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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:H9ZYCGQ0.xml</dcterms:identifier> <dcterms:creator identifier="GND:118785516">Musschenbroek, Petrus van</dcterms:creator> <dcterms:title xml:lang="la">Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1729</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> <log>0335.jpg was not typed during DE, but by KT during postprocessing 0079.jpg: replaced q by quote</log> </metadata> <text xml:lang="la" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/> <pb file="0002" n="2"/> <pb file="0003" n="3"/> <handwritten/> <pb file="0004" n="4"/> <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">PETRI <emph style="sc">VAN</emph> MUSSCHENBROEK</emph></head> <head xml:id="echoid-head2" style="it" xml:space="preserve">A. L. M. Med. & Phil. D. Phil. & Matheſ. <lb/>Profeſſ. in Acad. Ultraj.</head> <head xml:id="echoid-head3" xml:space="preserve"><emph style="red">PHYSICÆ</emph> <lb/>EXPERIMENTALES, <lb/>ET <lb/><emph style="red">GEOMETRICÆ,</emph> <lb/>DE <lb/>MAGNETE, TUBORUM CAPILLARIUM VITREORUM-<lb/>QUE SPECULORUM ATTRACTIONE, MAGNITUDINE <lb/>TERRÆ, COHÆRENTIA CORPORUM FIRMORUM</head> <head xml:id="echoid-head4" xml:space="preserve"><emph style="red">DISSERTATIONES:</emph> <lb/>UTET <lb/><emph style="red">EPHEMERIDES</emph> <lb/>METEOROLOGICÆ ULTRAJECTINÆ.</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-head5" xml:space="preserve">LUGDUNI BATAVORUM, <lb/>Apud <emph style="red">SAMUELEM LUCHTMANS,</emph> <emph style="sc">MDCCXXIX.</emph></head> <pb file="0006" n="6"/> <handwritten/> <pb file="0007" n="7"/> </div> <div xml:id="echoid-div4" type="section" level="1" n="4"> <head xml:id="echoid-head6" style="it" xml:space="preserve">NOBILISSIMIS ET AMPLISSIMIS</head> <head xml:id="echoid-head7" xml:space="preserve">VIRIS <lb/>LUCÆ <emph style="sc">VAN</emph> VOORST, <lb/>JCTO. <lb/>ET <lb/>HENRICO <emph style="sc">VAN</emph> SOESTDYK, <lb/>INCLYTÆ URBIS <lb/>TRAJECTINÆ <lb/>CONSULIBUS, <lb/>HAS DISSERTATIONES <lb/>EA QUA PAR EST <lb/>OBSERVANTIA</head> <head xml:id="echoid-head8" xml:space="preserve">D. D. D.</head> <head xml:id="echoid-head9" xml:space="preserve">PETRUS <emph style="sc">VAN</emph> MUSSCHENBROEK.</head> <pb file="0008" n="8"/> <pb file="0009" n="9"/> <figure> <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01"/> </figure> </div> <div xml:id="echoid-div5" type="section" level="1" n="5"> <head xml:id="echoid-head10" xml:space="preserve">LECTORI SALUTEM.</head> <p style="it"> <s xml:id="echoid-s1" xml:space="preserve">Quicquid de corporibus intelligunt mortales, <lb/>primum obſervationibus ſenſuum ope per-<lb/>actis; </s> <s xml:id="echoid-s2" xml:space="preserve">tum experimentis, caſu vel indu-<lb/>ſtria cum iis inſtitutis; </s> <s xml:id="echoid-s3" xml:space="preserve">tandem ratiocinio <lb/>ex obſervationibus aut Experimentis deducto, <lb/>debetur. </s> <s xml:id="echoid-s4" xml:space="preserve">Idcirco phænomena, quæ corpora <lb/>edunt quâcunque poſita in occaſione aut loco, ſunt data & </s> <s xml:id="echoid-s5" xml:space="preserve"><lb/>ratiocinii materies; </s> <s xml:id="echoid-s6" xml:space="preserve">ex quibus ſedulo collectis, ſollicite ad-<lb/>notatis, & </s> <s xml:id="echoid-s7" xml:space="preserve">inter ſe comparatis, geometrice, rationis viri-<lb/>bus colligi poſſunt, corporum proprietates, agendi virtutes, <lb/>harum proportiones, cauſæ, & </s> <s xml:id="echoid-s8" xml:space="preserve">effectus.</s> <s xml:id="echoid-s9" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s10" xml:space="preserve">Quo igitur plura cognoſcuntur corporum phænomena, eo <lb/>uberior ſuppeditatur materia ratiocinio, quod cæteroquin <lb/>brevi ad ſilentium reduceretur, datâ obſervationum pe-<lb/>nuriâ.</s> <s xml:id="echoid-s11" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s12" xml:space="preserve">Quod cum a multis retro temporibus animadverſum fuit, <lb/>nonnulli Philoſophi in colligendis obſervationibus & </s> <s xml:id="echoid-s13" xml:space="preserve">capiendis <lb/>Experimentis operam poſuerunt, præcipuè tamen elapſo, <lb/>& </s> <s xml:id="echoid-s14" xml:space="preserve">quod nunc decurrit, ſeculo: </s> <s xml:id="echoid-s15" xml:space="preserve">hinc eorum nata inſignis <pb file="0010" n="10" rhead="PRÆFATIO."/> multitudo, quam ſi quis prima fronte adſpiciat, phyſicam, <lb/>ſcientiam ditiſſimam, & </s> <s xml:id="echoid-s16" xml:space="preserve">ad magnam uſque amplitudinem <lb/>provectam judicaret: </s> <s xml:id="echoid-s17" xml:space="preserve">Verum ſi penitius ſingula inſpiciamus, <lb/>notando, quænam tentamina ſint accurate capta, rite deſcri-<lb/>pta, ita ut nihil omiſſum, nihil alieni ſit additum, merito <lb/>dubitandum, an quidem ulla ſcientia pauperior, pluribus <lb/>contaminata erroribus, aut incunabulis ſit propior.</s> <s xml:id="echoid-s18" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s19" xml:space="preserve">Homines enim, inquit magnus VERULAMIUS, do-<lb/>cti ſupini ſane & </s> <s xml:id="echoid-s20" xml:space="preserve">faciles, rumores quosdam Experientiæ, <lb/>& </s> <s xml:id="echoid-s21" xml:space="preserve">quaſi famas & </s> <s xml:id="echoid-s22" xml:space="preserve">auras ejus, ad Philoſophiam ſuam vel <lb/>conſtituendam vel confirmandam exceperunt, atque illis <lb/>nihilominus pondus legitimi teſtimonii attribuerunt: <lb/></s> <s xml:id="echoid-s23" xml:space="preserve">veluti ſi regnum aliquod aut ſtatus, non ex litteris <lb/>& </s> <s xml:id="echoid-s24" xml:space="preserve">relationibus a Legatis & </s> <s xml:id="echoid-s25" xml:space="preserve">nunciis fide dignis miſ-<lb/>ſis, ſed ex urbanorum ſermunculis & </s> <s xml:id="echoid-s26" xml:space="preserve">ex triviis con-<lb/>ſilia ſua & </s> <s xml:id="echoid-s27" xml:space="preserve">negotia gubernaret: </s> <s xml:id="echoid-s28" xml:space="preserve">omnino talis in Phi-<lb/>loſophiam adminiſtratio, quatenus ad experientiam <lb/>introducta eſt; </s> <s xml:id="echoid-s29" xml:space="preserve">nil fere debitis modis exquiſitum, <lb/>nil verificatum, nil numeratum, nil appenſum, nil <lb/>demenſum reperitur.</s> <s xml:id="echoid-s30" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s31" xml:space="preserve">Quibus elapſo ſeculo perſpectis immenſum pondus nugarum <lb/>ex Philoſophia eliminarunt Verulamius, Helmontius, Galilæus, <lb/>Torricellius, Mariottus, Redus, Boyleus, Newtonus, plureſque <lb/>alii, animo & </s> <s xml:id="echoid-s32" xml:space="preserve">ſolertia excellentes Viri, qui ad ſeverum examen <lb/>obſervationes aliorum revocantes, errores extemplo detexerunt, <lb/>ſuisque ſapientes præterea Experimentis, novam condere in-<lb/>choaverunt ſcientiam, ſtabilem & </s> <s xml:id="echoid-s33" xml:space="preserve">inconcuſſam.</s> <s xml:id="echoid-s34" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s35" xml:space="preserve">Horum veſtigia, quamvis impari paſſu, ſequi conatus, <pb file="0011" n="11" rhead="PRÆFATIO."/> plurima in diverſis corporibus feci ab aliquot retro annis pericula; <lb/></s> <s xml:id="echoid-s36" xml:space="preserve">idque eo lubentius, quod muneris ratio hæc poſtulabat, tum <lb/>neſcio quo impetu ſponte in ejuſmodi ſtudium trahebar; </s> <s xml:id="echoid-s37" xml:space="preserve">ea <lb/>harum Diſſertationum eſt origo, in quibus nonnulla, forte <lb/>minus buc uſque divulgata habentur, verum ſimul quoque a-<lb/>lia, quæ ab aliis inventa, novo tantum examini ſubjecta <lb/>fuerunt; </s> <s xml:id="echoid-s38" xml:space="preserve">ut quid verum, quid erroneum ſit, conſtaret.</s> <s xml:id="echoid-s39" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s40" xml:space="preserve">Auctorum nomina quandoque appoſita fuerunt; </s> <s xml:id="echoid-s41" xml:space="preserve">non ut do-<lb/>ctrinam oſtentarem, vel autoritatibus pugnarem, quæ in <lb/>Philoſophia nullius ſunt pretii, ſed ut inventoribus merita <lb/>adſcriberetur gloria.</s> <s xml:id="echoid-s42" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s43" xml:space="preserve">In inſtituendis experimentis omnem adhibui diligentiam & </s> <s xml:id="echoid-s44" xml:space="preserve"><lb/>attentionem ad phænomena; </s> <s xml:id="echoid-s45" xml:space="preserve">nonnullis perſpicaciam effugien-<lb/>tibus repetitum fuit periculum, imo inter dum frequentius, ut, ſi <lb/>non liceret omnes, ſaltem plurimos & </s> <s xml:id="echoid-s46" xml:space="preserve">craſſiores errores evitarem: <lb/></s> <s xml:id="echoid-s47" xml:space="preserve">verum nonnulla, uti ſunt ea, quæ Magnetem ſpectant, a <lb/>tam exiguis pendent circumſtantiis, ut vel centum oculatiſſi-<lb/>mos ſimul attendentes illudere poſſent, quæ animum non pa-<lb/>rum ſollicitum, ſed eo prudentiorem reddiderunt.</s> <s xml:id="echoid-s48" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s49" xml:space="preserve">Inchoavi tantummodo Magnetis examen, quod ſilentio pre-<lb/>mere in animum induxeram, cum nihil de bujus admir andi <lb/>Lapidis indole hucuſque detegere potueram, prudentia igitur, <lb/>ut ſobrie inter dum ratiocinarer, interdum Experimentum dun-<lb/>taxat commemorarem, ſuadebat. </s> <s xml:id="echoid-s50" xml:space="preserve">Verum amicorum votis <lb/>reſiſtere non licuit: </s> <s xml:id="echoid-s51" xml:space="preserve">interim in perpolienda hac doctrina, no-<lb/>viſque continuo obſervationibus & </s> <s xml:id="echoid-s52" xml:space="preserve">periculis capiendis de hoc <lb/>lapide occupor quotidie, ut aliquando ſupplere poſſim, quæ <lb/>nunc deficiunt, abſtruſumque ejus genium penitius perſcru-<lb/>ter.</s> <s xml:id="echoid-s53" xml:space="preserve"/> </p> <pb file="0012" n="12" rhead="PRÆFATIO."/> <p style="it"> <s xml:id="echoid-s54" xml:space="preserve">Doctrinam de Corporum firmitate etiam modo incepi, in <lb/>qua difficili materia longe plura reſtant, natura hic occul-<lb/>tante aut involvente cum aliis plurima. </s> <s xml:id="echoid-s55" xml:space="preserve">Quamobrem magni <lb/>atque præſtantes viri ſubinde aliquid humani in ea pertractan-<lb/>da paſſi ſunt, quod me non parum ſollicitum reddidit, haud <lb/>adeo magnifice de me ipſo ſentientem, quin cum iis in ſco-<lb/>pulos hos alioſve quandoque impegerim. </s> <s xml:id="echoid-s56" xml:space="preserve">Scrupulos auxerunt <lb/>tentaminum eventus, ſæpe adeo intricati, ut vel Alexandri <lb/>gladio opus eſſet, ſæpe quoque non parum ab aliorum obſer-<lb/>vatis abludentes, quod repetitis & </s> <s xml:id="echoid-s57" xml:space="preserve">ſæpe iiſdem Experi-<lb/>mentis occaſionem dedit. </s> <s xml:id="echoid-s58" xml:space="preserve">Hæc in uſum tironum ſunt con-<lb/>ſcripta, ut Experimenta, quorum maximam partem in Thea-<lb/>tro Academico demonſtratam viderunt, melius in memoriam <lb/>revocarent.</s> <s xml:id="echoid-s59" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s60" xml:space="preserve">Adjunguntur binæ Diſſertationes de Attractionibus Tubo-<lb/>rum Capillarium vitreorum, atque planorum ſpeculorum. </s> <s xml:id="echoid-s61" xml:space="preserve">Non <lb/>dubito fore pleroſque, qui Attractionis voce offendantur, <lb/>eamque contemnant, derideant, explodant: </s> <s xml:id="echoid-s62" xml:space="preserve">his autem ſi tanta <lb/>ſit animi æquitas, ut ſuſpenſo præjudicio Experimenta prius <lb/>legant, & </s> <s xml:id="echoid-s63" xml:space="preserve">inter ſe comparent; </s> <s xml:id="echoid-s64" xml:space="preserve">tum cauſam eorum eruere co-<lb/>nantibus facile apparebit, propter quasnam rationes hac voce <lb/>uſi fuimus. </s> <s xml:id="echoid-s65" xml:space="preserve">Hi ſciant præterea, Philoſophos, qui manum <lb/>operi admovendo, ſtrenue corpora explorarunt, multiſque <lb/>ſubjecerunt periculis, ſemper obſervaſſe & </s> <s xml:id="echoid-s66" xml:space="preserve">confeſſos fuiſſe in <lb/>Natura aliquid dari, quo corpora abſque externo cognito <lb/>impulſu ad ſe accederent; </s> <s xml:id="echoid-s67" xml:space="preserve">quod tamen rejectum perpetuo & </s> <s xml:id="echoid-s68" xml:space="preserve"><lb/>exploſum ab iis magiſtris, qui meditabundi tantum in <lb/>Muſeo ſedentes, cum ſuis opinionibus & </s> <s xml:id="echoid-s69" xml:space="preserve">hypotheſibus domi- <pb file="0013" n="13" rhead="PRÆFATIO."/> nari conſueverunt, nequaquam naturæ effectus obſervantes: <lb/></s> <s xml:id="echoid-s70" xml:space="preserve">non ex Hypotheſi quadam Attractionis vocabulum duxit apud <lb/>nos originem, quippe quodcunque Hypotheſin ſapit, non plu-<lb/>ris quam Romanenſem fabulam habemus.</s> <s xml:id="echoid-s71" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s72" xml:space="preserve">Addita eſt duplex Diſſertatio de Terræ Magnitudine, <lb/>quarum una, ſecundum Snellii menſuram, ab ipſo Autore <lb/>emendatam, nunc ê tenebris evoluta primum prodit; </s> <s xml:id="echoid-s73" xml:space="preserve">in al-<lb/>tera, menſuræ Snellianæ nonnulla adjunximus, atque correxi-<lb/>mus, accuratis organis angulos plurimorum Triangulorum <lb/>explorando de novo; </s> <s xml:id="echoid-s74" xml:space="preserve">quibus deprehendimus menſuram Cl. <lb/></s> <s xml:id="echoid-s75" xml:space="preserve">Picardi ferè accuratè cum noſtra conſentire.</s> <s xml:id="echoid-s76" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s77" xml:space="preserve">Ultimo tandem loco adnexui Ephemerides Meteorologicas, <lb/>morboſque, qui potiſſimum regnarunt Ultrajecti Anno <lb/>MDCCXXVIII; </s> <s xml:id="echoid-s78" xml:space="preserve">has eo incepi animo, ut quotannis ejuſmodi in <lb/>lucem emitterem, atque conſtaret ex plurimis tandem obſervatio-<lb/>nibus, quænam aëris temperies morborumEpidemicorum ſit cauſa; <lb/></s> <s xml:id="echoid-s79" xml:space="preserve">tum ut excitarem Medicos ad hanc partem Medicinæ, quam <lb/>Hippocrates excolere incepit, quam Sydenhamus, Ramazzi-<lb/>nus, Freindius, Scheuchzerus, aliique eleganter promoverunt, <lb/>perpoliendam, ut in generis humani utilitatem futuros <lb/>prædicere & </s> <s xml:id="echoid-s80" xml:space="preserve">avertere queamus morbos, quantum exſpe-<lb/>ctari ab induſtriâ humanâ poteſt: </s> <s xml:id="echoid-s81" xml:space="preserve">Cæterum errores Typogra-<lb/>phici hinc inde in opuſculum irrepſerunt, quod Leydæ im-<lb/>preſſum, alterius curæ committendum fuit, quos L. </s> <s xml:id="echoid-s82" xml:space="preserve">B, cor-<lb/>rigat optamus, & </s> <s xml:id="echoid-s83" xml:space="preserve">ut hos qualeſcunque primos conatus æqui bo-<lb/>nique conſulat.</s> <s xml:id="echoid-s84" xml:space="preserve"/> </p> <pb file="0014" n="14"/> </div> <div xml:id="echoid-div6" type="section" level="1" n="6"> <head xml:id="echoid-head11" xml:space="preserve">ERRATA TYPOGRAPHICA.</head> <note position="right" xml:space="preserve"> <lb/>Pag. # Lin. # Pro # Lege <lb/>17 # 6. # 12 pollicum # 12 linearum. <lb/>32 # 31. # {7/40} # {11/20} <lb/>94 # 26. # quorum # qui. <lb/>121 # 11. # actem # actum. <lb/>122 # 15. # Tab. V. fig. 1. # Tab. V. fig. 2. <lb/>304 # 18. # 0, 8 # 0, 08. <lb/>304 # 24. # 2°. # 9°. <lb/>485 # 13. # Tab. fig. XX. 1. # Tab. XX. fig. 1. <lb/>487 # 7. # fig. 10. # fig. 19. <lb/>487 # 12. # Tab. XX. # Tab. XXI. <lb/>488 # 2. # Tab XIX. # Tab. XX. <lb/>490 # 26. # Tab. XXI. # Tab. XXII. <lb/>657 # 3. # reant. # erant. <lb/>672 # 14. # examianari. # examinari. <lb/>673 # 13. # temperiei # temperie. <lb/>684 # 15. # corpus. # corporis. <lb/></note> </div> <div xml:id="echoid-div7" type="section" level="1" n="7"> <head xml:id="echoid-head12" xml:space="preserve">Berigt voor den Boekbinder.</head> <p> <s xml:id="echoid-s85" xml:space="preserve">NB. </s> <s xml:id="echoid-s86" xml:space="preserve">’t wit der Figuuren moet niet afgeſneeden, maar om in te vouwen <lb/>en uyt te ſlaan, gehouden werden.</s> <s xml:id="echoid-s87" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Tab. I. tot X. # agter pag. 270 in te voegen. <lb/>Tab. XI. tot XIII. # agter pag. 354 in te voegen. <lb/>Tab. XIV. tot XVI. # agter pag. 420 in te voegen. <lb/>Tab. XVII. tot XXVIII. # agter pag. 672 in te voegen. <lb/>Ephemerides agter pag. 686. <lb/></note> <pb file="0015" n="15"/> </div> <div xml:id="echoid-div8" type="section" level="1" n="8"> <head xml:id="echoid-head13" xml:space="preserve">DISSERTATIO <lb/>PHYSICA <lb/>EXPERIMENTALIS <lb/>DE <lb/>MAGNETE. <lb/>PRÆFATIO.</head> <p> <s xml:id="echoid-s88" xml:space="preserve">Quotquot in rerum Natura effectus a corporibus <lb/>editos conſpicimus, illi omnes motum, ut ſuam <lb/>cauſam agnoſcunt; </s> <s xml:id="echoid-s89" xml:space="preserve">quod quidem adeo perſpicu-<lb/>um eſt attendenti, ut de eo nemo ſanæ mentis <lb/>dubium movere poſſit: </s> <s xml:id="echoid-s90" xml:space="preserve">ſi ulterius indagationes nos-<lb/>tras promoveamus, atque inquiramus quænam <lb/>ſit cauſa eorum motuum, qui iſtos in ſenſus in-<lb/>currentes effectus excitant, tum nequaquam tan-<lb/>ta lux in vera cauſa aſſignanda ingenio humano affulget; </s> <s xml:id="echoid-s91" xml:space="preserve">imo e con-<lb/>trario, denſiſſimis ſæpe involuta cauſa tenebris illi videtur, qui re-<lb/>rum naturam ſumma cum diligentia & </s> <s xml:id="echoid-s92" xml:space="preserve">attentione perſcrutatur, o-<lb/>mniaque ſollicita evolvit cura: </s> <s xml:id="echoid-s93" xml:space="preserve">Videmus corpus motu concitatum & </s> <s xml:id="echoid-s94" xml:space="preserve"><lb/>occurrens alteri quieto mobilique, hoc movere, quod ita cauſa mo-<lb/>tus illius exiſtit: </s> <s xml:id="echoid-s95" xml:space="preserve">de hac cauſa motus non disputant inter ſe, ob ni-<lb/>miam ſenſuum evidentiam, Philoſophi; </s> <s xml:id="echoid-s96" xml:space="preserve">verum an omnis cauſa mo-<lb/>tus ſit corpus in motu conſtitutum, alterique occurrens, illudque at-<lb/>tingens & </s> <s xml:id="echoid-s97" xml:space="preserve">percutiens, controvertitur valde, quam multis id affir-<lb/>mantibus, pluribus autem in contrarias, & </s> <s xml:id="echoid-s98" xml:space="preserve">merito me judice, eunti- <pb o="2" file="0016" n="16" rhead="PRÆFATIO."/> bus partes, plurimasque eſſe motuum cauſas ſtatuentibus, in quibus <lb/>immediatus contactus locum non habet: </s> <s xml:id="echoid-s99" xml:space="preserve">Gravitatem enim oblerva-<lb/>mus in corporibus illud eſſe attributum univerſale, quo ea, quæ inter ſe <lb/>diſtant, libereque poſita ſunt, ad ſe invicem feruntur ſua ſponte, & </s> <s xml:id="echoid-s100" xml:space="preserve"><lb/>quidem ad centrum maxime corporeum, quamvis nullum corpus, ab <lb/>ullo mortalium huc usque cognitum, hæc ad ſe mutuo pellat, aut <lb/>extrinſecus percutiendo dirigat. </s> <s xml:id="echoid-s101" xml:space="preserve">Cauſam hujus motus vocamus quidem <lb/>Gravitatem, ſed hæc tantum vox eſt, qua prolata & </s> <s xml:id="echoid-s102" xml:space="preserve">applicata de-<lb/>ſcendentibus verſus ſe corporibus nihil plus intelligitur de ipſa cauſa <lb/>hujus motus, quam ſi quis nunquam vocem Gravitatis audiviſſet: <lb/></s> <s xml:id="echoid-s103" xml:space="preserve">Quicunque enim hanc eſſe Legem Naturæ ſtatuit a Deo omnibus in-<lb/>fuſam corporibus, non clarius intelligit, quomodo id principium, <lb/>vel attributum, in corporum interna ſubſtantia ſit poſitum, quomo-<lb/>do ibi comparatum ſit, quam ignorantiſſimus ex plebe. </s> <s xml:id="echoid-s104" xml:space="preserve">Sed præter <lb/>ea aliud in nonnullis corporibus obſervatur attributum, quod Elas-<lb/>ticitas vocatur; </s> <s xml:id="echoid-s105" xml:space="preserve">hæc cauſa motus aliorum corporum exiſtit, ea pre-<lb/>mendo vel percutiendo, adeoque attingendo corpora: </s> <s xml:id="echoid-s106" xml:space="preserve">ſed ipſa ope-<lb/>ratur Elaſticitas absque motu ſibi ab aliis corporibus communicato. </s> <s xml:id="echoid-s107" xml:space="preserve"><lb/>Inſuper Mens humana, & </s> <s xml:id="echoid-s108" xml:space="preserve">aliquid, quadantenus ipſi ſimile, quod in <lb/>Animalibus omnibus reperitur, cauſa motuum plurimorum eſt; </s> <s xml:id="echoid-s109" xml:space="preserve">poſt-<lb/>quam enim, omnibus fluidis in corpore placide tantum motis, in <lb/>affectus quis rapitur, hæc omnia vehementius commoventur; </s> <s xml:id="echoid-s110" xml:space="preserve">idemque <lb/>in omnibus obtinet brutis, quando paſſionibus aguntur: </s> <s xml:id="echoid-s111" xml:space="preserve">nonne mo-<lb/>veo determinato motu ea membra, quæ modo ante quieſcebant? </s> <s xml:id="echoid-s112" xml:space="preserve"><lb/>imo genero tantundem in iis fere motus, ac deſidero, excitatosque <lb/>iterum ſopio: </s> <s xml:id="echoid-s113" xml:space="preserve">quod mens hæc faciat, nullus, qui attendit, poteſt in <lb/>dubium vocare: </s> <s xml:id="echoid-s114" xml:space="preserve">nec ad excitandum motum repugnat indoles ejus <lb/>ſpiritualis; </s> <s xml:id="echoid-s115" xml:space="preserve">quomodo enim illud Ens Summum, quod totus Spiritus <lb/>eſt, potuiſſet pernices illos motus indere corporibus vaſtæ molis & </s> <s xml:id="echoid-s116" xml:space="preserve"><lb/>orbem terrarum centies millies, & </s> <s xml:id="echoid-s117" xml:space="preserve">ultra, magnitudine ſuperantibus, <lb/>quæ per cæleſtia ſpatia vagantur? </s> <s xml:id="echoid-s118" xml:space="preserve">Tandem obſervamus corpora ad <lb/>ſe invicem moveri, & </s> <s xml:id="echoid-s119" xml:space="preserve">in mutuos ultro ruere amplexus, non quia ad <lb/>ſe pelluntur a corpore quocunque externo, non a vi Gravitatis, non <lb/>a Mente cogitante, ſed a cauſa alia, quam æque ignoramus, ac <lb/>eam Gravitatis; </s> <s xml:id="echoid-s120" xml:space="preserve">hanc tamen inſignire nomine Attractionis nonnullis <lb/>placuit Philoſophis, non quia corpora ad ſe mutuo accederent, quaſi <pb o="3" file="0017" n="17" rhead="PRÆFATIO."/> Attractione proprie dicta trahuntur, ſed quoniam nomen qualecunque <lb/>huic ſive effectui, ſive cauſæ, dandum erat; </s> <s xml:id="echoid-s121" xml:space="preserve">optime enim illi, qui hac vo-<lb/>ce utuntur, intellexerunt, duo corpora ad ſe proprie tunc ſolum trahi, <lb/>quando ope intermedii corporis tertii, ſive funis, baculive jungun-<lb/>tur, atque extremitas alterutra, vel ambæ ſimul trahuntur; </s> <s xml:id="echoid-s122" xml:space="preserve">qua actio-<lb/>ne corpora connexa ad ſe accedunt: </s> <s xml:id="echoid-s123" xml:space="preserve">Sed ea quæ ſe attrahere dicun-<lb/>tur corpora, non ligantur ope alicujus lori baculive intermedii, verum <lb/>ſeparata vel ſoluta a ſe mutuo, ad ſe accedunt ſine auxilio, aut præſentia <lb/>aliorum corporum, fere eodem modo ac ſi in ſe invicem gravitarent; <lb/></s> <s xml:id="echoid-s124" xml:space="preserve">Vox Attractionis recepta erat in Philoſophia, eamque retinere vo-<lb/>luimus in hac ſignificatione, ſi quis tamen ea offenderetur, aliam af-<lb/>ferre ipſi licitum erit eodem jure: </s> <s xml:id="echoid-s125" xml:space="preserve">Nominum enim definitiones arbi-<lb/>trariæ ſunt, modo effectum intelligat eundem.</s> <s xml:id="echoid-s126" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s127" xml:space="preserve">Quoniam autem in omnibus, quæ hactenus nota ſunt, corporibus, <lb/>obtinet vis quædam, qua ad ſe accedunt, vel qua ſe ſuasve partes <lb/>retinent, cum ſeſe contingunt, Attractio a nonnullis Lex Naturæ <lb/>Univerſalis habetur: </s> <s xml:id="echoid-s128" xml:space="preserve">quæ omni corpuſculo infuſa ſolido, nunquam <lb/>deſtruitur, ſed in eo ſemper manet, quemadmodum Gravitas indita <lb/>a Creatore omni materiei, proportionalis eſt maſſæ, peritque aut ſi-<lb/>let nunquam.</s> <s xml:id="echoid-s129" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s130" xml:space="preserve">Philoſophi, qui Legem Attractionis condiderunt, neutiquam ex <lb/>Hypotheſi eam aſſumſerunt, verum quia experimentis & </s> <s xml:id="echoid-s131" xml:space="preserve">quotidianis <lb/>obſervationibus animadverterunt vim quandam dari in corporibus, <lb/>qua, ſi a ſe diſtant, verſus ſe mutuo feruntur; </s> <s xml:id="echoid-s132" xml:space="preserve">& </s> <s xml:id="echoid-s133" xml:space="preserve">ſi ſe contingunt, <lb/>firmiter ſe retinent, cum nullius corporis foris pellentis ſuſpicio, vel <lb/>preſſio obſervatur: </s> <s xml:id="echoid-s134" xml:space="preserve">hoc modo Hypotheſis ambientis & </s> <s xml:id="echoid-s135" xml:space="preserve">corpora pre-<lb/>mentis Fluidi qualiscunque Ætherei penitus ex Philoſophia elimina-<lb/>tur. </s> <s xml:id="echoid-s136" xml:space="preserve">Inter corpora quæ Attrahere ſe dicuntur, nulla ſunt hactenus <lb/>cognita, quæ aut manifeſtius, aut fortius, aut ad majorem interca-<lb/>pedinem in ſe operantur, quam Magnes & </s> <s xml:id="echoid-s137" xml:space="preserve">Ferrum, idcirco opina-<lb/>bar nunquam melius Leges Attractionis addiſci poſſe, quam ſi Ma-<lb/>gnetem accuratiſſime, & </s> <s xml:id="echoid-s138" xml:space="preserve">ab omni parte, diverſisque modis examina-<lb/>rem; </s> <s xml:id="echoid-s139" xml:space="preserve">rem igitur aggreſſus ſum, & </s> <s xml:id="echoid-s140" xml:space="preserve">quamvis nec ſumtibus nec labori <lb/>pepercerim, nequaquam voto potitus ſum: </s> <s xml:id="echoid-s141" xml:space="preserve">id tamen didici, Magne-<lb/>tis partes univerſali Legi Attractionis ſubjici, has cohærere inter ſe <lb/>vi ſimili, qua omnia corpora: </s> <s xml:id="echoid-s142" xml:space="preserve">verum ea vis Magnetis, quæ ad ma- <pb o="4" file="0018" n="18" rhead="PRÆFATIO."/> ximas diffunditur diſtantias, qua Ferrum aliusve Magnes attrahitur <lb/>ab alio, viſa mihi fuit omnino diſtinguenda a priori Attractione, hæc <lb/>enim mutabilis eſt, & </s> <s xml:id="echoid-s143" xml:space="preserve">fere penitus ex Magnete profligari poteſt, aut <lb/>ad ſilentium deduci; </s> <s xml:id="echoid-s144" xml:space="preserve">uti ex Experimentis inferius commemorandis <lb/>conſtabit: </s> <s xml:id="echoid-s145" xml:space="preserve">nemo autem facile dixerit Legem Naturæ mutabilem eſſe <lb/>in corporibus. </s> <s xml:id="echoid-s146" xml:space="preserve">Quamobrem duplicis generis obtinebit in Magneti-<lb/>bus Attractio, quarum una a Lege Naturæ pendebit univerſali, unde <lb/>autem altera pendeat, ignoro huc usque: </s> <s xml:id="echoid-s147" xml:space="preserve">Natura in hoc corpore in-<lb/>numera videtur abſcondidiſſe Myſteria, quorum quo plura revela-<lb/>mus, eo magis a divinanda cauſa removemur, & </s> <s xml:id="echoid-s148" xml:space="preserve">in majorem illapſi <lb/>hæſitationem quam ante, eo plura ignorari, quo plura ſcimus, <lb/>quo ea attentiori animo revolvimus, fateri continuo cogimur: </s> <s xml:id="echoid-s149" xml:space="preserve">Ali-<lb/>quando diu meditatus de nonnullis Experimentis, a pororum tum <lb/>Magnetis, tum Ferri figura, vim pendere doceri videbar, ſed illico <lb/>alia prodibant phænomena, quæ hujus opinionis imbecillitatem de-<lb/>monſtrabant: </s> <s xml:id="echoid-s150" xml:space="preserve">modo a parva quantitate corporea, quæ in ferro & </s> <s xml:id="echoid-s151" xml:space="preserve">in <lb/>Magnete hæret, vim deducendam credidiſſem, hoc quaſi probante <lb/>Analyſi Chemica utriusque corporis; </s> <s xml:id="echoid-s152" xml:space="preserve">ſed mox plurima ſurgebant ad-<lb/>verſus hanc ſententiam argumenta, cum ſimplex mallei percuſſio vim <lb/>ex ferro magneticam profligabat, non amiſſa ulla ſubſtantia. </s> <s xml:id="echoid-s153" xml:space="preserve">Similes <lb/>ſuſpiciones diverſiſſimæ ex inter ſe comparatis oboriebantur Experi-<lb/>mentis, ſed quarum infirmitas ex collatis aliis cum his iterum elu-<lb/>ceſcebat: </s> <s xml:id="echoid-s154" xml:space="preserve">unde ſemper, quo plura mecum verſabam, & </s> <s xml:id="echoid-s155" xml:space="preserve">inter ſe com-<lb/>parabam, eo incertior evaſi: </s> <s xml:id="echoid-s156" xml:space="preserve">Forſitan illa ſecundi generis Attractio, <lb/>qua Magnes ad longam operatur diſtantiam, non videbitur multis eſ-<lb/>ſe tam abſtruſa, ſed eam conſiſtere in Fluido aliquo, extrinſecus ambien-<lb/>te Magnetem, eumque premente verſus alium, aut verſus Ferrum; <lb/></s> <s xml:id="echoid-s157" xml:space="preserve">pace autem horum Doctiſſimorum Virorum dixerim, me nullam ob-<lb/>ſervaſſe Hypotheſin magis oppoſitam Experimentis & </s> <s xml:id="echoid-s158" xml:space="preserve">veritati, quam <lb/>hanc; </s> <s xml:id="echoid-s159" xml:space="preserve">argumenta, quæ eum in finem infra attuli, examinanda ſunt, <lb/>ex quibus liquebit, an feſtinanti conſilio hanc concluſionem forma-<lb/>verim: </s> <s xml:id="echoid-s160" xml:space="preserve">præterea obteſtor Philoſophorum, qui cuncta phænomena <lb/>Magnetica norunt, conſcientiam, an præjudicio omni exuto, convicti <lb/>penitus ſint ex obſervationibus aut Experimentis, Fluidum aliquod Ma-<lb/>gneticum, vel Effluvia quædam, (quocunque nomine vocentur perin-<lb/>de mihi erit) dari, atque ex iis poſſe omnia Mechanice explica- <pb o="5" file="0019" n="19" rhead="PRÆFATIO."/> ri ac demonſtrari phænomena, quæ Magnetes & </s> <s xml:id="echoid-s161" xml:space="preserve">Ferrum quotidie con-<lb/>ſpicienda præbent? </s> <s xml:id="echoid-s162" xml:space="preserve">Quod ſi enim ſenſus conſulant, neque Viſu, neque <lb/>Tactu, neque reſiſtentia, neque pondere Fluidum obſervatur magneti-<lb/>cum; </s> <s xml:id="echoid-s163" xml:space="preserve">adeoque cum id advocatur ad effectus explicandos, non niſi ex <lb/>mera hypotheſi aſſumitur, nequaquam demonſtratur; </s> <s xml:id="echoid-s164" xml:space="preserve">quonam igitur <lb/>fundamento ſevero rerum indagatori ejusmodi dari Fluidum perſuaderi <lb/>poterit? </s> <s xml:id="echoid-s165" xml:space="preserve">Quod ſi deinde maximos in arte viros conſulamus, qui noſtra <lb/>ætate quamplurimum operæ in explicandis Geometrice effectibus mag-<lb/>neticis poſuerunt, fluido tamen ad id uſi, hos vehementer ſuum torſiſſe <lb/>animum inani opera & </s> <s xml:id="echoid-s166" xml:space="preserve">fruſtraneo labore, deprehendimus, atque adver-<lb/>ſus Hydroſtraticas leges inceſſiſſe, neque tamen adhuc ſibi ipſis ſa-<lb/>tisfeciſſe; </s> <s xml:id="echoid-s167" xml:space="preserve">teſtimonium Præſtantiſſimi Whiſtoni pro omnibus ſufficiat, <lb/>qui non dubitavit profiteri palam, ſe nullo modo Mechanice explica-<lb/>re poſſe phænomena magnetica, neque meditando invenire ſe po-<lb/>tuiſſe ejusmodi motum Fluidi ſubtilis, quod vim Attractricem in <lb/>proportione illa, quæ inter Magnetes a ſe ſejunctos obtinet, operaretur: <lb/></s> <s xml:id="echoid-s168" xml:space="preserve">arbitror autem nec dari Fluidum magneticum, niſi in animo illud <lb/>fingentis, multo minus ex eo demonſtrari poſſe phænomena, quæ in-<lb/>ferius afferam: </s> <s xml:id="echoid-s169" xml:space="preserve">Agit Magnes in Magnetem, aut in Ferrum, vi attra-<lb/>ctrice, quæ quomodo comparata ſit in iis corporibus, non intelligi-<lb/>tur, uti nec ejus cauſa, unde hic ſi ullibi, recte convenit dictum <lb/>Ciceronis, facilius quid non ſit, quam quid ſit, de hujusmodi rebus <lb/>poſſe confirmari.</s> <s xml:id="echoid-s170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s171" xml:space="preserve">Mirabitur procul dubio Lector, me aliquid conſcripſiſſe de eo <lb/>corpore, cujus nonnullos quidem effectus intelligo, ſed quorum <lb/>cauſam me ignorare confiteor, de quibus proinde non multum diſſe-<lb/>rere, & </s> <s xml:id="echoid-s172" xml:space="preserve">pauciora adhucdum demonſtrare potero, de quibus idcirco non <lb/>niſi valde ſterilis doctrina erit; </s> <s xml:id="echoid-s173" xml:space="preserve">& </s> <s xml:id="echoid-s174" xml:space="preserve">in qua tractanda vix Philoſophi functus <lb/>ero officio, cum nullam hypotheſin condidi, ex qua effectus explicem; <lb/></s> <s xml:id="echoid-s175" xml:space="preserve">Hic intelligat volo, me eam profiteri Philoſophandi methodum, quæ <lb/>rejectis omnibus Hypotheſibus, nihil ponit in Phyſica firmum ratumque, <lb/>niſi quod abſolute demonſtratur: </s> <s xml:id="echoid-s176" xml:space="preserve">neque cum illis me conſentire, qui regu-<lb/>lam ſtabiliverunt. </s> <s xml:id="echoid-s177" xml:space="preserve">Præſtantius eſſe opinari de rebus difficillimis, quam <lb/>clara tantum velle ſcire & </s> <s xml:id="echoid-s178" xml:space="preserve">demonſtrare, aut ignor antiam fateri: </s> <s xml:id="echoid-s179" xml:space="preserve">Quid enim <lb/>differt Opinio aut Hypotheſis a fabula? </s> <s xml:id="echoid-s180" xml:space="preserve">utraque chimæra ludibundi <lb/>eſt ingenii; </s> <s xml:id="echoid-s181" xml:space="preserve">tamdiu placet vigetque, donec nova jocoſior exoritur;</s> <s xml:id="echoid-s182" xml:space="preserve"> <pb o="6" file="0020" n="20" rhead="PRÆFATIO."/> neque hæc viciſſitudinibus iterum erepta eſt; </s> <s xml:id="echoid-s183" xml:space="preserve">quippe ſimulac alia ſu-<lb/>perbiori induta ornatu in Scenam prodit, prior proſcribitur atque ſpreta <lb/>jacet: </s> <s xml:id="echoid-s184" xml:space="preserve">Quam apprime ingenioſus Buffierius in Tract. </s> <s xml:id="echoid-s185" xml:space="preserve">de primis veri-<lb/>tatibus part. </s> <s xml:id="echoid-s186" xml:space="preserve">5, Hypotheſium Phyſicarum Auctores comparat cum <lb/>Romannis, qui quidem id conantur quod veroſimile eſt, nequaquam <lb/>id, quod veritatem comprehendit; </s> <s xml:id="echoid-s187" xml:space="preserve">qui eo plus placent, quo magis aliena <lb/>ab exſpectatione & </s> <s xml:id="echoid-s188" xml:space="preserve">ratione noſtra, imo quæ nonnunquam dementiæ ſunt <lb/>propinqua, ponunt, modo contradictionem non involvant: </s> <s xml:id="echoid-s189" xml:space="preserve">ſed ecquis <lb/>ratione præditus ejusmodi fabulas ſibi pro veritate obtrudi ſine-<lb/>ret in hiſtoriis? </s> <s xml:id="echoid-s190" xml:space="preserve">quonam igitur meliori jure in Phyſicis? </s> <s xml:id="echoid-s191" xml:space="preserve">idcirco ma-<lb/>gnus Verulamius Hypotheſes Philoſophorum non niſi cerebella ho-<lb/>minum & </s> <s xml:id="echoid-s192" xml:space="preserve">potentes nugas vocavit, atque oravit & </s> <s xml:id="echoid-s193" xml:space="preserve">obſecravit homi-<lb/>nes, ut animos ſubmitterent, ſcientias quærerent rejecta libidine fin-<lb/>gendi, ipſamque potius Naturam obſervarent: </s> <s xml:id="echoid-s194" xml:space="preserve">Aurea hercle monita! <lb/>eaque ſequenda eſſe, ſi unquam aliquid certi cognoſcere in Phyſicis <lb/>conamur, fatentur omnes penetrantioris judicii Sapientes: </s> <s xml:id="echoid-s195" xml:space="preserve">Pauci ta-<lb/>men hæc tam bene obſervarunt, quam Iſacus Newtonus & </s> <s xml:id="echoid-s196" xml:space="preserve">Niewen-<lb/>tytius. </s> <s xml:id="echoid-s197" xml:space="preserve">Hi Hypotheſes, quantum potuerunt, rejecerunt: </s> <s xml:id="echoid-s198" xml:space="preserve">Quam pul-<lb/>cre igitur hoſce Philoſophos aut evolverunt, aut intellexerunt illi, qui <lb/>iis ubivis Hypotheſes adſcribunt, in quibus eorum demonſtrationes <lb/>fundatas arbitrantur? </s> <s xml:id="echoid-s199" xml:space="preserve">ſed ignoſcendum eſt aliquid iis Heroibus, qui <lb/>Matheſeos ignari, & </s> <s xml:id="echoid-s200" xml:space="preserve">ideo eam exoſi, atque ex Phyſica, veluti <lb/>Scientiam inutilem proſcribentes, ſcripta tantæ penetrationis in arca-<lb/>na Naturæ, ne quidem legere, multo minus intelligere potuerunt; <lb/></s> <s xml:id="echoid-s201" xml:space="preserve">ut hi tamen videantur Newtoniana legiſſe, nonnullos interpretes de-<lb/>ſcribunt, quorum verba hinc inde paulum immutando, turpes con-<lb/>tra prima Geometriæ fundamenta immiſcent errores, quo opinantur <lb/>jactitantque ſe clare conſcribere & </s> <s xml:id="echoid-s202" xml:space="preserve">emendare, quod Geometras reddere <lb/>obſcuriſſimum, criminantur: </s> <s xml:id="echoid-s203" xml:space="preserve">Quod ſi hi in Newtonianis verſati fo-<lb/>rent ſcriptis, cognoviſſent quid quondam Anno 1672. </s> <s xml:id="echoid-s204" xml:space="preserve">Philoſophus <lb/>reſpondit Pardieſio, qui Theoriam Lucis & </s> <s xml:id="echoid-s205" xml:space="preserve">Colorum Hypotheſin vo-<lb/>caverat, ſe id amice habere, ſiquidem ipſi nondum conſtabat, ſed alio <lb/>tamen conſilio ſe id propoſuiſſe, cum nihil aliud continere videtur, <lb/>quam proprietates quasdam Lucis. </s> <s xml:id="echoid-s206" xml:space="preserve">confer. </s> <s xml:id="echoid-s207" xml:space="preserve">Philoſoph. </s> <s xml:id="echoid-s208" xml:space="preserve">Transact. </s> <s xml:id="echoid-s209" xml:space="preserve">No. </s> <s xml:id="echoid-s210" xml:space="preserve"><lb/>84. </s> <s xml:id="echoid-s211" xml:space="preserve">pag. </s> <s xml:id="echoid-s212" xml:space="preserve">4039. </s> <s xml:id="echoid-s213" xml:space="preserve">qualem idcirco, hoc ictu ſapientior factus, Pardie-<lb/>ſius palinodiam cecinerit, vide ſis in Philoſoph. </s> <s xml:id="echoid-s214" xml:space="preserve">Transact. </s> <s xml:id="echoid-s215" xml:space="preserve">No. </s> <s xml:id="echoid-s216" xml:space="preserve">85. </s> <s xml:id="echoid-s217" xml:space="preserve">p.</s> <s xml:id="echoid-s218" xml:space="preserve"> <pb o="7" file="0021" n="21" rhead="PRÆFATIO."/> 5013. </s> <s xml:id="echoid-s219" xml:space="preserve">Sed ejusmodi Philoſophorum genus abunde ſuæ ignorantiæ <lb/>apud veros Phyſicæ cultores luit pœnas, uti liquet ex inclyti Keilii <lb/>Præfatione ad veram Phyſicam, hos ita deſcribentis; </s> <s xml:id="echoid-s220" xml:space="preserve">Quod, ut I-<lb/>gnavo & </s> <s xml:id="echoid-s221" xml:space="preserve">deſidi placeant Philoſophantum populo, nullum Geometriæ <lb/>uſum in Philoſophia adhibent: </s> <s xml:id="echoid-s222" xml:space="preserve">excogitantes quoque Philoſophiam, <lb/>quæ a veris Mechanicæ legibus tantum abhorret, quantum quæ lon-<lb/>giſſime: </s> <s xml:id="echoid-s223" xml:space="preserve">ideo umbram Philoſophiæ, non ipſam ſubſtantiam ample-<lb/>ctuntur: </s> <s xml:id="echoid-s224" xml:space="preserve">Sed hi terant ſuum tempus inutiliſſime in Hypotheſibus <lb/>fabulisque fingendis, pergant deridere Geometras, elatoque de-<lb/>ſpicere ſupercilio, hos facile ſuo genio indulgentes relinquimus, dum <lb/>interim ad alia tranſimus.</s> <s xml:id="echoid-s225" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s226" xml:space="preserve">Præterea hæc in lucem emiſi, quia ante paucos annos quædam Expe-<lb/>rimenta magnetica in Epiſtola communicaveram cum Viro Experientiſſi-<lb/>mo, Doctiſſimoque Diſaguillierio, qui ea pluris æſtimans, quam mere-<lb/>bantur, Actis Philoſophicis inſerendas eſſe voluit; </s> <s xml:id="echoid-s227" xml:space="preserve">Quum vero hæc non <lb/>eo transmiſeram ſcopo, quia nimis rudia & </s> <s xml:id="echoid-s228" xml:space="preserve">incondita erant, curamque <lb/>poſteriorem deſiderabant, nunc ea paulo magis, pro exiguo quo <lb/>fruor otio, elaboravi. </s> <s xml:id="echoid-s229" xml:space="preserve">Non tamen hæc vendito pro novis, plura <lb/>enim aliorum huc congeſſi, quæ tantum novo exploravi examine, <lb/>eo duntaxat ſcopo, ut appareat, quid huc usque in Scientia <lb/>Magnetica actum ſit, quid ulterius deſideretur; </s> <s xml:id="echoid-s230" xml:space="preserve">& </s> <s xml:id="echoid-s231" xml:space="preserve">ut veræ ob-<lb/>ſervationes ab erroneis, quæ frequentiſſime in hanc doctrinam <lb/>irrepſerant, diſtinguantur: </s> <s xml:id="echoid-s232" xml:space="preserve">Quoniam autem aliorum inventa meri-<lb/>tamque gloriam mihi vindicare nolui, candide Autores memoravi, <lb/>qui eadem experimenta primi inſtituerunt, ſeu cum eodem, ſeu cum <lb/>diverſo ſucceſſu. </s> <s xml:id="echoid-s233" xml:space="preserve">Nullos autem allegavi, niſi quos ipſe legi, quos <lb/>fateor eſſe admodum paucos, ſed malui in lucem hæc nudo & </s> <s xml:id="echoid-s234" xml:space="preserve">ſimpli-<lb/>ci induta ornatu emittere, prout Philoſophum decere arbitror, <lb/>quam cum magna oſtentatione eruditionis plurimos citare autores, <lb/>quos nunquam legi, aut vidi, quod haud difficile fuiſſet, ſi tantum <lb/>modo exſcripſiſſem Doctiſſimum Sturmium, & </s> <s xml:id="echoid-s235" xml:space="preserve">Acta Eruditorum Li-<lb/>pſienſium, aliaque Librorum extracta, atque citationes ex citationi-<lb/>bus, tam male quam bene per fortunam intellectis, accumulaſſem, <lb/>hæ vero artes ignavæ, quibus nonnulli utuntur, facile detectæ fu-<lb/>iſſent ab iis, qui mediocriter in Phyſica ſe exercuerunt. </s> <s xml:id="echoid-s236" xml:space="preserve">Quidnam <lb/>præſtiterim illi cognoſcent, qui plurima optimorum Autorum, qui <pb o="8" file="0022" n="22" rhead="PRÆFATIO."/> de Magnete ſcripſerunt, evolverunt ſcripta: </s> <s xml:id="echoid-s237" xml:space="preserve">Nihil addidi, quod ar-<lb/>tiſicia magnetica ſpectat, qualia congeſſerunt plurima Kircherus, <lb/>Schottus, Pugettus, aliique: </s> <s xml:id="echoid-s238" xml:space="preserve">nam hæc nihil faciunt ad amplifi-<lb/>candam Scientiam Phyſicam; </s> <s xml:id="echoid-s239" xml:space="preserve">attendere tantummodo volui ad pro-<lb/>prietates Magnetis, in iisque eruendis laborem impendere. </s> <s xml:id="echoid-s240" xml:space="preserve">Ante-<lb/>quam autem rem ipſam aggrediamur, nonnulla quæ Magnetem ſpe-<lb/>ctant prænoſcenda ſunt.</s> <s xml:id="echoid-s241" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s242" xml:space="preserve">Solet Magnes erui ex fodinis tum ſibi propriis, tum ex illis, ex <lb/>quibus Ferrum elicitur: </s> <s xml:id="echoid-s243" xml:space="preserve">nulla Terrarum orbis pars eſt, quæ non <lb/>præſtantes profert Magnetes, imo de meliori virtute diſputant æque <lb/>inter ſe Aſiatici & </s> <s xml:id="echoid-s244" xml:space="preserve">Europæi, quam Americani & </s> <s xml:id="echoid-s245" xml:space="preserve">qui in Africa in-<lb/>veniuntur.</s> <s xml:id="echoid-s246" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s247" xml:space="preserve">Videtur Magnes eſſe Ferri ditior Vena, unde recte & </s> <s xml:id="echoid-s248" xml:space="preserve">eleganter <lb/>Claudianus cecinit:</s> <s xml:id="echoid-s249" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div9" type="section" level="1" n="9"> <head xml:id="echoid-head14" style="it" xml:space="preserve">Ex Ferro meruit vitam, ferrique rigore <lb/>Veſcitur, has dulces epulas, hæc pabula novit.</head> <p> <s xml:id="echoid-s250" xml:space="preserve">In hac opinione plures mecum conſentiunt: </s> <s xml:id="echoid-s251" xml:space="preserve">Regis in Phyſiq. </s> <s xml:id="echoid-s252" xml:space="preserve">part. </s> <s xml:id="echoid-s253" xml:space="preserve">3. </s> <s xml:id="echoid-s254" xml:space="preserve">L. <lb/></s> <s xml:id="echoid-s255" xml:space="preserve">4. </s> <s xml:id="echoid-s256" xml:space="preserve">c. </s> <s xml:id="echoid-s257" xml:space="preserve">14. </s> <s xml:id="echoid-s258" xml:space="preserve">ideo dicit, Quamvis Magnes numeretur inter Lapides, nihilo-<lb/>minus ſimilis videtur miner alibus, & </s> <s xml:id="echoid-s259" xml:space="preserve">imprimis ferro: </s> <s xml:id="echoid-s260" xml:space="preserve">imo Voſſius teſtatur <lb/>in Idololatr. </s> <s xml:id="echoid-s261" xml:space="preserve">lib. </s> <s xml:id="echoid-s262" xml:space="preserve">6. </s> <s xml:id="echoid-s263" xml:space="preserve">c. </s> <s xml:id="echoid-s264" xml:space="preserve">11. </s> <s xml:id="echoid-s265" xml:space="preserve">quod effodiuntur Magnetes, plus Ferri ha-<lb/>bentes quam Lapidis. </s> <s xml:id="echoid-s266" xml:space="preserve">Magis hoc concludi poteſt ex colore ferru-<lb/>gineo; </s> <s xml:id="echoid-s267" xml:space="preserve">tum quod notante Gilberto Lib. </s> <s xml:id="echoid-s268" xml:space="preserve">1. </s> <s xml:id="echoid-s269" xml:space="preserve">cap. </s> <s xml:id="echoid-s270" xml:space="preserve">16. </s> <s xml:id="echoid-s271" xml:space="preserve">de Mag: </s> <s xml:id="echoid-s272" xml:space="preserve">ex Ma-<lb/>guete fuſo optimæ notæ Ferrum Chalybsque præparari poſſit: </s> <s xml:id="echoid-s273" xml:space="preserve">quod <lb/>etiam confirmat Lemmery in Curſu Chemiæ, cap. </s> <s xml:id="echoid-s274" xml:space="preserve">7. </s> <s xml:id="echoid-s275" xml:space="preserve">addens, ad id ma-<lb/>gnum requiri ignem. </s> <s xml:id="echoid-s276" xml:space="preserve">Tachenius in Clave Medicinæ Hipp. </s> <s xml:id="echoid-s277" xml:space="preserve">cap. </s> <s xml:id="echoid-s278" xml:space="preserve">9. </s> <s xml:id="echoid-s279" xml:space="preserve"><lb/>ideo vocat Magnetem, matrem Ferri, quæ Filii odorem percipit, <lb/>quia amat. </s> <s xml:id="echoid-s280" xml:space="preserve">&</s> <s xml:id="echoid-s281" xml:space="preserve">c Inſuper hoc concludo, quia ferrum infixum lapidi <lb/>foſſili & </s> <s xml:id="echoid-s282" xml:space="preserve">poroſo, quem Belgice Hardſteen vocamus, multaque per <lb/>ſecula corroſum in rubiginem, atque ulterius poris lapidis infuſum <lb/>cum illapſa pluvia, abit cum eo in præſtantiſſimos Magnetes, non di-<lb/>ſtinguendos a foſſilibus colore, duritie, aut pondere: </s> <s xml:id="echoid-s283" xml:space="preserve">Ejusmodi fragmen-<lb/>ta ferrea exſciſſa ex templis Trajectinæ urbis antiquiſſimis conſervo, <lb/>quæ eximiam vim attrahendi ferrum & </s> <s xml:id="echoid-s284" xml:space="preserve">Magnetem habent. </s> <s xml:id="echoid-s285" xml:space="preserve">Similia <lb/>magnetica ferramenta paucos ante annos Delphis quoque in ſummo <lb/>apice vetuſſiſſimi templi ſunt reperta, quorum nonnulla exploravi:</s> <s xml:id="echoid-s286" xml:space="preserve"> <pb o="9" file="0023" n="23" rhead="PRÆFATIO."/> aliaque deſcripſit Leewenhoekius in Phil. </s> <s xml:id="echoid-s287" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s288" xml:space="preserve">No. </s> <s xml:id="echoid-s289" xml:space="preserve">371. </s> <s xml:id="echoid-s290" xml:space="preserve">Haſce <lb/>generationes Magnetum ex ferro corroſo notavit etiam Vallemontius <lb/>in deſcriptione Magnetis Chartrenſis: </s> <s xml:id="echoid-s291" xml:space="preserve">tum Gaſſendus in Scientia Phyſi-<lb/>ca, Sect. </s> <s xml:id="echoid-s292" xml:space="preserve">3. </s> <s xml:id="echoid-s293" xml:space="preserve">pag. </s> <s xml:id="echoid-s294" xml:space="preserve">128. </s> <s xml:id="echoid-s295" xml:space="preserve">& </s> <s xml:id="echoid-s296" xml:space="preserve">ad Epicurum pag. </s> <s xml:id="echoid-s297" xml:space="preserve">205. </s> <s xml:id="echoid-s298" xml:space="preserve">Dechales in curſu <lb/>Mathematico: </s> <s xml:id="echoid-s299" xml:space="preserve">Philip. </s> <s xml:id="echoid-s300" xml:space="preserve">Coſta Mantuanus in Libro de compoſitionibus <lb/>Antidotorum. </s> <s xml:id="echoid-s301" xml:space="preserve">Schottus in Magia magnetica pag. </s> <s xml:id="echoid-s302" xml:space="preserve">225, 231. </s> <s xml:id="echoid-s303" xml:space="preserve">Ca-<lb/>bæus in Philoſ. </s> <s xml:id="echoid-s304" xml:space="preserve">Magn. </s> <s xml:id="echoid-s305" xml:space="preserve">Lib. </s> <s xml:id="echoid-s306" xml:space="preserve">1. </s> <s xml:id="echoid-s307" xml:space="preserve">cap. </s> <s xml:id="echoid-s308" xml:space="preserve">17. </s> <s xml:id="echoid-s309" xml:space="preserve">pag. </s> <s xml:id="echoid-s310" xml:space="preserve">62. </s> <s xml:id="echoid-s311" xml:space="preserve">Sturmius in Phyſi-<lb/>ca Electiva Tom. </s> <s xml:id="echoid-s312" xml:space="preserve">2. </s> <s xml:id="echoid-s313" xml:space="preserve">pag. </s> <s xml:id="echoid-s314" xml:space="preserve">1090 La Hire in Journal des Scavans <lb/>Ao. </s> <s xml:id="echoid-s315" xml:space="preserve">1691. </s> <s xml:id="echoid-s316" xml:space="preserve">Rohaultus in Phyſica, part. </s> <s xml:id="echoid-s317" xml:space="preserve">3. </s> <s xml:id="echoid-s318" xml:space="preserve">cap. </s> <s xml:id="echoid-s319" xml:space="preserve">8. </s> <s xml:id="echoid-s320" xml:space="preserve">§. </s> <s xml:id="echoid-s321" xml:space="preserve">39. </s> <s xml:id="echoid-s322" xml:space="preserve">imo Aldro-<lb/>vandus in ſuo muſæo ejusmodi fragmentum conſervabat, petitum ex <lb/>Templo Italico Arimini.</s> <s xml:id="echoid-s323" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s324" xml:space="preserve">Novi equidem Nob. </s> <s xml:id="echoid-s325" xml:space="preserve">Boyleum dubitaſſe an unquam ferrum <lb/>hoc modo in Magnetem abiret, ſimilem illis, qui eruuntur ex fodi-<lb/>nis, ſed maxima ſimilitudo quoad colorem, ſubſtantiam, duriti-<lb/>em, aliaque attributa intercedit inter fragmenta ferrea, quæ conſervo, <lb/>& </s> <s xml:id="echoid-s326" xml:space="preserve">inter Naturales Magnetes, ſi oculo attento aut Microſcopiis in-<lb/>ſpiciantur, ut dubium ſuperſit nullum.</s> <s xml:id="echoid-s327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s328" xml:space="preserve">Vallemontius hoc aliis adſtruxit argumentis: </s> <s xml:id="echoid-s329" xml:space="preserve">(1) ſi ſuper Magne-<lb/>tem generatum ex ferro fundatur Aqua fortis, Spiritus nitri, vel Spi-<lb/>ritus vitrioli, nulla fit ebullitio, effervelcentia, nec exhalatio: </s> <s xml:id="echoid-s330" xml:space="preserve">hi <lb/>iidem ſpiritus acidi affuſi Magneti nigro naturali, ſive ex fodinis ef-<lb/>foſſo, etiam non efferveſcunt, nec motus cient, notante eodem Auto-<lb/>re, atque etiam Grewo: </s> <s xml:id="echoid-s331" xml:space="preserve">hi tamen ſpiritus affuſi Limaturæ ferri, vehe-<lb/>menter ebulliunt. </s> <s xml:id="echoid-s332" xml:space="preserve">(2) in calcem reductus eſt in Igne Magnes naturalis, <lb/>tum Magnes Chartrenſis ex ferro, iisque ſeorſim poſitis ſuperaffuſa <lb/>fuit aqua fortis, ſpiritus nitri, & </s> <s xml:id="echoid-s333" xml:space="preserve">ſpiritus vitrioli; </s> <s xml:id="echoid-s334" xml:space="preserve">hi ſpiritus abſorpti <lb/>ſunt introrſum a calce utraque, ſed lente & </s> <s xml:id="echoid-s335" xml:space="preserve">eodem modo, cum in Lima-<lb/>turam ferri cito deſcendunt cum diverſis Phænomenis: </s> <s xml:id="echoid-s336" xml:space="preserve">Poſtquam Che-<lb/>mici Ferrum in Aere poſitum vim Magneticam acquirere obſervarunt, <lb/>ſtatuerunt Aerem generare Magnetem: </s> <s xml:id="echoid-s337" xml:space="preserve">Vid. </s> <s xml:id="echoid-s338" xml:space="preserve">Theatri Chymic. </s> <s xml:id="echoid-s339" xml:space="preserve">vol. </s> <s xml:id="echoid-s340" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s341" xml:space="preserve">pag. </s> <s xml:id="echoid-s342" xml:space="preserve">440.</s> <s xml:id="echoid-s343" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s344" xml:space="preserve">Sunt inter Magnetes ex ferro corrupto generatos aliqui tam for-<lb/>tes, ut viribus eos ſuperent, qui ex fodinis eruuntur, probante hoc <lb/>Chartrenſi, noſtrisque Trajectinis, aliisque: </s> <s xml:id="echoid-s345" xml:space="preserve">Generantur etiam Magne-<lb/>tes albi in ſpongiis marinis, quos obſervavit Kolbius, exhibuitque <lb/>in deſcriptione Promontorii Bonæ ſpei Tom. </s> <s xml:id="echoid-s346" xml:space="preserve">1. </s> <s xml:id="echoid-s347" xml:space="preserve">p. </s> <s xml:id="echoid-s348" xml:space="preserve">275. </s> <s xml:id="echoid-s349" xml:space="preserve">In quibus <pb o="10" file="0024" n="24" rhead="PRÆFATIO."/> quidem vis eſt Attrahendi ferrum, verum nequaquam illæ virtutes, de-<lb/>prehenduntur quas fabulatrix antiquitas Magneti attribuebat, quod foret <lb/>aut philtrum amoris, aut poſſeſſorem gratum acceptumque faciat prin-<lb/>cipibus, aut eloquentem: </s> <s xml:id="echoid-s350" xml:space="preserve">Ceilonenſes, ab Academiæ Regiæ Pariſi-<lb/>næ Sapientibus deſcriptos, nondum exploravi, neque matricem eo-<lb/>rum cognovi.</s> <s xml:id="echoid-s351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s352" xml:space="preserve">Eſt vulgaris Magnes, Lapis plerumque tam durus, ut percuſſus <lb/>chalybe malleove ſcintillas innumeras magnasque edat, quæ eas <lb/>excedunt, quæ ex vulgari ſilice eliciuntur, imo ex duobus Magne-<lb/>tibus percuſſis exit Ignis, etiamſi non tam copioſus, quam cum <lb/>alteruter chalybe percutitur, hoc teſtante Nob. </s> <s xml:id="echoid-s353" xml:space="preserve">Boyleo, qui plu-<lb/>rimos Magnetes examinavit.</s> <s xml:id="echoid-s354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s355" xml:space="preserve">Brevitatis ergo plurima de Magnete præteribo, tam quæ ſpectant <lb/>tempus, quo primum inventus eſt, quam inventorem, quia hæc <lb/>ſunt incerta; </s> <s xml:id="echoid-s356" xml:space="preserve">omittamque ejus Generationem & </s> <s xml:id="echoid-s357" xml:space="preserve">Loca natalia, in hoc <lb/>Terrarum orbe, de his vide Normannum in New. </s> <s xml:id="echoid-s358" xml:space="preserve">Attractiv. </s> <s xml:id="echoid-s359" xml:space="preserve">cap. </s> <s xml:id="echoid-s360" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s361" xml:space="preserve">nec attingam ejus nomina diverſa, varios colores, diverſiſſimasque <lb/>compactiones & </s> <s xml:id="echoid-s362" xml:space="preserve">ſubſtantias, de quibus fuſe & </s> <s xml:id="echoid-s363" xml:space="preserve">ſæpius a plurimis autori-<lb/>bus actum eſt, quorum nonnulli, uti Gilbertus, Kircherus, Cabeus, <lb/>integra volumina, ſolam doctrinam magneticam comprehendentia, <lb/>adimpleverunt.</s> <s xml:id="echoid-s364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s365" xml:space="preserve">Omnes effectus Magnetici huc usque cogniti ad quinque diverſas claſ-<lb/>ſes commode reduci poſſe videntur. </s> <s xml:id="echoid-s366" xml:space="preserve">(1) ad Actionem unius Magnetis in <lb/>alterum. </s> <s xml:id="echoid-s367" xml:space="preserve">(2) ad Actionem Magnetis in Ferrum. </s> <s xml:id="echoid-s368" xml:space="preserve">(3) ad Directionem <lb/>Magnetis & </s> <s xml:id="echoid-s369" xml:space="preserve">Ferri affricti Magneti verſus certas cæli plagas. </s> <s xml:id="echoid-s370" xml:space="preserve">(4) ad <lb/>Actionem ferri in aliud ferrum Magneti affrictum vel non affrictum, <lb/>& </s> <s xml:id="echoid-s371" xml:space="preserve">mutationes virium ex inflexione. </s> <s xml:id="echoid-s372" xml:space="preserve">(5) ad Effectus Ferri ſibi diu in <lb/>eodem ſitu commiſſi. </s> <s xml:id="echoid-s373" xml:space="preserve">Hunc ordinem, qui mihi commodiſſimus vi-<lb/>ſus eſt, in ſequentibus ſequar; </s> <s xml:id="echoid-s374" xml:space="preserve">idcirco hanc Diſſertationem in V. <lb/></s> <s xml:id="echoid-s375" xml:space="preserve">Capita diſtribui, quæ nunc aggrediar.</s> <s xml:id="echoid-s376" xml:space="preserve"/> </p> <pb o="11" file="0025" n="25"/> </div> <div xml:id="echoid-div10" type="section" level="1" n="10"> <head xml:id="echoid-head15" xml:space="preserve">DISSERTATIO <lb/>PHYSICA <lb/>EXPERIMENTALIS <lb/>DE <lb/>MAGNETE.</head> <head xml:id="echoid-head16" xml:space="preserve">CAPUT I.</head> <head xml:id="echoid-head17" style="it" xml:space="preserve">DE ACTIONE MAGNETUM IN SE MUTUO.</head> <p> <s xml:id="echoid-s377" xml:space="preserve">Eſt hac tempeſtate notiſſimum, Magnetes in ſe invicem agere, <lb/>ſejunctos mutuo quaſi amore ſe allicere, ad ſe appropinqua-<lb/>re, conjungi, atque cohærere, quo latere ſe attingunt, & </s> <s xml:id="echoid-s378" xml:space="preserve"><lb/>tum tam firmiter ſe amplecti, ut non niſi vi magna ſeparari <lb/>divellique queant: </s> <s xml:id="echoid-s379" xml:space="preserve">verum in hiſce Lapidibus altera reſidet proprie-<lb/>tas, qua ſeſe iterum fugant, majus ſpatium, quo diſtent, poſtulan-<lb/>tes; </s> <s xml:id="echoid-s380" xml:space="preserve">haud aliter, ac ſi odio ſemet ipſos proſequerentur, nec unus <lb/>alterius conſpectum ferre vellet. </s> <s xml:id="echoid-s381" xml:space="preserve">Non deprehenditur Amor aut odi-<lb/>um in hoc alterove tantum, ſed mutuo ſe amant, mutuo ſe oderunt: <lb/></s> <s xml:id="echoid-s382" xml:space="preserve">non appetit hic fortius ſocium quam alter, nec reſpuit eum inæ-<lb/>quali impetu; </s> <s xml:id="echoid-s383" xml:space="preserve">ſed quantum hic agit, tantum viciſſim reagitur ab <lb/>altero; </s> <s xml:id="echoid-s384" xml:space="preserve">ſuntque omnes actiones & </s> <s xml:id="echoid-s385" xml:space="preserve">reactiones inter ſe accuratiſſime <lb/>æquales: </s> <s xml:id="echoid-s386" xml:space="preserve">Imponantur enim duo Magnetes parvis ligneis ſcaphis, <lb/>libere innatantibus Aquæ ſtagnanti, poſitæque in loco a nullo vento <pb o="12" file="0026" n="26" rhead="DISSERTATIO"/> perflato, nec plus diſtent, quam ut in ſe agere queant; </s> <s xml:id="echoid-s387" xml:space="preserve">ambæ ſcaphæ <lb/>ſibi adnatabunt, & </s> <s xml:id="echoid-s388" xml:space="preserve">ſibi in medio quodam intervalli puncto occur-<lb/>rent; </s> <s xml:id="echoid-s389" xml:space="preserve">quod accurate medium fuiſſet, ſi tum ſcaphæ, tum Magnetes <lb/>ejusdem ponderis & </s> <s xml:id="echoid-s390" xml:space="preserve">magnitudinis fuiſſent.</s> <s xml:id="echoid-s391" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s392" xml:space="preserve">Attingent ſe ſcaphæ in aliquibus punctis, in quibus contactus ſem-<lb/>per repetetur, quotieſcunque ambas a ſe removeris. </s> <s xml:id="echoid-s393" xml:space="preserve">Invertatur au-<lb/>tem alterutra Scapha, ut latere priori oppoſito Magnes Magnetem <lb/>reſpiciat, a ſe invicem ambo recedent, atque æquali velocitate fu-<lb/>gient: </s> <s xml:id="echoid-s394" xml:space="preserve">Spectari iidem effectus facilius poſſunt hoc modo: </s> <s xml:id="echoid-s395" xml:space="preserve">Vide Tab. <lb/></s> <s xml:id="echoid-s396" xml:space="preserve">I. </s> <s xml:id="echoid-s397" xml:space="preserve">Fig. </s> <s xml:id="echoid-s398" xml:space="preserve">I. </s> <s xml:id="echoid-s399" xml:space="preserve">Magnes C funi alligatus ſuspendatur ex Bilancis brachio <lb/>B, factoque æquilibrio cum pondere Lanci A impoſito, infra C ali-<lb/>us ponatur Magnes D; </s> <s xml:id="echoid-s400" xml:space="preserve">illico cum impetu ruit C verſus D, elevat-<lb/>que pondus A, haud aliter ac ſi gravitatem, ſimilemve impetum ſibi <lb/>conciliaſſet.</s> <s xml:id="echoid-s401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s402" xml:space="preserve">Quod ſi converteris Magnetem D, ut oppoſito latere reſpiciat C, <lb/>fugit a D, adſcendit, ſeſe quaſi leviorem reddit, nec ad æquilibri-<lb/>um pervenit unquam, niſi vel pondere aggravetur, vel D removea-<lb/>tur: </s> <s xml:id="echoid-s403" xml:space="preserve">quod ſi D ponatur in ſuperiori loco E, iterum accedit Magnes <lb/>C ad E, ſed converſo Magnete E, recedit C deſcendendo in locum <lb/>inferiorem, quam ubi æquilibrium fecit. </s> <s xml:id="echoid-s404" xml:space="preserve">Ex hiſce binis igitur effe-<lb/>ctibus, quos edunt in ſe Magnetes, manifeſto liquet, eos in ſe agere, <lb/>actiones mutuas eſſe æquales, & </s> <s xml:id="echoid-s405" xml:space="preserve">proinde Reactionem dari æqualem <lb/>Actioni.</s> <s xml:id="echoid-s406" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s407" xml:space="preserve">Hæc Magnetis vis in admirationem rapuit Plinium, qui Lib. </s> <s xml:id="echoid-s408" xml:space="preserve">36. <lb/></s> <s xml:id="echoid-s409" xml:space="preserve">cap. </s> <s xml:id="echoid-s410" xml:space="preserve">16. </s> <s xml:id="echoid-s411" xml:space="preserve">in hæc verba erumpit: </s> <s xml:id="echoid-s412" xml:space="preserve">Quid Magnete mirabilius, aut qua <lb/>in parte Naturæ major improbitas? </s> <s xml:id="echoid-s413" xml:space="preserve">dederat vocem ſaxis reſponden-<lb/>tem homini, ſed quid Lapidis rigore pigrius? </s> <s xml:id="echoid-s414" xml:space="preserve">ecce ſenſus manusque <lb/>tribuit illi: </s> <s xml:id="echoid-s415" xml:space="preserve">quid Ferri duritie pugnacius? </s> <s xml:id="echoid-s416" xml:space="preserve">ſed cedit & </s> <s xml:id="echoid-s417" xml:space="preserve">patitur mo-<lb/>res: </s> <s xml:id="echoid-s418" xml:space="preserve">trahitur namque a Magnete Lapide, domitrixque illa rerum <lb/>omnium materia ad inane neſcio quid currit; </s> <s xml:id="echoid-s419" xml:space="preserve">atque ut propius ve-<lb/>nit, aſſiſtit, teneturque, & </s> <s xml:id="echoid-s420" xml:space="preserve">complexu hæret. </s> <s xml:id="echoid-s421" xml:space="preserve">Quando etiam Tha-<lb/>les Mileſius ad Magnetis operationes quondam attendebat, quæ ad-<lb/>miranda varietate ſuum percellebant animum, neque ab externa pro-<lb/>ficiſci cauſa videbantur, Animam Magneti attribuere non dubitavit, <lb/>ſecumque conſentientem in eadem ſententia poſtea habuit Scaligerum.</s> <s xml:id="echoid-s422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s423" xml:space="preserve">Cognito Magnetum verſus ſe invicem acceſſu, indagandum erat, <pb o="13" file="0027" n="27" rhead="DEMAGNETE."/> quomodo ad ſe appropinquent, an cum iisdem, an cum diverſis viribus <lb/>in variis diſtantiis? </s> <s xml:id="echoid-s424" xml:space="preserve">tum quænam proportio virium in dato intervallo <lb/>obtineret? </s> <s xml:id="echoid-s425" xml:space="preserve">deinde quærenda erat cauſa, quæ moveret pelleretve ver-<lb/>ſus ſe mutuo Magnetes in proportione diſtantiarum obſervata: </s> <s xml:id="echoid-s426" xml:space="preserve">ho-<lb/>rum enim cognitionem deſiderant Philoſophi, ut intelligant evidenter, <lb/>quid ſit Magnes, & </s> <s xml:id="echoid-s427" xml:space="preserve">quomodo intima hujus Lapidis natura ſit comparata: <lb/></s> <s xml:id="echoid-s428" xml:space="preserve">In cauſa divinanda multi plurimum operæ poſuerunt ab aliquot re-<lb/>tro ſeculis, verum qualis ſit virium Attractricium proportio ad di-<lb/>verſa intervalla indagaverunt pauci: </s> <s xml:id="echoid-s429" xml:space="preserve">Inter primos, qui ad Magnetis <lb/>proprietates intelligendas hoc poſtulari rite animadverterunt, & </s> <s xml:id="echoid-s430" xml:space="preserve">id-<lb/>circo proportionem quæſiverunt, fuit artificiofiſſimus Hauksbejus, <lb/>deinde Nobiliſſimus Taylor, tandem Eruditiſſimus Whiſtonus; </s> <s xml:id="echoid-s431" xml:space="preserve">qui <lb/>varia methodo id Problema ſolvere conati ſunt: </s> <s xml:id="echoid-s432" xml:space="preserve">Quoniam vero Hauks-<lb/>bejana methodus nequidem ipſis Britannis ſatisfecerat, neque mihi <lb/>adeo ſimplex viſa fuit, ac deſiderari poſſet, idem Problema arripui, <lb/>conatus id alio ſolvere modo, perquam ſimplici & </s> <s xml:id="echoid-s433" xml:space="preserve">naturali, ad <lb/>quem me conſpectus antea memoratorum Experimentorum deduxit: </s> <s xml:id="echoid-s434" xml:space="preserve"><lb/>Quemadmodum enim ope Stateræ corporum pondera expendimus, <lb/>ita vires Attractrices ope ponderum in Bilance cognoſci, & </s> <s xml:id="echoid-s435" xml:space="preserve">cum iis <lb/>comparari poſſe videbam, earumque magnitudo in variis oſtendi di-<lb/>ſtantiis: </s> <s xml:id="echoid-s436" xml:space="preserve">quod ut clare intelligatur, methodum deſcribam, ex qua ju-<lb/>dicium ferri poteſt, utrum ſatis accurrate experimenta inſtituta ſint, <lb/>tum ut repeti poſſent cum aliis, quam quibus uſus fui Magnetibus, <lb/>corumque virtus eodem modo explorari & </s> <s xml:id="echoid-s437" xml:space="preserve">adnotari.</s> <s xml:id="echoid-s438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s439" xml:space="preserve">Tab. </s> <s xml:id="echoid-s440" xml:space="preserve">1. </s> <s xml:id="echoid-s441" xml:space="preserve">Fig. </s> <s xml:id="echoid-s442" xml:space="preserve">2. </s> <s xml:id="echoid-s443" xml:space="preserve">Elegi accuratiſſimam Libram XG, cujus <lb/>axis admodum acutus politusque erat, ut ſuper eo jugum XG lu-<lb/>briciſſime moveretur, atque ab {1/20} grani parte alterutri extre-<lb/>mitati G vel X impoſita, deprimeretur; </s> <s xml:id="echoid-s444" xml:space="preserve">ut Libræ minima quoque <lb/>depreſſio manifeſto conſpiceretur, examen ejus in acutiſſimam termi-<lb/>nabatur cuſpidem, quæ opponebatur pinnulæ tenui V, deorfum promi-<lb/>nenti ex media ſuperiori parte trutinarum, hæ in latos expanſæ ibi an-<lb/>nulos, liberum relinquebant obſervationi locum, an examen accu-<lb/>rate reſponderet pinnulæ, an ab alterutro declinaret latere, & </s> <s xml:id="echoid-s445" xml:space="preserve">quan-<lb/>tum, hoc eſt, an æquilibrium ab utroque Libræ latere foret, an ſe-<lb/>cus: </s> <s xml:id="echoid-s446" xml:space="preserve">ad extremitatem G annexui funem GH, multos pedes longum, <lb/>ambientemque Magnetem H ſphæricum, quem Terrellam appel- <pb o="14" file="0028" n="28" rhead="DISSERTATIO"/> lant Philoſophi, poſtulabatur autem funis tam longus, ne Magnes <lb/>H in ipſam ageret Libram GX, quæ ex Chalybe eſt compoſita; </s> <s xml:id="echoid-s447" xml:space="preserve">ex <lb/>altero extremo Libræ X pendebat Lanx cuprea F, pondera excipi-<lb/>ens, quæ gravitate ſua menſurabant vires Magnetum Attractrices.</s> <s xml:id="echoid-s448" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s449" xml:space="preserve">Quoniam ad varias diſtantias Magnetum a ſe mutuo vires erant ex-<lb/>plorandæ, oportebat ut Libra attolli deprimive poſſet, & </s> <s xml:id="echoid-s450" xml:space="preserve">ut Mag-<lb/>nes ex ea ſuſpenſus ſemper eidem puncto alterius fixi Magnetis res-<lb/>ponderet, ita attollenda erat Bilanx, ut in eadem linea, ad hori-<lb/>zontem perpendiculari ſemper foret: </s> <s xml:id="echoid-s451" xml:space="preserve">quamobrem ejus uncum ſupe-<lb/>riorem Q immiſi crenæ parallelepipedi lignei QB, eique ope clavi E <lb/>affixi: </s> <s xml:id="echoid-s452" xml:space="preserve">transmittebatur parallelepipedum QB per foramen quadratum <lb/>Z, aſſeri DC inſculptum, qui parieti immobilis inhærebat, adeout cum <lb/>Ligno BQ Libra nunc attolli deprimique potuerit, quemadmodum de-<lb/>ſiderabatur, quod ut facillime fieret, ei annexus fuit funis B d c e M, <lb/>ſupra Cochleam A transmiſſus: </s> <s xml:id="echoid-s453" xml:space="preserve">ſi ex ſolo fune pependiſſet Libra, <lb/>perpetuo intorta fuiſſet, fune ſe convolvente aut evolvente ſemper <lb/>pro varia aeris ſiccitate, unde absque apparatu modo ante deſcripto <lb/>nihil obſervari poterat: </s> <s xml:id="echoid-s454" xml:space="preserve">Alter Magnes, in quem operari debebat <lb/>prior H, erat quoque Terrella NO, inſiſtens rotundo aſſeri, qui in <lb/>medio excavatus erat, ut eo facilius Magnes NO poneretur in ſitu <lb/>quolibetcunque; </s> <s xml:id="echoid-s455" xml:space="preserve">aſſer tripes inſiſtebat Menſæ firmæ ligneæ TT, quæ <lb/>nullos clavosferreos, nihilque ferri continebat, ne mutua in ſe Ma-<lb/>gnetum actio turbaretur.</s> <s xml:id="echoid-s456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s457" xml:space="preserve">Hoc apparatu præmiſſo, pondus Magnetis H, funisque GH ex-<lb/>ploravi, ſublato Magnete altero N O a Tabula: </s> <s xml:id="echoid-s458" xml:space="preserve">deinde ex unco G <lb/>demiſi pendulum aliquod ex tenui filo, ut notaretur locus huic ex-<lb/>tremitati Libræ G ſubjectus; </s> <s xml:id="echoid-s459" xml:space="preserve">in quo Magnetis ON polum locavi; <lb/></s> <s xml:id="echoid-s460" xml:space="preserve">converti tum ambos Magnetes, ut eorum axes, ſive Lineæ per polos <lb/>tranſeuntes, eſſent perpendiculariter ad horizontem erecti, atque in <lb/>una eademque linea producta: </s> <s xml:id="echoid-s461" xml:space="preserve">Polus Magnetis Hinferior attrahebat <lb/>acus Magneticæ polum auſtralem, ſed polus Magnetis N ſurſum <lb/>ſpectans, ejusdem acus polum Borealem alliciebat, quamobrem bini <lb/>poli Magnetum, ſibi amici, nunc ſe reſpiciebant: </s> <s xml:id="echoid-s462" xml:space="preserve">Experimenta in-<lb/>choaturus, attollebam prius Magnetem H ad magnam ab inferiori N <lb/>intercapedinem; </s> <s xml:id="echoid-s463" xml:space="preserve">& </s> <s xml:id="echoid-s464" xml:space="preserve">cum pondere lanci F immiſſo redegi in æquili-<lb/>brium; </s> <s xml:id="echoid-s465" xml:space="preserve">deinde paulatim relaxato fune M e c d B ad minores demiſi <pb o="15" file="0029" n="29" rhead="DEMAGNETE."/> Magnetem H diſtantias ab N, a quo cum attrahebatur, deprime-<lb/>batur, pereunte ita æquilibrio cum pondere lancis F; </s> <s xml:id="echoid-s466" xml:space="preserve">ſed id facile <lb/>reſtituebatur novis leviter & </s> <s xml:id="echoid-s467" xml:space="preserve">abſque concuſſione injectis ponduſculis, <lb/>quæ demonſtrabant, quantæ erant vires Magnetum in ſe in illis in-<lb/>tervallis: </s> <s xml:id="echoid-s468" xml:space="preserve">Diſtantiæ majores ope circini mere ænei menſurabantur, <lb/>in quibus hoc modo vires attractrices facile eruebam, ſed pergens <lb/>ad eas quoque in minoribus intervallis adnotandas, nimis difficile <lb/>obſervatu erat punctum æquilibrii, cum pondere F nondum ſatis <lb/>gravi, Magnes H propius accedebat ad N, pondere autem injecto <lb/>paulum graviori, nimium attollebatur Magnes H: </s> <s xml:id="echoid-s469" xml:space="preserve">huic incommodo <lb/>obviam ivi ſumendo lamellas æneas L L, vel in Fig 3. </s> <s xml:id="echoid-s470" xml:space="preserve">S. </s> <s xml:id="echoid-s471" xml:space="preserve">S. </s> <s xml:id="echoid-s472" xml:space="preserve">S, <lb/>quarum latitudo inter ſe diſcrepabat {1/12} pollicis, ejusmodi 12 præpa-<lb/>ravi, deinde alias quarum craſſities erat {1/24} tum {1/36}, & </s> <s xml:id="echoid-s473" xml:space="preserve">{1/48} pollicis: </s> <s xml:id="echoid-s474" xml:space="preserve">Impo-<lb/>ſita igitur aliqua lamella LL polo Magnetis NO, firmatoque in crena <lb/>capitis lignei K, demiſſus fuit Magnes ſuperior, donec lamellam ſuo <lb/>attingebat polo, atque examinis apex relpondebat pinnullæ V, quo <lb/>modo verum Magnetum intervallum dabatur, tum injecta fuerunt <lb/>Lanci F ponduscula, quæ erant grana Medica, donec vi At-<lb/>tractrice ſuperata Magnes H elevabatur: </s> <s xml:id="echoid-s475" xml:space="preserve">ne fallerer, bis ſemper re-<lb/>petii tentamen, prudentiſſime lanci immittendo & </s> <s xml:id="echoid-s476" xml:space="preserve">ſingulatim pon-<lb/>duſcula, quod ſi enim ex majori altitudine aliquod in eam incide-<lb/>rit, aut duo ſimul, avellitur Magnes H citius quam oportebat, ne-<lb/>que vera attractio in data diſtantia obtinetur: </s> <s xml:id="echoid-s477" xml:space="preserve">Inſuper dies elegi, <lb/>quibus experimenta capiebam, ſerenos, ſilentibus ventis; </s> <s xml:id="echoid-s478" xml:space="preserve">quoties-<lb/>cunque enim ventis agitatur Atmosphæra aëria, nunquam mobiliſſi-<lb/>ma noſtra Libra quieſcit, neque æquilibrium obſervari poteſt, etiam-<lb/>ſi in camera undique clauſa ſuſpendatur, Aer enim externus ſemper <lb/>cum eo, internas ædium partes occupante, communicat motum.</s> <s xml:id="echoid-s479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s480" xml:space="preserve">Tum ne aliquid omitterem, quod forſitan Experimento mutatio-<lb/>nem inferret, notavi diem Anni, altitudinem Baroſcopii, & </s> <s xml:id="echoid-s481" xml:space="preserve">Thermo-<lb/>ſcopii, cælique ſiccitatem, atque venti plagam, quod non inutile <lb/>fuiſſe animadverti poſtea, ita enim detexi Vires eorundem Magne-<lb/>tum variare diverſo anni tempore, atque idcirco ejus ſemper in his <lb/>Experimentis habendam eſſe rationem.</s> <s xml:id="echoid-s482" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s483" xml:space="preserve">Prolixior quidem fui in memoranda methodo tentaminum noſtro-<lb/>rum, ſed inde colligi poteſt, an cum ea, quæ deſiderari poſſet, fa- <pb o="16" file="0030" n="30" rhead="DISSERTATIO"/> cta ſint cura; </s> <s xml:id="echoid-s484" xml:space="preserve">quod ſi igitur error in illa irrepſerit, quemadmodum <lb/>raro absque ullo Experimenta multa fieri poſſunt, erit tamen par-<lb/>vus, neque ultra granum unum alterumve adſcendet.</s> <s xml:id="echoid-s485" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s486" xml:space="preserve">Quo brevior eſſe poſſem, conjeci in Tabellas eventus. </s> <s xml:id="echoid-s487" xml:space="preserve">Ecce cos, <lb/>quos collegi 10 Julii Anno 1725. </s> <s xml:id="echoid-s488" xml:space="preserve">Baroſcopio elevato ad 29 {3/12} polli-<lb/>ces Rhenolandicos: </s> <s xml:id="echoid-s489" xml:space="preserve">Thermoſcopio Fahrenheytii ex Mercurio fa-<lb/>cto, in aprico oſtendente gradum 61 {1/2}. </s> <s xml:id="echoid-s490" xml:space="preserve">Cælo humido, pluvioſo, <lb/>Vento leni Occidentali ſpirante, cum Magnetibus binis ſphæricis, <lb/>quorum ON habebat diametrum 6 {1/2} pollic. </s> <s xml:id="echoid-s491" xml:space="preserve">H vero 1 {1/2} pollic.</s> <s xml:id="echoid-s492" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div11" type="section" level="1" n="11"> <head xml:id="echoid-head18" xml:space="preserve">EXPERIMENTUMI</head> <note position="right" xml:space="preserve"> <lb/>In diſtantia \\ pollic. # Magnetum; \\ Lin. # Attractio æqualis \\ Granis Medicis <lb/>5 # 10 # 1 {1/4} <lb/>4 # 6 # 2 {1/4} <lb/>3 # 9 # 3 <lb/>2 # 4 # 9 <lb/>1 # 9 # 12 <lb/># 12 # 23 <lb/># 11 # 23 {1/2} <lb/># 10 # 26 {1/4} <lb/># 9 # 29 <lb/># 8 # 30 {3/4} <lb/># 7 # 33 <lb/># 6 # 38 {1/2} <lb/># 5 # 43 {1/2} <lb/># 4 # 50 {1/2} <lb/># 3 # 62. <lb/># 2 # 79. <lb/># 1 {3/4} # 81. <lb/># 1 # 140. <lb/># {1/2} # 186. <lb/># {1/3} # 240. <lb/># 0 # 340. <lb/></note> <pb o="17" file="0031" n="31" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s493" xml:space="preserve">Elicimus ex hiſce Experimentis ſequentia Corollaria.</s> <s xml:id="echoid-s494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s495" xml:space="preserve">(1) Magnetes duos ſe attrahere diverſis viribus in variis diſtantiis a <lb/>ſe invicem, & </s> <s xml:id="echoid-s496" xml:space="preserve">quidem eo fortius ſe appetere, quo ſibi propiores ſunt; <lb/></s> <s xml:id="echoid-s497" xml:space="preserve">unde in mutuo contactu fortiſſime in ſe agunt, nam vires quibus <lb/>ſe contingentes attrahebant, erant æquales ponderi 340 granorum, & </s> <s xml:id="echoid-s498" xml:space="preserve"><lb/>in diſtantia 12 pollicum modo æquabant 23 grana.</s> <s xml:id="echoid-s499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s500" xml:space="preserve">Corol. </s> <s xml:id="echoid-s501" xml:space="preserve">2. </s> <s xml:id="echoid-s502" xml:space="preserve">Et apparet ex inſpectis Experimentis vires attrahentes <lb/>nondum eſſe in tam alta ratione, quæ eſt inverſa diſtantiarum, ſed in <lb/>minori: </s> <s xml:id="echoid-s503" xml:space="preserve">Cum enim ad diſtantiam {1/2} lineæ ſit vis attrahens 186 gra-<lb/>norum, ad diſtantiam duplo majorem, ſive 1 lineæ, invenitur hæc vis <lb/>140 granorum, quod ſi in ratione inverſa diſtantiarum hæc vis fuiſſet, <lb/>pondera hæc darentur</s> </p> <note position="right" xml:space="preserve"> <lb/>Diſtant. # pond. ex calculo. # pondera vera <lb/>{1/2} # 186 # 186 <lb/>1 # 93 # 140 <lb/>2 # 46 {1/2} # 79 <lb/>4 # 23 {1/4} # 50 {1/2} <lb/>8 # 11 {5/8} # 33. <lb/></note> <p> <s xml:id="echoid-s504" xml:space="preserve">Si alias ſumamus obſervatas diſtantias, iterum invenimus attractio-<lb/>nes majores, quam calculus memoratus indicaret.</s> <s xml:id="echoid-s505" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtant. # pond. ex calculo. # pondera vera <lb/>{1/3} # 240 # 240 <lb/>1 # 80 # 140 <lb/>3 # 26 {1/3} # 62 <lb/>9 # 8 {7/9} # 29 <lb/>27 # 3 fere # 9. <lb/></note> <p> <s xml:id="echoid-s506" xml:space="preserve">Corol. </s> <s xml:id="echoid-s507" xml:space="preserve">3. </s> <s xml:id="echoid-s508" xml:space="preserve">Quod ſi attendamus ad proportionem virium attrahen-<lb/>tium, eam nequaquam deprehendimus eſſe aliquam conſtantem, nam <lb/>pondus ad {1/2} lineam diſtantiæ fuit 186 granorum, qui numerus eſt ad 140 <lb/>grana, uti 1 {23/70} ad 1. </s> <s xml:id="echoid-s509" xml:space="preserve">quæ proportio ſemper in aliis Sequentibus obti-<lb/>neret numeris, poſita quadam ratione conſtanti: </s> <s xml:id="echoid-s510" xml:space="preserve">verum 140 ſunt ad <lb/>79:</s> <s xml:id="echoid-s511" xml:space="preserve">: 1 {61/79}. </s> <s xml:id="echoid-s512" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s513" xml:space="preserve">Sunt 79 ad 50 {1/2}:</s> <s xml:id="echoid-s514" xml:space="preserve">: 1 {57/101} ad 1. </s> <s xml:id="echoid-s515" xml:space="preserve">tum 50 {1/2} ad 33:</s> <s xml:id="echoid-s516" xml:space="preserve">: 1 {35/66} ad 1.</s> <s xml:id="echoid-s517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s518" xml:space="preserve">In quibus omnibus profecto obtinet alia proportio. </s> <s xml:id="echoid-s519" xml:space="preserve">Quoniam in-<lb/>numeræ dari poſſunt proportiones, multum laboris impendi, ut ali-<lb/>quam eruerem ex datis numeris, ſive ſimplicem, ſive compoſitam ex <pb o="18" file="0032" n="32" rhead="DISSERTATIO"/> duabus, aut pluribus, ſed incaſſum hucusque adhibitus fuit omnis <lb/>labor.</s> <s xml:id="echoid-s520" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div12" type="section" level="1" n="12"> <head xml:id="echoid-head19" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s521" xml:space="preserve">Nolui vero acquieſcere in Experimentis cum hiſce tantum Mag-<lb/>netibus factis, quia ſperabam fortuito me obſervaturum aliquid <lb/>in aliis, quod hi bini ſuppeditare non potuerant: </s> <s xml:id="echoid-s522" xml:space="preserve">poſſet enim he-<lb/>terogeneitas materiæ alterutrius cauſa eſſe, quo minus quædam accu-<lb/>rata & </s> <s xml:id="echoid-s523" xml:space="preserve">conſtans proportio inter vires attrahentes & </s> <s xml:id="echoid-s524" xml:space="preserve">diſtantias obtine-<lb/>ret. </s> <s xml:id="echoid-s525" xml:space="preserve">Adeoque eundem Magnetem ſphæricum magnum NO reliqui in <lb/>eodem menſæ loco, ſed ex bilance GX ſuspendebam Magnetem ali-<lb/>um, nudum ſive non armatum, (quales ſemper Experimentis inſer-<lb/>vierunt;) </s> <s xml:id="echoid-s526" xml:space="preserve">forma hujus Magnetis erat parrallelepipedo ſimilis, altitu-<lb/>dinis 2 pollic. </s> <s xml:id="echoid-s527" xml:space="preserve">longitudinis 2 {1/2}, latitudinis 1 {7/12}: </s> <s xml:id="echoid-s528" xml:space="preserve">hunc etiam ita ſuspen-<lb/>debam, ut ambo poli eſſent in recta ad horizontem perpendiculari, <lb/>& </s> <s xml:id="echoid-s529" xml:space="preserve">in eadem linea cum ambobus polis Magnetis alterius, tum Expe-<lb/>rimenta dederunt attractionis ſequentes magnitudines.</s> <s xml:id="echoid-s530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s531" xml:space="preserve">Experimenta hæc ſunt facta 11 Julii Ao. </s> <s xml:id="echoid-s532" xml:space="preserve">1725. </s> <s xml:id="echoid-s533" xml:space="preserve">Baroſcopio elevato <lb/>ad 29 {5/24} pollic. </s> <s xml:id="echoid-s534" xml:space="preserve">Thermoſcopio Fahrenheiti ad 62 grad. </s> <s xml:id="echoid-s535" xml:space="preserve">flante Borea, <lb/>cælo ſicco & </s> <s xml:id="echoid-s536" xml:space="preserve">ſereno</s> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # Lin. # Attractiones æquales \\ granis Medicis <lb/>12 # 0 # 0 <lb/>9 # 0 # 1 {1/8}. <lb/>8 # 0 # 1 {1/2}. <lb/>7 # 6 # 2. <lb/>7 # 6 # 2 {1/2}. <lb/># 12 # 70 {1/2}. <lb/># 11 # 75 {1/2}. <lb/># 10 # 85. <lb/># 9 # 92. <lb/># 8 # 100. <lb/># 7 # 106. <lb/># 6 # 111. <lb/># 5 # 132. <lb/># 4 # 149. <lb/></note> <pb o="19" file="0033" n="33" rhead="DEMAGNETE."/> <note position="right" xml:space="preserve"> <lb/>Lin. # gran. Med. <lb/># 3 # 173. <lb/># 2 # 205. <lb/># 1 # 240. <lb/># {1/2} # 270. <lb/># 0 # 300. <lb/></note> </div> <div xml:id="echoid-div13" type="section" level="1" n="13"> <head xml:id="echoid-head20" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s537" xml:space="preserve">Explorandum duxi an ejusdem Magnetis vires Attractrices omni <lb/>tempore eſſent æque fortes; </s> <s xml:id="echoid-s538" xml:space="preserve">utrum caloris & </s> <s xml:id="echoid-s539" xml:space="preserve">frigoris viciſſitudo dis-<lb/>crepantiam inferret, atque Hyeme vires Magnetis diverſæ forent <lb/>ab iis, quæ Æſtate obſervatæ erant: </s> <s xml:id="echoid-s540" xml:space="preserve">Quamobrem repetii ponderatio-<lb/>nes virium Magneticarum die 24 menſis Decembris ejusdem anni, <lb/>cum iisdem Magnetibus, omni adhibito eodem apparatu, quo in <lb/>priori uſus fueram Experimento; </s> <s xml:id="echoid-s541" xml:space="preserve">& </s> <s xml:id="echoid-s542" xml:space="preserve">ecce eventus:</s> <s xml:id="echoid-s543" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # Lin. # Attractiones æquales \\ granis Medicis. <lb/>15 # 6 # 0 <lb/>13 # 6 # 0 <lb/>12 # 0 # vix {1/20} <lb/>11 # 0 # vix {1/8} <lb/>10 # 0 # vix {1/4} <lb/>9 # 0 # {1/2} <lb/>7 # 6 # 1 {1/2} <lb/>7 # 0 # 2 {1/2} <lb/># 12 # 70 {1/2} <lb/># 11 # 78 {1/2} <lb/># 10 # 87 <lb/># 9 # 94 <lb/># 8 # 106 <lb/># 7 # 114 <lb/># 6 # 131 <lb/># 5 # 146 <lb/># 4 # 172 <lb/># 3 # 190 <lb/></note> <pb o="20" file="0034" n="34" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Lin. # gran. Med. <lb/># 2 # 215 <lb/># 1 # 250 <lb/># {1/2} # 290 <lb/># 0 # 340 <lb/></note> <p> <s xml:id="echoid-s544" xml:space="preserve">In immediato contactu erant hic vires eædem attrahentes, atque <lb/>in immediato contactu prioris ſphærici Magnetis H cum hoc ſphæ-<lb/>rico NO in tabula poſito: </s> <s xml:id="echoid-s545" xml:space="preserve">verum in diſtantiis æqualibus a ſe invicem, <lb/>ac in prioribus Experimentis, magna videtur inter attractiones diffe-<lb/>rentia, & </s> <s xml:id="echoid-s546" xml:space="preserve">præterea notamus attractiones non eſſe in ratione inverſa <lb/>diſtantiarum, ſed in minori ratione, neque eas increſcere in quadam <lb/>conſtanti proportione, prout diſtantiæ increſcunt, aut minuuntur.</s> <s xml:id="echoid-s547" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s548" xml:space="preserve">Nam in Experimento ſecundo proportio virium ad diſtantias æqua-<lb/>les, inventa eſt juxta hos numeros.</s> <s xml:id="echoid-s549" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ. # vires. <lb/>{1/2} # 270 <lb/>1 # 240 <lb/>2 # 205 <lb/>4 # 149 <lb/>8 # 100 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # proportio. <lb/>1 {1/8} # 1 <lb/>1 {7/41} # 1 <lb/>1 {96/149} # 1 <lb/>1 {49/100} # 1 <lb/></note> <p> <s xml:id="echoid-s550" xml:space="preserve">Et in Experimento Tertio proportio virium ad diſtantias æquales <lb/>datur ſecundum hos numeros.</s> <s xml:id="echoid-s551" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ. # vires. # <lb/>{1/2} # 290 <lb/>1 # 250 <lb/>2 # 215 <lb/>4 # 172 <lb/>8 # 106 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # proportio. <lb/>1 {4/25} # 1 <lb/>1 {9/43} # 1 <lb/>1 {43/172} # 1 <lb/>1 {18/53} # 1 <lb/></note> <p> <s xml:id="echoid-s552" xml:space="preserve">Unde etiam liquet non obtinere eandem proportionem virium at-<lb/>trahentium Hyeme & </s> <s xml:id="echoid-s553" xml:space="preserve">Æſtate, modo inter ſeſe comparemus pro-<lb/>portiones in ambobus Experimentis erutas.</s> <s xml:id="echoid-s554" xml:space="preserve"/> </p> <pb o="21" file="0035" n="35" rhead="DEMAGNETE."/> </div> <div xml:id="echoid-div14" type="section" level="1" n="14"> <head xml:id="echoid-head21" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s555" xml:space="preserve">Verum præterea ſumſi duos alios Magnetes, qui ambo erant for-<lb/>mæ parallelepipedi, quorum unum ex Libra GX ſuspendebam, al-<lb/>terum menſæ TT imponebam, obſervando quantum fieri poteſt, <lb/>ut ambæ polares plagæ ſibi mutuo reſponderent in eadem linea ad ho-<lb/>rizontem perpendiculari: </s> <s xml:id="echoid-s556" xml:space="preserve">Magnitudo unius Magnetis erat hæc; </s> <s xml:id="echoid-s557" xml:space="preserve">longi-<lb/>tudo 2 {3/4} pollic. </s> <s xml:id="echoid-s558" xml:space="preserve">latitudo 2 {1/2} pollic. </s> <s xml:id="echoid-s559" xml:space="preserve">altitudo 1 {1/2} pollic. </s> <s xml:id="echoid-s560" xml:space="preserve">alter hujus Ma-<lb/>gnitudinis erat, altitudinis 2 poll, longitudinis 2 {1/2} latitudinis 1 {7/12} poll. <lb/></s> <s xml:id="echoid-s561" xml:space="preserve">eventus experimentorum cum his binis factorum repræſentatur in ſe-<lb/>quenti Tabula.</s> <s xml:id="echoid-s562" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # lin. # Attractiones æquales \\ granis Medicis. <lb/>9 # 4 # 0 <lb/>8 # 6 # 1 <lb/>7 # 9 # 1 <lb/>7 # 3 # 1 <lb/>6 # 5 # 1 <lb/>5 # 11 # 2 {1/2} <lb/>4 # 11 # 2 {1/2} <lb/>3 # 11 # 4 {1/2} <lb/>3 # 1 # 7 {1/2} <lb/>2 # 5 # 12 {1/2} <lb/>1 # 8 # 21 {1/2} <lb/># 10 # 45 <lb/># 5 # 95 <lb/># 0 # 128 <lb/></note> <p> <s xml:id="echoid-s563" xml:space="preserve">Ex quibus Experimentis nihil plus de proportione quadam viriùm <lb/>reſpondente diſtantiis, concludere poſſumus, quam ex præcedenti-<lb/>bus.</s> <s xml:id="echoid-s564" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div15" type="section" level="1" n="15"> <head xml:id="echoid-head22" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s565" xml:space="preserve">Adhibui deinde Magnetem magnum rotundum NO diametri 6 {1/2} pol- <pb o="22" file="0036" n="36" rhead="DISSERTATIO"/> licum, quem uti in Experimento I, II, III. </s> <s xml:id="echoid-s566" xml:space="preserve">impoſui TT menſæ, <lb/>cui inſiſtebat immobilis, & </s> <s xml:id="echoid-s567" xml:space="preserve">ex bilance ſuspendi Magnetem parallele-<lb/>pipedum, qui Experimento IV. </s> <s xml:id="echoid-s568" xml:space="preserve">inſerviit, fueratque longitudinis 2 {3/4} <lb/>poll. </s> <s xml:id="echoid-s569" xml:space="preserve">latitudinis 2 {1/2} poll. </s> <s xml:id="echoid-s570" xml:space="preserve">altitudinis 1 {1/2} poll. </s> <s xml:id="echoid-s571" xml:space="preserve">tum vero vires attractio-<lb/>nis fuerunt obſervatæ ſequentes.</s> <s xml:id="echoid-s572" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # Lin. # Grana \\ Medica. <lb/>19 # 0 # 0 <lb/>18 # 0 # 1 <lb/>17 # 4 # 1 {1/2} # idem fuit pondus in variis locis. <lb/>13 # 0 # 2 # idem pondus in variis diſtantiis. <lb/>9 # 9 # 2 {1/2} <lb/># 10 # 122 <lb/># 8 # 136 <lb/># 7 # 164 <lb/># 6 # 170 <lb/># 5 # 187 <lb/># 4 # 209 <lb/># 3 # 218 <lb/># 2 # 241 <lb/># 1 # 273 <lb/># 0 # 340 <lb/></note> <p> <s xml:id="echoid-s573" xml:space="preserve">Ex his rurſus patet nullam dari proportionem virium in diverſis <lb/>diſtantiis, nam Actiones horum Magnetum non fuerunt in ratione <lb/>ſimplici inverſa diſtantiarum a ſe, quippe cum diſtabant 1 linea, <lb/>actio erat æqualis 273 granis, cum 2 lineis aberant a ſe, Attractio <lb/>erat æqualis 241 granis.</s> <s xml:id="echoid-s574" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s575" xml:space="preserve">Si vero eſſent actiones in inverſa ratione diſtantiarum, tum ad di-<lb/>ſtantiam 2 linearum, pondus, attractioni æquipollens, requiſitum <lb/>fuiſſet 136 {1/2} gran. </s> <s xml:id="echoid-s576" xml:space="preserve">nempe dimidium 273 granorum.</s> <s xml:id="echoid-s577" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s578" xml:space="preserve">Sunt autem hæ vires in proportione ad ſe invicem uti 1 ad 1 {32/273}. <lb/></s> <s xml:id="echoid-s579" xml:space="preserve">quod ſi vires in eadem proportione manerent, decreſcendo in majoribus <lb/>diſtantiis, tum ad diſtantiam 4 linearum eſſent æquales 215 {218/305} granis. </s> <s xml:id="echoid-s580" xml:space="preserve">Sed <lb/>Experimentum eas exhibet æquales 309 granis, adeoque hic calculus non <lb/>reſpondet obſervationi: </s> <s xml:id="echoid-s581" xml:space="preserve">demonſtratu facile foret eodem modo Experi- <pb o="23" file="0037" n="37" rhead="DE MAGNETE."/> menta reliqua abludere a conſtanti proportione quacunque ope cal-<lb/>culi detegenda in diſtantiis aliis.</s> <s xml:id="echoid-s582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s583" xml:space="preserve">Atque hoc idem eſt quod Nobiliſſimus Taylor adnotavit, con-<lb/>cludendo ex ſuis Experimentis, vires Magneticas non reſpondere di-<lb/>ſtantiis, ſed proportiones magis decreſcere in diſtantiis majoribus, <lb/>quam in minoribus. </s> <s xml:id="echoid-s584" xml:space="preserve">Quod ex omnibus noſtris quoque Experimen-<lb/>tis colligi poteſt. </s> <s xml:id="echoid-s585" xml:space="preserve">Verum Philoſophus addidit, in ſuis Experi-<lb/>mentis cum duabus acubus factis, ad diſtantiam 2 {1/2} pollicum, vires <lb/>nondum mutari ut quadrata diſtantiarum, & </s> <s xml:id="echoid-s586" xml:space="preserve">ad 10 pollices, vires <lb/>plus mutari, quam ſunt Cubi diſtantiarum, cum exponens eſſet æ-<lb/>qualis 3 {1/4}. </s> <s xml:id="echoid-s587" xml:space="preserve">Vid. </s> <s xml:id="echoid-s588" xml:space="preserve">Philoſ. </s> <s xml:id="echoid-s589" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s590" xml:space="preserve">No. </s> <s xml:id="echoid-s591" xml:space="preserve">368. </s> <s xml:id="echoid-s592" xml:space="preserve">p. </s> <s xml:id="echoid-s593" xml:space="preserve">204.</s> <s xml:id="echoid-s594" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s595" xml:space="preserve">Addiſcimus tamen ex omnibus his V. </s> <s xml:id="echoid-s596" xml:space="preserve">Experimentis, (1) Actiones <lb/>duorum Magnetum non ſieri in quacunque diſtantia a ſe mutuo, ſed <lb/>diſtantiam Actionis eorum eſſe determinatam, nam in Experimento <lb/>IV. </s> <s xml:id="echoid-s597" xml:space="preserve">non extenditur ad 10 pollices, in Experimento V. </s> <s xml:id="echoid-s598" xml:space="preserve">non extendi-<lb/>tur ad 19 pollices, ſaltem mobiliſſima Libra nullum ſignum Actionis <lb/>mutuæ Magnetum in ſe invicem edidit; </s> <s xml:id="echoid-s599" xml:space="preserve">unde ſi ex Experimentis tan-<lb/>tum ratiocinabor, non poſſum concludere Actiones Magnetum ſe <lb/>ad maximas diffundere diſtantias: </s> <s xml:id="echoid-s600" xml:space="preserve">fateor tamen ex aliis Experimentis <lb/>cum verſoriis mobiliſſimis conſtare, Magnetes agere in hæc ad multo <lb/>majores diſtantias, quam ope hujus methodi oſtendi poſſit, quia <lb/>cum multo minori attritu verſorium ſupra ſuam cuſpidem, quam Li-<lb/>bra ſupra axin vertitur: </s> <s xml:id="echoid-s601" xml:space="preserve">ſed nihilominus idem colligere licebit ex <lb/>Actione Magnetis in verſoria, quia hæc ad multorum pedum di-<lb/>ſtantiam a Magnete non moventur, quippe nunquam deprehendi ad <lb/>majorem diſtantiam exporrectam fuiſſe vim, quam ad 14 pedes Rhe-<lb/>nolandicos, quando præſtantiſſimum verſorio 6 pollicum opponebam <lb/>Magnetem.</s> <s xml:id="echoid-s602" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s603" xml:space="preserve">(2) Quod ſi comparemus hæc V. </s> <s xml:id="echoid-s604" xml:space="preserve">Experimenta inter ſe, tum <lb/>obſervari poteſt Vim omnium Magnetum non exporrigi ad ean-<lb/>dem diſtantiam, ſed ab his ad majorem, ab aliis ad minorem, nam <lb/>in Experimento V. </s> <s xml:id="echoid-s605" xml:space="preserve">exporrigebatur ad 18 pollices, in Experimento <lb/>IV. </s> <s xml:id="echoid-s606" xml:space="preserve">ad 9 pollices, in tertio ad 13 pollices, in ſecundo Experimento <lb/>ad 12 pollices. </s> <s xml:id="echoid-s607" xml:space="preserve">Imo habui Magnetem magnum, cujus vis ſenſibilis <lb/>adhuc erat ad diſtantiam 11 pedum, imo aliquando ad 14.</s> <s xml:id="echoid-s608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s609" xml:space="preserve">(3) Præterea cum obſervamus vires Magnetum attractrices in Ex- <pb o="24" file="0038" n="38" rhead="DISSERTATIO"/> perimentis I, II, V. </s> <s xml:id="echoid-s610" xml:space="preserve">in diſtantiis æqualium linearum eſſe admodum <lb/>diverſas, in Experimento quinto eſſe majores quam in tertio, & </s> <s xml:id="echoid-s611" xml:space="preserve">in <lb/>tertio majores quam in primo, mirandum tamen eſt in immediato <lb/>contactu Magnetum vires eſſe easdem, nam ſunt æquales 340 gra-<lb/>nis: </s> <s xml:id="echoid-s612" xml:space="preserve">idque eo plus eſt mirandum, cum Magnetes ſuspenſi ex Libra, <lb/>qui tribus memoratis Experimentis inſervierunt, ſunt inæquales quo-<lb/>ad volumina, & </s> <s xml:id="echoid-s613" xml:space="preserve">gravitates, formasque habent diverſas: </s> <s xml:id="echoid-s614" xml:space="preserve">cumque vires <lb/>horum Magnetum etiam ſint valde diverſæ inter ſe, nam præſtan-<lb/>tiſſimus eſt Magnes rotundus primi Experimenti, licet ſit parvus; <lb/></s> <s xml:id="echoid-s615" xml:space="preserve">Sunt vires Magnetis Experimenti quinti mediocriter bonæ; </s> <s xml:id="echoid-s616" xml:space="preserve">ſed vires <lb/>illius adhibiti in tertio Experimento ſunt valde debiles. </s> <s xml:id="echoid-s617" xml:space="preserve">Accedit in-<lb/>ſuper, quod in primo Experimento duo globi ſe contingebant, in <lb/>tertio & </s> <s xml:id="echoid-s618" xml:space="preserve">quinto globus contingebat planam ſuperficiem: </s> <s xml:id="echoid-s619" xml:space="preserve">contactus <lb/>in his tribus caſubus eſt quidem in uno puncto, verum ultra conta-<lb/>ctus punctum ſuperſicies ſphæricæ illico magis a ſe recedendo diſtant, <lb/>quam ſuperficies ſphærica & </s> <s xml:id="echoid-s620" xml:space="preserve">plana: </s> <s xml:id="echoid-s621" xml:space="preserve">Cum mecum hæc omnia atten-<lb/>tius volvebam, incepi dubitare, an quidem Magnetum actio penderet <lb/>ab effluviis quibusdam Magneticis, vel Fluido quodam externo, <lb/>quocunque ſub nomine veniat; </s> <s xml:id="echoid-s622" xml:space="preserve">cui examini poſtea plus operæ impen-<lb/>di: </s> <s xml:id="echoid-s623" xml:space="preserve">Si enim pendeat Actio Magnetum duorum in ſe ab effluviis mu-<lb/>tuis, tum eo erit Actio major, quo effluvia ſunt copioſiora, & </s> <s xml:id="echoid-s624" xml:space="preserve">hæc <lb/>copia majori effluent ex Magnetibus generoſioribus, quam ex lan-<lb/>guidis; </s> <s xml:id="echoid-s625" xml:space="preserve">quamobrem multo plura exiviſſent eſfluvia ex iis, quibus <lb/>uſus fui in Experimento primo & </s> <s xml:id="echoid-s626" xml:space="preserve">quinto, quia hi præſtabant altero <lb/>in Experimento tertio adhibito: </s> <s xml:id="echoid-s627" xml:space="preserve">in immediato contactu tamen omni-<lb/>um vires æquales ſunt notatæ.</s> <s xml:id="echoid-s628" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div16" type="section" level="1" n="16"> <head xml:id="echoid-head23" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s629" xml:space="preserve">Huc usque examinaveram attractiones duorum polorum in ambo-<lb/>bus Magnetibus, verum indagandum duxi an corundem Magnetum <lb/>poli alteri ſibi obverſi easdem, an varias vires attrahentes exercerent, <lb/>quam bini priores examinati.</s> <s xml:id="echoid-s630" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s631" xml:space="preserve">Igitur Magnetem parvum ſphæricum H, qui primo Experimen-<lb/>to inſervierat, iterum ſuspendi ex fune Bilanci annexo, ſed ut po-<lb/>lus alter deorſum nunc eſſet converſus; </s> <s xml:id="echoid-s632" xml:space="preserve">tum Magnetem ſphæricum <pb o="25" file="0039" n="39" rhead="DE MAGNETE."/> NO majorem impoſui tabulæ TT ut antea, cujus polum alterum <lb/>ſurſum convertebam, binisque in linea perpendiculari ad horizon-<lb/>tem dispoſitis polis, obſervatisque omnibus cautelis, obſervavi attra-<lb/>ctiones mutuas ad varias Magnetum diſtantias, quas in ſequenti Ta-<lb/>bula adnotavi die 12 Julii Anni 1725.</s> <s xml:id="echoid-s633" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # lin. # Attractio. \\ gran. Medicor. <lb/>4 # 6 # 1 {3/4} <lb/>4 # 2 # 2 {1/4} <lb/>3 # 9 # 2 {3/4} <lb/>2 # 4 # 9 <lb/>1 # 9 # 12 <lb/># 12 # 26 <lb/># 11 # 28 <lb/># 10 # 31 <lb/># 9 # 34 <lb/># 8 # 36 <lb/># 7 # 39 <lb/># 6 # 44 <lb/># 5 # 48 <lb/># 4 # 59 <lb/># 3 # 68 <lb/># 2 # 89 <lb/># 1 # 132 <lb/># {1/2} # 155 <lb/># {1/3} # 225 <lb/># 0 # 310 <lb/></note> <p> <s xml:id="echoid-s634" xml:space="preserve">Quod ſi comparemus has vires cum iis, quas ſupra deſcripſi, ma-<lb/>gnam inter utrasque videmus differentiam, omnesque in his caſibus <lb/>eſſe minores, quam ſupra: </s> <s xml:id="echoid-s635" xml:space="preserve">quare poli bini Magnetis non exercent <lb/>easdem vires Attractionis in alium Magnetem, ſed diverſas.</s> <s xml:id="echoid-s636" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div17" type="section" level="1" n="17"> <head xml:id="echoid-head24" xml:space="preserve">EXPERIMENTUM VII. & VIII.</head> <p> <s xml:id="echoid-s637" xml:space="preserve">Videri poſſem non ſatis prudentis fuiſſe conſilii, ſi uno tantum rem <lb/>confectam credidiſſem Experimento, quamobrem plura feci: </s> <s xml:id="echoid-s638" xml:space="preserve">Adeo- <pb o="26" file="0040" n="40" rhead="DISSERTATIO"/> que Magnetem rotundum majorem ON, quo uſus fueram in Expe-<lb/>rimentis I, II, V. </s> <s xml:id="echoid-s639" xml:space="preserve">impoſui tabulæ immobilem, aliumque Magnetem, <lb/>quam quo hactenus uſus fueram, ſuspendi ex bilance, die 17 Februarii <lb/>Anni 1726. </s> <s xml:id="echoid-s640" xml:space="preserve">& </s> <s xml:id="echoid-s641" xml:space="preserve">polos ambos utriusque Magnetis ſe attrahentes, ſibi <lb/>obverti, ut notare attractionum æqualitatem vel inæqualitatem pos-<lb/>ſem, ecce igitur Experimenta in utroque caſu adnotata, quæ juxta <lb/>ſe poſui, ut melius uno oculi ictu conſpiceretur in eadem diſtantia <lb/>virium diverſitas.</s> <s xml:id="echoid-s642" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Exp. VII. <lb/>Poli duo amici \\ ad diſtantiam <lb/>Linear. # grana trahunt. <lb/>12 # 57 <lb/>11 # 63 <lb/>10 # 66 <lb/>9 # 70 <lb/>8 # 79 <lb/>7 # 83 <lb/>6 # 90 <lb/>5 # 101 <lb/>4 # 113 <lb/>3 # 124 <lb/>2 # 148 <lb/>1 # 168 <lb/>0 # 228 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Exp. VIII. <lb/>Poli duo amici alteri \\ ad diſtantiam <lb/>Linear. # grana trahunt. <lb/>12 # 72 <lb/>11 # 78 <lb/>10 # 87 <lb/>9 # 94 <lb/>8 # 106 <lb/>7 # 114 <lb/>6 # 131 <lb/>5 # 146 <lb/>4 # 172 <lb/>3 # 190 <lb/>2 # 215 <lb/>1 # 205 <lb/>0 # 340 <lb/></note> </div> <div xml:id="echoid-div18" type="section" level="1" n="18"> <head xml:id="echoid-head25" xml:space="preserve">EXPERIMENTUM IX, X, XI, XII.</head> <p> <s xml:id="echoid-s643" xml:space="preserve">Non acquieſcebam hifce Experimentis cum Magnetibus factis in <lb/>iis conditionibus, ut ambo poli eſſent directe ſibi obverſi in eadem <lb/>linea, itaque volui etiam videre quales quantæque forent attractio-<lb/>nes, quando Magnetes ſibi alio opponerentur modo, poſitis axibus <lb/>ſibi parallelis, vel ad rectos angulos: </s> <s xml:id="echoid-s644" xml:space="preserve">non quidem inde ſperabam me <lb/>multa detecturum, vel plurimum lucis in doctrina Magnetica fœ-<lb/>neraturum; </s> <s xml:id="echoid-s645" xml:space="preserve">ſed quia in Phyſicis aliquando caſu plus detegimus, quam <lb/>prævidemus; </s> <s xml:id="echoid-s646" xml:space="preserve">tum ne quædam omitterem ſpectantia hanc examinandi <lb/>methodum, denuo ſequentibus me accinxi tentaminibus: </s> <s xml:id="echoid-s647" xml:space="preserve">Magne- <pb o="27" file="0041" n="41" rhead="DE MAGNETE."/> tem rotundum majorem, qui binis præcedentibus Experimentis in-<lb/>ſervierat, uti ante in tabula immobilem locavi, ut linea polos jun-<lb/>gens eſſet horizonti perpendicularis, veluti in præcedentibus: </s> <s xml:id="echoid-s648" xml:space="preserve">ve-<lb/>rum Magnetem formæ parallelepipedi, quo modo ante uſus fueram, ita <lb/>ſuspendi ex Libra, ut linea jungens polos eſſet horizonti parallela; <lb/></s> <s xml:id="echoid-s649" xml:space="preserve">itaque quia 6 latera habebat, duo polaria ſuperius examinata, nunc <lb/>4 alia examinanda præbebat; </s> <s xml:id="echoid-s650" xml:space="preserve">examinavi igitur primum duo latera ſi-<lb/>bi oppoſita parallelaque; </s> <s xml:id="echoid-s651" xml:space="preserve">dein reliqua duo latera etiam ſibi oppoſita, <lb/>& </s> <s xml:id="echoid-s652" xml:space="preserve">adnotavi effectus ſequentes, quos in duabus tabulis exhibeo.</s> <s xml:id="echoid-s653" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s654" xml:space="preserve">Duo latera Magnetis ſibi oppoſita & </s> <s xml:id="echoid-s655" xml:space="preserve">polo eidem, rotundi Mague-<lb/>tis obverſa, ad diſtantiam in</s> </p> <note position="right" xml:space="preserve"> <lb/># Exp. IX. <lb/>Linear. # grana trahunt. <lb/>12 # 32 <lb/>11 # 34 <lb/>10 # 32 <lb/>9 # 34 <lb/>8 # 38 <lb/>7 # 43 <lb/>6 # 48 <lb/>5 # 56 <lb/>4 # 63 <lb/>3 # 74 <lb/>2 # 94 <lb/>1 # 114 <lb/>0 # 178 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Exp. X. <lb/>Linear. # grana trahunt. <lb/>12 # 32 <lb/>11 # 34 <lb/>10 # 37 <lb/>9 # 40 <lb/>8 # 46 <lb/>7 # 52 <lb/>6 # 56 <lb/>5 # 69 <lb/>4 # 76 <lb/>3 # 94 <lb/>2 # 115 <lb/>1 # 146 <lb/>0 # 196 <lb/></note> <p> <s xml:id="echoid-s656" xml:space="preserve">Duo alia latera ejusdem Magnetis ſibi oppoſita eidem polo rotun-<lb/>di Magnetis obverſa trahunt ad diſtantiam in</s> </p> <note position="right" xml:space="preserve"> <lb/># Exp. XI. <lb/># Linear. # grana. <lb/>12 # 20 <lb/>11 # 20 <lb/>10 # 24 <lb/>9 # 25 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Exp. XII. <lb/># Linear. # grana. <lb/>12 # 13 <lb/>11 # 13 <lb/>10 # 16 <lb/>9 # 16 <lb/></note> <pb o="28" file="0042" n="42" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># Exp. II. <lb/>Lin. # grana. <lb/>8 # 29 <lb/>7 # 34 <lb/>6 # 36 <lb/>5 # 44 <lb/>4 # 51 <lb/>3 # 59 <lb/>2 # 73 <lb/>1 # 93 <lb/>0 # 135 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Exp. 12. <lb/>Lin. # grana. <lb/>8 # 21 <lb/>7 # 24 <lb/>6 # 28 <lb/>5 # 34 <lb/>4 # 39 <lb/>3 # 51 <lb/>2 # 63 <lb/>1 # 82 <lb/>0 # 128 <lb/></note> <p> <s xml:id="echoid-s657" xml:space="preserve">Quantum variat horum 4 laterum attractio? </s> <s xml:id="echoid-s658" xml:space="preserve">quod ſi Magnes ſit <lb/>ſubſtantia homogenea, ſi polorum axis jaceat inter ambas ſuperficies <lb/>parallelepipedi intermedius, an non 4 laterum attractiones deberent <lb/>eſſe æquales? </s> <s xml:id="echoid-s659" xml:space="preserve">nullam video rationem, quæ non ſtabiliret hoc ratio-<lb/>cinium, verum Magnes, quo in examine uſus fui, tamen ita vide-<lb/>batur comparatus; </s> <s xml:id="echoid-s660" xml:space="preserve">nam an accuratiſſime ita ſe habuerit, nullo modo <lb/>me determinare poſſe fateor: </s> <s xml:id="echoid-s661" xml:space="preserve">nihilominus obſervationes inter ſe plu-<lb/>rimum diſcrepant, quæ virium magnitudinem oſtendunt.</s> <s xml:id="echoid-s662" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div19" type="section" level="1" n="19"> <head xml:id="echoid-head26" xml:space="preserve">EXPERIMENTUM XIII.</head> <p> <s xml:id="echoid-s663" xml:space="preserve">Magnetes ſeſe mutuo non tantum attrahunt, ſed etiam repellunt, <lb/>& </s> <s xml:id="echoid-s664" xml:space="preserve">æque ambo poli unius Magnetis ambos repellunt alterius polos; <lb/></s> <s xml:id="echoid-s665" xml:space="preserve">ſunt tamen alii poli, qui ſe repellunt, quam qui ſe attrahunt: </s> <s xml:id="echoid-s666" xml:space="preserve">Deſiderio <lb/>capiebar indagandi quomodo repulſiones Magnetum eſſent comparatæ, <lb/>an majores, an minores forent, quam attractiones, an etiam in pro-<lb/>portione quadam diſtantiarum vel in inconſtanti? </s> <s xml:id="echoid-s667" xml:space="preserve">ponderando <lb/>opinabar me abunde voto potiturum juxta methodum in attractioni-<lb/>bus adhibitam; </s> <s xml:id="echoid-s668" xml:space="preserve">ea tamen diſſerentia obſervanda erat, ut cum antea <lb/>Lanci eſſent imponenda ponduſcula, quæ attractionibus æquipolle-<lb/>bant, nunc ponduſcula Magneti eſſent imponenda, ut tanto gravior <lb/>fieret, accederetque ad inferiorem Magnetem, quo plus ab ipſo re-<lb/>pellebatur, hoc eſt, elevabatur ſurſum.</s> <s xml:id="echoid-s669" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s670" xml:space="preserve">Magnetem NO majorem rotundum iterum immobilem poſui in <lb/>menſa; </s> <s xml:id="echoid-s671" xml:space="preserve">aliumque magnetem parallelepipedum (quo uſus fueram <pb o="29" file="0043" n="43" rhead="DE MAGNETE."/> in Experimento V.) </s> <s xml:id="echoid-s672" xml:space="preserve">ſuſpendi ex Libræ brachio, quo prius ope pon-<lb/>deris Lanci injecti reducto ad æquilibrium, repulſionis magnitudines <lb/>obſervavi ſequentes.</s> <s xml:id="echoid-s673" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Repulſiones ad diſtantiam \\ poll. # Linear. # æquales granis Medicis. <lb/>14 # 0 # {1/2} <lb/>13 # 0 # {3/4} <lb/>11 # 9 # 1 <lb/>10 # 9 # {1/2} <lb/>10 # 4 # 0 # } # ſive ſimplex æquilibrium uti \\ ante inſtituta Experimenta. <lb/>9 # 10 # 0 <lb/>9 # 4 # {1/4} <lb/>9 # 0 # {1/4} <lb/>8 # 3 # {3/4} <lb/>7 # 9 # 1 <lb/>7 # 6 # 1 {1/2} <lb/>6 # 9 # 2 <lb/>6 # 4 # 2 {1/2} <lb/>5 # 9 # 2 <lb/>5 # 4 # 2 <lb/>5 # 2 # 2 {1/2} <lb/>4 # 9 # 3 <lb/>3 # 10 # 1 <lb/></note> <p> <s xml:id="echoid-s674" xml:space="preserve">Quando Magnetem alteri propius admovebam, non amplius re-<lb/>pellebatur, ſed attrahebatur: </s> <s xml:id="echoid-s675" xml:space="preserve">nam ad diſtantiam 3 pollic. </s> <s xml:id="echoid-s676" xml:space="preserve">6 linear. <lb/></s> <s xml:id="echoid-s677" xml:space="preserve">erat attractio æqualis 7 granis. </s> <s xml:id="echoid-s678" xml:space="preserve">Neſcio an quidem aliquid plus ano-<lb/>mali obſervari poſſit, quam repulſiones hæ demonſtrant, quæ in <lb/>magna diſtantia 14 pollicum ſunt notabiles, in minori æquali 10 poll. </s> <s xml:id="echoid-s679" xml:space="preserve"><lb/>obſervabatur nulla, tum iterum in propiori diſtantia usque ad 4 polli-<lb/>ces, increſcebat, dein in propiori decreſcebat, tum mutabatur in <lb/>vim attrahentem: </s> <s xml:id="echoid-s680" xml:space="preserve">Polinierius in Experienc. </s> <s xml:id="echoid-s681" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s682" xml:space="preserve">pag. </s> <s xml:id="echoid-s683" xml:space="preserve">279. </s> <s xml:id="echoid-s684" xml:space="preserve">etiam <lb/>adnotavit, quod Polus Magnetis, qui acus nauticæ extremitatem <lb/>repellebat in majori diſtantia, eam attrahebat cum propius admove-<lb/>batur: </s> <s xml:id="echoid-s685" xml:space="preserve">quicquid horum ſit, valde anomali ſunt hi effectus: </s> <s xml:id="echoid-s686" xml:space="preserve">quare <lb/>cum alio Magnete, quo uſus fui in Experimento III. </s> <s xml:id="echoid-s687" xml:space="preserve">idem tenta- <pb o="30" file="0044" n="44" rhead="DISSERTATIO"/> men repetendum eſſe opinabar, ut vel aliud quid circa repulſiones <lb/>Magnetum mutuas detegerem, vel anomaliam priorem confirmarem. <lb/></s> <s xml:id="echoid-s688" xml:space="preserve">Experimenta ſunt hæc.</s> <s xml:id="echoid-s689" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div20" type="section" level="1" n="20"> <head xml:id="echoid-head27" xml:space="preserve">EXPERIMENTUM XIV.</head> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # lin. # repulſ. æquales \\ granis Medicis. <lb/>13 # 0 # 0 <lb/>11 # 11 # {1/2} <lb/>10 # 9 # {3/4} <lb/>9 # 9 # 1 <lb/>6 # 1 # 2 <lb/>5 # 1 # 3 {1/2} <lb/>4 # 0 # 6 {1/2} <lb/>2 # 9 # 11 {1/2} <lb/>2 # 3 # 13 <lb/>1 # 11 # 12 <lb/>1 # 4 # 17 <lb/># 12 # 24 <lb/># 10 # 24 <lb/># 7 # 25 <lb/># 6 # 25 {1/2} <lb/># 5 # 27 {1/2} <lb/># 4 # 29 <lb/># 0 # 44 <lb/></note> <p> <s xml:id="echoid-s690" xml:space="preserve">Hæc Experimenta, quæ repulſiones Magnetum ſpectant, poſtu-<lb/>lant multo majorem dexteritatem, quam quæ in Attractionibus de-<lb/>ſiderabatur, quia obſervabam Magnetem ſuspenſum egredi perpetuo <lb/>ex recta linea per polos tranſeunte, hinc adnecti debuit filo cupreo, <lb/>& </s> <s xml:id="echoid-s691" xml:space="preserve">hoc Libræ, ut ſemper detineretur accurate ſupra alium Mague-<lb/>tem in eadem linea.</s> <s xml:id="echoid-s692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s693" xml:space="preserve">Major tamen ordo, (ſive, ut vocant) regularitas in hiſce Experimen-<lb/>tis obſervatur, quam in iis cum præcedenti Maguete factis, quoniam <lb/>increvit repulſio decreſcente diſtantia, & </s> <s xml:id="echoid-s694" xml:space="preserve">ad ipſum contactum usque <lb/>manſit.</s> <s xml:id="echoid-s695" xml:space="preserve"/> </p> <pb o="31" file="0045" n="45" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s696" xml:space="preserve">Sed apparet intuenti hanc repulſionis tabulam, quod nec certa <lb/>nec determinabilis proportio inter vires & </s> <s xml:id="echoid-s697" xml:space="preserve">diſtantias detur, uti nec <lb/>in attractione inveniri poterat.</s> <s xml:id="echoid-s698" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s699" xml:space="preserve">Attamen multo major eſt attractio quam repulſio; </s> <s xml:id="echoid-s700" xml:space="preserve">cum enim in <lb/>immediato contactu fuerit attractio æqualis 340 granis, repulſio <lb/>tantum fuit æqualis 44 granis, & </s> <s xml:id="echoid-s701" xml:space="preserve">comparando Experimentum terti-<lb/>um cum hoc, facile patet quanta diverſitas obſervetur.</s> <s xml:id="echoid-s702" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div21" type="section" level="1" n="21"> <head xml:id="echoid-head28" xml:space="preserve">EXPERIMENTUM XV.</head> <p> <s xml:id="echoid-s703" xml:space="preserve">Volui præterea obſervare, an vires repellentes utriusque poli ejus-<lb/>dem Magnetis forent æquales, aut quomodo variarent; </s> <s xml:id="echoid-s704" xml:space="preserve">itaque Ma-<lb/>guetem, qui poſtremo inſerviit experimento & </s> <s xml:id="echoid-s705" xml:space="preserve">ex Bilance pendebat, <lb/>converti, ut alter polus deorſum ſpectaret, converti quoque <lb/>Magnetem rotundum in tabula poſitum, tumque obſervationes notavi <lb/>ſequentes:</s> <s xml:id="echoid-s706" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Ad diſtantiam \\ Linearum. # fuit repulſio granorum. <lb/>12 # 30 <lb/>11 # 32 <lb/>10 # 32 <lb/>9 # 33 <lb/>8 # 34 <lb/>7 # 36 <lb/>6 # 36 <lb/>5 # 34 <lb/>4 # 32 <lb/>3 # 28 <lb/>2 # 27 <lb/>1 # 25 <lb/>0 # 13 <lb/></note> <p> <s xml:id="echoid-s707" xml:space="preserve">Ecce eventum, adeo admirandum, ut dubitaverim in initio, an qui-<lb/>dem Experimenta rite inſtituta eſſent, ſed repetens eadem, atque ma-<lb/>jori attendens cura, omnino easdem inveni repulſiones; </s> <s xml:id="echoid-s708" xml:space="preserve">Sunt hæ ad <lb/>diſtantiam 12 linearum magnæ, increscunt usque ad diſtantiam 7 li- <pb o="32" file="0046" n="46" rhead="DISSERTATIO"/> nearum, dein decreſcunt, donec in immediato contactu repulſio tan-<lb/>tum ſit æqualis 13 granis; </s> <s xml:id="echoid-s709" xml:space="preserve">quid igitur eſt in Magnetibus, quod hanc <lb/>Anomaliam producit? </s> <s xml:id="echoid-s710" xml:space="preserve">an dicam Lapidem, qui examini inſerviit, <lb/>conſtare ex partibus valde heterogeneis, quarum quædam attrahunt, <lb/>quædam repellunt, & </s> <s xml:id="echoid-s711" xml:space="preserve">quæ ambæ vires oppoſitæ ex eodem loco Ma-<lb/>guetis effluunt, hinc turbantes proportionem vel ſimplicis repulſio-<lb/>nis vel attractionis? </s> <s xml:id="echoid-s712" xml:space="preserve">veroſimile hoc apparet, quamobrem qui ſolam <lb/>repulſionem cognoſcere vellet, perſpectam habere deberet vim At-<lb/>trahentem eorundem polorum, eamque addere virtuti repellenti ob-<lb/>ſervatæ, tum ſumma indicaret totam vim repellentem: </s> <s xml:id="echoid-s713" xml:space="preserve">Attractionem <lb/>autem ſimul cum repulſione dari patet ex Experimento XIII. </s> <s xml:id="echoid-s714" xml:space="preserve">in <lb/>quo ad diſtantiam 3 pollic. </s> <s xml:id="echoid-s715" xml:space="preserve">6 lin. </s> <s xml:id="echoid-s716" xml:space="preserve">& </s> <s xml:id="echoid-s717" xml:space="preserve">ad minorem attractio præpolle-<lb/>bat repulſioni, hinc magnes ex Libra ſuspenſus attrahebatur, non <lb/>repellebatur, & </s> <s xml:id="echoid-s718" xml:space="preserve">in Experimento XV. </s> <s xml:id="echoid-s719" xml:space="preserve">ad diſtantiam 5 linearum <lb/>proportio repulſionis erat minor quam attractionis, unde quoque re-<lb/>pulſio imminui videbatur in minoribus diſtantiis, quæ tamen procul <lb/>dubio augebatur, quo Magnetes propius ſibi admovebantur, ſed <lb/>ab attractione tantopere turbabatur, ut inde oborta fuerit ſumma ir-<lb/>regularitas, quæ in ipſis obſervabatur Experimentis, cum ad diſtan-<lb/>tias 10, 11, & </s> <s xml:id="echoid-s720" xml:space="preserve">4 linearum æqualis repulſio obtinuerit, & </s> <s xml:id="echoid-s721" xml:space="preserve">maxima <lb/>in diſtantia 7 linearum fuerit: </s> <s xml:id="echoid-s722" xml:space="preserve">confirmabar in hac ſententia, poſt-<lb/>quam attractiones in Experimento III. </s> <s xml:id="echoid-s723" xml:space="preserve">inter hos Magnetes regnan-<lb/>tes, & </s> <s xml:id="echoid-s724" xml:space="preserve">notatas, addideram repulſionibus, tum enim quædam regu-<lb/>laritas dabatur, maximaque repulſio foret in contactu immediato, <lb/>minor in aliquo Magnetum intervallo, & </s> <s xml:id="echoid-s725" xml:space="preserve">ſemper decreſcens aucto inter-<lb/>vallo, quemadmodum patebit in hac Tabula, exhibente attractiones no-<lb/>tatas in Experimento tertio, & </s> <s xml:id="echoid-s726" xml:space="preserve">Repulſiones in Experimento XIV, ſi-<lb/>mul cum Summa ex attractione addita repulſioni, quam hic volumus.</s> <s xml:id="echoid-s727" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Attract. \\ poll. # Lin. # gran. <lb/>12 # 0 # {1/20} <lb/>11 # 0 # {1/8} <lb/># 12 # 70 {1/2} <lb/># 10 # 87 <lb/># 7 # 114 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Repulſ. \\ poll. # Lin. # gran. # Summ. tota \\ repulſion. <lb/>11 # 11 # {1/2} # {3/40} <lb/>10 # 9 # {3/4} # {7/8} <lb/># 12 # 24 # 94 {1/2} <lb/># 10 # 24 # 111 <lb/># 7 # 25 # 139 <lb/></note> <pb o="33" file="0047" n="47" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># Lin. # gran. <lb/># 6 # 131 <lb/># 4 # 172 <lb/># 0 # 340 <lb/></note> <note position="right" xml:space="preserve"> <lb/># Lin. # gran. # repulſion. <lb/># 6 # 25 {1/2} # 156 {1/2} <lb/># 4 # 29 # 201 <lb/># 0 # 44 # 384 <lb/></note> <p> <s xml:id="echoid-s728" xml:space="preserve">Attendens autem ad numeros, ſummam repulſionis exprimentes, <lb/>inter eos & </s> <s xml:id="echoid-s729" xml:space="preserve">diſtantias conſtantem proportionem non animadvertere <lb/>potui, ſed ſi quædam obtineat, non erit alta, & </s> <s xml:id="echoid-s730" xml:space="preserve">minor quam ſim-<lb/>plex inverſa diſtantiarum, incipiendo ſupputationem a contactu ipſo: <lb/></s> <s xml:id="echoid-s731" xml:space="preserve">nam 6. </s> <s xml:id="echoid-s732" xml:space="preserve">4:</s> <s xml:id="echoid-s733" xml:space="preserve">: 201. </s> <s xml:id="echoid-s734" xml:space="preserve">134. </s> <s xml:id="echoid-s735" xml:space="preserve">loco 156 {1/2}. </s> <s xml:id="echoid-s736" xml:space="preserve">tum 7. </s> <s xml:id="echoid-s737" xml:space="preserve">6:</s> <s xml:id="echoid-s738" xml:space="preserve">: 156 {1/2}. </s> <s xml:id="echoid-s739" xml:space="preserve">134 {1/7}. </s> <s xml:id="echoid-s740" xml:space="preserve">loco 139. </s> <s xml:id="echoid-s741" xml:space="preserve"><lb/>tum 10. </s> <s xml:id="echoid-s742" xml:space="preserve">7:</s> <s xml:id="echoid-s743" xml:space="preserve">: 139. </s> <s xml:id="echoid-s744" xml:space="preserve">97 {3/10} loco 111. </s> <s xml:id="echoid-s745" xml:space="preserve">tum 12. </s> <s xml:id="echoid-s746" xml:space="preserve">10:</s> <s xml:id="echoid-s747" xml:space="preserve">: 111. </s> <s xml:id="echoid-s748" xml:space="preserve">92 {3/4}. </s> <s xml:id="echoid-s749" xml:space="preserve">loco 94 {1/2}. </s> <s xml:id="echoid-s750" xml:space="preserve"><lb/>Attamen non dubito, quin conſtans proportio obtineat inter diſtan-<lb/>tias & </s> <s xml:id="echoid-s751" xml:space="preserve">repulſiones, modo hæ ſolæ, ſeparatæque ab omni alia cauſa <lb/>haberentur, imo attractiones ſolæ etiam in conſtanti ratione eſſe poſ-<lb/>ſunt, ſed turbantur forſitan a repulſionibus: </s> <s xml:id="echoid-s752" xml:space="preserve">nam uterque polus Mag-<lb/>netis vim repellentem æque oſtendit, ac attrahentem: </s> <s xml:id="echoid-s753" xml:space="preserve">& </s> <s xml:id="echoid-s754" xml:space="preserve">idcir-<lb/>co ex eodem polo vis attrahens & </s> <s xml:id="echoid-s755" xml:space="preserve">repellens exibit: </s> <s xml:id="echoid-s756" xml:space="preserve">quando poli Mag-<lb/>netum duorum ſibi amici obvertuntur, attractio præpollet repulſio-<lb/>ni; </s> <s xml:id="echoid-s757" xml:space="preserve">quando inimici ſe reſpiciunt poli, repulſio ſuperat attractionem; </s> <s xml:id="echoid-s758" xml:space="preserve"><lb/>quare ſemper actio datur compoſita ex attractione & </s> <s xml:id="echoid-s759" xml:space="preserve">repulſione: </s> <s xml:id="echoid-s760" xml:space="preserve">un-<lb/>de proportiones duæ componentes actionem in Experimentis obſerva-<lb/>tam, forent ex quantitatibus notatis extricandæ a ſe invicem, ut <lb/>ſolæ haberentur, quod difficillimum erit; </s> <s xml:id="echoid-s761" xml:space="preserve">nec prius veram propor-<lb/>tionem attractionis & </s> <s xml:id="echoid-s762" xml:space="preserve">repulſionis determinare poterimus. </s> <s xml:id="echoid-s763" xml:space="preserve">In hac <lb/>itaque rerum caligine, præſtabit ſuspendiſſe adhuc judicium, & </s> <s xml:id="echoid-s764" xml:space="preserve">can-<lb/>dide memoraſſe obſervationes, ex quibus ſerior ſapientiorque ætas <lb/>multa forte eruet, poſtquam plura data hoc in negotio acceperit: </s> <s xml:id="echoid-s765" xml:space="preserve"><lb/>Neque noſtrum ſilentium dedecori erit, cum ſapientiſſimi Philoſophi <lb/>Florentini de Magnete agentes, etiam Experimenta tantummodo at-<lb/>tulerint, nihil ratiocinii addentes, neque ullas ex iis elicientes ſeque-<lb/>las, ne ficta pro veris, ſive hypotheſin loco demonſtrationis darent, <lb/>carbonemque pro theſauro relinquerent.</s> <s xml:id="echoid-s766" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s767" xml:space="preserve">Quum his Experimentis inſtitutis nullam virium proportio-<lb/>nem inveneram, cæpi ſuspicari, an quidem unquam iis modis, <lb/>quibus tentamina feci, poſſet virium proportio detegi in variis di-<lb/>ſtantiis, etiamſi quædam daretur, quoniam Magnetes ambo in ſe <pb o="34" file="0048" n="48" rhead="DISSERTATIO"/> agunt, & </s> <s xml:id="echoid-s768" xml:space="preserve">hinc vires exeuntes forte ex ambobus, ſibique obviam <lb/>euntes, proportionem turbare poſſent: </s> <s xml:id="echoid-s769" xml:space="preserve">qua propter ſi haberem Mag-<lb/>netem unum activum, & </s> <s xml:id="echoid-s770" xml:space="preserve">alium ſpoliatum omnibus viribus, mihi <lb/>ſpes quædam affulgebat detegendi melius virium proportionem, ve-<lb/>rum ejusmodi Magnes iners eſſe tantum poterat ferrum purum bo-<lb/>numque, recenter ex Igne extractum, quod nequaquam ulla vi Mag-<lb/>netica foret imbutum, non arreptum aut percuſſum forcipe ferreo, ſed <lb/>leniter & </s> <s xml:id="echoid-s771" xml:space="preserve">prudenter tractatum, ideoque me converti ad Experimenta <lb/>cum Magnete & </s> <s xml:id="echoid-s772" xml:space="preserve">ferro facienda, quæ in Capite deſcribam ſequente.</s> <s xml:id="echoid-s773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s774" xml:space="preserve">Fui in hiſce Experimentis inſtituendis deſcribendisque ad tædium <lb/>usque prolixus, ſed non abſque ratione; </s> <s xml:id="echoid-s775" xml:space="preserve">fieri enim potuiſſet, ut in <lb/>uno deciperer, errorem autem agnoſcerem in altero: </s> <s xml:id="echoid-s776" xml:space="preserve">præterea quia <lb/>virium Magneticarum proportionem aliam aſſumſit Philoſophorum, <lb/>qui unquam extiterunt, princeps Iſacus Newtonus, non oportebat, <lb/>ut perfunctorie hoc negotium tractarem, paucisque contentus eſſem <lb/>Experimentis: </s> <s xml:id="echoid-s777" xml:space="preserve">Dixerat enim vir nunquam ſatis laudatus in Prine. <lb/></s> <s xml:id="echoid-s778" xml:space="preserve">Philoſ. </s> <s xml:id="echoid-s779" xml:space="preserve">Lib. </s> <s xml:id="echoid-s780" xml:space="preserve">1. </s> <s xml:id="echoid-s781" xml:space="preserve">Sect. </s> <s xml:id="echoid-s782" xml:space="preserve">13. </s> <s xml:id="echoid-s783" xml:space="preserve">prop. </s> <s xml:id="echoid-s784" xml:space="preserve">85. </s> <s xml:id="echoid-s785" xml:space="preserve">Si corporis attracti, ubi attra-<lb/>benti contiguum eſt, attractio longe fortior ſit, quam cum vel mi-<lb/>nimo intervallo ſeparatur ab invicem, vires particularum trabentis, <lb/>in receſſu corporis attracti, decreſcere in ratione plusquam duplicata <lb/>diſtantiarum a particulis: </s> <s xml:id="echoid-s786" xml:space="preserve">præterea in Lib. </s> <s xml:id="echoid-s787" xml:space="preserve">3. </s> <s xml:id="echoid-s788" xml:space="preserve">prop. </s> <s xml:id="echoid-s789" xml:space="preserve">6. </s> <s xml:id="echoid-s790" xml:space="preserve">Corol. </s> <s xml:id="echoid-s791" xml:space="preserve">5. </s> <s xml:id="echoid-s792" xml:space="preserve">pag. </s> <s xml:id="echoid-s793" xml:space="preserve"><lb/>368. </s> <s xml:id="echoid-s794" xml:space="preserve">Hæc habet: </s> <s xml:id="echoid-s795" xml:space="preserve">vis gravit at is diverſi eſt generis a vi Magnetica, <lb/>nam attractio Magnetica non eſt ut materia attracta. </s> <s xml:id="echoid-s796" xml:space="preserve">Corpora ali-<lb/>qua magis trabuntur, alia minus, plurima non trabuntur. </s> <s xml:id="echoid-s797" xml:space="preserve">Et vis <lb/>Magnetica in uno & </s> <s xml:id="echoid-s798" xml:space="preserve">eodem corpore intendi poteſt & </s> <s xml:id="echoid-s799" xml:space="preserve">remitti, eſtque <lb/>nonnunquam longe major pro quantitate materiæ, quam vis gravi-<lb/>tatis, & </s> <s xml:id="echoid-s800" xml:space="preserve">in receſſu a Magnete decreſcit in ratione diſtantiæ non du-<lb/>plicata, ſed fere triplicata, quantum ex craſſis quibusdam obſerva-<lb/>tionibus animadvertere potui. </s> <s xml:id="echoid-s801" xml:space="preserve">Utinam memoriæ prodita fuiſſent Ex-<lb/>perimenta, ex quibus Newtonus hæc collegit! forſitan enim Vir ſtu-<lb/>pendæ ſubtilitatis in Mathematicis diſciplinis methodum invenit ſepa-<lb/>randi attractiones a repulſionibus, quarum proportionem in diſtan-<lb/>tiæ ratione triplicata decreſcere deprehendit; </s> <s xml:id="echoid-s802" xml:space="preserve">ſed quia nihil de hac <lb/>re ulterius determinavit, nec rejicere, nec amplecti ejus ſententiam <lb/>poſſumus; </s> <s xml:id="echoid-s803" xml:space="preserve">ſi autem modo Experimenta noſtra conſulamus, tum vi-<lb/>res Magnetis attrahentes non in tam alta ratione diſtantiarum decreſ-<lb/>cere concluderemus.</s> <s xml:id="echoid-s804" xml:space="preserve"/> </p> <pb o="35" file="0049" n="49" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div22" type="section" level="1" n="22"> <head xml:id="echoid-head29" xml:space="preserve">CAPUT II.</head> <head xml:id="echoid-head30" style="it" xml:space="preserve">DE ACTIONE MAGNETIS IN FERRUM.</head> <p> <s xml:id="echoid-s805" xml:space="preserve">Si Magnes longo alligatus funi ſuspendatur ex Bilance, uti in <lb/>ſuperioribus Experimentis factum fuit, atque æquipondio <lb/>oppoſitæ Lanci immiſſo reducatur ad æquilibrium, tum maſſa <lb/>ferri immobilis ponatur infra Magnetem in linea perpendicula-<lb/>ri ad horizontem, quæ per ferrum & </s> <s xml:id="echoid-s806" xml:space="preserve">Magnetem tranſit, & </s> <s xml:id="echoid-s807" xml:space="preserve">ad di-<lb/>ſtantiam paucorum pollicum a ſe mutuo, deſcendet Magnes verſus fer-<lb/>rum, & </s> <s xml:id="echoid-s808" xml:space="preserve">quaſi</s> </p> </div> <div xml:id="echoid-div23" type="section" level="1" n="23"> <head xml:id="echoid-head31" style="it" xml:space="preserve">Flagrat anbela ſilex, & amicam ſaucia ſentit <lb/>Materiam, placidosque chalybs cognoſcit amores.</head> <p> <s xml:id="echoid-s809" xml:space="preserve">Si tamen eum retinere velimus in eadem a ferro diſtantia, erunt <lb/>plurima pondera lanci Libræ imponenda, quæ ſua gravitate Magne-<lb/>tem elevent, atque tantum a ferro avellant, quantum Magnes ſua <lb/>vi ad illud accedit: </s> <s xml:id="echoid-s810" xml:space="preserve">pondus quod de novo Lanci immittitur ultra <lb/>primum æquilibrium, demonſtrat quanta ſit Attractio Magnetis ad <lb/>ferrum, quamobrem beneficio hujus artificii addiſcimus modum de-<lb/>terminandi vires magneticas in ferrum ad varias a ſe mutuo diſtan-<lb/>tias.</s> <s xml:id="echoid-s811" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s812" xml:space="preserve">Quocunque modo Magnes convertatur, manens Libræ alligatus, <lb/>ſemper ad ferrum accedit.</s> <s xml:id="echoid-s813" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s814" xml:space="preserve">Hoc Experimentum probat, Magnetem non tantum agere in ali-<lb/>um Magnetem, ſed quoque in ferrum: </s> <s xml:id="echoid-s815" xml:space="preserve">Hoc non adeo mirandum <lb/>eſt; </s> <s xml:id="echoid-s816" xml:space="preserve">Quia Magnes eſt modo lapis, conſtans ex ferro bono cum in-<lb/>termiſtis partibus terreis: </s> <s xml:id="echoid-s817" xml:space="preserve">Lapis hic vim non habet quatenus compo-<lb/>nitur ex mera terra, ſed quatenus aliquam terram & </s> <s xml:id="echoid-s818" xml:space="preserve">ſimul ferrum <lb/>poſſidet; </s> <s xml:id="echoid-s819" xml:space="preserve">unde eo præſtantiorum eſt virium, quo plus ferri habet, <lb/>& </s> <s xml:id="echoid-s820" xml:space="preserve">quo gravior eſt: </s> <s xml:id="echoid-s821" xml:space="preserve">ferreas particulas vim Lapidi adferre, proba-<lb/>ri poſſet facile, nam quando ferrum Lapidi infixum diu per plu-<lb/>res annos fuit, & </s> <s xml:id="echoid-s822" xml:space="preserve">rubigine corroſæ partes permearunt lapidis poros, <lb/>Lapis evaſit Magnes, uti experientia frequenti conſtare ſupra monui, <pb o="36" file="0050" n="50" rhead="DISSERTATIO"/> & </s> <s xml:id="echoid-s823" xml:space="preserve">quod de La Hire ſuis obſervatis confirmavit in L’Hiſt. </s> <s xml:id="echoid-s824" xml:space="preserve">de L’A-<lb/>cad. </s> <s xml:id="echoid-s825" xml:space="preserve">Roy. </s> <s xml:id="echoid-s826" xml:space="preserve">Ao. </s> <s xml:id="echoid-s827" xml:space="preserve">1705. </s> <s xml:id="echoid-s828" xml:space="preserve">qui incluſit fila ferrea lapidi, ſed hæc diſpoſuit, <lb/>ut ſua longitudine reſponderent directioni acus Magneticæ, tum <lb/>poſt 10 annos lapis evaſit Magnes verus, filis nempe a rubigine corroſis: <lb/></s> <s xml:id="echoid-s829" xml:space="preserve">Nonnulla autem fila prius Magneti affricuerat, antequam alteri lapi-<lb/>di incluſerat, volens videre, an non ita fortior generaretur Magnes, <lb/>verum plus virium in hoc lapide non animadvertit. </s> <s xml:id="echoid-s830" xml:space="preserve">Ferrum igitur, <lb/>quod eſt in Magnete, ſimul cum ſua terra vim attrahendi habet; </s> <s xml:id="echoid-s831" xml:space="preserve"><lb/>ſi proinde hoc agat in ferreas partes conſtituentes alium Magnetem, <lb/>non admirandum eſt, hoc etiam agere in ferrum purum, ſive in Ma-<lb/>gnetem puriſſimum abſque lapide admiſto, ſic enim ferrum purum <lb/>vocare licebit: </s> <s xml:id="echoid-s832" xml:space="preserve">Eodem prorſus modo Magnes agit in quælibet cor-<lb/>pora, quibus ferrum eſt intermiſtum; </s> <s xml:id="echoid-s833" xml:space="preserve">imo forte in ea, quæ nihil <lb/>ferri habent, ſed eandem terreſtrem attractricem materiam: </s> <s xml:id="echoid-s834" xml:space="preserve">agit ita <lb/>in nonnullas plantas; </s> <s xml:id="echoid-s835" xml:space="preserve">in lateres coctos ruberrimi coloris, notante Ca-<lb/>bæo Lib. </s> <s xml:id="echoid-s836" xml:space="preserve">1. </s> <s xml:id="echoid-s837" xml:space="preserve">cap. </s> <s xml:id="echoid-s838" xml:space="preserve">17. </s> <s xml:id="echoid-s839" xml:space="preserve">p. </s> <s xml:id="echoid-s840" xml:space="preserve">63. </s> <s xml:id="echoid-s841" xml:space="preserve">in Colcotar vitrioli; </s> <s xml:id="echoid-s842" xml:space="preserve">in pulverem ſplen-<lb/>dentem nigrumque, qui ex arena Indica elicitur, & </s> <s xml:id="echoid-s843" xml:space="preserve">qui nunquam ru-<lb/>biginem contrahit, de quo plura inferius: </s> <s xml:id="echoid-s844" xml:space="preserve">in pulverem nigrum qui <lb/>remanet poſt deſtillationem olei Lini, & </s> <s xml:id="echoid-s845" xml:space="preserve">olei Therebinthinæ, uti <lb/>annotatum eſt in L’Hiſtoire de L’Academie Roy. </s> <s xml:id="echoid-s846" xml:space="preserve">Ao. </s> <s xml:id="echoid-s847" xml:space="preserve">1704. </s> <s xml:id="echoid-s848" xml:space="preserve">in Gra-<lb/>natum, gemmam, modo fuerit colore ſaturo tincta, affirmante Boy-<lb/>leo, vide Act. </s> <s xml:id="echoid-s849" xml:space="preserve">Lipſ. </s> <s xml:id="echoid-s850" xml:space="preserve">Ao. </s> <s xml:id="echoid-s851" xml:space="preserve">1693. </s> <s xml:id="echoid-s852" xml:space="preserve">pag 182. </s> <s xml:id="echoid-s853" xml:space="preserve">in Lapidem Lough neagh <lb/>calcinatum, notante Molyneux in Phil. </s> <s xml:id="echoid-s854" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s855" xml:space="preserve">No. </s> <s xml:id="echoid-s856" xml:space="preserve">166. </s> <s xml:id="echoid-s857" xml:space="preserve">atque in <lb/>impuritates vitri, monente Helmontio, pag. </s> <s xml:id="echoid-s858" xml:space="preserve">727. </s> <s xml:id="echoid-s859" xml:space="preserve">unde error Pli-<lb/>nii liquet, qui in Lib. </s> <s xml:id="echoid-s860" xml:space="preserve">34. </s> <s xml:id="echoid-s861" xml:space="preserve">cap. </s> <s xml:id="echoid-s862" xml:space="preserve">14. </s> <s xml:id="echoid-s863" xml:space="preserve">Hiſtor. </s> <s xml:id="echoid-s864" xml:space="preserve">Nat. </s> <s xml:id="echoid-s865" xml:space="preserve">dicit, de ferro <lb/>verba habens; </s> <s xml:id="echoid-s866" xml:space="preserve">Sola hæc materia vires ab eo lapide accipit.</s> <s xml:id="echoid-s867" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s868" xml:space="preserve">Quia autem omnis Actio eſt æqualis Reactioni, non poteſt Mag-<lb/>nes agere in ferrum, niſi hoc reciproce in Magnetem agat, adeo-<lb/>que eodem modo ferrum ad Magnetem accedat, quam hic ad fer-<lb/>rum; </s> <s xml:id="echoid-s869" xml:space="preserve">hoc tamen Experimento confirmare volui: </s> <s xml:id="echoid-s870" xml:space="preserve">Suspenſus fuit Mag-<lb/>nes ex fune longo Libræ alligato, reductusque ope æquipondii eſt <lb/>in æqualibrium; </s> <s xml:id="echoid-s871" xml:space="preserve">tum maſſa ferrea ejusdem gravitatis cum Magnete, e <lb/>quatuor a ſe diſtantibus funibus ſuspenſa ex altera Libra, ita ut Magnes <lb/>& </s> <s xml:id="echoid-s872" xml:space="preserve">ferrum fere in eadem linea perpendiculari forent, æquilibrium quo-<lb/>que quæſitum fuit; </s> <s xml:id="echoid-s873" xml:space="preserve">ſimulac autem tam prope ad ſe admovebantur, <lb/>ut manifeſto in ſe mutuo operarentur, acceſſit ferrum ad Magne- <pb o="37" file="0051" n="51" rhead="DE MAGNETE."/> tem, & </s> <s xml:id="echoid-s874" xml:space="preserve">Magnes reciproce tantopere ad ferrum, hinc ut manerent a <lb/>ſe ſejuncta hæc corpora; </s> <s xml:id="echoid-s875" xml:space="preserve">pondus majus imponendum erat Lanci ad-<lb/>nexæ oppoſito brachio I ibræ illius, ex quo Magnes pendebat, eo <lb/>attollebatur Magnes, tum accurate tantundem ponderi imponendum <lb/>erat ferro, a quo deprimebatur, atque a Magnete avellebatur; </s> <s xml:id="echoid-s876" xml:space="preserve">quibus <lb/>peractis æquilibrium obſervabatur in utraque libra: </s> <s xml:id="echoid-s877" xml:space="preserve">Hinc igitur ma-<lb/>nifeſto liquet, Actionem Magnetis in ferrum eſſe æqualem Reactioni <lb/>ferri ad Magnetem: </s> <s xml:id="echoid-s878" xml:space="preserve">idem evinci poteſt alio etiam modo, ſi nem-<lb/>pe tum ferrum, tum Magnetem parvis inmittamus cymbulis, in <lb/>quibus, Aqua labro amplo immiſſa, natent, accedunt enim ambæ <lb/>cymbulæ ad ſe æquali cum impetu, & </s> <s xml:id="echoid-s879" xml:space="preserve">in intermedia via ſibi eunt <lb/>obviam: </s> <s xml:id="echoid-s880" xml:space="preserve">Verum ad alia tranſeamus experimenta, in quibus opera-<lb/>tiones Magnetis in ferrum determinare calculo conati fuimus.</s> <s xml:id="echoid-s881" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div24" type="section" level="1" n="24"> <head xml:id="echoid-head32" xml:space="preserve">EXPERIMENTUM XVI.</head> <p> <s xml:id="echoid-s882" xml:space="preserve">Sumſi maſſam ferream, quod erat parallelepipedum, baſeos 224 <lb/>linearum pollicis quadratarum, longitudinis 5 {1/2} pollic. </s> <s xml:id="echoid-s883" xml:space="preserve">rhenol. </s> <s xml:id="echoid-s884" xml:space="preserve">hoc nun-<lb/>quam Magnetem attigerat, tabulæ id impoſui, ut immobiliter ſtaret: <lb/></s> <s xml:id="echoid-s885" xml:space="preserve">tum ſuspendi Magnetem, etiam formæ parallelepipedæ, qui Expe-<lb/>rimento quarto inſervierat, ex fune annexo Libræ, ita ut axis, <lb/>utrosque polos connectens, eſſet in horizontem perpendicularis, tran-<lb/>ſiretque per axem ferri: </s> <s xml:id="echoid-s886" xml:space="preserve">reductum Magnetem ad æquilibrium, pri-<lb/>usquam tentamina fierent, demiſi ad varias a ferro diſtantias ſucces-<lb/>ſive, quemadmodum in Experimento II. </s> <s xml:id="echoid-s887" xml:space="preserve">& </s> <s xml:id="echoid-s888" xml:space="preserve">notavi pondus alteri <lb/>imponendum lanci, ad æquilibrium reſtituendum, quod æquipolle-<lb/>bat ſemper ejus viribus attractricibus: </s> <s xml:id="echoid-s889" xml:space="preserve">eſſectum attractionis ex appo-<lb/>ſita conſpicere licet tabula.</s> <s xml:id="echoid-s890" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ pollic. # lin # Attractio. \\ gran. Medicor. <lb/>3 # 7 # 1 <lb/>2 # 11 # 1 {1/2} <lb/>2 # 6 # 2 <lb/>1 # 7 # 6 <lb/>1 # 4 {1/2} # 10 <lb/># 11 # 14 <lb/></note> <pb o="38" file="0052" n="52" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># Lin # gran. Med. <lb/># 10 # 16 <lb/># 9 # 17 <lb/># 8 # 21 <lb/># 7 # 29 <lb/># 6 # 32 <lb/># 5 # 44 <lb/># 4 # 52 <lb/># 3 # 72 <lb/># 2 # 96 <lb/># 1 # 110 <lb/># 0 # 180 <lb/></note> </div> <div xml:id="echoid-div25" type="section" level="1" n="25"> <head xml:id="echoid-head33" xml:space="preserve">EXPERIMENTUM XVII.</head> <p> <s xml:id="echoid-s891" xml:space="preserve">Quia autem parallelepipedum illud ferreum fuerat admodum ma-<lb/>gnum & </s> <s xml:id="echoid-s892" xml:space="preserve">grave, aliud fieri curavi, quod eſſet ejusdem gravitatis <lb/>cum Magnete altero, in Experimento IV. </s> <s xml:id="echoid-s893" xml:space="preserve">examinato, & </s> <s xml:id="echoid-s894" xml:space="preserve">quod ſu-<lb/>perſiciem æque magnam obvertebat Magneti ſuspenſo, ac alter Mag-<lb/>nes obtulerat, opinabar enim me ita inventurum vires attractrices <lb/>easdem, ac in Experimento IV. </s> <s xml:id="echoid-s895" xml:space="preserve">cum ferrum Magneti erat ſimile, ni-<lb/>ſi quod ob majorem gravitatem erat minus altum: </s> <s xml:id="echoid-s896" xml:space="preserve">cum eodem Ma-<lb/>gnete ac in præcedenti Experimento ſequentes notatæ fuerunt obſer-<lb/>vationes.</s> <s xml:id="echoid-s897" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Ad diſtant. \\ pollic. # Lin. # Attractiones erant \\ granor. Medic. <lb/>5 # 0 # 1 <lb/>3 # 3 # 2 <lb/>2 # 0 # 8 <lb/># 12 # 35 <lb/># 11 # 37 <lb/># 10 # 43 <lb/># 9 # 47 <lb/># 8 # 57 <lb/># 7 # 66 <lb/></note> <pb o="39" file="0053" n="53" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># Lin. # gran.Med. <lb/># 6 # 76 <lb/># 5 # 96 <lb/># 4 # 109 <lb/># 3 # 131 <lb/># 2 # 179 <lb/># 1 # 231 <lb/># {1/2} # 343 <lb/># 0 # 720 <lb/></note> </div> <div xml:id="echoid-div26" type="section" level="1" n="26"> <head xml:id="echoid-head34" xml:space="preserve">EXPERIMENTUM XVIII.</head> <p> <s xml:id="echoid-s898" xml:space="preserve">Hactenus Magnes fuerat ſuspenſus, volui igitur ferrum reciproce <lb/>ex Libra ſuspendere, & </s> <s xml:id="echoid-s899" xml:space="preserve">Magnetem menſæ impoſitum retinere quie <lb/>tum: </s> <s xml:id="echoid-s900" xml:space="preserve">Adeoque ſuspendi parallelepipedum ferreum, cujus baſis 224 li-<lb/>nearum longitudo 5 {1/2} pollic. </s> <s xml:id="echoid-s901" xml:space="preserve">rhenol. </s> <s xml:id="echoid-s902" xml:space="preserve">hoc ex bilancis brachio funi longo <lb/>alligatum pendebat juxta longitudinem, atque ad accuratiſſimum re-<lb/>ducebatur æquilibrium; </s> <s xml:id="echoid-s903" xml:space="preserve">dein Magnetem ſphæricum NO impoſui ta-<lb/>bulæ, polo ſurſum converſo, ita ut linea polorum tranſiret per axem <lb/>ferri, hoc vero ad varias a Magnete diſtantias, dedit eſſectus ſe-<lb/>quentes.</s> <s xml:id="echoid-s904" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Pollic. # Lin. # Grana <lb/>4 # 3 # 0 <lb/>3 # 10 # 1 <lb/>3 # 1 # 4 <lb/>2 # 11 # 7 <lb/>2 # 5 # 10 <lb/>1 # 7 # 24 <lb/>1 # 4 # 37 <lb/># 12 # 61 <lb/># 11 # 70 <lb/># 10 # 84 <lb/># 9 # 106 <lb/># 8 # 121 <lb/># 7 # 140 <lb/></note> <pb o="40" file="0054" n="54" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># Lin. # Gran. <lb/># 6 # 164 <lb/># 5 # 201 <lb/># 4 # 229 <lb/># 3 # 285 <lb/># 2 # 361 <lb/># 1 # 472 <lb/># 0 # 1312 <lb/></note> </div> <div xml:id="echoid-div27" type="section" level="1" n="27"> <head xml:id="echoid-head35" xml:space="preserve">EXPERIMENTUM XIX.</head> <p> <s xml:id="echoid-s905" xml:space="preserve">Antequam has obſervationes ad examen vocem, adnotabo prius <lb/>adhuc alias, quas non indignas attentione noſtra opinor: </s> <s xml:id="echoid-s906" xml:space="preserve">Eum in <lb/>finem autem ſequentia tentamina feci, ut viderem quænam ſoret <lb/>differentia inter attractiones ejusdem Magnetis, poſita maſſa ferrea <lb/>minori vel alterius figuræ, eademve locata in alio ſitu: </s> <s xml:id="echoid-s907" xml:space="preserve">ſumſi <lb/>igitur pedem armaturæ Magnetis prius ignitum, ut vim exueret Ma-<lb/>gneticam, quem refert Tab. </s> <s xml:id="echoid-s908" xml:space="preserve">6. </s> <s xml:id="echoid-s909" xml:space="preserve">Fig. </s> <s xml:id="echoid-s910" xml:space="preserve">4. </s> <s xml:id="echoid-s911" xml:space="preserve">erat hic pes A B C D modo <lb/>lamina ferri tenuis, ponderis ℥ij, cui parvus pes EF cubicus appen-<lb/>debat, cujus latus quadratum F, quod Magneti obvertebatur, erat <lb/>circiter 9 linearum quadratarum, attractiones illius fuerunt ſequen-<lb/>tes, ad diſtantias</s> </p> <note position="right" xml:space="preserve"> <lb/>Pollic. # Lin. # Granis æqualis attractio. <lb/>4 # 6 # 0 <lb/>3 # 10 # 1 <lb/>3 # 7 # 1 {1/4} <lb/>2 # 5 # 3 {1/2} <lb/>2 # 0 # 6 {1/2} <lb/>1 # 11 # 7 <lb/>1 # 6 # 10 <lb/>1 # 4 # 15 <lb/># 12 # 25 <lb/># 11 # 30 <lb/># 10 # 33 <lb/># 9 # 37 <lb/># 8 # 40 <lb/></note> <pb o="41" file="0055" n="55" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># Lin. # Grana. <lb/># 7 # 43 <lb/># 6 # 49 <lb/># 5 # 54 <lb/># 4 # 64 <lb/># 3 # 78 <lb/># 2 # 114 <lb/># 1 # 184 <lb/># 0 # 1024 <lb/></note> </div> <div xml:id="echoid-div28" type="section" level="1" n="28"> <head xml:id="echoid-head36" xml:space="preserve">EXPERIMENTUM XX.</head> <p> <s xml:id="echoid-s912" xml:space="preserve">Deinde eundem pedem Armaturæ ferreum A B C D E F in Tab. <lb/></s> <s xml:id="echoid-s913" xml:space="preserve">6. </s> <s xml:id="echoid-s914" xml:space="preserve">fig. </s> <s xml:id="echoid-s915" xml:space="preserve">4. </s> <s xml:id="echoid-s916" xml:space="preserve">ſuſpendi transverſè, ita ut major ſuperficies plana A B C D <lb/>polum Magnetis reſpiceret, ferrum erat multo tenuius eâ parte, <lb/>quæ directe polo Magnetis imminebat, quam in Experimento <lb/>præcedenti, tum notavi ſequentes effectus ad diſtantias a Magne-<lb/>te varias.</s> <s xml:id="echoid-s917" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Pollic. # Linear. # Grana <lb/>4 # 0 # 0 <lb/>3 # 10 # 1 <lb/>3 # 5 # 1 {1/4} <lb/>2 # 3 # 2 {1/2} <lb/>1 # 10 # 4 <lb/>1 # 2 # 15 {1/2} <lb/># 12 # 20 <lb/># 10 # 30 <lb/># 9 # 37 <lb/># 7 # 40 <lb/># 6 # 54 <lb/># 5 # 69 <lb/># 4 # 79 <lb/># 3 # 86 <lb/># 2 # 134 <lb/></note> <pb o="42" file="0056" n="56" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># Linear. # Grana <lb/># 1 # 214 <lb/># 0 # 574 <lb/></note> </div> <div xml:id="echoid-div29" type="section" level="1" n="29"> <head xml:id="echoid-head37" xml:space="preserve">EXPERIMENTUM XXI.</head> <p> <s xml:id="echoid-s918" xml:space="preserve">Deinde explorandum erat quomodo Magnes in limaturam ferri <lb/>ageret, ſumſi eum in finem capſulam ferream ejuſdem formæ & </s> <s xml:id="echoid-s919" xml:space="preserve"><lb/>magnitudinis, quam Magnes, quo uſus fui in Experimento tertio, <lb/>erat metallum capſulæ tenuiſſimum, vulgo dictum Blick, hanc <lb/>implevi penitus limatura ferri, & </s> <s xml:id="echoid-s920" xml:space="preserve">ponderavi, minorem autem <lb/>habuit gravitatem quam Magnes ipſi æqualis, quia limatura <lb/>non eſt maſſa compacta; </s> <s xml:id="echoid-s921" xml:space="preserve">pondus igitur deficiebat ab eo Magnetis 15 <lb/>drachmis: </s> <s xml:id="echoid-s922" xml:space="preserve">hæc capſula ſuſpendebatur ex Bilance, atque Magnes <lb/>rotundus idem, quo uſus fui in Experimento III. </s> <s xml:id="echoid-s923" xml:space="preserve">erat impoſitus ta-<lb/>bulæ immobilis, polo ſpectante ſurſum, uti in Experimento III. <lb/></s> <s xml:id="echoid-s924" xml:space="preserve">& </s> <s xml:id="echoid-s925" xml:space="preserve">obſervationes eodem modo cum ponderibus inſtituendo, quæ <lb/>attractiones menſurabant, tabulam condidi ſequentem.</s> <s xml:id="echoid-s926" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Pollic # Lin # Grana attractioni æqualia <lb/>9 # 0 # 0 <lb/>4 # 9 # vix aliquid. <lb/>4 # 0 # 1 <lb/>3 # 3 # 6 <lb/># 12 # 63 <lb/># 11 # 68 <lb/># 10 # 77 <lb/># 9 # 82 <lb/># 8 # 103 <lb/># 7 # 115 <lb/># 6 # 135 <lb/># 5 # 158 <lb/># 4 # 166 <lb/># 3 # 221 <lb/></note> <pb o="43" file="0057" n="57" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># Lineæ # Grana <lb/># 2 # 275 <lb/># 1 # 373 <lb/># {1/2} # 460 <lb/># 0 # 650 <lb/></note> </div> <div xml:id="echoid-div30" type="section" level="1" n="30"> <head xml:id="echoid-head38" xml:space="preserve">EXPERIMENTUM XXII.</head> <p> <s xml:id="echoid-s927" xml:space="preserve">Deinde vero eſſudi ex hac capſula aliquantum limaturæ, donec <lb/>haberet eandem altitudinem, quam maſſa ſolida ferri habebat, quæ <lb/>ejuſdem ponderis cum Magnete fuit, & </s> <s xml:id="echoid-s928" xml:space="preserve">experimenta dederunt effe-<lb/>ctus hos.</s> <s xml:id="echoid-s929" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Diſtant. Linear. # Grana Attractioni æqualia. <lb/># 12 # 59 <lb/># 11 # 62 <lb/># 10 # 72 <lb/># 9 # 78 <lb/># 8 # 94 <lb/># 7 # 108 <lb/># 6 # 134 <lb/># 5 # 149 <lb/># 4 # 182 <lb/># 3 # 221 <lb/># 2 # 275 <lb/># 1 # 415 <lb/># {1/2} # 460 <lb/># 0 # 710 imo 772. in aliis punctis <lb/></note> <p> <s xml:id="echoid-s930" xml:space="preserve">contactus ejuſdem capſulæ. </s> <s xml:id="echoid-s931" xml:space="preserve">Hiſce omnibus obſervatis, oportebit <lb/>Experimenta inter ſe comparare, ſequelas elicere, quæ inde fluunt, <lb/>fructumque ex tantis hic impenſis laboribus carpere, quantum tuto <lb/>fieri poteſt.</s> <s xml:id="echoid-s932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s933" xml:space="preserve">Corol. </s> <s xml:id="echoid-s934" xml:space="preserve">1. </s> <s xml:id="echoid-s935" xml:space="preserve">Manifeſto liquet Magnetem fortius ad ſe trahere fer-<lb/>rum, quam alterum Magnetem: </s> <s xml:id="echoid-s936" xml:space="preserve">nam in Experimento quarto, Ma-<lb/>gnetes ambo ſe contingentes exercuerant vim 128. </s> <s xml:id="echoid-s937" xml:space="preserve">granor. </s> <s xml:id="echoid-s938" xml:space="preserve">Sed <lb/>in Experimento XVI, idem Magnes attraxit ferrum in puncto conta-<lb/>ctus vi 180. </s> <s xml:id="echoid-s939" xml:space="preserve">granor. </s> <s xml:id="echoid-s940" xml:space="preserve">adeoque ferrum majori vi attractum fuit, <pb o="44" file="0058" n="58" rhead="DISSERTATIO"/> quam Magnes Hoc autem multo magis probat Experimentum XVII, <lb/>nam idem Magnes in puncto contactus cum ferro minoris formæ, <lb/>quam in Experimento XVI, habuit vim attrahendi = 720. </s> <s xml:id="echoid-s941" xml:space="preserve">granis, <lb/>quæ vis plus quam quinquies ſuperat 180. </s> <s xml:id="echoid-s942" xml:space="preserve">grana in Experimento <lb/>quarto: </s> <s xml:id="echoid-s943" xml:space="preserve">Imo hoc ulterius confirmat Experimentum V. </s> <s xml:id="echoid-s944" xml:space="preserve">nam in hoc <lb/>Magnes NO. </s> <s xml:id="echoid-s945" xml:space="preserve">rotundus attrahebat alium vi 340. </s> <s xml:id="echoid-s946" xml:space="preserve">granor. </s> <s xml:id="echoid-s947" xml:space="preserve">in puncto <lb/>contactus, ſed in Experimento XVIII, idem Magnes rotundus at-<lb/>traxit ferrum vi = 1312. </s> <s xml:id="echoid-s948" xml:space="preserve">granis. </s> <s xml:id="echoid-s949" xml:space="preserve">vel inExperimento XIX. </s> <s xml:id="echoid-s950" xml:space="preserve">attraxit fer-<lb/>rum vi = 1024. </s> <s xml:id="echoid-s951" xml:space="preserve">gran. </s> <s xml:id="echoid-s952" xml:space="preserve">& </s> <s xml:id="echoid-s953" xml:space="preserve">in Experimento XX. </s> <s xml:id="echoid-s954" xml:space="preserve">attraxit ferrum vi = <lb/>574 gran. </s> <s xml:id="echoid-s955" xml:space="preserve">Ex pluribus igitur Experimentis conſtat manifeſto, Magne-<lb/>tem fortius attrahere ferrum, quam alterum Magnetem. </s> <s xml:id="echoid-s956" xml:space="preserve">Ex hac ob-<lb/>ſervatione confirmor in ſententia, quam in Cap 1. </s> <s xml:id="echoid-s957" xml:space="preserve">attuli, Magnetes, <lb/>qui polis amicis ſe attrahunt, ſimul ſe repellere, ſed repulſionem <lb/>ſuperari ab attractione; </s> <s xml:id="echoid-s958" xml:space="preserve">quemadmodum Magnetes, quo tempore <lb/>polis ſe fugantibus ſibi obverſi recedunt, ſimul tamen attrahuntur, <lb/>ſed attractio a repulſione ſuperatur: </s> <s xml:id="echoid-s959" xml:space="preserve">Quomodo enim ferrum modo <lb/>ante ex Igne extractum, & </s> <s xml:id="echoid-s960" xml:space="preserve">nulla ferè vi, ſaltem perquam exigua <lb/>imprægnatum, poſſet fortius attrahi â Magnete, quam Magnes exi-<lb/>miâ donatus vi attrahente? </s> <s xml:id="echoid-s961" xml:space="preserve">niſi quod Ferrum attrahatur tantum, <lb/>nequaquam ſimul repellat: </s> <s xml:id="echoid-s962" xml:space="preserve">aut ſi repellat, parum agat.</s> <s xml:id="echoid-s963" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s964" xml:space="preserve">Corol. </s> <s xml:id="echoid-s965" xml:space="preserve">2. </s> <s xml:id="echoid-s966" xml:space="preserve">Datur in his attractionibus ferri ad Magnetem, maxi-<lb/>mum aliquod & </s> <s xml:id="echoid-s967" xml:space="preserve">minimum: </s> <s xml:id="echoid-s968" xml:space="preserve">Ferri enim maſſa determinatæ magni-<lb/>tudinis & </s> <s xml:id="echoid-s969" xml:space="preserve">formæ maxime attrahetur â Magnete magnitudinis de-<lb/>terminatæ Ferri maſſa alia major vel minor, minus attrahetur ab eo-<lb/>dem, & </s> <s xml:id="echoid-s970" xml:space="preserve">quo maſſæ, tam quoad exceſſum vel defectum, plus diffe-<lb/>runt â maſſâ, quæ maxime attrahitur, eo etiam minus attrahentur. <lb/></s> <s xml:id="echoid-s971" xml:space="preserve">Hoc probo ex Experimentis XVII, XVIII, XIX, XX, in qui-<lb/>bus idem Magnes rotundus NO Tab 1. </s> <s xml:id="echoid-s972" xml:space="preserve">fig. </s> <s xml:id="echoid-s973" xml:space="preserve">2 fuit in uſum vocatus: </s> <s xml:id="echoid-s974" xml:space="preserve"><lb/>Nam in Experimento XVIII ferri maſſa quædam mediæ magnitudinis, <lb/>attrahebatur in puncto contactus vi = 1312. </s> <s xml:id="echoid-s975" xml:space="preserve">granis. </s> <s xml:id="echoid-s976" xml:space="preserve">Verum paralle-<lb/>lopipedum ferreum multo gravius, in Experimento XVII, attrahebatur <lb/>tantum vi = 720. </s> <s xml:id="echoid-s977" xml:space="preserve">gran adeoque minus quam ferrum Experimenti <lb/>XVIII. </s> <s xml:id="echoid-s978" xml:space="preserve">ſed ferri moles minor in Experimento XIX. </s> <s xml:id="echoid-s979" xml:space="preserve">attrahebatur vi = <lb/>1024. </s> <s xml:id="echoid-s980" xml:space="preserve">gran. </s> <s xml:id="echoid-s981" xml:space="preserve">ergo minus quam moles in Experimento XVIII. </s> <s xml:id="echoid-s982" xml:space="preserve">qua par-<lb/>te autem in contactu attrahebatur hoc ferrum in Experimento XIX, <lb/>erat craſſius, quam ferrum in Experimento XX. </s> <s xml:id="echoid-s983" xml:space="preserve">quod hinc modo in con- <pb o="45" file="0059" n="59" rhead="DE MAGNETE."/> tactu attrahebatur vi = 574 granis. </s> <s xml:id="echoid-s984" xml:space="preserve">Ut hanc ſequelam magis confir-<lb/>mare poſſem, ſuſpendi ex bilance ferrum adhuc multo minus, nempe <lb/>pedem chaly beum pyramidalem circini vulgaris, cujus cuſpis acuta in <lb/>immediato contactu ad Magnetis ejuſdem rotundi polum attrahebatur <lb/>vi = 20. </s> <s xml:id="echoid-s985" xml:space="preserve">granis. </s> <s xml:id="echoid-s986" xml:space="preserve">tum con vertebam hunc pedem chalybeum, ut parte <lb/>obtuſiori eundem Magnetis polum contingeret, nuncattrahebatur viri-<lb/>bus 224 granorum, adcoque multo minus quam ullum ferrum in Expe-<lb/>rimentis XVII, XVIII, XIX. </s> <s xml:id="echoid-s987" xml:space="preserve">XX. </s> <s xml:id="echoid-s988" xml:space="preserve">Sed hanc ſequelam ulterius confir-<lb/>mant Experimenta duo cum limatura ferri inſtituta, uti Experimenta. <lb/></s> <s xml:id="echoid-s989" xml:space="preserve">XXI & </s> <s xml:id="echoid-s990" xml:space="preserve">XXII. </s> <s xml:id="echoid-s991" xml:space="preserve">nam limaturæ quantitas major attrahebatur in contactu <lb/>vi 650. </s> <s xml:id="echoid-s992" xml:space="preserve">granor. </s> <s xml:id="echoid-s993" xml:space="preserve">& </s> <s xml:id="echoid-s994" xml:space="preserve">quantitas minor vi 710. </s> <s xml:id="echoid-s995" xml:space="preserve">granor. </s> <s xml:id="echoid-s996" xml:space="preserve">verum quantitas li-<lb/>maturæ relicta in eadem capſula multo minor, attrahebatur 315. </s> <s xml:id="echoid-s997" xml:space="preserve">gra-<lb/>nis, adcoque manifeſtum eſt, dari determinatam magnitudinem ferri, <lb/>in quam Magnes fortiſſime agit, & </s> <s xml:id="echoid-s998" xml:space="preserve">ipſum in majorem vel minorem <lb/>ferri molem minoribus viribus tantum operari.</s> <s xml:id="echoid-s999" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1000" xml:space="preserve">Ex hiſce Experimentis opinor poſſe elici methodum optimam ar-<lb/>mandi Magnetem, ut ferri maximum elevet onus, ſi ponderando <lb/>inquireremus, in quam craſſam ferri molem viribus ageret ſummis; <lb/></s> <s xml:id="echoid-s1001" xml:space="preserve">ſique tum armatura fabrefieret ex inventa craſſitie. </s> <s xml:id="echoid-s1002" xml:space="preserve">Ex hoc Co-<lb/>rollario etiam fluit Magnetem non attrahere Ferrum vi Legis gene-<lb/>ralis Attractionis, qua omnia corpora ſeſe trahunt; </s> <s xml:id="echoid-s1003" xml:space="preserve">nam ponamus <lb/>particulis ferri æqualibus innatam eſſe eandem vim attrahendi Ma-<lb/>gnetem, tum erit magnitudo attractionis in maſſa ferrea, uti eſt <lb/>magnitudo maſſæ, & </s> <s xml:id="echoid-s1004" xml:space="preserve">idcirco maſſa major â Magnete fortius de-<lb/>beret attrahi, quam minor; </s> <s xml:id="echoid-s1005" xml:space="preserve">verum longe quid aliud experientia e-<lb/>vincit, & </s> <s xml:id="echoid-s1006" xml:space="preserve">maſſa major debilius attrahitur minori, quamobrem Ma-<lb/>gnetis actio ab alia cauſa, quam â Lege Univerſali attractionis pen-<lb/>debit, quod infra prolixius evincere conabor aliis adhuc argumentis.</s> <s xml:id="echoid-s1007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1008" xml:space="preserve">Corol. </s> <s xml:id="echoid-s1009" xml:space="preserve">3. </s> <s xml:id="echoid-s1010" xml:space="preserve">Non tamen ad eandem a ſe mutuo diſtantiam agit <lb/>Magnes in ferrum quam quidem agunt duo Magnetes in ſe invicem. <lb/></s> <s xml:id="echoid-s1011" xml:space="preserve">Intueamur enim Experimentum 1 in quo Magnes rotundus major ope-<lb/>rabatur in minorem ad diſtantiam 5. </s> <s xml:id="echoid-s1012" xml:space="preserve">poll. </s> <s xml:id="echoid-s1013" xml:space="preserve">10. </s> <s xml:id="echoid-s1014" xml:space="preserve">linear. </s> <s xml:id="echoid-s1015" xml:space="preserve">in Experimen-<lb/>to II. </s> <s xml:id="echoid-s1016" xml:space="preserve">ad diſtantiam 9. </s> <s xml:id="echoid-s1017" xml:space="preserve">pollic. </s> <s xml:id="echoid-s1018" xml:space="preserve">in Experimento III. </s> <s xml:id="echoid-s1019" xml:space="preserve">ad diſtantiam 12. </s> <s xml:id="echoid-s1020" xml:space="preserve"><lb/>pollic in Experimento V. </s> <s xml:id="echoid-s1021" xml:space="preserve">ad diſtantiam 18 pollic. </s> <s xml:id="echoid-s1022" xml:space="preserve">ſed in Experimen-<lb/>to XVIII. </s> <s xml:id="echoid-s1023" xml:space="preserve">idem Magnes modo agebat in ferrum ad diſtantiam 3. </s> <s xml:id="echoid-s1024" xml:space="preserve"><lb/>pollic 10. </s> <s xml:id="echoid-s1025" xml:space="preserve">linear. </s> <s xml:id="echoid-s1026" xml:space="preserve">uti & </s> <s xml:id="echoid-s1027" xml:space="preserve">in Experimento XIX. </s> <s xml:id="echoid-s1028" xml:space="preserve">& </s> <s xml:id="echoid-s1029" xml:space="preserve">XX. </s> <s xml:id="echoid-s1030" xml:space="preserve">ad 4. </s> <s xml:id="echoid-s1031" xml:space="preserve">polli- <pb o="46" file="0060" n="60" rhead="DISSERTATIO"/> ces in XXI. </s> <s xml:id="echoid-s1032" xml:space="preserve">Experimento. </s> <s xml:id="echoid-s1033" xml:space="preserve">Ex quibus ergo Experimentis abunde patet <lb/>corollarium elicitum: </s> <s xml:id="echoid-s1034" xml:space="preserve">attamen volui id ulterius confirmare, ſumſique <lb/>acum rotatilem, ſive verſorium, vulgo cen Compas naalde, non affrictam <lb/>Magneti, obſervavi in quanam diſtantia â Magnete in cipiebat rotari <lb/>moto Magnete, dein acum affricui Magneti, quæ viribus imprægnata <lb/>inſtar alterius Magnetis ſe habebat, hæc acus cardiniſuo impoſita con-<lb/>vertebatur ad diſtantiam 4. </s> <s xml:id="echoid-s1035" xml:space="preserve">pedum â Magnete rotundo, No, cum <lb/>antea ad diſtantiam 9. </s> <s xml:id="echoid-s1036" xml:space="preserve">pollicum nondum convertebatur. </s> <s xml:id="echoid-s1037" xml:space="preserve">Quam-<lb/>obrem hoc Corollarium ſatis demonſtratum erit; </s> <s xml:id="echoid-s1038" xml:space="preserve">atque ſimul in eo li-<lb/>quet, Magnetem vim ſuam ex ſe emittere extrorſum ad majorem <lb/>diſtantiam, quam Ferrum purum, id autem vires ad majus inter-<lb/>vallum ejaculare, poſtquam Magnetem attigit.</s> <s xml:id="echoid-s1039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1040" xml:space="preserve">Corol. </s> <s xml:id="echoid-s1041" xml:space="preserve">4. </s> <s xml:id="echoid-s1042" xml:space="preserve">Omnia autem hæc Experimenta inſtituta ſunt, ut ex-<lb/>plorarem quænam proportio inter vim attrahentem Magnetis & </s> <s xml:id="echoid-s1043" xml:space="preserve">di-<lb/>ſtantias daretur; </s> <s xml:id="echoid-s1044" xml:space="preserve">quod ſi Experimentum XVII. </s> <s xml:id="echoid-s1045" xml:space="preserve">ante oculos pona-<lb/>mus, atque examen incipiamus a diſtantia 12. </s> <s xml:id="echoid-s1046" xml:space="preserve">linearum uſque ad <lb/>3. </s> <s xml:id="echoid-s1047" xml:space="preserve">lineas, animadvertemus numeros, exprimentes magnitudinem <lb/>attractionis, eſſe fere in ratione inverſâ diſtantiarum, a quâ pro-<lb/>portione tamen abludunt attractiones in minoribus & </s> <s xml:id="echoid-s1048" xml:space="preserve">in majoribus <lb/>diſtantiis obſervatæ, incipiamus enim calculum a diſtantia 12. </s> <s xml:id="echoid-s1049" xml:space="preserve">li-<lb/>nearum, minorem verſus pergendo, tum numeros in inverſa ratione <lb/>diſtantiarum erutos deprehendemus ſequentes.</s> <s xml:id="echoid-s1050" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ in Lineis # Numeri \\ juxta Calculum # Attractiones \\ obſervatæ <lb/>12 # 35 # 35 <lb/>11 # 38 {1/11} # 37 <lb/>10 # 42 # 43 <lb/>9 # 46 {2/3} # 47 <lb/>8 # 52 {1/2} # 57 <lb/>7 # 60 # 66 <lb/>6 # 70 # 76 <lb/>5 # 84 # 96 <lb/>4 # 105 # 109 <lb/>3 # 140 # 131 <lb/></note> <p> <s xml:id="echoid-s1051" xml:space="preserve">Si in reliquis diſtantiis numeri ope calculi inventi tam ac- <pb o="47" file="0061" n="61" rhead="DE MAGNETE."/> curate congruerent cum iis, quos ipſa obſervatio dedit, non dubi-<lb/>tarem affirmare vires Magnetis attrahentes Ferrum eſſe in ratione <lb/>inverſa diſtantiarum, parva enim diſcrepantia, quæ inter ambos <lb/>numeros, tum ex calculo, tum ex obſervatione poſitos, datur, non <lb/>prohiberet, quominus hanc proportionem ſtabiliremus; </s> <s xml:id="echoid-s1052" xml:space="preserve">quippe <lb/>experimenta omnia phyſica ejus ſunt naturæ, ut ferè nunquam ac-<lb/>curatiſſime cum calculo congruant: </s> <s xml:id="echoid-s1053" xml:space="preserve">verum in diſtantiis minoribus <lb/>multo minus convenit calculus cum obſervationibus, nam priorem <lb/>proportionem continuando, ad diſtantiam 2. </s> <s xml:id="echoid-s1054" xml:space="preserve">linearum deberet eſſe <lb/>attractio 210. </s> <s xml:id="echoid-s1055" xml:space="preserve">granorum, quæ modo fuit 179. </s> <s xml:id="echoid-s1056" xml:space="preserve">gran· & </s> <s xml:id="echoid-s1057" xml:space="preserve">ad diſtantiam <lb/>1. </s> <s xml:id="echoid-s1058" xml:space="preserve">lineæ foret 420. </s> <s xml:id="echoid-s1059" xml:space="preserve">granor. </s> <s xml:id="echoid-s1060" xml:space="preserve">quæ obſervata fuit modo 231. </s> <s xml:id="echoid-s1061" xml:space="preserve">gran. </s> <s xml:id="echoid-s1062" xml:space="preserve">at-<lb/>que ad {1/2} lineam deſiderata fuiſſet 840. </s> <s xml:id="echoid-s1063" xml:space="preserve">gran. </s> <s xml:id="echoid-s1064" xml:space="preserve">quæ tantum 343. </s> <s xml:id="echoid-s1065" xml:space="preserve">gra-<lb/>nor. </s> <s xml:id="echoid-s1066" xml:space="preserve">fuit. </s> <s xml:id="echoid-s1067" xml:space="preserve">Unde autem hæc diſcrepantia oritur? </s> <s xml:id="echoid-s1068" xml:space="preserve">an quia, quod-<lb/>cunque fuerit ferrum, vim aliquam repellendi Magnetem habet, <lb/>quæ ad parvam diffuſa modo diſtantiam, attractionis aliquam par-<lb/>tem tollit, in quam nihil agit in majori intervallo? </s> <s xml:id="echoid-s1069" xml:space="preserve">an vero ipſa vis <lb/>repellens Magnetis hanc inæqualitatem attractioni affert?</s> <s xml:id="echoid-s1070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1071" xml:space="preserve">Alia Experimenta, nempe XVI. </s> <s xml:id="echoid-s1072" xml:space="preserve">& </s> <s xml:id="echoid-s1073" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s1074" xml:space="preserve">quoque ad examen <lb/>vocavi, explorans an in diſtantiis a 12 ad 3 lineas etiam daretur <lb/>attractio in ratione inverſa diſtantiarum, ſed in illis nequaquam <lb/>numeros tam prope accedentes obſervatis ſuppeditavit calcu-<lb/>lus, ecce eos juxta ſe poſitos, quos ex Experimento XVI. </s> <s xml:id="echoid-s1075" xml:space="preserve">erui-<lb/>mus:</s> <s xml:id="echoid-s1076" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantiæ \\ Linear. # Numeri \\ calculo inventi. # Attractio \\ obſervata <lb/>11 # 14 # 14 <lb/>10 # 15 {2/5} # 16 <lb/>9 # 17 {1/9} # 17 <lb/>8 # 19 {2/8} # 21 <lb/>7 # 22 # 29 <lb/>6 # 25 {2/3} # 32 <lb/>5 # 30 {4/5} # 44 <lb/>4 # 38 {1/2} # 52 <lb/>3 # 51 {1/3} # 72 <lb/>2 # 77 # 96 <lb/>1 # 154 # 110 <lb/></note> <pb o="48" file="0062" n="62" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s1077" xml:space="preserve">Sunt attractiones obſervatæ a linea 11. </s> <s xml:id="echoid-s1078" xml:space="preserve">ad 1. </s> <s xml:id="echoid-s1079" xml:space="preserve">majores quam cal-<lb/>culus indicat, ſed in diſtantia 1. </s> <s xml:id="echoid-s1080" xml:space="preserve">lineæ minores ſunt, quæ anoma-<lb/>lia procul dubio oritur a vi attrahente & </s> <s xml:id="echoid-s1081" xml:space="preserve">repellente, quæ ambæ ſimula-<lb/>gunt in ferrum, atque proportionem conſtantem turbant. </s> <s xml:id="echoid-s1082" xml:space="preserve">Ecce <lb/>veró numeros ex Experimento XVIII. </s> <s xml:id="echoid-s1083" xml:space="preserve">ſubductos juxta rationem in-<lb/>verſam diſtantiarum, in quibus eadem anomalia locum habet.</s> <s xml:id="echoid-s1084" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Calculus ad \\ Linearum # diſtantiam \\ dat grana # Obſervatio \\ dat grana <lb/>12 # 61 # 61 <lb/>11 # 66 {6/11} # 70 <lb/>10 # 73 {1/5} # 84 <lb/>9 # 81 {1/3} # 106 <lb/>8 # 91 {1/2} # 121 <lb/>7 # 104 {4/7} # 140 <lb/>6 # 122 # 164 <lb/>5 # 146 {2/5} # 201 <lb/>4 # 183 # 229 <lb/>3 # 244 # 285 <lb/>2 # 366 # 361 <lb/>1 # 732 # 472 <lb/></note> <p> <s xml:id="echoid-s1085" xml:space="preserve">Quantum igitur conjectando aſſequi poſſum, vires Magnetum <lb/>ſe invicem attrahentes & </s> <s xml:id="echoid-s1086" xml:space="preserve">repellentes erunt in ratione inverſa di-<lb/>ſtantiarum; </s> <s xml:id="echoid-s1087" xml:space="preserve">aut in proportione huic proxima; </s> <s xml:id="echoid-s1088" xml:space="preserve">& </s> <s xml:id="echoid-s1089" xml:space="preserve">quia Magnetes <lb/>ſimul ſe attrahunt & </s> <s xml:id="echoid-s1090" xml:space="preserve">repellunt, Experimenta priora Capitis primi <lb/>non poſſunt non exhibere numeros, attractionem exprimentes, <lb/>in proportione inconſtanti, cum nequaquam ſolam attractionem <lb/>vel repulſionem oſtendant; </s> <s xml:id="echoid-s1091" xml:space="preserve">nequaquam igitur in tam alta proportio-<lb/>ne, veluti duplicata aut triplicata intervallorum, vires Magnetum de-<lb/>creſcent, uti a nonnullis creditum fuit.</s> <s xml:id="echoid-s1092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1093" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s1094" xml:space="preserve">5. </s> <s xml:id="echoid-s1095" xml:space="preserve">Præterea ex memoratis Experimentis colligimus, non fieri <lb/>attractionem ferri ad Magnetem in proportione magnitudinis ſuperfi-<lb/>ciei, quæ Magneti opponitur; </s> <s xml:id="echoid-s1096" xml:space="preserve">ſed etiam dati hic maximum aliquid <lb/>& </s> <s xml:id="echoid-s1097" xml:space="preserve">minimum. </s> <s xml:id="echoid-s1098" xml:space="preserve">Nam in Exp. </s> <s xml:id="echoid-s1099" xml:space="preserve">XIX. </s> <s xml:id="echoid-s1100" xml:space="preserve">ſuperficies F pedis armaturæ <lb/>obvertebatur Magneti, vid. </s> <s xml:id="echoid-s1101" xml:space="preserve">Tab. </s> <s xml:id="echoid-s1102" xml:space="preserve">6, fig. </s> <s xml:id="echoid-s1103" xml:space="preserve">4. </s> <s xml:id="echoid-s1104" xml:space="preserve">reliqua ſuperficies ferri <pb o="49" file="0063" n="63" rhead="DE MAGNETE."/> t<unsure/>am ſuperior, quam inferior, demtis lateribus, erat parva: </s> <s xml:id="echoid-s1105" xml:space="preserve">fiebat ta-<lb/>men attractio ad eandem diſtantiam a Magnete, quam in Exper. <lb/></s> <s xml:id="echoid-s1106" xml:space="preserve">XX. </s> <s xml:id="echoid-s1107" xml:space="preserve">in quo ſuperficies ferri A B C D, Magneti eidem oppoſita, tam <lb/>ſuperior quam inferior, erat quidem duodecies, imo multo <lb/>amplior; </s> <s xml:id="echoid-s1108" xml:space="preserve">in diſtantiis tameu propioribus, idem ferrum Experimen-<lb/>ti XIX. </s> <s xml:id="echoid-s1109" xml:space="preserve">multo fortius attrahebatur, quam in Exp. </s> <s xml:id="echoid-s1110" xml:space="preserve">XX. </s> <s xml:id="echoid-s1111" xml:space="preserve">uti ex <lb/>comparatis tabulis videri poteſt: </s> <s xml:id="echoid-s1112" xml:space="preserve">in quibus obſervamus, ſuperficiem <lb/>minorem ferri attractam fuiſſe majoribus viribus, quam fuit ferri <lb/>ſuperficies major: </s> <s xml:id="echoid-s1113" xml:space="preserve">Non tamen deduci inde poteſt, quo ſuperficies <lb/>ferri minor obvertitur Magneti, eo fieri majorem attractionem, nam <lb/>alia attuli experimenta cum pede ferreo circini inſtituta, quæ ex-<lb/>hibuerunt attractionem ferri acuti ad Magnetem eſſe minorem, <lb/>quam ejuſdem ferri obtuſioris: </s> <s xml:id="echoid-s1114" xml:space="preserve">quamobrem dabitur ſuperficies deter-<lb/>minatæ magnitudinis, determinatæ ferreæ maſſæ, quæ à Magnete <lb/>maxime attrahetur, & </s> <s xml:id="echoid-s1115" xml:space="preserve">aliæ ſuperficies, hâc majores vel minores, mi-<lb/>nus attrahentur. </s> <s xml:id="echoid-s1116" xml:space="preserve">Plura corollaria ex his experimentis deducere po-<lb/>tuiſſem, verum præſtare ea opinabar, quæ evidentiſſima ſunt, & </s> <s xml:id="echoid-s1117" xml:space="preserve"><lb/>multis comprobantur obſervationibus, quam quæ ex hac aut illâ <lb/>tantum ſluerent,</s> </p> <p> <s xml:id="echoid-s1118" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s1119" xml:space="preserve">Primus, quantum novi, omnium Hauksbejus inqui-<lb/>quiſivit proportionem virium Magneticarum in variis diſtantiis <lb/>Magnetis a ferro: </s> <s xml:id="echoid-s1120" xml:space="preserve">methodus ejus, prorſus diverſa a noſtrâ, <lb/>quamvis omnium ſuffragia non latura ſit, tamen cognoſci meretur, <lb/>ob effectus in ea obſervatos: </s> <s xml:id="echoid-s1121" xml:space="preserve">proſtat autem deſcripta in Philoſ. <lb/></s> <s xml:id="echoid-s1122" xml:space="preserve">Tranſactions N° 335. </s> <s xml:id="echoid-s1123" xml:space="preserve">p. </s> <s xml:id="echoid-s1124" xml:space="preserve">506. </s> <s xml:id="echoid-s1125" xml:space="preserve">vel in Compendii vol. </s> <s xml:id="echoid-s1126" xml:space="preserve">4. </s> <s xml:id="echoid-s1127" xml:space="preserve">part.</s> <s xml:id="echoid-s1128" xml:space="preserve">, 2. </s> <s xml:id="echoid-s1129" xml:space="preserve">pag. </s> <s xml:id="echoid-s1130" xml:space="preserve"><lb/>295.</s> <s xml:id="echoid-s1131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1132" xml:space="preserve">Sumſit Vir artificio ſiſſimus Quadrantem, cujus radius 4. </s> <s xml:id="echoid-s1133" xml:space="preserve">ped. <lb/></s> <s xml:id="echoid-s1134" xml:space="preserve">quem poſuit ſupra ſolum, in centro ponebatur acus rotatilis; </s> <s xml:id="echoid-s1135" xml:space="preserve"><lb/>quæ ſibi commiſſa, ſtabat in Quadrante ad grad. </s> <s xml:id="echoid-s1136" xml:space="preserve">o. </s> <s xml:id="echoid-s1137" xml:space="preserve">tum Magnetem <lb/>imponebat aſſeri ita, ut polus ejus jaceret in eodem plano cum Qua-<lb/>drante & </s> <s xml:id="echoid-s1138" xml:space="preserve">acu, & </s> <s xml:id="echoid-s1139" xml:space="preserve">moveri poſſet juxta limbum Quadrantis a gradu <lb/>in gradum, & </s> <s xml:id="echoid-s1140" xml:space="preserve">a diſtantia una in aliam. </s> <s xml:id="echoid-s1141" xml:space="preserve">Magnes erat figuræ irregu-<lb/>laris, & </s> <s xml:id="echoid-s1142" xml:space="preserve">circiter 6. </s> <s xml:id="echoid-s1143" xml:space="preserve">Librarum. </s> <s xml:id="echoid-s1144" xml:space="preserve">fecit vero Experimenta cum duabus <lb/>acubus, quarum una fuit 3. </s> <s xml:id="echoid-s1145" xml:space="preserve">poll. </s> <s xml:id="echoid-s1146" xml:space="preserve">longa, altera 6. </s> <s xml:id="echoid-s1147" xml:space="preserve">poll. </s> <s xml:id="echoid-s1148" xml:space="preserve">ſed ſemper <lb/>invenit breviorem eſſe meliorem.</s> <s xml:id="echoid-s1149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1150" xml:space="preserve">In tabulis autem continentibus hæc Experimenta obſervandum eſt, <pb o="50" file="0064" n="64" rhead="DISSERTATIO."/> longiorem acum ad diſtantiam 9. </s> <s xml:id="echoid-s1151" xml:space="preserve">poll. </s> <s xml:id="echoid-s1152" xml:space="preserve">à Magnete efficere angulum <lb/>paulo majorem, quam acum breviorem ad diſtantiam 3. </s> <s xml:id="echoid-s1153" xml:space="preserve">pollicum. <lb/></s> <s xml:id="echoid-s1154" xml:space="preserve">Acum breviorem ad diſtant. </s> <s xml:id="echoid-s1155" xml:space="preserve">9. </s> <s xml:id="echoid-s1156" xml:space="preserve">poll. </s> <s xml:id="echoid-s1157" xml:space="preserve">facere angulum 9. </s> <s xml:id="echoid-s1158" xml:space="preserve">grad. </s> <s xml:id="echoid-s1159" xml:space="preserve">minorem, <lb/>quam longiorem in eadem diſtantia: </s> <s xml:id="echoid-s1160" xml:space="preserve">ſed hæc paradoxa facile in-<lb/>telligentur, ſi conſideramus diſproportionem longitudinis acus, nam <lb/>cuſpis longioris acus ad diſt. </s> <s xml:id="echoid-s1161" xml:space="preserve">9. </s> <s xml:id="echoid-s1162" xml:space="preserve">poll. </s> <s xml:id="echoid-s1163" xml:space="preserve">erat propior Magneti 1. </s> <s xml:id="echoid-s1164" xml:space="preserve">poll. </s> <s xml:id="echoid-s1165" xml:space="preserve"><lb/>quam cuſpis brevioris acûs; </s> <s xml:id="echoid-s1166" xml:space="preserve">& </s> <s xml:id="echoid-s1167" xml:space="preserve">cuſpis brevioris acûs in diſtantia <lb/>9. </s> <s xml:id="echoid-s1168" xml:space="preserve">pollic. </s> <s xml:id="echoid-s1169" xml:space="preserve">a Magnete, diſtabat 5. </s> <s xml:id="echoid-s1170" xml:space="preserve">poll. </s> <s xml:id="echoid-s1171" xml:space="preserve">plus, quam acus majoris, <lb/>cum Magnes in eodem gradu Quadrantis erat: </s> <s xml:id="echoid-s1172" xml:space="preserve">Unde ad hanc diſpro-<lb/>portionem attendendum. </s> <s xml:id="echoid-s1173" xml:space="preserve">Notandum præterea, Magnetem in diſtantia <lb/>5. </s> <s xml:id="echoid-s1174" xml:space="preserve">ped. </s> <s xml:id="echoid-s1175" xml:space="preserve">ab acu, facere angulum 2. </s> <s xml:id="echoid-s1176" xml:space="preserve">grad. </s> <s xml:id="echoid-s1177" xml:space="preserve">cum una acu, & </s> <s xml:id="echoid-s1178" xml:space="preserve">2 {1/2} grad. </s> <s xml:id="echoid-s1179" xml:space="preserve"><lb/>cum altera acu: </s> <s xml:id="echoid-s1180" xml:space="preserve">ſed in majori diſtantiâ non fieri obſer vabilem mutatio-<lb/>nem in Acu: </s> <s xml:id="echoid-s1181" xml:space="preserve">Ita ut vis Magnetica extendatur eouſque ad 5. </s> <s xml:id="echoid-s1182" xml:space="preserve">ped. </s> <s xml:id="echoid-s1183" xml:space="preserve">in <lb/>quibus proportiones capi poſſunt, ſed in majoribus diſtantiis, vis <lb/>Magnetis eſt adeo debilis, ut nihil certi obſervetur.</s> <s xml:id="echoid-s1184" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # # Experimenta cum breviori # # # # Experimenta cum Longiori Acu <lb/>Diſtantiæ \\ Acus a \\ Magn. in \\ poll. # # Anguli ad \\ quaſſibet \\ diſtantias \\ facti ab Acu # Differentiæ \\ comparatæ \\ inter ſe, in \\ Minutis # Diſtantiæ \\ Acus a \\ Magn. in \\ poll. # # Anguli ad \\ quaſlibet \\ diſtantias \\ factiab Acu # Differentiæ \\ comparatæ \\ cum priori- \\ bus in Mi- \\ nutis. <lb/># Gr. # M. # # # Gr. # M. <lb/>3 # 87 # 0 # 180 # 9 # 87 # 30 # 345 <lb/>6 # 84 # 0 # 330 # 12 # 81 # 45 # 570 <lb/>9 # 78 # 30 # 570 # 15 # 72 # 15 # 1137 <lb/>12 # 69 # 0 # 735 # 18 # 53 # 20 # 1100 <lb/>15 # 56 # 45 # 795 # 21 # 35 # 0 # 660 <lb/>18 # 43 # 30 # 630 # 24 # 24 # 10 # 380 <lb/>21 # 33 # 0 # 540 # 27 # 17 # 50 # 280 <lb/>24 # 24 # 0 # 360 # 30 # 13 # 10 # 180 <lb/>27 # 18 # 0 # 270 # 33 # 10 # 10 # 130 <lb/>30 # 13 # 30 # 150 # 36 # 8 # 0 # 90 <lb/>33 # 11 # 0 # 135 # 39 # 6 # 30 # 75 <lb/>36 # 8 # 45 # 105 # 42 # 5 # 15 # 65 <lb/>39 # 7 # 0 # 90 # 45 # 4 # 10 # 40 <lb/>42 # 5 # 30 # 60 # 48 # 3 # 30 # 30 <lb/></note> <pb o="51" file="0065" n="65" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/>45 # 4 # 30 # 40 # 51 # 3 # 0 # 25 <lb/>48 # 3 # 50 # 30 # 54 # 2 # 35 # 20 <lb/>51 # 3 # 20 # 20 # 57 # 2 # 15 # 15 <lb/>54 # 3 # 0 # 15 # 60 # 2 # 0 # 0 <lb/>57 # 2 # 45 # 15 <lb/>60 # 2 # 30 # 0 <lb/></note> <p> <s xml:id="echoid-s1185" xml:space="preserve">Quia in his Experimentis non accurate videre poſſumus diſtantias <lb/>Magnetis ab acu; </s> <s xml:id="echoid-s1186" xml:space="preserve">juſſit Societas Regia, ut Nob. </s> <s xml:id="echoid-s1187" xml:space="preserve">Brook Taylor caperet <lb/>experimenta alio & </s> <s xml:id="echoid-s1188" xml:space="preserve">clariori modo de viribus Magnetis, adeoque hic <lb/>ſubtilis egregiuſque Mathematicus poſuit acum in centro Quadrantis <lb/>prioris, & </s> <s xml:id="echoid-s1189" xml:space="preserve">Magnetem, cujus axis in plano horizontali jacebat, admovit <lb/>removitque ab Acu in linea recta, quæ cum naturali directione Acus <lb/>faceret angulum rectum: </s> <s xml:id="echoid-s1190" xml:space="preserve">tunc diſtantias menſurans perlineam inter <lb/>centrum & </s> <s xml:id="echoid-s1191" xml:space="preserve">Magnetem interjacentem; </s> <s xml:id="echoid-s1192" xml:space="preserve">condidit ſequentem tabulam.</s> <s xml:id="echoid-s1193" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia \\ in pedibus # Variatio \\ Acus <lb/># Gr. # m. <lb/>1 # 81 # 45 <lb/>2 # 58 # 0 <lb/>3 # 30 # 0 <lb/>4 # 16 # 0 <lb/>5 # 9 # 20 <lb/>6 # 5 # 35 <lb/>7 # 3 # 30 <lb/>8 # 2 # 20 <lb/>9 # 1 # 35 <lb/></note> <p> <s xml:id="echoid-s1194" xml:space="preserve">Hæc Experimenta facta ſunt cum Magnete præſtantiſſimo Socie-<lb/>tatis Regiæ; </s> <s xml:id="echoid-s1195" xml:space="preserve">ſed quoniam in hiſce non obſervata fuit ſimilis poſitio <lb/>Lineæ, in qua movebatur Magnes verſus acum, quod erat admo-<lb/>dum neceſſarium, non multum ex his concludi poterat, obſervante <lb/>Whiſtono, qui idcirco alia experimenta de novo inſtituit: </s> <s xml:id="echoid-s1196" xml:space="preserve">imo ar-<lb/>bitror hiſce methodis nos voti compotes fieri non poſſe, uti pate-<lb/>bit ex ſcrupulo, quem in medium proferam, poſtquam Whiſtoni ob-<lb/>ſervationes annotavero. </s> <s xml:id="echoid-s1197" xml:space="preserve">Operæ pretium autem eſſe indicavi Præſtan- <pb o="52" file="0066" n="66" rhead="DISSERTATIO"/> tiſſimi hujus Philoſophi Experimenta adjungere, quia facta ſunt <lb/>cum Magnete & </s> <s xml:id="echoid-s1198" xml:space="preserve">Ferro, prius imprægnato vi Magnetica, quamobrem <lb/>diverſum hoc eſt penitus examen a noſtro, cum uſus ego tantum <lb/>fuerim vel duobus Magnetibus, vel Magnete & </s> <s xml:id="echoid-s1199" xml:space="preserve">Ferro puro, non poſ-<lb/>ſidente vim a Magnete ſibi communicatam: </s> <s xml:id="echoid-s1200" xml:space="preserve">Sumſit duas acus ver-<lb/>ſorias impoſitas cuſpidibus, quarum una erat 4 {1/2} pollices, altera 4 pedes <lb/>longa, atque Magnetem ſphæricum diametri 2 {8/10} pollicum; </s> <s xml:id="echoid-s1201" xml:space="preserve">hujus po-<lb/>lum Auſtralem ſemper oppoſuit acuum cuſpidibus Borealibus, admo-<lb/>vendo Magnetem verſus acum ita, ut hæc ſemper cum linea directrice <lb/>Magnetis conſtitueret angulum rectum: </s> <s xml:id="echoid-s1202" xml:space="preserve">tum chordas arcuum men-<lb/>ſuravit, quibus acus declinabat â naturali directione, quarum lon-<lb/>gitudines ſumebat pro iis quantitatibus, quæ exprimerent vires attra-<lb/>ctrices, loco Chordarum Sinus poſuit, quia hi ſunt dimidia Chorda-<lb/>rum, Tabulamque obſervationum dedit ſequentem.</s> <s xml:id="echoid-s1203" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia \\ in pollic. # Gradus \\ declinat. # Sinus dimidiorum \\ arcuum. <lb/>3 # 0 # 0 <lb/>6 # 0 # 0 <lb/>6 {1/2} # 90 # 7071 <lb/>9 # 27 # 2334 <lb/>12 # 13 # 1132 <lb/>15 # 9 {1/4} # 848 <lb/>18 # 6 {3/4} # 588 <lb/>21 # 4 {1/2} # 392 <lb/>24 # 3 # 262 <lb/>27 # 2 # 174 <lb/>30 # 1 {5/6} # 160 <lb/>33 # 1 {1/2} # 131 <lb/>36 # 1 {1/4} # 109 <lb/>39 # 0 {5/6} # 73 <lb/>42 # 0 {3/4} # 65 <lb/>45 # {2/3} # 58 <lb/>48 # {1/2} # 44 <lb/></note> <p> <s xml:id="echoid-s1204" xml:space="preserve">Quærantur nunc numeri diſtantiarum, & </s> <s xml:id="echoid-s1205" xml:space="preserve">Sinuum iis reſponden- <pb o="53" file="0067" n="67" rhead="DE MAGNETE."/> tium, uti diſtantiæ 9 pollicum reſpondet Sinus 2334. </s> <s xml:id="echoid-s1206" xml:space="preserve">& </s> <s xml:id="echoid-s1207" xml:space="preserve">diſtantiæ <lb/>18 pollicum Sinus 588. </s> <s xml:id="echoid-s1208" xml:space="preserve">Sunt hi numeri Sinuum ad ſe invicem accu-<lb/>rate, uti 3 {285/294} ad 1. </s> <s xml:id="echoid-s1209" xml:space="preserve">ſive circiter uti 4 ad 1 hoc eſt in ratione inverſa dupli-<lb/>cata diſtantiarum. </s> <s xml:id="echoid-s1210" xml:space="preserve">Sinus appoſiti diſtantiis 12 & </s> <s xml:id="echoid-s1211" xml:space="preserve">24, ſunt 1132 & </s> <s xml:id="echoid-s1212" xml:space="preserve">262, qui <lb/>ſunt inter ſe uti 4 {42/131} ad 1, adeoque hi ſunt in majori proportione ad ſe in-<lb/>vicem, quam ſuperiores Sinus appoſiti diſtantiis 15 & </s> <s xml:id="echoid-s1213" xml:space="preserve">30 pollicum, ſunt <lb/>848 & </s> <s xml:id="echoid-s1214" xml:space="preserve">131, qui ſunt inter ſe. </s> <s xml:id="echoid-s1215" xml:space="preserve">uti 6 {62/131} ad 1. </s> <s xml:id="echoid-s1216" xml:space="preserve">Sinus reſpondentes di-<lb/>ſtantiis 18 & </s> <s xml:id="echoid-s1217" xml:space="preserve">36, ſunt 588 & </s> <s xml:id="echoid-s1218" xml:space="preserve">109. </s> <s xml:id="echoid-s1219" xml:space="preserve">ſunt uti 5 {43/109} ad 1. </s> <s xml:id="echoid-s1220" xml:space="preserve">Sinus appoſi-<lb/>ti diſtantiis 21 & </s> <s xml:id="echoid-s1221" xml:space="preserve">42 pollicibus, ſunt 392 & </s> <s xml:id="echoid-s1222" xml:space="preserve">65, quorum proportio <lb/>eſt 6 {2/65} ad 1.</s> <s xml:id="echoid-s1223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1224" xml:space="preserve">Ex quibus mihi colligendum videtur proportionem dari valde in-<lb/>conſtantem, quæ aliquando eſſet minor quam duplicata, aliquando <lb/>paulum major, aliquando multo major duplicata. </s> <s xml:id="echoid-s1225" xml:space="preserve">Poſuit nihilo-<lb/>minus Whiſtonus rationem hic obtinere Sesquiduplicatam, quoniam <lb/>in Experimentis quædam laxitas Geometrica habenda eſt, id con-<lb/>cedendum omnino, niſi laxitas nimium extendatur, quod hic <lb/>fieri videtur, nimia enim intercedit diſcrepantia, cum Experimenta <lb/>in uno caſu dent proportionem uti 3 {285/294} ad 1. </s> <s xml:id="echoid-s1226" xml:space="preserve">& </s> <s xml:id="echoid-s1227" xml:space="preserve">in altero 6 {62/131} ad 1. <lb/></s> <s xml:id="echoid-s1228" xml:space="preserve">ut hæ ambæ pro unâ eademque proportione habeantur: </s> <s xml:id="echoid-s1229" xml:space="preserve">Idcirco non <lb/>video, cur non potius fateamur nullam conſtantem hic dari propor-<lb/>tionem, quam tam mirifice intorquendo Experimenta, ut propor-<lb/>tionem inveniamus, ubi eam Natura negat.</s> <s xml:id="echoid-s1230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1231" xml:space="preserve">Verum in hac methodo explorandi vires Magneticas difficultas <lb/>quædam latet. </s> <s xml:id="echoid-s1232" xml:space="preserve">Agitur Magnes aut Acus nautica viribus duabus a <lb/>ſe diſtinctis, una attractrice, aliâ directrice verſus quoſdam in <lb/>Terrâ polos: </s> <s xml:id="echoid-s1233" xml:space="preserve">vi directrice Acus in hoc Experimento quoque dirigitur <lb/>ad polos. </s> <s xml:id="echoid-s1234" xml:space="preserve">Cum Magnes Acui opponitur ad diverſas diſtantias, eamque <lb/>a directione priori deflectit, tum vi ſua Attractrice agit in vim di-<lb/>rectricem Acus; </s> <s xml:id="echoid-s1235" xml:space="preserve">atque eam deflectit, donec vis directrix, in eam ob-<lb/>liquam poſitionem acus agens, æquilibrium inveniat cum vi attra-<lb/>ctrice Magnetis: </s> <s xml:id="echoid-s1236" xml:space="preserve">adeoque non ita detegitur quantitas virium ſe mu-<lb/>tuo attrahentium in Acu & </s> <s xml:id="echoid-s1237" xml:space="preserve">Magnete, ſed longe quid aliud: </s> <s xml:id="echoid-s1238" xml:space="preserve">Conci-<lb/>piamus enim Acum rotatilem ſupra pinnam fixam, poſitam in medio <lb/>flumine quodam, dirigique juxta ejus curſum; </s> <s xml:id="echoid-s1239" xml:space="preserve">& </s> <s xml:id="echoid-s1240" xml:space="preserve">lateraliter cuſpi-<lb/>dem Acus trahi per funem annexum ripam verſus ita, ut funis ſem-<lb/>per ſit perpendicularis ad Acum, tum ut inflectatur in angulum, <pb o="54" file="0068" n="68" rhead="DISSERTATIO"/> non modo potentia trahens agit in Acum, ſed in fluvium quoque, & </s> <s xml:id="echoid-s1241" xml:space="preserve"><lb/>ſuperandam habet vim fluminis in illam incurrentis lateraliter, eam-<lb/>que propellentis recta, juxta ſui curſus determinationem eſtque flu-<lb/>minis incurrentis vis ſemper eo major, quo Acus ſitum flumini plus <lb/>oppoſitum accipit: </s> <s xml:id="echoid-s1242" xml:space="preserve">vis trahens & </s> <s xml:id="echoid-s1243" xml:space="preserve">inflectens Acum, agit hic igitur in <lb/>Acum & </s> <s xml:id="echoid-s1244" xml:space="preserve">ſimul in vim directricem fluminis, & </s> <s xml:id="echoid-s1245" xml:space="preserve">non in Acum ſolam, <lb/>quatenus eſt modo corpus movendum. </s> <s xml:id="echoid-s1246" xml:space="preserve">Eodem modo Acus rotati-<lb/>lis Magneti aſſricta a vi directrice univerſali verſus ſuos in Terra <lb/>polos agitur, æque in hanc, ac in acum, Magnes in Experimento vi <lb/>attractrice agit, haud aliter ac in ſuperiori exemplo potentia ope <lb/>intermedii lori traheret acum in flumine; </s> <s xml:id="echoid-s1247" xml:space="preserve">cum hac vi directrice æ-<lb/>quilibrium ad varias diſtantias & </s> <s xml:id="echoid-s1248" xml:space="preserve">varias obliquas poſitiones acûs Ma-<lb/>gnes agit; </s> <s xml:id="echoid-s1249" xml:space="preserve">unde ex his experimentis non poteſt concludi, quanta vi <lb/>attrahuntur, per ſolam vim attractricem, duo Magnetes ad ſe, vel <lb/>Magnes ad Acum Ferrumque. </s> <s xml:id="echoid-s1250" xml:space="preserve">Non tamen hæc Eperimenta ſuâ ca-<lb/>rent utilitate, quippe, ſuppoſita Acu abſque attritu poſſe ſupra cardi-<lb/>nem converti, evincunt vim attractricem Magnetis agere in vim di-<lb/>rectricem ad certas diſtantias ſecundum ſuperius indicatas rationes: </s> <s xml:id="echoid-s1251" xml:space="preserve">& </s> <s xml:id="echoid-s1252" xml:space="preserve"><lb/>cognita vi attrahente Magnetis, indagari poteſt quantitas virtutis <lb/>directricis ad quamcunque obliquitatem acus ex regulis Mechanices: <lb/></s> <s xml:id="echoid-s1253" xml:space="preserve">Sit enim acus Tab. </s> <s xml:id="echoid-s1254" xml:space="preserve">5. </s> <s xml:id="echoid-s1255" xml:space="preserve">fig. </s> <s xml:id="echoid-s1256" xml:space="preserve">6. </s> <s xml:id="echoid-s1257" xml:space="preserve">ACB, cujus axis in C, quæ vi directrice agen-<lb/>tejuxta B C A teneatur in eadem determinatione, trahatur acus per <lb/>vim D, in ſitum obliquum a C b, ita tamen, ut angulus C a b ſit re-<lb/>ctus: </s> <s xml:id="echoid-s1258" xml:space="preserve">ducatur quæcunquerecta E a parallela ad A C B, quæ vim directri-<lb/>cem indicat, tum perpendicularis E C in aC; </s> <s xml:id="echoid-s1259" xml:space="preserve">concipiaturque reſolvi vis <lb/>directrix in unam perpendicularem ad acum, quæ eſt E C, & </s> <s xml:id="echoid-s1260" xml:space="preserve">in aliam <lb/>a C, erit E C directe oppoſita ipſi a D directioni potentiæ D, atque tria <lb/>latera T rianguli E a C ſuis magnitudinibus expriment vires, quæ hic <lb/>adſunt: </s> <s xml:id="echoid-s1261" xml:space="preserve">C E notabit vim potentiæ trahentis D. </s> <s xml:id="echoid-s1262" xml:space="preserve">E a ſive A C totam <lb/>vim directricem, & </s> <s xml:id="echoid-s1263" xml:space="preserve">a c partem virium directricium remanentium: </s> <s xml:id="echoid-s1264" xml:space="preserve"><lb/>cognita igitur longitudine Acus a c, tum angulo E C a, & </s> <s xml:id="echoid-s1265" xml:space="preserve">quantita-<lb/>te virium attractricium ſive E C, invenitur E a ſive A C, hoc eſt <lb/>quantitas virtutis directricis.</s> <s xml:id="echoid-s1266" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1267" xml:space="preserve">quando mecum pervolvebam vim univerſalem directricem Ma-<lb/>gneticam, qua dirigitur & </s> <s xml:id="echoid-s1268" xml:space="preserve">deprimitur Verſorium infra horizon-<lb/>tis paralleliſmum in his Europæ regionibus, uti poſtea liquebit quan- <pb o="55" file="0069" n="69" rhead="DE MAGNETE."/> do de Acu Inclinatoria agam; </s> <s xml:id="echoid-s1269" xml:space="preserve">ſuſpicabar an in noſtris Experimentis, <lb/>in quibus Magnetem unum ſupra alterum ſuſpendebam ex Libra, et-<lb/>iam non oriretur quædam depreſſio Magnetis horizontem verſus ra-<lb/>tione virtutis Univerſalis directricis, atque ita pertur baretur accura-<lb/>ta menſura virium attractricium; </s> <s xml:id="echoid-s1270" xml:space="preserve">verum evanuit ſcrupulus, cum <lb/>animadvertebam hanc vim directricem deprimentem Magnetem ef-<lb/>ficere quaſi quandam partem gravitatis Magnetis; </s> <s xml:id="echoid-s1271" xml:space="preserve">& </s> <s xml:id="echoid-s1272" xml:space="preserve">quia hæc vis <lb/>ope ponderis ſimul cum gravitate ad æquilibrium reducebatur ante <lb/>inſtitutum Experimentum, & </s> <s xml:id="echoid-s1273" xml:space="preserve">ſemper manebat æque magna, non <lb/>poterat turbare obſervationes circa attractiones factas.</s> <s xml:id="echoid-s1274" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div31" type="section" level="1" n="31"> <head xml:id="echoid-head39" xml:space="preserve">EXPERIMENTUM XXIII.</head> <p> <s xml:id="echoid-s1275" xml:space="preserve">Parallelopipedum ferreum, pondere 5 librarum, in lance ænea <lb/>poſitum, pendente ex æneis catenis Libræ adnexis ad æquilibrium <lb/>ope ponderum oppoſitæ lanci immiſſorum reductum fuit, tum igni <lb/>commiſſum eſt vehementi, donec ruberet, non tamen ſcintillaret, <lb/>deinde rurſus eidem impoſitum eſt lanci, infra quam Magnes ſphæ-<lb/>ricus major NO Tab. </s> <s xml:id="echoid-s1276" xml:space="preserve">1 fig. </s> <s xml:id="echoid-s1277" xml:space="preserve">2. </s> <s xml:id="echoid-s1278" xml:space="preserve">habebatur, ad diſtantiam duorum accurate <lb/>pollicum: </s> <s xml:id="echoid-s1279" xml:space="preserve">ſtatim deorſum tractum fuit hoc ignitum ferrum a Magne-<lb/>te; </s> <s xml:id="echoid-s1280" xml:space="preserve">tum vero vis attractrix explorabatur, injectis alteri lanci pon-<lb/>deribus uſque ad æquilibrium; </s> <s xml:id="echoid-s1281" xml:space="preserve">inter refrigerandum continuo magis <lb/>magiſque increvit Magnetis attractio, quæ æqualis erat 3 granis, <lb/>â ſummo calore uſque ad eum, quem manus vix vix ferebat; </s> <s xml:id="echoid-s1282" xml:space="preserve">ſed <lb/>ferro ad eundem calorem cum atmoſphærico aere redeunte, iterum <lb/>increſcebat attractio 4 granis, adeo ut tora diſſerentia attractionis <lb/>a ſummo calore uſque ad eum, qui in aere erat, fuerit in diſtantia <lb/>2 pollicum æqualis 7 granis; </s> <s xml:id="echoid-s1283" xml:space="preserve">vis tamen hujus Magnetis in idem fer-<lb/>rum frigidum fuit 16 granorum, adeoque fere ad dimidium decre-<lb/>vit poſito ferro calidiſſimo. </s> <s xml:id="echoid-s1284" xml:space="preserve">Repetitum poſtea fuit Experimentum cum <lb/>eodem Magnete & </s> <s xml:id="echoid-s1285" xml:space="preserve">Ferro, a ſe invicem uno pollice remotis; </s> <s xml:id="echoid-s1286" xml:space="preserve">frigidum <lb/>adhuc ferrum a Magnete attrahebatur vi 61 granorum, ſed igne ſum-<lb/>mo candefactum vi 26 granorum; </s> <s xml:id="echoid-s1287" xml:space="preserve">adco ut differentia attractionis fue-<lb/>rit 35 granorum, vehementius in hoc Experimento calebat ferrum <lb/>quam in priori, & </s> <s xml:id="echoid-s1288" xml:space="preserve">ideo vis Magnetis in hoc magis decrevit. </s> <s xml:id="echoid-s1289" xml:space="preserve">Si <pb o="56" file="0070" n="70" rhead="DISSERTATIO"/> hæc tentamina operoſiora viderentur, facilius demonſtrabitur Ma-<lb/>gnetem non tantundem ferri calefacti, quam frigidi attrahere, aut <lb/>ſibi applicatum ſuſtinere, ſi ipſi, aut inermi, aut armato, prius appen-<lb/>ſum fuerit ferrum frigidum tanti ponderis, quantum vix elevatur, <lb/>id enim poſtea calefactum & </s> <s xml:id="echoid-s1290" xml:space="preserve">denuo appoſitum non a Magnete feretur.</s> <s xml:id="echoid-s1291" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1292" xml:space="preserve">Nob. </s> <s xml:id="echoid-s1293" xml:space="preserve">Boyleus olim animadvertit Magnetem in alium Ignitum non <lb/>æquali vi operari quam in frigidum: </s> <s xml:id="echoid-s1294" xml:space="preserve">tres Magnetes compactæ ſub-<lb/>ſtantiæ igni immiſit, donec rubebant, calefactos argenteæ lamel-<lb/>læ impoſuit, inſra quam alter locatus Magnes attrahebat quidem <lb/>ignitos, ſed imbecillius, increſcente tamen continuo attractione, <lb/>prout magis refrigerabantur Magnetes.</s> <s xml:id="echoid-s1295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1296" xml:space="preserve">Præterire igitur ſilentio errorem Kircheri nequeo, affirmantis in <lb/>Lib. </s> <s xml:id="echoid-s1297" xml:space="preserve">1. </s> <s xml:id="echoid-s1298" xml:space="preserve">§. </s> <s xml:id="echoid-s1299" xml:space="preserve">31. </s> <s xml:id="echoid-s1300" xml:space="preserve">pag. </s> <s xml:id="echoid-s1301" xml:space="preserve">140. </s> <s xml:id="echoid-s1302" xml:space="preserve">de Magnete, operationem Magnetis in fer-<lb/>rum frigidum & </s> <s xml:id="echoid-s1303" xml:space="preserve">ignitum eſſe penitus eandem: </s> <s xml:id="echoid-s1304" xml:space="preserve">in errorem incidiſſe <lb/>videtur vir Magnus, quod rudiori modo experimenta ceperit, fer-<lb/>rum ignitum applicando tantum Magneti armato, id enim quidem <lb/>attrahitur, ſed nunquam tantis viribus, quam ferrum frigidiſſi-<lb/>mum.</s> <s xml:id="echoid-s1305" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1306" xml:space="preserve">An hinc non intelligitur Magnetem minori vi ferrum, æſtivo <lb/>calore imprægnatum, attracturum, quam quando hyemali frigore <lb/>riget & </s> <s xml:id="echoid-s1307" xml:space="preserve">condenſatum eſt, quod memoravi in Experimento III.</s> <s xml:id="echoid-s1308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1309" xml:space="preserve">Demonſtrabitur in Capite V. </s> <s xml:id="echoid-s1310" xml:space="preserve">hujus Diſſertationis, Ferrum quod-<lb/>cunque vi Magnetica imprægnari quando refrigeratur; </s> <s xml:id="echoid-s1311" xml:space="preserve">& </s> <s xml:id="echoid-s1312" xml:space="preserve">in Cap. <lb/></s> <s xml:id="echoid-s1313" xml:space="preserve">III. </s> <s xml:id="echoid-s1314" xml:space="preserve">Ignem eandem vim, aut majorem cum Ferro a Magnete com-<lb/>municatam expellere; </s> <s xml:id="echoid-s1315" xml:space="preserve">ideo Ferrum candidiſſimum, magnâ parte vir-<lb/>tutis attrahentis ſpoliatum, nequit â Magnete tanto cum impetu <lb/>attrahi, quam frigidum, vi donatum Magneticâ: </s> <s xml:id="echoid-s1316" xml:space="preserve">præterea motus <lb/>vibratorius, quo igniti ferri partes contremiſcunt, vires Magneti-<lb/>cas impediunt, irritasque reddunt: </s> <s xml:id="echoid-s1317" xml:space="preserve">ulterius hic quidem quæri poſ-<lb/>ſet, quomodo Ignis in has vires operetur, verum quia nondum ex-<lb/>plicui, quomodo hæ comparatæ ſint, an corporeæ, an alterius <lb/>indolis? </s> <s xml:id="echoid-s1318" xml:space="preserve">præſtabit hic nihil amplius addidiſſe, ſed in iis indagandis <lb/>aliquem impendiſſe laborem.</s> <s xml:id="echoid-s1319" xml:space="preserve"/> </p> <pb o="57" file="0071" n="71" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div32" type="section" level="1" n="32"> <head xml:id="echoid-head40" xml:space="preserve">EXPERIMENTUM XXIV.</head> <p> <s xml:id="echoid-s1320" xml:space="preserve">Quoniam plurimorum Eruditorum animis inſedit opinio, effectus <lb/>Magnetum in ſe mutuo pendere ab Effluviis ſubtilibus ab omni late-<lb/>re continuo egredientibus, aut a fluido Æthereo Magnetes undiqua-<lb/>que ambiente, premente aut propellente tum eos ſe invicem verſus, <lb/>tum Ferrum, tum alia Corpora, quæ ab iis attrahuntur, ſedulo in-<lb/>veſtigavi, quibusnam innixa argumentis hæc opinio foret; </s> <s xml:id="echoid-s1321" xml:space="preserve">excutien-<lb/>ti apparuerunt nulla, aut adeo imbecillia, ut temeritatis merito ar-<lb/>guerer, ſi abſque aliis, firmioribusque ratiociniis Effluvia Magneti-<lb/>ca, aut Æthereum fluidum cauſam effectuum Magneticorum ſtatuiſ-<lb/>ſem: </s> <s xml:id="echoid-s1322" xml:space="preserve">poſtquam vero manum operi admovendo, Effluvia aut Æthe-<lb/>rem quærere incepi, nulla ſeſe obtulerunt Experimenta, ex quibus <lb/>vel minima eorum ſuſpicio foveri poſſet, è contrario ea prodierunt <lb/>data, quæ me penitus convicerunt, nec Effluviis nec Æthere regi <lb/>Magnetes, nec poſſe. </s> <s xml:id="echoid-s1323" xml:space="preserve">Ut hoc clare appareat, ſupponamus ex Ma-<lb/>gnete Effluvia exire, quæ effluendo repulſionis, & </s> <s xml:id="echoid-s1324" xml:space="preserve">affluendo attra-<lb/>ctionis ſint cauſæ, atque ante oculos poſitum fingamus Magnetem <lb/>ſuſpenſum ex libra accuratiſſima, in Tab. </s> <s xml:id="echoid-s1325" xml:space="preserve">2. </s> <s xml:id="echoid-s1326" xml:space="preserve">fig. </s> <s xml:id="echoid-s1327" xml:space="preserve">2. </s> <s xml:id="echoid-s1328" xml:space="preserve">alterumque in-<lb/>fra ipſum ſupra menſam locatum; </s> <s xml:id="echoid-s1329" xml:space="preserve">Effluvia ex utroque libere egre-<lb/>dientur, regredientur, atque vi maximâ ſe Magnetes at-<lb/>trahent: </s> <s xml:id="echoid-s1330" xml:space="preserve">verum concipiamus nunc corpus ſolidum denſumque <lb/>inter eos interponi, an Effluvia utriuſque Magnetis in hoc non incur-<lb/>rent, nonneintercipientur, & </s> <s xml:id="echoid-s1331" xml:space="preserve">aliorſum determinabuntur, atque ita At-<lb/>tractio aut Repulſio ſublata erit? </s> <s xml:id="echoid-s1332" xml:space="preserve">novi equidem regeri poſſe, omnia <lb/>corpora eſſe admodum poroſa, Effluvia valde ſubtilia, ita ut poros fa-<lb/>cile permeare poſſint, atque Attractionem & </s> <s xml:id="echoid-s1333" xml:space="preserve">Repulſionem eodem mo-<lb/>do obſervandam eſſe, ac ſi nihil inter Magnetes fuiſſet interpoſitum: <lb/></s> <s xml:id="echoid-s1334" xml:space="preserve">concedendum eſt, firma quæcunque corpora plurimis eſſe pertuſa po-<lb/>ris, nihilominus conſtant ex plurimis quoque partibus ſolidis, im-<lb/>penetrabilibus, & </s> <s xml:id="echoid-s1335" xml:space="preserve">proinde Effluvia intercipientibus, quæ in ipſas <lb/>moventur: </s> <s xml:id="echoid-s1336" xml:space="preserve">quo corpora graviora ſunt, eo ſunt ſolidiora, & </s> <s xml:id="echoid-s1337" xml:space="preserve">mi-<lb/>nus poroſa, hæc intercipient longe plura Effluvia aliorum corporum, <lb/>utcunque ſubtilia fuerint: </s> <s xml:id="echoid-s1338" xml:space="preserve">Odores quicunque non tranſeunt per po-<lb/>ros vitrorum, metallorum, ſaxorum, aliorumque ſolidorum cor- <pb o="58" file="0072" n="72" rhead="DISSERTATIO"/> porum: </s> <s xml:id="echoid-s1339" xml:space="preserve">Lux, quæ eſt ſubtiliſſimum, quod novimus, Fluidum, inci-<lb/>dat in vitrum, metallum, ſilicem, aquam, oleum, vel quodlibet <lb/>aliud corpus, magna ejus portio â partibus repercutietur ſoli-<lb/>dis, portio tranſibit per poros, ita ut longe rarior, poſt tranſitum <lb/>per corpora diaphana habeatur, nec tam læte fulgeat & </s> <s xml:id="echoid-s1340" xml:space="preserve">adhuc mul-<lb/>to rarior ſit, quæ per opacorum poros permeavit, ſi quædam trans-<lb/>ierit: </s> <s xml:id="echoid-s1341" xml:space="preserve">Nonne plurimum Lucis ipſa atmoſphæra aërea, vapores tenuiſ-<lb/>ſimi, nebulæ, nubeſve rariſſimæ intercipiunt? </s> <s xml:id="echoid-s1342" xml:space="preserve">Ignis ſubtilitas forſi-<lb/>tan non multum cedit Luci, ſupra ipſum detine Thermoſcopium mo-<lb/>biliſſimum, illico fluidum rarefieri obſervabitur; </s> <s xml:id="echoid-s1343" xml:space="preserve">ſed inter Ignem <lb/>& </s> <s xml:id="echoid-s1344" xml:space="preserve">Thermoſcopium pone vitrum, lamellam metallicam, chartam, <lb/>lignum, vel quodcunque aliud firmum corpus, intercipietur Ignis <lb/>ab his omnibus, nam fluidum in initio non adſcendet in Thermo-<lb/>ſcopio, & </s> <s xml:id="echoid-s1345" xml:space="preserve">aliquo elapſo tempore lentè & </s> <s xml:id="echoid-s1346" xml:space="preserve">parum rarefieri obſerva-<lb/>bitur; </s> <s xml:id="echoid-s1347" xml:space="preserve">removeatur denuo corpus interpoſitum, & </s> <s xml:id="echoid-s1348" xml:space="preserve">Ignis abſque im-<lb/>pedimento ad fluidum allatus, id ſubito & </s> <s xml:id="echoid-s1349" xml:space="preserve">multum rarefaciet: </s> <s xml:id="echoid-s1350" xml:space="preserve">Spi-<lb/>ritus maxime volatilis, qui ulla unquam arte præparatus fuit, coër-<lb/>cetur ita in vaſis vitreis, ut non, aut parum & </s> <s xml:id="echoid-s1351" xml:space="preserve">lente per eorum po-<lb/>ros tranſſudet: </s> <s xml:id="echoid-s1352" xml:space="preserve">Aer ab omni corpore ſolido ſiſtitur, ut vel nequa-<lb/>quam vel difficilius poros pervadat: </s> <s xml:id="echoid-s1353" xml:space="preserve">in genere dixero, nullum eſſe <lb/>cognitum corporis genus, quin a metallis, vitris, aliisque firmis <lb/>retineatur omnino, vel pro maxima parte: </s> <s xml:id="echoid-s1354" xml:space="preserve">Quod ſi igitur metal-<lb/>la, aliaque ſolidiſſima corpora ſubtiles Odorum particulas, & </s> <s xml:id="echoid-s1355" xml:space="preserve">quoſ-<lb/>cunque volatiles Spiritus, tum Ignem & </s> <s xml:id="echoid-s1356" xml:space="preserve">Lucem intercipiant, vel <lb/>penitus, vel eorum maximam partem, an etiam non intercipient <lb/>aliquomodo Effluvia Magnetica, ita ut ultra impedimentum inter-<lb/>medium nequaquam tam copioſa ſint, quam forent eo ſublato? </s> <s xml:id="echoid-s1357" xml:space="preserve">An <lb/>autem hæc Effluvia æque facile per ſolidiſſima tranſibunt corpora, <lb/>ac ſi nihil adfuiſſet? </s> <s xml:id="echoid-s1358" xml:space="preserve">Opinor neminem, qui ex Experimentis inter <lb/>ſe collatis ratiocinatur, aut Mechanicos claroſque de corporibus, <lb/>eorumque fabrica conceptus format, in hanc ultimam abire poſſe <lb/>ſententiam, quæ omnem Analogiam reſpueret, & </s> <s xml:id="echoid-s1359" xml:space="preserve">corpora impe-<lb/>netrabilia, perfecte penetrabilia poneret: </s> <s xml:id="echoid-s1360" xml:space="preserve">Quamobrem ſtatuendum <lb/>erit, ſi ex Magnete Effluvia perpetuo emittantur, quæ attrahunt <lb/>alterum Magnetem aut Ferrum, hæc interceptum iri a metallo, vi-<lb/>tro, aut quocunque alio ſolidiſſimo corpore interpoſito, neque <pb o="59" file="0073" n="73" rhead="DE MAGNETE."/> tum æque magnam attrahendi vim exerciturum Magnetem in alium, <lb/>ac ſi ambo ſibi libere abſque ullo obſtaculo, in æquali diſtantia ob-<lb/>verſi fuiſſent: </s> <s xml:id="echoid-s1361" xml:space="preserve">Si vero eandem vim attrahendi habeat uterque poſi-<lb/>to intermedio quolibet obſtaculo, vel nullo, non dabuntur Efflu-<lb/>via, ſed ab alia cauſa Magnetum effectus pendebunt; </s> <s xml:id="echoid-s1362" xml:space="preserve">ad ipſa igitur <lb/>Experimenta accedamus & </s> <s xml:id="echoid-s1363" xml:space="preserve">exploremus, utrum corpora ſolidiſſima <lb/>inter binos Magnetes poſita, vires attrahentes tollant, imminuant, <lb/>mutent, an eas integras relinquant.</s> <s xml:id="echoid-s1364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1365" xml:space="preserve">1. </s> <s xml:id="echoid-s1366" xml:space="preserve">Suſpenſus fuit ex Libra Magnes H, Tab 1. </s> <s xml:id="echoid-s1367" xml:space="preserve">fig. </s> <s xml:id="echoid-s1368" xml:space="preserve">2. </s> <s xml:id="echoid-s1369" xml:space="preserve">infra quem <lb/>ad diſtantiam 1 {9/12} pollicis poſita Terrella NO fuit, atque explorata <lb/>quantitas virium attrahentium: </s> <s xml:id="echoid-s1370" xml:space="preserve">deinde inter utrumque Magnetem <lb/>interpoſita eſt moles plumbea, admodum lata, ſed craſſitiei 1 {9/12} pol-<lb/>licis, vires autem attrahentes Magnetum permanſerunt eædem ac <lb/>ante, interpolatis vicibus remotum eſt plumbum, atque denuo in-<lb/>terpoſitum, manente ſemper Attractione omnino eadem.</s> <s xml:id="echoid-s1371" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1372" xml:space="preserve">2. </s> <s xml:id="echoid-s1373" xml:space="preserve">Loco Plumbi ſumebatur parallelopipedum Stanni, craſſi-<lb/>tiei quoque 1 {9/12} pollic: </s> <s xml:id="echoid-s1374" xml:space="preserve">quo inter eoſdem Magnetes interpoſito, nul-<lb/>lum virium decrementum, incrementum, aut differentia obſervata <lb/>fuit: </s> <s xml:id="echoid-s1375" xml:space="preserve">plurimi orbes ſtannei, majorem craſſitiem facientes non mu-<lb/>tare potuerunt, vel tantillum vires attrahentes, ſed eas reliquerunt <lb/>eaſdem ac ſi in vacuo ſe liberrime reſpexiſſent Magnetes.</s> <s xml:id="echoid-s1376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1377" xml:space="preserve">3. </s> <s xml:id="echoid-s1378" xml:space="preserve">Tum maſſa Cuprea unum pollicem craſſa, lata plurimos, <lb/>intermedia, nihil quoque mutationis Attractioni induxit, ſive adeſ-<lb/>ſet ſive abeſſet.</s> <s xml:id="echoid-s1379" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1380" xml:space="preserve">4. </s> <s xml:id="echoid-s1381" xml:space="preserve">Nec nummi Argentei, nec Aurei interpoſiti vel tantillum <lb/>differentiæ viribus attractricibus attulerunt.</s> <s xml:id="echoid-s1382" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1383" xml:space="preserve">5. </s> <s xml:id="echoid-s1384" xml:space="preserve">Ne autem Metallorum tenuitas argueretur cauſa, quæ abſ-<lb/>que impedimento vires Magneticas tranſmiſiſſet, parallelopipedum <lb/>electum fuit Plumbeum, unum pedem craſſum, & </s> <s xml:id="echoid-s1385" xml:space="preserve">generoſior Ma-<lb/>gnes, quam qui prioribus Experimentis inſerviit, in menſa fuit po-<lb/>ſitus, ut alterum H, ſuſpenſum ex fune majoribus deprimeret viri-<lb/>bus, nihilominus obſervabatur eadem vis attrahens tam ſepoſito <lb/>quam applicato Magneti Plumbo.</s> <s xml:id="echoid-s1386" xml:space="preserve"/> </p> <pb o="60" file="0074" n="74" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div33" type="section" level="1" n="33"> <head xml:id="echoid-head41" xml:space="preserve">EXPERIMENTUM XXV.</head> <p> <s xml:id="echoid-s1387" xml:space="preserve">Oborta fuit in præcedentibus Experimentis ſuſpicio, an non Ef-<lb/>fluvia Magnetica a metallis intercepta, juxta horum latitudinem <lb/>excurrerint, & </s> <s xml:id="echoid-s1388" xml:space="preserve">deinde delata ad margines ſe inflexerint, ambie-<lb/>rintque Magnetes æque ſurſum & </s> <s xml:id="echoid-s1389" xml:space="preserve">deorſum eundo, & </s> <s xml:id="echoid-s1390" xml:space="preserve">Magnetem <lb/>ſuſpenſum verſus inferiorem deprimendo, ac ſi nullum corpus me-<lb/>tallicum intermedium fuiſſet: </s> <s xml:id="echoid-s1391" xml:space="preserve">ut mihi ipſi in hac quæſtione ſatis fa-<lb/>cerem, fieri curavi tres capſulas metallicas, unam ex Plumbo, al-<lb/>teram ex Stanno, tertiam ex Cupro, quibus includi poterat Magnes, <lb/>quo uſus fui in Experimento 7°. </s> <s xml:id="echoid-s1392" xml:space="preserve">& </s> <s xml:id="echoid-s1393" xml:space="preserve">8°. </s> <s xml:id="echoid-s1394" xml:space="preserve">Magnete alicui capſulæ im-<lb/>miſſo agglutinatum ope ferruminis fuit capſulæ operculum, quo <lb/>medio in metallo hærebat Lapis, ex fune longo ſuſpendebatur capſu-<lb/>la, annexo Libræ, quemadmodum in Experimentis præcedentibus, <lb/>atque ad varias demiſſa diſtantias, attracta fuit viribus, quas Ta-<lb/>bula exhibebit, notandum vero eoſdem in uſum fuiſſe vocatos Ma-<lb/>gnetes, ac in Experimento ſeptimo.</s> <s xml:id="echoid-s1395" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Magnes \\ ad diſtant. \\ Linear. # attractus \\ fuit vi æquali \\ in capſula \\ Plumbea \\ granis. # Magnes \\ in capſula \\ Cuprea \\ gran. # Magnes \\ in capſula \\ Stannea \\ gran. <lb/>12 # 57 # 57 # 57 <lb/>11 # 62 # 63 # 63 <lb/>10 # 66 # 65 # 66 <lb/>9 # 70 # 70 # 71 <lb/>8 # 79 # 78 {1/2} # 79 <lb/>7 # 83 # 83 # 83 <lb/>6 # 91 # 90 # 90 <lb/>5 # 101 # 101 # 101 <lb/>4 # 115 # 113 # 114 <lb/>3 # 124 # 114 # 124 <lb/>2 # 148 # 148 # 148 <lb/>1 # 168 # 168 # 168 <lb/></note> <p> <s xml:id="echoid-s1396" xml:space="preserve">Comparando has tres tabulas inter ſe, & </s> <s xml:id="echoid-s1397" xml:space="preserve">cum ea Experimenti <pb o="61" file="0075" n="75" rhead="DE MAGNETE."/> VII. </s> <s xml:id="echoid-s1398" xml:space="preserve">convenientiam Attractionis in æqualibus diſtantiis videmus hic <lb/>dari magnam: </s> <s xml:id="echoid-s1399" xml:space="preserve">quod autem nonnullos attinet numeros, qui paulum <lb/>diſcrepant, & </s> <s xml:id="echoid-s1400" xml:space="preserve">variam dari Attractionem hinc inde oſtenderent, ſcien-<lb/>dum eſt, nunquam tam accurate in totidem Experimentis dirigi poſſe <lb/>Magnetem ſuſpenſum ex fune, ut eædem plagæ ſuperioris ſpectent <lb/>eaſdem inferioris Magnetis, unde oritur quædam Attractionis di-<lb/>verſitas, malui autem candide obſervationes cum ſuis Anomaliis <lb/>apponere, quam nonnullas corrigere aut immutare, quod ſi enim <lb/>aliquis eadem repetat Experimenta, facile obfervabit, non poſſe <lb/>dexteritate quâcunque eadem reperiri in omnibus diſtantiis Magne-<lb/>tum a ſe invicem Attractio, quia converſo per evolutionem funis <lb/>H G vel tantillum Magnete H ex priori ſitu, extemplo alia vis at-<lb/>tractrix N O verſus obſervatur.</s> <s xml:id="echoid-s1401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1402" xml:space="preserve">Liquet igitur ex his Experimentis Metalla non remorari vires Ma-<lb/>gneticas, neque eas imminuere aut turbare: </s> <s xml:id="echoid-s1403" xml:space="preserve">ſed poſſent Metalla eſſe <lb/>reſpectu Effluviorum Magneticorum, quod ſunt vitra, & </s> <s xml:id="echoid-s1404" xml:space="preserve">diaphana <lb/>corpora reſpectu Lucis, quæ hujus maximam per ſe tranſmittunt <lb/>copiam, idcirco cum aliis corporibus ſolidis ſimilia inſtituenda ad-<lb/>hucdum eſſe Experimenta ratus fui, hæc enim poſſent eſſe ita com-<lb/>parata cum Effluviis, quemadmodum opaca ſunt reſpectu Lucis: </s> <s xml:id="echoid-s1405" xml:space="preserve">In-<lb/>cluſus fuit Magnes capſulæ ex terra porcellanica Chinenſi confectæ; <lb/></s> <s xml:id="echoid-s1406" xml:space="preserve">poſtea incluſus fuit capſulæ vitreæ, atque in hoc duplici tentami-<lb/>ne eodem modo vires exploratæ fuerunt ac in Experimento præce-<lb/>denti, ſed utraque capſula nullam viribus Magneticis intulit moram, <lb/>decrementum nullum; </s> <s xml:id="echoid-s1407" xml:space="preserve">æque facile hæ per utramque tranſiverunt, <lb/>ac ſi ambo Magnetes abſque ullo intermedio obſtaculo ſe ſpectaſſent. </s> <s xml:id="echoid-s1408" xml:space="preserve"><lb/>Immiſſus tandem fuit Magnes recipienti Boyleano, atque ex eo <lb/>omnis, quantum fieri poteſt ope Antliæ Pneumaticæ, eductus <lb/>aër elaſticus, alter Magnes, & </s> <s xml:id="echoid-s1409" xml:space="preserve">extra recipiens ex Libra noſtra ſu-<lb/>ſpenſus, ad varias demiſſus diſtantias, iiſdem attrahebatur viribus <lb/>ac in primo Experimento, poſitis ambobus Magnetibus in aëre aper-<lb/>to: </s> <s xml:id="echoid-s1410" xml:space="preserve">Novi equidem magnum Boyleum parumper diverſum eventum <lb/>ſimilis Experimenti adnotaſſe in Continuat. </s> <s xml:id="echoid-s1411" xml:space="preserve">1. </s> <s xml:id="echoid-s1412" xml:space="preserve">Exper. </s> <s xml:id="echoid-s1413" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s1414" xml:space="preserve">Mech. </s> <s xml:id="echoid-s1415" xml:space="preserve"><lb/>Exper. </s> <s xml:id="echoid-s1416" xml:space="preserve">31. </s> <s xml:id="echoid-s1417" xml:space="preserve">qui Magnetem oneravit tanta Ferri quantitate ac trahere <lb/>potuit, tum ex unco recipientis ſuſpendit, aërem Antliâ eduxit; </s> <s xml:id="echoid-s1418" xml:space="preserve"><lb/>quo ſublato Magnes aliquamdiu Ferrum geſtavit, ſed poſtea demiſit<unsure/>, <pb o="62" file="0076" n="76" rhead="DISSERTATIO"/> quod probare videretur Magnetem in Vacuo viribus minoribus pol-<lb/>lere quam in aëre aperto; </s> <s xml:id="echoid-s1419" xml:space="preserve">verum Ferri delapſum potius eveniſſe ſu-<lb/>ſpicor ex motu concuſſionis cum Magnete communicato, qui inter <lb/>evacuandum non poteſt non contingere; </s> <s xml:id="echoid-s1420" xml:space="preserve">præterea in Vacuo maſſa <lb/>ferrea gravior eſt, quam in aëre, quod nonnihil ad lapſum ejus <lb/>faciliorem reddendum contulit. </s> <s xml:id="echoid-s1421" xml:space="preserve">Cæteroquin in vacuo recipiente <lb/>Magnetem in Verſorium operari facillime demonſtratur, modo am-<lb/>bo eidem includantur recipienti, eductoque aëre Magnes circa Ver-<lb/>ſorium vertatur, hocinſtar obedientiſſimi Magnetis pediſſequi, ipſum <lb/>ſequitur, moveturque vel ad minimos illius motus, quod modo <lb/>paulum a noſtro differente etiam experientiâ comprobavit Boy-<lb/>leus.</s> <s xml:id="echoid-s1422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1423" xml:space="preserve">Tum ex noſtro, tum ex Experimento Boyleano conſtat eviden-<lb/>ter, Magnetem in aëre rariori non plus ponderis geſtare quam in <lb/>denſiori, quare opinor erroneam eſſe Hartſoekeri obſervationem in <lb/>L’Eclairciſſ. </s> <s xml:id="echoid-s1424" xml:space="preserve">ſur les Conjectur. </s> <s xml:id="echoid-s1425" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s1426" xml:space="preserve">Magnetem eo plus ferri <lb/>elevare, quo aër Atmosphæricus foret levior, & </s> <s xml:id="echoid-s1427" xml:space="preserve">Mercurius in Ba-<lb/>roſcopio depreſſior: </s> <s xml:id="echoid-s1428" xml:space="preserve">Tutius concludam, aëris raritatem aut denſi-<lb/>tatem nihil diverſitatis attrahentibus viribus adferre, nec VacuumBoy-<lb/>leanum augere, aut imminuere vires: </s> <s xml:id="echoid-s1429" xml:space="preserve">Admiratus profecto fui Stur-<lb/>mii, judicioſi cæteroquin Viri errorem, opinantis ab aëre elaſtico <lb/>effectus Magneticos pendere, ejuſque gravitate apprimi Magnetem <lb/>ad alterum aut ad Ferrum, ſed optime errorem hunc detexit Cele-<lb/>berrimus Wolfius.</s> <s xml:id="echoid-s1430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1431" xml:space="preserve">Primus non ſum, qui Magnetum vim per omnia penetrantem <lb/>corpora notavi; </s> <s xml:id="echoid-s1432" xml:space="preserve">attamen eam accurate eandem manfiſſe abſque ul-<lb/>lo decremento non novi demonſtratum hactenus; </s> <s xml:id="echoid-s1433" xml:space="preserve">Gilbertus Lib. </s> <s xml:id="echoid-s1434" xml:space="preserve">2. </s> <s xml:id="echoid-s1435" xml:space="preserve">Cap. <lb/></s> <s xml:id="echoid-s1436" xml:space="preserve">16. </s> <s xml:id="echoid-s1437" xml:space="preserve">de Magnete memoriæ prodidit, Magnetis vim tranſire per aquam, <lb/>pyxidem, aut vas; </s> <s xml:id="echoid-s1438" xml:space="preserve">non enim, inquit, obſtant craſſa tabulata, non <lb/>figulina, non marmorea vaſa, nec metalla ipſa: </s> <s xml:id="echoid-s1439" xml:space="preserve">nihil tam ſolidum, <lb/>quod vires tollat aut impediat. </s> <s xml:id="echoid-s1440" xml:space="preserve">Interpoſita omnia, licet denſiſſima, <lb/>uti non tollunt virtutem ejus, nec viam obſtruunt, ita neque ullo <lb/>modo impediunt, diminuunt, aut retardant. </s> <s xml:id="echoid-s1441" xml:space="preserve">Kircherus Lib. </s> <s xml:id="echoid-s1442" xml:space="preserve">1. </s> <s xml:id="echoid-s1443" xml:space="preserve">prop. </s> <s xml:id="echoid-s1444" xml:space="preserve"><lb/>2. </s> <s xml:id="echoid-s1445" xml:space="preserve">Theor. </s> <s xml:id="echoid-s1446" xml:space="preserve">7. </s> <s xml:id="echoid-s1447" xml:space="preserve">pag. </s> <s xml:id="echoid-s1448" xml:space="preserve">72. </s> <s xml:id="echoid-s1449" xml:space="preserve">eadem verba fere repetit: </s> <s xml:id="echoid-s1450" xml:space="preserve">Schottus deſcri-<lb/>bendo kircherum plane eadem notat in Magia Magnetica Cap. </s> <s xml:id="echoid-s1451" xml:space="preserve">3. </s> <s xml:id="echoid-s1452" xml:space="preserve"><lb/>§ 1. </s> <s xml:id="echoid-s1453" xml:space="preserve">pag. </s> <s xml:id="echoid-s1454" xml:space="preserve">245. </s> <s xml:id="echoid-s1455" xml:space="preserve">Gaſſendus hæc omnia confirmat in Lib. </s> <s xml:id="echoid-s1456" xml:space="preserve">x. </s> <s xml:id="echoid-s1457" xml:space="preserve">Diog.</s> <s xml:id="echoid-s1458" xml:space="preserve"> <pb o="63" file="0077" n="77" rhead="DE MAGNETE."/> Laërt. </s> <s xml:id="echoid-s1459" xml:space="preserve">pag. </s> <s xml:id="echoid-s1460" xml:space="preserve">197. </s> <s xml:id="echoid-s1461" xml:space="preserve">Philoſophi Florentini, ſuis ſapientes obſervatis, <lb/>deprehenderunt in Experimentis cum Magnete captis in Experien-<lb/>ces Academie del Cimento pag. </s> <s xml:id="echoid-s1462" xml:space="preserve">247. </s> <s xml:id="echoid-s1463" xml:space="preserve">virtutem Magnetis eandem man-<lb/>ſiſſe, quæ penetraverat per Mercurium, per capſulam ligneam plenam <lb/>arena, vel limaturâ metallorum (excepta ea ex ferro) per parallelo-<lb/>pipeda ſolida lapidea, marmorea, per 50 patinas aureas ſibi impofitas, <lb/>tandem per ſpiritum vini ardentem Cl. </s> <s xml:id="echoid-s1464" xml:space="preserve">Wolfius ſimilia fecit cum <lb/>Magnete Experimenta, eoſdemque effectus adnotavit, vide ejus Ver-<lb/>nuftige Gedachten Tom. </s> <s xml:id="echoid-s1465" xml:space="preserve">3. </s> <s xml:id="echoid-s1466" xml:space="preserve">Leeuwenhoekius in philoſ. </s> <s xml:id="echoid-s1467" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s1468" xml:space="preserve">N°. <lb/></s> <s xml:id="echoid-s1469" xml:space="preserve">226. </s> <s xml:id="echoid-s1470" xml:space="preserve">& </s> <s xml:id="echoid-s1471" xml:space="preserve">N°. </s> <s xml:id="echoid-s1472" xml:space="preserve">227. </s> <s xml:id="echoid-s1473" xml:space="preserve">per aquam tranſiiſſe vim Magnetis quoque probavit.</s> <s xml:id="echoid-s1474" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1475" xml:space="preserve">Poſtquam Kircherus vim Magnetis adeo permeantem per cuncta <lb/>corpora cognoverat, adverſus Epicurum, ponentem Atomos circum-<lb/>fluentes & </s> <s xml:id="echoid-s1476" xml:space="preserve">pellentes Magnetem cauſas omnium effectuum, in hæc <lb/>verba erumpit Lib. </s> <s xml:id="echoid-s1477" xml:space="preserve">1. </s> <s xml:id="echoid-s1478" xml:space="preserve">part. </s> <s xml:id="echoid-s1479" xml:space="preserve">2. </s> <s xml:id="echoid-s1480" xml:space="preserve">Quomodo Magnes hujusmodi tenuiſſi-<lb/>ma atomorum corpuſcula æqua facilitate & </s> <s xml:id="echoid-s1481" xml:space="preserve">tranſitu momentaneo, <lb/>per duriſſima & </s> <s xml:id="echoid-s1482" xml:space="preserve">ſolidiſſima quævis corpora in ferrum traducet? </s> <s xml:id="echoid-s1483" xml:space="preserve">Vn-<lb/>de veriſimile eſt hanc circumpulſionem non in Magnete, ſed in E-<lb/>picuri cerebro exiſtentem, hanc abſonam prorſus opinionem pepe-<lb/>riſſe. </s> <s xml:id="echoid-s1484" xml:space="preserve">In eundem tamen ſcopulum impegerunt plurimi recentiores <lb/>Philoſophi, qui vel ad hoc, vel ad aliud Fluidorum, aut Effluvio-<lb/>rum corporeorum genus recurrunt, ut Magnetis actiones explicent; <lb/></s> <s xml:id="echoid-s1485" xml:space="preserve">ſed quantis, præter allatas, premantur difficultatibus ejuſmodi hy-<lb/>potheſes, in ſequentibus demonſtrabitur.</s> <s xml:id="echoid-s1486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1487" xml:space="preserve">Fingamus enim dari Effluvia, vel Fluida exeuntia ex magnete, <lb/>quæ corporea ſint: </s> <s xml:id="echoid-s1488" xml:space="preserve">vel Odores cum Tachenio vocentur; </s> <s xml:id="echoid-s1489" xml:space="preserve">nam hic <lb/>Magnetem odore trahere ferrum dixit. </s> <s xml:id="echoid-s1490" xml:space="preserve">Tum. </s> <s xml:id="echoid-s1491" xml:space="preserve">vid. </s> <s xml:id="echoid-s1492" xml:space="preserve">Tab. </s> <s xml:id="echoid-s1493" xml:space="preserve">2. </s> <s xml:id="echoid-s1494" xml:space="preserve">fig. </s> <s xml:id="echoid-s1495" xml:space="preserve">1. </s> <s xml:id="echoid-s1496" xml:space="preserve">& </s> <s xml:id="echoid-s1497" xml:space="preserve"><lb/>ſit Magnes A, cujus Effluvia ferantur directione A E, & </s> <s xml:id="echoid-s1498" xml:space="preserve">A F, ſit <lb/>præterea corpus B D C, facillime mobile fupra cardinem D, quem-<lb/>admodum Acus nautica verti ſolet; </s> <s xml:id="echoid-s1499" xml:space="preserve">ſitque B D C ex quocunque me-<lb/>tallo denſiſſimo; </s> <s xml:id="echoid-s1500" xml:space="preserve">hoc conſtabit partim ex poris, partim ex partibus <lb/>ſolidis, quatenus igitur effluvia A E incurrunt in partes ſolidas <lb/>metalli B C, (neceſſario enim nonnulla incurrunt in ſolidas partes) <lb/>eas movebunt, adeoque pars B D debebit elevari in K, & </s> <s xml:id="echoid-s1501" xml:space="preserve">C de-<lb/>primi in L: </s> <s xml:id="echoid-s1502" xml:space="preserve">eritque eo major elevatio K verſus, quo B D C eſt mi-<lb/>nus poroſum: </s> <s xml:id="echoid-s1503" xml:space="preserve">ſed ejuſmodi effectus nunquam contingit ſi B D C <lb/>fuerit Acus ex quolibet metallo, Ferro excepto, verum manet per- <pb o="64" file="0078" n="78" rhead="DISSERTATIO"/> fecte immobilis, Magnete ſupra vel infra B D C poſito: </s> <s xml:id="echoid-s1504" xml:space="preserve">ſola ferrea <lb/>Acus movetur, poſito Magnete in A. </s> <s xml:id="echoid-s1505" xml:space="preserve">Nemo, qui ope microſcopio-<lb/>rum corporum ſoliditatem examinavit, hic ſtatuet omnia metalla <lb/>eſſe adeo poroſa, ut per ea Effluvia liberrime tranſeant, Ferrum con-<lb/>tra eſſe ſolidius, vix poroſum, atque excipere omnem Effluviorum <lb/>actionem in ſe, ideo tantum hoc moveri, quieſcentibus reliquis. </s> <s xml:id="echoid-s1506" xml:space="preserve">Ne-<lb/>que poni poteſt Effluviorum A E vim eſſe nimis imbecillem ad Acum <lb/>B D C ex Cupro, aliove metallo factam, commovendam, cum vi æ-<lb/>quali plurimorum granorum ponderi Acus ſimilis ferrea, poſita in <lb/>eodem loco, a Magnete movetur.</s> <s xml:id="echoid-s1507" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1508" xml:space="preserve">Præterea ſi Effluvia ex Magnete A egrediantur directione A E, <lb/>occurrantque Acui ferreæ B D C, nonne eam a Magnete repellent <lb/>ulterius K verſus, hâc enim determinatione moventur, eâdem igi-<lb/>tur Acum promovebunt; </s> <s xml:id="echoid-s1509" xml:space="preserve">verum ſi Acus ex ferro puro, nondum im-<lb/>buto vi Magnetica, ponatur ſupra Magnetem A, non ab eo repel-<lb/>letur recedendo, ſed attrahetur accedendo; </s> <s xml:id="echoid-s1510" xml:space="preserve">hic acceſſus igitur po-<lb/>tius Effluvia poſtulat ingredientia Magnetem, delataque motu <lb/>E A, quæ autem accedunt ad aliquod corpus, Effluvia illius dici <lb/>nequeunt; </s> <s xml:id="echoid-s1511" xml:space="preserve">Quamobrem ex hiſce concludi poteſt Philoſophos non <lb/>ſatis attente omnia conſideraſſe, qui Magnetis vires ab Effluviis cor-<lb/>poreis deduxerunt.</s> <s xml:id="echoid-s1512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1513" xml:space="preserve">Quicunque autem ſupponet Fluidum aliquod extus ambiens ac-<lb/>cedenſque ad Magnetem eſſe effectuum memoratorum cauſam, etiam <lb/>non carebit inextricabilibus difficultatibus: </s> <s xml:id="echoid-s1514" xml:space="preserve">Hoc enim Fluidum ſit <lb/>quoque corporeum, & </s> <s xml:id="echoid-s1515" xml:space="preserve">feratur directione E A Magnetem verſus, <lb/>tum illud corpus quodcunque ſolidum B D C poſitum in parvâ a Ma-<lb/>gnete diſtantiâ, ad ipſum propellet æque Cuprum ac Ferrum, <lb/>illud enim fluidum neceſſario occurret eodem modo partibus Cupri <lb/>ſolidis, quo Ferri: </s> <s xml:id="echoid-s1516" xml:space="preserve">Hoc tamen non probat experientia, manente <lb/>Acu cuprea B D C perfecte immota, ſed ferreâ attracta verſus A.</s> <s xml:id="echoid-s1517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1518" xml:space="preserve">Neque explicatio Gaſſendi aliquem locum habet, dicentis: <lb/></s> <quote><s xml:id="echoid-s1519" xml:space="preserve">Ra-<lb/>dios Magneticos non pellicere marmor, cum tamen ferrum pelli-<lb/>ciunt; </s> <s xml:id="echoid-s1520" xml:space="preserve">imo neque feſtucas, aliave leviora interpoſita; </s> <s xml:id="echoid-s1521" xml:space="preserve">quoniam præ-<lb/>ter ferrum Magnetemque, cætera corpora non habent neque ra-<lb/>dios reciprocos, neque eam pororum, meatuumve diſpoſitio-<lb/>nem, propter quam & </s> <s xml:id="echoid-s1522" xml:space="preserve">radios refringant, & </s> <s xml:id="echoid-s1523" xml:space="preserve">ab iis ſtringantur.</s></quote> <pb o="65" file="0079" n="79" rhead="DE MAGNETE."/> <s xml:id="echoid-s1524" xml:space="preserve">Sed Gaſſendum rogo, an marmor, feſtucæ aliave corpuſcula non <lb/>habeant partes ſolidas? </s> <s xml:id="echoid-s1525" xml:space="preserve">concedam in iis poros eſſe diverſiſſimo fabre-<lb/>factos modo ab iis in Ferro, nihilominus radii Magnetici, quos Ef-<lb/>fluvia corporea eſſe ſupponit, partibus ſolidis marmoris occurrent, ut-<lb/>cunque paucas habuerit marmor, utcunque poris rectis donatas id <lb/>ſtatuatur, ferrum contra intortis; </s> <s xml:id="echoid-s1526" xml:space="preserve">adeoque radii aliqualem motum, <lb/>etiamſi parvum, marmori feſtucisque dabunt, ſed nihil percipitur <lb/>communicari cum feſtucis levibus, marmore metallisve aliis, quam-<lb/>obrem hæc opinio corruit.</s> <s xml:id="echoid-s1527" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1528" xml:space="preserve">Præterea quæro, quam ob rationem fluidum illud moveatur verſus <lb/>A? </s> <s xml:id="echoid-s1529" xml:space="preserve">an hæc eſt vis attractrix Magnetis? </s> <s xml:id="echoid-s1530" xml:space="preserve">tum attractio corporum ad <lb/>ſe in vicem per aliam attractionem æque obſcuram explicabitur; </s> <s xml:id="echoid-s1531" xml:space="preserve">quod <lb/>eſt abſurdum. </s> <s xml:id="echoid-s1532" xml:space="preserve">Inſuper quare illud fluidum eo vehementius aget in a-<lb/>lio corpore pellendo, quo hoc Magneti eſt propius, niſi ejus mo-<lb/>tus perpetuo acceleretur, ſed quænam erit cauſa hujus accelerati <lb/>motus? </s> <s xml:id="echoid-s1533" xml:space="preserve">niſi vis attractrix Magnetica ſupponatur, agens diverſis vi-<lb/>ribus ad varias diſtantias.</s> <s xml:id="echoid-s1534" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1535" xml:space="preserve">Denuo ſit Magnes in A, ferrum in E, aliudque in F, hæc ambo <lb/>accedent ad Magnetem vi validâ, & </s> <s xml:id="echoid-s1536" xml:space="preserve">undiquaque circa A poſita cor-<lb/>puſcula ferrea accedent ad Magnetem, qui acceſſus argueret flui-<lb/>dum quaquaverſum accedere ad Magnetem; </s> <s xml:id="echoid-s1537" xml:space="preserve">ubi hoc fluidum ma-<lb/>net, an egreditur iterum ex Magnete? </s> <s xml:id="echoid-s1538" xml:space="preserve">Forte patroni illius hoc ſtatuent <lb/>& </s> <s xml:id="echoid-s1539" xml:space="preserve">ex repulſione id affirmabunt: </s> <s xml:id="echoid-s1540" xml:space="preserve">ſed ſciant hi velim, omnem repul-<lb/>ſionem in experimentis detectam eſſe multo imbecilliorem attra-<lb/>ctione, ut cuilibet experimenta noſtra comparanti apparebit: </s> <s xml:id="echoid-s1541" xml:space="preserve">ecce <lb/>igitur majori vi & </s> <s xml:id="echoid-s1542" xml:space="preserve">copia affluet ad Magnetem fluidum quam ex eo <lb/>exibit; </s> <s xml:id="echoid-s1543" xml:space="preserve">quare opplebuntur breviori vel longiori tempore ejus pori <lb/>omnino, & </s> <s xml:id="echoid-s1544" xml:space="preserve">vis Magnetica peribit; </s> <s xml:id="echoid-s1545" xml:space="preserve">quod iterum non obſervatur <lb/>contingere, nam Magnetes eandem vim retinere deprehenduntur per <lb/>plurima annorum ſpatia.</s> <s xml:id="echoid-s1546" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1547" xml:space="preserve">Tandem ſit Ferrum in F, immobile poſitum ſupra menſam, & </s> <s xml:id="echoid-s1548" xml:space="preserve"><lb/>Magnes ex Libra ſuſpenſus in A; </s> <s xml:id="echoid-s1549" xml:space="preserve">ſit fluidum motum directione F A <lb/>quod pellat Ferrum verſus Magnetem, & </s> <s xml:id="echoid-s1550" xml:space="preserve">ſit hæc vis accuratiſſime <lb/>ponderata, interF & </s> <s xml:id="echoid-s1551" xml:space="preserve">A tum immediate infraF ponatur cubus plumbiut-<lb/>cunque craſſus, an hic non impediet aliquomodo affluxum fluidi verſus <lb/>A? </s> <s xml:id="echoid-s1552" xml:space="preserve">ſi non impediat, plumbum penitus poroſum absque partibus fingen- <pb o="66" file="0080" n="80" rhead="DISSERTATIO"/> dum eſt ſolidis, cui nemo adſtipulabitur; </s> <s xml:id="echoid-s1553" xml:space="preserve">ſed plumbum interpoſi-<lb/>tum fuerit vel non, eadem manet actio Ferri in Magnetem; </s> <s xml:id="echoid-s1554" xml:space="preserve">quare <lb/>niſi aliquid abſurdiſſimum ſupponatur, fluidum ejuſmodi fingi ne-<lb/>quit.</s> <s xml:id="echoid-s1555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1556" xml:space="preserve">Sed ulterius hæc hypotheſis fluidi alicujus externi, vel effluvio-<lb/>rum Magneticorum enecanda erit, quod ope ſequentium experi-<lb/>mentorum ſatis facile fiet.</s> <s xml:id="echoid-s1557" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div34" type="section" level="1" n="34"> <head xml:id="echoid-head42" xml:space="preserve">EXPERIMENTUM. XXVI.</head> <p> <s xml:id="echoid-s1558" xml:space="preserve">Magnes & </s> <s xml:id="echoid-s1559" xml:space="preserve">lamella aut virga chalybea vel ferrea ſeorſim accura-<lb/>tiſſime ponderentur, Magneti affricetur lamella aut virga, tumque <lb/>iterum amborum pondus ſeorſim exploretur, deprehenditur pon-<lb/>dus in utroque corpore manſiſſe idem.</s> <s xml:id="echoid-s1560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1561" xml:space="preserve">Primus hoc Experimentum inſtituit Normannus capiendo 2 vel <lb/>3 fragmenta oblonga fili ferrei, quæ primum in aurificis ſtatera pon-<lb/>deravit; </s> <s xml:id="echoid-s1562" xml:space="preserve">tum Magneti affricta iterum ponderavit, idemque man-<lb/>ſiſſe deprehendit pondus vid New. </s> <s xml:id="echoid-s1563" xml:space="preserve">Attract. </s> <s xml:id="echoid-s1564" xml:space="preserve">cap. </s> <s xml:id="echoid-s1565" xml:space="preserve">5. </s> <s xml:id="echoid-s1566" xml:space="preserve">Gilbertus idem <lb/>fecit Lib. </s> <s xml:id="echoid-s1567" xml:space="preserve">5. </s> <s xml:id="echoid-s1568" xml:space="preserve">Cap. </s> <s xml:id="echoid-s1569" xml:space="preserve">3. </s> <s xml:id="echoid-s1570" xml:space="preserve">Merſennus & </s> <s xml:id="echoid-s1571" xml:space="preserve">Gaſſendus apud Zygoſtatam mo-<lb/>netalem libellâ accuratiſſima pondus explorantes ferri ante & </s> <s xml:id="echoid-s1572" xml:space="preserve">poſt <lb/>applicationem ad Magnetem, idem manſiſſe notant, vid. </s> <s xml:id="echoid-s1573" xml:space="preserve">Gaſſen-<lb/>dusin Lib. </s> <s xml:id="echoid-s1574" xml:space="preserve">x. </s> <s xml:id="echoid-s1575" xml:space="preserve">Diog. </s> <s xml:id="echoid-s1576" xml:space="preserve">Laertii pag. </s> <s xml:id="echoid-s1577" xml:space="preserve">200. </s> <s xml:id="echoid-s1578" xml:space="preserve">& </s> <s xml:id="echoid-s1579" xml:space="preserve">in Tomo 2. </s> <s xml:id="echoid-s1580" xml:space="preserve">operum pag. </s> <s xml:id="echoid-s1581" xml:space="preserve">129. <lb/></s> <s xml:id="echoid-s1582" xml:space="preserve">Verum Whiſtonus hoc obſervatum dubium reddidit in Tractatu of <lb/>The dipping needle pag. </s> <s xml:id="echoid-s1583" xml:space="preserve">9. </s> <s xml:id="echoid-s1584" xml:space="preserve">leviusque fieri affirmat Ferrum poſtquam <lb/>Magneti applicatum fuit; </s> <s xml:id="echoid-s1585" xml:space="preserve">ſumſit enim virgam 4 pedes longam pon-<lb/>deris 4015 {3/8} granorum antequam Magnetem olfecerat, poſt appli-<lb/>cationem pondus decreverat 2 granis: </s> <s xml:id="echoid-s1586" xml:space="preserve">aliam ſumſit 4584 {1/8} granorum, <lb/>cujus pondus poſt applicationem ad Magnetem decrevit 2 {1/8} granis: </s> <s xml:id="echoid-s1587" xml:space="preserve"><lb/>aliam ſumſit 14792 {1/2} granorum, cujus pondus decrevit 2 {1/2} granis. </s> <s xml:id="echoid-s1588" xml:space="preserve"><lb/>Aliam adhibuit 65726 granorum, cujus pondus decrevit 14 granis, <lb/>teſtemque Experimentorum advocat Hauksbejum. </s> <s xml:id="echoid-s1589" xml:space="preserve">Deſiderio ca-<lb/>piebar ſimilia repetendi Experimenta ſumma cum cura, Libram ac-<lb/>curatiſſimam adhibui, quæ etiamſi magna ſatis ſit, nihilominus <lb/>{1/20}grani parte movebatur, onerata pondereLibrarum 2. </s> <s xml:id="echoid-s1590" xml:space="preserve">Ne igitur ferrum <lb/>cujus pondus explorarem, aliquid ageret in ipſam Libram, id ex filo <lb/>æneo longo 5 pedes ſuſpendi: </s> <s xml:id="echoid-s1591" xml:space="preserve">nolui enim Lanci imponere, quia <lb/>ejus margines circumflexi in ſe filum ferreum continent, ita enim <pb o="67" file="0081" n="81" rhead="DE MAGNETE."/> fabri lances facere ſolent: </s> <s xml:id="echoid-s1592" xml:space="preserve">tum ſumſi ferreos cylindros longos, aut <lb/>virgas, quorum pondera fuerunt 2500, 6800, 14580 granorum, <lb/>his prius accuratiſſime notatis, ferramenta affricui præſtanti <lb/>Magneti, & </s> <s xml:id="echoid-s1593" xml:space="preserve">ſingula ſeorſim iterum examinavi in media camera, <lb/>ne ulla actio in ferream Libram, aut in aliquod Ferrum pavimenti <lb/>vel lacunaris exerceri poſſet per vim Magnetis communicatam: </s> <s xml:id="echoid-s1594" xml:space="preserve">fa-<lb/>teor autem me in hiſce omnibus caſibus nullam differentiam pon-<lb/>deris obſervare potuiſſe: </s> <s xml:id="echoid-s1595" xml:space="preserve">ut certior fierem, an Libra quidem ſatis <lb/>mobilis foret, grani dimidium alterutri imponebam parti, a quo <lb/>deprimebatur, unde de illius mobilitate dubitare non poteram. </s> <s xml:id="echoid-s1596" xml:space="preserve">Mi-<lb/>rabar hoc omnino, quia hæc Experimenta non congruebant cum <lb/>Whiſtonianis, quæ profecto etiam a Viris exercitatiſſimis inſtituta <lb/>ſunt, quibus plus dexteritatis & </s> <s xml:id="echoid-s1597" xml:space="preserve">accurationis in capiendis experi-<lb/>mentis, quam mihi ipſi adſcribo; </s> <s xml:id="echoid-s1598" xml:space="preserve">mihi itaque primum non confiſus, <lb/>cum aliis virgis & </s> <s xml:id="echoid-s1599" xml:space="preserve">parallelopipedis ferreis cùm 8050, tum 15565 gra-<lb/>norum alio die inſtitui tentamina, & </s> <s xml:id="echoid-s1600" xml:space="preserve">attendi ad omnia quæ Expe-<lb/>rimentum turbare poſſent, deponens quicquid ferri gerebam, axin <lb/>trutinamque Libræ abſterſi, acuique, ut mobiliſſima omnino eſſet <lb/>Libra, inſtitutis vero iterum tentaminibus, idem pondus manſiſſe <lb/>obſervavi: </s> <s xml:id="echoid-s1601" xml:space="preserve">Quamobrem hic varius Experimentorum eventus pen-<lb/>det, vel a diverſâ vi, qua varii Magnetes in Ferrum agunt, quorum <lb/>alius Ferrum redderet levius, alter idem pondus in eo relinqueret; <lb/></s> <s xml:id="echoid-s1602" xml:space="preserve">vel a diverſa cura, quacum experimenta capta ſunt; </s> <s xml:id="echoid-s1603" xml:space="preserve">quod ſi Whi-<lb/>ſtoniana examinemus, aliquid miri in ſe comprehendere videntur: </s> <s xml:id="echoid-s1604" xml:space="preserve"><lb/>Ferrum 4585 {1/8} granorum amittit 2 {5/8} grana: </s> <s xml:id="echoid-s1605" xml:space="preserve">aliud gravius & </s> <s xml:id="echoid-s1606" xml:space="preserve">14792 {1/2} <lb/>granorum amittit 2 {1/2} grana: </s> <s xml:id="echoid-s1607" xml:space="preserve">adeoque Ferrum gravius minus ponderis a-<lb/>miſiſſet, quam levius, cum in alio Experimento graviſſimum Ferrum <lb/>65726 granorum amiſerit 14 grana, adeoque iterum plus; </s> <s xml:id="echoid-s1608" xml:space="preserve">quæ non ad-<lb/>modum inter ſe congruere videntur, cur enim illudFerrum 14792 {1/2} gra-<lb/>norum non amiſit plus ponderis poſtquam Magneti affrictum fuit <lb/>quam illud 4585 {1/8} gran.</s> <s xml:id="echoid-s1609" xml:space="preserve">? attamen Whiſtoniana obſervata negari ne-<lb/>queunt, quia continent modo Experimenta: </s> <s xml:id="echoid-s1610" xml:space="preserve">facile autem in ponderan-<lb/>do corpore aliquem errorem committimus ſi adminimas circumſtantias <lb/>non attendamus, ut expertus didici Cum enim in initio Experimentum <lb/>Whiſtonirepetebam, ſuſpendi virgas ferreas ex fune cannabino, longo, <lb/>anſerini calami craſſitie; </s> <s xml:id="echoid-s1611" xml:space="preserve">quid fit? </s> <s xml:id="echoid-s1612" xml:space="preserve">ignem forte in loco, in quo Ex- <pb o="68" file="0082" n="82" rhead="DISSERTATIO"/> perimentum capiebam, inſtruxeram, obſervavique omnino Libram <lb/>a parte appenſæ virgæ leviorem eſſe redditam, imprimis poſtquam <lb/>aliquamdiu exſpectaveram; </s> <s xml:id="echoid-s1613" xml:space="preserve">unde concludebam Whiſtonum recte <lb/>animadvertiſſe Ferrum Magneti affrictum fieri levius, ſed neſcio quo <lb/>caſu diutius exſpectabam, ut accuratius differentiam ponderis nota-<lb/>rem, vidique tum perpetuo Libram ab eadem parte leviorem fieri; <lb/></s> <s xml:id="echoid-s1614" xml:space="preserve">omnia hæc tum ſibi commiſi uſque in ſequentem diem, quo Libra <lb/>ab eadem parte non levior erat utante, ſed præponderabat, ex qui-<lb/>bus manifeſto apparebat hanc ponderis diverſitatem pendere ab <lb/>humido in fune hærente & </s> <s xml:id="echoid-s1615" xml:space="preserve">expulſo ab Igne, poſteroque die quo <lb/>ignis aberat, iterumſe inſinuante. </s> <s xml:id="echoid-s1616" xml:space="preserve">Unde poſtea ſemper inſtitui expe-<lb/>rimenta ſuſpendendo virgas ferreas ex filo æneo; </s> <s xml:id="echoid-s1617" xml:space="preserve">(Lances Libræ <lb/>ob idem incommodum diu ante a me obſervatum, ex catenis æneis <lb/>ſemper ſuſpenſæ quoque fuerunt) tumque nunquam aliquam ponderis <lb/>varietatem vidi, & </s> <s xml:id="echoid-s1618" xml:space="preserve">ne aliquid in hoc tentamine omitteretur, non <lb/>modo virgas uno ſuſpendi modo, ſed poſtea quoque inverſas iterum <lb/>ponderavi, præterea eas ap plicui polo Magnetis Boreali, affricui etiam <lb/>polo Auſtrali, ſed ſemper cum eodem ſucceſſu: </s> <s xml:id="echoid-s1619" xml:space="preserve">diverſis diebus cepi <lb/>centamen, regnantibuſque variis ventis, imo intercedente intervallo <lb/>menſis, ſed nunquam alius eventus mihi contigit. </s> <s xml:id="echoid-s1620" xml:space="preserve">Ex noſtris igitur <lb/>tuto concludam experimentis pondus Ferri ante & </s> <s xml:id="echoid-s1621" xml:space="preserve">poſt affrictionem <lb/>ad Magnetem noſtrum idem manere. </s> <s xml:id="echoid-s1622" xml:space="preserve">Dentur igitur Effluvia Magne-<lb/>tica ex hypotheſi, hæc ſuum pondus habebunt, quemadmodum omnia <lb/>alia corpora, hactenus nota, gravitate donantur: </s> <s xml:id="echoid-s1623" xml:space="preserve">effluant ex Magne-<lb/>te, ingrediantur Ferrum, hujus pondus tantillum neceſſario auge-<lb/>bitur, manente Ferri eodem volumine: </s> <s xml:id="echoid-s1624" xml:space="preserve">ſed nec Incrementum nec <lb/>decrementum ullum ponderis obſervatur; </s> <s xml:id="echoid-s1625" xml:space="preserve">quo igitur jure Effluvia <lb/>corporea hic adeſſe dicentur? </s> <s xml:id="echoid-s1626" xml:space="preserve">Exemplum forte ex corporibus odo-<lb/>riferis petetur, quæ abſque ſenſibili ponderis jactura diu exſpirant, <lb/>ſed hæc tamen aliquod corporeum exſpirant, quod a metallis poteſt <lb/>retineri, capi & </s> <s xml:id="echoid-s1627" xml:space="preserve">ponderari, adeo ut ex odoribus nihil probari poſ-<lb/>ſit. </s> <s xml:id="echoid-s1628" xml:space="preserve">Operoſus fui in his experimentis examinandis, quia ſi in pon-<lb/>dere ferri affricti ad Magnetem differentia oritur, tum duo videntur <lb/>inde ſequi ſatis manifeſto, 1°. </s> <s xml:id="echoid-s1629" xml:space="preserve">Magnetem regi ab Effluviis corporeis, <lb/>caque cumFerro communicari. </s> <s xml:id="echoid-s1630" xml:space="preserve">2°. </s> <s xml:id="echoid-s1631" xml:space="preserve">Si Ferrum levius fit, Effluvia dabun-<lb/>@ur orbata gravitate, & </s> <s xml:id="echoid-s1632" xml:space="preserve">deſtruentia partem gravitatis ex corporibus, <pb o="69" file="0083" n="83" rhead="DE MAGNETE."