echoid-s13087" xml:space="preserve">IL terminatum, vocatur ſpatium <lb/> <anchor type="note" xlink:label="note-0511-01a" xlink:href="note-0511-01"/> attractionis.</s> <s xml:id="echoid-s13088" xml:space="preserve"/> </p> <div xml:id="echoid-div1936" type="float" level="2" n="1"> <note position="right" xlink:label="note-0511-01" xlink:href="note-0511-01a" xml:space="preserve">632.</note> </div> <note position="right" xml:space="preserve">TAB. IV. <lb/>fig. 1.</note> <p> <s xml:id="echoid-s13089" xml:space="preserve">Inter plana quæ his lineis repreſentantur attractio obtinet, <lb/>non ultra <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13090" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">619.</note> <p style="it"> <s xml:id="echoid-s13091" xml:space="preserve">Directio hujus actionis eſt perpendicularis ad ſuperficiem <lb/> <anchor type="note" xlink:label="note-0511-04a" xlink:href="note-0511-04"/> media dirimentem, ideoque ad ſuperficiem IL; </s> <s xml:id="echoid-s13092" xml:space="preserve">& </s> <s xml:id="echoid-s13093" xml:space="preserve">inæqualis <lb/>eſt ad varias diſtantias ab hac ſuperficie <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13094" xml:space="preserve">Ad æquales ve- <anchor type="note" xlink:label="note-0511-05a" xlink:href="note-0511-05"/> rò diſtantias æqualis eſt, quia media ambo homogenea & </s> <s xml:id="echoid-s13095" xml:space="preserve">u-<lb/>bique ſibi ſimilia ponuntur.</s> <s xml:id="echoid-s13096" xml:space="preserve"/> </p> <div xml:id="echoid-div1937" type="float" level="2" n="2"> <note position="right" xlink:label="note-0511-04" xlink:href="note-0511-04a" xml:space="preserve">633.</note> <note symbol="*" position="right" xlink:label="note-0511-05" xlink:href="note-0511-05a" xml:space="preserve">619.</note> </div> <p> <s xml:id="echoid-s13097" xml:space="preserve">Motus radii AC poteſt reſolvi in duos alios motus juxta <lb/>directiones AO & </s> <s xml:id="echoid-s13098" xml:space="preserve">OC <anchor type="note" xlink:href="" symbol="*"/>, quarum prima ſuperficiei <anchor type="note" xlink:href="" symbol="*"/><unsure/> F <anchor type="note" xlink:label="note-0511-06a" xlink:href="note-0511-06"/> <anchor type="note" xlink:label="note-0511-07a" xlink:href="note-0511-07"/> parallela eſt, ſecunda huic eidem ſuperficiei perpendicula-<lb/>ris; </s> <s xml:id="echoid-s13099" xml:space="preserve">quorum motuum celeritates reſpectivè proportionales <lb/>erunt hiſce lineis AO & </s> <s xml:id="echoid-s13100" xml:space="preserve">OC dum AC ipſius radii ce-<lb/>leritatem denotat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13101" xml:space="preserve"/> </p> <div xml:id="echoid-div1938" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0511-06" xlink:href="note-0511-06a" xml:space="preserve">192.</note> <note symbol="*" position="right" xlink:label="note-0511-07" xlink:href="note-0511-07a" xml:space="preserve">E</note> </div> <note symbol="*" position="right" xml:space="preserve">192.</note> <p style="it"> <s xml:id="echoid-s13102" xml:space="preserve">Motus juxta directionem AO ex attractione perpendicu-<lb/> <anchor type="note" xlink:label="note-0511-09a" xlink:href="note-0511-09"/> lari ad ſuperficiem IL non mutatur, ſolus motus juxta OC <lb/>acceleratur.</s> <s xml:id="echoid-s13103" xml:space="preserve"/> </p> <div xml:id="echoid-div1939" type="float" level="2" n="4"> <note position="right" xlink:label="note-0511-09" xlink:href="note-0511-09a" xml:space="preserve">634.</note> </div> <p> <s xml:id="echoid-s13104" xml:space="preserve">Poteſt ſervatâ lineâ AC, celeritate nempe ipſius radii, <lb/> <anchor type="note" xlink:label="note-0511-10a" xlink:href="note-0511-10"/> hujus inclinatio mutari, quo etiam mutatur celeritas juxta <lb/>directionem OC, quæ celeritas in totum evaneſcit, ſi mi-<lb/>nimus ſit angulus A a G. </s> <s xml:id="echoid-s13105" xml:space="preserve">In quo caſu ſi poſt ingreſſum <lb/>luminis in medium denſius, illius motus in duos reſolvatur, <lb/>ita ut unius directio ſit ſuperficiei IL perpendicularis, hu-<lb/>jus celeritas in totum tribuenda erit attractioni ſæpius me-<lb/>moratæ. </s> <s xml:id="echoid-s13106" xml:space="preserve">In ingreſſu enim in ſpatium attractionis generatur <lb/>motus juxta hanc directionem, & </s> <s xml:id="echoid-s13107" xml:space="preserve">in tranſitu per hoc ſpatium, <lb/>in quo ubique nova actio juxta eandem directionem in lumen <lb/>agit, continuò acceleratur. </s> <s xml:id="echoid-s13108" xml:space="preserve">Quæ acceleratio in omnilumi-<lb/>nis tranſitu per ſpatium attractionis obtinet, ſed diverſa eſt, <lb/>pro varia celeritate qua lumen perpendiculariter ad ſuperfi-<lb/>ciem media dirimentem accedit.</s> <s xml:id="echoid-s13109" xml:space="preserve"/> </p> <div xml:id="echoid-div1940" type="float" level="2" n="5"> <note position="right" xlink:label="note-0511-10" xlink:href="note-0511-10a" xml:space="preserve">635.</note> </div> <p> <s xml:id="echoid-s13110" xml:space="preserve">Si æquabilis foret attractio per totam latitudinem ſpatii at-<lb/>tractionis, poſſent, quæ accelerationem memoratam ſpectant, <pb o="(24)" file="0512" n="562" rhead="PHYSICES ELEMENTA"/> ut de acceleratione gravium dictum eſt poſt n. </s> <s xml:id="echoid-s13111" xml:space="preserve">130.</s> <s xml:id="echoid-s13112" xml:space="preserve">, deter-<lb/> <anchor type="note" xlink:label="note-0512-01a" xlink:href="note-0512-01"/> minari ope trianguli rectanguli PQR, in quo lineæ pa-<lb/>rallelæ ad baſin celeritates repreſentant, dum portiones areæ <lb/>trianguli ſpatia percurſa deſignant. </s> <s xml:id="echoid-s13113" xml:space="preserve">Hìc autem de eo-<lb/>dem ſpatio percurſo ſemper agitur, latitudine nempe ſpatii <lb/>attractionis, quia ſolum motum ad ſuperficiem Media diri-<lb/>mentem perpendicularem conſideramus; </s> <s xml:id="echoid-s13114" xml:space="preserve">idcirco per por-<lb/>tiones æquales areæ trianguli PQR ſpatium hoc percur-<lb/>ſum ſemper repreſentatur. </s> <s xml:id="echoid-s13115" xml:space="preserve">Sit portio hæc Pdc quando <lb/>cum celeritate o. </s> <s xml:id="echoid-s13116" xml:space="preserve">lumen ſpatium attractionis juxta memora-<lb/>tam directionem perpendicularemintrat, id eſt, quando ra-<lb/>dius incidens cum ſuperficie media ſeparante angulum mini-<lb/>mum format; </s> <s xml:id="echoid-s13117" xml:space="preserve">dc in hoc caſu deſignabit celeritatem attra-<lb/>ctione acquiſitam, & </s> <s xml:id="echoid-s13118" xml:space="preserve">quâ lumen ſpatium attractionis exit.</s> <s xml:id="echoid-s13119" xml:space="preserve"/> </p> <div xml:id="echoid-div1941" type="float" level="2" n="6"> <note position="left" xlink:label="note-0512-01" xlink:href="note-0512-01a" xml:space="preserve">TAB. IV. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s13120" xml:space="preserve">Si autem lumen cum celeritate quæ per fg deſignatur <lb/>perpendiculariter ſpatium attractionis intret, exibit ſpatium <lb/>cum celeritate hi poſitis areis Pdc & </s> <s xml:id="echoid-s13121" xml:space="preserve">fgih æqualibus <lb/>inter ſe, ut ex dictis patet. </s> <s xml:id="echoid-s13122" xml:space="preserve">Triangula Pdc, Pfg, Phi <lb/>ſunt ſimilia, ideoque horum areæ ſunt inter ſe ut quadrata <lb/>laterum homologorum dc, fg, hi ſumma autem arearum <lb/>Pdc, Pfg æqualis eſt areæ phi, (propter areas æ-<lb/>quales Pdc & </s> <s xml:id="echoid-s13123" xml:space="preserve">fgih); </s> <s xml:id="echoid-s13124" xml:space="preserve">ergo & </s> <s xml:id="echoid-s13125" xml:space="preserve">ſumma quadratorum li-<lb/>nearum dc & </s> <s xml:id="echoid-s13126" xml:space="preserve">fg æqualis eſt quadrato lineæ hi; </s> <s xml:id="echoid-s13127" xml:space="preserve">unde <lb/>ſequitur tribus memoratis lineis formari poſſe triangulum re-<lb/>ctangulum cujus hypotenuſa erit hi. </s> <s xml:id="echoid-s13128" xml:space="preserve">Ergo</s> </p> <p style="it"> <s xml:id="echoid-s13129" xml:space="preserve">In triangulo rectangulo, cujus latus unum eſt celeritas quâ <lb/> <anchor type="note" xlink:label="note-0512-02a" xlink:href="note-0512-02"/> lumen perpendiculariter ſpatium attractionis intrat, latus <lb/>alterum celeritas percurrendo hoc ſpatium acquiſita, quando <lb/>lumen celeritate o. </s> <s xml:id="echoid-s13130" xml:space="preserve">hoc intrat, hypotenuſa trianguli deſignat <lb/>celeritatem qua lumen ad partem oppoſitam ſpatium attractio-<lb/>nis perpendiculariter exit. </s> <s xml:id="echoid-s13131" xml:space="preserve">Quod univerſaliter obtinet, quo-<lb/>modocunque mutetur attractio in ſpatio attractionis pro va-<lb/>ria diſtantia a planis quibus hoc ſpatium terminatur. </s> <s xml:id="echoid-s13132" xml:space="preserve">Quod <lb/>ur probetur,</s> </p> <div xml:id="echoid-div1942" type="float" level="2" n="7"> <note position="left" xlink:label="note-0512-02" xlink:href="note-0512-02a" xml:space="preserve">636.</note> </div> <p> <s xml:id="echoid-s13133" xml:space="preserve">Ponamus ſpatium attractionis in duas partes, ſive æquales <lb/>ſive utcunque inæquales ſecari plano parallelo ad ſuperficies <lb/>quibus terminatur. </s> <s xml:id="echoid-s13134" xml:space="preserve">Ponamus ulterius attractionem dari diver- <pb o="(25)" file="0513" n="563" rhead="MATHEMATICA LIB. III. CAP. VI."/> ſam in his partibus, in eadem tamen illam non variari. </s> <s xml:id="echoid-s13135" xml:space="preserve">Con-<lb/>ſiderandæ ſunt hæ partes ut duo diverſa ſpatia attractionis. <lb/></s> <s xml:id="echoid-s13136" xml:space="preserve"> <anchor type="note" xlink:label="note-0513-01a" xlink:href="note-0513-01"/> Sit A celeritas, quam lumen primam partem ſpatii percurren-<lb/>do acquirit, quando ſpatium intrat celeritate o.</s> <s xml:id="echoid-s13137" xml:space="preserve">; ſit B cele-<lb/>ritas ſecundam partem ſpatii percurrendo acquiſita, quan-<lb/>do itidem lumen hanc partem celeritate o. </s> <s xml:id="echoid-s13138" xml:space="preserve">intrat. </s> <s xml:id="echoid-s13139" xml:space="preserve">Notan-<lb/>dum in hac demonſtratione ubique agi de motu perpendicu-<lb/>lari ad ſuperficiem, qua media ſeparantur.</s> <s xml:id="echoid-s13140" xml:space="preserve"/> </p> <div xml:id="echoid-div1943" type="float" level="2" n="8"> <note position="right" xlink:label="note-0513-01" xlink:href="note-0513-01a" xml:space="preserve">TAB. IV. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13141" xml:space="preserve">Intret lumen primam partem ſpatii memorati celeritate <lb/>o. </s> <s xml:id="echoid-s13142" xml:space="preserve">ad ſecundam partem accedet celeritate A; </s> <s xml:id="echoid-s13143" xml:space="preserve">ſi ergo lateri-<lb/>bus A & </s> <s xml:id="echoid-s13144" xml:space="preserve">B triangulum formetur rectangulum ECD, hy-<lb/>potenuſa ED deſignabit celeritatem qua lumen ex ſpatio <lb/>attractionis exibit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13145" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">636.</note> <p> <s xml:id="echoid-s13146" xml:space="preserve">Si lumen celeritate FG ſpatium attractionis intret, for-<lb/>metur triangulum rectangulum HFG lateribus FG & </s> <s xml:id="echoid-s13147" xml:space="preserve"><lb/>A; </s> <s xml:id="echoid-s13148" xml:space="preserve">hypotenuſa HG erit celeritas, qua lumen prima par-<lb/> <anchor type="note" xlink:label="note-0513-03a" xlink:href="note-0513-03"/> te ſpatii attractionis exit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s13149" xml:space="preserve">in ſecundam penetrat; </s> <s xml:id="echoid-s13150" xml:space="preserve">for- mando autem triangulum rectangulum HGI cujus perpen-<lb/>dicularis æqualis ſit lineæ B, datur hypotenuſa IG deſignans <lb/>celeritatem qua lumen exit, & </s> <s xml:id="echoid-s13151" xml:space="preserve">poſt totum ſpatium attractio-<lb/>nis percurſum motum continuat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13152" xml:space="preserve"/> </p> <div xml:id="echoid-div1944" type="float" level="2" n="9"> <note symbol="*" position="right" xlink:label="note-0513-03" xlink:href="note-0513-03a" xml:space="preserve">636.</note> </div> <note symbol="*" position="right" xml:space="preserve">636.</note> <p> <s xml:id="echoid-s13153" xml:space="preserve">Demonſtrandum autem eſt celeritatem IG etiam eſſe <lb/>hypotenuſam trianguli rectanguli NML, cujus latus ML <lb/>æquale eſt FG celeritati, qua lumen ſpatium attractionis <lb/>intrat, & </s> <s xml:id="echoid-s13154" xml:space="preserve">cujus latus alterum LN æquale eſt lineæ ED, <lb/>celeritati, quam lumen acquirit totam latitudinem ſpatii re-<lb/>fractionis percurrendo, quando hoc intravit celeritateo.</s> <s xml:id="echoid-s13155" xml:space="preserve">; quo <lb/>demonſtrato & </s> <s xml:id="echoid-s13156" xml:space="preserve">in hoc caſu, in quo duæ diverſæ vires at-<lb/>tractionis agunt, propoſitionem n. </s> <s xml:id="echoid-s13157" xml:space="preserve">636. </s> <s xml:id="echoid-s13158" xml:space="preserve">obtineri patebit.</s> <s xml:id="echoid-s13159" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13160" xml:space="preserve">Lineas vero I <anchor type="note" xlink:href="" symbol="*"/><unsure/> & </s> <s xml:id="echoid-s13161" xml:space="preserve">NM æquales eſſe ex conſideratio- <anchor type="note" xlink:label="note-0513-05a" xlink:href="note-0513-05"/> ne triangulorum rectangulorum facile liquet. </s> <s xml:id="echoid-s13162" xml:space="preserve">Quadratum <lb/>lineæ NM valet quadrata linearum NL & </s> <s xml:id="echoid-s13163" xml:space="preserve">LM aut <lb/>FG: </s> <s xml:id="echoid-s13164" xml:space="preserve">NL æqualis lineæ ED, cujus quadratum valet quadra-<lb/>ta linearum EC & </s> <s xml:id="echoid-s13165" xml:space="preserve">CD, aut linearum A & </s> <s xml:id="echoid-s13166" xml:space="preserve">B, æqualium <lb/>lineis FH & </s> <s xml:id="echoid-s13167" xml:space="preserve">HI: </s> <s xml:id="echoid-s13168" xml:space="preserve">Æquale ergo eſt quadratum hypotenu-<lb/>ſæ NM tribus quadratis linearum FG, FH, & </s> <s xml:id="echoid-s13169" xml:space="preserve">HI. </s> <s xml:id="echoid-s13170" xml:space="preserve">Qui-<lb/>bus iiſdem tribus quadratis æquale eſt quadratum lineæ <pb o="26" file="0514" n="564" rhead="PHYSICES ELEMENTA"/> GI; </s> <s xml:id="echoid-s13171" xml:space="preserve">hoc enim valet quadrata linearum HI & </s> <s xml:id="echoid-s13172" xml:space="preserve">HG, quod <lb/>ultimum æquale eſt quadratis linearum HF & </s> <s xml:id="echoid-s13173" xml:space="preserve">FG.</s> <s xml:id="echoid-s13174" xml:space="preserve"/> </p> <div xml:id="echoid-div1945" type="float" level="2" n="10"> <note symbol="*" position="right" xlink:label="note-0513-05" xlink:href="note-0513-05a" xml:space="preserve">G</note> </div> <p> <s xml:id="echoid-s13175" xml:space="preserve">Si ſpatium refractionis in ſpatia quotcunque dividatur pla-<lb/>nis parallelis ſuperficiebus, quibus ſpatium hoc terminatur, & </s> <s xml:id="echoid-s13176" xml:space="preserve"><lb/>in partibus diverſis vires attractionis diverſæ obtineant, ea-<lb/>dem demonſtratio locum habebit; </s> <s xml:id="echoid-s13177" xml:space="preserve">& </s> <s xml:id="echoid-s13178" xml:space="preserve">poteſt utcunque etiam <lb/> <anchor type="note" xlink:label="note-0514-01a" xlink:href="note-0514-01"/> in infinitum augeri diviſionum numerus; </s> <s xml:id="echoid-s13179" xml:space="preserve">qui caſus extat in <lb/>refractione, quam lumen tranſeundo ex medio quocunque <lb/>in aliud diverſæ denſitatis patitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13180" xml:space="preserve">cui ergo applicari po- <anchor type="note" xlink:label="note-0514-02a" xlink:href="note-0514-02"/> teſt regula n. </s> <s xml:id="echoid-s13181" xml:space="preserve">636.</s> <s xml:id="echoid-s13182" xml:space="preserve"/> </p> <div xml:id="echoid-div1946" type="float" level="2" n="11"> <note position="left" xlink:label="note-0514-01" xlink:href="note-0514-01a" xml:space="preserve">637.</note> <note symbol="*" position="left" xlink:label="note-0514-02" xlink:href="note-0514-02a" xml:space="preserve">633.</note> </div> <p> <s xml:id="echoid-s13183" xml:space="preserve">Sit Z medium rarius, X medium denſius, ſeparentur plano <lb/> <anchor type="note" xlink:label="note-0514-03a" xlink:href="note-0514-03"/> EF; </s> <s xml:id="echoid-s13184" xml:space="preserve">detur radius luminis AC obliquè in ſuperficiem EF <lb/>incidens; </s> <s xml:id="echoid-s13185" xml:space="preserve">deſignet AC celeritatem luminis in medio Z, ſit-<lb/>que hæc linea AC conſtans; </s> <s xml:id="echoid-s13186" xml:space="preserve">id eſt, maneat quæcunque <lb/>fuerit radii inclinatio. </s> <s xml:id="echoid-s13187" xml:space="preserve">Centro C ſemidiametro CA deſcriba-<lb/>tur circulus; </s> <s xml:id="echoid-s13188" xml:space="preserve">detur NCM ad EF perpendicularis; </s> <s xml:id="echoid-s13189" xml:space="preserve">ex A du-<lb/>cantur perpendiculares AO ad NC, & </s> <s xml:id="echoid-s13190" xml:space="preserve">AQ ad EF.</s> <s xml:id="echoid-s13191" xml:space="preserve"/> </p> <div xml:id="echoid-div1947" type="float" level="2" n="12"> <note position="left" xlink:label="note-0514-03" xlink:href="note-0514-03a" xml:space="preserve">TAB. IV. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s13192" xml:space="preserve">Motus per AC concipiatur reſolutus in duos alios, unum <lb/>juxta AO, alterum juxta AQ aut OC <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13193" xml:space="preserve">deſignabit linea <anchor type="note" xlink:label="note-0514-04a" xlink:href="note-0514-04"/> OC radii celeritatem perpendicularem ſuperficiei EF, quæ <lb/>celeritas ſola ex attractione medii augetur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13194" xml:space="preserve"/> </p> <div xml:id="echoid-div1948" type="float" level="2" n="13"> <note symbol="*" position="left" xlink:label="note-0514-04" xlink:href="note-0514-04a" xml:space="preserve">192.</note> </div> <note symbol="*" position="left" xml:space="preserve">634.</note> <p> <s xml:id="echoid-s13195" xml:space="preserve">Sit CP celeritas, quam lumen acquirit perpendiculariter <lb/>percurrendo ſpatium attractionis medii X; </s> <s xml:id="echoid-s13196" xml:space="preserve">poſitâ luminis ce-<lb/>leritate in ingreſſu o.</s> <s xml:id="echoid-s13197" xml:space="preserve">; hypotenuſa OP trianguli rectanguli <lb/>PCO erit celeritas radii AC in medio X, juxta directio-<lb/>nem perpendicularem ſuperficiei EF <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13198" xml:space="preserve">celeritas luminis jux- <anchor type="note" xlink:label="note-0514-06a" xlink:href="note-0514-06"/> ta directionem AO aut QC, parallelam ſuperficiei EF, non <lb/>mutatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13199" xml:space="preserve">Sit ideo CV æqualis AO aut QC, & </s> <s xml:id="echoid-s13200" xml:space="preserve">VB <anchor type="note" xlink:label="note-0514-07a" xlink:href="note-0514-07"/> perpendicularis ad EF, æqualis hypotenuſæ PO, ducatur-<lb/>que CB; </s> <s xml:id="echoid-s13201" xml:space="preserve">erit motus per CB motus ex ambobus compoſi-<lb/>tus, & </s> <s xml:id="echoid-s13202" xml:space="preserve">determinat linea hæc ſitu ſuo directionem, & </s> <s xml:id="echoid-s13203" xml:space="preserve">longi-<lb/>tudine ſua celeritatem luminis in medio X <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13204" xml:space="preserve">quæ celeritas <anchor type="note" xlink:label="note-0514-08a" xlink:href="note-0514-08"/> variâ inclinatione radii AC non mutatur. </s> <s xml:id="echoid-s13205" xml:space="preserve">Quadratum e-<lb/> <anchor type="note" xlink:label="note-0514-09a" xlink:href="note-0514-09"/> nim lineæ CB valet quadratum lineæ BV aut PO, & </s> <s xml:id="echoid-s13206" xml:space="preserve">qua-<lb/>dratum lineæ CV aut AO; </s> <s xml:id="echoid-s13207" xml:space="preserve">quadratum vero lineæ PO valet <lb/>quadrata linearum PC & </s> <s xml:id="echoid-s13208" xml:space="preserve">CO: </s> <s xml:id="echoid-s13209" xml:space="preserve">æquale ergo eſt quadratum <lb/>lineæ CB tribus quadratis linearum PC, CO, & </s> <s xml:id="echoid-s13210" xml:space="preserve">AO, quæ <pb o="27" file="0515" n="565" rhead="MATHEMATICA. LIB. III. CAP. VI."/> duo ultima ſi jungantur habebimus quadratum ſemi diametri <lb/>AC aut CN; </s> <s xml:id="echoid-s13211" xml:space="preserve">id eſt, CB æqualis eſt PN, cujus quadratum <lb/>valet etiam quadrata linearum PC & </s> <s xml:id="echoid-s13212" xml:space="preserve">CN, & </s> <s xml:id="echoid-s13213" xml:space="preserve">quæ ex mu-<lb/>tata inclinatione radii AC nullam mutationem ſubit.</s> <s xml:id="echoid-s13214" xml:space="preserve"/> </p> <div xml:id="echoid-div1949" type="float" level="2" n="14"> <note symbol="*" position="left" xlink:label="note-0514-06" xlink:href="note-0514-06a" xml:space="preserve">637.</note> <note symbol="*" position="left" xlink:label="note-0514-07" xlink:href="note-0514-07a" xml:space="preserve">634</note> <note position="left" xlink:label="note-0514-08" xlink:href="note-0514-08a" xml:space="preserve">638.</note> <note symbol="*" position="left" xlink:label="note-0514-09" xlink:href="note-0514-09a" xml:space="preserve">191.</note> </div> <p> <s xml:id="echoid-s13215" xml:space="preserve">Linea CB ſecat in T circulum ſemidiametro CA de-<lb/>ſcriptum; </s> <s xml:id="echoid-s13216" xml:space="preserve">a punctis B & </s> <s xml:id="echoid-s13217" xml:space="preserve">T perpendiculares BS & </s> <s xml:id="echoid-s13218" xml:space="preserve">TR du-<lb/>cantur ad CM: </s> <s xml:id="echoid-s13219" xml:space="preserve">propter triangula ſimilia CBS, CTR, <lb/>BC erit ad TC aut CA, ut BS ad TR; </s> <s xml:id="echoid-s13220" xml:space="preserve">quæ ergo li-<lb/>neæ, propter conſtantes BC & </s> <s xml:id="echoid-s13221" xml:space="preserve">CA, eandem ſemper ratio-<lb/>nem habebunt, quicunque fuerit angulus incidentiæ. </s> <s xml:id="echoid-s13222" xml:space="preserve">TR <lb/>eſt ſinus anguli refractionis TCR; </s> <s xml:id="echoid-s13223" xml:space="preserve">& </s> <s xml:id="echoid-s13224" xml:space="preserve">B æqualis CV, <lb/> <anchor type="note" xlink:label="note-0515-01a" xlink:href="note-0515-01"/> æqualis AO, eſt ſinus anguli incidentiæ ACO.</s> <s xml:id="echoid-s13225" xml:space="preserve"/> </p> <div xml:id="echoid-div1950" type="float" level="2" n="15"> <note position="right" xlink:label="note-0515-01" xlink:href="note-0515-01a" xml:space="preserve">S<unsure/></note> </div> <p style="it"> <s xml:id="echoid-s13226" xml:space="preserve">In omni ergo radii incidentis inclinatione conſtans & </s> <s xml:id="echoid-s13227" xml:space="preserve">im-<lb/> <anchor type="note" xlink:label="note-0515-02a" xlink:href="note-0515-02"/> mutabilis datur ratio inter ſinus angulorum incidentiæ & </s> <s xml:id="echoid-s13228" xml:space="preserve">re-<lb/>fractionis.</s> <s xml:id="echoid-s13229" xml:space="preserve"/> </p> <div xml:id="echoid-div1951" type="float" level="2" n="16"> <note position="right" xlink:label="note-0515-02" xlink:href="note-0515-02a" xml:space="preserve">639.</note> </div> <p> <s xml:id="echoid-s13230" xml:space="preserve">Cum autem BC & </s> <s xml:id="echoid-s13231" xml:space="preserve">CA, quæ ſunt ut memorati ſinus, <lb/>etiam deſignent celeritates luminis in mediis X & </s> <s xml:id="echoid-s13232" xml:space="preserve">Z, ſequi-<lb/>tur ſinus hos eſſe inverſè ut ſunt celeritates in iſtis mediis.</s> <s xml:id="echoid-s13233" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">640.</note> <p> <s xml:id="echoid-s13234" xml:space="preserve">Si medium Z ſit aër & </s> <s xml:id="echoid-s13235" xml:space="preserve">X aqua, ſinus prædicti ſunt ut 4. <lb/></s> <s xml:id="echoid-s13236" xml:space="preserve">ad 3.</s> <s xml:id="echoid-s13237" xml:space="preserve">, & </s> <s xml:id="echoid-s13238" xml:space="preserve">celeritas luminis in aëre ad hujus celeritatem in <lb/>aqua, ut 3. </s> <s xml:id="echoid-s13239" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s13240" xml:space="preserve">Si vero, manente Z aëre, X ſit vitrum, <lb/>ſinus ſunt ut 17. </s> <s xml:id="echoid-s13241" xml:space="preserve">ad 11. </s> <s xml:id="echoid-s13242" xml:space="preserve">circa omnia media illud unico expe-<lb/>rimento determinaſſe ſufficit.</s> <s xml:id="echoid-s13243" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13244" xml:space="preserve">Ratio quæ datur inter ſinus angulorum quorumcunque eſt <lb/> <anchor type="note" xlink:label="note-0515-04a" xlink:href="note-0515-04"/> inverſa ſecantium comp.</s> <s xml:id="echoid-s13245" xml:space="preserve">, ut in hac figura patet, conci-<lb/>piendo circulum ſemi diametro CQ aut CV ductum: </s> <s xml:id="echoid-s13246" xml:space="preserve">tunc <lb/>enim AC æqualis CT, & </s> <s xml:id="echoid-s13247" xml:space="preserve">CB ſunt ſecantes angulorum <lb/>ACQ & </s> <s xml:id="echoid-s13248" xml:space="preserve">BCV complementorum angulorum incidentiæ <lb/>& </s> <s xml:id="echoid-s13249" xml:space="preserve">refractionis, & </s> <s xml:id="echoid-s13250" xml:space="preserve">ſunt inverſè ut BS æqualis AO & </s> <s xml:id="echoid-s13251" xml:space="preserve">TR, <lb/>quæ in majori circulo ſunt ſinus incidentiæ & </s> <s xml:id="echoid-s13252" xml:space="preserve">refractionis. <lb/></s> <s xml:id="echoid-s13253" xml:space="preserve">Hæcque ſecantium proportio methodum dat facillimè vo-<lb/>candi ad experimentum Propoſitionem N. </s> <s xml:id="echoid-s13254" xml:space="preserve">639.</s> <s xml:id="echoid-s13255" xml:space="preserve"/> </p> <div xml:id="echoid-div1952" type="float" level="2" n="17"> <note position="right" xlink:label="note-0515-04" xlink:href="note-0515-04a" xml:space="preserve">641.</note> </div> </div> <div xml:id="echoid-div1954" type="section" level="1" n="482"> <head xml:id="echoid-head645" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s13256" xml:space="preserve">In hoc Experimento, lumen eodem modo ac in præce-<lb/> <anchor type="note" xlink:label="note-0515-05a" xlink:href="note-0515-05"/> dentibus in cubiculum obſcurum per ſciſſuram intromitti-<lb/>tur, & </s> <s xml:id="echoid-s13257" xml:space="preserve">a ſpeculo reflexum per ſciſſuram verticalem in tabella <lb/>T tranſmittitur.</s> <s xml:id="echoid-s13258" xml:space="preserve"/> </p> <div xml:id="echoid-div1954" type="float" level="2" n="1"> <note position="right" xlink:label="note-0515-05" xlink:href="note-0515-05a" xml:space="preserve">TAB IV. <lb/>fig. 6.</note> </div> <pb o="28" file="0516" n="566" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s13259" xml:space="preserve">Datur Pixis P, ejuſdem præterpropter magnitudinis cum <lb/>illa, qua in præcedentibus experimentis utimur; </s> <s xml:id="echoid-s13260" xml:space="preserve">in hac uni-<lb/>cum latus, & </s> <s xml:id="echoid-s13261" xml:space="preserve">quidem ex minoribus, vitreum eſt abcd. <lb/></s> <s xml:id="echoid-s13262" xml:space="preserve">Ad dimidiam altitudinem aquâ repletur Pixis.</s> <s xml:id="echoid-s13263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13264" xml:space="preserve">Radius luminis verticalis in fg obliquè in latus vitreum <lb/>pixidis inpingit; </s> <s xml:id="echoid-s13265" xml:space="preserve">pars radii ſupra aqua rectâ tranſit & </s> <s xml:id="echoid-s13266" xml:space="preserve">in h <lb/>ad latus majus pixidis pertingit; </s> <s xml:id="echoid-s13267" xml:space="preserve">pars verò radii in aqua re-<lb/>fracta per g i procedit & </s> <s xml:id="echoid-s13268" xml:space="preserve">in i in idem pixidis latus impin-<lb/>git. </s> <s xml:id="echoid-s13269" xml:space="preserve">Quicunque fuerit angulus a radio cum latere abcd <lb/>pixidis formatus, lineæ fh & </s> <s xml:id="echoid-s13270" xml:space="preserve">gi ſemper ſunt inter ſe ut <lb/>3. </s> <s xml:id="echoid-s13271" xml:space="preserve">ad 4.</s> <s xml:id="echoid-s13272" xml:space="preserve">; ut commodè oſtenditur in variis inclinationibus, ſi <lb/>ſcalæ duæ dentur, ſingulæ in partes exiguas æquales diviſæ, <lb/>& </s> <s xml:id="echoid-s13273" xml:space="preserve">quarum diviſiones ſunt inter ſe ut 3. </s> <s xml:id="echoid-s13274" xml:space="preserve">ad 4; </s> <s xml:id="echoid-s13275" xml:space="preserve">tot enim ſem-<lb/>per continebit partes majores linea gi, quot minores conti-<lb/>net linea fh. </s> <s xml:id="echoid-s13276" xml:space="preserve">Angulus, quem fh cum plano abcd format, <lb/>eſt complementum anguli incidentiæ ad angulum rectum, <lb/>& </s> <s xml:id="echoid-s13277" xml:space="preserve">angulus, a linea gi cum eodem plano formatus, eſt com-<lb/>plementum anguli refractionis ad angulum rectum; </s> <s xml:id="echoid-s13278" xml:space="preserve">ſunt ideo <lb/>gh & </s> <s xml:id="echoid-s13279" xml:space="preserve">gi ſecantes comp. </s> <s xml:id="echoid-s13280" xml:space="preserve">angulorum incidentiæ & </s> <s xml:id="echoid-s13281" xml:space="preserve">refra-<lb/>ctionis, quas conſtantem inter ſe rationem habere experi-<lb/>mento erat confirmandum.</s> <s xml:id="echoid-s13282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13283" xml:space="preserve">Hucuſque radium è medio rariori in denſius intrantem <lb/> <anchor type="note" xlink:label="note-0516-01a" xlink:href="note-0516-01"/> conſideravimus, ſed eadem conſtans ſinuum proportio, in n. <lb/></s> <s xml:id="echoid-s13284" xml:space="preserve">639.</s> <s xml:id="echoid-s13285" xml:space="preserve">, memorata in motu radiorum contrario obtinet; </s> <s xml:id="echoid-s13286" xml:space="preserve">anguli <lb/>ACN, MCB non mutantur quicunque ſit radius inci-<lb/> <anchor type="note" xlink:label="note-0516-02a" xlink:href="note-0516-02"/> dens, ſive AC ſive BC <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13287" xml:space="preserve">In hoc caſu ſi BC ſit celeritas <anchor type="note" xlink:label="note-0516-03a" xlink:href="note-0516-03"/> radii incidentis, CA erit celeritas radii refracti; </s> <s xml:id="echoid-s13288" xml:space="preserve">eodem e-<lb/>nim modo, ex attractione verſus medium X, motus radii <lb/>ex X in Z tranſeuntis retardatur, ac in motu contrario ac-<lb/>celeratur.</s> <s xml:id="echoid-s13289" xml:space="preserve"/> </p> <div xml:id="echoid-div1955" type="float" level="2" n="2"> <note position="left" xlink:label="note-0516-01" xlink:href="note-0516-01a" xml:space="preserve">642.</note> <note position="left" xlink:label="note-0516-02" xlink:href="note-0516-02a" xml:space="preserve">TAB. IV. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0516-03" xlink:href="note-0516-03a" xml:space="preserve">626.</note> </div> </div> <div xml:id="echoid-div1957" type="section" level="1" n="483"> <head xml:id="echoid-head646" xml:space="preserve">CAPUT VII.</head> <head xml:id="echoid-head647" style="it" xml:space="preserve">De luminis refractione, quando media ſuperficie <lb/>planâ ſeparantur.</head> <head xml:id="echoid-head648" xml:space="preserve"><emph style="sc">Definitio i</emph>.</head> <p style="it"> <s xml:id="echoid-s13290" xml:space="preserve">RAdii ab eodem puncto, quaſi centro, procedentes & </s> <s xml:id="echoid-s13291" xml:space="preserve">ſic con-<lb/> <anchor type="note" xlink:label="note-0516-04a" xlink:href="note-0516-04"/> tinuo magis a ſe mutuo recedentes, dicuntur divergentes.</s> <s xml:id="echoid-s13292" xml:space="preserve"/> </p> <div xml:id="echoid-div1957" type="float" level="2" n="1"> <note position="left" xlink:label="note-0516-04" xlink:href="note-0516-04a" xml:space="preserve">643.</note> </div> <pb file="0517" n="567"/> <pb file="0517a" n="568"/> <figure> <image file="0517a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0517a-01"/> </figure> <pb file="0518" n="569"/> <pb o="29" file="0519" n="570" rhead="MATHEMATICA LIB. III. CAP. VII."/> </div> <div xml:id="echoid-div1959" type="section" level="1" n="484"> <head xml:id="echoid-head649" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s13293" xml:space="preserve">Magis divergentes ſunt, qui majorem Angulum inter ſe for-<lb/> <anchor type="note" xlink:label="note-0519-01a" xlink:href="note-0519-01"/> mant.</s> <s xml:id="echoid-s13294" xml:space="preserve"/> </p> <div xml:id="echoid-div1959" type="float" level="2" n="1"> <note position="right" xlink:label="note-0519-01" xlink:href="note-0519-01a" xml:space="preserve">644.</note> </div> </div> <div xml:id="echoid-div1961" type="section" level="1" n="485"> <head xml:id="echoid-head650" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s13295" xml:space="preserve">Punctum, a quo radii divergentes procedunt, dicitur Pun-<lb/> <anchor type="note" xlink:label="note-0519-02a" xlink:href="note-0519-02"/> ctum radians.</s> <s xml:id="echoid-s13296" xml:space="preserve"/> </p> <div xml:id="echoid-div1961" type="float" level="2" n="1"> <note position="right" xlink:label="note-0519-02" xlink:href="note-0519-02a" xml:space="preserve">645.</note> </div> <p style="it"> <s xml:id="echoid-s13297" xml:space="preserve">Quo magis radii ſunt divergentes, poſitâ eâdem inter hos <lb/> <anchor type="note" xlink:label="note-0519-03a" xlink:href="note-0519-03"/> diſtantiâ, quo minus diſtat punctum radians & </s> <s xml:id="echoid-s13298" xml:space="preserve">contra.</s> <s xml:id="echoid-s13299" xml:space="preserve"/> </p> <div xml:id="echoid-div1962" type="float" level="2" n="2"> <note position="right" xlink:label="note-0519-03" xlink:href="note-0519-03a" xml:space="preserve">646.</note> </div> <p> <s xml:id="echoid-s13300" xml:space="preserve">Sæpe per refractionem radii ita moventur, quaſi a puncto <lb/> <anchor type="note" xlink:label="note-0519-04a" xlink:href="note-0519-04"/> radiante procederent, licet revera a tali puncto non proce-<lb/>dant; </s> <s xml:id="echoid-s13301" xml:space="preserve">id eſt, ſi radii continuarentur, verſus partem a qua <lb/>procedunt, in unum punctum concurrerent. </s> <s xml:id="echoid-s13302" xml:space="preserve">In hoc caſu <lb/>etiam divergentes radii dicuntur.</s> <s xml:id="echoid-s13303" xml:space="preserve"/> </p> <div xml:id="echoid-div1963" type="float" level="2" n="3"> <note position="right" xlink:label="note-0519-04" xlink:href="note-0519-04a" xml:space="preserve">647.</note> </div> </div> <div xml:id="echoid-div1965" type="section" level="1" n="486"> <head xml:id="echoid-head651" xml:space="preserve"><emph style="sc">Definitiones</emph> 4. & 5.</head> <p> <s xml:id="echoid-s13304" xml:space="preserve">Radii qui in unum punctum concurrunt, aut continuati <lb/> <anchor type="note" xlink:label="note-0519-05a" xlink:href="note-0519-05"/> concurrerent, vocantur convergentes; </s> <s xml:id="echoid-s13305" xml:space="preserve">& </s> <s xml:id="echoid-s13306" xml:space="preserve">magis convergen-<lb/> <anchor type="note" xlink:label="note-0519-06a" xlink:href="note-0519-06"/> tes, qui majorem angulum formant.</s> <s xml:id="echoid-s13307" xml:space="preserve"/> </p> <div xml:id="echoid-div1965" type="float" level="2" n="1"> <note position="right" xlink:label="note-0519-05" xlink:href="note-0519-05a" xml:space="preserve">648.</note> <note position="right" xlink:label="note-0519-06" xlink:href="note-0519-06a" xml:space="preserve">649.</note> </div> </div> <div xml:id="echoid-div1967" type="section" level="1" n="487"> <head xml:id="echoid-head652" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s13308" xml:space="preserve">Punctum concurſus radiorum convergentium vocatur Focus.</s> <s xml:id="echoid-s13309" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">650.</note> </div> <div xml:id="echoid-div1968" type="section" level="1" n="488"> <head xml:id="echoid-head653" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p> <s xml:id="echoid-s13310" xml:space="preserve">Punctum, in quo radii convergentes, & </s> <s xml:id="echoid-s13311" xml:space="preserve">ante concurſum in-<lb/> <anchor type="note" xlink:label="note-0519-08a" xlink:href="note-0519-08"/> tercepti aut deflexi, continuati concurrerent, vocatur Focus <lb/>imaginarius; </s> <s xml:id="echoid-s13312" xml:space="preserve">quo nomine etiam datur punctum, ex quo fluere <lb/>concipiuntur radii divergentes, qui ex puncto radiante non <lb/>procedunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13313" xml:space="preserve"/> </p> <div xml:id="echoid-div1968" type="float" level="2" n="1"> <note position="right" xlink:label="note-0519-08" xlink:href="note-0519-08a" xml:space="preserve">651.</note> </div> <note symbol="*" position="right" xml:space="preserve">647.</note> <p style="it"> <s xml:id="echoid-s13314" xml:space="preserve">Quo magis radii convergunt, poſitâ eâdem inter hos di-<lb/> <anchor type="note" xlink:label="note-0519-10a" xlink:href="note-0519-10"/> ſtantiâ, eo minus diſtat focus ſive verus ſive imaginarius.</s> <s xml:id="echoid-s13315" xml:space="preserve"/> </p> <div xml:id="echoid-div1969" type="float" level="2" n="2"> <note position="right" xlink:label="note-0519-10" xlink:href="note-0519-10a" xml:space="preserve">652.</note> </div> <p> <s xml:id="echoid-s13316" xml:space="preserve">Si radii paralleli tranſeant è medio quocunque in aliud <lb/> <anchor type="note" xlink:label="note-0519-11a" xlink:href="note-0519-11"/> alterius denſitatis, poſt refractionem etiam ſunt paralleli: </s> <s xml:id="echoid-s13317" xml:space="preserve">quia <lb/>omnes æqualiter inflectuntur, in toto enim hoc capite agi-<lb/>tur de mediis ſuperficie planâ ſeparatis.</s> <s xml:id="echoid-s13318" xml:space="preserve"/> </p> <div xml:id="echoid-div1970" type="float" level="2" n="3"> <note position="right" xlink:label="note-0519-11" xlink:href="note-0519-11a" xml:space="preserve">653.</note> </div> <p> <s xml:id="echoid-s13319" xml:space="preserve">Dentur media X & </s> <s xml:id="echoid-s13320" xml:space="preserve">Z, hoc rarius illud verò denſius, pla-<lb/> <anchor type="note" xlink:label="note-0519-12a" xlink:href="note-0519-12"/> no ES ſeparata; </s> <s xml:id="echoid-s13321" xml:space="preserve">procedant à puncto R radii divergentes <lb/> <anchor type="note" xlink:label="note-0519-13a" xlink:href="note-0519-13"/> RC, R o, R n, mediumque denſius intrent: </s> <s xml:id="echoid-s13322" xml:space="preserve">inter hos ſit <lb/>RC, perpendicularis ad ſuperficiem ES; </s> <s xml:id="echoid-s13323" xml:space="preserve">hic a via non <lb/>deflectitur <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s13324" xml:space="preserve">per CG motum continuat. </s> <s xml:id="echoid-s13325" xml:space="preserve">Radii R o, <anchor type="note" xlink:label="note-0519-14a" xlink:href="note-0519-14"/> R n refractionem patiuntur verſus perpendiculares, quæ in <pb o="30" file="0520" n="571" rhead="PHYSICES ELEMENTA"/> punctis o & </s> <s xml:id="echoid-s13326" xml:space="preserve">n ad ſuperficiem ES concipiuntur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13327" xml:space="preserve">Hi radií in <anchor type="note" xlink:label="note-0520-01a" xlink:href="note-0520-01"/> medio denſiori ita moventur, quaſi procederent omnes a foco <lb/>imaginario r, magis a ſuperficie diſtanti, quam ipſum R, ſi <lb/>radii non nimium diſpergantur; </s> <s xml:id="echoid-s13328" xml:space="preserve">quod tamen non mathema-<lb/>ticè eſt intelligendum, per punctum enim ſpatium exiguum, <lb/>quod aliter punctum phyſicum vocatur, intelligimus.</s> <s xml:id="echoid-s13329" xml:space="preserve"/> </p> <div xml:id="echoid-div1971" type="float" level="2" n="4"> <note position="right" xlink:label="note-0519-12" xlink:href="note-0519-12a" xml:space="preserve">654.</note> <note position="right" xlink:label="note-0519-13" xlink:href="note-0519-13a" xml:space="preserve">TAB. V. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0519-14" xlink:href="note-0519-14a" xml:space="preserve">629.</note> <note symbol="*" position="left" xlink:label="note-0520-01" xlink:href="note-0520-01a" xml:space="preserve">624.</note> </div> <p> <s xml:id="echoid-s13330" xml:space="preserve">Ut hanc demonſtremus propoſitionem, conſiderandum eſt, <lb/>angulum Ro C eſſe complementum anguli incidentiæ ad <lb/>angulum rectum, & </s> <s xml:id="echoid-s13331" xml:space="preserve">angulum roC eſſe etiam complemen-<lb/>tum anguli refractionis ad angulum rectum; </s> <s xml:id="echoid-s13332" xml:space="preserve">ideoque lineas <lb/>Ro, ro eſſe ſecantes comp. </s> <s xml:id="echoid-s13333" xml:space="preserve">angulorum incidentiæ & </s> <s xml:id="echoid-s13334" xml:space="preserve">refra-<lb/>ctionis, poſito ſemidiametro oC; </s> <s xml:id="echoid-s13335" xml:space="preserve">inter quas ſecantes con-<lb/>ſtans datur proportio <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13336" xml:space="preserve">In diſperſione exigua Ro & </s> <s xml:id="echoid-s13337" xml:space="preserve">RC, <anchor type="note" xlink:label="note-0520-02a" xlink:href="note-0520-02"/> ut & </s> <s xml:id="echoid-s13338" xml:space="preserve">ro, & </s> <s xml:id="echoid-s13339" xml:space="preserve">rC, ſenſibiliter non differunt, & </s> <s xml:id="echoid-s13340" xml:space="preserve">inter RC <lb/>& </s> <s xml:id="echoid-s13341" xml:space="preserve">rC etiam conſtans datur ratio; </s> <s xml:id="echoid-s13342" xml:space="preserve">id eſt r æquè fixum eſt <lb/>ac R, licet inclinatio radii mutetur: </s> <s xml:id="echoid-s13343" xml:space="preserve">idcirco Rn ita etiam re-<lb/>fringitur per nA quaſi ab r procederet.</s> <s xml:id="echoid-s13344" xml:space="preserve"/> </p> <div xml:id="echoid-div1972" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0520-02" xlink:href="note-0520-02a" xml:space="preserve">641. 639.</note> </div> <p> <s xml:id="echoid-s13345" xml:space="preserve">Si nimium diſpergantur radii, hæc demonſttatio locum <lb/> <anchor type="note" xlink:label="note-0520-03a" xlink:href="note-0520-03"/> non habet, & </s> <s xml:id="echoid-s13346" xml:space="preserve">locus concurſus r pro puncto haberi non po-<lb/>teſt; </s> <s xml:id="echoid-s13347" xml:space="preserve">in hoc caſu circellus ibi concipiendus eſt, in quem omnes <lb/>radii concurrunt, qui eo major erit, quo majorem angulum <lb/>radii divergentes formant.</s> <s xml:id="echoid-s13348" xml:space="preserve"/> </p> <div xml:id="echoid-div1973" type="float" level="2" n="6"> <note position="left" xlink:label="note-0520-03" xlink:href="note-0520-03a" xml:space="preserve">655.</note> </div> <p style="it"> <s xml:id="echoid-s13349" xml:space="preserve">Si radii quidam ex R procedentes non admodum diſper-<lb/> <anchor type="note" xlink:label="note-0520-04a" xlink:href="note-0520-04"/> gantur, ſed valdè obliquè incidant in ſuperficiem ES, re-<lb/>fringuntur quaſi procederent ex puncto non admodum a pun-<lb/>cto r remoto: </s> <s xml:id="echoid-s13350" xml:space="preserve">ut ex dictis ſatis liquet.</s> <s xml:id="echoid-s13351" xml:space="preserve"/> </p> <div xml:id="echoid-div1974" type="float" level="2" n="7"> <note position="left" xlink:label="note-0520-04" xlink:href="note-0520-04a" xml:space="preserve">656.</note> </div> <p> <s xml:id="echoid-s13352" xml:space="preserve">Radii qui ut An, Bo, GC convergentes ex medio denſiori <lb/> <anchor type="note" xlink:label="note-0520-05a" xlink:href="note-0520-05"/> X in rarius Z tranſeunt, citius concurrunt, quam concur-<lb/>rerent, ſi in medio denſiori motum continuarent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13353" xml:space="preserve">id eſt, ma- <anchor type="note" xlink:label="note-0520-06a" xlink:href="note-0520-06"/> gis convergentes fiunt, & </s> <s xml:id="echoid-s13354" xml:space="preserve">focus verus minus quam imagina-<lb/>rius diſtat. </s> <s xml:id="echoid-s13355" xml:space="preserve">In hac figura focus imaginarius eſt r, focus autem <lb/>verus R <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13356" xml:space="preserve">Propoſitio hæc propriè eſt inverſa propoſitionis <anchor type="note" xlink:label="note-0520-07a" xlink:href="note-0520-07"/> n. </s> <s xml:id="echoid-s13357" xml:space="preserve">654. </s> <s xml:id="echoid-s13358" xml:space="preserve">ideoque eodem experimento probantur ambæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13359" xml:space="preserve"/> </p> <div xml:id="echoid-div1975" type="float" level="2" n="8"> <note position="left" xlink:label="note-0520-05" xlink:href="note-0520-05a" xml:space="preserve">657.</note> <note symbol="*" position="left" xlink:label="note-0520-06" xlink:href="note-0520-06a" xml:space="preserve">625.</note> <note symbol="*" position="left" xlink:label="note-0520-07" xlink:href="note-0520-07a" xml:space="preserve">652.</note> </div> <note symbol="*" position="left" xml:space="preserve">626.</note> </div> <div xml:id="echoid-div1977" type="section" level="1" n="489"> <head xml:id="echoid-head654" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s13360" xml:space="preserve">Per globum G, in feneſtra mobilem, & </s> <s xml:id="echoid-s13361" xml:space="preserve">in quo foramen <lb/> <anchor type="note" xlink:label="note-0520-09a" xlink:href="note-0520-09"/> per centrum tranſiens datur, radius ſolaris cylindricus in cu-<lb/>biculum obſcurum intromittitur, & </s> <s xml:id="echoid-s13362" xml:space="preserve">a ſpeculo Shorizontaliter <pb o="31" file="0521" n="572" rhead="MATHEMATICA LIB. III. CAP. VII."/> reflectitur; </s> <s xml:id="echoid-s13363" xml:space="preserve">tranſmittitur per lentem vitream convexam in <lb/>tabella T, & </s> <s xml:id="echoid-s13364" xml:space="preserve">radii in R colliguntur, & </s> <s xml:id="echoid-s13365" xml:space="preserve">poſt R moventur quaſi <lb/>ab hoc puncto procederent; </s> <s xml:id="echoid-s13366" xml:space="preserve">quod ergo eſt punctum radians.</s> <s xml:id="echoid-s13367" xml:space="preserve"/> </p> <div xml:id="echoid-div1977" type="float" level="2" n="1"> <note position="left" xlink:label="note-0520-09" xlink:href="note-0520-09a" xml:space="preserve">TAB. V. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s13368" xml:space="preserve">Lentes vitreæ convexæ ſunt admodum vulgares; </s> <s xml:id="echoid-s13369" xml:space="preserve">de ha-<lb/>rum proprietatibus in ſequentibus agam <anchor type="note" xlink:href="" symbol="*"/>, hasque memorare <anchor type="note" xlink:label="note-0521-01a" xlink:href="note-0521-01"/> hujus loci non eſt; </s> <s xml:id="echoid-s13370" xml:space="preserve">in hoc experimento indigemus puncto ra-<lb/>diante, & </s> <s xml:id="echoid-s13371" xml:space="preserve">ſatis eſt hujus formationem memoraſſe.</s> <s xml:id="echoid-s13372" xml:space="preserve"/> </p> <div xml:id="echoid-div1978" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0521-01" xlink:href="note-0521-01a" xml:space="preserve">691. 697.</note> </div> <p> <s xml:id="echoid-s13373" xml:space="preserve">Detur Pixis P cujus latus abcd eſt vitreum, aquâ im-<lb/>pleatur; </s> <s xml:id="echoid-s13374" xml:space="preserve">radii, divergentes a puncto R, aquam ingreſſi mi-<lb/>nus divergentes erunt.</s> <s xml:id="echoid-s13375" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13376" xml:space="preserve">Quando radii convergentes, ut HD, I p, L q, habentes <lb/> <anchor type="note" xlink:label="note-0521-02a" xlink:href="note-0521-02"/> focum imaginarium f, è medio rariori Z in denſius X pene-<lb/> <anchor type="note" xlink:label="note-0521-03a" xlink:href="note-0521-03"/> trant, minus convergentes fiunt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s13377" xml:space="preserve">in focum F, magis <anchor type="note" xlink:label="note-0521-04a" xlink:href="note-0521-04"/> diſtantem a ſuperficie ES <anchor type="note" xlink:href="" symbol="*"/>, concurrunt ut patet hic appli- <anchor type="note" xlink:label="note-0521-05a" xlink:href="note-0521-05"/> cando demonſtrationem datam in n. </s> <s xml:id="echoid-s13378" xml:space="preserve">654.</s> <s xml:id="echoid-s13379" xml:space="preserve"/> </p> <div xml:id="echoid-div1979" type="float" level="2" n="3"> <note position="right" xlink:label="note-0521-02" xlink:href="note-0521-02a" xml:space="preserve">658.</note> <note position="right" xlink:label="note-0521-03" xlink:href="note-0521-03a" xml:space="preserve">TAB. V. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0521-04" xlink:href="note-0521-04a" xml:space="preserve">624.</note> <note symbol="*" position="right" xlink:label="note-0521-05" xlink:href="note-0521-05a" xml:space="preserve">652.</note> </div> <p> <s xml:id="echoid-s13380" xml:space="preserve">Radii ex puncto F procedentes, & </s> <s xml:id="echoid-s13381" xml:space="preserve">ex medio denſiori in <lb/> <anchor type="note" xlink:label="note-0521-06a" xlink:href="note-0521-06"/> rarius penetrantes, magis divergentes fiunt, & </s> <s xml:id="echoid-s13382" xml:space="preserve">moventur <lb/>quaſi ex f procederent; </s> <s xml:id="echoid-s13383" xml:space="preserve">quæ propoſitio eſt inverſa præce-<lb/>dentis, & </s> <s xml:id="echoid-s13384" xml:space="preserve">cum hac eodem Experimento confirmatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13385" xml:space="preserve"/> </p> <div xml:id="echoid-div1980" type="float" level="2" n="4"> <note position="right" xlink:label="note-0521-06" xlink:href="note-0521-06a" xml:space="preserve">659.</note> </div> <note symbol="*" position="right" xml:space="preserve">626.</note> </div> <div xml:id="echoid-div1982" type="section" level="1" n="490"> <head xml:id="echoid-head655" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s13386" xml:space="preserve">Eâdem, cum præcedenti Experimento, pixide P inſtituitur; <lb/></s> <s xml:id="echoid-s13387" xml:space="preserve"> <anchor type="note" xlink:label="note-0521-08a" xlink:href="note-0521-08"/> in hoc, lumen ſolare in cubiculum obſcurum intromittitur per <lb/>duo foramina in orbe mobili O, qui in feneſtra datur; </s> <s xml:id="echoid-s13388" xml:space="preserve">à ſpeculo <lb/>horizontaliter reflectantur radiiambo, & </s> <s xml:id="echoid-s13389" xml:space="preserve">per lentes convexas, <lb/>ſimiles tranſmittantur; </s> <s xml:id="echoid-s13390" xml:space="preserve">quo radii, ex quibus radii primi con-<lb/>ſtant, convergentes fiunt, habentes focos ad eandem diſtan-<lb/>tiam; </s> <s xml:id="echoid-s13391" xml:space="preserve">ſi autem radii convergentes in aquam, pixide conten-<lb/>tam, per latus vitreum abcd penetrent, ad majorem di-<lb/>ſtantiam colligentur; </s> <s xml:id="echoid-s13392" xml:space="preserve">quod clarè patet, comparando inter ſe <lb/>ſitus punctorum F in aëre & </s> <s xml:id="echoid-s13393" xml:space="preserve">f in aqua.</s> <s xml:id="echoid-s13394" xml:space="preserve"/> </p> <div xml:id="echoid-div1982" type="float" level="2" n="1"> <note position="right" xlink:label="note-0521-08" xlink:href="note-0521-08a" xml:space="preserve">TAB. V. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div1984" type="section" level="1" n="491"> <head xml:id="echoid-head656" xml:space="preserve">CAPUT VIII.</head> <head xml:id="echoid-head657" style="it" xml:space="preserve">De refractione luminis, poſitis mediis ſuperficie <lb/>ſphæricâ ſeparatis.</head> <p> <s xml:id="echoid-s13395" xml:space="preserve">SInt Media denſitate differentia X & </s> <s xml:id="echoid-s13396" xml:space="preserve">Z, hoc rarius illud <lb/> <anchor type="note" xlink:label="note-0521-09a" xlink:href="note-0521-09"/> denſius; </s> <s xml:id="echoid-s13397" xml:space="preserve">ſeparentur ſuperficie ſphæricâ ES, cujus cen-<lb/>trum eſt C, & </s> <s xml:id="echoid-s13398" xml:space="preserve">cujus convexitas eſt ad partem medii rarioris.</s> <s xml:id="echoid-s13399" xml:space="preserve"/> </p> <div xml:id="echoid-div1984" type="float" level="2" n="1"> <note position="right" xlink:label="note-0521-09" xlink:href="note-0521-09a" xml:space="preserve">TAB. VI. <lb/>fig. 1.</note> </div> <pb o="32" file="0522" n="573" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s13400" xml:space="preserve">Ut caſum ſimpliciſſimum ante alios examinemus, ponamus <lb/> <anchor type="note" xlink:label="note-0522-01a" xlink:href="note-0522-01"/> radios parallelos ut BO & </s> <s xml:id="echoid-s13401" xml:space="preserve">An, ex medio rariori in denſius <lb/>penetrantes, in memoratam convexam ſuperficiem incidere; <lb/></s> <s xml:id="echoid-s13402" xml:space="preserve">deturque inter hos BO, qui continuatus per centrum C <lb/>tranſit, & </s> <s xml:id="echoid-s13403" xml:space="preserve">perpendiculariter cadit in ſuperficiem ES; </s> <s xml:id="echoid-s13404" xml:space="preserve">ideo-<lb/>que a recta non deflectitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13405" xml:space="preserve">Radii omnes non nimium ab <anchor type="note" xlink:label="note-0522-02a" xlink:href="note-0522-02"/> hoc diſtantes ad hunc refractione medii denſioris accedunt, <lb/>& </s> <s xml:id="echoid-s13406" xml:space="preserve">in unum punctum F colliguntur. </s> <s xml:id="echoid-s13407" xml:space="preserve">Sit ex. </s> <s xml:id="echoid-s13408" xml:space="preserve">gr. </s> <s xml:id="echoid-s13409" xml:space="preserve">radius An, <lb/>qui refringitur per n F; </s> <s xml:id="echoid-s13410" xml:space="preserve">per punctum n ducatur ad centrum <lb/>C ſemidiameter C n continuata ad p; </s> <s xml:id="echoid-s13411" xml:space="preserve">cùm hæc perpendicu-<lb/>laris ſit ad ſuperficiem media dirimentem, angulus inciden-<lb/>tiæ eſt A np, æqualis angulo nCO: </s> <s xml:id="echoid-s13412" xml:space="preserve">angulus refractionis <lb/>eſt C n F. </s> <s xml:id="echoid-s13413" xml:space="preserve">Si arcus n O fuerit exiguus, anguli hi ſunt ut ho-<lb/>rum ſinus, quorum ratio eſt conſtans <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13414" xml:space="preserve">In eadem ergo ra- <anchor type="note" xlink:label="note-0522-03a" xlink:href="note-0522-03"/> tione creſcunt & </s> <s xml:id="echoid-s13415" xml:space="preserve">minuuntur hi anguli n CO & </s> <s xml:id="echoid-s13416" xml:space="preserve">CnF, ut & </s> <s xml:id="echoid-s13417" xml:space="preserve"><lb/>horum differentia angulus n FO, qui igitur ſequitur propor-<lb/>tionem arcus n O, menſuræ anguli n CO; </s> <s xml:id="echoid-s13418" xml:space="preserve">Quamdiu arcus <lb/>n O, 15. </s> <s xml:id="echoid-s13419" xml:space="preserve">gr. </s> <s xml:id="echoid-s13420" xml:space="preserve">non ſuperat, angulus nFO in eadem ratione cum <lb/>hoc arcu ſenſibiliter augetur & </s> <s xml:id="echoid-s13421" xml:space="preserve">minuitur; </s> <s xml:id="echoid-s13422" xml:space="preserve">ideoque omnes <lb/>radii inter A n & </s> <s xml:id="echoid-s13423" xml:space="preserve">BO, refractione, ſenſibiliter in punctum <lb/>F concurrunt.</s> <s xml:id="echoid-s13424" xml:space="preserve"/> </p> <div xml:id="echoid-div1985" type="float" level="2" n="2"> <note position="left" xlink:label="note-0522-01" xlink:href="note-0522-01a" xml:space="preserve">660.</note> <note symbol="*" position="left" xlink:label="note-0522-02" xlink:href="note-0522-02a" xml:space="preserve">629.</note> <note symbol="*" position="left" xlink:label="note-0522-03" xlink:href="note-0522-03a" xml:space="preserve">639.</note> </div> </div> <div xml:id="echoid-div1987" type="section" level="1" n="492"> <head xml:id="echoid-head658" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s13425" xml:space="preserve">Radius ſolaris cylindricus diametri unius pollicis, ex in-<lb/> <anchor type="note" xlink:label="note-0522-04a" xlink:href="note-0522-04"/> numeris aliis parallelis, propter immenſam Solis diſtantiam, <lb/>conſtans, in cubiculum obſcurum intromittitur, ut in exp. </s> <s xml:id="echoid-s13426" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s13427" xml:space="preserve">capitis præcedentis, & </s> <s xml:id="echoid-s13428" xml:space="preserve">a ſpeculo Shorizontaliter reflectitur.</s> <s xml:id="echoid-s13429" xml:space="preserve"/> </p> <div xml:id="echoid-div1987" type="float" level="2" n="1"> <note position="left" xlink:label="note-0522-04" xlink:href="note-0522-04a" xml:space="preserve">TAB. VI. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s13430" xml:space="preserve">Pixis P, latitudinis ad & </s> <s xml:id="echoid-s13431" xml:space="preserve">altitudinis ba circiter trium pol-<lb/>licum, longitudinis unius pedis, aquâ repletur. </s> <s xml:id="echoid-s13432" xml:space="preserve">In medio la-<lb/>teris abcd datur vitrum V; </s> <s xml:id="echoid-s13433" xml:space="preserve">eſt hoc ſphæræ portio, tenue, <lb/>& </s> <s xml:id="echoid-s13434" xml:space="preserve">ubique ejuſdem craſſitiei; </s> <s xml:id="echoid-s13435" xml:space="preserve">vulgo vitris talibus indices ob-<lb/>teguntur in horologiis portatilibus.</s> <s xml:id="echoid-s13436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13437" xml:space="preserve">Diſponitur vitrum V, ut pars convexa ſit exterior, & </s> <s xml:id="echoid-s13438" xml:space="preserve">a-<lb/>qua, cavitatem vitri implens, adipiſcatur ſuperficiem ſphæri-<lb/>cam convexam. </s> <s xml:id="echoid-s13439" xml:space="preserve">Si radii memorati pixidem per hoc vitrum <lb/>intrent, propter vitri tenuitatem & </s> <s xml:id="echoid-s13440" xml:space="preserve">quia hoc faciebus pa-<lb/>rallelis terminatur, non ſenſibilis datur mutatio in motu lu-<lb/>minis ex vitri refractione, & </s> <s xml:id="echoid-s13441" xml:space="preserve">lumen aquam intrat, eodem <pb file="0523" n="574"/> <pb file="0523a" n="575"/> <anchor type="figure" xlink:label="fig-0523a-01a" xlink:href="fig-0523a-01"/> <pb file="0524" n="576"/> <pb o="(33)" file="0525" n="577" rhead="MATHEMATICA, LIB. III. CAP. VIII."/> modo ac ſi vitrum non daretur. </s> <s xml:id="echoid-s13442" xml:space="preserve">Diſponatur pixis, ut unus <lb/>ex radiis per centrum ſuperficiei ſphæricæ aquæ tranſeat, a-<lb/>lii ad hunc accedent, & </s> <s xml:id="echoid-s13443" xml:space="preserve">in F cum hoc concurrent.</s> <s xml:id="echoid-s13444" xml:space="preserve"/> </p> <div xml:id="echoid-div1988" type="float" level="2" n="2"> <figure xlink:label="fig-0523a-01" xlink:href="fig-0523a-01a"> <image file="0523a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0523a-01"/> </figure> </div> <p> <s xml:id="echoid-s13445" xml:space="preserve">Detur iterum X medium denſius, Z rarius, ſeparentur <lb/> <anchor type="note" xlink:label="note-0525-01a" xlink:href="note-0525-01"/> ſuperficie ſphæricâ ES, cujus centrum eſt C, & </s> <s xml:id="echoid-s13446" xml:space="preserve">cujus con-<lb/>vexitas eſt ad partem medii rarioris; </s> <s xml:id="echoid-s13447" xml:space="preserve">Ex puncto radiante R <lb/> <anchor type="note" xlink:label="note-0525-02a" xlink:href="note-0525-02"/> procedant radii, & </s> <s xml:id="echoid-s13448" xml:space="preserve">in medium denſius per memoratam ſuperfi-<lb/>ciem penetrent, ita ut inter hos radius RO continuatus per <lb/>centrum C tranſeat; </s> <s xml:id="echoid-s13449" xml:space="preserve">hic non refringitur dum aquam intrat, <lb/>& </s> <s xml:id="echoid-s13450" xml:space="preserve">ad hunc refractione reliqui omnes accedunt, & </s> <s xml:id="echoid-s13451" xml:space="preserve">quando <lb/>parum diſperguntur in unum punctum, ut F, colliguntur, eo-<lb/>dem modo ac de radiis parallelis dictum; </s> <s xml:id="echoid-s13452" xml:space="preserve">cum hac differen-<lb/>tiâ, quod focus F in hoc caſu magis diſtet. </s> <s xml:id="echoid-s13453" xml:space="preserve">Eadem etiam de-<lb/>monſtratio hìc locum habet ac circa radios parallelos, quæ <lb/>hoc fundamento nititur, quod angulus incidentiæ, cum ar-<lb/>cu n O in eadem ratione creſcat, quod & </s> <s xml:id="echoid-s13454" xml:space="preserve">hìc obtinet, ſiarcus <lb/>n O gradus 15. </s> <s xml:id="echoid-s13455" xml:space="preserve">non ſuperet. </s> <s xml:id="echoid-s13456" xml:space="preserve">Detur radius R n, per n ex <lb/>centro C ducatur C np: </s> <s xml:id="echoid-s13457" xml:space="preserve">angulus R np erit angulus inci-<lb/>dentiæ; </s> <s xml:id="echoid-s13458" xml:space="preserve">dividatur hic in duas partes lineâ nq, parallelâ li-<lb/>neæ ROC; </s> <s xml:id="echoid-s13459" xml:space="preserve">pars pnq æqualis eſt angulo n CO, qui arcu <lb/>n O menſuratur, & </s> <s xml:id="echoid-s13460" xml:space="preserve">qui ideo cum hoc arcu eandem ſequitur <lb/>proportionem; </s> <s xml:id="echoid-s13461" xml:space="preserve">quam etiam, poſito hoc exiguo, ſequitur <lb/>angulus n RO, æqualis ſecundæ parti anguli incidentiæ, <lb/>qui igitur in totum etiam cum arcu n O in eadem ratione <lb/>creſcit & </s> <s xml:id="echoid-s13462" xml:space="preserve">minuitur, quæ enim ratio in ſingulis partibus lo-<lb/>cum habet, reſpectu totius etiam obtinet.</s> <s xml:id="echoid-s13463" xml:space="preserve"/> </p> <div xml:id="echoid-div1989" type="float" level="2" n="3"> <note position="right" xlink:label="note-0525-01" xlink:href="note-0525-01a" xml:space="preserve">TAB. VI. <lb/>fig. 3.</note> <note position="right" xlink:label="note-0525-02" xlink:href="note-0525-02a" xml:space="preserve">661.</note> </div> <p> <s xml:id="echoid-s13464" xml:space="preserve">Similis demonſtratio poteſt applicari radiis quibuſcunque <lb/> <anchor type="note" xlink:label="note-0525-03a" xlink:href="note-0525-03"/> divergentibus, aut convergentibus, qui in quocunque caſu <lb/>in ſuperficie ſphæricâ refringuntur, & </s> <s xml:id="echoid-s13465" xml:space="preserve">qui ut hac demonſtra-<lb/>tione conſtat, in exiguâ diſperſione, focum habent aut ve-<lb/>rum, aut imaginarium, aut paralleli ſunt inter ſe. </s> <s xml:id="echoid-s13466" xml:space="preserve">Quod in <lb/>genere hic notaſſe ſufficiat.</s> <s xml:id="echoid-s13467" xml:space="preserve"/> </p> <div xml:id="echoid-div1990" type="float" level="2" n="4"> <note position="right" xlink:label="note-0525-03" xlink:href="note-0525-03a" xml:space="preserve">662.</note> </div> <p> <s xml:id="echoid-s13468" xml:space="preserve">Focus F radiorum ab R procedentium, accedente R rece-<lb/> <anchor type="note" xlink:label="note-0525-04a" xlink:href="note-0525-04"/> dit & </s> <s xml:id="echoid-s13469" xml:space="preserve">vice verſa. </s> <s xml:id="echoid-s13470" xml:space="preserve">Accedente puncto radiante, ſi maneat <lb/>punctum n, augetur angulus incidentiæ, quo creſcente, au-<lb/>getur etiam angulus refractionis F n C, & </s> <s xml:id="echoid-s13471" xml:space="preserve">n F ad majorem <lb/>diſtantiam interſecat RC.</s> <s xml:id="echoid-s13472" xml:space="preserve"/> </p> <div xml:id="echoid-div1991" type="float" level="2" n="5"> <note position="right" xlink:label="note-0525-04" xlink:href="note-0525-04a" xml:space="preserve">663.</note> </div> <pb o="(34)" file="0526" n="578" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div1993" type="section" level="1" n="493"> <head xml:id="echoid-head659" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s13473" xml:space="preserve">Differt hoc experimentum cum præcedenti in eo ſolo, <lb/> <anchor type="note" xlink:label="note-0526-01a" xlink:href="note-0526-01"/> quod radius ſolaris cylindricus, horizontaliter reflexus, tranſ-<lb/>mittatur per lentem convexam in tabella T, ut in experi-<lb/>mentis capitis præcedentis, quo formatur punctum radians <lb/>R. </s> <s xml:id="echoid-s13474" xml:space="preserve">Radii ab hoc procedentes in aquâ colliguntur in F ad ma-<lb/>jorem diſtantiam, quàm ſi paralleli forent.</s> <s xml:id="echoid-s13475" xml:space="preserve"/> </p> <div xml:id="echoid-div1993" type="float" level="2" n="1"> <note position="left" xlink:label="note-0526-01" xlink:href="note-0526-01a" xml:space="preserve">TAB. VI. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13476" xml:space="preserve">Motu tabellæ T movetur punctum R; </s> <s xml:id="echoid-s13477" xml:space="preserve">recedente hoc a <lb/>ſuperficie media dirimente, ad hanc accedit F; </s> <s xml:id="echoid-s13478" xml:space="preserve">contra ac-<lb/>cedente R recedit F.</s> <s xml:id="echoid-s13479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13480" xml:space="preserve">Ita poteſt admoveri punctum radians ad ſuperficiem me-<lb/> <anchor type="note" xlink:label="note-0526-02a" xlink:href="note-0526-02"/> dia dirimentem, ut focus ad diſtantiam infinitam recedat, <lb/>id eſt, ut radii refracti paralleli fiant.</s> <s xml:id="echoid-s13481" xml:space="preserve"/> </p> <div xml:id="echoid-div1994" type="float" level="2" n="2"> <note position="left" xlink:label="note-0526-02" xlink:href="note-0526-02a" xml:space="preserve">664.</note> </div> </div> <div xml:id="echoid-div1996" type="section" level="1" n="494"> <head xml:id="echoid-head660" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s13482" xml:space="preserve">Rebus, ut in Experimento præcedenti, diſpoſitis; </s> <s xml:id="echoid-s13483" xml:space="preserve">motu <lb/> <anchor type="note" xlink:label="note-0526-03a" xlink:href="note-0526-03"/> tabellæ T admoveatur R ad pixidem, & </s> <s xml:id="echoid-s13484" xml:space="preserve">in tali ſitu facile <lb/>diſponetur, ut refracti radii paralleli ſint.</s> <s xml:id="echoid-s13485" xml:space="preserve"/> </p> <div xml:id="echoid-div1996" type="float" level="2" n="1"> <note position="left" xlink:label="note-0526-03" xlink:href="note-0526-03a" xml:space="preserve">TAB. VI. <lb/>fig. 5.</note> </div> </div> <div xml:id="echoid-div1998" type="section" level="1" n="495"> <head xml:id="echoid-head661" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s13486" xml:space="preserve">Iiſdem manentibus, ſi magis accedat ad pixidem punctum <lb/> <anchor type="note" xlink:label="note-0526-04a" xlink:href="note-0526-04"/> radians R, divergentes fient radii refracti, minus tamen <lb/> <anchor type="note" xlink:label="note-0526-05a" xlink:href="note-0526-05"/> divergentes quam incidentes;</s> <s xml:id="echoid-s13487" xml:space="preserve"/> </p> <div xml:id="echoid-div1998" type="float" level="2" n="1"> <note position="left" xlink:label="note-0526-04" xlink:href="note-0526-04a" xml:space="preserve">665.</note> <note position="left" xlink:label="note-0526-05" xlink:href="note-0526-05a" xml:space="preserve">TAB. VII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s13488" xml:space="preserve">Si radii, qui ex medio rariori in denſius per ſuperficiem <lb/> <anchor type="note" xlink:label="note-0526-06a" xlink:href="note-0526-06"/> convexam intrant, convergentes ſint, & </s> <s xml:id="echoid-s13489" xml:space="preserve">ad centrum ſuperfi-<lb/>ciei dirigantur, nullam patiuntur refractionem <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13490" xml:space="preserve">Si ver- <anchor type="note" xlink:label="note-0526-07a" xlink:href="note-0526-07"/> ſus aliud punctum dirigantur, cùm verſus perpendicularem <lb/> <anchor type="note" xlink:label="note-0526-08a" xlink:href="note-0526-08"/> refringantur <anchor type="note" xlink:href="" symbol="*"/>, ita inflectuntur radii, ut focus radiorum ho- <anchor type="note" xlink:label="note-0526-09a" xlink:href="note-0526-09"/> rum convergentium ſemper detur inter centrum ſuperficiei <lb/>media dirimentis, (ad quod perpendiculares omnes diri-<lb/>guntur), & </s> <s xml:id="echoid-s13491" xml:space="preserve">punctum verſus quod radii incidentes tendunt. <lb/></s> <s xml:id="echoid-s13492" xml:space="preserve">Id eſt, ſi focus imaginarius incidentium detur ad minorem <lb/>diſtantiam quàm centrum, minus convergentes ſunt radii re-<lb/>fracti: </s> <s xml:id="echoid-s13493" xml:space="preserve">ſi ultra centrum detur hicce focus imaginarius, magis <lb/>convergentes erunt radii refracti.</s> <s xml:id="echoid-s13494" xml:space="preserve"/> </p> <div xml:id="echoid-div1999" type="float" level="2" n="2"> <note position="left" xlink:label="note-0526-06" xlink:href="note-0526-06a" xml:space="preserve">666.</note> <note symbol="*" position="left" xlink:label="note-0526-07" xlink:href="note-0526-07a" xml:space="preserve">629.</note> <note position="left" xlink:label="note-0526-08" xlink:href="note-0526-08a" xml:space="preserve">667.</note> <note symbol="*" position="left" xlink:label="note-0526-09" xlink:href="note-0526-09a" xml:space="preserve">624.</note> </div> </div> <div xml:id="echoid-div2001" type="section" level="1" n="496"> <head xml:id="echoid-head662" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s13495" xml:space="preserve">Iiſdem adhibitis, quæ in experimentis præcedentibus, faci-<lb/> <anchor type="note" xlink:label="note-0526-10a" xlink:href="note-0526-10"/> le hæ propoſitiones experimentis confirmantur; </s> <s xml:id="echoid-s13496" xml:space="preserve">ita enim <lb/>diſponi poteſt tabella T, ut radii convergentes aquam in- <pb file="0527" n="579"/> <pb file="0527a" n="580"/> <anchor type="figure" xlink:label="fig-0527a-01a" xlink:href="fig-0527a-01"/> <pb file="0528" n="581"/> <pb o="(35)" file="0529" n="582" rhead="MATHEMATICA. LIB. III. CAP. VIII."/> trent, & </s> <s xml:id="echoid-s13497" xml:space="preserve">horum focus imaginarius detur ad diſtantiam <lb/>quamcunque in aquâ.</s> <s xml:id="echoid-s13498" xml:space="preserve"/> </p> <div xml:id="echoid-div2001" type="float" level="2" n="1"> <note position="left" xlink:label="note-0526-10" xlink:href="note-0526-10a" xml:space="preserve">TAB. VII. <lb/>fig. 2.</note> <figure xlink:label="fig-0527a-01" xlink:href="fig-0527a-01a"> <image file="0527a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0527a-01"/> </figure> </div> <p> <s xml:id="echoid-s13499" xml:space="preserve">Ex hucuſque dictis, quæ in motu radiorum contrario ob <lb/> <anchor type="note" xlink:label="note-0529-01a" xlink:href="note-0529-01"/> tinent facile determinamus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13500" xml:space="preserve">id eſt, motum radiorum ex <anchor type="note" xlink:label="note-0529-02a" xlink:href="note-0529-02"/> medio denſiori in rarius, manente ſuperficie convexâ ad par-<lb/>tem medii rarioris.</s> <s xml:id="echoid-s13501" xml:space="preserve"/> </p> <div xml:id="echoid-div2002" type="float" level="2" n="2"> <note position="right" xlink:label="note-0529-01" xlink:href="note-0529-01a" xml:space="preserve">668.</note> <note symbol="*" position="right" xlink:label="note-0529-02" xlink:href="note-0529-02a" xml:space="preserve">626.</note> </div> <p style="it"> <s xml:id="echoid-s13502" xml:space="preserve">Radii paralleli poſt refractionem in focum concurrunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13503" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">664.</note> <p style="it"> <s xml:id="echoid-s13504" xml:space="preserve">Etiam in punctum aut focum conveniunt radii ex puncto <lb/> <anchor type="note" xlink:label="note-0529-04a" xlink:href="note-0529-04"/> radiante manantes, <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s13505" xml:space="preserve">accedente hoc recedit illud, &</s> <s xml:id="echoid-s13506" xml:space="preserve"> <anchor type="note" xlink:label="note-0529-05a" xlink:href="note-0529-05"/> contra <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13507" xml:space="preserve"/> </p> <div xml:id="echoid-div2003" type="float" level="2" n="3"> <note position="right" xlink:label="note-0529-04" xlink:href="note-0529-04a" xml:space="preserve">669.</note> <note symbol="*" position="right" xlink:label="note-0529-05" xlink:href="note-0529-05a" xml:space="preserve">661.</note> </div> <note symbol="*" position="right" xml:space="preserve">663.</note> <p> <s xml:id="echoid-s13508" xml:space="preserve">Ita poteſt diſponi punctum radians, ut focus ad diſtantiam <lb/> <anchor type="note" xlink:label="note-0529-07a" xlink:href="note-0529-07"/> infinitam detur, id eſt, ut radii refracti paralleli ſint. </s> <s xml:id="echoid-s13509" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13510" xml:space="preserve"/> </p> <div xml:id="echoid-div2004" type="float" level="2" n="4"> <note position="right" xlink:label="note-0529-07" xlink:href="note-0529-07a" xml:space="preserve">670.</note> </div> <note symbol="*" position="right" xml:space="preserve">660.</note> <p style="it"> <s xml:id="echoid-s13511" xml:space="preserve">Si ulterius accedat punctum radians, refracti divergen-<lb/> <anchor type="note" xlink:label="note-0529-09a" xlink:href="note-0529-09"/> tes ſunt; </s> <s xml:id="echoid-s13512" xml:space="preserve">minus divergentes quam incidentes, ſi punctum <lb/>radians magis diſtet à ſuperficie quàm centrum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13513" xml:space="preserve"/> </p> <div xml:id="echoid-div2005" type="float" level="2" n="5"> <note position="right" xlink:label="note-0529-09" xlink:href="note-0529-09a" xml:space="preserve">671.</note> </div> <note symbol="*" position="right" xml:space="preserve">667.</note> <p style="it"> <s xml:id="echoid-s13514" xml:space="preserve">Si autem punctum radians detur inter ſuperficiem & </s> <s xml:id="echoid-s13515" xml:space="preserve">cen-<lb/> <anchor type="note" xlink:label="note-0529-11a" xlink:href="note-0529-11"/> trum, radii refracti magis divergentes erunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13516" xml:space="preserve"/> </p> <div xml:id="echoid-div2006" type="float" level="2" n="6"> <note position="right" xlink:label="note-0529-11" xlink:href="note-0529-11a" xml:space="preserve">672.</note> </div> <note symbol="*" position="right" xml:space="preserve">667.</note> <p> <s xml:id="echoid-s13517" xml:space="preserve">Si radii fuerint convergentes, magis in omni caſu fiunt <lb/> <anchor type="note" xlink:label="note-0529-13a" xlink:href="note-0529-13"/> convergentes, quod ex refractione a perpendiculari <anchor type="note" xlink:href="" symbol="*"/> ſequi- <anchor type="note" xlink:label="note-0529-14a" xlink:href="note-0529-14"/> tur, & </s> <s xml:id="echoid-s13518" xml:space="preserve">etiam deducitur ex n. </s> <s xml:id="echoid-s13519" xml:space="preserve">665.</s> <s xml:id="echoid-s13520" xml:space="preserve"/> </p> <div xml:id="echoid-div2007" type="float" level="2" n="7"> <note position="right" xlink:label="note-0529-13" xlink:href="note-0529-13a" xml:space="preserve">673.</note> <note symbol="*" position="right" xlink:label="note-0529-14" xlink:href="note-0529-14a" xml:space="preserve">625.</note> </div> <p> <s xml:id="echoid-s13521" xml:space="preserve">Ponamus iterum radios ex medio rariori Z in denſius X <lb/> <anchor type="note" xlink:label="note-0529-15a" xlink:href="note-0529-15"/> intrare, cavitatem autem ſuperficiei ſphæricæ ES, media ſe-<lb/> <anchor type="note" xlink:label="note-0529-16a" xlink:href="note-0529-16"/> parantis, dari ad partem medii rarioris. </s> <s xml:id="echoid-s13522" xml:space="preserve">Si radii fuerint <lb/>paralleli, ut BO, A n; </s> <s xml:id="echoid-s13523" xml:space="preserve">BO, qui per centrum C ſuperficiei <lb/>ES tranſit, nullam patitur refractionem; </s> <s xml:id="echoid-s13524" xml:space="preserve">A n verò ad per-<lb/>pendicularem C p per n G refringitur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s13525" xml:space="preserve">verſus Z conti- <anchor type="note" xlink:label="note-0529-17a" xlink:href="note-0529-17"/> nuatus interſecat BCO in f, quod etiam reſpectu radio-<lb/>rum inter BO & </s> <s xml:id="echoid-s13526" xml:space="preserve">A n obtinet <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13527" xml:space="preserve">fiunt ergo hi radii diver- <anchor type="note" xlink:label="note-0529-18a" xlink:href="note-0529-18"/> gentes, hàbentes focum imaginarium f in medio rariori.</s> <s xml:id="echoid-s13528" xml:space="preserve"/> </p> <div xml:id="echoid-div2008" type="float" level="2" n="8"> <note position="right" xlink:label="note-0529-15" xlink:href="note-0529-15a" xml:space="preserve">674.</note> <note position="right" xlink:label="note-0529-16" xlink:href="note-0529-16a" xml:space="preserve">TAB. VII. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0529-17" xlink:href="note-0529-17a" xml:space="preserve">624.</note> <note symbol="*" position="right" xlink:label="note-0529-18" xlink:href="note-0529-18a" xml:space="preserve">662.</note> </div> </div> <div xml:id="echoid-div2010" type="section" level="1" n="497"> <head xml:id="echoid-head663" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s13529" xml:space="preserve">In eo ſolo experimentum hoc a primo hujus capitis dif-<lb/> <anchor type="note" xlink:label="note-0529-19a" xlink:href="note-0529-19"/> fert, quod vitrum V, habeat cavitatem ad partem aëris, de <lb/>cætero pixis P à prima pixide non differt; </s> <s xml:id="echoid-s13530" xml:space="preserve">In hoc caſu ra-<lb/>dii, ex quibus radius cylindricus conſtat, in aquâ diſpergun-<lb/>tur.</s> <s xml:id="echoid-s13531" xml:space="preserve"/> </p> <div xml:id="echoid-div2010" type="float" level="2" n="1"> <note position="right" xlink:label="note-0529-19" xlink:href="note-0529-19a" xml:space="preserve">TAB. VII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13532" xml:space="preserve">Si à puncto radiante in CB ultra C, radii emanant, mi-<lb/> <anchor type="note" xlink:label="note-0529-20a" xlink:href="note-0529-20"/> nuitur angulus incidentiæ A n C, & </s> <s xml:id="echoid-s13533" xml:space="preserve">idcirco etiam angulus <lb/> <anchor type="note" xlink:label="note-0529-21a" xlink:href="note-0529-21"/> <pb o="(36)" file="0530" n="583" rhead="PHYSICES ELEMENTA"/> refractionis G np; </s> <s xml:id="echoid-s13534" xml:space="preserve">id eſt, radii refracti magis divergentes <lb/>fiunt, & </s> <s xml:id="echoid-s13535" xml:space="preserve">ad C accedit focus imaginarius f <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13536" xml:space="preserve">donec acceſſu <anchor type="note" xlink:label="note-0530-01a" xlink:href="note-0530-01"/> puncti radiantis tandem hoc coincidat cum foco imaginario <lb/>in C; </s> <s xml:id="echoid-s13537" xml:space="preserve">in hoc enim caſu radii nullam patiuntur refractionem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13538" xml:space="preserve"/> </p> <div xml:id="echoid-div2011" type="float" level="2" n="2"> <note position="right" xlink:label="note-0529-20" xlink:href="note-0529-20a" xml:space="preserve">675.</note> <note position="right" xlink:label="note-0529-21" xlink:href="note-0529-21a" xml:space="preserve">TAB. VII. <lb/>fig. 3.</note> <note symbol="*" position="left" xlink:label="note-0530-01" xlink:href="note-0530-01a" xml:space="preserve">646.</note> </div> <note symbol="*" position="left" xml:space="preserve">629.</note> <p> <s xml:id="echoid-s13539" xml:space="preserve">Si ulterius accedat punctum radians, inter C & </s> <s xml:id="echoid-s13540" xml:space="preserve">O ma-<lb/> <anchor type="note" xlink:label="note-0530-03a" xlink:href="note-0530-03"/> gis diſtet focus imaginarius ab O, quàm punctum radians, in-<lb/>ter hoc enim & </s> <s xml:id="echoid-s13541" xml:space="preserve">C ſemper ille datur, propter angulos refra-<lb/>ctionis minores angulis incidentiæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13542" xml:space="preserve"/> </p> <div xml:id="echoid-div2012" type="float" level="2" n="3"> <note position="left" xlink:label="note-0530-03" xlink:href="note-0530-03a" xml:space="preserve">676.</note> </div> <note symbol="*" position="left" xml:space="preserve">624.</note> </div> <div xml:id="echoid-div2014" type="section" level="1" n="498"> <head xml:id="echoid-head664" xml:space="preserve"><emph style="sc">Experimentum</emph>. 7.</head> <p> <s xml:id="echoid-s13543" xml:space="preserve">Si eadem dentur, quæ in experimento præcedenti, ad-<lb/>hibitâ tabellâ cum lente convexâ, de qua ſæpius jam di-<lb/>ctum, ad punctum radians formandum, facilia ſunt experi-<lb/>menta circa has propoſitiones.</s> <s xml:id="echoid-s13544" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s13545" xml:space="preserve">Si radii fuerint convergentes, & </s> <s xml:id="echoid-s13546" xml:space="preserve">punctum concurſus detur <lb/> <anchor type="note" xlink:label="note-0530-05a" xlink:href="note-0530-05"/> in medio denſiori, in viciniis ſuperficiei media ſeparantis, re-<lb/>fracti radii etiam convergunt, ſed minus convergunt, quàm <lb/>incidentes.</s> <s xml:id="echoid-s13547" xml:space="preserve"/> </p> <div xml:id="echoid-div2014" type="float" level="2" n="1"> <note position="left" xlink:label="note-0530-05" xlink:href="note-0530-05a" xml:space="preserve">677.</note> </div> <p> <s xml:id="echoid-s13548" xml:space="preserve">Si ab O magis ac magis recedat focus imaginarius radio-<lb/>rum incidentium, id eſt, ſi hi minus convergant, etiam mi-<lb/> <anchor type="note" xlink:label="note-0530-06a" xlink:href="note-0530-06"/> nus convergent radii refracti; </s> <s xml:id="echoid-s13549" xml:space="preserve">donec, receſſu foci imagina-<lb/>rii, refracti paralleli ſint.</s> <s xml:id="echoid-s13550" xml:space="preserve"/> </p> <div xml:id="echoid-div2015" type="float" level="2" n="2"> <note position="left" xlink:label="note-0530-06" xlink:href="note-0530-06a" xml:space="preserve">678.</note> </div> <p style="it"> <s xml:id="echoid-s13551" xml:space="preserve">In ulteriori receſſu foci imaginarii divergentes fiunt refra-<lb/> <anchor type="note" xlink:label="note-0530-07a" xlink:href="note-0530-07"/> cti radii.</s> <s xml:id="echoid-s13552" xml:space="preserve"/> </p> <div xml:id="echoid-div2016" type="float" level="2" n="3"> <note position="left" xlink:label="note-0530-07" xlink:href="note-0530-07a" xml:space="preserve">679.</note> </div> </div> <div xml:id="echoid-div2018" type="section" level="1" n="499"> <head xml:id="echoid-head665" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s13553" xml:space="preserve">In hoc ad pixidem ita admovenda eſt tabella T, ut ra-<lb/> <anchor type="note" xlink:label="note-0530-08a" xlink:href="note-0530-08"/> dii convergentes aquam intrent; </s> <s xml:id="echoid-s13554" xml:space="preserve">& </s> <s xml:id="echoid-s13555" xml:space="preserve">in motu tabellæ prædi-<lb/>cta ad oculum patent.</s> <s xml:id="echoid-s13556" xml:space="preserve"/> </p> <div xml:id="echoid-div2018" type="float" level="2" n="1"> <note position="left" xlink:label="note-0530-08" xlink:href="note-0530-08a" xml:space="preserve">TAB. VII. <lb/>fig 5.</note> </div> <p> <s xml:id="echoid-s13557" xml:space="preserve">Radii, qui e medio denſiori in rarius penetrant, manente <lb/> <anchor type="note" xlink:label="note-0530-09a" xlink:href="note-0530-09"/> ſuperficie cavâ ad partem hujus medii, iiſdem fere legibus <lb/>ſubjiciuntur.</s> <s xml:id="echoid-s13558" xml:space="preserve"/> </p> <div xml:id="echoid-div2019" type="float" level="2" n="2"> <note position="left" xlink:label="note-0530-09" xlink:href="note-0530-09a" xml:space="preserve">680.</note> </div> <p style="it"> <s xml:id="echoid-s13559" xml:space="preserve">Radii paralleli refractione divergunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13560" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">678. 626.</note> <p style="it"> <s xml:id="echoid-s13561" xml:space="preserve">Si à puncto radianti procedant, magis ſunt divergentes <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13562" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">681.</note> <note symbol="*" position="left" xml:space="preserve">677.</note> <p style="it"> <s xml:id="echoid-s13563" xml:space="preserve">Et cum acceſſu puncti radiantis continuo magis ac magïs <lb/> <anchor type="note" xlink:label="note-0530-13a" xlink:href="note-0530-13"/> divergunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13564" xml:space="preserve"/> </p> <div xml:id="echoid-div2020" type="float" level="2" n="3"> <note position="left" xlink:label="note-0530-13" xlink:href="note-0530-13a" xml:space="preserve">682.</note> </div> <note symbol="*" position="left" xml:space="preserve">678.</note> <p style="it"> <s xml:id="echoid-s13565" xml:space="preserve">Convergentes radii, qui ad centrum ſuperficiei ſphæricæ <lb/> <anchor type="note" xlink:label="note-0530-15a" xlink:href="note-0530-15"/> tendunt, nullam ſubeunt mutationem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13566" xml:space="preserve"/> </p> <div xml:id="echoid-div2021" type="float" level="2" n="4"> <note position="left" xlink:label="note-0530-15" xlink:href="note-0530-15a" xml:space="preserve">683.</note> </div> <note symbol="*" position="left" xml:space="preserve">629.</note> <p style="it"> <s xml:id="echoid-s13567" xml:space="preserve">Si magis aut minus convergant, focus imaginarius inciden-<lb/> <anchor type="note" xlink:label="note-0530-17a" xlink:href="note-0530-17"/> <pb file="0531" n="584"/> <pb file="0531a" n="585"/> <anchor type="figure" xlink:label="fig-0531a-01a" xlink:href="fig-0531a-01"/> <pb file="0532" n="586"/> <pb o="(37)" file="0533" n="587" rhead="MATHEMATICA LIB. III. CAP. VIII."/> tium ſemper datur inter centrum ſuperficiei media ſeparan-<lb/> <anchor type="note" xlink:label="note-0533-01a" xlink:href="note-0533-01"/> tis, & </s> <s xml:id="echoid-s13568" xml:space="preserve">focum refractorum <anchor type="note" xlink:href="" symbol="*"/>, qui poteſt in infinitum recedere, <anchor type="note" xlink:label="note-0533-02a" xlink:href="note-0533-02"/> ita ut radii refracti paralleli ſint <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13569" xml:space="preserve"/> </p> <div xml:id="echoid-div2022" type="float" level="2" n="5"> <note position="left" xlink:label="note-0530-17" xlink:href="note-0530-17a" xml:space="preserve">684.</note> <figure xlink:label="fig-0531a-01" xlink:href="fig-0531a-01a"> <image file="0531a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0531a-01"/> </figure> <note position="right" xlink:label="note-0533-01" xlink:href="note-0533-01a" xml:space="preserve">685.</note> <note symbol="*" position="right" xlink:label="note-0533-02" xlink:href="note-0533-02a" xml:space="preserve">675. 676.</note> </div> <note symbol="*" position="right" xml:space="preserve">674.</note> <p> <s xml:id="echoid-s13570" xml:space="preserve">Huc uſque conſideravimus radios parum ad ſuperfi-<lb/>ciem media ſeparantem inclinatos; </s> <s xml:id="echoid-s13571" xml:space="preserve">nam de incidentibus <lb/>egimus, inter quos datur radius ad ſeparationem mediorum <lb/>perpendicularem, & </s> <s xml:id="echoid-s13572" xml:space="preserve">qui parum diſperguntur. </s> <s xml:id="echoid-s13573" xml:space="preserve">In radiis <lb/> <anchor type="note" xlink:label="note-0533-04a" xlink:href="note-0533-04"/> obliquis fere eædem propoſitiones locum habent, in hoc tamen <lb/>caſu omnes inflectuntur, quod in directis non æquè; </s> <s xml:id="echoid-s13574" xml:space="preserve">radius <lb/>enim ad ſuperficiem perpendicularis non inflectitur. </s> <s xml:id="echoid-s13575" xml:space="preserve">In ob-<lb/> <anchor type="note" xlink:label="note-0533-05a" xlink:href="note-0533-05"/> liquis etiam omnes majorem patiuntur refractionem, id eſt, <lb/>magis ad ſe mutuò aut à ſe mutuò radii inter ſe vicini infle-<lb/>ctuntur, quàm in directis, poſitis iiſdem circumſtantiis.</s> <s xml:id="echoid-s13576" xml:space="preserve"/> </p> <div xml:id="echoid-div2023" type="float" level="2" n="6"> <note position="right" xlink:label="note-0533-04" xlink:href="note-0533-04a" xml:space="preserve">686.</note> <note position="right" xlink:label="note-0533-05" xlink:href="note-0533-05a" xml:space="preserve">687.</note> </div> <p> <s xml:id="echoid-s13577" xml:space="preserve">Sit Z medium rarius, X denſius, ES ſuperficies cujus <lb/> <anchor type="note" xlink:label="note-0533-06a" xlink:href="note-0533-06"/> centrum C, quæ media ſeparat; </s> <s xml:id="echoid-s13578" xml:space="preserve">radii A n, B m paralleli <lb/>concurrunt in F. </s> <s xml:id="echoid-s13579" xml:space="preserve">Radii, qui procedunt ex puncto radian-<lb/>te R, concurrunt in focum f.</s> <s xml:id="echoid-s13580" xml:space="preserve"/> </p> <div xml:id="echoid-div2024" type="float" level="2" n="7"> <note position="right" xlink:label="note-0533-06" xlink:href="note-0533-06a" xml:space="preserve">TAB. VIII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s13581" xml:space="preserve">Si convertatur ſuperficies, ut cavitas ſit ad partem medii <lb/> <anchor type="note" xlink:label="note-0533-07a" xlink:href="note-0533-07"/> rarioris, radii A n & </s> <s xml:id="echoid-s13582" xml:space="preserve">B m paralleli habebunt focum imagi-<lb/>narium in f; </s> <s xml:id="echoid-s13583" xml:space="preserve">hujus autem diſtantia a ſuperficie ES, ut & </s> <s xml:id="echoid-s13584" xml:space="preserve"><lb/>memoratorum focorum F & </s> <s xml:id="echoid-s13585" xml:space="preserve">f in fig. </s> <s xml:id="echoid-s13586" xml:space="preserve">1. </s> <s xml:id="echoid-s13587" xml:space="preserve">minor eſt, quam ſi <lb/>radii forent directi.</s> <s xml:id="echoid-s13588" xml:space="preserve"/> </p> <div xml:id="echoid-div2025" type="float" level="2" n="8"> <note position="right" xlink:label="note-0533-07" xlink:href="note-0533-07a" xml:space="preserve">TAB. VIII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s13589" xml:space="preserve">Corporis lucidi ſingula puncta ſunt puncta radiantia & </s> <s xml:id="echoid-s13590" xml:space="preserve">ha-<lb/> <anchor type="note" xlink:label="note-0533-08a" xlink:href="note-0533-08"/> bent ſingula ſuum focum. </s> <s xml:id="echoid-s13591" xml:space="preserve">Quod dat explicationem experi-<lb/>menti ſequentis, quod, quæ deradiis obliquis dicta ſunt, con-<lb/>firmat.</s> <s xml:id="echoid-s13592" xml:space="preserve"/> </p> <div xml:id="echoid-div2026" type="float" level="2" n="9"> <note position="right" xlink:label="note-0533-08" xlink:href="note-0533-08a" xml:space="preserve">688.</note> </div> </div> <div xml:id="echoid-div2028" type="section" level="1" n="500"> <head xml:id="echoid-head666" xml:space="preserve"><emph style="sc">Experimentum</emph> 9.</head> <p> <s xml:id="echoid-s13593" xml:space="preserve">Detur pixis P, de qua in Exp. </s> <s xml:id="echoid-s13594" xml:space="preserve">1. </s> <s xml:id="echoid-s13595" xml:space="preserve">aquâ plena; </s> <s xml:id="echoid-s13596" xml:space="preserve">vitrum V ob-<lb/> <anchor type="note" xlink:label="note-0533-09a" xlink:href="note-0533-09"/> tegatur ita, ut pars detecta ſit circularis & </s> <s xml:id="echoid-s13597" xml:space="preserve">diametri circiter <lb/>ſemi pollicis; </s> <s xml:id="echoid-s13598" xml:space="preserve">in pixide detur tabella T alba & </s> <s xml:id="echoid-s13599" xml:space="preserve">mobilis. </s> <s xml:id="echoid-s13600" xml:space="preserve">Si <lb/>candela A ad diſtantiam detur trium aut quatuor pedum a <lb/>pixide, & </s> <s xml:id="echoid-s13601" xml:space="preserve">tabella T per aquam moveatur, ubi pervenerit <lb/>ad diſtantiam focorum flammæ A, flamma hæc in tabella exa-<lb/>ctiſſimè repræſentata apparebit; </s> <s xml:id="echoid-s13602" xml:space="preserve">focis omnibus picturam for-<lb/>mantibus. </s> <s xml:id="echoid-s13603" xml:space="preserve">Hoc autem obtinet ſive radii à candela obliquè in <lb/>vitrum V incidant ſive directè, in ſitu tamen obliquo, manen-<lb/>te diſtantia candelæ A, minuitur diſtantia tabellæ T ab V.</s> <s xml:id="echoid-s13604" xml:space="preserve"> <pb o="38" file="0534" n="588" rhead="PHYSICES ELEMENTA"/> In hoc etiam caſu candela & </s> <s xml:id="echoid-s13605" xml:space="preserve">vitrum V non ſunt in eadem <lb/>linea recta cum repreſentatione illius, quod in ſitu directo <lb/>obtinet; </s> <s xml:id="echoid-s13606" xml:space="preserve">quo confirmatur n. </s> <s xml:id="echoid-s13607" xml:space="preserve">686.</s> <s xml:id="echoid-s13608" xml:space="preserve"/> </p> <div xml:id="echoid-div2028" type="float" level="2" n="1"> <note position="right" xlink:label="note-0533-09" xlink:href="note-0533-09a" xml:space="preserve">TAB. VIII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s13609" xml:space="preserve">Repræ ſentatur candela in ſitu everſo, quia radii, à diver-<lb/> <anchor type="note" xlink:label="note-0534-01a" xlink:href="note-0534-01"/> ſis punctis procedentes, tranſeundo per V. </s> <s xml:id="echoid-s13610" xml:space="preserve">ſeſe mutuò inter-<lb/>ſecant, ut per inſpectionem fig. </s> <s xml:id="echoid-s13611" xml:space="preserve">1. </s> <s xml:id="echoid-s13612" xml:space="preserve">clarè patet. </s> <s xml:id="echoid-s13613" xml:space="preserve">Ex qua eadem <lb/>cauſa, ſi duæ dentur candelæ ut A & </s> <s xml:id="echoid-s13614" xml:space="preserve">B, repræſentatio hujus <lb/>dabitur in b illius in a.</s> <s xml:id="echoid-s13615" xml:space="preserve"/> </p> <div xml:id="echoid-div2029" type="float" level="2" n="2"> <note position="left" xlink:label="note-0534-01" xlink:href="note-0534-01a" xml:space="preserve">689.</note> </div> <p> <s xml:id="echoid-s13616" xml:space="preserve">Omnes mutationes in lumine, de quibus in hoc capite a-<lb/> <anchor type="note" xlink:label="note-0534-02a" xlink:href="note-0534-02"/> ctum, eò magis ſunt ſenſibiles, quo ſuperficies media diri-<lb/>mens eſt magis curva, id eſt, minoris ſphæræ portio.</s> <s xml:id="echoid-s13617" xml:space="preserve"/> </p> <div xml:id="echoid-div2030" type="float" level="2" n="3"> <note position="left" xlink:label="note-0534-02" xlink:href="note-0534-02a" xml:space="preserve">690.</note> </div> </div> <div xml:id="echoid-div2032" type="section" level="1" n="501"> <head xml:id="echoid-head667" xml:space="preserve">CAPUT IX.</head> <head xml:id="echoid-head668" style="it" xml:space="preserve">De Motu Luminis trans Medium denſius. Vbi de <lb/>Lentium affectionibus.</head> <p> <s xml:id="echoid-s13618" xml:space="preserve">VItrorum frequens uſus eſt, aëre denſiora ſunt, & </s> <s xml:id="echoid-s13619" xml:space="preserve">ex aëre <lb/> <anchor type="note" xlink:label="note-0534-03a" xlink:href="note-0534-03"/> in aërem trans vitrum radii penetrant. </s> <s xml:id="echoid-s13620" xml:space="preserve">Pro variis ſuper-<lb/>ficiebus, quibus terminatur vitrum, diverſas in hoc motu lu-<lb/>men mutationes ſubit, quæ ut determinentur, vitra, aut <lb/>media quæcunque medio rariori circumdata, & </s> <s xml:id="echoid-s13621" xml:space="preserve">variis ſuper-<lb/>ficiebus terminata, examinanda ſunt. </s> <s xml:id="echoid-s13622" xml:space="preserve">Conſiderando ſolas ſu-<lb/>perficies planas & </s> <s xml:id="echoid-s13623" xml:space="preserve">ſphæricas, ſex Claſſes dantur.</s> <s xml:id="echoid-s13624" xml:space="preserve"/> </p> <div xml:id="echoid-div2032" type="float" level="2" n="1"> <note position="left" xlink:label="note-0534-03" xlink:href="note-0534-03a" xml:space="preserve">691.</note> </div> <p> <s xml:id="echoid-s13625" xml:space="preserve">I. </s> <s xml:id="echoid-s13626" xml:space="preserve">Medium hoc planum eſt ab utraque parte. </s> <s xml:id="echoid-s13627" xml:space="preserve">2. </s> <s xml:id="echoid-s13628" xml:space="preserve">Ab una <lb/>parte planum ab altera convexum. </s> <s xml:id="echoid-s13629" xml:space="preserve">3. </s> <s xml:id="echoid-s13630" xml:space="preserve">Ab utraque parte <lb/>convexum. </s> <s xml:id="echoid-s13631" xml:space="preserve">4. </s> <s xml:id="echoid-s13632" xml:space="preserve">Ab una parte planum ab altera cavum. </s> <s xml:id="echoid-s13633" xml:space="preserve">5. </s> <s xml:id="echoid-s13634" xml:space="preserve">ca-<lb/>vum utrimque. </s> <s xml:id="echoid-s13635" xml:space="preserve">6. </s> <s xml:id="echoid-s13636" xml:space="preserve">Terminatur ſuperficie cavâ, & </s> <s xml:id="echoid-s13637" xml:space="preserve">oppoſita <lb/>convexa eſt.</s> <s xml:id="echoid-s13638" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2034" type="section" level="1" n="502"> <head xml:id="echoid-head669" xml:space="preserve"><emph style="sc">Definitio i</emph>.</head> <p> <s xml:id="echoid-s13639" xml:space="preserve">Si de vitro agatur & </s> <s xml:id="echoid-s13640" xml:space="preserve">craſſitiem non magnam habeat in quin-<lb/> <anchor type="note" xlink:label="note-0534-04a" xlink:href="note-0534-04"/> que ultimis caſibus, vitrum tale Lens vitrea dicitur.</s> <s xml:id="echoid-s13641" xml:space="preserve"/> </p> <div xml:id="echoid-div2034" type="float" level="2" n="1"> <note position="left" xlink:label="note-0534-04" xlink:href="note-0534-04a" xml:space="preserve">692.</note> </div> <p> <s xml:id="echoid-s13642" xml:space="preserve">In ſecundo & </s> <s xml:id="echoid-s13643" xml:space="preserve">tertio caſu lens dicitur convexa; </s> <s xml:id="echoid-s13644" xml:space="preserve">ſi tamen <lb/>hi caſus diſtinguendi ſint, in ſecundo caſu dicitur plano-con-<lb/>vexa. </s> <s xml:id="echoid-s13645" xml:space="preserve">Eodem modo in quarto caſu dicitur plano-cava; </s> <s xml:id="echoid-s13646" xml:space="preserve">licèt <lb/>& </s> <s xml:id="echoid-s13647" xml:space="preserve">hicce caſus cum quinto ſequenti ad cavas lentes generali-<lb/>ter referatur. </s> <s xml:id="echoid-s13648" xml:space="preserve">Lens autem cavo-convexa ad cavas aut con-<lb/>vexas lentes refertur, pro illa aut hac ſuperficie prævalente;</s> <s xml:id="echoid-s13649" xml:space="preserve"> <pb o="39" file="0535" n="589" rhead="MATHEMATICA LIB. III. CAP. IX."/> prævalet autem cujus curvatura major eſt, id eſt, quæ mi-<lb/>noris ſphæræ portio eſt.</s> <s xml:id="echoid-s13650" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2036" type="section" level="1" n="503"> <head xml:id="echoid-head670" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s13651" xml:space="preserve">In omni lente, aut medio quocunque ut dictum terminato, axis <lb/> <anchor type="note" xlink:label="note-0535-01a" xlink:href="note-0535-01"/> vocatur linea recta, quæ ad ambas ſuperficies perpendicularis <lb/>eſt. </s> <s xml:id="echoid-s13652" xml:space="preserve">Quando ambæ ſuperficies ſunt ſphæricæ per ambarum <lb/>centra tranſit axis; </s> <s xml:id="echoid-s13653" xml:space="preserve">poſitâ verò alterâ ſuperficie planâ, per-<lb/>pendiculariter ad hanc per aliûs centrum procedit.</s> <s xml:id="echoid-s13654" xml:space="preserve"/> </p> <div xml:id="echoid-div2036" type="float" level="2" n="1"> <note position="right" xlink:label="note-0535-01" xlink:href="note-0535-01a" xml:space="preserve">693.</note> </div> <p> <s xml:id="echoid-s13655" xml:space="preserve">In tranſitu luminis per medium, duabus ſuperficiebus pla-<lb/>nis terminatum, radiorum directio non mutatur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13656" xml:space="preserve">qui caſus <anchor type="note" xlink:label="note-0535-02a" xlink:href="note-0535-02"/> in vitris planis extat.</s> <s xml:id="echoid-s13657" xml:space="preserve"/> </p> <div xml:id="echoid-div2037" type="float" level="2" n="2"> <note position="right" xlink:label="note-0535-02" xlink:href="note-0535-02a" xml:space="preserve">694.</note> </div> <note symbol="*" position="right" xml:space="preserve">628.</note> <p> <s xml:id="echoid-s13658" xml:space="preserve">Lentium convexarum quarumcunque proprietas eſt, quod <lb/> <anchor type="note" xlink:label="note-0535-04a" xlink:href="note-0535-04"/> radii in tranſitu verſus ſe mutuò inflectantur; </s> <s xml:id="echoid-s13659" xml:space="preserve">eò magis, quo <lb/>major eſt convexitas: </s> <s xml:id="echoid-s13660" xml:space="preserve">cavarum autem quod radii à ſe mu-<lb/> <anchor type="note" xlink:label="note-0535-05a" xlink:href="note-0535-05"/> tuo deflectantur; </s> <s xml:id="echoid-s13661" xml:space="preserve">magis pro majori cavitate. </s> <s xml:id="echoid-s13662" xml:space="preserve">Nam per vitrum <lb/>planum radiorum directio non mutatur <anchor type="note" xlink:href="" symbol="*"/>, inflectendo autem <anchor type="note" xlink:label="note-0535-06a" xlink:href="note-0535-06"/> unam aut ambas ſuperficies, alia datur radiorum directio: </s> <s xml:id="echoid-s13663" xml:space="preserve">ma-<lb/>gis verſus lentis axem inflectuntur ex convexitate ſuperficiei <lb/>vitri, & </s> <s xml:id="echoid-s13664" xml:space="preserve">excavando ſuperficiem ab axe deflectuntur; </s> <s xml:id="echoid-s13665" xml:space="preserve">ut cla-<lb/>rè patet in omni caſu, comparando inflexionem in ſuperfi-<lb/>cie plana ad axem perpendiculari, cum inflexione in ſuper-<lb/>ficie ſphærica ad diſtantiam quamcunque ab axe. </s> <s xml:id="echoid-s13666" xml:space="preserve">Et diffe-<lb/>rentia inſlexionum, id eſt, directionis radiorum mutatio, <lb/>cum diſtantia ab axe creſcit; </s> <s xml:id="echoid-s13667" xml:space="preserve">& </s> <s xml:id="echoid-s13668" xml:space="preserve">in quacunque radiorum di-<lb/>rectione locum habet; </s> <s xml:id="echoid-s13669" xml:space="preserve">æquè in radiis obliquis, quàm in di-<lb/>rectis; </s> <s xml:id="echoid-s13670" xml:space="preserve">ſed in radiis obliquis propter majores angulos inci-<lb/> <anchor type="note" xlink:label="note-0535-07a" xlink:href="note-0535-07"/> dentiæ mutationes majores ſunt. </s> <s xml:id="echoid-s13671" xml:space="preserve">Ex quibus Lentium pro-<lb/>prietates ſequentes deducimus.</s> <s xml:id="echoid-s13672" xml:space="preserve"/> </p> <div xml:id="echoid-div2038" type="float" level="2" n="3"> <note position="right" xlink:label="note-0535-04" xlink:href="note-0535-04a" xml:space="preserve">695.</note> <note position="right" xlink:label="note-0535-05" xlink:href="note-0535-05a" xml:space="preserve">696.</note> <note symbol="*" position="right" xlink:label="note-0535-06" xlink:href="note-0535-06a" xml:space="preserve">694.</note> <note position="right" xlink:label="note-0535-07" xlink:href="note-0535-07a" xml:space="preserve">697.</note> </div> <p style="it"> <s xml:id="echoid-s13673" xml:space="preserve">Radios parallelos, tranſeundo per lentem convexam, in fo-<lb/> <anchor type="note" xlink:label="note-0535-08a" xlink:href="note-0535-08"/> cum concurrere.</s> <s xml:id="echoid-s13674" xml:space="preserve"/> </p> <div xml:id="echoid-div2039" type="float" level="2" n="4"> <note position="right" xlink:label="note-0535-08" xlink:href="note-0535-08a" xml:space="preserve">698.</note> </div> <p> <s xml:id="echoid-s13675" xml:space="preserve">Radios divergentes aut minus divergere, aut parallelos <lb/> <anchor type="note" xlink:label="note-0535-09a" xlink:href="note-0535-09"/> fieri, aut tandem convergere; </s> <s xml:id="echoid-s13676" xml:space="preserve">in quo caſu recedente puncto <lb/>radiante accedit focus, & </s> <s xml:id="echoid-s13677" xml:space="preserve">vice verſa: </s> <s xml:id="echoid-s13678" xml:space="preserve">Caſus autem hic ex-<lb/>tat; </s> <s xml:id="echoid-s13679" xml:space="preserve">quando punctum radians à lente magis removetur, quàm <lb/>ab hac diſtat focus radiorum parallelorum.</s> <s xml:id="echoid-s13680" xml:space="preserve"/> </p> <div xml:id="echoid-div2040" type="float" level="2" n="5"> <note position="right" xlink:label="note-0535-09" xlink:href="note-0535-09a" xml:space="preserve">699.</note> </div> <p> <s xml:id="echoid-s13681" xml:space="preserve">Tandem radios convergentes magis in egreſſu luminis con-<lb/> <anchor type="note" xlink:label="note-0535-10a" xlink:href="note-0535-10"/> vergere.</s> <s xml:id="echoid-s13682" xml:space="preserve"/> </p> <div xml:id="echoid-div2041" type="float" level="2" n="6"> <note position="right" xlink:label="note-0535-10" xlink:href="note-0535-10a" xml:space="preserve">700.</note> </div> <pb o="40" file="0536" n="590" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s13683" xml:space="preserve">Hæc etiam obtinent in radiis obliquis; </s> <s xml:id="echoid-s13684" xml:space="preserve">circa quos notan-<lb/> <anchor type="note" xlink:label="note-0536-01a" xlink:href="note-0536-01"/> dum diſtantias focorum radiorum exeuntium, minores eſſe quàm <lb/>in radiis directis, & </s> <s xml:id="echoid-s13685" xml:space="preserve">reliquas mutationes magis ſenſibiles eſſe <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13686" xml:space="preserve"/> </p> <div xml:id="echoid-div2042" type="float" level="2" n="7"> <note position="left" xlink:label="note-0536-01" xlink:href="note-0536-01a" xml:space="preserve">701.</note> </div> <note symbol="*" position="left" xml:space="preserve">697.</note> <p> <s xml:id="echoid-s13687" xml:space="preserve">Hæc eadem omnia ex examine duplicis refractionis in in <lb/>greſſu & </s> <s xml:id="echoid-s13688" xml:space="preserve">egreſſu luminis deducuntur. </s> <s xml:id="echoid-s13689" xml:space="preserve">Hæc autem duplex <lb/>refractio in caſu quocunque ſub oculis ponitur, in experi-<lb/>mentis ſequentibus; </s> <s xml:id="echoid-s13690" xml:space="preserve">quibus lentium convexarum affectiones <lb/>memoratæ confirmantur.</s> <s xml:id="echoid-s13691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13692" xml:space="preserve">Pixides ut P variæ dantur, quæ aquam continent, & </s> <s xml:id="echoid-s13693" xml:space="preserve">per <lb/> <anchor type="note" xlink:label="note-0536-03a" xlink:href="note-0536-03"/> quas lumen tranſmittitur per vitra V & </s> <s xml:id="echoid-s13694" xml:space="preserve">V, quæ dantur in <lb/> <anchor type="note" xlink:label="note-0536-04a" xlink:href="note-0536-04"/> lateribus oppoſitis pixidis, a ſe mutuò diſtantibus circiter <lb/>pollicem unum. </s> <s xml:id="echoid-s13695" xml:space="preserve">Vitra hæc ſunt tenuia; </s> <s xml:id="echoid-s13696" xml:space="preserve">in pixide, quæ re-<lb/>præſentat lentem convevam ab utraque parte unum datur, <lb/>ſimile illi, de quo in exp. </s> <s xml:id="echoid-s13697" xml:space="preserve">1. </s> <s xml:id="echoid-s13698" xml:space="preserve">capitis præcedentis, quæ diſpo-<lb/>nuntur ut convexitates ſint extra pixidem. </s> <s xml:id="echoid-s13699" xml:space="preserve">Quando lens plano <lb/>convexa repræſentanda eſt, ad unam partem datur vitrum <lb/>planum. </s> <s xml:id="echoid-s13700" xml:space="preserve">Lens cavo-convexa repreſentatur adhibitis duobus <lb/>vitris ſphæricis variarum ſphærarum portionibus, & </s> <s xml:id="echoid-s13701" xml:space="preserve">convexi-<lb/>tas portionis majoris ſphæræ, ad interiorem pixidis partem <lb/>datur.</s> <s xml:id="echoid-s13702" xml:space="preserve"/> </p> <div xml:id="echoid-div2043" type="float" level="2" n="8"> <note position="left" xlink:label="note-0536-03" xlink:href="note-0536-03a" xml:space="preserve">702.</note> <note position="left" xlink:label="note-0536-04" xlink:href="note-0536-04a" xml:space="preserve">TAB. VIII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13703" xml:space="preserve">Dum lumen per has pixides tranſit, ad oculum patent lu-<lb/>minis mutationes in ingreſſu & </s> <s xml:id="echoid-s13704" xml:space="preserve">egreſſu medii denſioris, & </s> <s xml:id="echoid-s13705" xml:space="preserve"><lb/>harum ope omnia, quæ lentes convcxas ſpcctant, clarè de-<lb/>monſtrantur.</s> <s xml:id="echoid-s13706" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2045" type="section" level="1" n="504"> <head xml:id="echoid-head671" xml:space="preserve"><emph style="sc">Experimentum i</emph>.</head> <p> <s xml:id="echoid-s13707" xml:space="preserve">Sit una ex memoratis pixidibus P, ex.</s> <s xml:id="echoid-s13708" xml:space="preserve">gr.</s> <s xml:id="echoid-s13709" xml:space="preserve">cum vitris V, V, <lb/>ſphæricis, poſitis convexitatibus externè; </s> <s xml:id="echoid-s13710" xml:space="preserve">aquâ repleatur; <lb/></s> <s xml:id="echoid-s13711" xml:space="preserve">detur in cubiculo obſcuro radius Solis cylindricus a ſpeculo <lb/>S horizontaliter reflexus; </s> <s xml:id="echoid-s13712" xml:space="preserve">intret hic pixidem; </s> <s xml:id="echoid-s13713" xml:space="preserve">radii paralleli <lb/>ex quibus formatur ad ſe mutuò inflectentur, & </s> <s xml:id="echoid-s13714" xml:space="preserve">convergent; </s> <s xml:id="echoid-s13715" xml:space="preserve"><lb/>in egreſſu magis convergent & </s> <s xml:id="echoid-s13716" xml:space="preserve">in F concurrent. </s> <s xml:id="echoid-s13717" xml:space="preserve">Circa ra-<lb/>dios incidentes, qui divergunt aut convergunt, experimenta <lb/>inſtituuntur, adhibitâ tabellâ cum lente convexa, ut in expe-<lb/>rimentis capitis præcedentis.</s> <s xml:id="echoid-s13718" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13719" xml:space="preserve">Singula puncta corporis lucidi, ut antea memoratum, ſunt <lb/>puncta radiantia <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s13720" xml:space="preserve">poſita juſta diſtantia à convexâ lente, <anchor type="note" xlink:label="note-0536-05a" xlink:href="note-0536-05"/> ſingula focum ſuum habent <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13721" xml:space="preserve"/> </p> <div xml:id="echoid-div2045" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0536-05" xlink:href="note-0536-05a" xml:space="preserve">688.</note> </div> <note symbol="*" position="left" xml:space="preserve">698.</note> <pb file="0537" n="591"/> <pb file="0537a" n="592"/> <figure> <image file="0537a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0537a-01"/> </figure> <pb file="0538" n="593"/> <pb o="41" file="0539" n="594" rhead="MATHEMATICA LIB. III. CAP. IX."/> </div> <div xml:id="echoid-div2047" type="section" level="1" n="505"> <head xml:id="echoid-head672" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s13722" xml:space="preserve">Detur candela lucens, à lente convexâ remota ultra fo-<lb/>cum radiorum parallelorum, ad oppoſitam lentis partem ſu-<lb/>per plano albo, per focos punctorum flammæ, hæc repræ-<lb/>ſentabitur & </s> <s xml:id="echoid-s13723" xml:space="preserve">quidem inverſa, propter radiorum interſectio. <lb/></s> <s xml:id="echoid-s13724" xml:space="preserve">nem in tranſitu per vitrum.</s> <s xml:id="echoid-s13725" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13726" xml:space="preserve">Lentes convexæ ſunt etiam vitra uſtoria, quia colligunt <lb/> <anchor type="note" xlink:label="note-0539-01a" xlink:href="note-0539-01"/> radios ſolares <anchor type="note" xlink:href="" symbol="*"/>, qui, propter Solis immenſam diſtantiam, pro <anchor type="note" xlink:label="note-0539-02a" xlink:href="note-0539-02"/> parallelis habentur. </s> <s xml:id="echoid-s13727" xml:space="preserve">Radii verò in foco collecti, propter i-<lb/>gnem antea diſperſum, nunc collectum, & </s> <s xml:id="echoid-s13728" xml:space="preserve">propter ignis <lb/>motum juxta varias directiones, violenter urunt.</s> <s xml:id="echoid-s13729" xml:space="preserve"/> </p> <div xml:id="echoid-div2047" type="float" level="2" n="1"> <note position="right" xlink:label="note-0539-01" xlink:href="note-0539-01a" xml:space="preserve">703.</note> <note symbol="*" position="right" xlink:label="note-0539-02" xlink:href="note-0539-02a" xml:space="preserve">698.</note> </div> </div> <div xml:id="echoid-div2049" type="section" level="1" n="506"> <head xml:id="echoid-head673" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s13730" xml:space="preserve">Detur lens convexa cujuſcunque magnitudinis, exponatur <lb/>hæc radiis ſolaribus ita, ut lentis axis cum directione radio-<lb/>rum conveniat; </s> <s xml:id="echoid-s13731" xml:space="preserve">ſi corpus quodcunque combuſtibile in foco <lb/>radiorum ſolarium ponatur, uritur.</s> <s xml:id="echoid-s13732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13733" xml:space="preserve">Quando propter lentis magnitudinem non ſatis exactè col-<lb/>liguntur radii, antequam ad focum perveniant, per ſecun-<lb/>dam minorem convexam lentem tranſmittuntur, quo in mi-<lb/>nus ſpatium rediguntur, ita ut magis violenter comburant.</s> <s xml:id="echoid-s13734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13735" xml:space="preserve">Quod ſpectat lentes cavas, & </s> <s xml:id="echoid-s13736" xml:space="preserve">harum proprietates ex di-<lb/>ctis <anchor type="note" xlink:href="" symbol="*"/> facile deducuntur.</s> <s xml:id="echoid-s13737" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">696.</note> <p style="it"> <s xml:id="echoid-s13738" xml:space="preserve">Radii paralteli divergentes fiunt, per lentem cavam <lb/> <anchor type="note" xlink:label="note-0539-04a" xlink:href="note-0539-04"/> tranſeundo.</s> <s xml:id="echoid-s13739" xml:space="preserve"/> </p> <div xml:id="echoid-div2049" type="float" level="2" n="1"> <note position="right" xlink:label="note-0539-04" xlink:href="note-0539-04a" xml:space="preserve">704.</note> </div> <p style="it"> <s xml:id="echoid-s13740" xml:space="preserve">Divergentes magis divergunt.</s> <s xml:id="echoid-s13741" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">705.</note> <p> <s xml:id="echoid-s13742" xml:space="preserve">Convergentes, aut minus convergunt; </s> <s xml:id="echoid-s13743" xml:space="preserve">aut paralleli fiunt; <lb/></s> <s xml:id="echoid-s13744" xml:space="preserve"> <anchor type="note" xlink:label="note-0539-06a" xlink:href="note-0539-06"/> aut, quod in minus convergentibus obtinet, divergentes <lb/>lentem exeunt.</s> <s xml:id="echoid-s13745" xml:space="preserve"/> </p> <div xml:id="echoid-div2050" type="float" level="2" n="2"> <note position="right" xlink:label="note-0539-06" xlink:href="note-0539-06a" xml:space="preserve">706.</note> </div> <p style="it"> <s xml:id="echoid-s13746" xml:space="preserve">Quæ omnia, æquè in obliquis radiis, ac in directis locum <lb/> <anchor type="note" xlink:label="note-0539-07a" xlink:href="note-0539-07"/> habent, in illis tamen magis ſenſibiliter <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13747" xml:space="preserve"/> </p> <div xml:id="echoid-div2051" type="float" level="2" n="3"> <note position="right" xlink:label="note-0539-07" xlink:href="note-0539-07a" xml:space="preserve">707.</note> </div> <note symbol="*" position="right" xml:space="preserve">697.</note> <p> <s xml:id="echoid-s13748" xml:space="preserve">Pixides, repræſentantes lentes cavas, eodem modo con-<lb/> <anchor type="note" xlink:label="note-0539-09a" xlink:href="note-0539-09"/> ſtruuntur, ac illæ cum quibus experimenta circa lentes con-<lb/> <anchor type="note" xlink:label="note-0539-10a" xlink:href="note-0539-10"/> vexas inſtituuntur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13749" xml:space="preserve">Sola differentia datur in ſitu vitro- <anchor type="note" xlink:label="note-0539-11a" xlink:href="note-0539-11"/> rum: </s> <s xml:id="echoid-s13750" xml:space="preserve">In pixide primâ vitrorum duorum ſphæricorum V, V <lb/>cavitates externæ ſunt. </s> <s xml:id="echoid-s13751" xml:space="preserve">In ſecundâ, loco unius illorum vi-<lb/>trorum, datur vitrum planum. </s> <s xml:id="echoid-s13752" xml:space="preserve">In tertiâ, duo quidem vitra <lb/>dantur ſphærica, ſed diverſarum ſphærarum ſectiones, majo- <pb o="42" file="0540" n="595" rhead="PHYSICES ELEMENTA"/> ris ſphæræ ſectio convexitatem externè habet, aliûs con-<lb/>vexitas internè datur.</s> <s xml:id="echoid-s13753" xml:space="preserve"/> </p> <div xml:id="echoid-div2052" type="float" level="2" n="4"> <note position="right" xlink:label="note-0539-09" xlink:href="note-0539-09a" xml:space="preserve">708.</note> <note position="right" xlink:label="note-0539-10" xlink:href="note-0539-10a" xml:space="preserve">TAB. IX. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0539-11" xlink:href="note-0539-11a" xml:space="preserve">702.</note> </div> </div> <div xml:id="echoid-div2054" type="section" level="1" n="507"> <head xml:id="echoid-head674" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s13754" xml:space="preserve">Radii ſolares paralleli, in cubiculo obſcuro à ſpeculo Sho-<lb/>rizontaliter reflexi, per pixidem P, lentem utrinque con-<lb/>cavam repræſentantem & </s> <s xml:id="echoid-s13755" xml:space="preserve">aquâ plenam, tranſmittuntur; </s> <s xml:id="echoid-s13756" xml:space="preserve">in <lb/>ingreſſu divergentes fiunt, & </s> <s xml:id="echoid-s13757" xml:space="preserve">egreſſu magis diſperguntur.</s> <s xml:id="echoid-s13758" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13759" xml:space="preserve">Reliqua experimenta circa lentes cavas eodem modo in-<lb/>ſtituuntur, ac de lentibus convexis in exp. </s> <s xml:id="echoid-s13760" xml:space="preserve">1. </s> <s xml:id="echoid-s13761" xml:space="preserve">dictum.</s> <s xml:id="echoid-s13762" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2055" type="section" level="1" n="508"> <head xml:id="echoid-head675" xml:space="preserve">CAPUT X.</head> <head xml:id="echoid-head676" style="it" xml:space="preserve">De Viſu, ubi de Oculi conſtructione.</head> <p> <s xml:id="echoid-s13763" xml:space="preserve">QUas luminis proprietates refractioniſque leges explicavi-<lb/>mus, mirandum, in objectis menti noſtræ repræſentan-<lb/>dis, uſum habent.</s> <s xml:id="echoid-s13764" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13765" xml:space="preserve">His legibus objecta in fundo oculi pulcherrimè, propriis <lb/>ſuis coloribus ornata, depinguntur; </s> <s xml:id="echoid-s13766" xml:space="preserve">hæcque pictura, ut in <lb/>ſequentibus dicam <anchor type="note" xlink:href="" symbol="*"/>, occaſio eſt idearum, quæ in mente cir- <anchor type="note" xlink:label="note-0540-01a" xlink:href="note-0540-01"/> ca res viſas excitantur.</s> <s xml:id="echoid-s13767" xml:space="preserve"/> </p> <div xml:id="echoid-div2055" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0540-01" xlink:href="note-0540-01a" xml:space="preserve">716.</note> </div> <p> <s xml:id="echoid-s13768" xml:space="preserve">Quomodo autem hæc pictura in oculo detur explicarinon <lb/>poteſt, niſi examinatâ novâ luminis proprietate; </s> <s xml:id="echoid-s13769" xml:space="preserve">radiorum <lb/>nempe diviſibilitate captum noſtrum ſuperante.</s> <s xml:id="echoid-s13770" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2057" type="section" level="1" n="509"> <head xml:id="echoid-head677" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s13771" xml:space="preserve">Corpus, quod non eſt lucidum & </s> <s xml:id="echoid-s13772" xml:space="preserve">lumen intercipit, vocatur <lb/> <anchor type="note" xlink:label="note-0540-02a" xlink:href="note-0540-02"/> opacum.</s> <s xml:id="echoid-s13773" xml:space="preserve"/> </p> <div xml:id="echoid-div2057" type="float" level="2" n="1"> <note position="left" xlink:label="note-0540-02" xlink:href="note-0540-02a" xml:space="preserve">709.</note> </div> <p> <s xml:id="echoid-s13774" xml:space="preserve">Corpora pleraque inter hæc opaca omnia, exactiſſimè poli-<lb/> <anchor type="note" xlink:label="note-0540-03a" xlink:href="note-0540-03"/> ta, ut & </s> <s xml:id="echoid-s13775" xml:space="preserve">perfectè nigra excipias, ſi quæ dantur, dividendi <lb/>luminis proprietatem habent; </s> <s xml:id="echoid-s13776" xml:space="preserve">repercutiunt lumen ita, ut à <lb/>ſingulis punctis radii repercuſſi dividantur, & </s> <s xml:id="echoid-s13777" xml:space="preserve">verſus omnes <lb/>partes recedant, & </s> <s xml:id="echoid-s13778" xml:space="preserve">ſingula puncta corporis ſint quaſi pun-<lb/>cta radiantia, ex quibus lumen verſus omnes partes procedit.</s> <s xml:id="echoid-s13779" xml:space="preserve"/> </p> <div xml:id="echoid-div2058" type="float" level="2" n="2"> <note position="left" xlink:label="note-0540-03" xlink:href="note-0540-03a" xml:space="preserve">710.</note> </div> <p> <s xml:id="echoid-s13780" xml:space="preserve">Unde deducimus Methodum depingendorum objectorum <lb/> <anchor type="note" xlink:label="note-0540-04a" xlink:href="note-0540-04"/> in plano albo; </s> <s xml:id="echoid-s13781" xml:space="preserve">ſingula enim puncta corporis illuminati, ex <lb/>quibus radii ad lentem convexam perveniunt, poſt len-<lb/>tem focum ſuum habent <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s13782" xml:space="preserve">Objectorum diſtantium, li- <anchor type="note" xlink:label="note-0540-05a" xlink:href="note-0540-05"/> cèt inæqualiter, foci ſenſibiliter eandem ad diſtantiam à <pb o="43" file="0541" n="596" rhead="MATHEMATICA LIB. III. CAP. X."/> lente dantur; </s> <s xml:id="echoid-s13783" xml:space="preserve">hiſce in eodem plano, objecta hæc, repræ-<lb/>ſentari poſſunt; </s> <s xml:id="echoid-s13784" xml:space="preserve">quæ repræſentatio inverſa eſt, propter ra-<lb/>diorum interſectionem tranſeundo per vitrum; </s> <s xml:id="echoid-s13785" xml:space="preserve">& </s> <s xml:id="echoid-s13786" xml:space="preserve">ſenſi-<lb/>bilis, eſt in loco obſcuro, in quo lumen per ſolam len-<lb/>tem intrat, & </s> <s xml:id="echoid-s13787" xml:space="preserve">quidem illud ſolum quo objecta depingun-<lb/>tur.</s> <s xml:id="echoid-s13788" xml:space="preserve"/> </p> <div xml:id="echoid-div2059" type="float" level="2" n="3"> <note position="left" xlink:label="note-0540-04" xlink:href="note-0540-04a" xml:space="preserve">711.</note> <note symbol="*" position="left" xlink:label="note-0540-05" xlink:href="note-0540-05a" xml:space="preserve">699.</note> </div> <p> <s xml:id="echoid-s13789" xml:space="preserve">Hæc obtinent ubicunque lens ponatur, & </s> <s xml:id="echoid-s13790" xml:space="preserve">quidem circa <lb/>omnia objectorum puncta, luminis radiis illuſtrata, à quibus <lb/>lineæ rectæ non interruptæ ad lentem duci poſſunt; </s> <s xml:id="echoid-s13791" xml:space="preserve">ita ut <lb/>ſequenti Experimento probetur diviſibilitas memorata in lu-<lb/>mine, & </s> <s xml:id="echoid-s13792" xml:space="preserve">dividendi luminis capacitas in corporibus lumen <lb/>repercutientibus.</s> <s xml:id="echoid-s13793" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2061" type="section" level="1" n="510"> <head xml:id="echoid-head678" xml:space="preserve"><emph style="sc">Experimentum i</emph>.</head> <p> <s xml:id="echoid-s13794" xml:space="preserve">In loco obſcuro foramen detur, cui varia reſpondeant <lb/> <anchor type="note" xlink:label="note-0541-01a" xlink:href="note-0541-01"/> objecta, ad diſtantiam ad minimum quinquaginta pedum, & </s> <s xml:id="echoid-s13795" xml:space="preserve"><lb/>majorem. </s> <s xml:id="echoid-s13796" xml:space="preserve">Sit hoc V, & </s> <s xml:id="echoid-s13797" xml:space="preserve">in hoc detur lens convexa, quæ col-<lb/>ligit radios parallelos ad diſtantiam quatuor aut quinque pe-<lb/>dum; </s> <s xml:id="echoid-s13798" xml:space="preserve">ſi ad diſtantiam paululum majorem poſt lentem detur <lb/>planum album, in hoc objecta memorata pulcherrimis co-<lb/>loribus depinguntur. </s> <s xml:id="echoid-s13799" xml:space="preserve">Notandum lentem in ſitu ad planum <lb/>parallelo ponendam eſſe; </s> <s xml:id="echoid-s13800" xml:space="preserve">& </s> <s xml:id="echoid-s13801" xml:space="preserve">motu plani aut lentis detegi di-<lb/>ſtantiam ad quam objecta exactiſſimè repræſentantur.</s> <s xml:id="echoid-s13802" xml:space="preserve"/> </p> <div xml:id="echoid-div2061" type="float" level="2" n="1"> <note position="right" xlink:label="note-0541-01" xlink:href="note-0541-01a" xml:space="preserve">TAB. IX. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s13803" xml:space="preserve">Hæc objectorum repræſentatio magnam cum illa, qua in <lb/>fundo oculi objecta viſa depinguntur, affinitatem habet, ut <lb/>ex oculi conſtructione patebit.</s> <s xml:id="echoid-s13804" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13805" xml:space="preserve">Oculi figura, ſi capite extrahatur, præterpropter eſt <lb/> <anchor type="note" xlink:label="note-0541-02a" xlink:href="note-0541-02"/> ſphærica: </s> <s xml:id="echoid-s13806" xml:space="preserve">nihilominus pars anterior eſt paululum magis con-<lb/>vexa.</s> <s xml:id="echoid-s13807" xml:space="preserve"/> </p> <div xml:id="echoid-div2062" type="float" level="2" n="2"> <note position="right" xlink:label="note-0541-02" xlink:href="note-0541-02a" xml:space="preserve">712.</note> </div> <p> <s xml:id="echoid-s13808" xml:space="preserve">Oculi ſectio in hac figurâ repræſentatur.</s> <s xml:id="echoid-s13809" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">TAB. IX. <lb/>fig. 3.</note> <p> <s xml:id="echoid-s13810" xml:space="preserve">Pars magis convexa A A, eſt tranſlucida & </s> <s xml:id="echoid-s13811" xml:space="preserve">tunica cor-<lb/>nea vocatur.</s> <s xml:id="echoid-s13812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13813" xml:space="preserve">Totum oculi integumentum, corneâ exceptâ, vocatur <lb/>ſclerotica B A A B; </s> <s xml:id="echoid-s13814" xml:space="preserve">pars ſcleroticæ quæ corneæ adjacet, <lb/>vocatur adnata, ſive album oculi.</s> <s xml:id="echoid-s13815" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13816" xml:space="preserve">Ab interiori parte cornea obtegitur tunicâ uvea dictâ, quæ <lb/>in medio foramen habet p p, quod nominatur pupilla.</s> <s xml:id="echoid-s13817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13818" xml:space="preserve">Uvea conſtat ex fibris circularibus concentricis, ad angu- <pb o="44" file="0542" n="597" rhead="PHYSICES ELEMENTA"/> los rectos per rectas fibras interſectis. </s> <s xml:id="echoid-s13819" xml:space="preserve">Si primæ inflentur <lb/>relaxantur ſecundæ, & </s> <s xml:id="echoid-s13820" xml:space="preserve">pupilla minuitur; </s> <s xml:id="echoid-s13821" xml:space="preserve">augetur motu fi-<lb/>brarum contrario.</s> <s xml:id="echoid-s13822" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13823" xml:space="preserve">In medio oculi, magis tamen verſus partem anteriorem, <lb/>datur corpus molle tranſlucidum C C, lenti convexæ ſimi-<lb/>le, cujus ſuperficies poſterior convexitate anteriorem ſupe-<lb/>rat. </s> <s xml:id="echoid-s13824" xml:space="preserve">Vocatur humor cryſtallinus. </s> <s xml:id="echoid-s13825" xml:space="preserve">Axis hujus cum oculi <lb/>axe, per centra pupillæ & </s> <s xml:id="echoid-s13826" xml:space="preserve">totius oculi tranſeunte, coinci-<lb/>dit.</s> <s xml:id="echoid-s13827" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13828" xml:space="preserve">Suſtinetur cryſtallinus humor filis, quæ in ſingulis punctis <lb/>circumferentiæ hujus cohærent, & </s> <s xml:id="echoid-s13829" xml:space="preserve">interiori parte oculi <lb/>annectuntur: </s> <s xml:id="echoid-s13830" xml:space="preserve">in formam arcus inflectuntur, & </s> <s xml:id="echoid-s13831" xml:space="preserve">muſculi ſunt; <lb/></s> <s xml:id="echoid-s13832" xml:space="preserve">nominantur ligamenta ciliaria, duo videntur in l C, l C. </s> <s xml:id="echoid-s13833" xml:space="preserve"><lb/>Omnia inter ſe cohærent, & </s> <s xml:id="echoid-s13834" xml:space="preserve">cum cryſtallino ſeparationem <lb/>in oculo formant, huncque in duas cavitates, unam ante-<lb/>riorem p p, alteram poſteriorem SS, dividunt.</s> <s xml:id="echoid-s13835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13836" xml:space="preserve">Anterior cavitas repletur liquido aquæ ſimili, dicitur hu-<lb/>mor aquens.</s> <s xml:id="echoid-s13837" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13838" xml:space="preserve">Cavitas poſterior repletur humore tranſlucido, ejuſdem <lb/>circiter denſitatis cum humore aqueo, ſed non æquè fluido; <lb/></s> <s xml:id="echoid-s13839" xml:space="preserve">humor vitreus vocatur.</s> <s xml:id="echoid-s13840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13841" xml:space="preserve">Superficies poſterior & </s> <s xml:id="echoid-s13842" xml:space="preserve">interior oculi tunicâ obtegitur, <lb/>choroides dictâ, quam iterum obtegit membrana tenuiſſima, <lb/>cui nomen retinæ datur.</s> <s xml:id="echoid-s13843" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13844" xml:space="preserve">Nervus opticus NN, ad poſteriorem bulbi oculi partem, <lb/>paululum ad latus, datur; </s> <s xml:id="echoid-s13845" xml:space="preserve">& </s> <s xml:id="echoid-s13846" xml:space="preserve">ita cum oculo jungitur; </s> <s xml:id="echoid-s13847" xml:space="preserve">ut hic <lb/>ſit quaſi expanſio nervi optici; </s> <s xml:id="echoid-s13848" xml:space="preserve">tunicæ enim nervi expanſæ <lb/>choroidem & </s> <s xml:id="echoid-s13849" xml:space="preserve">ſcleroticam formant; </s> <s xml:id="echoid-s13850" xml:space="preserve">Fibræ autem ex quibus <lb/>retina conſtat concurrunt & </s> <s xml:id="echoid-s13851" xml:space="preserve">medullam nervi formant.</s> <s xml:id="echoid-s13852" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13853" xml:space="preserve">Oculus in capite movetur variis muſculis cum ſclerotica <lb/>cohærentibus; </s> <s xml:id="echoid-s13854" xml:space="preserve">de his hìc non agitur; </s> <s xml:id="echoid-s13855" xml:space="preserve">oculi conſtructionem <lb/>cum relatione ad motum luminis conſidero, de omnibus cæ-<lb/>teris loqui conſultò abſtineo.</s> <s xml:id="echoid-s13856" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13857" xml:space="preserve">Radii à puncto quocunque procedentes, & </s> <s xml:id="echoid-s13858" xml:space="preserve">qui per pupil-<lb/> <anchor type="note" xlink:label="note-0542-01a" xlink:href="note-0542-01"/> lam oculum intrant, ex medio rariori in denſius per ſuperfi-<lb/>ciem ſphæricam tranſeunt, ideoque poſitâ juſtâ puncti diſtan-<lb/>tiâ ab oculo, radii poſt refractionem convergunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13859" xml:space="preserve">planè eo- <anchor type="note" xlink:label="note-0542-02a" xlink:href="note-0542-02"/> <pb o="45" file="0543" n="598" rhead="MATHEMATICA. LIB. III. CAP. X."/> dem modo ac in experimento n. </s> <s xml:id="echoid-s13860" xml:space="preserve">663. </s> <s xml:id="echoid-s13861" xml:space="preserve">in quo vitrum V oculi <lb/> <anchor type="note" xlink:label="note-0543-01a" xlink:href="note-0543-01"/> tunicam corneam tranſlucidam repræſentat, dum aqua in <lb/>pixide humoris aquei vices gerit; </s> <s xml:id="echoid-s13862" xml:space="preserve">ideoque poſitis corneâ <lb/> <anchor type="note" xlink:label="note-0543-02a" xlink:href="note-0543-02"/> & </s> <s xml:id="echoid-s13863" xml:space="preserve">humore aqueo, dabitur pictura inverſa objectorum in <lb/>oculo <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13864" xml:space="preserve"/> </p> <div xml:id="echoid-div2063" type="float" level="2" n="3"> <note position="left" xlink:label="note-0542-01" xlink:href="note-0542-01a" xml:space="preserve">713.</note> <note symbol="*" position="left" xlink:label="note-0542-02" xlink:href="note-0542-02a" xml:space="preserve">661.</note> <note position="right" xlink:label="note-0543-01" xlink:href="note-0543-01a" xml:space="preserve">TAB. VI. <lb/>fig. 4.</note> <note position="right" xlink:label="note-0543-02" xlink:href="note-0543-02a" xml:space="preserve">714.</note> </div> <note symbol="*" position="right" xml:space="preserve">710. 711:</note> </div> <div xml:id="echoid-div2065" type="section" level="1" n="511"> <head xml:id="echoid-head679" xml:space="preserve"><emph style="sc">Experimentum 2</emph>.</head> <p> <s xml:id="echoid-s13865" xml:space="preserve">Sit P pixis ſtatim memorata, aquam continens; </s> <s xml:id="echoid-s13866" xml:space="preserve">detur hæc <lb/> <anchor type="note" xlink:label="note-0543-04a" xlink:href="note-0543-04"/> in loco obſcuro, in quo foramen datur diametri circiter ſe-<lb/>mi pollicis, & </s> <s xml:id="echoid-s13867" xml:space="preserve">cui ad certam diſtantiam reſpondent objecta <lb/>illuminata ita, ut per hoc foramen viſibilia ſint; </s> <s xml:id="echoid-s13868" xml:space="preserve">applice-<lb/>tur vitrum V pixidis huic foramini, & </s> <s xml:id="echoid-s13869" xml:space="preserve">pictura inverſa ob-<lb/>jectorum, in tabella alba T, dabitur: </s> <s xml:id="echoid-s13870" xml:space="preserve">motu tabeIlæ diſtantia <lb/>ad quam repræſentatio eſt exacta, detegitur.</s> <s xml:id="echoid-s13871" xml:space="preserve"/> </p> <div xml:id="echoid-div2065" type="float" level="2" n="1"> <note position="right" xlink:label="note-0543-04" xlink:href="note-0543-04a" xml:space="preserve">TAB. IX. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13872" xml:space="preserve">Pictura ſtatim memorata in oculo, & </s> <s xml:id="echoid-s13873" xml:space="preserve">cujus imitationem <lb/>in hoc experimento habemus, ad nimiam diſtantiam à cor-<lb/>neâ, & </s> <s xml:id="echoid-s13874" xml:space="preserve">ultra fundum oculi, daretur; </s> <s xml:id="echoid-s13875" xml:space="preserve">minuitur idcirco <lb/>diſtantia ope humoris Cryſtallini denſioris mediis illum cir-<lb/> <anchor type="note" xlink:label="note-0543-05a" xlink:href="note-0543-05"/> cumdantibus; </s> <s xml:id="echoid-s13876" xml:space="preserve">radii enim convergentes in humore aqueo trans <lb/>cryſtallinum in humorem vitreum penetrant; </s> <s xml:id="echoid-s13877" xml:space="preserve">id eſt, ex <lb/>medio rariori trans denſius, duabus ſuperficiebus ſphæricis <lb/>convexis terminatum, in rarius; </s> <s xml:id="echoid-s13878" xml:space="preserve">quo motu convergentes <lb/>radii magis convergentes fiunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13879" xml:space="preserve">ideoque citius concurrunt, <anchor type="note" xlink:label="note-0543-06a" xlink:href="note-0543-06"/> & </s> <s xml:id="echoid-s13880" xml:space="preserve">pictura memorata intra oculum cadit.</s> <s xml:id="echoid-s13881" xml:space="preserve"/> </p> <div xml:id="echoid-div2066" type="float" level="2" n="2"> <note position="right" xlink:label="note-0543-05" xlink:href="note-0543-05a" xml:space="preserve">715.</note> <note symbol="*" position="right" xlink:label="note-0543-06" xlink:href="note-0543-06a" xml:space="preserve">700.</note> </div> </div> <div xml:id="echoid-div2068" type="section" level="1" n="512"> <head xml:id="echoid-head680" xml:space="preserve"><emph style="sc">Experimentum 3</emph>.</head> <p> <s xml:id="echoid-s13882" xml:space="preserve">Iiſdem poſitis, quæ in experimento præcedenti, detur lens <lb/> <anchor type="note" xlink:label="note-0543-07a" xlink:href="note-0543-07"/> vitrea convexa C inter vitrum V & </s> <s xml:id="echoid-s13883" xml:space="preserve">tabellam T, multò ta-<lb/>men minus à vitro quam à tabellâ diſtans; </s> <s xml:id="echoid-s13884" xml:space="preserve">ut pictura exacta <lb/>detur, verſus V admovenda erit tabella. </s> <s xml:id="echoid-s13885" xml:space="preserve">In quo experimen-<lb/>to Oculum artificialem habemus, qui exactiſſimè quantum <lb/>ad motum luminis, naturalem imitatur. </s> <s xml:id="echoid-s13886" xml:space="preserve">Vitrum V, ut in ex-<lb/>perimento præcedenti dictum, corneam repræſentat; </s> <s xml:id="echoid-s13887" xml:space="preserve">lens <lb/>convexa vitrea C cryſtallini vices gerit; </s> <s xml:id="echoid-s13888" xml:space="preserve">tabella T pro fun-<lb/>do oculi habetur; </s> <s xml:id="echoid-s13889" xml:space="preserve">aqua humorum aquei & </s> <s xml:id="echoid-s13890" xml:space="preserve">vitrei locum te-<lb/>net, in his enim humoribus lumen æqualem patitur refra-<lb/>ctionem.</s> <s xml:id="echoid-s13891" xml:space="preserve"/> </p> <div xml:id="echoid-div2068" type="float" level="2" n="1"> <note position="right" xlink:label="note-0543-07" xlink:href="note-0543-07a" xml:space="preserve">TAB. IX. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s13892" xml:space="preserve">Objecta, quæ ut explicavi in fundo oculi depinguntur, in <lb/> <anchor type="note" xlink:label="note-0543-08a" xlink:href="note-0543-08"/> retinâ delineantur; </s> <s xml:id="echoid-s13893" xml:space="preserve">& </s> <s xml:id="echoid-s13894" xml:space="preserve">motu luminis fibræ tenuiſſimæ, ex <pb o="(46)" file="0544" n="599" rhead="PHYSICES ELEMENTA"/> quibus retina conſtat, agitantur; </s> <s xml:id="echoid-s13895" xml:space="preserve">qua agitatione ideæ obje-<lb/>ctorum, in oculo depictorum, in mente excitantur. </s> <s xml:id="echoid-s13896" xml:space="preserve">Nexus in-<lb/>ter ideas & </s> <s xml:id="echoid-s13897" xml:space="preserve">motus quibus excitantur, ut ante dictum <anchor type="note" xlink:href="" symbol="*"/>, nos <anchor type="note" xlink:label="note-0544-01a" xlink:href="note-0544-01"/> latet: </s> <s xml:id="echoid-s13898" xml:space="preserve">in cauſis ſenſationum determinandis, non ultra ner-<lb/>vorum agitationes penetrare poſiumus.</s> <s xml:id="echoid-s13899" xml:space="preserve"/> </p> <div xml:id="echoid-div2069" type="float" level="2" n="2"> <note position="right" xlink:label="note-0543-08" xlink:href="note-0543-08a" xml:space="preserve">716.</note> <note symbol="*" position="left" xlink:label="note-0544-01" xlink:href="note-0544-01a" xml:space="preserve">502.</note> </div> <p> <s xml:id="echoid-s13900" xml:space="preserve">Quo pictura memorat a magis eſt exacta, quo objecta diſtin-<lb/> <anchor type="note" xlink:label="note-0544-02a" xlink:href="note-0544-02"/> ctius apparent. </s> <s xml:id="echoid-s13901" xml:space="preserve">Quando radii ab eodem puncto manantes <lb/> <anchor type="note" xlink:label="note-0544-03a" xlink:href="note-0544-03"/> non exactè in retinâ junguntur, illius pictura non eſt pun-<lb/>ctum ſed macula, quæ confunditur cum picturis punctorum <lb/>vicinorum; </s> <s xml:id="echoid-s13902" xml:space="preserve">in quo caſu viſio confuſa eſt.</s> <s xml:id="echoid-s13903" xml:space="preserve"/> </p> <div xml:id="echoid-div2070" type="float" level="2" n="3"> <note position="left" xlink:label="note-0544-02" xlink:href="note-0544-02a" xml:space="preserve">717.</note> <note position="left" xlink:label="note-0544-03" xlink:href="note-0544-03a" xml:space="preserve">718.</note> </div> <p> <s xml:id="echoid-s13904" xml:space="preserve">Cùm autem, pro varíâ puncti radiantis diſtantiâ, hujus <lb/> <anchor type="note" xlink:label="note-0544-04a" xlink:href="note-0544-04"/> focus magis aut minus removeatur <anchor type="note" xlink:href="" symbol="*"/>, neceſſe eſt, ut mutatio <anchor type="note" xlink:label="note-0544-05a" xlink:href="note-0544-05"/> detur in oculo, ne locus in quo pictura eſt exacta, ante aut <lb/>poſt retinam cadat, & </s> <s xml:id="echoid-s13905" xml:space="preserve">viſio confuſa ſit.</s> <s xml:id="echoid-s13906" xml:space="preserve"/> </p> <div xml:id="echoid-div2071" type="float" level="2" n="4"> <note position="left" xlink:label="note-0544-04" xlink:href="note-0544-04a" xml:space="preserve">719.</note> <note symbol="*" position="left" xlink:label="note-0544-05" xlink:href="note-0544-05a" xml:space="preserve">663.</note> </div> <p> <s xml:id="echoid-s13907" xml:space="preserve">Quænam autem hæc ſit mutatio difficulter admodum de-<lb/>terminatur, variæque dantur Philoſophorum ſententiæ; </s> <s xml:id="echoid-s13908" xml:space="preserve">cir-<lb/>ca quas in genere notabo, minimè probabile eſſe totius oculi <lb/> <anchor type="note" xlink:label="note-0544-06a" xlink:href="note-0544-06"/> figuram mutari, ad removendam aut admovendam retinam, <lb/>& </s> <s xml:id="echoid-s13909" xml:space="preserve">in interiori oculo mutationem quærendam eſſe.</s> <s xml:id="echoid-s13910" xml:space="preserve"/> </p> <div xml:id="echoid-div2072" type="float" level="2" n="5"> <note position="left" xlink:label="note-0544-06" xlink:href="note-0544-06a" xml:space="preserve">720.</note> </div> <p> <s xml:id="echoid-s13911" xml:space="preserve">Nam ſi figura oculi mutaretur, cùm in omnibus Animali-<lb/>bus æquè neceſſaria ſit mutatio de qua agitur, in omnibus <lb/>animalibus oculi figura eaſdem ſubibit mutationes; </s> <s xml:id="echoid-s13912" xml:space="preserve">ejuſdem <lb/>enim effectus cauſas varias in rerum natura non deprehen-<lb/>dimus. </s> <s xml:id="echoid-s13913" xml:space="preserve">In Balenâ verò ſclerotica nimium eſt dura, ut va-<lb/>riationi obnoxia ſit. </s> <s xml:id="echoid-s13914" xml:space="preserve">Ulterius, ſi talis detur mutatio in toto <lb/>oculo, orietur hæc ex muſculorum externorum preſſione, <lb/>quæ pro variò oculi ſitu diverſa erit, & </s> <s xml:id="echoid-s13915" xml:space="preserve">tantum regularis in <lb/>unico oculi ſitu.</s> <s xml:id="echoid-s13916" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13917" xml:space="preserve">Si nunc oculum in interiori examinemus, mutationem in <lb/>cryſtallino neceſſariò dari patebit; </s> <s xml:id="echoid-s13918" xml:space="preserve">qui tranſlatione in ocu-<lb/>lo, aut mutatione figuræ, deſideratum effectum præſtabit; <lb/></s> <s xml:id="echoid-s13919" xml:space="preserve">Radii enim retinam ante concurſum ſecantes, in retinâ con-<lb/>current, ſi convexior fiat cryſtallinus humor <anchor type="note" xlink:href="" symbol="*"/>, aut ſi, ſer- <anchor type="note" xlink:label="note-0544-07a" xlink:href="note-0544-07"/> vatâ hujus figurâ, ipſe magis verſus anteriorem oculi partem <lb/>feratur.</s> <s xml:id="echoid-s13920" xml:space="preserve"/> </p> <div xml:id="echoid-div2073" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0544-07" xlink:href="note-0544-07a" xml:space="preserve">695.</note> </div> <p> <s xml:id="echoid-s13921" xml:space="preserve">Cryſtallini humoris ſitum facile mutari, illumque ad reti-<lb/> <anchor type="note" xlink:label="note-0544-08a" xlink:href="note-0544-08"/> nam accedere & </s> <s xml:id="echoid-s13922" xml:space="preserve">ab hac recedere, manente illius axe, ex eo <pb o="(47)" file="0545" n="600" rhead="MATHEMATICA LIB. III. CAP. X."/> liquet, quod ligamina ciliaria muſculoſa ſint: </s> <s xml:id="echoid-s13923" xml:space="preserve">quando hi mu-<lb/>ſculi inflantur, & </s> <s xml:id="echoid-s13924" xml:space="preserve">breviores fiunt, minuitur cavitas quæ exin-<lb/>flexione horum ligaminum formatur in C l, C l; </s> <s xml:id="echoid-s13925" xml:space="preserve">quo com-<lb/>primitur humor vitreus, qui ipſe in humorem cryſtallinum <lb/>premit & </s> <s xml:id="echoid-s13926" xml:space="preserve">hunc propellit, hujuſque diſtantiam à retinâ auget; <lb/></s> <s xml:id="echoid-s13927" xml:space="preserve">quod in viſione objectorum propinquorum requiritur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13928" xml:space="preserve"/> </p> <div xml:id="echoid-div2074" type="float" level="2" n="7"> <note position="left" xlink:label="note-0544-08" xlink:href="note-0544-08a" xml:space="preserve">721.</note> </div> <note symbol="*" position="right" xml:space="preserve">663. 699.</note> <p> <s xml:id="echoid-s13929" xml:space="preserve">Aliam præter hanc in oculo mutationem dari, ex experi-<lb/>mento, in ſequentibus memorando <anchor type="note" xlink:href="" symbol="*"/>, demonſtratum fuit, <anchor type="note" xlink:label="note-0545-02a" xlink:href="note-0545-02"/> quæ cum hac contrariè agit; </s> <s xml:id="echoid-s13930" xml:space="preserve">quod unde deductum fuerit <lb/>dicetur. </s> <s xml:id="echoid-s13931" xml:space="preserve">Mutatio autem ſecunda etiam ad ipſum cryſtalli-<lb/>num referenda eſt; </s> <s xml:id="echoid-s13932" xml:space="preserve">hic quando à ligaminibus ciliaribus tra-<lb/> <anchor type="note" xlink:label="note-0545-03a" xlink:href="note-0545-03"/> hitur, quo à fundo oculi recedit, etiam planior fit, quare <lb/>ut magis recedat, quàm ſi figuram immutabilem baberet, ne-<lb/> <anchor type="note" xlink:label="note-0545-04a" xlink:href="note-0545-04"/> ceſſe eſt: </s> <s xml:id="echoid-s13933" xml:space="preserve">id eſt, mutationem magis ſenſibilem eſſe, quod <lb/>uſum ſuum habere videbimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s13934" xml:space="preserve"/> </p> <div xml:id="echoid-div2075" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0545-02" xlink:href="note-0545-02a" xml:space="preserve">753.</note> <note position="right" xlink:label="note-0545-03" xlink:href="note-0545-03a" xml:space="preserve">722.</note> <note position="right" xlink:label="note-0545-04" xlink:href="note-0545-04a" xml:space="preserve">723.</note> </div> <note symbol="*" position="right" xml:space="preserve">730.</note> <p> <s xml:id="echoid-s13935" xml:space="preserve">Limites ſuos habent hæ mutationes in oculo, inde etiam <lb/>objecta tantum diſtincta apparent inter certos limites, ad <lb/> <anchor type="note" xlink:label="note-0545-06a" xlink:href="note-0545-06"/> varias diſtantias pro variis oculis poſitos; </s> <s xml:id="echoid-s13936" xml:space="preserve">& </s> <s xml:id="echoid-s13937" xml:space="preserve">ſæpiſſimè in <lb/> <anchor type="note" xlink:label="note-0545-07a" xlink:href="note-0545-07"/> eodem bomine, non pro ſingulis oculis iidem limites dan-<lb/>tur, quod ejuſdem ferè eſt utilitatis, ac ſi pro ambobus <lb/>oculis limites magis inte ſe diſtarent; </s> <s xml:id="echoid-s13938" xml:space="preserve">unico enim oculo ob-<lb/>jectum diſtinctè videri ſat eſt. </s> <s xml:id="echoid-s13939" xml:space="preserve">In quibuſdam etiam, proxi-<lb/>mus limes reſpectu unius oculi, magis diſtat quàm maximè <lb/>remotus reſpectu alterius, in hoc caſu objecta propinqua & </s> <s xml:id="echoid-s13940" xml:space="preserve"><lb/>valdè remota diſtinctè videntur, intermedia confuſa apparent.</s> <s xml:id="echoid-s13941" xml:space="preserve"/> </p> <div xml:id="echoid-div2076" type="float" level="2" n="9"> <note position="right" xlink:label="note-0545-06" xlink:href="note-0545-06a" xml:space="preserve">724.</note> <note position="right" xlink:label="note-0545-07" xlink:href="note-0545-07a" xml:space="preserve">725.</note> </div> <p> <s xml:id="echoid-s13942" xml:space="preserve">Pictura in fundo oculi, ut dictum <anchor type="note" xlink:href="" symbol="*"/>, eſt inverſa; </s> <s xml:id="echoid-s13943" xml:space="preserve">unde <anchor type="note" xlink:label="note-0545-08a" xlink:href="note-0545-08"/> quæſitum, quare objecta erecta appareant? </s> <s xml:id="echoid-s13944" xml:space="preserve">Quæſtione re-<lb/> <anchor type="note" xlink:label="note-0545-09a" xlink:href="note-0545-09"/> ſpondemus, an quis melius concipiat nexum inter ideam in <lb/>mente, & </s> <s xml:id="echoid-s13945" xml:space="preserve">figuram erectam, quàm everſam? </s> <s xml:id="echoid-s13946" xml:space="preserve">nexum in neu-<lb/>tro caſu nos nullum percipere fatemur: </s> <s xml:id="echoid-s13947" xml:space="preserve">Experientia autem <lb/>docet, dari nexum inter picturam inverſam in oculo & </s> <s xml:id="echoid-s13948" xml:space="preserve">ob-<lb/>jecti erecti ideam; </s> <s xml:id="echoid-s13949" xml:space="preserve">& </s> <s xml:id="echoid-s13950" xml:space="preserve">præterea nihil novimus.</s> <s xml:id="echoid-s13951" xml:space="preserve"/> </p> <div xml:id="echoid-div2077" type="float" level="2" n="10"> <note position="right" xlink:label="note-0545-08" xlink:href="note-0545-08a" xml:space="preserve">726.</note> <note symbol="*" position="right" xlink:label="note-0545-09" xlink:href="note-0545-09a" xml:space="preserve">714.</note> </div> <p> <s xml:id="echoid-s13952" xml:space="preserve">Ambobus oculis ſi idem objectum intueamur unicum appa-<lb/> <anchor type="note" xlink:label="note-0545-10a" xlink:href="note-0545-10"/> ret; </s> <s xml:id="echoid-s13953" xml:space="preserve">illudque in eo caſu ſolo, quando objectum in punctis re-<lb/>ſpondentibus retinæ depingitur; </s> <s xml:id="echoid-s13954" xml:space="preserve">quod probabiliter ex con-<lb/>curſu nervorum opticorum ſequitur. </s> <s xml:id="echoid-s13955" xml:space="preserve">Obſervatur enim in <lb/>omnibus animalibus, quæ idem objectum ambobus oculis <pb o="(48)" file="0546" n="601" rhead="PHYSICES ELEMENTA"/> vident, nervos opticos concurrere, antequam ad cerebrum <lb/>perveniant, ad quod iterum ſeparati pertingunt; </s> <s xml:id="echoid-s13956" xml:space="preserve">in animali-<lb/>bus verò quæ ſingulis oculis diverſa objecta intuentur, nervi <lb/>optici ab oculis ad cerebrum uſque ſeparantur.</s> <s xml:id="echoid-s13957" xml:space="preserve"/> </p> <div xml:id="echoid-div2078" type="float" level="2" n="11"> <note position="right" xlink:label="note-0545-10" xlink:href="note-0545-10a" xml:space="preserve">727.</note> </div> <p> <s xml:id="echoid-s13958" xml:space="preserve">Vnicum tantum punctum eodem tempore diſtinctiſſimè vi-<lb/> <anchor type="note" xlink:label="note-0546-01a" xlink:href="note-0546-01"/> deri poteſt, quod nempe in axe oculi repreſentatur; </s> <s xml:id="echoid-s13959" xml:space="preserve">ſi am-<lb/>bobus oculis punctum quis intueatur, ita ſunt dirigendi ocu-<lb/>li, ut axes amborum oculorum continuati in illo concur-<lb/>rant; </s> <s xml:id="echoid-s13960" xml:space="preserve">quod obtinet, quando in aliquod punctum intentos <lb/>oculos habemus.</s> <s xml:id="echoid-s13961" xml:space="preserve"/> </p> <div xml:id="echoid-div2079" type="float" level="2" n="12"> <note position="left" xlink:label="note-0546-01" xlink:href="note-0546-01a" xml:space="preserve">728.</note> </div> <p> <s xml:id="echoid-s13962" xml:space="preserve">Hæc ipſa axium directio in judicio circa diſtantiam obje-<lb/>ctorum viſorum uſum habet; </s> <s xml:id="echoid-s13963" xml:space="preserve">ſitus enim diverſus oculorum <lb/>pro vario angulo ab axibus formato datur, & </s> <s xml:id="echoid-s13964" xml:space="preserve">pendet hic ab <lb/>objecti diſtantiâ: </s> <s xml:id="echoid-s13965" xml:space="preserve">unde, ne quidem ad illud attendendo, uſu <lb/>facultatem acquirimus, de diſtantiâ dijudicandi, ex axium di-<lb/> <anchor type="note" xlink:label="note-0546-02a" xlink:href="note-0546-02"/> rectione; </s> <s xml:id="echoid-s13966" xml:space="preserve">quæ nobis ſenſibilis eſt, quia à motu oculi, nobis ſen-<lb/>ſibili, pendet. </s> <s xml:id="echoid-s13967" xml:space="preserve">Videmus ergo uſum duorum oculorum ad <lb/>certam â ſe mutuo diſtantiam poſitorum; </s> <s xml:id="echoid-s13968" xml:space="preserve">quamdiu hæc o-<lb/>culorum diſtantia ſenſibilem rationem babet ad objectorum <lb/>diſtantiam, de bac judicium ſatis certum eſt.</s> <s xml:id="echoid-s13969" xml:space="preserve"/> </p> <div xml:id="echoid-div2080" type="float" level="2" n="13"> <note position="left" xlink:label="note-0546-02" xlink:href="note-0546-02a" xml:space="preserve">729.</note> </div> <p> <s xml:id="echoid-s13970" xml:space="preserve">De minoribus diſtantiis etiam unico oculo dijudicamus; <lb/></s> <s xml:id="echoid-s13971" xml:space="preserve"> <anchor type="note" xlink:label="note-0546-03a" xlink:href="note-0546-03"/> quia in variatione exiguæ diſtantiæ mutatio in oculo <anchor type="note" xlink:href="" symbol="*"/> ſenſi- <anchor type="note" xlink:label="note-0546-04a" xlink:href="note-0546-04"/> bilis eſt.</s> <s xml:id="echoid-s13972" xml:space="preserve"/> </p> <div xml:id="echoid-div2081" type="float" level="2" n="14"> <note position="left" xlink:label="note-0546-03" xlink:href="note-0546-03a" xml:space="preserve">730.</note> <note symbol="*" position="left" xlink:label="note-0546-04" xlink:href="note-0546-04a" xml:space="preserve">721. 723.</note> </div> <p> <s xml:id="echoid-s13973" xml:space="preserve">De magnis diſtantiis, ſi de objectis notis agatur, judicium <lb/> <anchor type="note" xlink:label="note-0546-05a" xlink:href="note-0546-05"/> ex magnitudine apparente & </s> <s xml:id="echoid-s13974" xml:space="preserve">colore fertur.</s> <s xml:id="echoid-s13975" xml:space="preserve"/> </p> <div xml:id="echoid-div2082" type="float" level="2" n="15"> <note position="left" xlink:label="note-0546-05" xlink:href="note-0546-05a" xml:space="preserve">731.</note> </div> <p style="it"> <s xml:id="echoid-s13976" xml:space="preserve">De maximis impoſſibile eſt judicium, niſi ex diverſis locis <lb/> <anchor type="note" xlink:label="note-0546-06a" xlink:href="note-0546-06"/> idem objectum obſervetur.</s> <s xml:id="echoid-s13977" xml:space="preserve"/> </p> <div xml:id="echoid-div2083" type="float" level="2" n="16"> <note position="left" xlink:label="note-0546-06" xlink:href="note-0546-06a" xml:space="preserve">732.</note> </div> <p> <s xml:id="echoid-s13978" xml:space="preserve">Magnitudo apparens objecti, pendet à magnitudine picturæ <lb/> <anchor type="note" xlink:label="note-0546-07a" xlink:href="note-0546-07"/> in fundo oculi, quæ ipſa pendet ab angulo ſub quo objectum <lb/>videtur, id eſt, qui formatur à lineis ab extremitatibus ob-<lb/>jecti ad oculum ductis.</s> <s xml:id="echoid-s13979" xml:space="preserve"/> </p> <div xml:id="echoid-div2084" type="float" level="2" n="17"> <note position="left" xlink:label="note-0546-07" xlink:href="note-0546-07a" xml:space="preserve">733.</note> </div> <p> <s xml:id="echoid-s13980" xml:space="preserve">Magnitudo hæc apparens diſtinguenda eſt à magnitudine, <lb/> <anchor type="note" xlink:label="note-0546-08a" xlink:href="note-0546-08"/> quam mens noſtra tribuit objecto viſo, quæ ultima judicio <lb/>nititur, quod non ſolam apparentiam pro fundamento habet. <lb/></s> <s xml:id="echoid-s13981" xml:space="preserve">Notum eſt unicuique, objectum eo minus apparêre, quo ma-<lb/>gis diſtat; </s> <s xml:id="echoid-s13982" xml:space="preserve">unde pro majori diſtantiâ objecti, ſi nota ſit, ma-<lb/>gnitudo apparens objecti augetur in judicio à mente lato, <pb o="(49)" file="0547" n="602" rhead="MATHEMATICA LIB. III. CAP. XI."/> quod fit ne quidem ad illud attendendo. </s> <s xml:id="echoid-s13983" xml:space="preserve">Ideò idem obje-<lb/>ctum, ad eandem diſtantiam, diverſae; </s> <s xml:id="echoid-s13984" xml:space="preserve">apparet magnitudinis, <lb/>ſi judicium de diſtantiâ fuerit diverſum.</s> <s xml:id="echoid-s13985" xml:space="preserve"/> </p> <div xml:id="echoid-div2085" type="float" level="2" n="18"> <note position="left" xlink:label="note-0546-08" xlink:href="note-0546-08a" xml:space="preserve">734.</note> </div> <p> <s xml:id="echoid-s13986" xml:space="preserve">Exemplum notabile habemus in Sole & </s> <s xml:id="echoid-s13987" xml:space="preserve">Lunâ, majoribus <lb/> <anchor type="note" xlink:label="note-0547-01a" xlink:href="note-0547-01"/> apparentibus propè horizontem, quàm ad majorem altitudi-<lb/>nim; </s> <s xml:id="echoid-s13988" xml:space="preserve">licèt, ut Aſtronomis notum, pictura Solis in fundo oculi <lb/>ſit eadem in utroque caſu, & </s> <s xml:id="echoid-s13989" xml:space="preserve">Lunæ pictura minor ſit, quando <lb/>propè horizontem major apparet; </s> <s xml:id="echoid-s13990" xml:space="preserve">de diſtantiâ in neutro caſu <lb/>judicium ferre non poſſumus <anchor type="note" xlink:href="" symbol="*"/>, ſed major, ex interpoſitis <anchor type="note" xlink:label="note-0547-02a" xlink:href="note-0547-02"/> campis & </s> <s xml:id="echoid-s13991" xml:space="preserve">coelo, hæc videtur propè horizontem. </s> <s xml:id="echoid-s13992" xml:space="preserve">Per tubum <lb/>ſi intueamur corpora memorata, diſtantia apparens evaneſcit, <lb/>& </s> <s xml:id="echoid-s13993" xml:space="preserve">cum hac magnitudo quæ ex ipſà deducitur. </s> <s xml:id="echoid-s13994" xml:space="preserve">Ab infantiâ <lb/>continuò, & </s> <s xml:id="echoid-s13995" xml:space="preserve">adhucdum omnibus momentis, ideam diſtan-<lb/>tiæ cum augmento in magnitudine apparente jungimus, <lb/>(quod ad verum de magnitudine judicium ferendum neceſſe <lb/>eſt,) quo hæ ideæ ita intimè junguntur, ut ſeparari ne-<lb/>queant, ne quidem in illis caſibus, in quibus novimus illas <lb/>nos in errorem ducere. </s> <s xml:id="echoid-s13996" xml:space="preserve">Quòt errores tribuendi ſint ideis <lb/>ita junctis norunt logici.</s> <s xml:id="echoid-s13997" xml:space="preserve"/> </p> <div xml:id="echoid-div2086" type="float" level="2" n="19"> <note position="right" xlink:label="note-0547-01" xlink:href="note-0547-01a" xml:space="preserve">735.</note> <note symbol="*" position="right" xlink:label="note-0547-02" xlink:href="note-0547-02a" xml:space="preserve">732.</note> </div> </div> <div xml:id="echoid-div2088" type="section" level="1" n="513"> <head xml:id="echoid-head681" xml:space="preserve">CAPUT XI.</head> <head xml:id="echoid-head682" style="it" xml:space="preserve">De viſione trans vitra, & corrigendis quibuſdam <lb/>oculorum vitiis.</head> <p> <s xml:id="echoid-s13998" xml:space="preserve">OBjectum viſibile eſt, quia ſingula hujus puncta ſunt quaſi <lb/>puncta radiantia <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s13999" xml:space="preserve">Punctum ergo apparet in illo loco, <anchor type="note" xlink:label="note-0547-03a" xlink:href="note-0547-03"/> ex quo radii divergentes emittuntur.</s> <s xml:id="echoid-s14000" xml:space="preserve"/> </p> <div xml:id="echoid-div2088" type="float" level="2" n="1"> <note position="right" xlink:label="note-0547-03" xlink:href="note-0547-03a" xml:space="preserve">736.</note> </div> <note symbol="*" position="right" xml:space="preserve">713. 714. 715.</note> <p> <s xml:id="echoid-s14001" xml:space="preserve">Si radii utcunque in flexi divergentes oculum intrent, da-<lb/> <anchor type="note" xlink:label="note-0547-05a" xlink:href="note-0547-05"/> bitur punctum viſibile in radiorum foco imaginario; </s> <s xml:id="echoid-s14002" xml:space="preserve">planè e-<lb/>nim eodem modo radii hi oculum intrant, ac radii directè <lb/>ex illo foco procedentes; </s> <s xml:id="echoid-s14003" xml:space="preserve">idemque ut in retinâ concur-<lb/>rant, cryſtallini ſitus requiritur: </s> <s xml:id="echoid-s14004" xml:space="preserve">ita ut reſpectu ſpectatoris <lb/>non interſit, utrum illi radii refracti, an hi directi oculum <lb/>intrent; </s> <s xml:id="echoid-s14005" xml:space="preserve">& </s> <s xml:id="echoid-s14006" xml:space="preserve">idem motus detur in oculo, cùm ſe conſtituit <lb/>ut viſio ſit diſtincta <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14007" xml:space="preserve"/> </p> <div xml:id="echoid-div2089" type="float" level="2" n="2"> <note position="right" xlink:label="note-0547-05" xlink:href="note-0547-05a" xml:space="preserve">737.</note> </div> <note symbol="*" position="right" xml:space="preserve">719. 730.</note> <p style="it"> <s xml:id="echoid-s14008" xml:space="preserve">Punctum eo magis illuminatum apparet, quo plures radii <lb/> <anchor type="note" xlink:label="note-0547-07a" xlink:href="note-0547-07"/> ab boc procedentes oculum intrant.</s> <s xml:id="echoid-s14009" xml:space="preserve"/> </p> <div xml:id="echoid-div2090" type="float" level="2" n="3"> <note position="right" xlink:label="note-0547-07" xlink:href="note-0547-07a" xml:space="preserve">738.</note> </div> <pb o="(50)" file="0548" n="603" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s14010" xml:space="preserve">Objecta viſa trans vitrum planum, ſuperficiebus inter. </s> <s xml:id="echoid-s14011" xml:space="preserve">ſe <lb/> <anchor type="note" xlink:label="note-0548-01a" xlink:href="note-0548-01"/> parallelis terminatum, ad minorem diſtantiam, quàm nudis <lb/> <anchor type="note" xlink:label="note-0548-02a" xlink:href="note-0548-02"/> oculis apparent. </s> <s xml:id="echoid-s14012" xml:space="preserve">Sit A punctum viſibile; </s> <s xml:id="echoid-s14013" xml:space="preserve">radii ex hoc pro-<lb/>cedentes, & </s> <s xml:id="echoid-s14014" xml:space="preserve">oculum intrantes, dantur inter A b, & </s> <s xml:id="echoid-s14015" xml:space="preserve">A b; <lb/></s> <s xml:id="echoid-s14016" xml:space="preserve">hi refracti in vitro V V moventur per b c, b c; </s> <s xml:id="echoid-s14017" xml:space="preserve">& </s> <s xml:id="echoid-s14018" xml:space="preserve">exeunt <lb/>per c d, c d parallelas lineis A b, A b <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s14019" xml:space="preserve">quia autem <anchor type="note" xlink:label="note-0548-03a" xlink:href="note-0548-03"/> b c, b c ad perpendicularem refringuntur <anchor type="note" xlink:href="" symbol="*"/>, c d, c d, in- <anchor type="note" xlink:label="note-0548-04a" xlink:href="note-0548-04"/> ter b A & </s> <s xml:id="echoid-s14020" xml:space="preserve">b A cadunt; </s> <s xml:id="echoid-s14021" xml:space="preserve">id eſt, ſeſe mutuò ſecant in a mi-<lb/>nus diſtanti quam A; </s> <s xml:id="echoid-s14022" xml:space="preserve">focus ergo imaginarius radiorum ocu-<lb/>lum intrantium eſt a, in quo punctum A apparet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14023" xml:space="preserve"/> </p> <div xml:id="echoid-div2091" type="float" level="2" n="4"> <note position="left" xlink:label="note-0548-01" xlink:href="note-0548-01a" xml:space="preserve">739.</note> <note position="left" xlink:label="note-0548-02" xlink:href="note-0548-02a" xml:space="preserve">TAB. X. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0548-03" xlink:href="note-0548-03a" xml:space="preserve">628.</note> <note symbol="*" position="left" xlink:label="note-0548-04" xlink:href="note-0548-04a" xml:space="preserve">624.</note> </div> <note symbol="*" position="left" xml:space="preserve">737.</note> <p> <s xml:id="echoid-s14024" xml:space="preserve">Punctum hoc etiam magis illuminatum apparet, viſum <lb/> <anchor type="note" xlink:label="note-0548-06a" xlink:href="note-0548-06"/> trans vitrum memoratum. </s> <s xml:id="echoid-s14025" xml:space="preserve">Nam omnes radii inter A b & </s> <s xml:id="echoid-s14026" xml:space="preserve"><lb/>A b pupillam intrant inter d & </s> <s xml:id="echoid-s14027" xml:space="preserve">d; </s> <s xml:id="echoid-s14028" xml:space="preserve">cùm verò lineæ A b, A b <lb/>ſint parallelæ lineis c d, c d, & </s> <s xml:id="echoid-s14029" xml:space="preserve">hæ dentur inter illas, A b <lb/>& </s> <s xml:id="echoid-s14030" xml:space="preserve">A b continuatæ ultra d & </s> <s xml:id="echoid-s14031" xml:space="preserve">d caderent; </s> <s xml:id="echoid-s14032" xml:space="preserve">ideoque ſublato vi-<lb/>tro, radii qui nunc pupillam intrant majus ſpatium occupa-<lb/>rent, & </s> <s xml:id="echoid-s14033" xml:space="preserve">non omnes oculum intrarent.</s> <s xml:id="echoid-s14034" xml:space="preserve"/> </p> <div xml:id="echoid-div2092" type="float" level="2" n="5"> <note position="left" xlink:label="note-0548-06" xlink:href="note-0548-06a" xml:space="preserve">740.</note> </div> <p> <s xml:id="echoid-s14035" xml:space="preserve">Magnitudo apparens objecti augetur interpoſito vitro pla-<lb/> <anchor type="note" xlink:label="note-0548-07a" xlink:href="note-0548-07"/> no; </s> <s xml:id="echoid-s14036" xml:space="preserve">Objectum A E nudo oculo videtur ſub angulo A d E; <lb/></s> <s xml:id="echoid-s14037" xml:space="preserve"> <anchor type="note" xlink:label="note-0548-08a" xlink:href="note-0548-08"/> poſito verò vitro V V, ob refractionem per A b c d & </s> <s xml:id="echoid-s14038" xml:space="preserve">E b c d, <lb/>videtur ſub angulo c d c, qui præcedente major eſt. </s> <s xml:id="echoid-s14039" xml:space="preserve">Non ta-<lb/> <anchor type="note" xlink:label="note-0548-09a" xlink:href="note-0548-09"/> men pro ratione auctæ magnitudinis, apparentis objectum <lb/>majus videtur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14040" xml:space="preserve">nam ad minorem diſtantiam apparet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14041" xml:space="preserve"/> </p> <div xml:id="echoid-div2093" type="float" level="2" n="6"> <note position="left" xlink:label="note-0548-07" xlink:href="note-0548-07a" xml:space="preserve">741.</note> <note position="left" xlink:label="note-0548-08" xlink:href="note-0548-08a" xml:space="preserve">TAB. X. <lb/>fig. 2.</note> <note position="left" xlink:label="note-0548-09" xlink:href="note-0548-09a" xml:space="preserve">742.</note> </div> <note symbol="*" position="left" xml:space="preserve">734.</note> <p> <s xml:id="echoid-s14042" xml:space="preserve">Augmentum magnitudinis apparentis eo major eſt, quo ma-<lb/> <anchor type="note" xlink:label="note-0548-11a" xlink:href="note-0548-11"/> <anchor type="note" xlink:label="note-0548-12a" xlink:href="note-0548-12"/> gis differunt anguli a d E & </s> <s xml:id="echoid-s14043" xml:space="preserve">c d c; </s> <s xml:id="echoid-s14044" xml:space="preserve">quorum differentia creſcit <lb/>cum acceſſu interſectionum linearum A d cum b c & </s> <s xml:id="echoid-s14045" xml:space="preserve">E d <lb/>cum b c, verſus puncta b & </s> <s xml:id="echoid-s14046" xml:space="preserve">b; </s> <s xml:id="echoid-s14047" xml:space="preserve">quod obtinet in acceſſu objecti <lb/>ad vitrum; </s> <s xml:id="echoid-s14048" xml:space="preserve">ideoque omnium maxima eſt, quando objectum <lb/>vitrum tangit; </s> <s xml:id="echoid-s14049" xml:space="preserve">quod probat objecta in ipſo vitro etiam am-<lb/>plificata apparêre.</s> <s xml:id="echoid-s14050" xml:space="preserve"/> </p> <div xml:id="echoid-div2094" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0548-11" xlink:href="note-0548-11a" xml:space="preserve">739.</note> <note position="left" xlink:label="note-0548-12" xlink:href="note-0548-12a" xml:space="preserve">743.</note> </div> <p> <s xml:id="echoid-s14051" xml:space="preserve">Et in genere, poſito oculo in medio rariori, objectum quod <lb/> <anchor type="note" xlink:label="note-0548-13a" xlink:href="note-0548-13"/> in medio denſiori videtur majus apparere, quod etiam refra-<lb/>ctione appropinquatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14052" xml:space="preserve">Confirmantur hæc quotidianâ ex- <anchor type="note" xlink:label="note-0548-14a" xlink:href="note-0548-14"/> perientiâ, reſpectu objectorum in aquâ viſorum.</s> <s xml:id="echoid-s14053" xml:space="preserve"/> </p> <div xml:id="echoid-div2095" type="float" level="2" n="8"> <note position="left" xlink:label="note-0548-13" xlink:href="note-0548-13a" xml:space="preserve">744.</note> <note symbol="*" position="left" xlink:label="note-0548-14" xlink:href="note-0548-14a" xml:space="preserve">659.</note> </div> <p> <s xml:id="echoid-s14054" xml:space="preserve">Detur punctum A trans lentem convexam V V viſum, ra-<lb/> <anchor type="note" xlink:label="note-0548-15a" xlink:href="note-0548-15"/> dii A b, A b in c d, c d minus divergentes exeunt, quaſi <lb/> <anchor type="note" xlink:label="note-0548-16a" xlink:href="note-0548-16"/> nempe ex a procederent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14055" xml:space="preserve">ideoque punctum hoc ad majo- <anchor type="note" xlink:label="note-0548-17a" xlink:href="note-0548-17"/> <pb o="(51)" file="0549" n="604" rhead="MATHEMATICA LIB. III. CAP. XI."/> rem diſtantiam apparet <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14056" xml:space="preserve">Etiam magis illuminatum; </s> <s xml:id="echoid-s14057" xml:space="preserve">nam <anchor type="note" xlink:label="note-0549-01a" xlink:href="note-0549-01"/> tranſeundo per vitrum ad ſe mutuo accedunt radii, <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s14058" xml:space="preserve">in <anchor type="note" xlink:label="note-0549-02a" xlink:href="note-0549-02"/> minus ſpatium rediguntur, quare etiam majori numero pu-<lb/> <anchor type="note" xlink:label="note-0549-03a" xlink:href="note-0549-03"/> pillam intrant.</s> <s xml:id="echoid-s14059" xml:space="preserve"/> </p> <div xml:id="echoid-div2096" type="float" level="2" n="9"> <note position="left" xlink:label="note-0548-15" xlink:href="note-0548-15a" xml:space="preserve">745.</note> <note position="left" xlink:label="note-0548-16" xlink:href="note-0548-16a" xml:space="preserve">TAB. X. <lb/>fig. 3.</note> <note symbol="*" position="left" xlink:label="note-0548-17" xlink:href="note-0548-17a" xml:space="preserve">699.</note> <note position="right" xlink:label="note-0549-01" xlink:href="note-0549-01a" xml:space="preserve">746.</note> <note symbol="*" position="right" xlink:label="note-0549-02" xlink:href="note-0549-02a" xml:space="preserve">737.</note> <note symbol="*" position="right" xlink:label="note-0549-03" xlink:href="note-0549-03a" xml:space="preserve">695.</note> </div> <p> <s xml:id="echoid-s14060" xml:space="preserve">Magnitudo apparens objecti etiam augetur; </s> <s xml:id="echoid-s14061" xml:space="preserve">id eſt, Ob-<lb/> <anchor type="note" xlink:label="note-0549-04a" xlink:href="note-0549-04"/> jectum ſub majori angulo trans vitrum convexum vide-<lb/> <anchor type="note" xlink:label="note-0549-05a" xlink:href="note-0549-05"/> tur, quod ex inſpectione figurarum patet: </s> <s xml:id="echoid-s14062" xml:space="preserve">Objectum A E <lb/>nudis oculis videtur ſub angulo A d E, nunc autem ſub an-<lb/>gulo majori c d c; </s> <s xml:id="echoid-s14063" xml:space="preserve">nam (in fig. </s> <s xml:id="echoid-s14064" xml:space="preserve">4.) </s> <s xml:id="echoid-s14065" xml:space="preserve">radii A b, E b conver-<lb/>gentes, magis convergunt ex lente exeuntes <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14066" xml:space="preserve">aut (in fig. </s> <s xml:id="echoid-s14067" xml:space="preserve">5.)</s> <s xml:id="echoid-s14068" xml:space="preserve"> <anchor type="note" xlink:label="note-0549-06a" xlink:href="note-0549-06"/> divergentes, convergentes ad oculum perveniunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14069" xml:space="preserve">Idcir- <anchor type="note" xlink:label="note-0549-07a" xlink:href="note-0549-07"/> co objectum amplificatum apparet, & </s> <s xml:id="echoid-s14070" xml:space="preserve">ex remotâ apparen-<lb/>tiâ <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14071" xml:space="preserve">ex auctâ hujus magnitudine <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14072" xml:space="preserve">ideo non ſequitur <anchor type="note" xlink:label="note-0549-08a" xlink:href="note-0549-08"/> magnitudo, quam objecto tribuimus, eandem proportionem <lb/> <anchor type="note" xlink:label="note-0549-09a" xlink:href="note-0549-09"/> cum magnitudine apparente; </s> <s xml:id="echoid-s14073" xml:space="preserve">quare non inhæremus in de-<lb/> <anchor type="note" xlink:label="note-0549-10a" xlink:href="note-0549-10"/> monſtrandis quæ hanc ſpectant. </s> <s xml:id="echoid-s14074" xml:space="preserve">Sed generaliter notamus;</s> <s xml:id="echoid-s14075" xml:space="preserve"/> </p> <div xml:id="echoid-div2097" type="float" level="2" n="10"> <note position="right" xlink:label="note-0549-04" xlink:href="note-0549-04a" xml:space="preserve">747.</note> <note position="right" xlink:label="note-0549-05" xlink:href="note-0549-05a" xml:space="preserve">TAB. X. <lb/>fig. 4. & 5.</note> <note symbol="*" position="right" xlink:label="note-0549-06" xlink:href="note-0549-06a" xml:space="preserve">700.</note> <note symbol="*" position="right" xlink:label="note-0549-07" xlink:href="note-0549-07a" xml:space="preserve">699.</note> <note position="right" xlink:label="note-0549-08" xlink:href="note-0549-08a" xml:space="preserve">748.</note> <note symbol="*" position="right" xlink:label="note-0549-09" xlink:href="note-0549-09a" xml:space="preserve">745.</note> <note symbol="*" position="right" xlink:label="note-0549-10" xlink:href="note-0549-10a" xml:space="preserve">734.</note> </div> <p style="it"> <s xml:id="echoid-s14076" xml:space="preserve">Angulum, ſub quo objectum trans vitrum convexum vide-<lb/> <anchor type="note" xlink:label="note-0549-11a" xlink:href="note-0549-11"/> tur, minui in receſſu oculi à vitro; </s> <s xml:id="echoid-s14077" xml:space="preserve">quamdiu objectum non <lb/>diſtat à vitro ultra punctum, in quo radii paralleli colligun-<lb/>tur: </s> <s xml:id="echoid-s14078" xml:space="preserve">poſito verò objecto ad majorem diſtantiam, augetur ma-<lb/>gnitudo apparens in oculi receſſu.</s> <s xml:id="echoid-s14079" xml:space="preserve"/> </p> <div xml:id="echoid-div2098" type="float" level="2" n="11"> <note position="right" xlink:label="note-0549-11" xlink:href="note-0549-11a" xml:space="preserve">749.</note> </div> <p> <s xml:id="echoid-s14080" xml:space="preserve">Eodem modo, poſito oculo inter vitrum & </s> <s xml:id="echoid-s14081" xml:space="preserve">focum radio-<lb/> <anchor type="note" xlink:label="note-0549-12a" xlink:href="note-0549-12"/> rum parallelorum, in receſſu objecti minuitur angulus memo-<lb/>ratus; </s> <s xml:id="echoid-s14082" xml:space="preserve">poſito oculo ad majorem diſtantiam, idem angulus in <lb/>receſſu objecti augetur; </s> <s xml:id="echoid-s14083" xml:space="preserve">in quo ultimo caſu ita poteſt remo-<lb/>veri objectum, ut trans vitrum non ſit viſibile, ut ſtatim <lb/>dicetur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14084" xml:space="preserve"/> </p> <div xml:id="echoid-div2099" type="float" level="2" n="12"> <note position="right" xlink:label="note-0549-12" xlink:href="note-0549-12a" xml:space="preserve">750.</note> </div> <note symbol="*" position="right" xml:space="preserve">754.</note> <p> <s xml:id="echoid-s14085" xml:space="preserve">In ipſis etiam caſibus, in quibus objecta ſunt viſibilia, non <lb/>ſemper diſtinctè apparent.</s> <s xml:id="echoid-s14086" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14087" xml:space="preserve">Nam ut punctum diſtinctum appareat requiritur, ut ra-<lb/> <anchor type="note" xlink:label="note-0549-14a" xlink:href="note-0549-14"/> dii à puncto procedentes divergentes oculum intrent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14088" xml:space="preserve">& </s> <s xml:id="echoid-s14089" xml:space="preserve">ut <anchor type="note" xlink:label="note-0549-15a" xlink:href="note-0549-15"/> focus imaginarius borum radiorum detur, reſpectu ſpectato-<lb/>ris, inter limites diſtinctæ viſionis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14090" xml:space="preserve"/> </p> <div xml:id="echoid-div2100" type="float" level="2" n="13"> <note position="right" xlink:label="note-0549-14" xlink:href="note-0549-14a" xml:space="preserve">751.</note> <note symbol="*" position="right" xlink:label="note-0549-15" xlink:href="note-0549-15a" xml:space="preserve">736.</note> </div> <note symbol="*" position="right" xml:space="preserve">737. 724.</note> <p> <s xml:id="echoid-s14091" xml:space="preserve">Si objectum removeatur ultra focum radiorum parallelo-<lb/> <anchor type="note" xlink:label="note-0549-17a" xlink:href="note-0549-17"/> rum, radii à puncto objecti manantes convergentes oculum <lb/>intrant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14092" xml:space="preserve">qui caſus nudis oculis impoſſibilis eſt: </s> <s xml:id="echoid-s14093" xml:space="preserve">in hoc vi- <anchor type="note" xlink:label="note-0549-18a" xlink:href="note-0549-18"/> ſio ſemper confufa datur, & </s> <s xml:id="echoid-s14094" xml:space="preserve">oculus ſeſe diſponit ut viſio <pb o="(52)" file="0550" n="605" rhead="PHYSICES ELEMENTA"/> omnium minimè ſit confuſa; </s> <s xml:id="echoid-s14095" xml:space="preserve">ex hac diſpoſitione de diſtan-<lb/>tià dijudicamus, ut in omni caſu in quo unico oculo de hac <lb/>judicium fertur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14096" xml:space="preserve"/> </p> <div xml:id="echoid-div2101" type="float" level="2" n="14"> <note position="right" xlink:label="note-0549-17" xlink:href="note-0549-17a" xml:space="preserve">752.</note> <note symbol="*" position="right" xlink:label="note-0549-18" xlink:href="note-0549-18a" xml:space="preserve">699.</note> </div> <note symbol="*" position="left" xml:space="preserve">730.</note> <p> <s xml:id="echoid-s14097" xml:space="preserve">Hæc autem diſtantia non ſemper eadem videtur, unde <lb/> <anchor type="note" xlink:label="note-0550-02a" xlink:href="note-0550-02"/> deducuntur, quæ de mutatione figuræ cryſtallini dicta ſunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14098" xml:space="preserve"> <anchor type="note" xlink:label="note-0550-03a" xlink:href="note-0550-03"/> Si enim, poſito cryſtallino mobili, figuram immutatam ha-<lb/>beat, in omni objecti & </s> <s xml:id="echoid-s14099" xml:space="preserve">oculi ſitu, in quo radii ex puncto <lb/>manantes convergentes oculum intrant, minima dabitur <lb/>confuſio, ſi cryſtallinus quantum poteſt ad retinam accedat; <lb/></s> <s xml:id="echoid-s14100" xml:space="preserve">ita ut in omni caſu eadem daretur oculi diſpoſitio, & </s> <s xml:id="echoid-s14101" xml:space="preserve">idem <lb/>judicium circa diſtantiam; </s> <s xml:id="echoid-s14102" xml:space="preserve">quod ut dictum, experientiæ <lb/>adverſatur: </s> <s xml:id="echoid-s14103" xml:space="preserve">ſi autem in receſſu à retinâ cryſtallinus planior <lb/>fiat, mutationes dantur in oculo, quæ congruunt cum variis <lb/>judiciis circa diſtantiam in vario objecti & </s> <s xml:id="echoid-s14104" xml:space="preserve">oculi ſitu.</s> <s xml:id="echoid-s14105" xml:space="preserve"/> </p> <div xml:id="echoid-div2102" type="float" level="2" n="15"> <note position="left" xlink:label="note-0550-02" xlink:href="note-0550-02a" xml:space="preserve">753.</note> <note symbol="*" position="left" xlink:label="note-0550-03" xlink:href="note-0550-03a" xml:space="preserve">722.</note> </div> <p> <s xml:id="echoid-s14106" xml:space="preserve">Si in caſu ultimo, in quo radii à puncto convergunt, ita <lb/> <anchor type="note" xlink:label="note-0550-04a" xlink:href="note-0550-04"/> removeatur oculus, ut concurrant radii antequam ad oculum <lb/>perveniant, dantur in ſingulis punctis, in quo radii concur-<lb/>runt, puncta radiantia; </s> <s xml:id="echoid-s14107" xml:space="preserve">nempe foci ſingulorum punctorum <lb/>objecti, quibus objectum inverſum in plano albo repræſenta-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14108" xml:space="preserve">& </s> <s xml:id="echoid-s14109" xml:space="preserve">qui ſunt puncta viſibilia reſpectu oculi, ad quem <anchor type="note" xlink:label="note-0550-05a" xlink:href="note-0550-05"/> radii poſt interſectionem pervenire poſſunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14110" xml:space="preserve">In hoc caſu <anchor type="note" xlink:label="note-0550-06a" xlink:href="note-0550-06"/> objectum inverſum apparet, quia objectum ipſum non vide-<lb/>mus, ſed hujus repræſentationem poſt vitrum, quam inver-<lb/>ſam dari diximus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14111" xml:space="preserve"/> </p> <div xml:id="echoid-div2103" type="float" level="2" n="16"> <note position="left" xlink:label="note-0550-04" xlink:href="note-0550-04a" xml:space="preserve">754.</note> <note symbol="*" position="left" xlink:label="note-0550-05" xlink:href="note-0550-05a" xml:space="preserve">711.</note> <note symbol="*" position="left" xlink:label="note-0550-06" xlink:href="note-0550-06a" xml:space="preserve">736.</note> </div> <note symbol="*" position="left" xml:space="preserve">711.</note> <p> <s xml:id="echoid-s14112" xml:space="preserve">Nudis oculis dixi caſum impoſſibilem eſſe, in quo radii à <lb/> <anchor type="note" xlink:label="note-0550-08a" xlink:href="note-0550-08"/> puncto convergentes oculum intrant; </s> <s xml:id="echoid-s14113" xml:space="preserve">ideoque viſionem talem <lb/>ſemper confuſam eſſe; </s> <s xml:id="echoid-s14114" xml:space="preserve">quia nempe ad caſum impoſſibilem <lb/>oculorum conſtructio non adaptatur: </s> <s xml:id="echoid-s14115" xml:space="preserve">aliquando tamen, ſed <lb/>rarò, & </s> <s xml:id="echoid-s14116" xml:space="preserve">in hoc caſu objecta diſtinctè videntur, quod cùm <lb/>ex vitio oculi oriatur, quo omnis diſtincta viſio nudis oculis <lb/>tollitur, ad has exceptiones regulæ generalis attendendum <lb/>non eſle credidi.</s> <s xml:id="echoid-s14117" xml:space="preserve"/> </p> <div xml:id="echoid-div2104" type="float" level="2" n="17"> <note position="left" xlink:label="note-0550-08" xlink:href="note-0550-08a" xml:space="preserve">755.</note> </div> <p> <s xml:id="echoid-s14118" xml:space="preserve">Plerorumque ſenum vitium in oculis eſt, quod niſi obje-<lb/> <anchor type="note" xlink:label="note-0550-09a" xlink:href="note-0550-09"/> cta longinqua diſtinctè non videant, propinqua confuſe4; <lb/></s> <s xml:id="echoid-s14119" xml:space="preserve">quod, interpoſitâ lente convexâ, vitium corrigitur. </s> <s xml:id="echoid-s14120" xml:space="preserve">Radii, <lb/>à puncto propinquo manantes, ultra retinam concurrunt; </s> <s xml:id="echoid-s14121" xml:space="preserve"><lb/>per vitrum convexum minus divergunt dum oculum intrant, <pb o="(53)" file="0551" n="606" rhead="MATHEMATICA LIB. III. CAP XI."/> & </s> <s xml:id="echoid-s14122" xml:space="preserve">in oculo citius concurrunt; </s> <s xml:id="echoid-s14123" xml:space="preserve">id eſt ad oculum perveniunt <lb/>quaſi à puncto remotiori, quod à ſene diſtinctè videtur, <lb/>procederent.</s> <s xml:id="echoid-s14124" xml:space="preserve"/> </p> <div xml:id="echoid-div2105" type="float" level="2" n="18"> <note position="left" xlink:label="note-0550-09" xlink:href="note-0550-09a" xml:space="preserve">756.</note> </div> <p style="it"> <s xml:id="echoid-s14125" xml:space="preserve">Trans lentem cavam objecta minus diſtantia, minus illumi-<lb/> <anchor type="note" xlink:label="note-0551-01a" xlink:href="note-0551-01"/> nata, & </s> <s xml:id="echoid-s14126" xml:space="preserve">minora, apparent.</s> <s xml:id="echoid-s14127" xml:space="preserve"/> </p> <div xml:id="echoid-div2106" type="float" level="2" n="19"> <note position="right" xlink:label="note-0551-01" xlink:href="note-0551-01a" xml:space="preserve">757.</note> </div> <p> <s xml:id="echoid-s14128" xml:space="preserve">Radii A b, A b, & </s> <s xml:id="echoid-s14129" xml:space="preserve">omnes intermedii, tranſeundo per <lb/> <anchor type="note" xlink:label="note-0551-02a" xlink:href="note-0551-02"/> Ientem cavam magis divergentes fiunt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14130" xml:space="preserve">oculum intrant <anchor type="note" xlink:label="note-0551-03a" xlink:href="note-0551-03"/> quaſi à puncto minus diſtanti a procederent <anchor type="note" xlink:href="" symbol="*"/>, in quo pun- <anchor type="note" xlink:label="note-0551-04a" xlink:href="note-0551-04"/> ctum A apparet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14131" xml:space="preserve"/> </p> <div xml:id="echoid-div2107" type="float" level="2" n="20"> <note position="right" xlink:label="note-0551-02" xlink:href="note-0551-02a" xml:space="preserve">TAB. X. <lb/>fig. 6.</note> <note symbol="*" position="right" xlink:label="note-0551-03" xlink:href="note-0551-03a" xml:space="preserve">705.</note> <note symbol="*" position="right" xlink:label="note-0551-04" xlink:href="note-0551-04a" xml:space="preserve">652.</note> </div> <note symbol="*" position="right" xml:space="preserve">737.</note> <p> <s xml:id="echoid-s14132" xml:space="preserve">Ex radiorum divergentiâ auctâ magis diſperguntur radii, <lb/>& </s> <s xml:id="echoid-s14133" xml:space="preserve">minori numero oculum intrant, quod minuit puncti illu-<lb/>minationem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14134" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">738.</note> <p> <s xml:id="echoid-s14135" xml:space="preserve">Minuitur etiam magnitudo apparens, quia radii A b, E b, <lb/> <anchor type="note" xlink:label="note-0551-07a" xlink:href="note-0551-07"/> quibus extremitates objecti videntur minus convergentes ad <lb/>oculum perveniunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14136" xml:space="preserve">ideò angulus c d c ſub quo trans <anchor type="note" xlink:label="note-0551-08a" xlink:href="note-0551-08"/> lentem objectum videtur, minor eſt angulo A d E, ſub quo <lb/>nudis oculis apparet: </s> <s xml:id="echoid-s14137" xml:space="preserve">quare & </s> <s xml:id="echoid-s14138" xml:space="preserve">ex imminutâ diſtantiâ & </s> <s xml:id="echoid-s14139" xml:space="preserve">ex <lb/>imminuto angulo memorato, imminutum apparet objectum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14140" xml:space="preserve"/> </p> <div xml:id="echoid-div2108" type="float" level="2" n="21"> <note position="right" xlink:label="note-0551-07" xlink:href="note-0551-07a" xml:space="preserve">TAB. X. <lb/>fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0551-08" xlink:href="note-0551-08a" xml:space="preserve">706.</note> </div> <note symbol="*" position="right" xml:space="preserve">734.</note> <p> <s xml:id="echoid-s14141" xml:space="preserve">Illis inſervit lens cava, qui objecta propinqua tantum di-<lb/> <anchor type="note" xlink:label="note-0551-10a" xlink:href="note-0551-10"/> ſtinctè vident; </s> <s xml:id="echoid-s14142" xml:space="preserve">Myopes vocantur; </s> <s xml:id="echoid-s14143" xml:space="preserve">trans hanc lentem puncta <lb/>remota appropinquantur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14144" xml:space="preserve">radii, qui ante retinam con- <anchor type="note" xlink:label="note-0551-11a" xlink:href="note-0551-11"/> currebant, magis divergentes oculum intrantes, in retinâ <lb/>concurrunt.</s> <s xml:id="echoid-s14145" xml:space="preserve"/> </p> <div xml:id="echoid-div2109" type="float" level="2" n="22"> <note position="right" xlink:label="note-0551-10" xlink:href="note-0551-10a" xml:space="preserve">758.</note> <note symbol="*" position="right" xlink:label="note-0551-11" xlink:href="note-0551-11a" xml:space="preserve">757.</note> </div> <p> <s xml:id="echoid-s14146" xml:space="preserve">Vitra dantur unicâ ſuperſicie planâ ab unâ parte termina-<lb/>ta, ad aliam variis ſuperficiebus planis, angulos inter ſe for-<lb/>mantibus, per has radii, ab eodem puncto procedentes, di-<lb/>verſas patiuntur refractiones; </s> <s xml:id="echoid-s14147" xml:space="preserve">& </s> <s xml:id="echoid-s14148" xml:space="preserve">pro ſingulis ſuperficiebus o-<lb/>culum intrant juxta diverſam directionem, & </s> <s xml:id="echoid-s14149" xml:space="preserve">quaſi à puncto <lb/>diverſo procederent: </s> <s xml:id="echoid-s14150" xml:space="preserve">id eſt, format idem punctum varios <lb/>focos imaginarios; </s> <s xml:id="echoid-s14151" xml:space="preserve">& </s> <s xml:id="echoid-s14152" xml:space="preserve">idcirco multiplicatum apparet: </s> <s xml:id="echoid-s14153" xml:space="preserve">vide-<lb/>tur nempe in ſingulis focis imaginariis <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s14154" xml:space="preserve">quod cùm obti- <anchor type="note" xlink:label="note-0551-12a" xlink:href="note-0551-12"/> neat reſpectu ſingulorum punctorum objecti, per talem len-<lb/> <anchor type="note" xlink:label="note-0551-13a" xlink:href="note-0551-13"/> tem polygonam objectum multiplicatum apparet.</s> <s xml:id="echoid-s14155" xml:space="preserve"/> </p> <div xml:id="echoid-div2110" type="float" level="2" n="23"> <note symbol="*" position="right" xlink:label="note-0551-12" xlink:href="note-0551-12a" xml:space="preserve">737.</note> <note position="right" xlink:label="note-0551-13" xlink:href="note-0551-13a" xml:space="preserve">759.</note> </div> <pb o="(54)" file="0552" n="607" rhead="PHYSICES ELEMENTA CAPUT XII."/> </div> <div xml:id="echoid-div2112" type="section" level="1" n="514"> <head xml:id="echoid-head683" style="it" xml:space="preserve">De Microſcopiis & Teleſcopiis.</head> <p> <s xml:id="echoid-s14156" xml:space="preserve">VItrorum, ſphæricis ſuperficiebus terminatorum, uſus, <lb/>in corrigendis oculorum Senum & </s> <s xml:id="echoid-s14157" xml:space="preserve">Myopum vitiis, vi-<lb/>dimus <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14158" xml:space="preserve">Quantum valeant, in minimis objectis detegen- <anchor type="note" xlink:label="note-0552-01a" xlink:href="note-0552-01"/> dis, & </s> <s xml:id="echoid-s14159" xml:space="preserve">in longè diſtantibus quaſi ſub oculis ponendis, dicen-<lb/>dum eſt.</s> <s xml:id="echoid-s14160" xml:space="preserve"/> </p> <div xml:id="echoid-div2112" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0552-01" xlink:href="note-0552-01a" xml:space="preserve">756. 758.</note> </div> <p> <s xml:id="echoid-s14161" xml:space="preserve">Vitra convexa objecta amplificare diximus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14162" xml:space="preserve">quæ ampli- <anchor type="note" xlink:label="note-0552-02a" xlink:href="note-0552-02"/> ficatio pendet à refractione radiorum, tranſeundo per lentem <lb/>convexam, unde ſequitur illam augeri, ſi ſervatis iiſdem <lb/>conditionibus, refractio augeatur; </s> <s xml:id="echoid-s14163" xml:space="preserve">quem effectum obtine-<lb/>mus, augendo convexitatem lentis; </s> <s xml:id="echoid-s14164" xml:space="preserve">quæ eò convexior eſt, <lb/>quo ſuperficies, hanc terminantes, ſunt portiones minoris <lb/>ſphæræ quod niſi in exiguis vitris locum habere non poteſt.</s> <s xml:id="echoid-s14165" xml:space="preserve"/> </p> <div xml:id="echoid-div2113" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0552-02" xlink:href="note-0552-02a" xml:space="preserve">747.</note> </div> </div> <div xml:id="echoid-div2115" type="section" level="1" n="515"> <head xml:id="echoid-head684" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s14166" xml:space="preserve">Tales lentes exiguæ Microſcopia vocantur.</s> <s xml:id="echoid-s14167" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">760.</note> <p> <s xml:id="echoid-s14168" xml:space="preserve">Microſcopio exigua objecta in immenſum amplificantur <lb/> <anchor type="note" xlink:label="note-0552-04a" xlink:href="note-0552-04"/> ita, ut quæ nudis oculis detegi non poſſunt, hoc median-<lb/>te, diſtinctiſſimè videantur.</s> <s xml:id="echoid-s14169" xml:space="preserve"/> </p> <div xml:id="echoid-div2115" type="float" level="2" n="1"> <note position="left" xlink:label="note-0552-04" xlink:href="note-0552-04a" xml:space="preserve">761.</note> </div> </div> <div xml:id="echoid-div2117" type="section" level="1" n="516"> <head xml:id="echoid-head685" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s14170" xml:space="preserve">Spatium per Microſcopium viſum, id eſt, circulus in quo <lb/> <anchor type="note" xlink:label="note-0552-05a" xlink:href="note-0552-05"/> objecta per Microſcopium viſibilia ſunt, vocatur Microſco-<lb/>pii campus.</s> <s xml:id="echoid-s14171" xml:space="preserve"/> </p> <div xml:id="echoid-div2117" type="float" level="2" n="1"> <note position="left" xlink:label="note-0552-05" xlink:href="note-0552-05a" xml:space="preserve">762.</note> </div> </div> <div xml:id="echoid-div2119" type="section" level="1" n="517"> <head xml:id="echoid-head686" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s14172" xml:space="preserve">Per Microſcopium V ſi intueamur objectum exiguum <lb/> <anchor type="note" xlink:label="note-0552-06a" xlink:href="note-0552-06"/> A E, in a e amplificatum apparebit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14173" xml:space="preserve"/> </p> <div xml:id="echoid-div2119" type="float" level="2" n="1"> <note position="left" xlink:label="note-0552-06" xlink:href="note-0552-06a" xml:space="preserve">TAB. IX. <lb/>fig. 5.</note> </div> <note symbol="*" position="left" xml:space="preserve">745. 747.</note> <p> <s xml:id="echoid-s14174" xml:space="preserve">Dantur & </s> <s xml:id="echoid-s14175" xml:space="preserve">Microſcopia compoſita, ex duabus aut tribus <lb/>lentibus conſtantia; </s> <s xml:id="echoid-s14176" xml:space="preserve">quo fundamento nitantur, explicatione <lb/>illius, quod ex duabus lentibus conſtat, ſatis patebit.</s> <s xml:id="echoid-s14177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14178" xml:space="preserve">Detur lens exigua, admodum convexa, V V, ad talem ab <lb/> <anchor type="note" xlink:label="note-0552-08a" xlink:href="note-0552-08"/> hac diſtantiam detur objectum A E, ut ſingula illius puncta <lb/>poſt lentem focum ſuum habeant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14179" xml:space="preserve">admoveatur ita obje- <anchor type="note" xlink:label="note-0552-09a" xlink:href="note-0552-09"/> ctum, ut foci removeantur ad a e <anchor type="note" xlink:href="" symbol="*"/>, dabitur ibi objecti re- <anchor type="note" xlink:label="note-0552-10a" xlink:href="note-0552-10"/> præſentatio, admodum amplificata, quæ ſuper plano albo <lb/>ſi recipiatur ſenſibilis fiet <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14180" xml:space="preserve"/> </p> <div xml:id="echoid-div2120" type="float" level="2" n="2"> <note position="left" xlink:label="note-0552-08" xlink:href="note-0552-08a" xml:space="preserve">TAB XI. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0552-09" xlink:href="note-0552-09a" xml:space="preserve">710. 699.</note> <note symbol="*" position="left" xlink:label="note-0552-10" xlink:href="note-0552-10a" xml:space="preserve">699.</note> </div> <note symbol="*" position="left" xml:space="preserve">711.</note> <pb file="0553" n="608"/> <pb file="0553a" n="609"/> <figure> <image file="0553a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0553a-01"/> </figure> <pb file="0554" n="610"/> <pb o="55" file="0555" n="611" rhead="MATHEMATICA LIB. III. CAP. XII."/> </div> <div xml:id="echoid-div2122" type="section" level="1" n="518"> <head xml:id="echoid-head687" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s14181" xml:space="preserve">Lens memorata in tubi extremitate firmatur in V, altera <lb/> <anchor type="note" xlink:label="note-0555-01a" xlink:href="note-0555-01"/> latior tubi extremitas, chartâ tenuiſſimâ CC obtegitur; </s> <s xml:id="echoid-s14182" xml:space="preserve">ob-<lb/>jectum AE ita diſponitur, ut foci punctorum hujus objecti <lb/>dentur ad chartæ diſtantiam; </s> <s xml:id="echoid-s14183" xml:space="preserve">ſi tunc objectum probè fuerit <lb/>illuminatum, dabitur hujus repræſentatio inverſa, trans char-<lb/>tam viſibilis, in a e. </s> <s xml:id="echoid-s14184" xml:space="preserve">Motu objecti detegitur hujus ſitus ut <lb/>repræſentatio in chartâ ſit exacta.</s> <s xml:id="echoid-s14185" xml:space="preserve"/> </p> <div xml:id="echoid-div2122" type="float" level="2" n="1"> <note position="right" xlink:label="note-0555-01" xlink:href="note-0555-01a" xml:space="preserve">TAB. XI. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s14186" xml:space="preserve">Puncta ſingula repræſentationis a e ſunt puncta radiantia, <lb/> <anchor type="note" xlink:label="note-0555-02a" xlink:href="note-0555-02"/> & </s> <s xml:id="echoid-s14187" xml:space="preserve">viſibilia <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14188" xml:space="preserve">quæ per microſcopium majus VV viſa, auctam <anchor type="note" xlink:label="note-0555-03a" xlink:href="note-0555-03"/> repræſentationem a e exhibent in a e <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14189" xml:space="preserve">id eſt, radii ab ob- <anchor type="note" xlink:label="note-0555-04a" xlink:href="note-0555-04"/> jecto AE procedentes, poſt refractionem per ambas lentes <lb/>VV, VV, oculum intrabunt, quaſi ex objecto in a e pro-<lb/>cederent.</s> <s xml:id="echoid-s14190" xml:space="preserve"/> </p> <div xml:id="echoid-div2123" type="float" level="2" n="2"> <note position="right" xlink:label="note-0555-02" xlink:href="note-0555-02a" xml:space="preserve">TAB. XI. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0555-03" xlink:href="note-0555-03a" xml:space="preserve">736. 754.</note> <note symbol="*" position="right" xlink:label="note-0555-04" xlink:href="note-0555-04a" xml:space="preserve">761.</note> </div> <p style="it"> <s xml:id="echoid-s14191" xml:space="preserve">Objectum itaque inverſum, & </s> <s xml:id="echoid-s14192" xml:space="preserve">multò magis amplificatum, <lb/> <anchor type="note" xlink:label="note-0555-05a" xlink:href="note-0555-05"/> per hoc Microſcopium compoſitum apparet, quàm per Mi-<lb/>croſcopium ſimplex.</s> <s xml:id="echoid-s14193" xml:space="preserve"/> </p> <div xml:id="echoid-div2124" type="float" level="2" n="3"> <note position="right" xlink:label="note-0555-05" xlink:href="note-0555-05a" xml:space="preserve">763.</note> </div> </div> <div xml:id="echoid-div2126" type="section" level="1" n="519"> <head xml:id="echoid-head688" xml:space="preserve"><emph style="sc">Definitio</emph> 3. & 4.</head> <p style="it"> <s xml:id="echoid-s14194" xml:space="preserve">In hoc Microſcopio lens minima objecto vicina vocatur <lb/> <anchor type="note" xlink:label="note-0555-06a" xlink:href="note-0555-06"/> objectiva, alia ocularis dicitur.</s> <s xml:id="echoid-s14195" xml:space="preserve"/> </p> <div xml:id="echoid-div2126" type="float" level="2" n="1"> <note position="right" xlink:label="note-0555-06" xlink:href="note-0555-06a" xml:space="preserve">764.</note> </div> <p> <s xml:id="echoid-s14196" xml:space="preserve">Ne hæc nimium ſit exigua requiritur: </s> <s xml:id="echoid-s14197" xml:space="preserve">nam puncta repræ-<lb/>ſentationis ab, licèt ſint puncta radiantia, non tamen verſus <lb/>omnes partes lumen emittunt; </s> <s xml:id="echoid-s14198" xml:space="preserve">radii ſoli, qui per lentem ob-<lb/>jectivam tranſeunt, ſeſe mutuò interſecant in ſingulis pun-<lb/>ctis repræſentationis a b; </s> <s xml:id="echoid-s14199" xml:space="preserve">quæ ergo per lentem ocularem vi-<lb/>ſibilis non erit, niſi radii, per lentem objectivam tranſeun-<lb/>tes, ad lentem ocularem perveniant. </s> <s xml:id="echoid-s14200" xml:space="preserve">Campus ideò pendet <lb/> <anchor type="note" xlink:label="note-0555-07a" xlink:href="note-0555-07"/> à magnitudine hujus lentis.</s> <s xml:id="echoid-s14201" xml:space="preserve"/> </p> <div xml:id="echoid-div2127" type="float" level="2" n="2"> <note position="right" xlink:label="note-0555-07" xlink:href="note-0555-07a" xml:space="preserve">765.</note> </div> <p> <s xml:id="echoid-s14202" xml:space="preserve">Oculus etiam ita diſponendus eſt, ut omnes radii, qui ad <lb/> <anchor type="note" xlink:label="note-0555-08a" xlink:href="note-0555-08"/> lentem ocularem pertingunt, per hanc tranſeundo, ad o-<lb/>culum perveniant; </s> <s xml:id="echoid-s14203" xml:space="preserve">quod obtinemus, diſponendo oculum <lb/>in d, puncto, in quo radii à centro lentis objectivæ provenien-<lb/>tes, ocularem tranſeundo, colliguntur.</s> <s xml:id="echoid-s14204" xml:space="preserve"/> </p> <div xml:id="echoid-div2128" type="float" level="2" n="3"> <note position="right" xlink:label="note-0555-08" xlink:href="note-0555-08a" xml:space="preserve">766.</note> </div> <p> <s xml:id="echoid-s14205" xml:space="preserve">Per Microſcopia objecta ſatis illuminata apparent; </s> <s xml:id="echoid-s14206" xml:space="preserve">quia <lb/>parum à vitro diſtant, & </s> <s xml:id="echoid-s14207" xml:space="preserve">ita radii iidem per exiguam len-<lb/>tem tranſeunt, qui ad diſtantiam majorem, niſi per majus fo-<lb/>ramen, non tranſirent. </s> <s xml:id="echoid-s14208" xml:space="preserve">Sæpe tamen, in maximis amplifica-<lb/> <anchor type="note" xlink:label="note-0555-09a" xlink:href="note-0555-09"/> <pb o="56" file="0556" n="612" rhead="PHYSICES ELEMENTA"/> tionibus, neceſſe eſt, ut objecta illuminentur radiis, tranſeun-<lb/>do per lentem convexam, collectis.</s> <s xml:id="echoid-s14209" xml:space="preserve"/> </p> <div xml:id="echoid-div2129" type="float" level="2" n="4"> <note position="right" xlink:label="note-0555-09" xlink:href="note-0555-09a" xml:space="preserve">767.</note> </div> <p> <s xml:id="echoid-s14210" xml:space="preserve">Magnam cum Microſcopio compoſito affinitatem habet <lb/>Teleſcopium Aſtronomicum.</s> <s xml:id="echoid-s14211" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2131" type="section" level="1" n="520"> <head xml:id="echoid-head689" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s14212" xml:space="preserve">Teleſcopia vocantur, inſtrumenta ad objecta longinqua vi-<lb/> <anchor type="note" xlink:label="note-0556-01a" xlink:href="note-0556-01"/> denda adaptata.</s> <s xml:id="echoid-s14213" xml:space="preserve"/> </p> <div xml:id="echoid-div2131" type="float" level="2" n="1"> <note position="left" xlink:label="note-0556-01" xlink:href="note-0556-01a" xml:space="preserve">768.</note> </div> <p> <s xml:id="echoid-s14214" xml:space="preserve">De quo nunc agimus, vocatur Aſtronomicum, quia rebus <lb/> <anchor type="note" xlink:label="note-0556-02a" xlink:href="note-0556-02"/> terreſtribus videndis minimè eſt aptum, objecta enim inver-<lb/>ſa repræſentat: </s> <s xml:id="echoid-s14215" xml:space="preserve">de ſitu autèm apparentiæ minimè ſolliciti <lb/>ſunt Aſtronomi.</s> <s xml:id="echoid-s14216" xml:space="preserve"/> </p> <div xml:id="echoid-div2132" type="float" level="2" n="2"> <note position="left" xlink:label="note-0556-02" xlink:href="note-0556-02a" xml:space="preserve">769.</note> </div> <p> <s xml:id="echoid-s14217" xml:space="preserve">Teleſcopium hoc conſtat ex duabus lentibus convexis, unâ <lb/>objectivâ, quæ verſus objecta diſponitur, alterâ oculari, quæ <lb/>ad partem oculi datur. </s> <s xml:id="echoid-s14218" xml:space="preserve">Ope primæ, objecta longinqua ad <lb/>certam diſtantiam poſt lentem repræſentantur <anchor type="note" xlink:href="" symbol="*"/>, ut in mi- <anchor type="note" xlink:label="note-0556-03a" xlink:href="note-0556-03"/> croſcopio compoſito objecta propinqua. </s> <s xml:id="echoid-s14219" xml:space="preserve">Per lentem ocula-<lb/>rem ſi obſervetur hæc repræſentatio, amplificata & </s> <s xml:id="echoid-s14220" xml:space="preserve">inverſa <lb/>apparet, ut de Microſcopio dictum. </s> <s xml:id="echoid-s14221" xml:space="preserve">Campum etiam in hoc <lb/> <anchor type="note" xlink:label="note-0556-04a" xlink:href="note-0556-04"/> caſu, ut in Microſcopio, à magnitudine lentis ocularis pen-<lb/>dere, clarè liquet; </s> <s xml:id="echoid-s14222" xml:space="preserve">ut & </s> <s xml:id="echoid-s14223" xml:space="preserve">ſitum oculi eodem modo pro Teleſco-<lb/> <anchor type="note" xlink:label="note-0556-05a" xlink:href="note-0556-05"/> pio, quàm pro Microſcopio, determinari <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s14224" xml:space="preserve">differt enim Te- <anchor type="note" xlink:label="note-0556-06a" xlink:href="note-0556-06"/> leſcopium Aſtronomicum à Microſcopio compoſito in eo ſo-<lb/>lo, quod in hoc lentes ſint magis convexæ, quæ objectis lon-<lb/>ginquis videndis minimè ſunt aptæ, præcipuè quod ſpectat <lb/>lentes objectivas. </s> <s xml:id="echoid-s14225" xml:space="preserve">In Microſcopio lens objectiva ocularem <lb/>convexitate ſuperat; </s> <s xml:id="echoid-s14226" xml:space="preserve">in Teleſcopio contrarium obtinet.</s> <s xml:id="echoid-s14227" xml:space="preserve"/> </p> <div xml:id="echoid-div2133" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0556-03" xlink:href="note-0556-03a" xml:space="preserve">711.</note> <note position="left" xlink:label="note-0556-04" xlink:href="note-0556-04a" xml:space="preserve">770.</note> <note position="left" xlink:label="note-0556-05" xlink:href="note-0556-05a" xml:space="preserve">771.</note> <note symbol="*" position="left" xlink:label="note-0556-06" xlink:href="note-0556-06a" xml:space="preserve">766.</note> </div> <p> <s xml:id="echoid-s14228" xml:space="preserve">Teleſcopia, quantumvis longa, ſideribus obſervandis apta <lb/>ſunt: </s> <s xml:id="echoid-s14229" xml:space="preserve">quæ viginti pedes excedunt, ad objecta, in terræ ſuper-<lb/>ſicie, videnda nullius uſus ſunt; </s> <s xml:id="echoid-s14230" xml:space="preserve">propter aëris continuam agita-<lb/>tionem, in tantâ objectorum amplificatione nimium ſenſibilem.</s> <s xml:id="echoid-s14231" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14232" xml:space="preserve">Brevius autem Teleſcopium Aſtronomicum, rebus terreſtri-<lb/> <anchor type="note" xlink:label="note-0556-07a" xlink:href="note-0556-07"/> bus videndis, adaptatur, additis duabus lentibus convexis, <lb/>quæ etiam oculares dicuntur; </s> <s xml:id="echoid-s14233" xml:space="preserve">tres autèm oculares ſimiles <lb/>ſunt, & </s> <s xml:id="echoid-s14234" xml:space="preserve">minus convexæ quàm in Teleſcopio Aſtronomico, <lb/>ſervatâ eâdem lente objectivâ.</s> <s xml:id="echoid-s14235" xml:space="preserve"/> </p> <div xml:id="echoid-div2134" type="float" level="2" n="4"> <note position="left" xlink:label="note-0556-07" xlink:href="note-0556-07a" xml:space="preserve">772.</note> </div> <p> <s xml:id="echoid-s14236" xml:space="preserve">Detur lens objectiva VV, quæ objectum longinquum in-<lb/> <anchor type="note" xlink:label="note-0556-08a" xlink:href="note-0556-08"/> verſum repræſentat in e a; </s> <s xml:id="echoid-s14237" xml:space="preserve">Dentur ulterius lentes oculares <lb/> <anchor type="note" xlink:label="note-0556-09a" xlink:href="note-0556-09"/> <pb file="0557" n="613"/> <pb file="0557a" n="614"/> <anchor type="figure" xlink:label="fig-0557a-01a" xlink:href="fig-0557a-01"/> <pb file="0558" n="615"/> <pb o="57" file="0559" n="616" rhead="MATHEMATICA. LIB. III. CAP. XII."/> tres DD, DD, DD. </s> <s xml:id="echoid-s14238" xml:space="preserve">Prima diſponitur, ut radii, à punctis <lb/>repræſentationis e a procedentes, paralleli lentem exeant <anchor type="note" xlink:href="" symbol="*"/>:</s> <s xml:id="echoid-s14239" xml:space="preserve"> <anchor type="note" xlink:label="note-0559-01a" xlink:href="note-0559-01"/> in hoc caſu radii, qui à puncto medio lentis objectivæ pro. <lb/></s> <s xml:id="echoid-s14240" xml:space="preserve">cedunt, colliguntur in G; </s> <s xml:id="echoid-s14241" xml:space="preserve">ſecunda lens diſponitur, ut ra-<lb/>dii hi in G collecti, ibique ſeſe mutuo interſecantes, & </s> <s xml:id="echoid-s14242" xml:space="preserve">quaſi <lb/>ex illo puncto procedentes, paralleli exeant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14243" xml:space="preserve">quibus poſitis, <anchor type="note" xlink:label="note-0559-02a" xlink:href="note-0559-02"/> radii à vitro objectivo ad e provenientes, ibique ſeſe mutuo <lb/>interſecantes, & </s> <s xml:id="echoid-s14244" xml:space="preserve">punctum hoc repræſentationis objecti for-<lb/>mantes, per primam lentem refracti, per G paralleli inter <lb/>ſe moventur; </s> <s xml:id="echoid-s14245" xml:space="preserve">per ſecundam lentem refringuntur juxta dire-<lb/>ctionem D e & </s> <s xml:id="echoid-s14246" xml:space="preserve">in e colliguntur <anchor type="note" xlink:href="" symbol="*"/> ita, ut hoc punctum ſit <anchor type="note" xlink:label="note-0559-03a" xlink:href="note-0559-03"/> punctum novæ repræſentationis. </s> <s xml:id="echoid-s14247" xml:space="preserve">Eodem modo puncto a <lb/>primæ repræſentationis reſpondet punctum a ſecundæ repræ-<lb/>ſentationis; </s> <s xml:id="echoid-s14248" xml:space="preserve">quod cùm etiam locum habeat reſpectu puncto-<lb/>rum intermediorum, datur objecti repræſentatio erecta in a e.</s> <s xml:id="echoid-s14249" xml:space="preserve"/> </p> <div xml:id="echoid-div2135" type="float" level="2" n="5"> <note position="left" xlink:label="note-0556-08" xlink:href="note-0556-08a" xml:space="preserve">773.</note> <note position="left" xlink:label="note-0556-09" xlink:href="note-0556-09a" xml:space="preserve">TAB. XI. <lb/>fig. 3.</note> <figure xlink:label="fig-0557a-01" xlink:href="fig-0557a-01a"> <image file="0557a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0557a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0559-01" xlink:href="note-0559-01a" xml:space="preserve">699.</note> <note symbol="*" position="right" xlink:label="note-0559-02" xlink:href="note-0559-02a" xml:space="preserve">699.</note> <note symbol="*" position="right" xlink:label="note-0559-03" xlink:href="note-0559-03a" xml:space="preserve">698.</note> </div> </div> <div xml:id="echoid-div2137" type="section" level="1" n="521"> <head xml:id="echoid-head690" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s14250" xml:space="preserve">Tres tabellæ D, D, D, cum vitris ocularibus, quæ ad <lb/> <anchor type="note" xlink:label="note-0559-04a" xlink:href="note-0559-04"/> diſtantiam quinque circiter pollicum radios parallelos colli-<lb/>gunt, ſuper plano inter duas regulas moventur ita, ut tria <lb/>vitra ſint in eadem lineâ, in quâ etiam foramen datur V, <lb/>per quod ſolum in cubiculum lumen intrat, & </s> <s xml:id="echoid-s14251" xml:space="preserve">in quo datur <lb/>lens objectiva, quæ tubo brevi continetur, ad excludendum <lb/>lumen laterale.</s> <s xml:id="echoid-s14252" xml:space="preserve"/> </p> <div xml:id="echoid-div2137" type="float" level="2" n="1"> <note position="right" xlink:label="note-0559-04" xlink:href="note-0559-04a" xml:space="preserve">TAB. XI. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s14253" xml:space="preserve">Lens hæc objectiva talis eſt, ut ad diſtantiam circiter trium <lb/>pedum ab V, repræſentet objecta longinqua inverſa in F, <lb/>quæ repræſentatio videtur, ſi plano albo radii intercipian-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14254" xml:space="preserve">Ad diſtantiam quinque pollicum ab F datur prima <anchor type="note" xlink:label="note-0559-05a" xlink:href="note-0559-05"/> lens ocularis, à qua decem pollices diſtat lens ſecunda; </s> <s xml:id="echoid-s14255" xml:space="preserve">in f, <lb/>ad diſtantiam quinque pollicum ab hac, datur repræſentatio <lb/>erecta eorundèm objectorum, quæ etiam interpoſito plano <lb/>albo ſenſibilis eſt.</s> <s xml:id="echoid-s14256" xml:space="preserve"/> </p> <div xml:id="echoid-div2138" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0559-05" xlink:href="note-0559-05a" xml:space="preserve">711.</note> </div> <p> <s xml:id="echoid-s14257" xml:space="preserve">Si repræſentatio a e videatur per tertiam lentem ocula-<lb/> <anchor type="note" xlink:label="note-0559-06a" xlink:href="note-0559-06"/> rem, poſito oculo in o, in quo colliguntur radii paralleli <lb/>a D, e D, amplificatum, appropinquatum & </s> <s xml:id="echoid-s14258" xml:space="preserve">erectum, obje-<lb/> <anchor type="note" xlink:label="note-0559-07a" xlink:href="note-0559-07"/> ctum apparet; </s> <s xml:id="echoid-s14259" xml:space="preserve">videtur enim ſub angulo D o D, dum nudis <lb/>oculis ſub angulo exiguo apparet; </s> <s xml:id="echoid-s14260" xml:space="preserve">etiam objectum appro-<lb/>pinquatum habemus, quia, licèt ultra a e videatur, diſtantia <pb o="58" file="0560" n="617" rhead="PHYSICES ELEMENTA"/> tamen ad quam apparet, relationem ſenſibilem non habet ad <lb/>objecti longinqui diſtantiam.</s> <s xml:id="echoid-s14261" xml:space="preserve"/> </p> <div xml:id="echoid-div2139" type="float" level="2" n="3"> <note position="right" xlink:label="note-0559-06" xlink:href="note-0559-06a" xml:space="preserve">TAB. XI. <lb/>fig. 3.</note> <note position="right" xlink:label="note-0559-07" xlink:href="note-0559-07a" xml:space="preserve">774.</note> </div> </div> <div xml:id="echoid-div2141" type="section" level="1" n="522"> <head xml:id="echoid-head691" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s14262" xml:space="preserve">Poſitis quæ in Experimento præcedenti; </s> <s xml:id="echoid-s14263" xml:space="preserve">ad diſtantiam <lb/> <anchor type="note" xlink:label="note-0560-01a" xlink:href="note-0560-01"/> decem pollicum à ſecundâ lente oculari detur tertia, à qua <lb/>quinque pollices diſtet tabella O cum foramine; </s> <s xml:id="echoid-s14264" xml:space="preserve">ſi oculus de-<lb/>tur in O, objectum, ut dictum, erectum, amplificatum, & </s> <s xml:id="echoid-s14265" xml:space="preserve">ap-<lb/>propinquatum, apparet. </s> <s xml:id="echoid-s14266" xml:space="preserve">Si tabella O tranſponatur, id eſt, <lb/>accedat aut recedat, campus Teleſcopii minuitur; </s> <s xml:id="echoid-s14267" xml:space="preserve">quia uni-<lb/>cus tantum oculi datur ſitus, in quo omnes radii, per lentes <lb/>oculares tranſeuntes ad oculum, perveniunt.</s> <s xml:id="echoid-s14268" xml:space="preserve"/> </p> <div xml:id="echoid-div2141" type="float" level="2" n="1"> <note position="left" xlink:label="note-0560-01" xlink:href="note-0560-01a" xml:space="preserve">TAB. XI. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s14269" xml:space="preserve">Notandum lentes oculares, hìc adhibitas, non ſatis eſſe <lb/>convexas reſpectu lentis objectivæ V; </s> <s xml:id="echoid-s14270" xml:space="preserve">ſed hæ in experimen-<lb/>to 3. </s> <s xml:id="echoid-s14271" xml:space="preserve">magis ſunt commodæ.</s> <s xml:id="echoid-s14272" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14273" xml:space="preserve">Singula etiam objecti puncta magis illuminata apparent; <lb/></s> <s xml:id="echoid-s14274" xml:space="preserve"> <anchor type="note" xlink:label="note-0560-02a" xlink:href="note-0560-02"/> radii enim qui, ab aliquo puncto ad ſingula lentis objectivæ <lb/>puncta advenientes, in puncto repræſentationis ſeſe mutuò <lb/>interſecant, propter exiguam lentis ocularis ab hac repræ-<lb/>ſentatione diſtantiam, parum diſperguntur antequam ad o-<lb/>culum perveniant; </s> <s xml:id="echoid-s14275" xml:space="preserve">ita ut omnes hunc intrent. </s> <s xml:id="echoid-s14276" xml:space="preserve">Eſt itaque <lb/>illuminatio, per Teleſcopium, ad hanc, nudis oculis, ut ſuper-<lb/>ficies lentis objectivæ, per quam radii tranſeunt, ad pupillæ <lb/>ſuperficiem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14277" xml:space="preserve"/> </p> <div xml:id="echoid-div2142" type="float" level="2" n="2"> <note position="left" xlink:label="note-0560-02" xlink:href="note-0560-02a" xml:space="preserve">775.</note> </div> <note symbol="*" position="left" xml:space="preserve">738.</note> <p> <s xml:id="echoid-s14278" xml:space="preserve">Conſtruuntur etiam ex duabus lentibus Teleſcopia, per quæ <lb/> <anchor type="note" xlink:label="note-0560-04a" xlink:href="note-0560-04"/> objecta erecta, illuminata, & </s> <s xml:id="echoid-s14279" xml:space="preserve">amplificata, apparent. </s> <s xml:id="echoid-s14280" xml:space="preserve">Bre-<lb/>viora hæc ſunt, nam propter arctum campum, ſi longitudine <lb/>pedem unicum excedant, ferè nullius uſus ſunt.</s> <s xml:id="echoid-s14281" xml:space="preserve"/> </p> <div xml:id="echoid-div2143" type="float" level="2" n="3"> <note position="left" xlink:label="note-0560-04" xlink:href="note-0560-04a" xml:space="preserve">776.</note> </div> <p> <s xml:id="echoid-s14282" xml:space="preserve">Sit VV lens objectiva; </s> <s xml:id="echoid-s14283" xml:space="preserve">repræſentatio inverſa objecti di-<lb/> <anchor type="note" xlink:label="note-0560-05a" xlink:href="note-0560-05"/> ſtantis datur in e a <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s14284" xml:space="preserve">lente cavâ DD intercipiuntur radii <anchor type="note" xlink:label="note-0560-06a" xlink:href="note-0560-06"/> ita, ut qui à centro lentis VV procedunt, inflectantur quaſi <lb/>à puncto f procederent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14285" xml:space="preserve">eâdem refractione radii concur- <anchor type="note" xlink:label="note-0560-07a" xlink:href="note-0560-07"/> rentes in a, divergentes fiunt <anchor type="note" xlink:href="" symbol="*"/>, habentes focum imaginarium <anchor type="note" xlink:label="note-0560-08a" xlink:href="note-0560-08"/> in a; </s> <s xml:id="echoid-s14286" xml:space="preserve">quod idem in ſingulis punctis repræſentationis e a obti-<lb/>net, & </s> <s xml:id="echoid-s14287" xml:space="preserve">loco hujus datur repræſentatio imaginaria, erecta, <lb/>in a e; </s> <s xml:id="echoid-s14288" xml:space="preserve">id eſt, radii oculum intrant, quaſi ex objecto in a e <lb/>procederent.</s> <s xml:id="echoid-s14289" xml:space="preserve"/> </p> <div xml:id="echoid-div2144" type="float" level="2" n="4"> <note position="left" xlink:label="note-0560-05" xlink:href="note-0560-05a" xml:space="preserve">TAB. XI. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0560-06" xlink:href="note-0560-06a" xml:space="preserve">711.</note> <note symbol="*" position="left" xlink:label="note-0560-07" xlink:href="note-0560-07a" xml:space="preserve">705.</note> <note symbol="*" position="left" xlink:label="note-0560-08" xlink:href="note-0560-08a" xml:space="preserve">706.</note> </div> <p> <s xml:id="echoid-s14290" xml:space="preserve">Radii, omni reſpectu, divergentes ex lente oculari <lb/> <anchor type="note" xlink:label="note-0560-09a" xlink:href="note-0560-09"/> <pb file="0561" n="618"/> <pb file="0561a" n="619"/> <anchor type="figure" xlink:label="fig-0561a-01a" xlink:href="fig-0561a-01"/> <pb file="0562" n="620"/> <pb o="59" file="0563" n="621" rhead="MATHEMATICA LIB. III. CAP. XIII."/> exeunt; </s> <s xml:id="echoid-s14291" xml:space="preserve">ideò quantum poteſt oculus huic lenti admovendus <lb/>eſt.</s> <s xml:id="echoid-s14292" xml:space="preserve"/> </p> <div xml:id="echoid-div2145" type="float" level="2" n="5"> <note position="left" xlink:label="note-0560-09" xlink:href="note-0560-09a" xml:space="preserve">777.</note> <figure xlink:label="fig-0561a-01" xlink:href="fig-0561a-01a"> <image file="0561a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0561a-01"/> </figure> </div> <p> <s xml:id="echoid-s14293" xml:space="preserve">Campus in hoc Teleſcopio pendet à magnitudine lentis ob-<lb/> <anchor type="note" xlink:label="note-0563-01a" xlink:href="note-0563-01"/> jectivæ; </s> <s xml:id="echoid-s14294" xml:space="preserve">radii enim, qui à puncto obliquè ad centrum hujus <lb/>lentis perveniunt, ſæpe oculum non intrant, dum radii ab <lb/>eodem puncto, qui per lentem verſus periferiam tranſeunt, <lb/>ad oculum pertingunt.</s> <s xml:id="echoid-s14295" xml:space="preserve"/> </p> <div xml:id="echoid-div2146" type="float" level="2" n="6"> <note position="right" xlink:label="note-0563-01" xlink:href="note-0563-01a" xml:space="preserve">778.</note> </div> </div> <div xml:id="echoid-div2148" type="section" level="1" n="523"> <head xml:id="echoid-head692" xml:space="preserve">CAPUT XIII.</head> <head xml:id="echoid-head693" style="it" xml:space="preserve">De Reflexione Luminis.</head> <p> <s xml:id="echoid-s14296" xml:space="preserve">LUmen à corporibus opacis repercuti vidimus, & </s> <s xml:id="echoid-s14297" xml:space="preserve">quidem <lb/>in omnibus punctis verſus omnes partes <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14298" xml:space="preserve">In cauſâ eſt <anchor type="note" xlink:label="note-0563-02a" xlink:href="note-0563-02"/> inæqualitas ſuperficierum, quæ conſtant ex innumeris pla-<lb/>nis minimis, quæ, in omnibus punctis ſenſibilibus, ver-<lb/>ſus omnes partes diriguntur; </s> <s xml:id="echoid-s14299" xml:space="preserve">quod facilè concipitur, ſi ſuper-<lb/>ficiem innumeris hemiſphæriis minimis obtectam concipia-<lb/>mus. </s> <s xml:id="echoid-s14300" xml:space="preserve">Hoc revera ſic ſe haberi deducimus, ex reflexione lu-<lb/>minis, â ſuperficie politâ, id eſt, cujus æqualitates ſunt <lb/> <anchor type="note" xlink:label="note-0563-03a" xlink:href="note-0563-03"/> ſublatæ; </s> <s xml:id="echoid-s14301" xml:space="preserve">quæ verſus unicam tantum partem in ſingulis pun-<lb/>ctis lumen reflectit; </s> <s xml:id="echoid-s14302" xml:space="preserve">quod æquè in curvis ac planis ſuperfi-<lb/>ciebus locum habet. </s> <s xml:id="echoid-s14303" xml:space="preserve">Etiam, à ſuperficiebus minimé politis, <lb/>lumen maximâ copiâ reflecti verſus illam partem, verſus <lb/>quam, ſi politæ forent, in totum reflecteretur, quotidianis <lb/>experimentis extra dubium eſt.</s> <s xml:id="echoid-s14304" xml:space="preserve"/> </p> <div xml:id="echoid-div2148" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0563-02" xlink:href="note-0563-02a" xml:space="preserve">710.</note> <note position="right" xlink:label="note-0563-03" xlink:href="note-0563-03a" xml:space="preserve">779.</note> </div> <p> <s xml:id="echoid-s14305" xml:space="preserve">Sit radius luminis AC, obliquè in ſuperficiem planam im-<lb/> <anchor type="note" xlink:label="note-0563-04a" xlink:href="note-0563-04"/> pingens; </s> <s xml:id="echoid-s14306" xml:space="preserve">ſit ad hanc perpendicularis CO, & </s> <s xml:id="echoid-s14307" xml:space="preserve">reflectatur ra-<lb/>dius per CB,</s> </p> <div xml:id="echoid-div2149" type="float" level="2" n="2"> <note position="right" xlink:label="note-0563-04" xlink:href="note-0563-04a" xml:space="preserve">TAB. XII. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div2151" type="section" level="1" n="524"> <head xml:id="echoid-head694" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s14308" xml:space="preserve">Radius CB, vocatur Radius reflexus.</s> <s xml:id="echoid-s14309" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2152" type="section" level="1" n="525"> <head xml:id="echoid-head695" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <note position="right" xml:space="preserve">780.</note> <p> <s xml:id="echoid-s14310" xml:space="preserve">Angulus OCB vocatur angulus reflexionis.</s> <s xml:id="echoid-s14311" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">781.</note> <p style="it"> <s xml:id="echoid-s14312" xml:space="preserve">Radius reflexus eſt cum incidente in eodem plano perpendi-<lb/> <anchor type="note" xlink:label="note-0563-07a" xlink:href="note-0563-07"/> culari ad planum reflectens.</s> <s xml:id="echoid-s14313" xml:space="preserve"/> </p> <div xml:id="echoid-div2152" type="float" level="2" n="1"> <note position="right" xlink:label="note-0563-07" xlink:href="note-0563-07a" xml:space="preserve">782.</note> </div> <p> <s xml:id="echoid-s14314" xml:space="preserve">Hujus enim plani actio, qua lumen repercutitur, perpen-<lb/> <anchor type="note" xlink:label="note-0563-08a" xlink:href="note-0563-08"/> diculariter dirigitur ad hoc planum, quod ſibi ſimile ponitur <lb/>in omnibus punctis.</s> <s xml:id="echoid-s14315" xml:space="preserve"/> </p> <div xml:id="echoid-div2153" type="float" level="2" n="2"> <note position="right" xlink:label="note-0563-08" xlink:href="note-0563-08a" xml:space="preserve">783.</note> </div> <pb o="60" file="0564" n="622" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s14316" xml:space="preserve">Angulus reflexionis æqualis eſt angulo incidentiæ.</s> <s xml:id="echoid-s14317" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">784.</note> </div> <div xml:id="echoid-div2155" type="section" level="1" n="526"> <head xml:id="echoid-head696" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s14318" xml:space="preserve">Detur in loco obſcuro ſpeculum planum S, quod, ope <lb/> <anchor type="note" xlink:label="note-0564-02a" xlink:href="note-0564-02"/> globi mobilis pede ſuſtentati, ad libitum conſtituitur; </s> <s xml:id="echoid-s14319" xml:space="preserve">per fo-<lb/>ramen in laminâ metallicâ L, quæ in feneſtrâ datur, radius <lb/>ſolaris diametri circiter quartæ partis pollicis, in cubiculum <lb/>intromittitur; </s> <s xml:id="echoid-s14320" xml:space="preserve">ita ſpeculum diſponitur ut radius tranſeat per <lb/>cavitatem cylindricam obliquam, (cujus diameter radii dia-<lb/>metrum æquat,) in tabellâ T: </s> <s xml:id="echoid-s14321" xml:space="preserve">ſi hæc tranſponatur, reflexus <lb/>radius per eandem cavitatem tranſibit. </s> <s xml:id="echoid-s14322" xml:space="preserve">Obtinet hoc quæ-<lb/>cunque fuerit cavitatis inclinatio, ut adhibitis variis tabellis <lb/>demonſtratur.</s> <s xml:id="echoid-s14323" xml:space="preserve"/> </p> <div xml:id="echoid-div2155" type="float" level="2" n="1"> <note position="left" xlink:label="note-0564-02" xlink:href="note-0564-02a" xml:space="preserve">TAB. XII. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s14324" xml:space="preserve">Quo experimento cum n. </s> <s xml:id="echoid-s14325" xml:space="preserve">784. </s> <s xml:id="echoid-s14326" xml:space="preserve">etiam probatur n. </s> <s xml:id="echoid-s14327" xml:space="preserve">779.</s> <s xml:id="echoid-s14328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14329" xml:space="preserve">Siradius reflexus fiat radius incidens, id eſt, ſi lumen ac-<lb/> <anchor type="note" xlink:label="note-0564-03a" xlink:href="note-0564-03"/> cedat per lineam BC, redibit per CA, id eſt, primus in-<lb/> <anchor type="note" xlink:label="note-0564-04a" xlink:href="note-0564-04"/> cidens fiet reflexus; </s> <s xml:id="echoid-s14330" xml:space="preserve">ut patet ex æqualitate angulorum BCO, <lb/>OCA.</s> <s xml:id="echoid-s14331" xml:space="preserve"/> </p> <div xml:id="echoid-div2156" type="float" level="2" n="2"> <note position="left" xlink:label="note-0564-03" xlink:href="note-0564-03a" xml:space="preserve">785.</note> <note position="left" xlink:label="note-0564-04" xlink:href="note-0564-04a" xml:space="preserve">TAB. XII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s14332" xml:space="preserve">Ex hac æqualitate angulorum incidentiæ & </s> <s xml:id="echoid-s14333" xml:space="preserve">reflectionis, <lb/>ulterius deducimus, lumen eâdem cum vi à corpore poſt im-<lb/> <anchor type="note" xlink:label="note-0564-05a" xlink:href="note-0564-05"/> pactum recedere, qua acceſſit. </s> <s xml:id="echoid-s14334" xml:space="preserve">Reſolvatur motus per AC, <lb/>in duos motus per AO & </s> <s xml:id="echoid-s14335" xml:space="preserve">OC <anchor type="note" xlink:href="" symbol="*"/>, poſitis AO ad planum <anchor type="note" xlink:label="note-0564-06a" xlink:href="note-0564-06"/> reflectens parallelâ, & </s> <s xml:id="echoid-s14336" xml:space="preserve">OC ad hoc perpendiculari. </s> <s xml:id="echoid-s14337" xml:space="preserve">Con-<lb/>tinuetur AO; </s> <s xml:id="echoid-s14338" xml:space="preserve">motus juxta hanc directionem non mutatur <lb/>ex plani actione: </s> <s xml:id="echoid-s14339" xml:space="preserve">ſint ideò AO & </s> <s xml:id="echoid-s14340" xml:space="preserve">OB æquales; </s> <s xml:id="echoid-s14341" xml:space="preserve">ſi lumen re-<lb/>cedat â plano eâ cum vi, cum qua acceſſit, motus ex repul-<lb/>ſione repræſentatur per CO, & </s> <s xml:id="echoid-s14342" xml:space="preserve">in hoc caſu radius reflexus <lb/>tranſit per B <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14343" xml:space="preserve">id eſt, angulus OCB æqualis eſt angulo <anchor type="note" xlink:label="note-0564-07a" xlink:href="note-0564-07"/> OCA, quod cum experimento congruit.</s> <s xml:id="echoid-s14344" xml:space="preserve"/> </p> <div xml:id="echoid-div2157" type="float" level="2" n="3"> <note position="left" xlink:label="note-0564-05" xlink:href="note-0564-05a" xml:space="preserve">786.</note> <note symbol="*" position="left" xlink:label="note-0564-06" xlink:href="note-0564-06a" xml:space="preserve">192.</note> <note symbol="*" position="left" xlink:label="note-0564-07" xlink:href="note-0564-07a" xml:space="preserve">191.</note> </div> <p> <s xml:id="echoid-s14345" xml:space="preserve">Circa luminis reflexionem notatu digniſſimum eſt, lumen <lb/> <anchor type="note" xlink:label="note-0564-08a" xlink:href="note-0564-08"/> non incurrere in partes ſolidas corporum, dum ab his refle-<lb/>ctitur, ſed ibi reflecti, ubi liberrimè pertranſire poteſt. </s> <s xml:id="echoid-s14346" xml:space="preserve">Va-<lb/>riis illud probabo experimentis, quibus aliæ miræ reflexionis <lb/>proprietates deteguntur.</s> <s xml:id="echoid-s14347" xml:space="preserve"/> </p> <div xml:id="echoid-div2158" type="float" level="2" n="4"> <note position="left" xlink:label="note-0564-08" xlink:href="note-0564-08a" xml:space="preserve">787.</note> </div> <p> <s xml:id="echoid-s14348" xml:space="preserve">Quotidianum eſt experimentum à nemine non obſerva-<lb/>tum, lumen dum per medium quodcunque movetur, ex. </s> <s xml:id="echoid-s14349" xml:space="preserve">gr. <lb/></s> <s xml:id="echoid-s14350" xml:space="preserve"> <anchor type="note" xlink:label="note-0564-09a" xlink:href="note-0564-09"/> vitrum, aquam, aërem, ſenſibilem & </s> <s xml:id="echoid-s14351" xml:space="preserve">regularem non pati re-<lb/>flexionem; </s> <s xml:id="echoid-s14352" xml:space="preserve">ibi autem reflecti, ubi media duo diverſæ denſi- <pb o="61" file="0565" n="623" rhead="MATHEMATICA LIB. III. CAP. XIII."/> tatis ſeparantur; </s> <s xml:id="echoid-s14353" xml:space="preserve">ſic in ſuperficie aquæ aut vitri reflectitur.</s> <s xml:id="echoid-s14354" xml:space="preserve"/> </p> <div xml:id="echoid-div2159" type="float" level="2" n="5"> <note position="left" xlink:label="note-0564-09" xlink:href="note-0564-09a" xml:space="preserve">788.</note> </div> <p> <s xml:id="echoid-s14355" xml:space="preserve">An tantâ copiâ lumen, ubi media ſeparantur, in horum <lb/>particulas poteſt incurrere, dum per utrumque per ſpatium <lb/>magnum in has non incurrendo movetur? </s> <s xml:id="echoid-s14356" xml:space="preserve">An tales particu-<lb/>læ majori numero verſus ſuperficiem dantur quam alibi?</s> <s xml:id="echoid-s14357" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s14358" xml:space="preserve">Lumen etiam majori copiâ reflectitur, in denſiori medio, <lb/> <anchor type="note" xlink:label="note-0565-01a" xlink:href="note-0565-01"/> incurrendo in ſuperficiem rarioris, quàm contra in rariori, <lb/>impingendo in ſuperficiem denſioris.</s> <s xml:id="echoid-s14359" xml:space="preserve"/> </p> <div xml:id="echoid-div2160" type="float" level="2" n="6"> <note position="right" xlink:label="note-0565-01" xlink:href="note-0565-01a" xml:space="preserve">789.</note> </div> </div> <div xml:id="echoid-div2162" type="section" level="1" n="527"> <head xml:id="echoid-head697" xml:space="preserve"><emph style="sc">Experimentum</emph>. 2.</head> <p> <s xml:id="echoid-s14360" xml:space="preserve">In loco obſcuro, in quo lumen per foramen in lamina L <lb/> <anchor type="note" xlink:label="note-0565-02a" xlink:href="note-0565-02"/> intrat, detur priſma triangulare vitreum AB; </s> <s xml:id="echoid-s14361" xml:space="preserve">lumen prif-<lb/>ma intret per latus unum; </s> <s xml:id="echoid-s14362" xml:space="preserve">ſi ad vicinum latus perveniat, & </s> <s xml:id="echoid-s14363" xml:space="preserve"><lb/>efficiat angulum incidentiæ majorem grad. </s> <s xml:id="echoid-s14364" xml:space="preserve">40. </s> <s xml:id="echoid-s14365" xml:space="preserve">in totum re-<lb/>flectitur, & </s> <s xml:id="echoid-s14366" xml:space="preserve">nihil in aërem penetrat; </s> <s xml:id="echoid-s14367" xml:space="preserve">lumen autem in aëre à <lb/>vitro nunquam in totum reflectitur.</s> <s xml:id="echoid-s14368" xml:space="preserve"/> </p> <div xml:id="echoid-div2162" type="float" level="2" n="1"> <note position="right" xlink:label="note-0565-02" xlink:href="note-0565-02a" xml:space="preserve">TAB. XII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s14369" xml:space="preserve">Si verò reflexio fiat ex impactu luminis in partes ſolidas <lb/>corporum, plures tales dantur partes in aëre, quàm in vitro, <lb/>nam ſi ab ipſo vitro in hoc lumen reflecteretur, ad ſepara-<lb/>tionem mediorum lumen nunquam pertingeret; </s> <s xml:id="echoid-s14370" xml:space="preserve">ex vitro e-<lb/>tiam lumen poſſe exire, ubi reflectitur, in Exp. </s> <s xml:id="echoid-s14371" xml:space="preserve">ſequentibus <lb/>probatur. </s> <s xml:id="echoid-s14372" xml:space="preserve">In viciniis idcirco vitri tot requiruntur partes in <lb/>aëre, ut lumini via non detur, ita ut in totum in vitrum re-<lb/>flectatur; </s> <s xml:id="echoid-s14373" xml:space="preserve">tales tamen non dari patet, quia per aërem juxta <lb/>omnes directiones ad vitrum uſque pervenit lumen & </s> <s xml:id="echoid-s14374" xml:space="preserve">vitrum <lb/>intrat. </s> <s xml:id="echoid-s14375" xml:space="preserve">Etiam in eodem loco ſuperficiei, ſeparantis vitrum <lb/>& </s> <s xml:id="echoid-s14376" xml:space="preserve">aërem, lumen ab unâ parte accedens reflectitur, dum <lb/>quod à parte oppoſitâ advenit, tranſmittitur. </s> <s xml:id="echoid-s14377" xml:space="preserve">Quod clarè <lb/>probat lumen ibi reflecti, ubi pertranſire poteſt.</s> <s xml:id="echoid-s14378" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2164" type="section" level="1" n="528"> <head xml:id="echoid-head698" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s14379" xml:space="preserve">Iiſdem poſitis, quæ in Experimento præcedenti, fi mi <lb/> <anchor type="note" xlink:label="note-0565-03a" xlink:href="note-0565-03"/> nuatur luminis obliquitas, pro parte in aërem tranſibit.</s> <s xml:id="echoid-s14380" xml:space="preserve"/> </p> <div xml:id="echoid-div2164" type="float" level="2" n="1"> <note position="right" xlink:label="note-0565-03" xlink:href="note-0565-03a" xml:space="preserve">790.</note> </div> <note position="right" xml:space="preserve">TAB. XII. <lb/>fig. 3.</note> <p> <s xml:id="echoid-s14381" xml:space="preserve">Quis concipiet lumen, quod ex vitro in aërem tranſit & </s> <s xml:id="echoid-s14382" xml:space="preserve"><lb/>in partes ſolidas non incurrit, illud totum, ſi paululum au-<lb/>geatur obliquitas, incurrere in tales partes; </s> <s xml:id="echoid-s14383" xml:space="preserve">cùm in utroque <lb/>medio, ut dictum, meatus juxta omnes directiones dentur.</s> <s xml:id="echoid-s14384" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2166" type="section" level="1" n="529"> <head xml:id="echoid-head699" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s14385" xml:space="preserve">Priſma vitreum triangulare AB, volubile eſt circa axem; <lb/></s> <s xml:id="echoid-s14386" xml:space="preserve"> <anchor type="note" xlink:label="note-0565-05a" xlink:href="note-0565-05"/> <anchor type="note" xlink:label="note-0565-06a" xlink:href="note-0565-06"/> <pb o="62" file="0566" n="624" rhead="PHYSICES ELEMENTA"/> quod præſtatur baſibus jungendo laminas æneas, quibus fila <lb/>ænea perpendiculariter cohærent; </s> <s xml:id="echoid-s14387" xml:space="preserve">pixidi P ſuperimponitur <lb/>priſma ita, ut memorata fila ab oris pixidis ſuſtineantur; </s> <s xml:id="echoid-s14388" xml:space="preserve">oræ <lb/>etiam paululum excavantur, ad fila recipienda; </s> <s xml:id="echoid-s14389" xml:space="preserve">quæ facilè <lb/>circumaguntur, quo motu priſma circa axem revolvitur, & </s> <s xml:id="echoid-s14390" xml:space="preserve"><lb/>facilè diſponitur, ut lumen reflectat eodem modo, ac in <lb/>exp. </s> <s xml:id="echoid-s14391" xml:space="preserve">2. </s> <s xml:id="echoid-s14392" xml:space="preserve">Pixis impletur aquâ, quæ ad priſma pertingit; </s> <s xml:id="echoid-s14393" xml:space="preserve">& </s> <s xml:id="echoid-s14394" xml:space="preserve">lu-<lb/>men, quod in aërem impingendo, in totum reflectebatur, <lb/>nunc in aquam incurrens, pro parte in hanc penetrat, & </s> <s xml:id="echoid-s14395" xml:space="preserve"><lb/>pro parte tantum reflectitur.</s> <s xml:id="echoid-s14396" xml:space="preserve"/> </p> <div xml:id="echoid-div2166" type="float" level="2" n="1"> <note position="right" xlink:label="note-0565-05" xlink:href="note-0565-05a" xml:space="preserve">791.</note> <note position="right" xlink:label="note-0565-06" xlink:href="note-0565-06a" xml:space="preserve">TAB. XII. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s14397" xml:space="preserve">Quod experimentum cum reflexione, ex impactu in par-<lb/>tes ſolidas, minimè congruit.</s> <s xml:id="echoid-s14398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14399" xml:space="preserve">In parte tertiâ hujus libri etiam videbimus, tenues lami-<lb/>nas, quæ lumen reflectunt, illud tranſmittere, ſi craſſiores <lb/>fiant <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14400" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">894.</note> <p> <s xml:id="echoid-s14401" xml:space="preserve">Probat etiam Exp. </s> <s xml:id="echoid-s14402" xml:space="preserve">4. </s> <s xml:id="echoid-s14403" xml:space="preserve">vim reflectentem eo eſſe majorem, quo <lb/> <anchor type="note" xlink:label="note-0566-02a" xlink:href="note-0566-02"/> media, quæ à ſuperficie reflectente ſeparantur, magis denſita-<lb/>te differant; </s> <s xml:id="echoid-s14404" xml:space="preserve">vitrum enim & </s> <s xml:id="echoid-s14405" xml:space="preserve">aër, magis quàm illud cum a-<lb/>quâ, denſitate differunt.</s> <s xml:id="echoid-s14406" xml:space="preserve"/> </p> <div xml:id="echoid-div2167" type="float" level="2" n="2"> <note position="left" xlink:label="note-0566-02" xlink:href="note-0566-02a" xml:space="preserve">792.</note> </div> <p style="it"> <s xml:id="echoid-s14407" xml:space="preserve">In hoc Experimento etiam videmus reflexionem fieri ex <lb/> <anchor type="note" xlink:label="note-0566-03a" xlink:href="note-0566-03"/> eâdem vi, qua radii refringuntur, quæ in diverſis circum-<lb/>ſtantiis varios edit effectus.</s> <s xml:id="echoid-s14408" xml:space="preserve"/> </p> <div xml:id="echoid-div2168" type="float" level="2" n="3"> <note position="left" xlink:label="note-0566-03" xlink:href="note-0566-03a" xml:space="preserve">793.</note> </div> <p> <s xml:id="echoid-s14409" xml:space="preserve">Radius, qui ex medio denſiori in rarius tranſit, attractio-<lb/>ne illius medii à perpendiculari recedit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14410" xml:space="preserve">ſi incidentis obli- <anchor type="note" xlink:label="note-0566-04a" xlink:href="note-0566-04"/> quitas augeatur, augetur & </s> <s xml:id="echoid-s14411" xml:space="preserve">refracti obliquitas, donec tan-<lb/>dem hic, in ipſâ ſuperficie media dirimente, moveatur. <lb/></s> <s xml:id="echoid-s14412" xml:space="preserve">Quod obtinet, quando ſinus anguli incidentiæ eſt ad ſi-<lb/>num totum, ut ſinus incidentiæ in medio denſiori, ad ſi-<lb/>num refractionis in rariori; </s> <s xml:id="echoid-s14413" xml:space="preserve">in hoc enim caſu angulus refra-<lb/>ctionis eſt rectus. </s> <s xml:id="echoid-s14414" xml:space="preserve">Si ulterius incidentis radii obliquitas au-<lb/>geatur, radium in rarius non poſſe penetrare clarè patet; </s> <s xml:id="echoid-s14415" xml:space="preserve"><lb/>hicce eſt caſus, in quo lumen in totum reflectitur; </s> <s xml:id="echoid-s14416" xml:space="preserve">quæ re-<lb/>flexio pendet ab attractione qua radii refringuntur. </s> <s xml:id="echoid-s14417" xml:space="preserve">Nam <lb/>radius, dum per ſpatium attractionis movetur, incurvatur <lb/>verſus medium denſius <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14418" xml:space="preserve">ſi in denſiori medio detur & </s> <s xml:id="echoid-s14419" xml:space="preserve">ita <anchor type="note" xlink:label="note-0566-05a" xlink:href="note-0566-05"/> incurvetur, ut antequam per totum penetraverit ſpatium at-<lb/>tractionis, tangens ad curvam parallela ſit ſuperficiei media <pb o="63" file="0567" n="625" rhead="MATHEMATICA LIB. III. CAP. XIII."/> ſeparanti, curva continuata regreditur, idèoque radius refle-<lb/>ctitur ex attractione medii denſioris, hæcque curvæ conti-<lb/>nuatio ſimilis & </s> <s xml:id="echoid-s14420" xml:space="preserve">æqualis eſt primæ portioni, & </s> <s xml:id="echoid-s14421" xml:space="preserve">efficit angu-<lb/>lum reflexionis æqualem angulo incidentiæ; </s> <s xml:id="echoid-s14422" xml:space="preserve">quia per ean-<lb/>dem partem ſpatii attractionis lumen redit, & </s> <s xml:id="echoid-s14423" xml:space="preserve">eædem vires <lb/>attrahentes in punctis reſpondentibus portionum curvæ in <lb/>lumen agunt. </s> <s xml:id="echoid-s14424" xml:space="preserve">Sic corpus projectum, in aſcenſu & </s> <s xml:id="echoid-s14425" xml:space="preserve">deſcen-<lb/>ſu, curvas ſimiles & </s> <s xml:id="echoid-s14426" xml:space="preserve">æquales deſcribit.</s> <s xml:id="echoid-s14427" xml:space="preserve"/> </p> <div xml:id="echoid-div2169" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0566-04" xlink:href="note-0566-04a" xml:space="preserve">625.</note> <note symbol="*" position="left" xlink:label="note-0566-05" xlink:href="note-0566-05a" xml:space="preserve">619.</note> </div> <p> <s xml:id="echoid-s14428" xml:space="preserve">Non tamen omnem reflectionem ab hac attractione eodem <lb/> <anchor type="note" xlink:label="note-0567-01a" xlink:href="note-0567-01"/> modo pendêre, clarum eſt; </s> <s xml:id="echoid-s14429" xml:space="preserve">nam in eo caſu in quo refractio <lb/>datur, lumen pro parte reflectitur; </s> <s xml:id="echoid-s14430" xml:space="preserve">ne quidem in totum ex <lb/>rariori medio in denſius penetrat lumen; </s> <s xml:id="echoid-s14431" xml:space="preserve">nam & </s> <s xml:id="echoid-s14432" xml:space="preserve">in hoc ca-<lb/>ſu, in quo attractio quam maximè reflectioni opponitur, <lb/>quidam radii repercutiuntur.</s> <s xml:id="echoid-s14433" xml:space="preserve"/> </p> <div xml:id="echoid-div2170" type="float" level="2" n="5"> <note position="right" xlink:label="note-0567-01" xlink:href="note-0567-01a" xml:space="preserve">794.</note> </div> <p> <s xml:id="echoid-s14434" xml:space="preserve">Reflexionem tamen, in omni caſu, cum vi refringente re-<lb/> <anchor type="note" xlink:label="note-0567-02a" xlink:href="note-0567-02"/> lationem habere, in dubium vocari non poteſt.</s> <s xml:id="echoid-s14435" xml:space="preserve"/> </p> <div xml:id="echoid-div2171" type="float" level="2" n="6"> <note position="right" xlink:label="note-0567-02" xlink:href="note-0567-02a" xml:space="preserve">795.</note> </div> <p> <s xml:id="echoid-s14436" xml:space="preserve">Vbi lumen ſine refractione tranſit, ibi non reflectitur<anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s14437" xml:space="preserve"> <anchor type="note" xlink:label="note-0567-03a" xlink:href="note-0567-03"/> <anchor type="note" xlink:label="note-0567-04a" xlink:href="note-0567-04"/> ubi autem refractio maxima eſt, ibi etiam reflexio fortior <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s14438" xml:space="preserve"> <anchor type="note" xlink:label="note-0567-05a" xlink:href="note-0567-05"/> quod non modo obtinet, quando lumen, in medio denſiori <lb/>motum, in rarius impingit, ut in exp. </s> <s xml:id="echoid-s14439" xml:space="preserve">4.</s> <s xml:id="echoid-s14440" xml:space="preserve">, ſed idem obſerva-<lb/>tur, quando lumen in denſius medium impingit: </s> <s xml:id="echoid-s14441" xml:space="preserve">ſic poſito <lb/>lumine in aëre, ſuperficies vitri fortius reflectit, quam aquæ; <lb/></s> <s xml:id="echoid-s14442" xml:space="preserve">adamantis ſuperficies iterum fortius. </s> <s xml:id="echoid-s14443" xml:space="preserve">Immerſis, aquâ, vitro & </s> <s xml:id="echoid-s14444" xml:space="preserve"><lb/>adamante, in ſeparatione horum corporum cum aquâ vis re-<lb/>fringens minor eſt, quàm in viciniis aëris, & </s> <s xml:id="echoid-s14445" xml:space="preserve">eorundem cor-<lb/>porum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14446" xml:space="preserve">minus etiam fortiter in aquâ, quàm in aëre, re- <anchor type="note" xlink:label="note-0567-06a" xlink:href="note-0567-06"/> flectunt lumen hæc corpora. </s> <s xml:id="echoid-s14447" xml:space="preserve">Ex hac relatione vis reflecten-<lb/>tis cum vi refringente deducimus, lumen repercuti ad certam <lb/> <anchor type="note" xlink:label="note-0567-07a" xlink:href="note-0567-07"/> diſtantiam à corporibus, eodem modo ac vis refringens ad <lb/>certam à corpore diſtantiam agit; </s> <s xml:id="echoid-s14448" xml:space="preserve">confirmatur hæc propoſitio <lb/>ex demonſtratis circa reflexionem, quæ non pendet ab im-<lb/>pactu in partes ſolidas corporum; </s> <s xml:id="echoid-s14449" xml:space="preserve">& </s> <s xml:id="echoid-s14450" xml:space="preserve">pleniſſimè evincitur ſi <lb/>conſideremus, corpora polita regulariter lumen reflectere, <lb/> <anchor type="note" xlink:label="note-0567-08a" xlink:href="note-0567-08"/> quod in ſpeculis obſervamus, licèt in horum ſuperficiebus in-<lb/>numeræ dentur raſuræ: </s> <s xml:id="echoid-s14451" xml:space="preserve">nam pulveris attritu poliuntur, & </s> <s xml:id="echoid-s14452" xml:space="preserve"><lb/>quantumvis ſint exiguæ hujus particulæ, reſpectu luminis ra-<lb/>ſuras magnas in ſuperficie relinquunt; </s> <s xml:id="echoid-s14453" xml:space="preserve">unde in ipſâ ſuperfi- <pb o="64" file="0568" n="626" rhead="PHYSICES ELEMENTA"/> cie reflectio neceſſario irregularis eſt; </s> <s xml:id="echoid-s14454" xml:space="preserve">ſi autem ad exiguam <lb/>à ſuperficie diſtantiam reflexionem fieri concipiamus, minu-<lb/>untur, & </s> <s xml:id="echoid-s14455" xml:space="preserve">ferè in totum tolluntur irregularitates, ut atten-<lb/>dendo facilè liquet.</s> <s xml:id="echoid-s14456" xml:space="preserve"/> </p> <div xml:id="echoid-div2172" type="float" level="2" n="7"> <note position="right" xlink:label="note-0567-03" xlink:href="note-0567-03a" xml:space="preserve">796.</note> <note symbol="*" position="right" xlink:label="note-0567-04" xlink:href="note-0567-04a" xml:space="preserve">617. 788.</note> <note symbol="*" position="right" xlink:label="note-0567-05" xlink:href="note-0567-05a" xml:space="preserve">631. 792.</note> <note symbol="*" position="right" xlink:label="note-0567-06" xlink:href="note-0567-06a" xml:space="preserve">631.</note> <note position="right" xlink:label="note-0567-07" xlink:href="note-0567-07a" xml:space="preserve">797.</note> <note position="right" xlink:label="note-0567-08" xlink:href="note-0567-08a" xml:space="preserve">798.</note> </div> </div> <div xml:id="echoid-div2174" type="section" level="1" n="530"> <head xml:id="echoid-head700" xml:space="preserve">CAPUT XIV.</head> <head xml:id="echoid-head701" style="it" xml:space="preserve">De Speculis planis.</head> <p> <s xml:id="echoid-s14457" xml:space="preserve">SIt bc ſuperficies ſpeculi plani; </s> <s xml:id="echoid-s14458" xml:space="preserve">A punctum radians. </s> <s xml:id="echoid-s14459" xml:space="preserve">Con-<lb/> <anchor type="note" xlink:label="note-0568-01a" xlink:href="note-0568-01"/> tinuetur planum ſpeculi, & </s> <s xml:id="echoid-s14460" xml:space="preserve">ad hoc à radiante A dimitta-<lb/>tur perpendicularis AC; </s> <s xml:id="echoid-s14461" xml:space="preserve">ſi continuetur hæc, & </s> <s xml:id="echoid-s14462" xml:space="preserve">fiat C a <lb/>æqualis CA, a erit focus imaginarius reflexorum radiorum <lb/>ex A procedentium. </s> <s xml:id="echoid-s14463" xml:space="preserve">Sit A b radius incidens; </s> <s xml:id="echoid-s14464" xml:space="preserve">b f radius re-<lb/>flexus; </s> <s xml:id="echoid-s14465" xml:space="preserve">continuetur hoc ultra ſpeculum; </s> <s xml:id="echoid-s14466" xml:space="preserve">propter angulos in-<lb/>cidentiæ & </s> <s xml:id="echoid-s14467" xml:space="preserve">reflexionis æquales inter ſe <anchor type="note" xlink:href="" symbol="*"/>, æquantur etiam <anchor type="note" xlink:label="note-0568-02a" xlink:href="note-0568-02"/> horum complementa anguli A b C, f b d; </s> <s xml:id="echoid-s14468" xml:space="preserve">huic æqualis <lb/>eſt oppoſitus ad verticem ab C: </s> <s xml:id="echoid-s14469" xml:space="preserve">Triangula A b C, ab C <lb/>rectangula habent latus commune C b & </s> <s xml:id="echoid-s14470" xml:space="preserve">angulos æquales <lb/>C b a, C b A; </s> <s xml:id="echoid-s14471" xml:space="preserve">in omnibus ergo conveniunt, & </s> <s xml:id="echoid-s14472" xml:space="preserve">ſunt æ-<lb/>quales inter ſe CA & </s> <s xml:id="echoid-s14473" xml:space="preserve">C a: </s> <s xml:id="echoid-s14474" xml:space="preserve">quæ demonſtratio omnibus a-<lb/>liis radiis, ex A profluentibus, competit, in quocunque <lb/>plano perpendiculari ad planum ſpeculi concipiantur. </s> <s xml:id="echoid-s14475" xml:space="preserve">ld-<lb/>circo ubicunque oculus detur, ſi ad hunc radii reflexi per-<lb/>veniant, oculum intrabunt quaſi ex a procederent; </s> <s xml:id="echoid-s14476" xml:space="preserve">& </s> <s xml:id="echoid-s14477" xml:space="preserve">in hoc <lb/>puncto apparebit punctum A <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14478" xml:space="preserve">hujus autem puncti appa- <anchor type="note" xlink:label="note-0568-03a" xlink:href="note-0568-03"/> rentia eundem ſitum habet reſpectu ſpeculi, ad partem poſti-<lb/> <anchor type="note" xlink:label="note-0568-04a" xlink:href="note-0568-04"/> cam, quâm habet ipſum punctum radians ad partem anticam.</s> <s xml:id="echoid-s14479" xml:space="preserve"/> </p> <div xml:id="echoid-div2174" type="float" level="2" n="1"> <note position="left" xlink:label="note-0568-01" xlink:href="note-0568-01a" xml:space="preserve">799.</note> <note symbol="*" position="left" xlink:label="note-0568-02" xlink:href="note-0568-02a" xml:space="preserve">384.</note> <note position="left" xlink:label="note-0568-03" xlink:href="note-0568-03a" xml:space="preserve">800.</note> <note symbol="*" position="left" xlink:label="note-0568-04" xlink:href="note-0568-04a" xml:space="preserve">737.</note> </div> <p> <s xml:id="echoid-s14480" xml:space="preserve">Quod ſi applicetur ad ſingula puncta objecti, patebit, ob-<lb/> <anchor type="note" xlink:label="note-0568-05a" xlink:href="note-0568-05"/> jectum poſt ſpeculum apparêre, in eo ſitu, in quo reverâ da-<lb/>tur ante ſpeculum.</s> <s xml:id="echoid-s14481" xml:space="preserve"/> </p> <div xml:id="echoid-div2175" type="float" level="2" n="2"> <note position="left" xlink:label="note-0568-05" xlink:href="note-0568-05a" xml:space="preserve">801.</note> </div> </div> <div xml:id="echoid-div2177" type="section" level="1" n="531"> <head xml:id="echoid-head702" xml:space="preserve">CAPUT XV.</head> <head xml:id="echoid-head703" style="it" xml:space="preserve">De Speculis ſphæricis.</head> <p> <s xml:id="echoid-s14482" xml:space="preserve">OMnis ſuperficies ſphærica conſiderari poteſt, quaſi for-<lb/>mata ex innumeris ſuperficiebus planis minimis; </s> <s xml:id="echoid-s14483" xml:space="preserve">pla-<lb/>numque, ſphæram in puncto quocunque tangens, eſt quaſi <lb/>continuatio talis plani exigui.</s> <s xml:id="echoid-s14484" xml:space="preserve"/> </p> <pb o="65" file="0569" n="627" rhead="MATHEMATICA LIB. III. CAP. XV."/> <p> <s xml:id="echoid-s14485" xml:space="preserve">Specula ſphærica ſunt aut cava aut convexa.</s> <s xml:id="echoid-s14486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14487" xml:space="preserve">Prima formantur ex portione ſphæræ cavæ & </s> <s xml:id="echoid-s14488" xml:space="preserve">politæ.</s> <s xml:id="echoid-s14489" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14490" xml:space="preserve">Secunda ſunt portiones ſphærarum ab exteriori parte po-<lb/>litarum.</s> <s xml:id="echoid-s14491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14492" xml:space="preserve">Radius in ſpeculum quodcunque ſphæricum impingens, cum <lb/> <anchor type="note" xlink:label="note-0569-01a" xlink:href="note-0569-01"/> ſuo reflexo, dantur in plano, quod continuatum per ſphæræ cen-<lb/>trum tranſit <anchor type="note" xlink:href="" symbol="*"/>, eſt enim tale planum ad ſuperficiem ſphæræ <anchor type="note" xlink:label="note-0569-02a" xlink:href="note-0569-02"/> perpendiculare. </s> <s xml:id="echoid-s14493" xml:space="preserve">Linea, quæ per centrum ſphæræ & </s> <s xml:id="echoid-s14494" xml:space="preserve">punctum <lb/> <anchor type="note" xlink:label="note-0569-03a" xlink:href="note-0569-03"/> incidentiæ ducitur, continuata, cum radio incidente & </s> <s xml:id="echoid-s14495" xml:space="preserve">re-<lb/>flexo angulos æquales format <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14496" xml:space="preserve">nam linea hæc eſt perpen- <anchor type="note" xlink:label="note-0569-04a" xlink:href="note-0569-04"/> dicularis ad ſuperficiem & </s> <s xml:id="echoid-s14497" xml:space="preserve">hi ſunt anguli incidentiæ & </s> <s xml:id="echoid-s14498" xml:space="preserve">re-<lb/>flexionis: </s> <s xml:id="echoid-s14499" xml:space="preserve">ideoque radius per centrum tranſiens, aut qui con-<lb/> <anchor type="note" xlink:label="note-0569-05a" xlink:href="note-0569-05"/> tinuatus per centrum tranſiret, reflexus in ſe redit.</s> <s xml:id="echoid-s14500" xml:space="preserve"/> </p> <div xml:id="echoid-div2177" type="float" level="2" n="1"> <note position="right" xlink:label="note-0569-01" xlink:href="note-0569-01a" xml:space="preserve">804.</note> <note symbol="*" position="right" xlink:label="note-0569-02" xlink:href="note-0569-02a" xml:space="preserve">782;</note> <note position="right" xlink:label="note-0569-03" xlink:href="note-0569-03a" xml:space="preserve">805.</note> <note symbol="*" position="right" xlink:label="note-0569-04" xlink:href="note-0569-04a" xml:space="preserve">784.</note> <note position="right" xlink:label="note-0569-05" xlink:href="note-0569-05a" xml:space="preserve">806.</note> </div> <note position="right" xml:space="preserve">TAB. XII. <lb/>fig. 5.</note> <p> <s xml:id="echoid-s14501" xml:space="preserve">Sit b c portio ſpeculi convexi; </s> <s xml:id="echoid-s14502" xml:space="preserve">punctum radians A; </s> <s xml:id="echoid-s14503" xml:space="preserve">ſint <lb/>A b, A d, A e, radii incidentes; </s> <s xml:id="echoid-s14504" xml:space="preserve">reflexi erunt b f, d g, <lb/> <anchor type="note" xlink:label="note-0569-07a" xlink:href="note-0569-07"/> e b; </s> <s xml:id="echoid-s14505" xml:space="preserve">ſi à puncto radiante A ducatur tangens ad ſpeculum, <lb/>radius reflexus erit continuatio incidentis, aut potius in <lb/>puncto contactus terminatur radiorum reflexio.</s> <s xml:id="echoid-s14506" xml:space="preserve"/> </p> <div xml:id="echoid-div2178" type="float" level="2" n="2"> <note position="right" xlink:label="note-0569-07" xlink:href="note-0569-07a" xml:space="preserve">807.</note> </div> <p> <s xml:id="echoid-s14507" xml:space="preserve">Si radii à ſpeculo convexo reflexi b f, d g, e b continuentur, <lb/> <anchor type="note" xlink:label="note-0569-08a" xlink:href="note-0569-08"/> cum omnibus intermediis, interſectionibus ſuis formant cur-<lb/>vam a a, quam omnes hi radii tangunt, & </s> <s xml:id="echoid-s14508" xml:space="preserve">radii vicini ſeſe <lb/>mutuo interſecant in ipſa periferia curvæ; </s> <s xml:id="echoid-s14509" xml:space="preserve">ita ut ſemper ocu-<lb/>lum intrent quaſi à puncto periferiæ procederent; </s> <s xml:id="echoid-s14510" xml:space="preserve">in qua <lb/>ideò punctum A ſemper apparet <anchor type="note" xlink:href="" symbol="*"/>, quamdiu reflexi ad ocu- <anchor type="note" xlink:label="note-0569-09a" xlink:href="note-0569-09"/> lum pervenire poſſunt, & </s> <s xml:id="echoid-s14511" xml:space="preserve">oculus movetur in plano, quod <lb/>per centrum ſphæræ tranſit: </s> <s xml:id="echoid-s14512" xml:space="preserve">remoto verò oculo ex hoc pla-<lb/>no, in aliâ curvâ apparet radians, quia tales curvæ dantur in <lb/>ſingulis planis, quæ per A & </s> <s xml:id="echoid-s14513" xml:space="preserve">C concipi poſſunt.</s> <s xml:id="echoid-s14514" xml:space="preserve"/> </p> <div xml:id="echoid-div2179" type="float" level="2" n="3"> <note position="right" xlink:label="note-0569-08" xlink:href="note-0569-08a" xml:space="preserve">808.</note> <note symbol="*" position="right" xlink:label="note-0569-09" xlink:href="note-0569-09a" xml:space="preserve">737.</note> </div> <p> <s xml:id="echoid-s14515" xml:space="preserve">Cùm omnes hæ curvæ & </s> <s xml:id="echoid-s14516" xml:space="preserve">quidem integræ dentur poſt <lb/>ſpeculum, omnia etiam objecta poſt ſpeculi ſuperficiem appa-<lb/> <anchor type="note" xlink:label="note-0569-10a" xlink:href="note-0569-10"/> rent.</s> <s xml:id="echoid-s14517" xml:space="preserve"/> </p> <div xml:id="echoid-div2180" type="float" level="2" n="4"> <note position="right" xlink:label="note-0569-10" xlink:href="note-0569-10a" xml:space="preserve">809.</note> </div> <p> <s xml:id="echoid-s14518" xml:space="preserve">Objecta etiam apparent erecta. </s> <s xml:id="echoid-s14519" xml:space="preserve">Nam ſi punctum A mo-<lb/> <anchor type="note" xlink:label="note-0569-11a" xlink:href="note-0569-11"/> veatur circa ſpeculum, eodem motu fertur tota curva a a; <lb/></s> <s xml:id="echoid-s14520" xml:space="preserve">quod probat, quantum ad ſitum erectum aut inverſum, pun-<lb/>cta repræſentationis eandem inter ſe habere relationem, <lb/>quam ipſius objecti puncta.</s> <s xml:id="echoid-s14521" xml:space="preserve"/> </p> <div xml:id="echoid-div2181" type="float" level="2" n="5"> <note position="right" xlink:label="note-0569-11" xlink:href="note-0569-11a" xml:space="preserve">810.</note> </div> <p> <s xml:id="echoid-s14522" xml:space="preserve">Recedente puncto A à ſpeculo, recedit & </s> <s xml:id="echoid-s14523" xml:space="preserve">tota curva mo- <pb o="66" file="0570" n="628" rhead="PHYSICES ELEMENTA"/> tu contrario; </s> <s xml:id="echoid-s14524" xml:space="preserve">poſito autem A ad diſtantiam infinitam, pun-<lb/>ctum curvæ à ſuperficie maximè remotum, ab hac diſtabit <lb/>quartam partem diametri: </s> <s xml:id="echoid-s14525" xml:space="preserve">Unde ſequitur imminuta appare-<lb/> <anchor type="note" xlink:label="note-0570-01a" xlink:href="note-0570-01"/> re objecta; </s> <s xml:id="echoid-s14526" xml:space="preserve">repræſentationes enim omnes inter arctos limites <lb/>continentur.</s> <s xml:id="echoid-s14527" xml:space="preserve"/> </p> <div xml:id="echoid-div2182" type="float" level="2" n="6"> <note position="left" xlink:label="note-0570-01" xlink:href="note-0570-01a" xml:space="preserve">811.</note> </div> <p> <s xml:id="echoid-s14528" xml:space="preserve">Si moveatur oculus, movetur & </s> <s xml:id="echoid-s14529" xml:space="preserve">objecti apparentia, cujus <lb/> <anchor type="note" xlink:label="note-0570-02a" xlink:href="note-0570-02"/> figura etiam mutatur: </s> <s xml:id="echoid-s14530" xml:space="preserve">ſingula enim puncta per ſuas curvas <lb/>moventur, & </s> <s xml:id="echoid-s14531" xml:space="preserve">quidem inæqualiter pro diverſo oculi ſitu, re-<lb/>ſpectu ſingularum curvarum; </s> <s xml:id="echoid-s14532" xml:space="preserve">unde neceſſario ſigura mutatur.</s> <s xml:id="echoid-s14533" xml:space="preserve"/> </p> <div xml:id="echoid-div2183" type="float" level="2" n="7"> <note position="left" xlink:label="note-0570-02" xlink:href="note-0570-02a" xml:space="preserve">812.</note> </div> </div> <div xml:id="echoid-div2185" type="section" level="1" n="532"> <head xml:id="echoid-head704" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s14534" xml:space="preserve">Si, in ſpeculo ſphærico convexo, aliquis ut A ſe ipſum in-<lb/>tueatur, faciem ſuam in a, erectam, imminutam, & </s> <s xml:id="echoid-s14535" xml:space="preserve">à vera <lb/> <anchor type="note" xlink:label="note-0570-03a" xlink:href="note-0570-03"/> diſſimilem, videbit; </s> <s xml:id="echoid-s14536" xml:space="preserve">motu oculi reliqua memorata obſerva-<lb/>bit reſpectu objectorum fixorum.</s> <s xml:id="echoid-s14537" xml:space="preserve"/> </p> <div xml:id="echoid-div2185" type="float" level="2" n="1"> <note position="left" xlink:label="note-0570-03" xlink:href="note-0570-03a" xml:space="preserve">TAB. XII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s14538" xml:space="preserve">Sit b d ſpeculum cavum, portio ſphæræ cujus centrum <lb/> <anchor type="note" xlink:label="note-0570-04a" xlink:href="note-0570-04"/> eſt C; </s> <s xml:id="echoid-s14539" xml:space="preserve">cadant in ſpeculi ſuperficiem radii paralleli, inter <lb/> <anchor type="note" xlink:label="note-0570-05a" xlink:href="note-0570-05"/> quos detur C d per centrum tranſiens; </s> <s xml:id="echoid-s14540" xml:space="preserve">reflexione hic in ſe <lb/>redit <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14541" xml:space="preserve">radii vicini, reflexi, convergentes fiunt, &</s> <s xml:id="echoid-s14542" xml:space="preserve"> <anchor type="note" xlink:label="note-0570-06a" xlink:href="note-0570-06"/> cum hoc concurrunt in focum F, punctum medium inter <lb/>d & </s> <s xml:id="echoid-s14543" xml:space="preserve">C. </s> <s xml:id="echoid-s14544" xml:space="preserve">Sit A b radius parum à C d diſtans; </s> <s xml:id="echoid-s14545" xml:space="preserve">ducatur ſemi-<lb/>diameter C b; </s> <s xml:id="echoid-s14546" xml:space="preserve">angulus incidentiæ erit A b C, cui æqualis <lb/>eſt angulus reflexionis C b F <anchor type="note" xlink:href="" symbol="*"/>, ut & </s> <s xml:id="echoid-s14547" xml:space="preserve">angulus alternus b C <anchor type="note" xlink:label="note-0570-07a" xlink:href="note-0570-07"/> F; </s> <s xml:id="echoid-s14548" xml:space="preserve">Eſt ergo iſoſceles triangulum b FC, & </s> <s xml:id="echoid-s14549" xml:space="preserve">latera FC & </s> <s xml:id="echoid-s14550" xml:space="preserve"><lb/>F b ſunt æqualia: </s> <s xml:id="echoid-s14551" xml:space="preserve">propter exiguum b d, F d & </s> <s xml:id="echoid-s14552" xml:space="preserve">F b ſenſibi-<lb/>liter non differunt; </s> <s xml:id="echoid-s14553" xml:space="preserve">idè FC & </s> <s xml:id="echoid-s14554" xml:space="preserve">F d ſunt æquales: </s> <s xml:id="echoid-s14555" xml:space="preserve">quæ de-<lb/>monſtratio omnibus radiis à C d parum diſtantibus competit.</s> <s xml:id="echoid-s14556" xml:space="preserve"/> </p> <div xml:id="echoid-div2186" type="float" level="2" n="2"> <note position="left" xlink:label="note-0570-04" xlink:href="note-0570-04a" xml:space="preserve">813.</note> <note position="left" xlink:label="note-0570-05" xlink:href="note-0570-05a" xml:space="preserve">TAB. XIII. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0570-06" xlink:href="note-0570-06a" xml:space="preserve">806.</note> <note symbol="*" position="left" xlink:label="note-0570-07" xlink:href="note-0570-07a" xml:space="preserve">805.</note> </div> <p> <s xml:id="echoid-s14557" xml:space="preserve">Si radii paralleli magis à C d diſtent, in F non conve-<lb/>niunt; </s> <s xml:id="echoid-s14558" xml:space="preserve">omnes tamen in circellum exiguum concurrunt, ſi <lb/>ſpeculi diametrum non excedat ſextam aut quintam partem <lb/>diametri ſphæræ, cujus portio eſt ſpeculum.</s> <s xml:id="echoid-s14559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14560" xml:space="preserve">Hoc fundamento nituntur ſpecula uſtoria, quæ radios ſo-<lb/> <anchor type="note" xlink:label="note-0570-08a" xlink:href="note-0570-08"/> lares parallelos in focum colligunt.</s> <s xml:id="echoid-s14561" xml:space="preserve"/> </p> <div xml:id="echoid-div2187" type="float" level="2" n="3"> <note position="left" xlink:label="note-0570-08" xlink:href="note-0570-08a" xml:space="preserve">814.</note> </div> </div> <div xml:id="echoid-div2189" type="section" level="1" n="533"> <head xml:id="echoid-head705" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s14562" xml:space="preserve">Detur ſpeculum concavum S, ex metallo, aut vitro hy-<lb/> <anchor type="note" xlink:label="note-0570-09a" xlink:href="note-0570-09"/> drargyro à poſteriori parte induto; </s> <s xml:id="echoid-s14563" xml:space="preserve">ſuſtineatur hoc pede li-<lb/>gneo P, in cujus ſuperiori parte datur cavitas cylindrica, <lb/>quæ cylindro ligneo impletur, qui cum tranſverſo ligno <pb file="0571" n="629"/> <pb file="0571a" n="630"/> <anchor type="figure" xlink:label="fig-0571a-01a" xlink:href="fig-0571a-01"/> <pb file="0572" n="631"/> <pb o="67" file="0573" n="632" rhead="MATHEMATICA LIB. III. CAP. XV."/> AA cohœret, quod ope cylindri hujus circa punctum <lb/>ſuum medium horizontaliter rotatur; </s> <s xml:id="echoid-s14564" xml:space="preserve">inter ſuſtentacula <lb/>AB, AB, ſpeculum utcunque inclinatur, & </s> <s xml:id="echoid-s14565" xml:space="preserve">ope cochlea-<lb/>rum in B, B, in ſitu quocunque firmatur.</s> <s xml:id="echoid-s14566" xml:space="preserve"/> </p> <div xml:id="echoid-div2189" type="float" level="2" n="1"> <note position="left" xlink:label="note-0570-09" xlink:href="note-0570-09a" xml:space="preserve">TAB. XIII. <lb/>fig. 2.</note> <figure xlink:label="fig-0571a-01" xlink:href="fig-0571a-01a"> <image file="0571a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0571a-01"/> </figure> </div> <p> <s xml:id="echoid-s14567" xml:space="preserve">Expoſito ſpeculo radiis ſolaribus ita, ut radius, qui ad ſpe-<lb/>culi punctum medium pertingit, ad ſuperficiem ſit perpen-<lb/>dicularis, cùm omnes alii huic ſint paralleli, colliguntur in <lb/>focum, ad diſtantiam à ſpeculo quartæ partis diametri ſphæ-<lb/>ræ, ibique violenter urunt.</s> <s xml:id="echoid-s14568" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14569" xml:space="preserve">Si diameter ſuperficiei ſpeculi, ut in noſtro, ſit circiter <lb/>quindecim pollicum, & </s> <s xml:id="echoid-s14570" xml:space="preserve">focus detur ad diſtantiam ſeſqui pe-<lb/>dis, lignum ſtatim flammam concpiit, & </s> <s xml:id="echoid-s14571" xml:space="preserve">laminæ tenues <lb/>plumbi brevi liqueſcunt.</s> <s xml:id="echoid-s14572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14573" xml:space="preserve">Si conſideremus radios à C d remotos & </s> <s xml:id="echoid-s14574" xml:space="preserve">huic parallelos, <lb/>ſi vicini fuerint, reflexi ſeſe mutuo interſecant antequam ad <lb/>C d perveniant, & </s> <s xml:id="echoid-s14575" xml:space="preserve">in hoc caſu, id eſt, ubi incidentes pa-<lb/> <anchor type="note" xlink:label="note-0573-01a" xlink:href="note-0573-01"/> ralleli obliquè in ſpeculum impingunt, parum diſperſi refle-<lb/>ctione in unum punctum colliguntur.</s> <s xml:id="echoid-s14576" xml:space="preserve"/> </p> <div xml:id="echoid-div2190" type="float" level="2" n="2"> <note position="right" xlink:label="note-0573-01" xlink:href="note-0573-01a" xml:space="preserve">815.</note> </div> <p style="it"> <s xml:id="echoid-s14577" xml:space="preserve">Si focus, in quo radii paralleli â ſpeculo cavo colligun-<lb/> <anchor type="note" xlink:label="note-0573-02a" xlink:href="note-0573-02"/> tur, fiat punctum radians, radii parum diſperſi, reflectun-<lb/>tur paralleli inter ſe <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14578" xml:space="preserve"/> </p> <div xml:id="echoid-div2191" type="float" level="2" n="3"> <note position="right" xlink:label="note-0573-02" xlink:href="note-0573-02a" xml:space="preserve">816.</note> </div> <note symbol="*" position="right" xml:space="preserve">813. 785.</note> <p> <s xml:id="echoid-s14579" xml:space="preserve">Ex hiſce ſpeculi cavi proprietatibus deducimus metho-<lb/> <anchor type="note" xlink:label="note-0573-04a" xlink:href="note-0573-04"/> dum repræſentandi objecta in loco obſcuro, ſimilem illi, de <lb/>qua antèa, adhibitâ lente convexâ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14580" xml:space="preserve"/> </p> <div xml:id="echoid-div2192" type="float" level="2" n="4"> <note position="right" xlink:label="note-0573-04" xlink:href="note-0573-04a" xml:space="preserve">817.</note> </div> <note symbol="*" position="right" xml:space="preserve">711.</note> <p> <s xml:id="echoid-s14581" xml:space="preserve">Detur foramen F in pariete; </s> <s xml:id="echoid-s14582" xml:space="preserve">ſit a b ſpeculum cavum ita <lb/> <anchor type="note" xlink:label="note-0573-06a" xlink:href="note-0573-06"/> diſpoſitum, ut colligat in F radios parallelos, & </s> <s xml:id="echoid-s14583" xml:space="preserve">ad parie-<lb/>tem perpendiculares: </s> <s xml:id="echoid-s14584" xml:space="preserve">juxta hanc directionem radii ex F pro-<lb/>cedentes reflectuntur <anchor type="note" xlink:href="" symbol="*"/>, quales ſunt radii, qui ab objectis re- <anchor type="note" xlink:label="note-0573-07a" xlink:href="note-0573-07"/> percuſſi in F ſeſe mutuò interſecant.</s> <s xml:id="echoid-s14585" xml:space="preserve"/> </p> <div xml:id="echoid-div2193" type="float" level="2" n="5"> <note position="right" xlink:label="note-0573-06" xlink:href="note-0573-06a" xml:space="preserve">TAB. XIII. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0573-07" xlink:href="note-0573-07a" xml:space="preserve">816.</note> </div> <p> <s xml:id="echoid-s14586" xml:space="preserve">Sint AF radii à puncto objecti longinqui manantes; </s> <s xml:id="echoid-s14587" xml:space="preserve">re-<lb/>flectuntur hi à ſpeculo perpendiculariter ad parietem; </s> <s xml:id="echoid-s14588" xml:space="preserve">& </s> <s xml:id="echoid-s14589" xml:space="preserve"><lb/>quia radii ex puncto longinquo, per exiguum foramen tran-<lb/>ſeuntes, pro parallelis haberi poſſunt, colliguntur hi, poſt <lb/>reflexionem, in unum punctum a, ad diſtantiam parietis <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0573-08a" xlink:href="note-0573-08"/> id eſt, in ſuperficie hujus; </s> <s xml:id="echoid-s14590" xml:space="preserve">ubi idcirco punctum repræſen-<lb/>tatur. </s> <s xml:id="echoid-s14591" xml:space="preserve">Eodem modo radii per BF, à puncto profluentes, <lb/>colliguntur in b, quod cùm reſpectu omnium punctorum <pb o="(68)" file="0574" n="633" rhead="PHYSICES ELEMENTA"/> objecti locum habeat, datur hujus repræſentatio in pariete; <lb/></s> <s xml:id="echoid-s14592" xml:space="preserve">qui ſi albus fuerit, & </s> <s xml:id="echoid-s14593" xml:space="preserve">objectum Solis radiis illuſtratum, vivi-<lb/>dis coloribus depictum objectum erit.</s> <s xml:id="echoid-s14594" xml:space="preserve"/> </p> <div xml:id="echoid-div2194" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0573-08" xlink:href="note-0573-08a" xml:space="preserve">815.</note> </div> </div> <div xml:id="echoid-div2196" type="section" level="1" n="534"> <head xml:id="echoid-head706" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s14595" xml:space="preserve">In loco obſcuro feneſtra chartâ albâ obtegitur, in cujus <lb/> <anchor type="note" xlink:label="note-0574-01a" xlink:href="note-0574-01"/> medio foramen datur, cujus diameter ſemi pollicem paulu-<lb/>lum excedit, & </s> <s xml:id="echoid-s14596" xml:space="preserve">quod cum foramine in feneſtrâ congruit, cui <lb/>ad dìſtantiam ad minimum quinquaginta pedum reſpondent <lb/>objecta varia à Sole illuminata; </s> <s xml:id="echoid-s14597" xml:space="preserve">ſpeculum concavum cujus <lb/>ſuperficiei diameter eſt quindecim pollicum, & </s> <s xml:id="echoid-s14598" xml:space="preserve">quod ad di-<lb/>ſtantiam octodecim pollicum colligit radios parallelos, ad <lb/>hanc diſtantiam à feneſtrâ diſponitur ita, ut linea, per cen-<lb/>trum foraminis, & </s> <s xml:id="echoid-s14599" xml:space="preserve">centrum ſuperficiei ſpeculi tranſiens, ad <lb/>planum chartæ, & </s> <s xml:id="echoid-s14600" xml:space="preserve">ſpeculi ſuperficiem perpendicularis ſit. <lb/></s> <s xml:id="echoid-s14601" xml:space="preserve">Objecta tunc ſuper chartâ repræſentantur in circulo concen-<lb/>trico cum foramine, & </s> <s xml:id="echoid-s14602" xml:space="preserve">cujus diameter æqualis eſt diametro <lb/>ſpeculi. </s> <s xml:id="echoid-s14603" xml:space="preserve">Conus truncatus excavatus cum foramine extra <lb/>cubiculum jungitur ad excludendum lumen, quod non ab <lb/>objectis repræſentandis advenit.</s> <s xml:id="echoid-s14604" xml:space="preserve"/> </p> <div xml:id="echoid-div2196" type="float" level="2" n="1"> <note position="left" xlink:label="note-0574-01" xlink:href="note-0574-01a" xml:space="preserve">TAB. XIII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s14605" xml:space="preserve">Sit ſpeculum cavum b e; </s> <s xml:id="echoid-s14606" xml:space="preserve">centrum cavitatis C; </s> <s xml:id="echoid-s14607" xml:space="preserve">punctum <lb/> <anchor type="note" xlink:label="note-0574-02a" xlink:href="note-0574-02"/> radians A, ultra centrum C à ſpeculo diſtans; </s> <s xml:id="echoid-s14608" xml:space="preserve">radii inci-<lb/> <anchor type="note" xlink:label="note-0574-03a" xlink:href="note-0574-03"/> dentes A b, A d, A e, quorum reflexi b f, dg, eb, cum <lb/>intermediis, mutuis interſectionibus, formant curvam a a, <lb/>quam omnes tangunt; </s> <s xml:id="echoid-s14609" xml:space="preserve">Punctum ideo A in hac curvâ appa-<lb/>ret <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14610" xml:space="preserve">moto oculo in plano curvæ apparentia per hanc <anchor type="note" xlink:label="note-0574-04a" xlink:href="note-0574-04"/> curvam transfertur. </s> <s xml:id="echoid-s14611" xml:space="preserve">In ſingulis autem planis quæ per C A <lb/>concipi poſſunt talis datur curva, omnes concurrunt in linea <lb/>C A, nempe in a. </s> <s xml:id="echoid-s14612" xml:space="preserve">In hoc puncto a ergo maximâ copiâ col-<lb/> <anchor type="note" xlink:label="note-0574-05a" xlink:href="note-0574-05"/> liguntur radii reflexi, quod ideò vocatur focus radiorum ex <lb/>A profluentium. </s> <s xml:id="echoid-s14613" xml:space="preserve">Vice verſa A eſt focus, poſito radiante <lb/>in a <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14614" xml:space="preserve"/> </p> <div xml:id="echoid-div2197" type="float" level="2" n="2"> <note position="left" xlink:label="note-0574-02" xlink:href="note-0574-02a" xml:space="preserve">818.</note> <note position="left" xlink:label="note-0574-03" xlink:href="note-0574-03a" xml:space="preserve">TAB. XIII. <lb/>fig. 5.</note> <note symbol="*" position="left" xlink:label="note-0574-04" xlink:href="note-0574-04a" xml:space="preserve">808.</note> <note position="left" xlink:label="note-0574-05" xlink:href="note-0574-05a" xml:space="preserve">819.</note> </div> <note symbol="*" position="left" xml:space="preserve">785.</note> <p> <s xml:id="echoid-s14615" xml:space="preserve">In hac figura pars curvæ, quæ ab unâ parte lineæ A C <lb/>datur, tantum delineata eſt; </s> <s xml:id="echoid-s14616" xml:space="preserve">pars ſimilis ad aliam partem <lb/>concipi debet; </s> <s xml:id="echoid-s14617" xml:space="preserve">ambæ junguntur in foco puncti radiantis.</s> <s xml:id="echoid-s14618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14619" xml:space="preserve">Recedente puncto radiante ad ſpeculum accedit curva.</s> <s xml:id="echoid-s14620" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">820.</note> <p> <s xml:id="echoid-s14621" xml:space="preserve">Accedente radiante recedit à ſpeculo curva & </s> <s xml:id="echoid-s14622" xml:space="preserve">verſus <lb/>ipſum radians movetur; </s> <s xml:id="echoid-s14623" xml:space="preserve">donec in centro C concurrant; </s> <s xml:id="echoid-s14624" xml:space="preserve">in <lb/> <anchor type="note" xlink:label="note-0574-08a" xlink:href="note-0574-08"/> <pb o="(69)" file="0575" n="634" rhead="MATHEMATICA. LIB. III. CAP. XV."/> quo ſi detur radians, omnes radii reflexi cum incidentibus <lb/>coincidunt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14625" xml:space="preserve">tota curva quaſi coacta eſt in ipſo centro.</s> <s xml:id="echoid-s14626" xml:space="preserve"/> </p> <div xml:id="echoid-div2198" type="float" level="2" n="3"> <note position="left" xlink:label="note-0574-08" xlink:href="note-0574-08a" xml:space="preserve">821.</note> </div> <note symbol="*" position="right" xml:space="preserve">806.</note> <p> <s xml:id="echoid-s14627" xml:space="preserve">Si ulterius accedat radians, ut inter centrum & </s> <s xml:id="echoid-s14628" xml:space="preserve">ſpeculum <lb/> <anchor type="note" xlink:label="note-0575-02a" xlink:href="note-0575-02"/> detur, magis etiam recedit curva, quæ tunc ultra centrum <lb/>datur, & </s> <s xml:id="echoid-s14629" xml:space="preserve">in curvâ omnium maximè recedit punctum, in quo <lb/>omnes curvæ quæ in variis planis concipiuntur concurrunt, <lb/>id eſt, focus puncti radiantis, qui ad diſtantiam infinitam <lb/>datur, quando radians diſtat à ſpeculo quartam partem diame-<lb/> <anchor type="note" xlink:label="note-0575-03a" xlink:href="note-0575-03"/> tri ſphæræ <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s14630" xml:space="preserve">Tuncque curva in infinitum extenditur & </s> <s xml:id="echoid-s14631" xml:space="preserve">duæ <anchor type="note" xlink:label="note-0575-04a" xlink:href="note-0575-04"/> partes quæ in foco radiantis concurrunt ſeparantur; </s> <s xml:id="echoid-s14632" xml:space="preserve">talis <lb/>pars ſeparata videtur in a a; </s> <s xml:id="echoid-s14633" xml:space="preserve">ſi magis accedat radians magis <lb/> <anchor type="note" xlink:label="note-0575-05a" xlink:href="note-0575-05"/> à ſe mutuo declinant curvæ partes, quia radii ut A b cum <lb/> <anchor type="note" xlink:label="note-0575-06a" xlink:href="note-0575-06"/> vicinis reflexi curvam non tangunt, ſed divergentes ſunt; <lb/></s> <s xml:id="echoid-s14634" xml:space="preserve">id eſt, reflexi ultra ſpeculum continuati ſeſe mutuo interſe-<lb/>cant, & </s> <s xml:id="echoid-s14635" xml:space="preserve">formant novam curvam poſt ſpeculum, quæ conſtat <lb/>ex duobus cruribus, quorum unum videtur in a a; </s> <s xml:id="echoid-s14636" xml:space="preserve">concur-<lb/>runt in lineâ C A continuatâ, nempe in a, & </s> <s xml:id="echoid-s14637" xml:space="preserve">recedendo à <lb/>ſpeculo in infinitum porriguntur. </s> <s xml:id="echoid-s14638" xml:space="preserve">Daturque ab utraque <lb/>parte puncti radiantis, in ſuperficie punctum ut d, quod ſe-<lb/>parat radios formantes curvas a a & </s> <s xml:id="echoid-s14639" xml:space="preserve">a a; </s> <s xml:id="echoid-s14640" xml:space="preserve">radiuſque A d re-<lb/>flexus in d g neutram curvam tangit, ſi verſus utramque <lb/>partem g, g, in infinitum continuetur, licèt continuò ma-<lb/>gis ac magis ad utramque curvam accedat. </s> <s xml:id="echoid-s14641" xml:space="preserve">Si tota ſphæra <lb/>abſolveretur, reſpectu partis oppoſitæ ſphæræ, ultra cen-<lb/>trum diſtaret radians, & </s> <s xml:id="echoid-s14642" xml:space="preserve">radii reflexi formarent curvam, <lb/>de qua antea <anchor type="note" xlink:href="" symbol="*"/>, qua conjungerentur crura ſeparata ut a a.</s> <s xml:id="echoid-s14643" xml:space="preserve"> <anchor type="note" xlink:label="note-0575-07a" xlink:href="note-0575-07"/> His præ miſſis phænomena ſpeculorum concavorum expli-<lb/>canda ſunt.</s> <s xml:id="echoid-s14644" xml:space="preserve"/> </p> <div xml:id="echoid-div2199" type="float" level="2" n="4"> <note position="right" xlink:label="note-0575-02" xlink:href="note-0575-02a" xml:space="preserve">822.</note> <note position="right" xlink:label="note-0575-03" xlink:href="note-0575-03a" xml:space="preserve">823.</note> <note symbol="*" position="right" xlink:label="note-0575-04" xlink:href="note-0575-04a" xml:space="preserve">813. 816.</note> <note position="right" xlink:label="note-0575-05" xlink:href="note-0575-05a" xml:space="preserve">824.</note> <note position="right" xlink:label="note-0575-06" xlink:href="note-0575-06a" xml:space="preserve">TAB. XIII. <lb/>fig. 6.</note> <note symbol="*" position="right" xlink:label="note-0575-07" xlink:href="note-0575-07a" xml:space="preserve">818.</note> </div> <p> <s xml:id="echoid-s14645" xml:space="preserve">Si corpore lucido illuminetur ſpeculum, radii à ſingulis <lb/> <anchor type="note" xlink:label="note-0575-08a" xlink:href="note-0575-08"/> punctis corporis manantes reflexi, curvas formant, ſed maxi-<lb/>mâ copiâ in horum punctorum focis colliguntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14646" xml:space="preserve">ſi idèo foci <anchor type="note" xlink:label="note-0575-09a" xlink:href="note-0575-09"/> hi in ſuperficie plani albi dentur, dabitur ibi corporis lucidi <lb/> <anchor type="note" xlink:label="note-0575-10a" xlink:href="note-0575-10"/> repræſentatio, ut in exp. </s> <s xml:id="echoid-s14647" xml:space="preserve">2. </s> <s xml:id="echoid-s14648" xml:space="preserve">cap. </s> <s xml:id="echoid-s14649" xml:space="preserve">9.</s> <s xml:id="echoid-s14650" xml:space="preserve">; & </s> <s xml:id="echoid-s14651" xml:space="preserve">quidem inverſa, <lb/>nam linea quæ jungit punctum radians cum ſuo foco, tranſit <lb/>per centrum ſphæræ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14652" xml:space="preserve">in quo idcirco omnes tales lineæ <anchor type="note" xlink:label="note-0575-11a" xlink:href="note-0575-11"/> ſeſe mutuo interſecant; </s> <s xml:id="echoid-s14653" xml:space="preserve">& </s> <s xml:id="echoid-s14654" xml:space="preserve">hæc interſectio, datur inter pun-<lb/>ctum radians & </s> <s xml:id="echoid-s14655" xml:space="preserve">focum <anchor type="note" xlink:href="" symbol="*"/>, in quo punctum repræſentatur.</s> <s xml:id="echoid-s14656" xml:space="preserve"/> </p> <div xml:id="echoid-div2200" type="float" level="2" n="5"> <note position="right" xlink:label="note-0575-08" xlink:href="note-0575-08a" xml:space="preserve">825.</note> <note position="right" xlink:label="note-0575-09" xlink:href="note-0575-09a" xml:space="preserve">826.</note> <note symbol="*" position="right" xlink:label="note-0575-10" xlink:href="note-0575-10a" xml:space="preserve">819.</note> <note symbol="*" position="right" xlink:label="note-0575-11" xlink:href="note-0575-11a" xml:space="preserve">819.</note> </div> <note symbol="*" position="right" xml:space="preserve">818.</note> <pb o="(70)" file="0576" n="635" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div2202" type="section" level="1" n="535"> <head xml:id="echoid-head707" xml:space="preserve">Accedente autem ad ſpeculum corpore lucido, recedit ap-<lb/>parentia <anchor type="note" xlink:href="" symbol="*"/>, quæ in eo caſu major eſt.</head> <note symbol="*" position="left" xml:space="preserve">820.</note> </div> <div xml:id="echoid-div2203" type="section" level="1" n="536"> <head xml:id="echoid-head708" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s14657" xml:space="preserve">Candela lucens ponitur inter ſpeculum cavum & </s> <s xml:id="echoid-s14658" xml:space="preserve">centrum <lb/>ſphæræ, cujus ſectio ſpeculum eſt, ita tamen, ut magis à <lb/>ſpeculo quàm ab hoc centro diſtet: </s> <s xml:id="echoid-s14659" xml:space="preserve">ſi tunc planum album <lb/>detur perpendiculare ad lineam, quæ per candelam & </s> <s xml:id="echoid-s14660" xml:space="preserve">cen-<lb/>trum ſphæræ tranſit, & </s> <s xml:id="echoid-s14661" xml:space="preserve">ultra centrum ponatur, dabitur in <lb/>illo repræſentatio candelæ inverſa; </s> <s xml:id="echoid-s14662" xml:space="preserve">plani diſtantia à ſpeculo <lb/>movendo illud, detegitur; </s> <s xml:id="echoid-s14663" xml:space="preserve">etiam hac proportione; </s> <s xml:id="echoid-s14664" xml:space="preserve">ut dif-<lb/>ferentia diſtantiarum candelæ â centro ſphæræ & </s> <s xml:id="echoid-s14665" xml:space="preserve">â ſpecu-<lb/>lo, ſe habet ad quartam partem diametri ſphæræ, ita di-<lb/>ſtantia candelæ à ſpeculo ad diſtantiam quæſitam. </s> <s xml:id="echoid-s14666" xml:space="preserve">Dum <lb/>candela accedit ad ſpeculum, planum removendum eſt, <lb/>& </s> <s xml:id="echoid-s14667" xml:space="preserve">augetur repræſentatio.</s> <s xml:id="echoid-s14668" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14669" xml:space="preserve">Objecta, ultra centrum poſita, inter ſpeculum & </s> <s xml:id="echoid-s14670" xml:space="preserve">cen-<lb/> <anchor type="note" xlink:label="note-0576-02a" xlink:href="note-0576-02"/> trum apparent, nam ſingula puncta in curvâ ut a a appa-<lb/> <anchor type="note" xlink:label="note-0576-03a" xlink:href="note-0576-03"/> rent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14671" xml:space="preserve">etiam imminuta & </s> <s xml:id="echoid-s14672" xml:space="preserve">inverſa ſunt objectorum idola:</s> <s xml:id="echoid-s14673" xml:space="preserve"> <anchor type="note" xlink:label="note-0576-04a" xlink:href="note-0576-04"/> nam in arctum ſpatium rediguntur; </s> <s xml:id="echoid-s14674" xml:space="preserve">& </s> <s xml:id="echoid-s14675" xml:space="preserve">in deſcenſu puncti <lb/> <anchor type="note" xlink:label="note-0576-05a" xlink:href="note-0576-05"/> A adſcendit repræſentatio hujus; </s> <s xml:id="echoid-s14676" xml:space="preserve">linea enim a a eundem <lb/>ſervat ſitum reſpectu A C a rotantis circa centrum C.</s> <s xml:id="echoid-s14677" xml:space="preserve"/> </p> <div xml:id="echoid-div2203" type="float" level="2" n="1"> <note position="left" xlink:label="note-0576-02" xlink:href="note-0576-02a" xml:space="preserve">827.</note> <note position="left" xlink:label="note-0576-03" xlink:href="note-0576-03a" xml:space="preserve">TAB. XIII. <lb/>fig. 5.</note> <note position="left" xlink:label="note-0576-04" xlink:href="note-0576-04a" xml:space="preserve">828</note> <note symbol="*" position="left" xlink:label="note-0576-05" xlink:href="note-0576-05a" xml:space="preserve">818.</note> </div> </div> <div xml:id="echoid-div2205" type="section" level="1" n="537"> <head xml:id="echoid-head709" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s14678" xml:space="preserve">Ne lumine extraneo minus vivida ſit objectorum repræ-<lb/> <anchor type="note" xlink:label="note-0576-06a" xlink:href="note-0576-06"/> ſentatio, pixide includendum ſpeculum. </s> <s xml:id="echoid-s14679" xml:space="preserve">Detur ſpeculum <lb/>cujus ſuperficiei diameter eſt circiter octo pollicum, & </s> <s xml:id="echoid-s14680" xml:space="preserve">quod <lb/>eſt portio ſphæræ diametri unius pedis cum ſemiſſe; </s> <s xml:id="echoid-s14681" xml:space="preserve">inclu-<lb/>datur hoc pixide P, in cujus anteriori parte datur foramen <lb/>diametri circiter ſex pollicum, & </s> <s xml:id="echoid-s14682" xml:space="preserve">â quo ſpeculum diſtat <lb/>pollices ſex aut ſeptem; </s> <s xml:id="echoid-s14683" xml:space="preserve">ut apertura hæc à lumine ſit aver-<lb/>ſa neceſſe eſt. </s> <s xml:id="echoid-s14684" xml:space="preserve">Si nunc quis, ut A ad diſtantiam circiter <lb/>duorum pedum à ſpeculo, ſe ipſum intueatur; </s> <s xml:id="echoid-s14685" xml:space="preserve">facies ejus <lb/>inverſa in pixide verſus aperturam apparebit, ſi accedat <lb/>ſpectator, caput ex pixide prominens videbit.</s> <s xml:id="echoid-s14686" xml:space="preserve"/> </p> <div xml:id="echoid-div2205" type="float" level="2" n="1"> <note position="left" xlink:label="note-0576-06" xlink:href="note-0576-06a" xml:space="preserve">TAB. XIII. <lb/>fig. 7.</note> </div> <p style="it"> <s xml:id="echoid-s14687" xml:space="preserve">Repræſentatio puncti, in centro ſphæræ poſiti, cum ipſo <lb/> <anchor type="note" xlink:label="note-0576-07a" xlink:href="note-0576-07"/> puncto radiante coincidit, & </s> <s xml:id="echoid-s14688" xml:space="preserve">ab hoc quaſi abſorbetur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14689" xml:space="preserve"/> </p> <div xml:id="echoid-div2206" type="float" level="2" n="2"> <note position="left" xlink:label="note-0576-07" xlink:href="note-0576-07a" xml:space="preserve">829.</note> </div> <note symbol="*" position="left" xml:space="preserve">821.</note> <p> <s xml:id="echoid-s14690" xml:space="preserve">Poſuo oculo in hoc centro nullum objectum ab hoc poterit <lb/> <anchor type="note" xlink:label="note-0576-09a" xlink:href="note-0576-09"/> videri; </s> <s xml:id="echoid-s14691" xml:space="preserve">ſoli enim radii ab oculo provenientes ad ipſum re-<lb/>flectuntur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14692" xml:space="preserve"/> </p> <div xml:id="echoid-div2207" type="float" level="2" n="3"> <note position="left" xlink:label="note-0576-09" xlink:href="note-0576-09a" xml:space="preserve">830.</note> </div> <note symbol="*" position="left" xml:space="preserve">806.</note> <pb o="(71)" file="0577" n="636" rhead="MATHEMATICA LIB. III. CAP. XV."