/> quæ duo magnam ſequelam in Phyſica ſecum traherent, nec parvam <lb/>mutationem Philoſophiæ, inprimis Newtonianæ inferrent.</s> <s xml:id="echoid-s1633" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div35" type="section" level="1" n="35"> <head xml:id="echoid-head43" xml:space="preserve">EXPERIMENTUM XXVII.</head> <p> <s xml:id="echoid-s1634" xml:space="preserve">Tab. </s> <s xml:id="echoid-s1635" xml:space="preserve">2. </s> <s xml:id="echoid-s1636" xml:space="preserve">fig. </s> <s xml:id="echoid-s1637" xml:space="preserve">2. </s> <s xml:id="echoid-s1638" xml:space="preserve">Sit Acus nautica poſita in meridiano ſuo A B, <lb/>incluſa capſulæ cupreæ, quæ ſuperne tegatur vitro, cujus margi-<lb/>nes ope cæmenti conglutinentur cum capſula, ne ullus aër egredi aut <lb/>ingredi in capſulam queat, Magnes C ponatur fixus in quadam ab <lb/>Acu diſtantia, ita ut hæc cuſpidem A dirigat, in a b, a ſuo meri-<lb/>diano ad certum gradum, qui obſervetur; </s> <s xml:id="echoid-s1639" xml:space="preserve">tum in vaſe cupreo D <lb/>aër condenſetur ope Antliæ pneumaticæ, quantum fieri arte poteſt; <lb/></s> <s xml:id="echoid-s1640" xml:space="preserve">ponatur vas D eo modo infra rectam lineam A B C continuatam, <lb/>ut orificium D directe illi reſpondeat, tum aperiatur ſubito orifi-<lb/>cium D, atque attendatur an Acus A moveatur: </s> <s xml:id="echoid-s1641" xml:space="preserve">aër ex æneo vaſe <lb/>erumpens vehementiſſium excitabit ventum, aliquamdiu duran-<lb/>tem, interim tamen Acus manere obſervatur immota: </s> <s xml:id="echoid-s1642" xml:space="preserve">finge nunc <lb/>iterum Effluvia Magnetica, velaliud fluidum ex Magnete dirigi ad A-<lb/>cum, rogo, an hujus fluidi motus ab impetuoſiſſimo vento non aliquo-<lb/>modo mutabitur, & </s> <s xml:id="echoid-s1643" xml:space="preserve">proinde interea vis Acus directrix ab a verſus <lb/>A aget, hæc enim antequam aperiebatur orificium D, cum vi at-<lb/>tractrice Magnetis erat in æquilibrio, quod ſi hic ventus dicatur <lb/>nihil poſſe agere in illud fluidum, cujus igitur erit naturæ? </s> <s xml:id="echoid-s1644" xml:space="preserve">hercle <lb/>non corporeæ! nam fieri nequit, ut ventus artificialis denſiſſimus, <lb/>qui ventum naturalem impetu & </s> <s xml:id="echoid-s1645" xml:space="preserve">velocitate aliquoties ſuperat, in <lb/>illud non agat, nec ſurſum propellat ejusque motum turbet; </s> <s xml:id="echoid-s1646" xml:space="preserve">quo-<lb/>niam vero nulla turba nulluſque in Acu a b, obſervatus fuit motus, <lb/>iterum tum Effluvia Magnetica, tum quodcumque aliud Magnetem <lb/>ambiens ſuppoſitum fluidum, utcunque ſubtile, vi hujus Experi-<lb/>menti proſcribuntur.</s> <s xml:id="echoid-s1647" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div36" type="section" level="1" n="36"> <head xml:id="echoid-head44" xml:space="preserve">EXPERIMENTUM. XXVIII.</head> <p> <s xml:id="echoid-s1648" xml:space="preserve">Tab. </s> <s xml:id="echoid-s1649" xml:space="preserve">2. </s> <s xml:id="echoid-s1650" xml:space="preserve">fig. </s> <s xml:id="echoid-s1651" xml:space="preserve">2. </s> <s xml:id="echoid-s1652" xml:space="preserve">Verſorio A B, capſulæ incluſo ſibique commiſſo, <lb/>in Meridiano ſuo A B, ad diſtantiam 6 pollicum ponebatur Magnes <lb/>C, â quo dirigebatur in ſitum a b, tum loco vaſis D lata patina <pb o="70" file="0084" n="84" rhead="DISSERTATIO"/> ſpiritu vini plena adhibita fuit, hujus accenſi alta & </s> <s xml:id="echoid-s1653" xml:space="preserve">latiſſima flam-<lb/>ma omne ſpatium inter Verſorium Magnetemque implevit, arſit <lb/>flamma, quam diu ſpiritus idoneum pabulum ſuppeditabat, quod <lb/>majori copia ſubminiſtrabatur, ut diu obſervatio protraheretur, & </s> <s xml:id="echoid-s1654" xml:space="preserve"><lb/>accuratius adnotari poſſet, an Verſorium a, b, eandem reſpiceret ſem-<lb/>per plagam, an aliam: </s> <s xml:id="echoid-s1655" xml:space="preserve">nulla aberratio â lineâ a, b, facta fuit roto <lb/>obſervationis tempore, extinctâque flammâ penitus immotum man-<lb/>ſit Verſorium: </s> <s xml:id="echoid-s1656" xml:space="preserve">eundem tentaminis eventum a ſe obſervatum, me-<lb/>morant quoque Florentini in Ezperien. </s> <s xml:id="echoid-s1657" xml:space="preserve">fattes in Acad. </s> <s xml:id="echoid-s1658" xml:space="preserve">del Cimen-<lb/>to. </s> <s xml:id="echoid-s1659" xml:space="preserve">Wolfius in phyſ. </s> <s xml:id="echoid-s1660" xml:space="preserve">Tom. </s> <s xml:id="echoid-s1661" xml:space="preserve">3. </s> <s xml:id="echoid-s1662" xml:space="preserve">& </s> <s xml:id="echoid-s1663" xml:space="preserve">Polinierius in Exper. </s> <s xml:id="echoid-s1664" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s1665" xml:space="preserve">pag. <lb/></s> <s xml:id="echoid-s1666" xml:space="preserve">295. </s> <s xml:id="echoid-s1667" xml:space="preserve">Quoniam flamma accenſi ſpiritus perquam tenuis & </s> <s xml:id="echoid-s1668" xml:space="preserve">rara eſt, <lb/>nec multum calet; </s> <s xml:id="echoid-s1669" xml:space="preserve">vehementiorem, & </s> <s xml:id="echoid-s1670" xml:space="preserve">denſiorem flammam exci-<lb/>tandam eſſe ratus ſum, ut validius argumentum ex Experimento <lb/>peti poſſet: </s> <s xml:id="echoid-s1671" xml:space="preserve">Accenſa fuit Lampas ingens Encauſtica O. </s> <s xml:id="echoid-s1672" xml:space="preserve">Tab. </s> <s xml:id="echoid-s1673" xml:space="preserve">2. </s> <s xml:id="echoid-s1674" xml:space="preserve">fig. </s> <s xml:id="echoid-s1675" xml:space="preserve"><lb/>6. </s> <s xml:id="echoid-s1676" xml:space="preserve">cujus flamma, nutrita raparum oleo, valde calens, & </s> <s xml:id="echoid-s1677" xml:space="preserve">conden-<lb/>ſata vi impetuoſi venti ex folle magno expreſſi, vitrum & </s> <s xml:id="echoid-s1678" xml:space="preserve">metal-<lb/>lum quodcunque intra momentum temporis liquefacit; </s> <s xml:id="echoid-s1679" xml:space="preserve">hæc ita di-<lb/>rigebatur, ut lineam rectam a Verſorio A B continuatam uſque ad <lb/>Magnetem C ad angulum rectum ſecaret: </s> <s xml:id="echoid-s1680" xml:space="preserve">Verſorium A B a Meri-<lb/>diano ſuo per attractionem Magnetis C deflexum erat, inter lam-<lb/>padem O & </s> <s xml:id="echoid-s1681" xml:space="preserve">Verſorium A B vitrea tenebatur lamella, ne a motu <lb/>venti per flammam tranſeuntis Verſorium moveretur: </s> <s xml:id="echoid-s1682" xml:space="preserve">quamdiu lam-<lb/>pas arſit, non mutata fuit Verſorii directio, ſed in abſolutâ per-<lb/>manſit quiete.</s> <s xml:id="echoid-s1683" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1684" xml:space="preserve">Finge nunc iterum Effluvia Magnetica, vel aliud fluidum ex Ma-<lb/>gnete C ad Verſorium A B deferri, id a Meridiano ſuo detorquere, <lb/>& </s> <s xml:id="echoid-s1685" xml:space="preserve">cum ejus viribus directricibus æquilibrari, an hæc, quæ fingis <lb/>fluida, abſque ullo virium decremento, abſque ulla directionis mu-<lb/>tatione tranſibunt per flammam denſiſſimam, calentiſſimam, cujus <lb/>partes admodum ſolidæ infinitâ rapiditate moventur?</s> <s xml:id="echoid-s1686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1687" xml:space="preserve">Si autem vires fluidi per flammam tranſeuntis decreſcant, Ver-<lb/>ſorium illico antiquum appetet Meridianum, directum viribus a <lb/>parte antica in ipſum agentibus: </s> <s xml:id="echoid-s1688" xml:space="preserve">ſed immotum ſtetit, quamdiu con-<lb/>tinuatum fuit Experimentum.</s> <s xml:id="echoid-s1689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1690" xml:space="preserve">Motorem in Rerum univerſo Igne majorem nemo mortalium ha-<lb/>ctenus novit, ſua quippe tenuitate, duritie, celeritate omnia diſ- <pb o="71" file="0085" n="85" rhead="DE MAGNETE."/> ſolvit corpora, proſternit, diruit, diſſipat: </s> <s xml:id="echoid-s1691" xml:space="preserve">an igitur, qui cuncta <lb/>movet, ineptus erit profligandis effluviis Magneticis? </s> <s xml:id="echoid-s1692" xml:space="preserve">quodnam i-<lb/>taque hæc corporum genus erunt? </s> <s xml:id="echoid-s1693" xml:space="preserve">Si mole exilia, mobilia, & </s> <s xml:id="echoid-s1694" xml:space="preserve">ſolida, <lb/>quemadmodum omnium aliorum fluidorum partes ſunt comparatæ, <lb/>tum ab aliis corpuſculis in ipſa incurrentibus poterunt percuti, re-<lb/>tardari, retrorſum pelli, aliâ determinatione moveri, veluti cor-<lb/>pora majora; </s> <s xml:id="echoid-s1695" xml:space="preserve">ab Igne igitur & </s> <s xml:id="echoid-s1696" xml:space="preserve">flamma, cujus partes non poſſunt <lb/>non Effluviis occurrere, propellentur, atque idcirco directio Ver-<lb/>ſorii A B immutanda fuiſſet, eo immoto manente ſequitur non trans-<lb/>iiſſe Effluvia e Magnete per flammam, neque operari hunc lapidem <lb/>Fluidi aut Effluviorum quorumlibet ope.</s> <s xml:id="echoid-s1697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1698" xml:space="preserve">Si quis cuncta argumenta, quæ adverſus hypotheſin Fluidi Aerei, <lb/>Ætherei, Effluviorum, quæ Magneticos operari effectus dicta fuerunt, <lb/>examinaverit, comparaverit inter ſe, ſibique addiderit, non poteſt <lb/>non eſſe convictus ab alia Magnetem regi cauſa, & </s> <s xml:id="echoid-s1699" xml:space="preserve">hæc fuiſſe quon-<lb/>dam ex hypotheſi modo aſſumta, ab Empedocle, Democrito, Leu-<lb/>ſippo, Epicuro, Lucretio, Carteſio, Sturmio aliiſque Clariſſimis <lb/>Viris, nequaquam demonſtrata, corruunt igitur ſua ſponte quæcun-<lb/>que alicui harum ſententiarum innituntur.</s> <s xml:id="echoid-s1700" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div37" type="section" level="1" n="37"> <head xml:id="echoid-head45" xml:space="preserve">EXPERIMENTUM XXIX.</head> <p> <s xml:id="echoid-s1701" xml:space="preserve">Magnes, qui Verſorio obverſus, aut ſupra ferri limaturam reten-<lb/>tus, attrahentium ſuarum virium præclara edebat ſpecimina, igni <lb/>commiſſus fuit in furno anemi, ex carbonibus foſſilibus ligneisque <lb/>exſtructo, ita ut canduerit 5 horarum ſpatio: </s> <s xml:id="echoid-s1702" xml:space="preserve">refrigeratus, & </s> <s xml:id="echoid-s1703" xml:space="preserve">ferri <lb/>limaturæ impoſitus, nequidem leviſſimam ejus particulam attraxit, <lb/>neque geſtavit, viribus, ut prima fronte apparebat, omnino de-<lb/>ſtructis, quod impoſuiſſe videtur Clariſſimis Viris de Lanis & </s> <s xml:id="echoid-s1704" xml:space="preserve">Boy-<lb/>leo, affirmantibus Ignem ex Magnete omnem expellere virtutem <lb/>attrahentem; </s> <s xml:id="echoid-s1705" xml:space="preserve">quod alio tentamine Lemmerius in L’Hiſt. </s> <s xml:id="echoid-s1706" xml:space="preserve">de L’A-<lb/>cad. </s> <s xml:id="echoid-s1707" xml:space="preserve">Royal A°. </s> <s xml:id="echoid-s1708" xml:space="preserve">1706. </s> <s xml:id="echoid-s1709" xml:space="preserve">comprobare etiam adniſus fuit, obſervando <lb/>Magnetem radiis ſolaribus in foco ſpeculi uſtorii poſitum, quamvis <lb/>non tam diu ut in vitrum abiret, omnem vim attrahendi amiſiſſe: <lb/></s> <s xml:id="echoid-s1710" xml:space="preserve">attamen Magnes a nobis examinatus ad intervallum dimidii digiti a <lb/>Verſorio, 6 pollices longo, mobiliſſimoque, manifeſta ſuperſtitum <pb o="72" file="0086" n="86" rhead="DISSERTATIO"/> rium edidit ſigna, id movendo, ad ſe adducendo repellendoque; <lb/></s> <s xml:id="echoid-s1711" xml:space="preserve">crediderim in Magnetibus a memoratis Eruditis examinatis, ejus-<lb/>modi parvas vires quoque ſuperſtites fuiſſe, quas oſtendiſſent, ſi <lb/>potius Verſorio, quam limaturæ Martis fuiſſent appoſiti: </s> <s xml:id="echoid-s1712" xml:space="preserve">Nam adeo <lb/>vehementiMagnetem urſiIgne, ut dubitem an ſimili expoſuerint deLa-<lb/>nis, Boyleusque ſuos calori, excepto illo, quem focus ſpeculi largitur. </s> <s xml:id="echoid-s1713" xml:space="preserve"><lb/>ne quis vero opinetur ignem diutius continuatum majores editurum <lb/>effectus in Magnetem, vireſque omnes proſtraturum, infra enim in A-<lb/>naly ſi hujus Lapidis Chemica conſtabit, nunquam igne, etiamſi ſæpius <lb/>repetito, vires ex Magnete omnes periiſſe. </s> <s xml:id="echoid-s1714" xml:space="preserve">Quoniam in præcedenti <lb/>Experimento adſtruximus, Ignem non agere in vires Magnetis, in <lb/>hoc autem liquet Ignem ejus vim admodum imminuere, admirari <lb/>debemus Ignis efficaciam adeo diverſam in unum idemque corpus: </s> <s xml:id="echoid-s1715" xml:space="preserve"><lb/>ſuſpicabar, intuitus Experimenti eventum, Ignem ex Magnete ex-<lb/>puliſſe nonnullas particulas, ferreas, aliasve, a quibus tota vis at-<lb/>tractrix penderet, hinc ſcobem Martis non amplius ab illo appeti; </s> <s xml:id="echoid-s1716" xml:space="preserve"><lb/>ſed tutudi Magnetem in pulverem ſubtilem, eique ad duorum trium-<lb/>ve pollicum intervallum oppoſui alium generoſum Magnetem, hic <lb/>totum allexit pulverem, elevavit, geſtavit, ac ſi limatura ferri fuiſ-<lb/>ſet. </s> <s xml:id="echoid-s1717" xml:space="preserve">Non igitur ex Magnete ignis expulerat illas particulas, in qui-<lb/>bus vis attractrix reſidebat, tum enim pulvis hic iners jacuiſſet, nec <lb/>alteri advolaſſet Magneti, eo autem indicabat in ſe attrahendi ſu-<lb/>pereſſe vim, cum nulla detur actio, ubi reactio non ſimul adſit, <lb/>omniaque corpora ſeſe æqua vi & </s> <s xml:id="echoid-s1718" xml:space="preserve">reciproca neceſſario attrahunt.</s> <s xml:id="echoid-s1719" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1720" xml:space="preserve">Ignis figuram pororum in hoc Lapide mutaverat, levior enim, <lb/>rubicundioriſque coloris evaſerat, ſed ideo non poteſt dici virtutem <lb/>ſuam amiſiſſe, quid enim porus eſt, præterquam pars ſpatii, quod <lb/>ſua natura eſt iners, & </s> <s xml:id="echoid-s1721" xml:space="preserve">ſive terminis hoc illove modo poſitis cir-<lb/>cumſcribatur, vires acquirere nequit, quamobrem pororum im-<lb/>mutata figura nequit ſtatui cauſa jacturæ virium: </s> <s xml:id="echoid-s1722" xml:space="preserve">egit tamen ignis <lb/>in aliquid, quod fuit in Magnete, egit procul omni dubio, in ali-<lb/>quid quod corporeum eſt: </s> <s xml:id="echoid-s1723" xml:space="preserve">ita autem in illud operatus fuit, ut cum <lb/>antea vires attrahendi magnas habebat, nunc eas aliquomodo ex-<lb/>pulerit, aut potius ad ſilentium redegerit, nam in pulvere Magne-<lb/>tico iterum obſervabatur, & </s> <s xml:id="echoid-s1724" xml:space="preserve">ab altero Magnete excitatum revi-<lb/>viſcebat iisdem viribus, quibus unquam donatum fuit: </s> <s xml:id="echoid-s1725" xml:space="preserve">Fortiſſimus <pb o="73" file="0087" n="87" rhead="DE MAGNETE."/> Ignis tantummodo illud domat, quippe leni Igne Magnes calefactus <lb/>vires non perdit: </s> <s xml:id="echoid-s1726" xml:space="preserve">Sæpe jungunt artifices multa Magnetum fragmenta <lb/>ſecum invicem, circa illa circumfundendo liquefactum plumbum, <lb/>ſtannum, vel aliud compoſitum metallum, neque vires ab eo cor-<lb/>rumpuntur calore, ſed manent integræ ſtabileſque: </s> <s xml:id="echoid-s1727" xml:space="preserve">quamobrem hæ <lb/>fortiter inhærent Magneti, non expellendæ niſi vi ſumma diutiſſi-<lb/>me continuati Ignis, aut ab eo tantum domandæ: </s> <s xml:id="echoid-s1728" xml:space="preserve">Attamen reſtat <lb/>hic aliquid obſcuriſſimum, quidnam nempe ſit illud in Lapide, in <lb/>quo vires ſedent? </s> <s xml:id="echoid-s1729" xml:space="preserve">& </s> <s xml:id="echoid-s1730" xml:space="preserve">quomodo id ab Igne agitatur, mutaturve, ut <lb/>ex agenti fiat iners? </s> <s xml:id="echoid-s1731" xml:space="preserve">hic mentis acies hebeſcit, hoc ſolo autem in-<lb/>tellecto omnis Magnetum effectus & </s> <s xml:id="echoid-s1732" xml:space="preserve">operationes cognoſcerentur: <lb/></s> <s xml:id="echoid-s1733" xml:space="preserve">Si id corporeum ſit, & </s> <s xml:id="echoid-s1734" xml:space="preserve">ex Magnete exeat, quando operatur, daren-<lb/>tur Effluvia, a quorum affluxu, & </s> <s xml:id="echoid-s1735" xml:space="preserve">refluxu omnia phænomena ori-<lb/>rentur, verum ſuperius monuimus, quibuſnam Effluviorum doctri-<lb/>na urgeatur difficultatibus, adeo ut hoc ſtatui nequeat: </s> <s xml:id="echoid-s1736" xml:space="preserve">Si corporeum <lb/>ſit; </s> <s xml:id="echoid-s1737" xml:space="preserve">& </s> <s xml:id="echoid-s1738" xml:space="preserve">ex Magnete non exeat, quomodo tum corpora ad multorum <lb/>pedum intervallum agitabit, movebit, ad ſe alliciet? </s> <s xml:id="echoid-s1739" xml:space="preserve">Neque hoc <lb/>animus ullomodo comprehendit. </s> <s xml:id="echoid-s1740" xml:space="preserve">Verum an non eſt ſtabilita Lex <lb/>Naturæ; </s> <s xml:id="echoid-s1741" xml:space="preserve">atque â Creatore impreſſa omnibus corporibus, ut poſitis <lb/>his ſibi propinquis, vel ad aliquod intervallum, ſe attrahant, ad <lb/>ſe accedant, & </s> <s xml:id="echoid-s1742" xml:space="preserve">cohæreant, quamvis nihil extrinſecus pellat, nihilque <lb/>in intermedio ſpatio ſit, quod ea attrahat, an poſita hac Lege Magnes <lb/>non accedet ad Magnetem aut ad Ferrum, omneſque ejus operationes <lb/>inde fluent? </s> <s xml:id="echoid-s1743" xml:space="preserve">Quamvis ejuſmodi Legem ab omnipotente Creatore <lb/>latam eſſe conceſſero, non tamen vi ejus fluent, aut ex ea explicari <lb/>poterunt phænomena, quæ Magnes conſpicienda præbet: </s> <s xml:id="echoid-s1744" xml:space="preserve">Quippe <lb/>ſive Igni commiſſus fuerit, ſive ex fodina modo ante erutus, ſub eo-<lb/>dem volumine manente ejus eadem maſſa corporea, eædem quoque <lb/>vires attrahentes obtinerent: </s> <s xml:id="echoid-s1745" xml:space="preserve">in Naturæ Legem Ignis non egit, nec <lb/>eam immutare, nec deſtruere potuit: </s> <s xml:id="echoid-s1746" xml:space="preserve">Ignis tamen potiſſimum virtutis <lb/>ex Magnete fugavit: </s> <s xml:id="echoid-s1747" xml:space="preserve">verum pluribus obnoxia eſt hæc ſententia dif-<lb/>ficultatibus, conſtantis enim eſt obſervationis, Magnetem fortiter <lb/>Malleo percuſſum, ita ut omnes contremuerint partes; </s> <s xml:id="echoid-s1748" xml:space="preserve">aut in pul-<lb/>verem contritum, rubigine obductum, aëri humido diu expoſitum, <lb/>ſitu inverſo in Meridiano ſuo jacentem, prope alium fortioribus vi-<lb/>ribus donatum, virtute orbari, infringi, debilitari, id teſtanti- <pb o="74" file="0088" n="88" rhead="DISSERTATIO"/> bus tum propriis obſervationibus, tum Carteſio in princ. </s> <s xml:id="echoid-s1749" xml:space="preserve">philoſ. </s> <s xml:id="echoid-s1750" xml:space="preserve">part. <lb/></s> <s xml:id="echoid-s1751" xml:space="preserve">4. </s> <s xml:id="echoid-s1752" xml:space="preserve">§. </s> <s xml:id="echoid-s1753" xml:space="preserve">145. </s> <s xml:id="echoid-s1754" xml:space="preserve">N°. </s> <s xml:id="echoid-s1755" xml:space="preserve">33, 34. </s> <s xml:id="echoid-s1756" xml:space="preserve">Schotto de morbis Magnetum. </s> <s xml:id="echoid-s1757" xml:space="preserve">pag. </s> <s xml:id="echoid-s1758" xml:space="preserve">286. </s> <s xml:id="echoid-s1759" xml:space="preserve">Wol-<lb/>fio in Meditationibus Ingenioſis, Lemmerio in L’Hiſt. </s> <s xml:id="echoid-s1760" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s1761" xml:space="preserve"><lb/>Roy. </s> <s xml:id="echoid-s1762" xml:space="preserve">A°. </s> <s xml:id="echoid-s1763" xml:space="preserve">1706. </s> <s xml:id="echoid-s1764" xml:space="preserve">pag. </s> <s xml:id="echoid-s1765" xml:space="preserve">146. </s> <s xml:id="echoid-s1766" xml:space="preserve">Boyleo in Magnetics edito a Shaw, aliisque <lb/>pluribus Viris eruditis, In omnibus his occaſionibus Lapidis manet <lb/>eadem ſubſtantia, eadem magnitudo, adeoque vi Legis innatæ non <lb/>minorem attractionem exerceret. </s> <s xml:id="echoid-s1767" xml:space="preserve">Nec tempeſtatis aëriſque viciſ-<lb/>ſitudines minimam viribus diſcrepantiam afferrent, quemadmodum <lb/>tamen contingere an notavit Doctiſſimus Derhamus in Philoſ. </s> <s xml:id="echoid-s1768" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s1769" xml:space="preserve"><lb/>N°. </s> <s xml:id="echoid-s1770" xml:space="preserve">303. </s> <s xml:id="echoid-s1771" xml:space="preserve">Egregius enim ille Magnes, qui penes Regiam ſervatur <lb/>Societatem Londinenſem, aliquando Ferrum ſuſpendit, ut alteri <lb/>adhæreat, ad intervallum 8, 9, 10. </s> <s xml:id="echoid-s1772" xml:space="preserve">pedum, aliquando id non ſu-<lb/>ſtinet in diſtantia 3 vel 4 pedum. </s> <s xml:id="echoid-s1773" xml:space="preserve">Legi naturæ tempeſtates mu-<lb/>tationes adferre nemo facile dixerit: </s> <s xml:id="echoid-s1774" xml:space="preserve">quamobrem hanc non eſſe <lb/>cauſam Magneticorum effectuum liquido patet: </s> <s xml:id="echoid-s1775" xml:space="preserve">pendet hujus La-<lb/>pidis vis a cauſa alia; </s> <s xml:id="echoid-s1776" xml:space="preserve">oportetque bene diſtingui ejus attractio <lb/>ab aliis plurimis, quæ in corporibus obſervantur, & </s> <s xml:id="echoid-s1777" xml:space="preserve">quæ <lb/>æque aliis proprietatibus gaudent, ac variæ legi ſubjiciuntur.</s> <s xml:id="echoid-s1778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1779" xml:space="preserve">Hiſce perpenſis difficultatibus circa cauſam virium Magnetis ab <lb/>Eruditis variis propoſitam, exſpectatur forte, ut ipſe aliam aſſi-<lb/>gnem, ex qua Mechanice reſolvi & </s> <s xml:id="echoid-s1780" xml:space="preserve">demonſtrari poſſint omnia phæ-<lb/>nomena, & </s> <s xml:id="echoid-s1781" xml:space="preserve">quam ſolidis probem argumentis eſſe unicam & </s> <s xml:id="echoid-s1782" xml:space="preserve">veram: <lb/></s> <s xml:id="echoid-s1783" xml:space="preserve">non parum circa eam occupatus fui, comparando plurima Experi-<lb/>menta interſe, hypotheſes varias fingendo, novisque modis tenta-<lb/>mina inſtituendo, ſed quo plus operæ impendi, eo longius me ſem-<lb/>per ab ea divinanda abfuiſſe deprehendi: </s> <s xml:id="echoid-s1784" xml:space="preserve">quam ob rem laborum pertæ-<lb/>ſus, & </s> <s xml:id="echoid-s1785" xml:space="preserve">tenuitatis conſcius, tandem cogor candide profiteri palam, cau-<lb/>ſam Magnetis eſſe adhuc abſconditam, ignoratamque ab omnibus <lb/>mortalibus: </s> <s xml:id="echoid-s1786" xml:space="preserve">Doctiſſimus & </s> <s xml:id="echoid-s1787" xml:space="preserve">verſatiſſimus in ſcientia Magnetica Whiſto-<lb/>nus ſe plurimum laboris inſumſiſſe in Magnetis cauſa detegenda etiam <lb/>fatetur, at ſe ſibi in nulla Hypotheſi ſatisfacere potuiſſe, ex qua Me-<lb/>chanice cuncta reſolveret, idcirco noluit aliquam Litterato orbi obtru-<lb/>dere: </s> <s xml:id="echoid-s1788" xml:space="preserve">Doctiſſimus Hambergerus in Elementis Phyſ. </s> <s xml:id="echoid-s1789" xml:space="preserve">Cap. </s> <s xml:id="echoid-s1790" xml:space="preserve">9. </s> <s xml:id="echoid-s1791" xml:space="preserve">Fluidum <lb/>quoddam Magnetem ambiens cauſam effectuum opinatur addit tamen: </s> <s xml:id="echoid-s1792" xml:space="preserve"><lb/>Quale ſit iſtud Fluidum, qualis motus ejuſdem, & </s> <s xml:id="echoid-s1793" xml:space="preserve">qualis diſpoſitio poro-<lb/>rum, & </s> <s xml:id="echoid-s1794" xml:space="preserve">quomodo ex hiſce fluant phænomena, non niſi bypothetice & </s> <s xml:id="echoid-s1795" xml:space="preserve">ne ſic <pb o="75" file="0089" n="89" rhead="DE MAGNETE."/> quidem ſufficienter, explicare licet. </s> <s xml:id="echoid-s1796" xml:space="preserve">Quod â confeſſione ignoran-<lb/>tiæ totius cauſæ non differt, & </s> <s xml:id="echoid-s1797" xml:space="preserve">quam poſtea in programmate Inau-<lb/>gurali de partialitate Acus Magneticæ agnovit, dicendo in §. </s> <s xml:id="echoid-s1798" xml:space="preserve">17. <lb/></s> <s xml:id="echoid-s1799" xml:space="preserve">Genuinam inimicitiæ atque amicitiæ polorum Magnetum, vel A-<lb/>cus Magneticæ cauſam eſſe incognitam ſe credere. </s> <s xml:id="echoid-s1800" xml:space="preserve">Propterea con-<lb/>venit hic apprime Aphrodiſæi dictum, qui cum attentiſſimus ad <lb/>Magnetem fuerat, ejus vim attractricem ſoli Deo notam excla-<lb/>mat: </s> <s xml:id="echoid-s1801" xml:space="preserve">Si Galenum & </s> <s xml:id="echoid-s1802" xml:space="preserve">Avicennam conſulamus, hi vim Magnetis <lb/>non comprehendentes, divinam eſſe judicant: </s> <s xml:id="echoid-s1803" xml:space="preserve">quod ſi teſtimo-<lb/>nia plurium Eruditiſſimorum Virorum afferre vellem, qui exa-<lb/>minatis ſollicite Magneticis phænomenis, cauſam eorum huc uſ-<lb/>que latere confitentur, etiam Camerarium prudenter in Epiſtolis <lb/>Taurinenſibus diſſerentem afferrem, fatentemque ingenue rationes <lb/>Magneticorum effectuum eſſe adhuc quam maxime occultas, & </s> <s xml:id="echoid-s1804" xml:space="preserve">ſpe-<lb/>ciatim quidem illas, quæ declinare Magnetem cogunt: </s> <s xml:id="echoid-s1805" xml:space="preserve">cui quoque <lb/>eximius Wolfius in Cogitatis Ingenioſis adſtipulatur. </s> <s xml:id="echoid-s1806" xml:space="preserve">Ex noſtris <lb/>enim hactenus allatis experimentis & </s> <s xml:id="echoid-s1807" xml:space="preserve">argumentis conſtat, non eſſe <lb/>eam quærendam in Effluviis Magneticis, aut in ambientis fictitii æthe-<lb/>ris vorticibus, nam (Whiſtoni liceat uti verbis) divinare nequeo ejuſ-<lb/>modi motum Fluidi ſubtilis pertinentis ad Magnetem quod vim attra-<lb/>ctricem in ratione reciproca ſesquiduplicata diſtantiarum exerceret; </s> <s xml:id="echoid-s1808" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s1809" xml:space="preserve">ſi talem Fluidi motum concipere poſſem, id non ſufficeret ad po-<lb/>nendum, ejuſmodi Fluidum eſſe veram cauſam horum phænome-<lb/>norum, quemadmodum Coteſius recte obſervavit in ſimili caſu in <lb/>Præfatione Operis Newtoni. </s> <s xml:id="echoid-s1810" xml:space="preserve">An autem conſiſtit in Blaſmotivo & </s> <s xml:id="echoid-s1811" xml:space="preserve"><lb/>locali, prout Helmontius voluit? </s> <s xml:id="echoid-s1812" xml:space="preserve">Sed hoc nihil eſt præter mera <lb/>verba, quæ a nemine intelliguntur. </s> <s xml:id="echoid-s1813" xml:space="preserve">An vero erit anima, Spiri-<lb/>tus aliquis Univerſalis Magnetis motor, ut Hermes, Zoroaſter, <lb/>Orpheus, aliique Seriores Philoſophi crediderunt? </s> <s xml:id="echoid-s1814" xml:space="preserve">tum profecto cauſa <lb/>mechanica non erit: </s> <s xml:id="echoid-s1815" xml:space="preserve">verum prius hujus Spiritus exiſtentia, & </s> <s xml:id="echoid-s1816" xml:space="preserve">de-<lb/>inde ejus facultas attrahendi, aut apprimendi corpora demonſtranda <lb/>foret, quod huc uſque fieri non potuit; </s> <s xml:id="echoid-s1817" xml:space="preserve">niſi per illum intelligamus <lb/>DEUM, Sapientiſſimum Auctorem omnium, quæ in Univerſo exi-<lb/>ſtunt, primum motorem omnium potentiſſimum, per cujus vim & </s> <s xml:id="echoid-s1818" xml:space="preserve"><lb/>efficaciam effectus Magnetici fierent, fluerentque immediate abſque <lb/>ulla alia, vel ſine pluribus intercedentibus cauſis; </s> <s xml:id="echoid-s1819" xml:space="preserve">ſed immediatam <pb o="76" file="0090" n="90" rhead="DISSERTATIO"/> hanc Dei operationem in Magnetem quoque probare non poſſu-<lb/>mus, licet certo certius ad Deum uſque perventuri ſimus ſequen-<lb/>do effectuum cauſas, atque in eo, vere cauſâ omnium rerum <lb/>prima, determinaremur: </s> <s xml:id="echoid-s1820" xml:space="preserve">videtur profecto inter Deum ut cauſam <lb/>& </s> <s xml:id="echoid-s1821" xml:space="preserve">inter vires Magnetis, alia adhuc intercedere cauſa, nam idem <lb/>Magnes vires acquirit vel amittit pro diverſo ſitu quem tenuit: <lb/></s> <s xml:id="echoid-s1822" xml:space="preserve">Vires in igne amittit quodammodo: </s> <s xml:id="echoid-s1823" xml:space="preserve">Ferrum cudendo acquirit vi-<lb/>res, & </s> <s xml:id="echoid-s1824" xml:space="preserve">prout plus cuditur, eo majores, quæ in me ſuſpicionem <lb/>alterius cauſæ intercedentis excitant. </s> <s xml:id="echoid-s1825" xml:space="preserve">Præteribo plures aliorum <lb/>Philoſophorum abſonas Hypotheſes, quæ apud Gilbertum: </s> <s xml:id="echoid-s1826" xml:space="preserve">Lib. </s> <s xml:id="echoid-s1827" xml:space="preserve"><lb/>1. </s> <s xml:id="echoid-s1828" xml:space="preserve">Cap. </s> <s xml:id="echoid-s1829" xml:space="preserve">1. </s> <s xml:id="echoid-s1830" xml:space="preserve">& </s> <s xml:id="echoid-s1831" xml:space="preserve">Cabeum in Lib. </s> <s xml:id="echoid-s1832" xml:space="preserve">2 Cap. </s> <s xml:id="echoid-s1833" xml:space="preserve">2. </s> <s xml:id="echoid-s1834" xml:space="preserve">videri poſſunt.</s> <s xml:id="echoid-s1835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1836" xml:space="preserve">Si quis hæc ſerio ſecum conſideraverit, facile perſpiciet, quan-<lb/>tum abſumus a cognitione Naturæ corporum, quam quidam ſibi <lb/>perſpectam jactitant, quaſi in hoc alterove attributo univerſali <lb/>hæreret; </s> <s xml:id="echoid-s1837" xml:space="preserve">hi vires ſuas explorent, an è Natura corporum ſibi, ut <lb/>opinantur, cognita, etiam Naturam Magnetis, Naturam ejus vi-<lb/>rium deducere queant, non hypotheſes nobis obtrudendo, ut fieri <lb/>ſolet, ſed probas demonſtrationes concinnando.</s> <s xml:id="echoid-s1838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1839" xml:space="preserve">Unica via detegendi Magnetis cauſam hæc fupereſt, ut Philoſo-<lb/>phi, abjecta libidine hypotheſes fingendi, quod ſatis repeti & </s> <s xml:id="echoid-s1840" xml:space="preserve">in-<lb/>culcari nequit, capiendis Experimentis, adnotandisque Magnetis <lb/>effectibus dent operam, ipſi manum labori admoveant, nec tantum <lb/>ſedeant meditabundi in Muſæis, recte enim Sapiens Reaumurius <lb/>animadvertit, eo modo in genere nimis excoli Phyſicam, & </s> <s xml:id="echoid-s1841" xml:space="preserve">per-<lb/>verſe: </s> <s xml:id="echoid-s1842" xml:space="preserve">tum autem ſpes affulget, aliquando datum iri aliquem tam <lb/>felicem, qui ex inter ſe plurimis comparatis Magnetis operationi-<lb/>bus, manifeſto earum cauſam demonſtrabit; </s> <s xml:id="echoid-s1843" xml:space="preserve">tumque poſteritas ad-<lb/>mirabitur nos tam aperta, quæ ſe ſua ſponte offerunt, & </s> <s xml:id="echoid-s1844" xml:space="preserve">quibus <lb/>hac tempeſtate adeo propinqui fuimus, neſciviſſe.</s> <s xml:id="echoid-s1845" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div38" type="section" level="1" n="38"> <head xml:id="echoid-head46" xml:space="preserve">EXPERIMENTUM XXX.</head> <p> <s xml:id="echoid-s1846" xml:space="preserve">Quoniam ope Analyſeos Chemicæ non raro detegimus partes di-<lb/>verſas, quæ corpora majora componunt; </s> <s xml:id="echoid-s1847" xml:space="preserve">Magnetem etiam hac me-<lb/>thodo examinare ſtatuebam, ſuſpicatus hoc corpus non ſimplex eſſe, <lb/>ſed ex pluribus diverſis conflatum, quæ ſi ſeparare a ſe mutuo poſ- <pb o="77" file="0091" n="91" rhead="DE MAGNETE."/> ſem, ſperabam me acquiſiturum partes inertes nullaque vi donatas <lb/>attractrice, aliaſque in quibus omnis vis hæreret; </s> <s xml:id="echoid-s1848" xml:space="preserve">ex quibus Mi-<lb/>croſcopio, vel alia methodo examinatis, quænam fabrica Magne-<lb/>tis, & </s> <s xml:id="echoid-s1849" xml:space="preserve">cauſa virtutis foret, detegeretur: </s> <s xml:id="echoid-s1850" xml:space="preserve">Omnem igitur huc direxi <lb/>animi meditationem, ut Magnetem, quem corpus compoſitum <lb/>tum ex aliis ſupponebam, in ſua ſimpliciora diſſolverem: </s> <s xml:id="echoid-s1851" xml:space="preserve">Boyleus <lb/>in his Tentaminibus mihi aliquomodo præiverat, ſed tam paucos <lb/>progreſſus faciendo, & </s> <s xml:id="echoid-s1852" xml:space="preserve">nequaquam ſatis ſollicita inſtituendo exa-<lb/>mina, ut ex Boyleanis nihil vel parum lucis foenerari potuerim: <lb/></s> <s xml:id="echoid-s1853" xml:space="preserve">addenda autem illa noſtris judicavi, quia paucis comprehendi poſſunt. </s> <s xml:id="echoid-s1854" xml:space="preserve"><lb/>Candefecit Philoſophus diverſos Magnetes in Igne, tum in eo-<lb/>rum ſubſtantia magnam animadvertit heterogeneitatem: </s> <s xml:id="echoid-s1855" xml:space="preserve">Nonnulli <lb/>inter refrigerandum cadebant in pulverem; </s> <s xml:id="echoid-s1856" xml:space="preserve">alii friabiles evadebant; </s> <s xml:id="echoid-s1857" xml:space="preserve"><lb/>alii integri perſtabant; </s> <s xml:id="echoid-s1858" xml:space="preserve">alii diffracti intus apparebant inſtar ſquam-<lb/>marum Ferri; </s> <s xml:id="echoid-s1859" xml:space="preserve">alii referebant lamellas colore variegatas, ſibi mutuo <lb/>parallelas; </s> <s xml:id="echoid-s1860" xml:space="preserve">alii vix apparebant mutati colore & </s> <s xml:id="echoid-s1861" xml:space="preserve">ſoliditate.</s> <s xml:id="echoid-s1862" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1863" xml:space="preserve">Nulli horum in Igne flammam cæruleam, quæ indicium præſen-<lb/>tis ſulphuris foret, emiſerunt, etiamſi id affirmet Del Porta, ſup-<lb/>ponens vim Magneticam in Sulphure conſiſtere. </s> <s xml:id="echoid-s1864" xml:space="preserve">Ex qua diverſiſ-<lb/>ſima Magnetum igni commiſſorum forma conſtat, varias ad eos <lb/>componendos concurrere ſubſtantias, quarum nonnullæ plus, aliæ <lb/>minus volatiles fiunt. </s> <s xml:id="echoid-s1865" xml:space="preserve">Sed ad Analyſin Magnetis properemus, <lb/>diverſiſſimas ineundo vias, ut, quod una non eruitur, altera in-<lb/>veniatur.</s> <s xml:id="echoid-s1866" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div39" type="section" level="1" n="39"> <head xml:id="echoid-head47" xml:space="preserve">PROCESSUS PRIMUS.</head> <p> <s xml:id="echoid-s1867" xml:space="preserve">Quia Magnes integer in Igne aliquamdiu toſtus, vim attrahendi <lb/>Ferrum eo uſque amittit, ut limaturam non attrahat, attamen agat <lb/>in Verſorium 6 pollicum Magneticâ vi imbutum; </s> <s xml:id="echoid-s1868" xml:space="preserve">exploravi, an non <lb/>poſſet penitus omnis vis attractrix expelli; </s> <s xml:id="echoid-s1869" xml:space="preserve">quod facilius videretur <lb/>poſſe fieri, quando Magnes in pulverem ſubtiliſſimum prius redu-<lb/>ceretur, tumque igni committeretur. </s> <s xml:id="echoid-s1870" xml:space="preserve">idcirco Magnetem elegi bo-<lb/>num, præſtantiſque virtutis, nigreſcentis coloris, qui in mor-<lb/>tario in pulverem ſubtiliſſimum contuſus fuit: </s> <s xml:id="echoid-s1871" xml:space="preserve">ſuſpicabar in hocpul-<lb/>vere datum iri partes, quæ â Magnete attraherentur, alias, quæ nul- <pb o="78" file="0092" n="92" rhead="DISSERTATIO"/> lum ſignum virtutis ederent; </s> <s xml:id="echoid-s1872" xml:space="preserve">itaque beneficio egregii Magnetis pul-<lb/>verem unum ex alio ſeparare nitebar, verum erat adeo homogeneus, <lb/>ut, totus quantus erat, attraheretur: </s> <s xml:id="echoid-s1873" xml:space="preserve">tum menſuravi ad quanmam <lb/>a Magnete diſtantiam attrahebatur, ut poſtea cognoſcerem, an quod <lb/>produceretur arte, vi majori an minori polleret: </s> <s xml:id="echoid-s1874" xml:space="preserve">pulverem immiſ-<lb/>ſum crucibulo, ſuperius aperto, in furno Anemi poſui, urſique ve-<lb/>hementi igne, excitato è carbonibus ligneis, quibus undique obrue-<lb/>batur, ſpatio trium horarum, quo toto tempore valde candeſce-<lb/>bat: </s> <s xml:id="echoid-s1875" xml:space="preserve">omnibus poſtea refrigeratis, examinanti quid in crucibulo e-<lb/>rat, apparuit pulvis idem, ejuſdem coloris, ac ante ignitionem: <lb/></s> <s xml:id="echoid-s1876" xml:space="preserve">pulverem in crucibulo impactum antequam igni committebam, ob-<lb/>verti Verſorio 6 pollicum, gradatim propius admovendo, ut in qua-<lb/>nam diſtantia illud agitaret, accuratius intelligerem, diſtantiam <lb/>notaveram, nunc iterum crucibulum cum injecto pulvere Verſorio <lb/>eidem objeci, idque in eadem diſtantia, ac ante, attraxit: </s> <s xml:id="echoid-s1877" xml:space="preserve">Deinde <lb/>ſupra pulverem ex crucibulo excuſſum Magnetem tenui eundem, qui <lb/>in eadem diſtantia ac ante non attrahebatur quidem illico, ſed poſt-<lb/>quam per Minutum ſecundum unum alterumve exſpectaveram, tum <lb/>vero attractus fuit æque valide, quam ante Ignitionem.</s> <s xml:id="echoid-s1878" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1879" xml:space="preserve">Ad pondus Magnetis ante & </s> <s xml:id="echoid-s1880" xml:space="preserve">poſt Ignitionem non attendi, quia <lb/>præcavere non poteram, quin cineres carbonum in crucibulum aper-<lb/>tum inciderint, qui pondus verum mutabant.</s> <s xml:id="echoid-s1881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1882" xml:space="preserve">Ex hoc eventu igitur liquet vim attrahentem Magnetis non <lb/>facile penitus expelli poſſe ope Ignitionis, licet ea ex integro Magne-<lb/>te multum imminuatur, unde videtur, quando ad certum uſque gra-<lb/>dum vis periit, non ulterius eam ignitione paucarum horarum de-<lb/>creſcere; </s> <s xml:id="echoid-s1883" xml:space="preserve">quod oſtendit principium attractionis in Magnete non eſſe <lb/>admodum volatile.</s> <s xml:id="echoid-s1884" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div40" type="section" level="1" n="40"> <head xml:id="echoid-head48" xml:space="preserve">PROCESSUS SECUNDUS.</head> <p> <s xml:id="echoid-s1885" xml:space="preserve">Exploravi deinde, an principium attractionis Magneticæ non <lb/>volatile reddi poſſet, Magnetis pulveri admiſcendo corpora Sali-<lb/>na, quæ ſubtiliſſime omnia penetrare ſolent, & </s> <s xml:id="echoid-s1886" xml:space="preserve">ſecum abripere, <lb/>atque in altum elevare, quæcunque levia & </s> <s xml:id="echoid-s1887" xml:space="preserve">ſubtilia reddi poſſunt: <lb/></s> <s xml:id="echoid-s1888" xml:space="preserve">Hunc in finem ſumſi Magnetis ejuſdem in pollinem reducti, & </s> <s xml:id="echoid-s1889" xml:space="preserve">Mer- <pb o="79" file="0093" n="93" rhead="DE MAGNETE."/> curii ſublimati corroſivi ana ℨiij. </s> <s xml:id="echoid-s1890" xml:space="preserve">quos binos pulveres bene miſtos, <lb/>phialæ immiſi vitreæ, quam expoſui igni arenæ trihorii ſpatio; </s> <s xml:id="echoid-s1891" xml:space="preserve">ad-<lb/>ſcendit omnis Mercurius ſublimatus, atque adhæſit ſuperiori phia-<lb/>læ fornici, ejuſque collo, quemadmodum in omni ſublimationeejus <lb/>contingit; </s> <s xml:id="echoid-s1892" xml:space="preserve">ſed nihil ex Magnete ſecum elevavit; </s> <s xml:id="echoid-s1893" xml:space="preserve">qui ſub forma <lb/>pulveris remanſit in phialæ fundo: </s> <s xml:id="echoid-s1894" xml:space="preserve">hac diffracta & </s> <s xml:id="echoid-s1895" xml:space="preserve">pulvere exemto, <lb/>obſervata fuit vis eadem attratrix ſuperſtes in eo, quæ ante inſtitu-<lb/>tam operationem adnotata fuerat.</s> <s xml:id="echoid-s1896" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1897" xml:space="preserve">2. </s> <s xml:id="echoid-s1898" xml:space="preserve">Quia in Chemiâ aliquando deprehendimus unâ operatione non <lb/>peragi, quod repetita abſolvitur, Mercurium ſublimatum priorem <lb/>collegi, ipſique crudi Mercurii ℈ij. </s> <s xml:id="echoid-s1899" xml:space="preserve">admiſcui, & </s> <s xml:id="echoid-s1900" xml:space="preserve">pulverem tandem <lb/>Magnetis eundem: </s> <s xml:id="echoid-s1901" xml:space="preserve">hæc tria phialæ vitreæ immiſſa iterum igni ex-<lb/>poſui arenæ per tres horas, quibus elapſis deprehendebam Mercu-<lb/>rium omnem quidem fuiſſe ad ſuperiorem phialæ fornicem ſublima-<lb/>tum, attamen eum nihil ex Magnere ſecum elevaſſe, qui ſub forma <lb/>pulveris, ejuſdem ac ante coloris, ad fundum phialæ manſit, & </s> <s xml:id="echoid-s1902" xml:space="preserve">qui <lb/>poſtea examinatus per Magnetem alium ſupra ipſum detentum, ni-<lb/>hil de ſuâ virtute perdidiſſe deprehendebatur.</s> <s xml:id="echoid-s1903" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1904" xml:space="preserve">Omnem quem colligere potui Mercurium in hac operatione, miſcui <lb/>iterum accurate cum pulvere Magnetis eodem, immiſique crucibulo <lb/>terreo, ſuperne aperto, viſurus quid major ignis, & </s> <s xml:id="echoid-s1905" xml:space="preserve">apertus in <lb/>hæc ambo corpora operaretur, ex diverſa enim Ignis applicatione <lb/>haud raro diverſiſſima conficiuntur producta, per horam igitur in <lb/>furno anemi igni commiſi maſſam, avolavit Mercurius, relinquens <lb/>cundem pulverem Magnetis in crucibulo, nec mutatum copia, co-<lb/>lore, aut vi attractrice, quam in Verſorium & </s> <s xml:id="echoid-s1906" xml:space="preserve">Magnetem manifeſto <lb/>exercebat; </s> <s xml:id="echoid-s1907" xml:space="preserve">adeo ut ex hac operatione plane conſter Mercurium ne-<lb/>quicquam agere in Magnetem, nihilque in ipſo mutare, corrum-<lb/>pere, volatile reddere, ſeparare, ſed ipſum penitus relinquere in-<lb/>tactum.</s> <s xml:id="echoid-s1908" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div41" type="section" level="1" n="41"> <head xml:id="echoid-head49" xml:space="preserve">PROCESSUS TERTIUS.</head> <p> <s xml:id="echoid-s1909" xml:space="preserve">Quamvis Mercurius ſublimatus nihil in Magnete volatile reddi-<lb/>derit, concludere tamen ut Phyſicus non poteram, ergo nullum <lb/>Sal Magnetem reddet volatilem, quia Salia diverſiſſimæ indolis <pb o="80" file="0094" n="94" rhead="DISSERTATIO"/> ſunt, unumque ſæpe in corpora quædam operatur, alterius vi in <lb/>ea abſolute ſilente; </s> <s xml:id="echoid-s1910" xml:space="preserve">uti quidem non ex hoc, ſed ex aliis liquebit <lb/>Proceſſibus: </s> <s xml:id="echoid-s1911" xml:space="preserve">Sumſi igitur novum pulverem Magneticum, ſed ex <lb/>eodem Magnete, qui præcedentibus & </s> <s xml:id="echoid-s1912" xml:space="preserve">omnibus aliis ſequentibus <lb/>operationibus inſerviit; </s> <s xml:id="echoid-s1913" xml:space="preserve">huic addidi Arſenici ana ℨiij, ambos pul-<lb/>veres diu & </s> <s xml:id="echoid-s1914" xml:space="preserve">bene miſcui, incluſos phialæ vitreæ expoſui igni are-<lb/>næ bihorii ſpatio, omne Arſenicum ſublimatum fuit, magnaque e-<lb/>jus pars ex collo phialæ avolavit, relinquens in fundo pulverem Ma-<lb/>gnetis, nullo modo immutatum, copiâ, colore, aut vi attractrice <lb/>reſpectu Verſorii, aut alterius Magnetis: </s> <s xml:id="echoid-s1915" xml:space="preserve">ex quâ operatione nihil <lb/>diſcimus, niſi Arſenicum non agere in Magnetem.</s> <s xml:id="echoid-s1916" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div42" type="section" level="1" n="42"> <head xml:id="echoid-head50" xml:space="preserve">PROCESSUS QUARTUS.</head> <p> <s xml:id="echoid-s1917" xml:space="preserve">Quia Sal Ammoniacus Ferrum volatile reddit, & </s> <s xml:id="echoid-s1918" xml:space="preserve">cum eo ſubli-<lb/>matur, arbitrabar Magnetem vel partim vel penitus volatilem reddi-<lb/>tum iri, ſi cum hoc Sale urgeretur, neque ê ſpe excidi: </s> <s xml:id="echoid-s1919" xml:space="preserve">Sumſi <lb/>Salis Ammoniaci & </s> <s xml:id="echoid-s1920" xml:space="preserve">Magnetis pulveris novi ana ℨiij. </s> <s xml:id="echoid-s1921" xml:space="preserve">ambos pulve-<lb/>res diu contritos & </s> <s xml:id="echoid-s1922" xml:space="preserve">miſtos immiſi phialæ vitreæ, quam impoſui igni <lb/>arenæ, continuato per 3 horas, quem tamen non excitaviſummum, <lb/>cum lebes arenam continens non ſatis profunde fornaci immiſſus fue-<lb/>rat: </s> <s xml:id="echoid-s1923" xml:space="preserve">exemta & </s> <s xml:id="echoid-s1924" xml:space="preserve">diffracta phiala, obſervabatur maſſa in fundo phia-<lb/>læ cohærens, tamen mollis, & </s> <s xml:id="echoid-s1925" xml:space="preserve">facile friabilis in pulverem, parum <lb/>olens, quæ per medium diffracta, â parte inferiori verſus ſuperio-<lb/>ra, exhibebat aliquod ſtrata hoc ordine poſita: </s> <s xml:id="echoid-s1926" xml:space="preserve">Infimum ſtratum erat <lb/>tenuiſſimum omnium, coloris obſcuri: </s> <s xml:id="echoid-s1927" xml:space="preserve">Stratum ſecundum colorem <lb/>habebat fulvum; </s> <s xml:id="echoid-s1928" xml:space="preserve">tertium colore donabatur luteo: </s> <s xml:id="echoid-s1929" xml:space="preserve">quartum erat gry-<lb/>ſeum, conſtans ex miſtis partibus Magnetis nigris cum albis Salis <lb/>Ammoniaci: </s> <s xml:id="echoid-s1930" xml:space="preserve">quintum ſtratum ſive ſupremum conſtabat ex puris <lb/>floribus Salis Ammoniaci albiſſimis, levibus, & </s> <s xml:id="echoid-s1931" xml:space="preserve">vix cohærenti-<lb/>bus.</s> <s xml:id="echoid-s1932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1933" xml:space="preserve">Maſſa hæc prope Verſorium 6 pollicum locata, manifeſtos in eo <lb/>excitavit motus, tam attrahentes, quam repellentes.</s> <s xml:id="echoid-s1934" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1935" xml:space="preserve">Ex hoc colore diverſo ſtratorum, tum ex varia eorum gravitate, <lb/>liquebat Magnetem non eſſe corpus homogeneum & </s> <s xml:id="echoid-s1936" xml:space="preserve">ſimplex, ſed <lb/>eſſe aliquod compoſitum ex pluribus partibus diverſis.</s> <s xml:id="echoid-s1937" xml:space="preserve"/> </p> <pb o="81" file="0095" n="95" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s1938" xml:space="preserve">In animum induxeram ſingula hæc ſtrata ſeorſim examinare, <lb/>verum aliis diſtrictus negotiis, uſque in ſequentem diſtuli hoc nego-<lb/>tium diem; </s> <s xml:id="echoid-s1939" xml:space="preserve">quo animadverti maſſam ab humido aëris fuiſſe molliorem <lb/>redditam, ut ſtrata accurate ſeorſim ſeparare non potuerim, adeo-<lb/>que omnia modo inter ſe permiſcui.</s> <s xml:id="echoid-s1940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1941" xml:space="preserve">2. </s> <s xml:id="echoid-s1942" xml:space="preserve">Hujus maſſæ drachmis tribus phialæ immiſſis ſuperaffudiaquam <lb/>putealem ad eminentiam unius digiti, digeſſique in furnulo ligneo <lb/>octo diebus, quibus eliciebatur Tinctura, pellucida, mediocriter <lb/>ſpiſſa, ex fulvo flaveſcens, quaſi in aqua rubigo ferri ſoluta fuiſſet: <lb/></s> <s xml:id="echoid-s1943" xml:space="preserve">manſit in fundo phialæ potiſſima pars Magnetis non ſoluta.</s> <s xml:id="echoid-s1944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1945" xml:space="preserve">3. </s> <s xml:id="echoid-s1946" xml:space="preserve">Tincturam leniter effuſam, ut nihil pulveris adeſſet, inſpiſſavi <lb/>& </s> <s xml:id="echoid-s1947" xml:space="preserve">exſiccavi in vaſe puro porcellanico, quæ dedit pulverem auran-<lb/>tii coloris, ſaporis ſalſi & </s> <s xml:id="echoid-s1948" xml:space="preserve">adſtringentis, quaſi aliquid vitrioli mar-<lb/>tis admiſtum fuiſſet; </s> <s xml:id="echoid-s1949" xml:space="preserve">qui pulvis nequaquam a Magnete attractus <lb/>fuit, licet armaturæ pes ipſi immediate applicaretur.</s> <s xml:id="echoid-s1950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1951" xml:space="preserve">4. </s> <s xml:id="echoid-s1952" xml:space="preserve">Hunc pulverem aurantium inditum crucibulo, igni commiſi <lb/>aperto, ſolvebatur primo in fluidum, quod ebulliit, inſtar aquæ, <lb/>perpetuo emittens fumos copioſos, poſtea manſit pulvis nigreſcens, <lb/>ejuſdem coloris ac Magnes ante inſtitutam operationem, & </s> <s xml:id="echoid-s1953" xml:space="preserve">quiab <lb/>alio Magnete iterum vehementer attrahebatur, imo æque valide, <lb/>ac ſi pulvis Magnetis nullam actionem Ignis expertus fuiſſet.</s> <s xml:id="echoid-s1954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1955" xml:space="preserve">5. </s> <s xml:id="echoid-s1956" xml:space="preserve">Aliam portionem maſſæ deſcriptæ in §. </s> <s xml:id="echoid-s1957" xml:space="preserve">1. </s> <s xml:id="echoid-s1958" xml:space="preserve">ſumſi ad ℨiij, ei-<lb/>que immiſſæ phialæ altæ ſuperaffuſum eſt Alcohol vini per ſe de-<lb/>ſtillatum, cum quo digeſtum eſt per octiduum, elicita fuit Tinctu-<lb/>ra ſpiſſior, viridiuſcula, manente ad fundum maxima parte pulve-<lb/>ris Magnetis non ſoluta: </s> <s xml:id="echoid-s1959" xml:space="preserve">hæc Tinctura habuit ſaporem acrem ſub-<lb/>ſalſum.</s> <s xml:id="echoid-s1960" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1961" xml:space="preserve">6. </s> <s xml:id="echoid-s1962" xml:space="preserve">Ex hac Tinctura eduxi omnem Spiritum vini, remanente in <lb/>fundo vaſis quamplurimo pulvere ex flavo fuſco, ſaporis ſalſi, ſed <lb/>acerrimi & </s> <s xml:id="echoid-s1963" xml:space="preserve">rodentis, qui nullum indicium attractionis edidit, Ver-<lb/>ſorio aut Magnete ipſi appoſitis.</s> <s xml:id="echoid-s1964" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1965" xml:space="preserve">7. </s> <s xml:id="echoid-s1966" xml:space="preserve">Hic pulvis igni aperto commiſſus in crucibulo, edidit eadem <lb/>phænomena, quæ pulvis in §. </s> <s xml:id="echoid-s1967" xml:space="preserve">4. </s> <s xml:id="echoid-s1968" xml:space="preserve">deſcriptus, abiitque in eundem <lb/>pulverem Magneticum nigreſcentem.</s> <s xml:id="echoid-s1969" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1970" xml:space="preserve">8. </s> <s xml:id="echoid-s1971" xml:space="preserve">Manſerat igitur in phialis pulvis Magnetis non ſolutus, nec in aqua, <lb/>necin Alcohole vini, hunc igitur inditum crucibulo, leniter exſiccavi, <pb o="82" file="0096" n="96" rhead="DISSERTATIO"/> evaſit pulvis nigri coloris, qui â Magnete attrahebatur; </s> <s xml:id="echoid-s1972" xml:space="preserve">ſed deinde <lb/>hunc violentiori Igni expoſui in eodem crucibulo ſpatio unius horæ, <lb/>prodiitque pulvis ex fulvo rubicundus, qui â Magnete fortiter at-<lb/>trahebatur, imo ad majorem diſtantiam, quam Magnetis pulvis <lb/>ante ullam inſtitutam operationem.</s> <s xml:id="echoid-s1973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1974" xml:space="preserve">9. </s> <s xml:id="echoid-s1975" xml:space="preserve">Quia non ſatis fortem ignem admoveram, repetiiExperimentum, <lb/>novum pulverem Magnetis cum Salis Ammoniaciæquali copia ſubli-<lb/>mando, & </s> <s xml:id="echoid-s1976" xml:space="preserve">in phiala fortiſſimo igni exponendo; </s> <s xml:id="echoid-s1977" xml:space="preserve">in hac operatione <lb/>Salem Ammoniacum reddidi penitus volatilem, qui ſecum elevave-<lb/>rat ad phialæ fornicem ex Magnete pulverem flavum, eundem, <lb/>quem in priori operatione ope Alcoholis vini & </s> <s xml:id="echoid-s1978" xml:space="preserve">aquæ ſub forma <lb/>Tincturæ collegeram: </s> <s xml:id="echoid-s1979" xml:space="preserve">remanſitque in fundo phialæ maſſa coloris ex <lb/>rubro fuſci, quæ in aëre aperto intra diem per deliquium ſolve-<lb/>batur.</s> <s xml:id="echoid-s1980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1981" xml:space="preserve">10. </s> <s xml:id="echoid-s1982" xml:space="preserve">Poſtea ſumſi Magnetis novi pulveriſati & </s> <s xml:id="echoid-s1983" xml:space="preserve">Salis Ammoniaci <lb/>iterum ℨiij. </s> <s xml:id="echoid-s1984" xml:space="preserve">quas perfecte miſtas in crucibulo expoſui igni aperto in <lb/>furno Anemi, ſpatio unius horæ, quo avolavit omnis Sal Ammonia-<lb/>cus, ſecum ſimul abripiens multum ex Magnete, relinquens tamen <lb/>in fundo crucibuli pulverem roſei coloris, qui quidem attrahitur â <lb/>Magnete, ſed parum, & </s> <s xml:id="echoid-s1985" xml:space="preserve">modo in parvâ diſtantiâ.</s> <s xml:id="echoid-s1986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1987" xml:space="preserve">11. </s> <s xml:id="echoid-s1988" xml:space="preserve">Quod ſi ad omnia, quæ in hoc Proceſſu occurrunt, atten-<lb/>damus, patet in Magnete dari nonnullas partes, quæ citius red-<lb/>di poſſunt volatiles, quam aliæ nam illæ, quæ colorem flavum <lb/>conſtituebant in §. </s> <s xml:id="echoid-s1989" xml:space="preserve">1, 2, 4, 5, 7, 9. </s> <s xml:id="echoid-s1990" xml:space="preserve">cum Sale Ammoniaco adſcen-<lb/>derunt; </s> <s xml:id="echoid-s1991" xml:space="preserve">quæ vero coloris propius ad nigreſcentem accedentis erant, <lb/>magis fixæ aut gravioresviſæ ſunt, cum in fundo phialæ remanebant: <lb/></s> <s xml:id="echoid-s1992" xml:space="preserve">Sed hac operatione non penetramus in artem ſeparandi ex Magnete <lb/>partes inertes ab iis, quæ maxima virtute donantur, quia, quæ vo-<lb/>latiles factæ ſunt, æque vim attractricem retinuerunt, quam fixiſſi-<lb/>mæ, cum partes volatiles orbatæ tantummodo ab adhærente Sale <lb/>iterum perfecte eandem, quam antea, vim Magneticam oſtende-<lb/>runt, uti in §. </s> <s xml:id="echoid-s1993" xml:space="preserve">4, 7. </s> <s xml:id="echoid-s1994" xml:space="preserve">videre licet.</s> <s xml:id="echoid-s1995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1996" xml:space="preserve">12. </s> <s xml:id="echoid-s1997" xml:space="preserve">Mirandum tamen eſt, Tincturam Magnetis ſive cum Aqua, <lb/>ſive cum Alcohole factam, exſiccatam, ut redierit in pulverem §. </s> <s xml:id="echoid-s1998" xml:space="preserve">3. <lb/></s> <s xml:id="echoid-s1999" xml:space="preserve">6, nullum indicium Attractionis habuiſſe, etiamſi Magnetem inſe <lb/>contineat, qui poſt ulteriorem ignis actionem perpeſſam, ſuas vires <pb o="83" file="0097" n="97" rhead="DE MAGNETE."/> luculenter probat: </s> <s xml:id="echoid-s2000" xml:space="preserve">verum Tinctura exſiccata plurimum Salis in ſe <lb/>habet, Sal Magnetem vehementer attrahit, efficitque, ut hu-<lb/>jus vis in ſe terminetur, nec proinde in alium Magnetem agere poſ-<lb/>ſit: </s> <s xml:id="echoid-s2001" xml:space="preserve">conſtanter id obtinere didici ex omnibus Experimentis, quod <lb/>nihil, præterquam Salem, vim Magnetis impedit, quo minus ad <lb/>notabilem diffundatur diſtantiam; </s> <s xml:id="echoid-s2002" xml:space="preserve">ſed omnis Sal, ejus virtutem co-<lb/>hibet, æque Sal Ammoniacus, quam Marinus, Gemmæ, Nitrum, <lb/>ut in ſequentibus conſtabit: </s> <s xml:id="echoid-s2003" xml:space="preserve">Eſt igitur ita aliquid hic admirandum <lb/>inter Salem & </s> <s xml:id="echoid-s2004" xml:space="preserve">Magnetem, eo prohibente aliquid, quod nec Metal-<lb/>la, Gemmæ, Lapides, Vitra, Ligna, Terræve prohibere potue-<lb/>runt.</s> <s xml:id="echoid-s2005" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div43" type="section" level="1" n="43"> <head xml:id="echoid-head51" xml:space="preserve">PROCESSUS QUINTUS.</head> <p> <s xml:id="echoid-s2006" xml:space="preserve">Cum voti non factus eram compos in præcedenti operatione, ad <lb/>examen cum alio Sale me converti, verebar tamen me aliorum <lb/>ope non multum præſtiturum, cum docente conſtanti experientia, <lb/>nullum melius Sale Ammoniaco corpora aperiat, ſed a priori in Phy-<lb/>ſicis non multum concludi poteſt, & </s> <s xml:id="echoid-s2007" xml:space="preserve">ideo me potius cæcum opera-<lb/>torem gerere malui, quam ſubtilem ratiocinatorem, a quo vix quid-<lb/>quam, præter aliquod hypotheticum argumentum produceretur: </s> <s xml:id="echoid-s2008" xml:space="preserve">Ma-<lb/>gnetis in pulverem contuſi & </s> <s xml:id="echoid-s2009" xml:space="preserve">Salis Marini ana ℨiij. </s> <s xml:id="echoid-s2010" xml:space="preserve">accurate permi-<lb/>ſtas ſubtileſque immiſi crucibulo, eaſque urſi igne vehementi in <lb/>furno Anemi, ſpatio trium horarum: </s> <s xml:id="echoid-s2011" xml:space="preserve">coibant pulveres in maſſam <lb/>ſolidam, parietibus crucibuli valde adhærentem, nec niſi eo fracto <lb/>avellendam, maſſa colorem ex rubro nigrum accepit, inſtar colco-<lb/>taris vitrioli, quæ ubivis per totam ſuam ſubſtantiam habebat parva <lb/>puncta, ſplendentia valde, æmula partibus ferri diffracti: </s> <s xml:id="echoid-s2012" xml:space="preserve">hæc re-<lb/>ducta in pulverem, a Magnete, ſupra eam poſito, vehementer fuit <lb/>attracta: </s> <s xml:id="echoid-s2013" xml:space="preserve">quamobrem Sal marinus non eliminat ex Magnete partes <lb/>aliquas, in quibus vis reſideret, neque etiam ex illo partes ejicit <lb/>inertes.</s> <s xml:id="echoid-s2014" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2015" xml:space="preserve">2. </s> <s xml:id="echoid-s2016" xml:space="preserve">Sed hac una operatione non contentus, iterum priorem pul-<lb/>verem, jam ſemel ignis vim paſſum, miſcui cum æquali copia Sa-<lb/>lis marini atque in crucibulo aperto expoſui igni fortiſſimo in furno <lb/>reverberii ſpatio 2 {1/2} horarum, ex qua operatione prodiit maſſa firma, <pb o="84" file="0098" n="98" rhead="DISSERTATIO"/> arcte cohærens cum crucibulo, ſpongioſa, cujus pars ſuperior co-<lb/>lorem gryſeum, inferior rufeſcentem habebat: </s> <s xml:id="echoid-s2017" xml:space="preserve">ambas diverſi co-<lb/>loris partes a ſe ſollicite ſeparavi, ſperans me hoc modo ex Magne-<lb/>te ſejunxiſſe iners ab attrahenti; </s> <s xml:id="echoid-s2018" xml:space="preserve">maſſa utraque in pulverem reda-<lb/>cta a Magnete attrahebatur, gryſea tamen fortius, rufa debi-<lb/>lius.</s> <s xml:id="echoid-s2019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2020" xml:space="preserve">3. </s> <s xml:id="echoid-s2021" xml:space="preserve">Ex quo progreſſu concludebam Magnetem eſſe revera corpus <lb/>aliquod compoſitum ex terra nigra, inerti, & </s> <s xml:id="echoid-s2022" xml:space="preserve">ex aliqua alia mate-<lb/>ria, in qua vis potiſſimum reſidet; </s> <s xml:id="echoid-s2023" xml:space="preserve">ſed hæc tenaciſſime adhæret ſuæ <lb/>Terræ, atque ideo nondum in hac operatione ſeparata penitus fuit; <lb/></s> <s xml:id="echoid-s2024" xml:space="preserve">tum enim in Terra nihil virium deprehendi debuiſſet, & </s> <s xml:id="echoid-s2025" xml:space="preserve">in pul-<lb/>vere gryſeo major attractio.</s> <s xml:id="echoid-s2026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2027" xml:space="preserve">4. </s> <s xml:id="echoid-s2028" xml:space="preserve">Pulverem itaque hunc gryſeum nitebar in ulteriori operatione <lb/>perfectius ſeparare a ſua Terra, ipſique admiſcui Salis Marini æqua-<lb/>lem quantitatem, atque in crucibulo urſi per 3 horas in Igne vehe-<lb/>mentiſſimo rotæ, vi carbonum Ligneorum & </s> <s xml:id="echoid-s2029" xml:space="preserve">foſſilium; </s> <s xml:id="echoid-s2030" xml:space="preserve">refrigeratis <lb/>deinde omnibus, pulvis erat ejuſdem coloris ac ante, & </s> <s xml:id="echoid-s2031" xml:space="preserve">qui a Ma-<lb/>gnete attrahebatur ut ante, necita ullam obtinui partium terreſtrium <lb/>ab aliis ſeparationem: </s> <s xml:id="echoid-s2032" xml:space="preserve">adeoque vel id quod maxima vi gaudet, avo-<lb/>lavit, vel in hac operatione ignis nihil mutationis induxit: </s> <s xml:id="echoid-s2033" xml:space="preserve">hac <lb/>igitur via non amplius pergendum eſſe ratus ſum, quia pulvis ab hoc <lb/>fortiſſimo Igne non mutatus fuit.</s> <s xml:id="echoid-s2034" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2035" xml:space="preserve">5. </s> <s xml:id="echoid-s2036" xml:space="preserve">Adeoque explorabam, an non tantopere aperuiſſem Magnetem, <lb/>ut ex eo nunc elicere poſſem Tincturam: </s> <s xml:id="echoid-s2037" xml:space="preserve">hunc in finem pulveri af-<lb/>fuſa fuit aqua, cum qua digeſſi 8 diebus; </s> <s xml:id="echoid-s2038" xml:space="preserve">ſed Sal modo in aqua ſol-<lb/>vebatur, cæteroquin nulla oriebatur Tinctura: </s> <s xml:id="echoid-s2039" xml:space="preserve">quo viſo affudi pul-<lb/>veri copioſam aquam, eum lavi effundendo ſalſam, & </s> <s xml:id="echoid-s2040" xml:space="preserve">reaffunden-<lb/>do inſipidam, donec aqua penitus inſipida redibat: </s> <s xml:id="echoid-s2041" xml:space="preserve">poſtea pulvis <lb/>exſiccatus exhibebat eundem colorem, quem pulvis Magnetis ante <lb/>ullam cum eo inſtitutam operationem, & </s> <s xml:id="echoid-s2042" xml:space="preserve">iterum æque fortiter â <lb/>Magnete attrahebatur: </s> <s xml:id="echoid-s2043" xml:space="preserve">in principio, quando ſupra eum tenetur <lb/>Magnes, aliquantum ſilet virtus, ſedelapſo uno alterove Secundo Mi-<lb/>nuto, attractio fit, pulvis qui ſemel attractus fuit & </s> <s xml:id="echoid-s2044" xml:space="preserve">abſterſus dein-<lb/>ceps, multo facilius de novo attrahitur, atque ad majorem diſtan-<lb/>tiam a Magnete commovetur, elevatur, ipſique advolat: </s> <s xml:id="echoid-s2045" xml:space="preserve">hæcſola <lb/>eſt differentia, quam ignis vehementis tortura pulveri intulit, quod <pb o="85" file="0099" n="99" rhead="DE MAGNETE."/> nunc in principio non attrahatur tam ſubito, quam pulvis nulli <lb/>igni immiſſus.</s> <s xml:id="echoid-s2046" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div44" type="section" level="1" n="44"> <head xml:id="echoid-head52" xml:space="preserve">PROCESSUS SEXTUS.</head> <p> <s xml:id="echoid-s2047" xml:space="preserve">Examinaveram ita quidem Magnetem cum Sale neutro, quale eſt <lb/>Ammoniacum, & </s> <s xml:id="echoid-s2048" xml:space="preserve">cum Sale muriatico, uti eſt marinum; </s> <s xml:id="echoid-s2049" xml:space="preserve">nunc ex-<lb/>ponendus quoque erat actioni Salis Alcalini fixi; </s> <s xml:id="echoid-s2050" xml:space="preserve">quamobrem ſumſi <lb/>Magnetis in pulverem contuſi, & </s> <s xml:id="echoid-s2051" xml:space="preserve">Salis Tartari ana ℨiij. </s> <s xml:id="echoid-s2052" xml:space="preserve">amboſque <lb/>pulveres diu & </s> <s xml:id="echoid-s2053" xml:space="preserve">bene tritos miſtoſque immiſi crucibulo, quod apertum <lb/>ſuperne impoſitum eſtIgni carbonumLigneorum in furno anemi, trium <lb/>horarum ſpatio: </s> <s xml:id="echoid-s2054" xml:space="preserve">omnibus refrigeratis pulverem recepi ejuſdem co-<lb/>loris ac ante quam igni commiſſus erat, qui nullo modo immutatus <lb/>apparebat, movebatque Verſorium 6 pollicum in eadem ac ante <lb/>diſtantia, & </s> <s xml:id="echoid-s2055" xml:space="preserve">ab alio Magnete attrahebatur manifeſto.</s> <s xml:id="echoid-s2056" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2057" xml:space="preserve">2. </s> <s xml:id="echoid-s2058" xml:space="preserve">Cum ſolet Sal Tartari eſſe impatiens ſiccitatis, & </s> <s xml:id="echoid-s2059" xml:space="preserve">fortiſſimus <lb/>Magnes humidi aërei exiſtit, experiebar an nunc quoque per deli-<lb/>quium flueret, eoque modo magis forſitan aperiret Magnetem; </s> <s xml:id="echoid-s2060" xml:space="preserve">ſed <lb/>contra ſuam indolem ſiccus manſit; </s> <s xml:id="echoid-s2061" xml:space="preserve">quod videtur pendere a vima-<lb/>gna, quâ Magnetem attrahendo occupabatur.</s> <s xml:id="echoid-s2062" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2063" xml:space="preserve">3. </s> <s xml:id="echoid-s2064" xml:space="preserve">Quamobrem pulveri phialæ immiſſo ſuperaſſuſa fuit aqua ad <lb/>exceſſum unius digiti, ut viderem, an Tinctura exinde poſt longam <lb/>digeſtionem eliceretur, continuavi operationem per 16 dies; </s> <s xml:id="echoid-s2065" xml:space="preserve">ma-<lb/>nente nihilominus aqua pellucida, albaque, in qua nil niſi Sal Al-<lb/>calinum, quod pulveri adhæſerat, ſolvebatur: </s> <s xml:id="echoid-s2066" xml:space="preserve">hoc obſervato edul-<lb/>coravi pulverem larga ablutione cum aqua pura, eumque tandem <lb/>exſiccavi; </s> <s xml:id="echoid-s2067" xml:space="preserve">hic vires attrahendi ferrum manifeſtas habuit, vix iis <lb/>cedentes, quas in pulvere ante ullam inſtitutam operationem ani-<lb/>madverteram: </s> <s xml:id="echoid-s2068" xml:space="preserve">Hic pulvis tamen non erat purus Magneticus, quia <lb/>cineres a Sale Tartari relictos ſibique permixtos poſſidebat, a qui-<lb/>bus cum ſeparabatur ope alterius Magnetis, qui quidem in pulve-<lb/>rem Magneticum, non in cineres agit, recipiebam pulverem Ma-<lb/>gneticum, nullo modo mutatum: </s> <s xml:id="echoid-s2069" xml:space="preserve">non continuavi ulterius hanc <lb/>operationem, quia nihil ex ea didiceram, niſi Sal Alcalinum acer-<lb/>rimum nihil agere in Magnetem, nec ulterius quid ſperabam, ideo <lb/>potius ad examen cum alio Sale me contuli.</s> <s xml:id="echoid-s2070" xml:space="preserve"/> </p> <pb o="86" file="0100" n="100" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div45" type="section" level="1" n="45"> <head xml:id="echoid-head53" xml:space="preserve">PROCESSUS SEPTIMUS.</head> <p> <s xml:id="echoid-s2071" xml:space="preserve">Magnetis in pulverem reducti & </s> <s xml:id="echoid-s2072" xml:space="preserve">Nitri ana ℨiij. </s> <s xml:id="echoid-s2073" xml:space="preserve">bene miſtas in <lb/>crucibulo expoſui igni in furno anemi, per trihorium, in quo abie-<lb/>runt in maſſam ſirmam, ſpongioſam, non ſplendentem, nigreſcen-<lb/>tem, crucibulo adeo pertinaciter adhærentem, ut non niſi eo dif-<lb/>fracto ſeparari potuerit: </s> <s xml:id="echoid-s2074" xml:space="preserve">hæc in pulverem contuſa a Magnete attra-<lb/>hebatur, ſaporem parumper ſalſum retinuerat ab Alcali, in quod <lb/>Nitrum in Igne converſum fuit: </s> <s xml:id="echoid-s2075" xml:space="preserve">cum Maſſa homogenei fuerat co-<lb/>loris in hac prima operatione, nihil ſeparati diſtinctique dedit, quare <lb/>illam alteri exponebam operationi.</s> <s xml:id="echoid-s2076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2077" xml:space="preserve">2. </s> <s xml:id="echoid-s2078" xml:space="preserve">Pulveri priori admiſcui Nitri æqualem copiam, atque eum in <lb/>crucibulo per horas 2 {1/2} vehementiſſimo Igni carbonum foſſilium in <lb/>furno reverberii expoſui; </s> <s xml:id="echoid-s2079" xml:space="preserve">tum abiit in maſſam valde friabilem, ſo-<lb/>lisque digitis in pulverem conterendam, rubeſcentem, ſed ubivis <lb/>homogeneam, nihilque diſtincti præbentem: </s> <s xml:id="echoid-s2080" xml:space="preserve">reduxi eam in pulve-<lb/>rem, ſed qui parum a Magnete attrahebatur; </s> <s xml:id="echoid-s2081" xml:space="preserve">unde concluſiſſem <lb/>partem viribus donatam cum Nitro avolaſſe, niſi certo certius ſci-<lb/>viſſem, hoc tantum provenire a copia Salis, undique pulveri ad-<lb/>hærentis, & </s> <s xml:id="echoid-s2082" xml:space="preserve">vim Magnetis in alia corpora prohibentis.</s> <s xml:id="echoid-s2083" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2084" xml:space="preserve">3. </s> <s xml:id="echoid-s2085" xml:space="preserve">Pulverem immiſſum phialæ cum Aqua digeſſi, coxique ſpatio <lb/>8 dierum, obſervaturus an tincturam daret, ſed nullomodo ſol-<lb/>vebatur: </s> <s xml:id="echoid-s2086" xml:space="preserve">tum pulverem in copioſiſſima diluebam & </s> <s xml:id="echoid-s2087" xml:space="preserve">lavabam A qua, <lb/>donec inſipidus evadebat; </s> <s xml:id="echoid-s2088" xml:space="preserve">poſtea exſiccatus, manſit rubeſcentis <lb/>coloris, & </s> <s xml:id="echoid-s2089" xml:space="preserve">multo fortius a Magnete attrahebatur quam antea in §. <lb/></s> <s xml:id="echoid-s2090" xml:space="preserve">2: </s> <s xml:id="echoid-s2091" xml:space="preserve">imo dubitabam an in attractione differentia obtineret inter præ-<lb/>ſentem & </s> <s xml:id="echoid-s2092" xml:space="preserve">eam ante inſtitutam ullam operationem cum pulvere.</s> <s xml:id="echoid-s2093" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2094" xml:space="preserve">Iterum ex hujus Salis operatione nihil ulterius ſperabam; </s> <s xml:id="echoid-s2095" xml:space="preserve">videbam <lb/>equidem hujus corroſionem aliam fuiſſe, quam Salis Tartari, <lb/>aut Salis Marini, quia pulvis alio colore donabatur; </s> <s xml:id="echoid-s2096" xml:space="preserve">nunc enim erat <lb/>rubeſcens, quiantea gryſeus, rubeſcens, nigreſcenſque habebatur, ſed <lb/>ita non ad ſcopum perveniebam: </s> <s xml:id="echoid-s2097" xml:space="preserve">quare ad aliud examen me ac-<lb/>cinxi.</s> <s xml:id="echoid-s2098" xml:space="preserve"/> </p> <pb o="87" file="0101" n="101" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div46" type="section" level="1" n="46"> <head xml:id="echoid-head54" xml:space="preserve">PROCESSUS OCTAVUS.</head> <p> <s xml:id="echoid-s2099" xml:space="preserve">Sumebantur Magnetis in pulverem fracti & </s> <s xml:id="echoid-s2100" xml:space="preserve">Salis Gemmæ ana <lb/>ℨiij. </s> <s xml:id="echoid-s2101" xml:space="preserve">ambos pulveres diu inter ſe contritos & </s> <s xml:id="echoid-s2102" xml:space="preserve">optime miſtos immiſi <lb/>crucibulo, quod expoſitum fuitigni in furno Anemi, per trihorium; <lb/></s> <s xml:id="echoid-s2103" xml:space="preserve">tum refrigeratis omnibus maſſa dabatur firma, crucibulo valde ad-<lb/>hærens, ubivis interſperſa puncta micantia habens, quæ per Mi-<lb/>croſcopium conſpecta, erant modo partes Salis Gemmæ pellucidiſ-<lb/>fimæ in ſuperſicie maſſæ color ferreus apparebat, ex quo plurimum <lb/>Ferri in hac maſſa hærere ſuſpicabar, in parte inferiori erat maſſa-<lb/>aſpera, & </s> <s xml:id="echoid-s2104" xml:space="preserve">multo nigrior. </s> <s xml:id="echoid-s2105" xml:space="preserve">Non poteram pro voto partem ſupe-<lb/>riorem ſeparare ab inferiori, quod ſperabam me melius facturum, <lb/>ſi ſecundæ operationi maſſam committerem: </s> <s xml:id="echoid-s2106" xml:space="preserve">Eam igitur prius in <lb/>pulverem redegi, qui ſaporem acrem ſalſumque retinebat, atque a <lb/>Magnete fortiter attrahebatur.</s> <s xml:id="echoid-s2107" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2108" xml:space="preserve">2. </s> <s xml:id="echoid-s2109" xml:space="preserve">Huic pulveri iterum addidi Salis Gemmæ, æqualem copiam, <lb/>& </s> <s xml:id="echoid-s2110" xml:space="preserve">ut ante in crucibulo commiſi Igni vehementiſſimo, in furno Ane-<lb/>mi, per 2 {1/2} horas, maſſa refrigerata erat firma, cujus ſtratum ſuperius <lb/>colorem Ferri æmulabatur, pars inferior erat ſpongioſa, rufa, mol-<lb/>lior; </s> <s xml:id="echoid-s2111" xml:space="preserve">ambo hæc ſtrata a ſe mutuo ſeparata redegi in pulverem; <lb/></s> <s xml:id="echoid-s2112" xml:space="preserve">pulvis ſtrati ſuperioris multo vehementius a Magnete attraheba-<lb/>tur, quam ſtrati inferioris; </s> <s xml:id="echoid-s2113" xml:space="preserve">imo erant in ſtrato inferiori plu-<lb/>rimæ partes, quæ non a Magnete attrahebantur, cum e contrario <lb/>omnes in ſtrato ſuperiori alliciebantur.</s> <s xml:id="echoid-s2114" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2115" xml:space="preserve">3. </s> <s xml:id="echoid-s2116" xml:space="preserve">Erat itaque multum in ſtrato inſeriori, ſimile illi, quod in ſtrato <lb/>ſuperiori deprehendebatur, hinc quicquid a Magnete attrahebatur, <lb/>eliciebam ex ſtrato inferiori, addidique pulveri ſtrati ſuperioris: <lb/></s> <s xml:id="echoid-s2117" xml:space="preserve">huic iterum admiſcui copiam Salis Gemmæ æqualem, quam immiſ-<lb/>ſam crucibulo, impoſui Igni fortiſſimo rotæ, excitato ex Carbo-<lb/>nibus ligneis & </s> <s xml:id="echoid-s2118" xml:space="preserve">foſſilibus, continuatoque per 4 horas; </s> <s xml:id="echoid-s2119" xml:space="preserve">maſſa dein-<lb/>de refrigerata exhibebat ſubſtantiam nigram non multum cohæren-<lb/>tem, valde friabilem, ſed homogeneam: </s> <s xml:id="echoid-s2120" xml:space="preserve">adhærebant lateribus <lb/>crucibuli pelliculæ metalli alicujus, ſed mihi incogniti, argentei <lb/>coloris, ſplendentes, quæ nullo modo a Magnete attraheban-<lb/>tur: </s> <s xml:id="echoid-s2121" xml:space="preserve">maſſa tota erat in hac operatione valde imminuta, adeo ut <pb o="88" file="0102" n="102" rhead="DISSERTATIO"/> pars magna tum Salis, tum Magnetis avolaverit, non tamen omnis <lb/>Sal abierat, quippe ſapor ſalſus maſſæ manifeſtus inerat: </s> <s xml:id="echoid-s2122" xml:space="preserve">In omni-<lb/>bus tenuiſſime contuſis vis parva Magnetis obſervabatur, uti quidem <lb/>ante ſuſpicatus eram, quia Sal undequaque penetraverat in partes <lb/>Magneticas, cum quibus vehementer cohærebat, adeo ut vis for-<lb/>tiſſimi ignis tamdiu continuati eas a ſe avellere non potuerit: </s> <s xml:id="echoid-s2123" xml:space="preserve">ſed <lb/>id quod Ignis præſtare nequit, aqua facile abſolvit.</s> <s xml:id="echoid-s2124" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2125" xml:space="preserve">4. </s> <s xml:id="echoid-s2126" xml:space="preserve">Quamobrem huic pulveri in phiala ſuperaffundebatur aqua ad <lb/>exceſſum unius digiti, qua cum digeſſi per octiduum, viſurus an <lb/>tincturam præberet; </s> <s xml:id="echoid-s2127" xml:space="preserve">ſed nullam dedit, ſolummodo Sal Gemmæ <lb/>reſiduum fuit in aqua ſolutum, eo cognito, pulverem lavi copio-<lb/>ſa aqua, uſque dum inſipida redibat; </s> <s xml:id="echoid-s2128" xml:space="preserve">pulvis exſiccatus, erat ni-<lb/>grioris coloris, quam pulvis Magneticus ante operationem; </s> <s xml:id="echoid-s2129" xml:space="preserve">& </s> <s xml:id="echoid-s2130" xml:space="preserve">at-<lb/>trahebatur a Magnete fortius quam unquam antea; </s> <s xml:id="echoid-s2131" xml:space="preserve">quod evincebat <lb/>Salem admiſtum impediviſſe actionem ejus Magneticam; </s> <s xml:id="echoid-s2132" xml:space="preserve">& </s> <s xml:id="echoid-s2133" xml:space="preserve">aliquam <lb/>Terram inertem fuiſſe ſeparatam ex Magnetis ſubſtantia; </s> <s xml:id="echoid-s2134" xml:space="preserve">quam procul <lb/>dubio in §. </s> <s xml:id="echoid-s2135" xml:space="preserve">3. </s> <s xml:id="echoid-s2136" xml:space="preserve">ſepoſueram: </s> <s xml:id="echoid-s2137" xml:space="preserve">non autem dubitavi quin in hac maſſa <lb/>reſidua adhuc multum materiæ inertis contineretur, quæ ulteriori-<lb/>bus operationibus diutiſſime continuatis poſſet ſeparari ab omni effi-<lb/>caci, verum non ſatis otii fruebar, ut id ulterius indagarem; </s> <s xml:id="echoid-s2138" xml:space="preserve">po-<lb/>tius ad alias methodos feſtinavi, ſperans me facilius voti compotem <lb/>futurum. </s> <s xml:id="echoid-s2139" xml:space="preserve">Id tamen ex hiſce omnibus tentaminibus colligitur, vim <lb/>Magnetis ex Magnete non poſle tam facile expelli omnem, uti cre-<lb/>diderunt antea Philoſophi, videntes Magnetem magnum & </s> <s xml:id="echoid-s2140" xml:space="preserve">inte-<lb/>grum in Igne corrumpi, ſuaſque vires amittere; </s> <s xml:id="echoid-s2141" xml:space="preserve">ſed Lapis non <lb/>omnes amittit, & </s> <s xml:id="echoid-s2142" xml:space="preserve">quomodocunque tractetur, aliquid retinet, veluti <lb/>ex his huc uſque expoſitis patet tentaminibus, & </s> <s xml:id="echoid-s2143" xml:space="preserve">in ſequentibus <lb/>etiam ulterius liquebit.</s> <s xml:id="echoid-s2144" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div47" type="section" level="1" n="47"> <head xml:id="echoid-head55" xml:space="preserve">PROCESSUS NONUS.</head> <p> <s xml:id="echoid-s2145" xml:space="preserve">Deſiderio flagrabam explorandi, an Magnes in vitrum converſus <lb/>vim attrahendi retineret, quoniam vitriſicatio eſt ultimus finis ope-<lb/>rationum Chemicarum, & </s> <s xml:id="echoid-s2146" xml:space="preserve">quæ corpora maxime immutat: </s> <s xml:id="echoid-s2147" xml:space="preserve">Magne-<lb/>tem per ſe, aut ope Borracis ſolius non in vitrum mutaveram hacte-<lb/>nus, licet diu & </s> <s xml:id="echoid-s2148" xml:space="preserve">vehementiſſimo Igni expoſuerim; </s> <s xml:id="echoid-s2149" xml:space="preserve">ideo Minium <pb o="89" file="0103" n="103" rhead="DE MAGNETE."/> Plumbi additum fuit, quod cum corporibus pluribus terreſtribus, <lb/>& </s> <s xml:id="echoid-s2150" xml:space="preserve">imprimis cum ſilicibus abit in vitrum elegans, pellucidum, fla-<lb/>vum, pulchritudine certans cum Pruſſico ſuccino: </s> <s xml:id="echoid-s2151" xml:space="preserve">Primum igitur <lb/>indagandum erat, cum quanta copia Minii Magnes in vitrum redu-<lb/>ceretur, a minima Minii quantitate incipiendum fuit, ut certior <lb/>ſierem de vi ſuperſtite vel deſtructa Magnetica: </s> <s xml:id="echoid-s2152" xml:space="preserve">Adeoque Minii, <lb/>Magnetis, Borracis ana ℨiij. </s> <s xml:id="echoid-s2153" xml:space="preserve">optime miſtas impoſui crucibulo, quod <lb/>per 3 horas Igni expoſitum validiſſimo, exhibuit modo maſſam ali-<lb/>quam vix cohærentem, quæ minabatur quaſi in ſolidam ſubſtan-<lb/>tiam abire vellet, ſi modo plus fluidi admiſtum fuiſſet: </s> <s xml:id="echoid-s2154" xml:space="preserve">hæc attra-<lb/>hebatur a Magnete adhuc ut ante, imo tota ſubſtantia attraheba-<lb/>tur, æque Minium, Sal, quam Magnes: </s> <s xml:id="echoid-s2155" xml:space="preserve">patebat igitur plus Minii <lb/>addendum eſſe, & </s> <s xml:id="echoid-s2156" xml:space="preserve">quia Arenæ triplo plus Minii eſt addendum, ut <lb/>vitrum inde formetur; </s> <s xml:id="echoid-s2157" xml:space="preserve">addidi quoque maſſæ noſtræ tantundem Mi-<lb/>nii, ut nunc eſſet ejus triplo major copia quam Magnetis, adjecta <lb/>etiam fuit Borracis drachma: </s> <s xml:id="echoid-s2158" xml:space="preserve">hæc maſſa in crucibulo per trihorium <lb/>ſummo Igni commiſſa, abiit in vitrum opacum fuſci coloris, ad-<lb/>modum grave, quod fundi ducique poterat, ut vitrum ſolet; </s> <s xml:id="echoid-s2159" xml:space="preserve">erat-<lb/>que homogeneum ubivis. </s> <s xml:id="echoid-s2160" xml:space="preserve">Adeoque Magnes in vitrum ſic erat mu-<lb/>tatus, ſummamque proinde operationem paſſus, quam unquam po-<lb/>terit: </s> <s xml:id="echoid-s2161" xml:space="preserve">[Cauſtici ſpeculi foco excepto] in qua ſi vim ſuam retinet, <lb/>eam quidem ſemper retinebit.</s> <s xml:id="echoid-s2162" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2163" xml:space="preserve">Hoc vitrum itaque oblatum Verſorio, id æque manifeſto attra-<lb/>xit, quam ante ullam perpeſſam operationem ab Igne: </s> <s xml:id="echoid-s2164" xml:space="preserve">Attraheba-<lb/>tur a Magnete etiam haud aliter, ac ſi verus Magnes fuiſſet quam-<lb/>obrem hoc vitrum in pulverem tritum a Magnete attrahebatur, ut <lb/>inſtar barbæ ipſius polis adhæſerit: </s> <s xml:id="echoid-s2165" xml:space="preserve">Plumbum in vitrum reductum <lb/>& </s> <s xml:id="echoid-s2166" xml:space="preserve">undiquaque ambiens partes Magnetis non ita impediit ejus vires, <lb/>quam quidem parva Salis copia in præcedentibus proceſſibus, quod <lb/>clarius per Experientiam, quam quidem ex ratione intelligitur, ſed <lb/>plurima in Phyſicis ita comparata ſunt.</s> <s xml:id="echoid-s2167" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div48" type="section" level="1" n="48"> <head xml:id="echoid-head56" xml:space="preserve">PROCESSUS DECIMUS.</head> <p> <s xml:id="echoid-s2168" xml:space="preserve">Quum Antimonium ſolet ferè omnia metalla in Igne reddere vo-<lb/>latilia, ea penetrando uſque in intimam medullam, in ſubtiliſſimas <lb/>ſolvendo partes, & </s> <s xml:id="echoid-s2169" xml:space="preserve">ſecum avehendo, tentatum fuit an Antimonium <pb o="90" file="0104" n="104" rhead="DISSERTATIO"/> etiam non aliquid in Magnete operaretur, & </s> <s xml:id="echoid-s2170" xml:space="preserve">volatile ex eo faceret <lb/>id omne, quod poſſet, relinquendo inertem terreſtremque maſſam: <lb/></s> <s xml:id="echoid-s2171" xml:space="preserve">Igitur ſumſi Magnetis & </s> <s xml:id="echoid-s2172" xml:space="preserve">Antimonii in pulverem contuſi ana ℨiij, <lb/>quæ ambo accurate miſta inditaque crucibulo, aperto impoſita ſunt <lb/>Igni carbonum foſſilium in furno Anemitrium horarum ſpatio: </s> <s xml:id="echoid-s2173" xml:space="preserve">maſſæ <lb/>refrigerio commiſſæ deprehendebatur plurimum imminutum pondus <lb/>& </s> <s xml:id="echoid-s2174" xml:space="preserve">copia, ſed erat compacta, valde friabilis, nigreſcens, quæ Ver-<lb/>ſorium movebat, & </s> <s xml:id="echoid-s2175" xml:space="preserve">trita in pulverem a Magnete haud aliter attra-<lb/>hebatur, quam ſi nullum Ignem experta fuiſſet.</s> <s xml:id="echoid-s2176" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2177" xml:space="preserve">2. </s> <s xml:id="echoid-s2178" xml:space="preserve">Manſerat in hac maſſa aliquid Antimonii, quod ulteriori ope-<lb/>ratione expellere volui, quem in finem ſumſi maſſæ prioris ℨiiij, <lb/>Sulphuris vulgaris ℨj. </s> <s xml:id="echoid-s2179" xml:space="preserve">Borracis Veneti ℨij. </s> <s xml:id="echoid-s2180" xml:space="preserve">(per infortunium hunc <lb/>Salem loco Nitri addideram) omniaque bene contuſa & </s> <s xml:id="echoid-s2181" xml:space="preserve">miſta in <lb/>crucibulo commiſi Igni ſummo reverberii, bihorii ſpatio: </s> <s xml:id="echoid-s2182" xml:space="preserve">liquefa-<lb/>cta hoc tempore aliquantum fuit maſſa, quæ fuit unita, ferreæ <lb/>duritiëi, ſpongioſaque: </s> <s xml:id="echoid-s2183" xml:space="preserve">hæc oppoſita Verſorio 6 pollicum, illud <lb/>nunc attrahebat nunc repellebat, quamobrem in hac operatione vis <lb/>ex Magnete non expellebatur.</s> <s xml:id="echoid-s2184" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2185" xml:space="preserve">3. </s> <s xml:id="echoid-s2186" xml:space="preserve">Huic maſſæ iterum redactæ in pulverem addidi Nitri ℨij, <lb/>cum quo igni vehementiſſimo per bihorium rurſus commiſi; </s> <s xml:id="echoid-s2187" xml:space="preserve">ex eo <lb/>rediit maſſa nigra, dura, fragilis, cohærens, ſed valde ſpongioſa <lb/>& </s> <s xml:id="echoid-s2188" xml:space="preserve">poroſa, ac heterogenea: </s> <s xml:id="echoid-s2189" xml:space="preserve">quæ oblata Verſorio, id nihilominus <lb/>manifeſto attraxit, & </s> <s xml:id="echoid-s2190" xml:space="preserve">reducta in pulverem, tamen tota a Magnete <lb/>fortiter attrahebatur, etiamſi paulum forte minus quam ante ope-<lb/>rationem ullam: </s> <s xml:id="echoid-s2191" xml:space="preserve">Quare Antimonium non ſecum abripit ex Magnete <lb/>partem, in qua vis attractrix reſidet, licet ejus aliquam exiguam <lb/>portionem volatilem reddat.</s> <s xml:id="echoid-s2192" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div49" type="section" level="1" n="49"> <head xml:id="echoid-head57" xml:space="preserve">PROCESSUS UNDECIMUS.</head> <p> <s xml:id="echoid-s2193" xml:space="preserve">Tandem Magnetem etiam vexandum arbitrabar Salibus Acidis, <lb/>quibus hactenus non uſus fueram, quapropter Magnetis in pulve-<lb/>rem contriti ℨiij. </s> <s xml:id="echoid-s2194" xml:space="preserve">immiſi phialæ vitreæ alti colli, ſuperaffudi Spiri-<lb/>tum Salis marini ad exceſſum duorum digitorum; </s> <s xml:id="echoid-s2195" xml:space="preserve">magna oborta fuit <lb/>efferveſcentia, ex qua fumi aſſurgebant fætentes, magnæ in phiala <lb/>excitabantur bullæ, haud aliter ac ſi limaturæ ferri hic Spiritus in- <pb o="91" file="0105" n="105" rhead="DE MAGNETE."/> jectus fuiſſet; </s> <s xml:id="echoid-s2196" xml:space="preserve">ſedatus fuit elapſo aliquo tempore hic tumultus, <lb/>tum digeſta materia octo diebus, dedit Tincturam intenſe flavam, <lb/>in qua totus Magnes ſolutus continebatur, abſque ullis fere fæci-<lb/>bus; </s> <s xml:id="echoid-s2197" xml:space="preserve">hæc Tinctura non oſtendit ullam actionem in Acum nauti-<lb/>cam.</s> <s xml:id="echoid-s2198" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2199" xml:space="preserve">Nob Boyleus hunc Proceſſum inchoaverat, verum non produxerat <lb/>multum, memorat tamen ſe paucas hujus Tincturæ guttas inje-<lb/>ciſſe infuſo Gallarum, quod abibat in atramentum nigrum, & </s> <s xml:id="echoid-s2200" xml:space="preserve"><lb/>quod diverſimode poſitum apparebat cæruleum inſtar Tincturæ di-<lb/>lutæ Chalybis.</s> <s xml:id="echoid-s2201" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2202" xml:space="preserve">Tincturæ quoque huic Magnetis affudit Salem Tartari, a quo <lb/>præcipitatio fiebat, quæ evadebat ſimilis ſolutioni Vitrioli: </s> <s xml:id="echoid-s2203" xml:space="preserve">Alteri <lb/>parti hujus Tincturæ Magnetis immiſit Spiritum Urinæ fermentatæ, <lb/>cujus ope acquirebat præcipitatum ex flavo rubrum: </s> <s xml:id="echoid-s2204" xml:space="preserve">Verum non <lb/>examinavit magnus Philoſophus quaſnam vires hæc præcipitata <lb/>continebant, & </s> <s xml:id="echoid-s2205" xml:space="preserve">idcirco longe accuratius hæc tentamina inſtituere <lb/>tenebar.</s> <s xml:id="echoid-s2206" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2207" xml:space="preserve">2. </s> <s xml:id="echoid-s2208" xml:space="preserve">Ex Tincturâ immiſſa retortæ, lento Igne elicui omnem Spi-<lb/>ritum Salis Marini, donec remanebat materia perfecte ſicca, in qua <lb/>operatione obſervavi Magnetem fuiſſe ſemivolatilem factum in fo-<lb/>lutione Spiritus Salis, non enim in fundo retortæ hæſit materia <lb/>ſicca, ſed ad ſuperiorem ejus partem & </s> <s xml:id="echoid-s2209" xml:space="preserve">in collum uſque adſcen-<lb/>derat: </s> <s xml:id="echoid-s2210" xml:space="preserve">erat quoque duplicis coloris, purpureo donabatur pars in-<lb/>fima, luteo ſuprema, ſed hic a Spiritu ſalis imprimis relictus vi-<lb/>debatur.</s> <s xml:id="echoid-s2211" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2212" xml:space="preserve">3. </s> <s xml:id="echoid-s2213" xml:space="preserve">Fracta retorta ſeparatim collegi utramque materiam: </s> <s xml:id="echoid-s2214" xml:space="preserve">Neutra <lb/>ullomodo attrahebatur a Magnete, aut Verſorium nauticum com-<lb/>movebat. </s> <s xml:id="echoid-s2215" xml:space="preserve">Utraque erat in aëre aperto impatiens ſiccitatis: </s> <s xml:id="echoid-s2216" xml:space="preserve">Ecce <lb/>igitur iterum vis Magnetica ad ſilentium reducta; </s> <s xml:id="echoid-s2217" xml:space="preserve">prima fronte <lb/>credebam vim fore deſtructam, neque redituram in has partes, <lb/>quæ tamen poſtea reverſa fuit, ut in ſequentibus patebit.</s> <s xml:id="echoid-s2218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2219" xml:space="preserve">4. </s> <s xml:id="echoid-s2220" xml:space="preserve">Maſſam utramque permiſcui, phialæque immiſſæ affudi aquam, <lb/>cum qua digeſſi per biduum, prodibat Tinctura intenſe flava, ſa-<lb/>poris acidi & </s> <s xml:id="echoid-s2221" xml:space="preserve">adſtringentis, atque ad fundum ſubſedit pulvis ni-<lb/>gricans: </s> <s xml:id="echoid-s2222" xml:space="preserve">effudi Tincturam, & </s> <s xml:id="echoid-s2223" xml:space="preserve">reſiduo novam adjeci aquam puram, <lb/>quâcum iterum illud digeſſi, ſimilemque priori acquiſivi Tinctu- <pb o="92" file="0106" n="106" rhead="DISSERTATIO"/> ram, quâ effuſâ, rurſuſque reſiduo aquâ, additâ, Tincturamque no-<lb/>vam elicui, id repetens, quamdiu Tinctura oriebatur.</s> <s xml:id="echoid-s2224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2225" xml:space="preserve">5. </s> <s xml:id="echoid-s2226" xml:space="preserve">Omnes Tincturæ in vaſe commiſtæ per triduum, acquire-<lb/>bant in ſuperficie pelliculam, quæ cryſtallorum eſt ſpecies, conſta-<lb/>batque ex fibris rectiſſimis, tenuibus, ſibique perfecté parallelis: <lb/></s> <s xml:id="echoid-s2227" xml:space="preserve">interim ſubſedit pulvis flaveſcens ad fundum vaſis, quem collegi, <lb/>lente & </s> <s xml:id="echoid-s2228" xml:space="preserve">caute prius educta aqua: </s> <s xml:id="echoid-s2229" xml:space="preserve">pulvis hic exſiccatus erat flavi <lb/>coloris, ſaporis ſalſi, acidi, ſed valde adſtringentis, qui nequa-<lb/>quam a Magnete attrahebatur.</s> <s xml:id="echoid-s2230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2231" xml:space="preserve">6. </s> <s xml:id="echoid-s2232" xml:space="preserve">Alter pulvis nigreſcens, qui poſt digeſtionem & </s> <s xml:id="echoid-s2233" xml:space="preserve">ablutionem <lb/>cum aqua ſubſederat in §. </s> <s xml:id="echoid-s2234" xml:space="preserve">4, exſiccatus leniter, nullomodo ab ar-<lb/>mato Magnete attrahebatur: </s> <s xml:id="echoid-s2235" xml:space="preserve">Hunc itaque in crucibulo per bihorium <lb/>Igni fortiſſimo reverberii commiſi, frigefactus colorem nigrum ha-<lb/>bebat, ſed continebat parva fruſta duriſſima, quæ in Igne coalue-<lb/>rant, quaſi metallum continerent; </s> <s xml:id="echoid-s2236" xml:space="preserve">Totus hic pulvis a Magnete ite-<lb/>rum attrahebatur, apparebat tamen vis in initio minor, quam pul-<lb/>veris Magnetici ante actionem ullam Ignis.</s> <s xml:id="echoid-s2237" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2238" xml:space="preserve">Ecce Magnetem perfecte ſolubilem in menſtruo; </s> <s xml:id="echoid-s2239" xml:space="preserve">in quodigitur ve-<lb/>hementer operatur ſua viattrahente, cum omnis ſolutio corporum in <lb/>menſtruo ab ejuſmodi vi, reciproca inter hæc ambo, dependeat: </s> <s xml:id="echoid-s2240" xml:space="preserve">unde <lb/>mirum non eſt, vim Magneticam non apparere in alia corpora, quam-<lb/>diu menſtruum adeſt, quod in Magnetis partes tam vehementer ope-<lb/>ratur: </s> <s xml:id="echoid-s2241" xml:space="preserve">Verum menſtruo expulſo redeunt in conſpectum Vires, præ-<lb/>cipue altero Magnete appoſito.</s> <s xml:id="echoid-s2242" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div50" type="section" level="1" n="50"> <head xml:id="echoid-head58" xml:space="preserve">PROCESSUS DUODECIMUS.</head> <p> <s xml:id="echoid-s2243" xml:space="preserve">Sumſi Spiritum Nitri more Glauberiano confectum ad ℥iij, cui <lb/>in Phiala alta immiſi ℨiij. </s> <s xml:id="echoid-s2244" xml:space="preserve">Magnetis in pulverem comminuti, vix <lb/>efferveſcentia oborta fuit; </s> <s xml:id="echoid-s2245" xml:space="preserve">digeſſi hæc ſpatio 16 dierum, eliciebatur <lb/>Tinctura, perfecte pellucida, ſpiſſa tamen, coloris ex viri-<lb/>diuſculo flaveſcentis; </s> <s xml:id="echoid-s2246" xml:space="preserve">remanente in fundo phialæ pulvere non ſo-<lb/>luto.</s> <s xml:id="echoid-s2247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2248" xml:space="preserve">2. </s> <s xml:id="echoid-s2249" xml:space="preserve">Tincturam leniter effudi, pulveremque reſiduum & </s> <s xml:id="echoid-s2250" xml:space="preserve">non ſo-<lb/>lutum exſiccavi; </s> <s xml:id="echoid-s2251" xml:space="preserve">qui deinde oppoſitus polo Magnetis præſtantiſſimi, <lb/>hinc inde parte aliqua ſimulabat, quaſi vellet attrahi, attamen non <pb o="93" file="0107" n="107" rhead="DE MAGNETE."/> attrahebatur, niſi in immediato contactu: </s> <s xml:id="echoid-s2252" xml:space="preserve">adeo ut vis Magnetica fere <lb/>penitus in hoc reſiduo pulvere ſileat, quod ſequenti operatione <lb/>exploravi.</s> <s xml:id="echoid-s2253" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2254" xml:space="preserve">3. </s> <s xml:id="echoid-s2255" xml:space="preserve">Hunc pulverem in crucibulo commiſi Igni in furno Anemi per <lb/>horam unam, evaſit pulvis rubicundus, lætioris ruboris, quam <lb/>creta rubra eſſe ſolet; </s> <s xml:id="echoid-s2256" xml:space="preserve">hic oppoſitus Verſorio 6 pollicum, id nequa-<lb/>quam attraxit, aut movit, nec ullomodo â polo Magnetis for-<lb/>tiſſimi attractus, vel tantillum motus fuit.</s> <s xml:id="echoid-s2257" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2258" xml:space="preserve">Hæc igitur fuit Terra iners Magnetis, in qua nulla virtus ſuper-<lb/>ſtes erat; </s> <s xml:id="echoid-s2259" xml:space="preserve">hanc Spiritus Nitri proinde non ſolvit, ſed modo illud <lb/>ex Magnete elicit, quod virtutem habet.</s> <s xml:id="echoid-s2260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2261" xml:space="preserve">4. </s> <s xml:id="echoid-s2262" xml:space="preserve">Idcirco Tincturam exſiccavi, quæ præbuit plurimum ſubſtan-<lb/>tiæ rubræ inſtar Colcotar vitrioli: </s> <s xml:id="echoid-s2263" xml:space="preserve">hæc in pulverem redacta non <lb/>attrahebatur a Magnete, quod mirabar primum, opinatus vim Ma-<lb/>gneticam penitus eſſe in hac operatione deſtructam; </s> <s xml:id="echoid-s2264" xml:space="preserve">ſed judicium <lb/>ſuſpendebam detegens ex ſapore, pulverem abundare Sale acido in <lb/>evaporatione relicto & </s> <s xml:id="echoid-s2265" xml:space="preserve">qui eaſdem fabulas cum reliquis Salibus agere <lb/>poſſet: </s> <s xml:id="echoid-s2266" xml:space="preserve">idcirco pulverem in crucibulo expoſui igni fortiſſimo rever-<lb/>berii per bihorium, & </s> <s xml:id="echoid-s2267" xml:space="preserve">recepi pulverem, copiâ vix imminutum, co-<lb/>loris fulvi, inſipidum, qui vehementiſſime â Magnete attrahebatur, <lb/>fere tam fortiter, quam limatura Ferri, quæ fortius â Magnete attra-<lb/>hitur, quam Magnes in pulverem minutus: </s> <s xml:id="echoid-s2268" xml:space="preserve">Vere igitur dixerim me <lb/>hoc modo ſeparaſſe ex Magnete partem aliquam intertem ex eâ, quæ <lb/>virtute pollet; </s> <s xml:id="echoid-s2269" xml:space="preserve">ſed hæc pars non niſi mera eſſe terra videbatur, quam <lb/>aliis viis forte immutare, forte non poſſem; </s> <s xml:id="echoid-s2270" xml:space="preserve">Sublimavi eam <lb/>quidem cum Sale Ammonico, qui penitus volatilis eſt factus ipſa <lb/>manente fixa, & </s> <s xml:id="echoid-s2271" xml:space="preserve">coloris multo obſcurioris, quam antea fuerat, Sal <lb/>nihil ex ipſa reddidit volatile: </s> <s xml:id="echoid-s2272" xml:space="preserve">poſtea materiam Magneticam lavi atque <lb/>edulcoravi aqua, ut ſi quid Salis a prioribus operationibus relictum <lb/>fuiſſet, id omne omnino tolleretur, pulvis exſiccatus colorem re-<lb/>ferebat obſcurum, qui a Magnete in initio parum attrahebatur, <lb/>ſed qui cum ſemel vim Magnetis leniter ſupraducti ſubolfecerat, <lb/>vehementiſſime omnium pulverum attractus fuit, atque ad notabi-<lb/>lem a Magnete diſtantiam elevabatur: </s> <s xml:id="echoid-s2273" xml:space="preserve">Si hujus examini plus incum-<lb/>beremus, forſitan aliquid, quod labores penſaret, invenerimus; <lb/></s> <s xml:id="echoid-s2274" xml:space="preserve">nunquam enim ars Analytica ingrata fuit cultoribus, ſed inſperata <pb o="94" file="0108" n="108" rhead="DISSERTATIO"/> detegens, opimos ſemper dedit fructus tam fortunæ quam famæ, <lb/>atque admirandis productis omne tædium, ab improbo ortum labore, <lb/>ex animo delevit.</s> <s xml:id="echoid-s2275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2276" xml:space="preserve">Sufficiat ex his omnibus operationibus didiciſſe, Magnetem quo-<lb/>modocunque tractatum manere Magnetem, neque vi Ignis, vel <lb/>Menſtruorum ſolventium, vel Salium ita deſtrui, ut vim penitus amit-<lb/>tat nunquam recuperandam, cum in omnibus deſcriptis proceſſibus <lb/>ſemper eamdem retinuerit: </s> <s xml:id="echoid-s2277" xml:space="preserve">Sed a Sale compedibus quaſi vincieba-<lb/>tur. </s> <s xml:id="echoid-s2278" xml:space="preserve">Alias inſtitui præterea operationes cum Magnete, ſed quæ pa-<lb/>rum mihi ſatis faciebant; </s> <s xml:id="echoid-s2279" xml:space="preserve">ita eam ſolvi in oleo vitrioli poſt digeſtio-<lb/>nem 16 dierum, quod oleum abiit in lapillum durum, qui in aqua <lb/>ſolutus, præcipitem dabat pulverem gryſei coloris, ſalſum, ſed a <lb/>Magnete fortiter attractum, qui in Igne rotæ per bihorium poſitus <lb/>in pulverem rubrum abiit, æque ac antea vi gaudentem Magne-<lb/>tica.</s> <s xml:id="echoid-s2280" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2281" xml:space="preserve">Nob. </s> <s xml:id="echoid-s2282" xml:space="preserve">Boyleus Magnetem diſſolvit in aquâ regiâ, obtinuitque ſo-<lb/>lutionem, qualis ab Auro puro fiëri ſolet: </s> <s xml:id="echoid-s2283" xml:space="preserve">poſſet hoc corpus di-<lb/>verſiſſimis adhuc tractari aliis modis, & </s> <s xml:id="echoid-s2284" xml:space="preserve">procul dubio varia daret <lb/>pulcra producta, quæ ſua utilitate ſe commendarent, ſed hæc tem-<lb/>pori committenda, nobis ſufficit aliqua tentaſſe, & </s> <s xml:id="echoid-s2285" xml:space="preserve">aliquem pro-<lb/>greſſum, etiamſi exiguum, in hac materia feciſſe.</s> <s xml:id="echoid-s2286" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2287" xml:space="preserve">Sed redeamus in viam, ad alios properemus effectus, quos Ma-<lb/>gnes in Ferrum edit, quorum licet cauſam ignoremus, nihilominus <lb/>plurimum ad clariorem Lapidis cognitionem conferent, nonnullos <lb/>ex comparatis cum aliis exponere licebit, alios tantummodo me-<lb/>morare, quorum non prius, quam virium Magneticarum eruta erit <lb/>cauſa, explicari & </s> <s xml:id="echoid-s2288" xml:space="preserve">intelligi poterunt: </s> <s xml:id="echoid-s2289" xml:space="preserve">hæſitavi aliquamdiu, an ſe-<lb/>quentia adnecterem prioribus Experimenta, quia maxima parte <lb/>aliorum ſunt, nec magnam redolent ſubtilitatem, & </s> <s xml:id="echoid-s2290" xml:space="preserve">modo inſtar <lb/>collectionis indigeſtæ haberi poſſunt: </s> <s xml:id="echoid-s2291" xml:space="preserve">Verum quia ex proprietatibus <lb/>rerum, earum indoles eruitur, etiam ex Experimentis Magneticis <lb/>cauſa virtutis attractricis indaganda erit, nunquam idcirco multa <lb/>reſpuenda erunt data, in quibus omnis ſpes ſolvendi problema con-<lb/>cipienda eſt; </s> <s xml:id="echoid-s2292" xml:space="preserve">quod quo abſtruſius fuerit, eo plura poſtulat cogni-<lb/>ta, ut ſolvatur & </s> <s xml:id="echoid-s2293" xml:space="preserve">intelligatur, Sylvam idcirco Experimentorum <lb/>conſivimus, quæ etiamſi nunc parvi, poſtea majoris uſus videbun- <pb o="95" file="0109" n="109" rhead="DE MAGNETE"/> tur, meliorique ordine diſponi poterunt, nam nunc modo <lb/>Hoc genus in rebus firmandum eſt, multa priuſquam <lb/>Ipſius rei rationem reddere poſſis: <lb/></s> <s xml:id="echoid-s2294" xml:space="preserve">Et nimium longis ambagibus eſt adeundum. </s> <s xml:id="echoid-s2295" xml:space="preserve"><lb/>teſtante Lucretio Lib. </s> <s xml:id="echoid-s2296" xml:space="preserve">6. </s> <s xml:id="echoid-s2297" xml:space="preserve">dolendum vero eſt plurima ab autoribus, <lb/>qui de Magnete egerunt, commemorari, quæ dubiæ ſunt fidei, <lb/>ſaltem quæ noſtra ætate, hac in regione, noſtrisque in Magneti-<lb/>bus nequaquam deprehenduntur, quia non cum ſufficienti cura ob-<lb/>fervationes inſtituerunt Philoſophi; </s> <s xml:id="echoid-s2298" xml:space="preserve">aut quædam audita, & </s> <s xml:id="echoid-s2299" xml:space="preserve">male <lb/>intellecta, ſuis inſeruerunt ſcriptis, quod etiam conqueſtus fuit <lb/>quondam Cabbeus in præfatione Philofophiæ Magneticæ præfixa: </s> <s xml:id="echoid-s2300" xml:space="preserve"><lb/>Certius ſcio, inquit, multos ſcriptores, etiam non infimæ notæ, <lb/>ſpecioſa quædam de Magnete commenta ex aliis tranſcripſiſſe, quæ <lb/>re ipſa vera non ſunt, ſi Experimenti ſubeant examen. </s> <s xml:id="echoid-s2301" xml:space="preserve">Non ta-<lb/>men erroris illico accuſare aliquem licet, qui obſervationem mul-<lb/>tum a noſtra diſcrepantem adnotavit: </s> <s xml:id="echoid-s2302" xml:space="preserve">Experientiâ enim frequenti <lb/>didici, quantum interſe differant phænomena Magnetica variis anni <lb/>temporibus, aut quæ eodem die cum diverſis Magnetibus excitan-<lb/>tur & </s> <s xml:id="echoid-s2303" xml:space="preserve">obſervantur: </s> <s xml:id="echoid-s2304" xml:space="preserve">Verum multa ex cerebello protruſerunt ficta ex-<lb/>perimenta Philoſophi, ut hypotheſin, ſemel ſtabilitam, tuerentur, <lb/>vel melioribus quaſi confirmarent argumentis, aut in Experimentis <lb/>ea, quæ hypotheſi favebant, viderunt, omiſſis aliis, quæ ſimul <lb/>concurrebant: </s> <s xml:id="echoid-s2305" xml:space="preserve">tantâ enim abripiuntur plurimi mortales philautiâ, <lb/>ut modo videant, quæ videre volunt, quæ præjudiciis conveniunt, <lb/>in reliquis cæcutiant.</s> <s xml:id="echoid-s2306" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2307" xml:space="preserve">Ut igitur fabulas & </s> <s xml:id="echoid-s2308" xml:space="preserve">figmenta a veritate ſegregarem, omnia re-<lb/>petenda erant, & </s> <s xml:id="echoid-s2309" xml:space="preserve">ad novum examen vocanda Experimenta, quæ un-<lb/>quam ab Autoribus memoriæ ſunt prodita; </s> <s xml:id="echoid-s2310" xml:space="preserve">quo modo nonnun-<lb/>quam errorum cauſam detexi, haud raro ortam, quod concluſio <lb/>univerſalis ex particulari obſervatione deducta eſt, ſæpe inter ex-<lb/>plorandum in nova incidi tentamina, eaque, quæ alii inchoave-<lb/>runt, ulterius produxi; </s> <s xml:id="echoid-s2311" xml:space="preserve">quidnam actum fuerit ex ipſis tentamini-<lb/>bus intelligetur.</s> <s xml:id="echoid-s2312" xml:space="preserve"/> </p> <pb o="96" file="0110" n="110" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div51" type="section" level="1" n="51"> <head xml:id="echoid-head59" xml:space="preserve">EXPERIMENTUM XXXI.</head> <p> <s xml:id="echoid-s2313" xml:space="preserve">Communis eſt ſententia, Ferrum ſuper polo Magnetis ductum vi-<lb/>ribus attrahentibus imprægnari, eam tamen obſervatione oppoſita <lb/>dubiam olim reddidit Cl. </s> <s xml:id="echoid-s2314" xml:space="preserve">de La Hire in L’Hiſt. </s> <s xml:id="echoid-s2315" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s2316" xml:space="preserve">Roy. <lb/></s> <s xml:id="echoid-s2317" xml:space="preserve">A°. </s> <s xml:id="echoid-s2318" xml:space="preserve">1692. </s> <s xml:id="echoid-s2319" xml:space="preserve">Quum virgæ ferreæ, 6 pollices longæ, 4 lineas craſſæ, <lb/>præſtantem Magnetem aliquoties applicatum nullas attrahendi vires <lb/>communicaſſe memorat, etiamſi virgis tenuioribus quamplurimum <lb/>virtutis impertiretur, quamobrem determinatæ craſſitiei deſidera-<lb/>retur Ferrum, quod a Magnete vim recipere poſſet, nequaquam <lb/>ad id conducente Ferro admodum craſſo: </s> <s xml:id="echoid-s2320" xml:space="preserve">examine dignum viſum <lb/>fuit hoc Experimentum, ut inde cognoſceretur, quomodo Magnes <lb/>cum Ferro vires ſuas communicat: </s> <s xml:id="echoid-s2321" xml:space="preserve">Parallelopipedum ferreum, 6 <lb/>longum pollices, unum latum altumque; </s> <s xml:id="echoid-s2322" xml:space="preserve">ſuper Magnetis, (cujus <lb/>pondus erat 1 {1/4} libræ, & </s> <s xml:id="echoid-s2323" xml:space="preserve">tanta vis, ut ex armatura 7 Librarum ge-<lb/>ſtaret) polo aliquoties juxta longitudinem ductum fuit, hujus pla-<lb/>næ extremitati, æque ac marginibus & </s> <s xml:id="echoid-s2324" xml:space="preserve">angulis adhærebat pulvis <lb/>Indicus, & </s> <s xml:id="echoid-s2325" xml:space="preserve">ſcobs ferrea attracta, ab angulo aut margine Acus te-<lb/>nuiſſima, vix {3/4} ponderis grani, parumper attrahebatur, non tamen <lb/>tota geſtari potuit; </s> <s xml:id="echoid-s2326" xml:space="preserve">quamobrem hoc Ferrum vi Magnetica, licet exi-<lb/>gua, imprægnatum fuiſſe, liquido conſtabat: </s> <s xml:id="echoid-s2327" xml:space="preserve">deinde exploratum <lb/>fuit, an eadem moles ferrea majores acquireret tempore longiori <lb/>ab eodem Magnete vires, hæc applicata ideo diei ſpatio Lapidi man-<lb/>ſit, tum iterum pulveri Indico immiſſa, Acui chalybeæ tenui ap-<lb/>poſita, eaſdem, non majores, attractrices vires oſtendit, quas <lb/>nec auxerunt repetiti eidem Magnetis polo affrictus.</s> <s xml:id="echoid-s2328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2329" xml:space="preserve">2°. </s> <s xml:id="echoid-s2330" xml:space="preserve">Tres fuerunt præparati cylindri ferrei, æque longi, ſinguli <lb/>4 pollicum & </s> <s xml:id="echoid-s2331" xml:space="preserve">unius lineæ: </s> <s xml:id="echoid-s2332" xml:space="preserve">extremitate una plana & </s> <s xml:id="echoid-s2333" xml:space="preserve">circulari ter-<lb/>minabantur, altera conica; </s> <s xml:id="echoid-s2334" xml:space="preserve">fuerunt omnium conorum altitudines <lb/>{2/10} pollicis: </s> <s xml:id="echoid-s2335" xml:space="preserve">diameter craſſiſſimi cylindri fuit {50/100} pollic. </s> <s xml:id="echoid-s2336" xml:space="preserve">cylindro <lb/>hoc ſecundum totam longitudinem aliquoties ſuper Magnetis polo <lb/>ducto, tum perpendiculariter ſuſpenſo ad horizontem, baſi circu-<lb/>lari deorſum ſpectante, appoſita fuit Acus chalybea nova, graviſſi-<lb/>ma, quæ elevari poterat, quod variis explorabatur tentaminibus, <lb/>tum vix ex circulari ſuperficie ſuſtenta fuit Acus tenuiſſima, non- <pb o="97" file="0111" n="111" rhead="DE MAGNETE."/> dum ponderis grani unius: </s> <s xml:id="echoid-s2337" xml:space="preserve">inverſi deinde cylindri apici conico etiam <lb/>apponebatur Acus chalybea, graviſfima fuit ponderis 1 {9/10} grani, <lb/>quæ geſtari potuit.</s> <s xml:id="echoid-s2338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2339" xml:space="preserve">Diameter ſecundi cylindri fuit {36/100} pollicis, qui etiam ſecundum <lb/>longitudinem ſuper eodem Magnetis polo ductus fuit, ex illius ex-<lb/>tremo circulari etiam tantum Acus, gravitate grani unius, appendi <lb/>potuit, ſed ab omni puncto ſuperficiei circularis attracta ſuſpende-<lb/>batur: </s> <s xml:id="echoid-s2340" xml:space="preserve">Verum inverſo hoc cylindro, ex coni apice deorſum ſpe-<lb/>ctante ſuſpendi potuerunt aliquot Acus, quarum omnium pondus <lb/>fuit 7 {1/2} granorum.</s> <s xml:id="echoid-s2341" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2342" xml:space="preserve">Tertii cylindri Diameter fuit {12/100} pollicis, ex cujus extremo cir-<lb/>culari ſuſpendi etiam modo potuit Acus Chalybea ponderis unius <lb/>grani; </s> <s xml:id="echoid-s2343" xml:space="preserve">verum ab apice conico plurimæ gerebantur Acus, quarum <lb/>omnium ſibi adhærentium pondus erat 8 granorum.</s> <s xml:id="echoid-s2344" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2345" xml:space="preserve">Ex quatuor his tentaminibus ſequitur, quo Ferrum eſt craſſius, <lb/>eo minori viâ Magnete eodem imprægnari, tenuiſſimum enim plu-<lb/>rimam virtutem, quia maximum onus geſtabat, recepit: </s> <s xml:id="echoid-s2346" xml:space="preserve">An tamen <lb/>Ferrum, quo plus attenuatum, fed ejuſdem longitudinis, ſemper <lb/>eo majori vi Magnetica imprægnabitur? </s> <s xml:id="echoid-s2347" xml:space="preserve">hoc etiam exploratum fuit, <lb/>eventu tamen probante determinatam poſtulari Ferri craſſitiem, quæ <lb/>maximum pondus attrahat, aliam vero omnem minorem etiam exi-<lb/>liori gaudere virtute.</s> <s xml:id="echoid-s2348" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2349" xml:space="preserve">Cylindrus enim tenuior, Diametri {12/100} pol. </s> <s xml:id="echoid-s2350" xml:space="preserve">ejuſdemque cum priori-<lb/>bus longitudinis, tantummodo ex apice conico pondus ferreum 4 <lb/>granorum geſtavit: </s> <s xml:id="echoid-s2351" xml:space="preserve">& </s> <s xml:id="echoid-s2352" xml:space="preserve">fila tenuiora ferrea ſuper eodem deducta Ma-<lb/>gnetis polo, iterum pondera ferrea leviora tantum attraxerunt: <lb/></s> <s xml:id="echoid-s2353" xml:space="preserve">quare datur craſſities Ferri, quæ a polo dati Magnetis, maxima vi <lb/>attractrice induitur, aliaque omnia ferramenta, craſſiora vel te-<lb/>nuiora minorem vim ab eodem Magnete recipiunt.</s> <s xml:id="echoid-s2354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2355" xml:space="preserve">Extremitates autem conicæ cylindrorum videntur ad apicem ob-<lb/>tuſum condenſare aut colligere vim Magneticam, quia ex hiſce api-<lb/>cibus pondus ferreum multo gravius, quam ex plano extremo cir-<lb/>culari geſtatum fuit: </s> <s xml:id="echoid-s2356" xml:space="preserve">Cylindros deſcriptos eum in finem præparave-<lb/>ram, ut detegerem an inter craſſities, longitudines, & </s> <s xml:id="echoid-s2357" xml:space="preserve">vires a Ma-<lb/>gnete cum ipſis communicatas quædam proportio daretur, ſed mihi <lb/>ipſi in hiſce Experimentis non ſatisfeci, neſciens utrum majori dexte- <pb o="98" file="0112" n="112" rhead="DISSERTATIO"/> ritate aliisque auxiliis non plus Ferri conorum apicibus applicari po-<lb/>tuiſſet, præterea ab apicum figura varia oritur magna inter vires at-<lb/>trahentes differentia, atque hic quid aliud latet ſubtile, quod ma-<lb/>jori labore eruendum erit poſtea.</s> <s xml:id="echoid-s2358" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2359" xml:space="preserve">Nunc videamus quantum variet virium Magneticarum communi-<lb/>catio poſito alterius figuræ ferro; </s> <s xml:id="echoid-s2360" xml:space="preserve">parallelopipeda ſequentibus inſer-<lb/>vierunt Experimentis, quorum omnium longitudo erat 4 pollicum.</s> <s xml:id="echoid-s2361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2362" xml:space="preserve">3. </s> <s xml:id="echoid-s2363" xml:space="preserve">Parallelopipedi primi latitudo erat {48/100} pollicis, altitudo {18/100} poll. <lb/></s> <s xml:id="echoid-s2364" xml:space="preserve">in quo, lentè & </s> <s xml:id="echoid-s2365" xml:space="preserve">aliquoties ſupra eundem polum Magnetis ducto ſe-<lb/>cundum longitudinem, ita ut latitudine ſua Magnetem attigerit, <lb/>vis tanta attractrix obſervata fuit, ut ab extremitate plana ſuſpendi <lb/>potuerit onus 25 granorum: </s> <s xml:id="echoid-s2366" xml:space="preserve">Deinde idem parallelopipedum eidem <lb/>polo Magnetis appoſitum, eadem directione Lapidi affrictum fuit <lb/>aliquoties, ſed altitudine Magnetem contingente, tum ex eadem <lb/>extremitate ſuſpenſum fuit pondus ferreum 35 granorum; </s> <s xml:id="echoid-s2367" xml:space="preserve">adeo ut <lb/>cum eodem ferro diverſa vis attractrix communicetur a Magnete, <lb/>prout hic varium ferri latus attigerit.</s> <s xml:id="echoid-s2368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2369" xml:space="preserve">Secundi parallelopipedi latitudo fuit {39/100} pollic. </s> <s xml:id="echoid-s2370" xml:space="preserve">altitudo {13/100} poll. <lb/></s> <s xml:id="echoid-s2371" xml:space="preserve">quod ſecundum longitudinem ſuper eodem polo Magnetis ductum, <lb/>ita ut ſua latitudine Lapidem attigerit, ad extremam planamque ſu-<lb/>perficiem geſtare potuit pondus 145 granorum: </s> <s xml:id="echoid-s2372" xml:space="preserve">Deinde eadem di-<lb/>rectione ſuper eodem polo Magnetis latum, ut altitudine lapidem <lb/>attigerit, ex extremo eodem geſtavit modo 64 grana.</s> <s xml:id="echoid-s2373" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2374" xml:space="preserve">Tertii parallelopipedi latitudo fuit {25/100} poll. </s> <s xml:id="echoid-s2375" xml:space="preserve">altitudo {5/100} poll. </s> <s xml:id="echoid-s2376" xml:space="preserve">quod <lb/>latitudine ſua Magnetem attingens, ſuper eodem ejus polo ductum, <lb/>tandem ab extremitate geſtavit 267 grana: </s> <s xml:id="echoid-s2377" xml:space="preserve">Verum poſtea ſecundum <lb/>altitudinem ductum, eâque attingens lapidem, modo attrahere potuit <lb/>grana 57.</s> <s xml:id="echoid-s2378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2379" xml:space="preserve">Corol. </s> <s xml:id="echoid-s2380" xml:space="preserve">1. </s> <s xml:id="echoid-s2381" xml:space="preserve">Ex hiſce liquet Experimentis Ferrum oblongum & </s> <s xml:id="echoid-s2382" xml:space="preserve">pla-<lb/>num ab eodem polo Magnetis majoribus viribus donari, quam cy-<lb/>lindricum: </s> <s xml:id="echoid-s2383" xml:space="preserve">vires fuiſſe cum parallelopipedis majores communicatas <lb/>patet, 1°. </s> <s xml:id="echoid-s2384" xml:space="preserve">quia primum geſtavit ab extremo ſuo 25 grana: </s> <s xml:id="echoid-s2385" xml:space="preserve">cylindrus <lb/>autem ſecundus modo grana. </s> <s xml:id="echoid-s2386" xml:space="preserve">7 {1/2}. </s> <s xml:id="echoid-s2387" xml:space="preserve">2°. </s> <s xml:id="echoid-s2388" xml:space="preserve">parallelopipedi extremitas erat ſu-<lb/>perficies plana, nondum deſinens in cuſpidem, cæteroquin plus <lb/>ponderis geſtaſſet, cum cylindrus ex apice tantum potuit ferre gra-<lb/>na 1 {9/10} 3°. </s> <s xml:id="echoid-s2389" xml:space="preserve">pondus parallelopipedi erat gravius eo cylindri, & </s> <s xml:id="echoid-s2390" xml:space="preserve">lati- <pb o="99" file="0113" n="113" rhead="DE MAGNETE."/> tudo major quoque diametro cylindri.</s> <s xml:id="echoid-s2391" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2392" xml:space="preserve">Corol. </s> <s xml:id="echoid-s2393" xml:space="preserve">2. </s> <s xml:id="echoid-s2394" xml:space="preserve">Quanta quoque eſt diſcrepantia virium communicatarum <lb/>cum parallelopipedis, prout latitudine vel altitudine ſua Magnetem at-<lb/>tigerint? </s> <s xml:id="echoid-s2395" xml:space="preserve">Suſpicaremur Ferrum latitudine & </s> <s xml:id="echoid-s2396" xml:space="preserve">altitudine ſimul ſuper <lb/>Magnete ductum majores ablaturum vires, quam ſi modo latitudi-<lb/>ne ſua Magneti affrictum fuiſſet, quod in primo parallelopipedo vi-<lb/>debatur obſervari, ſed in ſecundo & </s> <s xml:id="echoid-s2397" xml:space="preserve">tertio obtinet contrarium, cum <lb/>in iis vires, antea magnæ, imminuantur plurimum, affrictu alti-<lb/>tudinis, ſequente eum latitudinis.</s> <s xml:id="echoid-s2398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2399" xml:space="preserve">Corol. </s> <s xml:id="echoid-s2400" xml:space="preserve">3. </s> <s xml:id="echoid-s2401" xml:space="preserve">Si comparemus vim attractricem in parallelopipedo 6 <lb/>pollices longo, unum pollicem alto latoque, cum iis parallelopipe-<lb/>di primi 4 pollices longo, erunt circiter ut 1 ad 50. </s> <s xml:id="echoid-s2402" xml:space="preserve">attamen ſi ut-<lb/>riuſque craſſitiei habeatur ratio, erit hæc primi Ferri ad alterius ut <lb/>11 {496/864} ad 1. </s> <s xml:id="echoid-s2403" xml:space="preserve">quamobrem ſi vis proportionalis craſſitiei communica-<lb/>retur. </s> <s xml:id="echoid-s2404" xml:space="preserve">geſtanda fuiſſent a parallelopipedo unum pollicem craſſo, 2 <lb/>circiter grana, cum modo {1/4} attracta fuit; </s> <s xml:id="echoid-s2405" xml:space="preserve">datur igitur quædam craſ-<lb/>ſities Ferri in determinata longitudine, quæ viribus ſummis a Ma-<lb/>gnete imprægnatur, ultra quam craſſiora ferramenta, æque ac te-<lb/>nuiora minores vires recipiunt; </s> <s xml:id="echoid-s2406" xml:space="preserve">Nam lamella 4 longa pollices lata <lb/>{25/100} poll. </s> <s xml:id="echoid-s2407" xml:space="preserve">alta {1/100} affricta eidem polo Magnetis, inde abſtulit vires, <lb/>quibus modo 12 grana geſtabat.</s> <s xml:id="echoid-s2408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2409" xml:space="preserve">Incideram, memorata intuitus Experimenta, in ſuſpicionem; <lb/></s> <s xml:id="echoid-s2410" xml:space="preserve">Magnetem vibrationibus tremulis agitari, in his vim conſiſtere, eas <lb/>cum Ferro ſibi applicato communicari, idcirco in hoc obſervari ma-<lb/>jores quam in altero, quia facilius recipiuntur. </s> <s xml:id="echoid-s2411" xml:space="preserve">& </s> <s xml:id="echoid-s2412" xml:space="preserve">melius retinentur: </s> <s xml:id="echoid-s2413" xml:space="preserve"><lb/>Quoniam vero pannus fidibus pulſatis ſonantibuſque applicatus, ex-<lb/>templo tremores ſonoſque ſuffocat, videbatur quoque vibrationes <lb/>Magnetis imminuturus aut deleturus; </s> <s xml:id="echoid-s2414" xml:space="preserve">ſuper polo eodem Magnetis <lb/>triplicato panno obducto parallelopipedum tertium (ejus prioribus <lb/>viribus in Igne expulſis) aliquoties ductum fuit, nihilominus inde <lb/>abſtulit vim attractricem 9 granorum. </s> <s xml:id="echoid-s2415" xml:space="preserve">Deinde pannus duplicatus <lb/>modo obductus fuit polo, idem Ferrum ſupra pannum trajectum vim <lb/>recepit elevandi grana 17. </s> <s xml:id="echoid-s2416" xml:space="preserve">tandem ſimplici obducebatur polus pan-<lb/>no, idemque trajectum ferrum vim habuit geſtandi 47 grana: </s> <s xml:id="echoid-s2417" xml:space="preserve">ex-<lb/>pulſa in Igne vi Magnetica ex ferro, ad intervallum 3 linearum <lb/>a Magnete iterum juxta polum trajectum eſt parallelopipedum, ni- <pb o="100" file="0114" n="114" rhead="DISSERTATIO"/> hilominus vim recepit geſtandi pondus 4 granorum.</s> <s xml:id="echoid-s2418" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2419" xml:space="preserve">Omnia hæc Experimenta clare probaverunt Magnetis vim non in-<lb/>tremore partium conſiſtere, quum communicetur cum Ferro ipſum <lb/>non attingente, aut ducto ſupra pannum tremores ſuſfocaturum; </s> <s xml:id="echoid-s2420" xml:space="preserve">ſed <lb/>ad intervallum a Magnete inſigne fieri virtutis attrahentis commu-<lb/>nicationem; </s> <s xml:id="echoid-s2421" xml:space="preserve">hæc indicant Magnetem medium in Atmoſphæra ſuarum <lb/>virium, quæ ad notabilem diſtantiam diffunduntur, hærere.</s> <s xml:id="echoid-s2422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2423" xml:space="preserve">4. </s> <s xml:id="echoid-s2424" xml:space="preserve">Quoniam Experimenta cum prioribus cylindris aut parallelo-<lb/>pipedis ferreis mihi non ſatisfecerant, confectæ fuerunt 6 laminæ <lb/>rectangulæ, accurate æque craſſæ, quam proxime {1/100} pollic. <lb/></s> <s xml:id="echoid-s2425" xml:space="preserve">erant quoque æque longæ, nempe 4 pollicum, latitudi-<lb/>ne erant 1, 2, 3, 4, 5, 6 linearum: </s> <s xml:id="echoid-s2426" xml:space="preserve">hæ omnes ter ſuper eo-<lb/>dem polo Magnetis cum eadem vi applicatæ, æque celeriter ductæ <lb/>fuerunt, ut æquabiliter vi Magneticâ imprægnarentur: </s> <s xml:id="echoid-s2427" xml:space="preserve">tenuiſſima <lb/>erat prima, quæ modo pondus 1 {1/4} grani ab una ſui extremitate ſu-<lb/>ſpendit.</s> <s xml:id="echoid-s2428" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2429" xml:space="preserve">Altera latitudinis duarum linearum geſtavit 10 {3/8} gran.</s> <s xml:id="echoid-s2430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2431" xml:space="preserve">Tertia latitudinis 3 linearum geſtavit 7 {5/8} gran.</s> <s xml:id="echoid-s2432" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2433" xml:space="preserve">Quarta latitudinis 4 linearum tulit 2 grana.</s> <s xml:id="echoid-s2434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2435" xml:space="preserve">Quinta latitudinis 5 linearum tulit 1 {1/2} gran.</s> <s xml:id="echoid-s2436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2437" xml:space="preserve">Sexta latitudinis 6 linearum tulit 1 {1/10} gran.</s> <s xml:id="echoid-s2438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2439" xml:space="preserve">Quæ Experimenta etiam modo probant id, quod ſuperius innui-<lb/>mus, Ferrum determinatæ latitudinis viribus attrahentibus maximis <lb/>a Magnete imprægnari, alia autem magis minuſve lata ferramenta <lb/>minori vi donari; </s> <s xml:id="echoid-s2440" xml:space="preserve">præterea nulla proportio inter latitudines & </s> <s xml:id="echoid-s2441" xml:space="preserve">vires <lb/>obſervatas datur conſtans.</s> <s xml:id="echoid-s2442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2443" xml:space="preserve">5. </s> <s xml:id="echoid-s2444" xml:space="preserve">Tandem explorandum erat, an Ferrum altero longius majo-<lb/>ribus viribus a Magnete imbueretur. </s> <s xml:id="echoid-s2445" xml:space="preserve">Quamobrem lamina ferrea, <lb/>ejuſdem craſſitiei cum 6 prioribus, 5 lineas lata, pollices 13 {1/4} lon-<lb/>ga ſuper eodem Magnetis polo ter ducta fuit, uti ſuperiores; </s> <s xml:id="echoid-s2446" xml:space="preserve">hæc ab <lb/>extremo geſtavit pondus ferreum 25 granorum: </s> <s xml:id="echoid-s2447" xml:space="preserve">abbreviata ut mo-<lb/>do eſſet 10 pollices longa, iterumque ter ducta ſuper eodem Ma-<lb/>gnetis polo geſtavit 33 grana; </s> <s xml:id="echoid-s2448" xml:space="preserve">cum erat 9 pollicum ſuſtinuit modo <lb/>19 gran. </s> <s xml:id="echoid-s2449" xml:space="preserve">cum erat 8 pollicum geſtavit 17 grana. </s> <s xml:id="echoid-s2450" xml:space="preserve">& </s> <s xml:id="echoid-s2451" xml:space="preserve">4 longa polli-<lb/>ces geſtavit modo 1 {1/2} gran.</s> <s xml:id="echoid-s2452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2453" xml:space="preserve">Ex hoc Experimento etiam conſtat poſito ejuſdem latitudinis & </s> <s xml:id="echoid-s2454" xml:space="preserve">craſ- <pb o="101" file="0115" n="115" rhead="DE MAGNETE."/> ſitiei Ferro, id quod eſt longius majoribus viribus imprægnari breviori, <lb/>attamen modo uſque ad aliquam cum perventum ſit longitudinem, tum <lb/>maximis donari viribus, a qua ſi receſſerit longitudine majori, aut bre-<lb/>vitate, minores a Magnete vires aufert: </s> <s xml:id="echoid-s2455" xml:space="preserve">Sed maxima virium obſerva-<lb/>tur differentia inter longitudinem 10 poll. </s> <s xml:id="echoid-s2456" xml:space="preserve">& </s> <s xml:id="echoid-s2457" xml:space="preserve">4 pollic. </s> <s xml:id="echoid-s2458" xml:space="preserve">hæc enim <lb/>tantum pondus 1 {1/2} grani tulit, altera geſtante 33 grana: </s> <s xml:id="echoid-s2459" xml:space="preserve">non quo-<lb/>que videtur proportio dari inter ferri longitudinem & </s> <s xml:id="echoid-s2460" xml:space="preserve">virium quan-<lb/>titatem.</s> <s xml:id="echoid-s2461" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div52" type="section" level="1" n="52"> <head xml:id="echoid-head60" xml:space="preserve">EXPERIMENTUM XXXII.</head> <p> <s xml:id="echoid-s2462" xml:space="preserve">Lamella Chalybea temperata, 4 pollices longa, {4/10} pollic. </s> <s xml:id="echoid-s2463" xml:space="preserve">lata, <lb/>{1/10} pollic. </s> <s xml:id="echoid-s2464" xml:space="preserve">alta, ſuper polo Magnetis ducta ter, lente & </s> <s xml:id="echoid-s2465" xml:space="preserve">cum de-<lb/>terminata appreſſione, ab extremo ſuo geſtavit pondus ferreum 72 <lb/>granorum: </s> <s xml:id="echoid-s2466" xml:space="preserve">lamella ferrea mollis, accurate ſimilis & </s> <s xml:id="echoid-s2467" xml:space="preserve">æqualis priori <lb/>ſuper eodem polo Magnetis ter ducta quoque, cum eadem appreſ-<lb/>ſione, ab extremo ſuo geſtare tantum potuit ferrum 10 granorum; <lb/></s> <s xml:id="echoid-s2468" xml:space="preserve">repetiti affrictus ad eundem Magnetem non communicaverunt ma-<lb/>jores ferro vires; </s> <s xml:id="echoid-s2469" xml:space="preserve">adeo ut Magnes multo majores vires cum Chaly-<lb/>be communicet quam cum Ferro, & </s> <s xml:id="echoid-s2470" xml:space="preserve">ſecundum hoc Experimentum, <lb/>quidem ſepties Majores; </s> <s xml:id="echoid-s2471" xml:space="preserve">an eadem proportio in aliis corporibus æ-<lb/>qualibus ex Chalybe & </s> <s xml:id="echoid-s2472" xml:space="preserve">Ferro confectis obtineat, non determino. </s> <s xml:id="echoid-s2473" xml:space="preserve"><lb/>Notaverunt plurimi Autores cum Chalybe Magnetem plus virtutis-<lb/>quam cum ferro communicare, ſed eorum nemo proportionem ac-<lb/>curate obſervavit; </s> <s xml:id="echoid-s2474" xml:space="preserve">multum differentiæ procul dubio dabitur, prout <lb/>Chalybs eſt purior impuriorve, & </s> <s xml:id="echoid-s2475" xml:space="preserve">Ferrum hujus alteriuſve indolis, <lb/>ex Sueciæ vel Germaniæ fodinis effoſſum.</s> <s xml:id="echoid-s2476" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div53" type="section" level="1" n="53"> <head xml:id="echoid-head61" xml:space="preserve">EXPERIMENTUM XXXIII.</head> <p> <s xml:id="echoid-s2477" xml:space="preserve">Magnes fortius trahit Ferrum quam Chalybem, & </s> <s xml:id="echoid-s2478" xml:space="preserve">fortius Cha-<lb/>lybem mollem quam temperatum, fortius temperatum, quam qui <lb/>ſummopere induratus eſt.</s> <s xml:id="echoid-s2479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2480" xml:space="preserve">Memini hoc olim Hartſoekerum quoque obſervaſſe, adnotantem, <lb/>ſi Magnes poſſit elevare regulam Chaly beam gravitatis 3 unciarum, <lb/>ipſum tum ad minimum regulam Ferri molliſſimi unciarum quatuor <pb o="102" file="0116" n="116" rhead="DISSERTATIO"/> elevaturum: </s> <s xml:id="echoid-s2481" xml:space="preserve">Dechales contrarium quidem ſtatuit, niſi forte de vi-<lb/>ribus Magnetis, cum Chalybe in majore quantitate communica-<lb/>tis hæc opinatus fuerit, uti in præcedenti Experimento monitum <lb/>fuit.</s> <s xml:id="echoid-s2482" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div54" type="section" level="1" n="54"> <head xml:id="echoid-head62" xml:space="preserve">EXPERIMENTUM XXXIV.</head> <p> <s xml:id="echoid-s2483" xml:space="preserve">Nonnulli Magnetes multo plus virium communicant cum Ferro, <lb/>quam alii: </s> <s xml:id="echoid-s2484" xml:space="preserve">neque illi, qui fortiſſime trahunt magnam Ferri molem, <lb/>aut qui maximi ſunt, ſemper tantum virtutis dant Ferro, quam par-<lb/>vi debileſque.</s> <s xml:id="echoid-s2485" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2486" xml:space="preserve">Hoc diu obſervaverunt omnes fabri Acuum nauticarum, idcirco <lb/>ſemper quærentes Liberales, ut vocant, Magnetes, licet non ma-<lb/>gnam molem Ferri attrahant: </s> <s xml:id="echoid-s2487" xml:space="preserve">Experimentum cepi cum Magnete <lb/>præſtantiſſimo, ſuam virtutem manifeſto ad 14 pedum Rhenolandico-<lb/>rum diſtantiam exſerente, qui ſi bene armatus fuiſſet, forte 50 Li-<lb/>bras & </s> <s xml:id="echoid-s2488" xml:space="preserve">ultra, ferri, geſtaſſet. </s> <s xml:id="echoid-s2489" xml:space="preserve">Hujus polo Boreali lamellæ ferreæ <lb/>affrictæ ſunt, quarum vis, appendendo extremitatibus ponduſcula, <lb/>explorata fuit: </s> <s xml:id="echoid-s2490" xml:space="preserve">his deinde ignitis, ut vi accepta orbarentur, a Ma-<lb/>gnete parvo debilique, qui tantum Libras 4 elevabat, communica-<lb/>ta fuit vis attrahens multo major: </s> <s xml:id="echoid-s2491" xml:space="preserve">inſtituens hoc Experimentum cu-<lb/>ravi, ut ſuper polis cognominibus utriuſque Magnetis Ferrum du-<lb/>ceretur, cum æquali celeritate, eadem appreſſione, & </s> <s xml:id="echoid-s2492" xml:space="preserve">æqualibus <lb/>repetitionibus, cæteroquin nihil accurati concludi potuiſſet: </s> <s xml:id="echoid-s2493" xml:space="preserve">Cl. <lb/></s> <s xml:id="echoid-s2494" xml:space="preserve">Whiſtonus idem confirmat tam ex ſua experientia, quam ex ea <lb/>præſtantis Fatii, & </s> <s xml:id="echoid-s2495" xml:space="preserve">Colonelli Windhami: </s> <s xml:id="echoid-s2496" xml:space="preserve">Sed attendit ad celerita-<lb/>tem vibrationum, quibus eadem Acus oſcillabat affricta diverſis Ma-<lb/>gnetibus; </s> <s xml:id="echoid-s2497" xml:space="preserve">atque ita ſimul adnotavit vim directricem non melius im-<lb/>pertiri Acui a Magnete magno quam ab exiguo: </s> <s xml:id="echoid-s2498" xml:space="preserve">Notandum autem <lb/>plerumque Magnetes fortiores plus virium cum Ferro communicare <lb/>quam debiliores:</s> <s xml:id="echoid-s2499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2500" xml:space="preserve">Ex hoc Experimento videtur ſequi, vires in omnibus Magneti-<lb/>bus non eſſe eodem modo comparatas, has melius a Ferro recipi <lb/>poſſe aliis: </s> <s xml:id="echoid-s2501" xml:space="preserve">Nam probabiliſſimum eſt Magnetem fortiſſimum plures <lb/>vires ex ſe emittere, quam debilem, quomodo enim poſſet alio-<lb/>quin fortiſſimus eſſe, ſive maximam Ferri quantitatem geſtare, niſi <pb o="103" file="0117" n="117" rhead="DE MAGNETE."/> plurimas vires de ſe ſpargeret; </s> <s xml:id="echoid-s2502" xml:space="preserve">hæ tamen a Ferro non recipiuntur <lb/>ſemper in tanta copia, quam quidem illæ, quæ ex Magnete debili <lb/>effluunt, & </s> <s xml:id="echoid-s2503" xml:space="preserve">copia minores ſunt: </s> <s xml:id="echoid-s2504" xml:space="preserve">quare nonnullorum vires magis <lb/>conveniunt cum fabrica partium Ferri, quam aliorum.</s> <s xml:id="echoid-s2505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2506" xml:space="preserve">Datur ita etiam Ferrum, quod a Magnete parum virtutis accipit, <lb/>dum interim aliud Ferrum ab eodem Magnete majori vi donatur.</s> <s xml:id="echoid-s2507" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div55" type="section" level="1" n="55"> <head xml:id="echoid-head63" xml:space="preserve">EXPERIMENTUM. XXXV.</head> <p> <s xml:id="echoid-s2508" xml:space="preserve">Si Ferrum ſubitiſſime ſupra Magnetem ſemel ducatur, aliquantum <lb/>virtutis acquirit, ſi repetatur affrictio ſupra eundem Magnetis lo-<lb/>cum & </s> <s xml:id="echoid-s2509" xml:space="preserve">cum eadem directione, ferrum a Magnete elevando, quando <lb/>ad extremum perductum eſt, augetur vis in Ferro, donec poſt ali-<lb/>quot repetitos affrictus acceperit omnem vim, quam poteſt: </s> <s xml:id="echoid-s2510" xml:space="preserve">poſtea <lb/>enim ſæpius reiterati affrictus ſupra eundem Magnetem, nihil plus <lb/>virium Ferro concedunt.</s> <s xml:id="echoid-s2511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2512" xml:space="preserve">Hoc confirmavit Sturmius in Pbyſic. </s> <s xml:id="echoid-s2513" xml:space="preserve">Elect. </s> <s xml:id="echoid-s2514" xml:space="preserve">Tom. </s> <s xml:id="echoid-s2515" xml:space="preserve">2.</s> <s xml:id="echoid-s2516" xml:space="preserve">pag. </s> <s xml:id="echoid-s2517" xml:space="preserve">1090. <lb/></s> <s xml:id="echoid-s2518" xml:space="preserve">In hoc Experimento Ferrum a Magnete tantum determinatas acqui-<lb/>rit vires non auctas, etiamſi millies Lapidi affricetur, quod non <lb/>evenit, quia pluribus viribus accipiendis foret impar, ſed quoniam <lb/>Magnes ille huic moli majores aut plures tribuere nequit; </s> <s xml:id="echoid-s2519" xml:space="preserve">ſi enim <lb/>hoc Ferrum ſuper liberaliori Magnete ducatur, majorem vim attra-<lb/>hendi acquirit.</s> <s xml:id="echoid-s2520" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2521" xml:space="preserve">Si Ferrum non ductum fuerit ſuper Magnete, ſed tantummodo <lb/>applicatum, tum non niſi elapſis aliquot horis imprægnatur vi Ma-<lb/>gnetica, quemadmodum recte adnotavit Cl. </s> <s xml:id="echoid-s2522" xml:space="preserve">Wolfius, non tamen <lb/>tot vires hoc modo recipit, ac ſi duceretur ſuper Magnete: </s> <s xml:id="echoid-s2523" xml:space="preserve">Quo-<lb/>niam igitur mera Ferri applicatio ad Magnetem, aut velox ſuper eo <lb/>ductus non largitur multum virtutis Ferro, præſtat hoc lente & </s> <s xml:id="echoid-s2524" xml:space="preserve"><lb/>cum valida appreſſione Magnetis polo attriviſſe.</s> <s xml:id="echoid-s2525" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div56" type="section" level="1" n="56"> <head xml:id="echoid-head64" xml:space="preserve">EXPERIMENTUM. XXXVI.</head> <p> <s xml:id="echoid-s2526" xml:space="preserve">Si Ferrum affrictum forti liberalique Magneti vim magnam acce-<lb/>perit elevandi aliud Ferrum; </s> <s xml:id="echoid-s2527" xml:space="preserve">tum rurſus ducatur ſuper polo Magne-<lb/>tis debiliorum virium, plurimum de vi accepta priori amittet, multo <pb o="104" file="0118" n="118" rhead="DISSERTATIO"/> minus Ferri elevabit, gaudens tantum virtute, quam cum eo debi-<lb/>lior Magnes communicaſſet.</s> <s xml:id="echoid-s2528" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div57" type="section" level="1" n="57"> <head xml:id="echoid-head65" xml:space="preserve">EXPERIMENTUM XXXVII.</head> <p> <s xml:id="echoid-s2529" xml:space="preserve">Si lamina ferrea, ſuper alterutro Magnetis polo ducta ſiniſtror-<lb/>ſum, vi attractrice imbuta fuerit, deinde reducatur dextrorſum, <lb/>maximam virtutis partem, quam in priori tractu acquiſivit, amittet, <lb/>ea quæ ſupereſt hæret in laminæ extremitate, quæ ultimo Magne-<lb/>tem attigit.</s> <s xml:id="echoid-s2530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2531" xml:space="preserve">Nunquam igitur Ferrum Magneti affricandum eſt, illud ducendo <lb/>dextrorſum, & </s> <s xml:id="echoid-s2532" xml:space="preserve">reducendo ſiniſtrorſum, nam poſt plurimos ejuſ-<lb/>modi itus redituſque Ferrum nihil virtutis accipiet: </s> <s xml:id="echoid-s2533" xml:space="preserve">hoc recte quon-<lb/>dam obſervavit Barlow, & </s> <s xml:id="echoid-s2534" xml:space="preserve">Riccioli in Geograpb. </s> <s xml:id="echoid-s2535" xml:space="preserve">pag, 338. </s> <s xml:id="echoid-s2536" xml:space="preserve">Ani-<lb/>madvertit præterea Eruditiſſimus Derhamus, Ferrum ita affrictum <lb/>non in ſuis extremitatibus habere polos, ſed in centro, vel prope <lb/>illud: </s> <s xml:id="echoid-s2537" xml:space="preserve">aliquando unum polum eſſe prope centrum, alterum ad alte-<lb/>rutrum extremum: </s> <s xml:id="echoid-s2538" xml:space="preserve">aliquando ambo extrema attrahi ab eodem polo <lb/>Magnetis, ab altero ejus polo repelli: </s> <s xml:id="echoid-s2539" xml:space="preserve">in quo caſu polus repellens <lb/>ſemper inveniebat partem attrahentem prope centrum: </s> <s xml:id="echoid-s2540" xml:space="preserve">In aliis ob-<lb/>ſervavit ferramentis, vim directricem eſſe converſam, eorumque <lb/>extrema attrahi & </s> <s xml:id="echoid-s2541" xml:space="preserve">repelli plane contrario modo quam naturaliter ſo-<lb/>let. </s> <s xml:id="echoid-s2542" xml:space="preserve">Confer. </s> <s xml:id="echoid-s2543" xml:space="preserve">Philoſ. </s> <s xml:id="echoid-s2544" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s2545" xml:space="preserve">N°. </s> <s xml:id="echoid-s2546" xml:space="preserve">303.</s> <s xml:id="echoid-s2547" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div58" type="section" level="1" n="58"> <head xml:id="echoid-head66" xml:space="preserve">EXPERIMENTUM XXXVIII.</head> <p> <s xml:id="echoid-s2548" xml:space="preserve">Viribus alicujus Magnetis in Ferrum, datâ diſtantiâ remotum, <lb/>ſecundum noſtram ponderandi methodum accuratiſſime cognitis, la-<lb/>pidi affricentur plurima corpora ferrea, quæ vi Magnetica impræ-<lb/>gnentur; </s> <s xml:id="echoid-s2549" xml:space="preserve">tum ſtatim exploretur vis denuo Magnetis in Ferrum; </s> <s xml:id="echoid-s2550" xml:space="preserve">an <lb/>permanſerit, utrum decreverit: </s> <s xml:id="echoid-s2551" xml:space="preserve">obſervabitur perpetuo perſeveraſſe <lb/>ſine ullo decremento,</s> </p> <p> <s xml:id="echoid-s2552" xml:space="preserve">Plures hanc obſervationem memoriæ prodiderunt, uti Norman-<lb/>nus in New. </s> <s xml:id="echoid-s2553" xml:space="preserve">attract. </s> <s xml:id="echoid-s2554" xml:space="preserve">Cap. </s> <s xml:id="echoid-s2555" xml:space="preserve">1. </s> <s xml:id="echoid-s2556" xml:space="preserve">Gilbertus, & </s> <s xml:id="echoid-s2557" xml:space="preserve">Hartſoekerus tandem, <lb/>qui mihi ſuum nonnunquam teſtatus dolorem, ſe ex Jobloti aſler-<lb/>tis in errorem illapſum, contrarium ſuis inſeruiſſe ſcriptis, Magne- <pb o="105" file="0119" n="119" rhead="DE MAGNETE."/> tes enim nunquam aliquid de virtute amittere, quamvis eodem die <lb/>plurima ferramenta ipſis applicata fuerint.</s> <s xml:id="echoid-s2558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2559" xml:space="preserve">Eſt hoc profecto admodum paradoxon, nam ſi Magnes tantun-<lb/>dem ſuæ virtutis cum Ferro communicet, quantum Ferrum recipit, <lb/>tum ſæpe lamella magnitudinis determinatæ acquiſiviſſet {1/8} partem vi-<lb/>rium Magnetis, adeoque 8 lamellæ vim æqualem illi, quam Ma-<lb/>gnes habet, accepiſſent; </s> <s xml:id="echoid-s2560" xml:space="preserve">& </s> <s xml:id="echoid-s2561" xml:space="preserve">64 lamellæ octies vim totam Magnetis <lb/>adeptæ fuiſſent, ſive octies orbatus fuiſſet Magnes penitus ſuâ vir-<lb/>tute: </s> <s xml:id="echoid-s2562" xml:space="preserve">verum Magnes eandem vim ſemper conſervat, etiamſi intra <lb/>horam non modo 64 ferramenta, ſed duplo plura ſuper eo ducan-<lb/>tur, imo obſervante Normanno, etiamſi 10000 laminæ, Acuſve <lb/>ipſi affrictæ fuerint.</s> <s xml:id="echoid-s2563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2564" xml:space="preserve">An igitur Magnes novam vim aliunde continuo acquirit, illi æ-<lb/>qualem, quam communicat? </s> <s xml:id="echoid-s2565" xml:space="preserve">Nam ope ex ſe emiſſorum effluvio-<lb/>rum fieri communicatio nequit, quia horum tam æquabilis & </s> <s xml:id="echoid-s2566" xml:space="preserve">ſubita-<lb/>nea generatio, qualis deſideraretur cum ferramenta plurima ſubito in-<lb/>tra anguſtiſſimum temporis ſpatium ipſi applicantur, fieri non poteſt. <lb/></s> <s xml:id="echoid-s2567" xml:space="preserve">Unde igitur hæ vires attrahentes, & </s> <s xml:id="echoid-s2568" xml:space="preserve">tam æquabili copia accedent ad <lb/>Magnetem, ut nihil ullo affrictu hic amiſiſſe videatur? </s> <s xml:id="echoid-s2569" xml:space="preserve">An non potius <lb/>Lapis nihil de ſua ſubſtantia communicat cum ferro, ſed tantum vim, <lb/>in metallo ſemper latentem, excitat, & </s> <s xml:id="echoid-s2570" xml:space="preserve">quietam deducit in actum? </s> <s xml:id="echoid-s2571" xml:space="preserve">Nam <lb/>nonnunquam contingit, ut Ferrum ſuper Magnete ductum, majus <lb/>pondus elevet, quam ipſe Magnes, obſervante de la Hirio in <lb/>L’Hiſt. </s> <s xml:id="echoid-s2572" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s2573" xml:space="preserve">Roy. </s> <s xml:id="echoid-s2574" xml:space="preserve">A°. </s> <s xml:id="echoid-s2575" xml:space="preserve">1717. </s> <s xml:id="echoid-s2576" xml:space="preserve">Hic virium in Ferro ſupra Ma-<lb/>gnetem exceſſus, an ab ipſo Magnete orietur? </s> <s xml:id="echoid-s2577" xml:space="preserve">tum minus erit in <lb/>cauſa quam in effectu, quod repugnat: </s> <s xml:id="echoid-s2578" xml:space="preserve">ſed ſi vis major in Ferro la-<lb/>tuerit, quæ a Magnete in actum modo deducitur, intelligi poteſt <lb/>aliquid, ut & </s> <s xml:id="echoid-s2579" xml:space="preserve">quomodo Magnes in innumeris ferramentis eodem <lb/>die vim excitaverit. </s> <s xml:id="echoid-s2580" xml:space="preserve">demonſtrari hic tamen poteſt nihil.</s> <s xml:id="echoid-s2581" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div59" type="section" level="1" n="59"> <head xml:id="echoid-head67" xml:space="preserve">EXPERIMENTUM XXXIX.</head> <p> <s xml:id="echoid-s2582" xml:space="preserve">Magnes multo fortius attrahit Ferrum purum, quam rubiginoſum: <lb/></s> <s xml:id="echoid-s2583" xml:space="preserve">quia rubigo eſt ſpecies Vitrioli, ſive Sal mixtum cum Ferri particu-<lb/>lis; </s> <s xml:id="echoid-s2584" xml:space="preserve">demonſtravimus autem ſupra in Chemicâ Magnetis Analyſi, <lb/>Salem vires Magneticas coërcere, atque ad ſilentium deducere, id- <pb o="106" file="0120" n="120" rhead="DISSERTATIO"/> circo vis Magnetis non tanta cum efficaciâ in Ferrum rubiginoſum <lb/>agit quam in purum: </s> <s xml:id="echoid-s2585" xml:space="preserve">quamobrem nequaquam conſentio cum Ta-<lb/>chenio in Clave Hippocr. </s> <s xml:id="echoid-s2586" xml:space="preserve">Medic. </s> <s xml:id="echoid-s2587" xml:space="preserve">Cap. </s> <s xml:id="echoid-s2588" xml:space="preserve">9. </s> <s xml:id="echoid-s2589" xml:space="preserve">hoc explicante, quod ex <lb/>rubigine acidum ferri exſpiravit, & </s> <s xml:id="echoid-s2590" xml:space="preserve">ob id ejus odorem mater (Ma-<lb/>gnes ſcilicet) non percipit.</s> <s xml:id="echoid-s2591" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div60" type="section" level="1" n="60"> <head xml:id="echoid-head68" xml:space="preserve">EXPERIMENTUM XL.</head> <p> <s xml:id="echoid-s2592" xml:space="preserve">Magnes inermis, qui poteſt elevare maſſam ferream duarum un-<lb/>ciarum, quod eſt maximum pondus ab eo ſuſtinendum; </s> <s xml:id="echoid-s2593" xml:space="preserve">non pote-<lb/>rit tamen elevare aliud Ferrum unciæ unius cum uncia alterius me-<lb/>talli, etiamſi ſuperficiem ſimilem priori maſſæ habuerit: </s> <s xml:id="echoid-s2594" xml:space="preserve">quemad-<lb/>modum recte obſervavit Dechales.</s> <s xml:id="echoid-s2595" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div61" type="section" level="1" n="61"> <head xml:id="echoid-head69" xml:space="preserve">EXPERIMENTUM. XLI.</head> <p> <s xml:id="echoid-s2596" xml:space="preserve">Magnes in aliquot partes ope ſerræ dividatur, ne concuſſione in-<lb/>teriora ejus turbentur, tum ſumma ponderum Ferri, quam omnia fra-<lb/>gmenta ſeorſim examinata ſuſtinent, multum ſuperat illud pondus, <lb/>quod antea â Magnete integro elevabatur.</s> <s xml:id="echoid-s2597" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2598" xml:space="preserve">Raro grandis datur Magnes, qui ſuum geſtare poteſt pondus: </s> <s xml:id="echoid-s2599" xml:space="preserve">mi-<lb/>nores novi plurimos, qui vim attrahentem decies, vigeſies & </s> <s xml:id="echoid-s2600" xml:space="preserve">ultra <lb/>ſuperantem ſuum pondus poſſident; </s> <s xml:id="echoid-s2601" xml:space="preserve">minimos vidi, quorum virtus <lb/>quingenties gravitatem excedebat: </s> <s xml:id="echoid-s2602" xml:space="preserve">Quia autem grandis Magnes con-<lb/>ſiderari poteſt inſtar congeriei plurimorum parvorum, in unam con-<lb/>junctorum maſſam, hi ſibi additi nequeunt tantam vim in Ferrum <lb/>exercere, quam ſeparati: </s> <s xml:id="echoid-s2603" xml:space="preserve">Demonſtratum enim eſt in Experimento <lb/>XVI. </s> <s xml:id="echoid-s2604" xml:space="preserve">Vim Magnetis in Ferrum decreſcere, prout majori ab eo ab-<lb/>eſt diſtantia: </s> <s xml:id="echoid-s2605" xml:space="preserve">Sit Magnes A Tab. </s> <s xml:id="echoid-s2606" xml:space="preserve">2. </s> <s xml:id="echoid-s2607" xml:space="preserve">fig. </s> <s xml:id="echoid-s2608" xml:space="preserve">3. </s> <s xml:id="echoid-s2609" xml:space="preserve">qui attollere poſſit Fer-<lb/>rum B, concipiatur diviſus in 9 partes, quas figura exhibet, appa-<lb/>rebit intuenti, Ferrum B eſſe quidem immediate applicatum parti-<lb/>bus 1, 2, 3. </s> <s xml:id="echoid-s2610" xml:space="preserve">Sed diſtare a partibus 4, 5, 6 craſſitie partium in ſe-<lb/>rie anteriori, quamobrem hæ agent modo in Ferrum, quemadmo-<lb/>dum Magnes in id, tantopere a ſe remotum, operatus fuiſſet: </s> <s xml:id="echoid-s2611" xml:space="preserve">Quia <lb/>autem partes 7, 8, 9. </s> <s xml:id="echoid-s2612" xml:space="preserve">multo plus diſtant â Ferro B, quam ſeries <lb/>media, iterum minus in illud operabuntur; </s> <s xml:id="echoid-s2613" xml:space="preserve">adjuvabunt tamen ſuâ <pb o="107" file="0121" n="121" rhead="DE MAGNETE."/> virtute actionem ſeriei primæ in Ferrum: </s> <s xml:id="echoid-s2614" xml:space="preserve">Quod ſi 9 partes a ſe ſe-<lb/>paratæ fuiſſent, atque ſingulis Ferrum immediate apponeretur, id <lb/>ſingulas contingens ſumma vi attractum fuiſſet, unde ſumma pon-<lb/>derum ab his 9 attractorum multum ſuperaret pondus ab unitâ maſ-<lb/>ſâ A geſtatum: </s> <s xml:id="echoid-s2615" xml:space="preserve">quo A in minores partes erit diviſum, quibus ſin-<lb/>gulis Ferrum geſtandum traditur, eo plus ponderis elevabitur ab omni-<lb/>bus ſimul: </s> <s xml:id="echoid-s2616" xml:space="preserve">quo autem A grandior moles exiſtit, eo partes poſterio-<lb/>res magis diſtant ab iis, quibus Ferrum applicatur, & </s> <s xml:id="echoid-s2617" xml:space="preserve">idcirco mi-<lb/>nus in id operari poſſunt.</s> <s xml:id="echoid-s2618" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div62" type="section" level="1" n="62"> <head xml:id="echoid-head70" xml:space="preserve">EXPERIMENTUM. XLII.</head> <p> <s xml:id="echoid-s2619" xml:space="preserve">Quo Magnetes ſunt majores, licet non fuerint eximiæ virtutis, <lb/>eo ad majorem diſtantiam vires ſuas diffundunt: </s> <s xml:id="echoid-s2620" xml:space="preserve">Quare præſtantes, <lb/>ſed parvi Magnetes non tam late ſuam vim exſerunt, quam magni, <lb/>licet inertiores; </s> <s xml:id="echoid-s2621" xml:space="preserve">quod etiam experientia ſe didiciſſe confirmat Hart-<lb/>ſoekerus, ideo tres quatuorve Magnetes bene ſecum invicem jun-<lb/>cti ad majorem diſtantiam agunt, quam ſinguli ſeorſim.</s> <s xml:id="echoid-s2622" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2623" xml:space="preserve">Ad magnum ſæpe intervallum a lapide vis attractrix diffunditur; <lb/></s> <s xml:id="echoid-s2624" xml:space="preserve">Experimenta nonnulla feci cum aliquo grandiori, qui manifeſto o-<lb/>perabatur in diſtantia 14 pedum Rhenolandicorum. </s> <s xml:id="echoid-s2625" xml:space="preserve">Optime cogno-<lb/>ſcetur ad quodnam intervallum vis ex Magnete extendatur duobus <lb/>ſequentibus modis. </s> <s xml:id="echoid-s2626" xml:space="preserve">1°. </s> <s xml:id="echoid-s2627" xml:space="preserve">Acus Chalybea tenuiſſima imponatur ſuperfi-<lb/>ciei Aquæ, ut natet in medio, tum in magna diſtantia poſitus Magnes <lb/>primum ſit, qui admoveatur ſenſim, & </s> <s xml:id="echoid-s2628" xml:space="preserve">ita ut linea tranſiens perpolos <lb/>Acum verſus dirigatur, appropinquet Magnes eousque, donec Acus <lb/>moveri incipiat, quæ tandem adnatabit parieti vaſis Magnetem ſpe-<lb/>ctanti. </s> <s xml:id="echoid-s2629" xml:space="preserve">2°. </s> <s xml:id="echoid-s2630" xml:space="preserve">Vel Verſorium mobiliſſimum, 6 pollices plureſvelon-<lb/>gum in Meridiano ſuo locetur, notato gradu cui cuſpis reſpondet, <lb/>tum Magnes ex longo intervallo ſenſim admoveatur, ita ut axis ſit <lb/>ad Acum perpendicularis in eodem horizontali plano, donec a ſitu <lb/>incipiat Verſorium detorqueri; </s> <s xml:id="echoid-s2631" xml:space="preserve">hæc diſtantia erit longitudo virium <lb/>Magneticarum, ſive radii activi; </s> <s xml:id="echoid-s2632" xml:space="preserve">hujus methodi mentionem quo-<lb/>que fecit Fontenellius in L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s2633" xml:space="preserve">Roy. </s> <s xml:id="echoid-s2634" xml:space="preserve">A°. </s> <s xml:id="echoid-s2635" xml:space="preserve">1717.</s> <s xml:id="echoid-s2636" xml:space="preserve"/> </p> <pb o="108" file="0122" n="122" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div63" type="section" level="1" n="63"> <head xml:id="echoid-head71" xml:space="preserve">EXPERIMENTUM XLIII.</head> <p> <s xml:id="echoid-s2637" xml:space="preserve">Poſſunt fragmenta Magnetum varia conjungi in unam maſſam, <lb/>quæ multas vires exercebit, modo inter & </s> <s xml:id="echoid-s2638" xml:space="preserve">circum partes fundatur <lb/>plumbum: </s> <s xml:id="echoid-s2639" xml:space="preserve">ſunt fragmenta hoc ordine locanda, ut Poli ejuſdem <lb/>nominis ſpectent eandem partem: </s> <s xml:id="echoid-s2640" xml:space="preserve">tum enim diſpoſita ſunt, <lb/>quemadmodum a Natura partes locatæ fuiſſent magni Ma-<lb/>gnetis, ars hic imitata Naturam e parvis componit majorem molem: <lb/></s> <s xml:id="echoid-s2641" xml:space="preserve">Dechales aliique plurimi hoc noverunt & </s> <s xml:id="echoid-s2642" xml:space="preserve">experientia comproba-<lb/>runt.</s> <s xml:id="echoid-s2643" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div64" type="section" level="1" n="64"> <head xml:id="echoid-head72" xml:space="preserve">EXPERIMENTUM XLIV.</head> <p> <s xml:id="echoid-s2644" xml:space="preserve">Nonnunquam contingit, ut grandis Magnetica moles non oſten-<lb/>dat multum virium attrahentium, cum eadem in fragmenta plurima <lb/>diſſecta, aliquam exiguam portionem exhibeat magnis viribus do-<lb/>natam, a qua, in medio Lapide, tanquam a corde molis, vis omnis <lb/>pependit, quæ diſperſa per totam majorem maſſam, aut egredi <lb/>impediebatur, vel quaquaverſum per totam molem diſtributa de-<lb/>bilitabat loca polaria.</s> <s xml:id="echoid-s2645" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div65" type="section" level="1" n="65"> <head xml:id="echoid-head73" xml:space="preserve">EXPERIMENTUM. XLV.</head> <p> <s xml:id="echoid-s2646" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2647" xml:space="preserve">2. </s> <s xml:id="echoid-s2648" xml:space="preserve">fig. </s> <s xml:id="echoid-s2649" xml:space="preserve">4. </s> <s xml:id="echoid-s2650" xml:space="preserve">Supra Magnetem generoſum & </s> <s xml:id="echoid-s2651" xml:space="preserve">grandem A, ad <lb/>notabilem ab ipſo diſtantiam teneantur duæ claves ferreæ B, C, <lb/>nunquam antea vi Magnetica imprægnatæ, ex clave C ſuſpendetur <lb/>B K, imo hæ ambæ nonnunquam feruntur a tertia clavi D: </s> <s xml:id="echoid-s2652" xml:space="preserve">ſi ad <lb/>majorem diſtantiam a Magnete attollatur D, ſimul cum adhærentibus <lb/>ſibi clavibus C, B, tum ſolutæ a ſe mutuo decidunt: </s> <s xml:id="echoid-s2653" xml:space="preserve">Ad magnam <lb/>autem diſtantiam a Magnete removeri claves poſſunt, antequam <lb/>ſolvantur, quippe obſervavit Derhamus in Philoſ. </s> <s xml:id="echoid-s2654" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s2655" xml:space="preserve">N°. <lb/></s> <s xml:id="echoid-s2656" xml:space="preserve">303. </s> <s xml:id="echoid-s2657" xml:space="preserve">Magnetem Societatis Regiæ Brittannicæ ſuſpendiſſe claves duas <lb/>ex ſe mutuo ad intervallum 8, 9, vel 10 pedum ab ipſo Ma-<lb/>gnete.</s> <s xml:id="echoid-s2658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2659" xml:space="preserve">Obſervamus in hoc Experimento vim Magnetis attractricem per <pb o="109" file="0123" n="123" rhead="DE MAGNETE."/> ipſum tranſire Ferrum, & </s> <s xml:id="echoid-s2660" xml:space="preserve">ita ad inſignem diſtantiam extendi: </s> <s xml:id="echoid-s2661" xml:space="preserve">mira-<lb/>mur hic tamen Clavim B K non tantopere trahi a Magnete A, quam <lb/>a clave C, huic enim adhæret, non Magneti; </s> <s xml:id="echoid-s2662" xml:space="preserve">attamen Magnes eſt <lb/>cauſa attractionis, ſolvuntur enim illico a ſe claves, ſimulac altius <lb/>ſupra Magnetem elevantur: </s> <s xml:id="echoid-s2663" xml:space="preserve">Cur itaque clavis C adeo remota â Ma-<lb/>gnete, fortius trahit clavim B, quam Magnes A eam trahit? </s> <s xml:id="echoid-s2664" xml:space="preserve">forſi-<lb/>tan aliquis opinaretur clavim B non trahi a Magnete, ſed repelli <lb/>contra C, quod verum non eſt; </s> <s xml:id="echoid-s2665" xml:space="preserve">nam trahitur B fortiſſime a Ma-<lb/>gnete; </s> <s xml:id="echoid-s2666" xml:space="preserve">hoc pater, ſi polus Magnetis fuerit in E, & </s> <s xml:id="echoid-s2667" xml:space="preserve">clavis B circa <lb/>eum circulariter, ſed ad notabilem diſtantiam, in latioris ſcilicet <lb/>circuli peripheriâ, circumferatur, pars K inferior verſus E trahetur, <lb/>totaque clavis ſitum acquiret valde obliquum, & </s> <s xml:id="echoid-s2668" xml:space="preserve">circumducta ſu-<lb/>perficiem conicam deſcribere videbitur: </s> <s xml:id="echoid-s2669" xml:space="preserve">in inſtituendo hoc Expe-<lb/>rimento præterea obſervatur, axe Magnetis perpendiculari ad ho-<lb/>rizontem poſito, claves altius ſupra Magnetem attolli poſſe ſalvâ at-<lb/>tractione, quam axe horizonti parallelo: </s> <s xml:id="echoid-s2670" xml:space="preserve">& </s> <s xml:id="echoid-s2671" xml:space="preserve">ſi polus Boreus Ma-<lb/>gnetis ſurſum ſpectaverit, tum omnium altiſſime & </s> <s xml:id="echoid-s2672" xml:space="preserve">in maximo a <lb/>lapide intervallo claves attolli poterunt ſuperſtite cohærentia mu-<lb/>tua.</s> <s xml:id="echoid-s2673" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div66" type="section" level="1" n="66"> <head xml:id="echoid-head74" xml:space="preserve">EXPERIMENTUM XLVI.</head> <p> <s xml:id="echoid-s2674" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2675" xml:space="preserve">2. </s> <s xml:id="echoid-s2676" xml:space="preserve">fig. </s> <s xml:id="echoid-s2677" xml:space="preserve">5. </s> <s xml:id="echoid-s2678" xml:space="preserve">Aliquot parvi globi ferrei, C, D, E, ſibi applicati, <lb/>& </s> <s xml:id="echoid-s2679" xml:space="preserve">ex ſeſuſpenſi attrahantur ſerie rectâ ad horizontem perpendiculari <lb/>a polo A Magnetis P A, deinde polus cognominis A, alterius Ma-<lb/>gnetis B lente admoveatur globo infimo E, a quo notabili adhuc <lb/>remotus intervallo, ſeparabit globum E â D, totamque globorum <lb/>ſeriem D C fugabit, obliquum ei ſitum dando.</s> <s xml:id="echoid-s2680" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2681" xml:space="preserve">Eſt perpetuæ obſervationis polos cognomines duorum Magnetum <lb/>ſe invicem fugare; </s> <s xml:id="echoid-s2682" xml:space="preserve">hoc poſito, polus A Magnetis A P ad ſe trahit <lb/>globorum ſeriem E D C, directione ab E ad C, adeoque <lb/>omnes globorum infimæ partes erunt poli cognomines ipſius A, <lb/>& </s> <s xml:id="echoid-s2683" xml:space="preserve">ſupremæ partes erunt cognomines poli P. </s> <s xml:id="echoid-s2684" xml:space="preserve">poſito igitur Magne-<lb/>tis B S polo B cognomine ipſius A, hoc eſt infimarum partium glo-<lb/>borum, debebunt hæ omnes a polo B fugari, ſi vis fugans ipſius <lb/>B, ſit major vi trahente poli A in globum remotiſſimum E, in quem <lb/>parum tantummodo operari poteſt, globus E fugatus nimium a po- <pb o="110" file="0124" n="124" rhead="DISSERTATIO"/> lo B, ſeparabitur a reliquis. </s> <s xml:id="echoid-s2685" xml:space="preserve">Loco globulorum ferreorum idem Ex-<lb/>perimentum etiam optime inſtituitur cum acubus, quæ ex ſuis ſu-<lb/>ſpenſæ extremis, ſibi adhæreſcendo longam conſtituunt ſeriem, ſi <lb/>circa infimam Magnes B S circumagatur, eam fugabit, atque in <lb/>circulum deducet, uti etiam eleganter adnotavit Cl. </s> <s xml:id="echoid-s2686" xml:space="preserve">Wolfius in <lb/>Meditat, Ingen. </s> <s xml:id="echoid-s2687" xml:space="preserve">Tom. </s> <s xml:id="echoid-s2688" xml:space="preserve">3. </s> <s xml:id="echoid-s2689" xml:space="preserve">Si vero polus S, Magnetis B S Acui infi-<lb/>mæ obferatur, hæc illi advolabit extemplo.</s> <s xml:id="echoid-s2690" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div67" type="section" level="1" n="67"> <head xml:id="echoid-head75" xml:space="preserve">EXPERIMENTUM XLVII.</head> <p> <s xml:id="echoid-s2691" xml:space="preserve">Si polo Magnetis majorum virium apponatur aliquod oblongum <lb/>Ferrum, jacens in plano horizontali lævigato, alterique extremo <lb/>Ferri polus alterius nominis, ſed Magnetis debilioris virtutis appli-<lb/>cetur, huic Magneti lente retro tracto, ut Ferrum in plano ma-<lb/>neat, ſæpe adhærebit Ferrum, avulſum a fortiori Magnete.</s> <s xml:id="echoid-s2692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2693" xml:space="preserve">Plurimi hunc obſervaverunt effectum, uti Kircherus in Lib. </s> <s xml:id="echoid-s2694" xml:space="preserve">de <lb/>Magn. </s> <s xml:id="echoid-s2695" xml:space="preserve">Gaſſendus ad Diog. </s> <s xml:id="echoid-s2696" xml:space="preserve">Laërt. </s> <s xml:id="echoid-s2697" xml:space="preserve">p. </s> <s xml:id="echoid-s2698" xml:space="preserve">205. </s> <s xml:id="echoid-s2699" xml:space="preserve">Rohaultus in Phyſic. <lb/></s> <s xml:id="echoid-s2700" xml:space="preserve">part. </s> <s xml:id="echoid-s2701" xml:space="preserve">3. </s> <s xml:id="echoid-s2702" xml:space="preserve">Cap. </s> <s xml:id="echoid-s2703" xml:space="preserve">8. </s> <s xml:id="echoid-s2704" xml:space="preserve">§. </s> <s xml:id="echoid-s2705" xml:space="preserve">54. </s> <s xml:id="echoid-s2706" xml:space="preserve">de la Hire in L’Hiſt. </s> <s xml:id="echoid-s2707" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s2708" xml:space="preserve">Roy. </s> <s xml:id="echoid-s2709" xml:space="preserve"><lb/>A°. </s> <s xml:id="echoid-s2710" xml:space="preserve">1717.</s> <s xml:id="echoid-s2711" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div68" type="section" level="1" n="68"> <head xml:id="echoid-head76" xml:space="preserve">EXPERIMENTUM XLVIII.</head> <p> <s xml:id="echoid-s2712" xml:space="preserve">Acus Magnetica ponatur in æquatore Magnetis Sphærici, pa-<lb/>rallele ad axin Magnetis, acus extremo apponatur regula ferrea, quæ <lb/>ei adhærebit tam firmiter, ut regula eam circum ducere circa totum <lb/>Magnetem queat, & </s> <s xml:id="echoid-s2713" xml:space="preserve">in ſitum quemcunque protrahere.</s> <s xml:id="echoid-s2714" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div69" type="section" level="1" n="69"> <head xml:id="echoid-head77" xml:space="preserve">EXPERIMENTUM XLIX.</head> <p> <s xml:id="echoid-s2715" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2716" xml:space="preserve">6. </s> <s xml:id="echoid-s2717" xml:space="preserve">fig. </s> <s xml:id="echoid-s2718" xml:space="preserve">1. </s> <s xml:id="echoid-s2719" xml:space="preserve">Si Magneti præſtantis virtutis A adhæſeritſphæ-<lb/>rula ferrea B, attracta, atque regula ferrea C D tetigerit punctum <lb/>Sphæræ oppoſitum puncto contactus cum Magnete; </s> <s xml:id="echoid-s2720" xml:space="preserve">poterit regula <lb/>C D adimere Sphæram a Magnete, ſed ſi Magnes debilium fuerit <lb/>virium, tum regula non poterit Sphæram B a Magnete avellere: </s> <s xml:id="echoid-s2721" xml:space="preserve">Cl. <lb/></s> <s xml:id="echoid-s2722" xml:space="preserve">de la Hirius inſtituens hoc Experimentum cum duabus regulis fer-<lb/>reis, quarum ea minima erat, quæ adhærebat Magneti, notat, ma- <pb o="111" file="0125" n="125" rhead="DE MAGNETE."/> jorem regulam abſtuliſſe quidem minorem a Magnete, ſed ambas â <lb/>ſe ſeparatas fuiſſe, poſtquam a Magnete duobus tribuſve pollicibus <lb/>receſſerant.</s> <s xml:id="echoid-s2723" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div70" type="section" level="1" n="70"> <head xml:id="echoid-head78" xml:space="preserve">EXPERIMENTUM L.</head> <p> <s xml:id="echoid-s2724" xml:space="preserve">Cuſpis Acus chalybeæ hebetata fuit, capite manente craſſiori, <lb/>cuſpide applicata Magneti fortiſſimo & </s> <s xml:id="echoid-s2725" xml:space="preserve">capite virgæ ferreæ, ſemper <lb/>deductæ a Lapide virgæ adhæſit firmiter Acus, a Magnete ademta: <lb/></s> <s xml:id="echoid-s2726" xml:space="preserve">capite Acus deinde applicato Magneti, & </s> <s xml:id="echoid-s2727" xml:space="preserve">cuſpide regulæ ferreæ, <lb/>aliquando avellebatur Acus a Magnete, aliquando non, remotâ ut <lb/>ante regulâ.</s> <s xml:id="echoid-s2728" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2729" xml:space="preserve">Tum cuſpis Acus reddita fuit acutiſſima, & </s> <s xml:id="echoid-s2730" xml:space="preserve">caput optime appla-<lb/>natum, cuſpide applicata Magneti, & </s> <s xml:id="echoid-s2731" xml:space="preserve">capite virgæ ferreæ, huic <lb/>ſemper Acus adhæſit, tollique â Magnete potuit. </s> <s xml:id="echoid-s2732" xml:space="preserve">Sed capite Acûs <lb/>applicato Magneti, cuſpide virgæ, nunquam adhæſit virgæ, ſed <lb/>applicata Magneti manſit: </s> <s xml:id="echoid-s2733" xml:space="preserve">idcirco prima fronte opinabar, cum aliis <lb/>Philoſophis Acum adhærere corpori, quod pluribus attingebat pun-<lb/>ctis, attamen erroneam hanc fuiſſe opinionem plura me docuerunt Ex-<lb/>perimenta, nam clavis, cujus planities magna, appoſita fuit plano Ma-<lb/>gnetis polo, adeo ut contactus in lata ſuperficie daretur, tum caput <lb/>alterius clavis rotundum applicatum fuit capiti rotundo prioris cla-<lb/>vis, ut contactus ambarum in puncto tantum fuerit, nihilo-<lb/>minus clavis ſecunda abſtulit primam a Magnete; </s> <s xml:id="echoid-s2734" xml:space="preserve">inſtitui hoc Ex-<lb/>perimentum cum Cl. </s> <s xml:id="echoid-s2735" xml:space="preserve">Hartſoekero, tum affirmante, ſe idem parado-<lb/>xon ſemper obſervaſſe, quod etiam adnotavit de la Hirius in L’Hiſt. <lb/></s> <s xml:id="echoid-s2736" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s2737" xml:space="preserve">Roy. </s> <s xml:id="echoid-s2738" xml:space="preserve">A°. </s> <s xml:id="echoid-s2739" xml:space="preserve">1717. </s> <s xml:id="echoid-s2740" xml:space="preserve">ratus, Ferrum eſſe fortiorem <lb/>Magnetem ad attrahendum Ferrum ipſo Lapide, hinc regulam fer-<lb/>ream adimere aliam a Magnete: </s> <s xml:id="echoid-s2741" xml:space="preserve">Hoc tamen videtur nimis precario <lb/>aſſumtum, cum a Magnete præſtantiſſimo Ferrum vix viribus do-<lb/>natum adimit aliud Ferrum: </s> <s xml:id="echoid-s2742" xml:space="preserve">præterea ita non ſolvitur difficultas, <lb/>quomodo Magnes debilior a fortiori abripiat Ferrum in Experimen-<lb/>to XLVII. </s> <s xml:id="echoid-s2743" xml:space="preserve">Supponit quidem Philoſophus debiliorem Magnetem vi-<lb/>res acquirere a fortiori, ſed demonſtrandum foret debiliorem fieri <lb/>fortiorem ipſo Magnete præſtantiſſimo, quod an concipi concedive <lb/>queat vehementer dubito: </s> <s xml:id="echoid-s2744" xml:space="preserve">Sunt hercle multiplicia Magnetum phæ- <pb o="112" file="0126" n="126" rhead="DISSERTATIO"/> nomena, & </s> <s xml:id="echoid-s2745" xml:space="preserve">pauciſſima quæ ab animo intelligi poſſunt noſtro, hæc <lb/>ab Exp. </s> <s xml:id="echoid-s2746" xml:space="preserve">XLVII. </s> <s xml:id="echoid-s2747" xml:space="preserve">ad L, ſunt quidem inter ea, quæ omnium minime <lb/>comprehenduntur.</s> <s xml:id="echoid-s2748" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div71" type="section" level="1" n="71"> <head xml:id="echoid-head79" xml:space="preserve">EXPERIMENTUM LI.</head> <p> <s xml:id="echoid-s2749" xml:space="preserve">Si aliquot Acus vulgares, vel laminæ parvæ ferreæ ponantur in <lb/>ſerie quadam juxta ſe invicem, Magnete attingente unam Acum vel <lb/>laminam, cohærebunt omnes inter ſe & </s> <s xml:id="echoid-s2750" xml:space="preserve">cum Magnete, cohærebit <lb/>tamen fortius ſecunda cum prima, quam tertia cum ſecunda, vel <lb/>quarta cum tertia, erit enim eo minor cohærentia, quo Acus vel <lb/>virgæ magis â Magnete diſtiterint: </s> <s xml:id="echoid-s2751" xml:space="preserve">tranſit igitur vis Magnetis ex Fer-<lb/>ro in Ferrum; </s> <s xml:id="echoid-s2752" xml:space="preserve">aut ſuſcitata vi Magnetica in hoc Ferro, ſuſcitatur quo-<lb/>que in vicino, & </s> <s xml:id="echoid-s2753" xml:space="preserve">ſic porro uſque ad ultimum: </s> <s xml:id="echoid-s2754" xml:space="preserve">Effectus hiſce ana-<lb/>logi conſpiciuntur in duobus turbinibus ferreis, quorum hic attin-<lb/>git Magnetem, alter ex priori ſuſpenditur, ambobusſe contingen-<lb/>tibus in puncto, cohærent tamen attracti vi Magnetica, poteſtque <lb/>in gyrum velocem & </s> <s xml:id="echoid-s2755" xml:space="preserve">oppoſitæ directionis uterque moveri, gyratio <lb/>enim attractionem non tollit.</s> <s xml:id="echoid-s2756" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div72" type="section" level="1" n="72"> <head xml:id="echoid-head80" xml:space="preserve">EXPERIMENTUM LII.</head> <p> <s xml:id="echoid-s2757" xml:space="preserve">Si lamina ferrea Magneti affricetur ſecundum longitudinem ſuam, <lb/>pars, quæ ultimo Magnetem tetigit, plus virium habet, quam quæ <lb/>primo applicabatur Lapidi, ut igitur extremitas Ferri imbecillior <lb/>eaſdem vires ac altera recipiat, affricanda eſt polo oppoſito Ma-<lb/>gnetis.</s> <s xml:id="echoid-s2758" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div73" type="section" level="1" n="73"> <head xml:id="echoid-head81" xml:space="preserve">EXPERIMENTUM. LIII.</head> <p> <s xml:id="echoid-s2759" xml:space="preserve">Regula Chalybea temperata ſecetur in aliquot partesrectangulas, <lb/>quæ omnes ſuper lamina poſitæ cuprea diverſo ſitu juxta ſe invicem <lb/>quam antea cohæſerant, bene apprimantur, ut quaſi corpus unitum <lb/>forment: </s> <s xml:id="echoid-s2760" xml:space="preserve">Supra hunc apparatum tranſeat Magnes fortiter appreſſus, <lb/>tum regula viribus imprægnabitur, eo majoribus, quo partes ſe ar-<lb/>ctius contigerint, ſi autem vix ſe contigerint, non niſi paucæ cum <lb/>iis communicatæ erunt vires,</s> </p> <pb o="113" file="0127" n="127" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div74" type="section" level="1" n="74"> <head xml:id="echoid-head82" xml:space="preserve">EXPERIMENTUM. LIV.</head> <p> <s xml:id="echoid-s2761" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2762" xml:space="preserve">6. </s> <s xml:id="echoid-s2763" xml:space="preserve">fig. </s> <s xml:id="echoid-s2764" xml:space="preserve">2. </s> <s xml:id="echoid-s2765" xml:space="preserve">Tabulæ D inſiſtat Acus C D perpendicularis, at-<lb/>tracta a Magnete ſuperius poſita A B, tum admoveatur Acus F G <lb/>tranſverſe, quæ ulterius promota tranſiret inter Acum C D & </s> <s xml:id="echoid-s2766" xml:space="preserve">Ma-<lb/>gnetem A B, illico cadet Acus C D, non amplius attracta.</s> <s xml:id="echoid-s2767" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2768" xml:space="preserve">Quantum igitur a viâ ſuâ detorqueri poteſt vis Magnetica, imo <lb/>quam facilea parva cauſa? </s> <s xml:id="echoid-s2769" xml:space="preserve">nam acus F G omnem vim, antea determi-<lb/>natam ſecundum C D, abripit, inflectitque ſecundum F G: </s> <s xml:id="echoid-s2770" xml:space="preserve">Qui-<lb/>cunque Aquarum motus Fluidorumque decurſus cognoſcit, facile <lb/>perſpiciet hoc phænomenon reſpuere omnes Fluidorum currentium <lb/>Leges, & </s> <s xml:id="echoid-s2771" xml:space="preserve">idcirco Magnetem non operari effluviis, aut Fluido quo-<lb/>cunque alio.</s> <s xml:id="echoid-s2772" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div75" type="section" level="1" n="75"> <head xml:id="echoid-head83" xml:space="preserve">EXPERIMENTUM LV.</head> <p> <s xml:id="echoid-s2773" xml:space="preserve">Lamina ferrea, ſuper præſtantiſſimo ducta Magnete, viribus inſi-<lb/>gnibus imprægnata fuit, hæc impoſita incudi, malleo aliquamdiu <lb/>tuſa fuit, quo omnes amiſit a Magnete antea acceptas vires, non <lb/>enim niſi leviſſimas ſcobis| particulas geſtabat, vi â pulſatione com-<lb/>municata, qualem omne Ferrum malleis contuſum, acquirit; </s> <s xml:id="echoid-s2774" xml:space="preserve">ſed <lb/>nequaquam vel leviſſimam attollere potuit Acum.</s> <s xml:id="echoid-s2775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2776" xml:space="preserve">Grimaldi in Phyſica eundem Experimenti ſucceſſum adnotavit: <lb/></s> <s xml:id="echoid-s2777" xml:space="preserve">Quid hic vires ex Ferro expellit? </s> <s xml:id="echoid-s2778" xml:space="preserve">Partes Ferri, quod cuditur, a <lb/>ſe removentur, pori mutantur, aliarum partium fit contactus mu-<lb/>tuus, nil aliud in Ferro mutatur, id tamen aptum eſt turbandis, <lb/>& </s> <s xml:id="echoid-s2779" xml:space="preserve">profligandis viribus Magneticis, ut nullæ ſuperſint: </s> <s xml:id="echoid-s2780" xml:space="preserve">an igitur <lb/>pororum figura erit cauſa attractionis aut virtutis Magneticæ? </s> <s xml:id="echoid-s2781" xml:space="preserve">ne-<lb/>quaquam, quid enim porus eſt præter ſpatium vacuum, quod ſua <lb/>natura eſt iners, ſed an, cum ſitus partium mutatus eſt, etiam non <lb/>expulſa eſt vis, in quam cum Malleus egit, an non erit ſub-<lb/>ſtantia corporea? </s> <s xml:id="echoid-s2782" xml:space="preserve">corpus enim in aliud agere clare intelligi-<lb/>tur, ſed in diverſas ſubſtantias quomodo agat, non compre-<lb/>hendi poteſt; </s> <s xml:id="echoid-s2783" xml:space="preserve">agit tamen corpus in mentem humanam, rem <lb/>diſtinctiſſimam, an ſic mallei pulſatio non poſſet in vim Ma-<lb/>gneticam agere, etiamſi hæc non foret ſubſtantia corporea, ſedal- <pb o="114" file="0128" n="128" rhead="DISSERTATIO"/> terius naturæ; </s> <s xml:id="echoid-s2784" xml:space="preserve">ſi quoque ejuſmodirelatio, acinter mentem & </s> <s xml:id="echoid-s2785" xml:space="preserve">corpus <lb/>noſtrum exiſtit, daretur. </s> <s xml:id="echoid-s2786" xml:space="preserve">Quia autem obſervamus limaturam Ferri a <lb/>Magnete viribus donatam, extemplo earum jacturam facere, ſimulac <lb/>partes inter ſe miſcentur, an eodem modo Ferrum cuſum vires amit-<lb/>tit, quoniam quoque variæ partes inter ſe miſcentur, alioque po-<lb/>nuntur ordine? </s> <s xml:id="echoid-s2787" xml:space="preserve">Hoc quidem probabiliſſimum videtur: </s> <s xml:id="echoid-s2788" xml:space="preserve">reſtat tamen <lb/>difficultas quomodo vires pereant ordine partium turbato.</s> <s xml:id="echoid-s2789" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div76" type="section" level="1" n="76"> <head xml:id="echoid-head84" xml:space="preserve">EXPERIMENTUM LVI.</head> <p> <s xml:id="echoid-s2790" xml:space="preserve">Lamina ferrea, quæ fortiſſimo affricta Magneti viribus imprægna-<lb/>ta fuit eximiis, imponatur Igni, ut penitus candeſcat, calida appo-<lb/>natur Limaturæ Ferri, ejus nullam particulam attrahet: </s> <s xml:id="echoid-s2791" xml:space="preserve">manifeſto <lb/>indicio in hac calente lamina nullas ſupereſſe vires attrahentes. </s> <s xml:id="echoid-s2792" xml:space="preserve">Con-<lb/>venit hoc cum Experimento XXIX. </s> <s xml:id="echoid-s2793" xml:space="preserve">Magnetem Igni commiſſum <lb/>ſpectante, qui etiam vires ſuas ſcobem attrahendi amiſit: </s> <s xml:id="echoid-s2794" xml:space="preserve">non dif-<lb/>fert Ferrum a Magnete, neque vis Magnetica diverſa eſt in Ferro <lb/>& </s> <s xml:id="echoid-s2795" xml:space="preserve">Magnete, ſi igitur Ignis eam ejiciat ex uno, cur non expunge-<lb/>ret ex altero, Ecce mirandas virtutis Magneticæ proprietates nunc <lb/>in eam agit Ignis, nunc nihil agit, tranſit vis per flammam Spiri-<lb/>tus & </s> <s xml:id="echoid-s2796" xml:space="preserve">olei accenſi illibata, expellitur tamen & </s> <s xml:id="echoid-s2797" xml:space="preserve">deſtruitur ab Igne, <lb/>hærens in corporibus ferreis & </s> <s xml:id="echoid-s2798" xml:space="preserve">lapideis.</s> <s xml:id="echoid-s2799" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div77" type="section" level="1" n="77"> <head xml:id="echoid-head85" xml:space="preserve">EXPERIMENTUM LVII.</head> <p> <s xml:id="echoid-s2800" xml:space="preserve">Quoniam lamina vires Magneticas in Igne deponit, explorandum <lb/>erat, an Magnes cum Ferro ignito vim communicaret, atque an com-<lb/>municata in Ferro maneret? </s> <s xml:id="echoid-s2801" xml:space="preserve">ſuperfluum prima fronte judicabitur <lb/>hoc Experimentum, ſi enim Ignis in Exp. </s> <s xml:id="echoid-s2802" xml:space="preserve">LVI. </s> <s xml:id="echoid-s2803" xml:space="preserve">vim ex Ferro eji-<lb/>ciat Magneticam, etiam nunc ex eo vim qualemcumque acceptam <lb/>expellet, qui enim in Ferro valde ignito hæret ignis, non diſcre-<lb/>pat ab alio Igne, ſed ecce quam oppoſita phænomena mihi ita ra-<lb/>tiocinanti evenerunt, quæ docere poſſunt Experimentatores, quam <lb/>lente, quam caute in Phyſica pergendum ſit, & </s> <s xml:id="echoid-s2804" xml:space="preserve">quam parum Ex-<lb/>perimentis, niſi crebro repetitis a dexterrimis obſervatoribus, con-<lb/>fidere poſſumus; </s> <s xml:id="echoid-s2805" xml:space="preserve">convenit in hac ſcientia id, quoda Chemicis ſemper <lb/>inculcatur, omnem feſtinationem eſſe â Diabolo, feſtinans enim & </s> <s xml:id="echoid-s2806" xml:space="preserve">ra- <pb o="115" file="0129" n="129" rhead="DE MAGNETE."/> tiocinium ex una alterave obſervatione deducens non poteſt non ſæ-<lb/>piſſime illabi in errores: </s> <s xml:id="echoid-s2807" xml:space="preserve">Anno 1725. </s> <s xml:id="echoid-s2808" xml:space="preserve">lamella valde ignita, ſuper <lb/>polo egregii Magnetis ducta, & </s> <s xml:id="echoid-s2809" xml:space="preserve">immiſſa limaturæ Ferri, nullum <lb/>indicium virium attractricium edidit, repetitus fuit ad Magnetem <lb/>affrictus, cum Ferro nulla vis communicata fuit, refrigerata lamella <lb/>non majorem virtutem attrahendi habuit, quam quælibet alia lamella <lb/>poſſidere ſolet. </s> <s xml:id="echoid-s2810" xml:space="preserve">Anno 1727 cum alio præſtanti Magnete, ſed ar-<lb/>mato, idem Experimentum coram plurimis repetii ſpectatoribus, <lb/>eadem lamella ferrea, vehementer ignita, ſuper pede ſive polo ar-<lb/>mati Magnetis ducta fuit, tum ſcobi immiſſa, oſtendit inſignem vim, <lb/>ſcobe undiquaque inſtar barbæ ſibi adhærente, frigefacta eandem vim <lb/>retinuit. </s> <s xml:id="echoid-s2811" xml:space="preserve">Admiratus eventum inſperatum & </s> <s xml:id="echoid-s2812" xml:space="preserve">priori oppoſitum, ſe-<lb/>quenti die tentamen repetii cum filo ferreo, novam capiendo ſco-<lb/>bem, & </s> <s xml:id="echoid-s2813" xml:space="preserve">caute ad omnia attendens, ne ſeducerer, ſed fuit idem ten-<lb/>taminis ſucceſſus, vi Magnetica imprægnatum fuit filum ignitum, <lb/>eandem retinuit refrigerio commiſſum. </s> <s xml:id="echoid-s2814" xml:space="preserve">Quid ex tam oppoſito eventu <lb/>concludi poteſt? </s> <s xml:id="echoid-s2815" xml:space="preserve">an non, Magnetes nonnullos vim cum Ferro poſſe <lb/>communicare ignito, alios non poſſe: </s> <s xml:id="echoid-s2816" xml:space="preserve">aut hoc tempore phænomenon <lb/>a Magnete excitari, quodalia tempeſtate non excitatur: </s> <s xml:id="echoid-s2817" xml:space="preserve">an vero arma-<lb/>tura aliquid contribuit? </s> <s xml:id="echoid-s2818" xml:space="preserve">an pendet â certo gradu candefactionis? </s> <s xml:id="echoid-s2819" xml:space="preserve">an <lb/>â Ferro? </s> <s xml:id="echoid-s2820" xml:space="preserve">Sed præſtat ſobrie ex ejuſmodi ratiocinari Experimentis.</s> <s xml:id="echoid-s2821" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div78" type="section" level="1" n="78"> <head xml:id="echoid-head86" xml:space="preserve">EXPERIMENTUM LVIII.</head> <p> <s xml:id="echoid-s2822" xml:space="preserve">Magnes poſitus fuit in tabula rotatili, in altera tabula Verſorium, <lb/>quod diſtabat a Magnete 10 pedibus, ita ut axis Lapidis & </s> <s xml:id="echoid-s2823" xml:space="preserve">Verſorium eſ-<lb/>ſentin eodem plano horizontali; </s> <s xml:id="echoid-s2824" xml:space="preserve">Verſorio ad quietem reducto, conver-<lb/>ſa fuit Tabula cum Magnete, motus Verſorii obſervatus fuit, ante-<lb/>quam tamen moveri incipiebat, tempus interceſſit, brevius minuto <lb/>ſecundo; </s> <s xml:id="echoid-s2825" xml:space="preserve">propius deinde admotus fuit Magnes Verſorio, illiuſque <lb/>tabulâ ſeptem pedibus diſtante, rurſuſque converſâ, Verſorium motum <lb/>fuit, brevius tamen tempus inter initium motus Magnetis & </s> <s xml:id="echoid-s2826" xml:space="preserve">Ver-<lb/>ſorii interceſſit, quam antea: </s> <s xml:id="echoid-s2827" xml:space="preserve">iterum propius Magnes admotus Ver-<lb/>ſorio fuit, intervallo 3 pedum inter utrumque intercedente; </s> <s xml:id="echoid-s2828" xml:space="preserve">con-<lb/>verſo Magnete ſimul converſum fuit Verſorium, neque temporis <lb/>mora obſervari potuit: </s> <s xml:id="echoid-s2829" xml:space="preserve">Nimis breve tempus eſt, quod inter motum <pb o="116" file="0130" n="130" rhead="DISSERTATIO"/> Magnetis & </s> <s xml:id="echoid-s2830" xml:space="preserve">Verſorii intercedit, quam ut accurate obſervaripoſſit, <lb/>operam impendi, ut detegerem proportionem inter tempora, quibus <lb/>motus dabatur, & </s> <s xml:id="echoid-s2831" xml:space="preserve">diſtantias horum corporum a ſe invicem, ut per-<lb/>nicitatem virium Magneticarum invenirem, ſed nimia celeritas pro-<lb/>hibuit hucuſque, quo minus aliquid accurati determinem: </s> <s xml:id="echoid-s2832" xml:space="preserve">pulcrius <lb/>tamen hoc rude tentamen mihi viſum fuit, quam ut ſilentio preme-<lb/>retur.</s> <s xml:id="echoid-s2833" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div79" type="section" level="1" n="79"> <head xml:id="echoid-head87" xml:space="preserve">EXPERIMENTUM LIX.</head> <p> <s xml:id="echoid-s2834" xml:space="preserve">Si Verſorium & </s> <s xml:id="echoid-s2835" xml:space="preserve">Magnes in eâ ponantur diſtantia, ut in ſe agant, <lb/>Verſorium a polo Magnetis attrahitur, cuſpide alterius nominis <lb/>verſus polum directa; </s> <s xml:id="echoid-s2836" xml:space="preserve">tum juxta priorem ponatur alius Magnes, in <lb/>codem plano horizontali, & </s> <s xml:id="echoid-s2837" xml:space="preserve">in eâdem â Verſorio diſtantiâ, polis <lb/>cognominibus eandem plagam ſpectantibus, dirigetur Acus verſus me-<lb/>dium interſtitii inter ambos relicti Magnetes, in quo loco eſt cen-<lb/>trum virium Magnetum, haud aliter fere ac centrum gravitatis in-<lb/>ter duo ſejuncta corpora intermedium jacet. </s> <s xml:id="echoid-s2838" xml:space="preserve">Si autem Magnetis, <lb/>juxta priorem poſiti, polus ſit alterius nominis, Verſorium dirigi-<lb/>tur, ut ſit perpendiculare ad amborum Magnetum axes, tum enim <lb/>cuſpis illius æque attrahitur ab uno, quam repellitur ab altero ſe-<lb/>cundi Magnetis polo.</s> <s xml:id="echoid-s2839" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div80" type="section" level="1" n="80"> <head xml:id="echoid-head88" xml:space="preserve">EXPERIMENTUM LX.</head> <p> <s xml:id="echoid-s2840" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2841" xml:space="preserve">3. </s> <s xml:id="echoid-s2842" xml:space="preserve">fig. </s> <s xml:id="echoid-s2843" xml:space="preserve">1. </s> <s xml:id="echoid-s2844" xml:space="preserve">Tabulæ A B, quæ ope rotæ P velociſſime cir-<lb/>cumverti poterat, impoſitus alligatuſque fuit Magnes C, ita ut axis <lb/>perpendiculariter inſiſteret horizonti, polus autem Boreus ſurſum <lb/>ſpectaret: </s> <s xml:id="echoid-s2845" xml:space="preserve">tum Verſorium Magneticum alteri impoſitum fuit menſæ <lb/>immobili; </s> <s xml:id="echoid-s2846" xml:space="preserve">atque in eodem plano horizontali cum A B, tegebatur <lb/>campana vitrea, ne a motu aëris per circumgyrationem tabulæ A <lb/>B, turbaretur, admovebatur Verſorium tam prope Magneti C, ut <lb/>intra ejus virtutis ſphæram hæreret: </s> <s xml:id="echoid-s2847" xml:space="preserve">Verſorio quieſcente, tabula A B <lb/>velociter circumagebatur, in principio viſa fuit Acus oſeillari nunc <lb/>dextrorſum, nunc ſiniſtrorſum, primum ſitum relinquendo parum-<lb/>per: </s> <s xml:id="echoid-s2848" xml:space="preserve">ſed aucta velocitate tabulæ A B, quantum fieri potuit, Ver-<lb/>ſorium manſit fixum in ſuo meridiano, neque ullum motus minimi <lb/>dedit ſignum.</s> <s xml:id="echoid-s2849" xml:space="preserve"/> </p> <pb o="117" file="0131" n="131" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div81" type="section" level="1" n="81"> <head xml:id="echoid-head89" xml:space="preserve">EXPERIMENTUM LXI.</head> <p> <s xml:id="echoid-s2850" xml:space="preserve">Omni apparatu præcedentis Experimenti manente eodem, Ver-<lb/>ſorium altius fuit poſitum, ut eſſet in plano ſupra polum Magne-<lb/>tis C, quorſum Acus illico dirigebatur, inclinata quoque a viribus <lb/>attrahentis poli deorſum; </s> <s xml:id="echoid-s2851" xml:space="preserve">fuit Verſorium ita poſitum, ut ex meri-<lb/>diano ſuo egreſſum fueritper attractionem Magnetis: </s> <s xml:id="echoid-s2852" xml:space="preserve">hoc lapide C <lb/>velociſſime circumacto ope rotæ P, manſit Acus inclinata, quieta, <lb/>& </s> <s xml:id="echoid-s2853" xml:space="preserve">directa, ut modo ante: </s> <s xml:id="echoid-s2854" xml:space="preserve">Quare hæc velociſſima circumgy-<lb/>ratio non impedivit, quominus Magnes in Verſorium egerit.</s> <s xml:id="echoid-s2855" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div82" type="section" level="1" n="82"> <head xml:id="echoid-head90" xml:space="preserve">EXPERIMENTUM LXII.</head> <p> <s xml:id="echoid-s2856" xml:space="preserve">Idem Magnes binorum præcedentium Experimentorum C tabu-<lb/>læ A B ita alligatus fuit, ut ejus ambo poli, ſive axis, jaceret in <lb/>plano horizontali A C B. </s> <s xml:id="echoid-s2857" xml:space="preserve">Verſorium in alia poſitum fuit tabula im-<lb/>mobili, ita ut in eodem producto plano horizontali A C B foret: <lb/></s> <s xml:id="echoid-s2858" xml:space="preserve">Magnete velociter circumacto, cuſpis Verſorii Borea inverteba-<lb/>tur, directa verſus Magnetem, manebatque in hoc ſitu immobilis, <lb/>quamdiu Magnes velociſſime circumvolvebatur, ſed eo tardius mo-<lb/>to oſcillabat Verſorium: </s> <s xml:id="echoid-s2859" xml:space="preserve">idem erat effectus poſito Verſorio ad Bo-<lb/>ream, Ortum, Meridiem vel Occaſum Magnetis, cuſpis enim Borea <lb/>ſemper verſus Magnetem trahebatur.</s> <s xml:id="echoid-s2860" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2861" xml:space="preserve">Hoc Experimentum iterum docet, circumgyrationem Magnetis <lb/>velociſſimam non impedire, quominus Acus attrahatur: </s> <s xml:id="echoid-s2862" xml:space="preserve">hujus cuſpis <lb/>Borea ad Magnetem dirigebatur, quia polus Meridionalis Magne-<lb/>tis, cui Verſorium affrictum fuit, in hac regione majores attrahendi <lb/>vires habet, quam Boreus.</s> <s xml:id="echoid-s2863" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div83" type="section" level="1" n="83"> <head xml:id="echoid-head91" xml:space="preserve">EXPERIMENTUM. LXIII.</head> <p> <s xml:id="echoid-s2864" xml:space="preserve">Magnes attrahit Ferrum purum, & </s> <s xml:id="echoid-s2865" xml:space="preserve">id quod eſt imprægnatum vi <lb/>a Magnete, agit in hoc ad majorem diſtantiam, quam in illud: <lb/></s> <s xml:id="echoid-s2866" xml:space="preserve">ſunt diſtantiæ, in quibus actio incipit ſpectari, Magnetis in Ferrum <lb/>imprægnatum, ad eas in Ferrum non imprægnatum, circiter uti 5 <lb/>ad 2.</s> <s xml:id="echoid-s2867" xml:space="preserve"/> </p> <pb o="118" file="0132" n="132" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s2868" xml:space="preserve">Hoc ſubtiliſſime primus obſervavit Whiſtonus: </s> <s xml:id="echoid-s2869" xml:space="preserve">Ferrum igitur, <lb/>quod ſuper Magnete ductum fuit, & </s> <s xml:id="echoid-s2870" xml:space="preserve">vires accepit, hæret quaſi in <lb/>centro virium ad aliquam diſtantiam diffuſarum, & </s> <s xml:id="echoid-s2871" xml:space="preserve">vires Magnetis <lb/>& </s> <s xml:id="echoid-s2872" xml:space="preserve">Ferri ſibi obviam quaſi eunt, atque in intermedio ſpatio in ſe a-<lb/>gunt; </s> <s xml:id="echoid-s2873" xml:space="preserve">niſi Ferrum, vi donatum, mobilius ſit altero, & </s> <s xml:id="echoid-s2874" xml:space="preserve">ideo ab exi-<lb/>lioribus Magnetis viribus in diſtantia majori commoveri poſſit.</s> <s xml:id="echoid-s2875" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div84" type="section" level="1" n="84"> <head xml:id="echoid-head92" xml:space="preserve">EXPERIMENTUM LXIV.</head> <p> <s xml:id="echoid-s2876" xml:space="preserve">Si Magnes homogeneæ ſubſtantiæ undiquaque obruatur limatura <lb/>Ferri tenuiſſima, vel pulvere Indico, nullum fere erit in ſuperſicie <lb/>punctum, cui attracta limatura non adhæret: </s> <s xml:id="echoid-s2877" xml:space="preserve">majori tamen copia adhæ-<lb/>ret angulis & </s> <s xml:id="echoid-s2878" xml:space="preserve">polis, quam lateralibus planiſque Magnetis partibus; </s> <s xml:id="echoid-s2879" xml:space="preserve">at-<lb/>trahit igitur omne punctum Magnetis Ferrum, etiamſi non æque valide.</s> <s xml:id="echoid-s2880" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div85" type="section" level="1" n="85"> <head xml:id="echoid-head93" xml:space="preserve">EXPERIMENTUM LXV.</head> <p> <s xml:id="echoid-s2881" xml:space="preserve">Si limatura Ferri rarè, & </s> <s xml:id="echoid-s2882" xml:space="preserve">æquabiliter ſpargatur ſupra corporis non <lb/>admodum denſi ſuperficiem planam (ne quidem Ferro excepto) & </s> <s xml:id="echoid-s2883" xml:space="preserve"><lb/>Magnes directe infra id corpus ponatur, alterutro polo ſpectante <lb/>ſurſum, primo plurimæ particulæ limaturæ conjungentur in formam <lb/>oblongæ Acus, illæ perpendiculariter ſupra ſuperficiem erigentur, <lb/>quæ directe e regione poli Magnetis ſunt: </s> <s xml:id="echoid-s2884" xml:space="preserve">moto Magnete dextror-<lb/>ſum ſecundum longitudinem plani ſuſtinentis, cadunt omnes partes <lb/>limaturæ ſiniſtrorſum; </s> <s xml:id="echoid-s2885" xml:space="preserve">redeunte Magnete ſiniſtrorſum, eriguntur <lb/>partes, caduntque dextrorſum: </s> <s xml:id="echoid-s2886" xml:space="preserve">idem ſpectatur effectus, quicun-<lb/>que Magnetis polus ſurſum fuerit converſus. </s> <s xml:id="echoid-s2887" xml:space="preserve">Poſt itus reditusque <lb/>aliquot Magnetis infra planum ſuſtinens ſcobem, ordinatur lima-<lb/>tura in ſeries oblongas.</s> <s xml:id="echoid-s2888" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2889" xml:space="preserve">Si pars Magnetis lateralis plano obverſa, ſed infra illud promo-<lb/>veatur dextrorſum, vel ſiniſtrorſum, etiam erigitur limatura, ca-<lb/>ditque contraria directione, quam qua Magnes movetur, cadit tamen <lb/>paulum oblique, magis nempe a polis utrimque attracta, quam a <lb/>meridiano Magnetis.</s> <s xml:id="echoid-s2890" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2891" xml:space="preserve">Si aliquoties infra planum Magnetem, alterutro polo ſurſum ſpe-<lb/>ctante, dextrorſum & </s> <s xml:id="echoid-s2892" xml:space="preserve">ſiniſtrorſum promoveris, ut limatura ſit in ſeries <pb o="119" file="0133" n="133" rhead="DE MAGNETE."/> ordinata, tum invertatur Magnes, & </s> <s xml:id="echoid-s2893" xml:space="preserve">altero polo ſurſum ſpectante, <lb/>commoveatur; </s> <s xml:id="echoid-s2894" xml:space="preserve">primo limatura hærebit quaſi anceps, neſcia quor-<lb/>ſum ſe vertat cadatque, ſed repetito Magnetis itu erigitur, & </s> <s xml:id="echoid-s2895" xml:space="preserve">cadit <lb/>contraria directione, quam qua Magnes movebatur.</s> <s xml:id="echoid-s2896" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2897" xml:space="preserve">Si autem ſupra limaturam Ferri Magnetem protraxeris, erigitur <lb/>rectà ea limaturæ pars, quæ Magneti ſubjacet, cæteroquin ſequitur <lb/>motum Magnetis, unde ipſo moto dextrorſum, limatura cadit dex-<lb/>trorſum, & </s> <s xml:id="echoid-s2898" xml:space="preserve">contra: </s> <s xml:id="echoid-s2899" xml:space="preserve">Optime fit hoc Experimentum limaturam ſpar-<lb/>gendo ſupra tenues laminas metallicas: </s> <s xml:id="echoid-s2900" xml:space="preserve">Lucretius quondam hoc in-<lb/>ſtituiſſe videtur, cum canebat, <lb/>Exſultare etiam Samothracia ferrea vidi, <lb/>Et ramenta ſimul Ferri furere intus ahenis <lb/>In ſcaphis, lapis hic Magnes cum ſubditus eſſet, <lb/>Vſque adeo fugere a ſaxo geſtire videtur <lb/>Ære interpoſito, diſcordia tanta creatur.</s> <s xml:id="echoid-s2901" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2902" xml:space="preserve">Quemadmodum eriguntur caduntque partes ſcobis in hoc Experi-<lb/>mento, ita erigi diſponique partes in ſolido Ferro, quod Magneti <lb/>aſſricatur, opinatus fuit Gaſſendus, ideoque in Ferro partes jacere <lb/>ſiniſtrorſum Magnete ſuper ipſo ducto dextrorſum, & </s> <s xml:id="echoid-s2903" xml:space="preserve">contra, veluti <lb/>campus frumento conſitus ariſtas verſus unum latus a vento afflante <lb/>jacentes gerit, & </s> <s xml:id="echoid-s2904" xml:space="preserve">in oppoſitum protenſas a vento contrario. </s> <s xml:id="echoid-s2905" xml:space="preserve">Attamen <lb/>mihi partes ſolidi Ferri fortius cohærere videntur, quam ut a vi <lb/>Magnetica ita ordinarentur: </s> <s xml:id="echoid-s2906" xml:space="preserve">ſedeo conceſſo, non clarius intelligitur, <lb/>quomodo ex ejuſmodi partium ſitu vis attrahendi aliud Ferrum ſe-<lb/>quetur, aut quid ſitus ad directionem Ferri verſus aliquas cæli pla-<lb/>gas conferet, niſi fluidum advocetur.</s> <s xml:id="echoid-s2907" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2908" xml:space="preserve">Explicantur autem memorata phænomena facile, modo in ante-<lb/>ceſſum notemus, parva fragmenta Acuum oblonga, loco ſcobis <lb/>impoſita plano, a Magnete infra moto, plane eodem modo erigi, & </s> <s xml:id="echoid-s2909" xml:space="preserve"><lb/>cadere ad oppoſitam partem ac Magnes movetur; </s> <s xml:id="echoid-s2910" xml:space="preserve">Quare ſcobs po-<lb/>terit| conſiderari, inſtar congeriei exiguorum, ſed oblongorum fra-<lb/>gmentorum: </s> <s xml:id="echoid-s2911" xml:space="preserve">Concipiatur Magnes directe infra unam particulam, <lb/>hæc erigetur ſupra planum perpendiculariter, atque ambas extre-<lb/>mitates nanciſcitur polares, quarum ea, quæ plano contigua, eſt <lb/>polus alterius nominis, quam Magnetis, planum ibi tangentis, (poli <lb/>enim Magnetum diverſi nominis tantum ſe attrahunt), extremitas <pb o="120" file="0134" n="134" rhead="DISSERTATIO"/> particulæ ſuperior erit polus cognominis poli Magnetici, & </s> <s xml:id="echoid-s2912" xml:space="preserve">quia <lb/>poli cognomines Magnetum ſemet fugant, hic quoque a polo Ma-<lb/>gnetis fugari concipiendus eſt: </s> <s xml:id="echoid-s2913" xml:space="preserve">promoveatur nunc Magnes infra <lb/>particulam ſiniſtrorſum, adeoque ſecum trahere nitetur eam parti-<lb/>culæ extremitatem, quæ plano eſt contigua, ſed hæc ab aſperitate <lb/>plani impeditur ſequi, manetque in priori loco, polus vero Ma-<lb/>gnetis fugans ſuperiorem particulæ extremitatem, oblique in eam <lb/>agit, & </s> <s xml:id="echoid-s2914" xml:space="preserve">quidem dextrorſum, quare pelletur dextrorſum, obliquum <lb/>accipiendo ſitum; </s> <s xml:id="echoid-s2915" xml:space="preserve">promoto tandem ulterius Magnete, ut in eam par-<lb/>ticulam non amplius agat, hæc cadet ſua gravitate dextrorſum: </s> <s xml:id="echoid-s2916" xml:space="preserve">quod <lb/>in una conceptum fuit particula, obtinet in omnibus, idcirco moto <lb/>Magnete ſiniſtrorſum infra planum, erigetur prius perpendiculariter <lb/>ipſi impoſita Scobs, delapſura dextrorſum poſtea.</s> <s xml:id="echoid-s2917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2918" xml:space="preserve">Cum vero Magnes ſupra Scobem & </s> <s xml:id="echoid-s2919" xml:space="preserve">planum poſitus promovetur, <lb/>erigitur quoque quælibet particula perpendiculariter, cujus ſuperior <lb/>extremitas fit polus alterius nominis ac polus Magnetis, quem ſpe-<lb/>ctat, a quo proinde attrahitur, cujus motum ſequitur, & </s> <s xml:id="echoid-s2920" xml:space="preserve">ideo moto <lb/>Magnete ſupra Scobem ſiniſtrorſum, cadet Scobs ſiniſtrorſum, <lb/>eventu plane contrario, quam cum Magnes infra Scobem promo-<lb/>vebatur.</s> <s xml:id="echoid-s2921" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div86" type="section" level="1" n="86"> <head xml:id="echoid-head94" xml:space="preserve">EXPERIMENTUM LXVI.</head> <p> <s xml:id="echoid-s2922" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2923" xml:space="preserve">6. </s> <s xml:id="echoid-s2924" xml:space="preserve">fig. </s> <s xml:id="echoid-s2925" xml:space="preserve">3. </s> <s xml:id="echoid-s2926" xml:space="preserve">Si circa Magnetem A B, impoſitum plano, ſpar-<lb/>gatur Limatura Ferri, aut potius pulvis Indicus, ad aliquam uſque <lb/>latitudinem, leviterque planum concutiatur, diſponitur pulvis in <lb/>ſeries ordinatas oblongas, intercapedinem relinquentes, quales <lb/>figura exhibet; </s> <s xml:id="echoid-s2927" xml:space="preserve">in quibus duæ ſunt plagæ A A, B B, plerumque <lb/>rectilineas ſeries formantes, ſed aliæ circa utrumque Magnetis latus, <lb/>incurvantur, uti D D, C C. </s> <s xml:id="echoid-s2928" xml:space="preserve">quæ curvarum perpetuo ampliatarum, <lb/>prout plus â Magnete diſtant, ſunt portiones: </s> <s xml:id="echoid-s2929" xml:space="preserve">omnes ſeries non <lb/>æquale intervallum inter ſe relinquunt, ſed prope Magnetem pau-<lb/>lum arctius: </s> <s xml:id="echoid-s2930" xml:space="preserve">quod circiter adæquat {6/10} lineæ: </s> <s xml:id="echoid-s2931" xml:space="preserve">poll. </s> <s xml:id="echoid-s2932" xml:space="preserve">Rhen intervalla non <lb/>penitus ſunt ſine pulvere interſperſo, adhærente ſeriei alicui, & </s> <s xml:id="echoid-s2933" xml:space="preserve">excur-<lb/>rente irregulariter uſque ad ſeriem vicinam, id tamen plus obtinet in <lb/>majoria Magnete diſtantia, quam prope ipſum: </s> <s xml:id="echoid-s2934" xml:space="preserve">Optime hæc omnia <pb o="121" file="0135" n="135" rhead="DE MAGNETE."/> conſpici poſſunt poſito Magnete ſupra ſpeculum vitreum, infra quod <lb/>alba jacet charta; </s> <s xml:id="echoid-s2935" xml:space="preserve">nulla enim ſuperficies datur lævigatior, ſupra quam <lb/>ferrea Scobs, vel pulvis Indicus, in ſeries magis ordinatas diſponi <lb/>poteſt.</s> <s xml:id="echoid-s2936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2937" xml:space="preserve">Quicunque has ſeries circa Magnetem primo intuetur, extemplo <lb/>judicaret eas a circumfluente circa lapidem Fluido pendere, quod <lb/>delatum inter Ferri partes, eas tam juſto diſponeret ordine, cum <lb/>viam ſibi quærit, atque Scobis partes, ut totidem obſtacula, removet: <lb/></s> <s xml:id="echoid-s2938" xml:space="preserve">attendenti autem nihil minus verum eſſe apparet; </s> <s xml:id="echoid-s2939" xml:space="preserve">cum enim Scobs <lb/>ferrea ſit admodum gravis & </s> <s xml:id="echoid-s2940" xml:space="preserve">craſſa, debebit id fluidum, quod eam <lb/>e loco moveret, ordinaretque, eſſe copioſum, veloci actem motu, & </s> <s xml:id="echoid-s2941" xml:space="preserve"><lb/>magnarum virium; </s> <s xml:id="echoid-s2942" xml:space="preserve">id igitur facilius movebit, propellet, disjiciet aut <lb/>ordinabit Scobem parteſve corporum leviſſimas, uti farinam frumenti, <lb/>Scobem Ligni, Eboris, Stanni, Cupri; </s> <s xml:id="echoid-s2943" xml:space="preserve">quam graviſſimas Ferri: </s> <s xml:id="echoid-s2944" xml:space="preserve">verum <lb/>hæc omnia circa Magnetem ſparſa non in ſeries diſponuntur, non mo-<lb/>ventur, ſed jacent quieta, uti ceciderunt, ac ſi nullus afforet Magnes, an <lb/>igitur fingipoteſt fluidum, quod corpora moveret craſſiora & </s> <s xml:id="echoid-s2945" xml:space="preserve">gravia, in <lb/>leviſſima autem operari non poſſet? </s> <s xml:id="echoid-s2946" xml:space="preserve">ſed non fluere in intervallis <lb/>ſerierum dicatur fluidum, verum per ipſam Scobis ſubſtantiam, & </s> <s xml:id="echoid-s2947" xml:space="preserve"><lb/>ea ideo ita ordinari; </s> <s xml:id="echoid-s2948" xml:space="preserve">hoc conceſſo, quæram quomodo id fluidum <lb/>non moveat partes leviſſimas farinæ, quibus occurrit, & </s> <s xml:id="echoid-s2949" xml:space="preserve">quas penetrat, <lb/>cum moveat Ferri partes graviſſimas? </s> <s xml:id="echoid-s2950" xml:space="preserve">& </s> <s xml:id="echoid-s2951" xml:space="preserve">2°. </s> <s xml:id="echoid-s2952" xml:space="preserve">quomodo Scobs ferrea <lb/>in ſeries intervalla relinquentes ordinetur, & </s> <s xml:id="echoid-s2953" xml:space="preserve">non partes juxta ſe <lb/>poſitas tantum habeat? </s> <s xml:id="echoid-s2954" xml:space="preserve">Quas difficultates nemo ſolvet facile, prius-<lb/>quam indolem virium Magneticarum melius intellexerimus.</s> <s xml:id="echoid-s2955" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div87" type="section" level="1" n="87"> <head xml:id="echoid-head95" xml:space="preserve">EXPERIMENTUM LXVII.</head> <p> <s xml:id="echoid-s2956" xml:space="preserve">Sternebatur limatura Ferri ſupra parallelopipedum ferreum 6 <lb/>pollices craſſum, cujus inferiori extremo applicatus fuit Magnes, <lb/>illico Limatura recta ſurſum erigebatur: </s> <s xml:id="echoid-s2957" xml:space="preserve">indicio vim Magnetis tranſire <lb/>quoque per Ferrum, etiamſi craſſiſſimum.</s> <s xml:id="echoid-s2958" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2959" xml:space="preserve">Deinde ſupra aliud parallelopipedum ferreum, unum pollicem craſ-<lb/>ſum, limatura Ferri ſatis denſe ſpargebatur, huic iterum præcedens <lb/>parallelopipedum 6 pollicum impoſitum, ejuſque parti ſuperiori in-<lb/>jecta quoque fuit Ferri Limatura, tum Magnes infimo applicatus <pb o="122" file="0136" n="136" rhead="DISSERTATIO"/> parallelopipedo, vires ſuas transfudit per omnem hunc apparatum <lb/>uſque ad Limaturam ſuperiorem, quam erexit ut ante, unde non <lb/>modo vis tranſit per ſolidum Ferrum, ſed per interruptum, imo per <lb/>diſſolutam Scobem uſque in ſolidam maſſam.</s> <s xml:id="echoid-s2960" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div88" type="section" level="1" n="88"> <head xml:id="echoid-head96" xml:space="preserve">EXPERIMENTUM LXVIII.</head> <p> <s xml:id="echoid-s2961" xml:space="preserve">Ponantur duo Magnetes juxta ſe invicem, ita ut amborum poli <lb/>cognomines ſurſum ſpectent, atque in eadem ſint altitudine, his impo-<lb/>natur ſpeculum vitreum, ſuper quo ſparſa Scobs ferrea ordinatur <lb/>in eaſdem ſeries formaſque, quas alteruter Magnes formaviſſet, niſi <lb/>quod in loco inter ambos polos medio, ſit centrum polare ſive cen-<lb/>trum virium, quod pro uno polo habendum eſt: </s> <s xml:id="echoid-s2962" xml:space="preserve">cæteroquin ad ma-<lb/>jorem quaquaverſum latitudinem vis diffuſa conſpicitur, ambobus <lb/>Magnetibus ſe mutuo adjuvantibus.</s> <s xml:id="echoid-s2963" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div89" type="section" level="1" n="89"> <head xml:id="echoid-head97" xml:space="preserve">EXPERIMENTUM LXIX.</head> <p> <s xml:id="echoid-s2964" xml:space="preserve">Tab. </s> <s xml:id="echoid-s2965" xml:space="preserve">5. </s> <s xml:id="echoid-s2966" xml:space="preserve">fig. </s> <s xml:id="echoid-s2967" xml:space="preserve">1. </s> <s xml:id="echoid-s2968" xml:space="preserve">Duo Magnetes formæ Cubicæ, polis cognomini-<lb/>bus ſurſum ſpectantibus, quorum ſuperſicies ſint planæ & </s> <s xml:id="echoid-s2969" xml:space="preserve">lævigatæ, <lb/>jungantur ſecum invicem, ſed ita, ut inter ambos A & </s> <s xml:id="echoid-s2970" xml:space="preserve">B jaceat <lb/>C lamella tenuis, ferrea; </s> <s xml:id="echoid-s2971" xml:space="preserve">aſſeri iis impoſito inſpergatur limatura <lb/>Ferri, hæc diſponetur in ſeries, quas repræſentat figura, in qua <lb/>locus polaris fortiſſimi Magnetis B ſatis bene indicatur, cæteroquin <lb/>ſupra laminam C vix conſpicitur aliquid Scobis, & </s> <s xml:id="echoid-s2972" xml:space="preserve">ultra hunc lo-<lb/>cum omnia ſunt confuſo ordine poſita.</s> <s xml:id="echoid-s2973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2974" xml:space="preserve">Differt hoc Experimentum a præcedenti, lamellâ C ferreâ inter-<lb/>poſitâ, quæ omnes has irregularitates attractionis producit, impe-<lb/>diendo quominus poli ambo ſe conjungant in medio, polum vi-<lb/>rium communem faciendo, ſed efficit ut vires utriuſque Magnetis <lb/>diſtinctæ maneant; </s> <s xml:id="echoid-s2975" xml:space="preserve">quia autem Magnes B præſtantior eſt quam A, <lb/>ad latera ſe ſpectantia vires ſuas fortius emittit, quæ tranſilientes <lb/>ſepimentum ferreum, ordinem Limaturæ ab A factum perturbant.</s> <s xml:id="echoid-s2976" xml:space="preserve"/> </p> <pb o="123" file="0137" n="137" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div90" type="section" level="1" n="90"> <head xml:id="echoid-head98" xml:space="preserve">EXPERIMENTUM LXX.</head> <p> <s xml:id="echoid-s2977" xml:space="preserve">Ambo iidem Magnetes juxta ſe, nihilo interpuncto, ponantur; </s> <s xml:id="echoid-s2978" xml:space="preserve">ſedut <lb/>poli alterni nominis ſurſum ſpectent, ſupra aſſerculum, illis impoſitum, <lb/>ſpargatur Scobs ferrea, hæc uti in Tab. </s> <s xml:id="echoid-s2979" xml:space="preserve">5. </s> <s xml:id="echoid-s2980" xml:space="preserve">fig. </s> <s xml:id="echoid-s2981" xml:space="preserve">1. </s> <s xml:id="echoid-s2982" xml:space="preserve">ambos polos mon-<lb/>ſtrabit ad A, a. </s> <s xml:id="echoid-s2983" xml:space="preserve">inter quos loco intermedio Scobs in curvilineam, <lb/>ab utraque parte convexam, figuram diſponetur, cæteroquin qua-<lb/>quaverſum vis rectà exiens Scobem quoque rectà conformat: </s> <s xml:id="echoid-s2984" xml:space="preserve">in-<lb/>termedia inter polos A, a, Scobis figura eſt eadem, ac ſi ambo Ma-<lb/>gnetes in eodem jacentes horizontali plano polis alterni nominis ſc <lb/>ſpectaſſent, non Scobis fit fuga, ſed amica attractio, a viribus <lb/>conſpirantium polorum excitata.</s> <s xml:id="echoid-s2985" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div91" type="section" level="1" n="91"> <head xml:id="echoid-head99" xml:space="preserve">EXPERIMENTUM LXXI.</head> <p> <s xml:id="echoid-s2986" xml:space="preserve">Si Limatura Ferri infundatur tubis vitreis, atque arcte compin-<lb/>gatur, fit æque apta recipiendo vim Magnetis, quam Ferri fruſtum <lb/>unitum, ut docet ejus affrictio ad Magnetem, & </s> <s xml:id="echoid-s2987" xml:space="preserve">vis deinde explo-<lb/>rata, nam ab hoc non differt, niſi quod partes in maſſa ſunt ar-<lb/>ctius unitæ inter ſe, quam in Limatura attamen in Limatura com-<lb/>pactâ ſe bene contingunt: </s> <s xml:id="echoid-s2988" xml:space="preserve">ſi vero hæc Limatura commoveatur, <lb/>quaſſeturque, ut partes locum ſuum mutent, illico omnis earum vis <lb/>perit: </s> <s xml:id="echoid-s2989" xml:space="preserve">nam fricantur partes inter ſe diverſiſſimis directionibus; </s> <s xml:id="echoid-s2990" xml:space="preserve">quem-<lb/>admodum autem virtus ex Ferro auferebatur, cum contraria directio-<lb/>ne eidem polo Magnetis affricabatur quam ante, ita per ſimiles con-<lb/>trarias frictiones vis ex Limatura perit.</s> <s xml:id="echoid-s2991" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div92" type="section" level="1" n="92"> <head xml:id="echoid-head100" xml:space="preserve">EXPERIMENTUM LXXII.</head> <p> <s xml:id="echoid-s2992" xml:space="preserve">Conſtitit quidem huc uſque Magnetem attrahere Ferrum; </s> <s xml:id="echoid-s2993" xml:space="preserve">quia <lb/>autem Ferrum eſt maſſa admodum compoſita, ex Sulphure, Sale, <lb/>Terra, examinandum erat, quid inſit Ferro, quod attrahitur: </s> <s xml:id="echoid-s2994" xml:space="preserve">an <lb/>Sulphur, an Sal, an Terra, an autem hæc omnia ſimul poſtulen-<lb/>tur permixta?</s> <s xml:id="echoid-s2995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2996" xml:space="preserve">Si Ferrum in Carbonibus foſſilibus vehementiſſime igniatur, ita <pb o="124" file="0138" n="138" rhead="DISSERTATIO"/> ut ſcintillet, tumque ex Igne eximatur, & </s> <s xml:id="echoid-s2997" xml:space="preserve">colligantur Scintillæ <lb/>expulſæ, Sphæricæ, quæ in vitrum abiverunt, hæ nec attrahun-<lb/>tur a Magnete, nec Acum Nauticam ullo modo ex ſuâ viâ detorquent: <lb/></s> <s xml:id="echoid-s2998" xml:space="preserve">Eſt vitrificatio productum ultimum, ad quod metallum aliudve cor-<lb/>pus reduci poteſt: </s> <s xml:id="echoid-s2999" xml:space="preserve">conſtat hoc vitrum ex Terrâ, ſed an alia admixta <lb/>habeat, diſtinguere non licet. </s> <s xml:id="echoid-s3000" xml:space="preserve">Quamobrem terra Ferri ſummo acta <lb/>Igne non amplius vim Magneticam habet, imo nequidem recipere <lb/>poteſt.</s> <s xml:id="echoid-s3001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3002" xml:space="preserve">Scoriæ Ferri, quæ ſupra incudem ex cuſo Ferro decidunt, & </s> <s xml:id="echoid-s3003" xml:space="preserve"><lb/>latæ planæque ſunt, attrahuntur fortiſſime a Magnete, & </s> <s xml:id="echoid-s3004" xml:space="preserve">ſemel <lb/>attractæ vim recipiunt, quam aliquamdiu retinent: </s> <s xml:id="echoid-s3005" xml:space="preserve">cæteroquin <lb/>modo exceptæ a Ferro, tumque oppoſitæ Acui Magneticæ; </s> <s xml:id="echoid-s3006" xml:space="preserve">non <lb/>multum in ipſam agunt, eam tamen detorquent a ſua viâ.</s> <s xml:id="echoid-s3007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3008" xml:space="preserve">Sunt hæ Scoriæ minus combuſtæ ab Igne, quam globi vitrificati, <lb/>orbatæ tamen ſunt Sulphure, & </s> <s xml:id="echoid-s3009" xml:space="preserve">Sale, hinc non amplius in Igne <lb/>liqueſcunt, nec ardent: </s> <s xml:id="echoid-s3010" xml:space="preserve">continent hæ itaque in ſe vel illud princi-<lb/>pium, vel corporum genus, quod adhuc a Magnete attrahitur, & </s> <s xml:id="echoid-s3011" xml:space="preserve"><lb/>quod Igne vehementi continuato tandem avolat, ante quam maſſa in <lb/>vitrum abit: </s> <s xml:id="echoid-s3012" xml:space="preserve">quamobrem id corporis genus, quod in Ferro eſt, <lb/>& </s> <s xml:id="echoid-s3013" xml:space="preserve">quod ſolum attrahitur, non videtur magnam in eo conſtituere <lb/>copiam, cum Ferrum conſtet ex maxima patte Sulphuris, & </s> <s xml:id="echoid-s3014" xml:space="preserve">ex ma-<lb/>teria copioſa, quæ in vitrum abit; </s> <s xml:id="echoid-s3015" xml:space="preserve">eſt id autem valde fixum, nam <lb/>non avolat ex tota maſſa, niſi cum in vitrum abibit, quod modo <lb/>ſit Igne terreſtri vehementiſſimo omnium, quem excitare ars po-<lb/>teſt.</s> <s xml:id="echoid-s3016" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3017" xml:space="preserve">Quod ſi ex Ferro, id quod attrahitur a Magnete, elici poſſet <lb/>ſolum, id vehementiſſime attraheret & </s> <s xml:id="echoid-s3018" xml:space="preserve">attraheretur, & </s> <s xml:id="echoid-s3019" xml:space="preserve">quo pro-<lb/>piores ſumus ad id purum habendum, eo maſſam fortius attrahen-<lb/>tem poſſidemus. </s> <s xml:id="echoid-s3020" xml:space="preserve">Eum in finem conatus fui Ferrum ſpoliare reliquo <lb/>omni, quod non attrahitur a Magnete, ſequenti modo; </s> <s xml:id="echoid-s3021" xml:space="preserve">Limatu-<lb/>ram Ferri in aliqua diſtantia ab Acu, 6 pollices longa, poſui, eam <lb/>admovi, donec manifeſto percipiebam Acum agere in Limaturam & </s> <s xml:id="echoid-s3022" xml:space="preserve"><lb/>a ſuâ directione turbari: </s> <s xml:id="echoid-s3023" xml:space="preserve">tum Limaturam indidi phialæ parvæ vi-<lb/>treæ, quam in eodem arcu circuli, quem cuſpis Acûs deſcribit, <lb/>poſui, ad diſtantiam {1/2} pollicis a ſe mutuo, cuſpis Acus attracta ad-<lb/>hæſit ſuperficiei phialæ, huic ita quieſcenti infudi leniter oleum Vi- <pb o="125" file="0139" n="139" rhead="DE MAGNETE."/> trioli, quod Limaturam ſolvebat, elapſis circiter duobus minutis, <lb/>Acus reliquit phialam aliquomodo, petens directionem priſtinam <lb/>ſibique naturalem; </s> <s xml:id="echoid-s3024" xml:space="preserve">quo Limaturæ major quantitas ſolvebatur, eo <lb/>Acus etiam magis recedebat a phiala; </s> <s xml:id="echoid-s3025" xml:space="preserve">nunquam tamen accurate in <lb/>ſitum priſtinum rediit: </s> <s xml:id="echoid-s3026" xml:space="preserve">idem contigit cum ſolvebam Ferrum in Spi-<lb/>ritu Nitri Glauberi, aut Aqua forti vulgari: </s> <s xml:id="echoid-s3027" xml:space="preserve">vis attrahens ſemper <lb/>imminuta erat, non penitus tamen ſublata: </s> <s xml:id="echoid-s3028" xml:space="preserve">Ex ſolutione Ferri præ-<lb/>paravi vitriolum Martis, quod admodum ſiccum, & </s> <s xml:id="echoid-s3029" xml:space="preserve">oppoſitum cuſ-<lb/>pidi Acus 6 pollicum, eam parum attraxit, attamen oculo diſtin-<lb/>gui poterat cuſpide ad {1/4} gradus ex ſuo loco recedente, ſimulac vi-<lb/>triolum prope ipſam tenebatur: </s> <s xml:id="echoid-s3030" xml:space="preserve">repetii hoc Experimentum aliquo-<lb/>ties, in initio opinatus me decipi, cum acutus Lemmerius in L’Hiſt. <lb/></s> <s xml:id="echoid-s3031" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s3032" xml:space="preserve">Roy. </s> <s xml:id="echoid-s3033" xml:space="preserve">A°. </s> <s xml:id="echoid-s3034" xml:space="preserve">1706. </s> <s xml:id="echoid-s3035" xml:space="preserve">obſervaverit, vitriolum Martis non <lb/>attrahere Magnetem, forte non inſtituit cum Acu tam longa, nam <lb/>in breviori & </s> <s xml:id="echoid-s3036" xml:space="preserve">vulgari Acu nequidem oculatiſſimus motum ullum at-<lb/>tractionis obſervabit, ſed tantum in longiſſima conſpici potuit: </s> <s xml:id="echoid-s3037" xml:space="preserve">De-<lb/>creverat hæc vis attractionis ex Limatura, cum ſolvebatur, quia omnes <lb/>ejus partes a ſe removebantur, variiſque directionibus ſimul agita-<lb/>tæ, haud aliter quam Limatura in præcedenti Experimento con-<lb/>cuſſa, vim ſuam amittunt. </s> <s xml:id="echoid-s3038" xml:space="preserve">Hæc ſolutio Ferri præmiſſa fuit, ut <lb/>melius poſſet Ferrum ſuo Sulphure orbari, id enim fortiſſime ad-<lb/>hæret Spiritibus acidis, & </s> <s xml:id="echoid-s3039" xml:space="preserve">cum iis ope Ignis facile avolat: </s> <s xml:id="echoid-s3040" xml:space="preserve">Ex Vi-<lb/>triolo immiſſo retortæ eduxi Spiritum acidum cum Sulphure mixtum <lb/>vi Ignis, donec materia in fundo reſtans rubri eſſet coloris, quæ <lb/>vocatur vulgo Colcotar Vitrioli: </s> <s xml:id="echoid-s3041" xml:space="preserve">hoc appoſitum Acui eidem lon-<lb/>giſſimæ, motum excitavit, ſed parvum, majorem tamen priori, <lb/>quem ſolum Vitriolum ediderat: </s> <s xml:id="echoid-s3042" xml:space="preserve">Spiritus acidus in phiala collectus <lb/>appoſitusque apici nullum ſignum attractionis oſtendit; </s> <s xml:id="echoid-s3043" xml:space="preserve">quamob-<lb/>rem concludo; </s> <s xml:id="echoid-s3044" xml:space="preserve">Sulphur Ferri non eſſe cauſam virtutis Magneticæ.</s> <s xml:id="echoid-s3045" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3046" xml:space="preserve">Deinde Colcotar impoſui igni violentiſſimo in crucibulo terreo, <lb/>quod evaſit tandem maſſa nigra & </s> <s xml:id="echoid-s3047" xml:space="preserve">rara, in qua non amplius ullum indi-<lb/>eium Sulphuris erat, quemadmodum bene adnotavit Cl. </s> <s xml:id="echoid-s3048" xml:space="preserve">Lemmerius: <lb/></s> <s xml:id="echoid-s3049" xml:space="preserve">hæc enim erat friabilis facile in pulverem, injecta Igni non ſcintillabat, <lb/>veluti limatura Ferri facit, & </s> <s xml:id="echoid-s3050" xml:space="preserve">Sale omni etiam orbata videtur, cum <lb/>nunquam rubiginem contrahat nec in aëre, nec in aqua ſalſa; </s> <s xml:id="echoid-s3051" xml:space="preserve">etiam <lb/>vix dat Tincturam, non efferveſcit cum Oleo Vitrioli, nec cum Spi-<lb/>ritu Salis, aut Spiritu Nitri.</s> <s xml:id="echoid-s3052" xml:space="preserve"/> </p> <pb o="126" file="0140" n="140" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s3053" xml:space="preserve">Sed hæc maſſa ſive integra, ſive in pulverem tuſa, vehementer <lb/>& </s> <s xml:id="echoid-s3054" xml:space="preserve">a Magnete & </s> <s xml:id="echoid-s3055" xml:space="preserve">ab Acu Nautica attrahitur, & </s> <s xml:id="echoid-s3056" xml:space="preserve">ad longe majorem <lb/>diſtantiam quam Limatura Ferri recens: </s> <s xml:id="echoid-s3057" xml:space="preserve">quod manifeſto probat ne-<lb/>que Sulphur, neque Salem Ferri eſſe materiam attractioni propriam, <lb/>ſed aliquam aliam, quæ eo fortius attrahitur, quo accuratius orbata <lb/>eſt Sulphure & </s> <s xml:id="echoid-s3058" xml:space="preserve">Sale.</s> <s xml:id="echoid-s3059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3060" xml:space="preserve">Hæc materia cohærebat hactenus cum terra ſolida, quam in vi-<lb/>trum abire ſuperius monui, & </s> <s xml:id="echoid-s3061" xml:space="preserve">quæ nullam vim in ſe habet: </s> <s xml:id="echoid-s3062" xml:space="preserve">igitur <lb/>ſeparanda erat ab hac terrâ inerti, quantum poterat; </s> <s xml:id="echoid-s3063" xml:space="preserve">in eo ſecutus <lb/>fui Cl. </s> <s xml:id="echoid-s3064" xml:space="preserve">Lemmerium, qui ad pulverem redactæ materiæ affudit Spi-<lb/>ritum Nitri; </s> <s xml:id="echoid-s3065" xml:space="preserve">abſque efferveſcentia ſenſibili ſolvebatur pulvis, atque <lb/>ad ſuperficiem abibat in pulverem album, pinguiuſculum, qui ſæ-<lb/>pe aliquamdiu candorem retinet, aliquando fulvus fit; </s> <s xml:id="echoid-s3066" xml:space="preserve">hic pulvis <lb/>collectus ſeorſim, & </s> <s xml:id="echoid-s3067" xml:space="preserve">prope exſiccatus attrahitur vi majori adhuc a <lb/>Magnete vel a lamina Chalybea, quam maſſa præcedens attracta <lb/>fuit: </s> <s xml:id="echoid-s3068" xml:space="preserve">videtur hoc corpus id ſolum eſſe, quod in Ferro cauſa attractio-<lb/>nis exiſtit, quodque miſtum cum aliis corporum generibus, ut Fer-<lb/>rum conſtituat, agere impeditur aliquomodo.</s> <s xml:id="echoid-s3069" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3070" xml:space="preserve">Forſitan ſimile aut idem corpus in Magnete eſt ſolum id, quod at-<lb/>tractionem in eo excitat, quod quo purius eſt & </s> <s xml:id="echoid-s3071" xml:space="preserve">in majori quantita-<lb/>te, eo Magnetem præſtantiorum virium facit: </s> <s xml:id="echoid-s3072" xml:space="preserve">Id autem quadante-<lb/>nus colligi poteſt ex Magnetibus, qui tempore generantur in aëre ex <lb/>Ferro: </s> <s xml:id="echoid-s3073" xml:space="preserve">quod cum ab aëre in rubiginem corroditur, ſuos Sales miſcet <lb/>cum materia terreſtri, Sulphur miſcetur cum Salibus per aërem na-<lb/>tantibus, & </s> <s xml:id="echoid-s3074" xml:space="preserve">idcirco ex Ferro ſeparantur ex ſe ejus principia com-<lb/>ponentia: </s> <s xml:id="echoid-s3075" xml:space="preserve">ſcilicet terra, materia Magnetica, Sal, Sulphur; </s> <s xml:id="echoid-s3076" xml:space="preserve">cum igi-<lb/>tur materia Magnetica ſimul cum pluvia ingreditur poros lapidis, <lb/>cui Ferrum inhæret, eos in veros Magnetes mutat, quos, expe-<lb/>rientia teſte, deprehendimus perpetuo ubicunque modo Ferrum aëri <lb/>diu expoſitum lapidique infixum ſpongioſo fuerit.</s> <s xml:id="echoid-s3077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3078" xml:space="preserve">Ex hac Analyſi liquet manifeſto, cur Chalybs melius imbuatur <lb/>vi Magnetica, eandemque retineat, quam Ferrum: </s> <s xml:id="echoid-s3079" xml:space="preserve">Chalybs enim <lb/>antequam uſibus convenit, aliquoties eſt igniendus & </s> <s xml:id="echoid-s3080" xml:space="preserve">cudendus, in <lb/>Igne certo certius deponens aliquantum ſui Sulphuris vel Olei, unde <lb/>nunquam tam flexilis eſt poſtea, quam Ferrum, tum igitur Chalybs <lb/>depuratur magis ab heterogenea materia adhærente, & </s> <s xml:id="echoid-s3081" xml:space="preserve">pro quanti- <pb o="127" file="0141" n="141" rhead="DE MAGNETE."/> tate maſſæ plus illius materiæ, quæ Magnetica eſt, in ſe retinet, <lb/>fortioremque attractionem exercet: </s> <s xml:id="echoid-s3082" xml:space="preserve">imo inde intelligitur, Ferrum eo <lb/>majori vi Magnetica imbui poſſe, quo plus illius materiæ Magne-<lb/>ticæ in ſe continet, & </s> <s xml:id="echoid-s3083" xml:space="preserve">omne Ferrum non ejus æqualem copiam ha-<lb/>bere docet experientia, cum datur Ferrum quod longe majorem vim <lb/>attrahendi accipit â Magnete, quam alterum.</s> <s xml:id="echoid-s3084" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3085" xml:space="preserve">Si Vitriolum Martis affricetur polo Magnetis, vi majori imbui-<lb/>tur, & </s> <s xml:id="echoid-s3086" xml:space="preserve">Acum Nauticam longe fortius attrahit, & </s> <s xml:id="echoid-s3087" xml:space="preserve">ex ſua ſede pro-<lb/>turbat, quam Vitriolum purum.</s> <s xml:id="echoid-s3088" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3089" xml:space="preserve">Boyleus Ocram Brittannicam, quæ eſt rubigo Ferri, ſed a natura-<lb/>libus Salibus acidis corroſi miſtique cum terra, exploravit an vim <lb/>Magneticam oſtenderet; </s> <s xml:id="echoid-s3090" xml:space="preserve">hujus nequicquam detexit: </s> <s xml:id="echoid-s3091" xml:space="preserve">cum autem <lb/>poſtea Igni commiſerat Ocram, partesque Sulphureas, Salinas, aliaſ-<lb/>que plurimas expulerat; </s> <s xml:id="echoid-s3092" xml:space="preserve">Ferrum in maſſa reſiduum ſuas vires attra-<lb/>ctrices oſtendere & </s> <s xml:id="echoid-s3093" xml:space="preserve">exſerere potuit, quibus egit in Acum Nauticam: <lb/></s> <s xml:id="echoid-s3094" xml:space="preserve">Vid. </s> <s xml:id="echoid-s3095" xml:space="preserve">Magnet. </s> <s xml:id="echoid-s3096" xml:space="preserve">pag. </s> <s xml:id="echoid-s3097" xml:space="preserve">499.</s> <s xml:id="echoid-s3098" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div93" type="section" level="1" n="93"> <head xml:id="echoid-head101" xml:space="preserve">EXPERIMENTUM LXXIII.</head> <p> <s xml:id="echoid-s3099" xml:space="preserve">Memoravimus in initio hujus Capitis 2, Magnetem vi valida at-<lb/>trahere aliquam arenæ ſpeciem, nigri coloris, ſplendentem, nun-<lb/>quam rubigine infectam, quæ ex Virginia affertur, atque Magnetis <lb/>ope ex alio ſecernitur pulvere; </s> <s xml:id="echoid-s3100" xml:space="preserve">gravitate ſpecifica donatur, quæ <lb/>eſt ad arenam vulgarem, uti 161 ad 71. </s> <s xml:id="echoid-s3101" xml:space="preserve">Operæ pretium erat inda-<lb/>gare an hæc Arena eſſet Ferrum, ejuſve quædam ſpecies, an nihil <lb/>metalli in ſe concluderet: </s> <s xml:id="echoid-s3102" xml:space="preserve">hoc ſi foret, Magnes in alia corpora, <lb/>præterquam in Ferrum operaretur: </s> <s xml:id="echoid-s3103" xml:space="preserve">Moulenus hanc Arenam variis <lb/>torſit modis, ſuorumque Experimentorum ſucceſſus inſeruit Philoſ. <lb/></s> <s xml:id="echoid-s3104" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3105" xml:space="preserve">N°. </s> <s xml:id="echoid-s3106" xml:space="preserve">197. </s> <s xml:id="echoid-s3107" xml:space="preserve">alia addidi tentamina, quæ ad clariorem ejus in-<lb/>tellectum conducere arbitratus fui.</s> <s xml:id="echoid-s3108" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3109" xml:space="preserve">1. </s> <s xml:id="echoid-s3110" xml:space="preserve">Si hæc arena Igni committatur & </s> <s xml:id="echoid-s3111" xml:space="preserve">calcinetur, poſt calcinatio-<lb/>nem vehementius a Magnete attrahitur, quam antea.</s> <s xml:id="echoid-s3112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3113" xml:space="preserve">2. </s> <s xml:id="echoid-s3114" xml:space="preserve">Arena calcinata mixta fuit cum Carbone in pulverem redacto, <lb/>impoſitaque fornaci probatoriæ per horæ ſpatium non abiit in Re-<lb/>gulum, ſed adhuc vehementiori impetu a Magnete attrahebatur.</s> <s xml:id="echoid-s3115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3116" xml:space="preserve">Quamobrem Ignis ſolus aliquid ex hoc pulvere ſeparat, quod at- <pb o="128" file="0142" n="142" rhead="DISSERTATIO"/> tractionem paulum impediebat; </s> <s xml:id="echoid-s3117" xml:space="preserve">non tamen eam materiam, quæ at-<lb/>trahitur, reddit volatilem, licet avolare queat, ut mox patebit.</s> <s xml:id="echoid-s3118" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3119" xml:space="preserve">3. </s> <s xml:id="echoid-s3120" xml:space="preserve">Arena mixta fuit cum Nitro fixo, impoſitaque fornaci fuſoriæ <lb/>ſpatio horæ non abiit in Regulum. </s> <s xml:id="echoid-s3121" xml:space="preserve">Reliqua maſſa non attraheba-<lb/>tur â Magnete exceptâ tenui cruſta, quæ Carboni in crucibulum <lb/>injecto adhærebat.</s> <s xml:id="echoid-s3122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3123" xml:space="preserve">4. </s> <s xml:id="echoid-s3124" xml:space="preserve">Deinde mixta fuit cum Nitro & </s> <s xml:id="echoid-s3125" xml:space="preserve">Carbone in pulverem contu-<lb/>ſo, atque per horam fuſoriæ fornaci immiſſa non abiit in regulum: <lb/></s> <s xml:id="echoid-s3126" xml:space="preserve">maſſa inde producta non â Magnete attrahebatur, exceptis iis par-<lb/>tibus, quæ Carboni adhærebant.</s> <s xml:id="echoid-s3127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3128" xml:space="preserve">5. </s> <s xml:id="echoid-s3129" xml:space="preserve">Arenæ alia pars mixta fuit cum Nitro & </s> <s xml:id="echoid-s3130" xml:space="preserve">floribus Sulphuris, <lb/>quæ in fornace aliquamdiu poſita, etiam Regulum non dedit.</s> <s xml:id="echoid-s3131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3132" xml:space="preserve">Liquet ergo ex his 1°, Nitrum reddere illud volatile, quod in <lb/>hac Arena a Magnete attrahitur, idcirco enim actionem Nitri paſſa, <lb/>non amplius patitur Magnetis actionem in ſe.</s> <s xml:id="echoid-s3133" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3134" xml:space="preserve">6. </s> <s xml:id="echoid-s3135" xml:space="preserve">Volatile autem reddi poſſe id quod attrahitur a Magnete patet <lb/>ex hoc proceſſu.</s> <s xml:id="echoid-s3136" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3137" xml:space="preserve">Arenæ Indicæ ℨiij, miſtæ cum Salis Ammoniaci ℨiij, expoſitæ <lb/>fuerunt in crucibulo aperto Igni modico, â quo tamen Sal Ammo-<lb/>niacus volatilis eſt factus expulſuſque: </s> <s xml:id="echoid-s3138" xml:space="preserve">totum reſiduum pondus ha-<lb/>bebat ℨij. </s> <s xml:id="echoid-s3139" xml:space="preserve">cum granis 23, adeoque pondus Arenæ amiſſum fuit 37 <lb/>granorum, poſito nihil Salis in Arenâ ſuperſtes fuiſle: </s> <s xml:id="echoid-s3140" xml:space="preserve">inerant re-<lb/>ſiduo grana majora, quam ante fuerant, coloris elegantis Cinnaba-<lb/>rini; </s> <s xml:id="echoid-s3141" xml:space="preserve">omnes reliquæ partes amiſſâ priori nigredine ad obſcure ru-<lb/>brum vergebant: </s> <s xml:id="echoid-s3142" xml:space="preserve">Magnes ſupra hæc omnia poſitus, ductus, imo <lb/>iis applicatus, vix aliquid attrahere potuit, dabatur tamen attractio <lb/>obſcura: </s> <s xml:id="echoid-s3143" xml:space="preserve">Reſiduum Aqua lotum & </s> <s xml:id="echoid-s3144" xml:space="preserve">edulcoratum, deinde exſicca-<lb/>tum, non majori vi quam ante a Magnere attractum fuit: </s> <s xml:id="echoid-s3145" xml:space="preserve">mani-<lb/>feſto indicio ſimul cum Sale Ammoniaco avolaſſe ex hac Arena, <lb/>quicquid a Magnete attrahitur.</s> <s xml:id="echoid-s3146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3147" xml:space="preserve">Non tamen id valde volatile eſt, aut cum leviſſimis Salis Ammo-<lb/>niaci partibus adſcendit, licet ex hac Arena, ſimul cum illispartes <lb/>quædam Aurantii coloris in auras adſcendant, uti ex ſequenti pro-<lb/>ceſſu liquebit.</s> <s xml:id="echoid-s3148" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3149" xml:space="preserve">7. </s> <s xml:id="echoid-s3150" xml:space="preserve">Mixtæ fuerunt Arenæ ℨiij, cum Salis Ammoniaci ℨiij, quæ <lb/>incluiæ phialæ committebantur Igni Arenæ trihorii ſpatio, quo ferè <pb o="129" file="0143" n="143" rhead="DE MAGNETE."/> omnis Sal ſublimabatur, adhærens lateribus & </s> <s xml:id="echoid-s3151" xml:space="preserve">fornici lagenæ, cum <lb/>partibus Arenæ aurantii coloris miſtus, relictâ materia in fundo, <lb/>ex fulvo atra, quæ expoſita Magneti aliquantum, ſed parum attra-<lb/>hebatur: </s> <s xml:id="echoid-s3152" xml:space="preserve">Maſſa in aqua ſoluta, dedit ſpiſſam Tincturam coloris <lb/>ferruginei, relicto craſſiori pulvere in fundo; </s> <s xml:id="echoid-s3153" xml:space="preserve">ſolutio cum notabili <lb/>efferveſcentia conjungebatur: </s> <s xml:id="echoid-s3154" xml:space="preserve">Tinctura exſiccata non a Magnete <lb/>attracta fuit; </s> <s xml:id="echoid-s3155" xml:space="preserve">pulvis, qui ſubſederat, erat craſſus, conſtans ex fra-<lb/>gmentis pluribus, duris, concretis, coloris elegantis rubicundi, <lb/>quæ exſiccata a Magnete vehementer attrahebantur: </s> <s xml:id="echoid-s3156" xml:space="preserve">hæc volatilia <lb/>nondum erant a Sale facta, & </s> <s xml:id="echoid-s3157" xml:space="preserve">ideo vim attrahentem, retinuerant; <lb/></s> <s xml:id="echoid-s3158" xml:space="preserve">quamobrem Sal Ammoniacus non illico eam abigit in auras, etiamſi <lb/>majori molimine expungatur.</s> <s xml:id="echoid-s3159" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3160" xml:space="preserve">Conſtat quoque ex præcedentibus operationibus, hanc Arenam non <lb/>abire in Regulum, unde concludendum eſt, eam nihil, aut ſaltem parum <lb/>Metalli in ſe habere; </s> <s xml:id="echoid-s3161" xml:space="preserve">niſi aliquod Sulphur ipſi adeo firmiter adhæ-<lb/>reat, ut a vi ignis & </s> <s xml:id="echoid-s3162" xml:space="preserve">Salium abſorberi nequeat, quodque impediit <lb/>quominus ad fluxionem reduci, & </s> <s xml:id="echoid-s3163" xml:space="preserve">in Regulum abire potuerit: </s> <s xml:id="echoid-s3164" xml:space="preserve">Sed <lb/>an poſtulatur metallum, ut Magnes in corpus aliquod operetur? </s> <s xml:id="echoid-s3165" xml:space="preserve">Nul-<lb/>la profecto eſt neceſſitas, & </s> <s xml:id="echoid-s3166" xml:space="preserve">alia dari quoque corpora, in quibus <lb/>non demonſtratum eſt Ferrum eſſe, monui ſupra, quæ tamen actio-<lb/>nem Magnetis in ſe experiuntur. </s> <s xml:id="echoid-s3167" xml:space="preserve">Non penitus probabilitate caret, <lb/>in hac Arena nihil Ferri aut metalli contineri, quia non efferveſcit <lb/>cum Spiritu Salis Marini; </s> <s xml:id="echoid-s3168" xml:space="preserve">nec cum Spiritu Nitri fortiſſimo, eove cum <lb/>Aqua diluto; </s> <s xml:id="echoid-s3169" xml:space="preserve">nec cum Aqua forti ſimplici, nec cum Aqua forti <lb/>duplici; </s> <s xml:id="echoid-s3170" xml:space="preserve">nec cum Aqua Regia; </s> <s xml:id="echoid-s3171" xml:space="preserve">nec cum Oleo Vitrioli forti, eove <lb/>diluto cum Aqua; </s> <s xml:id="echoid-s3172" xml:space="preserve">imo ſive hæc Arena calcinata fuerit vel non; <lb/></s> <s xml:id="echoid-s3173" xml:space="preserve">frigida vel calida, nunquam cum memoratis Spiritibus acidiſſimis <lb/>efferveſcit, quibuscum tamen omne Ferrum acriter efferveſcit; </s> <s xml:id="echoid-s3174" xml:space="preserve"><lb/>an igitur ulla ſuſpicio Ferri latentis in hac Arena poteſt foveri?</s> <s xml:id="echoid-s3175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3176" xml:space="preserve">8. </s> <s xml:id="echoid-s3177" xml:space="preserve">Miſtæ fuerunt hujus Arenæ ℨiij. </s> <s xml:id="echoid-s3178" xml:space="preserve">cum Minii Drachmis novem, <lb/>quæ in Crucibulo igni vehementi in furno Anemi, trium horarum <lb/>ſpatio, commiſſæ, abiverunt in maſſam firmam, duriſſimam, valde <lb/>ſpongioſam, coloris ferrei, ſuperficiei inæqualis, in qua plurimæ <lb/>partes plumbi, in globulos coaliti, ſirmiter alteri materiei adhærebant: <lb/></s> <s xml:id="echoid-s3179" xml:space="preserve">Ne minimum ſignum vitri ullius conſpiciebatur, ad quod con-<lb/>ficiendum, Experimentum inſtitueram; </s> <s xml:id="echoid-s3180" xml:space="preserve">potius Minium in Plumbum <pb o="130" file="0144" n="144" rhead="DISSERTATIO"/> renatum erat, quod cultro hinc inde ſeparatum ab alia materia, <lb/>erat purum Plumbum: </s> <s xml:id="echoid-s3181" xml:space="preserve">Alia autem duriorque maſſa, in pulverem <lb/>trita, a Magnete æque fortiter attrahebatur, quam ipſa Arena In-<lb/>dica, pulvis tamen minus ſplendebat, nec erat tam atri coloris: <lb/></s> <s xml:id="echoid-s3182" xml:space="preserve">Adeo ut Plumbum non valeat vires attrahentes ex hac Arena proflige-<lb/>re. </s> <s xml:id="echoid-s3183" xml:space="preserve">Cum vero ſolet Minium cum Arena vulgari aut ſilice abire in <lb/>vitrum, uti quoque ſupra demonſtravimus Magnetem ipſius ope in <lb/>vitrum mutari, manifeſtum eſt, hanc Virginiæ Arenam non eſſe ter-<lb/>ram facile penetrabilem aut ſolubilem ab eo metallo, quod iguitum per <lb/>omnia fere tranſit alia corpora: </s> <s xml:id="echoid-s3184" xml:space="preserve">non tamen eſſe ſubſtantiam ſimpli-<lb/>cem, docuit vis Salis Ammoniaci & </s> <s xml:id="echoid-s3185" xml:space="preserve">Nitri in ipſam; </s> <s xml:id="echoid-s3186" xml:space="preserve">ex quibus au-<lb/>tem componatur partibus ſimplicioribus nondum deprehendere po-<lb/>tui.</s> <s xml:id="echoid-s3187" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div94" type="section" level="1" n="94"> <head xml:id="echoid-head102" xml:space="preserve">DE METHODO ARMANDI MAGNETES.</head> <p> <s xml:id="echoid-s3188" xml:space="preserve">Magnes ex fodinis erutus, non ſolet multum Ferri elevare atque <lb/>geſtare, ideo armatura induitur, qua adjutus multo plus ferreipon-<lb/>deris gerit, hæc enim ejus vires, cæteroquin quaquaverſum dif-<lb/>fundendas colligit, dirigit, condenſat, atque eas amborum polo-<lb/>rum congregat, ut in eandem agant molem ferream, eamque ſimul <lb/>trahant: </s> <s xml:id="echoid-s3189" xml:space="preserve">Inter varias armandi tentatas methodos optimam elegi, <lb/>quæ huc uſque innotuit, hanc tamen eſſe abſolute perfectiſſimam <lb/>non niſi temere affirmarem.</s> <s xml:id="echoid-s3190" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3191" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3192" xml:space="preserve">6. </s> <s xml:id="echoid-s3193" xml:space="preserve">fig. </s> <s xml:id="echoid-s3194" xml:space="preserve">3, Fingamus molem Magnetis informem, & </s> <s xml:id="echoid-s3195" xml:space="preserve">modo <lb/>ex fodina erutam proponi, quæ ita ſit armanda, ut plurimum Ferri <lb/>elevet geratque: </s> <s xml:id="echoid-s3196" xml:space="preserve">Circa eam in Tabula poſitam ſpargatur limatura <lb/>Martis, atque ita invertatur, donec duas exhibeat plagas, ſibi op-<lb/>poſitas, quæ limaturam in ſeries rectas ordinant. </s> <s xml:id="echoid-s3197" xml:space="preserve">Hæ plagæ erunt <lb/>Magnetis poli, qui accuratiſſime determinabuntur, Acu brevi gra-<lb/>cilique iis impoſita, quæ perpendiculariter polis inſiſtit, oblique <lb/>inflexa & </s> <s xml:id="echoid-s3198" xml:space="preserve">attracta ab aliis Magnetis lateribus.</s> <s xml:id="echoid-s3199" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3200" xml:space="preserve">2. </s> <s xml:id="echoid-s3201" xml:space="preserve">Ambo inventa loca ſupra cotem verſatilem, aut planum lapi-<lb/>dem aſperum, lævigentur & </s> <s xml:id="echoid-s3202" xml:space="preserve">applanentur, ut ſuperficiebus ſibi paral-<lb/>lelis, & </s> <s xml:id="echoid-s3203" xml:space="preserve">perpendicularibus ad directionem impoſitæ Acus, donen- <pb o="131" file="0145" n="145" rhead="DE MAGNETE."/> tur: </s> <s xml:id="echoid-s3204" xml:space="preserve">hæ bales ſunt totius operis, his bene poſitis, Magneti poterit elegans <lb/>quæcunque induci forma, cubica, parallelopipeda, vel quæcun-<lb/>que alia deſideratur, a locis enim polaribus omnis virtus Magnetica <lb/>exſpectanda eſt, & </s> <s xml:id="echoid-s3205" xml:space="preserve">fere tota dependet. </s> <s xml:id="echoid-s3206" xml:space="preserve">Notandum hic imprimts eſt, <lb/>nunquam Magnetem eſle abbreviandum, locis polaribus bene appla-<lb/>natis, quia abbreviando ſemper aliquid ſuæ virtutis amitteret, ve-<lb/>rum poſſunt abſque detrimento alia latera circa axin abſcindi, uti <lb/>Vallemontius, aliique plures recte animadverterunt.</s> <s xml:id="echoid-s3207" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3208" xml:space="preserve">3. </s> <s xml:id="echoid-s3209" xml:space="preserve">Formentur deinde ex Ferro molliſſimo, in quo nullæ ſunt ſpinæ, <lb/>aliquot corpora illius formæ, quam fig, 4. </s> <s xml:id="echoid-s3210" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3211" xml:space="preserve">6. </s> <s xml:id="echoid-s3212" xml:space="preserve">repræſentat: </s> <s xml:id="echoid-s3213" xml:space="preserve">Sit <lb/>A B C D pars tenuiſſima, longitudinis & </s> <s xml:id="echoid-s3214" xml:space="preserve">latitudinis ejuſdem ac to-<lb/>tum latus polare armandi Magnetis: </s> <s xml:id="echoid-s3215" xml:space="preserve">ad angulum rectum inflexam <lb/>habeat partem E F craſſiorem, inferius rotundam, ſive in promi-<lb/>nentiam deſinentem, quæ Pes Armaturæ vocari ſolet.</s> <s xml:id="echoid-s3216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3217" xml:space="preserve">Obſervandum eſt in formando hoc pede a fabro, ut B E ſit pars <lb/>inflexa Ferri A B, atque ita ſtriarum ferrearum ductus A B E con-<lb/>tinuati jaceant, exercitati enim in Magnetica arte fabri obſervave-<lb/>runt, ex pede armaturæ dicto modo formato, Magnetem plus ponde-<lb/>ris elevare. </s> <s xml:id="echoid-s3218" xml:space="preserve">Monui ex Ferro molliſſimo hæc corpora eſſe forman-<lb/>da, & </s> <s xml:id="echoid-s3219" xml:space="preserve">non ex Chalybe, uti perverſe a nonnullis annotatum eſt, <lb/>ex ferrea enim armatura multo plus ponderis geſtant Magnetes, quam <lb/>ex Chalybea.</s> <s xml:id="echoid-s3220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3221" xml:space="preserve">4. </s> <s xml:id="echoid-s3222" xml:space="preserve">Sed quantæ craſſitiei poſtulatur Ferrum A B C D? </s> <s xml:id="echoid-s3223" xml:space="preserve">hoc deter-<lb/>minatu a priori eſt difficillimum: </s> <s xml:id="echoid-s3224" xml:space="preserve">laminæ craſſitiei diverſæ & </s> <s xml:id="echoid-s3225" xml:space="preserve">lon-<lb/>gitudinis A B prius ſuper polo Magnetis ducantur, atque explore-<lb/>tur, quænam maximis ab eo viribus imprægnetur, ſecundum Ex-<lb/>perimentum XXXI. </s> <s xml:id="echoid-s3226" xml:space="preserve">hujus craſſities erit ea, quæ deſideratur in <lb/>A B C D: </s> <s xml:id="echoid-s3227" xml:space="preserve">ſolet cæteroquin tentando explorari ex quanam armatura <lb/>plurimum Ferri geſtetur, conficiuntur aliquot nempe ferramenta <lb/>A B C D E F diverſæ craſſitiei, his armatur Magnes, & </s> <s xml:id="echoid-s3228" xml:space="preserve">quæ fortiſ-<lb/>ſime Ferrum elevant, eliguntur. </s> <s xml:id="echoid-s3229" xml:space="preserve">Alii ſupra laminam A B, Magneti <lb/>applicatam, ſcobem ſpargunt, quæ ſi valde attrahatur & </s> <s xml:id="echoid-s3230" xml:space="preserve">erigatur, <lb/>nimis tenuem eſſe A B judicant: </s> <s xml:id="echoid-s3231" xml:space="preserve">ſi vero vix aut nequaquam attra-<lb/>hitur, eam minus craſſam pronunciant, atque eo uſque eſſe atte-<lb/>nuandam, donec aliquid ſcobis attrahat.