/> <p> <s xml:id="echoid-s14693" xml:space="preserve">Si objectum detur inter centrum & </s> <s xml:id="echoid-s14694" xml:space="preserve">punctum, in quo radii <lb/> <anchor type="note" xlink:label="note-0577-01a" xlink:href="note-0577-01"/> paralleli reflexi colliguntur; </s> <s xml:id="echoid-s14695" xml:space="preserve">apparet etiam objectum extra <lb/>ſpeculum, ad majorem diſtantiam à ſpeculo, quàm ipſum obje-<lb/>ctum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14696" xml:space="preserve">inverſa eſt repræſentatio, quod eodem modo pro- <anchor type="note" xlink:label="note-0577-02a" xlink:href="note-0577-02"/> batur ac in n. </s> <s xml:id="echoid-s14697" xml:space="preserve">828; </s> <s xml:id="echoid-s14698" xml:space="preserve">& </s> <s xml:id="echoid-s14699" xml:space="preserve">amplificatur, quia hæc magis remo <lb/>vetur â centro, quàm ipſum objectum ab hoc diſtat; </s> <s xml:id="echoid-s14700" xml:space="preserve">in <lb/>infinitum enim à centro recedit repræſentatio, dum obje-<lb/>ctum quartam partem diametri ſphæræ percurrit.</s> <s xml:id="echoid-s14701" xml:space="preserve"/> </p> <div xml:id="echoid-div2208" type="float" level="2" n="4"> <note position="right" xlink:label="note-0577-01" xlink:href="note-0577-01a" xml:space="preserve">831.</note> <note symbol="*" position="right" xlink:label="note-0577-02" xlink:href="note-0577-02a" xml:space="preserve">822.</note> </div> <p> <s xml:id="echoid-s14702" xml:space="preserve">Si objectum non diſtet â ſpeculo quartam partem diametri <lb/> <anchor type="note" xlink:label="note-0577-03a" xlink:href="note-0577-03"/> ſphæræ, pro diver ſo oculi ſitu, aut ante aut poſt ſpeculum <lb/> <anchor type="note" xlink:label="note-0577-04a" xlink:href="note-0577-04"/> objectum apparet. </s> <s xml:id="echoid-s14703" xml:space="preserve">Poſito oculo, ut radii reflexi ad hunc <lb/>perveniant, qui formant curvam a a, ut verſus f, videbit <lb/>objecti apparentiam ultra ſpeculum <anchor type="note" xlink:href="" symbol="*"/>, amplificatam; </s> <s xml:id="echoid-s14704" xml:space="preserve">quia <anchor type="note" xlink:label="note-0577-05a" xlink:href="note-0577-05"/> curvæ ut a a, quæ ad varia puncta pertinent divergentes <lb/>ſunt.</s> <s xml:id="echoid-s14705" xml:space="preserve"/> </p> <div xml:id="echoid-div2209" type="float" level="2" n="5"> <note position="right" xlink:label="note-0577-03" xlink:href="note-0577-03a" xml:space="preserve">832.</note> <note position="right" xlink:label="note-0577-04" xlink:href="note-0577-04a" xml:space="preserve">TAB. XIII. <lb/>fig. 6.</note> <note symbol="*" position="right" xlink:label="note-0577-05" xlink:href="note-0577-05a" xml:space="preserve">824.</note> </div> <p> <s xml:id="echoid-s14706" xml:space="preserve">Si ad oculum perveniant radii formantes curvam a a, ob-<lb/>jectum extra ſpeculum apparet: </s> <s xml:id="echoid-s14707" xml:space="preserve">& </s> <s xml:id="echoid-s14708" xml:space="preserve">in utroque caſu repræ-<lb/> <anchor type="note" xlink:label="note-0577-06a" xlink:href="note-0577-06"/> ſentatio eſt erecta; </s> <s xml:id="echoid-s14709" xml:space="preserve">adſcendente enim aut deſcendente <lb/>puncto A, eodem motu curvæ a a, a a, in quibus repræ-<lb/>ſentatur, agitantur.</s> <s xml:id="echoid-s14710" xml:space="preserve"/> </p> <div xml:id="echoid-div2210" type="float" level="2" n="6"> <note position="right" xlink:label="note-0577-06" xlink:href="note-0577-06a" xml:space="preserve">833.</note> </div> <p> <s xml:id="echoid-s14711" xml:space="preserve">Si oculus detur in puncto, in quo radii reflexi pertinentes <lb/> <anchor type="note" xlink:label="note-0577-07a" xlink:href="note-0577-07"/> ad utramque curvam ſeſe mutuo interſecant, ut in O, duplex <lb/>dabitur objecti apparentia.</s> <s xml:id="echoid-s14712" xml:space="preserve"/> </p> <div xml:id="echoid-div2211" type="float" level="2" n="7"> <note position="right" xlink:label="note-0577-07" xlink:href="note-0577-07a" xml:space="preserve">834.</note> </div> <p> <s xml:id="echoid-s14713" xml:space="preserve">Facilè patet in omni caſu apparentiæ, puncta non ean-<lb/>dem inter ſe habere relationem, quam habent objecti pun-<lb/>cta; </s> <s xml:id="echoid-s14714" xml:space="preserve">ideoque ſpeculum cavum nunquam objectum exactè re-<lb/> <anchor type="note" xlink:label="note-0577-08a" xlink:href="note-0577-08"/> præſentare: </s> <s xml:id="echoid-s14715" xml:space="preserve">maximè tamen irregularis repræſentatio eſt, <lb/>quæ datur in lineis ut a a.</s> <s xml:id="echoid-s14716" xml:space="preserve"/> </p> <div xml:id="echoid-div2212" type="float" level="2" n="8"> <note position="right" xlink:label="note-0577-08" xlink:href="note-0577-08a" xml:space="preserve">835.</note> </div> <p> <s xml:id="echoid-s14717" xml:space="preserve">Dantur & </s> <s xml:id="echoid-s14718" xml:space="preserve">ſpæcula cylindrica convexa & </s> <s xml:id="echoid-s14719" xml:space="preserve">cava, uno re-<lb/> <anchor type="note" xlink:label="note-0577-09a" xlink:href="note-0577-09"/> ſpectu ſunt plana, alio reſpectu ſphærica; </s> <s xml:id="echoid-s14720" xml:space="preserve">idcirco objecto-<lb/>rum repræſentatio admodum irregularis eſt, quæ irregula-<lb/>ritas, cùm à regulari figurâ pendeat, determinari poteſt ita, <lb/>ut ſiguræ delineantur, quæ dum revera irregulares ſunt, <lb/>in tali ſpeculo, in determinato oculi ſitu, regulares vi-<lb/>dentur.</s> <s xml:id="echoid-s14721" xml:space="preserve"/> </p> <div xml:id="echoid-div2213" type="float" level="2" n="9"> <note position="right" xlink:label="note-0577-09" xlink:href="note-0577-09a" xml:space="preserve">836.</note> </div> <pb o="(72)" file="0578" n="637" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div2215" type="section" level="1" n="538"> <head xml:id="echoid-head710" xml:space="preserve">CAPUT XVI.</head> <head xml:id="echoid-head711" style="it" xml:space="preserve">De Lucerna Magica.</head> <p> <s xml:id="echoid-s14722" xml:space="preserve">VAriæ conſtruuntur Machinæ, in quibus, ſpeculis & </s> <s xml:id="echoid-s14723" xml:space="preserve"><lb/>lentibus conjunctis, & </s> <s xml:id="echoid-s14724" xml:space="preserve">utilia & </s> <s xml:id="echoid-s14725" xml:space="preserve">amoena videntur ſpecta-<lb/>cula; </s> <s xml:id="echoid-s14726" xml:space="preserve">quorum explicatio ex ante dictis haud difficulter de-<lb/>ducitur.</s> <s xml:id="echoid-s14727" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14728" xml:space="preserve">Unicam explicandam inter cæteras eligam, quâ in vitro <lb/>exiguo figuræ depictæ, giganteæ in plano albo repræſentan-<lb/>tur. </s> <s xml:id="echoid-s14729" xml:space="preserve">Phoenomenon ſatis ſtupendum, ut peculiarem merea-<lb/>tur explicationem! Lucerna Magica vocatur machina, quâ <lb/>exhibetur, à ſcriptoribus opticis non quidem intacta, ſa-<lb/>tis tamen neglecta.</s> <s xml:id="echoid-s14730" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14731" xml:space="preserve">Pixis datur lignea, longitudinis circiter unius pedis cum <lb/> <anchor type="note" xlink:label="note-0578-01a" xlink:href="note-0578-01"/> ſemiſſe, lata & </s> <s xml:id="echoid-s14732" xml:space="preserve">alta quatuordecim pollices; </s> <s xml:id="echoid-s14733" xml:space="preserve">in hac datur <lb/> <anchor type="note" xlink:label="note-0578-02a" xlink:href="note-0578-02"/> ſpeculum cavum S, diametri octo pollicum, & </s> <s xml:id="echoid-s14734" xml:space="preserve">ſectio ſphæ-<lb/>ræ diametri ſeſquipedalis: </s> <s xml:id="echoid-s14735" xml:space="preserve">ſpeculum hoc ſuſtentaculo ap-<lb/>plicatur, quod inter regulas juxta longitudinem pixidis <lb/>movetur.</s> <s xml:id="echoid-s14736" xml:space="preserve"/> </p> <div xml:id="echoid-div2215" type="float" level="2" n="1"> <note position="left" xlink:label="note-0578-01" xlink:href="note-0578-01a" xml:space="preserve">837.</note> <note position="left" xlink:label="note-0578-02" xlink:href="note-0578-02a" xml:space="preserve">TAB. XIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s14737" xml:space="preserve">Datur & </s> <s xml:id="echoid-s14738" xml:space="preserve">in hac lampas L, quæ pede ligneo ſuſtinetur, <lb/>inter regulas ad latus pixidis, juxta hujus longitudinem <lb/>mobili. </s> <s xml:id="echoid-s14739" xml:space="preserve">Prominet lampadis tubus ita, ut centrum flammæ <lb/>reſpondeat centro ſuperficiei ſpeculi; </s> <s xml:id="echoid-s14740" xml:space="preserve">conſtat hæc flamma <lb/>ex quatuor flammis, quæ cum ſeſe mutuò tangant flammam <lb/>quadratam formant, cujus latus excedit duos pollices.</s> <s xml:id="echoid-s14741" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14742" xml:space="preserve">Oblonga datur apertura in ſuperiori pixidis plano, quæ <lb/>operculo inter regulas mobili obtegitur; </s> <s xml:id="echoid-s14743" xml:space="preserve">per hoc tranſit ca-<lb/>minus C, qui (ut in fig. </s> <s xml:id="echoid-s14744" xml:space="preserve">3. </s> <s xml:id="echoid-s14745" xml:space="preserve">videtur) ſupra pixidem ad alti-<lb/>tudinem circiter ſeſquipedis prominet. </s> <s xml:id="echoid-s14746" xml:space="preserve">Caminus cum oper-<lb/>culo eſt mobilis, aperturâ memoratâ manente clauſâ; </s> <s xml:id="echoid-s14747" xml:space="preserve">ut <lb/>lampadi reſpondeat diſponitur caminus.</s> <s xml:id="echoid-s14748" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14749" xml:space="preserve">In Pixidis latere minori datur foramen rotundum, dia-<lb/>metri quinque pollicum; </s> <s xml:id="echoid-s14750" xml:space="preserve">in quo datur vitrum convexum <lb/>ejuſdem diametri V: </s> <s xml:id="echoid-s14751" xml:space="preserve">terminatur hoc utrimque convexâ ſu-<lb/>perficie, portione ſphæræ, cujus diameter pedem unum æ-<lb/>quat: </s> <s xml:id="echoid-s14752" xml:space="preserve">axis hujus vitri ſi concipiatur, ad ſpeculi ſuperficiem in <pb file="0579" n="638"/> <pb file="0579a" n="639"/> <anchor type="figure" xlink:label="fig-0579a-01a" xlink:href="fig-0579a-01"/> <pb file="0580" n="640"/> <pb o="(73)" file="0581" n="641" rhead="MATHEMATICA LIB. III. CAP. XVI."/> hujus centro perpendicularis erit, ut & </s> <s xml:id="echoid-s14753" xml:space="preserve">ad planum flammæ <lb/>per cujus punctum medium tranſit.</s> <s xml:id="echoid-s14754" xml:space="preserve"/> </p> <div xml:id="echoid-div2216" type="float" level="2" n="2"> <figure xlink:label="fig-0579a-01" xlink:href="fig-0579a-01a"> <image file="0579a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0579a-01"/> </figure> </div> <p> <s xml:id="echoid-s14755" xml:space="preserve">Clauditur & </s> <s xml:id="echoid-s14756" xml:space="preserve">reſeratur hoc foramen plano inter regulas <lb/>mobili, quod cylindro, in E ex pixide prominente, agi-<lb/>tatur.</s> <s xml:id="echoid-s14757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14758" xml:space="preserve">Huic foramini extra pixidem reſpondet tubus T, longitu-<lb/>dinis & </s> <s xml:id="echoid-s14759" xml:space="preserve">diametri circiter ſex pollicum, in cujus extremo da-<lb/>tur annulus, in quo movetur tubus ſecundus t, diametri cir-<lb/>citer quatuor pollicum, & </s> <s xml:id="echoid-s14760" xml:space="preserve">longitudinis quinque aut ſex pol-<lb/>licum.</s> <s xml:id="echoid-s14761" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14762" xml:space="preserve">In hoc tubo minori dantur lentes duæ; </s> <s xml:id="echoid-s14763" xml:space="preserve">prima in extre-<lb/>mitate quæ tubo T intruditur, & </s> <s xml:id="echoid-s14764" xml:space="preserve">eſt ejuſdem convexitatis <lb/>cum vitro V, & </s> <s xml:id="echoid-s14765" xml:space="preserve">diametri trium pollicum cum ſemiſſe. </s> <s xml:id="echoid-s14766" xml:space="preserve">Se-<lb/>cunda lens pollices tres à primâ diſtat, planior eſt, termina-<lb/>tur portionibus ſphæræ diametri quatuor pedum. </s> <s xml:id="echoid-s14767" xml:space="preserve">Inter has <lb/>lentes, diſtans à ſecundâ pollicem unum, diſponitur an-<lb/>nulus ligneus, quo tubus clauditur, relictâ aperturâ circula-<lb/>ri, cujus diameter quartâ parte pollicem unum excedit.</s> <s xml:id="echoid-s14768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14769" xml:space="preserve">Objecta repræſentanda in vitro plano & </s> <s xml:id="echoid-s14770" xml:space="preserve">tenui depingun-<lb/>tur, quod extra pixidem juxta vitrum V, inter hoc & </s> <s xml:id="echoid-s14771" xml:space="preserve">tu-<lb/>bum T movetur, poſitâ picturâ in ſitu inverſo. </s> <s xml:id="echoid-s14772" xml:space="preserve">Si vitra hæc <lb/>fuerint rotunda, habent diametrum quinque pollicum; </s> <s xml:id="echoid-s14773" xml:space="preserve">ut <lb/>commodè moveantur, in plano ligneo firmantur, & </s> <s xml:id="echoid-s14774" xml:space="preserve">tres in <lb/>eodem plano poſſunt conjungi. </s> <s xml:id="echoid-s14775" xml:space="preserve">Etiam in vitris longioribus <lb/>depinguntur figuræ, quæ ſucceſſivè juxta vitrum V tran-<lb/>ſeunt.</s> <s xml:id="echoid-s14776" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14777" xml:space="preserve">Tota hæc pixis pede ſuſtinetur, quo, inter certos limites, <lb/> <anchor type="note" xlink:label="note-0581-01a" xlink:href="note-0581-01"/> ad altitudinem quamcunque firmatur; </s> <s xml:id="echoid-s14778" xml:space="preserve">Plana lignea cum <lb/>pixide cohoerent, & </s> <s xml:id="echoid-s14779" xml:space="preserve">inter regulas juxta plana quæ pedem <lb/>formant moventur; </s> <s xml:id="echoid-s14780" xml:space="preserve">in utroque illorum datur ſciſſura; </s> <s xml:id="echoid-s14781" xml:space="preserve">ad <lb/>altitudinem deſideratam, ope cochlearum in pede fixarum, <lb/>& </s> <s xml:id="echoid-s14782" xml:space="preserve">per ſciſſuras mobilium, conſtituitur pixis.</s> <s xml:id="echoid-s14783" xml:space="preserve"/> </p> <div xml:id="echoid-div2217" type="float" level="2" n="3"> <note position="right" xlink:label="note-0581-01" xlink:href="note-0581-01a" xml:space="preserve">TAB. XIV. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s14784" xml:space="preserve">Diſponitur tota machina ad diſtantiam, quindecim, viginti, <lb/>aut triginta pedum à plano albo, diverſam pro magnitudine <lb/>plani; </s> <s xml:id="echoid-s14785" xml:space="preserve">hæc enim diſtantia poteſt plani longitudinem æquare; <lb/></s> <s xml:id="echoid-s14786" xml:space="preserve">ad talem altitudinem firmatur pixis ut tubi, in latere pixidis, <lb/>medio plani reſpondeant. </s> <s xml:id="echoid-s14787" xml:space="preserve">Accenſâ lampade pixis clauditur <pb o="(74)" file="0582" n="642" rhead="PHYSICES ELEMENTA"/> & </s> <s xml:id="echoid-s14788" xml:space="preserve">figuræ, in vitro depictæ, in plano albo repræſentantur. <lb/></s> <s xml:id="echoid-s14789" xml:space="preserve">Motu tubi, in quo lentes duæ dantur, detegitur hujus ſitus, <lb/>ad repræſentationem diſtinctam exhibendam, requiſitus. </s> <s xml:id="echoid-s14790" xml:space="preserve"><lb/>Diſpoſitio autem partium machinæ, quæ immediatè huic <lb/>ſpectaculo exhibendo inſerviunt, peculiarius eſt explicanda.</s> <s xml:id="echoid-s14791" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14792" xml:space="preserve">Sint hæ partes ſeparatæ; </s> <s xml:id="echoid-s14793" xml:space="preserve">S S ſpeculum; </s> <s xml:id="echoid-s14794" xml:space="preserve">flamma in l l, <lb/> <anchor type="note" xlink:label="note-0582-01a" xlink:href="note-0582-01"/> conſtat hæc ex quatuor flammis in lineâ l l; </s> <s xml:id="echoid-s14795" xml:space="preserve">V V eſt vitrum <lb/> <anchor type="note" xlink:label="note-0582-02a" xlink:href="note-0582-02"/> V. </s> <s xml:id="echoid-s14796" xml:space="preserve">fig. </s> <s xml:id="echoid-s14797" xml:space="preserve">I.</s> <s xml:id="echoid-s14798" xml:space="preserve">; O O pictura in vitro plano tenui; </s> <s xml:id="echoid-s14799" xml:space="preserve">a a lens major; <lb/></s> <s xml:id="echoid-s14800" xml:space="preserve">d d lens planior; </s> <s xml:id="echoid-s14801" xml:space="preserve">b b annulus ligneus inter lentes; </s> <s xml:id="echoid-s14802" xml:space="preserve">f apertura <lb/>annuli, id eſt, foramen in medio hujus.</s> <s xml:id="echoid-s14803" xml:space="preserve"/> </p> <div xml:id="echoid-div2218" type="float" level="2" n="4"> <note position="left" xlink:label="note-0582-01" xlink:href="note-0582-01a" xml:space="preserve">838.</note> <note position="left" xlink:label="note-0582-02" xlink:href="note-0582-02a" xml:space="preserve">TAB. XIV. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s14804" xml:space="preserve">Hiſce omnibus ut jam explicatum, & </s> <s xml:id="echoid-s14805" xml:space="preserve">ut in hac figurâ vi-<lb/>detur diſpoſitis; </s> <s xml:id="echoid-s14806" xml:space="preserve">radii, qui à puncto picturæ O O procedunt, <lb/>per lentem a a tranſeundo, minus divergentes ſunt, & </s> <s xml:id="echoid-s14807" xml:space="preserve">quaſi <lb/>à puncto remotiori procederent, ad lentem d d perveniunt <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0582-03a" xlink:href="note-0582-03"/> ex qua convergentes exeunt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s14808" xml:space="preserve">in ſuperficie plani albi col- <anchor type="note" xlink:label="note-0582-04a" xlink:href="note-0582-04"/> liguntur, & </s> <s xml:id="echoid-s14809" xml:space="preserve">picturam puncti, figuræ in vitro, exhibent <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14810" xml:space="preserve"> <anchor type="note" xlink:label="note-0582-05a" xlink:href="note-0582-05"/> Figura in vitro illuminatur & </s> <s xml:id="echoid-s14811" xml:space="preserve">à radiis à flammâ l l proceden-<lb/>tibus & </s> <s xml:id="echoid-s14812" xml:space="preserve">à radiis à ſpeculo S S reflexis.</s> <s xml:id="echoid-s14813" xml:space="preserve"/> </p> <div xml:id="echoid-div2219" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0582-03" xlink:href="note-0582-03a" xml:space="preserve">699.</note> <note symbol="*" position="left" xlink:label="note-0582-04" xlink:href="note-0582-04a" xml:space="preserve">699.</note> <note symbol="*" position="left" xlink:label="note-0582-05" xlink:href="note-0582-05a" xml:space="preserve">711.</note> </div> <p> <s xml:id="echoid-s14814" xml:space="preserve">Ad perfectionem hujus machinæ requiritur; </s> <s xml:id="echoid-s14815" xml:space="preserve">1. </s> <s xml:id="echoid-s14816" xml:space="preserve">ut figura <lb/> <anchor type="note" xlink:label="note-0582-06a" xlink:href="note-0582-06"/> O O quantum fieri poteſt ſit illuminata; </s> <s xml:id="echoid-s14817" xml:space="preserve">2. </s> <s xml:id="echoid-s14818" xml:space="preserve">ut in omnibus <lb/>punctis æqualiter illuminetur; </s> <s xml:id="echoid-s14819" xml:space="preserve">3. </s> <s xml:id="echoid-s14820" xml:space="preserve">ut omne lumen, quo ſingu-<lb/>la picturæ puncta illuminantur, per lentes a a & </s> <s xml:id="echoid-s14821" xml:space="preserve">d d ad pla-<lb/>num album perveniat & </s> <s xml:id="echoid-s14822" xml:space="preserve">repræſentationi exhibendæ inſer-<lb/>viat; </s> <s xml:id="echoid-s14823" xml:space="preserve">4. </s> <s xml:id="echoid-s14824" xml:space="preserve">tandem ut ſolum hoc lumen ex pixide exeat, ne <lb/>lumine extraneo minus vivida ſit repræſentatio.</s> <s xml:id="echoid-s14825" xml:space="preserve"/> </p> <div xml:id="echoid-div2220" type="float" level="2" n="6"> <note position="left" xlink:label="note-0582-06" xlink:href="note-0582-06a" xml:space="preserve">839.</note> </div> <p> <s xml:id="echoid-s14826" xml:space="preserve">A magnitudine flammæ & </s> <s xml:id="echoid-s14827" xml:space="preserve">ſpeculi, ut & </s> <s xml:id="echoid-s14828" xml:space="preserve">hujus cavitate, <lb/>pendet requiſitum primum; </s> <s xml:id="echoid-s14829" xml:space="preserve">quo magis excavatur ſpeculum, <lb/>eo propius flammæ admovendum eſt, & </s> <s xml:id="echoid-s14830" xml:space="preserve">majori numero <lb/>radii intercipiuntur, & </s> <s xml:id="echoid-s14831" xml:space="preserve">reflectuntur; </s> <s xml:id="echoid-s14832" xml:space="preserve">cavendum tamen, ne <lb/>nimium incaleſcat ſpeculum, quod optimè ex vitro confla-<lb/>tur.</s> <s xml:id="echoid-s14833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14834" xml:space="preserve">Datis autem flammâ & </s> <s xml:id="echoid-s14835" xml:space="preserve">ſpeculo, ut quantum fieri poteſt <lb/>maximè illuminetur pictura, & </s> <s xml:id="echoid-s14836" xml:space="preserve">ubique æqualiter, ita flamma <lb/>& </s> <s xml:id="echoid-s14837" xml:space="preserve">ſpeculum conſtituuntur, ut repræſentatio inverſa flammæ <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0582-07a" xlink:href="note-0582-07"/> cadat in ipſam picturam: </s> <s xml:id="echoid-s14838" xml:space="preserve">cùm autem repræſentatio flammæ <lb/>augeri & </s> <s xml:id="echoid-s14839" xml:space="preserve">minui poſſit <anchor type="note" xlink:href="" symbol="*"/>, ita ſpeculum & </s> <s xml:id="echoid-s14840" xml:space="preserve">flamma diſponenda <anchor type="note" xlink:label="note-0582-08a" xlink:href="note-0582-08"/> ſunt, ut flammæ repræſentatio totam picturam in vitro obte- <pb o="(75)" file="0583" n="643" rhead="MATHEMATICA. LIB. III. CAP. XVII."/> gat & </s> <s xml:id="echoid-s14841" xml:space="preserve">hanc non excedat. </s> <s xml:id="echoid-s14842" xml:space="preserve">Tunc enim pictura quantum poteſt <lb/>fieri maximè à lumine reflexo illuminatur, & </s> <s xml:id="echoid-s14843" xml:space="preserve">ſingula illius <lb/>puncta æqualiter illuſtrantur; </s> <s xml:id="echoid-s14844" xml:space="preserve">directè etiam in ſingula pictu-<lb/>ræ puncta lumen, ſenſibiliter æquale, cadit; </s> <s xml:id="echoid-s14845" xml:space="preserve">admotâ flam-<lb/>mâ, lumen hoc quidem augeretur, ſed minueretur reflexum, <lb/>& </s> <s xml:id="echoid-s14846" xml:space="preserve">diminutio hujus augmentum illius ſuperaret.</s> <s xml:id="echoid-s14847" xml:space="preserve"/> </p> <div xml:id="echoid-div2221" type="float" level="2" n="7"> <note symbol="*" position="left" xlink:label="note-0582-07" xlink:href="note-0582-07a" xml:space="preserve">826.</note> <note symbol="*" position="left" xlink:label="note-0582-08" xlink:href="note-0582-08a" xml:space="preserve">826.</note> </div> <p> <s xml:id="echoid-s14848" xml:space="preserve">Uſus vitri V V eſt inflexio luminis, quo pictura O O il-<lb/>luminatur, antequam illud ad hanc perveniat; </s> <s xml:id="echoid-s14849" xml:space="preserve">qua infle-<lb/>ctione lumen omne ad lentem a a pervenit, & </s> <s xml:id="echoid-s14850" xml:space="preserve">repræſenta-<lb/>tioni in plano albo inſervit.</s> <s xml:id="echoid-s14851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14852" xml:space="preserve">Omne lumen, quod huic repræſentationi utile eſt, tranſit <lb/>per foramen f; </s> <s xml:id="echoid-s14853" xml:space="preserve">radiique à variis punctis procedentes ibi ſeſe <lb/>mutuo interſecant; </s> <s xml:id="echoid-s14854" xml:space="preserve">quare pictura inverſa in vitro, erecta da-<lb/>tur in plano albo; </s> <s xml:id="echoid-s14855" xml:space="preserve">annulo b b omnes radii, qui repræſenta-<lb/>tioni formandæ non inſerviunt, intercipiuntur, ne cubiculum <lb/>intrent & </s> <s xml:id="echoid-s14856" xml:space="preserve">minus vivida ſit pictura. </s> <s xml:id="echoid-s14857" xml:space="preserve">Annulus etiam hicce <lb/>intercipit radios, quibus unum punctum magis quàm aliud il-<lb/>luminatur, quo lumen, quod ex ante dictis quidem æqua-<lb/>bile ſatis eſt, magis adhucdum æquabile fit. </s> <s xml:id="echoid-s14858" xml:space="preserve">Niſi exactè <lb/>detur annulus b b in radiorum interſectione, magnoperè <lb/>nocet.</s> <s xml:id="echoid-s14859" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2223" type="section" level="1" n="539"> <head xml:id="echoid-head712" style="it" xml:space="preserve">LIBRI III. Pars III.</head> <head xml:id="echoid-head713" xml:space="preserve">De Opaco & Coloribus.</head> <head xml:id="echoid-head714" xml:space="preserve">CAPUT XVII.</head> <head xml:id="echoid-head715" style="it" xml:space="preserve">De Corporum Opacitate</head> <head xml:id="echoid-head716" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s14860" xml:space="preserve">COrpora quæ lumen tranſmittunt vocantur pellucida. </s> <s xml:id="echoid-s14861" xml:space="preserve">Ta-<lb/> <anchor type="note" xlink:label="note-0583-01a" xlink:href="note-0583-01"/> lia ſunt omnia media <anchor type="note" xlink:href="" symbol="*"/>, vacuo excepto.</s> <s xml:id="echoid-s14862" xml:space="preserve"/> </p> <div xml:id="echoid-div2223" type="float" level="2" n="1"> <note position="right" xlink:label="note-0583-01" xlink:href="note-0583-01a" xml:space="preserve">840.</note> </div> <note symbol="*" position="right" xml:space="preserve">615.</note> <p> <s xml:id="echoid-s14863" xml:space="preserve">Nullum datur corpus, cujus partes minimæ non ſint pelluci-<lb/> <anchor type="note" xlink:label="note-0583-03a" xlink:href="note-0583-03"/> dæ; </s> <s xml:id="echoid-s14864" xml:space="preserve">hoc in dubium nemo vocabit, qui mycroſcopiis ſæpe u-<lb/>ſus eſt: </s> <s xml:id="echoid-s14865" xml:space="preserve">partes quædam metallicæ, quæ licèt exiguæ, lumen <lb/>non tranſmittunt, ſi in menſtruis diſſolvantur, id eſt, in <pb o="(76)" file="0584" n="644" rhead="PHYSICES ELEMENTA"/> partes multò minores dividantur, tranſlucidæ fiunt. </s> <s xml:id="echoid-s14866" xml:space="preserve">Facili <lb/>etiam experimento probatur, lumen per pleraque corpora o-<lb/>paca tranſire poſſe.</s> <s xml:id="echoid-s14867" xml:space="preserve"/> </p> <div xml:id="echoid-div2224" type="float" level="2" n="2"> <note position="right" xlink:label="note-0583-03" xlink:href="note-0583-03a" xml:space="preserve">841.</note> </div> </div> <div xml:id="echoid-div2226" type="section" level="1" n="540"> <head xml:id="echoid-head717" xml:space="preserve"><emph style="sc">Experimentum</emph>. 1.</head> <p> <s xml:id="echoid-s14868" xml:space="preserve">In cubiculo obſcuro, in quo lumen ſolare per foramen in-<lb/>trat, obtegatur foramen hoc laminâ tenui corporis opaci, <lb/>per hanc tranſibit lumen; </s> <s xml:id="echoid-s14869" xml:space="preserve">lignum craſſitiei decimæ partis pol-<lb/>licis lumen omne non intercipit. </s> <s xml:id="echoid-s14870" xml:space="preserve">Hoc autem experimento <lb/>perfecta partium tranſluciditas in corporibus opacis non pro-<lb/>batur, talis enim in minimis partibus tantum obtinet.</s> <s xml:id="echoid-s14871" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14872" xml:space="preserve">Opacitas non oritur, ut vulgò creditur, ex eo, quod viæ, <lb/> <anchor type="note" xlink:label="note-0584-01a" xlink:href="note-0584-01"/> per quas lumen tranſire poſſet, obturentur à materiæ parti-<lb/>culis, per ſingulas enim corporis partes minores lumen tran-<lb/>ſit; </s> <s xml:id="echoid-s14873" xml:space="preserve">inutilis etiam ad opacitatem talis eſt luminis interceptio; <lb/></s> <s xml:id="echoid-s14874" xml:space="preserve">ad opacitatem requiritur luminis reflectio & </s> <s xml:id="echoid-s14875" xml:space="preserve">deflectio à lineâ <lb/>rectâ, ad quod ſeparatio duorum mediorum tantum requi-<lb/>ritur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s14876" xml:space="preserve"/> </p> <div xml:id="echoid-div2226" type="float" level="2" n="1"> <note position="left" xlink:label="note-0584-01" xlink:href="note-0584-01a" xml:space="preserve">842.</note> </div> <note symbol="*" position="left" xml:space="preserve">631. 796.</note> <p> <s xml:id="echoid-s14877" xml:space="preserve">Concipiamus corpus conſtans ex particulis minimis, per-<lb/>fectè tranſlucidis, (quales ſunt particulæ ex quibus corpora <lb/>conſtant <anchor type="note" xlink:href="" symbol="*"/>) poris inter ſe ſeparatis; </s> <s xml:id="echoid-s14878" xml:space="preserve">interſtitiaque aut vacua <anchor type="note" xlink:label="note-0584-03a" xlink:href="note-0584-03"/> dari aut repleta medio denſitate differente cum ipſis parti-<lb/>culis; </s> <s xml:id="echoid-s14879" xml:space="preserve">lumen ſi intret hoc corpus, omnibus momentis incidet <lb/>in ſuperficiem media, denſitate differentia, ſeparantem; </s> <s xml:id="echoid-s14880" xml:space="preserve">in-<lb/>numeras ergo patietur reflectiones & </s> <s xml:id="echoid-s14881" xml:space="preserve">refractiones in illo cor-<lb/>pore <anchor type="note" xlink:href="" symbol="*"/>, ita ut pertranſire non poterit. </s> <s xml:id="echoid-s14882" xml:space="preserve">Videmus ergo opa- <anchor type="note" xlink:label="note-0584-04a" xlink:href="note-0584-04"/> citatem à poris pendêre; </s> <s xml:id="echoid-s14883" xml:space="preserve">Repletis enim poris, medio ejuſdem <lb/>denſitatis cum particulis ipſis corporis, nullam in corpore <lb/>lumen patietur reflectionem, aut refractionem, ſed rectâ <lb/>tranſibit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s14884" xml:space="preserve">& </s> <s xml:id="echoid-s14885" xml:space="preserve">corpus erit tranſlucidum.</s> <s xml:id="echoid-s14886" xml:space="preserve"/> </p> <div xml:id="echoid-div2227" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0584-03" xlink:href="note-0584-03a" xml:space="preserve">841.</note> <note symbol="*" position="left" xlink:label="note-0584-04" xlink:href="note-0584-04a" xml:space="preserve">631. 796. <lb/>843.</note> </div> <note symbol="*" position="left" xml:space="preserve">841. 631. 796.</note> <p> <s xml:id="echoid-s14887" xml:space="preserve">Licèt non poſſimus experimenta inſtituere, in quibus pori <lb/>exactiſſimè medio ejuſdem denſitatis cum particulis replean-<lb/>tur, ſequentia nihilominus, ſatis clarè doctrinam Newto-<lb/>nianam, de opacitate, evincunt.</s> <s xml:id="echoid-s14888" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2229" type="section" level="1" n="541"> <head xml:id="echoid-head718" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s14889" xml:space="preserve">Charta, ſi aquâ madefiat magis fit tranſlucida; </s> <s xml:id="echoid-s14890" xml:space="preserve">hæc im-<lb/>plet poros & </s> <s xml:id="echoid-s14891" xml:space="preserve">minus quàm aër denſitate cum particulis <lb/>chartæ differt. </s> <s xml:id="echoid-s14892" xml:space="preserve">Oleum eundem edit effectum.</s> <s xml:id="echoid-s14893" xml:space="preserve"/> </p> <pb file="0585" n="645"/> <pb file="0585a" n="646"/> <figure> <image file="0585a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0585a-01"/> </figure> <pb file="0586" n="647"/> <pb o="(77)" file="0587" n="648" rhead="MATHEMATICA LIB. III. CAP. XVII."/> </div> <div xml:id="echoid-div2230" type="section" level="1" n="542"> <head xml:id="echoid-head719" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s14894" xml:space="preserve">Detur fruſtum vitri, craſſitiei duorum pollicum; </s> <s xml:id="echoid-s14895" xml:space="preserve">dentur <lb/>variæ laminæ ejuſdem vitri, quæ, ad ſe mutuo applicatæ, <lb/>omnes ſimul craſſitie duos pollices non æquant; </s> <s xml:id="echoid-s14896" xml:space="preserve">hæ minus <lb/>erunt tranſlucidæ, propter aërem interjectum inter laminas, <lb/>quàm fruſtum cujus omnes partes cohoerent.</s> <s xml:id="echoid-s14897" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2231" type="section" level="1" n="543"> <head xml:id="echoid-head720" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s14898" xml:space="preserve">Dentur, ex eodem vitro, duodecim laminæ, quantum <lb/>fieri poteſt ejuſdem craſſitiei; </s> <s xml:id="echoid-s14899" xml:space="preserve">ſex & </s> <s xml:id="echoid-s14900" xml:space="preserve">ſex ad ſe invicem ap-<lb/>plicentur; </s> <s xml:id="echoid-s14901" xml:space="preserve">ex duabus hiſce congeriebus ſi minus tranſlucida <lb/>aquæ immergatur, extracta, tranſluciditate, aliam vincet; <lb/></s> <s xml:id="echoid-s14902" xml:space="preserve">quia aqua, quæ in hoc caſu interſtitia inter plana replet, <lb/>denſitate cum vitro minus differt quàm aër.</s> <s xml:id="echoid-s14903" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14904" xml:space="preserve">Confirmantur ulterius, & </s> <s xml:id="echoid-s14905" xml:space="preserve">extra omne dubium ponuntur, <lb/>quæ de opacitate dicta ſunt innumeris experimentis, quibus <lb/>corpora perfectè tranſlucida, ſeparatione partium, non in-<lb/> <anchor type="note" xlink:label="note-0587-01a" xlink:href="note-0587-01"/> terveniente corpore ullo opaco, opaca fiunt.</s> <s xml:id="echoid-s14906" xml:space="preserve"/> </p> <div xml:id="echoid-div2231" type="float" level="2" n="1"> <note position="right" xlink:label="note-0587-01" xlink:href="note-0587-01a" xml:space="preserve">844.</note> </div> </div> <div xml:id="echoid-div2233" type="section" level="1" n="544"> <head xml:id="echoid-head721" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s14907" xml:space="preserve">Agitetur liquidum quodcunque, perfectè tranſlucidum, <lb/>quod in ſpumam poteſt converti, donec in bullas extenſum <lb/>ſit; </s> <s xml:id="echoid-s14908" xml:space="preserve">ſtatim opacum erit, ex interſtitiis aëre repletis.</s> <s xml:id="echoid-s14909" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2234" type="section" level="1" n="545"> <head xml:id="echoid-head722" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s14910" xml:space="preserve">Reſina terebinthina, & </s> <s xml:id="echoid-s14911" xml:space="preserve">aqua, ſunt corpora tranſlucida; <lb/></s> <s xml:id="echoid-s14912" xml:space="preserve">commixta corpus formant opacum.</s> <s xml:id="echoid-s14913" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2235" type="section" level="1" n="546"> <head xml:id="echoid-head723" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s14914" xml:space="preserve">Aqua & </s> <s xml:id="echoid-s14915" xml:space="preserve">oleum commixta ſunt opaca; </s> <s xml:id="echoid-s14916" xml:space="preserve">licèt ſeparata ſint <lb/>tranſlucida.</s> <s xml:id="echoid-s14917" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2236" type="section" level="1" n="547"> <head xml:id="echoid-head724" xml:space="preserve"><emph style="sc">Experimentum</emph> 8.</head> <p> <s xml:id="echoid-s14918" xml:space="preserve">Vitrum quantumvis tranſlucidum, ſi in pulverem redi-<lb/>gatur fit opacum. </s> <s xml:id="echoid-s14919" xml:space="preserve">Etiam ex rimis in vitro hoc opa-<lb/>cum eſt.</s> <s xml:id="echoid-s14920" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14921" xml:space="preserve">In hiſce omnibus clarè videmus opacitatem dari, quia <lb/>inter partes tranſlucidas interjacet medium diverſæ denſi-<lb/>tatis; </s> <s xml:id="echoid-s14922" xml:space="preserve">quod etiam in nubibus obſervatur, quæ opacæ ſunt <lb/>ex aëre inter aquæ particulas interpoſito.</s> <s xml:id="echoid-s14923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14924" xml:space="preserve">Si hiſce addamus, quæ de tenuium laminarum coloribus <lb/>in capite 22. </s> <s xml:id="echoid-s14925" xml:space="preserve">ſequenti dicuntur; </s> <s xml:id="echoid-s14926" xml:space="preserve">nova habebimus experi- <pb o="(78)" file="0588" n="649" rhead="PHYSICES ELEMENTA"/> menta, quibus ſolis pleniſſimè probatur corpora lumen in-<lb/>tercipere, quia ex particulis tenuibus, medio, denſitate cum <lb/>ipſis particulis differente, circumdatis, conſtant.</s> <s xml:id="echoid-s14927" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14928" xml:space="preserve">Corpora quædam opaca exiguam luminis copiam refle-<lb/>ctunt, reliquum lumen, innumeris diviſionibus, quas in re-<lb/>flectionibus & </s> <s xml:id="echoid-s14929" xml:space="preserve">refractionibus memoratis patitur, in corpore <lb/>extinguitur; </s> <s xml:id="echoid-s14930" xml:space="preserve">talia funt corpora nigra; </s> <s xml:id="echoid-s14931" xml:space="preserve">ſi perfectè nigra da-<lb/> <anchor type="note" xlink:label="note-0588-01a" xlink:href="note-0588-01"/> rentur, nullum reflecterent lumen; </s> <s xml:id="echoid-s14932" xml:space="preserve">corpus enim omne, ſi <lb/>nullo illuſtretur lumine, & </s> <s xml:id="echoid-s14933" xml:space="preserve">ita nullos radios reflectat, nigrum <lb/>apparet.</s> <s xml:id="echoid-s14934" xml:space="preserve"/> </p> <div xml:id="echoid-div2236" type="float" level="2" n="1"> <note position="left" xlink:label="note-0588-01" xlink:href="note-0588-01a" xml:space="preserve">845.</note> </div> <p> <s xml:id="echoid-s14935" xml:space="preserve">Corpora reliqua opaca coloribus variis induta videntur, <lb/>quædam etiam tranſlucida coloribus tinguntur: </s> <s xml:id="echoid-s14936" xml:space="preserve">Unde hi <lb/>oriantur examinandum nunc eſt.</s> <s xml:id="echoid-s14937" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2238" type="section" level="1" n="548"> <head xml:id="echoid-head725" xml:space="preserve">CAPUT XVIII.</head> <head xml:id="echoid-head726" style="it" xml:space="preserve">De diverſâ radiorum ſolarium refrangibilitate.</head> <p> <s xml:id="echoid-s14938" xml:space="preserve">COrpora variè colorata apparent, licèt iiſdem radiis ſo-<lb/>laribus, qui ab illis reflectuntur, illuminentur: </s> <s xml:id="echoid-s14939" xml:space="preserve">multa <lb/>præterea lucis phoenomena, circa colores, minimè negli-<lb/>genda dantur.</s> <s xml:id="echoid-s14940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14941" xml:space="preserve">In his ad tria attendendum eſt: </s> <s xml:id="echoid-s14942" xml:space="preserve">1. </s> <s xml:id="echoid-s14943" xml:space="preserve">Ipſi radii examinandi <lb/> <anchor type="note" xlink:label="note-0588-02a" xlink:href="note-0588-02"/> ſunt. </s> <s xml:id="echoid-s14944" xml:space="preserve">2. </s> <s xml:id="echoid-s14945" xml:space="preserve">Animadvertenda eſt radiorum reflectio. </s> <s xml:id="echoid-s14946" xml:space="preserve">3. </s> <s xml:id="echoid-s14947" xml:space="preserve">Inqui-<lb/>rendum in conſtitutionem ſuperficierum corporum diverſè <lb/>coloratorum.</s> <s xml:id="echoid-s14948" xml:space="preserve"/> </p> <div xml:id="echoid-div2238" type="float" level="2" n="1"> <note position="left" xlink:label="note-0588-02" xlink:href="note-0588-02a" xml:space="preserve">846.</note> </div> <p> <s xml:id="echoid-s14949" xml:space="preserve">Quod radios ſpectat, prima harum proprietas, hìc no-<lb/>tanda, eſt, non omnes radios, in circumſtantiis ſimilibus, <lb/> <anchor type="note" xlink:label="note-0588-03a" xlink:href="note-0588-03"/> eandem pati refractionem.</s> <s xml:id="echoid-s14950" xml:space="preserve"/> </p> <div xml:id="echoid-div2239" type="float" level="2" n="2"> <note position="left" xlink:label="note-0588-03" xlink:href="note-0588-03a" xml:space="preserve">847.</note> </div> </div> <div xml:id="echoid-div2241" type="section" level="1" n="549"> <head xml:id="echoid-head727" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s14951" xml:space="preserve">Radii, qui talem diverſam refractionem patiuntur, di-<lb/> <anchor type="note" xlink:label="note-0588-04a" xlink:href="note-0588-04"/> verſæ refrangibilitatis dicuntur, & </s> <s xml:id="echoid-s14952" xml:space="preserve">magis refrangibiles, qui <lb/>magis refractione inflectuntur.</s> <s xml:id="echoid-s14953" xml:space="preserve"/> </p> <div xml:id="echoid-div2241" type="float" level="2" n="1"> <note position="left" xlink:label="note-0588-04" xlink:href="note-0588-04a" xml:space="preserve">848.</note> </div> </div> <div xml:id="echoid-div2243" type="section" level="1" n="550"> <head xml:id="echoid-head728" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s14954" xml:space="preserve">Homogenei radii dicuntur, qui refrangibilitate inter ſe <lb/> <anchor type="note" xlink:label="note-0588-05a" xlink:href="note-0588-05"/> non differunt.</s> <s xml:id="echoid-s14955" xml:space="preserve"/> </p> <div xml:id="echoid-div2243" type="float" level="2" n="1"> <note position="left" xlink:label="note-0588-05" xlink:href="note-0588-05a" xml:space="preserve">849.</note> </div> </div> <div xml:id="echoid-div2245" type="section" level="1" n="551"> <head xml:id="echoid-head729" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s14956" xml:space="preserve">Heterogenei, qui non omnes æqualiter, in iiſdem circum-<lb/> <anchor type="note" xlink:label="note-0588-06a" xlink:href="note-0588-06"/> ſtantiis, refractione inflectuntur.</s> <s xml:id="echoid-s14957" xml:space="preserve"/> </p> <div xml:id="echoid-div2245" type="float" level="2" n="1"> <note position="left" xlink:label="note-0588-06" xlink:href="note-0588-06a" xml:space="preserve">850.</note> </div> <pb o="(79)" file="0589" n="650" rhead="MATHEMATICA LIB. III. CAP. XVIII."/> <p> <s xml:id="echoid-s14958" xml:space="preserve">Sit inter A B & </s> <s xml:id="echoid-s14959" xml:space="preserve">C D radius ſolaris, ex innumeris aliis, <lb/> <anchor type="note" xlink:label="note-0589-01a" xlink:href="note-0589-01"/> inter ſe parallelis, formatus; </s> <s xml:id="echoid-s14960" xml:space="preserve">non omnes hi æqualem patiun-<lb/>tur refractionem, ſi enim obliquè in ſuperficiem BD me-<lb/>dii denſioris incidant, quidam inter BE & </s> <s xml:id="echoid-s14961" xml:space="preserve">DG refringun-<lb/>tur, & </s> <s xml:id="echoid-s14962" xml:space="preserve">juxta hanc directionem in denſiori medio moventur; <lb/></s> <s xml:id="echoid-s14963" xml:space="preserve">alii magis inflectuntur, & </s> <s xml:id="echoid-s14964" xml:space="preserve">inter BF & </s> <s xml:id="echoid-s14965" xml:space="preserve">DH, juxta harum <lb/>linearum ſitum, motum dirigunt; </s> <s xml:id="echoid-s14966" xml:space="preserve">nulla denique directio <lb/>concipi poteſt inter media juxta quam radii quidam non mo-<lb/>ventur, in ſingulis punctis inter B & </s> <s xml:id="echoid-s14967" xml:space="preserve">D: </s> <s xml:id="echoid-s14968" xml:space="preserve">ita ut radius quan-<lb/>tumvis exiguus refractione in innumeros alios dividatur, quia <lb/>omnis radius, ut à Sole profluit, quantumvis exiguus hete-<lb/>rogeneus eſt, & </s> <s xml:id="echoid-s14969" xml:space="preserve">conſtans ex innumeris minoribus radiis re-<lb/>frangibilibus juxta omnes gradus refrangibilitatis.</s> <s xml:id="echoid-s14970" xml:space="preserve"/> </p> <div xml:id="echoid-div2246" type="float" level="2" n="2"> <note position="right" xlink:label="note-0589-01" xlink:href="note-0589-01a" xml:space="preserve">TAB. XV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s14971" xml:space="preserve">Radii memorati paralleli, incidentes in ſuperficiem pla-<lb/>nam, refractione moventur inter BE & </s> <s xml:id="echoid-s14972" xml:space="preserve">DH; </s> <s xml:id="echoid-s14973" xml:space="preserve">quæ lineæ <lb/>divergunt inter ſe, & </s> <s xml:id="echoid-s14974" xml:space="preserve">continuatæ magis ac magis ſeparan-<lb/>tur; </s> <s xml:id="echoid-s14975" xml:space="preserve">ita ut radii memorati refractione diſpergantur. </s> <s xml:id="echoid-s14976" xml:space="preserve">In <lb/>n. </s> <s xml:id="echoid-s14977" xml:space="preserve">653. </s> <s xml:id="echoid-s14978" xml:space="preserve">radios conſideravimus homogeneos, ut ubique in tota <lb/> <anchor type="note" xlink:label="note-0589-02a" xlink:href="note-0589-02"/> parte præcedenti; </s> <s xml:id="echoid-s14979" xml:space="preserve">ſatis eſt exigua differentia refrangibilita-<lb/>tis in radiis ſolaribus, ut in præcedentibus negligi potuit. <lb/></s> <s xml:id="echoid-s14980" xml:space="preserve">Quid in homogeneis radiis obtineat etiam prius fuit exami-<lb/>nandum, & </s> <s xml:id="echoid-s14981" xml:space="preserve">quid ex diverſâ refrangibilitate in propoſitioni-<lb/>bus mutandum ſit unuſquiſque facile videbit.</s> <s xml:id="echoid-s14982" xml:space="preserve"/> </p> <div xml:id="echoid-div2247" type="float" level="2" n="3"> <note position="right" xlink:label="note-0589-02" xlink:href="note-0589-02a" xml:space="preserve">851.</note> </div> <p> <s xml:id="echoid-s14983" xml:space="preserve">Ut hæc radiorum refrangibilitas ad oculum pateat, au-<lb/> <anchor type="note" xlink:label="note-0589-03a" xlink:href="note-0589-03"/> genda eſt divergentia memorata; </s> <s xml:id="echoid-s14984" xml:space="preserve">quod fit, ſi radii memora-<lb/>ti incidant in ſuperficiem EH, medium denſius terminan-<lb/>tem, & </s> <s xml:id="echoid-s14985" xml:space="preserve">hoc à rariori ſeparantem, quæ cum ſuperficie BD <lb/>angulum quemcunque format, & </s> <s xml:id="echoid-s14986" xml:space="preserve">ad hanc ita inclinatur, ut <lb/>in illam radii magis refrangibiles obliquius incidant, quàm <lb/>minus refrangibiles; </s> <s xml:id="echoid-s14987" xml:space="preserve">ita ut illi, tranſeundo in medium ra-<lb/>rius, ex duplici cauſa, majori refrangibilitate & </s> <s xml:id="echoid-s14988" xml:space="preserve">majori in-<lb/>clinatione, magis detorqueantur, & </s> <s xml:id="echoid-s14989" xml:space="preserve">ab aliis magis diver-<lb/>gant. </s> <s xml:id="echoid-s14990" xml:space="preserve">Radii minus refrangibiles inter BE & </s> <s xml:id="echoid-s14991" xml:space="preserve">DG, ſecun-<lb/>dò refracti inter EI & </s> <s xml:id="echoid-s14992" xml:space="preserve">GL motum continuant; </s> <s xml:id="echoid-s14993" xml:space="preserve">alii inter <lb/>FM & </s> <s xml:id="echoid-s14994" xml:space="preserve">HN: </s> <s xml:id="echoid-s14995" xml:space="preserve">in quo caſu, ſi, ad diſtantiam quindecim <lb/>aut viginti pedum, in plano hi radii cadant, ſenſibiliter <lb/>maximè & </s> <s xml:id="echoid-s14996" xml:space="preserve">minimè refrangibiles ſeparantur, & </s> <s xml:id="echoid-s14997" xml:space="preserve">totum in- <pb o="(80)" file="0590" n="651" rhead="PHYSICES ELEMENTA"/> termedium ſpatium radiis mediâ refrangibilitate præditis il-<lb/>luminatur.</s> <s xml:id="echoid-s14998" xml:space="preserve"/> </p> <div xml:id="echoid-div2248" type="float" level="2" n="4"> <note position="right" xlink:label="note-0589-03" xlink:href="note-0589-03a" xml:space="preserve">852.</note> </div> </div> <div xml:id="echoid-div2250" type="section" level="1" n="552"> <head xml:id="echoid-head730" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s14999" xml:space="preserve">Detur in laminâ metallicâ in feneſtrâ foramen, diametri <lb/> <anchor type="note" xlink:label="note-0590-01a" xlink:href="note-0590-01"/> quartæ partis pollicis, per quod radii ſolares cubiculum <lb/>obſcurum intrent, cadant hi in priſma vitreum triangulare <lb/>AA, ut in totum ab inferiori ſuperficie reflectantur, (vi-<lb/>de exp. </s> <s xml:id="echoid-s15000" xml:space="preserve">n. </s> <s xml:id="echoid-s15001" xml:space="preserve">789.) </s> <s xml:id="echoid-s15002" xml:space="preserve">Duabus refractionibus, quas lumen pati-<lb/>tur, radii diverſè refrangibiles non divergunt, & </s> <s xml:id="echoid-s15003" xml:space="preserve">reflexi ad <lb/>ſecundum priſma, etiam vitreum & </s> <s xml:id="echoid-s15004" xml:space="preserve">triangulare, BB per-<lb/>veniunt, eodem modo ac ſi directè à Sole procederent. <lb/></s> <s xml:id="echoid-s15005" xml:space="preserve">Priſmata hæc ambo circa axes ſunt volubilia, ut ante expli-<lb/>catum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15006" xml:space="preserve">primum AA ligno imponitur & </s> <s xml:id="echoid-s15007" xml:space="preserve">huic alligatur, ita <anchor type="note" xlink:label="note-0590-02a" xlink:href="note-0590-02"/> tamen, ut rotatio circa axem non impediatur; </s> <s xml:id="echoid-s15008" xml:space="preserve">lignum hoc <lb/>cum globo mobili conjungitur, qui â tripode ſuſtinetur, <lb/>quæ machina in praxi geometriæ vulgaris eſt. </s> <s xml:id="echoid-s15009" xml:space="preserve">Priſma ſe-<lb/>cundum BB imponitur ſuſtentaculo S, in cujus lateribus <lb/>ſciſſuræ variæ dantur, reſpondentes inter ſe in ſingulis lateri-<lb/>bus; </s> <s xml:id="echoid-s15010" xml:space="preserve">illis priſma ad varias altitudines ſuſtinetur, ſemper ta-<lb/>men horizontaliter, ambabus axeos extremitatibus in ſciſſu-<lb/>ris reſpondentibus poſitis.</s> <s xml:id="echoid-s15011" xml:space="preserve"/> </p> <div xml:id="echoid-div2250" type="float" level="2" n="1"> <note position="left" xlink:label="note-0590-01" xlink:href="note-0590-01a" xml:space="preserve">TAB. XV. <lb/>fig. 2.</note> <note symbol="*" position="left" xlink:label="note-0590-02" xlink:href="note-0590-02a" xml:space="preserve">791.</note> </div> <p> <s xml:id="echoid-s15012" xml:space="preserve">Lumen ad priſma BB perpendiculariter ad axem accedit <lb/>& </s> <s xml:id="echoid-s15013" xml:space="preserve">tranſmittitur, ut in fig. </s> <s xml:id="echoid-s15014" xml:space="preserve">1. </s> <s xml:id="echoid-s15015" xml:space="preserve">demonſtratur, in qua BD & </s> <s xml:id="echoid-s15016" xml:space="preserve"><lb/>EH latera priſmatis deſignant; </s> <s xml:id="echoid-s15017" xml:space="preserve">etiam ad utrumque latus <lb/>æqualiter inclinatur lumen: </s> <s xml:id="echoid-s15018" xml:space="preserve">quod obtinetur, ſi circa axem <lb/>priſma agitetur, lumen enim Solis in hac agitatione adſcen-<lb/>dit iterumque deſcendit, ſituſque quæſitus, eſt ubi lumen <lb/>maximè elevatur: </s> <s xml:id="echoid-s15019" xml:space="preserve">ita autem ambo ſunt diſponenda priſma-<lb/>ta, ut in hoc caſu lumen horizontaliter ex priſmate BB <lb/>exeat. </s> <s xml:id="echoid-s15020" xml:space="preserve">Radius hicce horizontalis, ad diſtantiam quindecim <lb/>aut viginti pedum, cadit in tabulam T, chartâ albâ obte-<lb/>ctam, quæ pede ſuſtinetur, quo ad varias altitudines eleva-<lb/>tur & </s> <s xml:id="echoid-s15021" xml:space="preserve">firmatur. </s> <s xml:id="echoid-s15022" xml:space="preserve">Radii divergentes ad tabulam perveniunt <lb/>& </s> <s xml:id="echoid-s15023" xml:space="preserve">in hac formant imaginem oblongam RV, terminatam, <lb/>ad latera, lineis parallelis, in R & </s> <s xml:id="echoid-s15024" xml:space="preserve">V verò ſemicirculis.</s> <s xml:id="echoid-s15025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15026" xml:space="preserve">Radii ſolares, per foramen rotundum tranſeuntes, ſi ad <lb/>certam diſtantiam in planum cadant, in hoc videtur macula <pb o="(81)" file="0591" n="652" rhead="MATHEMATICA LIB. III. CAP. XVIII."/> illuminata rotunda, eo major, quo planum magis à foramine <lb/>diſtat, quod oritur ex radiis à lateribus Solis provenientibus, <lb/>cum illis, qui à centro ad foramen perveniunt angulum <lb/>formantibus, & </s> <s xml:id="echoid-s15027" xml:space="preserve">in foramine hos interſecantibus, ita ut in <lb/>plano quaſi imago Solis detur.</s> <s xml:id="echoid-s15028" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15029" xml:space="preserve">Si radii per priſma BB non tranſirent, & </s> <s xml:id="echoid-s15030" xml:space="preserve">ad diſtantiam <lb/>tabulæ T in planum caderent, Solis imago haberet diametrum <lb/>æqualem latitudini imaginis RV; </s> <s xml:id="echoid-s15031" xml:space="preserve">quæ latitudo refractione <lb/>non mutatur; </s> <s xml:id="echoid-s15032" xml:space="preserve">quia radii, perpendiculariter ad axem, priſma <lb/>intrant, & </s> <s xml:id="echoid-s15033" xml:space="preserve">ad hoc, reſpectu latitudinis imaginis, non in-<lb/>clinantur. </s> <s xml:id="echoid-s15034" xml:space="preserve">Cum autem alio reſpectu oblonga ſit Solis imago, <lb/> <anchor type="note" xlink:label="note-0591-01a" xlink:href="note-0591-01"/> clarè inde ſequitur, non omnes radios æqualem paſſos re-<lb/>fractionem; </s> <s xml:id="echoid-s15035" xml:space="preserve">radiis homogeneis rotundam, licèt refractis, <lb/>dantibus Solis imaginem. </s> <s xml:id="echoid-s15036" xml:space="preserve">Minimè refrangibiles radii pertin-<lb/>gunt ad R, maximè refrangibiles ad V; </s> <s xml:id="echoid-s15037" xml:space="preserve">& </s> <s xml:id="echoid-s15038" xml:space="preserve">ſemicirculis in <lb/>R & </s> <s xml:id="echoid-s15039" xml:space="preserve">V terminatur tota imago RV; </s> <s xml:id="echoid-s15040" xml:space="preserve">quia ex circularibus <lb/>imaginibus tota conſtat: </s> <s xml:id="echoid-s15041" xml:space="preserve">inter R & </s> <s xml:id="echoid-s15042" xml:space="preserve">V autem dantur imagi-<lb/>nes circulares innumeræ, ex radiis refrangibilitatum inter-<lb/>mediarum omnium poſſibilium; </s> <s xml:id="echoid-s15043" xml:space="preserve">aliter ad latera non lineis <lb/>rectis imago RV terminaretur.</s> <s xml:id="echoid-s15044" xml:space="preserve"/> </p> <div xml:id="echoid-div2251" type="float" level="2" n="2"> <note position="right" xlink:label="note-0591-01" xlink:href="note-0591-01a" xml:space="preserve">853.</note> </div> <p> <s xml:id="echoid-s15045" xml:space="preserve">In plurimis experimentis, per ſciſſuram aut foramen lu-<lb/>men intromitti in locum obſcurum, vidimus, quod ad arbi-<lb/>trium artificis reliquimus; </s> <s xml:id="echoid-s15046" xml:space="preserve">nos autem hac methodo uſi ſumus.</s> <s xml:id="echoid-s15047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15048" xml:space="preserve">In plano ligneo, quo feneſtræ apertura obturatur, datur <lb/> <anchor type="note" xlink:label="note-0591-02a" xlink:href="note-0591-02"/> foramen quadratum, cujus latus eſt quatuor pollicum; </s> <s xml:id="echoid-s15049" xml:space="preserve">cir-<lb/> <anchor type="note" xlink:label="note-0591-03a" xlink:href="note-0591-03"/> cumdatur hoc tribus regulis ligneis AB, BC, CD, quæ <lb/>retinent tabellam ligneam quadratam R, longitudinis & </s> <s xml:id="echoid-s15050" xml:space="preserve">la-<lb/>titudinis ſex pollicum. </s> <s xml:id="echoid-s15051" xml:space="preserve">Extrahi poteſt hæc, & </s> <s xml:id="echoid-s15052" xml:space="preserve">variæ dantur <lb/>variis experimentis inſervientes. </s> <s xml:id="echoid-s15053" xml:space="preserve">Quæ in experimento ſe-<lb/>quenti adhibetur, à parte poſteriori in medio excavatur, ut <lb/>contineat lentem convexam, objectivam Teleſcopii ſedecim <lb/>aut viginti pedum; </s> <s xml:id="echoid-s15054" xml:space="preserve">& </s> <s xml:id="echoid-s15055" xml:space="preserve">in medio datur foramen rotundum f, <lb/>cujus diameter ſemi pollicem ſuperat, per quod, tranſeun-<lb/>do per vitrum, radii ſolares cubiculum intrant. </s> <s xml:id="echoid-s15056" xml:space="preserve">In ante-<lb/>riori parte quoque excavatur tabella Q, non tamen in medio; <lb/></s> <s xml:id="echoid-s15057" xml:space="preserve">continet cavitas hæc orbem æneum rotundum L, verſus pe-<lb/>ripheriam perforatum in f, quod foramen æquale eſt foramini <pb o="(82)" file="0592" n="653" rhead="PHYSICES ELEMENTA"/> in ipſâ tabellâ Q, & </s> <s xml:id="echoid-s15058" xml:space="preserve">cum hoc congruit. </s> <s xml:id="echoid-s15059" xml:space="preserve">Cum orbe L alius <lb/>minor concentricus & </s> <s xml:id="echoid-s15060" xml:space="preserve">circa centrum mobilis conjungitur; <lb/></s> <s xml:id="echoid-s15061" xml:space="preserve">Continet hicce foramina varia inæqualia, quæ ſucceſſivè <lb/>dum orbis rotatur tranſeunt in f; </s> <s xml:id="echoid-s15062" xml:space="preserve">ita ut ad libitum, per fo-<lb/>ramen majus aut minus, lumen locum obſcurum intret; </s> <s xml:id="echoid-s15063" xml:space="preserve">quod <lb/>in multis experimentis, quæ, ſublatâ lente memoratâ, inſti-<lb/>tuuntur, uſu venit. </s> <s xml:id="echoid-s15064" xml:space="preserve">Clavulo m cum orbe conjuncto, in gy-<lb/>rum hicce rotatur.</s> <s xml:id="echoid-s15065" xml:space="preserve"/> </p> <div xml:id="echoid-div2252" type="float" level="2" n="3"> <note position="right" xlink:label="note-0591-02" xlink:href="note-0591-02a" xml:space="preserve">854.</note> <note position="right" xlink:label="note-0591-03" xlink:href="note-0591-03a" xml:space="preserve">TAB. XV. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div2254" type="section" level="1" n="553"> <head xml:id="echoid-head731" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15066" xml:space="preserve">Trans lentem memoratam radii ſolares, per foramen dia-<lb/>metri quartæ partis pollicis, in cubiculum obſcurum intrant; <lb/></s> <s xml:id="echoid-s15067" xml:space="preserve">his, ad diſtantiam ad quam radii paralleli à lente colliguntur, <lb/>Sol exactiſſimè repræſentatur, & </s> <s xml:id="echoid-s15068" xml:space="preserve">hujus imago circìnatis li-<lb/>mitibus terminatur. </s> <s xml:id="echoid-s15069" xml:space="preserve">Nam radii à ſingulis punctis Solis, qui, <lb/>propter hujus immenſam diſtantiam, pro parallelis haberi <lb/>poſſunt, ad talem diſtantiam in unum punctum colliguntur.</s> <s xml:id="echoid-s15070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15071" xml:space="preserve">Si nunc hiſce radiis experimentum ſtatim memoratum in-<lb/> <anchor type="note" xlink:label="note-0592-01a" xlink:href="note-0592-01"/> ſtituatur, ſingulæ imagines ex radiis homogeneis, poſitâ ta-<lb/>bulâ T ad juſtam diſtantiam, exactè terminantur, ideòque <lb/>imago oblonga RV, quæ ex omnibus illis imaginibus for-<lb/>matur.</s> <s xml:id="echoid-s15072" xml:space="preserve"/> </p> <div xml:id="echoid-div2254" type="float" level="2" n="1"> <note position="left" xlink:label="note-0592-01" xlink:href="note-0592-01a" xml:space="preserve">TAB. XV. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s15073" xml:space="preserve">Procedit eodem modo hoc experimentum, ſi radii tran-<lb/>ſeant per priſma cujuſcunque materiæ aëre denſioris.</s> <s xml:id="echoid-s15074" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2256" type="section" level="1" n="554"> <head xml:id="echoid-head732" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15075" xml:space="preserve">Detur ex ligno & </s> <s xml:id="echoid-s15076" xml:space="preserve">duobus planis vitreis, priſma triangula-<lb/> <anchor type="note" xlink:label="note-0592-02a" xlink:href="note-0592-02"/> re, quod aquâ repletur; </s> <s xml:id="echoid-s15077" xml:space="preserve">tale videtur in BB, (Tab. </s> <s xml:id="echoid-s15078" xml:space="preserve">XVII. <lb/></s> <s xml:id="echoid-s15079" xml:space="preserve">fig. </s> <s xml:id="echoid-s15080" xml:space="preserve">3.) </s> <s xml:id="echoid-s15081" xml:space="preserve">hoc ſi adhibeatur loco priſmatis BB in hac fig.</s> <s xml:id="echoid-s15082" xml:space="preserve">, ex-<lb/>perimentum eodem modo procedit; </s> <s xml:id="echoid-s15083" xml:space="preserve">&</s> <s xml:id="echoid-s15084" xml:space="preserve">, tranſeundo per a-<lb/>quam, radii heterogenei eodem modo refractionibus ſepa-<lb/>rantur.</s> <s xml:id="echoid-s15085" xml:space="preserve"/> </p> <div xml:id="echoid-div2256" type="float" level="2" n="1"> <note position="left" xlink:label="note-0592-02" xlink:href="note-0592-02a" xml:space="preserve">TAB. XV. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div2258" type="section" level="1" n="555"> <head xml:id="echoid-head733" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s15086" xml:space="preserve">Si ſpectator ad diſtantiam quindecim, aut viginti pedum, <lb/>intueatur foramen, per quod lumen in cubiculum intromit-<lb/>titur, rotundum illud apparet; </s> <s xml:id="echoid-s15087" xml:space="preserve">ſi priſma triangulare vitreum, <lb/>aut aqueum in ultimo experimento memoratum, ante oculos <lb/>ponatur ita, ut radii à foramine procedentes, poſt refractio-<lb/>nes, ſimiles illis quas lumen in experimentis præcedentibus <pb o="(83)" file="0593" n="654" rhead="MATHEMATICA. LIB. III. CAP. XVIII."/> patitur, ad oculos perveniant, foramen oblongum apparebit. <lb/></s> <s xml:id="echoid-s15088" xml:space="preserve">Situs priſmatis detegitur, ſi, poſito hoc in ſitu horizontali <lb/>& </s> <s xml:id="echoid-s15089" xml:space="preserve">acie ſupernè, paululum circa axem agitetur, quo mo-<lb/>tu adſcendit & </s> <s xml:id="echoid-s15090" xml:space="preserve">deſcendit imago foraminis, & </s> <s xml:id="echoid-s15091" xml:space="preserve">priſma re-<lb/>tineatur in ſitu, in quo foramen maximè depreſſum ap-<lb/>paret.</s> <s xml:id="echoid-s15092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15093" xml:space="preserve">Probat hoc experimentum, æquè ac præcedentia, diver-<lb/>ſam radiorum refrangibilitatem; </s> <s xml:id="echoid-s15094" xml:space="preserve">nam, radiis homogeneis u-<lb/>nius cujuſque refrangibilitatis, foramen apparet in focis ima-<lb/>ginariis radiorum à ſingulis punctis foraminis procedentium <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0593-01a" xlink:href="note-0593-01"/> quæ imago rotunda eſt; </s> <s xml:id="echoid-s15095" xml:space="preserve">radii, qui variam patiuntur refra-<lb/>ctionem, juxta varias directiones oculos intrant, & </s> <s xml:id="echoid-s15096" xml:space="preserve">imagi-<lb/>nes dantur diverſæ, quæ omnes imaginem oblongam, quæ <lb/>reverâ videtur, formant.</s> <s xml:id="echoid-s15097" xml:space="preserve"/> </p> <div xml:id="echoid-div2258" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0593-01" xlink:href="note-0593-01a" xml:space="preserve">737.</note> </div> <p> <s xml:id="echoid-s15098" xml:space="preserve">Hanc autem diverſam refrangibilitatem non à medio re-<lb/> <anchor type="note" xlink:label="note-0593-02a" xlink:href="note-0593-02"/> fringente pendere, ſed ab ipſorum radiorum conſtitutione, ex <lb/>eo probatur, quod radii, qui in uno caſu maximam patiun-<lb/>tur refractionem, in tefractione quacunque à viâ maximè <lb/>deflectantur.</s> <s xml:id="echoid-s15099" xml:space="preserve"/> </p> <div xml:id="echoid-div2259" type="float" level="2" n="2"> <note position="right" xlink:label="note-0593-02" xlink:href="note-0593-02a" xml:space="preserve">855.</note> </div> </div> <div xml:id="echoid-div2261" type="section" level="1" n="556"> <head xml:id="echoid-head734" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s15100" xml:space="preserve">Iiſdem poſitis quæ in Experimento 1, ad diſtantiam quam-<lb/> <anchor type="note" xlink:label="note-0593-03a" xlink:href="note-0593-03"/> cunque à priſmate BB, cadat oblonga Solis imago in priſma <lb/>CC verticale, etiam circa axem volubile; </s> <s xml:id="echoid-s15101" xml:space="preserve">dum radii tran-<lb/>ſeunt, agitetur hoc circa axem, ſixumque relinquatur ubi <lb/>radii quantum poteſt minimè, per refractiones trans priſma, <lb/>à rectâ viâ deflectuntur; </s> <s xml:id="echoid-s15102" xml:space="preserve">in hoc caſu radii eodem modo per <lb/>hoc priſma ac per primum refranguntur; </s> <s xml:id="echoid-s15103" xml:space="preserve">non autem eo-<lb/>dem modo diſperguntur, quod quadratam formaret imagi-<lb/>nem. </s> <s xml:id="echoid-s15104" xml:space="preserve">Hæc autem, manente hujus latitudine, inclinatur in <lb/>RV, radiis in V maximè ex viâ deſlexis, ut in refractione <lb/>per primum priſma BB.</s> <s xml:id="echoid-s15105" xml:space="preserve"/> </p> <div xml:id="echoid-div2261" type="float" level="2" n="1"> <note position="right" xlink:label="note-0593-03" xlink:href="note-0593-03a" xml:space="preserve">TAB. XV. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s15106" xml:space="preserve">Demonſtratio, antea data <anchor type="note" xlink:href="" symbol="*"/>, de conſtanti ratione inter <anchor type="note" xlink:label="note-0593-04a" xlink:href="note-0593-04"/> ſinus angulorum incidentiæ & </s> <s xml:id="echoid-s15107" xml:space="preserve">refractionis, ad radios quoſcun-<lb/> <anchor type="note" xlink:label="note-0593-05a" xlink:href="note-0593-05"/> que homogeneos referri debet, poſitâ verò diverſâ refrangi-<lb/>bilitate, proportio hæc variat, ut ex experimentis hujus <lb/>capitis clarè ſequitur.</s> <s xml:id="echoid-s15108" xml:space="preserve"/> </p> <div xml:id="echoid-div2262" type="float" level="2" n="2"> <note position="right" xlink:label="note-0593-04" xlink:href="note-0593-04a" xml:space="preserve">856.</note> <note symbol="*" position="right" xlink:label="note-0593-05" xlink:href="note-0593-05a" xml:space="preserve">639.</note> </div> <p> <s xml:id="echoid-s15109" xml:space="preserve">Refrangibilitatem autem, in ſingulis radiis, omni modo eſſe <lb/> <anchor type="note" xlink:label="note-0593-06a" xlink:href="note-0593-06"/> <pb o="(84)" file="0594" n="655" rhead="PHYSICES ELEMENTA"/> immutabilem experimentis, in ſequentibus memorandis, ex-<lb/>tra omne dubium erit.</s> <s xml:id="echoid-s15110" xml:space="preserve"/> </p> <div xml:id="echoid-div2263" type="float" level="2" n="3"> <note position="right" xlink:label="note-0593-06" xlink:href="note-0593-06a" xml:space="preserve">857.</note> </div> </div> <div xml:id="echoid-div2265" type="section" level="1" n="557"> <head xml:id="echoid-head735" xml:space="preserve">CAPUT XIX.</head> <head xml:id="echoid-head736" style="it" xml:space="preserve">De Radiorum Coloribus & horum immutabilitate.</head> <p style="it"> <s xml:id="echoid-s15111" xml:space="preserve">Diverſa radiorum refrangibilitas cum diverſo colore con-<lb/> <anchor type="note" xlink:label="note-0594-01a" xlink:href="note-0594-01"/> juncta eſt; </s> <s xml:id="echoid-s15112" xml:space="preserve">& </s> <s xml:id="echoid-s15113" xml:space="preserve">ſinguli radii, pro ut magis aut minus refra-<lb/>ctione inflectuntur, colorem ſibi peculiarem, & </s> <s xml:id="echoid-s15114" xml:space="preserve">omnino im-<lb/>mutabilem, habent.</s> <s xml:id="echoid-s15115" xml:space="preserve"/> </p> <div xml:id="echoid-div2265" type="float" level="2" n="1"> <note position="left" xlink:label="note-0594-01" xlink:href="note-0594-01a" xml:space="preserve">858.</note> </div> <p> <s xml:id="echoid-s15116" xml:space="preserve">Circa colores notandum, quod circa alias ſenſationes jam <lb/>fuit notatum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15117" xml:space="preserve">colores ſunt ideæ, quæ nihil cum radiis, <anchor type="note" xlink:label="note-0594-02a" xlink:href="note-0594-02"/> quibus excitantur, commune habent: </s> <s xml:id="echoid-s15118" xml:space="preserve">definiendum ideo, <lb/>quid per radios coloratos & </s> <s xml:id="echoid-s15119" xml:space="preserve">objecta colorata intelligamus.</s> <s xml:id="echoid-s15120" xml:space="preserve"/> </p> <div xml:id="echoid-div2266" type="float" level="2" n="2"> <note symbol="*" position="left" xlink:label="note-0594-02" xlink:href="note-0594-02a" xml:space="preserve">502. 580. 716.</note> </div> </div> <div xml:id="echoid-div2268" type="section" level="1" n="558"> <head xml:id="echoid-head737" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s15121" xml:space="preserve">Objectum illo colore tinctum dicitur, cujus idea, radiis ab <lb/> <anchor type="note" xlink:label="note-0594-03a" xlink:href="note-0594-03"/> objecto reflexis, in mente excitatur.</s> <s xml:id="echoid-s15122" xml:space="preserve"/> </p> <div xml:id="echoid-div2268" type="float" level="2" n="1"> <note position="left" xlink:label="note-0594-03" xlink:href="note-0594-03a" xml:space="preserve">859.</note> </div> </div> <div xml:id="echoid-div2270" type="section" level="1" n="559"> <head xml:id="echoid-head738" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s15123" xml:space="preserve">Radii homogenei, qui in retinam impingentes, ideam ali-<lb/> <anchor type="note" xlink:label="note-0594-04a" xlink:href="note-0594-04"/> cujus coloris in mente excitant, vocantur radii illius coloris.</s> <s xml:id="echoid-s15124" xml:space="preserve"/> </p> <div xml:id="echoid-div2270" type="float" level="2" n="1"> <note position="left" xlink:label="note-0594-04" xlink:href="note-0594-04a" xml:space="preserve">860.</note> </div> <p> <s xml:id="echoid-s15125" xml:space="preserve">Dicimus radios ideam excitare, intelligimus radios ſi-<lb/>bras agitare, &</s> <s xml:id="echoid-s15126" xml:space="preserve">, occaſione hujus agitationis, ideam in men-<lb/>te dari.</s> <s xml:id="echoid-s15127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15128" xml:space="preserve">Ex experimentis capitis præcedentis, diverſum colorem <lb/> <anchor type="note" xlink:label="note-0594-05a" xlink:href="note-0594-05"/> habere radios diverſæ refrangibilitatis pleniſſimè conſtat; <lb/></s> <s xml:id="echoid-s15129" xml:space="preserve">Variis enim coloribus tincta eſt imago Solis, oblonga in illis <lb/>experimentis demonſtrata. </s> <s xml:id="echoid-s15130" xml:space="preserve">Qui radii minimè refractione à <lb/> <anchor type="note" xlink:label="note-0594-06a" xlink:href="note-0594-06"/> viâ deflectuntur rubri ſunt, reliqui colores hoc ordine ſequun-<lb/>tur, aureus, flavus, viridis, cæruleus, indicus, violaceus, <lb/>cujus ultimi coloris ſunt radii maximâ refrangibilitate præ-<lb/>diti. </s> <s xml:id="echoid-s15131" xml:space="preserve">Oblonga memorata Solis imago, ut dictum <anchor type="note" xlink:href="" symbol="*"/>, for- <anchor type="note" xlink:label="note-0594-07a" xlink:href="note-0594-07"/> matur innumeris imaginibus rotundis, ſi harum diametri mi-<lb/>nuantur, quod fit interceptis radiis ſolaribus ita, ut ſoli per <lb/>priſma tranſeant à centro Solis manantes, non mutantur cen-<lb/>tra imaginum peculiarium oblongam formantium; </s> <s xml:id="echoid-s15132" xml:space="preserve">idcirco <lb/>longitudo ah imaginis inter lineas parallelas non mutatur; </s> <s xml:id="echoid-s15133" xml:space="preserve">& </s> <s xml:id="echoid-s15134" xml:space="preserve"><lb/>hæc ſola ſupereſſet ſi infinitè parva daretur imaginis latitu- <pb file="0595" n="656"/> <pb file="0595a" n="657"/> <anchor type="figure" xlink:label="fig-0595a-01a" xlink:href="fig-0595a-01"/> <pb file="0596" n="658"/> <pb o="(85)" file="0597" n="659" rhead="MATHEMATICA LIB. III. CAP. XIX."/> do: </s> <s xml:id="echoid-s15135" xml:space="preserve">ita, ut hæc longitudo ſola conſideranda ſit in determi-<lb/>nandis colorum limitibus, in ipſâ imagine, hi in hac figurâ <lb/>litteris a, b, c, d, e, f, g, h, notantur, & </s> <s xml:id="echoid-s15136" xml:space="preserve">numerus uni-<lb/>cuique colori adſcriptus ſpatium ab hoc in imagine occupa-<lb/>tum deſignat, diviſâ totâ imaginis longitudine in partes 360.</s> <s xml:id="echoid-s15137" xml:space="preserve"/> </p> <div xml:id="echoid-div2271" type="float" level="2" n="2"> <note position="left" xlink:label="note-0594-05" xlink:href="note-0594-05a" xml:space="preserve">TAB. XVI. <lb/>fig. 1.</note> <note position="left" xlink:label="note-0594-06" xlink:href="note-0594-06a" xml:space="preserve">861.</note> <note symbol="*" position="left" xlink:label="note-0594-07" xlink:href="note-0594-07a" xml:space="preserve">853.</note> <figure xlink:label="fig-0595a-01" xlink:href="fig-0595a-01a"> <image file="0595a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0595a-01"/> </figure> </div> <p> <s xml:id="echoid-s15138" xml:space="preserve">Si latitudo imaginis Solis oblonga minuatur, magis in i-<lb/> <anchor type="note" xlink:label="note-0597-01a" xlink:href="note-0597-01"/> magine colores heterogenei ſeparantur, quia in ſingulis pun-<lb/>ctis minori numero confunduntur imagines peculiares, ex <lb/>radiis variarum refrangibilitatum parum inter ſe differentium.</s> <s xml:id="echoid-s15139" xml:space="preserve"/> </p> <div xml:id="echoid-div2272" type="float" level="2" n="3"> <note position="right" xlink:label="note-0597-01" xlink:href="note-0597-01a" xml:space="preserve">862.</note> </div> <p style="it"> <s xml:id="echoid-s15140" xml:space="preserve">Color cujuſcunque radii, ut & </s> <s xml:id="echoid-s15141" xml:space="preserve">hujus refrangibilitas, nul-<lb/> <anchor type="note" xlink:label="note-0597-02a" xlink:href="note-0597-02"/> lis refractionibus, neque reflexionibus, aut per mixtionibus <lb/>quibuſcunque mutatur.</s> <s xml:id="echoid-s15142" xml:space="preserve"/> </p> <div xml:id="echoid-div2273" type="float" level="2" n="4"> <note position="right" xlink:label="note-0597-02" xlink:href="note-0597-02a" xml:space="preserve">863.</note> </div> <p> <s xml:id="echoid-s15143" xml:space="preserve">De refractione & </s> <s xml:id="echoid-s15144" xml:space="preserve">reflectione in hoc capite, de permixtio-<lb/>ne in ſequenti, agam.</s> <s xml:id="echoid-s15145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15146" xml:space="preserve">Refrangibilitatem refractione non mutari in exp. </s> <s xml:id="echoid-s15147" xml:space="preserve">5. </s> <s xml:id="echoid-s15148" xml:space="preserve">cap. <lb/></s> <s xml:id="echoid-s15149" xml:space="preserve"> <anchor type="note" xlink:label="note-0597-03a" xlink:href="note-0597-03"/> præcedentis probatur; </s> <s xml:id="echoid-s15150" xml:space="preserve">quod & </s> <s xml:id="echoid-s15151" xml:space="preserve">etiam ad colorem referri po-<lb/>teſt; </s> <s xml:id="echoid-s15152" xml:space="preserve">hæc eadem experimento ſequenti clariùs evincuntur. <lb/></s> <s xml:id="echoid-s15153" xml:space="preserve">Circa quod notandum, quod & </s> <s xml:id="echoid-s15154" xml:space="preserve">de ſequentibus etiam dicen-<lb/>dum eſt, experimenta inſtituenda eſſe cum priſmatibus ex <lb/>vitro puro venulis immune, his enim irregulariter lumen in <lb/>priſmate movetur & </s> <s xml:id="echoid-s15155" xml:space="preserve">radii refractionibus non ritè ſeparantur.</s> <s xml:id="echoid-s15156" xml:space="preserve"/> </p> <div xml:id="echoid-div2274" type="float" level="2" n="5"> <note position="right" xlink:label="note-0597-03" xlink:href="note-0597-03a" xml:space="preserve">864.</note> </div> </div> <div xml:id="echoid-div2276" type="section" level="1" n="560"> <head xml:id="echoid-head739" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s15157" xml:space="preserve">Rebus diſpoſitis ut in exp. </s> <s xml:id="echoid-s15158" xml:space="preserve">1. </s> <s xml:id="echoid-s15159" xml:space="preserve">capitis præcedentis, inſti-<lb/> <anchor type="note" xlink:label="note-0597-04a" xlink:href="note-0597-04"/> tuitur experimentum cum radio ſolari per foramen intrante, <lb/>cujus diameter eſt ſemi pollicis; </s> <s xml:id="echoid-s15160" xml:space="preserve">ſuſtentaculum autem S <lb/>priſmatis tale eſt, ut inter latera moveatur tabella t, quæ in <lb/>hoc experimento uſu venit, in hac datur foramen F diame-<lb/>tri octavæ partis unius pollicis, per hoc tranſmittitur lumen <lb/>à priſmate refractum, quo radii in oblongâ imagine melius <lb/>inter ſe ſeparantur, radiis magnâ parte interceptis; </s> <s xml:id="echoid-s15161" xml:space="preserve">imago <lb/>hæc oblonga RV, ad diſtantiam decem aut duodecim pe-<lb/>dum à priſmate, cadit in tabellam t, ſuſtentaculi ſimilis <lb/>priori, in quâ tabellâ etiam exiguum, ut in primâ, datur <lb/>foramen F; </s> <s xml:id="echoid-s15162" xml:space="preserve">per quod radii tranſeunt, qui in ſecundum ca-<lb/>dunt priſma, huic ſuſtentaculo impoſitum, & </s> <s xml:id="echoid-s15163" xml:space="preserve">refringuntur <lb/>eodem modo ac per primum; </s> <s xml:id="echoid-s15164" xml:space="preserve">paululum circa axem agitan-<lb/>do primum priſma, adſcendit aut deſcendit imago RV, quo <pb o="(86)" file="0598" n="660" rhead="PHYSICES ELEMENTA"/> ſucceſſivè per foramen radii varii tranſmittuntur; </s> <s xml:id="echoid-s15165" xml:space="preserve">in omni <lb/>caſu radii, per ſecundum priſma refracti, & </s> <s xml:id="echoid-s15166" xml:space="preserve">in tabulam T, <lb/>chartâ albâ obtectam, impingentes, in H non diſperguntur <lb/>ſed rotunda eſt imago, ſi radii perpendiculariter in chartam <lb/>cadant, etiam ejuſdem coloris cum radiis in ſecundum priſ-<lb/>ma cadentibus. </s> <s xml:id="echoid-s15167" xml:space="preserve">Imago tamen Heo magis elevatur, quo ra-<lb/>dii, in refractione, per priſma primum magis à viâ deflectun-<lb/>tur, id eſt, magis refrangibiles in uno caſu, in alio caſu <lb/>etiam majorem patiuntur refractionem.</s> <s xml:id="echoid-s15168" xml:space="preserve"/> </p> <div xml:id="echoid-div2276" type="float" level="2" n="1"> <note position="right" xlink:label="note-0597-04" xlink:href="note-0597-04a" xml:space="preserve">TAB. XVI. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s15169" xml:space="preserve">Refrangibilitatem & </s> <s xml:id="echoid-s15170" xml:space="preserve">colorem neque reflectione mutari <lb/> <anchor type="note" xlink:label="note-0598-01a" xlink:href="note-0598-01"/> experimentis ſequentibus patebit.</s> <s xml:id="echoid-s15171" xml:space="preserve"/> </p> <div xml:id="echoid-div2277" type="float" level="2" n="2"> <note position="left" xlink:label="note-0598-01" xlink:href="note-0598-01a" xml:space="preserve">865.</note> </div> </div> <div xml:id="echoid-div2279" type="section" level="1" n="561"> <head xml:id="echoid-head740" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15172" xml:space="preserve">Radii partem, ex. </s> <s xml:id="echoid-s15173" xml:space="preserve">gr. </s> <s xml:id="echoid-s15174" xml:space="preserve">rubram, imaginis oblongæ colora-<lb/>tæ ſæpius memoratæ formantes, à quocunque corpore re-<lb/>flectantur, rubri ſunt; </s> <s xml:id="echoid-s15175" xml:space="preserve">id eſt, omnia corpora in illo lumine <lb/>rubra ſunt: </s> <s xml:id="echoid-s15176" xml:space="preserve">in lumine violaceo ſunt violacea; </s> <s xml:id="echoid-s15177" xml:space="preserve">in viride ſunt <lb/>viridia; </s> <s xml:id="echoid-s15178" xml:space="preserve">& </s> <s xml:id="echoid-s15179" xml:space="preserve">ſic de cæteris. </s> <s xml:id="echoid-s15180" xml:space="preserve">Patet hoc, ſi illud tentetur cum <lb/>minio, auripigmento, cœruleo montano, panno utcunque <lb/>tincto, &</s> <s xml:id="echoid-s15181" xml:space="preserve">c.</s> <s xml:id="echoid-s15182" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2280" type="section" level="1" n="562"> <head xml:id="echoid-head741" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15183" xml:space="preserve">Intret lumen cubiculum obſcurum per duo foramina, dia-<lb/> <anchor type="note" xlink:label="note-0598-02a" xlink:href="note-0598-02"/> metri quartæ partis pollicis, in laminâ retundâ volubili, quæ <lb/>in feneſtrâ datur; </s> <s xml:id="echoid-s15184" xml:space="preserve">ſit diſtantia inter hæc circiter duorum pol-<lb/>licum; </s> <s xml:id="echoid-s15185" xml:space="preserve">radii à ſpeculo plano S reflectantur.</s> <s xml:id="echoid-s15186" xml:space="preserve"/> </p> <div xml:id="echoid-div2280" type="float" level="2" n="1"> <note position="left" xlink:label="note-0598-02" xlink:href="note-0598-02a" xml:space="preserve">TAB. XVI. <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s15187" xml:space="preserve">Ita diſponenda lamina & </s> <s xml:id="echoid-s15188" xml:space="preserve">ſpeculum, ut radii in duo priſma-<lb/>ta AA, AA, quæ eidem ſuſtentaculo horizontaliter im-<lb/>ponuntur, incidant; </s> <s xml:id="echoid-s15189" xml:space="preserve">& </s> <s xml:id="echoid-s15190" xml:space="preserve">ut imagines oblongæ, refractionibus <lb/>horum priſmatum formatæ, ad latus ſeſe mutuo tangant. </s> <s xml:id="echoid-s15191" xml:space="preserve">Pau-<lb/>lulum circa axem agitetur priſma unum, ut color ruber u-<lb/>nius imaginis detur ad latus violacei alterius. </s> <s xml:id="echoid-s15192" xml:space="preserve">Intercipiantur <lb/>hi colores, & </s> <s xml:id="echoid-s15193" xml:space="preserve">quidem ſoli, regulâ ligneâ LL, chartâ albâ <lb/>obtectâ, in qua color ille in R hicce in V videtur, dum reli-<lb/>quum utriuſque imaginis in parietem, panno nigro obte-<lb/>ctum, cadit. </s> <s xml:id="echoid-s15194" xml:space="preserve">Si ſpectator in O, per priſma BB, intueatur <lb/>colores hos R & </s> <s xml:id="echoid-s15195" xml:space="preserve">V, ut de foramine in exp. </s> <s xml:id="echoid-s15196" xml:space="preserve">4. </s> <s xml:id="echoid-s15197" xml:space="preserve">capitis præ-<lb/>cedentis dictum, videbit colores, inter ſe ſeparatos, ru-<lb/>brum in r, violaceum in v; </s> <s xml:id="echoid-s15198" xml:space="preserve">qui ergo reflexus, tranſeundo per <pb o="(87)" file="0599" n="661" rhead="MATHEMATICA LIB. III. CAP. XIX."/> priſma BB, majorem patitur refractionem.</s> <s xml:id="echoid-s15199" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15200" xml:space="preserve">In experimento 1. </s> <s xml:id="echoid-s15201" xml:space="preserve">hujus capitis dedimus methodum, qua <lb/>radii heterogenei melius ſeparantur quàm in aliis experimen-<lb/>tis; </s> <s xml:id="echoid-s15202" xml:space="preserve">in ſequenti experimento lumina diverſorum colorum <lb/> <anchor type="note" xlink:label="note-0599-01a" xlink:href="note-0599-01"/> multò magis homogenea fiunt, quod in ſexto hujus capitis <lb/>experimento requiritur.</s> <s xml:id="echoid-s15203" xml:space="preserve"/> </p> <div xml:id="echoid-div2281" type="float" level="2" n="2"> <note position="right" xlink:label="note-0599-01" xlink:href="note-0599-01a" xml:space="preserve">866.</note> </div> </div> <div xml:id="echoid-div2283" type="section" level="1" n="563"> <head xml:id="echoid-head742" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s15204" xml:space="preserve">Intret lumen cubiculum tenebricoſum per foramen, cujus <lb/> <anchor type="note" xlink:label="note-0599-02a" xlink:href="note-0599-02"/> diameter ſit pars octava pollicis; </s> <s xml:id="echoid-s15205" xml:space="preserve">radius Solis, priſmate AA, <lb/>ad lentem convexam V, pede ſuſtentatam & </s> <s xml:id="echoid-s15206" xml:space="preserve">cujus diameter <lb/>eſt trium aut quatuor pollicum, reflectitur; </s> <s xml:id="echoid-s15207" xml:space="preserve">longitudo ra-<lb/>diorum incidentis & </s> <s xml:id="echoid-s15208" xml:space="preserve">reflexi conjunctorum, eſt circiter ſe-<lb/>ptem pedum; </s> <s xml:id="echoid-s15209" xml:space="preserve">lentis convexitas talis eſt, ut, ad diſtantiam <lb/>decem aut duodecim pedum à lente, dentur foci radiorum à <lb/>ſingulis punctis foraminis procedentium, quibus focis fora-<lb/>men poteſt in chartâ repræſentari <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15210" xml:space="preserve">Immediatè poſt len- <anchor type="note" xlink:label="note-0599-03a" xlink:href="note-0599-03"/> tem ponitur priſma BB, quo radii, ut in exp. </s> <s xml:id="echoid-s15211" xml:space="preserve">1. </s> <s xml:id="echoid-s15212" xml:space="preserve">cap. </s> <s xml:id="echoid-s15213" xml:space="preserve">præceden-<lb/>tis, diſperguntur; </s> <s xml:id="echoid-s15214" xml:space="preserve">poſitâ autem tabulâ T, ad diſtantiam ad <lb/>quam à ſingulis punctis foraminis radii colliguntur, dabitur <lb/>circinata imago oblonga colorata RV, cujus longitudo ad <lb/>latitudinem majorem proportionem habebit, quàm in aliis ex-<lb/>perimentis; </s> <s xml:id="echoid-s15215" xml:space="preserve">& </s> <s xml:id="echoid-s15216" xml:space="preserve">quæ ideò conſtat ex radiis magis homoge-<lb/>neis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15217" xml:space="preserve">& </s> <s xml:id="echoid-s15218" xml:space="preserve">eo minus permixtis, quo foramen in feneſtrâ mi- <anchor type="note" xlink:label="note-0599-04a" xlink:href="note-0599-04"/> nus eſt. </s> <s xml:id="echoid-s15219" xml:space="preserve">Admovendo & </s> <s xml:id="echoid-s15220" xml:space="preserve">removendo tabulam T, detegitur <lb/>diſtantia, ad quam imago maximè eſt diſtincta & </s> <s xml:id="echoid-s15221" xml:space="preserve">ſine penum-<lb/>brâ terminata.</s> <s xml:id="echoid-s15222" xml:space="preserve"/> </p> <div xml:id="echoid-div2283" type="float" level="2" n="1"> <note position="right" xlink:label="note-0599-02" xlink:href="note-0599-02a" xml:space="preserve">TAB. XVII. <lb/>fig 1.</note> <note symbol="*" position="right" xlink:label="note-0599-03" xlink:href="note-0599-03a" xml:space="preserve">711.</note> <note symbol="*" position="right" xlink:label="note-0599-04" xlink:href="note-0599-04a" xml:space="preserve">862.</note> </div> <p> <s xml:id="echoid-s15223" xml:space="preserve">Radios autèm in hoc Experimento ſeparatos, ſatis eſſe <lb/>homogeneos, ex eo probatur, quod novâ refractione non <lb/>diſpergantur; </s> <s xml:id="echoid-s15224" xml:space="preserve">hanc autem eſſe homogeneorum proprietatem, <lb/>ex æquali refrangibilitate ſequitur; </s> <s xml:id="echoid-s15225" xml:space="preserve">quod jam experimento <lb/>fuit confirmatum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15226" xml:space="preserve">plenius ſequenti demonſtratur.</s> <s xml:id="echoid-s15227" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">864.</note> </div> <div xml:id="echoid-div2285" type="section" level="1" n="564"> <head xml:id="echoid-head743" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s15228" xml:space="preserve">Si duo circuli chartacei, diametri circiter unius pollicis, <lb/>illuminentur, unus radiis homogeneis coloris cujuſcunque, <lb/>alter radiis ſolaribus; </s> <s xml:id="echoid-s15229" xml:space="preserve">ſi ambo per priſma ad diſtantiam ali-<lb/>quot pedum obſerventur, ut in exp. </s> <s xml:id="echoid-s15230" xml:space="preserve">3. </s> <s xml:id="echoid-s15231" xml:space="preserve">hujus capitis; </s> <s xml:id="echoid-s15232" xml:space="preserve">circu-<lb/>lus, colore heterogeneo illuminatus, oblongus apparet, & </s> <s xml:id="echoid-s15233" xml:space="preserve">va- <pb o="(88)" file="0600" n="662" rhead="PHYSICES ELEMENTA"/> riis coloribus tinctus, ut in Exp. </s> <s xml:id="echoid-s15234" xml:space="preserve">4. </s> <s xml:id="echoid-s15235" xml:space="preserve">capitis præceden-<lb/>tis; </s> <s xml:id="echoid-s15236" xml:space="preserve">alterius verò circuli neque color neque figura mu-<lb/>tatur.</s> <s xml:id="echoid-s15237" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2286" type="section" level="1" n="565"> <head xml:id="echoid-head744" xml:space="preserve"><emph style="sc">Experimentum</emph> 6.</head> <p> <s xml:id="echoid-s15238" xml:space="preserve">In chartâ albâ ducantur lineæ nigræ inter ſe parallelæ, & </s> <s xml:id="echoid-s15239" xml:space="preserve"><lb/>latæ circiter decimam ſextam pollicis partem; </s> <s xml:id="echoid-s15240" xml:space="preserve">illuminentur <lb/>hæ oblongâ imagine, de qua in experimento quarto, ita, <lb/>ut lineæ juxta imaginis longitudinem dirigantur. </s> <s xml:id="echoid-s15241" xml:space="preserve">Detur ul-<lb/>terius lens convexa, diametri quinque aut ſex pollicum, pe-<lb/>de ſuſtentata, qualis datur in V (Tab. </s> <s xml:id="echoid-s15242" xml:space="preserve"><emph style="sc">XIX</emph>. </s> <s xml:id="echoid-s15243" xml:space="preserve">fig. </s> <s xml:id="echoid-s15244" xml:space="preserve">2.)</s> <s xml:id="echoid-s15245" xml:space="preserve">, quæ ra-<lb/>dios rubros, à puncto radiante emiſſos à vitro ſex pedes di-<lb/>ſtanti, ad diſtantiam æqualem colligit. </s> <s xml:id="echoid-s15246" xml:space="preserve">Si lens hæc detur ad <lb/>diſtantiam ſex pedum ab imagine memoratâ, partes linea-<lb/>rum, quæ in colore rubro dantur, in chartâ, per radios à <lb/>lente collectos, ad diſtantiam etiam ſex pedum exactè re-<lb/>præſentantur, in imagine rubrâ; </s> <s xml:id="echoid-s15247" xml:space="preserve">admovenda autem eſt char-<lb/>ta circiter tres pollices cum ſemiſle, ut partes linearum, <lb/>colore indico illuminatæ, dìſtinctæ appareant, in imagine <lb/>ejuſdem coloris; </s> <s xml:id="echoid-s15248" xml:space="preserve">colores intermedii dant imagines ad di-<lb/>ſtantias intermedias; </s> <s xml:id="echoid-s15249" xml:space="preserve">violaceus adeo eſt debilis, ut fila in hoc <lb/>repræſentari nequeant.</s> <s xml:id="echoid-s15250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15251" xml:space="preserve">Confirmat ergo & </s> <s xml:id="echoid-s15252" xml:space="preserve">hoc experimentum, reflexorum radio-<lb/>rum colorem novâ refractione per lentem non mutari; </s> <s xml:id="echoid-s15253" xml:space="preserve">ut <lb/>& </s> <s xml:id="echoid-s15254" xml:space="preserve">radios maximè refrangibiles, tranſeundo per lentem aliis <lb/>magis inflecti.</s> <s xml:id="echoid-s15255" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15256" xml:space="preserve">Probat etiam Experimentum hoc ultimum, diverſam ra-<lb/> <anchor type="note" xlink:label="note-0600-01a" xlink:href="note-0600-01"/> diorum refrangibilitatem in cauſâ eſſe, quo minus Teleſcopia <lb/>ſint perfecta. </s> <s xml:id="echoid-s15257" xml:space="preserve">Foci enim punctorum æquè diſtantium, ad <lb/>varias à lente diſtantias dantur, pro vario colore; </s> <s xml:id="echoid-s15258" xml:space="preserve">unde e-<lb/>tiam inæqualiter, â lente oculari diſtant, punctorum repræ-<lb/>ſentationes; </s> <s xml:id="echoid-s15259" xml:space="preserve">quæ ideo per hanc non omnes perfectè videri <lb/>queunt.</s> <s xml:id="echoid-s15260" xml:space="preserve"/> </p> <div xml:id="echoid-div2286" type="float" level="2" n="1"> <note position="left" xlink:label="note-0600-01" xlink:href="note-0600-01a" xml:space="preserve">867.</note> </div> <p> <s xml:id="echoid-s15261" xml:space="preserve">Circa reflexionem radiorum notandum, radios in totum <lb/> <anchor type="note" xlink:label="note-0600-02a" xlink:href="note-0600-02"/> facilius reflecti, qui majorem habent refrangibilitatem; </s> <s xml:id="echoid-s15262" xml:space="preserve">nam <lb/>quo major datur radiorum refractio, quo minor requiritur <lb/>obliquitas ut omnes reflectantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15263" xml:space="preserve"/> </p> <div xml:id="echoid-div2287" type="float" level="2" n="2"> <note position="left" xlink:label="note-0600-02" xlink:href="note-0600-02a" xml:space="preserve">868.</note> </div> <note symbol="*" position="left" xml:space="preserve">793.</note> <pb o="(89)" file="0601" n="663" rhead="MATHEMATICA LIB. III. CAP. XX."/> </div> <div xml:id="echoid-div2289" type="section" level="1" n="566"> <head xml:id="echoid-head745" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s15264" xml:space="preserve">Detur priſma diſpoſitum ut ante memoratum <anchor type="note" xlink:href="" symbol="*"/>, ubi vi- <anchor type="note" xlink:label="note-0601-01a" xlink:href="note-0601-01"/> dimus, agitando priſma circa axem, radios primò tranſeun-<lb/>tes, auctâ horum inclinatione, in totum reflecti; </s> <s xml:id="echoid-s15265" xml:space="preserve">ſi autem <lb/>lentè in hoc caſu priſma moveatur, videmus radios violaceos <lb/>ante omnes alios in totum reflecti, deinde indicos; </s> <s xml:id="echoid-s15266" xml:space="preserve">& </s> <s xml:id="echoid-s15267" xml:space="preserve">cæ-<lb/>teros alios eo ordine, quo in imagine Solis oblongâ, ſæpiſſi-<lb/>mè memorata, diſponuntur: </s> <s xml:id="echoid-s15268" xml:space="preserve">quod patet ſi reflexi, priſmatis <lb/>refractione, ſeparentur.</s> <s xml:id="echoid-s15269" xml:space="preserve"/> </p> <div xml:id="echoid-div2289" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0601-01" xlink:href="note-0601-01a" xml:space="preserve">790.</note> </div> </div> <div xml:id="echoid-div2291" type="section" level="1" n="567"> <head xml:id="echoid-head746" xml:space="preserve">CAPUT XX.</head> <head xml:id="echoid-head747" style="it" xml:space="preserve">De Colorum permixtione, ubi de Albore.</head> <p> <s xml:id="echoid-s15270" xml:space="preserve">RAdiorum refrangibilitatem, & </s> <s xml:id="echoid-s15271" xml:space="preserve">colorem, permixtione <lb/> <anchor type="note" xlink:label="note-0601-02a" xlink:href="note-0601-02"/> radiorum variæ refrangibilitatis non mutari dictum <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s15272" xml:space="preserve"> <anchor type="note" xlink:label="note-0601-03a" xlink:href="note-0601-03"/> quod experimentis probandum eſt.</s> <s xml:id="echoid-s15273" xml:space="preserve"/> </p> <div xml:id="echoid-div2291" type="float" level="2" n="1"> <note position="right" xlink:label="note-0601-02" xlink:href="note-0601-02a" xml:space="preserve">869.</note> <note symbol="*" position="right" xlink:label="note-0601-03" xlink:href="note-0601-03a" xml:space="preserve">863.</note> </div> </div> <div xml:id="echoid-div2293" type="section" level="1" n="568"> <head xml:id="echoid-head748" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s15274" xml:space="preserve">Inſtituitur hoc, ut tertium capitis præcedentis; </s> <s xml:id="echoid-s15275" xml:space="preserve">in hoc co-<lb/> <anchor type="note" xlink:label="note-0601-04a" xlink:href="note-0601-04"/> lor ruber R, & </s> <s xml:id="echoid-s15276" xml:space="preserve">violaceus V, confunduntur, in eodem lo-<lb/>co regulæ LL cadentes, quæ purpurea in eo loco appa-<lb/>ret. </s> <s xml:id="echoid-s15277" xml:space="preserve">Spectatori tamen, qui hos per priſma BB intuetur, <lb/>ſeparati apparent colores, & </s> <s xml:id="echoid-s15278" xml:space="preserve">neque color, neque refran-<lb/>gibilitas, hac colorum confuſione mutantur.</s> <s xml:id="echoid-s15279" xml:space="preserve"/> </p> <div xml:id="echoid-div2293" type="float" level="2" n="1"> <note position="right" xlink:label="note-0601-04" xlink:href="note-0601-04a" xml:space="preserve">TAB. XVI. <lb/>fig. 3.</note> </div> </div> <div xml:id="echoid-div2295" type="section" level="1" n="569"> <head xml:id="echoid-head749" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15280" xml:space="preserve">Si oblonga colorata Solis imago, (de qua in exp. </s> <s xml:id="echoid-s15281" xml:space="preserve">1. </s> <s xml:id="echoid-s15282" xml:space="preserve">cap. </s> <s xml:id="echoid-s15283" xml:space="preserve">18.) <lb/></s> <s xml:id="echoid-s15284" xml:space="preserve"> <anchor type="note" xlink:label="note-0601-05a" xlink:href="note-0601-05"/> cadat in RV in lentem convexam L, in exp. </s> <s xml:id="echoid-s15285" xml:space="preserve">4. </s> <s xml:id="echoid-s15286" xml:space="preserve">cap. </s> <s xml:id="echoid-s15287" xml:space="preserve">præ-<lb/>cedentis memoratam, & </s> <s xml:id="echoid-s15288" xml:space="preserve">ad diſtantiam ſex aut ſeptem pe-<lb/>dum à priſmate BB diſpoſitam, radii divergentes refra-<lb/>ctione lentis convergunt, & </s> <s xml:id="echoid-s15289" xml:space="preserve">ad diſtantiam novem aut de-<lb/>cem pedum ſeſe mutuo interſecant in A; </s> <s xml:id="echoid-s15290" xml:space="preserve">ſi ad majorem di-<lb/>ſtantiam detur Tabula T, radii, qui poſt interſectionem ite-<lb/>rum divergunt, diſperſi ad hanc perveniunt; </s> <s xml:id="echoid-s15291" xml:space="preserve">daturque ite-<lb/>rum imago oblonga colorata, ſed colores, propter interſe-<lb/>ctionem in A, contrario ordine diſponuntur, non tamen, <lb/>permixtione in A, mutantur.</s> <s xml:id="echoid-s15292" xml:space="preserve"/> </p> <div xml:id="echoid-div2295" type="float" level="2" n="1"> <note position="right" xlink:label="note-0601-05" xlink:href="note-0601-05a" xml:space="preserve">TAB. XVII. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div2297" type="section" level="1" n="570"> <head xml:id="echoid-head750" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15293" xml:space="preserve">Omnibus manentibus, ut in Exp. </s> <s xml:id="echoid-s15294" xml:space="preserve">præcedenti; </s> <s xml:id="echoid-s15295" xml:space="preserve">ſi chartâ <lb/> <anchor type="note" xlink:label="note-0601-06a" xlink:href="note-0601-06"/> <pb o="(90)" file="0602" n="664" rhead="PHYSICES ELEMENTA"/> nigrâ radii quidam imaginis RV intercipiantur, quod mu-<lb/>tat permixtionem, quæ hac methodo ad libitum variatur, <lb/>radiorum cæterorum iterum ſeparatorum colores non mu-<lb/>tantur.</s> <s xml:id="echoid-s15296" xml:space="preserve"/> </p> <div xml:id="echoid-div2297" type="float" level="2" n="1"> <note position="right" xlink:label="note-0601-06" xlink:href="note-0601-06a" xml:space="preserve">TAB. XVII <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s15297" xml:space="preserve">Si radii ſolares, ut ad nos perveniunt, in totum ab ali-<lb/> <anchor type="note" xlink:label="note-0602-01a" xlink:href="note-0602-01"/> quo corpore reflectantur, hoc album apparet; </s> <s xml:id="echoid-s15298" xml:space="preserve">radii autem hi <lb/>ſunt congeries radiorum variorum colorum <anchor type="note" xlink:href="" symbol="*"/>, unde deduci- <anchor type="note" xlink:label="note-0602-02a" xlink:href="note-0602-02"/> mus permixtionem colorum variorum conſtituere albedinem; <lb/></s> <s xml:id="echoid-s15299" xml:space="preserve"> <anchor type="note" xlink:label="note-0602-03a" xlink:href="note-0602-03"/> ſi enim colores, qui obſervantur in oblongâ Solis imagine, <lb/>ſæpius memoratâ, eâ proportione, qua in illâ imagine dantur, <lb/>inter ſe confundantur, conflatur albedo: </s> <s xml:id="echoid-s15300" xml:space="preserve">quod & </s> <s xml:id="echoid-s15301" xml:space="preserve">eo reſpectu <lb/>radios immutabiles probat. </s> <s xml:id="echoid-s15302" xml:space="preserve">A Sole procedentes radii albi ap-<lb/>parent, ſi ſeparantur horum colores deteguntur, iterum per-<lb/>mixti reſtituitur albor.</s> <s xml:id="echoid-s15303" xml:space="preserve"/> </p> <div xml:id="echoid-div2298" type="float" level="2" n="2"> <note position="left" xlink:label="note-0602-01" xlink:href="note-0602-01a" xml:space="preserve">870.</note> <note symbol="*" position="left" xlink:label="note-0602-02" xlink:href="note-0602-02a" xml:space="preserve">847. 858.</note> <note position="left" xlink:label="note-0602-03" xlink:href="note-0602-03a" xml:space="preserve">871.</note> </div> </div> <div xml:id="echoid-div2300" type="section" level="1" n="571"> <head xml:id="echoid-head751" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s15304" xml:space="preserve">Omnibus manentibus, ut in Experimentis duobus præce-<lb/> <anchor type="note" xlink:label="note-0602-04a" xlink:href="note-0602-04"/> dentibus; </s> <s xml:id="echoid-s15305" xml:space="preserve">ponatur tabula T in A, in ipſo loco ubi omnes <lb/>radii imaginis RV confunduntur; </s> <s xml:id="echoid-s15306" xml:space="preserve">albedo dabitur in A; </s> <s xml:id="echoid-s15307" xml:space="preserve">ſi <lb/>color ruber imaginis RV chartâ nigrâ intercipiatur, eva-<lb/>neſcit albedo, & </s> <s xml:id="echoid-s15308" xml:space="preserve">color in A ad cæruleum vergit; </s> <s xml:id="echoid-s15309" xml:space="preserve">interceptis <lb/>verò radiis violaceis & </s> <s xml:id="echoid-s15310" xml:space="preserve">cæruleis, rubeſcit albor.</s> <s xml:id="echoid-s15311" xml:space="preserve"/> </p> <div xml:id="echoid-div2300" type="float" level="2" n="1"> <note position="left" xlink:label="note-0602-04" xlink:href="note-0602-04a" xml:space="preserve">TAB. XVII. <lb/>fig. 2.</note> </div> </div> <div xml:id="echoid-div2302" type="section" level="1" n="572"> <head xml:id="echoid-head752" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s15312" xml:space="preserve">Dentur priſmata triangularia tria, ex ligno, & </s> <s xml:id="echoid-s15313" xml:space="preserve">laminis vi-<lb/> <anchor type="note" xlink:label="note-0602-05a" xlink:href="note-0602-05"/> treis, conſtructa, aquam continentia, BB, DD, DD; <lb/></s> <s xml:id="echoid-s15314" xml:space="preserve">laminæ vitreæ in ſingulis inter ſe formant angulos æquales, <lb/>circiter 70. </s> <s xml:id="echoid-s15315" xml:space="preserve">gr.</s> <s xml:id="echoid-s15316" xml:space="preserve">; longitudo laminarum eſt ſex aut ſeptem <lb/>pollicum, latitudo trium pollicum; </s> <s xml:id="echoid-s15317" xml:space="preserve">hæ aliter in priſmati-<lb/>bus DD, DD, quâm in priſmate BB, diſponuntur; </s> <s xml:id="echoid-s15318" xml:space="preserve">ita <lb/>ut illorum baſes majores ſint. </s> <s xml:id="echoid-s15319" xml:space="preserve">Refringuntur radii ſolares per <lb/>priſma BB, ut in Exp. </s> <s xml:id="echoid-s15320" xml:space="preserve">3. </s> <s xml:id="echoid-s15321" xml:space="preserve">capitis 18.</s> <s xml:id="echoid-s15322" xml:space="preserve">, & </s> <s xml:id="echoid-s15323" xml:space="preserve">ad diſtantiam trium <lb/>aut quatuor pedum cadit oblonga Solis imàgo in faciem <lb/>priſmatis DD, poſitam in ſitu parallelo faciei priſmatis BB <lb/>ex qua radii exeunt. </s> <s xml:id="echoid-s15324" xml:space="preserve">In ſecundo priſmate radii contrariam <lb/>patiuntur refractionem, quàm in primo; </s> <s xml:id="echoid-s15325" xml:space="preserve">proprer paralle-<lb/>liſmum memoratum, & </s> <s xml:id="echoid-s15326" xml:space="preserve">quia acies anguli à planis vitreis for-<lb/>mati in priſmate BB ſurſum, in DD deorſum datur. </s> <s xml:id="echoid-s15327" xml:space="preserve">Id-<lb/>circo ſecundâ refractione deſtruitur prima, & </s> <s xml:id="echoid-s15328" xml:space="preserve">radii paralleli <pb file="0603" n="665"/> <pb file="0603a" n="666"/> <anchor type="figure" xlink:label="fig-0603a-01a" xlink:href="fig-0603a-01"/> <pb file="0604" n="667"/> <pb o="91" file="0605" n="668" rhead="MATHEMATICA LIB. III. CAP. XX."/> inter ſe ex priſmate DD in RV exeunt, nam admotis <lb/>priſmatibus ita, ut facies parallelæ ſeſe mutuo tangant, tran-<lb/>ſibit lumen per medium planis parallelis terminatum, quod <lb/>ambo priſmata conjuncta formant, per quod lumen cu-<lb/>juſcunque refrangibilitatis ſine directionis mutatione tran-<lb/>ſit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15329" xml:space="preserve">Separantur autem priſmata, ut radii heterogenei ſe- <anchor type="note" xlink:label="note-0605-01a" xlink:href="note-0605-01"/> parentur, antequam paralleli iterum fiant; </s> <s xml:id="echoid-s15330" xml:space="preserve">ſi hi radii colora-<lb/>ti cadant in tertium priſma DD, &</s> <s xml:id="echoid-s15331" xml:space="preserve">, per hoc tranſeundo, <lb/>patiantur refractionem ſimilem illi, quàm in primo aut ſecun-<lb/>do priſmate paſſi ſunt; </s> <s xml:id="echoid-s15332" xml:space="preserve">radii in rv exeuntes convergunt, <lb/>ex inæqualibus refractionibus in radiis diverſorum colorum, <lb/>& </s> <s xml:id="echoid-s15333" xml:space="preserve">in A concurrunt, in quo loco etiam albor datur, ut in <lb/>Experimento præcedenti.</s> <s xml:id="echoid-s15334" xml:space="preserve"/> </p> <div xml:id="echoid-div2302" type="float" level="2" n="1"> <note position="left" xlink:label="note-0602-05" xlink:href="note-0602-05a" xml:space="preserve">TAB. XVII. <lb/>fig. 3.</note> <figure xlink:label="fig-0603a-01" xlink:href="fig-0603a-01a"> <image file="0603a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0603a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0605-01" xlink:href="note-0605-01a" xml:space="preserve">628.</note> </div> </div> <div xml:id="echoid-div2304" type="section" level="1" n="573"> <head xml:id="echoid-head753" xml:space="preserve"><emph style="sc">Experimentum</emph>. 6.</head> <p> <s xml:id="echoid-s15335" xml:space="preserve">Si imago Solis oblonga colorata, ut in Exp. </s> <s xml:id="echoid-s15336" xml:space="preserve"><emph style="sc">I</emph>. </s> <s xml:id="echoid-s15337" xml:space="preserve">Cap. </s> <s xml:id="echoid-s15338" xml:space="preserve">18.</s> <s xml:id="echoid-s15339" xml:space="preserve">; <lb/>detur, & </s> <s xml:id="echoid-s15340" xml:space="preserve">ſpectator ad diſtantiam priſmatis, lumen refrin-<lb/>gentis, imaginem intueatur, ut de formaine in Exp. </s> <s xml:id="echoid-s15341" xml:space="preserve">4. </s> <s xml:id="echoid-s15342" xml:space="preserve">ejuſ-<lb/>dem Capitis dictum, rotundam & </s> <s xml:id="echoid-s15343" xml:space="preserve">albam videbit imagi-<lb/>nem; </s> <s xml:id="echoid-s15344" xml:space="preserve">ſecundâ refractione primam deſtruente; </s> <s xml:id="echoid-s15345" xml:space="preserve">quo radii <lb/>iterum permixti oculum intrant, quibus in hoc caſu ima-<lb/>go alba apparet.</s> <s xml:id="echoid-s15346" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15347" xml:space="preserve">Non omnium, qui in imagine Solis oblongâ obſervantur, <lb/> <anchor type="note" xlink:label="note-0605-02a" xlink:href="note-0605-02"/> colorum permixtio ad albedinem conflandam neceſſaria eſt, <lb/>ipſe radiorum ſolarium albor paululum ad flavum vergit, <lb/>radiis flavis pro parte ex permixtione ſublatis albor datur <lb/>magis perfectus. </s> <s xml:id="echoid-s15348" xml:space="preserve">Ex quatuor aut quinque colorum permix-<lb/>tione, juſtâ ſervatâ proportione, albedo naſcitur.</s> <s xml:id="echoid-s15349" xml:space="preserve"/> </p> <div xml:id="echoid-div2304" type="float" level="2" n="1"> <note position="right" xlink:label="note-0605-02" xlink:href="note-0605-02a" xml:space="preserve">872.</note> </div> <p> <s xml:id="echoid-s15350" xml:space="preserve">Colores etiam innumeros primarii, id eſt, homogenei, <lb/> <anchor type="note" xlink:label="note-0605-03a" xlink:href="note-0605-03"/> permixti generant, ab homogeneis aut primariis, diverſos. <lb/></s> <s xml:id="echoid-s15351" xml:space="preserve">Sæpe color homogeneo ſimilis ex aliorum permixtione con-<lb/>flatur; </s> <s xml:id="echoid-s15352" xml:space="preserve">ſed quando nudis oculis inter homogeneum & </s> <s xml:id="echoid-s15353" xml:space="preserve">permix-<lb/> <anchor type="note" xlink:label="note-0605-04a" xlink:href="note-0605-04"/> tum differentia nulla obſervatur, trans priſma ſenſibilis <lb/>hæc eſt.</s> <s xml:id="echoid-s15354" xml:space="preserve"/> </p> <div xml:id="echoid-div2305" type="float" level="2" n="2"> <note position="right" xlink:label="note-0605-03" xlink:href="note-0605-03a" xml:space="preserve">873.</note> <note position="right" xlink:label="note-0605-04" xlink:href="note-0605-04a" xml:space="preserve">874.</note> </div> </div> <div xml:id="echoid-div2307" type="section" level="1" n="574"> <head xml:id="echoid-head754" xml:space="preserve"><emph style="sc">Experimentum</emph> 7.</head> <p> <s xml:id="echoid-s15355" xml:space="preserve">Trans priſma obſerventur objecta quæcunque exigua, ut <lb/>litteræ in chartâ, muſcæ & </s> <s xml:id="echoid-s15356" xml:space="preserve">alia ſimilia; </s> <s xml:id="echoid-s15357" xml:space="preserve">ſi lumini aperto <lb/>exponantur, confuſa apparent; </s> <s xml:id="echoid-s15358" xml:space="preserve">ſi lumine homogeneo, Fx- <pb o="92" file="0606" n="669" rhead="PHYSICES ELEMENTA"/> perimenti 4, hujus capitis, illuminentur, trans priſma viſa, <lb/>diſtinctis limitibus terminantur.</s> <s xml:id="echoid-s15359" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2308" type="section" level="1" n="575"> <head xml:id="echoid-head755" xml:space="preserve">CAPUT XXI.</head> <head xml:id="echoid-head756" style="it" xml:space="preserve">De Iride.</head> <p> <s xml:id="echoid-s15360" xml:space="preserve">PEractis quæ radios, quibus corpora illuminantur, ſpe-<lb/>ctant, antequam hanc materiam miſſam faciamus, expli-<lb/>candum eſt phænomenon, nimium notabile & </s> <s xml:id="echoid-s15361" xml:space="preserve">vulgare ut <lb/>ſilentio prætereatur.</s> <s xml:id="echoid-s15362" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15363" xml:space="preserve">Arcus cæleſtis, aut Iris, à nemine ſæpiſſimè non fuit ob-<lb/>ſervatus; </s> <s xml:id="echoid-s15364" xml:space="preserve">quibuſdam præmiſſis, explicandum erit unde oria-<lb/>tur</s> </p> <p> <s xml:id="echoid-s15365" xml:space="preserve">Detur medium denſius, rariori circumdatum, circulo BD <lb/> <anchor type="note" xlink:label="note-0606-01a" xlink:href="note-0606-01"/> FH terminatum. </s> <s xml:id="echoid-s15366" xml:space="preserve">Incidant in illud radii homogenei paralle-<lb/> <anchor type="note" xlink:label="note-0606-02a" xlink:href="note-0606-02"/> li inter ſe, quorum unus eſt AB; </s> <s xml:id="echoid-s15367" xml:space="preserve">ducatur ſemidiameter <lb/>CB continuata ad N; </s> <s xml:id="echoid-s15368" xml:space="preserve">perpendicularis eſt hæc ad ſuperfi-<lb/>ciem media dirimentem; </s> <s xml:id="echoid-s15369" xml:space="preserve">ABN eſt ergo angulus inciden-<lb/>tiæ hic æqualis eſt angulo oppoſito ad verticem CBL, cu-<lb/>jus ſinus eſt CL, per centrum ad BL perpendicularis; </s> <s xml:id="echoid-s15370" xml:space="preserve">re-<lb/>fringitur radius ad perpendicularem <anchor type="note" xlink:href="" symbol="*"/>, eſtque angulus re- <anchor type="note" xlink:label="note-0606-03a" xlink:href="note-0606-03"/> fractionis CBM, cujus ſinus eſt CM, à C ad BD perpen-<lb/>dicularis: </s> <s xml:id="echoid-s15371" xml:space="preserve">pro ſingulis radiis, ut AB, datur eadem ratio in-<lb/>ter lineas, ut CL & </s> <s xml:id="echoid-s15372" xml:space="preserve">CM <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15373" xml:space="preserve">Radius BD pro parte in me- <anchor type="note" xlink:label="note-0606-04a" xlink:href="note-0606-04"/> dium rarius penetrat juxta DE, pro parte reflectitur per <lb/>DF; </s> <s xml:id="echoid-s15374" xml:space="preserve">efficitque angulum reflectionis CDF æqualem angulo <lb/>incidentiæ BDC<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15375" xml:space="preserve">unde BD & </s> <s xml:id="echoid-s15376" xml:space="preserve">DF æquales ſunt. </s> <s xml:id="echoid-s15377" xml:space="preserve">Ra- <anchor type="note" xlink:label="note-0606-05a" xlink:href="note-0606-05"/> dius DF pro parte etiam ex denſiori medio exit per FG, <lb/>pro parte reflectitur per FH; </s> <s xml:id="echoid-s15378" xml:space="preserve">qui eodem modo pro parte <lb/>exit per HI, & </s> <s xml:id="echoid-s15379" xml:space="preserve">pro parte reflectitur: </s> <s xml:id="echoid-s15380" xml:space="preserve">hanc autem refle-<lb/>ctionem, ulterioresque reflectiones & </s> <s xml:id="echoid-s15381" xml:space="preserve">refractiones non <lb/>conſideramus; </s> <s xml:id="echoid-s15382" xml:space="preserve">nimium debiles ſunt, propter varias quas lu-<lb/>men paſſum eſt diviſiones.</s> <s xml:id="echoid-s15383" xml:space="preserve"/> </p> <div xml:id="echoid-div2308" type="float" level="2" n="1"> <note position="left" xlink:label="note-0606-01" xlink:href="note-0606-01a" xml:space="preserve">875.</note> <note position="left" xlink:label="note-0606-02" xlink:href="note-0606-02a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0606-03" xlink:href="note-0606-03a" xml:space="preserve">624.</note> <note symbol="*" position="left" xlink:label="note-0606-04" xlink:href="note-0606-04a" xml:space="preserve">639.</note> <note symbol="*" position="left" xlink:label="note-0606-05" xlink:href="note-0606-05a" xml:space="preserve">805.</note> </div> <p> <s xml:id="echoid-s15384" xml:space="preserve">Radius FG, qui poſt unicam reflectionem medium den-<lb/>ſius exit, cum radio incidente AB format angulum GPA, <lb/>qui variat in diverſis radiis incidentibus; </s> <s xml:id="echoid-s15385" xml:space="preserve">Ideò, licèt hi paral-<lb/>leli fuerint, diſperguntur, poſt unicam reflectionem exeuntes, <lb/> <anchor type="note" xlink:label="note-0606-06a" xlink:href="note-0606-06"/> ut ex inſpectione figuræ patet.</s> <s xml:id="echoid-s15386" xml:space="preserve"/> </p> <div xml:id="echoid-div2309" type="float" level="2" n="2"> <note position="left" xlink:label="note-0606-06" xlink:href="note-0606-06a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 2.</note> </div> <pb file="0607" n="670"/> <pb file="0607a" n="671"/> <figure> <image file="0607a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0607a-01"/> </figure> <pb file="0608" n="672"/> <pb o="93" file="0609" n="673" rhead="MATHEMATICA LIB. III. CAP. XXI."/> <p> <s xml:id="echoid-s15387" xml:space="preserve">Radius EE, qui continuatus per centrum C tranſit, neque <lb/>reflectione neque refractione à viâ deflectitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15388" xml:space="preserve"> <anchor type="note" xlink:label="note-0609-01a" xlink:href="note-0609-01"/> </s> </p> <div xml:id="echoid-div2310" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0609-01" xlink:href="note-0609-01a" xml:space="preserve">806. 629.</note> </div> <p> <s xml:id="echoid-s15389" xml:space="preserve">Recedendo ab hoc radio, ad incidentem continuò minus <lb/>ac minus inclinatur radius, qui redit. </s> <s xml:id="echoid-s15390" xml:space="preserve">Sic radius DD, qui <lb/>per dd exit ex medio denſiori, & </s> <s xml:id="echoid-s15391" xml:space="preserve">per hanc lineam regredi-<lb/>tur, cum dd majorem angulum format, quàm, cum ſuis re-<lb/>deuntibus, & </s> <s xml:id="echoid-s15392" xml:space="preserve">ex medio denſiori exeuntibus, efficiunt radii <lb/>intermedii inter DD & </s> <s xml:id="echoid-s15393" xml:space="preserve">EE.</s> <s xml:id="echoid-s15394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15395" xml:space="preserve">Datur radius ut BB, cujus reſpectu inclinatio hæc eſt <lb/> <anchor type="note" xlink:label="note-0609-02a" xlink:href="note-0609-02"/> omnium minima, id eſt, qui efficit angulum ut GPA <lb/>(fig. </s> <s xml:id="echoid-s15396" xml:space="preserve">1.) </s> <s xml:id="echoid-s15397" xml:space="preserve">omnium maximum. </s> <s xml:id="echoid-s15398" xml:space="preserve">Ultra BB, magis ad inci-<lb/>dentes inclinantur radii redeuntes; </s> <s xml:id="echoid-s15399" xml:space="preserve">ſic AA per aa redit.</s> <s xml:id="echoid-s15400" xml:space="preserve"/> </p> <div xml:id="echoid-div2311" type="float" level="2" n="4"> <note position="right" xlink:label="note-0609-02" xlink:href="note-0609-02a" xml:space="preserve">876.</note> </div> <p> <s xml:id="echoid-s15401" xml:space="preserve">Ex hac radiorum redeuntium diſperſione, recedendo à <lb/>medio denſiori debiliores continuò ſunt, & </s> <s xml:id="echoid-s15402" xml:space="preserve">horum color non, <lb/> <anchor type="note" xlink:label="note-0609-03a" xlink:href="note-0609-03"/> per totum ſpatium quod implent, percipi poteſt, licèt inciden-<lb/>tium color vividus ſit. </s> <s xml:id="echoid-s15403" xml:space="preserve">Color, in radiis redeuntibus, ſenſibilis <lb/>tantùm eſt, ubi radii vicini paralleli ſunt & </s> <s xml:id="echoid-s15404" xml:space="preserve">adjacentes pa-<lb/>rum admodum divergunt, ita ut ad magnam diſtantiam ſatis <lb/>denſi ſint, ut percipiantur. </s> <s xml:id="echoid-s15405" xml:space="preserve">Hi ſoli efficaces dicuntur, & </s> <s xml:id="echoid-s15406" xml:space="preserve"><lb/>dantur, ubi radii vicini incidentes refracti concurrunt in <lb/>ipſo puncto reflectionis.</s> <s xml:id="echoid-s15407" xml:space="preserve"/> </p> <div xml:id="echoid-div2312" type="float" level="2" n="5"> <note position="right" xlink:label="note-0609-03" xlink:href="note-0609-03a" xml:space="preserve">877.</note> </div> <p> <s xml:id="echoid-s15408" xml:space="preserve">Sint AB, ab radii vicini, paralleli inter ſe, incidentes <lb/> <anchor type="note" xlink:label="note-0609-04a" xlink:href="note-0609-04"/> in ſuperficiem circularem medium denſius terminantem; </s> <s xml:id="echoid-s15409" xml:space="preserve">ſi <lb/>hi refracti, per BD, bd, concurrant in D, puncto reflexio-<lb/>nis, reflexi, DF, D f, æquales angulos cum F f formabunt, <lb/>ac DB, D b cum B b; </s> <s xml:id="echoid-s15410" xml:space="preserve">ideoque refracti FG, f g paralleli <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0609-05a" xlink:href="note-0609-05"/> & </s> <s xml:id="echoid-s15411" xml:space="preserve">efficaces erunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15412" xml:space="preserve">In hoc caſu ſequenti methodo deter- <anchor type="note" xlink:label="note-0609-06a" xlink:href="note-0609-06"/> minatur angulus ab incidente cum redeunte formatus, id eſt, <lb/>angulus APG, qui hìc eſt omnium maximus.</s> <s xml:id="echoid-s15413" xml:space="preserve"/> </p> <div xml:id="echoid-div2313" type="float" level="2" n="6"> <note position="right" xlink:label="note-0609-04" xlink:href="note-0609-04a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0609-05" xlink:href="note-0609-05a" xml:space="preserve">627.</note> <note symbol="*" position="right" xlink:label="note-0609-06" xlink:href="note-0609-06a" xml:space="preserve">877.</note> </div> <p> <s xml:id="echoid-s15414" xml:space="preserve">Ponamus inter ſinus angulorum incidentiæ & </s> <s xml:id="echoid-s15415" xml:space="preserve">refractionis, <lb/> <anchor type="note" xlink:label="note-0609-07a" xlink:href="note-0609-07"/> quando lumen ex medio rariori, quo denſius circumdatur, <lb/>in denſius, ipſo circulo contentum, penetrat, rationem <lb/>dari, quæ datur inter J & </s> <s xml:id="echoid-s15416" xml:space="preserve">R. </s> <s xml:id="echoid-s15417" xml:space="preserve">Eſt ergo, ductis perpendicu-<lb/>lari C m ad b D, & </s> <s xml:id="echoid-s15418" xml:space="preserve">arcu mn centro C, & </s> <s xml:id="echoid-s15419" xml:space="preserve">ſemidiametro <lb/>C m,</s> </p> <div xml:id="echoid-div2314" type="float" level="2" n="7"> <note position="right" xlink:label="note-0609-07" xlink:href="note-0609-07a" xml:space="preserve">878.</note> </div> </div> <div xml:id="echoid-div2316" type="section" level="1" n="576"> <head xml:id="echoid-head757" xml:space="preserve">J, R:: CL, CM:: C l, C m:: CL--C l = L l, <lb/>CM--C m = M n.</head> <pb o="94" file="0610" n="674" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s15420" xml:space="preserve">Ducatur B o ad BL perpendicularis; </s> <s xml:id="echoid-s15421" xml:space="preserve">ut & </s> <s xml:id="echoid-s15422" xml:space="preserve">B p ad BD nor-<lb/>malis; </s> <s xml:id="echoid-s15423" xml:space="preserve">deturque bp, quæ cum B p angulum rectum format; <lb/></s> <s xml:id="echoid-s15424" xml:space="preserve">tandem lineis jungantur puncta B, C, & </s> <s xml:id="echoid-s15425" xml:space="preserve">M, m.</s> <s xml:id="echoid-s15426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15427" xml:space="preserve">Triangula B bo, BCL ſunt ſimilia; </s> <s xml:id="echoid-s15428" xml:space="preserve">ſunt enium rectangula, <lb/>& </s> <s xml:id="echoid-s15429" xml:space="preserve">anguli o B b & </s> <s xml:id="echoid-s15430" xml:space="preserve">CBL, quorum ſingulorum differentia cum <lb/>angulo recto eſt angulus o BC, ſunt æquales.</s> <s xml:id="echoid-s15431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15432" xml:space="preserve">Eodem modo probatur, ſimilia eſſe triangula BMC & </s> <s xml:id="echoid-s15433" xml:space="preserve"><lb/>B bp; </s> <s xml:id="echoid-s15434" xml:space="preserve">huic etiam ſimile eſt triangulum M mn rectangulum <lb/>in n, nam latera M n, B p, perpendicularia lineæ BD, ſunt <lb/>parallela; </s> <s xml:id="echoid-s15435" xml:space="preserve">ut & </s> <s xml:id="echoid-s15436" xml:space="preserve">M m & </s> <s xml:id="echoid-s15437" xml:space="preserve">B b, quia in partes æquales, in M <lb/>& </s> <s xml:id="echoid-s15438" xml:space="preserve">m, biſecantur lineæ BD, b D. </s> <s xml:id="echoid-s15439" xml:space="preserve">Idcirco etiam B b eſt <lb/>dupla M m, & </s> <s xml:id="echoid-s15440" xml:space="preserve">B p dupla mn. </s> <s xml:id="echoid-s15441" xml:space="preserve">Ex hiſce deducimus</s> </p> </div> <div xml:id="echoid-div2317" type="section" level="1" n="577"> <head xml:id="echoid-head758" xml:space="preserve">BC, BL:: B b, B o.</head> <head xml:id="echoid-head759" xml:space="preserve">BC, BM:: B b, B p.</head> <p> <s xml:id="echoid-s15442" xml:space="preserve">ergo</s> </p> <p> <s xml:id="echoid-s15443" xml:space="preserve">BL, BM:</s> <s xml:id="echoid-s15444" xml:space="preserve">: B o = L l, B p = 2 M n:</s> <s xml:id="echoid-s15445" xml:space="preserve">: J, 2R:</s> <s xml:id="echoid-s15446" xml:space="preserve">: CL, <lb/>2 CM, conferendo haſce proportiones cum ante memo-<lb/>ratâ proportione.</s> <s xml:id="echoid-s15447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15448" xml:space="preserve">Cùm proportionalium quantitatum, quadrata proportio-<lb/>nalia ſint, datur</s> </p> <p> <s xml:id="echoid-s15449" xml:space="preserve">B L<emph style="super">q</emph>, CL<emph style="super">q</emph>:</s> <s xml:id="echoid-s15450" xml:space="preserve">: BM<emph style="super">q</emph>, 4CM<emph style="super">q</emph>.</s> <s xml:id="echoid-s15451" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15452" xml:space="preserve">Unde deducimus</s> </p> <p> <s xml:id="echoid-s15453" xml:space="preserve">BL<emph style="super">q</emph> + CL<emph style="super">q</emph> = BC<emph style="super">q</emph>, BL<emph style="super">q</emph>:</s> <s xml:id="echoid-s15454" xml:space="preserve">: BM<emph style="super">q</emph> + 4CM<emph style="super">q</emph> = BC<emph style="super">q</emph> + <lb/>3CM<emph style="super">q</emph>, BM<emph style="super">q</emph> = BC<emph style="super">q</emph>-CM<emph style="super">q</emph> = BL<emph style="super">q</emph> + LC<emph style="super">q</emph>-CM<emph style="super">q</emph>.</s> <s xml:id="echoid-s15455" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15456" xml:space="preserve">Subtrahendo primum & </s> <s xml:id="echoid-s15457" xml:space="preserve">ſecundum terminum è tertio & </s> <s xml:id="echoid-s15458" xml:space="preserve"><lb/>quarto, quo proportio non mutatur, habemus <lb/>BC<emph style="super">q</emph>, BL<emph style="super">q</emph>:</s> <s xml:id="echoid-s15459" xml:space="preserve">: 3CM<emph style="super">q</emph>, LC<emph style="super">q</emph>-CM<emph style="super">q</emph>:</s> <s xml:id="echoid-s15460" xml:space="preserve">: 3R<emph style="super">q</emph>, J<emph style="super">q</emph>-R<emph style="super">q</emph>; <lb/></s> <s xml:id="echoid-s15461" xml:space="preserve">datur enim inter CM & </s> <s xml:id="echoid-s15462" xml:space="preserve">LC eadem ratio ac inter <lb/>R & </s> <s xml:id="echoid-s15463" xml:space="preserve">J.</s> <s xml:id="echoid-s15464" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15465" xml:space="preserve">Si ergo nota ſit ratio inter R & </s> <s xml:id="echoid-s15466" xml:space="preserve">J, innoteſcit ratio inter <lb/>ſemidiametrum BC, & </s> <s xml:id="echoid-s15467" xml:space="preserve">lineam BL, quæ eſt ſinus anguli <lb/>BCL, qui angulus idcirco datur; </s> <s xml:id="echoid-s15468" xml:space="preserve">notus eſt igitur arcus <lb/>BN, ut & </s> <s xml:id="echoid-s15469" xml:space="preserve">FG, ſunt enim hi æquales.</s> <s xml:id="echoid-s15470" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15471" xml:space="preserve">Dato ſinu BL, datur & </s> <s xml:id="echoid-s15472" xml:space="preserve">BM ſinus anguli BCM; </s> <s xml:id="echoid-s15473" xml:space="preserve">quia ut <lb/>ante vidimus</s> </p> </div> <div xml:id="echoid-div2318" type="section" level="1" n="578"> <head xml:id="echoid-head760" xml:space="preserve">BL, BM:: J, 2 R.</head> <p> <s xml:id="echoid-s15474" xml:space="preserve">Determinatur ergo arcus BD cui æqualis eſt DF.</s> <s xml:id="echoid-s15475" xml:space="preserve"/> </p> <pb o="95" file="0611" n="675" rhead="MATHEMATICA LIB. III. CAP. XXI."/> <p> <s xml:id="echoid-s15476" xml:space="preserve">Ex hiſce facilè deducimus arcus NH & </s> <s xml:id="echoid-s15477" xml:space="preserve">BF; </s> <s xml:id="echoid-s15478" xml:space="preserve">ſi ex hoc <lb/> <anchor type="note" xlink:label="note-0611-01a" xlink:href="note-0611-01"/> ille ſubtrahatur, & </s> <s xml:id="echoid-s15479" xml:space="preserve">reſiduum in duas partes æquales divida-<lb/>tur, habetur, ut notum eſt, menſura anguli APG.</s> <s xml:id="echoid-s15480" xml:space="preserve"/> </p> <div xml:id="echoid-div2318" type="float" level="2" n="1"> <note position="right" xlink:label="note-0611-01" xlink:href="note-0611-01a" xml:space="preserve">879.</note> </div> <p> <s xml:id="echoid-s15481" xml:space="preserve">Quando ratio inter J & </s> <s xml:id="echoid-s15482" xml:space="preserve">R variat, mutatur angulus APG; <lb/></s> <s xml:id="echoid-s15483" xml:space="preserve">qui idèo diverſus eſt pro variâ radiorum refrangibilitate.</s> <s xml:id="echoid-s15484" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15485" xml:space="preserve">Si Radiis hæterogeneis, ut à Sole profluunt, illuſtretur ſu-<lb/> <anchor type="note" xlink:label="note-0611-02a" xlink:href="note-0611-02"/> perficies memorata, efficaces diverſorum colorum non angulos <lb/>æquales cum incidentibus efficiunt, & </s> <s xml:id="echoid-s15486" xml:space="preserve">ſic ope hujus refractionis <lb/>ſeparantur colores.</s> <s xml:id="echoid-s15487" xml:space="preserve"/> </p> <div xml:id="echoid-div2319" type="float" level="2" n="2"> <note position="right" xlink:label="note-0611-02" xlink:href="note-0611-02a" xml:space="preserve">880.</note> </div> </div> <div xml:id="echoid-div2321" type="section" level="1" n="579"> <head xml:id="echoid-head761" xml:space="preserve"><emph style="sc">Experimentum</emph> I.</head> <p> <s xml:id="echoid-s15488" xml:space="preserve">Intret lumen ſolare in cubiculum obſcurum, per ſciſluram in <lb/> <anchor type="note" xlink:label="note-0611-03a" xlink:href="note-0611-03"/> orbe mobili O, & </s> <s xml:id="echoid-s15489" xml:space="preserve">à ſpeculo S horizontaliter reflexum, tranſeat <lb/>per ſciſſuram in tabellâ T; </s> <s xml:id="echoid-s15490" xml:space="preserve">ut ante explicatum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15491" xml:space="preserve">Detur phiala <anchor type="note" xlink:label="note-0611-04a" xlink:href="note-0611-04"/> exactè cylindrica, ex vitro puro, aquâ repleta. </s> <s xml:id="echoid-s15492" xml:space="preserve">Incidat ra-<lb/>dius in phialæ ſuperficiem in fg, in aquâ refringitur verſus <lb/>hi, & </s> <s xml:id="echoid-s15493" xml:space="preserve">ibi reflectitur, & </s> <s xml:id="echoid-s15494" xml:space="preserve">in lm phialam exit. </s> <s xml:id="echoid-s15495" xml:space="preserve">Facilè ita di-<lb/>ſponitur hæc, ut radii hi ſint efficaces; </s> <s xml:id="echoid-s15496" xml:space="preserve">&</s> <s xml:id="echoid-s15497" xml:space="preserve">, propter latitudi-<lb/>nem radii incidentis, efficaces omnium colorum eodem <lb/>tempore exeunt; </s> <s xml:id="echoid-s15498" xml:space="preserve">nam parum hi in incidentiâ diſtant. </s> <s xml:id="echoid-s15499" xml:space="preserve">Si hi <lb/>radii efficaces in chartam albam, ad diſtantiam quatuor aut <lb/>quinque pedum à phialâ, impingant, dantur in chartâ faſciæ <lb/>verticales, variorum colorum homogeneorum, ex radiis ef-<lb/>ficacibus ſingulorum colorum oriundæ, ſi etiam, ad diſtan-<lb/>tiam aliquot pedum à phialâ, oculus detur ubicunque ut in <lb/>N, in radiis hiſce efficacibus, videt in phialâ illum colorem, <lb/>cujus radii oculum intrant; </s> <s xml:id="echoid-s15500" xml:space="preserve">& </s> <s xml:id="echoid-s15501" xml:space="preserve">motu oculi ſucceſſivè omnes <lb/>percipit colores antea memoratos <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15502" xml:space="preserve"> <anchor type="note" xlink:label="note-0611-05a" xlink:href="note-0611-05"/> </s> </p> <div xml:id="echoid-div2321" type="float" level="2" n="1"> <note position="right" xlink:label="note-0611-03" xlink:href="note-0611-03a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 4.</note> <note symbol="*" position="right" xlink:label="note-0611-04" xlink:href="note-0611-04a" xml:space="preserve">630.</note> <note symbol="*" position="right" xlink:label="note-0611-05" xlink:href="note-0611-05a" xml:space="preserve">861.</note> </div> <p> <s xml:id="echoid-s15503" xml:space="preserve">Quod autem ſpectat radios, qui poſt duplam in medio den-<lb/> <anchor type="note" xlink:label="note-0611-06a" xlink:href="note-0611-06"/> ſiori reflectionem hoc exeunt, efficaces erunt, ſi poſt pri-<lb/> <anchor type="note" xlink:label="note-0611-07a" xlink:href="note-0611-07"/> mam reflectionem paralleli ſint: </s> <s xml:id="echoid-s15504" xml:space="preserve">tunc enim FH, fh ad <lb/>H h eodem modo inclinantur ac BD, bd ad B b; </s> <s xml:id="echoid-s15505" xml:space="preserve">ideòque <lb/>poſitis incidentibus AB, ab parallelis, exeuntes HI, hi, e-<lb/>tiam paralleli erunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15506" xml:space="preserve"> <anchor type="note" xlink:label="note-0611-08a" xlink:href="note-0611-08"/> </s> </p> <div xml:id="echoid-div2322" type="float" level="2" n="2"> <note position="right" xlink:label="note-0611-06" xlink:href="note-0611-06a" xml:space="preserve">881.</note> <note position="right" xlink:label="note-0611-07" xlink:href="note-0611-07a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0611-08" xlink:href="note-0611-08a" xml:space="preserve">627.</note> </div> <p> <s xml:id="echoid-s15507" xml:space="preserve">In hoc caſu d D eſt dimidium differentiæ inter arcus <lb/>DF & </s> <s xml:id="echoid-s15508" xml:space="preserve">df, aut DB & </s> <s xml:id="echoid-s15509" xml:space="preserve">db; </s> <s xml:id="echoid-s15510" xml:space="preserve">horum autem differentia eſt <lb/>B b minus D d; </s> <s xml:id="echoid-s15511" xml:space="preserve">ſi ergo hicce ex illo ſubtrahatur, ſupere-<lb/>rit duplum arcus D d, cujus triplum eſt idcirco B b. </s> <s xml:id="echoid-s15512" xml:space="preserve">Si <pb o="96" file="0612" n="676" rhead="PHYSICES ELEMENTA"/> lineis jungantur puncta D, d, & </s> <s xml:id="echoid-s15513" xml:space="preserve">B, b, triangula BE b & </s> <s xml:id="echoid-s15514" xml:space="preserve"><lb/>DE d erunt ſimilia, ut notum eſt; </s> <s xml:id="echoid-s15515" xml:space="preserve">quod ergo etiam obti-<lb/>net, ſi ipſi arcus B b, D d fuerint minimi, ita ut pro lineis <lb/>rectis haberi poſſint.</s> <s xml:id="echoid-s15516" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15517" xml:space="preserve">Datur idcirco inter ED & </s> <s xml:id="echoid-s15518" xml:space="preserve">E b ratio, quæ inter hos ar-<lb/>cus obtinet, id eſt ED eſt pars tertia ipſius E b, aut EB; <lb/></s> <s xml:id="echoid-s15519" xml:space="preserve">quia exiguum admodum ponimus arcum B b. </s> <s xml:id="echoid-s15520" xml:space="preserve">Dividitur <lb/>igitur MD in duas partes æquales in E; </s> <s xml:id="echoid-s15521" xml:space="preserve">& </s> <s xml:id="echoid-s15522" xml:space="preserve">ME eſt pars <lb/>tertia ipſius EB.</s> <s xml:id="echoid-s15523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15524" xml:space="preserve">Si nunc, ut in fig. </s> <s xml:id="echoid-s15525" xml:space="preserve">3.</s> <s xml:id="echoid-s15526" xml:space="preserve">, formentur triangula B ob, B pb <lb/>& </s> <s xml:id="echoid-s15527" xml:space="preserve">M mn, erit M m pars tertia B b, & </s> <s xml:id="echoid-s15528" xml:space="preserve">B p triplum ipſius <lb/>M n; </s> <s xml:id="echoid-s15529" xml:space="preserve">ſi nunc, mutatis mutandis, ad hanc figuram appli-<lb/>cemus quæ reſpectu fig. </s> <s xml:id="echoid-s15530" xml:space="preserve">3. </s> <s xml:id="echoid-s15531" xml:space="preserve">demonſtrata ſunt <anchor type="note" xlink:href="" symbol="*"/>, quia in hac <anchor type="note" xlink:label="note-0612-01a" xlink:href="note-0612-01"/> B p valet 3 M n, cujus quadratum eſt 9 M n<emph style="super">9</emph>, habe-<lb/>mus</s> </p> <div xml:id="echoid-div2323" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0612-01" xlink:href="note-0612-01a" xml:space="preserve">878.</note> </div> </div> <div xml:id="echoid-div2325" type="section" level="1" n="580"> <head xml:id="echoid-head762" xml:space="preserve">BC<emph style="super">q</emph>, BL<emph style="super">q</emph>:: 8 R<emph style="super">q</emph>, J<emph style="super">q</emph>-R<emph style="super">q</emph></head> <p> <s xml:id="echoid-s15532" xml:space="preserve">Ex qua proportione, ut de fig. </s> <s xml:id="echoid-s15533" xml:space="preserve">3. </s> <s xml:id="echoid-s15534" xml:space="preserve">dictum, detegitur ar-<lb/>cus BN, cui æqualis HG; </s> <s xml:id="echoid-s15535" xml:space="preserve">& </s> <s xml:id="echoid-s15536" xml:space="preserve">quia in hoc caſu</s> </p> </div> <div xml:id="echoid-div2326" type="section" level="1" n="581"> <head xml:id="echoid-head763" xml:space="preserve">BL, BM:: J, 3R,</head> <p> <s xml:id="echoid-s15537" xml:space="preserve">Innoteſcit etiam arcus BD, cui propter angulos reflectio-<lb/>nis, æquales angulis incidentiæ <anchor type="note" xlink:href="" symbol="*"/>, æquales ſunt DF & </s> <s xml:id="echoid-s15538" xml:space="preserve">FH.</s> <s xml:id="echoid-s15539" xml:space="preserve"> <anchor type="note" xlink:label="note-0612-02a" xlink:href="note-0612-02"/> </s> </p> <div xml:id="echoid-div2326" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0612-02" xlink:href="note-0612-02a" xml:space="preserve">805.</note> </div> <p> <s xml:id="echoid-s15540" xml:space="preserve">Ex quibus datis, facilè eliciuntur arcus GFDN & </s> <s xml:id="echoid-s15541" xml:space="preserve">BH, <lb/> <anchor type="note" xlink:label="note-0612-03a" xlink:href="note-0612-03"/> quorum ſemi differentia eſt menſura anguli HPB, ab ex-<lb/>eunte radio cum incidente formato; </s> <s xml:id="echoid-s15542" xml:space="preserve">qui angulus in hoc <lb/>caſu omnium ſimilium eſt minimus, & </s> <s xml:id="echoid-s15543" xml:space="preserve">pro diversâ radiorum <lb/>refrangibilitâte diverſus. </s> <s xml:id="echoid-s15544" xml:space="preserve">Unde etiam in hoc caſu poſt du-<lb/> <anchor type="note" xlink:label="note-0612-04a" xlink:href="note-0612-04"/> plicem reflectionem efficaces variorum colorum, poſitis inci-<lb/>dentibus parallelis, ſeparantur.</s> <s xml:id="echoid-s15545" xml:space="preserve"/> </p> <div xml:id="echoid-div2327" type="float" level="2" n="2"> <note position="left" xlink:label="note-0612-03" xlink:href="note-0612-03a" xml:space="preserve">882.</note> <note position="left" xlink:label="note-0612-04" xlink:href="note-0612-04a" xml:space="preserve">883.</note> </div> </div> <div xml:id="echoid-div2329" type="section" level="1" n="582"> <head xml:id="echoid-head764" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15546" xml:space="preserve">Eodem modo ac præcedens experimentum hoc inſtitui-<lb/> <anchor type="note" xlink:label="note-0612-05a" xlink:href="note-0612-05"/> tur, ſitus phialæ tantum paululum mutatur, ut, poſt duas in <lb/>phialâ reflexiones, radii ad oculum aut chartam verſus N per-<lb/>veniant.</s> <s xml:id="echoid-s15547" xml:space="preserve"/> </p> <div xml:id="echoid-div2329" type="float" level="2" n="1"> <note position="left" xlink:label="note-0612-05" xlink:href="note-0612-05a" xml:space="preserve"><emph style="sc">TAB. XVIII</emph>. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s15548" xml:space="preserve">Huc uſque explicata ad Iridem applicari poſſunt; </s> <s xml:id="echoid-s15549" xml:space="preserve">ad quod <lb/> <anchor type="note" xlink:label="note-0612-06a" xlink:href="note-0612-06"/> phænomenon guttæ aqueæ in aëre ſuſpenſæ requiruntur; </s> <s xml:id="echoid-s15550" xml:space="preserve">ut <lb/>ſpectator, adverſo Sole inter hunc & </s> <s xml:id="echoid-s15551" xml:space="preserve">guttas collocetur; </s> <s xml:id="echoid-s15552" xml:space="preserve">& </s> <s xml:id="echoid-s15553" xml:space="preserve">ut <lb/>poſt guttas nubes detur obſcura, ut magis ſenſibiles ſint colo- <pb o="97" file="0613" n="677" rhead="MATHEMATIC A LIB. III. CAP. XXI."/> res, qui vix percipiuntur, ſi lumen vividum eodem tempo-<lb/>re oculos intret.</s> <s xml:id="echoid-s15554" xml:space="preserve"/> </p> <div xml:id="echoid-div2330" type="float" level="2" n="2"> <note position="left" xlink:label="note-0612-06" xlink:href="note-0612-06a" xml:space="preserve">884.</note> </div> <p> <s xml:id="echoid-s15555" xml:space="preserve">Si, hiſce poſitis, concipiamus ſingulas guttas ſecari planis, <lb/>per Solem & </s> <s xml:id="echoid-s15556" xml:space="preserve">oculum ſpectatoris tranſeuntibus, quæ de me-<lb/>dio, ſuperficie circulari terminato, demonſtrata ſunt <anchor type="note" xlink:href="" symbol="*"/>, ad <anchor type="note" xlink:label="note-0613-01a" xlink:href="note-0613-01"/> ſingulas haſce ſectiones poterunt applicari.</s> <s xml:id="echoid-s15557" xml:space="preserve"/> </p> <div xml:id="echoid-div2331" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0613-01" xlink:href="note-0613-01a" xml:space="preserve">878. 879. 880. <lb/>881. 882. 883.</note> </div> <p> <s xml:id="echoid-s15558" xml:space="preserve">Hìc autem agitur de radiis ex aëre in aquam penetranti-<lb/>bus. </s> <s xml:id="echoid-s15559" xml:space="preserve">In radiis rubris, id eſt, minimè omnium refrangibili-<lb/>bus, ratio inter ſinum anguli incidentiæ & </s> <s xml:id="echoid-s15560" xml:space="preserve">ſinum anguli re-<lb/>fractionis, id eſt, inter J & </s> <s xml:id="echoid-s15561" xml:space="preserve">R, eſt 108. </s> <s xml:id="echoid-s15562" xml:space="preserve">ad 81. </s> <s xml:id="echoid-s15563" xml:space="preserve">aut quæ ea-<lb/>dem eſt, 4. </s> <s xml:id="echoid-s15564" xml:space="preserve">ad 3.</s> <s xml:id="echoid-s15565" xml:space="preserve">; cum quibus numeris ſi computatio inea-<lb/>tur, angulus APG (fig. </s> <s xml:id="echoid-s15566" xml:space="preserve">3.) </s> <s xml:id="echoid-s15567" xml:space="preserve">erit 42. </s> <s xml:id="echoid-s15568" xml:space="preserve">gr. </s> <s xml:id="echoid-s15569" xml:space="preserve">2 <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15570" xml:space="preserve">angulus <anchor type="note" xlink:label="note-0613-02a" xlink:href="note-0613-02"/> API (fig. </s> <s xml:id="echoid-s15571" xml:space="preserve">4.) </s> <s xml:id="echoid-s15572" xml:space="preserve">erit 50. </s> <s xml:id="echoid-s15573" xml:space="preserve">gr. </s> <s xml:id="echoid-s15574" xml:space="preserve">57′. </s> <s xml:id="echoid-s15575" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15576" xml:space="preserve">ſi de radiis violaceis aga- <anchor type="note" xlink:label="note-0613-03a" xlink:href="note-0613-03"/> tur, J eſt ad R, ut 109. </s> <s xml:id="echoid-s15577" xml:space="preserve">ad 81.</s> <s xml:id="echoid-s15578" xml:space="preserve">; qui numeri dant angulos <lb/>APG (fig. </s> <s xml:id="echoid-s15579" xml:space="preserve">3.) </s> <s xml:id="echoid-s15580" xml:space="preserve">40. </s> <s xml:id="echoid-s15581" xml:space="preserve">gr. </s> <s xml:id="echoid-s15582" xml:space="preserve">17′. </s> <s xml:id="echoid-s15583" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15584" xml:space="preserve">API (fig. </s> <s xml:id="echoid-s15585" xml:space="preserve">4.) </s> <s xml:id="echoid-s15586" xml:space="preserve">54. </s> <s xml:id="echoid-s15587" xml:space="preserve">gr. </s> <s xml:id="echoid-s15588" xml:space="preserve">7′. </s> <s xml:id="echoid-s15589" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15590" xml:space="preserve"> <anchor type="note" xlink:label="note-0613-04a" xlink:href="note-0613-04"/> <anchor type="note" xlink:label="note-0613-05a" xlink:href="note-0613-05"/> </s> </p> <div xml:id="echoid-div2332" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0613-02" xlink:href="note-0613-02a" xml:space="preserve">879.</note> <note symbol="*" position="right" xlink:label="note-0613-03" xlink:href="note-0613-03a" xml:space="preserve">882.</note> <note symbol="*" position="right" xlink:label="note-0613-04" xlink:href="note-0613-04a" xml:space="preserve">879.</note> <note symbol="*" position="right" xlink:label="note-0613-05" xlink:href="note-0613-05a" xml:space="preserve">882.</note> </div> <p> <s xml:id="echoid-s15591" xml:space="preserve">Sint nunc guttæ per aërem diffuſæ, & </s> <s xml:id="echoid-s15592" xml:space="preserve">radiis ſolaribus <lb/> <anchor type="note" xlink:label="note-0613-06a" xlink:href="note-0613-06"/> illuſtratæ, parallelis inter ſe & </s> <s xml:id="echoid-s15593" xml:space="preserve">lineæ OF, per oculum ſpe-<lb/>ctatoris tranſeunti. </s> <s xml:id="echoid-s15594" xml:space="preserve">Concipiantur lineæ e O, EO, b O, <lb/>BO & </s> <s xml:id="echoid-s15595" xml:space="preserve">ſint anguli e OF 40. </s> <s xml:id="echoid-s15596" xml:space="preserve">gr. </s> <s xml:id="echoid-s15597" xml:space="preserve">17′.</s> <s xml:id="echoid-s15598" xml:space="preserve">, EOF 42. </s> <s xml:id="echoid-s15599" xml:space="preserve">gr. </s> <s xml:id="echoid-s15600" xml:space="preserve">2′.</s> <s xml:id="echoid-s15601" xml:space="preserve">, <lb/>b OF 50. </s> <s xml:id="echoid-s15602" xml:space="preserve">gr. </s> <s xml:id="echoid-s15603" xml:space="preserve">57′.</s> <s xml:id="echoid-s15604" xml:space="preserve">, BOF 54. </s> <s xml:id="echoid-s15605" xml:space="preserve">gr. </s> <s xml:id="echoid-s15606" xml:space="preserve">7′.</s> <s xml:id="echoid-s15607" xml:space="preserve">: eædem hæ lineæ cum radiis <lb/>incidentibus de, DE, ab, AB, angulos formant memo-<lb/>ratis reſpectivè æquales; </s> <s xml:id="echoid-s15608" xml:space="preserve">ideò, ſi guttæ concipiantur in e, E, <lb/>b, B, radii efficaces violacei, poſt unicam reflectionem in gut-<lb/>tâ e, oculum intrant; </s> <s xml:id="echoid-s15609" xml:space="preserve">& </s> <s xml:id="echoid-s15610" xml:space="preserve">ad oculum efficaces rubri ex guttâ E <lb/>perveniunt; </s> <s xml:id="echoid-s15611" xml:space="preserve">itidem poſt unicam reflectionem, reliqui colo-<lb/>res intermedii inter e & </s> <s xml:id="echoid-s15612" xml:space="preserve">E obſervantur, ordine antea memo-<lb/>rato <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15613" xml:space="preserve">Poſt duas in guttâ reflectiones ex guttâ b radii ef- <anchor type="note" xlink:label="note-0613-07a" xlink:href="note-0613-07"/> ficaces rubri ad oculum perveniunt; </s> <s xml:id="echoid-s15614" xml:space="preserve">& </s> <s xml:id="echoid-s15615" xml:space="preserve">violacei efficaces ex <lb/>guttâ B; </s> <s xml:id="echoid-s15616" xml:space="preserve">inter has guttas colores intermedii apparent, eo-<lb/>dem modo ac inter E, e, ſed ordine contrario diſpo-<lb/>nuntur, & </s> <s xml:id="echoid-s15617" xml:space="preserve">propter duplicem reflectionem etiam debiliores <lb/>ſunt.</s> <s xml:id="echoid-s15618" xml:space="preserve"/> </p> <div xml:id="echoid-div2333" type="float" level="2" n="5"> <note position="right" xlink:label="note-0613-06" xlink:href="note-0613-06a" xml:space="preserve"><emph style="sc">TAB. XIX</emph>. <lb/>fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0613-07" xlink:href="note-0613-07a" xml:space="preserve">861.</note> </div> <p> <s xml:id="echoid-s15619" xml:space="preserve">Concipiamus lineam ut O e, circa lineam OF fixam, ſer-<lb/>vato angulo e OF, revolvi, & </s> <s xml:id="echoid-s15620" xml:space="preserve">conum aut partem ſuperficiei <lb/>coni formare; </s> <s xml:id="echoid-s15621" xml:space="preserve">in omni ſitu linea e O cum radiis ſolaribus, <lb/>parallelis inter ſe & </s> <s xml:id="echoid-s15622" xml:space="preserve">lineæ OF, formabit angulum 40. </s> <s xml:id="echoid-s15623" xml:space="preserve">gr. </s> <s xml:id="echoid-s15624" xml:space="preserve">17′. <lb/></s> <s xml:id="echoid-s15625" xml:space="preserve">Siergo guttæ juxta partem ſuperficiei hujus coni ſive ad ean-<lb/> <anchor type="note" xlink:label="note-0613-08a" xlink:href="note-0613-08"/> <pb o="(98)" file="0614" n="678" rhead="PHYSICES ELEMENTA"/> dem ſive ad diverſas diſtantias diffuſæ fuerint, videbit oculus <lb/>arcum violaceum: </s> <s xml:id="echoid-s15626" xml:space="preserve">idem dicendum eſt de cæteris coloribus; <lb/></s> <s xml:id="echoid-s15627" xml:space="preserve">ideòque, datis guttis, in aëre ſuſpenſis, videt arcum latitudinis <lb/>eE, coloribus homogeneis, ante memoratis <anchor type="note" xlink:href="" symbol="*"/>, tinctum, eodem <anchor type="note" xlink:label="note-0614-01a" xlink:href="note-0614-01"/> ordine diſpoſitis ac in experimentis cum priſmatibus; </s> <s xml:id="echoid-s15628" xml:space="preserve">quia <lb/>in guttis æquè ac inpriſmate radii hæterogenii ſeparantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15629" xml:space="preserve"> <anchor type="note" xlink:label="note-0614-02a" xlink:href="note-0614-02"/> </s> </p> <div xml:id="echoid-div2334" type="float" level="2" n="6"> <note position="right" xlink:label="note-0613-08" xlink:href="note-0613-08a" xml:space="preserve">885.</note> <note symbol="*" position="left" xlink:label="note-0614-01" xlink:href="note-0614-01a" xml:space="preserve">861.</note> <note symbol="*" position="left" xlink:label="note-0614-02" xlink:href="note-0614-02a" xml:space="preserve">852. 880.</note> </div> <p> <s xml:id="echoid-s15630" xml:space="preserve">Simili ratiocinio patet dari arcum, latiorem, primum cir-<lb/> <anchor type="note" xlink:label="note-0614-03a" xlink:href="note-0614-03"/> cumdantem, in quo colores iidem, ſed contrario ordine, & </s> <s xml:id="echoid-s15631" xml:space="preserve"><lb/>debiliores, apparent.</s> <s xml:id="echoid-s15632" xml:space="preserve"/> </p> <div xml:id="echoid-div2335" type="float" level="2" n="7"> <note position="left" xlink:label="note-0614-03" xlink:href="note-0614-03a" xml:space="preserve">886.</note> </div> </div> <div xml:id="echoid-div2337" type="section" level="1" n="583"> <head xml:id="echoid-head765" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15633" xml:space="preserve">Panno nigro ſuſpenſo, radiis ſolaribus expoſito; </s> <s xml:id="echoid-s15634" xml:space="preserve">detur, <lb/>inter hunc & </s> <s xml:id="echoid-s15635" xml:space="preserve">Solem, ſpectator pannum reſpiciens; </s> <s xml:id="echoid-s15636" xml:space="preserve">& </s> <s xml:id="echoid-s15637" xml:space="preserve">inter <lb/>pannum & </s> <s xml:id="echoid-s15638" xml:space="preserve">ſpectatorem diſpergatur aqua, ut in guttas exi-<lb/>guas reſolvatur, videbit ſpectator Iridem ſaltem interiorem.</s> <s xml:id="echoid-s15639" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2338" type="section" level="1" n="584"> <head xml:id="echoid-head766" xml:space="preserve">CAPUT XXII. <lb/>De tenuium Laminarum Coloribus.</head> <p> <s xml:id="echoid-s15640" xml:space="preserve">TRanſimus ad corporum naturalium colores, & </s> <s xml:id="echoid-s15641" xml:space="preserve">ante <lb/>omnia examinandas credimus tenues lamellas. </s> <s xml:id="echoid-s15642" xml:space="preserve">Qui vi-<lb/>trum tenue, aut globos ex aquâ cum ſapone formatos, atten-<lb/>tè conſideravit, varios colores in illis obſervare facillimè potuit.</s> <s xml:id="echoid-s15643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15644" xml:space="preserve">Radii luminis, ope laminæ tenuis & </s> <s xml:id="echoid-s15645" xml:space="preserve">tranſlucidæ, inter ſe <lb/>ſeparantur, & </s> <s xml:id="echoid-s15646" xml:space="preserve">pro variâ craſſitie laminæ, radii quorundam co-<lb/> <anchor type="note" xlink:label="note-0614-04a" xlink:href="note-0614-04"/> lorum tranſmittuntur, aliorum reflectuntur; </s> <s xml:id="echoid-s15647" xml:space="preserve">& </s> <s xml:id="echoid-s15648" xml:space="preserve">eadem lamina <lb/>tenuiſſima aliûs coloris eſt, ſiradiis tranſmiſſis, quàm ſi reflexis <lb/>videatur.</s> <s xml:id="echoid-s15649" xml:space="preserve"/> </p> <div xml:id="echoid-div2338" type="float" level="2" n="1"> <note position="left" xlink:label="note-0614-04" xlink:href="note-0614-04a" xml:space="preserve">887.</note> </div> </div> <div xml:id="echoid-div2340" type="section" level="1" n="585"> <head xml:id="echoid-head767" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s15650" xml:space="preserve">Si duo vitra objectiva, majoribus teleſcopiis inſervientia, <lb/> <anchor type="note" xlink:label="note-0614-05a" xlink:href="note-0614-05"/> AB & </s> <s xml:id="echoid-s15651" xml:space="preserve">CD, ſuper ſe mutuo imponantur, & </s> <s xml:id="echoid-s15652" xml:space="preserve">arctè compri-<lb/>mantur, in medio ubi vitra ſeſe mutuo tangunt datur macu-<lb/>la tranſlucida, quæ circulis coloratis circumdatur. </s> <s xml:id="echoid-s15653" xml:space="preserve">Si lumen <lb/>reflexum ab aëre, inter vitra interjacente, ad oculum in Oper-<lb/>veniat, macula tranſlucida nigra apparet, & </s> <s xml:id="echoid-s15654" xml:space="preserve">colores, quià cen-<lb/>tro recedendo ita diſponuntur ut ad varios ordines, propter co-<lb/>lores repetitos, referri poſſint, ſequentes ſunt; </s> <s xml:id="echoid-s15655" xml:space="preserve">NIGER, cœ-<lb/>ruleus, albus, flavus, rubeus: </s> <s xml:id="echoid-s15656" xml:space="preserve">VIOLACEUS, cœruleus, viri-<lb/>dis, flavus, rubeus: </s> <s xml:id="echoid-s15657" xml:space="preserve">PURPUREUS, cœruleus, viridis, flavus, <pb o="(99)" file="0615" n="679" rhead="MATHEMATICA LIB. III. CAP. XXII."/> rubeus: </s> <s xml:id="echoid-s15658" xml:space="preserve">VIRIDIS, rubeus: </s> <s xml:id="echoid-s15659" xml:space="preserve">qui colores etiam aliis circum-<lb/>dantur, ſed recedendo à centro continuò debiliores.</s> <s xml:id="echoid-s15660" xml:space="preserve"/> </p> <div xml:id="echoid-div2340" type="float" level="2" n="1"> <note position="left" xlink:label="note-0614-05" xlink:href="note-0614-05a" xml:space="preserve">TAB. XVIII. <lb/>fig. 6.</note> </div> <p> <s xml:id="echoid-s15661" xml:space="preserve">Si lumen trans vitra ad oculum Operveniat, macula trans-<lb/>lucida, omnes tranſmittens radios, alba eſt, & </s> <s xml:id="echoid-s15662" xml:space="preserve">juxta hanc ſe-<lb/>riem recedendo à centro apparent colores, qui etiam ad <lb/>varios ordines referuntur, ordinibus memoratis oppoſitos: <lb/></s> <s xml:id="echoid-s15663" xml:space="preserve">ALBUS, rubeus flaveſcens, niger, violaceus, cœruleus: </s> <s xml:id="echoid-s15664" xml:space="preserve">AL-<lb/>BUS, flavus, rubeus, violaceus, cœruleus: </s> <s xml:id="echoid-s15665" xml:space="preserve">VIRIDIS, flavus, <lb/>rubeus, viridis ſubcœruleus: </s> <s xml:id="echoid-s15666" xml:space="preserve">RUBEUS, viridis ſubcœruleus: </s> <s xml:id="echoid-s15667" xml:space="preserve"><lb/>qui etiam colores aliis debilioribus circumdantur.</s> <s xml:id="echoid-s15668" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2342" type="section" level="1" n="586"> <head xml:id="echoid-head768" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15669" xml:space="preserve">Lamina tenuis ex aquâ formatur, ſi hæc paululum ſapo-<lb/>ne incraſſata fuerit, & </s> <s xml:id="echoid-s15670" xml:space="preserve">in bullam infletur. </s> <s xml:id="echoid-s15671" xml:space="preserve">Obtegatur hæc <lb/>vitro admodum tranſlucido, ne, aëris agitatione, colores <lb/>qui in hac bullâ obſervantur, motu aquæ, confundantur. <lb/></s> <s xml:id="echoid-s15672" xml:space="preserve">Bulla talis, quia aqua continuò verſus omnes partes defluit, <lb/>tenuiſſima eſt in ſupremâ parte, & </s> <s xml:id="echoid-s15673" xml:space="preserve">craſſities deſcendendo con-<lb/>tinuò augetur, & </s> <s xml:id="echoid-s15674" xml:space="preserve">totius craſſities ex eâdem cauſa de mo-<lb/>mento in momentum minuitur. </s> <s xml:id="echoid-s15675" xml:space="preserve">Antequam bulla diſrumpa-<lb/>tur, ſummitas ipſius ita tenuis fit, ut omne lumen tranſmit-<lb/>tat, & </s> <s xml:id="echoid-s15676" xml:space="preserve">nigra appareat. </s> <s xml:id="echoid-s15677" xml:space="preserve">Si in hoc caſu bulla hæc reflexo lu-<lb/>mine obſervetur, dum cœli ſubalbidioris reflectione illuſtra-<lb/>tur, & </s> <s xml:id="echoid-s15678" xml:space="preserve">lumen extraneum intercipitur, corpore quocunque <lb/>nigro ultra bullam poſito; </s> <s xml:id="echoid-s15679" xml:space="preserve">macula nigra ſtatim memorata <lb/>iiſdem circulis coloratis circumdatur & </s> <s xml:id="echoid-s15680" xml:space="preserve">eodem ordine di-<lb/>ſpoſitis, quàm circa maculam nigram in præcedenti ex peri-<lb/>mento. </s> <s xml:id="echoid-s15681" xml:space="preserve">Deſcenſu aquæ continuò dilatantur annuli colorati <lb/>donec frangatur bulla.</s> <s xml:id="echoid-s15682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15683" xml:space="preserve">Si, ubi extremus bullæ circuitus, reflexis radiis, rubeus <lb/>apparet, ſpectator illum, tranſmiſſis radiis, intueatur, cæru-<lb/>leus erit; </s> <s xml:id="echoid-s15684" xml:space="preserve">& </s> <s xml:id="echoid-s15685" xml:space="preserve">in genere colores, tranſmiſſis & </s> <s xml:id="echoid-s15686" xml:space="preserve">reflexis radiis, eo-<lb/>dem modo ac in præcedenti experimento, ſibi mutuo op-<lb/>ponuntur.</s> <s xml:id="echoid-s15687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15688" xml:space="preserve">Ex hiſce experimentis coliatis, ſequitur augendo tenuiſſimæ <lb/> <anchor type="note" xlink:label="note-0615-01a" xlink:href="note-0615-01"/> laminæ craſſitiem; </s> <s xml:id="echoid-s15689" xml:space="preserve">hujus colorem mutari, & </s> <s xml:id="echoid-s15690" xml:space="preserve">quidem mutationes <lb/>dari ſucceſſivè eaſdem, eodem ordine, ſive ex rarioriaut denſiori <lb/>medio formetur lamella. </s> <s xml:id="echoid-s15691" xml:space="preserve">Nam in laminâ aëreâ inter vitra & </s> <s xml:id="echoid-s15692" xml:space="preserve">a- <pb o="(100)" file="0616" n="680" rhead="PHYSICES ELEMENTA"/> queâ in bullâ, quarum craſſities recedendoà medio creſcunt, <lb/>eodem ordine colores diſponuntur. </s> <s xml:id="echoid-s15693" xml:space="preserve">In laminâ tamen den-<lb/> <anchor type="note" xlink:label="note-0616-01a" xlink:href="note-0616-01"/> ſiori minor craſſities requiritur, quàm in rariori, ut eodem <lb/>colore tingantur.</s> <s xml:id="echoid-s15694" xml:space="preserve"/> </p> <div xml:id="echoid-div2342" type="float" level="2" n="1"> <note position="right" xlink:label="note-0615-01" xlink:href="note-0615-01a" xml:space="preserve">888.</note> <note position="left" xlink:label="note-0616-01" xlink:href="note-0616-01a" xml:space="preserve">889.</note> </div> </div> <div xml:id="echoid-div2344" type="section" level="1" n="587"> <head xml:id="echoid-head769" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15695" xml:space="preserve">Iiſdem poſitis quæ in Experimento 1.</s> <s xml:id="echoid-s15696" xml:space="preserve">; madefactis paulu-<lb/>lum ab unâ parte vitrorum marginibus, aqua paulatim inter <lb/>vitra penetrabit; </s> <s xml:id="echoid-s15697" xml:space="preserve">in aquâ non alii, quàm in aëre, circulorum <lb/>colores obſervantur, neque horum ordo mutatur, ſed circuli <lb/>contrahuntur; </s> <s xml:id="echoid-s15698" xml:space="preserve">ubi ad centrum pervenit aqua, omnes circu-<lb/>lorum portiones in aquâ à portionìbus in aëre ſeparantur, & </s> <s xml:id="echoid-s15699" xml:space="preserve"><lb/>in minus ſpatium rediguntur.</s> <s xml:id="echoid-s15700" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15701" xml:space="preserve">Laminæ color ab illius craſſitie <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15702" xml:space="preserve">denſitate <anchor type="note" xlink:href="" symbol="*"/>, pen- <anchor type="note" xlink:label="note-0616-02a" xlink:href="note-0616-02"/> <anchor type="note" xlink:label="note-0616-03a" xlink:href="note-0616-03"/> <anchor type="note" xlink:label="note-0616-04a" xlink:href="note-0616-04"/> det, non à medio circumdante.</s> <s xml:id="echoid-s15703" xml:space="preserve"/> </p> <div xml:id="echoid-div2344" type="float" level="2" n="1"> <note position="left" xlink:label="note-0616-02" xlink:href="note-0616-02a" xml:space="preserve">890.</note> <note symbol="*" position="left" xlink:label="note-0616-03" xlink:href="note-0616-03a" xml:space="preserve">887.</note> <note symbol="*" position="left" xlink:label="note-0616-04" xlink:href="note-0616-04a" xml:space="preserve">889.</note> </div> </div> <div xml:id="echoid-div2346" type="section" level="1" n="588"> <head xml:id="echoid-head770" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s15704" xml:space="preserve">Si lamella ex lapide ſpeculari ita tenuis detur, ut colorata <lb/>appareat, colores non mutantur ſi madefacta fuerit, id eſt, <lb/>ſi, loco aëris, aquâ circumdetur lamella.</s> <s xml:id="echoid-s15705" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15706" xml:space="preserve">Ejuſdem lamellæ color eſt eo magis vividus, quo illius denſitas <lb/> <anchor type="note" xlink:label="note-0616-05a" xlink:href="note-0616-05"/> magis differt cum denſitate medii circumambientis. </s> <s xml:id="echoid-s15707" xml:space="preserve">Hoc præ-<lb/>cedenti Experimento probatur, in quo colores laminæ made-<lb/>factæ languidiores ſunt, quàm laminæ aëre circumdatæ. </s> <s xml:id="echoid-s15708" xml:space="preserve">Etiam <lb/>in Exp. </s> <s xml:id="echoid-s15709" xml:space="preserve">3. </s> <s xml:id="echoid-s15710" xml:space="preserve">minus vividi ſunt colores quàm in ſecundo; </s> <s xml:id="echoid-s15711" xml:space="preserve">in utroque <lb/>lamina aquea datur, in hoc aëre, in illo vitro circumdata; </s> <s xml:id="echoid-s15712" xml:space="preserve">minus <lb/>autem aqua & </s> <s xml:id="echoid-s15713" xml:space="preserve">vitrum denſitate differunt, quàm aër & </s> <s xml:id="echoid-s15714" xml:space="preserve">aqua.</s> <s xml:id="echoid-s15715" xml:space="preserve"/> </p> <div xml:id="echoid-div2346" type="float" level="2" n="1"> <note position="left" xlink:label="note-0616-05" xlink:href="note-0616-05a" xml:space="preserve">891.</note> </div> <p> <s xml:id="echoid-s15716" xml:space="preserve">Si media denſitate æqualiter differant, colores vividiores <lb/> <anchor type="note" xlink:label="note-0616-06a" xlink:href="note-0616-06"/> erunt, ſi denſius rariori circumdetur: </s> <s xml:id="echoid-s15717" xml:space="preserve">nam in laminâ vitreâ <lb/>tenuiſſimâ, quæ coloribus ex tenuitate tingitur, aëre circum-<lb/>datâ, colores magis vividi erunt, quàm in Exper. </s> <s xml:id="echoid-s15718" xml:space="preserve">1. </s> <s xml:id="echoid-s15719" xml:space="preserve">in quo <lb/>lamina aërea vitro circumdatur.</s> <s xml:id="echoid-s15720" xml:space="preserve"/> </p> <div xml:id="echoid-div2347" type="float" level="2" n="2"> <note position="left" xlink:label="note-0616-06" xlink:href="note-0616-06a" xml:space="preserve">892.</note> </div> <p> <s xml:id="echoid-s15721" xml:space="preserve">Ejuſdem denſitatis lamina, eodem medio circumdata, eo <lb/> <anchor type="note" xlink:label="note-0616-07a" xlink:href="note-0616-07"/> majori copiâ lumen reflectit, quo tenuior eſt. </s> <s xml:id="echoid-s15722" xml:space="preserve">Nimium tamen <lb/> <anchor type="note" xlink:label="note-0616-08a" xlink:href="note-0616-08"/> ſi minuatur craſſities, non reflectit lumen. </s> <s xml:id="echoid-s15723" xml:space="preserve">Patent hæc expe-<lb/>rimentis præcedentibus; </s> <s xml:id="echoid-s15724" xml:space="preserve">in tribus primis circuli colorati mi-<lb/>nores, qui etiam ſunt tenuiores, omnium optimè lumen re-<lb/>flectunt; </s> <s xml:id="echoid-s15725" xml:space="preserve">in centro verò, ubi lamina eſt omnium tenuiſſi-<lb/>ma, nulla ſenſibilis datur reflectio; </s> <s xml:id="echoid-s15726" xml:space="preserve">ut illud in ſecundo clarè <pb o="(101)" file="0617" n="681" rhead="MATHEMATICA LIB. III. CAP. XXII."/> patet: </s> <s xml:id="echoid-s15727" xml:space="preserve">in primo datur etiam lamina tenuiſſima aërea, quæ lu-<lb/>men non reflectit; </s> <s xml:id="echoid-s15728" xml:space="preserve">nam macula in centro tranſlucida ſuperat <lb/>magnitudine ſuperficies vitrorum, quæ ex introceſſione par-<lb/>tium immediatè ſeſe mutuo tangunt.</s> <s xml:id="echoid-s15729" xml:space="preserve"/> </p> <div xml:id="echoid-div2348" type="float" level="2" n="3"> <note position="left" xlink:label="note-0616-07" xlink:href="note-0616-07a" xml:space="preserve">893.</note> <note position="left" xlink:label="note-0616-08" xlink:href="note-0616-08a" xml:space="preserve">894.</note> </div> <p> <s xml:id="echoid-s15730" xml:space="preserve">Si dentur laminæ ejuſdem medii, quarum craſſities ſint in <lb/> <anchor type="note" xlink:label="note-0617-01a" xlink:href="note-0617-01"/> progreſſione arithmeticâ numerorum naturalium 1. </s> <s xml:id="echoid-s15731" xml:space="preserve">2. </s> <s xml:id="echoid-s15732" xml:space="preserve">3. </s> <s xml:id="echoid-s15733" xml:space="preserve">4. </s> <s xml:id="echoid-s15734" xml:space="preserve">5. <lb/></s> <s xml:id="echoid-s15735" xml:space="preserve">6. </s> <s xml:id="echoid-s15736" xml:space="preserve">7. </s> <s xml:id="echoid-s15737" xml:space="preserve">&</s> <s xml:id="echoid-s15738" xml:space="preserve">c.</s> <s xml:id="echoid-s15739" xml:space="preserve">, ſi omnium tenuiſſima reflectat radios homogeneos <lb/>quoſcunque, ſecunda eoſdem tranſmittet, tertia iterum re-<lb/>flectet, & </s> <s xml:id="echoid-s15740" xml:space="preserve">alternis vicibus radiir eflectuntur & </s> <s xml:id="echoid-s15741" xml:space="preserve">tranſmit-<lb/>tuntur: </s> <s xml:id="echoid-s15742" xml:space="preserve">id eſt, laminæ, quarum craſſities in progreſſione <lb/>memoratâ reſpondent numeris imparibus 1. </s> <s xml:id="echoid-s15743" xml:space="preserve">3. </s> <s xml:id="echoid-s15744" xml:space="preserve">5. </s> <s xml:id="echoid-s15745" xml:space="preserve">7. </s> <s xml:id="echoid-s15746" xml:space="preserve">&</s> <s xml:id="echoid-s15747" xml:space="preserve">c.</s> <s xml:id="echoid-s15748" xml:space="preserve">, re-<lb/>flectunt radios, quos tranſmittunt reliquæ, quarum craſſities <lb/>reſpondent numeris paribus 2. </s> <s xml:id="echoid-s15749" xml:space="preserve">4. </s> <s xml:id="echoid-s15750" xml:space="preserve">6. </s> <s xml:id="echoid-s15751" xml:space="preserve">8. </s> <s xml:id="echoid-s15752" xml:space="preserve">& </s> <s xml:id="echoid-s15753" xml:space="preserve">c.</s> <s xml:id="echoid-s15754" xml:space="preserve"/> </p> <div xml:id="echoid-div2349" type="float" level="2" n="4"> <note position="right" xlink:label="note-0617-01" xlink:href="note-0617-01a" xml:space="preserve">895.</note> </div> <p> <s xml:id="echoid-s15755" xml:space="preserve">Hæc laminarum proprietas obtinet reſpectu radiorum ho-<lb/>mogeneorum quorumcunque: </s> <s xml:id="echoid-s15756" xml:space="preserve">cum hac differentiâ, quod craſ-<lb/>ſities diverſæ pro coloribus diverſis requirantur, ut ante di-<lb/>ctum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15757" xml:space="preserve">omnium minima eſt in coloris violacei reflectione;</s> <s xml:id="echoid-s15758" xml:space="preserve"> <anchor type="note" xlink:label="note-0617-02a" xlink:href="note-0617-02"/> in rubri reflectione omnium maxima; </s> <s xml:id="echoid-s15759" xml:space="preserve">poſitis craſſitiebus in-<lb/>termediis, radii refrangibilitatis intermediæ reflectuntur, <lb/>id eſt, creſcente radii refrangibilitate etiam minuitur craſ-<lb/> <anchor type="note" xlink:label="note-0617-03a" xlink:href="note-0617-03"/> ſities laminæ, quæ illum reflectit.</s> <s xml:id="echoid-s15760" xml:space="preserve"/> </p> <div xml:id="echoid-div2350" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0617-02" xlink:href="note-0617-02a" xml:space="preserve">887.</note> <note position="right" xlink:label="note-0617-03" xlink:href="note-0617-03a" xml:space="preserve">896.</note> </div> </div> <div xml:id="echoid-div2352" type="section" level="1" n="589"> <head xml:id="echoid-head771" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s15761" xml:space="preserve">Inſtituatur experimentum in loco obſcuro, in quo imago <lb/>Solis oblonga, in Exp. </s> <s xml:id="echoid-s15762" xml:space="preserve">1. </s> <s xml:id="echoid-s15763" xml:space="preserve">cap. </s> <s xml:id="echoid-s15764" xml:space="preserve">18. </s> <s xml:id="echoid-s15765" xml:space="preserve">memorata, in chartâ re-<lb/>præſentatur. </s> <s xml:id="echoid-s15766" xml:space="preserve">Dentur, ut in exp. </s> <s xml:id="echoid-s15767" xml:space="preserve">1. </s> <s xml:id="echoid-s15768" xml:space="preserve">hujus cap. </s> <s xml:id="echoid-s15769" xml:space="preserve">duo vitra ob-<lb/>jectiva, teleſcopiorum majorum, ſuper ſe mutuo compreſ-<lb/>ſorum, & </s> <s xml:id="echoid-s15770" xml:space="preserve">ita diſponantur, ut in his, quaſi in ſpeculo, ſuc-<lb/>ceſſivè videantur colores ſinguli imaginis memoratæ id eſt, <lb/>vitra ſucceſſivè illuminentur radiis homogeneis diverſis; <lb/></s> <s xml:id="echoid-s15771" xml:space="preserve">quod obtinetur paululum circa axem agitando priſma, quo <lb/>radii in imagine oblongâ ſeparantur. </s> <s xml:id="echoid-s15772" xml:space="preserve">Annuli, in experimen-<lb/>to primo memorati, apparent, ſed majori numero, & </s> <s xml:id="echoid-s15773" xml:space="preserve">unius <lb/>tantum coloris; </s> <s xml:id="echoid-s15774" xml:space="preserve">propter coloris immutabilitatem in radiis <lb/>homogeneis <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s15775" xml:space="preserve">in interſtitiis horum annulorum radii tranſ- <anchor type="note" xlink:label="note-0617-04a" xlink:href="note-0617-04"/> mittuntur ut in chartâ, diſpoſitâ poſt vitra, in quam radii <lb/>tranſmiſſi impingunt, clarè patet; </s> <s xml:id="echoid-s15776" xml:space="preserve">annuli omnium ſunt mi-<lb/>nimi, quando ſunt violacei; </s> <s xml:id="echoid-s15777" xml:space="preserve">dilatantur ſucceſſivè conſideran- <pb o="(102)" file="0618" n="682" rhead="PHYSICES ELEMENTA"/> do colores ſequentes ad rubrum uſque. </s> <s xml:id="echoid-s15778" xml:space="preserve">Si, poſitis annulis <lb/>coloris cujuſcunque, diametri exactè menſurentur ci culo-<lb/>rum, qui in medio latitudinis ſingulorum annulorum conci-<lb/>piuntur, quadrata diametrorum erunt inter ſe ut numeri im-<lb/>pares 1. </s> <s xml:id="echoid-s15779" xml:space="preserve">3. </s> <s xml:id="echoid-s15780" xml:space="preserve">5. </s> <s xml:id="echoid-s15781" xml:space="preserve">&</s> <s xml:id="echoid-s15782" xml:space="preserve">c. </s> <s xml:id="echoid-s15783" xml:space="preserve">& </s> <s xml:id="echoid-s15784" xml:space="preserve">eodem modo, menſuratis diametris cir-<lb/>culorum, in medio ſingulorum interſtitiorum inter annu-<lb/>los, illarum quadrata erunt, ut numeri pares 2. </s> <s xml:id="echoid-s15785" xml:space="preserve">4. </s> <s xml:id="echoid-s15786" xml:space="preserve">6. </s> <s xml:id="echoid-s15787" xml:space="preserve">&</s> <s xml:id="echoid-s15788" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s15789" xml:space="preserve">Cùm autem agatur de vitris ſphæricis, craſſities laminæ aëreæ, <lb/>in circulis memoratis, ſunt ut numeri pares & </s> <s xml:id="echoid-s15790" xml:space="preserve">impares.</s> <s xml:id="echoid-s15791" xml:space="preserve"/> </p> <div xml:id="echoid-div2352" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0617-04" xlink:href="note-0617-04a" xml:space="preserve">863.</note> </div> </div> <div xml:id="echoid-div2354" type="section" level="1" n="590"> <head xml:id="echoid-head772" xml:space="preserve"><emph style="sc">Definitio</emph></head> <p> <s xml:id="echoid-s15792" xml:space="preserve">Color homogencus, in laminâ medii cujuſcunque, dicitur <lb/> <anchor type="note" xlink:label="note-0618-01a" xlink:href="note-0618-01"/> primi ordinis, ſi lamina fuerit omnium tenuiſſima, quæ talem <lb/>colorem reflectit; </s> <s xml:id="echoid-s15793" xml:space="preserve">in laminâ, cujus craſſities tripla eſt, dici-<lb/>tur ſecundi ordinis, &</s> <s xml:id="echoid-s15794" xml:space="preserve">c.</s> <s xml:id="echoid-s15795" xml:space="preserve"/> </p> <div xml:id="echoid-div2354" type="float" level="2" n="1"> <note position="left" xlink:label="note-0618-01" xlink:href="note-0618-01a" xml:space="preserve">897.</note> </div> <p style="it"> <s xml:id="echoid-s15796" xml:space="preserve">Color primi ordinis eſt omnium maximè vividus; </s> <s xml:id="echoid-s15797" xml:space="preserve">& </s> <s xml:id="echoid-s15798" xml:space="preserve">ſucceſ-<lb/> <anchor type="note" xlink:label="note-0618-02a" xlink:href="note-0618-02"/> ſivè, in ordinibus ſequentibus, ſecundo, tertio, &</s> <s xml:id="echoid-s15799" xml:space="preserve">c, minus <lb/>ac minus vividus eſt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15800" xml:space="preserve"> <anchor type="note" xlink:label="note-0618-03a" xlink:href="note-0618-03"/> </s> </p> <div xml:id="echoid-div2355" type="float" level="2" n="2"> <note position="left" xlink:label="note-0618-02" xlink:href="note-0618-02a" xml:space="preserve">898.</note> <note symbol="*" position="left" xlink:label="note-0618-03" xlink:href="note-0618-03a" xml:space="preserve">893.</note> </div> <p> <s xml:id="echoid-s15801" xml:space="preserve">Quando radiis hæterogeneis illuſtratur lamina aërea, inter <lb/>vitra Teleſcopiorum, aut lamina ſimilis ex aliâ quacunque <lb/>materiá, ut in Exp. </s> <s xml:id="echoid-s15802" xml:space="preserve">1. </s> <s xml:id="echoid-s15803" xml:space="preserve">& </s> <s xml:id="echoid-s15804" xml:space="preserve">2. </s> <s xml:id="echoid-s15805" xml:space="preserve">varii ex annulis, in ultimo ex-<lb/>perimento viſis, inter ſe confunduntur, & </s> <s xml:id="echoid-s15806" xml:space="preserve">color videtur, <lb/>qui ex horum permixtione conflatur; </s> <s xml:id="echoid-s15807" xml:space="preserve">nam eadem laminæ <lb/> <anchor type="note" xlink:label="note-0618-04a" xlink:href="note-0618-04"/> craſſities, ad colores diverſos, variorum or dinum, reflecten-<lb/>dos, ſæpè requiritur: </s> <s xml:id="echoid-s15808" xml:space="preserve">ſic lamina, quæ violaceum tertii ordi-<lb/>nis reflectit, etiam repercutit rubrum ſecundi ordinis, ut, <lb/>ad hoc attendendo, ex ultimo experimento deducitur: </s> <s xml:id="echoid-s15809" xml:space="preserve">ideò-<lb/>que in Exp. </s> <s xml:id="echoid-s15810" xml:space="preserve">1. </s> <s xml:id="echoid-s15811" xml:space="preserve">& </s> <s xml:id="echoid-s15812" xml:space="preserve">2.</s> <s xml:id="echoid-s15813" xml:space="preserve">, violaceus annulus tertius cum parte ex-<lb/>teriori annuli rubri ſecundi confunditur, & </s> <s xml:id="echoid-s15814" xml:space="preserve">color datur pur-<lb/>pureus; </s> <s xml:id="echoid-s15815" xml:space="preserve">non tamen omnis ruber color ſecundi ordinis abſor-<lb/>betur; </s> <s xml:id="echoid-s15816" xml:space="preserve">quia annulus ruber violaceum latitudine ſuperat.</s> <s xml:id="echoid-s15817" xml:space="preserve"/> </p> <div xml:id="echoid-div2356" type="float" level="2" n="3"> <note position="left" xlink:label="note-0618-04" xlink:href="note-0618-04a" xml:space="preserve">899.</note> </div> <p> <s xml:id="echoid-s15818" xml:space="preserve">Quo magis augetur laminæ craſſities, eo plures colores re-<lb/> <anchor type="note" xlink:label="note-0618-05a" xlink:href="note-0618-05"/> flectit, varios, ex diverſis ordinibus. </s> <s xml:id="echoid-s15819" xml:space="preserve">Lamina violacea de-<lb/>cimi ordinis, congruit cum cæruleâ noni ordinis, & </s> <s xml:id="echoid-s15820" xml:space="preserve">flavâ <lb/>octavi ordinis, & </s> <s xml:id="echoid-s15821" xml:space="preserve">tandem cum rubrâ ſeptimi ordinis, & </s> <s xml:id="echoid-s15822" xml:space="preserve">color <lb/>laminæ ex permixtione horum colorum conflatur.</s> <s xml:id="echoid-s15823" xml:space="preserve"/> </p> <div xml:id="echoid-div2357" type="float" level="2" n="4"> <note position="left" xlink:label="note-0618-05" xlink:href="note-0618-05a" xml:space="preserve">900.</note> </div> <p> <s xml:id="echoid-s15824" xml:space="preserve">Si, in Exp. </s> <s xml:id="echoid-s15825" xml:space="preserve">1. </s> <s xml:id="echoid-s15826" xml:space="preserve">& </s> <s xml:id="echoid-s15827" xml:space="preserve">2.</s> <s xml:id="echoid-s15828" xml:space="preserve">, obliquè ſpectator intueatur laminas, <lb/> <anchor type="note" xlink:label="note-0618-06a" xlink:href="note-0618-06"/> aëream, & </s> <s xml:id="echoid-s15829" xml:space="preserve">aqueam, dilantantur annuli cum oculi obliquitate, <pb o="(103)" file="0619" n="683" rhead="MATHEMATICA LIB. III. CAP. XXIII."/> id eſt, in hcc motu oculi laminæ color in determinato loco <lb/>mutatur: </s> <s xml:id="echoid-s15830" xml:space="preserve">major tamen eſt in Exp. </s> <s xml:id="echoid-s15831" xml:space="preserve">1. </s> <s xml:id="echoid-s15832" xml:space="preserve">dilatatio; </s> <s xml:id="echoid-s15833" xml:space="preserve">quod pro-<lb/>bat obliquitate radiorum colorem magis mutari, ſilamina den-<lb/> <anchor type="note" xlink:label="note-0619-01a" xlink:href="note-0619-01"/> ſiori medio, quàm ſi rariori circumdetur.</s> <s xml:id="echoid-s15834" xml:space="preserve"/> </p> <div xml:id="echoid-div2358" type="float" level="2" n="5"> <note position="left" xlink:label="note-0618-06" xlink:href="note-0618-06a" xml:space="preserve">901.</note> <note position="right" xlink:label="note-0619-01" xlink:href="note-0619-01a" xml:space="preserve">902.</note> </div> <p> <s xml:id="echoid-s15835" xml:space="preserve">Cujus propoſitionis demonſtrationem ex refractionis legi-<lb/> <anchor type="note" xlink:label="note-0619-02a" xlink:href="note-0619-02"/> bus facile deducimus. </s> <s xml:id="echoid-s15836" xml:space="preserve">Sint L & </s> <s xml:id="echoid-s15837" xml:space="preserve">l laminæ tenues; </s> <s xml:id="echoid-s15838" xml:space="preserve">hæc me-<lb/>dio denſiori, illa medio rariori circumdata; </s> <s xml:id="echoid-s15839" xml:space="preserve">ſint ambæ ejuſ-<lb/>dem craſſitiei: </s> <s xml:id="echoid-s15840" xml:space="preserve">ſi in has incidant radii AB, ab, æqualiter <lb/>ad laminas inclinati; </s> <s xml:id="echoid-s15841" xml:space="preserve">in L refractio fiet, accedendo ad per-<lb/>pendicularem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15842" xml:space="preserve">in l contra refringitur radius recedendo a <anchor type="note" xlink:label="note-0619-03a" xlink:href="note-0619-03"/> perpendiculari <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15843" xml:space="preserve">& </s> <s xml:id="echoid-s15844" xml:space="preserve">licèt BD & </s> <s xml:id="echoid-s15845" xml:space="preserve">bd ſint æquales, bc longitudi- <anchor type="note" xlink:label="note-0619-04a" xlink:href="note-0619-04"/> ne ſuperat BC, ideòque major datur mutatio in motu lu-<lb/>minis in laminâ l quàm in L. </s> <s xml:id="echoid-s15846" xml:space="preserve">Auctâ denſitate laminæ L, <lb/> <anchor type="note" xlink:label="note-0619-05a" xlink:href="note-0619-05"/> manente medio rariori quo circumdatur, minor dabitur diffe-<lb/>rentia inter BC & </s> <s xml:id="echoid-s15847" xml:space="preserve">BD, ideoque minor mutatio coloris; </s> <s xml:id="echoid-s15848" xml:space="preserve">& </s> <s xml:id="echoid-s15849" xml:space="preserve"><lb/>ſi ita augeatur vis refringens laminæ, ut radii refracti, quæ-<lb/> <anchor type="note" xlink:label="note-0619-06a" xlink:href="note-0619-06"/> cunque fuerit incidentis obliquitas, ſenſibiliter inter ſe non <lb/>differant, ſenſibilis non dabitur differentia in colore laminæ, <lb/>in quocunque ſitu oculus ponatur.</s> <s xml:id="echoid-s15850" xml:space="preserve"/> </p> <div xml:id="echoid-div2359" type="float" level="2" n="6"> <note position="right" xlink:label="note-0619-02" xlink:href="note-0619-02a" xml:space="preserve">TAB. XVIII. <lb/>fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0619-03" xlink:href="note-0619-03a" xml:space="preserve">624.</note> <note symbol="*" position="right" xlink:label="note-0619-04" xlink:href="note-0619-04a" xml:space="preserve">625.</note> <note position="right" xlink:label="note-0619-05" xlink:href="note-0619-05a" xml:space="preserve">903.</note> <note position="right" xlink:label="note-0619-06" xlink:href="note-0619-06a" xml:space="preserve">904.</note> </div> <p> <s xml:id="echoid-s15851" xml:space="preserve">Ex hiſce facile deducimus, quarundam laminarum colorem <lb/> <anchor type="note" xlink:label="note-0619-07a" xlink:href="note-0619-07"/> ex mutato oculi ſitu variari, aliarum colorem permanere.</s> <s xml:id="echoid-s15852" xml:space="preserve"/> </p> <div xml:id="echoid-div2360" type="float" level="2" n="7"> <note position="right" xlink:label="note-0619-07" xlink:href="note-0619-07a" xml:space="preserve">905.</note> </div> </div> <div xml:id="echoid-div2362" type="section" level="1" n="591"> <head xml:id="echoid-head773" xml:space="preserve">CAPUT XXIII. <lb/>De Corporum naturalium Coloribus.</head> <p> <s xml:id="echoid-s15853" xml:space="preserve">QUæ Corporum quorumcunque colores ſpectant, ex huc <lb/>uſque explicatis facilè deducuntur.</s> <s xml:id="echoid-s15854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15855" xml:space="preserve">Vidimus radios luminis colores ſibi peculiares & </s> <s xml:id="echoid-s15856" xml:space="preserve">im-<lb/>mutabiles habere, ita ut reflectione non mutentur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15857" xml:space="preserve"> <anchor type="note" xlink:label="note-0619-08a" xlink:href="note-0619-08"/> </s> </p> <div xml:id="echoid-div2362" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0619-08" xlink:href="note-0619-08a" xml:space="preserve">863.</note> </div> <p style="it"> <s xml:id="echoid-s15858" xml:space="preserve">Ideò radii à corporibus reflexi, pro majori aut minori re-<lb/> <anchor type="note" xlink:label="note-0619-09a" xlink:href="note-0619-09"/> frangibilitate, quæ competit colori ipſius corporis, majorem <lb/>aut minorem refrangibilitatem habent.</s> <s xml:id="echoid-s15859" xml:space="preserve"/> </p> <div xml:id="echoid-div2363" type="float" level="2" n="2"> <note position="right" xlink:label="note-0619-09" xlink:href="note-0619-09a" xml:space="preserve">906.</note> </div> </div> <div xml:id="echoid-div2365" type="section" level="1" n="592"> <head xml:id="echoid-head774" xml:space="preserve"><emph style="sc">Experimentum</emph> 1.</head> <p> <s xml:id="echoid-s15860" xml:space="preserve">In medio chartæ nigræ duo fruſta quadrata, duorum cir-<lb/>citer pollicum, vittæ ſericæ, unum rubeum alterum viola-<lb/>ceum, junguntur ita, ut ſeſe mutuo ad latera tangant, eo-<lb/>dem modo ac colores ruber & </s> <s xml:id="echoid-s15861" xml:space="preserve">violaceus in Exp. </s> <s xml:id="echoid-s15862" xml:space="preserve">3. </s> <s xml:id="echoid-s15863" xml:space="preserve">cap. </s> <s xml:id="echoid-s15864" xml:space="preserve">19.</s> <s xml:id="echoid-s15865" xml:space="preserve">; <pb o="(104)" file="0620" n="684" rhead="PHYSICES ELEMENTA"/> diſponintur charta nigra, ut à lumine per feneſtram cubicu-<lb/>lum intranti vittæ probè illuminentur: </s> <s xml:id="echoid-s15866" xml:space="preserve">ſi ſpectator trans <lb/>priſma vittas intueatur, ut in exp. </s> <s xml:id="echoid-s15867" xml:space="preserve">ſtatim memorato, eodem <lb/>modo, ac in illo experimento, colores ſeparati apparent.</s> <s xml:id="echoid-s15868" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2366" type="section" level="1" n="593"> <head xml:id="echoid-head775" xml:space="preserve"><emph style="sc">Experimentum</emph> 2.</head> <p> <s xml:id="echoid-s15869" xml:space="preserve">Dentur in R & </s> <s xml:id="echoid-s15870" xml:space="preserve">V vittæ ſericæ in Experimento præceden-<lb/> <anchor type="note" xlink:label="note-0620-01a" xlink:href="note-0620-01"/> ti memoratæ hæc violacea, illa rubra eſt; </s> <s xml:id="echoid-s15871" xml:space="preserve">flammâ candelæ <lb/>illuminentur; </s> <s xml:id="echoid-s15872" xml:space="preserve">ad ſex pedum diſtantiam detur lens convexa <lb/>V, de qua in Exp. </s> <s xml:id="echoid-s15873" xml:space="preserve">6. </s> <s xml:id="echoid-s15874" xml:space="preserve">cap. </s> <s xml:id="echoid-s15875" xml:space="preserve">19; </s> <s xml:id="echoid-s15876" xml:space="preserve">ad diſtantiam circiter ſex <lb/>pedum, in chartâ albâ dabitur in r repræſentatio vittæ R, <lb/>ad minorem diſtantiam in v aliûs repræſentationem exactam <lb/>habemus. </s> <s xml:id="echoid-s15877" xml:space="preserve">Determinatur ubi repræſentationes ſunt exactæ, <lb/>ſi fila nigra trajiciant ſuperficiem vittarum, nam hæc fila di-<lb/>ſtincta apparent in exactâ repræſentatione.</s> <s xml:id="echoid-s15878" xml:space="preserve"/> </p> <div xml:id="echoid-div2366" type="float" level="2" n="1"> <note position="left" xlink:label="note-0620-01" xlink:href="note-0620-01a" xml:space="preserve">TAB. XIX. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s15879" xml:space="preserve">Corporum colores varios dari, quia radii diverſi à corpori-<lb/> <anchor type="note" xlink:label="note-0620-02a" xlink:href="note-0620-02"/> bus diverſê coloratis reflectuntur, & </s> <s xml:id="echoid-s15880" xml:space="preserve">corpus illius coloris ap-<lb/>parere, qui oritur ex permixtione radiorum reflexorum, <lb/>non modo ex præcedentibus experimentis deducitur, ſed <lb/>etiam directis demonſtratur.</s> <s xml:id="echoid-s15881" xml:space="preserve"/> </p> <div xml:id="echoid-div2367" type="float" level="2" n="2"> <note position="left" xlink:label="note-0620-02" xlink:href="note-0620-02a" xml:space="preserve">907.</note> </div> </div> <div xml:id="echoid-div2369" type="section" level="1" n="594"> <head xml:id="echoid-head776" xml:space="preserve"><emph style="sc">Experimentum</emph> 3.</head> <p> <s xml:id="echoid-s15882" xml:space="preserve">Dentur duo corpora quæcunque unum rubrum, alterum <lb/>cœruleum, illuminentur hæc ſucceſſivè, in loco obſcuro, <lb/>coloribus imaginis coloratæ, refractione priſmatis formatæ, <lb/>ſinguli colores ab ambobus quidem reflectuntur, ſed radii <lb/>rubri magnâ copia à corpore rubro repercutiuntur, dum pau-<lb/>cos ex his reflectit corpus cœruleum, ut ex collatione coloris <lb/>rubri amborum corporum clarè patet; </s> <s xml:id="echoid-s15883" xml:space="preserve">contrarium obſer-<lb/>vatur in radiis cœruleis, qui à corpore cœruleo magnâ co-<lb/>piâ reflectuntur, dum à corpore rubro pauci tantum, re-<lb/>flectione redeunt.</s> <s xml:id="echoid-s15884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15885" xml:space="preserve">Radii, qui à corpore non reflectuntur, in hoc penetrant, ibi-<lb/>que innumeras reflectiones & </s> <s xml:id="echoid-s15886" xml:space="preserve">refractiones patiuntur, ut inter <lb/>num. </s> <s xml:id="echoid-s15887" xml:space="preserve">842. </s> <s xml:id="echoid-s15888" xml:space="preserve">& </s> <s xml:id="echoid-s15889" xml:space="preserve">843. </s> <s xml:id="echoid-s15890" xml:space="preserve">explicavimus; </s> <s xml:id="echoid-s15891" xml:space="preserve">donec tandem ſeſe jungant <lb/> <anchor type="note" xlink:label="note-0620-03a" xlink:href="note-0620-03"/> particulis ipſius corporis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s15892" xml:space="preserve">Idèo corpus eo citius incaleſcit, <anchor type="note" xlink:label="note-0620-04a" xlink:href="note-0620-04"/> quo minori copiâ reflectit lumen. </s> <s xml:id="echoid-s15893" xml:space="preserve">Idcirco corpus album, <lb/> <anchor type="note" xlink:label="note-0620-05a" xlink:href="note-0620-05"/> quod ferè omnes radios quibus illuſtratur reflectit <anchor type="note" xlink:href="" symbol="*"/>, omnium, <anchor type="note" xlink:label="note-0620-06a" xlink:href="note-0620-06"/> lentiſſimè incaleſcit, dum corpus nigrum, in quod ferè omnes <pb file="0621" n="685"/> <pb file="0621a" n="686"/> <anchor type="figure" xlink:label="fig-0621a-01a" xlink:href="fig-0621a-01"/> <pb file="0622" n="687"/> <pb o="(105)" file="0623" n="688" rhead="MATHEMATICA LIB. III. CAP. XXIII."/> radii penetrant, quia pauci tantùm reflectuntur <anchor type="note" xlink:href="" symbol="*"/>, citius aliis <anchor type="note" xlink:label="note-0623-01a" xlink:href="note-0623-01"/> calorem acquirit.</s> <s xml:id="echoid-s15894" xml:space="preserve"/> </p> <div xml:id="echoid-div2369" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0620-03" xlink:href="note-0620-03a" xml:space="preserve">546.</note> <note position="left" xlink:label="note-0620-04" xlink:href="note-0620-04a" xml:space="preserve">908.</note> <note position="left" xlink:label="note-0620-05" xlink:href="note-0620-05a" xml:space="preserve">909.</note> <note symbol="*" position="left" xlink:label="note-0620-06" xlink:href="note-0620-06a" xml:space="preserve">870.</note> <figure xlink:label="fig-0621a-01" xlink:href="fig-0621a-01a"> <image file="0621a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0621a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0623-01" xlink:href="note-0623-01a" xml:space="preserve">845.</note> </div> <p> <s xml:id="echoid-s15895" xml:space="preserve">Ut autem determinemus conſtitutionem ſuperficierum <lb/>corporum, à qua color pendet, debemus attendere ad mi-<lb/>nimas particulas, ex quibus hæ ſuperficies formantur; </s> <s xml:id="echoid-s15896" xml:space="preserve">Par-<lb/>ticulæ hæ ſunt tranſlucidæ <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15897" xml:space="preserve">ſeparantur medio, denſitate <anchor type="note" xlink:label="note-0623-02a" xlink:href="note-0623-02"/> differente cum ipſis particulis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15898" xml:space="preserve">ſunt etiam tenues, aliter <anchor type="note" xlink:label="note-0623-03a" xlink:href="note-0623-03"/> ſuperficies quaſi corpore tranſlucido obtegeretur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s15899" xml:space="preserve">color à <anchor type="note" xlink:label="note-0623-04a" xlink:href="note-0623-04"/> particulis infra has pendêret. </s> <s xml:id="echoid-s15900" xml:space="preserve">In omni ergo ſuperficie cor-<lb/>poris colorati dantur laminæ innumeræ exiguæ tenues; </s> <s xml:id="echoid-s15901" xml:space="preserve">mi-<lb/>nuendo autem laminam, ſervatâ hujus craſſitie, non hujus <lb/>proprietates, quantum ad luminis reflectionem, mutantur; <lb/></s> <s xml:id="echoid-s15902" xml:space="preserve">nam lamina minima, cum relatione ad radios luminis, magna <lb/>admodum eſt: </s> <s xml:id="echoid-s15903" xml:space="preserve">Idcirco demonſtrata in Capite præcedenti, ad <lb/>haſce laminas in ſuperficiebus corporum applicari poſſunt. </s> <s xml:id="echoid-s15904" xml:space="preserve"><lb/>Unde ſequentes deducimus concluſiones.</s> <s xml:id="echoid-s15905" xml:space="preserve"/> </p> <div xml:id="echoid-div2370" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0623-02" xlink:href="note-0623-02a" xml:space="preserve">841.</note> <note symbol="*" position="right" xlink:label="note-0623-03" xlink:href="note-0623-03a" xml:space="preserve">843.</note> <note symbol="*" position="right" xlink:label="note-0623-04" xlink:href="note-0623-04a" xml:space="preserve">843.</note> </div> <p style="it"> <s xml:id="echoid-s15906" xml:space="preserve">Pendet color corporis à craſſitie, & </s> <s xml:id="echoid-s15907" xml:space="preserve">denſitate partium cor-<lb/> <anchor type="note" xlink:label="note-0623-05a" xlink:href="note-0623-05"/> poris, quæ in ſuperficie interjacent meatus in corpore <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15908" xml:space="preserve"> <anchor type="note" xlink:label="note-0623-06a" xlink:href="note-0623-06"/> </s> </p> <div xml:id="echoid-div2371" type="float" level="2" n="3"> <note position="right" xlink:label="note-0623-05" xlink:href="note-0623-05a" xml:space="preserve">910.</note> <note symbol="*" position="right" xlink:label="note-0623-06" xlink:href="note-0623-06a" xml:space="preserve">890.</note> </div> <p style="it"> <s xml:id="echoid-s15909" xml:space="preserve">Eo magis vividus & </s> <s xml:id="echoid-s15910" xml:space="preserve">magis homogeneus eſt color, quo par-<lb/> <anchor type="note" xlink:label="note-0623-07a" xlink:href="note-0623-07"/> tes ſunt tenuiores <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15911" xml:space="preserve"> <anchor type="note" xlink:label="note-0623-08a" xlink:href="note-0623-08"/> </s> </p> <div xml:id="echoid-div2372" type="float" level="2" n="4"> <note position="right" xlink:label="note-0623-07" xlink:href="note-0623-07a" xml:space="preserve">911.</note> <note symbol="*" position="right" xlink:label="note-0623-08" xlink:href="note-0623-08a" xml:space="preserve">898. 899. 900.</note> </div> <p style="it"> <s xml:id="echoid-s15912" xml:space="preserve">Cæteris paribus, partes memoratæ craſſitiem omnium <lb/> <anchor type="note" xlink:label="note-0623-09a" xlink:href="note-0623-09"/> maximam habent, ſi corpus fuerit rubrum, omnium minimam <lb/>ſi violaceum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15913" xml:space="preserve"> <anchor type="note" xlink:label="note-0623-10a" xlink:href="note-0623-10"/> </s> </p> <div xml:id="echoid-div2373" type="float" level="2" n="5"> <note position="right" xlink:label="note-0623-09" xlink:href="note-0623-09a" xml:space="preserve">912.</note> <note symbol="*" position="right" xlink:label="note-0623-10" xlink:href="note-0623-10a" xml:space="preserve">896. 861.</note> </div> <p style="it"> <s xml:id="echoid-s15914" xml:space="preserve">Partes corporum denſitate medium in interſtitiis multum <lb/> <anchor type="note" xlink:label="note-0623-11a" xlink:href="note-0623-11"/> ſuperant <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15915" xml:space="preserve"> <anchor type="note" xlink:label="note-0623-12a" xlink:href="note-0623-12"/> </s> </p> <div xml:id="echoid-div2374" type="float" level="2" n="6"> <note position="right" xlink:label="note-0623-11" xlink:href="note-0623-11a" xml:space="preserve">913.</note> <note symbol="*" position="right" xlink:label="note-0623-12" xlink:href="note-0623-12a" xml:space="preserve">902. 903. 904.</note> </div> <p> <s xml:id="echoid-s15916" xml:space="preserve">Denſitas hæc minor eſt in caudis pavonum & </s> <s xml:id="echoid-s15917" xml:space="preserve">in quibuſdam <lb/> <anchor type="note" xlink:label="note-0623-13a" xlink:href="note-0623-13"/> pannis ſericis, & </s> <s xml:id="echoid-s15918" xml:space="preserve">in genere in omnibus corporibus, quorum co-<lb/>lor pro diverſo oculi ſitu variat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15919" xml:space="preserve"> <anchor type="note" xlink:label="note-0623-14a" xlink:href="note-0623-14"/> </s> </p> <div xml:id="echoid-div2375" type="float" level="2" n="7"> <note position="right" xlink:label="note-0623-13" xlink:href="note-0623-13a" xml:space="preserve">914.</note> <note symbol="*" position="right" xlink:label="note-0623-14" xlink:href="note-0623-14a" xml:space="preserve">901. 903.</note> </div> <p> <s xml:id="echoid-s15920" xml:space="preserve">Color corporis obſcurior & </s> <s xml:id="echoid-s15921" xml:space="preserve">fuſcior eſt, ſi medium denſius po-<lb/> <anchor type="note" xlink:label="note-0623-15a" xlink:href="note-0623-15"/> ros intret <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s15922" xml:space="preserve">tunc enim partes à quibus color pendet, medio <anchor type="note" xlink:label="note-0623-16a" xlink:href="note-0623-16"/> denſiori quàm ante, circumdantur.</s> <s xml:id="echoid-s15923" xml:space="preserve"/> </p> <div xml:id="echoid-div2376" type="float" level="2" n="8"> <note position="right" xlink:label="note-0623-15" xlink:href="note-0623-15a" xml:space="preserve">915.</note> <note symbol="*" position="right" xlink:label="note-0623-16" xlink:href="note-0623-16a" xml:space="preserve">891.</note> </div> <p> <s xml:id="echoid-s15924" xml:space="preserve">Experimur hoc in omnibus corporibus, quæ intimè ab aquâ <lb/>aut oleo penetrantur: </s> <s xml:id="echoid-s15925" xml:space="preserve">exſiccatis corporibus priſtinum recu-<lb/>perant colorem, niſi in quibuſdam occaſionibus, in quibus, <lb/>actione aquæ aut olei, quædam partes ſunt ſublatæ, aut quan-<lb/>do partes quædam aquæ aut olei, cum partibus corporis ita <lb/>conjunguntur, ut lamellarum craſſities mutetur.</s> <s xml:id="echoid-s15926" xml:space="preserve"/> </p> <pb o="(106)" file="0624" n="689" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s15927" xml:space="preserve">Ex ſimili cauſà deducuntur mutationes in coloribus quo-<lb/>rundam liquidorum, ex permixtione cum aliis liquidis. </s> <s xml:id="echoid-s15928" xml:space="preserve">Sæ-<lb/> <anchor type="note" xlink:label="note-0624-01a" xlink:href="note-0624-01"/> pè particulæ ſalinæ, natantes inuno liquido, ſeſe jungunt par-<lb/>ticulis ſalinis natantibus in alio; </s> <s xml:id="echoid-s15929" xml:space="preserve">aut, ex actione particularum <lb/>ſupervenientium, ſeparantur particulæ junctæ, quibus omnibus <lb/>mutatur particularum craſſities, & </s> <s xml:id="echoid-s15930" xml:space="preserve">cum hac liquidorum co-<lb/>lor <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15931" xml:space="preserve"> <anchor type="note" xlink:label="note-0624-02a" xlink:href="note-0624-02"/> </s> </p> <div xml:id="echoid-div2377" type="float" level="2" n="9"> <note position="left" xlink:label="note-0624-01" xlink:href="note-0624-01a" xml:space="preserve">916.</note> <note symbol="*" position="left" xlink:label="note-0624-02" xlink:href="note-0624-02a" xml:space="preserve">888.</note> </div> <p style="it"> <s xml:id="echoid-s15932" xml:space="preserve">Liquidi aliquando diverſus eſt color, ſiradiis reflexis, quàm <lb/> <anchor type="note" xlink:label="note-0624-03a" xlink:href="note-0624-03"/> ſi tranſmiſſis, videatur: </s> <s xml:id="echoid-s15933" xml:space="preserve">unde hoc oriatur antea vidimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15934" xml:space="preserve"/> </p> <div xml:id="echoid-div2378" type="float" level="2" n="10"> <note position="left" xlink:label="note-0624-03" xlink:href="note-0624-03a" xml:space="preserve">917.</note> </div> <note symbol="*" position="left" xml:space="preserve">887.</note> </div> <div xml:id="echoid-div2380" type="section" level="1" n="595"> <head xml:id="echoid-head777" xml:space="preserve"><emph style="sc">Experimentum</emph> 4.</head> <p> <s xml:id="echoid-s15935" xml:space="preserve">Infuſio ligni nephritici, non nimium ſatura, reflexis radiis, <lb/>coerulea apparet, flava videtur, ſi inter lumen & </s> <s xml:id="echoid-s15936" xml:space="preserve">oculum de-<lb/>tur phiala infuſionem continens.</s> <s xml:id="echoid-s15937" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2381" type="section" level="1" n="596"> <head xml:id="echoid-head778" xml:space="preserve"><emph style="sc">Experimentum</emph> 5.</head> <p> <s xml:id="echoid-s15938" xml:space="preserve">Si in infuſione ligni nephritici infundatur ſpiritus aceti vi-<lb/>ni, flava apparet quomodocunque videatur.</s> <s xml:id="echoid-s15939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15940" xml:space="preserve">In hoc caſu particularum craſſities mutatur, & </s> <s xml:id="echoid-s15941" xml:space="preserve">radii per <lb/>ſingulas particulas tranſmiſſi intercipiuntur; </s> <s xml:id="echoid-s15942" xml:space="preserve">licèt verò liquor <lb/>inter oculum & </s> <s xml:id="echoid-s15943" xml:space="preserve">lumen ponatur radiis reflexis videtur, nam <lb/>tales radios ad oculum pervenire ex variis reflectionibus, quas <lb/>lumen in liquido patitur, facile concipimus. </s> <s xml:id="echoid-s15944" xml:space="preserve">Hicce autem <lb/>color ſolus ſenſibilis eſt, quia radii directè per liquidum pe-<lb/>netrare non poſſunt.</s> <s xml:id="echoid-s15945" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15946" xml:space="preserve">Ex hoc ipſo deducimus, quare liquidum coloratum, in vi-<lb/> <anchor type="note" xlink:label="note-0624-05a" xlink:href="note-0624-05"/> tro figuræ coni inverſi, ſi detur inter oculum & </s> <s xml:id="echoid-s15947" xml:space="preserve">lumen, di-<lb/>verſi coloris appareat, in variis vaſeos partibus; </s> <s xml:id="echoid-s15948" xml:space="preserve">Inferiori <lb/>parte non omnes radii per particulas tranſmiſſi intercipiun-<lb/>tur, magis ac magis intercipiuntur, quo majori copiâ liqui-<lb/>dum inter oculum & </s> <s xml:id="echoid-s15949" xml:space="preserve">lumen detur; </s> <s xml:id="echoid-s15950" xml:space="preserve">donec tandem omnes in-<lb/>tercipiantur & </s> <s xml:id="echoid-s15951" xml:space="preserve">ſoli à particulis reflexi liquidum penetrent; </s> <s xml:id="echoid-s15952" xml:space="preserve">in <lb/>quo calu color coincidit cum colore liquidi, radiis reflexis viſi.</s> <s xml:id="echoid-s15953" xml:space="preserve"/> </p> <div xml:id="echoid-div2381" type="float" level="2" n="1"> <note position="left" xlink:label="note-0624-05" xlink:href="note-0624-05a" xml:space="preserve">918.</note> </div> <p> <s xml:id="echoid-s15954" xml:space="preserve">Nubes ſæpe pulcherrimè coloratæ apparent; </s> <s xml:id="echoid-s15955" xml:space="preserve">conſtant ex <lb/> <anchor type="note" xlink:label="note-0624-06a" xlink:href="note-0624-06"/> particulis aqueis quibus interjacet aër, pro variâ idèo partï-<lb/>cularum aquearum craſſitie, color diverſus in nube dabitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s15956" xml:space="preserve"> <anchor type="note" xlink:label="note-0624-07a" xlink:href="note-0624-07"/> </s> </p> <div xml:id="echoid-div2382" type="float" level="2" n="2"> <note position="left" xlink:label="note-0624-06" xlink:href="note-0624-06a" xml:space="preserve">920.</note> <note symbol="*" position="left" xlink:label="note-0624-07" xlink:href="note-0624-07a" xml:space="preserve">888.</note> </div> </div> <div xml:id="echoid-div2384" type="section" level="1" n="597"> <head xml:id="echoid-head779" xml:space="preserve">FINIS LIBRI TERTII.</head> <pb file="0625" n="690"/> <pb file="0625a" n="691"/> <figure> <image file="0625a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0625a-01"/> </figure> <pb file="0626" n="692"/> <pb o="(107)" file="0627" n="693"/> </div> <div xml:id="echoid-div2385" type="section" level="1" n="598"> <head xml:id="echoid-head780" xml:space="preserve">PHYSICES</head> <head xml:id="echoid-head781" xml:space="preserve">ELEMENTA MATHEMATICA, <lb/>EXPERIMENTIS CONFIRMATA.</head> <head xml:id="echoid-head782" style="it" xml:space="preserve">LIBER IV. <lb/>Pars I. De Mundi Syſtemate.</head> <head xml:id="echoid-head783" xml:space="preserve">CAPUT I. <lb/>Idea Generalis Syſtematis Planetarii.</head> <p> <s xml:id="echoid-s15957" xml:space="preserve">Spatium nullis limitibus terminari poſſe <anchor type="note" xlink:href="" symbol="*"/> qui atten- <anchor type="note" xlink:label="note-0627-01a" xlink:href="note-0627-01"/> tè conſideraverit, vix inficias ire poterit, ſupre-<lb/>mam omnipotentem intelligentiam, quam terri-<lb/>colis arcto in campo demonſtravit, ſapientiam <lb/>ubique manifeſtam feciſſe. </s> <s xml:id="echoid-s15958" xml:space="preserve">Quem hìc arctum dico campum, <lb/>in immenſum captum noſtrum ſuperat; </s> <s xml:id="echoid-s15959" xml:space="preserve">arctum tamen cum <lb/>ſpatio infinito collatum.</s> <s xml:id="echoid-s15960" xml:space="preserve"/> </p> <div xml:id="echoid-div2385" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0627-01" xlink:href="note-0627-01a" xml:space="preserve">15.</note> </div> <p> <s xml:id="echoid-s15961" xml:space="preserve">Tellus noſtra cum ſedecim aliis corporibus, (non plura no-<lb/> <anchor type="note" xlink:label="note-0627-02a" xlink:href="note-0627-02"/> vimus) in determinato ſpatio movetur; </s> <s xml:id="echoid-s15962" xml:space="preserve">non ultra determina-<lb/>tos limites, neque à ſe mutuo recedunt; </s> <s xml:id="echoid-s15963" xml:space="preserve">neque ad ſe mutuo <lb/>accedunt hæc corpora; </s> <s xml:id="echoid-s15964" xml:space="preserve">& </s> <s xml:id="echoid-s15965" xml:space="preserve">immutatis legibus motus horum <lb/>ſubjiciuntur.</s> <s xml:id="echoid-s15966" xml:space="preserve"/> </p> <div xml:id="echoid-div2386" type="float" level="2" n="2"> <note position="right" xlink:label="note-0627-02" xlink:href="note-0627-02a" xml:space="preserve">921.</note> </div> </div> <div xml:id="echoid-div2388" type="section" level="1" n="599"> <head xml:id="echoid-head784" xml:space="preserve"><emph style="sc">Definitio</emph> I.</head> <p style="it"> <s xml:id="echoid-s15967" xml:space="preserve">Congeries hæc ſeptemdecim corporum vocatur Syſtema <lb/> <anchor type="note" xlink:label="note-0627-03a" xlink:href="note-0627-03"/> Planetarium.</s> <s xml:id="echoid-s15968" xml:space="preserve"/> </p> <div xml:id="echoid-div2388" type="float" level="2" n="1"> <note position="right" xlink:label="note-0627-03" xlink:href="note-0627-03a" xml:space="preserve">922.</note> </div> <p> <s xml:id="echoid-s15969" xml:space="preserve">Circa hæc ſola ferè tota verſatur ars Aſtronomica; </s> <s xml:id="echoid-s15970" xml:space="preserve">de his <lb/>etiam præcipuè acturus ſum in hoc opere: </s> <s xml:id="echoid-s15971" xml:space="preserve">reliqua Univer-<lb/>ſum conſtituentia corpora nimium à nobis diſtant, ut horum <lb/>motus, ſi moventur, à nobis obſervari poſſint; </s> <s xml:id="echoid-s15972" xml:space="preserve">inter hæc <lb/>nobis ſenſibilia ſunt ſola lucida, & </s> <s xml:id="echoid-s15973" xml:space="preserve">quidem inſigniora tan-<lb/>tùm, & </s> <s xml:id="echoid-s15974" xml:space="preserve">quæ à nobis cæteris minus diſtant: </s> <s xml:id="echoid-s15975" xml:space="preserve">etiam illorum, <lb/>quæ Teleſcopio deteguntur, plurima oculo inermi viſibilia <lb/>non ſunt.</s> <s xml:id="echoid-s15976" xml:space="preserve"/> </p> <pb o="(108)" file="0628" n="694" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s15977" xml:space="preserve">Corpora hæc omnia dicuntur Stellæ fixæ.</s> <s xml:id="echoid-s15978" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">923.</note> <p> <s xml:id="echoid-s15979" xml:space="preserve">Fixæ vocantur, quia eundem ſitum inter ſe ſenſibiliter ſer-<lb/>vant; </s> <s xml:id="echoid-s15980" xml:space="preserve">circa hæc peculiaria quædam, in ſequentibus, memo-<lb/>randa erunt.</s> <s xml:id="echoid-s15981" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s15982" xml:space="preserve">Quod autem Syſtema Planetarium ſpectat; </s> <s xml:id="echoid-s15983" xml:space="preserve">In hoc ſe-<lb/> <anchor type="note" xlink:label="note-0628-02a" xlink:href="note-0628-02"/> ptemdecim dari corpora diximus: </s> <s xml:id="echoid-s15984" xml:space="preserve">Omnia ſunt ſphærica: </s> <s xml:id="echoid-s15985" xml:space="preserve">V-<lb/>nicum proprio lumine lucet; </s> <s xml:id="echoid-s15986" xml:space="preserve">reliqua ſunt opaca, & </s> <s xml:id="echoid-s15987" xml:space="preserve">mutuato <lb/>lumine viſibilia ſunt.</s> <s xml:id="echoid-s15988" xml:space="preserve"/> </p> <div xml:id="echoid-div2389" type="float" level="2" n="2"> <note position="left" xlink:label="note-0628-02" xlink:href="note-0628-02a" xml:space="preserve">924.</note> </div> <p style="it"> <s xml:id="echoid-s15989" xml:space="preserve">Sol eſt corpus illud lucidum, & </s> <s xml:id="echoid-s15990" xml:space="preserve">omnium in Syſtemate Pla-<lb/> <anchor type="note" xlink:label="note-0628-03a" xlink:href="note-0628-03"/> netario longè maximum; </s> <s xml:id="echoid-s15991" xml:space="preserve">in hujus medio quieſcit, ſaltem exi-<lb/>guo motu tantùm agitatur.</s> <s xml:id="echoid-s15992" xml:space="preserve"/> </p> <div xml:id="echoid-div2390" type="float" level="2" n="3"> <note position="left" xlink:label="note-0628-03" xlink:href="note-0628-03a" xml:space="preserve">925.</note> </div> </div> <div xml:id="echoid-div2392" type="section" level="1" n="600"> <head xml:id="echoid-head785" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s15993" xml:space="preserve">Reliqua ſedecim vocantur Planetæ.</s> <s xml:id="echoid-s15994" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">926.</note> <p> <s xml:id="echoid-s15995" xml:space="preserve">Hi in duas claſſes dividuntur; </s> <s xml:id="echoid-s15996" xml:space="preserve">ſex dicuntur Planetæ pri-<lb/>marii; </s> <s xml:id="echoid-s15997" xml:space="preserve">decem vocantur Planetæ ſecundarii. </s> <s xml:id="echoid-s15998" xml:space="preserve">Quando de <lb/>Planetis, nullâ adjectâ diſtinctione, loquimur, primarios in-<lb/>telligimus.</s> <s xml:id="echoid-s15999" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16000" xml:space="preserve">Primarii Planetæ motibus ſuis Solem cingunt, & </s> <s xml:id="echoid-s16001" xml:space="preserve">ad di-<lb/> <anchor type="note" xlink:label="note-0628-05a" xlink:href="note-0628-05"/> verſas ab hoc diſtantias, in curvis, in ſe redeuntibus, feruntur.</s> <s xml:id="echoid-s16002" xml:space="preserve"/> </p> <div xml:id="echoid-div2392" type="float" level="2" n="1"> <note position="left" xlink:label="note-0628-05" xlink:href="note-0628-05a" xml:space="preserve">927.</note> </div> <p> <s xml:id="echoid-s16003" xml:space="preserve">Planeta ſecundarius circa primarium revolvitur, & </s> <s xml:id="echoid-s16004" xml:space="preserve">hunc <lb/> <anchor type="note" xlink:label="note-0628-06a" xlink:href="note-0628-06"/> in motu ſuo circa Solem comitatur.</s> <s xml:id="echoid-s16005" xml:space="preserve"/> </p> <div xml:id="echoid-div2393" type="float" level="2" n="2"> <note position="left" xlink:label="note-0628-06" xlink:href="note-0628-06a" xml:space="preserve">928.</note> </div> <p> <s xml:id="echoid-s16006" xml:space="preserve">Planetæ in motibus ſuis lineas Ellipticas, à circulis non <lb/> <anchor type="note" xlink:label="note-0628-07a" xlink:href="note-0628-07"/> admodum differentes, deſcribunt.</s> <s xml:id="echoid-s16007" xml:space="preserve"/> </p> <div xml:id="echoid-div2394" type="float" level="2" n="3"> <note position="left" xlink:label="note-0628-07" xlink:href="note-0628-07a" xml:space="preserve">929.</note> </div> <p> <s xml:id="echoid-s16008" xml:space="preserve">Et ſingulæ lineæ hæ fixæ ſunt, ſaltem, niſi poſt longum <lb/>tempus, exigua in ſitu mutatio obſervatur.</s> <s xml:id="echoid-s16009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16010" xml:space="preserve">Linea Elliptica formatur, ſi filum, cujus extremitates in <lb/> <anchor type="note" xlink:label="note-0628-08a" xlink:href="note-0628-08"/> duobus punctis F & </s> <s xml:id="echoid-s16011" xml:space="preserve">f fixæ ſunt, moveatur manens tenſum; <lb/></s> <s xml:id="echoid-s16012" xml:space="preserve"> <anchor type="note" xlink:label="note-0628-09a" xlink:href="note-0628-09"/> ut in hac figura videtur, in qua filum repræſentatur in F d f, <lb/>FE f, FB f. </s> <s xml:id="echoid-s16013" xml:space="preserve">Puncta F, f, vocantur foci; </s> <s xml:id="echoid-s16014" xml:space="preserve">linea A a, quæ <lb/>per hos tranſit, & </s> <s xml:id="echoid-s16015" xml:space="preserve">ab utraque parte, in peripheriâ Ellipſeos <lb/>terminatur, vocatur axis major; </s> <s xml:id="echoid-s16016" xml:space="preserve">eſt recta omnium maxima <lb/>quæ in Ellipſi duci poteſt. </s> <s xml:id="echoid-s16017" xml:space="preserve">Punctum hujus axeos medium C, <lb/>eſt Ellipſeos centrum; </s> <s xml:id="echoid-s16018" xml:space="preserve">per hoc, ad axem majorem normalis, <lb/>tranſit axis minor D d.</s> <s xml:id="echoid-s16019" xml:space="preserve"/> </p> <div xml:id="echoid-div2395" type="float" level="2" n="4"> <note position="left" xlink:label="note-0628-08" xlink:href="note-0628-08a" xml:space="preserve">930.</note> <note position="left" xlink:label="note-0628-09" xlink:href="note-0628-09a" xml:space="preserve"><emph style="sc">TAB. XXIV.</emph> <lb/>fig 3.</note> </div> <p style="it"> <s xml:id="echoid-s16020" xml:space="preserve">Ita ſingulorum Planetarum primariorum orbitæ diſponun-<lb/> <anchor type="note" xlink:label="note-0628-10a" xlink:href="note-0628-10"/> tur, ut focorum alter cadat in centro Solis; </s> <s xml:id="echoid-s16021" xml:space="preserve">ſi Ellipſis AD a d <lb/>repræſentet orbitam Planetæ, centrum Solis eſt F.</s> <s xml:id="echoid-s16022" xml:space="preserve"/> </p> <div xml:id="echoid-div2396" type="float" level="2" n="5"> <note position="left" xlink:label="note-0628-10" xlink:href="note-0628-10a" xml:space="preserve">931.</note> </div> <pb o="(109)" file="0629" n="695" rhead="MATHEMATICA LIB. IV. CAP. I."/> </div> <div xml:id="echoid-div2398" type="section" level="1" n="601"> <head xml:id="echoid-head786" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p style="it"> <s xml:id="echoid-s16023" xml:space="preserve">Diſtantia, inter centrum Solis & </s> <s xml:id="echoid-s16024" xml:space="preserve">centrum orbitæ, vocatur <lb/> <anchor type="note" xlink:label="note-0629-01a" xlink:href="note-0629-01"/> Planetæ Excentricitas: </s> <s xml:id="echoid-s16025" xml:space="preserve">ut FC.</s> <s xml:id="echoid-s16026" xml:space="preserve"/> </p> <div xml:id="echoid-div2398" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-01" xlink:href="note-0629-01a" xml:space="preserve">932.</note> </div> <p> <s xml:id="echoid-s16027" xml:space="preserve">In ſingulis revolutionibus Planeta ſemel ad Solem accedit, <lb/> <anchor type="note" xlink:label="note-0629-02a" xlink:href="note-0629-02"/> & </s> <s xml:id="echoid-s16028" xml:space="preserve">ſemel ab hoc recedit; </s> <s xml:id="echoid-s16029" xml:space="preserve">daturque ad diſtantiam omnium <lb/>maximam in extremitate a axeos majoris orbitæ; </s> <s xml:id="echoid-s16030" xml:space="preserve">& </s> <s xml:id="echoid-s16031" xml:space="preserve">ad di-<lb/>ſtantiam omnium minimam in extremitate oppoſitâ A.</s> <s xml:id="echoid-s16032" xml:space="preserve"/> </p> <div xml:id="echoid-div2399" type="float" level="2" n="2"> <note position="right" xlink:label="note-0629-02" xlink:href="note-0629-02a" xml:space="preserve">933.</note> </div> </div> <div xml:id="echoid-div2401" type="section" level="1" n="602"> <head xml:id="echoid-head787" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s16033" xml:space="preserve">Diſtantia Planetæ à Sole vocatur Media, quæ æqualiter <lb/> <anchor type="note" xlink:label="note-0629-03a" xlink:href="note-0629-03"/> cum maximâ & </s> <s xml:id="echoid-s16034" xml:space="preserve">minimâ differt. </s> <s xml:id="echoid-s16035" xml:space="preserve">Ad hanc datur Planeta in <lb/>extremitatibus D, d, axeos minoris.</s> <s xml:id="echoid-s16036" xml:space="preserve"/> </p> <div xml:id="echoid-div2401" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-03" xlink:href="note-0629-03a" xml:space="preserve">934.</note> </div> </div> <div xml:id="echoid-div2403" type="section" level="1" n="603"> <head xml:id="echoid-head788" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s16037" xml:space="preserve">Punctum orbitæ, in quo Planeta à Sole maximè diſtat, <lb/> <anchor type="note" xlink:label="note-0629-04a" xlink:href="note-0629-04"/> vocatur Aphelium. </s> <s xml:id="echoid-s16038" xml:space="preserve">Ut a.</s> <s xml:id="echoid-s16039" xml:space="preserve"/> </p> <div xml:id="echoid-div2403" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-04" xlink:href="note-0629-04a" xml:space="preserve">935.</note> </div> </div> <div xml:id="echoid-div2405" type="section" level="1" n="604"> <head xml:id="echoid-head789" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p style="it"> <s xml:id="echoid-s16040" xml:space="preserve">Punctum orbitæ, in quo planeta minimè à Solè diſtat, vo-<lb/> <anchor type="note" xlink:label="note-0629-05a" xlink:href="note-0629-05"/> catur Perihelium.</s> <s xml:id="echoid-s16041" xml:space="preserve"/> </p> <div xml:id="echoid-div2405" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-05" xlink:href="note-0629-05a" xml:space="preserve">936.</note> </div> </div> <div xml:id="echoid-div2407" type="section" level="1" n="605"> <head xml:id="echoid-head790" xml:space="preserve"><emph style="sc">Definitio</emph> 8.</head> <p> <s xml:id="echoid-s16042" xml:space="preserve">Nomine communi puncta hæc vocantur Auges ſeu Apſi-<lb/> <anchor type="note" xlink:label="note-0629-06a" xlink:href="note-0629-06"/> des.</s> <s xml:id="echoid-s16043" xml:space="preserve"/> </p> <div xml:id="echoid-div2407" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-06" xlink:href="note-0629-06a" xml:space="preserve">937.</note> </div> </div> <div xml:id="echoid-div2409" type="section" level="1" n="606"> <head xml:id="echoid-head791" xml:space="preserve"><emph style="sc">Definitio</emph> 9.</head> <p> <s xml:id="echoid-s16044" xml:space="preserve">Linea quæ aplides conjungit, id eſt, axis major orbitæ, <lb/> <anchor type="note" xlink:label="note-0629-07a" xlink:href="note-0629-07"/> vocatur linea Apſidum.</s> <s xml:id="echoid-s16045" xml:space="preserve"/> </p> <div xml:id="echoid-div2409" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-07" xlink:href="note-0629-07a" xml:space="preserve">938.</note> </div> <p style="it"> <s xml:id="echoid-s16046" xml:space="preserve">Orbita unaquæque in plano datur, quod per centrum Solis <lb/> <anchor type="note" xlink:label="note-0629-08a" xlink:href="note-0629-08"/> tranſit.</s> <s xml:id="echoid-s16047" xml:space="preserve"/> </p> <div xml:id="echoid-div2410" type="float" level="2" n="2"> <note position="right" xlink:label="note-0629-08" xlink:href="note-0629-08a" xml:space="preserve">939.</note> </div> </div> <div xml:id="echoid-div2412" type="section" level="1" n="607"> <head xml:id="echoid-head792" xml:space="preserve"><emph style="sc">Definitio</emph> 10.</head> <p style="it"> <s xml:id="echoid-s16048" xml:space="preserve">Planum orbitæ Telluris vocatur Planum Eclipticæ.</s> <s xml:id="echoid-s16049" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">940.</note> <p> <s xml:id="echoid-s16050" xml:space="preserve">Hoc quaquaverſum continuatum concipitur; </s> <s xml:id="echoid-s16051" xml:space="preserve">& </s> <s xml:id="echoid-s16052" xml:space="preserve">ad ſitum <lb/>planorum reliquarum orbitarum, reſpectu hujus, attendunt <lb/>Aſtronomi.</s> <s xml:id="echoid-s16053" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2413" type="section" level="1" n="608"> <head xml:id="echoid-head793" xml:space="preserve"><emph style="sc">Definitio</emph> 11.</head> <p style="it"> <s xml:id="echoid-s16054" xml:space="preserve">Puncta in quibus orbitæ ſecant planum Eclipticæ vo-<lb/> <anchor type="note" xlink:label="note-0629-10a" xlink:href="note-0629-10"/> cantur Nodi.</s> <s xml:id="echoid-s16055" xml:space="preserve"/> </p> <div xml:id="echoid-div2413" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-10" xlink:href="note-0629-10a" xml:space="preserve">941.</note> </div> </div> <div xml:id="echoid-div2415" type="section" level="1" n="609"> <head xml:id="echoid-head794" xml:space="preserve"><emph style="sc">Definitio</emph> 12.</head> <p> <s xml:id="echoid-s16056" xml:space="preserve">Linea quæ jungit orbitæ cujuſcunque Nodos, id eſt, co-<lb/> <anchor type="note" xlink:label="note-0629-11a" xlink:href="note-0629-11"/> munis ſectio plani orbitæ, cum Plano Eclipticæ, vocatur <lb/>Linea Nodorum.</s> <s xml:id="echoid-s16057" xml:space="preserve"/> </p> <div xml:id="echoid-div2415" type="float" level="2" n="1"> <note position="right" xlink:label="note-0629-11" xlink:href="note-0629-11a" xml:space="preserve">942.</note> </div> <pb o="(110)" file="0630" n="696" rhead="PHYSICES ELEMENTA"/> <p style="it"> <s xml:id="echoid-s16058" xml:space="preserve">Planeta non æquali celeritate in omnibus punctis orbitæ ſuæ <lb/> <anchor type="note" xlink:label="note-0630-01a" xlink:href="note-0630-01"/> fertur; </s> <s xml:id="echoid-s16059" xml:space="preserve">quo minus à Sole diſtat, eo celerius movetur; </s> <s xml:id="echoid-s16060" xml:space="preserve">& </s> <s xml:id="echoid-s16061" xml:space="preserve">tem-<lb/> <anchor type="note" xlink:label="note-0630-02a" xlink:href="note-0630-02"/> pora, in quibus arcus varii orbitæ percurruntur, ſunt inter ſe <lb/>ut areæ, lineis ad centrum Solis ductis, formatæ; </s> <s xml:id="echoid-s16062" xml:space="preserve">Arcus AB <lb/>& </s> <s xml:id="echoid-s16063" xml:space="preserve">a E percurruntur in temporibus, quæ ſunt inter ſe, ut areæ <lb/>triangulorum mixtorum AFB, a FE.</s> <s xml:id="echoid-s16064" xml:space="preserve"/> </p> <div xml:id="echoid-div2416" type="float" level="2" n="2"> <note position="left" xlink:label="note-0630-01" xlink:href="note-0630-01a" xml:space="preserve">943.</note> <note position="left" xlink:label="note-0630-02" xlink:href="note-0630-02a" xml:space="preserve">944.</note> </div> <p> <s xml:id="echoid-s16065" xml:space="preserve">Omnes Planetæ verſus eandem partem feruntur; </s> <s xml:id="echoid-s16066" xml:space="preserve">& </s> <s xml:id="echoid-s16067" xml:space="preserve">ho-<lb/> <anchor type="note" xlink:label="note-0630-03a" xlink:href="note-0630-03"/> rum motus, in orbitis ſuis, eſt contrarius motui, quem quoti-<lb/>die in omnibus corporibus cœleſtibus obſervamus, quo in <lb/>uno die tellurem circumferri videntur, de quo in ſequen-<lb/>tibus.</s> <s xml:id="echoid-s16068" xml:space="preserve"/> </p> <div xml:id="echoid-div2417" type="float" level="2" n="3"> <note position="left" xlink:label="note-0630-03" xlink:href="note-0630-03a" xml:space="preserve">945.</note> </div> </div> <div xml:id="echoid-div2419" type="section" level="1" n="610"> <head xml:id="echoid-head795" xml:space="preserve"><emph style="sc">Definitio</emph> 13.</head> <p> <s xml:id="echoid-s16069" xml:space="preserve">Motus, qualis eſt Planetarum in orbitis, dicitur in conſe-<lb/> <anchor type="note" xlink:label="note-0630-04a" xlink:href="note-0630-04"/> quentiâ, & </s> <s xml:id="echoid-s16070" xml:space="preserve">directus.</s> <s xml:id="echoid-s16071" xml:space="preserve"/> </p> <div xml:id="echoid-div2419" type="float" level="2" n="1"> <note position="left" xlink:label="note-0630-04" xlink:href="note-0630-04a" xml:space="preserve">946.</note> </div> </div> <div xml:id="echoid-div2421" type="section" level="1" n="611"> <head xml:id="echoid-head796" xml:space="preserve"><emph style="sc">Definitio</emph> 14.</head> <p style="it"> <s xml:id="echoid-s16072" xml:space="preserve">Motus contrarius dicitur in antecedentiâ; </s> <s xml:id="echoid-s16073" xml:space="preserve">aliquando etiam <lb/> <anchor type="note" xlink:label="note-0630-05a" xlink:href="note-0630-05"/> retrogradus.</s> <s xml:id="echoid-s16074" xml:space="preserve"/> </p> <div xml:id="echoid-div2421" type="float" level="2" n="1"> <note position="left" xlink:label="note-0630-05" xlink:href="note-0630-05a" xml:space="preserve">947.</note> </div> <p> <s xml:id="echoid-s16075" xml:space="preserve">Quo à Sole magis removentur Planetæ, eo in orbitis lentiùs <lb/> <anchor type="note" xlink:label="note-0630-06a" xlink:href="note-0630-06"/> feruntur; </s> <s xml:id="echoid-s16076" xml:space="preserve">ita ut tempora periodica magis diſtantium majora <lb/>ſint, & </s> <s xml:id="echoid-s16077" xml:space="preserve">ex majori orbitâ percurſâ, & </s> <s xml:id="echoid-s16078" xml:space="preserve">ex lentiori motu.</s> <s xml:id="echoid-s16079" xml:space="preserve"/> </p> <div xml:id="echoid-div2422" type="float" level="2" n="2"> <note position="left" xlink:label="note-0630-06" xlink:href="note-0630-06a" xml:space="preserve">948.</note> </div> </div> <div xml:id="echoid-div2424" type="section" level="1" n="612"> <head xml:id="echoid-head797" xml:space="preserve"><emph style="sc">Definitio</emph> 15.</head> <p style="it"> <s xml:id="echoid-s16080" xml:space="preserve">Axis Planetæ dicitur linea, quæ per centrum Planetæ tran-<lb/> <anchor type="note" xlink:label="note-0630-07a" xlink:href="note-0630-07"/> ſit, & </s> <s xml:id="echoid-s16081" xml:space="preserve">circa quam hicce rotatur.</s> <s xml:id="echoid-s16082" xml:space="preserve"/> </p> <div xml:id="echoid-div2424" type="float" level="2" n="1"> <note position="left" xlink:label="note-0630-07" xlink:href="note-0630-07a" xml:space="preserve">949.</note> </div> <p> <s xml:id="echoid-s16083" xml:space="preserve">Planetæ, ſaltem plerique, & </s> <s xml:id="echoid-s16084" xml:space="preserve">Sol ipſer circa axes revol-<lb/> <anchor type="note" xlink:label="note-0630-08a" xlink:href="note-0630-08"/> vuntur: </s> <s xml:id="echoid-s16085" xml:space="preserve">duo dantur circa quos, hujus reſpectu, obſervationes <lb/>inſtituere non licuit, qui hoc motu probabiliter non deſti-<lb/>tuuntur.</s> <s xml:id="echoid-s16086" xml:space="preserve"/> </p> <div xml:id="echoid-div2425" type="float" level="2" n="2"> <note position="left" xlink:label="note-0630-08" xlink:href="note-0630-08a" xml:space="preserve">950.</note> </div> <p> <s xml:id="echoid-s16087" xml:space="preserve">Motus hicce conſpirat cum motu Planetarum in orbitis, <lb/> <anchor type="note" xlink:label="note-0630-09a" xlink:href="note-0630-09"/> id eſt, eſt in antecedentiâ.</s> <s xml:id="echoid-s16088" xml:space="preserve"/> </p> <div xml:id="echoid-div2426" type="float" level="2" n="3"> <note position="left" xlink:label="note-0630-09" xlink:href="note-0630-09a" xml:space="preserve">951.</note> </div> <p> <s xml:id="echoid-s16089" xml:space="preserve">Axes ipſi motu parallelo feruntur, ita, ut ſingula axeos <lb/> <anchor type="note" xlink:label="note-0630-10a" xlink:href="note-0630-10"/> Planetæ puncta lineas æquales & </s> <s xml:id="echoid-s16090" xml:space="preserve">ſimiles deſcribant.</s> <s xml:id="echoid-s16091" xml:space="preserve"/> </p> <div xml:id="echoid-div2427" type="float" level="2" n="4"> <note position="left" xlink:label="note-0630-10" xlink:href="note-0630-10a" xml:space="preserve">952.</note> </div> </div> <div xml:id="echoid-div2429" type="section" level="1" n="613"> <head xml:id="echoid-head798" xml:space="preserve"><emph style="sc">Definitio</emph> 16.</head> <p style="it"> <s xml:id="echoid-s16092" xml:space="preserve">Axeos extremitates dicuntur Planetæ Poli.</s> <s xml:id="echoid-s16093" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">953.</note> <p> <s xml:id="echoid-s16094" xml:space="preserve">Planetarum à Sole diſtantias ſatis accuratè inter ſe con-<lb/> <anchor type="note" xlink:label="note-0630-12a" xlink:href="note-0630-12"/> ferunt Aſtronomi; </s> <s xml:id="echoid-s16095" xml:space="preserve">ita ut totius Syſtematis ideam habeamus. <lb/></s> <s xml:id="echoid-s16096" xml:space="preserve"> <anchor type="note" xlink:label="note-0630-13a" xlink:href="note-0630-13"/> Orbium dimenſiones in hoc ſchemate repræſentantur, in quo <lb/>puncta NN, ſingulorum orbium Nodos deſignant.</s> <s xml:id="echoid-s16097" xml:space="preserve"/> </p> <div xml:id="echoid-div2429" type="float" level="2" n="1"> <note position="left" xlink:label="note-0630-12" xlink:href="note-0630-12a" xml:space="preserve">954.</note> <note position="left" xlink:label="note-0630-13" xlink:href="note-0630-13a" xml:space="preserve"><emph style="sc">TAB. XX.</emph> <lb/>fig. 1.</note> </div> <pb o="(111)" file="0631" n="697" rhead="MATHEMATICA LIB. IV. CAP. I."/> <p style="it"> <s xml:id="echoid-s16098" xml:space="preserve">Nondum tamen hujus ſyſtematis dimenſiones, cum ullâ <lb/> <anchor type="note" xlink:label="note-0631-01a" xlink:href="note-0631-01"/> menſurâ nobis notâ, in ſuperficie Telluris, conferre poſſu-<lb/>mus; </s> <s xml:id="echoid-s16099" xml:space="preserve">obſervationes enim, circa talem collationem inſtitutas, <lb/>erroris expertes eſſe Aſtronomus non aſſeret.</s> <s xml:id="echoid-s16100" xml:space="preserve"/> </p> <div xml:id="echoid-div2430" type="float" level="2" n="2"> <note position="right" xlink:label="note-0631-01" xlink:href="note-0631-01a" xml:space="preserve">955.</note> </div> <p> <s xml:id="echoid-s16101" xml:space="preserve">Ut autem variæ ſyſtematis partes inter ſe conferantur, <lb/> <anchor type="note" xlink:label="note-0631-02a" xlink:href="note-0631-02"/> ponimus mediam Telluris à Sole diſtantiam, dividi in 1000. <lb/></s> <s xml:id="echoid-s16102" xml:space="preserve">partes æquales, quæ, in menſurandis reliquis dimenſionibus, <lb/>adhibentur.</s> <s xml:id="echoid-s16103" xml:space="preserve"/> </p> <div xml:id="echoid-div2431" type="float" level="2" n="3"> <note position="right" xlink:label="note-0631-02" xlink:href="note-0631-02a" xml:space="preserve">956.</note> </div> <p> <s xml:id="echoid-s16104" xml:space="preserve">Solo in medio ſyſtematis, ut ante dictum, exiguo motu agi-<lb/> <anchor type="note" xlink:label="note-0631-03a" xlink:href="note-0631-03"/> tatur; </s> <s xml:id="echoid-s16105" xml:space="preserve">circa axem revolvitur in ſpatio 25. </s> <s xml:id="echoid-s16106" xml:space="preserve">dierum: </s> <s xml:id="echoid-s16107" xml:space="preserve">& </s> <s xml:id="echoid-s16108" xml:space="preserve">axis ad <lb/>planum Eclipticæ inclinatur, efficiens angulum 87. </s> <s xml:id="echoid-s16109" xml:space="preserve">gr. </s> <s xml:id="echoid-s16110" xml:space="preserve">30′.</s> <s xml:id="echoid-s16111" xml:space="preserve"/> </p> <div xml:id="echoid-div2432" type="float" level="2" n="4"> <note position="right" xlink:label="note-0631-03" xlink:href="note-0631-03a" xml:space="preserve">957.</note> </div> <p> <s xml:id="echoid-s16112" xml:space="preserve">Planetarum omnium minimè à Sole diſtat Mercurius ☿; <lb/></s> <s xml:id="echoid-s16113" xml:space="preserve"> <anchor type="note" xlink:label="note-0631-04a" xlink:href="note-0631-04"/> Hujus diſtantia media à Sole eſt 387: </s> <s xml:id="echoid-s16114" xml:space="preserve">Excentricitas eſt 80.</s> <s xml:id="echoid-s16115" xml:space="preserve">; <lb/>Inclinatio orbitæ, id eſt, angulus à plano orbitæ cum plano <lb/>Eclipticæ formatus, eſt 6. </s> <s xml:id="echoid-s16116" xml:space="preserve">gr. </s> <s xml:id="echoid-s16117" xml:space="preserve">52′.</s> <s xml:id="echoid-s16118" xml:space="preserve">: In tempore 87. </s> <s xml:id="echoid-s16119" xml:space="preserve">dierum, <lb/>23. </s> <s xml:id="echoid-s16120" xml:space="preserve">horarum, revolutionem circa Solem peragit.</s> <s xml:id="echoid-s16121" xml:space="preserve"/> </p> <div xml:id="echoid-div2433" type="float" level="2" n="5"> <note position="right" xlink:label="note-0631-04" xlink:href="note-0631-04a" xml:space="preserve">958.</note> </div> <p> <s xml:id="echoid-s16122" xml:space="preserve">Inſequitur Venus ♀; </s> <s xml:id="echoid-s16123" xml:space="preserve">cujus diſtantia media à Sole eſt 723: <lb/></s> <s xml:id="echoid-s16124" xml:space="preserve"> <anchor type="note" xlink:label="note-0631-05a" xlink:href="note-0631-05"/> Excentricitas 5: </s> <s xml:id="echoid-s16125" xml:space="preserve">Inclinatio orbitæ 3. </s> <s xml:id="echoid-s16126" xml:space="preserve">gr. </s> <s xml:id="echoid-s16127" xml:space="preserve">23′: </s> <s xml:id="echoid-s16128" xml:space="preserve">Tempus pe-<lb/>riodicum 224. </s> <s xml:id="echoid-s16129" xml:space="preserve">dier. </s> <s xml:id="echoid-s16130" xml:space="preserve">17. </s> <s xml:id="echoid-s16131" xml:space="preserve">hor.</s> <s xml:id="echoid-s16132" xml:space="preserve">: Circa axem rotatur in 23. <lb/></s> <s xml:id="echoid-s16133" xml:space="preserve">horis.</s> <s xml:id="echoid-s16134" xml:space="preserve"/> </p> <div xml:id="echoid-div2434" type="float" level="2" n="6"> <note position="right" xlink:label="note-0631-05" xlink:href="note-0631-05a" xml:space="preserve">959.</note> </div> <p> <s xml:id="echoid-s16135" xml:space="preserve">Planeta tertius ordine à Sole, eſt Tellus noſtra ♁, hujus <lb/> <anchor type="note" xlink:label="note-0631-06a" xlink:href="note-0631-06"/> diſtantia media à Sole eſt 1000.</s> <s xml:id="echoid-s16136" xml:space="preserve">: Excentricitas 169: </s> <s xml:id="echoid-s16137" xml:space="preserve">In ipſo <lb/>plano Eclipticæ movetur. </s> <s xml:id="echoid-s16138" xml:space="preserve">Tempus periodicum eſt 365. </s> <s xml:id="echoid-s16139" xml:space="preserve">dier. <lb/></s> <s xml:id="echoid-s16140" xml:space="preserve">5. </s> <s xml:id="echoid-s16141" xml:space="preserve">hor. </s> <s xml:id="echoid-s16142" xml:space="preserve">51′: </s> <s xml:id="echoid-s16143" xml:space="preserve">Circa axem in ſpatio 23. </s> <s xml:id="echoid-s16144" xml:space="preserve">hor. </s> <s xml:id="echoid-s16145" xml:space="preserve">56′. </s> <s xml:id="echoid-s16146" xml:space="preserve">4″. </s> <s xml:id="echoid-s16147" xml:space="preserve">revolvi-<lb/>tur: </s> <s xml:id="echoid-s16148" xml:space="preserve">Axis cum plano Eclipticæ efficit angulum 66. </s> <s xml:id="echoid-s16149" xml:space="preserve">gr. </s> <s xml:id="echoid-s16150" xml:space="preserve">31′.</s> <s xml:id="echoid-s16151" xml:space="preserve"/> </p> <div xml:id="echoid-div2435" type="float" level="2" n="7"> <note position="right" xlink:label="note-0631-06" xlink:href="note-0631-06a" xml:space="preserve">960.</note> </div> <p> <s xml:id="echoid-s16152" xml:space="preserve">Mars ♂ à Sole in mediâ diſtantiâ removetur 1524.</s> <s xml:id="echoid-s16153" xml:space="preserve">: Ex-<lb/> <anchor type="note" xlink:label="note-0631-07a" xlink:href="note-0631-07"/> centricitas eſt 141.</s> <s xml:id="echoid-s16154" xml:space="preserve">: Inclinatio orbitæ 1. </s> <s xml:id="echoid-s16155" xml:space="preserve">gr. </s> <s xml:id="echoid-s16156" xml:space="preserve">52′.</s> <s xml:id="echoid-s16157" xml:space="preserve">: Tempus <lb/>periodicum 686. </s> <s xml:id="echoid-s16158" xml:space="preserve">dier. </s> <s xml:id="echoid-s16159" xml:space="preserve">23. </s> <s xml:id="echoid-s16160" xml:space="preserve">hor.</s> <s xml:id="echoid-s16161" xml:space="preserve">. Circa axem revolutionem <lb/>peragit in 24. </s> <s xml:id="echoid-s16162" xml:space="preserve">hor. </s> <s xml:id="echoid-s16163" xml:space="preserve">40′.</s> <s xml:id="echoid-s16164" xml:space="preserve"/> </p> <div xml:id="echoid-div2436" type="float" level="2" n="8"> <note position="right" xlink:label="note-0631-07" xlink:href="note-0631-07a" xml:space="preserve">961.</note> </div> <p> <s xml:id="echoid-s16165" xml:space="preserve">Jupiter ♃ Planetarum maximus, à Sole diſtat mediâ re-<lb/> <anchor type="note" xlink:label="note-0631-08a" xlink:href="note-0631-08"/> motione 5201.</s> <s xml:id="echoid-s16166" xml:space="preserve">: Excentricitas 250.</s> <s xml:id="echoid-s16167" xml:space="preserve">: Inclinatio orbitæ, <lb/>1. </s> <s xml:id="echoid-s16168" xml:space="preserve">gr. </s> <s xml:id="echoid-s16169" xml:space="preserve">20′.</s> <s xml:id="echoid-s16170" xml:space="preserve">: Tempus periodicum 4332. </s> <s xml:id="echoid-s16171" xml:space="preserve">dier. </s> <s xml:id="echoid-s16172" xml:space="preserve">12. </s> <s xml:id="echoid-s16173" xml:space="preserve">hor.</s> <s xml:id="echoid-s16174" xml:space="preserve">: Circa <lb/>axem revolvitur in 9. </s> <s xml:id="echoid-s16175" xml:space="preserve">hor. </s> <s xml:id="echoid-s16176" xml:space="preserve">56′.</s> <s xml:id="echoid-s16177" xml:space="preserve"/> </p> <div xml:id="echoid-div2437" type="float" level="2" n="9"> <note position="right" xlink:label="note-0631-08" xlink:href="note-0631-08a" xml:space="preserve">962.</note> </div> <p> <s xml:id="echoid-s16178" xml:space="preserve">Saturni ♄ Planetarum remotiſſimi à Sole diſtantia media <lb/> <anchor type="note" xlink:label="note-0631-09a" xlink:href="note-0631-09"/> eſt 9538.</s> <s xml:id="echoid-s16179" xml:space="preserve">: Excentricitas 547.</s> <s xml:id="echoid-s16180" xml:space="preserve">: Orbitæ inclinatio 2. </s> <s xml:id="echoid-s16181" xml:space="preserve">gr. </s> <s xml:id="echoid-s16182" xml:space="preserve">30′.</s> <s xml:id="echoid-s16183" xml:space="preserve">: <lb/>Tempus periodicum 10759. </s> <s xml:id="echoid-s16184" xml:space="preserve">dier. </s> <s xml:id="echoid-s16185" xml:space="preserve">7. </s> <s xml:id="echoid-s16186" xml:space="preserve">hor.</s> <s xml:id="echoid-s16187" xml:space="preserve">. Hic annulo cir-<lb/>cumdatur, qui Planetam non tangit, & </s> <s xml:id="echoid-s16188" xml:space="preserve">hunc nunquam de- <pb o="(112)" file="0632" n="698" rhead="PHYSICES ELEMENTA"/> ſerit: </s> <s xml:id="echoid-s16189" xml:space="preserve">niſi adhibito Teleſcopio viſibilis non eſt.</s> <s xml:id="echoid-s16190" xml:space="preserve"/> </p> <div xml:id="echoid-div2438" type="float" level="2" n="10"> <note position="right" xlink:label="note-0631-09" xlink:href="note-0631-09a" xml:space="preserve">963.</note> </div> <p> <s xml:id="echoid-s16191" xml:space="preserve">Datâ diſtantiâ mediâ, addendo excentricitatem, detegitur <lb/>maxima diſtantia; </s> <s xml:id="echoid-s16192" xml:space="preserve">ſubtractâ verò excentricitate ex mediâ di-<lb/>ſtantiâ, determinatur diſtantia minima <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16193" xml:space="preserve"> <anchor type="note" xlink:label="note-0632-01a" xlink:href="note-0632-01"/> </s> </p> <div xml:id="echoid-div2439" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0632-01" xlink:href="note-0632-01a" xml:space="preserve">836.</note> </div> <p> <s xml:id="echoid-s16194" xml:space="preserve">T@es Planetæ, Mars, Jupiter, & </s> <s xml:id="echoid-s16195" xml:space="preserve">Saturnus, qui ultra <lb/> <anchor type="note" xlink:label="note-0632-02a" xlink:href="note-0632-02"/> Tellurem à Sole removentur, dicuntur ſuperiores. </s> <s xml:id="echoid-s16196" xml:space="preserve">Inferio-<lb/>res Planetæ vocantur Venus & </s> <s xml:id="echoid-s16197" xml:space="preserve">Mercurius.</s> <s xml:id="echoid-s16198" xml:space="preserve"/> </p> <div xml:id="echoid-div2440" type="float" level="2" n="12"> <note position="left" xlink:label="note-0632-02" xlink:href="note-0632-02a" xml:space="preserve">964.</note> </div> <p style="it"> <s xml:id="echoid-s16199" xml:space="preserve">Inter primarios Planetas tres ſecundariis ſtipantur.</s> <s xml:id="echoid-s16200" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">965.</note> <p> <s xml:id="echoid-s16201" xml:space="preserve">Circa Saturnum quinque Planetæ, ſatellites dicti, moventur: <lb/></s> <s xml:id="echoid-s16202" xml:space="preserve">Circa Jovem quatuor: </s> <s xml:id="echoid-s16203" xml:space="preserve">Circa Tellurem unus, Luna nempe.</s> <s xml:id="echoid-s16204" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16205" xml:space="preserve">Planetæ ſecundarii, Lunâ exceptâ, nudis oculis non dete-<lb/>guntur.</s> <s xml:id="echoid-s16206" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s16207" xml:space="preserve">Satellites circa primarios deſcribunt areas, lineis ad cen-<lb/> <anchor type="note" xlink:label="note-0632-04a" xlink:href="note-0632-04"/> tra primariorum, ductis, temporibus proportionales; </s> <s xml:id="echoid-s16208" xml:space="preserve">ut re-<lb/>ſpectu centri Solis de primariis dictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16209" xml:space="preserve"> <anchor type="note" xlink:label="note-0632-05a" xlink:href="note-0632-05"/> </s> </p> <div xml:id="echoid-div2441" type="float" level="2" n="13"> <note position="left" xlink:label="note-0632-04" xlink:href="note-0632-04a" xml:space="preserve">966.</note> <note symbol="*" position="left" xlink:label="note-0632-05" xlink:href="note-0632-05a" xml:space="preserve">944.</note> </div> <p> <s xml:id="echoid-s16210" xml:space="preserve">Luna circa Tellurem in ellipſi movetur, cujus focorum al-<lb/> <anchor type="note" xlink:label="note-0632-06a" xlink:href="note-0632-06"/> ter occupat Telluris centrum, à quo Lunæ diſtantia media <lb/>eſt ſemidiametrorum Telluris 60 {2/9}.</s> <s xml:id="echoid-s16211" xml:space="preserve">: Excentricitas mutatio-<lb/> <anchor type="note" xlink:label="note-0632-07a" xlink:href="note-0632-07"/> ni obnoxia eſt, media eſt ſemidiametrorum 3 {1/3}.</s> <s xml:id="echoid-s16212" xml:space="preserve">: Planum or-<lb/> <anchor type="note" xlink:label="note-0632-08a" xlink:href="note-0632-08"/> bitæ, cum plano Eclipticæ, efficit angulum circiter 5. </s> <s xml:id="echoid-s16213" xml:space="preserve">gr.</s> <s xml:id="echoid-s16214" xml:space="preserve">, ſed <lb/>non conſtans eſt hæc inclinatio. </s> <s xml:id="echoid-s16215" xml:space="preserve">In motu Lunæ circa Tellurem, <lb/> <anchor type="note" xlink:label="note-0632-09a" xlink:href="note-0632-09"/> non motu parallelo feruntur, neque linea Apſidum, neque li-<lb/>nea Nodorum; </s> <s xml:id="echoid-s16216" xml:space="preserve">ſed hæc in antecedentia, illa in conſequentia <lb/>fertur; </s> <s xml:id="echoid-s16217" xml:space="preserve">prima in 9. </s> <s xml:id="echoid-s16218" xml:space="preserve">circiter annis revolutionem peragit, ſe-<lb/>cunda in 19. </s> <s xml:id="echoid-s16219" xml:space="preserve">Annis. </s> <s xml:id="echoid-s16220" xml:space="preserve">Lunæ tempus periodicum, circa tellu-<lb/>rem eſt 27. </s> <s xml:id="echoid-s16221" xml:space="preserve">dierum & </s> <s xml:id="echoid-s16222" xml:space="preserve">7. </s> <s xml:id="echoid-s16223" xml:space="preserve">circiter horarum; </s> <s xml:id="echoid-s16224" xml:space="preserve">& </s> <s xml:id="echoid-s16225" xml:space="preserve">exactiſſimè in <lb/>eodem tempore circa axem rotatur.</s> <s xml:id="echoid-s16226" xml:space="preserve"/> </p> <div xml:id="echoid-div2442" type="float" level="2" n="14"> <note position="left" xlink:label="note-0632-06" xlink:href="note-0632-06a" xml:space="preserve">967.</note> <note position="left" xlink:label="note-0632-07" xlink:href="note-0632-07a" xml:space="preserve">968.</note> <note position="left" xlink:label="note-0632-08" xlink:href="note-0632-08a" xml:space="preserve">969.</note> <note position="left" xlink:label="note-0632-09" xlink:href="note-0632-09a" xml:space="preserve">970</note> </div> <p> <s xml:id="echoid-s16227" xml:space="preserve">Planetarum circumjovialium primus ſeu intimus, à Jovis <lb/> <anchor type="note" xlink:label="note-0632-10a" xlink:href="note-0632-10"/> centro diſtat diametros Jovis 2 {5/6}.</s> <s xml:id="echoid-s16228" xml:space="preserve">: circa Jovem circumvol-<lb/> <anchor type="note" xlink:label="note-0632-11a" xlink:href="note-0632-11"/> vitur in uno die 18. </s> <s xml:id="echoid-s16229" xml:space="preserve">hor. </s> <s xml:id="echoid-s16230" xml:space="preserve">28′.</s> <s xml:id="echoid-s16231" xml:space="preserve"/> </p> <div xml:id="echoid-div2443" type="float" level="2" n="15"> <note position="left" xlink:label="note-0632-10" xlink:href="note-0632-10a" xml:space="preserve">971.</note> <note position="left" xlink:label="note-0632-11" xlink:href="note-0632-11a" xml:space="preserve"><emph style="sc">TAB. XX.</emph> <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s16232" xml:space="preserve">Secundi diſtantia eſt diametrorum Jovis 4 {1/2}.</s> <s xml:id="echoid-s16233" xml:space="preserve">: tempus pe-<lb/>riodicum 3. </s> <s xml:id="echoid-s16234" xml:space="preserve">dier. </s> <s xml:id="echoid-s16235" xml:space="preserve">13. </s> <s xml:id="echoid-s16236" xml:space="preserve">hor. </s> <s xml:id="echoid-s16237" xml:space="preserve">18′.</s> <s xml:id="echoid-s16238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16239" xml:space="preserve">Tertii diſtantia eſt 7 {1/6}. </s> <s xml:id="echoid-s16240" xml:space="preserve">diam.</s> <s xml:id="echoid-s16241" xml:space="preserve">: Tempus periodicum 7. </s> <s xml:id="echoid-s16242" xml:space="preserve">dier. <lb/></s> <s xml:id="echoid-s16243" xml:space="preserve">4. </s> <s xml:id="echoid-s16244" xml:space="preserve">hor.</s> <s xml:id="echoid-s16245" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16246" xml:space="preserve">Quartus diſtat 12 {2/3}. </s> <s xml:id="echoid-s16247" xml:space="preserve">diam.</s> <s xml:id="echoid-s16248" xml:space="preserve">: Revolvitur in tempore 16. </s> <s xml:id="echoid-s16249" xml:space="preserve">dier. <lb/></s> <s xml:id="echoid-s16250" xml:space="preserve">18. </s> <s xml:id="echoid-s16251" xml:space="preserve">hor. </s> <s xml:id="echoid-s16252" xml:space="preserve">5′.</s> <s xml:id="echoid-s16253" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16254" xml:space="preserve">Primus ſeu intimus Saturni Satelles, à centro Saturni di-<lb/> <anchor type="note" xlink:label="note-0632-12a" xlink:href="note-0632-12"/> <pb o="(113)" file="0633" n="699" rhead="MATHEMATICA LIB. IV. CAP. I."/> ſtat {39/40}. </s> <s xml:id="echoid-s16255" xml:space="preserve">diam. </s> <s xml:id="echoid-s16256" xml:space="preserve">Annuli: </s> <s xml:id="echoid-s16257" xml:space="preserve">Tempus periodicum 1. </s> <s xml:id="echoid-s16258" xml:space="preserve">diei, 21. </s> <s xml:id="echoid-s16259" xml:space="preserve">hor. </s> <s xml:id="echoid-s16260" xml:space="preserve">18′.</s> <s xml:id="echoid-s16261" xml:space="preserve"/> </p> <div xml:id="echoid-div2444" type="float" level="2" n="16"> <note position="left" xlink:label="note-0632-12" xlink:href="note-0632-12a" xml:space="preserve">972. <lb/><emph style="sc">TAB. XX.</emph> <lb/>fig. 3.</note> </div> <p> <s xml:id="echoid-s16262" xml:space="preserve">Secundi diſtantia eſt diam. </s> <s xml:id="echoid-s16263" xml:space="preserve">Ann. </s> <s xml:id="echoid-s16264" xml:space="preserve">1 {1/4}.</s> <s xml:id="echoid-s16265" xml:space="preserve">: Tempus periodicum <lb/>2. </s> <s xml:id="echoid-s16266" xml:space="preserve">dier. </s> <s xml:id="echoid-s16267" xml:space="preserve">17. </s> <s xml:id="echoid-s16268" xml:space="preserve">hor. </s> <s xml:id="echoid-s16269" xml:space="preserve">41′.</s> <s xml:id="echoid-s16270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16271" xml:space="preserve">Tertii diſtantia eſt 1 {3/4}. </s> <s xml:id="echoid-s16272" xml:space="preserve">diam. </s> <s xml:id="echoid-s16273" xml:space="preserve">Ann.</s> <s xml:id="echoid-s16274" xml:space="preserve">: Tempus periodicum <lb/>4. </s> <s xml:id="echoid-s16275" xml:space="preserve">dier. </s> <s xml:id="echoid-s16276" xml:space="preserve">13. </s> <s xml:id="echoid-s16277" xml:space="preserve">hor. </s> <s xml:id="echoid-s16278" xml:space="preserve">47′.</s> <s xml:id="echoid-s16279" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16280" xml:space="preserve">Quarti diſtantia 4. </s> <s xml:id="echoid-s16281" xml:space="preserve">diam. </s> <s xml:id="echoid-s16282" xml:space="preserve">Ann.</s> <s xml:id="echoid-s16283" xml:space="preserve">: Tempus periodicum <lb/>15. </s> <s xml:id="echoid-s16284" xml:space="preserve">dier. </s> <s xml:id="echoid-s16285" xml:space="preserve">22. </s> <s xml:id="echoid-s16286" xml:space="preserve">hor. </s> <s xml:id="echoid-s16287" xml:space="preserve">41′.</s> <s xml:id="echoid-s16288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16289" xml:space="preserve">Quinti diſtantia 12. </s> <s xml:id="echoid-s16290" xml:space="preserve">diam. </s> <s xml:id="echoid-s16291" xml:space="preserve">Ann.</s> <s xml:id="echoid-s16292" xml:space="preserve">: Tempus periodicum <lb/>79. </s> <s xml:id="echoid-s16293" xml:space="preserve">dier. </s> <s xml:id="echoid-s16294" xml:space="preserve">7. </s> <s xml:id="echoid-s16295" xml:space="preserve">hor. </s> <s xml:id="echoid-s16296" xml:space="preserve">53′.</s> <s xml:id="echoid-s16297" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16298" xml:space="preserve">Demotu horum, ut & </s> <s xml:id="echoid-s16299" xml:space="preserve">Jovialium Satellitum, circa axes, nil certi <lb/> <anchor type="note" xlink:label="note-0633-01a" xlink:href="note-0633-01"/> huc uſque ex obſervationibus Aſtronomicis determinari poteſt.</s> <s xml:id="echoid-s16300" xml:space="preserve"/> </p> <div xml:id="echoid-div2445" type="float" level="2" n="17"> <note position="right" xlink:label="note-0633-01" xlink:href="note-0633-01a" xml:space="preserve">973.</note> </div> <p> <s xml:id="echoid-s16301" xml:space="preserve">Si ad diſtantias & </s> <s xml:id="echoid-s16302" xml:space="preserve">Tempora periodica Planetarum attenda-<lb/>mus, hanc regulam in noſtro Syſtemate, ubicunque plurima <lb/>corpora circa idem punctum revolvuntur, id eſt, circa So-<lb/> <anchor type="note" xlink:label="note-0633-02a" xlink:href="note-0633-02"/> lem, Saturnum, & </s> <s xml:id="echoid-s16303" xml:space="preserve">Jovem, obtinêre videmus; </s> <s xml:id="echoid-s16304" xml:space="preserve">Quadrata <lb/>Temporum periodicorum eſſe inter ſe, ut ſunt cubi diſtantia-<lb/>rum mediarum à centro.</s> <s xml:id="echoid-s16305" xml:space="preserve"/> </p> <div xml:id="echoid-div2446" type="float" level="2" n="18"> <note position="right" xlink:label="note-0633-02" xlink:href="note-0633-02a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s16306" xml:space="preserve">Dimenſionum ipſorum corporum, in noſtro ſyſtemate, i-<lb/> <anchor type="note" xlink:label="note-0633-03a" xlink:href="note-0633-03"/> deam damus in fig. </s> <s xml:id="echoid-s16307" xml:space="preserve">4.</s> <s xml:id="echoid-s16308" xml:space="preserve">, in qua omnes Planetæ primarii, ut & </s> <s xml:id="echoid-s16309" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0633-04a" xlink:href="note-0633-04"/> Saturni annulus, ſecundum dimenſiones ſuas, delineantur; <lb/></s> <s xml:id="echoid-s16310" xml:space="preserve">Sol, cujus magnitudo omnes alias excedit, repræſentatur cir-<lb/>culo maximo fig. </s> <s xml:id="echoid-s16311" xml:space="preserve">1.</s> <s xml:id="echoid-s16312" xml:space="preserve">, id eſt, figuram terminante.</s> <s xml:id="echoid-s16313" xml:space="preserve"/> </p> <div xml:id="echoid-div2447" type="float" level="2" n="19"> <note position="right" xlink:label="note-0633-03" xlink:href="note-0633-03a" xml:space="preserve">975.</note> <note position="right" xlink:label="note-0633-04" xlink:href="note-0633-04a" xml:space="preserve"><emph style="sc">TAB. XX.</emph> <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s16314" xml:space="preserve">Hæ dimenſiones ſatis exactè proportiones corporum inter <lb/>ſe exhibent, ſi tellurem excipiamus, quæ, ex ratione jam <lb/>tradita <anchor type="note" xlink:href="" symbol="*"/>, cum cæteris corporibus ita conferri non poteſt, ut <anchor type="note" xlink:label="note-0633-05a" xlink:href="note-0633-05"/> de errore dubium nullum ſuperſit.</s> <s xml:id="echoid-s16315" xml:space="preserve"/> </p> <div xml:id="echoid-div2448" type="float" level="2" n="20"> <note symbol="*" position="right" xlink:label="note-0633-05" xlink:href="note-0633-05a" xml:space="preserve">955.</note> </div> <p> <s xml:id="echoid-s16316" xml:space="preserve">Menſuratur tamen Telluris diameter, & </s> <s xml:id="echoid-s16317" xml:space="preserve">eſt 340069. </s> <s xml:id="echoid-s16318" xml:space="preserve">per-<lb/> <anchor type="note" xlink:label="note-0633-06a" xlink:href="note-0633-06"/> ticarum, quarum ſingulæ continent 12. </s> <s xml:id="echoid-s16319" xml:space="preserve">pedes Rhynlandicos; <lb/></s> <s xml:id="echoid-s16320" xml:space="preserve">ſed licèt inter ſe, & </s> <s xml:id="echoid-s16321" xml:space="preserve">cumSolis diametro, conferantur cætero-<lb/>rum Planetarum diametri, quot pedes hæ contineant exactè, <lb/>niſi poſt, in tempore opportuno, inſtituendas obſervationes, <lb/>determinari non poterit.</s> <s xml:id="echoid-s16322" xml:space="preserve"/> </p> <div xml:id="echoid-div2449" type="float" level="2" n="21"> <note position="right" xlink:label="note-0633-06" xlink:href="note-0633-06a" xml:space="preserve">976.</note> </div> <p> <s xml:id="echoid-s16323" xml:space="preserve">Inter corpora Syſtema Planetarium componentia, ſola Lu-<lb/> <anchor type="note" xlink:label="note-0633-07a" xlink:href="note-0633-07"/> na cum Tellure confertur; </s> <s xml:id="echoid-s16324" xml:space="preserve">hujus diameter eſt ad Lunæ dia-<lb/>metrum, ut 40. </s> <s xml:id="echoid-s16325" xml:space="preserve">ad 11.</s> <s xml:id="echoid-s16326" xml:space="preserve"/> </p> <div xml:id="echoid-div2450" type="float" level="2" n="22"> <note position="right" xlink:label="note-0633-07" xlink:href="note-0633-07a" xml:space="preserve">977.</note> </div> <p> <s xml:id="echoid-s16327" xml:space="preserve">Planetæ ſecundarii reliqui, ab Aſtronomis non menſuran-<lb/> <anchor type="note" xlink:label="note-0633-08a" xlink:href="note-0633-08"/> tur, quoſdam tamen magnitudine Tellurem excedere, in du-<lb/>bium vix vocari poterit.</s> <s xml:id="echoid-s16328" xml:space="preserve"/> </p> <div xml:id="echoid-div2451" type="float" level="2" n="23"> <note position="right" xlink:label="note-0633-08" xlink:href="note-0633-08a" xml:space="preserve">978.</note> </div> <pb o="(114)" file="0634" n="700" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s16329" xml:space="preserve">Præter corpora huc uſque memorata, in ſyſtemate plane-<lb/>tario, quædam alia per tempus videntur, quæ ad Solem ac-<lb/>cedunt, deinde ab hoc recedunt, & </s> <s xml:id="echoid-s16330" xml:space="preserve">inviſibilia fiunt; </s> <s xml:id="echoid-s16331" xml:space="preserve">Come-<lb/> <anchor type="note" xlink:label="note-0634-01a" xlink:href="note-0634-01"/> tæ dicuntur. </s> <s xml:id="echoid-s16332" xml:space="preserve">Hi plerumque caudati apparent, & </s> <s xml:id="echoid-s16333" xml:space="preserve">cauda <lb/>ſemper à Sole averſa datur. </s> <s xml:id="echoid-s16334" xml:space="preserve">In motu ſuo deſcribunt areas, <lb/> <anchor type="note" xlink:label="note-0634-02a" xlink:href="note-0634-02"/> lineis ad centrum Solis ductis, temporibus proportionales, <lb/>ut de Planetis dictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16335" xml:space="preserve"> <anchor type="note" xlink:label="note-0634-03a" xlink:href="note-0634-03"/> </s> </p> <div xml:id="echoid-div2452" type="float" level="2" n="24"> <note position="left" xlink:label="note-0634-01" xlink:href="note-0634-01a" xml:space="preserve">979.</note> <note position="left" xlink:label="note-0634-02" xlink:href="note-0634-02a" xml:space="preserve">980.</note> <note symbol="*" position="left" xlink:label="note-0634-03" xlink:href="note-0634-03a" xml:space="preserve">944. 966.</note> </div> <p> <s xml:id="echoid-s16336" xml:space="preserve">Circa Cometas probabile eſt, illos in orbitis ellipticis ad-<lb/> <anchor type="note" xlink:label="note-0634-04a" xlink:href="note-0634-04"/> modum excontricis moveri; </s> <s xml:id="echoid-s16337" xml:space="preserve">ita ut inviſibiles ſint, quando â <lb/>Sole remotiorem orbitæ partem occupant; </s> <s xml:id="echoid-s16338" xml:space="preserve">quod ex quo-<lb/>rundam periodis ſatis regularibus deducitur; </s> <s xml:id="echoid-s16339" xml:space="preserve">& </s> <s xml:id="echoid-s16340" xml:space="preserve">ex obſer-<lb/>vationibus conſtat, quoſdam pertiones Ellipſium valdè ex-<lb/> <anchor type="note" xlink:label="note-0634-05a" xlink:href="note-0634-05"/> centricarum, in quarum foco centrum Solis erat, in motu <lb/>ſuo deſcripſiſſe.</s> <s xml:id="echoid-s16341" xml:space="preserve"/> </p> <div xml:id="echoid-div2453" type="float" level="2" n="25"> <note position="left" xlink:label="note-0634-04" xlink:href="note-0634-04a" xml:space="preserve">981.</note> <note position="left" xlink:label="note-0634-05" xlink:href="note-0634-05a" xml:space="preserve">982.</note> </div> <p> <s xml:id="echoid-s16342" xml:space="preserve">Quam huc uſque ideam Syſtematis Planetarii dedi, Aſtro-<lb/>nomicis nititur obſervationibus; </s> <s xml:id="echoid-s16343" xml:space="preserve">&</s> <s xml:id="echoid-s16344" xml:space="preserve">, de huc uſque dictis, nul-<lb/>la lis eſt inter Aſtronomos, ſi excipiamus, quæ lineam ellipti-<lb/>cam & </s> <s xml:id="echoid-s16345" xml:space="preserve">motum Telluris ſpectant.</s> <s xml:id="echoid-s16346" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16347" xml:space="preserve">Quidam Planetarum orbitas non eſſe ellipticas, ſed illos, <lb/>in motu, aliam ovalem deſcribere contendunt: </s> <s xml:id="echoid-s16348" xml:space="preserve">ex obſerva-<lb/>tionibus Tichonis Brahe deduxit Keplerus, lineas has eſſe el-<lb/>lipticas; </s> <s xml:id="echoid-s16349" xml:space="preserve">& </s> <s xml:id="echoid-s16350" xml:space="preserve">curvas alias à Planetis non poſſe deſcribi, in par-<lb/>te ſequenti videbimus.</s> <s xml:id="echoid-s16351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16352" xml:space="preserve">Qui Tellurem quieſcere contendunt, nullo Aſtronomico <lb/>aut Phyſico nituntur argumento; </s> <s xml:id="echoid-s16353" xml:space="preserve">id eſt, ex Phoenomenis <lb/>non ratiocinantur: </s> <s xml:id="echoid-s16354" xml:space="preserve">neglectâ Syſtematis ſimplicitate, & </s> <s xml:id="echoid-s16355" xml:space="preserve">in <lb/>hoc motuum analogià, ſententiam ſuam obſervationibus <lb/>non contrariari defendunt; </s> <s xml:id="echoid-s16356" xml:space="preserve">in quo illos errare, in parte ſe-<lb/>quenti videbimus.</s> <s xml:id="echoid-s16357" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2455" type="section" level="1" n="614"> <head xml:id="echoid-head799" xml:space="preserve">CAPUT II.</head> <head xml:id="echoid-head800" style="it" xml:space="preserve">De motu apparenti.</head> <p> <s xml:id="echoid-s16358" xml:space="preserve">QUi, lecto capite præcedenti, coelum intuebitur, illud ſe, <lb/>quod ibi exponitur, ſyſtema contemplari vix credet; <lb/></s> <s xml:id="echoid-s16359" xml:space="preserve">& </s> <s xml:id="echoid-s16360" xml:space="preserve">exactior motuum coeleſtium conſideratio dubium <lb/>augebit. </s> <s xml:id="echoid-s16361" xml:space="preserve">Nil mirum, in cœlis præter falſas apparentias vix <lb/> <anchor type="note" xlink:label="note-0634-06a" xlink:href="note-0634-06"/> quicquam obſervamus.</s> <s xml:id="echoid-s16362" xml:space="preserve"/> </p> <div xml:id="echoid-div2455" type="float" level="2" n="1"> <note position="left" xlink:label="note-0634-06" xlink:href="note-0634-06a" xml:space="preserve">983.</note> </div> <pb file="0635" n="701"/> <pb file="0635a" n="702"/> <figure> <image file="0635a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0635a-01"/> </figure> <pb file="0636" n="703"/> <pb o="(115)" file="0637" n="704" rhead="MATHEMATICA LIB. IV. CAP. II."/> <p> <s xml:id="echoid-s16363" xml:space="preserve">Variis motibus agitatus ſpectator, qui ſe quieſcere cogitat, <lb/>& </s> <s xml:id="echoid-s16364" xml:space="preserve">intuetur corpora, circa quorum diſtantiam & </s> <s xml:id="echoid-s16365" xml:space="preserve">magnitudi-<lb/>nem falſa fert judicia, vulgaris eſt cœlorum contemplator. <lb/></s> <s xml:id="echoid-s16366" xml:space="preserve">Per multa ſæcula verum Mundi Syſtema, cœlum etiam ex-<lb/>actius obſervantes, latuit.</s> <s xml:id="echoid-s16367" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16368" xml:space="preserve">Explicandum autem nobis eſt, quomodo omnia, quæ circa <lb/> <anchor type="note" xlink:label="note-0637-01a" xlink:href="note-0637-01"/> corpora cœleſtia obſervantur, reſpectu ſpectatoris in Tel-<lb/>lure, locum habeant in Syſtemate expoſito; </s> <s xml:id="echoid-s16369" xml:space="preserve">id eſt, ex ve-<lb/>ris motibus apparentias deducemus. </s> <s xml:id="echoid-s16370" xml:space="preserve">Quod fieri non poteſt, <lb/>niſi quibuſdam generalibus præmiſſis, de motu apparenti in <lb/>genere.</s> <s xml:id="echoid-s16371" xml:space="preserve"/> </p> <div xml:id="echoid-div2456" type="float" level="2" n="2"> <note position="right" xlink:label="note-0637-01" xlink:href="note-0637-01a" xml:space="preserve">984.</note> </div> <p> <s xml:id="echoid-s16372" xml:space="preserve">Motum verum nullâ arte à nobis obſervari poſſe, extra o-<lb/>mne dubium eſt; </s> <s xml:id="echoid-s16373" xml:space="preserve">ſolus motus relativus ſub ſenſus cadit; </s> <s xml:id="echoid-s16374" xml:space="preserve">de <lb/>eo etiam tantùm agitur in capite præcedenti: </s> <s xml:id="echoid-s16375" xml:space="preserve">Quis affirma. <lb/></s> <s xml:id="echoid-s16376" xml:space="preserve">re aut negare cum ratione poterit, non motu communi o-<lb/>mnia corpora nobis nota, per ſpatia immenſa transferri?</s> <s xml:id="echoid-s16377" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16378" xml:space="preserve">Motus relativus ab apparenti diſtinguendus eſt; </s> <s xml:id="echoid-s16379" xml:space="preserve">hic enim <lb/> <anchor type="note" xlink:label="note-0637-02a" xlink:href="note-0637-02"/> eſt mutâtio viſa in ſitu corporum, & </s> <s xml:id="echoid-s16380" xml:space="preserve">pendet à mutatione in <lb/>picturâ in fundo oculi; </s> <s xml:id="echoid-s16381" xml:space="preserve">nam objecta illam inter ſe relationem <lb/>apparentem habent, quæ datur in oculo inter objectorum <lb/>repræſentationes; </s> <s xml:id="echoid-s16382" xml:space="preserve">videntur enim ut in oculo depinguntur<anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s16383" xml:space="preserve"> <anchor type="note" xlink:label="note-0637-03a" xlink:href="note-0637-03"/> & </s> <s xml:id="echoid-s16384" xml:space="preserve">mutatio in hac picturâ ex corporum motu, ferè ſemper <lb/>differt cum mutatione relationis inter ipſa corpora; </s> <s xml:id="echoid-s16385" xml:space="preserve">ut ex <lb/>picturæ formatione ſequitur.</s> <s xml:id="echoid-s16386" xml:space="preserve"/> </p> <div xml:id="echoid-div2457" type="float" level="2" n="3"> <note position="right" xlink:label="note-0637-02" xlink:href="note-0637-02a" xml:space="preserve">985.</note> <note symbol="*" position="right" xlink:label="note-0637-03" xlink:href="note-0637-03a" xml:space="preserve">716.</note> </div> <p> <s xml:id="echoid-s16387" xml:space="preserve">Cœlum nibil eſt prœter ſpatium immenſum, quod videri <lb/> <anchor type="note" xlink:label="note-0637-04a" xlink:href="note-0637-04"/> non poteſt, & </s> <s xml:id="echoid-s16388" xml:space="preserve">nigrum apparêret <anchor type="note" xlink:href="" symbol="*"/>, niſi continuò radii lumi- <anchor type="note" xlink:label="note-0637-05a" xlink:href="note-0637-05"/> nis innumeri, à corporibus cœleſtibus manantes Atmoſphæ-<lb/>ram penetrarent. </s> <s xml:id="echoid-s16389" xml:space="preserve">Plerique per rectas lineas, à corporibus <lb/>ad nos, perveniunt, multi tamen in Atmoſphærâ varias pa-<lb/>tiuntur reflectiones & </s> <s xml:id="echoid-s16390" xml:space="preserve">totam Atmoſphæram illuminant; </s> <s xml:id="echoid-s16391" xml:space="preserve">in-<lb/>de de die, etiam abſque nubium reflectione, corpora illu-<lb/>ſtrantur, ad quæ radii ſolares directè pervenire nequeunt.</s> <s xml:id="echoid-s16392" xml:space="preserve"/> </p> <div xml:id="echoid-div2458" type="float" level="2" n="4"> <note position="right" xlink:label="note-0637-04" xlink:href="note-0637-04a" xml:space="preserve">986.</note> <note symbol="*" position="right" xlink:label="note-0637-05" xlink:href="note-0637-05a" xml:space="preserve">845.</note> </div> <p> <s xml:id="echoid-s16393" xml:space="preserve">Radii hi ſunt hæterogenei, & </s> <s xml:id="echoid-s16394" xml:space="preserve">quidem albi; </s> <s xml:id="echoid-s16395" xml:space="preserve">nam corpora <lb/>dantur hiſce radiis illuſtrata, quæ alba apparent; </s> <s xml:id="echoid-s16396" xml:space="preserve">& </s> <s xml:id="echoid-s16397" xml:space="preserve">hæc, per <lb/>priſmata viſa, ad extremitates coloribus tinguntur; </s> <s xml:id="echoid-s16398" xml:space="preserve">quod in <lb/>colore homogeneo non obtinet <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16399" xml:space="preserve">etiam circulus chartæ al- <anchor type="note" xlink:label="note-0637-06a" xlink:href="note-0637-06"/> bæ, diametri ſemi pollicis, panno nigro ſuper impoſitus, ſi <pb o="(116)" file="0638" n="705" rhead="PHYSICES ELEMENTA"/> hiſce radiis illuminetur, per priſma oblongus apparet, & </s> <s xml:id="echoid-s16400" xml:space="preserve"><lb/>iidem colores, qui in radiis ſolaribus obſervantur <anchor type="note" xlink:href="" symbol="*"/>, eodem <anchor type="note" xlink:label="note-0638-01a" xlink:href="note-0638-01"/> modo hìc videntur; </s> <s xml:id="echoid-s16401" xml:space="preserve">quæ omnia minimè obtinerent, ſi aër, ut <lb/>à plurimis ſtatuitur, foret liquidum cœruleum, id eſt, per <lb/>quod ſoli radii cœrulei, ſaltem maximâ copiâ, tranſeunt.</s> <s xml:id="echoid-s16402" xml:space="preserve"/> </p> <div xml:id="echoid-div2459" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0637-06" xlink:href="note-0637-06a" xml:space="preserve">874.</note> <note symbol="*" position="left" xlink:label="note-0638-01" xlink:href="note-0638-01a" xml:space="preserve">861.</note> </div> <p> <s xml:id="echoid-s16403" xml:space="preserve">Dum cœlum nigrum intuemur, radii albi memorati oculos <lb/> <anchor type="note" xlink:label="note-0638-02a" xlink:href="note-0638-02"/> intrant, unde color cœruleus cœlorum oritur. </s> <s xml:id="echoid-s16404" xml:space="preserve">Quia adſueti <lb/>ſumus colorem videre, ubi objectum datur coloratum, etiam <lb/>ad objectum refertur color cœlorum; </s> <s xml:id="echoid-s16405" xml:space="preserve">cùm autem hic ver-<lb/>ſus omnes partes æqualiter obſervetur, concipimus ſuperfi-<lb/> <anchor type="note" xlink:label="note-0638-03a" xlink:href="note-0638-03"/> ciem cavam ſphœricam, in cujus centro ipſi poſiti ſumus; </s> <s xml:id="echoid-s16406" xml:space="preserve">ſu-<lb/>perficies hœc ut opaca, ideoque ultra omnia corpora nobis <lb/>viſibilia remota, imaginatur.</s> <s xml:id="echoid-s16407" xml:space="preserve"/> </p> <div xml:id="echoid-div2460" type="float" level="2" n="6"> <note position="left" xlink:label="note-0638-02" xlink:href="note-0638-02a" xml:space="preserve">987.</note> <note position="left" xlink:label="note-0638-03" xlink:href="note-0638-03a" xml:space="preserve">988.</note> </div> <p> <s xml:id="echoid-s16408" xml:space="preserve">Quando inter planum & </s> <s xml:id="echoid-s16409" xml:space="preserve">oculum datur Corpus, de cujus <lb/>diſtantiâ judicium ferre non poſſumus, plano applicatum no-<lb/>bis apparet corpus, quæcunque fuerit diſtantia inter hoc & </s> <s xml:id="echoid-s16410" xml:space="preserve"><lb/>planum; </s> <s xml:id="echoid-s16411" xml:space="preserve">nulla enim datur ratio, quare partes plani, quæ ad <lb/>latera imaginis corporis in oculo depinguntur, non ad ean-<lb/>dem diſtantiam cum corpore apparêrent.</s> <s xml:id="echoid-s16412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16413" xml:space="preserve">Inde etiam omnia corpora cœleſtia, (quorum minimè à <lb/> <anchor type="note" xlink:label="note-0638-04a" xlink:href="note-0638-04"/> nobis diſtans, Luna nempè, ita removetur, ut judicium de <lb/>diſtantiâ non detur <anchor type="note" xlink:href="" symbol="*"/>,) ad ſphœram imaginariam, memora- <anchor type="note" xlink:label="note-0638-05a" xlink:href="note-0638-05"/> tam, referuntur; </s> <s xml:id="echoid-s16414" xml:space="preserve">& </s> <s xml:id="echoid-s16415" xml:space="preserve">omnia œque remota apparent; </s> <s xml:id="echoid-s16416" xml:space="preserve">& </s> <s xml:id="echoid-s16417" xml:space="preserve">in ſu-<lb/>perficie ſphœrœ cavœ moveri videntur. </s> <s xml:id="echoid-s16418" xml:space="preserve">Sic Luna inter ſtellas <lb/>fixas concipitur, licet illius diſtantia vix rationem ſenſibilem <lb/>habeat ad Saturni diſtantiam, quæ ipſa evaneſcit collata cum <lb/>immenſâ ſtellarum fixarum remotione. </s> <s xml:id="echoid-s16419" xml:space="preserve">Non mirum eſt igi-<lb/>tur, ſi de magnitudine corporum cœleſtium & </s> <s xml:id="echoid-s16420" xml:space="preserve">cœlorum im-<lb/>menſitate nil noſcat vulgus.</s> <s xml:id="echoid-s16421" xml:space="preserve"/> </p> <div xml:id="echoid-div2461" type="float" level="2" n="7"> <note position="left" xlink:label="note-0638-04" xlink:href="note-0638-04a" xml:space="preserve">989.</note> <note symbol="*" position="left" xlink:label="note-0638-05" xlink:href="note-0638-05a" xml:space="preserve">732.</note> </div> <p> <s xml:id="echoid-s16422" xml:space="preserve">Videmus ex dictis, quomodo ex dato motu corporis cu-<lb/>juſcunque, & </s> <s xml:id="echoid-s16423" xml:space="preserve">noto motu Telluris, motus apparens determi-<lb/>netur.</s> <s xml:id="echoid-s16424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16425" xml:space="preserve">Sphæram diximus imaginari ultra ſtellas fixas, in cujus cen-<lb/>tro datur ſpectator <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s16426" xml:space="preserve">orbita Telluris adeò eſt exigua re- <anchor type="note" xlink:label="note-0638-06a" xlink:href="note-0638-06"/> ſpectu diametri hujus ſphæræ, ut ex tranſlato cum Tellure, <lb/>ſpectatore, centrum ſphæræ ſenſibiliter non mutetur; </s> <s xml:id="echoid-s16427" xml:space="preserve">Qua-<lb/>re in omnibus ſuperficiei Tellur is punctis, & </s> <s xml:id="echoid-s16428" xml:space="preserve">in tempore quo-<lb/> <anchor type="note" xlink:label="note-0638-07a" xlink:href="note-0638-07"/> <pb o="(117)" file="0639" n="706" rhead="MATHEMATICA LIB. IV. CAP. III."/> cunque, eandem Terricolœ imaginantur ſphæram, ad quam <lb/>corpora cœleſtia referunt; </s> <s xml:id="echoid-s16429" xml:space="preserve">& </s> <s xml:id="echoid-s16430" xml:space="preserve">quam, in ſequentibus, nomina-<lb/>bimus ſphœram ſtellarum fixarum.</s> <s xml:id="echoid-s16431" xml:space="preserve"/> </p> <div xml:id="echoid-div2462" type="float" level="2" n="8"> <note symbol="*" position="left" xlink:label="note-0638-06" xlink:href="note-0638-06a" xml:space="preserve">988.</note> <note position="left" xlink:label="note-0638-07" xlink:href="note-0638-07a" xml:space="preserve">990.</note> </div> <p> <s xml:id="echoid-s16432" xml:space="preserve">Hiſce poſitis, ſi per Tellurem, & </s> <s xml:id="echoid-s16433" xml:space="preserve">corpus, lineam concipia-<lb/> <anchor type="note" xlink:label="note-0639-01a" xlink:href="note-0639-01"/> mus, quœ ultra corpus continuata ſphœram memoratam ſecat, <lb/>habemus punctum, ad quod corpus memoratum refertur, & </s> <s xml:id="echoid-s16434" xml:space="preserve"><lb/>quod eſt locus apparens corporis.</s> <s xml:id="echoid-s16435" xml:space="preserve"/> </p> <div xml:id="echoid-div2463" type="float" level="2" n="9"> <note position="right" xlink:label="note-0639-01" xlink:href="note-0639-01a" xml:space="preserve">991.</note> </div> <p> <s xml:id="echoid-s16436" xml:space="preserve">Dum corpus, aut Tellus, aut ambo, moventur, agitatur <lb/>hæc linea, & </s> <s xml:id="echoid-s16437" xml:space="preserve">motus apparens eſt linea, quam inter ſtellas <lb/> <anchor type="note" xlink:label="note-0639-02a" xlink:href="note-0639-02"/> fixas deſcribit extremitas lineœ memoratæ, tranſeuntis per <lb/>Tellurem & </s> <s xml:id="echoid-s16438" xml:space="preserve">corpus, cujus motus apparens obſervatur.</s> <s xml:id="echoid-s16439" xml:space="preserve"/> </p> <div xml:id="echoid-div2464" type="float" level="2" n="10"> <note position="right" xlink:label="note-0639-02" xlink:href="note-0639-02a" xml:space="preserve">992.</note> </div> <p> <s xml:id="echoid-s16440" xml:space="preserve">Idcirco eœdem apparentiœ ex tranſlatâ Tellure ſequuntur, <lb/> <anchor type="note" xlink:label="note-0639-03a" xlink:href="note-0639-03"/> quàm ex tranſlato corpore, & </s> <s xml:id="echoid-s16441" xml:space="preserve">eædem etiam ex motu amborum <lb/>deduci poßunt.</s> <s xml:id="echoid-s16442" xml:space="preserve"/> </p> <div xml:id="echoid-div2465" type="float" level="2" n="11"> <note position="right" xlink:label="note-0639-03" xlink:href="note-0639-03a" xml:space="preserve">993.</note> </div> <p> <s xml:id="echoid-s16443" xml:space="preserve">Si autem Corpus & </s> <s xml:id="echoid-s16444" xml:space="preserve">Tellus ita moveantur, ut linea, quœ <lb/> <anchor type="note" xlink:label="note-0639-04a" xlink:href="note-0639-04"/> per bœc corpora tranſit, motu parallelo feratur, corpus in-<lb/>ter ſtellas fixas quieſcere videbitur; </s> <s xml:id="echoid-s16445" xml:space="preserve">quia ſpatium, in hoc <lb/>caſu, ab extremitate lineæ inter ſtellas percurſum, non <lb/>poteſt ſuperare ſpatium à Tellure percurſum; </s> <s xml:id="echoid-s16446" xml:space="preserve">linea autem <lb/>æqualis toti ſpatio, quod à Tellure poteſt percurri, ad diſtan-<lb/>tiam ſtellarum fixarum remota, nobis ſenſibilis non eſt.</s> <s xml:id="echoid-s16447" xml:space="preserve"/> </p> <div xml:id="echoid-div2466" type="float" level="2" n="12"> <note position="right" xlink:label="note-0639-04" xlink:href="note-0639-04a" xml:space="preserve">994.</note> </div> <p> <s xml:id="echoid-s16448" xml:space="preserve">Ex motu Telluris circa axem etiam datur motus apparens, <lb/> <anchor type="note" xlink:label="note-0639-05a" xlink:href="note-0639-05"/> qui ſuo tempore, ex fundamentis in hoc capite poſitis, fa-<lb/>cilè deducetur.</s> <s xml:id="echoid-s16449" xml:space="preserve"/> </p> <div xml:id="echoid-div2467" type="float" level="2" n="13"> <note position="right" xlink:label="note-0639-05" xlink:href="note-0639-05a" xml:space="preserve">995.</note> </div> <p> <s xml:id="echoid-s16450" xml:space="preserve">Motum apparentem à relativo differre, & </s> <s xml:id="echoid-s16451" xml:space="preserve">ex motu ſpe-<lb/>ctatoris variari, navigantes quotidie experiuntur.</s> <s xml:id="echoid-s16452" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2469" type="section" level="1" n="615"> <head xml:id="echoid-head801" xml:space="preserve">CAPUT III.</head> <head xml:id="echoid-head802" style="it" xml:space="preserve">De Phœnomenis Solis ex motu Telluris in orbitâ.</head> <p> <s xml:id="echoid-s16453" xml:space="preserve">SIt Sol in S; </s> <s xml:id="echoid-s16454" xml:space="preserve">Tellus in orbitâ ſuâ in T; </s> <s xml:id="echoid-s16455" xml:space="preserve">rs ſphæra ſtella-<lb/> <anchor type="note" xlink:label="note-0639-06a" xlink:href="note-0639-06"/> rum fixarum; </s> <s xml:id="echoid-s16456" xml:space="preserve">locus apparens Solis eſt s <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s16457" xml:space="preserve">Dum Tellus <anchor type="note" xlink:label="note-0639-07a" xlink:href="note-0639-07"/> in orbit â transfertur à Tin t, Sol moveri videtur, & </s> <s xml:id="echoid-s16458" xml:space="preserve">percur-<lb/> <anchor type="note" xlink:label="note-0639-08a" xlink:href="note-0639-08"/> rere arcum s r <anchor type="note" xlink:href="" symbol="*"/>, qui menſurat angulum r S s, æqualem <anchor type="note" xlink:label="note-0639-09a" xlink:href="note-0639-09"/> angulo T S t; </s> <s xml:id="echoid-s16459" xml:space="preserve">ita, ut celeritas motus apparentis Solis pen-<lb/>deat, à celeritate motus angularis Telluris, reſpectu centri <lb/>Solis; </s> <s xml:id="echoid-s16460" xml:space="preserve">qui motus ex duplici cauſâ creſcit; </s> <s xml:id="echoid-s16461" xml:space="preserve">ex imminutâ di- <pb o="(118)" file="0640" n="707" rhead="PHYSICES ELEMENTA"/> ſtantiâ à Sole, & </s> <s xml:id="echoid-s16462" xml:space="preserve">ex auctâ celeritate Telluris: </s> <s xml:id="echoid-s16463" xml:space="preserve">quæ ambæ <lb/> <anchor type="note" xlink:label="note-0640-01a" xlink:href="note-0640-01"/> cauſæ ſemper concurrunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16464" xml:space="preserve">quare motus apparentis Solis <anchor type="note" xlink:label="note-0640-02a" xlink:href="note-0640-02"/> inœqualitas ſenſibilis eſt. </s> <s xml:id="echoid-s16465" xml:space="preserve">In integr â Telluris revolutione, e-<lb/> <anchor type="note" xlink:label="note-0640-03a" xlink:href="note-0640-03"/> tiam integrum circulum Sol percurrere videtur.</s> <s xml:id="echoid-s16466" xml:space="preserve"/> </p> <div xml:id="echoid-div2469" type="float" level="2" n="1"> <note position="right" xlink:label="note-0639-06" xlink:href="note-0639-06a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig. 1.</note> <note position="right" xlink:label="note-0639-07" xlink:href="note-0639-07a" xml:space="preserve">996.</note> <note symbol="*" position="right" xlink:label="note-0639-08" xlink:href="note-0639-08a" xml:space="preserve">991.</note> <note symbol="*" position="right" xlink:label="note-0639-09" xlink:href="note-0639-09a" xml:space="preserve">992.</note> <note symbol="*" position="left" xlink:label="note-0640-01" xlink:href="note-0640-01a" xml:space="preserve">944.</note> <note position="left" xlink:label="note-0640-02" xlink:href="note-0640-02a" xml:space="preserve">797.</note> <note position="left" xlink:label="note-0640-03" xlink:href="note-0640-03a" xml:space="preserve">998.</note> </div> </div> <div xml:id="echoid-div2471" type="section" level="1" n="616"> <head xml:id="echoid-head803" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s16467" xml:space="preserve">Via hæc apparens Solis, Linea Ecliptica vocatur. </s> <s xml:id="echoid-s16468" xml:space="preserve">Eſt ſe-<lb/> <anchor type="note" xlink:label="note-0640-04a" xlink:href="note-0640-04"/> ctio ſphæræ ſtellarum fixarum cum plano Eclipticæ, ad hanc <lb/>ſphæram uſque continuato.</s> <s xml:id="echoid-s16469" xml:space="preserve"/> </p> <div xml:id="echoid-div2471" type="float" level="2" n="1"> <note position="left" xlink:label="note-0640-04" xlink:href="note-0640-04a" xml:space="preserve">999.</note> </div> <p> <s xml:id="echoid-s16470" xml:space="preserve">Dividitur hæc via in duodecim partes æquales, quæ ſin-<lb/>gulæ continent 30. </s> <s xml:id="echoid-s16471" xml:space="preserve">gr.</s> <s xml:id="echoid-s16472" xml:space="preserve">; partes hæ vocantur Signa, & </s> <s xml:id="echoid-s16473" xml:space="preserve">no-<lb/>minibus dantur; </s> <s xml:id="echoid-s16474" xml:space="preserve">Aries ♈, Taurus ♉, Gemini II, Cancer ♋, <lb/>Leo ♌, Virgo ♍, Libra ♎, Scorpius ♏, Sagittarius ♐, <lb/>Capricornus <unsure/>, Aquarius ♒, Piſces <unsure/>. </s> <s xml:id="echoid-s16475" xml:space="preserve">Unde hæ partes <lb/>nomina mutuatæ ſint, ubi de ſtellis fixis acturi ſumus vide-<lb/>bimus.</s> <s xml:id="echoid-s16476" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s16477" xml:space="preserve">Diutius in percurrendis ſex ſignis primis bœret Sol, quàm <lb/> <anchor type="note" xlink:label="note-0640-05a" xlink:href="note-0640-05"/> in ſex poſterioribus, daturque differentia novem dierum.</s> <s xml:id="echoid-s16478" xml:space="preserve"/> </p> <div xml:id="echoid-div2472" type="float" level="2" n="2"> <note position="left" xlink:label="note-0640-05" xlink:href="note-0640-05a" xml:space="preserve">1000.</note> </div> <p> <s xml:id="echoid-s16479" xml:space="preserve">Licèt circulus nullum habeat principium aut finem, ubi <lb/> <anchor type="note" xlink:label="note-0640-06a" xlink:href="note-0640-06"/> tamen, in hoc, puncta varia determinanda ſunt, quoddam <lb/>punctum pro principio habendum eſt; </s> <s xml:id="echoid-s16480" xml:space="preserve">hoc, in lineâ Eclipti-<lb/>câ, eſt primum punctum Arietis; </s> <s xml:id="echoid-s16481" xml:space="preserve">quomodo determinetur, in <lb/>ſequentibus videbimus. </s> <s xml:id="echoid-s16482" xml:space="preserve">Non eſt ſixum inter ſtellas fixas; </s> <s xml:id="echoid-s16483" xml:space="preserve">id-<lb/>circo orbitæ Planetarum, quæ adeò parum mutantur, ut pro <lb/> <anchor type="note" xlink:label="note-0640-07a" xlink:href="note-0640-07"/> immutabilibus haberi poſſint <anchor type="note" xlink:href="" symbol="*"/>, non eundem reſpectu bujus <anchor type="note" xlink:label="note-0640-08a" xlink:href="note-0640-08"/> puncti ſitum ſervant.</s> <s xml:id="echoid-s16484" xml:space="preserve"/> </p> <div xml:id="echoid-div2473" type="float" level="2" n="3"> <note position="left" xlink:label="note-0640-06" xlink:href="note-0640-06a" xml:space="preserve">1001.</note> <note position="left" xlink:label="note-0640-07" xlink:href="note-0640-07a" xml:space="preserve">1002.</note> <note symbol="*" position="left" xlink:label="note-0640-08" xlink:href="note-0640-08a" xml:space="preserve">929.</note> </div> </div> <div xml:id="echoid-div2475" type="section" level="1" n="617"> <head xml:id="echoid-head804" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s16485" xml:space="preserve">Diſtantia Solis à primo puncto Arietis, in conſequentiâ, <lb/> <anchor type="note" xlink:label="note-0640-09a" xlink:href="note-0640-09"/> menſurata, dicitur Solis Longitudo.</s> <s xml:id="echoid-s16486" xml:space="preserve"/> </p> <div xml:id="echoid-div2475" type="float" level="2" n="1"> <note position="left" xlink:label="note-0640-09" xlink:href="note-0640-09a" xml:space="preserve">1003.</note> </div> <p style="it"> <s xml:id="echoid-s16487" xml:space="preserve">Longitudines cœterorum corporum cœleſtium, eodem modo in <lb/> <anchor type="note" xlink:label="note-0640-10a" xlink:href="note-0640-10"/> Eclipticâ menſurantur; </s> <s xml:id="echoid-s16488" xml:space="preserve">Ad banc referuntur, ſi circulus ma-<lb/> <anchor type="note" xlink:label="note-0640-11a" xlink:href="note-0640-11"/> jor per corpus concipiatur perpendicularis ad Eclipticam; <lb/></s> <s xml:id="echoid-s16489" xml:space="preserve">punctum enim, in quo hæc ab illo circulo ſecatur, determi-<lb/>nat corporis longitudinem.</s> <s xml:id="echoid-s16490" xml:space="preserve"/> </p> <div xml:id="echoid-div2476" type="float" level="2" n="2"> <note position="left" xlink:label="note-0640-10" xlink:href="note-0640-10a" xml:space="preserve">1004.</note> <note position="left" xlink:label="note-0640-11" xlink:href="note-0640-11a" xml:space="preserve">1005.</note> </div> </div> <div xml:id="echoid-div2478" type="section" level="1" n="618"> <head xml:id="echoid-head805" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s16491" xml:space="preserve">Diſtantia corporis cœieſtis à lineâ Eclipticâ, vocatur il-<lb/> <anchor type="note" xlink:label="note-0640-12a" xlink:href="note-0640-12"/> lius Latitudo. </s> <s xml:id="echoid-s16492" xml:space="preserve">Eſt arcus circuli majoris, ad Eclipticam per-<lb/>pendicularis, inter corpus & </s> <s xml:id="echoid-s16493" xml:space="preserve">Eclipticam interceptus.</s> <s xml:id="echoid-s16494" xml:space="preserve"/> </p> <div xml:id="echoid-div2478" type="float" level="2" n="1"> <note position="left" xlink:label="note-0640-12" xlink:href="note-0640-12a" xml:space="preserve">1006.</note> </div> <pb o="(119)" file="0641" n="708" rhead="MATHEMATICA LIB. IV. CAP. IV."/> </div> <div xml:id="echoid-div2480" type="section" level="1" n="619"> <head xml:id="echoid-head806" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p style="it"> <s xml:id="echoid-s16495" xml:space="preserve">Si in centro ſphæræ ſtellarum fixarum, ad planum Eclipti-<lb/> <anchor type="note" xlink:label="note-0641-01a" xlink:href="note-0641-01"/> cæ, concipiamus lineam perpendicularem, puncta, in quibus bæc <lb/>memoratam ſphæram ſecant, vocantur Poli Eclipticæ.</s> <s xml:id="echoid-s16496" xml:space="preserve"/> </p> <div xml:id="echoid-div2480" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-01" xlink:href="note-0641-01a" xml:space="preserve">1007.</note> </div> </div> <div xml:id="echoid-div2482" type="section" level="1" n="620"> <head xml:id="echoid-head807" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p style="it"> <s xml:id="echoid-s16497" xml:space="preserve">Zodiacus eſt Zona, quæ concipitur in cœlis, quam in duas <lb/> <anchor type="note" xlink:label="note-0641-02a" xlink:href="note-0641-02"/> partes æqualès ſecat linea Ecliptica, & </s> <s xml:id="echoid-s16498" xml:space="preserve">quæ, ab utraque par-<lb/>te terminatur circulo line æ Eclipticæ parallelo, & </s> <s xml:id="echoid-s16499" xml:space="preserve">ab hac octo <lb/>gradibus diſtanti. </s> <s xml:id="echoid-s16500" xml:space="preserve">Propter exiguam orbium Planetarum, ut <lb/>& </s> <s xml:id="echoid-s16501" xml:space="preserve">Lunæ, inclinationem ad planum Eclipticæ, nunquam <lb/> <anchor type="note" xlink:label="note-0641-03a" xlink:href="note-0641-03"/> extra Zodiacum, corpora ulla ſyſtematis Planetarii apparent.</s> <s xml:id="echoid-s16502" xml:space="preserve"/> </p> <div xml:id="echoid-div2482" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-02" xlink:href="note-0641-02a" xml:space="preserve">1008.</note> <note position="right" xlink:label="note-0641-03" xlink:href="note-0641-03a" xml:space="preserve">1009.</note> </div> </div> <div xml:id="echoid-div2484" type="section" level="1" n="621"> <head xml:id="echoid-head808" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s16503" xml:space="preserve">Inter hæc, quæ eandem habent longitudinem dicuntur in <lb/> <anchor type="note" xlink:label="note-0641-04a" xlink:href="note-0641-04"/> conjunctione.</s> <s xml:id="echoid-s16504" xml:space="preserve"/> </p> <div xml:id="echoid-div2484" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-04" xlink:href="note-0641-04a" xml:space="preserve">1010.</note> </div> </div> <div xml:id="echoid-div2486" type="section" level="1" n="622"> <head xml:id="echoid-head809" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p> <s xml:id="echoid-s16505" xml:space="preserve">In oppoſitione dicuntur, quorum longitudines differunt <lb/> <anchor type="note" xlink:label="note-0641-05a" xlink:href="note-0641-05"/> 180. </s> <s xml:id="echoid-s16506" xml:space="preserve">gr.</s> <s xml:id="echoid-s16507" xml:space="preserve"/> </p> <div xml:id="echoid-div2486" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-05" xlink:href="note-0641-05a" xml:space="preserve">1011.</note> </div> </div> <div xml:id="echoid-div2488" type="section" level="1" n="623"> <head xml:id="echoid-head810" xml:space="preserve">CAPUT IV.</head> <head xml:id="echoid-head811" style="it" xml:space="preserve">De Phænomenis Planetarum inferiorum, ex horum, <lb/>& Telluris, motibus in orbitis ſuis.</head> <p> <s xml:id="echoid-s16508" xml:space="preserve">SIt S Sol; </s> <s xml:id="echoid-s16509" xml:space="preserve">AVB v orbita Planetæ inferioris; </s> <s xml:id="echoid-s16510" xml:space="preserve">Tellus in or-<lb/> <anchor type="note" xlink:label="note-0641-06a" xlink:href="note-0641-06"/> bitâ ſuâ T; </s> <s xml:id="echoid-s16511" xml:space="preserve">a v b portio ſphæræ ſtellarum fixarum; </s> <s xml:id="echoid-s16512" xml:space="preserve">Lo-<lb/>cus apparens Solis eſt v <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16513" xml:space="preserve"> <anchor type="note" xlink:label="note-0641-07a" xlink:href="note-0641-07"/> </s> </p> <div xml:id="echoid-div2488" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-06" xlink:href="note-0641-06a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig. 2.</note> <note symbol="*" position="right" xlink:label="note-0641-07" xlink:href="note-0641-07a" xml:space="preserve">991.</note> </div> <p> <s xml:id="echoid-s16514" xml:space="preserve">Si ex Tellure, ad orbitam Planetæ, ducantur tangentes <lb/>T A a, TB b, clarè patet, nunquam ad majorem diſtan-<lb/>tiam, quàm v a aut v b à Sole, in motu apparenti, removeri <lb/>Planetam; </s> <s xml:id="echoid-s16515" xml:space="preserve">& </s> <s xml:id="echoid-s16516" xml:space="preserve">hunc illum, in motu apparenti circa Tellurem, <lb/>quaſi comitari.</s> <s xml:id="echoid-s16517" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2490" type="section" level="1" n="624"> <head xml:id="echoid-head812" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s16518" xml:space="preserve">Diſtantia apparens Planetæ à Sole, dicitur illius Elongatio. <lb/></s> <s xml:id="echoid-s16519" xml:space="preserve"> <anchor type="note" xlink:label="note-0641-08a" xlink:href="note-0641-08"/> v a aut v b eſt elongatio maxima: </s> <s xml:id="echoid-s16520" xml:space="preserve">hæc ex duabus cauſis va-<lb/> <anchor type="note" xlink:label="note-0641-09a" xlink:href="note-0641-09"/> riat; </s> <s xml:id="echoid-s16521" xml:space="preserve">quia nempè & </s> <s xml:id="echoid-s16522" xml:space="preserve">Tellus & </s> <s xml:id="echoid-s16523" xml:space="preserve">Planeta in lineis ellipticis re-<lb/>volvuntur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16524" xml:space="preserve"> <anchor type="note" xlink:label="note-0641-10a" xlink:href="note-0641-10"/> </s> </p> <div xml:id="echoid-div2490" type="float" level="2" n="1"> <note position="right" xlink:label="note-0641-08" xlink:href="note-0641-08a" xml:space="preserve">1012.</note> <note position="right" xlink:label="note-0641-09" xlink:href="note-0641-09a" xml:space="preserve">1013.</note> <note symbol="*" position="right" xlink:label="note-0641-10" xlink:href="note-0641-10a" xml:space="preserve">929.</note> </div> <p> <s xml:id="echoid-s16525" xml:space="preserve">Planeta, citiùs quàm Tellus, revolutionem peragit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16526" xml:space="preserve">ideò, <anchor type="note" xlink:label="note-0641-11a" xlink:href="note-0641-11"/> in motu ſuo, inter Tellurem & </s> <s xml:id="echoid-s16527" xml:space="preserve">Solem tranſit, & </s> <s xml:id="echoid-s16528" xml:space="preserve">deinde ultra <lb/> <anchor type="note" xlink:label="note-0641-12a" xlink:href="note-0641-12"/> <pb o="(120)" file="0642" n="709" rhead="PHYSICES ELEMENTA"/> Solem reſpectu Telluris movetur: </s> <s xml:id="echoid-s16529" xml:space="preserve">ita, ut duobus modis cum <lb/>Sole in conjunctione ſit, nunquam autem in oppoſitione.</s> <s xml:id="echoid-s16530" xml:space="preserve"/> </p> <div xml:id="echoid-div2491" type="float" level="2" n="2"> <note position="right" xlink:label="note-0641-11" xlink:href="note-0641-11a" xml:space="preserve">1014.</note> <note symbol="*" position="right" xlink:label="note-0641-12" xlink:href="note-0641-12a" xml:space="preserve">948.</note> </div> <p> <s xml:id="echoid-s16531" xml:space="preserve">Ut ideam habeamus motus apparentis Planetæ, concipe-<lb/>re debemus, cum Tellure moveri lineas TBb, TS v, TAa; <lb/></s> <s xml:id="echoid-s16532" xml:space="preserve">ita ut puncta A, V, B, & </s> <s xml:id="echoid-s16533" xml:space="preserve">v, dum Tellus revolutionem pera-<lb/>git, orbitam Planetæ circumrotentur; </s> <s xml:id="echoid-s16534" xml:space="preserve">Planeta verò, qui <lb/>celerius revolvitur, per hæc puncta ſucceſſivè iterum atque <lb/>iterum tranſit.</s> <s xml:id="echoid-s16535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16536" xml:space="preserve">Dum ab V in Din orbitâ fertur, inter fixas ab v verſus d <lb/> <anchor type="note" xlink:label="note-0642-01a" xlink:href="note-0642-01"/> moveri videtur; </s> <s xml:id="echoid-s16537" xml:space="preserve">in hoc caſu, motus apparens eſt in antece-<lb/>dentiâ & </s> <s xml:id="echoid-s16538" xml:space="preserve">Planeta eſt retrogradus. </s> <s xml:id="echoid-s16539" xml:space="preserve">In D ſtationarius dicitur; <lb/></s> <s xml:id="echoid-s16540" xml:space="preserve"> <anchor type="note" xlink:label="note-0642-02a" xlink:href="note-0642-02"/> quia per aliquod tempus, in eodem loco, inter ſtellas fixas ap-<lb/>paret: </s> <s xml:id="echoid-s16541" xml:space="preserve">hoc obtinet, ubi Planetæ orbita, in loco, in quo Pla-<lb/>neta verſatur, ad orbitam Telluris, in loco in quo hæc da-<lb/>tur, ita inclinatur, ut ductâ linea t d lineæ T D parallelâ, & </s> <s xml:id="echoid-s16542" xml:space="preserve"><lb/>parum ab hac diſtanti, D d ſit ad T t, ut Planetæ celeritas, <lb/>in orbitâ, ad Telluris celeritatem; </s> <s xml:id="echoid-s16543" xml:space="preserve">hæ lineolæ eodem tem-<lb/>pore percurruntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16544" xml:space="preserve">& </s> <s xml:id="echoid-s16545" xml:space="preserve">linea, quæ per Tellurem & </s> <s xml:id="echoid-s16546" xml:space="preserve">Plane- <anchor type="note" xlink:label="note-0642-03a" xlink:href="note-0642-03"/> tam ducitur, motu parallelo fertur, quo locus Planetæ ap-<lb/>parens non mutatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16547" xml:space="preserve"> <anchor type="note" xlink:label="note-0642-04a" xlink:href="note-0642-04"/> </s> </p> <div xml:id="echoid-div2492" type="float" level="2" n="3"> <note position="left" xlink:label="note-0642-01" xlink:href="note-0642-01a" xml:space="preserve">1015.