</s> <s xml:id="echoid-s3232" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3233" xml:space="preserve">Duo ejuſmodi corpora ferrea accuratiſſime polita & </s> <s xml:id="echoid-s3234" xml:space="preserve">explanata <pb o="132" file="0146" n="146" rhead="DISSERTATIO"/> Magneti apponantur, ſingulo lateri polari unum, pes B E etiam <lb/>accurate tangat inferiorem Magnetis partem; </s> <s xml:id="echoid-s3235" xml:space="preserve">ambo arcte cum Ma-<lb/>gnete ligentur, qui ita præparatus, vocatur Armatus Magnes, qua-<lb/>lem exhibet figura 5, Tab. </s> <s xml:id="echoid-s3236" xml:space="preserve">6. </s> <s xml:id="echoid-s3237" xml:space="preserve">Hac methodo fere omnis vis Magne-<lb/>tis, rectà ex polis egrediens, intrat in armaturam, ad pedem E F di-<lb/>rigitur, qui cum inferius ſit rotundiuſculus, vim condenſat in ar-<lb/>ctius ſpatium, in quo ea quaſi concentrata hæret, ex quo proinde <lb/>maximum Ferri pondus geſtabitur.</s> <s xml:id="echoid-s3238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3239" xml:space="preserve">Formam armaturæ aliam deſcripſit Gaſſendus & </s> <s xml:id="echoid-s3240" xml:space="preserve">Cabeus in Phi-<lb/>loſ. </s> <s xml:id="echoid-s3241" xml:space="preserve">Mag. </s> <s xml:id="echoid-s3242" xml:space="preserve">Lib. </s> <s xml:id="echoid-s3243" xml:space="preserve">4. </s> <s xml:id="echoid-s3244" xml:space="preserve">Cap. </s> <s xml:id="echoid-s3245" xml:space="preserve">44. </s> <s xml:id="echoid-s3246" xml:space="preserve">pag. </s> <s xml:id="echoid-s3247" xml:space="preserve">408. </s> <s xml:id="echoid-s3248" xml:space="preserve">Magnetem ſecundum axin per-<lb/>forando, tum virgam Chalybeam, foramen exquiſite complen-<lb/>tem, tranſmittendo, hæc ex ſuis extremitatibus magnam virtutem <lb/>exercet: </s> <s xml:id="echoid-s3249" xml:space="preserve">Nulli tamen auctor ſum, ut præſtantem Magnetem hoc mo-<lb/>do perforet, quia magna pars præſtantis virtutis exſculpitur, & </s> <s xml:id="echoid-s3250" xml:space="preserve">tan-<lb/>rum ab uno extremo tranſmiſſæ virgæ pondus geſtatur, ſeſe non ad-<lb/>juvantibus ambobus polis, uti in noſtrâ methodo.</s> <s xml:id="echoid-s3251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3252" xml:space="preserve">Solent in Magnete plurimæ anomaliæ obſervari, quas nemo mor-<lb/>talium facile explicabit, quamdiu, quid ſit vis Magnetica, ignora-<lb/>tur; </s> <s xml:id="echoid-s3253" xml:space="preserve">ecce enim quænam obſervavit Cl. </s> <s xml:id="echoid-s3254" xml:space="preserve">Butterfield, memorante <lb/>Hartſoekero, dari aliquos Magnetes, qui inermes plus videntur a-<lb/>gere, quam armati, eludentes ita armati omnem exſpecta-<lb/>tionem: </s> <s xml:id="echoid-s3255" xml:space="preserve">alios, qui inermes admodum imbecilles videntur, arma-<lb/>tos plurimum virtutis poſſidere. </s> <s xml:id="echoid-s3256" xml:space="preserve">An igitur nonnullorum Magnetum <lb/>vis facilius per Ferrum tranſit, aliorum difficilius? </s> <s xml:id="echoid-s3257" xml:space="preserve">An hoc pendet <lb/>a diverſa indole Ferri? </s> <s xml:id="echoid-s3258" xml:space="preserve">Ad hæc nondum ſatis attenderunt mortales, <lb/>& </s> <s xml:id="echoid-s3259" xml:space="preserve">idcirco nihil certi concludi poteſt.</s> <s xml:id="echoid-s3260" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div95" type="section" level="1" n="95"> <head xml:id="echoid-head103" xml:space="preserve">EXPERIMENTUM LXXIV.</head> <p> <s xml:id="echoid-s3261" xml:space="preserve">Magnes, deſcripto armatus modo, attrahit ſuſtinetque Ferrum <lb/>multo majoris ponderis applicatum ſuis pedibus, quam inermis ex <lb/>utroque polo elevaverat.</s> <s xml:id="echoid-s3262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3263" xml:space="preserve">Eſt enim mihi Magnes, qui inermis ex ſingulo polo ſuſtinet cir-<lb/>citer 5 Ferri Uncias, adeoque ex utroque ſimul ſuſtineret modo 10 <lb/>Uncias, hic autem armatus elevat Libras 7 Ferri.</s> <s xml:id="echoid-s3264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3265" xml:space="preserve">Utque aliorum teſtimoniis mea confirmem obſervata, Merſen- <pb o="133" file="0147" n="147" rhead="DE MAGNETE"/> num conſulamus annotantem ſe vidiſſe Magnetem ponderis Librar 3, <lb/>qui inermis elevabat tantum Unciam ſemiſſem, armatus autem ge-<lb/>ſtabat Libras 10.</s> <s xml:id="echoid-s3266" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3267" xml:space="preserve">De Lanis in Magiſt. </s> <s xml:id="echoid-s3268" xml:space="preserve">Nat. </s> <s xml:id="echoid-s3269" xml:space="preserve">& </s> <s xml:id="echoid-s3270" xml:space="preserve">Artis Tom. </s> <s xml:id="echoid-s3271" xml:space="preserve">3. </s> <s xml:id="echoid-s3272" xml:space="preserve">Lib. </s> <s xml:id="echoid-s3273" xml:space="preserve">23. </s> <s xml:id="echoid-s3274" xml:space="preserve">Cap. </s> <s xml:id="echoid-s3275" xml:space="preserve">1. </s> <s xml:id="echoid-s3276" xml:space="preserve">§. <lb/></s> <s xml:id="echoid-s3277" xml:space="preserve">15. </s> <s xml:id="echoid-s3278" xml:space="preserve">Magnetem ſe habuiſſe, inquit, qui armatus elevabat grana 864, <lb/>ſed idem inermis ſuſtinuit modo grana 54. </s> <s xml:id="echoid-s3279" xml:space="preserve">Memoratque Romæ Ma-<lb/>gnetem fuiſſe, qui inermis vix drachmam, armatus vero Uncias 5 <lb/>elevabat Ex quibus obſervatis liquido conſtat, exarmatura plus pon-<lb/>deris geri, quam ex nudo Magnete, quia autem non credibile eſt, <lb/>Magnetes memoratos fuiſſe eodem modo, & </s> <s xml:id="echoid-s3280" xml:space="preserve">cum ſumma cautelà <lb/>armatos, dici nequit vires proportione eadem, aut diverſa ad ele-<lb/>vandum Ferrum acquiri.</s> <s xml:id="echoid-s3281" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div96" type="section" level="1" n="96"> <head xml:id="echoid-head104" xml:space="preserve">EXPERIMENTUM. LXXV.</head> <p> <s xml:id="echoid-s3282" xml:space="preserve">Si Magnes ex uno ſui polo poteſt ſuſpenſos tenere aliquot annu-<lb/>los ferreos, ſibi libere appenſos, unus vero ex iis ita ſuſpendatur, ut <lb/>ambos Magnetis polos ſimul tangat, tum hic unus tantum ſuſtineri <lb/>poteſt a Magnete, omneſque alii, qui huic applicantur, deci-<lb/>dunt.</s> <s xml:id="echoid-s3283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3284" xml:space="preserve">Primo intuitu crederemus vim unitam fortiorem fore, cum enim <lb/>unus polus plures elevat annulos, duo poli plures elevarent, impri-<lb/>miscum multo plus Ferri ex ambobus polis ſimul ſuſpendi poteſt, quam <lb/>ex uno; </s> <s xml:id="echoid-s3285" xml:space="preserve">ſed contrarium obtinet: </s> <s xml:id="echoid-s3286" xml:space="preserve">Infirmitatis igitur ratio pendebit ex <lb/>figura annulari ipſius Ferri, efficiente, ut vis exiens ex Magnetis <lb/>uno polo, deſtruat eam ex altero, poſtquam contrariâ directione ſibii <lb/>occurrerint, unde nihil amplius ex primo annulo geſtari poterit.</s> <s xml:id="echoid-s3287" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div97" type="section" level="1" n="97"> <head xml:id="echoid-head105" xml:space="preserve">EXPERIMENTUM LXXVI.</head> <p> <s xml:id="echoid-s3288" xml:space="preserve">Si pedi Magnetis armati affricetur lamella ferrea, imbuitur ma-<lb/>jori vi attractrice, quam ſi eadem lamella eidem polo Magnetis in-<lb/>ermis affricta fuiſſet.</s> <s xml:id="echoid-s3289" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3290" xml:space="preserve">Hoc in controverſum vocatum fuit a nonnullis, qui eandem vim <lb/>communicari ab inermi, quam ab armato Magnete ſtatuerunt, cum <lb/>hiſce tamen conſentire nequeo, refragante experientia: </s> <s xml:id="echoid-s3291" xml:space="preserve">& </s> <s xml:id="echoid-s3292" xml:space="preserve">nonnera- <pb o="134" file="0148" n="148" rhead="DISSERTATIO"/> tio quoque pro nobis militat, cum enim vis Magnetica concentra-<lb/>tur in pede armaturæ ita, ut multo plus Ferri ab eo, quam ab ipſo <lb/>Magnete ſuſtineri poſſit, nonne etiam plus virtutis in lamellam <lb/>affrictam tranſibit, quemadmodum a fortiori Magnete plerumque <lb/>fieri ſolet?</s> <s xml:id="echoid-s3293" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div98" type="section" level="1" n="98"> <head xml:id="echoid-head106" xml:space="preserve">EXPERIMENTUM LXXVII.</head> <p> <s xml:id="echoid-s3294" xml:space="preserve">Si utrique pedi armaturæ adhæſerit lamella ferrea, atque in eo-<lb/>dem plano cum armaturâ & </s> <s xml:id="echoid-s3295" xml:space="preserve">lamellâ fuerit Acus verſatilis Nautica, <lb/>qui diſtat â Magnete, jacetque in perpendiculari inter utroſque pedes <lb/>media, hæc nequaquam in tam longa diſtantia â Magnete movebitur, <lb/>quam ſi Magnes inermis fuiſſet, aut armatura non geſtaſſet lamel-<lb/>lam.</s> <s xml:id="echoid-s3296" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3297" xml:space="preserve">Quod fit, quia vis Magnetis operatur in lamellam pedibus appli-<lb/>catam, unde nequaquam ad tantam longitudinem extenditur, quam <lb/>ſi nulla ferrea lamella adſit.</s> <s xml:id="echoid-s3298" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div99" type="section" level="1" n="99"> <head xml:id="echoid-head107" xml:space="preserve">EXPERIMENTUM LXXVIII.</head> <p> <s xml:id="echoid-s3299" xml:space="preserve">Si Ferrum ſecundum longitudinem ſuamaſſricetur utrique pedi Ar-<lb/>maturæ ſimul, non tantas viresattrahendi acquirit, quam ſi uni tan-<lb/>tum pedi affricetur.</s> <s xml:id="echoid-s3300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3301" xml:space="preserve">Quia Ferrum ab utroque polo directionis vires acquirit contra-<lb/>rias, quibus ſe deſtruentibus, minor earum copia in Ferro remanet: <lb/></s> <s xml:id="echoid-s3302" xml:space="preserve">quare ut Ferrum magna vi imbuatur, ſupra unum polum pedemve <lb/>Magnetis modo fricandum erit.</s> <s xml:id="echoid-s3303" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div100" type="section" level="1" n="100"> <head xml:id="echoid-head108" xml:space="preserve">EXPERIMENTUM. LXXIX.</head> <p> <s xml:id="echoid-s3304" xml:space="preserve">Vis attrahens variorum Magnetum armatorum in elevando fer-<lb/>reo pondere, eſt cæteris paribus in ratione duplicata Diametrorum, <lb/>aut in ratione ſuperficierum.</s> <s xml:id="echoid-s3305" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3306" xml:space="preserve">Whiſtonus in Tractatu of the dipping Needle, pag. </s> <s xml:id="echoid-s3307" xml:space="preserve">11. </s> <s xml:id="echoid-s3308" xml:space="preserve">hanc pro-<lb/>portionem commemorat repertam a Nobiliſſimo Viro Paisley; </s> <s xml:id="echoid-s3309" xml:space="preserve">cum <lb/>enim vis ex ſuperficie Magnetis exeat, quo atmatura majorem partem <pb o="135" file="0149" n="149" rhead="DE MAGNETE."/> ſuperficiei occupat, eo plus virium a Magnete recipit, atque eo majus <lb/>pondus Ferri elevabit. </s> <s xml:id="echoid-s3310" xml:space="preserve">Videmus hinc quantum hæc vis Magnetis <lb/>differat a gravitate, quæ eſt in ratione ſoliditatis corporum, ſive in <lb/>eorum Diametrorum ratione triplicata: </s> <s xml:id="echoid-s3311" xml:space="preserve">& </s> <s xml:id="echoid-s3312" xml:space="preserve">ideo evidenter liquet, vim <lb/>Magnetis non poſſe pendere a lege Naturæ, quâ poſitis corporibus <lb/>duobus, ad ſe acceſſus fiet, quippe tum vis foret in ratione quan-<lb/>titatis corporeæ, hoc eſt utigravitas, cum ea nunc obſervatur in ra-<lb/>tione ſuperficiei corporeæ tantum exiſtere.</s> <s xml:id="echoid-s3313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div101" type="section" level="1" n="101"> <head xml:id="echoid-head109" xml:space="preserve">EXPERIMENTUM LXXX.</head> <p> <s xml:id="echoid-s3314" xml:space="preserve">Æqualis vis bonorum Magnetum inermium, non ſenſibiliter inæ-<lb/>qualium vi, ſimilis figuræ & </s> <s xml:id="echoid-s3315" xml:space="preserve">poſitionis, ſed inæqualis magnitudi-<lb/>nis, eſt aliquando paulum major vel minor, quam in ratione ſuarum <lb/>Diametrorum.</s> <s xml:id="echoid-s3316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3317" xml:space="preserve">Memorat Whiſtonus ſe hoc etiam ex variis didiciſſe Experimen-<lb/>tis; </s> <s xml:id="echoid-s3318" xml:space="preserve">attamen fatetur magnam eſſe difficultatem determinandi, an <lb/>diverſi Magnetes, aut diverſæ partes ejuſdem Magnetis ſint æque <lb/>bonæ, ut fere perveniri nequeat ad aliquem accuratum ſucceſſum <lb/>Experimenti.</s> <s xml:id="echoid-s3319" xml:space="preserve"/> </p> <pb o="136" file="0150" n="150" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div102" type="section" level="1" n="102"> <head xml:id="echoid-head110" xml:space="preserve">CAPUT TERTIUM.</head> <head xml:id="echoid-head111" xml:space="preserve">De Directione Magnetis & Ferri ſuper ipſo <lb/>ducti.</head> <p> <s xml:id="echoid-s3320" xml:space="preserve">Donatus eſt Magnes plerumque duobus polis, qui ſunt plagæ <lb/>alicujus latitudinis, non puncta Mathematica, inſtar polo-<lb/>rum terreſtrium, aut coeleſtium: </s> <s xml:id="echoid-s3321" xml:space="preserve">Supra memoravimus vim attrahen-<lb/>tem Magnetis maximam ab hiſce polis exerceri; </s> <s xml:id="echoid-s3322" xml:space="preserve">qui ideo facile de-<lb/>teguntur, circumquaque circa Magnetem Ferrum applicando, & </s> <s xml:id="echoid-s3323" xml:space="preserve"><lb/>explorando quibuſnam in locis id fortiſſime attrahatur: </s> <s xml:id="echoid-s3324" xml:space="preserve">Innoteſcunt <lb/>tamen facilius ope Scobis ferreæ circumſperſæ, vel Acum nauti-<lb/>cam ſupra Stylum mobilem circumducendo, quæ maximo cum <lb/>impetu verſus hos polos dirigetur.</s> <s xml:id="echoid-s3325" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3326" xml:space="preserve">Sunt aliquando bini poli ſibi in recta diametraliter oppoſiti, ali-<lb/>quando in curva: </s> <s xml:id="echoid-s3327" xml:space="preserve">Non quoque in omnibus Magnetibus neceſſario <lb/>duo tantum poli deprehenduntur, quippe & </s> <s xml:id="echoid-s3328" xml:space="preserve">ipſe vidi, atque alii nota-<lb/>verunt Auctores, Magnetes, in quibus tres, idem teſtante Fournierio, <lb/>tum in quibus quatuor manifeſto poli obſervabantur: </s> <s xml:id="echoid-s3329" xml:space="preserve">Cl. </s> <s xml:id="echoid-s3330" xml:space="preserve">Pugettus <lb/>in Tractatu Experimentorum Magneticorum Sermone Gallico con-<lb/>ſcriptorum, Magnetis meminit, vide Tab. </s> <s xml:id="echoid-s3331" xml:space="preserve">7. </s> <s xml:id="echoid-s3332" xml:space="preserve">fig. </s> <s xml:id="echoid-s3333" xml:space="preserve">1. </s> <s xml:id="echoid-s3334" xml:space="preserve">Sphærici <lb/>A B C D, pedi eburneo inſiſtentis, a cujus polo A, Acus nauticæ cuſpis <lb/>attrahitur, quæ a parte, priori oppoſita, C, etiam allicitur, indi-<lb/>cio A & </s> <s xml:id="echoid-s3335" xml:space="preserve">C eſſe polos cognomines: </s> <s xml:id="echoid-s3336" xml:space="preserve">a parte B attrahitur ejuſdem A-<lb/>cus cauda, quam pariter allicit oppoſitum punctum D: </s> <s xml:id="echoid-s3337" xml:space="preserve">poſſidet A-<lb/>cuum nauticarum artifex inſignis Rotterodamenſis, Dykgraaf, Ma-<lb/>gnetem, quem mihi explorandum accommodavit, formæ utcun-<lb/>que cubicæ, quam repræſentat Tab. </s> <s xml:id="echoid-s3338" xml:space="preserve">7. </s> <s xml:id="echoid-s3339" xml:space="preserve">fig. </s> <s xml:id="echoid-s3340" xml:space="preserve">2. </s> <s xml:id="echoid-s3341" xml:space="preserve">in cujus latere ante-<lb/>riori N, Z, ſunt duo poli, quorum unus N eſt Boreus, alter Z Au-<lb/>ſtralis, latus N Z priori oppoſitum, etiam duos habet polos, quo-<lb/>rum hic N eſt Boreus, alter Z Auſtralis: </s> <s xml:id="echoid-s3342" xml:space="preserve">penes eundem artificem <lb/>alius proſtat Magnes formæ oblongæ, Tab. </s> <s xml:id="echoid-s3343" xml:space="preserve">7. </s> <s xml:id="echoid-s3344" xml:space="preserve">fig. </s> <s xml:id="echoid-s3345" xml:space="preserve">3. </s> <s xml:id="echoid-s3346" xml:space="preserve">in quo pri-<lb/>mum tres obſervabantur poli, unus B Boreus, erant M, M. </s> <s xml:id="echoid-s3347" xml:space="preserve">duo Meri-<lb/>dionales, Magnete autem diviſo ſectione F K, fragmentum A ob- <pb o="137" file="0151" n="151" rhead="DEMAGNETE."/> ſervatum eſt habuiſſe quatuor polos, duos Boreos B, B, duos <lb/>Auſtrales M, M: </s> <s xml:id="echoid-s3348" xml:space="preserve">alium examinavi Magnetem, qui in omni fe-<lb/>re puncto ſuæ ſuperficiei polo donatus videbatur, & </s> <s xml:id="echoid-s3349" xml:space="preserve">circumquaque <lb/>vim attrahendi fere æqualem exercebat: </s> <s xml:id="echoid-s3350" xml:space="preserve">Verum hi ſunt Magnetes <lb/>Anomali, minima tamen pars eorum duobus gaudet polis ſibi directe <lb/>oppoſitis, de Regularibus Magnetibus in ſequentibus modo agam.</s> <s xml:id="echoid-s3351" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div103" type="section" level="1" n="103"> <head xml:id="echoid-head112" xml:space="preserve">EXPERIMENTUM LXXXI.</head> <p> <s xml:id="echoid-s3352" xml:space="preserve">Magnes parvæ impoſitus Cymbæ ligneæ, ut Aquæ in vaſe am-<lb/>plo innater, jaceatque axe ad horizontem parallelo, ſeconvertet, do-<lb/>nec ſuis polis reſpiciat determinatas cæli plagas, quarum una in hac <lb/>Regione eſt utcunque Borea, altera utcunque Auſtralis.</s> <s xml:id="echoid-s3353" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3354" xml:space="preserve">Minus exactè loquuntur, nec accuratas inſtituerunt obſerva-<lb/>tiones, qui Magnetem ſe ad Boream & </s> <s xml:id="echoid-s3355" xml:space="preserve">Auſtrum convertere dixe-<lb/>runt, inferius enim liquebit pauca tantum in hoc terrarum orbe nunc <lb/>dari loca, in quibus Magnes accurate Boream Auſtrumque ſpectat, <lb/>nam ſunt modo tres Meridiani ejuſmodi hucuſque cogniti; </s> <s xml:id="echoid-s3356" xml:space="preserve">ſufficiat <lb/>id annotaſſe pro hoc Experimento, mox enim prolixius de iis age-<lb/>mus.</s> <s xml:id="echoid-s3357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3358" xml:space="preserve">Non requiritur, ut Cymbæ innatet Magnes, cujus directionem ex-<lb/>ploramus, ea enim obſervatur quoque, ſuſpenſo Magnete ex filo ſeri-<lb/>ceo tenui, non intorto, ſed texto, ejuſque axe ad horizontem parallelo: <lb/></s> <s xml:id="echoid-s3359" xml:space="preserve">Neque differentia obſervatur, ſive ſit Magnes grandis, ſive exiguus, <lb/>ſive unitus, ſive in partes diſſectus, omnes quippe ejus particulæ <lb/>eâdem directione aguntur.</s> <s xml:id="echoid-s3360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3361" xml:space="preserve">D<emph style="sc">EFINITIO.</emph></s> <s xml:id="echoid-s3362" xml:space="preserve">Polus Magnetis, Boream ſemper ſpectans, vocatur <lb/>Boreus, qui Auſtro obvertitur polus Auſtralis.</s> <s xml:id="echoid-s3363" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3364" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s3365" xml:space="preserve">Incertum eſt, quo tempore Magnetis, & </s> <s xml:id="echoid-s3366" xml:space="preserve">Ferri ſuper <lb/>ipſo ducti, directio ad plagas Cæli Boreas & </s> <s xml:id="echoid-s3367" xml:space="preserve">Auſtrales detecta fuit: <lb/></s> <s xml:id="echoid-s3368" xml:space="preserve">uti & </s> <s xml:id="echoid-s3369" xml:space="preserve">quando a nautis cœpit in uſum vocari, aptarique Acus in for-<lb/>mam Compaſſi, maritimis accommodati uſibus. </s> <s xml:id="echoid-s3370" xml:space="preserve">Probabile eſt, ali-<lb/>quem caſu primum inveniſſe Magnetis impoſiti cymbulæ, natanti <lb/>in Aqua, alterum polum conſtanter dirigi Boream verſus, alterum <lb/>Auſtrum verſus: </s> <s xml:id="echoid-s3371" xml:space="preserve">deinde Ferrum Magneti aſſrictum in ſimili cym-<lb/>bula agi eâdem directione: </s> <s xml:id="echoid-s3372" xml:space="preserve">poſtea Ferrum acutæ fuit impoſitum <pb o="138" file="0152" n="152" rhead="DISSERTATIO"/> pinnæ, ut liberius citiuſque moveretur; </s> <s xml:id="echoid-s3373" xml:space="preserve">deinde deliberatum fuit, <lb/>an non poſſet inſervire Nautis, ut hi, cælo nubibus obducto atris, nec <lb/>Sole, nec ſideribus fulgentibus, cognoſcerent Boream Auſtrumque, <lb/>ſicque tutum dirigerent per æquora curſum: </s> <s xml:id="echoid-s3374" xml:space="preserve">Acûs, ſolummodo impo-<lb/>ſitæ pinnæ, obſervati defectus, ex navis orti concuſſibus, dederunt ori-<lb/>ginem Compaſſo marino, atque ita gradatim hoc inventum perfectum <lb/>videtur, id callidiſſime conjectante Walliſio in Philoſ. </s> <s xml:id="echoid-s3375" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3376" xml:space="preserve">N°. </s> <s xml:id="echoid-s3377" xml:space="preserve">278.</s> <s xml:id="echoid-s3378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3379" xml:space="preserve">Uſus Compaſſi maritimus primum innotuiſſe videtur Gallis, ma-<lb/>ris Mediterranei accolis: </s> <s xml:id="echoid-s3380" xml:space="preserve">Quiſnam vero primus in navi, & </s> <s xml:id="echoid-s3381" xml:space="preserve">quo <lb/>tempore, uſus fuerit Compaſſo, non conſtat: </s> <s xml:id="echoid-s3382" xml:space="preserve">innotuit ante annum <lb/>1180 poſt Chr. </s> <s xml:id="echoid-s3383" xml:space="preserve">Nat. </s> <s xml:id="echoid-s3384" xml:space="preserve">Quia tum vixit ſcripſitque Poëta, Gallus, <lb/>Gujotus Provineus, qui Compaſſum vocavit Marinettam, artifici-<lb/>um non decipiens; </s> <s xml:id="echoid-s3385" xml:space="preserve">cujus carmina ita ſonant. </s> <s xml:id="echoid-s3386" xml:space="preserve">Icolle eſtoile ne ſe <lb/>muet, Vn art font, qui montir ne peut, Par vertu de la Mari-<lb/>nette, Vne Pierre laide, & </s> <s xml:id="echoid-s3387" xml:space="preserve">noirette, Ou li fer volontiers ſejoint: <lb/></s> <s xml:id="echoid-s3388" xml:space="preserve">Quæ reperiri poſſunt in Fauchet, Les Antiquités de la France; </s> <s xml:id="echoid-s3389" xml:space="preserve"><lb/>aut apud Perrault, Parallele des Anciens & </s> <s xml:id="echoid-s3390" xml:space="preserve">Modernes Tom. </s> <s xml:id="echoid-s3391" xml:space="preserve">3. </s> <s xml:id="echoid-s3392" xml:space="preserve">tum <lb/>apud Gaſſendum in Lib. </s> <s xml:id="echoid-s3393" xml:space="preserve">X. </s> <s xml:id="echoid-s3394" xml:space="preserve">Diog. </s> <s xml:id="echoid-s3395" xml:space="preserve">Laërtii Tom. </s> <s xml:id="echoid-s3396" xml:space="preserve">1. </s> <s xml:id="echoid-s3397" xml:space="preserve">p. </s> <s xml:id="echoid-s3398" xml:space="preserve">193. </s> <s xml:id="echoid-s3399" xml:space="preserve">qui & </s> <s xml:id="echoid-s3400" xml:space="preserve"><lb/>addit hoc argumentum, ut inventum Gallorum eſſe demonſtret: </s> <s xml:id="echoid-s3401" xml:space="preserve"><lb/>Acum Nauticam Lilio donari, quod regni Galliarum eſt inſigne. </s> <s xml:id="echoid-s3402" xml:space="preserve"><lb/>Proſerpſit hoc inventum pedetentim juxta littora Maris Mediterra-<lb/>nei, atque ita pervenit ad Venetos, apud quos primum adhibitum <lb/>fuit a Paulo Veneto, cui idcirco gloria inventi Anno 1260 adſcri-<lb/>bitur: </s> <s xml:id="echoid-s3403" xml:space="preserve">tum etiam ad urbem Amalphim in Regno Neapolitano dela-<lb/>tum eſt, in qua primo a Johanne Goya, circa annum 1300 in uſum <lb/>vocatus fuit Compaſſus, unde verſiculus,</s> </p> <p> <s xml:id="echoid-s3404" xml:space="preserve">Prima dedit Nautis uſum Magnetis Amalphis.</s> <s xml:id="echoid-s3405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3406" xml:space="preserve">Hiſce binis a ſuis popularibus attributa fuit inventi gloria; </s> <s xml:id="echoid-s3407" xml:space="preserve">procul <lb/>dubio tantum, quia primi inter ſuos fuerunt, qui Compaſſo uſi ſunt, <lb/>etiamſi diu ante Gallis innotuerit.</s> <s xml:id="echoid-s3408" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div104" type="section" level="1" n="104"> <head xml:id="echoid-head113" xml:space="preserve">EXPERIMENTUM LXXXII.</head> <p> <s xml:id="echoid-s3409" xml:space="preserve">Si Magnes parvæ impoſitus Cymbæ ligneæ, ne ſub Aqua ſubmer-<lb/>gatur, axim gerat perpendicularem ad horizontem, natetque in vaſe <lb/>amplo, eandem ſemper faciem convertet ad plagam Boream, aliam-<lb/>que ad Auſtralem.</s> <s xml:id="echoid-s3410" xml:space="preserve"/> </p> <pb o="139" file="0153" n="153" rhead="DEMAGNETE."/> <p> <s xml:id="echoid-s3411" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3412" xml:space="preserve">7. </s> <s xml:id="echoid-s3413" xml:space="preserve">fig. </s> <s xml:id="echoid-s3414" xml:space="preserve">4. </s> <s xml:id="echoid-s3415" xml:space="preserve">Magnes A innatans Cymbæ in vaſe aquæ pleno <lb/>C B D, polo m Auſtrali reſpiciat Zenith; </s> <s xml:id="echoid-s3416" xml:space="preserve">ſupra vaſis medium pen-<lb/>deat acus ferrea E, in quam agat Magnes, ut eo melius in medio <lb/>vaſis teneatur; </s> <s xml:id="echoid-s3417" xml:space="preserve">Magnetis aliquamdiu ſibi commiſſi notetur pars pla-<lb/>gam Boream ſpectans; </s> <s xml:id="echoid-s3418" xml:space="preserve">deinde convertatur, iterum ſibi relictus, eô-<lb/>dem latere ad plagam Boream convertetur, quemadmodum primus <lb/>obſervavit Grandamicus.</s> <s xml:id="echoid-s3419" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div105" type="section" level="1" n="105"> <head xml:id="echoid-head114" xml:space="preserve">EXPERIMENTUM LXXXIII.</head> <p> <s xml:id="echoid-s3420" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3421" xml:space="preserve">7. </s> <s xml:id="echoid-s3422" xml:space="preserve">fig. </s> <s xml:id="echoid-s3423" xml:space="preserve">5. </s> <s xml:id="echoid-s3424" xml:space="preserve">Sit Magnes A, C, D, K, cujus ambo poli <lb/>A, D, proinde cujus axis ſit A D, dividatur bifariam in C K, ſectio-<lb/>ne perpendiculari ad axim, erit unius ſegmenti polus A, antea Au-<lb/>ſtralis, adhuc Auſtralis, & </s> <s xml:id="echoid-s3425" xml:space="preserve">B Boreus: </s> <s xml:id="echoid-s3426" xml:space="preserve">alterius ſegmenti pars a, quæ <lb/>adhæſit polo Boreo B, erit polus Auſtralis, pars D polus Boreus, ut <lb/>ante.</s> <s xml:id="echoid-s3427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3428" xml:space="preserve">Eſt hoc Experimentum in controverſo, & </s> <s xml:id="echoid-s3429" xml:space="preserve">ideo merebatur exa-<lb/>men accuratius & </s> <s xml:id="echoid-s3430" xml:space="preserve">novum: </s> <s xml:id="echoid-s3431" xml:space="preserve">quicunque autem non poſſidet viles Ma-<lb/>gnetes, aut artem eos ſeparandi non callet, idem inſtituere poteſt <lb/>cum filo ferreo, prius ſuper Magnete ducto, hoc enim in partes <lb/>diviſum eadem præbebit phænomena: </s> <s xml:id="echoid-s3432" xml:space="preserve">Del Porta in Magia Nat. </s> <s xml:id="echoid-s3433" xml:space="preserve">& </s> <s xml:id="echoid-s3434" xml:space="preserve"><lb/>poſtea Ridley, in Treatiſe of Magnetic Bodies Ch. </s> <s xml:id="echoid-s3435" xml:space="preserve">9. </s> <s xml:id="echoid-s3436" xml:space="preserve">contrarium <lb/>affirmant, ſtatuentes polum Auſtralem A mutatum iri in Borealem <lb/>factâ ſectione: </s> <s xml:id="echoid-s3437" xml:space="preserve">An hoc ipſis contigerit neſcio, & </s> <s xml:id="echoid-s3438" xml:space="preserve">dubito: </s> <s xml:id="echoid-s3439" xml:space="preserve">mihi con-<lb/>trarium evenit, atque mecum conſentiunt Gilbertus Lib. </s> <s xml:id="echoid-s3440" xml:space="preserve">2. </s> <s xml:id="echoid-s3441" xml:space="preserve">Cap. </s> <s xml:id="echoid-s3442" xml:space="preserve">5. <lb/></s> <s xml:id="echoid-s3443" xml:space="preserve">de Magnete, tum Barlow in Magnetical advertiſements, Chap. </s> <s xml:id="echoid-s3444" xml:space="preserve">2. </s> <s xml:id="echoid-s3445" xml:space="preserve"><lb/>Non tamen falſitatis argui poteſt del Porta aut Ridleyus, quia <lb/>forſitan facturi hoc Experimentum, cuneo fiderunt Magnetem, <lb/>magnam ipſi vim inferendo, quo mutata eſt vis directrix Magnetis; </s> <s xml:id="echoid-s3446" xml:space="preserve"><lb/>obſervavi enim, quando filum ferreum in partes ope limæ lente, <lb/>ſed penitus ſecabam, directricem vim in omnibus ſegmentis man-<lb/>ſiſſe eandem; </s> <s xml:id="echoid-s3447" xml:space="preserve">cum vero partes fili tantummodo uſque ad medium <lb/>lima ſeparaveram, & </s> <s xml:id="echoid-s3448" xml:space="preserve">reliquum inflectendo frangebam, vel cuneo <lb/>malleoque findebam, polum Auſtralem mutatum eſſe in ſemi-<lb/>boreum, imo aliquando penitus in Boreum, unde ejuſmodi ſegmen-<lb/>tum duos polos Boreos in ſuis extremitatibus habebat.</s> <s xml:id="echoid-s3449" xml:space="preserve"/> </p> <pb o="140" file="0154" n="154" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div106" type="section" level="1" n="106"> <head xml:id="echoid-head115" xml:space="preserve">EXPERIMENTUM LXXXIV.</head> <p> <s xml:id="echoid-s3450" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3451" xml:space="preserve">7. </s> <s xml:id="echoid-s3452" xml:space="preserve">fig. </s> <s xml:id="echoid-s3453" xml:space="preserve">6. </s> <s xml:id="echoid-s3454" xml:space="preserve">Magnetis rotundi A B E F axis ſit C D, C polus <lb/>Auſtralis, D Boreus, dividatur Magnes bifariam ſectione per axem <lb/>tranſeunte, habebit pars C O A B P D polum Auſtralem in O, Bo-<lb/>reum in P: </s> <s xml:id="echoid-s3455" xml:space="preserve">ſegmentum C X E F Z D habebit polum Auſtralem in <lb/>X & </s> <s xml:id="echoid-s3456" xml:space="preserve">Boreum in Z.</s> <s xml:id="echoid-s3457" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3458" xml:space="preserve">Retinent igitur hæc ſegmenta eoſdem polos, quibus antea dona-<lb/>ta erant, ſola mutatio in eorum axe contingit, qui fit X Z, & </s> <s xml:id="echoid-s3459" xml:space="preserve"><lb/>O P, tranſeundo per medium cujuſlibet ſegmenti: </s> <s xml:id="echoid-s3460" xml:space="preserve">idem obtinetin omni <lb/>ſectione parallelâ ad axim: </s> <s xml:id="echoid-s3461" xml:space="preserve">ergo patet totum latus E X C O A eſſe <lb/>polare, & </s> <s xml:id="echoid-s3462" xml:space="preserve">eodem modo conſtructum, cæteroquin videri poſſet, <lb/>quaſi plagæ quædam, quales hic C & </s> <s xml:id="echoid-s3463" xml:space="preserve">D, ſoli forent poli, cum quod-<lb/>libet punctum lateris A C E, aut B D F polare ſit, ſed in Magnete <lb/>integro poli C & </s> <s xml:id="echoid-s3464" xml:space="preserve">D, erant concurſus virium, ſive centrum polorum <lb/>ab utroque latere.</s> <s xml:id="echoid-s3465" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div107" type="section" level="1" n="107"> <head xml:id="echoid-head116" xml:space="preserve">EXPERIMENTUM LXXXV.</head> <p> <s xml:id="echoid-s3466" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3467" xml:space="preserve">7. </s> <s xml:id="echoid-s3468" xml:space="preserve">fig. </s> <s xml:id="echoid-s3469" xml:space="preserve">7. </s> <s xml:id="echoid-s3470" xml:space="preserve">Duorum Magnetum A B, a b poli Auſtrales ſint <lb/>A, a, Borei B, b, hi in eodem plano horizontali poſiti, ad ſe <lb/>accedere queant, tum polus Boreus unius attrahet, ſibique junget, <lb/>polum Auſtralem alterius: </s> <s xml:id="echoid-s3471" xml:space="preserve">ideo ſi Tab. </s> <s xml:id="echoid-s3472" xml:space="preserve">7. </s> <s xml:id="echoid-s3473" xml:space="preserve">fig. </s> <s xml:id="echoid-s3474" xml:space="preserve">8. </s> <s xml:id="echoid-s3475" xml:space="preserve">Magnes A B ſu-<lb/>pra alterum a b teneatur, & </s> <s xml:id="echoid-s3476" xml:space="preserve">alteruter libere converti poſſit, con-<lb/>vertetur, ut polus Auſtralis A ſit directe ſub polo Boreo b, & </s> <s xml:id="echoid-s3477" xml:space="preserve">po-<lb/>lus Boreus B ſub Auſtrali a.</s> <s xml:id="echoid-s3478" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3479" xml:space="preserve">Ne alicui hæc converſio mira videatur, patebit intuenti Magnetem <lb/>ante unitum, ſed nunc diſſectum, partes hoc ordine habuiſſe compoſi-<lb/>tas; </s> <s xml:id="echoid-s3480" xml:space="preserve">ſi enim ambo Magnetes AB, a b conſtituiſſent antea maſſam unam, <lb/>nonne pars a adhæſiſſet parti B, atque hæ ambæ partes ſe attraxiſ-<lb/>ſent: </s> <s xml:id="echoid-s3481" xml:space="preserve">verum an hæ nunc ſolutæ non iterum ſe attrahent? </s> <s xml:id="echoid-s3482" xml:space="preserve">adeoque <lb/>poli nominis alterni ſe conjungent; </s> <s xml:id="echoid-s3483" xml:space="preserve">poli cognomines, uti bini Borei <lb/>vel bini Auſtrales ſe mutuo fugabunt, hi enim nunquam natura-<lb/>liter in Magnete cohæſerunt.</s> <s xml:id="echoid-s3484" xml:space="preserve"/> </p> <pb o="141" file="0155" n="155" rhead="DEMAGNETE."/> </div> <div xml:id="echoid-div108" type="section" level="1" n="108"> <head xml:id="echoid-head117" xml:space="preserve">EXPERIMENTUM LXXXVI.</head> <p> <s xml:id="echoid-s3485" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3486" xml:space="preserve">7. </s> <s xml:id="echoid-s3487" xml:space="preserve">fig. </s> <s xml:id="echoid-s3488" xml:space="preserve">9. </s> <s xml:id="echoid-s3489" xml:space="preserve">Sint duo Magnetes priſmatici a, A, quorum <lb/>poli Meridionales ſint M, M; </s> <s xml:id="echoid-s3490" xml:space="preserve">Borei B, B, ita facti, ut alteruter <lb/>polus deſinat in punctum, jungantur ambo Magnetes, ut conſtitu-<lb/>ant unam maſſam parallelopipedam, hæc tantum duobus donata <lb/>erit polis, & </s> <s xml:id="echoid-s3491" xml:space="preserve">axe per medium maſſæ tranſeunte.</s> <s xml:id="echoid-s3492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3493" xml:space="preserve">Ex hoc Experimento iterum patet, polarem plagam Magnetis eſſe <lb/>tantum collectionem polorum; </s> <s xml:id="echoid-s3494" xml:space="preserve">tum polum eſſe eorum centrum vi-<lb/>rium: </s> <s xml:id="echoid-s3495" xml:space="preserve">ideo tota vis poli B inferioris Magnetis receſſit verſus polunt <lb/>ſuperioris, qui etiam deſcendit paulum inferius, atque ita ambo poli <lb/>in unum coaluerunt, ſitum in loco intermedio lateris B, B.</s> <s xml:id="echoid-s3496" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div109" type="section" level="1" n="109"> <head xml:id="echoid-head118" xml:space="preserve">EXPERIMENTUM LXXXVII.</head> <p> <s xml:id="echoid-s3497" xml:space="preserve">Magnes homogeneus ſphæricus imponatur Mercurio, ita ut ipſi libere <lb/>innatet, axe tamen ad horizontem parallelo; </s> <s xml:id="echoid-s3498" xml:space="preserve">ſibi commiſſus, ex ſitu <lb/>horizontali abibit, polum Boreum inclinando in hac regione deor-<lb/>ſum, & </s> <s xml:id="echoid-s3499" xml:space="preserve">polum Auſtralem elevando: </s> <s xml:id="echoid-s3500" xml:space="preserve">quæ inclinatio variat ſingulis <lb/>annis in eadem regione, & </s> <s xml:id="echoid-s3501" xml:space="preserve">eodem anno in diverſis regionibus, quem-<lb/>admodum accuratius infra patebit in Experimentis cum Acu nauti-<lb/>ca factis.</s> <s xml:id="echoid-s3502" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div110" type="section" level="1" n="110"> <head xml:id="echoid-head119" xml:space="preserve">EXPERIMENTUM LXXXVIII.</head> <p> <s xml:id="echoid-s3503" xml:space="preserve">Si Magnes oblongus igni committatur brevi temporis intervallo, <lb/>ut tantum rubeat, tum ad horizontem perpendiculariter poſitus re-<lb/>frigeretur, ejus infima extremitas in hac regione evadit polus Bo-<lb/>reus: </s> <s xml:id="echoid-s3504" xml:space="preserve">idem adnotabimus Cap. </s> <s xml:id="echoid-s3505" xml:space="preserve">5. </s> <s xml:id="echoid-s3506" xml:space="preserve">contingere in Ferro, eodem in <lb/>ſitu refrigerio commiſſo.</s> <s xml:id="echoid-s3507" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div111" type="section" level="1" n="111"> <head xml:id="echoid-head120" xml:space="preserve">EXPERIMENTUM LXXXIX.</head> <p> <s xml:id="echoid-s3508" xml:space="preserve">Si Magnes oblongus, ignituſque perpendiculariter imponatur po-<lb/>lo Magnetis fortioris Boreo, & </s> <s xml:id="echoid-s3509" xml:space="preserve">in hoc ſitu refrigeretur, Magnes <pb o="142" file="0156" n="156" rhead="DISSERTATIO"/> ignitus multum virtutis acquiret a fortiori, ejuſque polus inferior <lb/>nunc non evadet Boreus, ſed Auſtralis, appetetque impetuoſe po-<lb/>lum Acûs nauticæ Boreum: </s> <s xml:id="echoid-s3510" xml:space="preserve">Si Magnes antequam igni committeba-<lb/>tur, imbecillis fuerit, impoſitus fortiori quamdiu calet, multis vi-<lb/>ribus donabitur, & </s> <s xml:id="echoid-s3511" xml:space="preserve">majoribus, quam unquam habuit: </s> <s xml:id="echoid-s3512" xml:space="preserve">Notat Nob. <lb/></s> <s xml:id="echoid-s3513" xml:space="preserve">Boyle, ſe exploraſſe Magnetem, qui frigidus vix fruſtulum Acus ele-<lb/>vabat, ſed poſtquam candens impoſitus fuerat generoſo Magneti <lb/>donec frigebat, eum geſtaſſe multo plus ferri. </s> <s xml:id="echoid-s3514" xml:space="preserve">Si Magnes debilis, <lb/>frigensque, fortiori imponatur, virium incrementum acquirit, non <lb/>tamen tam cito, nec tantum, ac ſi Magnes ignitus alteri impoſitus <lb/>fuiſſet.</s> <s xml:id="echoid-s3515" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3516" xml:space="preserve">Ignis Magnetem rarefaciendo partes omnes aſe removet, minuſ-<lb/>que cohærentes reddit, ita enim metalla ex duriſſimis ſubſtantiis <lb/>fluida facit, idcirco Magnes generoſus, poſitus infra alium ignitum <lb/>partibuſque facile concutiendis, alioque locandis ordine conſtantem, <lb/>hujus partes ita agitat, ordinat, dirigitque, penetrando per eas ſuâ <lb/>virtute, ut poſtea multo majorem vim attrahentem poſſideant. </s> <s xml:id="echoid-s3517" xml:space="preserve">Sed <lb/>Magnes frigidus non conſtat ex partibustam facile mobilibus, alio-<lb/>que ordine diſponendis, idcirco frigidi, impoſiti generoſiori Magne-<lb/>ti, partes non tam bene mutantur, aliove ordinantur modo, nec <lb/>totidem viribus imprægnari poſſunt.</s> <s xml:id="echoid-s3518" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3519" xml:space="preserve">Ope hujus methodi convertere polos Magnetum poſſumus. </s> <s xml:id="echoid-s3520" xml:space="preserve">2°. <lb/></s> <s xml:id="echoid-s3521" xml:space="preserve">Magnetibus imbecillioribus vires addere.</s> <s xml:id="echoid-s3522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3523" xml:space="preserve">Sunt hæc primaria phænomena, quæ Magnetes ſua directione <lb/>oſtendunt, plura alia omiſi ſtudio, tum quia parvi videbantur mo-<lb/>menti, tum ne nimium prolixus evadam, tranſeundum potius ra-<lb/>tus ad examen directionis Ferri, cum quo accuratiores capi poſſunt <lb/>obſervationes; </s> <s xml:id="echoid-s3524" xml:space="preserve">nihil autem hic explico, quomodo phænomena fiant, <lb/>cum theoriam Halleyi ſub finem adnectendam eſſe duxi, ſimul cum <lb/>aliquot animadverſionibus, quibus intellectis, quid de cauſa dire-<lb/>ctionum ſtatuendum ſit, liquebit.</s> <s xml:id="echoid-s3525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3526" xml:space="preserve">D<emph style="sc">EFINITIO.</emph></s> <s xml:id="echoid-s3527" xml:space="preserve">Verſorium, vel Acum Magneticam, vel Acum Nau-<lb/>ticam vocamus, vid. </s> <s xml:id="echoid-s3528" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3529" xml:space="preserve">4 fig. </s> <s xml:id="echoid-s3530" xml:space="preserve">9. </s> <s xml:id="echoid-s3531" xml:space="preserve">Acum Chalybeam E F, in me-<lb/>dio O capitulo aurichalceo inſtructam, excavatam intus, ut pinnæ <lb/>cupreæ K imponi queat, & </s> <s xml:id="echoid-s3532" xml:space="preserve">ſupra eam libere quaquaverſum con-<lb/>verti: </s> <s xml:id="echoid-s3533" xml:space="preserve">Dicitur punctum E, cuſpis Verſorii, F cauda.</s> <s xml:id="echoid-s3534" xml:space="preserve"/> </p> <pb o="143" file="0157" n="157" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div112" type="section" level="1" n="112"> <head xml:id="echoid-head121" xml:space="preserve">EXPERIMENTUM XC.</head> <p> <s xml:id="echoid-s3535" xml:space="preserve">Extremitas fili ferrei apponatur polo Magnetis, non affricando <lb/>id, ſed tantum applicando & </s> <s xml:id="echoid-s3536" xml:space="preserve">avellendo Magnetem, filum oſtendet <lb/>per totam longitudinem puncta Magnetica polaria in diverſis locis, <lb/>quæ vocantur Puncta Conſequentia, quia attrahunt alternatim po-<lb/>lum Boreum & </s> <s xml:id="echoid-s3537" xml:space="preserve">Auſtralem Verſorii, cujus apex lente ſecundum lon-<lb/>gitudinem fili promovetur ad diſtantiam {1/2} pollicis.</s> <s xml:id="echoid-s3538" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3539" xml:space="preserve">Verſorium novum, modo ante igni commiſſum, & </s> <s xml:id="echoid-s3540" xml:space="preserve">nondum vi-<lb/>ribus Magneticis imprægnatum, 12 {1/2} pollices longum, erat mihi ad <lb/>manus, quod loco fili vel virgæ ferreæ ſumſi; </s> <s xml:id="echoid-s3541" xml:space="preserve">id ſupra pin-<lb/>nam mobiliſſimum, a viribus Magneticis exiguis e quiete <lb/>turbabatur: </s> <s xml:id="echoid-s3542" xml:space="preserve">Secundum hujus longitudinem tenui duxique apicem <lb/>Verſorii Boreum, quod Magneti affrictum fuit, tumque 6 Puncta <lb/>Conſequentia obſervabantur: </s> <s xml:id="echoid-s3543" xml:space="preserve">apex novi Verſorii attrahebatur, locus <lb/>1 {1/2} pollice inde diſtans repellebatur, eratque quidem 6 pollices la-<lb/>tus; </s> <s xml:id="echoid-s3544" xml:space="preserve">tum iterum dabatur locus attrahens, tum iterum repellens, at-<lb/>trahebatur plage ſequens, repellebatur tandem altera extremitas: <lb/></s> <s xml:id="echoid-s3545" xml:space="preserve">ſed apice Auſtrali ducto ſecundum longitudinem Verſorii novi, ob-<lb/>ſervabantur modo tria Puncta Conſequentia, atque in aliis locis <lb/>quam in quibus antea Puncta conſequentia animadverteram; </s> <s xml:id="echoid-s3546" xml:space="preserve">extre-<lb/>mitas enim novi Verſorii repellebatur, quæ repulſio per 1 {1/2} pollicem <lb/>durabat, tum ſequebatur attractio exigua; </s> <s xml:id="echoid-s3547" xml:space="preserve">ſed ad finem fere perdu-<lb/>rans, tum fortiſſima attractio a priori diſtincta: </s> <s xml:id="echoid-s3548" xml:space="preserve">quæ omnia longe <lb/>clarius conſpiciebantur, poſtquam Apex novi Verſorii polo Magnetis <lb/>femel applicatus fuerat.</s> <s xml:id="echoid-s3549" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3550" xml:space="preserve">Primi hoc Experimentum deſcripſerunt Cl. </s> <s xml:id="echoid-s3551" xml:space="preserve">Diſaguillierius & </s> <s xml:id="echoid-s3552" xml:space="preserve">Nob. <lb/></s> <s xml:id="echoid-s3553" xml:space="preserve">Taylor in Philoſ. </s> <s xml:id="echoid-s3554" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3555" xml:space="preserve">N°. </s> <s xml:id="echoid-s3556" xml:space="preserve">368, hic 5 Acus Chalybeas, 2 polliceslon-<lb/>gas, quarum extremitates Magneti antea applicatæ fuerant, impoſuit. </s> <s xml:id="echoid-s3557" xml:space="preserve"><lb/>Aquæ ſtagnanti, atque Verſorii cuſpidem ſecundum harum lon-<lb/>gitudinem promovit, ita tamen ut eas non attingeret, tum â pun-<lb/>ctis notatis in Tab. </s> <s xml:id="echoid-s3558" xml:space="preserve">5. </s> <s xml:id="echoid-s3559" xml:space="preserve">fig. </s> <s xml:id="echoid-s3560" xml:space="preserve">5. </s> <s xml:id="echoid-s3561" xml:space="preserve">attrahebatur Verſorii polus Auſtralis <lb/>vel Septentrionalis, prout litteræ A & </s> <s xml:id="echoid-s3562" xml:space="preserve">S. </s> <s xml:id="echoid-s3563" xml:space="preserve">indicant: </s> <s xml:id="echoid-s3564" xml:space="preserve">In ſuprema Acu <lb/>obſervabantur 5 poli, quemadmodum quoque in ſecunda, inter <lb/>quas intercedit differentia hæc tantum; </s> <s xml:id="echoid-s3565" xml:space="preserve">quod unius extrema ambo <lb/>attrahant polum Septentrionalem. </s> <s xml:id="echoid-s3566" xml:space="preserve">In tertiâ 6 dantur poli, in quarta <lb/>7, in quinta 4.</s> <s xml:id="echoid-s3567" xml:space="preserve"/> </p> <pb o="144" file="0158" n="158" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s3568" xml:space="preserve">An non pendent hæc phænomena a ſpinis Ferri, pluribus vel <lb/>paucioribus, & </s> <s xml:id="echoid-s3569" xml:space="preserve">Ferrum quaſi interſecantibus in fragmenta varia, <lb/>ad quorum extremitates diverſi poli attrahentes ſunt, fortiores aut <lb/>imbecilliores, pro ſpinarum fabrica & </s> <s xml:id="echoid-s3570" xml:space="preserve">ſitu? </s> <s xml:id="echoid-s3571" xml:space="preserve">Hoc probabile eſt, con-<lb/>ſtat enim in omni Ferro & </s> <s xml:id="echoid-s3572" xml:space="preserve">Chalybe ſpinas dari, quæ ſunt quidem <lb/>Ferrum, ſed durius diverſumque à reliquo & </s> <s xml:id="echoid-s3573" xml:space="preserve">aliquando ita diſtin-<lb/>ctum, ac nodus ligni ab aſſere reliquo: </s> <s xml:id="echoid-s3574" xml:space="preserve">quia hæ ſpinæ nullo ſunt <lb/>poſitæ ordine, ideo etiam non ſervant Puncta Conſequentia diſtan-<lb/>tias a ſe æquales, aut proportionales.</s> <s xml:id="echoid-s3575" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div113" type="section" level="1" n="113"> <head xml:id="echoid-head122" xml:space="preserve">EXPERIMENTUM XCI.</head> <p> <s xml:id="echoid-s3576" xml:space="preserve">Verſorii novi, 12 {1/2} pollices longi, medium impoſitum fuit <lb/>polo Magnetis Auſtrali, tum avulſum, directum fuit cuſpide ad <lb/>plagam Boream, caudâ ad Auſtralem: </s> <s xml:id="echoid-s3577" xml:space="preserve">2°. </s> <s xml:id="echoid-s3578" xml:space="preserve">hujus Verſorii, in medio <lb/>ſuper polo Magnetis Auſtrali poſiti, pars Borea ducta fuit a medio <lb/>cuſpidem Boream verſus, longitudine circiter 2 pollicum, tum pin-<lb/>næ impoſiti extremitas Borea vix dirigebatur, torpente Acu, ſpe-<lb/>ctabat tamen Boream, tumque alterius Verſorii cuſpide Boreali ſe-<lb/>cundum illius longitudinem promota, obſervabantur tantum duo po-<lb/>li, quorum unus & </s> <s xml:id="echoid-s3579" xml:space="preserve">valde torpens, erat Boreus, atque ad diſtan-<lb/>tiam 2 pollicum ab hinc, tota Verſorii longitudo attrahebatur a cu-<lb/>ſpide Borea alterius Verſorii; </s> <s xml:id="echoid-s3580" xml:space="preserve">cuſpis tamen Auſtralis non torpebat, <lb/>ſed vehementiſſime attrahebatur. </s> <s xml:id="echoid-s3581" xml:space="preserve">3°. </s> <s xml:id="echoid-s3582" xml:space="preserve">Medium ejuſdem Verſorii <lb/>iterum impoſitum fuit polo Auſtrali Magnetis, cujus pars Septen-<lb/>trionalis ſuper eo ducta fuit uſque ad locum ubi Punctum Conſe-<lb/>quens, modo ante obſervatum fuit, non tamen uſque ad extremita-<lb/>tem Verſorii; </s> <s xml:id="echoid-s3583" xml:space="preserve">erat hujus directio ut ante, multo tamen vividius <lb/>obſervabatur moveri, neque tum plures polos habuit, quam duos, <lb/>in qualibet extremitate unum, atque vis ſingulorum deſinebat in <lb/>medio Verſorii.</s> <s xml:id="echoid-s3584" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3585" xml:space="preserve">4. </s> <s xml:id="echoid-s3586" xml:space="preserve">Omnia phænomena fuerunt eadem, poſito hujus Verſorii me-<lb/>dio ſuper polo Magnetis Auſtrali, & </s> <s xml:id="echoid-s3587" xml:space="preserve">ſuper eo ducta parte Septen-<lb/>trionali Verſorii uſque ad apicem.</s> <s xml:id="echoid-s3588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3589" xml:space="preserve">5. </s> <s xml:id="echoid-s3590" xml:space="preserve">Tum iterum Verſorii medium impoſitum fuit Magnetis polo <lb/>Auſtrali, atque illius pars Auſtralis producta aliquouſque a medio <pb o="145" file="0159" n="159" rhead="DE MAGNETE"/> verſus extremum, Verſorium valde torpere incepit, vix directa, <lb/>plerumque declinans a Meridiano Magnetico, cuſpis tamen antea <lb/>Borea, ita permanfit, iterum vero 4 poli in Verſorio obſervabantur, <lb/>duo, ſed ſibi conſequentes, in parte ejus Borea, duo alii conſe-<lb/>quentes in parte Auſtrali.</s> <s xml:id="echoid-s3591" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3592" xml:space="preserve">6. </s> <s xml:id="echoid-s3593" xml:space="preserve">Rurſus Verſorii medium imponebatur polo Magnetis Auſtrali, <lb/>atque illius parte Auſtrali producta ſuper polum ad diſtantiam 1 {1/2} <lb/>pollicis uſque ab extremo, Verſorium ſupra pinnam converſum fuit, <lb/>atque extremitas, antea Auſtralis, evaſit Borea: </s> <s xml:id="echoid-s3594" xml:space="preserve">utraque tamen <lb/>extremitas fugabatur a cuſpide Borea alterius Verſorii, atque obſer-<lb/>vabantur tria Puncta Conſequentia.</s> <s xml:id="echoid-s3595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3596" xml:space="preserve">Omnia phænomena manſerunt eadem ac in §. </s> <s xml:id="echoid-s3597" xml:space="preserve">6. </s> <s xml:id="echoid-s3598" xml:space="preserve">poſtquam Ver-<lb/>ſorii dimidum, nempe pars Auſtralis ſuper polo Magnetis Auſtrali <lb/>producta fuit, atque utraque extremitas adhuc fugabatur a cuſpide <lb/>Borea alterius Verſorii.</s> <s xml:id="echoid-s3599" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3600" xml:space="preserve">In his Experimentis patet 1°. </s> <s xml:id="echoid-s3601" xml:space="preserve">Puncta Conſequentia, quæ in Verſo-<lb/>rio longo habentur, plura vel pauciora obſervari, prout ſuper Magnete <lb/>vario modo ductum fuit Verſorium. </s> <s xml:id="echoid-s3602" xml:space="preserve">2°. </s> <s xml:id="echoid-s3603" xml:space="preserve">Eundem polum Magnetis <lb/>duas oppoſitas directiones Verſorio poſſe conciliare, prout hoc a <lb/>medio ſuo dextrorſum vel ſiniſtrorſum ſuper Magnete ducitur. </s> <s xml:id="echoid-s3604" xml:space="preserve">3°. <lb/></s> <s xml:id="echoid-s3605" xml:space="preserve">Partem Verſorii ultimo applicatam Magneti majoribus viribus imbui <lb/>reliqua parte, ideo enim converſum fuit Verſorium in §. </s> <s xml:id="echoid-s3606" xml:space="preserve">6. </s> <s xml:id="echoid-s3607" xml:space="preserve">& </s> <s xml:id="echoid-s3608" xml:space="preserve">7. </s> <s xml:id="echoid-s3609" xml:space="preserve"><lb/>4°. </s> <s xml:id="echoid-s3610" xml:space="preserve">Et patet error Regulæ a plurimis ſtabilitæ Doctis, polum Bo-<lb/>reum attrahere Auſtralem alterius Acus, dantur enim multi caſus, <lb/>in quibus polus Verſorii Auſtralis fugatur ab alterius polo Boreo, <lb/>quemadmodum in Experimento notatum fuit. </s> <s xml:id="echoid-s3611" xml:space="preserve">Hinc immerito Gil-<lb/>bertus L. </s> <s xml:id="echoid-s3612" xml:space="preserve">1. </s> <s xml:id="echoid-s3613" xml:space="preserve">C. </s> <s xml:id="echoid-s3614" xml:space="preserve">6. </s> <s xml:id="echoid-s3615" xml:space="preserve">refutavit Albertum magnum, dicentem ſuâ ætate <lb/>Magnetem inventum eſſe, qui una parte Ferrum ad ſe traheret, al-<lb/>tero autem polo ſui Ferri contrariam extremitatem â ſe abigeret, <lb/>cum attrahere debuiſſet; </s> <s xml:id="echoid-s3616" xml:space="preserve">hoc autem veriſſimum fuit, modo Al-<lb/>bertus cum Verſorio, quali nos uſi fuimus, tentamen inſtituerit.</s> <s xml:id="echoid-s3617" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div114" type="section" level="1" n="114"> <head xml:id="echoid-head123" xml:space="preserve">EXPERIMENTUM XCII.</head> <p> <s xml:id="echoid-s3618" xml:space="preserve">Sive Verſorii ſuperficies inferior, ſive ſuperior, ſiveanterior, ſive <lb/>poſterior lateralis, ducatur â medio ad extremum, tum ſiniſtrorſum, <pb o="146" file="0160" n="160" rhead="DISSERTATIO"/> tum dextrorſum, ſupra eundem polum Magnetis, eadem omnino <lb/>phænomena tam quoad directionem, quam Puncta Conſequentia, <lb/>obſervantur, quæ in Experimento præcedenti.</s> <s xml:id="echoid-s3619" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div115" type="section" level="1" n="115"> <head xml:id="echoid-head124" xml:space="preserve">EXPERIMENTUM XCIII.</head> <p> <s xml:id="echoid-s3620" xml:space="preserve">Omni vi Magnetica in igne ex Verſorio præcedentium Experi-<lb/>mentorum expulſa, nihilominus id inter refrigerandum vim directri-<lb/>cem acquiſiverat, quâ cuſpide dirigebatur Boream verſus, cauda <lb/>Auſtrum verſus, uti fuſius in Cap. </s> <s xml:id="echoid-s3621" xml:space="preserve">5. </s> <s xml:id="echoid-s3622" xml:space="preserve">demonſtrabo: </s> <s xml:id="echoid-s3623" xml:space="preserve">nunc autem Verſo-<lb/>rium modo in extremitate polarem vim oſtendebat, ipſi admoto altero <lb/>Verſorio, ſed nulla Puncta Conſequentia in intermedia parte: </s> <s xml:id="echoid-s3624" xml:space="preserve">cu-<lb/>ſpide Verſorii Borea applicata polo Magnetis Auſtrali, affricabatur <lb/>hoc a cuſpide medium verſus, ducta tamen modo ſupra Ma-<lb/>gnetem ad {1/4} totius ſuæ longitudinis partem: </s> <s xml:id="echoid-s3625" xml:space="preserve">ubi avulſum fuit â la-<lb/>pide, cuſpis Borea manſit Borea, torpida tamen in ipſâ regnante vi <lb/>directrice; </s> <s xml:id="echoid-s3626" xml:space="preserve">ſed accurate ad Meridianum reducente Acum: </s> <s xml:id="echoid-s3627" xml:space="preserve">Alterius <lb/>Verſorii cuſpis Borea, retenta prope cuſpidem Boream hujus, attrahe-<lb/>bat polum Boreum: </s> <s xml:id="echoid-s3628" xml:space="preserve">attamen in diſtantia 1 {1/2} pollicum ab extremo regna-<lb/>bat vis repellens, tum iterum vis attrahens dabatur uſque ad cuſpidem <lb/>Auſtralem, adeo ut ambo extrema Verſorii attracta fuerint a cuſpi-<lb/>de Borea alterius Verſorii.</s> <s xml:id="echoid-s3629" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3630" xml:space="preserve">2. </s> <s xml:id="echoid-s3631" xml:space="preserve">Tum affrictus Verſorii productus fuit ab extremo Boreo uſque <lb/>ad medium, vel centrum, ſuper eodem polo Magnetis, Verſorium <lb/>ſtylo impoſitum convertebatur, parte nempe Auſtrali directa Bo-<lb/>ream verſus, & </s> <s xml:id="echoid-s3632" xml:space="preserve">Borea Auſtrum verſus, utraque extremitas attra-<lb/>hebatur ab alterius Verſorii cuſpide Borea prope illas poſita, nam <lb/>ab uno extremo ad longitudinem 4 pollicum circiter fiebat attractio, <lb/>ad longitudinem 4 pollicum abhinc adeoque ultra centrum Verſorii, <lb/>exercebatur repulſio, abhincuſque ad oppoſitum extremum regnabat <lb/>iterum vis attrahens: </s> <s xml:id="echoid-s3633" xml:space="preserve">ſed alterius Verſorii cuſpis, polo Auſtrali ſpectan-<lb/>te Verſorii, quod examinatur, cuſpidem Boream, hanc Boream repelle-<lb/>bat, regnante repulſione ad diſtantiam 4 pollicum ab apice, hinc uſque <lb/>ad medium erat indifferentia, ſive nec attractio, nec repulſio; </s> <s xml:id="echoid-s3634" xml:space="preserve">a me-<lb/>dio apicem oppoſitum verſus in longitudine 2 pollicum exercebatur <lb/>attractio, hinc uſque ad extremum iterum repulſio dabatur. </s> <s xml:id="echoid-s3635" xml:space="preserve">Vi- <pb o="147" file="0161" n="161" rhead="DE MAGNETE."/> detur Doctiſſimus Hambergerus ſimile aliquid obſervaſſe inProgram-<lb/>mate Inaugurali de Partialitate Acus Magneticæ, cujus obſerva-<lb/>tiones, etiamſi non accurate cum noſtris conveniant, non dubito <lb/>quin veræ ſint, & </s> <s xml:id="echoid-s3636" xml:space="preserve">bene adnotatæ, nam dabitur in his Experimen-<lb/>tis ſemper diſcrepantia, pro varia tempeſtate diei, anni, longitudine <lb/>& </s> <s xml:id="echoid-s3637" xml:space="preserve">ſtructura Ferri, tum pro vario Magnete, qui in uſum vocatur: <lb/></s> <s xml:id="echoid-s3638" xml:space="preserve">Acum, inquit, in ſuperficie ſuperiori polo Magnetis Boreali ſtrinxi <lb/>ab extremitate verſus centrum, hæc impoſita ſtilo, nec ſeſe ſponte <lb/>verſus Septentrionem dirigebat, ſed in quovis fere ſitu quie ſcebat, <lb/>aliqualem tamen conatum ſeſe dirigendi verſus Septentrionem obſer-<lb/>vabam: </s> <s xml:id="echoid-s3639" xml:space="preserve">Nobis autem ſemper contigit obſervare Acum accurate dirigi <lb/>in Meridiano Magnetico, etiamſi non tetigerit Magnetem, verum <lb/>centrum O AcûsTab.</s> <s xml:id="echoid-s3640" xml:space="preserve">4.</s> <s xml:id="echoid-s3641" xml:space="preserve">fig.</s> <s xml:id="echoid-s3642" xml:space="preserve">9 probe deterſum fuit a ſquammis, quæ igni-<lb/>tione oriuntur, & </s> <s xml:id="echoid-s3643" xml:space="preserve">mobilitatem ſua aſperitate tollunt: </s> <s xml:id="echoid-s3644" xml:space="preserve">pergit deinde, Ad-<lb/>moto polo Magnetis Boreali ad Acus cuſpidem, hæc recedebat a Ma-<lb/>gnete, cauda Acus haud accedebat, ſedtota Acus poſt aliquot vibrationes <lb/>reciprocas ita ſubſiſtebat, ut ad lineam per polos Magnetis ad <lb/>centrum Acus ductam eſſet perpendicularis, admoto vero polo Ma-<lb/>gnetis Auſtrali ad caudam, hæc ad polum accedebat, ejuſque mo-<lb/>tum ſequebatur, eodem polo ad cuſpidem accedente, etiam hæc ac-<lb/>cedebat ad polum Magnetis, eumque commotum ſequebatur, minori <lb/>tamen celeritate quam cauda. </s> <s xml:id="echoid-s3645" xml:space="preserve">Polus ergo Magnetis Auſtralis utrique <lb/>extremo amicus, ipſa vero acus reſpectu totius Magnetis partialis <lb/>erat. </s> <s xml:id="echoid-s3646" xml:space="preserve">In noſtro Experimento utraque Verſorii extremitas erat amica <lb/>polo Boreo alterius Verſorii, quod directe eſt oppoſitum obſervationi <lb/>Hambergeri; </s> <s xml:id="echoid-s3647" xml:space="preserve">elapſo menſerepetii Experimentum, eventu conveniente <lb/>cum obſervationibusHambergerianis, nam Verſorii utraque extremitas <lb/>erat amica polo Auſtrali alterius; </s> <s xml:id="echoid-s3648" xml:space="preserve">adeo Natura in Magneticis luxuriat, <lb/>ut oppoſitos nonnunquam effectus producat, quibus virium ſuarum <lb/>cauſam magis occultando, cum mortalium ſolertia late ludit, arrogan-<lb/>temque ſagacitatis fiduciam compeſcit. </s> <s xml:id="echoid-s3649" xml:space="preserve">Intelligi tamen facile poteſt <lb/>quomodo in tentamine primo ambæ Verſorii extremitates a cuſpide <lb/>eâdem alterius Verſorii attrahebantur: </s> <s xml:id="echoid-s3650" xml:space="preserve">Verſorii enim propoſiti extre-<lb/>mitasAuſtralis aCuſpideBorea alterius ante ullum Magnetis contactum <lb/>attrahebatur, vis hæc in Ferro longiſſimo permanſit, etiamſi Ma-<lb/>gnes extremo oppoſito fuerit applicatus: </s> <s xml:id="echoid-s3651" xml:space="preserve">Concipiatur ergo ſuper <pb o="148" file="0162" n="162" rhead="DISSERTATIO"/> Magnete duci aliquouſque extremitas Borea, quæ Auſtralis ideo <lb/>evadit, & </s> <s xml:id="echoid-s3652" xml:space="preserve">modo ſufficientes vires haberet, converteret acum, uti <lb/>fit, ſi Magnes ulterius ſupra ipſum ducatur; </s> <s xml:id="echoid-s3653" xml:space="preserve">ſed Auſtralis polus a <lb/>Boreo polo alterius Verſorii attrahitur, eodem modo cuſpis Ver-<lb/>ſorii, Auſtralis poli vim nacta, a cuſpide Borea alterius attrahenda <lb/>eſt.</s> <s xml:id="echoid-s3654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3655" xml:space="preserve">3. </s> <s xml:id="echoid-s3656" xml:space="preserve">Deinde Verſorium ſecundum totam longitudinem, directione <lb/>priori continuata, ſuper polo Magnetis Auſtrali ductum fuit; </s> <s xml:id="echoid-s3657" xml:space="preserve">quo <lb/>facto, directum fuit uti modo ante in §. </s> <s xml:id="echoid-s3658" xml:space="preserve">2, ſed Puncta intermedia <lb/>Conſequentia habuit nulla, cuſpide Borea attracta ab alterius Au-<lb/>ſtrali, & </s> <s xml:id="echoid-s3659" xml:space="preserve">cauda Auſtrali attracta ab alterius Verſorii Boreo polo.</s> <s xml:id="echoid-s3660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3661" xml:space="preserve">4. </s> <s xml:id="echoid-s3662" xml:space="preserve">Tandem hujus Verſorii cauda Auſtrum ſpectans appoſita fuit <lb/>Magnetis polo Boreo, & </s> <s xml:id="echoid-s3663" xml:space="preserve">ſuper eo ducta ad longitudinem 2 polli-<lb/>cum; </s> <s xml:id="echoid-s3664" xml:space="preserve">permanſit Verſorii directio, quæ ſupra, ſed utraque extre-<lb/>mitas ejus repellebatur ab alterius Verſorii polo Boreo, atque pars <lb/>media Acus ab hoc polo tantum attrahebatur; </s> <s xml:id="echoid-s3665" xml:space="preserve">quod phænomenon <lb/>codem modo explicandum eſt ac primum.</s> <s xml:id="echoid-s3666" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div116" type="section" level="1" n="116"> <head xml:id="echoid-head125" xml:space="preserve">EXPERIMENTUM XCIV.</head> <p> <s xml:id="echoid-s3667" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3668" xml:space="preserve">4. </s> <s xml:id="echoid-s3669" xml:space="preserve">fig. </s> <s xml:id="echoid-s3670" xml:space="preserve">7. </s> <s xml:id="echoid-s3671" xml:space="preserve">& </s> <s xml:id="echoid-s3672" xml:space="preserve">9. </s> <s xml:id="echoid-s3673" xml:space="preserve">Sit A B C D latus polare Magnetis, Verſo-<lb/>rium vero E F mobile ſupra ſtylum K, apponatur cuſpis E puncto <lb/>Magnetis A, D, B, vel C, tum Verſorium ſecundum totam longi-<lb/>tudinem E F, ab E ad F ducatur directione A B, aut D C, B A aut <lb/>C D, vel quacunque ſimili aliâ inter has intermedia; </s> <s xml:id="echoid-s3674" xml:space="preserve">Verſorii ſty-<lb/>lo K impoſiti cuſpis E dirigetur ſemper verſus eandem cœli pla-<lb/>gam.</s> <s xml:id="echoid-s3675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3676" xml:space="preserve">2. </s> <s xml:id="echoid-s3677" xml:space="preserve">Deinde cauda F Verſorii applicetur iiſdem punctis Magnetis <lb/>A, D, B, C, & </s> <s xml:id="echoid-s3678" xml:space="preserve">Verſorium ſecundum totam longitudinem F E, ab <lb/>F uſque ad E, Magneti affricetur directionibus ex A in B, ex D in <lb/>C, uti ſupra, Verſori iterum impoſiti ſtylo K, cuſpis E ſpectabit <lb/>plagam cœli oppoſitam, quam in præcedenti tentamine.</s> <s xml:id="echoid-s3679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3680" xml:space="preserve">3. </s> <s xml:id="echoid-s3681" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3682" xml:space="preserve">4. </s> <s xml:id="echoid-s3683" xml:space="preserve">fig. </s> <s xml:id="echoid-s3684" xml:space="preserve">8. </s> <s xml:id="echoid-s3685" xml:space="preserve">Idem Magnes invertatur, ut alium polum G N <lb/>LM nobis obvertat, Verſorii cuſpis E imponatur punctis G, N, LvelM <lb/>Magnetis, & </s> <s xml:id="echoid-s3686" xml:space="preserve">totum Verſorium ab E uſque ad F ducatur ſuper polo <lb/>directionibus G L, vel N M, L G aut M N, cuſpis E Verſorii, impoſiti <pb o="149" file="0163" n="163" rhead="DE MAGNETE."/> ſtylo K, dirigetur verſus eandem cœli plagam, ac in tentamine ſe-<lb/>cundo.</s> <s xml:id="echoid-s3687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3688" xml:space="preserve">4. </s> <s xml:id="echoid-s3689" xml:space="preserve">Si vero cauda F Verſorii imponatur punctis G, N, L, M Ma-<lb/>gnetis, & </s> <s xml:id="echoid-s3690" xml:space="preserve">Verſorium totum ab F uſque ad E ipſi affricetur, dire-<lb/>ctionibus G L, N M, L G vel M N, cuſpis E dirigetur verſus ean-<lb/>dem cœli plagam, ac in tentamine primo.</s> <s xml:id="echoid-s3691" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div117" type="section" level="1" n="117"> <head xml:id="echoid-head126" xml:space="preserve">EXPERIMENTUM XCV.</head> <p> <s xml:id="echoid-s3692" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3693" xml:space="preserve">4. </s> <s xml:id="echoid-s3694" xml:space="preserve">fig. </s> <s xml:id="echoid-s3695" xml:space="preserve">7. </s> <s xml:id="echoid-s3696" xml:space="preserve">& </s> <s xml:id="echoid-s3697" xml:space="preserve">9. </s> <s xml:id="echoid-s3698" xml:space="preserve">Si A D B C fuerit polus Magnetis Auſtralis, <lb/>cui Verſorii cuſpis E applicatur, atque affrictus frat ab E ad F, di-<lb/>rigetur cuſpis E Verſorii, ſtylo K poſtea impoſiti, verſus plagam Au-<lb/>ſtralem, cauda verſus Borealem. </s> <s xml:id="echoid-s3699" xml:space="preserve">Si autem cauda Verſorii F fuerit <lb/>appoſita polo Auſtrali Magnetis, & </s> <s xml:id="echoid-s3700" xml:space="preserve">affrictus fiat ab F ad E, dirige-<lb/>tur cuſpis E verſus plagam cæli Boream: </s> <s xml:id="echoid-s3701" xml:space="preserve">ideo ut cuſpis E Verſorii <lb/>Boream ſpectet, oportebit ſemper caudam F applicare polo Ma-<lb/>gnetis Auſtrali, & </s> <s xml:id="echoid-s3702" xml:space="preserve">ſuper eodem ducere Verſorium a cauda ad cuſpi-<lb/>dem.</s> <s xml:id="echoid-s3703" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div118" type="section" level="1" n="118"> <head xml:id="echoid-head127" xml:space="preserve">EXPERIMENTUM XCVI.</head> <p> <s xml:id="echoid-s3704" xml:space="preserve">Tab. </s> <s xml:id="echoid-s3705" xml:space="preserve">5. </s> <s xml:id="echoid-s3706" xml:space="preserve">fig. </s> <s xml:id="echoid-s3707" xml:space="preserve">4. </s> <s xml:id="echoid-s3708" xml:space="preserve">Sit Scyphus vitreus D, aquâ plenus, ope furcæ <lb/>tenuis F G, Acus nautica M S, imprægnata vi Magnetica, vel acus <lb/>tenuis vulgaris nova, imponatur ſuperficiei Aquæ, ut ſupra eam na-<lb/>tet; </s> <s xml:id="echoid-s3709" xml:space="preserve">tum Magnetis A B polus Boreus B obvertatur Acui, cujus cu-<lb/>ſpis M Auſtralis attrahetur ab hoc Magnetis polo: </s> <s xml:id="echoid-s3710" xml:space="preserve">Sed invertatur <lb/>Magnes, ut polo Auſtrali A ſpectet idem Scyphi punctum, Acus M S <lb/>intorquebitur, deſcribendo lineam curvam S E M, atque caudâ Sre-<lb/>ſpiciet polum A Magnetis.</s> <s xml:id="echoid-s3711" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3712" xml:space="preserve">Notandum erat hoc Experimentum, a Pe<unsure/>linierio deſcriptum in <lb/>Experienc. </s> <s xml:id="echoid-s3713" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s3714" xml:space="preserve">pag. </s> <s xml:id="echoid-s3715" xml:space="preserve">290, ob curvam lineam S E M, quam A-<lb/>cus ſupra aquam deſcribit; </s> <s xml:id="echoid-s3716" xml:space="preserve">videretur enim ſe modo converſura ſupra <lb/>centrum gravitatis, veluti Acus nautica ſupra ſtylum rotatur, verum <lb/>curvam deſcribit, illi ſimilem, quam limatura circa Magnetem con-<lb/>ſperſa format.</s> <s xml:id="echoid-s3717" xml:space="preserve"/> </p> <pb o="150" file="0164" n="164" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div119" type="section" level="1" n="119"> <head xml:id="echoid-head128" xml:space="preserve">EXPERIMENTUM XCVII.</head> <p> <s xml:id="echoid-s3718" xml:space="preserve">Si Verſorium multis donatum viribus magneticis, & </s> <s xml:id="echoid-s3719" xml:space="preserve">ſuper ſtylo <lb/>liberrime mobile, imponatur Meridiano terreſtri, tendenti a vero <lb/>Septentrione ad Auſtrum, deprehenditur in nonnullis Terræ locis <lb/>cum hoc Meridiano congruere, atque in eo dirigi; </s> <s xml:id="echoid-s3720" xml:space="preserve">in aliis autem re-<lb/>gionibus ab eo recedere.</s> <s xml:id="echoid-s3721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3722" xml:space="preserve">Vocatur hic â Meridiano receſſus, Declinatio, Variatio, De-<lb/>viatio, ?</s> <s xml:id="echoid-s3723" xml:space="preserve">??</s> <s xml:id="echoid-s3724" xml:space="preserve">??</s> <s xml:id="echoid-s3725" xml:space="preserve">??</s> <s xml:id="echoid-s3726" xml:space="preserve">??</s> <s xml:id="echoid-s3727" xml:space="preserve">??</s> <s xml:id="echoid-s3728" xml:space="preserve">?.</s> <s xml:id="echoid-s3729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3730" xml:space="preserve">Quando hæc Declinatio fit ortum verſus, dicitur Acus Græciſſa-<lb/>re. </s> <s xml:id="echoid-s3731" xml:space="preserve">(Belgice de Naald Ooſtert) cum autem Declinatio fit occaſum ver-<lb/>ſus, dicitur Acus Magiſtriſſare (Belgice de Naald Weſtert).</s> <s xml:id="echoid-s3732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3733" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s3734" xml:space="preserve">Superius annotavimus vim directricem Magnetis verſus <lb/>Septentrionem & </s> <s xml:id="echoid-s3735" xml:space="preserve">Auſtrum ante Annum 1200 poſt Chr. </s> <s xml:id="echoid-s3736" xml:space="preserve">Nat. </s> <s xml:id="echoid-s3737" xml:space="preserve">inno-<lb/>tuiſſe: </s> <s xml:id="echoid-s3738" xml:space="preserve">Controvertitur, quiſnam primus Declinationem Acûs obſer-<lb/>vaverit: </s> <s xml:id="echoid-s3739" xml:space="preserve">Ut hæc quæſtio bene intelligatur, diſtinguenda eſt Decli-<lb/>natio in ſimplicem, & </s> <s xml:id="echoid-s3740" xml:space="preserve">in Declinationem declinationis: </s> <s xml:id="echoid-s3741" xml:space="preserve">illa eſt tan-<lb/>tum declinatio a Septentrione; </s> <s xml:id="echoid-s3742" xml:space="preserve">hæc eſt perpetua mutatio declina-<lb/>tionis in eodem Terræ loco.</s> <s xml:id="echoid-s3743" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3744" xml:space="preserve">De ſimplici Declinatione ergo primum agam: </s> <s xml:id="echoid-s3745" xml:space="preserve">Thevenottus in Iti-<lb/>nerario prodit, ſe Epiſtolam vidiſte, conſcriptam Anno 1269. </s> <s xml:id="echoid-s3746" xml:space="preserve">a <lb/>Petro Adſigerio, in qua declinare Acûs à vero Septentrione quin-<lb/>quegradibus commemoratur: </s> <s xml:id="echoid-s3747" xml:space="preserve">neque hoc fidem ſuperat, quippe ſimul <lb/>ac obſervatum fuit, Magnetem dirigi verſus Septentrionem, deſiderio <lb/>obſervandi accurate directionem capi potuerunt eodem ſeculo nau-<lb/>tæ aut Philoſophi: </s> <s xml:id="echoid-s3748" xml:space="preserve">Non tamen divulgata ſummopere fuit hæc obſer-<lb/>vatio, cæteroquin poſteri, aliquot ſerioribus viventes ſeculis, ſibi <lb/>gloriam inventi non adſcripſiſſent. </s> <s xml:id="echoid-s3749" xml:space="preserve">Cl. </s> <s xml:id="echoid-s3750" xml:space="preserve">Deliſle, Geographus, Ma-<lb/>nuſcriptum poſſidet alicujus nautæ Diepenſis, vocati Crignon, quod <lb/>dedicatum fuit Architalaſſo Chaboto, Anno 1534, in quo mentio <lb/>fit Declinationis Verſorii, vide L’Hiſt. </s> <s xml:id="echoid-s3751" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s3752" xml:space="preserve">Roy. </s> <s xml:id="echoid-s3753" xml:space="preserve">A°. </s> <s xml:id="echoid-s3754" xml:space="preserve">1712. <lb/></s> <s xml:id="echoid-s3755" xml:space="preserve">adeoque inventio adſcribetur immerito Sebaſtiano Chaboto, Ve-<lb/>neto, etiamſi Declinationem cognoverit. </s> <s xml:id="echoid-s3756" xml:space="preserve">Alii enumerant inter in-<lb/>ventores Gonzalum de Oviedo, Robertum Normannum, Dalençè: </s> <s xml:id="echoid-s3757" xml:space="preserve"><lb/>Seculo autem decimo ſexto admodum innotuiſſe videtur in pluribus <pb o="151" file="0165" n="165" rhead="DE MAGNETE."/> terræ locis; </s> <s xml:id="echoid-s3758" xml:space="preserve">nam in Germania Anno 1536 Hartmannum eam ob-<lb/>ſervaſſe Graduum 10, Minutorum 15, tradit Hulſius in navigatione <lb/>Indiam verſus, quod confirmat Keplerus in Stereometria: </s> <s xml:id="echoid-s3759" xml:space="preserve">in initio <lb/>autem credebatur non bene inſtituta obſervatio, quare Petrus Me-<lb/>dinenſis Lib. </s> <s xml:id="echoid-s3760" xml:space="preserve">6. </s> <s xml:id="echoid-s3761" xml:space="preserve">Cap. </s> <s xml:id="echoid-s3762" xml:space="preserve">3. </s> <s xml:id="echoid-s3763" xml:space="preserve">Declinationem adſcribit erroneæ obſerva-<lb/>tioni nauclerorum, ortæ ex imperfectione & </s> <s xml:id="echoid-s3764" xml:space="preserve">imperitia magnetifi-<lb/>candi Acum; </s> <s xml:id="echoid-s3765" xml:space="preserve">imo Celeberrimus Nonnius eam tribuebat magneticæ <lb/>Acus virtuti paulatim deficienti, aut ipſius Magnetis longo uſu at-<lb/>triti vigori magis magiſque remiſſo: </s> <s xml:id="echoid-s3766" xml:space="preserve">Verum poſtea innumeris obſer-<lb/>vationibus confirmata eſt, ut de Declinatione Acus nemo amplius <lb/>dubitet; </s> <s xml:id="echoid-s3767" xml:space="preserve">ſi quis interim cognoſcere cupiat quinam autores de Acûs <lb/>Declinatione fuſe egerint, conſulat Doctiſſimi Riccioli Geogra-<lb/>phiam Lib. </s> <s xml:id="echoid-s3768" xml:space="preserve">8. </s> <s xml:id="echoid-s3769" xml:space="preserve">Sect. </s> <s xml:id="echoid-s3770" xml:space="preserve">2, Cap. </s> <s xml:id="echoid-s3771" xml:space="preserve">XII. </s> <s xml:id="echoid-s3772" xml:space="preserve">pag. </s> <s xml:id="echoid-s3773" xml:space="preserve">337. </s> <s xml:id="echoid-s3774" xml:space="preserve">tum ea, quæ proſtant <lb/>ſparſim in L’Hiſtoire de L’Academie Royale, des Sciences; </s> <s xml:id="echoid-s3775" xml:space="preserve">& </s> <s xml:id="echoid-s3776" xml:space="preserve">in <lb/>Philoſophical Tranſactions. </s> <s xml:id="echoid-s3777" xml:space="preserve">Hæc ſufficiant de ſimplici Declinatione <lb/>Acus monuiſſe.</s> <s xml:id="echoid-s3778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3779" xml:space="preserve">Tranſeamus igitur ad Declinationem declinationis, quæ eſt mu-<lb/>tatio Declinationis, cui in eodem Terræ loco obnoxia eſt Acus; <lb/></s> <s xml:id="echoid-s3780" xml:space="preserve">obſervatur in directione Magnetis perpetuus quaſi motus, ita ut ſin-<lb/>gulo Anno, Menſe, die, horâ, verſus aliam cœleſtem plagam diri-<lb/>gatur, quod plurimis confirmabo obſervationibus. </s> <s xml:id="echoid-s3781" xml:space="preserve">Non autem an-<lb/>tiquiores habemus, quam quæ in Galliis, & </s> <s xml:id="echoid-s3782" xml:space="preserve">præcipue Pariſiis, ca-<lb/>ptæ ſunt, quamobrem Tabulam obſervationum hic adnectam, ex <lb/>quâ conſtat Gallos primos fuiſſe, qui Declinationem Declinationis <lb/>obſervaverunt: </s> <s xml:id="echoid-s3783" xml:space="preserve">Anno enim 1550 Pariſiiis regnabat Declinatio 8 <lb/>graduum verſus ortum, Anno 1580 fuit 11 grad. </s> <s xml:id="echoid-s3784" xml:space="preserve">30 Minut. </s> <s xml:id="echoid-s3785" xml:space="preserve">verſus <lb/>ortum. </s> <s xml:id="echoid-s3786" xml:space="preserve">Anno 1610 fuit 8 grad. </s> <s xml:id="echoid-s3787" xml:space="preserve">verſus ortum: </s> <s xml:id="echoid-s3788" xml:space="preserve">poſtea tamen inter <lb/>Brittannos Gellibrandus accuratiſſime ad hanc mutationem declina-<lb/>tionis attendiſſe videtur, quando Anno 1625 in Horto Londinenſi, <lb/>vocato The Privy Garden at Whitehall, ſollicite Meridianam li-<lb/>neam duxit, ut ope longæ Acus Magneticæ declinationis declina-<lb/>tionem obſervaret; </s> <s xml:id="echoid-s3789" xml:space="preserve">notante Walliſio in Philoſ. </s> <s xml:id="echoid-s3790" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3791" xml:space="preserve">N°. </s> <s xml:id="echoid-s3792" xml:space="preserve">276. </s> <s xml:id="echoid-s3793" xml:space="preserve">& </s> <s xml:id="echoid-s3794" xml:space="preserve"><lb/>N°. </s> <s xml:id="echoid-s3795" xml:space="preserve">278. </s> <s xml:id="echoid-s3796" xml:space="preserve">Inter primos, qui huic rei obſervandæ quoque operam <lb/>dederunt, fuit Petrus Gaſſendi, deinde Lynſchoten, & </s> <s xml:id="echoid-s3797" xml:space="preserve">Hacklvith, <lb/>qui Indias petentes, experiebantur declinationem mutari in iiſdem <lb/>locis, poſtea vero ab omnibus confirmata fuit obſervatoribus. </s> <s xml:id="echoid-s3798" xml:space="preserve">Erat <pb o="152" file="0166" n="166" rhead="DISSERTATIO"/> hoc inventum illius naturæ, ut aliquem temporis lapſum poſtula-<lb/>ret, quo obſervationes repeterentur: </s> <s xml:id="echoid-s3799" xml:space="preserve">Gratulari nobis poſſumus Pa-<lb/>riſiis & </s> <s xml:id="echoid-s3800" xml:space="preserve">Londini a plurimis retro annis Viros vixiſſe, qui in Obſer-<lb/>vationibus capiendis plurimum operæ poſuerunt, atque Declinatio-<lb/>nes magneticas quoque adnotaverunt variis annis. </s> <s xml:id="echoid-s3801" xml:space="preserve">Ecce Tabulam, <lb/>theſauro, cariorem, ex qua multa colligi poterunt, ſpectantia <lb/>magneticam doctrinam.</s> <s xml:id="echoid-s3802" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div120" type="section" level="1" n="120"> <head xml:id="echoid-head129" style="it" xml:space="preserve">Tabula Declinationis Acus Magneticæ Pariſiis obſervatæ.</head> <note position="right" xml:space="preserve"> <lb/>Anno. # Grad. # Minut. <lb/>1550 # 8 # 0 <lb/>1580 # 11 # 30 # Verſus \\ Ortum <lb/>1610 # 8 # 0 <lb/>1640 # 3 # 0 <lb/>1664 # 0 # 40 <lb/>1666 # 0 # 0 <lb/>1670 # 1 # 30 <lb/>1680 # 2 # 40 <lb/>1681 # 2 # 30 <lb/>1683 # 3 # 50 <lb/>1684 # 4 # 10 <lb/>1685 # 4 # 10 <lb/>1686 # 4 # 30 <lb/>1692 # 5 # 50 <lb/>1693 # 6 # 20 # Verſus \\ Occaſum <lb/>1695 # 6 # 48 <lb/>1696 # 7 # 8 <lb/>1698 # 7 # 40 <lb/>1699 # 8 # 10 <lb/>1700 # 8 # 12 <lb/>1701 # 8 # 25 <lb/>1702 # 8 # 48 <lb/>1703 # 9 # 6 <lb/>1704 # 9 # 20 <lb/>1705 # 9 # 35 <lb/>1706 # 9 # 48 <lb/></note> <note position="right" xml:space="preserve"> <lb/>Anno. # Grad. # Minut. <lb/>1707 # 10 # 10 <lb/>1708 # 10 # 15 <lb/>1709 # 10 # 15 <lb/>1710 # 10 # 50 <lb/>1711 # 10 # 50 <lb/>1712 # 11 # 15 <lb/>1713 # 11 # 12 <lb/>1714 # 11 # 30 <lb/>1715 # 11 # 10 <lb/>1716 # 12 # 20 <lb/>1717 # 12 # 20 <lb/>Alio menſe # 12 # 45 <lb/>1718 # 12 # 30 # Verſus Occaſum. <lb/>1719 # 12 # 30 <lb/>1720 # 13 # 0 <lb/>1721 # 13 # 0 <lb/>1722 # 13 # 0 <lb/>1723 # 13 # 0 <lb/>1724 # 13 # 0 <lb/>1725 <lb/>6 Novemb. # 13 # 15 <lb/>30 Decemb. # 13 # 15 <lb/>1726:6 Dec. # 13 # 45 <lb/>1727:1 Dec. # 14 # 0 <lb/>1728:3 Jan. # 14 # 0 <lb/></note> <pb o="153" file="0167" n="167" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s3803" xml:space="preserve">Quinque ultimas obſervationes, mecum communicare voluerunt <lb/>Viri præſtantiſſimi Fontenellius & </s> <s xml:id="echoid-s3804" xml:space="preserve">Maraldi.</s> <s xml:id="echoid-s3805" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3806" xml:space="preserve">Ex omnibus hiſce obſervationibus nonnulla Corollaria elicere nunc <lb/>licebit.</s> <s xml:id="echoid-s3807" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3808" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3809" xml:space="preserve">1. </s> <s xml:id="echoid-s3810" xml:space="preserve">Mutatio Declinationis non eſt proportionalis Tempori <lb/>in eodem loco Terræ. </s> <s xml:id="echoid-s3811" xml:space="preserve">Si enim obtineret hæc proportio, ſingulo <lb/>anno Declinatio æqualiter mutari deberet; </s> <s xml:id="echoid-s3812" xml:space="preserve">quod non fit, nam Sta-<lb/>tionarius fuit Magnes annis 1720, 1721, 1722. </s> <s xml:id="echoid-s3813" xml:space="preserve">quibus declinavit <lb/>13 gradibus verſus occaſum. </s> <s xml:id="echoid-s3814" xml:space="preserve">Stationarius fuit annis 1718, 1719, <lb/>quibus declinavit 12°, 30`. </s> <s xml:id="echoid-s3815" xml:space="preserve">itidem annis 1716, 1717, quibus de-<lb/>clinavit 12°, 20`. </s> <s xml:id="echoid-s3816" xml:space="preserve">verum aliis annis mutata fuit Declinatio, cum enim <lb/>anno 1700 declinabat 8°, 12`. </s> <s xml:id="echoid-s3817" xml:space="preserve">anno 1701 declinavit 8°, 25`, anno <lb/>1702. </s> <s xml:id="echoid-s3818" xml:space="preserve">8°, 48`. </s> <s xml:id="echoid-s3819" xml:space="preserve">& </s> <s xml:id="echoid-s3820" xml:space="preserve">ſic porro uſque ad annum 1711 ſingulis annis paſſa <lb/>fuit Declinatio mutationem.</s> <s xml:id="echoid-s3821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3822" xml:space="preserve">Si æqualem decurſum plurium annorum ſimul ſumamus, pariter <lb/>obſervabimus, admodum inæqualem mutationem Declinationis, ne-<lb/>quaquam tempori proportionalem; </s> <s xml:id="echoid-s3823" xml:space="preserve">ſumamus enim 10 annos ſimul, <lb/>ab anno 1710 ad 1720. </s> <s xml:id="echoid-s3824" xml:space="preserve">quibus Declinatio obſervata fuit 10°, 50`, <lb/>& </s> <s xml:id="echoid-s3825" xml:space="preserve">13°. </s> <s xml:id="echoid-s3826" xml:space="preserve">quibus Declinationis differentia eſt 2°, 10. </s> <s xml:id="echoid-s3827" xml:space="preserve">ſed ab anno 1700 <lb/>ad 1710 differentia eſt 2°, 38`. </s> <s xml:id="echoid-s3828" xml:space="preserve">ab anno 1670, ad 1680 differentia <lb/>fuit 1°, 10. </s> <s xml:id="echoid-s3829" xml:space="preserve">quare intra 10 annorum decurſum etiam non eſt æqua-<lb/>lis Declinationis differentia, quod probat Declinationem admodum <lb/>inæquali progreſſu temporis æquali intervallo, promoveri.</s> <s xml:id="echoid-s3830" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3831" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3832" xml:space="preserve">2 Neque ſemper Declinatio progreditur, ſed quoque re-<lb/>trogreditur aliquando: </s> <s xml:id="echoid-s3833" xml:space="preserve">Nam anno 1712 Declinatio fuit 11°, 15`. </s> <s xml:id="echoid-s3834" xml:space="preserve">& </s> <s xml:id="echoid-s3835" xml:space="preserve"><lb/>anno 1713 fuit 11°, 12`. </s> <s xml:id="echoid-s3836" xml:space="preserve">adeoque retrogreſſa fuit 3 Minutis. </s> <s xml:id="echoid-s3837" xml:space="preserve">ita quo-<lb/>que anno 1714 fuit Declinatio 11°, 30`. </s> <s xml:id="echoid-s3838" xml:space="preserve">quæ anno 1715 tantum fuit <lb/>11°, 10`. </s> <s xml:id="echoid-s3839" xml:space="preserve">ſic anno 1717 fuit 12°, 45`. </s> <s xml:id="echoid-s3840" xml:space="preserve">& </s> <s xml:id="echoid-s3841" xml:space="preserve">1718 fuit 12°, 30`. </s> <s xml:id="echoid-s3842" xml:space="preserve">nec mo-<lb/>do his ultimis temporibus retrograda fuit, ſed etiam anno 1681, quo <lb/>declinabat Acus 2°, 30`. </s> <s xml:id="echoid-s3843" xml:space="preserve">cum declinaverat Anno 1680, 2°, 40`.</s> <s xml:id="echoid-s3844" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3845" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3846" xml:space="preserve">3. </s> <s xml:id="echoid-s3847" xml:space="preserve">Cum igitur motus Declinationis ſit adeo diverſus, mo-<lb/>tus aliquis medius pro ſingulis annis inveniri poteſt, quia enim ſpa-<lb/>tio 56 annorum Declinatio mutata fuit 13 gradubus, hi dividantur <lb/>per 56 annos, prodeunt 13 {52/76} Minuta, ſive circiter 14 Minuta pro quo-<lb/>libet anno, qui Declinationis progreſſus poteſt vocari Motus medius.</s> <s xml:id="echoid-s3848" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3849" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3850" xml:space="preserve">4. </s> <s xml:id="echoid-s3851" xml:space="preserve">Eſt progreſſus Declinationis a vero Septentrione ad Occaſum <pb o="154" file="0168" n="168" rhead="DISSERTATIO"/> celerior, quam fuit ab Ortu ad verum Septentrionem, nam anno 1610 <lb/>declinabat Acus 8 gradibus verſus Ortum, excurrerunt inter 1610 & </s> <s xml:id="echoid-s3852" xml:space="preserve"><lb/>1666 anni 56, quemadmodum inter 1666 & </s> <s xml:id="echoid-s3853" xml:space="preserve">1722. </s> <s xml:id="echoid-s3854" xml:space="preserve">cum igitur mo-<lb/>tus ab Ortu ad Boream fuit 8 graduum, poſtea æquali annorum in-<lb/>tervallo fuit a Borea ad Occaſum 13 graduum, patet ergo hunc po-<lb/>ſteriorem motum eſſe celeriorem.</s> <s xml:id="echoid-s3855" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3856" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3857" xml:space="preserve">5. </s> <s xml:id="echoid-s3858" xml:space="preserve">Ut igitur motu medio 14 Minutorum Acus <lb/>Declinatio integrum circuitum abſolvat, indigebit ſpatio 1542 <lb/>Annorum circiter, uti patet, ſi integer circulus 360 Graduum divi-<lb/>datur per 14 Minuta. </s> <s xml:id="echoid-s3859" xml:space="preserve">Fatendum tamen eſt, hoc eſſe admodum incer-<lb/>tum: </s> <s xml:id="echoid-s3860" xml:space="preserve">imo de ejuſmodi motu medio non interſe conveniunt Philo-<lb/>ſophi, Noëllius enim in Obſerv. </s> <s xml:id="echoid-s3861" xml:space="preserve">in China factis. </s> <s xml:id="echoid-s3862" xml:space="preserve">pag. </s> <s xml:id="echoid-s3863" xml:space="preserve">111. </s> <s xml:id="echoid-s3864" xml:space="preserve">ponit <lb/>9 {1/2} vel 10 Minuta: </s> <s xml:id="echoid-s3865" xml:space="preserve">Caſſini attribuit 11 vel 12 Minuta in L’ Hiſt. </s> <s xml:id="echoid-s3866" xml:space="preserve">de <lb/>L’ Acad. </s> <s xml:id="echoid-s3867" xml:space="preserve">Roy. </s> <s xml:id="echoid-s3868" xml:space="preserve">A°. </s> <s xml:id="echoid-s3869" xml:space="preserve">1701. </s> <s xml:id="echoid-s3870" xml:space="preserve">ipſique alii modo attribuunt 9 Minuta, in-<lb/>nixi obſervationibus captis Londini; </s> <s xml:id="echoid-s3871" xml:space="preserve">quas hic adjungendas eum in <lb/>finem duxi: </s> <s xml:id="echoid-s3872" xml:space="preserve">fuit igitur Declinatio obſervata</s> </p> <note position="right" xml:space="preserve"> <lb/># Anno # Grad. # M. <lb/>a Burrough # 1576 # 11 # 15 <lb/># 1612 # 6 # 10 <lb/>a Guntero # 1622 # 6 # 0 # Verſus Ortum. <lb/>a Gellibrando # 1634 # 4 # 5 <lb/>a Bondio # 1657 # 0 # 0 <lb/># 1665 # 1 # 22 {1/2} <lb/># 1666 # 1 # 35? 36? <lb/>ab Halleyo # 1672 # 2 # 30 # Verſus Occaſum. <lb/># 1683 # 4 # 30 <lb/># 1692 # 6 # 0 <lb/># 1700 # 8 # 0 <lb/></note> <p> <s xml:id="echoid-s3873" xml:space="preserve">Excurrerunt ab Anno 1576. </s> <s xml:id="echoid-s3874" xml:space="preserve">ad 1700 Anni 124. </s> <s xml:id="echoid-s3875" xml:space="preserve">quibus facta fuit <lb/>Declinationis mutatio 19°, 15`. </s> <s xml:id="echoid-s3876" xml:space="preserve">quibus diviſis per 124 Annos pro-<lb/>deunt pro uno Anno 9 {39/124} Minuta: </s> <s xml:id="echoid-s3877" xml:space="preserve">Kirchius obſervans Declinatio-<lb/>nem Magnetis Berolini, hanc adnotavit</s> </p> <pb o="155" file="0169" n="169" rhead="DE MAGNETE"/> <note position="right" xml:space="preserve"> <lb/>Anno # # Grad. # Minut. <lb/>1717 # circa initium æſtatis # 10 # 42 <lb/># 26 Novembris # 10 # 55 <lb/>1724 # 13 Auguſti # 11 # 45 <lb/>1725 # 14 Junii # 11 # 56 <lb/></note> <p> <s xml:id="echoid-s3878" xml:space="preserve">Ex quibus obſervationibus attribuit Acui progreſſum 9, 15``, pro <lb/>quolibet Anno: </s> <s xml:id="echoid-s3879" xml:space="preserve">Si numerus rotundus 9 ſumatur pro vero, tum ſpa-<lb/>tio 2400 Annorum integrum circuitum Declinatio abſolveret. </s> <s xml:id="echoid-s3880" xml:space="preserve">Su-<lb/>ſpicatur Whiſtonus revolutionem peractum iri intra 1920 Annos: <lb/></s> <s xml:id="echoid-s3881" xml:space="preserve">Revera reſtant in hac doctrinâ Magnetica, quæ nequaquam accu-<lb/>rate determinari hucuſque poſſunt: </s> <s xml:id="echoid-s3882" xml:space="preserve">Verſamur tantum in principio <lb/>hujus ſcientiæ, quæ modo poſt plurimos annos, ac poſt multas <lb/>obſervationes perfici & </s> <s xml:id="echoid-s3883" xml:space="preserve">demonſtrari poterit.</s> <s xml:id="echoid-s3884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3885" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s3886" xml:space="preserve">Videntur Brittanni primi de integrâ revolutione Acus, <lb/>aut poli Magnetici terreſtris cogitaſſe, unde aliquis, nomine Phi-<lb/>lips, aſſeruit, hanc revolutionem peractum iriſpatio 370 annorum: <lb/></s> <s xml:id="echoid-s3887" xml:space="preserve">deinde Bondius eam intra 600 annos perfici credidit, in Treatiſe <lb/>Longitude found, p. </s> <s xml:id="echoid-s3888" xml:space="preserve">2. </s> <s xml:id="echoid-s3889" xml:space="preserve">ad 9. </s> <s xml:id="echoid-s3890" xml:space="preserve">Magnus in arte Halleyus conjecta-<lb/>bat eam abſolvi intra 700 circiter annos.</s> <s xml:id="echoid-s3891" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3892" xml:space="preserve">Corol. </s> <s xml:id="echoid-s3893" xml:space="preserve">6. </s> <s xml:id="echoid-s3894" xml:space="preserve">Si Tabulam Brittannicam comparemus cum Pariſienſi, <lb/>obſervamus in Brittannia Acum 9 annis citius verum Boream indi-<lb/>caſſe, quam Pariſiis; </s> <s xml:id="echoid-s3895" xml:space="preserve">quod provenire videtur, quia Londinum 2°, <lb/>25` jacet occidentalius.</s> <s xml:id="echoid-s3896" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3897" xml:space="preserve">Auzoutus Romæ obſervavit Anno 1670 Declinationem eſſe vel <lb/>2 Graduum, vel 2°, 30` verſus Occaſum, uti notatum eſt in Phi-<lb/>loſ. </s> <s xml:id="echoid-s3898" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3899" xml:space="preserve">N°. </s> <s xml:id="echoid-s3900" xml:space="preserve">58. </s> <s xml:id="echoid-s3901" xml:space="preserve">Jacet autem Roma Orientalius 11°, 48` Lutetiis, <lb/>quare major Declinatio verſus Occaſum Romæ fuit, quam eodem <lb/>anno Lutetiis, imo & </s> <s xml:id="echoid-s3902" xml:space="preserve">major fuit Londini hoc anno, licet Londi-<lb/>num jaceat occidentalius, & </s> <s xml:id="echoid-s3903" xml:space="preserve">fuit hic Declinatio fere eadem, quæ Ro-<lb/>mæ, quod indicat, fere æqualiter utrimque a linea experte Decli-<lb/>nationis Londinum & </s> <s xml:id="echoid-s3904" xml:space="preserve">Romam tum abfuiſſe.</s> <s xml:id="echoid-s3905" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3906" xml:space="preserve">Interim admirandum eſt, cum Pariſiis anno 1666 nulla fuerit De-<lb/>clinatio, uti Londini Anno 1657, & </s> <s xml:id="echoid-s3907" xml:space="preserve">ante hoc tempus Acus græciſſabat, <lb/>ipſam tamen Regiomonti diu ante fuiſſe Occidentalem & </s> <s xml:id="echoid-s3908" xml:space="preserve">poſtea ita <lb/>manſiſſe: </s> <s xml:id="echoid-s3909" xml:space="preserve">notat enim Hevelius, ſuum præceptorem Crugerum, an- <pb o="156" file="0170" n="170" rhead="DISSERTATIO"/> no 1628 obſervaſſe Declinationem 1 gradus occidentalem, anno <lb/>1642 eam ſe cum Linnemanno deprehendiſſe 3°, 5 occidentalem, <lb/>anno 1670 graduum 7, Minut. </s> <s xml:id="echoid-s3910" xml:space="preserve">20. </s> <s xml:id="echoid-s3911" xml:space="preserve">vide Philoſ. </s> <s xml:id="echoid-s3912" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s3913" xml:space="preserve">N°. </s> <s xml:id="echoid-s3914" xml:space="preserve">64. </s> <s xml:id="echoid-s3915" xml:space="preserve">pag. <lb/></s> <s xml:id="echoid-s3916" xml:space="preserve">2060.</s> <s xml:id="echoid-s3917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3918" xml:space="preserve">Obſervatum autem eſt præterea, non in omni loco Terræ fieri in-<lb/>tra idem tempus eandem quantitatem variationis: </s> <s xml:id="echoid-s3919" xml:space="preserve">Nam Caſſini ad-<lb/>notavit intra 37 Annos eam in Quebecq modo fuiſſe 30 Minutorum: <lb/></s> <s xml:id="echoid-s3920" xml:space="preserve">Deliſle etiam obſervavit intra 11 annos variationem ibi fuiſſe 1 gra-<lb/>dus. </s> <s xml:id="echoid-s3921" xml:space="preserve">vid. </s> <s xml:id="echoid-s3922" xml:space="preserve">L’ Hiſtoir. </s> <s xml:id="echoid-s3923" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s3924" xml:space="preserve">Roy. </s> <s xml:id="echoid-s3925" xml:space="preserve">1712. </s> <s xml:id="echoid-s3926" xml:space="preserve">Sed Pariſiis fuit ab A°. </s> <s xml:id="echoid-s3927" xml:space="preserve"><lb/>1666. </s> <s xml:id="echoid-s3928" xml:space="preserve">ad 1696 æqualis 7°, 8`. </s> <s xml:id="echoid-s3929" xml:space="preserve">& </s> <s xml:id="echoid-s3930" xml:space="preserve">intra 11 annos ultimo obſervatos fuit <lb/>æqualis 1°, 48`.</s> <s xml:id="echoid-s3931" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3932" xml:space="preserve">Monui autem ſuperius, non modo ſingulo anno, ſed ſingulo menſe <lb/>& </s> <s xml:id="echoid-s3933" xml:space="preserve">die Declinationem eſſe diverſam; </s> <s xml:id="echoid-s3934" xml:space="preserve">quod conſtat ex obſervationi-<lb/>bus a Patre Guy Tachart factis anno 1682; </s> <s xml:id="echoid-s3935" xml:space="preserve">cum enim coram Rege <lb/>Siammenſi in urbe Louvo ejuſdem Regni ad Acum attendebat, in-<lb/>venit eam declinaſſe verſus Occidentem uno die 16 Minutis, ſecun-<lb/>do die 31 M`. </s> <s xml:id="echoid-s3936" xml:space="preserve">tertio die 35 M`. </s> <s xml:id="echoid-s3937" xml:space="preserve">quarto die 38 M`. </s> <s xml:id="echoid-s3938" xml:space="preserve">Aliis autem die-<lb/>bus ejuſdem anni, inter quos non interceſſit longum intervallum, <lb/>obſervavit Deviationem 28 Minutorum, altero die 33 M`. </s> <s xml:id="echoid-s3939" xml:space="preserve">tertio die <lb/>21 M`. </s> <s xml:id="echoid-s3940" xml:space="preserve">vide Itinerarium ejuſdem pag. </s> <s xml:id="echoid-s3941" xml:space="preserve">224, 225. </s> <s xml:id="echoid-s3942" xml:space="preserve">Septem hæ obſer-<lb/>vationes procul dubio ſunt intra menſis ſpatium factæ; </s> <s xml:id="echoid-s3943" xml:space="preserve">ex quibus <lb/>liquet, Acum ſingulo die aliam variationem oſtendere. </s> <s xml:id="echoid-s3944" xml:space="preserve">Neſcio an <lb/>ante huncPatrem aliquis hanc quotidianam mutationem obſervaverit: <lb/></s> <s xml:id="echoid-s3945" xml:space="preserve">Eandem confirmare poſſum propriâ experientiâ, nam</s> </p> <note position="right" xml:space="preserve"> <lb/># # # Grad. # Minut. <lb/>Anno 1728. # 8 # Martii fuit Trajecti Declinatio # 13 # 20 <lb/># 8 # Aprilis # 13 # 15 <lb/># 10 # # 13 # 19 <lb/># 11 # # 13 # 20 <lb/># 12 # # 13 # 20 <lb/># 15 # # 13 # 14 <lb/># 16 # # 13 # 15 <lb/># 17 # # 13 # 15 <lb/># 18 # # 13 # 15 <lb/># 19 # # 13 # 15 <lb/></note> <pb o="157" file="0171" n="171" rhead="de MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # # Grad. # Min. <lb/>Anno 1728. # 20 # Aprilis # 13 # 18 <lb/># 21 # # 13 # 15 <lb/># 22 # # 13 # 15 <lb/># 23 # # 13 # 15 <lb/></note> <p> <s xml:id="echoid-s3946" xml:space="preserve">Verum Inſignis artifex Londinenſis Graham accuratius ad hanc <lb/>rem attendit, plurimaſque inſtituit obſervationes, quas inſeruit <lb/>Actis Philoſophicis Anglicanis N°. </s> <s xml:id="echoid-s3947" xml:space="preserve">383. </s> <s xml:id="echoid-s3948" xml:space="preserve">A°. </s> <s xml:id="echoid-s3949" xml:space="preserve">1724. </s> <s xml:id="echoid-s3950" xml:space="preserve">pag. </s> <s xml:id="echoid-s3951" xml:space="preserve">96. </s> <s xml:id="echoid-s3952" xml:space="preserve">quas, <lb/>utpote præſtantiſſimas, hic adnectam, quoniam ex iis cum noſtra, <lb/>tum obſervata Tachartii, quæ prima fronte dubiæ fidei viderentur, <lb/>penitus confirmantur & </s> <s xml:id="echoid-s3953" xml:space="preserve">illuſtrantur.</s> <s xml:id="echoid-s3954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3955" xml:space="preserve">Accuratiſſimam conſtruxit Acum, longam, fortiſſimo Magneti <lb/>bene affrictam, incluſam capſulæ cupreæ, quæ arcum circuli con-<lb/>tinebat, in quo Gradus & </s> <s xml:id="echoid-s3956" xml:space="preserve">Minuta habebantur; </s> <s xml:id="echoid-s3957" xml:space="preserve">capſula hâc impo-<lb/>ſitâ Meridianæ lineæ, ut melius obſervaretur Declinatio Acus ver-<lb/>ſus occidentem, invenit ſequentia</s> </p> <note position="right" xml:space="preserve"> <lb/>8 Martii # # Declinatio \\ Acus erat # # # # Alia Acus incluſa \\ capſulæ ligneæ <lb/>1722. # Grad. # M. # Hora, # Min. # Gr. # Minuta: <lb/>+ hoc ſignum \\ notat plus \\ aliquid. # 14 # 30 # 3 # 0 # 14 # 25 + <lb/># 14 # 20 # 3 # 15 # 14 # 20 <lb/># 14 # 15 + # 4 # 0 # 14 # 10 <lb/>--- hoc minus \\ aliquid. # 14 # 20 # 4 # 15 # 14 # 15 <lb/># 14 # 25 # 5 # 0 # 14 # 20 <lb/># 14 # 25 # 5 # 30 # 14 # 20 <lb/># 14 # 15 # 5 # 45 # 14 # 10 <lb/># 14 # 0 # 5 # 57 # 14 # 0---<lb/># 14 # 0--- # 6 # 8 # 13 # 55 <lb/># 13 # 50 # 6 # 15 # 13 # 40 <lb/># 14 # 20 # 6 # 38 # 14 # 15 + <lb/># 14 # 0 + # 6 # 48 # 14 # 0 <lb/># 14 # 0 # 6 # 54 # 14 # 0---<lb/># 14 # 5 # 7 # 5 # 14 # 0 + <lb/># 14 # 10 # 7 # 15 # 14 # 5 <lb/># 14 # 0 + # 12 # 0 # 14 # 0 + <lb/></note> <pb o="158" file="0172" n="172" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s3958" xml:space="preserve">Colligimus ex his Experimentis Declinationem Acus variare fere <lb/>qualibet hora, imo forte quolibet Minuto, uti nonnullæ obſerva-<lb/>tiones demonſtrant.</s> <s xml:id="echoid-s3959" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3960" xml:space="preserve">2°. </s> <s xml:id="echoid-s3961" xml:space="preserve">Duas Acus, eidem Magneti affrictas, habere diverſam Declina-<lb/>tionem, unâ declinante in Cupro 14°. </s> <s xml:id="echoid-s3962" xml:space="preserve">30`. </s> <s xml:id="echoid-s3963" xml:space="preserve">alterâ in capſulâ li-<lb/>gnea 14°. </s> <s xml:id="echoid-s3964" xml:space="preserve">25`.</s> <s xml:id="echoid-s3965" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3966" xml:space="preserve">3°. </s> <s xml:id="echoid-s3967" xml:space="preserve">Patet quodDeclinatio major & </s> <s xml:id="echoid-s3968" xml:space="preserve">minor mutabatur in utraque Acu <lb/>ſimul, ſed non æqualiter, nunc enim fiebat in hoc Acu major, nuncin <lb/>alterâ: </s> <s xml:id="echoid-s3969" xml:space="preserve">ambæ primæ obſervationes cum Acu in cuprea capſula pro-<lb/>bant variationem = 10 M`. </s> <s xml:id="echoid-s3970" xml:space="preserve">cum in ligno variatio nis differentia erat <lb/>æqualis 5 M`. </s> <s xml:id="echoid-s3971" xml:space="preserve">Sed tertia variatio in Cupro differt a ſecunda modo 5 M`. <lb/></s> <s xml:id="echoid-s3972" xml:space="preserve">tertia vero in Ligno differt a ſecunda 10 M?</s> <s xml:id="echoid-s3973" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s3974" xml:space="preserve">4°. </s> <s xml:id="echoid-s3975" xml:space="preserve">Sed intra ſpatium 3 hor. </s> <s xml:id="echoid-s3976" xml:space="preserve">8`. </s> <s xml:id="echoid-s3977" xml:space="preserve">variatio fuit in utraque acu = <lb/>30 M.</s> <s xml:id="echoid-s3978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3979" xml:space="preserve">Utinam obſervator ſimul attendiſſet ad ventos, eorumque muta-<lb/>tiones! forte enim inde aliquid detegere potuiſſet.</s> <s xml:id="echoid-s3980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3981" xml:space="preserve">Sed annectere lubet alias obſervationes dierum ſequentium, ut <lb/>ex iis conſtet, ſemper, & </s> <s xml:id="echoid-s3982" xml:space="preserve">quotidie eas Acûs mutationes contingere, <lb/>imo & </s> <s xml:id="echoid-s3983" xml:space="preserve">qualibet hora.</s> <s xml:id="echoid-s3984" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Declin. # Grad. # M. # Hora. # M. <lb/>Martii \\ 9 # 14 # 10 # 9 # 30 <lb/># 14 # 10 + # 10 # 0 <lb/># 14 # 10 # 10 # 15 <lb/># 14 # 10 + # 10 # 30 <lb/># 14 # 15 # 11 # 0 <lb/># 14 # 0 # 8 # 15 <lb/># 14 # 0 # 11 # 50 <lb/>Martii \\ 10. # 14 # 10 + # 10 # 0 <lb/># 14 # 15 # 11 # 0 <lb/># 14 # 15 # 12 # 0 <lb/># 14 # 15 + # 12 # 45 <lb/># 14 # 15 + # 2 # 0 <lb/># 14 # 15 # 3 # 30 <lb/># 14 # 15 + # 4 # 0 <lb/># 14 # 15-- # 5 # 30 <lb/># 14 # 10 # 6 # 0 <lb/># 14 # 0 # 6 # 15 <lb/># 14 # --- # 6 # 30 <lb/></note> <pb o="159" file="0173" n="173" rhead="de MAGNETE."/> <note position="right" xml:space="preserve"> <lb/>Grad. # M. # Horæ # M. <lb/>14 + # # 7 # 30 <lb/>14 # 5 # 7 # 45 <lb/>14 + # # 12 # 0 <lb/></note> <p> <s xml:id="echoid-s3985" xml:space="preserve">Plures obſervationes in citatis actis conſpici poſſunt: </s> <s xml:id="echoid-s3986" xml:space="preserve">notat ob-<lb/>ſervator ſe ultra 1000 obſervationes feciſſe in eodem loco cum iiſ-<lb/>dem Acubus, quæ omnes ſibi fuerunt ſimiles. </s> <s xml:id="echoid-s3987" xml:space="preserve">Sunt hæc Experi-<lb/>menta plane contraria iis, quæ Cabeus Lib. </s> <s xml:id="echoid-s3988" xml:space="preserve">1. </s> <s xml:id="echoid-s3989" xml:space="preserve">Cap. </s> <s xml:id="echoid-s3990" xml:space="preserve">16. </s> <s xml:id="echoid-s3991" xml:space="preserve">notavit, <lb/>in eodem loco eandem perpetuo Declinationem fore, audacter pro-<lb/>nuncians.</s> <s xml:id="echoid-s3992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3993" xml:space="preserve">Cl. </s> <s xml:id="echoid-s3994" xml:space="preserve">Mullerus in Collegio Experim. </s> <s xml:id="echoid-s3995" xml:space="preserve">pag. </s> <s xml:id="echoid-s3996" xml:space="preserve">237. </s> <s xml:id="echoid-s3997" xml:space="preserve">Obſervationem ſui <lb/>fratris affert, notantis Acum in verticibus montium 10, 20, 50, <lb/>imo 90 gradibus plus aberrare, quam ad eorum radicem, idque ob-<lb/>tinere in montibus Bohemiæ & </s> <s xml:id="echoid-s3998" xml:space="preserve">prope vetus Briſacum, dicitur etiam <lb/>ibidem, id obſervatum in montibus Saxoniæ fuiſſe: </s> <s xml:id="echoid-s3999" xml:space="preserve">meretur hoc pa-<lb/>radaxon ulterius examinari in locis montoſis, ut & </s> <s xml:id="echoid-s4000" xml:space="preserve">confirmetur, & </s> <s xml:id="echoid-s4001" xml:space="preserve"><lb/>inde multum lucis doctrinæ Magneticæ adferatur; </s> <s xml:id="echoid-s4002" xml:space="preserve">nam Ferrum, quod <lb/>plurimi montes gerunt, etiam magnam varietatem hiſce & </s> <s xml:id="echoid-s4003" xml:space="preserve">ſimili-<lb/>bus obſervationibus adferre potuiſſet.</s> <s xml:id="echoid-s4004" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4005" xml:space="preserve">Manifeſto igitur ex ſuperioribus obſervationibus conſtat: </s> <s xml:id="echoid-s4006" xml:space="preserve">Decli-<lb/>nationem Acus Magneticæ eſſe obnoxiam perpetuis mutationibus <lb/>in eodem Terræ loco, uti Pariſiis & </s> <s xml:id="echoid-s4007" xml:space="preserve">Londini; </s> <s xml:id="echoid-s4008" xml:space="preserve">& </s> <s xml:id="echoid-s4009" xml:space="preserve">idem obtinere per-<lb/>univerſum Terrarum orbem: </s> <s xml:id="echoid-s4010" xml:space="preserve">Nunc nonnulla loca ſunt libera a De-<lb/>clinatione, in quibus Magnes directe reſpicit Boream & </s> <s xml:id="echoid-s4011" xml:space="preserve">Auſtrum, <lb/>verum ſequentianno in iis declinabit Magnes verſus Ortum vel Occa-<lb/>ſum. </s> <s xml:id="echoid-s4012" xml:space="preserve">In aliis Terræ plagis nunc parum declinat, ſequentiautem anno <lb/>magis, ita ut perpetua in Declinatione Magnetis per Univerſam Ter-<lb/>ram obtineat varietas; </s> <s xml:id="echoid-s4013" xml:space="preserve">hæc adfert ſummam difficultatem doctrinæ Ma-<lb/>gneticæ, imprimis cum nondum multas poſſidemus obſervationes, & </s> <s xml:id="echoid-s4014" xml:space="preserve"><lb/>quas habemus earum plurimæ adhuc non ſunt cum cura ſufficienti fa-<lb/>ctæ, præſtaret, ſi inſtituerentur eodem anno in omnibus partibus Terræ <lb/>& </s> <s xml:id="echoid-s4015" xml:space="preserve">Oceanorum ſimul, atque per plurimos continuarentur annos, tum <lb/>enim decurſus Declinationis innoteſceret, & </s> <s xml:id="echoid-s4016" xml:space="preserve">forſitan ex eo ſimul cauſa <lb/>& </s> <s xml:id="echoid-s4017" xml:space="preserve">virtus Magnetis detegeretur: </s> <s xml:id="echoid-s4018" xml:space="preserve">Ex rudi tamen Chao obſervationum Vir <lb/>Sagaciſſimus ſummoque præditus ingenio, Edm Halleyus Syſthema <lb/>aliquod condidit quod licet (ipſo fatente Philoſopho) rude adhuc ſit, &</s> <s xml:id="echoid-s4019" xml:space="preserve"> <pb o="160" file="0174" n="174" rhead="DISSERTATIO"/> expoliendum tempore, nihilominus magis magiſque confirmatur quo-<lb/>tidianis obſervationibus; </s> <s xml:id="echoid-s4020" xml:space="preserve">hinc illud pro baſi eſt aſſumendum, quem-<lb/>admodum quoque Academiæ Regiæ Pariſinæ Sapientes eo uſi, con-<lb/>ferunt illud cum novis in itinere factis obſervationibus, atque re-<lb/>jectis omnibus aliis hypotheſibus, hoc ſolummodo poliunt, exco-<lb/>lunt, amplificant, illuſtrant. </s> <s xml:id="echoid-s4021" xml:space="preserve">Confer. </s> <s xml:id="echoid-s4022" xml:space="preserve">L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s4023" xml:space="preserve">Roy. <lb/></s> <s xml:id="echoid-s4024" xml:space="preserve">A°. </s> <s xml:id="echoid-s4025" xml:space="preserve">1712 Utigitur hoc negotium, quod valdequam intricatum eſt, cla-<lb/>re intelligatur, Mappa Magnetica Halley ana ponatur ante oculos; </s> <s xml:id="echoid-s4026" xml:space="preserve">vid. </s> <s xml:id="echoid-s4027" xml:space="preserve"><lb/>Tab. </s> <s xml:id="echoid-s4028" xml:space="preserve">X. </s> <s xml:id="echoid-s4029" xml:space="preserve">hæc baſis erit omnium, quæ in ſequentibus dicentur, quam <lb/>ideo hic adferre debui: </s> <s xml:id="echoid-s4030" xml:space="preserve">Mappa repræſentat fere integrum terrarum <lb/>orbem, tum lineas continet rectas, exhibentes Meridianos ductos <lb/>a polo Auſtrali ad Borealem: </s> <s xml:id="echoid-s4031" xml:space="preserve">præterea lineas Latitudinis habet, qua-<lb/>les in Mappis vulgaribus obſervantur: </s> <s xml:id="echoid-s4032" xml:space="preserve">Inſuper conſpiciuntur lineæ <lb/>curvæ, quæ pertinent ad demonſtrandam directionem Magnetis: </s> <s xml:id="echoid-s4033" xml:space="preserve"><lb/>Eſt hæc Mappa confecta pro anno 1700, quo Declinatio Magne-<lb/>tis fuit in illis locis, qualis depingitur. </s> <s xml:id="echoid-s4034" xml:space="preserve">1°. </s> <s xml:id="echoid-s4035" xml:space="preserve">datur curva, quæ in-<lb/>cipit in America ad Carolinam, tranſiens per Inſulam Bermudos, per <lb/>Oceanum Æthyopicum Auſtrum verſus, deſinens ad latitudinem Au-<lb/>ſtralem 58 Grad. </s> <s xml:id="echoid-s4036" xml:space="preserve">in Meridiano Londinenſi: </s> <s xml:id="echoid-s4037" xml:space="preserve">hæc curva anno 1700 <lb/>tranſiit ſupra omnia loca Terræ mariſque, quæ immunia erant a De-<lb/>clinatione Magnetis: </s> <s xml:id="echoid-s4038" xml:space="preserve">unde vocatur ab Halleyo Linea expers Va-<lb/>riationis.</s> <s xml:id="echoid-s4039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4040" xml:space="preserve">2°. </s> <s xml:id="echoid-s4041" xml:space="preserve">Supra hanc lineam verſus Boream conſpiciuntur aliæ curvæ, <lb/>quibus appoſiti ſunt numeri Arithmetici 5, 10, 15, 20, 25, tranſ-<lb/>euntque ſupra Oceanum occidentalem: </s> <s xml:id="echoid-s4042" xml:space="preserve">numeri indicant Acum to-<lb/>tidem gradibus declinare verſus occaſum in locis ſubjacentibus ſub <lb/>his curvis.</s> <s xml:id="echoid-s4043" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4044" xml:space="preserve">Pro baſi firma hoc ponendum eſt, nam ex obſervationibus bene <lb/>captis & </s> <s xml:id="echoid-s4045" xml:space="preserve">comparatis cum aliis hæ lineæ ductæ ſunt: </s> <s xml:id="echoid-s4046" xml:space="preserve">Sed his Hal-<lb/>leyanis addamus obſervationes Declinationis captas anno 1720 in <lb/>mari Baltico, quæ proſtant in Philoſ. </s> <s xml:id="echoid-s4047" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4048" xml:space="preserve">N°. </s> <s xml:id="echoid-s4049" xml:space="preserve">366, & </s> <s xml:id="echoid-s4050" xml:space="preserve">quæ ſunt <lb/>Prope</s> </p> <note position="right" xml:space="preserve"> <lb/># # # Latitudo # # Declinat. # Magnetis Occidentali <lb/>Revel # 58° # 58` # 14° # 53 # Differentia locorum \\ in longitud. 1°. 50` <lb/>Gottſand # 58 # 21 # 14 # 50 <lb/>Bornholme # 56 # 0 # 14 # 44 <lb/></note> <p> <s xml:id="echoid-s4051" xml:space="preserve">Præterea adjungatur ex Philoſopb. </s> <s xml:id="echoid-s4052" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4053" xml:space="preserve">N°. </s> <s xml:id="echoid-s4054" xml:space="preserve">393. </s> <s xml:id="echoid-s4055" xml:space="preserve">Anni 1726. <lb/></s> <s xml:id="echoid-s4056" xml:space="preserve">Tabula.</s> <s xml:id="echoid-s4057" xml:space="preserve"/> </p> <pb o="161" file="0175" n="175" rhead="de MAGNETE."/> <p> <s xml:id="echoid-s4058" xml:space="preserve">Tabula continens Declinationem Magneticam obſervatam in <lb/>4 Itineribus verſus Fretum Hudſoni, ab Anno 1721 ad <lb/>1725. </s> <s xml:id="echoid-s4059" xml:space="preserve">ex Philoſ. </s> <s xml:id="echoid-s4060" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s4061" xml:space="preserve">N°. </s> <s xml:id="echoid-s4062" xml:space="preserve">393.</s> <s xml:id="echoid-s4063" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 12 # 0 # 14 # 0 <lb/>51 # 0 # 12 # 0 # 14 # 15 <lb/>52 # 0 # 12 # 0 # 14 # 30 <lb/>53 # 0 # 12 # 0 # 14 # 45 <lb/>54 # 0 # 12 # 0 # 15 # 0 <lb/>55 # 0 # 12 # 0 # 15 # 15 <lb/>56 # 0 # 12 # 0 # 15 # 30 <lb/>57 # 0 # 12 # 0 # 15 # 45 <lb/>58 # 0 # 12 # 0 # 16 # 0 <lb/>59 # 0 # 12 # 0 # 16 # 15 <lb/>50 # 0 # 14 # 15 # 15 # 0 <lb/>51 # 0 # 14 # 15 # 15 # 15 <lb/>52 # 0 # 14 # 15 # 15 # 30 <lb/>53 # 0 # 14 # 15 # 15 # 45 <lb/>54 # 0 # 14 # 15 # 16 # 0 <lb/>55 # 0 # 14 # 15 # 16 # 15 <lb/>56 # 0 # 14 # 15 # 16 # 30 <lb/>57 # 0 # 14 # 15 # 16 # 45 <lb/>58 # 0 # 14 # 15 # 17 # 0 <lb/>59 # 0 # 14 # 15 # 17 # 15 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 16 # 30 # 16 # 0 <lb/>51 # 0 # 16 # 30 # 16 # 15 <lb/>52 # 0 # 16 # 30 # 16 # 30 <lb/>53 # 0 # 16 # 30 # 16 # 45 <lb/>54 # 0 # 16 # 30 # 17 # 0 <lb/>55 # 0 # 16 # 30 # 17 # 15 <lb/>56 # 0 # 16 # 30 # 17 # 30 <lb/>57 # 0 # 16 # 30 # 17 # 45 <lb/>58 # 0 # 16 # 30 # 18 # 0 <lb/>59 # 0 # 16 # 30 # 18 # 15 <lb/>50 # 0 # 18 # 45 # 17 # 0 <lb/>51 # 0 # 18 # 45 # 17 # 15 <lb/>52 # 0 # eadem ubi- \\ que longi \\ tudo. # 17 # 30 <lb/>53 # 0 # # # 17 # 45 <lb/>54 # 0 # # # 18 # 0 <lb/>55 # 0 # # # 18 # 15 <lb/>56 # 0 # # # 18 # 30 <lb/>57 # 0 # # # 18 # 45 <lb/>58 # 0 # # # 19 # 0 <lb/>59 # 0 # # # 19 # 15 <lb/></note> <pb o="162" file="0176" n="176" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Ubivis \\ eadem \\ Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 21 # 0 # 18 # 0 <lb/>51 # 0 # # # 18 # 15 <lb/>52 # 0 # # # 18 # 30 <lb/>53 # 0 # # # 18 # 45 <lb/>54 # 0 # # # 19 # 0 <lb/>55 # 0 # # # 19 # 15 <lb/>56 # 0 # # # 19 # 30 <lb/>57 # 0 # # # 19 # 45 <lb/>58 # 0 # # # 20 # 0 <lb/>59 # 0 # # # 20 # 15 <lb/>50 # 0 # 23 # 15 # 19 # 0 <lb/>51 # 0 # # # 19 # 15 <lb/>52 # 0 # # # 19 # 30 <lb/>53 # 0 # # # 19 # 45 <lb/>54 # 0 # # # 20 # 0 <lb/>55 # 0 # # # 20 # 15 <lb/>56 # 0 # # # 20 # 30 <lb/>57 # 0 # # # 20 # 45 <lb/>58 # 0 # # # 21 # 0 <lb/>59 # 0 # # # 21 # 15 <lb/>50 # 0 # 25 # 30 # 20 # 0 <lb/>51 # 0 # # # 20 # 15 <lb/>52 # 0 # # # 20 # 30 <lb/>53 # 0 # # # 20 # 45 <lb/>54 # 0 # # # 21 # 0 <lb/>55 # 0 # # # 21 # 15 <lb/>56 # 0 # # # 21 # 30 <lb/>57 # 0 # # # 21 # 45 <lb/>58 # 0 # # # 22 # 0 <lb/>59 # 0 # # # 22 # 15 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Ubivis \\ eadem \\ Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 27 # 45 # 21 # 0 <lb/>51 # 0 # # # 21 # 15 <lb/>52 # 0 # # # 21 # 30 <lb/>53 # 0 # # # 21 # 45 <lb/>54 # 0 # # # 22 # 0 <lb/>55 # 0 # # # 22 # 15 <lb/>56 # 0 # # # 22 # 30 <lb/>57 # 0 # # # 22 # 45 <lb/>58 # 0 # # # 23 # 0 <lb/>59 # 0 # # # 23 # 15 <lb/>50 # 0 # 30 # 0 # 22 # 0 <lb/>51 # 0 # # # 22 # 15 <lb/>52 # 0 # # # 22 # 30 <lb/>53 # 0 # # # 22 # 45 <lb/>54 # 0 # # # 23 # 0 <lb/>55 # 0 # # # 23 # 15 <lb/>56 # 0 # # # 23 # 30 <lb/>57 # 0 # # # 23 # 45 <lb/>58 # 0 # # # 24 # 0 <lb/>59 # 0 # # # 24 # 15 <lb/>50 # 0 # 32 # 15 # 23 # 0 <lb/>51 # 0 # # # 23 # 15 <lb/>52 # 0 # # # 23 # 30 <lb/>53 # 0 # # # 23 # 45 <lb/>54 # 0 # # # 24 # 0 <lb/>55 # 0 # # # 24 # 15 <lb/>56 # 0 # # # 24 # 30 <lb/>57 # 0 # # # 24 # 45 <lb/>58 # 0 # # # 25 # 0 <lb/>59 # 0 # # # 25 # 15 <lb/></note> <pb o="163" file="0177" n="177" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Ubivis \\ eadem \\ Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 34 # 30 # 24 # 0 <lb/>51 # 0 # # # 24 # 15 <lb/>52 # 0 # # # 24 # 30 <lb/>53 # 0 # # # 24 # 45 <lb/>54 # 0 # # # 25 # 0 <lb/>55 # 0 # # # 25 # 15 <lb/>56 # 0 # # # 25 # 30 <lb/>57 # 0 # # # 25 # 45 <lb/>58 # 0 # # # 26 # 0 <lb/>59 # 0 # # # 26 # 15 <lb/>50 # 0 # 36 # 45 # 25 # 0 <lb/>51 # 0 # # # 25 # 15 <lb/>52 # 0 # # # 25 # 30 <lb/>53 # 0 # # # 25 # 45 <lb/>54 # 0 # # # 26 # 0 <lb/>55 # 0 # # # 26 # 15 <lb/>56 # 0 # # # 26 # 30 <lb/>57 # 0 # # # 26 # 45 <lb/>58 # 0 # # # 27 # 0 <lb/>59 # 0 # # # 27 # 15 <lb/>50 # 0 # 39 # 0 # 26 # 0 <lb/>51 # 0 # # # 26 # 15 <lb/>52 # 0 # # # 26 # 30 <lb/>53 # 0 # # # 26 # 45 <lb/>54 # 0 # # # 27 # 0 <lb/>55 # 0 # # # 27 # 15 <lb/>56 # 0 # # # 27 # 30 <lb/>57 # 0 # # # 27 # 45 <lb/>58 # 0 # # # 28 # 0 <lb/>59 # 0 # # # 28 # 15 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Ubivis \\ eadem \\ Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>50 # 0 # 41 # 15 # 27 # 0 <lb/>51 # 0 # # # 27 # 15 <lb/>52 # 0 # # # 27 # 30 <lb/>53 # 0 # # # 27 # 45 <lb/>54 # 0 # # # 28 # 0 <lb/>56 # 0 # # # 28 # 15 <lb/>57 # 0 # # # 28 # 30 <lb/>58 # 0 # # # 28 # 45 <lb/>59 # 0 # # # 29 # 0 <lb/>50 # 0 # 43 # 30 # 28 # 0 <lb/>51 # 0 # # # 28 # 15 <lb/>52 # 0 # # # 28 # 30 <lb/>53 # 0 # # # 28 # 45 <lb/>54 # 0 # # # 29 # 0 <lb/>55 # 0 # # # 29 # 15 <lb/>56 # 0 # # # 29 # 30 <lb/>57 # 0 # # # 29 # 45 <lb/>58 # 0 # # # 30 # 0 <lb/>59 # 0 # # # 30 # 15 <lb/>51 # 0 # 46 # 0 # 29 # 0 <lb/>52 # 0 # # # 29 # 15 <lb/>53 # 0 # # # 29 # 30 <lb/>54 # 0 # # # 29 # 45 <lb/>55 # 0 # # # 30 # 0 <lb/>56 # 0 # # # 30 # 15 <lb/>57 # 0 # # # 30 # 30 <lb/>58 # 0 # # # 30 # 45 <lb/>59 # 0 # # # 31 # 0 <lb/></note> <pb o="164" file="0178" n="178" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>52 # 0 # 48 # 30 # 30 # 0 <lb/>53 # 0 # # # 30 # 15 <lb/>54 # 0 # # # 30 # 30 <lb/>55 # 0 # # # 30 # 45 <lb/>56 # 0 # # # 31 # 0 <lb/>57 # 0 # # # 31 # 15 <lb/>58 # 0 # # # 31 # 30 <lb/>59 # 0 # # # 31 # 45 <lb/>53 # 0 # 51 # 0 # 31 # 0 <lb/>54 # 0 # # # 31 # 15 <lb/>55 # 0 # # # 31 # 30 <lb/>56 # 0 # # # 31 # 45 <lb/>57 # 0 # # # 32 # 0 <lb/>58 # 0 # # # 32 # 15 <lb/>59 # 0 # # # 32 # 30 <lb/>60 # 0 # # # 32 # 45 <lb/>54 # 0 # 54 # 0 # 32 # 0 <lb/>55 # 0 # # # 32 # 15 <lb/>56 # 0 # # # 32 # 30 <lb/>57 # 0 # # # 32 # 45 <lb/>58 # 0 # # # 33 # 0 <lb/>59 # 0 # # # 33 # 15 <lb/>60 # 0 # # # 33 # 30 <lb/>61 # 0 # # # 33 # 45 <lb/>54 # 0 # 57 # 0 # 33 # 0 <lb/>55 # 0 # # # 33 # 15 <lb/>56 # 0 # # # 33 # 30 <lb/>57 # 0 # # # 33 # 45 <lb/>58 # 0 # # # 34 # 0 <lb/>59 # 0 # # # 34 # 30 <lb/>60 # 0 # # # 35 # 0 <lb/>61 # 0 # # # 35 # 30 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>55 # 0 # 60 # 0 # 34 # 0 <lb/>56 # 0 # # # 34 # 30 <lb/>57 # 0 # # # 35 # 0 <lb/>58 # 0 # # # 35 # 30 <lb/>59 # 0 # # # 36 # 0 <lb/>60 # 0 # # # 36 # 30 <lb/>61 # 0 # # # 37 # 0 <lb/>57 # 0 # 63 # 0 # 35 # 0 <lb/>58 # 0 # # # 35 # 30 <lb/>59 # 0 # # # 36 # 0 <lb/>60 # 0 # # # 36 # 30 <lb/>61 # 0 # # # 37 # 0 <lb/>62 # 0 # # # 37 # 30 <lb/>59 # 0 # 66 # 0 # 37 # 0 <lb/>60 # 0 # # # 37 # 40 <lb/>61 # 0 # # # 38 # 20 <lb/>62 # 0 # # # 39 # 0 <lb/>63 # 0 # # # 39 # 40 <lb/>60 # 0 # 69 # 0 # 41 # 0 <lb/>61 # 0 # # # 41 # 40 <lb/>62 # 0 # # # 42 # 20 <lb/>60 # 0 # 72 # 0 # 40 # 0 <lb/>61 # 0 # # # 42 # 0 <lb/>61 # 40 # # # 42 # 40 <lb/>62 # 0 # 78 # 0 # 43 # 0 <lb/>63 # 0 # # # 44 # 0 <lb/>63 # 50 # # # 46 # 0 <lb/>61 # 0 # 75 # 0 # 38 # 0 <lb/>62 # 0 # # # 43 # 0 <lb/>62 # 50 # # # 45 # 0 <lb/></note> <pb o="165" file="0179" n="179" rhead="de MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>63 # 0 # 81 # 0 # 43 # 0 <lb/>64 # 0 # 81 # 0 # 46 # 0 <lb/>62 # 0 # 82 # 0 # 39 # 0 <lb/>63 # 0 # 82 # 0 # 44 # 0 <lb/>61 # 0 # 84 # 0 # 33 # 45 <lb/>62 # 0 # 84 # 0 # 40 # 0 <lb/>63 # 0 # 84 # 0 # 42 # 0 <lb/>60 # 0 # 86 # 0 # 30 # 0 <lb/>61 # 0 # 86 # 0 # 33 # 0 <lb/>62 # 0 # 86 # 0 # 35 # 0 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio. <lb/>Gr. # M. # Gr. # M. # Gr. # M <lb/>59 # 0 # 88 # 0 # 28 # 0 <lb/>60 # 0 # 88 # 0 # 28 # 40 <lb/>61 # 0 # 88 # 0 # 29 # 20 <lb/>57 # 0 # 90 # 0 # 24 # 0 <lb/>58 # 0 # 90 # 0 # 24 # 30 <lb/>59 # 0 # 90 # 0 # 25 # 0 <lb/>57 # 0 # 94 # 0 # 23 # 0 <lb/>58 # 0 # 95 # 0 # 22 # 30 <lb/>59 # 0 # 95 # 0 # 21 # 0 <lb/></note> <p> <s xml:id="echoid-s4064" xml:space="preserve">A Longitudine 68 Graduum uſque ad 81 obſervationes ſunt factæ <lb/>in ſinu Hudſoni, in quo eſt maxima Variatio & </s> <s xml:id="echoid-s4065" xml:space="preserve">in quo Acus diffi-<lb/>culter ſuam directionem oſtendit.</s> <s xml:id="echoid-s4066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4067" xml:space="preserve">Ex inſpectis liquet Tabulispag. </s> <s xml:id="echoid-s4068" xml:space="preserve">152 & </s> <s xml:id="echoid-s4069" xml:space="preserve">Mappâ Halleyi, Declinatio-<lb/>nem Magnetis increviſſe Pariſiis, ita ut anno 1728 fuerit 14 graduum <lb/>verſus Occaſum. </s> <s xml:id="echoid-s4070" xml:space="preserve">Inſuper, notante Cl. </s> <s xml:id="echoid-s4071" xml:space="preserve">Deliſle in L’Hiſt. </s> <s xml:id="echoid-s4072" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s4073" xml:space="preserve">Roy. <lb/></s> <s xml:id="echoid-s4074" xml:space="preserve">1712. </s> <s xml:id="echoid-s4075" xml:space="preserve">in urbibus plurimis Galliæ fere eodem modo Declinatio increvit <lb/>ac Pariſiis; </s> <s xml:id="echoid-s4076" xml:space="preserve">etiam æqualiter Genevæ progreſſa fuit: </s> <s xml:id="echoid-s4077" xml:space="preserve">quod ulterius pro-<lb/>batur, quia in Tabula Geographica Maris Caſpii, facta anno 1720, & </s> <s xml:id="echoid-s4078" xml:space="preserve"><lb/>quæ proſtat in L’Hiſt. </s> <s xml:id="echoid-s4079" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s4080" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4081" xml:space="preserve">1721. </s> <s xml:id="echoid-s4082" xml:space="preserve">Acus obſervata fuit de-<lb/>clinare in Caſpio Mari nunc 12°, 9`. </s> <s xml:id="echoid-s4083" xml:space="preserve">nunc 11°, 44`. </s> <s xml:id="echoid-s4084" xml:space="preserve">alibi 13°, 51`. </s> <s xml:id="echoid-s4085" xml:space="preserve"><lb/>&</s> <s xml:id="echoid-s4086" xml:space="preserve">c. </s> <s xml:id="echoid-s4087" xml:space="preserve">unde concludendum, curvas lineas in Mappa Halleyana, Tab. </s> <s xml:id="echoid-s4088" xml:space="preserve"><lb/>X. </s> <s xml:id="echoid-s4089" xml:space="preserve">quæ occidentalem Declinationem in parte Boreali Terræ oſten-<lb/>dunt, motas fuiſſe, tam deſcendendo verfus Æquatorem, quam <lb/>ſe convertendo ab Occaſu verſus Ortum, quaſi circa centrum quod-<lb/>dam, commune omnibus illis lineis: </s> <s xml:id="echoid-s4090" xml:space="preserve">qua converſione linea 10 graduum <lb/>Declinationis primum tranſiit per Hiberniam, Scotiam, Brittanniam, <lb/>tum per Hollandiam, Daniam, Gallias, Curlandiam; </s> <s xml:id="echoid-s4091" xml:space="preserve">tandemque per <lb/>mare Caſpium, quam omnes aliæ ſecutæ fuerunt Declinationum ma-<lb/>jorum lineæ: </s> <s xml:id="echoid-s4092" xml:space="preserve">imo ipſam lineam, continentem 5 gradus Declinationis <lb/>Occidentalis, huic motui verſus Æquatorem obtemperaſſe, patet ex ob-<lb/>ſervationibus notatis in L’ Hiſtoire de L’ Academ. </s> <s xml:id="echoid-s4093" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4094" xml:space="preserve">A°. </s> <s xml:id="echoid-s4095" xml:space="preserve">1710. </s> <s xml:id="echoid-s4096" xml:space="preserve">erant <pb o="166" file="0180" n="180" rhead="DISSERTATIO"/> ipſæ obſervationes captæ anno 1706. </s> <s xml:id="echoid-s4097" xml:space="preserve">In his vero habetur, 25 mil-<lb/>liaribus a porto Santo prope Maderam Declinationem fuiſſe 5 grad. <lb/></s> <s xml:id="echoid-s4098" xml:space="preserve">verſus Occaſum, cum prope Maderam, ſed ad Occaſum declinabat <lb/>Acus 4°. </s> <s xml:id="echoid-s4099" xml:space="preserve">30`. </s> <s xml:id="echoid-s4100" xml:space="preserve">atque inter Maderam & </s> <s xml:id="echoid-s4101" xml:space="preserve">Inſulam Ferri 4 gradibus, cum <lb/>in Mappa Halleyi minor in his locis declinatio habeatur.</s> <s xml:id="echoid-s4102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4103" xml:space="preserve">Verum omnes curvas Septentrionales ſimul deſcendiſſe verſus Æ-<lb/>quatorem, etiam liquet ex Tabula ſuperiori, nam A°. </s> <s xml:id="echoid-s4104" xml:space="preserve">1700, ad latitu-<lb/>dinem Boream 55°, ad longitudinem a Londino 60°. </s> <s xml:id="echoid-s4105" xml:space="preserve">occidentalem erat <lb/>Declinatio inter 20 & </s> <s xml:id="echoid-s4106" xml:space="preserve">25 gradus: </s> <s xml:id="echoid-s4107" xml:space="preserve">verum anno 1721 ibidem loci obſer-<lb/>vata fuit Declinatio 34 graduum: </s> <s xml:id="echoid-s4108" xml:space="preserve">Pariter cum anno 1700 ad latitudinem <lb/>Boream 50°, & </s> <s xml:id="echoid-s4109" xml:space="preserve">longitudinem occidentalem 43° a Londino declina-<lb/>tio erat 15 graduum, Anno 1721 hæc ibidem fuit 28°. </s> <s xml:id="echoid-s4110" xml:space="preserve">idem obtinet in <lb/>aliis lineis: </s> <s xml:id="echoid-s4111" xml:space="preserve">cumque illæ omnes tantopere deſcenderint, alias pro-<lb/>diiſſe concipiendum ex vicinia poli, in quibus major declinatio nunc <lb/>obſervatur, quam anno hujus ſæculi primo.</s> <s xml:id="echoid-s4112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4113" xml:space="preserve">Præterea id in genere notare poſſumus, Declinationem occiden-<lb/>talem increſcere ad majorem latitudinem Borealem, & </s> <s xml:id="echoid-s4114" xml:space="preserve">eſſe maxi-<lb/>mam in Sinu Hudſoni.</s> <s xml:id="echoid-s4115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4116" xml:space="preserve">Nunc examinemus Lineam expertem Variationis, ortam ad Ca-<lb/>rolinam, & </s> <s xml:id="echoid-s4117" xml:space="preserve">videamus quamnam hæc mutationem quoque paſſa ſit <lb/>in toto ſui decurſu: </s> <s xml:id="echoid-s4118" xml:space="preserve">ſed duo tantum in ipſâ loca adnotabo.</s> <s xml:id="echoid-s4119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4120" xml:space="preserve">Hæc ſecundum obſervationes anno 1706 factas in Oceano Atlantico, <lb/>deſcriptas in Philoſ. </s> <s xml:id="echoid-s4121" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s4122" xml:space="preserve">N°. </s> <s xml:id="echoid-s4123" xml:space="preserve">310. </s> <s xml:id="echoid-s4124" xml:space="preserve">tranſiit ſuper loca latitudinis Au-<lb/>ſtrinæ 3°, 17` longitudinis occidentalis a Londino 20°, 5`. </s> <s xml:id="echoid-s4125" xml:space="preserve">Halleyus eam <lb/>notaverat pro Anno 1700 ad longitudinem 20°. </s> <s xml:id="echoid-s4126" xml:space="preserve">& </s> <s xml:id="echoid-s4127" xml:space="preserve">ad latitudinem Borea-<lb/>lem 5 grad. </s> <s xml:id="echoid-s4128" xml:space="preserve">adeoque hæc pars Lineæ mota fuiſſet ibidem loci verſus <lb/>Americam: </s> <s xml:id="echoid-s4129" xml:space="preserve">Sed Feuillee A°. </s> <s xml:id="echoid-s4130" xml:space="preserve">1708 in itinere Americano eam notat ad <lb/>latitud. </s> <s xml:id="echoid-s4131" xml:space="preserve">Bor. </s> <s xml:id="echoid-s4132" xml:space="preserve">5°, 24`. </s> <s xml:id="echoid-s4133" xml:space="preserve">ad Longitudinem 357°, 3`. </s> <s xml:id="echoid-s4134" xml:space="preserve">qui eſt ipſe locusab Hal-<lb/>leyo notatus; </s> <s xml:id="echoid-s4135" xml:space="preserve">unde ſecundum hunc remanſiſſet immota: </s> <s xml:id="echoid-s4136" xml:space="preserve">Præterea alia <lb/>pars hujus Lineæ ibidem in iiſdem Tranſact. </s> <s xml:id="echoid-s4137" xml:space="preserve">obſervata fuit ad lati-<lb/>tudinem Auſtralem 34°, 31`. </s> <s xml:id="echoid-s4138" xml:space="preserve">& </s> <s xml:id="echoid-s4139" xml:space="preserve">ad longitudinem Oc. </s> <s xml:id="echoid-s4140" xml:space="preserve">1°, 29`, 30?</s> <s xml:id="echoid-s4141" xml:space="preserve">. cum <lb/>Halleyus eam poſuerit in eadem Latitudine ad longitudinem 4 gra-<lb/>duum a Meridiano Londinenſi, quapropter hæc pars Lineæ acceſ-<lb/>ſiſſet ad Ortum, contrario motu, quam pars ſuperior; </s> <s xml:id="echoid-s4142" xml:space="preserve">verum anno <lb/>1721, eadem pars obſervata fuit ferè ad longitudinem 12°, 57`. </s> <s xml:id="echoid-s4143" xml:space="preserve">a <lb/>Meridiano Londinenſi verſus Ortum, nam in Philoſoph Tranſact. </s> <s xml:id="echoid-s4144" xml:space="preserve">N°.</s> <s xml:id="echoid-s4145" xml:space="preserve"> <pb o="167" file="0181" n="181" rhead="DEMAGNETE."/> 371. </s> <s xml:id="echoid-s4146" xml:space="preserve">proſtat ejuſmodi obſervatio, adeoque confirmatur præcedens <lb/>nota, nempe hanc partem Lineæ motam fuiſſe verſus Ortum, hoc eſt <lb/>verſus Promontorium Bonæ Spei: </s> <s xml:id="echoid-s4147" xml:space="preserve">Sed operæ pretium erit mo-<lb/>tum hujus Lineæ, quam Meridianum Magneticum haud incongrue <lb/>vocaremus, ex vetuſtioribus eruere obſervatis: </s> <s xml:id="echoid-s4148" xml:space="preserve">Anno 1638 Vien-<lb/>næ in Auſtria non declinavit Magnes, nec Londini Anno 1657, <lb/>nec Pariſiis anno 1666. </s> <s xml:id="echoid-s4149" xml:space="preserve">nec anno 1600 in Promontorio Africæ das <lb/>Aguilhas: </s> <s xml:id="echoid-s4150" xml:space="preserve">ante hæc tempora in memoratis locis, & </s> <s xml:id="echoid-s4151" xml:space="preserve">in omnibus Eu-<lb/>ropæ Africæque regionibus magis ad Occidentem fitis, Declinatio <lb/>Magnetis Orientem verſus obſervabatur: </s> <s xml:id="echoid-s4152" xml:space="preserve">è contrario in locis magis <lb/>ad Orientem vergentibus regnabat Magnetis Declinatio Occidenta-<lb/>lis: </s> <s xml:id="echoid-s4153" xml:space="preserve">Meridianus hic Magneticus ita comparatus eſt, ut ad ſuum la-<lb/>tus occidentale Declinationem Orientalem habeat, ad latus orti-<lb/>vum occidentalem: </s> <s xml:id="echoid-s4154" xml:space="preserve">Quamobrem hic idem fuit, qui annis ſupe-<lb/>rioribus tranſiit ſupra Viennam, Londinum, Lutetias, promonto-<lb/>riumque das Aguilhas, atque progreſſus fuit verſus Occaſum, ſimul <lb/>â parte Boreâ Terræ deſcendendo quaſi verſus Auſtrum, velociori-<lb/>que motu percurrendo Europæ regiones & </s> <s xml:id="echoid-s4155" xml:space="preserve">Atlanticum Oceanum, <lb/>quam quidem Africæ ultimas terras, & </s> <s xml:id="echoid-s4156" xml:space="preserve">Æthyopici maris partem, <lb/>& </s> <s xml:id="echoid-s4157" xml:space="preserve">quia Halleyus pro anno 1700, atque Feuillejus octo annis poſt, <lb/>ad latitudinem Bor. </s> <s xml:id="echoid-s4158" xml:space="preserve">5°, 24?</s> <s xml:id="echoid-s4159" xml:space="preserve">, & </s> <s xml:id="echoid-s4160" xml:space="preserve">ad longitudinem 357°, 3? </s> <s xml:id="echoid-s4161" xml:space="preserve">Meridia-<lb/>num hunc permanſiſie in eodem loco notant, cujus tamen pars Bo-<lb/>rea perpetuo magis Occaſum verſus declinare pergit, cum pars Au-<lb/>ſtralis Ortum verſus incedat, uti modo adnotavimus, liquet locum <lb/>a Feuillejo inventum eſſe inſtar alicujus centriſuper quo Meridianus <lb/>Magneticus librationis ſpeciem patitur, ita ut cum unâ parte Oc-<lb/>caſum verſus moveatur, altera Orientem verſus incedat; </s> <s xml:id="echoid-s4162" xml:space="preserve">plureshu-<lb/>jus Meridiani motus poſtera deteget ætas, modo ab omnibus nau-<lb/>tis Oceanos Atlanticos & </s> <s xml:id="echoid-s4163" xml:space="preserve">Æthyopicos ac Indicos tranſcurrentibus <lb/>accuratæ capiantur quotidie Declinationum Magneticarum obſer-<lb/>vationes.</s> <s xml:id="echoid-s4164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4165" xml:space="preserve">Sinunciterum introſpiciamus Mappam Halleyi, dantur aliæ curvæ <lb/>inter Lineam expertem Declinationis & </s> <s xml:id="echoid-s4166" xml:space="preserve">Americam, quæ ductæ ſunt <lb/>ſupraloca eam paſſa Declinationis quantitatem, quæ deſignantur nu-<lb/>meris 5, 10, 15, 20, 25: </s> <s xml:id="echoid-s4167" xml:space="preserve">Eſt vero in omnibus his locis occidentalibus <lb/>Declinatio verſus Ortum: </s> <s xml:id="echoid-s4168" xml:space="preserve">Linea, cui adſcriptus eſt numerus 5, ſatis <pb o="168" file="0182" n="182" rhead="DISSERTATIO"/> bene congruit cum obſervationibus factis anno 1706, & </s> <s xml:id="echoid-s4169" xml:space="preserve">quæ pro-<lb/>ſtant in Philoſ. </s> <s xml:id="echoid-s4170" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4171" xml:space="preserve">N°. </s> <s xml:id="echoid-s4172" xml:space="preserve">310. </s> <s xml:id="echoid-s4173" xml:space="preserve">Sed ad latitudinem Auſtralem <lb/>18 & </s> <s xml:id="echoid-s4174" xml:space="preserve">19 graduum videtur paulo magis eſſe erigenda verſus Lineam <lb/>abſque Declinatione, ut patebit facile, ſi quis tabulas Obſervatio-<lb/>num, quas infra appoſui, comparare cum hac Linea voluerit; </s> <s xml:id="echoid-s4175" xml:space="preserve">aliæ <lb/>curvæ etiam ſatis accurate obſervationibus reſpondent; </s> <s xml:id="echoid-s4176" xml:space="preserve">curvam <lb/>tranſeuntem ſupra loca, in quibus Magnes 10 gradibus declinat in <lb/>Mari Pacifico, ulterius continuavi, traduxique per urbem Valpa-<lb/>raiſo, quia Frezier inſuo Itinerario talem ibi notavit Declinationem. <lb/></s> <s xml:id="echoid-s4177" xml:space="preserve">licet Feuillèe eam modo poſuerit 9°, 30?</s> <s xml:id="echoid-s4178" xml:space="preserve">, Halleyus enim nullas ob-<lb/>ſervationes in eo Mari captas poſſedit: </s> <s xml:id="echoid-s4179" xml:space="preserve">Si omnes cognoſceremus Decli-<lb/>nationes, quæ regnant in littoribus Americæ, mare Pacificum ſpe-<lb/>ctantibus; </s> <s xml:id="echoid-s4180" xml:space="preserve">ea, quæ Halleyus inchoavit, abſolvere poſſemus: </s> <s xml:id="echoid-s4181" xml:space="preserve">nunc tan-<lb/>tum 5 alia loca addere utcunque potui, ex obſervationibus Frezierii <lb/>& </s> <s xml:id="echoid-s4182" xml:space="preserve">Feuilleji. </s> <s xml:id="echoid-s4183" xml:space="preserve">ad Californiam, Santam Guaram & </s> <s xml:id="echoid-s4184" xml:space="preserve">Aricam.</s> <s xml:id="echoid-s4185" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4186" xml:space="preserve">Verum tranſeundum eſt ad alias curvas, jacentes ad Ortum Li-<lb/>neæ expertis Declinationis; </s> <s xml:id="echoid-s4187" xml:space="preserve">hæ ductæ ſunt partim ſupra Oceanum <lb/>Æthyopicum, tumſupra Indicum, in quibus omnibus obtinet Declina-<lb/>tio Occidentalis, quæ maxima eſt ad latitudinem Auſtralem 54 gra-<lb/>dum, & </s> <s xml:id="echoid-s4188" xml:space="preserve">ad longitudinem Orientalem 50 grad. </s> <s xml:id="echoid-s4189" xml:space="preserve">a MeridianoLondinenſi, <lb/>maxima hæc Declinatio eſt 30 graduum. </s> <s xml:id="echoid-s4190" xml:space="preserve">Si conſulamus obſervatio-<lb/>nes ex Philoſophic. </s> <s xml:id="echoid-s4191" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4192" xml:space="preserve">N°. </s> <s xml:id="echoid-s4193" xml:space="preserve">371. </s> <s xml:id="echoid-s4194" xml:space="preserve">factas anno 1721. </s> <s xml:id="echoid-s4195" xml:space="preserve">tum pa-<lb/>ret has curvas receſſiſſe verſus Ortum; </s> <s xml:id="echoid-s4196" xml:space="preserve">nam ſub latitudine 32°, 40?</s> <s xml:id="echoid-s4197" xml:space="preserve">, <lb/>ſub longitudine 120, 1?</s> <s xml:id="echoid-s4198" xml:space="preserve">, obſervatur Declinatio 3 graduum modo, <lb/>ubi Halleyus eam ponit 7 vel 8 graduum: </s> <s xml:id="echoid-s4199" xml:space="preserve">itidem ſub latitudine <lb/>Auſtrali 31°, 22?</s> <s xml:id="echoid-s4200" xml:space="preserve">, & </s> <s xml:id="echoid-s4201" xml:space="preserve">longitudine 37°, 7?</s> <s xml:id="echoid-s4202" xml:space="preserve">, ponitur Declinatio 10 <lb/>graduum 57 Minut. </s> <s xml:id="echoid-s4203" xml:space="preserve">ubi Halleyus eam ſtatuit fere 20 graduum: </s> <s xml:id="echoid-s4204" xml:space="preserve">iti-<lb/>dem in aliis obſervationibus eorundem Actorum ad latitudinem <lb/>Auſtr. </s> <s xml:id="echoid-s4205" xml:space="preserve">26°, 17?</s> <s xml:id="echoid-s4206" xml:space="preserve">. & </s> <s xml:id="echoid-s4207" xml:space="preserve">longitudinem 41°, 41?</s> <s xml:id="echoid-s4208" xml:space="preserve">. ponitur Declinatio 14°, <lb/>30?</s> <s xml:id="echoid-s4209" xml:space="preserve">. ubi Halleyuseam ultra 20 gradus ponit: </s> <s xml:id="echoid-s4210" xml:space="preserve">ex quibus liquet hanc <lb/>Declinationem auctam eſſe verſus Ortum.</s> <s xml:id="echoid-s4211" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4212" xml:space="preserve">Sequitur tandem in Mappa Halleyi, plus verſus Ortum, alia linea <lb/>expers omnis Declinationis, quæ tranſit ſupra Hollandiam novam, <lb/>inſulam Timor, Celebes, Mindoram, & </s> <s xml:id="echoid-s4213" xml:space="preserve">partem Chinenſis Regni, <lb/>100 milliaribus a Peking.</s> <s xml:id="echoid-s4214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4215" xml:space="preserve">Ultra hanc lineam verſus Ortum unam Halleyus depinxit curvam, <lb/>quæ tranſiret ſupra loca, in quibus Declinatio Magnetis iterum eſt <pb o="169" file="0183" n="183" rhead="DEMAGNETE."/> Orientalis; </s> <s xml:id="echoid-s4216" xml:space="preserve">poſuit autem eam 5 graduum; </s> <s xml:id="echoid-s4217" xml:space="preserve">nihil vero ulterius pro ma-<lb/>ri Pacifico notavit; </s> <s xml:id="echoid-s4218" xml:space="preserve">ſed ab anno 1700 facta ſunt per illum immen-<lb/>ſum Oceanum nonnulla itinera, & </s> <s xml:id="echoid-s4219" xml:space="preserve">ſimul notatæ ſunt Magnetis De-<lb/>clinationes, quibus uſus fui ad alias lineas ducendas, quæ in mari <lb/>Pacifico conſpiciuntur. </s> <s xml:id="echoid-s4220" xml:space="preserve">In Philo ſophic. </s> <s xml:id="echoid-s4221" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4222" xml:space="preserve">N°. </s> <s xml:id="echoid-s4223" xml:space="preserve">368 proſtant <lb/>obſervationes captæ a Wooden Rogers Anno 1710, in quibus ad la-<lb/>titudinem Boream 14°, 24?</s> <s xml:id="echoid-s4224" xml:space="preserve">. adlongitudinem 126°, 45? </s> <s xml:id="echoid-s4225" xml:space="preserve">Declinatio fuit <lb/>40? </s> <s xml:id="echoid-s4226" xml:space="preserve">orientalis: </s> <s xml:id="echoid-s4227" xml:space="preserve">ſed ad latitudinem Boream 14°, 36? </s> <s xml:id="echoid-s4228" xml:space="preserve">fuit Declinatio 50? <lb/></s> <s xml:id="echoid-s4229" xml:space="preserve">orientalis; </s> <s xml:id="echoid-s4230" xml:space="preserve">& </s> <s xml:id="echoid-s4231" xml:space="preserve">ad latitudinem eandem 14°, 14? </s> <s xml:id="echoid-s4232" xml:space="preserve">fuit Declinatio 45 orien-<lb/>talis: </s> <s xml:id="echoid-s4233" xml:space="preserve">quare dabitur inter latitudinem Boream 14°, 36?</s> <s xml:id="echoid-s4234" xml:space="preserve">, & </s> <s xml:id="echoid-s4235" xml:space="preserve">14°, 14?</s> <s xml:id="echoid-s4236" xml:space="preserve">. lo-<lb/>cus, in quo Declinatio erit nulla: </s> <s xml:id="echoid-s4237" xml:space="preserve">tum vero ab utraque parte hujus loci <lb/>iterum obſervatur Declinatio orientalis. </s> <s xml:id="echoid-s4238" xml:space="preserve">De Liſle alias accepit obſerva-<lb/>tiones eodem anno factas in Pacifico Oceano, ex quibus collegit etiam <lb/>dari Lineam expertem Declinationis, quæ incederet a Boreâ verſus <lb/>Auſtrum, circiter inſtar Meridiani terreſtris: </s> <s xml:id="echoid-s4239" xml:space="preserve">Hæc proinde eſt tertia <lb/>Linea Declinationis expers. </s> <s xml:id="echoid-s4240" xml:space="preserve">vid. </s> <s xml:id="echoid-s4241" xml:space="preserve">L? </s> <s xml:id="echoid-s4242" xml:space="preserve">Hiſtoire de L? </s> <s xml:id="echoid-s4243" xml:space="preserve">Acad. </s> <s xml:id="echoid-s4244" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4245" xml:space="preserve">A°. </s> <s xml:id="echoid-s4246" xml:space="preserve">1712. </s> <s xml:id="echoid-s4247" xml:space="preserve"><lb/>quam duxi in Tab. </s> <s xml:id="echoid-s4248" xml:space="preserve">X. </s> <s xml:id="echoid-s4249" xml:space="preserve">â California incipiendo. </s> <s xml:id="echoid-s4250" xml:space="preserve">Habet hæcid peculiare, <lb/>ut ad utramque ſui partem Declinationem ſentiat orientalem, cum <lb/>aliæ binæ lineæ Variationis expertes, ab Halleyo detectæ, habeant <lb/>ad unum ſui latus Declinationem orientalem, ad alterum occiduam.</s> <s xml:id="echoid-s4251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4252" xml:space="preserve">Forſitan hæc Linea erit modo continuatio Meridiani primi Ma-<lb/>gnetici, qui tranſit ſupra Bermudos, Carolinam, & </s> <s xml:id="echoid-s4253" xml:space="preserve">Americæ par-<lb/>tem Septentrionalem uſque ad Californiam, inde recta deſcendens <lb/>Æquatorem terreſtrem verſus, inſtar Meridiani Terræ decurrit, aut <lb/>parum ab eo aberrat: </s> <s xml:id="echoid-s4254" xml:space="preserve">Hujus lineæ, per mare Pacificum ducendæ, <lb/>decurſum accurate hactenus determinare non poſſumus, priuſquam <lb/>multo plures obſervationes æque in latitudinibus variis Boreis, ac <lb/>Auſtralibus captas erimus adepti: </s> <s xml:id="echoid-s4255" xml:space="preserve">Obſervationum penuriâ lineas <lb/>aliarum Declinationum tantummodo indicavi ſub formâ parvarum <lb/>rectarum, terreſtri Meridiano parallelarum; </s> <s xml:id="echoid-s4256" xml:space="preserve">procul dubio enimre-<lb/>ctæ erunt, quia linea ſecunda Declinationis expers, quæ per Chi-<lb/>nam atque Hollandiam novam tranſit, fere rectà inſtar Meridiani <lb/>terreſtris procurrit, tum quia ad rectam adhuc propius accedit li-<lb/>nea, quæ tranſit ſupra loca, in quibus Declinatio ſex graduum ob-<lb/>ſervatur, cujus ductum neceſſario ſequentur lineæ aliarum Declina-<lb/>tionum, inter hanc & </s> <s xml:id="echoid-s4257" xml:space="preserve">Meridianum tertium Magneticum intermediæ:</s> <s xml:id="echoid-s4258" xml:space="preserve"> <pb o="170" file="0184" n="184" rhead="DISSERTATIO"/> puncta, quibus adſcribuntur numeri, ſunt ipſa in Pacifico Oceano <lb/>obſervata loca: </s> <s xml:id="echoid-s4259" xml:space="preserve">hæc maximam Declinationem 12 graduum oſten-<lb/>dunt; </s> <s xml:id="echoid-s4260" xml:space="preserve">quamobrem in hoc Oceano regnat minor Magnetis Decli-<lb/>natio, quam in Atlantico, Æthyopico, aut Indico.</s> <s xml:id="echoid-s4261" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4262" xml:space="preserve">Tres igitur hac tempeſtate deteximus Meridianos Magneticos; <lb/></s> <s xml:id="echoid-s4263" xml:space="preserve">an autem plures non ſint affirmari nequit, quia ignoramus <lb/>huc uſque quomodo comparata ſit Magnetis Declinatio in ingenti <lb/>Terræ tractu, quæ Terra Æſonis vocatur, quam Oceani Pacifici <lb/>pars Borea alluit: </s> <s xml:id="echoid-s4264" xml:space="preserve">Auſtralia loca, tam terreſtria, quam marina ex-<lb/>ploravit hactenus nemo: </s> <s xml:id="echoid-s4265" xml:space="preserve">quam vaſta tandem regio eſt Tartaria, ſed <lb/>quænam in ea regnet Magnetis directio latet; </s> <s xml:id="echoid-s4266" xml:space="preserve">nemo igitur huc uſque <lb/>glorietur ſe cunctos Meridianos Magneticos noviſſe. </s> <s xml:id="echoid-s4267" xml:space="preserve">Mappæ Hal-<lb/>leyanæ prolixiorem deſcriptionem dare nolui, eam enim L. </s> <s xml:id="echoid-s4268" xml:space="preserve">B. </s> <s xml:id="echoid-s4269" xml:space="preserve">ante <lb/>oculos pone, & </s> <s xml:id="echoid-s4270" xml:space="preserve">brevi clariſſime cuncta intelliges, quæ verbis tam <lb/>concinne tradi non poſſent: </s> <s xml:id="echoid-s4271" xml:space="preserve">Tranſeo adtabulas obſervationum, quas <lb/>collegi ex L? </s> <s xml:id="echoid-s4272" xml:space="preserve">Hiſtoire de L? </s> <s xml:id="echoid-s4273" xml:space="preserve">Academie Roy. </s> <s xml:id="echoid-s4274" xml:space="preserve">des Scienc. </s> <s xml:id="echoid-s4275" xml:space="preserve">tum ex Phi-<lb/>loſoph. </s> <s xml:id="echoid-s4276" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s4277" xml:space="preserve">has ſuperius commemoravi, atque ex iis nonnullas <lb/>deduxi ſequelas, addendas ergo judicavi, præterea ut conſtaret, quo-<lb/>modo curvæ Halleyanæ congruant cum ipſis obſervationibus, & </s> <s xml:id="echoid-s4278" xml:space="preserve"><lb/>quomodo Declinatio Magnetis in certis terræ locis intra datum tem-<lb/>pus, ſive Ortum ſive Occaſum verſus, progrederetur, atque ut <lb/>examinanti pateret, an per to tum alicujus curvæ ductum pari aut <lb/>impari paſſu Declinatio incederet: </s> <s xml:id="echoid-s4279" xml:space="preserve">Utinam accuratius longitudines <lb/>obſervare poſſent nautæ! tum enim ſubtilius de progreſſu Declina-<lb/>tionum diſſerere liceret, cum prudentia nunc ſubito frænum ratioci-<lb/>nio immittat.</s> <s xml:id="echoid-s4280" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4281" xml:space="preserve">Obſervationes Declinationis Magneticæ captæ Anno 1675. </s> <s xml:id="echoid-s4282" xml:space="preserve">a Ley-<lb/>dekkero, deſcriptæ in Ephemerid. </s> <s xml:id="echoid-s4283" xml:space="preserve">German. </s> <s xml:id="echoid-s4284" xml:space="preserve">Curioſ. </s> <s xml:id="echoid-s4285" xml:space="preserve">Decur. </s> <s xml:id="echoid-s4286" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s4287" xml:space="preserve">A°. </s> <s xml:id="echoid-s4288" xml:space="preserve">2. </s> <s xml:id="echoid-s4289" xml:space="preserve">Meridiano primo ducto per Teneriffam.</s> <s xml:id="echoid-s4290" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Dies Anni # # Latitudo. # # # Longitudo. # # Declinatio. # Orientem \\ verſus <lb/># # Gr. # M. # Gr. # M?. # S?. # Gr. # M. <lb/>April. 12 # Bor. 0 # 20 # 358 # 0 # 0 # 1 # 36 <lb/>22 # Auſtr. 4 # 25 # # # # 2 # 3 <lb/>23 # 5 # 55 # 357 # 31 # 15 # 3 # 48 <pb o="171" file="0185" n="185" rhead="DEMAGNETE."/> April. # # Latitudo. # # # Longitudo. # # Declinatio. <lb/>24 # Auſtr. 7 # 23 # 357 # 31 # 15 # 4 # 0 # Orientem \\ verſus. <lb/>25 # 8 # 40 # # # # 4 # 15 <lb/>26 # 9 # 52 # 356 # 51 # 30 # 4 # 30 <lb/>27 # 11 # 21 # # # # 4 # 48 <lb/>28 # 13 # 6 # 356 # 33 # 45 # 5 # 15 <lb/>29 # 14 # 13 # 356 # 20 # 30 # 5 # 52 <lb/>30 # 15 # 14 # # # # 6 # 30 <lb/>Mayus 2 # 17 # 8 # 356 # 1 # 45 # 6 # 37 <lb/>8 # 25 # 36 # 352 # 5 # 55 # 11 # 55 <lb/>15 # 34 # 26 # 2 # 50 # 0 # 11 # 15 <lb/>17 # 34 # 14 # 7 # 23 # 15 # 7 # 30 <lb/>21 # 35 # 30 # 15 # 2 # 0 # 4 # 2 <lb/>23 # 36 # 8 # 18 # 47 # 15 # 3 # 28 <lb/>26 # 35 # 15 # 25 # 58 # 15 # 0 # 48 # Occidentem\\verſus. <lb/>27 # 34 # 42 # 27 # 33 # 0 # 2 # 8 <lb/>29 # 34 # 9 # 32 # 52 # 45 # 5 # 28 <lb/>30 # 33 # 46 # 36 # 40 # 0 # 7 # 30 <lb/>Jun. 20 # 36 # 35 # 39 # 20 # 0 <lb/>22 # 38 # 25 # 41 # 14 # 0 # 11 # 30 <lb/>25 # # # 50 # 20 # 0 # 16 # 0 <lb/>28 # 37 # 28 # 57 # 40 # 0 # 20 # 40 <lb/>29 # 37 # 49 # 60 # 0 # 0 # 21 # 45 <lb/>30 # 38 # 3 # 62 # 4 # 15 # 23 # 0 <lb/>Julius 5 # 37 # 33 # 77 # 25 # 30 # 26 # 30 <lb/>6 # 37 # 45 # 80 # 18 # 0 # 26 # 45 <lb/>7 # # # 82 # 0 # 0 # 25 # 44 <lb/>9 # 38 # 14 # 87 # 25 # 45 # 25 # 30 <lb/>12 # 38 # 3 # 96 # 20 # 0 # 22 # 44 <lb/>13 # 37 # 1 # 98 # 0 # 0 # 21 # 30 <lb/>15 # 35 # 54 # 103 # 0 # 0 # 18 # 40 <lb/>19 # 28 # 46 # 111 # 36 # 30 # 10 # 3 <lb/>21 # 26 # 50 # # # # 7 # 54 <lb/>22 # 25 # 22 # 116 # 17 # 45 # 7 # 30 <lb/>23 # 23 # 30 # # # # 7 # 0 <lb/>25 # 20 # 26 # 118 # 43 # 0 # 6 # 40 <lb/>29 # 14 # 10 # 122 # 6 # 0 # 4 # 15 <lb/>30 # 12 # 0 # 122 # 12 # 15 # 3 # 45 <lb/>31 # 11 # 28 # 112 # 30 # 0 # 2 # 0 <lb/>Aug. 1 # 9 # 0 # 123 # 1 # 45 # 2 # 10 <lb/></note> <pb o="172" file="0186" n="186" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s4291" xml:space="preserve">Declinationes Magnetis obſervatæ a Noëllio, Anno 1706, in Iti-<lb/>nere ad Indias Orientales inſtituto.</s> <s xml:id="echoid-s4292" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ loci # Longitudo # # Declinatio Acus \\ Magneticæ. <lb/># # # # Gr. # Min. <lb/>Gr. # M. # Lisbonæ. # 6 # 30 Occ. <lb/>18 # 20 Bor. # 50 Milliar. a Cabo \\ verde, # 1 # 15 <lb/>14 # # paulum propius \\ ad Cabo. # 0 # 0 <lb/>4 # # 2 gr. ab inſula Ferro. \\ Occid. # 0 # 0 <lb/>Sub Æquinoct. # # 3 gr. ab inſula Ferro. \\ Occ. # 1 # 30 Or. <lb/>7 # 28 Auſt. # 150 Mill. à Braſilia. # 3 # 0 <lb/>11 # 20 # In ead. longitud. # 4 # 0 <lb/>15 # 55 # In eadem longit. # 4 # 45 <lb/>25 # 40 # 700 Mill. a Cabo de \\ bona Eſperanc. # 3 # 20 <lb/>27 # 10 # 600 Milliar. a Cabo de \\ Eſper. # 2 # 30` Orien. <lb/>31 # 45 # 360 Milliar. ab \\ eodem. # 0 # 0 <lb/>33 # 48 # 250 Milliar. ab \\ eodem. # 4 # 0 Occ. <lb/>35 # 10 # In Conſpectu Cabo d’bona \\ Eſper. # 13 # 40 <lb/>36 # 40 # 200 Milliaria a Cabo \\ eodem verſus Ortum. # 18 # 30 <lb/>35 # 40 # 250 Mill. ab eodem \\ verſus Ortum. # 22 # 0 <lb/>36 # 0 # Sub Meridiano Inſulæ \\ Madagaſcar. # 36 # 0 <pb o="173" file="0187" n="187" rhead="DE MAGNETE."/> # # Auſtr. Latitudo \\ loci. # Longitudo. # # Declinatio \\ Acus. <lb/>Gr. <lb/>34 # 44 # 600 Milliar. a Cabo bona \\ Eſperan. # 22 # 0 <lb/>30 # 40 # 800 Milliar. ab eodem \\ Cabo. # 20 # 0 <lb/>28 # 15 # In itinere eodem verſus \\ Ortum. # 16 # 0 <lb/>27 # 44 # 950 Milliar. ab eodem \\ Cabo. # 15 # 0 <lb/>24 # 54 # 1200 Milliar. ab eodem \\ Cabo. # 10 # 0 <lb/>23 # 8 # 1300 Milliar. ab \\ eodem. # 8 40 <lb/>19 # 39 # { 1450 Milliar. ab eodem. \\ Plagâ Borrapheliote. # 6 # 0 Occ. <lb/>14 # 37 # # 2 # 40 <lb/>4 # 20 # 30 Mill. a Sumatra. # 0 # 0 <lb/>2 # 40 # Sub Meridiano urbis Achem \\ in hac inſula. # 1 # 30 Occ. <lb/># Sub Æquatore \\ Borealis # # Sub Meridiano Bengalæ. # 3 # 0 Occ. <lb/>4 # 50 # Inter præcedent: Meridia- \\ num & Ceilon. # 4 # 0 <lb/>7 # 50 # Prope Baticalon in \\ Ceilon. # 5 # 0 <lb/>9 # 0 # In littore urbis Co- \\ chim. # 6 # 20 <lb/>13 # 30 # Prope Urbem Goa. # 6 # 40 <lb/></note> <pb o="174" file="0188" n="188" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s4293" xml:space="preserve">Anno 1718. </s> <s xml:id="echoid-s4294" xml:space="preserve">In Itinere Maris de La Sonde verſus Braſiliam.</s> <s xml:id="echoid-s4295" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># Auſtr. \\ Latitudo \\ loci. # Longitudo. # # Declinatio \\ Acus. <lb/>Gr. M. <lb/>10 # 15 # 100 Milliar. à Mari la \\ Sonde. # 3 # 0 Occ. <lb/>13 # 50 # 180 Mill. à loco \\ priori. # 4 # 20 <lb/>16 # 0 # 80 Milliar. à loco \\ ultimo. # 7 # 0 <lb/>18 # 48` # 144 Mill. a loco \\ ultimo. # 9 # 0 Occ. <lb/>21 # 4 # 120 Mill. à loco \\ ultimo. # 11 # 20 <lb/>22 # 8 # 40 Mill. à loco \\ ultimo. # 11 # 20 <lb/>24 # 8 # 100 Milliar. à loco \\ ultimo. # 16 # 50 <lb/>26 # 27 # 80 Milliar. à loco \\ ultimo. # 19 # 20 <lb/>28 # 47 # 124 Milliar. à loco \\ ultimo. # 24 # 0 <lb/>30 # 12 # 86 Mill, à loco \\ ultimo. # 26 # 16 <lb/>30 # 60 # 70 Mill. à loco \\ ultimo. # 24 # 30 <lb/>31 # 0 # 23 Mill. à loco \\ ultimo. # 23 # 0 <lb/>33 # 21 # 100 Mill. à loco \\ ultimo. # 20 # 0 <pb o="175" file="0189" n="189" rhead="DE MAGNETE."/> # Latitudo \\ loci \\ Auſtr. # Longitudo \\ loci. # # Declinatio \\ Acus. <lb/>Gr. M. <lb/>35 # 30 # 180 Milliar. à loco \\ ultimo. # 15 # 40 <lb/>34 # 50 # 70 Milliar. à loco ultimo \\ id eſt, e regione Cabo de \\ bona Eſperanza. # 14 # 0 <lb/>34 # 45 # 70 Mill. a Cabo verſus \\ Braſil. # 11 # 0 <lb/>30 # 4 # 139 Mill. a loco \\ ultimo. # 4 # 30 <lb/>18 # 57 # 250 Milliar. a loco \\ ultimo. # 2 # 0 Orient. <lb/>13 # 30 # 320 Mill. a loco \\ ultimo. # 6 # 0 <lb/>13 # 10 # Prope portum Boha in \\ Braſilia. # 11 # 30 <lb/></note> <p> <s xml:id="echoid-s4296" xml:space="preserve">Declinationes Magnetis obſervatæ Anno 1706. </s> <s xml:id="echoid-s4297" xml:space="preserve">in Oceano Atlan-<lb/>tico & </s> <s xml:id="echoid-s4298" xml:space="preserve">Æthiopico, inſertæ Philoſ. </s> <s xml:id="echoid-s4299" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s4300" xml:space="preserve">N°. </s> <s xml:id="echoid-s4301" xml:space="preserve">310. </s> <s xml:id="echoid-s4302" xml:space="preserve">pag. <lb/></s> <s xml:id="echoid-s4303" xml:space="preserve">2433.</s> <s xml:id="echoid-s4304" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ Loci. # # Longitudo \\ a Londino # # Declinatio \\ Acus. <lb/>Grad. Min. # Grad. Min. # Grad. Min. <lb/>49 # 18 Septen. # 7 # 29 Occid. # 8 # 32 Occid. <lb/>44 # 31 # 13 # 45 # 6 # 42 <lb/>41 # 6 # 15 # 8 # 5 # 30 <lb/>40 # 22 # 14 # 54 # 5 # 4 <lb/>39 # 11 # 15 # 35 # 4 # 22 <lb/>32 # 21 # 15 # 39 # 3 # 30 <lb/>32 # 42 # 15 # 38 # 3 # 35 <lb/>18 # 50 # 20 # 52 # 1 # 20 <lb/>9 # 26 # 17 # 59 # 1 # 14 <lb/>0 # 49 # 18 # 42 # 1 # 10 <lb/></note> <pb o="176" file="0190" n="190" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo \\ a Londino # # Variatio \\ Acus. <lb/>Grad. # Min. # Grad. # Min. # Grad. # Min. <lb/>1 # 9 Auſtr. # 18 # 58 Occ. # 1 # 0 <lb/>2 # 32 # 19 # 48 # 0 # 16 <lb/>3 # 17 # 20 # 5 # 0 # 0 <lb/>3 # 58 # 20 # 27 # 0 # 40 Orient. <lb/>5 # 9 # 21 # 39 # 1 # 2 <lb/>6 # 21 # 22 # 8 # 1 # 30 <lb/>8 # 3 # 23 # 15 # 1 # 50 <lb/>9 # 7 # 23 # 35 # 2 # 10 <lb/>12 # 3 # 25 # 3 # 3 # 32 <lb/>18 # 53 # 26 # 30 # 6 # 4 <lb/>19 # 51 # 27 # 2 # 6 # 19 <lb/>21 # 26 # 28 # 14 # 6 # 20 <lb/>21 # 48 # 28 # 10 # 6 # 30 <lb/>21 # 58 # 28 # 23 # 7 # 0 <lb/>24 # 45 # 27 # 56 # 6 # 45 <lb/>27 # 11 # 27 # 17 # 6 # 36 <lb/>33 # 53 # 16 # 58 # 5 # 4 <lb/>34 # 21 # 1 # 29 30? # 0 # 0 <lb/>34 # 15 # 1 # 33 Orient. # 1 # 0 Occid. <lb/>33 # 41 # 6 # 23 # 4 # 16 <lb/>34 # 39 # 13 # 2 # 8 # 46 <lb/>34 # 30 # 16 # 15 # 11 # 56 <lb/>32 # 51 # 13 # 41 # 11 # 30 <lb/>30 # 21 # 11 # 46 # 10 # 0 <lb/>29 # 51 # 11 # 44 # 9 # 44 <lb/>29 # 28 # 11 # 31 # 9 # 34 <lb/>28 # 56 # 11 # 5 # 9 # 22 <lb/>27 # 38 # 10 # 1 # 9 # 4 <lb/>26 # 55 # 8 # 45 # 8 # 30 <lb/>25 # 41 # 7 # 22 # 8 # 2 <lb/>24 # 32 # 5 # 43 # 7 # 32 <lb/>16 # 0 # 6 # 30 # 1 # 52 <lb/></note> <pb o="177" file="0191" n="191" rhead="DE MAGNETE"/> <p> <s xml:id="echoid-s4305" xml:space="preserve">Declinationes Magneticæ obſervatæ Anno 1703. </s> <s xml:id="echoid-s4306" xml:space="preserve">Deſcriptæ in <lb/>L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s4307" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4308" xml:space="preserve">A°. </s> <s xml:id="echoid-s4309" xml:space="preserve">1705. </s> <s xml:id="echoid-s4310" xml:space="preserve">Meridianus primus per <lb/>Inſulam Ferri tranſire ſupponitur.</s> <s xml:id="echoid-s4311" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Longitudo. # # Latitudo. <lb/>A°. 1703. # Grad. # M`. # Grad. # M`. # Grad. # M. <lb/># 1 # 30 Occ. # 358 # 0` # 5 # 40 S. <lb/># 1 # 0 Or. # 356 # # 5 # 20 M. <lb/># 1 # 30 Or. # 352 # 40` # 11 # 15 M. <lb/># 6 # 30 Or. # 350 # 0 # 21 # 0 M. <lb/># 3 # 15 Or. # 7 # 45 # 34 # 40 M. <lb/># 3 # 0 Occ. # 24 # 10 # 36 # 0 M. <lb/>Banc des Aiguilles. # 13 # 0 Occ # 41 # 0 # 36 # 20 M. <lb/># 19 # 0 Occ. # 53 # 30 # 35 # 35 M. <lb/># 25 # 30 Occ. # 69 # 0 # 32 # 50 M. <lb/># 19 # 0 Occ. # 98 # 30 # 28 # 0 M. <lb/># 15 # 0 Occ. # 96 # 35 # 22 # 40 M. <lb/># 4 # 0 Occ. # 106 # 40 # 1 # 20 M. <lb/># 4 # 45 Occ. # 105 # 20 # 14 # 40 M. <lb/></note> <p> <s xml:id="echoid-s4312" xml:space="preserve">Omnes hæ Declinationes obſervatæ ſunt â Caſſino ſatis benere-<lb/>ſpondiſſe curvis Halleyi in Tabula X. </s> <s xml:id="echoid-s4313" xml:space="preserve">depictis.</s> <s xml:id="echoid-s4314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4315" xml:space="preserve">Tabula Declinationis Magneticæ, facta ab Houſſaye Annis 1704. <lb/></s> <s xml:id="echoid-s4316" xml:space="preserve">& </s> <s xml:id="echoid-s4317" xml:space="preserve">1705 Meridiano tranſeunte per Pico de Teneriffa. </s> <s xml:id="echoid-s4318" xml:space="preserve">vide L’Hiſ-<lb/>toire de L’Acad. </s> <s xml:id="echoid-s4319" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4320" xml:space="preserve">A°. </s> <s xml:id="echoid-s4321" xml:space="preserve">1708.</s> <s xml:id="echoid-s4322" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Longitudo. # # Latitudo. <lb/>Port Louis. # Gr. # M. # Gr. # M. # Gr. # M. <lb/># # 5 # 0 Occ. <lb/># # 0 # 0 # 357 # 0 # 22 # 0 S. <lb/># # 2 # 30 Or. # 353 # 45 # 16 # 30 M. <lb/># # 3 # 30 Or. # 354 # 0 # 18 # 0 M. <lb/>1682 # { 3 # 30 OR # 354 # 0 # 23 # 0 M. # \\ 11 # 0 Or # ibidem <lb/># # 6 # 0 Or. # 357 # 0 # 28 # 0 M. <lb/></note> <pb o="178" file="0192" n="192" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # Longitudo. # # Latitudo. <lb/>In proſpectu Cabo \\ de bona Eſper. # 9 # vel 10 Occ. <lb/>Banc des Aiguilles \\ a parte Occidentali. 1704 \\ Banc des Aiguilles # 12 # 0 Occ. <lb/># # 13 # 30 vel 14°. Occ. <lb/>a parte Orientali. # 1705. # 13 # 0 Occ. <lb/>Cabo deBonaEſper. A°. # 1680 # 7 # 30 Occ. <lb/># 1705 # 9 # 30 <lb/>In Canali Moſambicq. # # 22°, # vel 23° Occ. # Anno 1711. Kolbe \\ obſervavit hic De- \\ clinat. 11°, 55`. ver- \\ ſus Occ. Septent. <lb/>uſque ad Bay St Auguſtin. \\ ſed Anno # 1682 # 18°, # vel 19° Occ. <lb/>Ad Conſpectum # # 22° # 0 Occ. <lb/>Inſulæ Jean de Noüa. <lb/>In Conſpectu Inſulæ # # 20 # 30` Occ. <lb/>Majotte. Amznam. # # # Longitudo. # # Latitudo. <lb/># # # # Gr. M. # Gr. M. <lb/># 16 # 0 Occ. # 70 0 # 0 0 <lb/># 10 # 30 Occ. # 87 0 # 15 0 S. <lb/>ad Conſpectum. \\ Canaræ, & juxta Malabar. # 6 # 30 Occ. # 16 30S. <lb/>Cap Comorin. # 7 # 30 Occ. <lb/>In Ceylon ad punctum \\ Galle. # 5 # 30 Occ. <lb/>Prope Cormandel. # 5 # 0 Occ. <lb/>Prope Inſulas Andamam \\ & Nicobare. # 3 # 0 Occ. <lb/>In conſpectu Inſulæ \\ Diego Rodrigo. # 16 # 30` Occ. <lb/>In conſpectu Inſulæ. \\ Mauritii. # 21 # 0 Occ. <lb/>Inſula Bourbon. # 21 # 30 Occ. <lb/># 23 # 30` Occ. # 74 # 0 # 25 0 M. <lb/></note> <pb o="179" file="0193" n="193" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Longitudo. # # Latitudo. <lb/># Gr. # M. # Gr # M. # Gr. # M. <lb/># 24 # 30 Occ. # 72 # 45 # 27 # 15 M. <lb/># 14 # 30 Occ. # 65 # 45 # 33 # 10 M. <lb/>Inſula St. Helenæ. # 1 # 0 Occ. <lb/>Inſula Adſcenſion. # 0 vel # 1°. # Or. <lb/># 0 # 0 # 357 # 0 # 0 # 0 <lb/>Ad Conſpectum \\ Inſulæ Corvo. # 4 # 30` Occ. <lb/>ad Terre neuve. # 7° vel # 8° Occ. <lb/>Bretagne. # 5 # 0 Occ. <lb/></note> <p> <s xml:id="echoid-s4323" xml:space="preserve">Conveniunt hæc ſatis accuratè cum Mappa Halleyi.</s> <s xml:id="echoid-s4324" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4325" xml:space="preserve">Tabula declinationis Magneticæ deſcripta in L’Hiſtoire de L’Acad. <lb/></s> <s xml:id="echoid-s4326" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4327" xml:space="preserve">A. </s> <s xml:id="echoid-s4328" xml:space="preserve">1710. </s> <s xml:id="echoid-s4329" xml:space="preserve">Meridiano tranſeunte per Teneriffam.</s> <s xml:id="echoid-s4330" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Latitudo. # # Longitudo. <lb/>120 Milliaribus # Gr. # M. # Gr. # M. # Gr. # M. <lb/>a littoribus Galliæ. # 8 # 0 Occ. # 44 # 45 S. <lb/>Anno 1709. <lb/>Anno 1708. # 8 # 0 Occ. # ibidem. <lb/># 6 # 30 Occ. # 45 # 7 S. # 11 # 31 <lb/># 11 # 0 Occ. # 45 # 20 S. # 358 # 15 <lb/>Anno 1708. # 4 # 35 Occ. # 35 # 35 S. # 0 # 0 <lb/># 4 # 32 # 27 # 58 S. # 353 # 40 <lb/>a Rochelle Anno # 5 # 8 # 36 # 0 S. # 325 # 46 <lb/>230 Milliar. 1709 # 7 # 50 # 46 # 50 S. <lb/># 6 # 0 # 33 # 45 S. # 5 # 0 <lb/># 13 # 0 # 43 # 45 S. # 340 # 46 <lb/>a Cap. Finis Terræ # 1707 # 7 # 20 # 44 # 45 <lb/>52 Milliar. # 7 # 20 navigando 60 Milliaria ad Oc- \\ caſum. <lb/></note> <pb o="180" file="0194" n="194" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Latitudo. # # Longitudo. <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/># 2 # 30 # 7 # 15M. # 1 # 50 <lb/>In Guinea Juda. 1708 # 8 # 20 <lb/>1705 # 8 # 0 <lb/>St. Thomas. # 11 # 30 <lb/></note> <p> <s xml:id="echoid-s4331" xml:space="preserve">A Congo verſus Fluvium de la Plata navigando Auſtro Occ. </s> <s xml:id="echoid-s4332" xml:space="preserve">& </s> <s xml:id="echoid-s4333" xml:space="preserve"><lb/>Occ. </s> <s xml:id="echoid-s4334" xml:space="preserve">Auſtro Occ. </s> <s xml:id="echoid-s4335" xml:space="preserve">erat Declinatio Acus Occidentalis quolibet die <lb/>minor, & </s> <s xml:id="echoid-s4336" xml:space="preserve">peractis 560 Milliaribus, erat Declinatio = 0. </s> <s xml:id="echoid-s4337" xml:space="preserve">Dein ulte-<lb/>rius erat Declinatio ad Ortum.</s> <s xml:id="echoid-s4338" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # Declinatio. # # Latitudo. # # Longitudo. <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/>A°. 1709. # 1 # 30 Occ. # 28 # 30`S. # 316 # 30 <lb/># 4 # 10 Occ. # 32 # 15 S. # 321 # 45 <lb/># 7 # 10 Occ. # 36 # 50 S. # 329 # 0 <lb/># 10 # 10 # 45 # 8 S. # 305 # 30 <lb/></note> <p> <s xml:id="echoid-s4339" xml:space="preserve">Si hæ obſervationes ſint bene captæ.</s> <s xml:id="echoid-s4340" xml:space="preserve">; tum ad parallelam 22 <lb/>grad latitudinis Auſtralis Linea expers Declinationis Magneticæ ac-<lb/>ceſſiſſet ad occaſum 120 Milliaribus ab A°. </s> <s xml:id="echoid-s4341" xml:space="preserve">1700. </s> <s xml:id="echoid-s4342" xml:space="preserve">uſque ad 1708.</s> <s xml:id="echoid-s4343" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4344" xml:space="preserve">Tabula Declinationis Magneticæ, Anno 1721 in Oceano Æthyo-<lb/>pico obſervatæ, exhibita in Philoſophical Tranſactions N°. </s> <s xml:id="echoid-s4345" xml:space="preserve">371. <lb/></s> <s xml:id="echoid-s4346" xml:space="preserve">in qua Meridiana diſtantia ſupputatur â St. </s> <s xml:id="echoid-s4347" xml:space="preserve">Jago.</s> <s xml:id="echoid-s4348" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Meridiana # # Longitudo. # # Declinatio. <lb/>Gr. # M. # # Diſtantia. # Gr. # M. # Grad # M. <lb/>9 # 8` Mer. # 9 # 23` Occ. # 9° # 25` Occ # 2° # 13` Or. <lb/>11 # 12 # 10 # 46 # 10 # 50 # 4 # 30 Or. <lb/>11 # 34 # 11 # 28 # 11 # 41 # 4 # 29 Or. <lb/>12 # 32 # 11 # 31 # 11 # 43 # 4 # 27 Or. <lb/>15 # 46 # 10 # 53 # 11 # 6 # 6 # 10 <lb/>16 # 26 # 8 # 25 # 8 # 30 # 7 # 16 <lb/>18 # 45 # 9 # 31 # 9 # 39 # 6 # 17 <lb/>19 # 47 # 9 # 10 # 10 # 0 # 8 # 6 <lb/></note> <pb o="181" file="0195" n="195" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Meridiana # # Longitudo. # # Declinatio. <lb/>Gr. # M. # # Diſtantia. # Gr. # M. # Grad. # M <lb/>28 # 43 Mer. # 1 # 7 Occ. # 1 # 9 Or. # 5 # 53 Or. <lb/>31 # 33 # 3 # 41 Or. # 3 # 56 # 4 # 10 <lb/>33 # 30 # 11 # 29 # 12 # 57 # 0 # 11 Occ. <lb/>32 # 40 # 19 # 6 # 12 # 1 # 3 # 0 Occ. <lb/>32 # 53 # 21 # 18 # 24 # 59 # 5 # 41 <lb/>32 # 30 # 25 # 33 # 30 # 0 # 7 # 47 <lb/>32 # 28 # 30 # 37 # 35 # 52 # 8 # 44 <lb/>31 # 22 # 31 # 40 # 37 # 7 # 10 # 57 <lb/>31 # 11 # 32 # 4 # 37 # 47 # 11 # 20 <lb/></note> <p> <s xml:id="echoid-s4349" xml:space="preserve">Obſervationes factæ juxta littora Africæ A°. </s> <s xml:id="echoid-s4350" xml:space="preserve">1721. </s> <s xml:id="echoid-s4351" xml:space="preserve">deſcriptæ in <lb/>iiſdem Actis.</s> <s xml:id="echoid-s4352" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo. # # Variatio Acus. <lb/>Gr. # M. # Gr. # M. # Grad. # Min. <lb/>26 # 17 Mer. # 41 # 41 Or. # 14 # 30 Occ. <lb/>19 # 41 Mer. # # # 12 # 22 Occ. <lb/>17 # 4 Mer. # # # 14 # 29 Occ. <lb/>13 # 56 Mer. # # # 14 # 48 Occ. <lb/>10 # 57 Mer. # # # 13 # 11 Occ. <lb/>8 # 19 Mer. # # # 15 # 14 Occ. <lb/>5 # 0 Mer. # # in Cabenda Bay. # 14 # 33 Occ. <lb/></note> <p> <s xml:id="echoid-s4353" xml:space="preserve">A Cabenda uſque ad Londinum.</s> <s xml:id="echoid-s4354" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>3 # 25` Mer. # 11 # 43` Occ. # 11 # 32` Occ. <lb/>3 # 30 Mer. # 21 # 24 Occ. # 1 # 5 Occ. <lb/>0 # 30 Mer. # 30 # 46 Occ. <lb/>10 # 50 Sept. # 39 # 16 Occ. # 1 # 1 Or. <lb/>17 # 15 Sept. # 43 # 29 Occ. # 1 # 41 Or. <lb/></note> <pb o="182" file="0196" n="196" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s4355" xml:space="preserve">Obſervationes Declinationum captæ Anno 1706. </s> <s xml:id="echoid-s4356" xml:space="preserve">a de La Verune <lb/>deſcriptæ in L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s4357" xml:space="preserve">Roy. </s> <s xml:id="echoid-s4358" xml:space="preserve">A°. </s> <s xml:id="echoid-s4359" xml:space="preserve">1708. </s> <s xml:id="echoid-s4360" xml:space="preserve">in quibus <lb/>ſupponitur Meridianus primus per Pico de Teneriffa.</s> <s xml:id="echoid-s4361" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # Latitudo. # # Longitudo. # # Declinatio. <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/>1706 # 20 # 44 M. # 345 # 44 # 7 # 30 # Or. # Prope Inſulam \\ Adſcenſion. <lb/>1707 # 56 # 6 M. # 297 # 12 # 20 # 0 # Or. # Prope Hermitan. <lb/># 52 # 19 M. # 310 # 30 # 23 # 0 # Or. # Inſula Sebald. <lb/># 13 # 6 M. # 300 # 10 # 7 # 0 # Or. # Prope punctum. \\ Cannette. <lb/># 14 # 1 M. # 296 # 27 # 7 # 0 # Or. # Prope Piſco. <lb/># 31 # 49 M. # 297 # 30 # 8 # 0 # Or. # Valparezo. <lb/># 36 # 30 M. # 299 # 25 # 10 # 0 # Or. # PropeConception. <lb/># 44 # 49 M. # # In his parva # 12 # 0 # Or. <lb/># 48 # 58`M. # # diſtantia a \\ littoribus Americæ # 13 # 0 # Or. <lb/># 53 # 37 # # Occident. # 15 # 0 # Or. <lb/># 56 # 42 # # 17 # 0 # Or. <lb/></note> <p> <s xml:id="echoid-s4362" xml:space="preserve">Obſervationes Declinationum Magneticarum collectæ <lb/>ex Itinerario Dampierii.</s> <s xml:id="echoid-s4363" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Anno 1683. # # Latitud. # # Declinat. <lb/>Inſulæ de Waard. # 51 # 25 M. # 23 # 10 Or. <lb/>A° 1707. # # # 23 # 0 <lb/>1683. # 47 # 10 M. in Mari Pacif # 15 # 30 Or. <lb/># 36 # 0 # in eodem. # 8 # 0 Or. <lb/></note> <pb o="183" file="0197" n="197" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s4364" xml:space="preserve">Obſervationes Declinationum Anni 1706. </s> <s xml:id="echoid-s4365" xml:space="preserve">deſcriptæ in L’Hiſtoire <lb/>de L’Academie Roy. </s> <s xml:id="echoid-s4366" xml:space="preserve">1710.</s> <s xml:id="echoid-s4367" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Latitudo. # # Longitudo. <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/>25 Milliaribus a <lb/>porto Santo prope \\ Maderam. # 5 # 0 Occ. <lb/>Prope Maderam \\ ſed Auſtro Occ. # 4 # 30 Occ. <lb/>Inter Maderam \\ & inſulam Ferri. # 4 # 0 Occ. <lb/>50 Milliaribus verſus <lb/>Auſtr. Auſtr Occ. \\ ab Inſula Ferri. # 3 # 0 Occ. <lb/># 2 # 30 # 18 # 15 S. # 357 # 0 <lb/>Inter locum priorem \\ & Banc Bisagos in littoribus Guineæ ſemper Declinatio \\ obſervata # 2° # 30` <lb/># 2 # 0 Occ. # 6 # 0 S. # 358 # 0 <lb/># 2 # 0 # 3 # 15 S. # 0 # 10 <lb/># 2 # 0 # 0 # 0 # 7 # 0 <lb/>Sed 50 Milliaribus # 3 # 0 navigando a loco priori verſus \\ Auſtr. Or. <lb/>& ulterius 50 Mill # a 3 ad 4° navigando eodem modo. <lb/>& ulterius 50 Mill. # a 4 ad 5° navigando eodem modo. <lb/># 5 # 0 # 9 # 0 M. # 356 # 15` <lb/>& ulterius 50 Mill. # a 5° ad 4° avigando verſus Auſtro Occ. <lb/>ulterius 50 Mill. # a 4° ad 3 eodem tractu. <lb/>ulterius 50 Mill # a 2 ad 1 eodem tractu. <lb/>unde poſt 250 Mill. # 0 # 0 <lb/>ulterius 50 Milliar. # 1 # 0 Or. <lb/>20 Milliar. ad Boreo Or. \\ ab inſula Adſcenſion. # 6 # 0 # Or. <lb/>Inſula Grande \\ in Braſilia. # 11 # 40 Or. <lb/></note> <pb o="184" file="0198" n="198" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Locus. # # Declinatio. # # Latitudo. # # Longitudo. <lb/># Gr. # M. # Gr. # M. # Gr. # M. <lb/>Ad ſretum Magellanes # 12 # 0 # Or. <lb/># 13 # 0 <lb/># 16 # 0 <lb/># 17 <lb/># 18 <lb/># 19 # # 40 # 30 M. & manfit ſub <lb/>eadem latitudine per 60 Milliaria eadem Declinatio. # 26 # 0 Or. # 57 # 10 M. 60 Milliaribus \\ a Freto leMaire. \\ Auſtro Occ. <lb/>Per 40 Milliaria, # 26 # 0 Or. ad # 57 # 40` <lb/>la Conception. # 9 # 30 <lb/>Piſco. # 8 # 0 <lb/>Canette. # 6 # 30 <lb/>Callao. # 6 # 0 <lb/></note> <p> <s xml:id="echoid-s4368" xml:space="preserve">Hic notandum, quo iter fiebat, ad majorem latitudinem, eo De-<lb/>clinationem majorem fuiſſe: </s> <s xml:id="echoid-s4369" xml:space="preserve">ſed manendo in eadem parallela ver-<lb/>ſus Occaſum, Declinationem decreviſſe.</s> <s xml:id="echoid-s4370" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># 12 # 0 # 44 # 45 # M. 30 Milliar. a \\ Chili. <lb/># 7 # 0 # 44 # 45 # 120 Milliar. a \\ Chili. <lb/># 9 # 0 inter # 40 & # 41° # 10 Milliaribus \\ a littore. <lb/># 6 # 0 inter # 40 & # 41 # 6 Milliaribus \\ a littore. <lb/># 7 # 0 inter # 30 & # 31 # 60 Milliaribus \\ a littore. <lb/># 5 # 0 inter # 30 & # 31° # 220 Milliaribus \\ a littore. <lb/>Anno 1707 \\ A Gallegue. # 23 # 0 Or. <lb/>60 Milliaribus a Gallegue Verſus Cabo Bona Eſperanza # 22 # 0 Or. <lb/></note> <pb o="185" file="0199" n="199" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># Locus. # # Declinatio. # # Latitudo. <lb/># # Gr. # M. # Gr. # M. <lb/>30 Mill. ulterius # 20 # 0 Or. <lb/>150 Mill. ulterius # 18 # 0 Or. <lb/>110 Mill. ulterius # 16 # 0 Or. <lb/>150 Mill. ulterius # 14 # 0 Or. <lb/>60 Mill. ulterius # 13 # 0 Or. <lb/>50 Mill. ulterius # 12 # 0 Or. <lb/>20 Mill. ulterius # 11 # 0 Or. <lb/>30 Mill. ulterius # 10 # 0 Or. <lb/>20 Mill. ulterius # 8 # 0 Or. <lb/>100 Mill. ulterius # 4 # 0 Or. <lb/>120 Mill. ulterius # 0 # 0 Or. <lb/>60 Mill. ulterius # 2 # 0 Occ. navis petebat Ortum. <lb/>80 Mill. ulterius # 4 # 0 Occ. <lb/>60 Mill. ulterius # 7 # 0 Occ. <lb/>140 Mill. ulterius # 9 # 30 Occ. <lb/>60 Mill. ulterius # 8 # 0 Occ. prope Cabo de Bona Eſper. <lb/></note> <p> <s xml:id="echoid-s4371" xml:space="preserve">Ergo ab Anno 1700 uſque ad 1709 linea directionis fuit mutata <lb/>50 Milliaribus verſus Occaſum, ad latitudinem 35 Grad. </s> <s xml:id="echoid-s4372" xml:space="preserve">Meridio-<lb/>nalem.</s> <s xml:id="echoid-s4373" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>A Cabo de Bona Eſp. # 24 # 30` Occ # 33 # 30` <lb/>530 Mill. verſusOrt. <lb/></note> <p> <s xml:id="echoid-s4374" xml:space="preserve">Declinationes Magneticæ a Fueilleo obſervatæ Anno 1708 in Itine-<lb/>re verſus Americam.</s> <s xml:id="echoid-s4375" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ loci. # # Longitudo. # # Declinatio Acus. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/># # # # Calliari in Sardinia # 10 # 19 Occident. <lb/>35 # 35 # # Malta # 10 # 25 <lb/>39 # 54 # # in portu Mahon. # 10 # 26 <lb/>5 # 49 # 354 # 52 # 0 # 7 <lb/></note> <pb o="186" file="0200" n="200" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ loci. # # Longitudo. # # Declinatio Acus. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>5 # 24 # 357 # 3 # 0 # 0 <lb/># # Sub Æquatore # 354 # 0 # 0 # 37 Orientalis. <lb/>2 # 26 Auſtr. # 353 # 3 # 1 # 5 <lb/>8 # 4 # 352 # 39 # 1 # 17 <lb/>13 # 3 # 351 # 46 # 3 # 32 <lb/>20 # 21 # 350 # 27 # 8 # 11 <lb/>21 # 10 # 349 # 21 # 8 # 4 <lb/>21 # 53 # 348 # 8 # 7 # 46 <lb/>22 # 8 # 347 # 25 # 9 # 8 <lb/>22 # 20 {1/2} # 346 # 58 {1/4} # 9 # 28 <lb/>22 # 44 {1/2} # 346 # 6 {1/2} # 9 # 0 <lb/>27 # 5 # 355 # 52 # 12 # 17 <lb/>28 # 55 # 331 # 21 # 12 # 0 <lb/>31 # 0 # 329 # 7 # 16 # 24 <lb/>34 # 18 # 327 # 49 # 18 # 17 <lb/>41 # 11 # 322 # 46 # 19 # 19 <lb/>42 # 16 # 322 # 15 # 17 # 57 <lb/>43 # 24 # 321 # 49 # 19 # 57 <lb/>46 # 24 # 319 # 44 # 19 # 16 <lb/>53 # 0 # 315 # 29 # 23 # 5 <lb/>55 # 45 {1/3} # 318 # 9 # 23 # 3 {1/2} <lb/>51 # 26 # 299 # 29 # 15 # 0 <lb/>49 # 51 {1/3} # 299 # 54 # 13 # 30 <lb/>41 # 4 # 303 # 20 # 11 # 33 <lb/>33 # 1 # # Valporaiſo # 9 # 30 <lb/>13 # 9 {1/2} # # Lima # 6 # 15 <lb/></note> <pb o="187" file="0201" n="201" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s4376" xml:space="preserve">Tabula Declinationis in Mari Pacifico obſervatæ A°. </s> <s xml:id="echoid-s4377" xml:space="preserve">1710. </s> <s xml:id="echoid-s4378" xml:space="preserve">deſcri-<lb/>pta in Philoſophical Tranſactions N°. </s> <s xml:id="echoid-s4379" xml:space="preserve">368.</s> <s xml:id="echoid-s4380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4381" xml:space="preserve">Ab Auſtrali parte Caleforniæ uſque ad Inſulam Guanam, quæunaeſt <lb/>ex Ladronibus: </s> <s xml:id="echoid-s4382" xml:space="preserve">Meridiano tranſeunte per Londinum.</s> <s xml:id="echoid-s4383" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo \\ Occid. a Londino. # # Declinatio \\ Orientalis. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>22 # 16 # 114 # 9 # 3 # 0 <lb/>21 # 18 # 114 # 42 # 2 # 50 <lb/>20 # 24 # 115 # 15 # 2 # 50 <lb/>19 # 25 # 115 # 45 # 2 # 50 <lb/>18 # 56 # 116 # 24 # 2 # 45 <lb/>18 # 0 # 117 # 6 # 2 # 45 <lb/>17 # 11 # 117 # 30 # 2 # 15 <lb/>16 # 32 # 118 # 5 # 2 # 0 <lb/>15 # 44 # 118 # 54 # 1 # 50 <lb/>15 # 0 # 120 # 15 # 1 # 30 <lb/>14 # 49 # 122 # 5 # 1 # 10 <lb/>14 # 36 # 124 # 25 # 0 # 50 <lb/>14 # 24 # 126 # 45 # 0 # 40 <lb/>14 # 14 # 129 # 5 # 0 # 45 <lb/>13 # 50 # 131 # 23 # 0 # 50 <lb/>13 # 29 # 132 # 58 # 1 # 0 <lb/>13 # 29 # 134 # 41 # 1 # 10 <lb/>13 # 22 # 136 # 48 # 1 # 15 <lb/>13 # 27 # 139 # 21 # 1 # 25 <lb/>13 # 32 # 142 # 7 # 1 # 30 <lb/>13 # 32 # 144 # 37 # 1 # 40 <lb/>13 # 36 # 147 # 32 # 1 # 50 <lb/>13 # 26 # 150 # 18 # 2 # 0 <lb/>13 # 26 # 153 # 2 # 2 # 10 <lb/>13 # 26 # 155 # 19 # 2 # 25 <lb/>13 # 26 # 157 # 43 # 2 # 30 <lb/>13 # 25 # 160 # 31 # 2 # 50 <lb/>13 # 41 # 163 # 0 # 3 # 0 <lb/>13 # 41 # 165 # 18 # 3 # 20 <lb/>13 # 44 # 167 # 26 # 3 # 30 <lb/></note> <pb o="188" file="0202" n="202" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # Latitudo. # # Longitudo \\ a Londino. # # Declinatio \\ Orientalis. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>13 # 36 # 169 # 56 # 3 # 45 <lb/>13 # 33 # 172 # 27 # 4 # 0 <lb/>13 # 36 # 175 # 0 # 4 # 30 <lb/>13 # 32 # 177 # 21 # 5 # 20 <lb/>13 # 40 # 179 # 28 # 6 # 30 <lb/>13 # 47 # 181 # 24 # 7 # 0 <lb/>13 # 54 # 183 # 22 # 7 # 30 <lb/>13 # 52 # 185 # 37 # 9 # 0 <lb/>13 # 40 # 187 # 42 # 10 # 15 <lb/>13 # 28 # 189 # 49 # 11 # 0 <lb/>13 # 21 # 191 # 30 # 11 # 30 <lb/>13 # 12 # 193 # 25 # 12 # 0 <lb/>13 # 7 # 194 # 37 # 11 # 50 <lb/>13 # 10 # 195 # 51 # 11 # 0 <lb/>13 # 3 # 197 # 51 # 10 # 0 <lb/>13 # 0 # 199 # 3 # 9 # 50 <lb/>12 # 57 # 200 # 16 # 9 # 30 <lb/>12 # 54 # 202 # 20 # 9 # 0 <lb/>12 # 58 # 204 # 12 # 8 # 40 <lb/>13 # 4 # 206 # 6 # 8 # 20 <lb/>13 # 5 # 207 # 33 # 8 # 0 <lb/>13 # 5 # 209 # 4 # 7 # 50 <lb/>13 # 2 # 211 # 54 # 7 # 30 <lb/>13 # 7 # 212 # 42 # 7 # 10 <lb/>13 # 7 # 214 # 7 # 7 # 0 <lb/>13 # 3 # 215 # 28 # 6 # 50 <lb/>13 # 8 # 217 # 11 # 6 # 30 <lb/>13 # 16 # 218 # 27 # 5 # 40 <lb/># # # # # # In proſpectu Guanæ. <lb/></note> </div> <div xml:id="echoid-div121" type="section" level="1" n="121"> <head xml:id="echoid-head130" xml:space="preserve">EXPERIMENTUM XCVIII.</head> <p> <s xml:id="echoid-s4384" xml:space="preserve">Verſorium Chalybeum E O F Tabulæ 4. </s> <s xml:id="echoid-s4385" xml:space="preserve">fig. </s> <s xml:id="echoid-s4386" xml:space="preserve">9. </s> <s xml:id="echoid-s4387" xml:space="preserve">novum, utrim-<lb/>que â centro motus O æque longum, & </s> <s xml:id="echoid-s4388" xml:space="preserve">æque grave, ut ſtylo K <lb/>impoſitum, ſit horizonti parallelum; </s> <s xml:id="echoid-s4389" xml:space="preserve">ducatur ſupra eum Magnetis <lb/>polum, ut cuſpis E Septentrionem verſus dirigatur: </s> <s xml:id="echoid-s4390" xml:space="preserve">poſtea Verſo-<lb/>rii iterum impoſiti ſuo ſtylo deprimetur pars Septentrionalis E O <pb o="189" file="0203" n="203" rhead="DE MAGNETE."/> infra horizontem in regionibus Europæis, angulum aliquem cum eo <lb/>faciendo; </s> <s xml:id="echoid-s4391" xml:space="preserve">ſupra horizontem proinde pars F O tantopere elevabi-<lb/>tur.</s> <s xml:id="echoid-s4392" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4393" xml:space="preserve">Depreſſionem Acus infra horizontem Philoſophi hodierni vocant <lb/>Inclinationem, Gilbertus Lib. </s> <s xml:id="echoid-s4394" xml:space="preserve">5. </s> <s xml:id="echoid-s4395" xml:space="preserve">Declinationem vocavit.</s> <s xml:id="echoid-s4396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4397" xml:space="preserve">Illam primus invenit Robertus Normannus, Brittannus, Anno <lb/>1576, teſte Gilberto Lib. </s> <s xml:id="echoid-s4398" xml:space="preserve">1. </s> <s xml:id="echoid-s4399" xml:space="preserve">C. </s> <s xml:id="echoid-s4400" xml:space="preserve">1. </s> <s xml:id="echoid-s4401" xml:space="preserve">Hic, inquit, eſt ille Robertus <lb/>Normannus, nauta peritus & </s> <s xml:id="echoid-s4402" xml:space="preserve">ingenioſus artifex, qui primus De-<lb/>clinationem magnetici ferri invenit: </s> <s xml:id="echoid-s4403" xml:space="preserve">ante Gilbertum etiam Gui-<lb/>lelmus Borough in præfatione libelli de variatione pyxidis, Nor-<lb/>mannum inventorem deprædicavit: </s> <s xml:id="echoid-s4404" xml:space="preserve">Commemorat Normannus in <lb/>ſuo Tractatu New Attractive Cap. </s> <s xml:id="echoid-s4405" xml:space="preserve">3. </s> <s xml:id="echoid-s4406" xml:space="preserve">quo caſu in hoc inventum in-<lb/>cidit: </s> <s xml:id="echoid-s4407" xml:space="preserve">Acus elaborare ſolebat Nauticas, quæ in ſitu horizontali ſi-<lb/>bi æquilibratæ, ſimulac ſuper Magnete ducebantur, cuſpide Boreâ <lb/>infra horizontem inclinabant, quamobrem oppoſitæ parti Acûs te-<lb/>nebatur tantillum ceræ affigere, quæ ſuo pondere æquilibrium re-<lb/>ſtitueret; </s> <s xml:id="echoid-s4408" xml:space="preserve">poſtea ab Acûs ſex pollicum parte Boreâ aliquid abſcidit. <lb/></s> <s xml:id="echoid-s4409" xml:space="preserve">ſed paulo plus per infortunium, hinc perdito æquilibrio indignatus, <lb/>ope machinæ alterius explorandum prius duxit, quantum Acus, prius <lb/>æquilibrata, infra horizontem deprimeretur, poſtquam vim Magne-<lb/>ticam accepiſſet, machinam perfecit, quam deſcripſit in Cap. </s> <s xml:id="echoid-s4410" xml:space="preserve">4. </s> <s xml:id="echoid-s4411" xml:space="preserve">ſui <lb/>libelli.</s> <s xml:id="echoid-s4412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4413" xml:space="preserve">Hac Inclinatione igitur Acui nauticæ nova veluti gravitas additur <lb/>in hac regione â parte Septentrionali, quare ut horizonti parallela <lb/>maneat, artifices caudam Auſtralem graviorem cuſpide Borea fabri-<lb/>cantur: </s> <s xml:id="echoid-s4414" xml:space="preserve">ſed in terræ hemiſphærio Auſtrali Acûs cauda, quæ in Eu-<lb/>ropa ſurſum elevata erat, infra horizontem inclinat, cuſpide Borea <lb/>ſurſum ſpectante: </s> <s xml:id="echoid-s4415" xml:space="preserve">Quamobrem nautæ ea in telluris parte aliis Ver-<lb/>ſoriis uti tenentur, quorum cauda eſt cuſpide levior: </s> <s xml:id="echoid-s4416" xml:space="preserve">Operæ pre-<lb/>tium erit de Inclinatione Acus prolixius agere, cum â recentiſſimis <lb/>Philoſophis in lucem iterum ê tenebris protracta, maximi in doctri-<lb/>nâ Magneticâ, & </s> <s xml:id="echoid-s4417" xml:space="preserve">ad locorum longitudines determinandas, creditur <lb/>eſſe momenti; </s> <s xml:id="echoid-s4418" xml:space="preserve">licet huic ſcopo forte minus conveniat, promoven-<lb/>dæ nihilominus doctrinæ Magneticæ inſerviet.</s> <s xml:id="echoid-s4419" xml:space="preserve"/> </p> <pb o="190" file="0204" n="204" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div122" type="section" level="1" n="122"> <head xml:id="echoid-head131" xml:space="preserve">DE ACU INCLINATORIA.</head> <p> <s xml:id="echoid-s4420" xml:space="preserve">Vulgarium Verſoriorum horizontalium centrum gravitatis & </s> <s xml:id="echoid-s4421" xml:space="preserve">mo-<lb/>tus non eſt unum idemque punctum, ſed elevatius eſt centrum mo-<lb/>tus in ænei capituli excavati vertice, ſupra quem movetur, hinc <lb/>ſimulac Verſorium alterutro latere deprimitur, centrum gravitatis <lb/>elevatur ab oppofitâ parte, adeoque gravitas totius Verſorii iterum <lb/>deſcendere nitetur, atque hæc ita agendo in vim deprimentem Ver-<lb/>ſorii, impedit quominus accurate quantitas Inclinationis obſervari <lb/>queat, ideo vulgare Verſorium huic uſui ineptum eſt, aliudque di-<lb/>verſæ fabricandum erat formæ, cujus centrum motus & </s> <s xml:id="echoid-s4422" xml:space="preserve">gravitatis <lb/>unum idemque punctum foret: </s> <s xml:id="echoid-s4423" xml:space="preserve">Normannus acum conſtruxit ob-<lb/>longam, per cujus centrum gravitatis axem tranſfixit, quemadmo-<lb/>dum per Libræ jugum fieriſolet: </s> <s xml:id="echoid-s4424" xml:space="preserve">tum Acu Magneti affricta, & </s> <s xml:id="echoid-s4425" xml:space="preserve">axe <lb/>utrimque impoſito vitreo plano, deprehendit partem Boream incli-<lb/>naſſe Londini 71 gradibus, 50 Minutis. </s> <s xml:id="echoid-s4426" xml:space="preserve">Anno 1576. </s> <s xml:id="echoid-s4427" xml:space="preserve">Leotaudus, <lb/>improbata procul dubio Normanni machinâ, aliam invenit, quam <lb/>nos exhibemus Tab. </s> <s xml:id="echoid-s4428" xml:space="preserve">7. </s> <s xml:id="echoid-s4429" xml:space="preserve">fig. </s> <s xml:id="echoid-s4430" xml:space="preserve">10. </s> <s xml:id="echoid-s4431" xml:space="preserve">Eſt H I Acus oblonga, ab utraque <lb/>parte ſui axeos E F æque gravis: </s> <s xml:id="echoid-s4432" xml:space="preserve">axis excipitur ab annulo cupreo <lb/>D G E F, qui ex ſeta equina A D ſuſpenditur; </s> <s xml:id="echoid-s4433" xml:space="preserve">medius in circulo <lb/>æneo A K B C L, in 360 gradus diviſo, quorum initium eſt in ho-<lb/>rizontali K L, ponduſculum E annulo annexum ſuâ gravitate hunc <lb/>in ſitu ad horizontem perpendiculari dirigit; </s> <s xml:id="echoid-s4434" xml:space="preserve">hac machinâ nonnulli <lb/>Inclinationem Acus obſervaverunt, non tamen accurate, quia non-<lb/>nullis vitiis eſt ſubjecta, nec ob Acus brevitatem, utpote qui 3 vel <lb/>4 pollicum modo exiſtit, bene Inclinatio in gradibus & </s> <s xml:id="echoid-s4435" xml:space="preserve">minutis <lb/>obſervari poteſt: </s> <s xml:id="echoid-s4436" xml:space="preserve">præterea ope ponduſculi E non exacte poteſt con-<lb/>ſpici Nadir, imo attritus axeos G F in annulo ſupra idem metallum <lb/>mobilitatem acus adeo imminuit, ut vera Inclinatio obtineri nequeat. <lb/></s> <s xml:id="echoid-s4437" xml:space="preserve">Hiſce defectibus obſervatis aliam compoſui machinam multo majo-<lb/>rem, cui Acus longiſſimæ imponi poterant, ut mobilitatem earum <lb/>nanciſcerer ſummam, & </s> <s xml:id="echoid-s4438" xml:space="preserve">ſimul Inclinationem notarem exactiſſime, <lb/>machinam repræſentat Tabula 8. </s> <s xml:id="echoid-s4439" xml:space="preserve">Eſt A A A Tabula lignea qua-<lb/>drata, cujus quodlibet latus A A eſt 26 pollicum: </s> <s xml:id="echoid-s4440" xml:space="preserve">huic inſculpti <lb/>ſunt tres quadrantes circulorum concentricorum G G, H H, K K, <pb o="191" file="0205" n="205" rhead="DE MAGNETE."/> qui acubus diverſæ longitudinis explorandis inſerviunt: </s> <s xml:id="echoid-s4441" xml:space="preserve">inſiſtit pedi <lb/>firmo ligneo L L L, ope trium ænearum cochlearum ita dirigendo, <lb/>ut Tabula accurate horizonti perpendicularis ponatur: </s> <s xml:id="echoid-s4442" xml:space="preserve">hoc explo-<lb/>ratur ope penduli D C in cuſpidem deſinentis, quæ apici promi-<lb/>nentis ſtyli B reſpondet, ſimulac tabula bene eſt locata: </s> <s xml:id="echoid-s4443" xml:space="preserve">verticilli <lb/>E ope pendulum C D abbreviari elongarique poteſt. </s> <s xml:id="echoid-s4444" xml:space="preserve">Omnium qua-<lb/>drantum eſt centrum commune I, in quo haud exiguum artificium <lb/>latet. </s> <s xml:id="echoid-s4445" xml:space="preserve">lamina cuprea denſa firme annexa eſt lateri Tabulæ, ipſi im-<lb/>poſita ſunt duo capita ſeu excipula, quæ quia non ſatis clare con-<lb/>ſpici poſſunt, inferius depicta ſunt N, M: </s> <s xml:id="echoid-s4446" xml:space="preserve">utrumque in O laminam <lb/>politiſſimam vitream planamque continet, ſupra quam in capitis <lb/>commiſſurâ axis Acus poſitus libere convertitur abſque ullo fere at-<lb/>tritu; </s> <s xml:id="echoid-s4447" xml:space="preserve">ſupra ſuperficiem vitri enim axim mobiliſſime circumvertiob-<lb/>ſervaverunt recte Normannus & </s> <s xml:id="echoid-s4448" xml:space="preserve">Whiſtonus: </s> <s xml:id="echoid-s4449" xml:space="preserve">ex hac deſcriptione ſatis <lb/>intelligi poterit machina, accedamus igitur ad Acus, quarum non-<lb/>nullas præparavi diverſæ longitudinis & </s> <s xml:id="echoid-s4450" xml:space="preserve">fabricæ. </s> <s xml:id="echoid-s4451" xml:space="preserve">longiſſima S S erat 4 <lb/>pedum, in medio {1/2} pollicem lata, {3/12} pollic. </s> <s xml:id="echoid-s4452" xml:space="preserve">craſſa, utrimque de-<lb/>ſinens in apices acutiſſimos: </s> <s xml:id="echoid-s4453" xml:space="preserve">per medium, hoc eſt per centrum gra-<lb/>vitatis tranſibat axis indurati chalybis, tenuis, perfecte rotundus, <lb/>ac politiſſimus pp, ita Acus impoſita excipulis M N, lubriciſſime & </s> <s xml:id="echoid-s4454" xml:space="preserve">li-<lb/>bere poterat converti: </s> <s xml:id="echoid-s4455" xml:space="preserve">attamen præterea deſiderabatur, ut hæc Acus <lb/>excepta capitibus, ab utraque ſui parte foret accurate æquilibrata, <lb/>& </s> <s xml:id="echoid-s4456" xml:space="preserve">in ſitu poſita horizontali, vel in quocunque alio obliquo, abſo-<lb/>lute quieſceret: </s> <s xml:id="echoid-s4457" xml:space="preserve">hoc facile dictu & </s> <s xml:id="echoid-s4458" xml:space="preserve">conceptu, aſt factu difficilius <lb/>nihil, non enim, ut hujus indolis præparetur Acus, ſumma duntaxat <lb/>poſtulatur dexteritas, ſed improbus labor, conjunctus cum infan-<lb/>do tædio, quo maxima artificum patientia opprimeretur, nam me-<lb/>dium axeos per centrum gravitatis tranſire debet, quod ut obtinea-<lb/>tur accuratiſſime, nunc aliquid â latere acus dextro, nunc â ſini-<lb/>ſtro limâ abradendum eſt, nunc iterum aliquid a parte ſuperiori; <lb/></s> <s xml:id="echoid-s4459" xml:space="preserve">nunc ab inferiori, atque non niſi poſt infinita tentamina voti com-<lb/>potes evadimus: </s> <s xml:id="echoid-s4460" xml:space="preserve">difficultates ejuſmodi etiam experti fuerunt Whi-<lb/>ſtonus, & </s> <s xml:id="echoid-s4461" xml:space="preserve">poſtea Grahamus in Philoſ. </s> <s xml:id="echoid-s4462" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s4463" xml:space="preserve">N°. </s> <s xml:id="echoid-s4464" xml:space="preserve">389. </s> <s xml:id="echoid-s4465" xml:space="preserve">præparatâ <lb/>tamen Acu dubitavi valde, an præter binos memoratos viros aliquis <lb/>unquam bonam Acum Inclinatoriam poſſederit, neminementionem <lb/>faciente quanto cum labore præparari modo poſſit; </s> <s xml:id="echoid-s4466" xml:space="preserve">imo hinc opi- <pb o="192" file="0206" n="206" rhead="DISSERTATIO"/> nor pendere diſcrepantiam inter obſervatas Inclinationes in iiſdem <lb/>Terræ locis ſummam, etiamſi parvum temporis intervallum inter-<lb/>ceſſerit, uti conſtare poteſt ex obſervationibus Noëllii & </s> <s xml:id="echoid-s4467" xml:space="preserve">Poundii, <lb/>inferius commemorandis: </s> <s xml:id="echoid-s4468" xml:space="preserve">Acus alias breviores & </s> <s xml:id="echoid-s4469" xml:space="preserve">tenuiores quoque <lb/>conſtruxi, quarum una exhibetur R R, cujus axis æneus erat P P, <lb/>brachia P R, P R; </s> <s xml:id="echoid-s4470" xml:space="preserve">hujuſmodi acus præ gravitate ſuperabat Chalybis <lb/>rigiditatem, ita ut R R, non manſerit linea abſolute recta, poſt-<lb/>quam axis P P capitulis impoſitus fuerat, ſed parum in formam ar-<lb/>cus incurvabatur, minus tamen, quam ut ope oculi, vel regulæ ob-<lb/>ſervari potuerit; </s> <s xml:id="echoid-s4471" xml:space="preserve">centrum gravitatis igitur parum deſcendit infra <lb/>axin, vel centrum motus P P. </s> <s xml:id="echoid-s4472" xml:space="preserve">cum hujuſmodi acus in obliquo ad <lb/>horizontem poſita ſitu non valebat ad menſurandam Magnetis Incli-<lb/>nationem, corpuſculum cupreum Q, vix eminens ſupra acum, ta-<lb/>men ſatis ponderoſum, impoſitum fuit tum medio acûs, tum axeos, <lb/>quo centrum gravitatis adſcendens, redibat ad medium axeos, & </s> <s xml:id="echoid-s4473" xml:space="preserve"><lb/>acus utcunque perficiebatur, nontamen exactiſſime, pro omni ſi-<lb/>tu, nam incurvatio maxima eſt poſita acu in ſitu horizontali, & </s> <s xml:id="echoid-s4474" xml:space="preserve"><lb/>minor in quocunque ſitu obliquo, minima in perpendiculari, ut <lb/>ex natura vectis facile intelligitur, huic defectui tamen obviam ivi-<lb/>mus annulis æneis tenuiſſimis ſupra brachia P R mobilibus, locan-<lb/>diſque in variis punctis: </s> <s xml:id="echoid-s4475" xml:space="preserve">multo autem melius eſt virgas denſas rigi-<lb/>daſque ſumſiſſe, quæ non inflectantur: </s> <s xml:id="echoid-s4476" xml:space="preserve">His præmiſſis ad experimen-<lb/>ta cum deſcriptis capta acubus pergamus.</s> <s xml:id="echoid-s4477" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div123" type="section" level="1" n="123"> <head xml:id="echoid-head132" xml:space="preserve">EXPERIMENTUM XCIX.</head> <p> <s xml:id="echoid-s4478" xml:space="preserve">Tabula AAA. </s> <s xml:id="echoid-s4479" xml:space="preserve">primum ita locata fuit, ut ſtaret in eodem plano <lb/>verticali, quod Verſorium horizontale & </s> <s xml:id="echoid-s4480" xml:space="preserve">vulgare determinabat; <lb/></s> <s xml:id="echoid-s4481" xml:space="preserve">tum Acus 4 pedum Inclinatoria ducta fuit ſupra polum Boreum Ma-<lb/>gnetis armati, ſecundum totam ſuam longitudinem, poſtquam vi <lb/>Magnetis imprægnata fuit, impoſita eſt excipulis M N in ſitu hori-<lb/>zontali; </s> <s xml:id="echoid-s4482" xml:space="preserve">illico cuſpis Boream ſpectans deprimebatur, atque ultra <lb/>perpendiculum D C eundo, rediit ſurſum, oſcillationes plurimas <lb/>penduli inſtar abſolvens, donec tandem quievit, tum vero inclina-<lb/>vit ſub horizonte Anno 1728. </s> <s xml:id="echoid-s4483" xml:space="preserve">Martii 23. </s> <s xml:id="echoid-s4484" xml:space="preserve">Trajecti Batavorum gra-<lb/>dibus 67. </s> <s xml:id="echoid-s4485" xml:space="preserve">Sæpius autem ex hoc ſitu turbata, ut obſervarem an con-<lb/>ſtans foret Inclinatio, Acus rediit ad gradus 67, aliquando tamen <pb o="193" file="0207" n="207" rhead="DE MAGNETE."/> ad 66, aliquando ad 68, aut ad Minuta diverſa inter gradus 66 & </s> <s xml:id="echoid-s4486" xml:space="preserve"><lb/>68 intermedia: </s> <s xml:id="echoid-s4487" xml:space="preserve">ſequenti die inclinationes conſpexi eaſdem, quæ <lb/>tamen plerumque 67 gradum ſignabant: </s> <s xml:id="echoid-s4488" xml:space="preserve">Has autem tanta cum cura ob-<lb/>ſervavi, ut nunquam in aliquo Experimento capiendo quis magis ſolli-<lb/>citus eſſe queat, aut majori curâ ad omnes circumſtantias, & </s> <s xml:id="echoid-s4489" xml:space="preserve">ad ferrum, <lb/>quod adeſſe poſſet, removendum, attendere. </s> <s xml:id="echoid-s4490" xml:space="preserve">Admiramur Acum eodem <lb/>die, & </s> <s xml:id="echoid-s4491" xml:space="preserve">fere eâdem horâ non æqualiter inclinaſſe, quod ab axeos minus <lb/>perfecta rotunditate, aut ab Acu non ſatis accurata pendere videretur, <lb/>ſed affirmare audeo vitium machinæ attribui non poſſe; </s> <s xml:id="echoid-s4492" xml:space="preserve">cum axis <lb/>chalybeus rotundus perfecte & </s> <s xml:id="echoid-s4493" xml:space="preserve">vitri ſuperficies politiſſima fuerit: <lb/></s> <s xml:id="echoid-s4494" xml:space="preserve">ſimiles inæquales Inclinationes Acus accuratiſſimæ unum pedem <lb/>longæ, obſervavit quoque artificioſiſſimus Grahamus, in Philoſoph. </s> <s xml:id="echoid-s4495" xml:space="preserve"><lb/>Tranſact. </s> <s xml:id="echoid-s4496" xml:space="preserve">N°. </s> <s xml:id="echoid-s4497" xml:space="preserve">389. </s> <s xml:id="echoid-s4498" xml:space="preserve">qui plurimas cum ſuâ Acu accuratiſſimas inſtituit <lb/>obſervationes, variis repetitas diebus, quarum nonnullas hic adne-<lb/>ctam. </s> <s xml:id="echoid-s4499" xml:space="preserve">A M. </s> <s xml:id="echoid-s4500" xml:space="preserve">notat ante Meridiem, P M. </s> <s xml:id="echoid-s4501" xml:space="preserve">poſt Meridiem.</s> <s xml:id="echoid-s4502" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # # # Anno 1723. Inclinatio. hora diei. <lb/># Gr. # M. <lb/>Martii 29 # 75 # 0 # 10 # 0 # AM. <lb/># 74 # 53 # 4 # 15 # PM. <lb/>30 # 74 # 55+ # 1 # 0 # PM. <lb/># 74 # 50 # 4 # 0 # PM. <lb/>Aprilis 1 # 74 # 25 # 6 # 45 # AM. <lb/># 74 # 20 # 9 # 0 <lb/>3 # 74 # 20 # 9 # 30 # AM. <lb/># 74 # 50 # 4 # 15 # PM. <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # # 1723. Inclinat. hora diei. <lb/># Gr. # M. <lb/>April 4 # 74 # 55 # 10 # 0 <lb/># 74 # 50 # 11 # 15 <lb/># 74 # 40 # 12 # 45 <lb/># 74 # 35 # 7 # 30 # PM. <lb/>5 # 74 # 40 # 9 # 15 # AM. <lb/># 74 # 30 # 8 # 15 # PM. <lb/>6 # 74 # 35 # 10 # 0 <lb/>7 # 74 # 35 # 10 # 20 <lb/>8 # 74 # 40 # 12 # 15 <lb/></note> <p> <s xml:id="echoid-s4503" xml:space="preserve">Multo autem plures loco citato conſpici poſſunt, hæ ſufficiunt inæ-<lb/>quali inclinationi Acus intra breviſſimum temporis ſpatium confirman-<lb/>dæ. </s> <s xml:id="echoid-s4504" xml:space="preserve">Eſt longiſſima noſtra AcusSS. </s> <s xml:id="echoid-s4505" xml:space="preserve">Tab. </s> <s xml:id="echoid-s4506" xml:space="preserve">8. </s> <s xml:id="echoid-s4507" xml:space="preserve">adeo lubricemobilis ſupra axin, <pb o="194" file="0208" n="208" rhead="DISSERTATIO"/> ut nunquam Minuti ſpatio quieſcat, ſed perpetuo motu & </s> <s xml:id="echoid-s4508" xml:space="preserve">oſcilla-<lb/>tionibus agitetur, non ab aëris motu pendentibus, verum a ſuâ vir-<lb/>tute Magnetica.</s> <s xml:id="echoid-s4509" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div124" type="section" level="1" n="124"> <head xml:id="echoid-head133" xml:space="preserve">EXPERIMENTUM. C.</head> <p> <s xml:id="echoid-s4510" xml:space="preserve">Acus Inclinatoriæ diverſæ longitudinis etiam varia Inclinatione <lb/>aguntur eodem tempore & </s> <s xml:id="echoid-s4511" xml:space="preserve">in eodem loco, poſitæ in Meridiano <lb/>Magnetico.</s> <s xml:id="echoid-s4512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4513" xml:space="preserve">Memoravi Acum noſtram 48 pollices longam inclinaſſe gradibus <lb/>67 plerumque; </s> <s xml:id="echoid-s4514" xml:space="preserve">alia eſt mihi Acus, vid. </s> <s xml:id="echoid-s4515" xml:space="preserve">Tab. </s> <s xml:id="echoid-s4516" xml:space="preserve">8. </s> <s xml:id="echoid-s4517" xml:space="preserve">R R Cylindrica, <lb/>utrimque tamen in cuſpidem deſinens, 42 pollices longa, ſupra <lb/>cujus axem PP exiguus proſtat ſtylus, conſervans centrum gravita-<lb/>tis aliquomodo in axe, quia acûs ambæ extremitates R R ſua gra-<lb/>vitate parum perpendent; </s> <s xml:id="echoid-s4518" xml:space="preserve">hæc Acus ſupra eundem polum Magnetis <lb/>ducta, excipuliſque N M impoſita, inclinavit 72 gradibus plerum-<lb/>que, differentia enim diverſarum Inclinationum intra gradum manſit. <lb/></s> <s xml:id="echoid-s4519" xml:space="preserve">tum tertiam Acum duos pedes longam, eidem Magnetis polo affri-<lb/>ctam, obſervavi inclinaſſe 60 gradibus plerumque, nam nunc 59, <lb/>nunc 61, nunc gradum intermedium aut aliquod Minutum indica-<lb/>bat.</s> <s xml:id="echoid-s4520" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4521" xml:space="preserve">Ejuſmodi eventus acuum variæ longitudinis adnotavit etiam Whi-<lb/>ſtonus, qui in uſum vocans Acum unius pedis, Londini Inclinatio-<lb/>nem 73°, 45? </s> <s xml:id="echoid-s4522" xml:space="preserve">deprehendit, quam ope alterius 4 pedes longæ 75°, <lb/>10? </s> <s xml:id="echoid-s4523" xml:space="preserve">obſervavit: </s> <s xml:id="echoid-s4524" xml:space="preserve">imo Grahamus Acu unius pedis uſus Inclinationem <lb/>74, vel 75 grad. </s> <s xml:id="echoid-s4525" xml:space="preserve">adnotavit, aut aliquot Minutorum inter hos am-<lb/>bos intermediorum.</s> <s xml:id="echoid-s4526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4527" xml:space="preserve">Præcedenti Experimento XCIX, indicante variam Inclinatio-<lb/>nemAcus eodem die, & </s> <s xml:id="echoid-s4528" xml:space="preserve">hoc centeſimo diverſarum Acuum etiam diver-<lb/>fam Inclinationem eſſe oſtendente, liquet, antiquorum obſervationes <lb/>circa Inclinationem non eſſe magni uſus, quia ad has anomalias <lb/>non accurate attenderunt, nec longitudinem ſuarum Acuum adno-<lb/>taverunt. </s> <s xml:id="echoid-s4529" xml:space="preserve">Londini Anno 1576 Normannus Inclinationem ponit 71°, <lb/>50?</s> <s xml:id="echoid-s4530" xml:space="preserve">. Gilbertus ſua ætate eam ſtatuit 72 grad. </s> <s xml:id="echoid-s4531" xml:space="preserve">Ridleyus Anno 1613 <lb/>inter 72 & </s> <s xml:id="echoid-s4532" xml:space="preserve">73 grad. </s> <s xml:id="echoid-s4533" xml:space="preserve">obſervavit in Magnetic Motions C. </s> <s xml:id="echoid-s4534" xml:space="preserve">35, 39, 40. <lb/></s> <s xml:id="echoid-s4535" xml:space="preserve">Bondius Anno 1676 grad. </s> <s xml:id="echoid-s4536" xml:space="preserve">73°, 30?</s> <s xml:id="echoid-s4537" xml:space="preserve">, Whiſtonus Anno 1720 grad.</s> <s xml:id="echoid-s4538" xml:space="preserve"> <pb o="195" file="0209" n="209" rhead="DE MAGNETE."/> 73°, 45?</s> <s xml:id="echoid-s4539" xml:space="preserve">. Sed his omnibus ſides haberi nequit, niſi longitudo <lb/>Acus, quæ Experimento inſerviit adnotaretur; </s> <s xml:id="echoid-s4540" xml:space="preserve">cæteroquin ex hiſ-<lb/>ce obſervationibus colligi poſſet, a tempore Normanni uſque ad <lb/>hodiernum Inclinationem Acus increviſſe; </s> <s xml:id="echoid-s4541" xml:space="preserve">antequam tamen hoc <lb/>verum eſſe aſſeratur, in eodem Terræloco cum eadem Acu per pluri-<lb/>mos annos obſervationes capiendæ adhuc erunt: </s> <s xml:id="echoid-s4542" xml:space="preserve">Inclinationem autem <lb/>ſingulis mutari annis probabile reddit Declinationum mutatio, ſed <lb/>præſtat exſpectare, & </s> <s xml:id="echoid-s4543" xml:space="preserve">videre quomodo ipſa Natura operetur, obſer-<lb/>vationes enim ſibi oppoſitas, tam quæ Inclinationem increſcere, <lb/>quam decreſcere tempore monſtrarent, poſſidemus. </s> <s xml:id="echoid-s4544" xml:space="preserve">Nam Feuilleè <lb/>in urbe Americæ Coquimbo memoravit Inclinationem fuiſſe graduum <lb/>47 & </s> <s xml:id="echoid-s4545" xml:space="preserve">20 Minutorum, & </s> <s xml:id="echoid-s4546" xml:space="preserve">aliquantum poſt fuiſſe ibidem 47°, 30?</s> <s xml:id="echoid-s4547" xml:space="preserve">. ad-<lb/>eoque increviſſet Inclinatio, verum Grahamus ope ſuæ accuratiſſi-<lb/>mæ Acus Anno 1723, Martii 29. </s> <s xml:id="echoid-s4548" xml:space="preserve">Inclinationem notavit 75°, aut <lb/>74°, 53?</s> <s xml:id="echoid-s4549" xml:space="preserve">. & </s> <s xml:id="echoid-s4550" xml:space="preserve">27. </s> <s xml:id="echoid-s4551" xml:space="preserve">Maji 74°, 50?</s> <s xml:id="echoid-s4552" xml:space="preserve">. adeoque decreviſſet intermedio <lb/>tempore; </s> <s xml:id="echoid-s4553" xml:space="preserve">hanc poſteritas litem dirimet, uſura obſervationibus, quas <lb/>diligentes accuratique hujus & </s> <s xml:id="echoid-s4554" xml:space="preserve">ſequentium ſeculorum Phyſicæ cul-<lb/>tores accumulabunt.</s> <s xml:id="echoid-s4555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4556" xml:space="preserve">Poſtquam cognoveram Acus variæ longitudinis diverſimode in-<lb/>clinare, intelligere incepi obſervationes, quas Noëllius, Poundiuſ-<lb/>que per Mare Æthyopicum & </s> <s xml:id="echoid-s4557" xml:space="preserve">Indicum navigantes, inſtituerunt, <lb/>eas enim inter ſe comparans, tantam deprehendi differentiam, ut <lb/>conciliare ſecum invicem nequaquam potuerim; </s> <s xml:id="echoid-s4558" xml:space="preserve">fuerunt nempe hi <lb/>obſervatores uſi variæ longitudinis Acu, & </s> <s xml:id="echoid-s4559" xml:space="preserve">plus minuſve accurate <lb/>elaboratâ: </s> <s xml:id="echoid-s4560" xml:space="preserve">Quanta enim non intercedit differentia inter Inclinatio-<lb/>nes noſtrarum Acuum, unâ inclinante 72 gradibus, alterâ tantum <lb/>60? </s> <s xml:id="echoid-s4561" xml:space="preserve">quare non poteſt non ſumma obſervari Inclinationum diſcre-<lb/>pantia a variis Autoribus, uſis Acubus diverſis.</s> <s xml:id="echoid-s4562" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div125" type="section" level="1" n="125"> <head xml:id="echoid-head134" xml:space="preserve">EXPERIMENTUM CI.</head> <p> <s xml:id="echoid-s4563" xml:space="preserve">Auſtrali Extremitati Acus Inclinatoriæ 4 pedum impoſitum fuit <lb/>pondus 1 {1/2} grani, quo rediit in ſitum horizontalem; </s> <s xml:id="echoid-s4564" xml:space="preserve">tota hujus A-<lb/>cus gravitas eſt 6105 granorum. </s> <s xml:id="echoid-s4565" xml:space="preserve">Hoc etiam obſervavit Whiſtonus, <lb/>Acus enim 4 pedum, quæ Londini 75 gradibus 10 Minutis incli-<lb/>nabat, erat ponderis 4012 {3/8} granorum, hæc in æquilibrium, ſive <lb/>horizontalem ſitum redibat appenſo 1 {1/3} grano: </s> <s xml:id="echoid-s4566" xml:space="preserve">alia Acus ponde- <pb o="196" file="0210" n="210" rhead="DISSERTATIO"/> ris 4582 {1/8} granorum horizonti parallela fiebat impoſito grano 1 {1/4}.</s> <s xml:id="echoid-s4567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4568" xml:space="preserve">Ex quibus concludimus vim Magneticam directricem non eſſe <lb/>magnam, cæteroquin plus ponderis extremitati Auſtrali Acus ap-<lb/>ponendum fuiſſet ad ſitum horizontalem reſtituendum.</s> <s xml:id="echoid-s4569" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div126" type="section" level="1" n="126"> <head xml:id="echoid-head135" xml:space="preserve">EXPERIMENTUM CII.</head> <p> <s xml:id="echoid-s4570" xml:space="preserve">Acus Inclinatoria ſuis impoſita excipulis, oſcillationibus agitur, <lb/>ſurſum deorſumque circa punctum quietis eundo, haud aliter ac pen-<lb/>dulum horologii adſcendit deſcenditque in vibrationes concitatum. <lb/></s> <s xml:id="echoid-s4571" xml:space="preserve">Quoniam ex Oſcillationibus Acûs, Magnitudo virtutis directricis <lb/>Magneticæ cognoſci & </s> <s xml:id="echoid-s4572" xml:space="preserve">cum gravitate comparari poſſe videbatur, <lb/>oportebat ut ad tempus in ſingulâ impenſum oſcillatione accurate <lb/>attenderetur.</s> <s xml:id="echoid-s4573" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4574" xml:space="preserve">Acus Inclinatoria longiſſima 4 pedum ita directa fuit, ut in Me-<lb/>ridiano Magnetico vibraretur, comparato pendulo, cujus oſcilla-<lb/>tiones Minuto ſecundo abſolvebantur, Acus dimiſſa fuit ex loco 5 <lb/>gradibus altiore quam punctum quietis erat, adeo ut arcum 10 gra-<lb/>duum in initio deſcriberet, decem primæ vibrationes Acus peractæ <lb/>fuerunt in tribus Minutis & </s> <s xml:id="echoid-s4575" xml:space="preserve">32 ſecundis: </s> <s xml:id="echoid-s4576" xml:space="preserve">decem ſequentes in tribus <lb/>Minutis & </s> <s xml:id="echoid-s4577" xml:space="preserve">12 ſecundis, decem ſequentes in duobus Minutis & </s> <s xml:id="echoid-s4578" xml:space="preserve">54 <lb/>ſecundis: </s> <s xml:id="echoid-s4579" xml:space="preserve">hæc obſervavi Anno 1728, Martii 26. </s> <s xml:id="echoid-s4580" xml:space="preserve">Ex quibus con-<lb/>ſtat eo breviori tempore oſcillationes abſolvi, quo arcum minorem <lb/>deſcribit Acus; </s> <s xml:id="echoid-s4581" xml:space="preserve">hoc alia omnia tentamina cum diverſis acubus facta <lb/>conſirmarunt: </s> <s xml:id="echoid-s4582" xml:space="preserve">Acu enim Inclinatoriâ 42 pollic. </s> <s xml:id="echoid-s4583" xml:space="preserve">etiam in arcubus <lb/>10 grad. </s> <s xml:id="echoid-s4584" xml:space="preserve">oſcillante, 10 primæ vibrationes poſtularunt tempus 2?</s> <s xml:id="echoid-s4585" xml:space="preserve">, <lb/>44?</s> <s xml:id="echoid-s4586" xml:space="preserve">, & </s> <s xml:id="echoid-s4587" xml:space="preserve">decem aliis adhuc peractis fuit totum elapſum tempus 4?</s> <s xml:id="echoid-s4588" xml:space="preserve">, <lb/>45?</s> <s xml:id="echoid-s4589" xml:space="preserve">. Acu Inclinatoriâ 2 pedes longa oſcillante in arcu 10 grad. </s> <s xml:id="echoid-s4590" xml:space="preserve">de-<lb/>cem primæ oſcillationes peractæ fuerunt 1?</s> <s xml:id="echoid-s4591" xml:space="preserve">, 45?</s> <s xml:id="echoid-s4592" xml:space="preserve">, oſcillationibus de-<lb/>cem ſequentibus abſolutis totum tempus impenſum fuit 2?</s> <s xml:id="echoid-s4593" xml:space="preserve">, 15?</s> <s xml:id="echoid-s4594" xml:space="preserve">. idem <lb/>obſervavit etiam Grahamus in Philoſ. </s> <s xml:id="echoid-s4595" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s4596" xml:space="preserve">N°. </s> <s xml:id="echoid-s4597" xml:space="preserve">389, atque plu-<lb/>rimis probavit Experimentis, quæ cum Acu unum pedem longa fe-<lb/>cit, & </s> <s xml:id="echoid-s4598" xml:space="preserve">quæ hic apponenda ſunt, quia ex iis patet vibrationes varia <lb/>velocitate peragi diebus diverſis, atque eas fere nunquam inter ſe <lb/>congruere; </s> <s xml:id="echoid-s4599" xml:space="preserve">Unde colligimus vim Magnetis directricem non ſemper <lb/>æqualem eſſe; </s> <s xml:id="echoid-s4600" xml:space="preserve">quia gravitas corporum terreſtrium manet conſtans <pb o="197" file="0211" n="211" rhead="DE MAGNETE."/> & </s> <s xml:id="echoid-s4601" xml:space="preserve">æquabilis, pendula æque longa in eadem Terræ regione ſemper <lb/>æque velociter eoſdem circulorum arcus deſcribunt; </s> <s xml:id="echoid-s4602" xml:space="preserve">ſi gravitas au-<lb/>geretur nonnunquam, & </s> <s xml:id="echoid-s4603" xml:space="preserve">alia tempeſtate decreſceret, admodum <lb/>inæquali velocitate pendula concitarentur; </s> <s xml:id="echoid-s4604" xml:space="preserve">pendula igitur Magneti-<lb/>ca, ita enim Acus Magneticas vocare licet, vi admodum inæqua-<lb/>li agentur, majori quando velocius deſcribunt arcus ſuos, minori <lb/>cum lentius decurrunt per æqualia ſpatia: </s> <s xml:id="echoid-s4605" xml:space="preserve">Congruit hæc obſervatio, <lb/>cum iis quæ in capite ſecundo memoravimus, vim Magnetis non <lb/>ſemper ad elevandum Ferrum eandem eſſe, tum eam aliquando ex-<lb/>porrigi ad diſtantiam duplo vel triplo majorem, uti eſſectus in idem <lb/>Verſorium evincunt.</s> <s xml:id="echoid-s4606" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4607" xml:space="preserve">Ecce Grahami accuratiſſima Experimenta, cum Acu Inclinatoria <lb/>capta, oſcillationem incipiente in arcu 10 graduum.</s> <s xml:id="echoid-s4608" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>1723. # # Vibrationes. # # Tempus. <lb/># # # M. # Sec. <lb/>April. # 1. # primæ 50 # 3? # 2? <lb/># # ultimæ 50 # 2 # 45 <lb/># 2. # primæ 50 # 3 # 3 <lb/># # ultimæ 50 # 2 # 43 <lb/># 3. # primæ 50 # 2 # 52 <lb/># # ultimæ 50 # 2 # 39 <lb/># # eodem die # primæ 50 # 2 # 53 <lb/># # elapſâ horâ <lb/># # ultimæ 50 # 2 # 35 <lb/># 4. # primæ 50 # 2 # 54 <lb/># # ultimæ 50 # 2 # 30 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # Vibrationes. # # Tempus. <lb/># # # Min. # Sec. <lb/>April. # 28. # primæ 50 # 2 # 48 <lb/># # ultimæ 50 # 2 # 16 <lb/># # eodem die # primæ 50 # 2 # 47 <lb/># # ultimæ 50 # 2 # 16 <lb/>Maji # 20. # primæ 50 # 3 # 11 <lb/># # ultimæ 50 # 3 # 1 <lb/># # # # # Acu denuo ſuper Magnete ducta. <lb/># # primæ 50 # 2 # 38 <lb/># # ultimæ 50 # 2 # 23 <lb/># # eodem die # primæ 50 # 2 # 38 <lb/># # elapſa horâ <lb/># # ultimæ 50 # 2 # 20 <lb/></note> <pb o="198" file="0212" n="212" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Maji. # 21. # primæ 50 # 2 # 41 <lb/># # ultimæ 50 # 2 # 28 <lb/># 23. # primæ 50 # 2 # 40 <lb/># # ultimæ 50 # 2 # 27 <lb/></note> <note position="right" xml:space="preserve"> <lb/># 25. # primæ 50 # 2 # 41 <lb/># # ultimæ 50 # 2 # 30 <lb/># 27. # primæ 50 # 2 # 41 <lb/># # ultimæ 50 # 2 # 28 <lb/></note> <p> <s xml:id="echoid-s4609" xml:space="preserve">Intuiti prima fronte hæc Experimenta ſuſpicaremur Aëris rarita-<lb/>tem majorem minoremve variis diebus, plus minuſve reſiſtere oſcil-<lb/>lanti Acui, & </s> <s xml:id="echoid-s4610" xml:space="preserve">ideo eam varia velocitate arcus ſuos abſolvere, ve-<lb/>rum tanta raritatis, & </s> <s xml:id="echoid-s4611" xml:space="preserve">proinde reſiſtentiæ, differentia in aëre non <lb/>obtinet horæ intervallo, ut inde in oſcillationibus adeo notabilis <lb/>diverſitas oriatur, quæ obtinuit in Experimentis tertio Aprilis & </s> <s xml:id="echoid-s4612" xml:space="preserve"><lb/>Vigeſimo Maji captis: </s> <s xml:id="echoid-s4613" xml:space="preserve">An inde non ſequitur vim Magnetis omni <lb/>fere temporis minuto eſſe diverſam, nunc majorem, ſequenti mo-<lb/>mento autem minorem abſque ordine ullo? </s> <s xml:id="echoid-s4614" xml:space="preserve">Hoc colligo ulterius ex <lb/>aliis Experimentis, quum enim Acus primas oſcillationes 50 abſol-<lb/>vit intra determinatum tempus, & </s> <s xml:id="echoid-s4615" xml:space="preserve">ſecundas 50 etiam intra aliud, <lb/>ſed determinatum tempus; </s> <s xml:id="echoid-s4616" xml:space="preserve">an non deberet ſemper ultimas 50 vi-<lb/>brationes deſcribere intra idem tempus, deſcriptis 50 primis in tem-<lb/>poribus æqualibus, & </s> <s xml:id="echoid-s4617" xml:space="preserve">poſita vi Magnetica aliquamdiu conſtanti, <lb/>verum ea perpetuo variante etiam ultimæ 50 vibrationes brevius <lb/>longiuſve tempus poſtulabunt: </s> <s xml:id="echoid-s4618" xml:space="preserve">Ecce Vigeſimo Maji in duobus ul-<lb/>timis tentaminibus, primæ 50 Vibrationes peractæ ſunt 2?</s> <s xml:id="echoid-s4619" xml:space="preserve">, 38?</s> <s xml:id="echoid-s4620" xml:space="preserve">. ſed <lb/>ultimæ 50 in medio tentamine abſolvebantur 2?</s> <s xml:id="echoid-s4621" xml:space="preserve">, 2?</s> <s xml:id="echoid-s4622" xml:space="preserve">, & </s> <s xml:id="echoid-s4623" xml:space="preserve">ultimæ 50 <lb/>in poſtremo tentamine peragebantur 2?</s> <s xml:id="echoid-s4624" xml:space="preserve">, 20?</s> <s xml:id="echoid-s4625" xml:space="preserve">. Ita comparemus ten-<lb/>tamina inſtituta Maji 21 & </s> <s xml:id="echoid-s4626" xml:space="preserve">25. </s> <s xml:id="echoid-s4627" xml:space="preserve">ubi primæ 50 Vibrationes abſolu-<lb/>tæ ſunt 2?</s> <s xml:id="echoid-s4628" xml:space="preserve">, 41?</s> <s xml:id="echoid-s4629" xml:space="preserve">. ſed 50 ultimæ in primo tentamine 2?</s> <s xml:id="echoid-s4630" xml:space="preserve">, 48?</s> <s xml:id="echoid-s4631" xml:space="preserve">. & </s> <s xml:id="echoid-s4632" xml:space="preserve">50 <lb/>ultimæ in poſtremo tentamine 2?</s> <s xml:id="echoid-s4633" xml:space="preserve">, 30?</s> <s xml:id="echoid-s4634" xml:space="preserve">. In hac ſententia me conſir-<lb/>maverunt plurima alia Experimenta cum Magnete capta; </s> <s xml:id="echoid-s4635" xml:space="preserve">Magnetis <lb/>Declinatio ope longæ Acus explorata, perpetuo mutatur, veluti <lb/>ſupra in Exp. </s> <s xml:id="echoid-s4636" xml:space="preserve">XC. </s> <s xml:id="echoid-s4637" xml:space="preserve">oſtendimus: </s> <s xml:id="echoid-s4638" xml:space="preserve">Inclinatio Acus fere nunquam <lb/>eſt eadem, licet uno die 10 tentamina inſtituantur; </s> <s xml:id="echoid-s4639" xml:space="preserve">quæ modo me-<lb/>moratis addita obſervationibus, luce Meridiana clarius evincunt, <lb/>perpetuis mutationibus vim Magneticam eſſe obnoxiam, ſive di-<lb/>rectionem, ſive virium magnitudinem ſpectemus. </s> <s xml:id="echoid-s4640" xml:space="preserve">Hoc forſitan cauſa <pb o="199" file="0213" n="213" rhead="DE MAGNETE."/> quoque fuit, cur conſtantem proportionem virium Magneticarum <lb/>ſe attrahentium, in Capite primo & </s> <s xml:id="echoid-s4641" xml:space="preserve">ſecundo invenire non potuerim, <lb/>quia veroſimile eſt eandem inconſtantiam in viribus attractricibus da-<lb/>ri, quæ in directricibus obſervatur.</s> <s xml:id="echoid-s4642" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4643" xml:space="preserve">Omnis proinde virtutis Magneticæ comparatio cum gravitate non <lb/>magni momenti exiſtit, quippe hoc temporis minuto cum gravitate <lb/>hanc faciat proportionem, ſequenti minuto in alia iterum cum ipſa <lb/>erit.</s> <s xml:id="echoid-s4644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4645" xml:space="preserve">Jucundum tamen & </s> <s xml:id="echoid-s4646" xml:space="preserve">utile erit aliquid determinaſſe, quod etiamſi <lb/>non ſemper ſit verum, erit tamen vero proximum. </s> <s xml:id="echoid-s4647" xml:space="preserve">Ponamus igi-<lb/>tur Acum, unum pedem longam, oſcillationem unam quoque ab-<lb/>ſolvere tempore 330 Minutorum tertiorum, idenim tempusplerum-<lb/>que impendi obſervatum fuit; </s> <s xml:id="echoid-s4648" xml:space="preserve">oportebit in memoriam revocare do-<lb/>ctrinam pendulorum a nonnullis eximiis Philoſophis, Hugenio, <lb/>s’Gravezandio, aliisque egregie explicatam; </s> <s xml:id="echoid-s4649" xml:space="preserve">quam demonſtratam <lb/>ſupponere licebit, uti 1°. </s> <s xml:id="echoid-s4650" xml:space="preserve">Pendulum, cujus longitudo eſt 39 {2/10} poll. <lb/></s> <s xml:id="echoid-s4651" xml:space="preserve">Britt. </s> <s xml:id="echoid-s4652" xml:space="preserve">vi gravitatis unam oſcillationem abſolvere intra 60 Minuta <lb/>tertia. </s> <s xml:id="echoid-s4653" xml:space="preserve">2°. </s> <s xml:id="echoid-s4654" xml:space="preserve">Pendulum, cujus longitudo eſt 4 pollicum, oſcillatio-<lb/>nem unam perficere intra 19 {2/10} Minuta tertia, quia longitudines pen-<lb/>dulorum ſunt in duplicata ratione Temporum quibus oſcillationes <lb/>peraguntur. </s> <s xml:id="echoid-s4655" xml:space="preserve">3°. </s> <s xml:id="echoid-s4656" xml:space="preserve">Pendulum, quod eſt cylindrus, priſma, vel paral-<lb/>lelopipedum, habere centrum oſcillationis ad {2/3} ſuæ longitudinis, <lb/>adeoque penduli cylindrici 6 pollicum oſcillationis centrum eſſe ad <lb/>diſtantiam 4 pollicum a puncto ſuſpenſionis, hinc eſſe Iſochronon <lb/>cum pendulo 4 pollices longo, & </s> <s xml:id="echoid-s4657" xml:space="preserve">ſemel vibrari in 19``` {2/10}. </s> <s xml:id="echoid-s4658" xml:space="preserve">4°. </s> <s xml:id="echoid-s4659" xml:space="preserve">Si <lb/>dentur duo pendula, quorum longitudines ſint interſe, ut viresgra-<lb/>vitatis, quibus aguntur, oſcillationes eſſe æque diuturnas. </s> <s xml:id="echoid-s4660" xml:space="preserve">5°. </s> <s xml:id="echoid-s4661" xml:space="preserve">Et <lb/>ſi hæc ambo ad eandem reducantur longitudinem, eſſe durationes <lb/>oſcillationum in ratione ſubduplicata inverſa gravitatum: </s> <s xml:id="echoid-s4662" xml:space="preserve">quæ omnia <lb/>tironibus ſunt nota. </s> <s xml:id="echoid-s4663" xml:space="preserve">Loco diverſarum virium gravitatis, pona-<lb/>mus vim directricem, quia hæc eadem operatur in Acum Inclina-<lb/>toriam, quam vis gravitatis, adeoque ſecundum memoratas pro-<lb/>poſitiones formabitur hæc proportio: </s> <s xml:id="echoid-s4664" xml:space="preserve">uti 330 Minuta tertia impenſa <lb/>in oſcillatione Acus, ad 19 {2/10} Minuta tertia impenſa a pendulo, 6 <lb/>pollicum, ſed cylindrico, hoc eſt æque longo cum dimidia Acu, <lb/>ita eſt radix quadrata gravitatis, ad radicem quadratam virtutis di- <pb o="200" file="0214" n="214" rhead="DISSERTATIO"/> rectricis Magneticæ, quæ ſtant hoc modo</s> </p> <p> <s xml:id="echoid-s4665" xml:space="preserve">330```. </s> <s xml:id="echoid-s4666" xml:space="preserve">ad 19``` {2/10}:</s> <s xml:id="echoid-s4667" xml:space="preserve">: ?</s> <s xml:id="echoid-s4668" xml:space="preserve">gravitatis, ?</s> <s xml:id="echoid-s4669" xml:space="preserve">virtutis directricis. </s> <s xml:id="echoid-s4670" xml:space="preserve">Ut ſigna <lb/>radicalia tollantur, capiantur numerorum quadrata, quæ ſunt, <lb/>10890000, & </s> <s xml:id="echoid-s4671" xml:space="preserve">36864. </s> <s xml:id="echoid-s4672" xml:space="preserve">hæc ſunt inter ſe, uti 295 {15120/36864} ad 1. </s> <s xml:id="echoid-s4673" xml:space="preserve">quæ <lb/>exprimunt vires gravitatis & </s> <s xml:id="echoid-s4674" xml:space="preserve">directrices Magneticas: </s> <s xml:id="echoid-s4675" xml:space="preserve">quare ponere <lb/>licebit vim gravitatis eſſe ad vim Magneticam directricem ſuper Acu 6 <lb/>pollicum, uti 295 ad 1. </s> <s xml:id="echoid-s4676" xml:space="preserve">Eodem modo poteſt ſubduci vis directrix <lb/>ſuper Acu 4 pollicum, & </s> <s xml:id="echoid-s4677" xml:space="preserve">cum gravitate comparari. </s> <s xml:id="echoid-s4678" xml:space="preserve">Obſervat Whiſto-<lb/>nus Acum Inclinatoriam 4 pedum ſuas vibrationes minimas, proin-<lb/>de æquidiuturnas, abſolvere intra 22 Minuta ſecunda, velocius ſuas <lb/>abſolvit noſtra Acus, ſed poſitâ ea velocitate, erit visgravitatis ad <lb/>vim directricem Magneticam uti 600 ad 1 proxime.</s> <s xml:id="echoid-s4679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4680" xml:space="preserve">Ecce iterum miram virtutis directricis proprietatem, qua minus <lb/>agat in Acus ferreas longiſſimas, magis in breviores: </s> <s xml:id="echoid-s4681" xml:space="preserve">ita tamen vis <lb/>attractrix quoque comparata eſt, quæ proportionaliter major eſt in <lb/>minoribus quam in grandioribus Magnetibus.</s> <s xml:id="echoid-s4682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4683" xml:space="preserve">Corol. </s> <s xml:id="echoid-s4684" xml:space="preserve">1. </s> <s xml:id="echoid-s4685" xml:space="preserve">Ponamus Acum pedalem actam fuiſſe vi directrice, <lb/>quæ ſit ad gravitatem uti 1 ad 300, & </s> <s xml:id="echoid-s4686" xml:space="preserve">Acum 4 pedum actam vi di-<lb/>rectrice, quæ ſit reſpectu gravitatis, uti 1 ad 600, erit vis directrix <lb/>in utraque Acu, in ratione ſubduplicata longitudinum Acuum reci-<lb/>procê. </s> <s xml:id="echoid-s4687" xml:space="preserve">Nam ſunt longitudines 1, 4, & </s> <s xml:id="echoid-s4688" xml:space="preserve">vires directrices 2, 1.</s> <s xml:id="echoid-s4689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4690" xml:space="preserve">Corol. </s> <s xml:id="echoid-s4691" xml:space="preserve">2. </s> <s xml:id="echoid-s4692" xml:space="preserve">Et ſunt tempora oſcillationum uti longitudines Acuum, <lb/>poſito enim tempore 5 {1/2} Minutorum ſecundorum, quibus ſemel oſcil-<lb/>lat Acus unius pedis, & </s> <s xml:id="echoid-s4693" xml:space="preserve">22 Minutis ſecundis, quibus oſcillat Acus <lb/>4 pedum, ſunt 5 {1/2} ad 22:</s> <s xml:id="echoid-s4694" xml:space="preserve">: 1, 4. </s> <s xml:id="echoid-s4695" xml:space="preserve">hæc omnia erunt modo proxime <lb/>vera, quia oſcillationum tempora non ſunt æqualia: </s> <s xml:id="echoid-s4696" xml:space="preserve">Præterea du-<lb/>bito an hæc regula vera ſit, quoniam inſtitutis Experimentis cum <lb/>Acubus horizontalibus deprehendi, quadrata Temporum ab oſcilla-<lb/>tionibus impenſorum eſſe in ratione compoſita, ex directa longitu-<lb/>dinis & </s> <s xml:id="echoid-s4697" xml:space="preserve">gravitatis Acuum.</s> <s xml:id="echoid-s4698" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div127" type="section" level="1" n="127"> <head xml:id="echoid-head136" xml:space="preserve">EXPERIMENTUM. CIII.</head> <p> <s xml:id="echoid-s4699" xml:space="preserve">Acum Inclinatoriam in præcedenti Experimento poſuimus, ut <lb/>oſcillaret in Meridiano Magnetico; </s> <s xml:id="echoid-s4700" xml:space="preserve">nunc immutato Machinæ Tab. <lb/></s> <s xml:id="echoid-s4701" xml:space="preserve">8. </s> <s xml:id="echoid-s4702" xml:space="preserve">Situ, ita Acum direximus, ut oſcillaret in plano ad angulos re- <pb o="201" file="0215" n="215" rhead="DE MAGNETE."/> ctos Meridianum ſecante; </s> <s xml:id="echoid-s4703" xml:space="preserve">ceſſantibus oſcillationibus cuſpis Acus <lb/>deorſum ſpectans, & </s> <s xml:id="echoid-s4704" xml:space="preserve">ad Orientem converſa, quieſcebat in gradu <lb/>84, cum antea in 67°. </s> <s xml:id="echoid-s4705" xml:space="preserve">ſteterat.</s> <s xml:id="echoid-s4706" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4707" xml:space="preserve">Ex hoc ſitu iterum fuit turbata, ut oſcillando arcum decem gra-<lb/>duum deſcriberet, primas 10 vibrationes abſolvit tempore 4?</s> <s xml:id="echoid-s4708" xml:space="preserve">, 43?</s> <s xml:id="echoid-s4709" xml:space="preserve">. <lb/>peractis adhuc 10 aliis vibrationibus tempus 9 Minutorum elapſum <lb/>fuit; </s> <s xml:id="echoid-s4710" xml:space="preserve">hæc inſtituta ſunt cum acu 4 pedum: </s> <s xml:id="echoid-s4711" xml:space="preserve">multo lentius peractæ <lb/>hæ vibrationes, quam in Meridiano Magnetico, demonſtrant po-<lb/>tentiam moventem fuiſſe imbecilliorem, aſt quantum, ex ſequen-<lb/>ti patebit propoſitione Whiſtoni.</s> <s xml:id="echoid-s4712" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s4713" xml:space="preserve">Quantitas potentiæ Magneticæ accelerantis eandem Acum Incli-<lb/>natoriam, oſcillantem in variis planis verticalibus, eſt ſemper ut <lb/>Coſinus angulorum factorum ab his planis & </s> <s xml:id="echoid-s4714" xml:space="preserve">Meridiano Magnetico, <lb/>ſumto ſupra horizontem.</s> <s xml:id="echoid-s4715" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4716" xml:space="preserve">Tab. </s> <s xml:id="echoid-s4717" xml:space="preserve">3. </s> <s xml:id="echoid-s4718" xml:space="preserve">fig. </s> <s xml:id="echoid-s4719" xml:space="preserve">4. </s> <s xml:id="echoid-s4720" xml:space="preserve">Repræſentet A I maximam potentiam in Meri-<lb/>diano Magnetico, ſitque circuli radius.</s> <s xml:id="echoid-s4721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4722" xml:space="preserve">Sit A punctum, ubi Acus Inclinatoria ſecat horizontem, cum <lb/>ad ipſum eſt perpendicularis, & </s> <s xml:id="echoid-s4723" xml:space="preserve">vibretur ſecundum Tangentem <lb/>A B. </s> <s xml:id="echoid-s4724" xml:space="preserve">Sit I punctum in lineâ Sinuum applicatorum circulo, ubi ea-<lb/>dem Acus ſuſpenſa ex eodem centro ſecat horizontem in propriâ <lb/>Inclinatione ſecundum Meridianum Magneticum: </s> <s xml:id="echoid-s4725" xml:space="preserve">Ex A ducantur <lb/>Chordæ quæcunque A C, A D, A E, A F, A G, quæ hic ſub-<lb/>tenduntur arcubus ſeſe 15 gradibus ſuperantibus: </s> <s xml:id="echoid-s4726" xml:space="preserve">ex puncto I ducan-<lb/>tur perpendiculares in has Chordas, quæ ſint I g, I f, I e, I d, <lb/>I c. </s> <s xml:id="echoid-s4727" xml:space="preserve">quæ abſcindant partes Chordarum A c, A d, A e, A f, A g, <lb/>ſunt hæ abſciſſæ Coſinus angulorum factorum â Lineâ A I maximæ <lb/>potentiæ, & </s> <s xml:id="echoid-s4728" xml:space="preserve">ſingulorum planorum A C, A D, A E, A F, A G.</s> <s xml:id="echoid-s4729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4730" xml:space="preserve">Quia igitur vis A I, ex doctrinâ compoſitionis & </s> <s xml:id="echoid-s4731" xml:space="preserve">reſolutionis <lb/>motus, reſolvitur in A g + g I, vel in A f + f I, vel in A e + e I, <lb/>vel in A d + d I. </s> <s xml:id="echoid-s4732" xml:space="preserve">vel in A c + c I, erit vis, qua acceleratur Acus <lb/>Inclinatoria in quolibet plano, ut hi Coſinus.</s> <s xml:id="echoid-s4733" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4734" xml:space="preserve">Corol. </s> <s xml:id="echoid-s4735" xml:space="preserve">1. </s> <s xml:id="echoid-s4736" xml:space="preserve">Quia adſcenſus Acus Inclinatoriæ capti â puncto Nadir <lb/>A juxta circulum Acus, neceſiario increſcunt, donec veniant proxi-<lb/>mi puncto I, in quo ſolo cum pervenerunt, Acus quieſcit, adſcen-<lb/>ſus Acûs, vel complementa Inclinationis infra horizontem erunt in <lb/>ratione horum Coſinuum reſpective.</s> <s xml:id="echoid-s4737" xml:space="preserve"/> </p> <pb o="202" file="0216" n="216"/> </div> <div xml:id="echoid-div128" type="section" level="1" n="128"> <head xml:id="echoid-head137" xml:space="preserve">DISSERTATIO</head> <p> <s xml:id="echoid-s4738" xml:space="preserve">Corol 2. </s> <s xml:id="echoid-s4739" xml:space="preserve">Quoniam ſinus 3 ?</s> <s xml:id="echoid-s4740" xml:space="preserve">graduum æqualis eſt dimidio radio, adſcen-<lb/>ſus Acus Inclinatoriæ ſecundum lineam vel planum A D, in diſtan-<lb/>tia 60 graduum a Meridiano Magnetico A I, erit hic dimidium ma-<lb/>ximi adſcenſus.</s> <s xml:id="echoid-s4741" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4742" xml:space="preserve">Londini, ubi Inclinatio Acus pedis unius eſt 73 {3/4} graduum, & </s> <s xml:id="echoid-s4743" xml:space="preserve"><lb/>adſcenſus ejus â Nadir 16 {1/4} graduum: </s> <s xml:id="echoid-s4744" xml:space="preserve">ſed Inclinatio Acus 4 pedum <lb/>eſt 75 {1/6} graduum, adeoque ejus adſcenſus eſt â Nadir 14 {1/6} graduum: <lb/></s> <s xml:id="echoid-s4745" xml:space="preserve">Ideo adſcenſus in diſtantia 60 graduum abhinc, erit 8 {1/8} grad. </s> <s xml:id="echoid-s4746" xml:space="preserve">per-<lb/>Acum unius pedis, & </s> <s xml:id="echoid-s4747" xml:space="preserve">7 {5/12} graduum per Acum 4 pedum. </s> <s xml:id="echoid-s4748" xml:space="preserve">Notat Whi-<lb/>ſtonus ſe hoc variis temporibus exploraſſe, an experientia compro-<lb/>baretur, ſeſeque eam reſpondere demonſtrationi non modo in hoc <lb/>angulo, ſed in aliis deprehendiſſe.</s> <s xml:id="echoid-s4749" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4750" xml:space="preserve">Corol. </s> <s xml:id="echoid-s4751" xml:space="preserve">3. </s> <s xml:id="echoid-s4752" xml:space="preserve">Conſtructio præcedens ſupponatur in plano perpendicu-<lb/>lari ad horizontem, ſupra eandem A I, tanquam ſemidiametrum <lb/>ejuſdem circuli: </s> <s xml:id="echoid-s4753" xml:space="preserve">tum id ſupponatur locari a centro Acus Inclinato-<lb/>riæ ſecundum Magneticam directionem, ita ut ſinus A c, A d &</s> <s xml:id="echoid-s4754" xml:space="preserve">c, <lb/>repræſentent vires obliquas, ut antea: </s> <s xml:id="echoid-s4755" xml:space="preserve">tum inde ſupputare poſſumus <lb/>quantitatem iſtarum virium, tam in horizontali, quam in verticali <lb/>ſitu Acuum; </s> <s xml:id="echoid-s4756" xml:space="preserve">uti una enim linea exhibet vires Acus horizontalis, ita <lb/>altera exhibebit vires Acus Inclinatoriæ, cujus planum eſt in Ma-<lb/>gnetico æquatore. </s> <s xml:id="echoid-s4757" xml:space="preserve">Si quantitatem virium deſideramus in plano verti-<lb/>cali, prout Londini eſt, in Acubus unum pedem longis, hoc eſt <lb/>reſpectu totius virtutis ſecundum Magneticum Meridianum, hæc <lb/>eſt, uti ſinus 73 {3/4} graduum ad ſinum totum, qui eſt uti 96 ad 100. <lb/></s> <s xml:id="echoid-s4758" xml:space="preserve">adeoque tempora oſcillationum duarum Acuum Londini, vel in <lb/>Meridiano poſitarum Magnetico ſunt, uti hi numeri, vel proxime, ut <lb/>98 ad 100, vel 49 ad 50, quod congruit cum experientia. </s> <s xml:id="echoid-s4759" xml:space="preserve">Si eo-<lb/>dem modo deſideramus quantitatem virium in plano horizontali, <lb/>erit hæc reſpectu virium abſolutarum in Meridiano Magnetico, po-<lb/>ſita Acu unius pedis, uti ſinus 16 {1/4} graduum ad Sinum totum, ſive <lb/>ut 28 ad 100, & </s> <s xml:id="echoid-s4760" xml:space="preserve">poſita Acu 4 pedum, uti ſinus 14 {5/6} graduum ad <lb/>Sinum totum, vel ut 2560 ad 10000, ſive proxime uti 1 ad 4. </s> <s xml:id="echoid-s4761" xml:space="preserve">ad-<lb/>eoque tempora vibrationum ab his A cubus peractarum, quæ ſunt in <lb/>ſubduplicata proportione horum numerorum, ſunt in primo caſu <lb/>uti 52 {9/19} ad 100, & </s> <s xml:id="echoid-s4762" xml:space="preserve">in ſecundo proxime, uti 500 ad 1000, hoc eſt <lb/>uti 1 ad 2, quod convenit cum Experientia.</s> <s xml:id="echoid-s4763" xml:space="preserve"/> </p> <pb o="203" file="0217" n="217" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s4764" xml:space="preserve">Corol 4. </s> <s xml:id="echoid-s4765" xml:space="preserve">Quia A cus horizontalis movetur tantum a parte potentiæ, <lb/>quæ movet Acum Inclinatoriam, quando hæc ſtabit erecta perpen-<lb/>diculariter ad horizontem, tum Acus horizontalis non dirigetur <lb/>verſus aliquam cæli plagam, ſed erit indiſſerens ad quemcunque ſi-<lb/>tum, quia ſupra polum rectà ſtabit.</s> <s xml:id="echoid-s4766" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4767" xml:space="preserve">Detecta Acus Inclinatione, illico nonnulli Eruditi concluſerunt, <lb/>eam ſub æquatore Terreſtri fore nullam, adeoque Acum Horizonti <lb/>parallelam futuram; </s> <s xml:id="echoid-s4768" xml:space="preserve">ita Whrigtius in Epiſtola ad Gilbertum, & </s> <s xml:id="echoid-s4769" xml:space="preserve"><lb/>Sturmius in Phyſ. </s> <s xml:id="echoid-s4770" xml:space="preserve">Electiva Tom. </s> <s xml:id="echoid-s4771" xml:space="preserve">2. </s> <s xml:id="echoid-s4772" xml:space="preserve">pag. </s> <s xml:id="echoid-s4773" xml:space="preserve">1090. </s> <s xml:id="echoid-s4774" xml:space="preserve">Unde alii collegerunt, <lb/>in latitudine ab Æquatore eadem Inclinationem fore æque magnam; <lb/></s> <s xml:id="echoid-s4775" xml:space="preserve">Et quemadmodum Declinatio quondam credebatur firma & </s> <s xml:id="echoid-s4776" xml:space="preserve">immu-<lb/>tabilis in iiſdem Terræ locis, ita etiam Inclinatio ſtabilis & </s> <s xml:id="echoid-s4777" xml:space="preserve">ſixa ha-<lb/>bita fuit: </s> <s xml:id="echoid-s4778" xml:space="preserve">quæ utraque opinio erronea eſt: </s> <s xml:id="echoid-s4779" xml:space="preserve">inſpectis enim Noëllii <lb/>obſervationibus, in Itinere verſus Indias Orientales captis, ſuit ſub <lb/>Æquatore Inclinatio 10 grad. </s> <s xml:id="echoid-s4780" xml:space="preserve">30 Minut. </s> <s xml:id="echoid-s4781" xml:space="preserve">quod olim etiam nuncia-<lb/>tum Kirchero ſuit in Epiſtola, ab Indicis Itineratoribus ſibi miſſa, <lb/>inſertaque Lib. </s> <s xml:id="echoid-s4782" xml:space="preserve">2. </s> <s xml:id="echoid-s4783" xml:space="preserve">Artis Magn. </s> <s xml:id="echoid-s4784" xml:space="preserve">part. </s> <s xml:id="echoid-s4785" xml:space="preserve">5. </s> <s xml:id="echoid-s4786" xml:space="preserve">§. </s> <s xml:id="echoid-s4787" xml:space="preserve">5. </s> <s xml:id="echoid-s4788" xml:space="preserve">ubi hæc habentur: </s> <s xml:id="echoid-s4789" xml:space="preserve"><lb/>Cum vero appropinquaſſemus Æquinoctiali, Verſorium perpetuo <lb/>motu agitatum, quaſi ſecum deliberando, quam in plagam reſpice-<lb/>ret, ſe ſiſtere nolebat. </s> <s xml:id="echoid-s4790" xml:space="preserve">Vbi nota, quod facie Inſtrumenti gyrata <lb/>verſus Orientem, Verſorium elevabatur ad unam certam altitudi. </s> <s xml:id="echoid-s4791" xml:space="preserve"><lb/>nem, æ eâdem verſâ ad Occidentem, diverſâ ratione elevabatur, <lb/>quod particulariter accidit ultra Lineam Æquinoctialem, verſus <lb/>polum Auſtralem, diſſerentia vero ſemper erat quaſi eadem, vide-<lb/>licet 10 graduum. </s> <s xml:id="echoid-s4792" xml:space="preserve">Ex qua obſervatione idem colligo, quod quon-<lb/>dam Riccioli in Geograph. </s> <s xml:id="echoid-s4793" xml:space="preserve">Reform. </s> <s xml:id="echoid-s4794" xml:space="preserve">Lib. </s> <s xml:id="echoid-s4795" xml:space="preserve">7. </s> <s xml:id="echoid-s4796" xml:space="preserve">Acus partem Borealem <lb/>ſub Æquinoctiali & </s> <s xml:id="echoid-s4797" xml:space="preserve">ultra verſus Auſtrum inclinari 10 gradibus: </s> <s xml:id="echoid-s4798" xml:space="preserve">Imo <lb/>in alio Oceano Noëllius ſub Æquatore Inclinationem obſervavit 55 <lb/>grad. </s> <s xml:id="echoid-s4799" xml:space="preserve">Memoratus ex Kirchero locus videtur effugiſſe perſpicientiam <lb/>Sturmii, qui alioquin ſententiam de paralleliſmo Acûs ad horizon-<lb/>tem ſub Æquinoctiali non foviſſet.</s> <s xml:id="echoid-s4800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4801" xml:space="preserve">Eraſſe quoque eos, qui æqualem Acus Inclinationem in eadem <lb/>latitudine ſtatuerunt, patet ex obſervationibus: </s> <s xml:id="echoid-s4802" xml:space="preserve">inſpiciamus enim <lb/>Tabulas Obſervationum Noëllii & </s> <s xml:id="echoid-s4803" xml:space="preserve">Poundii, ex quibus conſtat Noël-<lb/>lium ſub latitudine Boreali 14 grad. </s> <s xml:id="echoid-s4804" xml:space="preserve">animadvertiſſe Inclinationem <lb/>25 grad. </s> <s xml:id="echoid-s4805" xml:space="preserve">Poundio eam modo 4 grad. </s> <s xml:id="echoid-s4806" xml:space="preserve">deprehendente: </s> <s xml:id="echoid-s4807" xml:space="preserve">ita ad latitu- <pb o="204" file="0218" n="218" rhead="DISSERTATIO"/> dinem Auſtralem 5 grad. </s> <s xml:id="echoid-s4808" xml:space="preserve">57?</s> <s xml:id="echoid-s4809" xml:space="preserve">. Poundius notavit Inclinationem 10 grad. </s> <s xml:id="echoid-s4810" xml:space="preserve">& </s> <s xml:id="echoid-s4811" xml:space="preserve">alibi in latitudine 6 grad. </s> <s xml:id="echoid-s4812" xml:space="preserve">12?</s> <s xml:id="echoid-s4813" xml:space="preserve">, (quæ latitudines parum di- ſcrepant,) Inclinationem 38 grad. </s> <s xml:id="echoid-s4814" xml:space="preserve">Ita Noëllius ſub latitudine Au- ſtrali 2 grad. </s> <s xml:id="echoid-s4815" xml:space="preserve">46?</s> <s xml:id="echoid-s4816" xml:space="preserve">. experiebatur Inclinationem 5 grad. </s> <s xml:id="echoid-s4817" xml:space="preserve">30?</s> <s xml:id="echoid-s4818" xml:space="preserve">, alibi in latitudine Auſtrali 2 grad. </s> <s xml:id="echoid-s4819" xml:space="preserve">40? </s> <s xml:id="echoid-s4820" xml:space="preserve">Inelinationem acus 62 graduum: </s> <s xml:id="echoid-s4821" xml:space="preserve">com- paravimus ita obiervationes cum eadem Acu factas inter ſe; </s> <s xml:id="echoid-s4822" xml:space="preserve">poſſet cæteroquin error ex aliis demonſtrari quoque autoribus, nam Granda- micus obſervavit Turonibus Inclinationem 70 graduum, jacet hæ urbs Galliæ ſub latitudine 47°, 38?</s> <s xml:id="echoid-s4823" xml:space="preserve">. Rothomagi Inclinatio tum erat 72 Grad. </s> <s xml:id="echoid-s4824" xml:space="preserve">quæ urbs ſub latitudine 49 grad. </s> <s xml:id="echoid-s4825" xml:space="preserve">Sita eſt: </s> <s xml:id="echoid-s4826" xml:space="preserve">adeoque in Incli natione major diſſerentia, quam inter latitudines locorum foret.</s> <s xml:id="echoid-s4827" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4828" xml:space="preserve">Incepit hoc ſeculo ſuſpicio foveri, ac ſi ope Acus Inclinatoriæ <lb/>locorum Longitudines, tam avide quæſitæ ab omnibus Geographis, <lb/>& </s> <s xml:id="echoid-s4829" xml:space="preserve">præcipue a Nautis, determinari poſſent; </s> <s xml:id="echoid-s4830" xml:space="preserve">ſummæ proinde utilita-<lb/>tis & </s> <s xml:id="echoid-s4831" xml:space="preserve">neceſſitatis eſſe hanc Acum, quæ a nautis conſulta, & </s> <s xml:id="echoid-s4832" xml:space="preserve">cum <lb/>Acu horizontali vulgari comparata, locum verum, in quo navis <lb/>verſaretur, indicaret.</s> <s xml:id="echoid-s4833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4834" xml:space="preserve">Inclinatoriam Acum omni utilitate eſſe deſtitutam non niſi teme-<lb/>rarius affirmabit, eam tamen ſolutioni problematis, locorum lon-<lb/>gitudines ſpectantis, ſatis facere poſſe vix conſido: </s> <s xml:id="echoid-s4835" xml:space="preserve">omnes, quibus <lb/>premitur hæc opinio, diſſicultates non adſeram, ſed illas tantum, <lb/>ex quibus ejus inſirmitas ſatis clare ſequitur: </s> <s xml:id="echoid-s4836" xml:space="preserve">1°. </s> <s xml:id="echoid-s4837" xml:space="preserve">Nunquam enim in <lb/>codem loco per integram diem Acus eædem Inclinationi ſubjicitur, <lb/>demonſtrantibus enim tum noſtris, tum Grahami obſervationibus, <lb/>Acus inclinat 66, 67, 68 gradibus, aut a 75° ad 74°, 53?</s> <s xml:id="echoid-s4838" xml:space="preserve">: & </s> <s xml:id="echoid-s4839" xml:space="preserve">intra <lb/>Menſis ſpatium diſſerentia Londini fuit a 75 gradibus ad 74°, 20?</s> <s xml:id="echoid-s4840" xml:space="preserve">. <lb/>quemadmodum Tabulam Experimentorum Grahami conſulenti ap-<lb/>parebit: </s> <s xml:id="echoid-s4841" xml:space="preserve">Quomodo igitur verus Terræ locus ex Inclinatione adeo <lb/>inſtabili eruetur? </s> <s xml:id="echoid-s4842" xml:space="preserve">error non poſſet non inde oriri aliquot Milliari-<lb/>bus æqualis. </s> <s xml:id="echoid-s4843" xml:space="preserve">2°. </s> <s xml:id="echoid-s4844" xml:space="preserve">Adnotavit Poundius ſe in Oceano Indico inter ſco-<lb/>pulos & </s> <s xml:id="echoid-s4845" xml:space="preserve">inſulas obſervaſſe motum Acus perpetuum verſus quamlibet <lb/>plagam, ita ut nulla ejus directio obſervari potuerit, quidnam uti-<lb/>litatis ergo in his locis Acus afferet? </s> <s xml:id="echoid-s4846" xml:space="preserve">3°. </s> <s xml:id="echoid-s4847" xml:space="preserve">Sed quod propius attinet <lb/>Acus Inclinatorias, Noëllii obſervationes inſpiciamus. </s> <s xml:id="echoid-s4848" xml:space="preserve">Acus In-<lb/>clinatoria deprehenditur ſub Latitudinibus & </s> <s xml:id="echoid-s4849" xml:space="preserve">Longitudinibus diver-<lb/>ſiſſimis perpendiculariter ad horizontem ſtetiſſe: </s> <s xml:id="echoid-s4850" xml:space="preserve">Nam ſub Latitu- <pb o="205" file="0219" n="219" rhead="DE MAGNETE."/> dine Auſtrali 35°, 25?</s> <s xml:id="echoid-s4851" xml:space="preserve">, ſub Meridiano Madagaſcar, erat Inclinatio <lb/>90 graduum; </s> <s xml:id="echoid-s4852" xml:space="preserve">ſub latitudine 34°, 44?</s> <s xml:id="echoid-s4853" xml:space="preserve">, plaga verſus Hypocæciam, <lb/>ſeu N, O, O. </s> <s xml:id="echoid-s4854" xml:space="preserve">eadem Inclinatio vigebat: </s> <s xml:id="echoid-s4855" xml:space="preserve">ſub latitudine 34°. </s> <s xml:id="echoid-s4856" xml:space="preserve">44? </s> <s xml:id="echoid-s4857" xml:space="preserve">& </s> <s xml:id="echoid-s4858" xml:space="preserve"><lb/>600 Milliaribus a Promontorio Bonæ Spei erat iterum eadem In-<lb/>clinatio: </s> <s xml:id="echoid-s4859" xml:space="preserve">ſub latitudine 30°, 40?</s> <s xml:id="echoid-s4860" xml:space="preserve">, & </s> <s xml:id="echoid-s4861" xml:space="preserve">800 Milliaribus ab eodem Pro-<lb/>montorio adhuc erat eadem Inclinatio; </s> <s xml:id="echoid-s4862" xml:space="preserve">imo & </s> <s xml:id="echoid-s4863" xml:space="preserve">ſub latitudine 29°, <lb/>47? </s> <s xml:id="echoid-s4864" xml:space="preserve">ulterius verſus Hypocæciam erat eadem Inclinatio: </s> <s xml:id="echoid-s4865" xml:space="preserve">data igitur <lb/>eadem Inclinatione ſub longitudine diverſiſſima, æquali pluribus <lb/>centenis Milliaribus itineris, & </s> <s xml:id="echoid-s4866" xml:space="preserve">ſub latitudine diverſiſſima, quid nam <lb/>certi ſtabiliri de vero loco, in quo navis verſatur, poterit? </s> <s xml:id="echoid-s4867" xml:space="preserve">Inſpectis <lb/>quoque Poundii obſervationibus, eadem animadvertentur, nam in <lb/>illis notatur ſub latitudine Auſtrali 36°, 56? </s> <s xml:id="echoid-s4868" xml:space="preserve">& </s> <s xml:id="echoid-s4869" xml:space="preserve">longitudine 71°, 12? <lb/></s> <s xml:id="echoid-s4870" xml:space="preserve">a Promontorio Bonæ Spei, Inclinatio 68 graduum, quæ eadem per-<lb/>manſit in latitudine 34°, 7?</s> <s xml:id="echoid-s4871" xml:space="preserve">, & </s> <s xml:id="echoid-s4872" xml:space="preserve">longitudine 78°, 32?</s> <s xml:id="echoid-s4873" xml:space="preserve">. tum in lati-<lb/>tudine 30°. </s> <s xml:id="echoid-s4874" xml:space="preserve">11?</s> <s xml:id="echoid-s4875" xml:space="preserve">. & </s> <s xml:id="echoid-s4876" xml:space="preserve">longitudine 86°, 28?</s> <s xml:id="echoid-s4877" xml:space="preserve">. Opinor has diſſicultates <lb/>tanti eſſe ponderis, ut nemo ex Acu Inclinatoria amplius tam opi-<lb/>mos, exſpectet fructus, aut hac via longitudines locorum inve-<lb/>ſtigandas eſſe exiſtimet.</s> <s xml:id="echoid-s4878" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4879" xml:space="preserve">Multo melius hujus Acûs ope polorum Magneticorum in ter-<lb/>ra veri ſitus, magnitudines, perpetuaque converſio demonſtrabi-<lb/>tur; </s> <s xml:id="echoid-s4880" xml:space="preserve">hoc ſcopo cum illa ab Itineratoribus & </s> <s xml:id="echoid-s4881" xml:space="preserve">Philoſophis obſer-<lb/>vationes capiendæ ſunt, quas nunc modo in utilitatem poſteri-<lb/>tatis colligere licet, & </s> <s xml:id="echoid-s4882" xml:space="preserve">par eſt. </s> <s xml:id="echoid-s4883" xml:space="preserve">Utinam deſiderio doctrinam <lb/>Magneticam promovendi ſlagrent plurimi rerum Naturalium ſcru-<lb/>tatores, ut Lapidis miriſicam & </s> <s xml:id="echoid-s4884" xml:space="preserve">adeo abſtruſam Naturam eruant <lb/>cognoſcantque; </s> <s xml:id="echoid-s4885" xml:space="preserve">nam ex ea non unius Lapidis tantum, ſed plu-<lb/>rimorum, imo omnium corporum vis attractrix forſitan intelli-<lb/>getur, qua cognita magnus in Phyſica foret factus progroſſus: <lb/></s> <s xml:id="echoid-s4886" xml:space="preserve">Si autem poſteritati prodeſſe cupiamus, oportet ut cum Acubus <lb/>Inclinatoriis, æque longis, æque gravibus, ſiguræ ſibi ſimillimis, <lb/>perfectiſſime elaboratis, obſervationes ubivis terrarum capiamus; </s> <s xml:id="echoid-s4887" xml:space="preserve">vix <lb/>autem tantus hominum conſenſus ſperari poteſt, aut tanta laborum <lb/>conſtantia, cum plurimi pulcrius, ſaltem jucundius eſſe, judicent, <lb/>rerum cauſas divinare, callide de iis ex hypotheſi diſſerere, <lb/>quam tædioſis obſervationibus capiendis dare operam: </s> <s xml:id="echoid-s4888" xml:space="preserve">quibus ac-<lb/>œdit, diſſicillime & </s> <s xml:id="echoid-s4889" xml:space="preserve">tantum a pauciſſimis accurata poſſe capi Ex- <pb o="206" file="0220" n="220" rhead="DISSERTATIO"/> perimenta, cum ad fingendam hypotheſin, quilibet, vel ineptiſſi- mus Philoſophus, ſatis accommodatus deprehendatur; </s> <s xml:id="echoid-s4890" xml:space="preserve">Ecquis enim jucundæ non facile foret autor fabulæ?</s> <s xml:id="echoid-s4891" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4892" xml:space="preserve">Inceperunt obſervationes componere cumInclinatoriis A cubusNo-<lb/>ëllius, Indias Orientales petens, tumPoundius & </s> <s xml:id="echoid-s4893" xml:space="preserve">Cunninghamus, quas <lb/>magniab omnibus veræ Phyſicæ cultoribus æſtimandas, noſtris adne-<lb/>ctere voluimus: </s> <s xml:id="echoid-s4894" xml:space="preserve">Inſtituit alias Feuillejus in Americano itinere, alias in <lb/>Britannia Whiſtonus; </s> <s xml:id="echoid-s4895" xml:space="preserve">alias tandem in Germania Semlerus. </s> <s xml:id="echoid-s4896" xml:space="preserve">Illas, <lb/>quas Poundius adnotavit, inſerui Mappæ Geographicæ Tab. </s> <s xml:id="echoid-s4897" xml:space="preserve">X. </s> <s xml:id="echoid-s4898" xml:space="preserve">in <lb/>qua parvis numeris deſignantur, libere hinc inde poſitis cum pun-<lb/>cto, ſigno loci, præſixo. </s> <s xml:id="echoid-s4899" xml:space="preserve">Noëllianas lubenter quoque addidiſſem, <lb/>ſed hæ tantopere abludunt a Poundianis obſervationibus, ut ni-<lb/>hil ſimile indicare videantur, hinc potius lectorem confudiſſent <lb/>atque turbaſſent, quam clarum de Inclinatione in Mappa dediſ-<lb/>ſent conceptum.</s> <s xml:id="echoid-s4900" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # # # # Obſervationes Inclinationum Acus Magneticæ captæ a Cunning- \\ hamo, Anno 1700 deſcriptæ in Philoſophic. Tranſactionibus N°. 292. <lb/># # Latitudo. \\ Septentr. # # Longitudo. \\ Orient. a St. Jago. # # Inclinatio Acus. \\ cum Cuſpide Septentrionali. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>1 # 26 # 6 # 16 # 8 # 30 <lb/>Auſtralis # # cum Cuſpide Auſtrali. <lb/>1 # 46 # 5 # 8 # 3 # 30 <lb/>5 # 57 # 3 # 54 # 10 # 0 <lb/>15 # 9 # 1 # 10 # 19 # 0 <lb/>19 # 14 # 1 # 29 # 30 # 0 <lb/>26 # 38 # 4 # 9 # 39 # 0 <lb/>31 # 16 # 13 # 57 # 42 # 0 <lb/>34 # 59 # 33 # 27 # 47 # 0 <lb/>34 # 3 # 50 # 36 # 48 # 0 <lb/># a Capite Bonæ Spei. # <lb/>37 # 41 # 19 # 10 # 60 # 0 <lb/></note> <pb o="207" file="0221" n="221" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ Auſtralis # # Longitudo. \\ a Cap. Bonæ Spei. # # Inclinatio \\ cum Cuſpid. Auſtr. <lb/>Gr. # M. # Gr. # M. # Gr. # M. <lb/>38 # 43 # 36 # 20 # 66 # 0 <lb/>38 # 17 # 42 # 7 # 69 # 0 <lb/>38 # 30 # 52 # 41 # 72 # 0 <lb/>37 # 10 # 60 # 54 # 75 # 0 <lb/>36 # 53 # 65 # 4 # 70 # 0 <lb/>36 # 56 # 71 # 12 # 68 # 0 <lb/>34 # 7 # 78 # 32 # 68 # 0 <lb/>30 # 11 # 86 # 28 # 68 # 0 <lb/>22 # 49 # 91 # 32 # 62 # 0 <lb/>15 # 2 # 95 # 15 # 53 # 0 <lb/>13 # 1 # 95 # 42 # 52 # 0 <lb/>8 # 45 # 97 # 37 # 46 # 0 <lb/># # in Batavia \\ Longitudo a Batavia \\ Orientalis. # 40 # 0 <lb/>6 # 12 # 1 # 51 # 38 # 0 <lb/>6 # 35 # 3 # 49 # 45 # 0 <lb/>6 # 50 # 5 # 37 # 41 # 0 <lb/>4 # 15 # 7 # 6 # 40 # 0 <lb/>4 # 1 # 0 # 13 # 35 # 0 <lb/># # Septentr. # # Longitudo a \\ pulo Condore \\ Orientalis. <lb/>1 # 25 # 0 # 0 # 31 # 0 <lb/>12 # 4 # 4 # 33 # 5 # 30 <lb/>14 # 5 # 5 # 58 # 4 # 0 <lb/>21 # 17 # 7 # 2 # 2 # 30 <lb/># # # cum Cuſpide Borea. <lb/>22 # 15 # 7 # 47 # 6 # 0 <lb/>24 # 22 # 10 # 43 # 12 # 0 <lb/>29 # 6 # 14 # 49 # 17 # 30 <lb/>30 # 25 # 14 # 20 # 21 # 0 <lb/></note> <pb o="208" file="0222" n="222" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s4901" xml:space="preserve">Hudſon in Itinere verſus polum Septentrionalem Anno 1608, ad <lb/>latitudinem Boream 61°. </s> <s xml:id="echoid-s4902" xml:space="preserve">11 obſervavit Inclinationem 79 grad. </s> <s xml:id="echoid-s4903" xml:space="preserve">& </s> <s xml:id="echoid-s4904" xml:space="preserve"><lb/>ad latitudinem Borealem 75°, 22 inclinationem invenit 89°, 30. <lb/></s> <s xml:id="echoid-s4905" xml:space="preserve">quæ obſervationes habentur in Vol. </s> <s xml:id="echoid-s4906" xml:space="preserve">3. </s> <s xml:id="echoid-s4907" xml:space="preserve">of Purchas Pilgrim, notante <lb/>Whiſtono.</s> <s xml:id="echoid-s4908" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4909" xml:space="preserve">Halleyus Anno 1700 Inclinationem prope inſulas Cabo Verde <lb/>obſervavit nullam, ſed Acum eſſe horizontalem.</s> <s xml:id="echoid-s4910" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # # # # # Obſervationes Noëllii Inclinationem Acus ſpectantes in diverſis \\ Terræ locis. <lb/># # Latitudo loci \\ Borea. # Longitudo. # # Acus \\ Inclinatio. # # Diſtantia \\ a Zenith. <lb/>Gr. # M. # # Gr. # M. <lb/>38 # 40 # Liſſabon. # 48 # 10 <lb/># # Sub horizont. <lb/>18 # 20 # 50 Milliar. \\ a Cabo Verde. # 29 # 0 <lb/>14 # 0 # paulo minus. # 25 # 0 <lb/>13 # 12 # 1 Grad. remotius <lb/># # ad Occaſum \\ quam inſula \\ Palma # 24 # 0 # 17 # 30 <lb/>9 # 20 # Sub eod. Merid. # 21 # 0 # 23 # 30 <lb/>8 # 0 # Sub eodem. # 19 # 0 # 26 # 0 <lb/>5 # 5 # Sub eodem. # 16 # 0 # 33 # 0 <lb/>4 # 0 # Sub eodem. # 14 # 30 # 36 # 0 <lb/>2 # 45 # paulo plus \\ ad Occaſ. # 13 # 0 # 40 # 0 <lb/>1 # 55 # paulo plus \\ ad Occaſ. # 12 # 30 # 44 # 30 <lb/># # Sub Æquatore. # ad Occaſ. # 10 # 30 # 49 # 30 <lb/># # Auſtralis. <lb/>1 # 30 # Verſus Occaſ. # 8 # 30 # 55 # 0 <lb/>2 # 46 # # 5 # 30 # 61 # 0 <lb/>4 # 15 # # 3 # 30 # 78 # 0 <lb/>6 # 30 # # 3 # 0 # 84 # 0 <lb/></note> <pb o="209" file="0223" n="223" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # Auſtralis \\ Latitudo \\ loci. # Longitudo. # # Inclinatio \\ Acus. # # Diſtantia \\ à Zenith. <lb/>Gr. # M # # Gr. # M. # Gr. # M. <lb/>7 # 20 # 150 Milliar. a Bra- \\ ſilia. # 5 # 0 # 90 # adeoque horizontalis <lb/>8 # 45 # verſus Occaſ. # 11 # 0 # 89 # verſus Zenith redit. <lb/>10 # 19 # # 28 # 30 # 85 # 30 <lb/>12 # 15 # # 34 # 30 # 84 # 0 <lb/>14 # 20 # # 42 # 0 # 81 # 0 <lb/>15 # 55 # # 49 # 0 # 79 # 0 <lb/>17 # 15 # # 51 # 30 # 77 # 0 <lb/>18 # 24 # # 53 # 30 # 76 # 0 <lb/>20 # 22 # # 56 # 0 # 74 # 0 <lb/>22 # 25 # # 54 # 30 # 72 # 0 <lb/>24 # 20 # Verſus Ortum. \\ ad Cabo d?Eſperan. # 64 # 0 # 70 # 0 <lb/>25 # 40 # 700 Milliar. a Cabo \\ Eſperan. # 67 # 0 # 68 # 30 <lb/>27 # 18 # Verſus Ortum. # 71 # 0 # 67 # 0 <lb/>28 # 57 # # 74 # 30 # 65 # 30 <lb/>30 # 15 # # 76 # 0 # 65 # 30 <lb/>31 # 45 # adhuc verſus \\ Ortum. # 78 # 0 # 63 # 0 <lb/># # 300 Mill. a Cabo <lb/>32 # 50 # # 79 # 0 # 62 # 0 <lb/>33 # 48 # # 80 # 0 # 61 # 0 <lb/>34 # 50 # verſus Ortum \\ in conſpectu # 81 # 30 # 60 # 0 <lb/>35 # 10 # Cabo de Eſper. # 82 # 0 # 59 # 0 <lb/>34 # 40 # Verſus Cabo de \\ Bona Eſperanza. # 83 # 0 # 58 # 30 <lb/>36 # 40 # plaga notape- \\ liotes # 85 # 0 # 57 # 0 <lb/>36 # 45 # Verſus Ortum. # 87 # 0 # 55 # 0 <lb/>36 # 10 # # 88 # 0 # 54 # 0 <lb/>35 # 40 # 300 Mill. à \\ Cabo, plaga Hy- \\ pocæcias. # 88 # 30 # 53 # 0 <lb/>35 # 40 # Verſus Ortum. # 89 # 0 # 51 # 30 <lb/>36 # 0 # Sub Meridiano \\ Madagaſcar. # 89 # 30 # 50 # 0 <lb/></note> <pb o="210" file="0224" n="224" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # Latitudo \\ loci \\ Auſtralis. # Longitudo. # # Inclinatio \\ Acus. # # Elongatio \\ a Zenith. <lb/>Gr. # M. # # Gr. # M. # Gr. # M. <lb/>35 # 25 # plaga Hypocæcias. # 90 # 0 # 48 # 30 <lb/>34 # 44 # 600 Milliar. à Cabo. # 90 # 0 # 46 # 30 <lb/>32 # 10 # verſus Hypocæcian. # 90 # 0 # 45 # 30 <lb/>31 # 25 # # 90 # 0 # 44 # 30 <lb/>30 # 40 # 800 Milliar à Cabo # adhuc Verticalis. # 44 # 30 <lb/>29 # 47 # adhuc verſus Hypo- \\ cæcian. # & Verticalis. # 44 # 30 <lb/>28 # 15 # # 89 # 30 <lb/>27 # 44 # verſus Hypocæcian. # 89 # ſupra horizontem. # 45 # 30 <lb/>26 # 10 # # 88 # 30 # 46 # 30 <lb/>24 # 54 # # 87 # 30 # 47 # 0 <lb/>23 # 12 # # 87 # 0 # 48 # 30 <lb/>23 # 8 # verſus Ortum 1300 \\ Mill. à Cabo. # 86 # 30 # 49 # 0 <lb/>19 # 30 # verſus Ortum & \\ Boream 1450 Mill. à Cabo. # 84 # 0 # 50 # 30 <lb/>18 # 10 # verſus Javam. # 83 # 0 # 52 # 0 <lb/>16 # 40 # verſus Cæcian. # 82 # 0 # 54 # 0 <lb/>14 # 37 # # 79 # 30 # 56 # 0 <lb/>12 # 0 # # 77 # 0 # 59 # 0 <lb/>10 # 30 # # 75 # 0 # 62 # 30 <lb/>8 # 30 # # 72 # 30 # 65 # 0 <lb/>7 # 40 # # 71 # 0 # 66 # 0 <lb/>4 # 20 # verſus Boream. # 66 # 0 # 68 # 30 <lb/>2 # 40 # verſus Circium e \\ regione Ceilon. # 62 # 0 # 70 # 0 <lb/>2 # 10 # # 60 # 30 # 71 # 0 <lb/># # Sub Æquatore. \\ Boreal. # # 55 # 0 # 73 # 30 <lb/>2 # 0 # # 51 # 0 # 75 # 30 <lb/>4 # 50 # # 42 # 0 # 78 # 30 <lb/>7 # 50 # in Baticalon Cei- \\ loniæ. # 30 # 0 # 85 # 0 <lb/>12 # 30 # ad littus Indiæ. # 0 # 0 # horizontalis \\ Acus. <lb/></note> <pb o="211" file="0225" n="225" rhead="DE MAGNETE."/> <note position="right" xml:space="preserve"> <lb/># # # # # # Obſervationes Inclinationum captæ a Fueilleo Anno 1706. in iti- \\ nere Americam verſus. <lb/># # Latitudo \\ loci \\ Auſtralis. # # Longitudo. # # Inclinatio \\ Acus. <lb/>Gr. # M. # Gr. # M # Gr. # M. <lb/>13 # 42 # 2 # 27 # 7 # 14 <lb/>14 # 53 # 5 # 52 # 22 # 40 <lb/>15 # 11 # 7 # 31 # 24 # 0 <lb/>16 # 16 # 7 # 4 # 26 # 30 <lb/>17 # 10 # 7 # 34 # 28 # 0 <lb/>18 # 10 # 7 # 52 # 30 # 45 <lb/>19 # 11 # 8 # 48 # 32 # 30 <lb/>20 # 50 # 9 # 34 # 36 # 0 <lb/>22 # 30 # 10 # 1 # 38 # 15 <lb/>24 # 0 # 10 # 28 # 41 # 30 <lb/>27 # 35 # 13 # 2 # 44 # 0 <lb/>29 # 2 # 11 # 43 # 46 # 0 <lb/>32 # 20 # 8 # 19 # 49 # 30 <lb/>35 # 43 # 6 # 2 # 53 # 30 <lb/>35 # 48 # 4 # 27 # 54 # 15 <lb/>36 # 33 # 3 # 0 # 55 # 30 <lb/>36 # 50 # 2 ab urbe # 55 # 45 <lb/># # Conception. # 55 # 0 <lb/>37 # 0 # 1 # 0 # 55 \\ 55 \\ 55 # 45 \\ 55 # 35 \\ 55 # 25 <lb/>diverſo tempore in eadem urbe \\ In urbe Coquimbo fuit Inclin. # 47 # 20 <lb/>alio tempore. # 47 # 30 <lb/>In urbe Ylo. # # 27 # 45 <lb/></note> <p style="it"> <s xml:id="echoid-s4911" xml:space="preserve"><emph style="sc">Definit</emph>. </s> <s xml:id="echoid-s4912" xml:space="preserve">Polus Magneticus Terræ vocatur illud punctum, vel <lb/>locus, â quo Magnes & </s> <s xml:id="echoid-s4913" xml:space="preserve">Acus Nautica trabuntur, & </s> <s xml:id="echoid-s4914" xml:space="preserve">quo dirigun-<lb/>tur.</s> <s xml:id="echoid-s4915" xml:space="preserve"/> </p> <pb o="212" file="0226" n="226" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s4916" xml:space="preserve">Quæſitum fuit a Philoſophis quot poli Magnetici in Terrâ den-<lb/>tur? </s> <s xml:id="echoid-s4917" xml:space="preserve">Ubinam ſiti? </s> <s xml:id="echoid-s4918" xml:space="preserve">An in ſuperficie Terræ, an ad aliquam ſub ipſa <lb/>profunditatem demerſi? </s> <s xml:id="echoid-s4919" xml:space="preserve">Quanam latitudine donati? </s> <s xml:id="echoid-s4920" xml:space="preserve">An firmi ſtabi-<lb/>leſque, an moveantur, & </s> <s xml:id="echoid-s4921" xml:space="preserve">qua velocitate? </s> <s xml:id="echoid-s4922" xml:space="preserve">Quæ omnia ſi a morta-<lb/>libus cognoſcerentur, quam plurimum lucis doctrinæ Magneticæ <lb/>affunderent, tum enim a priori poſſet determinari, qualis & </s> <s xml:id="echoid-s4923" xml:space="preserve">quan-<lb/>ta Declinatio aut Inclinatio Acuum Magneticarum hoc tempore in <lb/>dato loco regnaret, quod in re nautica magni foret momenti, cum <lb/>ex eo longitudines locorum, adeo avide â nautis deſideratas, cogno-<lb/>ſceremus exactius, quam ullis aliis hucuſque cognitis modis.</s> <s xml:id="echoid-s4924" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4925" xml:space="preserve">Quoniam Acus ferrea impoſita polo Magnetis perpendiculariter <lb/>erigitur, etiam Acus Inclinatoria delata ſupra eum in Terra locum, <lb/>qui vel polus eſt, aut ſupra polum directe jacet, perpendiculariter <lb/>ad horizontem erigetur, adeoque oportebit ea quærere Telluris <lb/>loca, in quibus obſervatur A cus Inclinatoria perpendiculariter eri-<lb/>gi: </s> <s xml:id="echoid-s4926" xml:space="preserve">Videtur igitur hoc tempore polus dari Boreus Magneticus, ad <lb/>latitudinem 76 grad. </s> <s xml:id="echoid-s4927" xml:space="preserve">30 Minut proinde 13°, 30 a polo Boreo Ter-<lb/>ræ. </s> <s xml:id="echoid-s4928" xml:space="preserve">hujus longitudo eſt circiter 30 graduum ad Ortum Meridiani <lb/>Londinenſis: </s> <s xml:id="echoid-s4929" xml:space="preserve">Polum hic poni arbitramur, quia Hudſonus in itine-<lb/>re Septentrionem verſus Anno 1607 & </s> <s xml:id="echoid-s4930" xml:space="preserve">1608 inſtituto, perveniens <lb/>adlatitudinem 75°, 22?</s> <s xml:id="echoid-s4931" xml:space="preserve">, Bor. </s> <s xml:id="echoid-s4932" xml:space="preserve">obſervavit Inclinationem Acus fuiſſe 89 <lb/>grad. </s> <s xml:id="echoid-s4933" xml:space="preserve">vel 89°, 30?</s> <s xml:id="echoid-s4934" xml:space="preserve">. bis vero deprehendit depreſſionem 84° ad di-<lb/>ſtantiam circiter 12, vel 13 grad. </s> <s xml:id="echoid-s4935" xml:space="preserve">magni circuli, ſemel, antequam <lb/>perveniebat ad locum dictum Noordcaap, & </s> <s xml:id="echoid-s4936" xml:space="preserve">deinde in nova Zem-<lb/>la. </s> <s xml:id="echoid-s4937" xml:space="preserve">Whiſtonus hic polum Magnetis primus locavit, candide tamen <lb/>confeſſus, hanc poli determinationem inniti tantum uni obſervatio-<lb/>ni Hudſoni, atque ab eo forſitan Inclinationem Acus potius ſcri-<lb/>ptam eſſe 86°, 30?</s> <s xml:id="echoid-s4938" xml:space="preserve">, quam 89°, 30?</s> <s xml:id="echoid-s4939" xml:space="preserve">. neque poſt Hudſonum alias ob-<lb/>ſervationes in parte Borea terræ cum Acu Inclinatoria factas acce-<lb/>pimus, quamobrem abſolute demonſtrari nequit polum Magneticum <lb/>ibi loci jacere: </s> <s xml:id="echoid-s4940" xml:space="preserve">abſque ullo dubio Occidentem & </s> <s xml:id="echoid-s4941" xml:space="preserve">Boream verſus <lb/>noſtri reſpectu polus jacet, quia Acus plus declinat in Anglia quam <lb/>in Hollandia, & </s> <s xml:id="echoid-s4942" xml:space="preserve">magis adhuc, quo locus eſt Borealior, & </s> <s xml:id="echoid-s4943" xml:space="preserve">Occi-<lb/>dentalior, id tamen non ſufficit ad abſolutam ſcientiam veri loci <lb/>comparandam, quare optandum eſſet, ut nautæ, qui in piſcandis balæ-<lb/>nis occupati, Boreas regiones inviſunt, ope probæ Acus Inclinato- <pb o="213" file="0227" n="227" rhead="DEMAGNETE."/> riæ obſervent Inclinationem in iis regionibus regnantem: </s> <s xml:id="echoid-s4944" xml:space="preserve">utinam quo-<lb/>que obſervaretur hæc Inclinatio in ultimis Moſcoviæ, Tartariæ, <lb/>terræque Æſoneæ finibus, ut conſtaret, num unus, num plures po-<lb/>li Magnetis Borei darentur! nec prius hæc ſcientia ablolvetur, nec <lb/>propoſita modo problemata extricabuntur. </s> <s xml:id="echoid-s4945" xml:space="preserve">Sed ad polos Auſtrales <lb/>properemus, ſi Acus Inclinatoria Poundii vitiis caruerit, Magnetis <lb/>polum Auſtralem in veniſſent mortales adhuc nullum, in ejus enim <lb/>obſervationibus Inclinatio maxima fuit tantum 75 graduum, adlon-<lb/>gitudinem 60°, 54? </s> <s xml:id="echoid-s4946" xml:space="preserve">a Promontorio Bonæ Spei, adeoque a polo Ma-<lb/>gnetico procul hic locus abeſſet: </s> <s xml:id="echoid-s4947" xml:space="preserve">Verum Noëllius idem iter Orien-<lb/>tem verſus inſtituit, atque longe aliam Inclinationem ſuæ Acus ad-<lb/>notavit, quæ ſi probe fuerit fabrefacta, polum Auſtralem quen-<lb/>dam indicaſſet, nam ad latitudinem Auſtr. </s> <s xml:id="echoid-s4948" xml:space="preserve">35°, 25?</s> <s xml:id="echoid-s4949" xml:space="preserve">, plaga Hypo-<lb/>cori a Meridiano tranſeunte ſupra Madagaſcar, Acus Inclinatoria ſte-<lb/>tit perpendicularis ad horizontem, atque ita manſit in latitudi-<lb/>nibus Auſtralibus non multum diſcrepantibus ultra diſtantiam 800 <lb/>Milliarium â Promontorio Bonæ Spei Orientem verſus: </s> <s xml:id="echoid-s4950" xml:space="preserve">Præterea <lb/>capitaneus Taſman obſervavit Anno 1642, cum non procul ad occi-<lb/>dentem aberat a Terra Diemenſi, ſuum horizontale Verſorium non <lb/>dirigi verſus ullam plagam, nulla enim directione agi debebit Acus, <lb/>quæ polo impoſita eſt Magnetico: </s> <s xml:id="echoid-s4951" xml:space="preserve">quamobrem ex binorum obſer-<lb/>vationibus ſequi videtur polum Auſtralem Magneticum hic dari, <lb/>eamque eſſe plagam admodum latam: </s> <s xml:id="echoid-s4952" xml:space="preserve">Quæri autem hic poteſt, an <lb/>Verſorium horizontale Noëllii & </s> <s xml:id="echoid-s4953" xml:space="preserve">aliorum, qui eadem maris Indi-<lb/>ci loca tranſcurrerunt, non debuiſſet eſſe indifferens ad quamlibet <lb/>directionem, quando ſupra polum ferebatur, veluti Taſman in ſuo <lb/>itinere obſervavit? </s> <s xml:id="echoid-s4954" xml:space="preserve">quod tamen â nautis Batavicis non adnotatur <lb/>ibidem obtinere: </s> <s xml:id="echoid-s4955" xml:space="preserve">opinor tum Acum modo eſſe indifferentem ad <lb/>quamlibet directionem, quando centro loci polaris Magnetici im-<lb/>ponitur, verum quia polus Auſtralis latam admodum plagam ſecun-<lb/>dum obſervationes Noëllii occuparet, Acus poſita in diverſis hujus <lb/>plagæ locis, nihilominus directione agi conſtanti debebit, nempe <lb/>verſus centrum, ad quod omnes vires conſpirant.</s> <s xml:id="echoid-s4956" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4957" xml:space="preserve">Ita duos Magneticos in Terra utcunque deſignavimus polos, Boreum <lb/>unum, Auſtralem alterum; </s> <s xml:id="echoid-s4958" xml:space="preserve">an hi omnes ſunt, an plures dantur? </s> <s xml:id="echoid-s4959" xml:space="preserve">utinam <lb/>plures captæ fuiſſent cum Acu Inclinatoria obſervationes ab itinera- <pb o="214" file="0228" n="228" rhead="DISSERTATIO"/> toribus mare Indicum & </s> <s xml:id="echoid-s4960" xml:space="preserve">Pacificum tranſcurrentibus! tum enim certi <lb/>quid affirmare poſſemus, ubi nunc reticendum eſt, niſi plus, quam <lb/>demonſtrari poteſt, ſtatuamus.</s> <s xml:id="echoid-s4961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4962" xml:space="preserve">Ex Verſoriis horizontalibus nihil colligere licet, quod abſque <lb/>ſcrupulo polos indicabit, cæteroquin cum iis multo plures captas <lb/>poſſidemus obſervationes, ex quibus fere hoc negotium poſſet abſol-<lb/>vi: </s> <s xml:id="echoid-s4963" xml:space="preserve">Nam Verſorium horizontale non dirigitur recta verſus polos <lb/>Magneticos Terræ, aut jacet in plano verticali tranſeunte per duos <lb/>polos, quia in nonnullis locis plane nihil declinat a vero Borea & </s> <s xml:id="echoid-s4964" xml:space="preserve">Au-<lb/>ſtro, adeoque ibi indicaret polos Magneticos & </s> <s xml:id="echoid-s4965" xml:space="preserve">Terræ eſſe eosdem, <lb/>cum tamen in aliis ejuſdem Meridiani terreſtris punctis poſitum de-<lb/>clinat 5, 10, vel 15 & </s> <s xml:id="echoid-s4966" xml:space="preserve">ultra gradibus Occaſum aut Ortum verſus, <lb/>atque ita polum Magnetis procul a terreſtri polo ſejunctum eſſe de-<lb/>monſtraret, quæ ambo ſimul obtinere nequeunt: </s> <s xml:id="echoid-s4967" xml:space="preserve">Si autem duo tan-<lb/>tum darentur in Terra poli Magnetici, Boreus & </s> <s xml:id="echoid-s4968" xml:space="preserve">Auſtralis, quacun-<lb/>que in plagâ Boreâ aut Auſtrali ſiti Verſorium horizontale ſemper <lb/>dirigeretur recta ad utroſque, atque planum verticale, quod per <lb/>ipſum concipitur ductum, per utroſque polos tranſiret, unde poſi-<lb/>tis duabus acubus in varia longitudine terreſtri, ex concurſu dire-<lb/>ctionum polus detegeretur; </s> <s xml:id="echoid-s4969" xml:space="preserve">nam poſitis pluribus acubus in eadem <lb/>latitudine, ſed longitudine diverſa, plana verticalia, quæ peripſas <lb/>ducta conciperentur, ſe in polis ſecarent: </s> <s xml:id="echoid-s4970" xml:space="preserve">id nunc non fit, quam-<lb/>obrem ſuſpicio oritur non levis, plures dari æque in hemiſphærio <lb/>Terræ Boreo polos Magneticos, ac in Auſtrali; </s> <s xml:id="echoid-s4971" xml:space="preserve">veluti quoque <lb/>magnus Halleyus callide conjectavit, quatuor opinatus eſſe Ma-<lb/>gneticos polos, duos in Terræ parte Septentrionali, duos in Me-<lb/>ridionali; </s> <s xml:id="echoid-s4972" xml:space="preserve">horum quatuor illum prædominari, Acumque maxime ad <lb/>ſe trahere, qui ſibi foret proximus, remotiorem quidem aliquid, <lb/>attamen parum in Acum acturum: </s> <s xml:id="echoid-s4973" xml:space="preserve">candide tamen confitetur Phi-<lb/>loſophus polos Geometrice determinari non poſſe: </s> <s xml:id="echoid-s4974" xml:space="preserve">unum prope Me-<lb/>ridianum tranſeuntem per partem Brittanniæ, Terræ finem voca-<lb/>tam, 7 gradibus a polo Arctico, ſitum eſſe opinatur, cujus vi de-<lb/>clinaret Acus in Europa, Tartaria, Mari Boreo, reſpectu tamen <lb/>habito alterius poli, ſiti in Meridiano terreſtri tranſeunte per me-<lb/>dium Californiæ, & </s> <s xml:id="echoid-s4975" xml:space="preserve">circiter 15 gradibus a polo Terræ Boreo; </s> <s xml:id="echoid-s4976" xml:space="preserve">hu-<lb/>jus vi Acus declinaret in Septentrionali Americâ, atque in ambo- <pb o="215" file="0229" n="229" rhead="DEMAGNETE."/> bus Oceanis utrimque ipſam alluentibus, ab Azoribus occidentali-<lb/>ter uſque ad Japoniam.</s> <s xml:id="echoid-s4977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4978" xml:space="preserve">Polum Magneticum Auſtralem ponit in Meridiano terreſtri, 20 <lb/>gradibus occidentalius freto Magellanico & </s> <s xml:id="echoid-s4979" xml:space="preserve">16 gradibus a polo Ter-<lb/>ræ Auſtrali, qui regeret Acum in America Auſtrali, Oceano Paci-<lb/>fico & </s> <s xml:id="echoid-s4980" xml:space="preserve">in Æthyopico: </s> <s xml:id="echoid-s4981" xml:space="preserve">Alterum polum Magneticum Auſtralem lo-<lb/>cat 20 gradibus a polo Terræ Auſtrali in Meridiano terreſtri tranſ-<lb/>eunte ſupra Hollandiam novam, cujus vi regeretur Acus in Aſri-<lb/>ca, Arabia, Mari rubro, Perſia, India, inſulisque maris Indici, <lb/>atque hujus hypotheſeos beneficio feliciſſime explicat declinationes <lb/>Acuum in variis locis, cum tamen nondum ſufficientia data poſſi-<lb/>deamus ad demonſtrandum verum horum polorum locum, melius <lb/>erit aliquamdiu adhuc exſpectaſſe, quam ut præmaturo ardore ex-<lb/>plicandi cuncta correpti, in errores incidamus, quos poſteriores <lb/>obſervationes detegerent, quæ operam omnem a nobis adhibitam <lb/>admodum inutilem fuiſſe arguerent, præſtabit itaque ſilere & </s> <s xml:id="echoid-s4982" xml:space="preserve">in <lb/>colligendis obſervationibus Acuum horizontalium & </s> <s xml:id="echoid-s4983" xml:space="preserve">Inclinatoria-<lb/>rum operam impendiſſe: </s> <s xml:id="echoid-s4984" xml:space="preserve">Inſolutum ergo manet problema, quot <lb/>poli Magnetici in Terra dantur? </s> <s xml:id="echoid-s4985" xml:space="preserve">ubi ſiti? </s> <s xml:id="echoid-s4986" xml:space="preserve">quam latitudinem occu-<lb/>pant? </s> <s xml:id="echoid-s4987" xml:space="preserve">quam profunde in ipſa terra demerſi? </s> <s xml:id="echoid-s4988" xml:space="preserve">Sed ad alia tranſeamus, <lb/>atque examinemus, an poli Magnetici in Terra ſint firmi ac ſtabi-<lb/>les, an e locis ſuis migrent perpetuo? </s> <s xml:id="echoid-s4989" xml:space="preserve">Adnotavimus ſuperius ſin-<lb/>gulis annis Declinationem Acûs horizontalis, ut & </s> <s xml:id="echoid-s4990" xml:space="preserve">Inclinationem <lb/>Acus inclinatoriæ in iisdem Terræ locis diſcrepare, quod fieri <lb/>nequit, niſi poli Magnetici mutentur, & </s> <s xml:id="echoid-s4991" xml:space="preserve">moveantur a parte Borea <lb/>Æquatoris Terræ ab Oriente Occidentem verſus, cum in Europa <lb/>Declinatio Acus Occaſum verſus augeri obſervetur.</s> <s xml:id="echoid-s4992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4993" xml:space="preserve">Quænam vero erit cauſa, in perpetuo poſita motu, quæ Magnetem ad <lb/>ſe dirigat? </s> <s xml:id="echoid-s4994" xml:space="preserve">eſt hoc determinatu difficillimum, & </s> <s xml:id="echoid-s4995" xml:space="preserve">forſitan nun quam po-<lb/>terit abſolute a mortalibus demonſtrari: </s> <s xml:id="echoid-s4996" xml:space="preserve">Sagaciſſimus Halleyus ſpeci-<lb/>men ſui feliciſſimi penetrantiſſimique ingenii in divinanda hac cauſa <lb/>mirandum dedit, fingendo hypotheſin, admodum probabilem, cu-<lb/>jus ope obſervationes plurimæ, ſi non omnes, facile explicantur, <lb/>& </s> <s xml:id="echoid-s4997" xml:space="preserve">difficultates ſolvuntur, quam idcirco aſſumſit Whiſtonus, Sem-<lb/>lerus, aliique qui eam probe intellexerunt, meretur igitur apponi. <lb/></s> <s xml:id="echoid-s4998" xml:space="preserve">Quoniam Acus nautica in hemiſphærio Terræ Boreo continuo plus <pb o="216" file="0230" n="230" rhead="DISSERTATIO"/> declinat Occaſum verſus, & </s> <s xml:id="echoid-s4999" xml:space="preserve">in hemiſphærio Auſtrali Ortum verſus, <lb/>non erit cauſa Magnetica Terræ parva, ſedin ipſa adingentem uſque <lb/>exporrecta longitudinem; </s> <s xml:id="echoid-s5000" xml:space="preserve">quod ulterius probatur, ſi ponamus unum <lb/>Magneticum polum jacere 13°, 30? </s> <s xml:id="echoid-s5001" xml:space="preserve">a polo Terræ Boreo, alterum <lb/>12° gradus a polo Auſtrali ſecundum obſervatas Inclinationes, <lb/>nam inter hæc bina loca ingens diſtantia interjacet. </s> <s xml:id="echoid-s5002" xml:space="preserve">2°. </s> <s xml:id="echoid-s5003" xml:space="preserve">Quia etiam <lb/>Declinatio & </s> <s xml:id="echoid-s5004" xml:space="preserve">Inclinatio Acus motu utcunque ordinato promove-<lb/>tur, cauſa Magnetica eodem motu agatur neceſſe erit, nam ab ea <lb/>Declinationis mutatio dependet. </s> <s xml:id="echoid-s5005" xml:space="preserve">3°, Cum Declinationis motus lentus <lb/>ſit, ſive verſus Occaſum aut Ortum, erit diverſus a motu Terræ <lb/>diurno aut annuo, quare cauſa utriuſque motus diverſa eſt. </s> <s xml:id="echoid-s5006" xml:space="preserve">4°. </s> <s xml:id="echoid-s5007" xml:space="preserve">Cum <lb/>Acus Inclinatoria, quæ â cauſa Magnetica dirigitur, valde depri-<lb/>matur, in his regionibus, indicatur cauſam Magneticam eſſe ad <lb/>aliquam profunditatem uſque in Terræ viſceribus demerſam, non <lb/>in ſuperficie poſitam. </s> <s xml:id="echoid-s5008" xml:space="preserve">5°. </s> <s xml:id="echoid-s5009" xml:space="preserve">Si Magnes ſphæricus includatur capſulæ <lb/>ligneæ, atque circa eam Acus in variis ponatur ſitubus, hæc nunc <lb/>declinat Ortum, nunc Occaſum verſus, atque inclinat diverſimo-<lb/>de, accurate exhibens omnia phænomena, quæ ſuperius comme-<lb/>moravimus obtinere in Terra & </s> <s xml:id="echoid-s5010" xml:space="preserve">Verſorio horizontali atque inclina-<lb/>torio: </s> <s xml:id="echoid-s5011" xml:space="preserve">quid igitur eſt veroſimilius, quam in Terræ gremio contineri <lb/>ingentem Magnetem, rotundum, Terræ concentricum, ut hujus <lb/>centrum gravitatis maneat ſemper idem, converſo Magnete quo-<lb/>cunque modo: </s> <s xml:id="echoid-s5012" xml:space="preserve">Hic internus Terræ Magnes moveatur perpetuo <lb/>neceſſe eſt. </s> <s xml:id="echoid-s5013" xml:space="preserve">cum Declinatio ferè ſemper progrediatur, adeoque oporte-<lb/>bit, ut Magnes ſit ſolutus a Terra, & </s> <s xml:id="echoid-s5014" xml:space="preserve">ab eâ inſtar nuclei a putamine <lb/>comprehenſus: </s> <s xml:id="echoid-s5015" xml:space="preserve">ut vero ſolutus maneat, diſtantiam inter ipſum <lb/>Terramque adimpleat aqua, aut quodcunque aliud fluidum, quo <lb/>eadem ſemper intercapedo conſervabitur: </s> <s xml:id="echoid-s5016" xml:space="preserve">Magnes ita ſeparatus ab <lb/>exteriori Terra, poterit cum hac ſimul contorqueri motu commu-<lb/>ni, qui diurnus eſt, ſed unà ferri motu quodam ſibi proprio len-<lb/>toque ab Ortu Occaſum verſus in plagâ Terræ Boreâ, & </s> <s xml:id="echoid-s5017" xml:space="preserve">contorqueri <lb/>circa ſuum axin, qui vel ipſi cum Terra communis eſt vel diverſus: <lb/></s> <s xml:id="echoid-s5018" xml:space="preserve">tum enim Acus Declinatio perpetuo mutari debebit Occaſum verſus, <lb/>poſitoque Magnetis axe ab eo Terræ diverſo, declinatio Acus, quæ <lb/>certi gradus eſt, non modo Ortum aut Occaſum verſus feretur, ſed <lb/>motu obliquo ad Æquatorem Terræ, qualis actu obſervatur. </s> <s xml:id="echoid-s5019" xml:space="preserve">Con.</s> <s xml:id="echoid-s5020" xml:space="preserve"> <pb o="217" file="0231" n="231" rhead="DE MAGNETE."/> cipiamus in hoc Magnete polos ab utraque parte ſui Æquatoris, <lb/>duos plureſve, atque ſubſtantiam eſſe heterogeneam, hinc inde præ-<lb/>ſtantiorum aut debiliorum virium, quemadmodum in vulgaribus <lb/>Magnetibus obſervatur, tumque directiones Acus in variis Terræ <lb/>plagis diverſas explicare poterimus, imo nihil erit hactenus obſer-<lb/>vatum, quod ex ſimplici hac hypotheſi non feliciſſime ſolvatur: <lb/></s> <s xml:id="echoid-s5021" xml:space="preserve">ne autem aliquis criminetur ſupponi hic Magnetem plurimis dona-<lb/>tum polis, cum plerique Magnetes duos tantum ſoleant poſſidere, <lb/>hic conſulat varia exempla, quæ ſupra attuli pag. </s> <s xml:id="echoid-s5022" xml:space="preserve">136, Magnetum <lb/>donatorum 4 polis, imo & </s> <s xml:id="echoid-s5023" xml:space="preserve">pluribus, unde nihil hic ſuppoſitum <lb/>fuit, quod non aliquando in natura obtinet: </s> <s xml:id="echoid-s5024" xml:space="preserve">Si igitur terra in ſuo <lb/>gremio complectatur ejuſmodi Magnetem, ad ejus polos Acus in <lb/>ſuperficie Terræ poſitæ dirigentur; </s> <s xml:id="echoid-s5025" xml:space="preserve">his polis non jacentibus in eo-<lb/>dem cum Terræ polis Meridiano, declinabit Acus a Borea & </s> <s xml:id="echoid-s5026" xml:space="preserve"><lb/>Auſtro, iis exceptis locis, in quibus duorum polorum vis ita ſibi <lb/>eſt æquilibrata, ut Acus motu amborum actæ ad Boream recta <lb/>determinentur, nec declinent. </s> <s xml:id="echoid-s5027" xml:space="preserve">Magnete hoc non tam rapide ſe-<lb/>quente motum Terræ circa axin ab Occaſu ad Ortum, videbitur ab <lb/>eo peragi motus ab Ortu ad Occaſum, atque Acus eodem modo <lb/>attractæ declinabunt ab Ortu ad Occaſum, hinc Declinationis mu-<lb/>tatio, quam Inclinatio ſequetur neceſſario: </s> <s xml:id="echoid-s5028" xml:space="preserve">Motu Terræ & </s> <s xml:id="echoid-s5029" xml:space="preserve">Ma-<lb/>gnetis aliquando æquilibrato ſibi per quoddam tempus, Acus ſta-<lb/>tionaria erit: </s> <s xml:id="echoid-s5030" xml:space="preserve">pars quædam hujus Magnetis fortioris debiliorisve <lb/>virtutis, obverſa Terræ alicui plagæ, efficiet, ut Acus in ea ma-<lb/>gis vel minus declinet, & </s> <s xml:id="echoid-s5031" xml:space="preserve">retrogrado vel celeri progreſſivo motu fe-<lb/>ratur, quæ omnia obſervata ſunt ſuperius in Tabulis Declinatio-<lb/>num & </s> <s xml:id="echoid-s5032" xml:space="preserve">Inclinationum ita obtinere: </s> <s xml:id="echoid-s5033" xml:space="preserve">ſi quis elegantius hæc adſtructa, <lb/>acuto & </s> <s xml:id="echoid-s5034" xml:space="preserve">plauſibili argumento ornata, deſideret, conſulat ipſum Sy-<lb/>ſtematis autorem, Halleyum in Philoſ. </s> <s xml:id="echoid-s5035" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5036" xml:space="preserve">N°. </s> <s xml:id="echoid-s5037" xml:space="preserve">195. </s> <s xml:id="echoid-s5038" xml:space="preserve">quibus <lb/>adjungat ea, quæ Whiſtonus etiam addiditin Tractatu of the dipping <lb/>Needle, tumque fatebitur hanc hypotheſin eſſe adeo ſimplicem, <lb/>adeo veroſimilem, ut ad id, quod fere demonſtratum eſt, proxi-<lb/>me accedat: </s> <s xml:id="echoid-s5039" xml:space="preserve">nolumus tamen hæc, quæ modo veroſimilia ſunt, pro <lb/>abſolute demonſtratis obtrudere, cum quotidiana doceat experien-<lb/>tia, quam facile in rerum cauſis aſſignandis hallucinemur, pruden-<lb/>tiamque ferè divinam, & </s> <s xml:id="echoid-s5040" xml:space="preserve">lentiſſimam in Phyſicis feſtinationem de- <pb o="218" file="0232" n="232" rhead="DISSERTATIO"/> ſiderari: </s> <s xml:id="echoid-s5041" xml:space="preserve">huc uſque tantum aliquid de Magnete ſubolfacimus, quem <lb/>ignoraverunt penitus antiqui: </s> <s xml:id="echoid-s5042" xml:space="preserve">id laudis nobis ſufficiat; </s> <s xml:id="echoid-s5043" xml:space="preserve">nos plura <lb/>illis tentaſſe, obſervaſſe aliquem progreſſum, aliquem motus ordi-<lb/>nem antea incognitum, idque noſtri temporis Philoſophis ſufficere <lb/>judicavit Fontenellius in L’Hiſt. </s> <s xml:id="echoid-s5044" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s5045" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5046" xml:space="preserve">A°. </s> <s xml:id="echoid-s5047" xml:space="preserve">1712, ne <lb/>animo deſpondeant in mediis Anomaliis, quibus Magnes abunde <lb/>luxuriat: </s> <s xml:id="echoid-s5048" xml:space="preserve">Hæreat igitur Magnes in imis Terræ viſceribus, ad quem o-<lb/>mnes noſtri Magnetes, omnes Acus Nauticæ & </s> <s xml:id="echoid-s5049" xml:space="preserve">Inclinatoriæ, omne <lb/>Ferrum denique dirigitur attractum, eodem modo ac a noſtris Magneti-<lb/>bus attrahuntur alii, nihilominus id reſtat, quomodo & </s> <s xml:id="echoid-s5050" xml:space="preserve">â quâ cauſâ iſta <lb/>attractio perficiatur: </s> <s xml:id="echoid-s5051" xml:space="preserve">Cauſa effectuum ſimilium procul omni dubio <lb/>erit eadem; </s> <s xml:id="echoid-s5052" xml:space="preserve">quæ enim noſtros Magnetes ad ſe appropinquare facit, <lb/>ea Magnetes in ſuperficie Terræ dirigit trahitque verſus grandem <lb/>iſtum in Terræ gremio concluſum Magnetem: </s> <s xml:id="echoid-s5053" xml:space="preserve">An hæc cauſa erunt <lb/>effluvia corporea, aut fluidum aliquod perpetuo curſu agitatum, <lb/>quod ex imis Terræ penetralibus egreſſum, circulum circa Terram <lb/>obit, per Aërem, & </s> <s xml:id="echoid-s5054" xml:space="preserve">ipſam Terræ ſubſtantiam circumlatum rapi-<lb/>diſſimi inſtar fluminis, quod ſecum abripit Magnetes noftros, Acus, <lb/>& </s> <s xml:id="echoid-s5055" xml:space="preserve">Ferrum omne, dirigitque certas verſus plagas? </s> <s xml:id="echoid-s5056" xml:space="preserve">Nequaquam profe-<lb/>cto, evicimus enim ſuperius plurimis argumentis ex experimentis <lb/>tantummodo petitis, Magnetes noſtros non regi ab effluviis, nec <lb/>quocunque alio admiſſo fluido explicari poſſe phænomena, con-<lb/>feſſi fuimus poſt totidem examina animum hebeſcere, neque cauſam <lb/>divinari, aut demonſtrari potuiſſe: </s> <s xml:id="echoid-s5057" xml:space="preserve">eadem abdita hic regnat cauſa; <lb/></s> <s xml:id="echoid-s5058" xml:space="preserve">priorem qui invenerit, hanc quoque intelliget, ab ea tantum di-<lb/>verſam magnitudine, non operatione attrahente vel dirigente: </s> <s xml:id="echoid-s5059" xml:space="preserve">an-<lb/>tequam igitur demonſtrari Geometrice poſſit directio Verſorii, In-<lb/>clinatio Acus, & </s> <s xml:id="echoid-s5060" xml:space="preserve">virium agentium quantitas, exſpectandum erit, do-<lb/>nec cauſa Magueticarum virium eruta fuerit.</s> <s xml:id="echoid-s5061" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5062" xml:space="preserve">Utcunque exiguum in Magnetica doctrina fecerimus progreſſum, <lb/>nihilominus experimentorum ope errores antiquorum deteximus, at <lb/>que eſſe abſonas eorum hypotheſes, nimiſque temere effictas, qua-<lb/>rum ope directionem Magnetis ſe explicare confifi ſunt: </s> <s xml:id="echoid-s5063" xml:space="preserve">Adeamus <lb/>veterum ſcholas, atque breviter percurramus opiniones præcipuas, <lb/>omnes enim examinaſſe non juvat.</s> <s xml:id="echoid-s5064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5065" xml:space="preserve">Fuerunt nonnulli, qui explicituri, quare ad Septentrionem diri- <pb o="219" file="0233" n="233" rhead="DE MAGNETE"/> geretur Acus nautica, vim polorum cœleſtium, & </s> <s xml:id="echoid-s5066" xml:space="preserve">imprimis poli Arctici, <lb/>vocabant, inter hos Petrus Peregrinus, Pedro de Media, Marſi-<lb/>lius Ficinus, & </s> <s xml:id="echoid-s5067" xml:space="preserve">Chemici plurimi exſtiterunt, hinc Menenſius in <lb/>Theatri Chemic. </s> <s xml:id="echoid-s5068" xml:space="preserve">vol. </s> <s xml:id="echoid-s5069" xml:space="preserve">5. </s> <s xml:id="echoid-s5070" xml:space="preserve">pag. </s> <s xml:id="echoid-s5071" xml:space="preserve">391. </s> <s xml:id="echoid-s5072" xml:space="preserve">inquit, Lapides virtutis aſtro-<lb/>rum conſortio frui inficiabitur nemo, qui ferreum pyxidis nauticæ <lb/>perpendiculum, Magnete confricatum, ſemper poli Septentrionalis <lb/>ſtellam ſpectare obſervabit. </s> <s xml:id="echoid-s5073" xml:space="preserve">Cadit hæc opinio ex ſolâ Inclinatione <lb/>Acûs ſupra axin mobilis, quæ non in hac regione elevatur 52 gra-<lb/>dibus ſupra horizontem, qualis eſt poli elevatio, ſed infra eum <lb/>deprimitur 67 gradibus.</s> <s xml:id="echoid-s5074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5075" xml:space="preserve">Corteſius ad punctum aliquod tractorium ultra cælum recurrit; <lb/></s> <s xml:id="echoid-s5076" xml:space="preserve">quodigitur plusquam infinito â Terrâ aberit intervallo, infinitum enim <lb/>Cœlum eſſe manifeſtum eſt, quia vacuum eſt, vacuum autem ex ſe <lb/>nulla ſuperficie limitante donatur, nec cum ea concipi poteſt, niſi <lb/>corpora ſimul adſint, quorum ſuperficies ſpatio terminos imponit; </s> <s xml:id="echoid-s5077" xml:space="preserve"><lb/>imo infinitum eſſe cælum alio agrumento probabile reddidit Halleyus <lb/>in Philoſ. </s> <s xml:id="echoid-s5078" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5079" xml:space="preserve">Quid vero tum punctum adeo remotum â Terrâ <lb/>operabitur? </s> <s xml:id="echoid-s5080" xml:space="preserve">ſed non ab uno regitur Magnes puncto, verum a pluri-<lb/>bus, neque tendit Acus vi Magnetis imbuta ad Cœlum, ſed ad Terram.</s> <s xml:id="echoid-s5081" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5082" xml:space="preserve">Dornæus in Vol. </s> <s xml:id="echoid-s5083" xml:space="preserve">1. </s> <s xml:id="echoid-s5084" xml:space="preserve">Theatr Chemic. </s> <s xml:id="echoid-s5085" xml:space="preserve">Cœleſti in fluentiâ Magnetem regi <lb/>opinabatur, non tamen quia Spiritus in eo eſſet: </s> <s xml:id="echoid-s5086" xml:space="preserve">vereor an Philoſophus <lb/>Cœleſtis influentiæ clarum conceptum formare unquam potuerit; <lb/></s> <s xml:id="echoid-s5087" xml:space="preserve">quid enim eſt influentia? </s> <s xml:id="echoid-s5088" xml:space="preserve">Spirituſne an corpus? </s> <s xml:id="echoid-s5089" xml:space="preserve">an quid aliud? </s> <s xml:id="echoid-s5090" xml:space="preserve">Spi-<lb/>ritum eſſe negat ipſe, quodnam igitur erit corpus, vel quænam alia <lb/>ſubſtantia? </s> <s xml:id="echoid-s5091" xml:space="preserve">niſi hæc prius definiatur, nihil plus intelligimus, quam <lb/>ſi nihil dixiſſet.</s> <s xml:id="echoid-s5092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5093" xml:space="preserve">Alii relicto Cœload Terram ſe converterunt, in ea cauſam reper-<lb/>turi; </s> <s xml:id="echoid-s5094" xml:space="preserve">idcirco Fracaſtorius â montibus quibuſdam Magneticis ſub <lb/>polo Septentrionali ſitis directionem Acus & </s> <s xml:id="echoid-s5095" xml:space="preserve">Magnetis derivabat. <lb/></s> <s xml:id="echoid-s5096" xml:space="preserve">Georgius Agricola Magnetem ita ſe dirigere cenſebat, ut ſe in pri-<lb/>ſtinum ſitum, quem in fodinis occupaverat reſtitueret: </s> <s xml:id="echoid-s5097" xml:space="preserve">Sententiam <lb/>ſuam uterque rejeciſſet, modo cognoviſſet directionem Acus & </s> <s xml:id="echoid-s5098" xml:space="preserve"><lb/>Magnetis perpetuis eſſe viciſſitudinibus obnoxiam.</s> <s xml:id="echoid-s5099" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5100" xml:space="preserve">Maurolycus ſupponebat Magneticam quandam inſulam, præter <lb/>polum ita conſtitutam, ut ad ſe ſemper Ferrum Magneremque diri-<lb/>geret; </s> <s xml:id="echoid-s5101" xml:space="preserve">ſed niſi hæc inſula, navigii inſtar perpetuo locum mutet, <pb o="220" file="0234" n="234" rhead="DISSERTATIO"/> explicari nequit Declinatio Declinationis, cui Magnes perpetuo ſub-<lb/>jicitur.</s> <s xml:id="echoid-s5102" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s5103" xml:space="preserve">Magneti naturalem ſenſationem adſcripſit Helmontius in Magn. <lb/></s> <s xml:id="echoid-s5104" xml:space="preserve">Vuln. </s> <s xml:id="echoid-s5105" xml:space="preserve">Curat. </s> <s xml:id="echoid-s5106" xml:space="preserve">pag. </s> <s xml:id="echoid-s5107" xml:space="preserve">727. </s> <s xml:id="echoid-s5108" xml:space="preserve">Si enim, inquit, Magnes ſe ad polum diri-<lb/>gat, eundem noviſſe oportet, ſi in directione ſuâ errorem non ſit <lb/>facturus, & </s> <s xml:id="echoid-s5109" xml:space="preserve">quomodo quæſo noverit, ſi non ſentiat ubi ſit? </s> <s xml:id="echoid-s5110" xml:space="preserve">ſimili-<lb/>ter ſi ad Ferrum eminus poſitum ſe torqueat polo neglecto, Ferrum <lb/>ſenſiſſe prius neceſſarium eſt, varios igitur ſenſus imaginis habet, <lb/>tum amoris & </s> <s xml:id="echoid-s5111" xml:space="preserve">philautiæ, adeoque phantaſiâ quâdam naturali dona-<lb/>tus eſt.</s> <s xml:id="echoid-s5112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5113" xml:space="preserve">Verum omnis noſtra ſcientia, omnis ſenſatio, amor, philautia, <lb/>ad mentem pertinent, rem â corpore diſtinctiſſimam, ergone Ma-<lb/>gnes quoque ex corpore & </s> <s xml:id="echoid-s5114" xml:space="preserve">animâ conjunctis conſtabit, quomodo <lb/>Philoſophus hoc novit? </s> <s xml:id="echoid-s5115" xml:space="preserve">an ex effectibus hactenus cognitis id probabi-<lb/>tur? </s> <s xml:id="echoid-s5116" xml:space="preserve">niſi aliis id evincat argumentis, aſſenſum a nemine extorquebit.</s> <s xml:id="echoid-s5117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5118" xml:space="preserve">Melioris proſapiæ viſa fuit acuti Carteſii opinio, qua ma-<lb/>teriam quandam Magneticam, inſtar ſtriarum exilium formatam, <lb/>perpetuo circa Terram volvi ſtatuit, quæ egreſſa & </s> <s xml:id="echoid-s5119" xml:space="preserve">ingreſſa Terræ <lb/>polos, delataque in ejus Meridiano, ſuâ determinatione Acum & </s> <s xml:id="echoid-s5120" xml:space="preserve"><lb/>Magnetem dirigeret, ſecumque abriperet: </s> <s xml:id="echoid-s5121" xml:space="preserve">At Acus non directa <lb/>Terræ polos verſus niſi in pauciſſimis locis, & </s> <s xml:id="echoid-s5122" xml:space="preserve">alii obnoxia ſemper <lb/>variis annis Declinationi hanc opinionem ipſa penitus refutat; </s> <s xml:id="echoid-s5123" xml:space="preserve">tranſ-<lb/>eo ſtrias breviſſimas fluidæ materiæ adſcriptas, quibus Magnes pro-<lb/>cul diſſitus Magneti adduceretur, legibus Mechanicis adeo adver-<lb/>ſari, ut intelligi nequeat tam abſona ex ſapienti progigni potuiſſe <lb/>cerebro: </s> <s xml:id="echoid-s5124" xml:space="preserve">quomodo enim cochleæ beneficio corpora ad ſe mutuo <lb/>movebuntur, niſi ejus longitudinis fuerit cochlea pater, ut & </s> <s xml:id="echoid-s5125" xml:space="preserve">in <lb/>matre immobili hæreat ab una parte, alterâ vero uſque ad corpus <lb/>movendum exporrigatur: </s> <s xml:id="echoid-s5126" xml:space="preserve">nec ſubtilior eſt explicatio Declinationis <lb/>Magneticæ, quæ penderet â Ferro & </s> <s xml:id="echoid-s5127" xml:space="preserve">Magnetibus, qui in viſceri-<lb/>bus Terræ aut in fundo maris hærerent; </s> <s xml:id="echoid-s5128" xml:space="preserve">cum magnus Terræ aut <lb/>maris tractus eidem declinationi ſubjiciatur, quæ etiam ordinatim <lb/>augetur, manente fundo immoto atque immutato: </s> <s xml:id="echoid-s5129" xml:space="preserve">inſuper Ferrum <lb/>ad tantam diſtantiam, quæ maris Indici profunditati æqualis eſt, in <lb/>alium Magnetem non videtur poſſe agere, quia experientia demon-<lb/>ſtrat, tormenta bellica ferrea in navibus ad 20 pedum diſtantiam <pb o="221" file="0235" n="235" rhead="DE MAGNETE."/> non agere in Verſorium, atque multo minori vi attrahente donatam <lb/>eſſe ipſam Ferri mineram alia docuerunt experimenta.</s> <s xml:id="echoid-s5130" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5131" xml:space="preserve">Gaſſendus in Terrâ exſculptas ſtrias ab Auſtro in Boream tenden-<lb/>tes, & </s> <s xml:id="echoid-s5132" xml:space="preserve">eodem ordine ſitas ac in Magnete partes ſupponebat, <lb/>unde directionem Magnetis deduxit: </s> <s xml:id="echoid-s5133" xml:space="preserve">ignoravit acutiſſimus Phi-<lb/>loſophus Magneticæ Declinationis perpetuam mutationem, quæ <lb/>ſitum partium in Terra æque ac in Magnete perpetuo mutari poſtu-<lb/>laret: </s> <s xml:id="echoid-s5134" xml:space="preserve">ſed an quoque ex ſitu partium Terræ ulla vis generabitur, <lb/>quæ in Magnetem ex ipſâ erutum, eamque non contingentem, <lb/>operabitur? </s> <s xml:id="echoid-s5135" xml:space="preserve">hoc ſanæ mentis intelligit nemo, alia ad vim expli-<lb/>candam deſideratur cauſa, quam ſi Fluidum aliquod eſſe voluerit <lb/>cum Carteſio, iisdem argumentis ſæpe allatis quoque ſupra re-<lb/>futaretur.</s> <s xml:id="echoid-s5136" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5137" xml:space="preserve">Gilbertus, & </s> <s xml:id="echoid-s5138" xml:space="preserve">cum ipſo conſentiens Cabeus Lib. </s> <s xml:id="echoid-s5139" xml:space="preserve">1. </s> <s xml:id="echoid-s5140" xml:space="preserve">Cap. </s> <s xml:id="echoid-s5141" xml:space="preserve">23. <lb/></s> <s xml:id="echoid-s5142" xml:space="preserve">Terram inſtar grandis Magnetis conſiderat, atque dirigi Acum <lb/>abſque Declinatione, ubi utrimque a Terræ continentibus ma-<lb/>joribus æqualiter trahitur, hinc in Azoribus nullam fieri Declina-<lb/>tionem, inter has inſulas & </s> <s xml:id="echoid-s5143" xml:space="preserve">Europam dirigi Ortum verſus, quia <lb/>ſoliditas Europæ plus traheret; </s> <s xml:id="echoid-s5144" xml:space="preserve">hanc ſententiam ipſi abjeciſſent <lb/>Patroni, ſi Declinationis perpetuam mutationem cognoviſſent, aut <lb/>lineam expertem Declinationis tranſiiſſe ſupra loca terreſtria, <lb/>marina, aliaque, in quibus æquabilis attractionis ſuſpicio dari <lb/>nulla poteſt: </s> <s xml:id="echoid-s5145" xml:space="preserve">tum, quod maximum eſt, Acum declinare rece-<lb/>dendo a littoribus Braſiliæ, atque mare petendo, non Terram.</s> <s xml:id="echoid-s5146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5147" xml:space="preserve">Hevelius librationem quandam in Terra advocat, ſimilem illi, <lb/>quæ in Luna obſervatur: </s> <s xml:id="echoid-s5148" xml:space="preserve">Sed an hæc tam lenta erit, ut modo <lb/>verſus unam partem oſcilletur centenorum aliquot annorum ſpa-<lb/>tio, dein reditura? </s> <s xml:id="echoid-s5149" xml:space="preserve">Nam anno 1580 Ortum verſus declinavit, <lb/>atque ab eo tempore in hoc uſque ad eandem partem progredi <lb/>perrexit directio Magnetis? </s> <s xml:id="echoid-s5150" xml:space="preserve">Similis libratio in Luna non datur; </s> <s xml:id="echoid-s5151" xml:space="preserve">an <lb/>vero hanc librationem Terræ Aſtronomi non obſervaſſent, quæ <lb/>ad plurimos gradus excurrit? </s> <s xml:id="echoid-s5152" xml:space="preserve">cum nondum redierit Acus ad Or-<lb/>tum in hac regione, ignoramus an reditura ſit, proinde ignora-<lb/>mus an libratio detur: </s> <s xml:id="echoid-s5153" xml:space="preserve">cæteroquin hic egregius Philoſophus ſibi <lb/>perſuaſit, perpenſis hypotheſibus aliorum, Magnetis Declinationem <lb/>non poſſe adſcribi Æthereis quibuſdam corpuſculis vid. </s> <s xml:id="echoid-s5154" xml:space="preserve">Philoſ. <lb/></s> <s xml:id="echoid-s5155" xml:space="preserve">Franſ. </s> <s xml:id="echoid-s5156" xml:space="preserve">N°. </s> <s xml:id="echoid-s5157" xml:space="preserve">64.</s> <s xml:id="echoid-s5158" xml:space="preserve"/> </p> <pb o="222" file="0236" n="236" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s5159" xml:space="preserve">Auzutus opinabatur materiam fluere per Terram ad axin pa-<lb/>rallelo motu, fluxum tamen continuo immutari ab alterationibus, <lb/>quas arte & </s> <s xml:id="echoid-s5160" xml:space="preserve">opera Terræ inducimus, eam excavando hic, alibi <lb/>accumulando & </s> <s xml:id="echoid-s5161" xml:space="preserve">montes & </s> <s xml:id="echoid-s5162" xml:space="preserve">acervos; </s> <s xml:id="echoid-s5163" xml:space="preserve">idem fieri a naturalibus cor-<lb/>roſionibus & </s> <s xml:id="echoid-s5164" xml:space="preserve">excavationibus, tum a metallorum generatione: </s> <s xml:id="echoid-s5165" xml:space="preserve">Verum <lb/>an tam exiguæ mutationes, quas foſſores Terræ inferunt, pote-<lb/>runt tantam varietatem, & </s> <s xml:id="echoid-s5166" xml:space="preserve">tam conſtantem inducere Declinationi <lb/>Magnetis? </s> <s xml:id="echoid-s5167" xml:space="preserve">Quomodo Magnes ſtationarius explicabitur, qui per <lb/>4 ſe ſequentes annos a 1720 ad 1725 eadem directione actus <lb/>fuit? </s> <s xml:id="echoid-s5168" xml:space="preserve">An toto hoc tempore foſſores metallorum per univerſum <lb/>terrarum orbem quieverunt? </s> <s xml:id="echoid-s5169" xml:space="preserve">Quomodo retrogradus explicabitur <lb/>Magnetis motus? </s> <s xml:id="echoid-s5170" xml:space="preserve">Hanc idcirco opinionem, in Philoſ. </s> <s xml:id="echoid-s5171" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5172" xml:space="preserve">N°. <lb/></s> <s xml:id="echoid-s5173" xml:space="preserve">51. </s> <s xml:id="echoid-s5174" xml:space="preserve">propoſitam, nemo amplius amplectitur, nec fovet.</s> <s xml:id="echoid-s5175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5176" xml:space="preserve">Sed ne tempus teramus in hypotheſibus enumerandis, ad ex-<lb/>perimenta redeamus potius, quæ quamdiu ſtabit Phyſicæ honos, <lb/>eadem permanebunt, & </s> <s xml:id="echoid-s5177" xml:space="preserve">firmam baſin ratiocinio ſemper ſtruent, <lb/>quæcunque inveniatur cauſa directionis, aut quocunque modo <lb/>comparata fuerit vis Magnetica.</s> <s xml:id="echoid-s5178" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div129" type="section" level="1" n="129"> <head xml:id="echoid-head138" xml:space="preserve">EXPERIMENTUM CIV.</head> <p> <s xml:id="echoid-s5179" xml:space="preserve">Conati fuerunt nonnulli Philoſophi Inclinationem & </s> <s xml:id="echoid-s5180" xml:space="preserve">Declinatio-<lb/>nem Acuum Magneticarum explicare ex effectibus, quos Magnes <lb/>in ejuſmodi Acus edit, fingentes ideo Magnetes globoſos, ſive <lb/>Terrellas, quia Terram Magnetem grandem habuerunt, in qua <lb/>omnia phænomena modo majora fiunt, quorum exiguas imagines <lb/>Magnes quoque conſpiciendas præberet: </s> <s xml:id="echoid-s5181" xml:space="preserve">globoſo lapidi inſculpſe-<lb/>runt Æquatorem, inter utrumque polum medium, & </s> <s xml:id="echoid-s5182" xml:space="preserve">Meridianos, <lb/>quales in artificialibus ſpectamus globis; </s> <s xml:id="echoid-s5183" xml:space="preserve">Ut Inclinatio Acus intel-<lb/>ligatur, ſit in Tab. </s> <s xml:id="echoid-s5184" xml:space="preserve">5. </s> <s xml:id="echoid-s5185" xml:space="preserve">fig. </s> <s xml:id="echoid-s5186" xml:space="preserve">7. </s> <s xml:id="echoid-s5187" xml:space="preserve">A B C D Magnes Sphæricus, Acus <lb/>ſit G H, per cujus centrum gravitatis I ducatur recta E K ex cen-<lb/>tro Magnetis, atque in hanc perpendicularis M N, repræſentans <lb/>horizontem, quæ ſit parallela Tangenti punctum L, tum menſuretur <lb/>angulus M I G, qui vocatur Inclinationis, menſuretur diſtantia pun-<lb/>cti L a polo A, quo facto habetur Inclinatio Acus in determinata di-<lb/>ſtantia â polo Magnetis: </s> <s xml:id="echoid-s5188" xml:space="preserve">hac methodo condiderunt Tabulam appo-<lb/>ſitam.</s> <s xml:id="echoid-s5189" xml:space="preserve"/> </p> <pb o="223" file="0237" n="237" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s5190" xml:space="preserve">Tabula Inclinationis Acus Magneticæ infra horizontem Borealem <lb/>ipſius Magnetis.</s> <s xml:id="echoid-s5191" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Altitudo poli Borealis \\ & diſtantia a polo \\ Magnetis. # Ex Gilberti & \\ Cabæi \\ Experimento. # Ex Grandamici \\ Experimento. # Ex \\ Whiſtono <lb/>Gradus # Minuta. # Grad. # Minut. # Gr. # M. # Gr. # M. <lb/>5 # 0 # 11 # 0 # 21 # 0 # # <lb/>9 # 0 # # # # # 25 # 50 <lb/>10 # 0 # 20 # 35 # 35 # 0 # # <lb/>15 # 0 # 30 # 25 # 44 # 0 # # <lb/>18 # 0 # # # # # 36 # 52 <lb/>20 # 0 # 37 # 35 # 51 # 0 # # <lb/>22 # 30 # # # # # 41 # 24 <lb/>25 # 0 # 44 # 55 # 56 # 0 # # <lb/>27 # 0 # # # # # 45 # 34 <lb/>30 # 0 # 51 # 8 # 60 # 0 # # <lb/>35 # 0 # 57 # 20 # 63 # 0 # # <lb/>36 # 0 # # # # # 53 # 7 <lb/>40 # 0 # 62 # 45 # 66 # 0 # # <lb/>45 # 0 # 67 # 50 # 69 # 0 # 60 # 0 <lb/>50 # 0 # 71 # 40 # 72 # 0 # # <lb/>54 # 0 # # # # # 60 # 20 <lb/>55 # 0 # 76 # 0 # 74 # 30 # # <lb/>60 # 0 # 78 # 30 # 77 # 0 # # <lb/>63 # 0 # # # # # 72 # 32 <lb/>65 # 0 # 81 # 30 # 79 # 30 # # <lb/>67 # 30 # # # # # 75 # 30 <lb/>70 # 0 # 84 # 0 # 82 # 0 # # <lb/>72 # 0 # # # # # 78 # 28 <lb/>75 # 0 # 86 # 30 # 84 # 0 # # <lb/>80 # 0 # 88 # 5 # 86 # 0 # # <lb/>81 # 0 # # # # # 84 # 15 <lb/>85 # 0 # 89 # 0 # 88 # 0 # # <lb/>90 # 0 # 90 # 0 # 90 # 0 # 90 # 0 <lb/></note> <pb o="224" file="0238" n="238" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s5192" xml:space="preserve">Quamvis Philoſophi hæc Experimenta cum cura inſtituerint, non <lb/>tamen magnos evitare errores potuerunt, quia polus Magnetis non <lb/>eſt punctum, ſed plaga lata: </s> <s xml:id="echoid-s5193" xml:space="preserve">Ex quo puncto igitur hujus plagæ <lb/>diſtantia menſurabitur, an ex medio, an ex aliquo margine? </s> <s xml:id="echoid-s5194" xml:space="preserve">Ideo <lb/>non miramur obſervationes Cabæi, Gilberti, Grandamici, Whi-<lb/>ſtoni valde inter ſe differre. </s> <s xml:id="echoid-s5195" xml:space="preserve">Cl. </s> <s xml:id="echoid-s5196" xml:space="preserve">de La Hire cum ejuſmodi Terrel-<lb/>la, Diametri unius pedis, experimenta inſtituit ſpectantia Declina-<lb/>tionem Acus, hanc variis imponendo Meridianis, obſervavit A-<lb/>cum aliquando declinaſſe verſus Orientem, aliquando verſus Oc-<lb/>cidentem, aliquando nihil, vid. </s> <s xml:id="echoid-s5197" xml:space="preserve">L‘Hiſt. </s> <s xml:id="echoid-s5198" xml:space="preserve">de L‘Academ. </s> <s xml:id="echoid-s5199" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5200" xml:space="preserve">A°. <lb/></s> <s xml:id="echoid-s5201" xml:space="preserve">1705. </s> <s xml:id="echoid-s5202" xml:space="preserve">Perperam tamen me judice ex his Experimentis concludere-<lb/>tur, ſimilem deprehenſum iri Inclinationem & </s> <s xml:id="echoid-s5203" xml:space="preserve">Declinationem A-<lb/>cuum in variis Terræ locis, nam ingens eſt differentia inter totum <lb/>Terrarum orbem, & </s> <s xml:id="echoid-s5204" xml:space="preserve">Terrellam Magneticam: </s> <s xml:id="echoid-s5205" xml:space="preserve">Terrella, quanta <lb/>eſt, Magnes eſt, Acum trahens dirigensque verſus ſuperficiem ex-<lb/>tremam & </s> <s xml:id="echoid-s5206" xml:space="preserve">plagas polares: </s> <s xml:id="echoid-s5207" xml:space="preserve">Verum tota noſtra Terra non eſt Ma-<lb/>gnes, qui Acum ad ſuos polos in ſuperficie ſitos determinat, ſed <lb/>verſus polos profunde locatos in intimo gremio, unde maxima <lb/>inter directionem Acus a Magnete, & </s> <s xml:id="echoid-s5208" xml:space="preserve">a Terra debet intercedere <lb/>diſcrepantia: </s> <s xml:id="echoid-s5209" xml:space="preserve">Varia Acus Declinatio, quam La Hire obſervavit, <lb/>procul dubio pendebat ab heterogeneitate Magnetis, qui nonnullas <lb/>partes in ſe generoſiores, alias imbecilliorum virium concludebat: </s> <s xml:id="echoid-s5210" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s5211" xml:space="preserve">prout Magnes plus minuſve homogeneæ ſit ſubſtantiæ, ita quo-<lb/>que diverſa phænomena Inclinationem ſpectantia, exhibebit, hinc <lb/>tanta quoque differentia inter experimenta Cabæi & </s> <s xml:id="echoid-s5212" xml:space="preserve">Grandamici, <lb/>qui variis uſi fuerunt Magnetibus.</s> <s xml:id="echoid-s5213" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div130" type="section" level="1" n="130"> <head xml:id="echoid-head139" xml:space="preserve">EXPERIMENTUM CV.</head> <p> <s xml:id="echoid-s5214" xml:space="preserve">Verſoria quæcunque rite compoſita ducantur ſuper eodem polo <lb/>Magnetis, hæc omnia impoſita ſtylis politiſſimis in eadem regio-<lb/>ne, eodem tempore dirigentur ad eandem cæli plagam: </s> <s xml:id="echoid-s5215" xml:space="preserve">Neque <lb/>directionis differentia obſervatur Verſoriis ad diverſiſſimorum Ma-<lb/>gnetum polos cognomines affrictis, ſive fortius, ſive lenius, imo <lb/>etiamſi in intervallo â polo.</s> <s xml:id="echoid-s5216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5217" xml:space="preserve">Cum pluribus diverſiſſimæ longitudinis Verſoriis tentamina feci, <pb o="225" file="0239" n="239" rhead="DE MAGNETE."/> directione omnium manente eâdem, atque effectus eosdem exper-<lb/>tus fui: </s> <s xml:id="echoid-s5218" xml:space="preserve">quod non eſt mirandum, quia eſt eadem cauſa Magnetica, <lb/>& </s> <s xml:id="echoid-s5219" xml:space="preserve">Univerſalis, quæ dirigit virtute imprægnatum Ferrum; </s> <s xml:id="echoid-s5220" xml:space="preserve">adeoque ea-<lb/>dem directione omne Ferrum agatur in eodem terræ loco neceſſum <lb/>erit: </s> <s xml:id="echoid-s5221" xml:space="preserve">obſervaverunt id plurimi autores a multis retro annis, quem-<lb/>admodum Normannus in New Attract. </s> <s xml:id="echoid-s5222" xml:space="preserve">Cap. </s> <s xml:id="echoid-s5223" xml:space="preserve">Gilbertus de Ma-<lb/>gnete Lib. </s> <s xml:id="echoid-s5224" xml:space="preserve">5. </s> <s xml:id="echoid-s5225" xml:space="preserve">Cap. </s> <s xml:id="echoid-s5226" xml:space="preserve">5. </s> <s xml:id="echoid-s5227" xml:space="preserve">Seller in Philoſ. </s> <s xml:id="echoid-s5228" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5229" xml:space="preserve">N°. </s> <s xml:id="echoid-s5230" xml:space="preserve">23. </s> <s xml:id="echoid-s5231" xml:space="preserve">de la Hire <lb/>in L‘Hiſt. </s> <s xml:id="echoid-s5232" xml:space="preserve">de L‘Acad. </s> <s xml:id="echoid-s5233" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5234" xml:space="preserve">A°. </s> <s xml:id="echoid-s5235" xml:space="preserve">1705. </s> <s xml:id="echoid-s5236" xml:space="preserve">Petitus addit, non obſer-<lb/>vari directionis differentiam, etiamſi Acus tetigerit Magnetem non <lb/>in polo, ſed in plaga quadam latiori a polo remota. </s> <s xml:id="echoid-s5237" xml:space="preserve">Vid. </s> <s xml:id="echoid-s5238" xml:space="preserve">Olden-<lb/>burgii Acta Philoſ. </s> <s xml:id="echoid-s5239" xml:space="preserve">pag. </s> <s xml:id="echoid-s5240" xml:space="preserve">428. </s> <s xml:id="echoid-s5241" xml:space="preserve">hinc erraſſe videntur, qui directio-<lb/>nis differentiam dari opinati ſunt, niſi figura compoſita aliquid con-<lb/>tribuerit, uti monebitur infra, pag. </s> <s xml:id="echoid-s5242" xml:space="preserve">232.</s> <s xml:id="echoid-s5243" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div131" type="section" level="1" n="131"> <head xml:id="echoid-head140" xml:space="preserve">EXPERIMENTUM CVI.</head> <p> <s xml:id="echoid-s5244" xml:space="preserve">Præterire etiam nequeo ſtupendam obſervationem â nautis circa <lb/>directionem Verſorii factam; </s> <s xml:id="echoid-s5245" xml:space="preserve">aliquoties enim annotatum eſt, Ful-<lb/>men prope Verſorium delatum, hujus directionem plane immutaſ-<lb/>ſe, ita ut polus Septentrionalis evaſerit Auſtralis: </s> <s xml:id="echoid-s5246" xml:space="preserve">proſtant ejuſmodi <lb/>obſervationes in Philoſ. </s> <s xml:id="echoid-s5247" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s5248" xml:space="preserve">N°. </s> <s xml:id="echoid-s5249" xml:space="preserve">127. </s> <s xml:id="echoid-s5250" xml:space="preserve">pag. </s> <s xml:id="echoid-s5251" xml:space="preserve">647. </s> <s xml:id="echoid-s5252" xml:space="preserve">N°. </s> <s xml:id="echoid-s5253" xml:space="preserve">157. <lb/></s> <s xml:id="echoid-s5254" xml:space="preserve">pag. </s> <s xml:id="echoid-s5255" xml:space="preserve">520. </s> <s xml:id="echoid-s5256" xml:space="preserve">in Compendii vol. </s> <s xml:id="echoid-s5257" xml:space="preserve">4 part. </s> <s xml:id="echoid-s5258" xml:space="preserve">2. </s> <s xml:id="echoid-s5259" xml:space="preserve">Cap. </s> <s xml:id="echoid-s5260" xml:space="preserve">4. </s> <s xml:id="echoid-s5261" xml:space="preserve">Walliſius hoc ob-<lb/>ſervatum memoriæ quoque prodidit, confirmavit Hartſoekerus in <lb/>Conject. </s> <s xml:id="echoid-s5262" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s5263" xml:space="preserve">idem ſanxerunt noſtri artifices Acuum Nautica-<lb/>rum, adeo ut de obſervatione ipſâ dubium moveri nequeat: </s> <s xml:id="echoid-s5264" xml:space="preserve">addi-<lb/>tur inſuper, chartam, in qua Verſorium latet, non fuiſſe combu-<lb/>ſtam: </s> <s xml:id="echoid-s5265" xml:space="preserve">ſed tam mirifice fulmen rebus in humanis ludit, ut gladium <lb/>in vagina candefaciat, imo liquefaciat, ne quidem combuſtâ læſâ-<lb/>ve vaginâ, eo etiam modo chalybeum Verſorium calefecit, non <lb/>comburendo chartam, illud vaginæ inſtar ambientem: </s> <s xml:id="echoid-s5266" xml:space="preserve">Ut autem <lb/>hoc phænomenon explicetur, quod admodum paradoxon eſt, con-<lb/>cipiamus fulmen Verſorium calefeciſſe; </s> <s xml:id="echoid-s5267" xml:space="preserve">adeoque id omni virtute <lb/>Magnetica ſpoliavit, quemadmodum Ferrum igni impoſitum vim <lb/>Magnetis exuit: </s> <s xml:id="echoid-s5268" xml:space="preserve">ſi autem fulmen non accurate ſecundum longitu-<lb/>dinem Verſorii projectum fuerit, ſed obliquitate quâcunque in id <lb/>impegerit, ut Verſorium converterit, id inverſo poſitum ſitu, at-<lb/>que frigefactum, directione plane oppoſitâ priori agetur, nam li- <pb o="226" file="0240" n="240" rhead="DISSERTATIO"/> quebit in Capite 5. </s> <s xml:id="echoid-s5269" xml:space="preserve">hujus Diſſertationis, Ferri prius igne candefa-<lb/>cti, deinde in Meridiano frigefacti, cuſpidem Boream verſus dire-<lb/>ctam, polum Boreum evadere, ſiigitur Verſorii cauda Auſtralis a fulmi-<lb/>ne converſa fuerit ad Boream, atque eo in ſitu frigefacta, hæc verſusBo-<lb/>ream dirigeretur neceſſum erat; </s> <s xml:id="echoid-s5270" xml:space="preserve">cuſpis autem Auſtrum verſus, ſitu op-<lb/>poſito priori: </s> <s xml:id="echoid-s5271" xml:space="preserve">ne autem ſuſpicemur ignem ſolum in Verſorium ada-<lb/>ctum ſufficere ad directionem immutandam, experimenta quædam <lb/>conſulenda erunt: </s> <s xml:id="echoid-s5272" xml:space="preserve">flammam lampadis encauſticæ excitavi magnam, <lb/>eamque vi follis condenſatam, ut fulmen ejuſque jactum æmulare-<lb/>tur, direxi in Verſorium, & </s> <s xml:id="echoid-s5273" xml:space="preserve">quidem ſecundum ejus longitudinem, <lb/>ictu tamen unico & </s> <s xml:id="echoid-s5274" xml:space="preserve">veloci ne id penitus igniretur; </s> <s xml:id="echoid-s5275" xml:space="preserve">poſtea explora-<lb/>ta Verſorii directio permanſiſſe eadem deprehenſa fuit: </s> <s xml:id="echoid-s5276" xml:space="preserve">tum flam-<lb/>ma tranſverſe in unum, deinde in alterum Verſorii brachium im-<lb/>pulſa fuit, ſuperſtes nihilominus antiqua directio fuit, quamobrem <lb/>ignis ſolus ineptus eſt ad vim directricem invertendam, licet eam <lb/>debiliter infringatque; </s> <s xml:id="echoid-s5277" xml:space="preserve">eodem modo fulmen quatenus ignis, quo-<lb/>cunque motu etiam determinatum, non convertit vim directricem <lb/>Verſorii, ſedigne ſuo vi priori Magnetica id orbavit, ſimulque inver-<lb/>tit, qua poſitione aliquamdiu illud relictum frigefactumque directio-<lb/>nem prorſus contrariam nactum fuit.</s> <s xml:id="echoid-s5278" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div132" type="section" level="1" n="132"> <head xml:id="echoid-head141" xml:space="preserve">EXPERIMENTUM CVII.</head> <p> <s xml:id="echoid-s5279" xml:space="preserve">Quotieſcunque Verſorium horizontale, Magneti affrictum, ſtylo <lb/>imponitur, ut non in Meridiano habeatur ſuo, ſibi commiſſum, ali-<lb/>quot vibrationibus agitur, donec tandem quieſcat in Meridiano: <lb/></s> <s xml:id="echoid-s5280" xml:space="preserve">obſervare conatus fui quot vibrationes data A cus intra datum tem-<lb/>pus abſolveret, ut inde virtutis directricis magnitudo erueretur, <lb/>quemadmodum ope Acus Inclinatoriæ & </s> <s xml:id="echoid-s5281" xml:space="preserve">oſcillantis factum fuit: </s> <s xml:id="echoid-s5282" xml:space="preserve"><lb/>Experimenta eum in finem capta fuerunt ſequentia cum acubus va-<lb/>riarum longitudinum.</s> <s xml:id="echoid-s5283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5284" xml:space="preserve">1°. </s> <s xml:id="echoid-s5285" xml:space="preserve">Acus 2 pollices longa abſolvit 10 primas vibrationes ſpatio <lb/>15?</s> <s xml:id="echoid-s5286" xml:space="preserve">. ſed 20 vibrationes in 29?</s> <s xml:id="echoid-s5287" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5288" xml:space="preserve">2°. </s> <s xml:id="echoid-s5289" xml:space="preserve">Acus 4 pollic. </s> <s xml:id="echoid-s5290" xml:space="preserve">4 linear. </s> <s xml:id="echoid-s5291" xml:space="preserve">cujus pondus 40 {1/2} granorum abſolvit <lb/>5 primas oſcillationes intra 16?</s> <s xml:id="echoid-s5292" xml:space="preserve">, ſed 10 intra 30?</s> <s xml:id="echoid-s5293" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5294" xml:space="preserve">3°. </s> <s xml:id="echoid-s5295" xml:space="preserve">Acus 4 poll. </s> <s xml:id="echoid-s5296" xml:space="preserve">11 linear. </s> <s xml:id="echoid-s5297" xml:space="preserve">cujus pondus erat 48 granorum abſol- <pb o="227" file="0241" n="241" rhead="de MAGNETE."/> vit 5 primas oſcillationes intra 20?</s> <s xml:id="echoid-s5298" xml:space="preserve">, ſed 10 oſcillationes intra <lb/>39?</s> <s xml:id="echoid-s5299" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5300" xml:space="preserve">4°. </s> <s xml:id="echoid-s5301" xml:space="preserve">Acus 6 poll. </s> <s xml:id="echoid-s5302" xml:space="preserve">6 linear. </s> <s xml:id="echoid-s5303" xml:space="preserve">cujus pondus 57 granorum abſolvit 5 <lb/>vibrationes intra 18?</s> <s xml:id="echoid-s5304" xml:space="preserve">. decem vibrationes intra 35?</s> <s xml:id="echoid-s5305" xml:space="preserve">. 15 vibrationes <lb/>intra 52?</s> <s xml:id="echoid-s5306" xml:space="preserve">, viginti vibrationes intra 1?</s> <s xml:id="echoid-s5307" xml:space="preserve">, 10?</s> <s xml:id="echoid-s5308" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5309" xml:space="preserve">5°. </s> <s xml:id="echoid-s5310" xml:space="preserve">Acus 6 poll. </s> <s xml:id="echoid-s5311" xml:space="preserve">6 linear. </s> <s xml:id="echoid-s5312" xml:space="preserve">cujus pondus 56 granorum abſolvit 20 <lb/>vibrationes intra 1?</s> <s xml:id="echoid-s5313" xml:space="preserve">, 14?</s> <s xml:id="echoid-s5314" xml:space="preserve">. in alio tentamine 10 vibrationes intra <lb/>40?</s> <s xml:id="echoid-s5315" xml:space="preserve">, viginti intra 1?</s> <s xml:id="echoid-s5316" xml:space="preserve">, 12?</s> <s xml:id="echoid-s5317" xml:space="preserve">. in alio tentamine 20 vibrationes perfecit <lb/>intra 1?</s> <s xml:id="echoid-s5318" xml:space="preserve">, 13?</s> <s xml:id="echoid-s5319" xml:space="preserve">. in alio tentamine viginti vibrationes deſcripſit intra <lb/>1?</s> <s xml:id="echoid-s5320" xml:space="preserve">, 16?</s> <s xml:id="echoid-s5321" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5322" xml:space="preserve">6°. </s> <s xml:id="echoid-s5323" xml:space="preserve">Acus 9 pollices longa, cujus pondus 95 granorum abſolvit <lb/>10 vibrationes intra 1 Minutum, in alio tentamine in 56?</s> <s xml:id="echoid-s5324" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5325" xml:space="preserve">7°. </s> <s xml:id="echoid-s5326" xml:space="preserve">Acus 12 pollic. </s> <s xml:id="echoid-s5327" xml:space="preserve">10 linear. </s> <s xml:id="echoid-s5328" xml:space="preserve">cujus pondus 205 gran. </s> <s xml:id="echoid-s5329" xml:space="preserve">abſolvit 5 <lb/>vibrationes intra 54?</s> <s xml:id="echoid-s5330" xml:space="preserve">. decem vibrationes intra 1?</s> <s xml:id="echoid-s5331" xml:space="preserve">, 46?</s> <s xml:id="echoid-s5332" xml:space="preserve">. quindecim <lb/>vibrationes intra 2?</s> <s xml:id="echoid-s5333" xml:space="preserve">, 39?</s> <s xml:id="echoid-s5334" xml:space="preserve">. viginti vibrationes intra 3?</s> <s xml:id="echoid-s5335" xml:space="preserve">, 30?</s> <s xml:id="echoid-s5336" xml:space="preserve">. triginta <lb/>vibrationes intra 5?</s> <s xml:id="echoid-s5337" xml:space="preserve">, 8?</s> <s xml:id="echoid-s5338" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5339" xml:space="preserve">8°. </s> <s xml:id="echoid-s5340" xml:space="preserve">Acus 5 pollic. </s> <s xml:id="echoid-s5341" xml:space="preserve">5 linear. </s> <s xml:id="echoid-s5342" xml:space="preserve">ponderis 30 granorum abſolvit 5 vi-<lb/>brationes in 35?</s> <s xml:id="echoid-s5343" xml:space="preserve">. decem in 1?</s> <s xml:id="echoid-s5344" xml:space="preserve">, 5?</s> <s xml:id="echoid-s5345" xml:space="preserve">. alias decem in 60?</s> <s xml:id="echoid-s5346" xml:space="preserve">.</s> </p> <p> <s xml:id="echoid-s5347" xml:space="preserve">Obſervamus in hiſce Experimentis anomalias, illis ſimiles, quas <lb/>in Acu Inclinatoria notavimus, æque multæ enim vibrationes non <lb/>abſolvuntur ſemper eodem tempore, ſed diverſo, etiamſi inter <lb/>tentamina repetita nequidem horæ quadrans interceſſerit, quia vero <lb/>pendent oſcillationes hæ â vi directrice Magnetica, quemadmodum <lb/>in Acu Inclinatoria, erit maxima hujus virtutis perpetua inæquali-<lb/>tas, uti ſupra indicavimus: </s> <s xml:id="echoid-s5348" xml:space="preserve">cæteroquin videntur eſſe Quadrata tem-<lb/>porum, quibus vibrationes duarum Acuum variæ longitudinis ab-<lb/>ſolvuntur, in ratione compoſita ex directâ longitudinis & </s> <s xml:id="echoid-s5349" xml:space="preserve">gravita-<lb/>tis. </s> <s xml:id="echoid-s5350" xml:space="preserve">ſive maſſæ.</s> <s xml:id="echoid-s5351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5352" xml:space="preserve">Nam Acûs 9 pollicum, ſive 108 linearum, pondus fuit 95 gra-<lb/>norum, hi duo numeri per ſe multiplicati, dant 10260: </s> <s xml:id="echoid-s5353" xml:space="preserve">Acus 12 poll. <lb/></s> <s xml:id="echoid-s5354" xml:space="preserve">10 linear.</s> <s xml:id="echoid-s5355" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5356" xml:space="preserve">10260, 31570:</s> <s xml:id="echoid-s5357" xml:space="preserve">: 3600, 11135 {115/171}. </s> <s xml:id="echoid-s5358" xml:space="preserve">11135 {115/171}=105 + </s> </p> <p> <s xml:id="echoid-s5359" xml:space="preserve">Sive 154 linear. </s> <s xml:id="echoid-s5360" xml:space="preserve">habet pondus 205 granorum, quæ per ſe mul-<lb/>tiplicata dant 31570. </s> <s xml:id="echoid-s5361" xml:space="preserve">a breviori Acu abſolvuntur 10 vibrationes <pb o="228" file="0242" n="242" rhead="DISSERTATIO"/> tempore 60?</s> <s xml:id="echoid-s5362" xml:space="preserve">. hujus quadratum eſt 3600, adeoque ſunt 10260 ad 31570, veluti 3600 ad 11135 {115/171}, hujus numeri radix eſt media in- ter 105 & </s> <s xml:id="echoid-s5363" xml:space="preserve">106 ſed tempus 10 vibrationum fuit obſervatum 106?</s> <s xml:id="echoid-s5364" xml:space="preserve">. quod ſatis accurate congruit; </s> <s xml:id="echoid-s5365" xml:space="preserve">non enim hæc proportio ſemper lo- cum habebit, cum tantopere tempora vibrationum inter ſe diffe- rant, ſufficit ad veritatem appropinquaſſe. </s> <s xml:id="echoid-s5366" xml:space="preserve">Quando hæc experi- menta inſtituuntur, ſollicite curandum eſt ut ſtylus, ſupra quem Acus vertitur, ſit acutus politiſſimuſque ſimul, & </s> <s xml:id="echoid-s5367" xml:space="preserve">cavitates Acuum etiam lævigatiſſimæ. </s> <s xml:id="echoid-s5368" xml:space="preserve">cæteroquin aſperitates motum vibratorium impediunt, atque tempus excurrit longius, quo vibratio abſolvi- tur, quam fieret poſitis omnibus lævigatiſſimis: </s> <s xml:id="echoid-s5369" xml:space="preserve">Cum elapſis qui- buſdam menſibus experimenta eadem repetierim, aliud tempus ex- currere, quo eædem vibrationes abſolvebantur, animadverti: </s> <s xml:id="echoid-s5370" xml:space="preserve">præ- terea novam longiſſimamque præparavi Acum, 36 {1/2} pollic. </s> <s xml:id="echoid-s5371" xml:space="preserve">Rheno- land. </s> <s xml:id="echoid-s5372" xml:space="preserve">fere ubivis ejuſdem craſſitiei, cujus pondus erat 1233 grano- rum, cujus tempora in repetitis tentaminibus fuerunt fere eadem, diſcrepantia tamen parum inter ſe, quorum unum hic adferam.</s> <s xml:id="echoid-s5373" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Vibrationes Tempora # M?. # M?. <lb/>1 # 0 # 18 <lb/>2 # 0 # 38 <lb/>3 # 0 # 56 <lb/>4 # 1 # 15 <lb/>5 # 1 # 33 <lb/>6 # 1 # 49 <lb/>7 # 2 # 11 <lb/>8 # 2 # 24 <lb/></note> <p> <s xml:id="echoid-s5374" xml:space="preserve">Tempus medium, quo una vibratio abſolvitur, eſt proinde æqua-<lb/>lis 18 {1/2} minuto ſecundo: </s> <s xml:id="echoid-s5375" xml:space="preserve">ſi nunc comparemus tempus vibrationis <lb/>impenſum ab hac Acu, cum tempore a pendulo acto gravitate & </s> <s xml:id="echoid-s5376" xml:space="preserve"><lb/>ejuſdem longitudinis, quod foret 34 circiter minutorum tertiorum, <lb/>erunt hæc tempora inter ſe uti 18 {1/2} Minuta ſecunda ad 34 Minuta <lb/>tertia ſive uti 1110 ad 34 quamobrem per ea Lemmata de pendulis <lb/>ſupra aſſumta, erit vis gravitatis ad vim directricem Magnetis, uti <pb o="229" file="0243" n="243" rhead="de MAGNETE."/> 1232100 ad 1117. </s> <s xml:id="echoid-s5377" xml:space="preserve">hoc eſt uti 1103 ad 1. </s> <s xml:id="echoid-s5378" xml:space="preserve">Vis gravitatis autem re-<lb/>ſpectu virtutis directricis inventa ſuperius fuit Exp. </s> <s xml:id="echoid-s5379" xml:space="preserve">CII. </s> <s xml:id="echoid-s5380" xml:space="preserve">uti 295 <lb/>ad 1. </s> <s xml:id="echoid-s5381" xml:space="preserve">nunc vero majorem rationem habet ad vim Magneticam, quod <lb/>oritur, quia Acus Inclinatoria â tota vi directrice agi poteſt, & </s> <s xml:id="echoid-s5382" xml:space="preserve"><lb/>verſus Magnetis polum, cum Acus horizontalis modo â parte vir-<lb/>tutis Magneticæ dirigi poſſit, nempe ab ea, quæ in latera Verſorii <lb/>horizonti perpendicularia agit, Acus vero Inclinatoria agatur a vi <lb/>deprimente, ſive â tota vi Magnetica.</s> <s xml:id="echoid-s5383" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div133" type="section" level="1" n="133"> <head xml:id="echoid-head142" xml:space="preserve">EXPERIMENTUM CVIII.</head> <p> <s xml:id="echoid-s5384" xml:space="preserve">Eadem Magnetis pars, quæ Verſorio communicat directionem <lb/>verſus Auſtrum, diviſo Magnete communicat Verſorio directionem <lb/>verſus Septentrionem.</s> <s xml:id="echoid-s5385" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5386" xml:space="preserve">Hoc, quod prima fronte paradoxon videretur apprime a Doctif-<lb/>ſimo Dechales fuit intellectum & </s> <s xml:id="echoid-s5387" xml:space="preserve">ſolutum. </s> <s xml:id="echoid-s5388" xml:space="preserve">Sit enim in Tab. </s> <s xml:id="echoid-s5389" xml:space="preserve">7 fig. <lb/></s> <s xml:id="echoid-s5390" xml:space="preserve">6. </s> <s xml:id="echoid-s5391" xml:space="preserve">Magnes rotundus ABEF, cujus hemiſphærium Boreale ſit <lb/>CXEFZD, in quo punctum, I diſſitum ab Æquatore, ſed parum: </s> <s xml:id="echoid-s5392" xml:space="preserve"><lb/>puncto I applicetur cuſpis Verſorii, quod ſuper eo ducatur, diri-<lb/>getur cuſpis verſus Septentrionem; </s> <s xml:id="echoid-s5393" xml:space="preserve">dividatur tum Magnes ſectione <lb/>tranſeunte per Æquatorem C D, tum E F manebit polus Borealis, <lb/>ſed C D evadit Auſtralis, eritque hujus ſegmenti Æquator in X Z, <lb/>adeoque punctum I evadit pars ſegmenti Auſtralis, huic nunc ite-<lb/>rum apponatur cuſpis Verſorii, & </s> <s xml:id="echoid-s5394" xml:space="preserve">affricetur, dirigetur verſus Au-<lb/>ſtrum, priori contraria directione.</s> <s xml:id="echoid-s5395" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div134" type="section" level="1" n="134"> <head xml:id="echoid-head143" xml:space="preserve">EXPERIMENTUM CIX. <lb/>DE FABRICA VERSORIORUM.</head> <p> <s xml:id="echoid-s5396" xml:space="preserve">Quoniam ab aliquot retro temporibus nonnulli Eruditi haud exi-<lb/>guam collocarunt operam, ut ſimplicem commodamque invenirent <lb/>& </s> <s xml:id="echoid-s5397" xml:space="preserve">conſtruerent machinam, cujus auxilio Declinatio Verſoriorum <lb/>accurate detegeretur, operæ pretium eſſe judicavimus hic adjungere <lb/>obſervationes, quas inter conſtruendam ejuſmodi machinam, tum <pb o="230" file="0244" n="244" rhead="DISSERTATIO"/> alias Acus Magneticas, adnotavimus</s> </p> <p> <s xml:id="echoid-s5398" xml:space="preserve">Acus Magneticæ, quas etiam Verſoria vocavimus, conſtruendæ <lb/>ſunt ex Chalybe puriſſimo, in quo nullæ ſunt ſpinæ, ſeu partes aliis <lb/>duriores, neque dentur fiſſuræ aut rimæ, hæ utcunque tenues fuerint, <lb/>ſollicite ſunt evitandæ; </s> <s xml:id="echoid-s5399" xml:space="preserve">hinc maſſa, ex quâ Acus fabrefiet, ſit bene <lb/>ſolida, unitaque quantum fieri poteſt: </s> <s xml:id="echoid-s5400" xml:space="preserve">Chalybs elegatur potius, <lb/>quam Ferrum, quia a Magnete multo majoribus, & </s> <s xml:id="echoid-s5401" xml:space="preserve">uti ſupra no-<lb/>tatum eſt, quidem ſepties fortio ribus, viribus imprægnari poteſt, <lb/>imo eas per longius temporis intervallum retinet.</s> <s xml:id="echoid-s5402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5403" xml:space="preserve">Quæſitum fuit â multis, quantæ longitudinis Acum componere <lb/>licet, ut mobiliſſima ſit, & </s> <s xml:id="echoid-s5404" xml:space="preserve">ſimul accuratiſſime dirigatur eam ver-<lb/>ſus coeli plagam, quo tendit Magnes: </s> <s xml:id="echoid-s5405" xml:space="preserve">ratio dictitat longiores uſi-<lb/>bus humanis fore maxime accommodatas, quia non tantum gradus, <lb/>quibus declinant a vero Septentrione, ſed etiam Minuta oſtende-<lb/>re poſſunt; </s> <s xml:id="echoid-s5406" xml:space="preserve">verum experientia arctos rationi ponit limites, nec <lb/>quamlibet longitudinem acubus concedit, monet Sturmius in Col-<lb/>leg. </s> <s xml:id="echoid-s5407" xml:space="preserve">Curioſ. </s> <s xml:id="echoid-s5408" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s5409" xml:space="preserve">part. </s> <s xml:id="echoid-s5410" xml:space="preserve">2. </s> <s xml:id="echoid-s5411" xml:space="preserve">pag. </s> <s xml:id="echoid-s5412" xml:space="preserve">235, tum in Phyſic. </s> <s xml:id="echoid-s5413" xml:space="preserve">Elect. </s> <s xml:id="echoid-s5414" xml:space="preserve">Tom. </s> <s xml:id="echoid-s5415" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s5416" xml:space="preserve">pag. </s> <s xml:id="echoid-s5417" xml:space="preserve">1103. </s> <s xml:id="echoid-s5418" xml:space="preserve">Acum unum pedem longam non valere, nec bene diri-<lb/>gi, quia præter binos ad extremitates polos, adhuc aliis duobus in <lb/>medio donata erat, qui mobilitatem & </s> <s xml:id="echoid-s5419" xml:space="preserve">vim directricem imminue-<lb/>bant & </s> <s xml:id="echoid-s5420" xml:space="preserve">turbabant, quos permanſiſſe obſervavit, etiamſi Acum ab-<lb/>breviaverit, ut longitudinem 7 pollicum non excederet; </s> <s xml:id="echoid-s5421" xml:space="preserve">quamob-<lb/>rem Vir experientiſſimus judicabat Acus non longiores 6 pollicibus <lb/>eſſe conſiciendas: </s> <s xml:id="echoid-s5422" xml:space="preserve">bini in medio Acus a Sturmio notati poli puncta <lb/>Conſequentia a nobis vocata fuerunt, quæcunque hæc ſpectant in <lb/>Acu aut virgâ longiori monui ſuperius. </s> <s xml:id="echoid-s5423" xml:space="preserve">Acus noſtra horizontalis, <lb/>quæ eſt 12 pollicum, 10 linearum ſtylo impoſita, mobiliſſima eſt, <lb/>ex meridiano turbata diutiſſime continuat ſuas oſcillationes, atque <lb/>lubrico motu ſuperat Acuum breviorum oſcillationes; </s> <s xml:id="echoid-s5424" xml:space="preserve">eſt autem in <lb/>perpetuo poſita motu, & </s> <s xml:id="echoid-s5425" xml:space="preserve">varia directione agitur, nunc excedenti <lb/>gradus 13°, 20?</s> <s xml:id="echoid-s5426" xml:space="preserve">; aliquot minutis, nunc ab iis deficienti, quemad-<lb/>modum Grahami obſervationes, ſupra a nobis allatæ, etiam oſten-<lb/>derunt, idcirco ejus ope determinari commode nequit, quanta ſit <lb/>Acus Declinatio; </s> <s xml:id="echoid-s5427" xml:space="preserve">Cl. </s> <s xml:id="echoid-s5428" xml:space="preserve">de la Hirius tamen commendavit Acum 12 <lb/>vel plures pollices longam in L’Hiſt. </s> <s xml:id="echoid-s5429" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s5430" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5431" xml:space="preserve">A°. </s> <s xml:id="echoid-s5432" xml:space="preserve">1716, ad <lb/>ſubtiles obſervationes capiendas, ſi Declinationem intellexerit, du- <pb o="231" file="0245" n="245" rhead="De MAGNETE"/> bito, an hanc quidem determinare auxilio tam longæ Acuspoſſet: </s> <s xml:id="echoid-s5433" xml:space="preserve">mihi <lb/>exploranti diverſiſſimas Acus uſque ad 3 pedes longas, arriſerunt <lb/>maxime, quæ 6 pollices non excedebant, quæ expertes ſunt Pun-<lb/>ctorum Conſequentium, modo fuerint ex bono confectæ Chaly-<lb/>be, & </s> <s xml:id="echoid-s5434" xml:space="preserve">rite ſuper Magnetis polo ductæ. </s> <s xml:id="echoid-s5435" xml:space="preserve">Neque poſtulantur lon-<lb/>giores ad obſervationes ſubtiliſſimas capiendas, earum enim ope <lb/>Declinationes uſque ad minuta obſervari & </s> <s xml:id="echoid-s5436" xml:space="preserve">diſtingui poſſe, mox <lb/>liquebit.</s> <s xml:id="echoid-s5437" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5438" xml:space="preserve">Non minoris momenti eſt craſſitiem Acuum notaſſe, quam lon-<lb/>gitudinem, quippe ſi Acus componantur admodum leves graciles-<lb/>que, non tam lubrice mobiles exiſtunt, nec tam conſtanter ad eun-<lb/>dem revertuntur locum, ex Meridiano ſuo turbatæ, quam quidem <lb/>craſſiores: </s> <s xml:id="echoid-s5439" xml:space="preserve">aliquam 6 longam pollices, ponderis 8 granorum ex-<lb/>ploravi, quæ vix in oſcillationes reducebatur, illico quieſcens, <lb/>nunquam ad verum rediens Magneticum Meridianum, & </s> <s xml:id="echoid-s5440" xml:space="preserve">quamvis <lb/>levitas attritum ſupra ſtylum imminuendo mobilitatem magnam ad-<lb/>ferre videretur, attamen nimis exigua Ferri moles deprehendeba-<lb/>tur, quæ dirigeretur a vi Magnetica, & </s> <s xml:id="echoid-s5441" xml:space="preserve">attritum qualemcunque <lb/>ſupra ſtylum ſuperaret: </s> <s xml:id="echoid-s5442" xml:space="preserve">difficile eſt determinatu quænam craſſities <lb/>Acubus diverſæ longitudinis conveniat: </s> <s xml:id="echoid-s5443" xml:space="preserve">ſi craſſiores feceris, pon-<lb/>dere nimio ſtylum prement, atque attritum augendo, immobilio-<lb/>res reddentur: </s> <s xml:id="echoid-s5444" xml:space="preserve">ſi Acus 6 pollicum conſtruatur, caveto ne ejus pon-<lb/>dus ſit minus 50 granis, pondus dico, hoc enim craſſitiem ſatis <lb/>determinat; </s> <s xml:id="echoid-s5445" xml:space="preserve">hujus longitudinis Acus 200 granorum adhuc agillima <lb/>eſt, hinc licebit ejuſmodi craſſitiem eligere, quæ pondus aliquod <lb/>intermedium inter 50 & </s> <s xml:id="echoid-s5446" xml:space="preserve">200 grana efficit: </s> <s xml:id="echoid-s5447" xml:space="preserve">craſſities aliarum longi-<lb/>tudinum exinde quodammodo colligi poſſunt, eas non tanta cum <lb/>cura exploravi, quali tamen præſtantes Acus pondere donari poſ-<lb/>ſunt, ex Experimento CVII. </s> <s xml:id="echoid-s5448" xml:space="preserve">ſatis apparet; </s> <s xml:id="echoid-s5449" xml:space="preserve">in genere notetur, pondus <lb/>majus, craſſiuſque corpus non adeo mobilitatem tollere, quam prima <lb/>fronte appareret, nihil vero plus nocet quam nimia gracilitas.</s> <s xml:id="echoid-s5450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5451" xml:space="preserve">Figura præſtat ſimpliciſſima, recta, utrimque in apicem deſi-<lb/>nens; </s> <s xml:id="echoid-s5452" xml:space="preserve">idem eſt ſive rotunda, cylindrica, conicave fuerit, ſive planis <lb/>ſuperficiebus donetur;</s> <s xml:id="echoid-s5453" xml:space="preserve">male autem inſtar ſagittæ formantur Acus, vel-<lb/>uti Tab. </s> <s xml:id="echoid-s5454" xml:space="preserve">4. </s> <s xml:id="echoid-s5455" xml:space="preserve">fig. </s> <s xml:id="echoid-s5456" xml:space="preserve">9 aliqua E O F picta eſt, ubi cuſpis lilio, cauda plumâ in-<lb/>ſtruitur, aut ſimilibus figuris: </s> <s xml:id="echoid-s5457" xml:space="preserve">præterquam enim quod hæ non tam <pb o="232" file="0246" n="246" rhead="DISSERTATIO"/> lubrice mobiles exiſtant, etiam magis a Septentrione declinant, <lb/>uti recte obſervavit de la Hirius in L’Hiſt. </s> <s xml:id="echoid-s5458" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s5459" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5460" xml:space="preserve">A°. <lb/></s> <s xml:id="echoid-s5461" xml:space="preserve">1717. </s> <s xml:id="echoid-s5462" xml:space="preserve">Natura profecto ubivis ſimplex, ſimplicitate gaudet, quæ eo <lb/>præſtantiorem reddit machinam, quo ad ſimplicitatem plus accedit, <lb/>ars Naturam imitetur oportet, hocagnoſcentibus omnibus Mechanicis.</s> <s xml:id="echoid-s5463" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5464" xml:space="preserve">Non modo ex Chalybe præſtanti componendæ ſunt Acus, ſed <lb/>quoque temperandæ ſunt, ita ut colore cæruleo eleganti tingantur, <lb/>& </s> <s xml:id="echoid-s5465" xml:space="preserve">valde elaſticæ fiant. </s> <s xml:id="echoid-s5466" xml:space="preserve">præterquam quod tum non tam cito rubigi-<lb/>nem contrahant, etiam majori vi Magnetica donari poſſunt, quam <lb/>multo diutius conſervant, notante Ridleyo in Magnetical Motions <lb/>Cap. </s> <s xml:id="echoid-s5467" xml:space="preserve">17. </s> <s xml:id="echoid-s5468" xml:space="preserve">Ab hactemperatura bonitas multum pendet: </s> <s xml:id="echoid-s5469" xml:space="preserve">non quilibet aër <lb/>regione quacunque æque illi favet, fatemur Cœlum Britannicum <lb/>Chalybi multo plus amicum eſſe quam noſtrum; </s> <s xml:id="echoid-s5470" xml:space="preserve">docuit frequens <lb/>experientia noſtros artiſices, Acus ab ipſis elaboratas, & </s> <s xml:id="echoid-s5471" xml:space="preserve">in Bri-<lb/>tannia temperatas, majorem vim Magneticam recepiſſe, & </s> <s xml:id="echoid-s5472" xml:space="preserve">eam <lb/>diutius conſervaſſe; </s> <s xml:id="echoid-s5473" xml:space="preserve">hæc ipſe non expertus ex aliorum, ſed ſide dig-<lb/>niſſimorum, relationibus appono.</s> <s xml:id="echoid-s5474" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5475" xml:space="preserve">Capitulum æneum, quod medio Acus imponitur, prius terebra <lb/>aliquouſque excavatum in ſinum conicum, poſtea acuto & </s> <s xml:id="echoid-s5476" xml:space="preserve">polito <lb/>Chalybeo ſtylo ope Mallei adacto, percutiatur, ut ſinus pau-<lb/>lum profundior reddatur, ſed præcipue percuſſio ope ſtyli fit, ut <lb/>centrum accuratiſſime ſit unum punctum, tum ut pori melius <lb/>occludantur, & </s> <s xml:id="echoid-s5477" xml:space="preserve">ſimul compactius fiat metallum, ubi ſupra cu-<lb/>ſpidem acutam convertendum eſt: </s> <s xml:id="echoid-s5478" xml:space="preserve">intrinſecus illinitur leviſſi-<lb/>meoleo, aut quod melius eſt plumbagine, qua lubricitas notabilis affer-<lb/>tur Verſorio, neque hæc inunctio unquam negligenda: </s> <s xml:id="echoid-s5479" xml:space="preserve">Magnum vero <lb/>latet arcanum in cuſpide ænei ſtyli, ſupra quem vertitur Acus, hæc <lb/>eſt bene polienda, nam Acûs mobilitas imprimis ab hujus politura <lb/>pendet: </s> <s xml:id="echoid-s5480" xml:space="preserve">non poſtulatur ſtylus valde tenuis & </s> <s xml:id="echoid-s5481" xml:space="preserve">lente in ſummam a-<lb/>cutiem deſinens, potius ejuſmodi rejiciendus eſt, cupro non ſatis <lb/>pondus ipſius Acûs in tam tenui maſſa ſuſtinente, quin inflectatur, <lb/>ſed cuſpis fiat ex obtuſo cito acuta, ſit rotundiſſima, & </s> <s xml:id="echoid-s5482" xml:space="preserve">lævigetur <lb/>ſupra lapidem Lydium, vel cotem mollem Lotharingienſem, qui nova-<lb/>culis acuendis inſervit, neulla lateralis aſperitas emineat, niſi hoc arti-<lb/>ficium bene obſervetur, nunquam lubrice movebitur Verſorium. </s> <s xml:id="echoid-s5483" xml:space="preserve">Suf-<lb/>ſiciat hæc in genere notaſſe de fabricâ Verſoriorum, ea enim, quæ <pb o="233" file="0247" n="247" rhead="DE MAGNETE."/> nauticos ſpectant Compaſſos, praetereo, cum ad obſervationesac-<lb/>curatas capiendas non multum conducunt, qui hæc tamen deſide-<lb/>rat, adeat Ricciolum, Gilbertum, Kircherum alioſque: </s> <s xml:id="echoid-s5484" xml:space="preserve">Accedamusad <lb/>Macbinæ Noſtræ Declinatoriæ deſcriptionem, quam ſecundum no-<lb/>ſtrum propoſitum fabrefecit dexterrimus artifex Amſtelodamenſis, <lb/>Didericus Mets, eamque ad ſummam perfectionem deduxit, ut <lb/>nihil commodius, nihil elegantius, nihil accuratius ab arte huma-<lb/>na exſpectari aut deſiderari poſſit, ſufficit artificis nomen, per totum <lb/>Terrarum orbem inclytum, tantum commemoraſſe, ad Inſtrumenti <lb/>concinnitatem & </s> <s xml:id="echoid-s5485" xml:space="preserve">elegantiam indicandam. </s> <s xml:id="echoid-s5486" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5487" xml:space="preserve">9. </s> <s xml:id="echoid-s5488" xml:space="preserve">fig. </s> <s xml:id="echoid-s5489" xml:space="preserve">2. </s> <s xml:id="echoid-s5490" xml:space="preserve">& </s> <s xml:id="echoid-s5491" xml:space="preserve">3. </s> <s xml:id="echoid-s5492" xml:space="preserve">eam, <lb/>ſed multo minorem, repræſentat: </s> <s xml:id="echoid-s5493" xml:space="preserve">Eſt A C B Acus Chalybea, 6 <lb/>pollices longa, cujus utrique extremitati A & </s> <s xml:id="echoid-s5494" xml:space="preserve">B arcus tenues cuprei <lb/>ope parvarum cochlearum ſunt impoſiti, qualis eſt E A D, ſunt hi <lb/>arcus utrimque æque graves & </s> <s xml:id="echoid-s5495" xml:space="preserve">æque magni, ut Acus impoſita ſtylo <lb/>G oſcillari poſſit in plano horizontali, haud aliter ac ſi arcus ab-<lb/>fuiſſent: </s> <s xml:id="echoid-s5496" xml:space="preserve">eſt pondus totius hujus apparatus 229 granorum Medico-<lb/>rum. </s> <s xml:id="echoid-s5497" xml:space="preserve">Eſt L O M capſula ænea, diametri 8 pollicum, in cujus <lb/>centro ſtylus æneus G eſt poſitus, cochleâ ſurſum deorſumve mo-<lb/>bilis: </s> <s xml:id="echoid-s5498" xml:space="preserve">capſulam internam ambit margo S, P, qui eſt annulus latus <lb/>planuſque, quater in 90 gradus diviſus: </s> <s xml:id="echoid-s5499" xml:space="preserve">Arcus A E ab A ad E con-<lb/>tinet 60 gradus, qui æquales ſunt 61 gradibus annulo S Pinſculptis, <lb/>quo artiſicio indicantur gradus & </s> <s xml:id="echoid-s5500" xml:space="preserve">Minuta, quibus Acus a vero Sep-<lb/>tentrione declinat: </s> <s xml:id="echoid-s5501" xml:space="preserve">in hoc annulo Acus cum arcubus libere conver-<lb/>titur, ita tamen ut modo {1/100} pollicis arcus ab annulo diſtent: </s> <s xml:id="echoid-s5502" xml:space="preserve">eſt <lb/>F L M K O lamella ænea firma, 2 pedes longa, cujus extremum <lb/>F L M K in Acumen deſinit, ut conſpici poſſit an accurate congruat <lb/>cum linea Meridiana, cui machina imponi debet: </s> <s xml:id="echoid-s5503" xml:space="preserve">prima nota di-<lb/>viſionis in annulo S tranſit accurate per F L M K, ſuperius tegitur <lb/>capſula vitro plano, ne aëris acceſſus Acum moveat, aut rubiginem <lb/>inducat, impoſita hac machina lineæ Meridianæ prius accurate de-<lb/>ſcriptæ, obſervatur illico Declinatio Acus in gradibus & </s> <s xml:id="echoid-s5504" xml:space="preserve">minutis.</s> <s xml:id="echoid-s5505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5506" xml:space="preserve">Adnotare oportet, ne machina imponatur ſolo ligneo clavis fer-<lb/>reis conjuncto, vel ne in vicinia ferramenti cujuſcunque fuerit, <lb/>tum ne obſervator claves ſecum ferreas habeat, aut quodcunque aliud <lb/>ferramentum, ſecus enim erroneas obſervationes inſtituet, imo me-<lb/>mini ab aciculis fibulæ, quibus calcei adducuntur, obſervationes <pb o="234" file="0248" n="248" rhead="DISSERTATIO"/> fuiſſe turbatas, tanta mobilitate donata eſt hæc Acus ut a minimi Ferri <lb/>viribus aliorſum dirigatur. </s> <s xml:id="echoid-s5507" xml:space="preserve">hac Machina Trajecti Anno 1728 Martil 20 <lb/>Declinatio Acus ad Occaſum obſervata fuit 13 graduum & </s> <s xml:id="echoid-s5508" xml:space="preserve">20 Minu-<lb/>torum in Specula Aſtronomica, aliæque ſequentibus diebus De-<lb/>clinationes ſupra memoratæ pag. </s> <s xml:id="echoid-s5509" xml:space="preserve">156. </s> <s xml:id="echoid-s5510" xml:space="preserve">notatæ fuerunt.</s> <s xml:id="echoid-s5511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5512" xml:space="preserve">Plurimi Eruditi aliarum formarum machinas finxerunt, eidem <lb/>deſtinatas ſcopo, de la Hirius in L’Hiſt. </s> <s xml:id="echoid-s5513" xml:space="preserve">de L’Acad Roy. </s> <s xml:id="echoid-s5514" xml:space="preserve">A°. </s> <s xml:id="echoid-s5515" xml:space="preserve">1716. <lb/></s> <s xml:id="echoid-s5516" xml:space="preserve">aliam deſcripſit; </s> <s xml:id="echoid-s5517" xml:space="preserve">Teuberus aliam molitus fuit, proſtantem in Actis <lb/>Lipſienſibus A°. </s> <s xml:id="echoid-s5518" xml:space="preserve">1686. </s> <s xml:id="echoid-s5519" xml:space="preserve">pag. </s> <s xml:id="echoid-s5520" xml:space="preserve">125. </s> <s xml:id="echoid-s5521" xml:space="preserve">diverſam methodum ſuppeditavit <lb/>Camerarius in Diſſertat. </s> <s xml:id="echoid-s5522" xml:space="preserve">Epiſt. </s> <s xml:id="echoid-s5523" xml:space="preserve">Taurin. </s> <s xml:id="echoid-s5524" xml:space="preserve">pag. </s> <s xml:id="echoid-s5525" xml:space="preserve">257. </s> <s xml:id="echoid-s5526" xml:space="preserve">aliam Hautefeuille <lb/>in Fournal des Scavans Anno 1683. </s> <s xml:id="echoid-s5527" xml:space="preserve">quam illuſtravit Sturmius in A-<lb/>ctis Lipſ. </s> <s xml:id="echoid-s5528" xml:space="preserve">A°. </s> <s xml:id="echoid-s5529" xml:space="preserve">1684. </s> <s xml:id="echoid-s5530" xml:space="preserve">Quia has Machinas non in uſum vocare poſ-<lb/>ſumus, niſi prius accurate lineam Meridianam duxerimus, quod nec <lb/>ſemper, nec in omnibus locis opportune fieri poteſt: </s> <s xml:id="echoid-s5531" xml:space="preserve">tum quoque <lb/>ab Itineratoribus brevi aliquo in loco commorantibus Declinationes <lb/>obſervari non poſſent, idcirco aliam invenit perfecitque Machinam <lb/>ingenioſus artifex, Henricus Sully, quæ proſtat dans une Deſcription <lb/>abregée d’un horloge A°. </s> <s xml:id="echoid-s5532" xml:space="preserve">1726. </s> <s xml:id="echoid-s5533" xml:space="preserve">quam exhibet Tab. </s> <s xml:id="echoid-s5534" xml:space="preserve">5. </s> <s xml:id="echoid-s5535" xml:space="preserve">fig. </s> <s xml:id="echoid-s5536" xml:space="preserve">3. </s> <s xml:id="echoid-s5537" xml:space="preserve">Qua-<lb/>drans eſt in ſuos diviſus gradus, firmiter affixus craſſo aſleri ligneo, <lb/>eique inſiſtens ad angulos rectos, in eodem cum quadrante plano ſty-<lb/>lus, ſupra quem Acus convertitur, ſtat erectus, Acus 6 pollicum <lb/>pyxidi æneæ, quater in 90 gradus diviſæ includitur. </s> <s xml:id="echoid-s5538" xml:space="preserve">Machina in-<lb/>ſiſtat tabulæ planæ, Lux Solis per foramen B transmiſſa incidat in <lb/>medium plani A affixi regulæ mobili B A, tempore Meridiano quæ-<lb/>ratur maxima Solis altitudo, atque ita intorqueatur Machina, do-<lb/>nec Sole culminante ſtet in Meridiano, tum ſimul pendulo C D <lb/>exploretur, an horizontalis ſit, alioquin cochleis I, I, I in <lb/>ſitum horizonti parallelum reducatur: </s> <s xml:id="echoid-s5539" xml:space="preserve">tum Verſorium indicabit De-<lb/>clinationem a vero Septentrione, hoc modo brevi & </s> <s xml:id="echoid-s5540" xml:space="preserve">cito obſervatio <lb/>fieri poteſt in quocunque loco, quem in finem hæc machina com-<lb/>mendanda eſt; </s> <s xml:id="echoid-s5541" xml:space="preserve">quamvis quidem ita ejus ope non accuratiſſime Decli-<lb/>natio Acus haberi poſſit, nihilominus errores orientur parvi, nec <lb/>opinor mari unquam obſervationem capi adhuc tam exactam, quam <lb/>ope hujus machinæ in continenti colligitur: </s> <s xml:id="echoid-s5542" xml:space="preserve">error omnis evitari po-<lb/>teſt eam in vero Meridiano locando ope obſervatarum fixarum ſecun-<lb/>dum methodum præſcriptam in Suite des Memoires de L’Acad. </s> <s xml:id="echoid-s5543" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5544" xml:space="preserve"><lb/>1718. </s> <s xml:id="echoid-s5545" xml:space="preserve">Part. </s> <s xml:id="echoid-s5546" xml:space="preserve">1. </s> <s xml:id="echoid-s5547" xml:space="preserve">Chap. </s> <s xml:id="echoid-s5548" xml:space="preserve">3. </s> <s xml:id="echoid-s5549" xml:space="preserve">§. </s> <s xml:id="echoid-s5550" xml:space="preserve">4.</s> <s xml:id="echoid-s5551" xml:space="preserve"/> </p> <pb o="235" file="0249" n="249" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div135" type="section" level="1" n="135"> <head xml:id="echoid-head144" xml:space="preserve">CAPUT QUARTUM.</head> <p style="it"> <s xml:id="echoid-s5552" xml:space="preserve">De actione Ferri, donati viribus Magneticis, in aliud Ferrum, <lb/>ſive purum, ſive viribus Magneticis imprægnatum.</s> <s xml:id="echoid-s5553" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5554" xml:space="preserve">Quoniam Ferrum, viribus Magneticis donatum, non differt a <lb/>Magneteipſo, ſive vim attractricem, quam in alterum exercet <lb/>Ferrum, ſive directricem, ſive communicantem virtutem <lb/>cum alio ſpectemus, ſuperſedere potuiſſem examini Ferri, quate-<lb/>nus attrahendo aliud, virtutem ſuam Magneticam oſtendit: </s> <s xml:id="echoid-s5555" xml:space="preserve">attamen <lb/>non licuit Magnetem omnibus tractare modis, quibus Ferrum agi-<lb/>tari poteſt; </s> <s xml:id="echoid-s5556" xml:space="preserve">non enim licuit lapidem inflectere in quamlibet formam, <lb/>nec unum circa alterum intorquere, nec prolongare, ipſum per fo-<lb/>ramen trahendo, nec cudendo figuram immutare, quibus inſlexio-<lb/>nibus & </s> <s xml:id="echoid-s5557" xml:space="preserve">mutationibus ductile metallum ſubjicitur; </s> <s xml:id="echoid-s5558" xml:space="preserve">igitur reſtabat <lb/>explorandum, quomodo virtus Magnetica ſe in Ferro haberet, quod <lb/>aliis diverſiſque tractatur & </s> <s xml:id="echoid-s5559" xml:space="preserve">torquetur modis, quam hucuſque exa-<lb/>minari Magnes potuit.</s> <s xml:id="echoid-s5560" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div136" type="section" level="1" n="136"> <head xml:id="echoid-head145" xml:space="preserve">EXPERIMENTUM CX.</head> <p> <s xml:id="echoid-s5561" xml:space="preserve">Scriptum video apud nonnullos Philoſophos, vim Magneticam <lb/>ex lamina Chalybea decreſcere, ſi ipſi alia tenuia, & </s> <s xml:id="echoid-s5562" xml:space="preserve">non grandia <lb/>ferramenta, nunquam ſuper Magnete ducta, affricentur; </s> <s xml:id="echoid-s5563" xml:space="preserve">ſed vim in-<lb/>tegram permanere, applicatis corporibus majoribus, quorum nimia <lb/>moles, ſpretis quaſi tenuioris laminæ Magneticis viribus, nihil <lb/>earum ſecum abriperet: </s> <s xml:id="echoid-s5564" xml:space="preserve">Hæc ſententia ſi vera foret, haud parum <lb/>quaſſaret ea, quæ de Magnete in Capite Secundo. </s> <s xml:id="echoid-s5565" xml:space="preserve">Experimento. <lb/></s> <s xml:id="echoid-s5566" xml:space="preserve">XXXVIII. </s> <s xml:id="echoid-s5567" xml:space="preserve">diximus, Magnetem ſcilicet nunquam aliquid ſuarum <lb/>amittere virium, quamvis ſexcenta ſuper ipſo ducta brevi tempore <lb/>fuiſſent ferramenta, tenuia, brevia, craſſa ſive longa fuerint; </s> <s xml:id="echoid-s5568" xml:space="preserve">hinc <lb/>ſuſpicabar non cum ſatis ſollicita attentione & </s> <s xml:id="echoid-s5569" xml:space="preserve">prudentia experimen-<lb/>tum cum Ferro fuiſſe captum, neque irritam me foviſſe ſuſpicio-<lb/>nem docuit experientia: </s> <s xml:id="echoid-s5570" xml:space="preserve">Lamina Chalybea 12 longa pollices, {3/4} la- <pb o="236" file="0250" n="250" rhead="DISSERTATIO"/> ta, {1/12} pollic. </s> <s xml:id="echoid-s5571" xml:space="preserve">craſſa, ſuper polo Magnetis ducta, vim attractricem <lb/>accepit; </s> <s xml:id="echoid-s5572" xml:space="preserve">exploravi quantum ponderis ferrei lamina ab extremitate <lb/>alterutra geſtabat, ut virium Magnitudinem cognoſcerem, ponde-<lb/>re cognito, eidem extremitati appoſitæ & </s> <s xml:id="echoid-s5573" xml:space="preserve">affrictæ fuerunt 20 lamel-<lb/>læ, quæ nunquam antea Magnetem olfecerant, quæ erant æquales <lb/>& </s> <s xml:id="echoid-s5574" xml:space="preserve">ſimiles priori; </s> <s xml:id="echoid-s5575" xml:space="preserve">omnes hæ vim Magneticam ab affrictu receperunt: <lb/></s> <s xml:id="echoid-s5576" xml:space="preserve">deinde iterum expertusfui, quantum ponderis lamina prior nunc ele-<lb/>varet, an vires attractrices decreviſſent, communicatæ cum 20 aliis <lb/>lamellis, an vero permanſiſſent; </s> <s xml:id="echoid-s5577" xml:space="preserve">idem omnino pondus geſtari cum <lb/>eadem facilitate deprehendi, ac ante; </s> <s xml:id="echoid-s5578" xml:space="preserve">unde concludendum erat, <lb/>vires quidem a Ferro communicari cum Ferro, ita tamen ut id, quod <lb/>liberalitatem ſuam hac communicatione oſtendit, nihil amittat. </s> <s xml:id="echoid-s5579" xml:space="preserve"><lb/>Unde vero aliorum error, vires imminui ſtatuentium? </s> <s xml:id="echoid-s5580" xml:space="preserve">Ecce fon-<lb/>tem: </s> <s xml:id="echoid-s5581" xml:space="preserve">Cum ſupra Ferrum plures laminæ traducuntur, ſordes abra-<lb/>duntur, quæ extremitati adhærent, huic igitur ſi pondus geſtandum <lb/>apponis, non id immediate metallo applicas, ſed corpuſculis inter-<lb/>poſitis, hinc aliquo intervallo pondus a Ferro ſejunctum tantis vi-<lb/>ribus attrahi nequit, quemadmodum Experimenta ſuperius in Ca-<lb/>pite primo & </s> <s xml:id="echoid-s5582" xml:space="preserve">ſecundo allata evicerunt: </s> <s xml:id="echoid-s5583" xml:space="preserve">hanc erroris eſſe veram <lb/>cauſam affirmo, mihi enim primum hoc tentanti viſa fuit eorum <lb/>Philoſophorum ſententia non repugnare veritati, quippe minus pon-<lb/>deris geſtabat lamina poſt, quam ante, aliarum affrictum, obſer-<lb/>vatis autem extremitati appenſis ſordibus, iiſque abſterſis, pondus <lb/>priſtinum a laminâ ferebatur.</s> <s xml:id="echoid-s5584" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div137" type="section" level="1" n="137"> <head xml:id="echoid-head146" xml:space="preserve">EXPERIMENTUM CXI.</head> <p> <s xml:id="echoid-s5585" xml:space="preserve">Explorandum deinde duxi, quantum virium 20 lamellæ ſupra <lb/>primam, Lapidi antea applicatam, frictæ, acceperant; </s> <s xml:id="echoid-s5586" xml:space="preserve">in omni-<lb/>bus vim attrahentem proxime æquam vigere deprehendi, in ſingu-<lb/>lis tamen minorem, quam in prima lamina fuerat: </s> <s xml:id="echoid-s5587" xml:space="preserve">Uni ex viginti <lb/>affricui cultrum majorem, qui vi Magnetica imprægnabatur, mi-<lb/>nori tamen, quam in lamina erat, cui applicabatur: </s> <s xml:id="echoid-s5588" xml:space="preserve">huic cultro <lb/>alium affricui, eidemque iterum alium, huic ultimo tandem quar-<lb/>tum; </s> <s xml:id="echoid-s5589" xml:space="preserve">verum hic tam parum virtutis accepit, ut vix limaturæ par-<lb/>ticulam, vel pulviſculum Virginienſis arenæ attraheret, qualem an- <pb o="237" file="0251" n="251" rhead="DE MAGNETE."/> tea attraxiſſet: </s> <s xml:id="echoid-s5590" xml:space="preserve">Si plures laminas Chalybeas inter ſe æquales habuiſ-<lb/>ſem animus erat, has ſibi affricare ſucceſſive, & </s> <s xml:id="echoid-s5591" xml:space="preserve">proportionem de-<lb/>crementi virium annotare, ſed iis deſtitutus, Experimentum dun-<lb/>taxat cum cultris cepi.</s> <s xml:id="echoid-s5592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5593" xml:space="preserve">Communicat igitur Ferrum vim ſuam cum Ferro, ſed minus tra-<lb/>dit, quam habet, quamobrem decreſcit communicata visperpetuo, <lb/>quo plura corpora ferrea ſibi invicem applicata ſucceſſive ſuerint, <lb/>Eſt igitur hæc proprietas virtutis Magneticæ, utmaneat eadem quan-<lb/>titate in Ferro, etiamſi id a plurimis ferramentis tangatur: </s> <s xml:id="echoid-s5594" xml:space="preserve">2° ut <lb/>generet aut excitet in æquali ferramento minus virtutis quam ipſa <lb/>eſt: </s> <s xml:id="echoid-s5595" xml:space="preserve">non enim tranſire ex Ferro in Ferrum poteſt, quia eadem ma-<lb/>net in Ferro, quod antea obſedit.</s> <s xml:id="echoid-s5596" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div138" type="section" level="1" n="138"> <head xml:id="echoid-head147" xml:space="preserve">EXPERIMENTUM CXII.</head> <p> <s xml:id="echoid-s5597" xml:space="preserve">Quia lamellæ ferreæ & </s> <s xml:id="echoid-s5598" xml:space="preserve">Chalybeæ Magneti affrictæ mutantur in <lb/>veros Magnetes, conati fuerunt Philoſophi ex pluribus ſibi impoſi-<lb/>tis laminis Magnetem artificialem componere, qui Ferrum attrahat, <lb/>elevet, geſtet, vim cum alio Ferro communicet inſtar veri Magne-<lb/>tis: </s> <s xml:id="echoid-s5599" xml:space="preserve">non injucundum, nec prorſus inutile erit fabricam ejuſmodi <lb/>Magnetis commemoraſſe: </s> <s xml:id="echoid-s5600" xml:space="preserve">Eligantur aliquotlaminæ Chalybeæ, tem-<lb/>peratæ, ſive induratæ ad eandem cum gladiis elaſticitatem; </s> <s xml:id="echoid-s5601" xml:space="preserve">per to-<lb/>tam ſuam longitudinem, ſint æque latæ, æque craſſæ & </s> <s xml:id="echoid-s5602" xml:space="preserve">politiſſi-<lb/>mæ, convenientiſſima menſura eſt ut ſint ad minimum 12 pollices <lb/>longæ, longiores tamen ſunt præſtantiores, {3/4} pollic. </s> <s xml:id="echoid-s5603" xml:space="preserve">latæ, {1/12} pol-<lb/>licis craſſæ: </s> <s xml:id="echoid-s5604" xml:space="preserve">Hæ bene imprægnatæ viribus liberalis & </s> <s xml:id="echoid-s5605" xml:space="preserve">egregii Ma-<lb/>gnetis ſibi mutuo imponantur, eo ordine, ut poli cognomines <lb/>ſe contingant, omnesque accurate congruentes, unitum quaſi cor-<lb/>pus, parallelopipedum, forment, quod repræſentatur Tab. </s> <s xml:id="echoid-s5606" xml:space="preserve">3. </s> <s xml:id="echoid-s5607" xml:space="preserve">fig. <lb/></s> <s xml:id="echoid-s5608" xml:space="preserve">2. </s> <s xml:id="echoid-s5609" xml:space="preserve">huic armatura applicanda eſt, qualis Magneti apponitur, quæ <lb/>vinculo æeo CC cochlea cuprea inſtructo adigatur, ut arctiſſime <lb/>extremitates laminarum cum pedibus armaturæ conjungantur, ſunt <lb/>quoque laminæ ſibi fortiter apprimendæ. </s> <s xml:id="echoid-s5610" xml:space="preserve">ut unum corpus conſti-<lb/>tuant, idcirco ſuperius jugum cupreum BB imponitur, quod ope 4 <lb/>ænearum cochlearum AAAA valde depreſſum, laminas coagmen-<lb/>tat in firmam unitamque maſſam.</s> <s xml:id="echoid-s5611" xml:space="preserve"/> </p> <pb o="238" file="0252" n="252" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s5612" xml:space="preserve">Quo plures laminæ Magnetem hunc componant, quo longiores <lb/>fuerint, quo ſupra liberaliorem ductæ lapidem, eo præſtantioris <lb/>virtutis erit; </s> <s xml:id="echoid-s5613" xml:space="preserve">nam ſingulæ lamellæ inſtar Magnetis ſunt, unius vis <lb/>adjuvat eam alterius, hinc aucto lamellarum numero, etiam ſum-<lb/>ma virium augetur, quemadmodum Magnetes plures in unum bene <lb/>coagmentati majorem vim attrahendi habent, quam unus alterve <lb/>ſeorſim ſumtus: </s> <s xml:id="echoid-s5614" xml:space="preserve">Non tamen quantitas virium attrahentium adutrum-<lb/>que armaturæ pedem ſequitur numerum lamellarum, ſed eſt in mi-<lb/>nori ratione, quia quo vis a pede plus diſtat, eo minor evadit, uti <lb/>ſuperius quoque demonſtravi in Magnetibus majoribus, quorum vis <lb/>ſemper eſt proportionaliter minor, quam in minoribus: </s> <s xml:id="echoid-s5615" xml:space="preserve">Memoranda hic <lb/>eſt obſervatio Hartſoekeri, quam inſeruit ſcripto, cui titulus Eclairciſ-<lb/>ſemens des Conjectur. </s> <s xml:id="echoid-s5616" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s5617" xml:space="preserve">pag. </s> <s xml:id="echoid-s5618" xml:space="preserve">92. </s> <s xml:id="echoid-s5619" xml:space="preserve">Vires attractrices, ſingularum <lb/>laminarum, quæ ejuſdem magnitudinis cum deſcriptis ſunt, deprehen-<lb/>dit eſſe 6 unciarum; </s> <s xml:id="echoid-s5620" xml:space="preserve">Magnes ex 18 ejuſmodi laminis compoſitus eleva-<lb/>bat pondus ferreum 6 vel 7 librarum: </s> <s xml:id="echoid-s5621" xml:space="preserve">Elapſis ſex ſeptimanis Magnes <lb/>hic fortior evaſit, & </s> <s xml:id="echoid-s5622" xml:space="preserve">plus ponderis tulit; </s> <s xml:id="echoid-s5623" xml:space="preserve">ſingulæ tamen lamellæ <lb/>ſeorſim examinatæ imbecilliores erant, ferentes tantum unciam ſes-<lb/>qui, aut uncias duas; </s> <s xml:id="echoid-s5624" xml:space="preserve">hæ denuo ſibi impoſitæ, tantundem quam <lb/>ante diſſolutionem geſtabant, interim earum ambo poli viribus æ-<lb/>qualibus gaudebant. </s> <s xml:id="echoid-s5625" xml:space="preserve">Nec de obſervatione dubitandum, quia idem <lb/>deprehendi in meo artiſiciali Magnete; </s> <s xml:id="echoid-s5626" xml:space="preserve">videtur vis Magnetica in <lb/>principio ab armatura lamellarum non tam bene capi potuiſſe, quam <lb/>quidem aliquo elapſo tempore, præterea per unitam maſſam æqua-<lb/>biliter diſtribuitur pedetentim, ita ut ambo ejus poli æquale pondus <lb/>geſtare queant.</s> <s xml:id="echoid-s5627" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div139" type="section" level="1" n="139"> <head xml:id="echoid-head148" xml:space="preserve">EXPERIMENTUM CXIII.</head> <p> <s xml:id="echoid-s5628" xml:space="preserve">Filum ferreum tenue, admodum flexile, ſuper Magnete ductum, <lb/>ejus viribus imprægnetur, deinde flectatur in varias formas, & </s> <s xml:id="echoid-s5629" xml:space="preserve">di-<lb/>verſos angulos; </s> <s xml:id="echoid-s5630" xml:space="preserve">& </s> <s xml:id="echoid-s5631" xml:space="preserve">ſint flexiones tam validæ, ut ſignum inflexio-<lb/>nis, ſive exaſperatæ ſuperficiei poſt ſe relinquant, omnis plerum-<lb/>que vis attractrix profligata ex filo obſervabitur.</s> <s xml:id="echoid-s5632" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5633" xml:space="preserve">In his inflexionibus ſitus partium mutatur, aliis ſe contingenti-<lb/>bus poſt flexionem, quam ante, nihil ſubſtantiæ periit, nihil ac- <pb o="239" file="0253" n="253" rhead="DE MAGNETE."/> ceſſit ad Ferrum, pori ejus non ſunt obturati, ſed parum mutati, <lb/>vis tamen Magnetica prius communicata, nunc abolita eſt; </s> <s xml:id="echoid-s5634" xml:space="preserve">idem <lb/>obſervavimus in Ferro, quod Magneticis donatum viribus, cum <lb/>cuderetur, eas penitus perdebat, quo etiam ſitus partium me-<lb/>talli tantummodo immutabatur. </s> <s xml:id="echoid-s5635" xml:space="preserve">Eſt igitur cauſa Magnetica illius <lb/>indolis, ut eum ſitum partium poſtulet in Ferro toto, quem id ha-<lb/>buit, cum ſuper Magnete ducebatur; </s> <s xml:id="echoid-s5636" xml:space="preserve">& </s> <s xml:id="echoid-s5637" xml:space="preserve">pereat vel avolet, Ferro <lb/>inducta quacunque alia partium alicubi, vel per totam maſſam diſ-<lb/>poſitione, in eo tamen vigere aut reviviſcere poteſt, modo Fer-<lb/>rum ita inflexum denuo Magneti aſſricetur: </s> <s xml:id="echoid-s5638" xml:space="preserve">id autem mirandum, <lb/>quod non maneat vis ſuperſtes in parte Ferri non Flexa, cujus par-<lb/>tes eundem ſitum retinuerunt.</s> <s xml:id="echoid-s5639" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div140" type="section" level="1" n="140"> <head xml:id="echoid-head149" xml:space="preserve">EXPERIMENTUM CXIV.</head> <p> <s xml:id="echoid-s5640" xml:space="preserve">Filum ferrcum aut lamina oblonga & </s> <s xml:id="echoid-s5641" xml:space="preserve">plana a Magnete plurimum <lb/>virtutis acceperit, quâ ex ſuis extremitatibus pondus ferreum ele-<lb/>vet; </s> <s xml:id="echoid-s5642" xml:space="preserve">deinde in flectatur in formam annuli, atque ambo extrema ſe <lb/>contingant; </s> <s xml:id="echoid-s5643" xml:space="preserve">illico omnis fere vis Magnetica ex Ferro peribit. </s> <s xml:id="echoid-s5644" xml:space="preserve">neque <lb/>ad juncturæ locum poterit appendi Ferrum alicujus magnitudinis, <lb/>imo maxima quoque pars virtutis directricis erit deſtructa.</s> <s xml:id="echoid-s5645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5646" xml:space="preserve">Obſervaverunt hoc multi Eruditi, Grimaldi in Lib. </s> <s xml:id="echoid-s5647" xml:space="preserve">de Lumine <lb/>& </s> <s xml:id="echoid-s5648" xml:space="preserve">Colore. </s> <s xml:id="echoid-s5649" xml:space="preserve">de la Hire in Philoſ. </s> <s xml:id="echoid-s5650" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5651" xml:space="preserve">N°. </s> <s xml:id="echoid-s5652" xml:space="preserve">188. </s> <s xml:id="echoid-s5653" xml:space="preserve">pag. </s> <s xml:id="echoid-s5654" xml:space="preserve">349. </s> <s xml:id="echoid-s5655" xml:space="preserve">Derhamus <lb/>in Philoſ. </s> <s xml:id="echoid-s5656" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5657" xml:space="preserve">N°. </s> <s xml:id="echoid-s5658" xml:space="preserve">303. </s> <s xml:id="echoid-s5659" xml:space="preserve">Quorum hic attentiſſimus ad ejuſmodi <lb/>phænomena ſimul adnotavit, totam vim directricem perire, ſi ho-<lb/>ris diurnis filum in orbem inflexum fuerit, & </s> <s xml:id="echoid-s5660" xml:space="preserve">deinde iterum in lon-<lb/>gum exporrectum; </s> <s xml:id="echoid-s5661" xml:space="preserve">ſed virium partem modo evaneſcere, facto hoc <lb/>experimento tempore veſpertino: </s> <s xml:id="echoid-s5662" xml:space="preserve">eædem tamen extremitates fili <lb/>attrahuntur ab eodem Magnetis polo ante & </s> <s xml:id="echoid-s5663" xml:space="preserve">poſt fili flexionem.</s> <s xml:id="echoid-s5664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5665" xml:space="preserve">Obſervandum eſt hoc Experimentum capienti, ne filum leviter <lb/>duntaxat inflectatur, ut ſibi relictum, ſponte priorem ſitum rectum <lb/>recuperet, ſed cum impetu flectatur, ut vis partibus inducatur, qua <lb/>filum inflexum poſtea maneat, hinc optime eventus Experimenti <lb/>ſpectatur, convoluto filo aliquoties circa cylindrum in formam ſpi-<lb/>ræ. </s> <s xml:id="echoid-s5666" xml:space="preserve">Fili ferrei altera extremitas polus Boreus, altera Auſtralis eva-<lb/>ſit, poſtquam ſuper Magnete ductum fuit: </s> <s xml:id="echoid-s5667" xml:space="preserve">filo flexo, ut uterque <pb o="240" file="0254" n="254" rhead="DISSERTATIO"/> polus ſe contigerit, vis directione oppoſita exiens & </s> <s xml:id="echoid-s5668" xml:space="preserve">ſibi æquilibra-<lb/>ta, ſe neceſſario deſtruit, ita ut Ferrum aliud attrahi nequeat, <lb/>quantum enim attraheretur ab uno fili polo, tantum repelleretur <lb/>ab altero, hinc actione nulla ab utroque ſimul movetur: </s> <s xml:id="echoid-s5669" xml:space="preserve">quia au-<lb/>tem uterque polus ſe attrahit, vim retinere deberet; </s> <s xml:id="echoid-s5670" xml:space="preserve">imo eam reti-<lb/>net & </s> <s xml:id="echoid-s5671" xml:space="preserve">immutatam, ſi filum ita tantummodo inflexum fuerit, ut <lb/>ſponte ſe reſtituat in priorem rectum ſitum; </s> <s xml:id="echoid-s5672" xml:space="preserve">ſed amittit partem vir-<lb/>tutis cum ita inflectatur, ut ſitus partium mutetur, aſperaque red-<lb/>datur ſuperſicies, quemadmodum ſupra in Exper. </s> <s xml:id="echoid-s5673" xml:space="preserve">CXIII. </s> <s xml:id="echoid-s5674" xml:space="preserve">demon-<lb/>ſtratum fuit: </s> <s xml:id="echoid-s5675" xml:space="preserve">aſt ſubtilem Derhami obſervationem nondum intelli-<lb/>gimus, quid enim dies aut veſpera afferre poteſt viribus magneti-<lb/>cis, ita ut hoc tempore maneant ſuperſtites, altero evaneſcant? </s> <s xml:id="echoid-s5676" xml:space="preserve">non <lb/>Lux aliquid hic contribuit, tum enim potius diurnis horis maneret <lb/>vis in filis inflexis, quam veſpertinis: </s> <s xml:id="echoid-s5677" xml:space="preserve">non calor aut frigus rarefa-<lb/>ctione aut condenſatione eſt cauſa, quippe dies hyemales ſunt fri-<lb/>gidiores noctibus æſtivis, quare hyeme ſemper ſuperſtes vis obſer-<lb/>varetur, ſi a frigore penderet: </s> <s xml:id="echoid-s5678" xml:space="preserve">nunc modo admirandam proprieta-<lb/>tem virtutis Magneticæ adnotare licet.</s> <s xml:id="echoid-s5679" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div141" type="section" level="1" n="141"> <head xml:id="echoid-head150" xml:space="preserve">EXPERIMENTUM CXV.</head> <p> <s xml:id="echoid-s5680" xml:space="preserve">Fili ferrei, Magneticâ vi imprægnati, altera extremitas in for-<lb/>cipe teneatur firme, prehenſa altera extremitate intorqueatur totum <lb/>filum, ita ut axis ſemper maneat idem, ſive immobilis & </s> <s xml:id="echoid-s5681" xml:space="preserve">proinde <lb/>omnium partium internus ſitus mutetur, variis abſolutis intorſioni-<lb/>bus obſervatur vis directrix fili multum debilitata, & </s> <s xml:id="echoid-s5682" xml:space="preserve">aliquando in-<lb/>verſa, ita ut extremitas, quæ attrahebatur antea â polo Magnetis <lb/>Boreo, nunc ab eo repellatur: </s> <s xml:id="echoid-s5683" xml:space="preserve">Cum variis filis hoc Experimentum <lb/>inſtitutum diverſa phænomena exhibet, cum enim filum nulla con-<lb/>ſequentia puncta habuerit ante intorſionem, eâ peractâ viſum <lb/>fuit accepiſſe Puncta Conſequentia varia, nunc ab axis cuſpide <lb/>Borea attracta, nunc repulſa, motâ nimirum Acu ſecundum to-<lb/>tam fili longitudinem, quemadmodum Doctiſſimus Derhamus etiam <lb/>obſervavit.</s> <s xml:id="echoid-s5684" xml:space="preserve"/> </p> <pb o="241" file="0255" n="255" rhead="DE MAGNETE."/> </div> <div xml:id="echoid-div142" type="section" level="1" n="142"> <head xml:id="echoid-head151" xml:space="preserve">EXPERIMENTUM CXVI.</head> <p> <s xml:id="echoid-s5685" xml:space="preserve">Sed oportebit demonſtrare, quomodo Ferrum vi Magneticâ im-<lb/>prægnatum agat in Scobem Ferri, aut in pulverem Indicum circa <lb/>ipſum conſperſum; </s> <s xml:id="echoid-s5686" xml:space="preserve">a ſimpliciſſimo Experimento initium capiamus: <lb/></s> <s xml:id="echoid-s5687" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5688" xml:space="preserve">3. </s> <s xml:id="echoid-s5689" xml:space="preserve">fig. </s> <s xml:id="echoid-s5690" xml:space="preserve">3. </s> <s xml:id="echoid-s5691" xml:space="preserve">Lamina Chalybea A C D B, 12 longa pollices; </s> <s xml:id="echoid-s5692" xml:space="preserve">de-<lb/>ſcripta in Experimento CXXII, ſuper Magnete ducta, impoſita fuit <lb/>plano vitreo ſpeculo; </s> <s xml:id="echoid-s5693" xml:space="preserve">erat lamina formæ parallelopipedæ, circum-<lb/>quaque ſparſa fuit Scobs ferrea vel arena Indica, rara, ut melius <lb/>ſeries obſervarentur, tum ſpeculo leviter concuſſo, in ſeries ordi-<lb/>natus fuit circumjectus pulvis, quales figura repræſentat; </s> <s xml:id="echoid-s5694" xml:space="preserve">diſtabant <lb/>omnes â ſe inæquali intervallo; </s> <s xml:id="echoid-s5695" xml:space="preserve">quæ è regione A & </s> <s xml:id="echoid-s5696" xml:space="preserve">B extremita-<lb/>tum erant, in eadem recta cum longitudine laminæ jacebant, qua-<lb/>les demonſtrant AE, BF: </s> <s xml:id="echoid-s5697" xml:space="preserve">ſeries ambientes utramque extremitatem <lb/>laminæ A & </s> <s xml:id="echoid-s5698" xml:space="preserve">B, ad diſtantiam ſesqui pollicis, hoc eſt ad C & </s> <s xml:id="echoid-s5699" xml:space="preserve">D, <lb/>etiam in rectis lineis extendebantur, quamvis extrema ambierint, <lb/>veluti oſtendunt GG, HH. </s> <s xml:id="echoid-s5700" xml:space="preserve">Media autem laminæ pars C D cinge-<lb/>batur a Scobe utrimque in curvilineas ſeries ordinata, quæ non vi-<lb/>dentur eſſe circulorum arcus, ſed aliarum curvarum portiones.</s> <s xml:id="echoid-s5701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5702" xml:space="preserve">Angulis laminæ excuſſis ita, ut utraque extremitas capite ro-<lb/>tundo terminaretur, circumſperſa arena Virginienſis in ſeries priori <lb/>ſimiles ordinabatur, quas repræſentat Tab. </s> <s xml:id="echoid-s5703" xml:space="preserve">4. </s> <s xml:id="echoid-s5704" xml:space="preserve">fig. </s> <s xml:id="echoid-s5705" xml:space="preserve">1. </s> <s xml:id="echoid-s5706" xml:space="preserve">Extremitati-<lb/>bus autem deſinentibus in Cuſpides acutas, paulum diverſo diſpo-<lb/>nebantur ſeries modo, quas in fig. </s> <s xml:id="echoid-s5707" xml:space="preserve">2. </s> <s xml:id="echoid-s5708" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5709" xml:space="preserve">4. </s> <s xml:id="echoid-s5710" xml:space="preserve">conſpicimus. </s> <s xml:id="echoid-s5711" xml:space="preserve">Ex-<lb/>tremitatibus vero bifidis factis, uti in fig. </s> <s xml:id="echoid-s5712" xml:space="preserve">3. </s> <s xml:id="echoid-s5713" xml:space="preserve">ordinatæ iterum <lb/>aliter fuerunt ſeries; </s> <s xml:id="echoid-s5714" xml:space="preserve">quæ ex quolibet angulo, veluti ex centro <lb/>circuli exporrigebantur rectæ, hinc verſus ſe inclinantes in hiulco <lb/>inter utramque cuſpidem ejuſdem lateris, non tamen ſeſe invi-<lb/>cem attingebant; </s> <s xml:id="echoid-s5715" xml:space="preserve">medium laminæ, uti ante, a rotundis ambie-<lb/>batur ſeriebus.</s> <s xml:id="echoid-s5716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5717" xml:space="preserve">Poſitâ ante oculos figura 3. </s> <s xml:id="echoid-s5718" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5719" xml:space="preserve">3, laminam quadrangularem <lb/>exhibente, exploratum fuit quomodo hæc lamina pulverem, cui <lb/>immittebatur, attraheret: </s> <s xml:id="echoid-s5720" xml:space="preserve">lateri o, p, tenuiſſimo maxima quan-<lb/>titas adhæſit, & </s> <s xml:id="echoid-s5721" xml:space="preserve">quidem imprimis adhæſit angulis o, p, atque <lb/>longiſſimo termino interjacenti angulis o, p, planæ ſuperſiciei ali-<lb/>quid, ſed parum.</s> <s xml:id="echoid-s5722" xml:space="preserve"/> </p> <pb o="242" file="0256" n="256" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div143" type="section" level="1" n="143"> <head xml:id="echoid-head152" xml:space="preserve">EXPERIMENTUM CXVII.</head> <p> <s xml:id="echoid-s5723" xml:space="preserve">Deinde duas laminas Chalybeas, vi Magnetica donatas, Tab. </s> <s xml:id="echoid-s5724" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s5725" xml:space="preserve">fig. </s> <s xml:id="echoid-s5726" xml:space="preserve">4, AB ita impoſui plano lævigato, ſive ſpeculo vitreo, ut am-<lb/>bo poli cognomines ſe ſpectarent, Indica arena circumſperſa in re-<lb/>ctas ſeries ex polari ſuperficie exeuntes ordinabatur, hæ tamen in <lb/>medio intervallo incurvabantur, ſeſe mutuo fugantes ita, ut nulla <lb/>particula arenæ in ſphærâ virium laminæ A attraheretur aut adhæ-<lb/>reret particulis circa laminam B jacentibus. </s> <s xml:id="echoid-s5727" xml:space="preserve">Inverſa autem alteru-<lb/>tra lamina, ut duo poli alterius nominis ſibi opponerentur, pror-<lb/>ſus diverſa ratione arena Indica ordinabatur, uti in Tab. </s> <s xml:id="echoid-s5728" xml:space="preserve">4. </s> <s xml:id="echoid-s5729" xml:space="preserve">fig. </s> <s xml:id="echoid-s5730" xml:space="preserve">5. </s> <s xml:id="echoid-s5731" xml:space="preserve"><lb/>ſeſe attrahebant arenulæ ab utriuſque laminæ viribus certo modo <lb/>directæ, in medio utriuſque intervalli recta exporrigebantur ſeries, <lb/>quæ mox utrimque incurvabantur, magis minuſve prout propiores <lb/>medio, vel plus ab eo aberant, figura accuratius omnia ob oculos <lb/>ponit, quam verbis deſcribi poſſent.</s> <s xml:id="echoid-s5732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5733" xml:space="preserve">Non diſcrepat hic ſerierum ordo ab eo, quem duo Magnetes ſibi <lb/>obverſi inſtruunt, polis enim cognominibus ſe ſpectantibus, lima-<lb/>tura Ferri dirigitur accurate uti in fig. </s> <s xml:id="echoid-s5734" xml:space="preserve">4.</s> <s xml:id="echoid-s5735" xml:space="preserve">: a laminis & </s> <s xml:id="echoid-s5736" xml:space="preserve">polis alterni <lb/>nominis ſe ſpectantibus, limatura ordinatur, quemadmodum in <lb/>fig. </s> <s xml:id="echoid-s5737" xml:space="preserve">5. </s> <s xml:id="echoid-s5738" xml:space="preserve">quod nequaquam eſt mirandum, quia Ferrum ſuper Magne-<lb/>te ductum, ejuſmodi viribus imprægnatur, quæ nullomodo a Ma-<lb/>gneticis diſcrepant.</s> <s xml:id="echoid-s5739" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div144" type="section" level="1" n="144"> <head xml:id="echoid-head153" xml:space="preserve">EXPERIMENTUM CXVIII.</head> <p> <s xml:id="echoid-s5740" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5741" xml:space="preserve">4. </s> <s xml:id="echoid-s5742" xml:space="preserve">fig. </s> <s xml:id="echoid-s5743" xml:space="preserve">6. </s> <s xml:id="echoid-s5744" xml:space="preserve">Sint duæ laminæ Chalybeæ A B, C D, ſibi junctæ <lb/>ad B & </s> <s xml:id="echoid-s5745" xml:space="preserve">C, extremo D Magnes apponatur, atque circa laminas <lb/>ſpargatur limatura, ejus parva portio lateribus adhærebit; </s> <s xml:id="echoid-s5746" xml:space="preserve">alia re-<lb/>motior in ſeries ordinabitur, anterius ê regione A rectâ exporrec-<lb/>tas, ad latera vero curvas, quæ eo magis inclinabunt ad Magne-<lb/>tem, quo ipſi propiores fuerint. </s> <s xml:id="echoid-s5747" xml:space="preserve">Ejuſmodi Experimentum a ſein-<lb/>ſtitutum memorat quoque de La Hire in L’Hiſt. </s> <s xml:id="echoid-s5748" xml:space="preserve">de L’ Academ. <lb/></s> <s xml:id="echoid-s5749" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5750" xml:space="preserve">A°. </s> <s xml:id="echoid-s5751" xml:space="preserve">1717 Comparemus hunc ſerierum ordinem cum eo, quem <lb/>fig. </s> <s xml:id="echoid-s5752" xml:space="preserve">1. </s> <s xml:id="echoid-s5753" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5754" xml:space="preserve">4. </s> <s xml:id="echoid-s5755" xml:space="preserve">repræſentat, & </s> <s xml:id="echoid-s5756" xml:space="preserve">magnam obſervabimus diſferentiam, <pb o="243" file="0257" n="257" rhead="DE MAGNETE."/> quæ tota pendet ab appoſito laminæ Magnete, vel ſublato; </s> <s xml:id="echoid-s5757" xml:space="preserve">tranſit <lb/>in fig. </s> <s xml:id="echoid-s5758" xml:space="preserve">6. </s> <s xml:id="echoid-s5759" xml:space="preserve">ejus vis recta per laminæ longitudinem, ex cujus lateri-<lb/>bus quoque fere recta exporrigitur, ita ut evaneſcat curvilineus or-<lb/>do, medium laminæ cæteroquin ambiturus.</s> <s xml:id="echoid-s5760" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div145" type="section" level="1" n="145"> <head xml:id="echoid-head154" xml:space="preserve">EXPERIMENTUM CXIX.</head> <p> <s xml:id="echoid-s5761" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5762" xml:space="preserve">6. </s> <s xml:id="echoid-s5763" xml:space="preserve">fig. </s> <s xml:id="echoid-s5764" xml:space="preserve">8. </s> <s xml:id="echoid-s5765" xml:space="preserve">Annulus integer Chalybeus A B diametri 2 polli-<lb/>cum, Experimento inſerviit, pars A ducta fuit ſuper polo Magne-<lb/>tis Boreo, pars B ſuper polo Auſtrali; </s> <s xml:id="echoid-s5766" xml:space="preserve">tum circa ipſum, ſpeculo vi-<lb/>treo impoſitum, circumſperſa fuit Ferri limatura vel Arena Indica; <lb/></s> <s xml:id="echoid-s5767" xml:space="preserve">ea, quæ loca affricta ſpectabat, in ſeries rectas dirigebatur, at in <lb/>aliquâ ab his locis diſtantiâ duæ ſeries curvilineæ, ſibi oppoſitæ for-<lb/>mabantur, quales ſunt C D. </s> <s xml:id="echoid-s5768" xml:space="preserve">Arena ſpatio annuli medio injecta le-<lb/>viter in ſeries curvas è regione C & </s> <s xml:id="echoid-s5769" xml:space="preserve">D ordinabatur, cæteroquin pro <lb/>maximâ parte eâdem directione diſponebatur, qua ſeries loca atta-<lb/>cta ſpectantes. </s> <s xml:id="echoid-s5770" xml:space="preserve">Celeb. </s> <s xml:id="echoid-s5771" xml:space="preserve">de la Hire primus inſtituit hoc Experimen-<lb/>tum, in Philoſ. </s> <s xml:id="echoid-s5772" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s5773" xml:space="preserve">N°. </s> <s xml:id="echoid-s5774" xml:space="preserve">188. </s> <s xml:id="echoid-s5775" xml:space="preserve">deſcriptum, addens ſe lamellam <lb/>Ferri, in cuſpidem terminatam inſtar cultri, Magneti affricuiſſe, <lb/>tum cuſpidem annulo obverſam, varias partes attraxiſſe, non modo <lb/>unam alteramve A vel B, quemadmodum in Verſorio vulgari con-<lb/>tigiſſet: </s> <s xml:id="echoid-s5776" xml:space="preserve">obſervavit inſuper annulum Chalybeum Magneti affrictum, <lb/>diu ſuam virtutem retinuiſſe, quamvis poli in ſitu contrario, ac <lb/>poli Mundi, poſiti fuerint. </s> <s xml:id="echoid-s5777" xml:space="preserve">Tum annulum Chalybeum fortiſſimo <lb/>Magneti affrictum, non niſi ægre contrariam directionem recipere, <lb/>ſi ſuper Magnete debiliore oppoſita determinatione ducatur, quam-<lb/>vis tamen in initio directionem amiſiſſe videatur, ſucceſſu temporis <lb/>priorem ipſum vim & </s> <s xml:id="echoid-s5778" xml:space="preserve">directionemrecipere, haudſecus, quam in duo-<lb/>bus Magnetibus inæqualium virium contingit, qui polis cognomi-<lb/>nibus ſibi appoſitis, vim directricem ex debiliori fugant, contra-<lb/>riamque inducunt, a ſe autem iterum remoti gradatim priſtinam <lb/>recuperant virtutem & </s> <s xml:id="echoid-s5779" xml:space="preserve">directionem.</s> <s xml:id="echoid-s5780" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div146" type="section" level="1" n="146"> <head xml:id="echoid-head155" xml:space="preserve">EXPERIMENTUM CXX.</head> <p> <s xml:id="echoid-s5781" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5782" xml:space="preserve">6. </s> <s xml:id="echoid-s5783" xml:space="preserve">fig. </s> <s xml:id="echoid-s5784" xml:space="preserve">6. </s> <s xml:id="echoid-s5785" xml:space="preserve">Duorum ſemicirculorum ferreorum AB, ab, ex- <pb o="244" file="0258" n="258" rhead="DISSERTATIO"/> tremitates, A, a affricabantur Magnetis polo Boreo, extremitates <lb/>B, b polo Magnetis Auſtrino, tum circa ambos, in plano vitreo <lb/>poſitos, parum a ſe remotos circumſperſa fuit Arena Indica, quæ <lb/>circa extrema A, a, ut & </s> <s xml:id="echoid-s5786" xml:space="preserve">B, b, in ſeries rectilineas ordinata fuit, <lb/>ad medium tamen utriuſque ſemicirculi formabantur ſeries cur-<lb/>vilineæ ad C & </s> <s xml:id="echoid-s5787" xml:space="preserve">D. </s> <s xml:id="echoid-s5788" xml:space="preserve">in ſpatio a circulo intercepto arena in re-<lb/>ctas quoque diſpoſita fuit lineas, parva excepta portione, quæ <lb/>e regione punctorum C & </s> <s xml:id="echoid-s5789" xml:space="preserve">D fuit: </s> <s xml:id="echoid-s5790" xml:space="preserve">ordines ſerierum ſimillimi fue-<lb/>runt iis, quos fig. </s> <s xml:id="echoid-s5791" xml:space="preserve">8. </s> <s xml:id="echoid-s5792" xml:space="preserve">Tab. </s> <s xml:id="echoid-s5793" xml:space="preserve">6. </s> <s xml:id="echoid-s5794" xml:space="preserve">in integro annulo exhibuit; </s> <s xml:id="echoid-s5795" xml:space="preserve">adeo <lb/>ut illi ex his intelligi & </s> <s xml:id="echoid-s5796" xml:space="preserve">exponi nunc queant. </s> <s xml:id="echoid-s5797" xml:space="preserve">In fig. </s> <s xml:id="echoid-s5798" xml:space="preserve">6. </s> <s xml:id="echoid-s5799" xml:space="preserve">ſunt a A, <lb/>duo poli cognomines, ſe fugantes, nam ambo hæc extrema ſu-<lb/>per eodem Magnetis polo ducta fuerunt; </s> <s xml:id="echoid-s5800" xml:space="preserve">ita B, b ſunt duo poli <lb/>cognomines ſe eodem modo fugantes; </s> <s xml:id="echoid-s5801" xml:space="preserve">quare hic dantur 4 poli ad <lb/>extremitates A, a, B, b, Quia vero hi excitant effectus omni-<lb/>no eoſdem, quos in integro adnotavimus annulo fig. </s> <s xml:id="echoid-s5802" xml:space="preserve">8, in hoc <lb/>quoque 4 poli dabuntur, quorum duo cognomines hærebunt ad <lb/>A, bini alii ad B. </s> <s xml:id="echoid-s5803" xml:space="preserve">Annulus hinc integer in duabus ſibi diametrali-<lb/>ter oppoſitis partibus ſuper Magnetis ambobus polis frictus, 4 po-<lb/>los accipiet, in utraque parte attractâ duos.</s> <s xml:id="echoid-s5804" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5805" xml:space="preserve">Converſus deinde alteruter ſemicirculus fuit uti in Tab. </s> <s xml:id="echoid-s5806" xml:space="preserve">6. </s> <s xml:id="echoid-s5807" xml:space="preserve">fig. <lb/></s> <s xml:id="echoid-s5808" xml:space="preserve">7. </s> <s xml:id="echoid-s5809" xml:space="preserve">polo A cognominem b ſpectante, & </s> <s xml:id="echoid-s5810" xml:space="preserve">B polo oppoſito ſuo cogno-<lb/>mini a, ita tamen ut aliquod intervallum interceſſerit. </s> <s xml:id="echoid-s5811" xml:space="preserve">tum cir-<lb/>cum extrema ſeries curvilineæ formabantur, ambientes A & </s> <s xml:id="echoid-s5812" xml:space="preserve">b, tum <lb/>B & </s> <s xml:id="echoid-s5813" xml:space="preserve">a, ad aliquam uſque latitudinem: </s> <s xml:id="echoid-s5814" xml:space="preserve">in toto 4 curvilineæ ſeries <lb/>conſpiciebantur, & </s> <s xml:id="echoid-s5815" xml:space="preserve">4 ſeries, inter has mediæ, rectilineæ, quas <lb/>eodem modo ordinatas eleganter quoque deſcripſit de la Hire in <lb/>Philoſ. </s> <s xml:id="echoid-s5816" xml:space="preserve">Tranſact. </s> <s xml:id="echoid-s5817" xml:space="preserve">N°. </s> <s xml:id="echoid-s5818" xml:space="preserve">188.</s> <s xml:id="echoid-s5819" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div147" type="section" level="1" n="147"> <head xml:id="echoid-head156" xml:space="preserve">EXPERIMENTUM CXXI.</head> <p> <s xml:id="echoid-s5820" xml:space="preserve">Inſtituit Cl. </s> <s xml:id="echoid-s5821" xml:space="preserve">Derhamus nonnulla Experimenta cum filis ferreis, <lb/>quæ, poſtquam Magneticis donata erant viribus, ſecundum longi-<lb/>tudinem findebantur, in quibus ſequentia animadvertit. </s> <s xml:id="echoid-s5822" xml:space="preserve">1°. </s> <s xml:id="echoid-s5823" xml:space="preserve">Polos <lb/>ſæpe inverti, ita ut Boreus evaſerit Auſtralis, haud aliter ac ſi fi-<lb/>lum de novo ſuper Magnete ductum fuiſſet directione priori oppo-<lb/>ſitâ 2°. </s> <s xml:id="echoid-s5824" xml:space="preserve">Aliquando dimidium fili vim Magneticam conſervare <pb o="245" file="0259" n="259" rhead="DE MAGNETE."/> eandem, directione alterius dimidii plane inverſâ. </s> <s xml:id="echoid-s5825" xml:space="preserve">3°. </s> <s xml:id="echoid-s5826" xml:space="preserve">Aliquando <lb/>nullam virtuti Magneticæ mutationem induci, præterquam decre-<lb/>mentum, quod ſemper contingit in omnibus fiſſis filis. </s> <s xml:id="echoid-s5827" xml:space="preserve">4° Quan-<lb/>do una pars fili poſt fiſſionem mutatur in directione, tum ſemper <lb/>pars fili eſt tenuior, quæ mutatur, craſſiori manente eadem. </s> <s xml:id="echoid-s5828" xml:space="preserve">5°. <lb/></s> <s xml:id="echoid-s5829" xml:space="preserve">Aliquando poſt fiſſionem alterius partis fili polus converſus eſt, al-<lb/>tera extremitate manente indifferenti, ita ut æque alliciatur â po-<lb/>lo Magnetis Boreo, quam ab Auſtrali. </s> <s xml:id="echoid-s5830" xml:space="preserve">6°. </s> <s xml:id="echoid-s5831" xml:space="preserve">Aliquando una pars fili <lb/>attrahitur ab uno polo, ſed eadem extremitas neque attrahitur, <lb/>neque repellitur ab altero Magnetis polo, neſciens quaſi quorſum <lb/>ſe vertet: </s> <s xml:id="echoid-s5832" xml:space="preserve">Suſpicabatur in principio Doctiſſimus Derhamus directio-<lb/>nis mutationem pendere â violentiâ filis inducta ferreis in fiſſione <lb/>& </s> <s xml:id="echoid-s5833" xml:space="preserve">flexione, ſed hanc ſententiam rejecit, obſervans nonnullorum <lb/>fiſſorum & </s> <s xml:id="echoid-s5834" xml:space="preserve">parum inflexorum filorum dimidium eſſe mutatum, al-<lb/>tera parte manente eadem: </s> <s xml:id="echoid-s5835" xml:space="preserve">tum nonnullorum valde inflexorum di-<lb/>rectionem permanſiſſe. </s> <s xml:id="echoid-s5836" xml:space="preserve">Præterea obſervavit perinde eſſe, ſive à <lb/>polo Boreo, ſive â polo Auſtrali fiſſio incepta fuerit.</s> <s xml:id="echoid-s5837" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div148" type="section" level="1" n="148"> <head xml:id="echoid-head157" xml:space="preserve">EXPERIMENTUM CXXII.</head> <p> <s xml:id="echoid-s5838" xml:space="preserve">Cum filum ferreum fiſſum acquirit unam ſuperficiem planam, <lb/>qua parte ſcilicet tranſit cuneus, alteram gibbam, magna eſt dire-<lb/>ctionis differentia, ſi filum impoſitum fuerit plano, ut planities <lb/>ſurſum ſpectet, ſive deorſum. </s> <s xml:id="echoid-s5839" xml:space="preserve">Gibba ſuperficies ſit ſuperior, plana <lb/>inferior fili horizontaliter jacentis, tum id attrahetur a duobus po-<lb/>lis Magnetis, & </s> <s xml:id="echoid-s5840" xml:space="preserve">ab iiſdem repelletur; </s> <s xml:id="echoid-s5841" xml:space="preserve">ſed invertatur filum, ut <lb/>planities ſurſum ſpectet, tum una extremitas attrahetur ab uno <lb/>Magnetis polo, repelletur ab altero. </s> <s xml:id="echoid-s5842" xml:space="preserve">Hoc etiam ſubtiliter ob-<lb/>ſervavit Derhamus, opinatus lubricitatem directionis pendere <lb/>a converſione polorum ex fiſſione, qua polus Boreus evaſiſſet <lb/>Auſtralis, ſed nunquam detegere potuit, latera cujusvis extre-<lb/>mi, alteriuſve partis, eſſe eadem, Magnete nunc huic, nunc alte-<lb/>ri lateri oppoſito.</s> <s xml:id="echoid-s5843" xml:space="preserve"/> </p> <pb o="246" file="0260" n="260" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div149" type="section" level="1" n="149"> <head xml:id="echoid-head158" xml:space="preserve">EXPERIMENTUM CXXIII.</head> <p> <s xml:id="echoid-s5844" xml:space="preserve">Lamina Chalybea, 12 pollicum, qualis Magneti artificiali inſervit, <lb/>vi Magnetica imprægnetur, tum alia virga nova aut lamina ferrea, <lb/>non admodum craſſa, ponatur in incude fabri, huic virgæ prioris <lb/>laminæ extremo appoſito magna attractio orietur, cohærente virga <lb/>fortiter cum lamina; </s> <s xml:id="echoid-s5845" xml:space="preserve">ſi autem virga impoſita fuerit ligno, lapidi, <lb/>manui, aliive corpori non ferreo, tum a lamina priori duplo vel <lb/>triplo minus attrahetur. </s> <s xml:id="echoid-s5846" xml:space="preserve">Quo incus, cui virga impoſita eſt, fuerit <lb/>major, eo majori vi virga attrahetur a lamina, atque ad majorem <lb/>elevatur ab incude altitudinem.</s> <s xml:id="echoid-s5847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5848" xml:space="preserve">Debetur hoc obſervatum Cl. </s> <s xml:id="echoid-s5849" xml:space="preserve">Reaumurio, in L’Hiſt. </s> <s xml:id="echoid-s5850" xml:space="preserve">de L’Acad. <lb/></s> <s xml:id="echoid-s5851" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5852" xml:space="preserve">A°. </s> <s xml:id="echoid-s5853" xml:space="preserve">1723. </s> <s xml:id="echoid-s5854" xml:space="preserve">in quo notamus idem fieri ab ingenti incude, quod <lb/>a Magnete præſtatur, duæ claves ſupra Magnetem ad notabile in-<lb/>tervallum ſibi applicatæ cohærebant vi ex lapide egreſſâ, eadem vis <lb/>ex incude egreditur, quæ duabus laminis ſibi appoſitis attractionem <lb/>excitat, aut excitatam auget, quod idem eſt; </s> <s xml:id="echoid-s5855" xml:space="preserve">quemadmodum cla-<lb/>ves altius ſupra Magnetem elevatæ, minori vi ad ſe attrahebantur, <lb/>atque ideo a ſe ſolutæ decidebant, ita quoque virga adhærens lami-<lb/>næ ſupra incudem elevatæ, decidit ſoluta, modo lamina magis ab <lb/>incude recedat: </s> <s xml:id="echoid-s5856" xml:space="preserve">Quare iterum evincitur Ferrum eſſe Magnetem, <lb/>& </s> <s xml:id="echoid-s5857" xml:space="preserve">ab hoc in eo tantum differre, quod vi minori polleat, niſi Ma-<lb/>gnetem attigerit.</s> <s xml:id="echoid-s5858" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div150" type="section" level="1" n="150"> <head xml:id="echoid-head159" xml:space="preserve">EXPERIMENTUM CXXIV.</head> <p> <s xml:id="echoid-s5859" xml:space="preserve">Intorquebam deinde duo fila ferrea circa ſe mutuo, quemadmo-<lb/>dum reſtiarii ex duobus funibus alium craſſiorem compoſituri faciunt; <lb/></s> <s xml:id="echoid-s5860" xml:space="preserve">filorum longitudo fuit 4 pollicum, diameter {1/12} pollic. </s> <s xml:id="echoid-s5861" xml:space="preserve">hæc ſuper Au-<lb/>ſtrali Magnetis polo ducta, utroque extremo repellebant Verſorii <lb/>tam polumBoreum, quam Auſtralem, media ſui parte utrum que polum <lb/>allicientes; </s> <s xml:id="echoid-s5862" xml:space="preserve">hæc intorta ut poli cognomines ſe contingerent, bifido <lb/>capite utrimque terminabantur, quorum alterutrum attrahebat Ver-<lb/>ſorii polum Boreum, repellebat alterum: </s> <s xml:id="echoid-s5863" xml:space="preserve">bina oppoſita capita at-<lb/>trahebant tum polum Auſtralem, tum Boreum: </s> <s xml:id="echoid-s5864" xml:space="preserve">totum intermedium <pb o="247" file="0261" n="261" rhead="DE MAGNETE."/> corpus filorum repulit Boreum, tenuit immobilem ſuſpenſumque <lb/>polum Auſtralem. </s> <s xml:id="echoid-s5865" xml:space="preserve">2°. </s> <s xml:id="echoid-s5866" xml:space="preserve">Duo alia ejuſdem longitudinis fila contorſi <lb/>circa ſe mutuo, quæ ambo attraxerant uno extremo polum Boreum, <lb/>altero Auſtralem, & </s> <s xml:id="echoid-s5867" xml:space="preserve">reciproce repulerant, quemadmodum bona <lb/>Verſoria faciunt: </s> <s xml:id="echoid-s5868" xml:space="preserve">hæc in unum contorta & </s> <s xml:id="echoid-s5869" xml:space="preserve">bifido deſinentia capi-<lb/>te, uno extremo polum Verſorii Boreum attraxerunt, altero ex-<lb/>tremo repulerunt, utroque tamen ſui extremo repulerunt polum <lb/>Verſorii Auſtralem: </s> <s xml:id="echoid-s5870" xml:space="preserve">media parte ſuæ longitudinis obverſa cuſpidi <lb/>Boreæ Verſorii, eam tenuerunt immobilem, nec attrahentia nec re-<lb/>pellentia; </s> <s xml:id="echoid-s5871" xml:space="preserve">attrahebant nihilominus cuſpidem Auſtralem: </s> <s xml:id="echoid-s5872" xml:space="preserve">Eſt hoc <lb/>Experimentum illius indolis, ut non facile intelligatur, quamvis <lb/>clare deſcriptum, niſi quis ipſe repetierit, variiſque exploraverit <lb/>tentaminibus.</s> <s xml:id="echoid-s5873" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div151" type="section" level="1" n="151"> <head xml:id="echoid-head160" xml:space="preserve">EXPERIMENTUM CXXV.</head> <p> <s xml:id="echoid-s5874" xml:space="preserve">Filum ferreum, ſuper Magnete ductum, 4 longum pollices, al-<lb/>tera ſui extremitate repellebat utrumque Verſorii polum, alterâ at-<lb/>trahebat Boreum, fugabat Auſtralem: </s> <s xml:id="echoid-s5875" xml:space="preserve">extremum, quod utrumque <lb/>polum repulerat, ſupra lapidem malleo percuſſum & </s> <s xml:id="echoid-s5876" xml:space="preserve">applanatum fu-<lb/>gabat, ſed vi imbecilli, polum Boreum Verſorii, attrahebat Au-<lb/>ſtralem: </s> <s xml:id="echoid-s5877" xml:space="preserve">alterum fili extremum etiam applanatum malleo attrahebat <lb/>polum Boreum, repellebat exigua vi Auſtralem, intermedia fili <lb/>portio donabatur duobus punctis conſequentibus, quorum unum <lb/>repellebat, alterum attrahebat cuſpidem Verſorii Boream. </s> <s xml:id="echoid-s5878" xml:space="preserve">2°. <lb/></s> <s xml:id="echoid-s5879" xml:space="preserve">Ducto hoc filo ſuper Magnetis polo Auſtrali, alterutra extremitas <lb/>obſervabatur allicere polum Verſorii Boreum, altera Auſtralem; </s> <s xml:id="echoid-s5880" xml:space="preserve"><lb/>tum percuſſo medio vi mallei, & </s> <s xml:id="echoid-s5881" xml:space="preserve">applanato ad longitudinem unius <lb/>pollicis, permanſit eadem in utraque extremitate vis directrix, ſed <lb/>multum debilitata, neque intermedia longitudo punctis conſequen-<lb/>ribus donata videbatur.</s> <s xml:id="echoid-s5882" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div152" type="section" level="1" n="152"> <head xml:id="echoid-head161" xml:space="preserve">EXPERIMENTUM CXXVI.</head> <p> <s xml:id="echoid-s5883" xml:space="preserve">Duo exploravi fila ferrea 4 pollicum, quæ Magneti affricta, uno <lb/>extremo attrahebant polum Verſorii Boreum, altero Auſtralem, po- <pb o="248" file="0262" n="262" rhead="DISSERTATIO"/> li filorum cognomines ſibi impoſiti fuerunt ad longitudinem dimi-<lb/>dii pollicis, atque aliquot ictibus mallei percuſſi ſupra lapideam in-<lb/>cudem, quibus ſupra ſe invicem applanabantur; </s> <s xml:id="echoid-s5884" xml:space="preserve">tum extremitas ap-<lb/>planata unius fili obverſa Verſorii cuſpidi Boreæ, quam ante re-<lb/>pulerat, nunc attraxit, alterius fili eadem extremitas polum <lb/>Boreum Verſorii repellebat, ut ante.</s> <s xml:id="echoid-s5885" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div153" type="section" level="1" n="153"> <head xml:id="echoid-head162" xml:space="preserve">EXPERIMENTUM CXXVII.</head> <p> <s xml:id="echoid-s5886" xml:space="preserve">Quoniam judicaremus ex prioribus Experimentis, mutatum par-<lb/>tium, ferream componentium maſſam, ſitum directioni Magneti-<lb/>cæ differentiam afferre, antequam eam ſtabilirem ſententiam, <lb/>alia tentamina capienda adhuc eſſe ratus ſum, in quibus partium <lb/>ſitus mutatur, ſed modo â prioribus paulum diverſo; </s> <s xml:id="echoid-s5887" xml:space="preserve">filum ferreum <lb/>4 longum pollices, ejuſdemque cum præcedentibus craſſitiei, ſu-<lb/>per polo Magnetis ductum, altero extremo Verſorii cuſpidem Bo-<lb/>ream attraxit, altero Auſtralem, neque ulla Punctorum Conſequen-<lb/>tium in intermedia aliquâ parte ſigna edidit; </s> <s xml:id="echoid-s5888" xml:space="preserve">fuit filumper foramen <lb/>anguſtius, laminæ inflictum Chalybeæ, trajectum, quo longitudi-<lb/>nem 5 {1/2} pollicum nactum fuit, manentibus ad utramque extremitatem <lb/>iiſdem polis, vireſque inſignes oſtendentibus, iterum nulla Puncta <lb/>Conſequentia in tota longitudine conſpecta fuerunt: </s> <s xml:id="echoid-s5889" xml:space="preserve">Eodem filo <lb/>per anguſtius foramen deinde trajecto, quo 7 pollices longum eva-<lb/>ſit, eadem directio, quæ ante, permanſit, attrahente nempe una <lb/>extremitate Verſorii polum Boreum, repellente Auſtralem, & </s> <s xml:id="echoid-s5890" xml:space="preserve">al-<lb/>tera extremitate trahente polum Auſtralem, repellente Boreum; <lb/></s> <s xml:id="echoid-s5891" xml:space="preserve">neque repetita ulterior fili attenuatio per anguſtius foramen novam <lb/>directionem induxit, aut priſtinam immutavit: </s> <s xml:id="echoid-s5892" xml:space="preserve">mutatus tamen fuit <lb/>in his tentaminibus partium fili ſitus, ita ut forſitan nullæ, quæ <lb/>ſe antea contigerant, ſibi adhæſerint aut in vicinia manſerint; </s> <s xml:id="echoid-s5893" xml:space="preserve">ſedad <lb/>inſigne intervallum â ſe mutuo fuerint remotæ.</s> <s xml:id="echoid-s5894" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5895" xml:space="preserve">Situs igitur partium mutatus non poteſt directionis inverſæ cauſa <lb/>univerſalis dici, dantur quippe caſus, in quibus aliter dirigitur Fer-<lb/>rum mutatâ ejus formâ, dantur alii, in quibus nulla diſcrepantia <lb/>directionis obſervatur. </s> <s xml:id="echoid-s5896" xml:space="preserve">Ecquis tam felix erit, qui eruta Magneti-<lb/>cæ virtutis cauſa, hæc phænomena clare intelliget, ſunt ea, quæ <pb o="249" file="0263" n="263" rhead="DE MAGNETE."/> in hoc Capite commemoravimus, non inter facillima intellectu po-<lb/>nenda; </s> <s xml:id="echoid-s5897" xml:space="preserve">nunc ignoratâ cauſâ, inſtar talparum fodimus, quærimus, <lb/>inveſtigamus, anfractuoſas ingredimur vias, aliquando ſteriles, ali-<lb/>quando exiguum laborum fructum afferentes; </s> <s xml:id="echoid-s5898" xml:space="preserve">id tamen poteſt nobis <lb/>eſſe ſolatii, Experimentum recte inſtitutum, accurate cum omnibus <lb/>circumſtantiis obſervatum, manere Experimentum, hoc eſt ſemper <lb/>verum, & </s> <s xml:id="echoid-s5899" xml:space="preserve">alicujus uſus; </s> <s xml:id="echoid-s5900" xml:space="preserve">neque illis unquam ſubjici viciſſitudinibus, <lb/>quibus ratiocinium, utcunque ſubtile, ex levi obortum hypo-<lb/>theſi.</s> <s xml:id="echoid-s5901" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div154" type="section" level="1" n="154"> <head xml:id="echoid-head163" xml:space="preserve">EXPERIMENTUM CXXVIII.</head> <p> <s xml:id="echoid-s5902" xml:space="preserve">Prope Verſorii alterutram extremitatem teneatur aliquod Ferrum, <lb/>non imprægnatum vi Magnetica, niſi quam ſua ſponte acquirit, <lb/>Verſorii directionem mutabit, ad ſe alliciet, non aliter quam verus <lb/>Magnes; </s> <s xml:id="echoid-s5903" xml:space="preserve">motum proinde ejus ſequetur Verſorium, quod in orbem <lb/>converti, variis in plagis ſiſti, dirigique poteſt pro lubitu, moto <lb/>tantummodo Ferro: </s> <s xml:id="echoid-s5904" xml:space="preserve">ſi autem vi donatum Magnetica ſit, Verſorium <lb/>longe vehementius attrahet in eadem diſtantiâ ac ante, aut multo <lb/>remotius poſitum nihilominus operationem ſuam demonſtrabit.</s> <s xml:id="echoid-s5905" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div155" type="section" level="1" n="155"> <head xml:id="echoid-head164" xml:space="preserve">EXPERIMENTUM CXXIX.</head> <p> <s xml:id="echoid-s5906" xml:space="preserve">Explorandum adhuc erat, quomodo duo Verſoria, vi Magneti-<lb/>câ donata, poſita in eodem horizontali plano intra mutuæ actionis <lb/>ſphæram in ſe operarentur: </s> <s xml:id="echoid-s5907" xml:space="preserve">unum Verſorium, quod huic Experi-<lb/>mento inſerviit, erat 6 {3/4} pol. </s> <s xml:id="echoid-s5908" xml:space="preserve">longum, alterum 9 poll. </s> <s xml:id="echoid-s5909" xml:space="preserve">utrumque ſuo <lb/>ſtylo, ſupra quem libere poterat converti, imponebatur: </s> <s xml:id="echoid-s5910" xml:space="preserve">erat alte-<lb/>rum alteri parallelum; </s> <s xml:id="echoid-s5911" xml:space="preserve">utrumque cuſpide Borea ſpectabat Boreum; <lb/></s> <s xml:id="echoid-s5912" xml:space="preserve">centra utriuſque ſive ſtyli jacebant in recta Æquatori Magnetico <lb/>parallela, in qua pro lubitu propius ſibi, aut remotius iterum, pone-<lb/>bantur, quo Verſoria tantundem ad ſe accedebant: </s> <s xml:id="echoid-s5913" xml:space="preserve">erat Verſorium <lb/>brevius ad Ortum longioris ſitum: </s> <s xml:id="echoid-s5914" xml:space="preserve">tum 1° diſtantibus ſtylis a ſe 4 <lb/>pollicibus, acceſſerunt ambo poli Borei ad ſe parum, atque tantun-<lb/>dem receſſerunt Auſtrales a ſe: </s> <s xml:id="echoid-s5915" xml:space="preserve">admotis propius ſtylis, ut tantum <lb/>3 poll: </s> <s xml:id="echoid-s5916" xml:space="preserve">a ſe diſtarent, receſſerunt a ſe poli Borei parum, acceſſerunt <pb o="250" file="0264" n="264" rhead="DISSERTATIO"/> tantundem Auſtrales; </s> <s xml:id="echoid-s5917" xml:space="preserve">qui eventus iidem obſervabantur remotis a <lb/>ſe ſtylis 2 {1/2}, 2, 1 {1/2} pollicibus, verum propius his admotis, conver-<lb/>tebantur Verſoria atque cuſpidibus alterni nominis ad ſe accedendo <lb/>in mutuos ibant amplexus.</s> <s xml:id="echoid-s5918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5919" xml:space="preserve">2°. </s> <s xml:id="echoid-s5920" xml:space="preserve">Eadem omnia obſervata fuerunt phænomena poſito Verſorio <lb/>breviori ad Ortum longioris.</s> <s xml:id="echoid-s5921" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5922" xml:space="preserve">3°. </s> <s xml:id="echoid-s5923" xml:space="preserve">Poſito Verſorio longiſſimo in Meridiano Magnetico, alterum <lb/>admotum fuit, ſed in eodem Meridiano; </s> <s xml:id="echoid-s5924" xml:space="preserve">tum utriuſque directio <lb/>in eodem Meridiano permanſit, cuspide Borea unius ſpectante <lb/>Auſtralem alterius, idque obtinebat in qualibet diſtantia centro-<lb/>rum a ſe, modo ſe non contigerint.</s> <s xml:id="echoid-s5925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5926" xml:space="preserve">4°. </s> <s xml:id="echoid-s5927" xml:space="preserve">Ambobus eundem Meridianum ſervantibus, fuit alterutrum <lb/>manu converſum, ejuſque cuſpis Borea ad Occaſum firme retenta, <lb/>tum cuſpis Borea alterius quoque directa fuit verſus Occaſum ſpon-<lb/>te, a vero tamen Occaſu aberat pluribus paucioribuſve gradibus, <lb/>prout centra ſibi propius fuerint, vel latius removerentur.</s> <s xml:id="echoid-s5928" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div156" type="section" level="1" n="156"> <head xml:id="echoid-head165" xml:space="preserve">EXPERIMENTUM CXXX.</head> <p> <s xml:id="echoid-s5929" xml:space="preserve">Tandem poterant duo Verſoria ſupra ſe invicem locari, ut am-<lb/>borum ſtyli eſſent in eadem recta ad horizontem perpendiculari, & </s> <s xml:id="echoid-s5930" xml:space="preserve"><lb/>proinde ambo Verſoria in diverſis planis: </s> <s xml:id="echoid-s5931" xml:space="preserve">tentamina cum hiſce varia <lb/>inſtituit quondam Cl. </s> <s xml:id="echoid-s5932" xml:space="preserve">de la Hire, quæ inſeruit L’Hiſt. </s> <s xml:id="echoid-s5933" xml:space="preserve">de L’A-<lb/>cad. </s> <s xml:id="echoid-s5934" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5935" xml:space="preserve">A°. </s> <s xml:id="echoid-s5936" xml:space="preserve">1692. </s> <s xml:id="echoid-s5937" xml:space="preserve">hæc rite capta, & </s> <s xml:id="echoid-s5938" xml:space="preserve">bene deſcripta ex ipſo Au-<lb/>tore depromenda ratus fui.</s> <s xml:id="echoid-s5939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5940" xml:space="preserve">1°. </s> <s xml:id="echoid-s5941" xml:space="preserve">Sumſit capſulam inſervientem Compaſſo, inſtructam circulo cu-<lb/>preo diviſo in 360 gradus; </s> <s xml:id="echoid-s5942" xml:space="preserve">ex cujus medio centro eminebat cuſpis, <lb/>cui imponebatur acus, libere mobilis, 3 {1/2} pollices longa: </s> <s xml:id="echoid-s5943" xml:space="preserve">capſulam <lb/>tamdiu convertit, donec Acus reſpondebat gradui 360°. </s> <s xml:id="echoid-s5944" xml:space="preserve">tum la-<lb/>mellæ vitreæ beneficio capſulâ clauſâ, ſumſit aliam Acum Magne-<lb/>ticam æque longam ac prior, quam tantummodo impoſuit lamellæ <lb/>vitreæ, ita ut ſuâ cuſpide reſpiceret Septentrionem, ſive ut hujus <lb/>cuſpis eſſet directe ſupra cuſpidem Acus in capſulâ, & </s> <s xml:id="echoid-s5945" xml:space="preserve">tota longi-<lb/>tudo hujus eſſet parallela longitudini alterius: </s> <s xml:id="echoid-s5946" xml:space="preserve">Acus ſupra vitrum <lb/>proinde jacebat immobilis: </s> <s xml:id="echoid-s5947" xml:space="preserve">tum vero cuſpis Acus in capſulâ con- <pb o="251" file="0265" n="265" rhead="DE MAGNETE."/> verſa fuit verſus Occaſum, & </s> <s xml:id="echoid-s5948" xml:space="preserve">poſt aliquot vibrationes manſit im-<lb/>mobilis ad 42 gradus verſus Occaſum.</s> <s xml:id="echoid-s5949" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5950" xml:space="preserve">2°. </s> <s xml:id="echoid-s5951" xml:space="preserve">Acu vero in capſula primo paulum vergente verſus Ortum re-<lb/>ſpectu Acus ſuperius impoſitæ, cuſpis Septentrionalis Acûs in ca-<lb/>pſula dirigebatur verſus Ortum, ſtabatque immobilis poſt aliquot <lb/>vibrationes ad 41 gradus verſus Ortum: </s> <s xml:id="echoid-s5952" xml:space="preserve">adeoque tantopere a pri-<lb/>mo ſitu declinabat verſus Ortum, quam in præcedenti experimento <lb/>verſus Occaſum.</s> <s xml:id="echoid-s5953" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5954" xml:space="preserve">3°. </s> <s xml:id="echoid-s5955" xml:space="preserve">Dein ſuperiori Acu remotâ, Acus in capſula redibat ad gra-<lb/>dum 360. </s> <s xml:id="echoid-s5956" xml:space="preserve">tum vero iterum imponebatur vitro altera Acus, ut cuſ-<lb/>pis Septentrionalis reſpiceret Occaſum, adeoque ut ambæ Acus <lb/>ſe ad rectos angulos ſecarent. </s> <s xml:id="echoid-s5957" xml:space="preserve">Tum cuſpis Septentrionalis A-<lb/>cus in capſula convertebatur verſus Ortum quantitate 13 gra-<lb/>duum.</s> <s xml:id="echoid-s5958" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5959" xml:space="preserve">4. </s> <s xml:id="echoid-s5960" xml:space="preserve">Iterum ſuperiori Acu remotâ, aliaque in capſulâ quieſcente, <lb/>Acus vitro impoſita fuit cuſpide Septentrionali ſpectante Ortum, <lb/>tum cuſpis Septentrionalis Acus in capſula mota fuit verſus Occa-<lb/>ſum quantitate 13 gràduum.</s> <s xml:id="echoid-s5961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5962" xml:space="preserve">5°. </s> <s xml:id="echoid-s5963" xml:space="preserve">Cum igitur cuſpis Septentrionalis Acûs in capſula diſtabat in <lb/>Experimento 4° a cuſpide Auſtrali Acus ſuſperioris gradibus 77. </s> <s xml:id="echoid-s5964" xml:space="preserve">hu-<lb/>jus cuſpis Auſtralis adducta fuit verſus Septentrionalem alterius A-<lb/>cûs quantitate 10 graduum, tum cuſpis Septentrionalis acceſſit ad <lb/>hanc 5 gradibus.</s> <s xml:id="echoid-s5965" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5966" xml:space="preserve">6°. </s> <s xml:id="echoid-s5967" xml:space="preserve">Quando Acus ſupra vitrum poſita adhuc ſua cuſpide Auſtrali <lb/>admovebatur 5 gradibus verſus Septentrionalem cuſpidem Acus in <lb/>capſula, tum ſubito cuſpis Septentrionalis accedebat ad Auſtralem <lb/>alterius, ita ut ambæ Acus immediate ſibi ſupra poſitæ quaſi eſſent, <lb/>imo elevabatur cuſpis Acus in capſula ſurſum tangendo vitrum, qua <lb/>parte Acus ſuperior jacebat.</s> <s xml:id="echoid-s5968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5969" xml:space="preserve">7°. </s> <s xml:id="echoid-s5970" xml:space="preserve">Experimenta autem adhuc erant inſtituenda cum duabus A-<lb/>cubus, quæ ambæ ſupra cuſpidem erant mobiles; </s> <s xml:id="echoid-s5971" xml:space="preserve">ſed hæ poneban-<lb/>tur ita, ut cuſpides jacerent in linea recta continuata, hoc eſt di-<lb/>recte ſupra ſe mutuo, & </s> <s xml:id="echoid-s5972" xml:space="preserve">in diſtantia 10 linearum. </s> <s xml:id="echoid-s5973" xml:space="preserve">tum ambæ cuſpi-<lb/>des Acuum directæ fuerunt verſus plagam quandam Septentriona-<lb/>lem, ita tamen ut non ſibi parallelæ fuerint Acus, ſed una tanto- <pb o="252" file="0266" n="266" rhead="DISSERTATIO"/> pere deviaret a Septentrione Ortum verſus, quam altera Occaſum <lb/>verſus.</s> <s xml:id="echoid-s5974" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5975" xml:space="preserve">8°. </s> <s xml:id="echoid-s5976" xml:space="preserve">Dein Acus impoſitæ fuerunt axibus brevioribus, ut ſibi pro-<lb/>piores eſſent quam in Experimento præcedenti & </s> <s xml:id="echoid-s5977" xml:space="preserve">tantum diſtarent <lb/>{4/12} pollicis; </s> <s xml:id="echoid-s5978" xml:space="preserve">cum ambæ cuſpides Septentrionales erant directæ in <lb/>Septentrionem, ſibi relictæ ſunt, tum a ſe ſponte ſeparatæ ſunt di-<lb/>ſtantia 46 graduum, & </s> <s xml:id="echoid-s5979" xml:space="preserve">quando alterutra petebat plagam Orien-<lb/>talem, altera Occidentalem petebat.</s> <s xml:id="echoid-s5980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5981" xml:space="preserve">9°. </s> <s xml:id="echoid-s5982" xml:space="preserve">Quando cuſpis Auſtralis unius Acus ponebatur ſupra cuſpi-<lb/>dem Septentrionalem alterius, ambæ ſeſe amplectebantur, mane-<lb/>bantque in loco in quo ſe primum amplexæ ſunt, adeoque non di-<lb/>rigebantur verſus verum Septentrionem & </s> <s xml:id="echoid-s5983" xml:space="preserve">Auſtrum.</s> <s xml:id="echoid-s5984" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5985" xml:space="preserve">10°. </s> <s xml:id="echoid-s5986" xml:space="preserve">Quando ambæ Acus velociter primum vertuntur, dein-<lb/>de ſibi relinquuntur, non quieſcunt priuſquam cuſpis Borealis <lb/>unius Acus amplectatur cuſpidem Auſtralem alterius Acus.</s> <s xml:id="echoid-s5987" xml:space="preserve"/> </p> <pb o="253" file="0267" n="267" rhead="DE MAGNETE"/> </div> <div xml:id="echoid-div157" type="section" level="1" n="157"> <head xml:id="echoid-head166" xml:space="preserve">CAPUT QUINTUM.</head> <head xml:id="echoid-head167" style="it" xml:space="preserve">De vi Magnetica Ferri.</head> <p> <s xml:id="echoid-s5988" xml:space="preserve">Admodum univerſalis eſt virtus Maguetica, in corpore quo-<lb/>cunque ex Ferro confecto latens; </s> <s xml:id="echoid-s5989" xml:space="preserve">five enim fuerit magnum <lb/>vel parvum, craſſum vel tenue ferramentum, manifeſto vim attra-<lb/>ctricem ſuam demonſtrat, quam exercet in Limaturam, Arenam <lb/>Virginienſem, aut in Acum Magneticam; </s> <s xml:id="echoid-s5990" xml:space="preserve">atque directrice virtute <lb/>ſæpegaudet, qua ad eaſdem cœliplagas, ſibi commiſium, convertitur, <lb/>quam Magnes aut Verſorium: </s> <s xml:id="echoid-s5991" xml:space="preserve">Hoc autem non admirandum eſt, <lb/>quia ſupra adnotavimus, Ferrum rubigine corroſum vetuſtate tem-<lb/>poris, atque Lapidis poris infuſum, in verum Magnetem abire & </s> <s xml:id="echoid-s5992" xml:space="preserve"><lb/>commutari; </s> <s xml:id="echoid-s5993" xml:space="preserve">neque magno indigemus molimine ad vim Magneticam <lb/>in corporibus ex Ferro fabrefactis inveniendam, omnis enim culter, <lb/>forceps, forfex, clavus, cuneus, acus, aut quodcunque aliud ad <lb/>manus inſtrumentum fuerit ferreum, Arenam Indicam aut ferream <lb/>ſcobem ad cuſpidem angulumve ſuum attrahendo affigit: </s> <s xml:id="echoid-s5994" xml:space="preserve">Cognita <lb/>hæc elapſo ſeculo fuerunt plurimis, præcipue tamen Viris ſtudio <lb/>& </s> <s xml:id="echoid-s5995" xml:space="preserve">doctrinâ præſtantiſſimis Gaſſendo, Rohaulto; </s> <s xml:id="echoid-s5996" xml:space="preserve">& </s> <s xml:id="echoid-s5997" xml:space="preserve">hac tempeſtate <lb/>ulterius confirmata â Wolfio, Reaumurioque in L’Hiſtoire de L’ A-<lb/>cad. </s> <s xml:id="echoid-s5998" xml:space="preserve">Roy. </s> <s xml:id="echoid-s5999" xml:space="preserve">A°. </s> <s xml:id="echoid-s6000" xml:space="preserve">1723. </s> <s xml:id="echoid-s6001" xml:space="preserve">De Magnete ejuſque viribus acturus, non <lb/>omittendas obſervationes de vi Ferri captas cenſui, cum ejuſdem <lb/>ſint naturæ ac priorcs, atque ex his lux quædam affulgeat il-<lb/>lis: </s> <s xml:id="echoid-s6002" xml:space="preserve">& </s> <s xml:id="echoid-s6003" xml:space="preserve">quemadmodum plurima, quæ de Magnete olim affirmaban-<lb/>tur, novo examini ſubmittens confirmavi, aut errorem detexi, ita <lb/>hic pergendum erat, exploranda erant aliorum inventa de novo, <lb/>hiulci ſupplendi, omiſſa & </s> <s xml:id="echoid-s6004" xml:space="preserve">præterviſa addenda, in ordinem redi-<lb/>genda, quæ ſparſim apud alios exſtabant; </s> <s xml:id="echoid-s6005" xml:space="preserve">hæc præmonenda duxi, <lb/>ne trita, aut aliorum inventa pro meis venditare videar.</s> <s xml:id="echoid-s6006" xml:space="preserve"/> </p> <pb o="254" file="0268" n="268" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div158" type="section" level="1" n="158"> <head xml:id="echoid-head168" xml:space="preserve">EXPERIMENTUM CXXXI.</head> <p> <s xml:id="echoid-s6007" xml:space="preserve">Virga ferrrea, cylindrica, diametri {1/12} poll. </s> <s xml:id="echoid-s6008" xml:space="preserve">ſed 6 longa, impo-<lb/>ſita fuit Igni luculento, ut ſecundum longitudinem in Meridiano <lb/>per Boream & </s> <s xml:id="echoid-s6009" xml:space="preserve">Auſtrum tranſeunte jaceret: </s> <s xml:id="echoid-s6010" xml:space="preserve">Ignis non erat exſtru-<lb/>ctus in loco prope Ferrum, ſed ubi modo lapides dabantur, ne vis <lb/>Ferri alterius Experimentum turbaret: </s> <s xml:id="echoid-s6011" xml:space="preserve">probe per totam longitudi-<lb/>nem candefacta, forcipe æneo, & </s> <s xml:id="echoid-s6012" xml:space="preserve">leni motu abſque ulla concuſſio-<lb/>ne, ex Igne exemta, atque horizontaliter retenta, admovebatur <lb/>illico admodum mobili Verſorio, vi donato Magnetica; </s> <s xml:id="echoid-s6013" xml:space="preserve">ita autem <lb/>movebatur, ut manſerit in eodem Meridiano; </s> <s xml:id="echoid-s6014" xml:space="preserve">tum vero Virgæ <lb/>cuſpis Auſtralis attrahebat polum Verſorii Boreum; </s> <s xml:id="echoid-s6015" xml:space="preserve">& </s> <s xml:id="echoid-s6016" xml:space="preserve">ejuſdem Vir-<lb/>gæ, ſed converſæ cuſpis Borealis attraxit quoque polum Verſorii <lb/>Boreum.</s> <s xml:id="echoid-s6017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6018" xml:space="preserve">2. </s> <s xml:id="echoid-s6019" xml:space="preserve">Loco hujus tenuis Virgæ alia duplo craſſioris diametri & </s> <s xml:id="echoid-s6020" xml:space="preserve">10 <lb/>longa pollices, novo tentamini inſerviit, hæc in Igne probe can-<lb/>defacta, deinde exemta, atque Verſorio oppoſita, ſuis extremita-<lb/>tibus eoſdem effectus Attractionis oſtendit, ac prior.</s> <s xml:id="echoid-s6021" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6022" xml:space="preserve">3. </s> <s xml:id="echoid-s6023" xml:space="preserve">Imo dedit plane eosdem eventus parallelopipedum ferreum, <lb/>5 pollices longum, baſeos quadratæ unius pollicis.</s> <s xml:id="echoid-s6024" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6025" xml:space="preserve">Hæc tentamina capi modo potuerunt cum Verſorio capſulæ <lb/>æneæ vitro tectæ incluſo, Ignis enim ex ferramentis explorandis <lb/>tanto cum impetu egreditur Verſoriumque concutit, nudum, ut <lb/>ipſi tremores, oſcillationes, motuſque alios inordinatos inducat, <lb/>impedientes, quominus aliquid obſervetur attractionem ſpe-<lb/>ctans.</s> <s xml:id="echoid-s6026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6027" xml:space="preserve">Agit ergo vis Magnetica, ſive in lapidea ſive in ferrea ſubſtantia <lb/>hæſerit, in Ferrum ignitum, illud attrahendo, Magnetem enim <lb/>Ferrum candefactum attrahere confirmarunt Colepreſſius in Philoſ. <lb/></s> <s xml:id="echoid-s6028" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6029" xml:space="preserve">tum Mullerus in Colleg. </s> <s xml:id="echoid-s6030" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s6031" xml:space="preserve">pag. </s> <s xml:id="echoid-s6032" xml:space="preserve">229, & </s> <s xml:id="echoid-s6033" xml:space="preserve">noſtra Expe-<lb/>rimenta in Cap. </s> <s xml:id="echoid-s6034" xml:space="preserve">2. </s> <s xml:id="echoid-s6035" xml:space="preserve">allata: </s> <s xml:id="echoid-s6036" xml:space="preserve">nunc obſervamus vim Magneticam Ver-<lb/>ſorii in Ferrum Ignitum operari, contra Gilbertum, id negantem <lb/>Lib. </s> <s xml:id="echoid-s6037" xml:space="preserve">2. </s> <s xml:id="echoid-s6038" xml:space="preserve">Cap 2. </s> <s xml:id="echoid-s6039" xml:space="preserve">pag. </s> <s xml:id="echoid-s6040" xml:space="preserve">52.</s> <s xml:id="echoid-s6041" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6042" xml:space="preserve">2. </s> <s xml:id="echoid-s6043" xml:space="preserve">Notamusvim directricem in Ferro ignito non dari, nam ſi polos <lb/>habuiſſet Ferrum candens, non attraxiſſet indifferentur utrumque <pb o="255" file="0269" n="269" rhead="DE MAGNETE."/> Verſorii polum; </s> <s xml:id="echoid-s6044" xml:space="preserve">id tamen ſi deprehenderetur in uno Ferro, non in <lb/>duobus aliis quoque obtineret, fatemur enim aliquando, raro ta-<lb/>men, fila dari, quorum ambo extrema eundem polum attrahunt <lb/>Verſorii, id vero nobis in tribus diverſis occaſionibus obſervari con-<lb/>tigit cum calido Ferro, nunquam contrarium: </s> <s xml:id="echoid-s6045" xml:space="preserve">adeoque vel non <lb/>datur vis directrix in calente Ferro, aut erit infinite parva:</s> <s xml:id="echoid-s6046" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div159" type="section" level="1" n="159"> <head xml:id="echoid-head169" xml:space="preserve">EXPERIMENTUM CXXXII.</head> <p> <s xml:id="echoid-s6047" xml:space="preserve">Si virgæ ferreæ tenuiſſimæ, Experimenti CXXXI, in Igne can-<lb/>defactæ, prudenter abſque ullâ concuſſione ex eo ſublatæ forcipe æ-<lb/>neo, ita ut horæ ſpatio jaceat in Meridiano terreſtri vel Magne-<lb/>tico ſuper lapideo ſolo, cuſpis Borea apponatur Verſorii polo Au-<lb/>ftrali, eum attrahet, ſed polum Boreum fugabit: </s> <s xml:id="echoid-s6048" xml:space="preserve">cuſpis autem Au-<lb/>ftralis virgæ attrahet Verſorii polum Boreum, fugabit Auſtralem.</s> <s xml:id="echoid-s6049" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6050" xml:space="preserve">Virgæ cylindricæ longæ & </s> <s xml:id="echoid-s6051" xml:space="preserve">tenues quæcunque, ſupra quas cor-<lb/>tinæ feneſtrarum aut cubilium vulgo protrahuntur, jacentes ali-<lb/>quamdiu horizonti parallelæ, & </s> <s xml:id="echoid-s6052" xml:space="preserve">in Meridiano terreſtri vel Magne-<lb/>tico, ſive ſolo impoſitæ, ſive altiores & </s> <s xml:id="echoid-s6053" xml:space="preserve">in aëre ſuſpenſæ, eadem <lb/>vi Magnetica directrice imbuuntur, atque cuſpidibus ſuis, quibus <lb/>Boream ſpectarunt, attrahunt Acûs Magneticæ polum Auſtralem, <lb/>repellunt Boreum.</s> <s xml:id="echoid-s6054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6055" xml:space="preserve">Obſervationem addam, ex quâ conſtabit Philoſophos plerumque <lb/>univerſalius proprietates Magnetis determinaſſe, neque fideliter <lb/>omnia, quæ in inſtituendo Experimento adhibuerint, accurate anno-<lb/>taſſe, quemadmodum tamen deſideratur, unde multiplici edoctus <lb/>experientiâ, cuncta, ne minimis circumſtantiis exceptis, addidi, <lb/>quibus prolixior quidem nonnullis videri poſſem, ſed niſi omnia <lb/>ſimul notentur, & </s> <s xml:id="echoid-s6056" xml:space="preserve">inter ſe comparentur, in errores incidimus: <lb/></s> <s xml:id="echoid-s6057" xml:space="preserve">Ecquis igitur, primâ fronte memorata hic Experimenta intuitus, <lb/>non pronunciaret, Ferrum in Meridiano poſitum vi Magnetica di-<lb/>rectrice imprægnari: </s> <s xml:id="echoid-s6058" xml:space="preserve">Sed lente feſtina, nam cum longis, & </s> <s xml:id="echoid-s6059" xml:space="preserve">te-<lb/>nuibus virgis capta duntaxat ſunt tentamina, an quidem eadem ob-<lb/>tinctbunt phænomena in craſſis? </s> <s xml:id="echoid-s6060" xml:space="preserve">Videamus & </s> <s xml:id="echoid-s6061" xml:space="preserve">hæc exploremus, ne-<lb/>que laboris pœnitebit: </s> <s xml:id="echoid-s6062" xml:space="preserve">Nam in ferramentis diametri unius pollicis, <lb/>aut craſſioribus, verum brevioribus quam 8 vel 10 poll. </s> <s xml:id="echoid-s6063" xml:space="preserve">nunquam <pb o="256" file="0270" n="270" rhead="DISSERTATIO"/> ejuſmodi vim directricem obſervare potui, imo etiamſi aliquotin <lb/>Meridiano eodem jacuerint diebus.</s> <s xml:id="echoid-s6064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6065" xml:space="preserve">Ecce aliquam Analogiam inter vim Magnetis in Ferrum, & </s> <s xml:id="echoid-s6066" xml:space="preserve"><lb/>inter vim univerſalem Magneticam, pendentem ex Magnete in <lb/>imo Terræ concluſo, & </s> <s xml:id="echoid-s6067" xml:space="preserve">Ferrum: </s> <s xml:id="echoid-s6068" xml:space="preserve">Magnes poſtulat lamellas fer-<lb/>reas certæ tantum craſſitiei, quibus ſuam vim communicat, il-<lb/>lam nequaquam craſſioribus impreſſurus: </s> <s xml:id="echoid-s6069" xml:space="preserve">Eodem modo Ferrum <lb/>deſideratur certæ longitudinis & </s> <s xml:id="echoid-s6070" xml:space="preserve">craſſitiei, quod ſibi commiſſum <lb/>ſponte vim Magneticam acquirat: </s> <s xml:id="echoid-s6071" xml:space="preserve">Non dubito, quin omne Fer-<lb/>rum, utcunque craſſum, vi Magnetica imprægnari poſſit, modo ſit <lb/>ſatis longum; </s> <s xml:id="echoid-s6072" xml:space="preserve">ſed proportio inter craſſitiem & </s> <s xml:id="echoid-s6073" xml:space="preserve">longitudinem re-<lb/>quiritur, qualis hæc ſit, defectu ſufficientium Experimentorum, <lb/>nondum mihi conſtat.</s> <s xml:id="echoid-s6074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6075" xml:space="preserve">Addunt, & </s> <s xml:id="echoid-s6076" xml:space="preserve">recte, autores harum obſervationum, Ferrum can-<lb/>defactum & </s> <s xml:id="echoid-s6077" xml:space="preserve">in Meridiano poſitum, ocyus vi Magnetica dire-<lb/>ctrice imbui, quam Ferrum frigidum. </s> <s xml:id="echoid-s6078" xml:space="preserve">Ferrum igitur tenue, & </s> <s xml:id="echoid-s6079" xml:space="preserve"><lb/>longum, ſua ſponte vim directricem acquirit, qua Acus nauticæ <lb/>ſive Verſoria aguntur, modo aliquamdiu in Meridiano jacuerit, <lb/>quamobrem abſque Magnetis auxilio Verſorium haberi poteſt, & </s> <s xml:id="echoid-s6080" xml:space="preserve"><lb/>directio ejus explorari: </s> <s xml:id="echoid-s6081" xml:space="preserve">Tenuem enim & </s> <s xml:id="echoid-s6082" xml:space="preserve">longam cape virgam, <lb/>quam per medium parvi ſuberis transfige, ut aquæ innatet in <lb/>labro magno, poſito in loco valde tranquillo, hujus cuſpidem <lb/>verſus Boream, haud aliter quam Verſorium, dirigi obſervabis, <lb/>lento tamen hæc converſio & </s> <s xml:id="echoid-s6083" xml:space="preserve">directio abſolvitur motu: </s> <s xml:id="echoid-s6084" xml:space="preserve">Idem <lb/>fit ſuſpenſâ virgâ ex filo tenuiſſimo, ſerico, non intorto, uti <lb/>monet Gilbertus Lib. </s> <s xml:id="echoid-s6085" xml:space="preserve">1. </s> <s xml:id="echoid-s6086" xml:space="preserve">Cap. </s> <s xml:id="echoid-s6087" xml:space="preserve">12. </s> <s xml:id="echoid-s6088" xml:space="preserve">pag. </s> <s xml:id="echoid-s6089" xml:space="preserve">32. </s> <s xml:id="echoid-s6090" xml:space="preserve">Adeoque vis, quam <lb/>Magnes Terræ interior cum Ferro communicat, non deſtruitur <lb/>illico, ſed aliquamdiu permanens, efficit ut Ferri pars, quæ ul-<lb/>timo Boream ſpectavit, pergat converti ad Boream.</s> <s xml:id="echoid-s6091" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div160" type="section" level="1" n="160"> <head xml:id="echoid-head170" xml:space="preserve">EXPERIMENTUM CXXXIII.</head> <p> <s xml:id="echoid-s6092" xml:space="preserve">Quemadmodum in tentamine ſuperiori Ferrum in Meridiano <lb/>poſitum exploratum fuit, ita examinandum erat, quid continge-<lb/>ret in Ferro jacente parallele ad Æquatorem Terræ ſitu prio-<lb/>rem ad angulos rectos ſecante: </s> <s xml:id="echoid-s6093" xml:space="preserve">Proinde virga ferrea tenuiſſima <pb o="257" file="0271" n="271" rhead="DE MAGNETE."/> Experimenti CXXXI. </s> <s xml:id="echoid-s6094" xml:space="preserve">in igne candefacta fuit, tum abſque con-<lb/>cuſſione intra æneam detenta volſellam, ſupra ſolum lapideum <lb/>refrigerio commiſſa fuit, in ſitu ad Æ quatorem terræ parallelo, <lb/>atque ſimul in plano horizontali: </s> <s xml:id="echoid-s6095" xml:space="preserve">frigida attraxit Verſorii polum <lb/>Auſtralem, repulit Boreum, cuſpide quæ Occaſum ſpectavit: <lb/></s> <s xml:id="echoid-s6096" xml:space="preserve">Verſorio tamen admovenda fuit propius uno pollice, ut virtutem <lb/>oſtenderet. </s> <s xml:id="echoid-s6097" xml:space="preserve">quamobrem in hoc ſitu frigeſacta debiliores nacta erat <lb/>vires, quam cum in Meridiano jacuerat. </s> <s xml:id="echoid-s6098" xml:space="preserve">Prævideram cuſpidis oc-<lb/>cidentalis vires attrahentes polum Auſtralem Verſorii; </s> <s xml:id="echoid-s6099" xml:space="preserve">nam decli-<lb/>nat hic terrarum hoc Anno Magnes 13°, 20 verſus Occaſum, adeo-<lb/>que poſita virga parallela ad Æ quatorem terræ, hærebat cuſpis Oc-<lb/>cidentalis in hemiſphærio virium Magneticarum Boreo, inde vim <lb/>& </s> <s xml:id="echoid-s6100" xml:space="preserve">directionem poli Borei nacta, non poterat non Verſorii polum <lb/>Auſtralem attrahere, repellere Boreum.</s> <s xml:id="echoid-s6101" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6102" xml:space="preserve">2. </s> <s xml:id="echoid-s6103" xml:space="preserve">Supra ſolum lapideum ducto Æ quatore Magnetico accura-<lb/>tiſſime, virgam eandem, prius in Igne candefactam, huic Æqua-<lb/>tori commiſi refrigerandam; </s> <s xml:id="echoid-s6104" xml:space="preserve">quo facto, cuſpide utraque attraxit <lb/>Verſorii polum Boreum & </s> <s xml:id="echoid-s6105" xml:space="preserve">Auſtralem, adeo ut vere indifferens fue-<lb/>rit virga, nullis donata polis, quemadmodum fieri debebat.</s> <s xml:id="echoid-s6106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6107" xml:space="preserve">3. </s> <s xml:id="echoid-s6108" xml:space="preserve">Iterum virgam eandem, in Igne candefactam, ſolo impoſui <lb/>lapideo, ut Meridianum Magneticum ſecaret angulo 45 graduum, <lb/>atque cuſpide una ſpectaret Ortum Septentrionem verſus, altera <lb/>Occaſum Auſtrum verſus. </s> <s xml:id="echoid-s6109" xml:space="preserve">Illius refrigeratæ cuſpis occidua attra-<lb/>xit Verſorii polum Boreum, nihil agens in Auſtralem, cuſpis O-<lb/>rientalis attraxit Verſorii polum Auſtralem, nihil agens in Boreum: <lb/></s> <s xml:id="echoid-s6110" xml:space="preserve">fuerunt hæc Experimenta ſummâ cum curâ capta in loco ab omni <lb/>Ferro remoto: </s> <s xml:id="echoid-s6111" xml:space="preserve">In attractione cuſpidum nihil anomali eſt, quippe <lb/>in §. </s> <s xml:id="echoid-s6112" xml:space="preserve">3. </s> <s xml:id="echoid-s6113" xml:space="preserve">cuſpis Auſtralis, evaſit polus Auſtralis, attrahens ideo Ver-<lb/>ſorii polum Boreum: </s> <s xml:id="echoid-s6114" xml:space="preserve">verum indifferentia alterius cuſpidis virgæ dif-<lb/>ficilius intelligitur, quippe hæc evincit attractioni æqualem fuiſſe <lb/>repulſionem, & </s> <s xml:id="echoid-s6115" xml:space="preserve">proinde hæc cuſpis bipolaris fuit reſpectu poli Au-<lb/>ſtralis: </s> <s xml:id="echoid-s6116" xml:space="preserve">ita quoque altera cuſpis Virgæ ſe habuit, indifferens hæc <lb/>enim reſpectu poli Borei, attraxit polum Verſorii Auſtralem: </s> <s xml:id="echoid-s6117" xml:space="preserve">adeo-<lb/>que hæc cuſpis bipolaris fuit reſpectu poli Borei, vi attrahente unius <lb/>æquilibrata cum repellente alterius poli. </s> <s xml:id="echoid-s6118" xml:space="preserve">Ter felicem profecto, qui <lb/>hæc clare intelligat, exponereque poſſit! proculdubio id facillimum <pb o="258" file="0272" n="272" rhead="DISSERTATIO"/> erit iis, qui corporum naturam jam callent, eamque determinant, <lb/>quod nobis ob nimiam mentis caliginem, & </s> <s xml:id="echoid-s6119" xml:space="preserve">obſcuras Mathemati-<lb/>cas cogitationes intelligi non poſſe videtur.</s> <s xml:id="echoid-s6120" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div161" type="section" level="1" n="161"> <head xml:id="echoid-head171" xml:space="preserve">EXPERIMENTUM CXXXIV.</head> <p> <s xml:id="echoid-s6121" xml:space="preserve">Virga ferrea tenuis & </s> <s xml:id="echoid-s6122" xml:space="preserve">longa, Experimenti CXXXI, in Igne can-<lb/>defacta fuit, ex quo ope ænei forcipis extracta, immergebatur <lb/>Aquæ, ſitu ad horizontem parallelo & </s> <s xml:id="echoid-s6123" xml:space="preserve">in Meridiano Magnetico; <lb/></s> <s xml:id="echoid-s6124" xml:space="preserve">extinctæ oſtendit illico cuſpis Borea vim poli Borei, qua Verſorii <lb/>polum Auſtralem attraxit; </s> <s xml:id="echoid-s6125" xml:space="preserve">cuſpis Auſtralis attraxit Verſoriipolum <lb/>Boreum: </s> <s xml:id="echoid-s6126" xml:space="preserve">erat autem Virgæ in Aquâ extinctæ vis attrahens multo <lb/>major, quam cum antea ſupra ſolum refrigerio committebatur: </s> <s xml:id="echoid-s6127" xml:space="preserve">Ad-<lb/>notarunt hoc mecum Gilbertus, Rohaultus, Boyleus, & </s> <s xml:id="echoid-s6128" xml:space="preserve">Wol-<lb/>fius; </s> <s xml:id="echoid-s6129" xml:space="preserve">verum nuper Cl. </s> <s xml:id="echoid-s6130" xml:space="preserve">Reaumurius hoc obſervatum in dubium vo-<lb/>cavit in L’Hiſt. </s> <s xml:id="echoid-s6131" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s6132" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6133" xml:space="preserve">A°. </s> <s xml:id="echoid-s6134" xml:space="preserve">1723. </s> <s xml:id="echoid-s6135" xml:space="preserve">affirmans ſe ſæpius <lb/>hoc tentaſſe, ſed nunquam immediate poſt Ferri extinctionem ul-<lb/>lam vim Magneticam deprehendiſſe: </s> <s xml:id="echoid-s6136" xml:space="preserve">ſuſpicatus igitur Gilbertum & </s> <s xml:id="echoid-s6137" xml:space="preserve"><lb/>Rohaultum non ſatis circumſpecte attendiſſe, & </s> <s xml:id="echoid-s6138" xml:space="preserve">concuſſiones aliquas <lb/>cum Ferro, cum extinguebatur, fuiſſe communicatas; </s> <s xml:id="echoid-s6139" xml:space="preserve">obſervave-<lb/>rat enim mallei ictus aut concuſſiones aptas eſſe ad Ferrum vi Ma-<lb/>gnetica imprægnandum: </s> <s xml:id="echoid-s6140" xml:space="preserve">Quid autem in hac controverſia agemus, <lb/>a cujus parte ſtabit veritas? </s> <s xml:id="echoid-s6141" xml:space="preserve">experientia me docuit, tum Gilbertum <lb/>cum ſibi aſſentientibus, tum Reaumurium fuiſſe veritatem aſſecu-<lb/>tos: </s> <s xml:id="echoid-s6142" xml:space="preserve">Ecce in quonam hic lateat ſubtilitas: </s> <s xml:id="echoid-s6143" xml:space="preserve">ſi capiatur virga longa <lb/>tenuiſque, quali nos uſi fuimus in Experimento CXXXI, ſemper <lb/>poſt exſtinctionem in Aqua obſervatur illico vis ingens Magnetica; </s> <s xml:id="echoid-s6144" xml:space="preserve"><lb/>verum ejuſdem virgæ portio unius pollicis duntaxat, aut virga ma-<lb/>joris craſſitiei & </s> <s xml:id="echoid-s6145" xml:space="preserve">ſimul admodum brevis, in Aqua extincta, nun-<lb/>quam acquirit vim Magneticam, ſenſibus obſervabilem: </s> <s xml:id="echoid-s6146" xml:space="preserve">idcirco <lb/>certum eſt, Reaumurium in ſuis Experimentis uſum fuiſſe virgis ni-<lb/>mis brevibus & </s> <s xml:id="echoid-s6147" xml:space="preserve">craſſis, in quibus vim Magneticam conſpicerenon <lb/>potuit; </s> <s xml:id="echoid-s6148" xml:space="preserve">Gilbertus, Rohaultus, Boyleus, Wolfius inſtituerunt Ex-<lb/>perimentum cum virgis tenuibus & </s> <s xml:id="echoid-s6149" xml:space="preserve">longis, ideo opinati vim Ma-<lb/>gneticam in omnibus extinctis obtinere ferramentis: </s> <s xml:id="echoid-s6150" xml:space="preserve">Diſcimus ex <lb/>ejuſmodi controverſiis, quanta cum cura ad omnes circumſtantias <pb o="259" file="0273" n="273" rhead="DE MAGNETE."/> in Experimentis attendendum ſit, plurimaque nimia feſtinatione <lb/>peragi, breviuſque deſcribi, quam oportebat; </s> <s xml:id="echoid-s6151" xml:space="preserve">tum quam parum <lb/>liceat ratiocinari in Phyſicis, atque ex uno obſervati genere con-<lb/>cluſionem generalem formare, id enim omnes memoratos Erudi-<lb/>tos in errorem conjecit; </s> <s xml:id="echoid-s6152" xml:space="preserve">particularis obſervatio omnium erat vera <lb/>in Ferro illo, quocum Experimenta inſtituerunt; </s> <s xml:id="echoid-s6153" xml:space="preserve">ſed non in omni <lb/>alio cujuſlibet longitudinis & </s> <s xml:id="echoid-s6154" xml:space="preserve">craſſitiei.</s> <s xml:id="echoid-s6155" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s6156" xml:space="preserve">Animadverti poſtea hoc olim fuiſſe optime memoriæ traditum in <lb/>Philoſ. </s> <s xml:id="echoid-s6157" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6158" xml:space="preserve">N°. </s> <s xml:id="echoid-s6159" xml:space="preserve">214, Anno 1694, â quodam anonymo, qui <lb/>Gilberti obſervationi hæc addit. </s> <s xml:id="echoid-s6160" xml:space="preserve">Sed hæc modo locum habet in non-<lb/>nullis caſibus, quando enim virga brevis eſt, non formari in ea <lb/>poterit polus hoc modo: </s> <s xml:id="echoid-s6161" xml:space="preserve">Cape filum rotundum, diametri {1/5} pollic. </s> <s xml:id="echoid-s6162" xml:space="preserve">lon-<lb/>gitudinis 10 pollicum, in eo non excitabis polum, licet igni commi-<lb/>ſeris: </s> <s xml:id="echoid-s6163" xml:space="preserve">ſed ſi hoc filum ſit longius, veluti 30 pollic. </s> <s xml:id="echoid-s6164" xml:space="preserve">tum candefactum <lb/>polo concipiendo eſt idoneum. </s> <s xml:id="echoid-s6165" xml:space="preserve">Ita cape virgamrotundam, diametri <lb/>unius pollicis, & </s> <s xml:id="echoid-s6166" xml:space="preserve">30 pollices longam, hæc non erit apta concipiendo <lb/>poto. </s> <s xml:id="echoid-s6167" xml:space="preserve">Deinde addit, non datur virga tam brevis, quin apta ſit po-<lb/>lo, modo ſatis attenuetur. </s> <s xml:id="echoid-s6168" xml:space="preserve">Terminus longitudinis requiſitus pro <lb/>uniuscujusque craſſitie plus increſcit, quam imaginari poſſemus: <lb/></s> <s xml:id="echoid-s6169" xml:space="preserve">Utinam hæc Experimenta vir accuratiſſimus adnectere voluiſſet! <lb/>videtur ea de induſtria omiſiſſe, quaſi parum utilia, quæ tamen, <lb/>me judice, forent inter utiliſſima ponenda.</s> <s xml:id="echoid-s6170" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div162" type="section" level="1" n="162"> <head xml:id="echoid-head172" xml:space="preserve">EXPERIMENTUM CXXXV.</head> <p> <s xml:id="echoid-s6171" xml:space="preserve">Virgam ferream tenuem, quæ Experimento CXXXI. </s> <s xml:id="echoid-s6172" xml:space="preserve">inſervierat, <lb/>iterum candefeci in Igne, quam in volſella ænea arreptam, hori-<lb/>zontaliter tenui, ut tamen ſemper in Meridiano terreſtri eſſet, hu-<lb/>jus partem dimidiam, Auſtro obverſam, extinxi in Aquâ, ita ut <lb/>fere manſerit horizontalis, quo facto, virgæ cuſpis Auſtralis, & </s> <s xml:id="echoid-s6173" xml:space="preserve"><lb/>Borea attrahebat Verſorii polum Boreum.</s> <s xml:id="echoid-s6174" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6175" xml:space="preserve">Ejuſdem virgæ iterum candefactæ partem dimidiam Boreæ ob-<lb/>verſam in Aquâ extinxi, manente altero dimidio extra aquam; </s> <s xml:id="echoid-s6176" xml:space="preserve">tum <lb/>virgæ cuſpis Borea fugavit Verſorii polum Boreum, & </s> <s xml:id="echoid-s6177" xml:space="preserve">attraxit Au-<lb/>ſtralem, quæ phænomena clarius intelligentur explicato Experimen-<lb/>to ſequenti.</s> <s xml:id="echoid-s6178" xml:space="preserve"/> </p> <pb o="260" file="0274" n="274" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div163" type="section" level="1" n="163"> <head xml:id="echoid-head173" xml:space="preserve">EXPERIMENTUM CXXXVI.</head> <p> <s xml:id="echoid-s6179" xml:space="preserve">Virga ferrea tenuis & </s> <s xml:id="echoid-s6180" xml:space="preserve">oblonga in Igne candefiat, quam in vol-<lb/>ſella ænea tene perpendiculariter ad horizontem: </s> <s xml:id="echoid-s6181" xml:space="preserve">hujus inferior <lb/>cuſpis, quamvis adhuc rubens, attrahit fortiter Verſorii polum <lb/>Auſtralem, & </s> <s xml:id="echoid-s6182" xml:space="preserve">fugat Boreum: </s> <s xml:id="echoid-s6183" xml:space="preserve">Cuſpis autem ſuperior attrahit Ver-<lb/>ſorii polum Boreum, fugat Auſtralem.</s> <s xml:id="echoid-s6184" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6185" xml:space="preserve">Adeoque Ferrum ignitum illico vi Magnetica donatur in hoc <lb/>ſitu perpendiculari, & </s> <s xml:id="echoid-s6186" xml:space="preserve">æque cito ac ſi Magneti affrictum fuiſ-<lb/>ſet.</s> <s xml:id="echoid-s6187" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6188" xml:space="preserve">2. </s> <s xml:id="echoid-s6189" xml:space="preserve">Virga hæc in eodem perpendiculari ſitu horæ ſpatio relicta, <lb/>oſtendit omnino eandem vim in Verſorium quam ante, illud ta-<lb/>men non tam fortiter attrahebat, nunc frigida, quam antea <lb/>ignita.</s> <s xml:id="echoid-s6190" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6191" xml:space="preserve">3. </s> <s xml:id="echoid-s6192" xml:space="preserve">Eandem virgam iterum in Igne candefactam immerſi Aquæ <lb/>perpendiculariter & </s> <s xml:id="echoid-s6193" xml:space="preserve">penitus, ejus cuſpis inferior polus Boreus eva-<lb/>ſit, nam Verſorii polum Auſtralem attraxit vi valida: </s> <s xml:id="echoid-s6194" xml:space="preserve">Non tamen <lb/>repetitæ candefactiones & </s> <s xml:id="echoid-s6195" xml:space="preserve">in Aquâ extinctiones vim attractricem <lb/>Virgæ auxiſſe mihi viſæ ſunt.</s> <s xml:id="echoid-s6196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6197" xml:space="preserve">4. </s> <s xml:id="echoid-s6198" xml:space="preserve">Eandem virgam denuo calentem, perpendiculariter Aquæ im-<lb/>miſi uſque ad dimidiam ſui longitudinem, ſic quoque cuſpis inferior <lb/>in Aqua extincta evaſit polus Boreus, cuſpis tamen ſuperior imme-<lb/>diate poſt extinctionem attrahebat æque polum Boreum quam Au-<lb/>ſtralem.</s> <s xml:id="echoid-s6199" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6200" xml:space="preserve">5. </s> <s xml:id="echoid-s6201" xml:space="preserve">Deinde patallelopipedum 5 pollices longum, baſeos quadratæ, <lb/>unius pollicis, ignitum, ſolo impoſui perpendiculariter erectum, cum <lb/>elapſâ horâ frigebat, baſis inferior attraxit polum Verſorii Boreum, <lb/>quem quoque attraxit baſis parallelopipedi ſuperior: </s> <s xml:id="echoid-s6202" xml:space="preserve">Quamobrem <lb/>in hoc ferreo parallelopipedo brevique vis Magnetica directrix non <lb/>colligitur intra tam anguſtum temporis ſpatium, quam quidem in <lb/>virgis tenuioribus: </s> <s xml:id="echoid-s6203" xml:space="preserve">imo non colligitur ſubito in Ferro tam craſſo, <lb/>quamvis etiam in Aqua extincto.</s> <s xml:id="echoid-s6204" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6205" xml:space="preserve">Cæteroquin obſervare licet in ferramentis univerſe omnibus, ne <lb/>quidem craſſiſſimis exceptis, imo in iis, quæ a Magnete ob magni-<lb/>tudinem non imprægnari vi Magnetica poterant, hæc ad horizon- <pb o="261" file="0275" n="275" rhead="DE MAGNETE."/> tem perpendiculariter erecta ſponte vi eâ donari; </s> <s xml:id="echoid-s6206" xml:space="preserve">craſſa tamen & </s> <s xml:id="echoid-s6207" xml:space="preserve"><lb/>brevia non niſi longinquitate temporis; </s> <s xml:id="echoid-s6208" xml:space="preserve">craſſa & </s> <s xml:id="echoid-s6209" xml:space="preserve">longa citius; </s> <s xml:id="echoid-s6210" xml:space="preserve">ſed <lb/>tenuia & </s> <s xml:id="echoid-s6211" xml:space="preserve">longa nequidem horæ minutum poſtulare, cape enim vir-<lb/>gam 6 pedes longam, diametri {1/5} pollicis, ad horizontem perpen-<lb/>diculariter tene, & </s> <s xml:id="echoid-s6212" xml:space="preserve">cuſpide inferiori polum Verſorii Auſtralem at-<lb/>trahet, fugabit Boreum: </s> <s xml:id="echoid-s6213" xml:space="preserve">cuſpide ſuperiori attrahet polum Boreum, <lb/>fugando Auſtralem: </s> <s xml:id="echoid-s6214" xml:space="preserve">ſtatim virgam inverte, & </s> <s xml:id="echoid-s6215" xml:space="preserve">intra Minutum ob-<lb/>ſervabis, cuſpidem inferiorem attracturam polum Verſorii Auſtra-<lb/>lem, quem modo ante reſpuerat, adeo ut poli in ejuſmodi Virga <lb/>ocyſſime mutentur: </s> <s xml:id="echoid-s6216" xml:space="preserve">Idem in Virga breviori, ſed ſimul multum te-<lb/>nuiori animadverti poteſt. </s> <s xml:id="echoid-s6217" xml:space="preserve">Horum nonnulla adnotavit quondam <lb/>Grimaldi in Tract. </s> <s xml:id="echoid-s6218" xml:space="preserve">de Lumine Prop. </s> <s xml:id="echoid-s6219" xml:space="preserve">6. </s> <s xml:id="echoid-s6220" xml:space="preserve">§. </s> <s xml:id="echoid-s6221" xml:space="preserve">51. </s> <s xml:id="echoid-s6222" xml:space="preserve">tum Boyle, Poli-<lb/>nierius in Exper. </s> <s xml:id="echoid-s6223" xml:space="preserve">Phyſiq. </s> <s xml:id="echoid-s6224" xml:space="preserve">pag. </s> <s xml:id="echoid-s6225" xml:space="preserve">283. </s> <s xml:id="echoid-s6226" xml:space="preserve">& </s> <s xml:id="echoid-s6227" xml:space="preserve">nuperrime Reaumurius in <lb/>L’Hiſt. </s> <s xml:id="echoid-s6228" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6229" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6230" xml:space="preserve">A°. </s> <s xml:id="echoid-s6231" xml:space="preserve">1723. </s> <s xml:id="echoid-s6232" xml:space="preserve">Addendum præterea eſt, dari <lb/>nonnunquam lamellas Chalybeas, quæ in aquâ perpendiculariter <lb/>ad horizontem extinctæ, acquirunt polos fixos, non mutabiles, <lb/>lamellis quomodocunque inverſis: </s> <s xml:id="echoid-s6233" xml:space="preserve">dantur quoque aliæ, quæ po-<lb/>los quidem fixos conſervant, verum inverſæ, non adeo vehemen-<lb/>ter vim ejuſdem poli exercent, quam antea, & </s> <s xml:id="echoid-s6234" xml:space="preserve">potius inclinatio-<lb/>nem tantum ejuſdem poli oſtendunt: </s> <s xml:id="echoid-s6235" xml:space="preserve">imo aliæ, poſtquam conver-<lb/>ſæ ſunt, evadunt indifferentes, ita ut nauticæ Acui admotæ, ver-<lb/>ſus Ortum & </s> <s xml:id="echoid-s6236" xml:space="preserve">Occaſum eam dirigant, atque in æquilibrio quaſi <lb/>teneant: </s> <s xml:id="echoid-s6237" xml:space="preserve">hæc autem omnia modo obtinent in tenuibus Chalybeis <lb/>lamellis; </s> <s xml:id="echoid-s6238" xml:space="preserve">nam in craſſioribus ferramentis ea, quæ ſuperius attuli, <lb/>tantum dantur, hujus obſervationis potiſſimam partem vide in Phi-<lb/>loſ. </s> <s xml:id="echoid-s6239" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6240" xml:space="preserve">N°. </s> <s xml:id="echoid-s6241" xml:space="preserve">246.</s> <s xml:id="echoid-s6242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6243" xml:space="preserve">Quod ſi ferramenta diu fixa ſteterint, quemadmodum cancelli <lb/>ferrei feneſtrarum, qui in ædibus antiquis per centenos hæſerunt <lb/>annos, hi vim maximam agendi in Acum Nauticam, imo ad di-<lb/>ſtantiam quidem 4 ulnarum & </s> <s xml:id="echoid-s6244" xml:space="preserve">amplius acquirunt, quemadmodum <lb/>Mantuæ obſervavit Cabeus Lib. </s> <s xml:id="echoid-s6245" xml:space="preserve">1. </s> <s xml:id="echoid-s6246" xml:space="preserve">Cap. </s> <s xml:id="echoid-s6247" xml:space="preserve">17.</s> <s xml:id="echoid-s6248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6249" xml:space="preserve">Ex his experimentis iterum conſtat, ſemper Verſorium haberi <lb/>poſſe, quod cuſpides ſuas dirigat verſus plagam cæli Boream & </s> <s xml:id="echoid-s6250" xml:space="preserve">Au-<lb/>ſtralem, etiamſi non affricetur Magneti, modo ſtet aliquamdiu ver-<lb/>ticaliter erectum, aut ignitum immergatur aquæ perpendiculari-<lb/>œ<unsure/>r.</s> <s xml:id="echoid-s6251" xml:space="preserve"/> </p> <pb o="262" file="0276" n="276" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s6252" xml:space="preserve">Si Virga pro hiſce Experimentis quædam longior eligatur, ejus <lb/>punctum attrahens polum Boreum Verſorii ſemper plus diſtat abex-<lb/>tremitate Ferri, quam punctum, quod polum Auſtralem Acus affi-<lb/>cit, quemadmodum olim in Philoſ. </s> <s xml:id="echoid-s6253" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6254" xml:space="preserve">A°. </s> <s xml:id="echoid-s6255" xml:space="preserve">1694 obſervatum <lb/>fuit, & </s> <s xml:id="echoid-s6256" xml:space="preserve">nuper etiam tradidit Reaumurius.</s> <s xml:id="echoid-s6257" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6258" xml:space="preserve">Eſt profecto admirandum, Ferrum candens, ſed perpendiculari-<lb/>ter ad horizontem poſitum, vi imbui Magneticâ, cum Magnes ipſe <lb/>candefactus, & </s> <s xml:id="echoid-s6259" xml:space="preserve">deinde perpendiculariter erectus, inter refrigeran-<lb/>dum nihil virtutis retineat, aut acquirat: </s> <s xml:id="echoid-s6260" xml:space="preserve">Boyleus eum in finem <lb/>Magnetes oblongos, in Igne canderactos, refrigerio expoſuit, aut <lb/>eos dirigendo verſus Boream & </s> <s xml:id="echoid-s6261" xml:space="preserve">Auſtrum, vel horizontaliter ponen-<lb/>do, vel perpendiculariter, vel in quocunque alio obliquo ſitu, ve-<lb/>rum nunquam vim attractricem aut directricem in iis ſuperſtitem ob. <lb/></s> <s xml:id="echoid-s6262" xml:space="preserve">ſervare potuit, vide Magnetic. </s> <s xml:id="echoid-s6263" xml:space="preserve">pag. </s> <s xml:id="echoid-s6264" xml:space="preserve">499.</s> <s xml:id="echoid-s6265" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div164" type="section" level="1" n="164"> <head xml:id="echoid-head174" xml:space="preserve">EXPERIMENTUM CXXXVII.</head> <p> <s xml:id="echoid-s6266" xml:space="preserve">Eadem extremitas Verſorii attrahitur vario modo ab extremitati-<lb/>bus iisdem Virgæ ferreæ, perpendiculariter ad horizontem deten-<lb/>tæ & </s> <s xml:id="echoid-s6267" xml:space="preserve">ipſi oppoſitæ, in diverſis locis Terræ.</s> <s xml:id="echoid-s6268" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6269" xml:space="preserve">Quod conſtat ex obſervationibus â nauta captis, inſertisque Phi-<lb/>loſophicis Tranſactionibus N°. </s> <s xml:id="echoid-s6270" xml:space="preserve">177. </s> <s xml:id="echoid-s6271" xml:space="preserve">quas nequaquam omittendas <lb/>judicavi, cum hactenus neminem offendi, qui ſimiles inſtituit: </s> <s xml:id="echoid-s6272" xml:space="preserve">con-<lb/>ſcriptæ autem fuerunt Anno 1684. </s> <s xml:id="echoid-s6273" xml:space="preserve">a nauta Æquatorem transanavi-<lb/>gante.</s> <s xml:id="echoid-s6274" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6275" xml:space="preserve">1. </s> <s xml:id="echoid-s6276" xml:space="preserve">Ab anglia uſque ad 10 gradus Latitudinis Boreæ, Verſorii <lb/>pars Borea attrahebat extremitatem Virgæ ferreæ ſuperiorem; </s> <s xml:id="echoid-s6277" xml:space="preserve">Ver-<lb/>ſorii pars Auſtralis, attrahebat Virgæ inferius extremum.</s> <s xml:id="echoid-s6278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6279" xml:space="preserve">2. </s> <s xml:id="echoid-s6280" xml:space="preserve">Ad Latitudinem Boream 9°, 42?</s> <s xml:id="echoid-s6281" xml:space="preserve">. ad Longitudinem a Lizard, <lb/>verſus Occaſum, extremum Verſorii Auſtralem fortiter attrahebat <lb/>Virgæ infimum: </s> <s xml:id="echoid-s6282" xml:space="preserve">Sed Verſorii extremitas Borea non tam fortiter <lb/>attrahebat partem ſuperiorem virgæ, quam ſupra.</s> <s xml:id="echoid-s6283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6284" xml:space="preserve">3. </s> <s xml:id="echoid-s6285" xml:space="preserve">Ad Latitudinem Boream 4°, 33?</s> <s xml:id="echoid-s6286" xml:space="preserve">. ad Lougitudinem 5°. </s> <s xml:id="echoid-s6287" xml:space="preserve">18? </s> <s xml:id="echoid-s6288" xml:space="preserve">a <lb/>Lizard, verſus Occaſum, Verſorii pars Borea incipiebat declinare <lb/>a parte ſuprema Virgæ, & </s> <s xml:id="echoid-s6289" xml:space="preserve">Verſorii Auſtralis pars inclinabat fortius <lb/>verſus partem infimam Virgæ.</s> <s xml:id="echoid-s6290" xml:space="preserve"/> </p> <pb o="263" file="0277" n="277" rhead="DE MAGNETE."/> <p> <s xml:id="echoid-s6291" xml:space="preserve">4. </s> <s xml:id="echoid-s6292" xml:space="preserve">ad Latitudinem o°, 52? </s> <s xml:id="echoid-s6293" xml:space="preserve">Meridionalem, & </s> <s xml:id="echoid-s6294" xml:space="preserve">ad Longitudinem <lb/>11°, 52? </s> <s xml:id="echoid-s6295" xml:space="preserve">a Lizard Occidentaliter: </s> <s xml:id="echoid-s6296" xml:space="preserve">Extremum Verſorii Boreum, <lb/>non attrahebatur a ſuprema parte virgæ, neque ab inferiori parte <lb/>hujus appetebatur; </s> <s xml:id="echoid-s6297" xml:space="preserve">Verſorii tamen extremum Auſtrale inclinabat ad <lb/>inferiorem virgæ partem, etiamſi non tam valide.</s> <s xml:id="echoid-s6298" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6299" xml:space="preserve">5. </s> <s xml:id="echoid-s6300" xml:space="preserve">Ad Latitudinem 5°, 17? </s> <s xml:id="echoid-s6301" xml:space="preserve">Meridionalem; </s> <s xml:id="echoid-s6302" xml:space="preserve">& </s> <s xml:id="echoid-s6303" xml:space="preserve">ad Longitudinem <lb/>15°, 9? </s> <s xml:id="echoid-s6304" xml:space="preserve">a Lizard Occidentaliter, extremum Verſorii Auſtrale verte-<lb/>batur ad inferiorem partem virgæ: </s> <s xml:id="echoid-s6305" xml:space="preserve">nequaquam tamen appetebat <lb/>partem virgæ ſuperiorem, quæ quoque non attrahebatur a Verſorii <lb/>extremo Boreo. </s> <s xml:id="echoid-s6306" xml:space="preserve">Cum autem virga ponebatur horizontaliter in li-<lb/>nea parallela Meridiano terreſtri; </s> <s xml:id="echoid-s6307" xml:space="preserve">tum extremum Verſorii Boreum <lb/>vertebatur verſus extremum Virgæ Auſtrale.</s> <s xml:id="echoid-s6308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6309" xml:space="preserve">6. </s> <s xml:id="echoid-s6310" xml:space="preserve">Ad Latitudinem 8, 17? </s> <s xml:id="echoid-s6311" xml:space="preserve">Meridionalem, & </s> <s xml:id="echoid-s6312" xml:space="preserve">ad Longitudinem <lb/>17°, 35? </s> <s xml:id="echoid-s6313" xml:space="preserve">a Lizard Occidentaliter, Verſorii extremum Boreum non <lb/>appetebat partem ſupremam Virgæ, potius ab ea fugiebat: </s> <s xml:id="echoid-s6314" xml:space="preserve">ſed Ver-<lb/>ſorii extremum Auſtrale appetebat aliquantum virgæ infimum, <lb/>ejuſque veram poſituram mutabat circiter 2 punctis: </s> <s xml:id="echoid-s6315" xml:space="preserve">Tum virga <lb/>ſupra Verſorium ita fuit diſpoſita, ut illius ſuprema pars reſpice-<lb/>ret cæli polum Meridionalem, & </s> <s xml:id="echoid-s6316" xml:space="preserve">infima pars polum Auſtralem, <lb/>tum Verſorii pars Borea appetebat partem virgæ infimam, ejuſque <lb/>motum ſequebatur: </s> <s xml:id="echoid-s6317" xml:space="preserve">ſi autem virga ponebatur horizontaliter, phæ-<lb/>nomena erant eadem, ac ſupra.</s> <s xml:id="echoid-s6318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6319" xml:space="preserve">7. </s> <s xml:id="echoid-s6320" xml:space="preserve">Ad Latitudinem 15° Meridionalem, & </s> <s xml:id="echoid-s6321" xml:space="preserve">ad Longitudinem 20° <lb/>Occidentaliter a Lizard, extremum Acus Auſtrale incipiebat appe-<lb/>rere ſuperiorem partem Virgæ ferreæ, & </s> <s xml:id="echoid-s6322" xml:space="preserve">Verſorii extremitas Bo-<lb/>rea attrahebat infimam partem virgæ, quam ſequebatur: </s> <s xml:id="echoid-s6323" xml:space="preserve">Sed poſita <lb/>Virga horizontaliter, tum Verſorii pars Borea appetebat Auſtralem <lb/>Virgæ.</s> <s xml:id="echoid-s6324" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6325" xml:space="preserve">8. </s> <s xml:id="echoid-s6326" xml:space="preserve">Ad Latitudinem 20°, 20? </s> <s xml:id="echoid-s6327" xml:space="preserve">Meridionalem, & </s> <s xml:id="echoid-s6328" xml:space="preserve">ad Longitudinem <lb/>19°, 20? </s> <s xml:id="echoid-s6329" xml:space="preserve">Occidentaliter a Lizard, Verſorii extremum Auſtrale ap-<lb/>petebat ſuperiorem partem Virgæ, & </s> <s xml:id="echoid-s6330" xml:space="preserve">extremum Boreum appetebat <lb/>fortiter inferiorem partem virgæ. </s> <s xml:id="echoid-s6331" xml:space="preserve">Quæ eadem obtinebant</s> </p> <p> <s xml:id="echoid-s6332" xml:space="preserve">9. </s> <s xml:id="echoid-s6333" xml:space="preserve">Ad Latitudinem 29°, 25?</s> <s xml:id="echoid-s6334" xml:space="preserve">, Meridionalem, & </s> <s xml:id="echoid-s6335" xml:space="preserve">ad Longitudinem <lb/>13° 10? </s> <s xml:id="echoid-s6336" xml:space="preserve">Occidentaliter a Lizard.</s> <s xml:id="echoid-s6337" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6338" xml:space="preserve">Hæc omnia â priori determinare potuiſſemus, poſtquam cogni-<lb/>tum fuit Verſorii extremum Boreum in Terræ hemiſphærio Boreo <pb o="264" file="0278" n="278" rhead="DISSERTATIO"/> deorſum premi horizontem verſus, atque extremum Auſtrale in <lb/>hemiſphærio Terræ Auſtrali inclinari deorſum, elevari autem Bo-<lb/>reum, quia polus Magnetis Terreſtris Boreus prævalet in Terræ <lb/>patte Borea atque ad ſe attrahit Verſorii extremum Boreum, <lb/>verum polus Auſtralis ejuſdem Magnetis prævalet in Terræ he-<lb/>miſphærio Auſtrali, unde verſus ſe extremum Auſtrale Acus deter-<lb/>minat: </s> <s xml:id="echoid-s6339" xml:space="preserve">Quoniam igitur per Experim CXXXVI. </s> <s xml:id="echoid-s6340" xml:space="preserve">inferior cuſpis virgæ <lb/>perpendiculariter poſitæ in hac regione polum Auſtralem Verſorii <lb/>attrahit, vi Borei poli a Terreſtri Magnete imprægnatur, quod fit, <lb/>quia inferior virgæ pars illi polo proxima eſt, adeoque tamdiu hæc <lb/>pars inferior virtutem poli Borei acci piet, quamdiu hæc propior <lb/>huic polo quam Auſtrali Magnetis fuerit, ſimulac vero cuſpis vir-<lb/>gæ inferior propius acceſſerit ad polum Magnetis Terreſtris Auſtra-<lb/>lem, hujus vim accipiet, plane oppoſitam priori, adeoque cuſpis <lb/>virgæ inferior attrahet polum Verſorii Boreum: </s> <s xml:id="echoid-s6341" xml:space="preserve">in eâ autem Ter-<lb/>ræ parte, in quâ vis utriuſque poli Magnetis Terreſtris ſibi eſt æ-<lb/>quilibrata, cuſpis virgæ inferior nulla vi donabitur: </s> <s xml:id="echoid-s6342" xml:space="preserve">Idcirco obſer-<lb/>vata fuit virgæ cuſpis inferior vi poli Borei Terreſtris imprægnata in <lb/>Terræ parte Septentrionali uſque ad latitudinem Auſtralem 8°, 17. <lb/></s> <s xml:id="echoid-s6343" xml:space="preserve">quia huc uſque visillius poliMagnetici ſeſe extendit; </s> <s xml:id="echoid-s6344" xml:space="preserve">ultraLatitudinem <lb/>vero 15 graduum Auſtralem vis poliMagnetisAuſtralis prædominari in-<lb/>cepit, atque cum virgæ infimo extremo virtutem ſuam communicans, <lb/>fecitut hoc Verſorii polum Boreum attraxerit: </s> <s xml:id="echoid-s6345" xml:space="preserve">Erat utriuſque poliMa-<lb/>gnetici virtus fere in æquilibrio a latitudine Meridionali 0°, 52? </s> <s xml:id="echoid-s6346" xml:space="preserve">ad <lb/>8°. </s> <s xml:id="echoid-s6347" xml:space="preserve">17. </s> <s xml:id="echoid-s6348" xml:space="preserve">hinc vix vi quadam imprægnabatur virgæ extremum utrum-<lb/>que. </s> <s xml:id="echoid-s6349" xml:space="preserve">Vidimus in Inclinationibus â Noellio obſervatis, Inclinatio-<lb/>nem Acus perpetuo imminui a latitudine Borea 38°, 40?</s> <s xml:id="echoid-s6350" xml:space="preserve">, uſque ad <lb/>Latitudinem Meridionalem 6°, 30?</s> <s xml:id="echoid-s6351" xml:space="preserve">. indicio vim poli Borei Magne-<lb/>tis Terreſtris eo uſque exporrigi: </s> <s xml:id="echoid-s6352" xml:space="preserve">inde autem recedendo magis ab <lb/>Æquatore Auſtrum verſus, inverſa fuit Inclinatoria Acus, & </s> <s xml:id="echoid-s6353" xml:space="preserve">cu-<lb/>ſpis, quæ in Septentrionali parte Terræ horizontem ſpectaverat, nunc <lb/>cœlum verſus dirigebatur, polo nempe Auſtralis Magnetis prædo-<lb/>minante, cujus vis fortior evaſit, donec ad latitudinem 35°, 25? </s> <s xml:id="echoid-s6354" xml:space="preserve"><lb/>validiſſima fuerit, atque Acum ad horizontem perpendiculariter <lb/>erexerit, ideo quoque in præſenti obſervatione recte notatum fuit, <lb/>ad latitudinem Meridionalem 20° & </s> <s xml:id="echoid-s6355" xml:space="preserve">ulterius uſque ad 29° virgæ in- <pb o="265" file="0279" n="279" rhead="DE MAGNETE."/> feriorem partem fortiter appetiiſſe Verſorii cuſpidem Boream: </s> <s xml:id="echoid-s6356" xml:space="preserve">imo <lb/>vis hæc fortior adhucdum obſervata fuiſſet, modo Experimentum <lb/>captum fuiſſet in majori latitudine Auſtrali, 35° grad. </s> <s xml:id="echoid-s6357" xml:space="preserve">& </s> <s xml:id="echoid-s6358" xml:space="preserve">longitu-<lb/>dine eadem, ſub qua Madagaſcar jacet.</s> <s xml:id="echoid-s6359" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div165" type="section" level="1" n="165"> <head xml:id="echoid-head175" xml:space="preserve">EXPERIMENTUM CXXXVIII.</head> <p> <s xml:id="echoid-s6360" xml:space="preserve">Virga ferrea ita impoſita fuit Incudi, ut ſitum Meridiano terreſtri <lb/>parallelum habuerit; </s> <s xml:id="echoid-s6361" xml:space="preserve">ejus extremum, Boream reſpiciens, malleo <lb/>tuſum, evaſit polus Boreus, extremum Auſtrale malleo ictum fa-<lb/>ctum eſt polus Auſtralis: </s> <s xml:id="echoid-s6362" xml:space="preserve">Succedit autem hoc Experimentum cum <lb/>virgis certæ longitudinis & </s> <s xml:id="echoid-s6363" xml:space="preserve">craſſitiei, non cum omnibus; </s> <s xml:id="echoid-s6364" xml:space="preserve">ſi enim <lb/>nimium craſſa reſpectu ſuæ longitudinis fuerit virga, licet alteru-<lb/>trum extremum Malleo cudatur, vis polorum directrix obſervabi-<lb/>tur nulla, niſi extremum tantopere attenuetur, ut virgæ ſubtilitas <lb/>certam proportionem ad ſuam longitudinem recipiat. </s> <s xml:id="echoid-s6365" xml:space="preserve">Quæcunque <lb/>de effectu Mallei dicta ſunt, etiam intelligenda ſunt de lima ſuper <lb/>Ferro ducta, de Ferri attritu ſupra quodcunque durum corpus, de <lb/>ſectione ope ſerræ, modo Ferrum ſit longum & </s> <s xml:id="echoid-s6366" xml:space="preserve">tenue: </s> <s xml:id="echoid-s6367" xml:space="preserve">Quo au-<lb/>tem memorata inſtrumenta vi fortiori in Ferrum adiguntur, eo Ma-<lb/>gnetiſmus illi major inducitur, qui tamen nunquam eo uſque in-<lb/>creſcit, qualis a Magnete, etiamſi mediocrium virium, cum Fer-<lb/>ro communicari poteſt. </s> <s xml:id="echoid-s6368" xml:space="preserve">Ut cudendo virgam ſupra incudem, extre-<lb/>mo alterutri polum Boreum inducamus alteri Auſtralem hac in re-<lb/>gione, viam ſequi oportet, quam Acus Inclinatoria præmonſtrat: <lb/></s> <s xml:id="echoid-s6369" xml:space="preserve">Ferri pars Auſtralis ſit ſupra incudem multo elevatior, pars Borea <lb/>depreſſior, hoc modo cuſa virga, ſemper binos polos in ſuis extre-<lb/>mitatibus habebit: </s> <s xml:id="echoid-s6370" xml:space="preserve">ſed ſi Ferrum alio ſupra incudem tenueris modo, <lb/>aliquando in utroque extremo polum Boreum obſervabis; </s> <s xml:id="echoid-s6371" xml:space="preserve">ſimilia <lb/>plura ſcripta video in Philoſ. </s> <s xml:id="echoid-s6372" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6373" xml:space="preserve">N°. </s> <s xml:id="echoid-s6374" xml:space="preserve">214.</s> <s xml:id="echoid-s6375" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div166" type="section" level="1" n="166"> <head xml:id="echoid-head176" xml:space="preserve">EXPERIMENTUM CXXXIX.</head> <p> <s xml:id="echoid-s6376" xml:space="preserve">Lamella Ferri mollioris intra roſtra forcipis, ultra quæ promi-<lb/>neat, capiatur; </s> <s xml:id="echoid-s6377" xml:space="preserve">tum vehementer inflectatur dextrorſum & </s> <s xml:id="echoid-s6378" xml:space="preserve">ſiniſtror-<lb/>ſum, donec poſt multas flexiones frangatur; </s> <s xml:id="echoid-s6379" xml:space="preserve">fractura limaturam <pb o="266" file="0280" n="280" rhead="DISSERTATIO"/> Ferri attrahet, haud aliter ac ſi lamella vi debilis Magnetis impræ-<lb/>gnata fuiſſet.</s> <s xml:id="echoid-s6380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6381" xml:space="preserve">Cl Reaumurius hoc Experimentum inſtituit cum ferramentis gran-<lb/>dibus, tum cum filis optimi ut & </s> <s xml:id="echoid-s6382" xml:space="preserve">mollis fragilisque Ferri; </s> <s xml:id="echoid-s6383" xml:space="preserve">cum <lb/>Chalybe temperato & </s> <s xml:id="echoid-s6384" xml:space="preserve">non temperato: </s> <s xml:id="echoid-s6385" xml:space="preserve">poſitis cæteris æqualibus, <lb/>quo Ferrum diffractum eſt mollius, eo eſt magis fibroſum, & </s> <s xml:id="echoid-s6386" xml:space="preserve">non <lb/>niſi pluribus flexionibus frangitur, ſed eo majorem vim attractri-<lb/>cem acquirit. </s> <s xml:id="echoid-s6387" xml:space="preserve">Ferrum fragile, citius ruptum, minori vi imprægna-<lb/>tur, minori adhucdum Chalybs temperatus; </s> <s xml:id="echoid-s6388" xml:space="preserve">qui prout mollior ri-<lb/>gidiorve fuerit, ita fortius vel imbecillius attrahit. </s> <s xml:id="echoid-s6389" xml:space="preserve">In genere, omne <lb/>Ferrum flexione fractum vim Magneticam habet, ſed interdum <lb/>modo diei ſpatio perdurantem: </s> <s xml:id="echoid-s6390" xml:space="preserve">Memorat inſuper Autor, non eſſe <lb/>ſenſibilem vim attractricem, ſi Ferrum tantummodo craſſitiem A-<lb/>cûs habuerit; </s> <s xml:id="echoid-s6391" xml:space="preserve">neque eam augeri in ratione craſſitiei laminarum, <lb/>ſed eſſe maximam in Ferro craſſitie digitum minimum æquante: </s> <s xml:id="echoid-s6392" xml:space="preserve">In <lb/>hiſce Experimentis iterum determinata longitudo Ferri requiritur; <lb/></s> <s xml:id="echoid-s6393" xml:space="preserve">flecte enim & </s> <s xml:id="echoid-s6394" xml:space="preserve">rumpe in medio Ferrum, cujus longitudo unius pedis, <lb/>ambo fragmenta vim manifeſtam oſtendent: </s> <s xml:id="echoid-s6395" xml:space="preserve">aſt ita crebro in flexum dif-<lb/>fringe, ut alterutrum fragmentum non ſuperet ſua longitudine di-<lb/>gitum, hoc limaturam, utcunque ſubtilem, attrahet nequaquam, <lb/>altero interim longiſſimo fragmento vi validâ eam alliciente.</s> <s xml:id="echoid-s6396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6397" xml:space="preserve">In hiſce Experimentis fractura duntaxat vim Magneticam acqui-<lb/>rit, alia extrema permanent comparata eodem modo ac ante in-<lb/>ſtitutum Experimentum.</s> <s xml:id="echoid-s6398" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div167" type="section" level="1" n="167"> <head xml:id="echoid-head177" xml:space="preserve">EXPERIMENTUM CXL.</head> <p> <s xml:id="echoid-s6399" xml:space="preserve">Sed plura elegantia tentamina cum Ferro debentur ſubtili Reau-<lb/>murio, inter quæ hoc etiam: </s> <s xml:id="echoid-s6400" xml:space="preserve">Filum ferreum craſſitiei circiter digiti <lb/>minimi, longitudinis 2 {1/2} pedum in forcipe tenuit, atque 5 digitis ab <lb/>extremo crebris flexionibus diffregit, utraque ſuperficies fracturæ <lb/>tantum virtutis Magneticæ habuit, qua clavum elevaret exi-<lb/>guum.</s> <s xml:id="echoid-s6401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6402" xml:space="preserve">Deinde longiſſimum fragmentum, eidem forcipi inſertum, ad di-<lb/>ſtantiam 1 {1/2} pollicis a fractura aliquoties inflexit, id tamen non fran-<lb/>gens; </s> <s xml:id="echoid-s6403" xml:space="preserve">hinc prioris fracturæ ſuperficies majorem vim attrahendi ac- <pb o="267" file="0281" n="281" rhead="DE MAGNETE."/> quiſivit; </s> <s xml:id="echoid-s6404" xml:space="preserve">poſtea in aliis locis, ſed ſemper accedendo verſus me-<lb/>dium, flexiones inſtituens, auctas vires Magneticas deprehendit; <lb/></s> <s xml:id="echoid-s6405" xml:space="preserve">Octo locis ita inſlexis fractura prior tantas nacta erat vires, ut <lb/>4 clavos ferreos elevaverit. </s> <s xml:id="echoid-s6406" xml:space="preserve">Taudem flexiones continuando a me-<lb/>dio Ferri uſque ad oppoſitum extremum, atque continuo vim u-<lb/>triuſque extremi examinando, fracturæ virtutem decreviſſe, incre-<lb/>ſcente eodem tempore illa alterius extremi deprehendit, donec poſt <lb/>plurimas flexiones in Ferri variis locis extremum acceperit vim ele-<lb/>vandi 4 clavos, ſuperficie fracturæ tum tantum capaci gerendi li-<lb/>maturæ particulas.</s> <s xml:id="echoid-s6407" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div168" type="section" level="1" n="168"> <head xml:id="echoid-head178" xml:space="preserve">EXPERIMENTUM CXLI.</head> <p> <s xml:id="echoid-s6408" xml:space="preserve">Si Filum ferreum in medio aliquoties flectatur, ejus ambo extre-<lb/>ma non nanciſcuntur vim manifeſtam: </s> <s xml:id="echoid-s6409" xml:space="preserve">concipiantur a medio Ferri <lb/>verſus utrumque extremum notæ æquali intervallo a ſe diſtantes, <lb/>atque Ferrum inflecti in duabus notis medio æqualiter utrimque re-<lb/>motis, atque ab eo incipiendo; </s> <s xml:id="echoid-s6410" xml:space="preserve">tum ambo Ferri extrema vim ac-<lb/>quirent, ſed debiliorem, quam ſi omnes flexiones ab una parte me-<lb/>dii factæ fuiſſent, imo tam debilis utriuſque extremitatis vis erit, <lb/>ut non adæquet {1/3} vel {1/4} illius, quam habuiſſet, factis flexionibus ab <lb/>una dimidia parte Ferri.</s> <s xml:id="echoid-s6411" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div169" type="section" level="1" n="169"> <head xml:id="echoid-head179" xml:space="preserve">EXPERIMENTUM CXLII.</head> <p> <s xml:id="echoid-s6412" xml:space="preserve">Si Filum ferreum variis inflexionibus acceperit in alterutro ex-<lb/>tremo vim notabilem attractricem, deinde autem in aliis adhuc lo-<lb/>cis, inter idem extremum & </s> <s xml:id="echoid-s6413" xml:space="preserve">notam mediam intermediis, inflecta-<lb/>tur, non augebitur vis attractrix ejuſdem extremi, ſed potius de-<lb/>ſtruetur, quemadmodum ſupra annotavi vim fili Magneti affricti & </s> <s xml:id="echoid-s6414" xml:space="preserve"><lb/>deinde aliquoties inflexi, perire.</s> <s xml:id="echoid-s6415" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div170" type="section" level="1" n="170"> <head xml:id="echoid-head180" xml:space="preserve">EXPERIMENTUM CXLIII.</head> <p> <s xml:id="echoid-s6416" xml:space="preserve">Tab. </s> <s xml:id="echoid-s6417" xml:space="preserve">9. </s> <s xml:id="echoid-s6418" xml:space="preserve">fig. </s> <s xml:id="echoid-s6419" xml:space="preserve">4. </s> <s xml:id="echoid-s6420" xml:space="preserve">Memorandum quoque eſt paradoxon quomodo <lb/>Ferrum, vario tuſum ope Mallei modo, vim Magneticam oſten- <pb o="268" file="0282" n="282" rhead="DISSERTATIO"/> dat. </s> <s xml:id="echoid-s6421" xml:space="preserve">Sit regula ferrea craſſa ABGM, quæ ſupra incudem tun-<lb/>datur Mallei parte plana lataque C, nullam vim attractricem <lb/>acquiret: </s> <s xml:id="echoid-s6422" xml:space="preserve">hâc tamen tuſâ parte Mallei acutiori D, incipiendo ab <lb/>E verſus B, acquiret extremitas A aliquam vim, quamquam de-<lb/>bilem, neque alibi, aut in aliqua parte circa loca pulſata vis ob-<lb/>ſervabitur: </s> <s xml:id="echoid-s6423" xml:space="preserve">Deinde autem pulſus fiant ſecundum longitudinem <lb/>FP in medio regulæ, cavendo ne cudantur partes FEBP, aut <lb/>FLMP, niſi exigua tantum recta plaga FP, & </s> <s xml:id="echoid-s6424" xml:space="preserve">ambo anguli A, <lb/>G vi donabuntur, nequaquam autem pars media inter AG.</s> <s xml:id="echoid-s6425" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div171" type="section" level="1" n="171"> <head xml:id="echoid-head181" xml:space="preserve">EXPERIMENTUM CXLIV.</head> <p> <s xml:id="echoid-s6426" xml:space="preserve">Simulac aliquod ferreum inſtrumentum ſecat aliud frigidum <lb/>Ferrum, vim attractricem acquirit; </s> <s xml:id="echoid-s6427" xml:space="preserve">ſed ſi ſecat vel abradit Fer-<lb/>rum igne candefactum nullam, imo quam antea habuit, amittit. <lb/></s> <s xml:id="echoid-s6428" xml:space="preserve">Si Chalybeus cuneus, Magnetica vi donatus, adigatur Malleo <lb/>ut Ferrum candens findat, vim quoque ſuam amittit.</s> <s xml:id="echoid-s6429" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div172" type="section" level="1" n="172"> <head xml:id="echoid-head182" xml:space="preserve">EXPERIMENTUM CXLV.</head> <p> <s xml:id="echoid-s6430" xml:space="preserve">Ferrea corpora, quæ in cuſpidem deſinunt. </s> <s xml:id="echoid-s6431" xml:space="preserve">majorem vim at-<lb/>tractricem nanciſcuntur, quam quæ deſinunt in latitudinem vel <lb/>planitiem, unde ceſtrum ſuâ cuſpide plus attrahit, quam culter: <lb/></s> <s xml:id="echoid-s6432" xml:space="preserve">Quo ceſtra ſunt breviora, eo minori vi donantur, obſervavit <lb/>enim Reaumurius, ceſtrum longitudinis unius pollicis, & </s> <s xml:id="echoid-s6433" xml:space="preserve">diametri <lb/>9 linearum, etiamſi bene perforaſſet Ferrum, non niſi aliquot ra-<lb/>menta; </s> <s xml:id="echoid-s6434" xml:space="preserve">contrà ceſtra 3 vel 4 pollicum, & </s> <s xml:id="echoid-s6435" xml:space="preserve">diametri 1 vel 1 {1/2} <lb/>lineæ parvos clavos attraxiſſe. </s> <s xml:id="echoid-s6436" xml:space="preserve">Videntur autem ceſtra virium <lb/>attractricium incremenra capere in ipſa rotatione, qua Ferrum <lb/>vel Cuprum, vel lapidem perforant, hoc recte annotantibus Hoo-<lb/>kio in Experimentis â Derhamo editis pag. </s> <s xml:id="echoid-s6437" xml:space="preserve">128, tum Ballardo in <lb/>Philoſ. </s> <s xml:id="echoid-s6438" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6439" xml:space="preserve">N°. </s> <s xml:id="echoid-s6440" xml:space="preserve">246, tum Reaumurio in L’Hiſt. </s> <s xml:id="echoid-s6441" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6442" xml:space="preserve"><lb/>Roy. </s> <s xml:id="echoid-s6443" xml:space="preserve">1723. </s> <s xml:id="echoid-s6444" xml:space="preserve">hinc non eſt admirandum Limaturam a ceſtro conta-<lb/>ctam atque ex foramine exſculptam vi Magnetica gaudere, quam <lb/>a ceſtro accepit.</s> <s xml:id="echoid-s6445" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div173" type="section" level="1" n="173"> <head xml:id="echoid-head183" xml:space="preserve">EXPERIMENTUM CXLVI.</head> <p> <s xml:id="echoid-s6446" xml:space="preserve">Inſtrumenta quæcunque nova Chalybea, temperata, in forcipe <pb o="269" file="0283" n="283" rhead="DE MAGNETE."/> retenta, fortiter limata, donec incipiant calere, magnam vim at-<lb/>tractricem habent, imo majorem quam frigefacta.</s> <s xml:id="echoid-s6447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6448" xml:space="preserve">Quodcunque corpus Chalybeum, valde ſupra ſolum frictum, <lb/>uſque ad caloris gradum notabilem, manifeſtam attractionem o-<lb/>ſtendit, quam tamen, ſimulac frigeſcit, amittit: </s> <s xml:id="echoid-s6449" xml:space="preserve">hæc jam inno-<lb/>tuere Boyleo, atque ab ipſo deſcripta ſunt in Mechan. </s> <s xml:id="echoid-s6450" xml:space="preserve">prod. </s> <s xml:id="echoid-s6451" xml:space="preserve">of Magne-<lb/>tics Sect. </s> <s xml:id="echoid-s6452" xml:space="preserve">1. </s> <s xml:id="echoid-s6453" xml:space="preserve">pag. </s> <s xml:id="echoid-s6454" xml:space="preserve">497. </s> <s xml:id="echoid-s6455" xml:space="preserve">& </s> <s xml:id="echoid-s6456" xml:space="preserve">a Ballardo in Philoſ. </s> <s xml:id="echoid-s6457" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6458" xml:space="preserve">N°. </s> <s xml:id="echoid-s6459" xml:space="preserve">246, <lb/>addente, attritu polos Ferri immutari: </s> <s xml:id="echoid-s6460" xml:space="preserve">cultrum enim Magneti af-<lb/>fricuit, quo cuſpis evaſit polus Auſtralis, tum cultro vehementer <lb/>attrito contra lignum durum ſiccumque uſque ad inſignem calorem, <lb/>cuſpis vim poli Auſtralis amiſit, mutata in polum Boreum, quod <lb/>ſæpius ipſi hoc repetenti, eodem modo obſervari contigit. </s> <s xml:id="echoid-s6461" xml:space="preserve">No-<lb/>tandum tamen hæc tantum evenire in cultro tenui, craſſior enim <lb/>attritu non amiſit polos, quos Magnes impreſſerat, partibus nem-<lb/>pe non ſatis concuſſis.</s> <s xml:id="echoid-s6462" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6463" xml:space="preserve">Sed longe pluribus hæc doctrina ditari poſſet, & </s> <s xml:id="echoid-s6464" xml:space="preserve">mereretur, ob-<lb/>ſervationibus, quæ vim Ferri attractricem, æque ac directricem <lb/>ſpectant, quia eruendæ cauſæ Magneticæ inſignem lucem afferre <lb/>aliquando poſſent; </s> <s xml:id="echoid-s6465" xml:space="preserve">aſt ſatis prolixus evaſi, brevem tantum diſſer-<lb/>tationem, non volumen conſcribere in animum induxi; </s> <s xml:id="echoid-s6466" xml:space="preserve">obſerva-<lb/>tiones quas attuli, primariæ ſunt, noſtraque inventæ aut demonſtratæ <lb/>tempeſtate, quibus coronæ loco addam aliquam, ſæpius a me notatam, <lb/>vim Univerſalem directricem confirmantem; </s> <s xml:id="echoid-s6467" xml:space="preserve">Tenuiſſimæ Ferri <lb/>ſquammæ, quæ inter cudendum aut tundendum ab Incude decidunt <lb/>in fabrorum officinis, ſeſe omnes attrahunt, dirigunturque Boream & </s> <s xml:id="echoid-s6468" xml:space="preserve"><lb/>Auſtrum verſus, jacentes exporrectæ ſecundum Magneticum Me-<lb/>ridianum, modo ſolum, cui Incus inſiſtit, fuerit planum, ligneum-<lb/>que.</s> <s xml:id="echoid-s6469" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6470" xml:space="preserve">Ex hiſce Experimentis colligimus vim Magnetis, gremio Terræ <lb/>incluſi, eſſe admodum univerſalem, eam ſe extendere per totum <lb/>Terrarum orbem, agere in omne Ferrum, id dirigere, haud aliter <lb/>quam Ferrum allici regique â Magnete ſupra diximus.</s> <s xml:id="echoid-s6471" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6472" xml:space="preserve">Aſt quomodo virtus illius grandis Magnetis comparata ſit, ne-<lb/>quaquam ex huc uſque commemoratis obſervationibus erui poteſt; <lb/></s> <s xml:id="echoid-s6473" xml:space="preserve">quamobrem alia a ſeris Nepotibus inſtituenda erunt tentamina, ut <lb/>voti compotes reddantur, & </s> <s xml:id="echoid-s6474" xml:space="preserve">problema hactenus adeo intricatum <pb o="270" file="0284" n="284" rhead="DISSERTATIO"/> atque abſtruſum ſolvant; </s> <s xml:id="echoid-s6475" xml:space="preserve">vera methodus erit ſi nobiscum ſe dun-<lb/>taxat obſervatores præſtiterint, Magnetemque aliis, variiſque <lb/>ſubjiciant periculis, nihil ratiocinii primum admiſcendo, nullaſque <lb/>hypotheſes fingendo, hæ enim fallaci blanditie in principio arriden-<lb/>tes, ulteriora tentamina & </s> <s xml:id="echoid-s6476" xml:space="preserve">progreſſus ſcientiæ remorantur, cum <lb/>ſoluti problematis ſpeciem præ ſe ferunt; </s> <s xml:id="echoid-s6477" xml:space="preserve">ſed quotquot fuerunt, <lb/>ſemper venenoſo decepiſſe hominum animos fuco deprehenſæ <lb/>fuerunt, & </s> <s xml:id="echoid-s6478" xml:space="preserve">nullam utilitatem, ſed poſteris prudentioribus novum <lb/>laborem examinandi & </s> <s xml:id="echoid-s6479" xml:space="preserve">excutiendi attuliſſe. </s> <s xml:id="echoid-s6480" xml:space="preserve">Neque a nobis ſa-<lb/>pientiſſimus Fontenellius diſſentit, qui in L’Hiſt. </s> <s xml:id="echoid-s6481" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6482" xml:space="preserve">Roy. <lb/></s> <s xml:id="echoid-s6483" xml:space="preserve">A°, 1723, Reaumurianis experimentis & </s> <s xml:id="echoid-s6484" xml:space="preserve">hypotheſibus elegantiſſime <lb/>explicitis, hæc addit: </s> <s xml:id="echoid-s6485" xml:space="preserve">Philoſophia optime contenta ejus labore fuiſſet, <lb/>ſi tantummodo omnia phænomena Magnetis detexiſſet: </s> <s xml:id="echoid-s6486" xml:space="preserve">Quid enim ſibi <lb/>volunt hypotheſes, utcunque ſubtiles & </s> <s xml:id="echoid-s6487" xml:space="preserve">ingenioſæ, ex quibus phæ-<lb/>nomena explicari aut Geometrice demonſtrari nequeunt? </s> <s xml:id="echoid-s6488" xml:space="preserve">Erutis phæ-<lb/>nomenis non amplius latebit cauſa: </s> <s xml:id="echoid-s6489" xml:space="preserve">Cauſa tandem inventa & </s> <s xml:id="echoid-s6490" xml:space="preserve">probe <lb/>intellecta, Mathematice cuncta phænomena probabuntur, atque tum <lb/>demum doctrina Magnetica inter partes mixtæ Matheſeos reponi <lb/>poterit. </s> <s xml:id="echoid-s6491" xml:space="preserve">Hoc tamen interea demonſtratum erit, lapidem hunc, <lb/>tam admirandis lateque ſe ſpargentibus donatum virtutibus, quæ ab <lb/>ingenio humano utcunque ſolerti & </s> <s xml:id="echoid-s6492" xml:space="preserve">ſagaci comprehendi nondum po-<lb/>tuerunt, non ex fortuito brutorum Atomorum concurſu coaluiſſe, ne-<lb/>que ex cauſâ minoribus donata vitutibus prodiiſſe, ſed ex aliâ longe ex-<lb/>cellentiori, fonte & </s> <s xml:id="echoid-s6493" xml:space="preserve">origine omnium rerum corporumque atque eorum <lb/>virium, cujus infinita ſapientia nihil, niſi quod ſapientiam ſpirat, pro-<lb/>duxit, cujus opera immenſa nobis finitis homuncionibus adſpicere, <lb/>venerari, atque admirari tantum licet, ut eo certius ex illis conſtaret, <lb/>debere dari Deum, & </s> <s xml:id="echoid-s6494" xml:space="preserve">infinitis donatum attributis, quorum quodlibet <lb/>infinitum eſt, qui infanda liberalitate, uti cætera omnia, ita hunc <lb/>lapidem creavit & </s> <s xml:id="echoid-s6495" xml:space="preserve">cum mortalibus communicavit, ut ejus beneficio <lb/>non plane incertus per vaſtos Oceanos nauta uſque in remotiſſimas <lb/>regiones navigaret, atque procul diſſitis gentibus afferret, repor-<lb/>taretque viciſſim ea, quæ ubivis Terrarum creſcunt aut effodiun-<lb/>tur, ita ut a ſingulis cognoſci queant quæcunque vaſtiſſima Tellus <lb/>gerit, eaque uſui cedant univerſis.</s> <s xml:id="echoid-s6496" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div174" type="section" level="1" n="174"> <head xml:id="echoid-head184" xml:space="preserve">FINIS.</head> <pb file="0285" n="285" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div175" type="section" level="1" n="175"> <head xml:id="echoid-head185" xml:space="preserve">PHYSICA <lb/>EXPERIMENTALIS <lb/>DE <lb/>TUBIS CAPILLARIBUS <lb/>VITREIS.</head> <pb file="0286" n="286"/> <pb o="273" file="0287" n="287" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div176" type="section" level="1" n="176"> <head xml:id="echoid-head186" xml:space="preserve">PHYSICA <lb/>EXPERIMENTALIS <lb/>DE <lb/>TUBIS CAPILLARIBUS <lb/>VITREIS. <lb/>PRÆFATIO.</head> <p> <s xml:id="echoid-s6497" xml:space="preserve">Præſtantiſſimos ſtudio & </s> <s xml:id="echoid-s6498" xml:space="preserve">doctrina, cum hujus, tum elapſi <lb/>ſæculi viros, admodum torſerunt phænomena, quæ vitrum <lb/>ſua vi attractrice edit, inter quæ haud infima fuerunt, quæ <lb/>tubi graciles, in ſe abſorbendo, atque ad inſignem altitu-<lb/>dinem elevando varios liquores, conſpicienda præbuerunt: </s> <s xml:id="echoid-s6499" xml:space="preserve">Quo-<lb/>niam omnes ab his tubis editi effectus adverſus generales huc uſque <lb/>traditas incedunt Hydroſtaticas leges, eorum cauſam dignam, quæ <lb/>inveſtigaretur, judicarunt plurimi; </s> <s xml:id="echoid-s6500" xml:space="preserve">partim ut regularum Hydroſta-<lb/>ticarum terminos intelligerent, partim ut hoc paradoxon, quod <lb/>ratiocinio tantopere adverſari videtur Mathematico, exponerent, <lb/>partim ut alias & </s> <s xml:id="echoid-s6501" xml:space="preserve">quidem frequentiſſimas accuratius perſpicerent Na-<lb/>turæ operationes, hiſce ſimillimas, & </s> <s xml:id="echoid-s6502" xml:space="preserve">ab eadem cauſa pendentes, <lb/>quales ſunt adſcenſus liquorum nutrientium ex radicibus plantarum <lb/>per anguſtiſſimos canales uſque ad earum vertices: </s> <s xml:id="echoid-s6503" xml:space="preserve">ingreſſus fluido-<lb/>rum, Aquæ, Mercurii, Oleorum, Medicamentorum, partium <lb/>ſubtiliſſimarum Emplaſtrorum, odorum, aliorumque corpori ani- <pb o="274" file="0288" n="288" rhead="PRÆFATIO."/> mali vivo extrinſecus applicatorum & </s> <s xml:id="echoid-s6504" xml:space="preserve">per vaſa capillaria anguſtiſſi-<lb/>ma, Abſorbentia vocata, uſque in ſanguinem delatorum: </s> <s xml:id="echoid-s6505" xml:space="preserve">ingreſſus <lb/>fluidorum, effuſorum in cavitatibus corporis, in vaſa abſorbentia <lb/>ſubtiliſſima; </s> <s xml:id="echoid-s6506" xml:space="preserve">veluti ſunt in plexubus Choroideis Cerebri, in cavitate <lb/>Pectoris, in Pericardio, abdominis Peritonæo, Scroto, tunica va-<lb/>ginali, in Iride Oculi, in ligamentis juncturas oſſium ambientibus <lb/>&</s> <s xml:id="echoid-s6507" xml:space="preserve">c. </s> <s xml:id="echoid-s6508" xml:space="preserve">Ingreſſus fluidorum, oleorumque in vaſa & </s> <s xml:id="echoid-s6509" xml:space="preserve">canales lapidum <lb/>omnium, ſive fuerint homogeneæ ſubſtantiæ, ſive diverſi coloris <lb/>& </s> <s xml:id="echoid-s6510" xml:space="preserve">duritiei maculas habeant; </s> <s xml:id="echoid-s6511" xml:space="preserve">ut plurima alia tranſeam corpora, quæ <lb/>canalibus poriſve pertuſa liquores in ſe rapiunt, quemadmodum vi-<lb/>trei tubi. </s> <s xml:id="echoid-s6512" xml:space="preserve">Ex quibus liquet, capillarium tuborum phænomena non <lb/>tam exigui in Phyſicis habenda eſſe momenti, aut adeo arctis eo-<lb/>rum utilitatem circumſcribi limitibus, ut modo cauſa ad ſolos hos <lb/>tubos, non ad plurimos in Natura alios, ex diverfâ compoſitos ma-<lb/>teriâ, pertineret.