</note> <note position="left" xlink:label="note-0642-02" xlink:href="note-0642-02a" xml:space="preserve">1016.</note> <note symbol="*" position="left" xlink:label="note-0642-03" xlink:href="note-0642-03a" xml:space="preserve">53.</note> <note symbol="*" position="left" xlink:label="note-0642-04" xlink:href="note-0642-04a" xml:space="preserve">994.</note> </div> <p> <s xml:id="echoid-s16548" xml:space="preserve">Inter d & </s> <s xml:id="echoid-s16549" xml:space="preserve">B magis ad orbitam Telluris inclinatur Planetæ <lb/>orbita, quare extremitas lineæ tranſeuntis per Tellurem & </s> <s xml:id="echoid-s16550" xml:space="preserve"><lb/>Planetam, licèt Planeta celerius Tellure moveatur, in con-<lb/> <anchor type="note" xlink:label="note-0642-05a" xlink:href="note-0642-05"/> ſequentiâ fertur; </s> <s xml:id="echoid-s16551" xml:space="preserve">verſus quam partem etiam dirigitur motus <lb/>apparens Planetæ<anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s16552" xml:space="preserve">Cùm tamen motus apparens Solis mo- <anchor type="note" xlink:label="note-0642-06a" xlink:href="note-0642-06"/> tum apparentem Planetæ ſuperet, elongatio augetur, quæ po-<lb/>ſito Planetâ in B eſt maxima. </s> <s xml:id="echoid-s16553" xml:space="preserve">Dum arcum B v Planeta per-<lb/>currit, in conſequentiâ etiam eſt motus apparens, & </s> <s xml:id="echoid-s16554" xml:space="preserve">motum <lb/>Solis apparentem ſuperat, ad quem accedit, & </s> <s xml:id="echoid-s16555" xml:space="preserve">transgredi-<lb/>tur, ab hoc recedendo, donec pervenerit ad A. </s> <s xml:id="echoid-s16556" xml:space="preserve">Inter A & </s> <s xml:id="echoid-s16557" xml:space="preserve"><lb/>E motus in conſequentiâ continuatur; </s> <s xml:id="echoid-s16558" xml:space="preserve">ſed Sol, cujus mo-<lb/>tus apparens in hoc caſu velocior eſt, ut de arcu d B expli-<lb/>catum, ad Planetam accedit, & </s> <s xml:id="echoid-s16559" xml:space="preserve">minuitur elongatio. </s> <s xml:id="echoid-s16560" xml:space="preserve">In E, <lb/>eodem modo ac in D, ſtationarius eſt Planeta, inter E & </s> <s xml:id="echoid-s16561" xml:space="preserve">V <lb/> <anchor type="note" xlink:label="note-0642-07a" xlink:href="note-0642-07"/> iterum retrogradus eſt.</s> <s xml:id="echoid-s16562" xml:space="preserve"/> </p> <div xml:id="echoid-div2493" type="float" level="2" n="4"> <note position="left" xlink:label="note-0642-05" xlink:href="note-0642-05a" xml:space="preserve">1017.</note> <note symbol="*" position="left" xlink:label="note-0642-06" xlink:href="note-0642-06a" xml:space="preserve">992.</note> <note position="left" xlink:label="note-0642-07" xlink:href="note-0642-07a" xml:space="preserve">1018.</note> </div> <p> <s xml:id="echoid-s16563" xml:space="preserve">Planetæ orbita ad planum Eclipticæ inclinatur<anchor type="note" xlink:href="" symbol="*"/>, idèo non <anchor type="note" xlink:label="note-0642-08a" xlink:href="note-0642-08"/> in lineâ Eclipticâ moveri videtur, ſed nunc minus nunc ma- <pb o="(121)" file="0643" n="710" rhead="MATHEMATICA LIB. IV. CAP. IV."/> gis ab hac diſtat, & </s> <s xml:id="echoid-s16564" xml:space="preserve">in curvâ irregulari ferri videtur, quæ <lb/>interdum Eclipticam ſecat.</s> <s xml:id="echoid-s16565" xml:space="preserve"/> </p> <div xml:id="echoid-div2494" type="float" level="2" n="5"> <note position="left" xlink:label="note-0642-08" xlink:href="note-0642-08a" xml:space="preserve">958. 959.</note> </div> <p> <s xml:id="echoid-s16566" xml:space="preserve">Sit NVN orbita Planetæ cujus nodi N, N; </s> <s xml:id="echoid-s16567" xml:space="preserve">ſit S Sol; <lb/></s> <s xml:id="echoid-s16568" xml:space="preserve"> <anchor type="note" xlink:label="note-0643-01a" xlink:href="note-0643-01"/> T t Telluris orbita in plano Eclipticæ; </s> <s xml:id="echoid-s16569" xml:space="preserve">Telius T; </s> <s xml:id="echoid-s16570" xml:space="preserve">Planeta <lb/>V. </s> <s xml:id="echoid-s16571" xml:space="preserve">Si V A concipiatur, per Planetam ad planum Eclipticæ <lb/>perpendicularis, angulus VTA, aut potius arcus, qui hunc <lb/>menſurat, eſt latitudo Planetæ <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s16572" xml:space="preserve">vocatur hæc latitudo Geo- <anchor type="note" xlink:label="note-0643-02a" xlink:href="note-0643-02"/> centrica, ut diſtinguatur à latitudine Planetæ ex Sole viſi, <lb/>quæ Heliocentrica dicitur, & </s> <s xml:id="echoid-s16573" xml:space="preserve">eſt in hoc caſu angulus VSA; <lb/></s> <s xml:id="echoid-s16574" xml:space="preserve">de illa hìc agitur, Phœnomena ex Tellure viſa examinamus.</s> <s xml:id="echoid-s16575" xml:space="preserve"/> </p> <div xml:id="echoid-div2495" type="float" level="2" n="6"> <note position="right" xlink:label="note-0643-01" xlink:href="note-0643-01a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig 5.</note> <note symbol="*" position="right" xlink:label="note-0643-02" xlink:href="note-0643-02a" xml:space="preserve">1006.</note> </div> <p> <s xml:id="echoid-s16576" xml:space="preserve">Quando Planeta eſt in Nodo, in lineâ Eclipticâ apparet, <lb/> <anchor type="note" xlink:label="note-0643-03a" xlink:href="note-0643-03"/> & </s> <s xml:id="echoid-s16577" xml:space="preserve">curva à Planetâ, motu apparenti in Zodiaco deſcripta, ſe-<lb/>cat lineam Eclipticam; </s> <s xml:id="echoid-s16578" xml:space="preserve">recedendo à Nodo augetur Planetæ <lb/> <anchor type="note" xlink:label="note-0643-04a" xlink:href="note-0643-04"/> latitudo, quæ etiam pro Telluris ſitu variatur; </s> <s xml:id="echoid-s16579" xml:space="preserve">ſic manente <lb/>Planetâ in V, major eſt latitudo ſi Tellus ſit in T, quàm ſi foret <lb/>in t. </s> <s xml:id="echoid-s16580" xml:space="preserve">Si, manente Tellure, Planetam ex V ad v tranſlatum <lb/>concipiamus, ex duplici cauſâ angulus v TB minor erit an-<lb/>gulo VTA, ex acceſſu Planetæ ad nodum, & </s> <s xml:id="echoid-s16581" xml:space="preserve">ex receſſu <lb/>ſpectatoris.</s> <s xml:id="echoid-s16582" xml:space="preserve"/> </p> <div xml:id="echoid-div2496" type="float" level="2" n="7"> <note position="right" xlink:label="note-0643-03" xlink:href="note-0643-03a" xml:space="preserve">1019.</note> <note position="right" xlink:label="note-0643-04" xlink:href="note-0643-04a" xml:space="preserve">1020.</note> </div> <p> <s xml:id="echoid-s16583" xml:space="preserve">Si nunc conſideremus Tellurem & </s> <s xml:id="echoid-s16584" xml:space="preserve">Planetam continuò <lb/>moveri, facilè concipiemus mutari omnibus momentis lati-<lb/>tudinem ex utraque cauſâ, quæ interdum contrariè agunt, <lb/>interdum, in augendâ aut minuendâ latitudine, conſpirant; <lb/></s> <s xml:id="echoid-s16585" xml:space="preserve">unde neceſſariò oritur motus apparens in curvâ irregulari, <lb/>ut ante dictum, quæ Eclipticam ſecat, quoties nodos trans-<lb/>greditur Planeta, id eſt, bis in ſingulis hujus revolutioni-<lb/>bus; </s> <s xml:id="echoid-s16586" xml:space="preserve">curva etiam hæc, ab utraque parte, non ultra certos <lb/>limites in Zodiaco ab Eclipticâ recedit.</s> <s xml:id="echoid-s16587" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16588" xml:space="preserve">Teleſcopio etiam deteguntur Phoenomena notabilia Pla-<lb/>netarum inferiorum, quæ ab horum opacitate pendent.</s> <s xml:id="echoid-s16589" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16590" xml:space="preserve">Sit S Sol; </s> <s xml:id="echoid-s16591" xml:space="preserve">T Tellus; </s> <s xml:id="echoid-s16592" xml:space="preserve">A, B, C, v, D, E, F, V, Planeta <lb/> <anchor type="note" xlink:label="note-0643-05a" xlink:href="note-0643-05"/> inferior, Venus ex gr.</s> <s xml:id="echoid-s16593" xml:space="preserve">, in orbitâ. </s> <s xml:id="echoid-s16594" xml:space="preserve">Hic mutuato à Sole lu-<lb/>mine lucet, & </s> <s xml:id="echoid-s16595" xml:space="preserve">hæmiſphærium Soli obverſum tantum illumi-<lb/>natur, hæmiſphærium alterum inviſibile eſt: </s> <s xml:id="echoid-s16596" xml:space="preserve">Idcirco ſola <lb/>pars hæmiſphærii illuminati, quæ Telluri obvertitur, ex hac <lb/>videri poteſt; </s> <s xml:id="echoid-s16597" xml:space="preserve">in V Planeta videri non poteſt, in v rotundus <lb/>apparêret, niſi radii ſolares impedirent quo minus videatur.</s> <s xml:id="echoid-s16598" xml:space="preserve"/> </p> <div xml:id="echoid-div2497" type="float" level="2" n="8"> <note position="right" xlink:label="note-0643-05" xlink:href="note-0643-05a" xml:space="preserve"><emph style="sc">TAB. XXI</emph>. <lb/>fig. 4.</note> </div> <pb o="122" file="0644" n="711" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s16599" xml:space="preserve">Ex v progrediendo, Planeta continuò decreſcit, in D ha. <lb/></s> <s xml:id="echoid-s16600" xml:space="preserve"> <anchor type="note" xlink:label="note-0644-01a" xlink:href="note-0644-01"/> bet figuram d, in e & </s> <s xml:id="echoid-s16601" xml:space="preserve">f delineatur, ut in E & </s> <s xml:id="echoid-s16602" xml:space="preserve">F apparet, <lb/>ulteriuſque decreſcit, donec evaneſcat in V; </s> <s xml:id="echoid-s16603" xml:space="preserve">deinde iterum <lb/>creſcit ſucceſſivè mutando figuram, donec totum hæmiſphæ-<lb/>rium illuminatum verſus Tellurem dirigatur.</s> <s xml:id="echoid-s16604" xml:space="preserve"/> </p> <div xml:id="echoid-div2498" type="float" level="2" n="9"> <note position="left" xlink:label="note-0644-01" xlink:href="note-0644-01a" xml:space="preserve">1021.</note> </div> <p> <s xml:id="echoid-s16605" xml:space="preserve">Quando nodus datur in V, aut in viciniis, Planeta in ipſo <lb/> <anchor type="note" xlink:label="note-0644-02a" xlink:href="note-0644-02"/> diſco Solis, & </s> <s xml:id="echoid-s16606" xml:space="preserve">quaſi Soli applicatum, videtur, & </s> <s xml:id="echoid-s16607" xml:space="preserve">obſervatur ma-<lb/>cula nigra, quæ ſuper Solis ſuper ficie movetur: </s> <s xml:id="echoid-s16608" xml:space="preserve">in hoc caſu, <lb/>propriè loquendo, Planetam non videmus, ſed ubi radios ſo-<lb/>lares intercipiat decernimus.</s> <s xml:id="echoid-s16609" xml:space="preserve"/> </p> <div xml:id="echoid-div2499" type="float" level="2" n="10"> <note position="left" xlink:label="note-0644-02" xlink:href="note-0644-02a" xml:space="preserve">1022.</note> </div> <p> <s xml:id="echoid-s16610" xml:space="preserve">Quo minus à Tellure diſtat Planeta, eo major apparet <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0644-03a" xlink:href="note-0644-03"/> & </s> <s xml:id="echoid-s16611" xml:space="preserve">magis lucidus; </s> <s xml:id="echoid-s16612" xml:space="preserve">ſed dum ad Tellurem accedit, pars lucida <lb/> <anchor type="note" xlink:label="note-0644-04a" xlink:href="note-0644-04"/> viſibilis minuitur, ita ut ex unâ cauſâ creſcat lumen, ex a-<lb/>liâ minuatur; </s> <s xml:id="echoid-s16613" xml:space="preserve">daturque diſtantia, ad quam lux reflexa eſt <lb/>maxima.</s> <s xml:id="echoid-s16614" xml:space="preserve"/> </p> <div xml:id="echoid-div2500" type="float" level="2" n="11"> <note position="left" xlink:label="note-0644-03" xlink:href="note-0644-03a" xml:space="preserve">1023.</note> <note symbol="*" position="left" xlink:label="note-0644-04" xlink:href="note-0644-04a" xml:space="preserve">733.</note> </div> </div> <div xml:id="echoid-div2502" type="section" level="1" n="625"> <head xml:id="echoid-head813" xml:space="preserve">CAPUT V.</head> <head xml:id="echoid-head814" style="it" xml:space="preserve">De Pbænomenis Planetarum ſuperiorum, ex horum <lb/>& Telluris motibus in orbitis ſuis.</head> <p> <s xml:id="echoid-s16615" xml:space="preserve">IN multis, cum explicatis circa Planetas inferiores, coin-<lb/>cidunt ſuperiorum motus apparentes, in multis differunt. <lb/></s> <s xml:id="echoid-s16616" xml:space="preserve">Non ſemper hi Solem comitantur, ſed ſæpe in oppoſitione <lb/> <anchor type="note" xlink:label="note-0644-05a" xlink:href="note-0644-05"/> obſervantur; </s> <s xml:id="echoid-s16617" xml:space="preserve">in motu tamen, ut de inferioribus dictum, <lb/>non ſemper in conſequentiâ ferri videntur, ſed ſæpe ſtationa-<lb/> <anchor type="note" xlink:label="note-0644-06a" xlink:href="note-0644-06"/> rii, ſæpe retrogradi ſunt.</s> <s xml:id="echoid-s16618" xml:space="preserve"/> </p> <div xml:id="echoid-div2502" type="float" level="2" n="1"> <note position="left" xlink:label="note-0644-05" xlink:href="note-0644-05a" xml:space="preserve">1024.</note> <note position="left" xlink:label="note-0644-06" xlink:href="note-0644-06a" xml:space="preserve">1025.</note> </div> <p> <s xml:id="echoid-s16619" xml:space="preserve">Sit M Planeta ſuperior, ex gr. </s> <s xml:id="echoid-s16620" xml:space="preserve">Mars, in orbitâ; </s> <s xml:id="echoid-s16621" xml:space="preserve">ATHB <lb/> <anchor type="note" xlink:label="note-0644-07a" xlink:href="note-0644-07"/> orbita Telluris. </s> <s xml:id="echoid-s16622" xml:space="preserve">Tempus periodicum Telluris brevius eſt <lb/> <anchor type="note" xlink:label="note-0644-08a" xlink:href="note-0644-08"/> tempore periodico Martis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16623" xml:space="preserve">ideò inter hunc & </s> <s xml:id="echoid-s16624" xml:space="preserve">Solem in <anchor type="note" xlink:label="note-0644-09a" xlink:href="note-0644-09"/> motu ſuo tranſit ellus, in quo caſu Planeta in F, inter ſtel-<lb/>las fixas Soli oppoſitus, apparet. </s> <s xml:id="echoid-s16625" xml:space="preserve">Per Mducantur lineæ BM; <lb/></s> <s xml:id="echoid-s16626" xml:space="preserve">AM, orbitam Telluris tangentes, quæ continuatæ in G & </s> <s xml:id="echoid-s16627" xml:space="preserve">D <lb/>in ſphærâ ſtellarum fixarum pertingunt. </s> <s xml:id="echoid-s16628" xml:space="preserve">Concipiamus, <lb/>dum Planeta in orbitâ transfertur, lineas has etiam moveri, <lb/>ita ut puncta A & </s> <s xml:id="echoid-s16629" xml:space="preserve">B, in quibus lineæ per Planetam tranſeun-<lb/>tes orbitam Telluris tangunt, in tempore periodico Pla-<lb/>netæ revolutionem peragant. </s> <s xml:id="echoid-s16630" xml:space="preserve">Cùm autem Tellus celerius <pb o="123" file="0645" n="712" rhead="MATHEMATICA LIB. IV. CAP. VI."/> revolvatur, per puncta A & </s> <s xml:id="echoid-s16631" xml:space="preserve">B, in motu ſuo tranſit. </s> <s xml:id="echoid-s16632" xml:space="preserve">In hoc <lb/>motu ultra FD & </s> <s xml:id="echoid-s16633" xml:space="preserve">FG à loco Planetæ è Sole viſo non re-<lb/>movetur locus apparens è Tellure. </s> <s xml:id="echoid-s16634" xml:space="preserve">Sit in hujus orbitâ pun-<lb/>ctum T tale, ut ductâ lineâ t m parallelâ lineæ TM, Tt ſit ad <lb/>Mm, ut Telluris celeritas ad Planetæ celeritatem; </s> <s xml:id="echoid-s16635" xml:space="preserve">in quo <lb/>caſu hæ lineolæ eodem tempore percurruntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16636" xml:space="preserve">interea <anchor type="note" xlink:label="note-0645-01a" xlink:href="note-0645-01"/> quieſcere videtur Planeta <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s16637" xml:space="preserve">ſtationarius dicitur. </s> <s xml:id="echoid-s16638" xml:space="preserve">Eodem <anchor type="note" xlink:label="note-0645-02a" xlink:href="note-0645-02"/> modo ſtationarius eſt, poſitâ Tellure in H. </s> <s xml:id="echoid-s16639" xml:space="preserve">In motu Tellu-<lb/>ris inter T & </s> <s xml:id="echoid-s16640" xml:space="preserve">H, Planeta ab E per F in antecedentiâ move-<lb/>ri videtur & </s> <s xml:id="echoid-s16641" xml:space="preserve">retrogradus dicitur, dum reliquam orbitæ ſuæ <lb/>partem percurrit Tellus, directus eſt Planeta.</s> <s xml:id="echoid-s16642" xml:space="preserve"/> </p> <div xml:id="echoid-div2503" type="float" level="2" n="2"> <note position="left" xlink:label="note-0644-07" xlink:href="note-0644-07a" xml:space="preserve">1026.</note> <note position="left" xlink:label="note-0644-08" xlink:href="note-0644-08a" xml:space="preserve">TAB. XXII. <lb/>fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0644-09" xlink:href="note-0644-09a" xml:space="preserve">948.</note> <note symbol="*" position="right" xlink:label="note-0645-01" xlink:href="note-0645-01a" xml:space="preserve">53.</note> <note symbol="*" position="right" xlink:label="note-0645-02" xlink:href="note-0645-02a" xml:space="preserve">994.</note> </div> <p style="it"> <s xml:id="echoid-s16643" xml:space="preserve">Phænomena circa latitudinem ſimilia ſunt iis, quæ expli-<lb/> <anchor type="note" xlink:label="note-0645-03a" xlink:href="note-0645-03"/> cata ſunt reſpectu Planetarnm inferiorum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16644" xml:space="preserve"/> </p> <div xml:id="echoid-div2504" type="float" level="2" n="3"> <note position="right" xlink:label="note-0645-03" xlink:href="note-0645-03a" xml:space="preserve">1027.</note> </div> <note symbol="*" position="right" xml:space="preserve">1018.</note> <p> <s xml:id="echoid-s16645" xml:space="preserve">Fupiter & </s> <s xml:id="echoid-s16646" xml:space="preserve">Saturnus ad magnam diſtantiam Telluris orbi-<lb/> <anchor type="note" xlink:label="note-0645-05a" xlink:href="note-0645-05"/> tam cingunt, quare ferè tota illorum hæmiſphæria, quæ â <lb/>Sole illuminantur, è Tellure viſibilia ſunt; </s> <s xml:id="echoid-s16647" xml:space="preserve">ideô ſemper rotun-<lb/>di apparent hi Planetæ.</s> <s xml:id="echoid-s16648" xml:space="preserve"/> </p> <div xml:id="echoid-div2505" type="float" level="2" n="4"> <note position="right" xlink:label="note-0645-05" xlink:href="note-0645-05a" xml:space="preserve">1028.</note> </div> <p> <s xml:id="echoid-s16649" xml:space="preserve">Quia minus diſtat Mars, paululum gibboſus apparet, in-<lb/> <anchor type="note" xlink:label="note-0645-06a" xlink:href="note-0645-06"/> ter conjunctionem & </s> <s xml:id="echoid-s16650" xml:space="preserve">oppoſitionem cum Sole.</s> <s xml:id="echoid-s16651" xml:space="preserve"/> </p> <div xml:id="echoid-div2506" type="float" level="2" n="5"> <note position="right" xlink:label="note-0645-06" xlink:href="note-0645-06a" xml:space="preserve">1029.</note> </div> </div> <div xml:id="echoid-div2508" type="section" level="1" n="626"> <head xml:id="echoid-head815" xml:space="preserve">CAPUT VI.</head> <head xml:id="echoid-head816" style="it" xml:space="preserve">De Phænomenis Satellitum, ex motu horum in orbi-<lb/>tis. Vbi de Eclipſibus Solis & Lunæ.</head> <p> <s xml:id="echoid-s16652" xml:space="preserve">SAtellites Fovis & </s> <s xml:id="echoid-s16653" xml:space="preserve">Saturni ſemper in motu primarios ſuos <lb/> <anchor type="note" xlink:label="note-0645-07a" xlink:href="note-0645-07"/> comitantur, & </s> <s xml:id="echoid-s16654" xml:space="preserve">nunquam ultra certos limites, qui ex ho-<lb/>rum, à primariis, diſtantiis facilè determinantur, ab utra-<lb/>que parte recedere videntur; </s> <s xml:id="echoid-s16655" xml:space="preserve">alterniſque vicibus in antece-<lb/>dentiâ & </s> <s xml:id="echoid-s16656" xml:space="preserve">in conſequentiâ feruntur. </s> <s xml:id="echoid-s16657" xml:space="preserve">Aliquando omnes ad <lb/>eandem partem primarii dantur, aliquando inter ipſos pri-<lb/>marius obſervatur; </s> <s xml:id="echoid-s16658" xml:space="preserve">omnes ſemper aut in eâdem lineâ rectâ <lb/> <anchor type="note" xlink:label="note-0645-08a" xlink:href="note-0645-08"/> diſponuntur, aut parum ab bac diſtant. </s> <s xml:id="echoid-s16659" xml:space="preserve">Quæ omnia ex mo-<lb/>tu circa primarios, in planis exiguos inter ſe, & </s> <s xml:id="echoid-s16660" xml:space="preserve">cum plano <lb/>Eclipticæ, angulos efficientibus, facilè deducuntur.</s> <s xml:id="echoid-s16661" xml:space="preserve"/> </p> <div xml:id="echoid-div2508" type="float" level="2" n="1"> <note position="right" xlink:label="note-0645-07" xlink:href="note-0645-07a" xml:space="preserve">1030.</note> <note position="right" xlink:label="note-0645-08" xlink:href="note-0645-08a" xml:space="preserve">1031.</note> </div> <p> <s xml:id="echoid-s16662" xml:space="preserve">Non omnes Saturni aut Jovis Satellites ſemper ſimul viſi-<lb/> <anchor type="note" xlink:label="note-0645-09a" xlink:href="note-0645-09"/> biles ſunt, aliquando à primario obteguntur, ſæpe in umbram <lb/>primarii immerguntur.</s> <s xml:id="echoid-s16663" xml:space="preserve"/> </p> <div xml:id="echoid-div2509" type="float" level="2" n="2"> <note position="right" xlink:label="note-0645-09" xlink:href="note-0645-09a" xml:space="preserve">1032.</note> </div> <pb o="124" file="0646" n="713" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div2511" type="section" level="1" n="627"> <head xml:id="echoid-head817" xml:space="preserve"><emph style="sc">Definitio i.</emph></head> <p> <s xml:id="echoid-s16664" xml:space="preserve">Talis in umbram immerſio dicitur Satellitis Eclipſis.</s> <s xml:id="echoid-s16665" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1033.</note> <p> <s xml:id="echoid-s16666" xml:space="preserve">Sit S Sol; </s> <s xml:id="echoid-s16667" xml:space="preserve">T t Telluris orbita, I Jupiter; </s> <s xml:id="echoid-s16668" xml:space="preserve">M m orbita ſe-<lb/> <anchor type="note" xlink:label="note-0646-02a" xlink:href="note-0646-02"/> cundarii Jovialis. </s> <s xml:id="echoid-s16669" xml:space="preserve">Dum ab M ad m movetur ſecundarius, E-<lb/>clipſin patitur; </s> <s xml:id="echoid-s16670" xml:space="preserve">& </s> <s xml:id="echoid-s16671" xml:space="preserve">à Sole non illuminatus inviſibilis eſt. </s> <s xml:id="echoid-s16672" xml:space="preserve">Po-<lb/>ſitâ Tellure verſus T, immerſio in umbram facile obſervatur, <lb/>emerſio contra magis ſenſibilis eſt, poſitâ Tellure verſus t.</s> <s xml:id="echoid-s16673" xml:space="preserve"/> </p> <div xml:id="echoid-div2511" type="float" level="2" n="1"> <note position="left" xlink:label="note-0646-02" xlink:href="note-0646-02a" xml:space="preserve">TAB XXII. <lb/>fig. 2.</note> </div> <p> <s xml:id="echoid-s16674" xml:space="preserve">Inter Saturni comites annulum dari diximus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16675" xml:space="preserve">circa quem <anchor type="note" xlink:label="note-0646-03a" xlink:href="note-0646-03"/> notandum, illum nunquam à ſpectatore in Tellure latiorem vi-<lb/> <anchor type="note" xlink:label="note-0646-04a" xlink:href="note-0646-04"/> deri, quam in fig. </s> <s xml:id="echoid-s16676" xml:space="preserve">4. </s> <s xml:id="echoid-s16677" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16678" xml:space="preserve">xx. </s> <s xml:id="echoid-s16679" xml:space="preserve">repræſentatur; </s> <s xml:id="echoid-s16680" xml:space="preserve">& </s> <s xml:id="echoid-s16681" xml:space="preserve">aliquando in-<lb/>viſibilem eſſe; </s> <s xml:id="echoid-s16682" xml:space="preserve">quando nempe planum annuli continuatum <lb/>per Tellurem tranſit; </s> <s xml:id="echoid-s16683" xml:space="preserve">annuli enim craſſities ſenſibilis non <lb/>eſt. </s> <s xml:id="echoid-s16684" xml:space="preserve">Etiam non videtur annulus, quando hujus planum conti-<lb/>nuatum, inter Solem & </s> <s xml:id="echoid-s16685" xml:space="preserve">Tellurem tranſit; </s> <s xml:id="echoid-s16686" xml:space="preserve">tunc enim ſuper-<lb/>ficies annuli illuminata à Tellure avertitur: </s> <s xml:id="echoid-s16687" xml:space="preserve">in utroque caſu <lb/>Saturnus rotundus apparet, in ultimo tamen, ex radiis ab an-<lb/>nulc interceptis, faſcia nigra in Planetæ ſuperficie obſervatur, <lb/>ſimilis illi, quæ ab umbrâ annuli pendet.</s> <s xml:id="echoid-s16688" xml:space="preserve"/> </p> <div xml:id="echoid-div2512" type="float" level="2" n="2"> <note position="left" xlink:label="note-0646-03" xlink:href="note-0646-03a" xml:space="preserve">1034.</note> <note symbol="*" position="left" xlink:label="note-0646-04" xlink:href="note-0646-04a" xml:space="preserve">963.</note> </div> <p> <s xml:id="echoid-s16689" xml:space="preserve">Telluris Satellitis, Lunæ nempe, Phoenomena noſtri re-<lb/>ſpectu notabiliora ſunt, & </s> <s xml:id="echoid-s16690" xml:space="preserve">peculiariter explicanda.</s> <s xml:id="echoid-s16691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16692" xml:space="preserve">Sæpiſſimè Soli conjungitur, totieſque buic opponitur, <lb/> <anchor type="note" xlink:label="note-0646-05a" xlink:href="note-0646-05"/> non tamen in ſingulis revolutionibus Lunæ in orbitâ; </s> <s xml:id="echoid-s16693" xml:space="preserve">nam <lb/>dum Luna poſt revolutionem integram 27. </s> <s xml:id="echoid-s16694" xml:space="preserve">dier. </s> <s xml:id="echoid-s16695" xml:space="preserve">7. </s> <s xml:id="echoid-s16696" xml:space="preserve">hor. </s> <s xml:id="echoid-s16697" xml:space="preserve">ite-<lb/>rum redit ad locum inter ſtellas fixas, in quo cum Sole fuit <lb/>conjuncta, Sol ex hoc loco receſſit, & </s> <s xml:id="echoid-s16698" xml:space="preserve">ab hoc circiter diſtat <lb/>27. </s> <s xml:id="echoid-s16699" xml:space="preserve">gr. </s> <s xml:id="echoid-s16700" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16701" xml:space="preserve">itaque conjunctiones vicinæ diſtant viginti novem <anchor type="note" xlink:label="note-0646-06a" xlink:href="note-0646-06"/> diebus cum ſemiſſe.</s> <s xml:id="echoid-s16702" xml:space="preserve"/> </p> <div xml:id="echoid-div2513" type="float" level="2" n="3"> <note position="left" xlink:label="note-0646-05" xlink:href="note-0646-05a" xml:space="preserve">1035.</note> <note position="left" xlink:label="note-0646-06" xlink:href="note-0646-06a" xml:space="preserve">1036.</note> </div> <note symbol="*" position="left" xml:space="preserve">960. 996. 998.</note> </div> <div xml:id="echoid-div2515" type="section" level="1" n="628"> <head xml:id="echoid-head818" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p> <s xml:id="echoid-s16703" xml:space="preserve">Menſis Lunaris periodicus, eſt tempus revolutionis Lunæ <lb/> <anchor type="note" xlink:label="note-0646-08a" xlink:href="note-0646-08"/> in orbitâ.</s> <s xml:id="echoid-s16704" xml:space="preserve"/> </p> <div xml:id="echoid-div2515" type="float" level="2" n="1"> <note position="left" xlink:label="note-0646-08" xlink:href="note-0646-08a" xml:space="preserve">1037.</note> </div> </div> <div xml:id="echoid-div2517" type="section" level="1" n="629"> <head xml:id="echoid-head819" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p> <s xml:id="echoid-s16705" xml:space="preserve">Menſis Lunaris Synodicus, ſeu lunatio, eſt tempus, quod Lu-<lb/> <anchor type="note" xlink:label="note-0646-09a" xlink:href="note-0646-09"/> na impendit inter conjunctiones cum Sole proximas.</s> <s xml:id="echoid-s16706" xml:space="preserve"/> </p> <div xml:id="echoid-div2517" type="float" level="2" n="1"> <note position="left" xlink:label="note-0646-09" xlink:href="note-0646-09a" xml:space="preserve">1038.</note> </div> <p> <s xml:id="echoid-s16707" xml:space="preserve">Inviſibilis eſt Luna in conjunctione cum Sole; </s> <s xml:id="echoid-s16708" xml:space="preserve">quia hæ-<lb/> <anchor type="note" xlink:label="note-0646-10a" xlink:href="note-0646-10"/> miſphærium illuminatum à Tellure avertitur. </s> <s xml:id="echoid-s16709" xml:space="preserve">Sit Tellus T; <lb/></s> <s xml:id="echoid-s16710" xml:space="preserve"> <anchor type="note" xlink:label="note-0646-11a" xlink:href="note-0646-11"/> Luna in N inter Solem & </s> <s xml:id="echoid-s16711" xml:space="preserve">Tellurem; </s> <s xml:id="echoid-s16712" xml:space="preserve">hemiſphærium illumi-<lb/>natum erit m l i, quod in Tellure videri non poteſt.</s> <s xml:id="echoid-s16713" xml:space="preserve"/> </p> <div xml:id="echoid-div2518" type="float" level="2" n="2"> <note position="left" xlink:label="note-0646-10" xlink:href="note-0646-10a" xml:space="preserve">1039.</note> <note position="left" xlink:label="note-0646-11" xlink:href="note-0646-11a" xml:space="preserve">TAB. XXII. <lb/>fig. 3.</note> </div> <pb file="0647" n="714"/> <pb file="0647a" n="715"/> <figure> <image file="0647a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0647a-01"/> </figure> <pb file="0648" n="716"/> <pb o="125" file="0649" n="717" rhead="MATHEMATICA LIB. IV. CAP. VI."/> <p> <s xml:id="echoid-s16714" xml:space="preserve">Dum Luna, in orbitâ, à conjunctione ad oppoſitionem, ſer-<lb/> <anchor type="note" xlink:label="note-0649-01a" xlink:href="note-0649-01"/> tur, pars illuminata, quæ ſemper verſus Solem dirigitur, <lb/>continuò magis ac magis ſpectatoribus in Tellure viſibilis eſt; <lb/></s> <s xml:id="echoid-s16715" xml:space="preserve">& </s> <s xml:id="echoid-s16716" xml:space="preserve">in punctis A, B, C, ſucceſſivè figuras a, b, c, acquirit Luna. </s> <s xml:id="echoid-s16717" xml:space="preserve"><lb/>In P, in oppoſitione cum Sole, rotunda apparet; </s> <s xml:id="echoid-s16718" xml:space="preserve">deinde per <lb/> <anchor type="note" xlink:label="note-0649-02a" xlink:href="note-0649-02"/> D, E, F, tranſeundo decreſcit, ut in d, e, f, repræſentatur.</s> <s xml:id="echoid-s16719" xml:space="preserve"/> </p> <div xml:id="echoid-div2519" type="float" level="2" n="3"> <note position="right" xlink:label="note-0649-01" xlink:href="note-0649-01a" xml:space="preserve">1040.</note> <note position="right" xlink:label="note-0649-02" xlink:href="note-0649-02a" xml:space="preserve">1041.</note> </div> </div> <div xml:id="echoid-div2521" type="section" level="1" n="630"> <head xml:id="echoid-head820" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s16720" xml:space="preserve">Conjunctio Lunæ cum Sole vocatur Novilunium. <lb/></s> <s xml:id="echoid-s16721" xml:space="preserve"> <anchor type="note" xlink:label="note-0649-03a" xlink:href="note-0649-03"/> Poſt conjunctionem Luna quaſi renaſci videtur.</s> <s xml:id="echoid-s16722" xml:space="preserve"/> </p> <div xml:id="echoid-div2521" type="float" level="2" n="1"> <note position="right" xlink:label="note-0649-03" xlink:href="note-0649-03a" xml:space="preserve">1042.</note> </div> </div> <div xml:id="echoid-div2523" type="section" level="1" n="631"> <head xml:id="echoid-head821" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p> <s xml:id="echoid-s16723" xml:space="preserve">Oppoſitio Lunæ cum Sole vocatur Plenilunium; </s> <s xml:id="echoid-s16724" xml:space="preserve">quia Luna <lb/> <anchor type="note" xlink:label="note-0649-04a" xlink:href="note-0649-04"/> tota lucida apparet.</s> <s xml:id="echoid-s16725" xml:space="preserve"/> </p> <div xml:id="echoid-div2523" type="float" level="2" n="1"> <note position="right" xlink:label="note-0649-04" xlink:href="note-0649-04a" xml:space="preserve">1043.</note> </div> </div> <div xml:id="echoid-div2525" type="section" level="1" n="632"> <head xml:id="echoid-head822" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s16726" xml:space="preserve">Nomine communi oppoſitio & </s> <s xml:id="echoid-s16727" xml:space="preserve">conjunctio Satellitis cum Sole <lb/> <anchor type="note" xlink:label="note-0649-05a" xlink:href="note-0649-05"/> vocantur Syzygiæ.</s> <s xml:id="echoid-s16728" xml:space="preserve"/> </p> <div xml:id="echoid-div2525" type="float" level="2" n="1"> <note position="right" xlink:label="note-0649-05" xlink:href="note-0649-05a" xml:space="preserve">1044.</note> </div> <p> <s xml:id="echoid-s16729" xml:space="preserve">In A & </s> <s xml:id="echoid-s16730" xml:space="preserve">F pars Lunæ obſcura, radiis à Tellure reflexis, <lb/> <anchor type="note" xlink:label="note-0649-06a" xlink:href="note-0649-06"/> paululum illuminatur; </s> <s xml:id="echoid-s16731" xml:space="preserve">ideò videtur à ſpectatore cui Sol viſi-<lb/>bilis non eſt, id eſt, in primo caſu poſt occaſum Solis, in <lb/>ſecundo ante hujus ortum.</s> <s xml:id="echoid-s16732" xml:space="preserve"/> </p> <div xml:id="echoid-div2526" type="float" level="2" n="2"> <note position="right" xlink:label="note-0649-06" xlink:href="note-0649-06a" xml:space="preserve">1045.</note> </div> </div> <div xml:id="echoid-div2528" type="section" level="1" n="633"> <head xml:id="echoid-head823" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p style="it"> <s xml:id="echoid-s16733" xml:space="preserve">Quando Solis lumen à Lunâ intercipitur ita ut in totum, <lb/> <anchor type="note" xlink:label="note-0649-07a" xlink:href="note-0649-07"/> aut pro parte, reſpectu ſpectatoris cujuſcunque in Tellure, <lb/>Sol obtegatur, Sol dicitur Eclipſin pati.</s> <s xml:id="echoid-s16734" xml:space="preserve"/> </p> <div xml:id="echoid-div2528" type="float" level="2" n="1"> <note position="right" xlink:label="note-0649-07" xlink:href="note-0649-07a" xml:space="preserve">1046.</note> </div> <p> <s xml:id="echoid-s16735" xml:space="preserve">Propriè loquendo, hæc eſt Eclipſis Telluris, in cujus ſu-<lb/>perficiem cadit Lunæ umbra aut penumbra.</s> <s xml:id="echoid-s16736" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2530" type="section" level="1" n="634"> <head xml:id="echoid-head824" xml:space="preserve"><emph style="sc">Definitio</emph> 8.</head> <p> <s xml:id="echoid-s16737" xml:space="preserve">Lunæ Eclipſis eſt obſcuratio Lunæ ex umbrâ Telluris. <lb/></s> <s xml:id="echoid-s16738" xml:space="preserve"> <anchor type="note" xlink:label="note-0649-08a" xlink:href="note-0649-08"/> </s> </p> <div xml:id="echoid-div2530" type="float" level="2" n="1"> <note position="right" xlink:label="note-0649-08" xlink:href="note-0649-08a" xml:space="preserve">1047.</note> </div> <p style="it"> <s xml:id="echoid-s16739" xml:space="preserve">Nunquam Solis Eclipſis obſervatur, niſi quando Novilu-<lb/> <anchor type="note" xlink:label="note-0649-09a" xlink:href="note-0649-09"/> nium celebratur.</s> <s xml:id="echoid-s16740" xml:space="preserve"/> </p> <div xml:id="echoid-div2531" type="float" level="2" n="2"> <note position="right" xlink:label="note-0649-09" xlink:href="note-0649-09a" xml:space="preserve">1048.</note> </div> <p style="it"> <s xml:id="echoid-s16741" xml:space="preserve">Nunquam Luna deliquium patitur, niſi in Plenilunio.</s> <s xml:id="echoid-s16742" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">1049.</note> <p> <s xml:id="echoid-s16743" xml:space="preserve">Non tamen in ſingulis Syzygiis Luminaria deficiunt; </s> <s xml:id="echoid-s16744" xml:space="preserve">quia <lb/> <anchor type="note" xlink:label="note-0649-11a" xlink:href="note-0649-11"/> Luna non in Plano Eclipticæ movetur <anchor type="note" xlink:href="" symbol="*"/>, in quo ſemper dan- <anchor type="note" xlink:label="note-0649-12a" xlink:href="note-0649-12"/> tur Sol & </s> <s xml:id="echoid-s16745" xml:space="preserve">Tellus; </s> <s xml:id="echoid-s16746" xml:space="preserve">quare, propter latitudinem Lunæ, hujus <lb/>umbra, in Novilunio, ſæpe Tellurem non tangit; </s> <s xml:id="echoid-s16747" xml:space="preserve">& </s> <s xml:id="echoid-s16748" xml:space="preserve">ipſa, <lb/>in Plenilunio, ad latus umbræ Telluris tranſit.</s> <s xml:id="echoid-s16749" xml:space="preserve"/> </p> <div xml:id="echoid-div2532" type="float" level="2" n="3"> <note position="right" xlink:label="note-0649-11" xlink:href="note-0649-11a" xml:space="preserve">1050.</note> <note symbol="*" position="right" xlink:label="note-0649-12" xlink:href="note-0649-12a" xml:space="preserve">969.</note> </div> <p> <s xml:id="echoid-s16750" xml:space="preserve">Quando autem Lunæ latitudo aut nulla aut exigua eſt, <lb/>id eſt, quando in Nodo, aut propè bunc, verſatur Luna in <lb/> <anchor type="note" xlink:label="note-0649-13a" xlink:href="note-0649-13"/> <pb o="126" file="0650" n="718" rhead="PHYSICES ELEMENTA."/> Syzygiis, Eclipſis obſervatur; </s> <s xml:id="echoid-s16751" xml:space="preserve">in hoc caſu in Eclipticâ, aut <lb/>parum ab hac diſtans, apparet Luna; </s> <s xml:id="echoid-s16752" xml:space="preserve">& </s> <s xml:id="echoid-s16753" xml:space="preserve">inde nomen ſuum <lb/>habet hæc linea.</s> <s xml:id="echoid-s16754" xml:space="preserve"/> </p> <div xml:id="echoid-div2533" type="float" level="2" n="4"> <note position="right" xlink:label="note-0649-13" xlink:href="note-0649-13a" xml:space="preserve">1051.</note> </div> <p> <s xml:id="echoid-s16755" xml:space="preserve">Ut quæ Lunæ Eclipſin ſpectant clariùs pateant, ſit Lunæ <lb/> <anchor type="note" xlink:label="note-0650-01a" xlink:href="note-0650-01"/> ſemita OO; </s> <s xml:id="echoid-s16756" xml:space="preserve">planum Eclipticæ RR; </s> <s xml:id="echoid-s16757" xml:space="preserve">in hoc ſemper datur <lb/>centrum umbræ Telluris <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16758" xml:space="preserve">Nodus orbitæ Lunæ eſt N.</s> <s xml:id="echoid-s16759" xml:space="preserve"/> </p> <div xml:id="echoid-div2534" type="float" level="2" n="5"> <note position="left" xlink:label="note-0650-01" xlink:href="note-0650-01a" xml:space="preserve">TAB. XXIII. <lb/>fig. 1.</note> </div> <note symbol="*" position="left" xml:space="preserve">940. 939.</note> <p> <s xml:id="echoid-s16760" xml:space="preserve">Si centrum umbræ Telluris ſit in A, non obſcuratur Lu-<lb/>na, quæ in F tranſit.</s> <s xml:id="echoid-s16761" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16762" xml:space="preserve">Si minus à Nodo diſtet Luna in Plenilunio, ut in G, um-<lb/> <anchor type="note" xlink:label="note-0650-03a" xlink:href="note-0650-03"/> bra Telluris datur in B, & </s> <s xml:id="echoid-s16763" xml:space="preserve">Luna pro parte obſcuratur; </s> <s xml:id="echoid-s16764" xml:space="preserve">hæc <lb/>Eclipſis dicitur Partialis.</s> <s xml:id="echoid-s16765" xml:space="preserve"/> </p> <div xml:id="echoid-div2535" type="float" level="2" n="6"> <note position="left" xlink:label="note-0650-03" xlink:href="note-0650-03a" xml:space="preserve">1052.</note> </div> <p> <s xml:id="echoid-s16766" xml:space="preserve">Si, poſitâ in D, Plenilunium celebretur, in totum <lb/> <anchor type="note" xlink:label="note-0650-04a" xlink:href="note-0650-04"/> tenebris obtegitur Luna in I; </s> <s xml:id="echoid-s16767" xml:space="preserve">in L in umbram cadit, in H <lb/>ex hac exit; </s> <s xml:id="echoid-s16768" xml:space="preserve">& </s> <s xml:id="echoid-s16769" xml:space="preserve">Eclipſis dicitur Totalis.</s> <s xml:id="echoid-s16770" xml:space="preserve"/> </p> <div xml:id="echoid-div2536" type="float" level="2" n="7"> <note position="left" xlink:label="note-0650-04" xlink:href="note-0650-04a" xml:space="preserve">1053.</note> </div> <p style="it"> <s xml:id="echoid-s16771" xml:space="preserve">Centralis vocatur Eclipſis, quando centrum Lunæ tranſit <lb/> <anchor type="note" xlink:label="note-0650-05a" xlink:href="note-0650-05"/> per centrum Vmbræ, quod in ipſo Nodo N tantùm obtinet.</s> <s xml:id="echoid-s16772" xml:space="preserve"/> </p> <div xml:id="echoid-div2537" type="float" level="2" n="8"> <note position="left" xlink:label="note-0650-05" xlink:href="note-0650-05a" xml:space="preserve">1054.</note> </div> <p> <s xml:id="echoid-s16773" xml:space="preserve">De Telluris umbrâ huc uſque locuti ſumus; </s> <s xml:id="echoid-s16774" xml:space="preserve">quia, quan-<lb/>do de Tellure loquimur, cum hac conjunctam etiam intelli-<lb/>gimus Atmoſphæram, de qua alibi <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16775" xml:space="preserve">de Atmoſpbæræ umbrâ <anchor type="note" xlink:label="note-0650-06a" xlink:href="note-0650-06"/> propriè agitur in Eclipſibus Lunaribus; </s> <s xml:id="echoid-s16776" xml:space="preserve">ipſius enim Tellu-<lb/> <anchor type="note" xlink:label="note-0650-07a" xlink:href="note-0650-07"/> ris umbra ad Lunam non pertingit.</s> <s xml:id="echoid-s16777" xml:space="preserve"/> </p> <div xml:id="echoid-div2538" type="float" level="2" n="9"> <note position="left" xlink:label="note-0650-06" xlink:href="note-0650-06a" xml:space="preserve">1055.</note> <note symbol="*" position="left" xlink:label="note-0650-07" xlink:href="note-0650-07a" xml:space="preserve">418.</note> </div> <p> <s xml:id="echoid-s16778" xml:space="preserve">Sit T Tellus, Atmoſphærâ FDGGDF circum. <lb/></s> <s xml:id="echoid-s16779" xml:space="preserve"> <anchor type="note" xlink:label="note-0650-08a" xlink:href="note-0650-08"/> data. </s> <s xml:id="echoid-s16780" xml:space="preserve">Radii ſolares BD, BD, Atmoſphæram tangen-<lb/>tes, rectâ progrediuntur, & </s> <s xml:id="echoid-s16781" xml:space="preserve">Atmoſphæræ umbram ter-<lb/>minant, extra quam ſi Luna detur, immediatè à radiis So-<lb/>laribus illuminatur, non verò eodem modo, inter BD & </s> <s xml:id="echoid-s16782" xml:space="preserve">BD, <lb/>illuſtratur.</s> <s xml:id="echoid-s16783" xml:space="preserve"/> </p> <div xml:id="echoid-div2539" type="float" level="2" n="10"> <note position="left" xlink:label="note-0650-08" xlink:href="note-0650-08a" xml:space="preserve">TAB. XXIV. <lb/>fig. 1.</note> </div> <p> <s xml:id="echoid-s16784" xml:space="preserve">Radii, qui obliquè Atmoſphæram intrant, refractionem pa-<lb/> <anchor type="note" xlink:label="note-0650-09a" xlink:href="note-0650-09"/> tiuntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16785" xml:space="preserve">& </s> <s xml:id="echoid-s16786" xml:space="preserve">dum ad Tellurem accedunt, continuò in me- <anchor type="note" xlink:label="note-0650-10a" xlink:href="note-0650-10"/> dium denſius atque denſius penetrant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16787" xml:space="preserve">ideoque omnibus <anchor type="note" xlink:label="note-0650-11a" xlink:href="note-0650-11"/> momentis inflectuntur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s16788" xml:space="preserve">& </s> <s xml:id="echoid-s16789" xml:space="preserve">per curvas moventur. </s> <s xml:id="echoid-s16790" xml:space="preserve">Sic radii <anchor type="note" xlink:label="note-0650-12a" xlink:href="note-0650-12"/> EF, EF, in curvis FG, FG, Tellurem tangentibus, <lb/>Atmoſphæram penetrant. </s> <s xml:id="echoid-s16791" xml:space="preserve">Omne lumen inter EF, EF, à <lb/>Tellure intercipitur, & </s> <s xml:id="echoid-s16792" xml:space="preserve">Radii GA, GA, terminant Tel-<lb/>luris umbram.</s> <s xml:id="echoid-s16793" xml:space="preserve"/> </p> <div xml:id="echoid-div2540" type="float" level="2" n="11"> <note position="left" xlink:label="note-0650-09" xlink:href="note-0650-09a" xml:space="preserve">1056.</note> <note symbol="*" position="left" xlink:label="note-0650-10" xlink:href="note-0650-10a" xml:space="preserve">617.</note> <note symbol="*" position="left" xlink:label="note-0650-11" xlink:href="note-0650-11a" xml:space="preserve">424. 429.</note> <note symbol="*" position="left" xlink:label="note-0650-12" xlink:href="note-0650-12a" xml:space="preserve">617.</note> </div> <p> <s xml:id="echoid-s16794" xml:space="preserve">Lumen autem inter EF & </s> <s xml:id="echoid-s16795" xml:space="preserve">BD, ab Atmoſphærâ refra-<lb/>ctum, diſpergitur inter GA & </s> <s xml:id="echoid-s16796" xml:space="preserve">BD continuatam, & </s> <s xml:id="echoid-s16797" xml:space="preserve">ultra A, <pb o="127" file="0651" n="719" rhead="MATHEMATICA LIB. IV. CAP. VI."/> mucronem umbræ Telluris, lumina ab omnibus partibus con-<lb/>funduntur, ſed recedendo à Tellure continuò debiliora ſunt: <lb/></s> <s xml:id="echoid-s16798" xml:space="preserve">ita ut Vmbra Atmoſphæræ non ſit umbra perfecta ſed lu-<lb/> <anchor type="note" xlink:label="note-0651-01a" xlink:href="note-0651-01"/> men debile, quo Luna in Eclipſi viſibilis eſt.</s> <s xml:id="echoid-s16799" xml:space="preserve"/> </p> <div xml:id="echoid-div2541" type="float" level="2" n="12"> <note position="right" xlink:label="note-0651-01" xlink:href="note-0651-01a" xml:space="preserve">1057.</note> </div> <p> <s xml:id="echoid-s16800" xml:space="preserve">Atmoſphæræ umbra eſt conica; </s> <s xml:id="echoid-s16801" xml:space="preserve">quia Solis diameter At-<lb/> <anchor type="note" xlink:label="note-0651-02a" xlink:href="note-0651-02"/> moſphæræ diametrum, quæ vix à Telluris diametro differt, <lb/>ſuperat; </s> <s xml:id="echoid-s16802" xml:space="preserve">& </s> <s xml:id="echoid-s16803" xml:space="preserve">conus hicce ad Martem non pertingit, ut ex <lb/>obſervationibus immediatis conſtat: </s> <s xml:id="echoid-s16804" xml:space="preserve">umbræ autem diame-<lb/>ter, in loco, ubi ab orbitâ Lunæ ſecatur, à Telluris diame-<lb/>tro vix quartâ parte ſuperatur.</s> <s xml:id="echoid-s16805" xml:space="preserve"/> </p> <div xml:id="echoid-div2542" type="float" level="2" n="13"> <note position="right" xlink:label="note-0651-02" xlink:href="note-0651-02a" xml:space="preserve">1058.</note> </div> <p> <s xml:id="echoid-s16806" xml:space="preserve">Simili ratiocinio, quo probavimus Lunam in Atmoſphæ-<lb/>ræ umbram cadere, quando in plenilunio Luna in Nodo, <lb/>aut propè hunc datur, probatur Lunæ umbram in Tellu-<lb/>rem cadere in Novilunio, quando aut in Nodo aut prope <lb/> <anchor type="note" xlink:label="note-0651-03a" xlink:href="note-0651-03"/> Nodum Luna verſatur, ideòque in hoc caſu Solem Eclipſin <lb/>pati; </s> <s xml:id="echoid-s16807" xml:space="preserve">circa quam varia ſunt notanda.</s> <s xml:id="echoid-s16808" xml:space="preserve"/> </p> <div xml:id="echoid-div2543" type="float" level="2" n="14"> <note position="right" xlink:label="note-0651-03" xlink:href="note-0651-03a" xml:space="preserve">1059.</note> </div> <p> <s xml:id="echoid-s16809" xml:space="preserve">Sit Sol S; </s> <s xml:id="echoid-s16810" xml:space="preserve">Luna T; </s> <s xml:id="echoid-s16811" xml:space="preserve">cadat hujus umbra in planum quod-<lb/> <anchor type="note" xlink:label="note-0651-04a" xlink:href="note-0651-04"/> cunque in GH. </s> <s xml:id="echoid-s16812" xml:space="preserve">Umbra hæc penumbrâ circumdatur; <lb/></s> <s xml:id="echoid-s16813" xml:space="preserve">nam ultra L & </s> <s xml:id="echoid-s16814" xml:space="preserve">E, planum hoc ab integro Solis Hæ-<lb/>miſphærio illuminatur; </s> <s xml:id="echoid-s16815" xml:space="preserve">ab L accedendo ad H, & </s> <s xml:id="echoid-s16816" xml:space="preserve">ab E <lb/>ad G lumen continuò minuitur, & </s> <s xml:id="echoid-s16817" xml:space="preserve">in viciniis G & </s> <s xml:id="echoid-s16818" xml:space="preserve">H, ra-<lb/>dii, ab exiguâtantùm parte ſuperficiei Solis, ad planum <lb/>perveniunt.</s> <s xml:id="echoid-s16819" xml:space="preserve"/> </p> <div xml:id="echoid-div2544" type="float" level="2" n="15"> <note position="right" xlink:label="note-0651-04" xlink:href="note-0651-04a" xml:space="preserve">TAB. XXII. <lb/>fig. 4.</note> </div> </div> <div xml:id="echoid-div2546" type="section" level="1" n="635"> <head xml:id="echoid-head825" xml:space="preserve"><emph style="sc">Definitio</emph> 9.</head> <p> <s xml:id="echoid-s16820" xml:space="preserve">Lux hæc imminuta, qua, ab omni parte, umbra GH cir-<lb/> <anchor type="note" xlink:label="note-0651-05a" xlink:href="note-0651-05"/> cumdatur vocatur penumbra.</s> <s xml:id="echoid-s16821" xml:space="preserve"/> </p> <div xml:id="echoid-div2546" type="float" level="2" n="1"> <note position="right" xlink:label="note-0651-05" xlink:href="note-0651-05a" xml:space="preserve">1060.</note> </div> <p> <s xml:id="echoid-s16822" xml:space="preserve">Simili penumbrâ Telluris umbra, in Eclipſi Lunari, cir-<lb/> <anchor type="note" xlink:label="note-0651-06a" xlink:href="note-0651-06"/> cumdatur, ſed hæc tantum in viciniis umbræ ſenſibilis eſt, & </s> <s xml:id="echoid-s16823" xml:space="preserve"><lb/>ideo exiguam babet latitudinem; </s> <s xml:id="echoid-s16824" xml:space="preserve">integra autem poteſt obſer-<lb/> <anchor type="note" xlink:label="note-0651-07a" xlink:href="note-0651-07"/> vari à ſpectatore, poſito in Plano, in quod umbra cadit, <lb/>qui caſus in Eclipſi Solari extat. </s> <s xml:id="echoid-s16825" xml:space="preserve">Spectator in I aut F ſe-<lb/>midiametrum Solis tantùm videre poteſt, reliquum diametri <lb/>à Lunâ obtegitur; </s> <s xml:id="echoid-s16826" xml:space="preserve">& </s> <s xml:id="echoid-s16827" xml:space="preserve">ab L progrediendo verſus H, Sol à Lu-<lb/>nâ continuò magis ac magis obtegitur, donec in ipſâ umbrâ <lb/>planè inviſibilis ſit.</s> <s xml:id="echoid-s16828" xml:space="preserve"/> </p> <div xml:id="echoid-div2547" type="float" level="2" n="2"> <note position="right" xlink:label="note-0651-06" xlink:href="note-0651-06a" xml:space="preserve">1061.</note> <note position="right" xlink:label="note-0651-07" xlink:href="note-0651-07a" xml:space="preserve">1062.</note> </div> <p> <s xml:id="echoid-s16829" xml:space="preserve">Ex hiſce ſequitur Solarem dari Eclipſin, licèt Lunæ um-<lb/> <anchor type="note" xlink:label="note-0651-08a" xlink:href="note-0651-08"/> bra Tellurem non tangat, ſi modo penumbra ad bujus ſuper- <pb o="128" file="0652" n="720" rhead="PHYSICES ELEMENTA"/> ficiem perveniat. </s> <s xml:id="echoid-s16830" xml:space="preserve">Etiam non in omnibus locis in quibus Sol <lb/> <anchor type="note" xlink:label="note-0652-01a" xlink:href="note-0652-01"/> viſibilis eſt, Eclipſin obſervari; </s> <s xml:id="echoid-s16831" xml:space="preserve">& </s> <s xml:id="echoid-s16832" xml:space="preserve">in locis, in quibus obſer-<lb/> <anchor type="note" xlink:label="note-0652-02a" xlink:href="note-0652-02"/> vatur, diverſam eſſe, pro ut umbra, aut pars varia penum-<lb/>bræ, per locum tranſit.</s> <s xml:id="echoid-s16833" xml:space="preserve"/> </p> <div xml:id="echoid-div2548" type="float" level="2" n="3"> <note position="right" xlink:label="note-0651-08" xlink:href="note-0651-08a" xml:space="preserve">1063.</note> <note position="left" xlink:label="note-0652-01" xlink:href="note-0652-01a" xml:space="preserve">1064.</note> <note position="left" xlink:label="note-0652-02" xlink:href="note-0652-02a" xml:space="preserve">1065.</note> </div> <p> <s xml:id="echoid-s16834" xml:space="preserve">Lunæ Eclipſis verô ubique eadem eſt, ubi Luna, durante E-<lb/> <anchor type="note" xlink:label="note-0652-03a" xlink:href="note-0652-03"/> clipſi, viſibilis eſt.</s> <s xml:id="echoid-s16835" xml:space="preserve"/> </p> <div xml:id="echoid-div2549" type="float" level="2" n="4"> <note position="left" xlink:label="note-0652-03" xlink:href="note-0652-03a" xml:space="preserve">1066.</note> </div> <p> <s xml:id="echoid-s16836" xml:space="preserve">Quando umbra ipſa Lunæ in Tellurem cadit, Totalis dici-<lb/> <anchor type="note" xlink:label="note-0652-04a" xlink:href="note-0652-04"/> tur Solis Eclipſis; </s> <s xml:id="echoid-s16837" xml:space="preserve">ſi penumbra tantùm pertingat ad Tellu-<lb/>rem, Partialis dicitur, illudque in genere conſiderando E-<lb/>clipſin.</s> <s xml:id="echoid-s16838" xml:space="preserve"/> </p> <div xml:id="echoid-div2550" type="float" level="2" n="5"> <note position="left" xlink:label="note-0652-04" xlink:href="note-0652-04a" xml:space="preserve">1067.</note> </div> <p> <s xml:id="echoid-s16839" xml:space="preserve">Quantum autem ad loca peculiaria, Totalis dicitur, in il-<lb/> <anchor type="note" xlink:label="note-0652-05a" xlink:href="note-0652-05"/> lis locis in quibus umbra tranſit; </s> <s xml:id="echoid-s16840" xml:space="preserve">Centralis in illis, in quibus <lb/>centrum umbræ tranſit, id eſt, in quibus centrum Lunæ ob-<lb/>tegit Solis centrum; </s> <s xml:id="echoid-s16841" xml:space="preserve">tandem Partialis dicitur, ubi penum-<lb/>bra tantùm tranſit, delineatur hæc in fig. </s> <s xml:id="echoid-s16842" xml:space="preserve">6.</s> <s xml:id="echoid-s16843" xml:space="preserve"/> </p> <div xml:id="echoid-div2551" type="float" level="2" n="6"> <note position="left" xlink:label="note-0652-05" xlink:href="note-0652-05a" xml:space="preserve">1068.</note> </div> <p> <s xml:id="echoid-s16844" xml:space="preserve">Quo umbra GH latior eſt, eo in pluribus locis Eclipſis <lb/> <anchor type="note" xlink:label="note-0652-06a" xlink:href="note-0652-06"/> totalis eſt, & </s> <s xml:id="echoid-s16845" xml:space="preserve">diutius Sol in totum obſcuratur. </s> <s xml:id="echoid-s16846" xml:space="preserve">Diverſa verò <lb/> <anchor type="note" xlink:label="note-0652-07a" xlink:href="note-0652-07"/> eſt hæc umbræ latitudo, pro variâ Lunæ à Tellure, & </s> <s xml:id="echoid-s16847" xml:space="preserve">hujus à <lb/>Sole, diſtantiâ.</s> <s xml:id="echoid-s16848" xml:space="preserve"/> </p> <div xml:id="echoid-div2552" type="float" level="2" n="7"> <note position="left" xlink:label="note-0652-06" xlink:href="note-0652-06a" xml:space="preserve">1069.</note> <note position="left" xlink:label="note-0652-07" xlink:href="note-0652-07a" xml:space="preserve">TAB. XXII. <lb/>fig. 4.</note> </div> <p> <s xml:id="echoid-s16849" xml:space="preserve">Si Lunæ Eclipſis detur, poſitâ Tellure in Peribelio, & </s> <s xml:id="echoid-s16850" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0652-08a" xlink:href="note-0652-08"/> Lunâ in Apogeo, id eſt, ad diſtantiam à Tellure maximam, <lb/>umbra Lunæ ad Tellurem non pertingit, & </s> <s xml:id="echoid-s16851" xml:space="preserve">Luna integrum <lb/>Solem non obtegit; </s> <s xml:id="echoid-s16852" xml:space="preserve">Annularis talis dicitur Eclipſis, & </s> <s xml:id="echoid-s16853" xml:space="preserve">re-<lb/>præſentatur in fig. </s> <s xml:id="echoid-s16854" xml:space="preserve">4.</s> <s xml:id="echoid-s16855" xml:space="preserve"/> </p> <div xml:id="echoid-div2553" type="float" level="2" n="8"> <note position="left" xlink:label="note-0652-08" xlink:href="note-0652-08a" xml:space="preserve">1070.</note> </div> </div> <div xml:id="echoid-div2555" type="section" level="1" n="636"> <head xml:id="echoid-head826" xml:space="preserve">CAPUT VII.</head> <head xml:id="echoid-head827" style="it" xml:space="preserve">De Pbænomenis ex motu Solis, Planetarum, & Lunæ, <lb/>circa axes.</head> <p> <s xml:id="echoid-s16856" xml:space="preserve">Solis motus circa axem, ſenſibilis eſt ex maculis, quæ in <lb/> <anchor type="note" xlink:label="note-0652-09a" xlink:href="note-0652-09"/> Solis ſuperficie ſæpiſſimè obſervantur; </s> <s xml:id="echoid-s16857" xml:space="preserve">hæ ſingulis diebus <lb/>ſitum ſuum & </s> <s xml:id="echoid-s16858" xml:space="preserve">figuram mutari, & </s> <s xml:id="echoid-s16859" xml:space="preserve">nunc celerius nunc tardius <lb/>ferri, videntur; </s> <s xml:id="echoid-s16860" xml:space="preserve">quæ omnia ex motu ſuperficiei ſphæricæ <lb/>facilè deducuntur: </s> <s xml:id="echoid-s16861" xml:space="preserve">& </s> <s xml:id="echoid-s16862" xml:space="preserve">Sol, qui, ſi tali motu non agitaretur, <lb/>ſemel tantùm in integro anno totam ſuperficiem Telluri ſuc-<lb/>ceſſivè obverteret, nunc illam integram, in minori quàm <lb/>unius menſis ſpatio, Terricolis videndam præbet.</s> <s xml:id="echoid-s16863" xml:space="preserve"/> </p> <div xml:id="echoid-div2555" type="float" level="2" n="1"> <note position="left" xlink:label="note-0652-09" xlink:href="note-0652-09a" xml:space="preserve">1071.</note> </div> <pb file="0653" n="721"/> <pb file="0653a" n="722"/> <figure> <image file="0653a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0653a-01"/> </figure> <pb file="0654" n="723"/> <pb o="(129)" file="0655" n="724" rhead="MATHEMATICA LIB. IV. CAP. VII."/> <p> <s xml:id="echoid-s16864" xml:space="preserve">Similia ſunt Phænomena ex rotatione Fovis, Martis, & </s> <s xml:id="echoid-s16865" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0655-01a" xlink:href="note-0655-01"/> Veneris, circa axes, qui motus, ex maculis in Planetarum <lb/>ſuperficiebus, ſenſibiles ſunt.</s> <s xml:id="echoid-s16866" xml:space="preserve"/> </p> <div xml:id="echoid-div2556" type="float" level="2" n="2"> <note position="right" xlink:label="note-0655-01" xlink:href="note-0655-01a" xml:space="preserve">1072.</note> </div> <p> <s xml:id="echoid-s16867" xml:space="preserve">Dum Tellus circa axem rotatur, ſpectator, qui transfertur, <lb/>ſe quieſcere, omnia verò corpora coeleſtia moveri, imagi-<lb/>natur.</s> <s xml:id="echoid-s16868" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2558" type="section" level="1" n="637"> <head xml:id="echoid-head828" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p style="it"> <s xml:id="echoid-s16869" xml:space="preserve">Puncta, in ſphærâ ſtellarum fixarum, in quibus axis Tel-<lb/> <anchor type="note" xlink:label="note-0655-02a" xlink:href="note-0655-02"/> luris, ab utraque parte continuatus, pertingit, vocantur <lb/>Poli Mundi.</s> <s xml:id="echoid-s16870" xml:space="preserve"/> </p> <div xml:id="echoid-div2558" type="float" level="2" n="1"> <note position="right" xlink:label="note-0655-02" xlink:href="note-0655-02a" xml:space="preserve">1073.</note> </div> </div> <div xml:id="echoid-div2560" type="section" level="1" n="638"> <head xml:id="echoid-head829" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s16871" xml:space="preserve">Motus apparens, ex motu Telluris circa axem, vocatur <lb/> <anchor type="note" xlink:label="note-0655-03a" xlink:href="note-0655-03"/> Motus diurnus.</s> <s xml:id="echoid-s16872" xml:space="preserve"/> </p> <div xml:id="echoid-div2560" type="float" level="2" n="1"> <note position="right" xlink:label="note-0655-03" xlink:href="note-0655-03a" xml:space="preserve">1074.</note> </div> </div> <div xml:id="echoid-div2562" type="section" level="1" n="639"> <head xml:id="echoid-head830" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s16873" xml:space="preserve">Concipitur Planum per centrum Telluris tranſiens, ad bu-<lb/> <anchor type="note" xlink:label="note-0655-04a" xlink:href="note-0655-04"/> jus axem perpendiculare, quaquaverſum continuatum, & </s> <s xml:id="echoid-s16874" xml:space="preserve">cir-<lb/>culus, in quo ſphæram ſtellarum fixarum ſecat, vocatur Æ-<lb/>quator coeleſtis.</s> <s xml:id="echoid-s16875" xml:space="preserve"/> </p> <div xml:id="echoid-div2562" type="float" level="2" n="1"> <note position="right" xlink:label="note-0655-04" xlink:href="note-0655-04a" xml:space="preserve">1075.</note> </div> <p> <s xml:id="echoid-s16876" xml:space="preserve">In motu Telluris circa Solem movetur Æquator, ſed cùm <lb/> <anchor type="note" xlink:label="note-0655-05a" xlink:href="note-0655-05"/> planum hujus circuli motu parallelo feratur, Æquator cœle-<lb/>ſtis non mutatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16877" xml:space="preserve"/> </p> <div xml:id="echoid-div2563" type="float" level="2" n="2"> <note position="right" xlink:label="note-0655-05" xlink:href="note-0655-05a" xml:space="preserve">1076.</note> </div> <note symbol="*" position="right" xml:space="preserve">994.</note> </div> <div xml:id="echoid-div2565" type="section" level="1" n="640"> <head xml:id="echoid-head831" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p style="it"> <s xml:id="echoid-s16878" xml:space="preserve">Circuli, quorum plana per axem Telluris tranſeunt, vocan-<lb/> <anchor type="note" xlink:label="note-0655-07a" xlink:href="note-0655-07"/> tur Meridiani.</s> <s xml:id="echoid-s16879" xml:space="preserve"/> </p> <div xml:id="echoid-div2565" type="float" level="2" n="1"> <note position="right" xlink:label="note-0655-07" xlink:href="note-0655-07a" xml:space="preserve">1077.</note> </div> <p style="it"> <s xml:id="echoid-s16880" xml:space="preserve">Omnes per polos Mundi tranſeunt, & </s> <s xml:id="echoid-s16881" xml:space="preserve">ad Æquatorem per-<lb/> <anchor type="note" xlink:label="note-0655-08a" xlink:href="note-0655-08"/> pendiculares ſunt.</s> <s xml:id="echoid-s16882" xml:space="preserve"/> </p> <div xml:id="echoid-div2566" type="float" level="2" n="2"> <note position="right" xlink:label="note-0655-08" xlink:href="note-0655-08a" xml:space="preserve">1078.</note> </div> </div> <div xml:id="echoid-div2568" type="section" level="1" n="641"> <head xml:id="echoid-head832" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p style="it"> <s xml:id="echoid-s16883" xml:space="preserve">Arcus Meridiani cujuſcunque, inter Æquatorem & </s> <s xml:id="echoid-s16884" xml:space="preserve">Sidus <lb/> <anchor type="note" xlink:label="note-0655-09a" xlink:href="note-0655-09"/> interceptus, vocatur Declinatio Sideris.</s> <s xml:id="echoid-s16885" xml:space="preserve"/> </p> <div xml:id="echoid-div2568" type="float" level="2" n="1"> <note position="right" xlink:label="note-0655-09" xlink:href="note-0655-09a" xml:space="preserve">1079.</note> </div> <p> <s xml:id="echoid-s16886" xml:space="preserve">Sit, in Tellure T, ſpectator, qui viſum dirigit per T A; <lb/></s> <s xml:id="echoid-s16887" xml:space="preserve"> <anchor type="note" xlink:label="note-0655-10a" xlink:href="note-0655-10"/> poſt aliquod tempus, ubi linea T A, ex motu Telluris, trans-<lb/>lata erit in T a, ſi per eandem lineam viſum ſpectator diri-<lb/>gat, corpus A tranſlatum apparebit per arcum a A; </s> <s xml:id="echoid-s16888" xml:space="preserve">ubi <lb/>verò linea ad priſtinum ſitum T A redierit, corpus inte-<lb/>gram revolutionem peregiſſe videbitur. </s> <s xml:id="echoid-s16889" xml:space="preserve">Si autem viſum per <lb/>Telluris axem dirigat, quia hic quieſcit, corpus, quod in axe <lb/>videtur, non tranſlatum apparebit; </s> <s xml:id="echoid-s16890" xml:space="preserve">ideò in Polis Mundi mo-<lb/> <anchor type="note" xlink:label="note-0655-11a" xlink:href="note-0655-11"/> <pb o="(130)" file="0656" n="725" rhead="PHYSICES ELEMENTA"/> tus diurnus non obſervatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s16891" xml:space="preserve">Corpora autem in horum vi- <anchor type="note" xlink:label="note-0656-01a" xlink:href="note-0656-01"/> ciniis, circa polos rotari clarum eſt; </s> <s xml:id="echoid-s16892" xml:space="preserve">& </s> <s xml:id="echoid-s16893" xml:space="preserve">corpus motu diurno <lb/>circulum eo majorem deſcribere, circa polum immobilem, <lb/>quo magis ab hoc diſtat. </s> <s xml:id="echoid-s16894" xml:space="preserve">Ideò tota ſphæra ſtellarum fixa-<lb/> <anchor type="note" xlink:label="note-0656-02a" xlink:href="note-0656-02"/> rum, circa axem Telluris continuatum, revolvere videtur, <lb/>in eo tempore, in quo Tellus revera circa axem rotatur. <lb/></s> <s xml:id="echoid-s16895" xml:space="preserve">Motus ergo diurnus communis eſt omnibus corporibus cœ-<lb/>leſtibus, niſi quatenus turbatur motibus antea memoratis.</s> <s xml:id="echoid-s16896" xml:space="preserve"/> </p> <div xml:id="echoid-div2569" type="float" level="2" n="2"> <note position="right" xlink:label="note-0655-10" xlink:href="note-0655-10a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>. <lb/>fig. 2.</note> <note position="right" xlink:label="note-0655-11" xlink:href="note-0655-11a" xml:space="preserve">1080.</note> <note symbol="*" position="left" xlink:label="note-0656-01" xlink:href="note-0656-01a" xml:space="preserve">1073.</note> <note position="left" xlink:label="note-0656-02" xlink:href="note-0656-02a" xml:space="preserve">1081.</note> </div> <p> <s xml:id="echoid-s16897" xml:space="preserve">Æquator ab utroque polo æqualiter diſtat, & </s> <s xml:id="echoid-s16898" xml:space="preserve">dividit cœlum <lb/>in duo hæmiſphæria, quorum puncta media ſunt Poli, qui <lb/>ergo à ſingulis punctis Æquatoris æqualiter diſtant; </s> <s xml:id="echoid-s16899" xml:space="preserve">corpora <lb/> <anchor type="note" xlink:label="note-0656-03a" xlink:href="note-0656-03"/> idcirco cæleſtia, quæ ſunt in Æquatore, motu diurno ipſum <lb/>Æquatorem deſcribere videntur, circulum omnium maximum, <lb/>qui motu diurno deſcribi poteſt; </s> <s xml:id="echoid-s16900" xml:space="preserve">reliqua corpora circulos <lb/> <anchor type="note" xlink:label="note-0656-04a" xlink:href="note-0656-04"/> Æquatori parallelos deſcribunt.</s> <s xml:id="echoid-s16901" xml:space="preserve"/> </p> <div xml:id="echoid-div2570" type="float" level="2" n="3"> <note position="left" xlink:label="note-0656-03" xlink:href="note-0656-03a" xml:space="preserve">1082.</note> <note position="left" xlink:label="note-0656-04" xlink:href="note-0656-04a" xml:space="preserve">1083.</note> </div> <p> <s xml:id="echoid-s16902" xml:space="preserve">Axis Telluris ad planum Eclipticæ inclinatur, & </s> <s xml:id="echoid-s16903" xml:space="preserve">efficit <lb/>angulum 66. </s> <s xml:id="echoid-s16904" xml:space="preserve">gr. </s> <s xml:id="echoid-s16905" xml:space="preserve">31′. </s> <s xml:id="echoid-s16906" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16907" xml:space="preserve">diſtant ideò Poli Mundi, à Polis E- <anchor type="note" xlink:label="note-0656-05a" xlink:href="note-0656-05"/> clipticæ, gradibus 23. </s> <s xml:id="echoid-s16908" xml:space="preserve">29′.</s> <s xml:id="echoid-s16909" xml:space="preserve">; & </s> <s xml:id="echoid-s16910" xml:space="preserve">angulum 23. </s> <s xml:id="echoid-s16911" xml:space="preserve">gr. </s> <s xml:id="echoid-s16912" xml:space="preserve">29′. </s> <s xml:id="echoid-s16913" xml:space="preserve">cum plano <lb/> <anchor type="note" xlink:label="note-0656-06a" xlink:href="note-0656-06"/> Eclipticæ format planum Æquatoris. </s> <s xml:id="echoid-s16914" xml:space="preserve">Planum utrumque per <lb/>Telluris centrum tranſit, cùm autem hoc pro centro ſphæ-<lb/>ræ ſtellarum fixarum haberi poſſit <anchor type="note" xlink:href="" symbol="*"/>, ſequitur Æquatorem <anchor type="note" xlink:label="note-0656-07a" xlink:href="note-0656-07"/> & </s> <s xml:id="echoid-s16915" xml:space="preserve">lineam Eclipticam eße circulos majores, qui ad ſe mutuo <lb/> <anchor type="note" xlink:label="note-0656-08a" xlink:href="note-0656-08"/> inclinantur, & </s> <s xml:id="echoid-s16916" xml:space="preserve">ſeſe mutuo ſecant, in duobus punctis oppoſitis, <lb/>principio Ariëtis & </s> <s xml:id="echoid-s16917" xml:space="preserve">principio Libræ quæ puncta in viâ Solis <lb/>hiſce interſectionibus determinantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16918" xml:space="preserve"/> </p> <div xml:id="echoid-div2571" type="float" level="2" n="4"> <note position="left" xlink:label="note-0656-05" xlink:href="note-0656-05a" xml:space="preserve">1084.</note> <note symbol="*" position="left" xlink:label="note-0656-06" xlink:href="note-0656-06a" xml:space="preserve">960.</note> <note position="left" xlink:label="note-0656-07" xlink:href="note-0656-07a" xml:space="preserve">1085.</note> <note symbol="*" position="left" xlink:label="note-0656-08" xlink:href="note-0656-08a" xml:space="preserve">988. 990.</note> </div> <note symbol="*" position="left" xml:space="preserve">1001.</note> <p> <s xml:id="echoid-s16919" xml:space="preserve">Quando Sol eſt in illis punctis, motu diurno Æquatorem de-<lb/> <anchor type="note" xlink:label="note-0656-10a" xlink:href="note-0656-10"/> ſcribere videtur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16920" xml:space="preserve">dum motu ſuo apparenti in Eclipticä <anchor type="note" xlink:label="note-0656-11a" xlink:href="note-0656-11"/> transfertur, continuò magis ac magis ab Æquatore recedit, <lb/> <anchor type="note" xlink:label="note-0656-12a" xlink:href="note-0656-12"/> augeturque hujus declinatio, & </s> <s xml:id="echoid-s16921" xml:space="preserve">circulos de die in diem mino-<lb/>res deſcribit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16922" xml:space="preserve">donec ad diſtantiam maximam ab Æquatore <anchor type="note" xlink:label="note-0656-13a" xlink:href="note-0656-13"/> pervenerit, quæ eſt 23. </s> <s xml:id="echoid-s16923" xml:space="preserve">gr. </s> <s xml:id="echoid-s16924" xml:space="preserve">29′. </s> <s xml:id="echoid-s16925" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s16926" xml:space="preserve">deinde iterum ad Æquato- <anchor type="note" xlink:label="note-0656-14a" xlink:href="note-0656-14"/> rem accedit, hunc prætergreditur, etiam 23. </s> <s xml:id="echoid-s16927" xml:space="preserve">gr. </s> <s xml:id="echoid-s16928" xml:space="preserve">29′.</s> <s xml:id="echoid-s16929" xml:space="preserve">, ad Po-<lb/> <anchor type="note" xlink:label="note-0656-15a" xlink:href="note-0656-15"/> lum oppoſitum accedens.</s> <s xml:id="echoid-s16930" xml:space="preserve"/> </p> <div xml:id="echoid-div2572" type="float" level="2" n="5"> <note position="left" xlink:label="note-0656-10" xlink:href="note-0656-10a" xml:space="preserve">1086.</note> <note position="left" xlink:label="note-0656-11" xlink:href="note-0656-11a" xml:space="preserve">1087.</note> <note symbol="*" position="left" xlink:label="note-0656-12" xlink:href="note-0656-12a" xml:space="preserve">1082.</note> <note symbol="*" position="left" xlink:label="note-0656-13" xlink:href="note-0656-13a" xml:space="preserve">1083.</note> <note position="left" xlink:label="note-0656-14" xlink:href="note-0656-14a" xml:space="preserve">1088.</note> <note symbol="*" position="left" xlink:label="note-0656-15" xlink:href="note-0656-15a" xml:space="preserve">1084.</note> </div> </div> <div xml:id="echoid-div2574" type="section" level="1" n="642"> <head xml:id="echoid-head833" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p> <s xml:id="echoid-s16931" xml:space="preserve">Circuli, à Sole motu diurno deſcripti, ab Æquatore maximè <lb/> <anchor type="note" xlink:label="note-0656-16a" xlink:href="note-0656-16"/> diſtantes, id eſt 23. </s> <s xml:id="echoid-s16932" xml:space="preserve">gr. </s> <s xml:id="echoid-s16933" xml:space="preserve">29′.</s> <s xml:id="echoid-s16934" xml:space="preserve">, vocantur Tropici.</s> <s xml:id="echoid-s16935" xml:space="preserve"/> </p> <div xml:id="echoid-div2574" type="float" level="2" n="1"> <note position="left" xlink:label="note-0656-16" xlink:href="note-0656-16a" xml:space="preserve">1089.</note> </div> <p> <s xml:id="echoid-s16936" xml:space="preserve">Unus tangit Lineam Eclipticam in primo gradu Cancri &</s> <s xml:id="echoid-s16937" xml:space="preserve"> <pb o="(131)" file="0657" n="726" rhead="MATHEMATICA LIB. IV. CAP. VII."/> dicitur Tropicus Cancri; </s> <s xml:id="echoid-s16938" xml:space="preserve">alter, Tropicus Capricorni nomina-<lb/>tus, per primum punctum ſigni Capricorni tranſit, ibique E-<lb/>clipticam lineam tangit.</s> <s xml:id="echoid-s16939" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2576" type="section" level="1" n="643"> <head xml:id="echoid-head834" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p> <s xml:id="echoid-s16940" xml:space="preserve">Polus Mundi Tropico Cancri vicinus, vocatur Polus Ar-<lb/> <anchor type="note" xlink:label="note-0657-01a" xlink:href="note-0657-01"/> cticus, & </s> <s xml:id="echoid-s16941" xml:space="preserve">Septentrionalis; </s> <s xml:id="echoid-s16942" xml:space="preserve">oppoſitus Antarcticus nuncupatur, <lb/>etiam Auſtralis.</s> <s xml:id="echoid-s16943" xml:space="preserve"/> </p> <div xml:id="echoid-div2576" type="float" level="2" n="1"> <note position="right" xlink:label="note-0657-01" xlink:href="note-0657-01a" xml:space="preserve">1090.</note> </div> </div> <div xml:id="echoid-div2578" type="section" level="1" n="644"> <head xml:id="echoid-head835" xml:space="preserve"><emph style="sc">Definitio</emph> 8.</head> <p> <s xml:id="echoid-s16944" xml:space="preserve">Circuli, à Polis Eclipticæ motu diurno deſcripti, id eſt, <lb/> <anchor type="note" xlink:label="note-0657-02a" xlink:href="note-0657-02"/> à Polis Mundi 23. </s> <s xml:id="echoid-s16945" xml:space="preserve">gr. </s> <s xml:id="echoid-s16946" xml:space="preserve">29′. </s> <s xml:id="echoid-s16947" xml:space="preserve">diſtantes, nominantur Circuli Po-<lb/>lares.</s> <s xml:id="echoid-s16948" xml:space="preserve"/> </p> <div xml:id="echoid-div2578" type="float" level="2" n="1"> <note position="right" xlink:label="note-0657-02" xlink:href="note-0657-02a" xml:space="preserve">1091.</note> </div> <p> <s xml:id="echoid-s16949" xml:space="preserve">Circulus Polaris Arcticus dicitur, qui Polum Arcticum <lb/>circumdat; </s> <s xml:id="echoid-s16950" xml:space="preserve">à Polo Antarctico alter nomen ſuum mutuatur.</s> <s xml:id="echoid-s16951" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s16952" xml:space="preserve">Supereſt Lunæ motus circa axem, cujus effectus eſt, quod <lb/> <anchor type="note" xlink:label="note-0657-03a" xlink:href="note-0657-03"/> eadem Lunæ facies in perpetuum Telluri obvertatur.</s> <s xml:id="echoid-s16953" xml:space="preserve"/> </p> <div xml:id="echoid-div2579" type="float" level="2" n="2"> <note position="right" xlink:label="note-0657-03" xlink:href="note-0657-03a" xml:space="preserve">1092.</note> </div> <p> <s xml:id="echoid-s16954" xml:space="preserve">Sit Luna in N, facies Telluri obverſa eſt m n i; </s> <s xml:id="echoid-s16955" xml:space="preserve">ſi Luna <lb/> <anchor type="note" xlink:label="note-0657-04a" xlink:href="note-0657-04"/> circa axem non rotaretur, & </s> <s xml:id="echoid-s16956" xml:space="preserve">ſingula puncta per lineas pa-<lb/> <anchor type="note" xlink:label="note-0657-05a" xlink:href="note-0657-05"/> rallelas tranſlatæ forent, linea m i coincideret cum lineâ l n <lb/>in ſitu Lunæ in B, & </s> <s xml:id="echoid-s16957" xml:space="preserve">hemiſphærium memoratum m n i <lb/>daretur in l m n; </s> <s xml:id="echoid-s16958" xml:space="preserve">ſed quia, dum Luna quartam partem or-<lb/>bitæ deſcribit, etiam quartam partem revolutionis circa <lb/>axem peragit, facies quæ daretur in l m n, nunc datur in <lb/>m n i, id eſt iterum Telluri obverſa. </s> <s xml:id="echoid-s16959" xml:space="preserve">Eodem modo proba-<lb/>tur, hanc eandem faciem m n i, in ſitu Lunæ in P, ſpectato-<lb/>ri in Tellure eſſe conſpicuam, & </s> <s xml:id="echoid-s16960" xml:space="preserve">in E etiam Telluri obver-<lb/>ti: </s> <s xml:id="echoid-s16961" xml:space="preserve">ut & </s> <s xml:id="echoid-s16962" xml:space="preserve">in omnibus aliis punctis orbitæ Lunæ.</s> <s xml:id="echoid-s16963" xml:space="preserve"/> </p> <div xml:id="echoid-div2580" type="float" level="2" n="3"> <note position="right" xlink:label="note-0657-04" xlink:href="note-0657-04a" xml:space="preserve"><emph style="sc">TAB. XXII</emph>.</note> <note position="right" xlink:label="note-0657-05" xlink:href="note-0657-05a" xml:space="preserve">fig. 3.</note> </div> <p> <s xml:id="echoid-s16964" xml:space="preserve">Axis Lunæ ad planum orbitæ non eſt perpendicularis, ſed <lb/> <anchor type="note" xlink:label="note-0657-06a" xlink:href="note-0657-06"/> paululum ad hoc inclinatur: </s> <s xml:id="echoid-s16965" xml:space="preserve">axis in motu ſuo circa Tellu-<lb/>rem paralleliſmum ſervat, ut de Planetis primariis dictum <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s16966" xml:space="preserve"> <anchor type="note" xlink:label="note-0657-07a" xlink:href="note-0657-07"/> idcirco ſitum ſuum mutat reſpectu ſpectatoris in Tellure, <lb/>cui nunc unus, deinde alter Lunæ Polus viſibilis eſt, unde <lb/>hæc motu quodam libratorio agitata videtur. </s> <s xml:id="echoid-s16967" xml:space="preserve">Alius etiam <lb/> <anchor type="note" xlink:label="note-0657-08a" xlink:href="note-0657-08"/> in Lunâ obſervatur motus libratorius; </s> <s xml:id="echoid-s16968" xml:space="preserve">motus circa axem <lb/>eſt æquabilis, & </s> <s xml:id="echoid-s16969" xml:space="preserve">in orbitâ celeritate inæquali fertur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s16970" xml:space="preserve">idcir- <anchor type="note" xlink:label="note-0657-09a" xlink:href="note-0657-09"/> co verſante Lunâ in Perigeo, id eſt, ad diſtantiam minimam <lb/>à Tellure ubi celerrimè in orbitâ movetur <anchor type="note" xlink:href="" symbol="*"/>, pars ſuperficiei, <anchor type="note" xlink:label="note-0657-10a" xlink:href="note-0657-10"/> quæ, ex motu in orbitâ, Telluri obvertitur, non tota ex mo- <pb o="(132)" file="0658" n="727" rhead="PHYSICES ELEMENTA"/> tu circa axem avertitur; </s> <s xml:id="echoid-s16971" xml:space="preserve">ideò pars ſuperficiei Lunæ, antea <lb/>non viſa, ad latus detegitur; </s> <s xml:id="echoid-s16972" xml:space="preserve">quæ, ubi Luna pervenit ad <lb/>Apogeum, iterum inviſibilis eſt.</s> <s xml:id="echoid-s16973" xml:space="preserve"/> </p> <div xml:id="echoid-div2581" type="float" level="2" n="4"> <note position="right" xlink:label="note-0657-06" xlink:href="note-0657-06a" xml:space="preserve">1093.</note> <note symbol="*" position="right" xlink:label="note-0657-07" xlink:href="note-0657-07a" xml:space="preserve">952.</note> <note position="right" xlink:label="note-0657-08" xlink:href="note-0657-08a" xml:space="preserve">1094.</note> <note symbol="*" position="right" xlink:label="note-0657-09" xlink:href="note-0657-09a" xml:space="preserve">966.</note> <note symbol="*" position="right" xlink:label="note-0657-10" xlink:href="note-0657-10a" xml:space="preserve">966.</note> </div> </div> <div xml:id="echoid-div2583" type="section" level="1" n="645"> <head xml:id="echoid-head836" xml:space="preserve">CAPUT VIII.</head> <head xml:id="echoid-head837" xml:space="preserve">De Phænomenis Telluris ſuperficiem, & peculiares <lb/>hujus partes, ſpectantibus.</head> <p> <s xml:id="echoid-s16974" xml:space="preserve">PHænomena cœleſtia, huc uſque examinata, explicavi-<lb/>mus, ſpectatorem conſiderando agitatum motibus, qui-<lb/>bus Tellus reverâ agitatur. </s> <s xml:id="echoid-s16975" xml:space="preserve">Illum nunc ſuperficiei Telluris <lb/>impoſitum, & </s> <s xml:id="echoid-s16976" xml:space="preserve">per varias hujus partes translatum, conſidera-<lb/>mus.</s> <s xml:id="echoid-s16977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16978" xml:space="preserve">Phænomenon primum hìc notandum, eſt ex interpoſit â <lb/> <anchor type="note" xlink:label="note-0658-01a" xlink:href="note-0658-01"/> Tellure, dimidium cælorum viſum fugere ſpectatoris, poſiti in <lb/>illius ſuperficie.</s> <s xml:id="echoid-s16979" xml:space="preserve"/> </p> <div xml:id="echoid-div2583" type="float" level="2" n="1"> <note position="left" xlink:label="note-0658-01" xlink:href="note-0658-01a" xml:space="preserve">1095.</note> </div> </div> <div xml:id="echoid-div2585" type="section" level="1" n="646"> <head xml:id="echoid-head838" xml:space="preserve"><emph style="sc">Definitio</emph> 1.</head> <p> <s xml:id="echoid-s16980" xml:space="preserve">Circulus in cælis, qui ſeparat partem viſibilem ab inviſibi-<lb/> <anchor type="note" xlink:label="note-0658-02a" xlink:href="note-0658-02"/> li, quando radii, inæqualitatibus in Telluris ſuperficie, non <lb/>intercipiuntur, vocatur Horizon.</s> <s xml:id="echoid-s16981" xml:space="preserve"/> </p> <div xml:id="echoid-div2585" type="float" level="2" n="1"> <note position="left" xlink:label="note-0658-02" xlink:href="note-0658-02a" xml:space="preserve">1096.</note> </div> <p> <s xml:id="echoid-s16982" xml:space="preserve">Cùm altitudo, ad quam ſpectator ſupra Telluris ſuperfi-<lb/>ciem poſſit elevari, admodum exigua ſit, relata ad Telluris <lb/>ſemidiametrum, oculus ſpectatoris poteſt haberi pro poſito <lb/>in ipſâ ſuperficie.</s> <s xml:id="echoid-s16983" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16984" xml:space="preserve">Sit Tellus T; </s> <s xml:id="echoid-s16985" xml:space="preserve">ſpectator in S; </s> <s xml:id="echoid-s16986" xml:space="preserve">P E p e ſphæra ſtellarum <lb/> <anchor type="note" xlink:label="note-0658-03a" xlink:href="note-0658-03"/> fixarum; </s> <s xml:id="echoid-s16987" xml:space="preserve">ſi per S concipiatur planum H H Tellurem tan-<lb/> <anchor type="note" xlink:label="note-0658-04a" xlink:href="note-0658-04"/> gens, erit hoc Horizontis planum, cujus ſectio cum ſphæ-<lb/>râ ſtellarum fixarum eſt Horizon. </s> <s xml:id="echoid-s16988" xml:space="preserve">Per centrum Telluris <lb/>concipitur planum h b, ad H H parallelum; </s> <s xml:id="echoid-s16989" xml:space="preserve">diſtantia h H <lb/>inſenſibilis eſt, propter immenſam ſtellarum fixarum diſtan-<lb/>tiam; </s> <s xml:id="echoid-s16990" xml:space="preserve">poteſt ideò hujus plani ſectio cum ſphærâ memo-<lb/>ratâ pro Horizonte H H uſurpari <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s16991" xml:space="preserve"/> </p> <div xml:id="echoid-div2586" type="float" level="2" n="2"> <note position="left" xlink:label="note-0658-03" xlink:href="note-0658-03a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>.</note> <note position="left" xlink:label="note-0658-04" xlink:href="note-0658-04a" xml:space="preserve">fig. 4.</note> </div> <note symbol="*" position="left" xml:space="preserve">994.</note> </div> <div xml:id="echoid-div2588" type="section" level="1" n="647"> <head xml:id="echoid-head839" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s16992" xml:space="preserve">Adſcenſus ſiderum ſupra Horizontem, vocatur horum Or-<lb/> <anchor type="note" xlink:label="note-0658-06a" xlink:href="note-0658-06"/> tus.</s> <s xml:id="echoid-s16993" xml:space="preserve"/> </p> <div xml:id="echoid-div2588" type="float" level="2" n="1"> <note position="left" xlink:label="note-0658-06" xlink:href="note-0658-06a" xml:space="preserve">1097.</note> </div> </div> <div xml:id="echoid-div2590" type="section" level="1" n="648"> <head xml:id="echoid-head840" xml:space="preserve"><emph style="sc">Definitio</emph> 3.</head> <p style="it"> <s xml:id="echoid-s16994" xml:space="preserve">Deſcenſus infra horizontem dicitur ſiderum Occaſus.</s> <s xml:id="echoid-s16995" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1098.</note> <pb o="(133)" file="0659" n="728" rhead="MATHEMATICA LIB. IV. CAP. VIII."/> </div> <div xml:id="echoid-div2591" type="section" level="1" n="649"> <head xml:id="echoid-head841" xml:space="preserve"><emph style="sc">Definitio</emph> 4.</head> <p> <s xml:id="echoid-s16996" xml:space="preserve">Si per centrum Telluris & </s> <s xml:id="echoid-s16997" xml:space="preserve">ſpectatorem concipiamus li-<lb/> <anchor type="note" xlink:label="note-0659-01a" xlink:href="note-0659-01"/> neam, quæ neceſſario horizonti perpendicularis eſt, inter <lb/>ſtellas fixas pertinget in puncto Z, quod vocatur Zenit.</s> <s xml:id="echoid-s16998" xml:space="preserve"/> </p> <div xml:id="echoid-div2591" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-01" xlink:href="note-0659-01a" xml:space="preserve">1099.</note> </div> </div> <div xml:id="echoid-div2593" type="section" level="1" n="650"> <head xml:id="echoid-head842" xml:space="preserve"><emph style="sc">Definitio</emph> 5.</head> <p style="it"> <s xml:id="echoid-s16999" xml:space="preserve">Punctum, huic oppoſitum N vocatur Nadir.</s> <s xml:id="echoid-s17000" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">1100.</note> </div> <div xml:id="echoid-div2594" type="section" level="1" n="651"> <head xml:id="echoid-head843" xml:space="preserve"><emph style="sc">Definitio</emph> 6.</head> <p style="it"> <s xml:id="echoid-s17001" xml:space="preserve">Sectio plani Meridiani, per ſpectatorem tranſeuntis, cum <lb/> <anchor type="note" xlink:label="note-0659-03a" xlink:href="note-0659-03"/> Horizonte, vocatur Linea Meridiana.</s> <s xml:id="echoid-s17002" xml:space="preserve"/> </p> <div xml:id="echoid-div2594" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-03" xlink:href="note-0659-03a" xml:space="preserve">1101.</note> </div> <p> <s xml:id="echoid-s17003" xml:space="preserve">A ſeptentrione ad auſtrum dirigitur.</s> <s xml:id="echoid-s17004" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2596" type="section" level="1" n="652"> <head xml:id="echoid-head844" xml:space="preserve"><emph style="sc">Definitio</emph> 7.</head> <p> <s xml:id="echoid-s17005" xml:space="preserve">Pars cœlorum Orientalis dicitur illa, ad quam corpora ſu-<lb/> <anchor type="note" xlink:label="note-0659-04a" xlink:href="note-0659-04"/> pra horizontem adſcendere videmus; </s> <s xml:id="echoid-s17006" xml:space="preserve">& </s> <s xml:id="echoid-s17007" xml:space="preserve">punctum Orientis <lb/>illud, in quo perpendicularis ad lineam Meridianam ver-<lb/>ſus hanc partem per ſpectatorem ducta, ſphæram ſtellarum <lb/>fixarum ſecat.</s> <s xml:id="echoid-s17008" xml:space="preserve"/> </p> <div xml:id="echoid-div2596" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-04" xlink:href="note-0659-04a" xml:space="preserve">1102.</note> </div> </div> <div xml:id="echoid-div2598" type="section" level="1" n="653"> <head xml:id="echoid-head845" xml:space="preserve"><emph style="sc">Definitio</emph> 8.</head> <p> <s xml:id="echoid-s17009" xml:space="preserve">Punctum huic oppoſitum vocatur punctum Occidentis; </s> <s xml:id="echoid-s17010" xml:space="preserve">& </s> <s xml:id="echoid-s17011" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0659-05a" xlink:href="note-0659-05"/> pars Occidentalis cœlorum Orientali opponitur.</s> <s xml:id="echoid-s17012" xml:space="preserve"/> </p> <div xml:id="echoid-div2598" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-05" xlink:href="note-0659-05a" xml:space="preserve">1103.</note> </div> </div> <div xml:id="echoid-div2600" type="section" level="1" n="654"> <head xml:id="echoid-head846" xml:space="preserve"><emph style="sc">Definitio</emph> 9.</head> <p> <s xml:id="echoid-s17013" xml:space="preserve">Amplitudo, eſt arcus Horizontis, inter punctum Orientis, <lb/> <anchor type="note" xlink:label="note-0659-06a" xlink:href="note-0659-06"/> aut Occidentis, & </s> <s xml:id="echoid-s17014" xml:space="preserve">punctum, in quo ſidus oritur aut occidit, in-<lb/>terceptus. </s> <s xml:id="echoid-s17015" xml:space="preserve">Prima dicitur ortiva, altera occidua: </s> <s xml:id="echoid-s17016" xml:space="preserve">utraque eſt <lb/>aut ſeptentrionâlis aut meridionalis.</s> <s xml:id="echoid-s17017" xml:space="preserve"/> </p> <div xml:id="echoid-div2600" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-06" xlink:href="note-0659-06a" xml:space="preserve">1104.</note> </div> </div> <div xml:id="echoid-div2602" type="section" level="1" n="655"> <head xml:id="echoid-head847" xml:space="preserve"><emph style="sc">Definitio</emph> 10.</head> <p> <s xml:id="echoid-s17018" xml:space="preserve">Altitudo ſideris ſupra horizontem, vocatur arcus circuli <lb/> <anchor type="note" xlink:label="note-0659-07a" xlink:href="note-0659-07"/> perpendicularis ad Horizontem, in cujus centro eſt ſpectator, <lb/>horizonte & </s> <s xml:id="echoid-s17019" xml:space="preserve">ſidere terminatus.</s> <s xml:id="echoid-s17020" xml:space="preserve"/> </p> <div xml:id="echoid-div2602" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-07" xlink:href="note-0659-07a" xml:space="preserve">1105.</note> </div> <p> <s xml:id="echoid-s17021" xml:space="preserve">Quando agitur de corporibus remotis, altitudo ſenſibiliter <lb/>non differt, ſive ſpectator detur in ſuperficie Telluris, ſive in <lb/>hujus centro. </s> <s xml:id="echoid-s17022" xml:space="preserve">Corpora minus diſtantia altiora apparent poſi-<lb/>to ſpectatore in centro.</s> <s xml:id="echoid-s17023" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2604" type="section" level="1" n="656"> <head xml:id="echoid-head848" xml:space="preserve"><emph style="sc">Definitio</emph> 11.</head> <p> <s xml:id="echoid-s17024" xml:space="preserve">Differentia altitudinis ſideris, pro diverſo ſitu ſpectatoris, <lb/> <anchor type="note" xlink:label="note-0659-08a" xlink:href="note-0659-08"/> in centro, aut in ſuperficie Telluris, vocatur Side s Paralaxis.</s> <s xml:id="echoid-s17025" xml:space="preserve"/> </p> <div xml:id="echoid-div2604" type="float" level="2" n="1"> <note position="right" xlink:label="note-0659-08" xlink:href="note-0659-08a" xml:space="preserve">1106.</note> </div> <p> <s xml:id="echoid-s17026" xml:space="preserve">Solius Lunæ Paralaxis obſervationibus determinatur: </s> <s xml:id="echoid-s17027" xml:space="preserve">re-<lb/> <anchor type="note" xlink:label="note-0659-09a" xlink:href="note-0659-09"/> liquorum corporum ſyſtematis Planetarii diſtantia nimia eſt, <pb o="(134)" file="0660" n="729" rhead="PHYSICES ELEMENTA"/> ut cum ſemidiametro Telluris conferantur; </s> <s xml:id="echoid-s17028" xml:space="preserve">& </s> <s xml:id="echoid-s17029" xml:space="preserve">Paralaxis pen-<lb/>det à ratione, quam ſemidiameter Telluris ad diſtantiam Pla-<lb/>netæ habet; </s> <s xml:id="echoid-s17030" xml:space="preserve">idcirco ipſius Martis, in oppoſitione cum Sole, <lb/> <anchor type="note" xlink:label="note-0660-01a" xlink:href="note-0660-01"/> Paralaxis obſervationes ſubtilliſſimas effugit.</s> <s xml:id="echoid-s17031" xml:space="preserve"/> </p> <div xml:id="echoid-div2605" type="float" level="2" n="2"> <note position="right" xlink:label="note-0659-09" xlink:href="note-0659-09a" xml:space="preserve">1107.</note> <note position="left" xlink:label="note-0660-01" xlink:href="note-0660-01a" xml:space="preserve">1108.</note> </div> <p> <s xml:id="echoid-s17032" xml:space="preserve">Ubi Parallaxis datur, adſcenſu corporis ſupra horizontem <lb/> <anchor type="note" xlink:label="note-0660-02a" xlink:href="note-0660-02"/> minuitur, & </s> <s xml:id="echoid-s17033" xml:space="preserve">in Zenit nulla eſt.</s> <s xml:id="echoid-s17034" xml:space="preserve"/> </p> <div xml:id="echoid-div2606" type="float" level="2" n="3"> <note position="left" xlink:label="note-0660-02" xlink:href="note-0660-02a" xml:space="preserve">1109.</note> </div> <p> <s xml:id="echoid-s17035" xml:space="preserve">Altitudo apparens ſiderum, mutatur etiam ex aliâ cauſâ, <lb/>quæ reſpectu omnium corporum Cœleſtium indeſcrimina-<lb/>tim locum habet. </s> <s xml:id="echoid-s17036" xml:space="preserve">Ex Atmoſphæræ refractione radii infle-<lb/> <anchor type="note" xlink:label="note-0660-03a" xlink:href="note-0660-03"/> ctuntur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s17037" xml:space="preserve">Sidera altiora apparent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17038" xml:space="preserve">quo tamen altiora <anchor type="note" xlink:label="note-0660-04a" xlink:href="note-0660-04"/> ſunt, eo minor eſt hæc inflectio <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17039" xml:space="preserve">quia radii minus obliquè <anchor type="note" xlink:label="note-0660-05a" xlink:href="note-0660-05"/> <anchor type="note" xlink:label="note-0660-06a" xlink:href="note-0660-06"/> <anchor type="note" xlink:label="note-0660-07a" xlink:href="note-0660-07"/> in Atmoſphæræ ſuperficiem incidunt. </s> <s xml:id="echoid-s17040" xml:space="preserve">In Zenit refractio <lb/> <anchor type="note" xlink:label="note-0660-08a" xlink:href="note-0660-08"/> nulla eſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17041" xml:space="preserve">etiam ad diſtantiam viginti, aut triginta, gra- <anchor type="note" xlink:label="note-0660-09a" xlink:href="note-0660-09"/> duum à Zenit ſenſibilis non eſt.</s> <s xml:id="echoid-s17042" xml:space="preserve"/> </p> <div xml:id="echoid-div2607" type="float" level="2" n="4"> <note position="left" xlink:label="note-0660-03" xlink:href="note-0660-03a" xml:space="preserve">1110.</note> <note position="left" xlink:label="note-0660-04" xlink:href="note-0660-04a" xml:space="preserve">1111.</note> <note symbol="*" position="left" xlink:label="note-0660-05" xlink:href="note-0660-05a" xml:space="preserve">1056.</note> <note symbol="*" position="left" xlink:label="note-0660-06" xlink:href="note-0660-06a" xml:space="preserve">624.</note> <note symbol="*" position="left" xlink:label="note-0660-07" xlink:href="note-0660-07a" xml:space="preserve">639.</note> <note position="left" xlink:label="note-0660-08" xlink:href="note-0660-08a" xml:space="preserve">1112.</note> <note symbol="*" position="left" xlink:label="note-0660-09" xlink:href="note-0660-09a" xml:space="preserve">629.</note> </div> <p> <s xml:id="echoid-s17043" xml:space="preserve">Cùm ex hac refractione Sidera eleventur, viſibilia ſunt <lb/> <anchor type="note" xlink:label="note-0660-10a" xlink:href="note-0660-10"/> antequam ad horizontem perveniant.</s> <s xml:id="echoid-s17044" xml:space="preserve"/> </p> <div xml:id="echoid-div2608" type="float" level="2" n="5"> <note position="left" xlink:label="note-0660-10" xlink:href="note-0660-10a" xml:space="preserve">1113.</note> </div> <p> <s xml:id="echoid-s17045" xml:space="preserve">Hæc omnia generaliter Telluris ſuperficies ſpectant, hu-<lb/> <anchor type="note" xlink:label="note-0660-11a" xlink:href="note-0660-11"/> jus variæ partes nunc ſunt examinandæ: </s> <s xml:id="echoid-s17046" xml:space="preserve">determinantur hæ, <lb/> <anchor type="note" xlink:label="note-0660-12a" xlink:href="note-0660-12"/> referendo ad Tellurem varios circulos, quos in cœlis antea <lb/>conſideravimus; </s> <s xml:id="echoid-s17047" xml:space="preserve">ſic in Tellure conſideramus Æquatorem, <lb/> <anchor type="note" xlink:label="note-0660-13a" xlink:href="note-0660-13"/> Meridianos, Tropicos, circulos Polares; </s> <s xml:id="echoid-s17048" xml:space="preserve">quibus circulis eo-<lb/>dem modo Telluris ſuperficies dividitur, ac, circulis in cœ-<lb/>lis, ſphæra ſtellarum fixarum: </s> <s xml:id="echoid-s17049" xml:space="preserve">Quare circuli hi ita ſibi mu-<lb/>tuo reſpondent, ut ductâ lineâ ex centro Telluris ad circu-<lb/>lum in cœlis, hæc per circulum in Tellure tranſeat. </s> <s xml:id="echoid-s17050" xml:space="preserve">Si po-<lb/>li fuerint P, p, Æquator erit E e, Tropici T T, t t, cir-<lb/>culi polares A A, a a.</s> <s xml:id="echoid-s17051" xml:space="preserve"/> </p> <div xml:id="echoid-div2609" type="float" level="2" n="6"> <note position="left" xlink:label="note-0660-11" xlink:href="note-0660-11a" xml:space="preserve"><emph style="sc">TAB. XXIV</emph>.</note> <note position="left" xlink:label="note-0660-12" xlink:href="note-0660-12a" xml:space="preserve">fig. 2.</note> <note position="left" xlink:label="note-0660-13" xlink:href="note-0660-13a" xml:space="preserve">1114.</note> </div> </div> <div xml:id="echoid-div2611" type="section" level="1" n="657"> <head xml:id="echoid-head849" xml:space="preserve"><emph style="sc">Definitio</emph> 12.</head> <p> <s xml:id="echoid-s17052" xml:space="preserve">Meridianus Loci dicitur ille, qui per locum ipſum tranſit.</s> <s xml:id="echoid-s17053" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1115.</note> <p> <s xml:id="echoid-s17054" xml:space="preserve">Hujus planum ad Horizontem eſt perpendiculare; </s> <s xml:id="echoid-s17055" xml:space="preserve">quia <lb/> <anchor type="note" xlink:label="note-0660-15a" xlink:href="note-0660-15"/> per centrum Telluris & </s> <s xml:id="echoid-s17056" xml:space="preserve">ſpectatorem tranſit.</s> <s xml:id="echoid-s17057" xml:space="preserve"/> </p> <div xml:id="echoid-div2611" type="float" level="2" n="1"> <note position="left" xlink:label="note-0660-15" xlink:href="note-0660-15a" xml:space="preserve">1116.</note> </div> <p> <s xml:id="echoid-s17058" xml:space="preserve">Linea Meridiana in Loco quocunque ducta, eſt pars Meri-<lb/> <anchor type="note" xlink:label="note-0660-16a" xlink:href="note-0660-16"/> diani Loci <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17059" xml:space="preserve"/> </p> <div xml:id="echoid-div2612" type="float" level="2" n="2"> <note position="left" xlink:label="note-0660-16" xlink:href="note-0660-16a" xml:space="preserve">1117.</note> </div> <note symbol="*" position="left" xml:space="preserve">1101.</note> </div> <div xml:id="echoid-div2614" type="section" level="1" n="658"> <head xml:id="echoid-head850" xml:space="preserve"><emph style="sc">Definitio</emph> 13.</head> <p> <s xml:id="echoid-s17060" xml:space="preserve">Latitudo Loci eſt hujus diſtantia ab Æquatore, id eſt, <lb/> <anchor type="note" xlink:label="note-0660-18a" xlink:href="note-0660-18"/> arcus interceptus inter Locum & </s> <s xml:id="echoid-s17061" xml:space="preserve">Æquatorem.</s> <s xml:id="echoid-s17062" xml:space="preserve"/> </p> <div xml:id="echoid-div2614" type="float" level="2" n="1"> <note position="left" xlink:label="note-0660-18" xlink:href="note-0660-18a" xml:space="preserve">1118.</note> </div> <pb o="(135)" file="0661" n="730" rhead="MATHEMATICA LIB. IV. CAP. VIII."/> </div> <div xml:id="echoid-div2616" type="section" level="1" n="659"> <head xml:id="echoid-head851" xml:space="preserve"><emph style="sc">Definitio</emph> 14.</head> <p> <s xml:id="echoid-s17063" xml:space="preserve">Circuli paralleli ad Æquatorem, vocantur Circuli Latitu-<lb/> <anchor type="note" xlink:label="note-0661-01a" xlink:href="note-0661-01"/> dinis; </s> <s xml:id="echoid-s17064" xml:space="preserve">ut B b.</s> <s xml:id="echoid-s17065" xml:space="preserve"/> </p> <div xml:id="echoid-div2616" type="float" level="2" n="1"> <note position="right" xlink:label="note-0661-01" xlink:href="note-0661-01a" xml:space="preserve">1119.</note> </div> <p> <s xml:id="echoid-s17066" xml:space="preserve">Determinatâ Latitudine Loci, determinatur circulus Latitu-<lb/>dinis, qui per Locum tranſit, ut autem ſitus variorum Locorum <lb/>inter ſe determinentur, in ſingulis circulis Loca determinan-<lb/>da ſunt, quod fit concipiendo Meridianum, per Locum quem-<lb/>cunque notabilem tranſeuntem, qui, ſectione ſuâ, in ſingulis <lb/>circulis Latitudinis, punctum determinat, à quo diſtantiæ <lb/>Locorum menſurantur.</s> <s xml:id="echoid-s17067" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2618" type="section" level="1" n="660"> <head xml:id="echoid-head852" xml:space="preserve"><emph style="sc">Definitio</emph> 15.</head> <p> <s xml:id="echoid-s17068" xml:space="preserve">Meridianus memoratus, ad arbitrium ſumtus, vocatur Pri-<lb/> <anchor type="note" xlink:label="note-0661-02a" xlink:href="note-0661-02"/> mus Meridianus.</s> <s xml:id="echoid-s17069" xml:space="preserve"/> </p> <div xml:id="echoid-div2618" type="float" level="2" n="1"> <note position="right" xlink:label="note-0661-02" xlink:href="note-0661-02a" xml:space="preserve">1120.</note> </div> </div> <div xml:id="echoid-div2620" type="section" level="1" n="661"> <head xml:id="echoid-head853" xml:space="preserve"><emph style="sc">Definitio</emph> 16.</head> <p style="it"> <s xml:id="echoid-s17070" xml:space="preserve">Diſtantia loci à primo Meridiano, in circulo Latitudinis <lb/> <anchor type="note" xlink:label="note-0661-03a" xlink:href="note-0661-03"/> Loci menſurata, vocatur Loci Longitudo.</s> <s xml:id="echoid-s17071" xml:space="preserve"/> </p> <div xml:id="echoid-div2620" type="float" level="2" n="1"> <note position="right" xlink:label="note-0661-03" xlink:href="note-0661-03a" xml:space="preserve">1121.</note> </div> <p style="it"> <s xml:id="echoid-s17072" xml:space="preserve">Aſtronomi omnia referunt ad Meridianum Loci, in quo ob-<lb/> <anchor type="note" xlink:label="note-0661-04a" xlink:href="note-0661-04"/> ſervationes ſuas inſtituunt.</s> <s xml:id="echoid-s17073" xml:space="preserve"/> </p> <div xml:id="echoid-div2621" type="float" level="2" n="2"> <note position="right" xlink:label="note-0661-04" xlink:href="note-0661-04a" xml:space="preserve">1122.</note> </div> <p> <s xml:id="echoid-s17074" xml:space="preserve">In explicandis Phænomenis, quæ varias Telluris ſuperfi-<lb/>ciei partes ſpectant, conſiderabimus ſpectatorem à Polo ver-<lb/>ſus Æquatorem incedentem; </s> <s xml:id="echoid-s17075" xml:space="preserve">ſolumque motum diurnum pri-<lb/>mò conſiderabimus.</s> <s xml:id="echoid-s17076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17077" xml:space="preserve">Quando ſpectator in ipſo Polo Telluris T, datur in S, <lb/> <anchor type="note" xlink:label="note-0661-05a" xlink:href="note-0661-05"/> cum Horizonte coincidit Æquator cœleſtis E e, & </s> <s xml:id="echoid-s17078" xml:space="preserve">Polus <lb/> <anchor type="note" xlink:label="note-0661-06a" xlink:href="note-0661-06"/> <anchor type="note" xlink:label="note-0661-07a" xlink:href="note-0661-07"/> Mundi P eſt in Zenit; </s> <s xml:id="echoid-s17079" xml:space="preserve">in hoc caſu, quia Circuli ad Hori-<lb/>zontem paralleli, etiam ad Æquatorem paralleli ſunt; </s> <s xml:id="echoid-s17080" xml:space="preserve">omnia <lb/>corpora cœleſtia motu parallelo ad Horizontem moveri vi-<lb/>dentur <anchor type="note" xlink:href="" symbol="*"/>, in circulis, qui repræſentantur per lineas A a, B b.</s> <s xml:id="echoid-s17081" xml:space="preserve"> <anchor type="note" xlink:label="note-0661-08a" xlink:href="note-0661-08"/> Stellæ fixæ in Hemiſphærio E P e nunquam occidunt, reli-<lb/>quæ nunquam videntur Horizon in hoc ſitu dicitur paralle-<lb/> <anchor type="note" xlink:label="note-0661-09a" xlink:href="note-0661-09"/> lus, aut ſphæra parallela.</s> <s xml:id="echoid-s17082" xml:space="preserve"/> </p> <div xml:id="echoid-div2622" type="float" level="2" n="3"> <note position="right" xlink:label="note-0661-05" xlink:href="note-0661-05a" xml:space="preserve">1123.</note> <note position="right" xlink:label="note-0661-06" xlink:href="note-0661-06a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>.</note> <note position="right" xlink:label="note-0661-07" xlink:href="note-0661-07a" xml:space="preserve">fig. 3.</note> <note symbol="*" position="right" xlink:label="note-0661-08" xlink:href="note-0661-08a" xml:space="preserve">1083.</note> <note position="right" xlink:label="note-0661-09" xlink:href="note-0661-09a" xml:space="preserve">1124.</note> </div> <p> <s xml:id="echoid-s17083" xml:space="preserve">Si ſpectator in Tellure T à polo recedat, & </s> <s xml:id="echoid-s17084" xml:space="preserve">detur in S, <lb/> <anchor type="note" xlink:label="note-0661-10a" xlink:href="note-0661-10"/> Horizon dicitur obliquus, aut ſphæra obliqua; </s> <s xml:id="echoid-s17085" xml:space="preserve">axis P p tunc <lb/> <anchor type="note" xlink:label="note-0661-11a" xlink:href="note-0661-11"/> <anchor type="note" xlink:label="note-0661-12a" xlink:href="note-0661-12"/> inclinatur ad Horizontem h b, eo magis, quo ſpectator ma-<lb/>gis à polo removetur.</s> <s xml:id="echoid-s17086" xml:space="preserve"/> </p> <div xml:id="echoid-div2623" type="float" level="2" n="4"> <note position="right" xlink:label="note-0661-10" xlink:href="note-0661-10a" xml:space="preserve">1125.</note> <note position="right" xlink:label="note-0661-11" xlink:href="note-0661-11a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>.</note> <note position="right" xlink:label="note-0661-12" xlink:href="note-0661-12a" xml:space="preserve">fig. 4.</note> </div> </div> <div xml:id="echoid-div2625" type="section" level="1" n="662"> <head xml:id="echoid-head854" xml:space="preserve"><emph style="sc">Definitio</emph> 17.</head> <p> <s xml:id="echoid-s17087" xml:space="preserve">Angulus, quem axis Telluris cum Horizonte efficit, vocatur <lb/> <anchor type="note" xlink:label="note-0661-13a" xlink:href="note-0661-13"/> Altitudo Poli <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17088" xml:space="preserve"/> </p> <div xml:id="echoid-div2625" type="float" level="2" n="1"> <note position="right" xlink:label="note-0661-13" xlink:href="note-0661-13a" xml:space="preserve">1126.</note> </div> <note symbol="*" position="right" xml:space="preserve">1105.</note> <pb o="(136)" file="0662" n="731" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s17089" xml:space="preserve">Hæc Poli altitudo æqualis eſt latitudini. </s> <s xml:id="echoid-s17090" xml:space="preserve">Altitudo Poli <lb/> <anchor type="note" xlink:label="note-0662-01a" xlink:href="note-0662-01"/> eſt angulus P T b, cujus menſura eſt arcus P b, latitudo <lb/>menſuratur arcu, qui in Tellure reſpondet arcui Z E in cœ-<lb/>lis <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17091" xml:space="preserve">Hic autem æqualis eſt arcui P b; </s> <s xml:id="echoid-s17092" xml:space="preserve">utriuſque enim com- <anchor type="note" xlink:label="note-0662-02a" xlink:href="note-0662-02"/> plementum, ad quadrantem circuli, eſt arcus Z P.</s> <s xml:id="echoid-s17093" xml:space="preserve"/> </p> <div xml:id="echoid-div2626" type="float" level="2" n="2"> <note position="left" xlink:label="note-0662-01" xlink:href="note-0662-01a" xml:space="preserve">1127.</note> <note symbol="*" position="left" xlink:label="note-0662-02" xlink:href="note-0662-02a" xml:space="preserve">1118.</note> </div> <p> <s xml:id="echoid-s17094" xml:space="preserve">In hoc ſitu ſpectatoris, quia Æquator ad Horizontem in-<lb/> <anchor type="note" xlink:label="note-0662-03a" xlink:href="note-0662-03"/> clinatur, omnia corpora cœleſtia in circulis ad Horizontem, <lb/>inclinatis lineis A a, B b, repræſentatis, motu diurno ferun-<lb/>tur.</s> <s xml:id="echoid-s17095" xml:space="preserve"/> </p> <div xml:id="echoid-div2627" type="float" level="2" n="3"> <note position="left" xlink:label="note-0662-03" xlink:href="note-0662-03a" xml:space="preserve">1128.</note> </div> <p> <s xml:id="echoid-s17096" xml:space="preserve">Quædam corpora cœleſtia in ſingulis Telluris revolutionibus <lb/> <anchor type="note" xlink:label="note-0662-04a" xlink:href="note-0662-04"/> oriuntur & </s> <s xml:id="echoid-s17097" xml:space="preserve">occidunt, illa nempe, quæ dantur inter paralle-<lb/>los ad Æquatorem B b & </s> <s xml:id="echoid-s17098" xml:space="preserve">h i; </s> <s xml:id="echoid-s17099" xml:space="preserve">quia omnes paralleli, inter hos, <lb/>Horizonte ſecantur.</s> <s xml:id="echoid-s17100" xml:space="preserve"/> </p> <div xml:id="echoid-div2628" type="float" level="2" n="4"> <note position="left" xlink:label="note-0662-04" xlink:href="note-0662-04a" xml:space="preserve">1129.</note> </div> <p> <s xml:id="echoid-s17101" xml:space="preserve">Plana Æquatoris & </s> <s xml:id="echoid-s17102" xml:space="preserve">Horizontis per Telluris centrum tran-<lb/>ſeunt; </s> <s xml:id="echoid-s17103" xml:space="preserve">hi circuli ideo ſeſe mutuo ſecant in duas partes æqua-<lb/>les, & </s> <s xml:id="echoid-s17104" xml:space="preserve">dimidium Æquatoris ſupra Horizontem datur: </s> <s xml:id="echoid-s17105" xml:space="preserve">Idcirco <lb/>corpora cœleſtia, quæ in Æquatore dantur, per ſemi revo-<lb/> <anchor type="note" xlink:label="note-0662-05a" xlink:href="note-0662-05"/> lutionem Telluris circa axem <anchor type="note" xlink:href="" symbol="*"/>, ſupra Horizontem verſan- <anchor type="note" xlink:label="note-0662-06a" xlink:href="note-0662-06"/> tur; </s> <s xml:id="echoid-s17106" xml:space="preserve">&</s> <s xml:id="echoid-s17107" xml:space="preserve">, propter æquabilitatem motus circa axem, per æ-<lb/>quale tempus inviſibilia ſunt.</s> <s xml:id="echoid-s17108" xml:space="preserve"/> </p> <div xml:id="echoid-div2629" type="float" level="2" n="5"> <note position="left" xlink:label="note-0662-05" xlink:href="note-0662-05a" xml:space="preserve">1130.</note> <note symbol="*" position="left" xlink:label="note-0662-06" xlink:href="note-0662-06a" xml:space="preserve">1082.</note> </div> <p> <s xml:id="echoid-s17109" xml:space="preserve">Hæc etiam in puncto Orientis oriuntur, & </s> <s xml:id="echoid-s17110" xml:space="preserve">in puncto Occi-<lb/> <anchor type="note" xlink:label="note-0662-07a" xlink:href="note-0662-07"/> dentis infra Horizontem cadunt; </s> <s xml:id="echoid-s17111" xml:space="preserve">nam ſectio planorum Æ-<lb/>quatoris, & </s> <s xml:id="echoid-s17112" xml:space="preserve">Horizontis, perpendicularis eſt ad planum per-<lb/>pendiculare ad ambo illa plana; </s> <s xml:id="echoid-s17113" xml:space="preserve">hoc autem planum eſt pla-<lb/>num Meridiani loci <anchor type="note" xlink:href="" symbol="*"/>, quare ſectio memorata ad lineam Me- <anchor type="note" xlink:label="note-0662-08a" xlink:href="note-0662-08"/> ridianam, normalis eſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17114" xml:space="preserve">ideòque per puncta Orientis & </s> <s xml:id="echoid-s17115" xml:space="preserve">Oc- <anchor type="note" xlink:label="note-0662-09a" xlink:href="note-0662-09"/> cidentis tranſit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17116" xml:space="preserve"/> </p> <div xml:id="echoid-div2630" type="float" level="2" n="6"> <note position="left" xlink:label="note-0662-07" xlink:href="note-0662-07a" xml:space="preserve">1131.</note> <note symbol="*" position="left" xlink:label="note-0662-08" xlink:href="note-0662-08a" xml:space="preserve">1078. 1116.</note> <note symbol="*" position="left" xlink:label="note-0662-09" xlink:href="note-0662-09a" xml:space="preserve">1117.</note> </div> <note symbol="*" position="left" xml:space="preserve">1102. 1103.</note> <p> <s xml:id="echoid-s17117" xml:space="preserve">Corpora inter Æquatorem & </s> <s xml:id="echoid-s17118" xml:space="preserve">parallelum B b, qui Horizon-<lb/> <anchor type="note" xlink:label="note-0662-11a" xlink:href="note-0662-11"/> tem tangit, ut in circulo A a, diutius ſupra Horizontem, <lb/>quàm infra Horizontem verſantur; </s> <s xml:id="echoid-s17119" xml:space="preserve">& </s> <s xml:id="echoid-s17120" xml:space="preserve">differentia hæc eſt eo <lb/>major, quo magis circulus ut A a, ad Polüm, qui ſupra <lb/>Horizontem elevatur, accedit; </s> <s xml:id="echoid-s17121" xml:space="preserve">Contra, ex acceſſu corporis <lb/> <anchor type="note" xlink:label="note-0662-12a" xlink:href="note-0662-12"/> ad Polum oppoſitum, minuitur mora ſupra Horizontem.</s> <s xml:id="echoid-s17122" xml:space="preserve"/> </p> <div xml:id="echoid-div2631" type="float" level="2" n="7"> <note position="left" xlink:label="note-0662-11" xlink:href="note-0662-11a" xml:space="preserve">1132.</note> <note position="left" xlink:label="note-0662-12" xlink:href="note-0662-12a" xml:space="preserve">1133.</note> </div> <p> <s xml:id="echoid-s17123" xml:space="preserve">Inæqualitas hæc inter moram corporis ſupra Horizontem & </s> <s xml:id="echoid-s17124" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0662-13a" xlink:href="note-0662-13"/> moram infra Horizontem, augetur, cum auctâ altitudine Poli, <lb/>propter diminutionem anguli ab Æquatore & </s> <s xml:id="echoid-s17125" xml:space="preserve">ejus parallelis <lb/>cum Horizonte formati.</s> <s xml:id="echoid-s17126" xml:space="preserve"/> </p> <div xml:id="echoid-div2632" type="float" level="2" n="8"> <note position="left" xlink:label="note-0662-13" xlink:href="note-0662-13a" xml:space="preserve">1134.</note> </div> <pb o="(137)" file="0663" n="732" rhead="MATHEMATICA LIB. IV. CAP. VIII."/> <p> <s xml:id="echoid-s17127" xml:space="preserve">Corpora, quorum diſtantia à Polo æqualis eſt hujus altitu-<lb/> <anchor type="note" xlink:label="note-0663-01a" xlink:href="note-0663-01"/> dini, nunquam occidunt, talis enim eſt diſtantia circuli B b, <lb/>qui Horizontem tangit, & </s> <s xml:id="echoid-s17128" xml:space="preserve">cujus pars nulla infra Horizontem <lb/>pervenit.</s> <s xml:id="echoid-s17129" xml:space="preserve"/> </p> <div xml:id="echoid-div2633" type="float" level="2" n="9"> <note position="right" xlink:label="note-0663-01" xlink:href="note-0663-01a" xml:space="preserve">1135.</note> </div> <p> <s xml:id="echoid-s17130" xml:space="preserve">Corpora, à Polo minus diſtantia, ne quidem ad Hori-<lb/>zontem pertingunt.</s> <s xml:id="echoid-s17131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17132" xml:space="preserve">Simili ratiocinio patet, Corpora, quorum diſtantia à Polo <lb/> <anchor type="note" xlink:label="note-0663-02a" xlink:href="note-0663-02"/> oppoſito, non ſuperat altitudinem Poli, nunquam ſupra Hori-<lb/>zontem adſcendere, & </s> <s xml:id="echoid-s17133" xml:space="preserve">ſemper inviſibilia eſſe.</s> <s xml:id="echoid-s17134" xml:space="preserve"/> </p> <div xml:id="echoid-div2634" type="float" level="2" n="10"> <note position="right" xlink:label="note-0663-02" xlink:href="note-0663-02a" xml:space="preserve">1136.</note> </div> <p> <s xml:id="echoid-s17135" xml:space="preserve">Per Zenit Z tranſeunt corpora, quorum diſtantia E Z, <lb/> <anchor type="note" xlink:label="note-0663-03a" xlink:href="note-0663-03"/> ab Æquatore, æqualis eſt altitudini Poli; </s> <s xml:id="echoid-s17136" xml:space="preserve">æqualis enim E Z <lb/>eſt latitudini loci, cui æqualis Poli altitudo <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17137" xml:space="preserve"/> </p> <div xml:id="echoid-div2635" type="float" level="2" n="11"> <note position="right" xlink:label="note-0663-03" xlink:href="note-0663-03a" xml:space="preserve">1137.</note> </div> <note symbol="*" position="right" xml:space="preserve">1126.</note> <p> <s xml:id="echoid-s17138" xml:space="preserve">Quando ſpectator S à Polo quantum poteſt receſſit, ad <lb/> <anchor type="note" xlink:label="note-0663-05a" xlink:href="note-0663-05"/> Æquatorem pervenit, cujus puncta æqualiter ab utroque <lb/> <anchor type="note" xlink:label="note-0663-06a" xlink:href="note-0663-06"/> <anchor type="note" xlink:label="note-0663-07a" xlink:href="note-0663-07"/> Polo diſtant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17139" xml:space="preserve">Tunc axis P p in Horizonte datur, cum quo <anchor type="note" xlink:label="note-0663-08a" xlink:href="note-0663-08"/> Æquator angulum rectum efficit <anchor type="note" xlink:href="" symbol="*"/>, quare Horizon dicitur <anchor type="note" xlink:label="note-0663-09a" xlink:href="note-0663-09"/> Rectus, aut ſphæra recta.</s> <s xml:id="echoid-s17140" xml:space="preserve"/> </p> <div xml:id="echoid-div2636" type="float" level="2" n="12"> <note position="right" xlink:label="note-0663-05" xlink:href="note-0663-05a" xml:space="preserve">1138.</note> <note position="right" xlink:label="note-0663-06" xlink:href="note-0663-06a" xml:space="preserve"><emph style="sc">TAB. XXIII</emph>.</note> <note position="right" xlink:label="note-0663-07" xlink:href="note-0663-07a" xml:space="preserve">fig. 5.</note> <note symbol="*" position="right" xlink:label="note-0663-08" xlink:href="note-0663-08a" xml:space="preserve">1075. 1114.</note> <note symbol="*" position="right" xlink:label="note-0663-09" xlink:href="note-0663-09a" xml:space="preserve">1075. 1114.</note> </div> <p> <s xml:id="echoid-s17141" xml:space="preserve">Horizon in duas partes æquales ſecat omnes circulos pa-<lb/>rallelos ad Æquatorem, qui per lineas A a, B b repræſen-<lb/>tantur; </s> <s xml:id="echoid-s17142" xml:space="preserve">ideò omnia corpora cœleſtia, ſingulis Telluris revo-<lb/> <anchor type="note" xlink:label="note-0663-10a" xlink:href="note-0663-10"/> lutionibus, oriuntur, & </s> <s xml:id="echoid-s17143" xml:space="preserve">occidunt, & </s> <s xml:id="echoid-s17144" xml:space="preserve">per tempora æqualia <lb/>viſibilia ſunt & </s> <s xml:id="echoid-s17145" xml:space="preserve">latent.</s> <s xml:id="echoid-s17146" xml:space="preserve"/> </p> <div xml:id="echoid-div2637" type="float" level="2" n="13"> <note position="right" xlink:label="note-0663-10" xlink:href="note-0663-10a" xml:space="preserve">1139.</note> </div> <p> <s xml:id="echoid-s17147" xml:space="preserve">Ipſe Æquator per Zenit tranſit; </s> <s xml:id="echoid-s17148" xml:space="preserve">ideòque omnia corpora <lb/> <anchor type="note" xlink:label="note-0663-11a" xlink:href="note-0663-11"/> quæ in hoc dantur.</s> <s xml:id="echoid-s17149" xml:space="preserve"/> </p> <div xml:id="echoid-div2638" type="float" level="2" n="14"> <note position="right" xlink:label="note-0663-11" xlink:href="note-0663-11a" xml:space="preserve">1140.</note> </div> <p> <s xml:id="echoid-s17150" xml:space="preserve">Si, quæ de motu diurno explicavimus, ad corpora appli-<lb/>centur, de quorum aliis motibus apparentibus antea actum, <lb/>facilè determinantur phœnomena ex motibus conjunctis; <lb/></s> <s xml:id="echoid-s17151" xml:space="preserve">quæ Solem ſpectant cæteris notabiliora ſunt, & </s> <s xml:id="echoid-s17152" xml:space="preserve">ideò peculia-<lb/>riter explicanda.</s> <s xml:id="echoid-s17153" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2640" type="section" level="1" n="663"> <head xml:id="echoid-head855" xml:space="preserve"><emph style="sc">Definitio</emph> 18.</head> <p style="it"> <s xml:id="echoid-s17154" xml:space="preserve">Dies Naturalis vocatur Tempus lapſum inter receſſum <lb/> <anchor type="note" xlink:label="note-0663-12a" xlink:href="note-0663-12"/> Solis à Meridiano loci, & </s> <s xml:id="echoid-s17155" xml:space="preserve">acceſſum ſequentem ad eundem Me-<lb/>ridianum.</s> <s xml:id="echoid-s17156" xml:space="preserve"/> </p> <div xml:id="echoid-div2640" type="float" level="2" n="1"> <note position="right" xlink:label="note-0663-12" xlink:href="note-0663-12a" xml:space="preserve">1141.</note> </div> <p> <s xml:id="echoid-s17157" xml:space="preserve">Dies hic differt à tempore revolutionis Telluris circa <lb/> <anchor type="note" xlink:label="note-0663-13a" xlink:href="note-0663-13"/> axem quæ tempora æqualia forent, ſi immobilis inter Stellas <lb/>fixas apparêret Sol; </s> <s xml:id="echoid-s17158" xml:space="preserve">ſed dum motu diurno, in tempore u-<lb/>nius revolutionis Telluris circa Axem, Sol circumfertur ab <pb o="138" file="0664" n="733" rhead="PHYSICES ELEMENTA"/> Oriente in Occidentem, id eſt, in antecedentiâ <anchor type="note" xlink:href="" symbol="*"/>, motu <anchor type="note" xlink:label="note-0664-01a" xlink:href="note-0664-01"/> contrario in Eclipticâ movetur <anchor type="note" xlink:href="" symbol="*"/>, quo tardius ad Meridia- <anchor type="note" xlink:label="note-0664-02a" xlink:href="note-0664-02"/> num pertingit.</s> <s xml:id="echoid-s17159" xml:space="preserve"/> </p> <div xml:id="echoid-div2641" type="float" level="2" n="2"> <note position="right" xlink:label="note-0663-13" xlink:href="note-0663-13a" xml:space="preserve">1142.</note> <note symbol="*" position="left" xlink:label="note-0664-01" xlink:href="note-0664-01a" xml:space="preserve">1080.</note> <note symbol="*" position="left" xlink:label="note-0664-02" xlink:href="note-0664-02a" xml:space="preserve">996.</note> </div> <p> <s xml:id="echoid-s17160" xml:space="preserve">Cùm autem non ſingulis diebus Sol ſpatium æquale per-<lb/> <anchor type="note" xlink:label="note-0664-03a" xlink:href="note-0664-03"/> currat in Eclipticâ <anchor type="note" xlink:href="" symbol="*"/>, non æqualiter ſinguli Dies Naturales <anchor type="note" xlink:label="note-0664-04a" xlink:href="note-0664-04"/> excedunt revolutionem Telluris circa axem; </s> <s xml:id="echoid-s17161" xml:space="preserve">ideoque Dies <lb/>hi ſunt inæquales inter ſe.</s> <s xml:id="echoid-s17162" xml:space="preserve"/> </p> <div xml:id="echoid-div2642" type="float" level="2" n="3"> <note position="left" xlink:label="note-0664-03" xlink:href="note-0664-03a" xml:space="preserve">1143.</note> <note symbol="*" position="left" xlink:label="note-0664-04" xlink:href="note-0664-04a" xml:space="preserve">997.</note> </div> <p> <s xml:id="echoid-s17163" xml:space="preserve">Etiam aliâ ex cauſâ dies naturales inæquales ſunt, nem-<lb/>pe ex inclinatione Eclipticæ reſpectu Æquatoris; </s> <s xml:id="echoid-s17164" xml:space="preserve">unde ſe-<lb/>quitur inæqualiter, in variis punctis, ad Æquatorem viam So-<lb/>lis annuam inclinari; </s> <s xml:id="echoid-s17165" xml:space="preserve">& </s> <s xml:id="echoid-s17166" xml:space="preserve">licet æqualiter in Eclipticâ ſin-<lb/>gulis diebus progrederetur Sol, non æqualiter dies natura-<lb/>les Tempus revolutionis circa axem excederent; </s> <s xml:id="echoid-s17167" xml:space="preserve">nam re-<lb/>ſoluto motu Solis in duos motus <anchor type="note" xlink:href="" symbol="*"/>, quorum unus parallelus <anchor type="note" xlink:label="note-0664-05a" xlink:href="note-0664-05"/> eſt Æquatori, alter huic perpendicularis, ille ſolus conſide-<lb/>randus erit in determinando exceſſu memorato, & </s> <s xml:id="echoid-s17168" xml:space="preserve">inæqua-<lb/>lem eſſe ex diverſà inclinatione indicatâ clarum eſt.</s> <s xml:id="echoid-s17169" xml:space="preserve"/> </p> <div xml:id="echoid-div2643" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0664-05" xlink:href="note-0664-05a" xml:space="preserve">191.</note> </div> <p> <s xml:id="echoid-s17170" xml:space="preserve">Hæ duæ cauſæ inæqualitatis ſæpe concurrunt, ſæpe con-<lb/>trariè agunt.</s> <s xml:id="echoid-s17171" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17172" xml:space="preserve">Dies ſinguli naturales dividuntur in viginti quatuor par-<lb/> <anchor type="note" xlink:label="note-0664-06a" xlink:href="note-0664-06"/> tes æquales, quæ Horæ dicuntur. </s> <s xml:id="echoid-s17173" xml:space="preserve">Singulæ Horæ dividun-<lb/>tur in Minuta ſexaginta, & </s> <s xml:id="echoid-s17174" xml:space="preserve">ſingula Minuta in Minuta ſecun-<lb/>da ſexaginta, & </s> <s xml:id="echoid-s17175" xml:space="preserve">ſic ulterius. </s> <s xml:id="echoid-s17176" xml:space="preserve">Partes bas Temporis in va-<lb/>riis diebus, variare, ex dictis <anchor type="note" xlink:href="" symbol="*"/>, clarè patet; </s> <s xml:id="echoid-s17177" xml:space="preserve">ad æqualita- <anchor type="note" xlink:label="note-0664-07a" xlink:href="note-0664-07"/> tem ab Aſtronomis reducuntur, conſiderando numerum <lb/>Horarum in integrâ Solis revolutione in Eclipticâ, & </s> <s xml:id="echoid-s17178" xml:space="preserve">totum <lb/>Tempus in tot partes æquales dividendo, quot dantur Horæ; <lb/></s> <s xml:id="echoid-s17179" xml:space="preserve">quarum viginti quatuor prouno die habentur. </s> <s xml:id="echoid-s17180" xml:space="preserve">Tempus, cujus <lb/> <anchor type="note" xlink:label="note-0664-08a" xlink:href="note-0664-08"/> partes hac methodo ad æqualitatem reducuntur, vocatur Tem-<lb/>pus medium; </s> <s xml:id="echoid-s17181" xml:space="preserve">& </s> <s xml:id="echoid-s17182" xml:space="preserve">ipſa reductio vocatur Temporis Æquatio.</s> <s xml:id="echoid-s17183" xml:space="preserve"/> </p> <div xml:id="echoid-div2644" type="float" level="2" n="5"> <note position="left" xlink:label="note-0664-06" xlink:href="note-0664-06a" xml:space="preserve">1144.</note> <note symbol="*" position="left" xlink:label="note-0664-07" xlink:href="note-0664-07a" xml:space="preserve">1143.</note> <note position="left" xlink:label="note-0664-08" xlink:href="note-0664-08a" xml:space="preserve">1145.</note> </div> <p style="it"> <s xml:id="echoid-s17184" xml:space="preserve">De diebus & </s> <s xml:id="echoid-s17185" xml:space="preserve">horis Temporis medii ſemper agitur in deter-<lb/> <anchor type="note" xlink:label="note-0664-09a" xlink:href="note-0664-09"/> minandis periodis motuum cæleſtium.</s> <s xml:id="echoid-s17186" xml:space="preserve"/> </p> <div xml:id="echoid-div2645" type="float" level="2" n="6"> <note position="left" xlink:label="note-0664-09" xlink:href="note-0664-09a" xml:space="preserve">1146.</note> </div> </div> <div xml:id="echoid-div2647" type="section" level="1" n="664"> <head xml:id="echoid-head856" xml:space="preserve"><emph style="sc">Definitio</emph> 19.</head> <p> <s xml:id="echoid-s17187" xml:space="preserve">Dies Artificialis eſt mora Solis ſupra Horizontem.</s> <s xml:id="echoid-s17188" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1147.</note> <p> <s xml:id="echoid-s17189" xml:space="preserve">De hoc ſemper agitur, quando de Die loquimur, hunc <lb/>opponendo Nocti. </s> <s xml:id="echoid-s17190" xml:space="preserve">In determinanda dierum artificialium <lb/> <anchor type="note" xlink:label="note-0664-11a" xlink:href="note-0664-11"/> longitudine ad Temporis æquationem non attendemus.</s> <s xml:id="echoid-s17191" xml:space="preserve"/> </p> <div xml:id="echoid-div2647" type="float" level="2" n="1"> <note position="left" xlink:label="note-0664-11" xlink:href="note-0664-11a" xml:space="preserve">1148.</note> </div> <pb file="0665" n="734"/> <pb file="0665a" n="735"/> <figure> <image file="0665a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0665a-01"/> </figure> <pb file="0666" n="736"/> <pb o="139" file="0667" n="737" rhead="MATHEMATICA LIB. IV. CAP. VIII."/> <p style="it"> <s xml:id="echoid-s17192" xml:space="preserve">Ortum Solis ſemper præcedit, & </s> <s xml:id="echoid-s17193" xml:space="preserve">occaſum inſequitur, cre-<lb/> <anchor type="note" xlink:label="note-0667-01a" xlink:href="note-0667-01"/> puſculum; </s> <s xml:id="echoid-s17194" xml:space="preserve">hoc nomine deſignamus lucem illam dubiam, quæ <lb/> <anchor type="note" xlink:label="note-0667-02a" xlink:href="note-0667-02"/> vulgo Aurora & </s> <s xml:id="echoid-s17195" xml:space="preserve">Veſper vocatur.</s> <s xml:id="echoid-s17196" xml:space="preserve"/> </p> <div xml:id="echoid-div2648" type="float" level="2" n="2"> <note position="right" xlink:label="note-0667-01" xlink:href="note-0667-01a" xml:space="preserve">1149.</note> <note position="right" xlink:label="note-0667-02" xlink:href="note-0667-02a" xml:space="preserve">1150.</note> </div> <p style="it"> <s xml:id="echoid-s17197" xml:space="preserve">Oriuntur crepuſcula ex Atmoſphærâ, quæ radiis ſolari-<lb/> <anchor type="note" xlink:label="note-0667-03a" xlink:href="note-0667-03"/> bus illuſtratur, & </s> <s xml:id="echoid-s17198" xml:space="preserve">cujus particulæ lumen quaquaverſum re-<lb/>flectunt; </s> <s xml:id="echoid-s17199" xml:space="preserve">unde radii quidam ad nos perveniunt, licèt Sol octo-<lb/>decim gradibus infra borizontem deprimatur.</s> <s xml:id="echoid-s17200" xml:space="preserve"/> </p> <div xml:id="echoid-div2649" type="float" level="2" n="3"> <note position="right" xlink:label="note-0667-03" xlink:href="note-0667-03a" xml:space="preserve">1151.</note> </div> <p> <s xml:id="echoid-s17201" xml:space="preserve">In ſphærâ parallelâ, id eſt, pro omnibus, quæ ſub Æ-<lb/> <anchor type="note" xlink:label="note-0667-04a" xlink:href="note-0667-04"/> quatore vivunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17202" xml:space="preserve">dies & </s> <s xml:id="echoid-s17203" xml:space="preserve">noctes per totum annum ſunt æqua- <anchor type="note" xlink:label="note-0667-05a" xlink:href="note-0667-05"/> les inter ſe <anchor type="note" xlink:href="" symbol="*"/>, nempe duodecim horarum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17204" xml:space="preserve"/> </p> <div xml:id="echoid-div2650" type="float" level="2" n="4"> <note position="right" xlink:label="note-0667-04" xlink:href="note-0667-04a" xml:space="preserve">1152.</note> <note symbol="*" position="right" xlink:label="note-0667-05" xlink:href="note-0667-05a" xml:space="preserve">1138.</note> </div> <note symbol="*" position="right" xml:space="preserve">1139.</note> <note symbol="*" position="right" xml:space="preserve">1144.</note> <p style="it"> <s xml:id="echoid-s17205" xml:space="preserve">In ſphærâ obliquâ dies majores aut minores ſunt, pro va-<lb/> <anchor type="note" xlink:label="note-0667-08a" xlink:href="note-0667-08"/> riâ diſtantiâ Solis ab Æquatore, verſus unum aut alterum <lb/>Polum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17206" xml:space="preserve">verſus quos ab Æquatore recedit 23. </s> <s xml:id="echoid-s17207" xml:space="preserve">gr. </s> <s xml:id="echoid-s17208" xml:space="preserve">29. </s> <s xml:id="echoid-s17209" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17210" xml:space="preserve"/> </p> <div xml:id="echoid-div2651" type="float" level="2" n="5"> <note position="right" xlink:label="note-0667-08" xlink:href="note-0667-08a" xml:space="preserve">1153.</note> </div> <note symbol="*" position="right" xml:space="preserve">1131. 1132.</note> <note symbol="*" position="right" xml:space="preserve">1087. 1088.</note> <p style="it"> <s xml:id="echoid-s17211" xml:space="preserve">In ipſo Æquatore datur circiter 22. </s> <s xml:id="echoid-s17212" xml:space="preserve">Martis, & </s> <s xml:id="echoid-s17213" xml:space="preserve">23. </s> <s xml:id="echoid-s17214" xml:space="preserve">Se-<lb/> <anchor type="note" xlink:label="note-0667-11a" xlink:href="note-0667-11"/> ptembris, & </s> <s xml:id="echoid-s17215" xml:space="preserve">dies nocti æquatur <anchor type="note" xlink:href="" symbol="*"/>, quod ubique terrarum ob- <anchor type="note" xlink:label="note-0667-12a" xlink:href="note-0667-12"/> tinet, ſolis Polis exceptis.</s> <s xml:id="echoid-s17216" xml:space="preserve"/> </p> <div xml:id="echoid-div2652" type="float" level="2" n="6"> <note position="right" xlink:label="note-0667-11" xlink:href="note-0667-11a" xml:space="preserve">1154.</note> <note symbol="*" position="right" xlink:label="note-0667-12" xlink:href="note-0667-12a" xml:space="preserve">1194.</note> </div> </div> <div xml:id="echoid-div2654" type="section" level="1" n="665"> <head xml:id="echoid-head857" xml:space="preserve"><emph style="sc">Definitio</emph> 20.</head> <note position="right" xml:space="preserve">1155.</note> <p> <s xml:id="echoid-s17217" xml:space="preserve">Puncta Eclipticæ, in quibus ab Æquatore ſecatur <anchor type="note" xlink:href="" symbol="*"/>, vo- <anchor type="note" xlink:label="note-0667-14a" xlink:href="note-0667-14"/> cantur Æquinoctialia. </s> <s xml:id="echoid-s17218" xml:space="preserve">Quia in his punctis verſatur Sol ubi <lb/>datur æqualitas memorata dierum & </s> <s xml:id="echoid-s17219" xml:space="preserve">noctium.</s> <s xml:id="echoid-s17220" xml:space="preserve"/> </p> <div xml:id="echoid-div2654" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0667-14" xlink:href="note-0667-14a" xml:space="preserve">1085.</note> </div> </div> <div xml:id="echoid-div2656" type="section" level="1" n="666"> <head xml:id="echoid-head858" xml:space="preserve"><emph style="sc">Definitio</emph> 21.</head> <p> <s xml:id="echoid-s17221" xml:space="preserve">Puncta Eclipticæ, in quibus Tropici circulum hunc tan-<lb/>gunt <anchor type="note" xlink:href="" symbol="*"/>, dicuntur Solſtitialia. </s> <s xml:id="echoid-s17222" xml:space="preserve">Quia per aliquot dies, quan- <anchor type="note" xlink:label="note-0667-15a" xlink:href="note-0667-15"/> do ad hæc accedit Sol, & </s> <s xml:id="echoid-s17223" xml:space="preserve">ultra tranſit, ſenſibiliter declina-<lb/>tionem non mutat, & </s> <s xml:id="echoid-s17224" xml:space="preserve">ſenſibiliter dierum longitudo non va-<lb/>riat.</s> <s xml:id="echoid-s17225" xml:space="preserve"/> </p> <div xml:id="echoid-div2656" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0667-15" xlink:href="note-0667-15a" xml:space="preserve">1089.</note> </div> <p> <s xml:id="echoid-s17226" xml:space="preserve">Sub Polis, ſidentur incolæ, ſemel in anno Solem orien-<lb/> <anchor type="note" xlink:label="note-0667-16a" xlink:href="note-0667-16"/> tem & </s> <s xml:id="echoid-s17227" xml:space="preserve">occidentem obſervant, & </s> <s xml:id="echoid-s17228" xml:space="preserve">dies unicus cum unicâ nocte <lb/>integrum annum obſolvunt. </s> <s xml:id="echoid-s17229" xml:space="preserve">Supra horizontem verſatur Sol, <lb/>dum dimidiam Eclipticæ partem percurrit <anchor type="note" xlink:href="" symbol="*"/>, per reliquum <anchor type="note" xlink:label="note-0667-17a" xlink:href="note-0667-17"/> Tempus ſub Horizonte latet. </s> <s xml:id="echoid-s17230" xml:space="preserve">Dies tamen protrahitur ex <lb/> <anchor type="note" xlink:label="note-0667-18a" xlink:href="note-0667-18"/> refractione <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s17231" xml:space="preserve">crepuſcula ſunt admodum diuturna, durant <anchor type="note" xlink:label="note-0667-19a" xlink:href="note-0667-19"/> enim quamdiu declinatio Solis verſus Polum latentem non <lb/>ſuperat 18. </s> <s xml:id="echoid-s17232" xml:space="preserve">gr. </s> <s xml:id="echoid-s17233" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17234" xml:space="preserve"/> </p> <div xml:id="echoid-div2657" type="float" level="2" n="2"> <note position="right" xlink:label="note-0667-16" xlink:href="note-0667-16a" xml:space="preserve">1156.</note> <note symbol="*" position="right" xlink:label="note-0667-17" xlink:href="note-0667-17a" xml:space="preserve">1085. 1123.</note> <note position="right" xlink:label="note-0667-18" xlink:href="note-0667-18a" xml:space="preserve">1157.</note> <note symbol="*" position="right" xlink:label="note-0667-19" xlink:href="note-0667-19a" xml:space="preserve">1113.</note> </div> <note symbol="*" position="right" xml:space="preserve">1151.</note> <p> <s xml:id="echoid-s17235" xml:space="preserve">In Polo Arctico in ſex ſignis primis, ab Ariete ad Libram, <lb/> <anchor type="note" xlink:label="note-0667-21a" xlink:href="note-0667-21"/> Sol ſupra Horizontem verſatur; </s> <s xml:id="echoid-s17236" xml:space="preserve">ideò in hoc Polo dies no-<lb/>ctem ſuperat novem diebus naturalibus <anchor type="note" xlink:href="" symbol="*"/>, præter diminutio- <anchor type="note" xlink:label="note-0667-22a" xlink:href="note-0667-22"/> nem noctis ex refractione <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17237" xml:space="preserve"/> </p> <div xml:id="echoid-div2658" type="float" level="2" n="3"> <note position="right" xlink:label="note-0667-21" xlink:href="note-0667-21a" xml:space="preserve">1158.</note> <note symbol="*" position="right" xlink:label="note-0667-22" xlink:href="note-0667-22a" xml:space="preserve">1000.</note> </div> <note symbol="*" position="right" xml:space="preserve">1157.</note> <pb o="140" file="0668" n="738" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s17238" xml:space="preserve">Hiſce generalibus, quæ ſpectant diverſos Horizontis ſi-<lb/>tus, expoſitis, quædam magis peculiaria ſunt examinanda.</s> <s xml:id="echoid-s17239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17240" xml:space="preserve">Dividitur tota Telluris ſuperficies in quinque Zonas. </s> <s xml:id="echoid-s17241" xml:space="preserve">Pri-<lb/> <anchor type="note" xlink:label="note-0668-01a" xlink:href="note-0668-01"/> ma inter duos Tropicos TT, t t, continetur, vocatur Zona <lb/> <anchor type="note" xlink:label="note-0668-02a" xlink:href="note-0668-02"/> Torrida; </s> <s xml:id="echoid-s17242" xml:space="preserve">duæ dantur Temperatæ, & </s> <s xml:id="echoid-s17243" xml:space="preserve">duæ Frigidæ. </s> <s xml:id="echoid-s17244" xml:space="preserve">Tempe-<lb/> <anchor type="note" xlink:label="note-0668-03a" xlink:href="note-0668-03"/> <anchor type="note" xlink:label="note-0668-04a" xlink:href="note-0668-04"/> rata Septentrionalis, Tropico Cancri TT, & </s> <s xml:id="echoid-s17245" xml:space="preserve">Circulo Polari <lb/> <anchor type="note" xlink:label="note-0668-05a" xlink:href="note-0668-05"/> Arctico AA, terminatur: </s> <s xml:id="echoid-s17246" xml:space="preserve">Zona Temperata Auſtralis inter <lb/>Tropicum t t, & </s> <s xml:id="echoid-s17247" xml:space="preserve">Circulum Polarem a a, continetur. </s> <s xml:id="echoid-s17248" xml:space="preserve">Fri-<lb/> <anchor type="note" xlink:label="note-0668-06a" xlink:href="note-0668-06"/> gidæ Zonæ circulis polaribus circumſcribuntur, & </s> <s xml:id="echoid-s17249" xml:space="preserve">Poli ba-<lb/>rum centra occupant.</s> <s xml:id="echoid-s17250" xml:space="preserve"/> </p> <div xml:id="echoid-div2659" type="float" level="2" n="4"> <note position="left" xlink:label="note-0668-01" xlink:href="note-0668-01a" xml:space="preserve">1159.</note> <note position="left" xlink:label="note-0668-02" xlink:href="note-0668-02a" xml:space="preserve">1160.</note> <note position="left" xlink:label="note-0668-03" xlink:href="note-0668-03a" xml:space="preserve">TAB. XXIV.</note> <note position="left" xlink:label="note-0668-04" xlink:href="note-0668-04a" xml:space="preserve">fig. 2.</note> <note position="left" xlink:label="note-0668-05" xlink:href="note-0668-05a" xml:space="preserve">1161.</note> <note position="left" xlink:label="note-0668-06" xlink:href="note-0668-06a" xml:space="preserve">1162.</note> </div> <p> <s xml:id="echoid-s17251" xml:space="preserve">In Zonâ Torridâ bis in anno, in meridie, per Zenit tran-<lb/> <anchor type="note" xlink:label="note-0668-07a" xlink:href="note-0668-07"/> ſit Sol <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17252" xml:space="preserve">Nam elevatio Poli minor eſt 23. </s> <s xml:id="echoid-s17253" xml:space="preserve">gr. </s> <s xml:id="echoid-s17254" xml:space="preserve">29. </s> <s xml:id="echoid-s17255" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s17256" xml:space="preserve"> <anchor type="note" xlink:label="note-0668-08a" xlink:href="note-0668-08"/> <anchor type="note" xlink:label="note-0668-09a" xlink:href="note-0668-09"/> diſtantia Solis ab Æquatore, verſus Polum qui ſupra Horizon-<lb/>tem datur, bis in anno æquatur altitudini Poli <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17257" xml:space="preserve">Ex quâ <anchor type="note" xlink:label="note-0668-10a" xlink:href="note-0668-10"/> eâdem ratione in ipſis Zonæ hujus limitibus, ſub Tropicis <lb/> <anchor type="note" xlink:label="note-0668-11a" xlink:href="note-0668-11"/> nempe, ſemel tantùm ad Zenit accedit Sol in integro anno <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17258" xml:space="preserve"/> </p> <div xml:id="echoid-div2660" type="float" level="2" n="5"> <note position="left" xlink:label="note-0668-07" xlink:href="note-0668-07a" xml:space="preserve">1163.</note> <note symbol="*" position="left" xlink:label="note-0668-08" xlink:href="note-0668-08a" xml:space="preserve">1137.</note> <note symbol="*" position="left" xlink:label="note-0668-09" xlink:href="note-0668-09a" xml:space="preserve">1160. 1127.</note> <note symbol="*" position="left" xlink:label="note-0668-10" xlink:href="note-0668-10a" xml:space="preserve">1087. 1088.</note> <note position="left" xlink:label="note-0668-11" xlink:href="note-0668-11a" xml:space="preserve">1164.</note> </div> <note symbol="*" position="left" xml:space="preserve">1087. 1089.</note> <p> <s xml:id="echoid-s17259" xml:space="preserve">In Zonis Temperatis & </s> <s xml:id="echoid-s17260" xml:space="preserve">Frigidis altitudo Poli minima ex-<lb/> <anchor type="note" xlink:label="note-0668-13a" xlink:href="note-0668-13"/> cedit maximam diſtantiam Solis ab Æquatore <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17261" xml:space="preserve">ideò nun- <anchor type="note" xlink:label="note-0668-14a" xlink:href="note-0668-14"/> <anchor type="note" xlink:label="note-0668-15a" xlink:href="note-0668-15"/> quam in hiſce per Zenit tranſit Sol <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17262" xml:space="preserve">Ad majorem tamen <anchor type="note" xlink:label="note-0668-16a" xlink:href="note-0668-16"/> <anchor type="note" xlink:label="note-0668-17a" xlink:href="note-0668-17"/> altitudinem eodem die adſcendit Sol, quo minor eſt altitudo <lb/>Poli; </s> <s xml:id="echoid-s17263" xml:space="preserve">quia eo minor etiam eſt inclinatio circulorum motus <lb/>diurni ad Horizontem.</s> <s xml:id="echoid-s17264" xml:space="preserve"/> </p> <div xml:id="echoid-div2661" type="float" level="2" n="6"> <note position="left" xlink:label="note-0668-13" xlink:href="note-0668-13a" xml:space="preserve">1165.</note> <note symbol="*" position="left" xlink:label="note-0668-14" xlink:href="note-0668-14a" xml:space="preserve">1087. 1161.</note> <note position="left" xlink:label="note-0668-15" xlink:href="note-0668-15a" xml:space="preserve">1162.</note> <note position="left" xlink:label="note-0668-16" xlink:href="note-0668-16a" xml:space="preserve">1166.</note> <note symbol="*" position="left" xlink:label="note-0668-17" xlink:href="note-0668-17a" xml:space="preserve">1137.</note> </div> <p> <s xml:id="echoid-s17265" xml:space="preserve">In Zonâ Torridâ, & </s> <s xml:id="echoid-s17266" xml:space="preserve">Zonis Temperatis, ſingulis diebus na-<lb/> <anchor type="note" xlink:label="note-0668-18a" xlink:href="note-0668-18"/> turalibus oritur & </s> <s xml:id="echoid-s17267" xml:space="preserve">occidit Sol <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17268" xml:space="preserve">nam diſtantia Solis â Polo <anchor type="note" xlink:label="note-0668-19a" xlink:href="note-0668-19"/> ſemper ſuperat Poli altitudinem <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17269" xml:space="preserve">Inæquales tamen ubi- <anchor type="note" xlink:label="note-0668-20a" xlink:href="note-0668-20"/> <anchor type="note" xlink:label="note-0668-21a" xlink:href="note-0668-21"/> que, ſolo Æquatore excepto <anchor type="note" xlink:href="" symbol="*"/>, ſunt Dies artificiales inter <anchor type="note" xlink:label="note-0668-22a" xlink:href="note-0668-22"/> ſe <anchor type="note" xlink:href="" symbol="*"/>, quæ inæqualitas eo major eſt, quo minus â Zona Fri- <anchor type="note" xlink:label="note-0668-23a" xlink:href="note-0668-23"/> <anchor type="note" xlink:label="note-0668-24a" xlink:href="note-0668-24"/> gida locus diſtat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17270" xml:space="preserve"/> </p> <div xml:id="echoid-div2662" type="float" level="2" n="7"> <note position="left" xlink:label="note-0668-18" xlink:href="note-0668-18a" xml:space="preserve">1167.</note> <note symbol="*" position="left" xlink:label="note-0668-19" xlink:href="note-0668-19a" xml:space="preserve">1129. 1137.</note> <note position="left" xlink:label="note-0668-20" xlink:href="note-0668-20a" xml:space="preserve">1168.</note> <note symbol="*" position="left" xlink:label="note-0668-21" xlink:href="note-0668-21a" xml:space="preserve">1087. 1160.</note> <note position="left" xlink:label="note-0668-22" xlink:href="note-0668-22a" xml:space="preserve">1161.</note> <note symbol="*" position="left" xlink:label="note-0668-23" xlink:href="note-0668-23a" xml:space="preserve">1152.</note> <note symbol="*" position="left" xlink:label="note-0668-24" xlink:href="note-0668-24a" xml:space="preserve">1132.</note> </div> <note symbol="*" position="left" xml:space="preserve">1134.</note> <p> <s xml:id="echoid-s17271" xml:space="preserve">In circulis autem Polaribus, in quibus Zonæ Temperatæ <lb/> <anchor type="note" xlink:label="note-0668-26a" xlink:href="note-0668-26"/> â Frigidis ſeparantur, altitudo Poli æqualis eſt diſtantiæ So-<lb/>lis â Polo, quando datur in Tropico vicino <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17272" xml:space="preserve">ideoque in <anchor type="note" xlink:label="note-0668-27a" xlink:href="note-0668-27"/> hoc caſu, id eſt, ſemel in anno, integram Sol, in motu diur-<lb/>no, peragit revolutionem, in qua infra Horizontem non <lb/>deſcendit.</s> <s xml:id="echoid-s17273" xml:space="preserve"/> </p> <div xml:id="echoid-div2663" type="float" level="2" n="8"> <note position="left" xlink:label="note-0668-26" xlink:href="note-0668-26a" xml:space="preserve">1169.</note> <note symbol="*" position="left" xlink:label="note-0668-27" xlink:href="note-0668-27a" xml:space="preserve">1089. 1091.</note> </div> <p> <s xml:id="echoid-s17274" xml:space="preserve">Vbique autem in Zonâ Frigidâ Altitudo Poli ſuperat di-<lb/> <anchor type="note" xlink:label="note-0668-28a" xlink:href="note-0668-28"/> ſtantiam minimam Solis à Polo <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17275" xml:space="preserve">idcirco, per aliquot revo- <anchor type="note" xlink:label="note-0668-29a" xlink:href="note-0668-29"/> lutiones Telluris, datur Sol ad diſtantiam à polo illâ alti- <pb o="141" file="0669" n="739" rhead="MATHEMATICA LIB. IV. CAP. VIII."/> tudine Poli minorem, & </s> <s xml:id="echoid-s17276" xml:space="preserve">per totum hocce tempus non occi-<lb/>dit, ne quidem ad Horizontem pertingit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17277" xml:space="preserve">Ubi autem di- <anchor type="note" xlink:label="note-0669-01a" xlink:href="note-0669-01"/> ſtantia à Polo, in receſſu Solis ab hoc, altitudinem Poli, <lb/>aut loci latitudinem <anchor type="note" xlink:href="" symbol="*"/>, ſuperat, ſingulis diebus naturalibus o- <anchor type="note" xlink:label="note-0669-02a" xlink:href="note-0669-02"/> ritur & </s> <s xml:id="echoid-s17278" xml:space="preserve">occidit Sol <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17279" xml:space="preserve">deinde infra Horizontem, motu ver- <anchor type="note" xlink:label="note-0669-03a" xlink:href="note-0669-03"/> <anchor type="note" xlink:label="note-0669-04a" xlink:href="note-0669-04"/> ſus Polum oppoſitum, eodem modo moratur, ac de motu ſu-<lb/>pra borizontem dictum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17280" xml:space="preserve"/> </p> <div xml:id="echoid-div2664" type="float" level="2" n="9"> <note position="left" xlink:label="note-0668-28" xlink:href="note-0668-28a" xml:space="preserve">1170.</note> <note symbol="*" position="left" xlink:label="note-0668-29" xlink:href="note-0668-29a" xml:space="preserve">1089. 1162.</note> <note symbol="*" position="right" xlink:label="note-0669-01" xlink:href="note-0669-01a" xml:space="preserve">1135.</note> <note symbol="*" position="right" xlink:label="note-0669-02" xlink:href="note-0669-02a" xml:space="preserve">1127.</note> <note position="right" xlink:label="note-0669-03" xlink:href="note-0669-03a" xml:space="preserve">1171.</note> <note symbol="*" position="right" xlink:label="note-0669-04" xlink:href="note-0669-04a" xml:space="preserve">1129.</note> </div> <note symbol="*" position="right" xml:space="preserve">1136.</note> <p> <s xml:id="echoid-s17281" xml:space="preserve">Tempora hæc, in quibus Sol integras revolutiones ſupra <lb/>Horizontem & </s> <s xml:id="echoid-s17282" xml:space="preserve">infra Horizontem in motu diurno peragit, <lb/>eo majora ſunt, id eſt, dies & </s> <s xml:id="echoid-s17283" xml:space="preserve">nox longiſſimæ, eo diutius du-<lb/> <anchor type="note" xlink:label="note-0669-06a" xlink:href="note-0669-06"/> rant, quo locus in Zonâ frigidâ minùs à Polo diſtat, donec <lb/>tandem in ipſo Polo integrum annum abſorbeant.</s> <s xml:id="echoid-s17284" xml:space="preserve"/> </p> <div xml:id="echoid-div2665" type="float" level="2" n="10"> <note position="right" xlink:label="note-0669-06" xlink:href="note-0669-06a" xml:space="preserve">1172.</note> </div> <p> <s xml:id="echoid-s17285" xml:space="preserve">Ex eâdem cauſâ, obliquitate nempe Eclipticæ reſpectu <lb/>Æquatoris, ex qua profluunt, quæ dierum inæqualitatem, <lb/>in variis locis diverſam, ſpectant, deducimus etiam diverſi-<lb/>tatem Tempeſtatum, quæ ſingulis annis ſibi mutuo ſucce-<lb/>dunt; </s> <s xml:id="echoid-s17286" xml:space="preserve">de his reſpectu Zonarum Frigidarum & </s> <s xml:id="echoid-s17287" xml:space="preserve">Temperata-<lb/>rum primò, deinde reſpectu Zonæ Torridæ, agam.</s> <s xml:id="echoid-s17288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17289" xml:space="preserve">Radii Solares calorem aëri communicant, non quidem <lb/>dum directè à Sole procedunt, ſed cùm à corporibus, aut <lb/>Telluris ſuperficie, irregulariter reflectuntur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17290" xml:space="preserve">Effectus <anchor type="note" xlink:label="note-0669-07a" xlink:href="note-0669-07"/> hic eo major eſt, quo radii minùs obliquè in Telluris ſuperfi-<lb/>ciem impingunt; </s> <s xml:id="echoid-s17291" xml:space="preserve">& </s> <s xml:id="echoid-s17292" xml:space="preserve">quidem ex duplici cauſâ. </s> <s xml:id="echoid-s17293" xml:space="preserve">1. </s> <s xml:id="echoid-s17294" xml:space="preserve">Reſoluto <lb/>motu luminis in duos <anchor type="note" xlink:href="" symbol="*"/>, quorum unus ad ſuperficiem paral- <anchor type="note" xlink:label="note-0669-08a" xlink:href="note-0669-08"/> lelus eſt, alter perpendicularis; </s> <s xml:id="echoid-s17295" xml:space="preserve">hoc ſolo in corpora lumen <lb/>agit, & </s> <s xml:id="echoid-s17296" xml:space="preserve">auctâ obliquitate minuitur. </s> <s xml:id="echoid-s17297" xml:space="preserve">2. </s> <s xml:id="echoid-s17298" xml:space="preserve">In eandem ſuperfi-<lb/>ciei Telluris partem eo majori numero agunt radii, quo <lb/>magis directè accedunt.</s> <s xml:id="echoid-s17299" xml:space="preserve"/> </p> <div xml:id="echoid-div2666" type="float" level="2" n="11"> <note symbol="*" position="right" xlink:label="note-0669-07" xlink:href="note-0669-07a" xml:space="preserve">582.</note> <note symbol="*" position="right" xlink:label="note-0669-08" xlink:href="note-0669-08a" xml:space="preserve">192.</note> </div> <p> <s xml:id="echoid-s17300" xml:space="preserve">Ex hiſce deducimus cauſas caloris augeri, dum ex acceſſu <lb/> <anchor type="note" xlink:label="note-0669-09a" xlink:href="note-0669-09"/> Solis verſus Polum, qui ſupra Horizontem datur Dies <lb/>creſcunt; </s> <s xml:id="echoid-s17301" xml:space="preserve">quia de die in diem ad majorem altitudinem ad-<lb/>ſcendit Sol; </s> <s xml:id="echoid-s17302" xml:space="preserve">ita ut imminutæ obliquitati ſeſe jungat mora <lb/>diuturnior Solis ſupra Horizontem, quæ ad augendum ca-<lb/>lorem concurrit; </s> <s xml:id="echoid-s17303" xml:space="preserve">etiam dum dies creſcunt noctes minuun-<lb/>tur, & </s> <s xml:id="echoid-s17304" xml:space="preserve">per tempus brevius decreſcit calor de die acquiſi-<lb/>tus.</s> <s xml:id="echoid-s17305" xml:space="preserve"/> </p> <div xml:id="echoid-div2667" type="float" level="2" n="12"> <note position="right" xlink:label="note-0669-09" xlink:href="note-0669-09a" xml:space="preserve">1173.</note> </div> <p> <s xml:id="echoid-s17306" xml:space="preserve">In Zonis Septentrionalibus, ut ex hiſce ſequitur, cauſa <pb o="142" file="0670" n="740" rhead="PHYSICES ELEMENTA"/> caloris eſt omnium maxima, cùm Sol Tropicum Cancri at-<lb/> <anchor type="note" xlink:label="note-0670-01a" xlink:href="note-0670-01"/> tingit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17307" xml:space="preserve">Non tamen, ubi cauſa caloris eſt maxima, ipſe ca- <anchor type="note" xlink:label="note-0670-02a" xlink:href="note-0670-02"/> lor eſt maximus; </s> <s xml:id="echoid-s17308" xml:space="preserve">nam hic augetur quamdiu calor, interdiu <lb/>acquiſitus, non in totum de nocte tollitur; </s> <s xml:id="echoid-s17309" xml:space="preserve">licèt enim quo-<lb/>tidiana augmenta minuantur, quamdiu augmentum datur, <lb/>creſcit calor. </s> <s xml:id="echoid-s17310" xml:space="preserve">Sic etiam frigus maximè intenſum non eſt in <lb/> <anchor type="note" xlink:label="note-0670-03a" xlink:href="note-0670-03"/> die breviſſimâ, in qua radiorum ſolarium obliquitas eſt ma-<lb/>xima, & </s> <s xml:id="echoid-s17311" xml:space="preserve">abſentia Solis maximè diuturna; </s> <s xml:id="echoid-s17312" xml:space="preserve">ſed frigus creſcit, <lb/>quamdiu diminutio caloris durat; </s> <s xml:id="echoid-s17313" xml:space="preserve">circa quam idem ratio-<lb/>cinium, quàm circa caloris augmentum, inſtitui poteſt.</s> <s xml:id="echoid-s17314" xml:space="preserve"/> </p> <div xml:id="echoid-div2668" type="float" level="2" n="13"> <note position="left" xlink:label="note-0670-01" xlink:href="note-0670-01a" xml:space="preserve">1174.</note> <note symbol="*" position="left" xlink:label="note-0670-02" xlink:href="note-0670-02a" xml:space="preserve">1090.</note> <note position="left" xlink:label="note-0670-03" xlink:href="note-0670-03a" xml:space="preserve">1175.</note> </div> <p style="it"> <s xml:id="echoid-s17315" xml:space="preserve">Dividitur annus in quatuor tempeſtates; </s> <s xml:id="echoid-s17316" xml:space="preserve">calidiſſima vo-<lb/> <anchor type="note" xlink:label="note-0670-04a" xlink:href="note-0670-04"/> catur Æſtas; </s> <s xml:id="echoid-s17317" xml:space="preserve">maximè frigida Hyems; </s> <s xml:id="echoid-s17318" xml:space="preserve">temperata quæ Hye-<lb/>mem ſequitur Ver; </s> <s xml:id="echoid-s17319" xml:space="preserve">Autumnus Æſtatem ab Hyeme ſeparat.</s> <s xml:id="echoid-s17320" xml:space="preserve"/> </p> <div xml:id="echoid-div2669" type="float" level="2" n="14"> <note position="left" xlink:label="note-0670-04" xlink:href="note-0670-04a" xml:space="preserve">1176.</note> </div> <p style="it"> <s xml:id="echoid-s17321" xml:space="preserve">In regionibus Septentrionalibus, in initio Veris, Sol in <lb/> <anchor type="note" xlink:label="note-0670-05a" xlink:href="note-0670-05"/> principio Arietis apparet: </s> <s xml:id="echoid-s17322" xml:space="preserve">in initio Æſtatis Sol ad Tropi-<lb/>cum cancri pertingit. </s> <s xml:id="echoid-s17323" xml:space="preserve">Vbi Sol ad principium Libræ perve-<lb/>nit incboatur Autumnus: </s> <s xml:id="echoid-s17324" xml:space="preserve">Tropicnm Capricorni percurrit <lb/>Sol motu diurno in initio Hyemis, quæ omnia ex explicatis <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0670-06a" xlink:href="note-0670-06"/> facilè deducuntur.</s> <s xml:id="echoid-s17325" xml:space="preserve"/> </p> <div xml:id="echoid-div2670" type="float" level="2" n="15"> <note position="left" xlink:label="note-0670-05" xlink:href="note-0670-05a" xml:space="preserve">1177.</note> <note symbol="*" position="left" xlink:label="note-0670-06" xlink:href="note-0670-06a" xml:space="preserve">1174. 1175.</note> </div> <p style="it"> <s xml:id="echoid-s17326" xml:space="preserve">In regionibus auſtralibus Æſtas cum Hyeme memoratâ coin-<lb/> <anchor type="note" xlink:label="note-0670-07a" xlink:href="note-0670-07"/> cidit, ver cum Autumno, & </s> <s xml:id="echoid-s17327" xml:space="preserve">vice verſâ.</s> <s xml:id="echoid-s17328" xml:space="preserve"/> </p> <div xml:id="echoid-div2671" type="float" level="2" n="16"> <note position="left" xlink:label="note-0670-07" xlink:href="note-0670-07a" xml:space="preserve">1178.</note> </div> <p> <s xml:id="echoid-s17329" xml:space="preserve">Cauſæ generales, à quibus diviſio memorata pendet, ſæ-<lb/>pe turbantur cauſis peculiaria loca ſpectantibus; </s> <s xml:id="echoid-s17330" xml:space="preserve">præcipuè <lb/>in Zonâ Torridâ, de qua ſeparatim agendum diximus. </s> <s xml:id="echoid-s17331" xml:space="preserve">In <lb/> <anchor type="note" xlink:label="note-0670-08a" xlink:href="note-0670-08"/> pleriſque hujus Zonæ locis duæ tantum obſervantur Tempe-<lb/>ſtates, Æſtas & </s> <s xml:id="echoid-s17332" xml:space="preserve">Hyems, quæ ſiccitate & </s> <s xml:id="echoid-s17333" xml:space="preserve">humiditate potiſſi-<lb/>mum diſtinguuntur.</s> <s xml:id="echoid-s17334" xml:space="preserve"/> </p> <div xml:id="echoid-div2672" type="float" level="2" n="17"> <note position="left" xlink:label="note-0670-08" xlink:href="note-0670-08a" xml:space="preserve">1179.</note> </div> <p> <s xml:id="echoid-s17335" xml:space="preserve">Quando Sol ad Zenit alicujus loci accedit, pluviæ dantur <lb/> <anchor type="note" xlink:label="note-0670-09a" xlink:href="note-0670-09"/> ferè continuæ, unde Calor minuitur; </s> <s xml:id="echoid-s17336" xml:space="preserve">quod tempus ad Hye-<lb/>mem refertur. </s> <s xml:id="echoid-s17337" xml:space="preserve">Recedente Sole, minuuntur pluviæ, calor <lb/> <anchor type="note" xlink:label="note-0670-10a" xlink:href="note-0670-10"/> augetur, & </s> <s xml:id="echoid-s17338" xml:space="preserve">tempus hoc ad Æſtatem refertur</s> </p> <div xml:id="echoid-div2673" type="float" level="2" n="18"> <note position="left" xlink:label="note-0670-09" xlink:href="note-0670-09a" xml:space="preserve">1180.</note> <note position="left" xlink:label="note-0670-10" xlink:href="note-0670-10a" xml:space="preserve">1181.</note> </div> <p> <s xml:id="echoid-s17339" xml:space="preserve">In medio Zonæ Torridæ duæ dantur Æſtates & </s> <s xml:id="echoid-s17340" xml:space="preserve">totidem <lb/> <anchor type="note" xlink:label="note-0670-11a" xlink:href="note-0670-11"/> Hyemes; </s> <s xml:id="echoid-s17341" xml:space="preserve">quia bis ad Zenit accedit Sol <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17342" xml:space="preserve"/> </p> <div xml:id="echoid-div2674" type="float" level="2" n="19"> <note position="left" xlink:label="note-0670-11" xlink:href="note-0670-11a" xml:space="preserve">1182.</note> </div> <note symbol="*" position="left" xml:space="preserve">1163.</note> <p> <s xml:id="echoid-s17343" xml:space="preserve">Ad latera hujus Zonæ, licèt Sol bis ad Zenit accedat; <lb/></s> <s xml:id="echoid-s17344" xml:space="preserve">cùm inter acceſlus breve tempus detur, ambo Hyemes con-<lb/>funduntur; </s> <s xml:id="echoid-s17345" xml:space="preserve">quare duæ tantum tempeſtates in integro anno <lb/>obſervantur.</s> <s xml:id="echoid-s17346" xml:space="preserve"/> </p> <pb o="143" file="0671" n="741" rhead="MATHEMATICA LIB. IV. CAP. IX."/> </div> <div xml:id="echoid-div2676" type="section" level="1" n="667"> <head xml:id="echoid-head859" xml:space="preserve">CAPUT IX.</head> <head xml:id="echoid-head860" xml:space="preserve">De Phænomenis ex motu Axeos Telluris.</head> <p> <s xml:id="echoid-s17347" xml:space="preserve">TElluris Axem motu Parallelo transferri diximus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17348" xml:space="preserve">non <anchor type="note" xlink:label="note-0671-01a" xlink:href="note-0671-01"/> conſideravimus motum exiguum, quo reverâ agitatur, <lb/>de quo nunc agendum nobis eſt.</s> <s xml:id="echoid-s17349" xml:space="preserve"/> </p> <div xml:id="echoid-div2676" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0671-01" xlink:href="note-0671-01a" xml:space="preserve">952.</note> </div> <p> <s xml:id="echoid-s17350" xml:space="preserve">Axis Telluris, ſervatâ inclinatione 66. </s> <s xml:id="echoid-s17351" xml:space="preserve">gr. </s> <s xml:id="echoid-s17352" xml:space="preserve">31. </s> <s xml:id="echoid-s17353" xml:space="preserve">ad planum <lb/> <anchor type="note" xlink:label="note-0671-02a" xlink:href="note-0671-02"/> Eclipticæ, in antecedentiâ revolvitur, id eſt, ſucceſſivè ver-<lb/>ſus omnes partes dirigitur; </s> <s xml:id="echoid-s17354" xml:space="preserve">& </s> <s xml:id="echoid-s17355" xml:space="preserve">hujus extremitates, Poli nem-<lb/> <anchor type="note" xlink:label="note-0671-03a" xlink:href="note-0671-03"/> pe Mundi, circa Polos Eclipticæ circulos deſcribunt ab O-<lb/>riente verſus Occidentem. </s> <s xml:id="echoid-s17356" xml:space="preserve">Hæc autem revolutio abſolvi-<lb/>tur circiter tempore viginti quinque millium annorum, quæ <lb/>periodus Annus Magnus vocatur.</s> <s xml:id="echoid-s17357" xml:space="preserve"/> </p> <div xml:id="echoid-div2677" type="float" level="2" n="2"> <note position="right" xlink:label="note-0671-02" xlink:href="note-0671-02a" xml:space="preserve">1183.</note> <note position="right" xlink:label="note-0671-03" xlink:href="note-0671-03a" xml:space="preserve">1184.</note> </div> <p> <s xml:id="echoid-s17358" xml:space="preserve">Cùm Tellus ab hujus incolis pro immobili habeatur, mo-<lb/>tus hic ad corpora cœleſtia refertur, ut de aliis motibus di-<lb/>ctum. </s> <s xml:id="echoid-s17359" xml:space="preserve">Ideò dum Poli mundi in antecedentiâ, circa Polos <lb/>Eclipticæ, moventur, & </s> <s xml:id="echoid-s17360" xml:space="preserve">ſucceſſivè per omnia puncta, 23. <lb/></s> <s xml:id="echoid-s17361" xml:space="preserve">gr. </s> <s xml:id="echoid-s17362" xml:space="preserve">29. </s> <s xml:id="echoid-s17363" xml:space="preserve">diſtantia ab his Polis, tranſeunt, hæc ipſa puncta, aut <lb/>potius Stellæ fixæ, quæ in his dantur, ſucceſſivè ad Polos <lb/>Mundi accedunt, & </s> <s xml:id="echoid-s17364" xml:space="preserve">in conſequentiâ ferri videntur, & </s> <s xml:id="echoid-s17365" xml:space="preserve">de-<lb/>ſcribere circulos, qui reverâ â Polis Mundi deſcribuntur, <lb/>circa Polos Eclipticæ, qui, in centris poſiti, ſoli quieſcunt. </s> <s xml:id="echoid-s17366" xml:space="preserve"><lb/>Nam cum ſtellis memoratis & </s> <s xml:id="echoid-s17367" xml:space="preserve">reliquæ, quia omnes eundem <lb/>ſitum erga ſe mutuo ſervant <anchor type="note" xlink:href="" symbol="*"/>, etiam tranſlatæ apparent.</s> <s xml:id="echoid-s17368" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">923.</note> <p> <s xml:id="echoid-s17369" xml:space="preserve">Idcirco integra ſphæra Stellarum fixarum circa Axem, per <lb/> <anchor type="note" xlink:label="note-0671-05a" xlink:href="note-0671-05"/> Polos Eclipticæ tranſeuntem, rotari in conſequentiâ videtur; <lb/></s> <s xml:id="echoid-s17370" xml:space="preserve">& </s> <s xml:id="echoid-s17371" xml:space="preserve">ſingulæ Stellæ circulos Eclipticæ parallelos, motu appa-<lb/>renti, deſcribunt; </s> <s xml:id="echoid-s17372" xml:space="preserve">quo motu latitudo Stellarum non muta-<lb/>tur.</s> <s xml:id="echoid-s17373" xml:space="preserve"/> </p> <div xml:id="echoid-div2678" type="float" level="2" n="3"> <note position="right" xlink:label="note-0671-05" xlink:href="note-0671-05a" xml:space="preserve">1185.</note> </div> <p> <s xml:id="echoid-s17374" xml:space="preserve">Planum Æquatoris cum Axe Telluris angulum efficit re-<lb/>ctum; </s> <s xml:id="echoid-s17375" xml:space="preserve">ideò, motu memorato Axeos, rotatur ſectio hujus <lb/>Plani cum Plano Eclipticæ; </s> <s xml:id="echoid-s17376" xml:space="preserve">quare prima puncta Ariëtis & </s> <s xml:id="echoid-s17377" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0671-06a" xlink:href="note-0671-06"/> Libræ <anchor type="note" xlink:href="" symbol="*"/>, quæ ſemper opponuntur, in ſpatio circiter vigin- <anchor type="note" xlink:label="note-0671-07a" xlink:href="note-0671-07"/> ti quinque millium annorum totam lineam Eclipticam in an-<lb/>tecedentiâ percurrunt: </s> <s xml:id="echoid-s17378" xml:space="preserve">pro immobilibus tamen habentur à <lb/>Terræ incolis, qui ipſas ſtellas fixas in conſequentiâ tranſla-<lb/>tas imaginantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17379" xml:space="preserve"/> </p> <div xml:id="echoid-div2679" type="float" level="2" n="4"> <note position="right" xlink:label="note-0671-06" xlink:href="note-0671-06a" xml:space="preserve">1186.</note> <note symbol="*" position="right" xlink:label="note-0671-07" xlink:href="note-0671-07a" xml:space="preserve">1085.</note> </div> <note symbol="*" position="right" xml:space="preserve">1185.</note> <pb o="144" file="0672" n="742" rhead="PHYSICES ELEMENTA"/> </div> <div xml:id="echoid-div2681" type="section" level="1" n="668"> <head xml:id="echoid-head861" xml:space="preserve">CAPUT X.</head> <head xml:id="echoid-head862" xml:space="preserve">De Stellis fixis.</head> <p> <s xml:id="echoid-s17380" xml:space="preserve">STellas fixas diximus eſſe corpora lucida, ita remota, ut <lb/>horum diſtantiæ cum diſtantiis ullis, in Syſtemate Plane-<lb/>tario, non conferri poſſint. </s> <s xml:id="echoid-s17381" xml:space="preserve">Non enim ſubtiliſſimis obſerva-<lb/> <anchor type="note" xlink:label="note-0672-01a" xlink:href="note-0672-01"/> tionibus Aſtronomi potuêre Polos Mundi tranſlatos obſervare <lb/>in motu Telluris annuo, licèt circulos orbitæ Telluris æqua-<lb/>les in cœlis deſcribant <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17382" xml:space="preserve"/> </p> <div xml:id="echoid-div2681" type="float" level="2" n="1"> <note position="left" xlink:label="note-0672-01" xlink:href="note-0672-01a" xml:space="preserve">1187.</note> </div> <note symbol="*" position="left" xml:space="preserve">952.</note> </div> <div xml:id="echoid-div2683" type="section" level="1" n="669"> <head xml:id="echoid-head863" xml:space="preserve"><emph style="sc">Definitio</emph> I.</head> <p> <s xml:id="echoid-s17383" xml:space="preserve">Tranſlatio hæc Poli vocatur Paralaxis annua.</s> <s xml:id="echoid-s17384" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">1188.</note> <p> <s xml:id="echoid-s17385" xml:space="preserve">Diſtantiam ſtellarum immenſam eſſe, etiam ex obſervatio-<lb/>nibus ope teleſcopiorum deducitur. </s> <s xml:id="echoid-s17386" xml:space="preserve">Si Stella fixa quæcun-<lb/> <anchor type="note" xlink:label="note-0672-04a" xlink:href="note-0672-04"/> que, ex maximê lucidis & </s> <s xml:id="echoid-s17387" xml:space="preserve">conſpicuis, conſpiciatur adhibito <lb/>Teleſcopio, per quod diameter Solis diametro orbitæ annuæ <lb/>æqualis apparêret, quaſi punctum lucidum, ſine ſenſibili ma-<lb/>gnitudine, apparebit; </s> <s xml:id="echoid-s17388" xml:space="preserve">minores enim omnes Stellæ per Te-<lb/>leſcopia, quàm nudis oculis, apparent, nam ex ſola ſcintilla-<lb/>tione magnitudinem ſenſibilem habere videntur.</s> <s xml:id="echoid-s17389" xml:space="preserve"/> </p> <div xml:id="echoid-div2683" type="float" level="2" n="1"> <note position="left" xlink:label="note-0672-04" xlink:href="note-0672-04a" xml:space="preserve">1189.</note> </div> <p style="it"> <s xml:id="echoid-s17390" xml:space="preserve">Vt Stellæ diſtinguantur, referuntur ad varias figuras, quæ <lb/> <anchor type="note" xlink:label="note-0672-05a" xlink:href="note-0672-05"/> in cælis imaginantur, & </s> <s xml:id="echoid-s17391" xml:space="preserve">Aſteriſmi vocantur.</s> <s xml:id="echoid-s17392" xml:space="preserve"/> </p> <div xml:id="echoid-div2684" type="float" level="2" n="2"> <note position="left" xlink:label="note-0672-05" xlink:href="note-0672-05a" xml:space="preserve">1190.</note> </div> <p style="it"> <s xml:id="echoid-s17393" xml:space="preserve">In Zodiaco duodecim Aſteriſmi concipiuntur, Zodiaci Signa <lb/> <anchor type="note" xlink:label="note-0672-06a" xlink:href="note-0672-06"/> dicti, nominantur ut animalia, aut res quas repræſentant: <lb/></s> <s xml:id="echoid-s17394" xml:space="preserve">Ariës, Taurus, Gemini, Cancer, Leo, Virgo, Libra, <lb/>Scorpius, Sagittarius, Capricornus, Aquarius, Piſces. </s> <s xml:id="echoid-s17395" xml:space="preserve">Si-<lb/> <anchor type="note" xlink:label="note-0672-07a" xlink:href="note-0672-07"/> gna hæc nomina ſua dedêre, duodecim partibus Eclipticæ de <lb/>quibus antea <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17396" xml:space="preserve"/> </p> <div xml:id="echoid-div2685" type="float" level="2" n="3"> <note position="left" xlink:label="note-0672-06" xlink:href="note-0672-06a" xml:space="preserve">1191.</note> <note position="left" xlink:label="note-0672-07" xlink:href="note-0672-07a" xml:space="preserve">1192.</note> </div> <note symbol="*" position="left" xml:space="preserve">999.</note> <p> <s xml:id="echoid-s17397" xml:space="preserve">Tempore Hiparchi, ſectiones Eclipticæ & </s> <s xml:id="echoid-s17398" xml:space="preserve">Æquatoris ſitæ <lb/>erant inter Aſteriſmos Piſcis & </s> <s xml:id="echoid-s17399" xml:space="preserve">Ariëtis, & </s> <s xml:id="echoid-s17400" xml:space="preserve">Virginis & </s> <s xml:id="echoid-s17401" xml:space="preserve">Li-<lb/>bræ, & </s> <s xml:id="echoid-s17402" xml:space="preserve">Aſteriſmi nomina dedêre illis Eclipticæ partibus, quæ <lb/>per ſingulos Aſteriſmos tranſibant: </s> <s xml:id="echoid-s17403" xml:space="preserve">& </s> <s xml:id="echoid-s17404" xml:space="preserve">partes Eclipticæ, po-<lb/> <anchor type="note" xlink:label="note-0672-09a" xlink:href="note-0672-09"/> nendo initium Ariëtis, & </s> <s xml:id="echoid-s17405" xml:space="preserve">Libræ in interſectionibus Æqua-<lb/>toris & </s> <s xml:id="echoid-s17406" xml:space="preserve">Eclipticæ, uti in illo tempore, nomina ſervarunt, <lb/>licet hæ interſectiones tranſlatæ ſint <anchor type="note" xlink:href="" symbol="*"/>, unde Sol in Tauro <anchor type="note" xlink:label="note-0672-10a" xlink:href="note-0672-10"/> dicitur, quando inter Stellas Aſteriſmi Ariëtis movetur.</s> <s xml:id="echoid-s17407" xml:space="preserve"/> </p> <div xml:id="echoid-div2686" type="float" level="2" n="4"> <note position="left" xlink:label="note-0672-09" xlink:href="note-0672-09a" xml:space="preserve">1193.</note> <note symbol="*" position="left" xlink:label="note-0672-10" xlink:href="note-0672-10a" xml:space="preserve">1186.</note> </div> <p> <s xml:id="echoid-s17408" xml:space="preserve">Zodiacus partem Cœli Septentrionalem à Meridionali ſe-<lb/>parat.</s> <s xml:id="echoid-s17409" xml:space="preserve"/> </p> <pb o="145" file="0673" n="743" rhead="MATHEMATICA LIB. IV. CAP. X."/> <p style="it"> <s xml:id="echoid-s17410" xml:space="preserve">In Septentrionali dantur Aſteriſmi, Vrſa minor, Vrſa <lb/> <anchor type="note" xlink:label="note-0673-01a" xlink:href="note-0673-01"/> major, Draco, Cepheus, Canes Venatici, Bootes, Corona <lb/>Septentrionalis, Hercules, Lyra, Cygnus, Lacerta, Caſio-<lb/>pèja, Camelopardus, Perſeus, Andromeda, Triangulum, <lb/>Triangulum minus, Muſca, Auriga, Pegaſus, Equuleus, <lb/>Delphin, Vulpecula, Anſer, Sagitta, Aquila, Antinous, <lb/>Scutum Sobieskianum, Serpentarius, Serpens, Mons Mæ-<lb/>nalus, Coma Berenicis, Leo minor, Linx.</s> <s xml:id="echoid-s17411" xml:space="preserve"/> </p> <div xml:id="echoid-div2687" type="float" level="2" n="5"> <note position="right" xlink:label="note-0673-01" xlink:href="note-0673-01a" xml:space="preserve">1194.</note> </div> <p style="it"> <s xml:id="echoid-s17412" xml:space="preserve">In parte Meridionali Cælorum Aſteriſmi, quorum multi à <lb/> <anchor type="note" xlink:label="note-0673-02a" xlink:href="note-0673-02"/> nobis videri non poſſunt <anchor type="note" xlink:href="" symbol="*"/>, ſunt, Cetus, Eridanus, Lepus, <anchor type="note" xlink:label="note-0673-03a" xlink:href="note-0673-03"/> Orion, Canis major, Monocerotes, Canis minor, Argo-navis, <lb/>Hydra, Vraniæ Sextans, Crater, Corvus, Centaurus, Lupus, <lb/>Ara, Corona Auſtralis, Piſcis Auſtrinus, Phænix, Grus, In-<lb/>dus, Pavo, Apus, Triangulum Auſtrale, Crux, Muſca, Cha-<lb/>mæleon, Quercus Carolinum, Piſcis volans, Toucan ſive <lb/>Anſer Americanus, Hydrus, Xiphias ſive Dorado.</s> <s xml:id="echoid-s17413" xml:space="preserve"/> </p> <div xml:id="echoid-div2688" type="float" level="2" n="6"> <note position="right" xlink:label="note-0673-02" xlink:href="note-0673-02a" xml:space="preserve">1195.</note> <note symbol="*" position="right" xlink:label="note-0673-03" xlink:href="note-0673-03a" xml:space="preserve">1131.</note> </div> </div> <div xml:id="echoid-div2690" type="section" level="1" n="670"> <head xml:id="echoid-head864" xml:space="preserve"><emph style="sc">Definitio</emph> 2.</head> <p style="it"> <s xml:id="echoid-s17414" xml:space="preserve">Stellæ, quæ inter Aſteriſmos dantur, vocantur informes.</s> <s xml:id="echoid-s17415" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">1196.</note> <p> <s xml:id="echoid-s17416" xml:space="preserve">Non omnes Stellæ æquè lucidæ apparent, & </s> <s xml:id="echoid-s17417" xml:space="preserve">ab Aſtrono-<lb/> <anchor type="note" xlink:label="note-0673-05a" xlink:href="note-0673-05"/> mis ad ſex claßes referuntur, omnium maximè lucidæ di-<lb/>cuntur Primæ Magnitudinis; </s> <s xml:id="echoid-s17418" xml:space="preserve">aliæ Secundæ, Tertiæ, &</s> <s xml:id="echoid-s17419" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s17420" xml:space="preserve">Magnitudinis, ad ſextam uſque.</s> <s xml:id="echoid-s17421" xml:space="preserve"/> </p> <div xml:id="echoid-div2690" type="float" level="2" n="1"> <note position="right" xlink:label="note-0673-05" xlink:href="note-0673-05a" xml:space="preserve">1197.</note> </div> <p style="it"> <s xml:id="echoid-s17422" xml:space="preserve">Quædam, ne quidem ad hanc ultimam claſſem referuntur, <lb/> <anchor type="note" xlink:label="note-0673-06a" xlink:href="note-0673-06"/> & </s> <s xml:id="echoid-s17423" xml:space="preserve">Nebuloſæ dicuntur.</s> <s xml:id="echoid-s17424" xml:space="preserve"/> </p> <div xml:id="echoid-div2691" type="float" level="2" n="2"> <note position="right" xlink:label="note-0673-06" xlink:href="note-0673-06a" xml:space="preserve">1198.</note> </div> <p> <s xml:id="echoid-s17425" xml:space="preserve">In Cælis etiam obſervamus Zonam quandam, non ubi-<lb/> <anchor type="note" xlink:label="note-0673-07a" xlink:href="note-0673-07"/> que ejuſdem latitudinis, quæ totum Cœlum circumdat, <lb/>& </s> <s xml:id="echoid-s17426" xml:space="preserve">in quibuſdam locis ſeparatur, ut dupla ſit. </s> <s xml:id="echoid-s17427" xml:space="preserve">Propter co-<lb/>lorem via Lactea vocatur. </s> <s xml:id="echoid-s17428" xml:space="preserve">Obſervationibus, ope Teleſco-<lb/>piorum conſtat, congeriem eſſe viam hanc Stellarum innume-<lb/> <anchor type="note" xlink:label="note-0673-08a" xlink:href="note-0673-08"/> rarum, quæ viſum oculi inermis fugiunt, aut quia cæteris <lb/>Stellis minores ſunt, aut quia magis diſtant.</s> <s xml:id="echoid-s17429" xml:space="preserve"/> </p> <div xml:id="echoid-div2692" type="float" level="2" n="3"> <note position="right" xlink:label="note-0673-07" xlink:href="note-0673-07a" xml:space="preserve">1199.</note> <note position="right" xlink:label="note-0673-08" xlink:href="note-0673-08a" xml:space="preserve">1200.</note> </div> <p style="it"> <s xml:id="echoid-s17430" xml:space="preserve">Verſus Polum Antarcticum duæ Nubeculæ, huic viæ ſimi-<lb/> <anchor type="note" xlink:label="note-0673-09a" xlink:href="note-0673-09"/> les, dantur, quæ etiam ſunt congeries Stellarum minimarum, <lb/>niſi per Teleſcopia Viſibilium. </s> <s xml:id="echoid-s17431" xml:space="preserve">Præter Stellas, quæ in hiſce Nu-<lb/>beculis, & </s> <s xml:id="echoid-s17432" xml:space="preserve">Viâ lacteâ, obſervantur, maximo numero per to-<lb/> <anchor type="note" xlink:label="note-0673-10a" xlink:href="note-0673-10"/> tum Cælum, adhibitis Teleſcopiis, minores Stellæ detegun-<lb/>tur, quæ nudis oculis non apparent. </s> <s xml:id="echoid-s17433" xml:space="preserve">Sæpiſſimè Stellarum <pb o="(146)" file="0674" n="744" rhead="PHYSICES ELEMENTA"/> congeries, innermi oculo, pro unicâ Stellâ habetur. <lb/></s> <s xml:id="echoid-s17434" xml:space="preserve"> <anchor type="note" xlink:label="note-0674-01a" xlink:href="note-0674-01"/> </s> </p> <div xml:id="echoid-div2693" type="float" level="2" n="4"> <note position="right" xlink:label="note-0673-09" xlink:href="note-0673-09a" xml:space="preserve">1201.</note> <note position="right" xlink:label="note-0673-10" xlink:href="note-0673-10a" xml:space="preserve">1202.</note> <note position="left" xlink:label="note-0674-01" xlink:href="note-0674-01a" xml:space="preserve">1203.</note> </div> <p> <s xml:id="echoid-s17435" xml:space="preserve">Inter Stellas, quædam per vices videntur, & </s> <s xml:id="echoid-s17436" xml:space="preserve">inviſibiles <lb/>fiunt, regulareſque periodos obſervant; </s> <s xml:id="echoid-s17437" xml:space="preserve">aliæ ſucceſſivè nunc <lb/>magis lucidæ, nunc hebetiori lumine præditæ, & </s> <s xml:id="echoid-s17438" xml:space="preserve">Teleſco-<lb/>piis tantùm viſibiles, apparent; </s> <s xml:id="echoid-s17439" xml:space="preserve">idque ſtatis temporibus.</s> <s xml:id="echoid-s17440" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s17441" xml:space="preserve">Non tamen ſingulis periodis æquè claræ ſunt.</s> <s xml:id="echoid-s17442" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s17443" xml:space="preserve">Aliquando ſubitò Stellæ apparuere, lumine lucidiores ſu-<lb/> <anchor type="note" xlink:label="note-0674-02a" xlink:href="note-0674-02"/> perantes, quæ deinde, ſucceſſivè decreſcentes, brevi evanue-<lb/>runt, & </s> <s xml:id="echoid-s17444" xml:space="preserve">adhucdum latent.</s> <s xml:id="echoid-s17445" xml:space="preserve"/> </p> <div xml:id="echoid-div2694" type="float" level="2" n="5"> <note position="left" xlink:label="note-0674-02" xlink:href="note-0674-02a" xml:space="preserve">1204.</note> </div> <p> <s xml:id="echoid-s17446" xml:space="preserve">Præter Stellas, etiam in Cælo obſervamus varias maculas al-<lb/> <anchor type="note" xlink:label="note-0674-03a" xlink:href="note-0674-03"/> bidiores & </s> <s xml:id="echoid-s17447" xml:space="preserve">quodammodo lucidas, quæ nudis oculis inviſibiles <lb/>ſunt; </s> <s xml:id="echoid-s17448" xml:space="preserve">horum enim lumen ad Stellas, quæ in ipſis dantur, re-<lb/>fertur aut pro Stellis nebuloſis habentur.</s> <s xml:id="echoid-s17449" xml:space="preserve"/> </p> <div xml:id="echoid-div2695" type="float" level="2" n="6"> <note position="left" xlink:label="note-0674-03" xlink:href="note-0674-03a" xml:space="preserve">1205.</note> </div> <p> <s xml:id="echoid-s17450" xml:space="preserve">Quid ſint hæ maculæ, determinari non poteſt, fortè ſunt <lb/>congeries Stellarum, quæ cum Stellis Teleſcopicis illam ha-<lb/>bent relationem, quàm quæ Viam lacteam formant, cum illis, <lb/>quæ nudis oculis deteguntur.</s> <s xml:id="echoid-s17451" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2697" type="section" level="1" n="671"> <head xml:id="echoid-head865" style="it" xml:space="preserve">LIBERI IV. Pars II.</head> <head xml:id="echoid-head866" xml:space="preserve">Motuum Cœleſtium Cauſæ Phyſicæ.</head> <head xml:id="echoid-head867" xml:space="preserve">CAPUT XI.</head> <head xml:id="echoid-head868" style="it" xml:space="preserve">De univerſali Gravitate.</head> <p> <s xml:id="echoid-s17452" xml:space="preserve">Expoſitis corporum cœleſtium motibus, ut & </s> <s xml:id="echoid-s17453" xml:space="preserve">Phœno-<lb/>menis inde oriundis, quibus legibus motus hi peragan-<lb/>tur explicandum erit.</s> <s xml:id="echoid-s17454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17455" xml:space="preserve">Leges, juxta quas corporum motus deriguntur, antea ex-<lb/>poſuimus <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17456" xml:space="preserve">Si hiſce unicam adamus, totum patet artificium, <anchor type="note" xlink:label="note-0674-04a" xlink:href="note-0674-04"/> quo ingens Machina, Syſtema Planetarium, regitur.</s> <s xml:id="echoid-s17457" xml:space="preserve"/> </p> <div xml:id="echoid-div2697" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0674-04" xlink:href="note-0674-04a" xml:space="preserve">124. 125. 126.</note> </div> <p> <s xml:id="echoid-s17458" xml:space="preserve">Lex, cæteris addenda, hæc eſt. </s> <s xml:id="echoid-s17459" xml:space="preserve">Omnia corpora in ſe <lb/> <anchor type="note" xlink:label="note-0674-05a" xlink:href="note-0674-05"/> mutuo gravia ſunt: </s> <s xml:id="echoid-s17460" xml:space="preserve">gravitas hæc materiæ quantitati pro-<lb/> <anchor type="note" xlink:label="note-0674-06a" xlink:href="note-0674-06"/> portionalis eſt: </s> <s xml:id="echoid-s17461" xml:space="preserve">ad inæquales diſtantias eſt inverſè, ut qua-<lb/> <anchor type="note" xlink:label="note-0674-07a" xlink:href="note-0674-07"/> dratum diſtantiæ. </s> <s xml:id="echoid-s17462" xml:space="preserve">Id eſt, omnia corpora ſeſe mutuo petunt, <lb/>aut verſus ſeſe mutuo tendunt, vi, quæ ſingulis particulis <pb o="(147)" file="0675" n="745" rhead="MATHEMATICA. LIB. IV. CAP XI."/> materiæ in ſingulas particulas competit; </s> <s xml:id="echoid-s17463" xml:space="preserve">& </s> <s xml:id="echoid-s17464" xml:space="preserve">vis, qua corpus <lb/>in alia agit, formatur ex omnibus viribus conjunctis <lb/>particularum, ex quibus corpus conſtat; </s> <s xml:id="echoid-s17465" xml:space="preserve">ideò vis hæc <lb/>creſcit in ratione, in qua materiæ quantitas augetur; </s> <s xml:id="echoid-s17466" xml:space="preserve">& </s> <s xml:id="echoid-s17467" xml:space="preserve">im-<lb/>mutabilis eſt in ſingulis particulis; </s> <s xml:id="echoid-s17468" xml:space="preserve">ad eandem diſtantiam <lb/>ſemper eadem; </s> <s xml:id="echoid-s17469" xml:space="preserve">auctâ autem diſtantiâ decreſcit vis, ut qua-<lb/>dratum diſtantiæ augetur.</s> <s xml:id="echoid-s17470" xml:space="preserve"/> </p> <div xml:id="echoid-div2698" type="float" level="2" n="2"> <note position="left" xlink:label="note-0674-05" xlink:href="note-0674-05a" xml:space="preserve">1206.</note> <note position="left" xlink:label="note-0674-06" xlink:href="note-0674-06a" xml:space="preserve">1207.</note> <note position="left" xlink:label="note-0674-07" xlink:href="note-0674-07a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s17471" xml:space="preserve">Vim hanc gravitatem nominamus, conſiderando corpus, <lb/> <anchor type="note" xlink:label="note-0675-01a" xlink:href="note-0675-01"/> quod verſus aliud ſponte tendit; </s> <s xml:id="echoid-s17472" xml:space="preserve">quia eo nomine vis hæc in <lb/>Telluris viciniis datur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17473" xml:space="preserve"> <anchor type="note" xlink:label="note-0675-02a" xlink:href="note-0675-02"/> </s> </p> <div xml:id="echoid-div2699" type="float" level="2" n="3"> <note position="right" xlink:label="note-0675-01" xlink:href="note-0675-01a" xml:space="preserve">1209.</note> <note symbol="*" position="right" xlink:label="note-0675-02" xlink:href="note-0675-02a" xml:space="preserve">73.</note> </div> <p> <s xml:id="echoid-s17474" xml:space="preserve">Conſiderando autem corpus, verſus quod aliud tendit, vim <lb/> <anchor type="note" xlink:label="note-0675-03a" xlink:href="note-0675-03"/> hanc vocamus attractionem. </s> <s xml:id="echoid-s17475" xml:space="preserve">His nominibus eundem effe-<lb/>ctum, & </s> <s xml:id="echoid-s17476" xml:space="preserve">nil præter effectum deſignamus; </s> <s xml:id="echoid-s17477" xml:space="preserve">nam, cum omnis <lb/>gravitas ſit reciproca <anchor type="note" xlink:href="" symbol="*"/>, corpora in ſe mutuo gravitare, <anchor type="note" xlink:label="note-0675-04a" xlink:href="note-0675-04"/> idem ſignificat, quàm corpora ſeſe mutuo attrahere, aut <lb/>ad ſe mutuo ſponte tendere.</s> <s xml:id="echoid-s17478" xml:space="preserve"/> </p> <div xml:id="echoid-div2700" type="float" level="2" n="4"> <note position="right" xlink:label="note-0675-03" xlink:href="note-0675-03a" xml:space="preserve">1210.</note> <note symbol="*" position="right" xlink:label="note-0675-04" xlink:href="note-0675-04a" xml:space="preserve">126.</note> </div> <p> <s xml:id="echoid-s17479" xml:space="preserve">Effectum hunc pro lege Naturæ habemus <anchor type="note" xlink:href="" symbol="*"/>, quia nunquam <anchor type="note" xlink:label="note-0675-05a" xlink:href="note-0675-05"/> failit, & </s> <s xml:id="echoid-s17480" xml:space="preserve">hujus cauſa nobis eſt ignota, & </s> <s xml:id="echoid-s17481" xml:space="preserve">ex legibus notis <lb/>minimè deduci poteſt, ut ſtatim dicetur. </s> <s xml:id="echoid-s17482" xml:space="preserve">Nunc autem talem <lb/>gravitatem reverâ dari, ex Phœnomenis probandum eſt.</s> <s xml:id="echoid-s17483" xml:space="preserve"/> </p> <div xml:id="echoid-div2701" type="float" level="2" n="5"> <note symbol="*" position="right" xlink:label="note-0675-05" xlink:href="note-0675-05a" xml:space="preserve">4</note> </div> <p> <s xml:id="echoid-s17484" xml:space="preserve">Planetæ primarii ſinguli in orbitis ſuis retinentur viribus, <lb/>quæ ad centrum Solis tendunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17485" xml:space="preserve">ideò datur vis, qua Plane- <anchor type="note" xlink:label="note-0675-06a" xlink:href="note-0675-06"/> tæ Solem verſus feruntur, & </s> <s xml:id="echoid-s17486" xml:space="preserve">qua Sol reciprocè ad illos <lb/>ſingulos tendit <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17487" xml:space="preserve">id eſt, Sol in Planetas, & </s> <s xml:id="echoid-s17488" xml:space="preserve">hi in Solem <anchor type="note" xlink:label="note-0675-07a" xlink:href="note-0675-07"/> gravitant. <lb/></s> <s xml:id="echoid-s17489" xml:space="preserve"> <anchor type="note" xlink:label="note-0675-08a" xlink:href="note-0675-08"/> </s> </p> <div xml:id="echoid-div2702" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0675-06" xlink:href="note-0675-06a" xml:space="preserve">944. 226.</note> <note position="right" xlink:label="note-0675-07" xlink:href="note-0675-07a" xml:space="preserve">1211.</note> <note symbol="*" position="right" xlink:label="note-0675-08" xlink:href="note-0675-08a" xml:space="preserve">126.</note> </div> <p> <s xml:id="echoid-s17490" xml:space="preserve">Eodem modo patet, ſecundarios Foviales in Fovem, & </s> <s xml:id="echoid-s17491" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0675-09a" xlink:href="note-0675-09"/> Fovem in ipſos; </s> <s xml:id="echoid-s17492" xml:space="preserve">ut & </s> <s xml:id="echoid-s17493" xml:space="preserve">Saturni Satellites in primarium, & </s> <s xml:id="echoid-s17494" xml:space="preserve"><lb/>hunc illos gravitare <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17495" xml:space="preserve"> <anchor type="note" xlink:label="note-0675-10a" xlink:href="note-0675-10"/> </s> </p> <div xml:id="echoid-div2703" type="float" level="2" n="7"> <note position="right" xlink:label="note-0675-09" xlink:href="note-0675-09a" xml:space="preserve">1212.</note> <note symbol="*" position="right" xlink:label="note-0675-10" xlink:href="note-0675-10a" xml:space="preserve">966. 226. 126.</note> </div> <p style="it"> <s xml:id="echoid-s17496" xml:space="preserve">Etiam Luna & </s> <s xml:id="echoid-s17497" xml:space="preserve">Tellus in ſe mutuo graves ſunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17498" xml:space="preserve"> <anchor type="note" xlink:label="note-0675-11a" xlink:href="note-0675-11"/> </s> </p> <div xml:id="echoid-div2704" type="float" level="2" n="8"> <note position="right" xlink:label="note-0675-11" xlink:href="note-0675-11a" xml:space="preserve">1213.</note> </div> <p> <s xml:id="echoid-s17499" xml:space="preserve">Secundarii omnes in Solem gravitatem habent. </s> <s xml:id="echoid-s17500" xml:space="preserve">Omnes <lb/> <anchor type="note" xlink:label="note-0675-12a" xlink:href="note-0675-12"/> enim, motu regulari, circa Primarios ita feruntur, quaſi Pri-<lb/> <anchor type="note" xlink:label="note-0675-13a" xlink:href="note-0675-13"/> marii quieſeerent; </s> <s xml:id="echoid-s17501" xml:space="preserve">unde liquet, illos motu communi cum <lb/>Primariis ferri; </s> <s xml:id="echoid-s17502" xml:space="preserve">id eſt, eandem vim, qua omnibus momen-<lb/>tis ad Solem feruntur Primarii, in Secundarios agere, & </s> <s xml:id="echoid-s17503" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0675-14a" xlink:href="note-0675-14"/> hos eâdem celeritate cum Primariis Solem verſus ferri. <lb/></s> <s xml:id="echoid-s17504" xml:space="preserve">Ipſæ Secundariorum irregularitates, quæ adeo ſunt exiguæ, <lb/>ut reſpectu ſolius Lunæ ſint ſenſibiles, confirmant hanc Se- <pb o="(148)" file="0676" n="746" rhead="PHYSICES ELEMENTA"/> cundariorum gravitatem in Solem; </s> <s xml:id="echoid-s17505" xml:space="preserve">nam irregularitates omnes <lb/>pendere à mutatâ gravitate Lunæ Solem verſus, pro variâ di-<lb/>ſtantiâ, & </s> <s xml:id="echoid-s17506" xml:space="preserve">ex eo quod lineæ, per quas ad Solem tendunt Tellus <lb/>& </s> <s xml:id="echoid-s17507" xml:space="preserve">Luna, non ſint omnino parallelæ, in ſequentibus videbimus.</s> <s xml:id="echoid-s17508" xml:space="preserve"/> </p> <div xml:id="echoid-div2705" type="float" level="2" n="9"> <note position="right" xlink:label="note-0675-12" xlink:href="note-0675-12a" xml:space="preserve">1214.</note> <note symbol="*" position="right" xlink:label="note-0675-13" xlink:href="note-0675-13a" xml:space="preserve">966. 226. 126.</note> <note position="right" xlink:label="note-0675-14" xlink:href="note-0675-14a" xml:space="preserve">1215.</note> </div> <p> <s xml:id="echoid-s17509" xml:space="preserve">Ex gravitate Secundariorum in Solem, ſequitur Solem in <lb/> <anchor type="note" xlink:label="note-0676-01a" xlink:href="note-0676-01"/> illos gravitare <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17510" xml:space="preserve"> <anchor type="note" xlink:label="note-0676-02a" xlink:href="note-0676-02"/> </s> </p> <div xml:id="echoid-div2706" type="float" level="2" n="10"> <note position="left" xlink:label="note-0676-01" xlink:href="note-0676-01a" xml:space="preserve">1216.</note> <note symbol="*" position="left" xlink:label="note-0676-02" xlink:href="note-0676-02a" xml:space="preserve">126.</note> </div> <p> <s xml:id="echoid-s17511" xml:space="preserve">Circa gravitatem Primariorum inter ſe, obſervarunt A ſtro-<lb/>nomi, Saturnum viam mutare ubi Jovi, Planetarum longè <lb/> <anchor type="note" xlink:label="note-0676-03a" xlink:href="note-0676-03"/> maximo, eſt proximus; </s> <s xml:id="echoid-s17512" xml:space="preserve">ita ut Fovem & </s> <s xml:id="echoid-s17513" xml:space="preserve">Saturnum in ſe mu-<lb/>tuo graves eſſe, immediatis obſervationibus conſtet.</s> <s xml:id="echoid-s17514" xml:space="preserve"/> </p> <div xml:id="echoid-div2707" type="float" level="2" n="11"> <note position="left" xlink:label="note-0676-03" xlink:href="note-0676-03a" xml:space="preserve">1217.</note> </div> <p> <s xml:id="echoid-s17515" xml:space="preserve">Saturnus etiam in hoc caſu, ut Flamſtedius obſervavit, tur-<lb/> <anchor type="note" xlink:label="note-0676-04a" xlink:href="note-0676-04"/> bat motum ſatellitum Fovis, hos paululum ad ſe trahens, <lb/>quod probat, & </s> <s xml:id="echoid-s17516" xml:space="preserve">hos Secundarios in Saturnum & </s> <s xml:id="echoid-s17517" xml:space="preserve">hunc in i-<lb/>pſos gravitare. </s> <s xml:id="echoid-s17518" xml:space="preserve">Ex quibus omnibus <anchor type="note" xlink:href="" symbol="*"/> collatis ſequitur, ſe- <anchor type="note" xlink:label="note-0676-05a" xlink:href="note-0676-05"/> ptemdecim, Syſtema Planetarium componentia, corpora in ſe <lb/>mutuo gravitare, licèt de ſingulorum in ſingulà gravitate ob-<lb/>ſervationes immediatas inſtituere non liceat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17519" xml:space="preserve"> <anchor type="note" xlink:label="note-0676-06a" xlink:href="note-0676-06"/> </s> </p> <div xml:id="echoid-div2708" type="float" level="2" n="12"> <note position="left" xlink:label="note-0676-04" xlink:href="note-0676-04a" xml:space="preserve">1218.</note> <note symbol="*" position="left" xlink:label="note-0676-05" xlink:href="note-0676-05a" xml:space="preserve">1211. 1212. 1213. 1214. 1216. 1217. 1218.</note> <note symbol="*" position="left" xlink:label="note-0676-06" xlink:href="note-0676-06a" xml:space="preserve">7</note> </div> <p> <s xml:id="echoid-s17520" xml:space="preserve">Legis pars ſecunda eſt <anchor type="note" xlink:href="" symbol="*"/>, gravitatem materiæ quantitati <anchor type="note" xlink:label="note-0676-07a" xlink:href="note-0676-07"/> proportionalem eſſe, id eſt, ſingulis materiæ particulis com-<lb/>petere in ſingulas, ideòque legem gravitatis univerſalem eſ-<lb/>ſe, & </s> <s xml:id="echoid-s17521" xml:space="preserve">ſingula corpora in alia corpora omnia gravitare; <lb/></s> <s xml:id="echoid-s17522" xml:space="preserve">quod ex Phœnomenis etiam deducitur.</s> <s xml:id="echoid-s17523" xml:space="preserve"/> </p> <div xml:id="echoid-div2709" type="float" level="2" n="13"> <note symbol="*" position="left" xlink:label="note-0676-07" xlink:href="note-0676-07a" xml:space="preserve">1207.</note> </div> <p> <s xml:id="echoid-s17524" xml:space="preserve">Vires gravitatis ſunt ut effectus æqualibus temporibus e-<lb/> <anchor type="note" xlink:label="note-0676-08a" xlink:href="note-0676-08"/> diti, & </s> <s xml:id="echoid-s17525" xml:space="preserve">ſunt hi ut quantitates materiæ translatæ, ſi transla-<lb/>tiones fuerint æquales; </s> <s xml:id="echoid-s17526" xml:space="preserve">idcirco, cùm corpora inæqualia, ad <lb/>eandem diſtantiam à corpore attrahente, æquè celeriter ex <lb/>gravitate moveantur <anchor type="note" xlink:href="" symbol="*"/>, vires gravitatis materiæ quantitatis <anchor type="note" xlink:label="note-0676-09a" xlink:href="note-0676-09"/> proportionem ſequi, clarum eſt. </s> <s xml:id="echoid-s17527" xml:space="preserve">Idem experimur in omni-<lb/>bus corporibus in Telluris viciniis, quæ Tellurem verſus, <lb/> <anchor type="note" xlink:label="note-0676-10a" xlink:href="note-0676-10"/> materiæ quantitati proportionalem, gravitatem habent <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17528" xml:space="preserve"> <anchor type="note" xlink:label="note-0676-11a" xlink:href="note-0676-11"/> Mutua autem horum omnium corporum gravitas ſenſibilis <lb/>non eſt; </s> <s xml:id="echoid-s17529" xml:space="preserve">quia reſpectu gravitatis Tellurem verſus admodum <lb/>eſt exigua, ideoque motum ex hac turbare non valet <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17530" xml:space="preserve">ſal- <anchor type="note" xlink:label="note-0676-12a" xlink:href="note-0676-12"/> tem ut ſenſibilis detur directionis mutatio.</s> <s xml:id="echoid-s17531" xml:space="preserve"/> </p> <div xml:id="echoid-div2710" type="float" level="2" n="14"> <note position="left" xlink:label="note-0676-08" xlink:href="note-0676-08a" xml:space="preserve">1219.</note> <note symbol="*" position="left" xlink:label="note-0676-09" xlink:href="note-0676-09a" xml:space="preserve">1215.</note> <note position="left" xlink:label="note-0676-10" xlink:href="note-0676-10a" xml:space="preserve">1220.</note> <note symbol="*" position="left" xlink:label="note-0676-11" xlink:href="note-0676-11a" xml:space="preserve">79.</note> <note symbol="*" position="left" xlink:label="note-0676-12" xlink:href="note-0676-12a" xml:space="preserve">190.</note> </div> <p> <s xml:id="echoid-s17532" xml:space="preserve">Et aliâ methodo, ex Phœnomenis, hanc univerſalitatem <lb/>gravitatis, ſingularum materiæ particulis in alias probari poſ-<lb/>ſe, ſtatim dicemus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17533" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">1222.</note> <pb o="(149)" file="0677" n="747" rhead="MATHEMATICA LIB. IV. CAP. XI."/> <p> <s xml:id="echoid-s17534" xml:space="preserve">Pars legis, quam examinamus, tertia eſt, gravitatem de-<lb/>creſcere, quando diſtantia augetur, & </s> <s xml:id="echoid-s17535" xml:space="preserve">eſſe inverſè ut quadra-<lb/>tum diſtantiæ; </s> <s xml:id="echoid-s17536" xml:space="preserve">quod ex Phœnomenis quoque ſequitur.</s> <s xml:id="echoid-s17537" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17538" xml:space="preserve">Corpora, in quæ vis gravitatis agit pro quantitate mate-<lb/> <anchor type="note" xlink:label="note-0677-01a" xlink:href="note-0677-01"/> riæ, ut in Syſtemate noſtro, eâdem, ut diximus, celeritate <lb/>feruntur, in circumſtantiis iiſdem; </s> <s xml:id="echoid-s17539" xml:space="preserve">ita ut non interſit, <lb/>utrum majora an minora ſint corpora, & </s> <s xml:id="echoid-s17540" xml:space="preserve">moveantur qua-<lb/>ſi eſſent æqualia. </s> <s xml:id="echoid-s17541" xml:space="preserve">In hoc autem caſu, ſi vis verſus pun-<lb/>ctum decreſcat in ratione inverſa quadrati diſtantiæ ab hoc <lb/>puncto, & </s> <s xml:id="echoid-s17542" xml:space="preserve">corpora ad varias ab hoc ipſo diſtantias revol-<lb/>vantur & </s> <s xml:id="echoid-s17543" xml:space="preserve">in circulis retineantur hac vi, quadrata temporum <lb/>periodicorum erunt inter ſe, ut diſtantiarum cubi <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17544" xml:space="preserve">Quod <anchor type="note" xlink:label="note-0677-02a" xlink:href="note-0677-02"/> æquè in lineis Ellipticis, ad quorum focos diriguntur vires, <lb/>reſpectu diſtantiarum mediarum, obtinere, à Geometris de-<lb/>monſtratur. </s> <s xml:id="echoid-s17545" xml:space="preserve">Hicce autem caſus in corporibus circa Solem, <lb/>Saturnum, & </s> <s xml:id="echoid-s17546" xml:space="preserve">Jovem <anchor type="note" xlink:href="" symbol="*"/>, revolventibus exſtat, unde ſequitur, <anchor type="note" xlink:label="note-0677-03a" xlink:href="note-0677-03"/> vim gravitatis, recedendo à centris horum corporum, decre-<lb/>ſcere in ratione inverſà quadratorum diſtantiarum.</s> <s xml:id="echoid-s17547" xml:space="preserve"/> </p> <div xml:id="echoid-div2711" type="float" level="2" n="15"> <note position="right" xlink:label="note-0677-01" xlink:href="note-0677-01a" xml:space="preserve">1221.</note> <note symbol="*" position="right" xlink:label="note-0677-02" xlink:href="note-0677-02a" xml:space="preserve">239.</note> <note symbol="*" position="right" xlink:label="note-0677-03" xlink:href="note-0677-03a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s17548" xml:space="preserve">Hoc ratiocinio, poſitâ gravitate materiæ quantitati pro-<lb/> <anchor type="note" xlink:label="note-0677-04a" xlink:href="note-0677-04"/> portionali, illam in ratione inverſâ quadrati diſtantiæ decre-<lb/>ſcere demonſtramus. </s> <s xml:id="echoid-s17549" xml:space="preserve">Ex eodem, poſitâ gravitatis diminu-<lb/>tione juxta hanc rationem, ſequitur, gravitatem materiæ quan-<lb/>titati proportionalem eſſe, ut facilè liquet.</s> <s xml:id="echoid-s17550" xml:space="preserve"/> </p> <div xml:id="echoid-div2712" type="float" level="2" n="16"> <note position="right" xlink:label="note-0677-04" xlink:href="note-0677-04a" xml:space="preserve">1222.</note> </div> <p> <s xml:id="echoid-s17551" xml:space="preserve">Probamus autem alio argumento, diminutionem gravitatis <lb/>ſæpius memoratam rationem inverſam quadrati diſtantiæ ſe-<lb/>qui; </s> <s xml:id="echoid-s17552" xml:space="preserve">ita ut circa ambas, de quibus agimus, gravitatis leges, <lb/>nullum dubium ſupereſſe poſſit.</s> <s xml:id="echoid-s17553" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17554" xml:space="preserve">Planetæ moventur in Orbibus quieſcentibus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17555" xml:space="preserve">& </s> <s xml:id="echoid-s17556" xml:space="preserve">in his <anchor type="note" xlink:label="note-0677-05a" xlink:href="note-0677-05"/> retinentur viribus, quæ ad punctum excentricum dirigun-<lb/> <anchor type="note" xlink:label="note-0677-06a" xlink:href="note-0677-06"/> tur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17557" xml:space="preserve">Conſtat autem hæc non obtinere, niſi vis centralis <anchor type="note" xlink:label="note-0677-07a" xlink:href="note-0677-07"/> decreſcat in ratione inverſâ quadrati diſtantiæ <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17558" xml:space="preserve"> <anchor type="note" xlink:label="note-0677-08a" xlink:href="note-0677-08"/> </s> </p> <div xml:id="echoid-div2713" type="float" level="2" n="17"> <note position="right" xlink:label="note-0677-05" xlink:href="note-0677-05a" xml:space="preserve">1223.</note> <note symbol="*" position="right" xlink:label="note-0677-06" xlink:href="note-0677-06a" xml:space="preserve">929.</note> <note symbol="*" position="right" xlink:label="note-0677-07" xlink:href="note-0677-07a" xml:space="preserve">931.</note> <note symbol="*" position="right" xlink:label="note-0677-08" xlink:href="note-0677-08a" xml:space="preserve">241. 243.</note> </div> <p> <s xml:id="echoid-s17559" xml:space="preserve">Gravitatem etiam recedendo â Telluris centro, juxta <lb/> <anchor type="note" xlink:label="note-0677-09a" xlink:href="note-0677-09"/> eandem legem decreſcere, ex ſimili ratiocinio ſequitur. <lb/></s> <s xml:id="echoid-s17560" xml:space="preserve">Luna enim in orbitâ retinetur vi, quæ ad Telluris cen-<lb/>trum, id eſt ad punctum excentricum, tendit <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17561" xml:space="preserve">& </s> <s xml:id="echoid-s17562" xml:space="preserve">licèt li- <anchor type="note" xlink:label="note-0677-10a" xlink:href="note-0677-10"/> nea Apſidum non feratur motu parallelo, agitatio hujus, ſi <lb/>ſingulas conſideremus revolutiones, admodum eſt exigua, ut <lb/>hic pro quieſcente haberi poſſit: </s> <s xml:id="echoid-s17563" xml:space="preserve">ſi enim computatio ineatur <pb o="(150)" file="0678" n="748" rhead="PHYSICES ELEMENTA"/> de vi quæ retinet Lunam in orbe ita agitato, diminutionem <lb/>vis gravitatis reſpectu Lunæ, parum admodum à ratione in-<lb/>verſâ quadrati diſtantiæ, differe detegimus, differentiamque <lb/>à Solis actione pendere in ſequentibus videbimus.</s> <s xml:id="echoid-s17564" xml:space="preserve"/> </p> <div xml:id="echoid-div2714" type="float" level="2" n="18"> <note position="right" xlink:label="note-0677-09" xlink:href="note-0677-09a" xml:space="preserve">1242.</note> <note symbol="*" position="right" xlink:label="note-0677-10" xlink:href="note-0677-10a" xml:space="preserve">967. 966. 226.</note> </div> <p> <s xml:id="echoid-s17565" xml:space="preserve">Nullumque dubium circa hanc diminutionem ſupererit, <lb/>ſi conſideremus, Lunam in orbitâ retineri ex ipſâ vi, qua <lb/> <anchor type="note" xlink:label="note-0678-01a" xlink:href="note-0678-01"/> corpora in Telluris viciniis Tellurem verſus feruntur, immi-<lb/>nutâ, juxta legem diminutionis ſæpiſſimè memoratam. </s> <s xml:id="echoid-s17566" xml:space="preserve">Di-<lb/>ſtantia media Lunæ eſt 60 {1/2} ſemid. </s> <s xml:id="echoid-s17567" xml:space="preserve">Telluris; </s> <s xml:id="echoid-s17568" xml:space="preserve">diametrum an-<lb/>tea vidimus continere perticas Rhenolandicas 3400669 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17569" xml:space="preserve">un- <anchor type="note" xlink:label="note-0678-02a" xlink:href="note-0678-02"/> de, ex noto tempore periodico, facilè detegimus in uno mi-<lb/>nuto primo temporis, Lunam in orbitâ percurrere perticas <lb/>Rhenolandicas 16425 {1/2}. </s> <s xml:id="echoid-s17570" xml:space="preserve">Hic arcus non eſt centeſima pars <lb/>unius gradus, & </s> <s xml:id="echoid-s17571" xml:space="preserve">pro ipſius ſubtenſâ uſurpari poteſt; </s> <s xml:id="echoid-s17572" xml:space="preserve">eſt ideò <lb/>orbitæ diameter ad hunc arcum, ut ipſe ad ſuum ſinum ver-<lb/>ſum; </s> <s xml:id="echoid-s17573" xml:space="preserve">qui detegitur pedum Rhenol. </s> <s xml:id="echoid-s17574" xml:space="preserve">15, 736.</s> <s xml:id="echoid-s17575" xml:space="preserve">, & </s> <s xml:id="echoid-s17576" xml:space="preserve">eſt acceſſus <lb/>mutuus Lunæ & </s> <s xml:id="echoid-s17577" xml:space="preserve">Telluris, ex horum corporum mutuâ actio-<lb/>ne, in uno minuto primo temporis. </s> <s xml:id="echoid-s17578" xml:space="preserve">Celeritas, qua corpus <lb/>gravitate ad aliud accedit, pendet à vi qua ab hoc alio attra-<lb/>hitur, cujus ſingulæ particulæ materiæ, illud attrahunt; </s> <s xml:id="echoid-s17579" xml:space="preserve">ideò <lb/>celeritates Lunæ & </s> <s xml:id="echoid-s17580" xml:space="preserve">Telluris, in mutuo acceſſu, ſunt inverſè ut <lb/>quantitates materiæ in his; </s> <s xml:id="echoid-s17581" xml:space="preserve">quod etiam ex æquali motus quanti-<lb/>tate in ut utroque corpore deducitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17582" xml:space="preserve">Hac ergo proportione <anchor type="note" xlink:label="note-0678-03a" xlink:href="note-0678-03"/> detegimus, quantum, ex memorato ſpatio 15, 736. </s> <s xml:id="echoid-s17583" xml:space="preserve">pedum, à <lb/>Lunâ percurratur; </s> <s xml:id="echoid-s17584" xml:space="preserve">ut quantitas materiæ in utroque corpore <lb/>ad quantitatem materiæ in Tellure, ita ſpatium in acceſſu <lb/>ad ſe mutuo ab ambobus percurſum, ad viam à ſolâ Lunâ <lb/>percurſam. </s> <s xml:id="echoid-s17585" xml:space="preserve">Quantitates autem materiæ in Lunâ & </s> <s xml:id="echoid-s17586" xml:space="preserve">Tellu-<lb/>re, ut in ſequentibus videbimus, ſunt inter ſe ut 1. </s> <s xml:id="echoid-s17587" xml:space="preserve">& </s> <s xml:id="echoid-s17588" xml:space="preserve">39, 37.</s> <s xml:id="echoid-s17589" xml:space="preserve">; <lb/>& </s> <s xml:id="echoid-s17590" xml:space="preserve">eſt 40, 37. </s> <s xml:id="echoid-s17591" xml:space="preserve">ad 39, 37.</s> <s xml:id="echoid-s17592" xml:space="preserve">, ut 15, 736. </s> <s xml:id="echoid-s17593" xml:space="preserve">ad 15, 344 ſpatium à <lb/>Lunâ percurſum; </s> <s xml:id="echoid-s17594" xml:space="preserve">quod ergo à corpore quocunque, in ſpa-<lb/>tio unius minuti primi, gravitate verſus Tellurem, ad di-<lb/>ſtantiam Lunæ percurreretur. </s> <s xml:id="echoid-s17595" xml:space="preserve">Creſcente hac vi, in ratione <lb/>inverſà quadrati diſtantiæ à centro, ſpatium eodem tempore <lb/>percurſum ad diſtantiam ſemidiametri Telluris, id eſt in hu-<lb/>jus ſuperficie, erit 60 {1/2} x 60 {1/2} x 15, 344, ſcil. </s> <s xml:id="echoid-s17596" xml:space="preserve">56158 pedum; <lb/></s> <s xml:id="echoid-s17597" xml:space="preserve">ſed quia in omni motu æquabiliter accelerato, ut hic, <lb/>(nam conſideramus vim ad diſtantiam ſuperficiei Telluris à <pb o="(151)" file="0679" n="749" rhead="MATHEMATICA LIB. IV. CAP. XI."/> centro) quadrata temporum ſunt, ut ſpatia cadendo percur-<lb/>ſa <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17598" xml:space="preserve">dividendo hunc numerum per 60 x 60 id eſt, 3600, <anchor type="note" xlink:label="note-0679-01a" xlink:href="note-0679-01"/> habemus ſpatium, in Telluris viciniis, in uno minuto ſecundo <lb/>à corpore percurſum, ex vi qua Luna in orbitâ retinetur, <lb/>quod detegitur 15, 6. </s> <s xml:id="echoid-s17599" xml:space="preserve">pedum Rhenolandicorum.</s> <s xml:id="echoid-s17600" xml:space="preserve"/> </p> <div xml:id="echoid-div2715" type="float" level="2" n="19"> <note position="left" xlink:label="note-0678-01" xlink:href="note-0678-01a" xml:space="preserve">1225.</note> <note symbol="*" position="left" xlink:label="note-0678-02" xlink:href="note-0678-02a" xml:space="preserve">976.</note> <note symbol="*" position="left" xlink:label="note-0678-03" xlink:href="note-0678-03a" xml:space="preserve">126. 65.</note> <note symbol="*" position="right" xlink:label="note-0679-01" xlink:href="note-0679-01a" xml:space="preserve">136.</note> </div> <p> <s xml:id="echoid-s17601" xml:space="preserve">Si nunc examinemus gravitatem, quam quotidie experi-<lb/>mur in omnibus corporibus, in Telluris viciniis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17602" xml:space="preserve">ex de- <anchor type="note" xlink:label="note-0679-02a" xlink:href="note-0679-02"/> monſtratis circa pendulorum motum <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s17603" xml:space="preserve">experimentis <anchor type="note" xlink:label="note-0679-03a" xlink:href="note-0679-03"/> circa pendula inſtitutis, conſtat, corpus cadendo etiam percur-<lb/>rere in uno minuto ſecundo pedes Rhenolandicos 15, 6. </s> <s xml:id="echoid-s17604" xml:space="preserve">ideo-<lb/>que cadere ex vi, quæ Lunam in orbitâ retinet.</s> <s xml:id="echoid-s17605" xml:space="preserve"/> </p> <div xml:id="echoid-div2716" type="float" level="2" n="20"> <note symbol="*" position="right" xlink:label="note-0679-02" xlink:href="note-0679-02a" xml:space="preserve">72.</note> <note symbol="*" position="right" xlink:label="note-0679-03" xlink:href="note-0679-03a" xml:space="preserve">157. 158.</note> </div> <p> <s xml:id="echoid-s17606" xml:space="preserve">In hac computatione negleximus conſiderationem actionis <lb/>Solis, quia hæc exigua eſt, & </s> <s xml:id="echoid-s17607" xml:space="preserve">alternatim nunc auget, nunc <lb/>minuit Lunæ gravitatem verſus Tellurem.</s> <s xml:id="echoid-s17608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17609" xml:space="preserve">Conſideravimus centra corporum in examine legis dimi-<lb/>nutionis gravitatis, licèt gravitas ſingulas corporum particu-<lb/>las ſpectet; </s> <s xml:id="echoid-s17610" xml:space="preserve">quia mathematicâ demonſtratione conſtat, actio-<lb/> <anchor type="note" xlink:label="note-0679-04a" xlink:href="note-0679-04"/> nem corporis ſphærici, in quo ubique partes à centro æquè <lb/>diſtantes ſunt homogeneæ, conſtantis ex particulis verſus <lb/>quas gravitas datur, quæ decreſcit recedendo à ſingulis, in <lb/>ratione inverſâ quadrati diſtantiæ, dirigi ad corporis cen-<lb/>trum, & </s> <s xml:id="echoid-s17611" xml:space="preserve">recedendo ab hoc minui in eâdem ratione inverſâ <lb/>quadrati diſtantiæ: </s> <s xml:id="echoid-s17612" xml:space="preserve">ita ut tale corpus agat, quaſi omnis mate-<lb/>ria ex qua conſtat, coacta foret in ipſo centro. </s> <s xml:id="echoid-s17613" xml:space="preserve">Unde ſequen-<lb/>tes deducimus concluſiones.</s> <s xml:id="echoid-s17614" xml:space="preserve"/> </p> <div xml:id="echoid-div2717" type="float" level="2" n="21"> <note position="right" xlink:label="note-0679-04" xlink:href="note-0679-04a" xml:space="preserve">1226.</note> </div> <p style="it"> <s xml:id="echoid-s17615" xml:space="preserve">In ſuperficiebus corporum, in quibus materia homogenea <lb/> <anchor type="note" xlink:label="note-0679-05a" xlink:href="note-0679-05"/> eſt ad diſtantias æquales à centro, gravitatem eſſe directè ut <lb/>materiæ quantitatem, & </s> <s xml:id="echoid-s17616" xml:space="preserve">inverſe ut quadratum diametri <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s17617" xml:space="preserve"> <anchor type="note" xlink:label="note-0679-06a" xlink:href="note-0679-06"/> nam in his corporibus diſtantiæ à centro ſunt ut diametri.</s> <s xml:id="echoid-s17618" xml:space="preserve"/> </p> <div xml:id="echoid-div2718" type="float" level="2" n="22"> <note position="right" xlink:label="note-0679-05" xlink:href="note-0679-05a" xml:space="preserve">1227.</note> <note symbol="*" position="right" xlink:label="note-0679-06" xlink:href="note-0679-06a" xml:space="preserve">1207. 1208.</note> </div> <p> <s xml:id="echoid-s17619" xml:space="preserve">In ſuperficiebus corporum ſphæricorum, homogeneorum, æ-<lb/> <anchor type="note" xlink:label="note-0679-07a" xlink:href="note-0679-07"/> qualium, gravitates eſſe ut corporum denſitates; </s> <s xml:id="echoid-s17620" xml:space="preserve">nam diſtan-<lb/>tiæ à centro ſunt æquales, in quo caſu gravitatis vires ſunt <lb/>ut quantitates materiæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17621" xml:space="preserve">quæ, in corporibus æqualibus, ſunt <anchor type="note" xlink:label="note-0679-08a" xlink:href="note-0679-08"/> ut denſitates <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17622" xml:space="preserve"> <anchor type="note" xlink:label="note-0679-09a" xlink:href="note-0679-09"/> </s> </p> <div xml:id="echoid-div2719" type="float" level="2" n="23"> <note position="right" xlink:label="note-0679-07" xlink:href="note-0679-07a" xml:space="preserve">1228.</note> <note symbol="*" position="right" xlink:label="note-0679-08" xlink:href="note-0679-08a" xml:space="preserve">1207.</note> <note symbol="*" position="right" xlink:label="note-0679-09" xlink:href="note-0679-09a" xml:space="preserve">288. 79.</note> </div> <p> <s xml:id="echoid-s17623" xml:space="preserve">In ſuperficiebus corporum ſphæricorum, inæqualium, ho-<lb/> <anchor type="note" xlink:label="note-0679-10a" xlink:href="note-0679-10"/> mogeneornm, æquè denſorum, gravitates ſunt inverſè, ut qua-<lb/>drata diametrorum <anchor type="note" xlink:href="" symbol="*"/>, quia in harum ratione ſunt diſtantiæ à <anchor type="note" xlink:label="note-0679-11a" xlink:href="note-0679-11"/> <pb o="(152)" file="0680" n="750" rhead="PHYSICES ELEMENTA"/> centris: </s> <s xml:id="echoid-s17624" xml:space="preserve">ſunt etiam gravitates directè ut diametrorum cubi <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s17625" xml:space="preserve"> <anchor type="note" xlink:label="note-0680-01a" xlink:href="note-0680-01"/> nam in hac ratione ſunt materiæ quantitates in ſphæris: </s> <s xml:id="echoid-s17626" xml:space="preserve">& </s> <s xml:id="echoid-s17627" xml:space="preserve"><lb/>ratio compoſita ex directà cuborum diametrorum, & </s> <s xml:id="echoid-s17628" xml:space="preserve">inver-<lb/>ſâ harum quadratorum, eſt directa ipſarum Diametrorum.</s> <s xml:id="echoid-s17629" xml:space="preserve"/> </p> <div xml:id="echoid-div2720" type="float" level="2" n="24"> <note position="right" xlink:label="note-0679-10" xlink:href="note-0679-10a" xml:space="preserve">1229.</note> <note symbol="*" position="right" xlink:label="note-0679-11" xlink:href="note-0679-11a" xml:space="preserve">1208.</note> <note symbol="*" position="left" xlink:label="note-0680-01" xlink:href="note-0680-01a" xml:space="preserve">1207.</note> </div> <p> <s xml:id="echoid-s17630" xml:space="preserve">Ideò, ſi & </s> <s xml:id="echoid-s17631" xml:space="preserve">denſitates & </s> <s xml:id="echoid-s17632" xml:space="preserve">diametri differant, gravitates in <lb/> <anchor type="note" xlink:label="note-0680-02a" xlink:href="note-0680-02"/> ſuperficiebus erunt in ratione compoſitâ denſitatum <anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s17633" xml:space="preserve">Dia- <anchor type="note" xlink:label="note-0680-03a" xlink:href="note-0680-03"/> metrorum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17634" xml:space="preserve">Idcirco diviſâ gravitate in ſuperficie, per dia- <anchor type="note" xlink:label="note-0680-04a" xlink:href="note-0680-04"/> metrum, detegitur denſitas; </s> <s xml:id="echoid-s17635" xml:space="preserve">quæ ergo ſequitur rationem di-<lb/> <anchor type="note" xlink:label="note-0680-05a" xlink:href="note-0680-05"/> rectam gravitatis in ſuperficie & </s> <s xml:id="echoid-s17636" xml:space="preserve">inverſam diametri.</s> <s xml:id="echoid-s17637" xml:space="preserve"/> </p> <div xml:id="echoid-div2721" type="float" level="2" n="25"> <note position="left" xlink:label="note-0680-02" xlink:href="note-0680-02a" xml:space="preserve">1230.</note> <note symbol="*" position="left" xlink:label="note-0680-03" xlink:href="note-0680-03a" xml:space="preserve">1228.</note> <note symbol="*" position="left" xlink:label="note-0680-04" xlink:href="note-0680-04a" xml:space="preserve">1229.</note> <note position="left" xlink:label="note-0680-05" xlink:href="note-0680-05a" xml:space="preserve">1231.</note> </div> <p> <s xml:id="echoid-s17638" xml:space="preserve">In ſphærâ homogeneâ, cavâ, ubique ejuſdem craſſitiei cor-<lb/> <anchor type="note" xlink:label="note-0680-06a" xlink:href="note-0680-06"/> pus ubicunque poſitum nullam gravitatem habet, gravitati-<lb/>bus oppoſitis ſeſe mutuo exactè deſtruentibus: </s> <s xml:id="echoid-s17639" xml:space="preserve">Unde ſequi-<lb/>tur, in ſphærâ homogeneâ, corpus accedendo ad centrum, <lb/> <anchor type="note" xlink:label="note-0680-07a" xlink:href="note-0680-07"/> verſus centrum gravitare ex ſolâ actione ſphæræ, cujus ſemi-<lb/>diameter eſt diſtantia corporis à centro, quæ gravitas de-<lb/>creſcit, accedendo ad centrum, in ratione diſtantiæ à cen-<lb/>tro <anchor type="note" xlink:href="" symbol="*"/>, nam omnis materia, quæ ad majorem à centro diſtan- <anchor type="note" xlink:label="note-0680-08a" xlink:href="note-0680-08"/> tiam datur, ſphæram cavam format, in qua actiones in cor-<lb/>pus ſeſe mutuo deſtruunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17640" xml:space="preserve"> <anchor type="note" xlink:label="note-0680-09a" xlink:href="note-0680-09"/> </s> </p> <div xml:id="echoid-div2722" type="float" level="2" n="26"> <note position="left" xlink:label="note-0680-06" xlink:href="note-0680-06a" xml:space="preserve">1232.</note> <note position="left" xlink:label="note-0680-07" xlink:href="note-0680-07a" xml:space="preserve">1233.</note> <note symbol="*" position="left" xlink:label="note-0680-08" xlink:href="note-0680-08a" xml:space="preserve">1229.</note> <note symbol="*" position="left" xlink:label="note-0680-09" xlink:href="note-0680-09a" xml:space="preserve">1232.</note> </div> <p> <s xml:id="echoid-s17641" xml:space="preserve">Gravitatem huc uſque, explicatam pro lege naturæ eſſe <lb/>habendam diximus, quia hujus cauſa nos latet, & </s> <s xml:id="echoid-s17642" xml:space="preserve">quia mi-<lb/>nimè pendet ab ullâ lege nobis notâ; </s> <s xml:id="echoid-s17643" xml:space="preserve">quod clarè patebit, ſi <lb/>ad ſequentia attendamus.</s> <s xml:id="echoid-s17644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17645" xml:space="preserve">Gravitatem requirere præſentiam corporis attrahentis; <lb/></s> <s xml:id="echoid-s17646" xml:space="preserve"> <anchor type="note" xlink:label="note-0680-10a" xlink:href="note-0680-10"/> ſic Satellites, ex gr. </s> <s xml:id="echoid-s17647" xml:space="preserve">Jovis, in Jovem gravitant, ubicunque <lb/>hic detur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17648" xml:space="preserve"/> </p> <div xml:id="echoid-div2723" type="float" level="2" n="27"> <note position="left" xlink:label="note-0680-10" xlink:href="note-0680-10a" xml:space="preserve">1234.</note> </div> <note symbol="*" position="left" xml:space="preserve">1212.</note> <p style="it"> <s xml:id="echoid-s17649" xml:space="preserve">Manente diſtantia, celeritatem, qua corpora ex gravitate <lb/> <anchor type="note" xlink:label="note-0680-12a" xlink:href="note-0680-12"/> feruntur, pendêre à quantitate materiæ in corpore attrahen-<lb/> <anchor type="note" xlink:label="note-0680-13a" xlink:href="note-0680-13"/> te <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17650" xml:space="preserve">Et celeritatem non variari, quæcunque fuerit maſſa cor- <anchor type="note" xlink:label="note-0680-14a" xlink:href="note-0680-14"/> poris gravitantis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17651" xml:space="preserve"> <anchor type="note" xlink:label="note-0680-15a" xlink:href="note-0680-15"/> </s> </p> <div xml:id="echoid-div2724" type="float" level="2" n="28"> <note position="left" xlink:label="note-0680-12" xlink:href="note-0680-12a" xml:space="preserve">1235.</note> <note symbol="*" position="left" xlink:label="note-0680-13" xlink:href="note-0680-13a" xml:space="preserve">1207.</note> <note position="left" xlink:label="note-0680-14" xlink:href="note-0680-14a" xml:space="preserve">1236.</note> <note symbol="*" position="left" xlink:label="note-0680-15" xlink:href="note-0680-15a" xml:space="preserve">1207.</note> </div> <p> <s xml:id="echoid-s17652" xml:space="preserve">Ulterius, ſi gravitas pendeat à lege motus notâ, ad impa-<lb/> <anchor type="note" xlink:label="note-0680-16a" xlink:href="note-0680-16"/> ctum corporis extranei referri debere, & </s> <s xml:id="echoid-s17653" xml:space="preserve">quia gravitas eſt <lb/>continua, impactum etiam continuum requiri.</s> <s xml:id="echoid-s17654" xml:space="preserve"/> </p> <div xml:id="echoid-div2725" type="float" level="2" n="29"> <note position="left" xlink:label="note-0680-16" xlink:href="note-0680-16a" xml:space="preserve">1237.</note> </div> <p> <s xml:id="echoid-s17655" xml:space="preserve">Si talis materia continuò in corpora impingens detur, ne-<lb/>ceſſario eſt fluida, & </s> <s xml:id="echoid-s17656" xml:space="preserve">quidem ſubtiliſſima, quæ penetrat cor-<lb/>pora quæcunque; </s> <s xml:id="echoid-s17657" xml:space="preserve">corpora enim in aliis utcunque incluſa <lb/>gravia ſunt.</s> <s xml:id="echoid-s17658" xml:space="preserve"/> </p> <pb o="(153)" file="0681" n="751" rhead="MATHEMATICA LIB. IV. CAP. XI."/> <p> <s xml:id="echoid-s17659" xml:space="preserve">Videat nunc Mathematicus, an fluidum adeo ſubtile, ut <lb/>corporum omnium poros liberrimè permeèt, & </s> <s xml:id="echoid-s17660" xml:space="preserve">adeò ra-<lb/>rum, ut motui corporum ſenſibiliter non obſtet, (in loco <lb/>enim aëre vacuo penduli motus diutiſſimè continuatur) cor-<lb/>pora ingentia tantâ cum vi ad ſe mutuo poſſit propellere? <lb/></s> <s xml:id="echoid-s17661" xml:space="preserve">Explicet quomodo hæc actio creſcat in ratione maſſæ corpo-<lb/>ris verſus quod aliud fertur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17662" xml:space="preserve">Tandem, quod omnium <anchor type="note" xlink:label="note-0681-01a" xlink:href="note-0681-01"/> mihi difficillimum videtur, dicat, quomodo omnia corpo-<lb/>ra, in quocunque ſitu, eâdem manente diſtantiâ, & </s> <s xml:id="echoid-s17663" xml:space="preserve">cor-<lb/>pore verſus quod gravitas datur, eadem velocitate feran-<lb/>tur <anchor type="note" xlink:href="" symbol="*"/>, id eſt, quomodo liquidum, quod niſi in ſuperfi- <anchor type="note" xlink:label="note-0681-02a" xlink:href="note-0681-02"/> cies, ſive ipſorum corporum, ſive illarum internarum par-<lb/>ticularum, ad quas acceſſus ex interpoſitis particulis non im-<lb/>peditur, actionem ſuam exerere non poteſt, communicet <lb/>corporibus motus quantitatem, quæ in omnibus corporibus <lb/>exactiſſimè ſequatur proportionem quantitatis materiæ in his, <lb/>quod in gravitate ubique obtineri, hoc capite probavimus, <lb/>& </s> <s xml:id="echoid-s17664" xml:space="preserve">quod directo experimento demonſtravimus reſpectu gra-<lb/>vitatis in Telluris viciniis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17665" xml:space="preserve"> <anchor type="note" xlink:label="note-0681-03a" xlink:href="note-0681-03"/> </s> </p> <div xml:id="echoid-div2726" type="float" level="2" n="30"> <note symbol="*" position="right" xlink:label="note-0681-01" xlink:href="note-0681-01a" xml:space="preserve">1235.</note> <note symbol="*" position="right" xlink:label="note-0681-02" xlink:href="note-0681-02a" xml:space="preserve">1236.</note> <note symbol="*" position="right" xlink:label="note-0681-03" xlink:href="note-0681-03a" xml:space="preserve">77.</note> </div> <p> <s xml:id="echoid-s17666" xml:space="preserve">Non tamen negamus, ab ullo impactu pendere gravita-<lb/> <anchor type="note" xlink:label="note-0681-04a" xlink:href="note-0681-04"/> tem, ſed illam non ſequi ex ullo impactu, juxta leges nobis <lb/>notas, clare patêre contendimus, gravitatiſque cauſam nos <lb/>omnino latêre fatemur.</s> <s xml:id="echoid-s17667" xml:space="preserve"/> </p> <div xml:id="echoid-div2727" type="float" level="2" n="31"> <note position="right" xlink:label="note-0681-04" xlink:href="note-0681-04a" xml:space="preserve">1238.</note> </div> </div> <div xml:id="echoid-div2729" type="section" level="1" n="672"> <head xml:id="echoid-head869" xml:space="preserve">CAPUT XII.</head> <head xml:id="echoid-head870" style="it" xml:space="preserve">De Materiâ Cœleſti; ubi Vacuum dari probatur.</head> <p> <s xml:id="echoid-s17668" xml:space="preserve">EXpoſitis legibus, quibus totum Syſtema Planetarium regi-<lb/>tur, varia præmittenda erunt, antequam ad ipſius Syſte-<lb/>matis explicationem Phyſicam accedamus. </s> <s xml:id="echoid-s17669" xml:space="preserve">De Materiâ cœ <lb/>leſti, id eſt de medio, in quibus corpora Syſtema compo-<lb/>nentia moventur, ante omnia quædam dicenda ſunt, quod <lb/>paucis fieri poſſet, ſi inter omnes conſtaret Philoſophos, in <lb/>rebus inane dari.</s> <s xml:id="echoid-s17670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17671" xml:space="preserve">Probavimus antea vacuum poſſibile eſſe <anchor type="note" xlink:href="" symbol="*"/>, nunc illud re- <anchor type="note" xlink:label="note-0681-05a" xlink:href="note-0681-05"/> verâ dari demonſtrandum nobis eſt.</s> <s xml:id="echoid-s17672" xml:space="preserve"/> </p> <div xml:id="echoid-div2729" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0681-05" xlink:href="note-0681-05a" xml:space="preserve">13.</note> </div> <p> <s xml:id="echoid-s17673" xml:space="preserve">Ex ſolâ motus conſideratione, vacuum dari deducitur, quod <lb/> <anchor type="note" xlink:label="note-0681-06a" xlink:href="note-0681-06"/> <pb o="(154)" file="0682" n="752" rhead="PHYSICES ELEMENTA"/> tritum & </s> <s xml:id="echoid-s17674" xml:space="preserve">vulgare admodum eſt argumentum, cujus vis ut pa-<lb/>teat, conſiderandum, non quidem omnes motus ſine vacuo <lb/>impoſſibiles eſſe, ſed pleroſque illorum, qui quotidie obſer-<lb/>vantur, quod longiori diſcuſſione pleniſſimè poſſe evinci, per-<lb/>ſuaſum habeo; </s> <s xml:id="echoid-s17675" xml:space="preserve">ſed ſequenti conſideratione ita clarè patêre <lb/>mihi videtur, ut plura addere inutile foret.</s> <s xml:id="echoid-s17676" xml:space="preserve"/> </p> <div xml:id="echoid-div2730" type="float" level="2" n="2"> <note position="right" xlink:label="note-0681-06" xlink:href="note-0681-06a" xml:space="preserve">1239.</note> </div> <p> <s xml:id="echoid-s17677" xml:space="preserve">Non mutabilem figuram habent particulæ omnium minimæ; <lb/></s> <s xml:id="echoid-s17678" xml:space="preserve">nam conſtat particula, cujus figura mutatur, ex particulis <lb/>minoribus, quæ inter ſe moventur, & </s> <s xml:id="echoid-s17679" xml:space="preserve">ideò, ſi figuram mu-<lb/>tabilem habet, non eſt ex particulis omnium minimis.</s> <s xml:id="echoid-s17680" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17681" xml:space="preserve">Si autem figura harum particularum ſit immutabilis, & </s> <s xml:id="echoid-s17682" xml:space="preserve"><lb/>corpus inter has poſſit moveri, ſine tali ſeparatione particula-<lb/>rum, quæ interſtitium vacuum relinquit, pendebit hoc à fi-<lb/>gurâ particularum, & </s> <s xml:id="echoid-s17683" xml:space="preserve">à relatione, quam habent inter ſe, quod <lb/>Mathematicus non negabit: </s> <s xml:id="echoid-s17684" xml:space="preserve">idcirco ſi hiſce ſervatis (figurâ & </s> <s xml:id="echoid-s17685" xml:space="preserve"><lb/>relatione) augeantur particulæ, & </s> <s xml:id="echoid-s17686" xml:space="preserve">in hoc caſu corpora ſine <lb/>vacuo moveri poterunt.</s> <s xml:id="echoid-s17687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17688" xml:space="preserve">Videat nunc quis, auctis particulis minimis, ut magnitu-<lb/>dine pedem cubicum æquent, quæcunque fuerit harum fi-<lb/>gura, & </s> <s xml:id="echoid-s17689" xml:space="preserve">cum cæteris particulis relatio, quas, in eadem ra-<lb/>tione, cum primis auctas ponimus, utrum corpora magnitu-<lb/>dinis cujuſcunque, inter has particulas poſſint ferri per rectas <lb/>lineas, & </s> <s xml:id="echoid-s17690" xml:space="preserve">per curvas quaſcunque, nunquam ſeparatis parti-<lb/>culis, ut ſpatia vacua inter has dentur.</s> <s xml:id="echoid-s17691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17692" xml:space="preserve">Particulas ſubtiliſſimas conceptu non aſſequimur, & </s> <s xml:id="echoid-s17693" xml:space="preserve">ideò <lb/>ſæpè his tribuimus proprietates, quæ ex harum figurâ non ſe-<lb/>quuntur, qui corriguntur errores, ſi particulas auctas ima-<lb/>ginemur.</s> <s xml:id="echoid-s17694" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17695" xml:space="preserve">Etiam argumento, ex reſiſtentiâ deducto, vacuum dari <lb/> <anchor type="note" xlink:label="note-0682-01a" xlink:href="note-0682-01"/> probamus.</s> <s xml:id="echoid-s17696" xml:space="preserve"/> </p> <div xml:id="echoid-div2731" type="float" level="2" n="3"> <note position="left" xlink:label="note-0682-01" xlink:href="note-0682-01a" xml:space="preserve">1240.</note> </div> <p> <s xml:id="echoid-s17697" xml:space="preserve">Materiam inertem eſſe diximus <anchor type="note" xlink:href="" symbol="*"/>, circa vocem quidam <anchor type="note" xlink:label="note-0682-02a" xlink:href="note-0682-02"/> contendunt, rem ipſam nemo negat; </s> <s xml:id="echoid-s17698" xml:space="preserve">Ex hac ſequitur, non <lb/>poſſe per fluidum corpus moveri, quin patiatur reſiſtentiam <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0682-03a" xlink:href="note-0682-03"/> ideoque retardationem <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17699" xml:space="preserve">Reſiſtentia ex materiæ inertiâ, <anchor type="note" xlink:label="note-0682-04a" xlink:href="note-0682-04"/> quam hic ſolam conſideramus, pendet à materiæ quantitate <lb/>ex loco removendæ, quæ eadem eſt, ſive partes fluidi ſint <lb/>majores, ſive minores, ſi corporis celeritas maneat: </s> <s xml:id="echoid-s17700" xml:space="preserve">unde ſe- <pb o="(155)" file="0683" n="753" rhead="MATHEMATICA LIB. IV. CAP. XII."/> quitur, in determinandis, quæ reſiſtentiam ſpectant, ad ſub-<lb/>tilitatem fluidi non eſſe attendendum, quamdiu hoc poros <lb/>corporum permeare non poteſt; </s> <s xml:id="echoid-s17701" xml:space="preserve">ſi enim ad illam pervenia-<lb/>mus partium tenuitatem, ut fluidum pro parte per corpus <lb/>penetret, corpori minori copiâ reſiſtet.</s> <s xml:id="echoid-s17702" xml:space="preserve"/> </p> <div xml:id="echoid-div2732" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0682-02" xlink:href="note-0682-02a" xml:space="preserve">12.</note> <note symbol="*" position="left" xlink:label="note-0682-03" xlink:href="note-0682-03a" xml:space="preserve">319.</note> <note symbol="*" position="left" xlink:label="note-0682-04" xlink:href="note-0682-04a" xml:space="preserve">330.</note> </div> <p> <s xml:id="echoid-s17703" xml:space="preserve">Concipiamus nunc Globum quemcunque, per medium e-<lb/>juſdem denſitatis cum globo, tranſlatum, & </s> <s xml:id="echoid-s17704" xml:space="preserve">cui per corpo-<lb/>ris poros tranſitus non patet; </s> <s xml:id="echoid-s17705" xml:space="preserve">omnibus momentis retarda-<lb/>tur, ita ut ejus velocitas tandem ad dimidium reducatur; <lb/></s> <s xml:id="echoid-s17706" xml:space="preserve">quod fieri, mathematicâ demonſtratione conſtat, antequam <lb/>corpus bis diametri longitudinem percurrat.</s> <s xml:id="echoid-s17707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17708" xml:space="preserve">Ut propoſitionem hanc ad motum in fluido ſubtiliſſimo, <lb/>omnium corporum poros liberrimè penetranti, & </s> <s xml:id="echoid-s17709" xml:space="preserve">omnia re-<lb/>plente, applicare poſſimus, concipiendum eſt, corpus ſphæ-<lb/>ricum, ſine poris, quod dari poſſe, intimè jungendo par-<lb/>ticulas materiæ, nemo inficias ibit.</s> <s xml:id="echoid-s17710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17711" xml:space="preserve">Talis corporis reſiſtentiam, in fluido quocunque, à magni-<lb/>tudine partium fluidi non pendere, & </s> <s xml:id="echoid-s17712" xml:space="preserve">eandem eſſe, ſive fluidi <lb/>partes ſint æquales, ſive utcunque inæquales inter ſe, patet.</s> <s xml:id="echoid-s17713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17714" xml:space="preserve">Si omnia ſint materiâ plena, niſi per fluidum, ejuſdem <lb/>denſitatis cum hoc corpore, poterit hoc moveri; </s> <s xml:id="echoid-s17715" xml:space="preserve">nam in-<lb/>currit in omnem materiam, quæ datur in locis, per quæ tran-<lb/>ſit, & </s> <s xml:id="echoid-s17716" xml:space="preserve">in his materia ſine interſtitiis, ut in corpore, datur; </s> <s xml:id="echoid-s17717" xml:space="preserve">id-<lb/>circo amittet dimidium velocitatis, antequam duarum dia-<lb/>metrorum ſuarum longitudinem percurrat.</s> <s xml:id="echoid-s17718" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17719" xml:space="preserve">Augeatur corpus manente materiæ quantitate, & </s> <s xml:id="echoid-s17720" xml:space="preserve">ſervato <lb/>hoc homogeneo; </s> <s xml:id="echoid-s17721" xml:space="preserve">id eſt, dentur pori in corpore, per quos <lb/>materiæ partes ſubſtiliſſimæ liberrimè tranſeant, & </s> <s xml:id="echoid-s17722" xml:space="preserve">ſint hi <lb/>pori æqualiter per totum corpus diſperſi. </s> <s xml:id="echoid-s17723" xml:space="preserve">Si corpus ſic mu-<lb/>tatum moveatur, non in totam ſuperficiem incurrit fluidum <lb/>ſubtiliſſimum de quo agimus, ſed tantùm in partes ſuperfi-<lb/>ciei, quæ poros interjacent, quæ partes ſimul ſumtæ, quia <lb/>corpus homogeneum ponimus, valent ſuperficiem corporis in <lb/>conſtitutione primâ, ſine poris; </s> <s xml:id="echoid-s17724" xml:space="preserve">Aucto enim corpore, ſuperfi-<lb/>cies non fuit mutata, ſed tantùm dilatata, interjectis poris: <lb/></s> <s xml:id="echoid-s17725" xml:space="preserve">ita ut corpus in utroque caſu eandem patiatur reſiſtentiam, <lb/>ex impactu in ſuperficiem; </s> <s xml:id="echoid-s17726" xml:space="preserve">& </s> <s xml:id="echoid-s17727" xml:space="preserve">reſiſtentia in corpore dilatato <pb o="156" file="0684" n="754" rhead="PHYSICES ELEMENTA"/> major eſt ex incurſu fluidi in particulas internas corporis: <lb/></s> <s xml:id="echoid-s17728" xml:space="preserve">quare corpus hoc citius dimidium ſui motus in ſecundo, quàm <lb/>in primo caſu, amittet; </s> <s xml:id="echoid-s17729" xml:space="preserve">id eſt, antequam duas diametros pri-<lb/>mæ magnitudinis percurrat; </s> <s xml:id="echoid-s17730" xml:space="preserve">& </s> <s xml:id="echoid-s17731" xml:space="preserve">ideò majorem motus quanti-<lb/>tatem amittit, dum per duas diametros ſecundæ magnitudi-<lb/>nis tranfertur.</s> <s xml:id="echoid-s17732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17733" xml:space="preserve">Hoc autem experientiæ adverſatur; </s> <s xml:id="echoid-s17734" xml:space="preserve">nam globus homo-<lb/>geneus, aureus, plumbeus, &</s> <s xml:id="echoid-s17735" xml:space="preserve">c. </s> <s xml:id="echoid-s17736" xml:space="preserve">quantitatem motus multò <lb/>minorem in aquâ & </s> <s xml:id="echoid-s17737" xml:space="preserve">aëre amittit; </s> <s xml:id="echoid-s17738" xml:space="preserve">unde ſequitur hypoteſin, <lb/>omnia materiâ repleri, falſam eſſe. </s> <s xml:id="echoid-s17739" xml:space="preserve">Vacuum ergo datur.</s> <s xml:id="echoid-s17740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17741" xml:space="preserve">Vacuum dari etiam cum Phænomenis circa gravitatem con-<lb/> <anchor type="note" xlink:label="note-0684-01a" xlink:href="note-0684-01"/> gruit, ex quibus ſequitur, hanc materiæ quantitati propor-<lb/>tionalem eſſe. </s> <s xml:id="echoid-s17742" xml:space="preserve">Si omnia materiâ replentur, gravitas verſus <lb/>omnes partes æqualis datur, & </s> <s xml:id="echoid-s17743" xml:space="preserve">vires quæ verſus partes oppo-<lb/>ſitas diriguntur, ſeſe mutuo deſtruunt, & </s> <s xml:id="echoid-s17744" xml:space="preserve">nulla ſenſibilis <lb/>gravitas obſervari poteſt, quod experientiæ adverſatur.</s> <s xml:id="echoid-s17745" xml:space="preserve"/> </p> <div xml:id="echoid-div2733" type="float" level="2" n="5"> <note position="left" xlink:label="note-0684-01" xlink:href="note-0684-01a" xml:space="preserve">1241.</note> </div> <p> <s xml:id="echoid-s17746" xml:space="preserve">Hiſce præmiſſis ad Materiam coeleſtem tranſeundum.</s> <s xml:id="echoid-s17747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17748" xml:space="preserve">A motu Materiæ coeleſtis, ſi quædam detur, non pen-<lb/>dent corporum coeleſtium motus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17749" xml:space="preserve">quo corruit illorum ſen- <anchor type="note" xlink:label="note-0684-02a" xlink:href="note-0684-02"/> tentia, qui motu communi cum materiâ, quæ Syſtema Plane-<lb/> <anchor type="note" xlink:label="note-0684-03a" xlink:href="note-0684-03"/> tarium replet, corpora cæleſtia tranſlata contendunt. </s> <s xml:id="echoid-s17750" xml:space="preserve">Quæ <lb/>etiam motu Cometarum evertitur ſententia; </s> <s xml:id="echoid-s17751" xml:space="preserve">ſi medium in <lb/>Syſtemate daretur, quod in motu ſuo Planetas ſecum fert, <lb/>& </s> <s xml:id="echoid-s17752" xml:space="preserve">etiam ſecum traheret Cometas, ſaltem ſenſibiliter hos in <lb/>motu turbaret, dum ferè directè ad Solem accedunt, aut ab <lb/>hoc recedunt, aut in antecedentia moventur, id eſt, motu <lb/>contrario motui talis materiæ; </s> <s xml:id="echoid-s17753" xml:space="preserve">qui motus cùm non turbari, & </s> <s xml:id="echoid-s17754" xml:space="preserve"><lb/>ſequi viam quæ à gravitate pendet, obſerventur, clarum eſt, <lb/>Materiam coeleſtem, ſi detur & </s> <s xml:id="echoid-s17755" xml:space="preserve">movetur, ſenſibilem in corpo-<lb/>ra Syſtematis Planetariinon exerere actionem; </s> <s xml:id="echoid-s17756" xml:space="preserve">quod etiam ex <lb/>parvâ hujus reſiſtentiâ deducitur; </s> <s xml:id="echoid-s17757" xml:space="preserve">nam, ex collatis antiquiſ-<lb/>ſimis cum recentioribus obſervationibus ſenſibiliter in moti-<lb/>bus non retardatos Planetas conſtat. </s> <s xml:id="echoid-s17758" xml:space="preserve">Reſiſtentia tamen in <lb/>aëre ſenſibilis eſt, quare denſitas medii in quo Planetæ mo-<lb/>verentur ferè in immenſum minor eſt, idcirco, niſi tali me-<lb/> <anchor type="note" xlink:label="note-0684-04a" xlink:href="note-0684-04"/> dio ſubtiliſſimo, non repletur Syſtema Planetarium.</s> <s xml:id="echoid-s17759" xml:space="preserve"/> </p> <div xml:id="echoid-div2734" type="float" level="2" n="6"> <note position="left" xlink:label="note-0684-02" xlink:href="note-0684-02a" xml:space="preserve">1242.</note> <note symbol="*" position="left" xlink:label="note-0684-03" xlink:href="note-0684-03a" xml:space="preserve">1238</note> <note position="left" xlink:label="note-0684-04" xlink:href="note-0684-04a" xml:space="preserve">1243.</note> </div> <p> <s xml:id="echoid-s17760" xml:space="preserve">Materiæ verò quantitatem, quantumvis exiguam, per totum <pb o="157" file="0685" n="755" rhead="MATHEMATICA LIB. IV. CAP. XIII."/> Syſtema poſſe diſpergi, relictis interſtitiis minimis, ex ma-<lb/>teriæ diviſibilitate, deducitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17761" xml:space="preserve"> <anchor type="note" xlink:label="note-0685-01a" xlink:href="note-0685-01"/> </s> </p> <div xml:id="echoid-div2735" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0685-01" xlink:href="note-0685-01a" xml:space="preserve">26.</note> </div> </div> <div xml:id="echoid-div2737" type="section" level="1" n="673"> <head xml:id="echoid-head871" xml:space="preserve">CAPUT XIII.</head> <head xml:id="echoid-head872" xml:space="preserve">De Motu Telluris.</head> <p> <s xml:id="echoid-s17762" xml:space="preserve">PRæter in Capite præcedenti diſcuſſam quæſtionem, & </s> <s xml:id="echoid-s17763" xml:space="preserve">a-<lb/>lia datur examinanda, antequam ad totius Syſtematis ex-<lb/>plicationem accedamus.</s> <s xml:id="echoid-s17764" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17765" xml:space="preserve">Ut nullum dubium ſuperſit circa Syſtema, in primo capite <lb/>hujus libri explicatum, probandus nobis hìc eſt Telluris mo-<lb/>tus, de quo non mirum ſi plures dubitaverint; </s> <s xml:id="echoid-s17766" xml:space="preserve">nullis enim, <lb/>niſi à ſpectatoribus in Tellure inſtitutis, obſervationibus, <lb/>motus coeleſtes à nobis determinari queunt, & </s> <s xml:id="echoid-s17767" xml:space="preserve">eadem Phoe-<lb/>nomena apparent, ſive corpora ipſa transferantur, ſive ſpecta-<lb/>tor moveatur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17768" xml:space="preserve">ita ut immediatis obſervationibus non conſtet, <anchor type="note" xlink:label="note-0685-02a" xlink:href="note-0685-02"/> utrum motus Telluris ad corpora coeleſtia non referri debeat.</s> <s xml:id="echoid-s17769" xml:space="preserve"/> </p> <div xml:id="echoid-div2737" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0685-02" xlink:href="note-0685-02a" xml:space="preserve">993.</note> </div> <p style="it"> <s xml:id="echoid-s17770" xml:space="preserve">Tellurem circa Solem circumferri, ex motuum analogiâ <lb/> <anchor type="note" xlink:label="note-0685-03a" xlink:href="note-0685-03"/> deducitur, & </s> <s xml:id="echoid-s17771" xml:space="preserve">ex examine legum naturæ demonſtratur.</s> <s xml:id="echoid-s17772" xml:space="preserve"/> </p> <div xml:id="echoid-div2738" type="float" level="2" n="2"> <note position="right" xlink:label="note-0685-03" xlink:href="note-0685-03a" xml:space="preserve">1244.</note> </div> <p> <s xml:id="echoid-s17773" xml:space="preserve">Quod motuum analogiam ſpectat, notandum, circa Jo-<lb/>vem & </s> <s xml:id="echoid-s17774" xml:space="preserve">Saturnum rotari Satellites corpore centrali minores; <lb/></s> <s xml:id="echoid-s17775" xml:space="preserve">Circa Tellurem Luna, Tellure minor, revolvitur; </s> <s xml:id="echoid-s17776" xml:space="preserve">Tandem <lb/>circa Solem girantur corpora minora Mercurius, Venus, <lb/>Mars, Jupiter, & </s> <s xml:id="echoid-s17777" xml:space="preserve">Saturnus; </s> <s xml:id="echoid-s17778" xml:space="preserve">Si cum his Telius rotetur, ubique <lb/>in Syſtemate noſtro corpora minora circa majora moventur; </s> <s xml:id="echoid-s17779" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0685-04a" xlink:href="note-0685-04"/> in hac autem regulâ exceptio dabitur reſpectu Solis, ſi ingens <lb/>hoc corpus, in motu, minimam Telluris maſſam <anchor type="note" xlink:href="" symbol="*"/> cingat.</s> <s xml:id="echoid-s17780" xml:space="preserve"/> </p> <div xml:id="echoid-div2739" type="float" level="2" n="3"> <note position="right" xlink:label="note-0685-04" xlink:href="note-0685-04a" xml:space="preserve">1245.</note> </div> <note symbol="*" position="right" xml:space="preserve">975.</note> <p> <s xml:id="echoid-s17781" xml:space="preserve">Circa Solem, Jovem, & </s> <s xml:id="echoid-s17782" xml:space="preserve">Saturnum, circa quos ſingulos <lb/>plurima corpora revolvuntur, lentius moventur, quæ magis à <lb/>corpore centrali diſtant, & </s> <s xml:id="echoid-s17783" xml:space="preserve">quidem juxta hanc regulam, qua-<lb/> <anchor type="note" xlink:label="note-0685-06a" xlink:href="note-0685-06"/> drata temporum periodicorum ſequi rationem cuborum di-<lb/>ſtantiarum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17784" xml:space="preserve">quæ regula applicari poteſt Telluri, ſi hæc <anchor type="note" xlink:label="note-0685-07a" xlink:href="note-0685-07"/> cum cæteris Planetis circa Solem circumferatur, ut patet, <lb/>ſi illius tempus periodicum, (tempus nempe in quo Sol in-<lb/>tegram revolutionem peragere videtur,) ut & </s> <s xml:id="echoid-s17785" xml:space="preserve">diſtantia à <lb/>Sole, cum cæterorum Planetarum diſtantiis & </s> <s xml:id="echoid-s17786" xml:space="preserve">temporibus <lb/>periodicis, conferantur.</s> <s xml:id="echoid-s17787" xml:space="preserve"/> </p> <div xml:id="echoid-div2740" type="float" level="2" n="4"> <note position="right" xlink:label="note-0685-06" xlink:href="note-0685-06a" xml:space="preserve">1246.</note> <note symbol="*" position="right" xlink:label="note-0685-07" xlink:href="note-0685-07a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s17788" xml:space="preserve">Vnicam autem patitur exceptionem regula hæc, ſi, Sole <pb o="158" file="0686" n="756" rhead="PHYSICES ELEMENTA"/> translato, Tellus quieſcat. </s> <s xml:id="echoid-s17789" xml:space="preserve">In hoc caſu Mercurius, Venus, <lb/>Mars, Jupiter, & </s> <s xml:id="echoid-s17790" xml:space="preserve">Saturnus, huic regulæ in motibus ſubji-<lb/>ciuntur, ut & </s> <s xml:id="echoid-s17791" xml:space="preserve">quinque Satellites Saturni, & </s> <s xml:id="echoid-s17792" xml:space="preserve">quatuor Jovia-<lb/>les Planetæ ſola Luna cum Sole, circa Tellurem, propor-<lb/>tionem omnino diverſam ſervant, & </s> <s xml:id="echoid-s17793" xml:space="preserve">non modo celeritas So-<lb/>lis major eſt, quàm quæ ex hac regulà requiritur, ſed & </s> <s xml:id="echoid-s17794" xml:space="preserve">ve-<lb/>locitate ad minimum vicies & </s> <s xml:id="echoid-s17795" xml:space="preserve">ſexies Lunam vincit, licèt ad <lb/>diſtantiam maximam, reſpectu Lunæ diſtantiæ, à Tellure re-<lb/>moveatur: </s> <s xml:id="echoid-s17796" xml:space="preserve">ita ut & </s> <s xml:id="echoid-s17797" xml:space="preserve">hoc reſpectu motuum coeleſtium analo-<lb/>gia turbetur.</s> <s xml:id="echoid-s17798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17799" xml:space="preserve">Hiſce argumentis alia addam, quibus, motum Telluris <lb/>ſequelam eſſe neceſſariam Legum naturæ, ex Phoenomenis <lb/>deductarum, clarè patebit.</s> <s xml:id="echoid-s17800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17801" xml:space="preserve">Omnia corpora in ſe mutuo gravia ſunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17802" xml:space="preserve">ideòque Sol <anchor type="note" xlink:label="note-0686-01a" xlink:href="note-0686-01"/> & </s> <s xml:id="echoid-s17803" xml:space="preserve">Tellus; </s> <s xml:id="echoid-s17804" xml:space="preserve">ſed motus, quo hæc duo corpora verſus ſe mutuo <lb/> <anchor type="note" xlink:label="note-0686-02a" xlink:href="note-0686-02"/> feruntur, ex directis obſervationibus deducitur. </s> <s xml:id="echoid-s17805" xml:space="preserve">Quodcun-<lb/>que horum corporum circa aliud moveatur, deſcribit areas, <lb/>lineis ad centrum hujus ductis, temporibus proportionales, <lb/>quod ex obſervationibus Aſtronomicis conſtat; </s> <s xml:id="echoid-s17806" xml:space="preserve">idcirco in <lb/>curvâ retinetur corpus motum, per vim, quæ ad aliûs cen-<lb/>trum dirigitur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17807" xml:space="preserve">Cùm autem actioni ſemper æqualis ſit re- <anchor type="note" xlink:label="note-0686-03a" xlink:href="note-0686-03"/> actio <anchor type="note" xlink:href="" symbol="*"/>, niſi Natur æ leges, quæ ubique conſtanter locum ba- <anchor type="note" xlink:label="note-0686-04a" xlink:href="note-0686-04"/> bent, in totum evertantur, duo hæc corpora motibus æqua-<lb/>libus ſeſe mutuo petunt, id eſt celeritatibus, quæ ſunt inver-<lb/>ſè ut horum maſſæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17808" xml:space="preserve">quod etiam ex lege gravitatis imme- <anchor type="note" xlink:label="note-0686-05a" xlink:href="note-0686-05"/> diatè deducitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17809" xml:space="preserve"> <anchor type="note" xlink:label="note-0686-06a" xlink:href="note-0686-06"/> </s> </p> <div xml:id="echoid-div2741" type="float" level="2" n="5"> <note position="left" xlink:label="note-0686-01" xlink:href="note-0686-01a" xml:space="preserve">1247.</note> <note symbol="*" position="left" xlink:label="note-0686-02" xlink:href="note-0686-02a" xml:space="preserve">1206.</note> <note symbol="*" position="left" xlink:label="note-0686-03" xlink:href="note-0686-03a" xml:space="preserve">226.</note> <note symbol="*" position="left" xlink:label="note-0686-04" xlink:href="note-0686-04a" xml:space="preserve">126.</note> <note symbol="*" position="left" xlink:label="note-0686-05" xlink:href="note-0686-05a" xml:space="preserve">65.</note> <note symbol="*" position="left" xlink:label="note-0686-06" xlink:href="note-0686-06a" xml:space="preserve">1235.</note> </div> <p> <s xml:id="echoid-s17810" xml:space="preserve">Materiæ quantitas in Tellure ferè nulla eſt reſpectu quanti-<lb/>tatis materiæ in Sole, ut in Capite ſequenti videbimus; </s> <s xml:id="echoid-s17811" xml:space="preserve">quare <lb/>hic lentiſſimè movetur, dum celerrimè ad hunc accedit Tellus.</s> <s xml:id="echoid-s17812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17813" xml:space="preserve">Unde ſequitur Tellurem circaSolem circumferri, ne in <lb/>hunc motu illo violentiſſimo cadat, quo in orbitâ retinetur.</s> <s xml:id="echoid-s17814" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17815" xml:space="preserve">Motus hic idem Telluris ex iiſdem principiis & </s> <s xml:id="echoid-s17816" xml:space="preserve">aliâ <lb/>methodo deducitur.</s> <s xml:id="echoid-s17817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17818" xml:space="preserve">Duo corpora, quæ vi quacunque ad ſe mutuo feruntur, <lb/>tandem concurrent, aut continuo magis à ſe mutuo rece-<lb/>dent, niſi utrumque ita moveatur, ut vim centrifugam ha-<lb/>beat æqualem illi, qua verſus aliud fertur; </s> <s xml:id="echoid-s17819" xml:space="preserve">cùm verò corpora <pb o="159" file="0687" n="757" rhead="MATHEMATICA LIB. IV. CAP. XIII."/> quæ in ſe mutuo gravitant, viribus æqualibus, ſeſe mutuo pe-<lb/> <anchor type="note" xlink:label="note-0687-01a" xlink:href="note-0687-01"/> tant <anchor type="note" xlink:href="" symbol="*"/>, aut quod idem eſt <anchor type="note" xlink:href="" symbol="*"/>, celeritatibus, quæ ſunt inverſè <anchor type="note" xlink:label="note-0687-02a" xlink:href="note-0687-02"/> ut quantitates materiæ <anchor type="note" xlink:href="" symbol="*"/>, non poterunt corpora hæc in <anchor type="note" xlink:label="note-0687-03a" xlink:href="note-0687-03"/> motu circum ſe mutuo perſeverare, niſi ambo ita moveantur, <lb/> <anchor type="note" xlink:label="note-0687-04a" xlink:href="note-0687-04"/> ut vires centrifugas æquales habeant, quod, niſi ambo cir-<lb/>ca commune ſuum gravitatis centrum, æqualibus tempori-<lb/>bus, rotentur, non obtinet; </s> <s xml:id="echoid-s17820" xml:space="preserve">id eſt, ſi propoſitio hæc ad <lb/>Solem & </s> <s xml:id="echoid-s17821" xml:space="preserve">Tellurem applicetur, niſi circa punctum, cujus diſtan-<lb/>tia à centro Solis eſt ad ipſius diſtantiam à centro Telluris, <lb/>ut quantitas materiæ in Tellure ad materiæ quantitatem in <lb/> <anchor type="note" xlink:label="note-0687-05a" xlink:href="note-0687-05"/> Sole, ambo moveantur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s17822" xml:space="preserve">quod punctum ergo parum admo- dum à centro Solis diſtat. </s> <s xml:id="echoid-s17823" xml:space="preserve">Cùm autem, quodcunque ho-<lb/>rum corporum moveatur, in motu circa aliud perſeveret, <lb/>ſequitur ambo motibus memoratis ſubjici, Solemque exiguo <lb/>motu agitari, dum Tellus orbem maximum deſcribit. </s> <s xml:id="echoid-s17824" xml:space="preserve">Ex <lb/>quibus ſequitur, motum Telluris ab illo negari non poſſe, <lb/>qui ex legibus motus, ex Phoenomenis deductis, ratiocina-<lb/>tur.</s> <s xml:id="echoid-s17825" xml:space="preserve"/> </p> <div xml:id="echoid-div2742" type="float" level="2" n="6"> <note symbol="*" position="right" xlink:label="note-0687-01" xlink:href="note-0687-01a" xml:space="preserve">126.</note> <note symbol="*" position="right" xlink:label="note-0687-02" xlink:href="note-0687-02a" xml:space="preserve">65.</note> <note position="right" xlink:label="note-0687-03" xlink:href="note-0687-03a" xml:space="preserve">1248.</note> <note symbol="*" position="right" xlink:label="note-0687-04" xlink:href="note-0687-04a" xml:space="preserve">1235.</note> <note symbol="*" position="right" xlink:label="note-0687-05" xlink:href="note-0687-05a" xml:space="preserve">234. 235.</note> </div> <p> <s xml:id="echoid-s17826" xml:space="preserve">Probato motu Telluris annuo, & </s> <s xml:id="echoid-s17827" xml:space="preserve">relatâ Tellure inter Pla-<lb/>netas, exigua tantùm difficultas ſupereſt reſpectu motus cir-<lb/>ca axem; </s> <s xml:id="echoid-s17828" xml:space="preserve">nemo enim qui de illo non dubitat, hunc negat; <lb/></s> <s xml:id="echoid-s17829" xml:space="preserve">multi, conceſſo motu circa axem, Telluris annuum motum <lb/> <anchor type="note" xlink:label="note-0687-06a" xlink:href="note-0687-06"/> negant; </s> <s xml:id="echoid-s17830" xml:space="preserve">ſatis ergo erit in tranſitu notare, omnes Planetas, <lb/>circa quos reſpectu hujus motus obſervationes inſtituere li-<lb/>cet, circa axes rotari; </s> <s xml:id="echoid-s17831" xml:space="preserve">& </s> <s xml:id="echoid-s17832" xml:space="preserve">motum ſimilem Telluri competere, <lb/>uniformem motum diurnum in corporibus, ad diſtantias quaſ-<lb/>cunque, ſatis indicare. </s> <s xml:id="echoid-s17833" xml:space="preserve">Quibus addendum, celeritatem <lb/>Stellarum fixarum, in minori quàm viginti quatuor horarum <lb/>ſpatio, revolutionem integram peragentium, vix magis pro-<lb/>babilem eſſe, quàm à nobis concipi poteſt.</s> <s xml:id="echoid-s17834" xml:space="preserve"/> </p> <div xml:id="echoid-div2743" type="float" level="2" n="7"> <note position="right" xlink:label="note-0687-06" xlink:href="note-0687-06a" xml:space="preserve">1249.</note> </div> <p> <s xml:id="echoid-s17835" xml:space="preserve">Etiam motus hic omnium corporum coeleſtium Naturæ <lb/>legibus adverſatur; </s> <s xml:id="echoid-s17836" xml:space="preserve">nam, ſi hæc rotentur, circulos, quo-<lb/> <anchor type="note" xlink:label="note-0687-07a" xlink:href="note-0687-07"/> rum centrum Tellus occupat, motu æquabili, ſingulis die-<lb/>bus, percurrunt; </s> <s xml:id="echoid-s17837" xml:space="preserve">id eſt, deſcribunt areas lineis ad centrum <lb/>Telluris ductis temporibus proportionales; </s> <s xml:id="echoid-s17838" xml:space="preserve">& </s> <s xml:id="echoid-s17839" xml:space="preserve">in orbitis reti-<lb/>nentur viribus, quæ ad centrum Telluris diriguntur <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s17840" xml:space="preserve"> <anchor type="note" xlink:label="note-0687-08a" xlink:href="note-0687-08"/> quibus, proprer omnis actionis reciprocationem <anchor type="note" xlink:href="" symbol="*"/>, Tellus <anchor type="note" xlink:label="note-0687-09a" xlink:href="note-0687-09"/> <pb o="160" file="0688" n="758" rhead="PHYSICES ELEMENTA"/> etiam continuò verſus illa corpora trahitur; </s> <s xml:id="echoid-s17841" xml:space="preserve">ita ut violentiſ-<lb/>ſimo motu neceſſario agitari debeat; </s> <s xml:id="echoid-s17842" xml:space="preserve">unde patet motum diur-<lb/>num non ad ipſa corpora coeleſtia referri debere, ſed ad <lb/>Tellurem circa axem rotantem.</s> <s xml:id="echoid-s17843" xml:space="preserve"/> </p> <div xml:id="echoid-div2744" type="float" level="2" n="8"> <note position="right" xlink:label="note-0687-07" xlink:href="note-0687-07a" xml:space="preserve">1250.</note> <note symbol="*" position="right" xlink:label="note-0687-08" xlink:href="note-0687-08a" xml:space="preserve">226.</note> <note symbol="*" position="right" xlink:label="note-0687-09" xlink:href="note-0687-09a" xml:space="preserve">126.</note> </div> <p> <s xml:id="echoid-s17844" xml:space="preserve">Objiciunt, qui Tellurem quieſcere contendunt, corpora <lb/> <anchor type="note" xlink:label="note-0688-01a" xlink:href="note-0688-01"/> in Telluris ſuperficie, ex vi centrifugâ, juxta tangentem ad <lb/>circulùm, Æquatori parallelum, debere à Tellure recede-<lb/>re <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17845" xml:space="preserve">Reſpondemus, corpora eodem motu cum ſuperficie <anchor type="note" xlink:label="note-0688-02a" xlink:href="note-0688-02"/> Telluris, in locis in quibus antur, transferri, & </s> <s xml:id="echoid-s17846" xml:space="preserve">ideò reſpe-<lb/>ctu punctorum ſuperficiei conari recedere per lineas ad axem <lb/>perpendiculares <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17847" xml:space="preserve">etiam corpora gravitate ad centrum Tel- <anchor type="note" xlink:label="note-0688-03a" xlink:href="note-0688-03"/> luris tendere <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17848" xml:space="preserve">& </s> <s xml:id="echoid-s17849" xml:space="preserve">ideò, motu ex hiſce ambobus compoſi- <anchor type="note" xlink:label="note-0688-04a" xlink:href="note-0688-04"/> to, corpus continuò, aut moveri aut moveri conari <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17850" xml:space="preserve">ſed <anchor type="note" xlink:label="note-0688-05a" xlink:href="note-0688-05"/> quia primus motus reſpectu ſecundi eſt admodum exiguus, <lb/>parum tantùm à directione verſus centrum detorquetur gra-<lb/>ve, & </s> <s xml:id="echoid-s17851" xml:space="preserve">paululum gravitas minuitur, eo magis, quo locus ma-<lb/>gis à polo diſtat; </s> <s xml:id="echoid-s17852" xml:space="preserve">Quod experientiæ congruit; </s> <s xml:id="echoid-s17853" xml:space="preserve">in ſequenti-<lb/>bus etiam videbimus, ubi de Telluris figurà agemus, directio-<lb/>nem memoratam gravium, ubique dirigi perpendiculariter ad <lb/>Telluris ſuperſiciem. </s> <s xml:id="echoid-s17854" xml:space="preserve">Corpus, quod in altum projicitur, <lb/>non modo motu quo projicitur gaudet, ſed etiam fertur mo-<lb/>tu impreſſo illi, qui hoc projicit, aut machinæ, ex qua pro-<lb/>pellitur, id eſt, motu communi cum ſuperficie Telluris fertur; <lb/></s> <s xml:id="echoid-s17855" xml:space="preserve">ideòque in eâdem lineêa, cum ſuperficie Telluris tranſlatâ <lb/>movetur, in qua tranſlatum foret ſi Tellus quieſceret.</s> <s xml:id="echoid-s17856" xml:space="preserve"/> </p> <div xml:id="echoid-div2745" type="float" level="2" n="9"> <note position="left" xlink:label="note-0688-01" xlink:href="note-0688-01a" xml:space="preserve">1251.</note> <note symbol="*" position="left" xlink:label="note-0688-02" xlink:href="note-0688-02a" xml:space="preserve">217.</note> <note symbol="*" position="left" xlink:label="note-0688-03" xlink:href="note-0688-03a" xml:space="preserve">223.</note> <note symbol="*" position="left" xlink:label="note-0688-04" xlink:href="note-0688-04a" xml:space="preserve">1226.</note> <note symbol="*" position="left" xlink:label="note-0688-05" xlink:href="note-0688-05a" xml:space="preserve">190. 198.</note> </div> </div> <div xml:id="echoid-div2747" type="section" level="1" n="674"> <head xml:id="echoid-head873" xml:space="preserve">CAPUT XIV.</head> <head xml:id="echoid-head874" xml:space="preserve">De Denſitate Planetarum.</head> <p> <s xml:id="echoid-s17857" xml:space="preserve">SUpereſt, antequam ad Syſtematis explicationem Phyſicam <lb/>tranſeamus, ut quantitates materiæ in quibuſdam corpo-<lb/>ribus, & </s> <s xml:id="echoid-s17858" xml:space="preserve">horum denſitates, determinemus; </s> <s xml:id="echoid-s17859" xml:space="preserve">quibus notis ef-<lb/>fectus legum, quibus hæc corpora reguntur, facilius pate-<lb/>bunt.</s> <s xml:id="echoid-s17860" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17861" xml:space="preserve">Quantitates materiæ, in variis corporibus, ſunt inter ſe, ut <lb/>gravitates ad eandem diſtantiam ab hiſce corporius <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17862" xml:space="preserve">quæ <anchor type="note" xlink:label="note-0688-06a" xlink:href="note-0688-06"/> gravitates ſunt inter ſe inverſè, ut quadrata temporum perio- <pb o="161" file="0689" n="759" rhead="MATHEMATICA LIB. IV. CAP. XI."/> dicorum corporum revolventium, circa varia illa corpora, ad <lb/>eandem illam diſtantiam <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17863" xml:space="preserve">Multiplicando quantitates, quæ <anchor type="note" xlink:label="note-0689-01a" xlink:href="note-0689-01"/> ſunt in hac ratione, per eandem quantitatem, cubum nempe <lb/>hujus diſtantiæ, non mutatur ratio harum quantitatum; </s> <s xml:id="echoid-s17864" xml:space="preserve">quæ <lb/>ergo ſunt inter ſe, ut quotientes diviſionum cubi memorati, <lb/>per quadrata temporum periodicorum memoratorum; </s> <s xml:id="echoid-s17865" xml:space="preserve">ſed <lb/>detegitur quotiens talis diviſionis, pro corpore quocunque, <lb/>dividendo cubum alterius diſtantiæ cujuſcunque, per quadra-<lb/>tum temporis periodici corporis ad hanc diſtantiam revol-<lb/>ventis: </s> <s xml:id="echoid-s17866" xml:space="preserve">quotientes enim tales ſunt æquales inter ſe, pro omni-<lb/>bus corporibus, circa idem, ad diſtantias quaſcunque revol-<lb/>ventibus; </s> <s xml:id="echoid-s17867" xml:space="preserve">ut ſequitur ex æqualitate rationis inter cubos di-<lb/>ſtantiarum, & </s> <s xml:id="echoid-s17868" xml:space="preserve">quadrata temporum periodicorum ad has <lb/>diſtantias <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s17869" xml:space="preserve">Ex qubius deducimus, quantitates materiæ in <anchor type="note" xlink:label="note-0689-02a" xlink:href="note-0689-02"/> corporibus quibuſcunque, in Syſtemate noſtro, eſſe inter ſe <lb/> <anchor type="note" xlink:label="note-0689-03a" xlink:href="note-0689-03"/> directè, ut cubos diſtantiarum ad quas, circa hæc, corpora a-<lb/>lia revolvuntur, & </s> <s xml:id="echoid-s17870" xml:space="preserve">inverſè ut quadrata temporum periodi-<lb/>corum horum corporum revolventium.</s> <s xml:id="echoid-s17871" xml:space="preserve"/> </p> <div xml:id="echoid-div2747" type="float" level="2" n="1"> <note symbol="*" position="left" xlink:label="note-0688-06" xlink:href="note-0688-06a" xml:space="preserve">1207.</note> <note symbol="*" position="right" xlink:label="note-0689-01" xlink:href="note-0689-01a" xml:space="preserve">236.</note> <note position="right" xlink:label="note-0689-02" xlink:href="note-0689-02a" xml:space="preserve">1252.</note> <note symbol="*" position="right" xlink:label="note-0689-03" xlink:href="note-0689-03a" xml:space="preserve">974.</note> </div> <p> <s xml:id="echoid-s17872" xml:space="preserve">Demonſtrantur hæc, ſeponendo agitationem corporis cen-<lb/>tralis, cujus materiæ quantitas quæritur.</s> <s xml:id="echoid-s17873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17874" xml:space="preserve">Propter Solis magnitudinem, reſpectu Veneris ex. </s> <s xml:id="echoid-s17875" xml:space="preserve">gr.</s> <s xml:id="echoid-s17876" xml:space="preserve">, <lb/>quem ex Planetis ſolum conſideramus, vix ex hujus actione <lb/>agitatur ille <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17877" xml:space="preserve">& </s> <s xml:id="echoid-s17878" xml:space="preserve">Venus poteſt conſiderari quaſi motus cir- <anchor type="note" xlink:label="note-0689-04a" xlink:href="note-0689-04"/> ca corpus quieſcens.</s> <s xml:id="echoid-s17879" xml:space="preserve"/> </p> <div xml:id="echoid-div2748" type="float" level="2" n="2"> <note symbol="*" position="right" xlink:label="note-0689-04" xlink:href="note-0689-04a" xml:space="preserve">1235.</note> </div> <p> <s xml:id="echoid-s17880" xml:space="preserve">Satellites Jovis & </s> <s xml:id="echoid-s17881" xml:space="preserve">Saturni, motu quidem communi cum <lb/>primariis feruntur, ſed circa ipſos, quaſi circa corpora qui-<lb/>eſcentia, propter primariorum magnitudinem, transferuntur.</s> <s xml:id="echoid-s17882" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17883" xml:space="preserve">Luna autem ſatis ſenſibiliter in Tellurem agit, & </s> <s xml:id="echoid-s17884" xml:space="preserve">hanc a-<lb/>gitat; </s> <s xml:id="echoid-s17885" xml:space="preserve">quare antequam, ope regulæ memoratæ <anchor type="note" xlink:href="" symbol="*"/>, cum motu <anchor type="note" xlink:label="note-0689-05a" xlink:href="note-0689-05"/> Lunæ computationem inire poſſimus, de conferendâ materiæ <lb/>quantitate in Tellure, cum materiæ quantitatibus in Sole, <lb/>Jove, & </s> <s xml:id="echoid-s17886" xml:space="preserve">Saturno, determinanda eſt diſtantia, ad quam Lu-<lb/> <anchor type="note" xlink:label="note-0689-06a" xlink:href="note-0689-06"/> na, circa Tellurem quieſcentem, id eſt actione Lunæ non <lb/>tranſlatam, revolvi poßet, in eodem tempore periodico, in <lb/>quo revolutionem ſuam reverâ peragit, Hìc etiam non at-<lb/>tendimus ad motum communem Telluri & </s> <s xml:id="echoid-s17887" xml:space="preserve">Lunæ, quo circa <lb/>Solem ambo feruntur.</s> <s xml:id="echoid-s17888" xml:space="preserve"/> </p> <div xml:id="echoid-div2749" type="float" level="2" n="3"> <note symbol="*" position="right" xlink:label="note-0689-05" xlink:href="note-0689-05a" xml:space="preserve">1252.</note> <note position="right" xlink:label="note-0689-06" xlink:href="note-0689-06a" xml:space="preserve">1253.</note> </div> <pb o="162" file="0690" n="760" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s17889" xml:space="preserve">Luna in motu ſuo circa Tellurem perſeverat; </s> <s xml:id="echoid-s17890" xml:space="preserve">ideò Tel-<lb/>lus & </s> <s xml:id="echoid-s17891" xml:space="preserve">illa circa commune gravitatis centrum rotantur: </s> <s xml:id="echoid-s17892" xml:space="preserve">ut <lb/> <anchor type="note" xlink:label="note-0690-01a" xlink:href="note-0690-01"/> ex demonſtratis circa Tellurem & </s> <s xml:id="echoid-s17893" xml:space="preserve">Solem <anchor type="note" xlink:href="" symbol="*"/> ſequitur, & </s> <s xml:id="echoid-s17894" xml:space="preserve">Lu- na, vi qua verſus Tellurem tendit, revolvitur in orbitâ, <lb/>cujus ſemi-diameter eſt diſtantia Lunæ à memorato commu-<lb/>ni centro gravitatis Lunæ & </s> <s xml:id="echoid-s17895" xml:space="preserve">Telluris.</s> <s xml:id="echoid-s17896" xml:space="preserve"/> </p> <div xml:id="echoid-div2750" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0690-01" xlink:href="note-0690-01a" xml:space="preserve">1248.</note> </div> <p> <s xml:id="echoid-s17897" xml:space="preserve">Sit L hæc Lunæ diſtantia à communi centro gravitatis; <lb/></s> <s xml:id="echoid-s17898" xml:space="preserve">T diſtantia Telluris ab eodem centro; </s> <s xml:id="echoid-s17899" xml:space="preserve">L + T eſt ergo di-<lb/>ſtantia Lunæ à Tellure, & </s> <s xml:id="echoid-s17900" xml:space="preserve">eſt 60 {1/2} ſemidiam. </s> <s xml:id="echoid-s17901" xml:space="preserve">Telluris; </s> <s xml:id="echoid-s17902" xml:space="preserve">me-<lb/>diam enim diſtantiam hìc conſideramus; </s> <s xml:id="echoid-s17903" xml:space="preserve">Sit D diſtantia <lb/>quam quærimus, ad quam, circa Tellurem quieſcentem, <lb/>gravitate ſuâ verſus Tellurem, poſſet moveri Luna, in tem-<lb/>pore, in quo revera ad diſtantiam L, circa commune gra-<lb/>vitatis centrum rotatur.</s> <s xml:id="echoid-s17904" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17905" xml:space="preserve">Propter hanc temporum periodicorum æqualitatem, vis, <lb/>qua Luna ad diſtantiam D poſſet in orbitâ retineri, eſt ad vim, <lb/>qua ad diſtantiam L, in orbe ſuo retinetur, ut D ad L <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17906" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">232.</note> <p> <s xml:id="echoid-s17907" xml:space="preserve">Sed vis, qua Luna ad Tellurem tenderet, & </s> <s xml:id="echoid-s17908" xml:space="preserve">in orbitâ <lb/>retineretur ad diſtantiam D, eſt ad vim, qua nunc in orbitâ <lb/>retinetur cûm â Tellure diſtat L + T, ut, L + T<emph style="super">9</emph> ad <lb/> <anchor type="note" xlink:label="note-0690-03a" xlink:href="note-0690-03"/> Dq <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17909" xml:space="preserve">Ergo D, L :</s> <s xml:id="echoid-s17910" xml:space="preserve">: <emph style="ol">L + T<emph style="super">q</emph></emph>, D<emph style="super">q</emph> <lb/>Ideoque D<emph style="super">c</emph> = L x <emph style="ol">L + T</emph><emph style="super">q</emph> & </s> <s xml:id="echoid-s17911" xml:space="preserve">D<emph style="super">c</emph> x <emph style="ol">L + T</emph> = L x <lb/><emph style="ol">L + T</emph><emph style="super">c</emph>: </s> <s xml:id="echoid-s17912" xml:space="preserve">unde ſequentem deducimus proportionem <lb/>Idcirco L + T, D : </s> <s xml:id="echoid-s17913" xml:space="preserve">: </s> <s xml:id="echoid-s17914" xml:space="preserve">L + T, ad primam ex dualbus <lb/>mediis proportionalibus inter l + T & </s> <s xml:id="echoid-s17915" xml:space="preserve">L.</s> <s xml:id="echoid-s17916" xml:space="preserve"/> </p> <div xml:id="echoid-div2751" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0690-03" xlink:href="note-0690-03a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s17917" xml:space="preserve">L + T eſt ad L, ut quantitas materiæ, in Tellure & </s> <s xml:id="echoid-s17918" xml:space="preserve"><lb/>Lunâ conjunctim, ad quantitatem materiæ in Tellure ſolâ *: <lb/></s> <s xml:id="echoid-s17919" xml:space="preserve"> <anchor type="note" xlink:label="note-0690-04a" xlink:href="note-0690-04"/> quæ quantitates materiæ, ut in ſequentibus videbimus, ſunt <lb/>inter ſe, ut 40, 37. </s> <s xml:id="echoid-s17920" xml:space="preserve">ad 39, 37.</s> <s xml:id="echoid-s17921" xml:space="preserve">, & </s> <s xml:id="echoid-s17922" xml:space="preserve">prima duarum mediarum <lb/>proportionalium, inter hos numeros, eſt 40, 035.</s> <s xml:id="echoid-s17923" xml:space="preserve">; ergo 40, 37. <lb/></s> <s xml:id="echoid-s17924" xml:space="preserve">eſt ad 40, 035.</s> <s xml:id="echoid-s17925" xml:space="preserve">, ut 60 {1/2} ad diſtantiam quæſitam, quæ dete-<lb/>gitur 60 ſemidiametrorum Telluris.</s> <s xml:id="echoid-s17926" xml:space="preserve"/> </p> <div xml:id="echoid-div2752" type="float" level="2" n="6"> <note symbol="*" position="left" xlink:label="note-0690-04" xlink:href="note-0690-04a" xml:space="preserve">234. 235.</note> </div> <p> <s xml:id="echoid-s17927" xml:space="preserve">Circa hanc operationem notandum eſt, diſtantiam D, non <lb/>detegi, niſi detur ratio inter maſlam Lunæ & </s> <s xml:id="echoid-s17928" xml:space="preserve">Telluris, quæ <pb o="163" file="0691" n="761" rhead="MATHEMATICA LIB. VI. CAP. XIV."/> determinari non poteſt, niſi detur ratio inter denſitatem So-<lb/>lis & </s> <s xml:id="echoid-s17929" xml:space="preserve">Telluris, ad quam detegendam, ut diſtantia D nota ſit, <lb/>neceſſe eſt. </s> <s xml:id="echoid-s17930" xml:space="preserve">Quare primo tentando detegitur D, & </s> <s xml:id="echoid-s17931" xml:space="preserve">approxi-<lb/>mando exactè determinatur. </s> <s xml:id="echoid-s17932" xml:space="preserve">Hanc autem eſſe 60 ſemi-<lb/>diam. </s> <s xml:id="echoid-s17933" xml:space="preserve">Telluris, conſtat; </s> <s xml:id="echoid-s17934" xml:space="preserve">quia hac poſitâ detegitur, inter quan-<lb/>titates materiæ Telluris & </s> <s xml:id="echoid-s17935" xml:space="preserve">Lunæ, ratio, quæ datur inter <lb/>39, 37. </s> <s xml:id="echoid-s17936" xml:space="preserve">& </s> <s xml:id="echoid-s17937" xml:space="preserve">I, ut in ſequentibus videbimus; </s> <s xml:id="echoid-s17938" xml:space="preserve">qua adhibitâ pro-<lb/>portione detegitur, ut vidimus, hæc ipſa diſtantia 60. </s> <s xml:id="echoid-s17939" xml:space="preserve">ſemi-<lb/>diametrorum.</s> <s xml:id="echoid-s17940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17941" xml:space="preserve">Hiſce præmiſſis ipſam aggredimur computationem.</s> <s xml:id="echoid-s17942" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17943" xml:space="preserve">Diſtantia Veneris à centro Solis eſt 723. </s> <s xml:id="echoid-s17944" xml:space="preserve">& </s> <s xml:id="echoid-s17945" xml:space="preserve">tempus pe-<lb/>riodicum 5393. </s> <s xml:id="echoid-s17946" xml:space="preserve">horarum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17947" xml:space="preserve"> <anchor type="note" xlink:label="note-0691-01a" xlink:href="note-0691-01"/> </s> </p> <div xml:id="echoid-div2753" type="float" level="2" n="7"> <note symbol="*" position="right" xlink:label="note-0691-01" xlink:href="note-0691-01a" xml:space="preserve">959.</note> </div> <p> <s xml:id="echoid-s17948" xml:space="preserve">Quartus Satelles Jovis diſtat à centro Jovis partibus 12, 507. <lb/></s> <s xml:id="echoid-s17949" xml:space="preserve">quarum Venus à Sole diſtat 723.</s> <s xml:id="echoid-s17950" xml:space="preserve">: hujus Satellitis tempus pe-<lb/>riodicum eſt 402 horarum 5′. </s> <s xml:id="echoid-s17951" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17952" xml:space="preserve"/> </p> <note symbol="*" position="right" xml:space="preserve">971.</note> <p> <s xml:id="echoid-s17953" xml:space="preserve">Quartus Satelles Saturni diſtat à centro Saturni, partibus <lb/>iiſdem 9,292.</s> <s xml:id="echoid-s17954" xml:space="preserve">; & </s> <s xml:id="echoid-s17955" xml:space="preserve">tempus periodicum eſt 382 horarum 41′ *</s> </p> <note symbol="*" position="right" xml:space="preserve">972.</note> <p> <s xml:id="echoid-s17956" xml:space="preserve">Tandem diſtantia Lunæ 60. </s> <s xml:id="echoid-s17957" xml:space="preserve">ſemidiam. </s> <s xml:id="echoid-s17958" xml:space="preserve">Telluris à cen-<lb/>tro hujus, eſt partium memoratarum 2,909. </s> <s xml:id="echoid-s17959" xml:space="preserve">tempus periodi-<lb/>cum medium 655. </s> <s xml:id="echoid-s17960" xml:space="preserve">hor. </s> <s xml:id="echoid-s17961" xml:space="preserve">43′.</s> <s xml:id="echoid-s17962" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17963" xml:space="preserve">Diviſis ſingulis cubis harum diſtantiarum, reſpectivè per <lb/> <anchor type="note" xlink:label="note-0691-04a" xlink:href="note-0691-04"/> ſuorum temporum periodicorum quadrata, dantur in quo-<lb/>tientibus numeri, qui ſunt inter ſe, ut materiæ quantitates <lb/>in dictis corporibus centralibus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17964" xml:space="preserve">qui quotientes ſunt inter <anchor type="note" xlink:label="note-0691-05a" xlink:href="note-0691-05"/> ſe ut numeri ſequentes,</s> </p> <div xml:id="echoid-div2754" type="float" level="2" n="8"> <note position="right" xlink:label="note-0691-04" xlink:href="note-0691-04a" xml:space="preserve">1254.</note> <note symbol="*" position="right" xlink:label="note-0691-05" xlink:href="note-0691-05a" xml:space="preserve">1252.</note> </div> <note position="right" xml:space="preserve"> <lb/>Quantitates # in Sole; # in Jove; # in Saturno; # in Tellure; <lb/># materiæ # 10000. # 9,248. # 4,223. # 0,0044. <lb/></note> <note position="right" xml:space="preserve">1255.</note> <p> <s xml:id="echoid-s17965" xml:space="preserve">Exobſervationibus aſtronomicis datur etiam proportio dia-<lb/>metrorum horum corporum.</s> <s xml:id="echoid-s17966" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diametri # Solis ; # Jovis ; # Saturni; # Telluris. <lb/># 10000. # 1077. # 889. # 104. <lb/></note> <note position="right" xml:space="preserve">1256.</note> <p> <s xml:id="echoid-s17967" xml:space="preserve">Si quantitates materiæ memoratæ per diametrorum qua-<lb/> <anchor type="note" xlink:label="note-0691-10a" xlink:href="note-0691-10"/> drata dividantur, quotientes erunt inter ſe, ut pondera in ſu-<lb/>perficiebus dictorum corporum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17968" xml:space="preserve">ſunt autem quotientes hi <anchor type="note" xlink:label="note-0691-11a" xlink:href="note-0691-11"/> ut numeri ſequentes.</s> <s xml:id="echoid-s17969" xml:space="preserve"/> </p> <div xml:id="echoid-div2755" type="float" level="2" n="9"> <note position="right" xlink:label="note-0691-10" xlink:href="note-0691-10a" xml:space="preserve">1257.</note> <note symbol="*" position="right" xlink:label="note-0691-11" xlink:href="note-0691-11a" xml:space="preserve">1227.</note> </div> <note position="right" xml:space="preserve"> <lb/>Gravitates # Solis; # Jovis: # Saturni; # Telluris <lb/>in ſuperficiebus, # 10000. # 797,15. # 534,337. # 407,832. <lb/></note> <note position="right" xml:space="preserve">1258.</note> <pb o="164" file="0692" n="762" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s17970" xml:space="preserve">Dividendo hos numeros per diametros, habemus propor-<lb/> <anchor type="note" xlink:label="note-0692-01a" xlink:href="note-0692-01"/> tionem denſitatum eorundem horum corporum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17971" xml:space="preserve"/> </p> <div xml:id="echoid-div2756" type="float" level="2" n="10"> <note position="left" xlink:label="note-0692-01" xlink:href="note-0692-01a" xml:space="preserve">1259.</note> </div> <note symbol="*" position="left" xml:space="preserve">1231.</note> <p> <s xml:id="echoid-s17972" xml:space="preserve">quotientes, hiſce diviſionibus detecti, ſequentium nume-<lb/>rorum relationem habent.</s> <s xml:id="echoid-s17973" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Deſitates # Solis; # Jovis; # Saturni; # Telluris. <lb/># 10000 # 7404. # 6011. # 39214. <lb/></note> <note position="left" xml:space="preserve">1260.</note> <p> <s xml:id="echoid-s17974" xml:space="preserve">Lunæ denſitatem in capite ultimo determinabimus.</s> <s xml:id="echoid-s17975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17976" xml:space="preserve">Minimè probabile eſt, corpora memorata quatuor homo-<lb/>genea eſſe; </s> <s xml:id="echoid-s17977" xml:space="preserve">circa Tellurem videbimus, in capite ſequenti 17.</s> <s xml:id="echoid-s17978" xml:space="preserve">, <lb/>illam verſus centrum denſiorem eſſe, quàm verſus ſuperſiciem; <lb/></s> <s xml:id="echoid-s17979" xml:space="preserve">unde ſequitur denſitates non exactè determinari poſſe, qua-<lb/>re tantùm determinantur denſitates mediæ, id eſt, quas cor-<lb/> <anchor type="note" xlink:label="note-0692-05a" xlink:href="note-0692-05"/> pora haberent, ſi ſervatâ materiæ quantitate & </s> <s xml:id="echoid-s17980" xml:space="preserve">magnitudi-<lb/>ne reſpectu ſingulorum, corpora forent homogenea.</s> <s xml:id="echoid-s17981" xml:space="preserve"/> </p> <div xml:id="echoid-div2757" type="float" level="2" n="11"> <note position="left" xlink:label="note-0692-05" xlink:href="note-0692-05a" xml:space="preserve">1261.</note> </div> <p> <s xml:id="echoid-s17982" xml:space="preserve">Proportio memorata <anchor type="note" xlink:href="" symbol="*"/>, inter denſitates reſpectu omnium cor- <anchor type="note" xlink:label="note-0692-06a" xlink:href="note-0692-06"/> rum, & </s> <s xml:id="echoid-s17983" xml:space="preserve">computationes reliquæ reſpectu Solis, Jovis, & </s> <s xml:id="echoid-s17984" xml:space="preserve">Sa-<lb/> <anchor type="note" xlink:label="note-0692-07a" xlink:href="note-0692-07"/> turni, ſenſibili errore expertes ſunt; </s> <s xml:id="echoid-s17985" xml:space="preserve">quantum ad Tellurem, <lb/>in his error fortè datur, corrigendus ex obſervationibus in <lb/>tempore inſtituendis: </s> <s xml:id="echoid-s17986" xml:space="preserve">Ponimus enim diſtantiam Lunæ, 60. <lb/></s> <s xml:id="echoid-s17987" xml:space="preserve">ſemi-diam.</s> <s xml:id="echoid-s17988" xml:space="preserve">, eſſe partium 2,909. </s> <s xml:id="echoid-s17989" xml:space="preserve">quarum Venus à Sole diſtat <lb/>723, id eſt, quarum Tellus à Sole diſtat, 1000 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17990" xml:space="preserve">quæ Lunæ <anchor type="note" xlink:label="note-0692-08a" xlink:href="note-0692-08"/> diſtantia detegitur, ponendo Solis Paralaxin horizontalem 10″, <lb/>quæ tamen pro verâ abſolutê haberi non poteſt, licèt ex obſer-<lb/>vationibus exactiſſimis, de Martis Telluri maximè vicini Paral-<lb/>laxi huc uſque inſtitutis, deducatur, ſed quæ nimium eſt <lb/>exigua, ut circa obſervationes nulla erroris ſuſpicio ſuperſit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s17991" xml:space="preserve"/> </p> <div xml:id="echoid-div2758" type="float" level="2" n="12"> <note position="left" xlink:label="note-0692-06" xlink:href="note-0692-06a" xml:space="preserve">1262.</note> <note symbol="*" position="left" xlink:label="note-0692-07" xlink:href="note-0692-07a" xml:space="preserve">1260.</note> <note symbol="*" position="left" xlink:label="note-0692-08" xlink:href="note-0692-08a" xml:space="preserve">959. 960.</note> </div> <note symbol="*" position="left" xml:space="preserve">1108.</note> <p> <s xml:id="echoid-s17992" xml:space="preserve">Errorem tamen ex malè determinatâ ratione, inter ſemi-<lb/>diametrum Telluris & </s> <s xml:id="echoid-s17993" xml:space="preserve">hujus â Sole diſtantiam, non mutare <lb/>determinatam Telluris denſitatem, ex ipſis computationi-<lb/>bus circa hanc inſtitutis, deducitur.</s> <s xml:id="echoid-s17994" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17995" xml:space="preserve">Ex hiſce enim ſequitur, denſitates corporum eſſe inter ſe, in <lb/>ratione compoſitâ ex directâ cuborum diſtantiarum corprum <lb/>quæ circumferentur, & </s> <s xml:id="echoid-s17996" xml:space="preserve">inverſâ quadratorum temporum pe-<lb/>riodicorum horum ipſorum corporum revolventium *: </s> <s xml:id="echoid-s17997" xml:space="preserve">Ut <lb/> <anchor type="note" xlink:label="note-0692-10a" xlink:href="note-0692-10"/> & </s> <s xml:id="echoid-s17998" xml:space="preserve">inverſâ cuborum diametrorum corporum centralium, <lb/>quorum denſitates quæruntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s17999" xml:space="preserve">ratio ex his compoſita, eſt <anchor type="note" xlink:label="note-0692-11a" xlink:href="note-0692-11"/> compoſita ex ratione directâ ſractionis, cujus numerator eſt <pb o="165" file="0693" n="763" rhead="MATHEMATICA LIB. IV. CAP. XV."/> cubus diſtantiæ corporis revoluti, & </s> <s xml:id="echoid-s18000" xml:space="preserve">denominator cubus <lb/>diametri corporis centralis, & </s> <s xml:id="echoid-s18001" xml:space="preserve">ratione inverſâ quadrati <lb/>temporis periodici corporis circumacti. </s> <s xml:id="echoid-s18002" xml:space="preserve">Fractio autem ta-<lb/>lis datur, ſi nota ſit ratio inter diametrum corporis centra-<lb/>lis & </s> <s xml:id="echoid-s18003" xml:space="preserve">diſtantiam corporis revoltventis ab hoc centro, licèt hæc <lb/>diſtantia cum nullâ aliâ poſſit conferri; </s> <s xml:id="echoid-s18004" xml:space="preserve">ratio autem hæ re-<lb/>ſpectu Telluris & </s> <s xml:id="echoid-s18005" xml:space="preserve">Lunæ, æque ac reſpectu cæterorum cor-<lb/>porum datur, quare & </s> <s xml:id="echoid-s18006" xml:space="preserve">Telluris denſitatis ratio ad reliquo-<lb/>rum corporum denſitates exactè detegitur.</s> <s xml:id="echoid-s18007" xml:space="preserve"/> </p> <div xml:id="echoid-div2759" type="float" level="2" n="13"> <note symbol="*" position="left" xlink:label="note-0692-10" xlink:href="note-0692-10a" xml:space="preserve">1254.</note> <note symbol="*" position="left" xlink:label="note-0692-11" xlink:href="note-0692-11a" xml:space="preserve">1257. 1259.</note> </div> </div> <div xml:id="echoid-div2761" type="section" level="1" n="675"> <head xml:id="echoid-head875" xml:space="preserve">CAPUT XV.</head> <head xml:id="echoid-head876" xml:space="preserve">Totius Syſtematis Planetarii explicatio Phyſica.</head> <p> <s xml:id="echoid-s18008" xml:space="preserve">IN parte primâ hujus libri, motus corporum in Syſtemate <lb/> <anchor type="note" xlink:label="note-0693-01a" xlink:href="note-0693-01"/> Planetario expoſuimus, quomodo hi, ex legibus Naturæ <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0693-02a" xlink:href="note-0693-02"/> ſequantur explicandum eſt; </s> <s xml:id="echoid-s18009" xml:space="preserve">id eſt, quomodo, corporibus <lb/> <anchor type="note" xlink:label="note-0693-03a" xlink:href="note-0693-03"/> his ſemel motis, in motibus quos obſervamus perſeverent.</s> <s xml:id="echoid-s18010" xml:space="preserve"/> </p> <div xml:id="echoid-div2761" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0693-01" xlink:href="note-0693-01a" xml:space="preserve">124. 125. 126.</note> <note position="right" xlink:label="note-0693-02" xlink:href="note-0693-02a" xml:space="preserve">1206. 1207.</note> <note position="right" xlink:label="note-0693-03" xlink:href="note-0693-03a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s18011" xml:space="preserve">Concipiamus Solem & </s> <s xml:id="echoid-s18012" xml:space="preserve">Mercurium, ſi ſibi permittantur ad <lb/> <anchor type="note" xlink:label="note-0693-04a" xlink:href="note-0693-04"/> ſe mutuo accedent <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18013" xml:space="preserve">Si autem projiciantur poterunt, cir- <anchor type="note" xlink:label="note-0693-05a" xlink:href="note-0693-05"/> ca commune gravitatis centrum, æqualibus temporibus, re-<lb/>volvi, & </s> <s xml:id="echoid-s18014" xml:space="preserve">Ellipticas lineas immobiles deſcribere <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18015" xml:space="preserve">in <anchor type="note" xlink:label="note-0693-06a" xlink:href="note-0693-06"/> illo motu perſeverare: </s> <s xml:id="echoid-s18016" xml:space="preserve">conſtat enim mathematicâ demon-<lb/> <anchor type="note" xlink:label="note-0693-07a" xlink:href="note-0693-07"/> ſtratione, in hoc caſu, corpora circa commune centrum gra-<lb/>vitatis deſcribere Ellipſes ſimiles illi, quam unum circa alte-<lb/>rum quieſcens, iiſdem viribus, poſſet deſcribere: </s> <s xml:id="echoid-s18017" xml:space="preserve">centrum <lb/>hoc, propter magnitudinem Solis <anchor type="note" xlink:href="" symbol="*"/>, vix ab ipſo Solis cen- <anchor type="note" xlink:label="note-0693-08a" xlink:href="note-0693-08"/> tro idſtat.</s> <s xml:id="echoid-s18018" xml:space="preserve"/> </p> <div xml:id="echoid-div2762" type="float" level="2" n="2"> <note position="right" xlink:label="note-0693-04" xlink:href="note-0693-04a" xml:space="preserve">1263.</note> <note symbol="*" position="right" xlink:label="note-0693-05" xlink:href="note-0693-05a" xml:space="preserve">1206.</note> <note symbol="*" position="right" xlink:label="note-0693-06" xlink:href="note-0693-06a" xml:space="preserve">1248. 1208.</note> <note position="right" xlink:label="note-0693-07" xlink:href="note-0693-07a" xml:space="preserve">241.</note> <note symbol="*" position="right" xlink:label="note-0693-08" xlink:href="note-0693-08a" xml:space="preserve">235.</note> </div> <p> <s xml:id="echoid-s18019" xml:space="preserve">Concipiamus ulterius, ad majorem à Sole diſtantiam, <lb/>Venerem projici, turbabit hic paululum Mercurii mo-<lb/>tum, qui etiam, actione ſuâ in Venerem, hunc paulu-<lb/>lum à viâ deflectet, & </s> <s xml:id="echoid-s18020" xml:space="preserve">ambo Solem,, nunc verſus eandem <lb/>partem, nunc ad partes diverſas, trahent; </s> <s xml:id="echoid-s18021" xml:space="preserve">ſed omnes has <lb/>irregularitates inſenſibiles eſſe videbimus, ſi Solis magnitudi-<lb/>nem conſideremus; </s> <s xml:id="echoid-s18022" xml:space="preserve">& </s> <s xml:id="echoid-s18023" xml:space="preserve">ideò hæc tria corpora tendere ad <lb/>punctum in viciniis Solis inter hæc corpora; </s> <s xml:id="echoid-s18024" xml:space="preserve">quod ergo pa-<lb/>rum admodum diſtat à communi centro gravitatis omnium.</s> <s xml:id="echoid-s18025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18026" xml:space="preserve">Si ſucceſſivé Tellus, Mars, & </s> <s xml:id="echoid-s18027" xml:space="preserve">reliqui Planetæ, ad diſtan- <pb o="(166)" file="0694" n="764" rhead="PHYSICES ELEMENTA"/> tias diverſas â Sole, projiciantur, idem ratiocinium locum <lb/>habebit. </s> <s xml:id="echoid-s18028" xml:space="preserve">Unde ſequitur omnes Planetas revolvi circa, <lb/> <anchor type="note" xlink:label="note-0694-01a" xlink:href="note-0694-01"/> omnium corporum Syſtema componentium, commune centrum <lb/>gravitatis, quod parum à Sole diſtat, & </s> <s xml:id="echoid-s18029" xml:space="preserve">Planetas ſeſe mu-<lb/>tuo ſenſibiliter in motibus non turbare; </s> <s xml:id="echoid-s18030" xml:space="preserve">unde ſinguli lineas <lb/> <anchor type="note" xlink:label="note-0694-02a" xlink:href="note-0694-02"/> deſcribunt, quas circa Solem deſcriberent, ſi quiſque ſolus <lb/>cum Sole in Syſtemate Planetario exiſteret; </s> <s xml:id="echoid-s18031" xml:space="preserve">id eſt, Ellipſes <lb/>immobiles: </s> <s xml:id="echoid-s18032" xml:space="preserve">nam has ex vi gravitatis deſcribi conſtat <anchor type="note" xlink:href="" symbol="*"/>, nul- <anchor type="note" xlink:label="note-0694-03a" xlink:href="note-0694-03"/> laſque alias lineas excentricas immobiles, ex vi centraliad di-<lb/>ſtantias æquales æqualiter agenti, deſcribi poſſe mathematicè <lb/>evincitur.</s> <s xml:id="echoid-s18033" xml:space="preserve"/> </p> <div xml:id="echoid-div2763" type="float" level="2" n="3"> <note position="left" xlink:label="note-0694-01" xlink:href="note-0694-01a" xml:space="preserve">1264.</note> <note position="left" xlink:label="note-0694-02" xlink:href="note-0694-02a" xml:space="preserve">1265.</note> <note symbol="*" position="left" xlink:label="note-0694-03" xlink:href="note-0694-03a" xml:space="preserve">1208. 241.