</s> <s xml:id="echoid-s6513" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6514" xml:space="preserve">Videntur hoc bene perſpexiſſe Eruditi, qui idcirco in eruenda <lb/>effectuum horum cauſa plurimum operæ poſuerunt, uti Hookius, <lb/>Honoratus Fabry, Sinclarius, Boyleus, Rohaultus, Sturmius, <lb/>Carreus, Hombergius, Bernouillius, Newtonus, Jurinus, Peti-<lb/>tus, Fayus. </s> <s xml:id="echoid-s6515" xml:space="preserve">Quia autem elapſo fæculo perverſa maxime viguit <lb/>philoſophandi methodus, innixa potius Hypotheſibus, quam Ex-<lb/>perimentis, atque ex paucis ſolvi problema ſatis poſſe credebatur; <lb/></s> <s xml:id="echoid-s6516" xml:space="preserve">variæ illico conditæ ſunt hypotheſes effictæque cauſæ, ex quibus <lb/>phænomena explicabantur; </s> <s xml:id="echoid-s6517" xml:space="preserve">ſed infeliciſſimo ſucceſſu; </s> <s xml:id="echoid-s6518" xml:space="preserve">nam indies <lb/>pluribus detectis effectibus prioris ratiocinii infirmitas apparebat; </s> <s xml:id="echoid-s6519" xml:space="preserve"><lb/>quare recentiores Philoſophi, refutatis antiquis, alias ſuggeſſerunt <lb/>cauſas; </s> <s xml:id="echoid-s6520" xml:space="preserve">quarum abſurdo iterum â poſterioribus detecto, novæ in ſce-<lb/>nam prodiere nec meliores nec magis ſtabiles; </s> <s xml:id="echoid-s6521" xml:space="preserve">unde hic, uti cum <lb/>aliis quoque accidit phænomenorum aſſumtis cauſis, quot capi-<lb/>ta, tot ſententias invenimus. </s> <s xml:id="echoid-s6522" xml:space="preserve">Sed omnis hæc turba orta fuit, quia <lb/>non ſatis Experimentis inſudatum eſt, & </s> <s xml:id="echoid-s6523" xml:space="preserve">nimium attribuebatur vi-<lb/>ribus rationis, quibus ſe in omnia Naturæ arcana penetrare poſſe <lb/>præcipiti feſtinatione Philoſophi conſiſi ſunt. </s> <s xml:id="echoid-s6524" xml:space="preserve">Hoc obſervato, di-<lb/>verſâ prorſus methodo Thema de Tubis capillaribus tractandum ju-<lb/>dicavi, plurima inſtituendo experimenta, & </s> <s xml:id="echoid-s6525" xml:space="preserve">ſobrie ratiocinando; </s> <s xml:id="echoid-s6526" xml:space="preserve"><lb/>Corollaria ex Experimentis deducta, iterum aliis confirmando, ſe- <pb o="275" file="0289" n="289" rhead="PRÆFATIO."/> cundum tutiſſimam optimamque Regulam a Nieuwentytio in Phy-<lb/>ſicis ſtabilitam. </s> <s xml:id="echoid-s6527" xml:space="preserve">Quamvis vero hic quædam præſtiterim, non ta-<lb/>men omnia abſolvere potui, quæ deſideraveram; </s> <s xml:id="echoid-s6528" xml:space="preserve">nam adeo ferti-<lb/>lis eſt Natura, ut ne quidem res abjectiſſima exhauriri penitus poſ-<lb/>ſit, ejuſve perfecta cognitio acquiri.</s> <s xml:id="echoid-s6529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6530" xml:space="preserve">Diviſi hoc Thema in 8 Capita, quorum</s> </p> <p> <s xml:id="echoid-s6531" xml:space="preserve">1. </s> <s xml:id="echoid-s6532" xml:space="preserve">Agit de Adſcenfu Aquæ in tubos rectos æqualium diametro-<lb/>rum, ſed diveræ longitudinis.</s> <s xml:id="echoid-s6533" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6534" xml:space="preserve">2. </s> <s xml:id="echoid-s6535" xml:space="preserve">De Adſcenſu in tubos ejuſdem longitudinis, ſed diverſæ dia-<lb/>metri.</s> <s xml:id="echoid-s6536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6537" xml:space="preserve">3. </s> <s xml:id="echoid-s6538" xml:space="preserve">De Adſcenſu variorum Fluidorum in eundem tubum.</s> <s xml:id="echoid-s6539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6540" xml:space="preserve">4. </s> <s xml:id="echoid-s6541" xml:space="preserve">Complectitur Experimenta cum tubis rectis, ſed inæqualis <lb/>capacitatis ad utrumque extremum.</s> <s xml:id="echoid-s6542" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6543" xml:space="preserve">5. </s> <s xml:id="echoid-s6544" xml:space="preserve">Agit de Tubis æqualis ubique diametri, ſed vario modo in-<lb/>flexis.</s> <s xml:id="echoid-s6545" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6546" xml:space="preserve">6. </s> <s xml:id="echoid-s6547" xml:space="preserve">De Tubis inæqualis diametri & </s> <s xml:id="echoid-s6548" xml:space="preserve">vario modo inflexis.</s> <s xml:id="echoid-s6549" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6550" xml:space="preserve">7. </s> <s xml:id="echoid-s6551" xml:space="preserve">De Tubis in recipiente aëre vacuo concluſis.</s> <s xml:id="echoid-s6552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6553" xml:space="preserve">8. </s> <s xml:id="echoid-s6554" xml:space="preserve">De adſcenſu liquorum in tubos ſibi mutuo immiſſos.</s> <s xml:id="echoid-s6555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6556" xml:space="preserve">D<emph style="sc">EFINITIO.</emph></s> <s xml:id="echoid-s6557" xml:space="preserve">Per tubum capillarem vitreum intelligo, canalem <lb/>vitreum, cavum, cylindricum, cujus cavitas adeo anguſta, ut dia-<lb/>meter ſit minor {1/10} parte pollicis.</s> <s xml:id="echoid-s6558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6559" xml:space="preserve">Monitum. </s> <s xml:id="echoid-s6560" xml:space="preserve">Omnia, quæ hic deſcribuntur, Experimenta, capta <lb/>ſunt cum tubis. </s> <s xml:id="echoid-s6561" xml:space="preserve">ex vitro albo, puro, in Hollandia confecto, re-<lb/>centiſſime conflatis, & </s> <s xml:id="echoid-s6562" xml:space="preserve">ſæpe modo elapſis paucis minutis aut horis: <lb/></s> <s xml:id="echoid-s6563" xml:space="preserve">quæ ideo moneo, quoniam brevi tempore cruſta quædam adnaſci-<lb/>tur ſuperficiei internæ tuborum, inſtar vitrioli vel ferruginis ad-<lb/>creſcentis metallis, quæ impedit, quominus accuratæ obſervatio-<lb/>nes inſtitui poſſint, imo quæ ſæpe omnem effectum plane tol-<lb/>lit, ut nequicquam liquoris tubos ingrediatur; </s> <s xml:id="echoid-s6564" xml:space="preserve">neque hoc præcave-<lb/>ri poteſt etiamſi capſulis probe incluſi tubi conſerventur; </s> <s xml:id="echoid-s6565" xml:space="preserve">nemo <lb/>igitur hæc tentamina repetat, niſi ipſe artem tubos componendi no-<lb/>rit, vel præſentem habeat artificem, atque eos, modo factos, in <lb/>uſum vocaverit, cæteroquin diverſiſſimos a noſtris obſervabit, ſed <lb/>erroneos, effectus: </s> <s xml:id="echoid-s6566" xml:space="preserve">in iis vero conſtruendis arcanum non latet, quod <lb/>tamen primâ fronte ſubeſle videretur, cum tuborum exiliſſimorum, <lb/>quorum craſſities vix capillum humanum ſuperat, mentio fit; </s> <s xml:id="echoid-s6567" xml:space="preserve">verum <pb o="276" file="0290" n="290" rhead="PRÆFATIO."/> non confido quemquam dari adeo imperitum, qui eos extemplo <lb/>juxta artificioſiſſimos conflare non poterit: </s> <s xml:id="echoid-s6568" xml:space="preserve">primum enim ſollicitus <lb/>quære tubos vitreos in officina vitraria ductos, accurate cylindri-<lb/>cos, quorum interna cavitas perfecte cylindrica eſt, nam niſi ejuſ-<lb/>modi electi fuerint, nunquam tubos capillares perfecte cylindricos, <lb/>quales tamen pro experimentis accuratis deſiderantur, compones: <lb/></s> <s xml:id="echoid-s6569" xml:space="preserve">perinde eſt fere cujuſnam fuerint diametri, nam ab una uſque ad ſex <lb/>plureſve lineas craſſities conducunt: </s> <s xml:id="echoid-s6570" xml:space="preserve">Tum cape Lampadem encau-<lb/>ſti inſtructam 100 pluribusve filis cotoneis, perpendiculariter ere-<lb/>ctis, atque in duos cumulos denſos congeſtis, in quorum medio <lb/>hiulcus maneat unius vel ſesqui linearum, quemadmodum conſpici <lb/>poteſt in Tab. </s> <s xml:id="echoid-s6571" xml:space="preserve">2. </s> <s xml:id="echoid-s6572" xml:space="preserve">fig. </s> <s xml:id="echoid-s6573" xml:space="preserve">8. </s> <s xml:id="echoid-s6574" xml:space="preserve">infuſo oleo, excitataque flamma tubum inflato-<lb/>rium tene eregione medii hiulci, ut ventum per eum pellas, flamma <lb/>condenſabitur, horizontali directione acta; </s> <s xml:id="echoid-s6575" xml:space="preserve">in hujus medio, ubi <lb/>fervor maximus regnat, tubum tene, ipſum perpetuo circumver-<lb/>tendo, ut æquabiliter calefiat, donec bene rubeat, ductilisque eva-<lb/>ſerit, tum ex flamma exemtum extrahe recta, ſponte tubum an-<lb/>guſtum formabis; </s> <s xml:id="echoid-s6576" xml:space="preserve">ſi cum impetu celeriterque extraxeris, acquires <lb/>anguſtiſſimum; </s> <s xml:id="echoid-s6577" xml:space="preserve">ſi tardius, latiorem: </s> <s xml:id="echoid-s6578" xml:space="preserve">ad anguſtiſſimos conflandos, ca-<lb/>piantur tubi minoris diametri, & </s> <s xml:id="echoid-s6579" xml:space="preserve">bene in igne candefiant antequam <lb/>extrahantur, tum & </s> <s xml:id="echoid-s6580" xml:space="preserve">anguſtiſſimos & </s> <s xml:id="echoid-s6581" xml:space="preserve">plurimos pedes longos habe-<lb/>bis; </s> <s xml:id="echoid-s6582" xml:space="preserve">ſolent omnes hi eſſe conici, in medio anguſtiores, latiores ad <lb/>utrumque finem, ideo pro experimentis partes mediæ exſcindendæ <lb/>ex longiſſimis ſunt, quæ ſatis bene cylindricæ erunt.</s> <s xml:id="echoid-s6583" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6584" xml:space="preserve">2. </s> <s xml:id="echoid-s6585" xml:space="preserve">Quia omne vitrum non æque magnam attrahendi vim habet, <lb/>etiam phænomenorum datur differentia; </s> <s xml:id="echoid-s6586" xml:space="preserve">ne quis igitur experimen-<lb/>ta noſtra imitatus, aliumque effectum paulo diverſum obſervans, <lb/>illico erroris nos arguat, ſi enim alterius indolis vitrum elegerit, <lb/>etiam diverſos a ſuis prioribus animadvertet effectus; </s> <s xml:id="echoid-s6587" xml:space="preserve">haud aliter ac <lb/>Magnetes debilioris aut præſtantioris virtutis cum Ferro plus mi-<lb/>nuſve virium communicant, Verſoriumque magis minuſve infra <lb/>horizontem deprimunt, atque variâ tempeſtate diverſas exhibent <lb/>operationes, uti ſæpe monui in Diſſertatione de Magnete.</s> <s xml:id="echoid-s6588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6589" xml:space="preserve">3. </s> <s xml:id="echoid-s6590" xml:space="preserve">Menſura in hoc Capite uſus fui Rhenolandica, in qua pes <lb/>dividitur in 12 pollices: </s> <s xml:id="echoid-s6591" xml:space="preserve">pollex in 12 lineas.</s> <s xml:id="echoid-s6592" xml:space="preserve"/> </p> <pb o="277" file="0291" n="291"/> </div> <div xml:id="echoid-div177" type="section" level="1" n="177"> <head xml:id="echoid-head187" xml:space="preserve">CAPUT PRIMUM.</head> <head xml:id="echoid-head188" style="it" xml:space="preserve">De Adſcenſu Fluidi in tubos diverſarum longitudinum & <lb/>ejuſdem diametri.</head> <head xml:id="echoid-head189" xml:space="preserve">EXPERIMENTUM I.</head> <p> <s xml:id="echoid-s6593" xml:space="preserve">Confectus fuit ex vitro albo puriſſimoque Tubus, perfecte cy-<lb/>lindricus, 3 {1/2} pollices longus; </s> <s xml:id="echoid-s6594" xml:space="preserve">cujus diameter interna erat {1/36} <lb/>pollicis. </s> <s xml:id="echoid-s6595" xml:space="preserve">Quia modo ante erat in Igne conflatus, erat quoque ſic-<lb/>ciſſimus, hunc utrimque apertum forcipe cepi tenello, ne manu <lb/>prehenſus calefieret, atque aër interioris cavitatis rarefieret, quo <lb/>experimenti ſucceſſus perturbaretur: </s> <s xml:id="echoid-s6596" xml:space="preserve">Tubus perpendiculariter ad <lb/>horizontem immiſſus fuit aquæ puræ frigidæque, ut tamen infi-<lb/>ma ora vix infra ſuperficiem liquoris demergeretur. </s> <s xml:id="echoid-s6597" xml:space="preserve">Hoc facto, <lb/>Aqua ſuâ ſponte rapta fuit ſurſum in tubum ad altitudinem 20 linea-<lb/>rum, ibique permanſit, menſurâ captâ a ſuperficie Aquæ in Va-<lb/>ſculo, ad ſuperficiem ſupremam Aquæ in tubo: </s> <s xml:id="echoid-s6598" xml:space="preserve">Aqua non cum <lb/>æquabili celeritate ab initio ad finem adſcendit, ſed primum ce-<lb/>lerrime, deinde lentius, tandem lentiſſime cum propemodum ad <lb/>20 linearum altitudinem pervenit.</s> <s xml:id="echoid-s6599" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6600" xml:space="preserve">Erat hic primus eventus, explorandum duxi, an hic ſemper <lb/>idem foret, repetito aliquoties Experimento, an autem Aqua ad <lb/>majorem minoremve altirudinem elevaretur; </s> <s xml:id="echoid-s6601" xml:space="preserve">quamobrem ori immiſſâ <lb/>extremitate tubi, quæ Aquæ immerſa fuerat, ſugendo tubum eva-<lb/>cuavi, ſimul curans ne pars ejus ſuperior, adhucdum ſicca, hu-<lb/>mectaretur: </s> <s xml:id="echoid-s6602" xml:space="preserve">Orificio tubi eodem Aquæ denuo impoſito, adſcen-<lb/>ſus accurate idem contigit, cum omnibus iiſdem phænomenis, & </s> <s xml:id="echoid-s6603" xml:space="preserve"><lb/>ad eandem altitudinem: </s> <s xml:id="echoid-s6604" xml:space="preserve">neque repetita tentamina differentiam ul-<lb/>lam dederunt.</s> <s xml:id="echoid-s6605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6606" xml:space="preserve">Quoniam animus eſt eruere cauſam horum phænomenorum ex <lb/>Experimentis, adhuc nihil explico, quamcunque enim cauſam af-<lb/>ferrem, eam nunc tanquam erutam ſupponere deberem, atque ita <pb o="278" file="0292" n="292" rhead="DISSERTATIO"/> hypothetice perrexiſſe merito viderer: </s> <s xml:id="echoid-s6607" xml:space="preserve">idcirco Experimentum nunc <lb/>modo commemoro: </s> <s xml:id="echoid-s6608" xml:space="preserve">Id tamen ſequitur ex eo, cauſam, quæcun-<lb/>que etiam fuerit, elevantem Aquam eſſe determinatæ virtutis, & </s> <s xml:id="echoid-s6609" xml:space="preserve"><lb/>cum gravitate aquæ elevatæ æquilibratam: </s> <s xml:id="echoid-s6610" xml:space="preserve">2° eam eſſe conſtantem, <lb/>ſive in tubo ſicciſſimo, & </s> <s xml:id="echoid-s6611" xml:space="preserve">in humido eandem. </s> <s xml:id="echoid-s6612" xml:space="preserve">3° altitudinem Aquæ <lb/>ſuperaſſe ſexagies diametrum cavitatis tubi hujus.</s> <s xml:id="echoid-s6613" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div178" type="section" level="1" n="178"> <head xml:id="echoid-head190" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s6614" xml:space="preserve">Tubus idem, in quem Aqua adſcendit ad altitudinem 20 linea-<lb/>rum, ex vaſculo ſublatus, atquein aëre perpendiculariter poſitus, o-<lb/>mnem Aquam in ſe retinet, nihil ejus demittens.</s> <s xml:id="echoid-s6615" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div179" type="section" level="1" n="179"> <head xml:id="echoid-head191" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s6616" xml:space="preserve">Idem tubus profundius Aquæ immerſus quam in Experimento I, <lb/>Aquam in ſe recepit ad altitudinem 20 linearum à ſuperficie, ut <lb/>antea.</s> <s xml:id="echoid-s6617" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6618" xml:space="preserve">Corol. </s> <s xml:id="echoid-s6619" xml:space="preserve">1. </s> <s xml:id="echoid-s6620" xml:space="preserve">Ergo Aqua vaſculi non habet in ſe cauſam adſcenſus <lb/>fluidi in tubum, tum enim tubo profundius immerſo, Aqua altius <lb/>in ipſum adſcenderet, quam eo ſuperficiem Aquæ tantum attingen-<lb/>te; </s> <s xml:id="echoid-s6621" xml:space="preserve">ubi enim major cauſa, ibi quoque major effectus foret: </s> <s xml:id="echoid-s6622" xml:space="preserve">ſed <lb/>Aqua Vaſculi cauſa adſcendentis & </s> <s xml:id="echoid-s6623" xml:space="preserve">ſuſpenſæ in tubo Aquæ eſſe ne-<lb/>quit, quippe in Experimento II, manet Aqua in tubo, hærente <lb/>tantum in aëre, & </s> <s xml:id="echoid-s6624" xml:space="preserve">in cujus infimam oram non amplius agit Aqua, <lb/>hæc idcirco ſua gravitate ex tubo elaberetur, cum potius æque ſu-<lb/>ſpenſa maneat: </s> <s xml:id="echoid-s6625" xml:space="preserve">errorem igitur cognoſcent, qui motum partibus A-<lb/>quæ in vaſculo proprium cauſam & </s> <s xml:id="echoid-s6626" xml:space="preserve">adſcendentis & </s> <s xml:id="echoid-s6627" xml:space="preserve">ſuſpenſæ in tu-<lb/>bis hiſce Aquæ opinati fuerunt.</s> <s xml:id="echoid-s6628" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div180" type="section" level="1" n="180"> <head xml:id="echoid-head192" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s6629" xml:space="preserve">Si idem tubus Experimenti III. </s> <s xml:id="echoid-s6630" xml:space="preserve">profundius Aquæ immiſſus, de-<lb/>nuo ex illa extrahatur, ex ejus, perpendiculariter in aëre erecti, <lb/>orificio inferiori, guttatim aqua effluit, donec ſere hæreat ad alti-<lb/>tudinem 20 linearum, hæret autem ſemper paulum altius, quia <pb o="279" file="0293" n="293" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> gutta, inferiori appendens orificio, fluidi deſcenſum impedit ali-<lb/>quomodo: </s> <s xml:id="echoid-s6631" xml:space="preserve">Accurate tamen iterum altitudo 20 linearum habetur, <lb/>ſi planæ ſuperficiei alicujus corporis imponatur alia aquæ gutta, <lb/>eique apponatur gutta tubi; </s> <s xml:id="echoid-s6632" xml:space="preserve">ambabus hiſce ſe permiſcentibus, flui-<lb/>dum ex tubo ad ſolitam deſcendit altitudinem. </s> <s xml:id="echoid-s6633" xml:space="preserve">Adnotavit hoc <lb/>etiam Cl. </s> <s xml:id="echoid-s6634" xml:space="preserve">Carrè: </s> <s xml:id="echoid-s6635" xml:space="preserve">idem cæteroquin obtineri poteſt, ſi gutta tubi <lb/>orificio appenſa prudenter linteo abſtergeatur: </s> <s xml:id="echoid-s6636" xml:space="preserve">Petitus in L’Hiſt. </s> <s xml:id="echoid-s6637" xml:space="preserve">de <lb/>L’Acad. </s> <s xml:id="echoid-s6638" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6639" xml:space="preserve">A°. </s> <s xml:id="echoid-s6640" xml:space="preserve">1724. </s> <s xml:id="echoid-s6641" xml:space="preserve">etiam obſervavit Aquam altius in tubo ex <lb/>vaſe ſublato hæſiſſe, cum enim tubum diametri {2/3} lineæ immerſerat <lb/>Aquæ, quæ ad altitudinem 5 linearum adſcendit, tubum ex Aqua <lb/>exemit, quæ in illo manſit ad altitudinem 6 {2/3} linearum ſuſpenſa: <lb/></s> <s xml:id="echoid-s6642" xml:space="preserve">Alia vice unico ictu eundem tubum ſubito ex Aqua extraxit, hac <lb/>manente in eo ſuſpenſa ad altitudinem 8 {1/2} lin. </s> <s xml:id="echoid-s6643" xml:space="preserve">cum tam ſubito ef-<lb/>fluere non poterat.</s> <s xml:id="echoid-s6644" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div181" type="section" level="1" n="181"> <head xml:id="echoid-head193" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s6645" xml:space="preserve">Idem tubus priorum IV. </s> <s xml:id="echoid-s6646" xml:space="preserve">Experimentorum, Aquæ ferventi im-<lb/>merſus, eam in ſe recepit ad altitudinem 19 {1/2} vel 20 linea-<lb/>rum.</s> <s xml:id="echoid-s6647" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6648" xml:space="preserve">Corollar. </s> <s xml:id="echoid-s6649" xml:space="preserve">Ergo Aqua frigida ad eandem, non ad minorem, altitudinem <lb/>in tubum adſcendit ac calida: </s> <s xml:id="echoid-s6650" xml:space="preserve">Quia autem partes Aquæ ferventis mul-<lb/>to vehementius moventur, quam frigidæ, patet motum partium A-<lb/>quæ non eſſe cauſam adſcenſus in tubos, uti aliqui opinati ſunt, <lb/>nam ſecundum hos Aqua fervens & </s> <s xml:id="echoid-s6651" xml:space="preserve">valde mota multo altius adſcen-<lb/>dere cogeretur: </s> <s xml:id="echoid-s6652" xml:space="preserve">Sed nec Ignis eſt cauſa adſcenſus, quia tum data <lb/>ejus majori copia altior adſcenſus fieri deberet, qui non fit: </s> <s xml:id="echoid-s6653" xml:space="preserve">In-<lb/>ſtituit etiam idem Experimentum Honoratus Fabry. </s> <s xml:id="echoid-s6654" xml:space="preserve">§. </s> <s xml:id="echoid-s6655" xml:space="preserve">1.</s> <s xml:id="echoid-s6656" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div182" type="section" level="1" n="182"> <head xml:id="echoid-head194" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s6657" xml:space="preserve">Tubus idem vacuus, oblique ad horizontem aquæ immiſſus, <lb/>in ſe Aquam recipit ad altitudinem perpendicularem 20 linea-<lb/>rum.</s> <s xml:id="echoid-s6658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6659" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s6660" xml:space="preserve">Adeoque vis Aquam elevans in tubum eſt revera æqualis <lb/>gravitati 20 linearum perpendicularium Aquæ: </s> <s xml:id="echoid-s6661" xml:space="preserve">Idcirco poſito tu- <pb o="280" file="0294" n="294" rhead="DISSERTATIO"/> bo ita inclinato ad horizontem, ut alterum extremum modo ha-<lb/>beat perpendicularem altitudinem 20 linearum ſupra ſuperficiem <lb/>Aquæ in vaſculo, totus tubus implebitur, uti etiam experientiâ <lb/>comprobatur.</s> <s xml:id="echoid-s6662" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div183" type="section" level="1" n="183"> <head xml:id="echoid-head195" xml:space="preserve">EXPERIMENTUM VII.</head> <p> <s xml:id="echoid-s6663" xml:space="preserve">Si idem tubus continens 20 lineas Aquæ inſe, ex vaſe ſublatus lente <lb/>inclinetur, ut parallelus horizonti evadat; </s> <s xml:id="echoid-s6664" xml:space="preserve">tum aqua in tubo mo-<lb/>vebitur ab uno extremo verſus aliud, ita tamen, ut occupet accu-<lb/>rate mediam tubi partem, relinquatque ambas extremitates vacuas <lb/>Aquâ, & </s> <s xml:id="echoid-s6665" xml:space="preserve">tantum aëre plenas.</s> <s xml:id="echoid-s6666" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div184" type="section" level="1" n="184"> <head xml:id="echoid-head196" xml:space="preserve">EXPERIMENTUM VIII.</head> <p> <s xml:id="echoid-s6667" xml:space="preserve">Extremum hujus tubi, quod Aquæ immerſum fuit, altius eleve-<lb/>tur ſupra horizontem, infra quem deprimatur alterum extremum, <lb/>tum Aqua deſcendit verſus humilius extremum, motu concitato; <lb/></s> <s xml:id="echoid-s6668" xml:space="preserve">ſubito tamen ſiſtitur ante tubi orificium ad diſtantiam {1/3} lineæ ab o-<lb/>ra, quæ tubi pars aëre impleta inſtar obturaculi ſe habet: </s> <s xml:id="echoid-s6669" xml:space="preserve">ſed tu-<lb/>bo elevato perpendiculariter, adeoque penitus inverſo, Aqua deſcen-<lb/>dit uſque ad ultimam oram, manetque in tubo ſuſpenſa ad eandem <lb/>altitudinem: </s> <s xml:id="echoid-s6670" xml:space="preserve">quod phænomenon in Capite 7 explicabo.</s> <s xml:id="echoid-s6671" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div185" type="section" level="1" n="185"> <head xml:id="echoid-head197" xml:space="preserve">EXPERIMENTUM IX.</head> <p> <s xml:id="echoid-s6672" xml:space="preserve">Hic tubus nunc omnino interne humectatus, iterum Aquæ im-<lb/>poſitus, perpendiculariter, eodem extremo fluidum attingente, ſi-<lb/>ve oppoſito, non rapuit Aquam ad majorem altitudinem quam 20 li-<lb/>nearum in ſe.</s> <s xml:id="echoid-s6673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6674" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s6675" xml:space="preserve">Quamobrem tubus ſiccus vel humidus Aquam abſque ulla <lb/>differentia altitudinis in ſe recipit: </s> <s xml:id="echoid-s6676" xml:space="preserve">Ex hoc Experimento detegimus <lb/>errorem Boylei, memorantis Aquam melius adſcendere in tubos <lb/>prius humidos, quam in ſiccos; </s> <s xml:id="echoid-s6677" xml:space="preserve">in eundem lapidem impegit Stur-<lb/>mius, cum in Colleg. </s> <s xml:id="echoid-s6678" xml:space="preserve">Cur. </s> <s xml:id="echoid-s6679" xml:space="preserve">tentam. </s> <s xml:id="echoid-s6680" xml:space="preserve">8. </s> <s xml:id="echoid-s6681" xml:space="preserve">Pag. </s> <s xml:id="echoid-s6682" xml:space="preserve">45. </s> <s xml:id="echoid-s6683" xml:space="preserve">dicit. </s> <s xml:id="echoid-s6684" xml:space="preserve">Canaliculus <lb/>humectatus prius, altius admittebat aquam, per cavitatem ſuam <pb o="281" file="0295" n="295" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> adſcendentem, quam exſiccatus, præſertim poſt humectationem <lb/>præcedaneam. </s> <s xml:id="echoid-s6685" xml:space="preserve">Error fuit ortus, quia hi Philoſophi non inſtitue-<lb/>runt Experimenta cum tubis novis, ſed cum iis, qui diu facti fue-<lb/>runt, quorum interna ſuperficies ab aëre corroſa, aſpera evaſit a <lb/>Salibus adhærentibus, quibus ablutis Aquâ tubus a novo vix dif-<lb/>fert; </s> <s xml:id="echoid-s6686" xml:space="preserve">ſed cum Experimentum ſemel cum tubo eſt factum, Aquæ quæ-<lb/>dam copia in cavitate manet, quæ accreſcit ſuperficiei, eamque <lb/>aſperam reddit, hinc iterum impeditur Aquæ adſcenſus, verum hac <lb/>cruſta abluta fit ſuperficies tubi inſtar novæ, iterumque Aquam uti <lb/>ante elevat. </s> <s xml:id="echoid-s6687" xml:space="preserve">Hoc quoque obſervavit Fayus in L’Hiſt. </s> <s xml:id="echoid-s6688" xml:space="preserve">de L’Acad. <lb/></s> <s xml:id="echoid-s6689" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6690" xml:space="preserve">A°. </s> <s xml:id="echoid-s6691" xml:space="preserve">1724, ideo exſiccans tubos valdequam ſupra lgnem vel <lb/>flammam.</s> <s xml:id="echoid-s6692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6693" xml:space="preserve">Si ad Adſcenſum Aquæ in tubos humectatos ſiccoſque attenda-<lb/>mus, non cum majori velocitate Aquam adſcendere in humidos, <lb/>quam in ſiccos novos, & </s> <s xml:id="echoid-s6694" xml:space="preserve">modo ante confectos obſervamus; </s> <s xml:id="echoid-s6695" xml:space="preserve">cæ-<lb/>teroquin multo lentius aſſurgit Aqua in tubos ſiccos antiquos, quam in <lb/>humidos.</s> <s xml:id="echoid-s6696" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div186" type="section" level="1" n="186"> <head xml:id="echoid-head198" xml:space="preserve">EXPERIMENTUM X.</head> <p> <s xml:id="echoid-s6697" xml:space="preserve">Si juxta externam ſuperficiem tubi, perpendiculariter ad horizon-<lb/>tem ſuſpenſi, gutta Aquæ defluat deorſum, hæc perveniens ad oram <lb/>infimam, ſurſum in tubi cavum rapitur ad altitudinem 20 linea-<lb/>rum.</s> <s xml:id="echoid-s6698" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6699" xml:space="preserve">Hoc etiam animadvertit Rohaultus in Phyſic. </s> <s xml:id="echoid-s6700" xml:space="preserve">Part. </s> <s xml:id="echoid-s6701" xml:space="preserve">1. </s> <s xml:id="echoid-s6702" xml:space="preserve">Cap. </s> <s xml:id="echoid-s6703" xml:space="preserve">22. <lb/></s> <s xml:id="echoid-s6704" xml:space="preserve">§ 88. </s> <s xml:id="echoid-s6705" xml:space="preserve">& </s> <s xml:id="echoid-s6706" xml:space="preserve">Carrè in L’Hiſt. </s> <s xml:id="echoid-s6707" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6708" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6709" xml:space="preserve">A°. </s> <s xml:id="echoid-s6710" xml:space="preserve">1705, atque idem <lb/>fieri in vacuo demonſtravit Cl. </s> <s xml:id="echoid-s6711" xml:space="preserve">Petitus in L’Hiſt. </s> <s xml:id="echoid-s6712" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6713" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6714" xml:space="preserve"><lb/>A°. </s> <s xml:id="echoid-s6715" xml:space="preserve">1724. </s> <s xml:id="echoid-s6716" xml:space="preserve">pag. </s> <s xml:id="echoid-s6717" xml:space="preserve">99. </s> <s xml:id="echoid-s6718" xml:space="preserve">Quotieſcunque hoc Experimentum inſtituitur <lb/>cum tubis capillaribus admodum gracilibus ſemper ſuccedit, quia <lb/>gutta Aquæ delapſa ad infimum tubi orificium, per totam illius baſin <lb/>diffunditur, atque ita cavitati oppoſita ſurſum rapitur: </s> <s xml:id="echoid-s6719" xml:space="preserve">ſi vero tu-<lb/>bus fuerit amplior, diametri nempe 3 {1/2} linearum, & </s> <s xml:id="echoid-s6720" xml:space="preserve">craſſioris vi-<lb/>tri, gutta Aquæ delapſa inferius non ſe per baſin totam diffundit, <lb/>ſed ejus parti tantum adhærens ſolidæ, introrſum non fluit.</s> <s xml:id="echoid-s6721" xml:space="preserve"/> </p> <pb o="282" file="0296" n="296" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div187" type="section" level="1" n="187"> <head xml:id="echoid-head199" xml:space="preserve">EXPERIMENTUM XI.</head> <p> <s xml:id="echoid-s6722" xml:space="preserve">Idem tubus, Aquam continens ad altitudinem 20 linearum, ex <lb/>vaſculo ſublatus, parum inclinetur ad horizontem, ut Aqua infimam <lb/>oram relinquens verſus medium tubi ſe recipiat, locum aëri cedens, <lb/>tum in hoc obliquo ſitu iterum imponatur Aquæ, quæ in ipſum ad-<lb/>ſcendet, intercipiens aëream bullam. </s> <s xml:id="echoid-s6723" xml:space="preserve">Tum tubo ex vaſe demto <lb/>& </s> <s xml:id="echoid-s6724" xml:space="preserve">perpendiculariter ſuſpenſo, obſervabitur effluere fere omnis A-<lb/>quæ inferior maſſa uſque ad aëream bullam, excepta altitudine <lb/>1 {1/3} vel 2, vel 3 linearum, ſupra quam hæret bulla aërea, & </s> <s xml:id="echoid-s6725" xml:space="preserve">ſupra <lb/>bullam, Aqua ſuperior ad altitudinem 20 linearum. </s> <s xml:id="echoid-s6726" xml:space="preserve">In hoc Ex-<lb/>perimento plus Aquæ in tubo deprehenditur, quam in ullis aliis, <lb/>quod mirum eſt: </s> <s xml:id="echoid-s6727" xml:space="preserve">Cur enim non expellitur omnis Aqua inferior <lb/>ſimul cum bullâ aëreâ: </s> <s xml:id="echoid-s6728" xml:space="preserve">hæc autem efficit, ut pars quædam Aquæ <lb/>non exeat, cæteroquin elapſura. </s> <s xml:id="echoid-s6729" xml:space="preserve">Videtur id fieri, quia aër val-<lb/>de adhæret parietibus tubi, atque ita ſuſtinet aliquomodo Fluidum <lb/>ſuperius ſibi incumbens, quominus tota gravitate deorſum ruat & </s> <s xml:id="echoid-s6730" xml:space="preserve"><lb/>premat Aquam infra bullam: </s> <s xml:id="echoid-s6731" xml:space="preserve">Aërem vero non niſi tarde, & </s> <s xml:id="echoid-s6732" xml:space="preserve">cum <lb/>quadam tenacitate per hos tubos moveri ſemper docuit experien-<lb/>tia: </s> <s xml:id="echoid-s6733" xml:space="preserve">licet ideo ſit multo levior quam Aqua, non tamen eam per-<lb/>rumpit adſcendendo, ſed tuborum occupat inferiorem partem, non <lb/>ſecus quam ſi Aquâ gravior foret, aut tubis inſtar ſolidi corporis <lb/>adhæreret.</s> <s xml:id="echoid-s6734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6735" xml:space="preserve">Fieri hoc modo poteſt, ut multo plus Aquæ, quam 20 li-<lb/>nearum, hæreat in tubo ſuſpenſum, modo partes frequentibus <lb/>bullis aëreis ſint interruptæ, nam omnes adhærendo tubi parie-<lb/>tibus, deſcenſum Aquæ impediunt. </s> <s xml:id="echoid-s6736" xml:space="preserve">Inde etiam clariſſime intel-<lb/>ligitur, quare, ſi in tubo hinc inde hæſerint parvæ guttæ Aquæ <lb/>bullas aëreas intercipientes, aqua non, vel vix in tubum ingredia-<lb/>tur, ſibi impoſitum, ingreſſum impedientibus bullis his aëreis in-<lb/>terceptis, quæ non niſi difficulter ſurſum adſcendunt: </s> <s xml:id="echoid-s6737" xml:space="preserve">Aëri enim <lb/>ineſt ſpecies quædam tenacitatis, aut immobilitatis, ideo etiam <lb/>hoſpitans in tubis majoribus, & </s> <s xml:id="echoid-s6738" xml:space="preserve">ad eorum in flexorum curv aturas, <lb/>transfluxum Aquæ valde impedit, & </s> <s xml:id="echoid-s6739" xml:space="preserve">ultra fidem, uti egregie ob-<lb/>ſervavit poſuitque Cl. </s> <s xml:id="echoid-s6740" xml:space="preserve">Disaguilliers in Philoſ. </s> <s xml:id="echoid-s6741" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s6742" xml:space="preserve">N°. </s> <s xml:id="echoid-s6743" xml:space="preserve">393.</s> <s xml:id="echoid-s6744" xml:space="preserve"/> </p> <pb o="283" file="0297" n="297" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> </div> <div xml:id="echoid-div188" type="section" level="1" n="188"> <head xml:id="echoid-head200" xml:space="preserve">EXPERIMENTUM XII.</head> <p> <s xml:id="echoid-s6745" xml:space="preserve">Tubi ejuſdem impleti Aquâ ad altitudinem 20 linearum, po-<lb/>ſitique perpendiculariter in aëre, orificium ſupremum hermeti-<lb/>ce fuit clauſum ope flammæ, aqua interim manente immota & </s> <s xml:id="echoid-s6746" xml:space="preserve"><lb/>ad eandem altitudinem: </s> <s xml:id="echoid-s6747" xml:space="preserve">obturaculo deinde diffracto, man-<lb/>ſit Aqua immota ut ante. </s> <s xml:id="echoid-s6748" xml:space="preserve">Quamobrem occluſio nihil mutatio-<lb/>nis adfert ad Aquam ſuſpenſam tenendam.</s> <s xml:id="echoid-s6749" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div189" type="section" level="1" n="189"> <head xml:id="echoid-head201" xml:space="preserve">EXPERIMENTUM XIII.</head> <p> <s xml:id="echoid-s6750" xml:space="preserve">Eundem Tubum Aquâ vacuum, ſuperius abruptum iterum hermetice <lb/>clauſi, omnibuſque refrigeratis, orificium apertum impoſui Aquæ, cu-<lb/>jus nulla guttula tubum ingreſſa fuit: </s> <s xml:id="echoid-s6751" xml:space="preserve">ſubmerſo deinde tubo ad <lb/>altitudinem unius pollicis infra Aquam, aliquid, quod tamen <lb/>vix conſpici poterat, in tubum intravit.</s> <s xml:id="echoid-s6752" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6753" xml:space="preserve">Aqua in hoc Experimento tubum ingredi non poterat, quin <lb/>condenſaret aërem, cujus vis elaſtica augetur in ratione denſita-<lb/>tis auctæ ſive inverſa ſpatiorum; </s> <s xml:id="echoid-s6754" xml:space="preserve">ideo ſi tubi vis elevans ſepona-<lb/>tur, facile cognoſci poteſt quouſque Aqua in ipſum aſſurgere de-<lb/>buiſſet, preſſa â gravitate unius pollicis Aquei: </s> <s xml:id="echoid-s6755" xml:space="preserve">Quo tempore ex-<lb/>perimentum inſtituebatur, erat Mercurius in Baroſcopio elevatus <lb/>ad 29 pollicum altitudinem, ſive ad 406 pollices Aquæ: </s> <s xml:id="echoid-s6756" xml:space="preserve">poſi-<lb/>ta hujus gravitate ad eam Mercurii uti 1 ad 14. </s> <s xml:id="echoid-s6757" xml:space="preserve">quamobrem aër, <lb/>qui erat in tubo comprimebatur viribus 406 pollicum Aquæ, ſed <lb/>tubo ſubmerſo profundius quantitate 1 pollicis, Aër in ipſo com-<lb/>primebatur vi 407 pollicum hinc denſior reddebatur, adeoque <lb/>ſpatium ab Aëre prius occupatum, debebat eſſe ad ſpatium ab eo <lb/>nunc occupatum, uti 407 ad 406, & </s> <s xml:id="echoid-s6758" xml:space="preserve">quia tubus erat longitudinis <lb/>3 {1/2} ſive 3 {407/814} pollicum, quod erat ſpatium prius ab aëre impletum, <lb/>nunc debebat eſſe ſpatium ejus 3 {400/814} pollic. </s> <s xml:id="echoid-s6759" xml:space="preserve">quæ differentia profecto <lb/>inſenſibilis eſt: </s> <s xml:id="echoid-s6760" xml:space="preserve">addamus nunc vim elevantem Aquæ, quæ in Ex-<lb/>perimento I deprehenſa fuit æqualis 20 lineis Aquæ, erit igitur <lb/>tota vis aërem condenſatura, compoſita ex 20 lineis + 1 pollice Aquæ, <lb/>hinc aër in tubo occupabit ſpatium 3 {388/814} pollic. </s> <s xml:id="echoid-s6761" xml:space="preserve">proximè, ſive aquæ <pb o="284" file="0298" n="298" rhead="DISSERTATIO"/> partes {12/814} pollicis ingreſſæ erunt in tubum, quæ quantitas eſt adeo <lb/>exigua, ut vix ab oculo diſcerni queat, idcirco in Experimento <lb/>etiam aliquid, ſed admodum parum Aquæ, tubum intravit Expe-<lb/>rimentum hoc etiam inſtituit Honor. </s> <s xml:id="echoid-s6762" xml:space="preserve">Fabry in Phyſ. </s> <s xml:id="echoid-s6763" xml:space="preserve">§. </s> <s xml:id="echoid-s6764" xml:space="preserve">3. </s> <s xml:id="echoid-s6765" xml:space="preserve">Boyle <lb/>in Exper. </s> <s xml:id="echoid-s6766" xml:space="preserve">phyſ. </s> <s xml:id="echoid-s6767" xml:space="preserve">Mech. </s> <s xml:id="echoid-s6768" xml:space="preserve">Exp. </s> <s xml:id="echoid-s6769" xml:space="preserve">9. </s> <s xml:id="echoid-s6770" xml:space="preserve">pag. </s> <s xml:id="echoid-s6771" xml:space="preserve">93. </s> <s xml:id="echoid-s6772" xml:space="preserve">tum Sturmius in Col-<lb/>leg. </s> <s xml:id="echoid-s6773" xml:space="preserve">Cur. </s> <s xml:id="echoid-s6774" xml:space="preserve">Tentam. </s> <s xml:id="echoid-s6775" xml:space="preserve">8. </s> <s xml:id="echoid-s6776" xml:space="preserve">p. </s> <s xml:id="echoid-s6777" xml:space="preserve">45. </s> <s xml:id="echoid-s6778" xml:space="preserve">qui tamen abſque demonſtratione id <lb/>reliquerunt: </s> <s xml:id="echoid-s6779" xml:space="preserve">Ex eo autem conſtat Aërem in tubis his contineri ejus-<lb/>dem denſitatis cum aëre ambiente, vel reliquæ atmoſphæræ: </s> <s xml:id="echoid-s6780" xml:space="preserve">pone <lb/>enim illum eſſe rariorem cum Rohaulto aliisque, an tum in tubum, <lb/>etiamſi ſuperne clauſum, non premetur a præponderante atmoſphæ-<lb/>râ liquor: </s> <s xml:id="echoid-s6781" xml:space="preserve">id omnino fieret, ſedipſa experientia obſtat, nihil ingredi-<lb/>tur, quia aër internus & </s> <s xml:id="echoid-s6782" xml:space="preserve">externus æque denſus vi ſua elaſtica reſiſtit.</s> <s xml:id="echoid-s6783" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div190" type="section" level="1" n="190"> <head xml:id="echoid-head202" xml:space="preserve">EXPERIMENTUM XIV.</head> <p> <s xml:id="echoid-s6784" xml:space="preserve">Tubi utrimque aperti, & </s> <s xml:id="echoid-s6785" xml:space="preserve">inclinati ad horizontem, extremum ſupe-<lb/>rius attingat guttam aquæ altius poſitam, hæc intus rapitur deſcenden-<lb/>do uſque ad inferius extremum, totuſque tubus penitus impletur: </s> <s xml:id="echoid-s6786" xml:space="preserve">Fluit <lb/>autem velocitate majori deſcendens liquor per tubum in hoc Experi-<lb/>mento, quam aſſurgit in ipſum erectum perpendiculariter in Exp. </s> <s xml:id="echoid-s6787" xml:space="preserve">I°, <lb/>quia duplici vi hic fertur, unâ, qua in tubum adſcendere poteſt ad alti-<lb/>tudinem perpendicularem 20 linearum, altera eſt ipſa gravitas, idcirco <lb/>hac vi liquor motu fertur accelerato, veluti omnia gravia, uſque ad <lb/>oram infimam tubi, ex quâ guttatim effluit. </s> <s xml:id="echoid-s6788" xml:space="preserve">Si vero eodem modo <lb/>teneatur alius tubus, cujus inferius orificium clauſum eſt, nihil A-<lb/>quæ ſuperius orificium ingreditur, nec deſcendit, excepta aliquâ, <lb/>ſed vix nudo oculo conſpicienda quantitate; </s> <s xml:id="echoid-s6789" xml:space="preserve">quia nec vis tubi in A-<lb/>quam, nec guttulæ orificio appoſitæ gravitas, ſufficiunt ad aërem <lb/>in tubo condenſandum, per demonſtrationem modo datam in Ex-<lb/>perimento XIII.</s> <s xml:id="echoid-s6790" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div191" type="section" level="1" n="191"> <head xml:id="echoid-head203" xml:space="preserve">EXPERIMENTUM. XV.</head> <p> <s xml:id="echoid-s6791" xml:space="preserve">Quo tubi vitrei majorem longitudinem habent, eo quoque altius <lb/>in ſe Aquam rapiunt; </s> <s xml:id="echoid-s6792" xml:space="preserve">non tamen ſecundum proportionem ali-<lb/>quam longitudini reſpondentem, cum duo diverlæ longitudinis tu- <pb o="285" file="0299" n="299" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> bi aliquando æque excelſe aquam elevant. </s> <s xml:id="echoid-s6793" xml:space="preserve">Hoc plurimis con-<lb/>firmabo Experimentis, quia Cl. </s> <s xml:id="echoid-s6794" xml:space="preserve">Carreus longitudinem Tubi nihil con-<lb/>ferre ad altitudinem adſcendentis Aquæ in L’Hiſt. </s> <s xml:id="echoid-s6795" xml:space="preserve">de L’Academ. <lb/></s> <s xml:id="echoid-s6796" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6797" xml:space="preserve">A°. </s> <s xml:id="echoid-s6798" xml:space="preserve">1705, poſuerat. </s> <s xml:id="echoid-s6799" xml:space="preserve">in quem errorem facile incidere potuit, <lb/>capiendo tantum experimenta in duobus tubis, longitudine non ad-<lb/>modum inter ſe diſcrepantibus, quia in his, ut mox liquebit, ali-<lb/>quando aqua æque alte elevata obſervatur. </s> <s xml:id="echoid-s6800" xml:space="preserve">niſi forſitan nimiâ præ-<lb/>cipitantiâ inſtituerit experimenta, nam ſi ad altitudinem 8, 10, vel <lb/>plurium pollicum Aqua in tubos longos adſcendat, ad minimum <lb/>12 eſt exſpectandum horis, antequam Aqua ad omnem pervenerit <lb/>altitudinem: </s> <s xml:id="echoid-s6801" xml:space="preserve">Miror Cl. </s> <s xml:id="echoid-s6802" xml:space="preserve">Carreum non conſuluiſſe obſervationes Ho-<lb/>nor. </s> <s xml:id="echoid-s6803" xml:space="preserve">Fabry in Phyſ. </s> <s xml:id="echoid-s6804" xml:space="preserve">Lib. </s> <s xml:id="echoid-s6805" xml:space="preserve">2. </s> <s xml:id="echoid-s6806" xml:space="preserve">Tract. </s> <s xml:id="echoid-s6807" xml:space="preserve">5.</s> <s xml:id="echoid-s6808" xml:space="preserve">§. </s> <s xml:id="echoid-s6809" xml:space="preserve">235 & </s> <s xml:id="echoid-s6810" xml:space="preserve">§. </s> <s xml:id="echoid-s6811" xml:space="preserve">169, atque <lb/>Sturmium in Colleg. </s> <s xml:id="echoid-s6812" xml:space="preserve">Curioſ. </s> <s xml:id="echoid-s6813" xml:space="preserve">Tentam. </s> <s xml:id="echoid-s6814" xml:space="preserve">8. </s> <s xml:id="echoid-s6815" xml:space="preserve">pag. </s> <s xml:id="echoid-s6816" xml:space="preserve">44. </s> <s xml:id="echoid-s6817" xml:space="preserve">§. </s> <s xml:id="echoid-s6818" xml:space="preserve">3. </s> <s xml:id="echoid-s6819" xml:space="preserve">qui obſer-<lb/>vaverunt, quo altius emineret tubulus ſuper Aquæ ſuperficiem, eo <lb/>altius in ipſum adſcendere aquam, cæteris ſcilicet paribus; </s> <s xml:id="echoid-s6820" xml:space="preserve">verum <lb/>auctoritatibus non pugnamus, ipſa rem demonſtrent experimen-<lb/>ta oportebit, quæ in tabellis conjecta ob oculos ponam.</s> <s xml:id="echoid-s6821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6822" xml:space="preserve">Tubus, cujus longitudo 3 {1/2} pollicum ad altitudinem 20 linearum <lb/>in ſe rapuit aquam, cum ab eodem amputata erat pars ſuperior, <lb/>ficca; </s> <s xml:id="echoid-s6823" xml:space="preserve">tumque eductâ Aquâ, orificium inferius iterum Aquæ im-<lb/>miſſum fuit, altitudines obſervatæ ſunt ſequentes.</s> <s xml:id="echoid-s6824" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6825" xml:space="preserve">Tubi longitudo poll. </s> <s xml:id="echoid-s6826" xml:space="preserve">lin. </s> <s xml:id="echoid-s6827" xml:space="preserve">Adſcenſ. </s> <s xml:id="echoid-s6828" xml:space="preserve">Aquæ adpoll. </s> <s xml:id="echoid-s6829" xml:space="preserve">lin.</s> <s xml:id="echoid-s6830" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>3 # 6 # 1 # 8 <lb/>2 # 0 # 1 # 6 <lb/>1 # 0 # 0 # 10 vel 10 {1/2} <lb/>0 # 9 # 0 # 8 <lb/>0 # 6 # 0 # 5 {1/4} <lb/>0 # 2 {1/2} # 0 # 2 {1/4} <lb/></note> <p> <s xml:id="echoid-s6831" xml:space="preserve">Cum alio tubo, cujus diameter erat {1/6} lineæ, quantum ope im-<lb/>miſſi Trianguli, & </s> <s xml:id="echoid-s6832" xml:space="preserve">Microſcopii detegere potui</s> </p> <pb o="286" file="0300" n="300" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s6833" xml:space="preserve">Tubi longit. </s> <s xml:id="echoid-s6834" xml:space="preserve">poll. </s> <s xml:id="echoid-s6835" xml:space="preserve">lin. </s> <s xml:id="echoid-s6836" xml:space="preserve">AdſcenſusAq ad poll. </s> <s xml:id="echoid-s6837" xml:space="preserve">lin.</s> <s xml:id="echoid-s6838" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>7 # 6 # 4 # 7 {1/5} <lb/>6 # 0 # 4 # 4 {4/5} <lb/>5 # 0 # 4 # 2 {2/5} <lb/>4 # 5 # 4 # 1 {1/5} <lb/></note> <p> <s xml:id="echoid-s6839" xml:space="preserve">Cum alio tubo aliquantum latiori</s> </p> <p> <s xml:id="echoid-s6840" xml:space="preserve">Tubi longit. </s> <s xml:id="echoid-s6841" xml:space="preserve">poll. </s> <s xml:id="echoid-s6842" xml:space="preserve">lin. </s> <s xml:id="echoid-s6843" xml:space="preserve">Adſcenſus ad poll. </s> <s xml:id="echoid-s6844" xml:space="preserve">lin.</s> <s xml:id="echoid-s6845" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>24 # 0 # 3 {9/10} <lb/>11 # 0 # 3 {7/10} <lb/>8 # 6 # 3 {7/10} <lb/>7 # 0 # 3 {6/10} <lb/>6 # 0 # 3 {4/10} <lb/>4 # 6 # 3 {3/10} <lb/>4 # 0 # 3 {3/10} <lb/>3 # 0 # fere ad orificium uſque. <lb/></note> <p> <s xml:id="echoid-s6846" xml:space="preserve">Cum alio tubo confecto ex alio vitri genere.</s> <s xml:id="echoid-s6847" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>24 # 0 # 3 {9/10} <lb/>12 # 0 # 3 {5/10} <lb/>11 # 0 # 3 {3/10} <lb/>10 # 0 # 3 {3/20} <lb/>8 # 0 # 3 <lb/>6 # 0 # 3 <lb/></note> <p> <s xml:id="echoid-s6848" xml:space="preserve">Præterea confeci tubum 3 {1/2} pedes longum, cujus cavitas erat ad-<lb/>eo anguſta, ut craſſitiem capilli humani non ſuperaverit, qui Aquam <lb/>in ſe recepit ad altitudinem 13 pollicum; </s> <s xml:id="echoid-s6849" xml:space="preserve">parte ejus abrupta, ut mo-<lb/>do longitudinem 2 pedum haberet, Aquam ſuſtulit ad 12 {1/2} pollices. </s> <s xml:id="echoid-s6850" xml:space="preserve">In-<lb/>ter reliquos erat mihi adhuc ad manus alius tubus anguſtus, diame-<lb/>tri {1/10} lineæ proxime, longitudinis 3 pollicum, qui aquam elevavit <lb/>ad altitudinem 2 {11/12} pollic. </s> <s xml:id="echoid-s6851" xml:space="preserve">parte abrupta ut modo 2 {3/4} pollic. </s> <s xml:id="echoid-s6852" xml:space="preserve">foret, <pb o="287" file="0301" n="301" rhead="DETUBIS CAPILLARIBUS VITREIS."/> aquam recepit ad altitudinem 2 pollic. </s> <s xml:id="echoid-s6853" xml:space="preserve">8 {1/4} lin. </s> <s xml:id="echoid-s6854" xml:space="preserve">rurſus abbreviatus ad <lb/>longitudinem 2 {1/2} pollic. </s> <s xml:id="echoid-s6855" xml:space="preserve">admiſit Aquam fere ad eandem altitudinem <lb/>2 poll. </s> <s xml:id="echoid-s6856" xml:space="preserve">8 {1/4} lin. </s> <s xml:id="echoid-s6857" xml:space="preserve">ſæpius tamen modo ad 2 pollices 3, 4, vel 5 lineas. <lb/></s> <s xml:id="echoid-s6858" xml:space="preserve">longitudinis tandem 2 pollicum abripuit Aquam uſque ad ſummam <lb/>oram, idque perpetuo fecit, cum abrumpendo portionem accipiebat <lb/>longitudinem 1, vel {1/2} pollicis, aut 5, 4, 3, linear. </s> <s xml:id="echoid-s6859" xml:space="preserve">in quibus ca-<lb/>ſibus Aqua ſemper totum tubum ab imo ad ſummum uſque imple-<lb/>vit: </s> <s xml:id="echoid-s6860" xml:space="preserve">prolixior videri in his tentaminibus poſſem, niſi cum Clariſſi-<lb/>mo Geometra aliter ſtatuente res nobis fuiſlet, atque ex his ſolis <lb/>hypotheſis valde ingenioſa ad explicanda tuborum capillarium phæ-<lb/>nomena penitus rueret, veneratio magno debita Viro jubebat, ne <lb/>præcipitantia aut temeritate pergeremus, ſed multis convinceremus <lb/>potius argumentis: </s> <s xml:id="echoid-s6861" xml:space="preserve">Contemplando noſtras obſervationes detegimus <lb/>facile quomodo in errorem labi potuiſſemus, ſiunum alterumve tan-<lb/>tum inſtituiſſemus tentamen, nam in tentamine hujus (15) tertio, <lb/>tubus longitudinis 11 pollic. </s> <s xml:id="echoid-s6862" xml:space="preserve">Aquam elevavit ad 3 {7/10} pollic. </s> <s xml:id="echoid-s6863" xml:space="preserve">quem-<lb/>admodum idem tubus longitudinis 8 {1/2} pollic. </s> <s xml:id="echoid-s6864" xml:space="preserve">ipſam abripuit: </s> <s xml:id="echoid-s6865" xml:space="preserve">imo <lb/>ſive longitudinem 4 {1/2} pollic. </s> <s xml:id="echoid-s6866" xml:space="preserve">ſive 4 pollic. </s> <s xml:id="echoid-s6867" xml:space="preserve">habuerit, ad eandem al-<lb/>titudinem 3 {3/10} pollic. </s> <s xml:id="echoid-s6868" xml:space="preserve">aquam ſuſpendit. </s> <s xml:id="echoid-s6869" xml:space="preserve">& </s> <s xml:id="echoid-s6870" xml:space="preserve">in quarto tentamine tu-<lb/>bus 8 pollic. </s> <s xml:id="echoid-s6871" xml:space="preserve">& </s> <s xml:id="echoid-s6872" xml:space="preserve">6 pollic. </s> <s xml:id="echoid-s6873" xml:space="preserve">aquam ejuſdem altitudinis 3 pollic. </s> <s xml:id="echoid-s6874" xml:space="preserve">in ſe <lb/>continuit quamobrem nonnulli dantur caſus, in quibus idem tubus <lb/>diverſæ longitudinis, ad eandem altitudinem Aquam elevat, qui <lb/>caſus procul dubio Cl. </s> <s xml:id="echoid-s6875" xml:space="preserve">Carreum in errorem conjecit.</s> <s xml:id="echoid-s6876" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6877" xml:space="preserve">Concludimus ex his Experimentis vim aut cauſam elevantem A-<lb/>quam per totam tubi longitudinem eſſe diffuſam, quo igitur longior <lb/>tubus exiſtit, eo major quantitas virium elevantium Aquam datur, <lb/>niſi id enim foret, ſed modo æqualis vis, tubo brevi longove poſi-<lb/>to, etiam ad eandem altitudinem aqua introrſum abriperetur: </s> <s xml:id="echoid-s6878" xml:space="preserve">Agit <lb/>igitur vis elevans tubi in diſtantiam & </s> <s xml:id="echoid-s6879" xml:space="preserve">quidem in magnam, nam tu-<lb/>bi 3 {1/2} pedum pars ſuperior 1 {1/2} pedum tantundem virium habet, qui-<lb/>bus Aquam ad {1/2} pollicem attollit, cum reliqua pars 2 pedum ipſam <lb/>ad 12 {1/2} pollices ſuſpendat, imo vim tubi ad majorem exporrigi di-<lb/>ſtantiam quam 1 {1/2} ped. </s> <s xml:id="echoid-s6880" xml:space="preserve">ex aliis experimentis cum tubis multo lon-<lb/>gioribus & </s> <s xml:id="echoid-s6881" xml:space="preserve">gracilioribus captis probari poſſet: </s> <s xml:id="echoid-s6882" xml:space="preserve">Occupatus fui ali-<lb/>quamdiu in eruenda quadam proportione inter longitudinem Tubi <lb/>& </s> <s xml:id="echoid-s6883" xml:space="preserve">altitudinem elevatæ Aquæ, abſque proportione enim non ope- <pb o="288" file="0302" n="302" rhead="DISSERTATIO"/> rabitur procul dubio natura, eam licet obvelet circumſtantiis, in <lb/>quibus mens illico non penetrat: </s> <s xml:id="echoid-s6884" xml:space="preserve">anomalias hic dari certum eſt, <lb/>quæ impediunt quominus aliquid ſtabilire audeamus, nam quomode <lb/>idem tubus diverſæ longitudinis aquam ad eandem aliquando altitudi-<lb/>nem attollit? </s> <s xml:id="echoid-s6885" xml:space="preserve">quare longior non ſemper excelſius eam elevat breviori? <lb/></s> <s xml:id="echoid-s6886" xml:space="preserve">ejuſmodi anomaliæ monent non nimis cito proportionem eſſe aſſu-<lb/>mendam inter altitudines Aquæ & </s> <s xml:id="echoid-s6887" xml:space="preserve">longitudines tuborum, priuſquam <lb/>cauſam impedimenti melius intellexerimus: </s> <s xml:id="echoid-s6888" xml:space="preserve">reſtat igitur hoc pro-<lb/>blema hactenus non ſolutum: </s> <s xml:id="echoid-s6889" xml:space="preserve">Notare tamen in genere poſſumus, <lb/>breviores tubos plus Aquæ, reſpectu ſuæ longitudinis habito, ele-<lb/>vare quam longiores, tubus enim duorum pedum elevavit modo <lb/>Aquam ad 3 {9/10} pollices, cum tubus unius pedis eam in ſe abripuit ad <lb/>3 {5/10} pollic. </s> <s xml:id="echoid-s6890" xml:space="preserve">atque tubus duorum pollicum Aquam ſuſtulit uſque ad <lb/>alterum extremum.</s> <s xml:id="echoid-s6891" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div192" type="section" level="1" n="192"> <head xml:id="echoid-head204" xml:space="preserve">EXPERIMENTUM XVI.</head> <p> <s xml:id="echoid-s6892" xml:space="preserve">Si capiantur tubi vitrei, ante aliquot tempus, menſes vel annos <lb/>confecti, qui jacuerunt aëri aperto expoſiti, aut optime ſervati fuerunt <lb/>in thecis capſulisve; </s> <s xml:id="echoid-s6893" xml:space="preserve">horum alterutrum extremum immittatur A-<lb/>quæ, hæc vel nequaquam, vel tantillum adſcendere obſervabitur, <lb/>& </s> <s xml:id="echoid-s6894" xml:space="preserve">ſi aliquantulum introiverit, immota manebit, tubo licet in-<lb/>verſo.</s> <s xml:id="echoid-s6895" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6896" xml:space="preserve">Videmus igitur aërem ſuperficiei internæ horum tuborum aliquid <lb/>illinire, quod inſtar olei vel obturaculi reſiſtit Aquæ, atque vim <lb/>elevantem tubi tollit, aut impedit, hoc forſitan in tubo inſtar Æ-<lb/>ruginis ſe habet, accreſcentis metallis: </s> <s xml:id="echoid-s6897" xml:space="preserve">hinc non dubito, quin Phi-<lb/>loſophi tentantes hæc Experimenta cum tubis aliquamdiu ante con-<lb/>fectis, & </s> <s xml:id="echoid-s6898" xml:space="preserve">hujuſmodi cruſtâ obſitis, ſæpe nullos effectus obſervarint; <lb/></s> <s xml:id="echoid-s6899" xml:space="preserve">videntur ejuſmodi profecto decepiſſe Sinclarium, dicentem, in tubum <lb/>ar idum vix, aut non, adſcendere Aquam. </s> <s xml:id="echoid-s6900" xml:space="preserve">Tract. </s> <s xml:id="echoid-s6901" xml:space="preserve">de Gravit. </s> <s xml:id="echoid-s6902" xml:space="preserve">pag. </s> <s xml:id="echoid-s6903" xml:space="preserve">161. </s> <s xml:id="echoid-s6904" xml:space="preserve"><lb/>tum quoque Cl. </s> <s xml:id="echoid-s6905" xml:space="preserve">Petitum in L’Hiſt. </s> <s xml:id="echoid-s6906" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s6907" xml:space="preserve">Roy. </s> <s xml:id="echoid-s6908" xml:space="preserve">A°. </s> <s xml:id="echoid-s6909" xml:space="preserve">1724. </s> <s xml:id="echoid-s6910" xml:space="preserve"><lb/>idem repetentem: </s> <s xml:id="echoid-s6911" xml:space="preserve">nam adſcendit Aqua in tubos aridiſſimos, no-<lb/>vos, brevi ante confectos, verum non in antiquos, quorum ſuper-<lb/>ficiei Aër cruſtam induxit, ſolvendo aut ſalia, ex quibus vitrum <lb/>conficitur, aut relinquendo aliquid terreſtre ſuæ ſubſtantiæ, e <pb o="289" file="0303" n="303" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> quibus permiſtis ærugo componitur, obturans cavitatem: </s> <s xml:id="echoid-s6912" xml:space="preserve">id tamen <lb/>omne tolli poteſt, tubique purificantur, ut experimentis inſerviant, <lb/>per eos Aquam puram ferventem aliquoties ſugendo, vel quod me-<lb/>lius eſt, Alcohol vini calidum, quibus interne loti inſtar novorum <lb/>fere ſe habent.</s> <s xml:id="echoid-s6913" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div193" type="section" level="1" n="193"> <head xml:id="echoid-head205" xml:space="preserve">EXPERIMENTUM XVII.</head> <p> <s xml:id="echoid-s6914" xml:space="preserve">Adſcendit Liquor ſurſum in canales ad horizontem perpendicula-<lb/>res motu retardato, incipiens primum ingredi motu celerrimo, <lb/>deinde tardiori, tardiſſimo denique, donec ad ſummam altitudi-<lb/>nem, in quâ quieſcit, pervenerit.</s> <s xml:id="echoid-s6915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6916" xml:space="preserve">Velocitatem adſcendentis Liquoris accuratiſſime obſervavi ope <lb/>penduli Minuta ſecunda oſtendentis: </s> <s xml:id="echoid-s6917" xml:space="preserve">Eſt autem motus in principio <lb/>adeo velox, ut accurate eum determinare non potuerim, quamvis <lb/>quoque duo Juvenes, acri viſu & </s> <s xml:id="echoid-s6918" xml:space="preserve">ingenio pollentes, mecum ſimul <lb/>obſervaverint: </s> <s xml:id="echoid-s6919" xml:space="preserve">In tabula ſequenti conſpiciuntur altitudines Aquæ <lb/>elevatæ in tubis, ad pollices lineasque, adſcripto ſimul tempore Mi-<lb/>nutorum, vel Minutorum ſecundorum, quibus ad eas altitudines <lb/>adſcenderat incipiendo ſupputationem temporis a primo momento <lb/>adſcenſus Aquæ.</s> <s xml:id="echoid-s6920" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # # # Longitudo Tubi fuit 35 {1/2} \\ pollic. Rhenoland. <lb/>Adſcenſus \\ ad poll. # lin. # Tempore \\ M. # M``. <lb/>4 # 7 # 2 # 7 <lb/>4 # 6 # 1 # 36 <lb/>4 # 3 # 0 # 48 <lb/>4 # 0 # 0 # 23 <lb/>3 # 9 # 0 # 15 <lb/>3 # 6 # 0 # 11 <lb/>3 # 3 # 0 # 9 <lb/>3 # 0 # 0 # 7 <lb/>2 # 9 # 0 # 4 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Longitudo Tubi ejuſdem fuit \\ 30 {1/2} poll. Rhenol. <lb/>Adſcenſ. \\ ad poll. # lin. # Tempore \\ M`. # M``. <lb/>4 # 9 # 2 # 7 <lb/>4 # 6 # 1 # 1 <lb/>4 # 3 # 0 # 34 <lb/>4 # 0 # 0 # 22 <lb/>3 # 9 # 0 # 15 <lb/>3 # 6 # 0 # 12 <lb/>3 # 3 # 0 # 9 <lb/>3 # 0 # 0 # 7 <lb/>2 # 9 # 0 # 5 <lb/></note> <pb o="290" file="0304" n="304" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>2 # 6 # 0 # 3 <lb/></note> <note position="right" xml:space="preserve"> <lb/>2 # 6 # 0 # 4 <lb/>2 # 3 # 0 # 3 <lb/>2 # 0 # 0 # 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Cum alio tubo ampliori longo \\ 14 {1/2} poll. Rhen. <lb/>Adſcenſus \\ ad poll. # lin. # Tempore \\ M`. # M``. <lb/>3 # 6 # 1 # 35 <lb/>3 # 3 # 0 # 24 <lb/>3 # 0 # 0 # 9 <lb/>2 # 9 # 0 # 5 <lb/>2 # 6 # 0 # 3 <lb/>2 # 3 # 0 # 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Cum eodem tubo longo 11 pol- \\ llic. Rhenol. <lb/>Adſcenſus \\ ad poll. # lin. # Tempore \\ M. # M``. <lb/>3 # 3 # 0 # 20 <lb/>3 # 0 # 0 # 8 <lb/>2 # 9 # 0 # 5 <lb/>2 # 6 # 0 # 4 <lb/>2 # 3 # 0 # 3 <lb/>2 # 0 # 0 # 2 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Cum alio tubo 20 {1/2} pollicum \\ & anguſtiori. <lb/>Adſcenſus \\ adpool. # lin. # Tempore \\M`. # M``. <lb/>4 # 11 # 3 # 54 <lb/>4 # 9 # 1 # 43 <lb/>4 # 6 # 0 # 54 <lb/>4 # 3 # 0 # 29 <lb/>4 # 0 # 0 # 19 <lb/>3 # 9 # 0 # 13 <lb/>3 # 6 # 0 # 10 <lb/>3 # 3 # 0 # 8 <lb/>3 # 0 # 0 # 5 <lb/>2 # 6 # 4 # 4 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Cum eodem tubo longo 15 {1/4} \\ pollic. Rhenol. <lb/>Adſcenſ. \\ ad poll. # lin. # Tempore \\ M`. # M``. <lb/>4 # 1 # 1 # 20 <lb/>4 # 0 # 0 # 30 <lb/>3 # 9 # 0 # 14 <lb/>3 # 6 # 0 # 10 <lb/>3 # 3 # 0 # 8 <lb/>3 # 0 # 0 # 6 <lb/>2 # 6 # 0 # 4 <lb/>2 # 0 # 0 # 2 <lb/></note> <pb o="291" file="0305" n="305" rhead="DETUBIS CAPILLARIBUS VITREIS."/> <note position="right" xml:space="preserve"> <lb/># # # # Cum eodem tubo 12 {3/4} pollic. <lb/>Adſcenſus \\ ad poll # lin. # Tempore \\ M`. # M``. <lb/>3 # 2 {1/2} # 2 # 0 <lb/>3 # 0 # 0 # 26 <lb/>2 # 9 # 0 # 13 <lb/>2 # 6 # 0 # 9 <lb/>2 # 3 # 0 # 6 <lb/>2 # 0 # 0 # 4 <lb/></note> <note position="right" xml:space="preserve"> <lb/># # # # Cum eodem tubo 10 pollic. <lb/>Adſcenſus \\ ad poll # lin. # Tempore \\ M`. # M``. <lb/>2 # 6 # 1 # 20 <lb/>2 # 3 # 0 # 24 <lb/>2 # 0 # 0 # 7 <lb/>1 # 9 # 0 # 3 <lb/></note> <p> <s xml:id="echoid-s6921" xml:space="preserve">Ex quibus obſervationibus conſtat, eo lentius rapi Aquam in tu-<lb/>bos ſurſum, quo ad majorem altitudinem pervenit: </s> <s xml:id="echoid-s6922" xml:space="preserve">cum enim in <lb/>obſervatione prima adſcenderat Aqua ab altitudine 2 poll. </s> <s xml:id="echoid-s6923" xml:space="preserve">6 lin. </s> <s xml:id="echoid-s6924" xml:space="preserve">ad <lb/>2 poll. </s> <s xml:id="echoid-s6925" xml:space="preserve">9 lineas, hoc eſt 3 lineas altius pervenerat, impendit tem-<lb/>pus unius Minuti ſecundi, ſed ut a 3 poll. </s> <s xml:id="echoid-s6926" xml:space="preserve">9 lin. </s> <s xml:id="echoid-s6927" xml:space="preserve">adſcenderet 3 li-<lb/>neas altius, hoc eſt perveniret ad 4 pollices, impendit tempus 8 <lb/>Minutorum ſecundorum: </s> <s xml:id="echoid-s6928" xml:space="preserve">& </s> <s xml:id="echoid-s6929" xml:space="preserve">ut 3 lineas altius adſcenderet impendit <lb/>tempus 25 Minutorum ſecundorum: </s> <s xml:id="echoid-s6930" xml:space="preserve">atque cum adhuc 3 lineas al-<lb/>tius adſcendit, elapſum fuit tempus 48 M. </s> <s xml:id="echoid-s6931" xml:space="preserve">ipſa rurſus adſcenden-<lb/>te ad 1 lineam tempus volvebatur 31 M. </s> <s xml:id="echoid-s6932" xml:space="preserve">Idem obtinet in obſerva-<lb/>tionibus aliis: </s> <s xml:id="echoid-s6933" xml:space="preserve">Adſcendit igitur Aqua in hos tubos capillares motu <lb/>retardato. </s> <s xml:id="echoid-s6934" xml:space="preserve">Retardatur motus a nonnullis cauſis ſimul: </s> <s xml:id="echoid-s6935" xml:space="preserve">1° Cauſa ad-<lb/>ſcendentis Aquæ in tubum eſt vis quædam; </s> <s xml:id="echoid-s6936" xml:space="preserve">qualiscunque fuerit: <lb/></s> <s xml:id="echoid-s6937" xml:space="preserve">hæc æque agit in Aquam, ſive ejus particula una, ſive 100, ſive <lb/>1000 fuerint in tubo, cum igitur una particula orificium tubi in-<lb/>greſſa incipit adſcendere, hæc ab omni vi agitur adeoque cum maſ-<lb/>ſam corporis exiguam conſtituat, velociſſime adſcendet; </s> <s xml:id="echoid-s6938" xml:space="preserve">ſed poſt-<lb/>quam 100 particulæ Aquæ, priorem ſequentes, ſibique adhærentes, tu-<lb/>bum ingreſſæ ſunt, iterum omnis vis tubi in 100 particulas impenditur, <lb/>quæ proinde minori velocitate agentur; </s> <s xml:id="echoid-s6939" xml:space="preserve">poſtquam 1000 particulæ tu-<lb/>bum ingreſſæſunt, hæ tantum ab eadem vi tubi aguntur, adeoque hæc, <lb/>per omnes diſtributa particulas, minori velocitate eas elevabit, <lb/>quamobrem quo plus Aquæ tubum intravit, eo lentius ipſam ferri <lb/>neceſium erit.</s> <s xml:id="echoid-s6940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6941" xml:space="preserve">Sed 2° Retardatur Liquoris adſcen ſus in tubos ab attritu, quem <lb/>particulæ patiuntur contra parietes tuborum; </s> <s xml:id="echoid-s6942" xml:space="preserve">licet enim parietes <pb o="292" file="0306" n="306" rhead="DISSERTATIO"/> ex vitro ſint, nihilominus ſuperficiem aſperam habent, ut Micro-<lb/>ſcopicæ evincunt obſervationes, in has cum liquoris particulæ in-<lb/>currunt aſperitates, retardantur, nec parum; </s> <s xml:id="echoid-s6943" xml:space="preserve">eſt Retardatio magna <lb/>in initio cum liquoris motus velox eſt, & </s> <s xml:id="echoid-s6944" xml:space="preserve">poſtea inſignis quoque eſt <lb/>cum magna Aquæ columna adimplevit tubos, atque magna ſuper-<lb/>ficic ſuperficiem tuborum attingens attritum auget, ſurſum adſcen-<lb/>dente tota columna. </s> <s xml:id="echoid-s6945" xml:space="preserve">3° Retardatur liquoris adſcenſus ab Aëre, in <lb/>tubis hoſpitante, qui ſurſum propellitur a liquore, ejiciturque, ni <lb/>hilominus movendus eſt aër, atque reſiſtentia ſua remoratur ad-<lb/>ſcenſum. </s> <s xml:id="echoid-s6946" xml:space="preserve">4°. </s> <s xml:id="echoid-s6947" xml:space="preserve">Solet autem aër tenaciter adhærere parietibus tubo-<lb/>rum, a quibus averruncandus eſt a liquore adſcendente, unde & </s> <s xml:id="echoid-s6948" xml:space="preserve"><lb/>hoc modo liquor retardatur: </s> <s xml:id="echoid-s6949" xml:space="preserve">a concurſu igitur quatuor cauſarum re-<lb/>moram perpetuo majorem experitur liquor adſcendens & </s> <s xml:id="echoid-s6950" xml:space="preserve">motu ſem-<lb/>per retardato feretur.</s> <s xml:id="echoid-s6951" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6952" xml:space="preserve">Præterea colligimus ex obſervationibus, liquorem eo velocius <lb/>adſcendere in tubos, quo hi longiores fuerint; </s> <s xml:id="echoid-s6953" xml:space="preserve">obſervationes <lb/>omnes, ſi ſecundam exceperimus, hoc ad oculum docent: </s> <s xml:id="echoid-s6954" xml:space="preserve">nec mi-<lb/>rum eſt, cum enim vis, quæ ſurſum elevat liquorem, pendet a lon-<lb/>gitudine tubi, uti in Experimento XV evictum eſt, erit vis eo ma-<lb/>jor, quo tubus, eadem manente diametro. </s> <s xml:id="echoid-s6955" xml:space="preserve">fuerit longior: </s> <s xml:id="echoid-s6956" xml:space="preserve">vis au-<lb/>tem magna eidem corpori majorem poterit celeritatem communi-<lb/>care quam exigua.</s> <s xml:id="echoid-s6957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6958" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s6959" xml:space="preserve">Ex veloci adſcenſu Aquæ in hos Tubos vitreos clarè <lb/>intelligimus, quomodo Aquain canales graciliſſimos Plantarum adeo <lb/>velociter adſcendat, attracta in radices, elevata in caulem, delata <lb/>in folia, flores, fructuſque, ut in vite 152 pollices abſolvat ſpatio <lb/>12 horarum, ſunt enim canales plantarum multo ſubtiliores tubis <lb/>vitreis a nobis examinatis hactenus, uti Microſcopia docent: </s> <s xml:id="echoid-s6960" xml:space="preserve">hinc <lb/>planta, cujus pondus modo eſt trium librarum tantundem Aquæ ex <lb/>Terra per radicem attrahit, velocique motu ſurſum determinat, ut <lb/>die æſtivo perſpiret 30 Uncias, ſpatio 12 horarum; </s> <s xml:id="echoid-s6961" xml:space="preserve">atque 17 plus <lb/>quam homo ſanus, ratione maſſæ utriuſque corporis habita. </s> <s xml:id="echoid-s6962" xml:space="preserve">Hinc <lb/>patet, quare planta flacceſcens ariditate, ſimulac Aquam modo lam-<lb/>bat, intra pauca horæ Minuta læte vireſcat, rigida turgidaque <lb/>oſtentans folia, floreſque; </s> <s xml:id="echoid-s6963" xml:space="preserve">cum Aqua rapidiſſimo deferatur motu per <lb/>canales radicum capillares, acta vi attractrice: </s> <s xml:id="echoid-s6964" xml:space="preserve">Et quia plantæ tan- <pb o="293" file="0307" n="307" rhead="DETUBIS CAPILLARIBUS VITREIS."/> tundem perſpirant, an non debet liquor nutrititius adſcendere ad <lb/>ſummitates vaſorum, veluti in Exp. </s> <s xml:id="echoid-s6965" xml:space="preserve">XV. </s> <s xml:id="echoid-s6966" xml:space="preserve">cum tubis vitreis fit, ut <lb/>exhalare poſſit, attractus ab aëre, & </s> <s xml:id="echoid-s6967" xml:space="preserve">rarefactus â radiis ſolaribus, <lb/>cumque igne adhærente ſurſum pulſus? </s> <s xml:id="echoid-s6968" xml:space="preserve">unde colligimus quantæ <lb/>ſubtilitatis ſint vaſcula plantarum, quæ liquorem ad ſuos apices uſ-<lb/>que elevant. </s> <s xml:id="echoid-s6969" xml:space="preserve">Inſuper ex hiſce Experimentis colligimus, quanta cum <lb/>velocitate ferantur liquores per vaſa abſorbentia noſtri corporis, <lb/>unde ingens quantitas fluidi extrinſecus applicati ſubito pervenit <lb/>ad ſanguinem reliquum, atque ita uſus Cataplaſmatum, Fomen-<lb/>torum, Inunctionum, Emplaſtrorum intelligitur: </s> <s xml:id="echoid-s6970" xml:space="preserve">licet igitur in <lb/>pectore, pericardio, abdomine, Scroto &</s> <s xml:id="echoid-s6971" xml:space="preserve">c. </s> <s xml:id="echoid-s6972" xml:space="preserve">ingens quantitas <lb/>ſubtilis vaporoſi dimittatur, vi circulantis ſanguinis magna cum <lb/>celeritate, hæcomnis iterum celerrime per vaſa abſorbentia refluit, vi <lb/>attrahente ipſorum vaſorum ſupplente vices cordis, quo alii humores <lb/>per corpus totum animale propelluntur: </s> <s xml:id="echoid-s6973" xml:space="preserve">hinc nulla vaporoſi in cavi-<lb/>tatibus corporis ſani collectio fit, quæ cæteroquin ad magnam <lb/>uſque increſcit molem obſtructis vaſis abſorbentibus a cauſa qua-<lb/>cunque, ut nonnulla Hydropum genera oſtendunt.</s> <s xml:id="echoid-s6974" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div194" type="section" level="1" n="194"> <head xml:id="echoid-head206" xml:space="preserve">EXPERIMENTUM XVIII.</head> <p> <s xml:id="echoid-s6975" xml:space="preserve">Indagandum reſtabat, ad quamnam altitudinem Aqua in tubos <lb/>vitreos adſcendere poſſet, poſito tubo graciliſſimo? </s> <s xml:id="echoid-s6976" xml:space="preserve">ſolvi poſlet <lb/>hoc problema, ſi prius magnitudinem uniuscujusque particulæ <lb/>Aquæ cognoſceremus. </s> <s xml:id="echoid-s6977" xml:space="preserve">2° quænam proportio inter altitudinem <lb/>Aquæ & </s> <s xml:id="echoid-s6978" xml:space="preserve">longitudinem Tubi daretur ex Exp. </s> <s xml:id="echoid-s6979" xml:space="preserve">XV. </s> <s xml:id="echoid-s6980" xml:space="preserve">3° quanta <lb/>foret aſperitas parietum ipſrus Tubi, nam vitri ſuperficies ad-<lb/>modum aſpera eſſe ſolet, unde Tubi non poſſunt fabrefieri tam <lb/>exiguæ capacitatis, ac ſi ſuperficies perfecte politas poſſiderent: <lb/></s> <s xml:id="echoid-s6981" xml:space="preserve">quamobrem Problema hactenus ſolvi Geometrice nequit. </s> <s xml:id="echoid-s6982" xml:space="preserve">quid <lb/>Phyſice præſtari poſſit addam; </s> <s xml:id="echoid-s6983" xml:space="preserve">confeci tubum graciliſſimum, cu-<lb/>jus interna cavitas diametrum habebat capillo humano æqualem, <lb/>longitudinis erat 3 {1/2} pedum, hic intra horæ ſpatium Aquam ab-<lb/>ripuit ad altitudinem 11 pollicum, atque adeo lente adſcende-<lb/>rat, ut quieviſſe viſa fuerit in eo Aqua, exſpectavi tamen ad-<lb/>huc 14 horis, quibus excelſius abrepta fuit, ita ut tota altitudo <lb/>13 pollicum fuerit.</s> <s xml:id="echoid-s6984" xml:space="preserve"/> </p> <pb o="294" file="0308" n="308" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s6985" xml:space="preserve">Præparavi alium tubum graciliſſimum 6 longum pedes, in quem <lb/>ad altitudinem 6 pollicum Aqua velociſſime ingreſſa fuit, elapſa <lb/>horâ ad 18 pollices pervenerat, verum poſt 24 horas modo ad <lb/>quietem reducta fuit, altitudinem 22 pollicum nacta: </s> <s xml:id="echoid-s6986" xml:space="preserve">ejuſmodi etiam <lb/>Experimentum, in quo Aqua ad altitudinem 21 pollic. </s> <s xml:id="echoid-s6987" xml:space="preserve">adſcendit, <lb/>commemorat Hooke in Microgr. </s> <s xml:id="echoid-s6988" xml:space="preserve">Obſ. </s> <s xml:id="echoid-s6989" xml:space="preserve">6.</s> <s xml:id="echoid-s6990" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6991" xml:space="preserve">Difficillimum eſt tubos longiſſimos & </s> <s xml:id="echoid-s6992" xml:space="preserve">graciliſſimos componere, <lb/>ideo nihil ulterius præſtare hic potui; </s> <s xml:id="echoid-s6993" xml:space="preserve">cum tamen tubi in immen-<lb/>fum ſubtiliores â natura fieri poſſint, quales illa molitur in vegeta-<lb/>bilibus, qui ad majorem altitudinem, non pollices, ſed centenos <lb/>pedes æquantem, Aquam abripiunt, ecquis terminos adſcendentis <lb/>Aquæ definiet?</s> <s xml:id="echoid-s6994" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6995" xml:space="preserve">Antequam hoc Caput claudam, aliquid etiam dicendum eſt de <lb/>figura ſuperficiei ſuperioris Aquæ in tubis, hæc cava eſt, altior ad <lb/>parietes, humilior in medio, ſimilis illi, quam Aqua ſcyphis vi-<lb/>treis infuſa habet, inferior ſuperficies, tubo perpendiculariter in <lb/>aëre ſuſpenſo, per Microſcopium apparet plana, & </s> <s xml:id="echoid-s6996" xml:space="preserve">in eodem cum <lb/>oris tubi horizontali plano; </s> <s xml:id="echoid-s6997" xml:space="preserve">ſi autem nimis Aquæ in tubo fuerit, <lb/>quam quæ contineri poſſit, hæc effluens ſuâ gravitate format ſphæ-<lb/>ram perfectam, pendentem ab extremitate tubi: </s> <s xml:id="echoid-s6998" xml:space="preserve">figura concava eſt <lb/>eadem, quam vitrum planum Aquæ immiſſum pro dimidia parte <lb/>format, de hac autem in Diſſertatione ſequenti.</s> <s xml:id="echoid-s6999" xml:space="preserve"/> </p> <pb o="295" file="0309" n="309" rhead="DETUBIS CAPILLARIBUS VITREIS."/> </div> <div xml:id="echoid-div195" type="section" level="1" n="195"> <head xml:id="echoid-head207" xml:space="preserve">CAPUT SECUNDUM.</head> <head xml:id="echoid-head208" style="it" xml:space="preserve">De Tubis æque longis diver ſarum diametrorum.</head> <p> <s xml:id="echoid-s7000" xml:space="preserve">Ut accuratiſſime menſurarem adſcenſum Aquæ in tubos æque <lb/>longos diverſarum diametrorum; </s> <s xml:id="echoid-s7001" xml:space="preserve">elegi tubos, 5 pollices Rhe-<lb/>nolandicos longos, intus puriſſimos, qui elapſâ tantum horâ erant <lb/>confecti, ne impuritas, aërisve ſordes aliquid adferrent impedi-<lb/>menti erroriſve experimentis: </s> <s xml:id="echoid-s7002" xml:space="preserve">magna difficultas latet in eligendis <lb/>tubis, quorum cavitates ſunt perfecte cylindricæ, his tamen dun-<lb/>taxat utendum eſt. </s> <s xml:id="echoid-s7003" xml:space="preserve">Ut cavitatum diametros exacte menſurarem, <lb/>ex charta tenui, ſed rigida Triangulum feci, cujus dorſum erat <lb/>{4/10} pollicis, longitudo 3 pollic. </s> <s xml:id="echoid-s7004" xml:space="preserve">quod accurate erat diviſum in par-<lb/>tes æquales, ita ut {1/100} partem pollicis manifeſto diſtinguere poſſem: <lb/></s> <s xml:id="echoid-s7005" xml:space="preserve">hæc Charta immiſſa tubis menſurabat utcunque diametros, & </s> <s xml:id="echoid-s7006" xml:space="preserve">mon-<lb/>ſtrabat ſimul, num tubi eſſent ovales, num perfecte cylindrici: </s> <s xml:id="echoid-s7007" xml:space="preserve">fa-<lb/>teor hac methodo non Mathematice menſurari diametros, quia <lb/>Charta craſſitiem habet, atque inſtar parallelopipedi craſſi exiſtit, <lb/>quod cylindrico immiſſum tubo, chordam aliquam circularis baſeos <lb/>metitur, non diametrum, ſed meliorem methodum invenire hacte-<lb/>nus non potui: </s> <s xml:id="echoid-s7008" xml:space="preserve">ope Microſcopii rem tentaveram, pejoriautem cum <lb/>ſucceſſu: </s> <s xml:id="echoid-s7009" xml:space="preserve">Tum vitrum planiſſimæ baſeos quæſitum, diametri 4 <lb/>pollicum, cui parum puræ Aquæ fuit affuſum, ut ne quidem al-<lb/>titudinem {1/20} pollicis acquireret, niſi hoc obſervetur, altitudines <lb/>veræ, ad quas in tubos Aqua adſcendit, notari nequeunt, cum A-<lb/>qua extrinſecus aſſurgens ad latera tuborum conſpectum impediat, <lb/>& </s> <s xml:id="echoid-s7010" xml:space="preserve">ſimul menſuram. </s> <s xml:id="echoid-s7011" xml:space="preserve">In hiſce autem & </s> <s xml:id="echoid-s7012" xml:space="preserve">ſequentibus uſus fui alia <lb/>menſura, quam ſupra, cum ſcalam commodiorem tum nactus eram, <lb/>in qua nempe pollex dividitur in 10 lineas, pollex tamen eſt Rhe-<lb/>nolandicus, idemque qui ante: </s> <s xml:id="echoid-s7013" xml:space="preserve">præterea uſus fui decimalium <lb/>notatione. </s> <s xml:id="echoid-s7014" xml:space="preserve">Experimenta fuerunt ſequentia.</s> <s xml:id="echoid-s7015" xml:space="preserve"/> </p> <pb o="296" file="0310" n="310" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/># # # Adſcenſus <lb/>Diametri \\ tuborum # pollic. # Aquæ # pollic. <lb/># 0.38 # # 0.09 <lb/># 0.13 # # 0.3 <lb/># 0.09 # # 0.41 <lb/># 0.08 # # 0.46 <lb/># 0.06 # # 0.61 <lb/># 0.05 # # 0.74 <lb/># 0.04 # # 0.93 <lb/># 0.02 # # 1.85 <lb/># 0.018 # # 2.80 <lb/></note> <p> <s xml:id="echoid-s7016" xml:space="preserve">Experimenta cum iiſdem tubis aliquoties repetita, dederunt ef-<lb/>fectus eoſdem. </s> <s xml:id="echoid-s7017" xml:space="preserve">Attendendum eſt, ut, ſi aqua ex tubis tollenda eſt, <lb/>puro ore illam exſugamus, os applicando extremo illi, quod <lb/>Aquæ in vaſculo immerſum fuit, nunquam ab altera parte tubum <lb/>inflando, tum enim ſuperficies vapore obducitur, & </s> <s xml:id="echoid-s7018" xml:space="preserve">Aqua ſequenti <lb/>vice ad paulo majorem vel minorem altitudinem raperetur, ſaltem <lb/>tum nunquam obſervatio accurata amplius cum tubo capi poteſt. <lb/></s> <s xml:id="echoid-s7019" xml:space="preserve">Tubi arctiſſimi maxima cum rapiditate Aquam in ſe recipiunt, mul-<lb/>to tardius tubi ampliores, celeritas autem omnium tanta fuit, ut <lb/>ad accuratam menſuram reducere eam non potuerim.</s> <s xml:id="echoid-s7020" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7021" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s7022" xml:space="preserve">1. </s> <s xml:id="echoid-s7023" xml:space="preserve">Sunt altitudines Aquæ in his tubis accurate in inverſa <lb/>ratione diametrorum tuborum. </s> <s xml:id="echoid-s7024" xml:space="preserve">Ex. </s> <s xml:id="echoid-s7025" xml:space="preserve">gr. </s> <s xml:id="echoid-s7026" xml:space="preserve">Exiſtente diametro 0,04 <lb/>pollicis, adſcenſus fuit 0.</s> <s xml:id="echoid-s7027" xml:space="preserve">93. </s> <s xml:id="echoid-s7028" xml:space="preserve">pollicis, & </s> <s xml:id="echoid-s7029" xml:space="preserve">data diametro 0,02 polli-<lb/>cis, adſcenſus fuit duplo major, æqualis nempe 1,85 poll. </s> <s xml:id="echoid-s7030" xml:space="preserve">minima <lb/>enim differentiola hic rejicienda eſt inter obſervationem & </s> <s xml:id="echoid-s7031" xml:space="preserve">calculum, <lb/>nemo enim tam ſubtiliter cuncta videre poteſt: </s> <s xml:id="echoid-s7032" xml:space="preserve">& </s> <s xml:id="echoid-s7033" xml:space="preserve">ſi calculus inea-<lb/>tur cum reliquis tubis, deprehendetur omnino regula tradita con-<lb/>venire.</s> <s xml:id="echoid-s7034" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7035" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7036" xml:space="preserve">2. </s> <s xml:id="echoid-s7037" xml:space="preserve">Et quia in cylindris, peripheriæ baſium ſunt inter ſe <lb/>ut diametri; </s> <s xml:id="echoid-s7038" xml:space="preserve">erunt adſcenſus Aquæ in hos tubos in ratione inverſa <lb/>peripheriarum baſium.</s> <s xml:id="echoid-s7039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7040" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7041" xml:space="preserve">3. </s> <s xml:id="echoid-s7042" xml:space="preserve">Quia in cylindris æque altis ſuperficies ſe habent uti <lb/>peripheriæ, ſunt adſcenſus Aquæ in tubos æque altos in ratione in-<lb/>verſâ ſuperficierum, quas tubi habent, interne.</s> <s xml:id="echoid-s7043" xml:space="preserve"/> </p> <pb o="297" file="0311" n="311" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> <p> <s xml:id="echoid-s7044" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7045" xml:space="preserve">4. </s> <s xml:id="echoid-s7046" xml:space="preserve">Erunt quantitates Aquæ elevatæ in omnibus his tu-<lb/>bis, tam amplis, quam anguſtis uti ſunt diametri baſium inter ſe.</s> <s xml:id="echoid-s7047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7048" xml:space="preserve">Nam quantitates ſunt uti altitudines multiplicatæ per ſuas baſes. <lb/></s> <s xml:id="echoid-s7049" xml:space="preserve">vocetur una altitudo a, adſcenſus nempe Aquæ in tubo ampliore, <lb/>ejuſque diameter baſeos vocetur B. </s> <s xml:id="echoid-s7050" xml:space="preserve">alterius tubi adſcenſus voce-<lb/>tur A, diameter b: </s> <s xml:id="echoid-s7051" xml:space="preserve">erit a. </s> <s xml:id="echoid-s7052" xml:space="preserve">A:</s> <s xml:id="echoid-s7053" xml:space="preserve">: b. </s> <s xml:id="echoid-s7054" xml:space="preserve">B. </s> <s xml:id="echoid-s7055" xml:space="preserve">per Corol. </s> <s xml:id="echoid-s7056" xml:space="preserve">1. </s> <s xml:id="echoid-s7057" xml:space="preserve">ergo multiplican-<lb/>do extrema & </s> <s xml:id="echoid-s7058" xml:space="preserve">media per ſe erit a B = A b. </s> <s xml:id="echoid-s7059" xml:space="preserve">ſed a BB, A bb expri-<lb/>munt quantitates Aquæ elevatæ in tubis, ergo his diviſis per a B, <lb/>A b æqualia, erunt quantitates uti B ad b. </s> <s xml:id="echoid-s7060" xml:space="preserve">ſive ut diametri.</s> <s xml:id="echoid-s7061" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7062" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7063" xml:space="preserve">5. </s> <s xml:id="echoid-s7064" xml:space="preserve">Quamobrem tubi ampliores majorem quantitatem A-<lb/>quæ elevant, quam anguſtiores, licet ad minorem altitudinem ele-<lb/>vent ſuam Aquam. </s> <s xml:id="echoid-s7065" xml:space="preserve">Nam ſemper ſunt quantitates elevatæ uti dia-<lb/>metri baſium.</s> <s xml:id="echoid-s7066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7067" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7068" xml:space="preserve">6. </s> <s xml:id="echoid-s7069" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7070" xml:space="preserve">XI. </s> <s xml:id="echoid-s7071" xml:space="preserve">fig. </s> <s xml:id="echoid-s7072" xml:space="preserve">1. </s> <s xml:id="echoid-s7073" xml:space="preserve">Sit Hyperbola H D d, ejuſque Aſym-<lb/>ptota B A, A a; </s> <s xml:id="echoid-s7074" xml:space="preserve">ſitque hyperbola ejus conditionis ut ſumta A a <lb/>= 9. </s> <s xml:id="echoid-s7075" xml:space="preserve">D a ſit = 38 partibus centeſimis pollicis & </s> <s xml:id="echoid-s7076" xml:space="preserve">ſi A a ſit = 30, <lb/>tum ? </s> <s xml:id="echoid-s7077" xml:space="preserve">? </s> <s xml:id="echoid-s7078" xml:space="preserve">ſit = 13 partibus centeſimis pollicis: </s> <s xml:id="echoid-s7079" xml:space="preserve">tum ex Naturâ Hy-<lb/>perbolæ omnes parallelæ ad Aſymptoton A B, inter Hyperbolam <lb/>& </s> <s xml:id="echoid-s7080" xml:space="preserve">Aſymptoton A a contentæ expriment diametros tuborum, & </s> <s xml:id="echoid-s7081" xml:space="preserve"><lb/>omnes A a expriment altitudines, ad quas Aqua in iis tubis eleva-<lb/>bitur: </s> <s xml:id="echoid-s7082" xml:space="preserve">ſi omnes tubi eandem longitudinem habuerint.</s> <s xml:id="echoid-s7083" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7084" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7085" xml:space="preserve">7. </s> <s xml:id="echoid-s7086" xml:space="preserve">Quia cognoſcitur gravitas Aquæ in dato tubo ex expe-<lb/>rimentis, cognoſcitur magnitudo virtutis, quæ Aquam elevat, nam <lb/>hæc æquipollet gravitati Aquæ.</s> <s xml:id="echoid-s7087" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7088" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s7089" xml:space="preserve">Quoniam igitur Aqua adſcendit altius in tubos angu-<lb/>ſtiores, quam in latos, an inde non patet, quare arbores proceræ <lb/>in ſtipite habeant vaſa ſubtiliſſima, per quæ liquor nutrititius ex ra-<lb/>dice ad verticem aſſurgit; </s> <s xml:id="echoid-s7090" xml:space="preserve">tum quare denſiores ſint ſtipites arbo-<lb/>rum valde procerarum, quam humilium, quarum lignum ſemper <lb/>laxius molliuſque deprehenditur, nam vaſa ſubtiliſſima requireban-<lb/>tur, ut ad maximam altitudinem Aqua adſcendere poſſet: </s> <s xml:id="echoid-s7091" xml:space="preserve">ideo plan-<lb/>tæ valde humiles etiam molles modo ſunt, vaſisque gaudent am-<lb/>plis, cum ad parvam altitudinem liquorem tantum attrahere tenen-<lb/>tur: </s> <s xml:id="echoid-s7092" xml:space="preserve">An ideo etiam non arbores juniores primis annis ſtipitem mol-<lb/>liorem habent, qui induratur in ſolidiorem ſubſtantiam graciliori-<lb/>bus canaliculis conſtantem, quo excelſiores fiunt?</s> <s xml:id="echoid-s7093" xml:space="preserve"/> </p> <pb o="298" file="0312" n="312" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div196" type="section" level="1" n="196"> <head xml:id="echoid-head209" xml:space="preserve">CAPUT TERTIUM.</head> <head xml:id="echoid-head210" style="it" xml:space="preserve">De Adſcenſu variorum Fluidorum in eundem Tubum.</head> <p> <s xml:id="echoid-s7094" xml:space="preserve">Sumſi tubum novum, longitudinis 43 linearum: </s> <s xml:id="echoid-s7095" xml:space="preserve">diametrum ejus <lb/>non accurate menſuravi, ſed erat minor {1/3} lineæ: </s> <s xml:id="echoid-s7096" xml:space="preserve">hic utrim-<lb/>que apertus, & </s> <s xml:id="echoid-s7097" xml:space="preserve">intra tenaculam captus, ne calor manus aliquid <lb/>mutationis experimentis afſerret; </s> <s xml:id="echoid-s7098" xml:space="preserve">tum ſuperficiei Aquæ immiſſus <lb/>tantillum, elevavit</s> </p> <p> <s xml:id="echoid-s7099" xml:space="preserve">Aquam ad altitudinem perpendicularem 26 linear.</s> <s xml:id="echoid-s7100" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7101" xml:space="preserve">Alcohol Vini purum ad 18 vel 19 lin.</s> <s xml:id="echoid-s7102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7103" xml:space="preserve">Oleum Tartari per deliq. </s> <s xml:id="echoid-s7104" xml:space="preserve">ad 25 & </s> <s xml:id="echoid-s7105" xml:space="preserve">26 lin.</s> <s xml:id="echoid-s7106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7107" xml:space="preserve">Spirit. </s> <s xml:id="echoid-s7108" xml:space="preserve">Nitri Glauberi ad 20 lineas.</s> <s xml:id="echoid-s7109" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7110" xml:space="preserve">Oleum Vitrioli ad 26 vel 27 lin.</s> <s xml:id="echoid-s7111" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7112" xml:space="preserve">Oleum Æthereum Therebinth. </s> <s xml:id="echoid-s7113" xml:space="preserve">ad 18 vel 19 lin.</s> <s xml:id="echoid-s7114" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7115" xml:space="preserve">Oleum vulgare raparum ad 21 lin.</s> <s xml:id="echoid-s7116" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7117" xml:space="preserve">Urinam ſani hominis matutinam ad 33, vel 34. </s> <s xml:id="echoid-s7118" xml:space="preserve">lin.</s> <s xml:id="echoid-s7119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7120" xml:space="preserve">Spiritum Salis Ammoniaci ad 30 vel 33. </s> <s xml:id="echoid-s7121" xml:space="preserve">lin.</s> <s xml:id="echoid-s7122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7123" xml:space="preserve">Mercurium ad --0. </s> <s xml:id="echoid-s7124" xml:space="preserve">ſive minus nihilo.</s> <s xml:id="echoid-s7125" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7126" xml:space="preserve">Hæc Experimenta ſequenti modo capta fuerunt, poſtquam alti-<lb/>tudinem Aquæ obſervaveram, tubum immiſi Alcoholi Vini fervi-<lb/>do, quod per cavum tubi trajeci aliquoties, deinde ipſum ſupra ig-<lb/>nem exſiccavi, ita interna ſuperficies æque pura reddebatur, quam <lb/>umquam fuerat; </s> <s xml:id="echoid-s7127" xml:space="preserve">tumque tubus examini alterius liquoris inſerviit, <lb/>qui cum fuerit Oleoſæ indolis, iterum ex tubo electus fuit ope Al-<lb/>coholis fervidi diu transmiſſi, ſi vero Salinæ fuerit indolis, prius <lb/>eluebatur Aqua calida, poſtea Alcohole, ita ut tubus ſemper in <lb/>eodem fuerit ſtatu, niſi enim puriſſimam habuiſſet internam ſuper-<lb/>ficiem & </s> <s xml:id="echoid-s7128" xml:space="preserve">ſiccam, accurata cum eo experimenta capi nequaquam po-<lb/>tuiſſent, quia reliquiæ alterius liquoris Oleoſæ adſcenſum Aqueo-<lb/>rum, & </s> <s xml:id="echoid-s7129" xml:space="preserve">horum partes introitum Oleoſorum impediviſſent.</s> <s xml:id="echoid-s7130" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7131" xml:space="preserve">Clar. </s> <s xml:id="echoid-s7132" xml:space="preserve">Carreus ſimilia deſcribit experimenta in L’ Hiſt. </s> <s xml:id="echoid-s7133" xml:space="preserve">de L’ Acad. <lb/></s> <s xml:id="echoid-s7134" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7135" xml:space="preserve">1705. </s> <s xml:id="echoid-s7136" xml:space="preserve">a ſe inſtituta, uſus eadem methodo, non conveniunt qui-<lb/>dem experimenta ipſius accurate cum noſtris, attamen non diſcre- <pb o="299" file="0313" n="313" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> pant valde; </s> <s xml:id="echoid-s7137" xml:space="preserve">afferam igitur ea, quæ præſtantiſſimus Mathemati-<lb/>cus adnotavit, ut noſtra magis confirmentur: </s> <s xml:id="echoid-s7138" xml:space="preserve">Sumſit Tubum dia-<lb/>metri {1/3} lineæ, longitudinis 12 {1/2} pollic. </s> <s xml:id="echoid-s7139" xml:space="preserve">Tubus hic elevavit ultro <lb/>inſe</s> </p> <p> <s xml:id="echoid-s7140" xml:space="preserve">Aquam ad 5 {3/4}, vel 7 {1/4} vel ad 10 lineas.</s> <s xml:id="echoid-s7141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7142" xml:space="preserve">Spiritum Vini ad 3 {1/2} vel ad 4 lin.</s> <s xml:id="echoid-s7143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7144" xml:space="preserve">Oleum Therebinthinæ ad 4 lin.</s> <s xml:id="echoid-s7145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7146" xml:space="preserve">Oleum Tartari per deliq. </s> <s xml:id="echoid-s7147" xml:space="preserve">ad 5 vel 6 lin.</s> <s xml:id="echoid-s7148" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7149" xml:space="preserve">Spiritum Nitri ad 4 lin.</s> <s xml:id="echoid-s7150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7151" xml:space="preserve">Oleum Olivarum ad 5 lin.</s> <s xml:id="echoid-s7152" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7153" xml:space="preserve">Repetiit hæc experimenta cum alio tubo longo 9 {1/2} pollices, fuit-<lb/>que Aquæ adſcenſus ad 10 lineas.</s> <s xml:id="echoid-s7154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7155" xml:space="preserve">Spiritus Vini ad 4 lineas.</s> <s xml:id="echoid-s7156" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7157" xml:space="preserve">Mercurii ad o lin.</s> <s xml:id="echoid-s7158" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7159" xml:space="preserve">Adhibuit dein alium tubum 15 pollices longum, diametri {1/6} lineæ.</s> <s xml:id="echoid-s7160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7161" xml:space="preserve">Aqua in eo elevata eſt ad 29 lineas.</s> <s xml:id="echoid-s7162" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7163" xml:space="preserve">Spiritus Vini ad 12 lineas.</s> <s xml:id="echoid-s7164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7165" xml:space="preserve">Tandem alium elegit tubum 5 pollices longum, ſed ejuſdem cum <lb/>præcedente diametri, in quo elevata fuit</s> </p> <p> <s xml:id="echoid-s7166" xml:space="preserve">Aqua ad 27 {1/2} lineas</s> </p> <p> <s xml:id="echoid-s7167" xml:space="preserve">Spiritus Vini ad 12 lineas.</s> <s xml:id="echoid-s7168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7169" xml:space="preserve">Sunt autem gravitates ſpecificæ horum fluidorum inter ſe, uti <lb/>hæc tabella oſtendit.</s> <s xml:id="echoid-s7170" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Alcohol # 866 # Oleum Tartari # 1550 <lb/>Oleum Thereb. # 874 # Oleum Vitrioli # 1700 <lb/>Oleum Rapar. # 913 # Mercurius # 14000 <lb/>Aqua # 1000 # Urina # 1030 <lb/>Spiritus Nitri # 1315 # Spirit. Sal. Ammon. # 1120 <lb/></note> <p> <s xml:id="echoid-s7171" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7172" xml:space="preserve">1. </s> <s xml:id="echoid-s7173" xml:space="preserve">Ex hiſce experimentis liquet adſcenſum Fluidorum non <lb/>fieri in ratione inverſa gravitatum ſuarum: </s> <s xml:id="echoid-s7174" xml:space="preserve">quippe Alcohol omnium <lb/>leviſſimum ad minimam adſcendit altitudinem, & </s> <s xml:id="echoid-s7175" xml:space="preserve">Oleum Vitrioli ad-<lb/>modum grave adſcendit ad majorem altitudinem, imo excelſius quam <lb/>Aqua elevatur: </s> <s xml:id="echoid-s7176" xml:space="preserve">Omnium vero altiſſime elevatur Urina & </s> <s xml:id="echoid-s7177" xml:space="preserve">Sp. </s> <s xml:id="echoid-s7178" xml:space="preserve">Salis <lb/>Ammoniaci; </s> <s xml:id="echoid-s7179" xml:space="preserve">è contrario minime omnium Mercurius adſcendit.</s> <s xml:id="echoid-s7180" xml:space="preserve"/> </p> <pb o="300" file="0314" n="314" rhead="DISSERTATIO"/> <p> <s xml:id="echoid-s7181" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7182" xml:space="preserve">2. </s> <s xml:id="echoid-s7183" xml:space="preserve">Unde etiam manifeſto ſequitur Adſcenſum Fluidorum <lb/>in tubos nequaquam pendere a premente aëre quocunque, magis <lb/>gravitante ſupra ſuperficiem Fluidorum in vaſe poſitorum, quam qui-<lb/>dem intus in tubis. </s> <s xml:id="echoid-s7184" xml:space="preserve">Conceperant enim Hooke in Micrographia <lb/>Obſerv. </s> <s xml:id="echoid-s7185" xml:space="preserve">6. </s> <s xml:id="echoid-s7186" xml:space="preserve">& </s> <s xml:id="echoid-s7187" xml:space="preserve">ex illo deinde Sinclarus in arte Gravit. </s> <s xml:id="echoid-s7188" xml:space="preserve">pag. </s> <s xml:id="echoid-s7189" xml:space="preserve">161. <lb/></s> <s xml:id="echoid-s7190" xml:space="preserve">tum Sturmius in Colleg. </s> <s xml:id="echoid-s7191" xml:space="preserve">Cur. </s> <s xml:id="echoid-s7192" xml:space="preserve">Tent. </s> <s xml:id="echoid-s7193" xml:space="preserve">8. </s> <s xml:id="echoid-s7194" xml:space="preserve">Honor. </s> <s xml:id="echoid-s7195" xml:space="preserve">Fabry in Phyſ. </s> <s xml:id="echoid-s7196" xml:space="preserve">Tr. </s> <s xml:id="echoid-s7197" xml:space="preserve"><lb/>5. </s> <s xml:id="echoid-s7198" xml:space="preserve">Lib. </s> <s xml:id="echoid-s7199" xml:space="preserve">2. </s> <s xml:id="echoid-s7200" xml:space="preserve">prop. </s> <s xml:id="echoid-s7201" xml:space="preserve">235 pag. </s> <s xml:id="echoid-s7202" xml:space="preserve">165. </s> <s xml:id="echoid-s7203" xml:space="preserve">Leeuwenhoek in Continuat. </s> <s xml:id="echoid-s7204" xml:space="preserve">Ar-<lb/>can. </s> <s xml:id="echoid-s7205" xml:space="preserve">Natur. </s> <s xml:id="echoid-s7206" xml:space="preserve">Epiſt. </s> <s xml:id="echoid-s7207" xml:space="preserve">131. </s> <s xml:id="echoid-s7208" xml:space="preserve">Bernouille de Gravit. </s> <s xml:id="echoid-s7209" xml:space="preserve">ætheris. </s> <s xml:id="echoid-s7210" xml:space="preserve">pag. </s> <s xml:id="echoid-s7211" xml:space="preserve">239. </s> <s xml:id="echoid-s7212" xml:space="preserve"><lb/>Rohaultus in Phyſica. </s> <s xml:id="echoid-s7213" xml:space="preserve">Mairan in L’ Hiſt. </s> <s xml:id="echoid-s7214" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s7215" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7216" xml:space="preserve">1722. </s> <s xml:id="echoid-s7217" xml:space="preserve"><lb/>in Tubis his, ob anguſtiam, contineri minus aëris, quam quidem <lb/>in atmoſphæra ambiente, & </s> <s xml:id="echoid-s7218" xml:space="preserve">idcirco Aquam in vaſculo, cui tubi <lb/>immerguntur, plus premi â gravitate atmoſphæræ, quam quidem <lb/>Aqua, quæ cavitati Tuborum reſpondet, & </s> <s xml:id="echoid-s7219" xml:space="preserve">idcirco Aquam in Tu-<lb/>bos adſcendere, quoniam minorem in iis repperiret reſiſtentiam: </s> <s xml:id="echoid-s7220" xml:space="preserve">ſed <lb/>ſi conceſſero Aërem non tam denſum copioſumve deprehendi in <lb/>Tubis, quam quidem eſt ille ambiens atmoſphæræ, a cujus preſſio-<lb/>ne majori Aqua & </s> <s xml:id="echoid-s7221" xml:space="preserve">Fluida plus elevabuntur in tubis; </s> <s xml:id="echoid-s7222" xml:space="preserve">neceſſe erit <lb/>ex legibus Hydroſtaticis, ut altitudines Fluidorum ſint in tubis in <lb/>ratione inverſa gravitatum ſuarum: </s> <s xml:id="echoid-s7223" xml:space="preserve">Sed hæc Lex non obtinet in <lb/>Experimentis, tum enim altiſſime elevari deberet Alcohol, tum O-<lb/>leum Therebinthinæ; </s> <s xml:id="echoid-s7224" xml:space="preserve">minus tum Oleum raparum, dein Aqua <lb/>iterum minus; </s> <s xml:id="echoid-s7225" xml:space="preserve">tum Urina adhuc minus, & </s> <s xml:id="echoid-s7226" xml:space="preserve">Sp Salis Ammoniaci ad huc <lb/>minus; </s> <s xml:id="echoid-s7227" xml:space="preserve">attamen nihil ejuſmodi obſervatur: </s> <s xml:id="echoid-s7228" xml:space="preserve">Quamobrem ſtatui ne-<lb/>quit, hunc adſcenſum pendere a preſſione aëris: </s> <s xml:id="echoid-s7229" xml:space="preserve">multo minus poteſt <lb/>pendere a preſſione inæquali alterius ſubtilioris aëris, quippe eadem <lb/>manet diſſicultas quoad adſcenſum, qui non eſt in ratione inverſa gra-<lb/>vitatis. </s> <s xml:id="echoid-s7230" xml:space="preserve">præterea ille aër tubos tam amplos facile ingrederetur. </s> <s xml:id="echoid-s7231" xml:space="preserve"><lb/>3° modo hypotheticè aſſumitur, at non demonſtratur: </s> <s xml:id="echoid-s7232" xml:space="preserve"><lb/>idcirco Viri Clariſſimi Carreus, Petitus aliique aërem, ut cauſam ad-<lb/>ſcendentium Fluidorum in Tubos penitus rejecerunt: </s> <s xml:id="echoid-s7233" xml:space="preserve">nec eum poſſe <lb/>eſſe cauſam ulterius patebit, quando demonſtrabimus in vacuo æque <lb/>elevari Fluida quam in aëre aperto. </s> <s xml:id="echoid-s7234" xml:space="preserve">Cæteroquin confoditur opinio <lb/>ex alio experimento, in quo tubus fuit ſumtus, per quem Oleum <lb/>Therebinthinæ, vel Olivarum tranſiit, quod tamen penitus poſtea <lb/>excuſſum reliquit aperturam tubi patulam: </s> <s xml:id="echoid-s7235" xml:space="preserve">ejuſmodi tubus Aquam <lb/>non elevat, etiamſi huic impoſitus: </s> <s xml:id="echoid-s7236" xml:space="preserve">cur Aqua non adſcendit, ſi <pb o="301" file="0315" n="315" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> aër exterior plus premat in reliquam Aquam, quam in eam, quæ <lb/>cavo tubi reſpondet? </s> <s xml:id="echoid-s7237" xml:space="preserve">Tandem cur Aqua non ingreditur tubos pa-<lb/>tulos, ſed ante annos aliquot confectos, an preſſio eadem aëris hic <lb/>deſinit? </s> <s xml:id="echoid-s7238" xml:space="preserve">affirmari hoc poteſt nullomodo.</s> <s xml:id="echoid-s7239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7240" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7241" xml:space="preserve">3. </s> <s xml:id="echoid-s7242" xml:space="preserve">Nimis feſtinanter autem concluſit Carreus Aquam <lb/>omnium altiſſime elevari; </s> <s xml:id="echoid-s7243" xml:space="preserve">id quidem conſtat ex ſuis experimentis, <lb/>verum non exploraverat adſcenſum Urinæ aut Sp. </s> <s xml:id="echoid-s7244" xml:space="preserve">Salis Ammo-<lb/>niaci, quos ambos liquores nos deprehendimus altius adſcendiſſe: <lb/></s> <s xml:id="echoid-s7245" xml:space="preserve">hinc tamen non concludo fieri non poſſe altiorem adſcenſum, quip-<lb/>pe omnes liquores dabiles non exploravi: </s> <s xml:id="echoid-s7246" xml:space="preserve">prudentius longe ratio-<lb/>cinandum eſt in Phyſicis, & </s> <s xml:id="echoid-s7247" xml:space="preserve">non niſi rariſſime ex innumeris ten-<lb/>taminibus concluſionem generalem formare poſſumus.</s> <s xml:id="echoid-s7248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7249" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7250" xml:space="preserve">4. </s> <s xml:id="echoid-s7251" xml:space="preserve">Non fiunt Fluidorum adſcenſus in ratione ſubtilitatis <lb/>Fluiditatis, aut tenacitatis ſuæ.</s> <s xml:id="echoid-s7252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7253" xml:space="preserve">Subtiliſſimum enim & </s> <s xml:id="echoid-s7254" xml:space="preserve">fluidiſſimum Fluidum eſt Alcohol, hoc <lb/>non adſcendit altiſſime, ſed humillime: </s> <s xml:id="echoid-s7255" xml:space="preserve">ſequitur ordine Sp. </s> <s xml:id="echoid-s7256" xml:space="preserve">Salis <lb/>Ammoniaci, quoad ſubtilitatem & </s> <s xml:id="echoid-s7257" xml:space="preserve">fluiditatem, verum hic valde-<lb/>quam alte adſcendit; </s> <s xml:id="echoid-s7258" xml:space="preserve">tenaciſſimum fluidum in noſtris experimentis <lb/>eſt Oleum raparum, ſed id adſcendit modo ad 21 lineas, cum mi-<lb/>nus tenax Oleum vitrioli altius elevetur nempe ad 27 lin. </s> <s xml:id="echoid-s7259" xml:space="preserve">Oleum porro <lb/>Therebinthinæ eſt tenacius Aqua, attamen non ad eandem cum hâc <lb/>adſcendit altitudinem: </s> <s xml:id="echoid-s7260" xml:space="preserve">ergo non fiunt adſcenſus eo majores quo <lb/>ſunt Fluda tenaciora: </s> <s xml:id="echoid-s7261" xml:space="preserve">ex quibus etiam cadit ſententia Virorum Do-<lb/>ctiſſimorum Iſaci Voſſii in Tract. </s> <s xml:id="echoid-s7262" xml:space="preserve">de Nilo Cap. </s> <s xml:id="echoid-s7263" xml:space="preserve">2. </s> <s xml:id="echoid-s7264" xml:space="preserve">p. </s> <s xml:id="echoid-s7265" xml:space="preserve">5. </s> <s xml:id="echoid-s7266" xml:space="preserve">& </s> <s xml:id="echoid-s7267" xml:space="preserve">6, tum <lb/>Carrei & </s> <s xml:id="echoid-s7268" xml:space="preserve">Petiti in L’ Hiſt. </s> <s xml:id="echoid-s7269" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s7270" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7271" xml:space="preserve">qui opinabantur, ad-<lb/>ſcenſum pendere ab adhæſione Fluidi ad latera tubi, & </s> <s xml:id="echoid-s7272" xml:space="preserve">ideo Flui-<lb/>dum in vaſe ambiens tubum plus deorſum premere, quam id, quod <lb/>cavo tubi reſpondet, hoc enim parietibus tubi adhærens ſua gravi-<lb/>tate minus deorſum poſſe niti & </s> <s xml:id="echoid-s7273" xml:space="preserve">agi, ambiens vero fluidum non adhæ-<lb/>rere, liberius gravitare & </s> <s xml:id="echoid-s7274" xml:space="preserve">deſcendere, atqueita majori preſſione va-<lb/>lere, ſurſumque pellere fluidum in tubi cavum: </s> <s xml:id="echoid-s7275" xml:space="preserve">At tum Oleum <lb/>raparum, quod maxime adhæret internis lateribus tubi, ad maximam <lb/>elevandum foret altitudinem, & </s> <s xml:id="echoid-s7276" xml:space="preserve">Oleum Therebinthinæ ad mino-<lb/>rem, quamvis ad majorem quam Aqua: </s> <s xml:id="echoid-s7277" xml:space="preserve">Spiritus Salis ammoniaci <lb/>cum Alcohole ad minimam nam in ambobus Spiritibus non facile <lb/>tenacitatem obſervabis: </s> <s xml:id="echoid-s7278" xml:space="preserve">Quæ omnia nequaquam reſpondent even- <pb o="302" file="0316" n="316" rhead="DISSERTATIO"/> tui: </s> <s xml:id="echoid-s7279" xml:space="preserve">prætereo eam Hypotheſin penitus cadere, quando intuemur <lb/>Experimenta cum tubis diverſæ longitudinis factis; </s> <s xml:id="echoid-s7280" xml:space="preserve">in his enim ſive <lb/>longis ſive brevibus eadem altitudo obſervanda foret, quæ non de-<lb/>prehenditur, cum evictum ſit, manifeſto altiorem fieri adſcenſum in <lb/>tubo longiori, quam in breviori: </s> <s xml:id="echoid-s7281" xml:space="preserve">Nec ex hac hypotheſi ullo modo <lb/>explicari poteſt, cur gutta minima extremo tubi appenſa penitus <lb/>intus & </s> <s xml:id="echoid-s7282" xml:space="preserve">ſurſum rapiatur, cum in hoc caſu nulla inæqualis preſſio <lb/>ambientis & </s> <s xml:id="echoid-s7283" xml:space="preserve">cavo tubi reſpondentis Aquæ fingi poſſit.</s> <s xml:id="echoid-s7284" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7285" xml:space="preserve">Inſuper ſupponamus fluidum adhærere lateribus tuborum interio-<lb/>ribus, id nihilominus eandem gravitatem habebit, qua deorſum <lb/>agitur, quam omne aliud fluidum, quippe nulla datur occaſio, <lb/>nullus locus, nullus ſitus, in quo corpus gravitatem ſuam nonſem-<lb/>per exerceat; </s> <s xml:id="echoid-s7286" xml:space="preserve">contra gravitatem ſuam adſcendit nihilominus in tu-<lb/>bos, adeoque gravitas fluidi ambientis cum ſit æqualis gravitati <lb/>fluidi interni, non poteſt eſſe cauſa hujus adſcenſus; </s> <s xml:id="echoid-s7287" xml:space="preserve">in opinione <lb/>Voſſii ſupponitur adhæſionem tollere gravitatem fluidi, vel ſaltem effi-<lb/>cere, quominus a fluido exerceatur, quod verum non eſt: </s> <s xml:id="echoid-s7288" xml:space="preserve">Unde <lb/>etiam Fayus in L’Hiſt. </s> <s xml:id="echoid-s7289" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s7290" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7291" xml:space="preserve">A°. </s> <s xml:id="echoid-s7292" xml:space="preserve">1724. </s> <s xml:id="echoid-s7293" xml:space="preserve">hanc opinio-<lb/>nem rejecit, concludens aliam eſſe cauſam phænomenãn, quam ad-<lb/>hæſionem, & </s> <s xml:id="echoid-s7294" xml:space="preserve">revera dari quandam vim agentem, tam quæ elevet <lb/>Aquam, quam quæ deprimat Mercurium infra libellam.</s> <s xml:id="echoid-s7295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7296" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7297" xml:space="preserve">5. </s> <s xml:id="echoid-s7298" xml:space="preserve">Inæquales proinde Fluidorum altitudines pendebunt a <lb/>cauſis ſingularibus, quæ ſpecifice obtinent inter Fluidum & </s> <s xml:id="echoid-s7299" xml:space="preserve">Tubum <lb/>vitreum.</s> <s xml:id="echoid-s7300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7301" xml:space="preserve">Quoniam Mercurius non adſcendit in Tubum ſibi leviter modo <lb/>impoſitum, experiundum erat, an nunquam eum ingrederetur, aut <lb/>quomodo? </s> <s xml:id="echoid-s7302" xml:space="preserve">Tubum itaque ſumſi diametri 0,5 lineæ, quem juxta <lb/>latera vaſculi vitrei continentis Mercurium demiſi, ad varias pro-<lb/>funditates, ingreſſus eum eſt Mercurius, ſed ſemper manſit in tubo <lb/>depreſſior, quam erat, qui ipſum in vaſculo ambiebat, eventus <lb/>brevitatis ergo in hac tabula adnotabo.</s> <s xml:id="echoid-s7303" xml:space="preserve"/> </p> <pb o="303" file="0317" n="317" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> <note position="right" xml:space="preserve"> <lb/>Altitudo Mercur. \\ in vaſe. \\ Lineæ # Altitudo Mercur. \\ in Tubo \\ Lin. Decimæ # Cum alio tubo anguſ- \\ tiori, diametri circi- \\ ter 0,07 lineæ # Altitud. in vaſe. \\ pol Lin. \\ in Tubo. \\ Lin. Decim. <lb/>3 # 1 <lb/>4 # 2 # 1.9 # 4.8 <lb/>5 # 3 # 2.1 # 7 <lb/>10 # 8 # 2.4 # 10 <lb/>19 # 16.8 # 2.8 # 13.7 <lb/>21 # 19 # 3.3 # 19 <lb/>24 # 21.7 # 3.7 # 23.5 <lb/>28 # 26 <lb/>33 # 30.8 <lb/>37 # 35.1 <lb/></note> <p> <s xml:id="echoid-s7304" xml:space="preserve">Cum aliis Tubis ſimilia inſtitui experimenta, quæ prolixiora ſunt <lb/>quam ut hic afferam: </s> <s xml:id="echoid-s7305" xml:space="preserve">Cl. </s> <s xml:id="echoid-s7306" xml:space="preserve">Jurinus in iiſdem tentaminibus aliquantum <lb/>quoque occupatus fuit, in omnibus vero a me factis experimentis <lb/>obtinent ſequelæ eædem, quas nunc ex propoſitis eliciam.</s> <s xml:id="echoid-s7307" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7308" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7309" xml:space="preserve">1. </s> <s xml:id="echoid-s7310" xml:space="preserve">Eadem obtinet differentia inter altitudinem Mercurii <lb/>in vaſculo, & </s> <s xml:id="echoid-s7311" xml:space="preserve">eam in tubo, nam capta cum uno tubo experimenta <lb/>oſtendunt differentiam utriuſque altitudinis æqualem duabus lineis; <lb/></s> <s xml:id="echoid-s7312" xml:space="preserve">alia cum altero tubo æqualem 14: </s> <s xml:id="echoid-s7313" xml:space="preserve">adeoque pars Tubi ſuperior vacua <lb/>Mercurio ſemper minuitur in ratione immerſionis.</s> <s xml:id="echoid-s7314" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7315" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7316" xml:space="preserve">2. </s> <s xml:id="echoid-s7317" xml:space="preserve">Eſt hæc differentia inter altitudinem Mercurii in Tubis, <lb/>& </s> <s xml:id="echoid-s7318" xml:space="preserve">in vaſculo eo major, quo Tubiſunt anguſtiores, & </s> <s xml:id="echoid-s7319" xml:space="preserve">videtur eſſe po-<lb/>ſitis Tubis æque longis, in ratione reciproca diametrorum Tuborum; <lb/></s> <s xml:id="echoid-s7320" xml:space="preserve">diametri enim eorum, quos examinavimus, ſunt inter ſe uti 50, ad 7. </s> <s xml:id="echoid-s7321" xml:space="preserve"><lb/>quæ ſunt inter ſe uti 7 ad 1 nam minutia eſt negligenda, quia non <lb/>perfecte menſurare poſſumus diametros Tuborum: </s> <s xml:id="echoid-s7322" xml:space="preserve">ſed ſunt differen-<lb/>tiæ altitudinum Mercurii in vaſculo & </s> <s xml:id="echoid-s7323" xml:space="preserve">in Tubis obſervatæ 2, & </s> <s xml:id="echoid-s7324" xml:space="preserve">14 <lb/>linear: </s> <s xml:id="echoid-s7325" xml:space="preserve">quæ ſunt uti 1 ad 7, quorum ratio inverſa eſt 7 ad 1.</s> <s xml:id="echoid-s7326" xml:space="preserve"/> </p> <pb o="304" file="0318" n="318" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div197" type="section" level="1" n="197"> <head xml:id="echoid-head211" xml:space="preserve">CAPUT QUARTUM.</head> <head xml:id="echoid-head212" style="it" xml:space="preserve">De Tubis rectis ſed diver ſam diametrum in ſua longitudine <lb/>continentibus.</head> <p> <s xml:id="echoid-s7327" xml:space="preserve">Poſſunt hujuſmodi tubi eſſe coni, vel cylindri duo ſibi applicati, <lb/>quorum unus capacior eſt altero Experimenta cum duplici ge-<lb/>nere inſtituta nunc adnotabo: </s> <s xml:id="echoid-s7328" xml:space="preserve">primum cum Tubis Conicis, qui <lb/>omnes 5 pollices longi erant & </s> <s xml:id="echoid-s7329" xml:space="preserve">recenter facti.</s> <s xml:id="echoid-s7330" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7331" xml:space="preserve">1. </s> <s xml:id="echoid-s7332" xml:space="preserve">Sumſi tubum conicum cujus exilior pars cava diametrum ha-<lb/>buit lineæ 0. </s> <s xml:id="echoid-s7333" xml:space="preserve">10 diameter partis ampliſſimæ erat lineæ 0. </s> <s xml:id="echoid-s7334" xml:space="preserve">15 anguſ-<lb/>tiori extremo aquæ immiſſo, adſcenſus ſupra ſuperficiem aquæ ob-<lb/>ſervatus fuit pollic. </s> <s xml:id="echoid-s7335" xml:space="preserve">2. </s> <s xml:id="echoid-s7336" xml:space="preserve">85. </s> <s xml:id="echoid-s7337" xml:space="preserve">parte latiori aquæ immiſſa, adſcenſus ob-<lb/>ſervabatur poll. </s> <s xml:id="echoid-s7338" xml:space="preserve">2. </s> <s xml:id="echoid-s7339" xml:space="preserve">78. </s> <s xml:id="echoid-s7340" xml:space="preserve">Eodem modo reliqua inſtitui experimenta, quæ <lb/>in hac tabula ſimul exhibentur.</s> <s xml:id="echoid-s7341" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># diameter \\ anguſt. part. \\ Lineæ # diameter \\ latior part. \\ Lineæ # adſcenſus \\ in part. ang. \\ poll. # adſcenſus \\ in part. latior \\ pollic. <lb/>2° # 0,10 # 0,60 # 2,6 0 # 0,8 0 <lb/>3° # 0,8 # 0,50 # 2,7 5 # 1,1 0 <lb/>4° # 0,11 # 0,60 # 2,6 8 # 0,8 5 <lb/>5° # 0,12 # 0,60 # 2,3 7 # 0,7 6 <lb/>6° # 0,40 # 0,80 # 1,6 0 # 0,6 0 <lb/>7° # 0,50 # 0,80 # 0,8 0 # 0,6 0 <lb/>8° # 0,50 # 0,150 # 0,8 0 # 0,3 5 <lb/>2° # 0,50 # 0,130 # 0,8 0 # 0,4 0 <lb/></note> <p> <s xml:id="echoid-s7342" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7343" xml:space="preserve">1. </s> <s xml:id="echoid-s7344" xml:space="preserve">Liquet ex his experimentis poſito uno extremo diver-<lb/>ſorum Tuborum æque lato, altero autem inæqualis latitudinis, al- <pb o="305" file="0319" n="319" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> tiores fieri adſcenſus in anguſtioribus, quam in latioribus: </s> <s xml:id="echoid-s7345" xml:space="preserve">nam in <lb/>Experimento ſecundo, quarto, & </s> <s xml:id="echoid-s7346" xml:space="preserve">quinto, extremitas una fuit <lb/>lin 0,60. </s> <s xml:id="echoid-s7347" xml:space="preserve">aliæ extremitates 0,10. </s> <s xml:id="echoid-s7348" xml:space="preserve">0,11. </s> <s xml:id="echoid-s7349" xml:space="preserve">0,12.</s> <s xml:id="echoid-s7350" xml:space="preserve">, tum vero adſcen-<lb/>ſusfuerunt poll. </s> <s xml:id="echoid-s7351" xml:space="preserve">2,60, & </s> <s xml:id="echoid-s7352" xml:space="preserve">2,68. </s> <s xml:id="echoid-s7353" xml:space="preserve">tum 2,37. </s> <s xml:id="echoid-s7354" xml:space="preserve">in Experimento quarto ali-<lb/>qua anomalia eſt: </s> <s xml:id="echoid-s7355" xml:space="preserve">hinc ſemper plurima ſunt inſtituenda Experimen-<lb/>ta antequam aliquid concludi poteſt: </s> <s xml:id="echoid-s7356" xml:space="preserve">idcirco Sextum & </s> <s xml:id="echoid-s7357" xml:space="preserve">Septimum <lb/>conſulatur, ea ambo confirmant iterum id, quod collegeram. </s> <s xml:id="echoid-s7358" xml:space="preserve">Si <lb/>experimenta intueamur, in quibus extremitates anguſtiores fuerunt <lb/>æquales, diſcrepantibus latioribus, aſſertum noſtrum eodem mo-<lb/>do ſtabit, uti patet ex Septimo, Octavo & </s> <s xml:id="echoid-s7359" xml:space="preserve">Nono Experimento.</s> <s xml:id="echoid-s7360" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div198" type="section" level="1" n="198"> <head xml:id="echoid-head213" xml:space="preserve">EXPERIMENTUM X.</head> <p> <s xml:id="echoid-s7361" xml:space="preserve">Si ſumatur Tubus cylindricus purus, in quo Aqua adſcendit ad alti-<lb/>tudinem 10 linearum; </s> <s xml:id="echoid-s7362" xml:space="preserve">dein depuretur ab Aqua ejusque orificium in <lb/>flamma pura coarctetur; </s> <s xml:id="echoid-s7363" xml:space="preserve">tum iterum immittatur Aquæ, parte co-<lb/>arctata ſubmerſa, nunquam elevabitur Aqua ad priorem altitudi-<lb/>nem, ſed ſemper ad minorem, deprehendi enim in memorato Tu-<lb/>bo eam modo adſcendiſſe ad 7 lineas.</s> <s xml:id="echoid-s7364" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div199" type="section" level="1" n="199"> <head xml:id="echoid-head214" xml:space="preserve">EXPERIMENTUM XI.</head> <p> <s xml:id="echoid-s7365" xml:space="preserve">Si Tubus cylindricus purus, longus, immittatur aquæ, cujus <lb/>notetur adſcenſus; </s> <s xml:id="echoid-s7366" xml:space="preserve">tum exſugatur aqua, & </s> <s xml:id="echoid-s7367" xml:space="preserve">extremitas ſuperior <lb/>Tubi, quæ non fuit aquæ immiſſa, igne paulum coarcte-<lb/>tur; </s> <s xml:id="echoid-s7368" xml:space="preserve">deinde extremitas Tubi eadem, quæ ante, aquæ immittatur, <lb/>nunquam hæc adſcendit ad eandem altitudinem, quam prius, ſed <lb/>ſemper ad minorem,</s> </p> <p> <s xml:id="echoid-s7369" xml:space="preserve">Corol.</s> <s xml:id="echoid-s7370" xml:space="preserve">. Hæc experimenta penitus proſternunt explicationem hy-<lb/>potheticam Cl. </s> <s xml:id="echoid-s7371" xml:space="preserve">Carrei, & </s> <s xml:id="echoid-s7372" xml:space="preserve">Petiti; </s> <s xml:id="echoid-s7373" xml:space="preserve">ſecundum hoſce enim Philoſo-<lb/>phos, ad majorem altitudinem aqua elevanda foret coarctatâ ex-<lb/>tremitate inferiori, uti in Exp. </s> <s xml:id="echoid-s7374" xml:space="preserve">X. </s> <s xml:id="echoid-s7375" xml:space="preserve">cum è contrario ad minorem <lb/>adſcendat altitudinem.</s> <s xml:id="echoid-s7376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7377" xml:space="preserve">Ambo Experimenta non videntur habere eandem cauſam, ſed <lb/>diverſam. </s> <s xml:id="echoid-s7378" xml:space="preserve">in Experimento X. </s> <s xml:id="echoid-s7379" xml:space="preserve">Altitudo Aquæ minor fuit anguſtatâ orâ <lb/>Tubi, quia hæc agit in Aquam, veluti Tubus anguſtior, eam altius vel <pb o="306" file="0320" n="320" rhead="DISSERTATIO"/> propius ad ſe rapiendo, idcirco Aqua, quæ adſcendit in Tubum, <lb/>magis agitur verſus oram inferiorem coarctatam, quam ſi ora ean-<lb/>dem cum Tubo amplitudinem retinuiſſet, unde minor Aquæ altitu-<lb/>do fit.</s> <s xml:id="echoid-s7380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7381" xml:space="preserve">Videretur proinde in Exper. </s> <s xml:id="echoid-s7382" xml:space="preserve">II°, in quo ora anguſtata eſt ad ſupre-<lb/>mum, Aquam altius debere adſcendere quam cum ora non anguſtata <lb/>erat; </s> <s xml:id="echoid-s7383" xml:space="preserve">imo procul dubio hoc eveniret: </s> <s xml:id="echoid-s7384" xml:space="preserve">ſed quia Tubi ſunt pleni aëre, at-<lb/>que Aër non niſi paulum difficilius per eos tranſit, longe difficilius <lb/>tranſibit per oram angſtatam, quam per ampliatam; </s> <s xml:id="echoid-s7385" xml:space="preserve">idcirco Aër <lb/>reſiſtit adſcendenti liquori, impeditque quominus eandem acquirat <lb/>altitudinem: </s> <s xml:id="echoid-s7386" xml:space="preserve">hoc ratiocinium penitus confirmatur. </s> <s xml:id="echoid-s7387" xml:space="preserve">ſi ad lentum <lb/>aquæ adſcenſum in Tubum attendimus, qui in cylindrico multo <lb/>conſpicitur rapidior.</s> <s xml:id="echoid-s7388" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div200" type="section" level="1" n="200"> <head xml:id="echoid-head215" xml:space="preserve">EXPERIMENTUM. XII.</head> <p> <s xml:id="echoid-s7389" xml:space="preserve">Sit in Fig. </s> <s xml:id="echoid-s7390" xml:space="preserve">2. </s> <s xml:id="echoid-s7391" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7392" xml:space="preserve">XI. </s> <s xml:id="echoid-s7393" xml:space="preserve">Tubus AB utrinque apertus, unum <lb/>duoſve pedes longus, cujus pars inferior deſinat in capillarem angu-<lb/>ſtiam B: </s> <s xml:id="echoid-s7394" xml:space="preserve">huic Mercurius inſuſus non effluet ex B, modo orificium B ſit <lb/>anguſtum: </s> <s xml:id="echoid-s7395" xml:space="preserve">tum vero immergatur Tubus vaſculo continenti alium <lb/>Mercurium, quem ſimulac ille in B, attingit, effluet omnis ex <lb/>Tubo A B per foramen B.</s> <s xml:id="echoid-s7396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7397" xml:space="preserve">Impleatur de novo Tubus Mercurio, tum apertura B paulum dif <lb/>fringatur, ut patentior fiat. </s> <s xml:id="echoid-s7398" xml:space="preserve">hæreatque perpendiculariter in Aëre <lb/>ſuſpenſus, ex apertura B effluet aliquantum Mercurii, non omnis, <lb/>dein menſuretur altitudo Mercurii ſuſpenſi in Tubo, & </s> <s xml:id="echoid-s7399" xml:space="preserve">comparetur <lb/>cum altitudine ſuperiori, invenietur eſſe in ratione reciproca dia-<lb/>metrorum utriuſque aperturæ.</s> <s xml:id="echoid-s7400" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7401" xml:space="preserve">Idem fit ſi Experimenrum inftituatur cum infundibulo vitreo in <lb/>caudam gracilem terminato, quemadmodum Cl. </s> <s xml:id="echoid-s7402" xml:space="preserve">Jurinus in Philoſ. <lb/></s> <s xml:id="echoid-s7403" xml:space="preserve">Tranſ. </s> <s xml:id="echoid-s7404" xml:space="preserve">N°. </s> <s xml:id="echoid-s7405" xml:space="preserve">355. </s> <s xml:id="echoid-s7406" xml:space="preserve">pag. </s> <s xml:id="echoid-s7407" xml:space="preserve">739. </s> <s xml:id="echoid-s7408" xml:space="preserve">adnotavit, huic enim Experimentum <lb/>debetur.</s> <s xml:id="echoid-s7409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7410" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7411" xml:space="preserve">1. </s> <s xml:id="echoid-s7412" xml:space="preserve">Ergo vis retinens Mercurium in Tubo videtur pendere a <lb/>certa conditione aperturæ B, qua poſitâ anguſtâ valde, vis reti-<lb/>nens eſt major, minor autem eſt eâ ampliatâ.</s> <s xml:id="echoid-s7413" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7414" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7415" xml:space="preserve">2. </s> <s xml:id="echoid-s7416" xml:space="preserve">Sed ea vis retinens Mercurium in Tubo ſuperatur ab alio <pb o="307" file="0321" n="321" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> Mercurio in vaſculo, unde ſtatim ad mutuum Mercurii contactum, <lb/>ſecundum leges gravitatis, deſcendit ex Tubo omnis, imo depreſſior <lb/>ad oram B eſt, quam ſecundum leges Hydroſtaticas deberet: </s> <s xml:id="echoid-s7417" xml:space="preserve">in-<lb/>dicio manifeſto, Mercurium plus agere in Mercurium, quam vi-<lb/>trum in eundem agit. </s> <s xml:id="echoid-s7418" xml:space="preserve">Memorabile eſt Experimentum â Cl. </s> <s xml:id="echoid-s7419" xml:space="preserve">Petito <lb/>deſcriptum in L’Hiſt. </s> <s xml:id="echoid-s7420" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s7421" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7422" xml:space="preserve">A°. </s> <s xml:id="echoid-s7423" xml:space="preserve">1724. </s> <s xml:id="echoid-s7424" xml:space="preserve">Sumſit ſi-<lb/>phonem inæqualium crurum A B C D. </s> <s xml:id="echoid-s7425" xml:space="preserve">Vid. </s> <s xml:id="echoid-s7426" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7427" xml:space="preserve">XI. </s> <s xml:id="echoid-s7428" xml:space="preserve">Fig. </s> <s xml:id="echoid-s7429" xml:space="preserve">3. </s> <s xml:id="echoid-s7430" xml:space="preserve">cruri <lb/>A B immiſit Mercurium uſque ad F F, cujus ſuperficies ſtetit con-<lb/>vexa, & </s> <s xml:id="echoid-s7431" xml:space="preserve">Mercurius ingreſſus fuit tubum graciliorem uſque ad <lb/>Ctantum, quodeſt infra ſuperſiciem F F, erat hæc quoque ſuperficies <lb/>convexa: </s> <s xml:id="echoid-s7432" xml:space="preserve">Effuſo Mercurio, crura ſiphonis obduxit interne cerâ lique-<lb/>factâ, vel ſebo; </s> <s xml:id="echoid-s7433" xml:space="preserve">& </s> <s xml:id="echoid-s7434" xml:space="preserve">iterum infudit Mercurium in A B uſque ad FF, <lb/>adſcendit tum Mercurius in Tubum graciliorem uſque ad K, ſupra <lb/>libellam F, F, habuitque ſuperficiem concavam.</s> <s xml:id="echoid-s7435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7436" xml:space="preserve">Vis, quæ in graciliore crure deprimebat Mercurium vel ipſi re-<lb/>ſiſtebat, ſublata aut impedita fuit a ſebo illiniente parietes, verum <lb/>vis Tubi elevans agit in Sebum, nam id, cum liqueſactum eſt, ele-<lb/>vatur quemadmodum Aqua; </s> <s xml:id="echoid-s7437" xml:space="preserve">idcirco hæc interna Tubi vis ad ſilen-<lb/>tium deducitur reſpectu Mercurii & </s> <s xml:id="echoid-s7438" xml:space="preserve">tota impenditur Sebo: </s> <s xml:id="echoid-s7439" xml:space="preserve">eleva-<lb/>tur enim nunc Mercurius in Tubum illinitum C D, quatenus elevatur <lb/>ab ipſo ſebo vel cerâ.</s> <s xml:id="echoid-s7440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7441" xml:space="preserve">Dein immiſſus fuit cruri ampliori A B, Tubus E E ejuſdem dia-<lb/>metri cum C D, quem ingreſſus fuit Mercurius ad altitudinem I, ean-<lb/>dem cum C in tubo C D.</s> <s xml:id="echoid-s7442" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div201" type="section" level="1" n="201"> <head xml:id="echoid-head216" xml:space="preserve">EXPERIMENTUM XIII.</head> <p> <s xml:id="echoid-s7443" xml:space="preserve">Nunc de Tubis cylindricis, quorum bini ſibi juncti ſunt, agendum <lb/>erit. </s> <s xml:id="echoid-s7444" xml:space="preserve">Sumatur Tubus C D Tab. </s> <s xml:id="echoid-s7445" xml:space="preserve">XI Fig. </s> <s xml:id="echoid-s7446" xml:space="preserve">4. </s> <s xml:id="echoid-s7447" xml:space="preserve">cujus una pars cylindri-<lb/>ca eſt amplior, altera anguſtior, breviſque: </s> <s xml:id="echoid-s7448" xml:space="preserve">immiſſâ parte graci-<lb/>liori Aquæ, adſcenſus fiet ad altitudinem æqualem longitudini A P, <lb/>ſi vero pars amplior C. </s> <s xml:id="echoid-s7449" xml:space="preserve">Aquæ immittitur, adſcenſus fiet ad altitudinem <lb/>B F: </s> <s xml:id="echoid-s7450" xml:space="preserve">Tubo hoc penitus adimpleto Aqua, pars C ſubmergatur infra <lb/>Aquæ ſuperficiem A B in vaſculo, manebit Aqua in Tubo ſuſpenſa.</s> <s xml:id="echoid-s7451" xml:space="preserve"/> </p> <pb o="308" file="0322" n="322" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div202" type="section" level="1" n="202"> <head xml:id="echoid-head217" xml:space="preserve">EXPERIMENTUM XIV.</head> <p> <s xml:id="echoid-s7452" xml:space="preserve">Sed quando pars Tubi gracilior D, in fig. </s> <s xml:id="echoid-s7453" xml:space="preserve">5. </s> <s xml:id="echoid-s7454" xml:space="preserve">immergitur aquæ, <lb/>converſo Tubo; </s> <s xml:id="echoid-s7455" xml:space="preserve">aqua illico ſubſidet, manetque ad altitudinem <lb/>DG = BF.</s> <s xml:id="echoid-s7456" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div203" type="section" level="1" n="203"> <head xml:id="echoid-head218" xml:space="preserve">EXPERIMENTUM XV.</head> <p> <s xml:id="echoid-s7457" xml:space="preserve">Sumatur Tubus, priori ſimilis, cujus una pars RC amplior, RD <lb/>gracilior, Tab. </s> <s xml:id="echoid-s7458" xml:space="preserve">XI. </s> <s xml:id="echoid-s7459" xml:space="preserve">fig. </s> <s xml:id="echoid-s7460" xml:space="preserve">4. </s> <s xml:id="echoid-s7461" xml:space="preserve">longitudine duntaxat diſcrepans â priori: </s> <s xml:id="echoid-s7462" xml:space="preserve">pars <lb/>amplior immittatur Aquæ, ſitque B F altitudo ad quam hæc ad-<lb/>ſcendit, tum ſit AP altitudo, ad quam Aqua adſcendit in tubo gra-<lb/>ciliori: </s> <s xml:id="echoid-s7463" xml:space="preserve">cum hujus amplioris Tubi orificium C ſit immerſum Aquæ <lb/>AB, & </s> <s xml:id="echoid-s7464" xml:space="preserve">Tubus impleatur ad minorem altitudinem, quam eſt longi-<lb/>tudo Tubi amplioris, Aqua illico deſcendet ad altitudinem æqua-<lb/>lem BF: </s> <s xml:id="echoid-s7465" xml:space="preserve">ſed cum modo pauxillum Aquæ intravit Tubum graciliorem <lb/>DR, manebit totus tubus DC impletus Aqua, imo quamvis in gra-<lb/>ciliori DR non fuerit Aqua æqualis longitudini AP.</s> <s xml:id="echoid-s7466" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div204" type="section" level="1" n="204"> <head xml:id="echoid-head219" xml:space="preserve">EXPERIMENTUM XVI.</head> <p> <s xml:id="echoid-s7467" xml:space="preserve">Quando idem Tubus invertitur, ut orificium gracilioris D, Vid. </s> <s xml:id="echoid-s7468" xml:space="preserve">fig. <lb/></s> <s xml:id="echoid-s7469" xml:space="preserve">5, ſit ſub Aquâ ſubmerſum, & </s> <s xml:id="echoid-s7470" xml:space="preserve">totus Tubus uſque ad C impletus Aquâ, <lb/>effluet Aqua omnis ex Tubo ampliori, & </s> <s xml:id="echoid-s7471" xml:space="preserve">in graciliori hærebit tan-<lb/>tum ſuſpenſa ad altitudinem BF, quæ eſt ea altitudo ad quam in am-<lb/>pliori Tubo hæſiſſet, cum tamen cæteroquin ad altitudinem AP in <lb/>graciliori adſcendere ſolet.</s> <s xml:id="echoid-s7472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7473" xml:space="preserve">Sunt hæc omnia Experimenta a Cl. </s> <s xml:id="echoid-s7474" xml:space="preserve">Jurino inſtituta, quæ demon-<lb/>ſtrant, quanta ſit vis retinens Aquam in Tubis gracilioribus: </s> <s xml:id="echoid-s7475" xml:space="preserve">ſimulac <lb/>enim Aqua impleverit penitus Tubum amplum, & </s> <s xml:id="echoid-s7476" xml:space="preserve">dein partem ali-<lb/>quam gracilioris Tubi, manet Aqua penitus ſuſpenſa in ambobus.</s> <s xml:id="echoid-s7477" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7478" xml:space="preserve">Ex hiſce vero Experimentis liquet clare, cauſam ſuſpendentem <lb/>non poſſe eſſe preſſionem alicujus ambientis fluidi majorem <lb/>circa tubum, quam intra: </s> <s xml:id="echoid-s7479" xml:space="preserve">nam a preſſione æquali idem modo effectus, <lb/>ſive eadem aquæ altitudo contingat neceſſe eſt; </s> <s xml:id="echoid-s7480" xml:space="preserve">non enim in fig. </s> <s xml:id="echoid-s7481" xml:space="preserve">4.</s> <s xml:id="echoid-s7482" xml:space="preserve"> <pb o="309" file="0323" n="323" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> a preſſione eadem poſſet ſuſtineri altitudo Aquæ FB, & </s> <s xml:id="echoid-s7483" xml:space="preserve">CRD, quæ <lb/>multo major eſt: </s> <s xml:id="echoid-s7484" xml:space="preserve">ut autem ulterius evincatur magnitudo virtutis <lb/>Aquam ſuſpendentis ex anguſto Tubo aut orificio, ſequentia Expe-<lb/>rimenta Jurinus fecit.</s> <s xml:id="echoid-s7485" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div205" type="section" level="1" n="205"> <head xml:id="echoid-head220" xml:space="preserve">EXPERIMENTUM XVII.</head> <p> <s xml:id="echoid-s7486" xml:space="preserve">Sumatur vas magnum cujuſcunque figuræ ut ABC in fig. </s> <s xml:id="echoid-s7487" xml:space="preserve">6. </s> <s xml:id="echoid-s7488" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7489" xml:space="preserve">XI. <lb/></s> <s xml:id="echoid-s7490" xml:space="preserve">jus extremitas C abeat in Tubum capillarem, hoc impleatur Aqua, <lb/>dein invertatur, & </s> <s xml:id="echoid-s7491" xml:space="preserve">margo AB attingat ſuperficiem alterius aquæ, <lb/>manebit totum vas ABC impletum.</s> <s xml:id="echoid-s7492" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div206" type="section" level="1" n="206"> <head xml:id="echoid-head221" xml:space="preserve">EXPERIMENTUM XVIII.</head> <p> <s xml:id="echoid-s7493" xml:space="preserve">Fig. </s> <s xml:id="echoid-s7494" xml:space="preserve">7 Tab. </s> <s xml:id="echoid-s7495" xml:space="preserve">XI. </s> <s xml:id="echoid-s7496" xml:space="preserve">Sit vas cylindricum BCFG, cujus pars ſuperior F A G <lb/>deſinat in Tubum capillarem, impleatur Aqua ad altitudinem FG, ita <lb/>tamen ut non attingat partem ſuperiorem infundibuli AFG tum tubus <lb/>A modo ſuperius humectetur digito. </s> <s xml:id="echoid-s7497" xml:space="preserve">manebit Aqua in hoc vaſe ſuſ-<lb/>penſa ad altitudinem FG, ſi loco Aquæ ſumatur Mercurius, idem <lb/>ſit experimenti ſucceſſus, niſi quod Mercurius ſtet depreſſior.</s> <s xml:id="echoid-s7498" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7499" xml:space="preserve">Hæc Experimenta ſunt eadem ſive inſtituantur cum Aqua vulgari, <lb/>ſive cum Aquâ, ex qua omnis eductus eſt Aër: </s> <s xml:id="echoid-s7500" xml:space="preserve">Prima fronte vide-<lb/>rentur hæc phænomena pendere a denegato aëris introitu per ori-<lb/>ficium ſubtilius C in Fig. </s> <s xml:id="echoid-s7501" xml:space="preserve">6. </s> <s xml:id="echoid-s7502" xml:space="preserve">vel A in Fig. </s> <s xml:id="echoid-s7503" xml:space="preserve">7. </s> <s xml:id="echoid-s7504" xml:space="preserve">unde Aër premens ſu-<lb/>pra vel contra ſuperficiem Aquæ inferiorem, eam in vaſis ſuſtine-<lb/>ret: </s> <s xml:id="echoid-s7505" xml:space="preserve">ſed huc non advocandam eſſe Aëris preſſionem Jurinus alio <lb/>probavit Experimento.</s> <s xml:id="echoid-s7506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7507" xml:space="preserve">Præparabatur Tubus 35 pollic. </s> <s xml:id="echoid-s7508" xml:space="preserve">longus, diametri {1/4} pollic. </s> <s xml:id="echoid-s7509" xml:space="preserve">cujus <lb/>una extremitas in apicem capillarem deſinebat: </s> <s xml:id="echoid-s7510" xml:space="preserve">hic penitus imple-<lb/>batur Aquâ, tum ponebatur ſub recipiente, ex quo omnis edu-<lb/>cebatur Aër, Aqua manente ſuſpenſa ad eandem in Tubo altitudi-<lb/>nem: </s> <s xml:id="echoid-s7511" xml:space="preserve">non ergo huc preſſio Aëris advocari poterit, quia, ab hac ſi <lb/>penderet phænomenon, in vacuo Aqua omnis ex Tubo ſuâ gravita-<lb/>te effluxiſſet.</s> <s xml:id="echoid-s7512" xml:space="preserve"/> </p> <pb o="310" file="0324" n="324" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div207" type="section" level="1" n="207"> <head xml:id="echoid-head222" xml:space="preserve">CAPUT QUINTUM.</head> <head xml:id="echoid-head223" style="it" xml:space="preserve">De Tubis ubivis æque latis, ſed vario modo inflexis.</head> <p> <s xml:id="echoid-s7513" xml:space="preserve">Sumſi Tubum, prius rectum, atque explorato ad quamnam alti-<lb/>tudinem Aquam perpendiculariter elevabat, ejus extremi-<lb/>tatem varios in ſlexus redegi, quos repreſentat fig. </s> <s xml:id="echoid-s7514" xml:space="preserve">8. </s> <s xml:id="echoid-s7515" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7516" xml:space="preserve">XI. <lb/></s> <s xml:id="echoid-s7517" xml:space="preserve">immiſsâque iterum extremitate A aquæ, perpendicularem annota-<lb/>vi altitudinem, ad quam adſcendebat, hancque deprehendi æqualem <lb/>altitudini priori.</s> <s xml:id="echoid-s7518" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div208" type="section" level="1" n="208"> <head xml:id="echoid-head224" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s7519" xml:space="preserve">Exploravi ad quam altitudinem Aquam elevaret alius Tubus re-<lb/>ctus, quo dein inſlexo in formam, qualem exhibet fig. </s> <s xml:id="echoid-s7520" xml:space="preserve">9. </s> <s xml:id="echoid-s7521" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7522" xml:space="preserve">XI. <lb/></s> <s xml:id="echoid-s7523" xml:space="preserve">iterumque immiſsâ extremitate A Aquæ, hæc adſcendit ad ean-<lb/>dem perpendicularem altitudinem quam ante.</s> <s xml:id="echoid-s7524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7525" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7526" xml:space="preserve">1. </s> <s xml:id="echoid-s7527" xml:space="preserve">Ergo vis Aquam in Tubos hos elevans eſt æqualis gra-<lb/>vitati altitudinis perpendicularis Aquæ Nunc enim major Aquæ quan-<lb/>titas adimplet Tubum inflexum, quam antea rectum: </s> <s xml:id="echoid-s7528" xml:space="preserve">ſed ma-<lb/>jor quantitas Aquæ non gravitat in cauſam quamcunque (ſive ſupe-<lb/>rius trahentem, vel prementem ſuperficiem reliquæ Aquæ, <lb/>nihil hucuſque de ea determino) cum ſuperfluum gravitatis ſuſtinea-<lb/>tur â parietibus Tuborum.</s> <s xml:id="echoid-s7529" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div209" type="section" level="1" n="209"> <head xml:id="echoid-head225" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s7530" xml:space="preserve">Sumatur Tubus ABCDE. </s> <s xml:id="echoid-s7531" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7532" xml:space="preserve">XI. </s> <s xml:id="echoid-s7533" xml:space="preserve">fig. </s> <s xml:id="echoid-s7534" xml:space="preserve">10. </s> <s xml:id="echoid-s7535" xml:space="preserve">cujus duo latera AB, <lb/>DE recta, quæ etiam ponantur horizonti parallelela: </s> <s xml:id="echoid-s7536" xml:space="preserve">altitudo CF <lb/>perpendicularis ſit minor ea, ad quam Aqua in Tubum eundem re-<lb/>ctum adſcendit: </s> <s xml:id="echoid-s7537" xml:space="preserve">extremitati E apponatur gutta Aquæ, rapietur Aqua in-<lb/>trorſum, adſcendet ſupra DC, deſcendet per BC, & </s> <s xml:id="echoid-s7538" xml:space="preserve">BA, uſque ad <lb/>alteram oram A, ubi quieſcet, nequaquam effluens.</s> <s xml:id="echoid-s7539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7540" xml:space="preserve">Eſt hic Tubus inſtar Siphonis æqualium crurum, qui dum magnæ <pb o="311" file="0325" n="325" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> foret capacitatis, & </s> <s xml:id="echoid-s7541" xml:space="preserve">Aquâ adimpletus, etiam non dimitteret ex ul-<lb/>la ora Aquam, modo CF ſit humilior 32 pedibus: </s> <s xml:id="echoid-s7542" xml:space="preserve">& </s> <s xml:id="echoid-s7543" xml:space="preserve">ſi Aqua attin-<lb/>gat alterutram oram E vel A etiam nihil dimittet ex altera, quic-<lb/>quid Cl. </s> <s xml:id="echoid-s7544" xml:space="preserve">Reiſelius adſeruerit.</s> <s xml:id="echoid-s7545" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div210" type="section" level="1" n="210"> <head xml:id="echoid-head226" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s7546" xml:space="preserve">Tubum capillarem inflectebam alio modo, ut tamen Siphonem <lb/>æqualium crurum repræſentaret, veluti in fig. </s> <s xml:id="echoid-s7547" xml:space="preserve">11. </s> <s xml:id="echoid-s7548" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7549" xml:space="preserve">XI. </s> <s xml:id="echoid-s7550" xml:space="preserve">ambo <lb/>extrema A, E, in eadem horiſontali linea ponebantur, altitudo per-<lb/>pendicularis CF erat minor, quam elevatio Aquæ in tubo recto eſſe ſo-<lb/>lebat: </s> <s xml:id="echoid-s7551" xml:space="preserve">impoſito extremo E aquæ, hæc ſponte ingreſſa ad D adſcendit <lb/>per DC, deſcendit per CB, fluens uſque ad A, ubi manſit, effluxit-<lb/>que nihil.</s> <s xml:id="echoid-s7552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7553" xml:space="preserve">Submerſi extremitatem E ſub Aquâ ſucceſſive, donec 3 lineis <lb/>infra ejus ſuperficiem depreſſa erat, & </s> <s xml:id="echoid-s7554" xml:space="preserve">tum modo ad A incipiebat <lb/>gutta formari, quæ tempore decidebat: </s> <s xml:id="echoid-s7555" xml:space="preserve">ad minorem altitudinis dif-<lb/>ferentiam inter Aquæ ſuperficiem & </s> <s xml:id="echoid-s7556" xml:space="preserve">oram A, nullus effluxus Aquæ <lb/>obſervabatur.</s> <s xml:id="echoid-s7557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7558" xml:space="preserve">Quondam Reiſelii Experimentum de Siphone æqualium crurum <lb/>diverſis examinans modis, Tubum BCD ferreum, 6 pedes longum, <lb/>confeceram, inflexum patiter ut fig. </s> <s xml:id="echoid-s7559" xml:space="preserve">11. </s> <s xml:id="echoid-s7560" xml:space="preserve">exhibet: </s> <s xml:id="echoid-s7561" xml:space="preserve">diametri {1/2} pol-<lb/>licis: </s> <s xml:id="echoid-s7562" xml:space="preserve">extremitates autem AB, DE erant Tubi capillares cuprei, ſin-<lb/>guli 4 poll. </s> <s xml:id="echoid-s7563" xml:space="preserve">longi: </s> <s xml:id="echoid-s7564" xml:space="preserve">ad C apertura erat cum epiſtomio, quo po-<lb/>terat inpleri Tubus aqua: </s> <s xml:id="echoid-s7565" xml:space="preserve">quamdiu eum adimplebam, ex utroque <lb/>extremo A & </s> <s xml:id="echoid-s7566" xml:space="preserve">E effluebat Aqua, ſub parvi radioli forma, eo autem <lb/>accurate impleto clauſoque epiſtomio ad E nihil amplius effluxit: <lb/></s> <s xml:id="echoid-s7567" xml:space="preserve">extremitate E, Aquæ impoſita, & </s> <s xml:id="echoid-s7568" xml:space="preserve">A manente in aëre libero, nullus <lb/>Aquæ ſpectabatur effluxus, neque prius guttatim ex A exivit, quam <lb/>Aquæ ſuperficies in vaſe, capiente crus ED, 2 pollicibus altior eſſet <lb/>quam ora A.</s> <s xml:id="echoid-s7569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7570" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7571" xml:space="preserve">1. </s> <s xml:id="echoid-s7572" xml:space="preserve">Hinc quo Tubus B C D eſt longior, eo profundius erit <lb/>E demergendum ſub Aquâ, antequam effluat ex orâ A.</s> <s xml:id="echoid-s7573" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7574" xml:space="preserve">Sed inquirendum hic eſt, cur tanto altior debeat eſſe ſuperficies <lb/>Aquæ, cui immerſum eſt crus D E, quam A B, ut effluat Aqua, <lb/>cum ſi ſypho habuiſſet majorem diametrum, Aqua elevatior pau- <pb o="312" file="0326" n="326" rhead="DISSERTATIO"/> lum ad E jam ingreſſa fuiſſet crus C D, & </s> <s xml:id="echoid-s7575" xml:space="preserve">effluxiſſet ex ora A: </s> <s xml:id="echoid-s7576" xml:space="preserve">hoc <lb/>provenire videtur, quia Aqua nimis adhæret parietibus anguſtorum tu-<lb/>borum, quam ut avelli ab iis moverique poſſit per gravitatis exi-<lb/>guum in uno crure exceſſum.</s> <s xml:id="echoid-s7577" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div211" type="section" level="1" n="211"> <head xml:id="echoid-head227" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s7578" xml:space="preserve">Tubum inflexi in formam A B C D E K Fig. </s> <s xml:id="echoid-s7579" xml:space="preserve">1. </s> <s xml:id="echoid-s7580" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7581" xml:space="preserve">XII. </s> <s xml:id="echoid-s7582" xml:space="preserve">ita ut <lb/>curvatura ſuperior D eſſet altior quam extremitas A, & </s> <s xml:id="echoid-s7583" xml:space="preserve">inferior <lb/>curvatura C depreſſior quam K: </s> <s xml:id="echoid-s7584" xml:space="preserve">erat tubus ejuſdem longitudinis & </s> <s xml:id="echoid-s7585" xml:space="preserve"><lb/>formæ ac depingitur, paulum tamen anguſtior: </s> <s xml:id="echoid-s7586" xml:space="preserve">Hujus immiſſa fuit <lb/>extremitas K, Aquæ, quæ ultro adſcendit ad D, atque curvaturâ ſu-<lb/>perata deſcendit ad C, qua pertranatâ adſcendit tantum uſque ad B, <lb/>non ad orificium ſummum A, manebatque diſtantia A B 1 {1/2} lineæ <lb/>vacua: </s> <s xml:id="echoid-s7587" xml:space="preserve">repetitumque aliquoties hoc Experimentum dedit effectum <lb/>eundem, imo ſive portio A B ſicca ſive Aqua humectata fuerit. <lb/></s> <s xml:id="echoid-s7588" xml:space="preserve">Deinde evacuato, atque inverſo Tubo, extremum ejus A immer-<lb/>ſum fuit aquæ, quæ adſcendit, implevitque tandem tubum D K <lb/>exceptâ parte ultimâ 1 {1/2} lineæ. </s> <s xml:id="echoid-s7589" xml:space="preserve">Tubum deinde iterum impletum po-<lb/>ſitumque ut in Fig. </s> <s xml:id="echoid-s7590" xml:space="preserve">1. </s> <s xml:id="echoid-s7591" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7592" xml:space="preserve">XII. </s> <s xml:id="echoid-s7593" xml:space="preserve">ex Aqua exemi, viſurus an efflue-<lb/>ret ex orificio K, an deſcenderet in crure B C, ſed manſit Aqua <lb/>in Tubo, effluxitque nihil. </s> <s xml:id="echoid-s7594" xml:space="preserve">Ecce ſimplex Experimentum: </s> <s xml:id="echoid-s7595" xml:space="preserve">non ta-<lb/>men extemplo liquet, quare Aqua adſcenderit in Tubum, vacuam <lb/>relinquendo partem ſeſqui lineæ: </s> <s xml:id="echoid-s7596" xml:space="preserve">non hoc contingit, quia ſi Tu-<lb/>bus rectus fuiſſet, â K, infimo orificio, uſque ad B Aqua adſcen-<lb/>diſſet, nam revera tum modo ad altitudinem perpendicularem 20 <lb/>linearum, hoc eſt in crure D G C, â K uſque ad G perveniſſet: </s> <s xml:id="echoid-s7597" xml:space="preserve"><lb/>per B ducta horozontali B H, non adſcendit, nec adſcendiſſet <lb/>Aqua modo uſque ad H, quia K H eſt tantum {9/10} pollicis, & </s> <s xml:id="echoid-s7598" xml:space="preserve"><lb/>Aqua, ſimulac attigerit orificium K, rapta fuit ſurſum uſque ad D <lb/>& </s> <s xml:id="echoid-s7599" xml:space="preserve">tranfluxit delabendo in C, inde adſcendendo ad B: </s> <s xml:id="echoid-s7600" xml:space="preserve">ſuſpicabar <lb/>in principio Aquam modo adſcenſuram ex K in H, quiâ poſito tu-<lb/>bo ita impleto Aquâ, ac hic exhibetur, gravitas columnæ B C eſt <lb/>æqualis gravitati GC, adeoque hæ ſibi æquilibrant, ut & </s> <s xml:id="echoid-s7601" xml:space="preserve"><lb/>gravitas DG æqualis DH, quæ etiam ſibi æquilibrare cenſeri <lb/>poſſunt, unde remanet tantum HK æqualis cauſæ elevanti, <pb o="313" file="0327" n="327" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> ab ea enim Aqua in tubo ſuſtinetur: </s> <s xml:id="echoid-s7602" xml:space="preserve">verum cauſam elevantem <lb/>majorem eſſe modo vidimus, unde ea ſuſpicio evanuit: </s> <s xml:id="echoid-s7603" xml:space="preserve">cur vero <lb/>impleto crure DGC Aquâ, etiam non impletur crus CBA uſque ad <lb/>A? </s> <s xml:id="echoid-s7604" xml:space="preserve">nam eſt gravitas columnæ deorſum nitentis DGC, major <lb/>quam ABC. </s> <s xml:id="echoid-s7605" xml:space="preserve">ut plus lucis fœnerarer, tubum amplum, 3 pedes <lb/>longum, diametri {3/10} pollicis inflexi in ſimilem formam ABCDK, <lb/>quem penitus implevi Aqua; </s> <s xml:id="echoid-s7606" xml:space="preserve">eo tum poſito in ſitu quem fig. </s> <s xml:id="echoid-s7607" xml:space="preserve">1. <lb/></s> <s xml:id="echoid-s7608" xml:space="preserve">monſtrat, effluxit Aqua ex crure DK, manſitque uſque ad F, quæ <lb/>erat in eadem horizontali cum A, nam replebatur pars FDGCBA. </s> <s xml:id="echoid-s7609" xml:space="preserve"><lb/>depreſſa parumper Aqua ab A uſque ad B, etiam promovebatur in <lb/>altero crure ab F uſque ad H, ſibi iterum relicta permanſit in hori-<lb/>zontali eadem BGH. </s> <s xml:id="echoid-s7610" xml:space="preserve">atque ulterius ex B verſus C depreſſa, etiam <lb/>ab H verſus K tantundem movebatur, manebatque ſemper in eâ-<lb/>dem horizontali: </s> <s xml:id="echoid-s7611" xml:space="preserve">hæc phænomena ſatis clare intelliguntur ex æ-<lb/>quilibrio liquorum, nam ad primum attendendo patet, ODF eſſe ſi-<lb/>phonem æqualium crurum horizontalium, qui ſemel impletus, ita <lb/>perſtabit, & </s> <s xml:id="echoid-s7612" xml:space="preserve">OCA, eſt modo tubus æqualium crurum inverſus, <lb/>in quo fluidum AC tantopere gravitat quam OC, hinc etiam æqui-<lb/>librium, ſimiliſque demonſtratio omnibus aliis caſibus convenit; </s> <s xml:id="echoid-s7613" xml:space="preserve"><lb/>verum nec hæc phænomena, nec eorum demonſtratio congruit <lb/>cum memoratis tuborum capillarium effectibus; </s> <s xml:id="echoid-s7614" xml:space="preserve">quamobrem nihil <lb/>lucis inde capimus, niſi quod diſcamus Leges Hydroſtaticas eſſe va-<lb/>rias in Tubis amplis & </s> <s xml:id="echoid-s7615" xml:space="preserve">anguſtis. </s> <s xml:id="echoid-s7616" xml:space="preserve">Exploravi an ad locum tubi B foret <lb/>quædam reſiſtentia contra adſcendentem Aquam, diffringendo cruris <lb/>C A partem, infimoque orificio ejus abruptæ partis Aquæ immiſſo, ad-<lb/>ſcenſus ultraB obſervabatur, imo uſque ad oram A fere; </s> <s xml:id="echoid-s7617" xml:space="preserve">quemadmodum <lb/>in Exper. </s> <s xml:id="echoid-s7618" xml:space="preserve">XV. </s> <s xml:id="echoid-s7619" xml:space="preserve">Cap. </s> <s xml:id="echoid-s7620" xml:space="preserve">1. </s> <s xml:id="echoid-s7621" xml:space="preserve">adnotavi. </s> <s xml:id="echoid-s7622" xml:space="preserve">quare in puncto B non eſt reſiſtentia <lb/>quædam conſtans contra Aquam, nam nunc adeſtin tubo longiſſimo <lb/>nunc evaneſcit in brevi: </s> <s xml:id="echoid-s7623" xml:space="preserve">Eſt profecto hic aliquid, quod mentis a-<lb/>ciem effugit.</s> <s xml:id="echoid-s7624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7625" xml:space="preserve">Sunt procul dubio vaſa abſorbentia in corpore vivo animali aut <lb/>recta, aut inflexa in ſimiles ſiphones incurvos, qualem figura hæc <lb/>prima repræſentat, cum autem in Cap. </s> <s xml:id="echoid-s7626" xml:space="preserve">1. </s> <s xml:id="echoid-s7627" xml:space="preserve">oſtendimus Tubos capillares <lb/>rectos, perpendiculariter ad horizontem poſitos, non in ſe Aquam <lb/>abripere uſque ad ſummum, niſi breviſſimi fuerint, & </s> <s xml:id="echoid-s7628" xml:space="preserve">nunc pa-<lb/>tet Aquam in ſiphone inflexo non uſque ad ſummam oram A, ſed <lb/>modo ad B adſcendere; </s> <s xml:id="echoid-s7629" xml:space="preserve">idem in abſorbentibus continget vaſis, qua- <pb o="314" file="0328" n="328" rhead="DISSERTATIO"/> re evacuari non poſiet liquor ex illis, nec cum reliquis permiſceri <lb/>corporis humoribus, niſi alia cauſa acceſſerit, quæ eſt pulſus arteria-<lb/>rum ſanguiferarum, vaſa comprimens, liquoremque propellens, <lb/>tum motus corporis qualiſcunque, vaſa hinc inde comprimens & </s> <s xml:id="echoid-s7630" xml:space="preserve"><lb/>ita evacuans.</s> <s xml:id="echoid-s7631" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div212" type="section" level="1" n="212"> <head xml:id="echoid-head228" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s7632" xml:space="preserve">Conſtruatur Sipho CFBA fig. </s> <s xml:id="echoid-s7633" xml:space="preserve">2. </s> <s xml:id="echoid-s7634" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7635" xml:space="preserve">XII. </s> <s xml:id="echoid-s7636" xml:space="preserve">crurum valde inæqua-<lb/>lium, ſit crus CF brevius, quam altitudo Aquæ eſt, quæ eleva-<lb/>tur in eodem Tubo recto: </s> <s xml:id="echoid-s7637" xml:space="preserve">& </s> <s xml:id="echoid-s7638" xml:space="preserve">ſit BA longius; </s> <s xml:id="echoid-s7639" xml:space="preserve">tum ora C immittatur <lb/>Aquæ DE, hæc adſcendit in crus CF, curvaturam ſuperat, influit <lb/>in crus longius BA, & </s> <s xml:id="echoid-s7640" xml:space="preserve">ex orâ A guttatim effluet, quemadmodum <lb/>in ſiphonibus amplis crurum inæqualium fieri ſolet.</s> <s xml:id="echoid-s7641" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7642" xml:space="preserve">Eundem ſucceſſum Experimenti adnotavit Boyle in novis Ex-<lb/>per. </s> <s xml:id="echoid-s7643" xml:space="preserve">Phyſ. </s> <s xml:id="echoid-s7644" xml:space="preserve">Mech. </s> <s xml:id="echoid-s7645" xml:space="preserve">Exp. </s> <s xml:id="echoid-s7646" xml:space="preserve">35. </s> <s xml:id="echoid-s7647" xml:space="preserve">tum Petitus in L’Hiſt. </s> <s xml:id="echoid-s7648" xml:space="preserve">de l’Acad. </s> <s xml:id="echoid-s7649" xml:space="preserve">Roy. <lb/></s> <s xml:id="echoid-s7650" xml:space="preserve">1722.</s> <s xml:id="echoid-s7651" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div213" type="section" level="1" n="213"> <head xml:id="echoid-head229" xml:space="preserve">EXPERIMENTUM VII.</head> <p> <s xml:id="echoid-s7652" xml:space="preserve">Sit iterum in Tab. </s> <s xml:id="echoid-s7653" xml:space="preserve">XII. </s> <s xml:id="echoid-s7654" xml:space="preserve">fig. </s> <s xml:id="echoid-s7655" xml:space="preserve">2. </s> <s xml:id="echoid-s7656" xml:space="preserve">CFBA Sipho capillaris inæqualium <lb/>crurum, orificium C cruris brevioris imponatur Aquæ, quæ ad-<lb/>ſcendat ad altitudinem CF, quod notetur, dein invertatur <lb/>Sipho & </s> <s xml:id="echoid-s7657" xml:space="preserve">impleatur Aquâ, tum iterum orificium C imponatur A-<lb/>quæ: </s> <s xml:id="echoid-s7658" xml:space="preserve">quod ſi pars BA cruris longioris ſit major quam CF, effluet <lb/>Aqua ex Siphone per orificium A, ſed ſi BA ſit brevior quam CF, <lb/>Sipho totus manebit impletus.</s> <s xml:id="echoid-s7659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7660" xml:space="preserve">1°, Conſideremus CFGB eſſe Siphonem vulgarem, amplum, bre-<lb/>viorem 32 pedibus, impletum Aqua, æqualium crurum, ejuſque ori-<lb/>ficia BC, in eadem horizontali BE, in hoc manebit Aqua ſuſpenſa, <lb/>quia æquali niſu tendit deorſum in GB, quam in FC, ſed ab Aëre <lb/>ſurſum æquali vi preſſa, manetin quiete, tubumque BGFC imple-<lb/>re pergit. </s> <s xml:id="echoid-s7661" xml:space="preserve">2°. </s> <s xml:id="echoid-s7662" xml:space="preserve">ſit nunc BA, pars extrema Tubi, æqualis FC, annexa <lb/>ipſi GB: </s> <s xml:id="echoid-s7663" xml:space="preserve">quia vis Tubi elevans Aquam eſt = FC, etiam hac eadem vi <lb/>manebit Aqua in Tubo; </s> <s xml:id="echoid-s7664" xml:space="preserve">quamobrem Tubus CFGBA per orificium C <lb/>implebitur Aqua uſque ad A, quæ nequaquam effluit, nam GB <lb/>nititur tantopere deorſum, quam CF, & </s> <s xml:id="echoid-s7665" xml:space="preserve">BA tendit deorſum, quan- <pb o="315" file="0329" n="329" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> tum a viribus Tubi elevatur ſurſum, manet ergo totus Tubus imple-<lb/>tus Aqua. </s> <s xml:id="echoid-s7666" xml:space="preserve">3°. </s> <s xml:id="echoid-s7667" xml:space="preserve">ſi vero AB excedat FC, erit gravitas Aquæ in Tubo <lb/>major quam eſt vis elevans, +FC, quare Aqua ex Tubo AB effluet, <lb/>evacuabiturque reliqua quæ eſt in vaſe DE, quemadmodum ope Si-<lb/>phonis ampli vulgaris contingit.</s> <s xml:id="echoid-s7668" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7669" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7670" xml:space="preserve">Hinc ſi CFGB ſit ſipho æqualium crurum, non prius ef-<lb/>fluet ex eo Aqua, niſi crus CF demergatur ſub Aqua ad altitudinem <lb/>F, tum enim crus alterum tanto profundius deſcendiſſe cenſeri po-<lb/>teſt, quemadmodum obſervavit Hauksbejus in Phyſic. </s> <s xml:id="echoid-s7671" xml:space="preserve">Mech. </s> <s xml:id="echoid-s7672" xml:space="preserve">Ex-<lb/>perim.</s> <s xml:id="echoid-s7673" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div214" type="section" level="1" n="214"> <head xml:id="echoid-head230" xml:space="preserve">EXPERIMENTUM VIII.</head> <p> <s xml:id="echoid-s7674" xml:space="preserve">Maneat idem Sipho fig. </s> <s xml:id="echoid-s7675" xml:space="preserve">2. </s> <s xml:id="echoid-s7676" xml:space="preserve">impletus Aquâ, & </s> <s xml:id="echoid-s7677" xml:space="preserve">extrahatur ex va-<lb/>ſculo DE, ſuſpendaturque in Aëre, tum Aqua manebit ſuſpenſa in <lb/>utroque crure, nec effluet, quamvis BA excedat FC.</s> <s xml:id="echoid-s7678" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div215" type="section" level="1" n="215"> <head xml:id="echoid-head231" xml:space="preserve">EXPERIMENTUM IX.</head> <p> <s xml:id="echoid-s7679" xml:space="preserve">Sed quando orificium C attingit modo Aquam, nec ei immergi-<lb/>tur, illico Aqua incipit effluere ex A, formans parvas guttas, <lb/>quamvis longitudo AB ſit notabiliter minor quam CF.</s> <s xml:id="echoid-s7680" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div216" type="section" level="1" n="216"> <head xml:id="echoid-head232" xml:space="preserve">EXPERIMENTUM X.</head> <p> <s xml:id="echoid-s7681" xml:space="preserve">Sit Sipho bicruralis ABGFC, fig. </s> <s xml:id="echoid-s7682" xml:space="preserve">2. </s> <s xml:id="echoid-s7683" xml:space="preserve">cujus crus FC ſit 4 linear. <lb/></s> <s xml:id="echoid-s7684" xml:space="preserve">GA 6 linearum, imponatur crus longius GA Aquæ, & </s> <s xml:id="echoid-s7685" xml:space="preserve">brevius <lb/>crus FC extra eam emineat, adſcendet Aqua ſurſum, ſuperat <lb/>flexuram FG, deſcenditque uſque ad oram breviorem C ad quam <lb/>hærebit, nulla effluente gutta.</s> <s xml:id="echoid-s7686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7687" xml:space="preserve">Iterum hic patet, quanta ſit differentia phænomenorum in ſiphoni-<lb/>bus amplioribus & </s> <s xml:id="echoid-s7688" xml:space="preserve">capillaribus: </s> <s xml:id="echoid-s7689" xml:space="preserve">Simulac enim poſito ſiphone am-<lb/>pliori Aquæ pleno, crus longius imponitur Aquæ, hæc relin-<lb/>quens crus brevius retrogreditur, & </s> <s xml:id="echoid-s7690" xml:space="preserve">flexuram ſuperando deſcendit <lb/>in longius, effluitque omnis.</s> <s xml:id="echoid-s7691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7692" xml:space="preserve">Si vero ex crure breviori, poſito Tubo capillari, efflueret A- <pb o="316" file="0330" n="330" rhead="DISSERTATIO"/> qua, haberetur mobile perpetuum, quod diu incaſſum quæſitum <lb/>fuit a Philoſophis.</s> <s xml:id="echoid-s7693" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div217" type="section" level="1" n="217"> <head xml:id="echoid-head233" xml:space="preserve">EXPERIMENTUM XI.</head> <p> <s xml:id="echoid-s7694" xml:space="preserve">Si utrique extremo ſiphonis CFGA fig. </s> <s xml:id="echoid-s7695" xml:space="preserve">2. </s> <s xml:id="echoid-s7696" xml:space="preserve">applicatur Aqua ſi-<lb/>mul, nihil ingreditur ab alterutrâ parte Tubum, impediente hoc <lb/>Aëre intus contento: </s> <s xml:id="echoid-s7697" xml:space="preserve">adeoque vis elevans Aquam in his Tubis <lb/>non videtur eſſe tanta, ut Aërem vel tantillum in ſe condenſare <lb/>poſſit, quod an pendeat ab immobilitate Aëris per Tubos, an quia <lb/>Aër repellat valide Aquam, hic determinare nolo.</s> <s xml:id="echoid-s7698" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div218" type="section" level="1" n="218"> <head xml:id="echoid-head234" xml:space="preserve">EXPERIMENTUM XII.</head> <p> <s xml:id="echoid-s7699" xml:space="preserve">Præparavi Tubum Capillarem incurvatum in modum arcus ABC, <lb/>fig. </s> <s xml:id="echoid-s7700" xml:space="preserve">3. </s> <s xml:id="echoid-s7701" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7702" xml:space="preserve">XII. </s> <s xml:id="echoid-s7703" xml:space="preserve">in medio B erat prominentia ſed aperta: </s> <s xml:id="echoid-s7704" xml:space="preserve">extremi-<lb/>tate A Aquæ immiſſâ, elevabatur hæc uſque ad B, cavitatemque <lb/>implebat, ſuperficiem vero ad B acquirebat cavam, ſupra quam, <lb/>tanquam ſupra ponticulum Aqua tranſcendebat, fluens verſus C, <lb/>atque ex ea elabebatur.</s> <s xml:id="echoid-s7705" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7706" xml:space="preserve">Hunc ita præparaveram, ut viderem an Aqua ex B non elabere-<lb/>tur, dum ſimul fluit verſus C, ſed effluit nihil: </s> <s xml:id="echoid-s7707" xml:space="preserve">quare ad oram B <lb/>datur vis elevans Aquam, haud aliter quam obtinet in A.</s> <s xml:id="echoid-s7708" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div219" type="section" level="1" n="219"> <head xml:id="echoid-head235" xml:space="preserve">EXPERIMENTUM XIII.</head> <p> <s xml:id="echoid-s7709" xml:space="preserve">Fiat, ut in fig. </s> <s xml:id="echoid-s7710" xml:space="preserve">4. </s> <s xml:id="echoid-s7711" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7712" xml:space="preserve">XII. </s> <s xml:id="echoid-s7713" xml:space="preserve">ſipho inæqualium crurum admo-<lb/>dum inflexus ACB, ſitque latus BC duos pollices longus: </s> <s xml:id="echoid-s7714" xml:space="preserve">D B ſit {1/2} <lb/>pollice longior, proinde tantopere infra oram A. </s> <s xml:id="echoid-s7715" xml:space="preserve">immiſſâ hac A <lb/>Aquæ, repit liquor per omnes flexuras, deſcenditque uſque ad B, <lb/>ſed effluit ex B nihil. </s> <s xml:id="echoid-s7716" xml:space="preserve">Si vero B immitatur Aquæ, hæc itidem <lb/>adſcendit per C uſque ad A, ubi ſtat immota, neque ex A ulla e-<lb/>labitur gutta.</s> <s xml:id="echoid-s7717" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7718" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7719" xml:space="preserve">Siveergo ſit ſipho capillaris inflexus admodum; </s> <s xml:id="echoid-s7720" xml:space="preserve">vel crura duo <lb/>recta poſſideat, eoſdem edit effectus.</s> <s xml:id="echoid-s7721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7722" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s7723" xml:space="preserve">Quantum non abludunt phænomena Tuborum Ca- <pb o="317" file="0331" n="331" rhead="DE TUBIS CAPILLARIBU SVITREIS."/> pillarium a regulis Hydroſtaticis hucuſque apud Geometras repe-<lb/>riundis! hi enim conſiderare modo ſolent preſſiones fluidorum a <lb/>gravitate pendentes, indeque oriundas altitudines fluidorum in Tu-<lb/>bis, nequaquam attendentes ad attractionem, quam fluida in Tu-<lb/>bos, & </s> <s xml:id="echoid-s7724" xml:space="preserve">hi viciſſim in fluida exercent: </s> <s xml:id="echoid-s7725" xml:space="preserve">hinc Theoreticam doctri-<lb/>nam quidem veram, congruamque ſuæ hypotheſi dederunt, nequa-<lb/>quam tamen veram in praxi, quia in hac attractionis ſimul ratio <lb/>habenda eſt: </s> <s xml:id="echoid-s7726" xml:space="preserve">Quo Tubus eſt amplior, eo minus ſuperficiei ratione <lb/>internæ capacitatis acquirit, atque ideo etiam minorem attractio-<lb/>nis effectum edere poteſt, quam Tubus anguſtior, quamobrem Le-<lb/>ges Hydroſtaticæ, hucuſque tradit@¦ a Geometris, magis conveniunt <lb/>Tubis amplis, quam anguſtis, imo in ampliſſimis vix abludunt ab <lb/>effectibus, quæ cauſa eſt ut pro veris abſolutiſque habitæ fuerint; <lb/></s> <s xml:id="echoid-s7727" xml:space="preserve">quod erroneum; </s> <s xml:id="echoid-s7728" xml:space="preserve">nam attractionis ratio ſimul habenda legibusque <lb/>vulgaribus addenda, antequam Lex abſolute vera & </s> <s xml:id="echoid-s7729" xml:space="preserve">experientiæ <lb/>congrua deprehendetur: </s> <s xml:id="echoid-s7730" xml:space="preserve">Geometræ enim detur Tubus vitreus u-<lb/>trimque apertus, rectus, cylindricus; </s> <s xml:id="echoid-s7731" xml:space="preserve">detur liquor, rogo ut deter-<lb/>minet altitudinem Fluidi ingreſſuri Tubum, quem perpendiculari-<lb/>ter ad horizontem Fluido immerget. </s> <s xml:id="echoid-s7732" xml:space="preserve">Si tantum preſſiones fluidi <lb/>conſideret, demonſtrabit ſuperficiem ejus in vaſe & </s> <s xml:id="echoid-s7733" xml:space="preserve">in Tubo fore <lb/>ad libellam; </s> <s xml:id="echoid-s7734" xml:space="preserve">fiat Experimentum, id non reſpondebit demonſtratio-<lb/>ni, ſed altius adſcendet libellâ fluidum, niſi fuerit Mercurius, <lb/>qui humilior manet, an ergo demonſtratio Geometrica falſa eſt? </s> <s xml:id="echoid-s7735" xml:space="preserve"><lb/>non, ſed non fuit completa, quippe demonſtrationi addenda erat <lb/>vis attrahens Tubi & </s> <s xml:id="echoid-s7736" xml:space="preserve">liquoris, qua additâ capiatur Experimentum, <lb/>& </s> <s xml:id="echoid-s7737" xml:space="preserve">reſpondebit calculo quam accuratiſſime. </s> <s xml:id="echoid-s7738" xml:space="preserve">Quadrat hercle <lb/>hic egregie ſapientis Fontenellii monitum in L’Hiſt. </s> <s xml:id="echoid-s7739" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s7740" xml:space="preserve"><lb/>Roy. </s> <s xml:id="echoid-s7741" xml:space="preserve">A°. </s> <s xml:id="echoid-s7742" xml:space="preserve">1723. </s> <s xml:id="echoid-s7743" xml:space="preserve">„ Si demonſtrandum foret, quantum Phyſica ſæpe <lb/>” differt â Geometria, quantum realis executio rerum diſtat ab <lb/>” eo, quod Geometra ope ſui calculi exſpectaſſet, nihil accomoda-<lb/>” tius foret quam hoc objectum, de quo agimus: </s> <s xml:id="echoid-s7744" xml:space="preserve">Quod non prove-<lb/>” nit, quia Geometria non ubivis obtinet ſine ulla exceptione, ſed <lb/>” eſt Phyſica plerumque valde compoſita, noſtrorumque ratiocinio-<lb/>” rum fundamenta ſunt nimis ſimplicia ad accurate eos effectus <lb/>” aſſequendos, qui in natura fiunt.</s> <s xml:id="echoid-s7745" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7746" xml:space="preserve">Quanta igitur cum prudentia ratiocinandum eſt in phyſicis? </s> <s xml:id="echoid-s7747" xml:space="preserve">quod <pb o="318" file="0332" n="332" rhead="DISSERTATIO"/> enim generaliter â Geometra demonſtratum eſt, nonſemper verum <lb/>eſt realiter, nec aſſumendum niſi Experimento probetur, in ejus <lb/>tentamine enim liquebit, an omnes, quæ concurrunt in phyſica cir-<lb/>cumſtantiæ, ſimul in demonſtratione comprehendantur, quod eſt <lb/>aureum Niewentytii monitum.</s> <s xml:id="echoid-s7748" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div220" type="section" level="1" n="220"> <head xml:id="echoid-head236" xml:space="preserve">CAPUT SEXTUM.</head> <head xml:id="echoid-head237" style="it" xml:space="preserve">De Tubis vario modo inflexis & inæqualis diametri.</head> <head xml:id="echoid-head238" xml:space="preserve">EXPERIMENTUM I.</head> <p> <s xml:id="echoid-s7749" xml:space="preserve">Sit Tubus capillaris AGB ſubtilior, fig. </s> <s xml:id="echoid-s7750" xml:space="preserve">5. </s> <s xml:id="echoid-s7751" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7752" xml:space="preserve">XII. </s> <s xml:id="echoid-s7753" xml:space="preserve">cui an-<lb/>nexus ſit alius Tubus amplior, ſed brevior, impleatur totus <lb/>quantus eſt Aquâ, dein invertatur, & </s> <s xml:id="echoid-s7754" xml:space="preserve">orificium A Tubi gracilio-<lb/>ris imponatur Aquæ in vaſe DE, tum Aqua ex parte ampliori <lb/>CFB adſcendet ex C in F & </s> <s xml:id="echoid-s7755" xml:space="preserve">in B, exibitque ex orificio A, ma-<lb/>nebit tamen Aqua in AB ſuſpenſa uſque ad altitudinem AB I-<lb/>dem phænomenon contingit ſive Tubus BFC ſit cylindricus ſive <lb/>conicus.</s> <s xml:id="echoid-s7756" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7757" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7758" xml:space="preserve">Eſt hoc phænomenon plane diverſum ab eo, quod nota-<lb/>vimus in capitis præced: </s> <s xml:id="echoid-s7759" xml:space="preserve">Exp. </s> <s xml:id="echoid-s7760" xml:space="preserve">X, in quo manebat Aqua in cru-<lb/>re BFC uſque ad oram C: </s> <s xml:id="echoid-s7761" xml:space="preserve">nunc autem retrogreditur, nec tamen <lb/>ſuperabat capacitas BFC multum eam in AGB nam idem contin-<lb/>git, ſi Tubus fuerit totus conicus & </s> <s xml:id="echoid-s7762" xml:space="preserve">diameter C modo ſuperet bis <lb/>diametrum in A.</s> <s xml:id="echoid-s7763" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7764" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7765" xml:space="preserve">2 Obſervatur igitur in hoc genere Tuborum idem, <lb/>quod in Siphonibus bicruralibus amplis, quoad retrogreſſum A-<lb/>quæ per CFB verſus A cum hac tamen differentia, quod Tubus <lb/>AGB maneat impletus: </s> <s xml:id="echoid-s7766" xml:space="preserve">vel ſi fuerit conicus, maneat ad eam im-<lb/>pletus altitudinem, ad quam ſuâ ſponte adſcendiſſet liquor ingreſ-<lb/>ſus per A.</s> <s xml:id="echoid-s7767" xml:space="preserve"/> </p> <pb o="319" file="0333" n="333" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> </div> <div xml:id="echoid-div221" type="section" level="1" n="221"> <head xml:id="echoid-head239" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s7768" xml:space="preserve">Si idem Tubus ABC prioris Experimenti, Aqua omnino im-<lb/>pletus, invertatur in Aëre, Aqua effluet guttatim ex orificio A, <lb/>nihil vero ex C, & </s> <s xml:id="echoid-s7769" xml:space="preserve">manebit ſuſpenſa in Tubo ABG, uſque ad <lb/>altitudinem AB.</s> <s xml:id="echoid-s7770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7771" xml:space="preserve">Sed in hoc Experimento obſervavit Jurinus, ut effluat Aqua ex <lb/>A, debere differentiam AG inter ambo crura Tuborum excede-<lb/>re FC. </s> <s xml:id="echoid-s7772" xml:space="preserve">eſt vero FC altitudo Aquæ, quæ ingreditur Tubum BFC <lb/>ſponte: </s> <s xml:id="echoid-s7773" xml:space="preserve">quod ſi AG non excedat FC, non effluet Aqua.</s> <s xml:id="echoid-s7774" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div222" type="section" level="1" n="222"> <head xml:id="echoid-head240" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s7775" xml:space="preserve">Fig. </s> <s xml:id="echoid-s7776" xml:space="preserve">6. </s> <s xml:id="echoid-s7777" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7778" xml:space="preserve">XII. </s> <s xml:id="echoid-s7779" xml:space="preserve">Sit A B C Sipho inæqualium crurum, tam <lb/>quoad longitudinem, quam amplitudinem: </s> <s xml:id="echoid-s7780" xml:space="preserve">in cujus graciliori & </s> <s xml:id="echoid-s7781" xml:space="preserve">bre-<lb/>viori crure AB, ſi ſufficientis foret longitudinis, columna Aquæ <lb/>poſſet ſuſpendi ad altitudinem æqualem EF. </s> <s xml:id="echoid-s7782" xml:space="preserve">ſed in crure longiori <lb/>& </s> <s xml:id="echoid-s7783" xml:space="preserve">ampliori Aqua intraret ad altitudinem H G. </s> <s xml:id="echoid-s7784" xml:space="preserve">Quando totus hic <lb/>Sipho impletur Aquâ, & </s> <s xml:id="echoid-s7785" xml:space="preserve">in eadem poſitione tenetur, quam figura <lb/>repræſentat, Aqua non effluet ex orificio Tubi C quamvis DC <lb/>(quæ eſt differentia inter longitudines amborum crurum ſuperet <lb/>longitudinem EF.</s> <s xml:id="echoid-s7786" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div223" type="section" level="1" n="223"> <head xml:id="echoid-head241" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s7787" xml:space="preserve">Si crus gracilius BC Tab. </s> <s xml:id="echoid-s7788" xml:space="preserve">XII. </s> <s xml:id="echoid-s7789" xml:space="preserve">fig. </s> <s xml:id="echoid-s7790" xml:space="preserve">7. </s> <s xml:id="echoid-s7791" xml:space="preserve">ſit longius quam crus <lb/>alterum BA, Aqua effluet ex C: </s> <s xml:id="echoid-s7792" xml:space="preserve">ſi DC, quæ eſt differentia longi-<lb/>tudinis amborum crurum, ſuperet longitudinem EF, ad quam ad-<lb/>ſcendit Aqua in crure ampliori, alioquin Aqua manebit in Sipho-<lb/>ne ſuſpenſa.</s> <s xml:id="echoid-s7793" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7794" xml:space="preserve">Ambo hæc Experimenta debentur Jurino. </s> <s xml:id="echoid-s7795" xml:space="preserve">Sunt autem valde <lb/>paradoxa, neque inter ſe conveniunt: </s> <s xml:id="echoid-s7796" xml:space="preserve">cur enim in Exp. </s> <s xml:id="echoid-s7797" xml:space="preserve">III. </s> <s xml:id="echoid-s7798" xml:space="preserve">non ef-<lb/>fluit Aqua ex DC, cujus longitudo ſuperat EF, cum Aqua fluat in <lb/>Exp 4. </s> <s xml:id="echoid-s7799" xml:space="preserve">ex DC cujus longitudo ſuperat EF Niſi Aër ejuſque preſ-<lb/>ſio hic aliquid conferat; </s> <s xml:id="echoid-s7800" xml:space="preserve">qui non tam facile ingredi poſſit orificium <lb/>A in fig. </s> <s xml:id="echoid-s7801" xml:space="preserve">7. </s> <s xml:id="echoid-s7802" xml:space="preserve">anguſtum, quam amplum in fig. </s> <s xml:id="echoid-s7803" xml:space="preserve">8. </s> <s xml:id="echoid-s7804" xml:space="preserve">& </s> <s xml:id="echoid-s7805" xml:space="preserve">ideo Sipho <pb o="320" file="0334" n="334" rhead="DISSERTATIO"/> ABDC fig. </s> <s xml:id="echoid-s7806" xml:space="preserve">7. </s> <s xml:id="echoid-s7807" xml:space="preserve">ſit conſiderandus quaſi clauſus ad A, unde Aër ſua <lb/>preſſione ſuſtinebit Aquam ad C ne exeat: </s> <s xml:id="echoid-s7808" xml:space="preserve">cum vero Aër in fig. </s> <s xml:id="echoid-s7809" xml:space="preserve">8. <lb/></s> <s xml:id="echoid-s7810" xml:space="preserve">per A, amplum facile irrepat, effluit Aqua ex C, modo DC ſu-<lb/>peret EF, quæ eſt = vi elevanti Aquam vel eam ſuſtinenti in <lb/>crure AB.</s> <s xml:id="echoid-s7811" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div224" type="section" level="1" n="224"> <head xml:id="echoid-head242" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s7812" xml:space="preserve">Sumatur Sipho fig. </s> <s xml:id="echoid-s7813" xml:space="preserve">3. </s> <s xml:id="echoid-s7814" xml:space="preserve">Tab. </s> <s xml:id="echoid-s7815" xml:space="preserve">XI. </s> <s xml:id="echoid-s7816" xml:space="preserve">æque longorum crurum, ſed <lb/>inæqualis diametri ADCB, qui ſit in ea poſitione ac hic exhibetur: <lb/></s> <s xml:id="echoid-s7817" xml:space="preserve">infundatur Mercurius in crus amplius A B, qui hoc replens uſque <lb/>ad F, adſcendit in cure graciliori modo ad C, manens multum de-<lb/>preſſus infra F.</s> <s xml:id="echoid-s7818" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7819" xml:space="preserve">Si loco Mercurii ſumatur Aqua, hac replente crus amplius uſ-<lb/>que ad F, obſervabitur ejus altitudo in crure graciliori uſque ad K. <lb/></s> <s xml:id="echoid-s7820" xml:space="preserve">Quare omnino contrarius obſervatur cum hoc Siphone in Aqua & </s> <s xml:id="echoid-s7821" xml:space="preserve"><lb/>Mercurio effectus.</s> <s xml:id="echoid-s7822" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div225" type="section" level="1" n="225"> <head xml:id="echoid-head243" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s7823" xml:space="preserve">Sit Tubus ABC inæqualium crurum, inflexus in gyros, quos <lb/>Tab. </s> <s xml:id="echoid-s7824" xml:space="preserve">XII. </s> <s xml:id="echoid-s7825" xml:space="preserve">fig. </s> <s xml:id="echoid-s7826" xml:space="preserve">8. </s> <s xml:id="echoid-s7827" xml:space="preserve">repræſentat, ſint ambo orificia A & </s> <s xml:id="echoid-s7828" xml:space="preserve">C in eadem <lb/>linea horizontali, tum applicatâ Aquâ oræ A, fiet ejus adſcenſus, <lb/>atque per omnes devoluta gyros fluet tandem ad C: </s> <s xml:id="echoid-s7829" xml:space="preserve">ſi extremum <lb/>C gracilius fuiſſet applicatum Aquæ, hæc etiam ingreſſa fuiſſet Tu-<lb/>bum, eumque impleviſſet uſque ad A: </s> <s xml:id="echoid-s7830" xml:space="preserve">Quod ſi Tubus hic ita im-<lb/>pletus, in Aëre erigatur, ut orificium C ſit ſupremum, A vero <lb/>infimum, manebit impletus Aqua, neque ex A aliquid effluet: </s> <s xml:id="echoid-s7831" xml:space="preserve">ſi <lb/>vero invertatur, ita ut A ſit ſupremum, C vero infimum, effluet <lb/>Aqua ex C, donec modo ea manſerit in crure C Aquæ copia, quæ <lb/>ſuâ ſponte elevaretur.</s> <s xml:id="echoid-s7832" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7833" xml:space="preserve">Non videtur hoc phænomenon diverſum ab iis, quæ memora-<lb/>vi Exp. </s> <s xml:id="echoid-s7834" xml:space="preserve">III. </s> <s xml:id="echoid-s7835" xml:space="preserve">& </s> <s xml:id="echoid-s7836" xml:space="preserve">IV. </s> <s xml:id="echoid-s7837" xml:space="preserve">atque ab eadem pendere cauſa.</s> <s xml:id="echoid-s7838" xml:space="preserve"/> </p> <pb o="321" file="0335" n="335" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> </div> <div xml:id="echoid-div226" type="section" level="1" n="226"> <head xml:id="echoid-head244" xml:space="preserve">EXPERIMENTUM VII.</head> <p> <s xml:id="echoid-s7839" xml:space="preserve">Si ſumatur Sipho uti in Tab. </s> <s xml:id="echoid-s7840" xml:space="preserve">XI. </s> <s xml:id="echoid-s7841" xml:space="preserve">fig 3. </s> <s xml:id="echoid-s7842" xml:space="preserve">& </s> <s xml:id="echoid-s7843" xml:space="preserve">crus capacius AB ſit lon-<lb/>gius quam crus gracilius BCD: </s> <s xml:id="echoid-s7844" xml:space="preserve">impleatur AB Aquâ uſque ad A, hæc <lb/>deſcendens exibit ex orificio cruris gracilioris, non tamen uſque <lb/>ad libellam cum hujus orâ, ſed ſtabit quidem 7 vel 8 lineis <lb/>altius in crure ampliori, quam eſt orificium ſupremum anguſtioris. <lb/></s> <s xml:id="echoid-s7845" xml:space="preserve">Et ſi loco Aquæ infundatur Mercurius cruri ampliori, idem erit <lb/>ſucceſſus, ſtabitque Mercurius in crure ampliori 7 vel 8 lineis ſupra <lb/>oram cruris exilioris.</s> <s xml:id="echoid-s7846" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7847" xml:space="preserve">Videretur prima fronte, quod fluida deberent exire uſque ad li-<lb/>bellam in utroque crure, juxta leges hydroſtaticas, ſed id fieri ne-<lb/>quit, cum vis major exerceatur in fluida a Tubo anguſtiori, quam <lb/>ampliori, hac vi retrotrahentur fluida ab ora extrema Tubi anguſtio-<lb/>ris, & </s> <s xml:id="echoid-s7848" xml:space="preserve">ideo effluere nequeunt uſque ad libellam. </s> <s xml:id="echoid-s7849" xml:space="preserve">debetur hoc Ex-<lb/>perimentum @l. </s> <s xml:id="echoid-s7850" xml:space="preserve">Fayo in L'Hiſt. </s> <s xml:id="echoid-s7851" xml:space="preserve">de L'Acad. </s> <s xml:id="echoid-s7852" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7853" xml:space="preserve">Ao. </s> <s xml:id="echoid-s7854" xml:space="preserve">1724.</s> <s xml:id="echoid-s7855" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div227" type="section" level="1" n="227"> <head xml:id="echoid-head245" xml:space="preserve">EXPERIMENTUM VIII.</head> <p> <s xml:id="echoid-s7856" xml:space="preserve">Sumtus fuit Sipho incurvus, cujus crura erant inæqualis diametri <lb/>& </s> <s xml:id="echoid-s7857" xml:space="preserve">longitudinis, digito clauſum fuit brachium brevius & </s> <s xml:id="echoid-s7858" xml:space="preserve">capacius, <lb/>& </s> <s xml:id="echoid-s7859" xml:space="preserve">brachium gracilius, quod & </s> <s xml:id="echoid-s7860" xml:space="preserve">longiſſimum erat, Mercurio impletum <lb/>fuit, tum ſublato digito, deſcendit Mercurius ex graciliori in amplius <lb/>crus, ex quo exivit, donec ſtaret ad libellam cum Mercurio <lb/>in graciliori Tubo: </s> <s xml:id="echoid-s7861" xml:space="preserve">Dein inclinatus parum fuit Tubus am-<lb/>plior, deſcenditque Mercurius ex graciliori paulum, manſitque <lb/>poſtea in eo humilius quam in capaciori: </s> <s xml:id="echoid-s7862" xml:space="preserve">quod etiam obſervatum <lb/>eſt â Fayo.</s> <s xml:id="echoid-s7863" xml:space="preserve"/> </p> <pb o="322" file="0336" n="336" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div228" type="section" level="1" n="228"> <head xml:id="echoid-head246" xml:space="preserve">CAPUT SEPTIMUM.</head> <head xml:id="echoid-head247" style="it" xml:space="preserve">De Tuborum Capillarium in Vacuo examinatorum phænomenis.</head> <head xml:id="echoid-head248" xml:space="preserve">EXPERIMENTUM I.</head> <p> <s xml:id="echoid-s7864" xml:space="preserve">Capiatur Aqua, quæ ſub recipiente Boyleano diu hæſit & </s> <s xml:id="echoid-s7865" xml:space="preserve">pro-<lb/>be depurata eſt ab omni Aëre: </s> <s xml:id="echoid-s7866" xml:space="preserve">huic immittatur perpendicula-<lb/>riter Tubus vitreus Capillaris, novus, utrimque apertus, & </s> <s xml:id="echoid-s7867" xml:space="preserve">obſer-<lb/>vetur altitudo ad quam Aqua adſcendit: </s> <s xml:id="echoid-s7868" xml:space="preserve">ille idem Tubus, Aquâ ex-<lb/>cuſſâ, ſuſpendatur perpendiculariter ex filo mobili, & </s> <s xml:id="echoid-s7869" xml:space="preserve">cum Aqua <lb/>ab aëre depurata includatur recipienti Vitreo, ita ut, quando lubuerit, <lb/>Tubus Aquæ immitti, vel ex ea tolli poſſit: </s> <s xml:id="echoid-s7870" xml:space="preserve">tum ope Antliæ pneu-<lb/>maticæ educatur Aër ex recipiente tam accurate ac fieri poteſt: </s> <s xml:id="echoid-s7871" xml:space="preserve">quo <lb/>facto, demittatur Tubus in Aquam; </s> <s xml:id="echoid-s7872" xml:space="preserve">hæc adſcendet, non ad mino-<lb/>rem, ſed potius ad majorem altitudinem, quam in Aëre libero ad-<lb/>ſcenderat.</s> <s xml:id="echoid-s7873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7874" xml:space="preserve">Plurimi Philoſophi hoc Experimentum inſtituerunt, quamvis non <lb/>quidem cum Aquâ prius ab Aëre depuratâ, & </s> <s xml:id="echoid-s7875" xml:space="preserve">ſucceſſum notant eun-<lb/>dem: </s> <s xml:id="echoid-s7876" xml:space="preserve">ita Boyle in Contin: </s> <s xml:id="echoid-s7877" xml:space="preserve">prima Experim: </s> <s xml:id="echoid-s7878" xml:space="preserve">ad Exp. </s> <s xml:id="echoid-s7879" xml:space="preserve">27. </s> <s xml:id="echoid-s7880" xml:space="preserve">pag. </s> <s xml:id="echoid-s7881" xml:space="preserve">63. <lb/></s> <s xml:id="echoid-s7882" xml:space="preserve">in Contin. </s> <s xml:id="echoid-s7883" xml:space="preserve">Secunda Exper. </s> <s xml:id="echoid-s7884" xml:space="preserve">ad Exp. </s> <s xml:id="echoid-s7885" xml:space="preserve">9. </s> <s xml:id="echoid-s7886" xml:space="preserve">pag. </s> <s xml:id="echoid-s7887" xml:space="preserve">93. </s> <s xml:id="echoid-s7888" xml:space="preserve">Carre in L’Hiſtoir. </s> <s xml:id="echoid-s7889" xml:space="preserve"><lb/>L’Acad. </s> <s xml:id="echoid-s7890" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7891" xml:space="preserve">Ao. </s> <s xml:id="echoid-s7892" xml:space="preserve">1705. </s> <s xml:id="echoid-s7893" xml:space="preserve">’sGravezandius in Elem. </s> <s xml:id="echoid-s7894" xml:space="preserve">phyſic. </s> <s xml:id="echoid-s7895" xml:space="preserve"><lb/>Lib. </s> <s xml:id="echoid-s7896" xml:space="preserve">1. </s> <s xml:id="echoid-s7897" xml:space="preserve">Newtonus in Optic. </s> <s xml:id="echoid-s7898" xml:space="preserve">pag. </s> <s xml:id="echoid-s7899" xml:space="preserve">367. </s> <s xml:id="echoid-s7900" xml:space="preserve">coram Societate <lb/>Regiâ Experimentum inſtitutum confirmat cum eodem <lb/>eventu.</s> <s xml:id="echoid-s7901" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div229" type="section" level="1" n="229"> <head xml:id="echoid-head249" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s7902" xml:space="preserve">Quando, omnibus manentibus ut in Experimento præcedenti, Aër <lb/>admittitur in recipiens: </s> <s xml:id="echoid-s7903" xml:space="preserve">& </s> <s xml:id="echoid-s7904" xml:space="preserve">Tubi, quibuscum tentamina capiun-<lb/>tur, fuerint breves, hoc eſt modo 4 vel 5 pollicum, in quibus <lb/>Aqua ad 3 vel 4 pollices hæret, tum manet Aqua immota ejuſdem-<lb/>que altitudinis, imo ſive Tubi manſerint in Aqua, vel ex ea extra- <pb o="323" file="0337" n="337" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> cti ſint: </s> <s xml:id="echoid-s7905" xml:space="preserve">Verum ſi Tubi longiores fuerint, uti 1, 2, vel 3 pedum, <lb/>oblervabitur Aqua adſcendere ad majorem altitudinem, quamdiu <lb/>Aër in recipiens admittitur: </s> <s xml:id="echoid-s7906" xml:space="preserve">eo vas penitus implente, elapſoque <lb/>aliquo tempore, Aqua iterum ſubſidet in Tubis ad priorem altitu-<lb/>dinem: </s> <s xml:id="echoid-s7907" xml:space="preserve">quod poſtremum phænomenon pendet ab Aëris preſſione, <lb/>quum hic enim recipiens ingreditur, longe citius preſſionem ſupra <lb/>Aquam vaſculi exercet, quam anguſtiſſimum ſupremum Tubi oriſi-<lb/>cium intrat, ideo premitur Aqua in Tubum altius, verum ſimulac Aër <lb/>penitus impleverit recipiens, Tubum ſucceſſu temporis quoque <lb/>implet, etiamſi lente, ceſſatque inæqualis preſſio ſupra Aquam <lb/>vaſculi & </s> <s xml:id="echoid-s7908" xml:space="preserve">Tubi, quamobrem Aqua deſcendit, cum non poſſit ſuſtineri <lb/>a cauſa, quæ ipſam elevavit, ad majorem altitudinem quam ante.</s> <s xml:id="echoid-s7909" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div230" type="section" level="1" n="230"> <head xml:id="echoid-head250" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s7910" xml:space="preserve">Si ſumantur Tubi variarum diametrorum, æque longi, & </s> <s xml:id="echoid-s7911" xml:space="preserve">an-<lb/>nexi filo æneo mobili, more ’sGravezandiano, Tab. </s> <s xml:id="echoid-s7912" xml:space="preserve"><emph style="sc">XII</emph> fig. </s> <s xml:id="echoid-s7913" xml:space="preserve">11. </s> <s xml:id="echoid-s7914" xml:space="preserve">tum <lb/>hi recipienti incluſi, ex quo omnis educatur Aër, aquæque immit-<lb/>tantur, hæc ipſos intrabit ad varias altitudines, quæ deprehendun-<lb/>tur in ratione inverſa diametrorum; </s> <s xml:id="echoid-s7915" xml:space="preserve">uti in Aëre aperto. </s> <s xml:id="echoid-s7916" xml:space="preserve">quod Boy-<lb/>leus utcunque expertus fuit loco Aquæ ſpiritum vini Cocco Baphica <lb/>tinctum ſumens, vid. </s> <s xml:id="echoid-s7917" xml:space="preserve">Continuat. </s> <s xml:id="echoid-s7918" xml:space="preserve">I. </s> <s xml:id="echoid-s7919" xml:space="preserve">Experimentum XXVII.</s> <s xml:id="echoid-s7920" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7921" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s7922" xml:space="preserve">Quando hæc Experimenta accurate inſtituenda ſunt, <lb/>nunquam ſumendus eſt liquor, in cujus interſtitiis Aër hæret; </s> <s xml:id="echoid-s7923" xml:space="preserve">hic enim <lb/>ſe explicans in vacuo bullas format, hinc inde parietibus adhæren-<lb/>tes vaſculi; </s> <s xml:id="echoid-s7924" xml:space="preserve">ſi Tubos capillares tum liquori immiſeris, illico illo-<lb/>rum oris bulla adhæret aërea, quæ prohibet, quominus liquor Tu-<lb/>bum ingrediatur, vel ſiquis ingreſſus eſt, ab Aëre in diverſas ſepara-<lb/>tur partes, quo impeditur accurata altitudinis obſervatio:</s> <s xml:id="echoid-s7925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7926" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s7927" xml:space="preserve">2. </s> <s xml:id="echoid-s7928" xml:space="preserve">Si Tubus prius aliquouſque impletus fuerit Aquâ <lb/>vulgari: </s> <s xml:id="echoid-s7929" xml:space="preserve">tum ſuſpenſus ex filo includatur recipienti, è quo Aër <lb/>educatur, hoc ſublato, Aqua paulum adſcendet, majuſque ſpatium <lb/>occupat, Aëre nempe ex ejus interſtitiis ſe quaquaverſum explican-<lb/>te, quemadmodum recte adnotarunt Boyle in Contin. </s> <s xml:id="echoid-s7930" xml:space="preserve">2. </s> <s xml:id="echoid-s7931" xml:space="preserve">Exper. <lb/></s> <s xml:id="echoid-s7932" xml:space="preserve">Carrè in L’Hiſt. </s> <s xml:id="echoid-s7933" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s7934" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7935" xml:space="preserve">A°. </s> <s xml:id="echoid-s7936" xml:space="preserve">1705. </s> <s xml:id="echoid-s7937" xml:space="preserve">Petitus in L’Hiſt. </s> <s xml:id="echoid-s7938" xml:space="preserve">de <lb/>L’Acad. </s> <s xml:id="echoid-s7939" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7940" xml:space="preserve">A°. </s> <s xml:id="echoid-s7941" xml:space="preserve">1724.</s> <s xml:id="echoid-s7942" xml:space="preserve"/> </p> <pb o="324" file="0338" n="338" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div231" type="section" level="1" n="231"> <head xml:id="echoid-head251" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s7943" xml:space="preserve">Sit Tubus rectus, cujus altera extremitas hermetice clauſa, altera <lb/>aperta, in quem Aquam non ingredi, etiamſi aliquouſque ipſi im-<lb/>merſum, ſupra vidimus; </s> <s xml:id="echoid-s7944" xml:space="preserve">hic recipienti immittatur, eductoque Aë-<lb/>re quantum vulgo fieri poteſt, extremitas aperta Tubi Aquæ immit-<lb/>tatur; </s> <s xml:id="echoid-s7945" xml:space="preserve">hæc intrat, adſcendens ad paulo minorem altitudinem, <lb/>quam ſi utrimque apertus Tubus fuiſſet: </s> <s xml:id="echoid-s7946" xml:space="preserve">Admiſſo deinde in re-<lb/>cipiens Aëre, altius adſcendit Aqua, fere uſque ad ſummitatem Tu-<lb/>bi, manente tamen exigua Aëris bulla, impediente quominus omni-<lb/>no Tubus impleatur.</s> <s xml:id="echoid-s7947" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7948" xml:space="preserve">Quia ope Antliæ Pneumaticæ Aërem rarefacere modo ſolemus in <lb/>recipientibus, non autem penitus educere, ejus tantillula quanti-<lb/>tas ſuperſtes manet, ſua elaſticitate impediens, quominus Aqua ad <lb/>eandem altitudinem in Tubum adſcendat, ad quam perveniſſet, ſi <lb/>liber Aëri fuiſſet exitus ſuperne conceſſus: </s> <s xml:id="echoid-s7949" xml:space="preserve">ſuperſtes tamen Aëris <lb/>in Tubo portio, multum rarefacta eſt, ideoque a gravitate atmo-<lb/>ſphæræ in recipiens admiſſæ comprimitur in minus ſpatium, donec ſua <lb/>elaſticitate & </s> <s xml:id="echoid-s7950" xml:space="preserve">pondere Aquæ Tubum implentis, æquilibrium cum <lb/>atmoſphæræ pondere acquiſiverit: </s> <s xml:id="echoid-s7951" xml:space="preserve">Adſcendit hinc Aqua in Tubum <lb/>preſſa vi atmoſphæræ, quemadmodum in Tubos amplos eodem mo-<lb/>do tractatos adſcendiſſet.</s> <s xml:id="echoid-s7952" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7953" xml:space="preserve">Quia ſemper aliquid Aëris relinquitur in recipientibus, quæ ope <lb/>Antliæ Pneumaticæ evacuantur, ſuſpicatus fuit Cl. </s> <s xml:id="echoid-s7954" xml:space="preserve">Fayus in L’Hiſt. <lb/></s> <s xml:id="echoid-s7955" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s7956" xml:space="preserve">Roy. </s> <s xml:id="echoid-s7957" xml:space="preserve">A°. </s> <s xml:id="echoid-s7958" xml:space="preserve">1724. </s> <s xml:id="echoid-s7959" xml:space="preserve">preſſionem hujus reſidui Aëris ſufficere <lb/>ad elevandam in Tubos Aquam, eamque penitus elapſuram, ſi <lb/>Tubi in vacuo perfecto ponerentur: </s> <s xml:id="echoid-s7960" xml:space="preserve">Ut hoc explorarem recipiens <lb/>omni Aëre evacuandum erat, quod quamvis difficile fieri poſſit, <lb/>nihilominus ſequenti methodo peractum fuit. </s> <s xml:id="echoid-s7961" xml:space="preserve">Vid. </s> <s xml:id="echoid-s7962" xml:space="preserve">Tab XII. </s> <s xml:id="echoid-s7963" xml:space="preserve">fig. </s> <s xml:id="echoid-s7964" xml:space="preserve"><lb/>11. </s> <s xml:id="echoid-s7965" xml:space="preserve">Tubos Capillares EE agglutinavi maſſæ ceraceæ OO, quam <lb/>tegebam recipiente R. </s> <s xml:id="echoid-s7966" xml:space="preserve">hoc, Antliæ laminæ S impoſitum, accura-<lb/>tiſſime implevi Aquâ, antea perfectiſſime orbata omni ſuo Aëre, <lb/>nullaque jam amplius in recipiente bulla aërea obſervari poterat: </s> <s xml:id="echoid-s7967" xml:space="preserve"><lb/>tum lente embolo â fundo Antliæ remoto, deſcendit Aqua ſua gra-<lb/>vitate ex recipiente, qua eductâ, Tubuli, qui prius omnino reple-<lb/>ti fuerant, aliquantum Aquæ ex ſe dimiſerunt, retinentes tamen <pb o="325" file="0339" n="339" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> eam ad paulo majorem altitudinem, quam huc uſque in Experi-<lb/>mentis obſervatum fuit: </s> <s xml:id="echoid-s7968" xml:space="preserve">ob guttam nempe inferius appenſam: <lb/></s> <s xml:id="echoid-s7969" xml:space="preserve">Hærebant nunc Tubi in recipiente privato omni Aëre craſſiori, ſive <lb/>in vacuo Torricellii; </s> <s xml:id="echoid-s7970" xml:space="preserve">quoniam in eo Tubi Aquam retinebant ſuſ-<lb/>penſam, Aër cauſa ſuſpenſæ aut elevatæ Aquæ eſſe non poterat: </s> <s xml:id="echoid-s7971" xml:space="preserve"><lb/>Hoc artificio ſemper ope Antliæ evacuari poteſt recipiens omni Aë-<lb/>re craſſo, eſtque hic ſummus apex, ad quem perveniri poteſt: </s> <s xml:id="echoid-s7972" xml:space="preserve"><lb/>non tamen ita vacuum perfectum conficitur, quemadmodum qui-<lb/>dam, minus periti in Phyſica, crediderunt, id enim nullâ arte hu-<lb/>manâ obtineri poteſt, quippe præterquam quod Lux omnia penetret, <lb/>Ignis ubivis per totam atmosphæram diſperſus, ſemper in pro-<lb/>portione ſpatiorum ſe recipit, vaſa omnia pervadit, eaque, ſibi <lb/>commiſſus, ſecundum hanc proportionem ſemper implet.</s> <s xml:id="echoid-s7973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7974" xml:space="preserve">Corol 1. </s> <s xml:id="echoid-s7975" xml:space="preserve">Sequitur ex omnibus hiſce Experimentis, Aërem non <lb/>eſſe cauſam elevatorum liquorum in Tubos, caditque Philoſophorum <lb/>opinio, qua ſtabiliebatur minus Aëris, vel illum magis rarefactum, <lb/>eſſe in Tubi cavitate interna ob anguſtiam, quam qui extrinſecus <lb/>Tubum ambit, & </s> <s xml:id="echoid-s7976" xml:space="preserve">idcirco abinæquali Aëris preſſione liquores elevari: <lb/></s> <s xml:id="echoid-s7977" xml:space="preserve">nam in vacuo adſcendunt liquores ad eandem ad minimum altitudi-<lb/>nem, quam in Aëre aperto.</s> <s xml:id="echoid-s7978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7979" xml:space="preserve">Corol. </s> <s xml:id="echoid-s7980" xml:space="preserve">2. </s> <s xml:id="echoid-s7981" xml:space="preserve">Quia poſito Tubo brevi utrimque aperto in vacuo conti-<lb/>nente Aquam, ad majorem altitudinem adſcenſus non fit, admiſſo <lb/>iterum aëre liquet Aërem ſubito ingredi cavitatem tuborum, alioquin <lb/>liquorem ſua inæquali preſſione altius elevaret, ut in Tubis ab unâ <lb/>parte clauſis evenit, ut & </s> <s xml:id="echoid-s7982" xml:space="preserve">in longiſſimis.</s> <s xml:id="echoid-s7983" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div232" type="section" level="1" n="232"> <head xml:id="echoid-head252" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s7984" xml:space="preserve">Explorandum adhuc reſtabat, an Tubi longiſſimi in vacuo ad <lb/>majorem altitudinem Aquam elevarent, quam multo breviores, <lb/>veluti in Exp XV. </s> <s xml:id="echoid-s7985" xml:space="preserve">Cap. </s> <s xml:id="echoid-s7986" xml:space="preserve">1. </s> <s xml:id="echoid-s7987" xml:space="preserve">id fieri in Aëre probavimus; </s> <s xml:id="echoid-s7988" xml:space="preserve">inde concluden-<lb/>tes vim totius, aut ferè totius Tubi, agere in Aquam, atque ideo <lb/>Tubos longiores ad majorem altitudinem Aquam rapturos breviori-<lb/>bus; </s> <s xml:id="echoid-s7989" xml:space="preserve">quam concluſionem non niſi poſt plurima tentamina & </s> <s xml:id="echoid-s7990" xml:space="preserve">exa-<lb/>mina a me ipſo extorſi, non ſuſpicante vim Tuborum ad notabi- <pb o="326" file="0340" n="340" rhead="DISSERTATIO"/> lem diſtantiam, majoremve hac alterave linea exporrigi, eandemque <lb/>idcirco altitudinem in Tubo brevi, ſcilicet 6 pollicum, quam in <lb/>alio 2, 3, 4, pedum datum iri: </s> <s xml:id="echoid-s7991" xml:space="preserve">dubitabam igitur an hic non lateret <lb/>cauſa compoſita, quæ mihi imponeret; </s> <s xml:id="echoid-s7992" xml:space="preserve">in vacuo autem poſitus <lb/>Tubus demonſtrare poterat, an veram an erroneam concluſionem <lb/>formaviſſem: </s> <s xml:id="echoid-s7993" xml:space="preserve">examini inſerviit Tubus duos pedes longus, qui re-<lb/>cipienti immiſſus, e quo Aër, quantum fieri poteſt, educebatur, <lb/>tandem Aquæ immerſus eſt, quam rapuit ad altitudinem 4 {3/4} polli-<lb/>cum; </s> <s xml:id="echoid-s7994" xml:space="preserve">deinde Tubi partem ſuperiorem abrupi, ita ut inferior pars <lb/>modo eſſet 6 {1/4} pollicum, ex qua prius omnis Aqua ore exſucta erat, <lb/>tum recipienti includebatur, ex quo Aër iterum evacuatus fuit: </s> <s xml:id="echoid-s7995" xml:space="preserve">in <lb/>hunc Tubum, Aquæ immerſum, adſcendit liquor modo ad altitu-<lb/>dinem 4 {1/12} pollicum, & </s> <s xml:id="echoid-s7996" xml:space="preserve">quamvis per ſemihoram exſpectaverim, <lb/>altius non adſcendit: </s> <s xml:id="echoid-s7997" xml:space="preserve">repetii Experimentum eventu eodem: </s> <s xml:id="echoid-s7998" xml:space="preserve">quam-<lb/>obrem tuto concludam liquores in Tubos longiores altius adſcende-<lb/>re quam in breviores; </s> <s xml:id="echoid-s7999" xml:space="preserve">proinde vim elevantem Tuborum eſſe ex-<lb/>porrectam ad magnam diſtantiam.</s> <s xml:id="echoid-s8000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8001" xml:space="preserve">Commemoravimus hucuſque nonnulla cum hiſce gracilibus Tu-<lb/>bis capta Experimenta, oportebit nunc cauſam indicare elevantem <lb/>liquores, potiſſimum enim in hunc finem omnis hic Experimentorum <lb/>apparatus præmiſſus fuit.</s> <s xml:id="echoid-s8002" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8003" xml:space="preserve">Hæc autem cauſa hæret vel extra Tubum & </s> <s xml:id="echoid-s8004" xml:space="preserve">liquores; </s> <s xml:id="echoid-s8005" xml:space="preserve">vel in <lb/>liquoribus; </s> <s xml:id="echoid-s8006" xml:space="preserve">vel in Tubo; </s> <s xml:id="echoid-s8007" xml:space="preserve">vel in Tubo & </s> <s xml:id="echoid-s8008" xml:space="preserve">liquoribus ſimul: </s> <s xml:id="echoid-s8009" xml:space="preserve">per-<lb/>curramus igitur hæc omnia, videamus quænam cauſa ſufficiens, <lb/>quænam non, eſſe poſſit, ut rejectis omnibus, quæ Experimentis <lb/>adverſantur, nec phænomena ſolvunt, reſtet tantum ſola vera & </s> <s xml:id="echoid-s8010" xml:space="preserve"><lb/>genuina.</s> <s xml:id="echoid-s8011" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8012" xml:space="preserve">1. </s> <s xml:id="echoid-s8013" xml:space="preserve">Cauſa, quæ extra Tubum & </s> <s xml:id="echoid-s8014" xml:space="preserve">liquores foret, hoſque in Tu-<lb/>bum adigeret, ageret, vel magis premendo ſuperficiem liquoris in <lb/>vaſculo quam in Tubo, vel liquorem attraheret in Tubum ſurſum.</s> <s xml:id="echoid-s8015" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8016" xml:space="preserve">Quæ ſupra ſuperficiem liquoris in vaſculo plus ageret quam ſu-<lb/>pra liquorem cavo Tubi reſpondentem, poſſet eſſe vel Aër atmosphæræ <lb/>craſſior, vel fluidum quodcunque aliud ſubtilius. </s> <s xml:id="echoid-s8017" xml:space="preserve">Demonſtravi-<lb/>mus autem ſupra aliquoties Aërem craſſiorem non poſſe eſſe cauſam; <lb/></s> <s xml:id="echoid-s8018" xml:space="preserve">quia fluida adſcendunt in Tubos Capillares poſitos in vacuo, tum <lb/>quia graviores liquores altius plerumque adſcendunt levioribus, & </s> <s xml:id="echoid-s8019" xml:space="preserve"><lb/>Mercurius nequaquam elevetur.</s> <s xml:id="echoid-s8020" xml:space="preserve"/> </p> <pb o="327" file="0341" n="341" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> <p> <s xml:id="echoid-s8021" xml:space="preserve">Quod autem fluidum Aëre ſubtilius attinet, id neque hic invo-<lb/>cari poteſt; </s> <s xml:id="echoid-s8022" xml:space="preserve">Quoniam enim Tubi recipienti Aëre vacuo incluſi ad ean-<lb/>dem altitudinem liquores elevent, oportebit ut id fluidum liberrime <lb/>tranſeat per poros vitrei recipientis, atque ita quoque plus agat in <lb/>ſuperficiem liquoris in vaſculo, quam in Tubo, prorſus eodem modo ac <lb/>de Aëre craſſiori dictum fuit; </s> <s xml:id="echoid-s8023" xml:space="preserve">verum quid impediet quominus illud flui-<lb/>dum ſubtiliſſimum ingrediatur liberrime ſupremum Tubi orificium & </s> <s xml:id="echoid-s8024" xml:space="preserve"><lb/>cavitatem totam, atque ita premendo tantundem agat ſupra ſu-<lb/>perficiem liquoris cavo Tubi reſpondentis, quam ſupra ſuperficiem <lb/>liquoris in vaſculo; </s> <s xml:id="echoid-s8025" xml:space="preserve">non poteſt anguſtia Tubi hic criminari, quip-<lb/>pe fluidum quod per poros recipientis liberrime tranſit, poterit ad-<lb/>huc multo liberius tranſire per cavitatem Tubi millies & </s> <s xml:id="echoid-s8026" xml:space="preserve">forſitan cen-<lb/>ties millies amplioris, procul dubio enim pororum vitreorum anguſtia <lb/>cſt plus quam millies ſubtilior quam apertura Tubi capillaris, præterea <lb/>eadem facilitate ac per poros recipientis id fluidum tranſit, etiam <lb/>tranſibit per poros vitrei Tubi uſque in internam cavitatem, atque <lb/>ita preſſionem eandem exercebit ſupra ſuperficiem liquoris in vaſ-<lb/>culo & </s> <s xml:id="echoid-s8027" xml:space="preserve">in Tubo, unde elevatio inæqualis fieri nequit, nec aliquid <lb/>in Tubum ultra reliquam ſuperficiem liquoris aſſurget: </s> <s xml:id="echoid-s8028" xml:space="preserve">præterea <lb/>conceſſo aliquo fluido ſubtiliori, quod ſua preſſione majori ſupra <lb/>vaſculum, quam cavum Tubi ageret, quæro an non effectus vir-<lb/>tuti prementi proportionales erunt? </s> <s xml:id="echoid-s8029" xml:space="preserve">Nemo erit qui hoc in dubium <lb/>vocabit; </s> <s xml:id="echoid-s8030" xml:space="preserve">an igitur non altiſſime premi debebunt in Tubum liquo-<lb/>res leviſſimi, humillime graviſſimi, & </s> <s xml:id="echoid-s8031" xml:space="preserve">an non ſecundum legem hy-<lb/>droſtaticam altitudines liquorum erunt in ratione reciproca gravi-<lb/>tatum ſpecificarum? </s> <s xml:id="echoid-s8032" xml:space="preserve">nec hoc negari poteſt: </s> <s xml:id="echoid-s8033" xml:space="preserve">ſed an hoc compro-<lb/>bant Experimenta in Capite 3 deſcripta? </s> <s xml:id="echoid-s8034" xml:space="preserve">nihil minus, apparet enim <lb/>in iis Mercurium non elevari, Aquam ſatis alte, altiſſime Uri-<lb/>nam, parum vero leviſſimum Alcohol: </s> <s xml:id="echoid-s8035" xml:space="preserve">quæ omnia hercle cla-<lb/>mitant evidentiſſime, non poſſe advocari fluidum ſubtilius quod, <lb/>ſua preſſione cauſa phænomenorum deſcriptorum foret: </s> <s xml:id="echoid-s8036" xml:space="preserve">non autem <lb/>opinor quemquam in tam abſonam & </s> <s xml:id="echoid-s8037" xml:space="preserve">& </s> <s xml:id="echoid-s8038" xml:space="preserve">adverſus omnes Hydroſta-<lb/>ticæ leges illapſurum opinionem, fluidum tamen poſſe ſtatui cau-<lb/>ſam, quia magna quantitate agit in magnam ſuperficiem liquoris in <lb/>vaſculo, minori tantum in cavum Tubi, atque inde tamen adſcen-<lb/>ſum futurum; </s> <s xml:id="echoid-s8039" xml:space="preserve">ſi quis id nihilominus tueretur, reſponſo indignus <pb o="328" file="0342" n="342" rhead="DISSERTATIO"/> habendus foret, atque mittendus ad leges Hydroſtaticæ addiſcen <lb/>das; </s> <s xml:id="echoid-s8040" xml:space="preserve">verum quicunque animadvertit Tubum Aqua plenum, in vacuo <lb/>recipiente ſuſpenſum extra vas, manere impletum, nec liquoris <lb/>guttulam demittere, intelligit in extremum Tubi ſuperius non <lb/>minorem preſſionem illius invocati fluidi fore, quam in extre-<lb/>mum inferius, æque latum, adeoque liquorem ſuâ gravitate elabi <lb/>ex Tubo debere, qui tamen ſuſpenſus manet. </s> <s xml:id="echoid-s8041" xml:space="preserve">Præterea ſi quædam <lb/>preſſio fluidi omnia præſtaret phænomena, quomodo tum ſuperfi-<lb/>cies liquoris in Tubis ſit concava, aut a Mercurio convexa? </s> <s xml:id="echoid-s8042" xml:space="preserve">ſe-<lb/>cundum leges preſſionum æqualium, ſuperficies accurate horizon-<lb/>ti parallela deſideraretur, nec poteſt unquam figura concava aut <lb/>convexa ab æquabili preſſione derivari: </s> <s xml:id="echoid-s8043" xml:space="preserve">ad figuram liquoris in Tu-<lb/>bo ſi accurate attendiſſent Philoſophi, dubito an quidem unquam ad <lb/>preſſionem, ut cauſam adſcenſus confugiſſent. </s> <s xml:id="echoid-s8044" xml:space="preserve">Multo minus preſ-<lb/>ſionem alicujus fluidi ad adſcenſum liquoris in Tubum explicandum, <lb/>invocare illi poſſunt, qui ſe ope Antliæ pneumaticæ, vel ope Mercurii <lb/>in Tubo, vacuum facere arbitrantur; </s> <s xml:id="echoid-s8045" xml:space="preserve">cum Capillares Tubi in eo <lb/>vacuo omnia exhibeant phænomena eadem, quæ memoravimus: <lb/></s> <s xml:id="echoid-s8046" xml:space="preserve">ſed ne in hiſce magis examinandis tempus teramus; </s> <s xml:id="echoid-s8047" xml:space="preserve">abunde enim <lb/>demonſtratum nunc eſt, preſſionem nullius fluidi hic poſſe invocari, <lb/>ejuſve auxilio detecta a nobis phænomena explicari. </s> <s xml:id="echoid-s8048" xml:space="preserve">An autem flui-<lb/>dum aliquod attrahens datur, quod penetrans in cavitatem Tubi <lb/>liquorem ex vaſculo ad ſe traheret uſque ad determinatam altitudi-<lb/>nem? </s> <s xml:id="echoid-s8049" xml:space="preserve">aut an aliquod aliud corporum genus aliunde adveniens ad <lb/>ſe in Tubum liquorem attrahet? </s> <s xml:id="echoid-s8050" xml:space="preserve">fateor me ejuſmodi attrahens flui-<lb/>dum aut aliud corporum genus, nec noviſſe, nec ejus ideam for-<lb/>mare poſſe, uti nec ejuſmodi attractionis: </s> <s xml:id="echoid-s8051" xml:space="preserve">nec opinor quemquam eo <lb/>ſagacitatis perveniſſe hactenus, ut clare aliquid ejuſmodi conce-<lb/>perit, aut demonſtraverit. </s> <s xml:id="echoid-s8052" xml:space="preserve">Neque externum ſpiritum attrahentem <lb/>in Tubos liquorem ineliori jure quis hic advocaverit, aut clare <lb/>conceperit, vel demonſtraverit. </s> <s xml:id="echoid-s8053" xml:space="preserve">Neque Ignem hic poſſe ſtatui cau-<lb/>ſam. </s> <s xml:id="echoid-s8054" xml:space="preserve">ſuperius evictum fuit in Capite primo, cum non ad majorem <lb/>altitudinem liquor adſcendat data Ignis magna copia, quam parva. </s> <s xml:id="echoid-s8055" xml:space="preserve"><lb/>Quamobrem concludimus nullam dari cauſam extra Tubum & </s> <s xml:id="echoid-s8056" xml:space="preserve">li-<lb/>quores hærentem, quæ phænomena Tuborum capillarium ex-<lb/>citer.</s> <s xml:id="echoid-s8057" xml:space="preserve"/> </p> <pb o="329" file="0343" n="343" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> <p> <s xml:id="echoid-s8058" xml:space="preserve">2. </s> <s xml:id="echoid-s8059" xml:space="preserve">Nunc ad ipſos liquores accedamus, indagemus an in ipſis cau-<lb/>ſa adſcenſus ſit, aut eſſe poſſit. </s> <s xml:id="echoid-s8060" xml:space="preserve">Nonnulli a tenacitate liquorum & </s> <s xml:id="echoid-s8061" xml:space="preserve"><lb/>proinde ab adhæſione eorum ad latera tubi crediderunt adſcenſum <lb/>oriri, quorum Syſtema in Capite tertio attulimus, & </s> <s xml:id="echoid-s8062" xml:space="preserve">inſolubiles ſi-<lb/>mul diſſicultates, quibus premitur: </s> <s xml:id="echoid-s8063" xml:space="preserve">Alii, hoc obſervato, potius a <lb/>motu perpetuo, quo omnium fluidorum partes agitari opinabantur, <lb/>adſcenſum in Tubos deduxerunt, hi ſimul ſupponebant internos <lb/>Tuborum parietes eſſe aſperos & </s> <s xml:id="echoid-s8064" xml:space="preserve">inæquales, atque inſtar ſpiræ <lb/>Archimedeæ habere inæqualitates contortas, has facile ſupra ſe ex-<lb/>cipere particulas liquorum, qui ſuo motu adſcendant, haud aliter <lb/>quam Aqua ope cochleæ Archimedeæ circumactæ elevatur: </s> <s xml:id="echoid-s8065" xml:space="preserve">ſuam <lb/>ſtabiliebant ſententiam eo Experimento, quo impediri adſcenſum <lb/>probabant lævigatâ internâ ſuperficie oleo vel pinguedine: </s> <s xml:id="echoid-s8066" xml:space="preserve">Ex hac <lb/>hypotheſi ſatis feliciter primâ fronte videbantur plurimis ſatisfeciſ-<lb/>ſe phænomenis: </s> <s xml:id="echoid-s8067" xml:space="preserve">attamen nonnullis difficultatibus laborat hæc opi-<lb/>nio: </s> <s xml:id="echoid-s8068" xml:space="preserve">1°. </s> <s xml:id="echoid-s8069" xml:space="preserve">Ex ea enim ſequitur, adſcenſum ejuſdem liquoris æque <lb/>altum fore, Tubo longiori vel breviori facto, quod Experimentis <lb/>adverſatur, quæ in Capite primo memoravimus. </s> <s xml:id="echoid-s8070" xml:space="preserve">2°. </s> <s xml:id="echoid-s8071" xml:space="preserve">præterea ne-<lb/>ſcio an quidem ullis demonſtrari poſſit argumentis, ſuperficiem Tu-<lb/>borum aſperam in modum ſpiræ eſſe formatam, aut liquo-<lb/>rem in gyrum agi ut ſpiras ſupraſcanderet: </s> <s xml:id="echoid-s8072" xml:space="preserve">ſed in gyrum aga-<lb/>tur liquor, dextrorſum vel ſiniſtrorſum agetur, agi dextrorſum <lb/>ſupponatur cum Tubum ingrediebatur: </s> <s xml:id="echoid-s8073" xml:space="preserve">nuncinvertatur Tubus, ejus <lb/>ſpiræ igitur contrarium priori ductum habebunt; </s> <s xml:id="echoid-s8074" xml:space="preserve">an liquor, cui Tu-<lb/>bus immergitur, directionem motus ſui ſimul invertit? </s> <s xml:id="echoid-s8075" xml:space="preserve">niſi intelli-<lb/>genti animo cognoſcat contrario turbine ſibi nunc eundum eſſe, ad-<lb/>ſcenſus non fiet, quitamen obſervatur. </s> <s xml:id="echoid-s8076" xml:space="preserve">3°. </s> <s xml:id="echoid-s8077" xml:space="preserve">Quicunque autem naturam <lb/>cochleæ Archimedeæ intelligit, novit in cochleam non adſcenſuram <lb/>Aquam, utcunque in turbinem agitatam, niſi ipſa cochlea cir-<lb/>cumvertatur, eam vero ita eſſe fabrefactam, ut Aqua in ipſa <lb/>ſemper deſcendat, cum adſcendit, quod hujus loci non eſt ut demon-<lb/>ſtrem. </s> <s xml:id="echoid-s8078" xml:space="preserve">Motus quoque inteſtinus partium non poteſt cauſa adſcenſus <lb/>poni, quippe foret tum adſcenſus eo major, quo motus inteſtinus eſ-<lb/>ſet major, adeoque liquores efferveſcentes, aut calidiſſimi, <lb/>quorum partes vehementer commoventur, altius adſcenderent fri-<lb/>gidis, non ita agitatis, quod nequaquam verum eſſe docuerunt <pb o="330" file="0344" n="344" rhead="DISSERTATIO"/> Experimenta Capitis primi. </s> <s xml:id="echoid-s8079" xml:space="preserve">Ex quibus igitur liquido conſtat cauſam <lb/>adſcenſus non ſitam eſſe, nec poni poſſe in ſolis liquoribus.</s> <s xml:id="echoid-s8080" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8081" xml:space="preserve">3. </s> <s xml:id="echoid-s8082" xml:space="preserve">Ipſos igitur Tubos adeamus, atque in iis quæramus cauſam: <lb/></s> <s xml:id="echoid-s8083" xml:space="preserve">Adſcendunt fluida in Tubos, motus igitur excitatur; </s> <s xml:id="echoid-s8084" xml:space="preserve">hic potentiam <lb/>moventem & </s> <s xml:id="echoid-s8085" xml:space="preserve">vim ſupponit, oportet igitur ut in ipſo Tubo vis la-<lb/>teat fluida elevans & </s> <s xml:id="echoid-s8086" xml:space="preserve">in ſe rapiens: </s> <s xml:id="echoid-s8087" xml:space="preserve">hoc mecum alii quoque animad-<lb/>verterunt Philoſophi: </s> <s xml:id="echoid-s8088" xml:space="preserve">ubi & </s> <s xml:id="echoid-s8089" xml:space="preserve">quænam hæc vis eritin Tubo quieſcente? </s> <s xml:id="echoid-s8090" xml:space="preserve"><lb/>vel hæret in cavitate, vel in Tubi ſolida ſubſtantia, inde in cavum <lb/>exeuns: </s> <s xml:id="echoid-s8091" xml:space="preserve">aſt poſito Tubo in vacuo nihil eſt in cavitate, quod ſen-<lb/>ſus aut ratio detegit: </s> <s xml:id="echoid-s8092" xml:space="preserve">adeoque erit in ſolida Tubiſubſtantia; </s> <s xml:id="echoid-s8093" xml:space="preserve">qualis hæc <lb/>erit? </s> <s xml:id="echoid-s8094" xml:space="preserve">ea, quæ admodum univerſalis eſt, qua duo corpora aſeremota, <lb/>ſua ſponte accedunt; </s> <s xml:id="echoid-s8095" xml:space="preserve">hanc Attractionem vocamus, quia eo nomi-<lb/>ne uti voluerunt Philoſophi, poſſet enim appellari alio quocunque <lb/>nomine, & </s> <s xml:id="echoid-s8096" xml:space="preserve">forſitan haud pejus, Acceſſus mutuus: </s> <s xml:id="echoid-s8097" xml:space="preserve">Obſervamus <lb/>enim in innumeris phænomenis, quæ corpora, fere omnia hacte-<lb/>nus cognita, edunt, eam dari Legem Naturæ, ut ſi a ſe mutuo <lb/>parum abſint bina, ad ſe accedant ſua ſponte, vel ſi alterutrum te-<lb/>neatur firmum, accedat alterum; </s> <s xml:id="echoid-s8098" xml:space="preserve">hæc ſe attingentia, vi ſe am-<lb/>plectuntur inſigni, qua ſeparationi reſiſtunt: </s> <s xml:id="echoid-s8099" xml:space="preserve">non ex Hypotheſi <lb/>quadam hæc profero, ſed tantum ex obſervatis phænomenis: </s> <s xml:id="echoid-s8100" xml:space="preserve">hanc <lb/>legem admittunt omnes Philoſophi, qui, non meditabundi ſedent <lb/>modo in muſæo, ſed ipſam Naturam explorant, & </s> <s xml:id="echoid-s8101" xml:space="preserve">obſervando <lb/>detegunt, quænam hæc moliatur. </s> <s xml:id="echoid-s8102" xml:space="preserve">Vi hujus legis omnia phæno-<lb/>mena Tuborum Capillarium ſiunt: </s> <s xml:id="echoid-s8103" xml:space="preserve">Immittatur enim Tubus novus <lb/>liquori, hunc adſe trahet, elevabitaliquam partem, quæ externæ ſu-<lb/>perſiciei adhærebit, donec gravitas liquoris cum hac viin æquilibrio <lb/>ſit: </s> <s xml:id="echoid-s8104" xml:space="preserve">elevabit intus in cavitatem ſuam partem liquoris aliam, & </s> <s xml:id="echoid-s8105" xml:space="preserve">quia ſu-<lb/>perficies cavæ ſibi propinquæ ſunt, ſeſeque reſpiciunt, mutuâque vi <lb/>ſibi auxiliantur, elevabitur major quantitas; </s> <s xml:id="echoid-s8106" xml:space="preserve">atque ad majorem <lb/>altitudinem in cavum adſcendet, donec quoquc inter gravitatem <lb/>ſublati liquoris & </s> <s xml:id="echoid-s8107" xml:space="preserve">vim elevantem detur æquilibrium. </s> <s xml:id="echoid-s8108" xml:space="preserve">Quando Tu-<lb/>bus ad horizontem parum inclinatur, atque Aqua pattem ſuperio-<lb/>rem occupans deorſum ruit, uti in Experimento. </s> <s xml:id="echoid-s8109" xml:space="preserve">VIII. </s> <s xml:id="echoid-s8110" xml:space="preserve">Cap. </s> <s xml:id="echoid-s8111" xml:space="preserve">I. </s> <s xml:id="echoid-s8112" xml:space="preserve">de-<lb/>ſcendit partim gravitate, partim hac vi attrahente, quam Tubi <lb/>pars inferior habet, ſi<unsure/>vero eo uſque deſcenderit liquor, ut vispar-<lb/>tis ſuperioris Tubi, quam reliquit, deorſum ruendo ſuperet gravi- <pb o="331" file="0345" n="345" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> tatem & </s> <s xml:id="echoid-s8113" xml:space="preserve">vim attrahentem partis inferioris Tubi, manebit liquor <lb/>ſuſpenſus in co aliquouſque, nec ad infimam oram appellet, aucta <lb/>autem gravitate abſoluta liquoris, quod ſit magis ad perpendiculum <lb/>elevando Tubum, aut plus Aquæ immittendo, deſcendet liquor <lb/>uſque ad infimam Tubi oram, cum vis attrahens partis ſuperioris <lb/>Tubi non poſſit elevare tantopere liquorem quam modo ante. </s> <s xml:id="echoid-s8114" xml:space="preserve">Et <lb/>quoniam hæc vis agit in diſtans, a Tubo longiori plus liquoris ele-<lb/>vatur quam â breviori; </s> <s xml:id="echoid-s8115" xml:space="preserve">decreſcit tamen virtutis robur, quo plus <lb/>a puncto corporeo, è quo quaſi exeundo agit, abeſt, hinc maxime <lb/>attrahetur liquor ſuperficiem immediate contingens, minus autem, qui <lb/>plus à ſuperficie diſtat, unde liquoris ſuperficies concava fit: </s> <s xml:id="echoid-s8116" xml:space="preserve">hinc etiam <lb/>a Tubo longiſſimo non multo plus liquoris elevatur, quam ab alio inſi-<lb/>gniter breviori: </s> <s xml:id="echoid-s8117" xml:space="preserve">Hæc vis agit in unum liquorem magis quam in alium, <lb/>veluti Magnes fortius attrahit hoc corpus alio, hinc altiſſime elevatur <lb/>Urina, humilius Spiritus Salis Ammoniaci, & </s> <s xml:id="echoid-s8118" xml:space="preserve">Aqua, minus adhuc ele-<lb/>vatur Alcohol Vini; </s> <s xml:id="echoid-s8119" xml:space="preserve">& </s> <s xml:id="echoid-s8120" xml:space="preserve">quia partes Mercurii ſe magis attrahunt, <lb/>quam a vitro attrahuntur, Mercurius nequaquam adſcendit, imo <lb/>potius repellitur a vitro, donec hujus ſuperficie obducta ſebo, in <lb/>quod vis attrahens vitri agit, etiam vis attrahens ſebi Mercurium <lb/>ad ſe rapiat tollatque in altum: </s> <s xml:id="echoid-s8121" xml:space="preserve">Hæc vis terminatur in cruſtam <lb/>aëream Tuborum antiquorum, in qua attrahendo ſe totam <lb/>conſumit, vel impendit maximam ſaltem ſui partem, hinc <lb/>inepta eſt elevando liquori, aut debilitata admodum. </s> <s xml:id="echoid-s8122" xml:space="preserve">Et quia <lb/>hæc vis eo eſt fortior, quo corporeo ſui puncto, e quo egre-<lb/>ditur, eſt propior, erit fortiſſima cum ſuperficies cava proxima <lb/>ſibi puncta habebit, ſive cum erit arctiſſima, idcirco altiſſime ele-<lb/>vabitur liquor a Tubis gracillimis, humilius ab amplioribus; </s> <s xml:id="echoid-s8123" xml:space="preserve">imo <lb/>in graciles majori velocitate adſcendet, utpote actus majoribus <lb/>viribus, quam in amplos: </s> <s xml:id="echoid-s8124" xml:space="preserve">Hæc vis ex quolibet puncto ſui corporis <lb/>emiſſa ad diſtantiam aliquam, non modo elevat particulas liquo-<lb/>ris ſuperficiei Tubi proximas, ſed quoque alias, contiguas prio-<lb/>ribus, aliaſque hiſce iterum contiguas, licet minori robore, quæ <lb/>tamen cum eandem gravitatem inter ſe habent, minus elevari poſ-<lb/>ſunt, idcirco ſuperficiem concavam componentes, eo depreſſio-<lb/>rem, quo plus a ſuperficie Tubi abſunt: </s> <s xml:id="echoid-s8125" xml:space="preserve">ſed hinc quoque major <lb/>quantitas liquoris â Tubis amplioribus quam â gracilioribus eleva- <pb o="332" file="0346" n="346" rhead="DISSERTATIO"/> bitur, cum pars virtutis modo in gracilioribus agere poſſit in liquo-<lb/>rem, non omnis, qualis in amplis agit: </s> <s xml:id="echoid-s8126" xml:space="preserve">quod ſi hanc vim ſub for-<lb/>ma radiorum recta ex quolibet ſuperficiei puncto conceperis, cla-<lb/>riſſimam ejus formabis ideam, atque nullum occurret phænomenon, <lb/>quod perſpicientiam eſfugiet, aut ſolvi illico non poterit: </s> <s xml:id="echoid-s8127" xml:space="preserve">tædio-<lb/>ſum foret omnia repetere Tuborum phænomena, atque demonſtra-<lb/>re, quomodo ea auxilio virtutis attractricis peragantur, ſufficit clavim <lb/>dediſle, & </s> <s xml:id="echoid-s8128" xml:space="preserve">veram canſam aſſignaſſe: </s> <s xml:id="echoid-s8129" xml:space="preserve">Eſt profecto admodum gene-<lb/>ralis corporum Magnetiſmus, quemadmodum ex Experientia e-<lb/>doctus fuit Magnus Newtonus, & </s> <s xml:id="echoid-s8130" xml:space="preserve">uti pariter Experientiſſimus & </s> <s xml:id="echoid-s8131" xml:space="preserve"><lb/>ingenioſus Mairanus, ad memorata attendens Tuborum phæno-<lb/>mena in L’Hiſt. </s> <s xml:id="echoid-s8132" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s8133" xml:space="preserve">Roy. </s> <s xml:id="echoid-s8134" xml:space="preserve">A°. </s> <s xml:id="echoid-s8135" xml:space="preserve">1724. </s> <s xml:id="echoid-s8136" xml:space="preserve">confitetur.</s> <s xml:id="echoid-s8137" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div233" type="section" level="1" n="233"> <head xml:id="echoid-head253" xml:space="preserve">CAPUT OCTAVUM.</head> <head xml:id="echoid-head254" style="it" xml:space="preserve">De Adſcenſu Liquorum in Tubos ſibi mutuo immiſſos.</head> <p> <s xml:id="echoid-s8138" xml:space="preserve">Antequam hanc materiam omnino relinquamus, non inutile <lb/>erit, ſi addiderimus quædam Experimenta prioribus analo-<lb/>ga, quondam ab Honorato Fabry in phyſic. </s> <s xml:id="echoid-s8139" xml:space="preserve">Tr. </s> <s xml:id="echoid-s8140" xml:space="preserve">5. </s> <s xml:id="echoid-s8141" xml:space="preserve">L. </s> <s xml:id="echoid-s8142" xml:space="preserve">2.</s> <s xml:id="echoid-s8143" xml:space="preserve">§. </s> <s xml:id="echoid-s8144" xml:space="preserve">235 de-<lb/>ſcripta; </s> <s xml:id="echoid-s8145" xml:space="preserve">a Sturmio in Colleg. </s> <s xml:id="echoid-s8146" xml:space="preserve">Curioſ. </s> <s xml:id="echoid-s8147" xml:space="preserve">Tent. </s> <s xml:id="echoid-s8148" xml:space="preserve">8, tum a Cl. </s> <s xml:id="echoid-s8149" xml:space="preserve">Petito in <lb/>L’Hiſt. </s> <s xml:id="echoid-s8150" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s8151" xml:space="preserve">Roy. </s> <s xml:id="echoid-s8152" xml:space="preserve">A°. </s> <s xml:id="echoid-s8153" xml:space="preserve">1724. </s> <s xml:id="echoid-s8154" xml:space="preserve">repetita, quæ ſpectant adſcen-<lb/>ſum liquorum in Tubos ſibi mutuo immiſſos. </s> <s xml:id="echoid-s8155" xml:space="preserve">Sumtus fuit, Tab. <lb/></s> <s xml:id="echoid-s8156" xml:space="preserve">XII. </s> <s xml:id="echoid-s8157" xml:space="preserve">ſig 9. </s> <s xml:id="echoid-s8158" xml:space="preserve">Tubus AB craſſus 2 lineas, cujus cavitas diametrum <lb/>habuit 1 lineæ hic immiſſus fuit vaſi CD, diametri 5 vel 6 linea-<lb/>rum, continenti Aquam uſque ad E, hæc adſcendit in Tubum <lb/>uſque ad F ſupra E; </s> <s xml:id="echoid-s8159" xml:space="preserve">in quo Experimento nihil inſoliti habetur, <lb/>ſed’id modo commemoratur, ut cum ſequenti comparari queat. </s> <s xml:id="echoid-s8160" xml:space="preserve"><lb/>Idem enim Tubus AB qui ante, immiſſus fuit. </s> <s xml:id="echoid-s8161" xml:space="preserve">Fig. </s> <s xml:id="echoid-s8162" xml:space="preserve">X. </s> <s xml:id="echoid-s8163" xml:space="preserve">alteri vaſi <lb/>GH, cujus diameter modo erat 2 {1/2} linear. </s> <s xml:id="echoid-s8164" xml:space="preserve">& </s> <s xml:id="echoid-s8165" xml:space="preserve">quod impletum erat <lb/>uſque ad I, I, Aqua, hæc tum in Tubum modo ingreſſa fuit uſ-<lb/>que ad K, hæſitque infra libellam I, I. </s> <s xml:id="echoid-s8166" xml:space="preserve">Si autem adimpleatur <lb/>vas GH ulterius, tum Aqua ultra oram G prominens convexam <lb/>acquirit ſuperficiem MG. </s> <s xml:id="echoid-s8167" xml:space="preserve">ſed eodem tempore Aqua ingreditur Tu- <pb o="333" file="0347" n="347" rhead="DE TUBIS CAPILLARIBUS VITREIS."/> bum AB uſque ad L, multo altius quam eſt extrema vaſis <lb/>ora G. </s> <s xml:id="echoid-s8168" xml:space="preserve">Quoniam diameter craſſitiei Tubi AB eſt 2 linearum, & </s> <s xml:id="echoid-s8169" xml:space="preserve">ea <lb/>vaſis GH 2 {1/2} linearum, patet, quod immiſſo Tubo AB in GH & </s> <s xml:id="echoid-s8170" xml:space="preserve"><lb/>quidem accurate in medio, ſuperficies interna vaſis GH & </s> <s xml:id="echoid-s8171" xml:space="preserve">externa <lb/>Tubi tantum a ſe diſtent {1/4} lineæ: </s> <s xml:id="echoid-s8172" xml:space="preserve">ſed ſuperſicies internæ Tubi <lb/>AB diſtant â ſe, I linea; </s> <s xml:id="echoid-s8173" xml:space="preserve">& </s> <s xml:id="echoid-s8174" xml:space="preserve">proinde plus, adeoque vis ambarum <lb/>ſuperficierum ſibi propiorum eſt major in Aquam, quam eſt illa <lb/>internæ ſuperſiciei Tubi: </s> <s xml:id="echoid-s8175" xml:space="preserve">adeoque altius debebit elevari Aqua intra <lb/>Tubum & </s> <s xml:id="echoid-s8176" xml:space="preserve">vas, quam in ipſo Tubo: </s> <s xml:id="echoid-s8177" xml:space="preserve">poſteaimpleto vaſe GH ultra <lb/>G ad M, ceſſat ea ratio, & </s> <s xml:id="echoid-s8178" xml:space="preserve">vas acquirit ſuperficiem ſive amplitu-<lb/>dinem indeterminatam, nam in Aquæ MMG ſuperficiem externam <lb/>non amplius agit vitri ſuperficies, ſed libera eſt, adeoque cum ſu-<lb/>perſicies interna Tubi agere pergat in Aquam, ea ultra M elevanda <lb/>erat uſque ad L.</s> <s xml:id="echoid-s8179" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8180" xml:space="preserve">Sequitur ex hoc Experimento, quo differentia inter capacitatem <lb/>vaſis GH, & </s> <s xml:id="echoid-s8181" xml:space="preserve">craſſitiem Tubi, eſt minor, eo altitudinem II Aquæ <lb/>in vaſe ſupra eam in K in Tubo eſſe majorem: </s> <s xml:id="echoid-s8182" xml:space="preserve">2°. </s> <s xml:id="echoid-s8183" xml:space="preserve">dari caſum in <lb/>quo altitudines in vaſe GH, & </s> <s xml:id="echoid-s8184" xml:space="preserve">Tubo AB erunt æquales, ſi nempe <lb/>diſtantiæ inter ſuperficies fuerint æquales.</s> <s xml:id="echoid-s8185" xml:space="preserve"/> </p> <pb o="334" file="0348" n="348"/> </div> <div xml:id="echoid-div234" type="section" level="1" n="234"> <head xml:id="echoid-head255" xml:space="preserve">DISSERTATIO</head> <head xml:id="echoid-head256" xml:space="preserve">PHYSICA <lb/>EXPERIMENTALIS <lb/>DE</head> <head xml:id="echoid-head257" xml:space="preserve">ATTRACTIONE SPECULORUM <lb/>PLANORUM VITREORUM.</head> <p> <s xml:id="echoid-s8186" xml:space="preserve">Demonſtravimus in præcedenti de Tubis Capillaribus Diſierta-<lb/>tione, vitrum vi attractrice eſſe donatum, eâque liquores <lb/>ad ſe rapere, atque ad varias altitudines elevare; </s> <s xml:id="echoid-s8187" xml:space="preserve">eo majores, quo <lb/>ſuperſicies attrahentes ſibi ſunt propiores; </s> <s xml:id="echoid-s8188" xml:space="preserve">eo minores, quo magis <lb/>a ſe mutuo ſuperficies deſtiterint: </s> <s xml:id="echoid-s8189" xml:space="preserve">Vis eadem vitri attractrix aliis ad-<lb/>huc probari poteſt modis, & </s> <s xml:id="echoid-s8190" xml:space="preserve">imprimis ope ſpeculorum planorum, <lb/>quorum phænomena cum facile obſervari queant, cum admodum <lb/>jucunda, & </s> <s xml:id="echoid-s8191" xml:space="preserve">primâ fronte admiranda ſint, atque ex iis nonnihil <lb/>lucis prioribus affundi poſſit, arbitrabar ea eſſe hujus loci, hanc-<lb/>que Diſſertationem priori ſubnectendam, quamvis non multum no-<lb/>vi contineat, ſed potiſſimum Experimenta ab Hauksbejo in Phy-<lb/>lico Mechanical Experiments deſcripta, aut a Cl Jurino in Phi-<lb/>loſopbicis Actis Britannicis relata, aut a magno ’sGravezandio, <lb/>Batavicæ Philoſophiæ decore, ſubtilius examinata: </s> <s xml:id="echoid-s8192" xml:space="preserve">Verum vitio <lb/>non vertitur Geometris eandem veritatem ſæpius diverfâ methodo <lb/>demonſtraſſe, non igitur nobis in Phyſicis ita etiam perrexiſie de-<lb/>decori fore ſp ro.</s> <s xml:id="echoid-s8193" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div235" type="section" level="1" n="235"> <head xml:id="echoid-head258" xml:space="preserve">EXPERIMENTUM I.</head> <p> <s xml:id="echoid-s8194" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8195" xml:space="preserve">13. </s> <s xml:id="echoid-s8196" xml:space="preserve">fig. </s> <s xml:id="echoid-s8197" xml:space="preserve">1. </s> <s xml:id="echoid-s8198" xml:space="preserve">Vitrum planum utrimque politum, quod ſpe- <pb o="335" file="0349" n="349" rhead="DE SPECULIS VITREIS."/> culo inſerviret, ſi alterutra ſuperficies Mercurio obduceretur, al-<lb/>titudinis 9 {4/10} pollic. </s> <s xml:id="echoid-s8199" xml:space="preserve">latitudinis 8 pollic. </s> <s xml:id="echoid-s8200" xml:space="preserve">FCD, mundum & </s> <s xml:id="echoid-s8201" xml:space="preserve">ſicciſ-<lb/>ſimum, impoſitum fuit perpendiculariter aquæ pluviæ, puriſſimæ <lb/>ADGB hæc adſcendit utrimque ad ſuperficiem Vitri, æque alte, <lb/>curvam quandam ſuperficiem C G, c g, formans, cujus altitudo <lb/>C D perpendicularis ſupra Aquam A B erat circiter æqualis {3/30} polli-<lb/>cis, circiter dico, quoniam tam accurate menſurare non potui ac <lb/>deſiderabam, cujus longitudo DG etiam circiter æqualis {5/30} pollic. <lb/></s> <s xml:id="echoid-s8202" xml:space="preserve">erat.</s> <s xml:id="echoid-s8203" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8204" xml:space="preserve">Ut attractio aquæ ad hoc Vitrum intelligatur clarius, ſit KLMO <lb/>Vitrum, & </s> <s xml:id="echoid-s8205" xml:space="preserve">particula quædam Aquæ X, tam parum remota, ut <lb/>agere in vitrum & </s> <s xml:id="echoid-s8206" xml:space="preserve">ab eo attrahi poſſit; </s> <s xml:id="echoid-s8207" xml:space="preserve">attrahetur igitur X a pun-<lb/>cto M in perpendiculari X M, & </s> <s xml:id="echoid-s8208" xml:space="preserve">Quia præter punctum M agit ma-<lb/>gna ſuperficies vitri, quæ exporrecta concipiatur uſque ad M L, <lb/>M O, etiam trahetur particula X. </s> <s xml:id="echoid-s8209" xml:space="preserve">ſecundum L X, ac O X, a <lb/>punctis L, O, atque ita a puncto quolibet intermedio inter L M <lb/>& </s> <s xml:id="echoid-s8210" xml:space="preserve">O M; </s> <s xml:id="echoid-s8211" xml:space="preserve">poſitis autem his punctis æque diſtantibus ab M, erit vis <lb/>attrahens æqualis quamobrem ſi centro M, radio quolibet ab M verſus <lb/>L tendente deſcribantur circuli ſupra ſuperficiem vitri, horum integræ <lb/>peripheriæ æquali vi attrahente in quolibet puncto pollebunt; </s> <s xml:id="echoid-s8212" xml:space="preserve">actio <lb/>autem harum omnium erit verſus M, quamobrem particula X fere-<lb/>tur in rectâ X M uſque ad M perpendiculari ſupra K O: </s> <s xml:id="echoid-s8213" xml:space="preserve">Si X nunc <lb/>fuerit gutta Aquæ, compoſita ex pluribus particulis, hæc etiam tra-<lb/>hetur, & </s> <s xml:id="echoid-s8214" xml:space="preserve">movebitur ſecundum rectam M X uſque ad contactum <lb/>M, tum vero partes laterales trahentur verſus L & </s> <s xml:id="echoid-s8215" xml:space="preserve">O, adeoque <lb/>explicabitur gutta quaquaverſum, eundo per varios ſibi concentri-<lb/>cos circulos, ſi ſua vis attrahens ſuperetur a vi attrahente vitri, <lb/>adeoque hac attractione agitur gutta haud aliter, ac ſi a ſui parte <lb/>poſtica ab alio plano premeretur, qua preſſione etiam explicaretur <lb/>& </s> <s xml:id="echoid-s8216" xml:space="preserve">applanaretur.</s> <s xml:id="echoid-s8217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8218" xml:space="preserve">Quia autem attractio puncti Mjuvatur ab attractionibus omnium <lb/>punctorum inter M L & </s> <s xml:id="echoid-s8219" xml:space="preserve">M O intermediorum, illæ attractiones <lb/>quæ ſunt proximæ puncto M, juvantur ab aliis remotis, ſed a pau-<lb/>cioribus, & </s> <s xml:id="echoid-s8220" xml:space="preserve">quæ plus diſtant a puncto M, iterum a paucioribus ma-<lb/>gis adhuc remotis, ſequitur vires attrahentes in puncto M eſſe ma-<lb/>ximas, omnium vero aliorum punctorum S, V, Q, P, L, O, <pb o="336" file="0350" n="350" rhead="DISSERTATIO"/> eſſe eo minores, quo plus diſtant a puncto M.</s> <s xml:id="echoid-s8221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8222" xml:space="preserve">Sed ipſa vis attrahens cujuslibet puncti decreſcit, quo corpus, <lb/>quod attrahitur, plus diſtat a puncto attrahente, igitur corpus X <lb/>attrahetur a punctis M, S, V, Q, P, L, eo minus, quo diſtan-<lb/>tiæ X M, X S, X V, X Q &</s> <s xml:id="echoid-s8223" xml:space="preserve">c. </s> <s xml:id="echoid-s8224" xml:space="preserve">ſuntmajores. </s> <s xml:id="echoid-s8225" xml:space="preserve">Sivero fuerint vires <lb/>attrahentes cujuslibet puncti, uti reciproce diſtantia attrahentis & </s> <s xml:id="echoid-s8226" xml:space="preserve"><lb/>attracti, tum erit vis puncti M in corpus X, ad vim puncti S in idem <lb/>X, uti S X ad M X. </s> <s xml:id="echoid-s8227" xml:space="preserve">& </s> <s xml:id="echoid-s8228" xml:space="preserve">eodem modo vis puncti L in X erit ad vim <lb/>puncti M in X, uti recta M X ad L X.</s> <s xml:id="echoid-s8229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8230" xml:space="preserve">Concipiatur X eſſe centrum circuli, X M radium, erit M L <lb/>Tangens circuli in puncto M, ducantur ex punctis S, V, Q, P, <lb/>L, Tangentis ad centrum X rectæ, erunt hæ ſecantes angulorum <lb/>S X M, V X M, Q X M, P X M, L X M, erit igitur vis <lb/>puncti L, qua trahit X, ad vim puncti S, quâ trahit idem X uti <lb/>S X ad L X, hoc eſt uti ſecans anguli S X M ad ſecantem anguli <lb/>L X M, ſive in ratione inverſa ſecantium angulorum, quos for-<lb/>mant diſtantiæ cum recta M X.</s> <s xml:id="echoid-s8231" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8232" xml:space="preserve">Supra autem innuimus vim attrahentem puncti M adjuvari ab at-<lb/>tractionibus omnium punctorum inter M & </s> <s xml:id="echoid-s8233" xml:space="preserve">K ab unâ parte: </s> <s xml:id="echoid-s8234" xml:space="preserve">ſit vis <lb/>attrahens hoc modo conſiderata, uti eſt diſtantia a puncto L, erit <lb/>tum vis in S ad eam in M, uti L S ad L M; </s> <s xml:id="echoid-s8235" xml:space="preserve">aſſumatur quæcunque <lb/>M Y in M X, atque ducantur ex punctis S, V, Q, P, L paral-<lb/>lelæ ad M X, erit vis in S ad eam in M, uti S a ad M Y: </s> <s xml:id="echoid-s8236" xml:space="preserve">Quam-<lb/>obrem ſi M Y foret maſſa fiuida, hac ratione elevaretur uſque ad <lb/>L formaretque Triangulum rectangulum M L Y. </s> <s xml:id="echoid-s8237" xml:space="preserve">Sed hæc vis at-<lb/>trahens accedit alteri virtuti, quæ eſt in ratione inverſâ Secantium <lb/>explicata, adeoque lineæ M Y adjungatur quædam Y X, quæ ſit <lb/>uti Secans anguli L X M, & </s> <s xml:id="echoid-s8238" xml:space="preserve">ad L jungatur linea æqualis radio cir-<lb/>culi, cujus Secans eſt Y X ſub angulo L X Y, tum ad S a jungatur <lb/>Secans anguli P X M quæ ſit a c, & </s> <s xml:id="echoid-s8239" xml:space="preserve">reciproce ad P a jungatur Se-<lb/>cans anguli S X M. </s> <s xml:id="echoid-s8240" xml:space="preserve">quæ ſit a f: </s> <s xml:id="echoid-s8241" xml:space="preserve">ita ut ad V a jungatur Secans an-<lb/>guli Q X M, quæ ſit a d, & </s> <s xml:id="echoid-s8242" xml:space="preserve">ad Z a jungatur Secans anguli V X M <lb/>quæ ſit e a: </s> <s xml:id="echoid-s8243" xml:space="preserve">puncta c, d, e, f, l jungantur, deſcripta erit cur-<lb/>va, ei ſimilis, quam Aquain Experimento exhibet: </s> <s xml:id="echoid-s8244" xml:space="preserve">l, f, e, d, c, x. <lb/></s> <s xml:id="echoid-s8245" xml:space="preserve">Eſſe curvam ideo patet, quia cum æquales capiuntur M S, S V, <lb/>V Q, Q P, P L. </s> <s xml:id="echoid-s8246" xml:space="preserve">evadent Tangentes a puncto M, duplo, tri- <pb o="337" file="0351" n="351" rhead="DE SPECULIS VITREIS."/> pio, quadruplo majores quam MS: </s> <s xml:id="echoid-s8247" xml:space="preserve">ita tamen non increſcunt Se-<lb/>cantes: </s> <s xml:id="echoid-s8248" xml:space="preserve">ſit enim MS Tangens anguli gradus unius 174551, erit Se-<lb/>cans 10001523: </s> <s xml:id="echoid-s8249" xml:space="preserve">ſed Tangens duplo major VM 349102 nondum <lb/>habebit reſpondentem eidem angulo Secantem 10006095. </s> <s xml:id="echoid-s8250" xml:space="preserve">ita QM <lb/>Tangenti triplo majori 523653 nondum reſpondebit Secans <lb/>10013723: </s> <s xml:id="echoid-s8251" xml:space="preserve">hiſce igitur non creſcentibus cum illis in eadem pro-<lb/>portione, non poterit L f, e, d, c, x eſſerecta, ſed debebit eſſe curva. </s> <s xml:id="echoid-s8252" xml:space="preserve">Si <lb/>accurate poſſemus obiervare altitudinem ML, & </s> <s xml:id="echoid-s8253" xml:space="preserve">longitudinem MX, <lb/>poſſent in curva ambæ viresattrahentes determinari, quod nunc im-<lb/>poſſibile manet: </s> <s xml:id="echoid-s8254" xml:space="preserve">& </s> <s xml:id="echoid-s8255" xml:space="preserve">magis, cum diverſæſpeciei vitrum, etiam diverſam <lb/>attrahendivim habet; </s> <s xml:id="echoid-s8256" xml:space="preserve">unde forſitan curvæ inter ſe admodum differen-<lb/>tes formabuntur, quarum naturam inveſtigaſſe non magnæ erit <lb/>utilitatis.</s> <s xml:id="echoid-s8257" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8258" xml:space="preserve">Redeamus nunc ad vitrum FCD, quod Aquæ immiſ-<lb/>fum fuit, quæ attrahitur â puncto D maxime & </s> <s xml:id="echoid-s8259" xml:space="preserve">agitur deter-<lb/>minatione B D, tum a punctis inter D & </s> <s xml:id="echoid-s8260" xml:space="preserve">C ſemper attrahitur mi-<lb/>nus: </s> <s xml:id="echoid-s8261" xml:space="preserve">concipiantur ductæ rectæ, Sc, Sd, Se perpendiculares in ſu-<lb/>perficiem, hæ repræſentabunt vires cujuslibet puncti attrahentis, <lb/>quarum ſumma erit æqualis quantitati attractæ, ſive gravitati A-<lb/>quæ C D G, deorſum nitentis, cum altitudo C D Aquæ manet <lb/>conſtans. </s> <s xml:id="echoid-s8262" xml:space="preserve">Si enim gravitas particularum Aquæ foret major, quam eſt <lb/>vis elevans, Aqua deſcenderet; </s> <s xml:id="echoid-s8263" xml:space="preserve">ſi vis elevans foret major, plus Aquæ <lb/>adſcenderet, donec ſibi gravitas & </s> <s xml:id="echoid-s8264" xml:space="preserve">vis elevans æquilibratæ eſſent.</s> <s xml:id="echoid-s8265" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8266" xml:space="preserve">Quia inferior pars vitri DR eſt ſub Aqua ſubmerſa, hujus quod <lb/>libet punctum Aquam ad ſe trahit, vi æquali, idcirco curva non <lb/>formatur ſub Aqua: </s> <s xml:id="echoid-s8267" xml:space="preserve">ut tamen demonſtremus curvam cæteroquin a <lb/>fluido attracto ad D R ſormatum iri, ſuperficiei Aquæ AB affunda-<lb/>tur quædam olei quantitas, deinde vitro FR immerſo Aquæ ad <lb/>profunditatem I vel 1 {1/2} lineæ exhibebitur ſuperſicies curva <lb/>olei attracti, æque ſub Aqua, quam ſupra Aquam: </s> <s xml:id="echoid-s8268" xml:space="preserve">ſi autem pro-<lb/>fundius demittatur vitrum, tum preſſio Aquæ ſuperans olei attra-<lb/>ctionem, id omne a vitro expellic, donec ſuperficiem parallelam <lb/>horizonti acquiſiverit.</s> <s xml:id="echoid-s8269" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8270" xml:space="preserve">Quia obſervaveram Tubos capillares longiſſimos, ad majorem <lb/>altitudinem elevare Aquam quam breviores, exploravi an quoque <lb/>vitrum FDK majus aut minus, differentiam elevatæ Aquæ exhi- <pb o="338" file="0352" n="352" rhead="DISSERTATIO"/> beret? </s> <s xml:id="echoid-s8271" xml:space="preserve">Sed nullam deprehendere potui, adſcendente Aqua juxta vi-<lb/>trum parvum æque alte, ut videbatur, quam juxta magnum.</s> <s xml:id="echoid-s8272" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div236" type="section" level="1" n="236"> <head xml:id="echoid-head259" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s8273" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8274" xml:space="preserve">13: </s> <s xml:id="echoid-s8275" xml:space="preserve">fig. </s> <s xml:id="echoid-s8276" xml:space="preserve">17. </s> <s xml:id="echoid-s8277" xml:space="preserve">& </s> <s xml:id="echoid-s8278" xml:space="preserve">18. </s> <s xml:id="echoid-s8279" xml:space="preserve">Si idem vitrum A B, immittatur Aquæ <lb/>oblique, cujus ſuperficies ſit C H, hæc ab eâ parte, quâ angulus <lb/>obtuſus formatur a vitro & </s> <s xml:id="echoid-s8280" xml:space="preserve">Aqua ipſa, parum adſcendit, atque eo <lb/>minus, quo angulus fuerit obtuſior, curvam deſcribendo, quam <lb/>repræſentat D E: </s> <s xml:id="echoid-s8281" xml:space="preserve">adſcendit autem Aqua alte, quâ parte angulus <lb/>acutus formatur, atque eo altius, quo angulus eſt acutior, forman-<lb/>do curvam F G.</s> <s xml:id="echoid-s8282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8283" xml:space="preserve">Primâ fronte videretur Aqua altius adſcenſura ſupra planum in-<lb/>clinatum, quam ſupra perpendiculare ad horizontem quod etiam fieret <lb/>vi attrahente puncti O in libella poſiti, ſed quia ſuperficies vitri BO <lb/>propius accedit ad ſuperficiem Aquæ C D O, quo vitrum A B plus <lb/>inclinatum eſt, hinc eo fortius trahit Aquam C D O ad ſe, quare <lb/>attractio ſupremæ partis O E A ſuperatur ab attractione partis O B, <lb/>unde eo minus adſcendit D E, quo O B propius acceſſit ad ſuper-<lb/>ficiem Aquæ C D, donec tandem vis D E fere penitus ſit ſublata, <lb/>& </s> <s xml:id="echoid-s8284" xml:space="preserve">C D E vix differat â rectâ horizontali: </s> <s xml:id="echoid-s8285" xml:space="preserve">hinc patet quare F C ſit <lb/>eo altius, quo vitrum magis inclinatum eſt ad ſuperficiem Aquæ <lb/>G H, nam eo propius Aquæ G H poſitum, majoribus viribus <lb/>ipſam attrahendo, altius quoque elevat: </s> <s xml:id="echoid-s8286" xml:space="preserve">curva autem eſt F G ſu-<lb/>perficies attractæ Aquæ, ob cauſam in Exper. </s> <s xml:id="echoid-s8287" xml:space="preserve">1. </s> <s xml:id="echoid-s8288" xml:space="preserve">allatam; </s> <s xml:id="echoid-s8289" xml:space="preserve">mu-<lb/>tatur autem curva perpetuo, mutata vitri inclinatione ad <lb/>Aquam.</s> <s xml:id="echoid-s8290" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div237" type="section" level="1" n="237"> <head xml:id="echoid-head260" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s8291" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8292" xml:space="preserve">13. </s> <s xml:id="echoid-s8293" xml:space="preserve">fig. </s> <s xml:id="echoid-s8294" xml:space="preserve">19. </s> <s xml:id="echoid-s8295" xml:space="preserve">Si ſpeculum A B, Aquæ immiſſum, perpen-<lb/>diculariter attollatur, atque lente & </s> <s xml:id="echoid-s8296" xml:space="preserve">pedetentim extrahatur ex A-<lb/>quâ; </s> <s xml:id="echoid-s8297" xml:space="preserve">hæc ſuperficiei inferioris marginis vitri B adhærebit, atque <lb/>perget utrimque formare curvam E D, F G, extremis D, G eo <lb/>propius ad ſe accedentibus, quo vitrum B altius ex Aquâ ſublatum <lb/>eſt: </s> <s xml:id="echoid-s8298" xml:space="preserve">quod ſi admodum craſſum fuerit, accedunt puncta E F propius <pb o="339" file="0353" n="353" rhead="DESPECULIS VITREIS."/> ad ſe mutuo imminuta curvarum D E, F G, diſtantiâ, quam eſt <lb/>craſſities vitri, cæteroquin manet E F ejuſdem latitudinis cum vi-<lb/>tri craſſitie; </s> <s xml:id="echoid-s8299" xml:space="preserve">elevato plus vitro extra Aquam, cadit E F D G ſepa-<lb/>rata â margine B. </s> <s xml:id="echoid-s8300" xml:space="preserve">Adhæret Aqua ipſi B, quamdiu vis attractrix vi-<lb/>tri ſuperat gravitatem Aquæ E F D G & </s> <s xml:id="echoid-s8301" xml:space="preserve">vim attrahentis Aquæ <lb/>C D G H: </s> <s xml:id="echoid-s8302" xml:space="preserve">gravitate autem & </s> <s xml:id="echoid-s8303" xml:space="preserve">vi attrahente Aquæ ſuperante vim at-<lb/>trahentem vitri, cadit ab eo ſoluta Aqua. </s> <s xml:id="echoid-s8304" xml:space="preserve">In hoc Experimento at-<lb/>tendendum eſt, curvas E D, F G formari ab attractione ipſius Aquæ <lb/>C D G H, quemadmodum enim in fig. </s> <s xml:id="echoid-s8305" xml:space="preserve">1. </s> <s xml:id="echoid-s8306" xml:space="preserve">demonſtravimus guttam X <lb/>a plano L M attractam induere curvam L e d c x ab una parte, <lb/>ſimilemque formatum iri ab alterâ parte MO, gutta major hic tan-<lb/>tum eſt E F D G in fig. </s> <s xml:id="echoid-s8307" xml:space="preserve">19. </s> <s xml:id="echoid-s8308" xml:space="preserve">elevata ſupra C D G H planum ſimile <lb/>illi L M fig. </s> <s xml:id="echoid-s8309" xml:space="preserve">1. </s> <s xml:id="echoid-s8310" xml:space="preserve">adeoque ab hoc attrahitur cum iiſdem phænomenis, <lb/>quæ in Exper. </s> <s xml:id="echoid-s8311" xml:space="preserve">1. </s> <s xml:id="echoid-s8312" xml:space="preserve">explicuimus.</s> <s xml:id="echoid-s8313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div238" type="section" level="1" n="238"> <head xml:id="echoid-head261" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s8314" xml:space="preserve">Sumta ſuerunt duo ſpecula ejuſdem magnitudinis ac in Experimento <lb/>I. </s> <s xml:id="echoid-s8315" xml:space="preserve">ex eodem vitro, ſatis accurate plana, pura, tam ſicca ac habe-<lb/>ri poſſunt, & </s> <s xml:id="echoid-s8316" xml:space="preserve">æqualia, inter quæ a parte dextra & </s> <s xml:id="echoid-s8317" xml:space="preserve">ſiniſtra inter-<lb/>ponebantur 40 lamellæ cupreæ, æque craſſæ, ut ſpeculorum ſuper-<lb/>perficies eſſent ſibi parallelæ; </s> <s xml:id="echoid-s8318" xml:space="preserve">tum lamellæ, compreſſæ ſimul cumſpe-<lb/>culis, relinquebant inter hæc diſtantiam pollicis R henolandici 0. </s> <s xml:id="echoid-s8319" xml:space="preserve">12, <lb/>ſpeculorum marginibus inferioribus Aquæ immerſis, hæc adſcendit <lb/>intra ſpecula ad altitudinem lin: </s> <s xml:id="echoid-s8320" xml:space="preserve">3, 1, ſuperficiem æquabilem ſuperio-<lb/>rem formando: </s> <s xml:id="echoid-s8321" xml:space="preserve">utrimque ſublatis 20 lamellis cupreis, & </s> <s xml:id="echoid-s8322" xml:space="preserve">ſiccatis <lb/>ſpeculorum ſuperficiebus, inter hæc erat diſtantia duplo minor <lb/>priori, ſpeculis ut ante Aquæ immiſſis, obſervatus adſcenſus fuit <lb/>ad lin. </s> <s xml:id="echoid-s8323" xml:space="preserve">6, 2.</s> <s xml:id="echoid-s8324" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8325" xml:space="preserve">Sublatis utrimque rurfus 10 lamellis, ita ut ſpeculorum diſtantia <lb/>iterum fuerit duplo minor, adſcendit Aqua inter ea ad poll. </s> <s xml:id="echoid-s8326" xml:space="preserve">1, <lb/>24 Et rurſus ſublatis 5 lamellis ex commiſſura, fiebat Aquæ intra <lb/>ſpecula adſcenſus ad pol, 2, 48.</s> <s xml:id="echoid-s8327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8328" xml:space="preserve">Corol. </s> <s xml:id="echoid-s8329" xml:space="preserve">Ergo eſt altitudo adſcendentis Aquæ intra ſpeculain ratione <lb/>inverſâ diſtantiarum a ſe invicem. </s> <s xml:id="echoid-s8330" xml:space="preserve">Hanc legem quoque ſupra depre-<lb/>hendimus locum habere in Tubis capillaribus æque longis; </s> <s xml:id="echoid-s8331" xml:space="preserve">in qui- <pb o="340" file="0354" n="354" rhead="DISSERTATIO"/> bus altitudines Aquæ erant in ratione inverſa diametrorum.</s> <s xml:id="echoid-s8332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8333" xml:space="preserve">Corob. </s> <s xml:id="echoid-s8334" xml:space="preserve">2. </s> <s xml:id="echoid-s8335" xml:space="preserve">Ergo quantitates Aquæ elevatæ intra hæc ſpecula ſem-<lb/>per fuerunt æquales inter ſe.</s> <s xml:id="echoid-s8336" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8337" xml:space="preserve">Scholium. </s> <s xml:id="echoid-s8338" xml:space="preserve">Quando duo ultima inſtituebantur Experimenta, Aqua <lb/>intra ſpecula adſcendit non æquabiliter, ſed motu & </s> <s xml:id="echoid-s8339" xml:space="preserve">ſuperſicie ad-<lb/>modum inæquabili, adſcendit enim ſub forma dentium ſerræ, nunc <lb/>uno dente aſſurgente, quaſi ad altitudinem 1 vel 2 linearum; </s> <s xml:id="echoid-s8340" xml:space="preserve">qui tum <lb/>paulum videtur quieſcere, nunc dentealiquo vicino aſſurgente; </s> <s xml:id="echoid-s8341" xml:space="preserve">inte-<lb/>rim incipit dens prior iterum aſſurgere; </s> <s xml:id="echoid-s8342" xml:space="preserve">ex quo dein novi oriun-<lb/>tur dentes, quorum nonnulli ſuam Aquam communicant vicinis, <lb/>nonnulli non, relinquendo in principio ſpatium intermedium non <lb/>humectatum, haud aliter ac ſi Aqua hinc inde ſordes deponeret; <lb/></s> <s xml:id="echoid-s8343" xml:space="preserve">ejuſmodi autem loca conſpiciuntur plurima. </s> <s xml:id="echoid-s8344" xml:space="preserve">Inæqualis Aquæ ad-<lb/>ſcenſus pendet 1°. </s> <s xml:id="echoid-s8345" xml:space="preserve">a reſiſtentia particularum aërearum, quæ inter ſpe-<lb/>cula interceptæ ſunt, nec facile avelluntur ab eorum ſuperficiebus, <lb/>aliæ tamen facilius aliis averruncantur, unde iſta inæqualitas inſtar <lb/>dentium, quibus Aqua aſſurgit. </s> <s xml:id="echoid-s8346" xml:space="preserve">2°. </s> <s xml:id="echoid-s8347" xml:space="preserve">ſuperficierum vitri ſcabrities <lb/>quoque cauſa eſt, cum enim vitrum ſit vallibus montibuſque exa-<lb/>ſperatum, valles vero magis a ſe diſtent, quam montr-<lb/>culi, attrahetur Aqua minus a remotioribus vallibus, quam <lb/>a ſibi proximis montibus: </s> <s xml:id="echoid-s8348" xml:space="preserve">hiſce vero ſe contingentibus, impeditur <lb/>Aquæ acceſſus, unde loca quædam in initio non humectari con-<lb/>ſpiciuntur: </s> <s xml:id="echoid-s8349" xml:space="preserve">3°. </s> <s xml:id="echoid-s8350" xml:space="preserve">Sunt etiam aliquando exiguæ ſordes, inconſpicuæ <lb/>oculo, quæ vitro adhærentes hinc inde, ſua vi repellente adſcen-<lb/>ſum Aquæ prohibent.</s> <s xml:id="echoid-s8351" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8352" xml:space="preserve">Schol. </s> <s xml:id="echoid-s8353" xml:space="preserve">2. </s> <s xml:id="echoid-s8354" xml:space="preserve">Hauksbejus in Appendice Phyſ. </s> <s xml:id="echoid-s8355" xml:space="preserve">Mech. </s> <s xml:id="echoid-s8356" xml:space="preserve">Exper. </s> <s xml:id="echoid-s8357" xml:space="preserve">pag: <lb/></s> <s xml:id="echoid-s8358" xml:space="preserve">329, eadem capiens Experimenta, eandem legem inter altitudi-<lb/>nem elevati fluidi & </s> <s xml:id="echoid-s8359" xml:space="preserve">ſpeculorum diſtantias obſervavit, verum quia <lb/>non menſuravit altitudinem Fluidi elevati ſupra ſuperficiem Fluidi <lb/>ſtagnantis, repetenda duxi hæc Experimenta; </s> <s xml:id="echoid-s8360" xml:space="preserve">uſus fuit Hauksbejus <lb/>ſpiritu Vini: </s> <s xml:id="echoid-s8361" xml:space="preserve">ſuccedunt vero Experimenta eodem modo cum Aqua; </s> <s xml:id="echoid-s8362" xml:space="preserve"><lb/>Vino, Aceto, Spiritu vini; </s> <s xml:id="echoid-s8363" xml:space="preserve">alios liquores non examinavi, nullus ta-<lb/>men dubito, quin idem ſit ſucceſſus futurus cum omnibus liquori-<lb/>bus tenuioribus.</s> <s xml:id="echoid-s8364" xml:space="preserve"/> </p> <pb o="341" file="0355" n="355" rhead="DE SPECULIS VITREIS."/> </div> <div xml:id="echoid-div239" type="section" level="1" n="239"> <head xml:id="echoid-head262" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s8365" xml:space="preserve">Si ambo ſpecula ſicciſſima & </s> <s xml:id="echoid-s8366" xml:space="preserve">puriſſima ſibi imponantur, ita ut <lb/>nihil ſit intermedium, quodilla ſeparet, atque apprima tur adſe, im-<lb/>poſita margine inferiori Aquæ, hæc adſcendet intra commiſſuram <lb/>ſub forma dentium ſerræ, uti ſupra expoſui, & </s> <s xml:id="echoid-s8367" xml:space="preserve">uſque ad margi-<lb/>nem ſuperiorem elevabitur, a quâ tamen diſtabit ſemper poll. <lb/></s> <s xml:id="echoid-s8368" xml:space="preserve">0. </s> <s xml:id="echoid-s8369" xml:space="preserve">1.</s> <s xml:id="echoid-s8370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8371" xml:space="preserve">An ad quamcunque altitudinem adſcenderet Aqua intra hæc ſpe-<lb/>cula non determino, ſpecula enim, quibuſcum hæc Experimenta inſti-<lb/>tui, parvam altitudinem, novem nempe pollicum modo habebant.</s> <s xml:id="echoid-s8372" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8373" xml:space="preserve">Adſcendit autem Aqua inter ſpecula, licet ſibi ſint impoſita, <lb/>quia aſperam habent ſuperſiciem; </s> <s xml:id="echoid-s8374" xml:space="preserve">& </s> <s xml:id="echoid-s8375" xml:space="preserve">ideo intetvalla ſatis patula re-<lb/>linquunt, quæ particulas Aquæ recipere poſſunt.</s> <s xml:id="echoid-s8376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8377" xml:space="preserve">Quoſuperficies fuerint magis politæ, eo propius ſibiſpecula apponi <lb/>poterunt, & </s> <s xml:id="echoid-s8378" xml:space="preserve">eo altius Aqua elevabitur; </s> <s xml:id="echoid-s8379" xml:space="preserve">quare diverſa altitudo <lb/>Aquæ obſervabitur pro variâ aſperitate vel politurâ ſuperſicie-<lb/>rum.</s> <s xml:id="echoid-s8380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8381" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s8382" xml:space="preserve">Attrahunt hæc ſpecula ſe mutuo vi inſigni, ſicciſſima <lb/>enim & </s> <s xml:id="echoid-s8383" xml:space="preserve">pura, ſibi tantum impoſita, adeo cohærent, ut elevato ſu-<lb/>premo horizontaliter, alterum maneat applicatum parti inferiori, <lb/>nec corpus videatur ad Magnetem propius accedere, quam ejuſmodi <lb/>vitrum: </s> <s xml:id="echoid-s8384" xml:space="preserve">ne autem quis preſſionem Aëris hic invocet, nam in va-<lb/>cuo Boyleano obſervatur omnino idem.</s> <s xml:id="echoid-s8385" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div240" type="section" level="1" n="240"> <head xml:id="echoid-head263" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s8386" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8387" xml:space="preserve">13. </s> <s xml:id="echoid-s8388" xml:space="preserve">fig. </s> <s xml:id="echoid-s8389" xml:space="preserve">16. </s> <s xml:id="echoid-s8390" xml:space="preserve">Hauksbejus in Appendice ad opus ſuum Expe-<lb/>rimentale adjecit aliquot notabilia obſervata in Exp. </s> <s xml:id="echoid-s8391" xml:space="preserve">19. </s> <s xml:id="echoid-s8392" xml:space="preserve">& </s> <s xml:id="echoid-s8393" xml:space="preserve">23, quæ <lb/>quoniam accurate ſatis inſtituta ſunt, digniſſima ſunt quæ recen-<lb/>ſeantur.</s> <s xml:id="echoid-s8394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8395" xml:space="preserve">Sumta ſunt duo ſpecula A B C D, A Z P K 20 pollices longa, quæ <lb/>ſibi ita imponebantur, ut ad unum latus A B ſe contingerent, & </s> <s xml:id="echoid-s8396" xml:space="preserve">ad <lb/>oppoſitam partem D C, K P a ſe diſtarent; </s> <s xml:id="echoid-s8397" xml:space="preserve">adeoque formabaut <lb/>duo plana, quæ angulum continebant D A K 20 minutorum:</s> <s xml:id="echoid-s8398" xml:space="preserve"> <pb o="342" file="0356" n="356" rhead="DISSERTATIO"/> hæc ita imponebantur Aquæ X Z, ut linea contactus A B <lb/>eſſet perpendicularis in horizontem, Aqua tum inter hæc ſpe-<lb/>cula adſcendit, humillime, quâ parte maxime â ſe diſtabant, <lb/>altiſſime, ubi ſe contingebant, & </s> <s xml:id="echoid-s8399" xml:space="preserve">formabat curvam, e f g <lb/>quam figura, una cum apparatu, repræſentat, quæ menſura-<lb/>ta accurate ad quamlibet diſtantiam a lineâ contactûs ha-<lb/>buit altitudinem ſupra ſuperficiem Aquæ ſibi adſcriptam, quam ex-<lb/>hibet quoque hæc Tabula.</s> <s xml:id="echoid-s8400" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia in \\ pollicibus, a linea \\ contactus # Numerus linearum \\ Aquæ elevatæ \\ ad quaslibet diſtantias. <lb/>13 # 1 <lb/>9 # 2 <lb/>7 # 3 <lb/>6 # 3 {3/4} <lb/>5 # 5 <lb/>4 # 6 {3/4} <lb/>3 # 9 <lb/>2 {1/2} # 12 <lb/>2 # 15 {1/2} <lb/>1 {3/4} # 18 <lb/>1 {1/2} # 21 {1/2} <lb/>1 {1/4} # 27 {1/2} <lb/>1 # 35 <lb/>{3/4} # 50 <lb/>{1/2} # 76 <lb/></note> <p> <s xml:id="echoid-s8401" xml:space="preserve">Deinde aperuit ſpecula magis, ita ut caperent angulum 40 minu-<lb/>torum, reliquis manentibus ut ante, & </s> <s xml:id="echoid-s8402" xml:space="preserve">menſuratâ altitudine liqui-<lb/>di elevati ad quamlibet a lineâ contactus diſtantiam, condidit Ta-<lb/>bulam ſequentem.</s> <s xml:id="echoid-s8403" xml:space="preserve"/> </p> <pb o="343" file="0357" n="357" rhead="DE SPECULIS VITREIS."/> <note position="right" xml:space="preserve"> <lb/>Diſtantia \\ pollicum \\ a contactu # Numerus \\ linearum \\ Aquæ elevatæ <lb/>9 # 1 <lb/>6 # 2 <lb/>4 {3/4} # 3 <lb/>3 # 4 {3/4} <lb/>2 {1/2} # 6 <lb/>2 # 7 {1/2} <lb/>1 {1/2} # 10 <lb/>1 {1/4} # 12 <lb/>1 # 15 <lb/>{3/4} # 19 <lb/>{1/2} # 28 <lb/>{1/4} # 50 <lb/></note> <p> <s xml:id="echoid-s8404" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8405" xml:space="preserve">XIII. </s> <s xml:id="echoid-s8406" xml:space="preserve">Fig. </s> <s xml:id="echoid-s8407" xml:space="preserve">2. </s> <s xml:id="echoid-s8408" xml:space="preserve">Quotieſcunque angulus inter ambo ſpecula <lb/>comprehenſus eſt exiguus & </s> <s xml:id="echoid-s8409" xml:space="preserve">linea juncturæ perpendicularisin Aquam <lb/>curva ab Aquâ deſcripta eſt Hyperbola inter aſymptotas ſuas con-<lb/>tenta, quarum una eſt ſuperficies Aquæ, altera, junctura ſpeculo-<lb/>rum. </s> <s xml:id="echoid-s8410" xml:space="preserve">Ducantur enim duæ rectæ A C, B C quæ repræſentent ſe-<lb/>ctionem ſpeculorum junctorum in C. </s> <s xml:id="echoid-s8411" xml:space="preserve">concipiatur B C diviſa in ali-<lb/>quot partes æquales & </s> <s xml:id="echoid-s8412" xml:space="preserve">parvas, quales ſunt e g, im. </s> <s xml:id="echoid-s8413" xml:space="preserve">& </s> <s xml:id="echoid-s8414" xml:space="preserve">quia angulus <lb/>A C B eſt parvus, poſſunt concipi d f e g, h lim, ut parallelogram-<lb/>ma: </s> <s xml:id="echoid-s8415" xml:space="preserve">quia autem poſitis ſpeculis a ſe diſtantibus & </s> <s xml:id="echoid-s8416" xml:space="preserve">parallelis copia <lb/>aquæ adſcendentis eſtæqualis per Corol. </s> <s xml:id="echoid-s8417" xml:space="preserve">2. </s> <s xml:id="echoid-s8418" xml:space="preserve">§. </s> <s xml:id="echoid-s8419" xml:space="preserve">3, erit inter d f e g, <lb/>æqualis Aquæ copia ac inter h i l m, adeoque erunt ea paralle-<lb/>lopipeda Aquæ æqualia, quorum altitudines ſunt reciproce ut ba-<lb/>ſes d e f g, h i l m. </s> <s xml:id="echoid-s8420" xml:space="preserve">& </s> <s xml:id="echoid-s8421" xml:space="preserve">quia hæ habent latus e g = i m, erunt <lb/>baſes uti de, ad hi, ſed ob triangula ſimilia d C e, h C i, eſt de, <lb/>h i:</s> <s xml:id="echoid-s8422" xml:space="preserve">: e C, i C. </s> <s xml:id="echoid-s8423" xml:space="preserve">quare erit altitudo Aquæ in e, ad eam in i, ut i C. <lb/></s> <s xml:id="echoid-s8424" xml:space="preserve">ad e C ſive reciproce ut diſtantiæ â C. </s> <s xml:id="echoid-s8425" xml:space="preserve">Quare ſi i C multiplicetur <lb/>in ſuam altitudinem, dabit productum æquale illi ex e C in ſuam; </s> <s xml:id="echoid-s8426" xml:space="preserve">ve-<lb/>rum nota hæc eſt natura Hyperbolæ, ut parallelogramma vid.</s> <s xml:id="echoid-s8427" xml:space="preserve"> <pb o="344" file="0358" n="358" rhead="DISSERTATIO"/> fig. </s> <s xml:id="echoid-s8428" xml:space="preserve">3. </s> <s xml:id="echoid-s8429" xml:space="preserve">d e C k, h i m C ſint æqualia, quæ continentur inter paral-<lb/>lelas aſymtotis AC, BC, quare etiam linea curva in Experimen-<lb/>tis notata eſt Hyperbola.</s> <s xml:id="echoid-s8430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8431" xml:space="preserve">Videamus an Experimenta reſpondeant demonſtrationi, in Ta-<lb/>bula prima obſervabitur anomalia hinc inde, quæ provenit, quia <lb/>non ſatis accnrate obſervare poſſumus altitudinem, videndo per craſ-<lb/>ſitiem vitri; </s> <s xml:id="echoid-s8432" xml:space="preserve">2°. </s> <s xml:id="echoid-s8433" xml:space="preserve">nec accurate ponere poſſumus ſpecula perpendicu-<lb/>laria, 3° nec hæc ſuperficies tam perfecte planas habentac poſtulatur. <lb/></s> <s xml:id="echoid-s8434" xml:space="preserve">4° accedit puritas vel impuritas vitri, ut & </s> <s xml:id="echoid-s8435" xml:space="preserve">Aquæ & </s> <s xml:id="echoid-s8436" xml:space="preserve">plurima alia: </s> <s xml:id="echoid-s8437" xml:space="preserve">ve-<lb/>rum tabula ſecunda melius reſpondet calculo; </s> <s xml:id="echoid-s8438" xml:space="preserve">nam ad diſtantiam <lb/>6 pollicum eſt altitudo = 2. </s> <s xml:id="echoid-s8439" xml:space="preserve">ad diſtantiam. </s> <s xml:id="echoid-s8440" xml:space="preserve">3 pollicum eſt altitudo <lb/>= 4 {1/4} eſt exceſſus hic = {3/4}. </s> <s xml:id="echoid-s8441" xml:space="preserve">ſupra calculum: </s> <s xml:id="echoid-s8442" xml:space="preserve">ad diſtantiam 1 {1/2} pol-<lb/>lic. </s> <s xml:id="echoid-s8443" xml:space="preserve">eſt altitudo = 10, quæ magnitudo eſt paulum plus quam du-<lb/>plo major quam 4 {3/4}: </s> <s xml:id="echoid-s8444" xml:space="preserve">& </s> <s xml:id="echoid-s8445" xml:space="preserve">ad diſtantiam {3/4} pollic. </s> <s xml:id="echoid-s8446" xml:space="preserve">= 19. </s> <s xml:id="echoid-s8447" xml:space="preserve">ubi eſt par-<lb/>Aus defectus, cum debuiſſet eſſe = 20. </s> <s xml:id="echoid-s8448" xml:space="preserve">verum ſatis hæc reſpon-<lb/>dent calculo. </s> <s xml:id="echoid-s8449" xml:space="preserve">ita ad diſtantiam 2 pollic. </s> <s xml:id="echoid-s8450" xml:space="preserve">eſt altitudo = 7 {1/2} lineis: </s> <s xml:id="echoid-s8451" xml:space="preserve"><lb/>ad diſtantiam duplo minorem eſt altitudo = 15. </s> <s xml:id="echoid-s8452" xml:space="preserve">duplo major, & </s> <s xml:id="echoid-s8453" xml:space="preserve"><lb/>ad {1/2} pollic: </s> <s xml:id="echoid-s8454" xml:space="preserve">eſt = 28, debuerat eſſe = 30 lineis, ut foret du-<lb/>plo major, verum hæc obſervata ſatis accurate reſpondent, ut cur-<lb/>va deſcripta poſſit haberi pro Hyperbola: </s> <s xml:id="echoid-s8455" xml:space="preserve">cujus ope igitur intelligi <lb/>& </s> <s xml:id="echoid-s8456" xml:space="preserve">demonſtrari poſſunt ſequentia obſervata, deſcripta ab Hauksbejo <lb/>in appendice, & </s> <s xml:id="echoid-s8457" xml:space="preserve">in Experimento XXIII.</s> <s xml:id="echoid-s8458" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8459" xml:space="preserve">Sint enim eadem ſpecula, quorum linea contactus ſit a c in om-<lb/>nibus caſibus, hæc ſubmergantur ſub Aqua uſque ad a b, ſub co <lb/>ſitu, quem figuræ 4, 5, 6, 7, 8, 10. </s> <s xml:id="echoid-s8460" xml:space="preserve">repræſentant, deſcribentur <lb/>curvæ d d hyperbolicæ, quarum aſymptotæ erunt a b, a c. </s> <s xml:id="echoid-s8461" xml:space="preserve">Et <lb/>ſi duo plana circularia fuerint, uti fig. </s> <s xml:id="echoid-s8462" xml:space="preserve">11. </s> <s xml:id="echoid-s8463" xml:space="preserve">repræſentat, erit iterum <lb/>Hyperbola d d, & </s> <s xml:id="echoid-s8464" xml:space="preserve">aſymptotæ a b, a c quarum una tangit circu-<lb/>lum in puncto c.</s> <s xml:id="echoid-s8465" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8466" xml:space="preserve">Quando latera ſe tangentia ſunt ſurſum poſita, parallela ſuperfi-<lb/>ciei Aquæ, veluti in fig. </s> <s xml:id="echoid-s8467" xml:space="preserve">9. </s> <s xml:id="echoid-s8468" xml:space="preserve">& </s> <s xml:id="echoid-s8469" xml:space="preserve">omnino ſub Aqua ſubmerſa, tum <lb/>extrahantur ſpecula lente in eadem poſitione, donec pondus Aquæ <lb/>inter plana ſuperet vim attractionis ſpeculorum, generabuntur duæ <lb/>curvæ, una â quolibet latere planorum, quæ ſe aperiunt, ſibique <lb/>occurruntin medio, uti figura repræſentat, ibi vero uniuntur forman-<lb/>do figuram, quam linea punctata refert, quæ nunc eſt in medio, <pb o="345" file="0359" n="359" rhead="DE SPECULIS VITREIS."/> nunc verſus alterutrum latus: </s> <s xml:id="echoid-s8470" xml:space="preserve">imo hæc curva ſemper deprehenditur <lb/>in mediâ diſtantiâ inter latera ſe tangentia a c & </s> <s xml:id="echoid-s8471" xml:space="preserve">ſuperſiciem Aquæ <lb/>a b.</s> <s xml:id="echoid-s8472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8473" xml:space="preserve">Scholium. </s> <s xml:id="echoid-s8474" xml:space="preserve">Quando angulus A C B inter ambo ſpecula contentus <lb/>non valdequam acutus eſt, ſed major evadit, vel obtuſus, non deſcribi-<lb/>tur ab Aqua accurate Hyperbola, quia tum d f, e g in fig. </s> <s xml:id="echoid-s8475" xml:space="preserve">2. </s> <s xml:id="echoid-s8476" xml:space="preserve">non <lb/>poſſunt poni parallela, ſed partim Hyperbola deſcribetur, par-<lb/>tim alia curva; </s> <s xml:id="echoid-s8477" xml:space="preserve">quemadmodum recte notavit. </s> <s xml:id="echoid-s8478" xml:space="preserve">Cl. </s> <s xml:id="echoid-s8479" xml:space="preserve">Gravezandius. <lb/></s> <s xml:id="echoid-s8480" xml:space="preserve">Forment enim ſpecula A B, B C angulum acutum, uti in fig. </s> <s xml:id="echoid-s8481" xml:space="preserve">12. </s> <s xml:id="echoid-s8482" xml:space="preserve">ma-<lb/>nentibus ſpeculis Aquæ perpendicularibus, etiam Aqua terminabi-<lb/>tur lineâ hyperbolicâ, cujus aſymptotos una eſt Aquæ ſuperficies, <lb/>altera habetur erigendo perpendicularem B F ad C B, in puncto B, <lb/>aſymptotos quæſita erit B E, quæ dividit bifariam F D perpen dicu-<lb/>larem in puncto quocunque ad B F, & </s> <s xml:id="echoid-s8483" xml:space="preserve">terminatam linea B A.</s> <s xml:id="echoid-s8484" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8485" xml:space="preserve">Si D F per punctum D Hyperbolæ tranſeat, B F erit ſemidiame-<lb/>ter conjugata cum ſemidiametro B D.</s> <s xml:id="echoid-s8486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8487" 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-s8488" xml:space="preserve">quidem pro diverſo, <lb/>quem inter ſe vitra continent, angulo, diverſam A B diſtantiam, <lb/>ab Hyperbolâ deflectitur curva, adſcenſuſque juxta B A conti-<lb/>nuatur.</s> <s xml:id="echoid-s8489" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8490" xml:space="preserve">Quando angulus A B C eſt obtuſus in fig. </s> <s xml:id="echoid-s8491" xml:space="preserve">13. </s> <s xml:id="echoid-s8492" xml:space="preserve">idem locum habet, <lb/>ultra F Hyperbola non continuatur, Aqua tamen ulterius adſcen-<lb/>dit, ſed alia terminatur curva.</s> <s xml:id="echoid-s8493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8494" xml:space="preserve">Explorandum deinde duxi qualis curva formaretur ab Aqua, ſi <lb/>una ſuperficies ſpeculi vi attrahente, altera Aquam repellente vir-<lb/>tute eſſet donata, quam ob cauſam unius ſpeculi ſuperficiem obduxi <lb/>oleo olivarum, abſterſique id rurſus linteo leviter, ita ut parum olei, & </s> <s xml:id="echoid-s8495" xml:space="preserve"><lb/>æquabiliter inuncti adhæreret: </s> <s xml:id="echoid-s8496" xml:space="preserve">hoc ſpeculo juncto cum altero mun-<lb/>do & </s> <s xml:id="echoid-s8497" xml:space="preserve">ſicco, ut ſpatium priſmatis trigoni interciperetur, infe-<lb/>riores oræ ſuerunt immiſſæ Aquæ; </s> <s xml:id="echoid-s8498" xml:space="preserve">quæ ſurſum rapta eſt ut ante, <lb/>hyperbolam formando: </s> <s xml:id="echoid-s8499" xml:space="preserve">Tum ambabus ſuperficiebus utriuſque ſpecu-<lb/>li oleum tenuiſſime & </s> <s xml:id="echoid-s8500" xml:space="preserve">æquabiliter illinivi, inter quas junctas, ut <lb/>ante, Aqua adſendit non ad minorem quam antea altitudinem, <lb/>accuratam formando Hyperbolam. </s> <s xml:id="echoid-s8501" xml:space="preserve">Tandem alterutrius ſpeculi ſu-<lb/>perficiem ſupra lampadis detinui flammam, ut fuligo applicaretur <pb o="346" file="0360" n="360" rhead="DISSERTATIO"/> oleo illito: </s> <s xml:id="echoid-s8502" xml:space="preserve">hoc ſpeculo alteri inuncto impoſito cum hiatu ut ante; <lb/></s> <s xml:id="echoid-s8503" xml:space="preserve">in initio non adſcendit inter eorum commiſſuram Aqua, cui im-<lb/>ponebantur, ſed aliquo elapſo tempore, avellebatur fuligo, ſur-<lb/>ſum ab Aqua propellebatur, quæ adſcendit, ſedinæquali formâ, & </s> <s xml:id="echoid-s8504" xml:space="preserve"><lb/>non admodum alte; </s> <s xml:id="echoid-s8505" xml:space="preserve">Ex hiſce Experimentis liquet vim attrahentem <lb/>vitri non impendi totam in oleum ſibi leviter inunctum, ſed per id <lb/>tranſire, & </s> <s xml:id="echoid-s8506" xml:space="preserve">agere adhuc in Aquam, eamque elevare, licet oleum ſua vi <lb/>repellente deprimat Aquam: </s> <s xml:id="echoid-s8507" xml:space="preserve">visigitur attrahens vitri in Aquam eſt ma-<lb/>jor virepellente oleitenuiter inuncti; </s> <s xml:id="echoid-s8508" xml:space="preserve">quando autem oleum craſſius& </s> <s xml:id="echoid-s8509" xml:space="preserve">in <lb/>majori copia illinitur, tum vis vitri pars major in oleum impenditur, <lb/>pars minor in Aquam: </s> <s xml:id="echoid-s8510" xml:space="preserve">quia autem oleum vim repellendi Aquam habet, <lb/>datur caſus, in quo eſt æquilibrium inter attractionem vitri in Aquam <lb/>& </s> <s xml:id="echoid-s8511" xml:space="preserve">repulſionem olei in eandem, tumque Aqua non aſſurgit, niſi olei pars <lb/>abſtergeatur: </s> <s xml:id="echoid-s8512" xml:space="preserve">ſi oleum aut ſebum craſſius adhuc illiniatur vitro, Aqua <lb/>non modo non aſſurgit, ſed repulſa humilior manet, atque infra <lb/>libellam depreſla.</s> <s xml:id="echoid-s8513" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div241" type="section" level="1" n="241"> <head xml:id="echoid-head264" xml:space="preserve">EXPERIMENTUM VII.</head> <p> <s xml:id="echoid-s8514" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8515" xml:space="preserve">13. </s> <s xml:id="echoid-s8516" xml:space="preserve">fig. </s> <s xml:id="echoid-s8517" xml:space="preserve">15. </s> <s xml:id="echoid-s8518" xml:space="preserve">Cum iiſdem ſpeculis inſtituit quoque Experi-<lb/>menta Cl. </s> <s xml:id="echoid-s8519" xml:space="preserve">Jurinus, quæ inſeruit Philoſ. </s> <s xml:id="echoid-s8520" xml:space="preserve">Tranſactionibus, ſed loco A-<lb/>quæ Mercurium, adhibendo, quæ cum profecto pulcra ſint, ad-<lb/>denda judicavi. </s> <s xml:id="echoid-s8521" xml:space="preserve">A B C D eſt lamella plana ſpeculi vitrei, quæ effi-<lb/>cit unum latus capſulæ ligneæ, in qua ponitur altera lamella ſpe-<lb/>culi, quæ contingit priorem juxta rectam A C, ſed quæ diſtat mul-<lb/>cum a parte B D, ita ut inter hæc ſpecula relinquatur ſpatium trian-<lb/>gulare, quod repleri poſſet à cuneo plano, acie ſc. </s> <s xml:id="echoid-s8522" xml:space="preserve">intrante uſque <lb/>ad C A, dorſo poſito in B D. </s> <s xml:id="echoid-s8523" xml:space="preserve">Quando infundebatur Mercurius in <lb/>capſulam uſque ad altitudinem C E, ita ut fomaret in reliqua par-<lb/>te capſulæ ſuperficiem E F, tum intra ambas lamellas aſſurgendo <lb/>ab inferioribus ſurſum, formabat curvam C G F. </s> <s xml:id="echoid-s8524" xml:space="preserve">quæ invenitur eſſe <lb/>hyperbola inſtituto examine, quando enim Cl. </s> <s xml:id="echoid-s8525" xml:space="preserve">Jurinus cum Hauks-<lb/>bejo menſurabant ope circini lineam E H, & </s> <s xml:id="echoid-s8526" xml:space="preserve">H G, oritur ex his mul-<lb/>tiplicatis rectangulum: </s> <s xml:id="echoid-s8527" xml:space="preserve">menſurando autem alias lineas parallelas <lb/>ad E C & </s> <s xml:id="echoid-s8528" xml:space="preserve">illas multiplicando per diſtantiam à puncto E, invenieban-<lb/>tur omnia rectangula inter ſe æqualia, quæ eſt natura hyperbo- <pb o="347" file="0361" n="361" rhead="DE SPECULIS VITREIS"/> læ inter aſymptota E C, E F deſcriptæ.</s> <s xml:id="echoid-s8529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8530" xml:space="preserve">Aſſurgit vero Mercurius ad diverſas altitudines, prout plana <lb/>vitrea ambo propius ad ſe accedunt, vel magis à ſe removentur.</s> <s xml:id="echoid-s8531" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8532" xml:space="preserve">Quando tamen ſpecula parum à ſe diſtant, tum inæqualitas ſu-<lb/>perſicierum ſolet facere ſenſibilem variationem in hac curvâ, nam <lb/>non poſſunt inveniri ſuperficies perfecte planæ, quales deſiderantur, <lb/>ut acquiratur linea Geometrica.</s> <s xml:id="echoid-s8533" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8534" xml:space="preserve">Eſt hæc curva contrario modo ſita, quam quando inſtituitur <lb/>Experimentum cum Aqua, vel Spiritu Vini, quia Mercurius ſe magis <lb/>attrahit, quam Vitrum: </s> <s xml:id="echoid-s8535" xml:space="preserve">idcirco ſe habet, quaſi à Vitro repelleretur; <lb/></s> <s xml:id="echoid-s8536" xml:space="preserve">cumque repulſio ſit oppoſita attactioni, etiam figura contraria à <lb/>liquore repulſo, quam ab attracto, formabitur.</s> <s xml:id="echoid-s8537" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div242" type="section" level="1" n="242"> <head xml:id="echoid-head265" xml:space="preserve">EXPERIMENTUM VIII.</head> <p> <s xml:id="echoid-s8538" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8539" xml:space="preserve">13 fig. </s> <s xml:id="echoid-s8540" xml:space="preserve">14. </s> <s xml:id="echoid-s8541" xml:space="preserve">Speculum D E ponatur horizonti parallelum, <lb/>cui affundatur gutta olei deſtillati B, tum alterum ſpeculum A C <lb/>imponatur priori, ita ut extremo A tangat alterius extremum D; </s> <s xml:id="echoid-s8542" xml:space="preserve">ſed <lb/>extremo C tantopere diſtet ab E, ut guttæ B ſuperiorem partem vix <lb/>vix contingat: </s> <s xml:id="echoid-s8543" xml:space="preserve">Quibus ita compoſitis, gutta B illico moveri incipit <lb/>verſus A D, in principio lente, ſed ſemper eo velocius, quo propius <lb/>accedit ad A D, explicata quoque continuo in majorem latitudi-<lb/>nem, tandemque prope juncturam A D ſpeculorum ſe utrimque <lb/>expandit ſecundum juncturæ longitudinem.</s> <s xml:id="echoid-s8544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8545" xml:space="preserve">Sit centrum gravitatis guttæ B in o, quia ſpeculum A C ad ſe <lb/>trahitguttam, agitur hæc directione o p, perpendiculari in ſuperſi-<lb/>ciem A C, atque directione O S perpendiculari in ſuperſiciem D E: <lb/></s> <s xml:id="echoid-s8546" xml:space="preserve">adeoque moveri debebit in diagonali o r parallelogrammi, cujus la-<lb/>tera duo ſunt directiones o p, o s, idcirco feretur gutta â B verſus A D. </s> <s xml:id="echoid-s8547" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s8548" xml:space="preserve">quia eadem ratio directionum trahentium obtinet quouſque <lb/>gutta ex B verſus A D perrexerit, continuabitur ejus motus uſque <lb/>ad A D. </s> <s xml:id="echoid-s8549" xml:space="preserve">Conſtat vero gutta ex materia non condenſabili, hinc in ar-<lb/>ctius delata ſpatium, ut expandatur pérpetuo magis magiſque neceſſe <lb/>erit. </s> <s xml:id="echoid-s8550" xml:space="preserve">Præterea adhæret pars guttæ ſuperior ſpeculo A C, quodpla-<lb/>num eſt inclinatum ad horizontem, ſuper quo omnia devoluta <lb/>gravia feruntur motu accelerato, ſive gutta adhæſerit inferiori hu-<lb/>jus plani ſuperficiei, ſive ſuper ipſo moveretur, idem eſt; </s> <s xml:id="echoid-s8551" xml:space="preserve">adeoque <lb/>quatenus gravitatem habet, motu accelerato feretur a p verſus A D: </s> <s xml:id="echoid-s8552" xml:space="preserve"><lb/>Inſuper quo centrum gravitatis o propius acceſſerit ad ſpeculorum <pb o="348" file="0362" n="362" rhead="DISSERTATIO"/> ſuperficies, eo fortius attrahetur; </s> <s xml:id="echoid-s8553" xml:space="preserve">ſed propius accedit, quo gutta <lb/>magis applanatur, hoc eſt, magis ad A D appropinquavit, adeo-<lb/>que fortius attracta gutta a ſuperficiebus, & </s> <s xml:id="echoid-s8554" xml:space="preserve">obliqua directione o p, <lb/>neceſſario velocius feretur, quæ eſt altera cauſa accelerati motus <lb/>in gutta obſervati: </s> <s xml:id="echoid-s8555" xml:space="preserve">Fortiſſima quoque ſpeculorum attractio cum ſit <lb/>in contactu A D, neceſſe eſt ut gutta ſecundum hunc contactum <lb/>expandatur per omnem ſpeculorum latitudinem.</s> <s xml:id="echoid-s8556" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8557" xml:space="preserve">Notandum eſt nonnulla ſpecula majori virtute attrahere oleum <lb/>quam alia, imo ſunt mihi, quæ vix attrahunt.</s> <s xml:id="echoid-s8558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8559" xml:space="preserve">Exploravi quænam olea forent huic Experimento maxime ido-<lb/>nea: </s> <s xml:id="echoid-s8560" xml:space="preserve">obſervavi in genere, omnia, quæ recenter deſtillata ſunt, & </s> <s xml:id="echoid-s8561" xml:space="preserve"><lb/>tenuia ſimul, maxima cum rapiditate ferri â B verſus A. </s> <s xml:id="echoid-s8562" xml:space="preserve">quæ craſ-<lb/>ſiora & </s> <s xml:id="echoid-s8563" xml:space="preserve">ſimul tenaciora ſunt, aut vetuſta, ſemper lentius ferun-<lb/>tur: </s> <s xml:id="echoid-s8564" xml:space="preserve">Ecce elenchum trium generum, quorum primum rapidiſſime <lb/>fertur; </s> <s xml:id="echoid-s8565" xml:space="preserve">ſecundum lentius; </s> <s xml:id="echoid-s8566" xml:space="preserve">tertium admodum tarde 1° rapidiſſime <lb/>currit oleum Saſſafras deſtill. </s> <s xml:id="echoid-s8567" xml:space="preserve">oleum Menthæ deſtill. </s> <s xml:id="echoid-s8568" xml:space="preserve">oleum Origani <lb/>deſtill. </s> <s xml:id="echoid-s8569" xml:space="preserve">oleum Rorismarini deſtill oleum Macis deſtill. </s> <s xml:id="echoid-s8570" xml:space="preserve">oleum Ta-<lb/>naceti deſtill. </s> <s xml:id="echoid-s8571" xml:space="preserve">oleum Ceræ deſtill. </s> <s xml:id="echoid-s8572" xml:space="preserve">oleum Meliſſæ deſtill. </s> <s xml:id="echoid-s8573" xml:space="preserve">oleum A-<lb/>rantiorum deſtill oleum Aniſi dſteill. </s> <s xml:id="echoid-s8574" xml:space="preserve">Inter hæc olea Rorismarini <lb/>& </s> <s xml:id="echoid-s8575" xml:space="preserve">Macis ſe diffundunt illico ſupra ſpeculum, ut gutta extemplo <lb/>applanetur inſtar ſpiritus vini, unde ſimul extenditur quaquaver-<lb/>ſum, ac verſus A rapitur.</s> <s xml:id="echoid-s8576" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8577" xml:space="preserve">2°. </s> <s xml:id="echoid-s8578" xml:space="preserve">Olea quæ lentius moventur, licet tamen inſigni lata motu, <lb/>ſunt oleum Carui deſtill. </s> <s xml:id="echoid-s8579" xml:space="preserve">oleum Abſinthii deſtill. </s> <s xml:id="echoid-s8580" xml:space="preserve">oleum Succini flavi; <lb/></s> <s xml:id="echoid-s8581" xml:space="preserve">oleum Succini albi, ol Juniperi deſtill. </s> <s xml:id="echoid-s8582" xml:space="preserve">ol Majoranæ nobilis deſtill.</s> <s xml:id="echoid-s8583" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8584" xml:space="preserve">3°. </s> <s xml:id="echoid-s8585" xml:space="preserve">Lente moventur hæc olea: </s> <s xml:id="echoid-s8586" xml:space="preserve">oleum Lavendulæ deſtill. </s> <s xml:id="echoid-s8587" xml:space="preserve">oleum <lb/>Hyſſopi deſtill. </s> <s xml:id="echoid-s8588" xml:space="preserve">oleum Cumini deſtill. </s> <s xml:id="echoid-s8589" xml:space="preserve">oleum Sabinæ deſtill. </s> <s xml:id="echoid-s8590" xml:space="preserve">oleum <lb/>Petroſelini deſtill. </s> <s xml:id="echoid-s8591" xml:space="preserve">oleum Fœniculi deſtill. </s> <s xml:id="echoid-s8592" xml:space="preserve">oleum Cinnamomi deſtill. <lb/></s> <s xml:id="echoid-s8593" xml:space="preserve">oleum Ligni Rhodii deſtill. </s> <s xml:id="echoid-s8594" xml:space="preserve">& </s> <s xml:id="echoid-s8595" xml:space="preserve">omnium lentiſſime fertur oleum Ca-<lb/>ryophyllorum deſtill.</s> <s xml:id="echoid-s8596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8597" xml:space="preserve">Quoniam omnia hæc olea non examinare potui ſimul, aut re-<lb/>centiſſime confecta, ſed nonnulla erant vetuſtiora aliis, in hanc <lb/>triplicem diviſionem error forte irrepſit, qui tamen parvi erit <lb/>momenti. </s> <s xml:id="echoid-s8598" xml:space="preserve">Succedit præterea hoc Experimentum cum oleo Oli-<lb/>varum, quod lente movetur; </s> <s xml:id="echoid-s8599" xml:space="preserve">aſt rapidius fertur ſpiritus Salis ma-<lb/>rini & </s> <s xml:id="echoid-s8600" xml:space="preserve">Aqua fortis: </s> <s xml:id="echoid-s8601" xml:space="preserve">non autem obſervavi motum à gutta Aquæ, nec <lb/>a gutta Aceti, nec Vini, nec ab oleo Tartari per deliquium, nec <lb/>ab Urina humana.</s> <s xml:id="echoid-s8602" xml:space="preserve"/> </p> <pb o="349" file="0363" n="363" rhead="DE SPECULIS VITREIS."/> </div> <div xml:id="echoid-div243" type="section" level="1" n="243"> <head xml:id="echoid-head266" xml:space="preserve">EXPERIMENTUM IX.</head> <p> <s xml:id="echoid-s8603" xml:space="preserve">Speculi una ſuperficies leviter obducatur oleo Arantiorum, & </s> <s xml:id="echoid-s8604" xml:space="preserve">po-<lb/>natur horizonti parallelum; </s> <s xml:id="echoid-s8605" xml:space="preserve">affundatur illi gutta olei Arantiorum, <lb/>alterumque ſpeculum apponatur, ita ut primum contingat in A, & </s> <s xml:id="echoid-s8606" xml:space="preserve"><lb/>guttam olei in B, illico oleum ſe expandit inter ambas ſuperficies: <lb/></s> <s xml:id="echoid-s8607" xml:space="preserve">tum manente ſpeculo inferiori immoto, elevetur ſuperius paulum <lb/>ad C, contactu in A manente, oleum ſtatim colligitur in corpus <lb/>formæ globoſæ, contingentis ambas ſuperficies, quod movetur ver-<lb/>ſus contactum A, ut in præcedenti Experimento. </s> <s xml:id="echoid-s8608" xml:space="preserve">Maneant in eadem <lb/>diſtantia ad Cambo ſpecula, ſitque hæc diſtantia {1/16} pollicis, elevetur <lb/>utrumque ſpeculum parte contactus ſui ad A, tum ad varias di-<lb/>ſtantias guttæ, a parte ſpeculorum C, varia elevatio in A efficie-<lb/>bat, ut gutta olei non adſcenderet, ſed maneret ſuſpenſa juxta hanc <lb/>tabulam.</s> <s xml:id="echoid-s8609" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia in \\ pollicibus ab \\ extremo C # # Angulus elevationis \\ partis A ſupra \\ horizontem <lb/># Gr. # # M. <lb/>2 # 0 # 15 <lb/>4 # 0 # 25 <lb/>6 # 0 # 35 <lb/>8 # 0 # 45 <lb/>10 # 1 # 0 <lb/>12 # 1 # 45 <lb/>14 # 2 # 45 <lb/>15 # 4 # 0 <lb/>16 # 6 # 0 <lb/>17 # 10 # 0 <lb/>18 # 22 # 0 <lb/></note> <p> <s xml:id="echoid-s8610" xml:space="preserve">Quando gutta olei ad 17. </s> <s xml:id="echoid-s8611" xml:space="preserve">pollices a C venerat, fiebat ovalis, & </s> <s xml:id="echoid-s8612" xml:space="preserve"><lb/>quo altius adſcendebat, eo plus ovalis reddebatur: </s> <s xml:id="echoid-s8613" xml:space="preserve">quando tandem <pb o="350" file="0364" n="364" rhead="DISSERTATIO"/> altiſſime adſcendit, pars guttæ ſeparabatur ab alia, deſcendens, <lb/>cum alia interim pergebat adſcendere. </s> <s xml:id="echoid-s8614" xml:space="preserve">Quia Oleum Arantiorum eſt <lb/>inter ea, quæ citiſſime adſcendunt, & </s> <s xml:id="echoid-s8615" xml:space="preserve">ideo Experimentum non tam <lb/>accurate obſervari poteſt, ac deſideratur, Hauksbejus idem repe-<lb/>tiit cum gutta Spiritus vini, quæ lentius movetur; </s> <s xml:id="echoid-s8616" xml:space="preserve">tabulamque ob-<lb/>ſervationum condidit ſequentem: </s> <s xml:id="echoid-s8617" xml:space="preserve">in qua notatur quando gutta non <lb/>adſcendebat verſus A. </s> <s xml:id="echoid-s8618" xml:space="preserve">Angulus C A B, quem ambo ſpecula formabant, <lb/>erat 18 Minutorum.</s> <s xml:id="echoid-s8619" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia in \\ pollicibus a \\ contactu A # # Angulus elevationis \\ partium contingentium ſe \\ in A, ſupra horizontem <lb/># Gr: # M. <lb/>18 {1/2} # 0 # 45 <lb/>16 {1/2} # 0 # 55 <lb/>14 {1/2} # 1 # 5 <lb/>12 {1/2} # 1 # 20 <lb/>10 {1/2} # 1 # 30 <lb/>9 {1/2} # 1 # 40 <lb/>8 {1/2} # 2 # 0 <lb/>7 {1/2} # 2 # 30 <lb/>6 {1/2} # 3 # 20 <lb/>5 {1/2} # 4 # 25 <lb/>4 {1/2} # 6 # 0 <lb/>4 # 7 # 23 <lb/>3 {3/4} # 8 # 40 <lb/>3 {1/2} # 9 # 25 <lb/>3 {1/4} # 10 # 30 <lb/>3 # 12 # 40 <lb/>2 {3/4} # 15 # 0 <lb/>2 {1/2} # 18 # 50 <lb/>2 {1/4} # 23 # 25 <lb/>2 # 30 # 0 <lb/></note> <p> <s xml:id="echoid-s8620" xml:space="preserve">Dein modo aperuit Hauksbejus ambo ſpecula, ut angulus B A C <pb o="351" file="0365" n="365" rhead="DE SPCULIS VITREIS."/> eſſet 10 Minutorum, & </s> <s xml:id="echoid-s8621" xml:space="preserve">notavit iterum ad quamnam elevationem <lb/>amborum ſpeculorum gutta ſiſtebatur.</s> <s xml:id="echoid-s8622" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Diſtantia pollicum \\ a contactu A # # Angulus elevationis \\ ſupra horizontem <lb/># Gr. # Min. <lb/>18 {1/2} # 1 # 30 <lb/>16 {1/2} # 1 # 50 <lb/>14 {1/2} # 2 # 10 <lb/>12 {1/2} # 2 # 40 <lb/>10 {1/2} # 3 # 10 <lb/>9 {1/2} # 3 # 30 <lb/>8 {1/2} # 4 # 0 <lb/>7 {1/2} # 5 # 5 <lb/>6 {1/2} # 7 # 40 <lb/>5 {1/2} # 10 # 50 <lb/>4 {1/2} # 14 # 18 <lb/>4 # 18 # 0 <lb/></note> <p> <s xml:id="echoid-s8623" xml:space="preserve">In hiſce omnibus Experimentis gutta ſive Olei ſive Spiritus vini <lb/>B, movetur verſus A, quia partes ſpeculorum in E ſibi propiores <lb/>ſunt quam in B, adeoque fortius agunt attrahendo guttam, quæ <lb/>ideo ex B movetur in E, ſed quia ſpeculorum partes propiores ad <lb/>A, ſibi etiam ſunt propiores, idcirco gutta continuo plus agitur <lb/>verſus A, adeoque adſcendit motu accelerato donec ad contactum <lb/>A pervenerit.</s> <s xml:id="echoid-s8624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8625" xml:space="preserve">Sed gutta gravitatem habet, & </s> <s xml:id="echoid-s8626" xml:space="preserve">quia inſiſtit plano inclinato, <lb/>quando ſpeculum inferius ab una parte eſt elevatum, poteſt ipſrus <lb/>gravitas relativa æqualis eſſe virtuti ſpeculorum ipſam elevanti, <lb/>ideo gutta quieſcit ſuſpenſa, poſita elevatione ad certum uſque <lb/>gradum; </s> <s xml:id="echoid-s8627" xml:space="preserve">quo hæc elevatio major eſt, eo gravitas relativa guttæ <lb/>eſt major: </s> <s xml:id="echoid-s8628" xml:space="preserve">ut igitur gutta ſuſpenſa maneat, inter portiones ſpeculo-<lb/>rum ſibi propiores hærere debet, tumque iterum vis ſpeculorum e-<lb/>levans guttam æquipollebit hujus gravitati relativæ.</s> <s xml:id="echoid-s8629" xml:space="preserve"/> </p> <pb o="352" file="0366" n="366" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div244" type="section" level="1" n="244"> <head xml:id="echoid-head267" xml:space="preserve">EXPERIMENTUM X.</head> <p> <s xml:id="echoid-s8630" xml:space="preserve">Si, poſito ſpeculo B horizontali, gutta notabilis Mercurii ſuper-<lb/>affundatur in B, tumque alterum ſpeculum A C ſuperponatur, donec <lb/>ſe contingant in A, ſimulac ſpeculum ſuperius attingit guttam B, <lb/>hæc applanatur, circularem, vel ſphæræ compreſſæ induendo ſi-<lb/>guram & </s> <s xml:id="echoid-s8631" xml:space="preserve">movetur verſus ſpeculorum hiatum C, quo autem ſpecu-<lb/>la ſibi arctius apponuntur, eo gutta B plus recedit ab A verſus C <lb/>adeoque contrarium fit in Mercurio quam in aliis liquoribus hacte-<lb/>nus examinatis, quemadmodum in Experimento VII. </s> <s xml:id="echoid-s8632" xml:space="preserve">etiam de-<lb/>prehendimus & </s> <s xml:id="echoid-s8633" xml:space="preserve">explicuimus.</s> <s xml:id="echoid-s8634" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div245" type="section" level="1" n="245"> <head xml:id="echoid-head268" xml:space="preserve">EXPERIMENTUM XI.</head> <p> <s xml:id="echoid-s8635" xml:space="preserve">Omnia hæc Experimenta ſortiuntur eoſdem eventus, ſive inſti-<lb/>tuantur in recipiente Boyleano, ex quo omnis eductus eſt Aër, <lb/>ſive in Aëre aperto: </s> <s xml:id="echoid-s8636" xml:space="preserve">adeoque cauſa eorum non poteſt dici preſſio <lb/>quædam Aëris elaſtici; </s> <s xml:id="echoid-s8637" xml:space="preserve">quippe ſublato Aëre, & </s> <s xml:id="echoid-s8638" xml:space="preserve">proinde preſſio-<lb/>ne, ceſſaret effectus: </s> <s xml:id="echoid-s8639" xml:space="preserve">neque poteſt preſſio, alterius fluidi ſubtilio-<lb/>ris dici cauſa horum admirandorum phænomen?</s> <s xml:id="echoid-s8640" xml:space="preserve">n, nam illud flui-<lb/>dum tranſibit tum facile per poros vitrei recipientis; </s> <s xml:id="echoid-s8641" xml:space="preserve">quia eadem <lb/>phænomena in vacuo contingunt; </s> <s xml:id="echoid-s8642" xml:space="preserve">igitur quæro an tum illud flui-<lb/>dum non facilius adhuc intrabit rimam inter ſpecula relictam, <lb/>millies forte ampliorem poro quocunque vitri? </s> <s xml:id="echoid-s8643" xml:space="preserve">quam ſi intraverit, <lb/>æque ſuperne, quam lateraliter, ac poſtice, nulla poterit ab hoc fluido <lb/>fieri inæqualis preſſio, nulluſque liquoris inter ſpecula adſcenſus. <lb/></s> <s xml:id="echoid-s8644" xml:space="preserve">Imo ex preſſione cujuſlibet fluidi, minore inter commiſſuram ſpecu-<lb/>lorum quam extrinſecus, explicetur quare gutta nonnullorum oleo-<lb/>rum mediis interjacens ſpeculis feratur rapide ſurſum, alia, ſive <lb/>denſioris ſive rarioris ſubſtantiæ, vix, imo non adſcendat, uti Ex-<lb/>perimentum VIII. </s> <s xml:id="echoid-s8645" xml:space="preserve">ejuſmodi exempla habet: </s> <s xml:id="echoid-s8646" xml:space="preserve">tum quare Mercu-<lb/>rius deſcendat, recedatque a junctura locum ampliorem verſus; </s> <s xml:id="echoid-s8647" xml:space="preserve"><lb/>hæc preſſionis cujuſlibet fluidi ope exponi nequeunt: </s> <s xml:id="echoid-s8648" xml:space="preserve">taceo flui-<lb/>dum id ſubtilius modo advocari, cujus exiſtentia nondum eſt pro-<lb/>bata, adeoque tuto concludam a preſſione nullius fluidi memorata <lb/>phænomena pendere poſſe.</s> <s xml:id="echoid-s8649" xml:space="preserve"/> </p> <pb o="353" file="0367" n="367" rhead="DE SPECULIS VITREIS."/> <p> <s xml:id="echoid-s8650" xml:space="preserve">Sed ſi preſſio nulla locum hic habere poſſit, an tum non reſtat pro <lb/>cauſa, vis quædam attrahens in ſpeculis latens, quæ elevat guttas li-<lb/>quorum vel eorum maſſam notabilem: </s> <s xml:id="echoid-s8651" xml:space="preserve">quæ attractio tum eſt ejusmo-<lb/>di Lex Naturæ a Deo corporibus indita, ut verſus ſe rapiantur ſub <lb/>ea proportione in tali diſtantia, ſub aliâ proportione in alia diſtan-<lb/>tia: </s> <s xml:id="echoid-s8652" xml:space="preserve">ut hæc corpora, compoſita ex corpuſculis minoribus certæ <lb/>denſitatis & </s> <s xml:id="echoid-s8653" xml:space="preserve">figuræ magis attrahantur ab illis corporibus, quam a-<lb/>lia, quorum corpuſcula minora aliam habent figuram & </s> <s xml:id="echoid-s8654" xml:space="preserve">denſita-<lb/>tem: </s> <s xml:id="echoid-s8655" xml:space="preserve">hinc nonnulla olea magis attrahuntur quam alia, aut plus <lb/>quam Aqua, vel Mercurius: </s> <s xml:id="echoid-s8656" xml:space="preserve">quæ omnia confirmantur tum ex Ex-<lb/>perimentis hiſce, tum ex aliis, in Diſſertatione de Tubis capilla-<lb/>ribus vitreis, memoratis.</s> <s xml:id="echoid-s8657" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div246" type="section" level="1" n="246"> <head xml:id="echoid-head269" xml:space="preserve">FINIS.</head> <pb file="0368" n="368"/> <pb file="0369" n="369"/> </div> <div xml:id="echoid-div247" type="section" level="1" n="247"> <head xml:id="echoid-head270" xml:space="preserve">DISSERTATIO <lb/><emph style="sc">DE</emph> <lb/>MAGNITUDINE <lb/>TERRÆ.</head> <pb file="0370" n="370"/> <pb o="357" file="0371" n="371"/> </div> <div xml:id="echoid-div248" type="section" level="1" n="248"> <head xml:id="echoid-head271" xml:space="preserve">DISSERTATIO <lb/><emph style="sc">DE</emph> <lb/>MAGNITUDINE <lb/>TERRÆ.</head> <p> <s xml:id="echoid-s8658" xml:space="preserve">Inter Mathematicorum principes a longiſſima uſque me-<lb/>moria agitatum fuit Problema de vera Magnitudine Ter-<lb/>ræ: </s> <s xml:id="echoid-s8659" xml:space="preserve">id arripuit Anaximander, deinde Eratoſthenes, <lb/>quem ſecutus fuit Hipparchus, hunc Poſidonius, dein-<lb/>de Ptolomæus: </s> <s xml:id="echoid-s8660" xml:space="preserve">poſt eos omnes, Arabes, Regum impenſis adjuti, <lb/>idem, ut memoriæ prodidit Abelfeda, tentaverunt: </s> <s xml:id="echoid-s8661" xml:space="preserve">Quoniam hi <lb/>varias iniverunt vias, quæ omnes etiamſi Geometriæ innituntur, <lb/>tamen in praxi multis incommodis ſubjiciuntur, admodum diver-<lb/>ſam Terræ magnitudinem aſſignaverunt. </s> <s xml:id="echoid-s8662" xml:space="preserve">Elapſo ſæculo Cl. </s> <s xml:id="echoid-s8663" xml:space="preserve">Snel-<lb/>lius idem Problema arripiens, difficultates methodorum veterum <lb/>probe perſpexit, quibus igitur rejectis in aliam incidit, admodum na-<lb/>turalem & </s> <s xml:id="echoid-s8664" xml:space="preserve">ſimpliciſſimam, quæ vere Geometrica erat, & </s> <s xml:id="echoid-s8665" xml:space="preserve">ſimul ſatis fa-<lb/>cile ipſa praxi abſolvi poterat: </s> <s xml:id="echoid-s8666" xml:space="preserve">hujus ſimplicitas ſe adeo commendavit, <lb/>ut inclyti Galliarum Mathematici, Picardus, Caſſini, La Hire aliique, <lb/>qui juſſu Regis Ludovici XIV, Terræ magnitudinem dimenſi nuper <lb/>fuerunt, eandem ſecuti ſint. </s> <s xml:id="echoid-s8667" xml:space="preserve">Snellii methodus hæc erat, primum men-<lb/>ſuravit quandam lineam rectam, quam in campo plano aſſumſit, ja-<lb/>centem transverſe inter urbem Leydam & </s> <s xml:id="echoid-s8668" xml:space="preserve">pagum Soeterwoudam, <lb/>hanc rectam poſuit baſin omnium aliarum diſtantiarum, quas Geo-<lb/>metrice exploraret: </s> <s xml:id="echoid-s8669" xml:space="preserve">ad utramque hujus lineæ extremitatem locando <lb/>Quadrantem, atque Turrim curiæ Leydenſis collineando angulos <lb/>menſuravit, quos quoque notavit viſum dirigendo Soeterwoudam <lb/>verſus; </s> <s xml:id="echoid-s8670" xml:space="preserve">tum primum ope Trigonometriæ diſtantiam inter utrasque <lb/>Turres calculo ſubduxit, Erat hoc primum notabile duorum locorum <pb o="358" file="0372" n="372" rhead="DISSERTATIO"/> vallum, quod ipſi manſit fundamentum omnium aliarum diſtantia-<lb/>rum, quas deinceps erueret: </s> <s xml:id="echoid-s8671" xml:space="preserve">ad utrumque enim hujus intervalli <lb/>extremum menſurando angulos, quos alia Turris cum hac linea <lb/>formabat, iterum Trigonometricarum regularum beneficio novam <lb/>diſtantiam inveniebat, ita unam deduxit ex altera, atque opus con-<lb/>tinuando tam Boream, quam Auſtrum verſus, determinavit quo-<lb/>nam intervallo diſtent Alcmaria & </s> <s xml:id="echoid-s8672" xml:space="preserve">Berga ad Zomum, quemadmo-<lb/>dum ex ſolutis problematibus patebit. </s> <s xml:id="echoid-s8673" xml:space="preserve">Deinde obſervavit quantum <lb/>Berga diſtabat a Meridiano Terreſtri tranſeunte per Alcmariam; <lb/></s> <s xml:id="echoid-s8674" xml:space="preserve">tandem exploravit Polorum altitudines Alcmariæ & </s> <s xml:id="echoid-s8675" xml:space="preserve">Bergæ, no-<lb/>tataque differentia latitudinis gradus unius, minutorum 11, ſecun-<lb/>dorum 30. </s> <s xml:id="echoid-s8676" xml:space="preserve">inter Alcmariam, & </s> <s xml:id="echoid-s8677" xml:space="preserve">circulum latitudinis tranſeuntem <lb/>per Bergam, dabatur longitudo portionis Meridiani terreſtris, quæ <lb/>ex menſura priori facile eruebatur. </s> <s xml:id="echoid-s8678" xml:space="preserve">Conſcripſit hæc omnia ſatis <lb/>prolixe & </s> <s xml:id="echoid-s8679" xml:space="preserve">clare ipſe Autor in Eratoſthene Batavo, quod opus in <lb/>lucem prodiit Lugduni Batavorum Anno 1617. </s> <s xml:id="echoid-s8680" xml:space="preserve">Snellius in erudi-<lb/>enda juventute, & </s> <s xml:id="echoid-s8681" xml:space="preserve">practica Geometria in campo demonſtranda oc-<lb/>cupatus, priſtinas pagorum circa Leydam jacentium diſtantias ex-<lb/>ercitationis ergo diſcipulis exhibiturus, animadvertit angulos non-<lb/>nullorum Triangulorum non accurate fuiſſe captos, atque male in <lb/>ſuo Eratoſthene deſcriptos, imo qui cruribus ſiniſtris interjacebant, <lb/>inter crura dextra locatos fuiſſe, confuſionemque ingentem in toto <lb/>opere fuiſſe commiſſam: </s> <s xml:id="echoid-s8682" xml:space="preserve">idcirco totum laborem à primordiis re-<lb/>petiit, omnes omnium Triangulorum angulos denuo menſuravit, <lb/>errores emendavit, atque iterum ſupputavit diſtantias omnium <lb/>urbium, progreſſus a Berga ad Zomum ulterius per Antverpiam uſ-<lb/>que ad Machlinias, ut in majori diſtantia ab Alcmaria, accuratius <lb/>graduum terreſtrium magnitudinem cognoſceret, atque hoc modo <lb/>aliam magnitudinem Terræ aſſignavit, quam ante: </s> <s xml:id="echoid-s8683" xml:space="preserve">retinuit tamen <lb/>baſin eandem inter Leydam & </s> <s xml:id="echoid-s8684" xml:space="preserve">Soeterwoudam interjacentem. </s> <s xml:id="echoid-s8685" xml:space="preserve">In <lb/>animum vero tum induxit Eratoſthenem ita emendatum in lucem <lb/>emittere, plurimaque inſerere hinc inde operi; </s> <s xml:id="echoid-s8686" xml:space="preserve">Cum ecce Anno <lb/>1622. </s> <s xml:id="echoid-s8687" xml:space="preserve">Aquæ omnia paſcua campoſque circa Leydam jacentes inun-<lb/>darent, quas mox Gelu menſe Januario in glaciem politiſſimam, pla-<lb/>niſſimum æquor æmulantem, coëgit; </s> <s xml:id="echoid-s8688" xml:space="preserve">hæc noſtro Geometræ occaſio-<lb/>nem dedit menſuras de novo capiendi, longe accuratiores, quam ulla <pb o="359" file="0373" n="373" rhead="DE MAGNITUDINE TERRÆ."/> gens Terrarum ullibi inſtituit, potuitve; </s> <s xml:id="echoid-s8689" xml:space="preserve">non enim datur ullibi <lb/>campus adeo æquatus, nullum littus tam planum, quin plurimis <lb/>aſperitatibus donetur, quarum cavitates catena decempedatoris <lb/>ingreditur, nec ope longorum baculorum evitatur error, quem <lb/>ſoli inæqualitas affert; </s> <s xml:id="echoid-s8690" xml:space="preserve">ſola glacies ſuperficiem æquam, accura-<lb/>tiſſime menſurandam, habet: </s> <s xml:id="echoid-s8691" xml:space="preserve">hanc igitur opportunitatem non ne-<lb/>glexit Snellius, atque intervallum aliquod inter pagum Voorſcho-<lb/>ten & </s> <s xml:id="echoid-s8692" xml:space="preserve">domum Douſianam aſſumens ſuper glacie, id accuratiſſime <lb/>menſuravit, imo ut tutius confidere poſſet, ter menſuram re-<lb/>petiit, deinde Quadrantis ope angulos obſervavit, quos Turris <lb/>Leydenſis cum aſſumta linea ad utrumque extremum compone-<lb/>bat; </s> <s xml:id="echoid-s8693" xml:space="preserve">idemque repetens adſpiciendo Turrim pagi Soeterwoudæ, <lb/>ex Trigonometria determinavit diſtantiam inter utramque Turrim <lb/>1097 perticarum, 1 pedis & </s> <s xml:id="echoid-s8694" xml:space="preserve">{17/100} pollicis. </s> <s xml:id="echoid-s8695" xml:space="preserve">cum antea eam modo <lb/>poſuerat 1092. </s> <s xml:id="echoid-s8696" xml:space="preserve">perticarum, 3 pedum, 3 pollicum. </s> <s xml:id="echoid-s8697" xml:space="preserve">Ultimam men-<lb/>ſuram omnino prætulit omnibus aliis, utpote ſupra glaciem politiſ-<lb/>ſimam ſummâ cum curâ captam. </s> <s xml:id="echoid-s8698" xml:space="preserve">Antea angulos omnium Trian-<lb/>gulorum correxerat, nunc baſin omnium longitudinum emendabat; <lb/></s> <s xml:id="echoid-s8699" xml:space="preserve">adeoque iterum ab initio calculus omnium Triangulorum erat re-<lb/>petendus: </s> <s xml:id="echoid-s8700" xml:space="preserve">pertæſus procul dubio laboris, quo jam bis perfun-<lb/>ctus erat Auctor, tantum adnotavit, ultimæ modo menſuræ fi-<lb/>dendum eſſe, non primæ, quam in Eratoſthene ſtatuit, atque <lb/>ulterius fecit nihil: </s> <s xml:id="echoid-s8701" xml:space="preserve">abſolviſſet procul dubio calculum, ſi cano-<lb/>nes Logarithmorum habuiſſet, quos hac tempeſtate poſſidemus, <lb/>& </s> <s xml:id="echoid-s8702" xml:space="preserve">quorum beneficio facillime & </s> <s xml:id="echoid-s8703" xml:space="preserve">breviſſime præſtamus, quod <lb/>veteres non niſi tædioſiſſimis multiplicationibus & </s> <s xml:id="echoid-s8704" xml:space="preserve">diviſionibus <lb/>maximorum numerorum peragebant, quibus non raro in errores <lb/>incidebant, â quibus Snellius immunis non fuit, deprehendi e-<lb/>nim illum uſum fuiſſe canonibus Sinuum & </s> <s xml:id="echoid-s8705" xml:space="preserve">Tangentium haud <lb/>accuratis, & </s> <s xml:id="echoid-s8706" xml:space="preserve">præterea propter longiſſimas Arithmeticas opera-<lb/>tiones commiſſiſſe alios errores, adeo ut ipſius calculo ſive <lb/>primo, ſive poſtea inſtituto non ſemper conſidi poſſit: </s> <s xml:id="echoid-s8707" xml:space="preserve">hinc <lb/>Galliarum Mathematici, qui Anno 1718 in lucem miſerunt men-<lb/>ſuram Terræ, merito in Snellium animadvertunt; </s> <s xml:id="echoid-s8708" xml:space="preserve">oſtendit-<lb/>que Cl. </s> <s xml:id="echoid-s8709" xml:space="preserve">Caſſini in L’Hiſt. </s> <s xml:id="echoid-s8710" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s8711" xml:space="preserve">Roy: </s> <s xml:id="echoid-s8712" xml:space="preserve">A°. </s> <s xml:id="echoid-s8713" xml:space="preserve">1702, ex diſtantia <lb/>inter Alcmariam & </s> <s xml:id="echoid-s8714" xml:space="preserve">Rotterodamum ſecundum Snellianam menſu- <pb o="360" file="0374" n="374" rhead="DISSERTATIO"/> ram, magnitudinem gradus unius eſſe 56612 hexapedarum Pariſien-<lb/>ſium; </s> <s xml:id="echoid-s8715" xml:space="preserve">vel ut poſtea ponitur in L’Hiſtoire A°. </s> <s xml:id="echoid-s8716" xml:space="preserve">1718 hexap. </s> <s xml:id="echoid-s8717" xml:space="preserve">58287. </s> <s xml:id="echoid-s8718" xml:space="preserve">atque <lb/>iterum ex aliâ menſura Snellii, inſpiciendo diſtantiam Alcmariam <lb/>inter & </s> <s xml:id="echoid-s8719" xml:space="preserve">Hagam comitis, magnitudinem gradus fore 56382 hexa-<lb/>pedarum Pariſienſium, cum ipſe Snellius gradui uni adſcribat tan-<lb/>tum hexapedas 55100, quæ magnitudines nequaquam inter ſe con-<lb/>veniunt, erroriſque arguunt obſervationes & </s> <s xml:id="echoid-s8720" xml:space="preserve">calculum Snellii: <lb/></s> <s xml:id="echoid-s8721" xml:space="preserve">hinc concluſerunt Celeberrimi Geometræ in L’Hiſt. </s> <s xml:id="echoid-s8722" xml:space="preserve">A°. </s> <s xml:id="echoid-s8723" xml:space="preserve">1718. </s> <s xml:id="echoid-s8724" xml:space="preserve">part. </s> <s xml:id="echoid-s8725" xml:space="preserve"><lb/>2. </s> <s xml:id="echoid-s8726" xml:space="preserve">Ch. </s> <s xml:id="echoid-s8727" xml:space="preserve">8. </s> <s xml:id="echoid-s8728" xml:space="preserve">Il paroît par toutes ces conſiderations, qu’on ne peut fai-<lb/>re aucun fondement ſolide ſur la meſure de la Terre de Snellius, <lb/>& </s> <s xml:id="echoid-s8729" xml:space="preserve">qu’ainſi il ne faut s’ etonner, ſi la grandeur du degré qu’il a <lb/>etablie ſe trouve ſi differente de celle, que nous avons determinée <lb/>dans le Voyage de la Meridienne. </s> <s xml:id="echoid-s8730" xml:space="preserve">Quoniam tamen ſi ulla regio <lb/>Terrarum poteſt eſſe accommodata menſuræ, erit profecto Hol-<lb/>landia ob ſummam planitiem qua gaudet, tum quia nemo mor-<lb/>talium opportunitatem nactus eſt primam menſuram ſupra glaciem <lb/>inſtituendi, quam Snellius, opinatus fui ejus menſuram funda-<lb/>tam ſuper ſuis emendationibus non eſſe prorſus rejiciendam; </s> <s xml:id="echoid-s8731" xml:space="preserve"><lb/>imo omnium maxime illi confiderem, ſi Snellius uſus fuiſſet <lb/>Quadrante Teleſcopiis & </s> <s xml:id="echoid-s8732" xml:space="preserve">filis duobus cruciatim ſe ſecantibus in <lb/>foco lentis ocularis inſtructo, ejus enim ope angulos multo accu-<lb/>ratius metimur, quam penullis, etiamſi exiliſſimis donatis crenis. </s> <s xml:id="echoid-s8733" xml:space="preserve"><lb/>Ne labor ingens, quem bis terve impendit noſter Geometra in per-<lb/>agrandis plurimis Fœderatarum provinciarum urbibus, menſuran-<lb/>diſque earum diſtantiis irritus maneret, in lucem emittendam eſſe <lb/>judicavi eam partem Eratoſthenis Batavi, quæ proprie de Magni-<lb/>tudine Terræ agit; </s> <s xml:id="echoid-s8734" xml:space="preserve">comprehenditur autem in 6. </s> <s xml:id="echoid-s8735" xml:space="preserve">capitibus, nempe <lb/>a Libri ſecundi Capite 6. </s> <s xml:id="echoid-s8736" xml:space="preserve">ad 11. </s> <s xml:id="echoid-s8737" xml:space="preserve">Bifariam autem hæc conſpiciuntur <lb/>diviſa: </s> <s xml:id="echoid-s8738" xml:space="preserve">in parte prima retinui omnia, quæ Autor ipſe in Manuſcripto <lb/>ſuo emendavit, poſtquam angulos Triangulorum ſecunda vice di-<lb/>menſus fuit, conſervando tamen baſin ſemel poſitam inter Ley-<lb/>dam & </s> <s xml:id="echoid-s8739" xml:space="preserve">Soeterwoudam perticarum 1092, 3, 3. </s> <s xml:id="echoid-s8740" xml:space="preserve">In altera parte <lb/>habentur, quæ ipſe ſupputavi, innixa menſuræ baſeos, quam Snellius <lb/>ſupra glaciem cepit, & </s> <s xml:id="echoid-s8741" xml:space="preserve">quam maxime commendavit; </s> <s xml:id="echoid-s8742" xml:space="preserve">quam aſſumere <lb/>tenebar, cum ejuſmodi opportunitas, qua uſus fuit Autor, ſe mihi <lb/>non obtulit: </s> <s xml:id="echoid-s8743" xml:space="preserve">verum de accurata menſura non dubitandum, cum <pb o="361" file="0375" n="375" rhead="DE MAGNITUDINE TERRÆ."/> ter repetita fuerit. </s> <s xml:id="echoid-s8744" xml:space="preserve">In hac parte proinde diſtantiæ deprehenduntur <lb/>locorum veræ, veraque magnitudo Gradus unius Terræ ſub noſtra <lb/>latitudine & </s> <s xml:id="echoid-s8745" xml:space="preserve">longitudine. </s> <s xml:id="echoid-s8746" xml:space="preserve">Dolendum eſt, cum ulterius menſuram <lb/>produxerat Geometra uſque ad Machliniam, veluti in Tab. </s> <s xml:id="echoid-s8747" xml:space="preserve">XVI. <lb/></s> <s xml:id="echoid-s8748" xml:space="preserve">repræſentatur, eas obſervationes periiſſe; </s> <s xml:id="echoid-s8749" xml:space="preserve">non enim illas in emen-<lb/>dationibus reperio, unde præter merum Schema ab ipſo Autore de-<lb/>pictum, nihil exhibere potui: </s> <s xml:id="echoid-s8750" xml:space="preserve">addita præterea ſunt alia Triangula, <lb/>quibus nonnullorum locorum diſtantiæ, quarum præcipua neceſſitas, <lb/>confirmantur, ut eo certiores veritatis evadamus; </s> <s xml:id="echoid-s8751" xml:space="preserve">quod in Geo-<lb/>metria Practica non prorſus eſt inutile; </s> <s xml:id="echoid-s8752" xml:space="preserve">docet enim experientia, <lb/>quam facile a verâ aberremus menſura, niſi ſummâ curâ obſerva-<lb/>tiones inſtrumentorum ope peregerimus, atque ideo ſolutionem <lb/>Problematis practici variis tentati modis menſuræ magnam fidem <lb/>conciliare: </s> <s xml:id="echoid-s8753" xml:space="preserve">præterea nonnullos Triangulorum angulos ope accu-<lb/>rati Quadrantis, Teleſcopiisque ornati ipſe exploravi, ut eo cer-<lb/>tior evaderem, an menſura Snelliana bene, an negligentius inſtituta <lb/>fuiſſet; </s> <s xml:id="echoid-s8754" xml:space="preserve">deprehendi plurimos angulos accuratiſſime fuiſſe captos, <lb/>aliquos uno alterove minuto aberraſſe, quos ideo correxi, hoc oc-<lb/>cupatus negotio non potui non dexteritatem Snellii admirari, qui <lb/>videndo tantum per penullarum crenas, tam accurate angulos tur-<lb/>rium valde diſſitarum & </s> <s xml:id="echoid-s8755" xml:space="preserve">vix nudo oculo diſtinguendarum obſer-<lb/>vare potuit: </s> <s xml:id="echoid-s8756" xml:space="preserve">omnes angulos de novo non examinavi, id vitæ meæ <lb/>ratio non permiſit, neque id neceſſarium judicabam, quum labores <lb/>ſecundi & </s> <s xml:id="echoid-s8757" xml:space="preserve">tertii Snellianitam accurate cum veritate conſentiebant, <lb/>quotieſcunque eos ad examen iterum vocabam: </s> <s xml:id="echoid-s8758" xml:space="preserve">Hæc monenda ju-<lb/>dicavi, ut intelligeretur, quare bis eadem menſura Terræ de-<lb/>ſcripta habeatur, & </s> <s xml:id="echoid-s8759" xml:space="preserve">quidnam a Snellio, quid a nobis in hoc negotio <lb/>peractum ſit.</s> <s xml:id="echoid-s8760" xml:space="preserve"/> </p> <pb o="362" file="0376" n="376" rhead="PARS PRIMA."/> </div> <div xml:id="echoid-div249" type="section" level="1" n="249"> <head xml:id="echoid-head272" xml:space="preserve">DE <lb/>MAGNITUDINE TERRÆ <lb/>MENSURATÆ <lb/>A <lb/>W. SNELLIO, <lb/>DESCRIPTÆ <lb/>IN <lb/>ERATOSTHENE BATAVO. <lb/>LIB. II. CAP. VI.</head> <head xml:id="echoid-head273" xml:space="preserve">Prima Gæodæſiæ ſtatio & diſtantia inter Lugdunum Bata-<lb/>vorum & Soeter woudam pagum definita.</head> <p> <s xml:id="echoid-s8761" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8762" xml:space="preserve">XIV. </s> <s xml:id="echoid-s8763" xml:space="preserve">fig. </s> <s xml:id="echoid-s8764" xml:space="preserve">1. </s> <s xml:id="echoid-s8765" xml:space="preserve">Ut ſtationum & </s> <s xml:id="echoid-s8766" xml:space="preserve">obſervationum loca, & </s> <s xml:id="echoid-s8767" xml:space="preserve">cal-<lb/>culi ratio clarius intelligatur totius regionis Chorographiam <lb/>hic exhibeo, unde tanto facilius locorum, ad quæ collineavimus, <lb/>poſitus perſpici poſſit. </s> <s xml:id="echoid-s8768" xml:space="preserve">Prima baſis & </s> <s xml:id="echoid-s8769" xml:space="preserve">totius operis fundamen-<lb/>tum erit recta, quæ urbem Leidam, Ptolomæo Lugdunum Ba-<lb/>tavorum dictam, & </s> <s xml:id="echoid-s8770" xml:space="preserve">pagum vicinum Soeterwoudam connectit. <lb/></s> <s xml:id="echoid-s8771" xml:space="preserve">Intervallo quaſi dodrantis horæ: </s> <s xml:id="echoid-s8772" xml:space="preserve">diſtantiam autem ad hunc mo-<lb/>dum dimenſus ſum. </s> <s xml:id="echoid-s8773" xml:space="preserve">Duo loca in intermedia camporum plani-<lb/>tie, quorum intercapedo illam lineam, quæ Leidam & </s> <s xml:id="echoid-s8774" xml:space="preserve">Soeterwoudam <lb/>connectit, transverſim ſecat, pro arbitrio oportuna ſelegi, & </s> <s xml:id="echoid-s8775" xml:space="preserve"><lb/>Quadrantem æreum in conſilium adhibui, cujus radius eſſet pe-<lb/>dum Rhynlandicorum duorum cum una quinta, limbus etiam in <lb/>terna ſcrupula, & </s> <s xml:id="echoid-s8776" xml:space="preserve">præterea per lineas tranſverſas in bina ita di-<lb/>viſus, ut etiam ſingula in eo nullo negotio notari poſſent. </s> <s xml:id="echoid-s8777" xml:space="preserve">Eſto <lb/>igitur Leidenſis curiæ turris I: </s> <s xml:id="echoid-s8778" xml:space="preserve">pagi Soeterwoudæ jam dicti turris, <lb/>hoc eodem Anno Magiſtratus urbici cura ac juſſu, qui hujus pagi <lb/>toparchiam non ita pridem redemerunt, priſtino nitori reſtituta, <lb/>cum per hæc bella diruta ſolas parietinas & </s> <s xml:id="echoid-s8779" xml:space="preserve">rudera tam calamitoſi <pb o="363" file="0377" n="377" rhead="DE MAGNITUDINE TERRÆ."/> belli reliquias oſtentaret, turris, inquam, ejus pagi ſit m. </s> <s xml:id="echoid-s8780" xml:space="preserve">Ejus ſitus <lb/>à turri curiæ Leidenſis ita in meridiem vergit, ut pauculis gradi-<lb/>bus in ortum declinet. </s> <s xml:id="echoid-s8781" xml:space="preserve">Stationum loca in camporum planitie a me <lb/>ad hanc primam Gæodæſiam ſelecta a. </s> <s xml:id="echoid-s8782" xml:space="preserve">& </s> <s xml:id="echoid-s8783" xml:space="preserve">e. </s> <s xml:id="echoid-s8784" xml:space="preserve">inter ſe trecentis vi-<lb/>ginti ſex Rhynlandicis perticis & </s> <s xml:id="echoid-s8785" xml:space="preserve">quatuor pedibus disjuncta. </s> <s xml:id="echoid-s8786" xml:space="preserve">Ve-<lb/>rum ut omnem ambiguitatem tollam, & </s> <s xml:id="echoid-s8787" xml:space="preserve">me ipſum hic clarius ex-<lb/>plicem, qua formula paſſim in hoc calculo uſus ſim prius indicabo. <lb/></s> <s xml:id="echoid-s8788" xml:space="preserve">Ut abacum facilem & </s> <s xml:id="echoid-s8789" xml:space="preserve">expeditum haberem decumanam numeratio-<lb/>nem uſurpavi. </s> <s xml:id="echoid-s8790" xml:space="preserve">Gæodætæ quidem noſtrates in agrorum metatione, <lb/>viarum dimenſione & </s> <s xml:id="echoid-s8791" xml:space="preserve">cæteris intervallis menſurandis, utuntur per-<lb/>tica, ipſi virgam vocant, een Roede, duodecim pedes longa, quas <lb/>duas orgyas veteres dicerent, eandem & </s> <s xml:id="echoid-s8792" xml:space="preserve">nos eadem longitudine re-<lb/>tinemus, ſed in partes tantum decem tributam. </s> <s xml:id="echoid-s8793" xml:space="preserve">Illi pedem ſuum <lb/>in uncias duodecim rurſum ſubdividunt; </s> <s xml:id="echoid-s8794" xml:space="preserve">Nos pedem noſtrum tan-<lb/>tum in partes decem, ita ut illis tota pertica ſit unciarum centum <lb/>quatuor & </s> <s xml:id="echoid-s8795" xml:space="preserve">quadraginta, nobis eadem pertica habeat tantum partes <lb/>centum. </s> <s xml:id="echoid-s8796" xml:space="preserve">Ut noſtri pedis in hoc calculo ad Rhynlandicum ratio ſit <lb/>ut 6 ad 5. </s> <s xml:id="echoid-s8797" xml:space="preserve">eadem ſcilicet, quæ Alexandrini aut Philetærei ad Roma-<lb/>num: </s> <s xml:id="echoid-s8798" xml:space="preserve">quamvis ipſæ perticæ omnino magnitudine eædem ſint. </s> <s xml:id="echoid-s8799" xml:space="preserve">He-<lb/>ro, ?</s> <s xml:id="echoid-s8800" xml:space="preserve"><unsure/>?</s> <s xml:id="echoid-s8801" xml:space="preserve">??</s> <s xml:id="echoid-s8802" xml:space="preserve">??</s> <s xml:id="echoid-s8803" xml:space="preserve">&</s> <s xml:id="echoid-s8804" xml:space="preserve"><unsure/> ?</s> <s xml:id="echoid-s8805" xml:space="preserve"><unsure/>?</s> <s xml:id="echoid-s8806" xml:space="preserve">?? </s> <s xml:id="echoid-s8807" xml:space="preserve"><lb/>?</s> <s xml:id="echoid-s8808" xml:space="preserve">??</s> <s xml:id="echoid-s8809" xml:space="preserve">?? </s> <s xml:id="echoid-s8810" xml:space="preserve">?</s> <s xml:id="echoid-s8811" xml:space="preserve">??</s> <s xml:id="echoid-s8812" xml:space="preserve">??</s> <s xml:id="echoid-s8813" xml:space="preserve">??</s> <s xml:id="echoid-s8814" xml:space="preserve">??</s> <s xml:id="echoid-s8815" xml:space="preserve">@?</s> <s xml:id="echoid-s8816" xml:space="preserve">?, <lb/>?</s> <s xml:id="echoid-s8817" xml:space="preserve">??</s> <s xml:id="echoid-s8818" xml:space="preserve">??</s> <s xml:id="echoid-s8819" xml:space="preserve">?@?</s> <s xml:id="echoid-s8820" xml:space="preserve">?@ Calamus, ha-<lb/>bet Philetæreos pedes decem, Italicos duodecim. </s> <s xml:id="echoid-s8821" xml:space="preserve">Ut plane noſter <lb/>pes decumanus Alexandrino æqualis ſit, cum Rhynlandicus Ro-<lb/>mano par ſit. </s> <s xml:id="echoid-s8822" xml:space="preserve">Atque hic tamen à conſueta appellatione non rece-<lb/>dimus, ut {1/10} Calami ſeu perticæ pedem, & </s> <s xml:id="echoid-s8823" xml:space="preserve">hujus pedis {1/10} digitum <lb/>vocemus. </s> <s xml:id="echoid-s8824" xml:space="preserve">Ea autem numeratione & </s> <s xml:id="echoid-s8825" xml:space="preserve">enuntiatione hoc aſſequimur, <lb/>ut ſolis integris numeris, non intercurrentibus partium particulis, <lb/>omnis calculus abſolvatur, neque conſuetam integrorum numera-<lb/>tionem quidquam turbent. </s> <s xml:id="echoid-s8826" xml:space="preserve">Exemplum, ſi quæratur 1575 digiti in <lb/>longum exporrecti quot ſint decempedæ? </s> <s xml:id="echoid-s8827" xml:space="preserve">Cum in pertica vel no-<lb/>ſtra decempeda ſint digiti centum, efficientur 15 decempedæ no-<lb/>ſtræ, 75 digiti; </s> <s xml:id="echoid-s8828" xml:space="preserve">hi per decem diviſi, tot enim digiti pedem effici-<lb/>ciunt, dabunt pedes 7. </s> <s xml:id="echoid-s8829" xml:space="preserve">digitos 5. </s> <s xml:id="echoid-s8830" xml:space="preserve">itaque ſola diſtinctione omniæ <lb/>iſta exprimentur, hoc modo 15, 7, 5. </s> <s xml:id="echoid-s8831" xml:space="preserve">Et contra idem numerus <lb/>non interrupto ordine in digitos vertetur, hoc modo, 1575 digiti. </s> <s xml:id="echoid-s8832" xml:space="preserve"><lb/>eodem modo intervallum ſtationum, quod diximus eſſe perticarum <lb/>326 pedum 4, ſecundum iſtam menſuram decumanam expreſſi, &</s> <s xml:id="echoid-s8833" xml:space="preserve"> <pb o="364" file="0378" n="378" rhead="DISSERTATIO"/> propterea mihi eſſent pedes 3264. </s> <s xml:id="echoid-s8834" xml:space="preserve">At ſi eundem numerum ſecun-<lb/>dum Gæodætarum morem in pedes commutare voles, quamvisper-<lb/>ticarum numerus omnino idem utrimque ſit, tamen cum in diver-<lb/>ſæ quantitatis pedes reſolvetur, alium quoque numerum inde effici <lb/>erit neceſſe. </s> <s xml:id="echoid-s8835" xml:space="preserve">Secundum hanc rationem cum iſti 10 pedes faciant <lb/>12 Rhynlandicos, itaque 3264 noſtri efficient Rhynlandicos 3916 {3/10} <lb/>pedes, qui tamen nihil ipſis ſunt aliud quam 326 perticæ, pedes 4 {3/10}. <lb/></s> <s xml:id="echoid-s8836" xml:space="preserve">Ut omnis differentia ad pedes & </s> <s xml:id="echoid-s8837" xml:space="preserve">digitos devolvatur. </s> <s xml:id="echoid-s8838" xml:space="preserve">Sed ad inſti-<lb/>tutam Gæodæſiam revertor. </s> <s xml:id="echoid-s8839" xml:space="preserve">Harum ſtationum a e intervallum <lb/>primum per triangulorum canones, deinde etiam applicata men-<lb/>ſura ſemel atque iterum ſum dimenſus. </s> <s xml:id="echoid-s8840" xml:space="preserve">Ejus Gæodæſiæ partes nunc <lb/>ſigillatim explicabo. </s> <s xml:id="echoid-s8841" xml:space="preserve">Ut à primo uſque principio & </s> <s xml:id="echoid-s8842" xml:space="preserve">ipſo fundamer-<lb/>to, nihil temere aſſumptum, ſed omnia certiſſimis demonſtrationi-<lb/>bus ſubſtructa & </s> <s xml:id="echoid-s8843" xml:space="preserve">firmata omnibus teſtatum faciam. </s> <s xml:id="echoid-s8844" xml:space="preserve">Ad invenien-<lb/>dam igitur diſtantiam a e aſſumpſi tranſverſim baſin t c 8705 di-<lb/>gitorum, vel 87 decempedarum 0 pedum, 5 digitorum. </s> <s xml:id="echoid-s8845" xml:space="preserve">Quem <lb/>numerum punctis ita diſtinguo 87. </s> <s xml:id="echoid-s8846" xml:space="preserve">0.</s> <s xml:id="echoid-s8847" xml:space="preserve">5. </s> <s xml:id="echoid-s8848" xml:space="preserve">ne ſemper decempedas, pe-<lb/>des, digitos appellare neceſſe habeam. </s> <s xml:id="echoid-s8849" xml:space="preserve">Porro angulus e t c ex obſer-<lb/>vatione datur 54 gr. </s> <s xml:id="echoid-s8850" xml:space="preserve">0 ſcr. </s> <s xml:id="echoid-s8851" xml:space="preserve">& </s> <s xml:id="echoid-s8852" xml:space="preserve">e c t 63. </s> <s xml:id="echoid-s8853" xml:space="preserve">gr. </s> <s xml:id="echoid-s8854" xml:space="preserve">52. </s> <s xml:id="echoid-s8855" xml:space="preserve">ſcr. </s> <s xml:id="echoid-s8856" xml:space="preserve">Unde latera e t <lb/>88. </s> <s xml:id="echoid-s8857" xml:space="preserve">4. </s> <s xml:id="echoid-s8858" xml:space="preserve">0. </s> <s xml:id="echoid-s8859" xml:space="preserve">e c 79. </s> <s xml:id="echoid-s8860" xml:space="preserve">6. </s> <s xml:id="echoid-s8861" xml:space="preserve">6. </s> <s xml:id="echoid-s8862" xml:space="preserve">per calculum inveniuntur. </s> <s xml:id="echoid-s8863" xml:space="preserve">Et rurſum cum <lb/>altrinſecus angulus a t c ex obſervatione ſit deprehenſus 78 gr. </s> <s xml:id="echoid-s8864" xml:space="preserve">30 <lb/>ſcr. </s> <s xml:id="echoid-s8865" xml:space="preserve">atque a c t 82 gr. </s> <s xml:id="echoid-s8866" xml:space="preserve">8 {1/2} ſcr. </s> <s xml:id="echoid-s8867" xml:space="preserve">dabitur per calculum a t 260. </s> <s xml:id="echoid-s8868" xml:space="preserve">1. </s> <s xml:id="echoid-s8869" xml:space="preserve">5. </s> <s xml:id="echoid-s8870" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s8871" xml:space="preserve">a c 256. </s> <s xml:id="echoid-s8872" xml:space="preserve">3. </s> <s xml:id="echoid-s8873" xml:space="preserve">0. </s> <s xml:id="echoid-s8874" xml:space="preserve">Atque ideo cum in triangulo e t a dentur latera e t <lb/>88. </s> <s xml:id="echoid-s8875" xml:space="preserve">4. </s> <s xml:id="echoid-s8876" xml:space="preserve">0. </s> <s xml:id="echoid-s8877" xml:space="preserve">atque a t 260. </s> <s xml:id="echoid-s8878" xml:space="preserve">1. </s> <s xml:id="echoid-s8879" xml:space="preserve">5. </s> <s xml:id="echoid-s8880" xml:space="preserve">Et præterea angulus e t a ab iſtis cru-<lb/>ribus comprehenſus 132 gr. </s> <s xml:id="echoid-s8881" xml:space="preserve">30 ſcr. </s> <s xml:id="echoid-s8882" xml:space="preserve">dabitur quoque baſis a e 326 4. </s> <s xml:id="echoid-s8883" xml:space="preserve"><lb/>3. </s> <s xml:id="echoid-s8884" xml:space="preserve">quam eandem applicata menſura ſemel atque iterum dimenſus <lb/>deprehendi 326 9. </s> <s xml:id="echoid-s8885" xml:space="preserve">0. </s> <s xml:id="echoid-s8886" xml:space="preserve">tantillo itaque calculus hic accuratior erit <lb/>iſta epharmoſi. </s> <s xml:id="echoid-s8887" xml:space="preserve">Atque ita jam definita baſe a e ſequitur deinceps <lb/>inventio diſtantiæ i m inter Leidam & </s> <s xml:id="echoid-s8888" xml:space="preserve">pagum Soeterwoudam, ſu-<lb/>periori calculo plane affinis.</s> <s xml:id="echoid-s8889" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Jam enim datur a e # 326. # 4. 3. <lb/>Ex obiervatione autem datur <lb/>Angulus i e a # 83 gr. # 20 ſcr. <lb/>Et angulus i a e # 67 gr. # 44 ſcr. <lb/>Unde per calculum dabitur latus a i. # 670. # 1. 9. <lb/>Et latus e i # 624. # 3. 0. <lb/></note> <pb o="365" file="0379" n="379" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Perro in triangulo a e m datur baſis a e ut ante # 326. 4. 3. <lb/>Angulus m a e ex obſervatione # 61 gr. 38 ſcr. <lb/>Et angulus m e a # 81 gr, 29 ſcr. <lb/>Unde dabitur latus a m # 537. 9. 0. <lb/>Et latus m e # 478. 5. 8. <lb/></note> <p> <s xml:id="echoid-s8890" xml:space="preserve">Quamobrem cum ex antecedentibus jam nobis cognita ſint crura <lb/>anguli i a m, & </s> <s xml:id="echoid-s8891" xml:space="preserve">angulus i a m 129 gr. </s> <s xml:id="echoid-s8892" xml:space="preserve">22 ſcr. </s> <s xml:id="echoid-s8893" xml:space="preserve">conflatus e duo-<lb/>bus i a e & </s> <s xml:id="echoid-s8894" xml:space="preserve">e a m, dabitur inde quoque baſis i m 1092. </s> <s xml:id="echoid-s8895" xml:space="preserve">3. </s> <s xml:id="echoid-s8896" xml:space="preserve">3.</s> <s xml:id="echoid-s8897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8898" xml:space="preserve">Atque ideo intervallum inter Leidenſis curiæ turrim & </s> <s xml:id="echoid-s8899" xml:space="preserve">turrim <lb/>pagi Soeterwoudæ interjectum erit digitorum 1092 33, vel decem-<lb/>pedarum 1092, pedum 3, digitorum 3. </s> <s xml:id="echoid-s8900" xml:space="preserve">Quo in calculo digitos <lb/>quoque admiſi & </s> <s xml:id="echoid-s8901" xml:space="preserve">pedes, non quod ita accurate ad unius digiti aut <lb/>pedis menſuram hanc diſtantiam explicatam exiſtimem, ſed ne er-<lb/>ror aliquis, leviculus initio, deinceps ulterius calculo procedente <lb/>in ipſas decempedas proſerpat, ut harum ſaltem menſura & </s> <s xml:id="echoid-s8902" xml:space="preserve">nume-<lb/>rus nobis integer & </s> <s xml:id="echoid-s8903" xml:space="preserve">a calculi vitio illibatus conſtet. </s> <s xml:id="echoid-s8904" xml:space="preserve">Nunc itaque <lb/>ad cætera cum bono Deo nos conferamus, hac baie totius operis <lb/>inter Leidam & </s> <s xml:id="echoid-s8905" xml:space="preserve">Soeterwoudam ita accurate & </s> <s xml:id="echoid-s8906" xml:space="preserve">bene juſte à nobis <lb/>definita.</s> <s xml:id="echoid-s8907" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div250" type="section" level="1" n="250"> <head xml:id="echoid-head274" xml:space="preserve">CAPUT VII.</head> <head xml:id="echoid-head275" xml:space="preserve">Diſtantia inter Lugdunum Batavorum & Hagam Comitis <lb/>definita.</head> <p> <s xml:id="echoid-s8908" xml:space="preserve">Tandem aliquando pedem è camporum planitie extulimus, & </s> <s xml:id="echoid-s8909" xml:space="preserve"><lb/>in turrium faſtigia conſcendimus: </s> <s xml:id="echoid-s8910" xml:space="preserve">Verum ut urbium longius <lb/>diſſitarum intervalla ſecure & </s> <s xml:id="echoid-s8911" xml:space="preserve">cum fide explicare queamus, inde jam in <lb/>vicinas quaſque & </s> <s xml:id="echoid-s8912" xml:space="preserve">operi noſtro opportunas turres transvolabimus. </s> <s xml:id="echoid-s8913" xml:space="preserve">Et <lb/>cum inter Hagam atque Leidam opportuna ſit duarum turrium ad <lb/>collineandum ſtatio, quaſi in medio itinere transverſim poſitarum, <lb/>in pagis Voorſchoten & </s> <s xml:id="echoid-s8914" xml:space="preserve">Waſſenaar, unde inclytæ Waſſenariæ gen. <lb/></s> <s xml:id="echoid-s8915" xml:space="preserve">tis nomen. </s> <s xml:id="echoid-s8916" xml:space="preserve">Harum intervalla primum cum Leida, deinde ipſarum <lb/>inter ipſas quoque explicabo.</s> <s xml:id="echoid-s8917" xml:space="preserve"/> </p> <pb o="366" file="0380" n="380" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div251" type="section" level="1" n="251"> <head xml:id="echoid-head276" xml:space="preserve">I. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head277" xml:space="preserve">Diſtantia pagorum Waſſenariæ & Soeterwoudæ.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XIV. fig. 3. Principio è capite ſexto datur \\ diſtantia inter Leidam & Soeterwoudam A E # 1092. # 3. 3. <lb/>Ex obſervatis autem angulis E A I # 63 gr. # 57 ſcr. <lb/>Et angulus A E I # 84 gr. # 5 ſcr. <lb/>Atque inde ſubductione, quia eo loco nulla oppor- \\ tuna ſtatio, angulus I # 31 gr # 58 ſcr. <lb/>Unde latus A I invenitur # 2052. # 1. 2. <lb/>Et latus E I # 1853. # 6. 3. <lb/></note> </div> <div xml:id="echoid-div252" type="section" level="1" n="252"> <head xml:id="echoid-head278" xml:space="preserve">II. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head279" xml:space="preserve">Diſtantia pagorum Soeterwoudæ & Voorſchoten.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XIV. fig. 4. Rurſum ut ante datur in hoc \\ triangulo latus A E # 1092. # 3. 3. <lb/>Ex obſervatis autem angulus E A I # 77 gr. # 12 ſcr. <lb/>Et angulus A E I # 45 gr. # 21 ſcr. <lb/>Inde ex horum ſubductione a duobus rectis A I E # 57 gr. # 27 ſcr. <lb/>Unde conſtabit latus A I # 921. # 9. 1. <lb/>Et latus E I # 1263. # 6. 8. <lb/></note> </div> <div xml:id="echoid-div253" type="section" level="1" n="253"> <head xml:id="echoid-head280" xml:space="preserve">III. <emph style="sc">Problema</emph>.</head> <head xml:id="echoid-head281" xml:space="preserve">Diſtantia pagorum Waſſenariæ & Voorſchoten.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XIV. fig. 6. E problemate ſecundo datur di- \\ ſtantia inter Leidam & pagum Voorſchoten, ſeu la- \\ tus A I # 1263. 6. 8. <lb/>Ex primo problemate datur diſtantia inter Leidam \\ & pagum Waſſenariam, ſeu latus A E # 1853. 6. 3. <lb/></note> <pb o="367" file="0381" n="381" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Ex obſervatis datur angulus E A I his cruribus \\ contentus # 38 gr. # 45 ſcr. <lb/>Unde eruetur baſis E I diſtantia inter pagos Waſ- \\ ſenariam & Voorſchoten. # 1174. # 4. 1. <lb/></note> </div> <div xml:id="echoid-div254" type="section" level="1" n="254"> <head xml:id="echoid-head282" xml:space="preserve">IV. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head283" xml:space="preserve">Diſtantia pagorum Waſſenariæ & Voorſchoten, iterata <lb/>Gæodæſia tentata & expreſſa.</head> <p> <s xml:id="echoid-s8918" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8919" xml:space="preserve">XV. </s> <s xml:id="echoid-s8920" xml:space="preserve">fig. </s> <s xml:id="echoid-s8921" xml:space="preserve">7. </s> <s xml:id="echoid-s8922" xml:space="preserve">Et vero ne quidquam dubii nobis hac in parte <lb/>relinquatur, eandem horum pagorum Waſſenariæ & </s> <s xml:id="echoid-s8923" xml:space="preserve">Voorſchoten <lb/>diſtantiam de novo experiri libuit. </s> <s xml:id="echoid-s8924" xml:space="preserve">Ut liquido conſtet in his nihil <lb/>à nobis commiſſum. </s> <s xml:id="echoid-s8925" xml:space="preserve">Et præterea illud planum fiat hunc calculum <lb/>atque locorum diſtantiam per triangulorum ambages derivatum non <lb/>aliter ad numeros redire, atque tanquam ſingulæ pro Gæodæſiæ <lb/>principio per artem à nobis eſſent conſtitutæ.</s> <s xml:id="echoid-s8926" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Loca ſtationum ſunto i & a inter iſtos pagos interjecta, quo- \\ rum intervallum a i & menſura applicata & per organa euthyme- \\ trica eſt deprehenſum decempedarum 348, pedis 1. # 348. # 1. <lb/>Et angulus a i E # 92 gr. # 10 ſcr. <lb/>Et angulus i a E # 66 gr. # 5 ſcr. <lb/>Unde datur angulus a E i # 21 gr. # 45 ſcr. <lb/>Atque ex his datis invenietur latus E i # 858. # 7. 3. <lb/>Et latus a E # 938. # 7. 2. <lb/>Rurſum in triangulo O a i datur ut antea a i # 348. # 1. <lb/>Ex obſervatis autem angulus O a i # 59 gr. # 20 ſcr. <lb/>Et angulus a i O # 60 gr. # 11 ſcr. <lb/>Unde dabitur angulus a O i # 60 gr. # 29 ſcr. <lb/>Atque hinc invenietur latus O i <lb/>Et præterea latus a O # 347. # 0. 6. <lb/>Quamobrem cum in triangulo O a E jam detur la- \\ tus a O # 347. # 0. 6. <lb/>Et latus a E # 938. # 7. 2. <lb/>Et angulus O a E conflatus ex O a i & i a E # 125 gr. # 25 ſcr. <lb/></note> <pb o="368" file="0382" n="382" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Dabitur quoque baſis O E diſtantia inter dictos pa- \\ gos, # 1174. # 4. 2. <lb/></note> <p> <s xml:id="echoid-s8927" xml:space="preserve">Qui calculus tam arcte cum ſuperiore conſentit, ut non ex obſer-<lb/>vatione notatus, ſed ex antecedente abaco derivatus videri poſſit, <lb/>niſi utriuſque obſervationis, inter quas amplius integro anno inter-<lb/>ceſſit, teſtes haberem fide dignos, & </s> <s xml:id="echoid-s8928" xml:space="preserve">harum rerum non ignaros. <lb/></s> <s xml:id="echoid-s8929" xml:space="preserve">Quin cum in illa prima obſervatione, quam tamen noviſſimam in-<lb/>ſtitui, ſemper ipſe præfuerim, ipſemet omnia Gæodæſiæ munia <lb/>obiverim; </s> <s xml:id="echoid-s8930" xml:space="preserve">hanc noviſſimam autem, excepta angulorum dimenſio-<lb/>ne, quam ſimul inſtituimus, totam per alios adminiſtraverim, & </s> <s xml:id="echoid-s8931" xml:space="preserve"><lb/>ſpatium a i per harum gnaros catena dimenſus ſim, idem tamen <lb/>intervallum utriuſque calculus in Abaco nobis repræſentavit. </s> <s xml:id="echoid-s8932" xml:space="preserve">Quam-<lb/>obrem harum turrium diſtantia tanta nobis eſto. </s> <s xml:id="echoid-s8933" xml:space="preserve">Atque hinc jam <lb/>ad intervallum Hagæ & </s> <s xml:id="echoid-s8934" xml:space="preserve">Leidæ, cui inveniundæ iſtam adeo ſollicite <lb/>& </s> <s xml:id="echoid-s8935" xml:space="preserve">anxie conquiſivimus, deinceps porro progrediamur.</s> <s xml:id="echoid-s8936" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div255" type="section" level="1" n="255"> <head xml:id="echoid-head284" xml:space="preserve">V. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head285" xml:space="preserve">Diſtantia Hagæ & Leidæ.</head> <p> <s xml:id="echoid-s8937" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8938" xml:space="preserve">XV. </s> <s xml:id="echoid-s8939" xml:space="preserve">fig. </s> <s xml:id="echoid-s8940" xml:space="preserve">8. </s> <s xml:id="echoid-s8941" xml:space="preserve">Cum in pagorum dictorum turribus minus eſ-<lb/>ſent oportunæ ad obſervandum ſtationes, angulos iſtos e turri tem-<lb/>pli Hagæ·comitani, quod prope forum piſcarium eſt, & </s> <s xml:id="echoid-s8942" xml:space="preserve">curiæ Lei-<lb/>denſis tantos obſervavimus, quemadmodum hic eos expreſſimus.</s> <s xml:id="echoid-s8943" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>E curia Leidenſi angulus I A O eſt # 15 gr. # 10 ſcr. <lb/>Et angulus O A E # 23 gr. # 36 ſcr. <lb/>Ex turri Hagienſi A O I # 6 gr. # 32 ſcr. <lb/>Et angulus A O E # 17 gr. # 9 ſcr. <lb/>Præterea quantitas lateris AI conſtante adeo cal- \\ culo comprobata # 1263. # 6. 8. <lb/>Et A E # 1853. # 6. 3. <lb/>Et E I # 1174. # 4. 1. <lb/>Unde anguli eruentur, E A I quidem, tantus \\ quoque ex obſervatione # 38 gr. # 45 ſcr. <lb/>Et angulus A I E # 98 gr. # 55 ſcr. <lb/></note> <pb o="369" file="0383" n="383" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Et præterea A EI # 42 gr. # 20 ſcr. <lb/>Cumque inſuper dentur E A O 23 gr. 36 ſcr. & A O E 17 \\ gr. 9 ſcr. dabitur quoque in triangulo A O E angulus tertius \\ A E O # 139 gr. # 5 ſcr. <lb/>Danturque ex obſervatis ſinguli O A E # 23 gr. # 36 ſcr. <lb/>Et angulus A O E # 17 gr. # 9 ſcr. <lb/>Et latus A E # 1853. # 6. 3. <lb/>Unde per triangulorum canones datur O E # 2516. # 6. 6. <lb/>Et denique A O diſtantia inter Hagam & Leidam # 4103. # 3. 6 <lb/></note> </div> <div xml:id="echoid-div256" type="section" level="1" n="256"> <head xml:id="echoid-head286" xml:space="preserve">VI. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head287" xml:space="preserve">Eadem diſtantia inter Hagam & Leidam aliter tentata.</head> <p> <s xml:id="echoid-s8944" xml:space="preserve">Tab. </s> <s xml:id="echoid-s8945" xml:space="preserve">XV. </s> <s xml:id="echoid-s8946" xml:space="preserve">fig. </s> <s xml:id="echoid-s8947" xml:space="preserve">12. </s> <s xml:id="echoid-s8948" xml:space="preserve">Necdum adeo ipſe mihi ſatisfeci, niſi hanc <lb/>eandem diſtantiam, quæ tam nobilis & </s> <s xml:id="echoid-s8949" xml:space="preserve">excellentis epichrematis ba-<lb/>ſis futura ſit, cum iſta conſentire etiam alia via demonſtraverim: <lb/></s> <s xml:id="echoid-s8950" xml:space="preserve">etſi non tanta cum fiducia hoc pronuntiare auſus fuiſſem, niſi inſti-<lb/>tuti operis arctus conſenſus me eo quaſi manu duxiſſet. </s> <s xml:id="echoid-s8951" xml:space="preserve">Quamob-<lb/>rem illud idem quoque ex prima baſi ſeuLeidæ & </s> <s xml:id="echoid-s8952" xml:space="preserve">Soeterwoudæ in-<lb/>tervallo explicare aggrediar.</s> <s xml:id="echoid-s8953" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Intercapedo inter Leidam & Soeterwoudam A E per ſexti capi- \\ tis calculum eſt # 1092. # 3. 3. <lb/>Et angulus I A E ex obſervatis # 60 gr. # 32 ſcr. <lb/>Et angulus I E A # 104 gr. # 32 ſcr. <lb/>Unde tertius A I E datur # 14 gr. # 56 ſcr. <lb/>Atque ideo per triangulorum doctrinam dabitur la- \\ tus A I # 4103. # 2. 1. <lb/>Et latus E I # 3690. # 5. 2. <lb/></note> <p> <s xml:id="echoid-s8954" xml:space="preserve">Certe ob exilitatem anguli A I E verebar ne calculus quidtur-<lb/>baret, & </s> <s xml:id="echoid-s8955" xml:space="preserve">vix ad unam aut alteram decempedam, vel etiam pluſcu-<lb/>las addicere auſus fuiſſem, niſi operis eventus arctiſſimum utriuſque <lb/>abaci conſenſum exhibuiſſet: </s> <s xml:id="echoid-s8956" xml:space="preserve">differentia enim inter hujus & </s> <s xml:id="echoid-s8957" xml:space="preserve">quinti <lb/>problematis numeros eſt duntaxat ſesquipedis, quod vel optare im-<lb/>probum videbatur. </s> <s xml:id="echoid-s8958" xml:space="preserve">Atque adeo cum utriuſque operis eventus eun- <pb o="370" file="0384" n="384" rhead="DISSERTATIO"/> dem numerum nobis addicat, de iſtorum locorum diſtantia amplius <lb/>dubitare fas non eſt Et ſuper hac baſi reliquam ſuſcepti operis <lb/>ſtructuram tuto inædificare licebit. </s> <s xml:id="echoid-s8959" xml:space="preserve">Quare alacri animo ad reliqua <lb/>nunc porro contendamus.</s> <s xml:id="echoid-s8960" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div257" type="section" level="1" n="257"> <head xml:id="echoid-head288" xml:space="preserve">CAPUT VIII.</head> <head xml:id="echoid-head289" xml:space="preserve">Omnium reliquorum locorum ad inſtitutam Gæodæſiam <lb/>adbibitorum intervalla definita.</head> <p> <s xml:id="echoid-s8961" xml:space="preserve">Priuſquam ad ſequentia tranſeam, ne novis ſemper opus ſitſche-<lb/>matis, ſemel hic tabellam expreſſi, in qua turrium & </s> <s xml:id="echoid-s8962" xml:space="preserve">urbium <lb/>loca exhibeo ſuis literis notata, quibus eas ſemper ſumus citaturi. <lb/></s> <s xml:id="echoid-s8963" xml:space="preserve">Ulterius itaque progreſſuris occurrit Gouda, ex cujus turri ad Lei-<lb/>dam & </s> <s xml:id="echoid-s8964" xml:space="preserve">Hagam collineavimus, & </s> <s xml:id="echoid-s8965" xml:space="preserve">angulorum quantitatem ſæpius <lb/>obſervavi majore Quadrante æreo, cujus ſupra mentio facta, aut ſemi-<lb/>circulo amplo diametri pedum Rhynlandicorum trium & </s> <s xml:id="echoid-s8966" xml:space="preserve">ſemis. </s> <s xml:id="echoid-s8967" xml:space="preserve">Ve-<lb/>rum ut via atque ordine horum tractatio procedat ſingula triangula <lb/>ſingularibus problematibus diſtinguam, ita enim commodius, quando <lb/>opus erit, citari à nobis poterunt.</s> <s xml:id="echoid-s8968" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div258" type="section" level="1" n="258"> <head xml:id="echoid-head290" xml:space="preserve">I. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head291" xml:space="preserve">Triangulum A E S, Leida, Haga, Gouda.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XVI. Ex V & VI antecedentis Capitis problemate jam nobis \\ inventa eſt diſtantia inter Leidam & Hagam, quæ propoſiti trian- \\ guli futura eſt baſis A E # 4103. # 3. <lb/>Ex obſervatione autem datur angulus A E S # 97 gr. # 11 ſcr. <lb/>Et angulus A S E # 32 gr. # 25 ſcr. <lb/>Et denique angulus E A S # 50 gr. # 23 ſcr. <lb/>Qui omnes in unam ſummam collecti efficiunt # 179 gr. # 59 ſcr. <lb/>Et propterea obſervationes noſtras quam diligentiſſime inſtitutas, \\ atque accuratiſſime notatas coarguunt. Unicum vero ſcrupulum, <lb/></note> <pb o="371" file="0385" n="385" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>quod è duobus rectis reliquum deſideratur, illud adjiciatur anguſo \\ E A S, ſitque is # 50 gr. # 24 ſcr. <lb/></note> <p> <s xml:id="echoid-s8969" xml:space="preserve">Id enim ad rei ſummam hic nihil admodum facit. </s> <s xml:id="echoid-s8970" xml:space="preserve">Ita enim non <lb/>ſemper omnia ad minutum redire mirum nemini videri debet, cum <lb/>turrium quantumvis longe diſſitarum aliqua ſit latitudo, & </s> <s xml:id="echoid-s8971" xml:space="preserve">in ocu-<lb/>lo obſervantis ſaltem aliquem notabilem angulum ſubtendat. </s> <s xml:id="echoid-s8972" xml:space="preserve">Ut <lb/>hoc clarius intelligatur, ſtatuamus turrim latitudine trium decem-<lb/>pedarum à nobis abeſſe intervallo decempedarum 4103. </s> <s xml:id="echoid-s8973" xml:space="preserve">Concipia-<lb/>mus itaque animo triangulum rectangulum, cujus hæc ipſa ſunt <lb/>crura, unde angulus, quem turris Hagienſis latitudo in turri Lei-<lb/>denſis curiæ ſubtendit, dabitur 0 gr. </s> <s xml:id="echoid-s8974" xml:space="preserve">2 ſcr. </s> <s xml:id="echoid-s8975" xml:space="preserve">31. </s> <s xml:id="echoid-s8976" xml:space="preserve">ſecundorum. </s> <s xml:id="echoid-s8977" xml:space="preserve">Ac ta-<lb/>metſi per dioptrarum crenas ad mediam turrium latitudinem colli-<lb/>neationem dirigere ſummo ſtudio coneris, radii illic quaſi in an-<lb/>guſtiis verſantes rei viſibilis ſpeciem ita atterunt, ut ipſa pene e <lb/>conſpectu evaneſcat, vel ſaltem minus diſtincte cernatur. </s> <s xml:id="echoid-s8978" xml:space="preserve">Sin ve-<lb/>ro utrinque dioptrarum latera viſu ſtringas, tunc refractio ab hu-<lb/>moribus oculi nata collineanti quoque non nihil illudit. </s> <s xml:id="echoid-s8979" xml:space="preserve">Ut plane <lb/>nemini intelligenti mirum videri debeat, ipſa adeo ſcrupula non <lb/>ad libitum ſemper redire; </s> <s xml:id="echoid-s8980" xml:space="preserve">cum turres a ſe nullum ſplendorem fun-<lb/>dant, quo claritatem aliquam obſervantium oculis affundant. </s> <s xml:id="echoid-s8981" xml:space="preserve">Quin <lb/>illud potius magis mirandum exiſtimem, tam accurate omnia nobis <lb/>ad calculum veniſſe. </s> <s xml:id="echoid-s8982" xml:space="preserve">Atque ea de cauſa non temere, niſi in an-<lb/>guſtias adactus, ullum angulum in iſtis abacis in conſilium advocem, <lb/>qui ſit valde acutus. </s> <s xml:id="echoid-s8983" xml:space="preserve">Horum enim dolos, & </s> <s xml:id="echoid-s8984" xml:space="preserve">in his minimam hal-<lb/>lucinationem pertimeſco, & </s> <s xml:id="echoid-s8985" xml:space="preserve">ne quid vitii faciant ſedulus circum-<lb/>ſpicio. </s> <s xml:id="echoid-s8986" xml:space="preserve">In ratione enim minoris inæqualitatis, terminis multum <lb/>differentibus, facilis eſt lapſus & </s> <s xml:id="echoid-s8987" xml:space="preserve">periculoſus. </s> <s xml:id="echoid-s8988" xml:space="preserve">Error enim ex mi-<lb/>nore termino in majoribus fit multiplex. </s> <s xml:id="echoid-s8989" xml:space="preserve">Contra vero, cum angu-<lb/>li omnes erunt majuſculi, tum ratio magis opportuna eſt, & </s> <s xml:id="echoid-s8990" xml:space="preserve">errori <lb/>minus obnoxia. </s> <s xml:id="echoid-s8991" xml:space="preserve">Atque ideo ſi in iſtis anguli ſinguli uno aut altero <lb/>ſcrupulo augeantur, aut multentur, differentia in calculo haud per-<lb/>inde erit notabilis: </s> <s xml:id="echoid-s8992" xml:space="preserve">Quia ratio horum ſinuum ut proxime eadem ta-<lb/>men manet. </s> <s xml:id="echoid-s8993" xml:space="preserve">Atque ideo laterum oppoſitorum quantitatis differen-<lb/>tia à juſto non erit admodum diverſa. </s> <s xml:id="echoid-s8994" xml:space="preserve">Ut ea ſæpe ſit paucorum <lb/>duntaxat pedum, quæ ſemel hic monere viſum eſt, ne ſæ pius no-<lb/>bis eadem eſſent iteranda. </s> <s xml:id="echoid-s8995" xml:space="preserve">Multa enim occurrunt in turrium faſti- <pb o="372" file="0386" n="386" rhead="DISSERTATIO"/> giis, quæ haud facile vitare poſſis, niſi ſingulis in locis diutiuſcu-<lb/>le hæreas, aut obſervationes aliquoties iteres. </s> <s xml:id="echoid-s8996" xml:space="preserve">Ut ſunt ventus in <lb/>ſummo aëre vehementior, cum etiam ad turrium baſin eum aut mo-<lb/>dicum, aut perſæpe nullum perſentiſcas: </s> <s xml:id="echoid-s8997" xml:space="preserve">ſtatio non ſemper in tur-<lb/>ris medio, ſed modo in hoc, modo in iſto angulo prout ſtructuræ <lb/>commoditas illud permittet aut locorum obſervandorum ſitus exi-<lb/>get. </s> <s xml:id="echoid-s8998" xml:space="preserve">Atque alia id genus compluria, quæ uſus te facilius docere <lb/>poſſit, quam ego verbis queam exprimere. </s> <s xml:id="echoid-s8999" xml:space="preserve">Neque vero minimam <lb/>difficultatem objecerit locorum ignorantia, cum ipſi ſpeculatores <lb/>turrim aliquam vicinam pro quæſita reponunt, ne quidquam igno-<lb/>rare videantur. </s> <s xml:id="echoid-s9000" xml:space="preserve">Atque ea ſane maxime res nos omnes triangulian-<lb/>gulos obſervare coëgit, ut tum demum legitimam obſervationem <lb/>probaremus, cum nobisad numeros veniunt. </s> <s xml:id="echoid-s9001" xml:space="preserve">Denique omniatan-<lb/>ta cum cura & </s> <s xml:id="echoid-s9002" xml:space="preserve">diligentia à nobis ſunt obita, ut tot moleſtiis & </s> <s xml:id="echoid-s9003" xml:space="preserve">dif-<lb/>ficultatibus fatigato, pene coeptum opus deſerere conſilium fuerit, <lb/>niſi publica utilitas, & </s> <s xml:id="echoid-s9004" xml:space="preserve">tot jam ſeculis fatigata tam nobilis cura ſti-<lb/>mulos mihi addidiſſet, & </s> <s xml:id="echoid-s9005" xml:space="preserve">rurſum calamum in manum, corpus & </s> <s xml:id="echoid-s9006" xml:space="preserve"><lb/>oculorum aciem in turrium faſtigia attollere coëgiſſet. </s> <s xml:id="echoid-s9007" xml:space="preserve">Hæc enim <lb/>ipſa, quæ hic afſero, vix milleſima pars ſunt laboris, moleſtiæ, & </s> <s xml:id="echoid-s9008" xml:space="preserve"><lb/>impenſarum, quas exantlavimus. </s> <s xml:id="echoid-s9009" xml:space="preserve">Et niſi animum contra omne <lb/>tœdium obfirmaviſſem, ad finem optatum perducere nunquampo-<lb/>tuiſſem. </s> <s xml:id="echoid-s9010" xml:space="preserve">Plura monere nunc ſuperſedeo & </s> <s xml:id="echoid-s9011" xml:space="preserve">ad inſtitutum rever-<lb/>tor.</s> <s xml:id="echoid-s9012" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Ex angulis igitur & baſe A E datis, latera quoque reliqua per trian- \\ gulorum canones dabuntur. Videlicet diſtantia inter Leidam & \\ Goudam E S # 5897. # 8. <lb/>Inter Hagam & Goudam A S # 7594. # 3. <lb/></note> </div> <div xml:id="echoid-div259" type="section" level="1" n="259"> <head xml:id="echoid-head292" xml:space="preserve">II. <emph style="sc">Problema</emph>.</head> <head xml:id="echoid-head293" xml:space="preserve">Triangulum E S R. Leida, Gouda, Dordracum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema I datur diſtantia inter Leidam, & \\ Goudam E S # 5897. # 8. <lb/>Ex obſervatis autem datur angulus R E S # 25 gr. # 49 ſcr. <lb/></note> <pb o="373" file="0387" n="387" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Et angulus E R S # 25 gr. # 50 ſcr. <lb/>Et angulus R S E # 128 gr. # 22 ſcr. <lb/>Omnium ſumma 180 gr. 1 ſcr. Ubi duntaxat unum ſcrupulum \\ redundat. Sit itaque angulus R E S # 25 gr. # 49 ſcr. <lb/>Et angulus E R S # 25 gr. # 49 ſcr. <lb/>Et angulus R S E # 128 gr. # 22 ſcr. <lb/>Unde per doctrinam triangulorum quoque dabitur \\ E R diſtantia inter Leidam & Dordracum # 10633. # 1. <lb/>Et S R diſtantia inter Goudam & Dordracum # 5897. # 8. <lb/></note> </div> <div xml:id="echoid-div260" type="section" level="1" n="260"> <head xml:id="echoid-head294" xml:space="preserve">III. <emph style="sc">Problema.</emph> <lb/>Triangulum E A R. Leida, Haga, Dordracum.</head> <note position="right" xml:space="preserve"> <lb/>Per Cap. VI. Probl. VI. datur diſtantia inter Hagam \\ & Leidam E A # 4103. # 3. <lb/>Ex obſervatis autem angulus E A R # 85 gr. # 51 ſcr. <lb/>Et angulus A E R # 71 gr. # 31 ſcr. <lb/>Unde angulus quoque tertius datur A R E. # 22 gr. # 38 ſcr. <lb/>Namque Dordraco Hagam non vidi. <lb/>Atque inde per doctrinam triangulorum diſtantia \\ inter Dordracum & Hagam A R # 10112. # 7. <lb/>Et E R diſtantia inter Dordracum & Leidam # 10634. # 7. <lb/>Quam eandem antecedente Problemate invenimus. # 10633. # 1. <lb/></note> <p> <s xml:id="echoid-s9013" xml:space="preserve">Differentia eſt vix duarum decempedarum, quæ omnino in tanto <lb/>intervallo nullius ſunt momenti.</s> <s xml:id="echoid-s9014" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div261" type="section" level="1" n="261"> <head xml:id="echoid-head295" xml:space="preserve">IV. <emph style="sc">Problema.</emph> <lb/>Triangulum A E F. Haga, Leida, Roterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Cap. VI. Probl. VI. datur diſtantia inter Hagam \\ & Leidam E A # 4103. # 3. <lb/></note> <pb o="374" file="0388" n="388" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Ex obſervatis angulus E A F # 90 gr. # 18 ſcr. <lb/>Et angulus A E F # 53 gr. # 40 ſcr. <lb/>Unde reliquus A F E dabitur # 36 gr. # 2 ſcr. <lb/>Atque inde per doctrinam triangulorum dabitur quo \\ que A F diſtantia inter Hagam & Rotterodamum # 5616. # 8. <lb/>Et E F diſtantia inter Leidam & Rotterodamum # 6975. # 3. <lb/></note> </div> <div xml:id="echoid-div262" type="section" level="1" n="262"> <head xml:id="echoid-head296" xml:space="preserve">V. <emph style="sc">Problema.</emph> <lb/>Triangulum E S F. Leida, Gouda, Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per problema I. datur E S diſtantia inter Leidam \\ & Goudam # 5897. # 8. <lb/>Ex obſervatis autem angulus S E F # 43 gr # 32 ſcr. <lb/>Et angulus E S F # 80 gr. # 0 ſcr. <lb/>Unde dabitur angulus E F S # 56 gr. # 28 ſcr. <lb/>Atque inde per triangulorum doctrinam dabitur \\ quoque S F diſtantia inter Goudam & Rotteroda- \\ mum # 4883. # 1. <lb/></note> </div> <div xml:id="echoid-div263" type="section" level="1" n="263"> <head xml:id="echoid-head297" xml:space="preserve">VI. <emph style="sc">Problema.</emph> <lb/>Triangulum E S V. Leida, Gouda, Trajectum.</head> <note position="right" xml:space="preserve"> <lb/>Diſtantia inter Leidam & Goudam datur per Pro- \\ blema primum E S # 5897. 8. <lb/>Et ex obſervatis angulus S E V # 37 gr. 40 ſcr. <lb/>Et angulus E S V # 114 gr. 48 ſcr. <lb/>Et angulus E V S # 27 gr. 32 ſcr. <lb/>His collectis ſcrupula duo redundant, quæ, ut mi-<lb/>nimum turbent, ita diſtribuam. <lb/>Angulus E S V ſit # 37 gr. 40 ſcr. <lb/>Et angulus E S V # 114 gr. 48 ſcr. <lb/>Et angulus E V S # 27 gr. 32 ſcr. <lb/></note> <pb o="375" file="0389" n="389" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Unde per triangulorum doctrinam dabitur EV diſtan- \\ tia inter Trajectum & Leidam # 11582. # 0. <lb/>Et S V diſtantia inter Goudam & Trajectum # 7847. # 5. <lb/></note> </div> <div xml:id="echoid-div264" type="section" level="1" n="264"> <head xml:id="echoid-head298" xml:space="preserve">VII. <emph style="sc">Problema.</emph> <lb/>Triangulum E R V. Leida, Dordracum, Trajectum.</head> <note position="right" xml:space="preserve"> <lb/>Per problema II. datur E R diſtantia inter Leidam \\ & Dordracum # 10633. # 1. <lb/>Et ex obſervatis angulus R E V # 63 gr. # 23 ſcr. <lb/>Et angulus E V R # 54 gr. # 29 ſcr. <lb/>Et angulus E R V # 62 gr. # 28 ſcr. <lb/>Unde per doctrinam triangulorum invenietur E V \\ diſtantia inter Leidam & Trajectum # 11584. # 0. <lb/>Et V R diſtantia inter Dordracum & Trajectum # 11646. # 1. <lb/>Atqui diſtantia inter Leidam & Trajectum antea Pro- \\ blemate VI inventa eſt # 11582. # 0. <lb/>Quamobrem hæc ludunt in confinio. <lb/></note> </div> <div xml:id="echoid-div265" type="section" level="1" n="265"> <head xml:id="echoid-head299" xml:space="preserve">VIII. <emph style="sc">Problema.</emph> <lb/>Triangulum E M V, Leida, Oude-Watera, Trajectum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema 6 datur E V diſtantia inter Leidam \\ & Trajectum # 11584. 0. <lb/>Ex obſervatis autem angulus M E V # 20 gr. 26 ſcr. <lb/>Et angulus E V M # 33 gr. 53 ſcr. <lb/>Et angulus E M V # 125 gr. 43 ſcr. <lb/>Ubi duo ſcrupula redundant. Atque ideo eſto an- \\ gulus M E V # 20 gr. 26 ſcr. <lb/>Et angulus E V M # 33 gr. 52 ſcr. <lb/>Et angulus E M V # 125 gr. 42 ſcr. <lb/></note> <pb o="376" file="0390" n="390" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Unde per doctrinam triangulorum invenietur \\ V M diſtantia inter Oude Wateram & Trajectum # 4980. # 6. <lb/>Et E M diſtantia inter Oude-Wateram & Lei- \\ dam # 7949. # 0. <lb/></note> </div> <div xml:id="echoid-div266" type="section" level="1" n="266"> <head xml:id="echoid-head300" xml:space="preserve">IX. <emph style="sc">Problema.</emph> <lb/>Triangulum E M S. Leida, Oude Watera, Gouda.</head> <note position="right" xml:space="preserve"> <lb/>Iterum diſtantiam inter Leidam & Oude-Wateram libet tentare, \\ ad operis veritatem explorandam, idque aſſumpta tertia Gouda. \\ Datur itaque hic per Problema II, E S diſtantia inter Leidam & \\ Goudam # 5897. # 8. <lb/>Ex obſervatis autem angulus S E M # 17 gr. # 23 ſcr. <lb/>Et angulus E S M # 125 gr. # 42 ſcr. <lb/>Et angulus E M S # 36 gr. # 53 ſcr. <lb/>In qua ſumma duo ſcrupula deſiderantur, quæ ita \\ ſupplebo, ut angulus S E M ſit # 17 gr. # 23 ſcr. <lb/>Et angulus E S M # 125 gr. # 43 ſcr. <lb/>Et angulus E M S # 36 gr. # 53 ſcr. <lb/>Quamobrem inde jam per planorum triangulorum doctrinam da- \\ bitur quoque diſtantia inter Oude-Wateram & Goudam, ſive latus \\ S M # 2921. # 3. <lb/>Et E M diſtantia inter Leidam & Oude-Wateram # 7962. # 0. <lb/>Atqui ea fuit Problemate VII. # 7949. # 0. <lb/>Differentia igitur inter has obſervationes intercedit undecim de- \\ cempedarum & ſemis, quæ paulo eſt major ſimul utriuſque turris \\ craſſitudine duplicata. Et ſi quamvis ſecundum octavi proble- \\ matis abacos potius pronuntiaverim, quod illic minimus angulus \\ ſit # 20 gr. # 26 ſcr. <lb/>Certe utraque eſt ſatis accurata. Si cui medium aſſumere libeat, \\ per me id quidem ei liceat, ut M E ſit # 7955. # 5. <lb/></note> <p> <s xml:id="echoid-s9015" xml:space="preserve">Verum enim vero ut noſtram induſtriam cunctis probem, at-<lb/>que ſumma cum ſedulitate ac diligentia in hoc opere nos verſatos <lb/>evidentiſſime oſtendam, novam hic Gæodæſiam exhibeo, qua de- <pb o="377" file="0391" n="391" rhead="DE MAGNITUDINE TERRÆ."/> nuo Oude. </s> <s xml:id="echoid-s9016" xml:space="preserve">Wateræ & </s> <s xml:id="echoid-s9017" xml:space="preserve">Goudæ diſtantiam legitimam hanc eſſe do-<lb/>ceam: </s> <s xml:id="echoid-s9018" xml:space="preserve">Quam non ex antecedentibus derivavi, ſed per artis præce-<lb/>pta ab initio inſtitutam exhibeo, ut deinceps ſecurus animi reliquam <lb/>partem inoffenſo pede percurram. </s> <s xml:id="echoid-s9019" xml:space="preserve">Cum enim Generoſiſſimi Baro-<lb/>nes Auſtriaci Eraſmus & </s> <s xml:id="echoid-s9020" xml:space="preserve">Caſparus Sterrenbergici, fratres germani <lb/>Arithmeticam & </s> <s xml:id="echoid-s9021" xml:space="preserve">Geometriam jam penitus cognoviſſent, & </s> <s xml:id="echoid-s9022" xml:space="preserve">in re-<lb/>ctarum circulo adſcriptarum Canonicis, quam triangulorum do-<lb/>ctrinam vulgo dicimus, verſarentur, placuit ipſis, ut Magno Ale-<lb/>xandro, ingenii ſui vires non in tenui pulvere periclitari: </s> <s xml:id="echoid-s9023" xml:space="preserve">Sed in <lb/>materia aliqua digniore, quæque uſum & </s> <s xml:id="echoid-s9024" xml:space="preserve">fructum ſuum ad plures <lb/>diffunderet. </s> <s xml:id="echoid-s9025" xml:space="preserve">Cum igitur longa & </s> <s xml:id="echoid-s9026" xml:space="preserve">diutina ſedulitate & </s> <s xml:id="echoid-s9027" xml:space="preserve">labore fati-<lb/>gatis animum per ferias caniculares recreare, & </s> <s xml:id="echoid-s9028" xml:space="preserve">à gravioribus ſtudiis <lb/>aliquantum remittere placeret, Vir doctiſſimus & </s> <s xml:id="echoid-s9029" xml:space="preserve">eorum aulæ ac <lb/>ſtudiis tum præfectus Joannes Philemon, & </s> <s xml:id="echoid-s9030" xml:space="preserve">ab ingenio & </s> <s xml:id="echoid-s9031" xml:space="preserve">à doctri-<lb/>na Magnus, quique in his jam tunc quoque non mediocres profe-<lb/>ctus fecerat, ne illud otium, liberale alioquin, nimis otioſe efflue-<lb/>ret, expeditionem in proximas Provincias ſe cogitare dixit, ut ita <lb/>regiones nobis vicinas cognoſcerent, & </s> <s xml:id="echoid-s9032" xml:space="preserve">ſimul, olim quoque judi-<lb/>cium de his ſuum ferre poſſent. </s> <s xml:id="echoid-s9033" xml:space="preserve">Id vero ipſum dum quam maxime <lb/>probo, & </s> <s xml:id="echoid-s9034" xml:space="preserve">illorum conſilium collaudo, Ecce! omnes uno ore ſimul <lb/>me quoque ejus itineris comitem rogare, nec illud ſibi negari ullo <lb/>modo paſſi: </s> <s xml:id="echoid-s9035" xml:space="preserve">Sed invitum pene domo me, & </s> <s xml:id="echoid-s9036" xml:space="preserve">à meis abduxere. </s> <s xml:id="echoid-s9037" xml:space="preserve">Ma-<lb/>xime quia hujus olim Gæodæſiæ mentionem injeceram, & </s> <s xml:id="echoid-s9038" xml:space="preserve">quan-<lb/>tam huic laudem à grata poſteritate ſperare deberet, ſi quis ea via <lb/>veram terreni gradus quantitatem definiviſſet. </s> <s xml:id="echoid-s9039" xml:space="preserve">Jam enim etiam ſphæ-<lb/>rica non leviter deguſtaverant. </s> <s xml:id="echoid-s9040" xml:space="preserve">Ecce quid facerem! illa quæ olim <lb/>tantum obiter à me dicta, ſerio ab ipſis accepta. </s> <s xml:id="echoid-s9041" xml:space="preserve">Inde igitur iter <lb/>omni diligentia procuramus, & </s> <s xml:id="echoid-s9042" xml:space="preserve">organa ad tantam rem depromimus, <lb/>ſemicirculum diametri pedum Rhynlandicorum trium & </s> <s xml:id="echoid-s9043" xml:space="preserve">ſemis, ad <lb/>Gæodæſias diſtantiarum & </s> <s xml:id="echoid-s9044" xml:space="preserve">angulorum quantitatem è turribus ob-<lb/>ſervandam. </s> <s xml:id="echoid-s9045" xml:space="preserve">Quadrantem etiam ampliſſimum ferreum, ære incru-<lb/>ſtatum, amplius quinque & </s> <s xml:id="echoid-s9046" xml:space="preserve">ſemis pedum, ad poli altitudinem ex-<lb/>plorandam. </s> <s xml:id="echoid-s9047" xml:space="preserve">Atque ita Oude-Wateram primum pauculos dies ruſti-<lb/>catum, & </s> <s xml:id="echoid-s9048" xml:space="preserve">in illo ſeceſſu ſtationem electuri contendimus; </s> <s xml:id="echoid-s9049" xml:space="preserve">ut ſimul <lb/>paternum atque avitum cinerem, qui ibi conditus diem quo ſibi <lb/>reſtituatur exſpectat: </s> <s xml:id="echoid-s9050" xml:space="preserve">& </s> <s xml:id="echoid-s9051" xml:space="preserve">præterea matrem meam anum ac jam vi- <pb o="378" file="0392" n="392" rhead="DISSERTATIO"/> duam, quæ poſt Viri Clariſſimi Rodolphi Snellii, chariſſimi Paren-<lb/>tis mei obitum, (qui anno æræ uſitatæ 1613 2 die Martii ſtylo Gre-<lb/>gor. </s> <s xml:id="echoid-s9052" xml:space="preserve">horâ 2, ſcrup 20. </s> <s xml:id="echoid-s9053" xml:space="preserve">à prandio animam Leidæ Deo Creatori red-<lb/>didit, corpus autem Oude-Wateram in avita monumenta illatum, <lb/>in qua urbe in hanc lucem eſt editus, anno 1546. </s> <s xml:id="echoid-s9054" xml:space="preserve">Oct. </s> <s xml:id="echoid-s9055" xml:space="preserve">18. </s> <s xml:id="echoid-s9056" xml:space="preserve">hora <lb/>quaſi 6. </s> <s xml:id="echoid-s9057" xml:space="preserve">matut. </s> <s xml:id="echoid-s9058" xml:space="preserve">vixit annos 66. </s> <s xml:id="echoid-s9059" xml:space="preserve">menſes 4. </s> <s xml:id="echoid-s9060" xml:space="preserve">dies 22. </s> <s xml:id="echoid-s9061" xml:space="preserve">horas 8 {1/3},) anno <lb/>ſuperiore eo conceſſerat extremum quoque vitæ diem illic inter ſuo-<lb/>rum monumenta clauſura, ſalutarem. </s> <s xml:id="echoid-s9062" xml:space="preserve">Eſt autem Oude-Watera op-<lb/>pidum ſoli Hollandici, in confinio Trajectenſis ditionis & </s> <s xml:id="echoid-s9063" xml:space="preserve">Hollan-<lb/>diæ ad illum Iſalam poſitum, qui Goudam quoque alluit, vallis & </s> <s xml:id="echoid-s9064" xml:space="preserve"><lb/>propugnaculis nunc undique probe munitum, ambitu ſeptingenta-<lb/>rum aut octingentarum decempedarum, longitudine ad latitudinem <lb/>fere ſesquialtera. </s> <s xml:id="echoid-s9065" xml:space="preserve">Olim fornicatis muris cinctum, ſitu amæniſſimo, <lb/>ſolo circumcirca feraci ac bono & </s> <s xml:id="echoid-s9066" xml:space="preserve">jam ante aliquot ſecula quoque <lb/>non ignobile; </s> <s xml:id="echoid-s9067" xml:space="preserve">ſemper autem incolarum frugalitate atque induſtria <lb/>celebratiſſimum: </s> <s xml:id="echoid-s9068" xml:space="preserve">Nunc vero etiam magis ob nobilem illam cladem, <lb/>quam Oude Watera ideo eſt perpeſſa, quod omnium prima patriæ <lb/>libertatem ſuo ſanguine redemerit. </s> <s xml:id="echoid-s9069" xml:space="preserve">Utpote, quæ prima graſſanti <lb/>Hiſpanorum tyrannidi ſeſe oppoſuerit, prima obſidione cincta & </s> <s xml:id="echoid-s9070" xml:space="preserve"><lb/>capta ſit. </s> <s xml:id="echoid-s9071" xml:space="preserve">Nardemum enim non vi, ſed ſponte in Albani poteſta-<lb/>rem venit. </s> <s xml:id="echoid-s9072" xml:space="preserve">Ea, inquam, prima poſt trium ſeptimanarum arctam <lb/>obſidionem, quaſſatosque noctu & </s> <s xml:id="echoid-s9073" xml:space="preserve">interdiu ariete tormentario mu-<lb/>ros, pauco milite præſidiario inſtructa, tamen virorum mulierum-<lb/>que & </s> <s xml:id="echoid-s9074" xml:space="preserve">viraginum junctis viribus, quæ non domi ſedere, ſed in mæ-<lb/>nibus, in vallo ſtare, ſuos hortari, hoſtem furentem & </s> <s xml:id="echoid-s9075" xml:space="preserve">rabidum <lb/>pice liquida & </s> <s xml:id="echoid-s9076" xml:space="preserve">ardente, ſabulo fervente, ſaxis ingentibus deturba-<lb/>re, tantum impetum tam diu ſuſtinuit, quem ne unicum quidem <lb/>diem latura videbatur. </s> <s xml:id="echoid-s9077" xml:space="preserve">Atque ſuo periculo potius & </s> <s xml:id="echoid-s9078" xml:space="preserve">malo patriæ <lb/>libertatis fundamenta jacere, quam in illius hoſtis ſe manum dede-<lb/>re, cui nihil ſacri, nihil ſancti præter libitum eſſet. </s> <s xml:id="echoid-s9079" xml:space="preserve">Inde jam capta <lb/>Urbe, fatali illa & </s> <s xml:id="echoid-s9080" xml:space="preserve">funeſta hora, omnes trucidari, rapi, rui. </s> <s xml:id="echoid-s9081" xml:space="preserve">nul-<lb/>lius ſexus aut ætatis habita reverentia: </s> <s xml:id="echoid-s9082" xml:space="preserve">foeminæ prægnantes è fori-<lb/>bus ſuarum ædium ſuſpenſæ: </s> <s xml:id="echoid-s9083" xml:space="preserve">embryones ex utero exciſi, in os ac <lb/>faciem matrum adhuc palpitantium, proh facinus in fandum! illiſi. <lb/></s> <s xml:id="echoid-s9084" xml:space="preserve">Alibi infantes aut pueruli tenellæ ætatis duo treſve, hominum <lb/>ac Deorum fidem implorantes, tanquam carnis fruſtra haſtis affixi.</s> <s xml:id="echoid-s9085" xml:space="preserve"> <pb o="379" file="0393" n="393" rhead="DEMAGNITUDINE TERRÆ."/> Nullum ſævitiæ genus relictum: </s> <s xml:id="echoid-s9086" xml:space="preserve">donectandem Urbs tota in favillas <lb/>& </s> <s xml:id="echoid-s9087" xml:space="preserve">cinerem abiit: </s> <s xml:id="echoid-s9088" xml:space="preserve">ut ſolæ ſeptem domus cum templo & </s> <s xml:id="echoid-s9089" xml:space="preserve">turri poſt <lb/>iſtam cladem ex tanto numero eſſent ſuperſtites. </s> <s xml:id="echoid-s9090" xml:space="preserve">Adeo autem illu-<lb/>ſtri incendio ea Urbs conflagravit, ut omnibus per univerſam Hol-<lb/>landiam tanquam ex aliqua pharo hoſtis crudeliſſimi adventum de-<lb/>nuntiaret. </s> <s xml:id="echoid-s9091" xml:space="preserve">Ut non Amſtolodami ſolum, ſed in ipſa Northollan-<lb/>dia, Hornæ & </s> <s xml:id="echoid-s9092" xml:space="preserve">Enchuſæ quoque, (quod longiſſimum eſt interval-<lb/>lum) viſum eſſe conſtet. </s> <s xml:id="echoid-s9093" xml:space="preserve">Tempus e R hetorico parentis mei politiſ-<lb/>ſimo dialogo, in quo Virum clariſſimum Johannem Magnum, ami-<lb/>cum ſuum veterem & </s> <s xml:id="echoid-s9094" xml:space="preserve">Illuſtr. </s> <s xml:id="echoid-s9095" xml:space="preserve">Princ. </s> <s xml:id="echoid-s9096" xml:space="preserve">Mauritio Haſſiæ Landtgravio <lb/>à conſiliis ſecum colloquentem introducit, ipſius verbis hic adſcri-<lb/>bam. </s> <s xml:id="echoid-s9097" xml:space="preserve">Veteraquinum arcte obſeſſum fuit, tandem captum VII Au-<lb/>guſti Juliani, anno c10 10 <emph style="sc">LXXV</emph>.</s> <s xml:id="echoid-s9098" xml:space="preserve">Sole medium coelum jam ſignan-<lb/>te, cives & </s> <s xml:id="echoid-s9099" xml:space="preserve">præſidiarii cæſi, nulli neque ætati nec ſexui parcitum, <lb/>pauciſſimi in ſemen ſervati, Oppidum incenſum, & </s> <s xml:id="echoid-s9100" xml:space="preserve">flamma ab-<lb/>ſumptum. </s> <s xml:id="echoid-s9101" xml:space="preserve">Sed neſcio quo me Patriæ amor, & </s> <s xml:id="echoid-s9102" xml:space="preserve">meorum dulciſſi-<lb/>ma recordatio abripuerit, quin ad inſtitutum potius revertor. </s> <s xml:id="echoid-s9103" xml:space="preserve">Hic, <lb/>inquam, dum verſamur, placuit initio ob loci oportunitatem no-<lb/>ſtræ Gæodæſiæ fundamenta jacere, & </s> <s xml:id="echoid-s9104" xml:space="preserve">baſin aliquam conſtituere. <lb/></s> <s xml:id="echoid-s9105" xml:space="preserve">Sunt enim illic tria oppida vicina haud admodum longo intervallo <lb/>inter ſe disjuncta, Oude Watera & </s> <s xml:id="echoid-s9106" xml:space="preserve">Woerda in ſolo Hollandico, Mont-<lb/>fortium in ditione Trajectenſi, ab Oude-Watera & </s> <s xml:id="echoid-s9107" xml:space="preserve">inter ſe quaſi <lb/>unius horæ intervallo diſtantia. </s> <s xml:id="echoid-s9108" xml:space="preserve">Ob iſtam vicinitatem intervallum <lb/>inter Oude Wateram & </s> <s xml:id="echoid-s9109" xml:space="preserve">Montfortium ante ſumus dimenſi, cujus <lb/>Gæodæſiam hic primum explicabo.</s> <s xml:id="echoid-s9110" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div267" type="section" level="1" n="267"> <head xml:id="echoid-head301" xml:space="preserve">IX. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head302" style="it" xml:space="preserve">Diſtantia inter Oude Wateram & Montſortium <lb/>quæſita.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XV. fig. 14. Baſis Gæodæſiæ in camporum \\ planitie fuit linea a o decempedarum # # 166. <lb/>Angulus e o a # 81 gr. # 57 ſcr. <lb/>Angulus o a e # 90 gr. # 6 ſcr. <lb/>Unde pertriangulorum do ctrinam invenitur diſtan-<lb/></note> <pb o="380" file="0394" n="394" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>tia o e # 1185. # 4 <lb/># Et latus o e <lb/>Secundo ex obſervatis datur angulus i o a # 65 gr. # 9 ſcr. <lb/>Et angulus i a o # 92 gr. # 19 ſcr. <lb/>Unde cognoſcitur angulus a i o # 22 gr. # 32 ſcr. <lb/>Atque in datur latus o i # 432. # 8. <lb/># Et latus a i <lb/>Dantur igitur in triangulo e o i latus e o # 1185. # 4. <lb/>Et latus o i # 432. # 8. <lb/>Cum angulo ab ipſis comprehenſo e o i # 147 gr. # 6 ſcr. <lb/>Unde invenitur latus e i # 1566. # 5. <lb/></note> <p> <s xml:id="echoid-s9111" xml:space="preserve">Tanta igitur erit diſtantia inter vicinas templorum turres Oude-<lb/>Wateræ & </s> <s xml:id="echoid-s9112" xml:space="preserve">Montfortii. </s> <s xml:id="echoid-s9113" xml:space="preserve">Unde Woerdæ ab utriſque diſtantia deri-<lb/>vatur, hoc modo.</s> <s xml:id="echoid-s9114" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9115" xml:space="preserve">(Error irrepſit in calculum Snellii, unde nec huic Problemati <lb/>I X, nec X, nec XI, multum confidi poterit. </s> <s xml:id="echoid-s9116" xml:space="preserve">Nam latus o e ope <lb/>calculi non invenitur 1185, 4. </s> <s xml:id="echoid-s9117" xml:space="preserve">ſed 1200, 2, 1. </s> <s xml:id="echoid-s9118" xml:space="preserve">& </s> <s xml:id="echoid-s9119" xml:space="preserve">latus e i 4384, <lb/>9. </s> <s xml:id="echoid-s9120" xml:space="preserve">quod plurimum differt. </s> <s xml:id="echoid-s9121" xml:space="preserve">a 1566, 5. </s> <s xml:id="echoid-s9122" xml:space="preserve">Videtur præterea minus ac-<lb/>curatus fuiſſe, cum diſtantia a o, nimis brevis capta fuerit:)</s> <s xml:id="echoid-s9123" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div268" type="section" level="1" n="268"> <head xml:id="echoid-head303" xml:space="preserve">X. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head304" style="it" xml:space="preserve">Triangulum M X C, Oude-Watera, Woerda, <lb/>Montfortium.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema IX. datur M X diſtantia inter Ou- \\ de-Wateram & Montfortium # 1566. # 5. <lb/>Ex obſervatis autem angulus C M X # 57 gr. # 3 ſcr. <lb/>Et angulus C X M # 71 gr. # 17 ſcr. <lb/>Et angulus X C M # 51 gr. # 40 ſcr. <lb/>Atque jam dabitur latus X C diſtantia inter Mont- \\ fortium & Woerdam # 1768. # 0. <lb/>Et M C diſtantia inter Oude-Wateram & Woerdam # 1891. # 4. <lb/></note> <pb o="381" file="0395" n="395" rhead="DEMAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div269" type="section" level="1" n="269"> <head xml:id="echoid-head305" xml:space="preserve">XI. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head306" style="it" xml:space="preserve">Triangulum M X S. Oude-Watera, Woerda, <lb/>Gouda.</head> <note position="right" xml:space="preserve"> <lb/>Per problema X datur M X diſtantia inter Oude- \\ Wateram & Woerdam # 1891. # 4. <lb/>Ex obſervatis autem angulus X M S # 104 gr. # 14 ſcr. <lb/>Et angulus X S M # 28 gr. # 25 ſcr. <lb/>Inde angulus S X M datur # 47 gr. # 21 ſcr. <lb/>Atque hinc per triangulorum doctrinam dabitur la- \\ tus S X diſtantia inter Goudam & Woerdam # 3852. # 5. <lb/>Et latus M S diſtantia inter Oude Wateram & Gou- \\ dam # 2923. # 3. <lb/>Atque eadem antea Problemate 8 inventa eſt # 2921. # 3. <lb/></note> <p> <s xml:id="echoid-s9124" xml:space="preserve">Quare hujus & </s> <s xml:id="echoid-s9125" xml:space="preserve">illius differentia eſt duntaxat decempedarum <lb/>duarum ad quam vicinitatem me perventurum ne ſperare quidem <lb/>auſus fuiſſem. </s> <s xml:id="echoid-s9126" xml:space="preserve">Cum diſtantia prima inter Oude Wateram & </s> <s xml:id="echoid-s9127" xml:space="preserve">Mont-<lb/>fortium tam anguſtis principiis ſit derivata. </s> <s xml:id="echoid-s9128" xml:space="preserve">Nam problemate IX di-<lb/>ſtantia inter Oude-Wateram & </s> <s xml:id="echoid-s9129" xml:space="preserve">Montfortium ex a o baſe trianguli <lb/>166 decempedarum, & </s> <s xml:id="echoid-s9130" xml:space="preserve">angulo adjacente e o a 81 gr. </s> <s xml:id="echoid-s9131" xml:space="preserve">57 ſcr. </s> <s xml:id="echoid-s9132" xml:space="preserve">ad-<lb/>modum amplo inventa eſt o e. </s> <s xml:id="echoid-s9133" xml:space="preserve">atqui iſtic tangentes & </s> <s xml:id="echoid-s9134" xml:space="preserve">ſecantes <lb/>admodum magnis differentiis augentur, ut exiguus error illic quo-<lb/>que periculoſus ſit. </s> <s xml:id="echoid-s9135" xml:space="preserve">Hic enim unius ſolum ſcrupuli error e tantilla <lb/>baſe 166 decempedarum, adjiciet decempedas duas cum ſemiſſe. </s> <s xml:id="echoid-s9136" xml:space="preserve">Si <lb/>enim angulus e o a illic aſſumatur 81 gr. </s> <s xml:id="echoid-s9137" xml:space="preserve">56 ſcr. </s> <s xml:id="echoid-s9138" xml:space="preserve">tum o e erit decem-<lb/>pedarum 1183. </s> <s xml:id="echoid-s9139" xml:space="preserve">0. </s> <s xml:id="echoid-s9140" xml:space="preserve">ſi 81 gr. </s> <s xml:id="echoid-s9141" xml:space="preserve">57 ſcr. </s> <s xml:id="echoid-s9142" xml:space="preserve">1185. </s> <s xml:id="echoid-s9143" xml:space="preserve">4. </s> <s xml:id="echoid-s9144" xml:space="preserve">ſi 81 gr. </s> <s xml:id="echoid-s9145" xml:space="preserve">58 ſcr. </s> <s xml:id="echoid-s9146" xml:space="preserve">1187. <lb/></s> <s xml:id="echoid-s9147" xml:space="preserve">8 atque ita deinceps porro magis magisque. </s> <s xml:id="echoid-s9148" xml:space="preserve">Ut tantum, & </s> <s xml:id="echoid-s9149" xml:space="preserve">am-<lb/>plius committi potuerit in Goudæ & </s> <s xml:id="echoid-s9150" xml:space="preserve">Oude-Wateræ intervallo, ſi <lb/>vel hic uno aut altero ſcrupulo erratum eſſet, quod tamen in hac <lb/>Gæodæſia addicere non eſſem auſus, ob impedimenta quædam illic <lb/>in campo nobis objecta. </s> <s xml:id="echoid-s9151" xml:space="preserve">Hanc autem difficultatem ubique decli-<lb/>navi, talem locorum poſitum captando, ubi nullus angulus in an-<lb/>guſtum cogeretur, ne inde nobis reliquus calculus evaderet lubri-<lb/>cus. </s> <s xml:id="echoid-s9152" xml:space="preserve">Attamen in hoc ipſo noſtræ diligentiæ ſpecimen elucet, quod <pb o="382" file="0396" n="396" rhead="DISSERTATIO"/> angulo o e a adeo acuto exiſtente 8 gr. </s> <s xml:id="echoid-s9153" xml:space="preserve">3 ſcr. </s> <s xml:id="echoid-s9154" xml:space="preserve">nihilominus tam pro- xime verum collineaverimus. </s> <s xml:id="echoid-s9155" xml:space="preserve">Atque hæc res nos adeo operoſe pri- mas noſtras Gæodæſias inſtituere & </s> <s xml:id="echoid-s9156" xml:space="preserve">toties iterare coëgit. </s> <s xml:id="echoid-s9157" xml:space="preserve">Quam- obrem, cum utriuſque calculi & </s> <s xml:id="echoid-s9158" xml:space="preserve">obſervationum quoque tantus ſit conſenſus, de reliqui operis fide dubium nullum cuiquam ſupereſſe poteſt. </s> <s xml:id="echoid-s9159" xml:space="preserve">Sed ad reliqua conficienda ſecurus deinceps procedam.</s> <s xml:id="echoid-s9160" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div270" type="section" level="1" n="270"> <head xml:id="echoid-head307" xml:space="preserve">XII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head308" style="it" xml:space="preserve">Triangulum A E I, Haga, Leida, Harlemum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VI. Cap. VI. datur A E diſtantia inter \\ Hagam & Leidam # 4103. # 3. <lb/>Et ex obſervatis angulus A E I # 147 gr. # 19 ſcr. <lb/>Itemque angulus E A I # 20 gr. # 45 ſcr. <lb/>Unde & reliquus A I E # 11 gr. # 56 ſcr. <lb/>Quare E I diſtantia inter Leidam & Harlemum dabitur # 7040. # 4. <lb/>Et latus A I diſtantia inter Hagam & Harlemum # 10725. # 7. <lb/></note> </div> <div xml:id="echoid-div271" type="section" level="1" n="271"> <head xml:id="echoid-head309" xml:space="preserve">XIII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head310" style="it" xml:space="preserve">Triangulum O E V, Amſtelodamum, Leida, <lb/>Trajectum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema V I I. datur E V diſtantia inter Lei- \\ dam & Trajectum # 11584. # 0. <lb/>Et ex obſervatis angulus O E V # 50 gr. # 40 ſcr. <lb/>Et angulus O V E # 54 gr. # 10 ſcr. <lb/>Unde reliquus E O V datur # 75 gr. # 10 ſcr. <lb/>Quare diſtantia O E inter Amſtelodamum & Lei- \\ dam # 9715. # 1. <lb/>Et O E diſtantia inter Amſtelodamum & Trajectum # 9201. # 0. <lb/></note> <pb o="383" file="0397" n="397" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div272" type="section" level="1" n="272"> <head xml:id="echoid-head311" xml:space="preserve">XIV. <emph style="sc">Proelema</emph></head> <head xml:id="echoid-head312" style="it" xml:space="preserve">Triangulum E I V, Leida, Harlemum, Trajectum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VII. datur E V diſtantia inter Lei- \\ dam & Trajectum # 11584. # 0. <lb/>Ex oblervatis autem angulus V E I # 77 gr. # 50 ſcr. <lb/>Et angulus V I E # 67 gr. # 51 ſcr. <lb/>Unde angulus E V I dabitur # 34 gr. # 19 ſcr. <lb/>Atque inde latus I V diſtantia inter Trajectum & \\ Harlemum # 12226. # 1. <lb/>Et E I diſtantia inter Leidam & Harlemum # 7051. # 1. <lb/></note> <p> <s xml:id="echoid-s9161" xml:space="preserve">Vides itaque diſtantiam Lcidæ & </s> <s xml:id="echoid-s9162" xml:space="preserve">Harlemi in utroque triangulo <lb/>quam proxime conſentire, quam vis alterum tot ambagibus ſit à no-<lb/>bis circumductum. </s> <s xml:id="echoid-s9163" xml:space="preserve">Nam initio diſtantiam Leidæ & </s> <s xml:id="echoid-s9164" xml:space="preserve">Noortwici non <lb/>eramus ex ipſo fundamento dimenſi, quod tamen poſtmodum ad <lb/>certiorem operis rationem oblatâ opportunitate hyberno tempore <lb/>per glaciem commodiſſime abſolvimus, argumenti eſt ſatis omnia <lb/>obſervandi munia à nobis legitime & </s> <s xml:id="echoid-s9165" xml:space="preserve">quam accuratiſſime obita, ut <lb/>in utram obſervationem inclinandum ſit vix conſtaret niſi in XIII. <lb/></s> <s xml:id="echoid-s9166" xml:space="preserve">Problemate angulus Harlemenſis exilis eſſet, ſed ſtatio Leidæ & </s> <s xml:id="echoid-s9167" xml:space="preserve"><lb/>Noortwici baſis per ſe prima. </s> <s xml:id="echoid-s9168" xml:space="preserve">Contra in Trajecto, Leida, Harle-<lb/>mo angulus Trajectenſis juſtæ quantitatis, utpote 34 gr. </s> <s xml:id="echoid-s9169" xml:space="preserve">19 ſcr. </s> <s xml:id="echoid-s9170" xml:space="preserve">di-<lb/>ſtantia inter Leidam & </s> <s xml:id="echoid-s9171" xml:space="preserve">Trajectum derivata quidem, ſed omnibus <lb/>modis ſatis accurata. </s> <s xml:id="echoid-s9172" xml:space="preserve">Itaque quamvis nihil admodum interſit inter <lb/>utrumque calculum diſſerentiæ maxime circa ſinem hunc verſantibus, <lb/>iſto tamen noviſſimo potius utemur.</s> <s xml:id="echoid-s9173" xml:space="preserve"/> </p> <pb o="384" file="0398" n="398" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div273" type="section" level="1" n="273"> <head xml:id="echoid-head313" xml:space="preserve">XV. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head314" style="it" xml:space="preserve">Triangulum E I O. Leyda, Harlemum, Amſtelo-<lb/>damum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XII. datur E I diſtantia inter Lei- \\ dam & Harlemum # 7049. # 2. <lb/>Ex obſervatis autem angulus O E I # 27 gr. # 11 ſcr. <lb/>Et angulus E O I # 43 gr. # 18 ſcr. <lb/>Et angulus E I O # 109 gr. # 31 ſcr. <lb/>Quare diſtantia O E inter Amſtelodamum & Lei- \\ dam dabitur # 9687. # 9. <lb/>Et O I diſtantia inter Amſtelodamum & Harle- \\ mum # 4695. # 6. <lb/></note> </div> <div xml:id="echoid-div274" type="section" level="1" n="274"> <head xml:id="echoid-head315" xml:space="preserve">XVI. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head316" style="it" xml:space="preserve">Triangulum I O ?. Harlemum, Amſtelodamum, <lb/>Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema 15 datur I O diſtantia inter Amſte- \\ lodamum & Harlemum # 4695. # 6. <lb/>Ex obſervatis autem angulus I O ? # 67 gr. # 36 ſcr. <lb/>Et angulus O I ? # 78 gr. # 2 ſcr. <lb/>Et angulus O ? I # 34 gr. # 22 ſcr. <lb/>Unde per doctrinam triangulorum dabitur O ? \\ diſtantia inter Amſtelodamum & Alcmariam # 8137. # 5. <lb/>Et I ? diſtantia inter Harlemum & Alcmariam # 7690. # 6. <lb/></note> <pb o="385" file="0399" n="399" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div275" type="section" level="1" n="275"> <head xml:id="echoid-head317" xml:space="preserve">XVII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head318" style="it" xml:space="preserve">Triangulum E O ?. Leida, Amſtelodamum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema X V. datur E O diſtantia inter Lei- \\ dam & Amſtelodamum # 9687. # 9. <lb/>Et per Problema XVI. O ? diſtantia inter Amſte- \\ lodamum & Alcmariam # 8137. # 5. <lb/>Ex obſervatione autem datur in Problemate XVI. an- \\ gulus I O ? # 67 gr. # 36 ſcr. <lb/>Et per Problema XV angulus E O I # 43 gr. # 18 ſcr. <lb/>Unde totus E O ? datur # 110 gr. # 54 ſcr. <lb/>Hinc jam per doctrinam triangulorum datis cru- \\ ribus & angulo ab ipſis comprehenſo datur baſis E ? \\ diſtantia inter Leidam & Alcmariam. # 14707. # 9. <lb/>Et angulus quoque O ? E # 37 gr # 59 ſcr. <lb/>Itemque angulus O E ? # 31 gr. # 7 ſcr. <lb/></note> <p style="it"> <s xml:id="echoid-s9174" xml:space="preserve">Nota. </s> <s xml:id="echoid-s9175" xml:space="preserve">in Problemate XIII Snellium poſuiſſe diſtantiam E O <lb/>9715, 1. </s> <s xml:id="echoid-s9176" xml:space="preserve">in Problemate XV autem 9687, 9. </s> <s xml:id="echoid-s9177" xml:space="preserve">quæ eſt differentia <lb/>27, 2. </s> <s xml:id="echoid-s9178" xml:space="preserve">hic præfert men ſuram Probl. </s> <s xml:id="echoid-s9179" xml:space="preserve">XV. </s> <s xml:id="echoid-s9180" xml:space="preserve">videturqne dubitaſſe de <lb/>probitate menſuræ Problematis XIII.</s> <s xml:id="echoid-s9181" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div276" type="section" level="1" n="276"> <head xml:id="echoid-head319" xml:space="preserve">XVIII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head320" style="it" xml:space="preserve">Triangulum M V L, Oude-Watera, Trajectum, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VIII. datur V M diſtantia inter \\ Oude Wateram & Trajectum # 4980. # 6. <lb/>Ex obſervatis autem angulus V M L # 65 gr # 23 ſcr. <lb/>Et angulus M V L # 82 gr. # 30 ſcr. <lb/>Atque inde reliquus V L M # 32 gr. # 7 ſcr. <lb/>Quare per doctrinam triangulorum dabitur L M, \\ diſtantia inter Oude-Wateram & Bommeliam # 9287. # 4. <lb/>Et V Ldiſtantia inter Trajectum & Bommeliam # 8516. # 5. <lb/></note> <pb o="386" file="0400" n="400" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div277" type="section" level="1" n="277"> <head xml:id="echoid-head321" xml:space="preserve">XIX. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head322" style="it" xml:space="preserve">Triangulum ? V L. Dordracum, Trajectum, <lb/>Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VII. datur R L, diſtantia inter Dor- \\ dracum & Trajectum # 11646. # 1. <lb/>Ex obſervatis autem angulus R V L # 62 gr. # 13 ſcr. <lb/>Et angulus V R L # 44 gr. # 27 ſcr. <lb/>Et inde reliquus angulus V L R # 73 gr. # 20 ſcr. <lb/>Atque inde per doctrinam triangulorum invenietur \\ R L, diſtantia inter Dordracum & Bommeliam # 10755. # 3. <lb/>Et V L diſtantia inter Trajectum & Bomme- \\ liam # 8513. # 3. <lb/></note> </div> <div xml:id="echoid-div278" type="section" level="1" n="278"> <head xml:id="echoid-head323" xml:space="preserve">XX. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head324" style="it" xml:space="preserve">Triangulum E V L. Leida, Trajectum, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VI. datur E V diſtantia inter Leidam \\ & Trajectum # 11584. # 0. <lb/>Per Problema XVIII & XIX aſſumam V L diſtan- \\ tiam inter Trajectum & Bommeliam # 85150. # 0. <lb/>Et ex obſervatis angulus E V L # 116 gr. # 23 ſcr. <lb/>Unde per doctrinam triangulorum dabitur E L di- \\ ſtantia inter Leidam & Bommeliam # 17156. # 9. <lb/>Et angulus V E L # 26 gr. # 24 ſcr. <lb/>Et angulus V L E # 37 gr. # 13 ſcr. <lb/></note> <pb o="387" file="0401" n="401" rhead="DEMAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div279" type="section" level="1" n="279"> <head xml:id="echoid-head325" xml:space="preserve">XXI. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head326" style="it" xml:space="preserve">Triangulum ? E L, Alcmaria, Leida, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XVII. datur ? E, diſtantia inter Lei- \\ dam & Alcmariam # 14707. # 9. <lb/>Per Problema XX. datur E L diſtantia inter Lei- \\ dam & Bommeliam # 17156. # 9. <lb/>Per Problema autem XVII datur angulus ? E O # 31 gr. # 7 ſcr. <lb/>Et angulus O E V ex ipſa obſervatione # 50 gr. # 36 ſcr. <lb/>Et angulus V E L per Problema XX # 26 gr. # 24 ſcr. <lb/>Quare totus ? E L datur # 108 gr. # 9 ſcr. <lb/>Atque inde datis cruribus cum angulo ab ipſis com- \\ prehenſo, dabitur quoque per doctrinam triangulo- \\ rum baſis ? L # 25843. # 7. <lb/>Et angulus E L ? # 34 gr. # 59 {1/2} ſcr. <lb/>Et angulus L ? E # 40 gr. # 22 {1/2} ſcr. <lb/></note> </div> <div xml:id="echoid-div280" type="section" level="1" n="280"> <head xml:id="echoid-head327" xml:space="preserve">XXII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head328" style="it" xml:space="preserve">Triangulum R L V, Dordracum, Bommelia, Breda.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XIX. datur R L diſtantia inter Dor- \\ dracum & Bommeliam # 10755. # 3. <lb/>Ex obſervatis autem angulus V R L # 72 gr. # 10 ſcr. <lb/>Et angulus L V R # 70 gr. # 7 ſcr. <lb/>Unde reliquus R L V datur # 37 gr. # 43 ſcr. <lb/>Atque inde R V, diſtantia inter Dordracum & Bre- \\ dam # 6996. # 5. <lb/>Et L V, diſtantia inter Bommeliam & Bredam # 10887. # 2. <lb/></note> </div> <div xml:id="echoid-div281" type="section" level="1" n="281"> <head xml:id="echoid-head329" xml:space="preserve">XXIII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head330" style="it" xml:space="preserve">Triangulum R S F. Dordracum, Gouda, Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema II datur R S diſtantia inter Goudam <lb/></note> <pb o="388" file="0402" n="402" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>& Dordracum # 5897. 8. <lb/>Ex obſervatis autem angulus S R F # 54 gr. 12 ſcr. <lb/>Et angulus R S F # 48 gr. 15 ſcr. <lb/>Unde reliquus R F S datur # 77 gr. 33 ſcr. <lb/>Quare per doctrinam triangulorum datur S F di \\ ſtantia inter Goudam & Rotterodamum # 4888. 8. <lb/>Et R F diſtantia inter Dordracum & Rotteroda- \\ mum # 4506. 1. <lb/>Atqui diſtantia inter Goudam & Rotterodamum an- \\ tea in Problemate V. fuit inventa # 4883. 1. <lb/></note> <p> <s xml:id="echoid-s9182" xml:space="preserve">Quamobrem iſta ſatis arcte inter ſe conſentiunt.</s> <s xml:id="echoid-s9183" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div282" type="section" level="1" n="282"> <head xml:id="echoid-head331" xml:space="preserve">XXIV. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head332" style="it" xml:space="preserve">Triangulum R T F, Dordracum, Willemſtadium, <lb/>Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXIII datur R F diſtantia inter Dor- \\ dracum & Rotterodamum # 4506. 1. <lb/>Et ex obſervatis angulus F R T # 86 gr. 19 ſcr. <lb/>Et angulus R T F # 41 gr. 10 ſcr. <lb/>Unde reliquus R F T datur # 52 gr. 31 ſcr. <lb/>Atque inde per doctrinam triangulorum quoque da- \\ bitur R T diſtantia inter Dordracum & Ilermopo- \\ lin # 5432. 0. <lb/>Et T F diſtantia inter Ilermopolin & Rotte roda- \\ mum # 6831. 2. <lb/></note> </div> <div xml:id="echoid-div283" type="section" level="1" n="283"> <head xml:id="echoid-head333" xml:space="preserve">XXV. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head334" style="it" xml:space="preserve">Triangulum R T V. Dordracum, Willemſtadium, <lb/>Breda.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXIV datur RT diſtantia inter Dor- \\ dracum & Ilermopolin # 5432. 0. <lb/>Ex obſervatis autem angulus T R V # 66 gr. 11 ſcr. <lb/></note> <pb o="389" file="0403" n="403" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Et angulus R T V # 67 gr. 51 ſcr. <lb/>Et angulus R V T # 45 gr. 59 ſcr. <lb/>Quæ ſumma duos rectos unico tantum ſcrupulo ex- \\ cedit, ſit itaque R V T # 45 gr. 58 ſcr. <lb/>Nam ob angulorum juſtam quantitatem hic unum \\ aut alterum ſcrupulum haud admodum magnam late- \\ rum differentiam poterit inducere. <lb/>Itaque ex his datis ſecundum artis præcepta inve- \\ nietur T V diſtantia inter Ilermopolin & Bredam # 6912. 1. <lb/>Et R V, diſtantia inter Dordracum & Bredam # 6998. 0. <lb/>Quam antea Problemate XXII, invenimus # 6996. 5. <lb/>Quæ differentia hic ſub finem nullius momenti ha- \\ benda eſt, & ſit propterea latus R V, ob numeri ro- \\ tundationem. # 7000. 0. <lb/></note> </div> <div xml:id="echoid-div284" type="section" level="1" n="284"> <head xml:id="echoid-head335" xml:space="preserve">XXVI. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head336" style="it" xml:space="preserve">Triangulum T V Q. Willemſtadium, Breda, Berga-<lb/>ad-Somum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXV datur V T diſtantia inter Bre- \\ dam & Ilermopolin ſive Willemſtadium # 6912. 1. <lb/>Ex obſervatione autem angulus V T Q # 89 gr. 25 ſcr. <lb/>Et angulus T V Q # 43 gr. 24 ſcr. <lb/>Et angulus V Q T # 47 gr. 15 ſcr. <lb/>Ubi quatuor omnino ſcrupula redundant, quæ ex \\ ipſis ita deducam, ut V T Q ſit # 89 gr. 23 ſcr. <lb/>Et angulus T V Q # 43 gr. 23 ſcr. <lb/>Et angulus V Q T # 47 gr. 14 ſcr. <lb/>Unde per artis præcepta dabitur T Q diſtantia inter \\ Ilermopolin & Bergam # 6467. 2. <lb/>Et V Q diſtantia inter Bredam & Bergam # 9414. 7. <lb/></note> <pb o="390" file="0404" n="404" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div285" type="section" level="1" n="285"> <head xml:id="echoid-head337" xml:space="preserve">XXVII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head338" xml:space="preserve">Triangulum R V Q Dordracum, Breda, Berga-ad-<lb/>Somum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXV datur V R diſtantia inter Dor- \\ dracum & Bredam # 7000. 0. <lb/>Et per Problema XXVI. Q V, diſtantia inter Bre- \\ dam & Bergam ad-Somum # 9414. 7. <lb/>Ex obſervatis autem denique datur angulus Q V R # 89 gr. 33 ſcr. <lb/>Unde per triangulorum doctrinam datis cruribus, & \\ angulo ab ipſis comprehenſo dabitur baſis Q R, di \\ ſtantia inter Dordracum & Bergam-ad-Somum # 11735. 6. <lb/>Et angulus V R Q # 53 gr. 39 {1/2} ſcr. <lb/>Et angulus V Q R # 36 gr. 47 {1/2} ſcr. <lb/></note> </div> <div xml:id="echoid-div286" type="section" level="1" n="286"> <head xml:id="echoid-head339" xml:space="preserve">XXVIII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head340" style="it" xml:space="preserve">Triangulum V L Q Breda, Bommelia, Berga-ad-<lb/>Somum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXII datur latus V L, diſtantia inter \\ Bredam & Bommeliam # 10887. 2. <lb/>Et per Problema XXVI datur V Q diſtantia inter \\ Bredam & Bergam-ad-Somum # 9414. 7. <lb/>Et per Problema XXII ex obſervatione ipſa datur \\ angulus L V R # 70 gr. 14 ſcr. <lb/>Et per Problema XXVII ex ipſis obſervatis datur \\ angulus R V Q # 89 gr. 33 ſcr. <lb/>Quare totus angulus L V Q dabitur # 159 gr. 47 ſcr. <lb/>Undeper doctrinam triangulorum dabitur baſis L Q \\ diſtantia inter Bommeliam & Bergam ad Somum # 19984. 9. <lb/>Et angulus V L Q # 9 gr. 25 ſcr. 20?. <lb/>Et angulus V Q L # 10 gr. 54 ſcr. 40?. <lb/></note> <pb o="391" file="0405" n="405" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div287" type="section" level="1" n="287"> <head xml:id="echoid-head341" xml:space="preserve">XXIX. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head342" style="it" xml:space="preserve">Datis quadrilateri L R V Q lateribus & diagonio R V, abſque <lb/>Triangulorum canonibus invenire reliquam diagonium Q L.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XVI. fig. 16. Per Problema XIX datur R L di- \\ ſtantia inter Dordracum & Bommeliam # 10755. 3. <lb/>Per Problema XXII datur RV, diſtantia inter Dor- \\ dracum & Bredam # 7000. 0. <lb/>Per Problema XXVII datur R Q diſtantia inter Dor- \\ dracum & Bergam ad-Somum # 11735. 6. <lb/>Per Problema XXVI datur V Q diſtantia inter Bre- \\ dam & Bergam-ad-Somum # 9414. 7. <lb/>Per Problema XXII datur V L diſtantia inter Bre- \\ dam & Bommeliam # 10887. 2. <lb/></note> <p> <s xml:id="echoid-s9184" xml:space="preserve">Quibus datis diagonius Q L diſtantia inter Bommeliam & </s> <s xml:id="echoid-s9185" xml:space="preserve">Ber-<lb/>gam-ad Somum eruetur hoc modo. </s> <s xml:id="echoid-s9186" xml:space="preserve">In triangulo R L V demitta-<lb/>tur à vertice L perpendicularis L V, in datam diagonium V R. <lb/></s> <s xml:id="echoid-s9187" xml:space="preserve">Et à Q itidem perpendicularis in eandem ſit Q M. </s> <s xml:id="echoid-s9188" xml:space="preserve">Cum itaque <lb/>in triangulo R L V tria dentur latera, dabuntur quoque ſegmenta <lb/>R V N V ab angulis ad perpendicularem L N. </s> <s xml:id="echoid-s9189" xml:space="preserve">Atque inde de-<lb/>mum cum in triangulo rectangulo R N L detur baſis recti R L & </s> <s xml:id="echoid-s9190" xml:space="preserve"><lb/>crus alterum R N, dabitur quoque perpendicularis L N. </s> <s xml:id="echoid-s9191" xml:space="preserve">Per ea-<lb/>dem præcepta invenientur ſegmenta M V & </s> <s xml:id="echoid-s9192" xml:space="preserve">V R, & </s> <s xml:id="echoid-s9193" xml:space="preserve">perpendicu-<lb/>laris Q M in triangulo R Q V. </s> <s xml:id="echoid-s9194" xml:space="preserve">Verum differentia ſegmentorum <lb/>R M & </s> <s xml:id="echoid-s9195" xml:space="preserve">R N eſt ipſa M N inter ſegmentum inter ipſas perpendicu-<lb/>laris interceptum. </s> <s xml:id="echoid-s9196" xml:space="preserve">Continuetur porro perpendicularis Q M uſque <lb/>in H æqualiter ipſi L M, & </s> <s xml:id="echoid-s9197" xml:space="preserve">connectatur L H. </s> <s xml:id="echoid-s9198" xml:space="preserve">Erit itaque L H <lb/>parallela & </s> <s xml:id="echoid-s9199" xml:space="preserve">æqualis perpendiculari L M, & </s> <s xml:id="echoid-s9200" xml:space="preserve">angulus H rectus: </s> <s xml:id="echoid-s9201" xml:space="preserve"><lb/>dantur autem Q M & </s> <s xml:id="echoid-s9202" xml:space="preserve">M H, datur itaque tota Q H. </s> <s xml:id="echoid-s9203" xml:space="preserve">Datur ve-<lb/>ro etiam ipſa M N; </s> <s xml:id="echoid-s9204" xml:space="preserve">hoc eſt L H ei parallela & </s> <s xml:id="echoid-s9205" xml:space="preserve">æqualis. </s> <s xml:id="echoid-s9206" xml:space="preserve">Quam-<lb/>obrem in triangulo rectangulo L H Q, datis cruribus Q H & </s> <s xml:id="echoid-s9207" xml:space="preserve"><lb/>H L, dabitur quoque baſis Q L diſtantia inter Bommeliam & </s> <s xml:id="echoid-s9208" xml:space="preserve"><lb/>Bredam quæſita. </s> <s xml:id="echoid-s9209" xml:space="preserve">Hujus problematis explicatio in numeris ita <lb/>habet.</s> <s xml:id="echoid-s9210" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Si quadratum ab R L # 11720227600. <lb/></note> <pb o="392" file="0406" n="406" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Addatur ad quadratum R V # 4900000000 <lb/>Summa erit # 16620227600 <lb/>Unde deductum quadratum L V # 12003831844 <lb/>Relinquit numerum # 4616395756 <lb/>Cujus dimidium # 2308197878 <lb/>Per R V diviſum dabit R N # 3297. 4. <lb/>Et ideo reliquam N V # 3702. 6. <lb/>Porro quadratum N V # 1370924676. <lb/>De quadrato V L ſubductum relinquet quadratum \\ perpendicularis N L # 10632907168. <lb/>Unde ipſa N L dabitur # 10311. 6. <lb/>Haud alia ratione invenietur R M # 7033. 3. <lb/>Et V M # 33. 0. <lb/>Unde ipſa perpendicularis M Q datur # 9414. 6. <lb/>Additis vero perpendicularibus M Q & L N, hoc \\ eſt ipſa M H, dabitur tota Q H # 19726. 2. <lb/>Deinde ſubducta R N de RV datur reliqua NV, hoc \\ eſt ipſa L H # 3735. 9. <lb/>Quamobrem junctis quadratis Q H & H L inve- \\ nietur diagonius Q L diſtantia inter Bergam & Bom- \\ meliam, quæ Problemate XXVIII. tanta quoque \\ fuit # 20076. 8. <lb/></note> </div> <div xml:id="echoid-div288" type="section" level="1" n="288"> <head xml:id="echoid-head343" xml:space="preserve">XXX. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head344" style="it" xml:space="preserve">Triangulum E I ?, Leida, Harlemum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XIV datur E I, diſtantia inter Lei- \\ dam & Harlemum # 7051. 1. <lb/>Per Problema XVI datur I ?, diſtantia inter Harle- \\ mum & Alcmariam # 7690. 6. <lb/>Ex obſervatione ipſa angulus E I ? # 172 gr. 11 ſcr. <lb/>Quamobrem E ? diſtantia Alcmariæ & Leidæ da- \\ bitur # 14708. 5. <lb/>Et angulus I E ? # 3 gr. 15 ſcr. <lb/>Et angulus E ? I # 3 gr. 8 ſcr. <lb/></note> <pb o="393" file="0407" n="407" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div289" type="section" level="1" n="289"> <head xml:id="echoid-head345" xml:space="preserve">XXXI. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head346" style="it" xml:space="preserve">Triangulum E V ?. Leida, Trajectum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema VI datur E V, diſtantia inter Leidam \\ & Trajectum # 11584. 0. <lb/>Per Problema XVII datur E ?, diſtantia inter Lei- \\ dam & Alcmariam # 14708. 5. <lb/>Ex obſervatis autem datur per Problema XIV angu- \\ lus V E I # 77 gr. 50 ſcr. <lb/>Et per Problema XXX angulus ? E I # 3 gr. 25 ſcr. <lb/>Unde conflatur totus V E ? # 81 gr. 15 ſcr. <lb/>Atque hinc datis cruribus cum angulo ab ipſis com- \\ prehenſo dabitur baſis V ?, diſtantia inter Trajectum \\ & Alcmariam # 17271. 2. <lb/>Et angulus E V ? # 57 gr. 17 ſcr. <lb/>Et angulus V ? E # 41 gr. 28 ſcr. <lb/></note> </div> <div xml:id="echoid-div290" type="section" level="1" n="290"> <head xml:id="echoid-head347" xml:space="preserve">XXXII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head348" style="it" xml:space="preserve">Triangulum V L ?. Trajectum, Bommelia, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XVIII & XIX datur V L diſtantia \\ inter Bommeliam & Trajectum # 8515. 0. <lb/>Et per Problema XXXI datur V ? diſtantia inter \\ Trajectum & Alcmariam # 17271. 2. <lb/>Ex obſervatis autem per Problema XIX datur an- \\ gulus L V R # 62 gr. 13 ſcr. <lb/>Ex obſervatis item angulus R V E per \\ Problema XIX # 54 gr. 29 ſcr. <lb/>Et angulus E V ? per Problema XXXI # 57 gr. 17 ſcr. <lb/>Unde totus L V ? datur # 173 gr. 59 ſcr. <lb/>Quare datis cruribus & angulo ab ipſis comprehen- \\ ſo dabitur baſis L ?, diſtantia inter Bommeliam & \\ Alcmariam # 25755. 2. <pb o="394" file="0408" n="408" rhead="DISSERTATIO"/> Et angulus V L ? # 4 gr. 1 ſcr. 20``. <lb/>Et angulus V ? L # 1 gr. 59 ſcr. 10``. <lb/></note> </div> <div xml:id="echoid-div291" type="section" level="1" n="291"> <head xml:id="echoid-head349" xml:space="preserve">XXXIII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head350" style="it" xml:space="preserve">Triangulum Q L ?. Berga-ad-Somum, Bommelia, <lb/>Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXIX. datur latus Q L diſtantia in- \\ ter Bergam & Bommeliam # 19984. 9. <lb/>Per Problema XXI L ? diſtantia inter Bommeliam, \\ & Alcmariam # 25755. 2. <lb/>Et angulus Q L ? quoque datur: namque per Pro. \\ blema XXXII datur angulus V L ? # 4 gr. 1`. 20``. <lb/>Et angulus V L R per XIX Problema # 73 gr. 20 ſcr. <lb/>Quare ? L R reliquus datur # 69 gr. 18. 40``. <lb/>Unde totus Q L ? dabitur # 97 gr. 36. 20``. <lb/>Datis igitur cruribus & angulo ab ipſis comprehen- \\ ſo dabitur baſis Q ? diſtantia inter Bergam-ad-Somum \\ & Alcmariam # 34626. 2. <lb/>Et angulus L Q ? # 45 gr. 56. 50``. <lb/>Et angulus L ? Q # 36 gr. 26. 50``. <lb/></note> <p> <s xml:id="echoid-s9211" xml:space="preserve">Ad quas turres in ſingulis urbibus collineavimus, & </s> <s xml:id="echoid-s9212" xml:space="preserve">quæ ſta-<lb/>tionum loca ad ſpeculandum delegerimus hic ad extremum quoque <lb/>annotabo. </s> <s xml:id="echoid-s9213" xml:space="preserve">Nam in quibuſdam plures ſunt, & </s> <s xml:id="echoid-s9214" xml:space="preserve">admodum ſubli-<lb/>mes.</s> <s xml:id="echoid-s9215" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9216" xml:space="preserve">Oude-Wateræ, turris templo conjuncta.</s> <s xml:id="echoid-s9217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9218" xml:space="preserve">Woerdæ, turris templo conjuncta.</s> <s xml:id="echoid-s9219" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9220" xml:space="preserve">Montfortii, turris templo conjuncta.</s> <s xml:id="echoid-s9221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9222" xml:space="preserve">Leidæ, turris curiæ conjuncta.</s> <s xml:id="echoid-s9223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9224" xml:space="preserve">Goudæ, turris templo majori conjuncta.</s> <s xml:id="echoid-s9225" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9226" xml:space="preserve">Hagæ, turris celſa templo prope forum piſcarium conjuncta.</s> <s xml:id="echoid-s9227" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9228" xml:space="preserve">Ultrajecti, turris celſiſſima templo cathedrali conjuncta.</s> <s xml:id="echoid-s9229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9230" xml:space="preserve">Dordraci, turris templo conjuncta, cui faſtigium deeſt.</s> <s xml:id="echoid-s9231" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9232" xml:space="preserve">Gorcomii, turris templo conjuncta.</s> <s xml:id="echoid-s9233" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9234" xml:space="preserve">Bommeliæ, turris celſiſſima templo conjuncta.</s> <s xml:id="echoid-s9235" xml:space="preserve"/> </p> <pb o="395" file="0409" n="409" rhead="DE MAGNITUDINE TERRÆ."/> <p> <s xml:id="echoid-s9236" xml:space="preserve">Bredæ, turris excelſa templo conjuncta.</s> <s xml:id="echoid-s9237" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9238" xml:space="preserve">Ilermopoli, ſive Willemſtadii, turricula ſupra templum.</s> <s xml:id="echoid-s9239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9240" xml:space="preserve">Bergæ-ad-Somum, turris templo anteriori prope forum con-<lb/>juncta, nam poſterius ſolas parietinas oſtentat.</s> <s xml:id="echoid-s9241" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9242" xml:space="preserve">Amſtelodami, turris veteri (ut vocant) templo conjuncta.</s> <s xml:id="echoid-s9243" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9244" xml:space="preserve">Harlemi, turricula medio templo impoſita.</s> <s xml:id="echoid-s9245" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9246" xml:space="preserve">Alcmariæ, turricula medio templo impoſita.</s> <s xml:id="echoid-s9247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9248" xml:space="preserve">Habeo longe plurium locorum obſervationes alteri fini â me <lb/>inſtitutas, verum iſtæ nunc huic inſtituto ſufficiant.</s> <s xml:id="echoid-s9249" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div292" type="section" level="1" n="292"> <head xml:id="echoid-head351" xml:space="preserve">CAPUT IX.</head> <head xml:id="echoid-head352" style="it" xml:space="preserve">Quantitas unius gradus in maximo Terræ circulo demum <lb/>definita.</head> <p> <s xml:id="echoid-s9250" xml:space="preserve">Cum igitur hactenus ita locorum diſtantias ſumma diligentia ex-<lb/>plicaverimus, ſupereſt tandem ut unius gradus quantitatem <lb/>ad extremum definiamus; </s> <s xml:id="echoid-s9251" xml:space="preserve">quo fine iſta omnia à nobis hactenus com-<lb/>parata & </s> <s xml:id="echoid-s9252" xml:space="preserve">conquiſita fuerunt. </s> <s xml:id="echoid-s9253" xml:space="preserve">Sed antea an extrema iſta loca, quo-<lb/>rum intervallis ad hanc rem utemur, ſub eodem meridiano ſita ſint, <lb/>quoque erit explorandum. </s> <s xml:id="echoid-s9254" xml:space="preserve">Et propterea angulum poſitionis, quem <lb/>Gouda cum meridiano Leidenſi faciat, hoc eſt, quantum à noſtro <lb/>meridiano ortum aut occaſum verſus declinet accurate notavi Sit <lb/>itaque ? </s> <s xml:id="echoid-s9255" xml:space="preserve">? </s> <s xml:id="echoid-s9256" xml:space="preserve">linea meridiana per Leidam educta, ut ? </s> <s xml:id="echoid-s9257" xml:space="preserve">ſeptentrionem, <lb/>? </s> <s xml:id="echoid-s9258" xml:space="preserve">meridiem ſpectet, Gouda hinc ortum verſus ita declinat ut angu-</s> </p> <note position="right" xml:space="preserve"> <lb/>lus ? E S, qui poſitionis vocatur, ſit # 45 gr. 31 ſcr. <lb/>Datur autem ex obſervatis angulus S E O # 88 gr. 21 ſcr. <lb/>Et per Problema XVII. angulus O E ? # 31 gr 7 ſcr. <lb/>Quare totus ? E ? datur # 164 gr. 59 ſcr. <lb/>Unde etiam reliquus ? E ? dabitur # 15 gr. 1 ſcr. <lb/>Atque ideo demiſſa perpendiculari ? ? erit angu- \\ lus E ? ? # 74 gr. 59 ſcr. <lb/>Datur autem per Problema XV I. ? E diſtantia \\ inter Leidam & Alcmariam # 14707. 9. <lb/>Dabitur igitur per doctrinam triangulorum perpen-<lb/></note> <pb o="396" file="0410" n="410" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>dicularis ? ? differentia longitudinis <lb/>Et ? E differentia latitudinis # 14203. 7. <lb/>Rurſum cum detur per Problema XXXIII. ? Q \\ diſtantia inter Alcmariam & Bergam # 34626. 2. <lb/>Datur autem per Problema XXXIII angulus \\ L ? Q # 36 gr. 26` ſcr. 50``. <lb/>Et per Problema XXI angulus L ? E # 40 gr. 22`. 30``. <lb/>Atque ideo reliquus E ? Q # 3 gr. 55`. 40``. <lb/>Qui additus ad ? ? E # 74 gr. 59 ſcr. <lb/>Conflabit ? ? Q ſive ? Q ? # 78 gr. 54 ſcr. <lb/>Et ideo angulum Q ? ? # 11 gr. 6. 20``. <lb/>Atque ideo Q ? differentia longitudinis inter Alc- \\ mariam & Bergam-ad-Somum erit. <lb/>Et ? ? differentia latitudinis inter Alcmariam & \\ Bergam-ad Somum # 33978. 1. <lb/></note> <p> <s xml:id="echoid-s9259" xml:space="preserve">Reliquum eſt igitur, ut poli altitudine, vel etiam ſola latitudi-<lb/>num differentia data, cætera concludamus. </s> <s xml:id="echoid-s9260" xml:space="preserve">Altitudo poli Alcma-<lb/>riani diligenter & </s> <s xml:id="echoid-s9261" xml:space="preserve">accurate obſervata eſt inventa 52 grad. </s> <s xml:id="echoid-s9262" xml:space="preserve">40 {1/2} ſcru-<lb/>pulorum. </s> <s xml:id="echoid-s9263" xml:space="preserve">Altitudo poli Bergæ-ad-Somum 51. </s> <s xml:id="echoid-s9264" xml:space="preserve">grad. </s> <s xml:id="echoid-s9265" xml:space="preserve">29 ſcrupulo-<lb/>rum. </s> <s xml:id="echoid-s9266" xml:space="preserve">Atque hinc differentia latitudinis inter Bergam & </s> <s xml:id="echoid-s9267" xml:space="preserve">Alcmariam <lb/>datur unius & </s> <s xml:id="echoid-s9268" xml:space="preserve">ſeptuaginta ſcrupulorum cum ſemiſſe. </s> <s xml:id="echoid-s9269" xml:space="preserve">Unde ſola <lb/>proportione unius gradus quantitatem in maximoterræ circulo con-<lb/>cludes 28513 perticarum. </s> <s xml:id="echoid-s9270" xml:space="preserve">Cum enim 71 {1/2} ſcrupula habeant 33978 <lb/>perticas, ſequitur ſcrupulis ſexaginta, quæ gradum implent, cede-<lb/>re perticas 28513. </s> <s xml:id="echoid-s9271" xml:space="preserve">Verum ut illud verum eſſe aliunde quoque e-<lb/>vincam. </s> <s xml:id="echoid-s9272" xml:space="preserve">Ecce iterum, Leidenſis & </s> <s xml:id="echoid-s9273" xml:space="preserve">Alcmarianæ elevationis differen-<lb/>tiam cum illarum diſtantia comparabo. </s> <s xml:id="echoid-s9274" xml:space="preserve">Altitudo poli Leidenſis plu-<lb/>ries, & </s> <s xml:id="echoid-s9275" xml:space="preserve">modis compluribus inventa eſt 52 graduum 10 {1/2} ſcrupulo-<lb/>rum. </s> <s xml:id="echoid-s9276" xml:space="preserve">Differentia igitur eſt ſcrupulorum triginta. </s> <s xml:id="echoid-s9277" xml:space="preserve">Atqui domus <lb/>mea à turri curiæ Leidenſis, e quâ tanquam ſpecula angulorum <lb/>quantitatem & </s> <s xml:id="echoid-s9278" xml:space="preserve">Gæodæſias obſervavimus, diſtat meridiem verſus, <lb/>ſi ad eundem meridianum revoces plane decempedis 95, quemad-<lb/>modum capite ſequenti Gæodætice & </s> <s xml:id="echoid-s9279" xml:space="preserve">accurate demonſtrabo. </s> <s xml:id="echoid-s9280" xml:space="preserve">Alc-<lb/>mariæ autem locus ille erat itidem à templi turricula ſupra notatus <lb/>abeſſe decempedis 55 præter propter, differentia utriuſque ſunt de-<lb/>cempedæ 40, ad diſtantiam parallelorum inter Alcmariam & </s> <s xml:id="echoid-s9281" xml:space="preserve">Lei- <pb o="397" file="0411" n="411" rhead="DE MAGNITUDINE TERRÆ."/> dam addendæ: </s> <s xml:id="echoid-s9282" xml:space="preserve">ea autem ſunt ſupra inventa 14204; </s> <s xml:id="echoid-s9283" xml:space="preserve">quare eâ ad <lb/>ædium ſtationes, in quibus poli altitudo obſervata fuit revocata, <lb/>erit 14244. </s> <s xml:id="echoid-s9284" xml:space="preserve">Atqui tot decempedæ cedunt ſcrupulis triginta. </s> <s xml:id="echoid-s9285" xml:space="preserve">Quam-<lb/>obrem uni gradui in maximo terræ circulo debentur decempedæ <lb/>28488. </s> <s xml:id="echoid-s9286" xml:space="preserve">Sed ante e diſtantia Alcmariæ atque Bergæ concluſimus <lb/>decempedas 28513 uno gradu contineri. </s> <s xml:id="echoid-s9287" xml:space="preserve">Calculus igitur uterque <lb/>eundem nobis numerum addicit, quam potuit proxime. </s> <s xml:id="echoid-s9288" xml:space="preserve">Atque ideo <lb/>ad numeri rotundationem aſſumatur numerus inter utrumque me-<lb/>dius. </s> <s xml:id="echoid-s9289" xml:space="preserve">Et vera ac juſta unius gradus quantitas in maximo terræ cir-<lb/>culo nobis eſto 28500 perticarum Rhynlandicarum. </s> <s xml:id="echoid-s9290" xml:space="preserve">Quarum ſin-<lb/>gulæ duodecim pedes Rhynlandicos continent, quamvis eam par-<lb/>titionem in calculo repudiaverimus ?</s> <s xml:id="echoid-s9291" xml:space="preserve">?? </s> <s xml:id="echoid-s9292" xml:space="preserve">?</s> <s xml:id="echoid-s9293" xml:space="preserve">? ?</s> <s xml:id="echoid-s9294" xml:space="preserve">??</s> <s xml:id="echoid-s9295" xml:space="preserve">??</s> <s xml:id="echoid-s9296" xml:space="preserve">??</s> <s xml:id="echoid-s9297" xml:space="preserve">?? </s> <s xml:id="echoid-s9298" xml:space="preserve">{?</s> <s xml:id="echoid-s9299" xml:space="preserve">??</s> <s xml:id="echoid-s9300" xml:space="preserve">} ?</s> <s xml:id="echoid-s9301" xml:space="preserve">??</s> <s xml:id="echoid-s9302" xml:space="preserve">??</s> <s xml:id="echoid-s9303" xml:space="preserve">??</s> <s xml:id="echoid-s9304" xml:space="preserve">??</s> <s xml:id="echoid-s9305" xml:space="preserve">, ne <lb/>intricata partium numeratio nobis negotium faceſſeret. </s> <s xml:id="echoid-s9306" xml:space="preserve">Hactenus <lb/>enim, ut ſupra capite V diſerte monui, tantum decumanam perticæ <lb/>diviſionem ſecutus ſum. </s> <s xml:id="echoid-s9307" xml:space="preserve">Ut ita {1/10} perticæ quoque in calculum ve-<lb/>niret, & </s> <s xml:id="echoid-s9308" xml:space="preserve">error ſi quis ex particularum neglectu in perticas uſque <lb/>irrepere poſſet, iſto modo commode declinaretur. </s> <s xml:id="echoid-s9309" xml:space="preserve">Præterea quo-<lb/>que haud ſum neſcius, ſi loca longiuſcule inter ſe diſtarent ſphæ-<lb/>ricorum triangulorum doctrina opus fore: </s> <s xml:id="echoid-s9310" xml:space="preserve">ſed peripheria unius gra-<lb/>dus, & </s> <s xml:id="echoid-s9311" xml:space="preserve">eo paulo etiam amplius ad rectam quam proxime accedunt, <lb/>ut in iſto epilogiſmo errorem nullum inducere potuerit. </s> <s xml:id="echoid-s9312" xml:space="preserve">Si enim <lb/>radium circuli aſſumas partium 100000000, unius gradus periphe-<lb/>ria erit 174533. </s> <s xml:id="echoid-s9313" xml:space="preserve">& </s> <s xml:id="echoid-s9314" xml:space="preserve">ejus ſubtenſa tantarum 174531. </s> <s xml:id="echoid-s9315" xml:space="preserve">quarum diffe-<lb/>rentia nullius admodum eſt momenti, & </s> <s xml:id="echoid-s9316" xml:space="preserve">ſolos pedes attin-<lb/>git.</s> <s xml:id="echoid-s9317" xml:space="preserve"/> </p> <pb o="398" file="0412" n="412"/> </div> <div xml:id="echoid-div293" type="section" level="1" n="293"> <head xml:id="echoid-head353" xml:space="preserve">PARS ALTERA. <lb/>DE <lb/>MAGNITUDINE TERRÆ <lb/>SECUNDUM MENSURAM ULTIMAM <lb/>SNELLII <lb/>ET <lb/>NOSTRAM.</head> <head xml:id="echoid-head354" xml:space="preserve"><emph style="sc">Problema</emph> I.</head> <head xml:id="echoid-head355" style="it" xml:space="preserve">Tab. XIV. fig. 2. Triangulum i e a connectens Leydam, <lb/>Douſæ arcem, locumque inter hanc & Voor-<lb/>ſchooten aſſumtum.</head> <note position="right" xml:space="preserve"> <lb/>Latus a e accuratiſſime ſupra glaciem menſuratum fuit catenâ, \\ qui labor ter repetitus eſt, ut eo tutius confidi poſſet, fuit \\ vero perticarum # 475, 0, 0 <lb/>Angulus i a e obſervatus # 54 gr. 36`. <lb/>Angulus i e a obſervatus # 89 gr. 31`. <lb/>Angulus a i e obſervatus eſt # 35 gr. 53`. <lb/>Ex quibus datis per regulas Trigonometriæ inventum eſt latus i e diſtantia Leidæ a Douſiana arce # 660, 5, 7. <lb/>Et latus i a # 810, 3, 6. <lb/></note> </div> <div xml:id="echoid-div294" type="section" level="1" n="294"> <head xml:id="echoid-head356" xml:space="preserve"><emph style="sc">Problema</emph> II.</head> <head xml:id="echoid-head357" style="it" xml:space="preserve">Triangulum a e m, nectens Douſæ arcem, pagum Soeterwoudam, <lb/>locumque inter illam & Voor ſchoten aſſumtum <lb/>eundem ac in Probl. I.</head> <note position="right" xml:space="preserve"> <lb/>Eſt obſervatus anguluse a m # 61 gr. 53`. <pb o="399" file="0413" n="413" rhead="DE MAGNITUDINE TERRÆ."/> Angulus a e m # 57 gr. 42. <lb/>Angulus e m a # 60 gr. 25`. <lb/>Latus a e datum # 475, 0, 0 <lb/>Ex quibus ope Regularum Trigonometriæ ſubducitur e m inter- \\ vallum inter Douſæ arcem & pagum Soeterwoudam # 481, 7, 4. <lb/></note> </div> <div xml:id="echoid-div295" type="section" level="1" n="295"> <head xml:id="echoid-head358" xml:space="preserve"><emph style="sc">Problema</emph> III.</head> <head xml:id="echoid-head359" style="it" xml:space="preserve">Triangulum i e m, jungens Leidam, Douſæ arcem & <lb/>Soeterwoudam.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus i e m # 147. gr. 13`. <lb/>Datur latus i e in Probl. I. # 660, 5, 7. <lb/>Et in Problemate II. datur latus e m # 481, 7, 4. <lb/>Adeoque datis duobus lateribus cum angulo intercep- \\ to dabunt regulæ Trigonometricæ <lb/>Latus i m # 1097, 1, 0. <lb/>Et erit angulus e m i # 19 gr. 1`, 40``. <lb/>Et angulus e i m # 13 gr. 45`, 20``. <lb/></note> <p> <s xml:id="echoid-s9318" xml:space="preserve">Adeoque ſecundum hanc menſuram eſt diſtantia inter Leidam & </s> <s xml:id="echoid-s9319" xml:space="preserve"><lb/>Soeterwoudam 1097 perticarum, 1 pedis, & </s> <s xml:id="echoid-s9320" xml:space="preserve">0 {17/100} pollicis: </s> <s xml:id="echoid-s9321" xml:space="preserve">aſt Snel-<lb/>lius hanc diſtantiam antea determinavit 1092, 3, 3, differentia eſt <lb/>4 perticarum 7 pedum, 6 pollicum cum fractione quadam, quæ <lb/>differentia admodum notabilis eſt: </s> <s xml:id="echoid-s9322" xml:space="preserve">Commendat vero Snellius fiden-<lb/>dum eſſe maxime ultimæ menſuræ, quia capta eſt ſupra glaciem <lb/>lævigatiſſimam diſtantia a e, repetitis vicibus & </s> <s xml:id="echoid-s9323" xml:space="preserve">magnâ cum curâ. <lb/></s> <s xml:id="echoid-s9324" xml:space="preserve">Quoniam igitur prima baſis totius operis multo longior depre-<lb/>henditur, quam Snellius eam primo poſuerat, non poterant <lb/>non diſtantiæ reliquorum locorum multum diſcrepare a menſu-<lb/>ra ante ſtabilita: </s> <s xml:id="echoid-s9325" xml:space="preserve">Tuto igitur ponemus diſtantiam i m eſſe pertica <lb/>rum 1097, 1, 0.</s> <s xml:id="echoid-s9326" xml:space="preserve"/> </p> <pb o="400" file="0414" n="414" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div296" type="section" level="1" n="296"> <head xml:id="echoid-head360" xml:space="preserve">IV. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head361" style="it" xml:space="preserve">Triangulum a i u, jungens Leidam, Voorſchoten, locumque <lb/>aſſumtum in Problemate I.</head> <note position="right" xml:space="preserve"> <lb/>Eſt angulus m i u obſervatus # 45 gr. 21`. <lb/>Eſt angulus e i m per III Problema # 13 gr 45`, 20``. <lb/>Eſt e i a angulus per I Problema # 35 gr 53`. <lb/>Adeoque eſt angulus m i a # 22 gr. 7`, 40``. <lb/>Hinc erit a i u # 23 gr. 13`, 20``. <lb/>Eſt quoque in Probl. I. angulus i a e # 54 gr. 36`. <lb/>Adeoque angulus i a u # 125 gr. 24`. <lb/>Et angulus i u a # 31 gr. 22`, 40``. <lb/>Datur autem latus i a in I Probl. # 810, 3, 6. <lb/>Ex quibus eruitur i u diſtantia inter Leidam & \\ Voorſchoten # 1268. 6, 3. <lb/></note> </div> <div xml:id="echoid-div297" type="section" level="1" n="297"> <head xml:id="echoid-head362" xml:space="preserve">V. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head363" style="it" xml:space="preserve">Diſtantia inter Leidam & Voor ſchoten alio modo quæſita, <lb/>ope Trianguli A E I nectentis Leidam, Soeterwou-<lb/>dam & Voorſchoten Tab. XIV. fig. 4.</head> <note position="right" xml:space="preserve"> <lb/>Eſt angulus E A I obſervatus # 77 gr. 10, 30``. <lb/>Angulus A I E obſervatus eſt # 57 gr. 28`, 30``. <lb/>Et angulus A E I # 45 gr. 21`, 0. <lb/>Datur latus A E per 3 Problema # 1097, 1, 0. <lb/>Unde eruitur latus E I, diſtantia inter Leidam & \\ Voorſchoten # 1268, 6, 2. <lb/></note> <p> <s xml:id="echoid-s9327" xml:space="preserve">Quoniam hæc diſtantia adeo accurate congruit cum ea quæ Pro-<lb/>blemate ſuperiori inventa fuit, ſequitur menſuras ambas fuiſſe ac-<lb/>curatiſſime captas, aſſignatamque diſtantiam eſſe veram: </s> <s xml:id="echoid-s9328" xml:space="preserve">quamob-<lb/>rem in hac erraverat Snellius, eam ponendo 1263, 6, 8. </s> <s xml:id="echoid-s9329" xml:space="preserve">minorem <lb/>verâ 4, 9, 5.</s> <s xml:id="echoid-s9330" xml:space="preserve"/> </p> <pb o="401" file="0415" n="415" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div298" type="section" level="1" n="298"> <head xml:id="echoid-head364" xml:space="preserve"><emph style="sc">Problema</emph> VI.</head> <head xml:id="echoid-head365" style="it" xml:space="preserve">Tab. XIV. fig. 2. Triangulum, imu, conjungens Leidam, <lb/>Soeterwoudam & Voorſchoten.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus m i u # 45 gr. 21`. <lb/>Tum obſervatus eſt angulus i m u # 57 gr. 28`, 30``. <lb/>Adeoque eſt angulus i u m # 77 gr. 10`, 30``. <lb/>Datur ex Problemate III latus i m # 1097, 1, 0. <lb/>Adeoque invenitur m u diſtantia inter Soeterwou- \\ dam & Voorſchooten # 925, 6, 0. <lb/></note> </div> <div xml:id="echoid-div299" type="section" level="1" n="299"> <head xml:id="echoid-head366" xml:space="preserve"><emph style="sc">Problema</emph> VII.</head> <head xml:id="echoid-head367" style="it" xml:space="preserve">Diſtantia inter Soeterwoudam & Voor ſchooten alio modo quæſita.</head> <p> <s xml:id="echoid-s9331" xml:space="preserve">Fuit hæc diſtantia quæſita Anno 1622. </s> <s xml:id="echoid-s9332" xml:space="preserve">tertio Februarii, quando <lb/>aſperrimâ hyeme, & </s> <s xml:id="echoid-s9333" xml:space="preserve">aquarum ſupra agrorum & </s> <s xml:id="echoid-s9334" xml:space="preserve">paſcuorum plani-<lb/>tiem inundatione per conglaciatum æquor accuratiſſima eſſet cate-<lb/>næ Geodæticæ explicatio, & </s> <s xml:id="echoid-s9335" xml:space="preserve">Quadrante ac Semicirculo adhibito <lb/>aſſumta fuit nova baſis, ut exploraretur, an diſtantia in Problema-<lb/>te VI eruta, foret vera.</s> <s xml:id="echoid-s9336" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Tab. XIV. fig. 5. Aſſumta fuit baſis, e o, Delphum verſus in- \\ ter Soeterwoudam & Voorſchooten, erat accurate menſurata Perti- \\ carum. # 250, 0, 0. <lb/>Obſervatus eſt angulus a e o # 78 gr. 38`. <lb/>Tum a o e angulus # 70 gr. 34. <lb/>Unde cognoſcitur latus a o # 478, 6, 6. <lb/>Eſt angulus i e o obſervatus # 40 gr. 2`, 35``. <lb/>Et angulus i o e obſervatus # 119 gr. 44`. <lb/>Unde cognoſcitur latus i o # 461, 6, 6. <lb/>Datis his binis lateribus a o, i o, & angulo inter- \\ cepto a o i, 159 gr. 42`. ope regularum Trigonometri- \\ carum eruitur latus a i diſtantia inter Voorſchooten & \\ Soeterwoudam # 925, 6, 0. <lb/>Et angulus o a i # 9 gr. 57`, 53``. <lb/>Et angulus o i a # 10 gr. 20`, 7``. <lb/></note> <pb o="402" file="0416" n="416" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div300" type="section" level="1" n="300"> <head xml:id="echoid-head368" xml:space="preserve"><emph style="sc">Problema</emph> VIII.</head> <head xml:id="echoid-head369" style="it" xml:space="preserve">Tab. XIV. fig. 3. Triangulum A E I, Leida, Soeterwouda, <lb/>Waſſenaria.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus E A I # 63 gr. 57`. <lb/>Angulus A E I # 84 gr. 5`. <lb/>Adeoque Angulus A I E eſt # 31 gr. 58`. <lb/>Datur latus A E ex III Problemate # 1097, 1, 0. <lb/>Unde eruitur latus A I diſtantia Soeterwoudæ & \\ Waſſenariæ # 2061, 0, 4. <lb/></note> </div> <div xml:id="echoid-div301" type="section" level="1" n="301"> <head xml:id="echoid-head370" xml:space="preserve"><emph style="sc">Problema</emph> IX.</head> <head xml:id="echoid-head371" style="it" xml:space="preserve">Tab. XIV. fig. 3. Triangulum E A I, diſtantia Leidæ & <lb/>Waſſenariæ quæſita.</head> <note position="right" xml:space="preserve"> <lb/>Datur latus A E # 1097, 1, 0. <lb/>Angulus A I E # 31 gr. 58`. <lb/>Angulus E A I # 63 gr. 57`. <lb/>Unde eruitur latus I E diſtantia Leidæ & Waſſena- \\ riæ # 1861, 5, 8. <lb/></note> </div> <div xml:id="echoid-div302" type="section" level="1" n="302"> <head xml:id="echoid-head372" xml:space="preserve"><emph style="sc">Problema</emph> X.</head> <head xml:id="echoid-head373" style="it" xml:space="preserve">Tab. XIV. fig. 6. Triangulum A E I, Leida, Waſſenaria, <lb/>Voorſchooten.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus E A I # 38 gr. 54`. <lb/>Datur latus A I in V Problemate # 1268, 6, 3. <lb/>Datur latus A E in IX. Problemate # 1861, 5, 8. <lb/>Ex quibus eruitur latus E I, intervallum Waſſena- \\ riæ a Voorſchooten # 1179, 4, 9. <lb/></note> <pb o="403" file="0417" n="417" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div303" type="section" level="1" n="303"> <head xml:id="echoid-head374" xml:space="preserve"><emph style="sc">Problema</emph> XI.</head> <head xml:id="echoid-head375" style="it" xml:space="preserve">Tab. XV. fig. 10. Triangulum aie, Leida, Noortvicum, <lb/>Voorſcbooten.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus a i e # 19 gr. 57?. <lb/>Angulus i a e # 38 gr. 58?. <lb/>Angulus i e a # 121 gr. 5?. <lb/>Datur latus e a in V problemate # 1268, 6, 3. <lb/>Hinc eruitur i e diſtantia inter Noortvicum & Lei- \\ dam # 2338, 2, 2. <lb/></note> </div> <div xml:id="echoid-div304" type="section" level="1" n="304"> <head xml:id="echoid-head376" xml:space="preserve">XII. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head377" style="it" xml:space="preserve">Tab. XV. fig. 9. Diſtantia inter Leidam & Noortvicum alio <lb/>modo quæſita.</head> <note position="right" xml:space="preserve"> <lb/>Aſſumta fuit baſis a e # 471, 5, 0. <lb/>Obſervatus fuit angulus o e a # 88 gr. 26?. <lb/>Angulus o a e # 68 gr. 50?. <lb/>Angulus a o e # 22 gr. 44?. <lb/>Unde eruitur latus a o # 1219, 6, 4. <lb/>Et latus o e # 1137, 7, 1. <lb/>In Triangulo a e u obſervatus eſt angulus u e a # 91 gr. 56?. <lb/>Angulus u a e # 67 gr. 4?. <lb/>Angulus a u e # 21 gr. 0. <lb/>Unde eruitur latus u e # 1210, 5, 0. <lb/>Datis vero lateribus o e, u e & angulo intercepto \\ oeu, datur recta ou # 2338, 0, 0 <lb/></note> </div> <div xml:id="echoid-div305" type="section" level="1" n="305"> <head xml:id="echoid-head378" xml:space="preserve">XIII. <emph style="sc">Problema</emph></head> <head xml:id="echoid-head379" style="it" xml:space="preserve">Tab. XV. fig. 11. Triangulum A E B, Haga, Leida, <lb/>Noortvicum.</head> <note position="right" xml:space="preserve"> <lb/>Obſervatus eſt angulus A E B # 106 gr. 3?. <lb/></note> <pb o="404" file="0418" n="418" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Angulus E B A # 48 gr. 42?. <lb/>Angulus E A B # 25 gr. 15?. <lb/>Datur latus E B in XI Problemate # 2338, 2, 2. <lb/>Unde eruitur latus A E diſtantia inter Hagam & \\ Leidam # 4118, 0, 7. <lb/></note> </div> <div xml:id="echoid-div306" type="section" level="1" n="306"> <head xml:id="echoid-head380" xml:space="preserve">XIV. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head381" style="it" xml:space="preserve">Eadem diſtantia inter Hagam & Leidam aliter tentata.</head> <note position="right" xml:space="preserve"> <lb/>Tab. XV. fig. 12. Eſt angulus I A E obſervatus # 60 gr. 32?. <lb/>Angulus I E A # 104 gr. 32?. <lb/>Unde tertius A I E datur # 14 gr. 56?. <lb/>Latus A E intercapedo inter Leidam & Soeterwou- \\ dam eſt # 1097, 1, 017. <lb/>Atque ideo per Triangulorum doctrinam dabitur la- \\ tus A I # 4120, 8, 1. <lb/>In ſuperiori problemate eadem diſtantia deprehen- \\ ditur # 4118, 0, 7. <lb/>Adeoque eſt differentia # 2, 7, 4. <lb/>Quæ quidem parva eſt, attamen nulla debuerat deprehendi, quo- \\ niam hæc diſtantia baſis eſt plurium aliarum menſurarum, priori cal- \\ culo magis fidendum erit quam huic, ob exiguitatem anguli A I E. \\ ideoque in poſterum aſſumam diſtantiam inter Hagam & Lei- \\ dam eſſe # 4118, 0, 7. <lb/></note> </div> <div xml:id="echoid-div307" type="section" level="1" n="307"> <head xml:id="echoid-head382" xml:space="preserve">XV. <emph style="sc">Problema.</emph></head> <head xml:id="echoid-head383" style="it" xml:space="preserve">Triangulum A E S nectens Leidam, Hagam, Goudam.</head> <note position="right" xml:space="preserve"> <lb/>Tab. X V I. Datur A E diſtantia inter Hagam & \\ Leidam # 4118 0, 7. <lb/>Ex obſervatione datur angulus A E S # 97 gr. 11?. <lb/>Et angulus A S E # 32 gr. 25?. <lb/>Denique angulus E A S # 50 gr. 24?. <lb/>Hinc diſtantia inter Leidam & Goudam # 5918, 9, 7. <lb/>Inter Hagam & Goudam # 7621, 5, 6. <lb/></note> <pb o="405" file="0419" n="419" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div308" type="section" level="1" n="308"> <head xml:id="echoid-head384" xml:space="preserve"><emph style="sc">Problema</emph> XVI.</head> <head xml:id="echoid-head385" style="it" xml:space="preserve">Triangulum E S R. Leida, Gouda, Dordracum.</head> <note position="right" xml:space="preserve"> <lb/>Datur per Probl. X V. diſtantia inter Leidam & \\ Goudam # 5918, 9, 7. <lb/>Ex obſervatis autem datur angulus R E S # 25 gr. 49?. <lb/>Angulus S R E # 25 gr. 49?. <lb/>Angulus R S E # 128 gr. 22?. <lb/>Unde per doctrinam Triangulorum eruitur diſtantia \\ inter Goudam & Dordracum # 5918, 9. 7. <lb/>Inter Leidam & Dordracum # 10663, 7. <lb/></note> </div> <div xml:id="echoid-div309" type="section" level="1" n="309"> <head xml:id="echoid-head386" xml:space="preserve"><emph style="sc">Problema</emph> XVII.</head> <head xml:id="echoid-head387" style="it" xml:space="preserve">Triangulum E A R, Leida, Haga, Dordracum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XIII datur diſtantia inter Hagam & \\ Leidam # 4118, 0, 7. <lb/>Ex obſervatis autem angulus E A R # 85 gr. 51?. <lb/>Angulus A E R # 71 gr. 31?. <lb/>Angulus A R E # 22 gr. 38?. <lb/>Unde latus E R diſtantia inter Dordracum & Lei- \\ dam # 10672, 7. <lb/></note> <p> <s xml:id="echoid-s9337" xml:space="preserve">Quæ major eſt quam inventa in problemate XVI, quare angulus <lb/>E A R major fuit obſervatus, quam revera eſt, poſitâ priori menſurâ <lb/>bonâ: </s> <s xml:id="echoid-s9338" xml:space="preserve">error irrepere in obſervationem Snellii potuit, quia Dordraco <lb/>Hagam non conſpicere ipſi licuit.</s> <s xml:id="echoid-s9339" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Eruitur vero diſtantia inter Hagam & Dordracum # 10148, 8. <lb/></note> </div> <div xml:id="echoid-div310" type="section" level="1" n="310"> <head xml:id="echoid-head388" xml:space="preserve"><emph style="sc">Problema</emph> XVIII.</head> <head xml:id="echoid-head389" style="it" xml:space="preserve">Triangulum A E F, Haga, Leida, Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XIII. Datur diſtantia inter Hagam Lei- \\ damque E A # 4118, 0, 7. <lb/>Ex obſervatis angulus E A F # 90 gr. 18?. <lb/></note> <pb o="406" file="0420" n="420" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Angulus A E F # 53 gr. 40?. <lb/>Unde reliquus A F E dabitur # 36 gr. 2?. <lb/>Hinc per doctrinam Triangulorum dabitur quoque \\ A F diſtantia inter Hagam & Rotterodamum # 5639, 1. <lb/>Et E F diſtantia inter Leidam & Rotterodamum # 7000, 2, 9. <lb/></note> <p> <s xml:id="echoid-s9340" xml:space="preserve">I n editione Snellii angulus E A F ponitur 39 gr. </s> <s xml:id="echoid-s9341" xml:space="preserve">53?</s> <s xml:id="echoid-s9342" xml:space="preserve">. & </s> <s xml:id="echoid-s9343" xml:space="preserve">A F E 86 gr. <lb/></s> <s xml:id="echoid-s9344" xml:space="preserve">27?</s> <s xml:id="echoid-s9345" xml:space="preserve">. hos angulos retinuit Caſſini ut veros, iiſque innixus ſupputan-<lb/>do deprehendit Snellium erraſſe, diſtantiam enim E F fore 6386 <lb/>perticarum & </s> <s xml:id="echoid-s9346" xml:space="preserve">A F, 5154 perticarum: </s> <s xml:id="echoid-s9347" xml:space="preserve">cum igitur nimia ſit differen-<lb/>tia inter numerum Snellianum 6972, 3, ſuumque 6386. </s> <s xml:id="echoid-s9348" xml:space="preserve">concluſit, <lb/>& </s> <s xml:id="echoid-s9349" xml:space="preserve">recte, angulos fuiſſe male hic poſitos a Snellio, quod veriſſi-<lb/>mum eſt, ideo Snellius in iterata obſervatione angulos aliter po-<lb/>ſuit, quos hic aſſumſimus.</s> <s xml:id="echoid-s9350" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div311" type="section" level="1" n="311"> <head xml:id="echoid-head390" xml:space="preserve"><emph style="sc">Problema.</emph> XIX.</head> <head xml:id="echoid-head391" style="it" xml:space="preserve">Triangulum E S F, Leida, Gouda, Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XV datur E S diſtantia inter Leidam \\ & Goudam # 5918, 9, 7. <lb/>Ex obſervatis autem angulus S E F # 43 gr. 32?. <lb/>Angulus E S F # 80 gr. 0?. <lb/>Unde dabitur angulus E F S # 56 gr. 28?. <lb/>Atque inde per Triangulorum doctrinam dabitur di- \\ ſtantia inter Goudam & Rotterodamum S F # 4890, 8, 6. <lb/></note> </div> <div xml:id="echoid-div312" type="section" level="1" n="312"> <head xml:id="echoid-head392" xml:space="preserve"><emph style="sc">Problema</emph> XX.</head> <head xml:id="echoid-head393" style="it" xml:space="preserve">Triangulum E S V. Leida, Vltrajectum, Gouda.</head> <note position="right" xml:space="preserve"> <lb/>Diſtantia inter Leidam & Goudam E S datur per \\ Problema XV. # 5918, 9, 7. <lb/>Et ex obſervatis angulus E V S # 27 gr. 45?. <lb/>Angulus E S V # 114 gr. 9?, 30?. <lb/>Angulus S E V # 38 gr. 5?, 30?. <lb/>Unde per doctrinam Triangulorum dabitur diſtan-<lb/></note> <pb o="407" file="0421" n="421" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>tia E V inter Trajectum & Leidam # 11589, 8. <lb/>Et V S inter Goudam & Trajectum # 7842, 4. <lb/></note> <p> <s xml:id="echoid-s9351" xml:space="preserve">Hos angulos accuratiſſime menſuravi, deprehendique eos diſcre-<lb/>pare ab iis, quos Snellius poſuit, quod factum videtur, quia quando <lb/>Leida e Turri Trajectina conſpicitur, duas ſibi vicinas turres ex-<lb/>hibet, quarum una pro altera facile ſumitur, imprimis ſi cælum non <lb/>fuerit admodum ſerenum, qui error ope Teleſcopiorum, quibus <lb/>Quadrans noſter inſtructus eſt, evitatus facile fuit.</s> <s xml:id="echoid-s9352" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div313" type="section" level="1" n="313"> <head xml:id="echoid-head394" xml:space="preserve"><emph style="sc">Problema</emph> XXI.</head> <head xml:id="echoid-head395" style="it" xml:space="preserve">Triangulum E R V, connectens Trajectum, Leidam, <lb/>Dordracum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XVI. datur diſtantia inter Leidam & \\ Dordracum # 10663, 7. <lb/>Et ex obſervatis angulus R E V # 63 gr. 23?. <lb/>Angulus E V R # 54 gr. 25?. <lb/>Angulus E R V # 62 gr. 12?. <lb/>Unde per doctrinam Triangulorum invenietur E V \\ diſtantia inter Leidam & Ultrajectum # 11589, 8. <lb/>Tum V R inter Dordracum & Trajectum # 11749, 9. <lb/>Non differt diſtantia inter Leidam & Trajectum in \\ hoc & præcedenti Problemate, eſtque exigua diffe- \\ rentia inter noſtram & Snellianam menſuram, quæ eſt # 11584, 0. <lb/></note> <p> <s xml:id="echoid-s9353" xml:space="preserve">Aſt ingens eſt diſcrepantia inter Dordracum & </s> <s xml:id="echoid-s9354" xml:space="preserve">Ultra-<lb/>jectum, ultra 100 perticarum.</s> <s xml:id="echoid-s9355" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div314" type="section" level="1" n="314"> <head xml:id="echoid-head396" xml:space="preserve"><emph style="sc">Problema.</emph> XXII.</head> <head xml:id="echoid-head397" style="it" xml:space="preserve">Triangulum E M V. Leida, Oudewatera, Vltrajectum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XX & XXI datur E V diſtantia # 11589, 8. <lb/>Et ex obſervatis angulus M E V # 20 gr. 26?. <lb/>Angulus E V M # 34 gr. 18?. <lb/>Et angulus E M V # 125 gr. 16. <lb/></note> <pb o="408" file="0422" n="422" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Unde eruitur V M diſtantia inter Ultrajectum & Ou- \\ dewateram # 4965, 2, 7. <lb/>Et E M diſtantia inter Leidam & Oudewateram # 7980, 2, 8. <lb/></note> </div> <div xml:id="echoid-div315" type="section" level="1" n="315"> <head xml:id="echoid-head398" xml:space="preserve"><emph style="sc">Problema</emph> XXIII.</head> <head xml:id="echoid-head399" style="it" xml:space="preserve">Triangulum E M S. Leidam, Oudewateram & Gou-<lb/>dam connectens.</head> <note position="right" xml:space="preserve"> <lb/>Datur diſtantia E S inter Leidam & Goudam per \\ Problema XV # 5918, 9, 7. <lb/>Obſervatur angulus S E M # 17 gr. 3`. <lb/>Angulus E M S # 36 gr. 53`. <lb/>Angulus E S M # 126 gr. 4`. <lb/>Quare datur diſtantia S M inter Oudewateram & \\ Goudam # 2891, 5, 6. <lb/></note> </div> <div xml:id="echoid-div316" type="section" level="1" n="316"> <head xml:id="echoid-head400" xml:space="preserve"><emph style="sc">Problema</emph> XXIV.</head> <head xml:id="echoid-head401" style="it" xml:space="preserve">In Triangulo A E I Haga, Leida, Harlemum.</head> <note position="right" xml:space="preserve"> <lb/>Ex Problemate XIII datur A E diſtantia inter Ha- \\ gam & Leidam # 4118, 0, 7. <lb/>Et ex obſervatis augulus A E I # 147 gr. 19`. <lb/>Itemque angulus E A I # 20 gr. 45`. <lb/>Unde reliquus A I E datur # 11 gr. 56`. <lb/>Quare invenitur diſtantia I E inter Harlemum & \\ Leidam # 7055, 9, 4. <lb/>Inter Hagam & Harlemum # 19754, 3. <lb/></note> </div> <div xml:id="echoid-div317" type="section" level="1" n="317"> <head xml:id="echoid-head402" xml:space="preserve"><emph style="sc">Problema</emph> XXV.</head> <head xml:id="echoid-head403" style="it" xml:space="preserve">Tab. XV. fig. 15. Diſtantia inter Harlemum & Leidam <lb/>alio modo quæſita in Triangulo I A E.</head> <note position="right" xml:space="preserve"> <lb/>Datur per Problema XI diſtantia inter Leidam & \\ Noortvicum # 2338, 2, 2. <lb/></note> <pb o="409" file="0423" n="423" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Ex obſervatis angulus I A E # 121 gr. 7`. <lb/>Angulus A E I # 42 gr. 24`. <lb/>Unde angulus A I E # 16 gr. 29`. <lb/>Atque eruitur latus I E ſive diſtantia inter Harlemum \\ & Leidam # 7053, 4, 8. <lb/>Adeoque differentia inter ambas diſtantias in hoc \\ & in Problemate XXIV inventa admodum parva eſt, \\ tutoque aſſumere licebit diſtantiam inter Harlemum \\ & Leidam eſſe # 7053, 4, 8. <lb/>Snellius aliam adhuc inſtituens Gæodæſiam, deter- \\ minat eam diſtantiam eſſe # 7049, 2. <lb/>Atque poſtea adhuc ex alio calculo # 7051, 1. <lb/></note> <p> <s xml:id="echoid-s9356" xml:space="preserve">Quamobrem mediam ponam inter Snellianam & </s> <s xml:id="echoid-s9357" xml:space="preserve">inventam in <lb/>Problemate XXIV. </s> <s xml:id="echoid-s9358" xml:space="preserve">quæ eſt hujus Problematis XXV.</s> <s xml:id="echoid-s9359" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div318" type="section" level="1" n="318"> <head xml:id="echoid-head404" xml:space="preserve"><emph style="sc">Problema</emph> XXVI.</head> <head xml:id="echoid-head405" style="it" xml:space="preserve">Tab. XVI. Triangulum O E V, Amſtelodamum, Leida, <lb/>Vltrajectum.</head> <note position="right" xml:space="preserve"> <lb/>Datur per Problema XX diſtantia E V inter Leidam \\ & Ultrajectum # 11589, 8. <lb/>Et ex obſervatis angulus O E V # 50 gr. 40`. <lb/>Angulus O V E # 54 gr. 10`. <lb/>Unde reliquus E O V datur # 75 gr. 10`. <lb/>Quare diſtantia O E inter Amſtelodamum & Lei- \\ dam erit # 9750, 0, 4. <lb/>Et O V diſtantia inter Amſtelodamum & Ultraje- \\ ctum. # 9280, 6, 5. <lb/></note> <pb o="410" file="0424" n="424" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div319" type="section" level="1" n="319"> <head xml:id="echoid-head406" xml:space="preserve"><emph style="sc">Problema</emph> XXVII.</head> <head xml:id="echoid-head407" style="it" xml:space="preserve">Triangulum E I V, Leida, Harlemum, Vltra-<lb/>jectum.</head> <note position="right" xml:space="preserve"> <lb/>Ex Problemate XX diſtantia E V inter Leidam & \\ Ultrajectum datur # 11589, 8. <lb/>Ex obſervatis autem angulus V E I # 77 gr. 51. 30``. <lb/>Angulus V I E # 67 gr. 51. <lb/>Et angulus E V I datur # 34 gr. 17`, 30``. <lb/>Unde eruitur I V diſtantia inter Harlemum & Ul- \\ trajectum # 12271, 1. <lb/>Atque diſtantia E I inter Harlemum & Leidam # 7055, 5, 4. <lb/></note> <p> <s xml:id="echoid-s9360" xml:space="preserve">Quæ diſtantia eſt proxime eadem ac in Proble-<lb/>mate XXIV inventa eſt.</s> <s xml:id="echoid-s9361" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div320" type="section" level="1" n="320"> <head xml:id="echoid-head408" xml:space="preserve"><emph style="sc">Problema</emph> XXVIII.</head> <head xml:id="echoid-head409" style="it" xml:space="preserve">Triangulum E I O, Leida, Harlemum, Amſtelo-<lb/>damum.</head> <note position="right" xml:space="preserve"> <lb/>Datur per Problema XXV diſtantia inter Leidam & \\ Harlemum # 7053, 4. 8. <lb/>Obſervatur Angulus O E I # 27 gr. 11`. <lb/>Et angulus E O I # 43 gr. 18. <lb/>Et angulus E I O # 109 gr. 31`. <lb/>Quare per doctrinam Triangulorum datur I O di- \\ ſtantia inter Harlemum & Amſtelodamum # 4698, 4, 8. <lb/>Angulos hos iteratis vicibus menſuravit inſtrumentis Snellius, \\ unde alios conſtituit, quam quidem in antiquo codice, in quo alia \\ methodo eos ſupputando deduxerat, & ideo magna inter hanc & \\ primam Snellianam menſuram intercedit differentia, exigua modo \\ inter noſtram & ultimam Snellianam, quæ eſt # 4695, 6. <lb/></note> <pb o="411" file="0425" n="425" rhead="DE MAGNITUDINE TERRÆ"/> </div> <div xml:id="echoid-div321" type="section" level="1" n="321"> <head xml:id="echoid-head410" xml:space="preserve"><emph style="sc">Problema</emph> XXIX.</head> <head xml:id="echoid-head411" style="it" xml:space="preserve">Triangulum I O ?, Harlemum, Amſtelodamum <lb/>Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>In Problemate XXVIII datur I O diſtantia inter Har- \\ lemum & Aſtelodamum # 4698, 4, 8. <lb/>Ex obſervatis autem angulus I O ? # 67 gr. 36`. <lb/>Angulus O I ? # 78 gr. 2`. <lb/>Angulus O ? I # 34 gr. 22`. <lb/>Unde per doctrinam Triangulorum dabitur O ? di- \\ ſtantia inter Amſtelodamum & Alcmariam # 8142, 5, 8. <lb/>Et I ? diſtantia inter Harlemum & Alcmariam # 7695, 4, 2. <lb/></note> </div> <div xml:id="echoid-div322" type="section" level="1" n="322"> <head xml:id="echoid-head412" xml:space="preserve"><emph style="sc">Problema</emph> XXX.</head> <head xml:id="echoid-head413" style="it" xml:space="preserve">Triangulum E O ? Leida, Amſtelodamum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>In Problemate XXVI datur E O diſtantia inter Lei- \\ dam & Amſtelodamum # 9750, 0, 4. <lb/>Et in Problemate XXIX datur O ? diſtantia inter \\ Amſtelodamum & Alcmariam # 8142, 5, 8. <lb/>Ex obſervatione autem datur angulus I O ? # 67 gr. 36`. <lb/>Et angulus E O I # 43 gr. 18`. <lb/>Unde totus E O ? datur # 110 gr. 54`. <lb/>Hinc ope doctrinæ Triangulorum, datis cruribus & \\ angulo ab ipſis comprehenſo, datur baſis E ? diſtantia \\ inter Leidam & Alcmariam. # 14730, 5. <lb/>Angulus O E ? # 31 gr. 0, 30``. <lb/>Angulus E ? O # 38 gr. 5`, 30``. <lb/></note> <pb o="412" file="0426" n="426" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div323" type="section" level="1" n="323"> <head xml:id="echoid-head414" xml:space="preserve"><emph style="sc">Problema</emph> XXXI.</head> <head xml:id="echoid-head415" style="it" xml:space="preserve">Triangulum M V L, Oude-Watera, Vltrajectum, <lb/>Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Ex Problemate XXII. datur V M diſtantia inter \\ Ultrajectum & Oudewateram # 4965, 2, 7. <lb/>Ex obſervatis autem angulus V M L # 65 gr. 23`. <lb/>Et angulus M V L # 82 gr. 30`. <lb/>Unde reliquus V L M # 32 gr. 7`. <lb/>Quare per doctrinam Triangulorum dabitur L M, \\ diſtantia inter Oude-Wateram & Bommeliam # 9259. 6, 1. <lb/>Et V L diſtantia inter Trajectum & Bommeliam # 8490. 6, 4. <lb/></note> </div> <div xml:id="echoid-div324" type="section" level="1" n="324"> <head xml:id="echoid-head416" xml:space="preserve"><emph style="sc">Problema</emph> XXXII.</head> <head xml:id="echoid-head417" style="it" xml:space="preserve">Trangulum R V L, Dordracum, Trajectum, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>In Problemate XXI, datur V R diſtantia inter \\ Dordracum & Trajectum # 11749, 9. <lb/>Ex obſervatis autem angulus R V L # 62 gr. 16`. <lb/>Angulus V R L # 44 gr. 4`. <lb/>Unde reliquus angulus V L R # 73 gr. 40`. <lb/>Hinc ope doctrinæ Triangulorum invenietur R L \\ diſtantia inter Dordracum & Bommeliam. # 10812, 7. <lb/></note> </div> <div xml:id="echoid-div325" type="section" level="1" n="325"> <head xml:id="echoid-head418" xml:space="preserve"><emph style="sc">Problema</emph> XXXIII.</head> <head xml:id="echoid-head419" style="it" xml:space="preserve">Triangulum E V L. Leida, Trajectum, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Datur per Probl. XXI. E V diſtantia inter Leidam \\ & Trajectum # 11589, 8. <lb/>Datur per Probl. XXXI, V L diſtantia inter Tra- \\ jectum & Bommeliam # 8490, 6, 4. <lb/>Et ex obſervatis angulus E V L # 116 gr. 41`. <lb/></note> <pb o="413" file="0427" n="427" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Unde per doctrinam Triangulorum dabitur E L, \\ diſtantia inter Leidam & Bommeliam. # 17510, 2. <lb/></note> </div> <div xml:id="echoid-div326" type="section" level="1" n="326"> <head xml:id="echoid-head420" xml:space="preserve"><emph style="sc">Problema</emph> XXXIV.</head> <head xml:id="echoid-head421" style="it" xml:space="preserve">Triangulum ? E L, Alcmaria, Leida, Bommelia.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXX datur ? E diſtantia inter Lei- \\ dam & Alcmariam # 14730, 5. <lb/>Per Problema XXXIII datur E L diſtantia inter \\ Leidam & Bommeliam # 17510, 2. <lb/>Eſt angulus ? E O per Problema XXX # 31 gr. 0`;, 30``;. <lb/>Eſt angulus O E V per Probl. XXVI # 50 gr. 40`;. <lb/>Eſt angulus V E L per Probl. XXXIII # 27 gr. 1`;, 40``;. <lb/>Quare totus ? E L datur # 108, 42`;, 10``;. <lb/>Atque inde datis cruribus cum angulo ab ipſis com- \\ prehenſo, dabitur quoque per doctrinam Triangu- \\ lorum baſis ? L # 26240, 3. <lb/>Et angulus E L ? # 32 gr. 7`;, 20`;. <lb/>Et angulus L ? E # 39 gr. 10`;, 30``;. <lb/></note> </div> <div xml:id="echoid-div327" type="section" level="1" n="327"> <head xml:id="echoid-head422" xml:space="preserve"><emph style="sc">Problema</emph> XXXV.</head> <head xml:id="echoid-head423" style="it" xml:space="preserve">Triangulum R L V. Dordracum, Bommelia, Breda.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXII datur R L diſtantia inter Dor- \\ dracum & Bommeliam # 10812, 7. <lb/>Ex obſervatis autem angulus V R L # 72 gr. 10`;. <lb/>Et angulus L V R # 70 gr. 7`;. <lb/>Unde reliquus R L V # 37 gr. 43`;. <lb/>Atque inde R V diſtantia inter Dordracum & Bre- \\ dam # 7034. <lb/>Et L V diſtantia inter Bommeliam & Bredam # 10945. <lb/></note> <pb o="414" file="0428" n="428" rhead="DISSERTATIO"/> </div> <div xml:id="echoid-div328" type="section" level="1" n="328"> <head xml:id="echoid-head424" xml:space="preserve"><emph style="sc">Problema</emph> XXXVI.</head> <head xml:id="echoid-head425" style="it" xml:space="preserve">Triangulum R S F. Dordracum, Gouda, Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XVI datur R S diſtantia inter Gou- \\ dam & Dordracum # 5918, 9, 7. <lb/>Ex obſervatis autem angulus S R F # 54 gr. 0`;. <lb/>Angulus R S F # 48 gr. 5`;. <lb/>Unde reliquus R F S datur # 77 gr. 55`;. <lb/>Quare per doctrinam Triangulorum datur S F di- \\ ſtantia inter Goudam & Rotterodamum # 4899, 7. <lb/>Et R F diſtantia inter Dordracum & Rotterodamum # 4504, 2. <lb/></note> <p> <s xml:id="echoid-s9362" xml:space="preserve">Deprehenditur diſtantia inter Goudam & </s> <s xml:id="echoid-s9363" xml:space="preserve">Rotterodamum 9 per-<lb/>ticis longior, quam in Problemate XIX quod arguit errorem, ſed <lb/>exiguum, irrepſiſſe in calculum, quod ſacile evenire potuit quia <lb/>angulorum minuta ſecunda non accurate ope Inſtrumentorum ca-<lb/>pi poſſunt.</s> <s xml:id="echoid-s9364" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div329" type="section" level="1" n="329"> <head xml:id="echoid-head426" xml:space="preserve"><emph style="sc">Problema</emph> XXXVII.</head> <head xml:id="echoid-head427" style="it" xml:space="preserve">Triangulum R T F, Dordracum, Willemſtadium, <lb/>Rotterodamum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXVI datur R F diſtantia inter \\ Dordracum & Rotterodamum # 4504, 2. <lb/>Et ex obſervatis angulus F R T # 86 gr 19`;. <lb/>Angulus R T F # 41 gr. 10`;. <lb/>Unde reliquus R F T datur # 52 gr. 31`;. <lb/>Atque inde per doctrinam Triangulorum dabitur \\ R T diſtantia inter Dordracum & Willemſtadium # 5429, 8, 7. <lb/>Tum T F diſtantia inter Willemſtadium & Rottero- \\ damum # 6828, 5, 4. <lb/></note> <pb o="415" file="0429" n="429" rhead="DE MAGNITUDINE TERRÆ."/> </div> <div xml:id="echoid-div330" type="section" level="1" n="330"> <head xml:id="echoid-head428" xml:space="preserve"><emph style="sc">Problema</emph> XXXVIII.</head> <head xml:id="echoid-head429" style="it" xml:space="preserve">Triangulum R T V. Dordracum, Willemſtadium, Breda.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXVII datur R T diſtantia inter Dor- \\ dracum & Willemſtadium # 5429, 8, 7. <lb/>Ex obſervatis autem angulus T R V # 66 gr. 13`;. <lb/>Angulus R T V # 67 gr. 59`;. <lb/>Angulus R V T # 45 gr. 48`;. <lb/>Unde datur T V diſtantia inter Willemſtadium & Bre- \\ dam # 6930, 7, 8. <lb/>Et R V diſtantia inter Dordracum & Bredam # 7038, 6. <lb/>Quam in Problemate XXXV invenimus # 7034. <lb/>Adeoque parum diſcrepant. <lb/></note> </div> <div xml:id="echoid-div331" type="section" level="1" n="331"> <head xml:id="echoid-head430" xml:space="preserve"><emph style="sc">Problema</emph> XXXIX.</head> <head xml:id="echoid-head431" style="it" xml:space="preserve">Triangulum T V Q Willemſtadium, Breda, <lb/>Bergaad Somum.</head> <note position="right" xml:space="preserve"> <lb/>In Problemate XXXVIII datur V T diſtantia inter \\ Bredam & Willemſtadium # 6930, 7, 8. <lb/>Obſervatur angulus V T Q # 89 gr. 23`;. <lb/>Angulus T V Q # 43 gr. 23`;. <lb/>Angulus V Q T # 47 gr. 14`;. <lb/>Hinc invenitur T Q diſtantia inter Willemſtadium \\ & Bergam # 6484, 7, 1. <lb/>Et Q V diſtantia Bredæ & Bergæ # 9440, 3, 2. <lb/></note> </div> <div xml:id="echoid-div332" type="section" level="1" n="332"> <head xml:id="echoid-head432" xml:space="preserve"><emph style="sc">Problema</emph> XL.</head> <head xml:id="echoid-head433" style="it" xml:space="preserve">Triangulum R V Q Dordracum, Breda, Berga <lb/>ad Somum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXV, datur V R diſtantia inter Dor- \\ dracum & Bredam # 7034. <lb/>Per Problema XXXIX datur V Q diſtantia inter Bre-<lb/></note> <pb o="416" file="0430" n="430" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>dam & Bergam ad Somum # 9440, 3, 2`. <lb/>Obſervatur angulus Q V R # 89 gr. 31`;. <lb/>Unde per Triangulorum doctrinam datis cruribus & \\ angulo ab ipſis comprehenſo dabitur baſis Q R diſtan- \\ tia inter Dordracum & Bergam ad Somum # 11725, 1`. <lb/>Et angulus V R Q # 53 gr. 37`;, 15``;. <lb/>Et angulus V Q R # 36 gr. 51`;, 45``;. <lb/></note> </div> <div xml:id="echoid-div333" type="section" level="1" n="333"> <head xml:id="echoid-head434" xml:space="preserve"><emph style="sc">Problema</emph> XLI.</head> <head xml:id="echoid-head435" style="it" xml:space="preserve">Triangulum V L Q Breda, Bommelia, Berga ad <lb/>Somum.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXV datur latus V L diſtantia in- \\ ter Bredam & Bommeliam # 10945. <lb/>Per Problema XXXIX datur V Q diſtantia inter Bre- \\ dam & Bergam ad Somum # 9440, 3, 2. <lb/>Eſt angulus Q V L inter ambo crura # 159 gr. 37`;. <lb/>Angulus V L Q # 9 gr. 26`;. <lb/>Angulus V Q L # 10 gr. 57`;. <lb/>Unde datur diſtantia L Q inter Bommeliam & Bergam \\ ad Somum. # 20061, 3. <lb/></note> </div> <div xml:id="echoid-div334" type="section" level="1" n="334"> <head xml:id="echoid-head436" xml:space="preserve"><emph style="sc">Problema</emph> XLII.</head> <head xml:id="echoid-head437" style="it" xml:space="preserve">Triangulum E I ?, Leida, Harlemum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXV datur E I diſtantia inter Lei- \\ dam & Harlemum # 7053, 4, 8. <lb/>Per Problema XXIX datur I ? diſtantia inter Har- \\ lemum & Alcmariam # 7695, 4, 2. <lb/>Ex obſervatione ipſa angulus E I ? # 172. 27`;. <lb/>Quamobrem E ? diſtantia Alcmariæ & Leida dabi- \\ tur. # 14724. <lb/>Et angulus I E ? # 3 gr. 56`;, 15``;. <lb/>Et angulus E ? I # 3 gr. 36`;, 45``;. <lb/></note> <pb o="417" file="0431" n="431" rhead="DE MAGNITUDINE TERRÆ."/> <p> <s xml:id="echoid-s9365" xml:space="preserve">Datur differentia 6 perticarum in diſtantia E ? </s> <s xml:id="echoid-s9366" xml:space="preserve">inter Proble-<lb/>ma XXX & </s> <s xml:id="echoid-s9367" xml:space="preserve">hoc XLII. </s> <s xml:id="echoid-s9368" xml:space="preserve">ſed hæc eſt exigua.</s> <s xml:id="echoid-s9369" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div335" type="section" level="1" n="335"> <head xml:id="echoid-head438" xml:space="preserve"><emph style="sc">Problema</emph> XLIII.</head> <head xml:id="echoid-head439" style="it" xml:space="preserve">Triangulum E V ?. Leida, Trajectum, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XX datur E V diſtantia inter Leidam \\ & Ultrajectum # 11589. 8. <lb/>Per Problema XXX datur E ? diſtantia inter Lei- \\ dam & Alcmariam # 14730. 5. <lb/>Ex obſervatis autem datur per Problema XXVII an- \\ gulus V E I # 77 gr. 51`; 30``;. <lb/>Et per Problema XLII angulus ? E I # 3 gr. 56`;, 15``;. <lb/>Unde conſlatur totus V E ? # 81 gr. 47`;, 45``;. <lb/>Atque hinc datis cruribus cum angulo ab ipſis com- \\ prehenſo dabitur baſis V ?, diſtantia inter Trajectum \\ & Alcmariam # 17406. 7. <lb/>Et angulus E V ? # 56 gr. 56`;, 25``;. <lb/>Et angulus V ? E # 41 gr. 15`;, 49``;. <lb/></note> </div> <div xml:id="echoid-div336" type="section" level="1" n="336"> <head xml:id="echoid-head440" xml:space="preserve"><emph style="sc">Problema</emph> XLIV.</head> <head xml:id="echoid-head441" style="it" xml:space="preserve">Triangulum V L ?. Trajectum, Bommelia, Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XXXI datur V L diſtantia inter Bom- \\ meliam & Trajectum # 8490, 6, 4. <lb/>Et per Problema XLIII datur V ? diſtantia inter Tra- \\ jectum & Alcmariam # 17406, 7. <lb/>Ex obſervatis datur in Prob. XXXII. angulus L V R # 62 gr. 16`;. <lb/>Angulus R V E per Probl. XXI. # 54 gr. 25``;. <lb/>Angulus E V ? per Probl. XLIII # 56 gr. 56`;, 25``;. <lb/>Unde totus L V ? datur # 173 gr. 37`;, 25``;. <lb/>Et per doctrinam Triangulorum eruetur baſis L ? \\ diſtantia inter Bommeliam & Alcmariam # 25953, 8. <lb/>Et angulus V L ? # 4, 16`;, 12``;. <lb/></note> <pb o="418" file="0432" n="432" rhead="DISSERTATIO"/> <note position="right" xml:space="preserve"> <lb/>Angulus V ? L # 2, 5?, 22?. <lb/></note> </div> <div xml:id="echoid-div337" type="section" level="1" n="337"> <head xml:id="echoid-head442" xml:space="preserve"><emph style="sc">Problema</emph> XLV.</head> <head xml:id="echoid-head443" style="it" xml:space="preserve">Triangulum Q L ?. Berga ad Somum, Bommelia, <lb/>Alcmaria.</head> <note position="right" xml:space="preserve"> <lb/>Per Problema XLI datur latus Q L diſtantia inter \\ Bergam & Bommeliam # 20061, 3. <lb/>Per Problema XLIV. datur L ? # 25953, 8. <lb/>Per Problemata datur quoque angulus Q L ?, utpote \\ compoſitus ex angulo V L ? per Probl. XLIV # 4, 16?, 12?. <lb/>Qui ſubtrahatur ex V L R Prob. XXXII. # 73. 40?. 0. <lb/>Reliquus ? L R erit # 69. 23?. 48?. <lb/>In Probl. XXXV. eſt V L R # 37. 43?. 0. <lb/>In Probl. XLI eſt V L Q. # 9. 26?. 0. <lb/>Qui ſubtractus ex priori dat. # 28. 17. 0. <lb/>Unde totus Q L ? dabitur # 97 gr. 40?, 48?. <lb/>Datis igitur cruribus & angulo ab ipſis compre- \\ henſo dabitur baſis Q ? diſtantia inter Bergam ad \\ Somum & Alcmariam # 34952, 5. <lb/>Et angulus L Q ? # 47. 24?, 15?. <lb/>Et angulus L ? Q # 34. 54?. 57?. <lb/></note> </div> <div xml:id="echoid-div338" type="section" level="1" n="338"> <head xml:id="echoid-head444" xml:space="preserve"><emph style="sc">Problema</emph> XLVI.</head> <p> <s xml:id="echoid-s9370" xml:space="preserve">Cognita diſtantia inter Alcmariam & </s> <s xml:id="echoid-s9371" xml:space="preserve">Bergam ad Somum, inda-<lb/>gandum reſtabat, an hæc loca ſub eodem, an ſub diverſo Meri-<lb/>diano Terreſtri jacerent, ſi ſub diverſo, ex alterutro loco ducen-<lb/>da erat recta parallela circulo latitudinis, quæ partem Meridiani <lb/>interciperet: </s> <s xml:id="echoid-s9372" xml:space="preserve">cujus longitudo ex menſura hactenus tradita eruenda <lb/>fuit, tumque altitudine poli in utroque obſervata loco, ejus diffe-<lb/>rentia, Gradus, eorumve partem, continet, quorum longitudinem <lb/>antea in perticis determinavimus, atque hoc modo quantitas unius <lb/>Gradus Terreſtris eruitur, ſed hæc clarius ex ſequentibus intelli-<lb/>gentur.</s> <s xml:id="echoid-s9373" xml:space="preserve"/> </p> <pb o="419" file="0433" n="433" rhead="DE MAGNITUDINE TERRÆ."/> <note position="right" xml:space="preserve"> <lb/>Sit ? ? linea Meridiana tranſeunsper Leidam, ? ſpectet Septentrio- \\ nem, ? Meridiem: obſervatur Gouda S ab hac Ortum verſus declinare \\ ita ut angulus ? E S, ſit # 45 gr. 31?. <lb/>Obſervatus autem eſt angulus S E O # 88 gr. 21?. <lb/>Et per Problema XXX. angulus O E ? # 31 gr. 0?. 30?. <lb/>Quare totus ? E ? datur # 164 gr. 52?. 30?. <lb/>Unde etiam reliquus ? E ? # 15 gr. 7?. 30?. <lb/>Atque ideo demiſſa perpendiculari ? ? erit angu- \\ lus E ? ? # 74 gr. 52?. 30?. <lb/>Datur per Problema XXX. ? E # 14730, 5. <lb/>Dabitur igitur per doctrinam Triangulorum perpen- \\ dicularis ? ?, differentia Longitudinis # 3843, 5, 7. <lb/>Et E ? differentia Latitudinis # 14220. 2. <lb/>Rurſus cum detur per Problema XLV. ? Q # 34952. 5. <lb/>Datur etiam per Problema XLV. angulus \\ L ? Q # 34 gr. 54?. 57?. <lb/>Et per Problema XXXIV angulus L ? E # 39 gr. 10?. 30?. <lb/>Atque ideo reliquus E ? Q # 4 gr. 15?. 33?. <lb/>Qui additus ad ? ? E # 74 gr. 52?. 30?. <lb/>Dabit ? ? Q ſive ? Q ? # 79 gr. 8?. 3?. <lb/>Et angulum Q ? ? # 10 gr. 51?. 57?. <lb/>Atque ideo Q ? differentia Longitudinis # 6589. <lb/>Et ? ? differentia Latitudinis inter Alcmariam & \\ Bergam ad Somum erit # 34326, 7. <lb/>Sed poli Alcmariani altitudo eſt, ut Caſſini bene \\ obſervavit, # 52 gr. 38?, 34. <lb/>Et poli altitudo Bergæ ad Somum eſt # 51 gr. 28?, 47?. <lb/></note> <p> <s xml:id="echoid-s9374" xml:space="preserve">Quare differentia inter utraſque polorum altitudines eſt 1 Gradus, <lb/>9 Minutorum, 47 Secundorum.</s> <s xml:id="echoid-s9375" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9376" xml:space="preserve">Adeoque Gradus Terreſtris conſtabit perticis Rhenolandicis <lb/>29514, 2, 3. </s> <s xml:id="echoid-s9377" xml:space="preserve">Nam recta ? </s> <s xml:id="echoid-s9378" xml:space="preserve">? </s> <s xml:id="echoid-s9379" xml:space="preserve">vix differet a curva (uti Snellius ſu-<lb/>pra annotavit) ſecundum rigorem tamen Mathematicum foret ? </s> <s xml:id="echoid-s9380" xml:space="preserve">? <lb/></s> <s xml:id="echoid-s9381" xml:space="preserve">modo chorda portionis circuli 69 minutorum, 47 ſecundorum. </s> <s xml:id="echoid-s9382" xml:space="preserve">Eſt <lb/>hæc noſtra menſura major quam Snelliana prima & </s> <s xml:id="echoid-s9383" xml:space="preserve">ſecunda; </s> <s xml:id="echoid-s9384" xml:space="preserve">quippe <lb/>prima ponit ? </s> <s xml:id="echoid-s9385" xml:space="preserve">? </s> <s xml:id="echoid-s9386" xml:space="preserve">28500 perticarum, & </s> <s xml:id="echoid-s9387" xml:space="preserve">ſecunda 28488. </s> <s xml:id="echoid-s9388" xml:space="preserve">perticarum. </s> <s xml:id="echoid-s9389" xml:space="preserve"><lb/>Lubet autem noſtram comparare cum ea, quam Celeberrimi Geo- <pb o="420" file="0434" n="434" rhead="DISSERTATIO DE MAGNITUDINE TERRÆ."/> metræ Galliarum in Tractatu vocato. </s> <s xml:id="echoid-s9390" xml:space="preserve">Suite des Memoires de l’ Acad. <lb/></s> <s xml:id="echoid-s9391" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9392" xml:space="preserve">A°. </s> <s xml:id="echoid-s9393" xml:space="preserve">1718. </s> <s xml:id="echoid-s9394" xml:space="preserve">dederunt: </s> <s xml:id="echoid-s9395" xml:space="preserve">Hi in parte I. </s> <s xml:id="echoid-s9396" xml:space="preserve">Cap. </s> <s xml:id="echoid-s9397" xml:space="preserve"><emph style="sc">XIII</emph> uni Gradui ad-<lb/>ſcribunt 57097 Hexapedas Pariſinas. </s> <s xml:id="echoid-s9398" xml:space="preserve">Eſt pes Rhenolandicus minor <lb/>Pariſino, & </s> <s xml:id="echoid-s9399" xml:space="preserve">quidem ſecundum Picardum in divers Ouvrages des <lb/>Meſſieurs de l’ Acad. </s> <s xml:id="echoid-s9400" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9401" xml:space="preserve">eſſet pes Rhenolandicus ad Pariſinum, uti <lb/>696 ad 720. </s> <s xml:id="echoid-s9402" xml:space="preserve">ſive 138 ad 144, vel ſecundum alios uti 139 ad 144 unde fo-<lb/>rent 29514, 2, 3. </s> <s xml:id="echoid-s9403" xml:space="preserve">perticæ Rhenolandicæ æquales hexapedis Pariſinis <lb/>57033. </s> <s xml:id="echoid-s9404" xml:space="preserve">0, 8. </s> <s xml:id="echoid-s9405" xml:space="preserve">& </s> <s xml:id="echoid-s9406" xml:space="preserve">Magnitudo Gradus unius terreſtris, a nobis deter-<lb/>minata, foret 64 hexapedis minor, quam Geometræ Galli <lb/>poſuerunt: </s> <s xml:id="echoid-s9407" xml:space="preserve">Accuratiſſimus Picardus determinaverat Magnitudinem <lb/>37 hexapedis minorem, nempe 57060. </s> <s xml:id="echoid-s9408" xml:space="preserve">hexapedarum, a cujus menſu-<lb/>ra ſuperatur iterum noſtra quantitate tantum 27 hexapedarum; </s> <s xml:id="echoid-s9409" xml:space="preserve">quæ <lb/>profecto admodum parva eſt diſcrepantia: </s> <s xml:id="echoid-s9410" xml:space="preserve">Unde concludere licebit <lb/>ex hoc conſenſu qualicunque, hodiernos Geometras non multum â <lb/>veritate aberrare; </s> <s xml:id="echoid-s9411" xml:space="preserve">nam abſolute hanc illamve eſſe veram Magnitu-<lb/>dinem nemo in Geometriâ practicâ verſatus affirmare audebit: </s> <s xml:id="echoid-s9412" xml:space="preserve">Cum <lb/>angulorum minuta ſecunda non niſi difficillime diſtinguere quea-<lb/>mus, & </s> <s xml:id="echoid-s9413" xml:space="preserve">ipſa Inſtrumenta, quibus utimur, utcunque accurate fabre-<lb/>facta, ſemper ab hominibus modo compoſita ſint, nec ad deſidera-<lb/>ram perfectionem unquam reducta fuerint, aut reduci poſſint, uti <lb/>ſummi artifices mecum confiteri tenebuntur: </s> <s xml:id="echoid-s9414" xml:space="preserve">præteribo plurima a-<lb/>lia, candorem Celeberrimorum Geometrarum Gallorum memoraſ-<lb/>ſe ſufficiet, qui definita Magnitudine Gradus Terræ, eaque compa-<lb/>rata cum Picardiana addunt: </s> <s xml:id="echoid-s9415" xml:space="preserve">Differentiam 37 Hexapedarum non <lb/>eſſe adeo notabilem, quin poſſit adſcribi erroribus illapſis partim in <lb/>ſuas, partim in Picardi obſervationes; </s> <s xml:id="echoid-s9416" xml:space="preserve">quia hic Autor fatetur, non <lb/>obſtante quâ cunque curâ adhibita, ſe non reſpondere poſſe de duo-<lb/>bus Minutis ſecundis, & </s> <s xml:id="echoid-s9417" xml:space="preserve">idcirco de quantitate circiter 32 hexape-<lb/>darum in quâlibet obſervatione: </s> <s xml:id="echoid-s9418" xml:space="preserve">Poſtquam tam propinquum con-<lb/>ſenſum inter calculum Picardi, aliorum Gallorum Geometrarum, <lb/>noſtrumque deprehenderam, in animum induxi eum cum publico <lb/>communicare, ne aliquid gloriæ Snellii, cui primæ baſeos menſu-<lb/>ram, & </s> <s xml:id="echoid-s9419" xml:space="preserve">aliquantum hujus ſupputationis debemus. </s> <s xml:id="echoid-s9420" xml:space="preserve">decedat: </s> <s xml:id="echoid-s9421" xml:space="preserve">integrum <lb/>interea ſit unicuique Picardianam, Gallicanam, aut hanc Snel-<lb/>lianam eligere menſuram, quæcunque enim eligetur, veritati pro-<lb/>xima erit.</s> <s xml:id="echoid-s9422" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div339" type="section" level="1" n="339"> <head xml:id="echoid-head445" xml:space="preserve">FINIS.</head> <pb file="0435" n="435"/> </div> <div xml:id="echoid-div340" type="section" level="1" n="340"> <head xml:id="echoid-head446" xml:space="preserve">INTRODUCTIO <lb/><emph style="sc">AD</emph> <lb/>COHÆ RENTIAM <lb/>CORPORUM FIRMORUM.</head> <pb file="0436" n="436"/> <pb o="423" file="0437" n="437"/> </div> <div xml:id="echoid-div341" type="section" level="1" n="341"> <head xml:id="echoid-head447" xml:space="preserve">INTRODUCTIO <lb/><emph style="sc">AD</emph> <lb/>COHÆRENTIAM <lb/>CORPORUM FIRMORUM.</head> <head xml:id="echoid-head448" xml:space="preserve">PRÆFATIO.</head> <p> <s xml:id="echoid-s9423" xml:space="preserve">Mechanica duas videtur habere partes, quarum una agens <lb/>de Potentiis moventibus, tradit regulas, quibus omnia <lb/>corpora motu percita ſubjiciuntur; </s> <s xml:id="echoid-s9424" xml:space="preserve">hanc partem plurimi <lb/>Philoſophi & </s> <s xml:id="echoid-s9425" xml:space="preserve">Mathematici, antiqui & </s> <s xml:id="echoid-s9426" xml:space="preserve">recentiores im-<lb/>penſe coluerunt, & </s> <s xml:id="echoid-s9427" xml:space="preserve">indies expoliunt, adeo ut hac tempeſtate The-<lb/>ma Mechanicæ nobiliſſimum, de quo ſubtiliſſime diſputatur, eva-<lb/>ſerit. </s> <s xml:id="echoid-s9428" xml:space="preserve">Sed altera pars Mechanicæ, quæ Reſiſtentias ſive Cohæren-<lb/>tias corporum examinat, pauciſſimos nacta fuit cultores: </s> <s xml:id="echoid-s9429" xml:space="preserve">Hanc, <lb/>Mechanicorum Princeps, Archimedes, intactam reliquit, nec ad <lb/>eam Priscorumullus animum applicuit: </s> <s xml:id="echoid-s9430" xml:space="preserve">Profecto admirandum! cum <lb/>hæc ſcientia utiliſſima & </s> <s xml:id="echoid-s9431" xml:space="preserve">perquam neceſſaria ſit in plurimis artibus, <lb/>imo fere in tota vita civili, ut probatu facillimum foret; </s> <s xml:id="echoid-s9432" xml:space="preserve">ſed ex <lb/>Mechanica atque Architectura vulgatiſſima exempla ſufficiant.</s> <s xml:id="echoid-s9433" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9434" xml:space="preserve">Quotieſcunque conſtruenda eſt inſignior compoſitaque ex multis <lb/>partibus Machina, ſolet â prudentioribus Architectis exiguum prius <lb/>fabrefieri prototypon, ut omnes forte oboriundæ difficultates ſu-<lb/>perentur, defectus minus præviſi ſuppleantur, male ordinata emen-<lb/>dentur, ne inutilis labor aut impenſæ ſupervacuæ fiant: </s> <s xml:id="echoid-s9435" xml:space="preserve">Sæpius e-<lb/>venit, ut exiguum prototypon omnibus perfectum ſit partibus. </s> <s xml:id="echoid-s9436" xml:space="preserve">ſa-<lb/>tis mobilibus firmisque, machina interim majori ſecundum illius <lb/>proportionem elaborata nequaquam valente propter partes nonnul-<lb/>las hinc inde minus firmas, quam ut vim iis applicandam ſuſtine- <pb o="424" file="0438" n="438" rhead="PRÆFATIO."/> ant: </s> <s xml:id="echoid-s9437" xml:space="preserve">Ideo inter Mechanicos Proverbium eſt natum, quæ in parvo <lb/>ſuccedunt, non eundem ſemper ſucceſſum in magno ſortiri: </s> <s xml:id="echoid-s9438" xml:space="preserve">Eſt hoc <lb/>aliquando verum, non tamen toties ac narratur; </s> <s xml:id="echoid-s9439" xml:space="preserve">infortunatus enim <lb/>majorum Machinarum eventus ab ignorantia Legum, tam motus, <lb/>quam firmitatis pendet: </s> <s xml:id="echoid-s9440" xml:space="preserve">Quippe ſi vires Cohærentiæ omnium cor-<lb/>porum bene exploratæ habeantur, a priori ſemper determinari poſ-<lb/>ſet craſſities requiſita partium Machinam conſtituentium deter-<lb/>minatæ longitudinis, & </s> <s xml:id="echoid-s9441" xml:space="preserve">ex quapræparandæ ſint partes materia, ut vi-<lb/>ribus motricibus datis excipiendis vel excitandis ſufficiant abſque ru-<lb/>pturæ periculo; </s> <s xml:id="echoid-s9442" xml:space="preserve">nempe ſecundum aliquam in Experimentis dete-<lb/>ctam proportionem, craſſitiem & </s> <s xml:id="echoid-s9443" xml:space="preserve">firmitatem earum conficiendo, <lb/>& </s> <s xml:id="echoid-s9444" xml:space="preserve">tum ſemper in magno ſuccedent, quæ in parvo prototypo era-<lb/>mus meditati: </s> <s xml:id="echoid-s9445" xml:space="preserve">Craſſitiem poſſe â priori unicuique parti Machinæ <lb/>aſſignare eſt idcirco magnus in Mechanica progreſſus: </s> <s xml:id="echoid-s9446" xml:space="preserve">& </s> <s xml:id="echoid-s9447" xml:space="preserve">fortunatum <lb/>eventum cujuslibet Machinæ grandis poſſe prædicere, eſt aliquid <lb/>egregium magnique momenti. </s> <s xml:id="echoid-s9448" xml:space="preserve">Eſt quoque utilitas hujus ſcientiæ <lb/>ingens in Architectura civili, ut præſcribamus craſſitiem, & </s> <s xml:id="echoid-s9449" xml:space="preserve">ex <lb/>illa firmitatem trabium aliorumque ſuſtentaculorum, quæ ad ex-<lb/>ſtruendas Ædes, Januarum poſtas, Tabulationes, & </s> <s xml:id="echoid-s9450" xml:space="preserve">Contignatio-<lb/>nes, quæ magnis oneribus gerendis ſunt deſtinatæ, deſiderantur: <lb/></s> <s xml:id="echoid-s9451" xml:space="preserve">nam ex inſtitutis quibuſdam experimentis in anteceſſum determina-<lb/>bimus, an Tabulatio data oneri dato ferendo par ſit: </s> <s xml:id="echoid-s9452" xml:space="preserve">quantæ craſ-<lb/>ſitiei poſtæ Januarum, quibus magna pars faciei ædificii incumbit, <lb/>fieri debeant, ut totum pondus impoſitorum lapidum ſuſtineant: </s> <s xml:id="echoid-s9453" xml:space="preserve">hoc <lb/>modo firmitatis Scientia noſtræ incolumitati proſpicit, liberatque <lb/>a periculo ruinæ inſtantis, aut ab inutilibus impenſis, quas multo <lb/>craſſiores Trabes, poſtæ, pali, fulcra, quam deſiderantur, ſecum <lb/>traherent. </s> <s xml:id="echoid-s9454" xml:space="preserve">Hydraulica ſuum quoque uſum ex hac doctrinâ capit, <lb/>ut â priori definiamus craſſitiem parietum canales formantium, per <lb/>quos Fluidum ad Fontem ſalientem componendum cum data velo-<lb/>citate fluet, aut quos gravitate ſua extrorſum premendo extendet: </s> <s xml:id="echoid-s9455" xml:space="preserve"><lb/>Verum ſuâ ſponte clarius eluceſcit hujus doctrinæ utilitas, ſeſeque <lb/>ſua præſtantia magis commendat, quam ut ipſi hederâ noſtrâ opus <lb/>ſit: </s> <s xml:id="echoid-s9456" xml:space="preserve">Agnoſcunt id præſtantiſſimi Mathematici, qui hoc Thema ſuis <lb/>lucubrationibus digniſſimum judicarunt, idque ſubtiliter enucleare <lb/>anniſi fuerunt: </s> <s xml:id="echoid-s9457" xml:space="preserve">Hos ordine memoraſſe, ut progreſſus Scientiæ me- <pb o="425" file="0439" n="439" rhead="PRÆFATIO."/> lius intelligatur, non plane ſupervacaneum puto.</s> <s xml:id="echoid-s9458" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9459" xml:space="preserve">Galilæus, Vir vaſti ingenii, & </s> <s xml:id="echoid-s9460" xml:space="preserve">perſpicientia in omnia penetrante <lb/>pollens, eaque, quæpræterviſa ab aliis in Philoſophia erant, detegens; <lb/></s> <s xml:id="echoid-s9461" xml:space="preserve">illico ad hanc Mechanicæ partem, quæ Corporum Firmitatem ſpectat, <lb/>animum applicuit, & </s> <s xml:id="echoid-s9462" xml:space="preserve">Geometrice Leges Cohærentiæ reſpectivæ ex <lb/>ſuppoſita Abſoluta dare anniſus fuit; </s> <s xml:id="echoid-s9463" xml:space="preserve">plurimaque abſtruſa phænomena <lb/>& </s> <s xml:id="echoid-s9464" xml:space="preserve">abſcondita Problemata feliciter reſolvit; </s> <s xml:id="echoid-s9465" xml:space="preserve">verum hinc inde aliquid <lb/>humani paſſus fuit, veluti cum Cohærentiam reſpectivam ſubduplam <lb/>Abſolutæ ponit, vel Solidum parabolicum utrimque fultum æqualis <lb/>ubique reſiſtentiæ pronunciat, aut ubi excavatorum corporum fir-<lb/>mitates cum ſolidis æque magnis comparat: </s> <s xml:id="echoid-s9466" xml:space="preserve">facile profecto in re <lb/>ardua vacillat ſubinde intellectus, præcipue quando quis primus <lb/>Scientiam novam, & </s> <s xml:id="echoid-s9467" xml:space="preserve">antea inauditam, condit, glaciemque frangit: </s> <s xml:id="echoid-s9468" xml:space="preserve">Sed <lb/>hi lapſus facillime condonabuntur ab omnibus æquis rerum arbitris, <lb/>quia Natura ſæpe profunde obvelat in reſiſtentiarum doctrina ve-<lb/>ctium & </s> <s xml:id="echoid-s9469" xml:space="preserve">fulcrorum ſitus, momentorum rationes, potentiarum di-<lb/>rectiones; </s> <s xml:id="echoid-s9470" xml:space="preserve">quibus in inextricabilem Labyrinthum Eruditos conjicit: </s> <s xml:id="echoid-s9471" xml:space="preserve"><lb/>Idcirco elegantiſſime Virorum Magnorum errores excuſat in nego-<lb/>tiis ejuſmodi intricatiſſimis eloquentiſſimus Fontenellus in L’Hiſt. </s> <s xml:id="echoid-s9472" xml:space="preserve"><lb/>de L’Acad. </s> <s xml:id="echoid-s9473" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9474" xml:space="preserve">A°. </s> <s xml:id="echoid-s9475" xml:space="preserve">1707. </s> <s xml:id="echoid-s9476" xml:space="preserve">Sed quodcunque horum fuerit, id fa-<lb/>mæ Galilæi nihil detrimenti afferet, agnoſcere enim ſemper tene-<lb/>buntur mortales, Galilæum eſſe hujus doctrinæ inventorem; </s> <s xml:id="echoid-s9477" xml:space="preserve">& </s> <s xml:id="echoid-s9478" xml:space="preserve">qui <lb/>ipſe ſubtilia cum explicuit, ad ulteriora viam aperuit: </s> <s xml:id="echoid-s9479" xml:space="preserve">Inventor au-<lb/>tem vere primus eſt, nam id, quod Ariſtoteles Mechanicis quæ-<lb/>ſtionibus inſeruit, indagans, Quare Ligna, quo longiora, eo de-<lb/>biliora ſint? </s> <s xml:id="echoid-s9480" xml:space="preserve">exigui eſt momenti, nec Scientiæ novæ initium, quem-<lb/>admodum nec ea, quæ Guevara doctiſſimis ſuis commentariis huic <lb/>Ariſtotelis loco addidit.</s> <s xml:id="echoid-s9481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9482" xml:space="preserve">Galilæum ſecutus fuit Blondellus, qui Anno 1661 Epiſtolam edi-<lb/>dit, in quâ famoſam Galilæi propoſitionem diſcuſſit, oſtendens So-<lb/>lidum non Parabolicum, ſed Ellipticum requiri, ut utrimque ful-<lb/>cris impoſitum ubivis æqualis reſiſtentiæ habeatur, memoratque ſi-<lb/>mul ſe Volumen de Reſiſtentia ſolidorum compoſuiſſe, cui titulum <lb/>Galilæi promoti præfixit: </s> <s xml:id="echoid-s9483" xml:space="preserve">Epiſtola prior deprehenditur quoque in <lb/>Libro, Regiis typis Anno 1676 Pariſiis edito, cui titulus, Recueil <lb/>de pluſieurs Traitez de Mathematique.</s> <s xml:id="echoid-s9484" xml:space="preserve"/> </p> <pb o="426" file="0440" n="440" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s9485" xml:space="preserve">Deinde Alexander Marchettus, Piſanæ Academiæ Philoſophus, <lb/>edidit Librum de Reſiſtentia Solidorum Anno 1669 Florentiæ, com-<lb/>prehendentem 156 Propoſitiones novas, quibus hanc doctrinam <lb/>amplificavit; </s> <s xml:id="echoid-s9486" xml:space="preserve">oſtenditque ſe ea tempeſtate in ſubtiliſſima arcana Ma-<lb/>theſeos penetraſſe, Magnitudines quorumcunque Solidorum, Pa-<lb/>raboloidum, Elliptoidum, Hyperboloidum menſurare, atque cen-<lb/>tra gravitatis in iis determinare noviſſe: </s> <s xml:id="echoid-s9487" xml:space="preserve">aſt materiæ difficultas non <lb/>abſque erroribus progredi egregio huic Geometræ conceſſit, quo-<lb/>rum nonnullos inclytus G. </s> <s xml:id="echoid-s9488" xml:space="preserve">Grandus annotavit in Rispoſta Apolo-<lb/>getica edita Luccæ Anno 1712.</s> <s xml:id="echoid-s9489" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9490" xml:space="preserve">Interim Honoratus Fabry Solidorum reſiſtentias quoque <lb/>Geometrice ſupputavit, conſcripſitque integrum de iis Li-<lb/>brum, qui quintus eſt in Tractatu Phyſicæ Secundo, atque <lb/>in Lucem prodiit Anno 1669 Lugduni, quo tempore Mar-<lb/>chettus ſuum opus edidit; </s> <s xml:id="echoid-s9491" xml:space="preserve">conſtat abunde ambos Autores nihil <lb/>de ſe invisem ſciviſſe aut ſaltem ſecum communicaſſe; </s> <s xml:id="echoid-s9492" xml:space="preserve">cum diverſa <lb/>inceſſerint via, propoſitioneſque plane contrarias habeant, ſæpius <lb/>tamen a veritate receſſiſſe videtur Fabry.</s> <s xml:id="echoid-s9493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9494" xml:space="preserve">Eandem materiam inchoavit poſtea G. </s> <s xml:id="echoid-s9495" xml:space="preserve">Pardieſius in Tractatu de vi-<lb/>ribus moventibus, paucisque propoſitionibus nonnulla demonſtravit.</s> <s xml:id="echoid-s9496" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9497" xml:space="preserve">Verum Mariottus, Experimentalem promovens Philoſophiam, <lb/>non modo Geometrice hoc Thema tractandum eſſe judicavit, uti <lb/>huc uſque factum fuerat, ſi Wurtſium exceperimus, ſed Experimen-<lb/>tis tentandum, ut vere demonſtraretur quænam proportio inter Re-<lb/>ſiſtentiam abſolutam & </s> <s xml:id="echoid-s9498" xml:space="preserve">reſpectivam Corporum Naturalium obtine-<lb/>ret: </s> <s xml:id="echoid-s9499" xml:space="preserve">Cum enim Blondellus memoriæ mandaverat, Paulum Wurt-<lb/>ſium Galilæanas demonſtrationes Experimentis exploraſſe, verum <lb/>hæc illis nequaquam reſpondiſſe, indagandum erat quænam phæno-<lb/>mena in Experimentis obſervarentur, & </s> <s xml:id="echoid-s9500" xml:space="preserve">quamobrem Galilæus in <lb/>errorem inciderat; </s> <s xml:id="echoid-s9501" xml:space="preserve">Mariottus ex inſtitutis â ſe nonnullis Tentamini-<lb/>bus invenit Reſiſtentiam abſolutam eſſe triplam, aut fere quadruplam <lb/>interdum, Reſiſtentiæ reſpectivæ, proportionem illius ad hanc majo-<lb/>rem deprehendens, quia Corpora omnia ſlexilia ſunt, pedetentim & </s> <s xml:id="echoid-s9502" xml:space="preserve"><lb/>ſucceſſive rumpuntur, quæ tranſverſe examinantur, cum Galilæus <lb/>omnia rigida, eodemque tempore frangi totam craſſitiem corporum <lb/>ſuppoſuerat.</s> <s xml:id="echoid-s9503" xml:space="preserve"/> </p> <pb o="427" file="0441" n="441" rhead="PRÆFATIO."/> <p> <s xml:id="echoid-s9504" xml:space="preserve">Hiſce inniſus Mariotti Experimentis Magnus Leibnitzius, de <lb/>Philoſophia Mathematiciſque diſciplinis, ſi quis unquam, optime <lb/>meritus, doctrinam Reſiſtentiarum in Actis Lipſienſibus Anni 1684 <lb/>ſubtilius expolivit, paucis propoſitionibus plurima complexus, no-<lb/>vamque demonſtrationem ſuppeditavit, quâ Reſiſtentiam abſolu-<lb/>tam triplo majorem reſpectiva probabat, ex iis quæ publicæ luci <lb/>commiſit, manifeſto colligi poteſt, Nobiliſſimum Mathematicum <lb/>non modo ea examinaſſe, quæ prodidit, ſed innumera alia, quæ <lb/>minoris exiſtimans pretii celavit.</s> <s xml:id="echoid-s9505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9506" xml:space="preserve">Anno 1686 de Lanis edidit ſuum opus Phyſicum, quod Magiſte-<lb/>rium naturæ & </s> <s xml:id="echoid-s9507" xml:space="preserve">artis vocavit, in quo fere nihil niſi quod ex Galilæo & </s> <s xml:id="echoid-s9508" xml:space="preserve"><lb/>Fabry depromtum eſt habetur, quod adhærentiam ſpectat, exceptis <lb/>quibusdam Phyſicis obſervationibus, quæ exigui ſunt pretii.</s> <s xml:id="echoid-s9509" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9510" xml:space="preserve">Leibnitzium proinde excepitinclytus Galliarum Mathematicus P. <lb/></s> <s xml:id="echoid-s9511" xml:space="preserve">Varignonus, qui ex ſublimi Geometria regulam Univerſalem concin-<lb/>navit, ſecundum quam Reſiſtentiæ omnium corporum Reſpectivæ ex <lb/>Abſoluta determinari poſſunt, ſive Galilæi Hypotheſin, ſive eam Ma-<lb/>riotti ſtatuamus veram, aut quamcunque aliam pro diverſa fibrarum <lb/>corporearum tenacitate condendam; </s> <s xml:id="echoid-s9512" xml:space="preserve">hujus regulæ ope non parum hanc <lb/>doctrinam promovit, imo fere exhauſit, proſtat autem in L’Hi-<lb/>ſtoire de L’Academie Roy. </s> <s xml:id="echoid-s9513" xml:space="preserve">A°. </s> <s xml:id="echoid-s9514" xml:space="preserve">1702.</s> <s xml:id="echoid-s9515" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9516" xml:space="preserve">Eodem Anno Cl. </s> <s xml:id="echoid-s9517" xml:space="preserve">Parentius, Regula uſus Varignoni, Reſiſtentias <lb/>corporum cavorum examinavit, erroreſque Galilæi oſtendit; </s> <s xml:id="echoid-s9518" xml:space="preserve">occu-<lb/>patus autem fuit hic Vir egregius plurimis annis eodem Themate, <lb/>alterque fuit, qui Mariottum imitatus Experimentis Cohærentiam <lb/>variorum Lignorum exploravit, pulcerrimiſque novis propoſitioni-<lb/>bus eam amplificavit in L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s9519" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9520" xml:space="preserve">A°. </s> <s xml:id="echoid-s9521" xml:space="preserve">1702, 1707, <lb/>1708, 1710.</s> <s xml:id="echoid-s9522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9523" xml:space="preserve">Magnus deinde Bernouillius, quamplurimis inventis, quibus <lb/>Mathematicas diſciplinas egregie promovit, inclytus, obſervavit, <lb/>hactenus Geometras conſideraſſe corpora, quæ transverſe rumpe-<lb/>bantur tantum diſſolvi aut diſtrahi per totam craſſitiem; </s> <s xml:id="echoid-s9524" xml:space="preserve">cum potius <lb/>ſuperiores fibræ extrahantur, inferiores comprimantur, quod ve-<lb/>rum eſſe arbitror, aliam generalem Regulam Cohærentiæ tradidit <lb/>Reſpectivæ, bene cum Experimentis Mariotti congruentem: </s> <s xml:id="echoid-s9525" xml:space="preserve">atque <lb/>ſimul Curvam definivit, quam Solida Elaſtica, cum franguntur, <pb o="428" file="0442" n="442" rhead="PRÆFATIO."/> deſcriberent; </s> <s xml:id="echoid-s9526" xml:space="preserve">hæc tradidit in L’Hiſt. </s> <s xml:id="echoid-s9527" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s9528" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9529" xml:space="preserve">A°. </s> <s xml:id="echoid-s9530" xml:space="preserve">1705.</s> <s xml:id="echoid-s9531" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9532" xml:space="preserve">Poſtea Paulus Hoſte integrum volumen de Cohærentia conſcrip-<lb/>ſit, quod conſtituit alteram partem Libri, cujus titulus eſt, Ma-<lb/>noeuvre des Vaiſſeaux.</s> <s xml:id="echoid-s9533" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9534" xml:space="preserve">Denique Celeb. </s> <s xml:id="echoid-s9535" xml:space="preserve">Grandi, re æque ac nomine magnus, in Libro <lb/>Italice conſcripto, Riſpoſta Apologetica dicto, adverſus Cl Mar-<lb/>chettum Reſiſtentias Solidorum tractavit, illaſque paucis propoſi-<lb/>tionibus ex ſublimi Geometriâ petitis mirifice amplificavit.</s> <s xml:id="echoid-s9536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9537" xml:space="preserve">Præter hos Autores neſcio an aliqui fuerint, qui hanc materiam <lb/>Geometrice tractarunt, niſi quod olim Romerus Tuborum metal-<lb/>licorum Fontibus inſervientium firmitatem exhibuerit in divers Ou-<lb/>vrages de Mathematique & </s> <s xml:id="echoid-s9538" xml:space="preserve">Phyſique, quam egregius Hermannus in <lb/>phoronomiæ Lib. </s> <s xml:id="echoid-s9539" xml:space="preserve">2. </s> <s xml:id="echoid-s9540" xml:space="preserve">prop. </s> <s xml:id="echoid-s9541" xml:space="preserve">8. </s> <s xml:id="echoid-s9542" xml:space="preserve">explicuit: </s> <s xml:id="echoid-s9543" xml:space="preserve">Veluti etiam Parentius in <lb/>L’Hiſt. </s> <s xml:id="echoid-s9544" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s9545" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9546" xml:space="preserve">A°. </s> <s xml:id="echoid-s9547" xml:space="preserve">1707. </s> <s xml:id="echoid-s9548" xml:space="preserve">tum quoque Merſennus in Har-<lb/>mon. </s> <s xml:id="echoid-s9549" xml:space="preserve">& </s> <s xml:id="echoid-s9550" xml:space="preserve">Reaumurius in L’Hiſt. </s> <s xml:id="echoid-s9551" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s9552" xml:space="preserve">Roy. </s> <s xml:id="echoid-s9553" xml:space="preserve">A°. </s> <s xml:id="echoid-s9554" xml:space="preserve">1711. </s> <s xml:id="echoid-s9555" xml:space="preserve">fidium <lb/>& </s> <s xml:id="echoid-s9556" xml:space="preserve">funium robur exploraverunt.</s> <s xml:id="echoid-s9557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9558" xml:space="preserve">Plurimi cæteroquin fuerunt Philoſophi, qui de Cohærentia ege-<lb/>runt, ſed modo Phyſice quærendo ejus cauſam, aut aliquam pro <lb/>lubitu fingendo, orbique obtrudendo, ut ex eâ phænomena, quæ <lb/>in Solidorum Cohærentia occurrunt, explicarent, hos ſicco pede <lb/>tranſimus, cum nihil boni ſtabiliſve noſtræ ſcientiæ attulerint, ſed <lb/>eam potius inutilibus opinionibus, acutioribus obtuſioribuſve ag-<lb/>gravaverint.