</note> </div> <p> <s xml:id="echoid-s18034" xml:space="preserve">Clarius etiam patebit, omnes Planetas ad punctum in vici-<lb/>niis Solis tendere, ſi conſideremus quantitatem materiæ in <lb/>Sole, millies & </s> <s xml:id="echoid-s18035" xml:space="preserve">magis, materiæ quantitatem in Jove, Planeta-<lb/>rum longè maximo, ſuperare <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18036" xml:space="preserve"> <anchor type="note" xlink:label="note-0694-04a" xlink:href="note-0694-04"/> </s> </p> <div xml:id="echoid-div2764" type="float" level="2" n="4"> <note symbol="*" position="left" xlink:label="note-0694-04" xlink:href="note-0694-04a" xml:space="preserve">1255.</note> </div> <p> <s xml:id="echoid-s18037" xml:space="preserve">Dum Planetæ omnes revolvuntur, licèt parum tantùm agi-<lb/> <anchor type="note" xlink:label="note-0694-05a" xlink:href="note-0694-05"/> tent Solem, hunc tamen agitant, & </s> <s xml:id="echoid-s18038" xml:space="preserve">diverſè trahunt, pro vario <lb/>illorum ſitu inter ſe, unde motus exiguus in Sole oritur, qui <lb/>ſemper pendet à motu jam acquiſito, & </s> <s xml:id="echoid-s18039" xml:space="preserve">mutatione in hoc ex <lb/>actione memoratâ, quæ omnibus momentis mutatur.</s> <s xml:id="echoid-s18040" xml:space="preserve"/> </p> <div xml:id="echoid-div2765" type="float" level="2" n="5"> <note position="left" xlink:label="note-0694-05" xlink:href="note-0694-05a" xml:space="preserve">1266.</note> </div> <p> <s xml:id="echoid-s18041" xml:space="preserve">Hujus verò Solis agitationis effectus eſt, Planetas ſeſe mu-<lb/> <anchor type="note" xlink:label="note-0694-06a" xlink:href="note-0694-06"/> tuo minus, in motibus Ellipticis circa Solem turbare, quàm <lb/>ſi Sol in medio Syſtematis quieſceret. </s> <s xml:id="echoid-s18042" xml:space="preserve">Jupiter, ex. </s> <s xml:id="echoid-s18043" xml:space="preserve">gr.</s> <s xml:id="echoid-s18044" xml:space="preserve">, ſi <lb/>æqualiter à Mercurio & </s> <s xml:id="echoid-s18045" xml:space="preserve">Sole diſter, æquali celeritate ad ſe <lb/>trahet hæc duo corpora <anchor type="note" xlink:href="" symbol="*"/>, unde ſitus reſpectu Solis minus <anchor type="note" xlink:label="note-0694-07a" xlink:href="note-0694-07"/> turbatur, quàm ſi Sol hoc motu non agitaretur, & </s> <s xml:id="echoid-s18046" xml:space="preserve">Mercurius <lb/>ſolus ad Jovem tenderet: </s> <s xml:id="echoid-s18047" xml:space="preserve">pro variis Mercurii & </s> <s xml:id="echoid-s18048" xml:space="preserve">Solis à Jo-<lb/>ve diſtantiis, unus aut alter magis attrahitur, & </s> <s xml:id="echoid-s18049" xml:space="preserve">ſemper in ſi-<lb/>tu reſpectivo minor mutatio datur, dum ambo verſus ean-<lb/>dem partem feruntur, quàm ſi, Sole quieſcente, Mercurius <lb/>ſolus verſus Jovem moveretur.</s> <s xml:id="echoid-s18050" xml:space="preserve"/> </p> <div xml:id="echoid-div2766" type="float" level="2" n="6"> <note position="left" xlink:label="note-0694-06" xlink:href="note-0694-06a" xml:space="preserve">1267.</note> <note symbol="*" position="left" xlink:label="note-0694-07" xlink:href="note-0694-07a" xml:space="preserve">1235.</note> </div> <p> <s xml:id="echoid-s18051" xml:space="preserve">Ratiocinium hoc ad omnes Planetarum magis à Sole diſtan-<lb/>tium actiones, in minus diſtantes, applicari poteſt. </s> <s xml:id="echoid-s18052" xml:space="preserve">Quod atti-<lb/>net horum actionem in illos, pro vario ſitu ad Solem trahunt <lb/>Planetam, aut hunc à Sole ſeparant, & </s> <s xml:id="echoid-s18053" xml:space="preserve">integram conſiderando <lb/>revolutionem reſpectivam, id eſt, motum à conjunctione ad <lb/>conjunctionem ſequentem, turbatio minor eſt, quam ſi Sol <lb/>immobilis ſtaret.</s> <s xml:id="echoid-s18054" xml:space="preserve"/> </p> <pb o="(167)" file="0695" n="765" rhead="MATHEMATICA LIB. IV. CAP. XV."/> <p> <s xml:id="echoid-s18055" xml:space="preserve">Magnitudo Solis, cum cæteris corporibus Syſtematis noſtri <lb/> <anchor type="note" xlink:label="note-0695-01a" xlink:href="note-0695-01"/> collati, in cauſâ eſt, ut ex ante demonſtratis patet, parum <lb/>Planetas ſeſe mutuo turbare, cùm tamen non infinita ſit hæc <lb/>magnitudo, non in totum actiones mutuæ contemnendæ <lb/>ſunt.</s> <s xml:id="echoid-s18056" xml:space="preserve"/> </p> <div xml:id="echoid-div2767" type="float" level="2" n="7"> <note position="right" xlink:label="note-0695-01" xlink:href="note-0695-01a" xml:space="preserve">1268.</note> </div> <p> <s xml:id="echoid-s18057" xml:space="preserve">Diximus obſervationibus Aſtronomicis conſtare, Jovem <lb/>viam Saturni mutare ubi huic eſt proximus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18058" xml:space="preserve">quare hæc <anchor type="note" xlink:label="note-0695-02a" xlink:href="note-0695-02"/> turbatio præ cæteris ſenſibilis ſit, ex lege gravitatis dedu-<lb/>citur.</s> <s xml:id="echoid-s18059" xml:space="preserve"/> </p> <div xml:id="echoid-div2768" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0695-02" xlink:href="note-0695-02a" xml:space="preserve">1217.</note> </div> <p> <s xml:id="echoid-s18060" xml:space="preserve">Actiones Jovis in Saturnum, quando huic eſt proximus, <lb/> <anchor type="note" xlink:label="note-0695-03a" xlink:href="note-0695-03"/> & </s> <s xml:id="echoid-s18061" xml:space="preserve">Solis in eundem Planetam, qua hic in orbitâ retinetur, <lb/>ſunt inter ſe directè ut quantitates materiæ in Jove & </s> <s xml:id="echoid-s18062" xml:space="preserve">Sole <anchor type="note" xlink:href="" symbol="*"/> <anchor type="note" xlink:label="note-0695-04a" xlink:href="note-0695-04"/> nempe ut 9,248. </s> <s xml:id="echoid-s18063" xml:space="preserve">ad 10000. </s> <s xml:id="echoid-s18064" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18065" xml:space="preserve">inverſè ut quadrata diſ- <anchor type="note" xlink:label="note-0695-05a" xlink:href="note-0695-05"/> tantiarum Jovis & </s> <s xml:id="echoid-s18066" xml:space="preserve">Solis à Saturno, id eſt directè ut 81. </s> <s xml:id="echoid-s18067" xml:space="preserve">ad <lb/>16.</s> <s xml:id="echoid-s18068" xml:space="preserve">; nam diſtantiæ, Saturni & </s> <s xml:id="echoid-s18069" xml:space="preserve">Jovis à Sole, ſunt ferè ut 9. </s> <s xml:id="echoid-s18070" xml:space="preserve">ad <lb/> <anchor type="note" xlink:label="note-0695-06a" xlink:href="note-0695-06"/> 5.</s> <s xml:id="echoid-s18071" xml:space="preserve">; quare, ubi Jupiter Saturno eſt proximus, diſtantiæ hujus à <lb/>Jove & </s> <s xml:id="echoid-s18072" xml:space="preserve">Sole ſunt ut 4. </s> <s xml:id="echoid-s18073" xml:space="preserve">ad 9. </s> <s xml:id="echoid-s18074" xml:space="preserve">Ratio compoſita ex memora-<lb/>tis duabus eſt 749. </s> <s xml:id="echoid-s18075" xml:space="preserve">ad 160000.</s> <s xml:id="echoid-s18076" xml:space="preserve">, aut 1. </s> <s xml:id="echoid-s18077" xml:space="preserve">ad 214.</s> <s xml:id="echoid-s18078" xml:space="preserve">; hæc Jovis <lb/>actio cum Saturni gravitate in Solem conſpirat, & </s> <s xml:id="echoid-s18079" xml:space="preserve">ideò banc <lb/>parte {1/214} auget: </s> <s xml:id="echoid-s18080" xml:space="preserve">unde non mirum turbationem ſenſibilem <lb/>eſſe.</s> <s xml:id="echoid-s18081" xml:space="preserve"/> </p> <div xml:id="echoid-div2769" type="float" level="2" n="9"> <note position="right" xlink:label="note-0695-03" xlink:href="note-0695-03a" xml:space="preserve">1269.</note> <note symbol="*" position="right" xlink:label="note-0695-04" xlink:href="note-0695-04a" xml:space="preserve">1207.</note> <note symbol="*" position="right" xlink:label="note-0695-05" xlink:href="note-0695-05a" xml:space="preserve">1255.</note> <note position="right" xlink:label="note-0695-06" xlink:href="note-0695-06a" xml:space="preserve">1270.</note> </div> <p> <s xml:id="echoid-s18082" xml:space="preserve">Non conſideramus hìc vim, qua Jupiter Solem trahit, nam <lb/>hac orbita Saturni non mutatur, & </s> <s xml:id="echoid-s18083" xml:space="preserve">explicandum erat, quare <lb/>Saturnum â viâ deflexum obſervent Aſtronomi; </s> <s xml:id="echoid-s18084" xml:space="preserve">actione ta-<lb/>men Jovis in Solem, magis ad Saturnum trahitur Sol, & </s> <s xml:id="echoid-s18085" xml:space="preserve">ſi-<lb/>tus reſpectivus horum corporum magis turbatur, quàm obſer-<lb/>vationibus Aſtronomicis detegitur. </s> <s xml:id="echoid-s18086" xml:space="preserve">Vis qua Jupiter in ſitu <lb/>memorato trahit Solem, & </s> <s xml:id="echoid-s18087" xml:space="preserve">qua ideò hic verſus Saturnum <lb/>trahitur, eſt ad vim qua Jupiter Saturnum trahit, ut 16. </s> <s xml:id="echoid-s18088" xml:space="preserve">ad <lb/>25. </s> <s xml:id="echoid-s18089" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, id eſt ut 479. </s> <s xml:id="echoid-s18090" xml:space="preserve">ad 749, qui numerus exprimit vim, <anchor type="note" xlink:label="note-0695-07a" xlink:href="note-0695-07"/> qua Saturnus ad Jovem tendit, quando gravitas Saturni in <lb/>Solem exprimitur per 160000. </s> <s xml:id="echoid-s18091" xml:space="preserve">Si colligamus in unam ſum-<lb/>mam vires Jovis, quibus Saturnum & </s> <s xml:id="echoid-s18092" xml:space="preserve">Solem trahit; </s> <s xml:id="echoid-s18093" xml:space="preserve">erit vis, <lb/>qua, ex interpoſito Jove, hæc corpora ad ſe mutuo ten-<lb/>dunt, ad gravitatem Saturni in Solem, ut 1228, ad 160000.</s> <s xml:id="echoid-s18094" xml:space="preserve">; <lb/>ſed gravitas hæc eſt ad gravitatem Solis in Saturnum, ut <lb/> <anchor type="note" xlink:label="note-0695-08a" xlink:href="note-0695-08"/> 160000. </s> <s xml:id="echoid-s18095" xml:space="preserve">ad 67, 5 <anchor type="note" xlink:href="" symbol="*"/>, quare acceſſus mutuus Solis & </s> <s xml:id="echoid-s18096" xml:space="preserve">Saturni, <anchor type="note" xlink:label="note-0695-09a" xlink:href="note-0695-09"/> <pb o="(168)" file="0696" n="766" rhead="PHYSICES ELEMENTA"/> eſt ad augmentum bujus acceſſus ex actione Jovis interpoſiti, ut <lb/>160067. </s> <s xml:id="echoid-s18097" xml:space="preserve">ad 1228. </s> <s xml:id="echoid-s18098" xml:space="preserve">aut ut 130.</s> <s xml:id="echoid-s18099" xml:space="preserve">, ad 1. </s> <s xml:id="echoid-s18100" xml:space="preserve">Hæc notabilis eſt, & </s> <s xml:id="echoid-s18101" xml:space="preserve">om-<lb/>nium longè maxima, turbatio in motu Planetæ primarii <lb/>cujuscunque, hæc etiam in unico tantum caſu obtinet; </s> <s xml:id="echoid-s18102" xml:space="preserve">nam, <lb/>recedente Jove à Saturno, brevi inſenſibilis eſt turbatio motus <lb/>Saturni.</s> <s xml:id="echoid-s18103" xml:space="preserve"/> </p> <div xml:id="echoid-div2770" type="float" level="2" n="10"> <note symbol="*" position="right" xlink:label="note-0695-07" xlink:href="note-0695-07a" xml:space="preserve">1208.</note> <note symbol="*" position="right" xlink:label="note-0695-08" xlink:href="note-0695-08a" xml:space="preserve">1207. 1255.</note> <note position="right" xlink:label="note-0695-09" xlink:href="note-0695-09a" xml:space="preserve">1271.</note> </div> <p> <s xml:id="echoid-s18104" xml:space="preserve">In eodem ſitu Jovis, Saturno proximi, hujus vis licèt in <lb/>hoc caſu ſit omnium maxima, non æquè ſenſibilis eſt, ad <lb/>viam Jovis circa Solem mutandam. </s> <s xml:id="echoid-s18105" xml:space="preserve">Actio Saturni ad Jovem <lb/>trahendum, eſtad hujus actionem, qua Solem trahit, ut 81. <lb/></s> <s xml:id="echoid-s18106" xml:space="preserve">ad 16 <anchor type="note" xlink:href="" symbol="*"/>, celerius ergo illum trahit, & </s> <s xml:id="echoid-s18107" xml:space="preserve">cûm verſus eandem <anchor type="note" xlink:label="note-0696-01a" xlink:href="note-0696-01"/> partem trahantur, differentia harum virium eſt vis, cum qua ex <lb/>Saturni actione, Jupiter & </s> <s xml:id="echoid-s18108" xml:space="preserve">Sol à ſe mutuo ſeparantur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18109" xml:space="preserve">quæ <anchor type="note" xlink:label="note-0696-02a" xlink:href="note-0696-02"/> ideo eſt ad gravitatem Solis in Saturnum, ut 65. </s> <s xml:id="echoid-s18110" xml:space="preserve">ad 16. </s> <s xml:id="echoid-s18111" xml:space="preserve">Hæc <lb/>autem Solis gravitas in Saturnum eſt ad gravitatem Jovis in <lb/>Solem, ut 4,223. </s> <s xml:id="echoid-s18112" xml:space="preserve">ad 10000. </s> <s xml:id="echoid-s18113" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18114" xml:space="preserve">ut 25. </s> <s xml:id="echoid-s18115" xml:space="preserve">ad 81. </s> <s xml:id="echoid-s18116" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, id eſt ut <anchor type="note" xlink:label="note-0696-03a" xlink:href="note-0696-03"/> <anchor type="note" xlink:label="note-0696-04a" xlink:href="note-0696-04"/> 106. </s> <s xml:id="echoid-s18117" xml:space="preserve">ad 810000, aut ut 16. </s> <s xml:id="echoid-s18118" xml:space="preserve">ad 122756; </s> <s xml:id="echoid-s18119" xml:space="preserve">eſt idcirco vis tur-<lb/>bans Saturni ad Jovis gravitatem in Solem, ut 65. </s> <s xml:id="echoid-s18120" xml:space="preserve">ad 122756, <lb/>aut ut 1. </s> <s xml:id="echoid-s18121" xml:space="preserve">ad 1888.</s> <s xml:id="echoid-s18122" xml:space="preserve">; ita ex actione maximâ Saturni, partetan-<lb/> <anchor type="note" xlink:label="note-0696-05a" xlink:href="note-0696-05"/> tùm {1/1888}, minuitur gravitas Jovis in Solem, quæ turbatio <lb/>inſenſibilis eſt.</s> <s xml:id="echoid-s18123" xml:space="preserve"/> </p> <div xml:id="echoid-div2771" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0696-01" xlink:href="note-0696-01a" xml:space="preserve">1208.</note> <note symbol="*" position="left" xlink:label="note-0696-02" xlink:href="note-0696-02a" xml:space="preserve">175.</note> <note symbol="*" position="left" xlink:label="note-0696-03" xlink:href="note-0696-03a" xml:space="preserve">1207. 1255.</note> <note symbol="*" position="left" xlink:label="note-0696-04" xlink:href="note-0696-04a" xml:space="preserve">1208.</note> <note position="left" xlink:label="note-0696-05" xlink:href="note-0696-05a" xml:space="preserve">1272.</note> </div> <p> <s xml:id="echoid-s18124" xml:space="preserve">Reliquæ Planetarum mutuæ perturbationes ſunt multò mi-<lb/>nores, ut patebit determinando illam, quæ omnium harum <lb/>maxima eſt, Jovis in Martem, quæ computatione ſimili præ-<lb/>cedenti detegitur.</s> <s xml:id="echoid-s18125" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18126" xml:space="preserve">Diſtantiæ Jovis à Marte & </s> <s xml:id="echoid-s18127" xml:space="preserve">Sole, quando Mars inter hunc <lb/>& </s> <s xml:id="echoid-s18128" xml:space="preserve">Jovem in eâdem lineâ datur, ſunt circiter ut 7. </s> <s xml:id="echoid-s18129" xml:space="preserve">ad 10. </s> <s xml:id="echoid-s18130" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18131" xml:space="preserve"> <anchor type="note" xlink:label="note-0696-06a" xlink:href="note-0696-06"/> quare vires, cum quibus Jupiter hæc corpora trahit, ſunt <lb/>ut 100. </s> <s xml:id="echoid-s18132" xml:space="preserve">ad 49. </s> <s xml:id="echoid-s18133" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, quarum virium differentia eſt ad gravitatem <anchor type="note" xlink:label="note-0696-07a" xlink:href="note-0696-07"/> Solis in Jovem, ut 51. </s> <s xml:id="echoid-s18134" xml:space="preserve">ad 49.</s> <s xml:id="echoid-s18135" xml:space="preserve">. Gravitas hæc Solis in Jovem, <lb/>eſt ad gravitatem Martis in Solem, ut 9,248. </s> <s xml:id="echoid-s18136" xml:space="preserve">ad 1000. </s> <s xml:id="echoid-s18137" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s18138" xml:space="preserve"> <anchor type="note" xlink:label="note-0696-08a" xlink:href="note-0696-08"/> ut 9. </s> <s xml:id="echoid-s18139" xml:space="preserve">ad 100 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18140" xml:space="preserve">id eſt ut 83. </s> <s xml:id="echoid-s18141" xml:space="preserve">ad 1000000.</s> <s xml:id="echoid-s18142" xml:space="preserve">; aut ut 49. </s> <s xml:id="echoid-s18143" xml:space="preserve">ad <anchor type="note" xlink:label="note-0696-09a" xlink:href="note-0696-09"/> 590443.</s> <s xml:id="echoid-s18144" xml:space="preserve">; & </s> <s xml:id="echoid-s18145" xml:space="preserve">vis perturbans Jovis ad gravitatem Martis in So-<lb/>lem, ut 51. </s> <s xml:id="echoid-s18146" xml:space="preserve">ad 590443; </s> <s xml:id="echoid-s18147" xml:space="preserve">aut ut 1. </s> <s xml:id="echoid-s18148" xml:space="preserve">ad 11577: </s> <s xml:id="echoid-s18149" xml:space="preserve">Quare Mar-<lb/> <anchor type="note" xlink:label="note-0696-10a" xlink:href="note-0696-10"/> tis gravitas in Solem, parte tantùm {1/11577}, actione Jovis illi <lb/>proximi minuitur.</s> <s xml:id="echoid-s18150" xml:space="preserve"/> </p> <div xml:id="echoid-div2772" type="float" level="2" n="12"> <note symbol="*" position="left" xlink:label="note-0696-06" xlink:href="note-0696-06a" xml:space="preserve">961. 962.</note> <note symbol="*" position="left" xlink:label="note-0696-07" xlink:href="note-0696-07a" xml:space="preserve">1280.</note> <note symbol="*" position="left" xlink:label="note-0696-08" xlink:href="note-0696-08a" xml:space="preserve">1207. 1255.</note> <note symbol="*" position="left" xlink:label="note-0696-09" xlink:href="note-0696-09a" xml:space="preserve">1208.</note> <note position="left" xlink:label="note-0696-10" xlink:href="note-0696-10a" xml:space="preserve">1273.</note> </div> <p> <s xml:id="echoid-s18151" xml:space="preserve">Quantumvis perturbationes hæ, ex actione Planetarum <lb/> <anchor type="note" xlink:label="note-0696-11a" xlink:href="note-0696-11"/> <pb o="(169)" file="0697" n="767" rhead="MATHEMATICA LIB. IV. CAP. XV."/> in ſe mutuo ſint exiguæ, & </s> <s xml:id="echoid-s18152" xml:space="preserve">licèt, quæ in ſitu Planetarum di-<lb/>verſo locum habent, quodammodo ſeſe mutuo compenſent, <lb/>hiſce tamen paululum mutatur proportio, in qua decreſcit <lb/>vis, quæ Planetas in orbitis retinet, ita ut non exactè minua-<lb/>tur in ratione inverlâ quadrati diſtantiæ, idcirco licèt ſenſibi-<lb/>liter quieſcant orbitæ, poſt multas revolutiones ſitus barum or-<lb/>bitarum paululum mutatus obſervatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18153" xml:space="preserve"> <anchor type="note" xlink:label="note-0697-01a" xlink:href="note-0697-01"/> </s> </p> <div xml:id="echoid-div2773" type="float" level="2" n="13"> <note position="left" xlink:label="note-0696-11" xlink:href="note-0696-11a" xml:space="preserve">1274.</note> <note symbol="*" position="right" xlink:label="note-0697-01" xlink:href="note-0697-01a" xml:space="preserve">243. 929.</note> </div> <p> <s xml:id="echoid-s18154" xml:space="preserve">Ex hiſce omnibus ſequitur Planetas in principio, ad diſ-<lb/> <anchor type="note" xlink:label="note-0697-02a" xlink:href="note-0697-02"/> tantias ad quas à Sole moventur, ſemel projectos, in moti-<lb/>bus, legibus ante expoſitis, perſeverare; </s> <s xml:id="echoid-s18155" xml:space="preserve">excentricitatemque <lb/>orbitarum pendere à celeritate, & </s> <s xml:id="echoid-s18156" xml:space="preserve">directione primæ projec-<lb/>tionis. </s> <s xml:id="echoid-s18157" xml:space="preserve">Motus autem hi diutiſſimè conſervari poſſunt, prop-<lb/>ter materiæ coeleſtis exiguam reſiſtentiam.</s> <s xml:id="echoid-s18158" xml:space="preserve"/> </p> <div xml:id="echoid-div2774" type="float" level="2" n="14"> <note position="right" xlink:label="note-0697-02" xlink:href="note-0697-02a" xml:space="preserve">1275.</note> </div> <p> <s xml:id="echoid-s18159" xml:space="preserve">Patet etiam, quare lineis ad centrum Solis ductis deſcribant <lb/>areas temporibus proportionales; </s> <s xml:id="echoid-s18160" xml:space="preserve">quia nempe cæteræ gravi-<lb/>tates in Syſtemate exiguæ ſunt, reſpectu gravitatis verſus So-<lb/>lem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18161" xml:space="preserve">ideòque hac ſolâ in orbitis retinentur Planetæ, un- <anchor type="note" xlink:label="note-0697-03a" xlink:href="note-0697-03"/> de hæc arearum proportio ſequitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18162" xml:space="preserve">Motus etiam in li- <anchor type="note" xlink:label="note-0697-04a" xlink:href="note-0697-04"/> neis Ellipticis lentiſſimè tranſlatis, ex lege gravitatis ſequitur; <lb/></s> <s xml:id="echoid-s18163" xml:space="preserve">hæ enim immobiles eſſent, ſi in Solem tantùm graves eſſent <lb/>Planetæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18164" xml:space="preserve">ex actione autem mutuâ Planetarum lenta orbium <anchor type="note" xlink:label="note-0697-05a" xlink:href="note-0697-05"/> agitatio deducitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18165" xml:space="preserve">Quod autem ſpectat proportionem, <anchor type="note" xlink:label="note-0697-06a" xlink:href="note-0697-06"/> quæ inter cubos diſtantiarum & </s> <s xml:id="echoid-s18166" xml:space="preserve">temporum periodicorum <lb/>quadrata obſervatur, ſequitur hæc quoque ex gravitatis le-<lb/>ge <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18167" xml:space="preserve">ita ut ſi hiſce addamus, quæ de deflectione Saturni dixi- <anchor type="note" xlink:label="note-0697-07a" xlink:href="note-0697-07"/> mus <anchor type="note" xlink:href="" symbol="*"/>, nihil explicandum ſuperſit, circa motum Planetarum <anchor type="note" xlink:label="note-0697-08a" xlink:href="note-0697-08"/> primariorum.</s> <s xml:id="echoid-s18168" xml:space="preserve"/> </p> <div xml:id="echoid-div2775" type="float" level="2" n="15"> <note symbol="*" position="right" xlink:label="note-0697-03" xlink:href="note-0697-03a" xml:space="preserve">1265.</note> <note symbol="*" position="right" xlink:label="note-0697-04" xlink:href="note-0697-04a" xml:space="preserve">225.</note> <note symbol="*" position="right" xlink:label="note-0697-05" xlink:href="note-0697-05a" xml:space="preserve">241. 1208.</note> <note symbol="*" position="right" xlink:label="note-0697-06" xlink:href="note-0697-06a" xml:space="preserve">1274.</note> <note symbol="*" position="right" xlink:label="note-0697-07" xlink:href="note-0697-07a" xml:space="preserve">239. 1208.</note> <note symbol="*" position="right" xlink:label="note-0697-08" xlink:href="note-0697-08a" xml:space="preserve">1217. 1270.</note> </div> <p> <s xml:id="echoid-s18169" xml:space="preserve">Cometarum motus à lege Gravitatis pendere, etiam ex ob-<lb/> <anchor type="note" xlink:label="note-0697-09a" xlink:href="note-0697-09"/> ſervationibus deducitur; </s> <s xml:id="echoid-s18170" xml:space="preserve">& </s> <s xml:id="echoid-s18171" xml:space="preserve">horum reſpectu, ut circa Pla-<lb/>netas dictum, Solis gravitas prævalet, & </s> <s xml:id="echoid-s18172" xml:space="preserve">hac gravitate à <lb/>viâ rectâ deflectuntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18173" xml:space="preserve">viæ autem curvaturam ab hac eâ- <anchor type="note" xlink:label="note-0697-10a" xlink:href="note-0697-10"/> dem gravitate etiam pendere ex eo ſequitur, quod corpus <lb/>ex hac gravitate deſcribat aut Ellipſin, aut Parabolam aut Hy-<lb/>perbolam <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18174" xml:space="preserve">quales lineas deſcripſiſſe hos Cometas conſtat, <anchor type="note" xlink:label="note-0697-11a" xlink:href="note-0697-11"/> quorum Trajectoriæ fuere determinatæ.</s> <s xml:id="echoid-s18175" xml:space="preserve"/> </p> <div xml:id="echoid-div2776" type="float" level="2" n="16"> <note position="right" xlink:label="note-0697-09" xlink:href="note-0697-09a" xml:space="preserve">1276.</note> <note symbol="*" position="right" xlink:label="note-0697-10" xlink:href="note-0697-10a" xml:space="preserve">980. 226.</note> <note symbol="*" position="right" xlink:label="note-0697-11" xlink:href="note-0697-11a" xml:space="preserve">241. 1208.</note> </div> <p> <s xml:id="echoid-s18176" xml:space="preserve">Satellites Jovis & </s> <s xml:id="echoid-s18177" xml:space="preserve">Saturni circa primarios iiſdem legibus <lb/> <anchor type="note" xlink:label="note-0697-12a" xlink:href="note-0697-12"/> moventur, quibus primarii circa Solem rotantur <anchor type="note" xlink:href="" symbol="*"/>, quare mo- <anchor type="note" xlink:label="note-0697-13a" xlink:href="note-0697-13"/> <pb o="(170)" file="0698" n="768" rhead="PHYSICES ELEMENTA"/> tuum horum explicatio <anchor type="note" xlink:href="" symbol="*"/> ad illos etiam referri poteſt, nam <anchor type="note" xlink:label="note-0698-01a" xlink:href="note-0698-01"/> in tribus hiſce caſibus, circa Solem, Jovem & </s> <s xml:id="echoid-s18178" xml:space="preserve">Saturnum, <lb/>dantur corpora minora, ad varias diſtantias, circa corpus <lb/>multò majus revolventia.</s> <s xml:id="echoid-s18179" xml:space="preserve"/> </p> <div xml:id="echoid-div2777" type="float" level="2" n="17"> <note position="right" xlink:label="note-0697-12" xlink:href="note-0697-12a" xml:space="preserve">1277.</note> <note symbol="*" position="right" xlink:label="note-0697-13" xlink:href="note-0697-13a" xml:space="preserve">944. 966. 974.</note> <note symbol="*" position="left" xlink:label="note-0698-01" xlink:href="note-0698-01a" xml:space="preserve">1275.</note> </div> <p> <s xml:id="echoid-s18180" xml:space="preserve">Dum ſecundarii circa primarium rotantur, omnes motu <lb/> <anchor type="note" xlink:label="note-0698-02a" xlink:href="note-0698-02"/> communi moveri poſſe, clarum eſt, quo non turbantur mo-<lb/>tus reſpectivi, quibus inter ſe agitantur, quia diverſis impreſ-<lb/>ſionibus corpus eodem tempore ferri poteſt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18181" xml:space="preserve">Motus pri- <anchor type="note" xlink:label="note-0698-03a" xlink:href="note-0698-03"/> mario cum ſatellitibus ſuis communis, eſt motus primarii circa <lb/>Solem.</s> <s xml:id="echoid-s18182" xml:space="preserve"/> </p> <div xml:id="echoid-div2778" type="float" level="2" n="18"> <note position="left" xlink:label="note-0698-02" xlink:href="note-0698-02a" xml:space="preserve">1278.</note> <note symbol="*" position="left" xlink:label="note-0698-03" xlink:href="note-0698-03a" xml:space="preserve">125.</note> </div> <p> <s xml:id="echoid-s18183" xml:space="preserve">Turbantur tamen ſecundariorum motus ex Solis actione, ver-<lb/> <anchor type="note" xlink:label="note-0698-04a" xlink:href="note-0698-04"/> ſus quem pro vario ſitu nunc primario celerius, nunc tardius <lb/>feruntur, plerumque etiam per directiones diverſas in cen-<lb/>tro Solis concurrentes; </s> <s xml:id="echoid-s18184" xml:space="preserve">hæ irregularites, quæ exiguæ ſunt, <lb/>in ſatellitibus Saturni & </s> <s xml:id="echoid-s18185" xml:space="preserve">Jovis obſervari non poſſunt, licètre-<lb/>verâ ſimiles ſint illis, quæ in motu Lunæ obſervantur; </s> <s xml:id="echoid-s18186" xml:space="preserve">mini-<lb/>ma hujus deviatio nobis admodum eſt ſenſibilis; </s> <s xml:id="echoid-s18187" xml:space="preserve">exactiſſimè <lb/>autem Lunæ irregularitates ex Theoriâ gravitatis ſequi, in ca-<lb/>pite ſequenti patebit.</s> <s xml:id="echoid-s18188" xml:space="preserve"/> </p> <div xml:id="echoid-div2779" type="float" level="2" n="19"> <note position="left" xlink:label="note-0698-04" xlink:href="note-0698-04a" xml:space="preserve">1279.</note> </div> </div> <div xml:id="echoid-div2781" type="section" level="1" n="676"> <head xml:id="echoid-head877" xml:space="preserve">CAPUT XVI.</head> <head xml:id="echoid-head878" style="it" xml:space="preserve">Motus Lunæ Explicatio Phyſica.</head> <p> <s xml:id="echoid-s18189" xml:space="preserve">LUnam & </s> <s xml:id="echoid-s18190" xml:space="preserve">Tellurem ſemel projectas, circa commune gravi-<lb/> <anchor type="note" xlink:label="note-0698-05a" xlink:href="note-0698-05"/> tatis centrum in motu perſeverare poſſe conſtat <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18191" xml:space="preserve">Si im- <anchor type="note" xlink:label="note-0698-06a" xlink:href="note-0698-06"/> preſſione communi quacunque ferantur, per lineas rectas pa-<lb/>rallelas inter ſe, ut de ſatellitibus Jovis & </s> <s xml:id="echoid-s18192" xml:space="preserve">Saturni dictum <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0698-07a" xlink:href="note-0698-07"/> motus hic non turbabit motum circa centrum commune gra-<lb/>vitatis, quod ſolum directionem hanc ſequetur; </s> <s xml:id="echoid-s18193" xml:space="preserve">quia reſ-<lb/>pectu amborum corporum quieſcit. </s> <s xml:id="echoid-s18194" xml:space="preserve">Corpora verò motu com-<lb/>poſito, ex hac impreſſione & </s> <s xml:id="echoid-s18195" xml:space="preserve">motu circa commune gravitatis <lb/>centrum feruntur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18196" xml:space="preserve">id eſt circa hoc tranſlatum girantur, ut <anchor type="note" xlink:label="note-0698-08a" xlink:href="note-0698-08"/> circa idem quieſcens ante hujus motum. </s> <s xml:id="echoid-s18197" xml:space="preserve">Si omnibus mo-<lb/>mentis novæ impreſſiones, communes ambobus corporibus, <lb/>in hæc agant, poterit omnibus momentis mutari via centri <lb/>gravitatis, quæ mutatio ſimilis erit illi, quam ſubirent cor-<lb/>pora ipſa, ſi motu reſpectivo carêrent.</s> <s xml:id="echoid-s18198" xml:space="preserve"/> </p> <div xml:id="echoid-div2781" type="float" level="2" n="1"> <note position="left" xlink:label="note-0698-05" xlink:href="note-0698-05a" xml:space="preserve">1280.</note> <note symbol="*" position="left" xlink:label="note-0698-06" xlink:href="note-0698-06a" xml:space="preserve">1263.</note> <note symbol="*" position="left" xlink:label="note-0698-07" xlink:href="note-0698-07a" xml:space="preserve">1278.</note> <note symbol="*" position="left" xlink:label="note-0698-08" xlink:href="note-0698-08a" xml:space="preserve">190.</note> </div> <pb o="(171)" file="0699" n="769" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> <p> <s xml:id="echoid-s18199" xml:space="preserve">Exhiſce deducimus, ſi, dum Luna & </s> <s xml:id="echoid-s18200" xml:space="preserve">Tellus circa commu-<lb/>ne centrum gravitatis in gyrum moventur, ambæ proji-<lb/>ciantur, viam centri gravitatis ex actione Solis, in utrum-<lb/>que corpus agenti, illam eſſe, quam corpus, eodem modo <lb/>projectum, circa Solem deſcribere poſſet.</s> <s xml:id="echoid-s18201" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s18202" xml:space="preserve">Unde ſequitur Lunam motum Telluris turbare, & </s> <s xml:id="echoid-s18203" xml:space="preserve">cen-<lb/> <anchor type="note" xlink:label="note-0699-01a" xlink:href="note-0699-01"/> trum commune gravitatis borum corporum de ſcribere orbitam, <lb/>circa Solem, quam buc uſque à Tellure ipſâ deſcriptam dixi-<lb/>mus; </s> <s xml:id="echoid-s18204" xml:space="preserve">quia ad actionem Lunæ huc uſque non attendimus; <lb/></s> <s xml:id="echoid-s18205" xml:space="preserve">Tellus autem deſcribit curvam irregularem. </s> <s xml:id="echoid-s18206" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0699-02a" xlink:href="note-0699-02"/> </s> </p> <div xml:id="echoid-div2782" type="float" level="2" n="2"> <note position="right" xlink:label="note-0699-01" xlink:href="note-0699-01a" xml:space="preserve">1281.</note> <note position="right" xlink:label="note-0699-02" xlink:href="note-0699-02a" xml:space="preserve">1282.</note> </div> <p> <s xml:id="echoid-s18207" xml:space="preserve">Poſito Sole in S; </s> <s xml:id="echoid-s18208" xml:space="preserve">ſit, in F, centrum commune gravita-<lb/> <anchor type="note" xlink:label="note-0699-03a" xlink:href="note-0699-03"/> tis Lunæ Q & </s> <s xml:id="echoid-s18209" xml:space="preserve">Telluris M, in Plenilunio: </s> <s xml:id="echoid-s18210" xml:space="preserve">poſt integram Lu-<lb/> <anchor type="note" xlink:label="note-0699-04a" xlink:href="note-0699-04"/> <anchor type="note" xlink:label="note-0699-05a" xlink:href="note-0699-05"/> nationem, id eſt iterum in Plenilunio, ſit hocce centrum in <lb/>A; </s> <s xml:id="echoid-s18211" xml:space="preserve">& </s> <s xml:id="echoid-s18212" xml:space="preserve">ſit FDA orbita, quam Telluris vocamus, & </s> <s xml:id="echoid-s18213" xml:space="preserve">in qua <lb/>memoratum centrum gravitatis reverâ movetur.</s> <s xml:id="echoid-s18214" xml:space="preserve"/> </p> <div xml:id="echoid-div2783" type="float" level="2" n="3"> <note position="right" xlink:label="note-0699-03" xlink:href="note-0699-03a" xml:space="preserve">1283.</note> <note position="right" xlink:label="note-0699-04" xlink:href="note-0699-04a" xml:space="preserve">TAB. XXIV.</note> <note position="right" xlink:label="note-0699-05" xlink:href="note-0699-05a" xml:space="preserve">fig. 4.</note> </div> <p> <s xml:id="echoid-s18215" xml:space="preserve">Sit Lunatio hæc diviſa in quatuor partes æquales; </s> <s xml:id="echoid-s18216" xml:space="preserve">poſt <lb/>primam centrum gravitatis erit in E, Luna in P, Tellus in <lb/>L; </s> <s xml:id="echoid-s18217" xml:space="preserve">lapsâ ſecundâ temporis parte, in Novilunio, centrum <lb/>gravitatis erit in D, Luna in R, Tellus in I; </s> <s xml:id="echoid-s18218" xml:space="preserve">in quadraturâ <lb/>ſequenti, centrum gravitatis erit in B, Luna in O, Tellus <lb/>in H; </s> <s xml:id="echoid-s18219" xml:space="preserve">tandem in Plenilunio poſito centro gravitatis in A, <lb/>Luna erit in N, Tellus in G: </s> <s xml:id="echoid-s18220" xml:space="preserve">quæ omnia ſequuntur ex re-<lb/>volutione Telluris & </s> <s xml:id="echoid-s18221" xml:space="preserve">Lunæ circa commune centrum gravi-<lb/>tatis, dum hoc in orbitâ circa Solem movetur.</s> <s xml:id="echoid-s18222" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18223" xml:space="preserve">Videmus ergo Tellurem moveri in curvâ MLIHG, quæ <lb/>in ſingulis Lunationibus bis inflectitur, quæ curva etiam in <lb/>ſe non redit, quia inflectiones, in variis revolutionibus circa <lb/>Solem, non coincidunt; </s> <s xml:id="echoid-s18224" xml:space="preserve">quia duodecim Lunationes cum <lb/>tertiâ parte circiter ſingulis annis abſolvuntur.</s> <s xml:id="echoid-s18225" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18226" xml:space="preserve">Irregularitas hæc motus Telluris, quæ ex legibus Naturæ <lb/> <anchor type="note" xlink:label="note-0699-06a" xlink:href="note-0699-06"/> deducitur, nimium eſt exigua, ut in obſervationibus Aſtro-<lb/>nomicis ſenſibilis ſit; </s> <s xml:id="echoid-s18227" xml:space="preserve">quare ſine errore ponimus, centrum ip-<lb/>ſum Telluris orbitam FDA percurrere; </s> <s xml:id="echoid-s18228" xml:space="preserve">nam MF, aut <lb/>DI, diſtantia maxima Telluris ab hac orbitâ, eſt circiter <lb/>pars quadrageſima diſtantiæ MR, quæ ipſa non eſt trecen-<lb/>teſima pars diſtantiæ FS.</s> <s xml:id="echoid-s18229" xml:space="preserve"/> </p> <div xml:id="echoid-div2784" type="float" level="2" n="4"> <note position="right" xlink:label="note-0699-06" xlink:href="note-0699-06a" xml:space="preserve">1284.</note> </div> <p> <s xml:id="echoid-s18230" xml:space="preserve">Etiam, in explicandis quæ Lunam ſpectant, negligimus con-<lb/> <anchor type="note" xlink:label="note-0699-07a" xlink:href="note-0699-07"/> <pb o="(172)" file="0700" n="770" rhead="PHYSICES ELEMENTA"/> ſiderationem motus Telluris, circa ſæpius memoratum cen-<lb/>trum gravitatis; </s> <s xml:id="echoid-s18231" xml:space="preserve">ſed ponimus banc revolvere ad diſtantiam <lb/>à centro Telluris 60. </s> <s xml:id="echoid-s18232" xml:space="preserve">ſemid.</s> <s xml:id="echoid-s18233" xml:space="preserve">; quia, ut antea demonſtravi-<lb/>mus <anchor type="note" xlink:href="" symbol="*"/>, ad hanc diſtantiam, in ſuo tempore periodico, re- <anchor type="note" xlink:label="note-0700-01a" xlink:href="note-0700-01"/> volvere poſſet circa Tellurem quieſcentem, aut tranſlatam <lb/>in orbitâ, in qua ex Lunæ actione non turbatur Tel-<lb/>lus. </s> <s xml:id="echoid-s18234" xml:space="preserve">Multo facilius hac methodo Lunæ irregularitates de-<lb/>teguntur, quæ eædem ſunt, ut facile patet, ſive Luna circa <lb/>commune centrum gravitatis Lunæ & </s> <s xml:id="echoid-s18235" xml:space="preserve">Telluris, ſive circa ip-<lb/>ſum Telluris centrum rotetur.</s> <s xml:id="echoid-s18236" xml:space="preserve"/> </p> <div xml:id="echoid-div2785" type="float" level="2" n="5"> <note position="right" xlink:label="note-0699-07" xlink:href="note-0699-07a" xml:space="preserve">1285.</note> <note symbol="*" position="left" xlink:label="note-0700-01" xlink:href="note-0700-01a" xml:space="preserve">1253.</note> </div> <p> <s xml:id="echoid-s18237" xml:space="preserve">Sit Sol S; </s> <s xml:id="echoid-s18238" xml:space="preserve">Tellus in T; </s> <s xml:id="echoid-s18239" xml:space="preserve">Lunæ orbita AL Bl; </s> <s xml:id="echoid-s18240" xml:space="preserve">Tandem <lb/> <anchor type="note" xlink:label="note-0700-02a" xlink:href="note-0700-02"/> detur Luna in A in quadraturâ; </s> <s xml:id="echoid-s18241" xml:space="preserve">per AS verſus Solem ten-<lb/> <anchor type="note" xlink:label="note-0700-03a" xlink:href="note-0700-03"/> <anchor type="note" xlink:label="note-0700-04a" xlink:href="note-0700-04"/> dit, eodem modo, & </s> <s xml:id="echoid-s18242" xml:space="preserve">eâdem cum vi, qua Tellus, verſus <lb/>S per TS fertur; </s> <s xml:id="echoid-s18243" xml:space="preserve">quia diſtantiæ AS & </s> <s xml:id="echoid-s18244" xml:space="preserve">TS ſunt æquales: <lb/></s> <s xml:id="echoid-s18245" xml:space="preserve">repræſentetur vis hæc per TS aut AS poterit vis, qua Lu-<lb/>na conatur deſcendere per AS, reſolvi in duas, formato <lb/>parallelogrammo ADST; </s> <s xml:id="echoid-s18246" xml:space="preserve">ita ut Luna conetur moveri per <lb/>AD & </s> <s xml:id="echoid-s18247" xml:space="preserve">AT, viribus, quæ hiſce lineis repræſentantur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18248" xml:space="preserve"/> </p> <div xml:id="echoid-div2786" type="float" level="2" n="6"> <note position="left" xlink:label="note-0700-02" xlink:href="note-0700-02a" xml:space="preserve">1286.</note> <note position="left" xlink:label="note-0700-03" xlink:href="note-0700-03a" xml:space="preserve">TAB. XXV.</note> <note position="left" xlink:label="note-0700-04" xlink:href="note-0700-04a" xml:space="preserve">fig. 1.</note> </div> <note symbol="*" position="left" xml:space="preserve">192.</note> <p> <s xml:id="echoid-s18249" xml:space="preserve">Vi per AD agenti, Luna eâdem cum celeritate, & </s> <s xml:id="echoid-s18250" xml:space="preserve">ver-<lb/>ſus eandem partem cum Tellure fertur; </s> <s xml:id="echoid-s18251" xml:space="preserve">propter lineas paral-<lb/>lelas & </s> <s xml:id="echoid-s18252" xml:space="preserve">æquales TS & </s> <s xml:id="echoid-s18253" xml:space="preserve">AD; </s> <s xml:id="echoid-s18254" xml:space="preserve">quare ex hoc motu relatioin-<lb/>ter Lunam & </s> <s xml:id="echoid-s18255" xml:space="preserve">Tellurem non mutatur; </s> <s xml:id="echoid-s18256" xml:space="preserve">vis autem per AT <lb/>cum gravitate Lunæ in Tellurem conſpirat, & </s> <s xml:id="echoid-s18257" xml:space="preserve">augetur gra-<lb/> <anchor type="note" xlink:label="note-0700-06a" xlink:href="note-0700-06"/> vitas hæc ex actione Solis, quando Luna in quadraturis da-<lb/>tur: </s> <s xml:id="echoid-s18258" xml:space="preserve">eſtque augmentum ad Telluris gravitatem in Solem, ut <lb/>AT, Lunæ diſtantia à Tellure, ad TS, Telluris diſtantiam <lb/>à Sole.</s> <s xml:id="echoid-s18259" xml:space="preserve"/> </p> <div xml:id="echoid-div2787" type="float" level="2" n="7"> <note position="left" xlink:label="note-0700-06" xlink:href="note-0700-06a" xml:space="preserve">1287.</note> </div> <p style="it"> <s xml:id="echoid-s18260" xml:space="preserve">Manente TS, Telluris diſtantiâ à Sole, creſcit & </s> <s xml:id="echoid-s18261" xml:space="preserve">minui-<lb/> <anchor type="note" xlink:label="note-0700-07a" xlink:href="note-0700-07"/> tur augmentum memoratum gravitatis in ratione lineæ AT, <lb/>diſtantiæ Lunæ à Tellure.</s> <s xml:id="echoid-s18262" xml:space="preserve"/> </p> <div xml:id="echoid-div2788" type="float" level="2" n="8"> <note position="left" xlink:label="note-0700-07" xlink:href="note-0700-07a" xml:space="preserve">1288.</note> </div> <p> <s xml:id="echoid-s18263" xml:space="preserve">Manente autem hac Lunæ diſtantiâ à Tellure AT, ſi au-<lb/>geatur TS minor erit AT reſpectu AS; </s> <s xml:id="echoid-s18264" xml:space="preserve">ideo licèt non mu-<lb/>taretur vis, qua Tellus & </s> <s xml:id="echoid-s18265" xml:space="preserve">Luna verſus Solem cadunt, aug-<lb/>mentum minus erit, & </s> <s xml:id="echoid-s18266" xml:space="preserve">eo minus, quo major eſt TS, id eſt, <lb/>erit inverſè ut TS; </s> <s xml:id="echoid-s18267" xml:space="preserve">vis autem gravitatis non manet, quando <lb/>TS augetur, ſed minuitur; </s> <s xml:id="echoid-s18268" xml:space="preserve">quare & </s> <s xml:id="echoid-s18269" xml:space="preserve">eo reſpectu minuitur <lb/>augmentum memoratum, & </s> <s xml:id="echoid-s18270" xml:space="preserve">quidem in eâdem ratione cum <pb file="0701" n="771"/> <pb file="0701a" n="772"/> <anchor type="figure" xlink:label="fig-0701a-01a" xlink:href="fig-0701a-01"/> <pb file="0702" n="773"/> <pb o="(173)" file="0703" n="774" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> hac vi gravitatis; </s> <s xml:id="echoid-s18271" xml:space="preserve">ideòque in ratione inverſa # ; </s> <s xml:id="echoid-s18272" xml:space="preserve">quadrati diſ-<lb/>tantiæ TS <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18273" xml:space="preserve">ſi hæc diminutio cum ſtatim memoratâ con- <anchor type="note" xlink:label="note-0703-01a" xlink:href="note-0703-01"/> jungatur, videmus augmentum, de quo agimus, ſequi ratio-<lb/> <anchor type="note" xlink:label="note-0703-02a" xlink:href="note-0703-02"/> nem inverſam cubi diſtantiæ Telluris à Sole.</s> <s xml:id="echoid-s18274" xml:space="preserve"/> </p> <div xml:id="echoid-div2789" type="float" level="2" n="9"> <figure xlink:label="fig-0701a-01" xlink:href="fig-0701a-01a"> <image file="0701a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0701a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0703-01" xlink:href="note-0703-01a" xml:space="preserve">1208.</note> <note position="right" xlink:label="note-0703-02" xlink:href="note-0703-02a" xml:space="preserve">1289.</note> </div> <p> <s xml:id="echoid-s18275" xml:space="preserve">Manente Telluris à Sole diſtantiá, Lunæ gravitas in Tel-<lb/> <anchor type="note" xlink:label="note-0703-03a" xlink:href="note-0703-03"/> lurem lentius in Quadraturis decreſcit, quàm pro ratione <lb/>inverſâ Quadrati diſtantiæ à Telluris centro; </s> <s xml:id="echoid-s18276" xml:space="preserve">nam ſi aug-<lb/>mentum, in hoc caſu, ſequeretur inverſam hanc rationem <lb/>quadrati diſtantiæ, quam ſequitur gravitas ex Telluris actione <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0703-04a" xlink:href="note-0703-04"/> non turbaretur hæc ratio; </s> <s xml:id="echoid-s18277" xml:space="preserve">augmentum verò creſcit, dum gra-<lb/>vitas ipſa minuitur; </s> <s xml:id="echoid-s18278" xml:space="preserve">quare augmentum, quando diſtantia au-<lb/>getur, ſemper majus eſt quàm requiritur, ideòque diminutio <lb/>minor.</s> <s xml:id="echoid-s18279" xml:space="preserve"/> </p> <div xml:id="echoid-div2790" type="float" level="2" n="10"> <note position="right" xlink:label="note-0703-03" xlink:href="note-0703-03a" xml:space="preserve">1290.</note> <note symbol="*" position="right" xlink:label="note-0703-04" xlink:href="note-0703-04a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s18280" xml:space="preserve">Augmentum hoc determinatur in mediis Lunæ à Tellure <lb/> <anchor type="note" xlink:label="note-0703-05a" xlink:href="note-0703-05"/> & </s> <s xml:id="echoid-s18281" xml:space="preserve">hujus à Sole diſtantiis: </s> <s xml:id="echoid-s18282" xml:space="preserve">ſint AT & </s> <s xml:id="echoid-s18283" xml:space="preserve">TS hæ diſtantiæ <lb/>mediæ; </s> <s xml:id="echoid-s18284" xml:space="preserve">eſt augmentum quæſitum ad gravitatem Telluris in <lb/>Solem ut AT ad TS <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18285" xml:space="preserve">eſt etiam hæc gravitas Telluris in <anchor type="note" xlink:label="note-0703-06a" xlink:href="note-0703-06"/> Solem ad gravitatem Lunæ in Tellurem, (quia corpora hæc <lb/>hiſce gravitatibus in orbitis retinentur) directè ut TS ad <lb/>TA, & </s> <s xml:id="echoid-s18286" xml:space="preserve">inverſè ut quadrata temporum periodicorum Tellu-<lb/>ris circa Solem & </s> <s xml:id="echoid-s18287" xml:space="preserve">Lunæ circa Tellurem <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18288" xml:space="preserve">eſt idcirco aug- <anchor type="note" xlink:label="note-0703-07a" xlink:href="note-0703-07"/> mentum quæſitum ad gravitatem Lunæ in Tellurem, in ra-<lb/>tione compoſitâ, ex hiſce rationibus; </s> <s xml:id="echoid-s18289" xml:space="preserve">id eſt, in ratione me-<lb/>moratâ inverſâ temporum periodicorum Telluris & </s> <s xml:id="echoid-s18290" xml:space="preserve">Lunæ, <lb/>cæteris rationibus ſeſe mutuo deſtruentibus. </s> <s xml:id="echoid-s18291" xml:space="preserve">Tempora hæc <lb/>dantur & </s> <s xml:id="echoid-s18292" xml:space="preserve">ſunt inverſè horum quadrata ut 1. </s> <s xml:id="echoid-s18293" xml:space="preserve">ad 178,73.</s> <s xml:id="echoid-s18294" xml:space="preserve"/> </p> <div xml:id="echoid-div2791" type="float" level="2" n="11"> <note position="right" xlink:label="note-0703-05" xlink:href="note-0703-05a" xml:space="preserve">1291.</note> <note symbol="*" position="right" xlink:label="note-0703-06" xlink:href="note-0703-06a" xml:space="preserve">1287.</note> <note symbol="*" position="right" xlink:label="note-0703-07" xlink:href="note-0703-07a" xml:space="preserve">237. 1236.</note> </div> <p> <s xml:id="echoid-s18295" xml:space="preserve">Sit nunc Luna in L, in quo ſitu Sol Lunam & </s> <s xml:id="echoid-s18296" xml:space="preserve">Tellurem, <lb/> <anchor type="note" xlink:label="note-0703-08a" xlink:href="note-0703-08"/> per eandem lineam, ad ſe trahit, ſed non æqualiter; </s> <s xml:id="echoid-s18297" xml:space="preserve">Lunam <lb/> <anchor type="note" xlink:label="note-0703-09a" xlink:href="note-0703-09"/> <anchor type="note" xlink:label="note-0703-10a" xlink:href="note-0703-10"/> majori cum vi, quia minus ab illo diſtat: </s> <s xml:id="echoid-s18298" xml:space="preserve">differentia harum <lb/>virium eſt vis, qua Luna à Tellure retrahitur, & </s> <s xml:id="echoid-s18299" xml:space="preserve">qua gravi-<lb/>tas Lunæ in Tellurem minuitur.</s> <s xml:id="echoid-s18300" xml:space="preserve"/> </p> <div xml:id="echoid-div2792" type="float" level="2" n="12"> <note position="right" xlink:label="note-0703-08" xlink:href="note-0703-08a" xml:space="preserve">1292.</note> <note position="right" xlink:label="note-0703-09" xlink:href="note-0703-09a" xml:space="preserve">TAB. XXV.</note> <note position="right" xlink:label="note-0703-10" xlink:href="note-0703-10a" xml:space="preserve">fig. 1.</note> </div> <p> <s xml:id="echoid-s18301" xml:space="preserve">Vires, quibus Luna in L, & </s> <s xml:id="echoid-s18302" xml:space="preserve">Tellus in T, verſus Solem <lb/>tendunt, ſunt inter ſe ut quadrata linearum ST & </s> <s xml:id="echoid-s18303" xml:space="preserve">SL <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0703-11a" xlink:href="note-0703-11"/> & </s> <s xml:id="echoid-s18304" xml:space="preserve">differentia virium, id eſt vis turbans, ad vim qua Tellus <lb/>verſus Solem deſcendit, ut differentia horum quadratorum ad <lb/>quadratum lineæ LS, id eſt, quam proximè, ut dupla <lb/>LT ad LS aut TS; </s> <s xml:id="echoid-s18305" xml:space="preserve">nam hæ lineæ parum admodum inter <pb o="(174)" file="0704" n="775" rhead="PHYSICES ELEMENTA"/> ſe differunt; </s> <s xml:id="echoid-s18306" xml:space="preserve">& </s> <s xml:id="echoid-s18307" xml:space="preserve">differentia quadratorum, quorum radices pa-<lb/> <anchor type="note" xlink:label="note-0704-01a" xlink:href="note-0704-01"/> rum inter ſe differunt, eſt ſervatâ proportione dupla illius, <lb/>quæ inter radices datur.</s> <s xml:id="echoid-s18308" xml:space="preserve"/> </p> <div xml:id="echoid-div2793" type="float" level="2" n="13"> <note symbol="*" position="right" xlink:label="note-0703-11" xlink:href="note-0703-11a" xml:space="preserve">1208.</note> <note position="left" xlink:label="note-0704-01" xlink:href="note-0704-01a" xml:space="preserve">1293.</note> </div> <p> <s xml:id="echoid-s18309" xml:space="preserve">Si ergo TS, ut antea, repræſentet vim, qua Tellus ver-<lb/>ſus Solem deſcendit, L l repræſentabit vim turbantem & </s> <s xml:id="echoid-s18310" xml:space="preserve"><lb/>gravitatem minuentem, dum in quadraturis vis turbans per <lb/>AT repræſentatur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18311" xml:space="preserve"/> </p> <note symbol="*" position="left" xml:space="preserve">1286.</note> <p> <s xml:id="echoid-s18312" xml:space="preserve">Detur Luna in l; </s> <s xml:id="echoid-s18313" xml:space="preserve">iterum cum Tellure, per eandem li-<lb/> <anchor type="note" xlink:label="note-0704-03a" xlink:href="note-0704-03"/> neam, à Sole attrahitur; </s> <s xml:id="echoid-s18314" xml:space="preserve">ſed quia Tellus minus diſtat, cele-<lb/>rius hæc verſus Solem movetur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18315" xml:space="preserve">ita ut deturvis, quæ Tel- <anchor type="note" xlink:label="note-0704-04a" xlink:href="note-0704-04"/> lurem à Lunâ ſeparat, differentia nempe virium Lunam & </s> <s xml:id="echoid-s18316" xml:space="preserve"><lb/>Tellurem trahentium; </s> <s xml:id="echoid-s18317" xml:space="preserve">quæ vis cum gravitate Lunæ in Tel-<lb/>lurem contrariè agit, & </s> <s xml:id="echoid-s18318" xml:space="preserve">hanc minuit; </s> <s xml:id="echoid-s18319" xml:space="preserve">eodem modo ac ex <lb/>majori gravitate Lunæ in Solem, poſitâ illâ in L, demon-<lb/>ſtratum fuit. </s> <s xml:id="echoid-s18320" xml:space="preserve">In L l etiam vis ſeparans à vi ſeparante in L vix <lb/>differt; </s> <s xml:id="echoid-s18321" xml:space="preserve">hæc enim ut vidimus proportionalis eſt differentiæ <lb/>quadratorum linearum TS & </s> <s xml:id="echoid-s18322" xml:space="preserve">LS, & </s> <s xml:id="echoid-s18323" xml:space="preserve">illa, ut ſimili demon-<lb/>ſtratione evincitur, differentiæ quadratorum linearum l S <lb/>& </s> <s xml:id="echoid-s18324" xml:space="preserve">TS; </s> <s xml:id="echoid-s18325" xml:space="preserve">quæ differentiæ, propter exiguam L l reſpectu TS, <lb/>vixinter ſe differunt; </s> <s xml:id="echoid-s18326" xml:space="preserve">ita ut vis, quæ minuit gravitatem Lunæ <lb/>in l etiam repræſentetur per L l.</s> <s xml:id="echoid-s18327" xml:space="preserve"/> </p> <div xml:id="echoid-div2794" type="float" level="2" n="14"> <note position="left" xlink:label="note-0704-03" xlink:href="note-0704-03a" xml:space="preserve">1294.</note> <note symbol="*" position="left" xlink:label="note-0704-04" xlink:href="note-0704-04a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s18328" xml:space="preserve">Major tamen paululum eſt vis perturbans in conjunctione in <lb/> <anchor type="note" xlink:label="note-0704-05a" xlink:href="note-0704-05"/> L, quam in oppoſitione in l; </s> <s xml:id="echoid-s18329" xml:space="preserve">nam poſitis differentiis æqua-<lb/>libus inter radices, quadrata ſervata proportione, eo magis <lb/>differunt, quo minora ſunt; </s> <s xml:id="echoid-s18330" xml:space="preserve">& </s> <s xml:id="echoid-s18331" xml:space="preserve">ſic ſervatâ proportione magis <lb/>differunt vires in L & </s> <s xml:id="echoid-s18332" xml:space="preserve">T quam in T & </s> <s xml:id="echoid-s18333" xml:space="preserve">l, quæ etiam mi-<lb/>nores ſunt <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18334" xml:space="preserve"/> </p> <div xml:id="echoid-div2795" type="float" level="2" n="15"> <note position="left" xlink:label="note-0704-05" xlink:href="note-0704-05a" xml:space="preserve">1295.</note> </div> <note symbol="*" position="left" xml:space="preserve">1208.</note> <p> <s xml:id="echoid-s18335" xml:space="preserve">Concludimus exhis, vim quæ in Syzygiis gravitatem Lunæ <lb/> <anchor type="note" xlink:label="note-0704-07a" xlink:href="note-0704-07"/> minuit, duplam eſſe illius, quæ banc auget in quadraturis; <lb/></s> <s xml:id="echoid-s18336" xml:space="preserve">nempe ut L l ad AT. </s> <s xml:id="echoid-s18337" xml:space="preserve">Quare in Syzygiis, Lunæ gravitas <lb/>ex actione Solis minuitur parte, quæ eſt adtotam gravitatem, <lb/>ut 1. </s> <s xml:id="echoid-s18338" xml:space="preserve">ad 89, 36; </s> <s xml:id="echoid-s18339" xml:space="preserve">nam in quadraturis augmentum gravitatis <lb/>eſt ad ipſam, ut I. </s> <s xml:id="echoid-s18340" xml:space="preserve">ad 178,73. </s> <s xml:id="echoid-s18341" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18342" xml:space="preserve"/> </p> <div xml:id="echoid-div2796" type="float" level="2" n="16"> <note position="left" xlink:label="note-0704-07" xlink:href="note-0704-07a" xml:space="preserve">1296.</note> </div> <note symbol="*" position="left" xml:space="preserve">1291.</note> <p> <s xml:id="echoid-s18343" xml:space="preserve">In Syzygiis vis perturbans ſequitur eandem proportionem <lb/> <anchor type="note" xlink:label="note-0704-09a" xlink:href="note-0704-09"/> cum ſemiſſe hujus, id eſt cum vi perturbante in quadratu-<lb/>ris <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18344" xml:space="preserve">eſt ergo directè ut diſtantia Lunæ à Tellure <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18345" xml:space="preserve">in- <anchor type="note" xlink:label="note-0704-10a" xlink:href="note-0704-10"/> <anchor type="note" xlink:label="note-0704-11a" xlink:href="note-0704-11"/> verſè ut cubus diſtantiæ Telluris à Sole <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18346" xml:space="preserve"/> </p> <div xml:id="echoid-div2797" type="float" level="2" n="17"> <note position="left" xlink:label="note-0704-09" xlink:href="note-0704-09a" xml:space="preserve">1297.</note> <note symbol="*" position="left" xlink:label="note-0704-10" xlink:href="note-0704-10a" xml:space="preserve">1296.</note> <note symbol="*" position="left" xlink:label="note-0704-11" xlink:href="note-0704-11a" xml:space="preserve">1288.</note> </div> <note symbol="*" position="left" xml:space="preserve">1289.</note> <pb o="(175)" file="0705" n="776" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> <p> <s xml:id="echoid-s18347" xml:space="preserve">In Syzygiis gravitas Lunæ in Tellurem, in receſſu illius <lb/> <anchor type="note" xlink:label="note-0705-01a" xlink:href="note-0705-01"/> ab bujus centro, magis minuitur, quam juxta rationem in-<lb/>verſam quadrati diſtantiæ, ab hoc centro; </s> <s xml:id="echoid-s18348" xml:space="preserve">in hac enim ra-<lb/>tione minueretur, ſi vis ablatitia perturbans eandem ſeque-<lb/>retur rationem; </s> <s xml:id="echoid-s18349" xml:space="preserve">cùm autem hæc contra creſcat, quando diſ-<lb/>tantia augetur <anchor type="note" xlink:href="" symbol="*"/> ſemper diminutio major eſt, quam juxta hanc <anchor type="note" xlink:label="note-0705-02a" xlink:href="note-0705-02"/> rationem.</s> <s xml:id="echoid-s18350" xml:space="preserve"/> </p> <div xml:id="echoid-div2798" type="float" level="2" n="18"> <note position="right" xlink:label="note-0705-01" xlink:href="note-0705-01a" xml:space="preserve">1298.</note> <note symbol="*" position="right" xlink:label="note-0705-02" xlink:href="note-0705-02a" xml:space="preserve">129@.</note> </div> <p> <s xml:id="echoid-s18351" xml:space="preserve">Tandem ſit Luna in F, loco quocunque intermedio inter <lb/> <anchor type="note" xlink:label="note-0705-03a" xlink:href="note-0705-03"/> Quadraturam & </s> <s xml:id="echoid-s18352" xml:space="preserve">Syzygiam, verſus Solem trahitur per FS, <lb/> <anchor type="note" xlink:label="note-0705-04a" xlink:href="note-0705-04"/> à quo cùm minus diſtet, quàm Tellus T, majori cum vi <lb/> <anchor type="note" xlink:label="note-0705-05a" xlink:href="note-0705-05"/> quàm Tellus trahitur: </s> <s xml:id="echoid-s18353" xml:space="preserve">Sit vis, quâ Luna ad Solem tendit, <lb/>ad vim, quâ Tellus ad eundem fertur, ut FM ad TS, <lb/>quæ etiam in præcedentibus, eandem Telluris gravitatem <lb/>deſignat. </s> <s xml:id="echoid-s18354" xml:space="preserve">Formetur Parallelogrammum FHMI, cujus dia-<lb/>gonalis ſit FM, & </s> <s xml:id="echoid-s18355" xml:space="preserve">cujus latus FH ſit parallelum, & </s> <s xml:id="echoid-s18356" xml:space="preserve">æqua-<lb/>le, lineæ TS. </s> <s xml:id="echoid-s18357" xml:space="preserve">Motus Lunæ verſus Solem reſolvitur in <lb/>duos, unum per FH, alterum per FI; </s> <s xml:id="echoid-s18358" xml:space="preserve">& </s> <s xml:id="echoid-s18359" xml:space="preserve">hæ lineæ de-<lb/>ſignant vires quibus Luna per ipſas moveri conatur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18360" xml:space="preserve">Mo- <anchor type="note" xlink:label="note-0705-06a" xlink:href="note-0705-06"/> tus per FH communis eſt Lunæ & </s> <s xml:id="echoid-s18361" xml:space="preserve">Telluri, quæ, æquali <lb/>vi per lineam huic parallelam, etiam ad Solem tendit; </s> <s xml:id="echoid-s18362" xml:space="preserve">ita ut, <lb/>hoc motu Lunæ, hujus ſitus reſpectu Telluris non mute-<lb/>tur, & </s> <s xml:id="echoid-s18363" xml:space="preserve">vis perturbans ſit ſolus motus per FI.</s> <s xml:id="echoid-s18364" xml:space="preserve"/> </p> <div xml:id="echoid-div2799" type="float" level="2" n="19"> <note position="right" xlink:label="note-0705-03" xlink:href="note-0705-03a" xml:space="preserve">1299.</note> <note position="right" xlink:label="note-0705-04" xlink:href="note-0705-04a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0705-05" xlink:href="note-0705-05a" xml:space="preserve">fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0705-06" xlink:href="note-0705-06a" xml:space="preserve">192.</note> </div> <p> <s xml:id="echoid-s18365" xml:space="preserve">Propter immenſam Solis diſtantiam, pars MS lineæ MF <lb/>exigua eſt reſpectu totius, & </s> <s xml:id="echoid-s18366" xml:space="preserve">angulus FST, ubi maximus <lb/>eſt, ut AST, vix ſextam unius gradus partem ſuperat; </s> <s xml:id="echoid-s18367" xml:space="preserve">un-<lb/>de ſequitur, lineas MI & </s> <s xml:id="echoid-s18368" xml:space="preserve">SN admodum eſſe vicinas, punc-<lb/>taque I & </s> <s xml:id="echoid-s18369" xml:space="preserve">N vix diſtare, & </s> <s xml:id="echoid-s18370" xml:space="preserve">ſine errore ſenſibili poſſe con-<lb/>fundi; </s> <s xml:id="echoid-s18371" xml:space="preserve">qui tamen error, quantumvis ſit contemnendus, in <lb/>conſideratione integræ revolutionis, compenſatur errore <lb/>contrario, poſitâ Lunâ in E. </s> <s xml:id="echoid-s18372" xml:space="preserve">Vis ergo perturbans deſignatur <lb/>per FN.</s> <s xml:id="echoid-s18373" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18374" xml:space="preserve">Notandum, quando lineæ ES ſola pars EF conſideratur, <lb/> <anchor type="note" xlink:label="note-0705-07a" xlink:href="note-0705-07"/> hane pro parallelâh aberi lineæ L l, propter exiguum angu-<lb/>lum, quem hæ lineæ efficiunt.</s> <s xml:id="echoid-s18375" xml:space="preserve"/> </p> <div xml:id="echoid-div2800" type="float" level="2" n="20"> <note position="right" xlink:label="note-0705-07" xlink:href="note-0705-07a" xml:space="preserve">1300.</note> </div> <p> <s xml:id="echoid-s18376" xml:space="preserve">Ex puncto N ducatur perpendiculum NQ ad lineam <lb/> <anchor type="note" xlink:label="note-0705-08a" xlink:href="note-0705-08"/> FT, continuatam ſi neceſſe fuerit, per quam Luna in Tel-<lb/>lurem gravitat; </s> <s xml:id="echoid-s18377" xml:space="preserve">& </s> <s xml:id="echoid-s18378" xml:space="preserve">conſtruatur parallelogrammum FPNQ rec- <pb o="(176)" file="0706" n="777" rhead="PHYSICES ELEMENTA"/> tangulum; </s> <s xml:id="echoid-s18379" xml:space="preserve">concipiamus vim per FN reſolutam in duas, per <lb/>FQ & </s> <s xml:id="echoid-s18380" xml:space="preserve">FP agentes, & </s> <s xml:id="echoid-s18381" xml:space="preserve">hiſce lineis repræſentatas <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18382" xml:space="preserve">Vi, per <anchor type="note" xlink:label="note-0706-01a" xlink:href="note-0706-01"/> FQ, vis gravitatis minuitur, in caſu hujus figuræ, augetur <lb/>quando punctum Q inter F & </s> <s xml:id="echoid-s18383" xml:space="preserve">T cadit; </s> <s xml:id="echoid-s18384" xml:space="preserve">vi autem per FP <lb/>Luna in orbitâ trahitur verſus Syzygiam vicinam L, & </s> <s xml:id="echoid-s18385" xml:space="preserve">ac-<lb/>celeratur aut retardatur Lunæ motus, pro ut vis hæc cum <lb/>motu Lunæ conſpirat, aut contrariè agit.</s> <s xml:id="echoid-s18386" xml:space="preserve"/> </p> <div xml:id="echoid-div2801" type="float" level="2" n="21"> <note position="right" xlink:label="note-0705-08" xlink:href="note-0705-08a" xml:space="preserve">1301.</note> <note symbol="*" position="left" xlink:label="note-0706-01" xlink:href="note-0706-01a" xml:space="preserve">192.</note> </div> <p> <s xml:id="echoid-s18387" xml:space="preserve">In viciniis Syzygiæ minuitur Lunæ gravitas, & </s> <s xml:id="echoid-s18388" xml:space="preserve">linea FQ, <lb/>quæ diminutionis hujus proportionem ſequitur, minuitur <lb/>recedendo à Syzygiâ donec evaneſcat, ad diſtantiam ab hac <lb/>54. </s> <s xml:id="echoid-s18389" xml:space="preserve">gr. </s> <s xml:id="echoid-s18390" xml:space="preserve">44′.</s> <s xml:id="echoid-s18391" xml:space="preserve">; ad majorem Lunæ à Syzygiâ diſtantiam Q inter <lb/>F & </s> <s xml:id="echoid-s18392" xml:space="preserve">T cadit, & </s> <s xml:id="echoid-s18393" xml:space="preserve">ex Solis actione gravitas Lunæ in Tellurem <lb/>augetur.</s> <s xml:id="echoid-s18394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18395" xml:space="preserve">Vis per FP in Syzygiâ L nulla eſt, recedendo ab hac au-<lb/>getur ad octantem uſque, punctum medium inter Syzygiam & </s> <s xml:id="echoid-s18396" xml:space="preserve"><lb/>Quadraturam, minuitur iterum donec in B etiam nulla ſit.</s> <s xml:id="echoid-s18397" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18398" xml:space="preserve">Inter B & </s> <s xml:id="echoid-s18399" xml:space="preserve">l aut l & </s> <s xml:id="echoid-s18400" xml:space="preserve">A, motus perturbantes eodem mo-<lb/> <anchor type="note" xlink:label="note-0706-02a" xlink:href="note-0706-02"/> do determinantur, ac in parte oppoſitâ inferiori ALB or-<lb/>bitæ ; </s> <s xml:id="echoid-s18401" xml:space="preserve">in E & </s> <s xml:id="echoid-s18402" xml:space="preserve">F æqualis eſt gravitatis diminutio, & </s> <s xml:id="echoid-s18403" xml:space="preserve">in illo <lb/>ſitu æquali vi in orbitâ verſus Syzygiam l trahitur, quâ <lb/>in F verſus Syzygiam L pellitur.</s> <s xml:id="echoid-s18404" xml:space="preserve"/> </p> <div xml:id="echoid-div2802" type="float" level="2" n="22"> <note position="left" xlink:label="note-0706-02" xlink:href="note-0706-02a" xml:space="preserve">1302.</note> </div> <p> <s xml:id="echoid-s18405" xml:space="preserve">Ex hiſce ſequitur, in motu Lunæ à Syzygiâ ad Quadra-<lb/> <anchor type="note" xlink:label="note-0706-03a" xlink:href="note-0706-03"/> turam, inter L & </s> <s xml:id="echoid-s18406" xml:space="preserve">B ut & </s> <s xml:id="echoid-s18407" xml:space="preserve">l & </s> <s xml:id="echoid-s18408" xml:space="preserve">A, gravitatem Lunæ in <lb/>Tellurem continuò augeri & </s> <s xml:id="echoid-s18409" xml:space="preserve">Lunam in motu continuò retarda-<lb/>ri. </s> <s xml:id="echoid-s18410" xml:space="preserve">In motu autem à Quadratur â ad Syzygiam, inter B & </s> <s xml:id="echoid-s18411" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0706-04a" xlink:href="note-0706-04"/> l ut & </s> <s xml:id="echoid-s18412" xml:space="preserve">A & </s> <s xml:id="echoid-s18413" xml:space="preserve">L, minuitur omnibus momentis Lunæ gravitas, <lb/>& </s> <s xml:id="echoid-s18414" xml:space="preserve">bujus motus in orbitâ acceleratur.</s> <s xml:id="echoid-s18415" xml:space="preserve"/> </p> <div xml:id="echoid-div2803" type="float" level="2" n="23"> <note position="left" xlink:label="note-0706-03" xlink:href="note-0706-03a" xml:space="preserve">1303.</note> <note position="left" xlink:label="note-0706-04" xlink:href="note-0706-04a" xml:space="preserve">1304.</note> </div> <p> <s xml:id="echoid-s18416" xml:space="preserve">Determinantur vires à quibus eſfectus hi pendent, conferen-<lb/>do has cum vi notâ, quâ gravitas in Quadraturis augetur <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s18417" xml:space="preserve"> <anchor type="note" xlink:label="note-0706-05a" xlink:href="note-0706-05"/> quæ per Lunæ diſtantiam à centro Telluris repræſentatur.</s> <s xml:id="echoid-s18418" xml:space="preserve"/> </p> <div xml:id="echoid-div2804" type="float" level="2" n="24"> <note symbol="*" position="left" xlink:label="note-0706-05" xlink:href="note-0706-05a" xml:space="preserve">1291.</note> </div> <p> <s xml:id="echoid-s18419" xml:space="preserve">Lineæ MI, HF, ST, ex conſtructione ſunt æquales; <lb/></s> <s xml:id="echoid-s18420" xml:space="preserve"> <anchor type="note" xlink:label="note-0706-06a" xlink:href="note-0706-06"/> ideò, cùm puncta I & </s> <s xml:id="echoid-s18421" xml:space="preserve">N confundantur, MN valet ST, & </s> <s xml:id="echoid-s18422" xml:space="preserve"><lb/>MS æqualis eſt NT. </s> <s xml:id="echoid-s18423" xml:space="preserve">Lineæ MF & </s> <s xml:id="echoid-s18424" xml:space="preserve">ST repræſentant vires, <lb/>quibus Luna in F & </s> <s xml:id="echoid-s18425" xml:space="preserve">Tellus in T verſus Solem S feruntur; <lb/></s> <s xml:id="echoid-s18426" xml:space="preserve">ſunt ergo ut quadratum lineæ TS ad quadratum lineæ FS <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18427" xml:space="preserve"> <anchor type="note" xlink:label="note-0706-07a" xlink:href="note-0706-07"/> quare, cùm FG ſit differentia harum linearum, differunt <lb/>inter ſe FM & </s> <s xml:id="echoid-s18428" xml:space="preserve">TS duplâ GF <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18429" xml:space="preserve">addendo GF li- <anchor type="note" xlink:label="note-0706-08a" xlink:href="note-0706-08"/> <pb o="(177)" file="0707" n="778" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> neæ FM, differentia inter GM & </s> <s xml:id="echoid-s18430" xml:space="preserve">TS, id eſt MS, <lb/>erit tripla lineæ FG; </s> <s xml:id="echoid-s18431" xml:space="preserve">quantum ergo etiam valet NT: <lb/></s> <s xml:id="echoid-s18432" xml:space="preserve">FE autem eſt dupla FG <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18433" xml:space="preserve">ideò NT ad FE ut tria ad duo.</s> <s xml:id="echoid-s18434" xml:space="preserve"/> </p> <div xml:id="echoid-div2805" type="float" level="2" n="25"> <note position="left" xlink:label="note-0706-06" xlink:href="note-0706-06a" xml:space="preserve">1305.</note> <note symbol="*" position="left" xlink:label="note-0706-07" xlink:href="note-0706-07a" xml:space="preserve">1208.</note> <note symbol="*" position="left" xlink:label="note-0706-08" xlink:href="note-0706-08a" xml:space="preserve">1293.</note> </div> <note symbol="*" position="right" xml:space="preserve">1300.</note> <p> <s xml:id="echoid-s18435" xml:space="preserve">Continuetur FT, ſi neceſſè fuerit, & </s> <s xml:id="echoid-s18436" xml:space="preserve">ad hanc, ex E, <lb/>ducatur perpendicularis EV; </s> <s xml:id="echoid-s18437" xml:space="preserve">triangula EVF, & </s> <s xml:id="echoid-s18438" xml:space="preserve">NQT, <lb/>rectangula, erunt ſimilia, propter angulos alternos VFE <lb/> <anchor type="note" xlink:label="note-0707-02a" xlink:href="note-0707-02"/> & </s> <s xml:id="echoid-s18439" xml:space="preserve">QTN <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18440" xml:space="preserve">Idcirco NT ad FE, id eſt, tria ad duo, ut NQ, æqualis FP, ad EV; </s> <s xml:id="echoid-s18441" xml:space="preserve">quæ ergo proportionalis <lb/>eſt duabus tertiis partibus vis, quæ exprimitur per FP; </s> <s xml:id="echoid-s18442" xml:space="preserve">ſed <lb/>EV eſt ſinus anguli ETV ad centrum, dupli anguli <lb/>EFV ad circumferentiam, æqualis angulo FTL, di-<lb/>ſtantiæ Lunæ à Syzygiâ. </s> <s xml:id="echoid-s18443" xml:space="preserve">Idcirco, ut radius, TA, aut <lb/> <anchor type="note" xlink:label="note-0707-03a" xlink:href="note-0707-03"/> TE, ad ſeſqui-ſinum duplæ diſtantiæ Lunæ à Syzygiâ, <lb/>nempe FP, ita augmentum gravitatis in quadraturis, <lb/>quod radio TA deſignatur, ad vim, quæ motum Lunæ in <lb/>orbitâ accelerat aut retardat.</s> <s xml:id="echoid-s18444" xml:space="preserve"/> </p> <div xml:id="echoid-div2806" type="float" level="2" n="26"> <note symbol="*" position="right" xlink:label="note-0707-02" xlink:href="note-0707-02a" xml:space="preserve">1300.</note> <note position="right" xlink:label="note-0707-03" xlink:href="note-0707-03a" xml:space="preserve">1306.</note> </div> <p> <s xml:id="echoid-s18445" xml:space="preserve">Computatio diminutionis gravitatis, &</s> <s xml:id="echoid-s18446" xml:space="preserve">, in minori diſtantiâ <lb/>à Quadraturis, hujus augmenti, exiiſdem principiis deducitur.</s> <s xml:id="echoid-s18447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18448" xml:space="preserve">Repræſentatur hæc diminutio lineâ FQ, quæ valet QT, <lb/>minus radio; </s> <s xml:id="echoid-s18449" xml:space="preserve">ſed ex conſideratione triangulorum ſtatim me-<lb/>moratorum ſeſqui VF, valet QT; </s> <s xml:id="echoid-s18450" xml:space="preserve">ideò ſeſqui VT plus <lb/>dimidio radio deſignat diminutionem gravitatis quæſitam; </s> <s xml:id="echoid-s18451" xml:space="preserve">& </s> <s xml:id="echoid-s18452" xml:space="preserve"><lb/>radius eſt ad ſummam aut differentiam ſeſqui co-ſinus duplæ <lb/> <anchor type="note" xlink:label="note-0707-04a" xlink:href="note-0707-04"/> diſtantiæ Lunæ à Syzygiâ & </s> <s xml:id="echoid-s18453" xml:space="preserve">dimidii radii, ut augmentum <lb/>gravitatis in Quadraturis ad diminutionem, aut augmentum, <lb/>gravitatis in ſitu Lunæ de quo computatio initur.</s> <s xml:id="echoid-s18454" xml:space="preserve"/> </p> <div xml:id="echoid-div2807" type="float" level="2" n="27"> <note position="right" xlink:label="note-0707-04" xlink:href="note-0707-04a" xml:space="preserve">1307.</note> </div> <p> <s xml:id="echoid-s18455" xml:space="preserve">Differentiâ co-ſinus à dimidio radio utimur, quando an-<lb/>gulus, cujus eſt co-ſinus, angulum rectum ſuperat; </s> <s xml:id="echoid-s18456" xml:space="preserve">quia in <lb/>hoc caſu utimur co-ſinu complementi anguli ad duos angu-<lb/>los rectos; </s> <s xml:id="echoid-s18457" xml:space="preserve">quando in hoc eodem caſu ſeſqui co-ſinus, quo <lb/>utimur, ſemi-radium ſuperat, quantitas detecta eſt addititia, <lb/>id eſt, gravitatem auget, quod ubique inter Quadraturam & </s> <s xml:id="echoid-s18458" xml:space="preserve"><lb/>35. </s> <s xml:id="echoid-s18459" xml:space="preserve">gr. </s> <s xml:id="echoid-s18460" xml:space="preserve">16′. </s> <s xml:id="echoid-s18461" xml:space="preserve">ab hac obtinet.</s> <s xml:id="echoid-s18462" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18463" xml:space="preserve">Vires hæ, quæcunque fuerint orbitæ Lunaris figura, exactè <lb/> <anchor type="note" xlink:label="note-0707-05a" xlink:href="note-0707-05"/> determinantur; </s> <s xml:id="echoid-s18464" xml:space="preserve">nam conferuntur cum augmento gravitatis <lb/>in Quadraturis, poſitâ Lunâ in Quadraturâ ad eandem diſtan-<lb/>tiam à Tellure, ad quam reverâ datur in loco de quo agitur;</s> <s xml:id="echoid-s18465" xml:space="preserve"> <pb o="(178)" file="0708" n="779" rhead="PHYSICES ELEMENTA"/> augmentum vero hoc in omni Caſu detegitur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18466" xml:space="preserve"/> </p> <div xml:id="echoid-div2808" type="float" level="2" n="28"> <note position="right" xlink:label="note-0707-05" xlink:href="note-0707-05a" xml:space="preserve">1308.</note> </div> <note symbol="*" position="left" xml:space="preserve">1291. 1288.</note> <p> <s xml:id="echoid-s18467" xml:space="preserve">Licèt extra ſcopum hujus operis ſit, computum, motus Lunæ <lb/> <anchor type="note" xlink:label="note-0708-02a" xlink:href="note-0708-02"/> tradere, neceſſè duxi breviter exponere, quâ methodo vires, <lb/>quibus Luna regitur, detegantur; </s> <s xml:id="echoid-s18468" xml:space="preserve">quia eo facilius effectum <lb/>generalem virium concipimus, quo exactius ipſas novimus.</s> <s xml:id="echoid-s18469" xml:space="preserve"/> </p> <div xml:id="echoid-div2809" type="float" level="2" n="29"> <note position="left" xlink:label="note-0708-02" xlink:href="note-0708-02a" xml:space="preserve">1289.</note> </div> <p> <s xml:id="echoid-s18470" xml:space="preserve">Ut nunc motum Lunæ examinemus, ſingulatim hujus va-<lb/>riæ irregularitates perpendendæ ſunt, quod ut ſine confuſio-<lb/>ne fiat, varias removemus irregularitates & </s> <s xml:id="echoid-s18471" xml:space="preserve">concipimus Lu-<lb/>nam, in circulo motam circa Tellurem, in quâ curvâ reti-<lb/>neri poſſe ex gravitate conſtat <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18472" xml:space="preserve">Ex actione Solis turba- <anchor type="note" xlink:label="note-0708-03a" xlink:href="note-0708-03"/> tur hic motus, & </s> <s xml:id="echoid-s18473" xml:space="preserve">orbita magis convexa eſt in Quadraturis <lb/>quàm in Syzygiis. </s> <s xml:id="echoid-s18474" xml:space="preserve">Curvæ, à corpore vi centrali deſcriptæ, <lb/>convexitas eo major eſt, quo vis centralis majori cum vi cor-<lb/>pus omnibus momentis ex viâ detorquet; </s> <s xml:id="echoid-s18475" xml:space="preserve">etiam eo major <lb/>eſt, quo corpus lentius movetur, quia vis centralis diutius a-<lb/>gens majorem edit effectum in inflectendâ corporis viâ. </s> <s xml:id="echoid-s18476" xml:space="preserve">Ex <lb/>cauſis contrariis minuitur convexitas curvæ. </s> <s xml:id="echoid-s18477" xml:space="preserve">Ambæ con-<lb/>currunt in augendâ orbitæ convexitate in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>, &</s> <s xml:id="echoid-s18478" xml:space="preserve"> <anchor type="note" xlink:label="note-0708-04a" xlink:href="note-0708-04"/> hac minuendà in Syzygiis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18479" xml:space="preserve"/> </p> <div xml:id="echoid-div2810" type="float" level="2" n="30"> <note symbol="*" position="left" xlink:label="note-0708-03" xlink:href="note-0708-03a" xml:space="preserve">241. 1208. <lb/>1309.</note> <note symbol="*" position="left" xlink:label="note-0708-04" xlink:href="note-0708-04a" xml:space="preserve">1303.</note> </div> <note symbol="*" position="left" xml:space="preserve">1304.</note> <p> <s xml:id="echoid-s18480" xml:space="preserve">Ex his ſequitur circularem orbitæ Lunaris figuram in ova-<lb/>lem mutari, cujus major axis per Quadraturas tranſit; </s> <s xml:id="echoid-s18481" xml:space="preserve">ut <lb/>partes magis convexæ in Quadraturis dentur. </s> <s xml:id="echoid-s18482" xml:space="preserve">Quare Luna <lb/> <anchor type="note" xlink:label="note-0708-06a" xlink:href="note-0708-06"/> minus à Tellure in Syzygiis, magis in Quadraturis diſtat; </s> <s xml:id="echoid-s18483" xml:space="preserve">& </s> <s xml:id="echoid-s18484" xml:space="preserve"><lb/>non mirum Lunam ad Tellurem accedere, dum gravitas <lb/>hujus minuitur; </s> <s xml:id="echoid-s18485" xml:space="preserve">quia acceſſus non eſt effectus immediatus <lb/>hujus diminutionis, ſed inflectionis orbitæ verſus Quadraturas.</s> <s xml:id="echoid-s18486" xml:space="preserve"/> </p> <div xml:id="echoid-div2811" type="float" level="2" n="31"> <note position="left" xlink:label="note-0708-06" xlink:href="note-0708-06a" xml:space="preserve">1310.</note> </div> <p> <s xml:id="echoid-s18487" xml:space="preserve">Motus Lunæ, ſublatâ Solis actione, non eſt in circulo, ſed <lb/>in Ellipſi, cujus focorum alter cum Telluris centro coincidit <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18488" xml:space="preserve"> <anchor type="note" xlink:label="note-0708-07a" xlink:href="note-0708-07"/> nam orbita Lunæ eſt excentrica & </s> <s xml:id="echoid-s18489" xml:space="preserve">vi gravitatis in hac retinetur.</s> <s xml:id="echoid-s18490" xml:space="preserve"/> </p> <div xml:id="echoid-div2812" type="float" level="2" n="32"> <note symbol="*" position="left" xlink:label="note-0708-07" xlink:href="note-0708-07a" xml:space="preserve">967. 241. <lb/>1208.</note> </div> <p> <s xml:id="echoid-s18491" xml:space="preserve">Demonſtrata ergo non exactè ad motum Lunæ applicari <lb/>poſſunt; </s> <s xml:id="echoid-s18492" xml:space="preserve">cùm autem vires, quæ deviationes explicatas gene-<lb/>rant, in Lunam reverâ agant, Ellipſis, quam Luna ſub-<lb/>lato Sole deſcriberet, mutatur, &</s> <s xml:id="echoid-s18493" xml:space="preserve">, cæteris paribus, propo-<lb/> <anchor type="note" xlink:label="note-0708-08a" xlink:href="note-0708-08"/> ſitiones n. </s> <s xml:id="echoid-s18494" xml:space="preserve">1309. </s> <s xml:id="echoid-s18495" xml:space="preserve">1310. </s> <s xml:id="echoid-s18496" xml:space="preserve">ad Lunæ motum applicari poſſunt.</s> <s xml:id="echoid-s18497" xml:space="preserve"/> </p> <div xml:id="echoid-div2813" type="float" level="2" n="33"> <note position="left" xlink:label="note-0708-08" xlink:href="note-0708-08a" xml:space="preserve">1311.</note> </div> <p> <s xml:id="echoid-s18498" xml:space="preserve">In Quadraturis & </s> <s xml:id="echoid-s18499" xml:space="preserve">Syzygiis, vis perturbans, cum vi gra-<lb/> <anchor type="note" xlink:label="note-0708-09a" xlink:href="note-0708-09"/> vitatis verſus Tellurem, in eâdem lineâ agit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18500" xml:space="preserve">ideòque vis <anchor type="note" xlink:label="note-0708-10a" xlink:href="note-0708-10"/> quæ continuò in Lunam agit, & </s> <s xml:id="echoid-s18501" xml:space="preserve">hanc in orbitâ retinet, ad cen-<lb/> <anchor type="note" xlink:label="note-0708-11a" xlink:href="note-0708-11"/> <pb o="(179)" file="0709" n="780" rhead="MATHEMATICA LIB. VI. CAP. XVI."/> trum Telluris dirigitur, & </s> <s xml:id="echoid-s18502" xml:space="preserve">Luna deſcribit areas, lineis ad <lb/>hoc centrum ductis, temporibus proportionales <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18503" xml:space="preserve"/> </p> <div xml:id="echoid-div2814" type="float" level="2" n="34"> <note position="left" xlink:label="note-0708-09" xlink:href="note-0708-09a" xml:space="preserve">1312.</note> <note symbol="*" position="left" xlink:label="note-0708-10" xlink:href="note-0708-10a" xml:space="preserve">1286. 1292.</note> <note position="left" xlink:label="note-0708-11" xlink:href="note-0708-11a" xml:space="preserve">1294.</note> </div> <note symbol="*" position="right" xml:space="preserve">225.</note> <p> <s xml:id="echoid-s18504" xml:space="preserve">In aliis orbitæ punctis, ut F, præter vim, quæ in Lineâ <lb/> <anchor type="note" xlink:label="note-0709-02a" xlink:href="note-0709-02"/> FT agit, datur & </s> <s xml:id="echoid-s18505" xml:space="preserve">alia, cujus directio ad FT eſt perpendi-<lb/> <anchor type="note" xlink:label="note-0709-03a" xlink:href="note-0709-03"/> <anchor type="note" xlink:label="note-0709-04a" xlink:href="note-0709-04"/> cularis <anchor type="note" xlink:href="" symbol="*"/>, quæ hìc per FP repræſentatur: </s> <s xml:id="echoid-s18506" xml:space="preserve">directio vis ex <anchor type="note" xlink:label="note-0709-05a" xlink:href="note-0709-05"/> ambabus compoſita dirigitur paululum ad latus lineæ FT, <lb/>& </s> <s xml:id="echoid-s18507" xml:space="preserve">non tendit ad Telluris centrum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18508" xml:space="preserve">quare areæ lineis ad cen- <anchor type="note" xlink:label="note-0709-06a" xlink:href="note-0709-06"/> trum Telluris ductis non ſunt exactè temporibus proportiona-<lb/>les <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18509" xml:space="preserve">In octantibus FP eſt omnium maxima; </s> <s xml:id="echoid-s18510" xml:space="preserve">& </s> <s xml:id="echoid-s18511" xml:space="preserve">vis, quæ <anchor type="note" xlink:label="note-0709-07a" xlink:href="note-0709-07"/> per hanc lineam repræſentatur, eſt ad gravitatem Lunæ ver-<lb/>ſus Tellurem, in hoc puncto, in mediis Lunæ & </s> <s xml:id="echoid-s18512" xml:space="preserve">Solis di-<lb/> <anchor type="note" xlink:label="note-0709-08a" xlink:href="note-0709-08"/> ſtantiis, ut 1. </s> <s xml:id="echoid-s18513" xml:space="preserve">ad 119,49. </s> <s xml:id="echoid-s18514" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18515" xml:space="preserve">quare directio vis compoſitæ, ex actionibus Solis & </s> <s xml:id="echoid-s18516" xml:space="preserve">Telluris in Lunam, cum lineâ FT effi-<lb/>cit angulum circiter ſemi gradus.</s> <s xml:id="echoid-s18517" xml:space="preserve"/> </p> <div xml:id="echoid-div2815" type="float" level="2" n="35"> <note position="right" xlink:label="note-0709-02" xlink:href="note-0709-02a" xml:space="preserve">1313.</note> <note position="right" xlink:label="note-0709-03" xlink:href="note-0709-03a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0709-04" xlink:href="note-0709-04a" xml:space="preserve">fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0709-05" xlink:href="note-0709-05a" xml:space="preserve">1301.</note> <note symbol="*" position="right" xlink:label="note-0709-06" xlink:href="note-0709-06a" xml:space="preserve">190.</note> <note symbol="*" position="right" xlink:label="note-0709-07" xlink:href="note-0709-07a" xml:space="preserve">226.</note> <note symbol="*" position="right" xlink:label="note-0709-08" xlink:href="note-0709-08a" xml:space="preserve">1306. 1307.</note> </div> <p> <s xml:id="echoid-s18518" xml:space="preserve">Variis irregularitatibus aliis ſubjicitur motus Lunæ, ita ut, <lb/>curvam omnino irregularem deſcribat; </s> <s xml:id="echoid-s18519" xml:space="preserve">quam ut computa-<lb/>tionibus, quantum fieri poteſt exactiſſimis, ſubjiciant, ad El-<lb/> <anchor type="note" xlink:label="note-0709-09a" xlink:href="note-0709-09"/> lipſin reducunt Aſtronomi, quam variis motibus agitatam, <lb/>etiam mutabilem, concipiunt, ne Luna banc deſerat.</s> <s xml:id="echoid-s18520" xml:space="preserve"/> </p> <div xml:id="echoid-div2816" type="float" level="2" n="36"> <note position="right" xlink:label="note-0709-09" xlink:href="note-0709-09a" xml:space="preserve">1314.</note> </div> <p> <s xml:id="echoid-s18521" xml:space="preserve">Circa vires centrales notavimus, corpus non deſcribere <lb/>Ellipſin, ſi vis centralis, qua in orbitâ retinetur, in aliâ ra-<lb/>tione decreſcat, quam in ratione inverſâ quadrati diſtantiæ; <lb/></s> <s xml:id="echoid-s18522" xml:space="preserve">curvam tamen ſæpe poſſe reduci ad Ellipſin mobilem <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18523" xml:space="preserve">cir- <anchor type="note" xlink:label="note-0709-10a" xlink:href="note-0709-10"/> ca quod notandum Ellipſin, in hoc motu, circa focum rotari, <lb/> <anchor type="note" xlink:label="note-0709-11a" xlink:href="note-0709-11"/> & </s> <s xml:id="echoid-s18524" xml:space="preserve">motum Ellipſeos dirigi ver ſus eandem partem, cummotu cor-<lb/>poris in bac, quando vis centralis celerius decreſcit quàm <lb/>pro ratione inverſâ quadrati diſtantiæ. </s> <s xml:id="echoid-s18525" xml:space="preserve">Si autem vis cen-<lb/> <anchor type="note" xlink:label="note-0709-12a" xlink:href="note-0709-12"/> tralis tardius decreſcat in receſſu à centro, Ellipſis in con-<lb/>trariam partem fertur; </s> <s xml:id="echoid-s18526" xml:space="preserve">ut hæc Mathematicâ demonſtratio-<lb/>ne conſtant.</s> <s xml:id="echoid-s18527" xml:space="preserve"/> </p> <div xml:id="echoid-div2817" type="float" level="2" n="37"> <note symbol="*" position="right" xlink:label="note-0709-10" xlink:href="note-0709-10a" xml:space="preserve">243.</note> <note position="right" xlink:label="note-0709-11" xlink:href="note-0709-11a" xml:space="preserve">1315.</note> <note position="right" xlink:label="note-0709-12" xlink:href="note-0709-12a" xml:space="preserve">1316.</note> </div> <p> <s xml:id="echoid-s18528" xml:space="preserve">Ex hiſce ſequitur, Lunæ orbitam ad Ellipticam referri non <lb/>poſſe, niſi quatuor motibus ſingulis revolutionibus hanc agi-<lb/>tatam concipiamus; </s> <s xml:id="echoid-s18529" xml:space="preserve">id eſt, niſi linea A pſidum, quæ per cen-<lb/>trum Telluris tranſit, bis progrediatur, & </s> <s xml:id="echoid-s18530" xml:space="preserve">bis regrediatur.</s> <s xml:id="echoid-s18531" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18532" xml:space="preserve">Progrediuntur Apſides Lunâ in Syzygiis verſante <anchor type="note" xlink:href="" symbol="*"/> aut po- <anchor type="note" xlink:label="note-0709-13a" xlink:href="note-0709-13"/> tius in motu Lunæ, inter puncta a Syzygiis 54. </s> <s xml:id="echoid-s18533" xml:space="preserve">gr. </s> <s xml:id="echoid-s18534" xml:space="preserve">44′. </s> <s xml:id="echoid-s18535" xml:space="preserve">dif-<lb/> <anchor type="note" xlink:label="note-0709-14a" xlink:href="note-0709-14"/> <anchor type="note" xlink:label="note-0709-15a" xlink:href="note-0709-15"/> tantia <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18536" xml:space="preserve">In Quadraturis, & </s> <s xml:id="echoid-s18537" xml:space="preserve">inter puncta ab his diſtantia 35.</s> <s xml:id="echoid-s18538" xml:space="preserve"> <anchor type="note" xlink:label="note-0709-16a" xlink:href="note-0709-16"/> <pb o="(180)" file="0710" n="781" rhead="PHYSICES ELEMENTA"/> gr. </s> <s xml:id="echoid-s18539" xml:space="preserve">16′, Apſides regrediuntur, id eſt in antecedentiâ moventur <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18540" xml:space="preserve"/> </p> <div xml:id="echoid-div2818" type="float" level="2" n="38"> <note position="right" xlink:label="note-0709-13" xlink:href="note-0709-13a" xml:space="preserve">1317.</note> <note symbol="*" position="right" xlink:label="note-0709-14" xlink:href="note-0709-14a" xml:space="preserve">1315. 1298.</note> <note symbol="*" position="right" xlink:label="note-0709-15" xlink:href="note-0709-15a" xml:space="preserve">1307.</note> <note position="right" xlink:label="note-0709-16" xlink:href="note-0709-16a" xml:space="preserve">1318.</note> </div> <note symbol="*" position="left" xml:space="preserve">1316. 1290. <lb/>1307.</note> <p> <s xml:id="echoid-s18541" xml:space="preserve">Vires à quibus progreſſus & </s> <s xml:id="echoid-s18542" xml:space="preserve">regreſſus Apſidum pendent <lb/> <anchor type="note" xlink:label="note-0710-02a" xlink:href="note-0710-02"/> ſunt vires motum Lunæ turbantes, antea explicatæ ; </s> <s xml:id="echoid-s18543" xml:space="preserve">ideo, <lb/>cùm vis turbans in Syzygiis, ſit dupla vis turbantis in Qua-<lb/>draturis <anchor type="note" xlink:href="" symbol="*"/>, progreſſus, integrâ conſideratâ Lunæ revolutione, <anchor type="note" xlink:label="note-0710-03a" xlink:href="note-0710-03"/> regreſſum ſuperat, cæteris paribus.</s> <s xml:id="echoid-s18544" xml:space="preserve"/> </p> <div xml:id="echoid-div2819" type="float" level="2" n="39"> <note position="left" xlink:label="note-0710-02" xlink:href="note-0710-02a" xml:space="preserve">1319.</note> <note symbol="*" position="left" xlink:label="note-0710-03" xlink:href="note-0710-03a" xml:space="preserve">1296.</note> </div> <p> <s xml:id="echoid-s18545" xml:space="preserve">In circulo, cujus centrum in centro virium datur, diminu-<lb/>tio vis, in receſſu à centro, nullum edit effectum; </s> <s xml:id="echoid-s18546" xml:space="preserve">quia in <lb/>hac lineâ non à centro recedit corpus; </s> <s xml:id="echoid-s18547" xml:space="preserve">Idcirco effectus di-<lb/>minutionis hujus eſt eo major, quo à tali circulo magis diſ-<lb/>fert curva, quam corpus deſcribit.</s> <s xml:id="echoid-s18548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s18549" xml:space="preserve">In orbitâ Ellipticâ, cujus Focorum alter cum virium cen-<lb/>tro coincidit, curvatura in Apſidibus omnium maximè à tali <lb/> <anchor type="note" xlink:label="note-0710-04a" xlink:href="note-0710-04"/> circulo differt, & </s> <s xml:id="echoid-s18550" xml:space="preserve">effectus diminutionis vis in receſſu à vi-<lb/>rium centro, eſt omniùm maximus. </s> <s xml:id="echoid-s18551" xml:space="preserve">Si orbita hæc parum fue-<lb/> <anchor type="note" xlink:label="note-0710-05a" xlink:href="note-0710-05"/> rit excentrica, in extremitatibus axeos minoris parum ad-<lb/>modum à circulo memorato differt Ellipſis, & </s> <s xml:id="echoid-s18552" xml:space="preserve">diminutionis <lb/>effectus eſt omnium minimus.</s> <s xml:id="echoid-s18553" xml:space="preserve"/> </p> <div xml:id="echoid-div2820" type="float" level="2" n="40"> <note position="left" xlink:label="note-0710-04" xlink:href="note-0710-04a" xml:space="preserve">1320.</note> <note position="left" xlink:label="note-0710-05" xlink:href="note-0710-05a" xml:space="preserve">1321.</note> </div> <p> <s xml:id="echoid-s18554" xml:space="preserve">Progreſſus, & </s> <s xml:id="echoid-s18555" xml:space="preserve">regreſſus, Apſidum pendent à proportio-<lb/> <anchor type="note" xlink:label="note-0710-06a" xlink:href="note-0710-06"/> ne, juxta quam decreſcit vis gravitatis recedendo à Tel-<lb/>luris centro <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18556" xml:space="preserve">eſt ideò effectus diminutionis vis centralis.</s> <s xml:id="echoid-s18557" xml:space="preserve"/> </p> <div xml:id="echoid-div2821" type="float" level="2" n="41"> <note position="left" xlink:label="note-0710-06" xlink:href="note-0710-06a" xml:space="preserve">1322.</note> </div> <note symbol="*" position="left" xml:space="preserve">1315. 1316.</note> <p> <s xml:id="echoid-s18558" xml:space="preserve">Varias ſubit mutationes explicatus Apſidum motus; </s> <s xml:id="echoid-s18559" xml:space="preserve">om-<lb/> <anchor type="note" xlink:label="note-0710-08a" xlink:href="note-0710-08"/> nium celerrimè progrediuntur Apſides, in Lunæ revolutione, <lb/> <anchor type="note" xlink:label="note-0710-09a" xlink:href="note-0710-09"/> poſitâ Apſidum lineâ in bis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18560" xml:space="preserve">& </s> <s xml:id="echoid-s18561" xml:space="preserve">in boc ipſo caſu omnium lentiſ- <anchor type="note" xlink:label="note-0710-10a" xlink:href="note-0710-10"/> <anchor type="note" xlink:label="note-0710-11a" xlink:href="note-0710-11"/> ſimè, in eâdem revolutione remeant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18562" xml:space="preserve">quia, propter exiguam <anchor type="note" xlink:label="note-0710-12a" xlink:href="note-0710-12"/> Lunæ excentricitatem, parum, ab extremitatibus axeos mi-<lb/> <anchor type="note" xlink:label="note-0710-13a" xlink:href="note-0710-13"/> noris orbitæ diſtant Quadraturæ.</s> <s xml:id="echoid-s18563" xml:space="preserve"/> </p> <div xml:id="echoid-div2822" type="float" level="2" n="42"> <note position="left" xlink:label="note-0710-08" xlink:href="note-0710-08a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0710-09" xlink:href="note-0710-09a" xml:space="preserve">fig. 2.</note> <note position="left" xlink:label="note-0710-10" xlink:href="note-0710-10a" xml:space="preserve">1323.</note> <note symbol="*" position="left" xlink:label="note-0710-11" xlink:href="note-0710-11a" xml:space="preserve">1317. 1322.</note> <note position="left" xlink:label="note-0710-12" xlink:href="note-0710-12a" xml:space="preserve">1320.</note> <note symbol="*" position="left" xlink:label="note-0710-13" xlink:href="note-0710-13a" xml:space="preserve">1318. 1322. <lb/>1321.</note> </div> <p style="it"> <s xml:id="echoid-s18564" xml:space="preserve">Poſitâ lineâ Apſiaum in Quadraturis, omnium minimè in <lb/> <anchor type="note" xlink:label="note-0710-14a" xlink:href="note-0710-14"/> Syzygiis in conſequentiâ feruntur Apſides <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18565" xml:space="preserve">celerrimè au- <anchor type="note" xlink:label="note-0710-15a" xlink:href="note-0710-15"/> <anchor type="note" xlink:label="note-0710-16a" xlink:href="note-0710-16"/> tem redeunt in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18566" xml:space="preserve">&</s> <s xml:id="echoid-s18567" xml:space="preserve">, in boc caſu, in integrâ <anchor type="note" xlink:label="note-0710-17a" xlink:href="note-0710-17"/> Lunæ revolutione, regreſſus progreſſum ſuperat.</s> <s xml:id="echoid-s18568" xml:space="preserve"/> </p> <div xml:id="echoid-div2823" type="float" level="2" n="43"> <note position="left" xlink:label="note-0710-14" xlink:href="note-0710-14a" xml:space="preserve">1324.</note> <note position="left" xlink:label="note-0710-15" xlink:href="note-0710-15a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0710-16" xlink:href="note-0710-16a" xml:space="preserve">fig. 3.</note> <note symbol="*" position="left" xlink:label="note-0710-17" xlink:href="note-0710-17a" xml:space="preserve">1317. 1322.</note> </div> <note position="left" xml:space="preserve">1321.</note> <note symbol="*" position="left" xml:space="preserve">1318. 1322.</note> <p> <s xml:id="echoid-s18569" xml:space="preserve">Dum Tellus in orbitâ transfertur, linea Apſidum ſucceſ-<lb/> <anchor type="note" xlink:label="note-0710-20a" xlink:href="note-0710-20"/> ſivè omnes acquirit ſitus reſpectu Solis; </s> <s xml:id="echoid-s18570" xml:space="preserve">quare plurimis re-<lb/> <anchor type="note" xlink:label="note-0710-21a" xlink:href="note-0710-21"/> volutionibus Lunæ ſimul conſideratis progrediuntur Apſides <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0710-22a" xlink:href="note-0710-22"/> & </s> <s xml:id="echoid-s18571" xml:space="preserve">ex obſervationibus conſtat, in ſpatio circiter octo anno-<lb/>rum lineam Apſidum integram peragere revolutionem.</s> <s xml:id="echoid-s18572" xml:space="preserve"/> </p> <div xml:id="echoid-div2824" type="float" level="2" n="44"> <note position="left" xlink:label="note-0710-20" xlink:href="note-0710-20a" xml:space="preserve">1320.</note> <note position="left" xlink:label="note-0710-21" xlink:href="note-0710-21a" xml:space="preserve">1325.</note> <note symbol="*" position="left" xlink:label="note-0710-22" xlink:href="note-0710-22a" xml:space="preserve">1319.</note> </div> <p> <s xml:id="echoid-s18573" xml:space="preserve">Orbitæ excentricitatem etiam inconſtantem eſſe diximus.</s> <s xml:id="echoid-s18574" xml:space="preserve"/> </p> <pb o="(181)" file="0711" n="782" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> <p> <s xml:id="echoid-s18575" xml:space="preserve">Augetur corporis excentricitas, ſi vis centralis, continuâ <lb/> <anchor type="note" xlink:label="note-0711-01a" xlink:href="note-0711-01"/> diminutione, celerius quàm ante decreſcat, dum corpus ab <lb/>Apſide imâ ad Apſidem ſummam transfertur; </s> <s xml:id="echoid-s18576" xml:space="preserve">tunc enim, om-<lb/>nibus momentis, minus trahitur, quam ſi vis non decreſceret; <lb/></s> <s xml:id="echoid-s18577" xml:space="preserve">& </s> <s xml:id="echoid-s18578" xml:space="preserve">ideò magis recedit. </s> <s xml:id="echoid-s18579" xml:space="preserve">Augetur etiam eâdem orbitæ excentri-<lb/>citas, in eodem caſu, in motu ab Apſide ſummâ adimam, quia <lb/>in hoc caſu, acceſſu ad centrum, celerius creſcit vis, quo ma-<lb/>gis verſus centrum deſcendit corpus; </s> <s xml:id="echoid-s18580" xml:space="preserve">ita ut in utroque caſu <lb/>differentia inter maximam & </s> <s xml:id="echoid-s18581" xml:space="preserve">minimam diſtantiam à centro vi-<lb/>rium, major fiat, ideòque excentricitas augeatur. </s> <s xml:id="echoid-s18582" xml:space="preserve">Simili ratio-<lb/> <anchor type="note" xlink:label="note-0711-02a" xlink:href="note-0711-02"/> cinio patet excentricitatem minui, quando vis centralis auge-<lb/>tur, in motu corporis ab Abſide imâ ad ſummam, & </s> <s xml:id="echoid-s18583" xml:space="preserve">quando <lb/>hæc minuitur in motu ab Apſide ſummâ ad imam, id eſt <lb/>quando lentius decreſcit, quàm ante, inreceſſu à centro.</s> <s xml:id="echoid-s18584" xml:space="preserve"/> </p> <div xml:id="echoid-div2825" type="float" level="2" n="45"> <note position="right" xlink:label="note-0711-01" xlink:href="note-0711-01a" xml:space="preserve">1326.</note> <note position="right" xlink:label="note-0711-02" xlink:href="note-0711-02a" xml:space="preserve">1327.</note> </div> <p> <s xml:id="echoid-s18585" xml:space="preserve">Hiſce ad motum Lunæ applicatis, patet: </s> <s xml:id="echoid-s18586" xml:space="preserve">Orbitæ excentrici-<lb/> <anchor type="note" xlink:label="note-0711-03a" xlink:href="note-0711-03"/> tatem, ſingulis revolutionibus, varias ſubire mutationes. </s> <s xml:id="echoid-s18587" xml:space="preserve">Eſ-<lb/> <anchor type="note" xlink:label="note-0711-04a" xlink:href="note-0711-04"/> ſeomnium maximam, poſitâ lineâ Apſidum in Syzygiis; </s> <s xml:id="echoid-s18588" xml:space="preserve">quia, vi-<lb/>ribus in Apſidibus collatis, celerius decreſcunt quàm pro ra-<lb/>tione inverſâ quadrati diſtantiæ <anchor type="note" xlink:href="" symbol="*"/>, unde augmentum hoc ſe- <anchor type="note" xlink:label="note-0711-05a" xlink:href="note-0711-05"/> quitur <anchor type="note" xlink:href="" symbol="*"/>, quod in hoc ſitu prævalet <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18589" xml:space="preserve">Orbitam verò omnium <anchor type="note" xlink:label="note-0711-06a" xlink:href="note-0711-06"/> minimè eſſe excentricam, verſante lineâ Apſidum in Quadra-<lb/> <anchor type="note" xlink:label="note-0711-07a" xlink:href="note-0711-07"/> turis, prævalente diminutione excentricitatis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18590" xml:space="preserve"/> </p> <div xml:id="echoid-div2826" type="float" level="2" n="46"> <note position="right" xlink:label="note-0711-03" xlink:href="note-0711-03a" xml:space="preserve">1328.</note> <note position="right" xlink:label="note-0711-04" xlink:href="note-0711-04a" xml:space="preserve">1329.</note> <note symbol="*" position="right" xlink:label="note-0711-05" xlink:href="note-0711-05a" xml:space="preserve">1298.</note> <note symbol="*" position="right" xlink:label="note-0711-06" xlink:href="note-0711-06a" xml:space="preserve">1326.</note> <note symbol="*" position="right" xlink:label="note-0711-07" xlink:href="note-0711-07a" xml:space="preserve">1320.</note> </div> <note symbol="*" position="right" xml:space="preserve">1290. 1327.</note> <p> <s xml:id="echoid-s18591" xml:space="preserve">Lunam diximus moveri in plano ad Eclipticæ planum in-<lb/> <anchor type="note" xlink:label="note-0711-09a" xlink:href="note-0711-09"/> clinatum; </s> <s xml:id="echoid-s18592" xml:space="preserve">lineam Nodorum rotari in antecedentiâ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18593" xml:space="preserve">& </s> <s xml:id="echoid-s18594" xml:space="preserve">in- <anchor type="note" xlink:label="note-0711-10a" xlink:href="note-0711-10"/> conſtantem eſſe Orbitæ inclinationem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18595" xml:space="preserve">effectus hi ex actio- <anchor type="note" xlink:label="note-0711-11a" xlink:href="note-0711-11"/> ne Solis in Lunam etiam deducuntur.</s> <s xml:id="echoid-s18596" xml:space="preserve"/> </p> <div xml:id="echoid-div2827" type="float" level="2" n="47"> <note position="right" xlink:label="note-0711-09" xlink:href="note-0711-09a" xml:space="preserve">1321.</note> <note symbol="*" position="right" xlink:label="note-0711-10" xlink:href="note-0711-10a" xml:space="preserve">970.</note> <note symbol="*" position="right" xlink:label="note-0711-11" xlink:href="note-0711-11a" xml:space="preserve">969.</note> </div> <p> <s xml:id="echoid-s18597" xml:space="preserve">Propter exiguam orbitæ Lunaris inclinationem, vires quas <lb/>huc uſque in plano Eclipticæ agentes non attendendo ad or-<lb/>bitæ inclinationem conſideravimus, ſine ſenſibili errore, ad <lb/>orbitæ planum, referuntur, & </s> <s xml:id="echoid-s18598" xml:space="preserve">Luna, in hoc, motibus ante <lb/>explicatis ſubjicitur: </s> <s xml:id="echoid-s18599" xml:space="preserve">Sed datur vis, quæ Lunam ex plano or-<lb/> <anchor type="note" xlink:label="note-0711-12a" xlink:href="note-0711-12"/> bitæ removet; </s> <s xml:id="echoid-s18600" xml:space="preserve">ita ut hoc planum agitatum concipere debea-<lb/>mus, ne Luna orbitam deſerat <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18601" xml:space="preserve"/> </p> <div xml:id="echoid-div2828" type="float" level="2" n="48"> <note position="right" xlink:label="note-0711-12" xlink:href="note-0711-12a" xml:space="preserve">1330.</note> </div> <note symbol="*" position="right" xml:space="preserve">1314.</note> <p> <s xml:id="echoid-s18602" xml:space="preserve">Sit Luna in F; </s> <s xml:id="echoid-s18603" xml:space="preserve">attendendo ad illa, quæ de actione Solis <lb/> <anchor type="note" xlink:label="note-0711-14a" xlink:href="note-0711-14"/> ſuperius dicta ſunt <anchor type="note" xlink:href="" symbol="*"/>, liquet planum parallelogrammi FHMI <anchor type="note" xlink:label="note-0711-15a" xlink:href="note-0711-15"/> <anchor type="note" xlink:label="note-0711-16a" xlink:href="note-0711-16"/> per lineam TS tranſire, quæ centra Solis & </s> <s xml:id="echoid-s18604" xml:space="preserve">Telluris jungit; <lb/></s> <s xml:id="echoid-s18605" xml:space="preserve"> <anchor type="note" xlink:label="note-0711-17a" xlink:href="note-0711-17"/> ideòque in plano Eclipticæ datur; </s> <s xml:id="echoid-s18606" xml:space="preserve">ita ut punctum N, ad <lb/>quod dirigitur vis FN turbans ex actione Solis, in hoc pla-<lb/>no detur.</s> <s xml:id="echoid-s18607" xml:space="preserve"/> </p> <div xml:id="echoid-div2829" type="float" level="2" n="49"> <note position="right" xlink:label="note-0711-14" xlink:href="note-0711-14a" xml:space="preserve">1331.</note> <note position="right" xlink:label="note-0711-15" xlink:href="note-0711-15a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0711-16" xlink:href="note-0711-16a" xml:space="preserve">fig. 1.</note> <note symbol="*" position="right" xlink:label="note-0711-17" xlink:href="note-0711-17a" xml:space="preserve">1299.</note> </div> <pb o="(182)" file="0712" n="783" rhead="PHYSICES ELEMENTA"/> <p> <s xml:id="echoid-s18608" xml:space="preserve">Repræſentetur hæc eâdem vis per FI; </s> <s xml:id="echoid-s18609" xml:space="preserve">in F ad orbitæ pla-<lb/> <anchor type="note" xlink:label="note-0712-01a" xlink:href="note-0712-01"/> num detur perpendicularis FR & </s> <s xml:id="echoid-s18610" xml:space="preserve">concipiatur parallelogram-<lb/> <anchor type="note" xlink:label="note-0712-02a" xlink:href="note-0712-02"/> <anchor type="note" xlink:label="note-0712-03a" xlink:href="note-0712-03"/> mum FRI i, cujus latus F i in plano orbitæ detur, & </s> <s xml:id="echoid-s18611" xml:space="preserve">cujus <lb/>diagonalis ſit FI; </s> <s xml:id="echoid-s18612" xml:space="preserve">vis turbans per F I reſolvitur in duas, per <lb/>FR & </s> <s xml:id="echoid-s18613" xml:space="preserve">F i, quas hæ lineæ repræſentant <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18614" xml:space="preserve">quarum hæc in <anchor type="note" xlink:label="note-0712-04a" xlink:href="note-0712-04"/> plano orbitæ agit: </s> <s xml:id="echoid-s18615" xml:space="preserve">ita ut ad hanc debeamus referre, quæ ſpec-<lb/>tant vim turbantem, de qua in n. </s> <s xml:id="echoid-s18616" xml:space="preserve">1299. </s> <s xml:id="echoid-s18617" xml:space="preserve">egimus; </s> <s xml:id="echoid-s18618" xml:space="preserve">lineæ enim F i <lb/>& </s> <s xml:id="echoid-s18619" xml:space="preserve">FI vix differunt, & </s> <s xml:id="echoid-s18620" xml:space="preserve">planum parallelogrammi FRI i ad pla-<lb/>num orbitæ Lunaris eſt perpendiculare.</s> <s xml:id="echoid-s18621" xml:space="preserve"/> </p> <div xml:id="echoid-div2830" type="float" level="2" n="50"> <note position="left" xlink:label="note-0712-01" xlink:href="note-0712-01a" xml:space="preserve">1332.</note> <note position="left" xlink:label="note-0712-02" xlink:href="note-0712-02a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0712-03" xlink:href="note-0712-03a" xml:space="preserve">fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0712-04" xlink:href="note-0712-04a" xml:space="preserve">192.</note> </div> <p> <s xml:id="echoid-s18622" xml:space="preserve">Determinanda eſt linea FR, quæ repræſentat vim, quæ ad <lb/> <anchor type="note" xlink:label="note-0712-05a" xlink:href="note-0712-05"/> planum orbitæ perpendiculariter agit, & </s> <s xml:id="echoid-s18623" xml:space="preserve">Lunam ex hoc plano <lb/>removet; </s> <s xml:id="echoid-s18624" xml:space="preserve">relatio autem lineæ FR aut I i ad radium ET, eſt <lb/>ratio vis turbantis, de qua hìc agitur, ad augmentum gravita-<lb/>tis in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18625" xml:space="preserve"/> </p> <div xml:id="echoid-div2831" type="float" level="2" n="51"> <note position="right" xlink:label="note-0712-05" xlink:href="note-0712-05a" xml:space="preserve">1333.</note> </div> <note symbol="*" position="left" xml:space="preserve">1286.</note> <p> <s xml:id="echoid-s18626" xml:space="preserve">In caſu hujus figuræ in quâ linea Nodorum N n in Quadra-<lb/> <anchor type="note" xlink:label="note-0712-07a" xlink:href="note-0712-07"/> turis verſatur, detegitur FR; </s> <s xml:id="echoid-s18627" xml:space="preserve">quia IT (quæ eſt NT fig. </s> <s xml:id="echoid-s18628" xml:space="preserve">I.) <lb/></s> <s xml:id="echoid-s18629" xml:space="preserve">datur <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18630" xml:space="preserve">quia IT ad I i aut FR, ut radius ad ſinum in- <anchor type="note" xlink:label="note-0712-08a" xlink:href="note-0712-08"/> clinationis crbitæ.</s> <s xml:id="echoid-s18631" xml:space="preserve"/> </p> <div xml:id="echoid-div2832" type="float" level="2" n="52"> <note position="left" xlink:label="note-0712-07" xlink:href="note-0712-07a" xml:space="preserve">1334.</note> <note symbol="*" position="left" xlink:label="note-0712-08" xlink:href="note-0712-08a" xml:space="preserve">1305.</note> </div> <p> <s xml:id="echoid-s18632" xml:space="preserve">Sed in omni caſu determinanda eſt vis, quæ Lunam ex pla-<lb/> <anchor type="note" xlink:label="note-0712-09a" xlink:href="note-0712-09"/> no pellit; </s> <s xml:id="echoid-s18633" xml:space="preserve">ponamus ideò lineam Nodorum tranſlatam ad ſitum <lb/>M m, quo, cæteris manentibus, mutatur I i. </s> <s xml:id="echoid-s18634" xml:space="preserve">Ad m M con-<lb/>tinuatam, ſi neceſſe fuerit, dentur perpendiculares i X & </s> <s xml:id="echoid-s18635" xml:space="preserve"><lb/>IX, quæ angulum efficiunt æqualem inclinationi plani orbitæ.</s> <s xml:id="echoid-s18636" xml:space="preserve"/> </p> <div xml:id="echoid-div2833" type="float" level="2" n="53"> <note position="left" xlink:label="note-0712-09" xlink:href="note-0712-09a" xml:space="preserve">1335.</note> </div> <p> <s xml:id="echoid-s18637" xml:space="preserve">Ratio inter ET & </s> <s xml:id="echoid-s18638" xml:space="preserve">I i, id eſt ratio inter augmentum gravi-<lb/> <anchor type="note" xlink:label="note-0712-10a" xlink:href="note-0712-10"/> tatis in Quadraturis & </s> <s xml:id="echoid-s18639" xml:space="preserve">vim, quam quærimus, quæ Lunam ex <lb/>orbitâ removet, eſt compoſita exrationibus lineæ ET ad TI, <lb/>lineæ TI ad IX, & </s> <s xml:id="echoid-s18640" xml:space="preserve">tandem lineæ IX ad I i. </s> <s xml:id="echoid-s18641" xml:space="preserve">Prima eſt ra-<lb/>tio inter radium & </s> <s xml:id="echoid-s18642" xml:space="preserve">ter ſinum diſtantiæ Lunæ à Quadraturâ <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18643" xml:space="preserve"> <anchor type="note" xlink:label="note-0712-11a" xlink:href="note-0712-11"/> ſecunda eſt ratio radii ad ſinum anguli ITX, id eſt diſtantiæ <lb/>Nodi à Syzygiâ; </s> <s xml:id="echoid-s18644" xml:space="preserve">tertia tandem eſt ratio radii ad ſinum incli-<lb/>nationis orbitæ: </s> <s xml:id="echoid-s18645" xml:space="preserve">& </s> <s xml:id="echoid-s18646" xml:space="preserve">ratio ex his compoſita, eſt ratio cubi radii <lb/>ad ter productum ſinu m diſtantiarum Lunæ à Quadratur â, & </s> <s xml:id="echoid-s18647" xml:space="preserve"><lb/>Nodi à Syzygiâ, ut & </s> <s xml:id="echoid-s18648" xml:space="preserve">inclinationis plani. </s> <s xml:id="echoid-s18649" xml:space="preserve">Ad hanc vim etiam <lb/>reſerendus n. </s> <s xml:id="echoid-s18650" xml:space="preserve">1308.</s> <s xml:id="echoid-s18651" xml:space="preserve"/> </p> <div xml:id="echoid-div2834" type="float" level="2" n="54"> <note position="left" xlink:label="note-0712-10" xlink:href="note-0712-10a" xml:space="preserve">1336.</note> <note symbol="*" position="left" xlink:label="note-0712-11" xlink:href="note-0712-11a" xml:space="preserve">1305.</note> </div> <p> <s xml:id="echoid-s18652" xml:space="preserve">Vis hæc in Quadraturis nulla eſt, quia punctum I cum <lb/> <anchor type="note" xlink:label="note-0712-12a" xlink:href="note-0712-12"/> puncto T, centro Telluris, coincidit, & </s> <s xml:id="echoid-s18653" xml:space="preserve">evaneſcit linea I i, li-<lb/>neis FI & </s> <s xml:id="echoid-s18654" xml:space="preserve">F i concurrentibus, in plano orbitæ; </s> <s xml:id="echoid-s18655" xml:space="preserve">quod etiam ex <pb o="(183)" file="0713" n="784" rhead="MATHEMATICA LIB. IV. CAP. XVI."/> computatione memoratâ <anchor type="note" xlink:href="" symbol="*"/> ſequitur; </s> <s xml:id="echoid-s18656" xml:space="preserve">evaneſcente ſinu diſtantiæ <anchor type="note" xlink:label="note-0713-01a" xlink:href="note-0713-01"/> Lunæ à Quadraturâ; </s> <s xml:id="echoid-s18657" xml:space="preserve">ideoque toto producto, quod per ſinum <lb/>hunc multiplicatur.</s> <s xml:id="echoid-s18658" xml:space="preserve"/> </p> <div xml:id="echoid-div2835" type="float" level="2" n="55"> <note position="left" xlink:label="note-0712-12" xlink:href="note-0712-12a" xml:space="preserve">1337.</note> <note symbol="*" position="right" xlink:label="note-0713-01" xlink:href="note-0713-01a" xml:space="preserve">1136.</note> </div> <p> <s xml:id="echoid-s18659" xml:space="preserve">Evaneſcit idem hoc productum, & </s> <s xml:id="echoid-s18660" xml:space="preserve">cum hoc vis, quam <lb/> <anchor type="note" xlink:label="note-0713-02a" xlink:href="note-0713-02"/> repræſentat, evaneſcente ſinu diſtantiæ Nodi à Syzygiâ, id <lb/> <anchor type="note" xlink:label="note-0713-03a" xlink:href="note-0713-03"/> <anchor type="note" xlink:label="note-0713-04a" xlink:href="note-0713-04"/> eſt, poſitâ lineâ Nodorum in Syzygiis; </s> <s xml:id="echoid-s18661" xml:space="preserve">etiam hoc ex eo de-<lb/>ducitur, quod linea Nodorum N n continuata per Solem tran-<lb/>ſit; </s> <s xml:id="echoid-s18662" xml:space="preserve">quare Sol in ipſo plano orbitæ datur; </s> <s xml:id="echoid-s18663" xml:space="preserve">ideoque Lunam, <lb/>niſi in hoc plano trahere non poteſt.</s> <s xml:id="echoid-s18664" xml:space="preserve"/> </p> <div xml:id="echoid-div2836" type="float" level="2" n="56"> <note position="right" xlink:label="note-0713-02" xlink:href="note-0713-02a" xml:space="preserve">1338.</note> <note position="right" xlink:label="note-0713-03" xlink:href="note-0713-03a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0713-04" xlink:href="note-0713-04a" xml:space="preserve">Fig. 5.</note> </div> <p style="it"> <s xml:id="echoid-s18665" xml:space="preserve">Vis etiam, quam examinamus, augetur in acceſſu Lunæ ad <lb/> <anchor type="note" xlink:label="note-0713-05a" xlink:href="note-0713-05"/> Syzygiam, & </s> <s xml:id="echoid-s18666" xml:space="preserve">in receſſu Nodi ab hac. </s> <s xml:id="echoid-s18667" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/></s> </p> <div xml:id="echoid-div2837" type="float" level="2" n="57"> <note position="right" xlink:label="note-0713-05" xlink:href="note-0713-05a" xml:space="preserve">1339.</note> </div> <note symbol="*" position="right" xml:space="preserve">1336.</note> <p> <s xml:id="echoid-s18668" xml:space="preserve">Sit P p planum Eclipticæ; </s> <s xml:id="echoid-s18669" xml:space="preserve">PA orbita Lunæ; </s> <s xml:id="echoid-s18670" xml:space="preserve">ubi Lu-<lb/> <anchor type="note" xlink:label="note-0713-07a" xlink:href="note-0713-07"/> na ad A pervenit, id eſt paululum à Nodo receſſit, ex plano <lb/> <anchor type="note" xlink:label="note-0713-08a" xlink:href="note-0713-08"/> <anchor type="note" xlink:label="note-0713-09a" xlink:href="note-0713-09"/> orbitæ removetur, & </s> <s xml:id="echoid-s18671" xml:space="preserve">in ſecundo momento non per AB, con-<lb/>tinuationem orbitæ PA, ſed per A b fertur; </s> <s xml:id="echoid-s18672" xml:space="preserve">quia per B b ad <lb/>planum Eclipticæ accedit; </s> <s xml:id="echoid-s18673" xml:space="preserve">itaque movetur, quaſi ex Nodo ma-<lb/>gis diſtante p procederet. </s> <s xml:id="echoid-s18674" xml:space="preserve">Unde patet Nodos regredi, dum <lb/> <anchor type="note" xlink:label="note-0713-10a" xlink:href="note-0713-10"/> Luna in orbitâ movetur, quamdiu à Nodo recedit: </s> <s xml:id="echoid-s18675" xml:space="preserve">etiam re-<lb/>meant Nodi in acceſſu Lunæ ad Nodum oppoſitum; </s> <s xml:id="echoid-s18676" xml:space="preserve">quia cùm <lb/>Luna continuò ex orbitâ verſus planum Eclipticæ pellatur, <lb/>continuò ad punctum minus diſtans dirigitur, & </s> <s xml:id="echoid-s18677" xml:space="preserve">citius ad No-<lb/>dum pervenit, quàm ſi tali motu non agitata eâdem celeritate <lb/>in motu continuaſſet.</s> <s xml:id="echoid-s18678" xml:space="preserve"/> </p> <div xml:id="echoid-div2838" type="float" level="2" n="58"> <note position="right" xlink:label="note-0713-07" xlink:href="note-0713-07a" xml:space="preserve">1340.</note> <note position="right" xlink:label="note-0713-08" xlink:href="note-0713-08a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0713-09" xlink:href="note-0713-09a" xml:space="preserve">Fig. 6.</note> <note position="right" xlink:label="note-0713-10" xlink:href="note-0713-10a" xml:space="preserve">1341.</note> </div> <p style="it"> <s xml:id="echoid-s18679" xml:space="preserve">Integram conſiderando Lunæ revolutionem, cæteris pari-<lb/> <anchor type="note" xlink:label="note-0713-11a" xlink:href="note-0713-11"/> bus, celerrimè in antecedentiâ moventur Nodi, verſante <lb/>Lunâ in Syzygiis <anchor type="note" xlink:href="" symbol="*"/>, deinde lentius atque lentius, donec <anchor type="note" xlink:label="note-0713-12a" xlink:href="note-0713-12"/> quieſcant, verſante Lunâ in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>,</s> </p> <div xml:id="echoid-div2839" type="float" level="2" n="59"> <note position="right" xlink:label="note-0713-11" xlink:href="note-0713-11a" xml:space="preserve">1342.</note> <note symbol="*" position="right" xlink:label="note-0713-12" xlink:href="note-0713-12a" xml:space="preserve">1339.</note> </div> <note symbol="*" position="right" xml:space="preserve">1337.</note> <p> <s xml:id="echoid-s18680" xml:space="preserve">Dum Tellus circa Solem rotatur, etiam non attendendo ad <lb/>motum ſtatim memoratum Nodorum, linea Nodorum ſuc-<lb/> <anchor type="note" xlink:label="note-0713-14a" xlink:href="note-0713-14"/> ceſſivè omnes ſitus poſſibiles acquirit reſpectu Solis; </s> <s xml:id="echoid-s18681" xml:space="preserve">&</s> <s xml:id="echoid-s18682" xml:space="preserve">, ſin-<lb/>gulis annis, bis per Syzygias, bis per Quadratur as tran-<lb/>ſit.</s> <s xml:id="echoid-s18683" xml:space="preserve"/> </p> <div xml:id="echoid-div2840" type="float" level="2" n="60"> <note position="right" xlink:label="note-0713-14" xlink:href="note-0713-14a" xml:space="preserve">1343.</note> </div> <p style="it"> <s xml:id="echoid-s18684" xml:space="preserve">Si nunc plurimas conſideremus Lunæ revolutiones, Nodi in <lb/> <anchor type="note" xlink:label="note-0713-15a" xlink:href="note-0713-15"/> integrâ revolutione celerrimè remeant, verſantibus No-<lb/>dis in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18685" xml:space="preserve">dein lentius, donec quieſcant, poſitâ <anchor type="note" xlink:label="note-0713-16a" xlink:href="note-0713-16"/> lineâ Nodorum in Syzygiis <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18686" xml:space="preserve"/> </p> <div xml:id="echoid-div2841" type="float" level="2" n="61"> <note position="right" xlink:label="note-0713-15" xlink:href="note-0713-15a" xml:space="preserve">1344.</note> <note symbol="*" position="right" xlink:label="note-0713-16" xlink:href="note-0713-16a" xml:space="preserve">1339.</note> </div> <note symbol="*" position="right" xml:space="preserve">1338.</note> <p> <s xml:id="echoid-s18687" xml:space="preserve">Hac eadem vi, qua Nodi moventur, mutatur etiam orbitæ <lb/> <anchor type="note" xlink:label="note-0713-18a" xlink:href="note-0713-18"/> <pb o="184" file="0714" n="785" rhead="PHYSICES ELEMENTA"/> inclinatio; </s> <s xml:id="echoid-s18688" xml:space="preserve">augetur in receſſu Lunæ à Nodo; </s> <s xml:id="echoid-s18689" xml:space="preserve">minuitur in <lb/>acceſſu ad Nodum.</s> <s xml:id="echoid-s18690" xml:space="preserve"/> </p> <div xml:id="echoid-div2842" type="float" level="2" n="62"> <note position="right" xlink:label="note-0713-18" xlink:href="note-0713-18a" xml:space="preserve">1345.</note> </div> <p> <s xml:id="echoid-s18691" xml:space="preserve">Angulus enim bp L, minor eſt angulo APL, & </s> <s xml:id="echoid-s18692" xml:space="preserve">eâdem <lb/> <anchor type="note" xlink:label="note-0714-01a" xlink:href="note-0714-01"/> de causâ continuo minuitur, & </s> <s xml:id="echoid-s18693" xml:space="preserve">inclinatio major fit; </s> <s xml:id="echoid-s18694" xml:space="preserve">ubi autem <lb/> <anchor type="note" xlink:label="note-0714-02a" xlink:href="note-0714-02"/> <anchor type="note" xlink:label="note-0714-03a" xlink:href="note-0714-03"/> Luna ad maximam diſtantiam à plano Eclipticæ pervenit, & </s> <s xml:id="echoid-s18695" xml:space="preserve"><lb/>ad Nodum oppoſitum accedit, continuò directio motus Lunæ <lb/>verſus planum Eclipticæ inflectitur, & </s> <s xml:id="echoid-s18696" xml:space="preserve">minus ad hoc inclina-<lb/>tur, quàm ſi in orbitâ motum continuaret: </s> <s xml:id="echoid-s18697" xml:space="preserve">ſit Npn planum <lb/>Eclipticæ; </s> <s xml:id="echoid-s18698" xml:space="preserve">curva Nn orbita Lunæ; </s> <s xml:id="echoid-s18699" xml:space="preserve">vi qua Luna continuo <lb/>ex hac removetur, mutatur Lunæ via, & </s> <s xml:id="echoid-s18700" xml:space="preserve">percurrit curvam Np, <lb/>quæ magis ad Npn in N inclinatur, quàm in p; </s> <s xml:id="echoid-s18701" xml:space="preserve">ita ut pla-<lb/>ni orbitæ inclinationem bis mutatam concipere debeamus <anchor type="note" xlink:href="" symbol="*"/>, dum <anchor type="note" xlink:label="note-0714-04a" xlink:href="note-0714-04"/> à Nodo ad Nodum movetur Luna: </s> <s xml:id="echoid-s18702" xml:space="preserve">ideòque quater in ſingulis <lb/> <anchor type="note" xlink:label="note-0714-05a" xlink:href="note-0714-05"/> Lunæ revolutionibus, bis minuitur, bis iterum augetur.</s> <s xml:id="echoid-s18703" xml:space="preserve"/> </p> <div xml:id="echoid-div2843" type="float" level="2" n="63"> <note position="left" xlink:label="note-0714-01" xlink:href="note-0714-01a" xml:space="preserve">1346.</note> <note position="left" xlink:label="note-0714-02" xlink:href="note-0714-02a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0714-03" xlink:href="note-0714-03a" xml:space="preserve">fig. 6.</note> <note symbol="*" position="left" xlink:label="note-0714-04" xlink:href="note-0714-04a" xml:space="preserve">1314.</note> <note position="left" xlink:label="note-0714-05" xlink:href="note-0714-05a" xml:space="preserve">1347.</note> </div> <p> <s xml:id="echoid-s18704" xml:space="preserve">Poſitis Nodis N, n, in Quadraturis, vires quæ in unicâ re-<lb/> <anchor type="note" xlink:label="note-0714-06a" xlink:href="note-0714-06"/> volutione augent inclinationem, & </s> <s xml:id="echoid-s18705" xml:space="preserve">hanc minuunt, ſunt æqua-<lb/> <anchor type="note" xlink:label="note-0714-07a" xlink:href="note-0714-07"/> <anchor type="note" xlink:label="note-0714-08a" xlink:href="note-0714-08"/> les inter ſe; </s> <s xml:id="echoid-s18706" xml:space="preserve">nam propter æqualem diſtantiam utriuſque Nodi <lb/>à Syzygiis, vires inclinationem mutantes in ND & </s> <s xml:id="echoid-s18707" xml:space="preserve">nE ſunt <lb/>æquales viribus, in punctis reſpondentibus, in D n & </s> <s xml:id="echoid-s18708" xml:space="preserve">EN<anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18709" xml:space="preserve"> <anchor type="note" xlink:label="note-0714-09a" xlink:href="note-0714-09"/> illis inclinatio augetur, his minuitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18710" xml:space="preserve">diminutio anguli inclina- <anchor type="note" xlink:label="note-0714-10a" xlink:href="note-0714-10"/> tionis ex primis ſecundarum actione inſtauratur, & </s> <s xml:id="echoid-s18711" xml:space="preserve">hic non <lb/>mutatur. </s> <s xml:id="echoid-s18712" xml:space="preserve">In motu memorato <anchor type="note" xlink:href="" symbol="*"/> lineæ Nodorum reſpectu Solis, <anchor type="note" xlink:label="note-0714-11a" xlink:href="note-0714-11"/> qui à ſitu parallelo lineæ hujus pender, Nodus N ad Syzygiam <lb/>E fertur. </s> <s xml:id="echoid-s18713" xml:space="preserve">Ubi ex gr. </s> <s xml:id="echoid-s18714" xml:space="preserve">linea Nodorum pervenit ad ſitum Mm, <lb/>Luna in receſſu à Nodis tranſit per Quadraturas N, n, in <lb/>quibus vis, quæ inclinationem mutat nulla eſt <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18715" xml:space="preserve">in quo- <anchor type="note" xlink:label="note-0714-12a" xlink:href="note-0714-12"/> rum viciniis omnium eſt minima <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18716" xml:space="preserve">in acceſſu autem ad Nodos <anchor type="note" xlink:label="note-0714-13a" xlink:href="note-0714-13"/> ubique Luna à Quadraturis diſtat, & </s> <s xml:id="echoid-s18717" xml:space="preserve">vis major in hanc agit <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18718" xml:space="preserve"> <anchor type="note" xlink:label="note-0714-14a" xlink:href="note-0714-14"/> ideòque integram conſiderando revolutionem, augmentum <lb/> <anchor type="note" xlink:label="note-0714-15a" xlink:href="note-0714-15"/> anguli inclinationis ſuperat hujus diminutionem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18719" xml:space="preserve">id eſt au- <anchor type="note" xlink:label="note-0714-16a" xlink:href="note-0714-16"/> getur ille angulus aut quod idem eſt minuitur inclinatio; </s> <s xml:id="echoid-s18720" xml:space="preserve">quod <lb/>ubique obtinet in motu Nodorum à Quadraturis ad Syzygias.</s> <s xml:id="echoid-s18721" xml:space="preserve"/> </p> <div xml:id="echoid-div2844" type="float" level="2" n="64"> <note position="left" xlink:label="note-0714-06" xlink:href="note-0714-06a" xml:space="preserve">1348.</note> <note position="left" xlink:label="note-0714-07" xlink:href="note-0714-07a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0714-08" xlink:href="note-0714-08a" xml:space="preserve">fig. 4.</note> <note symbol="*" position="left" xlink:label="note-0714-09" xlink:href="note-0714-09a" xml:space="preserve">1336.</note> <note symbol="*" position="left" xlink:label="note-0714-10" xlink:href="note-0714-10a" xml:space="preserve">1345.</note> <note symbol="*" position="left" xlink:label="note-0714-11" xlink:href="note-0714-11a" xml:space="preserve">1343.</note> <note symbol="*" position="left" xlink:label="note-0714-12" xlink:href="note-0714-12a" xml:space="preserve">1337.</note> <note symbol="*" position="left" xlink:label="note-0714-13" xlink:href="note-0714-13a" xml:space="preserve">1336.</note> <note symbol="*" position="left" xlink:label="note-0714-14" xlink:href="note-0714-14a" xml:space="preserve">1336.</note> <note position="left" xlink:label="note-0714-15" xlink:href="note-0714-15a" xml:space="preserve">1349.</note> <note symbol="*" position="left" xlink:label="note-0714-16" xlink:href="note-0714-16a" xml:space="preserve">1345.</note> </div> <p> <s xml:id="echoid-s18722" xml:space="preserve">Vbi ad Syzygias pervenêre Nodi, inclinatio plani orbi-<lb/> <anchor type="note" xlink:label="note-0714-17a" xlink:href="note-0714-17"/> tæ eſt omnium minima; </s> <s xml:id="echoid-s18723" xml:space="preserve">nam in motu Nodorum à Syzygiis ad <lb/> <anchor type="note" xlink:label="note-0714-18a" xlink:href="note-0714-18"/> Quadraturas, magis ac magis continuò inclinatur orbitæ pla-<lb/>num; </s> <s xml:id="echoid-s18724" xml:space="preserve">in hoc enim caſu in acceſſu ad Nodum per Quadratu-<lb/>ras tranſit Luna, in receſſu ab his diſtat à Quadraturis, & </s> <s xml:id="echoid-s18725" xml:space="preserve">in in- <pb o="185" file="0715" n="786" rhead="MATHEMATICA LIB. IV. CAP. XVII."/> tegrâ Lunæ revolutione, vis, quæ inclinationem auget, ſupe-<lb/> <anchor type="note" xlink:label="note-0715-01a" xlink:href="note-0715-01"/> ratillam, quæ hanc minuit<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18726" xml:space="preserve">idcirco augetur inclinatio; </s> <s xml:id="echoid-s18727" xml:space="preserve">& </s> <s xml:id="echoid-s18728" xml:space="preserve">eſt <anchor type="note" xlink:label="note-0715-02a" xlink:href="note-0715-02"/> omnium maxima verſantibus Nodis in Quadr aturis, ubi rer-<lb/>minatur diminutio anguli à Plano orbitæ cum plano Eclipticæ <lb/>formati <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18729" xml:space="preserve"/> </p> <div xml:id="echoid-div2845" type="float" level="2" n="65"> <note position="left" xlink:label="note-0714-17" xlink:href="note-0714-17a" xml:space="preserve">1350.</note> <note position="left" xlink:label="note-0714-18" xlink:href="note-0714-18a" xml:space="preserve">1351.</note> <note symbol="*" position="right" xlink:label="note-0715-01" xlink:href="note-0715-01a" xml:space="preserve">1337. 1345.</note> <note position="right" xlink:label="note-0715-02" xlink:href="note-0715-02a" xml:space="preserve">1352.</note> </div> <note symbol="*" position="right" xml:space="preserve">1349.</note> <p style="it"> <s xml:id="echoid-s18730" xml:space="preserve">Omnes, quos explicavimus, errores in motu Lunæ paululum <lb/> <anchor type="note" xlink:label="note-0715-04a" xlink:href="note-0715-04"/> majores ſunt in conjunctione quàm in oppoſitione<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18731" xml:space="preserve"/> </p> <div xml:id="echoid-div2846" type="float" level="2" n="66"> <note position="right" xlink:label="note-0715-04" xlink:href="note-0715-04a" xml:space="preserve">1353.</note> </div> <note symbol="*" position="right" xml:space="preserve">1295.</note> <p> <s xml:id="echoid-s18732" xml:space="preserve">Determinantur vires omnes perturbantes, detegendo ha-<lb/> <anchor type="note" xlink:label="note-0715-06a" xlink:href="note-0715-06"/> rum relationem cum augmento gravitatis in Quadraturis <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18733" xml:space="preserve"> <anchor type="note" xlink:label="note-0715-07a" xlink:href="note-0715-07"/> quare omnes easdem mutationes ſubeunt cum hoc augmento, <lb/> <anchor type="note" xlink:label="note-0715-08a" xlink:href="note-0715-08"/> id eſt, ſunt inversè, ut cubus diſtantiæ Solis à Tellure <anchor type="note" xlink:href="" symbol="*"/>, qua <anchor type="note" xlink:label="note-0715-09a" xlink:href="note-0715-09"/> manente, ſunt ut diſtantia Lunæ à Tellure <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18734" xml:space="preserve">Omnes vires <anchor type="note" xlink:label="note-0715-10a" xlink:href="note-0715-10"/> perturbantes ſimul conſiderando prævalet gravitatis diminu-<lb/> <anchor type="note" xlink:label="note-0715-11a" xlink:href="note-0715-11"/> tio <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18735" xml:space="preserve">quod ex progreſſu Apſidum <anchor type="note" xlink:href="" symbol="*"/>immediaté ſequitur; </s> <s xml:id="echoid-s18736" xml:space="preserve">nam <anchor type="note" xlink:label="note-0715-12a" xlink:href="note-0715-12"/> ex hoc patet, plurimis ſimul conſideratis revolutionibus, effe-<lb/> <anchor type="note" xlink:label="note-0715-13a" xlink:href="note-0715-13"/> ctum diminutionis gravitatis ſuperare effectum augmenti <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18737" xml:space="preserve"> <anchor type="note" xlink:label="note-0715-14a" xlink:href="note-0715-14"/> </s> </p> <div xml:id="echoid-div2847" type="float" level="2" n="67"> <note position="right" xlink:label="note-0715-06" xlink:href="note-0715-06a" xml:space="preserve">1354.</note> <note symbol="*" position="right" xlink:label="note-0715-07" xlink:href="note-0715-07a" xml:space="preserve">1306. 1307.</note> <note position="right" xlink:label="note-0715-08" xlink:href="note-0715-08a" xml:space="preserve">1336.</note> <note symbol="*" position="right" xlink:label="note-0715-09" xlink:href="note-0715-09a" xml:space="preserve">1289.</note> <note symbol="*" position="right" xlink:label="note-0715-10" xlink:href="note-0715-10a" xml:space="preserve">1288.</note> <note position="right" xlink:label="note-0715-11" xlink:href="note-0715-11a" xml:space="preserve">1355.</note> <note symbol="*" position="right" xlink:label="note-0715-12" xlink:href="note-0715-12a" xml:space="preserve">1296.</note> <note symbol="*" position="right" xlink:label="note-0715-13" xlink:href="note-0715-13a" xml:space="preserve">970. 1325.</note> <note symbol="*" position="right" xlink:label="note-0715-14" xlink:href="note-0715-14a" xml:space="preserve">1317. 1318.</note> </div> <p> <s xml:id="echoid-s18738" xml:space="preserve">Ergo motu Lunæ generaliter conſiderato, minuitur gra-<lb/> <anchor type="note" xlink:label="note-0715-15a" xlink:href="note-0715-15"/> vitas Lunæ in Tellurem acceſſu Solis <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18739" xml:space="preserve">ideòque, cùm mi- <anchor type="note" xlink:label="note-0715-16a" xlink:href="note-0715-16"/> nus à Tellure trahatur, ab hac magis recedit, quàm recederet, <lb/>ſi talis gravitatis diminutio non daretur; </s> <s xml:id="echoid-s18740" xml:space="preserve">augetur ergo in hoc <lb/>caſu Lunæ diſtantia, etiam tempus periodicum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18741" xml:space="preserve">& </s> <s xml:id="echoid-s18742" xml:space="preserve">tempus <anchor type="note" xlink:label="note-0715-17a" xlink:href="note-0715-17"/> hoc maximum eſt, ut & </s> <s xml:id="echoid-s18743" xml:space="preserve">diſtantia Lunæ, cæteris paribus, <lb/> <anchor type="note" xlink:label="note-0715-18a" xlink:href="note-0715-18"/> maxima, verſante Tellure in Perihelio <anchor type="note" xlink:href="" symbol="*"/>, quia omnium mi- <anchor type="note" xlink:label="note-0715-19a" xlink:href="note-0715-19"/> nime à Sole diſtat.</s> <s xml:id="echoid-s18744" xml:space="preserve"/> </p> <div xml:id="echoid-div2848" type="float" level="2" n="68"> <note position="right" xlink:label="note-0715-15" xlink:href="note-0715-15a" xml:space="preserve">1356.</note> <note symbol="*" position="right" xlink:label="note-0715-16" xlink:href="note-0715-16a" xml:space="preserve">1355. 1354.</note> <note position="right" xlink:label="note-0715-17" xlink:href="note-0715-17a" xml:space="preserve">1357.</note> <note symbol="*" position="right" xlink:label="note-0715-18" xlink:href="note-0715-18a" xml:space="preserve">224.</note> <note symbol="*" position="right" xlink:label="note-0715-19" xlink:href="note-0715-19a" xml:space="preserve">1354.</note> </div> </div> <div xml:id="echoid-div2850" type="section" level="1" n="677"> <head xml:id="echoid-head879" xml:space="preserve">CAPUT XVII.</head> <head xml:id="echoid-head880" style="it" xml:space="preserve">De Planetarum Figuris.</head> <p> <s xml:id="echoid-s18745" xml:space="preserve">Si ad Planetarum figuras attendamus, talibus illos præditos <lb/>detegimus, quæ ex ipſis, quibus ſyſtema regitur, legibus <lb/>ſequitur; </s> <s xml:id="echoid-s18746" xml:space="preserve">quod ordini mirabili, quem ubique obſervamus, ad-<lb/>modum congruum eſt, nullas in Planetas agere vires ad hos <lb/>deſtruendos; </s> <s xml:id="echoid-s18747" xml:space="preserve">id eſt illam eſſe Planetæ, ſive primarii, ſive ſe-<lb/> <anchor type="note" xlink:label="note-0715-20a" xlink:href="note-0715-20"/> cundarii, figuram, quam acquireret, ſi totus ex materiâ flui-<lb/>dâ conſtaret; </s> <s xml:id="echoid-s18748" xml:space="preserve">quod Phœnomenis congruit.</s> <s xml:id="echoid-s18749" xml:space="preserve"/> </p> <div xml:id="echoid-div2850" type="float" level="2" n="1"> <note position="right" xlink:label="note-0715-20" xlink:href="note-0715-20a" xml:space="preserve">1358.</note> </div> <p> <s xml:id="echoid-s18750" xml:space="preserve">Unde ſequitur Planetas omnes primarios, & </s> <s xml:id="echoid-s18751" xml:space="preserve">ſecundarios, <lb/> <anchor type="note" xlink:label="note-0715-21a" xlink:href="note-0715-21"/> eſſe ſphæricos; </s> <s xml:id="echoid-s18752" xml:space="preserve">conſtant enim ex materiâ cujus particulæ in <lb/>ſe mutuo graves ſunt <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18753" xml:space="preserve">ex qua mutuâ attractione figura <anchor type="note" xlink:label="note-0715-22a" xlink:href="note-0715-22"/> <pb o="186" file="0716" n="787" rhead="PHYSICES ELEMENTA"/> ſphærica generatur, codem modo ac gutta fit ſphærica ex aliâ <lb/>partium attractione <anchor type="note" xlink:href="" symbol="*"/></s> </p> <div xml:id="echoid-div2851" type="float" level="2" n="2"> <note position="right" xlink:label="note-0715-21" xlink:href="note-0715-21a" xml:space="preserve">1359.</note> <note symbol="*" position="right" xlink:label="note-0715-22" xlink:href="note-0715-22a" xml:space="preserve">1206. 1207.</note> </div> <note symbol="*" position="left" xml:space="preserve">34.</note> <p> <s xml:id="echoid-s18754" xml:space="preserve">Figura hæc ſphærica Planetarum ex motu circa Solem, <lb/> <anchor type="note" xlink:label="note-0716-02a" xlink:href="note-0716-02"/> aut ſecundariorum circa primarios, non mutatur; </s> <s xml:id="echoid-s18755" xml:space="preserve">quia ſingu-<lb/>læ particulæ eodem motu feruntur: </s> <s xml:id="echoid-s18756" xml:space="preserve">motu autem circa axem <lb/>mntationem figura ſubit, eo majorem, quo motus hic cele-<lb/>rior eſt.</s> <s xml:id="echoid-s18757" xml:space="preserve"/> </p> <div xml:id="echoid-div2852" type="float" level="2" n="3"> <note position="left" xlink:label="note-0716-02" xlink:href="note-0716-02a" xml:space="preserve">1360.</note> </div> <p> <s xml:id="echoid-s18758" xml:space="preserve">Sit PP axis Planetæ; </s> <s xml:id="echoid-s18759" xml:space="preserve">Ee diameter Æquatoris, ad axem <lb/> <anchor type="note" xlink:label="note-0716-03a" xlink:href="note-0716-03"/> perpendicularis; </s> <s xml:id="echoid-s18760" xml:space="preserve">detur canalis PCE fluido repletus; </s> <s xml:id="echoid-s18761" xml:space="preserve">pon-<lb/> <anchor type="note" xlink:label="note-0716-04a" xlink:href="note-0716-04"/> dere ſuo fluidum hoc verſus C in utroque crure deſcendit, <lb/> <anchor type="note" xlink:label="note-0716-05a" xlink:href="note-0716-05"/> & </s> <s xml:id="echoid-s18762" xml:space="preserve">non quieſcit, niſi preſſio in utroque crure æqualis ſit. <lb/></s> <s xml:id="echoid-s18763" xml:space="preserve">Si Planeta quieſcat, altitudo fluidi in utroque crure æqua-<lb/>lis eſt <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18764" xml:space="preserve">ſi vero Planeta circa axem Pp rotetur, vi centri- <anchor type="note" xlink:label="note-0716-06a" xlink:href="note-0716-06"/> fugâ omne liquidum in crure CE à centrò conatur rece-<lb/>dere <anchor type="note" xlink:href="" symbol="*"/>, quæ vis cum vi gravitatis contrariè agit <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18765" xml:space="preserve">ideò- <anchor type="note" xlink:label="note-0716-07a" xlink:href="note-0716-07"/> <anchor type="note" xlink:label="note-0716-08a" xlink:href="note-0716-08"/> que gravitatem minuit; </s> <s xml:id="echoid-s18766" xml:space="preserve">ita ut æquilibrium non detur, <lb/>niſi CE ſuperet CP. </s> <s xml:id="echoid-s18767" xml:space="preserve">Tollamus nunc canalem, preſſio latera-<lb/>lis fluidi, ex quo Planeta conſtat, non mutat gravitatem ver-<lb/>ſus C, neque differentiam inter altitudines columnarum CE, <lb/>CP<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18768" xml:space="preserve">altior idcirco ubique eſt Planeta in Æquatore, quam in <anchor type="note" xlink:label="note-0716-09a" xlink:href="note-0716-09"/> Polis, & </s> <s xml:id="echoid-s18769" xml:space="preserve">acquirit ex motu circa axem, figuram ſphæroidis <lb/>depreſſi in Polis; </s> <s xml:id="echoid-s18770" xml:space="preserve">elevatio enim continuò minuitur, acce-<lb/>dendo ad Polum; </s> <s xml:id="echoid-s18771" xml:space="preserve">quia vis centrifuga minuitur, propter immi-<lb/>nutam diſtantiam ab Axe <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18772" xml:space="preserve"> <anchor type="note" xlink:label="note-0716-10a" xlink:href="note-0716-10"/> </s> </p> <div xml:id="echoid-div2853" type="float" level="2" n="4"> <note position="left" xlink:label="note-0716-03" xlink:href="note-0716-03a" xml:space="preserve">1361.</note> <note position="left" xlink:label="note-0716-04" xlink:href="note-0716-04a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0716-05" xlink:href="note-0716-05a" xml:space="preserve">fig. 7.</note> <note symbol="*" position="left" xlink:label="note-0716-06" xlink:href="note-0716-06a" xml:space="preserve">1359.</note> <note symbol="*" position="left" xlink:label="note-0716-07" xlink:href="note-0716-07a" xml:space="preserve">217.</note> <note symbol="*" position="left" xlink:label="note-0716-08" xlink:href="note-0716-08a" xml:space="preserve">223.</note> <note symbol="*" position="left" xlink:label="note-0716-09" xlink:href="note-0716-09a" xml:space="preserve">280. 1362.</note> <note position="left" xlink:label="note-0716-10" xlink:href="note-0716-10a" xml:space="preserve">232</note> </div> <p> <s xml:id="echoid-s18773" xml:space="preserve">Si demonſtrata cum Phœnomenis conſerantur, patebit <lb/>quare omnia corpora ſint Sphærica in ſyſtemate noſtro <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18774" xml:space="preserve">hanc <anchor type="note" xlink:label="note-0716-11a" xlink:href="note-0716-11"/> tamen figuram non eſſe exactam, & </s> <s xml:id="echoid-s18775" xml:space="preserve">motibus circa axes paulu-<lb/>lum mutari <anchor type="note" xlink:href="" symbol="*"/>, licèt in pleriſque hoc obſervari non poſſit, ex <anchor type="note" xlink:label="note-0716-12a" xlink:href="note-0716-12"/> obſervationibus Jovis & </s> <s xml:id="echoid-s18776" xml:space="preserve">Telluris poterit deduci. </s> <s xml:id="echoid-s18777" xml:space="preserve">Fovis axem <lb/> <anchor type="note" xlink:label="note-0716-13a" xlink:href="note-0716-13"/> breviorem eſſe diametro Æquatoris obſervarunt Aſtrono-<lb/>mi; </s> <s xml:id="echoid-s18778" xml:space="preserve">hic licet omnium Planetarum ſit maximus, omnium ce-<lb/>lerrimè circa axem rotatur <anchor type="note" xlink:href="" symbol="*"/>, ideòque differentia hæc obſerva- <anchor type="note" xlink:label="note-0716-14a" xlink:href="note-0716-14"/> ri poteſt.</s> <s xml:id="echoid-s18779" xml:space="preserve"/> </p> <div xml:id="echoid-div2854" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0716-11" xlink:href="note-0716-11a" xml:space="preserve">924.</note> <note symbol="*" position="left" xlink:label="note-0716-12" xlink:href="note-0716-12a" xml:space="preserve">1362.</note> <note position="left" xlink:label="note-0716-13" xlink:href="note-0716-13a" xml:space="preserve">1363.</note> <note position="left" xlink:label="note-0716-14" xlink:href="note-0716-14a" xml:space="preserve">962.</note> </div> <p> <s xml:id="echoid-s18780" xml:space="preserve">Elevatio Telluris, in Æquatore, à nobis determi-<lb/> <anchor type="note" xlink:label="note-0716-15a" xlink:href="note-0716-15"/> natur, quamvis fortè aliorum Planetarum incolis, ſi dentur, <lb/>non magis eſt ſenſibilis, quam nobis elevationes in Marte & </s> <s xml:id="echoid-s18781" xml:space="preserve"><lb/>Venere, quas non percipimus.</s> <s xml:id="echoid-s18782" xml:space="preserve"/> </p> <div xml:id="echoid-div2855" type="float" level="2" n="6"> <note position="left" xlink:label="note-0716-15" xlink:href="note-0716-15a" xml:space="preserve">1364.</note> </div> <pb o="187" file="0717" n="788" rhead="MATHEMATICA LIB. IV. CAP. XVII."/> <p> <s xml:id="echoid-s18783" xml:space="preserve">Ponamus Tellurem fluidam, memoratam ſphæroidem ac-<lb/> <anchor type="note" xlink:label="note-0717-01a" xlink:href="note-0717-01"/> quiret figuram <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18784" xml:space="preserve">ſi cohæreant partes verſus centrum, non co <anchor type="note" xlink:label="note-0717-02a" xlink:href="note-0717-02"/> ſitus aliarum mutari poteſt, neque mutabitur, ſi in quibus-<lb/>dam locis partes ad ſuperſiciem uſque cohæreant inter ſe; </s> <s xml:id="echoid-s18785" xml:space="preserve">ita <lb/>ut Maris ſuperficies neceſſario acquirat ſphæroidem figuram <lb/>ad Polos depreſſam. </s> <s xml:id="echoid-s18786" xml:space="preserve">Cùm verò, parum tantùm, ubique lit-<lb/>tora ſupra Maris ſuperficiem, eleventur, continentem eandem <lb/>ſequi figuram extra dubium eſt.</s> <s xml:id="echoid-s18787" xml:space="preserve"/> </p> <div xml:id="echoid-div2856" type="float" level="2" n="7"> <note position="right" xlink:label="note-0717-01" xlink:href="note-0717-01a" xml:space="preserve">1365.</note> <note symbol="*" position="right" xlink:label="note-0717-02" xlink:href="note-0717-02a" xml:space="preserve">1362.</note> </div> <p> <s xml:id="echoid-s18788" xml:space="preserve">Ut nunc hanc menſuremus elevationem, id eſt quantum <lb/>diameter Æquatoris, ſuperet Axem, ad motum Telluris cir-<lb/>ca hunc in ſpatio 23 ho. </s> <s xml:id="echoid-s18789" xml:space="preserve">56′. </s> <s xml:id="echoid-s18790" xml:space="preserve">4″. </s> <s xml:id="echoid-s18791" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> attendendum eſt; </s> <s xml:id="echoid-s18792" xml:space="preserve">& </s> <s xml:id="echoid-s18793" xml:space="preserve">ſequen- <anchor type="note" xlink:label="note-0717-03a" xlink:href="note-0717-03"/> ti methodo, poſitâ Tellure homogeneâ computatio inſtitui-<lb/>tur.