</s> <s xml:id="echoid-s9559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9560" xml:space="preserve">Perſpectis his omnibus animadvertebam, quamcunque operam <lb/>Mathematici impenderint in Regula Univerſali Cohærentiæ Reſpe-<lb/>ctivæ invenienda, & </s> <s xml:id="echoid-s9561" xml:space="preserve">corporum variis donatorum figuris Firmitate <lb/>determinanda, nihilominus quam plurima deſiderari, & </s> <s xml:id="echoid-s9562" xml:space="preserve">quod qui-<lb/>dem palmarium erat, ipſa fundamenta.</s> <s xml:id="echoid-s9563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9564" xml:space="preserve">Supponamus enim dari Regulam Univerſalem, quæ determinet <lb/>proportionem inter Cohærentiam abſolutam & </s> <s xml:id="echoid-s9565" xml:space="preserve">reſpectivam Solido-<lb/>rum, ex ea demonſtrari nequit quanta erit alterutra Cohærentia <lb/>corporis dati, niſi ope Experimenti prius exploretur Cohærentia <lb/>abſoluta aut reſpectiva illius corporis: </s> <s xml:id="echoid-s9566" xml:space="preserve">Adeoque Experimenta deſi-<lb/>derabantur, quæ baſes forent ratiocinii Mathematici: </s> <s xml:id="echoid-s9567" xml:space="preserve">Pauciſſima <lb/>vero tantum facta ſunt a Romero, Mariotto, Parentio, Reaumu-<lb/>rio, cum plurima poſtulentur & </s> <s xml:id="echoid-s9568" xml:space="preserve">quidem inſtituenda cum omni- <pb o="429" file="0443" n="443" rhead="PRÆFATIO."/> bus corporum generibus, ex quibusGeometra calculi ope determinabit <lb/>firmitatem corporis datæ materiei, figuræ, & </s> <s xml:id="echoid-s9569" xml:space="preserve">magnitudinis.</s> <s xml:id="echoid-s9570" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9571" xml:space="preserve">Præterea obſervabam Regulam Univerſalem ab omnibus fuiſſe <lb/>quæſitam, poſitamque, quæ proportionem contineret inter Cohæ-<lb/>rentiam abſolutam & </s> <s xml:id="echoid-s9572" xml:space="preserve">reſpectivam, quam in Experimentis Mariot-<lb/>tus deprehenderat: </s> <s xml:id="echoid-s9573" xml:space="preserve">Quoniam vero pauca tantum capta erant Expe-<lb/>rimenta, quomodo & </s> <s xml:id="echoid-s9574" xml:space="preserve">ſcire & </s> <s xml:id="echoid-s9575" xml:space="preserve">convinci poteramus omnia corpora <lb/>eodem comparata eſſe modo, ac ea quæ Philoſophus examinaverat? <lb/></s> <s xml:id="echoid-s9576" xml:space="preserve">Idcirco dubitare incepi an non nimis cito Univerſalis Regula ſtabi-<lb/>lita fuiſſet; </s> <s xml:id="echoid-s9577" xml:space="preserve">& </s> <s xml:id="echoid-s9578" xml:space="preserve">quia in Phyſica ſæpiſſime deprehenderam corporum <lb/>ſingulares indoles reſpuiſſe nonnullas generales regulas, quas an-<lb/>tea Philoſophi poſuerant, hic idem poſſe obtinere ſuſpicabar: </s> <s xml:id="echoid-s9579" xml:space="preserve"><lb/>mecum præterea conſiderans corporis ejuſdem tenacitatem & </s> <s xml:id="echoid-s9580" xml:space="preserve">flexi-<lb/>litatem mire variari, aliam eſſe in ligno viridi, aliam in parum ſic-<lb/>cato, aliam in prorſus arido; </s> <s xml:id="echoid-s9581" xml:space="preserve">majorem in hoc corpore, minorem eſſe <lb/>in alio, ratus fui hanc doctrinam prius accuratius eſſe enuclean-<lb/>dam & </s> <s xml:id="echoid-s9582" xml:space="preserve">plurimis Tentaminibus illuſtrandam, quam poſſet Regula <lb/>Univerſalis ſtabiliri; </s> <s xml:id="echoid-s9583" xml:space="preserve">nec dubitaſſe poenituit me poſtea, cum ex Ex-<lb/>perimentis plurimis didici Regulam Univerſalem Cohærentiæ reſpe-<lb/>ctivæ non dari, quia valde differt proportio, quæ inter Abſo. </s> <s xml:id="echoid-s9584" xml:space="preserve"><lb/>lutam & </s> <s xml:id="echoid-s9585" xml:space="preserve">Reſpectivam viget, aliquando eſt illa ad hanc uti 3 ad 1, <lb/>aliquando uti 18 ad 1, imo plures proportiones inter memoratas <lb/>intermediæ dantur. </s> <s xml:id="echoid-s9586" xml:space="preserve">Inſuper unanimi conſenſu aſſumtum fuit cor-<lb/>porum variæ altitudinis Cohærentiam Reſpectivam eſſe in altitudi-<lb/>nis ratione duplicata; </s> <s xml:id="echoid-s9587" xml:space="preserve">hæc negari nequit, datur enim in nonnullis <lb/>corporibus, ſed alia quoque dantur quæ ad eam proxime accedunt, <lb/>alia quæ eam reſpuunt: </s> <s xml:id="echoid-s9588" xml:space="preserve">quam varietatem prævidebam facile, dete-<lb/>ctâ corporum mirâ flexilitate & </s> <s xml:id="echoid-s9589" xml:space="preserve">diverſiſſimâ proportione inter Co-<lb/>hærentiam abſolutam & </s> <s xml:id="echoid-s9590" xml:space="preserve">reſpectivam. </s> <s xml:id="echoid-s9591" xml:space="preserve">Quibus perpenſis ab ovo in-<lb/>choare materiam hanc volui, atque in ea diligenter & </s> <s xml:id="echoid-s9592" xml:space="preserve">accurate in-<lb/>ſtituere Experimenta, quæ vera & </s> <s xml:id="echoid-s9593" xml:space="preserve">inconcuſſa fundamenta forent: </s> <s xml:id="echoid-s9594" xml:space="preserve"><lb/>cum autem plurima deſiderentur, & </s> <s xml:id="echoid-s9595" xml:space="preserve">modo nonnulla hucuſque ce-<lb/>perim, Introductionem ad Cohærentiam Solidorum vocavi hanc Diſ-<lb/>tertationem.</s> <s xml:id="echoid-s9596" xml:space="preserve"/> </p> <pb o="430" file="0444" n="444" rhead="SERIES CAPITUM."/> <p style="it"> <s xml:id="echoid-s9597" xml:space="preserve">I. </s> <s xml:id="echoid-s9598" xml:space="preserve">De modis, quibus corpora majora ſecum invicem cohærent.</s> <s xml:id="echoid-s9599" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9600" xml:space="preserve">II. </s> <s xml:id="echoid-s9601" xml:space="preserve">De Cohærentia Abſoluta Lignorum.</s> <s xml:id="echoid-s9602" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9603" xml:space="preserve">III. </s> <s xml:id="echoid-s9604" xml:space="preserve">De Cohærentia Metallorum.</s> <s xml:id="echoid-s9605" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9606" xml:space="preserve">IV. </s> <s xml:id="echoid-s9607" xml:space="preserve">De Cohærentia Funium contortorum.</s> <s xml:id="echoid-s9608" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9609" xml:space="preserve">V. </s> <s xml:id="echoid-s9610" xml:space="preserve">De Cohærentia Lignorum Reſpectiva.</s> <s xml:id="echoid-s9611" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9612" xml:space="preserve">VI. </s> <s xml:id="echoid-s9613" xml:space="preserve">De Cohærentia Solidorum in medio ſui fulcro impoſitorum.</s> <s xml:id="echoid-s9614" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9615" xml:space="preserve">VII. </s> <s xml:id="echoid-s9616" xml:space="preserve">De Cohærentia Solidorum duobus fulcris libere impoſito-<lb/>rum.</s> <s xml:id="echoid-s9617" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9618" xml:space="preserve">VIII. </s> <s xml:id="echoid-s9619" xml:space="preserve">De Cohærentia Solidorum utrimque a foramine arcto excepto-<lb/>rum.</s> <s xml:id="echoid-s9620" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9621" xml:space="preserve">IX. </s> <s xml:id="echoid-s9622" xml:space="preserve">De Cohærentia Solidorum compreſſorum.</s> <s xml:id="echoid-s9623" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s9624" xml:space="preserve">X. </s> <s xml:id="echoid-s9625" xml:space="preserve">Tentamen de corporum Duritie.</s> <s xml:id="echoid-s9626" xml:space="preserve"/> </p> <pb o="431" file="0445" n="445"/> </div> <div xml:id="echoid-div342" type="section" level="1" n="342"> <head xml:id="echoid-head449" xml:space="preserve">INTRODUCTIO <lb/><emph style="sc">AD</emph> <lb/>COHÆRENTIAM <lb/>CORPORUM FIRMORUM.</head> <head xml:id="echoid-head450" xml:space="preserve">CAPUT PRIMUM,</head> <head xml:id="echoid-head451" style="it" xml:space="preserve">De Modis diverſis, quibus corpora ſoluta ſecum invicem in <lb/>maſſam unitam abeunt.</head> <p> <s xml:id="echoid-s9627" xml:space="preserve">DEFINITIO. </s> <s xml:id="echoid-s9628" xml:space="preserve">Vocamus Cohærentiam, Firmitatem vel Reſiſten-<lb/>tiam Solidorum eam vim corporum majorum, qua partes quo-<lb/>modocunque & </s> <s xml:id="echoid-s9629" xml:space="preserve">â quacunque cauſâ conjunctæ refiſtunt divulſioni <lb/>aut fracturæ, ita ut eadem vi â ſe mutuo removeri nequeant, qua <lb/>aut ſolæ moveri, aut ſibi tantummodo impoſitæ ſeparari poſſent, <lb/>ſed vim exigant multo majorem.</s> <s xml:id="echoid-s9630" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9631" xml:space="preserve">Ante oculos ponamus maſſam quamlibet firmam, Cubus Cupreus <lb/>ſit exempli loco, hic ex pluribus partibus ſupra ſe mutuo congeſtis <lb/>componitur, quæ tamen viribus noſtrorum digitorum reſiſtunt ita, <lb/>ut a ſe non avellantur; </s> <s xml:id="echoid-s9632" xml:space="preserve">ſed idem Cubus in pulverem limæ ope ſit <lb/>redactus, ſingulos pulviſculos facile ſeparabimus ab aliis; </s> <s xml:id="echoid-s9633" xml:space="preserve">nec ad <lb/>id major vis, quam quæ gravitatem unius cujusvis particulæ parum <lb/>ſuperat, requiritur: </s> <s xml:id="echoid-s9634" xml:space="preserve">Cum autem maſſæ unitæ partes non, aut dif-<lb/>ficillime, digitis cedebant, inerat tum in iis vis quædam, quæ eſt <lb/>vis Cohærentiæ, Firmitatis aut Reſiſtentiæ, quam in dagamus. </s> <s xml:id="echoid-s9635" xml:space="preserve">Eſt <lb/>hæc vis in nonnullis corporibus major quam in aliis: </s> <s xml:id="echoid-s9636" xml:space="preserve">in quibus ma-<lb/>xima eſt, ea duriſſima vocantur, in mollibus eſt minor, in molliſ-<lb/>ſimis, qualia ſunt Fluida, eſt minima; </s> <s xml:id="echoid-s9637" xml:space="preserve">ineſt tamen iis quædam vis, <pb o="432" file="0446" n="446" rhead="INTRODUCTIO AD COHÆRENTIAM"/> nam omnia Fluida renacia ſunt, in guttas rotundas abeunt, quæ ad-<lb/>hærent quibuſcunque Solidis fere, quamobrem nullum datur cor-<lb/>porum genus, hactenus mortalibus cognitum, quin componatur <lb/>ex partibus aliquam vim Cohærentiæ poſſidentibus.</s> <s xml:id="echoid-s9638" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9639" xml:space="preserve">Operæ pretium erit modos oſtendiſſe, quibus Ars vel Natura uti-<lb/>tur ad corpora ſejuncta unienda in Cohærentem maſſam.</s> <s xml:id="echoid-s9640" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9641" xml:space="preserve">§. </s> <s xml:id="echoid-s9642" xml:space="preserve">I. </s> <s xml:id="echoid-s9643" xml:space="preserve">Duo corpora, primum ſeparata, deinde ſibi mutuo impo-<lb/>ſita, a vi externa ad ſe compreſſa, cohærent, & </s> <s xml:id="echoid-s9644" xml:space="preserve">quidem quantum <lb/>â vi externâ ad ſe mutuo premuntur. </s> <s xml:id="echoid-s9645" xml:space="preserve">Cubi bini ambabus manibus <lb/>prehendantur & </s> <s xml:id="echoid-s9646" xml:space="preserve">comprimantur ſupra ſe invicem, cohærebunt, uni-<lb/>tam maſſam component; </s> <s xml:id="echoid-s9647" xml:space="preserve">non minori vi ſeparandam, quam quæ <lb/>manus removere poteſt: </s> <s xml:id="echoid-s9648" xml:space="preserve">Verum idem effectus continget, ſive cau-<lb/>ſa externa Solida, ſive Fluida fuerit; </s> <s xml:id="echoid-s9649" xml:space="preserve">ambiat enim memoratos Cu-<lb/>bos grave fluidum, tantopere ſecum cohærebunt, quantum gravi-<lb/>tat in ipſos fluidum, nec vi minori, quam quæ gravitatem aut preſ-<lb/>ſionem fluidi ſuperare poteſt, ſejungentur: </s> <s xml:id="echoid-s9650" xml:space="preserve">Guerickiana hemiſphæ-<lb/>ria Cuprea hoc luculenter probant; </s> <s xml:id="echoid-s9651" xml:space="preserve">ea enim cava intus, extus aëre <lb/>atmoſphærico & </s> <s xml:id="echoid-s9652" xml:space="preserve">gravi cincta, & </s> <s xml:id="echoid-s9653" xml:space="preserve">ope antliæ pneumaticæ intus e-<lb/>vacuata, omnique aëre orbata, tanta vi comprimuntur ab aëre ex-<lb/>terno, ut firmiſſime cohæreant, atque corpus unum, continuum <lb/>conſtituant, quod non divelli poteſt bifariam iterum, niſi vis ma-<lb/>xima adhibeatur, quæ gravitatem Aëris incumbentis vincat; </s> <s xml:id="echoid-s9654" xml:space="preserve">ita <lb/>hemiſphæria, quorum diameter {3/4} ulnæ Magdeburgicæ æqualis erat, <lb/>ſeparari non potuerunt niſi ope 16 equorum contrario niſu ea di-<lb/>ſtrahentium: </s> <s xml:id="echoid-s9655" xml:space="preserve">vid. </s> <s xml:id="echoid-s9656" xml:space="preserve">Guericke de Spat. </s> <s xml:id="echoid-s9657" xml:space="preserve">Vac. </s> <s xml:id="echoid-s9658" xml:space="preserve">Lib. </s> <s xml:id="echoid-s9659" xml:space="preserve">3. </s> <s xml:id="echoid-s9660" xml:space="preserve">Cap. </s> <s xml:id="echoid-s9661" xml:space="preserve">23. </s> <s xml:id="echoid-s9662" xml:space="preserve">Multa <lb/>corpora cohærent a pondere Aëris compreſſa, unde nonnulli Eru-<lb/>diti concluſerunt omnia cohærere, quatenus ab Aëre premuntur; <lb/></s> <s xml:id="echoid-s9663" xml:space="preserve">nimis cito hercle; </s> <s xml:id="echoid-s9664" xml:space="preserve">infra enim patebit hanc cauſam nec eſſe, nec <lb/>eſſe poſſe univerſalem.</s> <s xml:id="echoid-s9665" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9666" xml:space="preserve">§. </s> <s xml:id="echoid-s9667" xml:space="preserve">2. </s> <s xml:id="echoid-s9668" xml:space="preserve">Corpora etiam cohærent, quæ quando ſe contingunt, I° <lb/>vinaturali Magnetica, 2° vel vi quacunque attractrice ad ſe trahun-<lb/>tur. </s> <s xml:id="echoid-s9669" xml:space="preserve">Ferrum enim aut Magnes cum Magnete cohæret, unam maſ-<lb/>ſam conſtituens, & </s> <s xml:id="echoid-s9670" xml:space="preserve">ſeparari nequit, niſi vis præpollens attractioni <lb/>Magnetis advocetur.</s> <s xml:id="echoid-s9671" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9672" xml:space="preserve">Vim Magneticam diſtinxi a preſſione externa deſcripta modo an-<lb/>te, quoniam in Diſſertatione de Magnete demonſtravi, eam non <pb o="433" file="0447" n="447" rhead="CORPORUM FIRMORUM."/> pendere ab Aëre, nec ab Æthere, nec ab effluviis ullis, ſed â cau-<lb/>ſa alia, quæ huc uſque omnes latet Philoſophos.</s> <s xml:id="echoid-s9673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9674" xml:space="preserve">Cohærent corpora, quæ vi attractrice donata ſunt: </s> <s xml:id="echoid-s9675" xml:space="preserve">Capiantur <lb/>enim duo ſpecula vitrea, pura, ſicciſſimaque, aut laminæ planæ la-<lb/>pideæ, lateritiæ, metallicæ, has ſibi impoſitas cum avellere co-<lb/>naris, notabilem reſiſtentiam deprehendes, quod olim etiam Ga-<lb/>lilæus obſervavit in Dialogo I. </s> <s xml:id="echoid-s9676" xml:space="preserve">Mechan. </s> <s xml:id="echoid-s9677" xml:space="preserve">ne autem Aëris pondus hîc <lb/>invocemus ut cauſam, quippe intra laminarum commiſſuras aër hoſ-<lb/>pitatur, liberumque acceſſum exitumque habet, & </s> <s xml:id="echoid-s9678" xml:space="preserve">ſuâ vi elaſtica <lb/>tantopere removet laminas, quantum ab Aëris pondere extrinſecus <lb/>premuntur. </s> <s xml:id="echoid-s9679" xml:space="preserve">Aſt novo Brittannico Experimento id ulterius confir-<lb/>mabitur: </s> <s xml:id="echoid-s9680" xml:space="preserve">globos duosplumbeos ſibi impone, comprime, parum con-<lb/>torque, ut latiuſculam ſuperficiem adipiſcantur, & </s> <s xml:id="echoid-s9681" xml:space="preserve">ſeſe arctiſſime <lb/>contingant. </s> <s xml:id="echoid-s9682" xml:space="preserve">tum valde cohærebunt, & </s> <s xml:id="echoid-s9683" xml:space="preserve">multo fortius, quam un-<lb/>quam a pondere atmoſphæræ comprimi potuiſſent, quemadmodum <lb/>probavit inclytus Philoſophus Disaguillerius in Philoſ. </s> <s xml:id="echoid-s9684" xml:space="preserve">Tranſact. <lb/></s> <s xml:id="echoid-s9685" xml:space="preserve">N°. </s> <s xml:id="echoid-s9686" xml:space="preserve">389. </s> <s xml:id="echoid-s9687" xml:space="preserve">pag. </s> <s xml:id="echoid-s9688" xml:space="preserve">345.</s> <s xml:id="echoid-s9689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9690" xml:space="preserve">§. </s> <s xml:id="echoid-s9691" xml:space="preserve">3. </s> <s xml:id="echoid-s9692" xml:space="preserve">Corpora, quæ calore in Fluidum mutantur, frigore con-<lb/>creſcunt in maſſam firmam, ex admodum cohærentibus partibus <lb/>compoſitam: </s> <s xml:id="echoid-s9693" xml:space="preserve">Ita Metalla, Semimetalla, Salia, Reſinæ, Sulphu-<lb/>ra, Cera, Adeps, Vitrum &</s> <s xml:id="echoid-s9694" xml:space="preserve">c. </s> <s xml:id="echoid-s9695" xml:space="preserve">in Igne liquefiunt, & </s> <s xml:id="echoid-s9696" xml:space="preserve">conſtant ex <lb/>partibus a ſe mutuo facillime removendis, frigore autem in maſſas <lb/>admodum firmas abeunt.</s> <s xml:id="echoid-s9697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9698" xml:space="preserve">§. </s> <s xml:id="echoid-s9699" xml:space="preserve">4. </s> <s xml:id="echoid-s9700" xml:space="preserve">Ex molli maſſâ Ignis quoque corpus durum & </s> <s xml:id="echoid-s9701" xml:space="preserve">admodum <lb/>cohærens facit: </s> <s xml:id="echoid-s9702" xml:space="preserve">Lutum terreſtre humidum & </s> <s xml:id="echoid-s9703" xml:space="preserve">molle Igni imponatur, <lb/>coquatur, abit in laterem, ſuâ duritie ſilices æquantem, ſaxa non-<lb/>nulla ſuperantem. </s> <s xml:id="echoid-s9704" xml:space="preserve">Creta, corpus cæteroquin molle, igni aliquam-<lb/>diu inpoſita, magis magiſque induratur, etiamſi caleat. </s> <s xml:id="echoid-s9705" xml:space="preserve">Lignum <lb/>brevi temporis ſpatio igni committunt Indi, ut cuſpides ligneorum <lb/>telorum hac levi uſtulatione indurent. </s> <s xml:id="echoid-s9706" xml:space="preserve">Induratur igne Corium, Char-<lb/>ta, pergamena, & </s> <s xml:id="echoid-s9707" xml:space="preserve">alia plurima corpora: </s> <s xml:id="echoid-s9708" xml:space="preserve">& </s> <s xml:id="echoid-s9709" xml:space="preserve">ut copioſior ignis ma-<lb/>jores effectus edit, ita parcior minores, hinc lutum radiis Solari-<lb/>bus aërive calido & </s> <s xml:id="echoid-s9710" xml:space="preserve">ſiccanti expoſitum induratur, minus tamen <lb/>quam in fornace: </s> <s xml:id="echoid-s9711" xml:space="preserve">eodem modo Corallia ſe habent, quæ planta in <lb/>fundo maris creſcens primum educta, mollis eſt, ſed Soli aut Aëri <lb/>expoſita in lapideam duritiem abit. </s> <s xml:id="echoid-s9712" xml:space="preserve">Ita ſuccinum flavum in litto- <pb o="434" file="0448" n="448" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ra ejectum molle eſt, ſed Aëri expoſitum, durum evadit.</s> <s xml:id="echoid-s9713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9714" xml:space="preserve">§. </s> <s xml:id="echoid-s9715" xml:space="preserve">5. </s> <s xml:id="echoid-s9716" xml:space="preserve">Corpora majora ſoluta in unam molem concreſcunt ſæpe <lb/>firmiſſime cohærentem interpoſito Fluido vel Semifluido, quod <lb/>poſtea Fluidum manet, vel in maſſam firmam cum reliquis corpo-<lb/>ribus abit. </s> <s xml:id="echoid-s9717" xml:space="preserve">Specula duo plana & </s> <s xml:id="echoid-s9718" xml:space="preserve">ſicca ſibi imponantur, parum co-<lb/>hærent, verum iis interponatur Aqua, Oleum, Pinguedo ſoluta, <lb/>animalium liquidum Gluten, Therebinthina, Pix aliave ejuſmodi <lb/>glutinoſa, multo fortius cohærebunt: </s> <s xml:id="echoid-s9719" xml:space="preserve">Eodem modo elapidibus duo-<lb/>bus, interjecta cera, reſina, aut reſinoſis, maſſam unitam com-<lb/>ponemus: </s> <s xml:id="echoid-s9720" xml:space="preserve">Fabri Lignarii gluten ſemifluidum inter duo ligna inter-<lb/>ponunt, poros implent, ligna comprimunt, quæ ſæpe non minus <lb/>cohærent, quam ſi naturaliter concreviſſent: </s> <s xml:id="echoid-s9721" xml:space="preserve">Cæmentarii inter la-<lb/>teres maſſam interpungunt ſemifluidam, quæ eſt aqua cum arena <lb/>& </s> <s xml:id="echoid-s9722" xml:space="preserve">calce ſubacta, qua cum lateres in molem firmam abeunt: </s> <s xml:id="echoid-s9723" xml:space="preserve">Inter <lb/>duo duriora metalla aliud mollius aut facilius in igne liqueſcens ſe-<lb/>mifluidum fundatur, quo corpus unitum & </s> <s xml:id="echoid-s9724" xml:space="preserve">valde cohærens com-<lb/>ponitur: </s> <s xml:id="echoid-s9725" xml:space="preserve">hæc vulgaria ſunt, verum addere convenit alia experi-<lb/>menta quæ infra explicabo, ut & </s> <s xml:id="echoid-s9726" xml:space="preserve">rationem quare inſtituta ſint.</s> <s xml:id="echoid-s9727" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9728" xml:space="preserve">1°. </s> <s xml:id="echoid-s9729" xml:space="preserve">Præparata fuerunt ex vitro albo duo corpora ejus formæ quam <lb/>exhibet Tab. </s> <s xml:id="echoid-s9730" xml:space="preserve">XVII. </s> <s xml:id="echoid-s9731" xml:space="preserve">fig. </s> <s xml:id="echoid-s9732" xml:space="preserve">1. </s> <s xml:id="echoid-s9733" xml:space="preserve">A B C, quorum caput A craſſius & </s> <s xml:id="echoid-s9734" xml:space="preserve"><lb/>rotundiuſculum diametrum habet 2 {1/5} pollic. </s> <s xml:id="echoid-s9735" xml:space="preserve">Rhenol. </s> <s xml:id="echoid-s9736" xml:space="preserve">& </s> <s xml:id="echoid-s9737" xml:space="preserve">altitudinem <lb/>{1/2} pollicis; </s> <s xml:id="echoid-s9738" xml:space="preserve">pars inferior B C cylindrica eſt, diametri 1 {1/1 1/2} pollic. </s> <s xml:id="echoid-s9739" xml:space="preserve">al-<lb/>titudinis {3/4} pollic. </s> <s xml:id="echoid-s9740" xml:space="preserve">erat baſis B C & </s> <s xml:id="echoid-s9741" xml:space="preserve">planiſſima & </s> <s xml:id="echoid-s9742" xml:space="preserve">polita. </s> <s xml:id="echoid-s9743" xml:space="preserve">Dein-<lb/>de confectum fuit ex denſo Cupro corpus cavum F G. </s> <s xml:id="echoid-s9744" xml:space="preserve">fig. </s> <s xml:id="echoid-s9745" xml:space="preserve">2. </s> <s xml:id="echoid-s9746" xml:space="preserve">per-<lb/>foratum in G, ita ut Vitri A B C, partem inferiorem B C trans-<lb/>mitteret, arcte autem comprehenderet caput craſſius A. </s> <s xml:id="echoid-s9747" xml:space="preserve">in margine <lb/>interiori F donabatur cochlea, cui alia reſpondebat E operculi D E: <lb/></s> <s xml:id="echoid-s9748" xml:space="preserve">immiſſo vitro huic æneæ capſulæ appoſitum fuit operculum; </s> <s xml:id="echoid-s9749" xml:space="preserve">hic ap-<lb/>paratus ex unco K appenſus fuit Libræ brachio, reductusque in æ-<lb/>quilibrium: </s> <s xml:id="echoid-s9750" xml:space="preserve">alterum corpus vitreum, ſimile & </s> <s xml:id="echoid-s9751" xml:space="preserve">æquale priori etiam <lb/>ſimili apparatui æneo incluſum fuit, poſitumque in menſa, ita ut <lb/>baſin accurate horizontalem habuerit; </s> <s xml:id="echoid-s9752" xml:space="preserve">tum alterum dimiſſum ut <lb/>ſuâ baſi baſin inferioris attingeret, quemadmodum fig. </s> <s xml:id="echoid-s9753" xml:space="preserve">3. </s> <s xml:id="echoid-s9754" xml:space="preserve">oſtendit, <lb/>obſervatæ ſunt ambo corpora cohæſiſſe, aut ſe attraxiſſe vi 1 {1/2} gra-<lb/>norum Medicorum, quamvis utraque baſis fuerit ſicciſſima & </s> <s xml:id="echoid-s9755" xml:space="preserve">mo-<lb/>do ante mundata.</s> <s xml:id="echoid-s9756" xml:space="preserve"/> </p> <pb o="435" file="0449" n="449" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s9757" xml:space="preserve">2°. </s> <s xml:id="echoid-s9758" xml:space="preserve">Utrique baſi Aquâ puriſſimâ aſperſâ obſervata fuit ſecundum <lb/>priorem methodum Cohærentia 9 Unciarum: </s> <s xml:id="echoid-s9759" xml:space="preserve">quoniam Cohærentiam <lb/>majorem futuram exiſtimaveram, ſub Aqua in vaſe amplo demer-<lb/>ſos cylindros eodem modo exploravi, qui non plus, quam 9 Un-<lb/>ciarum viribus cohæſerunt, quamvis ſollicite curaverim ne latera-<lb/>liter moverentur.</s> <s xml:id="echoid-s9760" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9761" xml:space="preserve">3°. </s> <s xml:id="echoid-s9762" xml:space="preserve">Abſterſis ſuperſiciebus illivi oleum raparum, neque majorem <lb/>Cohærentiam quam 8 {1/2} Unciarum deprehendi.</s> <s xml:id="echoid-s9763" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9764" xml:space="preserve">4°. </s> <s xml:id="echoid-s9765" xml:space="preserve">Tum vitra ambo calefeci eouſque, ut ſebum candelarum ba-<lb/>ſibus eorum impoſitum cito liquefactum fuerit, utrâque baſi eo be-<lb/>ne illitâ ambo iterum ſibi impoſui, paulum ſupra ſe movendo, ne <lb/>aër ullus intrinſecus maneret, atque ad ſe appreſſa refrigerio com-<lb/>miſi, elapſâ horâ & </s> <s xml:id="echoid-s9766" xml:space="preserve">ſtante Fahrenheytii Thermoſcopio ad 50 gra-<lb/>dum exploravi Cohærentiam, quæ fuit æqualis libris 298.</s> <s xml:id="echoid-s9767" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9768" xml:space="preserve">5°. </s> <s xml:id="echoid-s9769" xml:space="preserve">Abſterſis baſibus, calefactisque magis quam ante, donec Ce-<lb/>ra flava facile ſuper iis liqueſceret, iterum ambo vitra ſibi impoſita <lb/>refrigerio commiſi, & </s> <s xml:id="echoid-s9770" xml:space="preserve">exſpectatâ horâ diei, qua Thermoſcopium <lb/>idem frigus notabat, Cohærentiam deprehendi fuiſſe librarum 230.</s> <s xml:id="echoid-s9771" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9772" xml:space="preserve">6°. </s> <s xml:id="echoid-s9773" xml:space="preserve">Mundatis iterum baſibus multo plus calefacta fuerunt, donec <lb/>pix nigra vulgaris, ſed pura, ſponte & </s> <s xml:id="echoid-s9774" xml:space="preserve">facile ſuper ea fluxerit; </s> <s xml:id="echoid-s9775" xml:space="preserve">ſibi <lb/>impoſita fuerunt & </s> <s xml:id="echoid-s9776" xml:space="preserve">quieverunt donec frigus æquale ac ante obſer-<lb/>vabatur, tum autem cohæſerunt vi 850. </s> <s xml:id="echoid-s9777" xml:space="preserve">librarnm.</s> <s xml:id="echoid-s9778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9779" xml:space="preserve">7°. </s> <s xml:id="echoid-s9780" xml:space="preserve">Deinde fabrefacti fuerunt duo cylindri ex Cupro flavo ejus <lb/>formæ, quam Tab. </s> <s xml:id="echoid-s9781" xml:space="preserve">XVII. </s> <s xml:id="echoid-s9782" xml:space="preserve">fig. </s> <s xml:id="echoid-s9783" xml:space="preserve">4. </s> <s xml:id="echoid-s9784" xml:space="preserve">exhibet, quorum baſes B C dia-<lb/>metrum 1 {11/12} poll. </s> <s xml:id="echoid-s9785" xml:space="preserve">Rhenol. </s> <s xml:id="echoid-s9786" xml:space="preserve">habebant, baſes ambæ erant planæ, læ-<lb/>vigatæ, non tamen uſque ad ſplendorem: </s> <s xml:id="echoid-s9787" xml:space="preserve">erat craſſities cujuslibet <lb/>A B {4/10} poll. </s> <s xml:id="echoid-s9788" xml:space="preserve">Uncus D & </s> <s xml:id="echoid-s9789" xml:space="preserve">annulus transmiſſus craſſus erat {3/10} poll. </s> <s xml:id="echoid-s9790" xml:space="preserve">hos <lb/>bene ſiccos mundosque ſibi impoſui. </s> <s xml:id="echoid-s9791" xml:space="preserve">veluti in hac figura 4 conſpi-<lb/>ciuntur, ab uno ex fune brachio Libræ alligato ut baſis eſſet hori-<lb/>zontalis, attrahebatur alterum vi 2 granorum.</s> <s xml:id="echoid-s9792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9793" xml:space="preserve">8°. </s> <s xml:id="echoid-s9794" xml:space="preserve">Aqua baſibus eorum affuſa effecit ut cohæſerint viduodecim <lb/>Unciarum.</s> <s xml:id="echoid-s9795" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9796" xml:space="preserve">9°. </s> <s xml:id="echoid-s9797" xml:space="preserve">Interpoſito baſibus oleo raparum, cohæſerunt viribus 18 Un-<lb/>ciarum.</s> <s xml:id="echoid-s9798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9799" xml:space="preserve">10°. </s> <s xml:id="echoid-s9800" xml:space="preserve">Intermiſſa baſibus Therebinthina Veneta prius calefacta co-<lb/>hæſerunt vi 24 Unciarum: </s> <s xml:id="echoid-s9801" xml:space="preserve">Sed calefactis interpoſitâ Colophoniâ, <lb/>frigidi rurſum cohæſerunt plus quam vi librarum 850.</s> <s xml:id="echoid-s9802" xml:space="preserve"/> </p> <pb o="436" file="0450" n="450" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s9803" xml:space="preserve">11°. </s> <s xml:id="echoid-s9804" xml:space="preserve">Illito animalium glutine calido, quo fabri lignarii utuntur, <lb/>erat poſtea frigefactorum Cohærentia minor quam librarum 100, <lb/>major tamen quam 90.</s> <s xml:id="echoid-s9805" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9806" xml:space="preserve">12°. </s> <s xml:id="echoid-s9807" xml:space="preserve">Interpoſito Sebo liquefacto, inter calidos, refrigerati ut ſu-<lb/>pra, cohæſerunt vi librarum 800.</s> <s xml:id="echoid-s9808" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9809" xml:space="preserve">13°. </s> <s xml:id="echoid-s9810" xml:space="preserve">Interpoſita Cera liquefacta cylindrisque bene calefactis ut <lb/>Ceram fuderint, refrigerati poſtea cohæſerunt vi librar. </s> <s xml:id="echoid-s9811" xml:space="preserve">900.</s> <s xml:id="echoid-s9812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9813" xml:space="preserve">14°. </s> <s xml:id="echoid-s9814" xml:space="preserve">Interpoſita Pice in Igne ſoluta cylindrisque prius probe ca-<lb/>lefactis, refrigeratorum poſtea obſervata fuit Cohærentia major <lb/>librarum 1400; </s> <s xml:id="echoid-s9815" xml:space="preserve">quanta ſit, definire nequeo, cum annuli cuprei, <lb/>D fig. </s> <s xml:id="echoid-s9816" xml:space="preserve">4. </s> <s xml:id="echoid-s9817" xml:space="preserve">uncique ferrei, ex quibus ſuſpendebantur, fuerint disru-<lb/>pti, manente tamen baſium conjunctione.</s> <s xml:id="echoid-s9818" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9819" xml:space="preserve">15°. </s> <s xml:id="echoid-s9820" xml:space="preserve">Duo cylindri, quos repræſentat fig. </s> <s xml:id="echoid-s9821" xml:space="preserve">5. </s> <s xml:id="echoid-s9822" xml:space="preserve">Tab. </s> <s xml:id="echoid-s9823" xml:space="preserve">XVII. </s> <s xml:id="echoid-s9824" xml:space="preserve">ex mar-<lb/>more albo confecti, planiſſimarum baſium, quarum diameter erat <lb/>2 {1/12} digitorum, interpoſitâ Aquâ cohæſerunt vi 6 Unciarum.</s> <s xml:id="echoid-s9825" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9826" xml:space="preserve">16°. </s> <s xml:id="echoid-s9827" xml:space="preserve">Sed iis affuſo oleo Cohærentia fuit 15 {1/2} Unciarum.</s> <s xml:id="echoid-s9828" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9829" xml:space="preserve">17°. </s> <s xml:id="echoid-s9830" xml:space="preserve">Calefactis cylindris & </s> <s xml:id="echoid-s9831" xml:space="preserve">interpoſitâ Cera liquefacta cohæſe-<lb/>runt frigidi vi 1250 librar.</s> <s xml:id="echoid-s9832" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9833" xml:space="preserve">18°. </s> <s xml:id="echoid-s9834" xml:space="preserve">Calidis baſibus affuſo ſebo candelarum, frigidi poſtea cylin-<lb/>dri cohæſerunt vi librarum 900.</s> <s xml:id="echoid-s9835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9836" xml:space="preserve">19°. </s> <s xml:id="echoid-s9837" xml:space="preserve">Alii cylindri majores ex marmore albo confecti, diametri <lb/>2 {7/12} digitorum calefacti & </s> <s xml:id="echoid-s9838" xml:space="preserve">interpoſito ſebo calido, deinde refrige-<lb/>rati cohæſerunt vi librarum 1150.</s> <s xml:id="echoid-s9839" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9840" xml:space="preserve">20°. </s> <s xml:id="echoid-s9841" xml:space="preserve">Alii minores ex eodem marmore, quorum diameter baſeos <lb/>erat {10/12} digiti, calefacti ut ſebum fuderint, frigidi ut supra, cohæſe-<lb/>runt vi librarum 200.</s> <s xml:id="echoid-s9842" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9843" xml:space="preserve">21°. </s> <s xml:id="echoid-s9844" xml:space="preserve">Confecti fuerunt ex marmore nigro alii cylindri, quorum <lb/>diameter fuit 2 {2/12} digitorum, qui eodem modo tractati interpoſito <lb/>ſebo cohæſerunt vi librarum 900.</s> <s xml:id="echoid-s9845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9846" xml:space="preserve">22°. </s> <s xml:id="echoid-s9847" xml:space="preserve">Ex Ebore tandem duo confecti ſunt, quorum diameter <lb/>2 {7/12} digitorum, hi interfuſo ſebo tantum cohæſerunt vi librarum <lb/>200.</s> <s xml:id="echoid-s9848" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9849" xml:space="preserve">§. </s> <s xml:id="echoid-s9850" xml:space="preserve">6 Ex miſturâ nonnullorum fluidorum oriuntur maſſæ firmæ, <lb/>quemadmodum fit in omni coagulatione; </s> <s xml:id="echoid-s9851" xml:space="preserve">Lac cum acido miſceatur, <lb/>in caſeum abibit: </s> <s xml:id="echoid-s9852" xml:space="preserve">Spiritus Urinæ Alcoholi vini affundatur, in Of-<lb/>fam Helmontii mutabitur, glaciei duritiem æmulantem: </s> <s xml:id="echoid-s9853" xml:space="preserve">miſcea- <pb o="437" file="0451" n="451" rhead="CORPORUM FIRMORUM."/> tur Oleum Vitrioli cum Oleo Alcalini Salis per deliquium ſoluti, <lb/>efferveſcentia fit, quâ ſedata in fundo vaſis concreſcit Salina ſoli-<lb/>da maſla; </s> <s xml:id="echoid-s9854" xml:space="preserve">ejuſmodi phænomena etiam fiunt quotieſcunque Sales re-<lb/>generantur.</s> <s xml:id="echoid-s9855" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9856" xml:space="preserve">§. </s> <s xml:id="echoid-s9857" xml:space="preserve">7. </s> <s xml:id="echoid-s9858" xml:space="preserve">Tandemex corporibus minoribus diſſolutis majores maſſas <lb/>componimus, transfigendo clavos ferreos ligneosve; </s> <s xml:id="echoid-s9859" xml:space="preserve">quod idem eſt <lb/>ac ſi corpora ramoſa ſe intricaſſent: </s> <s xml:id="echoid-s9860" xml:space="preserve">eo modo Aqua in glaciem du-<lb/>riſſimam concreſcere videtur, cum particulis Aquæ infiguntur cla-<lb/>vi, in Aëre natantes, forte nitroſæ indolis, qui ex plurimis ſub-<lb/>tilibus particulis aquæ, a ſe ſeparatis maſſam firmiſſimam compo-<lb/>nunt: </s> <s xml:id="echoid-s9861" xml:space="preserve">Vincula etiam circa minores maſſas circumjiciendo majores <lb/>moles componimus.</s> <s xml:id="echoid-s9862" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9863" xml:space="preserve">Hiſce modis natura & </s> <s xml:id="echoid-s9864" xml:space="preserve">ars utuntur ad corpora conjungenda in ma-<lb/>jores moles: </s> <s xml:id="echoid-s9865" xml:space="preserve">non tamen affirmo plures non dari; </s> <s xml:id="echoid-s9866" xml:space="preserve">cognitos tantum me-<lb/>moravi; </s> <s xml:id="echoid-s9867" xml:space="preserve">alios, procul dubio, ſedulæ nepotum obſervationes detegent.</s> <s xml:id="echoid-s9868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9869" xml:space="preserve">Ut autem memorata hucuſque phænomena in ſeptem enumeratis <lb/>modis exponamus, oportet quæramus cauſam Cohærentiæ uni-<lb/>verſalem, vel ſi plures dentur, tum omnes.</s> <s xml:id="echoid-s9870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9871" xml:space="preserve">Ordiamur igitur a rerum principiis, & </s> <s xml:id="echoid-s9872" xml:space="preserve">inveſtigemus, quænam <lb/>cauſa faciat, ut duo elementa, aut corpuscula minima & </s> <s xml:id="echoid-s9873" xml:space="preserve">ultima <lb/>inter ſe cohæreant, componantque moleculam aliquam unitam?</s> <s xml:id="echoid-s9874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9875" xml:space="preserve">Quotieſcunque bina elementa ſibi impoſita cohærent, ut non <lb/>eadem vi rurſus removeantur qua imponebantur, vis datur, quæ <lb/>partes conjungit; </s> <s xml:id="echoid-s9876" xml:space="preserve">ſimulac enim vi uteris ad ſolvenda elementa, <lb/>hæc reſiſtendo æqualem vim exercent; </s> <s xml:id="echoid-s9877" xml:space="preserve">quippe ubicunque actio po-<lb/>tentiæ datur, ibi quoque reactio æqualis virtutis adeſt: </s> <s xml:id="echoid-s9878" xml:space="preserve">adeoque <lb/>eſt vis quædam, quæ Elementa unit: </s> <s xml:id="echoid-s9879" xml:space="preserve">hanc ſi abeſſe ponas, ſoluta <lb/>ſunt, neque vi ſeparante indigent: </s> <s xml:id="echoid-s9880" xml:space="preserve">impone ſibi duo Elementa, ne-<lb/>que dari vim concipias retinentem, æque facile â ſe ſecedent ac ac-<lb/>cumulaveras, haud ſecus ac ſi arenam arenæ impoſuiſſes, quam æ-<lb/>que facile ab altera removeres, ac admoveras; </s> <s xml:id="echoid-s9881" xml:space="preserve">ſed cohæreant are-<lb/>næ, tum quid aliud acceſſit, vi indiges ut divellas, ergo ab illis <lb/>vis oppoſita exercetur, id igitur quod acceſſit, vis fuit: </s> <s xml:id="echoid-s9882" xml:space="preserve">neque ma-<lb/>jora corpora aliter ſecum cohærent quam ope virtutis alicujus, quia <lb/>nunquam in fragmenta ſeparari poſſunt niſi vi adhibita, cui reſtitit <lb/>vis oppoſita, quæ eſt vis unionis in partibus.</s> <s xml:id="echoid-s9883" xml:space="preserve"/> </p> <pb o="438" file="0452" n="452" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s9884" xml:space="preserve">Progrediamur, & </s> <s xml:id="echoid-s9885" xml:space="preserve">inveſtigemus quænam ſit vis unionis, quomo-<lb/>do ſit comparata, & </s> <s xml:id="echoid-s9886" xml:space="preserve">quibus donata proprietatibus: </s> <s xml:id="echoid-s9887" xml:space="preserve">Duplicis poteſt <lb/>modo eſſe indolis, Externa nempe aut Interna. </s> <s xml:id="echoid-s9888" xml:space="preserve">Nam nec expe-<lb/>rientia nec ratio aliam vim, præter has duas, detexit, nec dari alia <lb/>poteſt: </s> <s xml:id="echoid-s9889" xml:space="preserve">Externam prius examinemus, Internam poſtea.</s> <s xml:id="echoid-s9890" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9891" xml:space="preserve">A ſimpliciſſimis incipiamus elementis corporeis, atque duo ſibi <lb/>impoſita cohærere obſervemus, horum Cohærentia a vi externa <lb/>pendeat: </s> <s xml:id="echoid-s9892" xml:space="preserve">Vinculum ea ambiens circumquaque & </s> <s xml:id="echoid-s9893" xml:space="preserve">ſolidum non po-<lb/>terit eſſe cauſa vel virtus illius unionis, quærerem enim an id vin-<lb/>culum non conſtet ex partibus, ſive elementis ſibi impoſitis? </s> <s xml:id="echoid-s9894" xml:space="preserve">ne-<lb/>gari nequit; </s> <s xml:id="echoid-s9895" xml:space="preserve">ſed quomodo hæc inter ſe cohærent? </s> <s xml:id="echoid-s9896" xml:space="preserve">an etiam ope <lb/>vinculi ambientis? </s> <s xml:id="echoid-s9897" xml:space="preserve">tum circa hoc alterum vinculum eadem rediret <lb/>quæſtio in infinitum uſque continuanda: </s> <s xml:id="echoid-s9898" xml:space="preserve">quare omnis externi vin-<lb/>culi conceptus ſponte deſtruitur.</s> <s xml:id="echoid-s9899" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9900" xml:space="preserve">Melius vis externa in preſſione quadam reſidere affirmaretur, quæ <lb/>ſcilicet extrinſecus corporibus duobus incumbens, ea ita introrſum <lb/>comprimat, & </s> <s xml:id="echoid-s9901" xml:space="preserve">verſus ſe mutuo pellat, ut reſolvi nequeant niſi preſſione <lb/>ſuperata â vi quacumque aliâ contrarie agente: </s> <s xml:id="echoid-s9902" xml:space="preserve">Profecto fatendum eſt <lb/>nos â natura quaſi duci ad preſſionem externam ponendam, quia hæc <lb/>clariſſime poteſt concipi, & </s> <s xml:id="echoid-s9903" xml:space="preserve">nonnulla corpora ejus ope cohærent.</s> <s xml:id="echoid-s9904" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9905" xml:space="preserve">Sed quænam cauſa externa premens, & </s> <s xml:id="echoid-s9906" xml:space="preserve">omnia corpora uniens, <lb/>adeoque Univerſalis, eſſe poteſt? </s> <s xml:id="echoid-s9907" xml:space="preserve">Fluida tantum, quæ omnia am-<lb/>biat corpora, ſive in viſceribus Terræ, ſive in ejus ſuperficie, vel <lb/>ſupra eam poſita; </s> <s xml:id="echoid-s9908" xml:space="preserve">adeoque Fluidum Univerſale poſtulatur; </s> <s xml:id="echoid-s9909" xml:space="preserve">quod <lb/>erit vel Aër Elaſticus, vel Ignis, vel Æther ſubtilis: </s> <s xml:id="echoid-s9910" xml:space="preserve">Hinc Philo-<lb/>ſophi nonnulli ad Aërem, alii ad Ætherem confugerunt, opinati <lb/>hoc fluidum ſua gravitate comprimere corpora æque majora, ac <lb/>minora verſus ſe mutuo, inde eorum pendere Cohærentiam, cujus <lb/>magnitudo eſſet in ratione preſſionis; </s> <s xml:id="echoid-s9911" xml:space="preserve">Cohærentiam ſolvi non poſſe <lb/>niſi a cauſa, quæ pondus Aëris Ætheriſve ſuperaret: </s> <s xml:id="echoid-s9912" xml:space="preserve">Meretur ſenten-<lb/>tia utraque paulo fuſius examinari.</s> <s xml:id="echoid-s9913" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9914" xml:space="preserve">Qui Aëris Elaſtici gravitatem crediderunt eſſe cauſam firmitatis, <lb/>innixi fuerunt Experimento Magdeburgico, in quo duo hemiſphæ-<lb/>ria cuprea, cava, ſibi impoſita, aëre interno educto, validiſſime <lb/>cohæſerunt preſſa a pondere Aëris externi, uti ſupra tradidimus: <lb/></s> <s xml:id="echoid-s9915" xml:space="preserve">Ex quo concluſerunt, omnia corpora ſibi impoſita, ut Aërem in- <pb o="439" file="0453" n="453" rhead="CORPORUM FIRMORUM."/> ter ſuas ſuperficies non comprehenderent, ab Aëre externo com-<lb/>preſſa cohærere; </s> <s xml:id="echoid-s9916" xml:space="preserve">atque ita Univerſale hoc fluidum eſſe Cohærentiæ <lb/>cauſam univerſalem.</s> <s xml:id="echoid-s9917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9918" xml:space="preserve">Negari profecto nequit omnia fere corpora terreſtria comprimi <lb/>ab aëre elaſtico ambiente, atque ita compreſſa cohærere pro aliqua <lb/>parte: </s> <s xml:id="echoid-s9919" xml:space="preserve">verum omnem eorum Cohærentiam ab hujus Aëris preſſio-<lb/>ne pendere nego præfracte, niſi effectus ſtatuatur maior ipſâ cau-<lb/>ſâ; </s> <s xml:id="echoid-s9920" xml:space="preserve">quod abſurdum; </s> <s xml:id="echoid-s9921" xml:space="preserve">cum evidentiſſime demonſtratum ſit, cauſæ <lb/>ſemper adæquatum eſſe effectum: </s> <s xml:id="echoid-s9922" xml:space="preserve">Ecce vero difficultates, quibus <lb/>hæc opinio premitur: </s> <s xml:id="echoid-s9923" xml:space="preserve">Inter modos Cohærentiæ attuli experimenta <lb/>cum cylindris cupreis, vitreis, marmoreis, lævigatæ baſis, quæ <lb/>oleo, ſebo, cera, & </s> <s xml:id="echoid-s9924" xml:space="preserve">pice obducebatur, inſtituta: </s> <s xml:id="echoid-s9925" xml:space="preserve">ſebo, cera & </s> <s xml:id="echoid-s9926" xml:space="preserve">pice <lb/>interpoſitis inter ſuperficies, excluſus erat aër ex ſuperficiebus ſe <lb/>attingentibus, comprimebantur proinde ab aëre externo: </s> <s xml:id="echoid-s9927" xml:space="preserve">an igitur <lb/>compreſſio hæc non erit eadem (manente baroſcopio æque alto) ſive <lb/>inter eosdem cylindros interpoſitum ſit ſebum, ſive cera, ſive pix? <lb/></s> <s xml:id="echoid-s9928" xml:space="preserve">negari hoc nequit, quippe ſupra eandem ſuperficiem Aër idem pre-<lb/>mit eodem pondere: </s> <s xml:id="echoid-s9929" xml:space="preserve">quid vero docuit experientia? </s> <s xml:id="echoid-s9930" xml:space="preserve">maxime cohæ-<lb/>ſiſſe cylindros interpoſità pice, minus interpoſitâ cera, minus ad-<lb/>huc interpoſito animalium ſebo, minus adhuc interpoſito glutine <lb/>(Belgice Leim). </s> <s xml:id="echoid-s9931" xml:space="preserve">ubi igitur tantopere inter ſe discrepant magnitudi-<lb/>nes effectuum, an ibi cauſa eadem & </s> <s xml:id="echoid-s9932" xml:space="preserve">æque magna poni poterit?</s> <s xml:id="echoid-s9933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9934" xml:space="preserve">2°. </s> <s xml:id="echoid-s9935" xml:space="preserve">Aëris elaſtici gravitas eſt determinata & </s> <s xml:id="echoid-s9936" xml:space="preserve">cognita, quippe in <lb/>hac regione nunquam ſuperavit (quantum à longisſimâ usque me-<lb/>moriâ ex annalibus barometricis colligere datum eſt) pondus mer-<lb/>curii 30. </s> <s xml:id="echoid-s9937" xml:space="preserve">pollices Rhenolandicos alti, adeoque hoc pondus incum-<lb/>bens ſuperficiei cylindri, cujus baſis eſt 2 {7/10} pollic: </s> <s xml:id="echoid-s9938" xml:space="preserve">facile ſuppu-<lb/>tando detegitur, quod nondum aequale libris 90 Amſtelodamen-<lb/>ſibus deprehendetur: </s> <s xml:id="echoid-s9939" xml:space="preserve">verum marmorei cylindri dictæ baſeos, in-<lb/>terpoſito ſebo cohæſerunt vi librar. </s> <s xml:id="echoid-s9940" xml:space="preserve">1150. </s> <s xml:id="echoid-s9941" xml:space="preserve">alii minores adhuc, <lb/>interpoſita cerâ Cohæſerunt vi libr. </s> <s xml:id="echoid-s9942" xml:space="preserve">1250. </s> <s xml:id="echoid-s9943" xml:space="preserve">Cuprei multo mino-<lb/>ris diametri interpoſita pice cohæſerunt plusquam vi libr. </s> <s xml:id="echoid-s9944" xml:space="preserve">1400. <lb/></s> <s xml:id="echoid-s9945" xml:space="preserve">unde igitur hæc cohærentia oritur, quæ ſuperat toties pondus <lb/>aëris incumbentis: </s> <s xml:id="echoid-s9946" xml:space="preserve">concedam cylindros marmoreos diametri 2 {7/10} <lb/>pollic. </s> <s xml:id="echoid-s9947" xml:space="preserve">comprimi ab aëre pondere 90. </s> <s xml:id="echoid-s9948" xml:space="preserve">libr, & </s> <s xml:id="echoid-s9949" xml:space="preserve">tantopere cohæ-<lb/>rere, ſed obducti ſebo cohærent vi libr. </s> <s xml:id="echoid-s9950" xml:space="preserve">1150, adeoque duodecies <pb o="440" file="0454" n="454" rhead="INTRODUCTIO AD COHÆRENTIAM."/> plus quam ab aëre comprimebantur; </s> <s xml:id="echoid-s9951" xml:space="preserve">quamobrem Aëris gravitas <lb/>aut pondus nequit poni cauſa tanto majoris Cohærentiæ.</s> <s xml:id="echoid-s9952" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9953" xml:space="preserve">3°. </s> <s xml:id="echoid-s9954" xml:space="preserve">Si Aër Elaſticus ſit cauſa Cohærentiæ, quid eveniet corpo-<lb/>ribus poſitis in vacuo, in quo nullus Aër craſſior aut elaſticus ha-<lb/>betur, quale eſt vacuum Torricellianum? </s> <s xml:id="echoid-s9955" xml:space="preserve">hæc non amplius com-<lb/>preſſa, cohærere deſinent; </s> <s xml:id="echoid-s9956" xml:space="preserve">metalla, lapides, vitra, & </s> <s xml:id="echoid-s9957" xml:space="preserve">quæcunque <lb/>fuerint corpora firma modo inſtar cumuli arenarii ex ſolutis gra-<lb/>nis compoſiti, ſe habebunt, quæ minimo motu a ſe removentur <lb/>diffluuntque: </s> <s xml:id="echoid-s9958" xml:space="preserve">an vero ejusmodi aliquid in vacuo Torricelliano ob-<lb/>ſervatur unquam? </s> <s xml:id="echoid-s9959" xml:space="preserve">nihil minus, metalla manent firma, ſaxa ne-<lb/>quaquam in pulverem fatiscunt, & </s> <s xml:id="echoid-s9960" xml:space="preserve">vitrum magnam firmitatem <lb/>oſtendit: </s> <s xml:id="echoid-s9961" xml:space="preserve">forte vacuum Torricellianum non penitus orbatum Aëre <lb/>craſſo & </s> <s xml:id="echoid-s9962" xml:space="preserve">elaſtico ſtatuetur, atque idcirco corpora adhuc ab eo, <lb/>qui intus remanſit, Aëre comprimi & </s> <s xml:id="echoid-s9963" xml:space="preserve">firmitatem retinere: </s> <s xml:id="echoid-s9964" xml:space="preserve">dubito <lb/>tamen vehementer hoc reſponſum datum iri â Viris, qui unquam <lb/>Baroſcopium viderunt, examinarunt, aut confecerunt, quippe <lb/>apud omnes evictum eſt in ſuperiori parte Tubi Baroſcopici bene <lb/>confecti, nibil Aëris remanere, in hoc Vacuo tamen parietes Tu-<lb/>bi integri manent, ut & </s> <s xml:id="echoid-s9965" xml:space="preserve">quælibet incluſa ſolida: </s> <s xml:id="echoid-s9966" xml:space="preserve">addam in vacuo <lb/>Boyleano hemisphæria concluſa, quæ antea ab Aëre externo <lb/>compreſſa firmiter cohæſerant, pondere minimo â ſe divelli, hic <lb/>ceſſat preſſio, quia Aër ſublatus eſt; </s> <s xml:id="echoid-s9967" xml:space="preserve">ſi igitur ex recipiente vitreo <lb/>ope Antliæ pneumaticæ Aër tolli potuerit, qui Cohærentiam he-<lb/>misphæriorum Magdeburgicorum eſſecerat, multo magis Aër è ſu-<lb/>periori parte Tubi Torricelliani ſublatus erit; </s> <s xml:id="echoid-s9968" xml:space="preserve">in hoc autem va-<lb/>cuo, uti & </s> <s xml:id="echoid-s9969" xml:space="preserve">in Boyleano manent corpora firma, unita, dura, <lb/>cohærentia: </s> <s xml:id="echoid-s9970" xml:space="preserve">in recipientibus ſuspenſi cylindri marmorei inter-<lb/>poſito ſebo uniti, manent educto Aëre uniti, neque ab appenſis <lb/>centenis ponderibus, annexis filo cupreo tranſeunte inferius per <lb/>capſulam coriaceam, diſſolvuntur.</s> <s xml:id="echoid-s9971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9972" xml:space="preserve">4°. </s> <s xml:id="echoid-s9973" xml:space="preserve">Sed regeramus modo, quod olim de Lanis in hac opinione <lb/>obſervaverat: </s> <s xml:id="echoid-s9974" xml:space="preserve">Detur Cylindrus ſolidus ex cupro, alter priori æqua-<lb/>lis ex plumbo, tertius æque craſſus cum primo ex chalybe: </s> <s xml:id="echoid-s9975" xml:space="preserve">an <lb/>non premet Aër elaſticus hos omnes vi eadem? </s> <s xml:id="echoid-s9976" xml:space="preserve">habent enim <lb/>ſuperficiem eandem, habent poros anguſtiores, quam quos Aër <lb/>perrepere aut ingredi poteſt, adeoque vi eadem prementur, &</s> <s xml:id="echoid-s9977" xml:space="preserve"> <pb o="441" file="0455" n="455" rhead="CORPORUM FIRMORUM."/> æqualiter cohærebunt: </s> <s xml:id="echoid-s9978" xml:space="preserve">ſed patebit in examine firmitatis metallo-<lb/>rum, Chalybem fortiſſime cohærere, minus Cuprum, multo minus <lb/>Plumbum. </s> <s xml:id="echoid-s9979" xml:space="preserve">Arbitror hæc argumenta eſſe adeo convincentia; </s> <s xml:id="echoid-s9980" xml:space="preserve">ut <lb/>nemo amplius ſententiam eam, quæ Aërem craſſum Cohærentiæ <lb/>cauſam ſtatuit, amplecti poſſit.</s> <s xml:id="echoid-s9981" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9982" xml:space="preserve">Mecum plurimi alii idcirco Aërem craſſum ex cauſis univer-<lb/>ſalibus Cohærentiæ proſcripſerunt: </s> <s xml:id="echoid-s9983" xml:space="preserve">inter eos tamen nonnulli cau-<lb/>ſam externam debere dari exiſtimantes, ad Aërem quendam ſub-<lb/>tiliſſimum, quem Æthera vocant, confugerunt, qui longe majorum <lb/>foret virtutum, quam elaſticus atmosphæræ, & </s> <s xml:id="echoid-s9984" xml:space="preserve">qui ſuo pondere <lb/>efficere poſſet, ut corpora firmiſſime cohæreant, hæc plus, alia mi-<lb/>nus: </s> <s xml:id="echoid-s9985" xml:space="preserve">concipiunt hunc Ætherem eſſe ſluidum aliquod ſubtiliſſimum, <lb/>adimplentem omnesſpatii in hocUniverſo partes, omnesque corpo-<lb/>rum majorum poros; </s> <s xml:id="echoid-s9986" xml:space="preserve">hunc partibus corporum ſolidis incumbere, <lb/>eas ad ſe mutuo apprimere, appreſſasque retinere, quemadmodum <lb/>fautores ſententiæ modo ante allatæ, Aërem elaſticum hemisphæ-<lb/>ria Magdeburgica apprimere atque in unam maſſam conjungere <lb/>aſſeruerant: </s> <s xml:id="echoid-s9987" xml:space="preserve">quam hypotheſin eleganter adſtruere conati fuerunt <lb/>Malebranche in Lib. </s> <s xml:id="echoid-s9988" xml:space="preserve">6 de Inquirenda Veritate. </s> <s xml:id="echoid-s9989" xml:space="preserve">tum Jacobus Ber-<lb/>nouillius in erudito Tractatu de Gravitate Ætberis.</s> <s xml:id="echoid-s9990" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9991" xml:space="preserve">Verum utcunque ingenioſa ſit hæc Hypotheſis. </s> <s xml:id="echoid-s9992" xml:space="preserve">nihilominus in-<lb/>ſolubilibus implicita eſt difficultatibus, quæ ipſam a veritate alie-<lb/>nam eſſe oſtendunt.</s> <s xml:id="echoid-s9993" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9994" xml:space="preserve">1°. </s> <s xml:id="echoid-s9995" xml:space="preserve">Hypotheſis enim modo eſt, ponere Ætherem ſubtiliſſimum, <lb/>omnia hujus Univerſi ſpatia implentem, & </s> <s xml:id="echoid-s9996" xml:space="preserve">corpora prementem; <lb/></s> <s xml:id="echoid-s9997" xml:space="preserve">hic Æther nullo unquam argumento ab acutiſſimis etiamſi ejus pa-<lb/>tronis probari potuit; </s> <s xml:id="echoid-s9998" xml:space="preserve">omnem paginam Phyſicæ implere ſolebat, <lb/>omniaque fere corporum phænomena ipſi adſcribebantur; </s> <s xml:id="echoid-s9999" xml:space="preserve">quæ <lb/>poſtea penitus examinata aliam omnino cauſam habere deprehenſa <lb/>ſunt: </s> <s xml:id="echoid-s10000" xml:space="preserve">hinc ex Phyſica hodierna Æther proſcribitur merito.</s> <s xml:id="echoid-s10001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10002" xml:space="preserve">2°. </s> <s xml:id="echoid-s10003" xml:space="preserve">Sed major obſtat difficultas, ex qua evidenter liquebit Æthe-<lb/>rem non poſſe eſſe Cohærentiæ cauſam: </s> <s xml:id="echoid-s10004" xml:space="preserve">adeoque ipſum dari ſup-<lb/>ponam, imo ipſum corpora, eorumve partes ſibi impoſitas compri-<lb/>mere, quo igitur corpora ſint majora, aut quo ſuperſiciem ma-<lb/>jorem habeant, quæ fluidi iſtius preſſionem excipit, eo fortius pre-<lb/>mentur, validiusque cohærebunt: </s> <s xml:id="echoid-s10005" xml:space="preserve">Sit igitur in pede cubico {4/100} <pb o="442" file="0456" n="456" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pars ſolidi æquabiliter diſtributi, reliquum poroſum, ſolidum modo <lb/>premetur, nam poros libere pervadere Æther dicitur: </s> <s xml:id="echoid-s10006" xml:space="preserve">ſit in alte-<lb/>ro pede cubico {1/30} pars ſolidi, reliquum poroſum, adeoque duplo <lb/>major quantitas ſolidi plus premetur quam ante, cum majorem ſu-<lb/>perficiem, in quam fluidum illud aget, habeat, Sit iterum in <lb/>pede cubico {1/10} pars ſolidi æquabiliter diſtributi, reliquum poroſum, <lb/>adeoque iterum major erit ſolidi ſuperficies, quæ preſſionem exci-<lb/>piet: </s> <s xml:id="echoid-s10007" xml:space="preserve">quo igitur corpora erunt magis ſolida ſub eodem volumine, <lb/>eo majorem preſſionem excipient: </s> <s xml:id="echoid-s10008" xml:space="preserve">ſed demonſtratum eſt in Phy-<lb/>ſicis corporum gravitatem eſſe in eadem ratione cum ſoliditate, <lb/>quia omne ſolidum non modo grave eſt, ſed æque grave eſt, <lb/>ergo graviſſima ſolida maxime ab illo fluido prementur, minus <lb/>gravia prementur minus: </s> <s xml:id="echoid-s10009" xml:space="preserve">adeoque duo corpora graviſſima ſibi im-<lb/>poſita magis preſſa, quam alia leviora & </s> <s xml:id="echoid-s10010" xml:space="preserve">æque magna, etiam ma-<lb/>gis cohærebunt levioribus, eritque cohærentia partium in corpo-<lb/>ribus, in ratione gravitatis eorum: </s> <s xml:id="echoid-s10011" xml:space="preserve">exploremus an hoc ratiocinium <lb/>congruat cum experientia, examinemus an graviſſima ſint cohæ-<lb/>rentiſſima; </s> <s xml:id="echoid-s10012" xml:space="preserve">ſi enim id verum, Hypotheſis Ætheris maximam vero-<lb/>ſimilitudinem habebit; </s> <s xml:id="echoid-s10013" xml:space="preserve">ſi non reſpondeat rerum eventus, debilitata <lb/>haud parum erit: </s> <s xml:id="echoid-s10014" xml:space="preserve">gravitates corporum hoc ordine ſe ſequuntur, a <lb/>graviſſimo incipiendo, Aurum, Argentum vivum, Plumbum, Ar-<lb/>gentum, Cuprum, Ferrum, Stannum, Mineralia, Semimetalla, <lb/>Adamas reliquæque gemmæ pellucidæ &</s> <s xml:id="echoid-s10015" xml:space="preserve">c duriſſimum vero omnium <lb/>corporum, hoc eſt cujus partes maxime cohærent, eſt Adamas, <lb/>hunc ſequuntur Gemmæ pellucidæ pretioſæ, Silex; </s> <s xml:id="echoid-s10016" xml:space="preserve">inter metalla <lb/>Aurum, Ferrum, Argentum, Cuprum, Stannum, Plumbum, <lb/>eſt vero Mercurius admodum fluidus. </s> <s xml:id="echoid-s10017" xml:space="preserve">Quanta proinde eſt diffe-<lb/>rentia inter ordinem gravitatis in corporibus, & </s> <s xml:id="echoid-s10018" xml:space="preserve">Cohærentiæ in <lb/>iisdem? </s> <s xml:id="echoid-s10019" xml:space="preserve">Cur Ferri firmitas ſuperat eam Plumbi, hujus gravitate ſu-<lb/>perante pondus alterius? </s> <s xml:id="echoid-s10020" xml:space="preserve">ſed cur Mercurius adeo ſolidus maner <lb/>fluidus; </s> <s xml:id="echoid-s10021" xml:space="preserve">cur ejus partes non magis cohaerent appreſſæ ab illo flui-<lb/>do, quam partes leviſſimi ſuberis, aut lanæ rariſſimæ, fieri enim <lb/>nequit quin duabus ſuperficiebus pollicis quadrati tam ſuberis quam <lb/>Mercurii ſe contingentibus, multo plura & </s> <s xml:id="echoid-s10022" xml:space="preserve">majora loca contac-<lb/>tuum ſint in his ſuperficiebus, quam in illis, manet tamen Mercu-<lb/>rius fluidus, ſuber fit corpus ſolidum.</s> <s xml:id="echoid-s10023" xml:space="preserve"/> </p> <pb o="443" file="0457" n="457" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s10024" xml:space="preserve">3°. </s> <s xml:id="echoid-s10025" xml:space="preserve">Sed ecce aliam difficultatem, dentur duæ partes alicujus Flui-<lb/>di, quas voco A, B, hæ ſibi imponantur, premantur undiquaque <lb/>ab Æthere, ſint aliæ duæ partes æque magnæ corporis firmi D, E, <lb/>quæ etiam ſint ſibi impoſitæ, quæ eodem modo premantur ab Æ-<lb/>there, hæ cohærebunt, prioribus manentibus aut ſolutis aut facil-<lb/>lime a ſe ſolvendis, eadem conditio utriusque corporeæ maſſæ po-<lb/>nitur, cur una maſſa firma evadit, altera fluida. </s> <s xml:id="echoid-s10026" xml:space="preserve">Candidus & </s> <s xml:id="echoid-s10027" xml:space="preserve">per-<lb/>ſpicax Bernouillius hoc caſu examinato, non dubitavit confiteri <lb/>ſibi hærere aquam, utque ſe extricaret adhuc, quid aliud fingere co-<lb/>actus fuit, nempe partes fluidi ſe nunquam contingere immediate, <lb/>ſed libere rotari & </s> <s xml:id="echoid-s10028" xml:space="preserve">in Æthere natare, cum partes firmi corporis ſe-<lb/>ſe attingant, quieſcantque: </s> <s xml:id="echoid-s10029" xml:space="preserve">ſed ecce ſecundam hypotheſin inven-<lb/>tam ad hypotheſin aliam ſtabiliendam, imo hæc ſecunda hypothe-<lb/>ſis æque difficilis probatu foret quam prior, nec opinor aliquem <lb/>facile conceſſurum partes aquæ vaſculum implentes â ſeſe eſſe ita <lb/>ſeparatas, ut ſe nunquam contingant, & </s> <s xml:id="echoid-s10030" xml:space="preserve">facto contactu illico in <lb/>firmum corpus abirent ſecundum hypotheſin.</s> <s xml:id="echoid-s10031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10032" xml:space="preserve">4°. </s> <s xml:id="echoid-s10033" xml:space="preserve">Inter cylindros marmoreos deſcriptos ſit exigua quantitas ſebi <lb/>interpoſita, in alio caſu ſit paulum major quantitas ſebi, in tertio caſu <lb/>interponatur multo plus; </s> <s xml:id="echoid-s10034" xml:space="preserve">Cohærentiæ in omnibus his tribus caſibus <lb/>ſunt diverſiſſimæ, nam primi caſus cylindri non ſolventur niſi ap-<lb/>penſis libris 1150, ſecundi caſus ſolventur appenſis libris 800, ter-<lb/>tii caſus ſolventur appenſis libris 300: </s> <s xml:id="echoid-s10035" xml:space="preserve">in his tribus caſibus ſuperfi-<lb/>cies marmoris & </s> <s xml:id="echoid-s10036" xml:space="preserve">ſebi applicati eodem modo ſe habet, non plus <lb/>occluſi ſunt pori nec etiam magis aperti in primo quam in tertio <lb/>caſu, adeoque appreſſio ſebi ad marmoris ſuperficiem utramque de-<lb/>bebit eſſe eadem, & </s> <s xml:id="echoid-s10037" xml:space="preserve">Cohærentia eadem, quæ tamen diverſiſſima <lb/>exiſtit.</s> <s xml:id="echoid-s10038" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10039" xml:space="preserve">Quare clariſſime conſpicimus ex hypotheſi Ætheris nequaquam <lb/>fluere phænomena, quæ circa Cohærentiam experientia detegit, <lb/>meritoque hanc Hypotheſin ex Phyſica eſſe proſcribendam. </s> <s xml:id="echoid-s10040" xml:space="preserve">Hu-<lb/>jus ſententiæ tamen patroni, utcunque ſecuti fuerint Carteſium, <lb/>laudandi ſunt, quod apprime intellexerint, corpora nequaquam <lb/>cohærere niſi per vim quandam, quam idcirco in Scenam protulerunt, <lb/>rejicientes omnino doctrinam Carteſii, qui in Princ. </s> <s xml:id="echoid-s10041" xml:space="preserve">Philoſ. </s> <s xml:id="echoid-s10042" xml:space="preserve">parte 2. <lb/></s> <s xml:id="echoid-s10043" xml:space="preserve">§. </s> <s xml:id="echoid-s10044" xml:space="preserve">54. </s> <s xml:id="echoid-s10045" xml:space="preserve">Corpora dura eſſe dixerat, quorum partes juxta ſe quieſcunt;</s> <s xml:id="echoid-s10046" xml:space="preserve"> <pb o="444" file="0458" n="458" rhead="INTRODUCTIO AD COHÆRENTIAM"/> Fluida, quorum partes movebantur: </s> <s xml:id="echoid-s10047" xml:space="preserve">recte enim demonſtrarunt, in <lb/>quiete nullam eſſe vim, unde Cohærentiæ foret vis nulla, granum-<lb/>que cumuli arenarii æquali difficultate a reliquis ſepararetur, quam <lb/>Ferri portio a reliqua maſſa: </s> <s xml:id="echoid-s10048" xml:space="preserve">præterea contra hanc hypotheſin Car-<lb/>teſii adnoto, corporum firmorum partes celerrime aliquando mo-<lb/>veri manente tamen firmitate; </s> <s xml:id="echoid-s10049" xml:space="preserve">nam filum metallicum tenſum utrim-<lb/>que percutiatur ut ſonet, omnes ejus partes contremiſcent: </s> <s xml:id="echoid-s10050" xml:space="preserve">traha-<lb/>tur per foramen minoris diametri lamellæ chalybeæ inflictum, ut <lb/>duplo tenuius fiat, omnes ejus partes movebuntur, aliumque diver-<lb/>ſum a priori ſitum acquirunt, manente tamen in utroque caſu firmita-<lb/>te: </s> <s xml:id="echoid-s10051" xml:space="preserve">aliquantum caleſcat ad ignem Metallum, rarefiat, ne tamen fiat flui-<lb/>dum, partes motas acquiret, cohærebit nihilominus: </s> <s xml:id="echoid-s10052" xml:space="preserve">ſed alia plura & </s> <s xml:id="echoid-s10053" xml:space="preserve"><lb/>ponderoſa argumenta contra Carteſii ſententiam attulit inclytus <lb/>Bernouillius, cujus ſubtilis Tractatus de Grav. </s> <s xml:id="echoid-s10054" xml:space="preserve">Ætheris conſuli <lb/>poſſet. </s> <s xml:id="echoid-s10055" xml:space="preserve">Sunt binæ opiniones, tam quæ ſpectat gravitatem Aëris, <lb/>quam Ætheris, quidem omnium ſubtiliſſimæ, & </s> <s xml:id="echoid-s10056" xml:space="preserve">quæ genium vere <lb/>Philoſophicum ſapiunt, quamobrem eas primo ordine examinan-<lb/>das nobis propoſuimus:</s> <s xml:id="echoid-s10057" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10058" xml:space="preserve">Hæ cauſam externam corpora bina ſoluta conjungentem in unam <lb/>poſuerunt: </s> <s xml:id="echoid-s10059" xml:space="preserve">aliam vero cauſam externam non novimus, neque ejus ali-<lb/>quis ſuſpicionem fovit hactenus: </s> <s xml:id="echoid-s10060" xml:space="preserve">igitur cauſæ externæ impoſſibili-<lb/>rate demonſtratâ, an non reſtat cauſa interna in corporibus, qua <lb/>eorum partes cohærent? </s> <s xml:id="echoid-s10061" xml:space="preserve">antequam tamen hanc exponam prius percur-<lb/>rere alias diverſorum Philoſophorum de Cohærentia ſententias, ju-<lb/>vabit, quarum pleræque conditæ ſunt prius quam Phy ſica ad magnum <lb/>incrementum pervenerat; </s> <s xml:id="echoid-s10062" xml:space="preserve">unde breviter eas memoraſſe ſufficiet.</s> <s xml:id="echoid-s10063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10064" xml:space="preserve">Magnus Verulamius, inſtaurator ſanioris Philoſophiæ, quo tem-<lb/>pore ſub ſervitute & </s> <s xml:id="echoid-s10065" xml:space="preserve">tyrannide Peripateticorum gemebat, opinatus <lb/>fuit Cohærentiam pendere ab immediato contactu corporum diſ-<lb/>ſentientium, alienorum, aut alterius generis, & </s> <s xml:id="echoid-s10066" xml:space="preserve">exempla adfert <lb/>ſui argumenti petita ab unguentis, quæ ex oleo & </s> <s xml:id="echoid-s10067" xml:space="preserve">aqua inter ſe <lb/>mixtis componuntur, hæc fluiditatem ſuam amittunt, quæ in aqua <lb/>aut oleo ſolo obſervatur: </s> <s xml:id="echoid-s10068" xml:space="preserve">contra videmus papyrum aquâ madefactam <lb/>ſe ſolvere & </s> <s xml:id="echoid-s10069" xml:space="preserve">conſiſtentiam deponere, oleo autem reſperſam minus, <lb/>quia oleum papyro minus conſiſtit. </s> <s xml:id="echoid-s10070" xml:space="preserve">At pace hujus illuſtris Viri di-<lb/>xerim hoc modo non explicari quænam ſit cauſa Cohærentiæ, nam <pb o="445" file="0459" n="459" rhead="CORPORUM FIRMORUM."/> cohæreat corpus cum alio heterogeneo, quæritur quænam ſit cau-<lb/>ſa illius Cohærentiæ: </s> <s xml:id="echoid-s10071" xml:space="preserve">an quia corpus heterogeneum eſt? </s> <s xml:id="echoid-s10072" xml:space="preserve">an igitur <lb/>vis quædam naſcitur inter heterogenea, quæ abeſt in homogeneis; <lb/></s> <s xml:id="echoid-s10073" xml:space="preserve">quænam tum erit vis quæ naſcitur! Sed ab immediato contactu <lb/>corporum diſſentientium inquit oriri Cohærentiam; </s> <s xml:id="echoid-s10074" xml:space="preserve">id hercle eſſe <lb/>nequit, nam immediatus contactus corporum non ponit ullam vim, <lb/>qua ſe amplectentur: </s> <s xml:id="echoid-s10075" xml:space="preserve">imponantur enim duo corpora ſibi invicem, <lb/>ſeſeque contingant; </s> <s xml:id="echoid-s10076" xml:space="preserve">& </s> <s xml:id="echoid-s10077" xml:space="preserve">nihil aliud in iis adhuc concipias, an tum <lb/>non æque facile ea iterum ſepones, ac impoſueras? </s> <s xml:id="echoid-s10078" xml:space="preserve">revera; </s> <s xml:id="echoid-s10079" xml:space="preserve">nam <lb/>ſive ſe contingant, ſive ſe non contingant, inde non major cauſa <lb/>erit, quæ remotioni reſiſtit: </s> <s xml:id="echoid-s10080" xml:space="preserve">ſi dixeris inde cauſam reſiſtentem ori-<lb/>ri, ecce, vim ponis aliquam, diverſam a ſolo contactus conce-<lb/>ptu: </s> <s xml:id="echoid-s10081" xml:space="preserve">Mathematicus cubum imaginetur alteri cubo impoſitum, eum <lb/>iterum ab altero avulſurus nullam ideam reſiſtentiæ in animo de-<lb/>prehendit; </s> <s xml:id="echoid-s10082" xml:space="preserve">adeoque ex ſolo contactu etiam hæc non oritur, ſed ſi <lb/>acceſſerit, vis acceſſit diverſæ indolis & </s> <s xml:id="echoid-s10083" xml:space="preserve">naturæ a contactu, neque <lb/>ex eo fluens. </s> <s xml:id="echoid-s10084" xml:space="preserve">Explicuit Vir vere ſapiens egregiè, quomodo corpora <lb/>plerumque obſervantur ad Cohærentiam deduci interpoſito fluido <lb/>aut ſemi fluido heterogeneo, ſed non explicuit quare heterogenea <lb/>cohæreant. </s> <s xml:id="echoid-s10085" xml:space="preserve">Quæro proinde, quare heterogenea potius cohærebunt <lb/>quam homogenea? </s> <s xml:id="echoid-s10086" xml:space="preserve">hoc profecto exponendum foret: </s> <s xml:id="echoid-s10087" xml:space="preserve">ſi immedia-<lb/>tus corporum contactus hoc præſtaret, tum homogenea ſeſe contin-<lb/>gentia æque cohærebunt quam heterogenea. </s> <s xml:id="echoid-s10088" xml:space="preserve">Verum alia difficultas <lb/>latet, circa corpuſcula minima, quæ elementa vocabo: </s> <s xml:id="echoid-s10089" xml:space="preserve">hæc inter <lb/>ſe non differunt, aut ſaltem non poſſunt dici homogenea, vel he-<lb/>terogenea: </s> <s xml:id="echoid-s10090" xml:space="preserve">duo elementa ſibi impoſita conſtituunt maſſulam, hæc <lb/>cohærent, & </s> <s xml:id="echoid-s10091" xml:space="preserve">ex plurimis talibus compoſitis conficitur tandem <lb/>corpus magnum; </s> <s xml:id="echoid-s10092" xml:space="preserve">quomodo nunc prima elementa cohærent? </s> <s xml:id="echoid-s10093" xml:space="preserve">ex <lb/>ſolo contactu probavimus non exire vim reſiſtentiæ: </s> <s xml:id="echoid-s10094" xml:space="preserve">homogenea <lb/>& </s> <s xml:id="echoid-s10095" xml:space="preserve">heterogenea dici non poſſunt: </s> <s xml:id="echoid-s10096" xml:space="preserve">cauſa quæ hæc unit, eſt vera <lb/>cauſa cohærentiæ; </s> <s xml:id="echoid-s10097" xml:space="preserve">ex quibus patet hujus opinionis infirmitas.</s> <s xml:id="echoid-s10098" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10099" xml:space="preserve">Alii Philoſophi recurrerunt ad uliginem quandam ſeu viſcoſita-<lb/>tem, quæ interpoſita inter duas corporis partes, eas conjungeret. <lb/></s> <s xml:id="echoid-s10100" xml:space="preserve">Hi conſuluerunt quotidiana fabrorum experimenta, qui gluten <lb/>viſcidum binis lignis, quæ jungent, interponunt. </s> <s xml:id="echoid-s10101" xml:space="preserve">Hoſce rogatos <lb/>velim, an uligo vim quandam habeat, qua duo corpora ad ſe at- <pb o="446" file="0460" n="460" rhead="INTRODUCTIO AD COHÆRENTIAM"/> trahit, an nulla vi donetur: </s> <s xml:id="echoid-s10102" xml:space="preserve">ſi vi careat, quæſo quomodo efficiet, <lb/>ut corpora tantam vim reſiſtentiæ exerceant adverſus potentiam <lb/>ſeparantem? </s> <s xml:id="echoid-s10103" xml:space="preserve">niſi profecto ex uligine vis exire ſtatuatur, non poterit <lb/>vis oriri, quæ eſt in Cohærentiâ: </s> <s xml:id="echoid-s10104" xml:space="preserve">Inſuper an minima corpuſcula <lb/>etiam uliginem poſtulant ut cohæreant? </s> <s xml:id="echoid-s10105" xml:space="preserve">hoc dici quidem poteſt, <lb/>verum demonſtratione indigeret.</s> <s xml:id="echoid-s10106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10107" xml:space="preserve">Galilæus in Mechanicæ Dialogo 1. </s> <s xml:id="echoid-s10108" xml:space="preserve">pag. </s> <s xml:id="echoid-s10109" xml:space="preserve">12. </s> <s xml:id="echoid-s10110" xml:space="preserve">Vacui repugnantiam <lb/>opinatur ſufficere diviſioni partium cujuſcunque ſolidi, ſive lapidis <lb/>ſive Metalli, ſive cujuslibet materiæ magis denſæ & </s> <s xml:id="echoid-s10111" xml:space="preserve">conſolidatæ: <lb/></s> <s xml:id="echoid-s10112" xml:space="preserve">hanc repugnantiam vacui demonſtrat experimento ab Antlia petito, <lb/>â cujus fundo apprime clauſo embolus non niſi magna vi remove-<lb/>tur, vacuum vero fit inter fundum embolumque, hoc aliquan-<lb/>tis per ab illo recedente; </s> <s xml:id="echoid-s10113" xml:space="preserve">vis ad eum receſſum requiſita magni-<lb/>tudinem repugnantiæ vacui menſurat; </s> <s xml:id="echoid-s10114" xml:space="preserve">hæc ipſa Galilæi ſunt: </s> <s xml:id="echoid-s10115" xml:space="preserve">no-<lb/>ſtra vero ætate hæc vacui repugnantia evanuit, cum evidentiſſime <lb/>demonſtratur â gravitate & </s> <s xml:id="echoid-s10116" xml:space="preserve">preſſione Aeris embolo Antliæ incum-<lb/>bentis pendere difficultatem, quâcum â fundo removetur: </s> <s xml:id="echoid-s10117" xml:space="preserve">quid <lb/>autem eſt vacui repugnantia? </s> <s xml:id="echoid-s10118" xml:space="preserve">vox nihil explicans, cujus ideam <lb/>claram nemo formavit, idemque ſignificans ac id antiquum Peri-<lb/>pateticorum proverbium, a vacuo Naturam abhorrere. </s> <s xml:id="echoid-s10119" xml:space="preserve">Sed ſubla-<lb/>tus eſt e medio hic Naturæ horror, proſcripta eſt vacui repugnantia, <lb/>poſtquam ex rerum phænomenis demonſtratum eſt manifeſto, dari va-<lb/>cuum in Univerſo & </s> <s xml:id="echoid-s10120" xml:space="preserve">in omnibus corporibus magnis: </s> <s xml:id="echoid-s10121" xml:space="preserve">nihil plus admira-<lb/>tus fui unquam, quam Virum ſapientiſſimum, Philoſophiæ Mathema-<lb/>ticæ inſtauratorem, ſui ſæculi ornamentum, qui Scholaſticam doctri-<lb/>nam feliciſſime labefactaverat, illius fermentum hic tamen retinuiſſe.</s> <s xml:id="echoid-s10122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10123" xml:space="preserve">Honoratus Fabry in Phyſ. </s> <s xml:id="echoid-s10124" xml:space="preserve">Tr. </s> <s xml:id="echoid-s10125" xml:space="preserve">2. </s> <s xml:id="echoid-s10126" xml:space="preserve">lib. </s> <s xml:id="echoid-s10127" xml:space="preserve">5. </s> <s xml:id="echoid-s10128" xml:space="preserve">& </s> <s xml:id="echoid-s10129" xml:space="preserve">de Lanis in Magiſt. <lb/></s> <s xml:id="echoid-s10130" xml:space="preserve">Nat. </s> <s xml:id="echoid-s10131" xml:space="preserve">& </s> <s xml:id="echoid-s10132" xml:space="preserve">Art. </s> <s xml:id="echoid-s10133" xml:space="preserve">Lib. </s> <s xml:id="echoid-s10134" xml:space="preserve">XI. </s> <s xml:id="echoid-s10135" xml:space="preserve">cap. </s> <s xml:id="echoid-s10136" xml:space="preserve">3. </s> <s xml:id="echoid-s10137" xml:space="preserve">§. </s> <s xml:id="echoid-s10138" xml:space="preserve">5. </s> <s xml:id="echoid-s10139" xml:space="preserve">6. </s> <s xml:id="echoid-s10140" xml:space="preserve">opinantur cohærentiam <lb/>pendere a plexu & </s> <s xml:id="echoid-s10141" xml:space="preserve">ingreſſu mutuo partium heterogenearum <lb/>intra ſe, quemadmodum dentes duarum ſerrarum ſe excipiunt, <lb/>intricantque; </s> <s xml:id="echoid-s10142" xml:space="preserve">hi ſuam ſententiam adſtruunt exemplo fili, quod <lb/>cum longiſſimum fit, componitur ex filamentis plurimis brevibus <lb/>& </s> <s xml:id="echoid-s10143" xml:space="preserve">aſperis, quæ ſecum intorquentur: </s> <s xml:id="echoid-s10144" xml:space="preserve">tum quia omnia corpora ma-<lb/>gna firma conſtant ex aliis heterogeneis admixtis, quorum ope co-<lb/>hærent, uti docet ars Chemica, elice enim ex Ligno omnem aquam, <lb/>omne Oleum & </s> <s xml:id="echoid-s10145" xml:space="preserve">Salem, Lignum fatiſcet in cineres, qui ſunt me- <pb o="447" file="0461" n="461" rhead="CORPORUM FIRMORUM."/> rus ſubtilis pulvis; </s> <s xml:id="echoid-s10146" xml:space="preserve">homogenea vero & </s> <s xml:id="echoid-s10147" xml:space="preserve">heterogenea cohærent <lb/>plexu fibrillarum & </s> <s xml:id="echoid-s10148" xml:space="preserve">filaminum, quid ni etiam minima corpuſcula <lb/>eodem modo cohærebunt.</s> <s xml:id="echoid-s10149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10150" xml:space="preserve">Videtur hæc opinio inniti regulæ nonnullorum Philoſophorum, <lb/>Vt natura in magnis ita eſt in minimis. </s> <s xml:id="echoid-s10151" xml:space="preserve">quæ profecto generalis non <lb/>eſt: </s> <s xml:id="echoid-s10152" xml:space="preserve">ſi concedamus corpora magna cohærere intertextu vel mutuo <lb/>ingreſſu fibrarum in ſe invicem, nequaquam inde ſequitur demon-<lb/>ſtratum eſſe corpuſcula minima eodem modo cohærere; </s> <s xml:id="echoid-s10153" xml:space="preserve">ecquis de-<lb/>monſtravit ea ſuperficie aſperâ eſſe donata, ſupponi hoc poſſe fa-<lb/>teor, verum inter demonſtrationem & </s> <s xml:id="echoid-s10154" xml:space="preserve">hypotheſin magnum inter-<lb/>vallum intercedit; </s> <s xml:id="echoid-s10155" xml:space="preserve">ſed ſupponamus ſe intricantes dentes ſerrarum, <lb/>vel uncinulos, qualibus fructus Bardanæ donantur, ſeſe intrican-<lb/>tes firmiter & </s> <s xml:id="echoid-s10156" xml:space="preserve">profundè, qui nec ſolvuntur niſi fractis uncinulis; <lb/></s> <s xml:id="echoid-s10157" xml:space="preserve">tum quæram quomodo partes uncinulorum & </s> <s xml:id="echoid-s10158" xml:space="preserve">dentium cohærent? </s> <s xml:id="echoid-s10159" xml:space="preserve"><lb/>an hæ iterum ope uncinulorum & </s> <s xml:id="echoid-s10160" xml:space="preserve">dentium minorum? </s> <s xml:id="echoid-s10161" xml:space="preserve">ſi affirmetur, <lb/>redibit quæſtio an horum uncinulorum partes rurſus ope aliorum <lb/>cohæſerint, & </s> <s xml:id="echoid-s10162" xml:space="preserve">niſi progreſſus in Infinitum talium uncinulorum <lb/>ſuppoſueris, redibit ſemper eadem difficultas, an autem ita ad abſur-<lb/>dum non reducitur uncinulorum hypotheſis. </s> <s xml:id="echoid-s10163" xml:space="preserve">Aſt præterea ſi Co-<lb/>hærentias varias oſtendere poſſim, in quibus nulla uncorum ſuſpi-<lb/>cio eſt, neque hi, nec partium plexus cauſa generalis Cohærentiæ <lb/>poni poterit; </s> <s xml:id="echoid-s10164" xml:space="preserve">docent obſervationes microſcopicæ omnia olea con-<lb/>ſtare ex partibus globoſis; </s> <s xml:id="echoid-s10165" xml:space="preserve">ſumantur duo corpora politarum ſuper-<lb/>ſicierum, uti ſpecula plana vitrea, marmorea, lapides plani, la-<lb/>mellæ politæ ex cupro, inungantur oleo, ſibi apponantur, cohæ-<lb/>rebunt, ut non niſi vi inſigni a ſe iterum ſeparari queant: </s> <s xml:id="echoid-s10166" xml:space="preserve">an hic fit <lb/>partium ramoſarum, aut dentatarum plexus & </s> <s xml:id="echoid-s10167" xml:space="preserve">intricatio? </s> <s xml:id="echoid-s10168" xml:space="preserve">conce-<lb/>dam ſubtiles olei ſphæras ingredi poros in ſuperficiebus vitri, mar-<lb/>moris & </s> <s xml:id="echoid-s10169" xml:space="preserve">Cupri relictos, ſed quomodo a ſphæris intricatio partium <lb/>orietur, atque inde Cohærentia? </s> <s xml:id="echoid-s10170" xml:space="preserve">an magnes alteri magneti aut <lb/>ferro applicatus etiam cohæret propter plexum partium & </s> <s xml:id="echoid-s10171" xml:space="preserve">intrica-<lb/>tionem fibrillarum? </s> <s xml:id="echoid-s10172" xml:space="preserve">quamobrem hæc ſententia ſuas quoque patitur <lb/>manes, eamque egregie refutavit quondam Jac. </s> <s xml:id="echoid-s10173" xml:space="preserve">Bernouillius in <lb/>Tract. </s> <s xml:id="echoid-s10174" xml:space="preserve">de Gravitate Ætheris.</s> <s xml:id="echoid-s10175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10176" xml:space="preserve">Alii finxerunt ſingulas corporum durorum particulas eſſe duras, <lb/>eas gravitate, quâ verſus centrum Telluris aguntur, ſibi impoſitas <pb o="448" file="0462" n="462" rhead="INTRODUCTIO AD COHÆRENTIAM"/> comprimi ab omnibus corporibus incumbentibus, tum concreſcere <lb/>& </s> <s xml:id="echoid-s10177" xml:space="preserve">uniri in maſſas majores firmas cohærenteſque. </s> <s xml:id="echoid-s10178" xml:space="preserve">Quæ opinio nec <lb/>minoribus, nec levioribus eſt obnoxia erroribus, quam ulla præce-<lb/>dentium: </s> <s xml:id="echoid-s10179" xml:space="preserve">nam concedamus corporum partes ſibi apprimi gravitate <lb/>aliorum incumbentium corporum, atque ita cohærere, tum pro-<lb/>fecto non amplius inter ſe cohærebunt particulæ remotis rejectiſ-<lb/>que corporibus gravibus incumbentibus, adeoque corpora, quæ fir-<lb/>miſſima ſunt in terris viſceribus, quia valde comprimuntur, in pul-<lb/>verem fatiſcent ſponte, vel facile vi minimâ, ſimulac eruta ex fodi-<lb/>nis in ſuperficie terræ ponuntur, quippe tum nihil amplius eſt quod <lb/>illa comprimat: </s> <s xml:id="echoid-s10180" xml:space="preserve">verum dicuntur concreſcere quo tempore compri-<lb/>muntur, eſt hoc concreſcere pulcrum vocabulum, ſed quid ſigni-<lb/>ficat? </s> <s xml:id="echoid-s10181" xml:space="preserve">duæ particulæ duræ ſibi apprimantur a pondere quocunque <lb/>impoſito, quidnam nunc efficiet ut hæ particulæ ita uniantur, ut <lb/>poſtea non tam facile a ſe divelli poſſint, quam cum ſibi impone-<lb/>bantur: </s> <s xml:id="echoid-s10182" xml:space="preserve">propter preſſionem non cedunt introrſum, nam ſuppo-<lb/>nuntur duræ; </s> <s xml:id="echoid-s10183" xml:space="preserve">an igitur tempore accedit quid aliud ea conjunctu-<lb/>rum? </s> <s xml:id="echoid-s10184" xml:space="preserve">quid eſt quod accedit? </s> <s xml:id="echoid-s10185" xml:space="preserve">oportet ut ſit vis, corpora enim, <lb/>quæ cohærent, vim reſiſtentiæ habent: </s> <s xml:id="echoid-s10186" xml:space="preserve">an igitur vis generatur <lb/>in corporibus, quia tantummodo ſibi imponuntur & </s> <s xml:id="echoid-s10187" xml:space="preserve">comprimun-<lb/>tur? </s> <s xml:id="echoid-s10188" xml:space="preserve">quænam eſt ea vis? </s> <s xml:id="echoid-s10189" xml:space="preserve">quomodo generatur? </s> <s xml:id="echoid-s10190" xml:space="preserve">quomodo corpo-<lb/>ribus infunditur? </s> <s xml:id="echoid-s10191" xml:space="preserve">vel an corporibus ineſt ejuſmodi attributum aut <lb/>proprietas, ut vim Cohærentiæ generent? </s> <s xml:id="echoid-s10192" xml:space="preserve">ſi hoc, id demonſtran-<lb/>dum erit: </s> <s xml:id="echoid-s10193" xml:space="preserve">ſi vero vis aliunde acceſſerit, non ex ſola compreſſione <lb/>gravium incumbentium Cohærentia oritur: </s> <s xml:id="echoid-s10194" xml:space="preserve">ſed experiamur an cor-<lb/>pora dura, ſibi impoſita & </s> <s xml:id="echoid-s10195" xml:space="preserve">compreſſa concreſcant; </s> <s xml:id="echoid-s10196" xml:space="preserve">hoc eſt tem-<lb/>pore Cohærentiam accipiant: </s> <s xml:id="echoid-s10197" xml:space="preserve">Capiantur duo Cubi vitrei, cuprei <lb/>vel marmorei, perinde eſt ex quanam materia eligantur, hos pla-<lb/>niſſimæ ſuperficiei ſibi impone, prælo compreſſos per anni ſpatium <lb/>relinque (diutius enim hæc Experimenta non protraxi) ſolutâ <lb/>præli cochleâ obſervabis eos nequaquam concreviſſe, ſed æque <lb/>facile a ſe reponi, quam primo temporis momento, quo ſupra ſe <lb/>collocabantur: </s> <s xml:id="echoid-s10198" xml:space="preserve">corpora hæc compreſſa aliquamdiu fuerunt, pro-<lb/>inde in eodem ſtatu fuerunt ac ea, quæ in viſceribus Terræ ab aliis <lb/>incumbentibus gravibus compreſſa fuiſſent: </s> <s xml:id="echoid-s10199" xml:space="preserve">ſed intra prælum non <lb/>concreverunt; </s> <s xml:id="echoid-s10200" xml:space="preserve">an igitur in Terra, ſi nihil aliud acceſſerit, con- <pb o="449" file="0463" n="463" rhead="CORPORUM FIRMORUM."/> creſcent? </s> <s xml:id="echoid-s10201" xml:space="preserve">verum nimis magna forte dicar ſumſiſſe corpora, ea non <lb/>concreſcere, ſed tantum minima; </s> <s xml:id="echoid-s10202" xml:space="preserve">quaſi verò in Terrâ duo corpo-<lb/>ra magna in unam molem non abirent eadem cauſâ, qua corpu-<lb/>ſcula minima: </s> <s xml:id="echoid-s10203" xml:space="preserve">forte compreſſionem non ſatis diu protraxi, non u-<lb/>nus annus, ſed plures requirebantur, ut ex Elementis concreſceret <lb/>molecula ſecundæ magnitudinis; </s> <s xml:id="echoid-s10204" xml:space="preserve">Verum obſervamus Fluida ſæpe <lb/>citiſſime in ſolidam maſſam mutari paucis modo elapſis horæ mi-<lb/>nutis, veluti cum offa Helmontii conficitur; </s> <s xml:id="echoid-s10205" xml:space="preserve">aut cum liquefacta <lb/>metalla refrigerio committuntur. </s> <s xml:id="echoid-s10206" xml:space="preserve">Forſitan tamen in imis Terræ <lb/>viſceribus corpora concreſcere dicentur, non per ſolam compreſſio-<lb/>nem, ſed per hanc & </s> <s xml:id="echoid-s10207" xml:space="preserve">per allapſum interpoſitumque inter partes <lb/>fluidum: </s> <s xml:id="echoid-s10208" xml:space="preserve">ita enim revera concreſcunt & </s> <s xml:id="echoid-s10209" xml:space="preserve">excreſcunt omnia vege-<lb/>tabilia & </s> <s xml:id="echoid-s10210" xml:space="preserve">Animalia: </s> <s xml:id="echoid-s10211" xml:space="preserve">at tum id, quod â Philoſophis quæſitum fuit, <lb/>non ſolvitur: </s> <s xml:id="echoid-s10212" xml:space="preserve">quænam enim eſt cauſa, quæ Fluido inter duas inter-<lb/>poſito partes ſolidas efficit, ut in unam compactam firmamque <lb/>maſſam abeant? </s> <s xml:id="echoid-s10213" xml:space="preserve">quænam eſt quæ vim reſiſtentiæ contra potentiam <lb/>rumpentem tantam facit? </s> <s xml:id="echoid-s10214" xml:space="preserve">Quare Fluidum cohæret æque cum par-<lb/>te ſolida ſuperiori ac inferiori? </s> <s xml:id="echoid-s10215" xml:space="preserve">Ex quibus apparet, vocem illam <lb/>Concreſcere non plus explicare quam fictitia illa Abracadabra: </s> <s xml:id="echoid-s10216" xml:space="preserve">ita <lb/>Veteres Peripatetici ſe ſæpius decipiebant nominibus rebus impo-<lb/>nendis, uti Antipathiæ, Sympathiæ, Attractionis, Repulſionis, <lb/>quibus ſe res intellexiſſe arbitrabantur, quas penitus ignorabant.</s> <s xml:id="echoid-s10217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10218" xml:space="preserve">2°. </s> <s xml:id="echoid-s10219" xml:space="preserve">Quomodo ex ejuſmodi Hypotheſi explicari poteſt mutatio <lb/>duorum corporum fluidorum in ſuperficie Terræ poſirorum, & </s> <s xml:id="echoid-s10220" xml:space="preserve">ne-<lb/>quaquam compreſſorum in firmiſſimam ſubſtantiam, abeuntium uti <lb/>perpetuo contingit? </s> <s xml:id="echoid-s10221" xml:space="preserve">Quomodo liquefacta in Igne metalla, avo-<lb/>lante Igne, concreſcunt in duriſſimas maſſas, etiamſi in vacuo po-<lb/>nantur, nec partes ſuperiores ullâ gravitate, aut ſaltem notabili, <lb/>premantur? </s> <s xml:id="echoid-s10222" xml:space="preserve">Quomodo duo ſalini, oppoſitæque indolis liquores, <lb/>peractâ efferveſcentiâ in vacuo abeunt in ſalem firmum, ubi tamen <lb/>nulla cauſa comprimens adeſt, neque liquores in imis Terræ viſce-<lb/>ribus, ſed in ſuperficie habeantur?</s> <s xml:id="echoid-s10223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10224" xml:space="preserve">3°. </s> <s xml:id="echoid-s10225" xml:space="preserve">Præterea ſequitur ex hac Hypotheſi, corpora eo majorem <lb/>Cohærentiam habitura, quo ex profundioribus Terræ partibus ef-<lb/>fodiantur, atque compreſſa fuerint â plurimis graviſſimiſque pon-<lb/>deribus: </s> <s xml:id="echoid-s10226" xml:space="preserve">an autem hoc Experientia evincit? </s> <s xml:id="echoid-s10227" xml:space="preserve">fui ipſe in carbonaria <pb o="450" file="0464" n="464" rhead="INTRODUCTIO AD COHÆRENTIAM"/> fodina 250. </s> <s xml:id="echoid-s10228" xml:space="preserve">pedes alta, ex quâ carbones hærentes in terra molli ef-<lb/>fodiebantur; </s> <s xml:id="echoid-s10229" xml:space="preserve">cur hæc terra æquali pondere ac carbones compreſſa, <lb/>non in firmam maſſam concreverat? </s> <s xml:id="echoid-s10230" xml:space="preserve">Sæpe Ferrum deprehenditur <lb/>in gleba ad terræ ſuperficiem: </s> <s xml:id="echoid-s10231" xml:space="preserve">ecce igitur ex profunda fodina e-<lb/>rutam terram mollem, ex ſuperficie Terræ metallum cohærentiſſi-<lb/>mum: </s> <s xml:id="echoid-s10232" xml:space="preserve">Sed an Ferrum aliudve metallum ex profundiori fodinæ parte <lb/>effoſſum eſt durius, eo quod ex parte ſuperiori elicitur? </s> <s xml:id="echoid-s10233" xml:space="preserve">nec hoc <lb/>comprobat experientia: </s> <s xml:id="echoid-s10234" xml:space="preserve">præterea Mercurius ex profundis fodinis <lb/>colligitur fluidus, in his tamen valde compreſſus fuit ab ingentibus <lb/>impoſitis montibus.</s> <s xml:id="echoid-s10235" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10236" xml:space="preserve">4°. </s> <s xml:id="echoid-s10237" xml:space="preserve">Cohærentia partium eſt vis manens inter corporum partes, <lb/>quæ non niſi per vim oppoſitæ directionis ſuperari poteſt, uti liquet <lb/>in corporum diſſolutione: </s> <s xml:id="echoid-s10238" xml:space="preserve">ſed ex hac Hypotheſi non ſequitur ul-<lb/>la vis inter partes corporum, ſive interna, ſive externa, neque <lb/>etiam ullarum virium in ea fit mentio.</s> <s xml:id="echoid-s10239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10240" xml:space="preserve">Sed an non veroſimilior evadet, ſi addamus corpora cohærere <lb/>ob implexam partium texturam, accedentem prioribus? </s> <s xml:id="echoid-s10241" xml:space="preserve">conceda-<lb/>mus corpora majora ita aliquando cohærere, quæſo quomodo cor-<lb/>puſcula minima cohærebant, an minima etiam uncis ramiſve ſunt <lb/>donata? </s> <s xml:id="echoid-s10242" xml:space="preserve">ſi hoc, quomodo tum ſunt minima? </s> <s xml:id="echoid-s10243" xml:space="preserve">cum ipſi unci par-<lb/>tes diſtinctæ ſunt, ſed ſupra de his egimus,</s> </p> <p> <s xml:id="echoid-s10244" xml:space="preserve">Quas difficultates cum ſenſerint maturioris judicii Viri, arbitrati <lb/>ſunt mutuum ſuperficierum contactum additum hiſce tanquam <lb/>cauſam remotam, Cohærentiæ cauſas eſſe: </s> <s xml:id="echoid-s10245" xml:space="preserve">verum ſupra probavi-<lb/>mus ex ejuſmodi contactu non oriri ullam vim, qua corpora co-<lb/>hæreant, ſive enim ſe contingant, quæ ſibi imponuntur, ſive ſe-<lb/>orſum exſtent, ad unum ab alio ſeparandum valet eadem potentia, <lb/>quæ ad corpus æque magnum & </s> <s xml:id="echoid-s10246" xml:space="preserve">ſeorſim poſitum dimovendum po-<lb/>ſtulatur: </s> <s xml:id="echoid-s10247" xml:space="preserve">unde nec hoc modo opinioni pondus accedit.</s> <s xml:id="echoid-s10248" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10249" xml:space="preserve">Examinatis Philoſophorum opinionibus, reſtat ut probemus Co-<lb/>hærentiam ſolidorum pendere â vi internâ: </s> <s xml:id="echoid-s10250" xml:space="preserve">Demonſtravimus ſolida <lb/>tantum cohærere virium ope, vires autem ſunt externæ, vel in-<lb/>ternæ; </s> <s xml:id="echoid-s10251" xml:space="preserve">quæcunque vires externæ aſſignatæ fuerunt, aut non dan-<lb/>tur, aut quæ dantur non ſufficiunt exponendis phænomenis Cohæ-<lb/>rentiæ ut fuſe ſupra evictum eſt, reſtantigitur tantum vires internæ.</s> <s xml:id="echoid-s10252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10253" xml:space="preserve">Quomodo autem vires internas dari cognovimus; </s> <s xml:id="echoid-s10254" xml:space="preserve">non directe <pb o="451" file="0465" n="465" rhead="CORPORUM FIRMORUM."/> ſenſuum ope, quia his in corporum internam ſubſtantiam non pe-<lb/>netramus, ſed ſuperficies eorum tantum videmus, tangimus, gus-<lb/>tamus, olfacimus; </s> <s xml:id="echoid-s10255" xml:space="preserve">adeoque directe non poterunt cognoſci, quem-<lb/>admodum Extenſio, Figura, Mobilitas; </s> <s xml:id="echoid-s10256" xml:space="preserve">ſed dari intelligere licet <lb/>tantum ex editis effectibus; </s> <s xml:id="echoid-s10257" xml:space="preserve">qui ſi illius ſint naturæ, ut nequeant <lb/>niſi ex viribus internis ſluere, hæ aſſumendæ ſunt, tumque ſunt de-<lb/>monſtratæ; </s> <s xml:id="echoid-s10258" xml:space="preserve">nec aliter unquam probari poterunt.</s> <s xml:id="echoid-s10259" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10260" xml:space="preserve">Effectus univerſales hi ſunt, ut omne corpus ſive ſolidum, ſive <lb/>fluidum immediate alteri ſolido vel fluido applicatum in vacuo co-<lb/>hæreat, in exigua ab altero diſtantia minus cohæreat, tamen ver-<lb/>ſus alterum dirigatur, & </s> <s xml:id="echoid-s10261" xml:space="preserve">ſi poteſt, moveatur: </s> <s xml:id="echoid-s10262" xml:space="preserve">in majori autem <lb/>intervallo non cohæreat, neque ſenſibiliter dirigatur vel moveatur.</s> <s xml:id="echoid-s10263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10264" xml:space="preserve">Qui effectus cum conſtanter in vacuo, ubi nulla cauſa externa <lb/>datur, eveniunt, nequeunt fluere niſi ex vi interna; </s> <s xml:id="echoid-s10265" xml:space="preserve">adeoque ma-<lb/>nifeſto arguunt vim internam dari in corporibus, quæ agat exeun-<lb/>do aliquantum, maxime in immediato contactu, minus in inter-<lb/>vallo exiguo, minime in diſtantia notabili: </s> <s xml:id="echoid-s10266" xml:space="preserve">Quæ vis pellit corpus, <lb/>quod interne occupat, verſus alterum, & </s> <s xml:id="echoid-s10267" xml:space="preserve">hoc reciproce verſus <lb/>primum, donec ambo ſe contingant, & </s> <s xml:id="echoid-s10268" xml:space="preserve">nequeant propius acce-<lb/>dere; </s> <s xml:id="echoid-s10269" xml:space="preserve">in contactu ſe premunt directione oppoſita viribus mutuis, <lb/>& </s> <s xml:id="echoid-s10270" xml:space="preserve">quantum ſe premunt, tantum cohærent: </s> <s xml:id="echoid-s10271" xml:space="preserve">in exiguo intervallo <lb/>hæc vis pellit utrumque verſus ſe, ſed quia hæc vis undiquaque <lb/>exeundo ex corpore ſub forma radiorum Lucis e puncto lucente <lb/>emiſſorum, quorum denſitas decreſcit in diſtantiis a puncto lucen-<lb/>te, minus operari poteſt in corpus remotum, quam in ſibi conti-<lb/>guum, quod ita minus cohærebat, & </s> <s xml:id="echoid-s10272" xml:space="preserve">idcirco minime agens in pro-<lb/>cul diſſitum cum eo non cohærebit.</s> <s xml:id="echoid-s10273" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10274" xml:space="preserve">Hæc vis interna poteſt vocari Attrahens, quia agit quaſi corpus <lb/>attraheret alterum, poteſt quoque Interna apprimens vocari, ut <lb/>diſtinguatur a preſſione aut pulſione externa, nam nomina ab ar-<lb/>bitrio noſtro dependent.</s> <s xml:id="echoid-s10275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10276" xml:space="preserve">Hæc vis interna â Deo omnibus corporibus indita fuit, voluitque <lb/>infinite efficax Creator, ut hæc in ſe operarentur ſecundum vim illam: <lb/></s> <s xml:id="echoid-s10277" xml:space="preserve">adeoque hæc vis eſt Lex Naturæ: </s> <s xml:id="echoid-s10278" xml:space="preserve">cui ſimilis obſervatur altera, <lb/>Gravitas, appellata, quæ etiam vis eſt interna in corporibus, & </s> <s xml:id="echoid-s10279" xml:space="preserve"><lb/>univerſalis, nequaquam â cauſâ externa pendens, qua omnia cor- <pb o="452" file="0466" n="466" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pora terreſtria nituntur, aut deſcendunt in lineâ perpendiculari ad <lb/>Terræ ſuperſiciem, verſus centrum maxime corporeum: </s> <s xml:id="echoid-s10280" xml:space="preserve">Planetæ <lb/>autem in ſpatiis cœleſtibus vacuis poſiti in Solem vel in primarium <lb/>Planetam, atque unâ in ſe mutuo nituntur. </s> <s xml:id="echoid-s10281" xml:space="preserve">Eſt hæc vis interna <lb/>diverſa ab attractione ſuperiori, cum decreſcat in ratione duplica-<lb/>ta diſtantiarum, vis vero attrahens decreſcit in multo altiori ra-<lb/>tione, imo ſæpe in repulſionem mutatur in quam nunquam abit <lb/>Gravitas.</s> <s xml:id="echoid-s10282" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10283" xml:space="preserve">Præter quas vires internas corporum alia adhuc eſt, quæ vis In-<lb/>ertiæ vocatur, quâ reſiſtunt cuicunque oppoſita directione pre-<lb/>menti vel moto, & </s> <s xml:id="echoid-s10284" xml:space="preserve">quâ impetum habent mota.</s> <s xml:id="echoid-s10285" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10286" xml:space="preserve">Quamobrem vis attrahens non eſt ſola interna in corporibus, <lb/>cum adhuc duas alias verè dari cognoſcamus; </s> <s xml:id="echoid-s10287" xml:space="preserve">neque hypothetice <lb/>aſſumitur, cum ex effectibus fluat.</s> <s xml:id="echoid-s10288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10289" xml:space="preserve">Si introſpicere in corporum ſubſtantiam poſſemus, omnes pro-<lb/>prietates tum harum; </s> <s xml:id="echoid-s10290" xml:space="preserve">tum aliarum virium internarum; </s> <s xml:id="echoid-s10291" xml:space="preserve">quomodo <lb/>ſolidâ occupent; </s> <s xml:id="echoid-s10292" xml:space="preserve">ſub qua proportione agant exeundo; </s> <s xml:id="echoid-s10293" xml:space="preserve">aliaque plu-<lb/>ra intelligeremus, quæ nunc ignorantur.</s> <s xml:id="echoid-s10294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10295" xml:space="preserve">Poſſunt autem phænomena Cohærentiæ ex his viribus internis <lb/>nunc clarè explicari, cumque promiſerim ſupra me ſeptem mo-<lb/>dos Cohærentiarum expoſiturum, id breviter exſequar.</s> <s xml:id="echoid-s10296" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10297" xml:space="preserve">Primus modus ſpectabat corporum majorum cohærentiam, quæ <lb/>ab Aëre gravi externo comprimebantur; </s> <s xml:id="echoid-s10298" xml:space="preserve">eſt hujus Aëris preſſio ſu-<lb/>pra corpora tanta, ac ſi affuſus fuiſſet circa ea Mercurius ad alti-<lb/>tudinem eandem, quæ in Baroſcopio datur; </s> <s xml:id="echoid-s10299" xml:space="preserve">hæc enim cum Aëris <lb/>gravitate æquilibrium facit; </s> <s xml:id="echoid-s10300" xml:space="preserve">idcirco duo hemiſphæria cuprea, ca-<lb/>va, diametri 3 pollicum, ſibi impoſita eductoque aëre interno <lb/>compreſſa fuerunt ad ſe invicem, quo tempore Baroſcopium erat ad <lb/>29 pollices elevatum, libr. </s> <s xml:id="echoid-s10301" xml:space="preserve">112. </s> <s xml:id="echoid-s10302" xml:space="preserve">unciis 5, granis 33. </s> <s xml:id="echoid-s10303" xml:space="preserve">quia area <lb/>circuli, cujus diameter eſt 3 pollicum, eſt 7 {31/452} pollic: </s> <s xml:id="echoid-s10304" xml:space="preserve">quadrato-<lb/>rum: </s> <s xml:id="echoid-s10305" xml:space="preserve">pollex cubicus Mercurii eſt 8 unciarum, 6 drachmarum, <lb/>8 granorum, quod pondus ductum in 7 {31/452} & </s> <s xml:id="echoid-s10306" xml:space="preserve">tumin 29. </s> <s xml:id="echoid-s10307" xml:space="preserve">pollices dat <lb/>productum librarum 112. </s> <s xml:id="echoid-s10308" xml:space="preserve">unc. </s> <s xml:id="echoid-s10309" xml:space="preserve">5. </s> <s xml:id="echoid-s10310" xml:space="preserve">gr. </s> <s xml:id="echoid-s10311" xml:space="preserve">33. </s> <s xml:id="echoid-s10312" xml:space="preserve">veluti Experimentum <lb/>quoque oſtendit hanc cohærentiam, quæ tamen paulo major fuit, <lb/>quia margines cera obducuntur ad aërem arcendum, cujus tenaci-<lb/>tas quoque ſuperanda fuit: </s> <s xml:id="echoid-s10313" xml:space="preserve">ideo ſi voluerimus, ut Experimentum <pb o="453" file="0467" n="467" rhead="CORPORUM FIRMORUM."/> accurate cum calculo conveniat, non ſunt margines obducendi ce-<lb/>ra, ſed extrinſecus circa eos cera craſſiuſcule illiniatur, quæ Aërem <lb/>arceat, tumque intrinſecus evacuata non plus cohærebunt, quam <lb/>eſt pondus Aëris extrinſecus incumbens. </s> <s xml:id="echoid-s10314" xml:space="preserve">ſed hæc nimis innotue-<lb/>runt, quam ut fuſius demonſtrentur, viderique poſſent Gueric-<lb/>kius in Exper. </s> <s xml:id="echoid-s10315" xml:space="preserve">Magdeb. </s> <s xml:id="echoid-s10316" xml:space="preserve">aut Volderus in Diſput. </s> <s xml:id="echoid-s10317" xml:space="preserve">de Aëris gravit.</s> <s xml:id="echoid-s10318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10319" xml:space="preserve">Secundus Cohærentiæ modus in vi Magnetis ſitus eſſe demonſtra-<lb/>tus fuit, cujus cauſam ignorari hactenus prolixe oſtendi in Diſſerta-<lb/>tione de hoc lapide. </s> <s xml:id="echoid-s10320" xml:space="preserve">Vi attractrice cohærere ſibi impoſitas lami-<lb/>nas quaſcunque planas, lapideas, metallicas, vitreas Experientia <lb/>evincit, quod nunc exponam. </s> <s xml:id="echoid-s10321" xml:space="preserve">Demonſtratum fuit in omni parti <lb/>cula corporea vim attrahentem internam dari; </s> <s xml:id="echoid-s10322" xml:space="preserve">quotiescunque igi-<lb/>tur corpora planæ ſuperficiei ſibi imponuntur, partes quæ ſe con-<lb/>tingunt, ſeſe attrahent, & </s> <s xml:id="echoid-s10323" xml:space="preserve">quantum ſe attrahent, tantum cohæ-<lb/>rebunt: </s> <s xml:id="echoid-s10324" xml:space="preserve">Si corporum ſuperficies forent perfecte planæ, & </s> <s xml:id="echoid-s10325" xml:space="preserve">abſque <lb/>poris, tum ejuſmodi ſuperficies vi ſummâ cohærerent, quippe om-<lb/>nia in iis puncta ſeſe attraherent; </s> <s xml:id="echoid-s10326" xml:space="preserve">cum vero ſuperficies omnium <lb/>corporum ſunt poroſæ, & </s> <s xml:id="echoid-s10327" xml:space="preserve">ideo aſperæ, duæ ſibi incumbentes in <lb/>nonnullis punctis lociſve ſe tantum attingunt, quare attractio ea-<lb/>rum non eſt maxima, ſed eo propius ad eam accedit, quo ſuperfi-<lb/>cies propius ad perfecte planam denſamque accedunt & </s> <s xml:id="echoid-s10328" xml:space="preserve">eo attra-<lb/>ctio minor eſt, quo ſuperficies duæ magis â perfectè planâ denſâ-<lb/>que receſſerit: </s> <s xml:id="echoid-s10329" xml:space="preserve">idcirco ejuſdem corporis attractio ad alterum admo-<lb/>dum differre poteſt pro aſperitate aut politura ſuperficierum: </s> <s xml:id="echoid-s10330" xml:space="preserve">Sint <lb/>enim Tab. </s> <s xml:id="echoid-s10331" xml:space="preserve">XVII. </s> <s xml:id="echoid-s10332" xml:space="preserve">fig. </s> <s xml:id="echoid-s10333" xml:space="preserve">6. </s> <s xml:id="echoid-s10334" xml:space="preserve">duo corpora R S, X Z, aſperæ ſuperficiei, <lb/>quorum partes prominentes, quæ ſe contingunt, ſint p a, d a hæ <lb/>ſe attrahent, viribus aliquouſque utrimque ex punctis contactus <lb/>a, a, a, exeuntibus, verum ex toto corpore vis attrahens effluat uſ-<lb/>que ad f, f, f, & </s> <s xml:id="echoid-s10335" xml:space="preserve">b. </s> <s xml:id="echoid-s10336" xml:space="preserve">b. </s> <s xml:id="echoid-s10337" xml:space="preserve">b, imminutis igitur aſperitatibus d a, p a uſque <lb/>ad f & </s> <s xml:id="echoid-s10338" xml:space="preserve">b, contactus fiet earundem partium p a, d a in latioribus <lb/>ſuperficiebus, unde magis ſe attrahent, & </s> <s xml:id="echoid-s10339" xml:space="preserve">præterea augebitur at-<lb/>tractio a vi utriusque corporis R S, X Z: </s> <s xml:id="echoid-s10340" xml:space="preserve">imminutis aſperitatibus <lb/>ulterius, augebitur attractio ex utraque ratione. </s> <s xml:id="echoid-s10341" xml:space="preserve">Quo aſperitates <lb/>p a, d a ſint majores, quo ſint pauciores, quæ ſe attingunt, quo <lb/>acutius terminentur, eo minus ſe attrahere poterunt.</s> <s xml:id="echoid-s10342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10343" xml:space="preserve">Quæ omnia demonſtrantur experientiâ: </s> <s xml:id="echoid-s10344" xml:space="preserve">ſumſi enim cylindros <pb o="454" file="0468" n="468" rhead="INTRODUCTIO AD COHÆRENTIAM"/> vitreos diametri 1 {11/12} poll. </s> <s xml:id="echoid-s10345" xml:space="preserve">quorum alter baſin politam, alter aſpe-<lb/>ram habebat, hi ſibi impoſiti vix ſe attrahebant vi grani dimidii: </s> <s xml:id="echoid-s10346" xml:space="preserve">tum <lb/>tertium lævigatæ baſeos appoſui baſi lævi primi cylindri, qui am-<lb/>bo ſe attraxerunt vi 1 {1/2} grani: </s> <s xml:id="echoid-s10347" xml:space="preserve">duo cylindri cuprei ejusdem magnitu-<lb/>dinis, planæ baſeos ſed aſperæ, ſe non attraxerunt vi, quæ ope ac-<lb/>curatiſſimæ noſtræ bilancis obſervari potuit; </s> <s xml:id="echoid-s10348" xml:space="preserve">paulum lævigatæ, <lb/>attractio fuit {1/4} grani, ulterius politæ fuit æqualis grano 1. </s> <s xml:id="echoid-s10349" xml:space="preserve">politæ <lb/>quantum fieri poteſt, eos atterendo ſupra ſe mutuo interpoſito oleo <lb/>& </s> <s xml:id="echoid-s10350" xml:space="preserve">ſubtiliſſimo lapide Tripolitano, & </s> <s xml:id="echoid-s10351" xml:space="preserve">bene ſiccæ puræque ſe <lb/>attraxerunt vi granorum 2. </s> <s xml:id="echoid-s10352" xml:space="preserve">non tamen ſuperficies eo modo lævi-<lb/>gatiſſimæ ſunt factæ, quippe nondum ſplendebant. </s> <s xml:id="echoid-s10353" xml:space="preserve">Ex quibus <lb/>apparet, quare corpora aſperrimæ ſuperficiei ſibi impoſita non co-<lb/>hæreant, cum nimirum ſe in pauciſſimis attingant punctis, neque <lb/>vis attrahens ex toto egreſſa corpore eouſque ſeſe exporrigat, ut in <lb/>alterum corpus agat, idcirco attrahunt ſe minoribus viribus, quam <lb/>quæ ſub ſenſus cadunt. </s> <s xml:id="echoid-s10354" xml:space="preserve">Objectionibus plurimis ita obviam imus, cum <lb/>ſemper quæri ſoleat, data attractione, cur duo ligna ſibi impoſita non <lb/>cohæreant? </s> <s xml:id="echoid-s10355" xml:space="preserve">cur cubus metallicus alteri appoſitus non cohæreat, <lb/>ac ſi igne fuſus in unam maſſam uterque fuiſlet? </s> <s xml:id="echoid-s10356" xml:space="preserve">verum hæ evane-<lb/>ſcunt difficultates, ſi ad aſperitates ſuperficierum ſeſe attingentium <lb/>attendamus, impedientes quominus attractio ſenſibilis oriatur.</s> <s xml:id="echoid-s10357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10358" xml:space="preserve">Hinc intelligimus, quare corpora maxime cohærentia, uti A-<lb/>damas, Gemmæ, Silices, Vitra &</s> <s xml:id="echoid-s10359" xml:space="preserve">c. </s> <s xml:id="echoid-s10360" xml:space="preserve">diffracta ſuperſiciem ſplen-<lb/>dentem exhibeant, quæ ex planiſſimæ ſuperficiei partibus conſtare <lb/>videtur, quarum una alteram immediate attingere poteſt; </s> <s xml:id="echoid-s10361" xml:space="preserve">cum è <lb/>contrario corpora minoris firmitatis diffracta ſuperficiem exhibeant <lb/>aſperam & </s> <s xml:id="echoid-s10362" xml:space="preserve">inæqualem, utpote conſtantem ex corpuſculis, quorum <lb/>ſuperficies aſperiores etiam in paucioribus punctis attigerunt reli-<lb/>quas: </s> <s xml:id="echoid-s10363" xml:space="preserve">Et quia infinitis gradibus corpuſculorum ſuperficies quoad <lb/>aſperitatem inter ſe differre, & </s> <s xml:id="echoid-s10364" xml:space="preserve">majori minorive congruentia do-<lb/>nari poterunt, firmitas corporum majorum poteſt eſſe infinite varia.</s> <s xml:id="echoid-s10365" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10366" xml:space="preserve">Non alienum erit ab hoc loco demonſtraſſe Cohærentiam in im-<lb/>mediato cöntactu corporum poſſe eſſe maximam, quæ exigua eſt <lb/>in parvo corporum a ſe intervallo, prout ſecundum aliquam pro-<lb/>portionem decreſcit attractio in diſtantiis: </s> <s xml:id="echoid-s10367" xml:space="preserve">Sit enim centrum cir-<lb/>culi A, T ab. </s> <s xml:id="echoid-s10368" xml:space="preserve">XVII. </s> <s xml:id="echoid-s10369" xml:space="preserve">fig. </s> <s xml:id="echoid-s10370" xml:space="preserve">14. </s> <s xml:id="echoid-s10371" xml:space="preserve">cujus radius eſt A D ſupra aream hujus circuli <pb o="455" file="0469" n="469" rhead="CORPORUM FIRMORUM."/> erecta ſit perpendicularis P A, ſitque P quædam particula attracta ab <lb/>omnibus circuli partibus; </s> <s xml:id="echoid-s10372" xml:space="preserve">â P ad quodcunque punctum radii A D, <lb/>ducatur recta P E, in recta P A ducatur P F = P E, ex F ducatur <lb/>F K parallela ad A D, quæ repræſentet vires, quibus punctum E at-<lb/>trahit particulam P, ſitque I K L curva linea, quam punctum K <lb/>perpetuo tangit: </s> <s xml:id="echoid-s10373" xml:space="preserve">Occurrat eadem circuli plano in L. </s> <s xml:id="echoid-s10374" xml:space="preserve">in P A capia-<lb/>tur P H æqualis P D, & </s> <s xml:id="echoid-s10375" xml:space="preserve">erigatur perpendiculum H I cur væ oc-<lb/>currens in I. </s> <s xml:id="echoid-s10376" xml:space="preserve">demonſtravit Newtonus Lib. </s> <s xml:id="echoid-s10377" xml:space="preserve">1. </s> <s xml:id="echoid-s10378" xml:space="preserve">prop. </s> <s xml:id="echoid-s10379" xml:space="preserve">90. </s> <s xml:id="echoid-s10380" xml:space="preserve">Princ. </s> <s xml:id="echoid-s10381" xml:space="preserve">Philoſ. <lb/></s> <s xml:id="echoid-s10382" xml:space="preserve">corpuſculi P attractionem eſſe, ut area A H I L. </s> <s xml:id="echoid-s10383" xml:space="preserve">eſt ducta in alti-<lb/>tudinem A P.</s> <s xml:id="echoid-s10384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10385" xml:space="preserve">Vocetur P F x. </s> <s xml:id="echoid-s10386" xml:space="preserve">F K y, & </s> <s xml:id="echoid-s10387" xml:space="preserve">ſit F K, vel vis quâ punctum E <lb/>attrahit corpus P, reciproce ut aliqua potentia ipſius P F, ſit <lb/>hæc n. </s> <s xml:id="echoid-s10388" xml:space="preserve">tum æquatio curvæ erit y = {1/X<emph style="super">n</emph>} & </s> <s xml:id="echoid-s10389" xml:space="preserve">area A H I K L uti <lb/>{1/PA<emph style="super">n - 1</emph>} - {1/PH<emph style="super">n - 1</emph>} unde attractio corpuſculi P in circulum erit <lb/>ut {1/PA<emph style="super">n - 2</emph>} - {PA/PH<emph style="super">n - 1</emph>}.</s> <s xml:id="echoid-s10390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10391" xml:space="preserve">Hæc Cl. </s> <s xml:id="echoid-s10392" xml:space="preserve">Chynæus in Philoſophical Principles of Natural reli-<lb/>gion eleganter explicuit §. </s> <s xml:id="echoid-s10393" xml:space="preserve">44. </s> <s xml:id="echoid-s10394" xml:space="preserve">Si n = i, & </s> <s xml:id="echoid-s10395" xml:space="preserve">P A = 0. </s> <s xml:id="echoid-s10396" xml:space="preserve">tum radius cir-<lb/>culi attrahentis productus coincidet cum Aſy mptoto P O, in quo <lb/>caſu area A H I L erit infinita, cum curva ſit Hyperbola vulgaris; <lb/></s> <s xml:id="echoid-s10397" xml:space="preserve">& </s> <s xml:id="echoid-s10398" xml:space="preserve">P A = 0, ſive evaneſcente intervallo inter particulam & </s> <s xml:id="echoid-s10399" xml:space="preserve">circu-<lb/>lum attrahentem, erit attractio = P A X A H I L = 0 X ? </s> <s xml:id="echoid-s10400" xml:space="preserve">= i.</s> <s xml:id="echoid-s10401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10402" xml:space="preserve">Si n = 1, & </s> <s xml:id="echoid-s10403" xml:space="preserve">P A = ?</s> <s xml:id="echoid-s10404" xml:space="preserve">, hoc eſt quando planum attrahens A D <lb/>poſitum eſt ad concurſum Hyperbolæ, cum ſuâ Aſymptoto P H, <lb/>tum arcus D H, cujus centrum eſt P, & </s> <s xml:id="echoid-s10405" xml:space="preserve">cujus radius eſt P D = P A <lb/>= ?</s> <s xml:id="echoid-s10406" xml:space="preserve">, coincidet cum A D, & </s> <s xml:id="echoid-s10407" xml:space="preserve">ideo A L coincidet cum H I, unde <lb/>P A X A H I L = ? </s> <s xml:id="echoid-s10408" xml:space="preserve">X 0 = i.</s> <s xml:id="echoid-s10409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10410" xml:space="preserve">Si n = i. </s> <s xml:id="echoid-s10411" xml:space="preserve">& </s> <s xml:id="echoid-s10412" xml:space="preserve">P A = a tum A H vocetur y, & </s> <s xml:id="echoid-s10413" xml:space="preserve">P H = x = a + y, <lb/>unde corpuſculum P a circulo attrahetur vi = P A X A H I L = <lb/>{y-yy/2a} + {y<emph style="super">3</emph>/3aa} - {y<emph style="super">4</emph>/4a<emph style="super">3</emph>} &</s> <s xml:id="echoid-s10414" xml:space="preserve">c.</s> <s xml:id="echoid-s10415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10416" xml:space="preserve">Si n = 2 & </s> <s xml:id="echoid-s10417" xml:space="preserve">P A = 0. </s> <s xml:id="echoid-s10418" xml:space="preserve">tum area A H I L erit plus quam infinita, <lb/>unde attractio erit A P X A H I L = 0 multiplicato per pluſquam <lb/>infinitum, unde liquet attractionem in hoc caſu, poſito P A = 0.</s> <s xml:id="echoid-s10419" xml:space="preserve"> <pb o="456" file="0470" n="470" rhead="INTRODUCTIO AD COHÆRENTIAM"/> eſſe majorem quam in præcedenti; </s> <s xml:id="echoid-s10420" xml:space="preserve">cum n = i, & </s> <s xml:id="echoid-s10421" xml:space="preserve">P A = 0.</s> <s xml:id="echoid-s10422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10423" xml:space="preserve">Si n = 2, & </s> <s xml:id="echoid-s10424" xml:space="preserve">P A = ?</s> <s xml:id="echoid-s10425" xml:space="preserve">, tum area A H I L erit = 0. </s> <s xml:id="echoid-s10426" xml:space="preserve">ergo attractio <lb/>= P A X A H I L = ? </s> <s xml:id="echoid-s10427" xml:space="preserve">X 0 = 1. </s> <s xml:id="echoid-s10428" xml:space="preserve">Hinc apparet in hoc caſu, cum <lb/>P A = 0, attractionem fore majorem, quam cum P A = ?</s> <s xml:id="echoid-s10429" xml:space="preserve">: nam <lb/>duorum productorum eundem multiplicatorem habentium, illud eſt <lb/>majus, cujus multiplicandum eſt majus: </s> <s xml:id="echoid-s10430" xml:space="preserve">igitur ſi A notet attractio-<lb/>nem, cum P A = 0, & </s> <s xml:id="echoid-s10431" xml:space="preserve">a attractionem cum P A = ?</s> <s xml:id="echoid-s10432" xml:space="preserve">, erit A ad a, <lb/>veluti pluſquam Infinitum eſt ad Infinitum, contrarium ac contin-<lb/>git in primo caſu, cum n = 1, nam attractio in eo caſu erat ea-<lb/>dem ſive P A fuerit = 0 ſive = ?</s> <s xml:id="echoid-s10433" xml:space="preserve">, erat enim = 1.</s> <s xml:id="echoid-s10434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10435" xml:space="preserve">Si n =2, & </s> <s xml:id="echoid-s10436" xml:space="preserve">P A = a, tum A H vocato = y, erit attractio <lb/>= P A X A H I L = {y/a} - {y<emph style="super">2</emph>/a<emph style="super">2</emph>} + {y<emph style="super">3</emph>/a<emph style="super">3</emph>} - {y<emph style="super">4</emph>/a<emph style="super">4</emph>} + {y<emph style="super">5</emph>/a<emph style="super">5</emph>} &</s> <s xml:id="echoid-s10437" xml:space="preserve">c.</s> <s xml:id="echoid-s10438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10439" xml:space="preserve">Si n = 3. </s> <s xml:id="echoid-s10440" xml:space="preserve">& </s> <s xml:id="echoid-s10441" xml:space="preserve">P A = 0. </s> <s xml:id="echoid-s10442" xml:space="preserve">tum A H I L erit pluſquam Infinitum, ſed <lb/>A H I L in hoc tertio caſu erit majus quam A H I L in ſecundo ca-<lb/>ſu, ergo attractio, poſita P A = 0, pro utroque caſu, erit major in hoc <lb/>quam in ſecundo caſu, quoniam P A = 0 eſt communis multiplicator <lb/>utriusque, & </s> <s xml:id="echoid-s10443" xml:space="preserve">A H I L in hoc caſu eſt majus quam A H I L in ſecundo.</s> <s xml:id="echoid-s10444" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10445" xml:space="preserve">Si n = 3, & </s> <s xml:id="echoid-s10446" xml:space="preserve">P A = ?</s> <s xml:id="echoid-s10447" xml:space="preserve">, tum & </s> <s xml:id="echoid-s10448" xml:space="preserve">ante A H I L erit = 0, unde <lb/>attractio erit = ? </s> <s xml:id="echoid-s10449" xml:space="preserve">X 0 = 1.</s> <s xml:id="echoid-s10450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10451" xml:space="preserve">Si n = 3 & </s> <s xml:id="echoid-s10452" xml:space="preserve">P A = a, tum attractio erit æqualis {y/aa} - {3yy/2a<emph style="super">3</emph>}?</s> <s xml:id="echoid-s10453" xml:space="preserve">?+ <lb/>{2y<emph style="super">3</emph>/a<emph style="super">4</emph>} - {5y<emph style="super">4</emph>/2a<emph style="super">5</emph>} + {3y<emph style="super">5</emph>/a<emph style="super">6</emph>} - {21y<emph style="super">6</emph>/6a<emph style="super">7</emph>}. </s> <s xml:id="echoid-s10454" xml:space="preserve">Secundum hanc methodum vis at-<lb/>trahens plani circularis in corpuſculum P facile ſupputatur in quo <lb/>cunque aſſignabili caſu poſita proportione virium in diſtantiis datis <lb/>quacunque. </s> <s xml:id="echoid-s10455" xml:space="preserve">Ex hiſce omnibus manifeſto liquet ſi n = 3, attractio-<lb/>nem in quibuslibet finitis diſtantiis corporum multo magis decre-<lb/>ſcere, quam ſi n = 2, vel = 1. </s> <s xml:id="echoid-s10456" xml:space="preserve">fuerit: </s> <s xml:id="echoid-s10457" xml:space="preserve">cum vero attractio cor-<lb/>porum cohærentium in diſtantiis citiſſime decreſcat, erit dignitas <lb/>virium n, alta: </s> <s xml:id="echoid-s10458" xml:space="preserve">Quæ omnia pulcriora judicavi, quam ut omitte-<lb/>rentur.</s> <s xml:id="echoid-s10459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10460" xml:space="preserve">Tertium modum Cohærentiæ præbent corpora, quæ in Igne muta-<lb/>ta in fluidum, frigore in ſolidiſſimam maſſam abeunt, veluti me-<lb/>talla aliaque corpora ſuperius memorata ſe habent: </s> <s xml:id="echoid-s10461" xml:space="preserve">ut hoc cla-<lb/>rius intelligatur, primo corpus quodcunque veluti metallum, po- <pb o="457" file="0471" n="471" rhead="CORPORUM FIRMORUM."/> namus frigidum, cujus partes ſeſe attrahendo firmiter cohærent: <lb/></s> <s xml:id="echoid-s10462" xml:space="preserve">ignis accedat, qui eſt motor ſummus huc uſque notus, hic ingreſ-<lb/>ſus poros metalli, motu ſuo quaquaverſum removet metalli par-<lb/>tes, hoc eſt, rarefacit maſſam, attractionem ſuperando; </s> <s xml:id="echoid-s10463" xml:space="preserve">cum ve-<lb/>ro removere partes ulterius pergat, tandem ad tantam eas deducit <lb/>diſtantiam a ſe, ut vix amplius vi attrahente in ſe agere queant; </s> <s xml:id="echoid-s10464" xml:space="preserve">tum <lb/>vero ſolutæ ſunt partes, cuicunque determinationi facile cedunt, hoc <lb/>eſt maſſam fluidam componunt. </s> <s xml:id="echoid-s10465" xml:space="preserve">Deinde ignis avolare incipiat, tum <lb/>cauſa partes metallicas removens imminuetur, adeoque vis earum <lb/>attrahens partes iterum propius ad ſe reducet; </s> <s xml:id="echoid-s10466" xml:space="preserve">unde fluiditas de-<lb/>creſcet; </s> <s xml:id="echoid-s10467" xml:space="preserve">avolante igne ulterius, etiam cauſa partes removens magis <lb/>imminuitur, adeoque hæ per vim attrahentem propius ad ſe accedent, <lb/>& </s> <s xml:id="echoid-s10468" xml:space="preserve">maſſa ſimul fluiditatem amittendo firmitatis gradum acquirit, <lb/>quæ augetur, quo ignis plus avolat, & </s> <s xml:id="echoid-s10469" xml:space="preserve">partes vi attrahente pro-<lb/>pius ad ſe accedunt: </s> <s xml:id="echoid-s10470" xml:space="preserve">hinc proprie loquendo, frigus non reddit <lb/>corpora cohærentia, ſed attrahens vis partium, quæ maxima eſſe <lb/>poteſt in immediato contactu; </s> <s xml:id="echoid-s10471" xml:space="preserve">hoc eſt cum non datur Ignis eas a ſe <lb/>removens: </s> <s xml:id="echoid-s10472" xml:space="preserve">nam non eſt frigus quid aliud, præter Ignis abſentiam.</s> <s xml:id="echoid-s10473" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10474" xml:space="preserve">Zuartum modum Cohærentiæ poſuimus in Luto, quod prius <lb/>molle, dein igni commiſſum in laterem duriſſimum abit hoc modo: <lb/></s> <s xml:id="echoid-s10475" xml:space="preserve">Eſt Lutum ſive Argilla Terra compoſita ex nonnullis partibus Metal-<lb/>licis, Salinis, Arenoſis&</s> <s xml:id="echoid-s10476" xml:space="preserve">c. </s> <s xml:id="echoid-s10477" xml:space="preserve">mollis fit affuſâ, quæ quo copio-<lb/>ſior admiſceatur, eo molliorem argillam facit: </s> <s xml:id="echoid-s10478" xml:space="preserve">cum igitur partes <lb/>argillæ ſemet attrahant, ut corpus firmum componant, ex quo A-<lb/>qua maſſam mollem facit, removebit Aqua partes argillæ â ſe <lb/>invicem, earumque mutuam attractionem imminuet: </s> <s xml:id="echoid-s10479" xml:space="preserve">Hæc maſſa <lb/>igni admoveatur, qui ſecum illico abripit partes aqueas, utpote <lb/>admodum volatiles, unde argillæ partes vi attrahente propius ad <lb/>ſe accedent, maſſamque firmam componere incipient: </s> <s xml:id="echoid-s10480" xml:space="preserve">ignis tamen <lb/>partes a ſe removet, uti demonſtra vimus ſupra, unde, & </s> <s xml:id="echoid-s10481" xml:space="preserve">maſſa <lb/>quamdiu copioſus ignis adeſt, admodum firma evadere nequit. </s> <s xml:id="echoid-s10482" xml:space="preserve"><lb/>Ignis præterea Sales in argilla latentes ſolvit, fundit, inter partes <lb/>terreſtres diſtribuit, iiſque earum aſperitates implet, quæ idcirco <lb/>poſtea partim attrahuntur a ſe, partim a ſale utrimque interpoſito, <lb/>unde igne avolante maſſa fit, cujus partes ſeſe valde attrahunt, hoc <lb/>eſt, duriſſimum corpus componunt; </s> <s xml:id="echoid-s10483" xml:space="preserve">ſales autem fundi, atque per ar- <pb o="458" file="0472" n="472" rhead="INTRODUCTIO AD COHÆRENTIAM"/> gillæ partes diſtribui, docet vitrificatio, abeunt enim lateres vio-<lb/>lento igni expoſiti in vitrum, tumque evadunt duriſſimi</s> </p> <p> <s xml:id="echoid-s10484" xml:space="preserve">Creta cæteroquin mollis, durior in igne fit, expulfâ ex ipſa a-<lb/>quâ, quam copioſe concludit, unde partes ſolidæ propius ad ſe mu-<lb/>tuo accedunt, firmiuſque ſe attrahunt, quæ ratio etiam obtinet in <lb/>corio, pergameno, aliisque corporibus: </s> <s xml:id="echoid-s10485" xml:space="preserve">Lignum leviter uſtula-<lb/>tum, induratur, quia Aqua expellitur, parteſque ſolidæ propius <lb/>ad ſe accedunt, magiſque ſe attrahunt, tum quia reſina calore fuſa, <lb/>ad cuſpidem determinatur copioſius, quæ inter ſolidas diſtributa <lb/>partes attractionem mutuam; </s> <s xml:id="echoid-s10486" xml:space="preserve">& </s> <s xml:id="echoid-s10487" xml:space="preserve">proinde duritiem, auget. </s> <s xml:id="echoid-s10488" xml:space="preserve">Coral-<lb/>lia & </s> <s xml:id="echoid-s10489" xml:space="preserve">Succinum aëri expoſita calido indurantur non aliter, quam <lb/>quod fluida eorum cum igne ſimul avolent, relictis ſolidioribus <lb/>partibus, quæ ſeſe fortius tum attrahentes duritiem augent.</s> <s xml:id="echoid-s10490" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10491" xml:space="preserve">Ad Zuintum modum pervenimus, quo duo corpora cohærere <lb/>diximus interpoſito Fluido aut ſemifluido corpore, quod ita ma-<lb/>net, aut deinde in maſſam firmam abit. </s> <s xml:id="echoid-s10492" xml:space="preserve">Ut hunc modum quam cla-<lb/>riſſime intelligamus, ponatur Fig. </s> <s xml:id="echoid-s10493" xml:space="preserve">7. </s> <s xml:id="echoid-s10494" xml:space="preserve">T ab. </s> <s xml:id="echoid-s10495" xml:space="preserve">XVII. </s> <s xml:id="echoid-s10496" xml:space="preserve">ante oculos, in <lb/>qua conſpiciuntur corpora R S, X Z, aſperæ ſuperficiei (veluti <lb/>ſemper comparatæ ſunt corporum ſuperficies) ſibi impoſita: </s> <s xml:id="echoid-s10497" xml:space="preserve">hæc <lb/>ſe attingentia in paucis punctis a, a, parum ſe attrahunt, & </s> <s xml:id="echoid-s10498" xml:space="preserve">leviter <lb/>cohærent: </s> <s xml:id="echoid-s10499" xml:space="preserve">duas autem aſperitates duntaxat conſiderabo ap, ap ? <lb/></s> <s xml:id="echoid-s10500" xml:space="preserve">ad, ad in utraque ſuperficie, quippe quæ de his demonſtrabun-<lb/>tur, in omnibus aliis aſperitatibus obtinent. </s> <s xml:id="echoid-s10501" xml:space="preserve">Sit igitur inter pro-<lb/>minentes partes utriuſque ſuperficiei ap, ap. </s> <s xml:id="echoid-s10502" xml:space="preserve">ad, ad interpoſita <lb/>particula fluida F, quæ ſua vi attractrice attrahat ap, ap, â qui-<lb/>bus viciſſim attrahetur; </s> <s xml:id="echoid-s10503" xml:space="preserve">ſed eodem tempore attrahit prominentias <lb/>oppoſitas ad, ad, a quibus etiam reciproce attrahitur; </s> <s xml:id="echoid-s10504" xml:space="preserve">proinde <lb/>particula F ſeſe inſtar Magnetis habet, trahentis ad ſe latera pro-<lb/>minentiarum ap, ap, ad, ad; </s> <s xml:id="echoid-s10505" xml:space="preserve">hac attractione aguntur prominen-<lb/>tiæ ap, ap, ad, ad ad ſe mutuo, unde ſi vis quædam externa co-<lb/>naretur divellere bina corpora R S, X Z a ſe invicem, teneretur non <lb/>modo ſuperare attractionem mutui contactus in a, a. </s> <s xml:id="echoid-s10506" xml:space="preserve">ſed etiam <lb/>attractionem, qua tenet particula fluida F latera ap, ap, ad, ad. </s> <s xml:id="echoid-s10507" xml:space="preserve"><lb/>Hinc interpoſito inter quaslibet corporum ſuperficies fluido, co-<lb/>hærentia augeatur neceſſe eſt: </s> <s xml:id="echoid-s10508" xml:space="preserve">hæc eſt ratio quare in Exper. </s> <s xml:id="echoid-s10509" xml:space="preserve">2°, 80. </s> <s xml:id="echoid-s10510" xml:space="preserve"><lb/>15 interpoſita inter cylindrorum vitreorum, cupreorum, marmo- <pb o="459" file="0473" n="473" rhead="CORPORUM FIRMORUM."/> reorum baſes aquâ, obſervata fuerit aucta horum corporum Cohæ-<lb/>rentia.</s> <s xml:id="echoid-s10511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10512" xml:space="preserve">Verum quælibet particula fluidi non eſt Elementum corporeum, <lb/>ſed molecula ex aliis particulis minoribus congeſta; </s> <s xml:id="echoid-s10513" xml:space="preserve">hinc diverſæ <lb/>eſt denſitatis in variis ſluidis, adeoque poſita magnitudine & </s> <s xml:id="echoid-s10514" xml:space="preserve">ſigu-<lb/>ra eâdem non eandem vim attrahentem habebit: </s> <s xml:id="echoid-s10515" xml:space="preserve">ſit igitur particula <lb/>alterius Fluidi F rarioris vel denſioris inter eaſdem prominentias <lb/>ap, ap, ad, ad poſita, poterit has majori minorive virtute ad ſe <lb/>attrahere; </s> <s xml:id="echoid-s10516" xml:space="preserve">unde corporum R S, X Z major minorve Cohærentia <lb/>erit.</s> <s xml:id="echoid-s10517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10518" xml:space="preserve">Præterea ea corpora, quæ in Igne firmitatem deponunt & </s> <s xml:id="echoid-s10519" xml:space="preserve">lique-<lb/>facta inter prominentias ap, ad ponuntur, non eadem donata <lb/>ſunt figura: </s> <s xml:id="echoid-s10520" xml:space="preserve">fieri igitur poteſt, ut interponendæ partes habeant figu-<lb/>ram ſimilem, aut utcunque accedentem ad intervalli ap, ap, ad, <lb/>ad formam, veluti eſt particula D; </s> <s xml:id="echoid-s10521" xml:space="preserve">quæ totis fere ſuis lateribus attin-<lb/>gens prominentiarum ap, ap, ad, ad latera, vehementiſſime hæc <lb/>attrahet & </s> <s xml:id="echoid-s10522" xml:space="preserve">attrahetur, quamobrem non poterunt bina corpora R S, <lb/>X Z â ſe divelli, niſi vis ſeparans magna exſtiterit, hæc ratio eſt <lb/>quare in Exp. </s> <s xml:id="echoid-s10523" xml:space="preserve">14, pice inter cylindros cupreos interpoſita, tam <lb/>enormis Cohærentia obſervata fuerit, utpote major librarum 1400: <lb/></s> <s xml:id="echoid-s10524" xml:space="preserve">tum quare pice interpoſita major Cohærentia fuerit, quam ſi Cera, <lb/>aut Sebum, aut animale gluten illitum baſibus fuiſſet.</s> <s xml:id="echoid-s10525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10526" xml:space="preserve">Sed omnium firmorum aſperitates non ſunt eodem modo conſti-<lb/>tutæ, erunt aliæ pyramidales, veluti hic pinximus, aliæ ovales, aliæ <lb/>parallelopipedæ, aliæ alterius figuræ: </s> <s xml:id="echoid-s10527" xml:space="preserve">idcirco unum idemque cor-<lb/>pus liquefactum interpoſitum inter diverſorum corporum aſperas <lb/>baſes, non eandem attractionem exercere poterit; </s> <s xml:id="echoid-s10528" xml:space="preserve">ſed majorem, <lb/>ſi hæreat inter aſperitates, quibuſcum figurâ ſuâ convenit; </s> <s xml:id="echoid-s10529" xml:space="preserve">mino-<lb/>rem ſi non conveniat: </s> <s xml:id="echoid-s10530" xml:space="preserve">& </s> <s xml:id="echoid-s10531" xml:space="preserve">hinc quoque ſebo candelarum interpoſito <lb/>inter baſes vitreas Exper. </s> <s xml:id="echoid-s10532" xml:space="preserve">4. </s> <s xml:id="echoid-s10533" xml:space="preserve">aut inter cupreas Exp. </s> <s xml:id="echoid-s10534" xml:space="preserve">12. </s> <s xml:id="echoid-s10535" xml:space="preserve">tanta Cohæ-<lb/>rentiæ diſcrepantia obſervata fuit, ut vitrei cylindri modo cohæſe-<lb/>ſerint vi librarum 290, cuprei librar. </s> <s xml:id="echoid-s10536" xml:space="preserve">800. </s> <s xml:id="echoid-s10537" xml:space="preserve">aut interpoſita Cera vitreos <lb/>attraxerit cylindros vi librarum 230. </s> <s xml:id="echoid-s10538" xml:space="preserve">cupreos æque magnos in Exp. <lb/></s> <s xml:id="echoid-s10539" xml:space="preserve">13, vi librarum 900. </s> <s xml:id="echoid-s10540" xml:space="preserve">aut pix inter vitreos cohærere illos fecerit in <lb/>Exp. </s> <s xml:id="echoid-s10541" xml:space="preserve">6°, vi librarum 850 inter cupreos in Exp. </s> <s xml:id="echoid-s10542" xml:space="preserve">14. </s> <s xml:id="echoid-s10543" xml:space="preserve">plus quam li-<lb/>brarum 1400: </s> <s xml:id="echoid-s10544" xml:space="preserve">Ex quibus etiam intelliguntur reliqua Experimenta <pb o="460" file="0474" n="474" rhead="INTRODUCTIO AD COHÆRENTIAM"/> diverſam Cohærentiam ab interpoſito ſebo oſtendentia, cum lapi-<lb/>des marmorei albi, aut nigri, aut eburnei capti fuerunt.</s> <s xml:id="echoid-s10545" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10546" xml:space="preserve">Quotieſcunque Experimenta cum memoratis cylindris inſtituun-<lb/>tur, ſemper calefaciendi ſunt, ut ſebum, cera, pix, colophonia &</s> <s xml:id="echoid-s10547" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s10548" xml:space="preserve">ſuper eorum baſibus liqueſcat, differt autem eorum Cohærentia <lb/>plurimum, prout magis minuſve calidi ſibi fuerint impoſiti, nam quo <lb/>calidiores exſtiterint, & </s> <s xml:id="echoid-s10549" xml:space="preserve">illiti aliquo ex memoratis plus compriman-<lb/>tur, donec frigeant, eo validius cohærent: </s> <s xml:id="echoid-s10550" xml:space="preserve">calidi enim valde cylindri, <lb/>multum ſunt rarefacti, poroſque ampliores acquiſiverunt, ita ut <lb/>ſpatium a p, a p, a d, ad in Figura 7 ſit magnum: </s> <s xml:id="echoid-s10551" xml:space="preserve">quæ illiniuntur <lb/>corpora uti ſebum, cera, pix, fiunt eo fluidiora & </s> <s xml:id="echoid-s10552" xml:space="preserve">ſubtiliora, quo <lb/>plus calent; </s> <s xml:id="echoid-s10553" xml:space="preserve">quamobrem non una particula F ſpatium nunc amplius <lb/>a p, a p, a d, a d, ingredietur, ſed plures, uti in K, quæ penetra-<lb/>bunt uſque ad fundum p p, d d. </s> <s xml:id="echoid-s10554" xml:space="preserve">imo quatenus extrinſecus adhuc <lb/>premuntur, eo magis ad fundum utrumque determinabuntur, to-<lb/>tum ſpatium repleturæ: </s> <s xml:id="echoid-s10555" xml:space="preserve">deinde ipſa corpora R S, X Z frigori com-<lb/>miſſa con denſantur, ſpatium ap, ap, ad, ad anguſtius reddunt, <lb/>particulas incluſas fortiſſime concludunt, ut figuræ ſuæ congruant, <lb/>atque contactus fiat in magnis ſuperficiebus; </s> <s xml:id="echoid-s10556" xml:space="preserve">idcirco vis attrahens, <lb/>quæ ex toto corpore R S exit, & </s> <s xml:id="echoid-s10557" xml:space="preserve">tantum uſque ad ff in ipſo ſpa-<lb/>tio diffundebatur, nec antea in particulam F agebat, aut parum, <lb/>nunc valde attrahit particulas K concluſas, hæ reciproce ſemet <lb/>ipſas, tum corpus R S & </s> <s xml:id="echoid-s10558" xml:space="preserve">X Z, quamobrem non poteſt non attra-<lb/>ctio tum eſſe fortiſſima, & </s> <s xml:id="echoid-s10559" xml:space="preserve">Cohærentia maxima: </s> <s xml:id="echoid-s10560" xml:space="preserve">fuerint vero cy-<lb/>lindri frigidiores cum ſebo illiniebantur, nec comprimantur, non <lb/>tam profunde partes ſebi in poros penetrabunt, nec totidem in eos <lb/>ingredientur, unde neceſſario minor erit cum attractio, tum Co-<lb/>hærentia.</s> <s xml:id="echoid-s10561" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10562" xml:space="preserve">Præterea quo Sebum, Cera, Pix, denſius illita fuerint ſuperfi-<lb/>ciebus, eo minus cylindri cohærebunt, quia enim partes corporum <lb/>illitorum aſe diſtant, non valde ſe mutuo attrahunt, nec magnam fir-<lb/>mitatem exhibent, ideo non poterunt corpora R S, X Z ſe attrahere, <lb/>aut ſaltem non multum; </s> <s xml:id="echoid-s10563" xml:space="preserve">unde cohæreant parum neceſſe eſt: </s> <s xml:id="echoid-s10564" xml:space="preserve">con-<lb/>cipe enim hiulcum notabilem inter prominentias a p, ad, qui ſebo <lb/>ſit impletus, ſitque tam magnum intervallum, ut vis atrahens ap, non <lb/>amplius agat in ad, tum cohærebunt modo corpora, quatenus ab in- <pb o="461" file="0475" n="475" rhead="CORPORUM FIRMORUM."/> terpoſito ſebo attrahuntur, hoc eſt non magis cohærebunt, quam <lb/>eſt vis attrahens ipſarum ſebi partium, & </s> <s xml:id="echoid-s10565" xml:space="preserve">inſtituto experimento ob-<lb/>ſervatur fractura fieri per medium ſebi, etiamſi cum magnis inæqua-<lb/>litatibus: </s> <s xml:id="echoid-s10566" xml:space="preserve">Si paulo minor copia ſebi interpoſita fuerit, ut ad, ap as-<lb/>peritates in ſe operari queant, oritur Cohærentia major, compo-<lb/>ſita ex vi attrahente partium ap, ad, & </s> <s xml:id="echoid-s10567" xml:space="preserve">ex vi attrahente partium <lb/>ſebi ſed quia vis attrahens partium in alta proportione ad diſtan-<lb/>tias decreſcere videtur, maxima erit Cohærentia, quo minus ſebi <lb/>inter partes prominentes ap, ad, fuerit: </s> <s xml:id="echoid-s10568" xml:space="preserve">ideo etiam quo corpo-<lb/>rum ſuperficies R S, X Z accuratius congruerint ſibi impoſitæ an-<lb/>tequam ſebo obducuntur, ſobrie illitæ etiam eo fortius poſtea co-<lb/>hærent.</s> <s xml:id="echoid-s10569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10570" xml:space="preserve">Admirandum apparet corpora deſcripta adeo firmiter ſecum co-<lb/>hærere frigida, & </s> <s xml:id="echoid-s10571" xml:space="preserve">calida vix, ita ut cylindri, qui frigidi plus quam <lb/>vi librarum 1400. </s> <s xml:id="echoid-s10572" xml:space="preserve">cohæſerint, calidi, eademque pice interpoſitâ, ne <lb/>quidem pondus librarum 3 ferre potuerint: </s> <s xml:id="echoid-s10573" xml:space="preserve">ſed cogita quantum <lb/>motum ignis partibus communicet; </s> <s xml:id="echoid-s10574" xml:space="preserve">1°. </s> <s xml:id="echoid-s10575" xml:space="preserve">partes picis fluidas reddit, <lb/>adeoque tantopere a ſe removet, ut ſe aut non, aut vix attrahant: <lb/></s> <s xml:id="echoid-s10576" xml:space="preserve">partes metalli præterea concutit, eaſque etiam a ſe removet unde <lb/>partes tam metalli, quam picis in perpetuo ſunt motu, calente <lb/>maſſâ, neque ut ſeſe attrahant in iiſdem punctis tempus concedi-<lb/>tur.</s> <s xml:id="echoid-s10577" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10578" xml:space="preserve">In omnibus his experimentis notandum quoque eſt, Cohæren-<lb/>tiam non penitus pendere ab attrahentibus viribus, quibus tum cor-<lb/>pora, tum fluida ſemet & </s> <s xml:id="echoid-s10579" xml:space="preserve">corpora attrahunt; </s> <s xml:id="echoid-s10580" xml:space="preserve">ſed etiam a gravitate <lb/>Aëris elaſtici, hoc enim ex baſibus excluſo, externus ſortitur ef-<lb/>fectum, eoſque ſuo pondere tantopere comprimit, ac ſi undiqua-<lb/>que Mercurius circumfuſus foret, ad eandem altitudinem, quam <lb/>Baroſcopium oſtendit, quare hoc pondus ſubtrahendum eſt ab eo, <lb/>quod Cohærentiam totam exhibuit, tumque reſtat pondus expri-<lb/>mens attractionis magnitudinem.</s> <s xml:id="echoid-s10581" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10582" xml:space="preserve">Exploravi etiam quantum cohæreant cylindri marmorei Tab. <lb/></s> <s xml:id="echoid-s10583" xml:space="preserve">XVII. </s> <s xml:id="echoid-s10584" xml:space="preserve">fig. </s> <s xml:id="echoid-s10585" xml:space="preserve">5, quando potentiæ applicabantur uncis A & </s> <s xml:id="echoid-s10586" xml:space="preserve">B, atque trahe-<lb/>bant directione cylindrorum baſibus parallelâ; </s> <s xml:id="echoid-s10587" xml:space="preserve">cylindri qui inter-<lb/>poſito ſebo directe divulſi cohæſerant vi librarum 900, nunc co-<lb/>dem ſebo interpoſito frigefactique cohærebant tantum vi librarum <pb o="462" file="0476" n="476" rhead="INTRODUCTIO AD COHÆRENTIAM"/> 300, repetitumque tentamen eundem eventum dedit: </s> <s xml:id="echoid-s10588" xml:space="preserve">prima fronte <lb/>miraremur Cohærentiam hoc modo minorem dari, cum videatur <lb/>eadem vis attractionis ſuperanda in hoc Experimento, quam in directa <lb/>ſolutione: </s> <s xml:id="echoid-s10589" xml:space="preserve">verum in hoc longe quid aliud obtinet, nam potentiæ A & </s> <s xml:id="echoid-s10590" xml:space="preserve">B <lb/>trahentes parallele ad baſin, nihil operantur in attractionem amborum <lb/>cylindrorum, & </s> <s xml:id="echoid-s10591" xml:space="preserve">ſi baſes forent perfecte planæ, nec ulla donatæ aſperi-<lb/>tate, ac horizontales, potentia B, utcunque exigua ſufficeret ad ſepa-<lb/>randum cylindrum inſeriorem a ſuperiori, etiamſi hi viribus infinite <lb/>magnis ſe attraxiſſent; </s> <s xml:id="echoid-s10592" xml:space="preserve">demonſtrant quippe Mechanici, ſupra pla-<lb/>num horizontale perfecte lævigatum corpus utcunque grave planiſ-<lb/>ſimæque ſuperficiei a potentia quacunque exigua poſſe promoveri: <lb/></s> <s xml:id="echoid-s10593" xml:space="preserve">quia potentia non agit in gravitatem corporis, ſed hæc ſuſtinetur <lb/>a plano horizontali, unde corpus in æquilibrio poſitum a potentia <lb/>utcunque parva moveri poterit. </s> <s xml:id="echoid-s10594" xml:space="preserve">Sive igitur cylindrus ſuperior ap-<lb/>primatur inferioria gravitate, ſive a vi attracttrice, idem eſt, adeoque <lb/>poſſet ſuperior ab inferiori per potentiam admodum exiguam remo-<lb/>veri, quia hæc non ageret in vim eorum attracticem: </s> <s xml:id="echoid-s10595" xml:space="preserve">Quare ta-<lb/>men reſiſtunt? </s> <s xml:id="echoid-s10596" xml:space="preserve">quia ſuperſicies baſium ſunt aſperæ, & </s> <s xml:id="echoid-s10597" xml:space="preserve">appreſſione <lb/>ad ſe, prominentiæ unius ingreſſæ ſunt valles alterius, tum inter <lb/>amborum valles corpuſcula ſebi jacent, veluti in fig. </s> <s xml:id="echoid-s10598" xml:space="preserve">7. </s> <s xml:id="echoid-s10599" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10600" xml:space="preserve">XVII. </s> <s xml:id="echoid-s10601" xml:space="preserve"><lb/>corpuſculum F, vel D, vel plura K ponuntur: </s> <s xml:id="echoid-s10602" xml:space="preserve">non igitur poterunt <lb/>ſuperficies ſupra ſe moveri, niſi rumpantur aut ſlectantur partes ba-<lb/>ſium aſperæ, quæ in ſe intraverunt, atque ſimul frangantur par-<lb/>tes ſebi interpoſiti F, aut D: </s> <s xml:id="echoid-s10603" xml:space="preserve">harum partium Cohærentia reſiſten-<lb/>tiam facit adverſus potentias A & </s> <s xml:id="echoid-s10604" xml:space="preserve">B cylindros trahentes; </s> <s xml:id="echoid-s10605" xml:space="preserve">hæc ob-<lb/>ſervata fuit librarum 300, quæ proinde diverſiſſima eſt a reſiſtentiâ <lb/>directâ, quæ fuit librarum 900, unde hæc transverſa reſiſtentia <lb/>eſt ſubtripla cohærentiæ directæ: </s> <s xml:id="echoid-s10606" xml:space="preserve">congruit hoc abunde cum lege <lb/>Attritus ab Amontonſio ſtabilitâ, conſtat enim ex Experimentis hu-<lb/>jus Cl. </s> <s xml:id="echoid-s10607" xml:space="preserve">Philoſophi, corpus politæ ſuperficiei alteri polito atque <lb/>Horizontali impoſitum, motumque, attritum pati, ſive reſiſten-<lb/>tiam, quæ eſt æqualis {1/3} parti gravitatis corporis moti: </s> <s xml:id="echoid-s10608" xml:space="preserve">in noſtro <lb/>experimento gravitatis vices attractio ſupplet, cujus {2/3} parti æqua-<lb/>lis fuit attritus ex laterali motu cylindrorum ſupra ſe mutuo oriun-<lb/>dus.</s> <s xml:id="echoid-s10609" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10610" xml:space="preserve">Hujus loci quoque eſt explicuiſſe quomodo Calx ſubacta cum are- <pb o="463" file="0477" n="477" rhead="CORPORUM FIRMORUM."/> nâ & </s> <s xml:id="echoid-s10611" xml:space="preserve">aqua in paſtam ſemifluidam, & </s> <s xml:id="echoid-s10612" xml:space="preserve">interpoſita inter binos lapides, cum <lb/>his in unam molem cohærentemabit: </s> <s xml:id="echoid-s10613" xml:space="preserve">ponatur paſta inter duos lapides, <lb/>ſtatim ex illa attrahitur Aqua a lapidibus, quorum poros ingredi-<lb/>tur; </s> <s xml:id="echoid-s10614" xml:space="preserve">ſed ſolutos in ſe continens ſubtiliſſimos ſales Calcis, tum at-<lb/>tenuatiſſimas terreas particulas; </s> <s xml:id="echoid-s10615" xml:space="preserve">hos omnes ſecum abripit, lapidis <lb/>poros iis implet, lateribus prominentiarum accurate applicat, hinc <lb/>partes tenuiſſimæ Calcis & </s> <s xml:id="echoid-s10616" xml:space="preserve">arenæ incipiunt lapides attrahere, quæ <lb/>attractio augetur aqua ſe profundius in lapidem inſinuante, & </s> <s xml:id="echoid-s10617" xml:space="preserve">avo-<lb/>lante ſenſim cum Igne in atmosphæra ſemper hoſpitante, relinquun-<lb/>tur tum enim partes ſubtiliſſimæ Calcis accurate lapidibus applicatæ, <lb/>quos attrahunt, attrahunt ſimul ſe invicem, hinc quantum ſe attra-<lb/>hunt, tantopere una cum lapidibus cohærent: </s> <s xml:id="echoid-s10618" xml:space="preserve">quæri tamen hic poſſet, <lb/>cur Calx ſicca & </s> <s xml:id="echoid-s10619" xml:space="preserve">ſubtilem in pulverem reducta, interpoſita inter duos <lb/>lapides Cohærentiam eandem non efficiat, quam Calx prius aquâ <lb/>permixta, & </s> <s xml:id="echoid-s10620" xml:space="preserve">deinde exſiccata? </s> <s xml:id="echoid-s10621" xml:space="preserve">hoc fit, quia Calcis pulveriſatæ <lb/>partes ſunt ſatis craſſæ, aſperrimæque ſuperficiei, vix ſe attingen-<lb/>tes, & </s> <s xml:id="echoid-s10622" xml:space="preserve">ideo vix cohærentes: </s> <s xml:id="echoid-s10623" xml:space="preserve">ſed ſimulac aqua Calci affunditur, ef-<lb/>ferveſcentia quædam fit, attenuantur partes Calcis, craſſiora ſalia <lb/>ſolvuntur in ſubtiliſſimas particulas, quæ aſperas ſuperficies par-<lb/>tium terrearum implent, hoc modo eas quaſi lævigando, unde <lb/>partium terrearum ſibi incumbentium augetur contactus, & </s> <s xml:id="echoid-s10624" xml:space="preserve">attra-<lb/>ctio: </s> <s xml:id="echoid-s10625" xml:space="preserve">inſuper dubito an quidem omnis Aqua avolet ex paſta, & </s> <s xml:id="echoid-s10626" xml:space="preserve"><lb/>an non notabilis ejus copia, valide attracta a ſalibus Calcis, ſem-<lb/>per in ea hæreat, quæ proinde aſperitates omnium partium op-<lb/>plet, & </s> <s xml:id="echoid-s10627" xml:space="preserve">magnes intermedius inter terreſtres partes exiſtit: </s> <s xml:id="echoid-s10628" xml:space="preserve">ratio-<lb/>nes dubitationis hæ fuerunt: </s> <s xml:id="echoid-s10629" xml:space="preserve">quia Ignis per atmoſphæram diſperſus <lb/>non eſt copioſus, nec tantarum unquam virium, ut aliquod lixivium <lb/>exſiccare penitus queat; </s> <s xml:id="echoid-s10630" xml:space="preserve">ſed eſt Calx cum Aqua in paſtam ſubacta <lb/>lixivii ſpecies; </s> <s xml:id="echoid-s10631" xml:space="preserve">cum notiſſimum ſit quanta Salis alcalini copia in <lb/>Calce deprehendatur. </s> <s xml:id="echoid-s10632" xml:space="preserve">2°. </s> <s xml:id="echoid-s10633" xml:space="preserve">Si duos lapides ope calcis conjunctos diu <lb/>vehementiſſimo igni expoſuerimus, Calx in pulverem fatiſcit, & </s> <s xml:id="echoid-s10634" xml:space="preserve"><lb/>ſolvuntur a ſe lapides ſponte, aut viribus parvis. </s> <s xml:id="echoid-s10635" xml:space="preserve">Ignis autem ve-<lb/>hementiſſimus Aquam volatilem reddit, utcunque a ſale attractam: <lb/></s> <s xml:id="echoid-s10636" xml:space="preserve">vix ſtatui poteſt Sal aut Terra Calcis volatilis, quippe quæ in cal-<lb/>cinatione diutiſſime ignem ſuſtinuerunt, nec volatiles evaſerunt.</s> <s xml:id="echoid-s10637" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10638" xml:space="preserve">Efferveſcentiam oriri quando Calx cum Aqua ſubigitur in paſtam, <pb o="464" file="0478" n="478" rhead="INTRODUCTIO AD COHÆRENTIAM"/> eâque ipſâ partes attenuari, ab Aqua ſales ſolvi, atque ab his bi-<lb/>nis cauſis ſuperficies aſperas terreſtres impleri, mutuum partium <lb/>contactum augeri, & </s> <s xml:id="echoid-s10639" xml:space="preserve">Cohærentiam inde pendere, patet clare <lb/>nam loco Aquæ ſubigatur Calx cum oleo, ſive olivarum, ſive rapa-<lb/>rum, ſive alio craſſo: </s> <s xml:id="echoid-s10640" xml:space="preserve">manebit paſta ſemifluida nec firmitatem ac-<lb/>quirit unquam: </s> <s xml:id="echoid-s10641" xml:space="preserve">hæc inter binos poſita lapides, oleo quidem <lb/>quadantenus orbabitur attracto a lapidibus, nihilominus lapides <lb/>non conjunget: </s> <s xml:id="echoid-s10642" xml:space="preserve">eſt oleum fluidum aliquod veluti Aqua, cur hæc <lb/>igitur non eosdem effectus edit? </s> <s xml:id="echoid-s10643" xml:space="preserve">tantum, quia nec partes Calcis <lb/>attenuat, nec ſalia ſolvit, nec immediate partes lapidibus appli-<lb/>cat, aut contactuum puncta auget.</s> <s xml:id="echoid-s10644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10645" xml:space="preserve">Si de efferveſcentia paſtæ Calcis dubitemus, Gypſum ejus loco <lb/>ſubſtituamus: </s> <s xml:id="echoid-s10646" xml:space="preserve">qui in pulverem redactus, & </s> <s xml:id="echoid-s10647" xml:space="preserve">aqua permiſtus frigi-<lb/>da, inſignem calorem concipit, qui ab efferveſcentia tantummo-<lb/>do oritur, tum rarefit, & </s> <s xml:id="echoid-s10648" xml:space="preserve">illico in maſſam abit duriſſimam: </s> <s xml:id="echoid-s10649" xml:space="preserve">Gy-<lb/>pſum tamen cum oleo miſtum nec fervet, nec calorem concipit, <lb/>nec ullam duritiem acquirit, manens modo paſta ſemifluida.</s> <s xml:id="echoid-s10650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10651" xml:space="preserve">Nec nunc amplius latet, quare Calx facta ex lapidibus combuſtis <lb/>in multo majorem duritiem abeat, quam quæ ex conchis piſcium <lb/>conficitur: </s> <s xml:id="echoid-s10652" xml:space="preserve">quippe conchæ ſunt partes animalium, quæ potiſſi-<lb/>mum e ſale volatili, parum e ſale fixo conſtant. </s> <s xml:id="echoid-s10653" xml:space="preserve">Lapides contra non <lb/>volatilem, ſed fixum poſſident ſalem, unde plus ſalis fixi eſt in Cal-<lb/>celapidum, quam quidem concharum, & </s> <s xml:id="echoid-s10654" xml:space="preserve">hinc multo vehementius <lb/>efſerveſcit, quando in aqua extinguitur, ita mutuo attritu partes <lb/>multo ſubtiliores acquirit, & </s> <s xml:id="echoid-s10655" xml:space="preserve">poſtea inter lapides poſita, multo <lb/>profundius eorum aſperitates ingreditur; </s> <s xml:id="echoid-s10656" xml:space="preserve">accuratius implet; </s> <s xml:id="echoid-s10657" xml:space="preserve">in plu-<lb/>ribus punctis contingit; </s> <s xml:id="echoid-s10658" xml:space="preserve">fortius attrahitur; </s> <s xml:id="echoid-s10659" xml:space="preserve">validiusque cohæret, <lb/>quam partes concharum calcinatarum.</s> <s xml:id="echoid-s10660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10661" xml:space="preserve">Sexto modo corpora firmitatem acquirere & </s> <s xml:id="echoid-s10662" xml:space="preserve">in moles majores <lb/>abire monuimus, peractâ nonnullorum liquorum lecum mixtorum <lb/>efferveſcentiâ; </s> <s xml:id="echoid-s10663" xml:space="preserve">veluti ſi ſpiritus ſalini acidi cum alcalicis liquoribus <lb/>miſcentur: </s> <s xml:id="echoid-s10664" xml:space="preserve">efferveſcentia hæc oritur, quia partes ſe magno impetu <lb/>attrahunt, hinc ruunt verſus ſe invicem, magna vi in ſe impingunt, <lb/>ſeſe applanant; </s> <s xml:id="echoid-s10665" xml:space="preserve">quia elaſtica ſunt, ſæpe excutiuntur iterum, cor-<lb/>poribus nempe ſe reſtituentibus in priſtinam figuram; </s> <s xml:id="echoid-s10666" xml:space="preserve">ab aliis iterum <lb/>attrahuntur, cum attritu ſupra ſe invicem moventur, ignem colli- <pb o="465" file="0479" n="479" rhead="CORPORUM FIRMORUM."/> gunt; </s> <s xml:id="echoid-s10667" xml:space="preserve">alia applanata ſe tam fortiter attrahunt, ut ſe retineant, at-<lb/>trahunt alia, in maſſas concreſcunt majores, unde tandem firma <lb/>moles compingitur, cujus partes non amplius ſecedunt, ſedatur-<lb/>que efferveſcentia. </s> <s xml:id="echoid-s10668" xml:space="preserve">Spiritus Urinæ & </s> <s xml:id="echoid-s10669" xml:space="preserve">Viui Alcohol ſubtiliſſimum <lb/>ſemet fortiſſime attrahunt; </s> <s xml:id="echoid-s10670" xml:space="preserve">quare bina fluida, etiamſi ſint ſubti-<lb/>liſſima, illico in mutuos amplexus ruunt, ſeretinent, abeuntque in <lb/>glaciei duriſſimæ ſpeciem. </s> <s xml:id="echoid-s10671" xml:space="preserve">Acidum eſt magnes lactis, ejus partes <lb/>craſſiores firmiſſime attrahit, expellitur liquor ſubtilior, reliqua-<lb/>que maſſa in ſolidam ſubſtantiam, caſeum vocatam, abit.</s> <s xml:id="echoid-s10672" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10673" xml:space="preserve">Septimo tandem clavi ſolidi duobus immittuntur corporibus, <lb/>quæ in unam molem compinguntur, non facile ſolvendam; </s> <s xml:id="echoid-s10674" xml:space="preserve">quia cla-<lb/>vi ingreſſi corpora partes a ſe removent, his vero ſe attrahenti-<lb/>bus clavi inter duos Magnetes ponuntur, qui quo fortius ſe tra-<lb/>hunt, eo validius clavos retinent, præterea clavorum ſuperficies <lb/>aſpera eſſe ſolet, unde ſemel corporibus intruſi extrahi nequeunt, <lb/>niſi ſimul plurimæ partes tum clavorum, tum junctorum corporum <lb/>abradantur, hæ igitur reſiſtendo Cohærentiam validiorem faciunt. <lb/></s> <s xml:id="echoid-s10675" xml:space="preserve">Quomodo ejuſmodi exigui clavi partes aqueas transfigant, in gla-<lb/>ciem cogant, explicabo in alia Diſſertatione de Aqua & </s> <s xml:id="echoid-s10676" xml:space="preserve">Glacie: </s> <s xml:id="echoid-s10677" xml:space="preserve">ani-<lb/>mus modo fuit breviter expoſuiſſe ſeptem Cohærentiæ metho-<lb/>dos cognitas: </s> <s xml:id="echoid-s10678" xml:space="preserve">interim diffuſior evaſi in examine cauſarum, quas <lb/>Philoſophi Cohærentiæ affinxerunt; </s> <s xml:id="echoid-s10679" xml:space="preserve">abſtinere potuiſſem, niſi cre-<lb/>didiſſem alicujus uſus fore tironibus veterum ſententias noſſe, & </s> <s xml:id="echoid-s10680" xml:space="preserve"><lb/>errores; </s> <s xml:id="echoid-s10681" xml:space="preserve">alioquin cauſarum indagatio, qua adeo ſollicite nonnulli <lb/>occupantur, non magnam generi humano utilitatem affert; </s> <s xml:id="echoid-s10682" xml:space="preserve">cum e <lb/>contrario Legum Cohærentiæ cognitio ſit utiliſſima; </s> <s xml:id="echoid-s10683" xml:space="preserve">has plerique <lb/>negligunt, gloriam neſcio quam in cauſis aſſignandis captantes: </s> <s xml:id="echoid-s10684" xml:space="preserve"><lb/>Leges ſunt ſtabiles in natura, experimentis erui, & </s> <s xml:id="echoid-s10685" xml:space="preserve">auxilio Mathe-<lb/>ſeos explicari poſſunt, aut debent: </s> <s xml:id="echoid-s10686" xml:space="preserve">cauſæ â Natura profundiſſimis in-<lb/>volutæ tenebris, non niſi poſt magnos labores eruendæ, & </s> <s xml:id="echoid-s10687" xml:space="preserve">raro adeo <lb/>clarè, adeo directe demonſtrari queunt, unde de his acres, & </s> <s xml:id="echoid-s10688" xml:space="preserve">ple-<lb/>rumque vanæ Diſputationes, exſurgunt: </s> <s xml:id="echoid-s10689" xml:space="preserve">ab his igitur in poſterum <lb/>abſtinebimus, operam modo daturi legibus Cohærentiæ eruendis.</s> <s xml:id="echoid-s10690" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10691" xml:space="preserve">Poſſunt corpora, quæ cohærent, ſex diverſis modis examinari: <lb/></s> <s xml:id="echoid-s10692" xml:space="preserve">nam 1°. </s> <s xml:id="echoid-s10693" xml:space="preserve">ſecundum longitudinem ſuam directio potentiæ trahentis <lb/>applicari poteſt, uti in Tab. </s> <s xml:id="echoid-s10694" xml:space="preserve">XV III. </s> <s xml:id="echoid-s10695" xml:space="preserve">fig. </s> <s xml:id="echoid-s10696" xml:space="preserve">1. </s> <s xml:id="echoid-s10697" xml:space="preserve">ubi corpori AC ſecun- <pb o="466" file="0480" n="480" rhead="INTRODUCTIO AD COHÆRENTIAM"/> dum longitudinem ſuſpenſo, firmatoque in A, applicatur inferius <lb/>in C pondus B aut potentia alia, agens directione A C. </s> <s xml:id="echoid-s10698" xml:space="preserve">2°. </s> <s xml:id="echoid-s10699" xml:space="preserve">Poteſt <lb/>corpus uno extremo parietis foramini infigi, atque alteri extremo <lb/>appendi pondus, cujus directio eſt perpendicularis in corporis lon-<lb/>gitudinem, veluti eſt in Tab. </s> <s xml:id="echoid-s10700" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10701" xml:space="preserve">fig 2. </s> <s xml:id="echoid-s10702" xml:space="preserve">ubi lignum A C ponitur <lb/>parieti A infixum, & </s> <s xml:id="echoid-s10703" xml:space="preserve">pondus B applicatum alteri extremitati C, <lb/>quod transverſe agit in longitudinem A C. </s> <s xml:id="echoid-s10704" xml:space="preserve">3°. </s> <s xml:id="echoid-s10705" xml:space="preserve">Poteſt corpus D E. <lb/></s> <s xml:id="echoid-s10706" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10707" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10708" xml:space="preserve">fig. </s> <s xml:id="echoid-s10709" xml:space="preserve">iii. </s> <s xml:id="echoid-s10710" xml:space="preserve">imponi fulcro F medio quocunque in loco po-<lb/>ſito, atque utrique extremo D, E potentiæ P & </s> <s xml:id="echoid-s10711" xml:space="preserve">Q applicari, quæ <lb/>etiam transverſâ directione in longitudinem D E agant, & </s> <s xml:id="echoid-s10712" xml:space="preserve">frangere <lb/>corpus nitantur. </s> <s xml:id="echoid-s10713" xml:space="preserve">4°. </s> <s xml:id="echoid-s10714" xml:space="preserve">Poteſt corpus G K, vid. </s> <s xml:id="echoid-s10715" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10716" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10717" xml:space="preserve">fig. </s> <s xml:id="echoid-s10718" xml:space="preserve">3. </s> <s xml:id="echoid-s10719" xml:space="preserve">u-<lb/>trimque imponifulcro, atque ex medio appendipondus P, quodtrans-<lb/>verſâ directione in longitudinem G K agat. </s> <s xml:id="echoid-s10720" xml:space="preserve">5°. </s> <s xml:id="echoid-s10721" xml:space="preserve">Poteſt corpus L. </s> <s xml:id="echoid-s10722" xml:space="preserve">M. </s> <s xml:id="echoid-s10723" xml:space="preserve"><lb/>Tab. </s> <s xml:id="echoid-s10724" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10725" xml:space="preserve">fig. </s> <s xml:id="echoid-s10726" xml:space="preserve">4. </s> <s xml:id="echoid-s10727" xml:space="preserve">utroque extremo includi arctè foraminibus, at-<lb/>que ejus loco quocunque intermedio appendi pondus aut potentia, <lb/>cujus directio ſit transverſa in longitudinem corporis L M. </s> <s xml:id="echoid-s10728" xml:space="preserve">hic enim <lb/>ſitus corporis diſtinguendus eſt â priori in fig. </s> <s xml:id="echoid-s10729" xml:space="preserve">3, uti frequens e-<lb/>ventus comprobavit. </s> <s xml:id="echoid-s10730" xml:space="preserve">6°. </s> <s xml:id="echoid-s10731" xml:space="preserve">Tandem poteſt, Tab. </s> <s xml:id="echoid-s10732" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10733" xml:space="preserve">fig. </s> <s xml:id="echoid-s10734" xml:space="preserve">5. </s> <s xml:id="echoid-s10735" xml:space="preserve">corpus <lb/>ab C comprimi ſecundum longitudinem â pondere P impoſito, at-<lb/>que eo modo ejus Cohærentia explorari, quantum nempe ferre <lb/>poſſit, quid recuſet. </s> <s xml:id="echoid-s10736" xml:space="preserve">Poſſent innumeræ obliquæ directiones po-<lb/>tentiarum trahentium vel pellentium ſolidum, ut frangatur, conſide-<lb/>rari, aſt hæ omnes ex regulis Mechanices facile ad directas redu-<lb/>cuntur, quare inutile foret eas hic adjungere.</s> <s xml:id="echoid-s10737" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div343" type="section" level="1" n="343"> <head xml:id="echoid-head452" xml:space="preserve">CAPUT SECUNDUM.</head> <head xml:id="echoid-head453" style="it" xml:space="preserve">De Cohærentiâ Corporum abſolutà.</head> <p> <s xml:id="echoid-s10738" xml:space="preserve"><emph style="sc">Definitio</emph> 1. </s> <s xml:id="echoid-s10739" xml:space="preserve">Cohærentia vel reſiſtentia abſoluta, ea vocatur, <lb/>quâ corpus reſiſtit, ne frangatur, actum â viribus ſecundum <lb/>longitudinem ejus trahentibus: </s> <s xml:id="echoid-s10740" xml:space="preserve">ita in Tab. </s> <s xml:id="echoid-s10741" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10742" xml:space="preserve">fig. </s> <s xml:id="echoid-s10743" xml:space="preserve">1. </s> <s xml:id="echoid-s10744" xml:space="preserve">Cohæren-<lb/>tia abſoluta dicitur, qua corpus A C reſiſtit ponderi frangere co-<lb/>nanti B. </s> <s xml:id="echoid-s10745" xml:space="preserve">& </s> <s xml:id="echoid-s10746" xml:space="preserve">ſecundum longitudinem A C agenti.</s> <s xml:id="echoid-s10747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10748" xml:space="preserve">D<emph style="sc">EFINIT</emph>.</s> <s xml:id="echoid-s10749" xml:space="preserve">2. </s> <s xml:id="echoid-s10750" xml:space="preserve">Elementum voco particulam corpoream valde exi-<lb/>guam, quæ non amplius reſolvitur a viribus Naturæ, & </s> <s xml:id="echoid-s10751" xml:space="preserve">ex quibus <pb o="467" file="0481" n="481" rhead="CORPORUM FIRMORUM."/> plurimis ſibi accumulatis fibra oblonga minima vel ſimpliciſſima <lb/>componitur, aut componi poteſt.</s> <s xml:id="echoid-s10752" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div344" type="section" level="1" n="344"> <head xml:id="echoid-head454" xml:space="preserve">PROPOSITIO I.</head> <p style="it"> <s xml:id="echoid-s10753" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10754" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10755" xml:space="preserve">fig. </s> <s xml:id="echoid-s10756" xml:space="preserve">6. </s> <s xml:id="echoid-s10757" xml:space="preserve">Si fibra ſimpliciſſima A B, compoſita ex Ele-<lb/>mentis homogeneis 1, 2, 3, 4 & </s> <s xml:id="echoid-s10758" xml:space="preserve">æqualiter cohærentibus, lente trahatur <lb/>juxta longitudinem ſuam â potentia vel pondere B, extremitas <lb/>autem altera A ſit afſixa clavo immobili, atque fibra conſideretur <lb/>absque gravitate, tum potentia B, quæ ſolvere poterit fibræ Cohæ-<lb/>rentiam; </s> <s xml:id="echoid-s10759" xml:space="preserve">omnia Elementa a ſc mutuo æquali intervallo ſeparabit, <lb/>ut fatiſcant in pulverem.</s> <s xml:id="echoid-s10760" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10761" xml:space="preserve">Conſtet Fibra A B ex 4. </s> <s xml:id="echoid-s10762" xml:space="preserve">Elementis: </s> <s xml:id="echoid-s10763" xml:space="preserve">trahat potentia B Elementum <lb/>1. </s> <s xml:id="echoid-s10764" xml:space="preserve">directione A B lente; </s> <s xml:id="echoid-s10765" xml:space="preserve">hoc cohærens cum 2, trahit 2. </s> <s xml:id="echoid-s10766" xml:space="preserve">hoc cohærens <lb/>cum 3, trahit tantopere 3. </s> <s xml:id="echoid-s10767" xml:space="preserve">hoc 4. </s> <s xml:id="echoid-s10768" xml:space="preserve">adeo ut omnia Elementa æqualiter <lb/>trahantur, & </s> <s xml:id="echoid-s10769" xml:space="preserve">ſint in æquali tenſione: </s> <s xml:id="echoid-s10770" xml:space="preserve">ſed ſuppoſui elementa ho-<lb/>mogenea, ſive ejusdem magnitudinis, figuræ, ſoliditatis, & </s> <s xml:id="echoid-s10771" xml:space="preserve">vi-<lb/>rium, æqualiter ſecum cohærentia; </s> <s xml:id="echoid-s10772" xml:space="preserve">adeoque non ſeparabitur pri-<lb/>mum a ſecundo, quin hoc tantopere recedat a 3°, hoc a 4°. </s> <s xml:id="echoid-s10773" xml:space="preserve">quare <lb/>potentia B, quæ tractione ſeparare poterit 1 a 2. </s> <s xml:id="echoid-s10774" xml:space="preserve">eodem tempore <lb/>omnia a ſe ſeparabit, ſi tum ſeparare perrexerit, donec non amplius <lb/>vi ſua attrahente in ſe agant, tota ſibra fatiſcet in Elementa, hoc <lb/>eſt in pulveres, æquali intervallo a ſe remotos. </s> <s xml:id="echoid-s10775" xml:space="preserve">Hæc fient, poſita <lb/>tractione lentâ; </s> <s xml:id="echoid-s10776" xml:space="preserve">verum poſitâ celerrimâ, prius Elementum inſi-<lb/>mum B ſepararetur â 2, quam 2 â 3: </s> <s xml:id="echoid-s10777" xml:space="preserve">aut 3 â 4, motu prius com-<lb/>municato cum inſimo, nec tam cito æquabiliter per omnes reli-<lb/>quos C diſtributo.</s> <s xml:id="echoid-s10778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10779" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s10780" xml:space="preserve">Nonnulli pro Axiomate poſuerunt, corpus non poſſe <lb/>ſolvi in aliquo ſui puncto, ſi non datur plus rationis ad ſolutionem <lb/>in uno puncto, quam in altero. </s> <s xml:id="echoid-s10781" xml:space="preserve">Quod Axioma non eſt verum, nam <lb/>poterit corpus, cujus omnes partes æquali vi cohærent, ſolvi; </s> <s xml:id="echoid-s10782" xml:space="preserve">ſo-<lb/>lutio quidem non in uno puncto, ſed in omnibus ſimul continget; <lb/></s> <s xml:id="echoid-s10783" xml:space="preserve">niſi vis Cohærentiæ partium ponatur infinite magna: </s> <s xml:id="echoid-s10784" xml:space="preserve">verum quid <lb/>impediet quominus fibra ſimpliciſſima, cujus omnia elementa æ-<lb/>quali vi cohærent, aſt non inſinite magna, a potentia trahente <lb/>ſolvatur? </s> <s xml:id="echoid-s10785" xml:space="preserve">modo vis trahens ſit major vi, qua unum Elementum <lb/>cum altero cohæreat.</s> <s xml:id="echoid-s10786" xml:space="preserve"/> </p> <pb o="468" file="0482" n="482" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div345" type="section" level="1" n="345"> <head xml:id="echoid-head455" xml:space="preserve">PROPOSITIO II.</head> <p style="it"> <s xml:id="echoid-s10787" xml:space="preserve">Si eadem fibra A B ſimpliciſſima non habuerit Elementa homo-<lb/>genea & </s> <s xml:id="echoid-s10788" xml:space="preserve">æquali vi cohærentia, potentia B trahens fibram directio-<lb/>ne A B eam diſſolvet, quâ parte duo Elementa minus inter ſe co-<lb/>hærent.</s> <s xml:id="echoid-s10789" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10790" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10791" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10792" xml:space="preserve">fig. </s> <s xml:id="echoid-s10793" xml:space="preserve">6. </s> <s xml:id="echoid-s10794" xml:space="preserve">Sit Elementum 3 non homogeneum, ſed mi-<lb/>nus cohæreat cum 2, quam 2 cum 1. </s> <s xml:id="echoid-s10795" xml:space="preserve">tum trahente potentiâ B <lb/>elementum 1, hoc trahit 2, hoc 3. </s> <s xml:id="echoid-s10796" xml:space="preserve">hoc 4. </s> <s xml:id="echoid-s10797" xml:space="preserve">tractione potentiæ au-<lb/>cta cohærebit adhuc 1 cum 2; </s> <s xml:id="echoid-s10798" xml:space="preserve">quando 2 non amplius cum 3 cohæ-<lb/>ret, adeoque fibra ibidem rumpetur.</s> <s xml:id="echoid-s10799" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div346" type="section" level="1" n="346"> <head xml:id="echoid-head456" xml:space="preserve">PROPOSITIO III.</head> <p style="it"> <s xml:id="echoid-s10800" xml:space="preserve">Si fibra eadem A B homogenea fuerit, ſed gravis, & </s> <s xml:id="echoid-s10801" xml:space="preserve">trahatur <lb/>ſecundum longitudinem a pondere vel potentia B extremitati ap-<lb/>penſa, donec rumpatur, fiet fractura in ſuperiori parte A, quâ <lb/>clavo annectitur.</s> <s xml:id="echoid-s10802" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10803" xml:space="preserve">Tab | XVIII. </s> <s xml:id="echoid-s10804" xml:space="preserve">fig. </s> <s xml:id="echoid-s10805" xml:space="preserve">6. </s> <s xml:id="echoid-s10806" xml:space="preserve">Nam Elementum 4 deorſum agitur â pondere <lb/>ſuo & </s> <s xml:id="echoid-s10807" xml:space="preserve">pondere reliquorum trium Elementorum, quæ ipſi appenſa <lb/>ſunt: </s> <s xml:id="echoid-s10808" xml:space="preserve">inferiora Elementa minori pondere deorſum aguntur, quo <lb/>ſunt propiora extremo B: </s> <s xml:id="echoid-s10809" xml:space="preserve">poſita igitur Cohærentiâ omnium Ele-<lb/>mentorum æquali, & </s> <s xml:id="echoid-s10810" xml:space="preserve">agente potentia B, trahetur Elementum ſu-<lb/>perius 4, â pondere ſuo & </s> <s xml:id="echoid-s10811" xml:space="preserve">reliquorum trium & </s> <s xml:id="echoid-s10812" xml:space="preserve">actione potentiæ B. <lb/></s> <s xml:id="echoid-s10813" xml:space="preserve">verum ea, quæ ſunt infra Elementum 4, minus trahuntur. </s> <s xml:id="echoid-s10814" xml:space="preserve">adeoque <lb/>id ſolvetur, quod maxime trahitur, quare rumpetur fibra A B <lb/>in A.</s> <s xml:id="echoid-s10815" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10816" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s10817" xml:space="preserve">Comprobat hoc Experientia in funibus & </s> <s xml:id="echoid-s10818" xml:space="preserve">filis longis, <lb/>quibus ex alto ſuſpenſis pondus alligatur, franguntur enim ſemper <lb/>(ſi bona fuerint & </s> <s xml:id="echoid-s10819" xml:space="preserve">ubivis æqualiter cohæreant) ad partem altiſſi-<lb/>mam, quia ei adhæret maximum pondus.</s> <s xml:id="echoid-s10820" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div347" type="section" level="1" n="347"> <head xml:id="echoid-head457" xml:space="preserve">PROPOSITIOIV.</head> <p style="it"> <s xml:id="echoid-s10821" xml:space="preserve">Si fibra A B ſimpliciſſima, compoſita ex elementis homogeneis <pb o="469" file="0483" n="483" rhead="CORPORUM FIRMORUM."/> long a vel brevis fuerit, ſecundum longitudinem tracta, erit æque <lb/>cohærens, non conſider ando ejus gravitatem; </s> <s xml:id="echoid-s10822" xml:space="preserve">hac additâ, frange-<lb/>tur in parte ſuprema A ab eodem pondere in ſupremum elementum <lb/>A agente.</s> <s xml:id="echoid-s10823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10824" xml:space="preserve">Tab.</s> <s xml:id="echoid-s10825" xml:space="preserve">. XVIII. </s> <s xml:id="echoid-s10826" xml:space="preserve">fig. </s> <s xml:id="echoid-s10827" xml:space="preserve">6. </s> <s xml:id="echoid-s10828" xml:space="preserve">Sit enim fibra ſimpliciſſima & </s> <s xml:id="echoid-s10829" xml:space="preserve">brevis com-<lb/>poſita ex 4 Elementis, alia longiſſima ex 100 accurate ſimilibus, <lb/>quæ æqualibus viribus inter ſe cohæreant; </s> <s xml:id="echoid-s10830" xml:space="preserve">tum breviori applicatâ <lb/>potentiâ trahetur primum a ſecundo & </s> <s xml:id="echoid-s10831" xml:space="preserve">ſic deinceps quodlibet in eâ <lb/>elementum æqualiter: </s> <s xml:id="echoid-s10832" xml:space="preserve">& </s> <s xml:id="echoid-s10833" xml:space="preserve">longiori applicata potentia eâdem, trahe-<lb/>tur quoque primum â ſecundo, & </s> <s xml:id="echoid-s10834" xml:space="preserve">ſic deinceps quodlibet in ea Ele-<lb/>mentum æqualiter, hoc eſt æque ſupremum quam infimum: </s> <s xml:id="echoid-s10835" xml:space="preserve">quia <lb/>vero eadem vi ſuppoſita ſunt Elementa cohærere in breviori quam <lb/>in longiori fibra, æque tractum erit primum â ſecundo, & </s> <s xml:id="echoid-s10836" xml:space="preserve">ſic dein-<lb/>ceps quodlibet Elementum in fibra utraque; </s> <s xml:id="echoid-s10837" xml:space="preserve">adeoque ſi recedere <lb/>aliquantum potuerint Elementa a ſe nondum fracturâ factâ, ſive <lb/>attractione nondum ceſſante, eodem intervallo quodlibet Elemen-<lb/>tum brevioris, quam longioris fibræ diſtabit ab altero; </s> <s xml:id="echoid-s10838" xml:space="preserve">hinc aucta <lb/>potentia B, quæ trahere poſſit Elementum 1 a 2 ad majus interval-<lb/>lum, ut attractio ſuperetur, etiam attractio ſuperata erit in omni-<lb/>bus Elementis, æque in fibra breviori quam in longiori. </s> <s xml:id="echoid-s10839" xml:space="preserve">Si fibræ <lb/>conceptæ fuerint compoſitæ ex Elementis gravibus, tum ex ſupre-<lb/>mo elemento A poterit eadem potentia geſtari, ſive fibra longa ſi-<lb/>ve brevis fuerit, nam eadem Cohærentia utriusque fibræ ponitur: <lb/></s> <s xml:id="echoid-s10840" xml:space="preserve">quia autem Elementum ſupremum geſtare debet pondus omnium <lb/>aliorum appenſorum, maxima vi trahitur, adeoque fibræ utrius-<lb/>que fractura fiet in parte ſuprema.</s> <s xml:id="echoid-s10841" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10842" xml:space="preserve">Nota. </s> <s xml:id="echoid-s10843" xml:space="preserve">Non hic ponimus idem pondus poſſe geſtari ex extremita-<lb/>te fibræ gravis longioris quam ex breviori, nam fibræ longioris <lb/>Elementum ſupremum non modo geſtare debet pondus appenſum <lb/>extremo, ſed etiam pondus omnium aliorum Elementorum, quod <lb/>cum ſit majus in longiori fibra quam in breviori, erit pondus ap-<lb/>pendendum extremo longioris minus, quam quod ferri poterit ex <lb/>breviori. </s> <s xml:id="echoid-s10844" xml:space="preserve">ſed pondus Elementorum ſimul cum pondere appenſo, <lb/>erit æquale ponderi ſimul cum pondere appenſo in utraque fibra, <lb/>quando fiet ſolutio.</s> <s xml:id="echoid-s10845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10846" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s10847" xml:space="preserve">Nonnulli Philoſophi opinati ſunt, fibras funesque lon- <pb o="470" file="0484" n="484" rhead="INTRODUCTIO AD COHÆRENTIAM"/> giores magis cohærere brevioribus, quos olim refutavit Galilæus <lb/>in Dialog. </s> <s xml:id="echoid-s10848" xml:space="preserve">Mech. </s> <s xml:id="echoid-s10849" xml:space="preserve">2. </s> <s xml:id="echoid-s10850" xml:space="preserve">Mariottus in Traité de Mouv. </s> <s xml:id="echoid-s10851" xml:space="preserve">des Eaux part. <lb/></s> <s xml:id="echoid-s10852" xml:space="preserve">5 Diſ. </s> <s xml:id="echoid-s10853" xml:space="preserve">2. </s> <s xml:id="echoid-s10854" xml:space="preserve">ex Experientia determinavit, Corpora ex ferro, chartâ <lb/>aliâve materiâ confecta, ſive longa ſive brevia fuerint, æqualibus <lb/>viribus cohærere. </s> <s xml:id="echoid-s10855" xml:space="preserve">Merſennus Lib. </s> <s xml:id="echoid-s10856" xml:space="preserve">3. </s> <s xml:id="echoid-s10857" xml:space="preserve">prop. </s> <s xml:id="echoid-s10858" xml:space="preserve">16 Harmonic. </s> <s xml:id="echoid-s10859" xml:space="preserve">etiam <lb/>hanc quæſtionem agitavit, & </s> <s xml:id="echoid-s10860" xml:space="preserve">obſervavit, Experientias frequentes ſibi <lb/>contradicere, cum aliquando chordæ longæ plus ponderis gerant, <lb/>quam breves æque craſiæ, aliquando contrarium fiat: </s> <s xml:id="echoid-s10861" xml:space="preserve">hoc tamen <lb/>a parte quadam debiliori fieri recte opinatur; </s> <s xml:id="echoid-s10862" xml:space="preserve">unde concludit, ra-<lb/>tio nulla mihi ſuadet longiorem minus pondus ferre, ſed potius u-<lb/>traque, tam brevis quam longa, pondus æquale feret, niſi quid <lb/>aliud contingat.</s> <s xml:id="echoid-s10863" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10864" xml:space="preserve">Tentamina plurima feci cum fidibus metallicis clavicymbalo in-<lb/>ſervientibus, quæ ſive longæ ſive breves fuerint, idem pondus geſta-<lb/>verunt, funes filave contorta raro in longiſſimo tractu æque craſſa <lb/>& </s> <s xml:id="echoid-s10865" xml:space="preserve">proinde æque fortia fieri poſſunt, hinc Experimenta cum iis in-<lb/>ſtituta adeo mire variant.</s> <s xml:id="echoid-s10866" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div348" type="section" level="1" n="348"> <head xml:id="echoid-head458" xml:space="preserve">PROPOSITIO V.</head> <p style="it"> <s xml:id="echoid-s10867" xml:space="preserve">Si fibra A B homogenea, pendula ex clavo immobili A perpen-<lb/>diculariter ad horizontem, gravis fuerit, magnâque donata lon-<lb/>gitudine, in qua tantundem ſit gravitatis, ac antea pondus B an-<lb/>nexum extremo habuit, quod fibram rumpebat, nunc etiam â pro-<lb/>priâ gravitate in ſupremo A frangetur.</s> <s xml:id="echoid-s10868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10869" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10870" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10871" xml:space="preserve">fig. </s> <s xml:id="echoid-s10872" xml:space="preserve">6. </s> <s xml:id="echoid-s10873" xml:space="preserve">Agitur enim elementum ſupremum A tanto-<lb/>pere deorſum agravitate ſuæ fibræ, quam antea â pondere B appenſo; <lb/></s> <s xml:id="echoid-s10874" xml:space="preserve">quia autem fibræ Cohærentia in utroque caſu eſt eadem, nam non <lb/>mutatur ſive longa ſive brevis fuerit per Propoſ. </s> <s xml:id="echoid-s10875" xml:space="preserve">4. </s> <s xml:id="echoid-s10876" xml:space="preserve">adeoque rumpe-<lb/>tur fibra in A, quando pondus diſtrahens eſt idem, ſive oriundum <lb/>a propria gravitate, ſive ab inferius annexo alio pondere B.</s> <s xml:id="echoid-s10877" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10878" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s10879" xml:space="preserve">Hinc funis vel cylindrus corporeus quilibet poteſt eſſe <lb/>tam longus, ut â proprio frangatur pondere.</s> <s xml:id="echoid-s10880" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div349" type="section" level="1" n="349"> <head xml:id="echoid-head459" xml:space="preserve">PROPOSITIO VI.</head> <p style="it"> <s xml:id="echoid-s10881" xml:space="preserve">Omnia, quæ hactenus demonſtravimus de fibra ſimpliciſſima ex <pb o="471" file="0485" n="485" rhead="CORPORUM FIRMORUM."/> Elementis conſtante, vera erunt in fibra magis compoſita, con-<lb/>ſtante ex aliquot fibris homogeneis juxta ſe poſitis, cum trahitur <lb/>directione ſecundum longitudinem vel a potentia, pondere appen-<lb/>ſo, aut â propria gravitate.</s> <s xml:id="echoid-s10882" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10883" xml:space="preserve">Sint enim duæ fibræ ſimpliciſſimæ, quæ conſtent ex elementis <lb/>homogeneis & </s> <s xml:id="echoid-s10884" xml:space="preserve">æqualibus: </s> <s xml:id="echoid-s10885" xml:space="preserve">hæ juxta ſe poſitæ conjungantur vel <lb/>componantur in unam, tum potentia vel pondus, quæ ſeparare po-<lb/>terit hanc fibram compoſitam in aliqua ſectione transverſa, eandem <lb/>ſeparabit in qualibetalia, quia Cohærentia in qualibet ſectione eſt ea-<lb/>dem: </s> <s xml:id="echoid-s10886" xml:space="preserve">nam velutieſt Cohærentia Elementi in una fibra, ita eſt in altera, <lb/>idque in qualibet altitudine, ergo earum ſumma in utraque fibra, hoc <lb/>eſt in compoſita, erit eadem in quacunque altitudine: </s> <s xml:id="echoid-s10887" xml:space="preserve">2°. </s> <s xml:id="echoid-s10888" xml:space="preserve">quia fibra eſt <lb/>gravis, ſolvetur ab appenſo pondere in parte ſuperiori, cum illi appli-<lb/>catur vis maxima, nempe ponderis appenſi, & </s> <s xml:id="echoid-s10889" xml:space="preserve">propria omnium par <lb/>tium ab imo ad ſummum gravitas: </s> <s xml:id="echoid-s10890" xml:space="preserve">3°. </s> <s xml:id="echoid-s10891" xml:space="preserve">erit fibra æque cohærens ſi-<lb/>ve longa ſive brevis fuerit; </s> <s xml:id="echoid-s10892" xml:space="preserve">nam in ſectione transverſa qualibet <lb/>eandem Cohærentiam habet, ſive longa vel brevis fuerit, cum in <lb/>qualibet fibra ſimpliciſſima eadem Cohærentia demonſtrata ſit: </s> <s xml:id="echoid-s10893" xml:space="preserve">quæ <lb/>omnia fuerunt in præcedentibus Propoſitionibus probata obtinere <lb/>in fibra ſimpliciſſima.</s> <s xml:id="echoid-s10894" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10895" xml:space="preserve">Scholium. </s> <s xml:id="echoid-s10896" xml:space="preserve">Poſſunt corpora conſiderari tanquam compoſita ex-<lb/>fibris; </s> <s xml:id="echoid-s10897" xml:space="preserve">nam omnis funis conſtat ex filis, quodlibet filum ex fila-<lb/>mentis ſubtilioribus, uti docent Microſcopia: </s> <s xml:id="echoid-s10898" xml:space="preserve">omne lignum ſepara-<lb/>tur fiſſione in fibras oblongas, quæ inſpectæ Microſcopio componun-<lb/>tur ex fibrillis ſubtilioribus, cavis, harum parietes ex fibrillis ſo-<lb/>lidis ſubtiliſſimis: </s> <s xml:id="echoid-s10899" xml:space="preserve">eo modo omnia metalla, lapides, chordæ ex <lb/>inteſtinis animalium, aliaque corpora ſe habent: </s> <s xml:id="echoid-s10900" xml:space="preserve">quid eſt enim <lb/>cylindrus metalli ſolidus, cujus baſis unum pollicem adæquat, <lb/>præter quam congeries filamentorum metallicorum tenuium ſibi <lb/>conjunctorum, quæ eam craſſitiem formant; </s> <s xml:id="echoid-s10901" xml:space="preserve">quamobrem omnia <lb/>corpora conſiderari poſſunt uti congeries fibrarum, hinc omnia <lb/>demonſtrata hactenus de fibra ſimpliciſſima convenient quoque cor-<lb/>poribus magnis, ſi nullæ aliæ conditiones iis acceſſerint.</s> <s xml:id="echoid-s10902" xml:space="preserve"/> </p> <pb o="472" file="0486" n="486" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div350" type="section" level="1" n="350"> <head xml:id="echoid-head460" xml:space="preserve">PROPOSITIO VII.</head> <p style="it"> <s xml:id="echoid-s10903" xml:space="preserve">Si duo corpora oblonga, ejusdem materiæ, & </s> <s xml:id="echoid-s10904" xml:space="preserve">homogeneæ, ubivis <lb/>æque craſſa, (uti ſunt cubi, parallelopipeda, prismata, cylindri) <lb/>& </s> <s xml:id="echoid-s10905" xml:space="preserve">æque longa, trahantur directione longitudinibus ſuis parallela, <lb/>cohærebunt viribus æqualibus, & </s> <s xml:id="echoid-s10906" xml:space="preserve">tantum ab æquali pondere vel <lb/>potentia frangentur.</s> <s xml:id="echoid-s10907" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10908" xml:space="preserve">De duobus corporibus ejusdem figuræ, æque longis, æque craſ-<lb/>ſis, ejusdem materiæ homogeneæ dubium poteſt eſſe nullum, cum <lb/>enim componatur unum corpus ex 100 fibris, alterum etiam conſta-<lb/>bit ex 100 fibris, ſingulis æqualibus in hoc corpore quam in altero <lb/>adeoque erit ſumma omnium Cohærentiarum in uno corpore æ-<lb/>qualis ſummæ omnium Cohærentiarum in altero, ergo utrum-<lb/>que corpus æque cohærens: </s> <s xml:id="echoid-s10909" xml:space="preserve">ſed ſit unum corpus Cylindrus, alte-<lb/>rum Parallelopepidum, ſint ambo æque craſſa, ergo conſtant ex nu-<lb/>mero eodem fibrarum, & </s> <s xml:id="echoid-s10910" xml:space="preserve">quia ſingulæ fibræ æqualiter cohærent, <lb/>erit ſumma cohærentiarum in Cylindro, æqualis ſummæ cohæren-<lb/>tiarum in Parallelopipedo, adeoque eadem utriusque corporis fir-<lb/>mitas, eademque potentia diffringens deſiderabitur.</s> <s xml:id="echoid-s10911" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div351" type="section" level="1" n="351"> <head xml:id="echoid-head461" xml:space="preserve">PROPOSITIO VIII.</head> <p style="it"> <s xml:id="echoid-s10912" xml:space="preserve">Si duo corpora oblonga, regularia, per totam ſuam longitudinem æque <lb/>craſſa, habuerint eandem longitudinem, ſed diverſam craſſitiem, <lb/>fuerint vero ex eadem materia, & </s> <s xml:id="echoid-s10913" xml:space="preserve">trahantur ſecundum ſuas longi-<lb/>tudines, cohærebunt viribus, quæ ſunt in ratione craſſitierum.</s> <s xml:id="echoid-s10914" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10915" xml:space="preserve">Tab, XVIII. </s> <s xml:id="echoid-s10916" xml:space="preserve">fig. </s> <s xml:id="echoid-s10917" xml:space="preserve">7. </s> <s xml:id="echoid-s10918" xml:space="preserve">Sit enim corpus oblongum A B X, & </s> <s xml:id="echoid-s10919" xml:space="preserve">aliud <lb/>C K ex eadem materia homogenea, concipiatur C K diviſum in cor-<lb/>pora æque longa & </s> <s xml:id="echoid-s10920" xml:space="preserve">æque craſſa quam eſt A B, uti in C E D F, <lb/>E G F H, G I H K. </s> <s xml:id="echoid-s10921" xml:space="preserve">quodlibet horum tractum ſecundum longitudi-<lb/>nem, veluti etiam A B, cohærebit æquali vi ac A B, conſtat enim <lb/>ex totidem particulis cohærentibus & </s> <s xml:id="echoid-s10922" xml:space="preserve">æque cohærentibus ad quam-<lb/>libet ſectionem transverſam quam A B, quare vis cohærentiæ in <lb/>A B erit ad eam in C K, uti eſt A B ad numerum corporum æque <lb/>craſſorum in C K, hoc eſt uti craſſities B X ad D K.</s> <s xml:id="echoid-s10923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10924" xml:space="preserve">Corol. </s> <s xml:id="echoid-s10925" xml:space="preserve">1. </s> <s xml:id="echoid-s10926" xml:space="preserve">Ergo Priſmata, Parallelopipeda, & </s> <s xml:id="echoid-s10927" xml:space="preserve">Cylindri ex eadem <pb o="473" file="0487" n="487" rhead="CORPORUM FIRMORUM."/> materia & </s> <s xml:id="echoid-s10928" xml:space="preserve">æque longa, tracta ſecundum ſuam longitudinem cohæ-<lb/>rebunt in ratione ſuarum baſium, ſive ſolida memorata, quæ ſunt <lb/>ejusdem figuræ, cohærent in ratione duplicatâ diametrorum in baſi, <lb/>vel laterum homologorum in baſi, ſi fuerint ſimilia: </s> <s xml:id="echoid-s10929" xml:space="preserve">nam in hiſce <lb/>proportionibus ſunt craſſities</s> </p> <p> <s xml:id="echoid-s10930" xml:space="preserve">Corol 2. </s> <s xml:id="echoid-s10931" xml:space="preserve">Atque ſunt Cohærentiæ corporum memoratorum æque <lb/>longorum & </s> <s xml:id="echoid-s10932" xml:space="preserve">ejusdem materiæ in ratione quantitatum maſſarum; <lb/></s> <s xml:id="echoid-s10933" xml:space="preserve">cum Parallelopipedorum, Prismatum, Cylindrorum æque altorum <lb/>maſſæ ſint inter ſe veluti baſes.</s> <s xml:id="echoid-s10934" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10935" xml:space="preserve">Corol. </s> <s xml:id="echoid-s10936" xml:space="preserve">Ex hac Propoſitione proinde determinari poteſt robur fu-<lb/>nis utcunque craſſi, compoſiti ex filamentis ſibi parallelis, non in-<lb/>tortis, cognitâ modo Cohærentiâ unius fili tenuiſſimi, ex quorum <lb/>plurimis compoſitus eſt, nam robur tenuiſſimi eſt ad illud craſſiſſi-<lb/>mi, veluti ſunt amborum craſſities. </s> <s xml:id="echoid-s10937" xml:space="preserve">Sumſi filum vulgare Lini, <lb/>craſſitie ſua circiter adæquans ſetam equinam, hoc ſuſtinuit ple-<lb/>rumque libras 3 {1/2}. </s> <s xml:id="echoid-s10938" xml:space="preserve">7000 ejusmodi fila colligata & </s> <s xml:id="echoid-s10939" xml:space="preserve">non intorta <lb/>formant craſſitiem pollicis cylindrici proxime; </s> <s xml:id="echoid-s10940" xml:space="preserve">quare ejuſmodi funis <lb/>diametri 1 pollicis ſuſtineret libras 7000 X 3 {1/2}. </s> <s xml:id="echoid-s10941" xml:space="preserve">adeoque funis an-<lb/>chorarius navis bellicæ, cujus diameter eſt 5 pollicum, ſuſtinere <lb/>poſſet libras 7030 X 3 {1/2}X25. </s> <s xml:id="echoid-s10942" xml:space="preserve">Ex quo calculo patet clare, ejus-<lb/>modi funes ſuſtinere poſſe navim bellicam, etiamſi â procelloſis <lb/>fluctibus & </s> <s xml:id="echoid-s10943" xml:space="preserve">ventis agitatam quaſſatamque medio in Oceano.</s> <s xml:id="echoid-s10944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10945" xml:space="preserve">Poterit etiam vi hujus Propoſitionis determinari, quanta futuraſit <lb/>Cohærentia abſoluta uniuscujusvis corporis datæ craſſitiei & </s> <s xml:id="echoid-s10946" xml:space="preserve">longi-<lb/>tudinis, modo fuerit cylindricum vel parallelopipedum.</s> <s xml:id="echoid-s10947" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10948" xml:space="preserve">Datum enim corpus erit Vegetabile, Foſſile, vel Animale; </s> <s xml:id="echoid-s10949" xml:space="preserve">quæratur <lb/>primum ope Experimenti alicujus, deſcribendi infra in hoc Capite vel <lb/>in ſequenti, quanta ſit Cohærentia abſoluta illius ejusdem corpo-<lb/>ris in determinata craſſitie; </s> <s xml:id="echoid-s10950" xml:space="preserve">craſſitiem hanc vocabo = a b, & </s> <s xml:id="echoid-s10951" xml:space="preserve">Co-<lb/>hærentiam ſive pondus, quod geſtaripotuit = p. </s> <s xml:id="echoid-s10952" xml:space="preserve">tum menſuretur craſ-<lb/>ſiries corporis dati, quam vocabo = c d, ejuſque Cohærentiam in-<lb/>cognitam & </s> <s xml:id="echoid-s10953" xml:space="preserve">quæſitam = x. </s> <s xml:id="echoid-s10954" xml:space="preserve">erit a b. </s> <s xml:id="echoid-s10955" xml:space="preserve">p:</s> <s xml:id="echoid-s10956" xml:space="preserve">: c d, x. </s> <s xml:id="echoid-s10957" xml:space="preserve">unde x = {c d p.</s> <s xml:id="echoid-s10958" xml:space="preserve">/a b}</s> </p> <p> <s xml:id="echoid-s10959" xml:space="preserve">Si corporis dati longitudo fuerit magna, & </s> <s xml:id="echoid-s10960" xml:space="preserve">quæratur pondus, <lb/>quod inferius appendi poterit, id hoc modo invenietur: </s> <s xml:id="echoid-s10961" xml:space="preserve">quæra- <pb o="474" file="0488" n="488" rhead="INTRODUCTIO AD COHÆRENTIAM"/> tur primo Cohærentia abſoluta illius corporis priori methodo, quæ <lb/>ſit = {c d p.</s> <s xml:id="echoid-s10962" xml:space="preserve">/a b} tum quæratur pondus corporis dati in data longitudine, <lb/>ſitque illud = f. </s> <s xml:id="echoid-s10963" xml:space="preserve">tum pondus inferius appendendum corpori <lb/>rit = {c d p/a b} - f. </s> <s xml:id="echoid-s10964" xml:space="preserve">Si ergo tanta fiat longitudo ut ſit {c d p/a b} = f. </s> <s xml:id="echoid-s10965" xml:space="preserve">po-<lb/>terit nullum pondus extremo illius corporis appendi. </s> <s xml:id="echoid-s10966" xml:space="preserve">Si {c d p/a b} mi-<lb/>nor quam f. </s> <s xml:id="echoid-s10967" xml:space="preserve">nequidem poterit hoc corpus ſemet ipſum gerere, <lb/>niſi brevius fiat.</s> <s xml:id="echoid-s10968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10969" xml:space="preserve">Scbolion. </s> <s xml:id="echoid-s10970" xml:space="preserve">Hæc Propoſitio veriſſima eſt poſitis corporibus rigi-<lb/>dis: </s> <s xml:id="echoid-s10971" xml:space="preserve">in flexibilibus uti in Metallis, aliisve ſimilibus tantum appro-<lb/>pinquat ad veritatem; </s> <s xml:id="echoid-s10972" xml:space="preserve">uti ex Experimentis poſtea deſcribendis pa-<lb/>tebit.</s> <s xml:id="echoid-s10973" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div352" type="section" level="1" n="352"> <head xml:id="echoid-head462" xml:space="preserve">PROPOSITIO IX.</head> <p style="it"> <s xml:id="echoid-s10974" xml:space="preserve">Si duo corpor a oblong a ejusdem materiei & </s> <s xml:id="echoid-s10975" xml:space="preserve">craſſitiei, ſed diver-<lb/>ſæ longitudinis fuerint, & </s> <s xml:id="echoid-s10976" xml:space="preserve">ſuſpenſa perpendiculariter ad borizon-<lb/>tem gerant affixa inferius pondera, corpus longius minus ponderis <lb/>affixi ſuſtinere poterit, quam brevius.</s> <s xml:id="echoid-s10977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10978" xml:space="preserve">Nam ambo corpora ad ſupremam partem, quâ retinentur, æ-<lb/>que cohærent, adeoque ſuſtinere poterunt æqualem gravitatem an-<lb/>tequam rumpantur: </s> <s xml:id="echoid-s10979" xml:space="preserve">quoniam vero ipſa corpora gravitatem habent, <lb/>longius majorem, brevius minorem, & </s> <s xml:id="echoid-s10980" xml:space="preserve">tota gravitas, quæ agit in <lb/>Cohærentiam conſtet ex gravitate propria corporum, tum ex pon-<lb/>dere inferius appenſo, hinc ut ſummæ gravitatum fiant æquales, <lb/>erit pondus appendendum longiori tanto minus, quam quod bre-<lb/>viori adnectetur, quantum gravitas brevioris corporis eſt minor <lb/>gravitate longioris; </s> <s xml:id="echoid-s10981" xml:space="preserve">quare corpus longius poterit minus ponderis <lb/>appenſi extremo inferiori gerere quam brevius.</s> <s xml:id="echoid-s10982" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div353" type="section" level="1" n="353"> <head xml:id="echoid-head463" xml:space="preserve">PROPOSITIO X.</head> <p style="it"> <s xml:id="echoid-s10983" xml:space="preserve">Duo corpora oblonga, per totam ſuam longitudinem æquecraſſa, <pb o="475" file="0489" n="489" rhead="CORPORUM FIRMORUM."/> ejusdem materiæ, & </s> <s xml:id="echoid-s10984" xml:space="preserve">diverſæ craſſitiei, ſuſpenſa perpendiculariter <lb/>ad borizontem, quæ taniam longitudinem babent, ut gravitate <lb/>inde orta frangantur eruntæque longa.</s> <s xml:id="echoid-s10985" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10986" xml:space="preserve">Tab. </s> <s xml:id="echoid-s10987" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s10988" xml:space="preserve">fig. </s> <s xml:id="echoid-s10989" xml:space="preserve">7. </s> <s xml:id="echoid-s10990" xml:space="preserve">Sit A B X corpus tenuius, cujus longitudo <lb/>tanta, ut propria gravitate frangatur; </s> <s xml:id="echoid-s10991" xml:space="preserve">ſit C K corpus craſſius, con-<lb/>cipiatur hoc diviſum in corpora æque craſſa cum A B X, erit <lb/>Cohærentia in ſingulo corpore C F, E H, G K æqualis Cohæren-<lb/>tiæ corporis A B X, ſed æquales Cohærentiæ modo ferre poſſunt <lb/>idem pondus appenſum; </s> <s xml:id="echoid-s10992" xml:space="preserve">idem pondus reſider in corpore æque lon-<lb/>go, quamobrem ferri poterit a Cohærentia in C E corpus C F æque <lb/>longum quam A B, â Cohærentia in E G corpus æque longum quam <lb/>A B, a Cohærentia in G I corpus æque longum quam A B. </s> <s xml:id="echoid-s10993" xml:space="preserve">hinc a <lb/>tota ſumma Cohærentiarum C E G I ferri poterit corpus C K æque <lb/>longum quam eſt A B.</s> <s xml:id="echoid-s10994" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div354" type="section" level="1" n="354"> <head xml:id="echoid-head464" xml:space="preserve">PROPOSITIO XI. <emph style="sc">Problema</emph> 1.</head> <p style="it"> <s xml:id="echoid-s10995" xml:space="preserve">Invenire longitudinem corporis oblongi, quod ex alto libere ſus-<lb/>penſum propria gravitate frangetur</s> </p> <p> <s xml:id="echoid-s10996" xml:space="preserve">1°. </s> <s xml:id="echoid-s10997" xml:space="preserve">Quæratur pondus, quod corporis dati brevis portio gerere <lb/>non amplius poteſt, & </s> <s xml:id="echoid-s10998" xml:space="preserve">maximo, quod latum fuit, ſit proximum.</s> <s xml:id="echoid-s10999" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11000" xml:space="preserve">2°. </s> <s xml:id="echoid-s11001" xml:space="preserve">Quæratur pondus ejuſdem corporis in data longitudine.</s> <s xml:id="echoid-s11002" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11003" xml:space="preserve">3°. </s> <s xml:id="echoid-s11004" xml:space="preserve">Tum fiat, ut pondus in data longitudine inventum, ad pon-<lb/>dus paulo majus maximo, ita longitudo inventa modo ante in §. </s> <s xml:id="echoid-s11005" xml:space="preserve">2. <lb/></s> <s xml:id="echoid-s11006" xml:space="preserve">ad longitudinem quæſitam.</s> <s xml:id="echoid-s11007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11008" xml:space="preserve">Exemplum. </s> <s xml:id="echoid-s11009" xml:space="preserve">ſit filum Lini, quod fere, ſed nondum, gerere poteſt <lb/>libras 3 {1/2} antequam rumpitur: </s> <s xml:id="echoid-s11010" xml:space="preserve">pes hujus fili habeat pondus grano-<lb/>rum 2 adeoque fiat hæc proportio: </s> <s xml:id="echoid-s11011" xml:space="preserve">gran 2 ad 3 {1/2} libr:</s> <s xml:id="echoid-s11012" xml:space="preserve">: 1 pes ad <lb/>13440. </s> <s xml:id="echoid-s11013" xml:space="preserve">pedes. </s> <s xml:id="echoid-s11014" xml:space="preserve">quæ erit longitudo fili, cujus tanta gravitas, ut fi-<lb/>lum ex alto ſuſpenſum frangat.</s> <s xml:id="echoid-s11015" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div355" type="section" level="1" n="355"> <head xml:id="echoid-head465" xml:space="preserve">PROPOSITIO XII. <emph style="sc">Problema</emph> 2.</head> <p style="it"> <s xml:id="echoid-s11016" xml:space="preserve">Dato pondere geſtande a corpore datæ materiæ & </s> <s xml:id="echoid-s11017" xml:space="preserve">longitudinis, <lb/>formæ cylindricæ vel parallelopipedi. </s> <s xml:id="echoid-s11018" xml:space="preserve">invenire deſideratam corporis <lb/>craſſitiem, quæ ſit minima, ita ut â pondere tantillum aucto frangere-<lb/>tur.</s> <s xml:id="echoid-s11019" xml:space="preserve"/> </p> <pb o="476" file="0490" n="490" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s11020" xml:space="preserve">Primum inter Experimenta, inferius deſcribenda in hoc Capitevel <lb/>in ſequenti, quæratur quanta ſit Cohærentia abſoluta ejusdem cor-<lb/>poris ſub determinata craſſitie, hæc Cohærentia vocetur a. </s> <s xml:id="echoid-s11021" xml:space="preserve">& </s> <s xml:id="echoid-s11022" xml:space="preserve"><lb/>craſſities ſit b c. </s> <s xml:id="echoid-s11023" xml:space="preserve">Deinde quæratur quanta ſit gravitas corporis dati <lb/>in data longitudine, quæ ſit = g, & </s> <s xml:id="echoid-s11024" xml:space="preserve">pondus datum geſtandum ſit = p. <lb/></s> <s xml:id="echoid-s11025" xml:space="preserve">erit igitur Cohærentia abſoluta a ad ſuam craſſitiem b c. </s> <s xml:id="echoid-s11026" xml:space="preserve">velutigravitas <lb/>corporis cum pondere annexo = g + p ad craſſitiem quæſitam: </s> <s xml:id="echoid-s11027" xml:space="preserve"><lb/>quæ tum erit = {b c g + b c p.</s> <s xml:id="echoid-s11028" xml:space="preserve">/a}?</s> <s xml:id="echoid-s11029" xml:space="preserve">? nam pondus geſtandum g + p eſt æqua-<lb/>le Cohærentiæ abſolutæ corporis dati ſub determinata craſſitie.</s> <s xml:id="echoid-s11030" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11031" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s11032" xml:space="preserve">Hinc dato pondere ſuſpendendo ex catenis ferreis, filis <lb/>metallicis, funibuſve aut Lignis, aut datâ vi hæc corpora tenden-<lb/>te, â priori determinari ſemper poterit, quantæ craſſitiei deſide-<lb/>rantur, ne rumpantur: </s> <s xml:id="echoid-s11033" xml:space="preserve">Eſt hoc Problema magnæ utilitatis in praxi, <lb/>ne corpora ex quibus pondera ſunt ſuſpendenda, capiantur nimis <lb/>tenuia, atque ita olei & </s> <s xml:id="echoid-s11034" xml:space="preserve">operæ jactura fiat; </s> <s xml:id="echoid-s11035" xml:space="preserve">tum ne corpora craſ-<lb/>ſiora componantur, quam debent, inanesque fiant impenſæ.</s> <s xml:id="echoid-s11036" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div356" type="section" level="1" n="356"> <head xml:id="echoid-head466" xml:space="preserve">PROPOSITIO XIII.</head> <p style="it"> <s xml:id="echoid-s11037" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11038" xml:space="preserve">XVII. </s> <s xml:id="echoid-s11039" xml:space="preserve">fig. </s> <s xml:id="echoid-s11040" xml:space="preserve">10. </s> <s xml:id="echoid-s11041" xml:space="preserve">Sidetur Conusrectus B A F, cujus baſis B C la-<lb/>cunari affixa, ita ut axis C A ſit perpendicularis ad borizontem, <lb/>qui ſecetur plano borizontali D G, erit Cobærentia abſoluta baſeos <lb/>B F ad ſoliditatem coni A B F in minori ratione, quam Cobærentia <lb/>abſoluta baſeos D G in ſegmento ad ſuam ſoliditatem.</s> <s xml:id="echoid-s11042" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11043" xml:space="preserve">Concipiatur ſuper baſi B F factus cylindrus altitudinis C A, qui <lb/>fit B K P F, tum ſuper baſi ſegmenti D G cylindrus ſit æque altus <lb/>O I L M. </s> <s xml:id="echoid-s11044" xml:space="preserve">erit Cohærentia abſoluta cylindri B K P F ad Cohærentiam <lb/>cylindri O I L M abſolutam, uti baſis B F ad baſin O I per propoſ. <lb/></s> <s xml:id="echoid-s11045" xml:space="preserve">8. </s> <s xml:id="echoid-s11046" xml:space="preserve">& </s> <s xml:id="echoid-s11047" xml:space="preserve">eſt ſoliditas cylindri B K F P, ad ſoliditatem cylindri O I L M, <lb/>uti baſis B F ad O I baſin: </s> <s xml:id="echoid-s11048" xml:space="preserve">ergo Cohærentiæ & </s> <s xml:id="echoid-s11049" xml:space="preserve">Soliditates ſunt inter <lb/>ſe uti baſes: </s> <s xml:id="echoid-s11050" xml:space="preserve">ſed eſt baſis O I ad ſoliditatem O I L M in minori ra-<lb/>tione, quam eadem baſis O I ad ſoliditatis prioris portionem, ſive ad <lb/>D L M G. </s> <s xml:id="echoid-s11051" xml:space="preserve">Ergo erit Cohærentia, in O I, ſive in æquali D G, ad ſolidita-<lb/>tem D L M G in majori ratione, quam cohærentia O I ad ſoliditatem <lb/>O I L M: </s> <s xml:id="echoid-s11052" xml:space="preserve">unde quoque cohærentia in D G ad ſoliditatem D G L M <pb o="477" file="0491" n="491" rhead="CORPORUM FIRMORUM."/> erit in majori ratione, quam Cohærentia B F ad Soliditatem B K P F. <lb/></s> <s xml:id="echoid-s11053" xml:space="preserve">ſed Coni ſunt tertiæ partes Cylindrorum, hoceſt ſoliditatum hacte-<lb/>nus conſideratarum, adeoque erit Cohærentia D G ad ſoliditatem <lb/>coni D A G, in majori ratione, quam Cohærentia in B F ad ſolidi-<lb/>tatem Coni B A F.</s> <s xml:id="echoid-s11054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11055" xml:space="preserve">Corol. </s> <s xml:id="echoid-s11056" xml:space="preserve">1. </s> <s xml:id="echoid-s11057" xml:space="preserve">Quo igitur ſectio D G propior apici Coni A ponatur, <lb/>eo Cohærentia baſeos D G ad ſoliditatem abſciſſi coni majorem ra-<lb/>tionem habebit; </s> <s xml:id="echoid-s11058" xml:space="preserve">quare quo longior ſit Conus eo Cohærentia baſeos <lb/>ad ſuam Cohærentiam minorem rationem habebit.</s> <s xml:id="echoid-s11059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11060" xml:space="preserve">Corol. </s> <s xml:id="echoid-s11061" xml:space="preserve">2. </s> <s xml:id="echoid-s11062" xml:space="preserve">Eadem conveniunt Pyramidibus quibuſcunque rectis.</s> <s xml:id="echoid-s11063" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div357" type="section" level="1" n="357"> <head xml:id="echoid-head467" xml:space="preserve">PROPOSITIO XIV.</head> <p style="it"> <s xml:id="echoid-s11064" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11065" xml:space="preserve">XVII. </s> <s xml:id="echoid-s11066" xml:space="preserve">fig. </s> <s xml:id="echoid-s11067" xml:space="preserve">10. </s> <s xml:id="echoid-s11068" xml:space="preserve">Si Coni recti A B F, baſis B F cobæreat cum <lb/>lacunari, ut axis C A ſit ad borizontem perpendicularis, atque ſe-<lb/>cetur plano borizontali D G, erit Cobærentia abſoluta baſeos Coni <lb/>A B F, ad Cobærentiam baſeos ſegmenti D E G, in ratione duplicata <lb/>altitudinis C A ad E A.</s> <s xml:id="echoid-s11069" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11070" xml:space="preserve">Sit enim axis Coni A E C; </s> <s xml:id="echoid-s11071" xml:space="preserve">ducantur ex punctis E & </s> <s xml:id="echoid-s11072" xml:space="preserve">C, quæ ſunt <lb/>centra circulorum, rectæ C B, E D: </s> <s xml:id="echoid-s11073" xml:space="preserve">erit A E, A C:</s> <s xml:id="echoid-s11074" xml:space="preserve">: E D, C B. <lb/></s> <s xml:id="echoid-s11075" xml:space="preserve">per propoſ. </s> <s xml:id="echoid-s11076" xml:space="preserve">2. </s> <s xml:id="echoid-s11077" xml:space="preserve">Lib. </s> <s xml:id="echoid-s11078" xml:space="preserve">6. </s> <s xml:id="echoid-s11079" xml:space="preserve">Elem. </s> <s xml:id="echoid-s11080" xml:space="preserve">Eucli. </s> <s xml:id="echoid-s11081" xml:space="preserve">ſed eſt circulus radii E D ad cir-<lb/>culum radii C B, uti <emph style="ol">E D</emph><emph style="super">q</emph> ad <emph style="ol">C B</emph><emph style="super">q</emph> per prop. </s> <s xml:id="echoid-s11082" xml:space="preserve">2. </s> <s xml:id="echoid-s11083" xml:space="preserve">Lib. </s> <s xml:id="echoid-s11084" xml:space="preserve">12. </s> <s xml:id="echoid-s11085" xml:space="preserve">Elem. </s> <s xml:id="echoid-s11086" xml:space="preserve"><lb/>Euclid. </s> <s xml:id="echoid-s11087" xml:space="preserve">adeoque eſt circulus D E G ad circulum B C F:</s> <s xml:id="echoid-s11088" xml:space="preserve">: <emph style="ol">A E</emph><emph style="super">q</emph> <emph style="ol">A C</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s11089" xml:space="preserve"><lb/>verum Cohærentiæ abſolutæ baſium Conorum A D G, A B F, ſunt <lb/>inter ſe uti baſes D G E, B C F, adeoque ſunt Cohærentiæ ambo <lb/>rum Conorum in ratione duplicata altitudinum A E, A C.</s> <s xml:id="echoid-s11090" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div358" type="section" level="1" n="358"> <head xml:id="echoid-head468" xml:space="preserve">PROPOSITIO XV.</head> <p style="it"> <s xml:id="echoid-s11091" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11092" xml:space="preserve">XVII. </s> <s xml:id="echoid-s11093" xml:space="preserve">fig. </s> <s xml:id="echoid-s11094" xml:space="preserve">11. </s> <s xml:id="echoid-s11095" xml:space="preserve">Sit ſolidum parabolicum, ex circumacta Para-<lb/>bola circa axin natum, cujus baſis B F lacunari affixa ut axis C A <lb/>borizonti perpendicularis, ſecetur plano borizontali D E G, erit <lb/>Cobærentia baſeos B C F ad Cobærentiam ſegmenti D E G, in ratio-<lb/>ne altitudinis A C ad A E menſuratæ a vertice.</s> <s xml:id="echoid-s11096" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11097" xml:space="preserve">Sit enim B D A G F Parabola Apolloniana, cujus axis eſt A C, <pb o="478" file="0492" n="492" rhead="INTRODUCTIO AD COHÆRENTIAM"/> erit ex natura Parabolæ, <emph style="ol">B C</emph><emph style="super">q</emph> <emph style="ol">D E</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s11098" xml:space="preserve">: A C, A E. </s> <s xml:id="echoid-s11099" xml:space="preserve">ſed <emph style="ol">B C</emph><emph style="super">q</emph> eſt <lb/>ad <emph style="ol">D E</emph><emph style="super">q</emph>, uti circulus radii B C ad circulum radii D E, hoc eſt uti <lb/>baſis B F ad baſin D G. </s> <s xml:id="echoid-s11100" xml:space="preserve">hoc eſt uti Cohærentia in B F ad Cohæ-<lb/>rentiam in D G. </s> <s xml:id="echoid-s11101" xml:space="preserve">quare erit Cohærentia in B F ad eam in D G:</s> <s xml:id="echoid-s11102" xml:space="preserve">: C A <lb/>ad E A. </s> <s xml:id="echoid-s11103" xml:space="preserve">hoc eſt uti altitudines menſuratæ a vertice A.</s> <s xml:id="echoid-s11104" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div359" type="section" level="1" n="359"> <head xml:id="echoid-head469" xml:space="preserve">PROPOSITIO XVI.</head> <p style="it"> <s xml:id="echoid-s11105" xml:space="preserve">Tab XVII. </s> <s xml:id="echoid-s11106" xml:space="preserve">fig. </s> <s xml:id="echoid-s11107" xml:space="preserve">12. </s> <s xml:id="echoid-s11108" xml:space="preserve">Sit ſolidum planum Parabolicum B D E K F <lb/>L M. </s> <s xml:id="echoid-s11109" xml:space="preserve">cujus baſis B F G N lacunari affixa, ut axis A E Parabolæ ſit <lb/>ad borizontem perpendicularis, ſecetur plano borizontali D C K L, <lb/>erit Cobærentia baſeos B F G N, ad Cobærentiam ſegmenti D C K L <lb/>in ratione ſubduplicata diſtantiæ A E, ad C E a vertice.</s> <s xml:id="echoid-s11110" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11111" xml:space="preserve">Sunt Cohærentiæ baſeos B F G N & </s> <s xml:id="echoid-s11112" xml:space="preserve">ſegmenti D K L in ratione <lb/>ſuarum magnitudinum, ſed eſt planum B F G N ad planum D K L, <lb/>uti eſt B F ad D K, quia K L ponitur æquale F G: </s> <s xml:id="echoid-s11113" xml:space="preserve">dein ex natura Para-<lb/>bolæ eſt B F ad D K uti A E ad E C. </s> <s xml:id="echoid-s11114" xml:space="preserve">quare erit Cohærentia <lb/>baſeos ad Cohærentiam ſegmenti D K L, uti A E ad E C.</s> <s xml:id="echoid-s11115" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div360" type="section" level="1" n="360"> <head xml:id="echoid-head470" xml:space="preserve">PROPOSITIO XVII.</head> <p style="it"> <s xml:id="echoid-s11116" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11117" xml:space="preserve">XVII. </s> <s xml:id="echoid-s11118" xml:space="preserve">fig. </s> <s xml:id="echoid-s11119" xml:space="preserve">13. </s> <s xml:id="echoid-s11120" xml:space="preserve">Si detur cuneus par abolicus A F O B, cujus baſis <lb/>lacunari affixa, axis A F borizonti perpendicularis, ſeceturque <lb/>plano borizontali E C D. </s> <s xml:id="echoid-s11121" xml:space="preserve">erit Cobærentia baſeos ad eam ſegmenti in <lb/>ratione baſeos A O B ad eandem {A O B X E F X E F/A F X <emph style="sp">A F</emph>}.</s> <s xml:id="echoid-s11122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11123" xml:space="preserve">Vocentur A O = a. </s> <s xml:id="echoid-s11124" xml:space="preserve">O B = b. </s> <s xml:id="echoid-s11125" xml:space="preserve">F A = d. </s> <s xml:id="echoid-s11126" xml:space="preserve">E F = x.</s> <s xml:id="echoid-s11127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11128" xml:space="preserve">Ut habeatur C D, erit F A O B:</s> <s xml:id="echoid-s11129" xml:space="preserve">: F E. </s> <s xml:id="echoid-s11130" xml:space="preserve">C D. </s> <s xml:id="echoid-s11131" xml:space="preserve">ſive in terminis a-<lb/>nalyticis d. </s> <s xml:id="echoid-s11132" xml:space="preserve">b:</s> <s xml:id="echoid-s11133" xml:space="preserve">: x. </s> <s xml:id="echoid-s11134" xml:space="preserve">{b x.</s> <s xml:id="echoid-s11135" xml:space="preserve">/d} ut habeatur E C, erit F A.</s> <s xml:id="echoid-s11136" xml:space="preserve">F E:</s> <s xml:id="echoid-s11137" xml:space="preserve">: A O. <lb/></s> <s xml:id="echoid-s11138" xml:space="preserve">E C. </s> <s xml:id="echoid-s11139" xml:space="preserve">ſive in terminis Analyticis d.</s> <s xml:id="echoid-s11140" xml:space="preserve">x:</s> <s xml:id="echoid-s11141" xml:space="preserve">: a. </s> <s xml:id="echoid-s11142" xml:space="preserve">a {x.</s> <s xml:id="echoid-s11143" xml:space="preserve">/d} planum <pb o="479" file="0493" n="493" rhead="CORPORUM FIRMORUM."/> A O B habetur, ducendo A O in O B quod dabit a b eodem mo-<lb/>do planum F C D habebitur ducendo C E in C D ſive {bx/d} in <lb/>a {x/d} quod dat {a b x x/dd} ſive {A O B X E F X E F/A F X A F}</s> </p> <p> <s xml:id="echoid-s11144" xml:space="preserve">Scbolion. </s> <s xml:id="echoid-s11145" xml:space="preserve">Hoc modo conſiderari poſſunt Cohærentiæ abſolutæ, <lb/>quam habent corpora omnia poſſibilia tum in baſibus, tum in quo-<lb/>libet ſegmento baſi parallelo, ad id nihil aliud requiritur, quam <lb/>ut ea, quæ in Geometria demonſtrata ſunt, huc advocentur: </s> <s xml:id="echoid-s11146" xml:space="preserve">opi-<lb/>natus fui hanc levem ſcintillam ſufficere Tironibus, atque me ita <lb/>demonſtraſſe, quâ viâ & </s> <s xml:id="echoid-s11147" xml:space="preserve">methodo pergendum ſit.</s> <s xml:id="echoid-s11148" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div361" type="section" level="1" n="361"> <head xml:id="echoid-head471" xml:space="preserve">PROPOSITIO XVIII.</head> <p style="it"> <s xml:id="echoid-s11149" xml:space="preserve">In comparatis abſolutis Cobærentiis corporum ex diver ſa materia <lb/>confectorum, ejusdem vel diver ſæ baſeos, erunt inter ſe vires Co-<lb/>bærentiæ in ratione compoſita baſium & </s> <s xml:id="echoid-s11150" xml:space="preserve">Cobærentiarum in Ex-<lb/>perimentis fundæmentalibus obſer vatarum.</s> <s xml:id="echoid-s11151" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11152" xml:space="preserve">Nam poſitis corporibus ejuſdem materiæ & </s> <s xml:id="echoid-s11153" xml:space="preserve">diverſarum baſium, <lb/>erunt Cohærentiæ abſolutæ in ratione baſium; </s> <s xml:id="echoid-s11154" xml:space="preserve">poſitis corporibus di-<lb/>verſæ materiæ & </s> <s xml:id="echoid-s11155" xml:space="preserve">earundem baſium, erunt Cohærentiæ quemad-<lb/>modum Experimenta fundamentalia detegunt: </s> <s xml:id="echoid-s11156" xml:space="preserve">quare poſitis tum <lb/>baſibus, tum materiis corporum diverſis, erunt Cohærentiæ in ratio-<lb/>ne compoſita baſium & </s> <s xml:id="echoid-s11157" xml:space="preserve">Cohærentiarum in Experimentis fundamen-<lb/>talibus detectarum.</s> <s xml:id="echoid-s11158" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11159" xml:space="preserve">Corol. </s> <s xml:id="echoid-s11160" xml:space="preserve">Si Cohærentiæ corporum diverſæ materiæ ſint in ratio-<lb/>ne inverſa baſium ſuarum, erunt Cohærentiæ abſolutæ inter ſe æ-<lb/>quales.</s> <s xml:id="echoid-s11161" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div362" type="section" level="1" n="362"> <head xml:id="echoid-head472" style="it" xml:space="preserve">Experimenta fundamentalia Cobærentiæ abſolutæ <lb/>demonſtrandæ inſervientia.</head> <p> <s xml:id="echoid-s11162" xml:space="preserve">Viſis quibusdam generalibus propoſitionibus, convenit Experi-<lb/>mentorum ope explorare, quæ & </s> <s xml:id="echoid-s11163" xml:space="preserve">quantæ ſint corporum datæ craſſitiei <lb/>Cohærentiæ abſolutæ, hoc eſt, quando ſecundum longitudinem di-<lb/>ſtrahuntur: </s> <s xml:id="echoid-s11164" xml:space="preserve">hæc fundamentalia voco, (ſit venia verbo) quia baſes erunt, <pb o="480" file="0494" n="494" rhead="INTRODUCTIO AD COHÆRENTIAM"/> quibus omne ratiocinium ſcientiæ realis de ſolidorum reſiſtentia <lb/>ſuperſtruendum eſt, imo a quibus ordiendum eſt. </s> <s xml:id="echoid-s11165" xml:space="preserve">Ut autem bono <lb/>ordine dirigantur noſtri labores, in anteceſſum deſcribam metho-<lb/>dum, qua in examine Cohærentiæ ſolidorum uſus fui, ut conſtet, an Ex-<lb/>perimenta accurate ſint inſtituta, an fidem & </s> <s xml:id="echoid-s11166" xml:space="preserve">aſſenſum mereantur, aut <lb/>an in iis major cautela & </s> <s xml:id="echoid-s11167" xml:space="preserve">ad plures circumſtantias attentio deſideretur.</s> <s xml:id="echoid-s11168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11169" xml:space="preserve">Acturus de corporum Cohærentiâ, primo ſecutus fui me-<lb/>thodum ingenioſiſſimi Mariotti, deſcriptam in Libro de Mo-<lb/>tu Aquarum part. </s> <s xml:id="echoid-s11170" xml:space="preserve">5. </s> <s xml:id="echoid-s11171" xml:space="preserve">ſerm. </s> <s xml:id="echoid-s11172" xml:space="preserve">2. </s> <s xml:id="echoid-s11173" xml:space="preserve">quæ hæc eſt; </s> <s xml:id="echoid-s11174" xml:space="preserve">vid Tab XVIII. </s> <s xml:id="echoid-s11175" xml:space="preserve">fig 8. <lb/></s> <s xml:id="echoid-s11176" xml:space="preserve">Sumebatur Cylindrus ex ligno ſicco â tornione elaboratus, cujus <lb/>diameter erat {3/12} pollic: </s> <s xml:id="echoid-s11177" xml:space="preserve">extremitates deſinebant in capita majora <lb/>A, B, quos funes ambibant, qui alia methodo adnecti cylindro <lb/>firmiter non potuiſſent, quin citius ab extremitatibus remoti fuiſ-<lb/>ſent, quam quidem cylindrus diffringeretur: </s> <s xml:id="echoid-s11178" xml:space="preserve">caput ſupremum A me-<lb/>dium intra 4 funes ſuſpendebatur, qui trabi L annectebantur: </s> <s xml:id="echoid-s11179" xml:space="preserve">ex funi-<lb/>bus caput inferius B cingentibus appendebatur pondus C, quod in <lb/>initio exiguum. </s> <s xml:id="echoid-s11180" xml:space="preserve">augebatur ſucceſſive, donec cylindrus D B frange-<lb/>batur: </s> <s xml:id="echoid-s11181" xml:space="preserve">Mariottus inſtituens Experimentum cum cylindro ligneo, <lb/>deprehendit id ſuſtinuiſſe pondus 330 librar. </s> <s xml:id="echoid-s11182" xml:space="preserve">addere tamen ob-<lb/>litus fuit ex quonam genere lignum fuerit. </s> <s xml:id="echoid-s11183" xml:space="preserve">In hac methodo id in-<lb/>commodi deprehendi, quod pedes illius, qui Experimenta inſti-<lb/>tuebat, ſemper periculo læſionis exponebantur, cadente pondere C. </s> <s xml:id="echoid-s11184" xml:space="preserve"><lb/>2°, difficillimum eſt aliquot centenas libras Lanci imponere, <lb/>cum plurimorum diverſorumque corporum Cohærentia exploratur: </s> <s xml:id="echoid-s11185" xml:space="preserve"><lb/>3°. </s> <s xml:id="echoid-s11186" xml:space="preserve">aliquando etiam tenuis Ligni firmitas ſuperat craſſiorum funium <lb/>robur; </s> <s xml:id="echoid-s11187" xml:space="preserve">4°. </s> <s xml:id="echoid-s11188" xml:space="preserve">funes novi, aut tempeſtate humida quilibet, ſunt ni-<lb/>mis rigidi, quam ut bene circa capita A, B, flectantur: </s> <s xml:id="echoid-s11189" xml:space="preserve">5°. </s> <s xml:id="echoid-s11190" xml:space="preserve">novi quo-<lb/>que funes a ponderibus majoribus annexis valde quam elongantur, <lb/>ita ut ſuſpenſio ex Trabe L mutanda ſit aliquando; </s> <s xml:id="echoid-s11191" xml:space="preserve">quod & </s> <s xml:id="echoid-s11192" xml:space="preserve">difficile, & </s> <s xml:id="echoid-s11193" xml:space="preserve"><lb/>multum tædii laboriſque affert, ſimulque tempus nimis protrahendo <lb/>inutiliter conſumit: </s> <s xml:id="echoid-s11194" xml:space="preserve">Quamobrem his incommodis obſervatis Ma-<lb/>riotti methodum rejeci, animumque ad aliam iis expertem appli-<lb/>cui; </s> <s xml:id="echoid-s11195" xml:space="preserve">quæ ex voto ſucceſſit, & </s> <s xml:id="echoid-s11196" xml:space="preserve">ut fit inter tentantum, addendo o-<lb/>miſſa, immutando quæ obſtabant, emendandoque difficiliora, tan-<lb/>dem apparatum conſtruxi, qui commodiſſimus Cohærentiis abſo-<lb/>lutis quorumcunque ſolidorum examinandis revera deprehenſus fuit</s> </p> <pb o="481" file="0495" n="495" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s11197" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11198" xml:space="preserve">XIX. </s> <s xml:id="echoid-s11199" xml:space="preserve">fig 6. </s> <s xml:id="echoid-s11200" xml:space="preserve">Eſt A B Statera Romana ferrea, robuſta, cu-<lb/>jus ope corpus admodum grave, nempe librarum 1500 & </s> <s xml:id="echoid-s11201" xml:space="preserve">ultra, com-<lb/>mode ponderari poteſt, pondere C libere mobili ad varias diſtan-<lb/>tias applicato: </s> <s xml:id="echoid-s11202" xml:space="preserve">hæc ſuſpenditur ex unco craſſo D, excepto a Co-<lb/>chlea firma ferrea D E, quæ attollit demittitque ſtateram ad varias <lb/>altitudines, quod valde quam neceſſarium eſt, quia corpora quo-<lb/>rum Cohærentia examinabitur, non ſemper accurate æque longa <lb/>capi poſſunt: </s> <s xml:id="echoid-s11203" xml:space="preserve">ex capite ſtateræ A uncus firmus denſusque F pendet, <lb/>cui annectuntur corpora, quorum unum G hic conſpicitur, ut <lb/>clarius intelligeretur ea applicandi methodus: </s> <s xml:id="echoid-s11204" xml:space="preserve">ſunt K K duo ſtyli <lb/>lignei 6 pedes alti, e ligno quercico, quorum quodlibet latus 5 <lb/>pollices craſſum eſt, qui ſuperius conjunguntur ope trabis transver-<lb/>ſæ, per quam cochlea D E tranſit: </s> <s xml:id="echoid-s11205" xml:space="preserve">Inſiſtunt ambo trabi firmæ H L, <lb/>atque ut immobiles ſtarent, lateraliter applicata ſunt duo ferra-<lb/>menta O O. </s> <s xml:id="echoid-s11206" xml:space="preserve">ad partem anteriorem prominet uncus ferreus H, in-<lb/>fra trabem clavo retentus, ne extrahi poſſet, cum omnem vim cor-<lb/>porum examinandorum ſuſtinere debeat: </s> <s xml:id="echoid-s11207" xml:space="preserve">ad partem trabis L poſte-<lb/>riorem bini alii lignei ſtyli erecti ſunt P P, variis inciſuris donati <lb/>oblique deorſum inſculptis, quibus excipitur funis S S, utroque ex-<lb/>tremo donatus craſſiori nodo, qui per inciſuras transcurrere nequit <lb/>introrſum; </s> <s xml:id="echoid-s11208" xml:space="preserve">hic poſterior apparatus factus eſt, ut cauda ſtateræ B <lb/>non multum moveretur, neque contorſio totius ſtateræ, & </s> <s xml:id="echoid-s11209" xml:space="preserve">proin-<lb/>de corporum examinandorum G fieret: </s> <s xml:id="echoid-s11210" xml:space="preserve">præterea, quando rumpitur <lb/>corpus G, pondus C ſimul cum cauda ſtateræ cadit, magno cum <lb/>fragore & </s> <s xml:id="echoid-s11211" xml:space="preserve">periculo obſervatoris, cujus pedes facile læderentur, <lb/>idcirco funis S S in crenis jacet, qui ſtateram excipit, deciduam <lb/>modo ex tam parva altitudine ac volumus ob varias crenas; </s> <s xml:id="echoid-s11212" xml:space="preserve">unde nec <lb/>pondus C amplius cadit, & </s> <s xml:id="echoid-s11213" xml:space="preserve">â detrimento ſervetur ſtatera ob mollitiem <lb/>funis S S eam excipientis; </s> <s xml:id="echoid-s11214" xml:space="preserve">Trabs H L tribus rotis inſiſtit hic non <lb/>depictis, quarum beneficio in locum quemlibet facile apportatur, <lb/>nam graviſſima eſt tota machina, & </s> <s xml:id="echoid-s11215" xml:space="preserve">minus mobilis foret, nec le-<lb/>vior parari potuit propter vires maximas corporum cohærentium, <lb/>quæ explorandæ erant, quippe ſæpius 1000 librar. </s> <s xml:id="echoid-s11216" xml:space="preserve">vim exercet <lb/>cohærentia corporum tenuium abſoluta, ſæpe vim libr. </s> <s xml:id="echoid-s11217" xml:space="preserve">1500 & </s> <s xml:id="echoid-s11218" xml:space="preserve"><lb/>majorem, uti ex Experimentis infra deſcriptis apparebit.</s> <s xml:id="echoid-s11219" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11220" xml:space="preserve">Breviter quoque depinxiſſe formam corporum exploratorum.</s> <s xml:id="echoid-s11221" xml:space="preserve"> <pb o="482" file="0496" n="496" rhead="INTRODUCTIO AD COHÆRENTIAM"/> methodumque ea examinandi operæ pretium erit, cum poſt varia ten-<lb/>tamina modo inciderim in eam, quæ minimis difficultatibus ſubjici-<lb/>tur: </s> <s xml:id="echoid-s11222" xml:space="preserve">primum ligna deſcribam, quæ ſecundum longitudinem ſive fibra-<lb/>rum ductum examinavi, ut Cohærentiam eorum abiolutam experirer: <lb/></s> <s xml:id="echoid-s11223" xml:space="preserve">omnia Ligna ex aſſere craſſo ſecundum longitudinem fiſſo facta <lb/>fuerunt, ut fibræ tam recte decurrerent, quantum genium cujus-<lb/>vis Ligni permittebat; </s> <s xml:id="echoid-s11224" xml:space="preserve">niſi enim hoc religioſe obſervetur, nunquam <lb/>experimento conſidi poteſt; </s> <s xml:id="echoid-s11225" xml:space="preserve">præterea quodlibet lignum electum <lb/>fuit in ſuâ ſpecie bonum, firmum, modice ſiccum, abs-<lb/>que nodis: </s> <s xml:id="echoid-s11226" xml:space="preserve">formâ donabatur, quam Tab. </s> <s xml:id="echoid-s11227" xml:space="preserve">XX. </s> <s xml:id="echoid-s11228" xml:space="preserve">fig. </s> <s xml:id="echoid-s11229" xml:space="preserve">1. </s> <s xml:id="echoid-s11230" xml:space="preserve">repræſentat: </s> <s xml:id="echoid-s11231" xml:space="preserve"><lb/>Eſt A B B parallelopipedum, unum pedem longum, eſt B B {3/4} polli-<lb/>cis latum, B b {1/2} pollic: </s> <s xml:id="echoid-s11232" xml:space="preserve">profundum: </s> <s xml:id="echoid-s11233" xml:space="preserve">In medio longitudo G K 2 pol-<lb/>licum a Tornione exciſa fuit accurate in formam cylindri, ubi-<lb/>vis æque craſſi, cujus diameter erat 0, 27 pollicis Rhenolandici; </s> <s xml:id="echoid-s11234" xml:space="preserve"><lb/>extremitatibus ambabus A, B agglutinebatur utrimque par-<lb/>vum parallelopipedum D D ligni quercici, longum 2 pollic. </s> <s xml:id="echoid-s11235" xml:space="preserve">latum <lb/>{9/4} poll: </s> <s xml:id="echoid-s11236" xml:space="preserve">profundum {1/2} poll: </s> <s xml:id="echoid-s11237" xml:space="preserve">ita ut lignum explorandum in medio am-<lb/>borum hæreret: </s> <s xml:id="echoid-s11238" xml:space="preserve">fuit parallelopipedum A B tam craſſum electum, <lb/>& </s> <s xml:id="echoid-s11239" xml:space="preserve">in medio G K attenuatum, ne capita A & </s> <s xml:id="echoid-s11240" xml:space="preserve">B frangerentur, imo, <lb/>cum hæc nondum ſatis reſiſtant, corpuſcula lateralia D D agglutinata <lb/>fuerunt, quæ capitum robur adeo auxerunt, ut potius medium K G, <lb/>quam caput alterutrum A, B, diffractum fuerit: </s> <s xml:id="echoid-s11241" xml:space="preserve">Capita perforata <lb/>fuerunt in E E, F F, per hæc foramina enim clavi ferrei transmit-<lb/>tebantur, infra deſcribendi: </s> <s xml:id="echoid-s11242" xml:space="preserve">non modo ejusmodi corpora præpa-<lb/>rata fuerunt, ſed etiam ſimilia alia, quæ non erant in K G me-<lb/>dio cylindrica, ſed parallelopipeda quadrangula, quorum quodli-<lb/>bet latus erat 0, 27 poll. </s> <s xml:id="echoid-s11243" xml:space="preserve">cæteroquin craſſities Lignorum deſcri-<lb/>bitur in Experimentis, ſi diverſa fuerit: </s> <s xml:id="echoid-s11244" xml:space="preserve">ex quolibet ligni gene-<lb/>re igitur duo corpora confeceram. </s> <s xml:id="echoid-s11245" xml:space="preserve">quorum unum in medio <lb/>erat cylindricum, alterum quadrangulum, quia Cohæren-<lb/>tiam abſolutam cum reſpectiva binorum corporum compara-<lb/>re volueram, tum ut repetiti inſtar Experimenti unum alteri in-<lb/>ſerviret.</s> <s xml:id="echoid-s11246" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11247" xml:space="preserve">Deinde facti ſunt duo unci ferrei, quorum unum exhibet fig, 2. </s> <s xml:id="echoid-s11248" xml:space="preserve">Tab. <lb/></s> <s xml:id="echoid-s11249" xml:space="preserve">XX. </s> <s xml:id="echoid-s11250" xml:space="preserve">cujus crura L L perforata excipiebant clavum ferreum P P; </s> <s xml:id="echoid-s11251" xml:space="preserve">diſta-<lb/>bant crura hæc tantopere a ſe, ut capita Lignorum modo ante fig. </s> <s xml:id="echoid-s11252" xml:space="preserve">1.</s> <s xml:id="echoid-s11253" xml:space="preserve"> <pb o="483" file="0497" n="497" rhead="CORPORUM FIRMORUM."/> deſcriptorum D D D D comprehenderent, & </s> <s xml:id="echoid-s11254" xml:space="preserve">clavus P P trans-<lb/>iret tum per foramina unci, tum per foramina Lignorum E E, vel <lb/>F F. </s> <s xml:id="echoid-s11255" xml:space="preserve">quemadmodum Tab. </s> <s xml:id="echoid-s11256" xml:space="preserve">XIX. </s> <s xml:id="echoid-s11257" xml:space="preserve">fig. </s> <s xml:id="echoid-s11258" xml:space="preserve">6. </s> <s xml:id="echoid-s11259" xml:space="preserve">lignum cum ſuis annexis <lb/>uncis & </s> <s xml:id="echoid-s11260" xml:space="preserve">ſimul machinæ divulſoriæ applicatum, exhibet: </s> <s xml:id="echoid-s11261" xml:space="preserve">deſcripto <lb/>hoc apparatu ad ipſa tentamina accedamus, quorum eventus miri-<lb/>fice varius exigit, ut quodlibet Lignum ſeorſim adnotetur: </s> <s xml:id="echoid-s11262" xml:space="preserve">nihil <lb/>omittere conatus fui, quod vel tantillum lucis afferre huic doctrinæ <lb/>poſſet: </s> <s xml:id="echoid-s11263" xml:space="preserve">quem in finem etiam figuras lignorum fractorum depinxi, ex <lb/>quibus apparet an Lignum longas feſtucas, cum frangitur, format, an <lb/>nullas: </s> <s xml:id="echoid-s11264" xml:space="preserve">ut poſſet eligi pro pariete interno navium bellicarum, in <lb/>quibus fervente prælio plures vulnerantur a feſtucis ligni milites, quam <lb/>ab ipſis globis tormentariis; </s> <s xml:id="echoid-s11265" xml:space="preserve">Lignum, quod abſque feſtucis rumpitur, <lb/>huic malo obviam ire poſſet: </s> <s xml:id="echoid-s11266" xml:space="preserve">ſed præterea depinxeram alios in fines, ut <lb/>nempe quam clariſſime & </s> <s xml:id="echoid-s11267" xml:space="preserve">â primis fundamentis Cohærentias reſpe-<lb/>ctivas explicarem, in quibus tantum difficultatis poſtea deprehendi, <lb/>ut â plurimis ſubtilitatibus abſtinere huc uſque coactus fuerim.</s> <s xml:id="echoid-s11268" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div363" type="section" level="1" n="363"> <head xml:id="echoid-head473" xml:space="preserve">EXPERIMENTUM I.</head> <p> <s xml:id="echoid-s11269" xml:space="preserve">Lignum Tiliæ, cujus medium erat cylindricum, antequam rum-<lb/>pebatur, aliquamdiu ſuſtinuit libras Amſtelodamenſes 720, ab iis <lb/>tamen fractum fuit: </s> <s xml:id="echoid-s11270" xml:space="preserve">ante rupturam elongata fuit pars cylindrica <lb/>{2/100} pollicis, diameter interim contracta {1/100} pollic. </s> <s xml:id="echoid-s11271" xml:space="preserve">fuit: </s> <s xml:id="echoid-s11272" xml:space="preserve">rumpebatur in <lb/>medio cum feſtucis aliquibus eminentibus, quas exhibet Tab. </s> <s xml:id="echoid-s11273" xml:space="preserve">XXI. <lb/></s> <s xml:id="echoid-s11274" xml:space="preserve">fig. </s> <s xml:id="echoid-s11275" xml:space="preserve">1. </s> <s xml:id="echoid-s11276" xml:space="preserve">Notandum pro his & </s> <s xml:id="echoid-s11277" xml:space="preserve">omnibus Experimentis pondus C ſta-<lb/>teræ appenſum fuiſſe lentè ſecundum ejus longitudinem promotum, <lb/>& </s> <s xml:id="echoid-s11278" xml:space="preserve">aliquamdiu, fere per minutum horæ ad quamlibet diviſionem, <lb/>a 10 ad 10 libras increſcentem, relictum, non enim rumpitur lignum <lb/>uno ictu, ſed ſucceſſive fibræ ſolvuntur, & </s> <s xml:id="echoid-s11279" xml:space="preserve">ex ſe extricantur, unde <lb/>ſemper per aliquod tempus exſpectandum eſt, antequam pondus <lb/>ſupra ſtateram promoveatur.</s> <s xml:id="echoid-s11280" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div364" type="section" level="1" n="364"> <head xml:id="echoid-head474" xml:space="preserve">EXPERIMENTUM II.</head> <p> <s xml:id="echoid-s11281" xml:space="preserve">Lignum Tiliæ, cujus medium erat quadrilaterum parallelopipe-<lb/>dum, applicatum Machinæ noſtræ divulſoriæ, ruptum fuit a li- <pb o="484" file="0498" n="498" rhead="INTRODUCTIO AD COHÆRENTIAM"/> bris 1000; </s> <s xml:id="echoid-s11282" xml:space="preserve">exhibuit fractura feſtucam longam, quam vide ſis in <lb/>Tab. </s> <s xml:id="echoid-s11283" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11284" xml:space="preserve">fig. </s> <s xml:id="echoid-s11285" xml:space="preserve">2. </s> <s xml:id="echoid-s11286" xml:space="preserve">cujus pars A B hæſerat in parte craſſiori parallelo-<lb/>pipedi, tanquam in vagina: </s> <s xml:id="echoid-s11287" xml:space="preserve">Cohærentia hujus parallelopipedi fuit <lb/>paulum major, quam cylindri in Exper. </s> <s xml:id="echoid-s11288" xml:space="preserve">I cum enim circulus ſit ad <lb/>quadratum ſibi circumſcriptum proxime uti 11 ad 14, atque ita ſo-<lb/>liditates cylindri & </s> <s xml:id="echoid-s11289" xml:space="preserve">parallelopipedi æquo<unsure/> longi examinati, cohæ-<lb/>rentiæ utriusque in eadem proportione eſſe debuiſſent: </s> <s xml:id="echoid-s11290" xml:space="preserve">ſed ſunt <lb/>11, 14:</s> <s xml:id="echoid-s11291" xml:space="preserve">: 720, 916 {4/11}: </s> <s xml:id="echoid-s11292" xml:space="preserve">parallelopipedum vero ſuſtinuit plus quam 916 <lb/>nempe 1000 libras; </s> <s xml:id="echoid-s11293" xml:space="preserve">ſed poſtea ejusmodi anomalias explicabimus fa-<lb/>cile, demonſtraturi Lignum, ex eadem arbore propius cortici vel me-<lb/>ditullio ſumtum, variâ vi Cohærentiæ pollere.</s> <s xml:id="echoid-s11294" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div365" type="section" level="1" n="365"> <head xml:id="echoid-head475" xml:space="preserve">EXPERIMENTUM III.</head> <p> <s xml:id="echoid-s11295" xml:space="preserve">Lignum Alni, cujus medium fuit cylindricum antequam rumpe-<lb/>batur, ſuſtinuit aliquamdiu libras 800, a quibus tamen ſolutum: <lb/></s> <s xml:id="echoid-s11296" xml:space="preserve">fractura fuit admodum aſpera cum ſpinis acutis, quæ conſpici poſ-<lb/>ſunt in Tab. </s> <s xml:id="echoid-s11297" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11298" xml:space="preserve">fig. </s> <s xml:id="echoid-s11299" xml:space="preserve">3.</s> <s xml:id="echoid-s11300" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div366" type="section" level="1" n="366"> <head xml:id="echoid-head476" xml:space="preserve">EXPERIMENTUM IV.</head> <p> <s xml:id="echoid-s11301" xml:space="preserve">In uſum vocatum Lignum Alni, cujus medium erat parallelopi-<lb/>pedum quadrilaterum, ſuſtinuit hoc libras 1000. </s> <s xml:id="echoid-s11302" xml:space="preserve">tum vero fragor <lb/>magnus audiebatur, atque ſtatera deſcendebat; </s> <s xml:id="echoid-s11303" xml:space="preserve">opinabar Lignum <lb/>fuiſſe diffractum: </s> <s xml:id="echoid-s11304" xml:space="preserve">nihil profecto minus: </s> <s xml:id="echoid-s11305" xml:space="preserve">media pars, quæ Tab. </s> <s xml:id="echoid-s11306" xml:space="preserve">XX. <lb/></s> <s xml:id="echoid-s11307" xml:space="preserve">fig. </s> <s xml:id="echoid-s11308" xml:space="preserve">1. </s> <s xml:id="echoid-s11309" xml:space="preserve">notatur K G multum prolongata conſpiciebatur, omnibus <lb/>manentibus integris; </s> <s xml:id="echoid-s11310" xml:space="preserve">ſtateram igitur de novo elevabam, Cohæren-<lb/>tiam hujus Ligni exploraturus, ecce! educo parallelopipedum æque <lb/>craſſum ac erat G D ex reliqua craſſiori parte G A, quod longitu-<lb/>dinem habuit 4 pollicum, atque â G uſque ad E foramen capitis <lb/>pertingebat; </s> <s xml:id="echoid-s11311" xml:space="preserve">quod inſtar gladii e vaginâ extracti ſe habuit: </s> <s xml:id="echoid-s11312" xml:space="preserve">Liquet <lb/>in hoc Experimento partes, quæ fibram longitudinalem hujus Li-<lb/>gni componunt, fortius inter ſe cohærere, quam quæ transverſa-<lb/>les fibras faciunt, imo lateralem contactum, etiamſi in longitudi-<lb/>ne 4 pollicum, eſſe exiguum & </s> <s xml:id="echoid-s11313" xml:space="preserve">parvæ Cohærentiæ: </s> <s xml:id="echoid-s11314" xml:space="preserve">præterea con-<lb/>ſtat fibras hujus Ligni in rectas concreſcere lineas, cæteroquin per <pb o="485" file="0499" n="499" rhead="CORPORUM FIRMORUM."/> medium disruptæ fuiſſent: </s> <s xml:id="echoid-s11315" xml:space="preserve">quare autem cylindrus præcedentis Ex-<lb/>perimenti non eadem phænomena exhibuit? </s> <s xml:id="echoid-s11316" xml:space="preserve">quia idem Lignum <lb/>in omni arbore, etiam ſi ejusdem generis, non eodem modo con-<lb/>creſcit: </s> <s xml:id="echoid-s11317" xml:space="preserve">ſolum, in quo plantatur, eſt aquoſius vel oleoſius, ma-<lb/>gis minusve ſalinum: </s> <s xml:id="echoid-s11318" xml:space="preserve">imo differt ipſa Ligni denſitas, prout ſpecta-<lb/>verit arbor Boream vel Auſtrum, quippe denſior eſt, ſive circuli in <lb/>trunco transverſe ſecto ſibi ſunt propiores ea parte, quæ Boream <lb/>ſpectavit, quam quæ Auſtrum: </s> <s xml:id="echoid-s11319" xml:space="preserve">quæ diverſiſſima ejusdem trunci <lb/>ſtructura eventus Cohærentiæ diverſiſſimos etiam producit.</s> <s xml:id="echoid-s11320" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div367" type="section" level="1" n="367"> <head xml:id="echoid-head477" xml:space="preserve">EXPERIMENTUM V.</head> <p> <s xml:id="echoid-s11321" xml:space="preserve">Sumtum fuit Lignum Piceæ, cujus medium erat cylindricum, <lb/>quod cum ſuſtinuit libras 800, fragorem edidit, non tamen fractum <lb/>fuit: </s> <s xml:id="echoid-s11322" xml:space="preserve">At cylindrus, ejusdem craſſitiei ac in Tab. </s> <s xml:id="echoid-s11323" xml:space="preserve">fig. </s> <s xml:id="echoid-s11324" xml:space="preserve">XX. </s> <s xml:id="echoid-s11325" xml:space="preserve">1. </s> <s xml:id="echoid-s11326" xml:space="preserve">G K extra-<lb/>ctus ex capite craſſiori G A, veluti in Experimento 4. </s> <s xml:id="echoid-s11327" xml:space="preserve">obſervatum <lb/>fuit, quamobrem huic ligno conveniunt omnia, quæ monuimus <lb/>modo ante; </s> <s xml:id="echoid-s11328" xml:space="preserve">ejus igitur Cohærentiam abſolutam hac methodo ex-<lb/>plorare non potui, quæ vix niſi operoſiſſimâ aliâ detegetur, cui poſt-<lb/>ea operam forte impendam.</s> <s xml:id="echoid-s11329" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div368" type="section" level="1" n="368"> <head xml:id="echoid-head478" xml:space="preserve">EXPERIMENTUM VI.</head> <p> <s xml:id="echoid-s11330" xml:space="preserve">Lignum Abietis, cujus medium erat cylindricum, ſuſtinuit, ante-<lb/>quam frangebatur, libras 650, ruptum abiit in feſtucas oblongas a-<lb/>cutas, quales exhibet Tab. </s> <s xml:id="echoid-s11331" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11332" xml:space="preserve">fig. </s> <s xml:id="echoid-s11333" xml:space="preserve">4.</s> <s xml:id="echoid-s11334" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div369" type="section" level="1" n="369"> <head xml:id="echoid-head479" xml:space="preserve">EXPERIMENTUM VII.</head> <p> <s xml:id="echoid-s11335" xml:space="preserve">Lignum Abietis, cujus medium erat parallelopipedum quadrila-<lb/>terum, ſuſtinuit modo libras 600 tumque diffractum abiit in feſtu-<lb/>cas oblongas, quales exhibet Tab. </s> <s xml:id="echoid-s11336" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11337" xml:space="preserve">fig. </s> <s xml:id="echoid-s11338" xml:space="preserve">5. </s> <s xml:id="echoid-s11339" xml:space="preserve">hoc tamen minus <lb/>ſuſtinuit quam deberet, ratione Cohærentiæ in cylindro obſervatæ, <lb/>quia majorem craſſitiem habebat, ſed fibris longitudinalibus a ſe <lb/>magis diſtantibus conſtabat,</s> </p> <pb o="486" file="0500" n="500" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div370" type="section" level="1" n="370"> <head xml:id="echoid-head480" xml:space="preserve">EXPERIMENTUM VIII.</head> <p> <s xml:id="echoid-s11340" xml:space="preserve">Lignum, Quercus dictum, in medio Cylindricum a libris 1150 <lb/>penitus diffractum fuit, non in magnas aſperasve feſtucas abeundo, <lb/>quemadmodum fractura Tab. </s> <s xml:id="echoid-s11341" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11342" xml:space="preserve">fig, 6. </s> <s xml:id="echoid-s11343" xml:space="preserve">conſpicua oſtendit.</s> <s xml:id="echoid-s11344" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div371" type="section" level="1" n="371"> <head xml:id="echoid-head481" xml:space="preserve">EXPERIMENTUM IX.</head> <p> <s xml:id="echoid-s11345" xml:space="preserve">Lignum Quercicum, cujus medium erat parallelopipedum qua-<lb/>drangulum, ruptum fuit quoque a libris 1150, fractura non mul-<lb/>tum aſpera fuit, veluti oſtendit Tab. </s> <s xml:id="echoid-s11346" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11347" xml:space="preserve">fig. </s> <s xml:id="echoid-s11348" xml:space="preserve">7. </s> <s xml:id="echoid-s11349" xml:space="preserve">Lignum hoc vide-<lb/>batur conſtare ex fibris magis rectilineis, quam illud Experimenti <lb/>præcedentis, erat cæteroquin utrumque tam ſolidum, ac ex hoc <lb/>genere eligi poteſt, nec ratio apparuit, quare non plus cohæſerit <lb/>hoc quadrangulum, quam cylindricum.</s> <s xml:id="echoid-s11350" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div372" type="section" level="1" n="372"> <head xml:id="echoid-head482" xml:space="preserve">EXPERIMENTUM X.</head> <p> <s xml:id="echoid-s11351" xml:space="preserve">Factum fuit cum Ligno Ulmi, quod in medio erat cylindricum, <lb/>diametri 0, 26. </s> <s xml:id="echoid-s11352" xml:space="preserve">pollic. </s> <s xml:id="echoid-s11353" xml:space="preserve">hoc diffractum fuit penitus a libris 850, fractu-<lb/>ra non obſervabatur admodum aſpera, neque in feſtucas abierat, <lb/>veluti in Tab. </s> <s xml:id="echoid-s11354" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11355" xml:space="preserve">fig. </s> <s xml:id="echoid-s11356" xml:space="preserve">8. </s> <s xml:id="echoid-s11357" xml:space="preserve">conſpicitur.</s> <s xml:id="echoid-s11358" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div373" type="section" level="1" n="373"> <head xml:id="echoid-head483" xml:space="preserve">EXPERIMENTUM XI.</head> <p> <s xml:id="echoid-s11359" xml:space="preserve">Lignum Ulmi, cujus medium erat parallelopipedum quadran-<lb/>gulum, & </s> <s xml:id="echoid-s11360" xml:space="preserve">quodlibet latus erat 0, 27, pollic. </s> <s xml:id="echoid-s11361" xml:space="preserve">diffractum fuit penitus <lb/>in medio ab appenſo pondere librar. </s> <s xml:id="echoid-s11362" xml:space="preserve">950, abeundo in feſtucas oblon-<lb/>gas, quas Tab. </s> <s xml:id="echoid-s11363" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11364" xml:space="preserve">fig. </s> <s xml:id="echoid-s11365" xml:space="preserve">9. </s> <s xml:id="echoid-s11366" xml:space="preserve">exhibet.</s> <s xml:id="echoid-s11367" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div374" type="section" level="1" n="374"> <head xml:id="echoid-head484" xml:space="preserve">EXPERIMENTUM XII.</head> <p> <s xml:id="echoid-s11368" xml:space="preserve">Inſtitutum fuit cum Ligno Oleæ, cujus medium erat cylindricum, <lb/>quod penitus fuit diffractum a libris 650, ad partem cylindricam <lb/>ſuperiorem, ita tamen, ut ſimulipſi quædam portio parallelopipedi craſ- <pb o="487" file="0501" n="501" rhead="CORPORUM FIRMORUM."/> ſioris adhæſerit, veluti videtur in Tab. </s> <s xml:id="echoid-s11369" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11370" xml:space="preserve">fig. </s> <s xml:id="echoid-s11371" xml:space="preserve">10. </s> <s xml:id="echoid-s11372" xml:space="preserve">cæteroquin <lb/>ſuperficies fracturæ non fuit multum exaſperata.</s> <s xml:id="echoid-s11373" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div375" type="section" level="1" n="375"> <head xml:id="echoid-head485" xml:space="preserve">EXPERIMENTUM XIII.</head> <p> <s xml:id="echoid-s11374" xml:space="preserve">Lignum Oleæ, cujus medium erat parallelopipedum quadrangu-<lb/>lum, in quo latus quodlibet fuit 0, 26 pollic. </s> <s xml:id="echoid-s11375" xml:space="preserve">penitus diffractum <lb/>fuit a libris 850, relinquendo ſuperficiem vix aſperam & </s> <s xml:id="echoid-s11376" xml:space="preserve">absque <lb/>feſtucis. </s> <s xml:id="echoid-s11377" xml:space="preserve">vide Tab. </s> <s xml:id="echoid-s11378" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11379" xml:space="preserve">fig. </s> <s xml:id="echoid-s11380" xml:space="preserve">10.