</s> <s xml:id="echoid-s18794" xml:space="preserve"/> </p> <div xml:id="echoid-div2857" type="float" level="2" n="8"> <note symbol="*" position="right" xlink:label="note-0717-03" xlink:href="note-0717-03a" xml:space="preserve">960.</note> </div> <p> <s xml:id="echoid-s18795" xml:space="preserve">Telluris periſeria eſt pedum Rhenolandicorum 128202185.</s> <s xml:id="echoid-s18796" xml:space="preserve">; <lb/> <anchor type="note" xlink:label="note-0717-04a" xlink:href="note-0717-04"/> ideò in uno minuto ſecundo temporis, punctum Æquatoris per-<lb/>currit pedes 1488.</s> <s xml:id="echoid-s18797" xml:space="preserve">; cujus arcus ſinus verſus eſt pedum o, 054, <lb/>ſpatium quod in tali tempore ex vi centriſugâ à corpore per-<lb/>curri poteſt.</s> <s xml:id="echoid-s18798" xml:space="preserve"/> </p> <div xml:id="echoid-div2858" type="float" level="2" n="9"> <note position="right" xlink:label="note-0717-04" xlink:href="note-0717-04a" xml:space="preserve">1366.</note> </div> <p> <s xml:id="echoid-s18799" xml:space="preserve">Gravitate corpus, in uno minuto ſecundo, ut antea jam <lb/>vidimus, cadendo percurrit pedes 15, 607; </s> <s xml:id="echoid-s18800" xml:space="preserve">Sed hæc experi-<lb/>menta inſtituta ſuere ad diſtantiam 48. </s> <s xml:id="echoid-s18801" xml:space="preserve">gr. </s> <s xml:id="echoid-s18802" xml:space="preserve">ab Æquatore E e, <lb/> <anchor type="note" xlink:label="note-0717-05a" xlink:href="note-0717-05"/> <anchor type="note" xlink:label="note-0717-06a" xlink:href="note-0717-06"/> in pnncto A; </s> <s xml:id="echoid-s18803" xml:space="preserve">vis centriſuga in E eſt ad vim centriſugam <lb/>in A, ut CE, aut CA, nam parum admodum differunt hæ <lb/>lineæ, ad AB; </s> <s xml:id="echoid-s18804" xml:space="preserve">ſit vis hæ centrifuga Ab; </s> <s xml:id="echoid-s18805" xml:space="preserve">ductâ perpen-<lb/>diculari ba ad CA continuatam, relolvatur vis per A b, in <lb/>duas per A a & </s> <s xml:id="echoid-s18806" xml:space="preserve">ab<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18807" xml:space="preserve">illâ ſolâ minuitur gravitas, & </s> <s xml:id="echoid-s18808" xml:space="preserve">eſt Ab <anchor type="note" xlink:label="note-0717-07a" xlink:href="note-0717-07"/> ad vim illam minuentem, ut CA ad AB; </s> <s xml:id="echoid-s18809" xml:space="preserve">propter ſimilia trian-<lb/>gula rectangula, Aba, & </s> <s xml:id="echoid-s18810" xml:space="preserve">ABC, habentia in A angulos <lb/>oppoſitos ad verticem æquales; </s> <s xml:id="echoid-s18811" xml:space="preserve">eſt ideò vis centrifuga in Æ <lb/>quatore, qua corpus in minuto ſecundo percurrit O, 054; </s> <s xml:id="echoid-s18812" xml:space="preserve">ad <lb/>vim, gravitatem minuentem in A, in ratione duplicatâ <lb/>radii AC ad AB, co-ſinum latitudinis AE, 48. </s> <s xml:id="echoid-s18813" xml:space="preserve">gr.</s> <s xml:id="echoid-s18814" xml:space="preserve">; ita ut ex <lb/>hac vi minuente corpus in uno minuto ſecundo percurrat O, 0243.</s> <s xml:id="echoid-s18815" xml:space="preserve">; <lb/>quare, ſi Tellus quieſceret cadendo non percurreret pedes 15, 607.</s> <s xml:id="echoid-s18816" xml:space="preserve">, <lb/>ſed pedes 15, 632; </s> <s xml:id="echoid-s18817" xml:space="preserve">qua gravitate corpus ſub Polis cadit, quia <lb/>puncta hæc non moventur. </s> <s xml:id="echoid-s18818" xml:space="preserve">Ad Æquatorem vi centrifugâ per-<lb/>currit corpus O, 054. </s> <s xml:id="echoid-s18819" xml:space="preserve">& </s> <s xml:id="echoid-s18820" xml:space="preserve">tantum cadit, in eodem tempore ab <pb o="188" file="0718" n="789" rhead="PHYSICES ELEMENTA"/> altitudine pedum 15, 578.</s> <s xml:id="echoid-s18821" xml:space="preserve">; unde patet gravitatem ſub Polis eſſe <lb/>ad gravitatem ſub Æquatore, ut 289 ad 288.</s> <s xml:id="echoid-s18822" xml:space="preserve"/> </p> <div xml:id="echoid-div2859" type="float" level="2" n="10"> <note position="right" xlink:label="note-0717-05" xlink:href="note-0717-05a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0717-06" xlink:href="note-0717-06a" xml:space="preserve">fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0717-07" xlink:href="note-0717-07a" xml:space="preserve">192.</note> </div> <p> <s xml:id="echoid-s18823" xml:space="preserve">Si ſig. </s> <s xml:id="echoid-s18824" xml:space="preserve">7. </s> <s xml:id="echoid-s18825" xml:space="preserve">figuram Telluris repræſentat, pondus columnæ <lb/>liquidi CE erit ad pondus columnæ liquidi CA, quieſcente <lb/>Tellure, ut 289 ad 288; </s> <s xml:id="echoid-s18826" xml:space="preserve">aliter enim, motâ Tellure, æqui-<lb/>librium non dabitur; </s> <s xml:id="echoid-s18827" xml:space="preserve">quia pars {1/259} columnæ CE vi centrifu-<lb/>gâ ſuſtinetur; </s> <s xml:id="echoid-s18828" xml:space="preserve">decreſcit enim vis centrifuga accedendo ad cen-<lb/>trum in ratione diſtantiæ<anchor type="note" xlink:href="" symbol="*"/>, in qua etiam ratione decreſcitgra- <anchor type="note" xlink:label="note-0718-01a" xlink:href="note-0718-01"/> vitas <anchor type="note" xlink:href="" symbol="*"/>, ita ut in ſingulis columnæ punctis eadem pars ponde- <anchor type="note" xlink:label="note-0718-02a" xlink:href="note-0718-02"/> ris ſuſtineatur, quàm verſus ſuperſiciem.</s> <s xml:id="echoid-s18829" xml:space="preserve"/> </p> <div xml:id="echoid-div2860" type="float" level="2" n="11"> <note symbol="*" position="left" xlink:label="note-0718-01" xlink:href="note-0718-01a" xml:space="preserve">232.</note> <note symbol="*" position="left" xlink:label="note-0718-02" xlink:href="note-0718-02a" xml:space="preserve">1233.</note> </div> <p> <s xml:id="echoid-s18830" xml:space="preserve">Ex his deducimus altitudinem CP, ad Polum, eſſe ad alti-<lb/> <anchor type="note" xlink:label="note-0718-03a" xlink:href="note-0718-03"/> tudinem EC, ad Æquatorem, ut 229 ad 230; </s> <s xml:id="echoid-s18831" xml:space="preserve">poſitâ enim <lb/>hac ratione inter Axem & </s> <s xml:id="echoid-s18832" xml:space="preserve">Æquatoris diametrum, ſide gravita-<lb/>tibus in locis P & </s> <s xml:id="echoid-s18833" xml:space="preserve">E, Tellare quieſcente. </s> <s xml:id="echoid-s18834" xml:space="preserve">computatio inea-<lb/>tur, deteguntur eſſe inter ſe, ut 1121, 71. </s> <s xml:id="echoid-s18835" xml:space="preserve">ad 1120, 71.</s> <s xml:id="echoid-s18836" xml:space="preserve">; quæ ra-<lb/>tio ubique obtinet in punctis reſpondentibus, id eſt quæ diſtant <lb/>à centro ut CP ad PE; </s> <s xml:id="echoid-s18837" xml:space="preserve">quia in utroque crure decreſcit gra-<lb/>vitas in ratione diſtantiæ à centro <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18838" xml:space="preserve">Pondus habetur multi- <anchor type="note" xlink:label="note-0718-04a" xlink:href="note-0718-04"/> plicando materiæ quantitatem per gravitatem; </s> <s xml:id="echoid-s18839" xml:space="preserve">nam in utriuſque <lb/>ratione creſcit pondus: </s> <s xml:id="echoid-s18840" xml:space="preserve">multiplicando 1121, 71. </s> <s xml:id="echoid-s18841" xml:space="preserve">per 229, & </s> <s xml:id="echoid-s18842" xml:space="preserve"><lb/>1120. </s> <s xml:id="echoid-s18843" xml:space="preserve">71 per 230. </s> <s xml:id="echoid-s18844" xml:space="preserve">producta ſunt inter ſe, ut 288. </s> <s xml:id="echoid-s18845" xml:space="preserve">ad 289.</s> <s xml:id="echoid-s18846" xml:space="preserve">; <lb/>quæ eſt ratio ponderum ante detecta. </s> <s xml:id="echoid-s18847" xml:space="preserve">Diameter media Tellu-<lb/>ris eſt 3400669 perticarum <anchor type="note" xlink:href="" symbol="*"/>, ideò axis PP eſt 3393261, &</s> <s xml:id="echoid-s18848" xml:space="preserve"> <anchor type="note" xlink:label="note-0718-05a" xlink:href="note-0718-05"/> diameter Æquatoris Ee 3408078. </s> <s xml:id="echoid-s18849" xml:space="preserve">perticarum, quæ Axem <lb/>ſuperat perticis 14817, parte nempe {1/230}, & </s> <s xml:id="echoid-s18850" xml:space="preserve">Æquator magis <lb/> <anchor type="note" xlink:label="note-0718-06a" xlink:href="note-0718-06"/> elevatur perticis 7408, 5.</s> <s xml:id="echoid-s18851" xml:space="preserve"/> </p> <div xml:id="echoid-div2861" type="float" level="2" n="12"> <note position="left" xlink:label="note-0718-03" xlink:href="note-0718-03a" xml:space="preserve">1367.</note> <note symbol="*" position="left" xlink:label="note-0718-04" xlink:href="note-0718-04a" xml:space="preserve">1233.</note> <note symbol="*" position="left" xlink:label="note-0718-05" xlink:href="note-0718-05a" xml:space="preserve">976.</note> <note position="left" xlink:label="note-0718-06" xlink:href="note-0718-06a" xml:space="preserve">1368.</note> </div> <p> <s xml:id="echoid-s18852" xml:space="preserve">In hac computatione, ut monuimus, Tellurem homogeneam <lb/> <anchor type="note" xlink:label="note-0718-07a" xlink:href="note-0718-07"/> habuimus; </s> <s xml:id="echoid-s18853" xml:space="preserve">ſi autem magis denſa ſit ad centrum, materia quæ adji-<lb/>citur poterit haberi pro corpore ſeparato, à cujus centro pun-<lb/>cta P & </s> <s xml:id="echoid-s18854" xml:space="preserve">E inæqualiter diſtant, & </s> <s xml:id="echoid-s18855" xml:space="preserve">in quod ideò diverſam <lb/>gravitatem habent corpora in P & </s> <s xml:id="echoid-s18856" xml:space="preserve">E<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18857" xml:space="preserve">& </s> <s xml:id="echoid-s18858" xml:space="preserve">diſſerentia eo ma- <anchor type="note" xlink:label="note-0718-08a" xlink:href="note-0718-08"/> jor erit, quo hæ diſtantiæ magis differunt: </s> <s xml:id="echoid-s18859" xml:space="preserve">& </s> <s xml:id="echoid-s18860" xml:space="preserve">etiam erit eo <lb/>major reſpectu totius gravitatis, quo materiæ quantitas adje-<lb/>cta, aut quod idem eſt, denſitas verſus centrum major eſt.</s> <s xml:id="echoid-s18861" xml:space="preserve"/> </p> <div xml:id="echoid-div2862" type="float" level="2" n="13"> <note position="left" xlink:label="note-0718-07" xlink:href="note-0718-07a" xml:space="preserve">1369.</note> <note position="left" xlink:label="note-0718-08" xlink:href="note-0718-08a" xml:space="preserve">1266</note> </div> <p> <s xml:id="echoid-s18862" xml:space="preserve">Magis inter ſe differre vires gravitatis in Polis & </s> <s xml:id="echoid-s18863" xml:space="preserve">Æquarore, <lb/>quàmparte {1/289}, collatis experimentis ad varias Æquatoris diſtan-<lb/>tias, ope pendulorum inſtitutis, conſtat, quibus vires gravitatis <pb o="189" file="0719" n="790" rhead="MATHEMATICA LIB. IV. CAP. XVII."/> interſe conferri poſſe vidimus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18864" xml:space="preserve">& </s> <s xml:id="echoid-s18865" xml:space="preserve">differentia quæ revera datur <anchor type="note" xlink:label="note-0719-01a" xlink:href="note-0719-01"/> fere dupla eſt illius, quæ computatione detegitur; </s> <s xml:id="echoid-s18866" xml:space="preserve">unde ſe-<lb/>quitur elevationem Æquatoris fere duplam eſſe illius, quam <lb/> <anchor type="note" xlink:label="note-0719-02a" xlink:href="note-0719-02"/> determinavimus 7408, 5. </s> <s xml:id="echoid-s18867" xml:space="preserve">perticarum <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18868" xml:space="preserve"/> </p> <div xml:id="echoid-div2863" type="float" level="2" n="14"> <note symbol="*" position="right" xlink:label="note-0719-01" xlink:href="note-0719-01a" xml:space="preserve">164. 165.</note> <note position="right" xlink:label="note-0719-02" xlink:href="note-0719-02a" xml:space="preserve">1370.</note> </div> <note symbol="*" position="right" xml:space="preserve">1368.</note> <p> <s xml:id="echoid-s18869" xml:space="preserve">Si nunc ad ſphæroidem figuram Telluris attendamus, vide-<lb/>mus gravia non directe tendere ad centrum Telluris, niſi <lb/> <anchor type="note" xlink:label="note-0719-04a" xlink:href="note-0719-04"/> in Polis & </s> <s xml:id="echoid-s18870" xml:space="preserve">Æquatore, ſed ubique perpendiculariter ad ſu-<lb/>perficiem Sphæroidis; </s> <s xml:id="echoid-s18871" xml:space="preserve">nam liquidum non quieſcit, niſi ſupre-<lb/>ma ſuperficies cum directione gravium angulum rectum ſor-<lb/>met <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18872" xml:space="preserve">& </s> <s xml:id="echoid-s18873" xml:space="preserve">ſphæroidis figura formatur à fluidi quieſcentis ſuper- <anchor type="note" xlink:label="note-0719-05a" xlink:href="note-0719-05"/> ficie. </s> <s xml:id="echoid-s18874" xml:space="preserve">Hanc eandem gravium directionem etiam directè dedu-<lb/> <anchor type="note" xlink:label="note-0719-06a" xlink:href="note-0719-06"/> cimus ex vi centriſugâ. </s> <s xml:id="echoid-s18875" xml:space="preserve">Corpus in A gravitate tendit ad C, <lb/> <anchor type="note" xlink:label="note-0719-07a" xlink:href="note-0719-07"/> <anchor type="note" xlink:label="note-0719-08a" xlink:href="note-0719-08"/> vi centrifugâ fertur per Ab; </s> <s xml:id="echoid-s18876" xml:space="preserve">vis hæc in puncto A eſt ad <lb/>gravitatem per AC.</s> <s xml:id="echoid-s18877" xml:space="preserve">, ut I. </s> <s xml:id="echoid-s18878" xml:space="preserve">ad 430, 8.</s> <s xml:id="echoid-s18879" xml:space="preserve">: formato parallelogrammo <lb/>lateribus AC & </s> <s xml:id="echoid-s18880" xml:space="preserve">Ab, poſitis his inter ſe, ut 430, 8.</s> <s xml:id="echoid-s18881" xml:space="preserve">, ad I.</s> <s xml:id="echoid-s18882" xml:space="preserve">, dia-<lb/>gonalis deſignabit directionem gravium <anchor type="note" xlink:href="" symbol="*"/>, formantem exiguum <anchor type="note" xlink:label="note-0719-09a" xlink:href="note-0719-09"/> angulum cum lineâ AC. </s> <s xml:id="echoid-s18883" xml:space="preserve">Vis per Ab creſcit acceſlu ad Æqua-<lb/>torem, quo angulus hic augetur, ſed minuitur, propter au-<lb/>ctum angulum CAb; </s> <s xml:id="echoid-s18884" xml:space="preserve">ita ut in Æquatore, ubi vis centriſuga <lb/>eſt maxima, directio gravium cum EC coincidat: </s> <s xml:id="echoid-s18885" xml:space="preserve">in Polo co-<lb/>incidit cum PC; </s> <s xml:id="echoid-s18886" xml:space="preserve">quia vis centriſuga nulla datur.</s> <s xml:id="echoid-s18887" xml:space="preserve"/> </p> <div xml:id="echoid-div2864" type="float" level="2" n="15"> <note position="right" xlink:label="note-0719-04" xlink:href="note-0719-04a" xml:space="preserve">1371.</note> <note symbol="*" position="right" xlink:label="note-0719-05" xlink:href="note-0719-05a" xml:space="preserve">272.</note> <note position="right" xlink:label="note-0719-06" xlink:href="note-0719-06a" xml:space="preserve">1372.</note> <note position="right" xlink:label="note-0719-07" xlink:href="note-0719-07a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="right" xlink:label="note-0719-08" xlink:href="note-0719-08a" xml:space="preserve">fig. 7.</note> <note symbol="*" position="right" xlink:label="note-0719-09" xlink:href="note-0719-09a" xml:space="preserve">190.</note> </div> <p> <s xml:id="echoid-s18888" xml:space="preserve">In hac figurâ ſphæroidis determinatur latitudo loci angu-<lb/> <anchor type="note" xlink:label="note-0719-10a" xlink:href="note-0719-10"/> lo, ut ACE, quem cum Æquatore efficit linea, ex loco ad <lb/>centrum ducta. </s> <s xml:id="echoid-s18889" xml:space="preserve">Diviſo toto arcu PAE, hac methodo, in <lb/>partes nonaginta, id eſt in gradus, facile patet accedendo ad <lb/> <anchor type="note" xlink:label="note-0719-11a" xlink:href="note-0719-11"/> Polum, gradus inſuperficie augeri; </s> <s xml:id="echoid-s18890" xml:space="preserve">ſed hæc adeò exigua eſt <lb/>differentia, ut, in menſurandis gradibus non admodum diſtanti-<lb/>bus, detegi non poſſit; </s> <s xml:id="echoid-s18891" xml:space="preserve">quia error ex fabricâ, & </s> <s xml:id="echoid-s18892" xml:space="preserve">uſu inſtrumento-<lb/>rum, differentiam hanc ſuperat. </s> <s xml:id="echoid-s18893" xml:space="preserve">Inde differunt paululum <lb/>inter ſe gradus menſurati ad auſtrum & </s> <s xml:id="echoid-s18894" xml:space="preserve">boream Galliæ, ut & </s> <s xml:id="echoid-s18895" xml:space="preserve"><lb/>in Angliâ, & </s> <s xml:id="echoid-s18896" xml:space="preserve">medius eſt omnium minimus; </s> <s xml:id="echoid-s18897" xml:space="preserve">quare ex menſu-<lb/> <anchor type="note" xlink:label="note-0719-12a" xlink:href="note-0719-12"/> ris his de Telluris figurânil concludi poteſt.</s> <s xml:id="echoid-s18898" xml:space="preserve"/> </p> <div xml:id="echoid-div2865" type="float" level="2" n="16"> <note position="right" xlink:label="note-0719-10" xlink:href="note-0719-10a" xml:space="preserve">1373.</note> <note position="right" xlink:label="note-0719-11" xlink:href="note-0719-11a" xml:space="preserve">1374.</note> <note position="right" xlink:label="note-0719-12" xlink:href="note-0719-12a" xml:space="preserve">1375.</note> </div> </div> <div xml:id="echoid-div2867" type="section" level="1" n="678"> <head xml:id="echoid-head881" xml:space="preserve">CAPUT XVIII.</head> <head xml:id="echoid-head882" style="it" xml:space="preserve">Motus Axeos Telluris Explicatio Phyſica.</head> <p> <s xml:id="echoid-s18899" xml:space="preserve">Lunæ Nodos regredi, id eſt in antecedentiâ moveri <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s18900" xml:space="preserve">or- <anchor type="note" xlink:label="note-0719-13a" xlink:href="note-0719-13"/> bitæ inclinationem mutationibus eſſe obnoxiam <anchor type="note" xlink:href="" symbol="*"/>, demon- <anchor type="note" xlink:label="note-0719-14a" xlink:href="note-0719-14"/> <pb o="190" file="0720" n="791" rhead="PHYSICES ELEMENTA"/> ſtravimus; </s> <s xml:id="echoid-s18901" xml:space="preserve">concipiamus varias dari Lunas, ad eandem di-<lb/>ſtantiam, æqualibus temporibus, circa Tellurem revolventes, <lb/>in plano ad planum Eclipticæ inclinato; </s> <s xml:id="echoid-s18902" xml:space="preserve">ſingulas iiſdem moti-<lb/>bus agitari clarum eſt: </s> <s xml:id="echoid-s18903" xml:space="preserve">concipiamus numerum Lunarum auge-<lb/>ri, ita ut ſeſe mutuo tangant, & </s> <s xml:id="echoid-s18904" xml:space="preserve">annulum, cujus partes cohæ-<lb/>rent, forment; </s> <s xml:id="echoid-s18905" xml:space="preserve">dum annuli pars una trahitur, ut inclinationem <lb/>augeat, pars altera motu contrario agitatur, ad inclinationem <lb/>minuendam <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18906" xml:space="preserve">Vis major in hoc caſu prævalet, id eſt, in mo- <anchor type="note" xlink:label="note-0720-01a" xlink:href="note-0720-01"/> tu lineæ Nodorum à Quadraturis ad Syzygias annuli incli-<lb/> <anchor type="note" xlink:label="note-0720-02a" xlink:href="note-0720-02"/> natio minuitur in ſingulis hujus revolutionibus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18907" xml:space="preserve">& </s> <s xml:id="echoid-s18908" xml:space="preserve">eſt <anchor type="note" xlink:label="note-0720-03a" xlink:href="note-0720-03"/> omnium minima, verſante lineâ Nodorum in Syzygiis <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18909" xml:space="preserve">Con- <anchor type="note" xlink:label="note-0720-04a" xlink:href="note-0720-04"/> tra, augetur inclinatio dum linea Nodorum ex Syzygiis ad <lb/>Quadraturas transfertur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18910" xml:space="preserve">& </s> <s xml:id="echoid-s18911" xml:space="preserve">eſt omnium maxima, poſitâ <anchor type="note" xlink:label="note-0720-05a" xlink:href="note-0720-05"/> lineâ Nodorum in his<anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18912" xml:space="preserve">Linea Nodorum continuò in ante- <anchor type="note" xlink:label="note-0720-06a" xlink:href="note-0720-06"/> cedentiâ transfertur, niſi in Syzygiis ubi quieſcit<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18913" xml:space="preserve"> <anchor type="note" xlink:label="note-0720-07a" xlink:href="note-0720-07"/> </s> </p> <div xml:id="echoid-div2867" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0719-13" xlink:href="note-0719-13a" xml:space="preserve">1341.</note> <note symbol="*" position="right" xlink:label="note-0719-14" xlink:href="note-0719-14a" xml:space="preserve">1347.</note> <note position="left" xlink:label="note-0720-01" xlink:href="note-0720-01a" xml:space="preserve">1376.</note> <note position="left" xlink:label="note-0720-02" xlink:href="note-0720-02a" xml:space="preserve">1345.</note> <note position="left" xlink:label="note-0720-03" xlink:href="note-0720-03a" xml:space="preserve">1377.</note> <note position="left" xlink:label="note-0720-04" xlink:href="note-0720-04a" xml:space="preserve">1349.</note> <note position="left" xlink:label="note-0720-05" xlink:href="note-0720-05a" xml:space="preserve">1378.</note> <note position="left" xlink:label="note-0720-06" xlink:href="note-0720-06a" xml:space="preserve">1351.</note> <note position="left" xlink:label="note-0720-07" xlink:href="note-0720-07a" xml:space="preserve">1352. 1341 1344.</note> </div> <p> <s xml:id="echoid-s18914" xml:space="preserve">Si quantitas materiæ in annulo minuatur, non mutantur <lb/> <anchor type="note" xlink:label="note-0720-08a" xlink:href="note-0720-08"/> hujus motus; </s> <s xml:id="echoid-s18915" xml:space="preserve">quia à gravitate pendent, quæ æqualiter in ſin-<lb/>gulas materiæ particulas agit <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18916" xml:space="preserve"/> </p> <div xml:id="echoid-div2868" type="float" level="2" n="2"> <note position="left" xlink:label="note-0720-08" xlink:href="note-0720-08a" xml:space="preserve">1379.</note> </div> <note symbol="*" position="left" xml:space="preserve">1207.</note> <p> <s xml:id="echoid-s18917" xml:space="preserve">Si annuli diameter minuatur, in ratione hujus diminutio-<lb/>nis minuuntur motus <anchor type="note" xlink:href="" symbol="*"/>, ſed nullus in totum evaneſcit; </s> <s xml:id="echoid-s18918" xml:space="preserve">& </s> <s xml:id="echoid-s18919" xml:space="preserve">iiſ- <anchor type="note" xlink:label="note-0720-10a" xlink:href="note-0720-10"/> dem motibus agitatur.</s> <s xml:id="echoid-s18920" xml:space="preserve"/> </p> <div xml:id="echoid-div2869" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0720-10" xlink:href="note-0720-10a" xml:space="preserve">1354.</note> </div> <p> <s xml:id="echoid-s18921" xml:space="preserve">Concipiamus nunc Tellurem ſphæricam; </s> <s xml:id="echoid-s18922" xml:space="preserve">& </s> <s xml:id="echoid-s18923" xml:space="preserve">in plano Æ-<lb/> <anchor type="note" xlink:label="note-0720-11a" xlink:href="note-0720-11"/> quatoris, cum plano Eclipticæ efficiente angulum 23. </s> <s xml:id="echoid-s18924" xml:space="preserve">gr. </s> <s xml:id="echoid-s18925" xml:space="preserve">29′.</s> <s xml:id="echoid-s18926" xml:space="preserve">, <lb/>annulum dari, in eodem tempore cum Tellure revolventem; <lb/></s> <s xml:id="echoid-s18927" xml:space="preserve">minuatur hic ut Tellurem tangat, & </s> <s xml:id="echoid-s18928" xml:space="preserve">cum hac cohæreat; </s> <s xml:id="echoid-s18929" xml:space="preserve">hiſce <lb/>annulis motus memorati non tolluntur; </s> <s xml:id="echoid-s18930" xml:space="preserve">nam cùm Tellus nul-<lb/>lâ vi in determinato ſitu retineatur, cedit impreſſionibus annuli, <lb/>cujus agitationes tamen minuuntur, ex auctâ materiâ moven-<lb/>dâ, dum vis motrix eadem manet.</s> <s xml:id="echoid-s18931" xml:space="preserve"/> </p> <div xml:id="echoid-div2870" type="float" level="2" n="4"> <note position="left" xlink:label="note-0720-11" xlink:href="note-0720-11a" xml:space="preserve">1381.</note> </div> <p> <s xml:id="echoid-s18932" xml:space="preserve">Caſus hic revera extat, nam Telluris figura eſt ſphærica, an-<lb/>nulo in Æquatore circumdata, quo Tellus ad Æquatorem ma-<lb/>gis elevatur <anchor type="note" xlink:href="" symbol="*"/>, cujus annuli linea Nodorum eſt ſectio planorum <anchor type="note" xlink:label="note-0720-12a" xlink:href="note-0720-12"/> Æquatoris & </s> <s xml:id="echoid-s18933" xml:space="preserve">Eclipticæ. </s> <s xml:id="echoid-s18934" xml:space="preserve">Unde ſequentes deducimus conclu-<lb/>ſiones.</s> <s xml:id="echoid-s18935" xml:space="preserve"/> </p> <div xml:id="echoid-div2871" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0720-12" xlink:href="note-0720-12a" xml:space="preserve">1370.</note> </div> <p> <s xml:id="echoid-s18936" xml:space="preserve">In Æquinoctiis inclinatio Æquatoris eſt omnium minima <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s18937" xml:space="preserve"> <anchor type="note" xlink:label="note-0720-13a" xlink:href="note-0720-13"/> ideòque Axeos inclinatio omnium maxima; </s> <s xml:id="echoid-s18938" xml:space="preserve">nam cum plano <lb/> <anchor type="note" xlink:label="note-0720-14a" xlink:href="note-0720-14"/> Æquatoris angulum rectum efficit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18939" xml:space="preserve">Augetur inclinatio Æ- <anchor type="note" xlink:label="note-0720-15a" xlink:href="note-0720-15"/> <pb o="191" file="0721" n="792" rhead="MATHEMATICA LIB. IV. CAP. XIX."/> quatoris, id eſt minuitur Axeos inclinatio, donec Sol in <lb/> <anchor type="note" xlink:label="note-0721-01a" xlink:href="note-0721-01"/> Solticiis detur, ubi hæc eſt omnium minima, illa omnium <lb/> <anchor type="note" xlink:label="note-0721-02a" xlink:href="note-0721-02"/> maxima <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18940" xml:space="preserve">Idcirco bis in anno minuitnr Telluris Axeos in- <anchor type="note" xlink:label="note-0721-03a" xlink:href="note-0721-03"/> clinatio, bis inſtauratur. </s> <s xml:id="echoid-s18941" xml:space="preserve">Et Sectio plani Æquatoris cum <lb/> <anchor type="note" xlink:label="note-0721-04a" xlink:href="note-0721-04"/> plano Æclipticæ, quæ in Æquinoctiis quieſcit, per reli-<lb/>quum tempus in antecedentiâ movetur<anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s18942" xml:space="preserve"/> </p> <div xml:id="echoid-div2872" type="float" level="2" n="6"> <note position="left" xlink:label="note-0720-13" xlink:href="note-0720-13a" xml:space="preserve">1382.</note> <note position="left" xlink:label="note-0720-14" xlink:href="note-0720-14a" xml:space="preserve">1377.</note> <note symbol="*" position="left" xlink:label="note-0720-15" xlink:href="note-0720-15a" xml:space="preserve">1075.</note> <note position="right" xlink:label="note-0721-01" xlink:href="note-0721-01a" xml:space="preserve">1383.</note> <note symbol="*" position="right" xlink:label="note-0721-02" xlink:href="note-0721-02a" xml:space="preserve">1377.</note> <note position="right" xlink:label="note-0721-03" xlink:href="note-0721-03a" xml:space="preserve">1384.</note> <note position="right" xlink:label="note-0721-04" xlink:href="note-0721-04a" xml:space="preserve">1385.</note> </div> <note symbol="*" position="right" xml:space="preserve">1378.</note> <p> <s xml:id="echoid-s18943" xml:space="preserve">Ad planum orbitæ Lunaris etiam inclinatur planum Æqua-<lb/> <anchor type="note" xlink:label="note-0721-06a" xlink:href="note-0721-06"/> toris; </s> <s xml:id="echoid-s18944" xml:space="preserve">nam exiguum angulum illud cum Plano Eclipticæ eſſi-<lb/>cit <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s18945" xml:space="preserve">ideò eodem modo in annulum agit Luna, quàm Sol; </s> <s xml:id="echoid-s18946" xml:space="preserve">&</s> <s xml:id="echoid-s18947" xml:space="preserve"> <anchor type="note" xlink:label="note-0721-07a" xlink:href="note-0721-07"/> licèt illa minor ſit, quia Sole multo minus diſtat, in annulum <lb/>majorem exerit actionem. </s> <s xml:id="echoid-s18948" xml:space="preserve">Quare etiam ex actione Lunæ, bis <lb/> <anchor type="note" xlink:label="note-0721-08a" xlink:href="note-0721-08"/> in ſingulis hujus revolutionibus mutatur, & </s> <s xml:id="echoid-s18949" xml:space="preserve">bis inſtauratur, <lb/>Axeos Telluris inclinatio ad Planum orbitæ Lunæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18950" xml:space="preserve">ideò- <anchor type="note" xlink:label="note-0721-09a" xlink:href="note-0721-09"/> que ad planum Eclipticæ: </s> <s xml:id="echoid-s18951" xml:space="preserve">& </s> <s xml:id="echoid-s18952" xml:space="preserve">in antecedentiâ fertur Sectio <lb/>Plani Æquatoris cum plano orbitæ <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18953" xml:space="preserve">ex quo motu tranſla- <anchor type="note" xlink:label="note-0721-10a" xlink:href="note-0721-10"/> tio ſectionis illius plani cum plano Eclipticæ neceſſario ſe-<lb/>quitur.</s> <s xml:id="echoid-s18954" xml:space="preserve"/> </p> <div xml:id="echoid-div2873" type="float" level="2" n="7"> <note position="right" xlink:label="note-0721-06" xlink:href="note-0721-06a" xml:space="preserve">1386.</note> <note symbol="*" position="right" xlink:label="note-0721-07" xlink:href="note-0721-07a" xml:space="preserve">969.</note> <note position="right" xlink:label="note-0721-08" xlink:href="note-0721-08a" xml:space="preserve">1387.</note> <note symbol="*" position="right" xlink:label="note-0721-09" xlink:href="note-0721-09a" xml:space="preserve">1384.</note> <note symbol="*" position="right" xlink:label="note-0721-10" xlink:href="note-0721-10a" xml:space="preserve">1385.</note> </div> <p> <s xml:id="echoid-s18955" xml:space="preserve">Mutationes inclinationis Axeosnimium ſunt exiguæ, ut ob-<lb/> <anchor type="note" xlink:label="note-0721-11a" xlink:href="note-0721-11"/> ſerventur: </s> <s xml:id="echoid-s18956" xml:space="preserve">tranſlatio autem lineæ Æquinoctiorum, & </s> <s xml:id="echoid-s18957" xml:space="preserve">mo-<lb/> <anchor type="note" xlink:label="note-0721-12a" xlink:href="note-0721-12"/> tus Axeos, qui ex hac ſequitur, cùm ſemper verſus eandem <lb/>partem dirigantur, tandem ſenſibiles ſunt; </s> <s xml:id="echoid-s18958" xml:space="preserve">& </s> <s xml:id="echoid-s18959" xml:space="preserve">ex his Phœno-<lb/>mena antea explicata <anchor type="note" xlink:href="" symbol="*"/> ſequuntur.</s> <s xml:id="echoid-s18960" xml:space="preserve"/> </p> <div xml:id="echoid-div2874" type="float" level="2" n="8"> <note position="right" xlink:label="note-0721-11" xlink:href="note-0721-11a" xml:space="preserve">1388.</note> <note position="right" xlink:label="note-0721-12" xlink:href="note-0721-12a" xml:space="preserve">1389.</note> </div> <note symbol="*" position="right" xml:space="preserve">1185. 1186.</note> </div> <div xml:id="echoid-div2876" type="section" level="1" n="679"> <head xml:id="echoid-head883" xml:space="preserve">CAPUT XIX.</head> <head xml:id="echoid-head884" style="it" xml:space="preserve">De Æſtu Maris.</head> <p> <s xml:id="echoid-s18961" xml:space="preserve">Ut Æſtum Maris ex principiis traditis explicemus, conſi-<lb/>derandum eſt, Tellurem, ut & </s> <s xml:id="echoid-s18962" xml:space="preserve">etiam omnia corpora <lb/>in hujus viciniis, in Lunam gravitare <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18963" xml:space="preserve">ideò particulæ aqueæ, <anchor type="note" xlink:label="note-0721-14a" xlink:href="note-0721-14"/> in Telluris ſuperficie, quæ verſus centrum Telluris tendunt, <lb/>(hìc enim negligimus conſiderationem n. </s> <s xml:id="echoid-s18964" xml:space="preserve">1371.) </s> <s xml:id="echoid-s18965" xml:space="preserve">cum hac ver-<lb/>ſus Lunam feruntur. </s> <s xml:id="echoid-s18966" xml:space="preserve">Cùm etiam ſolida Telluris maſſa ad Lu-<lb/>nam feratur, juxta leges, quæ locum haberent, ſi omnis mate-<lb/> <anchor type="note" xlink:label="note-0721-15a" xlink:href="note-0721-15"/> ria ex quâ conſtat in centro coacta daretur<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18967" xml:space="preserve">poterunt demon- <anchor type="note" xlink:label="note-0721-16a" xlink:href="note-0721-16"/> ſtrata, in capite 16. </s> <s xml:id="echoid-s18968" xml:space="preserve">de actione Solis in Lunam, verſus Tel-<lb/>lurem cadentem, dum cum hac Solem petit, applicari ad <lb/>actionem Lunæ in particulas aqueas in Telluris ſuperfi-<lb/>cie, cum Telluris maſſa non cohærentes, ſed verſus hujus <pb o="192" file="0722" n="793" rhead="PHYSICES ELEMENTA"/> centrum tendentes, & </s> <s xml:id="echoid-s18969" xml:space="preserve">cum hujus maſſà, etiam verſus Lu-<lb/>nam continuò cadentes; </s> <s xml:id="echoid-s18970" xml:space="preserve">quâ vi, ut vidimus <anchor type="note" xlink:href="" symbol="*"/>, Tellus reti- <anchor type="note" xlink:label="note-0722-01a" xlink:href="note-0722-01"/> netur in orbitâ, circa commune gravitatis centrum hujus & </s> <s xml:id="echoid-s18971" xml:space="preserve"><lb/>Lunæ.</s> <s xml:id="echoid-s18972" xml:space="preserve"/> </p> <div xml:id="echoid-div2876" type="float" level="2" n="1"> <note symbol="*" position="right" xlink:label="note-0721-14" xlink:href="note-0721-14a" xml:space="preserve">1206.</note> <note symbol="*" position="right" xlink:label="note-0721-15" xlink:href="note-0721-15a" xml:space="preserve">1126.</note> <note position="right" xlink:label="note-0721-16" xlink:href="note-0721-16a" xml:space="preserve">1390.</note> <note symbol="*" position="left" xlink:label="note-0722-01" xlink:href="note-0722-01a" xml:space="preserve">1280.</note> </div> <p> <s xml:id="echoid-s18973" xml:space="preserve">Sit S Luna; </s> <s xml:id="echoid-s18974" xml:space="preserve">ALBl ſuperficies Telluris, cujus maſſa ad <lb/> <anchor type="note" xlink:label="note-0722-02a" xlink:href="note-0722-02"/> Lunam tendit, quaſi tota in T eſſet coacta; </s> <s xml:id="echoid-s18975" xml:space="preserve">ex actione Lu-<lb/> <anchor type="note" xlink:label="note-0722-03a" xlink:href="note-0722-03"/> <anchor type="note" xlink:label="note-0722-04a" xlink:href="note-0722-04"/> næ particulæ aqueæ A & </s> <s xml:id="echoid-s18976" xml:space="preserve">B verſus T majorem acquirunt gra-<lb/>vitatem <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s18977" xml:space="preserve">contra particulæ in L, l, ex gravitate amit- <anchor type="note" xlink:label="note-0722-05a" xlink:href="note-0722-05"/> tunt <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s18978" xml:space="preserve">Unde deducimus, ſi tota Tellus aquâ obtegatur, <anchor type="note" xlink:label="note-0722-06a" xlink:href="note-0722-06"/> æquilibrium non dari, niſi magis elevata ſit hæc aqua, in <lb/>punctis L & </s> <s xml:id="echoid-s18979" xml:space="preserve">l, quàm in toto circulo ab his punctis 90. </s> <s xml:id="echoid-s18980" xml:space="preserve">gr. <lb/></s> <s xml:id="echoid-s18981" xml:space="preserve">diſtanti; </s> <s xml:id="echoid-s18982" xml:space="preserve">& </s> <s xml:id="echoid-s18983" xml:space="preserve">ideò per puncta A & </s> <s xml:id="echoid-s18984" xml:space="preserve">B tranſeunti. </s> <s xml:id="echoid-s18985" xml:space="preserve">Idcirco, a-<lb/>ctione Lunæ, aqua adipiſcitur figuram ſphæroidis, forma-<lb/> <anchor type="note" xlink:label="note-0722-07a" xlink:href="note-0722-07"/> tam ex revolutione ovalis circa Axem majorem, qui conti-<lb/>nuatus per Lunam tranſit.</s> <s xml:id="echoid-s18986" xml:space="preserve"/> </p> <div xml:id="echoid-div2877" type="float" level="2" n="2"> <note position="left" xlink:label="note-0722-02" xlink:href="note-0722-02a" xml:space="preserve">1391.</note> <note position="left" xlink:label="note-0722-03" xlink:href="note-0722-03a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0722-04" xlink:href="note-0722-04a" xml:space="preserve">fig. 1.</note> <note symbol="*" position="left" xlink:label="note-0722-05" xlink:href="note-0722-05a" xml:space="preserve">1287.</note> <note symbol="*" position="left" xlink:label="note-0722-06" xlink:href="note-0722-06a" xml:space="preserve">1296.</note> <note position="left" xlink:label="note-0722-07" xlink:href="note-0722-07a" xml:space="preserve">1392.</note> </div> <p> <s xml:id="echoid-s18987" xml:space="preserve">Ponamus Lunam in Æquatore; </s> <s xml:id="echoid-s18988" xml:space="preserve">omnes Sectiones Telluris <lb/>parallelæ ad Æquatorem, cùm etiam ſphæroidis axi parallelæ <lb/>ſint <anchor type="note" xlink:href="" symbol="*"/>, ſunt ovales, quarum axes majores per Lunæ Meridia- <anchor type="note" xlink:label="note-0722-08a" xlink:href="note-0722-08"/> num tranſeunt; </s> <s xml:id="echoid-s18989" xml:space="preserve">unde ſequitur, Tellure quieſcente, in circulo <lb/> <anchor type="note" xlink:label="note-0722-09a" xlink:href="note-0722-09"/> quocunque latitudinis, aquam magis elevari in Meridia-<lb/>no in quo Luna datur, & </s> <s xml:id="echoid-s18990" xml:space="preserve">in Meridiano oppoſito, quàm in <lb/>Locis intermediis.</s> <s xml:id="echoid-s18991" xml:space="preserve"/> </p> <div xml:id="echoid-div2878" type="float" level="2" n="3"> <note symbol="*" position="left" xlink:label="note-0722-08" xlink:href="note-0722-08a" xml:space="preserve">1392.</note> <note position="left" xlink:label="note-0722-09" xlink:href="note-0722-09a" xml:space="preserve">1393.</note> </div> </div> <div xml:id="echoid-div2880" type="section" level="1" n="680"> <head xml:id="echoid-head885" xml:space="preserve"><emph style="sc">Definitio</emph>.</head> <p> <s xml:id="echoid-s18992" xml:space="preserve">DiesLunaris, eſt tempus lapſum interreceſſum Lunæ à Me-<lb/> <anchor type="note" xlink:label="note-0722-10a" xlink:href="note-0722-10"/> ridiano & </s> <s xml:id="echoid-s18993" xml:space="preserve">acceſſum ſequentem ad eundem. </s> <s xml:id="echoid-s18994" xml:space="preserve">Dies hæc in vi-<lb/>ginti quatuor horas Lunares dividitur. </s> <s xml:id="echoid-s18995" xml:space="preserve">Superat diem natura-<lb/>lem 50. </s> <s xml:id="echoid-s18996" xml:space="preserve">minutis.</s> <s xml:id="echoid-s18997" xml:space="preserve"/> </p> <div xml:id="echoid-div2880" type="float" level="2" n="1"> <note position="left" xlink:label="note-0722-10" xlink:href="note-0722-10a" xml:space="preserve">1394.</note> </div> <p> <s xml:id="echoid-s18998" xml:space="preserve">Ex motu Telluris circa axem, ſingulis diebus Lunaribus, loca <lb/>ſingula per Meridianum Lunæ & </s> <s xml:id="echoid-s18999" xml:space="preserve">Meridianum oppoſirum tran-<lb/>ſeunt, id eſt bis ibi tranſeunt, ubi aquâ ex actione Lunæ eleva-<lb/> <anchor type="note" xlink:label="note-0722-11a" xlink:href="note-0722-11"/> tur, & </s> <s xml:id="echoid-s19000" xml:space="preserve">bis ubi ex eâdem actione deprimitur <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19001" xml:space="preserve">& </s> <s xml:id="echoid-s19002" xml:space="preserve">ſic in die lu- <anchor type="note" xlink:label="note-0722-12a" xlink:href="note-0722-12"/> nari Mare bis elevatur, bis deprimitur, in loco quocunque.</s> <s xml:id="echoid-s19003" xml:space="preserve"/> </p> <div xml:id="echoid-div2881" type="float" level="2" n="2"> <note position="left" xlink:label="note-0722-11" xlink:href="note-0722-11a" xml:space="preserve">1395.</note> <note symbol="*" position="left" xlink:label="note-0722-12" xlink:href="note-0722-12a" xml:space="preserve">1393.</note> </div> <p> <s xml:id="echoid-s19004" xml:space="preserve">Ex motu Telluris circa axem, continuò aqua elevata à Meri-<lb/> <anchor type="note" xlink:label="note-0722-13a" xlink:href="note-0722-13"/> diano Lunæ recedit; </s> <s xml:id="echoid-s19005" xml:space="preserve">actione tamen Lunæ, Sphæroidis axis <lb/>per Lunam tranſit<anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19006" xml:space="preserve">ideò agitatur continuo aqua, ut eleva- <anchor type="note" xlink:label="note-0722-14a" xlink:href="note-0722-14"/> tio, ex motu Telluris, remota, infra Lunam inſtauretur. </s> <s xml:id="echoid-s19007" xml:space="preserve">Ideò <lb/> <anchor type="note" xlink:label="note-0722-15a" xlink:href="note-0722-15"/> <anchor type="note" xlink:label="note-0722-16a" xlink:href="note-0722-16"/> ab A & </s> <s xml:id="echoid-s19008" xml:space="preserve">B continuo verſus L & </s> <s xml:id="echoid-s19009" xml:space="preserve">l ſluit aqua. </s> <s xml:id="echoid-s19010" xml:space="preserve">dum ex motu <pb o="193" file="0723" n="794" rhead="MATHEMATICA LIB. IV. CAP. XIX."/> Telluris elevatio ab L verſus B & </s> <s xml:id="echoid-s19011" xml:space="preserve">ab l verſus A fertur; </s> <s xml:id="echoid-s19012" xml:space="preserve">id eſt, inter <lb/>L & </s> <s xml:id="echoid-s19013" xml:space="preserve">B, ut & </s> <s xml:id="echoid-s19014" xml:space="preserve">inter l & </s> <s xml:id="echoid-s19015" xml:space="preserve">A, dantur duo motus contrarii, quibus <lb/>aqua accumulatur; </s> <s xml:id="echoid-s19016" xml:space="preserve">ita ut elevationes maximæ inter hæc pun-<lb/>cta, ad latus Lunæ & </s> <s xml:id="echoid-s19017" xml:space="preserve">puncti oppoſiti, dentur. </s> <s xml:id="echoid-s19018" xml:space="preserve">Id eſt, in locis <lb/>quibuſcunque aqua maximè eſt elevata, duabus aut tribus <lb/> <anchor type="note" xlink:label="note-0723-01a" xlink:href="note-0723-01"/> horis poſtquam Luna per Meridianum loci, aut Meridia-<lb/>num oppoſitum, tranſivit.</s> <s xml:id="echoid-s19019" xml:space="preserve"/> </p> <div xml:id="echoid-div2882" type="float" level="2" n="3"> <note position="left" xlink:label="note-0722-13" xlink:href="note-0722-13a" xml:space="preserve">1396.</note> <note symbol="*" position="left" xlink:label="note-0722-14" xlink:href="note-0722-14a" xml:space="preserve">1392.</note> <note position="left" xlink:label="note-0722-15" xlink:href="note-0722-15a" xml:space="preserve"><emph style="sc">TAB. XXV</emph>.</note> <note position="left" xlink:label="note-0722-16" xlink:href="note-0722-16a" xml:space="preserve">Fig. 6.</note> <note position="right" xlink:label="note-0723-01" xlink:href="note-0723-01a" xml:space="preserve">1397.</note> </div> <p style="it"> <s xml:id="echoid-s19020" xml:space="preserve">Elevatio ad partem Lunæ paululum excedit oppoſitam <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s19021" xml:space="preserve"> <anchor type="note" xlink:label="note-0723-02a" xlink:href="note-0723-02"/> Minuitur aſcenſus aquarum acceſſu ad Polum, in quo nulla <lb/> <anchor type="note" xlink:label="note-0723-03a" xlink:href="note-0723-03"/> aquarum agitatio datur.</s> <s xml:id="echoid-s19022" xml:space="preserve"/> </p> <div xml:id="echoid-div2883" type="float" level="2" n="4"> <note position="right" xlink:label="note-0723-02" xlink:href="note-0723-02a" xml:space="preserve">1398.</note> <note symbol="*" position="right" xlink:label="note-0723-03" xlink:href="note-0723-03a" xml:space="preserve">1390. 1295.</note> </div> <note position="right" xml:space="preserve">1399.</note> <p> <s xml:id="echoid-s19023" xml:space="preserve">Quæ de Lunâ demonſtrata ſunt, ad Solem applicari poſſunt; <lb/></s> <s xml:id="echoid-s19024" xml:space="preserve">ideò, ex actione Solis, ſingulis diebus naturalibus, bis e-<lb/> <anchor type="note" xlink:label="note-0723-05a" xlink:href="note-0723-05"/> levatur Mare, bis deprimitur <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19025" xml:space="preserve">Agitatio hæc multò minor <anchor type="note" xlink:label="note-0723-06a" xlink:href="note-0723-06"/> eſt, propter Solis immenſam diſtantiam, quàm quæ à Lunâ <lb/> <anchor type="note" xlink:label="note-0723-07a" xlink:href="note-0723-07"/> pendet; </s> <s xml:id="echoid-s19026" xml:space="preserve">iiſdem tamen legibus ſubjicitur. <lb/></s> <s xml:id="echoid-s19027" xml:space="preserve"> <anchor type="note" xlink:label="note-0723-08a" xlink:href="note-0723-08"/> </s> </p> <div xml:id="echoid-div2884" type="float" level="2" n="5"> <note position="right" xlink:label="note-0723-05" xlink:href="note-0723-05a" xml:space="preserve">1400.</note> <note position="right" xlink:label="note-0723-06" xlink:href="note-0723-06a" xml:space="preserve">1401.</note> <note symbol="*" position="right" xlink:label="note-0723-07" xlink:href="note-0723-07a" xml:space="preserve">1395.</note> <note position="right" xlink:label="note-0723-08" xlink:href="note-0723-08a" xml:space="preserve">1402.</note> </div> <p> <s xml:id="echoid-s19028" xml:space="preserve">Non diſtinguuntur motus ab actione Lunæ, & </s> <s xml:id="echoid-s19029" xml:space="preserve">Solis, pen-<lb/> <anchor type="note" xlink:label="note-0723-09a" xlink:href="note-0723-09"/> dentes, ſed conſunduntur, & </s> <s xml:id="echoid-s19030" xml:space="preserve">ex hujus actione tantùm muta-<lb/>tur Maris ſluxus lunaris: </s> <s xml:id="echoid-s19031" xml:space="preserve">quæ mutatio ſingulis diebus va-<lb/> <anchor type="note" xlink:label="note-0723-10a" xlink:href="note-0723-10"/> riat, propter inæqualitatem inter diem Naturalem & </s> <s xml:id="echoid-s19032" xml:space="preserve">diem Lu-<lb/>narem <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s19033" xml:space="preserve"/> </p> <div xml:id="echoid-div2885" type="float" level="2" n="6"> <note position="right" xlink:label="note-0723-09" xlink:href="note-0723-09a" xml:space="preserve">1403.</note> <note position="right" xlink:label="note-0723-10" xlink:href="note-0723-10a" xml:space="preserve">1404.</note> </div> <note symbol="*" position="right" xml:space="preserve">1394.</note> <p> <s xml:id="echoid-s19034" xml:space="preserve">In Syzygiis elevationes, ex amborum Luminarium actioni-<lb/> <anchor type="note" xlink:label="note-0723-12a" xlink:href="note-0723-12"/> bus, concurrunt, & </s> <s xml:id="echoid-s19035" xml:space="preserve">magis elevatur Mare; </s> <s xml:id="echoid-s19036" xml:space="preserve">minus adſcendit <lb/>Mare in Quadr aturis; </s> <s xml:id="echoid-s19037" xml:space="preserve">nam ubi aqua Lunæ actione elevatur, <lb/>deprimitur ex actione Solis, & </s> <s xml:id="echoid-s19038" xml:space="preserve">vice versâ. </s> <s xml:id="echoid-s19039" xml:space="preserve">Idcircó, dum Lu-<lb/> <anchor type="note" xlink:label="note-0723-13a" xlink:href="note-0723-13"/> na à Syzygiâ ad Quadraturam tranſit, elevationes quotidia-<lb/>næ de die in diem minuuntur: </s> <s xml:id="echoid-s19040" xml:space="preserve">augentur contrà in motu à <lb/>Quadraturâ ad Syzygiam. </s> <s xml:id="echoid-s19041" xml:space="preserve">In Novilunio etiam, cæteris pari-<lb/> <anchor type="note" xlink:label="note-0723-14a" xlink:href="note-0723-14"/> bus, elevationes majores ſunt, & </s> <s xml:id="echoid-s19042" xml:space="preserve">quæ in eodem die ſeſe <lb/>mutuò ſequuntur, magis differunt, quàm in Plenilunio <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s19043" xml:space="preserve"/> </p> <div xml:id="echoid-div2886" type="float" level="2" n="7"> <note position="right" xlink:label="note-0723-12" xlink:href="note-0723-12a" xml:space="preserve">1405.</note> <note position="right" xlink:label="note-0723-13" xlink:href="note-0723-13a" xml:space="preserve">1406.</note> <note position="right" xlink:label="note-0723-14" xlink:href="note-0723-14a" xml:space="preserve">1407.</note> </div> <note symbol="*" position="right" xml:space="preserve">1398. 1402.</note> <p> <s xml:id="echoid-s19044" xml:space="preserve">Elevationes maximæ & </s> <s xml:id="echoid-s19045" xml:space="preserve">minimæ non obſervantur, niſiſe-<lb/> <anchor type="note" xlink:label="note-0723-16a" xlink:href="note-0723-16"/> cundâ, aut tertiâ, die poſt Novilunium, aut Plenilunium, <lb/>quia motus acquiſitus non ſtatim ex attritu, & </s> <s xml:id="echoid-s19046" xml:space="preserve">aliis cauſis, de-<lb/>ſtruitur, quo motu acquiſito adſcenſus aquarum augetur, licèt <lb/>minuatur actio quâ Mare elevatur: </s> <s xml:id="echoid-s19047" xml:space="preserve">ſimile quid circà calorem <lb/>alibi <anchor type="note" xlink:href="" symbol="*"/> demonſtravimus.</s> <s xml:id="echoid-s19048" xml:space="preserve"/> </p> <div xml:id="echoid-div2887" type="float" level="2" n="8"> <note position="right" xlink:label="note-0723-16" xlink:href="note-0723-16a" xml:space="preserve">1408.</note> </div> <note symbol="*" position="right" xml:space="preserve">1174.</note> <p> <s xml:id="echoid-s19049" xml:space="preserve">Si nunc Luminaria ex Æquatoris plano recedentia conſidere-<lb/>mus, videbimus agitationem minui, & </s> <s xml:id="echoid-s19050" xml:space="preserve">minorem dari, prò <lb/> <anchor type="note" xlink:label="note-0723-18a" xlink:href="note-0723-18"/> <pb o="(194)" file="0724" n="795" rhead="PHYSICES ELEMENTA"/> majori luminarium declinatione. </s> <s xml:id="echoid-s19051" xml:space="preserve">Quod clarè patet ſi hæc in <lb/>Polis concipiamus; </s> <s xml:id="echoid-s19052" xml:space="preserve">tunc enim Axis figuræ ſphæroidis cum Axe <lb/>Telluris coincidit; </s> <s xml:id="echoid-s19053" xml:space="preserve">& </s> <s xml:id="echoid-s19054" xml:space="preserve">omnes ſectiones ad Æquatorem paral-<lb/>lelæ ad Axem ſphæroidis ſunt perpendiculares; </s> <s xml:id="echoid-s19055" xml:space="preserve">ideòque cir-<lb/>culares. </s> <s xml:id="echoid-s19056" xml:space="preserve">Ita ut, aqua, in ſingulis circulis latitudinis, ubique <lb/>eandem habeat elevationem; </s> <s xml:id="echoid-s19057" xml:space="preserve">& </s> <s xml:id="echoid-s19058" xml:space="preserve">ſic in motu Telluris non mutatur <lb/>altitudo Maris in locis peculiaribus. </s> <s xml:id="echoid-s19059" xml:space="preserve">Si ex Polo recedant Lumi-<lb/>naria agitationem continuò magis ac magis augeri, facile vi-<lb/>demus, donec omnium ſit maxima, revolvente ſphæroide cir-<lb/>ca lineam ad Axem perpendicularem, poſitâ ſphæroidis axe in <lb/>plano Æquatoris.</s> <s xml:id="echoid-s19060" xml:space="preserve"/> </p> <div xml:id="echoid-div2888" type="float" level="2" n="9"> <note position="right" xlink:label="note-0723-18" xlink:href="note-0723-18a" xml:space="preserve">1409.</note> </div> <p> <s xml:id="echoid-s19061" xml:space="preserve">Hinc liquet, quare in Syzygiis, prope Æquinoctia, Æ-<lb/> <anchor type="note" xlink:label="note-0724-01a" xlink:href="note-0724-01"/> ſtus omnium maximi obſervantur, ambobus Luminaribus in <lb/>Æquatore aut prope hunc verſantibus.</s> <s xml:id="echoid-s19062" xml:space="preserve"/> </p> <div xml:id="echoid-div2889" type="float" level="2" n="10"> <note position="left" xlink:label="note-0724-01" xlink:href="note-0724-01a" xml:space="preserve">1410.</note> </div> <p> <s xml:id="echoid-s19063" xml:space="preserve">Actiones Lunæ & </s> <s xml:id="echoid-s19064" xml:space="preserve">Solis majores ſunt, quo minus hæc cor-<lb/> <anchor type="note" xlink:label="note-0724-02a" xlink:href="note-0724-02"/> pora à Tellure diſtant <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19065" xml:space="preserve">cùm autem minor Solis diſtantia <anchor type="note" xlink:label="note-0724-03a" xlink:href="note-0724-03"/> detur, hoc verſante in ſignis auſtralibus, ſæpe ambo Æſtus ma-<lb/>ximi Æquinoctiales in illo ſitu Solis obſervantur; </s> <s xml:id="echoid-s19066" xml:space="preserve">id eſt ante <lb/>Æquinoctium Vernum & </s> <s xml:id="echoid-s19067" xml:space="preserve">poſt Autumnale; </s> <s xml:id="echoid-s19068" xml:space="preserve">quod tamen non <lb/>ſingulis annis obtinet; </s> <s xml:id="echoid-s19069" xml:space="preserve">quia ex ſitu orbitæ Lunaris, & </s> <s xml:id="echoid-s19070" xml:space="preserve">diſtan-<lb/>tiâ Syzygiæ ab Æquinoctio variatio dari poteſt.</s> <s xml:id="echoid-s19071" xml:space="preserve"/> </p> <div xml:id="echoid-div2890" type="float" level="2" n="11"> <note position="left" xlink:label="note-0724-02" xlink:href="note-0724-02a" xml:space="preserve">1411.</note> <note symbol="*" position="left" xlink:label="note-0724-03" xlink:href="note-0724-03a" xml:space="preserve">1354. 1390.</note> </div> <p> <s xml:id="echoid-s19072" xml:space="preserve">In Locis ab Æquatore diſtantibus, receſſu Luminarium ab <lb/> <anchor type="note" xlink:label="note-0724-04a" xlink:href="note-0724-04"/> Æquatore, inæquales fiunt ejuſdem diei elevationes. </s> <s xml:id="echoid-s19073" xml:space="preserve">Sit <lb/> <anchor type="note" xlink:label="note-0724-05a" xlink:href="note-0724-05"/> <anchor type="note" xlink:label="note-0724-06a" xlink:href="note-0724-06"/> PP Telluris Axis; </s> <s xml:id="echoid-s19074" xml:space="preserve">EE Æquator; </s> <s xml:id="echoid-s19075" xml:space="preserve">L l circulus latitudinis; <lb/></s> <s xml:id="echoid-s19076" xml:space="preserve">AB axis ſphæroidis figuræ, quam format aqua: </s> <s xml:id="echoid-s19077" xml:space="preserve">quando locus <lb/>in circulo Ll, datur in L aut l, datur in eodem Meridiano cum <lb/>axe ſphæroidis & </s> <s xml:id="echoid-s19078" xml:space="preserve">aqua eſt maximè elevata, in utroque caſu; </s> <s xml:id="echoid-s19079" xml:space="preserve">in L <lb/>tamen magis quàm in l; </s> <s xml:id="echoid-s19080" xml:space="preserve">nam CL ſuperat Cl, quæ lineæ altitudines <lb/>aquarum, id eſt diſtantiæ à centro, menſurant: </s> <s xml:id="echoid-s19081" xml:space="preserve">æquales hæ <lb/>forent ſi AL & </s> <s xml:id="echoid-s19082" xml:space="preserve">B l diſtantiæ ab axe ſphæroidis forent æquales, <lb/>minor autem eſt Cl, quia Bl ſuperat AL, quod ex inclina-<lb/>tione Axeos ſphæroidis ad Æquatorem oritur.</s> <s xml:id="echoid-s19083" xml:space="preserve"/> </p> <div xml:id="echoid-div2891" type="float" level="2" n="12"> <note position="left" xlink:label="note-0724-04" xlink:href="note-0724-04a" xml:space="preserve">1412.</note> <note position="left" xlink:label="note-0724-05" xlink:href="note-0724-05a" xml:space="preserve">TAB. XXV.</note> <note position="left" xlink:label="note-0724-06" xlink:href="note-0724-06a" xml:space="preserve">fig. 8.</note> </div> <p style="it"> <s xml:id="echoid-s19084" xml:space="preserve">Quamdiù Luna ad eandem partem Æquatoris cum loco <lb/> <anchor type="note" xlink:label="note-0724-07a" xlink:href="note-0724-07"/> datur, id eſt, ad partem lineæ CA continuatæ, aquæ eleva-<lb/>tio maxima ſingulis diebus obſervatur, poſt tranſitum Lunæ <lb/>per Meridianum Loci, maxima enim datur elevatio, ubi locus <lb/>pervenit ad L; </s> <s xml:id="echoid-s19085" xml:space="preserve">ſi autem Æquator ſeparet Lunam & </s> <s xml:id="echoid-s19086" xml:space="preserve">locum, <lb/> <anchor type="note" xlink:label="note-0724-08a" xlink:href="note-0724-08"/> <pb o="(195)" file="0725" n="796" rhead="MATHEMATICA LIB. IV. CAP. XIX."/> de quo agitur, id eſt ſi detur illa ad partem lineæ CB conti-<lb/>nuatæ, aqua iterum in L, ad maximam pertingit altitudinem, <lb/>&</s> <s xml:id="echoid-s19087" xml:space="preserve">, ſingulis diebus, maxima Maris datur elevatio, poſt <lb/>tranſitum Lunæ per Meridianum oppoſitum.</s> <s xml:id="echoid-s19088" xml:space="preserve"/> </p> <div xml:id="echoid-div2892" type="float" level="2" n="13"> <note position="left" xlink:label="note-0724-07" xlink:href="note-0724-07a" xml:space="preserve">1413.</note> <note position="left" xlink:label="note-0724-08" xlink:href="note-0724-08a" xml:space="preserve">1414.</note> </div> <p> <s xml:id="echoid-s19089" xml:space="preserve">Omnia quæ huc uſque fuere expoſita, exactiſſimè obtine-<lb/>rent, ſi tota Telluris ſuperficies Mare obtegeretur; </s> <s xml:id="echoid-s19090" xml:space="preserve">cùm autem <lb/>non ubique Mare detur, mutationes inde oriuntur, non qui-<lb/>dem in Mare aperto; </s> <s xml:id="echoid-s19091" xml:space="preserve">quia ſatis extenditur Oceanus ut memo-<lb/>ratis motibus ſubjiciatur. </s> <s xml:id="echoid-s19092" xml:space="preserve">Sed ſitus littorum, freta, multa-<lb/> <anchor type="note" xlink:label="note-0725-01a" xlink:href="note-0725-01"/> que alia, à peculiari locorum ſitu pendentia, generales regulas <lb/>turbant. </s> <s xml:id="echoid-s19093" xml:space="preserve">Generalioribus tamen obſervationibus conſtat, Æſtum <lb/>leges explicatas ſequi. </s> <s xml:id="echoid-s19094" xml:space="preserve">Supereſt, ut ipſas vires quibus Sol & </s> <s xml:id="echoid-s19095" xml:space="preserve">Lu-<lb/>na Mare agitant determinemus, ut pateat has valere ad me-<lb/>moratos edendos effectus, & </s> <s xml:id="echoid-s19096" xml:space="preserve">illorum corporum actiones in <lb/>pendula & </s> <s xml:id="echoid-s19097" xml:space="preserve">cætera corpora inſenſibiles eſſe.</s> <s xml:id="echoid-s19098" xml:space="preserve"/> </p> <div xml:id="echoid-div2893" type="float" level="2" n="14"> <note position="right" xlink:label="note-0725-01" xlink:href="note-0725-01a" xml:space="preserve">1415.</note> </div> <p> <s xml:id="echoid-s19099" xml:space="preserve">Augmentum gravitatis Lunæ in Quadraturis, ex actione <lb/> <anchor type="note" xlink:label="note-0725-02a" xlink:href="note-0725-02"/> Solis, eſt ad ipſam Lunæ gravitatem in Tellurem, ut 1. </s> <s xml:id="echoid-s19100" xml:space="preserve">ad <lb/>178, 73. </s> <s xml:id="echoid-s19101" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> in quâ computatione poſuimus, Lunæ diſtantiam me- <anchor type="note" xlink:label="note-0725-03a" xlink:href="note-0725-03"/> diam à centro Telluris eſſe 60. </s> <s xml:id="echoid-s19102" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s19103" xml:space="preserve">Telluris <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19104" xml:space="preserve">gravitas ergo <anchor type="note" xlink:label="note-0725-04a" xlink:href="note-0725-04"/> Lunæ eſt ad gravitatem in Telluris ſuperficie, ut 1. </s> <s xml:id="echoid-s19105" xml:space="preserve">ad 60 x <lb/> <anchor type="note" xlink:label="note-0725-05a" xlink:href="note-0725-05"/> 60 = 3600 <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19106" xml:space="preserve">Eſt idcirco augmentum memoratum ad gravi- tatem in Telluris ſuperſicie, ut 1. </s> <s xml:id="echoid-s19107" xml:space="preserve">ad 643428.</s> <s xml:id="echoid-s19108" xml:space="preserve">, in quâ com-<lb/>putatione error datur corrigendus.</s> <s xml:id="echoid-s19109" xml:space="preserve"/> </p> <div xml:id="echoid-div2894" type="float" level="2" n="15"> <note position="right" xlink:label="note-0725-02" xlink:href="note-0725-02a" xml:space="preserve">1416.</note> <note symbol="*" position="right" xlink:label="note-0725-03" xlink:href="note-0725-03a" xml:space="preserve">1291.</note> <note symbol="*" position="right" xlink:label="note-0725-04" xlink:href="note-0725-04a" xml:space="preserve">1285.</note> <note symbol="*" position="right" xlink:label="note-0725-05" xlink:href="note-0725-05a" xml:space="preserve">1208.</note> </div> <p> <s xml:id="echoid-s19110" xml:space="preserve">Exacta foret computatio hæc, ſi augmentum, de quo agitur, <lb/>eſſet ad vim, quâ Tellus verſus Solem deſcendit, ut diſtan-<lb/>tia Lunæ 60. </s> <s xml:id="echoid-s19111" xml:space="preserve">ſemid. </s> <s xml:id="echoid-s19112" xml:space="preserve">Telluris ad diſtantiam Telluris à Sole <anchor type="note" xlink:href="" symbol="*"/>;</s> <s xml:id="echoid-s19113" xml:space="preserve"> <anchor type="note" xlink:label="note-0725-06a" xlink:href="note-0725-06"/> ſed eſt ut vera media Lunæ diſtantia, 60 {1/2} ſemid. </s> <s xml:id="echoid-s19114" xml:space="preserve">Telluris, ad <lb/>diſtantiam Telluris à Sole. </s> <s xml:id="echoid-s19115" xml:space="preserve">Quare augmentum ſtatim determi-<lb/>natum parte {1/120} augeri debet, & </s> <s xml:id="echoid-s19116" xml:space="preserve">ſe habebit ad vim gravitatis <lb/>in ſuperficie Telluris; </s> <s xml:id="echoid-s19117" xml:space="preserve">ut 1 {1/120} ad 643428, aut ut 1. </s> <s xml:id="echoid-s19118" xml:space="preserve">ad <lb/>638110,4.</s> <s xml:id="echoid-s19119" xml:space="preserve"/> </p> <div xml:id="echoid-div2895" type="float" level="2" n="16"> <note symbol="*" position="right" xlink:label="note-0725-06" xlink:href="note-0725-06a" xml:space="preserve">1287.</note> </div> <p> <s xml:id="echoid-s19120" xml:space="preserve">Augmentum hoc gravitatis Lunæ in quadraturis ex actione <lb/>Solis, eſt ad augmentum gravitatis aquæ in ſuperficie Telluris, <lb/>in locis à Sole 90. </s> <s xml:id="echoid-s19121" xml:space="preserve">gr. </s> <s xml:id="echoid-s19122" xml:space="preserve">diſtantibus, ex eâdem Solis actione, ut <lb/>60 {1/2} ad 1. </s> <s xml:id="echoid-s19123" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> ideo augmentum hoc gravitatis ad ipſam aquæ <anchor type="note" xlink:label="note-0725-07a" xlink:href="note-0725-07"/> graviratem, ut 1. </s> <s xml:id="echoid-s19124" xml:space="preserve">ad 38605679. </s> <s xml:id="echoid-s19125" xml:space="preserve">Diminutio gravitatis ſub Sole, <lb/>& </s> <s xml:id="echoid-s19126" xml:space="preserve">in loco oppoſito, eſt dupla hujus augmenti <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19127" xml:space="preserve">ideò eſt ad <anchor type="note" xlink:label="note-0725-08a" xlink:href="note-0725-08"/> <pb o="(196)" file="0726" n="797" rhead="PHYSICES ELEMENTA"/> gravitatem, ut 1. </s> <s xml:id="echoid-s19128" xml:space="preserve">ad 19302839, & </s> <s xml:id="echoid-s19129" xml:space="preserve">tota mutatio in gravita-<lb/> <anchor type="note" xlink:label="note-0726-01a" xlink:href="note-0726-01"/> te, ex actione Solis, eſt ad ipſam gravitatem, ut 1. </s> <s xml:id="echoid-s19130" xml:space="preserve">ad <lb/>12868560.</s> <s xml:id="echoid-s19131" xml:space="preserve"/> </p> <div xml:id="echoid-div2896" type="float" level="2" n="17"> <note symbol="*" position="right" xlink:label="note-0725-07" xlink:href="note-0725-07a" xml:space="preserve">1288.</note> <note symbol="*" position="right" xlink:label="note-0725-08" xlink:href="note-0725-08a" xml:space="preserve">1296.</note> <note position="left" xlink:label="note-0726-01" xlink:href="note-0726-01a" xml:space="preserve">1417.</note> </div> <p> <s xml:id="echoid-s19132" xml:space="preserve">Ut actionem Lunæ cum actione Solis comparemus, expe-<lb/> <anchor type="note" xlink:label="note-0726-02a" xlink:href="note-0726-02"/> rimenta ſunt inſtituenda in locis, in quibus, propter angu-<lb/>ſtias, Mare ſenſibiliter elevatur. </s> <s xml:id="echoid-s19133" xml:space="preserve">Prope Briſtoliam tempore <lb/>Autumnali & </s> <s xml:id="echoid-s19134" xml:space="preserve">Verno, in quo agitatio Maris eſt maxima <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0726-03a" xlink:href="note-0726-03"/> adſcendit aqua in Syzygiis, plus minus, pedibus 45.</s> <s xml:id="echoid-s19135" xml:space="preserve">; in Qua-<lb/>draturis pedibus, plus minus, 25.</s> <s xml:id="echoid-s19136" xml:space="preserve">, qui numeri ſunt inter ſe, <lb/>ut 9. </s> <s xml:id="echoid-s19137" xml:space="preserve">ad 4.</s> <s xml:id="echoid-s19138" xml:space="preserve"/> </p> <div xml:id="echoid-div2897" type="float" level="2" n="18"> <note position="left" xlink:label="note-0726-02" xlink:href="note-0726-02a" xml:space="preserve">1418.</note> <note symbol="*" position="left" xlink:label="note-0726-03" xlink:href="note-0726-03a" xml:space="preserve">1410.</note> </div> <p> <s xml:id="echoid-s19139" xml:space="preserve">Facillima foret determinatio virium, quas quærimus, ſi <lb/>elevationes maximæ & </s> <s xml:id="echoid-s19140" xml:space="preserve">minimæ exactè in Syzygiis darentur, <lb/>quod non obtinere antea vidimus <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0726-04a" xlink:href="note-0726-04"/> </s> </p> <div xml:id="echoid-div2898" type="float" level="2" n="19"> <note symbol="*" position="left" xlink:label="note-0726-04" xlink:href="note-0726-04a" xml:space="preserve">1408.</note> </div> <p> <s xml:id="echoid-s19141" xml:space="preserve">Diſtantia autem Lunæ à Syzygiâ, aut à Quadraturâ, non <lb/>ſemper eſt eadem in maximâ aut minimâ elevatione; </s> <s xml:id="echoid-s19142" xml:space="preserve">nam va-<lb/>riat hæc diſtantia, quia Luna nunc magis nunc minus à Me-<lb/>ridiano diſtat, quando per Syzygiam aut Quadraturam tran-<lb/>ſit. </s> <s xml:id="echoid-s19143" xml:space="preserve">Diſtantia media Lunæ à Syzygiâ, aut Quadraturâ, ad <lb/>quam obſervationes memoratæ referri debent eſt circiter 18. <lb/></s> <s xml:id="echoid-s19144" xml:space="preserve">gr. </s> <s xml:id="echoid-s19145" xml:space="preserve">30′; </s> <s xml:id="echoid-s19146" xml:space="preserve">ita ut non tota Solis actio, neque cum Lunæ actione <lb/>conſpiret in Syzygiis, neque contrariè agat in Quadraturis. </s> <s xml:id="echoid-s19147" xml:space="preserve"><lb/>Etiam in tali caſu, ſi in Syzygiâ, ambo luminaria in Æquatore <lb/>fuerint, in memoratâ diſtantiâ à Quadraturâ, declinatio Lu-<lb/>næ eſt plus minus 22. </s> <s xml:id="echoid-s19148" xml:space="preserve">gr. </s> <s xml:id="echoid-s19149" xml:space="preserve">13′; </s> <s xml:id="echoid-s19150" xml:space="preserve">quo minuitur Lunæ vis ad <lb/>Mare movendum <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19151" xml:space="preserve">Ulterius, cæteris paribus, diſtantia <anchor type="note" xlink:label="note-0726-05a" xlink:href="note-0726-05"/> Lunæ à Tellure in Syzygiis minor eſt, quàm in Quadratu-<lb/>ris <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19152" xml:space="preserve">unde etiam actio Lunæ in Quadraturis minuitur <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s19153" xml:space="preserve">ad <anchor type="note" xlink:label="note-0726-06a" xlink:href="note-0726-06"/> <anchor type="note" xlink:label="note-0726-07a" xlink:href="note-0726-07"/> quæ omnia attendendo detegitur, vim mediocrem Solis ad <lb/> <anchor type="note" xlink:label="note-0726-08a" xlink:href="note-0726-08"/> Mare movendum ſe habere ad vim mediocrem Lunæ ad i-<lb/>dem agitandum, ut 1. </s> <s xml:id="echoid-s19154" xml:space="preserve">ad 4,4815. </s> <s xml:id="echoid-s19155" xml:space="preserve">Sed vis Solis eſt ad vim <lb/> <anchor type="note" xlink:label="note-0726-09a" xlink:href="note-0726-09"/> gravitatis, ut 1. </s> <s xml:id="echoid-s19156" xml:space="preserve">ad 12868560. </s> <s xml:id="echoid-s19157" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19158" xml:space="preserve">quare vis Lunæ eſt ad ean- <anchor type="note" xlink:label="note-0726-10a" xlink:href="note-0726-10"/> dem vim gravitatis, ut 1. </s> <s xml:id="echoid-s19159" xml:space="preserve">ad 2871485. </s> <s xml:id="echoid-s19160" xml:space="preserve">Ex quibus ſequitur, <lb/>vires has Lunæ & </s> <s xml:id="echoid-s19161" xml:space="preserve">Solis nimium eſſe exiguas, ut in pendulis & </s> <s xml:id="echoid-s19162" xml:space="preserve"><lb/>aliis experimentis ſint ſenſibiles; </s> <s xml:id="echoid-s19163" xml:space="preserve">has autem ipſas valere ad Ma-<lb/>re agitandum facile probatur.</s> <s xml:id="echoid-s19164" xml:space="preserve"/> </p> <div xml:id="echoid-div2899" type="float" level="2" n="20"> <note symbol="*" position="left" xlink:label="note-0726-05" xlink:href="note-0726-05a" xml:space="preserve">1409.</note> <note symbol="*" position="left" xlink:label="note-0726-06" xlink:href="note-0726-06a" xml:space="preserve">1310. 1311.</note> <note symbol="*" position="left" xlink:label="note-0726-07" xlink:href="note-0726-07a" xml:space="preserve">1411.</note> <note position="left" xlink:label="note-0726-08" xlink:href="note-0726-08a" xml:space="preserve">1419.</note> <note symbol="*" position="left" xlink:label="note-0726-09" xlink:href="note-0726-09a" xml:space="preserve">1417.</note> <note position="left" xlink:label="note-0726-10" xlink:href="note-0726-10a" xml:space="preserve">1420.</note> </div> <p> <s xml:id="echoid-s19165" xml:space="preserve">Diminuendo gravitatem parte {1/289} Mare elevatur ad altitudi-<lb/>nem pedum Rhenolandicorum 88902. </s> <s xml:id="echoid-s19166" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>, perticæ enim ſin- <anchor type="note" xlink:label="note-0726-11a" xlink:href="note-0726-11"/> <pb file="0727" n="798"/> <pb file="0727a" n="799"/> <anchor type="figure" xlink:label="fig-0727a-01a" xlink:href="fig-0727a-01"/> <pb file="0728" n="800"/> <pb o="(197)" file="0729" n="801" rhead="MATHEMATICA LIB. IV. CAP. XX."/> gulæ continent pedes duodecim: </s> <s xml:id="echoid-s19167" xml:space="preserve">unde detegitur <anchor type="note" xlink:href="" symbol="*"/> ope regulæ <anchor type="note" xlink:label="note-0729-01a" xlink:href="note-0729-01"/> proportionum, Solis actionem mutare Maris altitudinem <lb/> <anchor type="note" xlink:label="note-0729-02a" xlink:href="note-0729-02"/> pedibus duobus, & </s> <s xml:id="echoid-s19168" xml:space="preserve">hanc ex Lunæ actione mutari pedibus <lb/> <anchor type="note" xlink:label="note-0729-03a" xlink:href="note-0729-03"/> 8,95 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19169" xml:space="preserve">& </s> <s xml:id="echoid-s19170" xml:space="preserve">ex ambabus actionibus conjunctis agitatio me- <anchor type="note" xlink:label="note-0729-04a" xlink:href="note-0729-04"/> diocris eſt circiter undecim pedum, quod cum obſervationi-<lb/> <anchor type="note" xlink:label="note-0729-05a" xlink:href="note-0729-05"/> bus ſatis congruit; </s> <s xml:id="echoid-s19171" xml:space="preserve">nam in Oceano aperto, pro ut Mare magis <lb/>aut minus patet, elevatur aqua, ad altitudinem ſex, novem, <lb/>duodecim, vel quindecim pedum; </s> <s xml:id="echoid-s19172" xml:space="preserve">in quibus elevationibus etiam <lb/>differentia datur ex profunditate aquarum. </s> <s xml:id="echoid-s19173" xml:space="preserve">Elevationes verò, <lb/>quæ has multum excedunt, locum habent, ubi magnâ vi <lb/> <anchor type="note" xlink:label="note-0729-06a" xlink:href="note-0729-06"/> Mare freta intrat, in quibus impetus non frangitur, niſi <lb/>majori adſcenſu.</s> <s xml:id="echoid-s19174" xml:space="preserve"/> </p> <div xml:id="echoid-div2900" type="float" level="2" n="21"> <note symbol="*" position="left" xlink:label="note-0726-11" xlink:href="note-0726-11a" xml:space="preserve">1368.</note> <figure xlink:label="fig-0727a-01" xlink:href="fig-0727a-01a"> <image file="0727a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0727a-01"/> </figure> <note symbol="*" position="right" xlink:label="note-0729-01" xlink:href="note-0729-01a" xml:space="preserve">1417.</note> <note position="right" xlink:label="note-0729-02" xlink:href="note-0729-02a" xml:space="preserve">1421.</note> <note position="right" xlink:label="note-0729-03" xlink:href="note-0729-03a" xml:space="preserve">1422.</note> <note symbol="*" position="right" xlink:label="note-0729-04" xlink:href="note-0729-04a" xml:space="preserve">1419.</note> <note position="right" xlink:label="note-0729-05" xlink:href="note-0729-05a" xml:space="preserve">1423.</note> <note position="right" xlink:label="note-0729-06" xlink:href="note-0729-06a" xml:space="preserve">1424.</note> </div> </div> <div xml:id="echoid-div2902" type="section" level="1" n="681"> <head xml:id="echoid-head886" xml:space="preserve">CAPUT XX.</head> <head xml:id="echoid-head887" style="it" xml:space="preserve">De Lunæ Denſitate & Figurâ.</head> <p> <s xml:id="echoid-s19175" xml:space="preserve">Vires Solis & </s> <s xml:id="echoid-s19176" xml:space="preserve">Lunæ ad Mare movendum, ſunt inter ſe in <lb/> <anchor type="note" xlink:label="note-0729-07a" xlink:href="note-0729-07"/> ratione compoſitâ, ex ratione quantitatum materiæ in <lb/>his corporibus <anchor type="note" xlink:href="" symbol="*"/>, (ſingulæ enim particulæ agunt) & </s> <s xml:id="echoid-s19177" xml:space="preserve">ratione in:</s> <s xml:id="echoid-s19178" xml:space="preserve"> <anchor type="note" xlink:label="note-0729-08a" xlink:href="note-0729-08"/> versâ cuborum diſtantiarum Solis & </s> <s xml:id="echoid-s19179" xml:space="preserve">Lunæ à Tellure <anchor type="note" xlink:href="" symbol="*"/>, <anchor type="note" xlink:label="note-0729-09a" xlink:href="note-0729-09"/> </s> </p> <div xml:id="echoid-div2902" type="float" level="2" n="1"> <note position="right" xlink:label="note-0729-07" xlink:href="note-0729-07a" xml:space="preserve">1425.</note> <note symbol="*" position="right" xlink:label="note-0729-08" xlink:href="note-0729-08a" xml:space="preserve">1207.</note> <note symbol="*" position="right" xlink:label="note-0729-09" xlink:href="note-0729-09a" xml:space="preserve">1390. 1402.</note> </div> <p> <s xml:id="echoid-s19180" xml:space="preserve">Quantitates materiæ ſunt in ratione compoſitâ, ex ratione <lb/> <anchor type="note" xlink:label="note-0729-10a" xlink:href="note-0729-10"/> voluminum, id eſt cuborum diametrorum, & </s> <s xml:id="echoid-s19181" xml:space="preserve">ratione denſita-<lb/>tum <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19182" xml:space="preserve">quare vires memoratæ ſunt directè ut denſitates &</s> <s xml:id="echoid-s19183" xml:space="preserve"> <anchor type="note" xlink:label="note-0729-11a" xlink:href="note-0729-11"/> cubi diametrorum, & </s> <s xml:id="echoid-s19184" xml:space="preserve">inversè ut cubi diſtantiarum.</s> <s xml:id="echoid-s19185" xml:space="preserve"/> </p> <div xml:id="echoid-div2903" type="float" level="2" n="2"> <note position="right" xlink:label="note-0729-10" xlink:href="note-0729-10a" xml:space="preserve">1354.</note> <note symbol="*" position="right" xlink:label="note-0729-11" xlink:href="note-0729-11a" xml:space="preserve">288. 79.</note> </div> <p> <s xml:id="echoid-s19186" xml:space="preserve">Diametri apparentes corporum, id eſt, anguli ſub quibus <lb/>videntur’, creſcunt ut ipſæ diametri, & </s> <s xml:id="echoid-s19187" xml:space="preserve">minuuntur ut diſtantiæ; <lb/></s> <s xml:id="echoid-s19188" xml:space="preserve">id eſt, ſunt directè ut diametri, & </s> <s xml:id="echoid-s19189" xml:space="preserve">inversè ut diſtantiæ; </s> <s xml:id="echoid-s19190" xml:space="preserve">id-<lb/>circo ratio compoſita ex ratione cuborum diametrorum appa-<lb/>rentium Solis & </s> <s xml:id="echoid-s19191" xml:space="preserve">Lunæ, & </s> <s xml:id="echoid-s19192" xml:space="preserve">ex ratione denſitatum, erit ratio vi-<lb/> <anchor type="note" xlink:label="note-0729-12a" xlink:href="note-0729-12"/> rium, quibus hæc corpora Mare movent. </s> <s xml:id="echoid-s19193" xml:space="preserve">Ideoque horum cor-<lb/>porum denſitates ſunt directè ut vires, quibus Mare movent, <lb/>& </s> <s xml:id="echoid-s19194" xml:space="preserve">inversè ut cubi diametrorum apparentium: </s> <s xml:id="echoid-s19195" xml:space="preserve">& </s> <s xml:id="echoid-s19196" xml:space="preserve">dividendo <lb/>vires per cubos harum diametrorum, datur ratio denſitatum.</s> <s xml:id="echoid-s19197" xml:space="preserve"/> </p> <div xml:id="echoid-div2904" type="float" level="2" n="3"> <note position="right" xlink:label="note-0729-12" xlink:href="note-0729-12a" xml:space="preserve">1426.</note> </div> <p> <s xml:id="echoid-s19198" xml:space="preserve">Vis Solis eſt ad vim Lunæ, ut 1. </s> <s xml:id="echoid-s19199" xml:space="preserve">ad 4,4815, <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19200" xml:space="preserve">media diame- <anchor type="note" xlink:label="note-0729-13a" xlink:href="note-0729-13"/> ter apparens Solis eſt 32′. </s> <s xml:id="echoid-s19201" xml:space="preserve">12″, & </s> <s xml:id="echoid-s19202" xml:space="preserve">media Lunæ diameter ap-<lb/>parens eſt 31′. </s> <s xml:id="echoid-s19203" xml:space="preserve">16 {1/2}″. </s> <s xml:id="echoid-s19204" xml:space="preserve">id eſt, ſunt inter ſe, ut 3864 ad 3753. </s> <s xml:id="echoid-s19205" xml:space="preserve">Eſt <lb/>igitur denſitas Solis ad Lunæ denſitatem, ut 10000 ad 48911.</s> <s xml:id="echoid-s19206" xml:space="preserve">: <lb/> <anchor type="note" xlink:label="note-0729-14a" xlink:href="note-0729-14"/> quæ Lunæ denſitas cum Jovis, Saturni, & </s> <s xml:id="echoid-s19207" xml:space="preserve">Telluris den- <pb o="(198)" file="0730" n="802" rhead="PHYSICES ELEMENTA"/> ſitatibus poteſt conferri <anchor type="note" xlink:href="" symbol="*"/>, eſtque Luna Tellure denſior.</s> <s xml:id="echoid-s19208" xml:space="preserve"> <anchor type="note" xlink:label="note-0730-01a" xlink:href="note-0730-01"/> </s> </p> <div xml:id="echoid-div2905" type="float" level="2" n="4"> <note symbol="*" position="right" xlink:label="note-0729-13" xlink:href="note-0729-13a" xml:space="preserve">1419.</note> <note position="right" xlink:label="note-0729-14" xlink:href="note-0729-14a" xml:space="preserve">1427.</note> <note symbol="*" position="left" xlink:label="note-0730-01" xlink:href="note-0730-01a" xml:space="preserve">1260.</note> </div> <p> <s xml:id="echoid-s19209" xml:space="preserve">Quantitates materiæ in duobus corporibus ſunt inter ſe in ra-<lb/>tione compoſitâ denſitatum & </s> <s xml:id="echoid-s19210" xml:space="preserve">voluminum <anchor type="note" xlink:href="" symbol="*"/>, id eſt, ſi de ſphæris <anchor type="note" xlink:label="note-0730-02a" xlink:href="note-0730-02"/> agatur, in ratione compoſitâ denſitatum & </s> <s xml:id="echoid-s19211" xml:space="preserve">cuborum diametrorum.</s> <s xml:id="echoid-s19212" xml:space="preserve"/> </p> <div xml:id="echoid-div2906" type="float" level="2" n="5"> <note symbol="*" position="left" xlink:label="note-0730-02" xlink:href="note-0730-02a" xml:space="preserve">288. 79.</note> </div> <p> <s xml:id="echoid-s19213" xml:space="preserve">Lunæ & </s> <s xml:id="echoid-s19214" xml:space="preserve">Telluris denſitates ſunt inter ſe, ut 48911. </s> <s xml:id="echoid-s19215" xml:space="preserve">ad <lb/> <anchor type="note" xlink:label="note-0730-03a" xlink:href="note-0730-03"/> 39214. </s> <s xml:id="echoid-s19216" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19217" xml:space="preserve">diametri ut 11. </s> <s xml:id="echoid-s19218" xml:space="preserve">ad 40,2. </s> <s xml:id="echoid-s19219" xml:space="preserve">ideò quantitates materiæ <anchor type="note" xlink:label="note-0730-04a" xlink:href="note-0730-04"/> in his corporibus, ut 1. </s> <s xml:id="echoid-s19220" xml:space="preserve">ad 39,13. </s> <s xml:id="echoid-s19221" xml:space="preserve">Licèt denſitates detegan-<lb/>tur, poſitis corporibus homogeneis, quantitates materiæ re-<lb/>ctè definiuntur, quamvis corpora homogenea non ſint; </s> <s xml:id="echoid-s19222" xml:space="preserve">nam <lb/>illam determinamus denſitatem, quam corpus haberet, ſimateria, <lb/>ex qua corpus reverâ conſtat, per hoc æqualiter diſpergeretur.</s> <s xml:id="echoid-s19223" xml:space="preserve"/> </p> <div xml:id="echoid-div2907" type="float" level="2" n="6"> <note position="left" xlink:label="note-0730-03" xlink:href="note-0730-03a" xml:space="preserve">1428.</note> <note symbol="*" position="left" xlink:label="note-0730-04" xlink:href="note-0730-04a" xml:space="preserve">1427. 1260.</note> </div> <p> <s xml:id="echoid-s19224" xml:space="preserve">Gravitates in ſuperficiebus Telluris & </s> <s xml:id="echoid-s19225" xml:space="preserve">Lunæ determi-<lb/> <anchor type="note" xlink:label="note-0730-05a" xlink:href="note-0730-05"/> nantur, multiplicando denſitates per diametros <anchor type="note" xlink:href="" symbol="*"/> id eſt ſunt in- <anchor type="note" xlink:label="note-0730-06a" xlink:href="note-0730-06"/> ter ſe, ut 2,93. </s> <s xml:id="echoid-s19226" xml:space="preserve">ad 1.</s> <s xml:id="echoid-s19227" xml:space="preserve">, aut ut 407,8. </s> <s xml:id="echoid-s19228" xml:space="preserve">ad 139,2. </s> <s xml:id="echoid-s19229" xml:space="preserve">qui nume-<lb/>rus etiam exprimit relationem gravitatis in ſuperficie Lunæ, <lb/>cum gravitate in ſuperficiebus Solis, Jovis, & </s> <s xml:id="echoid-s19230" xml:space="preserve">Saturni <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s19231" xml:space="preserve"> <anchor type="note" xlink:label="note-0730-07a" xlink:href="note-0730-07"/> </s> </p> <div xml:id="echoid-div2908" type="float" level="2" n="7"> <note position="left" xlink:label="note-0730-05" xlink:href="note-0730-05a" xml:space="preserve">1429.</note> <note symbol="*" position="left" xlink:label="note-0730-06" xlink:href="note-0730-06a" xml:space="preserve">1230.</note> <note symbol="*" position="left" xlink:label="note-0730-07" xlink:href="note-0730-07a" xml:space="preserve">1258.</note> </div> <p> <s xml:id="echoid-s19232" xml:space="preserve">Centrum commune gravitatis Lunæ & </s> <s xml:id="echoid-s19233" xml:space="preserve">Telluris, circa <lb/> <anchor type="note" xlink:label="note-0730-08a" xlink:href="note-0730-08"/> quod ambo corpora moventur, determinatur; </s> <s xml:id="echoid-s19234" xml:space="preserve">nam hujus à <lb/>Telluris centro diſtantia, eſt ad diſtantiam intra centra ambo-<lb/>rum corporum, ut quantitas materiæ in Lunâ ad quantitatem <lb/>materiæ in ambobus corporibus <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19235" xml:space="preserve">itaque 40,13. </s> <s xml:id="echoid-s19236" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s19237" xml:space="preserve">ut Lu- <anchor type="note" xlink:label="note-0730-09a" xlink:href="note-0730-09"/> næ diſtantia à Tellure ad diſtantiam quæſitam centri gravitatis <lb/>à centro Telluris, quæ detegitur 5126950. </s> <s xml:id="echoid-s19238" xml:space="preserve">perticarum, ut <lb/>ex notis Telluris diametro <anchor type="note" xlink:href="" symbol="*"/>, & </s> <s xml:id="echoid-s19239" xml:space="preserve">Lunæ diſtantiâ deducitur.</s> <s xml:id="echoid-s19240" xml:space="preserve"> <anchor type="note" xlink:label="note-0730-10a" xlink:href="note-0730-10"/> </s> </p> <div xml:id="echoid-div2909" type="float" level="2" n="8"> <note position="left" xlink:label="note-0730-08" xlink:href="note-0730-08a" xml:space="preserve">1430.</note> <note symbol="*" position="left" xlink:label="note-0730-09" xlink:href="note-0730-09a" xml:space="preserve">234. 235.</note> <note symbol="*" position="left" xlink:label="note-0730-10" xlink:href="note-0730-10a" xml:space="preserve">976.</note> </div> <p> <s xml:id="echoid-s19241" xml:space="preserve">Ut Lunæfiguram determinemus, examinanda eſt figura, quam, <lb/> <anchor type="note" xlink:label="note-0730-11a" xlink:href="note-0730-11"/> ſi fluida foret, acquireret <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19242" xml:space="preserve">Si Lunam ſolam conſideremus qui- <anchor type="note" xlink:label="note-0730-12a" xlink:href="note-0730-12"/> eſcentem, ſphærica erit <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19243" xml:space="preserve">Si actionem Telluris in Lunam con- <anchor type="note" xlink:label="note-0730-13a" xlink:href="note-0730-13"/> ſideremus, acquireret Luna figuram ſphæroidis, cujus axis per <lb/>Tellurem tranſiret <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19244" xml:space="preserve">Vis Telluris ad Lunæ figuram mutandam <anchor type="note" xlink:label="note-0730-14a" xlink:href="note-0730-14"/> eſt ad vim Lunæ in Tellurem, ut 39,13. </s> <s xml:id="echoid-s19245" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s19246" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> & </s> <s xml:id="echoid-s19247" xml:space="preserve">ut diameter <anchor type="note" xlink:label="note-0730-15a" xlink:href="note-0730-15"/> Lunæ ad Telluris diametrum <anchor type="note" xlink:href="" symbol="*"/>, quæ ſunt inter ſe, ut 11 ad 40.</s> <s xml:id="echoid-s19248" xml:space="preserve">2.</s> <s xml:id="echoid-s19249" xml:space="preserve"> <anchor type="note" xlink:label="note-0730-16a" xlink:href="note-0730-16"/> eſtque ratio compoſita ex his 10,7. </s> <s xml:id="echoid-s19250" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s19251" xml:space="preserve">Hæc vis Lunæ eſt ad <lb/>gravitatem in ſuperficie Telluris, ut 1. </s> <s xml:id="echoid-s19252" xml:space="preserve">ad 2871485 <anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19253" xml:space="preserve">quæ gra- <anchor type="note" xlink:label="note-0730-17a" xlink:href="note-0730-17"/> vitas in Telluris ſuperficie eſt ad gravitatem in ſuperficie Lu-<lb/>næ, ut 407,8. </s> <s xml:id="echoid-s19254" xml:space="preserve">ad 139,2. </s> <s xml:id="echoid-s19255" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/> aut ut 2871485′, ad 980028.</s> <s xml:id="echoid-s19256" xml:space="preserve">; <anchor type="note" xlink:label="note-0730-18a" xlink:href="note-0730-18"/> quare actio Telluris ad mutandam Lunæ figuram, ad gravita-<lb/> <anchor type="note" xlink:label="note-0730-19a" xlink:href="note-0730-19"/> tem in ſuperficie Lunæ, ut 10,7. </s> <s xml:id="echoid-s19257" xml:space="preserve">ad 980028, aut ut 1. </s> <s xml:id="echoid-s19258" xml:space="preserve">ad 91524.</s> <s xml:id="echoid-s19259" xml:space="preserve"> <pb o="(199)" file="0731" n="803" rhead="MATHEMATICA. LIB. IV. CAP. XXI,"/> mutatâ gravitate, in Telluris ſuperficie, parte {1/2871485}, aqua <lb/>elevatur pedibus 8,95. </s> <s xml:id="echoid-s19260" xml:space="preserve"><anchor type="note" xlink:href="" symbol="*"/>; </s> <s xml:id="echoid-s19261" xml:space="preserve">ideò, ſi gravitas parte {1/91524} mutare- <anchor type="note" xlink:label="note-0731-01a" xlink:href="note-0731-01"/> tur, elevatio foret pedum 280,7, ut regulâ aureâ detegitur: <lb/></s> <s xml:id="echoid-s19262" xml:space="preserve">ſi, ſervatâ hac diminutione gravitatis, de corpore minori a-<lb/>gatur, minuenda eſt hæc altitudo in ratione diametri; </s> <s xml:id="echoid-s19263" xml:space="preserve">ideò, <lb/>ex actione Telluris, elevatio in Lunâ eſt pedum 76,8.</s> <s xml:id="echoid-s19264" xml:space="preserve">: & </s> <s xml:id="echoid-s19265" xml:space="preserve"><lb/>æquilibrium non dabitur, ſi Luna ſit bomogenea, niſi axis <lb/> <anchor type="note" xlink:label="note-0731-02a" xlink:href="note-0731-02"/> ſphæroidis ſuperet diametrum ad bunc perpendicularem pe-<lb/>dibus 153,60.</s> <s xml:id="echoid-s19266" xml:space="preserve"/> </p> <div xml:id="echoid-div2910" type="float" level="2" n="9"> <note position="left" xlink:label="note-0730-11" xlink:href="note-0730-11a" xml:space="preserve">1431.</note> <note symbol="*" position="left" xlink:label="note-0730-12" xlink:href="note-0730-12a" xml:space="preserve">1358.</note> <note symbol="*" position="left" xlink:label="note-0730-13" xlink:href="note-0730-13a" xml:space="preserve">1359.</note> <note symbol="*" position="left" xlink:label="note-0730-14" xlink:href="note-0730-14a" xml:space="preserve">1392.</note> <note symbol="*" position="left" xlink:label="note-0730-15" xlink:href="note-0730-15a" xml:space="preserve">1428. 1207.</note> <note symbol="*" position="left" xlink:label="note-0730-16" xlink:href="note-0730-16a" xml:space="preserve">1390. 1354.</note> <note symbol="*" position="left" xlink:label="note-0730-17" xlink:href="note-0730-17a" xml:space="preserve">1420.</note> <note symbol="*" position="left" xlink:label="note-0730-18" xlink:href="note-0730-18a" xml:space="preserve">1429.</note> <note position="left" xlink:label="note-0730-19" xlink:href="note-0730-19a" xml:space="preserve">1432.</note> <note symbol="*" position="right" xlink:label="note-0731-01" xlink:href="note-0731-01a" xml:space="preserve">1420. 1422.</note> <note position="right" xlink:label="note-0731-02" xlink:href="note-0731-02a" xml:space="preserve">1433.</note> </div> <p> <s xml:id="echoid-s19267" xml:space="preserve">Unicâ proportione detegitur, ex notâ elevatione Maris <lb/> <anchor type="note" xlink:label="note-0731-03a" xlink:href="note-0731-03"/> ex Lunæ actione, elevatio in Lunâ ex Telluris actione; </s> <s xml:id="echoid-s19268" xml:space="preserve">nam <lb/>ſunt hæ elevationes in ratione duplicatâ inverſâ gravitatum <lb/>in ſuperficiebus illorum corporum.</s> <s xml:id="echoid-s19269" xml:space="preserve"/> </p> <div xml:id="echoid-div2911" type="float" level="2" n="10"> <note position="right" xlink:label="note-0731-03" xlink:href="note-0731-03a" xml:space="preserve">1434.</note> </div> <p> <s xml:id="echoid-s19270" xml:space="preserve">Si, poſitâ hac Lunæ figurâ, partes cohærere concipiamus, <lb/>æquilibrium inter Lunæ partes non dabitur, niſi axis ſphæ-<lb/> <anchor type="note" xlink:label="note-0731-04a" xlink:href="note-0731-04"/> roidis ad Tellurem dirigatur; </s> <s xml:id="echoid-s19271" xml:space="preserve">unde videmus, quare Luna <lb/>eandem faciem ſemper Telluri obvertat; </s> <s xml:id="echoid-s19272" xml:space="preserve">quâ continuâ agi-<lb/>tatione, Luna tandem acquiſivit motum circa axem, de quo <lb/> <anchor type="note" xlink:label="note-0731-05a" xlink:href="note-0731-05"/> antea egimus <anchor type="note" xlink:href="" symbol="*"/>: </s> <s xml:id="echoid-s19273" xml:space="preserve">qui motus neceſſario eodem tempore peragi.</s> <s xml:id="echoid-s19274" xml:space="preserve"> <anchor type="note" xlink:label="note-0731-06a" xlink:href="note-0731-06"/> tur, in quo Luna revolvitur; </s> <s xml:id="echoid-s19275" xml:space="preserve">nam ex actione memoratâ, ſe <lb/>ad celeritatem talem neceſſariò conſtituit; </s> <s xml:id="echoid-s19276" xml:space="preserve">ſi enim major fo-<lb/>ret celeritas, vi, quâ eadem facies ad Tellurem ſemper di-<lb/>rigitur, continuò retardaretur; </s> <s xml:id="echoid-s19277" xml:space="preserve">acceleraretur continuò ſi <lb/>minor foret. </s> <s xml:id="echoid-s19278" xml:space="preserve">Vis tamen hæc non eſt ſatis magna, ut in ſin-<lb/>gulis revolutionibus æquabilitatem motus acquiſiti circa <lb/>axem ſenſibiliter turbet: </s> <s xml:id="echoid-s19279" xml:space="preserve">Ideò motus circa axem æquabilis eſt, <lb/> <anchor type="note" xlink:label="note-0731-07a" xlink:href="note-0731-07"/> licèt motu inæquali in orbitâ moveatur Luna <anchor type="note" xlink:href="" symbol="*"/>. </s> <s xml:id="echoid-s19280" xml:space="preserve">Situs etiam <anchor type="note" xlink:label="note-0731-08a" xlink:href="note-0731-08"/> axis Lunæ, non vi memoratâ ita poteſt mutari, ut ad Planum <lb/>orbitæ, dum hujus inclinatio mutatur <anchor type="note" xlink:href="" symbol="*"/>, ſemper perpendi- <anchor type="note" xlink:label="note-0731-09a" xlink:href="note-0731-09"/> cularis ſit, idcircò ad Planum orbitæ aliquando inclinatur <lb/> <anchor type="note" xlink:label="note-0731-10a" xlink:href="note-0731-10"/> axis Lunæ, ut antea vidimus <anchor type="note" xlink:href="" symbol="*"/>.</s> <s xml:id="echoid-s19281" xml:space="preserve"> <anchor type="note" xlink:label="note-0731-11a" xlink:href="note-0731-11"/> </s> </p> <div xml:id="echoid-div2912" type="float" level="2" n="11"> <note position="right" xlink:label="note-0731-04" xlink:href="note-0731-04a" xml:space="preserve">1435.</note> <note position="right" xlink:label="note-0731-05" xlink:href="note-0731-05a" xml:space="preserve">1436.</note> <note symbol="*" position="right" xlink:label="note-0731-06" xlink:href="note-0731-06a" xml:space="preserve">970. 1092.</note> <note position="right" xlink:label="note-0731-07" xlink:href="note-0731-07a" xml:space="preserve">1437.</note> <note symbol="*" position="right" xlink:label="note-0731-08" xlink:href="note-0731-08a" xml:space="preserve">966.</note> <note symbol="*" position="right" xlink:label="note-0731-09" xlink:href="note-0731-09a" xml:space="preserve">1345.</note> <note position="right" xlink:label="note-0731-10" xlink:href="note-0731-10a" xml:space="preserve">1438.</note> <note symbol="*" position="right" xlink:label="note-0731-11" xlink:href="note-0731-11a" xml:space="preserve">1093.</note> </div> </div> <div xml:id="echoid-div2914" type="section" level="1" n="682"> <head xml:id="echoid-head888" xml:space="preserve">FINIS LIBRI QUARTI.</head> <figure> <image file="0731-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0731-01"/> </figure> <pb file="0732" n="804" rhead="CORRIGENDA."/> <note position="right" xml:space="preserve"> <lb/>Pag. # lin. # dele # lege <lb/>(2.) # 25. # major # majus. <lb/>(3.) # 3. in fine # Non tamen differentiam hanc in\vitto Anglicano obſervate potui, ni-\ſi illis diebus in quibus propter aëris\conſtitutionem languida eſt electri-\citas. <lb/>(4.) # 25. # abc # abd <lb/># 27. # turquæ # tur, quæ <lb/>(7.) # 5. # lamella # tabella <lb/># penult. & ult. # obteguntur & firmantur # obtegitur & firmatur. <lb/>(8.) # 16. # Gypſeis # ex Succino <lb/>(25.) # 30. # IL # IG <lb/>(28) # 6. # ſupra aqua # ſuper aquâ <lb/>(36.) # 5.6. # O magis diſtet # O, magis diſtas <lb/>(44.) # 18. # aquens # aqueus <lb/>(47.) # 21. # inte # inter <lb/>(66.) # 29. # diametrum # diameter <lb/>(94.) # 33. # FG # FH <lb/>(101.) # 9. # radiir eftectuntur # radii reflectuntur. <lb/>(110.) # 24. # ipſer # ipſe <lb/># 29. # antecedentiâ # conſequentiâ <lb/>(112.) # 8. # 60 {2/9} # 60 {1/2} <lb/>(113.) # 27 # 340069. # 3400669. <lb/>(117.) # 31. # videtur # videtur in conſequentiâ, <lb/>(128) # 20. # Luna # Solis <lb/>(130) # 5. # videtur # videtur in antecedentiâ <lb/>(134) # 16. # fuperficies # ſuperficiem <lb/>(135.) # 29. # Stella fixa # corpora caleſtia <lb/>(146.) # 12. # horum # harum <lb/>(173.) # 24. # inverſâ # inverſâ quadratorum <lb/>(174) # 15. # Ll # l <lb/>(185.) # 29. # ſequitur # ſequuntur <lb/>(187) # 24. # AB; # AB; <lb/>(189.) # 24. # centrum ducta # ſuperficiem perpendicularis <lb/>#### IN MARGINE. <lb/>(16.) # 33. # 291. # 190. <lb/>(60.) # 27. # 191. # 190. <lb/>(64) # 8. # TAB. XXI. \\ fig. 4. <lb/>(128) # 24. # fig 4. # fig. 5. <lb/>(138) # 14. # 191. # 192. <lb/>(187) # 24. # <anchor type="note" xlink:href="" symbol="*"/>232. </note> <figure> <image file="0732-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0732-01"/> </figure> <pb file="0733" n="805"/> </div> <div xml:id="echoid-div2915" type="section" level="1" n="683"> <head xml:id="echoid-head889" xml:space="preserve">INDEX <lb/>RERUM, <lb/>Numeri (1), (11), deſignant Tomum pri-<lb/>mum & ſecundum, p. denotat paginam, <lb/>& n. numerum in margine.</head> <note style="it" position="right" xml:space="preserve"> <lb/>A. Acceleratio gravium: (1) p. <lb/> # 38. n. 129. & ſeq. <lb/># --corporum ſuper <lb/># plano inclinato devol-<lb/># ventium. p. 42. n. 144. <lb/># & ſeq. n. 135. & ſeq. <lb/>Æoli Pila. (11) p. 16. n. 606. 607. <lb/>Æquatio Temporis (11) p. 138. n. 1145. <lb/>Æquator (11) p. 129. n. 1075.. p. 134. <lb/># n. 1114. <lb/>Æquinoctia. (11) p. 139. n. 1155. <lb/>borum præceſſio. p. 143. n. 1186. p. <lb/># 144. n. 1193. <lb/>motus bujus explicatio. p. 190. n. 1382. <lb/># & ſeq. <lb/>Aër inter fluida refertur. (1) p. 153. n. <lb/># 417. & ſeq. <lb/>--ponderatur. p. 163. n. 442. <lb/>--Elaſticitatem babet. p. 155. n. 426. <lb/># & ſeq. <lb/>--ex particulis ſeparatis conſtat. p. <lb/># 158. n. 431. <lb/>--experimenta bunc ſpectantia. p. <lb/># 163. n. 442. & ſeq. <lb/>--eſt vebiculum ſoni. p. 181. n. 504. <lb/>--bujus actio in ignem. vide Ignem. <lb/>Albor. (11) p. 90. n. 870. <lb/>--ex permixtione colorum. ibid. n. <lb/># 871. & 872. <lb/>corpus album citius aliis incaleſcit. p. <lb/># 104. n. 909. <lb/>Altitudo ſiderum. (11) p. 133. n. 1105. <lb/>--Poli. p. 135. n. 1126. <lb/>Amplitudo ſiderum. (11) p. 133. n. <lb/># 1104. <lb/>Angulus incidentiæ (11) p. 21. n. 621. <lb/>--Refractionis. ibid. n. 623. <lb/>--Reflectionis. p. 59. n. 781. <lb/>Animalia ad vivendum aëre indigent <lb/># (1) p. 169. n. 463. <lb/>--in aëre compreſſo. p. 170. n. <lb/># 465. <lb/>Annulus Saturni (11) p. 111. n. 963. <lb/># p. 124. n. 1034. <lb/>Antlia Pneumatica. (1) p. 160. n. 435. <lb/># & ſeq. <lb/>Antliæ vulgares. (1) p. 172. n. 472. <lb/>Aphelia Planetarum. (11) p. 109. n. <lb/># 935. <lb/>Apſides Planetarum. (11) p. 109. n. <lb/># 937. <lb/>linea Apſidum. n. 938. <lb/>Aqua eſt glacies liquefacta. (11) p. 15. <lb/># n. 604. <lb/>Arcus coeleſtis. Vide Iridem. <lb/>Aſcenſus fluidorum in tubos capillares, <lb/># (1) p. 10. n. 35. <lb/>--etiam in vacuo. n. 36. <lb/>--inter duo vitrea plana. n. 37. <lb/># 38. <lb/>Aſteriſmi. (11) p. 108. n. 1190. & ſeq. <lb/>Æſtus Maris. vide Mare. <lb/>Atmoſphæra. (1) p. 153. n. 418. <lb/> # (Cc 2) <lb/></note> <pb file="0734" n="806"/> <note position="right" xml:space="preserve"> <lb/>Attractio. (1) p. 9. n. 31. <lb/>-- bujus leges. ibid. <lb/>-- ex gravitate. (11) p. 147. n. <lb/># 1210. <lb/>Attractionis ſpatium. (11.) p. 23. n. 632. <lb/>Auges. vide Apſides. <lb/>Axiomata circa motum. (1) p. 15. n. 58. <lb/># & ſeq. <lb/>Axis Planetæ. (11) p. 110. n. 949. <lb/>Axeos Telluris motus. vide Æquino-<lb/># ctiorum præceſſionem. <lb/>Axis in Peritrochio. (1) p. 28. n. 112. <lb/>-- hujus proprietates. n. 113. & ſeq. <lb/>-- libræ. p. 20. n. 84. <lb/>B. <lb/>Bilanx vide Libram. <lb/>C. <lb/>Calor. (11) p. 10. n. 579. 580. p. 11. <lb/># n. 584. <lb/>Calorem non ſequi proportionem ignis. <lb/># p. 12. n. 588. <lb/>Calore corpora lucent. p. 12. n. 591. <lb/>-- corpora dilatantur. p. 13. n. 596. <lb/># 597. <lb/>-- corpora quædam liquefiunt. p. 15. <lb/># n. 602. <lb/>-- corpora quædam Elaſticitatem ac-<lb/># quirunt. p. 15. n. 605. <lb/>quæ corpora citius incaleſcant. p. 104. <lb/># n. 908. <lb/>Camera obſcura (11) p. 42. n. 711. p. 67. <lb/># n. 817. <lb/>Celeritas. (1) p. 15. n. 53. <lb/>-- relativa. p. 55. n. 175. <lb/>Centrum libræ. (1) p. 21. n. 85. <lb/>Centrum gravitatis. (1) p. 23. n. 95. <lb/>-- hujus proprietates. n. 96 & ſeq. <lb/>-- oſcillationis. p. 47. n. 161. <lb/>-- percuſſionis. p. 48. n. 162. <lb/>Centrales vires (1) p. 76. n. 220. <lb/>harum proprietates. n. 221. & ſeq. <lb/>harum comparatio. p. 82. n. 231. & <lb/># ſeq. <lb/>Centrifuga vis. (1) p. 76. n. 218. <lb/>Centripeta vis. (1) p. 76. n. 219. <lb/>Chordarum conſonantiæ. (1) p. 185. n. <lb/># 532. & ſeq. <lb/>-- motus aliis communicatus. p. <lb/># 186. n. 536. & ſeq. <lb/>Cochlea interior. (1) p. 33. n. 121. <lb/>-- exterior. ibid. <lb/>harum uſus. ibid. <lb/>Cochlea perpetua. (1) p. 34. n. 123. <lb/>Cœlum quid ſit. (11) p. 115. n. 986. <lb/>-- quare cœruleum. p. 116. n. 987. <lb/>Cohœſionis lex. (1) p. 9. n. 31. <lb/>Color objectorum. (11) p. 84. n. 859. <lb/>-- Radiorum. ibid. n. 860. <lb/>-- immutabilis hic eſt. p. 85. n. 863. & ſeq. <lb/># p. 89. n. 869. <lb/>Colorum ordo ex diverſâ refrangibili-<lb/># tate. p. 84. n. 861. <lb/>Colores permixti. p. 91. n. 873. 874. <lb/>unde Colores vividi & fuſci; p. 105. <lb/># n. 911. 915. <lb/>unde Colores in quibuſdam corporibus <lb/># varii ſint, pro oculi ſitu. ibid. n. 914. <lb/>mutatio Colorum in liquidis permixtis. <lb/># p. 106. n. 916. <lb/>liquidum Coloris diverſi, ſi radiis re-<lb/># flexis aut tranſmiſſis videatur. ibid. <lb/># n. 917. <lb/>Colores Nubium. ibid. n. 920. <lb/>-- tenuium lamellarum & horum <lb/># affectiones. p. 98. n. 887. & ſeq. <lb/>-- corporum unde oriantur p. 104. <lb/># n. 907. p. 105. n. 910. <lb/>Cometæ (11) p. 114. n. 979. & ſeq. <lb/>Cometarum motus explicatio. (11) p. <lb/># 169. n. 1276. <lb/>Conjunctio corporum cœleſtium. (11) <lb/># p. 119. n. 1010. <lb/>Conſonantiæ. (1) p. 185. n. 525. & ſeq. <lb/></note> <pb file="0735" n="807"/> <note position="right" xml:space="preserve"> <lb/>Corporis proprietates. (1) p. 3. n. 8. & <lb/># ſeq. <lb/>Crepuſcula. (11) p. 139. n. 1149. & <lb/># ſeq. <lb/>Cryſtallus montana ex attritu lucida. <lb/># (11) p. 2. n. 552. <lb/>Cuneus. (1) p. 31. n. 118. 119. <lb/>Curſus ſluminis. (1) p. 143. n. 392. & <lb/># ſeq. <lb/>hujus celeritatis menſura. p. 146. n. 399. <lb/># & ſeq. <lb/>D. <lb/>Declinatio Sideris. (11) p. 129. n. <lb/># 1079. <lb/>Denſitas. (1) p. 106. n. 284. <lb/>Denſitatum ſluidorum determinatio. (1) <lb/># p. 113, n. 309. & ſeq. <lb/>-- ſolidorum comparatio. p. 116. <lb/># n. 315. & ſeq. <lb/>Denſitates Planetarum. (11) p. 164. <lb/>-- n. 1260. p. <lb/>Dies Naturalis. (11) p. 137. n. 1141. <lb/>--artificialis. p. 138. n. 1147. <lb/>harum differentiæ. p. 139. n. 1152. <lb/># & ſeq. <lb/>Lunaris Dies. p. 192. n. 1394. <lb/>Dilatatio ex Calore. Vide Calorem. <lb/>Ditonus. (1) p. 185. n. 530. <lb/>Diviſibilitas Materiæ. (1) p. 3. n. 10. <lb/># p. 6. n. 17. & ſeq. p. 8. n. 26. <lb/>Durum corpus. (1) p. 8. n. 28. <lb/>E. <lb/>Echo. (1) p. 187. n. 542. <lb/>Eclipſis Satellitis. (11) p. 124. n. <lb/># 1033. <lb/>-- Lunæ. vide Lunam. <lb/>-- Solis. vide Solem. <lb/>Ecliptica linea. (11) p. 118. n. 999. <lb/>Eclipticæ planum. p. 109. n. 940. <lb/>Elaſticitas. (1) p. 13. n. 44. <lb/>-- perfecta. p. 56. n. 177. <lb/>Elaſticitatis lex. (1) p. 90. n. 251. <lb/>Fibrarum Elaſticitas. p. 88. n. 244. & <lb/># ſeq. <lb/>Laminarum Elaſticitas. p. 95. n. 262. & <lb/># ſeq. <lb/>globi Elaſticitas. p. 96. n. 266. <lb/>Elaſticitas ex calore. vid. Calorem. <lb/>Electricitas. (11) p. 2. n 551. <lb/>--Tubi vitrei. p. 2. n. 554. 555. <lb/>--Globi vitrei. p. 4. n. 559. & ſeq. <lb/>Conjecturæ circa hujus cauſam. p. 5. n. <lb/># 563. & ſeq. <lb/>Elongatio Planetarum. (11) p. 119. n. <lb/># 1012. <lb/>-- maxima. ibid. n. 1013. <lb/>Excentricitas Planetarum. (11) p. 109. <lb/># n. 932. <lb/>Extenſio. (1) p. 3. n. 8. p. 4. n. 13. <lb/>F. <lb/>Fibrarum Elaſticitas. (1) p. 88. n. <lb/># 244. & ſeq. <lb/>-- Vibrationes. p. 93. n. 257. & ſeq. <lb/>Flamma. (11) p. 11. n. 587. p. 12. n. 592. <lb/>Fluidum. (1) p. 8. n. 30. <lb/>Fluida, in quo cumſolidis congruant. (1) <lb/># p. 97. n. 270. <lb/>Fluidorum proprietates. p. 98. n. 272. <lb/># & ſeq. <lb/>-- actiones in fundos & lateravaſe-<lb/># rum. p. 101. n. 280. <lb/>horum motus. (1) p. 127. n. 354. <lb/>Fluida proſilientia verticaliter. p. 129. <lb/># n. 358. & ſeq. vide fonticulum. <lb/>-- proſilientia obliquè p. 133. n. 368. <lb/># & ſeq. <lb/>-- ex vaſis profluentia. p. 138. n. <lb/># 378. & ſeq. <lb/>comparatio temporum quibus vaſa eva-<lb/># cuantur. p. 139. n. 379. & ſeq. <lb/>Solida fluidis immerſa. p. 107. n. 290. & <lb/># ſeq. <lb/>-- graviora. p. 108. n. 292. n. 296. <lb/># & ſeq. <lb/></note> <pb file="0736" n="808"/> <note position="right" xml:space="preserve"> <lb/>-- leviora. p. 112. n 306. & ſeq. <lb/>Fluiditas, unde oriatur. (1) p. 97. n. 269. <lb/>-- an à calore pendeat? (11) p. 15. n. <lb/># 603. <lb/>Flumen. (1) p. 143. n. 390. <lb/>hujus ſectio. n. 391. <lb/>hujus curſus. n. 392. & ſeq. <lb/>Focus. (11) p. 29. n. 650. <lb/>Fonticulus Heronis. (1) p. 172. n. 474. <lb/>-- ex aëris compreſſione. p, 168. n. <lb/># 459. <lb/>Fonticuli duo. p. 167. n. 457. p. 168. n. <lb/># 458. <lb/>Fumus. (11) p. 11. n. 587. p. 12. n. <lb/># 592. <lb/>G. <lb/>Gradus latitudinis accedendo ad po-<lb/># los augentur. (11) p. 189. n. 1374. <lb/>Gravia non ad centrum Telluris tendunt. <lb/># (11) p. 189. n. 1371. <lb/>Gravitas. (1) p. 18. n. 73. (11) p. 147. <lb/># n. 1206. & ſeq. <lb/>Gravitatis Phœnomena. (1) p. 18. n. 72. <lb/># p. 19. n. 75. 77. <lb/>Gravitas reſpectiva. (1) p. 108. n. 295. <lb/>-- ſpecifica. (1) p. 107. n. 287. <lb/>-- univerſalis eſt. (11) p. 146. n. <lb/># 1206. <lb/>hujus leges. n. 1207. 1208. <lb/>probatur. p. 147. n. 1211. & ſeq. <lb/>propoſitiones hanc ſpectantes. p. 151. n. <lb/># 1226. & ſeq. <lb/>non tribuenda eſt impactui nobis noto. p. <lb/># 153. n. 1238. <lb/>Gravitas in ſuperficiebus Planetarum. <lb/># p. 62. n. 1258. <lb/>Gutta fit Sphærica (1) p. 9. n. 33. <lb/>Gypſum in vacuo lucet. (11) p. 8. n. 570. <lb/>H. <lb/>Heterogeneum corpus. (1) p. 107. <lb/># n. 286. <lb/>Heterogenei radii. (11) p. 78. n. 850. <lb/>Homogeneum corpus. (1) p. 106. n. <lb/># 285. <lb/>Homogenei radii. (11) p. 78. n. 849. <lb/>Homunculi vitrei in aquâ ſaltantes. (1) <lb/># p. 169. n. 462. <lb/>Horizon. (11) p. 132. n. 1096. <lb/>I. <lb/>Ignis proprietates. (11) p. 1. n. 544. <lb/># & ſeq. <lb/>Ignem corporibus contineri. (11) p. 2. <lb/># n. 552. & ſeq. <lb/>Aëris actio in Ignem. (11) p. 9. n. 577. <lb/># p. 13. n. 593. 594. <lb/>Inclinatum Planum. (1) p. 41. n. 139. <lb/>Inertia corporis. (1) p. 3. n. 12. <lb/>Iris, quando detur. (11) p. 96. n. 884. <lb/># 885. <lb/>ſæpe duæ obſervantur. p. 98. n. 886. <lb/>explicatio motus luminis in Iride forman-<lb/># dâ. p. 92. n. 875. & ſeq. <lb/>Judicium de diſtantiâ & magnitudine <lb/># objectorum. quære Viſum. <lb/>-- de magnitudine Solis & Lunæ <lb/># prope Horizontem. (11) p. 49. n. 735. <lb/>Jupiter. (11) p. 111. n. 962. <lb/>hujus pondus. p. 163. n. 1255. <lb/>gravitas in hujus ſuperficie. n. 1258. <lb/>hujus denſitas. p. 164. n. 1260. <lb/>-- vis in Saturnum. p. 167. n. <lb/># 1270. <lb/>-- in Martem. p. 168. n. <lb/># 1273. <lb/>Jovis ſigura. p. 186. n. 1363. <lb/>L. <lb/>Laminarum elaſticitas. (1) p. 95. n. <lb/># 262. & ſeq. <lb/>Latitudo corporis cœleſtis. (11) p. 118. <lb/># n. 1006. <lb/>-- loci. p. 134. n. 1118. <lb/></note> <pb file="0737" n="809"/> <note position="right" xml:space="preserve"> <lb/>circulus Latitudinis. p. 135. n. 1119. <lb/>Lex Naturæ. (1) p. 2. n. 4. <lb/>-- quomodo leges Naturæ detegan-<lb/># tur. ibid. <lb/>Lens vitrea. (11) p. 38. n. 692. <lb/>Lentium affectiones. (11) p. 38. & ſeq. <lb/>-- convexarum. p. 39. n. 698. & <lb/># ſeq. <lb/>-- cavarum. p. 41. n. 704. & <lb/># ſeq. <lb/>-- polygonarum. p. 53. n. 759. <lb/>Libræ proprietates. (1) p. 21. n. 87. & <lb/># ſeq. <lb/>-- perfectio. p. 25. n. 102. <lb/>-- falacia. p. 22. n. 92. <lb/>Bilanx Hydroſtatica. p. 98. n. 271. <lb/>Lignum lucidum. (11) p. 10. n. 578. <lb/>Liquefacta corpora. vid. Calorem. <lb/>Locus. (1) p. 14. n. 48. 49. 50 <lb/>Longitudo corporis cœleſtis. (11) p. 118. <lb/># n. 1003. 1004. <lb/>-- loci. p. 135. n. 1121. <lb/>Lucernæ Magicæ deſcriptio & uſus. <lb/># (11) p. 72. n. 837. & ſeq. <lb/>hujus perfectio. p. 74. n. 839. <lb/>Lumen. (11) p. 10. n. 581. & ſeq. <lb/>Lucent corpora calore. vide calorem. <lb/>Luminis Radius. vide Radium. <lb/>-- motus. (11) p. 12. n. 589. 590. <lb/>-- celeritas in variis mediis. p. 27. <lb/># n. 640. <lb/>-- inflectio. p. 17. n. 611. & ſeq. <lb/>-- Refractio; vide Refractionem. <lb/>-- Reflectio. vide Reflectionem. <lb/>Lunæ motus, diſtantia, & c. (11) p. <lb/># 112. n. 967. & ſeq. <lb/>-- dimenſiones. p. 113. n. 977. <lb/>-- diſtantia, ſi in ſuo tempore perio-<lb/># dico, circa Tellurem quieſcentem move-<lb/># retur. p. 161. n. 1253. <lb/>-- Phœnomena. (11) p. 124. n. 1035. <lb/># & ſeq. <lb/>quare major prope Horizontem appareai. <lb/># p. 49. n. 735. <lb/>circa axem rotatur. p. 112. n. 970. p. 131. <lb/># n. 1092. <lb/>eandem faciem T’elluri obvertit ſemper. <lb/># n. 1092. <lb/>Eclipſis Lunæ. (11) p. 125. n. 1047. <lb/>-- quando detur n. 1049 1051. <lb/>-- Partialis. p. 126. n. 1052. <lb/>-- Totalis. n. 1053. <lb/>-- Centralis. n. 1054. <lb/>Lunæ gravitas in Tellurem. p. 150. n. <lb/># 1225. <lb/>-- denſitas. p. 197. n. 1427. <lb/>-- gravitas in ſuperficie. p. 198. n. <lb/># 1429. <lb/>-- Pondus. n. 1428. <lb/>-- figura. n. 1431. <lb/>-- motus explicatio Phyſica. p. 170. <lb/># n. 1285. & ſeq. <lb/>Virium Lunam turbantium determi-<lb/># natio. p. 173. n. 1291. p. 147. n. <lb/># 1296. p. 177. n. 1306. 1307. p. 182. <lb/># n. 1336. <lb/>Lunæ Apſidum motus. p. 112. n. 970. p. <lb/># 180. n. 1325. <lb/>-- motus Nodorum. p. 112. n. 970. p. <lb/># 183. n. 1341. & ſeq. <lb/>-- Excentricitatis mutatio. p. 112. <lb/># n. 968. p. 181. n. 1328. 1329. <lb/>-- inclinationis orbitæ mutatio. p. 112. <lb/># n. 969. p. 183. n. 1345. & ſeq. <lb/>M. <lb/>Machinæ ſimplices. (1) p. 25. n. 103. <lb/># p. 28. n. 112. p. 29. n. 115. p. 31. <lb/># n. 119. p. 33. n. 121. <lb/>-- compoſitæ. p. 34. n. 122. & ſeq. <lb/>Machina, qua Cunei proprietates demon-<lb/># ſtrantur. (1) p. 32. n. 120. <lb/>-- ad accelerationem corporum caden-<lb/># tium determinandam. p 39. n. 132. <lb/></note> <pb file="0738" n="810"/> <note position="right" xml:space="preserve"> <lb/>Machina quaplani inclinati proprietates <lb/># demonſtrantur. (1) p. 41. n. 143. <lb/>-- qua experimenta de percuſſione in-<lb/># ſtituuntur. p. 50. n. 170. <lb/>-- pro experimentis de motu compo-<lb/># ſito & percuſſione obliquâ. p. 63. n. <lb/># 191. <lb/>-- pro potentiis obliquis. p. 67. n. 197. <lb/># p. 70. n. 203. 204. <lb/>-- progravium projectione. (1) p. 73. <lb/># n. 210. <lb/>-- ad vires centrales demonſtrandas. <lb/># p. 77. n. 222. <lb/>-- qua experimenta circa Elaſticita-<lb/># tem inſtituuntur. p. 89 n. 249. <lb/>-- quibus preſſiones fluidorum de-<lb/># monſtrantur. p. 101. n. 281. p. 104. <lb/># n. 282. p. 105. n. 283. <lb/>-- quibus denſitates fluidorumdete-<lb/># guntur. p. 114. n. 312. p. 115. n. <lb/># 314. <lb/>-- quibus denſitates ſolidorum confe-<lb/># runtur. p. 116. n. 317. p. 117. n. 318. <lb/>-- ad experimenta circa reſiſtentiam <lb/># fluidorum inſtituenda. p. 124. n. <lb/># 346. <lb/>-- quibus experimenta circa fluida <lb/># proſilientia inſtituuntur. p. 128. n. 356. <lb/># p. 133. n. 370. <lb/>-- quafluminis celeritas menſuratur. <lb/># p. 146. n. 398. <lb/>-- Pneumatica. p. 160. n. 435. & <lb/># ſeq. <lb/>-- qua corpora invacuo dimittuntur. <lb/># p. 19. n. 77. <lb/>-- qua corpora in vacuo circumvol-<lb/># vuntur. (11) p. 6. n. 567. <lb/>-- qua experimenta in aëre compreſ-<lb/># ſo inſtituuntur. (1) p. 166. n. 454 <lb/>-- qua Urinatores utuntur. p. 168. n. <lb/># 461. <lb/>Machinæ variæ, quarum effectusab aëris <lb/># actione pendet. (1) p. 170. n. 467. & ſeq. <lb/>-- quaglobus vitreus circumvolvitur. <lb/># (11) p. 3. n. 556. <lb/>-- qua luminis inflectio demonſtra-<lb/># tur. p. 17. n. 611. <lb/>-- quibus refractio luminis demon-<lb/># ſtratur. p. 21. n. 630. p. 28 inprinc. <lb/># p. 32. in med. p. 35. in fine; p. 40. n. <lb/># 702. p. 41. n. 708. <lb/>Maculæ albicantes in cœlis. (11) p. 146. <lb/># n. 1205. <lb/>Magnitudo apparens. vide Judicium & <lb/># viſum. <lb/>Maris Æſtus. (11) p. 192. n. 1395. & <lb/># ſeq. <lb/>-- -- ab actione Lunæ & Solis <lb/># derivatur. p. 191. n. 1390. & ſeq. <lb/>vires bædeterminantur. p. 195. n. 1416. <lb/># & ſeq. <lb/>Mars. (11) p. 111. n. 961. <lb/>Materia cœleſtis eſt ſubtiliſſima. (11) p. <lb/># 156. n. 1243. <lb/>-- --non movet corpora. n. 1244. <lb/>Materiæ quantitates in Planetis. (11) <lb/># p. 163. n. 1255. <lb/>Medium Luminis. (11) p. 19. n. 15. <lb/>Menſis Lunaris Periodicus. (11) p. 124. <lb/># n. 1037. <lb/>-- --Synodicus. n. 1038. <lb/>Mercurius in vacuo lucet. (11) p. 8. <lb/># n. 571. & ſeq. <lb/>-- Planeta. (11) p. 111. n. 958. <lb/>Meridiani. (11) p. 129. n. 1077. p. 134. <lb/># n. 1114. 1116. <lb/>primus Meridianus. p. 135. n. 120. <lb/>Meridiana linea. (11) p. 133. n. 1101. <lb/>Molle corpus. (1) p. 8. n. 29. <lb/>Mobile eſt corpus. (1) p. 3. n. 11. <lb/>Motus. (1) p. 14. n. 47. <lb/>hujus quantitas. p. 15. n. 54. <lb/>-- directio. n. 55. <lb/>-- leges. p. 36. n. 124. & ſeq. <lb/></note> <pb file="0739" n="811"/> <note position="right" xml:space="preserve"> <lb/>Motuum comparatio. (1) p. 16. n. 62. <lb/># & ſeq. <lb/>Motus acceleratus. (1) p. 37. n. 127. <lb/>-- retardatus. p. 38. n. 128. <lb/>-- compoſitus. p. 63. n. 190. & ſeq. <lb/>-- reſolutio. p. 65. n. 192. <lb/>-- relativus. (11) p. 115. n. 985. <lb/>-- apparens. n. 985. p. 117. n. 992. <lb/># & ſeq. <lb/>-- in conſequentiâ. p. 110. n. 946. <lb/>-- in antecedentiâ. n. 947. <lb/>-- diurnus. p. 129. n. 1074. p. 130. <lb/># n. 1081. & ſeq. <lb/>-- fluidorum. (1) p. 127. n. 354. <lb/># & ſeq. <lb/>-- Luminis. vid. Lumen. <lb/>-- quantitas in mundo non ſemper <lb/># eadem. (1) p. 61. n. 187. 188. <lb/>Mycroſcopium. (11) p. 54. n. 760. <lb/>-- amplificat objecta exigua. ibid. <lb/># n. 761. <lb/>-- compoſitum magis amplificat. <lb/># p. 55. n. 763. <lb/>Myops. vide Oculum. <lb/>N. <lb/>Nadir. (11) p. 133. n. 1100. <lb/>Nigredo. vide Reflectionem. <lb/>-- corpora nigra tardius cæteris <lb/># incaleſcunt. (11) p. 104. n. 909. <lb/>Nodi Planetarum. (11) p. 109. n. 941. <lb/>-- linea Nodorum. n. 942. <lb/>Novilunium. (11). p. 125. n. 1042. <lb/>Nubeculæ duæ in Cœlis. (11) p. 145. <lb/># n. 1201. <lb/>O. <lb/>Occaſus Siderum. (11) p. 132. n. <lb/># 1089. <lb/>Occidentis punctum. (11) p. 133. n. <lb/># 1103. <lb/>Octava. (1) p. 185. n. 527. <lb/>Oculi explicatio. (11) p. 43. n. 712. <lb/>Oculus Artificialis. (11) p. 45. <lb/>mutationes in Oculo p. 46. n. 719. & <lb/># ſeq. <lb/>vitium Senum corrigitur. p. 52. n. <lb/># 756. <lb/>vitium Myopum corrigitur. p. 53. n. <lb/># 758. <lb/>Opacum corpus. (11) p. 42. n. 709. <lb/>Opacitas a poris pendet. p. 76. n. 843. <lb/>Oppoſitio corporum cæleſtium. (11) p. <lb/># 119. n. 1011. <lb/>Ortus Siderum. (11) p. 132. n. 1097. <lb/>Orientis punctum. p. 133. n. 1102. <lb/>P. <lb/>Phænomena Naturalia. (1) p. 1. <lb/># n. 2. <lb/>Paralaxis Syderum. (11) p. 133. n. 1106. <lb/># & ſeq. <lb/>-- annua. p. 144. n. 1187. 1188. <lb/>Partium ſubtilitas. (1) p. 7. n. 20. & <lb/># ſeq. <lb/>Pellucidum corpus. (11) p. 75. n. 840. <lb/>Pellucidæ ſunt omnium corporum partes. <lb/># ibid. n. 841. <lb/>Pellucida corpora ſeparatione partium <lb/># ſiunt opaca. p. 77. n. 844. <lb/>Pendulum. (1) p. 44. n. 153. <lb/>-- compoſitum. p. 47. n. 161. <lb/>Pendulorum motus. p. 45. n. 154. & <lb/># ſeq. <lb/>Penumbra. (11) p. 127. n. 1060. <lb/>Percuſſio directa. (1) p. 49. n. 166. <lb/>-- corporum non Elaſticorum. p. 53. <lb/># n. 171. & ſeq. <lb/>-- corporum Elaſticorum. p. 56. n. <lb/># 179. & ſeq. <lb/>-- obliqua. p. 65. n. 193. & ſeq. <lb/>Perihelia Planetarum. (11) p. 109. n. <lb/># 936. <lb/>Phoſphorus urinæ. (11) p. 9. n. 575. <lb/>-- in vacuo. (11) p. 13. n. 595. <lb/>Phyſica. (1) p. 2. n. 3. <lb/></note> <pb file="0740" n="812"/> <note position="right" xml:space="preserve"> <lb/>Piſces aëre indigent. (1) p. 169. n. 464. <lb/>Planetæ. (11) p. 108. n. 926. <lb/>-- Primarii. ibid. n. 927. <lb/>-- Secundarii. ibid. n. 928. <lb/>-- inferiores. p. 112. n. 964. <lb/>-- ſuperiores. ibid. <lb/>Planetarum inferiorum apparentiæ. p. <lb/># 119. n. 1015. & ſeq. <lb/>-- ſuperiorum apparentiæ. p. 122. <lb/># n. 1024. & ſeq. <lb/>-- figuræ determinantur. p. 186. <lb/># n. 1360. <lb/>-- diſtantiæ. p. 111. n. 956. & ſeq. <lb/>-- dimenſiones. p. 113. n. 975. p. <lb/># 163. n. 1256. <lb/>-- pondera. p. 163. n. 1255. <lb/>-- denſitates. p. 164. n. 1260. <lb/>-- motus. p. 108. n. 929. & ſeq. <lb/>-- actionum mutuarum effectus. <lb/># p. 168. n. 1274. <lb/>Planetæ revolvuntur circa centrum gra-<lb/># vitatis totius Syſtematis. p. 166. <lb/># n. 1264. <lb/>horum orbitæ quieſcunt. p. 166. n. <lb/># 1265. <lb/>-- motuum explicatio Phyſica. p. <lb/># 169. n. 1275. <lb/>ſecundariorum motus diſtantiæ & c. <lb/># p. 112. n. 965. & ſeq. p. 123. n. <lb/># 1130. & ſeq. <lb/>-- horum motuum explicatio. p. 169. <lb/># n. 1277. & ſeq. <lb/>Plenilunium. (11) p. 125. n. 1043. <lb/>Poli Planetæ. (11) p. 110. n. 953. <lb/>-- Mundi. p. 129. n. 1073. <lb/>-- Arcticus. p. 131. n. 1090. <lb/>-- Antarcticus. n. 1091. <lb/>-- Eclipticæ. p. 119. n. 1007. <lb/>Circuli Polares. p. 131. n. 1091. p. <lb/># 134. n. 1114. <lb/>Potentia. (1) p. 15. n. 56. <lb/>hujus intenſitas. n. 57. <lb/>actionum Potentiarum comparatio. p. <lb/># 18. n. 67. & ſeq. <lb/>-- obliquarum determinatio. p. 67. <lb/># n. 196. & ſeq. <lb/>Præceſſio Æquinoctiorum. vide Æqui-<lb/># noctia. <lb/>Projectio gravium. (1) p. 72. n. 208. <lb/># & ſeq. <lb/>Puncta quietis in chordis agitatis. (1) <lb/># p. 185. n. 538. 539. <lb/>Q. <lb/>Quarta. (1) p. 185. n. 529. <lb/># Quinta. (1) p. 185. n. 528. <lb/>R. <lb/>Radians punctum. (11) p. 29. n 645. <lb/># Radius luminis. (11) p. 17. n. <lb/># 610. <lb/>Radii divergentes. (11) p. 28. n. 643. <lb/>-- convergentes. p. 29. n. 648. <lb/>-- incidens. p. 20. n. 620. <lb/>-- refractus. p. 21. n. 622. <lb/>-- reflexus. p. 59. n. 780. <lb/>-- Homogenei. p. 78. n. 849. <lb/>-- Heterogenei. ibid. n. 850. <lb/>-- per curvas in aëre moventur. p. <lb/># 126. n. 1056. <lb/>Reflectio luminis d corporibus. (11) <lb/># p. 42. n. 710. <lb/>-- à ſuperficie politâ. (11) p. 59. <lb/># n. 779. <lb/>-- hujus leges. ibid. n. 783. & ſeq. <lb/>-- cum refractione relationem ha-<lb/># bet. p. 63. n. 795. & ſeq. <lb/>corpora nigra lumen non reflectunt. p. <lb/># 78. n. 845. <lb/>Refractio luminis. (11) p. 19. n. 616. <lb/>-- quando detur. ibid. n. 617. <lb/>-- unde oriatur. ibid. n. 618. <lb/>-- hujus leges. p. 21. n. 624. & <lb/># ſeq. <lb/>conſtansratio inter ſinus incidentiæ & <lb/># Refractionis p. 27. n. 639. <lb/></note> <pb file="0741" n="813"/> <note position="right" xml:space="preserve"> <lb/>Hujus effectus cauſa. n. 633. & ſeq. <lb/>Leges Refractionis mediis ſuperficie <lb/># planâ ſeparatis. p. 28. & ſeq. <lb/>-- -- mediis ſuperficie ſphæricâ-<lb/># ſeparatis. p. 31. & ſeq. <lb/>Siderum Refractio. p. 134. n. 1110. & <lb/># ſeq. <lb/>Refrangibilitas diverſa in variis radiis. <lb/># (11) p. 78. n. 847. <lb/>-- in ſingulis conſtans eſt. p. 83. <lb/># n. 855. <lb/>-- quo major eſt, eo radii facilius <lb/># reflectuntur. p. 88. n. 868. <lb/>Regulæ philoſophandi. (1) p. 2. n. 5. <lb/># 6. & 7. <lb/>Res Naturales. (1) p. 1. n. 1. <lb/>Repulſio. (1) p. 11. n. 40. & ſeq. <lb/>Reſiſtentia fluidorum. (1) p. 118. n. <lb/># 319. & ſeq. <lb/>Retardatio corporum adſcendentium <lb/># verticaliter. (1) p 40. <lb/>-- -- adſcendentium ſuper pla-<lb/># no inclinato. p. 44. n. 151. & ſeq. <lb/>Retardatio corporum in fluidis moto-<lb/># rum. (1) p. 120. n. 329. <lb/>Retardationum comparatio. n. 331. & <lb/># ſeq. <lb/>-- collatio cum gravitate. p. 121. <lb/># n. 336. <lb/>Retardatio penduli in fluido. p. 122. n. <lb/># 339. & ſeq. <lb/>-- corporis in fluido deſcendentis. p. <lb/># 125. n. 347. & ſeq. <lb/>-- corporis in altum adſcendentis. p. <lb/># 126. n. 351. & ſeq. <lb/>Rotæ dentatæ. (1) p. 29. n. 114. <lb/>S. <lb/>SAtellites. vide Planetas Secunda-<lb/># rios. <lb/>Saturnus. (11) p. 111. n. 963. <lb/>hujus pondus. p. 163. n. 1255. <lb/>hujus gravitas in ſuperficie. n. 1258. <lb/>-- denſitas. p. 164. n. 1260. <lb/>-- vis in Jovem. p. 168. n. 1272. <lb/>Seſquiditonus. (1) p. 185. n. 531. <lb/>Signa Zodiaci. vide Zodiacum. <lb/>Sipho. (1) p. 170. n 467. 469-p. 171. <lb/># n 470. <lb/>Sol exiguo motu agitatur. (11) p. 111. n. <lb/># 957. p. 166. n 1266. <lb/>-- hujus motus effectus. p 166. n 1267. <lb/>-- circa axem rotatur. p. 111. n. 957. <lb/># p. 128. n. 1071. <lb/>--motu Telluris moveri videtur. p. <lb/># 117. n. 996. & ſeq. <lb/>quare major prope Horizontem appa-<lb/># reat p. 49. n. 735. <lb/>Eclipſis Solis. p. 125. n. 1046. <lb/>-- diverſa eſt in variis locis. p. 128. n. <lb/># 1065. <lb/>--quando detur. p. 127. n. 1059. <lb/>--Partialis. p. 128. n. 1067. 1068. <lb/>--Totatis. n. 1067. 1068. <lb/>--Centralis. n. 1068. <lb/>--Annularis. n. 1070. <lb/>Solis pondus. p. 163. n. 1255. <lb/>--gravitas in ſuperficie. n. 1258. <lb/>--denſitas. p. 164. n. 1260. <lb/>Soliditas Materiæ. (1) p. 3. n. 9. <lb/>Solſtitia. (11) p. 139. n. 1155. <lb/>Sonus ab aere pendet. (1) p. 181. n. 504. <lb/>hujus intenſitas. p. 184 n. 515. & ſeq. <lb/>augetur in aere compreſſo. p. 184. n. 516. <lb/>Soni celeritas. p. 182. n. 508. & ſeq. <lb/>Spatium. vide Vacuum. <lb/>Specula plana. (11) p. 64. n. 799. & <lb/>-- ſphærica convexa. p. 65. n. 806. <lb/># & ſeq. <lb/>-- ſphærica cava. p. 66. n. 813. & <lb/># ſeq. <lb/>-- uſtoria. ibid. n. 814. <lb/>-- cylindrica & conica. p. 71. n. <lb/># 863. <lb/></note> <pb file="0742" n="814"/> <note position="right" xml:space="preserve"> <lb/>Sphæra parallela. (11) p. 135. n. 1123. <lb/># 1124. <lb/>-- obliqua. n. 1125. & ſeq. <lb/>-- recta. p. 137. n. 1138. & ſeq. <lb/>Statera Romana. (1) p. 22. n. 91. <lb/>Stellæ fixæ. (11) p. 108. n. 923. p. 144. <lb/># n. 1190. & ſeq. <lb/>-- maximo numero Teleſcopiis dete-<lb/># guntur. p. 145. n. 1202. <lb/>-- quædam ſunt periodicæ. p. 146. <lb/># n. 1203 <lb/>-- quædam apparuere & in totum <lb/># evanuere. n. 1204. <lb/>Suſpenſionis puncta. (1) p. 21. n. 86. <lb/>Syſtema Planetarium. (11) p. 107. n. <lb/># 922. <lb/>hujus explicatio phyſica. (11) p. 169. <lb/># n. 1275. <lb/>Syzygiæ. (11) p. 125. n. 1044. <lb/>T. <lb/>Teleſcopium. (11) p. 56. n. 768. <lb/>-- Aſtronomicum. ibid. n. 769. <lb/>-- rebus terreſtribus videndis ap-<lb/># tum. ibid. n. 772. p. 58. n. 776. <lb/>quare minus ſunt perfecta Teleſcopia <lb/># p. 88. n. 867. <lb/>Tellus inter Planetas refertur. (11) p. <lb/># 111. n. 960. <lb/>hujus motus & diſtantia. n. 960. p. <lb/># 117. n. 996. & ſeq. p. 130. n. 1081 & <lb/># ſeq. p. 143. n. 1183. & ſeq. p. 157. <lb/># n. 1244. & ſeq. p. 171. n. 1281. <lb/>--dimenſiones. p. 113. n. 976. <lb/>--figura. p. 186. n. 1360. & ſeq. <lb/>-- --ex menſuris non poteſt deter-<lb/># minari. p. 189. n. 1375. <lb/>-- elevatio ad Æquatorem determi-<lb/># natur. p. 189. n. 1370. <lb/>in Telluris ſuperficie gradus acceden-<lb/># do ad Polos augentur. p. 189. n. <lb/># 1374. <lb/></note> <note position="right" xml:space="preserve"> <lb/>Tempeſtates annuæ. (11) p. 142. n. <lb/># 1176. & ſeq. <lb/>-- in Zonâ Torridâ. n. 1179. & <lb/># ſeq. <lb/>Tempus. (1) p. 15. n. 51. 52. <lb/>-- medium. (11) p. 138. n. 1145. <lb/>Thermometrum. (11) p. 14. n. 598. <lb/># 599. <lb/>Tonus. (1) p. 185. <lb/>-- gravis. ibid. <lb/>-- acutus. ibid. <lb/>Trochlea. (1) p. 20. n. 82. 83. p. 29. n. <lb/># 115. & ſeq. <lb/>Tropici. (11) p. 130. n. 1089. p. 134. <lb/># n. 1114 <lb/>Tubuli pulvere nitrato farti. (11) p. <lb/># 17. n. 609. <lb/>Tuba Stentoria. (1) p. 187. n. 543. <lb/>V. <lb/>Vacuum poſſibile eſt. (1) p. 4. n. <lb/># 13. <lb/>--hujus proprietates. (1) p. 5. n. 15. <lb/>-- datur. (11) p. 153. n. 1239. & <lb/># ſeq. <lb/>Vectis. (1) p. 25. n. 103. 104. <lb/># hujus proprietates. n. 103. & ſeq. <lb/>Velocitas. (1) p. 15. n. 53. <lb/>Venus. (11) p. 111. n. 959. <lb/>Via lactea. (11) p. 145. n. 1199. <lb/>-- eſt congeries Stellarum. n. 1200. <lb/>Vibrationes Pendulorum. vide Pen-<lb/># dula. <lb/>-- Fibrarum. vide Fibras. <lb/>Viſus. (11) p. 45. n. 716. <lb/>Viſio diſtincta. ibid. n. 717. p. 47. n. <lb/># 724. p. --48. n. 728. <lb/>confuſa. ibid. n. 718. <lb/>judicium de diſtantiâ. p. 48. n. 729. <lb/># & ſeq. <lb/>magnitudo apparens. ibid. n. 733. <lb/></note> <pb file="0743" n="815"/> <note position="right" xml:space="preserve"> <lb/>judicium de magnitudine. ibid. n. 734. <lb/>quidam objecta propinqua, & longin-<lb/># qua, diſtinctè vident, intermedia <lb/># confuſe. p. 47. n. 725. <lb/>Viſio per vitrum planum. (11) p. 50. n. <lb/># 739. & ſeq. <lb/>--per lentem convexam. ibid. n. 745. <lb/># & ſeq. <lb/>--per lentem cavam. (11) p. 53. <lb/># n. 757. <lb/>objecta in aquâ viſa ampliſicantur. <lb/># (11) p. 50. n. 744. <lb/>Vitra uſtoria. (11) p. 41. n. 703. <lb/>Vitrum lucidum ex atritu. (11) p. 2. n. <lb/># 553. p. 5. n. 557. 558. p. 7. n. 568. <lb/># 569. <lb/>Unda in fluidi ſuperficie. (1) p. 147. n. <lb/># 403. <lb/>hujus latitudo. p. 148. n. 404. <lb/>harum motus, reflectio &c. p. 147. n. <lb/># 402. p. 148. n. 405. & ſeq. <lb/>harum celeritas. p. 152. n. 415. 416. <lb/>Unda in aëre. p. 174. n. 476. <lb/>harum motus, celeritas &c. p. 175. <lb/># n. 477. & ſeq. <lb/>Uniſonus. (1) p. 185. n. 526. <lb/>Z. <lb/>Zenit. (11) p. 133. n. 1099. <lb/>Zodiacus. (11) p. 119. n. 1008. <lb/># 1009. <lb/>-- hujus ſigna. n. 999. p. 144. n. <lb/># 1191. 1192. <lb/>Zonæ. (11) p. 140. n. 1159. & ſeq. <lb/>phænomena Zonarum Frigidarum. n. <lb/># 1165. 1170. & ſeq. p. 142. n. 1176. <lb/># & ſeq. <lb/>-- Temperatarum. n. 1 65. & ſeq. <lb/># p. 142. n. 1176. & ſeq. <lb/>-- Torridæ Zonæ n. 1163. 1@67. <lb/># p. 142. n. 1179. & ſeq. <lb/></note> </div> <div xml:id="echoid-div2916" type="section" level="1" n="684"> <head xml:id="echoid-head890" xml:space="preserve">FINIS.</head> <head xml:id="echoid-head891" xml:space="preserve">CATALOGUE</head> <head xml:id="echoid-head892" xml:space="preserve">Des LIVRES Nouvellement Imprimez à LEIDE, chez <lb/>PIERRE <emph style="sc">VANDER</emph> Aa.</head> <p> <s xml:id="echoid-s19282" xml:space="preserve">Index alter Plantarum quae in Horto <lb/>Academico Lugduno-Batavo aluntur, <lb/>conſcriptus ab Hermanno Boerhaave, in 4°. <lb/></s> <s xml:id="echoid-s19283" xml:space="preserve">2 voll. </s> <s xml:id="echoid-s19284" xml:space="preserve">cum figuris.</s> <s xml:id="echoid-s19285" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19286" xml:space="preserve">-- Sermo Academicus de Chemia <lb/>ſuos Errores Expurgante, quem habuit, <lb/>Quum Chemiæ Profeſſionem in Acade-<lb/>mia Lugduno - Batavâ auſpicaretur XXI. <lb/></s> <s xml:id="echoid-s19287" xml:space="preserve">Septembris 1718. </s> <s xml:id="echoid-s19288" xml:space="preserve">4.</s> <s xml:id="echoid-s19289" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19290" xml:space="preserve">Oeuvres diverſes de Phyſique & </s> <s xml:id="echoid-s19291" xml:space="preserve">Me-<lb/>chanique, de Mrs. </s> <s xml:id="echoid-s19292" xml:space="preserve">C. </s> <s xml:id="echoid-s19293" xml:space="preserve">& </s> <s xml:id="echoid-s19294" xml:space="preserve">P. </s> <s xml:id="echoid-s19295" xml:space="preserve">Perrault, de <lb/>P Academie Royale des Sciences & </s> <s xml:id="echoid-s19296" xml:space="preserve">de l’ Aca-<lb/>demie Françoiſe. </s> <s xml:id="echoid-s19297" xml:space="preserve">in 4. </s> <s xml:id="echoid-s19298" xml:space="preserve">2 voll. </s> <s xml:id="echoid-s19299" xml:space="preserve">avec figures.</s> <s xml:id="echoid-s19300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19301" xml:space="preserve">La plus Nouvelle Academie Univerſelle <lb/>des Jeux, ou Divertiſſemens innocens, <lb/>contenant, les Regles des Jeux de Car-<lb/>ies permis; </s> <s xml:id="echoid-s19302" xml:space="preserve">des Echecs, du Trictrac, du <lb/>Revertier, du Toute-Table, du Tourne-<lb/>Cafe, des Dames Rabatues, du Plain & </s> <s xml:id="echoid-s19303" xml:space="preserve"><lb/>du Toc, comme auſſi, celles du Billard, <lb/>du Mail, de la Courte-Paume, de la Lon-<lb/>gue-Paume, &</s> <s xml:id="echoid-s19304" xml:space="preserve">c. </s> <s xml:id="echoid-s19305" xml:space="preserve">avec des Inſtructions <lb/>@ciles pour apprendre à les bien joüer. <lb/></s> <s xml:id="echoid-s19306" xml:space="preserve">Derniere Edition revûe, corrigée, aug-<lb/>mentée & </s> <s xml:id="echoid-s19307" xml:space="preserve">enrichie de Figures en taille-dou-<lb/>ce. </s> <s xml:id="echoid-s19308" xml:space="preserve">in 12°. </s> <s xml:id="echoid-s19309" xml:space="preserve">2 voll.</s> <s xml:id="echoid-s19310" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19311" xml:space="preserve">Recueil de pluſieurs Machines, de nou-<lb/>velle invention. </s> <s xml:id="echoid-s19312" xml:space="preserve">Ouvrage Poſthume de <lb/>Mr. </s> <s xml:id="echoid-s19313" xml:space="preserve">Claude Perrault, de l’Académie <lb/>Royale des Sciences, Docteur en Me-<lb/>decine, dela Faculté de Paris. </s> <s xml:id="echoid-s19314" xml:space="preserve">in 4°. </s> <s xml:id="echoid-s19315" xml:space="preserve">avec <lb/>figures.</s> <s xml:id="echoid-s19316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19317" xml:space="preserve">Les Colloques d’Eraſme, Owvrage très-<lb/>intéreſſant; </s> <s xml:id="echoid-s19318" xml:space="preserve">par la Diverſité des Sujets, par <lb/>l’ Enjoument, & </s> <s xml:id="echoid-s19319" xml:space="preserve">pour l’Utilité Mo ale: <lb/></s> <s xml:id="echoid-s19320" xml:space="preserve">Nouvelle Traduction, par Monſr.</s> <s xml:id="echoid-s19321" xml:space="preserve"> <pb file="0744" n="816" rhead="CATAL. DES LIVR. NOUV."/> Gueudeville, avec des Notes, & </s> <s xml:id="echoid-s19322" xml:space="preserve">des figu-<lb/>res trèsingenieuſes. </s> <s xml:id="echoid-s19323" xml:space="preserve">in 12°. </s> <s xml:id="echoid-s19324" xml:space="preserve">6 voll.</s> <s xml:id="echoid-s19325" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19326" xml:space="preserve">Voyages tres-renommées des S<emph style="super">rs</emph>. </s> <s xml:id="echoid-s19327" xml:space="preserve">Olearius <lb/>& </s> <s xml:id="echoid-s19328" xml:space="preserve">Mandelſlo, en Moſcovie, Tartarie, <lb/>Perſe, Indes Orientales, &</s> <s xml:id="echoid-s19329" xml:space="preserve">c. </s> <s xml:id="echoid-s19330" xml:space="preserve">&</s> <s xml:id="echoid-s19331" xml:space="preserve">c. </s> <s xml:id="echoid-s19332" xml:space="preserve">avec tres-<lb/>belles figures, in folio, 4 voll.</s> <s xml:id="echoid-s19333" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19334" xml:space="preserve">Les Comedies de Plaute, nouvellement <lb/>Traduites en Stile libre, naturel & </s> <s xml:id="echoid-s19335" xml:space="preserve">naif; <lb/></s> <s xml:id="echoid-s19336" xml:space="preserve">avec des Notes & </s> <s xml:id="echoid-s19337" xml:space="preserve">des Reflexions enjouées, <lb/>agreables & </s> <s xml:id="echoid-s19338" xml:space="preserve">utiles, deCritique, d’ Antiqui-<lb/>té, de Morale & </s> <s xml:id="echoid-s19339" xml:space="preserve">de Politique; </s> <s xml:id="echoid-s19340" xml:space="preserve">par Monſieur <lb/>Gueudeville. </s> <s xml:id="echoid-s19341" xml:space="preserve">Enrichi d’ Eſtampes en Taille-<lb/>douce à la Tête de chaque Tome & </s> <s xml:id="echoid-s19342" xml:space="preserve">de cha-<lb/>que Comedie. </s> <s xml:id="echoid-s19343" xml:space="preserve">Diviſées en dix Tomes. </s> <s xml:id="echoid-s19344" xml:space="preserve">en <lb/>grand douze.</s> <s xml:id="echoid-s19345" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19346" xml:space="preserve">Principia Trigonometriæ; </s> <s xml:id="echoid-s19347" xml:space="preserve">ſuccinctè <lb/>demonſtrata; </s> <s xml:id="echoid-s19348" xml:space="preserve">Auctore Joh. </s> <s xml:id="echoid-s19349" xml:space="preserve">Wilſon. </s> <s xml:id="echoid-s19350" xml:space="preserve">8°.</s> <s xml:id="echoid-s19351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19352" xml:space="preserve">Moſis Maimouidis Conſtitutiones de <lb/>Siclis; </s> <s xml:id="echoid-s19353" xml:space="preserve">quas Latinitate donavit & </s> <s xml:id="echoid-s19354" xml:space="preserve">notis <lb/>illuſtravit Joannis Eſgers, 4°.</s> <s xml:id="echoid-s19355" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19356" xml:space="preserve">Recueil des belles Tailles douces, en ma-<lb/>niere Noire, Peints, Deſſinées, ou Gravées <lb/>par les celebres Maitres, F. </s> <s xml:id="echoid-s19357" xml:space="preserve">Parmens, Spa-<lb/>gnolet, W. </s> <s xml:id="echoid-s19358" xml:space="preserve">Vaillant, J van Soomeren, D. <lb/></s> <s xml:id="echoid-s19359" xml:space="preserve">Teniers, P. </s> <s xml:id="echoid-s19360" xml:space="preserve">Picart, & </s> <s xml:id="echoid-s19361" xml:space="preserve">autres. </s> <s xml:id="echoid-s19362" xml:space="preserve">in fol.</s> <s xml:id="echoid-s19363" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19364" xml:space="preserve">Divers Owvrages de belles Figures; </s> <s xml:id="echoid-s19365" xml:space="preserve">Peints, <lb/>Deſſinées, ou Gravées par divers Maîtres <lb/>très Renommez, ſavoir: </s> <s xml:id="echoid-s19366" xml:space="preserve">A Carats, G. </s> <s xml:id="echoid-s19367" xml:space="preserve">Re-<lb/>ni, A. </s> <s xml:id="echoid-s19368" xml:space="preserve">Corregio, J. </s> <s xml:id="echoid-s19369" xml:space="preserve">Callot, Guarcin, S. <lb/></s> <s xml:id="echoid-s19370" xml:space="preserve">Vouet, J. </s> <s xml:id="echoid-s19371" xml:space="preserve">le Pautre, Rembrant, A. </s> <s xml:id="echoid-s19372" xml:space="preserve">F. </s> <s xml:id="echoid-s19373" xml:space="preserve">Van-<lb/>der Meulen, A. </s> <s xml:id="echoid-s19374" xml:space="preserve">Collart, & </s> <s xml:id="echoid-s19375" xml:space="preserve">autres. </s> <s xml:id="echoid-s19376" xml:space="preserve">in fol.</s> <s xml:id="echoid-s19377" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19378" xml:space="preserve">Marmorea Baſis Coloſſi Tiberio Cæ-<lb/>ſari erecti ob Civitates Aſiæ reſtitutas <lb/>poſt horrendos terræ tremores. </s> <s xml:id="echoid-s19379" xml:space="preserve">Primus <lb/>trans Alpes vulgavit, revocavit, notis <lb/>uberioribus & </s> <s xml:id="echoid-s19380" xml:space="preserve">novis obſervationibus ac <lb/>nummis illuſtravit Laurentius Theodo-<lb/>dorus Gronovius, in Octavo.</s> <s xml:id="echoid-s19381" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19382" xml:space="preserve">Vaillant diſcours ſur la ſtructure des Fleurs, <lb/>leurs differences & </s> <s xml:id="echoid-s19383" xml:space="preserve">l’uſage de leurs Par-<lb/>ties; </s> <s xml:id="echoid-s19384" xml:space="preserve">pr@noncé à l’Ouverture du Jardin Royal <lb/>de Paris, le X. </s> <s xml:id="echoid-s19385" xml:space="preserve">Jour du Mois de Juin 1717. <lb/></s> <s xml:id="echoid-s19386" xml:space="preserve">& </s> <s xml:id="echoid-s19387" xml:space="preserve">l’ Etabliſſement de trois nouveaux Genres <lb/>de Plantes, l’Araliaſtrum, la Scherardia, <lb/>la Boerhaavia. </s> <s xml:id="echoid-s19388" xml:space="preserve">Avec la Deſcription de deux <lb/>nouvelles Plantes, rapportée au dernier <lb/>Genre, in 4°.</s> <s xml:id="echoid-s19389" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19390" xml:space="preserve">Scamozzi Oeuvres d’ Architecture, conte-<lb/>nuës dans ſon Idée de l’Architecture Univer-<lb/>ſelle; </s> <s xml:id="echoid-s19391" xml:space="preserve">dont les Regles des cinq Ordres, que <lb/>le ſixiéme livre contient, ont ététraduites en <lb/>François par Mr. </s> <s xml:id="echoid-s19392" xml:space="preserve">Auguſtin Charles d’A-<lb/>viler, & </s> <s xml:id="echoid-s19393" xml:space="preserve">les autres parties traduites nouvel-<lb/>olement par Mr Du Ry; </s> <s xml:id="echoid-s19394" xml:space="preserve">avec les Planches <lb/>riginales: </s> <s xml:id="echoid-s19395" xml:space="preserve">Le tout revu & </s> <s xml:id="echoid-s19396" xml:space="preserve">exacte ment cor-<lb/>rigé ſur l’Original Italien. </s> <s xml:id="echoid-s19397" xml:space="preserve">On y a joint auſſi <lb/>pluſieurs nouveaux Deſſeins des plus beaux <lb/>Edifices de Rome, dont l’Auteur parle dans <lb/>ſon Ouvrage. </s> <s xml:id="echoid-s19398" xml:space="preserve">in fol.</s> <s xml:id="echoid-s19399" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19400" xml:space="preserve">Poſt Oewvres d’Architecture, in fol. </s> <s xml:id="echoid-s19401" xml:space="preserve">avec <lb/>très belles figures.</s> <s xml:id="echoid-s19402" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19403" xml:space="preserve">Vignole Regles descinqOrdres d’Architectu-<lb/>re, avec pluſieurs Augmentations de Michel <lb/>Ange Buonaroti, Nowvellement revûës, <lb/>corrigées & </s> <s xml:id="echoid-s19404" xml:space="preserve">augmentées par Mr. </s> <s xml:id="echoid-s19405" xml:space="preserve">Dury, 8°.</s> <s xml:id="echoid-s19406" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19407" xml:space="preserve">Vingboons Oewvres d’Architecture, conte-<lb/>nant les plans, elevations & </s> <s xml:id="echoid-s19408" xml:space="preserve">deſcription des <lb/>principaux & </s> <s xml:id="echoid-s19409" xml:space="preserve">desplus nowveaux Edifices par <lb/>lui ordonnéz dans le dernier agrandiſſement <lb/>de la Ville d’Amſterdam & </s> <s xml:id="echoid-s19410" xml:space="preserve">autres endroits <lb/>de ces Provinces, fol. </s> <s xml:id="echoid-s19411" xml:space="preserve">2 voll. </s> <s xml:id="echoid-s19412" xml:space="preserve">avec figures.</s> <s xml:id="echoid-s19413" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19414" xml:space="preserve">Delices de la Suiſſe, ou l’on void tout ce <lb/>qu’il y a de plus remarquable dans la Suiſſe, <lb/>& </s> <s xml:id="echoid-s19415" xml:space="preserve">dans ſes Alliez qui compoſent le Louable <lb/>Corps Helvetique: </s> <s xml:id="echoid-s19416" xml:space="preserve">la deſcription des Villes, <lb/>Bourgs, Chateaux; </s> <s xml:id="echoid-s19417" xml:space="preserve">la nature de l’air & </s> <s xml:id="echoid-s19418" xml:space="preserve"><lb/>du terroir; </s> <s xml:id="echoid-s19419" xml:space="preserve">les Antiquitez du Pays, & </s> <s xml:id="echoid-s19420" xml:space="preserve">les <lb/>raretez de la Nature; </s> <s xml:id="echoid-s19421" xml:space="preserve">le Naturel, les Mœurs <lb/>& </s> <s xml:id="echoid-s19422" xml:space="preserve">la Religion des habitans; </s> <s xml:id="echoid-s19423" xml:space="preserve">leurs Gouver-<lb/>nemens differens, leurs Alliances mutuelles <lb/>& </s> <s xml:id="echoid-s19424" xml:space="preserve">leurs interëts communs; </s> <s xml:id="echoid-s19425" xml:space="preserve">avec un Memoi-<lb/>re inſtructif ſur les cauſes de la guerre qui eſt <lb/>arrivée en Suiſſe, dans l’ An 1712. </s> <s xml:id="echoid-s19426" xml:space="preserve">Par le <lb/>Sr. </s> <s xml:id="echoid-s19427" xml:space="preserve">Gottlieb Kypſeler de Munſter, le tout <lb/>enrichi de très belles figures. </s> <s xml:id="echoid-s19428" xml:space="preserve">& </s> <s xml:id="echoid-s19429" xml:space="preserve">CartesGeo-<lb/>graphiques deſſinées ſur les originaux in, <lb/>12°. </s> <s xml:id="echoid-s19430" xml:space="preserve">4 voll.</s> <s xml:id="echoid-s19431" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s19432" xml:space="preserve">Oewvres de Mr. </s> <s xml:id="echoid-s19433" xml:space="preserve">Mariotte, de I’Acadé-<lb/>mie Royale des Sciences; </s> <s xml:id="echoid-s19434" xml:space="preserve">Diviſées en <lb/>deux tomes, comprenent tous les Traitez de <lb/>cet Auteur, tant ceux qui avoient déja paru <lb/>ſéparément, que ceux qui n’avoient pas en-<lb/>core été pubiez; </s> <s xml:id="echoid-s19435" xml:space="preserve">Imprimées ſur les Exem-<lb/>plaires les plus exacts & </s> <s xml:id="echoid-s19436" xml:space="preserve">les plus complets; <lb/></s> <s xml:id="echoid-s19437" xml:space="preserve">Revuës & </s> <s xml:id="echoid-s19438" xml:space="preserve">corrigées de nouveau. </s> <s xml:id="echoid-s19439" xml:space="preserve">in 4°. </s> <s xml:id="echoid-s19440" xml:space="preserve">2 voll. </s> <s xml:id="echoid-s19441" xml:space="preserve"><lb/>avec figures.</s> <s xml:id="echoid-s19442" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2917" type="section" level="1" n="685"> <head xml:id="echoid-head893" xml:space="preserve">FINIS.</head> <pb file="0745" n="817"/> <pb file="0745a" n="818"/> </div> <div xml:id="echoid-div2918" type="section" level="1" n="686"> <head xml:id="echoid-head894" style="it" xml:space="preserve">Tom. II. In fine poſt Indicem.</head> <head xml:id="echoid-head895" xml:space="preserve">USUS TABULÆ.</head> <p> <s xml:id="echoid-s19443" xml:space="preserve">CUm ſolus tomus primus de novo editus ſit, <lb/>inde reſpectu tomi ſecundi duo effluxere <lb/>incom moda, 1. </s> <s xml:id="echoid-s19444" xml:space="preserve">numeri in margine, qui propo-<lb/>ſitiones primi tomi indicant, propter mutatos <lb/>numeros in ſecunda editione, innutiles fiunt. <lb/></s> <s xml:id="echoid-s19445" xml:space="preserve">2. </s> <s xml:id="echoid-s19446" xml:space="preserve">Eadem de cauſa Index rerum, qui toti operi <lb/>deſtinatus eſt, tantum in tomo ſecundo uſu venit. </s> <s xml:id="echoid-s19447" xml:space="preserve"><lb/>Tabella adjecta ambo hæc tollit incommoda; </s> <s xml:id="echoid-s19448" xml:space="preserve"><lb/>ubi in margine tomi ſecundi numerus datur mi-<lb/>nor 543.</s> <s xml:id="echoid-s19449" xml:space="preserve">, qui ultimus eſt tomi primi in editione <lb/>prima, quærendus hìc eſt in prima columna <lb/>Tabellæ, & </s> <s xml:id="echoid-s19450" xml:space="preserve">numerus qui in ſecunda ipſi reſpon-<lb/>det eſt numerus in ſecunda editione quærendus.</s> <s xml:id="echoid-s19451" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19452" xml:space="preserve">Eodem modo ubi in indice agitur de tomo <lb/>primo, pag. </s> <s xml:id="echoid-s19453" xml:space="preserve">negligenda eſt, ſed numberus, qui <lb/>n. </s> <s xml:id="echoid-s19454" xml:space="preserve">notatur, quærendus eſt in hac tabella, ut <lb/>habeamus numerum in margine ſecundæ editio-<lb/>nis quærendus, & </s> <s xml:id="echoid-s19455" xml:space="preserve">qui propoſitioni in indi-<lb/>ce indicatæ reſpondet.</s> <s xml:id="echoid-s19456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19457" xml:space="preserve">Compendii cauſa tantum in hac tabella no-<lb/>tantur numeri, qui aut in margine tomi ſecun-<lb/>di, aut in indice ad calcem hujus, reperiuntur.</s> <s xml:id="echoid-s19458" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div2919" type="section" level="1" n="687"> <head xml:id="echoid-head896" xml:space="preserve">TABULA</head> <head xml:id="echoid-head897" style="it" xml:space="preserve">Demonſtrans quorundam numerorum 1<emph style="super">æ</emph>. & 2<emph style="super">dæ</emph>. Editionis <lb/>convenientiam.</head> <note position="right" xml:space="preserve"> <lb/>Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. # Ed. 1<emph style="super">a</emph>. # Ed. 2<emph style="super">a</emph>. <lb/>1 # 1 # 44 # 70 # 105 # 175 # 158 # 290 # # # 272 # 707 # 356 # 797 # 463 # 1120 <lb/>2 # 2 # 47 # 86 # 112 # 186 # # # 225 # {354 \\ 396 # 280 # 720 # 358 # 801 # 464 # 1121 <lb/>3 # 3 # 48 # 87 # 113 # 188 # 161 # {296 \\ 311 \\ 551 # # # 281 # 722 # 368 # 815 # 465 # 1121 <lb/>4 # 4 # 49 # 88 # 114 # 190 # # # # # 282 # 726 # 370 # 817 # 467 # 1124 <lb/>5 # 6 # 50 # 89 # 115 # 192 # 162 # 552 # 226 {355 \\ 397 # # 283 # 729 # 378 # 827 # 468 # 1125 <lb/>6 # 7 # 51 # 90 # 118 # 200 # 166 # 476 # # # 284 # 733 # 379 # 837 # 469 # 1126 <lb/>7 # 8 # 52 # 93 # # # # # 231 # 361 # 285 # 734 # 390 # 856 # 470 # 1127 <lb/>8 # 9 # 53 # 94 # 119 {204 \\ 205 \\ 212 # # 170 # {490 \\ 491 # # # # 286 # 735 # 391 # 857 # 472 # 1130 <lb/>9 # 10 # 55 # 96 # # # # # 232 {363 \\ 409 # # 287 # 736 # 392 # 858 # 474 # 1133 <lb/>10 # 11 # 56 # 97 # # # 171 # 519 # # # 288 # 737 # 398 # 868 # 476 # 1136 <lb/>11 # 12 # 57 # 104 # 120 {206 \\ 215 # # 175 # 473 # 234 # 367 # 290 # 742 # 399 # 869 # 477 # 1137 <lb/>13 # 15 # 62 # 450 # # # 177 # 557 # 235 # 369 # 292 # 748 # 402 # 872 # 502 # 1168 <lb/>14 # 17 # 63 # 447 # 121 # 208 # 179 # 565 # # # 295 # 753 # 403 # 873 # 504 # 1170 <lb/># # 64 # 470 # 122 # 217 # 190 # 246 # 236 {371 \\ 408 # # 296 # 754 # 404 # 874 # 508 # 1182 <lb/>15 {19 \\ 20 # # 67 # 107 # 123 # 218 # 191 # 615 # # # 306 # 769 # 405 # 875 # 515 # 1190 <lb/># # 72 # 113 # 124 # 243 # 192 # 604 # 237 # 373 # 309 # 774 # 415 # 889 # 516 # 1191 <lb/>20 # 25 # 73 # 114 # 125 # 245 # 193 # 612 # # # 312 # 778 # 416 # 890 # 525 # 1200 <lb/>26 # 23 # 75 # 116 # 126 # 247 # 196 # 220 # 239 {376 \\ 409 # # 314 # 781 # 417 # 1050 # 526 # 1201 <lb/>28 # 48 # 77 # 118 # 127 # 249 # 197 # 223 # # # 315 # 784 # 418 # 1051 # 527 # 1202 <lb/>29 # 49 # 78 # 119 # 128 # 250 # 198 # 221 # # # 317 # 786 # 424 # 1060 # 528 # 1203 <lb/>30 # 50 # 79 # 120 # 129 # 251 # 203 # 232 # 241 {381 \\ 411 # # 318 # 788 # 426 # 1063 # 529 # 1204 <lb/>31 # 51 # 82 # 123 # 131 # 255 # 204 # 233 # # # 319 # 891 # 429 # 1066 # 530 # 1205 <lb/>33 # 55 # 83 # 124 # # # 208 # 326 # # # 320 # 956 # 431 # 1092 # 531 # 1206 <lb/># # 84 # 125 # 132 {276 \\ 546 # # 210 # 328 # 243 {385 \\ 390 # # 330 # 942 # 435 # 1093 # 532 # 1207 <lb/>35 {56 \\ 78 # # 85 # 126 # # # 217 # 343 # # # 331 # 957 # # # 536 # 1211 <lb/># # 86 # 127 # 139 # 235 # 218 # 344 # 244 # 668 # 334 # 954 # 439 \\ 440} # 1096 # 538 # 1214 <lb/>36 # 57 # 87 # 128 # 143 # 239 # 219 # 345 # 249 # 673 # 335 # 958 # # # 539 # 1215 <lb/># # 91 # 135 # 144 # 263 # 220 # 346 # 251 # 675 # 336 # 928 # 442 # 1099 # 542 # 1218 <lb/>37 {59 \\ 85 # # 92 # 137 # 151 # 273 # 221 # 347 # 257 # 686 # 339 # 971 # 454 # 1111 # 543 # 1219 <lb/># # 95 # 143 # 153 # 278 # 222 # 348 # 262 # 692 # 346 # 977 # 457 # 1114 # # <lb/># # 96 # 144 # 154 # 279 # 223 # 349 # 266 # 697 # # # 458 # 1115 # # <lb/>38 {58 \\ 80 # # 102 # 155 # # # 224 # 351 # 269 # 702 # 347 \\ 351} # 965 # 459 # 1116 # # <lb/># # 103 # 172 # 157 {288 \\ 307 # # # # 270 # 704 # # # 461 # 1118 # # <lb/>40 # 61 # 104 # 174 # # # # # 271 # 705 # 354 # 794 # 462 # 1119 # # <lb/></note> <pb file="0746" n="819"/> <pb file="0747" n="820"/> <pb file="0748" n="821"/> <pb file="0749" n="822"/> <pb file="0750" n="823"/> </div></text> </echo>