</s> <s xml:id="echoid-s11381" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div376" type="section" level="1" n="376"> <head xml:id="echoid-head486" xml:space="preserve">EXPERIMENTUM XIV.</head> <p> <s xml:id="echoid-s11382" xml:space="preserve">Inſerviit Lignum Fagi, cujus medium erat cylindricum, diame-<lb/>tri 0, 26 pollic. </s> <s xml:id="echoid-s11383" xml:space="preserve">diffractum fuit penitus a libris 1150, abiitque fractu-<lb/>ra in multas aſperitates, & </s> <s xml:id="echoid-s11384" xml:space="preserve">feſtucam longam, quam repræſentat <lb/>Tab. </s> <s xml:id="echoid-s11385" xml:space="preserve">XX. </s> <s xml:id="echoid-s11386" xml:space="preserve">fig. </s> <s xml:id="echoid-s11387" xml:space="preserve">11.</s> <s xml:id="echoid-s11388" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div377" type="section" level="1" n="377"> <head xml:id="echoid-head487" xml:space="preserve">EXPERIMENTUM XV.</head> <p> <s xml:id="echoid-s11389" xml:space="preserve">Lignum Fagi, quod in medio erat parallelopipedum quadrangu-<lb/>lum, cujus ſingulum latus fuit 0, 26 pollic. </s> <s xml:id="echoid-s11390" xml:space="preserve">diffringi modo potuit a li-<lb/>bris 1250, abiitque in feſtucas 2 pollices longas & </s> <s xml:id="echoid-s11391" xml:space="preserve">valde aſperas, <lb/>quarum una proſtat in Tab. </s> <s xml:id="echoid-s11392" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11393" xml:space="preserve">fig. </s> <s xml:id="echoid-s11394" xml:space="preserve">16.</s> <s xml:id="echoid-s11395" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div378" type="section" level="1" n="378"> <head xml:id="echoid-head488" xml:space="preserve">EXPERIMENTUM XVI.</head> <p> <s xml:id="echoid-s11396" xml:space="preserve">Lignum Buxinum, cujus medium erat cylindricum diametri <lb/>0, 26. </s> <s xml:id="echoid-s11397" xml:space="preserve">pollic. </s> <s xml:id="echoid-s11398" xml:space="preserve">diffractum fuit a libris 850. </s> <s xml:id="echoid-s11399" xml:space="preserve">ſuperficies fracturæ parum <lb/>aſpera fuit, fere parallela baſi cylindricæ, ex qua una feſtuca ta-<lb/>men educta fuit, ut videri poteſt in Tab. </s> <s xml:id="echoid-s11400" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11401" xml:space="preserve">fig. </s> <s xml:id="echoid-s11402" xml:space="preserve">12.</s> <s xml:id="echoid-s11403" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div379" type="section" level="1" n="379"> <head xml:id="echoid-head489" xml:space="preserve">EXPERIMENTUM XVII.</head> <p> <s xml:id="echoid-s11404" xml:space="preserve">Factum fuit cum Ligno Buxino, quod in medio erat parallelopipe-<lb/>dum quadrangulare, cujus quodlibet latus fuit 0, 26 pollic. </s> <s xml:id="echoid-s11405" xml:space="preserve">ſuſtinuit <lb/>libras 950, hoc miro modo diffractum fuit, pars enim tenuior paral-<lb/>lelopipedi, quæexamini erat deſtinata, non diffracta fuit, ſed incipie- <pb o="488" file="0502" n="502" rhead="INTRODUCTIO AD COHÆRENTIAM"/> bat rumpi, contraxeratque rimam oblongam, verum pars capitis, <lb/>quæ in Tab. </s> <s xml:id="echoid-s11406" xml:space="preserve">XIX. </s> <s xml:id="echoid-s11407" xml:space="preserve">fig, 1. </s> <s xml:id="echoid-s11408" xml:space="preserve">notatur literis D G vel K D, diffracta <lb/>fuit, abiitque in feſtucam undulatam, 5 pollices longam, quam de-<lb/>pictam exhibet Tab. </s> <s xml:id="echoid-s11409" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11410" xml:space="preserve">fig. </s> <s xml:id="echoid-s11411" xml:space="preserve">17.</s> <s xml:id="echoid-s11412" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div380" type="section" level="1" n="380"> <head xml:id="echoid-head490" xml:space="preserve">EXPERIMENTUM XVIII.</head> <p> <s xml:id="echoid-s11413" xml:space="preserve">Captum fuit cum Ligno Piri, cujus medium erat cylindricum, <lb/>diametri 0, 24 pollic. </s> <s xml:id="echoid-s11414" xml:space="preserve">quod diffractum fuit penitus ab appenſis <lb/>libris 550, fracturæ ſuperficies non fuit multum aſpera, oblique <lb/>decurrens, veluti exhibet Tab. </s> <s xml:id="echoid-s11415" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11416" xml:space="preserve">fig. </s> <s xml:id="echoid-s11417" xml:space="preserve">13.</s> <s xml:id="echoid-s11418" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div381" type="section" level="1" n="381"> <head xml:id="echoid-head491" xml:space="preserve">EXPERIMENTUM XIX.</head> <p> <s xml:id="echoid-s11419" xml:space="preserve">Factum eſt cum Ligno Piri, cujus medium erat parallelopipedum <lb/>quadrangulare, hujus quodlibet latus fuit 0, 25 pollic. </s> <s xml:id="echoid-s11420" xml:space="preserve">diffractum fuit <lb/>penitus a libris 700, abeundo in longam feſtucam, ſuperficiei ad-<lb/>modum inæqualis, quæ proſtat Tab. </s> <s xml:id="echoid-s11421" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11422" xml:space="preserve">fig. </s> <s xml:id="echoid-s11423" xml:space="preserve">15.</s> <s xml:id="echoid-s11424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div382" type="section" level="1" n="382"> <head xml:id="echoid-head492" xml:space="preserve">EXPERIMENTUM XX.</head> <p> <s xml:id="echoid-s11425" xml:space="preserve">Lignum Nucis, quod ex Gallia affertur, cujus medium fuit cy-<lb/>lindricum, & </s> <s xml:id="echoid-s11426" xml:space="preserve">diametri 0, 26. </s> <s xml:id="echoid-s11427" xml:space="preserve">pollic. </s> <s xml:id="echoid-s11428" xml:space="preserve">rumpi modo potuit ab appenſis <lb/>libris 800, fracturæ pars quædam aſpera erat, pars manſerat cylin-<lb/>drica; </s> <s xml:id="echoid-s11429" xml:space="preserve">quæ aſpera, in feſtucam abiit longam ingredientem caput <lb/>ipſius Ligni aliquouſque; </s> <s xml:id="echoid-s11430" xml:space="preserve">videatur in Tab. </s> <s xml:id="echoid-s11431" xml:space="preserve">XXI. </s> <s xml:id="echoid-s11432" xml:space="preserve">fig. </s> <s xml:id="echoid-s11433" xml:space="preserve">14.</s> <s xml:id="echoid-s11434" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div383" type="section" level="1" n="383"> <head xml:id="echoid-head493" xml:space="preserve">EXPERIMENTUM XXI.</head> <p> <s xml:id="echoid-s11435" xml:space="preserve">Factum fuit cum parallelopipedo ex Ligno Nucis Gallico, cu-<lb/>jus quodlibet latus fuit 0, 26. </s> <s xml:id="echoid-s11436" xml:space="preserve">pollic. </s> <s xml:id="echoid-s11437" xml:space="preserve">hoc diffractum fuit a libris <lb/>800, eratque ſuperficies aſpera cum parva prominenti feſtuca, <lb/>vide Tab. </s> <s xml:id="echoid-s11438" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11439" xml:space="preserve">fig. </s> <s xml:id="echoid-s11440" xml:space="preserve">18.</s> <s xml:id="echoid-s11441" xml:space="preserve"/> </p> <pb o="489" file="0503" n="503" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div384" type="section" level="1" n="384"> <head xml:id="echoid-head494" xml:space="preserve">EXPERIMENTUM XXII.</head> <p> <s xml:id="echoid-s11442" xml:space="preserve">Lignum Salicis, cujus medium erat cylindricum diametri 0, 26 poll: <lb/></s> <s xml:id="echoid-s11443" xml:space="preserve">ſuſtinuit vim libr. </s> <s xml:id="echoid-s11444" xml:space="preserve">1000, a quibus tamen non eſt diffractum, ſed <lb/>ex capite Ligni parallelopipedi extractus fuit cylindrus 4 pollices <lb/>longus, qui erat productio cylindri medii: </s> <s xml:id="echoid-s11445" xml:space="preserve">conveniunt hic igitur ea <lb/>omnia dicenda de Cohærentiâ, quæ in Experimento IV monui.</s> <s xml:id="echoid-s11446" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div385" type="section" level="1" n="385"> <head xml:id="echoid-head495" xml:space="preserve">EXPERIMENTUM XXIII.</head> <p> <s xml:id="echoid-s11447" xml:space="preserve">Sumtum fuit iterum Lignum Salicis, cujus medium erat paralle-<lb/>lopipedum, & </s> <s xml:id="echoid-s11448" xml:space="preserve">quodlibet latus 0, 26 pollicis appenſis libris 900, <lb/>incipiebat extrahi parallelopipedum ex capite craſſiori ejuſdem craſ-<lb/>ſitiei ac erat medium parallelopipedum, quemadmodum in Expe-<lb/>rimento præcedenti: </s> <s xml:id="echoid-s11449" xml:space="preserve">interim tamen rumpebatur, abiitque in feſtu-<lb/>cam 3 pollices longam, quæ proſtat Tab. </s> <s xml:id="echoid-s11450" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11451" xml:space="preserve">fig. </s> <s xml:id="echoid-s11452" xml:space="preserve">20.</s> <s xml:id="echoid-s11453" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div386" type="section" level="1" n="386"> <head xml:id="echoid-head496" xml:space="preserve">EXPERIMENTUM XXIV.</head> <p> <s xml:id="echoid-s11454" xml:space="preserve">Spectandum præbuit Lignum Fraxini, cujus medium erat cylin-<lb/>dricum diametri 0, 26 pollicis, hoc appenſis libris 1050 non dif-<lb/>fractum fuit, ſed cylindrus Ligneus extractus ex medio capitis pa-<lb/>rallelopipedi ad longitudinem 4 pollicum, uti in Experimento IV,</s> </p> </div> <div xml:id="echoid-div387" type="section" level="1" n="387"> <head xml:id="echoid-head497" xml:space="preserve">EXPERIMENTVM XXV.</head> <p> <s xml:id="echoid-s11455" xml:space="preserve">Inſtitutum fuit cum Ligno Fraxini, cujus medium erat paralle-<lb/>lopipedum quadrangulare: </s> <s xml:id="echoid-s11456" xml:space="preserve">craſſities cujuslibet lateris fuit 0, 25 <lb/>pollicis, ſuſtinuit libras 1250, tum vero non diffractum fuit, ſed <lb/>parallelopipedum extrahebatur ex capite craſſiori, ad longitudinem <lb/>4 pollicum, uti ſupra.</s> <s xml:id="echoid-s11457" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div388" type="section" level="1" n="388"> <head xml:id="echoid-head498" xml:space="preserve">EXPERIMENTUM XXVI.</head> <p> <s xml:id="echoid-s11458" xml:space="preserve">Sumtum fuit Lignum Piceæ, (vulgo dictum Greynenhout) quod <lb/>in medio parallelopipedum, & </s> <s xml:id="echoid-s11459" xml:space="preserve">cujus quodlibet latus erat 0, 26 <pb o="490" file="0504" n="504" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pollicis, appenſis libris 550 extractum fuit parallelopipedum ex <lb/>capite craſſiori, inſtar gladii ex vagina adlongitudinem {1/2} pollicis, <lb/>ibidemque in theca diffractum fuit.</s> <s xml:id="echoid-s11460" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div389" type="section" level="1" n="389"> <head xml:id="echoid-head499" xml:space="preserve">EXPERIMENTUM XXVII.</head> <p> <s xml:id="echoid-s11461" xml:space="preserve">Lignum Piceæ, (vulgo dictum Greynenhout) in medio cylindri-<lb/>cum diametri 0, 26 pollic. </s> <s xml:id="echoid-s11462" xml:space="preserve">ſuſtinuit libras 850. </s> <s xml:id="echoid-s11463" xml:space="preserve">tum cylindrus, ejus-<lb/>dem craſſi tiei cum medio, extractus fuit ex capite craſſiori ad lon-<lb/>gitudinem 4 pollicum. </s> <s xml:id="echoid-s11464" xml:space="preserve">Examinans accurate Lignum tum hujus, <lb/>tum præcedentis Experimenti, nullam obſervare potui differentiam <lb/>aut in ductu, aut in propinquitate fibrarum Lignum componentium-<lb/>unum tamen altero tenacius videtur fuiſſe, quod unum altero an-<lb/>noſius fuerit.</s> <s xml:id="echoid-s11465" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div390" type="section" level="1" n="390"> <head xml:id="echoid-head500" xml:space="preserve">EXPERIMENTUM XXVIII.</head> <p> <s xml:id="echoid-s11466" xml:space="preserve">Factum fuit cum Pruno, cujus medium cylindricum diametri <lb/>erat 0, 25 pollicis, id diffractum fuit penitus ab appenſis libris 600, <lb/>nequeabiit in longas feſtucas, fracturam exhibet Tab. </s> <s xml:id="echoid-s11467" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11468" xml:space="preserve">fig. </s> <s xml:id="echoid-s11469" xml:space="preserve">21.</s> <s xml:id="echoid-s11470" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div391" type="section" level="1" n="391"> <head xml:id="echoid-head501" xml:space="preserve">EXPERIMENTUM XXIX.</head> <p> <s xml:id="echoid-s11471" xml:space="preserve">Factum fuit cum parallelopipedo ex eodem Ligno Pruni, cujus <lb/>quodlibet latus fuit 0, 25 pollic. </s> <s xml:id="echoid-s11472" xml:space="preserve">diffractum fuit penitus, ſed in craſſiori <lb/>parallelopipedo ad profunditatem 3 linearum, appenſas geſſit libras <lb/>550, in loco rupturæ, nec in toto ligno ulla heterogeneitas ap-<lb/>paruit, neque ulla ratio, ob quam potius in hoc loco quam in ullo <lb/>alio abruptum fuerit.</s> <s xml:id="echoid-s11473" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div392" type="section" level="1" n="392"> <head xml:id="echoid-head502" xml:space="preserve">EXPERIMENTUM XXX.</head> <p> <s xml:id="echoid-s11474" xml:space="preserve">Huic inſerviit Lignum Pomi, in medio cylindricum, & </s> <s xml:id="echoid-s11475" xml:space="preserve">diame-<lb/>tri 0, 25 pollicis, hoc transverſe penitus diffractum fuit a libris <lb/>500; </s> <s xml:id="echoid-s11476" xml:space="preserve">non abeundo in feſtucas, fracturam vide in Tab. </s> <s xml:id="echoid-s11477" xml:space="preserve">XXI. <lb/></s> <s xml:id="echoid-s11478" xml:space="preserve">fig. </s> <s xml:id="echoid-s11479" xml:space="preserve">22.</s> <s xml:id="echoid-s11480" xml:space="preserve"/> </p> <pb o="491" file="0505" n="505" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div393" type="section" level="1" n="393"> <head xml:id="echoid-head503" xml:space="preserve">EXPERIMENTUM XXXI.</head> <p> <s xml:id="echoid-s11481" xml:space="preserve">Lignum Pomi, cujus medium parallelopipedum, & </s> <s xml:id="echoid-s11482" xml:space="preserve">quod <lb/>libet latus erat 0, 25 pollicis, diffractum fuit a libris 550, <lb/>abiitque in oblongam feſtucam, proſtat fractura in Tab. </s> <s xml:id="echoid-s11483" xml:space="preserve">XXII. <lb/></s> <s xml:id="echoid-s11484" xml:space="preserve">fig. </s> <s xml:id="echoid-s11485" xml:space="preserve">23.</s> <s xml:id="echoid-s11486" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div394" type="section" level="1" n="394"> <head xml:id="echoid-head504" xml:space="preserve">EXPERIMENTUM XXXII.</head> <p> <s xml:id="echoid-s11487" xml:space="preserve">Inſtitutum fuit cum Ligno, quod colore, denſitate, ductu fibra-<lb/>rum Nuci eſt ſimillimum, in quo ex America Sacharum affertur, un-<lb/>de a noſtratibus vocatur Suyker kiſtenhout, hoc in medio cylin-<lb/>dricum, diametri 0, 25 pollicis, diffractum fuit a libris 700, abeun-<lb/>do in feſtucam oblongam, quam Tab. </s> <s xml:id="echoid-s11488" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11489" xml:space="preserve">fig. </s> <s xml:id="echoid-s11490" xml:space="preserve">24 repræſentat, <lb/>non autem hic cylindrus accurate ſecundum ductum fibrarum for-<lb/>matus fuit, cæteroquin multo tenacior fuiſſet, uti conſtabit ex Ex-<lb/>perimento ſequenti.</s> <s xml:id="echoid-s11491" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div395" type="section" level="1" n="395"> <head xml:id="echoid-head505" xml:space="preserve">EXPERIMENTUM XXXIII.</head> <p> <s xml:id="echoid-s11492" xml:space="preserve">Ex Ligno eodem, quocum Experimentum XXXII. </s> <s xml:id="echoid-s11493" xml:space="preserve">factum fuit, <lb/>paratum eſt parallelopipedum cujus quodlibet latus fuit 0, 26 polli-<lb/>cis, hoc ſuſtinuit libras 1500. </s> <s xml:id="echoid-s11494" xml:space="preserve">fuitque rupturæ proximum.</s> <s xml:id="echoid-s11495" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div396" type="section" level="1" n="396"> <head xml:id="echoid-head506" xml:space="preserve">EXPERIMENTUM XXXIV.</head> <p> <s xml:id="echoid-s11496" xml:space="preserve">Lignum Meſpili, cujus medium erat parallelopipedum, cujus quod-<lb/>libet latus 0, 26 pollicis, diffractum fuit penitus a libris 650, abeun-<lb/>do in feſtucam oblongam aſperamque Tab. </s> <s xml:id="echoid-s11497" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11498" xml:space="preserve">fig. </s> <s xml:id="echoid-s11499" xml:space="preserve">25.</s> <s xml:id="echoid-s11500" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div397" type="section" level="1" n="397"> <head xml:id="echoid-head507" xml:space="preserve">EXPERIMENTUM XXXV.</head> <p> <s xml:id="echoid-s11501" xml:space="preserve">Lignum Meſpili cujus medium erat cylindrum diametri 0, 26 <lb/>pollicis, ſuſtinuit libras 700, tum vero diffractum abiit in feſtu-<lb/>cam oblongam aſperam, pictam in Tab. </s> <s xml:id="echoid-s11502" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11503" xml:space="preserve">fig. </s> <s xml:id="echoid-s11504" xml:space="preserve">26.</s> <s xml:id="echoid-s11505" xml:space="preserve"/> </p> <pb o="492" file="0506" n="506" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div398" type="section" level="1" n="398"> <head xml:id="echoid-head508" xml:space="preserve">EXPERIMENTUM XXXVI.</head> <p> <s xml:id="echoid-s11506" xml:space="preserve">Confectum fuit ex Ligno Guajaci vel Sancto parallelopipedum <lb/>quadrangulum, cujus quodlibet latus fuit 0, 25 pollicis, diffractum <lb/>fuit penitus ab appenſis libris 855. </s> <s xml:id="echoid-s11507" xml:space="preserve">abiitque fractura in ſpinam aſpe-<lb/>ram. </s> <s xml:id="echoid-s11508" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11509" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11510" xml:space="preserve">fig. </s> <s xml:id="echoid-s11511" xml:space="preserve">27.</s> <s xml:id="echoid-s11512" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div399" type="section" level="1" n="399"> <head xml:id="echoid-head509" xml:space="preserve">EXPERIMENTUM XXXVII.</head> <p> <s xml:id="echoid-s11513" xml:space="preserve">Factum fuit cum Ceraſi nigri Ligno, cylindrico in medio, dia-<lb/>metri 0, 25 pollicis, quod ſuſtinuit libras 950, nec diffractum fuit, <lb/>ſed extractus cylindrus ex reliquo craſſiori capite, 4 pollices lon-<lb/>gus; </s> <s xml:id="echoid-s11514" xml:space="preserve">fuit hoc Lignum vix venoſum; </s> <s xml:id="echoid-s11515" xml:space="preserve">ſed uniformis admodum con-<lb/>ſiſtentiæ.</s> <s xml:id="echoid-s11516" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div400" type="section" level="1" n="400"> <head xml:id="echoid-head510" xml:space="preserve">EXPERIMENTUM XXXVIII.</head> <p> <s xml:id="echoid-s11517" xml:space="preserve">Ceraſi nigri aliud lignum, multis fibris & </s> <s xml:id="echoid-s11518" xml:space="preserve">colore variegatum ex <lb/>alia arbore captum fuit, hoc in medio erat parallelopipedum qua-<lb/>drangulare, cujus quodlibet latus fuit 0, 25 pollicis, diffractum <lb/>fuit penitus a libris 400 in feſtucam longam abeundo. </s> <s xml:id="echoid-s11519" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11520" xml:space="preserve">XXII. <lb/></s> <s xml:id="echoid-s11521" xml:space="preserve">fig. </s> <s xml:id="echoid-s11522" xml:space="preserve">28.</s> <s xml:id="echoid-s11523" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div401" type="section" level="1" n="401"> <head xml:id="echoid-head511" xml:space="preserve">EXPERIMENTUM XXXIX.</head> <p> <s xml:id="echoid-s11524" xml:space="preserve">Spectandum exhibuit Lignum Oxyacanthæ in medio Cylindri-<lb/>cum, cujus diameter fuit 0, 25 pollicis, ſuſtinuit libras 1000, a <lb/>quibus diffractum abiit in feſtucas valde aſperas, non tamen lon-<lb/>gas, depictas in Tab. </s> <s xml:id="echoid-s11525" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11526" xml:space="preserve">fig. </s> <s xml:id="echoid-s11527" xml:space="preserve">29.</s> <s xml:id="echoid-s11528" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div402" type="section" level="1" n="402"> <head xml:id="echoid-head512" xml:space="preserve">EXPERIMENTUM XL.</head> <p> <s xml:id="echoid-s11529" xml:space="preserve">Factum fuit cum parallelopipedo ejusdem Ligni Oxyacanthæ, <lb/>cujus quodlibet latus fuit 0, 25 pollicis, ab appenſis libris 900 <lb/>diffractum fuit, fracturæ ſuperficiem exhibet Tab. </s> <s xml:id="echoid-s11530" xml:space="preserve">XXII. </s> <s xml:id="echoid-s11531" xml:space="preserve">fig. </s> <s xml:id="echoid-s11532" xml:space="preserve">30.</s> <s xml:id="echoid-s11533" xml:space="preserve"/> </p> <pb o="493" file="0507" n="507" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div403" type="section" level="1" n="403"> <head xml:id="echoid-head513" xml:space="preserve">EXPERIMENTUM XLI.</head> <p> <s xml:id="echoid-s11534" xml:space="preserve">Lignum Ceraſi vulgaris, in medio cylindricum, diametri 0, 25 <lb/>pollicis ſuſtinuit libras 650, a quibus cylindrus non fuit diffractus, <lb/>ſed per medium uſque ad extremitatem capitis craſſioris fiſſus, <lb/>tum aucto pondere craſſius divulſum, vide Tab. </s> <s xml:id="echoid-s11535" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s11536" xml:space="preserve">fig. </s> <s xml:id="echoid-s11537" xml:space="preserve">32.</s> <s xml:id="echoid-s11538" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div404" type="section" level="1" n="404"> <head xml:id="echoid-head514" xml:space="preserve">EXPERIMENTUM XLII.</head> <p> <s xml:id="echoid-s11539" xml:space="preserve">Electum fuit Lignum rubri coloris, admodum ſolidum, quod <lb/>ex America affertur, & </s> <s xml:id="echoid-s11540" xml:space="preserve">a Belgis vocatur Caro Equina, propter <lb/>colorem, hujus medium erat parallelopipedum quadrangulum, cu-<lb/>jus quodlibet latus fuit 0, 25 pollicis, ſuſtinuit libras 1300, tum <lb/>autem tenuius parallelopipedum non diffractum fuit, ſed craſſior <lb/>pars oblique avulſa uſque ad extremitatem capitis. </s> <s xml:id="echoid-s11541" xml:space="preserve">vide Tab. </s> <s xml:id="echoid-s11542" xml:space="preserve">XXII. <lb/></s> <s xml:id="echoid-s11543" xml:space="preserve">fig. </s> <s xml:id="echoid-s11544" xml:space="preserve">31.</s> <s xml:id="echoid-s11545" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div405" type="section" level="1" n="405"> <head xml:id="echoid-head515" xml:space="preserve">EXPERIMENTUM XLIII.</head> <p> <s xml:id="echoid-s11546" xml:space="preserve">Factum fuit cum Ligno Americano, (a Belgis vocato Sakker-<lb/>daane) quod in medio parallelopipedum, cujus quodlibet latus <lb/>0, 25 pollicis ſuſtinuit libras 1350, tum non quidem diffractum fuit, <lb/>ſed ſpecies parallelopipedi latioris extracta ex craſſiori capite uſ-<lb/>que ad foramen, & </s> <s xml:id="echoid-s11547" xml:space="preserve">longitudinis 4 pollicum.</s> <s xml:id="echoid-s11548" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div406" type="section" level="1" n="406"> <head xml:id="echoid-head516" xml:space="preserve">EXPERIMENTUM XLIV.</head> <p> <s xml:id="echoid-s11549" xml:space="preserve">Lignum Americanum, (quod vocatur Granadille) elegantiſſime <lb/>fibris variegatum, cujus medium cylindricum diametri 0, 25 polli-<lb/>cis ſuſtinuit libras 950, â quibus tamen penitus diffractum fuit ab-<lb/>eundo in feſtucam oblongam aſperamque. </s> <s xml:id="echoid-s11550" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11551" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s11552" xml:space="preserve">fig. </s> <s xml:id="echoid-s11553" xml:space="preserve">33.</s> <s xml:id="echoid-s11554" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div407" type="section" level="1" n="407"> <head xml:id="echoid-head517" xml:space="preserve">EXPERIMENTUM XLV.</head> <p> <s xml:id="echoid-s11555" xml:space="preserve">Lignum idem Granadille in medio formatum in parallelopipedum <lb/>quadrangulum, cujus quodlibet latus fuit 0, 25 pollicis, hoc a libris <lb/>800 diffractum fuit p enitus in oblongam abeundo feſtucam. </s> <s xml:id="echoid-s11556" xml:space="preserve">Tab. <lb/></s> <s xml:id="echoid-s11557" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s11558" xml:space="preserve">fig. </s> <s xml:id="echoid-s11559" xml:space="preserve">34.</s> <s xml:id="echoid-s11560" xml:space="preserve"/> </p> <pb o="494" file="0508" n="508" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div408" type="section" level="1" n="408"> <head xml:id="echoid-head518" xml:space="preserve">EXPERIMENTUM XLVI.</head> <p> <s xml:id="echoid-s11561" xml:space="preserve">Santalum rubrum, in medio parallelopipedum quadrangulum <lb/>cujus quodlibet latus o, 25 pollicis, a libris 600 appenſis non dif-<lb/>fractum fuit, ſed ſpecies parallelopipedi extrahebatur ex <lb/>medio capitis craſſioris, quod findebatur.</s> <s xml:id="echoid-s11562" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div409" type="section" level="1" n="409"> <head xml:id="echoid-head519" xml:space="preserve">EXPERIMENTUM XLVII.</head> <p> <s xml:id="echoid-s11563" xml:space="preserve">Factum fuit cum parallelopipedo Ligni Ebeni, cujus quodlibet <lb/>latus fuit 0, 25 pollicis, hoc penitus diffractum fuit a libris 800 in <lb/>oblongam abeundo feſtucam, pictam in Tab. </s> <s xml:id="echoid-s11564" xml:space="preserve">XXIII fig. </s> <s xml:id="echoid-s11565" xml:space="preserve">35.</s> <s xml:id="echoid-s11566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11567" xml:space="preserve">Sunt hæc omnia Experimenta, quæ cum Lignis diverſis inſti-<lb/>tui, eodem modo explorari poſſunt reliqua omnia, ſi abſoluta re-<lb/>ſiſtentia eorum deſideratur: </s> <s xml:id="echoid-s11568" xml:space="preserve">Fuerunt hæc capta ſatis ſollicite, non <lb/>tamen dubito, quin ſi repetantur, aliquando diverſiſſimum eventum <lb/>exhibitura ſint: </s> <s xml:id="echoid-s11569" xml:space="preserve">nam prout Lignum in ſolo magis minusve aquoſo, <lb/>paludoſo, oleoſo, ſalſo concreverit, eo plus minusve tenax erit: <lb/></s> <s xml:id="echoid-s11570" xml:space="preserve">prout in regione calidiori frigidiorive plantatum fuerit, eo etiam <lb/>plus minusve cohærebit: </s> <s xml:id="echoid-s11571" xml:space="preserve">prout annoſior truncus, teneriorve ramus <lb/>fuerit, ex quo præparatur id, quod experimento inſerviet, eo rigi-<lb/>dius flexiliusve erit Lignum, ſive fortius debiliusve: </s> <s xml:id="echoid-s11572" xml:space="preserve">prout eligitur <lb/>Lignum fibris quam rectiſſimis, aut flexuoſis concretum, iterum <lb/>Cohærentia diverſa obſervabitur: </s> <s xml:id="echoid-s11573" xml:space="preserve">quod ſemel monuiſſe ſufficit.</s> <s xml:id="echoid-s11574" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div410" type="section" level="1" n="410"> <head xml:id="echoid-head520" xml:space="preserve">CAPUT TERTIUM.</head> <head xml:id="echoid-head521" style="it" xml:space="preserve">De Cohærentia Abſoluta Metallorum.</head> <p> <s xml:id="echoid-s11575" xml:space="preserve">Ut Metallorum firmitatem explorarem, confici ex iis curavi fi-<lb/>la cylindrica, ex quolibet Metallo quatuor, quorum diver-<lb/>ſa erat craſſities, ut non modo detegerem Cohærentiam Metalli <lb/>ſub craſſitie illius fili, ſed ſimul cognoſcerem an Metallorum firmi-<lb/>tas in ratione craſſitierum foret, an filum nempe duplo craſſius al-<lb/>tero, ex eodem præparatum Metallo, duplo majori firmitate gau- <pb o="495" file="0509" n="509" rhead="CORPORUM FIRMORUM."/> deret: </s> <s xml:id="echoid-s11576" xml:space="preserve">Supervacaneus videbitur Geometris noſter labor, imptimis <lb/>cum demonſtravimus in Propoſitione VIII. </s> <s xml:id="echoid-s11577" xml:space="preserve">duorum corporum cylin-<lb/>dricorum ejusdem materiæ, diverſam craſſitiem habentium, Cohæ-<lb/>rentiam fore in ratione craſſitierum: </s> <s xml:id="echoid-s11578" xml:space="preserve">quod veriſſimum eſt, & </s> <s xml:id="echoid-s11579" xml:space="preserve">in-<lb/>ſtar Axiomatis ponendum, ſi corpora, quibus vis infertur, ut fran-<lb/>gantur, maneant æque craſſa; </s> <s xml:id="echoid-s11580" xml:space="preserve">ſed an ea, quæ cedunt interim ob <lb/>flexilitatem, & </s> <s xml:id="echoid-s11581" xml:space="preserve">attenuantur, qualia ſunt Metalla, eidem Legi ſub-<lb/>jiciantur, mihi non ſatis liquido conſtabat; </s> <s xml:id="echoid-s11582" xml:space="preserve">de eo dubitaſſe poſtea <lb/>non pœnituit, cum Experientia evicerit, hic aliquid latere, acceden-<lb/>te Cohærentia quidem utcunque ad craſſitierum proportionem, non <lb/>tamen accurate. </s> <s xml:id="echoid-s11583" xml:space="preserve">Verum prius apparatum Experimentorum exacte <lb/>deſcribam: </s> <s xml:id="echoid-s11584" xml:space="preserve">Præparata fuerunt ex quolibet Metallo fila quatuor, <lb/>craſſiſſimi diameter erat {1/10} pollicis Rhenolandici, hoc in poſte-<lb/>rum inſigniam littera A. </s> <s xml:id="echoid-s11585" xml:space="preserve">Secundum, cujus craſſities minor erat, <lb/>habebat baſin vel craſſitiem, quæ ad eam in A fuit exacte uti 3 ad <lb/>4 hanc craſſitiem vocabo B. </s> <s xml:id="echoid-s11586" xml:space="preserve">Tertii fili craſſities ſive baſis erat ad <lb/>eam B uti 2 ad 3. </s> <s xml:id="echoid-s11587" xml:space="preserve">hanc craſſitiem vocabo C. </s> <s xml:id="echoid-s11588" xml:space="preserve">Quarti fili craſſities <lb/>erat ad eam C uti 1 and 2. </s> <s xml:id="echoid-s11589" xml:space="preserve">hanc vocabo D. </s> <s xml:id="echoid-s11590" xml:space="preserve">erant igitur baſes, ſive <lb/>craſſities filorum, uti 4, 3, 2, 1.</s> <s xml:id="echoid-s11591" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11592" xml:space="preserve">Fila omnia craſſitiei A ducta fuerunt per idem foramen lamellæ <lb/>indurati Chalybis inflictum, ut accuratiſſime forent æque craſſa: <lb/></s> <s xml:id="echoid-s11593" xml:space="preserve">ita per aliud foramen ducta fuerunt fila omnia B. </s> <s xml:id="echoid-s11594" xml:space="preserve">per aliud omnia <lb/>C. </s> <s xml:id="echoid-s11595" xml:space="preserve">per aliud omnia D.</s> <s xml:id="echoid-s11596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11597" xml:space="preserve">Quoniam omnia Metalla majorem rigiditatem acquirunt cum ita <lb/>ducuntur per hæc foramina, igni carbonum ligneorum puriſſimo-<lb/>rum immitebantur Aurum, Argentum, Cuprum, Ferrum, & </s> <s xml:id="echoid-s11598" xml:space="preserve">le-<lb/>viter candefacta, emollita fuerunt tam æquabiliter quantum fieri po-<lb/>teſt, cavendo ſimul ne ſuperficies ſcorias contraheret, atque ita te-<lb/>nuius fieret filum: </s> <s xml:id="echoid-s11599" xml:space="preserve">ut hæc ope Machinæ divulſoriæ examinaren-<lb/>tur, confecti fuerunt duo ferrei unci. </s> <s xml:id="echoid-s11600" xml:space="preserve">Tab. </s> <s xml:id="echoid-s11601" xml:space="preserve">XX. </s> <s xml:id="echoid-s11602" xml:space="preserve">fig. </s> <s xml:id="echoid-s11603" xml:space="preserve">3. </s> <s xml:id="echoid-s11604" xml:space="preserve">plusquam <lb/>duplo longiores & </s> <s xml:id="echoid-s11605" xml:space="preserve">craſſiores quam hic depinguntur, quorum capi-<lb/>tibus A, B inflicta erant foramina quadrata, quibus conveniebant <lb/>pinnæ fieret, formæ & </s> <s xml:id="echoid-s11606" xml:space="preserve">magnitudinis ac una proſtat in Tab. </s> <s xml:id="echoid-s11607" xml:space="preserve">XX. <lb/></s> <s xml:id="echoid-s11608" xml:space="preserve">fig. </s> <s xml:id="echoid-s11609" xml:space="preserve">4. </s> <s xml:id="echoid-s11610" xml:space="preserve">in medio erat cylindrica & </s> <s xml:id="echoid-s11611" xml:space="preserve">polita, circa quam partem fi-<lb/>lum metallicum circumvolvendum fuit, eratque ad latus pertuſum <lb/>foramine K, per quod filum transmittebatur, ut melius figi poſſet, <pb o="496" file="0510" n="510" rhead="INTRODUCTIO AD COHÆRENTIAM"/> quod eſt maxime neceſſarium, cæteroquin enim filum circumvol-<lb/>tur, licet aliquoties circumductum, circum ſuperficiem rotun-<lb/>dam cum ipſi pondus appenditur: </s> <s xml:id="echoid-s11612" xml:space="preserve">in E & </s> <s xml:id="echoid-s11613" xml:space="preserve">D ſunt partes quadrangu-<lb/>lares, quæ congruunt foraminibus quadratis inſculptis uncis, <lb/>hoc factum fuit ne pinna circumvolveretur in unco: </s> <s xml:id="echoid-s11614" xml:space="preserve">Caput C qua-<lb/>drangulum eſt, ut ope clavis circumverti poſſit pinna in un-<lb/>co, filumque circumduci metallicum: </s> <s xml:id="echoid-s11615" xml:space="preserve">quando autem circum-<lb/>vertitur pars D, paulum trahitur extra foramen unci B, tum enim <lb/>in foraminibus quadratis unci A & </s> <s xml:id="echoid-s11616" xml:space="preserve">B partes cylindricæ K & </s> <s xml:id="echoid-s11617" xml:space="preserve">F hu-<lb/>jus pinnæ jacent, quo modo commode filum metallicum ſupra fu-<lb/>ſum hoc quaſi ducitur. </s> <s xml:id="echoid-s11618" xml:space="preserve">Altera pinnæ extremitas F oblongo fora-<lb/>mine donata eſt, ut ope clavi P poſſit in uncis firmari. </s> <s xml:id="echoid-s11619" xml:space="preserve">Totus appara-<lb/>tus cum filo, aliquoties circum utramque pinnam circumducto, repræ-<lb/>ſentatur in Tab. </s> <s xml:id="echoid-s11620" xml:space="preserve">XX. </s> <s xml:id="echoid-s11621" xml:space="preserve">fig. </s> <s xml:id="echoid-s11622" xml:space="preserve">3. </s> <s xml:id="echoid-s11623" xml:space="preserve">atque eo modo Machinæ divulſoriæ fuit <lb/>applicatus, quemadmodum antea Ligna examinata: </s> <s xml:id="echoid-s11624" xml:space="preserve">pondus unius <lb/>cujusque unci fuit {3/4} libræ, quod cum uni extremitati ſtateræ appen-<lb/>debatur a reliquo pondere in ſtatera notato ſubducendum erat, ut <lb/>verum pondus, Cohærentiæ filorum æquale, haberetur: </s> <s xml:id="echoid-s11625" xml:space="preserve">Quibus <lb/>præmiſſis ad Experimentorum eventus accedam.</s> <s xml:id="echoid-s11626" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div411" type="section" level="1" n="411"> <head xml:id="echoid-head522" xml:space="preserve">EXPERIMENTUM XLVIII.</head> <p> <s xml:id="echoid-s11627" xml:space="preserve">Filum cylindricum craſſitiei A, Cupri rubri Suecici, per totam <lb/>ſuam longitudinem bene ſolidum & </s> <s xml:id="echoid-s11628" xml:space="preserve">abſque fiſſuris, rimis, aut inæquali-<lb/>tatibus, in igne adeo molle, ac fieri poteſt, redditum, ſuſtinuit tractum <lb/>perpendiculariter libr. </s> <s xml:id="echoid-s11629" xml:space="preserve">299 {1/4}, a quibus tamen rumpebatur, filum inter <lb/>medios uncos tenſum ab appenſo pondere attenuabatur interim eo <lb/>plus, quo plus ponderis applicabatur, unde diameter ejus, poſtquam <lb/>ruptum fuit, deprehendebatur {9/10} lineæ, quæ antea fuerat {18/10} li-<lb/>neæ: </s> <s xml:id="echoid-s11630" xml:space="preserve">præterea ſuperficies fracturæ fuit admodum aſpera & </s> <s xml:id="echoid-s11631" xml:space="preserve">trans-<lb/>verſa, ſed prope fracturam cylindrus abierat in ſpeciem coni trunca-<lb/>ti, longitudinis unius lineæ, diameter fracturæ fuit {7/10} lineæ.</s> <s xml:id="echoid-s11632" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div412" type="section" level="1" n="412"> <head xml:id="echoid-head523" xml:space="preserve">EXPERIMENTUM XLIX.</head> <p> <s xml:id="echoid-s11633" xml:space="preserve">Filum Cylindricum craſſitiei B, Cupri ejuſdem, ſuſtinuit plus <pb o="497" file="0511" n="511" rhead="CORPORUM FIRMORUM."/> quam libras 190, minus quam 200, antequam rumpebatur atte-<lb/>nuatum fuit, ita ut diametrum habuerit 0, 08 pollicis, prope fracturam <lb/>induit formam coni truncati ſuperficies fracturæ fuit obliqua, <lb/>etiamſi transverſa, paulum elliptica, ejusque diametri erant proxime <lb/>0, 075 pollicis, non enim abſolute diametros determinare poteram.</s> <s xml:id="echoid-s11634" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div413" type="section" level="1" n="413"> <head xml:id="echoid-head524" xml:space="preserve">EXPERIMENTUM L.</head> <p> <s xml:id="echoid-s11635" xml:space="preserve">Filum Cylindricum craſſitiei C, Cupri ejuſdem rubri, ruptum <lb/>fuit a libris 129 {1/4}, multum elongatum fuit antequam rumpebatur, <lb/>unde quoque ſimul attenuatum, ut acceperit diametrum 0, 06 pollicis, <lb/>fracturæ diameter tamen modo fuit 0, 04 pollicis, nam a fractura <lb/>ad diſtantiam unius lineæ conus truncatus formatus fuit.</s> <s xml:id="echoid-s11636" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div414" type="section" level="1" n="414"> <head xml:id="echoid-head525" xml:space="preserve">EXPERIMENTUM LI.</head> <p> <s xml:id="echoid-s11637" xml:space="preserve">Filum ejuſdem Cupri rubri craſſitiei D, ruptum fuit ab appenſis <lb/>ſenſim libris 79 {1/4}, elongatum interim & </s> <s xml:id="echoid-s11638" xml:space="preserve">attenuatum fuit, ut modo <lb/>retinuerit diametrum 0, 0 45 pollicis, diameter fracturæ modo fuit <lb/>0, 03 pollicis, nam ad diſtantiam unius lineæ â fractura abierat <lb/>in conum truncatum.</s> <s xml:id="echoid-s11639" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11640" xml:space="preserve">In his quatuor Experimentis præterea notandum, hæc fila non rupta <lb/>fuiſſe in loco aliquo medio inter ambos uncos, ſed ſemper ubiattige-<lb/>gerant ſty lum ſive pinnam ferream, circa quam circumvoluta fue-<lb/>rant, erantque ob preſſionem contra eandem paulum applanata.</s> <s xml:id="echoid-s11641" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11642" xml:space="preserve">Examinemus nunc an Cohærentiæ filorum fuerint accurate in <lb/>ratione craſſitierum ante inſtitutum Experimentum, an in ratione <lb/>craſſitierum poſt inſtitutum Experimentum, an in ratione magni-<lb/>tudinis fracturæ?</s> <s xml:id="echoid-s11643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11644" xml:space="preserve">Si Cohærentiæ eſſent in ratione craſſitierum ante Experimentum, <lb/>debuiſſent eſſe hæ, pro A 299 {1/4}. </s> <s xml:id="echoid-s11645" xml:space="preserve">pro B 224 {7/16}. </s> <s xml:id="echoid-s11646" xml:space="preserve">pro C 149 {5/8}. </s> <s xml:id="echoid-s11647" xml:space="preserve">pro D 74 {13/16}.</s> <s xml:id="echoid-s11648" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11649" xml:space="preserve">Si in ratione craſſitierum poſt Experimentum, fuiſſent hæ, pro <lb/>A 299 {1/4}. </s> <s xml:id="echoid-s11650" xml:space="preserve">pro B 236 {4/9}. </s> <s xml:id="echoid-s11651" xml:space="preserve">pro C 133. </s> <s xml:id="echoid-s11652" xml:space="preserve">pro D 74 {1113/1296}. </s> <s xml:id="echoid-s11653" xml:space="preserve">magnitudines fractu-<lb/>rarum conſiderari nequeunt, cum fractura fili B major fuerit quam <lb/>A, adeoque B plus ponderis geſtare debuiſſet, tenuius fuiſſet te-<lb/>nacius craſſiori, quod eſt abſurdum: </s> <s xml:id="echoid-s11654" xml:space="preserve">Verum ambæ proportiones <pb o="498" file="0512" n="512" rhead="INTRODUCTIO AD COHÆRENTIAM"/> abludunt ab Experimentis, aliquando calculus majorem indicat fo-<lb/>re Cohærentiam quam fuit obſervata; </s> <s xml:id="echoid-s11655" xml:space="preserve">aliquando minorem ſuppe-<lb/>dat: </s> <s xml:id="echoid-s11656" xml:space="preserve">arbitror hoc evenire, quia Metallum non eſt adeo homoge-<lb/>neum, quam nudo viſui apparet, ſed conſtat hinc inde partibus <lb/>magis minusve cohærentibus, vel quoniam hinc inde plus Sulphu-<lb/>ris, Salis, aut Mercurii poſitum eſt, quod impedit quominus <lb/>æquabilis firmitas detur; </s> <s xml:id="echoid-s11657" xml:space="preserve">adeoque ex hiſce Experimentis diſcimus, <lb/>Cohærentiam Cupri non ſequi accurate craſſitiem, unde ſi de-<lb/>ſideretur Machina quæcunque ex hoc Metallo, ex qua data <lb/>gravitas eſt ſuſpendenda, craſſius ſumendum erit Metallum, quam <lb/>calculus indicaret. </s> <s xml:id="echoid-s11658" xml:space="preserve">veluti ſi pondus 10000 librar. </s> <s xml:id="echoid-s11659" xml:space="preserve">ſuſpendendum fo-<lb/>ret ex filo Cupreo, ope calculi determinaretur fili craſſities, quæ <lb/>eſſet proxime æqualis 34 lineis cylindricis, ſed obſervata Cohæ-<lb/>rentiæ inæqualitate filum craſſius ſumendum eſſet, quod ſi foret <lb/>40 linearum cylindricarum, tuto pondus datum abſque rupturæ me-<lb/>tu geſtaret.</s> <s xml:id="echoid-s11660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11661" xml:space="preserve">Ex comparatis tamen aliorum Metallorum Cohærentiis videtur <lb/>colligendum, potius attendendum eſſe ad craſſitiem filorum ante <lb/>inſtitutum Experimentum, quam ad eam poſtea relictam, quia <lb/>proportiones eventuum propius ad illas craſſities appropinquant, <lb/>quam ad has.</s> <s xml:id="echoid-s11662" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div415" type="section" level="1" n="415"> <head xml:id="echoid-head526" xml:space="preserve">EXPERIMENTUM LII.</head> <p> <s xml:id="echoid-s11663" xml:space="preserve">Filum craſſitiei A ex Orichalco, ſive Cupro Calaminari ab ap-<lb/>penſis lente & </s> <s xml:id="echoid-s11664" xml:space="preserve">ſucceſſive libris 360. </s> <s xml:id="echoid-s11665" xml:space="preserve">fractum fuit; </s> <s xml:id="echoid-s11666" xml:space="preserve">antequam rum-<lb/>pebatur fuit plurimum elongatum & </s> <s xml:id="echoid-s11667" xml:space="preserve">attenuatum, ut modo reti-<lb/>nuerit diametrum 0, 08 pollicis, ſuperficies fracturæ fuit admodum <lb/>aſpera & </s> <s xml:id="echoid-s11668" xml:space="preserve">inæqualis, diametri 0, 075 pollicis, pars anterior abierat <lb/>quidem in conum, ſed vix viſibilem.</s> <s xml:id="echoid-s11669" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div416" type="section" level="1" n="416"> <head xml:id="echoid-head527" xml:space="preserve">EXPERIMENTUM LIII.</head> <p> <s xml:id="echoid-s11670" xml:space="preserve">Filum ex Orichalco craſſitiei B, fractum fuit â libris 260; </s> <s xml:id="echoid-s11671" xml:space="preserve">an-<lb/>tequam frangebatur, valde elongatum fuit, unde fracturâ factâ erat <lb/>modo craſſities 0, 07 pollicis in diametro; </s> <s xml:id="echoid-s11672" xml:space="preserve">fracturæ aſperæ diameter <pb o="499" file="0513" n="513" rhead="CORPORUM FIRMORUM."/> obſervabatur 0, 05 pollicis inceperatque filum ad diſtantiam unius li-<lb/>neæ â fractura in conum abire, vix conſpicuum.</s> <s xml:id="echoid-s11673" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div417" type="section" level="1" n="417"> <head xml:id="echoid-head528" xml:space="preserve">EXPERIMENTUM LIV.</head> <p> <s xml:id="echoid-s11674" xml:space="preserve">Filum Orichalci craſſitiei C diſſolutum fuit a libris 180, multum <lb/>quoque attenuatum & </s> <s xml:id="echoid-s11675" xml:space="preserve">elongatum, ut diametrum acceperit 0, 05 <lb/>pollicis: </s> <s xml:id="echoid-s11676" xml:space="preserve">aſperæ fracturæ ſuperficies habebat diametrum 0, 04 pollicis <lb/>abieratque ad diſtantiam {3/4} lineæ a fractura in ſpeciem Coni.</s> <s xml:id="echoid-s11677" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div418" type="section" level="1" n="418"> <head xml:id="echoid-head529" xml:space="preserve">EXPERIMENTUM LV.</head> <p> <s xml:id="echoid-s11678" xml:space="preserve">Filum Orichalci craſſitiei D diſſolutum fuit a libris 112, interim <lb/>multum elongatum, ita ut modo retinuerit diametrum 0, 04 pollicis, <lb/>ſuperficies fracturæ fuit 0, 03 pollicis, abierat enim ad diſtantiam {1/2} <lb/>lineæ â fractura in conum, ſed parum conſpicuum.</s> <s xml:id="echoid-s11679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11680" xml:space="preserve">Si ſecundum craſſities ante Experimentum Cohærentiæ ſeſe ha-<lb/>buiſſent, obſervatæ forent æquales 360 pro A. </s> <s xml:id="echoid-s11681" xml:space="preserve">270 pro B. </s> <s xml:id="echoid-s11682" xml:space="preserve">180 pro <lb/>C. </s> <s xml:id="echoid-s11683" xml:space="preserve">90 pro D. </s> <s xml:id="echoid-s11684" xml:space="preserve">quæ aberratio ab obſervationibus veris eſt multo mi-<lb/>nor, quam ſi ad craſſities poſt Experimenta attendamus, nam tum <lb/>forent pro A 360. </s> <s xml:id="echoid-s11685" xml:space="preserve">pro B 275 {5/8}. </s> <s xml:id="echoid-s11686" xml:space="preserve">pro C 140 {5/8}. </s> <s xml:id="echoid-s11687" xml:space="preserve">pro D 90.</s> <s xml:id="echoid-s11688" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div419" type="section" level="1" n="419"> <head xml:id="echoid-head530" xml:space="preserve">EXPERI MENTUM LVI.</head> <p> <s xml:id="echoid-s11689" xml:space="preserve">Quatuor ſequentia Experimenta facta ſunt cum filis ex Auro Pis-<lb/>tolettarum compoſitis.</s> <s xml:id="echoid-s11690" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11691" xml:space="preserve">Filum Aureum craſſitiei A a’libris 500 ſucceſſive appoſitis ruptum <lb/>fuit: </s> <s xml:id="echoid-s11692" xml:space="preserve">antequam frangebatur non multum elongatum aut attenua-<lb/>tum fuit, nam poſt fracturam retinuit diametrum 0, 095 pollicis: </s> <s xml:id="echoid-s11693" xml:space="preserve">fra-<lb/>ctura fuit valde aſpera diametri 0, 09 pollicis, nam ad diſtantiam <lb/>unius lineæ a fractura abierat in conicam formam, vix tamen ab <lb/>oculo diſtinguendam.</s> <s xml:id="echoid-s11694" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div420" type="section" level="1" n="420"> <head xml:id="echoid-head531" xml:space="preserve">EXPERIMENTUM LVII.</head> <p> <s xml:id="echoid-s11695" xml:space="preserve">Filum Aureum craſſitiei B ab appenſis ſenſim libris 350. </s> <s xml:id="echoid-s11696" xml:space="preserve">frange-<lb/>batur, elongatum & </s> <s xml:id="echoid-s11697" xml:space="preserve">attenuatum fuit, ut acceperit diametrum 0, 08 <pb o="500" file="0514" n="514" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pollicis, fractura fuit admodum aſpera, diametri 0, 065 pollicis, at-<lb/>que, addiſtantiam unius lineæ a fractura, acceperat filum coni trun-<lb/>cati figuram.</s> <s xml:id="echoid-s11698" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div421" type="section" level="1" n="421"> <head xml:id="echoid-head532" xml:space="preserve">EXPERIMENTUM LIX.</head> <p> <s xml:id="echoid-s11699" xml:space="preserve">Filum Aureum craſſitiei C diffractum fuit ab appenſis libris 240, <lb/>antequam frangebatur, elongatum & </s> <s xml:id="echoid-s11700" xml:space="preserve">attenuatum fuit, ut acce-<lb/>perit diametrum 0, 06 pollicis, fractura fuit admodumaſpera & </s> <s xml:id="echoid-s11701" xml:space="preserve">in-<lb/>æqualis diametri 0, 05 pollicis, abieratque ad diſtantiam {3/4} lineæ <lb/>â fractura in conum truncatum.</s> <s xml:id="echoid-s11702" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div422" type="section" level="1" n="422"> <head xml:id="echoid-head533" xml:space="preserve">EXPERIMENTUM LX.</head> <p> <s xml:id="echoid-s11703" xml:space="preserve">Filum Aureum craſſitiei D diffractum fuit a libris 150, ante ſo-<lb/>lutionem elongabatur atque attenuabatur, retinuitque diametrum <lb/>0, 04 pollicis, fractura fuit admodum aſpera, diametri 0, 03 pollicis <lb/>abieratque, ad diſtantiam {1/2} lineæ a fractura, in conum truncatum.</s> <s xml:id="echoid-s11704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11705" xml:space="preserve">Si Cohærentiæ horum filorum Aureorum ſeſe habuiſſent in ra-<lb/>tione craſſitierum ante Experimentum, fuiſſent pro A 500. </s> <s xml:id="echoid-s11706" xml:space="preserve">pro B <lb/>375. </s> <s xml:id="echoid-s11707" xml:space="preserve">pro C 250. </s> <s xml:id="echoid-s11708" xml:space="preserve">pro D 125. </s> <s xml:id="echoid-s11709" xml:space="preserve">ſed ſi fuiſſent in ratione craſſitierum <lb/>poſt Experimentum, fuiſſent pro A 500, pro B 354 {206/361}. </s> <s xml:id="echoid-s11710" xml:space="preserve">pro C 199 {261/362} <lb/>pro D 88 {232/361}. </s> <s xml:id="echoid-s11711" xml:space="preserve">quæ ultima proportio magis abludit ab Experimen-<lb/>tis quam prior, etiamſi & </s> <s xml:id="echoid-s11712" xml:space="preserve">illa nequaquam cum his congruat.</s> <s xml:id="echoid-s11713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11714" xml:space="preserve">Aurum multo minus attenuatum & </s> <s xml:id="echoid-s11715" xml:space="preserve">elongatum fuit quam Cuprum, <lb/>aut Orichalcum, quia eſt multo compactius, nec totidem poris per-<lb/>tuſum, imo ob ſoliditatem videtur eſſe adeo cohærens: </s> <s xml:id="echoid-s11716" xml:space="preserve">Soliditas <lb/>tamen non poteſt ſtatui ratio univerſalis majoris minoriſve Cohæ-<lb/>rentiæ, quippe hæc tum ſequeretur corporum gravitatem, hinc <lb/>Cohærentiam Auri ſequeretur ea Plumbi, cum tamen conſtabit ex <lb/>Experimentis ſequentibus Plumbum eſſe omnium Metallorum maxi-<lb/>me imbecille: </s> <s xml:id="echoid-s11717" xml:space="preserve">quamobrem figura partium hic invocanda erit: </s> <s xml:id="echoid-s11718" xml:space="preserve">quo <lb/>enim partes planioris ſuperficiei fuerint, eo in pluribus punctis ſe <lb/>contingent, majorique vi ſeſe attrahent, quo rotundiores fuerint, <lb/>eo minus ſe contingere poſſunt, & </s> <s xml:id="echoid-s11719" xml:space="preserve">minus attractæ facilius ſepara-<lb/>buntur.</s> <s xml:id="echoid-s11720" xml:space="preserve"/> </p> <pb o="501" file="0515" n="515" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div423" type="section" level="1" n="423"> <head xml:id="echoid-head534" xml:space="preserve">EXPERIMENTUM LXI.</head> <p> <s xml:id="echoid-s11721" xml:space="preserve">Filum Plumbeum craſſitiei A non plures libras geſſit quam 29 {1/4} <lb/>pedetentim & </s> <s xml:id="echoid-s11722" xml:space="preserve">lente ſibi appenſas: </s> <s xml:id="echoid-s11723" xml:space="preserve">retinere aliquamdiu aliud <lb/>filum potuit libras 35 ſubito applicatas, imo eas ſuſtinuit ſpatio <lb/>minuti ſecundi, verum lente applicari pondera tantum poſſunt 29{ /4}. <lb/></s> <s xml:id="echoid-s11724" xml:space="preserve">elongatum fuit valde, & </s> <s xml:id="echoid-s11725" xml:space="preserve">attenuatum, ita ut diameter modo man-<lb/>ſerito, 08 pollicis, fractura abiit in conum unam lineam altum, cuſpide <lb/>utcunque acuta terminatum, eratque toti coni ſuperficies polita.</s> <s xml:id="echoid-s11726" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div424" type="section" level="1" n="424"> <head xml:id="echoid-head535" xml:space="preserve">EXPERIMENTUM LXII.</head> <p> <s xml:id="echoid-s11727" xml:space="preserve">Filum Plumbeum craſſitiei B, fractum fuit a libris 21 {1/4} appenſis, <lb/>fractura abiit in conum unum pollicem longum, cuſpide acutâ ter-<lb/>minatum; </s> <s xml:id="echoid-s11728" xml:space="preserve">ante fracturam elongatum attenuatumque fuit, ut diameter <lb/>modo exſtiterit 0, 065 pollicis.</s> <s xml:id="echoid-s11729" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div425" type="section" level="1" n="425"> <head xml:id="echoid-head536" xml:space="preserve">EXPERIMENTUM LXIII.</head> <p> <s xml:id="echoid-s11730" xml:space="preserve">Filum Plumbeum craſſitiei C, ruptum fuit a libris 13 {1/4} abiit fra-<lb/>ctura in conum cum cuſpide acuta, elongatum fuit valde & </s> <s xml:id="echoid-s11731" xml:space="preserve">atte-<lb/>nuatum, habens diametrum 0, 055 pollicis.</s> <s xml:id="echoid-s11732" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div426" type="section" level="1" n="426"> <head xml:id="echoid-head537" xml:space="preserve">EXPERIMENTUM LXIV.</head> <p> <s xml:id="echoid-s11733" xml:space="preserve">Filum Plumbeum, craſſitiei D, ſolutum fuit a libris 8 {1/4} ſibi ſenſim <lb/>appenſis, abiitque fractura in Conum cum cuſpide acutâ.</s> <s xml:id="echoid-s11734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11735" xml:space="preserve">Si Cohærentiæ filorum plumbeorum ſequerentur proportionem <lb/>craſſitierum ante inſtitutum Experimentum, obſervatæ fuiſſent <lb/>pro A 29 {1/4}. </s> <s xml:id="echoid-s11736" xml:space="preserve">pro B 21 {15/36}. </s> <s xml:id="echoid-s11737" xml:space="preserve">pro C 14 {5/8}. </s> <s xml:id="echoid-s11738" xml:space="preserve">pro D 7 {5/56}. </s> <s xml:id="echoid-s11739" xml:space="preserve">qnæ videntur proxi-<lb/>me accedere ad eventus Experimentorum.</s> <s xml:id="echoid-s11740" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div427" type="section" level="1" n="427"> <head xml:id="echoid-head538" xml:space="preserve">EXPERIMENTUM LXV.</head> <p> <s xml:id="echoid-s11741" xml:space="preserve">Filum puriſſimi Stanni, craſſitiei A, fractum fuit a libris 49 {1/4} <lb/>lente & </s> <s xml:id="echoid-s11742" xml:space="preserve">pedetentim appoſitis; </s> <s xml:id="echoid-s11743" xml:space="preserve">ante fracturam multum elongatum <lb/>attenuatumque fuit, ut modo manſerit diameter 9, 09 pollicis, ad di- <pb o="502" file="0516" n="516" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſtantiam 0, 12 pollicis â fracturâ abiit in figuram conicam, dia-<lb/>meter fracturæ fuit; </s> <s xml:id="echoid-s11744" xml:space="preserve">0, 02 pollicis.</s> <s xml:id="echoid-s11745" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div428" type="section" level="1" n="428"> <head xml:id="echoid-head539" xml:space="preserve">EXPERIMENTUM LXVI.</head> <p> <s xml:id="echoid-s11746" xml:space="preserve">Filum Stanni ejuſdem, craſſitiei B, ſolutum fuit a libris 36 {1/4}, ante <lb/>rupturam elongatum & </s> <s xml:id="echoid-s11747" xml:space="preserve">attenuatum fuit, ut retinuerit diametrum <lb/>0, 075 pollicis, ad diſtantiam 0, 13 pollicis, a fractura abiit in co-<lb/>num truncatum, cujus ſuperior diameter erat 0, 03 pollicis.</s> <s xml:id="echoid-s11748" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div429" type="section" level="1" n="429"> <head xml:id="echoid-head540" xml:space="preserve">EXPERIMENTUM LXVII.</head> <p> <s xml:id="echoid-s11749" xml:space="preserve">Filum Stanneum craſſitiei C, frangebatur a libris 24 {1/4} ſenſim ap-<lb/>penſis, poſt fracturam retinuit modo diametrum 0, 065 pollicis, <lb/>fractura abiit in conum truncatum 0, 13 pollicis longum, cujus ſu-<lb/>perior diameter fuit 0, 02 pollicis.</s> <s xml:id="echoid-s11750" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div430" type="section" level="1" n="430"> <head xml:id="echoid-head541" xml:space="preserve">EXPERIMENTUM LXVIII.</head> <p> <s xml:id="echoid-s11751" xml:space="preserve">Filum Stanneum craſſitiei D ruptum fuit a libris 13 {1/4}, poſt fra-<lb/>cturam elongatum & </s> <s xml:id="echoid-s11752" xml:space="preserve">attenuatum deprehendebatur, ut diameter mo-<lb/>do fuerit 0, 0 15 pollicis, fractura abierat in conum truncatum <lb/>0, 13 pollicis longum.</s> <s xml:id="echoid-s11753" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11754" xml:space="preserve">Craſſitierum, ante experimenta inſtituta, proportio Cohærentiam <lb/>dediſſet pro A 49 {1/4}. </s> <s xml:id="echoid-s11755" xml:space="preserve">pro B 36 {15/16}. </s> <s xml:id="echoid-s11756" xml:space="preserve">pro C 24 {5/8}. </s> <s xml:id="echoid-s11757" xml:space="preserve">pro D 12 {5/16}. </s> <s xml:id="echoid-s11758" xml:space="preserve">quæ ſatis <lb/>accurate cum Experimentis congruunt.</s> <s xml:id="echoid-s11759" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div431" type="section" level="1" n="431"> <head xml:id="echoid-head542" xml:space="preserve">EXPERIMENTUM LXIX.</head> <p> <s xml:id="echoid-s11760" xml:space="preserve">Experimenta quatuor ſequentia capta ſunt cum Argenteis ſilis, <lb/>Argentum non fuit puriſſimum, ſed tantum magni Hollandici va-<lb/>loris, ſive ejuſdem, ex quo Nummi Philippæi conſtant</s> </p> <p> <s xml:id="echoid-s11761" xml:space="preserve">Filum craſſitiei A, antea optime ignitum, diffractum fuit a libris <lb/>370 ſenſim appenſis, ante fracturam elongatum & </s> <s xml:id="echoid-s11762" xml:space="preserve">attenuatum fuit, <lb/>ſuperficies fuit admodum aſpera, diametri 0; </s> <s xml:id="echoid-s11763" xml:space="preserve">05 pollicis, atque <lb/>ad diſtantiam 1 lineæ in conum truncatum abierat.</s> <s xml:id="echoid-s11764" xml:space="preserve"/> </p> <pb o="503" file="0517" n="517" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div432" type="section" level="1" n="432"> <head xml:id="echoid-head543" xml:space="preserve">EXPERIMENTUM LXX.</head> <p> <s xml:id="echoid-s11765" xml:space="preserve">Filum Argenteum craſſitiei B, diffractum fuit a libris 250, ante <lb/>fracturam elongatum & </s> <s xml:id="echoid-s11766" xml:space="preserve">attenuatum fuit, ut modo diameter man-<lb/>ſerit 0, 08 pollicis, fractura fuit admodum aſpera & </s> <s xml:id="echoid-s11767" xml:space="preserve">inæqualis, dia-<lb/>metri 0, 04 pollicis, abieratque ad longitudinem 0, 08 pollic. </s> <s xml:id="echoid-s11768" xml:space="preserve">in co-<lb/>num truncatum.</s> <s xml:id="echoid-s11769" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div433" type="section" level="1" n="433"> <head xml:id="echoid-head544" xml:space="preserve">EXPERIMENTUM LXXI.</head> <p> <s xml:id="echoid-s11770" xml:space="preserve">Filum Argenteum, craſſitiei C, a libris 170 appenſis diffractum fuit, <lb/>ante fracturam elongatum & </s> <s xml:id="echoid-s11771" xml:space="preserve">attenuatum fuit, ut modo retinuerit <lb/>diametrum 0, 06 pollicis, fracturæ ſuperficies erat admodum aſpera, <lb/>diametri 0, 035 pollicis, a fracturâ enim abierat in conum trunca-<lb/>tum {1/2} lineam longum.</s> <s xml:id="echoid-s11772" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div434" type="section" level="1" n="434"> <head xml:id="echoid-head545" xml:space="preserve">EXPERIMENTUM LXXII.</head> <p> <s xml:id="echoid-s11773" xml:space="preserve">Filum Argenteum, craſſitiei D, diffractum fuit a libirs 97 {1/4} appenſis’ <lb/>diameter poſt fracturam deprehendebatur 0, 04 pollicis, fracturæ <lb/>ſuperficies fuit aſpera diametri 0, 025 pollicis, abieratque in Co-<lb/>num truncatum {1/2} lineam longum.</s> <s xml:id="echoid-s11774" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11775" xml:space="preserve">Cohærentiæ horum 4 filorum Argenteorum, ſequentes craſſitie-<lb/>rum ante Experimenta inſtituta proportionem, ſe habuiſſent pro A <lb/>370. </s> <s xml:id="echoid-s11776" xml:space="preserve">pro B 277 {3/4}. </s> <s xml:id="echoid-s11777" xml:space="preserve">pro C 185. </s> <s xml:id="echoid-s11778" xml:space="preserve">pro D 92. </s> <s xml:id="echoid-s11779" xml:space="preserve">quæ omnia abludunt ali-<lb/>quantum ab ipſo eventu.</s> <s xml:id="echoid-s11780" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div435" type="section" level="1" n="435"> <head xml:id="echoid-head546" xml:space="preserve">EXPERIMENTUM LXXIII.</head> <p> <s xml:id="echoid-s11781" xml:space="preserve">Quatuor Experimenta ſequentia capta fuerunt cum filis Argen-<lb/>teis minoris valoris Hollandici, in quo plus Cupri habetur.</s> <s xml:id="echoid-s11782" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11783" xml:space="preserve">Filum craſſitiei A a libris 380 ſenſim appenſis ruptum fuit, filum <lb/>ante rupturam elongatum & </s> <s xml:id="echoid-s11784" xml:space="preserve">attenuatum, fuit, ut diametrum <pb o="504" file="0518" n="518" rhead="INTRODUCTIO AD COHÆRENTIAM"/> acceperit 0, 09 pollicis, fractura aſpera fuit, conica, cujus ſu-<lb/>perior diameter 0, 06 pollicis, longitudo unius lineæ.</s> <s xml:id="echoid-s11785" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div436" type="section" level="1" n="436"> <head xml:id="echoid-head547" xml:space="preserve">EXPERIMENTUM LXXIV.</head> <p> <s xml:id="echoid-s11786" xml:space="preserve">Filum argenteum craſſitiei B a libris 270. </s> <s xml:id="echoid-s11787" xml:space="preserve">appenſis pedetentim <lb/>fractum fuit, elongabatur & </s> <s xml:id="echoid-s11788" xml:space="preserve">attenuabatur, ut diameter evaſerit 0, 07 <lb/>pollicis; </s> <s xml:id="echoid-s11789" xml:space="preserve">ad diſtantiam unius lineæ â fracturâ abiit in conum trun-<lb/>catum, cujus ſuperficies valde aſpera erat, & </s> <s xml:id="echoid-s11790" xml:space="preserve">diametri 0, 05 pol-<lb/>licis.</s> <s xml:id="echoid-s11791" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div437" type="section" level="1" n="437"> <head xml:id="echoid-head548" xml:space="preserve">EXPERIMENTUM LXXV.</head> <p> <s xml:id="echoid-s11792" xml:space="preserve">Filum Argenteum craſſitiei C, ſolutum fuit a libris 180, elonga-<lb/>tum attenuatumque evaſit, ut modo diameter fuerit 0, 06. </s> <s xml:id="echoid-s11793" xml:space="preserve">pollicis; <lb/></s> <s xml:id="echoid-s11794" xml:space="preserve">ad diſtantiam unius lineæ â fractura abiit in conum truncatum, cu-<lb/>jus ſuperior ſuperficies aſpera erat diametri 0, 035 pollicis.</s> <s xml:id="echoid-s11795" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div438" type="section" level="1" n="438"> <head xml:id="echoid-head549" xml:space="preserve">EXPERIMENTUM LXXVI.</head> <p> <s xml:id="echoid-s11796" xml:space="preserve">Filum Argenteum craſſitiei D, non potuit ſuſtinere libras 110, <lb/>diffractum habuit craſſitiem cujus diameter erat 0, 04 pollicis, ad di-<lb/>ſtantiam 0, 05 pollicis â fracturâ abiit in conum truncatum, cujus <lb/>ſuperficies ſuperior erat aſpera, & </s> <s xml:id="echoid-s11797" xml:space="preserve">diametri 0, 02 pollicis.</s> <s xml:id="echoid-s11798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11799" xml:space="preserve">Cuprum igitur Argento additum auget Cohærentiam, nam ea in <lb/>his ultimis 4 filis argenteis major obſervata fuit, quam in filis Ar-<lb/>genti purioris: </s> <s xml:id="echoid-s11800" xml:space="preserve">Argentum tamen plus cohæret quam Cuprum, unde <lb/>videretur potius Cohærentiæ decrementum datum iri ab admiſto <lb/>Cupro: </s> <s xml:id="echoid-s11801" xml:space="preserve">ſed partes unius Metalli poros alterius ingrediuntur, atque <lb/>ita ſuperficierum contactum augent & </s> <s xml:id="echoid-s11802" xml:space="preserve">Cohærentiam; </s> <s xml:id="echoid-s11803" xml:space="preserve">veluti fluidum <lb/>inter duo corpora ſolida poſitum unionem facit & </s> <s xml:id="echoid-s11804" xml:space="preserve">magnam Cohæ-<lb/>rentiam. </s> <s xml:id="echoid-s11805" xml:space="preserve">Cohærentiæ in ratione craſſitierum filorum fuiſſent pro <lb/>A 380. </s> <s xml:id="echoid-s11806" xml:space="preserve">pro B 285. </s> <s xml:id="echoid-s11807" xml:space="preserve">pro C 190. </s> <s xml:id="echoid-s11808" xml:space="preserve">pro D 95. </s> <s xml:id="echoid-s11809" xml:space="preserve">quæ proportio non parum <lb/>abludit ab Experimentis, eſtque nunc major, nunc minor, quod ab <lb/>heterogenea maſſæ indole pendet.</s> <s xml:id="echoid-s11810" xml:space="preserve"/> </p> <pb o="505" file="0519" n="519" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div439" type="section" level="1" n="439"> <head xml:id="echoid-head550" xml:space="preserve">EXPERIMENTUM LXXVII.</head> <p> <s xml:id="echoid-s11811" xml:space="preserve">Filum Ferreum craſſitiei A, fractum fuit a libris 450 pedetentim <lb/>appenſis: </s> <s xml:id="echoid-s11812" xml:space="preserve">antequam frangebatur parumper elongatum fuit, ut vix <lb/>craſſities decreverit: </s> <s xml:id="echoid-s11813" xml:space="preserve">ad diſtantiam 1 lineæ a fractura obſervabatur, <lb/>licetægre, abiiſſe in conum truncatum, cujus diameter erat 0, 07 <lb/>pollic. </s> <s xml:id="echoid-s11814" xml:space="preserve">& </s> <s xml:id="echoid-s11815" xml:space="preserve">ſuperficies aſpera ac inæqualis.</s> <s xml:id="echoid-s11816" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div440" type="section" level="1" n="440"> <head xml:id="echoid-head551" xml:space="preserve">EXPERIMENTUM LXXVIII.</head> <p> <s xml:id="echoid-s11817" xml:space="preserve">Filum ferreum craſſitiei B, ruptum fuit â libris 310 appenſis; </s> <s xml:id="echoid-s11818" xml:space="preserve">atte-<lb/>nuatum fuit, ut diameter modo exſtiterit 0, 08 pollicis, ad diſtan-<lb/>tiam unius lineæ â fracturâ abierat in conum truncatum, cujus dia-<lb/>meter ſuperior modo erat 0, 06 pollicis.</s> <s xml:id="echoid-s11819" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div441" type="section" level="1" n="441"> <head xml:id="echoid-head552" xml:space="preserve">EXPERIMENTUM LXXIX.</head> <p> <s xml:id="echoid-s11820" xml:space="preserve">Filum ferreum craſſitiei C, modo ſuſtinere potuit libras 230, pa-<lb/>rum attenuatum fuit, cum retinuerit diametrum 0, 06 pollicis, ad <lb/>diſtantiam {1/2} lineæ a fractura in conum truncatum abierat, cujus <lb/>diameter ſuperior erat 0, 045 pollicis.</s> <s xml:id="echoid-s11821" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div442" type="section" level="1" n="442"> <head xml:id="echoid-head553" xml:space="preserve">EXPERIMENTUM LXXX.</head> <p> <s xml:id="echoid-s11822" xml:space="preserve">Filum ferreum craſſitiei D, ſolutum fuit ab appenſis libris 130, <lb/>parum elongatum, hinc diametrum retinuit 0, 05 pollicis, vix con-<lb/>ſpici poterat abiiſſe anterius in conum, cujus ſuperficies ſuperior <lb/>obſervabatur diametrum habere 0, 035 pollicis.</s> <s xml:id="echoid-s11823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11824" xml:space="preserve">Si Cohærentiæ hic proportionem craſſitierum obſervaſſent, qui-<lb/>bus fila ante inſtitutum Experimentum ſunt donata, debuiſſent eſſe <lb/>pro A 450. </s> <s xml:id="echoid-s11825" xml:space="preserve">pro B 337 {1/2}, pro C 225. </s> <s xml:id="echoid-s11826" xml:space="preserve">pro D 112 {1/2}. </s> <s xml:id="echoid-s11827" xml:space="preserve">ſed nunc major <lb/>nunc minor datur Cohærentia, quia Ferrum non videtur eſſe maſ-<lb/>ſa admodum homogenea.</s> <s xml:id="echoid-s11828" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11829" xml:space="preserve">Obſervavi in omnibus hiſce Experimentis, Fila cujuscunque Me-<lb/>ralli inſignem calorem concepiſſe, quando ab appenſo pondere e- <pb o="506" file="0520" n="520" rhead="INTRODUCTIO AD COHÆRENTIAM"/> logabantur & </s> <s xml:id="echoid-s11830" xml:space="preserve">rumpebantur: </s> <s xml:id="echoid-s11831" xml:space="preserve">calor hic ab attritu partium ſupra ſe <lb/>motarum & </s> <s xml:id="echoid-s11832" xml:space="preserve">valde preſſarum, cum attenuatur Metallum, oritur: <lb/></s> <s xml:id="echoid-s11833" xml:space="preserve">præterea ruptum Metallum, modo antea valde tenſum, in tremo-<lb/>res concitatiſſimos abit, quibus partes nunc excurrendo, nunc rede-<lb/>undo, ſeſe mutuo inſigniter fricabant, atterebantque, & </s> <s xml:id="echoid-s11834" xml:space="preserve">eo modo <lb/>ignem colligebant.</s> <s xml:id="echoid-s11835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11836" xml:space="preserve">Quicunque deſcripta a nobis Experimenta comparat cumiis, quæ <lb/>adfert de Lanis in Magiſterio naturæ & </s> <s xml:id="echoid-s11837" xml:space="preserve">artis Lib. </s> <s xml:id="echoid-s11838" xml:space="preserve">XI. </s> <s xml:id="echoid-s11839" xml:space="preserve">Cap. </s> <s xml:id="echoid-s11840" xml:space="preserve">1. </s> <s xml:id="echoid-s11841" xml:space="preserve">§ 22. <lb/></s> <s xml:id="echoid-s11842" xml:space="preserve">facile perſpiciet, hunc Autorem Experimenta ſpectantia corporum <lb/>Cohærentiam tantum exſuo cerebello extruſiſſe, tentaſſe vero nihil: </s> <s xml:id="echoid-s11843" xml:space="preserve"><lb/>hæc enim habet. </s> <s xml:id="echoid-s11844" xml:space="preserve">Nexus partium in metallis omnium robuſtiſſimus, <lb/>& </s> <s xml:id="echoid-s11845" xml:space="preserve">qui maxime reſiſtit fractioni videtur eſſe in Chalybe, tum in Fer-<lb/>ro, deinde vero in Ære, poſthæc in Argento, ac deinde in Auro, <lb/>demum in Stanno & </s> <s xml:id="echoid-s11846" xml:space="preserve">Plumbo; </s> <s xml:id="echoid-s11847" xml:space="preserve">nimirum ſi ſumas ſingula fila Cylin-<lb/>drica ex ſingulis metallis, inter ſe omnino æqualia ſecundum craſſi-<lb/>tiem, atque illis appendas diverſa pondera, donec frangantur, <lb/>filum chalybeum majus pondus ſuſtinebit, ac cætera deinceps, eo or-<lb/>dine, quem dicebamus,</s> </p> <p> <s xml:id="echoid-s11848" xml:space="preserve">Longe melius profecto Merſennus in Lib. </s> <s xml:id="echoid-s11849" xml:space="preserve">3. </s> <s xml:id="echoid-s11850" xml:space="preserve">Harmonices prop. </s> <s xml:id="echoid-s11851" xml:space="preserve">7. <lb/></s> <s xml:id="echoid-s11852" xml:space="preserve">ex Experientiâ metallorum Cohærentiam determinavit, quem ſi <lb/>conſuluiſſet de Lanis, Auro maximum robur competere deprehen-<lb/>diſſet: </s> <s xml:id="echoid-s11853" xml:space="preserve">convenit Merſenniana adduxiſſe, ut noſtra tentamina con-<lb/>ſirmentur. </s> <s xml:id="echoid-s11854" xml:space="preserve">Electæ fuerunt fides metallicæ, quarum craſſities fuit <lb/>{3/16} lineæ quam proxime, longæ 1 {1/2} pedes: </s> <s xml:id="echoid-s11855" xml:space="preserve">illi, quæ ex Auro puro <lb/>confecta fuit, appendi potuerunt libræ 23, a quibus frangebatur: </s> <s xml:id="echoid-s11856" xml:space="preserve"><lb/>hujus firmitati proxima fuit fides ex Auro mixto, quod erat 22 <lb/>partium: </s> <s xml:id="echoid-s11857" xml:space="preserve">fides ex Argento æqualis roboris cum binis præcedenti-<lb/>bus dicitur fuiſſe. </s> <s xml:id="echoid-s11858" xml:space="preserve">hoc tamen non bene convenit cum noſtris, qui-<lb/>bus minorem Cohærentiam Argenti deprehendimus: </s> <s xml:id="echoid-s11859" xml:space="preserve">fides ferrea <lb/>fracta fuit a libris 19. </s> <s xml:id="echoid-s11860" xml:space="preserve">chorda cuprea & </s> <s xml:id="echoid-s11861" xml:space="preserve">ænea æqualis fuit roboris <lb/>& </s> <s xml:id="echoid-s11862" xml:space="preserve">fracta a libris 18. </s> <s xml:id="echoid-s11863" xml:space="preserve">Chorda ex Inteſtinis ovium facta & </s> <s xml:id="echoid-s11864" xml:space="preserve">æque <lb/>craſſa cum priori fracta fuit a libris 7.</s> <s xml:id="echoid-s11865" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11866" xml:space="preserve">A methodo diverſa ſuſpenſionis facile potuit oriri diſcrepantia, <lb/>quæ inter Experimenta noſtra & </s> <s xml:id="echoid-s11867" xml:space="preserve">Merſenniana obtinet.</s> <s xml:id="echoid-s11868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11869" xml:space="preserve">Convenit hic quoque egiſſe de Cohærentia abſoluta Vitri, quod <lb/>quoniam maxime homogeneum corpus eſſe videtur, accuratiſſime <pb o="507" file="0521" n="521" rhead="CORPORUM FIRMORUM."/> erat examinandum, ut leges Cohærentiæ detegerentur.</s> <s xml:id="echoid-s11870" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div443" type="section" level="1" n="443"> <head xml:id="echoid-head554" xml:space="preserve">EXPERIMENTUM LXXXI.</head> <p> <s xml:id="echoid-s11871" xml:space="preserve">Confectus fuit in officina vitriaria ex puriſſimo albiſſimoque vi-<lb/>tro Cylindrus ſolidus 6 pollices longus, utrimque capite donatus <lb/>craſſiori inſtar piſtilli mortarii; </s> <s xml:id="echoid-s11872" xml:space="preserve">diameter, ubi gracillimus erat & </s> <s xml:id="echoid-s11873" xml:space="preserve"><lb/>fractus fuit, deprehenſa eſt accurate 0, 23 pollicis, hic ſecundum <lb/>longitudinem in machina noſtra divulſoria tractus, frangebatur a <lb/>libris 118.</s> <s xml:id="echoid-s11874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11875" xml:space="preserve">Alium deinde cylindrum elegi ejusdem vitri; </s> <s xml:id="echoid-s11876" xml:space="preserve">qui eodem modo <lb/>tentatus rumpebatur a libris 150, locus fracturæ diametrum habuit <lb/>0, 25 pollicis.</s> <s xml:id="echoid-s11877" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div444" type="section" level="1" n="444"> <head xml:id="echoid-head555" xml:space="preserve">EXPERIMENTUM LXXXII.</head> <p> <s xml:id="echoid-s11878" xml:space="preserve">Ex eodem vitro confectum fuit parallelopipedum quadrangulum, <lb/>cujus omnia latera ſupra laminam ferream applanata politaque fue-<lb/>rant, quodlibet latus erat 2 linearum, hoc ſecundum longitudinem <lb/>diſtractum frangebatur a libris 78.</s> <s xml:id="echoid-s11879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11880" xml:space="preserve">Aliud ex eodem vitro factum parallelopipedum quadrangulum, <lb/>cujus quodlibet latus erat 0, 16 pollicis, fractum fuit a libris 50.</s> <s xml:id="echoid-s11881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11882" xml:space="preserve">Modum, quo inſtitutum fuit Experimentum, adnectam: </s> <s xml:id="echoid-s11883" xml:space="preserve">Tab. <lb/></s> <s xml:id="echoid-s11884" xml:space="preserve">XVII. </s> <s xml:id="echoid-s11885" xml:space="preserve">fig. </s> <s xml:id="echoid-s11886" xml:space="preserve">8. </s> <s xml:id="echoid-s11887" xml:space="preserve">repræſentat AB cylindrum aut parallelopipedum ſoli-<lb/>dum vitreum, cui duo capita A & </s> <s xml:id="echoid-s11888" xml:space="preserve">B utrimque annexa fuerunt: </s> <s xml:id="echoid-s11889" xml:space="preserve">in fig. </s> <s xml:id="echoid-s11890" xml:space="preserve">9 <lb/>conſpicitur cylindrus A B ambabus aliis machinis annexus; </s> <s xml:id="echoid-s11891" xml:space="preserve">ſunt <lb/>C C. </s> <s xml:id="echoid-s11892" xml:space="preserve">duo unci ferrei, cochleâ D D utrimque affixi, circa quam <lb/>tamen libere converti poſſunt: </s> <s xml:id="echoid-s11893" xml:space="preserve">Sunt E E duo corpora ænea firma, <lb/>intus donata crenâ, conjuncta ope laminæ craſſæ æneæ F: </s> <s xml:id="echoid-s11894" xml:space="preserve">eſt G <lb/>lamina priori æqualis, ſed quæ ex crena inſculpta E E eximi poteſt, <lb/>ita ut cylindrus A B inter ambas laminas F, G, concludi poſſit, hinc <lb/>laminæ in medio foramen habent, anguſtius tamen quam eſt caput <lb/>A aut B cylindri vitrei: </s> <s xml:id="echoid-s11895" xml:space="preserve">Sunt K K duæ cochleæ connectentes am-<lb/>bas laminas G, F, ſecum invicem; </s> <s xml:id="echoid-s11896" xml:space="preserve">apparatus hic machinæ divulſo-<lb/>riæ applicatus fuit, ejusque ope Cohærentia Vitrorum explorata fuit.</s> <s xml:id="echoid-s11897" xml:space="preserve"/> </p> <pb o="508" file="0522" n="522" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div445" type="section" level="1" n="445"> <head xml:id="echoid-head556" xml:space="preserve">CAPUT QUARTUM.</head> <head xml:id="echoid-head557" xml:space="preserve">De Cohærentia Funis Intorti.</head> <p> <s xml:id="echoid-s11898" xml:space="preserve">Omnes fibrillæ aut Stamina, ex quibus fila vel funes conficiun-<lb/>tur, brevia ſunt, ſi ſericum exceperimus, quod a bombyce <lb/>in magnam uſque longitudinem producitur, cæteroquin filamenta <lb/>ſeminis Cotonei ſunt admodum brevia, Lana ovium, crines equi-<lb/>ni aut camelini, filamenta plantarum Lini aut Cannabis non ex-<lb/>cedunt longitudinem 3, 4, 5 vel 6 pedum: </s> <s xml:id="echoid-s11899" xml:space="preserve">Ex his inter ſe intortis <lb/>filum & </s> <s xml:id="echoid-s11900" xml:space="preserve">funis cujuslibet longitudinis componitur; </s> <s xml:id="echoid-s11901" xml:space="preserve">ex quo magna <lb/>pondera nonnunquam ſuſpenduntur: </s> <s xml:id="echoid-s11902" xml:space="preserve">Quæritur quamobrem brevia <lb/>Stamina filorum funiumve ex ſe non labantur appenſo pondere par-<lb/>tes a ſe diſtrahente, ſed potius continuum filum conſtituere per-<lb/>gant? </s> <s xml:id="echoid-s11903" xml:space="preserve">Contorſio fibrarum ſtaminumque inter ſe, tum aſperitates, <lb/>quibusper totam ſuperficiem donatæ ſunt, id efficere videntur. </s> <s xml:id="echoid-s11904" xml:space="preserve">Con-<lb/>torſione enim fibræ inter ſe intricantur, arcte ſibi applicantur; </s> <s xml:id="echoid-s11905" xml:space="preserve">aſ-<lb/>peritatibus irretiuntur ita ſecum invicem, ut iterum extricari abs-<lb/>que ingenti attritu & </s> <s xml:id="echoid-s11906" xml:space="preserve">abraſione partium in ſuperficiebus exſtantium <lb/>nequeant, unde tanta naſcitur reſiſtentia fibris, quæ ſe conarentur <lb/>quaſi extricare, ut potius rumpantur, quam extricentur. </s> <s xml:id="echoid-s11907" xml:space="preserve">Quan-<lb/>tum ſuperficierum aſperarum ingreſſus in ſe invicem faciat ad mo-<lb/>tum duorum corporum ſupra ſe impediendum clariſſime patet, cum <lb/>funis aliquoties circa cylindrum convolutus eſt ligneum, quemad-<lb/>modum fieri ſolet â Mechanicis circa fuſum Gerani bis terve funem <lb/>circumducendo, hujus enim alteri extremo pondus ingens moven-<lb/>dum applicetur, alterum manu leviter teneatur, circumacto fuſo <lb/>funis adeo arcte apprimitur, ut aſperitatibus mutuis ſe amborum ſu-<lb/>perficies ingrediantur aliquouſque, & </s> <s xml:id="echoid-s11908" xml:space="preserve">potius totus funis frangatur, <lb/>quam circa fuſum moveatur, volvi enim nequit niſi omnes exſtan-<lb/>tiores partes funis fuſique abradantur, quarum Cohærentiæ ſummâ <lb/>ſuperante Cohærentiam partium in ſectione funis transverſa poſita-<lb/>rum, potius funis frangetur, quam ut circa fuſum lubrice moveatur: <lb/></s> <s xml:id="echoid-s11909" xml:space="preserve">Siigitur duo tresve ambitus funis motum circa fuſum impediant, mul- <pb o="509" file="0523" n="523" rhead="CORPORUM FIRMORUM."/> to magis id impedient centum plureſve circumductiones, ideo fila-<lb/>mentum 3 vel 4 pedum circa alterum ejusdem longitudinis volutum <lb/>centies, non extricabitur, tractum licet ab uno extremo, ſed potius <lb/>ab appenſo pondere rumpetur, quemadmodum hoc eleganter ex-<lb/>plicuit Galilæus in Mechan. </s> <s xml:id="echoid-s11910" xml:space="preserve">Dialogo I. </s> <s xml:id="echoid-s11911" xml:space="preserve">Si vero fibrillæ & </s> <s xml:id="echoid-s11912" xml:space="preserve">ſtamina <lb/>circa ſe convoluta & </s> <s xml:id="echoid-s11913" xml:space="preserve">intorta ſuperficies perfecte politas æquatasque <lb/>poſſiderent; </s> <s xml:id="echoid-s11914" xml:space="preserve">nunquam ex iis ſola contorſione funis longus cohæ-<lb/>rens formari poſſet, quippe partes lubrice mobiles ſemper ſupra ſe <lb/>absque attritu & </s> <s xml:id="echoid-s11915" xml:space="preserve">reſiſtentia, a vi exigua extremo alterutri applicata <lb/>extricarentur; </s> <s xml:id="echoid-s11916" xml:space="preserve">quod ne fiat liberaliſſimus providit Creator, omnes <lb/>fibrillas Lini, Cannabis, Lanæ, Pilorum, Cotonei multis exſtan-<lb/>tiis exaſperando.</s> <s xml:id="echoid-s11917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11918" xml:space="preserve">Quando pauca memoratorum corporum Stamina ſimul intor-<lb/>quentur, fit id, quod Filum tenue vocatur; </s> <s xml:id="echoid-s11919" xml:space="preserve">Intorquendo fila te-<lb/>nuia duo, tria, quatuorve ſimul, fit Filum craſſius, vel ſecundæ <lb/>ſpeciei: </s> <s xml:id="echoid-s11920" xml:space="preserve">plura fila ſecundæ ſpeciei iterum ſimul capiendo & </s> <s xml:id="echoid-s11921" xml:space="preserve">intor-<lb/>quendo componitur filum craſſius tertiæ ſpeciei; </s> <s xml:id="echoid-s11922" xml:space="preserve">quorum plura eo-<lb/>dem modo intorta conſtituunt iterum Filum craſſius, adeo ut poſt <lb/>ejusmodi contorſiones Filorum diverſorum oriatur tandem Funis, <lb/>Rudensve deſideratæ craſſitiei.</s> <s xml:id="echoid-s11923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11924" xml:space="preserve">Viguit dui, vigetque adhuc inter quam plurimos, ne quidem Philo-<lb/>ſophis exceptis, opinio, funem ex aliis inter ſe contortis compoſi-<lb/>tum, fieri fortiorem ex hac ipſa contorſione, adeo ut ſi funis ex ſex <lb/>filamentis ſecum invicem convolutis conſtaret, fortior foret, majus-<lb/>que pondus gerere valeret, quam ſi eadem filamenta inter ſe parallela <lb/>haberentur & </s> <s xml:id="echoid-s11925" xml:space="preserve">non intorta, atque ex eorum extremitatibus idem pen-<lb/>deret pondus: </s> <s xml:id="echoid-s11926" xml:space="preserve">Imo nonnulli Viri eximii hoc demonſtrare anniſi ſunt, <lb/>inter quos eminet acutiſſimus Bellini in Tractatu de Motu cordis <lb/>cap. </s> <s xml:id="echoid-s11927" xml:space="preserve">5. </s> <s xml:id="echoid-s11928" xml:space="preserve">tum de Lanis Lib. </s> <s xml:id="echoid-s11929" xml:space="preserve">XI. </s> <s xml:id="echoid-s11930" xml:space="preserve">cap. </s> <s xml:id="echoid-s11931" xml:space="preserve">1. </s> <s xml:id="echoid-s11932" xml:space="preserve">Magiſt. </s> <s xml:id="echoid-s11933" xml:space="preserve">natur. </s> <s xml:id="echoid-s11934" xml:space="preserve">& </s> <s xml:id="echoid-s11935" xml:space="preserve">Art. </s> <s xml:id="echoid-s11936" xml:space="preserve">Tomo 2. <lb/></s> <s xml:id="echoid-s11937" xml:space="preserve">§. </s> <s xml:id="echoid-s11938" xml:space="preserve">21. </s> <s xml:id="echoid-s11939" xml:space="preserve">qui magis audacter quam vere pronunciat: </s> <s xml:id="echoid-s11940" xml:space="preserve">duo fila ſimul in-<lb/>torta majus pondus ſuſtinere antequam frangantur, quam non in-<lb/>torta: </s> <s xml:id="echoid-s11941" xml:space="preserve">at plus vice ſimplici animadverti hujus Philoſophi Experi-<lb/>mentis aſſertisque non multum fidei adhiberi poſſe: </s> <s xml:id="echoid-s11942" xml:space="preserve">procul dubio <lb/>autem hæc deſcripſerat ex Honor. </s> <s xml:id="echoid-s11943" xml:space="preserve">Fabry, qui in Phyſicæ Tract. </s> <s xml:id="echoid-s11944" xml:space="preserve">2. </s> <s xml:id="echoid-s11945" xml:space="preserve"><lb/>Lib. </s> <s xml:id="echoid-s11946" xml:space="preserve">5. </s> <s xml:id="echoid-s11947" xml:space="preserve">prop. </s> <s xml:id="echoid-s11948" xml:space="preserve">13. </s> <s xml:id="echoid-s11949" xml:space="preserve">dixit, duo fila ſimul intorta majus pondus gere-<lb/>re, quam non intorta, quod demonſtrare conatur, ſimul provo- <pb o="510" file="0524" n="524" rhead="INTRODUCTIO AD COHÆRENTIAM"/> cans Experientiam: </s> <s xml:id="echoid-s11950" xml:space="preserve">verum nullam commemoravit, unde concludo, <lb/>id modo ex vulgari opinione fuiſſe aſſumtum: </s> <s xml:id="echoid-s11951" xml:space="preserve">Sed receptam opinio-<lb/>nem eſſe erroneam, omni Experientiæ adverſam, & </s> <s xml:id="echoid-s11952" xml:space="preserve">cum ſana re-<lb/>pugnare ratione, primus omnium, quantum ſcio, Merſennus in <lb/>Lib. </s> <s xml:id="echoid-s11953" xml:space="preserve">3. </s> <s xml:id="echoid-s11954" xml:space="preserve">Harmonic. </s> <s xml:id="echoid-s11955" xml:space="preserve">prop. </s> <s xml:id="echoid-s11956" xml:space="preserve">16, oſtendit & </s> <s xml:id="echoid-s11957" xml:space="preserve">deinde Experientiſſimus <lb/>Reaumurius in L’Hiſtoire de L’Acad. </s> <s xml:id="echoid-s11958" xml:space="preserve">Roy: </s> <s xml:id="echoid-s11959" xml:space="preserve">des Scienc. </s> <s xml:id="echoid-s11960" xml:space="preserve">A°. </s> <s xml:id="echoid-s11961" xml:space="preserve">1711. <lb/></s> <s xml:id="echoid-s11962" xml:space="preserve">hic revera pluribus evicit Experimentis funem, ex contortis filis <lb/>factum, debiliorem eſſe, quam fila eadem non intorta, cum ex <lb/>his plus ponderis ſuſpendi queat.</s> <s xml:id="echoid-s11963" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11964" xml:space="preserve">Quoniam occupabar in examine Cohærentiæ ſolidorum, credi-<lb/>di nec inutile, nec injucundum fore, ſi Experimenta horum præ-<lb/>ſtantium Virorum repeterem, ulterius confirmarem, & </s> <s xml:id="echoid-s11965" xml:space="preserve">nonnulla <lb/>adderem, ut eo citius ex hominum animis erroneum præjudicium <lb/>tollatur; </s> <s xml:id="echoid-s11966" xml:space="preserve">& </s> <s xml:id="echoid-s11967" xml:space="preserve">alius modus funes componendi fortiores cum minori <lb/>impenſa inveſtigetur; </s> <s xml:id="echoid-s11968" xml:space="preserve">non inutile videri poteſt horum Experimen-<lb/>torum repetitum examen, cum verè ſapiens Fontenellius hoc ne-<lb/>gotium ulterius examinandum & </s> <s xml:id="echoid-s11969" xml:space="preserve">demonſtrandum commendaverit <lb/>Mathematicis: </s> <s xml:id="echoid-s11970" xml:space="preserve">inſuper a Cl. </s> <s xml:id="echoid-s11971" xml:space="preserve">Reaumurio ita plane exhauſtum non <lb/>eſt, quin pluribus obſervatis amplificari poſſit mereaturque.</s> <s xml:id="echoid-s11972" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11973" xml:space="preserve">Poſſet prima fronte videri, intorſionem filorum robur addituram <lb/>funi; </s> <s xml:id="echoid-s11974" xml:space="preserve">quia filum per totam ſuam longitudinem non eſt æque craſ-<lb/>ſum, nec æque tenax, ſed hic fortius, ibi debilius: </s> <s xml:id="echoid-s11975" xml:space="preserve">ponamus igi-<lb/>tur duo fila juxta ſe mutuo, atque unius pars debilior reſpondeat <lb/>fortiori alterius ſili, tum hæc ita ſibi applicata contorqueantur, <lb/>neceſſario exſurget inde robur aliquod æquabile per totum funem, <lb/>& </s> <s xml:id="echoid-s11976" xml:space="preserve">majus, quam ſi duo fila ſeorſim ponerentur, atque iis pondus <lb/>geſtandum appenderetur: </s> <s xml:id="echoid-s11977" xml:space="preserve">non inficiandum eſt hac ratione funem <lb/>ex intortis fibris compoſitum majorum virium evadere; </s> <s xml:id="echoid-s11978" xml:space="preserve">aſt contor-<lb/>ſio variis modis fibras debilitat, eſtque debilitatio major, quam <lb/>corroboratio ex priori cauſâ oriunda.</s> <s xml:id="echoid-s11979" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11980" xml:space="preserve">1°, Enim in formam ſpiræ torquentur filamenta, adeoque eorum <lb/>ſuperficies exterior fit major interiori; </s> <s xml:id="echoid-s11981" xml:space="preserve">hinc exteriores partes plus <lb/>tenduntur, quam interiores: </s> <s xml:id="echoid-s11982" xml:space="preserve">ſi igitur vis externa acceſſerit, hæc partes <lb/>plus tenſas, quam quæ ſunt minus, facilius franget, illisque fractis <lb/>etiam hæ cedent; </s> <s xml:id="echoid-s11983" xml:space="preserve">filamenti igitur intorti omnes partes non æqua-<lb/>liter reſiſtunt viribus frangentibus, ut quidem reſtitiſſent partes <pb o="511" file="0525" n="525" rhead="CORPORUM FIRMORUM."/> filamenti ſoluti & </s> <s xml:id="echoid-s11984" xml:space="preserve">recti, tractique ſecundum ſuam longitudinem: <lb/></s> <s xml:id="echoid-s11985" xml:space="preserve">Fateor hanc differentiam ſuperficiei exterioris & </s> <s xml:id="echoid-s11986" xml:space="preserve">interioris ſili in-<lb/>torti non eſſe magnam in tenui filo, ſed magna eſt in fune craſ-<lb/>ſo, qui propterea minus ponderis proportionaliter ſuſtinere valet, <lb/>quam tenuior, quemadmodum ex Experimentis infra deſcribendis <lb/>liquebit.</s> <s xml:id="echoid-s11987" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11988" xml:space="preserve">2°. </s> <s xml:id="echoid-s11989" xml:space="preserve">Filamenta quæcunque ſive Lini, Cannabina, Lanæ, alia-<lb/>que inæqualis ſunt craſſitiei; </s> <s xml:id="echoid-s11990" xml:space="preserve">plura nunc contorqueantur ſimul <lb/>formentque ſpiram, tum fieri nequit, quin in nonnullis locis par-<lb/>tes craſſiores plus tendantur, quam tenuiores; </s> <s xml:id="echoid-s11991" xml:space="preserve">ſit enim in Tab. <lb/></s> <s xml:id="echoid-s11992" xml:space="preserve">XXIIII. </s> <s xml:id="echoid-s11993" xml:space="preserve">fig. </s> <s xml:id="echoid-s11994" xml:space="preserve">1. </s> <s xml:id="echoid-s11995" xml:space="preserve">cylindrus, circa quem filum tenuius a, b, c, d, e, f, <lb/>ducatur, & </s> <s xml:id="echoid-s11996" xml:space="preserve">filum craſſius h, g, k, l, m: </s> <s xml:id="echoid-s11997" xml:space="preserve">tendentur hujus partes <lb/>tanto plus quam alterius fili, quanto circumferentia g, h, k ma-<lb/>j<unsure/>or eſt quam circumferentia a, b, c, d. </s> <s xml:id="echoid-s11998" xml:space="preserve">Fuerint vero æque cohæ-<lb/>rentes craſſiores tenuioreſque partes; </s> <s xml:id="echoid-s11999" xml:space="preserve">tum quia craſſiora loca non <lb/>poſſunt intorqueri, quin plus tendantur quam tenuiora, orietur Co-<lb/>hærentia filamentorum inæqualis, poteruntque minus cedere craſ-<lb/>ſiora, vi frangente aut tendente ipſis applicata, quam tenuiora: </s> <s xml:id="echoid-s12000" xml:space="preserve">unde <lb/>ob inæqualem filamentorum tenſionem facilius rumpetur funis, nec <lb/>tantundem ponderis geret, quam ſingula filamenta libere ſeorſim <lb/>poſita geſtaſſent.</s> <s xml:id="echoid-s12001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12002" xml:space="preserve">3°, Non poſſunt filamenta contorqueri, quin ſimul tendantur <lb/>partes, haud aliter ac ſi pondus appenſum foret; </s> <s xml:id="echoid-s12003" xml:space="preserve">quare non mirum <lb/>ſi funis non tantum ponderis gerere queat, quam ſingula filamenta <lb/>ſeorſum poſita ferunt: </s> <s xml:id="echoid-s12004" xml:space="preserve">quippe ponderi appenſo addendum eſt <lb/>quaſi pondus, quod æquale eſt tenſioni, ut fiat ponderum ſumma, <lb/>quæ â ſolutis filis geruntur: </s> <s xml:id="echoid-s12005" xml:space="preserve">Hinc quando fila valde contorquen-<lb/>tur, ut inde funis durior fiat, tantopere hæc tenduntur, ut modo <lb/>exiguum pondus appenſum ferre queant: </s> <s xml:id="echoid-s12006" xml:space="preserve">imo poteſt funis craſſus <lb/>tam valide intorqueri, ut vel inter contorquendum frangatur, vel <lb/>ſaltem âb exiguo appenſo pondere: </s> <s xml:id="echoid-s12007" xml:space="preserve">Quamobrem reſtiarii in eo ar-<lb/>tificium ponunt, ut craſſas compoſituri rudentes ex tenuibus filis <lb/>diverſæ ſpeciei, primum tria quatuorve fila tenuiora intorqueant <lb/>dextrorſum; </s> <s xml:id="echoid-s12008" xml:space="preserve">tum tria quatuorve ejuſmodi ſimul ſumta intorqueant <lb/>ſiniſtrorſum; </s> <s xml:id="echoid-s12009" xml:space="preserve">atque iterum tria quatuorve hujus generis ſimul con-<lb/>torqueant dextrorſum, ita enim relaxantur quaſi perpetuo fibrillæ, <pb o="512" file="0526" n="526" rhead="INTRODUCTIO AD COHÆRENTIAM"/> quæ antecedenti convolutione tenſæ erant; </s> <s xml:id="echoid-s12010" xml:space="preserve">quod licet aliquomodo <lb/>ſit verum, nihilominus nova convolutione plus tendi adhuc partes <lb/>eſt manifeſtum.</s> <s xml:id="echoid-s12011" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12012" xml:space="preserve">4°. </s> <s xml:id="echoid-s12013" xml:space="preserve">Quando funi ex contortis fibris compoſito, appenditur pon-<lb/>dus, elongatur, attenuatur, partes cedunt, moventur ſupra ſe, <lb/>contra ſe mutuo atteruntur, nonnullæ partes abraduntur, ideo vis <lb/>Cohærentiæ decreſcit, ut tandem a pondere ſuperetur: </s> <s xml:id="echoid-s12014" xml:space="preserve">ſed ille at-<lb/>tritus, atque abraſio partium non datur quando ſingula filamenta <lb/>libere juxta ſe ſunt poſita, ponduſque appenſum gerunt.</s> <s xml:id="echoid-s12015" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12016" xml:space="preserve">5°. </s> <s xml:id="echoid-s12017" xml:space="preserve">Sed ad debilitatem compoſiti funis etiam ductus obliquus fi. <lb/></s> <s xml:id="echoid-s12018" xml:space="preserve">lamentorum intortorum plurimum contribuit, uti ex Tab. </s> <s xml:id="echoid-s12019" xml:space="preserve">XXIIII. </s> <s xml:id="echoid-s12020" xml:space="preserve"><lb/>fig. </s> <s xml:id="echoid-s12021" xml:space="preserve">2. </s> <s xml:id="echoid-s12022" xml:space="preserve">patebit, quæ funem intortum repræſentat. </s> <s xml:id="echoid-s12023" xml:space="preserve">Sit enim unum <lb/>filamentum e, e, a, b, & </s> <s xml:id="echoid-s12024" xml:space="preserve">funi appenſum ſit pondus P, erit dire-<lb/>ctio actionis filamenti ſecundum ductum ſuum b, a, continuatum <lb/>ad lubitum uſque in C. </s> <s xml:id="echoid-s12025" xml:space="preserve">directio ponderis P eſt in rectâ continuata <lb/>b f P: </s> <s xml:id="echoid-s12026" xml:space="preserve">ſed filamentum a, b, g, f, ſuſtinet ſuperius ſibique incum-<lb/>bens e, e, a, b, quare reagit directione b d. </s> <s xml:id="echoid-s12027" xml:space="preserve">fiuntque tres poten-<lb/>tiæ agentes in unum punctum b, quarum magnitudo cognoſcitur, <lb/>ſi conſiderentur ſeorſum, ut in fig. </s> <s xml:id="echoid-s12028" xml:space="preserve">3. </s> <s xml:id="echoid-s12029" xml:space="preserve">b c exprimatur per b c: </s> <s xml:id="echoid-s12030" xml:space="preserve">b d <lb/>per b d. </s> <s xml:id="echoid-s12031" xml:space="preserve">b P per c d. </s> <s xml:id="echoid-s12032" xml:space="preserve">ducanturque in has tres directiones lineæ per-<lb/>pendiculares r s, s q r q, quæ coëundo forment Triangulum r s q, <lb/>hujus latera expriment magnitudines potentiarum in ſe agentium <lb/>& </s> <s xml:id="echoid-s12033" xml:space="preserve">ſibi æquilibratarum, uti demonſtravit Cl. </s> <s xml:id="echoid-s12034" xml:space="preserve">Varignonus in elabo-<lb/>ratiſſimo Mechanices opere. </s> <s xml:id="echoid-s12035" xml:space="preserve">Si igitur r s = s q exprimat vim Co-<lb/>hærentiæ fili c b & </s> <s xml:id="echoid-s12036" xml:space="preserve">b d, tum r q exprimet magnitudinem ponderis P, <lb/>æqualis ambabus Cohærentiæ viribus; </s> <s xml:id="echoid-s12037" xml:space="preserve">quia autem r q eſt minor <lb/>duabus r s + s q, pondus P erit minus quam ſumma utriulque Co-<lb/>hærentiæ c b + b d. </s> <s xml:id="echoid-s12038" xml:space="preserve">adeoque pondus P, quod ſolvet funem com-<lb/>poſitum tortumque, erit minus quam pondus, quodapplicatum filis <lb/>e e a b.</s> <s xml:id="echoid-s12039" xml:space="preserve">, a, b, g, f. </s> <s xml:id="echoid-s12040" xml:space="preserve">directe hæc fregiſſet, ſive funis compoſitus erit <lb/>debilior fibris ſolutis</s> </p> <p> <s xml:id="echoid-s12041" xml:space="preserve">Corol. </s> <s xml:id="echoid-s12042" xml:space="preserve">Sequitur ex hac demonſtratione, quod quo angulus c b d <lb/>in fig. </s> <s xml:id="echoid-s12043" xml:space="preserve">2. </s> <s xml:id="echoid-s12044" xml:space="preserve">eſt minor, eo angulum r s q in fig. </s> <s xml:id="echoid-s12045" xml:space="preserve">3. </s> <s xml:id="echoid-s12046" xml:space="preserve">eſſe majorem, & </s> <s xml:id="echoid-s12047" xml:space="preserve"><lb/>proinde manentibus s r, s q iiſdem, increſcet r q, donec evadat <lb/>fere æqualis s r + r q. </s> <s xml:id="echoid-s12048" xml:space="preserve">Quando autem angulus c b d eſt parvus, <lb/>repræſentat duo filamenta funem conſtituentia, & </s> <s xml:id="echoid-s12049" xml:space="preserve">vix intorta.</s> <s xml:id="echoid-s12050" xml:space="preserve"/> </p> <pb o="513" file="0527" n="527" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s12051" xml:space="preserve">Angulo c b d increſcente, decreſcit angulus r s q, & </s> <s xml:id="echoid-s12052" xml:space="preserve">ideo de-<lb/>creſcit longirudo lineæ r q, quæ exprimit rationem ponderis P: </s> <s xml:id="echoid-s12053" xml:space="preserve">ſed <lb/>angulo c b d increſcente, repræſentatur funis validius intortus; </s> <s xml:id="echoid-s12054" xml:space="preserve">qui-<lb/>cunque enim duo fila ſecum invicem torquebit, manifeſto obſer-<lb/>vabit, in initio angulum c b d eſſe parvum, eumque ſemper augeri, <lb/>quo fila vehementius intorquentur.</s> <s xml:id="echoid-s12055" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12056" xml:space="preserve">Ex hac demonſtratione manifeſto patet, quare funis contorſione <lb/>fibrarum factus, minus virium ad gerendum pondus habeat, quam <lb/>fibræ eum componentes, ſeorſim ſumtæ, habent: </s> <s xml:id="echoid-s12057" xml:space="preserve">tum 2°. </s> <s xml:id="echoid-s12058" xml:space="preserve">quare ro-<lb/>bur funis eo plus decreſcat, quo fibris vehementius intortis con-<lb/>ſtat: </s> <s xml:id="echoid-s12059" xml:space="preserve">Hæc omnia nunc nonnullis Experimentis confirmabo.</s> <s xml:id="echoid-s12060" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div446" type="section" level="1" n="446"> <head xml:id="echoid-head558" xml:space="preserve">EXPERIMENTUM LXXXIII.</head> <p> <s xml:id="echoid-s12061" xml:space="preserve">Sumſi funiculum tenuem, diametri 0, 03 pollicis Rhenolandici, <lb/>cui tres quatuorve ulnas longo appendere potui libras 12 {1/2}, ſed a li-<lb/>bris 13 rumpebatur: </s> <s xml:id="echoid-s12062" xml:space="preserve">ambo igitur fragmenta ſuſtinere potuerunt li-<lb/>bras 12 {1/2}. </s> <s xml:id="echoid-s12063" xml:space="preserve">Hæc conjuncta parum intorſi, ut funiculum acceperim <lb/>ex ambobus compoſitum, cujus extremitati appendi modo potue-<lb/>runt libræ 24. </s> <s xml:id="echoid-s12064" xml:space="preserve">Conatus fui menſurare angulum c b e in fig. </s> <s xml:id="echoid-s12065" xml:space="preserve">2. </s> <s xml:id="echoid-s12066" xml:space="preserve">quem <lb/>filum cum alio contorto conſtituebat, eum deprehendi angulum <lb/>16 {1/2} graduum, quare angulus c b d. </s> <s xml:id="echoid-s12067" xml:space="preserve">erat 33 graduum, tum vide fig. </s> <s xml:id="echoid-s12068" xml:space="preserve">4, <lb/>ambo ſimilia fila c b, b d, alligavi duobus clavis c & </s> <s xml:id="echoid-s12069" xml:space="preserve">d, & </s> <s xml:id="echoid-s12070" xml:space="preserve">ex me-<lb/>dio b appendi pondus pedetentim auctum uſque ad 24. </s> <s xml:id="echoid-s12071" xml:space="preserve">libras, obſer-<lb/>vans, ut angulus c b d etiam foret 33 graduum, elapſoque horæ minuto, <lb/>filum c b d diffractum fuit: </s> <s xml:id="echoid-s12072" xml:space="preserve">ſi ambo fila non intorta fuiſſent, tu-<lb/>liſſent ad minimum 25 libras, adeoque intorta evadunt gerendis <lb/>ponderibus ineptiora: </s> <s xml:id="echoid-s12073" xml:space="preserve">Cum autem angulus c b d eſt 33 graduum, eſt <lb/>in fig. </s> <s xml:id="echoid-s12074" xml:space="preserve">3. </s> <s xml:id="echoid-s12075" xml:space="preserve">angulus r s q graduum 147: </s> <s xml:id="echoid-s12076" xml:space="preserve">ponamus latus r s = s q ſingulum <lb/>eſſe 12 {1/2} partium, invenietur per regulas Trigonometriæ latus r q <lb/>24 partium, qui numerus exprimit pondus P, quod funem dif-<lb/>fregit.</s> <s xml:id="echoid-s12077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12078" xml:space="preserve">Reaumurius filum ſumſit longum, cui appendit pedetentim li-<lb/>bras 10, a quibus rumpebatur: </s> <s xml:id="echoid-s12079" xml:space="preserve">ambo fragmenta in unum contor-<lb/>ſit mediocriter, tum vero appendere huic novo funi tantum po-<lb/>tuit libras 16; </s> <s xml:id="echoid-s12080" xml:space="preserve">nam a pluribus frangebatur: </s> <s xml:id="echoid-s12081" xml:space="preserve">hæc fila non contorta <pb o="514" file="0528" n="528" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſuſtinuiſſent ad minimum libras 19, cum nunc minus tulerunt, <lb/>patet contorſionem debilitaſſe funem. </s> <s xml:id="echoid-s12082" xml:space="preserve">Merſennus exploravit <lb/>6 fidium robur, ex ſingula ſuſpendi potuerunt libræ 7. </s> <s xml:id="echoid-s12083" xml:space="preserve">unciæ 14, <lb/>poſtquam eas convolverat, tantum ferre potuerunt libras 41, cum <lb/>ſumma Cohærentiæ omnium ſeorſim examinatarum fuiſſet libra-<lb/>rum 47 {1/4}.</s> <s xml:id="echoid-s12084" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12085" xml:space="preserve">Sumſi aliud filum, quod a libris 12 {1/2} diffractum fuit, hujus am-<lb/>bo fragmenta colligavi, deinde intorſi multo plus, quam ante fe-<lb/>ceram; </s> <s xml:id="echoid-s12086" xml:space="preserve">ab appenſis libris 17 rumpebantur, cum ferre debuiſſent <lb/>libras 25, atque in præcedenti Experimento tulerint libras 24. </s> <s xml:id="echoid-s12087" xml:space="preserve">unde <lb/>liquet majorem contorſionem magis infringere vires funium.</s> <s xml:id="echoid-s12088" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12089" xml:space="preserve">Filum album ex Lino ruptum fuit a libris 3 {1/2}. </s> <s xml:id="echoid-s12090" xml:space="preserve">hujus am-<lb/>bo fragmenta colligata & </s> <s xml:id="echoid-s12091" xml:space="preserve">intorta plus quam mediocriter, fracta fue-<lb/>runt ab appenſis libris 4. </s> <s xml:id="echoid-s12092" xml:space="preserve">cum non contorta facile geſtaſſent libras 7. <lb/></s> <s xml:id="echoid-s12093" xml:space="preserve">Quoniam igitur in majoribus contorſionibus angulus c b d fig. </s> <s xml:id="echoid-s12094" xml:space="preserve">2 vel 3. </s> <s xml:id="echoid-s12095" xml:space="preserve"><lb/>augebatur, etiam per demonſtrationem ſupra datam, a minori pon-<lb/>dere funis rumpi debuit: </s> <s xml:id="echoid-s12096" xml:space="preserve">ut id ulterius evincerem, ſumſi ex eodem <lb/>glomere filum, quod ita duobus clavis rotundis, c, d, alligavi, <lb/>ut, vid. </s> <s xml:id="echoid-s12097" xml:space="preserve">fig 5? </s> <s xml:id="echoid-s12098" xml:space="preserve">& </s> <s xml:id="echoid-s12099" xml:space="preserve">6, angulus c b d eſſet major quam in priori caſu, <lb/>tumque pondus librarum 20, imo in alio tentamine fig. </s> <s xml:id="echoid-s12100" xml:space="preserve">6, pondus <lb/>P, 16 librarum, funem diffregit in b. </s> <s xml:id="echoid-s12101" xml:space="preserve">adeo ut ſit certiſſimum eo â mino-<lb/>ri pondere diffractum iri funem c b d duobus clavis annexum, quo an-<lb/>gulus c b d eſt major; </s> <s xml:id="echoid-s12102" xml:space="preserve">& </s> <s xml:id="echoid-s12103" xml:space="preserve">funem intortum eo etiam facilius diffringi, <lb/>quo in fig. </s> <s xml:id="echoid-s12104" xml:space="preserve">2. </s> <s xml:id="echoid-s12105" xml:space="preserve">funis eſt plus intortus, majoremque angulum c b d <lb/>format.</s> <s xml:id="echoid-s12106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12107" xml:space="preserve">Deinde in craſſioribus funibus hæc confirmanda erant; </s> <s xml:id="echoid-s12108" xml:space="preserve">funem igi-<lb/>tur Cannabinum elegi, cujus circumferentia erat 2 linearum, qui <lb/>ferre potuit pondus libr. </s> <s xml:id="echoid-s12109" xml:space="preserve">92. </s> <s xml:id="echoid-s12110" xml:space="preserve">bina ejus fragmenta contorſi in unum, <lb/>ita ut in fig. </s> <s xml:id="echoid-s12111" xml:space="preserve">2. </s> <s xml:id="echoid-s12112" xml:space="preserve">angulus a b e fuerit 33. </s> <s xml:id="echoid-s12113" xml:space="preserve">graduum, adeoque erat c b d <lb/>angulus 66 graduum, huic funi compoſito tantum appendi potue-<lb/>runt libræ 103. </s> <s xml:id="echoid-s12114" xml:space="preserve">Calculo igitur ſubducebam poſito latere c b = 92. <lb/></s> <s xml:id="echoid-s12115" xml:space="preserve">& </s> <s xml:id="echoid-s12116" xml:space="preserve">angulo c b d 66 graduum, quantum foret latus c d, quod depre-<lb/>hendebatur paulum majus quam 102 partium, adeo ut Experientia <lb/>cum calculo apprime congruerit: </s> <s xml:id="echoid-s12117" xml:space="preserve">Deinde ex eodem glomere cum <lb/>priori tres funes contorſi, ut iterum angulus a b e fig. </s> <s xml:id="echoid-s12118" xml:space="preserve">2. </s> <s xml:id="echoid-s12119" xml:space="preserve">eſſet 33 <lb/>graduum, funis inde compoſitus non tulit libras 160, conſtabat <pb o="515" file="0529" n="529" rhead="CORPORUM FIRMORUM."/> tamen reſoluta contorſione, quemlibet funem vires librar. </s> <s xml:id="echoid-s12120" xml:space="preserve">92 poſſi-<lb/>dere; </s> <s xml:id="echoid-s12121" xml:space="preserve">Quamobrem confirmamur iterum funes compoſitos ex aliis, <lb/>per contorſionem debilitari; </s> <s xml:id="echoid-s12122" xml:space="preserve">atque vires determinari poſſe ope <lb/>Trianguli formati ex perpendicularibus in directionem ſpiræ, reſi-<lb/>ſtentiæ, & </s> <s xml:id="echoid-s12123" xml:space="preserve">appenſi ponderis. </s> <s xml:id="echoid-s12124" xml:space="preserve">Sed Reaumuriana obſervata anne-<lb/>ctere libet, ut multitudine Experimentorum â variis captorum Phi-<lb/>loſophis magis convincamur, & </s> <s xml:id="echoid-s12125" xml:space="preserve">eo citius præjudicatam opinionem <lb/>exuamus: </s> <s xml:id="echoid-s12126" xml:space="preserve">Funem adhibuit Vir inclytus, qui geſtare poterat libras <lb/>72, hic erat compoſitus ex tribus funiculis, evolvit funem, ut ho-<lb/>rum trium robur ſeorſim examinaret; </s> <s xml:id="echoid-s12127" xml:space="preserve">unus deprehenſus fuit libras <lb/>27 ferre, alter libras 33. </s> <s xml:id="echoid-s12128" xml:space="preserve">tertius libras 35; </s> <s xml:id="echoid-s12129" xml:space="preserve">ſumma trium ponderum <lb/>eſt librar. </s> <s xml:id="echoid-s12130" xml:space="preserve">95. </s> <s xml:id="echoid-s12131" xml:space="preserve">quum tamen convoluti funes in unum modo libras 72 <lb/>geſtaverunt: </s> <s xml:id="echoid-s12132" xml:space="preserve">Præterea! alio uſus eſt fune, ex quo circiter ſuſpendebat <lb/>libras 70, nam a libris 72 frangebatur; </s> <s xml:id="echoid-s12133" xml:space="preserve">ex eo evolvit tres funicu-<lb/>los ipſum componentes, quorum unus ferebat libras 24, alter 28, <lb/>tertius 30; </s> <s xml:id="echoid-s12134" xml:space="preserve">ſumma horum ponderum eſt æqualis libris 82, quæ ma-<lb/>jor eſt, quam a fune compoſito lata fuit: </s> <s xml:id="echoid-s12135" xml:space="preserve">Si hæc Reaumuriana no-<lb/>ſtraque Experimenta non plane evicerint quemcunque funem com-<lb/>poſitum ex aliis debilitari convolutione in ſe mutuo, dubito an <lb/>quidem unquam aliquid demonſtratum fuerit: </s> <s xml:id="echoid-s12136" xml:space="preserve">prolixior evaſi quam <lb/>par erat, ſed ad errorem receptum eliminandum, ſemper quamplu-<lb/>rimum laboris impendi debet. </s> <s xml:id="echoid-s12137" xml:space="preserve">Reſtat ut determinemus robur non-<lb/>nullorum funium datæ craſſitiei, ut a priori cognoſcamus, quoties-<lb/>cunque aliquod pondus elevandum, vel grave onus movendum ſit, <lb/>cujus craſſitiei funis deſideretur, qui pondus geſtare valeat.</s> <s xml:id="echoid-s12138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12139" xml:space="preserve">Componuntur a reſtiariis funes tum albi, tum cinerei coloris, <lb/>quorum unum genus ex Cannabe inſolatione albefacta, alterum ex <lb/>Cannabe vulgari conficitur, utrumque genus examinavi, atque even-<lb/>tus tentaminum hi fuerunt.</s> <s xml:id="echoid-s12140" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div447" type="section" level="1" n="447"> <head xml:id="echoid-head559" xml:space="preserve">EXPERIMENTUM LXXXIV.</head> <p> <s xml:id="echoid-s12141" xml:space="preserve">Funis inſolatione candeſactus, cujus circumferentia erat 0, 15 <lb/>pollicis, compoſitus ex tribus funiculis in unum contortis, qui <lb/>ſinguli ex pluribus filamentis etiam contortis conſtabant, fuſtinuit <lb/>libras 31, ſed a libris 32 fractus fuit.</s> <s xml:id="echoid-s12142" xml:space="preserve"/> </p> <pb o="516" file="0530" n="530" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div448" type="section" level="1" n="448"> <head xml:id="echoid-head560" xml:space="preserve">EXPERIMENTUM LXXXV.</head> <p> <s xml:id="echoid-s12143" xml:space="preserve">Funis inſolatione candefactus, cujus circumferentia erat 0, 27 <lb/>pollicis, ruptus fuit a pondere librar. </s> <s xml:id="echoid-s12144" xml:space="preserve">87. </s> <s xml:id="echoid-s12145" xml:space="preserve">conſtabat ex 5 aliis funi-<lb/>culis intortis in unum.</s> <s xml:id="echoid-s12146" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div449" type="section" level="1" n="449"> <head xml:id="echoid-head561" xml:space="preserve">EXPERIMENTUM LXXXVI.</head> <p> <s xml:id="echoid-s12147" xml:space="preserve">Funis inſolatione candefactus, cujus circumferentia erat 0, 6 polli-<lb/>cis, compoſitus ex 6 aliis funiculis in unum convolutis, non plu-<lb/>res ferre potuit quam libras 210.</s> <s xml:id="echoid-s12148" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div450" type="section" level="1" n="450"> <head xml:id="echoid-head562" xml:space="preserve">EXPERIMENTUM LXXXVII.</head> <p> <s xml:id="echoid-s12149" xml:space="preserve">Funis Cannabinus vulgaris, cujus circumferentia erat 2 linearum, <lb/>compoſitus ex 6 aliis funiculis in unum convolutis geſtavit modo <lb/>libras 92.</s> <s xml:id="echoid-s12150" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div451" type="section" level="1" n="451"> <head xml:id="echoid-head563" xml:space="preserve">EXPERIMENTUM LXXXVIII.</head> <p> <s xml:id="echoid-s12151" xml:space="preserve">Funis Cannabinus vulgaris, ex 6 funiculis intortis fabrefactus, <lb/>cujus circumferentia erat 0, 4 pollic. </s> <s xml:id="echoid-s12152" xml:space="preserve">fractus fuit a libris 160 ap-<lb/>penſis.</s> <s xml:id="echoid-s12153" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div452" type="section" level="1" n="452"> <head xml:id="echoid-head564" xml:space="preserve">EXPERIMENTUM LXXXIX.</head> <p> <s xml:id="echoid-s12154" xml:space="preserve">Alius funis Cannabinus etiam ex 6 aliis compoſitus, & </s> <s xml:id="echoid-s12155" xml:space="preserve">circum-<lb/>ferentiæ 0, 54 pollicis geſtare modo potuit libras 240.</s> <s xml:id="echoid-s12156" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12157" xml:space="preserve">Hæc Experimenta inſtitui, ut detegerem an Cohærentiæ funium <lb/>forent in ratione craſſitierum, aut in quacunque alia, ut regulam <lb/>traderem ex data funis craſſitie determinandi ejus robur, aut ex <lb/>robore aſſignandi craſſitiem; </s> <s xml:id="echoid-s12158" xml:space="preserve">aut definiendi craſſitiem ad datum <lb/>pondus gerendum; </s> <s xml:id="echoid-s12159" xml:space="preserve">ſed ex iis liquet 1°. </s> <s xml:id="echoid-s12160" xml:space="preserve">Cohærentiam funium non <lb/>eſſe in ratione craſſitierum; </s> <s xml:id="echoid-s12161" xml:space="preserve">nam in Experimentis 84, 85, 86, ſunt <lb/>craſſities funium uti, 1, 3, 16. </s> <s xml:id="echoid-s12162" xml:space="preserve">& </s> <s xml:id="echoid-s12163" xml:space="preserve">Cohærentiæ uti 32, 87, 210, <lb/>cum fuiſſent ſecundum proportionem craſſitierum uti 32, 96, 512.</s> <s xml:id="echoid-s12164" xml:space="preserve"> <pb o="517" file="0531" n="531" rhead="CORPORUM FIRMORUM."/> ita in Experimentis 87, 88, 89. </s> <s xml:id="echoid-s12165" xml:space="preserve">craſſities ſunt uti 1, 4, 7 {29/100}, Co-<lb/>hærentiæ obſervatæ fuerunt uti 92, 160, 240, cum ſecundum pro-<lb/>portionem craſſitierum debuiſſent eſſe 92, 368, 644. </s> <s xml:id="echoid-s12166" xml:space="preserve">a proportione <lb/>craſſitierum maxime abludunt funes craſſiores, minus autem tenuio-<lb/>res; </s> <s xml:id="echoid-s12167" xml:space="preserve">decrementi non videtur dari proportio conſtans: </s> <s xml:id="echoid-s12168" xml:space="preserve">nam in com-<lb/>paratis tribus Experimentis 84, 85, 86. </s> <s xml:id="echoid-s12169" xml:space="preserve">Cohærentia ſecundi non <lb/>multum abludit a calculo, qui vim æqualem libris 96 ponit, ex-<lb/>perientia dante 87, ſed Cohærentia Experimenti 86 pluri-<lb/>mum abludit a calculo, cum hic ſuppeditet libras ferendas 512, Ex-<lb/>perientia nequaquam dimidium pondus afferente, cum id modo <lb/>fuerit librar. </s> <s xml:id="echoid-s12170" xml:space="preserve">210: </s> <s xml:id="echoid-s12171" xml:space="preserve">atque ejusmodi ingens abluſio quoque datur a <lb/>calculo in Experimento 89. </s> <s xml:id="echoid-s12172" xml:space="preserve">Quamobrem hactenus determinari <lb/>nequit, quantum futurum ſit robur funis datæ craſſitiei: </s> <s xml:id="echoid-s12173" xml:space="preserve">id quidem <lb/>ſemper admodum varium erit pro bonitate filamentorum Lini aut <lb/>Cannabis; </s> <s xml:id="echoid-s12174" xml:space="preserve">tum pro majori minorive filamentorum contorſione, <lb/>attamen dolendum eſt nihil poſſe a priori definiri calculi ope, quod <lb/>utcunque ad veritatem appropinquaret: </s> <s xml:id="echoid-s12175" xml:space="preserve">unicum remedium eſt, ut <lb/>ſemel tentamina capiantur cum funibus diverſiſſimarum craſſitie-<lb/>rum, a minima uſque ad maximam, exinde Tabulam condamus, <lb/>quæ, quotieſcunque opus eſt, conſulatur; </s> <s xml:id="echoid-s12176" xml:space="preserve">quod ſecum quidem <lb/>nonnihil laboris habebit, ſed emolumentum in genus humanum ex <lb/>his tentaminibus fundamentalibus non exiguum redundaret.</s> <s xml:id="echoid-s12177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12178" xml:space="preserve">Quoniam igitur funes per contorſiones adeo debilitantur, alſ<unsure/>-<lb/>quamdiu occupatus fui, ut remedium afferrem & </s> <s xml:id="echoid-s12179" xml:space="preserve">fila funeſque tam <lb/>fortes, ac fieri poteſt, conſervarem, ſic enim parcere magnis poſ<unsure/>-<lb/>ſemus impenſis; </s> <s xml:id="echoid-s12180" xml:space="preserve">quippe ſi rudens anchorarius, cujus circumferen-<lb/>tia eſt 21 pollicum, fieri poſſit æque cohærens & </s> <s xml:id="echoid-s12181" xml:space="preserve">modo conſter ex <lb/>{1/3} parte Cannabis, aut ex minori quantitate, ſumtus erunt triplo mi-<lb/>nores, quod inveniſſe & </s> <s xml:id="echoid-s12182" xml:space="preserve">demonſtraſſe omnibus navium poſſeſſori-<lb/>bus utiliſſimum exiſteret.</s> <s xml:id="echoid-s12183" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div453" type="section" level="1" n="453"> <head xml:id="echoid-head565" xml:space="preserve">EXPERIMENTUM XC.</head> <p> <s xml:id="echoid-s12184" xml:space="preserve">Cum ex obſervationibus præcedentibus conſtat, per contorſionem <lb/>omnia fila debilitari, neque tamen abſque convolutione ex lino aut <lb/>Cannabe, aut Lana, aut animalium pilis filum longum confici queat, <pb o="518" file="0532" n="532" rhead="INTRODUCTIO AD COHÆRENTIAM"/> oportebit, ut prima & </s> <s xml:id="echoid-s12185" xml:space="preserve">tenuiſſima fila parum contorqueantur, & </s> <s xml:id="echoid-s12186" xml:space="preserve"><lb/>fibrillæ modo tantum comprimantur, ut partes ex ſe non labantur, <lb/>ſed attritu contra ſe invicem reſiſtant lubrico motui. </s> <s xml:id="echoid-s12187" xml:space="preserve">Tum requi-<lb/>ritur, ut ejuſmodi fila tenuia plurima parallela ſibi ponantur, atque <lb/>colligantur in faſciculum cylindricum ope alterius ambientis fili, <lb/>ſpirali ductu colligentis, & </s> <s xml:id="echoid-s12188" xml:space="preserve">comprimentis omnia adverſus ſe, quo <lb/>unum continuum corpus conſtituant.</s> <s xml:id="echoid-s12189" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12190" xml:space="preserve">Funis ex hiſce parallelis filis compoſitus, erit tanti roboris ac <lb/>unquam fieri poteſt; </s> <s xml:id="echoid-s12191" xml:space="preserve">nam ſi illius extremo pondus appendatur, <lb/>omnia fila, æque tenſa in faſciculo, nequaquam ſecunda contorſione <lb/>debilitata, gerent tantum ponderis, quanta foret ſumma omnium <lb/>ſeorſim poſitorum: </s> <s xml:id="echoid-s12192" xml:space="preserve">conſtruxi eo modo funem, cujus circumferen-<lb/>tia erat 4 linearum, huic appendi potuerunt libræ 300 imo 320, <lb/>cum funis ex iisdem filis, contorſione vulgarem juxta methodum <lb/>compoſitus, rumpebatur â libris 160: </s> <s xml:id="echoid-s12193" xml:space="preserve">adeoque duplo cohærentior <lb/>funis tam exiguæ craſſitiei evadit, unde procul dubio rudens hoc mo-<lb/>do fabrefactus quidem decuplo fortior vulgari rudente foret: </s> <s xml:id="echoid-s12194" xml:space="preserve">Sed <lb/>id incommodi habet ejuſmodi textura, ut extimo filo, reliqua <lb/>ambiente, diffracto; </s> <s xml:id="echoid-s12195" xml:space="preserve">omnia exſiliant ex maſſa, quæ vix uſui ma-<lb/>net ſuperſtes, ſuccurrimus aliquomodo ex nonnullis filis faſciculum <lb/>componendo ope ambientis fili, atque iterum aliquos faſciculos <lb/>colligendo ope alterius ambientis fili, atque ejusmodi aliquot faſci-<lb/>culos iterum combinando ope circumvoluti alterius fili, donec fu-<lb/>nis quæſitam craſſitiem acceperit, ſed tum labor nimis multipli-<lb/>catur.</s> <s xml:id="echoid-s12196" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div454" type="section" level="1" n="454"> <head xml:id="echoid-head566" xml:space="preserve">EXPERIMENTUM XCI.</head> <p> <s xml:id="echoid-s12197" xml:space="preserve">Ad aliam proinde me converti methodum, ſemper id collineans, <lb/>ut fila prima maneant recta, ſibique parallela, quantum fieri poſſet: <lb/></s> <s xml:id="echoid-s12198" xml:space="preserve">Oculos ad faſciolas converti, (quas Belgæ vocant Zeelen) quæ <lb/>filis parallelis & </s> <s xml:id="echoid-s12199" xml:space="preserve">fere rectis conſtant, filum elegi, per totam ſuam <lb/>longitudinem æque craſſum ſatis, quod ſuſpendere fere poterat li-<lb/>bras 20: </s> <s xml:id="echoid-s12200" xml:space="preserve">hujuſmodi novem textori tradidi, qui eos ope alterius fu-<lb/>niculi texuit in faſciolæ formam: </s> <s xml:id="echoid-s12201" xml:space="preserve">hæc ad machinam divulſoriam <lb/>examinata ſuſtinuit libras 175. </s> <s xml:id="echoid-s12202" xml:space="preserve">quod pondus ſatis propinque accedit <pb o="519" file="0533" n="533" rhead="CORPORUM FIRMORUM."/> ad maximum, quod a 9 filis geri potuiſſet: </s> <s xml:id="echoid-s12203" xml:space="preserve">hinc colligimus faſcio-<lb/>las eſſe multo cohærentiores funibus, ex æquali quanti<unsure/>tate Can-<lb/>nabis & </s> <s xml:id="echoid-s12204" xml:space="preserve">æque longis, compoſitis.</s> <s xml:id="echoid-s12205" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div455" type="section" level="1" n="455"> <head xml:id="echoid-head567" xml:space="preserve">EXPERIMENTUM XCII.</head> <p> <s xml:id="echoid-s12206" xml:space="preserve">Sed faſciolæ omnibus humanis uſibus inſervire nequeunt ob pla-<lb/>nitiem & </s> <s xml:id="echoid-s12207" xml:space="preserve">latitudinem, adeoque alio fabrefeci funem modo; </s> <s xml:id="echoid-s12208" xml:space="preserve">Tres <lb/>funiculos ex glomere eodem ac ante ſumſi, quorum quilibet li-<lb/>bras 20 fere tulerat, hi contorti parum vulgari modo, ut reſtiarii <lb/>ſolent, ferre potuerunt fere libras 50, magisintorti modo libras 40. <lb/></s> <s xml:id="echoid-s12209" xml:space="preserve">tum tres alios funiculos ejuſdem glomeris intertexui, quemadmo-<lb/>dum mulieres capillos texunt, ſive quemadmodum tæniæ, quibus <lb/>thoraces adducuntur, fiunt: </s> <s xml:id="echoid-s12210" xml:space="preserve">hoc modo nulla vis funibus infereba-<lb/>tur; </s> <s xml:id="echoid-s12211" xml:space="preserve">unde ſuſtinuerunt libris 58: </s> <s xml:id="echoid-s12212" xml:space="preserve">funis igitur hac methodo confe-<lb/>ctus præſtat vulgari contorto, quod etiam ex ſequenti tentamine <lb/>liquebit: </s> <s xml:id="echoid-s12213" xml:space="preserve">Tres funiculos, qui ſinguli conſtabant ex tribus funiculis <lb/>contortis, etiam intorſi in modum funis vulgaris, funis inde factus <lb/>tulit tantum libras 155, compoſitus autem erat ex 9 aliis, quorum ſin-<lb/>guli geſtaſſent libras 20. </s> <s xml:id="echoid-s12214" xml:space="preserve">Verum 9 funiculos ejuſdem glomeris textui <lb/>inſtar capillorum muliebrium, indeque factus funis abſque ruptione <lb/>ſuſtinuit libras 170, adeoque fere tantundem ac faſciola lata, aut <lb/>funis parallelis filis & </s> <s xml:id="echoid-s12215" xml:space="preserve">rectis per aliud ambiens compoſitus.</s> <s xml:id="echoid-s12216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12217" xml:space="preserve">Eſt hic præſtantiſſimus modus conſtruendi funes uſibus humanis <lb/>aptos, qui multo tenuiores eſſe poſſunt vulgaribus, quando eadem <lb/>Cohærentiæ vis deſideratur; </s> <s xml:id="echoid-s12218" xml:space="preserve">eandem vero cum vulgaribus nacti <lb/>craſſitiem, multo fortiores erunt; </s> <s xml:id="echoid-s12219" xml:space="preserve">rotundi etiam ſunt, fractoque <lb/>uno alterove filo non exſiliunt reliqua; </s> <s xml:id="echoid-s12220" xml:space="preserve">flexilior manet quam funis <lb/>intortus, unde omnibus eſt accommodatior uſibus, quam funis in-<lb/>tortus.</s> <s xml:id="echoid-s12221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12222" xml:space="preserve">Præter hos modos humana ſagacitas alios quidem temporis ſuc-<lb/>ceſſu deteget, nobis ſufficit præjudicia exuiſſe inveterata, quibus <lb/>contorſio vires funibus addere credebatur, & </s> <s xml:id="echoid-s12223" xml:space="preserve">ſimul aliquod reme-<lb/>dium veteri incommodo attuliſſe, idque demonſtraſſe ex Expe-<lb/>rientia.</s> <s xml:id="echoid-s12224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12225" xml:space="preserve">Operæ pretium eſt explorare partium animalium Cohærentiam, <pb o="520" file="0534" n="534" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ut comparari cum ea vegetabilium poſſit, & </s> <s xml:id="echoid-s12226" xml:space="preserve">videri an major mi-<lb/>norve ſit: </s> <s xml:id="echoid-s12227" xml:space="preserve">ſi ad vim vitalem attendamus, quæ in animalibus partes <lb/>fluidas ſibi invicem apponit, compingitque in maſſam ſolidam, hæc <lb/>multo major videtur iis viribus, quam quæ idem in Vegetabilibus <lb/>efficiunt, in quibus lenta tantum humorum circulatio, & </s> <s xml:id="echoid-s12228" xml:space="preserve">debilior <lb/>partium appoſitio fit; </s> <s xml:id="echoid-s12229" xml:space="preserve">unde, fluidi nutrientis partibus æque magnis, <lb/>æque ſolidis, ejuſdemque figuræ poſitis, major Cohærentia fibrillæ <lb/>animalibus tenuiſſimæ videretur futura, quam fibrillæ vegetabilis <lb/>æque craſſæ.</s> <s xml:id="echoid-s12230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12231" xml:space="preserve">Verum non pendet Cohærentia fibrillæ tantum a vehementiori <lb/>impactu, quo particulæ ſibi impoſitæ ſunt, ſed ab earum ſolidita-<lb/>te majori minorive, tum a planiori aut aſperiori ſuperficie, quâ ſe <lb/>attingunt; </s> <s xml:id="echoid-s12232" xml:space="preserve">hinc enim plus minuſve ſe attrahunt: </s> <s xml:id="echoid-s12233" xml:space="preserve">Sint igitur partes <lb/>nutrientes animales ſolidiores quam vegetabiles, plus materiæ at-<lb/>trahentis in ſe continebunt; </s> <s xml:id="echoid-s12234" xml:space="preserve">ſint præterea planiori ſuperficie do-<lb/>natæ, ut ſe majori ſuperficie contingant, etiam fortius ſe attrahent; <lb/></s> <s xml:id="echoid-s12235" xml:space="preserve">quamobrem in animali partes fibram compoſituræ hoc modo con-<lb/>ſtitutæ, multo fortius ſe attrahent, & </s> <s xml:id="echoid-s12236" xml:space="preserve">proinde magis cohærebunt <lb/>quam aliæ rariores aſperioresque in vegetabili: </s> <s xml:id="echoid-s12237" xml:space="preserve">contra Vegetabile <lb/>ejuſmodi partibus donatum, fortius cohærebit quam animalis fibra <lb/>ê partibus rarioribus aſperioribuſque compoſita: </s> <s xml:id="echoid-s12238" xml:space="preserve">a priori igitur de-<lb/>terminari nequit, an vegetabile an animale ſolidum æque craſſum <lb/>firmius debiliusve futurum ſit, quamobrem ad Experientiam ve-<lb/>niendum erit, quæ omnia determinare ſolet: </s> <s xml:id="echoid-s12239" xml:space="preserve">a fibrilla tenuiſſima <lb/>tractabili incipiam ſenſim ad craſſiores perrecturus; </s> <s xml:id="echoid-s12240" xml:space="preserve">ſubtiliores non <lb/>novi tractabiles, quam quas Bombyx ſuppeditat.</s> <s xml:id="echoid-s12241" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div456" type="section" level="1" n="456"> <head xml:id="echoid-head568" xml:space="preserve">EXPERIMENTUM XCIII.</head> <p> <s xml:id="echoid-s12242" xml:space="preserve">Sumtum fuit filum unum ſerici, modo ante evolutum ex glome-<lb/>re, in quo Chryſalis latebat, hujus ſuperius extremum aliquoties <lb/>circumvolvi circa politum ſtylum cupreum, quemadmodum circa <lb/>alium ſtylum inferiorem extremitatem, huic ſtylo ſenſim appenſa <lb/>fuerunt grana Medica, donec filum rumpebatur: </s> <s xml:id="echoid-s12243" xml:space="preserve">varia inſtituta ſunt <lb/>tentamina, ut eo certius verum pondus cognoſceretur, aliquando <lb/>autem filo appendi potuerunt 80, aliquando 85, etiam 90 grana, <pb o="521" file="0535" n="535" rhead="CORPORUM FIRMORUM."/> a quibus frangebatur: </s> <s xml:id="echoid-s12244" xml:space="preserve">Convenit hic Experimentorum eventus ſatis <lb/>bene cum eo, quem Cl. </s> <s xml:id="echoid-s12245" xml:space="preserve">Reaumurius deprehendit, affirmans ſibi ê <lb/>multiplici tentamine conſtitiſſe, unum filum bombycinum ſuſti-<lb/>nuiſſe drachmam, nunc drachmam ſesqui, ſed hoc pondus a for-<lb/>tiſſimo filo tantum potuiſſe geſtari.</s> <s xml:id="echoid-s12246" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div457" type="section" level="1" n="457"> <head xml:id="echoid-head569" xml:space="preserve">EXPERIMENTUM XCIV.</head> <p> <s xml:id="echoid-s12247" xml:space="preserve">Fila 57 Serici modo â glomere eodem Chryſalidis evoluta ac in Expe-<lb/>rimento XCIII. </s> <s xml:id="echoid-s12248" xml:space="preserve">parum contorta conſtituerunt craſſitiem capillo hu-<lb/>mano æqualem, hæc circa duos convoluta aliquousque ſtylos, utro-<lb/>bur eorum exploraretur, fracta fuerunt a granis 4845, adeoque quodli-<lb/>bet geſtaverat 85 grana: </s> <s xml:id="echoid-s12249" xml:space="preserve">fila contorquebantur in unum, ut craſſities <lb/>comparari cum pilo poſſet: </s> <s xml:id="echoid-s12250" xml:space="preserve">evolvebantur iterum cum firmitas ex-<lb/>ploraretur; </s> <s xml:id="echoid-s12251" xml:space="preserve">nam minus ponderis geſtaſſent convoluta, uti ſuperius <lb/>demonſtratum eſt, atque Reaumurius Experimento probavit: </s> <s xml:id="echoid-s12252" xml:space="preserve">qui <lb/>filum compoſuit ex 832 ſericeis filamentis intortis, huic appendere <lb/>ſolummodo potuit 640 drachmas, ſive 5 libras, raro 5 {1/2} libras, cum <lb/>ponderum ſumma â filis omnibus geſtanda inveniri debuiſſet 1040 <lb/>drachmarum, tanta debilitatio filo propter contorſionem acceſſit.</s> <s xml:id="echoid-s12253" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div458" type="section" level="1" n="458"> <head xml:id="echoid-head570" xml:space="preserve">EXPERIMENTUM XCV.</head> <p> <s xml:id="echoid-s12254" xml:space="preserve">Capillus igitur humanus, qui quinquageſies & </s> <s xml:id="echoid-s12255" xml:space="preserve">ſepties craſſior fi-<lb/>lamentis bombycinis fuerat circa duos convolutus ſtylos, ſuſtinuit <lb/>modo grana 2069, tumque frangebatur: </s> <s xml:id="echoid-s12256" xml:space="preserve">erat capillus ſubtilis, modo <lb/>ante e capite evulſus, hominis ſani juveniſque: </s> <s xml:id="echoid-s12257" xml:space="preserve">de Lanis quoque <lb/>memorat ſe robur capilli ſui capitis indagaſſe, atque deprehendiſſe <lb/>1200 granorum, alium tamen geſtaſſe 1920 grana: </s> <s xml:id="echoid-s12258" xml:space="preserve">quæ diſcrepan-<lb/>tia ab ætate, pilorum cultura, craſſitieve varia pendere poteſt.</s> <s xml:id="echoid-s12259" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div459" type="section" level="1" n="459"> <head xml:id="echoid-head571" xml:space="preserve">EXPERIMENTUM XCVI.</head> <p> <s xml:id="echoid-s12260" xml:space="preserve">Deinde ſeptem elegi recentes ejuſdem hominis capillos, æque <lb/>craſſos, quantum microſcopio obſervare licuit, hi in unum contorti <lb/>componebant craſſitiem æqualem ſetæ equinæ, etiam modo ante <pb o="522" file="0536" n="536" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ex caudâ Equi vegeti extracto: </s> <s xml:id="echoid-s12261" xml:space="preserve">Septem hi capilli evoluti iterum, <lb/>non plus quam 9635. </s> <s xml:id="echoid-s12262" xml:space="preserve">grana ſuſtinuerunt.</s> <s xml:id="echoid-s12263" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div460" type="section" level="1" n="460"> <head xml:id="echoid-head572" xml:space="preserve">EXPERIMENTUM XCVII.</head> <p> <s xml:id="echoid-s12264" xml:space="preserve">Tum ſetæ equinæ firmitas explorata fuit, quæ in variis ten-<lb/>taminibus deprehenſa eſt 7970, vel 7920, granorum, vel alicujus <lb/>ponderis intermedii: </s> <s xml:id="echoid-s12265" xml:space="preserve">hujus craſſities ope Microſcopii examinata, <lb/>& </s> <s xml:id="echoid-s12266" xml:space="preserve">comparata cum ſcala transverſis diviſionibus diſtincta, videba-<lb/>tur paulo minoris diametri, quam 0, 01 pollicis Rhenolandici, fa-<lb/>teor tamen accuratiſſime craſſitiem non potuiſſe definiri.</s> <s xml:id="echoid-s12267" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12268" xml:space="preserve">Cum igitur ſeta hæc fuerit ſepties craſſior capillo humano, <lb/>humanus 57 craſſior bombycino, fuit ſeta 399. </s> <s xml:id="echoid-s12269" xml:space="preserve">craſſior bomby-<lb/>cino: </s> <s xml:id="echoid-s12270" xml:space="preserve">& </s> <s xml:id="echoid-s12271" xml:space="preserve">cum bombycis filum gerat 85 grana, ejuſmodi fila 399 <lb/>geſtare poſſent grana 33915, ſeta tamen modo tulit 7970 <lb/>grana.</s> <s xml:id="echoid-s12272" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div461" type="section" level="1" n="461"> <head xml:id="echoid-head573" xml:space="preserve">EXPERIMENTUM XCVIII.</head> <p> <s xml:id="echoid-s12273" xml:space="preserve">Sumta fuit tela Araneæ majoris, quæ ejus craſſitiei per microſco-<lb/>pium obſervabatur, ut 16 in unum convolutæ faſciculum compo-<lb/>ſuerint maſſam pilo humano Exper. </s> <s xml:id="echoid-s12274" xml:space="preserve">XCV æqualem: </s> <s xml:id="echoid-s12275" xml:space="preserve">quælibet fere <lb/>geſtare potuit pondus 150 granorum, totique faſciculo appendi po-<lb/>tuerunt 2400 grana.</s> <s xml:id="echoid-s12276" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div462" type="section" level="1" n="462"> <head xml:id="echoid-head574" xml:space="preserve">EXPERIMENTUM XCIX.</head> <p> <s xml:id="echoid-s12277" xml:space="preserve">Lini mediocriter ſubtilis, neque ulla alia adhuc arte tractati, <lb/>quam ut neri poſſit, elegi filamenta ſolitaria 23, quæ parum intorta <lb/>filum formabant æque craſſum ac ſeta equina Exper. </s> <s xml:id="echoid-s12278" xml:space="preserve">XCVII fuit; <lb/></s> <s xml:id="echoid-s12279" xml:space="preserve">horum firmitas tanta fuit, ut appendi potuerint grana 11710, aucto <lb/>pondere frangebantur: </s> <s xml:id="echoid-s12280" xml:space="preserve">Examinatum Microſcopii ope unum ex his <lb/>23 filamentum, deprehendebatur non fuiſſe ſolitarium, ſed con-<lb/>ſtare ad minimum ex 14. </s> <s xml:id="echoid-s12281" xml:space="preserve">aliis, in quæulteriori putrefactione aut <lb/>pulſione malleorum ſeparari potuiſſet, imo plura ſubtiliora in alio <lb/>filamento ſe exhibuerunt: </s> <s xml:id="echoid-s12282" xml:space="preserve">ut horum corporum firmitates compa- <pb o="523" file="0537" n="537" rhead="CORPORUM FIRMORUM."/> rentur ſecum invicem, ad eandem reducta ſupponantur craſſitiem, <lb/>quæ ſit ea ſetæ Equinæ, & </s> <s xml:id="echoid-s12283" xml:space="preserve">ſe habebunt ſecundum hanc Tabulam.</s> <s xml:id="echoid-s12284" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Sericum \\ Bombycis # Tela \\ Araneæ # Linum # Pilus \\ Humanus # Seta \\ Equina <lb/>33915, # 15800. # 11710. # 9635. # 7970. <lb/></note> <p> <s xml:id="echoid-s12285" xml:space="preserve">Ex quibus firmitatibus inter ſe comparatis colligo: </s> <s xml:id="echoid-s12286" xml:space="preserve">Eo partium <lb/>majorem Cohærentiam dari, quo Natura fibrillas format ſubtilio-<lb/>res, poſitis cæteris paribus: </s> <s xml:id="echoid-s12287" xml:space="preserve">Nam fibrilla omnium tenuiſſima eſt <lb/>Sericum, craſſior eſt Araneæ tela; </s> <s xml:id="echoid-s12288" xml:space="preserve">quam ſuperat Linum, quo craſ-<lb/>ſior eſt pilus humanus, qui iterum ſuperatur craſſitie ab equino.</s> <s xml:id="echoid-s12289" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12290" xml:space="preserve">Fateor equidem me ita conſiderare pilum humanum inſtar fi-<lb/>brillæ ſolidæ, qualis nequaquam eſt, cum beneficio Microſcopii con-<lb/>ſpiciatur per totam ſuam longitudinem innumeris ornari vaſculis, <lb/>inter ſe communicantibus, nunc ſeparatis, nunc iterum unitis, <lb/>inſulas ſub diverſiſſimis angulis conſtituentibus: </s> <s xml:id="echoid-s12291" xml:space="preserve">horum vaſculorum <lb/>nonnulla capillo nutrimentum afferunt, alia oleoſam medullam præ-<lb/>parant, quam medio cavo infundunt, quæ abundans ex apertis ex-<lb/>tremitatibus capilli effluit: </s> <s xml:id="echoid-s12292" xml:space="preserve">Vaſcula igitur hæc cava ſunt, formata <lb/>ex fibrillis multum ſubtilioribus, quam illæ ſunt, quæ Sericum vel <lb/>telam Araneæ formant: </s> <s xml:id="echoid-s12293" xml:space="preserve">ſumma Cohærentiæ harum efficit totam <lb/>Cohærentiam pili; </s> <s xml:id="echoid-s12294" xml:space="preserve">ſed quia vaſa, quæ formant, decurrunt variis <lb/>flexibus, & </s> <s xml:id="echoid-s12295" xml:space="preserve">vaſorum tegmen pilum componit, hinc ab appenſo <lb/>ipſi pilo pondere trahuntur inæqualiter, nec ſuæ Cohærentiæ vires <lb/>æquabiliter exercent.</s> <s xml:id="echoid-s12296" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12297" xml:space="preserve">Eadem ratio locum habet in Chordis Muſicis, quæ ex Inteſtinis <lb/>animalibus convolutis netisque formantur, quæ ſunt congeries in-<lb/>numerorum canalium, & </s> <s xml:id="echoid-s12298" xml:space="preserve">ſolidarum fibrarum hos componentium, <lb/>quæ omnes non decurrunt ſecundum longitudinum, ſed variis gyris <lb/>flexibuſque.</s> <s xml:id="echoid-s12299" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div463" type="section" level="1" n="463"> <head xml:id="echoid-head575" xml:space="preserve">EXPERIMENTUM C.</head> <p> <s xml:id="echoid-s12300" xml:space="preserve">Chordarum Cohærentiam etiam explorare anniſus fui, eas elegi, <lb/>quibus Muſici utuntur; </s> <s xml:id="echoid-s12301" xml:space="preserve">una, cujus diameter erat 0, 03 pollicis, <pb o="524" file="0538" n="538" rhead="INTRODUCTIO AD COHÆRENTIAM"/> geſtavit, antequam frangebatur, libras 27. </s> <s xml:id="echoid-s12302" xml:space="preserve">altera craſſior & </s> <s xml:id="echoid-s12303" xml:space="preserve">diame-<lb/>tri 0, 05 pollicis, ſuſtinuit ante rupturam libras 42.</s> <s xml:id="echoid-s12304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12305" xml:space="preserve">Ex quibus Experimentis concludo, chordas ex Inteſtinis eſſe fir-<lb/>miores pilis: </s> <s xml:id="echoid-s12306" xml:space="preserve">cum enim diameter chordæ primæ ſit triplo major <lb/>quam eſt ſetæ quinæ, erit illius craſſities novies major, & </s> <s xml:id="echoid-s12307" xml:space="preserve">proinde <lb/>novies plus ſubſtantiæ corporeæ habebit quam ſeta; </s> <s xml:id="echoid-s12308" xml:space="preserve">ſed ſetageſtavit <lb/>grana 7970, novem igitur ferent libras 9 + 2680 grana: </s> <s xml:id="echoid-s12309" xml:space="preserve">ſed chorda <lb/>ſuſtinuit libras 27 adeoque fere triplo robuſtior eſt ſetâ.</s> <s xml:id="echoid-s12310" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div464" type="section" level="1" n="464"> <head xml:id="echoid-head576" xml:space="preserve">EXPERIMENTUM CI.</head> <p> <s xml:id="echoid-s12311" xml:space="preserve">Ut Corii firmitatem experirer, ſumtum fuit Loramentum corii <lb/>Vitulini boni, 0, 4 pollicis latum, 0, 08 pollic. </s> <s xml:id="echoid-s12312" xml:space="preserve">craſſum, quod <lb/>vix ſuſtinuit libras 80, ab his enim aliquamdiu appenſis ruptum <lb/>fuit.</s> <s xml:id="echoid-s12313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div465" type="section" level="1" n="465"> <head xml:id="echoid-head577" xml:space="preserve">EXPERIMENTUM CII.</head> <p> <s xml:id="echoid-s12314" xml:space="preserve">Tandem cepi Experimentum cum Corii bubuli nova & </s> <s xml:id="echoid-s12315" xml:space="preserve">bene te-<lb/>naci lamellâ, unum pollicem lata, quæ in medio exſciſſa erat, ut <lb/>anguſtior foret, ejuſque Cohærentia ope Machinæ divulſoriæ ex-<lb/>ploraretur, habuit in medio latitudinem 0, 4 pollic. </s> <s xml:id="echoid-s12316" xml:space="preserve">craſſitiem 0, 18, <lb/>pollicis, fractum fuit a libris 380.</s> <s xml:id="echoid-s12317" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12318" xml:space="preserve">Inſtitutum fuit hoc Experimentum cum hoc Corio, ut conſtaret <lb/>robur Loramentorum, ex quibus currus Magnatum ſuſpenduntur: <lb/></s> <s xml:id="echoid-s12319" xml:space="preserve">Solent enim Carpentarii ex hoc Corio ejusdem craſſitiei quinque <lb/>loramenta, 2 {3/4} vel 3 pollices lata conſuere in unum, & </s> <s xml:id="echoid-s12320" xml:space="preserve">ex 4 ejusmo-<lb/>di conſutis currus ſuſpendere ad 4 angulos: </s> <s xml:id="echoid-s12321" xml:space="preserve">Quantum igitur eſt ro-<lb/>bur ejuſmodi 4 loramentorum compoſitorum? </s> <s xml:id="echoid-s12322" xml:space="preserve">cum loramentum 4 <lb/>lineas latum geſtat libras 380, aliud quod latitudinem 3 pollicum ha <lb/>bet, feret libras 3420. </s> <s xml:id="echoid-s12323" xml:space="preserve">adeoque ejuſmodi 5 conſuta in unum ſuſpen-<lb/>dere poterunt libras 17100, & </s> <s xml:id="echoid-s12324" xml:space="preserve">quatuor ejuſmodi compoſita gerent <lb/>libras 68400. </s> <s xml:id="echoid-s12325" xml:space="preserve">Poſſet tamen hoc pondus modo ferri ab iis ſecun-<lb/>dum longitudinem tractis, ſed quia obliquius affiguntur curribus, <lb/>non tantundem ponderis ſuſtinebunt, quemadmodum Statici de-<lb/>monſtrant.</s> <s xml:id="echoid-s12326" xml:space="preserve"/> </p> <pb o="525" file="0539" n="539" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div466" type="section" level="1" n="466"> <head xml:id="echoid-head578" xml:space="preserve">CAPUT QUINTUM. <lb/>De Cohærentia Corporum Reſpectiva.</head> <p> <s xml:id="echoid-s12327" xml:space="preserve">DEFINITIO. </s> <s xml:id="echoid-s12328" xml:space="preserve">Sit in Tab. </s> <s xml:id="echoid-s12329" xml:space="preserve">XVIII, fig. </s> <s xml:id="echoid-s12330" xml:space="preserve">2. </s> <s xml:id="echoid-s12331" xml:space="preserve">Corpus A C oblongum <lb/>parieti A infixum, cui applicetur pondus vel potentia B <lb/>agens directione perpendiculari ad AC, vel parallele ad baſin corpo-<lb/>ris A, vocabitur reſiſtentia adverſus vim frangentem B, Cohæren-<lb/>tia reſpectiva, aut Cohærentia transverſa.</s> <s xml:id="echoid-s12332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12333" xml:space="preserve">Magno labore indagare conati fuerunt Mathematici qualis & </s> <s xml:id="echoid-s12334" xml:space="preserve"><lb/>quanta Cohærentia reſpectiva ipſius abſolutæ foret, ita ut una co-<lb/>gnita, daretur & </s> <s xml:id="echoid-s12335" xml:space="preserve">altera, atque ex Experimentis in Capite II. </s> <s xml:id="echoid-s12336" xml:space="preserve">allatis de-<lb/>terminaretur, quantum corpus datæ materiæ & </s> <s xml:id="echoid-s12337" xml:space="preserve">figuræ reſiſteret <lb/>viribus, quæ ipſum transverſe ſolvere nituntur.</s> <s xml:id="echoid-s12338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12339" xml:space="preserve">Galilæus corpora perfecta rigida ſuppoſuit, ita ut cedere neſcia, <lb/>ſimulac quædam partes frangantur, eodem ictu omnes ſolvantur: <lb/></s> <s xml:id="echoid-s12340" xml:space="preserve">uti ſit in Tab. </s> <s xml:id="echoid-s12341" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12342" xml:space="preserve">fig. </s> <s xml:id="echoid-s12343" xml:space="preserve">10. </s> <s xml:id="echoid-s12344" xml:space="preserve">D E, cui infixum corpus A B K C, quod <lb/>vi ponderis F a pariete ſeparetur, eodem ictu temporis ſecedet <lb/>pars ſuprema B, quam media H, quam infima A, ſimul cum omni-<lb/>bus inter A & </s> <s xml:id="echoid-s12345" xml:space="preserve">B intermediis; </s> <s xml:id="echoid-s12346" xml:space="preserve">quibus poſitis pondus F, ſi A B C K <lb/>fuerit Cubus, erit modo dimidium illius, quod Cohærentiam ab-<lb/>ſolutam ejuſdem corporis valebat.</s> <s xml:id="echoid-s12347" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12348" xml:space="preserve">Quodut demonſtretur, ſit Tab. </s> <s xml:id="echoid-s12349" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12350" xml:space="preserve">fig. </s> <s xml:id="echoid-s12351" xml:space="preserve">11. </s> <s xml:id="echoid-s12352" xml:space="preserve">Idem corpus A B C K <lb/>ex materia perfecte rigida affixum baſi ED, quod trahatur perpen-<lb/>diculariter deorſum a pondere G, hoc eſt ſecundum longitudinem <lb/>& </s> <s xml:id="echoid-s12353" xml:space="preserve">ductum fibrarum, tum omnes ejus fibræ A C, H L, K B, & </s> <s xml:id="echoid-s12354" xml:space="preserve">quæ <lb/>ipſis ſunt parallelæ, æquali vi deorſum agentur, proinde æquali vi <lb/>reagent, hoc eſt reſiſtentiam æqualem exercebunt. </s> <s xml:id="echoid-s12355" xml:space="preserve">Quoniam reſi-<lb/>ſtentia eſt magnitudo, poterit exponi per aliam magnitudinem, ad-<lb/>eoque exponatur reſiſtentia fibræ B K ex puncto K per rectam B K <lb/>æqualem A B, reſiſtentiæ omnium ſibrarum inter A & </s> <s xml:id="echoid-s12356" xml:space="preserve">B interme-<lb/>diarum exprimentur per alias rectas æquales ad B K, ipſique paralle-<lb/>las quæ quia ſunt puncta inter A & </s> <s xml:id="echoid-s12357" xml:space="preserve">B infinita, etiam erunt infi-<lb/>nitæ, adeoque complebunt quadratum A B K C, quod ſummam <pb o="526" file="0540" n="540" rhead="INTRODUCTIO AD COHÆRENTIAM"/> reſiſtentiarum omnium abſolutarum exhibebit: </s> <s xml:id="echoid-s12358" xml:space="preserve">Quare ſtatui poteſt; <lb/></s> <s xml:id="echoid-s12359" xml:space="preserve">Cohærentiam abſolutam repræſentari ope Quadrati A B K C.</s> <s xml:id="echoid-s12360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12361" xml:space="preserve">Sit nunc corpus id ABKC in fig. </s> <s xml:id="echoid-s12362" xml:space="preserve">I0. </s> <s xml:id="echoid-s12363" xml:space="preserve">affixum parieti D E, ejuſ-<lb/>que extremo C appendatur pondus F id divulſurum â pariete, tum <lb/>ſi rumpetur corpus, id fiet in B A, quia pondus F applicatum <lb/>vecti A C maximam vim exercet in A B, â quo plurimum diſtat: <lb/></s> <s xml:id="echoid-s12364" xml:space="preserve">ſi deinde rumpatur, fiet rotatio circa punctum A, quamobrem <lb/>B A C hic poteſt conſiderari inſtar vectis incurvi, cujus bina crura <lb/>ſunt A B, A C, centrum motus in A, extremo C cruris A C ap-<lb/>plicatur potentia movens F, ſed omni puncto cruris A B applicatur <lb/>reſiſtentia ſuperanda, quæ eſt Cohærentia ejus cum pariete D E, <lb/>ſequitur ergo ex iis, quæ Mechanici de Vecte demonſtrant: </s> <s xml:id="echoid-s12365" xml:space="preserve">quo <lb/>punctum cruris A B eſt propius centro motus A, id eo minus mo-<lb/>menti reſpectu ponderis F, agentis ſemper ex eadem diſtantia A C, <lb/>habiturum: </s> <s xml:id="echoid-s12366" xml:space="preserve">quare ſi ſumatur punctum H, erit ad æquilibrium, vis re-<lb/>quiſita in H ad eam in C, uti A C ad A H: </s> <s xml:id="echoid-s12367" xml:space="preserve">& </s> <s xml:id="echoid-s12368" xml:space="preserve">in B ad eam in C, <lb/>uti A C ad A B. </s> <s xml:id="echoid-s12369" xml:space="preserve">Sed eſt Cohærentia omnium punctorum inter A <lb/>& </s> <s xml:id="echoid-s12370" xml:space="preserve">B æqualis, quare momentum virtutis, quæ agit ex ve-<lb/>cte A H erit ad eam ex A B, uti A H ad A B, hoc eſt uti <lb/>diſtantia a centro motus A; </s> <s xml:id="echoid-s12371" xml:space="preserve">quia autem ea in B eſt ad vim ſolven-<lb/>tem in C, uti A C ad A B, hoc eſt æqualis virtuti abſolutæ; </s> <s xml:id="echoid-s12372" xml:space="preserve">poteſt <lb/>vis Cohærentiæ puncti B exponi per BK, æquali B K in fig. </s> <s xml:id="echoid-s12373" xml:space="preserve">11, <lb/>tum ex quolibetpuncto rectæ A B ducatur recta parallela ad B K, & </s> <s xml:id="echoid-s12374" xml:space="preserve"><lb/>æqualis ſuæ diſtantiæ â centro A, hæc exponet vim illius puncti; </s> <s xml:id="echoid-s12375" xml:space="preserve"><lb/>ſumma vero omnium earum rectarum complebit Triangulum B A K, <lb/>quare ſumma Cohærentiæ lateris A B erit ut hoc Triangulum, quod <lb/>cum ſit dimidium quadrati B A K C exponentis Cohærentiam abſolu-<lb/>tam, erit Cohærentia reſpectiva dimidia abſolutæ: </s> <s xml:id="echoid-s12376" xml:space="preserve">ſi igitur corpus <lb/>A B C K in fig. </s> <s xml:id="echoid-s12377" xml:space="preserve">11. </s> <s xml:id="echoid-s12378" xml:space="preserve">a pondere G librarum 100 rumpatur, poterit trans-<lb/>verſe in fig. </s> <s xml:id="echoid-s12379" xml:space="preserve">10, a pondere F librar. </s> <s xml:id="echoid-s12380" xml:space="preserve">50 rumpi Hæc demonſtratio <lb/>competit omnibus corporibus rigidis, eam non dedit, ſed ſuppo-<lb/>ſuit Galilæus, eique hypotheſi Propoſitiones ſuas ſuperſtruxit: </s> <s xml:id="echoid-s12381" xml:space="preserve">An <lb/>igitur Cohærentia corporum reſpectiva non eritin hac proportione ad <lb/>abſolutam? </s> <s xml:id="echoid-s12382" xml:space="preserve">Revera, ſi corpora perſecte rigida ſint: </s> <s xml:id="echoid-s12383" xml:space="preserve">Verum nullum <lb/>novimus in hoc Univerſo corpus magnum abſolute rigidum, omnia <lb/>ſunt flexilia, omnia antequam franguntur, cedunt aliquomodo;</s> <s xml:id="echoid-s12384" xml:space="preserve"> <pb o="527" file="0541" n="541" rhead="CORPORUM FIRMORUM."/> Vitrum enim ponatur ante oculos, quod inter rigidiſſima huc uſque <lb/>cognita numeratur; </s> <s xml:id="echoid-s12385" xml:space="preserve">id nihilominus in fila ductum tenuia, valde <lb/>quam flexile obſervatur, uti plumæ ex eo confectæ, tum Tubi ca-<lb/>pillares probant, quorum aliquem, 3 pedes longum, in circulum <lb/>flectere potui integrum: </s> <s xml:id="echoid-s12386" xml:space="preserve">idcirco antequam vitrum frangitur, par-<lb/>tes aliquomodo ex ſe extricantur, ſucceſſive rumpuntur. </s> <s xml:id="echoid-s12387" xml:space="preserve">ſed id <lb/>multo clarius videtur in ligno transverſe frangendo: </s> <s xml:id="echoid-s12388" xml:space="preserve">ponamus enim <lb/>aliquod, uti in Tab. </s> <s xml:id="echoid-s12389" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12390" xml:space="preserve">fig. </s> <s xml:id="echoid-s12391" xml:space="preserve">12. </s> <s xml:id="echoid-s12392" xml:space="preserve">A B K C, cujus latus A B parieti <lb/>D B H A E applicatum firmiter, aut infixum ſit, quod a potentia vel <lb/>pondere Q deorſum trahatur; </s> <s xml:id="echoid-s12393" xml:space="preserve">hoc antequam frangetur, incurvabitur, <lb/>partes ſupremæ 1 B 2 B extrahentur ex ſe ad notabilem uſque diſtan-<lb/>tiam, deinde â ſe fatiſcent, cohærentibus tum nihilominus parti-<lb/>bus 1 H 2 H, quæ tantundem ac ſuperiores extrahendæ ſunt ante-<lb/>quam ſolvantur, ſequuntur tum aliæ propiores ipſi A, quæ minus <lb/>adhuc extricatæ, magis extrahendæ ſunt, priuſquam ſeſe relin-<lb/>quant, adeoque ſucceſſive fiet partium ſolutio, primo ſuperiorum, <lb/>tum mediarum, tandem inferiorum: </s> <s xml:id="echoid-s12394" xml:space="preserve">Hæc flexilitas omnium corpo-<lb/>rum & </s> <s xml:id="echoid-s12395" xml:space="preserve">ſucceſſiva abruptio demonſtrant, Galilæi hypotheſin non cum <lb/>Experimentis, quæ cum corporibus naturalibus inſtituentur, poſſe <lb/>congruere: </s> <s xml:id="echoid-s12396" xml:space="preserve">Cui accedit, quod fibræ corporum, quæ extrahuntur, <lb/>eo plus reſiſtunt viribus ſeparantibus, quo plus extrahuntur; </s> <s xml:id="echoid-s12397" xml:space="preserve">eo <lb/>minus autem reſiſtunt, quo minus extrahuntur; </s> <s xml:id="echoid-s12398" xml:space="preserve">quamobrem in <lb/>corpore ligneo, modo conſiderato, fibræ ſuperiores 1 B 2 B maxime <lb/>extractæ, maximâ vi ſe retrotrahent, hoc eſt reſiſtent, minus ex-<lb/>tractæ fibræ 1 H 2 H, etiam minori vi ſe retrotrahent, eritque vis <lb/>fibrarum retrotrahens ſemper eo minor, quo fibræ propius puncto <lb/>A fuerint: </s> <s xml:id="echoid-s12399" xml:space="preserve">Ex quo ſequitur, ab omnibus punctis lateralibus cor-<lb/>poris A 2 H 2 B vim reſiſtentiæ admodum inæ qualem contra poten-<lb/>tiam Q ſeparare nitentem eodem temporis momento exerceri, <lb/>quæ a Galilæo æqualis ſupponebatur: </s> <s xml:id="echoid-s12400" xml:space="preserve">Quamobrem hæ binæ ob-<lb/>ſervationes evincunt regulam Galilæi non reſponſuram Experimen-<lb/>tis cum corporibus flexilibus inſtituendis, uti etiam eventus com-<lb/>probavit, Mariottus enim nonnulla Cohærentiæ abſolutæ & </s> <s xml:id="echoid-s12401" xml:space="preserve">reſpe-<lb/>ctivæ inter ſe comparans Tentamina, obſervavit potentiam corpus <lb/>transverſe ſeparantem eſſe aliquando {1/3}, aliquando {1/4} illius, quæ <lb/>corpus directe fregerat: </s> <s xml:id="echoid-s12402" xml:space="preserve">Inclytus Leibnitſius etiam memoriæ pro- <pb o="528" file="0542" n="542" rhead="INTRODUCTIO AD COHÆRENTIAM"/> didit in Actis Lipſienſibus Anni 1684 ſibi a Blondellio relatum <lb/>fuiſſe, Paulum W urtſium, corporum firmitates explorantem depre-<lb/>hendiſſe, Experimenta nequaquam cum doctrina Galilæi conveni-<lb/>re, quemadmodum etiam omnia noſtra tentamina inferius traden-<lb/>da evincent.</s> <s xml:id="echoid-s12403" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12404" xml:space="preserve">Quoniam igitur omnia corpora flexilia ſunt, quænam propor-<lb/>tio, aut proportiones erunt inter Cohærentiam abſolutam & </s> <s xml:id="echoid-s12405" xml:space="preserve">reſpe-<lb/>ctivam? </s> <s xml:id="echoid-s12406" xml:space="preserve">ſupra memoravi quidnam Mariottus determinaverat ex <lb/>quibusdam a ſe captis Experimentis, quibus abſolutam eſſe ad re-<lb/>ſpectivam uti 3 ad 1, vel 4 ad 1 concluſerat: </s> <s xml:id="echoid-s12407" xml:space="preserve">nec negari poſle, quin <lb/>aliquando hæc obtineat proportio, noſtra tentamina evincent; </s> <s xml:id="echoid-s12408" xml:space="preserve">ve-<lb/>rum plurimas alias dari etiam ex illis conſtabit, & </s> <s xml:id="echoid-s12409" xml:space="preserve">quidem aliquan-<lb/>do eſſe uti 18 ad 1, imo omnes intermedias inter 3 ad 1 & </s> <s xml:id="echoid-s12410" xml:space="preserve">18 ad 1 <lb/>obtinere, quod probat Mariotti aſſertum non eſſe univerſale: </s> <s xml:id="echoid-s12411" xml:space="preserve">Pro-<lb/>fecto nihil difficilius determinatu datur; </s> <s xml:id="echoid-s12412" xml:space="preserve">magnus Leibnitſius omnes <lb/>fibras corporum, quæ transverſe franguntur, quo tempore frangun-<lb/>tur, conſideravit extrahi ex ſe mutuo a ponderibus appenſis; </s> <s xml:id="echoid-s12413" xml:space="preserve">Cele-<lb/>berrimus Bernouillius fibras corporum nonnullas extrahi, nonnul-<lb/>las ſimul comprimi demonſtravit: </s> <s xml:id="echoid-s12414" xml:space="preserve">eſt hæc ſententia veroſimilior <lb/>priori, ex utraque tamen diverſæ proportiones Cohærentiæ abſo-<lb/>lutæ & </s> <s xml:id="echoid-s12415" xml:space="preserve">reſpectivæ demonſtrari poſſunt; </s> <s xml:id="echoid-s12416" xml:space="preserve">& </s> <s xml:id="echoid-s12417" xml:space="preserve">cum utraque mereatur <lb/>cognoſci, primum Leibnitſianam demonſtrationem aggrediar.</s> <s xml:id="echoid-s12418" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12419" xml:space="preserve">Si in Tab. </s> <s xml:id="echoid-s12420" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12421" xml:space="preserve">fig. </s> <s xml:id="echoid-s12422" xml:space="preserve">12. </s> <s xml:id="echoid-s12423" xml:space="preserve">ſit corpus A B C K, parieti D B H A E <lb/>infixum, a quo, antequam penitus frangitur, ſecedere poſſit, quan-<lb/>tum hic conſpicitur, cum fibræ illud componentes, & </s> <s xml:id="echoid-s12424" xml:space="preserve">ſeſe necten-<lb/>tes tantopere extrahi ex ſe poſſint, quantum diſtat 1 B ab 2 B. </s> <s xml:id="echoid-s12425" xml:space="preserve">ſit <lb/>pondus vel potentia quædam Q applicata puncto extremo corpo-<lb/>ris C, ejus magnitudinis, ut aucta vel tantillum frangeret corpus, <lb/>adeoque id reducat in ſtatum fracturæ proximum, tum concipiatur <lb/>circa punctum infimum A, tanquam circa centrum, rotationem <lb/>vel motum fieri; </s> <s xml:id="echoid-s12426" xml:space="preserve">poteritque 2 B A C conſiderari ut vectis incurvus <lb/>æqualium brachiorum, totumque corpus absque gravitate, ergo <lb/>a potentia Q fibræ corporis tendentur, elongabuntur, ita ut pun-<lb/>ctum B ſuperius â pariete diſcedens veniat ad 2 B, ſecum trahat <lb/>fibram, eam tendat inſtar Chordæ, ipſam in violentum redigendo <lb/>ſtatum, quo acquirat longitudinem 1 B 2 B; </s> <s xml:id="echoid-s12427" xml:space="preserve">eodem modo pun- <pb o="529" file="0543" n="543" rhead="CORPORUM FIRMORUM."/> ctum H a pariete recedendo fibram ſuam tendit, elongatque ut ac-<lb/>quirat extenſionem 1H 2H, hoc modo omnes fibræ inter B & </s> <s xml:id="echoid-s12428" xml:space="preserve">A <lb/>tenduntur, extrahuntur, elongantur, maxime ſupremæ 1B 2B, <lb/>minus mediæ 1H 2H, omnium minime, quæ ſunt proximæ pun-<lb/>cto A. </s> <s xml:id="echoid-s12429" xml:space="preserve">proinde fibræ intermediæ 1H 2H minus reſiſtunt potentiæ <lb/>Q, quam 1B 2B propter duas rationes, 1°. </s> <s xml:id="echoid-s12430" xml:space="preserve">Quia B A C vectis eſt <lb/>incurvus, cujus unum crus eſt B A, adeoque vi eâdem applicatâ di-<lb/>verſis punctis 2B, 2H, erit momentum in 2B, ad id in 2H, uti <lb/>A B eſt ad A H; </s> <s xml:id="echoid-s12431" xml:space="preserve">hoc eſtuti diſtantia â puncto? </s> <s xml:id="echoid-s12432" xml:space="preserve">A: </s> <s xml:id="echoid-s12433" xml:space="preserve">quare momentum <lb/>Cohærentiæ in B, ad illud in H, erit uti diſtantia AB, ad AH, <lb/>quemadmodum ex natura vectis ſequitur. </s> <s xml:id="echoid-s12434" xml:space="preserve">2°. </s> <s xml:id="echoid-s12435" xml:space="preserve">Quoniam ambæ <lb/>fibræ 1B 2B, & </s> <s xml:id="echoid-s12436" xml:space="preserve">1H 2H ſimul tenduntur a potentia Q, minus ta-<lb/>men 1H 2H, quam 1B 2B: </s> <s xml:id="echoid-s12437" xml:space="preserve">ſupponamus vires retrotrahentes fi-<lb/>brarum tenſarum eſſe in ratione extenſionum, ita ut fibra tenſa & </s> <s xml:id="echoid-s12438" xml:space="preserve"><lb/>elongata aliquouſque a pondere uno, duplo plus elongetur a pon-<lb/>deribus duobus, triplo plus â tribus, & </s> <s xml:id="echoid-s12439" xml:space="preserve">ſic porro: </s> <s xml:id="echoid-s12440" xml:space="preserve">tum erunt vires <lb/>retrotrahentes, uti ſunt tenſiones, ſive elongationes, hoc eſt erit <lb/>vis in H, ad eam in B, uti 1H 2H, ad 1B 2B. </s> <s xml:id="echoid-s12441" xml:space="preserve">ſed ſunt A1 H <lb/>2H. </s> <s xml:id="echoid-s12442" xml:space="preserve">& </s> <s xml:id="echoid-s12443" xml:space="preserve">A 1B 2B duo Triangula ſimilia, & </s> <s xml:id="echoid-s12444" xml:space="preserve">1H 2H, ad 1B 2B <lb/>;</s> <s xml:id="echoid-s12445" xml:space="preserve">: A 1H ad A 1B. </s> <s xml:id="echoid-s12446" xml:space="preserve">quare erunt vires fibrarum retrotrahentes in <lb/>1H & </s> <s xml:id="echoid-s12447" xml:space="preserve">1B, uti A 1H ad A 1B ſed ob rationem vectis modo da-<lb/>tam. </s> <s xml:id="echoid-s12448" xml:space="preserve">erant momenta virium in H&</s> <s xml:id="echoid-s12449" xml:space="preserve">B, uti A 1H ad A 1B. </s> <s xml:id="echoid-s12450" xml:space="preserve">qua-<lb/>re ob duas rationes ſimul, erunt vires in H ad eas in B, in ra-<lb/>tione compoſita ex AH ad AB, & </s> <s xml:id="echoid-s12451" xml:space="preserve">ex AH ad AB, hoc <lb/>eſt in ratione duplicata diſtantiæ AH ad AB, a centro mo-<lb/>tus A.</s> <s xml:id="echoid-s12452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12453" xml:space="preserve">Quæcunque demonſtravimus de viribus duorum punctorum H & </s> <s xml:id="echoid-s12454" xml:space="preserve"><lb/>B conveniunt viribus omnium punctorum inter A & </s> <s xml:id="echoid-s12455" xml:space="preserve">B, ideoque <lb/>omnes vires in unam ſummam addendæ ſunt, ut habeatur tota <lb/>vis reſpectiva Cohærentiæ. </s> <s xml:id="echoid-s12456" xml:space="preserve">Hæc ſumma ſequenti modo cognoſce-<lb/>tur: </s> <s xml:id="echoid-s12457" xml:space="preserve">capiatur NR æqualis AB, in quâ fiat NP æqualis A H: </s> <s xml:id="echoid-s12458" xml:space="preserve">dein-<lb/>de ut NP<emph style="super">q</emph> ad NR<emph style="super">q</emph>. </s> <s xml:id="echoid-s12459" xml:space="preserve">ita ſit quæcunque PQ ad RS, quæ ad angulos <lb/>rectos inſiſtant ipſi NR, per puncta NQS deſcribatur parabola A-<lb/>polloniana, cujus vertex ſit in N, & </s> <s xml:id="echoid-s12460" xml:space="preserve">compleatur rectangulum NR <lb/>ST. </s> <s xml:id="echoid-s12461" xml:space="preserve">Tum ſi R S exponat vim Cohærentiæ puncti B, PQ exponet <lb/>eam puncti H, omnesque parallelæ ad RS utrimque terminatæ in <pb o="530" file="0544" n="544" rhead="INTRODUCTIO AD COHÆRENTIAM"/> NR & </s> <s xml:id="echoid-s12462" xml:space="preserve">in parabola, expriment vim illius puncti, quod ab A tan-<lb/>topere diſtat, ac diſtat ab N. </s> <s xml:id="echoid-s12463" xml:space="preserve">Omnes vero rectæ ex omnibus pun-<lb/>ctis NR ductæ ad NQS replent Trilineum parabolicum RSQN <lb/>PR, quare hocſpatium repræſentabit omnes vires Cohærentiæ to tius <lb/>lateris AB: </s> <s xml:id="echoid-s12464" xml:space="preserve">Verum quia vis puncti B poſita fuit æqualis RS, atque <lb/>vis Cohærentiæ abſolutæ omnium punctorum inter A & </s> <s xml:id="echoid-s12465" xml:space="preserve">B ſit eadem: <lb/></s> <s xml:id="echoid-s12466" xml:space="preserve">ſumma Cohærentiæ abſolutæ totius lateris AB exponetur ope re-<lb/>ctanguli NRST: </s> <s xml:id="echoid-s12467" xml:space="preserve">quamobrem vis ſuperans Cohærentiam reſpecti-<lb/>vam erit ad abſolutam, uti ſpatium Trilinei parabolici NQSRPN <lb/>ad rectangulum NRST: </s> <s xml:id="echoid-s12468" xml:space="preserve">verum conſtat apud Geometras, hoc ſpa-<lb/>tium trilineum eſſe {1/3} rectanguli, erit igitur Cohærentia reſpectiva <lb/>{2/3} Cohærentiæ abſolutæ: </s> <s xml:id="echoid-s12469" xml:space="preserve">hoc eſt ſi lignum ABCK traheretur â po-<lb/>tentia directione AC ſecundum longitudinem, & </s> <s xml:id="echoid-s12470" xml:space="preserve">rumperetur viribus <lb/>300 librarum, tum ex C pondus Q transverſe applicatum, & </s> <s xml:id="echoid-s12471" xml:space="preserve">modo <lb/>100 librarum, idem lignum frangeret.</s> <s xml:id="echoid-s12472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12473" xml:space="preserve">Eſt hæc demonſtratio veriſſima quotiescunque id obtinet in cor-<lb/>poribus, ut fibrarum tenſarum elongationes ſint proportionales vi-<lb/>ribus tendentibus, quemadmodum hic ſuppoſitum fuit: </s> <s xml:id="echoid-s12474" xml:space="preserve">verum id <lb/>non obtinet in omnibus omnium corporum tenſionibus, etiamſi <lb/>forte detur in nonnullis, nam in plurimis obſervamus, quando ten-<lb/>duntur ab aliquo pondere, extenſiones primum eſſe magnas, dein-<lb/>de æquali pondere addito minores quam ante, appenſo tertio pon-<lb/>dere multo minus elongari fibras quam â primo, atque æquali-<lb/>bus ponderibus aliis perpetuo annexis, decreſcere magis magis-<lb/>que elongationes, quod Clar. </s> <s xml:id="echoid-s12475" xml:space="preserve">Bernouillius ſequenti Experimento <lb/>confirmavit: </s> <s xml:id="echoid-s12476" xml:space="preserve">Sumta fuit Chorda ex Inteſtinis animalium facta, tres <lb/>longa pedes, cujus extremo ſucceſſive appenſæ fuerunt libræ, 2, 4, <lb/>6, 8. </s> <s xml:id="echoid-s12477" xml:space="preserve">elongationes Chordæ obſervatæ ſunt, 9, 17, 23, 27 linearum, <lb/>quæ fuiſſent 9, 18, 27, 36. </s> <s xml:id="echoid-s12478" xml:space="preserve">linearum, ſi elongationes fuiſſent pro-<lb/>portionales ponderibus tendentibus: </s> <s xml:id="echoid-s12479" xml:space="preserve">Verum ſint vires tendentes <lb/>in quacunque proportione ad fibrarum productiones, nihilominus <lb/>eadem methodo ope infinitarum parabolarum poterit Cohærentia <lb/>reſpectiva ex abſoluta deduci, atque demonſtrari quomodo, illa <lb/>poſſit eſſe {1/4}, {1/5}, {1/6}, {1/7} &</s> <s xml:id="echoid-s12480" xml:space="preserve">c. </s> <s xml:id="echoid-s12481" xml:space="preserve">hujus: </s> <s xml:id="echoid-s12482" xml:space="preserve">nam poſitis omnibus ut ante, ſit <lb/>vis retrotrahens in elongatione 1B 2B ad eam in elongatione 1H <lb/>2H, uti <emph style="ol">AB</emph><emph style="super">q</emph> ad <emph style="ol">AH</emph><emph style="super">q</emph>, erit vis tota puncti B ad eam in H, cum <pb o="531" file="0545" n="545" rhead="CORPORUM FIRMORUM."/> ex hac conſideratione, tum ex indole vectis, uti <emph style="ol">AB</emph><emph style="super">c</emph> ad <emph style="ol">AH</emph><emph style="super">c</emph> <lb/>atque in hac proportione agent omnes fibræ intermediæ: </s> <s xml:id="echoid-s12483" xml:space="preserve">ut capia-<lb/>tur ſumma virtutis omnium fibrarum inter A & </s> <s xml:id="echoid-s12484" xml:space="preserve">B intermedia-<lb/>rum, fiat NR = AB, in qua ſumatur NP = AH, tum fiat ut <lb/><emph style="ol">NP</emph><emph style="super">c</emph> ad <emph style="ol">NR</emph><emph style="super">c</emph>, ita quæpiam PQ ad RS, poteritque per tria pun-<lb/>cta NQS deſcribi parabola Cubica, cujus ſpatium NRS re-<lb/>ſiſtentiam reſpectivam exprimet: </s> <s xml:id="echoid-s12485" xml:space="preserve">completo autem parallelogram-<lb/>mo ſub NRS, quod reſiſtentiam abſolutam indicabit, erit Tri-<lb/>lineum parabolicum NRSN ad parallelogrammum NRST, uti 1 <lb/>ad 4.</s> <s xml:id="echoid-s12486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12487" xml:space="preserve">Si vero vis reſiſtentiæ fibrarum 1B 2B, 1H 2H in his elonga-<lb/>tionibus fuerit uti <emph style="ol">AB</emph><emph style="super">c</emph> ad <emph style="ol">AH</emph><emph style="super">c</emph>, erit additâ ratione vectis, tota <lb/>vis in B ad eam in H, uti <emph style="ol">AB</emph><emph style="super">4</emph> ad <emph style="ol">AH</emph><emph style="super">4</emph>, atque in eadem propor-<lb/>tione ſe habebunt omnes fibræ intermediæ, deſcripta iterum NR <lb/>= AB, & </s> <s xml:id="echoid-s12488" xml:space="preserve">NP = AH, atque aſſumta <emph style="ol">NR</emph><emph style="super">4</emph> ad <emph style="ol">NP</emph><emph style="super">4</emph>:</s> <s xml:id="echoid-s12489" xml:space="preserve">: RS. </s> <s xml:id="echoid-s12490" xml:space="preserve">PQ. <lb/></s> <s xml:id="echoid-s12491" xml:space="preserve">poterit iterum parabola, ſed ſurde ſolida deſcribi per puncta NQS, <lb/>ejuſque ſpatium NRSQN repræſentabit reſiſtentiam reſpectivam <lb/>hujus corporis: </s> <s xml:id="echoid-s12492" xml:space="preserve">completum vero parallelogrammum NRST abſo-<lb/>lutam, quia hoc ſpatium parabolicum NRSQN eſt ad parallelo-<lb/>grammum uti 1 ad 5, erit reſiſtentia reſpectiva ad abſolutam uti 1 <lb/>ad 5. </s> <s xml:id="echoid-s12493" xml:space="preserve">Eodem modo ſi vis fibrarum 1B 2B, & </s> <s xml:id="echoid-s12494" xml:space="preserve">1H 2H, in tali e-<lb/>longatione ac ſunt, quando corpus mox rumpetur, ſit uti <lb/>AB<emph style="super">4</emph> ad <emph style="ol">AH</emph><emph style="super">4</emph>, erit tota vis additâ ratione vectis uti <emph style="ol">AB</emph><emph style="super">5</emph> ad <emph style="ol">AH</emph><emph style="super">5</emph>. </s> <s xml:id="echoid-s12495" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s12496" xml:space="preserve">reperietur Cohærentia reſpectiva ad abſolutam uti 1 ad 6. </s> <s xml:id="echoid-s12497" xml:space="preserve">Hoc <lb/>modo pergendo ſemper determinabitur Cohærentia reſpectiva ex <lb/>abſoluta, ſint vires fibrarum tenſarum quælibetcunque in ſuis pro-<lb/>ductionibus; </s> <s xml:id="echoid-s12498" xml:space="preserve">quare ſpatia parabolarum infinitarum ſic inſervire poſ-<lb/>ſunt cognoſcendis Cohærentiis reſpectivis & </s> <s xml:id="echoid-s12499" xml:space="preserve">abſolutis, quamvis <lb/>vires retrotrahentes ad productiones non modo fuerint in rationi-<lb/>bus numerorum integrorum, ſed etiam ſecundum fractiones quaſ-<lb/>cunque: </s> <s xml:id="echoid-s12500" xml:space="preserve">ſi enim NT vocetur x, & </s> <s xml:id="echoid-s12501" xml:space="preserve">TS = y<emph style="super">m</emph>, erit ſpatium para-<lb/>bolicum NQSTN ad parallelogrammum NRST, uti m ad m + 1 <lb/>unde Trilineum parabolicum NRSQN ad parallelogrammum eſt <lb/>uti 1 ad m + 1, quemadmodum apud Mathematicos videri poteſt, <lb/>uti apud L’Hoſpital Sections Coniq. </s> <s xml:id="echoid-s12502" xml:space="preserve">Liv. </s> <s xml:id="echoid-s12503" xml:space="preserve">5. </s> <s xml:id="echoid-s12504" xml:space="preserve">§. </s> <s xml:id="echoid-s12505" xml:space="preserve">13. </s> <s xml:id="echoid-s12506" xml:space="preserve">Carreè Me- <pb o="532" file="0546" n="546" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſur. </s> <s xml:id="echoid-s12507" xml:space="preserve">des Surfaces Sect. </s> <s xml:id="echoid-s12508" xml:space="preserve">1. </s> <s xml:id="echoid-s12509" xml:space="preserve">§. </s> <s xml:id="echoid-s12510" xml:space="preserve">23. </s> <s xml:id="echoid-s12511" xml:space="preserve">Hayes Treatize of Fluxions Sect. </s> <s xml:id="echoid-s12512" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s12513" xml:space="preserve">§. </s> <s xml:id="echoid-s12514" xml:space="preserve">1. </s> <s xml:id="echoid-s12515" xml:space="preserve">Corol. </s> <s xml:id="echoid-s12516" xml:space="preserve">& </s> <s xml:id="echoid-s12517" xml:space="preserve">apud alios.</s> <s xml:id="echoid-s12518" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12519" xml:space="preserve">His licet demonſtratis, quanta ſutura ſit diverſorum corporum <lb/>Cohærentia reſpectiva ad abſolutam determinari tantum poterit ex <lb/>Experientia, quia a priori ignoramus, an in hoc corpore, quod <lb/>voco A, fibræ elongentur in ratione tenſionum, uti Leibnitſius <lb/>ſuppoſuit, an in ratione ſubduplicata, ſubtriplicata, aliave quali-<lb/>bet tenſionum ſuarum; </s> <s xml:id="echoid-s12520" xml:space="preserve">ſi id a priori cognoſceremus, etiam ope <lb/>explicatæ methodi extemplo reſpectivam Cohærentiam ex abſoluta <lb/>determinaremus, verum id Experientia prius oſtendere debet, ejus <lb/>ope cognita Cohærentia abſoluta & </s> <s xml:id="echoid-s12521" xml:space="preserve">reſpectiva, cognoſcetur ex iis, <lb/>quæ ſupra demonſtravimus, in quanam proportione ſe habeant vi-<lb/>res retrotrahentes fibrarum in variis elongationibus oriundis ex ten-<lb/>ſione.</s> <s xml:id="echoid-s12522" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12523" xml:space="preserve">Sit enim Cohærentia abſoluta alicujus corporis ad reſpectivam <lb/>uti 6 ad 1, tum erit hæc proprietas virium retrotrahentium in fi-<lb/>bris, ut ſint in ratione ſurde ſolida elongationum: </s> <s xml:id="echoid-s12524" xml:space="preserve">vidimus enim ſi <lb/>fibræ habeant vires retrotrahentes in ratione elongationum ſurde <lb/>ſolida, abſolutam Cohærentiam fore ad reſpectivam, uti 6 ad 1.</s> <s xml:id="echoid-s12525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12526" xml:space="preserve">Poſuimus in datâ demonſtratione omnes fibras totius lateris AHB <lb/>elongari & </s> <s xml:id="echoid-s12527" xml:space="preserve">diſtrahi, verum ſi accuratius attendamus, obſervabimus <lb/>in inflexione corporis ab appenſo pondere fibras partim extrahi, <lb/>partim comprimi: </s> <s xml:id="echoid-s12528" xml:space="preserve">Sit enim corpus Tab. </s> <s xml:id="echoid-s12529" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12530" xml:space="preserve">fig. </s> <s xml:id="echoid-s12531" xml:space="preserve">13. </s> <s xml:id="echoid-s12532" xml:space="preserve">ABCD, <lb/>primo horrizontale, atque infixum parieti AB, tum extremo CD <lb/>appendatur pondus P, quo deprimatur & </s> <s xml:id="echoid-s12533" xml:space="preserve">elongetur, atque fibra B <lb/>recedat uſque in F, evadatque corpus FAZX, erunt fibræ inter-<lb/>mediæ BAF quædam tenſæ: </s> <s xml:id="echoid-s12534" xml:space="preserve">ſed ſi hoc corpus ita ſibi relinquere-<lb/>tur, extenſione BF manente, & </s> <s xml:id="echoid-s12535" xml:space="preserve">concipiatur paries BA penetrabi-<lb/>lis, circa punctum F tanquam centrum converteretur deſcenden-<lb/>do uſque in ſitum GFXZ, adeoque parietem penetraſſet quanti-<lb/>tate Trianguli AGS, cum vero paries BA ponitur impenetrabilis, <lb/>corpus eum premit, quantum ingreſſum fuiſſet, adeoque tantope-<lb/>re comprimit fibras contra parietem.</s> <s xml:id="echoid-s12536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12537" xml:space="preserve">Ex quibus liquet, corporis ABCD, quo tempore id â pondere <lb/>P deprimitur, & </s> <s xml:id="echoid-s12538" xml:space="preserve">fibræ ſuperiores extenduntur, fibras inferiores <lb/>comprimi.</s> <s xml:id="echoid-s12539" xml:space="preserve"/> </p> <pb o="533" file="0547" n="547" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s12540" xml:space="preserve">Quo corpus ABCD ſit flexibilius, eò â pondere P, fibra BF <lb/>magis elongabitur, adeoque iterum concepto pariete penetrabili, <lb/>& </s> <s xml:id="echoid-s12541" xml:space="preserve">puncto f tanquam centro, magis penetrabit corpus parietem e-<lb/>vadendo gfZX, unde erit Triangulum AgS, exprimens quanti-<lb/>tatem, qua penetravit, majus quam Triangulum AGS præcedens; <lb/></s> <s xml:id="echoid-s12542" xml:space="preserve">poſito proinde iterum pariete AB impenetrabili, hoc corpus magis <lb/>premet parietem, ſive plus comprimet fibras inferiores, cum ſimul <lb/>plus extendat fibras ſuperiores.</s> <s xml:id="echoid-s12543" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12544" xml:space="preserve">Quo corporis fibræ plus comprimuntur, eo magis diſtant â ſolu-<lb/>tione, quæ hicin extractione conſiſtit; </s> <s xml:id="echoid-s12545" xml:space="preserve">quo minus comprimuntur, eo <lb/>ſolutioni ſunt propiores, adeoque propiores ſolutioni ſunt fibræ infe-<lb/>riores corporis rigidioris, quam flexibilioris; </s> <s xml:id="echoid-s12546" xml:space="preserve">unde in corpore val-<lb/>de flexibili omnes fibræ ſuperiores vim reſiſtentiæ contra pondus ex-<lb/>tremo appenſum P exercere debent, inferioribus fere nihil a-<lb/>gentibus, quum in corpore rigidiori plures ſuperiores ſimul reſi-<lb/>ſlant: </s> <s xml:id="echoid-s12547" xml:space="preserve">unde ſequitur â minori pondere diffractum iri fibras ſuperio-<lb/>res corporis flexiblis quam rigidioris, quod omnia noſtra tentami-<lb/>na penitus evincent, in iis quippe conſtabit, quo corpus eſt flexi-<lb/>bilius, eo Cohærentiam reſpectivam eſſe minorem, quo rigidius, eo <lb/>eſſe majorem.</s> <s xml:id="echoid-s12548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12549" xml:space="preserve">Viſis ita compreſſionibus fibrarum, examinemus earum elonga-<lb/>tiones, atque iterum ponamus fibram ſuperiorem BF corporis AB <lb/>CD eſſe extenſam quantitate BF, parietem penetrabilem, & </s> <s xml:id="echoid-s12550" xml:space="preserve">cor-<lb/>pus ſibi relinqui, ut deſcendendo circa F vertatur, & </s> <s xml:id="echoid-s12551" xml:space="preserve">fiat GFXZ, <lb/>tum elongabuntur fibræ componentes Triangulum SBF, hæ igitur <lb/>ſolæ ſunt, quæ ſe retrotrahendo reſiſtunt ponderi trahenti P, adeo-<lb/>que Triangulum poterit exprimere reſiſtentiam contra pondus P, <lb/>eritque hæc magnitudo Cohærentiæ reſpectivæ; </s> <s xml:id="echoid-s12552" xml:space="preserve">abſoluta autem eſt <lb/>æqualis Rectangulo, cujus unum latus AB, alterum BF, nam quan-<lb/>do corpus trahitur directione AD ſecundum longitudinem poterunt <lb/>omnes ejus fibræ in AB extendi, quantum extracta eſt fibra BF. <lb/></s> <s xml:id="echoid-s12553" xml:space="preserve">quia autem Triangulum BSF ſemper erit minus Triangulo ABF, <lb/>quod eſt dimidium rectanguli AB, BF, erit in omni corpore fle-<lb/>xibili ſemper Cohærentia reſpectiva minor quam {1/2} abſolutæ quo <lb/>nunc BF magis increſcit, manente pondere P eodem, uti fit in <lb/>corporibus flexibiliſſimis, eo punctum S magis adſcendit verſus B, at- <pb o="534" file="0548" n="548" rhead="INTRODUCTIO ad COHÆRENTIAM"/> que eo minus fit Triangulum S B F reſpectu rectanguli ſub A B, <lb/>B F, adeoque Cohærentia reſpectiva fit minor reſpectu abſolutæ, <lb/>unde poſito Triangulo S B F = {1/3} vel {1/4} vel {1/5} & </s> <s xml:id="echoid-s12554" xml:space="preserve">c. </s> <s xml:id="echoid-s12555" xml:space="preserve">rectanguli A B, B F, <lb/>erit Cohærentia reſpectiva {1/3}, vel {1/4} vel {1/5} abſolutæ; </s> <s xml:id="echoid-s12556" xml:space="preserve">& </s> <s xml:id="echoid-s12557" xml:space="preserve">fieri poteſt <lb/>Triangulum S B F multo minus adhuc, unde multum adhuc de-<lb/>creſcere Cohærentia reſpectiva poterit, quæ proinde pendebit a ri-<lb/>giditate vel flexibilitate majori minorive fibrarum, poteſtque ſub <lb/>variis obſervari proportionibus, non determinandis niſi ex Expe-<lb/>rientia.</s> <s xml:id="echoid-s12558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12559" xml:space="preserve">Sequitur ex his non dari in Natura unam regulam Univerſalem <lb/>exponentem proportionem eandem inter Cohærentiam reſpectivam <lb/>& </s> <s xml:id="echoid-s12560" xml:space="preserve">abſolutam, qualem Geometræ dare anniſi ſunt, cum diverſiſſi-<lb/>ma eſle debeat proportio pro variâ corporum flexibilitate, quemad-<lb/>modum revera Experientia evincit. </s> <s xml:id="echoid-s12561" xml:space="preserve">Si Philoſophi antequam ope-<lb/>ram huic doctrinæ navaſſent, prius plurima tentamina accurate <lb/>inſtituiſſent, multis peperciſſent laboribus, neque unquam uni u-<lb/>niverſali regulæ inveniendæ incubuiſſent: </s> <s xml:id="echoid-s12562" xml:space="preserve">quot enim fere diverſa <lb/>corpora dantur, totidem diverſæ proportiones inter Cohærentiam <lb/>abſolutam & </s> <s xml:id="echoid-s12563" xml:space="preserve">reſpectivam deprehenduntur.</s> <s xml:id="echoid-s12564" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12565" xml:space="preserve">Antequam eventum Experimentorum deſcribam, prius metho-<lb/>dum, qua peracta fuerunt notabo, ut judicium ferri poſſit an ac-<lb/>curate, an negligentius perrexerim.</s> <s xml:id="echoid-s12566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12567" xml:space="preserve">Tab. </s> <s xml:id="echoid-s12568" xml:space="preserve">XIX. </s> <s xml:id="echoid-s12569" xml:space="preserve">conſpicitur machina noſtra divulſoria in cujus bi-<lb/>nis perpendicularibus fulcris K K erat foramen Q & </s> <s xml:id="echoid-s12570" xml:space="preserve">R, hoc rotun-<lb/>dum, illud quadratum, ut infigi poſſent Ligna Cylindrica & </s> <s xml:id="echoid-s12571" xml:space="preserve">pa-<lb/>rallelopipeda, erat utrumque ejus amplitudinis, ut arctiſſime com-<lb/>plecteretur corpora ſibi immiſſa: </s> <s xml:id="echoid-s12572" xml:space="preserve">oræ foraminum Q & </s> <s xml:id="echoid-s12573" xml:space="preserve">R erant mu-<lb/>nitæ lamina craſſa cuprea, ne læderentur a corporibus immiſſis, <lb/>inflexiſque, & </s> <s xml:id="echoid-s12574" xml:space="preserve">ut accuratiſſime menſuraretur diſtantia appenſi pon-<lb/>deris a foramine: </s> <s xml:id="echoid-s12575" xml:space="preserve">Deinde præparavi tabulam Ligneam quadratam <lb/>Tab. </s> <s xml:id="echoid-s12576" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s12577" xml:space="preserve">fig, 9. </s> <s xml:id="echoid-s12578" xml:space="preserve">pedis quadrati, diviſam in 144 pollices quadra-<lb/>tos; </s> <s xml:id="echoid-s12579" xml:space="preserve">hæc applicabatur lateri fulcri K ad machinam divulſoriam, ut <lb/>linea, ubi diviſio prima incipit, eſſet in eadem horizontali cum <lb/>inferiori parte foraminis Q vel R: </s> <s xml:id="echoid-s12580" xml:space="preserve">Erat hæc tabula magnæ utilita-<lb/>tis & </s> <s xml:id="echoid-s12581" xml:space="preserve">commodi, quotieſcunque enim Ligno foramini machinæ im-<lb/>miſſo appenditur pondus, inflexio fit ante rupturam, neque facile <pb o="535" file="0549" n="549" rhead="CORPORUM FIRMORUM."/> obſervatur diſtantia lineæ directionis ponderis a foramine, quæ di-<lb/>ſtantiatamen accuratiſſime eſt notanda, ut Cohærentiæ abſolutæ & </s> <s xml:id="echoid-s12582" xml:space="preserve"><lb/>reſpectivæ proportio eruatur: </s> <s xml:id="echoid-s12583" xml:space="preserve">at ope hujus tabulæ facillime & </s> <s xml:id="echoid-s12584" xml:space="preserve">abſ-<lb/>que errore conſpicitur directionis ponderis diſtantia.</s> <s xml:id="echoid-s12585" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12586" xml:space="preserve">Præterea tabulam præparaveram, ut ſupra eam depingerem curvas, <lb/>quas qualibet inflexione corpora deſcriberent, ut obſervaretur, an <lb/>omnes ejuſdem naturæ, an diverſæ forent, & </s> <s xml:id="echoid-s12587" xml:space="preserve">quænam tum obtinerent: <lb/></s> <s xml:id="echoid-s12588" xml:space="preserve">unam enim ingenioſiſſimus Bernouillius examinaverat in L’ Hiſt. </s> <s xml:id="echoid-s12589" xml:space="preserve"><lb/>de L’ Acad. </s> <s xml:id="echoid-s12590" xml:space="preserve">Roy. </s> <s xml:id="echoid-s12591" xml:space="preserve">A° 1705. </s> <s xml:id="echoid-s12592" xml:space="preserve">cujus pulcerrimas proprietates detexe-<lb/>rat: </s> <s xml:id="echoid-s12593" xml:space="preserve">Sed in hiſce obſervandis mihi non ſatisfeci, quia lignorum <lb/>inflexio diu manet in motu ab eodem pondere, atque perpetuo <lb/>quaſi mutatur, cum fibræ corpus componentes non ſimul ex ſe mu-<lb/>tuo extrahuntur, quantum debent, ſed ſucceſſu temporis magis <lb/>magiſque ſolvuntur: </s> <s xml:id="echoid-s12594" xml:space="preserve">Si tamen rudem obſervationem afferre liceat, <lb/>quam fateor non ſecundum rigorem Mathematicum eſſe accipien-<lb/>dam; </s> <s xml:id="echoid-s12595" xml:space="preserve">Tot formantur curvæ diverſæ a ponderibus appenſis, quot diver-<lb/>ſa Ligna exploravi. </s> <s xml:id="echoid-s12596" xml:space="preserve">Ligna quæ examinibus inſervierunt, erant eadem <lb/>ac in Capite II. </s> <s xml:id="echoid-s12597" xml:space="preserve">adhibita, quæ eum in finem tantæ longitudinis <lb/>fumta fuerunt, ut iterum in hiſce tentaminibus explorarentur: </s> <s xml:id="echoid-s12598" xml:space="preserve"><lb/>quamvis quoque alia nova, earundemque arborum ligna præpara-<lb/>verim; </s> <s xml:id="echoid-s12599" xml:space="preserve">nam fibræ lignorum in Cap. </s> <s xml:id="echoid-s12600" xml:space="preserve">II. </s> <s xml:id="echoid-s12601" xml:space="preserve">examinatorum erant parum <lb/>ex ſe mutuo extractæ, adeoque hinc inde neceſſario fractæ fue-<lb/>runt, quod non poterat non Cohærentiam minorem verâ in ſe-<lb/>cundo tentamine exhibere: </s> <s xml:id="echoid-s12602" xml:space="preserve">nova ligna non audebam ſubſtituere exa-<lb/>minatis, quia etiamſi ex eadem arbore fuerint capta, nihilominus <lb/>ex alia parte depromebantur, quam non poteram ponere ejuſdem <lb/>eſſe Cohærentiæ cum alia; </s> <s xml:id="echoid-s12603" xml:space="preserve">imo infra oſtendam, hunc ſcrupulum va-<lb/>num non eſſe, atque ex eodem aſl<unsure/>ere partes, in diverſa a meditullio <lb/>diſtantiâ ſumtas, varia firmitate donari: </s> <s xml:id="echoid-s12604" xml:space="preserve">non tamen notabilem diſ-<lb/>crepantiam in hiſce Experimentis obſervavi, uti conſtabit in eorum <lb/>deſcriptis eventibus.</s> <s xml:id="echoid-s12605" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12606" xml:space="preserve">Ligna duplicis facta ſunt figuræ, cylindrica & </s> <s xml:id="echoid-s12607" xml:space="preserve">parallelopipeda, <lb/>qualia exhibet Tab. </s> <s xml:id="echoid-s12608" xml:space="preserve">XX. </s> <s xml:id="echoid-s12609" xml:space="preserve">fig. </s> <s xml:id="echoid-s12610" xml:space="preserve">5 & </s> <s xml:id="echoid-s12611" xml:space="preserve">6. </s> <s xml:id="echoid-s12612" xml:space="preserve">extremitas donabatur exiguo <lb/>capite A, impedituro ne funis, ex quo pondus pendebat, decide-<lb/>ret ab extremitate inflexi aliquousque ligni.</s> <s xml:id="echoid-s12613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12614" xml:space="preserve">Omnia ex fractis in Capite II. </s> <s xml:id="echoid-s12615" xml:space="preserve">confecta longitudinem 6 pollicum <pb o="536" file="0550" n="550" rhead="INTRODUCTIO ad COHÆRENTIAM"/> habuerunt, nova 11, vel 12. </s> <s xml:id="echoid-s12616" xml:space="preserve">pollicum: </s> <s xml:id="echoid-s12617" xml:space="preserve">immiſſa fuerunt foraminibus <lb/>Q & </s> <s xml:id="echoid-s12618" xml:space="preserve">R machinæ divulſoriæ ad profunditatem unius pollicis, adeo <lb/>ut eminerent illa 5, hæc 10, vel 11 poll. </s> <s xml:id="echoid-s12619" xml:space="preserve">diameter Cylindrorum fuit <lb/>eadem ac illorum qui ſecundum longitudinem explorati fuerunt, ple-<lb/>rumqueo, 25 pollicis: </s> <s xml:id="echoid-s12620" xml:space="preserve">latus quodlibet parallelopipedorum fuit exacte <lb/>idem quod ſupra examinatum erat: </s> <s xml:id="echoid-s12621" xml:space="preserve">pondus ad hæc frangenda uſurpa-<lb/>tum immittebatur patinæ lente & </s> <s xml:id="echoid-s12622" xml:space="preserve">prudenter, conſtans tantum ex <lb/>drachmis, ne Experimentum turbaretur a motu gravioris ponderis unâ <lb/>vice ſimul immiſſi: </s> <s xml:id="echoid-s12623" xml:space="preserve">patina funi tenui in annulum convoluto, & </s> <s xml:id="echoid-s12624" xml:space="preserve">Li-<lb/>gnum examinandum ambienti prope caput, alligata fuit, quo modo <lb/>revera accuratiſſime ponderis diſtantia a foramine conſpici poterat <lb/>contra Tabulam quadratam modo deſcriptam.</s> <s xml:id="echoid-s12625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12626" xml:space="preserve">Ut quam clariſſime Experimenta omnia intelligantur, unum ad-<lb/>notabo; </s> <s xml:id="echoid-s12627" xml:space="preserve">omnia eodem modo inſtituta fuerunt, quæ brevitatis er-<lb/>go in Tabellâ propoſui, ne repetere eadem ſæpe tenear.</s> <s xml:id="echoid-s12628" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12629" xml:space="preserve">Cylindrus Tiliæ foramini Q Machinæ divulſoriæ immiſſus, 10 <lb/>pollicibus prominebat: </s> <s xml:id="echoid-s12630" xml:space="preserve">patinæ ex fune prope caput cylindri pen-<lb/>denti injiciebantur pedetentim libræ 2 Amſtelodamenſes, patina erat <lb/>libræ{1/2} a quibus inflexus cylindrus deſcendit, ita ut ponderis directio <lb/>tantum 7 pollicibus a foramine diſtaret, tum ruptus fuit ad ipſam <lb/>foraminis oram: </s> <s xml:id="echoid-s12631" xml:space="preserve">gravitatis centri in cylindro & </s> <s xml:id="echoid-s12632" xml:space="preserve">capite habita <lb/>fuit ratio, idemque momentum habuit, ac ſi ſublata gravitate pon-<lb/>dus duarum drachmarum Lanci injectum fuiſſet.</s> <s xml:id="echoid-s12633" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12634" xml:space="preserve">Comparetur hoc Experimentum cum primo Capitis II. </s> <s xml:id="echoid-s12635" xml:space="preserve">in quo idem <lb/>Cylindrus ſecundum longitudinem exploratus ſuſtinuit libras 720 <lb/>antequam rumpebatur: </s> <s xml:id="echoid-s12636" xml:space="preserve">ſed obſervetur ex natura vectis, quantum <lb/>momenti exercuerit pondus librar. </s> <s xml:id="echoid-s12637" xml:space="preserve">2 {1/2} (similar drachmar. </s> <s xml:id="echoid-s12638" xml:space="preserve">2. </s> <s xml:id="echoid-s12639" xml:space="preserve">& </s> <s xml:id="echoid-s12640" xml:space="preserve">quodnam <lb/>pondus ad diſtantiam diametro cylindri æqualem â foramine idem <lb/>momentum exercuiſſet: </s> <s xml:id="echoid-s12641" xml:space="preserve">quia libræ 2 {1/2} & </s> <s xml:id="echoid-s12642" xml:space="preserve">drachmæ 2. </s> <s xml:id="echoid-s12643" xml:space="preserve">diſtiterint 28 <lb/>diametris cylindri a foramine, pondus 28 majus idem momentum <lb/>habuiſſet ad diſtantiam diametro æqualem, quod igitur foret li-<lb/>brar. </s> <s xml:id="echoid-s12644" xml:space="preserve">70 {7/16}. </s> <s xml:id="echoid-s12645" xml:space="preserve">quemadmodum hoc pondus 70 {7/16}. </s> <s xml:id="echoid-s12646" xml:space="preserve">ad libras 720, ita eſt <lb/>Cohærentia reſpectiva ad abſolutam, ſed hæ ſunt uti 1 ad 10 {259/1127}. <lb/></s> <s xml:id="echoid-s12647" xml:space="preserve">Quare ita ſe habent memoratæ Cohærentiæ, valde abludentes â <lb/>proportione Galilæanâ & </s> <s xml:id="echoid-s12648" xml:space="preserve">Mariottiana, ſecundum quas debuiſſet da-<lb/>ri uti 1 ad 2. </s> <s xml:id="echoid-s12649" xml:space="preserve">vel 1 ad 3, aut 1 ad 4.</s> <s xml:id="echoid-s12650" xml:space="preserve"/> </p> <pb file="0551" n="551"/> <pb file="0551a" n="552" rhead="TABULA"/> <note position="right" xml:space="preserve"> <lb/># # # # # # # # # # Continens Cohærentias Lignorum reſpectivas inſerenda Pag. 536. <lb/>Numerus Ex- \\ perimento- \\ rum. # Nomina Lignorum. \\ C. notat Cylindrum. \\ P. Parallelopiped. # Diſtantia ponderis \\ a foramine ante \\ inſtitutum Expe- \\ rim. cum novis \\ Lign. \\ Pollices. # Diſtantia ponderis \\ a foramine quan- \\ do frangitur. \\ Pollic. # Pondus applica- \\ tum extremo & \\ frangens. \\ Unciæ. # Proportio inter \\ Cohærentiam \\ abſolutam & \\ reſpectivam. # Ante Experimen- \\ tum diſtantia pon- \\ deris a foramine, \\ cum lignis exami- \\ natis in Cap. II. \\ Poll. # Diſtantia directionis \\ ponderis a forami- \\ ne cum frangitur. \\ pollic. # Pondus extremo \\ applicatum & fran- \\ gens. \\ Unciæ. # Proportio inter \\ Cohærentiam \\ abſolutam & \\ reſpectivam. <lb/>103 # C. Tiliæ # 10 # 7 # 40 {1/4} # 10 {250/1127} ad 1 # 5 # 3, 5 # 80 # 11 {13/1037} ad 1 <lb/>104 # C. Alni # 10 # 8 # 40 # 9 {151/161} ad 1 # 5 # 4 # 80 # 9 {151/161} ad 1 <lb/>105 # C. Piceæ # 6 # 4, 75 # 46 # 14 ad 1 # 5 # 4 # 72 # 12 ad 1 <lb/>106 # P. Piceæ # 10 # 9 # 40 # 5 {1/9} ad 1 <lb/>107 # C. Quercus # 10 # 7 # 53 {3/4} # 12 {68/301} ad 1 # 5 # 4, 3 # 102 # 11 {1434/4386} ad 1 <lb/>108 # P. Quercus # 10 # 8, 5 # 48 # 11 {28/50} ad 1 # 5 # 4, 5 # 100 # 11 {9/225} ad 1 <lb/>109 # C. Salicis # 10 # 8, 5 # 36 {12/17} # 13 {3/14} ad 1 # 5 # 4, 1 # 70 # 14 {142/287} ad 1 <lb/>110 # P. Salicis # 10 # 8 # 38 # 12 {1/2} ad 1 # 5 # 4 # 75 # 12 {36/75} ad 1 <lb/>111 # P. Ulmi # 10 # 9 # 64 # 6 {43/72} ad 1 # 5 # 4, 5 # 120 # 7 {356/540} ad 1 <lb/>112 # P. Ulmi aliud # 11 # 9 # 44 # 9 {519/119} ad 1 <lb/>113 # C. Pyri # 10 # 8 # 32 # 8 {13/32} ad 1 # 5 # 3, 7 # 51 # 11 {363/1887} ad 1 <lb/>114 # P. Pyri # 11 # 9 # 58 # 5 {190/511} ad 1 # 5 # 4 # 123 # 5 {170/246} ad 1 <lb/>115 # P. Grynen # 10 # 9 # 48 # 5 {5/54} ad 1 # 5 # 4, 5 # 58 # 8 {200/261} ad 1 <lb/>116 # C. Grynen # 10 # 8, 5 # 32 # 12 {19/34} ad 1 # 5 # 4, 5 # 59 # 13 {169/531} ad 1 <lb/>117 # C. Meſpili # 10 # 6 # 81 # 5 {183/243} ad 1 # 5 # 3 # 164 # 5 {113/123} ad 1 <lb/>118 # P. Meſpili # 10 # 6 # 100 {1/3} # 4 {126/131} ad 1 # 5 # 3 # 198 # 4 {164/297} ad 1 <lb/>119 # C. Abietis # 8 # 7, 5 # 37 # 8 {368/555}ad 1 # 5 # 4 # 69 # 10 {12/69} ad 1 <lb/>120 # P Abietis # 11 # 9, 5 # 36 {1/2} # 6 {702/1483} ad 1 # 5 # 4 # 71 # 9 {9/72} ad 1 <lb/>121 # C. Ulmi # 10 # 8, 5 # 36 # 11 {6/51}ad 1 # 5 # 4, 25 # 70 # 12 {92/287} ad 1 <lb/>122 # C. Fraxini # 10 # 7, 5 # 33 # 18 {14/237} ad 1 <lb/>123 # C. Fagi # 10 # 7, 25 # 38 # 16 {8/57} ad 1 # 5 # 4 # 79 # 15 {11/79} ad 1 <lb/>124 # C. Nucis # 10 # 8, 5 # 41 # 8 {224/697} ad 1 <lb/>125 # C. Buxi # 10 # 6, 5 # 82 # 3 {91/1103} ad 1 # 5 # 3, 8 # 161 # 5 {2395/3054} ad 1 <lb/>126 # P. Buxi # 10 # 7 # 96 # 5 {110/168} ad 1 # 5 # 3, 5 # 199 # 5 {6215/6965} ad 1 <lb/>127 # C. Pomi # 10 # 7 # 36 # 8 {108/476} ad 1 # 5 # 3, 5 # 79 # 7 {143/551} ad 1 <lb/>128 # P. Pomi # 10 # 7, 75 # 48 # 6 {154/341} ad 1 # 5 # 3, 5 # 80 # 7 {6/7} ad 1 <lb/>129 # P. Pomi alius # 9 # 5, 5 # 58 # 6 {286/319} ad 1 <lb/>130 # C. Oleæ # 10 # 8, 5 # 41 # 7 {642/1394} ad 1 # 5 # 4, 2 # 80 # 9 {121/287} ad 1 <lb/>131 # P. Oleæ # 10 # 9 # 65 # 5 {95/117} ad 1 # 5 # 3, 8 # 145 # 6 {230/551} ad 1 <lb/>132 # C. Suykerkiſte # 10 # 9, 5 # 56 # 5 {280/1064} ad 1 # 5 # 4, 5 # 114 # 5 {235/513} ad 1 <lb/>133 # P. Suykerkiſte # 10 # 9, 5 # 80 # 7 {17/19} ad 1 <lb/>134 # C. Ceraſi nigri # 9 # 7, 5 # 48 # 10 {5/9} ad 1 # 5 # 3, 3 # 100 # 11 {17/33} ad 1 <lb/>135 # P. Ceraſi nigri # 8 # 7 # 80 <lb/>136 # C. Oxyacanthæ # 9, 5 # 8 # 49 # 10 {80/392} ad 1 # 5 # 3,8 # 105 # 10 {10/399} ad 1 <lb/>137 # P. Oxyacanthæ # 9, 5 # 8 # 56 # 8 {16/448} ad 1 # 5 # 3, 8 # 110 # 8 {129/209} ad 1 <lb/>138 # C. Ceraſi # 8, 5 # 7, 75 # 44 # 7 {426/682} ad 1 <lb/>139 # P. Ceraſi # 8 # 7, 5 # 72 <lb/>140 # C. Pruni # 6 # 3 # 48 # 16 {16/283} ad 1 # 5 # 2, 5 # 60 # 16 ad 1 <lb/>141 # P. Pruni # 8, 5 # # 52 <lb/>142 # C. Granadille # 9, 5 # 7, 25 # 113 {1/2} # 4 {2036/3291} ad 1 # 5 # 3, 8 # 242 # 4 {1296/9176} ad 1 <lb/>143 # P. Granadille # 9 # 8, 25 # 153 # 2 {2702/5049} ad 1 # 5 # 3, 8 # 265 # 3 {179/1007} ad 1 <lb/>144 # P. Santali \\ rubri # 8 # 7, 5 # 80 # 4 ad 1 # 5 # 4, 1 # 153 # 3 {5181/6273} ad 1 <lb/>145 # P. Paardevlys # 9 # 8, 5 # 120 # 5 {25/99} ad 1 # 5 # 4, 25 # 230 # 5 {255/989} ad 1 <lb/>146 # P. Guajaci # 9, 5 # 9 # 64 # 5 {540/574} ad 1 # 5 # 4, 20 # 134 # 5 {2085/3003} ad 1 <lb/>147 # P. Sakkerdaane # 8, 5 # 8 # 71 {1/2} # 9 {108/288} ad 1 # 5 # 4, 4 # 149 # 8 {1552/6556} ad 1 <lb/>148 # P. Tiliæ # 10 # 8, 75 # 40 # 11 {3/7} ad 1 <lb/>149 # P. Fagi # 10 # 7 # 56 {1/2} # 12 {254/398} ad 1 # 5 # 4 # 90 # 14 {4/9} ad 1 <lb/>150 # P. Nucis # 10 # 8 # 67 {1/2} # 5 {50/54} ad 1 # 5 # 4 # 115 # 7 {27/115} ad 1 <lb/>151 # P. Alni # 10 # 9, 25 # 48 <lb/>152 # # # # # # # # # # P. Fraxini non potuit frangi, flexum fuit abſque ruptura, ita ut angulum \\ rectum pars flexa cum ea, quæ foramini inhæſit, conſtituerit. <lb/>153 # P. Vitri cujus \\ quodlibetla- \\ tus 2 lin. # 2, 42 # 2, 44 # 52 {1/6} # 1 {14203/15149} ad 1. \\ proxime 2 \\ ad 1 <lb/>154 # P. Vitri latus \\ 1 {6/10} lin. # 2, 44 # 2, 40 # 23 {13/16} # 2 {62/369} ad 1 <lb/>155 # C. Vitri dia- \\ metr. 2 {4/10} lin. # 3, 40 # 3, 40 # 49 {19/20} <lb/></note> <pb file="0552" n="553"/> <pb o="537" file="0553" n="554" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s12651" xml:space="preserve">Hæc Experimenta luce meridianâ clarius evincunt, nec regulam <lb/>Galilæi, nec Mariotti, nec aliorum eſſe Univerſalem, cum dentur <lb/>corpora, in quibus Cohærentia abſoluta ad reſpectivam eſt uti 18 <lb/>ad 1, veluti in Exp. </s> <s xml:id="echoid-s12652" xml:space="preserve">CXXII in aliis uti 16 ad 1, veluti in Exp. <lb/></s> <s xml:id="echoid-s12653" xml:space="preserve">CXXIII. </s> <s xml:id="echoid-s12654" xml:space="preserve">& </s> <s xml:id="echoid-s12655" xml:space="preserve">CXL. </s> <s xml:id="echoid-s12656" xml:space="preserve">in aliis uti 12 ad 1, veluti eſt in Exp. </s> <s xml:id="echoid-s12657" xml:space="preserve">CVII, <lb/>CX, CXIV, CXLIX. </s> <s xml:id="echoid-s12658" xml:space="preserve">dantur tamen ubi regnat proportio 3 ad 1 <lb/>veluti in Exp. </s> <s xml:id="echoid-s12659" xml:space="preserve">CXXV. </s> <s xml:id="echoid-s12660" xml:space="preserve">tum ubi eſt proportio 2 ad 1, ſicuti in Exp. </s> <s xml:id="echoid-s12661" xml:space="preserve"><lb/>CXLIII, CLIII, CLIV. </s> <s xml:id="echoid-s12662" xml:space="preserve">imo obtinent plurimæ aliæ proportiones <lb/>inter 18 ad 1, & </s> <s xml:id="echoid-s12663" xml:space="preserve">2 ad 1 intermediæ: </s> <s xml:id="echoid-s12664" xml:space="preserve">in hiſce fractiones negligimus, <lb/>quia non faciunt ad ſcopum.</s> <s xml:id="echoid-s12665" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12666" xml:space="preserve">In corporibus rigiditati proximis, veluti in Vitro, Galilæanæ <lb/>proportio datur: </s> <s xml:id="echoid-s12667" xml:space="preserve">in aliis paulo flexibilioribus datur Mariottiana: </s> <s xml:id="echoid-s12668" xml:space="preserve">ſed <lb/>in aliis quæ magis flecti poſſunt, aliæ regnant proportiones.</s> <s xml:id="echoid-s12669" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12670" xml:space="preserve">Qui hæc Experimenta accurate perpendit, dubitare poſſet, an <lb/>quidem cum ſufficienti cura ſint inſtituta, cum aliquando magna <lb/>Cohærentiæ diſcrepantia detur, licet corpora ex eodem ligno fuerint <lb/>confecta, ſed intelligat hic velim, Ligna non eſſe corpora homoge-<lb/>nea, ſed hinc inde poroſiora aut ſolidiora, magis minuſve reſinoſa, <lb/>fibris obliquioribus aut rectioribus compoſita, a quibus hæc diſcre-<lb/>pantia oritur, unde, ſi eadem repetantur tentamina, fere nunquam <lb/>cædem proportiones inter abſolutam & </s> <s xml:id="echoid-s12671" xml:space="preserve">reſpectivam Cohærentiam <lb/>deprehendentur, quamvis non multum ab his abluſuræ.</s> <s xml:id="echoid-s12672" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12673" xml:space="preserve">Obſervamus in his Experimentis fere omnium parallelopipedo-<lb/>rum Cohærentiam abſolutam majorem rationem habuiſie ad reſpe-<lb/>ctivam quam cylindrorum.</s> <s xml:id="echoid-s12674" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12675" xml:space="preserve">Quoniam ſingulis annis arborum trunci incrementum ca-<lb/>piunt, corticis interiori tunica ad lignum trunci accedente & </s> <s xml:id="echoid-s12676" xml:space="preserve"><lb/>accreſcente, non poteſt truncus per totam ſuam ſubſtantiam eſ-<lb/>ſe æque firmus: </s> <s xml:id="echoid-s12677" xml:space="preserve">meditullium enim annoſiſſimum eſt, pars huic <lb/>proxima ſequitur ætate, noviſſima eſt quæ cortici adhæret: </s> <s xml:id="echoid-s12678" xml:space="preserve">te-<lb/>nerum & </s> <s xml:id="echoid-s12679" xml:space="preserve">molle eſt lignum quod novum, quia parum eſt com-<lb/>preſſum, & </s> <s xml:id="echoid-s12680" xml:space="preserve">aquoſis plenum ſuccis, ſed durius eſt quod annoſius, <lb/>quia comprimitur circumquaque a novo ligno accedente, tum du-<lb/>rius eſt, quia plus reſinæ collegit: </s> <s xml:id="echoid-s12681" xml:space="preserve">explorandum duxi, quænam fo-<lb/>ret Cohærentia ejusdem ligni in diverſis a meditullio diſtantiis: </s> <s xml:id="echoid-s12682" xml:space="preserve">ex <lb/>Ligno Quercico electus fuit aſſer, qui ex medio trunco exſectus <pb o="538" file="0554" n="555" rhead="INTRODUCTIO AD COHÆRENTIAM"/> erat, proinde tranſiens per meditullium omnesque partes, quæ ſingulis <lb/>annis accreverant: </s> <s xml:id="echoid-s12683" xml:space="preserve">Ex eo confecta fuerunt parallelopipeda, 12 lon-<lb/>ga pollices, æque craſſa, o, 25 pollices lata; </s> <s xml:id="echoid-s12684" xml:space="preserve">unum erat ex medi-<lb/>tullio, alterum ex parte meditullio proxima, tertium ab eo remotius, ut <lb/>& </s> <s xml:id="echoid-s12685" xml:space="preserve">quartum, quintumque, ſextum cortici adhæſerat: </s> <s xml:id="echoid-s12686" xml:space="preserve">ſingula im-<lb/>miſſa fuerunt foramini quadrato R machinæ divulſoriæ ad diſtan-<lb/>tiam unius pollicis, exſtantia igitur 11 pollicibus; </s> <s xml:id="echoid-s12687" xml:space="preserve">extremitati ap-<lb/>penſa ſunt pondera ejus gravitatis donec Lignum fregerint, eventus <lb/>Experimentorum fuerunt ſequentes.</s> <s xml:id="echoid-s12688" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div467" type="section" level="1" n="467"> <head xml:id="echoid-head579" xml:space="preserve">EXPERIMENTUM CLVI.</head> <p> <s xml:id="echoid-s12689" xml:space="preserve">Parallelopipedum ex meditullio ſuſtinuit libras 4 {1/2}, inflexum fuit <lb/>antequam rumpebatur ita, ut directionis linea a foramine diſtiterit <lb/>9 pollicibus.</s> <s xml:id="echoid-s12690" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div468" type="section" level="1" n="468"> <head xml:id="echoid-head580" xml:space="preserve">EXPERIMENTUM CLVII.</head> <p> <s xml:id="echoid-s12691" xml:space="preserve">Quod meditullio proximum fuerat ſuſtinuit libras 4, inflexum fuit, <lb/>ſed minus quam præcedens, adeo ut ponderis directio a foramine <lb/>diſtaret 9 {1/4} pollicibus.</s> <s xml:id="echoid-s12692" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div469" type="section" level="1" n="469"> <head xml:id="echoid-head581" xml:space="preserve">EXPERIMENTUM CLVIII.</head> <p> <s xml:id="echoid-s12693" xml:space="preserve">Ordine huic proximum ſuſtinuit libras 4. </s> <s xml:id="echoid-s12694" xml:space="preserve">inflexum fuit minus <lb/>præcedenti, atque directio ponderis a foramine diſtabat 9 {1/2} pollici-<lb/>bus cum frangeretur.</s> <s xml:id="echoid-s12695" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div470" type="section" level="1" n="470"> <head xml:id="echoid-head582" xml:space="preserve">EXPERIMENTUM CLIX.</head> <p> <s xml:id="echoid-s12696" xml:space="preserve">Parallelopipedum a meditullio remotius ſuſtinuit libras 4, minus <lb/>inflexum fuit cum frangeretur, nam directio ponderis a foramine <lb/>diſtabat tantum 9 {3/4} pollicibus.</s> <s xml:id="echoid-s12697" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div471" type="section" level="1" n="471"> <head xml:id="echoid-head583" xml:space="preserve">EXPERIMENTUM CLX.</head> <p> <s xml:id="echoid-s12698" xml:space="preserve">Parallelopipedum adhuc a meditullio remotius præcedenti ſuſti- <pb o="539" file="0555" n="556" rhead="CORPORUM FIRMORUM."/> nuit libras 3 {10/16}, ſed directio ponderis â foramine, cum frangeretur. <lb/></s> <s xml:id="echoid-s12699" xml:space="preserve">diſtabat tantum 9 {1/2} pollicibus.</s> <s xml:id="echoid-s12700" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div472" type="section" level="1" n="472"> <head xml:id="echoid-head584" xml:space="preserve">EXPERIMENTUM CLXI.</head> <p> <s xml:id="echoid-s12701" xml:space="preserve">Quod Cortici proximum fractum fuit a libris 3 {3/16} extremo appen-<lb/>ſis, inflectebatur omnium minime, nam 10 pollicibus ponderis di-<lb/>rectio a foramine diſtabat, cum frangeretur.</s> <s xml:id="echoid-s12702" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12703" xml:space="preserve">Liquet ex his Experimentis omnes Trunci partes non eſſe æque <lb/>flexiles, meditullio proximas eſſe flexiliores iis, quæ corticiſunt <lb/>propinquiores: </s> <s xml:id="echoid-s12704" xml:space="preserve">nam parallelopipedum 11 pollicum meditullii, an-<lb/>tequam frangebatur, inflexum fuit, ut modo 9 pollicibus a forami-<lb/>ne diſtaret ponderis directio, cum quod cortici proximum ad 10 <lb/>pollicum diſtantiam â foramine ponderis directionem habuerit, <lb/>quando rumpebatur: </s> <s xml:id="echoid-s12705" xml:space="preserve">Vulgari opinioni hoc penitus adverſatur quip-<lb/>pe magis flexibile creditur lignum quod recentius, fragilius quod <lb/>annoſius eſt, in trunci ſubſtantia id falſum, verum in ramis exiſtit: <lb/></s> <s xml:id="echoid-s12706" xml:space="preserve">oleum, quo meditullium trunci copioſius gaudet, quam partes cor-<lb/>tici proximæ, facit ut meditullium flexibilius exiſtat.</s> <s xml:id="echoid-s12707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12708" xml:space="preserve">Præterea obſervamus in his Experimentis, Cohærentiam partium <lb/>per totam Trunci craſſitiem admodum diſcrepare: </s> <s xml:id="echoid-s12709" xml:space="preserve">tanta quippe pa-<lb/>rallelopipedi ex meditullio Cohærentia eſt, ut ruptum fuiſſet a li-<lb/>bris 162. </s> <s xml:id="echoid-s12710" xml:space="preserve">ad diſtantiam o, 25 pollicis a foramine applicatis; </s> <s xml:id="echoid-s12711" xml:space="preserve">ſed pa-<lb/>rallelopipedum ſecundum ad eandem diſtantiam frangeretur a libris <lb/>148: </s> <s xml:id="echoid-s12712" xml:space="preserve">Tertium a libris 152. </s> <s xml:id="echoid-s12713" xml:space="preserve">quartum a libris 156. </s> <s xml:id="echoid-s12714" xml:space="preserve">quintum a libris <lb/>138. </s> <s xml:id="echoid-s12715" xml:space="preserve">ſextum a libris 128. </s> <s xml:id="echoid-s12716" xml:space="preserve">Adeoque firmiſſimum eſt meditullium: <lb/></s> <s xml:id="echoid-s12717" xml:space="preserve">debiliſſimum Lignum cortici proximum: </s> <s xml:id="echoid-s12718" xml:space="preserve">in intermediis lignis in-<lb/>æqualitas datur, quæ pendet a diverſo modo, quo partes concre-<lb/>verunt, quod fieri potuit, quia uno anno æſtas fuerit calidior, fri-<lb/>gidiorve; </s> <s xml:id="echoid-s12719" xml:space="preserve">humidior, ſicciorve altero, ita ut partes a cortice for-<lb/>matæ fuerint nunc denſiores & </s> <s xml:id="echoid-s12720" xml:space="preserve">rigidiores, nunc rariores & </s> <s xml:id="echoid-s12721" xml:space="preserve">mollio-<lb/>res: </s> <s xml:id="echoid-s12722" xml:space="preserve">Idcirco arbitror Cohærentiam truncorum omnium arborum <lb/>fore admodum diverſam, nec id ipſum præciſe ſemper obſervatum <lb/>iri, quod mihi in hiſce Experimentis videre contigit.</s> <s xml:id="echoid-s12723" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12724" xml:space="preserve">Lignum unius ejuſdemque generis diverſa firmitate donati anno-<lb/>tavit Cl. </s> <s xml:id="echoid-s12725" xml:space="preserve">Parentius in L’Hiſt de L’Acad. </s> <s xml:id="echoid-s12726" xml:space="preserve">Roy: </s> <s xml:id="echoid-s12727" xml:space="preserve">A<emph style="super">o</emph>. </s> <s xml:id="echoid-s12728" xml:space="preserve">1707. </s> <s xml:id="echoid-s12729" xml:space="preserve">cum enim <pb o="540" file="0556" n="557" rhead="INTRODUCTIO AD COHÆRENTIAM"/> parallelopipedum ex ligno tenero quercico, mediocriter duro & </s> <s xml:id="echoid-s12730" xml:space="preserve">ſic-<lb/>co conſtruxerat, latum 5 lineas, altum 6 lineas, longum 5{1/2} polli-<lb/>ces, id foramini immiſſum horizontaliter a libris 23 extremo ap-<lb/>penſis fractum fuit: </s> <s xml:id="echoid-s12731" xml:space="preserve">deinde aliud parallelopipedum præparavit, æ-<lb/>que longum, latum & </s> <s xml:id="echoid-s12732" xml:space="preserve">altum ac prius, ſed ex Ligno quercico du-<lb/>riori, id antequam rumpebatur, ſuſtinuit libras 52. </s> <s xml:id="echoid-s12733" xml:space="preserve">ab extremo: <lb/></s> <s xml:id="echoid-s12734" xml:space="preserve">Aliud parallelopipedum quercicum durum ſiccumque, 3 {1/3} lineas <lb/>craſſum, 13 {2/3} lineas latum, 6 {1/2} pollices longum, planitiei impoſi-<lb/>tum, ſuſtinuit ante rupturam libras 38 {1/2} extremitati appenſas: </s> <s xml:id="echoid-s12735" xml:space="preserve">per-<lb/>petuæ eſt obſervationis ramorum Lignum eſſe flexibilius, ſed infir-<lb/>mius; </s> <s xml:id="echoid-s12736" xml:space="preserve">truncorum rigidius & </s> <s xml:id="echoid-s12737" xml:space="preserve">fortius: </s> <s xml:id="echoid-s12738" xml:space="preserve">creſcunt autem arbores certo <lb/>tempore, deinde ſtant, poſtea decreſcunt; </s> <s xml:id="echoid-s12739" xml:space="preserve">ſolet meditullium primo <lb/>corrumpi, cortex diutiſſime perſtare: </s> <s xml:id="echoid-s12740" xml:space="preserve">hinc meditullium trunci non <lb/>ſemper eſt firmiſſimum, quemadmodum noſtra Experimenta evi-<lb/>cerant, imo aliquando rami erunt fortiſſimi truncus debiliſſimus <lb/>omnium partium.</s> <s xml:id="echoid-s12741" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12742" xml:space="preserve">Sunt hæc pauca Tentamina fundamenta vera doctrinæ de Cohæ-<lb/>rentia ſolidorum; </s> <s xml:id="echoid-s12743" xml:space="preserve">utinam Philoſophi reliqua corpora, quæ in Terra <lb/>dantur, ſecundum hanc ſimilemve methodum explorarent! abſque <lb/>Experimentis enim hæc doctrina promoveri non poterit, mortalium <lb/>enim nemo â priori determinabit, quanta erit corporis dati, & </s> <s xml:id="echoid-s12744" xml:space="preserve">in <lb/>præcedentibus nondum explorati firmitas abſoluta. </s> <s xml:id="echoid-s12745" xml:space="preserve">aut reſpectiva: <lb/></s> <s xml:id="echoid-s12746" xml:space="preserve">imo ex data reſpectiva non fluit magnitudo abſolutæ, uti nec ex <lb/>abſolutâ reſpectiva cognoſcitur: </s> <s xml:id="echoid-s12747" xml:space="preserve">nam ignoramus quanta ſit in <lb/>dato corpore reſiſtentia tenſarum fibrarum in qualibet productione, <lb/>hoc Experientia tantum detegit: </s> <s xml:id="echoid-s12748" xml:space="preserve">propterea orandi ſunt homines, <lb/>ut animos ſubmittant, ſcientiam ſolidam quærant, tentamina cum <lb/>corporibus inſtituant, relinquantque inanem Philoſophiam, in <lb/>qua de cauſis tantum diſputatur, Hypotheſes finguntur, quæ diſci-<lb/>pulis pro demonſtrationibus venduntur, quorum animi vanâ im-<lb/>plentur doctrinâ, tempus peſſime eripitur, crumenæ turpiter eva-<lb/>cuantur.</s> <s xml:id="echoid-s12749" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12750" xml:space="preserve">Ordo exigeret, ut Metallorum Cohærentiam reſpectivam quoque <lb/>traderem, eorum enim maximus per totam vitam eſt uſus: </s> <s xml:id="echoid-s12751" xml:space="preserve">ſed hæc <lb/>adeo flexilia ſunt, ut horizontaliter foramini immiſſa, a pondere <lb/>extremitatibus appenſo, ad angulum rectum inflectantur, nec fran- <pb o="541" file="0557" n="558" rhead="CORPORUM FIRMORUM."/> gantur: </s> <s xml:id="echoid-s12752" xml:space="preserve">hac inflexione impediunt quo minus examini Cohærentia <lb/>eorum reſpectiva ſubmittatur.</s> <s xml:id="echoid-s12753" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12754" xml:space="preserve">Conveniunt huic loco Experimenta a Mariotto capta, quæ ta-<lb/>men non repetii: </s> <s xml:id="echoid-s12755" xml:space="preserve">Cylindrus vitri, diametri {5/3} linearum, longitudi-<lb/>nis 6 pedum, infixus foramini horizontaliter, propria gravltate <lb/>fuit diffractus.</s> <s xml:id="echoid-s12756" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12757" xml:space="preserve">2°. </s> <s xml:id="echoid-s12758" xml:space="preserve">Cylindrus marmoris nigri, diametri 0, 5 pollicis ad diſtantiam <lb/>4 pollicum â foramine ſuſtinuit ab extremo libras 10 {1/2}, a quibus <lb/>rumpebatur.</s> <s xml:id="echoid-s12759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12760" xml:space="preserve">3°. </s> <s xml:id="echoid-s12761" xml:space="preserve">Gladius oblique ſurſum infixus foramini geſtavit ab extremi-<lb/>tate libras 68.</s> <s xml:id="echoid-s12762" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12763" xml:space="preserve">4°. </s> <s xml:id="echoid-s12764" xml:space="preserve">Lamina parva ferri albi ſuſtinuit libras 80.</s> <s xml:id="echoid-s12765" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12766" xml:space="preserve">Sed ad alia properemus Tentamina, exploremus in quanam pro-<lb/>portione altitudinum, & </s> <s xml:id="echoid-s12767" xml:space="preserve">latitudinum corpora diverſæ craſſitiei co-<lb/>hæreant. </s> <s xml:id="echoid-s12768" xml:space="preserve">Hunc in finem parallelopipeda Lignea ex uno & </s> <s xml:id="echoid-s12769" xml:space="preserve">eodem <lb/>aſſere confeci, quorum omnium latitudo erat eadem, nempe 0, 26 <lb/>pollic: </s> <s xml:id="echoid-s12770" xml:space="preserve">altitudine tamen diverſa donabantur: </s> <s xml:id="echoid-s12771" xml:space="preserve">ne autem obſcuritas <lb/>maneat, quid latitudinem aut altitudinem vocem, inſpiciatur Tab. <lb/></s> <s xml:id="echoid-s12772" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s12773" xml:space="preserve">fig. </s> <s xml:id="echoid-s12774" xml:space="preserve">14. </s> <s xml:id="echoid-s12775" xml:space="preserve">in qua parallelopipedum X proponitur, cujus E F <lb/>altitudo, F G latitudo, G S longitudo appellatur: </s> <s xml:id="echoid-s12776" xml:space="preserve">Parallelopipe-<lb/>dum quodlibet uno extremo immittebatur foramini aſſeris querci-<lb/>ci, cui accurate conveniebat, & </s> <s xml:id="echoid-s12777" xml:space="preserve">cujus latus infimum perfecte hori-<lb/>zonti parallelum ponebatur, hinc quot diverſæ altitudinis paralle-<lb/>lopipeda dabantur, totidem diverſa foramina in aſſere exſculpta <lb/>erant: </s> <s xml:id="echoid-s12778" xml:space="preserve">alteri extremo parallelopipedi appendebatur pondus, quod <lb/>pedetentim auctum inflectebat Lignum, tandem rumpebat; </s> <s xml:id="echoid-s12779" xml:space="preserve">quo-<lb/>niam igitur ob inflexionem linea directionis ponderis â foramine per-<lb/>petuo imminuebatur, curavi adducendo ad foramen aut reducendo <lb/>ab illo funem, ex quo pondus pendebat, ut diſtantia lineæ di-<lb/>rectionis ponderis ſemper 9 pollicum fuerit, & </s> <s xml:id="echoid-s12780" xml:space="preserve">ſucceſſus notavi <lb/>ſequentes.</s> <s xml:id="echoid-s12781" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div473" type="section" level="1" n="473"> <head xml:id="echoid-head585" xml:space="preserve">EXPERIMENTUM CLXII.</head> <p> <s xml:id="echoid-s12782" xml:space="preserve">Parallelopipedum Quercium, altum 0, 33 pollic. </s> <s xml:id="echoid-s12783" xml:space="preserve">ad diſtantiam 9 <lb/>pollicum a foramine fractum fuit a libris 5.</s> <s xml:id="echoid-s12784" xml:space="preserve"/> </p> <pb o="542" file="0558" n="559" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div474" type="section" level="1" n="474"> <head xml:id="echoid-head586" xml:space="preserve">EXPERIMENTUM CLXIII.</head> <p> <s xml:id="echoid-s12785" xml:space="preserve">Parallelopipedum Quercium, altum 0, 40 pollic: </s> <s xml:id="echoid-s12786" xml:space="preserve">ad diſtantiam <lb/>9 pollic. </s> <s xml:id="echoid-s12787" xml:space="preserve">a foramine, fractum fuit a libris 8.</s> <s xml:id="echoid-s12788" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div475" type="section" level="1" n="475"> <head xml:id="echoid-head587" xml:space="preserve">EXPERIMENTUM CLXIV.</head> <p> <s xml:id="echoid-s12789" xml:space="preserve">Parallelopipedum' Quercicum altum 0, 52 pollic: </s> <s xml:id="echoid-s12790" xml:space="preserve">ad diſtantiam <lb/>eandem a foramine fractum a libris 11 (similar 15 unciis.</s> <s xml:id="echoid-s12791" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div476" type="section" level="1" n="476"> <head xml:id="echoid-head588" xml:space="preserve">EXPERIMENTUM CLXV.</head> <p> <s xml:id="echoid-s12792" xml:space="preserve">Parallopipedum Quercicum altum 0, 58. </s> <s xml:id="echoid-s12793" xml:space="preserve">poll: </s> <s xml:id="echoid-s12794" xml:space="preserve">ad diſtantiam ean-<lb/>dem a foramine fractum fuit â libris 14 (similar unciis 15 (similar drach-<lb/>mis 2.</s> <s xml:id="echoid-s12795" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div477" type="section" level="1" n="477"> <head xml:id="echoid-head589" xml:space="preserve">EXPERIMENTUM CLXVI.</head> <p> <s xml:id="echoid-s12796" xml:space="preserve">Parallelopipedum Quercicum altum 0, 68 pollic: </s> <s xml:id="echoid-s12797" xml:space="preserve">ad diſtantiam <lb/>9 pollic: </s> <s xml:id="echoid-s12798" xml:space="preserve">a foramine fractum fuit a libris 20 (similar unciis 7.</s> <s xml:id="echoid-s12799" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div478" type="section" level="1" n="478"> <head xml:id="echoid-head590" xml:space="preserve">EXPERIMENTUM CLXVII.</head> <p> <s xml:id="echoid-s12800" xml:space="preserve">Parallelopipedum Quercium altum 0, 74. </s> <s xml:id="echoid-s12801" xml:space="preserve">pollic: </s> <s xml:id="echoid-s12802" xml:space="preserve">ad diſtantiam <lb/>9 pollic: </s> <s xml:id="echoid-s12803" xml:space="preserve">a foramine fractum fuit a libris 24.</s> <s xml:id="echoid-s12804" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12805" xml:space="preserve">Si hæc Experimenta inter ſe comparemus, obſervamus Cohæ-<lb/>rentiam horum parallelopipedorum Quercicorum æque latorum, <lb/>ſed diverſæ altitudinis eſſe circiter in ratione duplicata altitudinis, <lb/>a qua proportione tamen plus recedunt craſſiora, quam tenuiora, <lb/>quod etiam obſervavi poſtea in aliis Experimentis ab CLXXXVII. <lb/></s> <s xml:id="echoid-s12806" xml:space="preserve">ad CXCII. </s> <s xml:id="echoid-s12807" xml:space="preserve">ſi accurate reſponderent Experimenta proportioni du-<lb/>plicatæ altitudinum, ecce quales Cohærentiæ debuiſſent eſſe in <lb/>uno conſpectæ tabellæ.</s> <s xml:id="echoid-s12808" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines lignorum # 33. # 40. # 52. # 58. # 68. # 74. <lb/>Altitudinum quadrata # 1089. # 1600. # 2704. # 3364. # 4624. # 5476. <lb/>Cohærentiæ in Experiment. # 5. # 8. # 11 {15/16}. # 14 {122/128}. # 20 {7/16}. # 24. <lb/>Cohærentiæ ex Calculo. # 5. # 7 {377/1089}. # 12 {452/1089}. # 15 {425/1089}, # 21 {251/1089}. # 25 {155/1089}. <lb/></note> <pb o="543" file="0559" n="560" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s12809" xml:space="preserve">Sunt hæ aberrationes a calculo non magnæ, quæ facile ab inæ-<lb/>quali ligni Cohærentia oriri potuerunt, quam prævidens, curaveram <lb/>ut omnia exploranda Ligna exloco fere aſſeris eodem ſumta fuerint, <lb/>aut ſaltem ſibi proximo, & </s> <s xml:id="echoid-s12810" xml:space="preserve">electa ex optima parte aſſeris maxi-<lb/>meque homogenea, quæ fibris tantum rectis conſtabat: </s> <s xml:id="echoid-s12811" xml:space="preserve">Deinde <lb/>explorandum duxi, an eadem proportio duplicata altitudinis in <lb/>Cohærentiis aliorum lignorum daretur, quamobrem ex Ulmo præ-<lb/>paravi parallelopipeda æque lata ac præcedentia, ſed diverſæ alti-<lb/>tudinis, quibuscum capta tentamina hæc fuerunt.</s> <s xml:id="echoid-s12812" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div479" type="section" level="1" n="479"> <head xml:id="echoid-head591" xml:space="preserve">EXPERIMENTUM CLXVIII.</head> <p> <s xml:id="echoid-s12813" xml:space="preserve">Parallelopipedum Ulmi 0, 26 pollic: </s> <s xml:id="echoid-s12814" xml:space="preserve">latum, 0, 25 pollic: </s> <s xml:id="echoid-s12815" xml:space="preserve">altum, <lb/>ad diſtantiam 7 {1/2} pollicum a foramine, tantopere enim linea dire-<lb/>ctionis ponderis â foramine diſtabat, fractum fuit a libris 2 (similar <lb/>drachma 1. </s> <s xml:id="echoid-s12816" xml:space="preserve">quia autem in ſequentibus Experimentis non curavi, ut <lb/>linea directionis ponderis a foramine æqualiter diſtaret, ſed tan-<lb/>tum eminerent parallelopipeda, antequam pondera appendebantur, <lb/>9 pollicibus, inflexa fuerunt a ponderibus vario modo; </s> <s xml:id="echoid-s12817" xml:space="preserve">idcirco <lb/>concipiantur reducta ad eam longitudinem, qua ponderis directio â <lb/>foramine diſtaret 8 pollicibus, quo tempore fracta ſunt, tumque <lb/>hoc parallelopipedum tuliſſet libram 1 (similar uncias 14 (similar {15/16} drachmæ.</s> <s xml:id="echoid-s12818" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div480" type="section" level="1" n="480"> <head xml:id="echoid-head592" xml:space="preserve">EXPERIMENTUM CLXIX.</head> <p> <s xml:id="echoid-s12819" xml:space="preserve">Parallelopipedum Ulmi, 0, 35 pollic: </s> <s xml:id="echoid-s12820" xml:space="preserve">altum, ad diſtantiam 8{/2} <lb/>pollic: </s> <s xml:id="echoid-s12821" xml:space="preserve">a foramine fractum fuit a libris 3 {1/2}. </s> <s xml:id="echoid-s12822" xml:space="preserve">adeoque ad diſtantiam <lb/>8 pollic: </s> <s xml:id="echoid-s12823" xml:space="preserve">a foramine ruptum fuiſſet a libris 3 + unciis 11 {1/2}.</s> <s xml:id="echoid-s12824" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div481" type="section" level="1" n="481"> <head xml:id="echoid-head593" xml:space="preserve">EXPERIMENTUM CLXX.</head> <p> <s xml:id="echoid-s12825" xml:space="preserve">Aliud parallelopipedum Ulmi 0, 43. </s> <s xml:id="echoid-s12826" xml:space="preserve">pollic: </s> <s xml:id="echoid-s12827" xml:space="preserve">altum ad diſtantiam <lb/>9 pollic: </s> <s xml:id="echoid-s12828" xml:space="preserve">a foramine ſuſtinere potuit libras 5 + unciam 1. </s> <s xml:id="echoid-s12829" xml:space="preserve">adeoque <lb/>ad diſtantiam 8 pollicum tuliſſet libras 5 {89/128}</s> </p> <pb o="544" file="0560" n="561" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div482" type="section" level="1" n="482"> <head xml:id="echoid-head594" xml:space="preserve">EXPERIMENTUM CLXXI.</head> <p> <s xml:id="echoid-s12830" xml:space="preserve">Parallelopipedum Ulmi altum 0, 52. </s> <s xml:id="echoid-s12831" xml:space="preserve">pollic. </s> <s xml:id="echoid-s12832" xml:space="preserve">ad diſtantiam 8 pol-<lb/>lic. </s> <s xml:id="echoid-s12833" xml:space="preserve">a foramine fractum fuit a libris 9 {1/4}.</s> <s xml:id="echoid-s12834" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12835" xml:space="preserve">Obſervamus in his quatuor Experimentis Cohærentiam eſſe in <lb/>majori proportione, quam quæ eſt duplicata altitudinum; </s> <s xml:id="echoid-s12836" xml:space="preserve">quod <lb/>etiam poſtea deprehendi in Experimentis ab CXCII ad CXCVI. </s> <s xml:id="echoid-s12837" xml:space="preserve">ecce <lb/>enim in Tabella numeros calculo erutos, qui exprimerent Cohæ-<lb/>rentiam in altitudinis duplicata ratione.</s> <s xml:id="echoid-s12838" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines lignorum # 25. # 35. # 43. # 52. <lb/>Altitudinum quadrata # 625. # 1225. # 1849. # 2704. <lb/>Cohærentiæ in Experim. # 1 {113/128}. # 3 {23/32}. # 5 {89/128}. # 9 {1/4}. <lb/>Cohærentiæ ſecundum Calcul. # 1 {113/128}. # 2 {2209/3200}. # 5 {45609/80000}. # 8 {11664/80000}. <lb/></note> <p> <s xml:id="echoid-s12839" xml:space="preserve">In ſuperioribus Experimentis dabantur Cohærentiæ Ligni Quer-<lb/>cici in minori proportione quam altitudinum duplicata, quare ali-<lb/>quando exceſſus ſupra hanc proportionem datur, aliquando defe-<lb/>ctus ab eadem, quod ab admiranda fibrarum flexilitate diverſa pen-<lb/>dere videtur: </s> <s xml:id="echoid-s12840" xml:space="preserve">Erant adhuc ad manus duo parallelopipeda ejuſdem <lb/>Ligni Ulmi, ſed quorum baſes erant quadratæ, cum quibus Expe-<lb/>rimenta cepi ſequentia.</s> <s xml:id="echoid-s12841" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div483" type="section" level="1" n="483"> <head xml:id="echoid-head595" xml:space="preserve">EXPERIMENTUM CLXXII.</head> <p> <s xml:id="echoid-s12842" xml:space="preserve">Parallelopipedum Ulmi 0, 35 poll. </s> <s xml:id="echoid-s12843" xml:space="preserve">altum & </s> <s xml:id="echoid-s12844" xml:space="preserve">latum ad diſtantiam <lb/>8 pollic. </s> <s xml:id="echoid-s12845" xml:space="preserve">a foramine frangebatur a libris 6 {1/2}.</s> <s xml:id="echoid-s12846" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div484" type="section" level="1" n="484"> <head xml:id="echoid-head596" xml:space="preserve">EXPERIMENTUM CLXXIII.</head> <p> <s xml:id="echoid-s12847" xml:space="preserve">Aliud parallelopipedum Ulmi, 0, 43 pollic, altum & </s> <s xml:id="echoid-s12848" xml:space="preserve">latum, ad <lb/>diſtantiam 9 pollic. </s> <s xml:id="echoid-s12849" xml:space="preserve">a foramine frangebatur ab appenſis libris 10. <lb/></s> <s xml:id="echoid-s12850" xml:space="preserve">adeoque ad diſtantiam 8 pollicum geſtaſſet libras 11 {1/4}.</s> <s xml:id="echoid-s12851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12852" xml:space="preserve">Ex quibus binis Experimentis tamen ſequeretur, Cohærentiam <lb/>non fuiſſe in ratione tam alta, quæ eſt duplicata altitudinum & </s> <s xml:id="echoid-s12853" xml:space="preserve"><lb/>ſimplici latitudinum, quippe tum parallelopipedum Experimenti <pb o="545" file="0561" n="562" rhead="CORPORUM FIRMORUM."/> CLXXIII ferre debuiſſet libras 12 {4591/85750}, quod ab inæquali firmitate <lb/>Ligni provenit.</s> <s xml:id="echoid-s12854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12855" xml:space="preserve">Deinde ad examen Ligni Piceæ acceſſi, ex quo etiam præparata <lb/>fuerunt 4 parallelopipeda, ex eodem aſſere exſculpta, quæque ſibi <lb/>proxima jacuerant, omnium latitudo fuit 0, 26 pollic. </s> <s xml:id="echoid-s12856" xml:space="preserve">altitudines <lb/>vero diverſæ, quas in Experimentis indicamus.</s> <s xml:id="echoid-s12857" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div485" type="section" level="1" n="485"> <head xml:id="echoid-head597" xml:space="preserve">EXPERIMENTUM CLXXIV.</head> <p> <s xml:id="echoid-s12858" xml:space="preserve">Parallelopipedum Piceæ, altum 0, 25 pollic. </s> <s xml:id="echoid-s12859" xml:space="preserve">ad diſtantiam 9 pol-<lb/>lic. </s> <s xml:id="echoid-s12860" xml:space="preserve">a foramine ruptum fuit a libris 2 {1/2}.</s> <s xml:id="echoid-s12861" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div486" type="section" level="1" n="486"> <head xml:id="echoid-head598" xml:space="preserve">EXPERIMENTUM CLXXV.</head> <p> <s xml:id="echoid-s12862" xml:space="preserve">Parallelopipedum Piceæ altum 0, 35 pollic. </s> <s xml:id="echoid-s12863" xml:space="preserve">ad diſtantiam 9 pol-<lb/>lic. </s> <s xml:id="echoid-s12864" xml:space="preserve">â foramine fractum fuit a libris 5.</s> <s xml:id="echoid-s12865" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div487" type="section" level="1" n="487"> <head xml:id="echoid-head599" xml:space="preserve">EXPERIMENTUM CLXXVI.</head> <p> <s xml:id="echoid-s12866" xml:space="preserve">Parallelopipedum Piceæ altum 0, 41. </s> <s xml:id="echoid-s12867" xml:space="preserve">poll. </s> <s xml:id="echoid-s12868" xml:space="preserve">ad diſtantiam 9 pollic. <lb/></s> <s xml:id="echoid-s12869" xml:space="preserve">a foramine fructam fuit a libris 5 {5/9}.</s> <s xml:id="echoid-s12870" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div488" type="section" level="1" n="488"> <head xml:id="echoid-head600" xml:space="preserve">EXPERIMENTUM CLXXVII.</head> <p> <s xml:id="echoid-s12871" xml:space="preserve">Parallelopipedum Piceæ altum 0, 52 pollic. </s> <s xml:id="echoid-s12872" xml:space="preserve">ad diſtantiam 9 pol-<lb/>lic. </s> <s xml:id="echoid-s12873" xml:space="preserve">a foramine fractum fuit a libris 9 {1/2}.</s> <s xml:id="echoid-s12874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12875" xml:space="preserve">In hac tabula ſubduxi Cohærentias, quæ forent in ratione dupli-<lb/>cata altitudinum.</s> <s xml:id="echoid-s12876" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 25, # 35, # 41, # 52. <lb/>Altitudinum Quadrata # 625. # 1225. # 1681. # 2704. <lb/>Cohærentiæ in Experim. # 2 {1/2}. # 5. # 5 {5/9}. # 9 {1/2}. <lb/>Cohærentiæ ſecundum Calcul. # 2 {1/2}. # 5 {9/10}. # 6 {181/250}. # 10 {204/256}. <lb/></note> <p> <s xml:id="echoid-s12877" xml:space="preserve">Ex quibus liquet Cohærentiam non accurate eſſe in ratione alti-<lb/>tudinum duplicata, ſed paulo minorem. </s> <s xml:id="echoid-s12878" xml:space="preserve">Quæ aberratio ab hac <lb/>proportione poſtea pluribus confirmabitur Experimentis: </s> <s xml:id="echoid-s12879" xml:space="preserve">Videtur <lb/>fibrarum diverſa flexilitas hanc anomaliam afferre, nam in corpo- <pb o="546" file="0562" n="563" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ribus perfecte rigidis datur proportio duplicata, quæ etiam a priori <lb/>Geometrice demonſtrari poteſt, de Flexibilibus omnibus nondum de-<lb/>monſtrari potuit, latet profecto in fibrarum lentitiâ adhuc aliquid, <lb/>quod perſpicientiam efſugit, atque Philoſophorum ſagacitatem eluſit.</s> <s xml:id="echoid-s12880" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12881" xml:space="preserve">Quoniam Vitrum inter corpora maxime homogenea merito poni-<lb/>tur, ratus fui cum eo inſtituta Experimenta regulam accurate ex-<lb/>hibitura, quæ revera ita prodiit; </s> <s xml:id="echoid-s12882" xml:space="preserve">monere oportet, difficillime cum <lb/>Vitro Experimenta accurata capi poſſe, quia Vitrum facilius vel dif-<lb/>ficilius frangitur pro duritie vel mollitie diverſa oræ foraminis, ex <lb/>quo eminet; </s> <s xml:id="echoid-s12883" xml:space="preserve">ſi ora cuprea vel ferrea ſit, tum idem Vitrum frange-<lb/>tur a libris 4 appenſis, quod ab 8 libris modo frangitur, ſi ora <lb/>fuerit lignea, vel plumbo aut Stanno obducta, cujus rei rationem fru-<lb/>ſtra ex Mechanicâ quæſiveris: </s> <s xml:id="echoid-s12884" xml:space="preserve">poſt varios igitur incaſſum tentatos <lb/>labores; </s> <s xml:id="echoid-s12885" xml:space="preserve">hanc methodum eſſe optimam Experientia docuit.</s> <s xml:id="echoid-s12886" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12887" xml:space="preserve">Ex vitreo ſpeculo, utrimque lævigato, & </s> <s xml:id="echoid-s12888" xml:space="preserve">per totam magnitudi, <lb/>nem æque craſſo exſectæ ſunt lamellæ, rectangulæ, diverſarum <lb/>latitudinum: </s> <s xml:id="echoid-s12889" xml:space="preserve">harum Sectiones, quæ inæquales ſemper ſunt ab ada-<lb/>mante fiſſæ, lævigatæ fuerunt & </s> <s xml:id="echoid-s12890" xml:space="preserve">rectangulæ factæ, ita ut quælibet <lb/>lamella fuerit parallelopipedum rectangulum ab omni parte: </s> <s xml:id="echoid-s12891" xml:space="preserve">Tum <lb/>in majori mole Ligni Buxini inciſura facta fuit, ejus amplitudinis, <lb/>ut accurate craſſitiem laminæ caperet, inciſuræ baſis planiſſima fuit <lb/>facta, & </s> <s xml:id="echoid-s12892" xml:space="preserve">Lignum ita affixum Tabulæ, ut hæc baſis quoque fuerit <lb/>accuratiſſime horizontalis, niſi enim id fiat, nunquam confidi <lb/>poſſet Experimento; </s> <s xml:id="echoid-s12893" xml:space="preserve">tum ex ligno eodem aſſerculus inciſuræ con-<lb/>gruens etiam factus qui minus magiſque profunde ipſi immitti poſſet, <lb/>& </s> <s xml:id="echoid-s12894" xml:space="preserve">ſuperius ope binarum cochlearum retineri: </s> <s xml:id="echoid-s12895" xml:space="preserve">baſi inciſuræ impoſita <lb/>fuit tenuis lamella ſtanni, circiter o, 03 pollicis craſſa, quæ impe-<lb/>diebat, quominus ora anterior ligni a vitro læderetur: </s> <s xml:id="echoid-s12896" xml:space="preserve">huic inci-<lb/>ſuræ immiſſæ fuerunt vitreæ lamellæ, cujus ſuperior ſuperficies, <lb/>adacto ligneo aſſerculo, horizonti erat parallela, atque aliud latus <lb/>ipſi perpendiculare; </s> <s xml:id="echoid-s12897" xml:space="preserve">erat omnium craſſities 0, 16 pollicis, diſtantia <lb/>applicati ponderis a foramine fuit accurate 3 pollicum Rhenolandi-<lb/>corum in primis tribus Experimentis, in tribus ſequentibus fuit 2 <lb/>pollicum.</s> <s xml:id="echoid-s12898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12899" xml:space="preserve">Præterea ſollicite admodum curandum eſt, ut hæc tentamina ca-<lb/>piantur in loco quietiſſimo; </s> <s xml:id="echoid-s12900" xml:space="preserve">ſi enim ambulaveris, aut currus per ſtrata <pb o="547" file="0563" n="564" rhead="CORPORUM FIRMORUM."/> viarum vicinarum inceſſerint, a tremore multo citius franguntur <lb/>Vitra, quam debuiſſent, aut feciſſent in loco quieto, ut mihi ali-<lb/>quoties contigit.</s> <s xml:id="echoid-s12901" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div489" type="section" level="1" n="489"> <head xml:id="echoid-head601" xml:space="preserve">EXPERIMENTUM CLXXVIII.</head> <p> <s xml:id="echoid-s12902" xml:space="preserve">Vitrea Lamella altitudinis o, 73 pollicis, ad diſtantiam 3 polli-<lb/>cum a foramine fracta fuit a libris 23 + unciis 14 + drachm. </s> <s xml:id="echoid-s12903" xml:space="preserve">7 <lb/>+ ſcrup. </s> <s xml:id="echoid-s12904" xml:space="preserve">2. </s> <s xml:id="echoid-s12905" xml:space="preserve">ſive a 9191 granis,</s> </p> </div> <div xml:id="echoid-div490" type="section" level="1" n="490"> <head xml:id="echoid-head602" xml:space="preserve">EXPERIMENTUM CLXXIX.</head> <p> <s xml:id="echoid-s12906" xml:space="preserve">Vitrea Lamella altitudinis o, 56 pollicis, ad diſtantiam 3 polli-<lb/>cum a foramine fracta fuit a granis 5410.</s> <s xml:id="echoid-s12907" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div491" type="section" level="1" n="491"> <head xml:id="echoid-head603" xml:space="preserve">EXPERIMENTUM CLXXX.</head> <p> <s xml:id="echoid-s12908" xml:space="preserve">Vitrea Lamella altitudinis o, 47 pollicis ad diſtantiam 3 pollic. </s> <s xml:id="echoid-s12909" xml:space="preserve">a <lb/>foramine fracta fuit a granis 3459.</s> <s xml:id="echoid-s12910" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div492" type="section" level="1" n="492"> <head xml:id="echoid-head604" xml:space="preserve">EXPERIMENTUM CLXXXI.</head> <p> <s xml:id="echoid-s12911" xml:space="preserve">Vitrea lamella altitudinis 0, 32 pollicis ad diſtantiam 2 pollicum <lb/>a foramine fracta fuit ab 2855 granis.</s> <s xml:id="echoid-s12912" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div493" type="section" level="1" n="493"> <head xml:id="echoid-head605" xml:space="preserve">EXPERIMENTUM CLXXXII.</head> <p> <s xml:id="echoid-s12913" xml:space="preserve">Vitrea lamella altitudinis 0, 45 pollicis ad diſtantiam 2 pollic. </s> <s xml:id="echoid-s12914" xml:space="preserve">a <lb/>foramine fracta fuit a 5644 granis.</s> <s xml:id="echoid-s12915" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div494" type="section" level="1" n="494"> <head xml:id="echoid-head606" xml:space="preserve">EXPERIMENTUM CLXXXIII.</head> <p> <s xml:id="echoid-s12916" xml:space="preserve">Vitrea lamella altitudinis 0, 4 pollicis ad diſtantiam 2 pollic. </s> <s xml:id="echoid-s12917" xml:space="preserve">a <lb/>foramine fracta fuit a 4469 granis.</s> <s xml:id="echoid-s12918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12919" xml:space="preserve">Congruunt hæc Experimenta, hercle pleniſſima laboris, accu-<lb/>rate ſatis cum regula, Cohærentiam nempe corporum æque craſ-<lb/>ſorum eſſe in ratione duplicata altitudinum: </s> <s xml:id="echoid-s12920" xml:space="preserve">Si enim calculus ineatur, <lb/>in Experimento CLXXIX. </s> <s xml:id="echoid-s12921" xml:space="preserve">Cohærentia debebit eſſe 5408 granorum, <pb o="548" file="0564" n="565" rhead="INTRODUCTIO AD COHÆRENTIAM"/> obſervata fuit 5410 granorum: </s> <s xml:id="echoid-s12922" xml:space="preserve">Calculus indicat pro Experimento <lb/>CLXXX Cohærentiam eſſe 3464, quæ obſervata fuit 3459. </s> <s xml:id="echoid-s12923" xml:space="preserve">grano-<lb/>rum. </s> <s xml:id="echoid-s12924" xml:space="preserve">Eodem modo eruitur ſupputando Cohærentia pro Experimento <lb/>CLXXXII æqualis 5646 granis, quæfuit 5644 obſervata: </s> <s xml:id="echoid-s12925" xml:space="preserve">& </s> <s xml:id="echoid-s12926" xml:space="preserve">pro Ex-<lb/>perimento CLXXXIII æqualis 4456, quam experientia dedit 4469. <lb/></s> <s xml:id="echoid-s12927" xml:space="preserve">quæ adeo accurate conveniunt, acunquamExperimenta poterunt, non <lb/>tamen diffiteor me plura alia inſtituiſſe, ex quibus hæc elegi, allis <lb/>non tam accurate reſpondentibus, ſed minimus tremor ab homini-<lb/>bus, currubus, equis in diſtantia etiamſi 70 pedum a loco obſerva-<lb/>tionis excitatus, valde notabilem, & </s> <s xml:id="echoid-s12928" xml:space="preserve">ultra omnem fidem, diſcre-<lb/>pantiam affert: </s> <s xml:id="echoid-s12929" xml:space="preserve">Ad quot & </s> <s xml:id="echoid-s12930" xml:space="preserve">quam exiguas circumſtantias in Expe-<lb/>rimentali Philoſophiâ attendendum non eſt? </s> <s xml:id="echoid-s12931" xml:space="preserve">hinc ſæpiſſime illudi-<lb/>mur, nec videtur humanum ingenium ſatis amplum ad omnia, quæ <lb/>concurrunt in aliquo Phænomeno, ſimul complectenda.</s> <s xml:id="echoid-s12932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12933" xml:space="preserve">Fundamentis hiſce præmiſſis, non absque fructu & </s> <s xml:id="echoid-s12934" xml:space="preserve">uſu Galilæi <lb/>doctrina de Cohærentiâ reſpectivâ, quæ pars Matbeſeos mixtæ <lb/>evaſit, addi poterit, quam in gratiam Tironum â prima origine <lb/>inchoabo.</s> <s xml:id="echoid-s12935" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12936" xml:space="preserve">D<emph style="sc">EFINITIO. I.</emph></s> <s xml:id="echoid-s12937" xml:space="preserve">Momentum voco vim totam Potentiæ agentis, quæ <lb/>oritur ex magnitudine Potentiæ ductâ in diſtantiam a centro mo-<lb/>tus, ſi vecti ſit applicata, aut in velocitatem quacum movetur.</s> <s xml:id="echoid-s12938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12939" xml:space="preserve">D<emph style="sc">EFINITIO.</emph></s> <s xml:id="echoid-s12940" xml:space="preserve"> 2. </s> <s xml:id="echoid-s12941" xml:space="preserve">Centrum gravitatis voco punctum aliquod, circa <lb/>quod corpus quocunque modo converſum, & </s> <s xml:id="echoid-s12942" xml:space="preserve">libere ex eo ſuſpen-<lb/>ſum, ſemper eſt undiquaque æquilibratum & </s> <s xml:id="echoid-s12943" xml:space="preserve">in quiete.</s> <s xml:id="echoid-s12944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12945" xml:space="preserve">In ſequentibus Propoſitionibus indicabo ubinam centrum gravi-<lb/>tatis corporum variâ figurâ donatorum ponatur, ſupponam tamen <lb/>in Mechanica hoc eſſe demonſtratum, ne a ſcopo latius aberrem; <lb/></s> <s xml:id="echoid-s12946" xml:space="preserve">cæteroquin, qui hoc deſideret, conſulat Walliſium in Mechanica, <lb/>aut Carreum in Libro vocato Traitè des Centres de Peſanteur. </s> <s xml:id="echoid-s12947" xml:space="preserve"><lb/>Hayes Treatiſe of Fluxions Sect. </s> <s xml:id="echoid-s12948" xml:space="preserve">XI. </s> <s xml:id="echoid-s12949" xml:space="preserve">qui hoc Thema pulcre & </s> <s xml:id="echoid-s12950" xml:space="preserve"><lb/>univerſaliter tractaverunt.</s> <s xml:id="echoid-s12951" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div495" type="section" level="1" n="495"> <head xml:id="echoid-head607" xml:space="preserve">PROPOSITIO XIX.</head> <p style="it"> <s xml:id="echoid-s12952" xml:space="preserve">Tab. </s> <s xml:id="echoid-s12953" xml:space="preserve">XIX. </s> <s xml:id="echoid-s12954" xml:space="preserve">fig. </s> <s xml:id="echoid-s12955" xml:space="preserve">3. </s> <s xml:id="echoid-s12956" xml:space="preserve">Si parallelopipedum FEAD, aut Priſma, <lb/>aut Cubus, aut Cylindrus, parieti infixus horizontaliter emineat, <pb o="549" file="0565" n="566" rhead="CORPORUM FIRMORUM."/> atque Potentia frangens extremitati D applicata agat directione <lb/>ad horizontem perpendiculari, fiet ruptura in orâ foraminis A E F.</s> <s xml:id="echoid-s12957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12958" xml:space="preserve">Poteſt conſiderari longitudo corporis A D ut vectis, cujus ful-<lb/>crum eſt ad A, potentia in D, eligatur quæcunque ſectio intermedia <lb/>C parallelela baſi A E F, in hac C, erit Cohærentia eadem ac in baſi <lb/>A E F, quia corpus eſt ubique æque craſſum: </s> <s xml:id="echoid-s12959" xml:space="preserve">eſt vero momentum po-<lb/>tentiæ D majus, applicatum vecti A D, quam D C breviori; </s> <s xml:id="echoid-s12960" xml:space="preserve">adeoque <lb/>potius ſuperabitur Cohærentia in A E F quam in C, & </s> <s xml:id="echoid-s12961" xml:space="preserve">quia vectis <lb/>A D eſt longiſſimus omnium in latere A D, cujus ope potentia maxi-<lb/>mum momentum exercet, franget hæc corpus in ora foraminis A E F.</s> <s xml:id="echoid-s12962" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div496" type="section" level="1" n="496"> <head xml:id="echoid-head608" xml:space="preserve">PROPOSITIO XX.</head> <p style="it"> <s xml:id="echoid-s12963" xml:space="preserve">Tab. </s> <s xml:id="echoid-s12964" xml:space="preserve">XIX. </s> <s xml:id="echoid-s12965" xml:space="preserve">fig. </s> <s xml:id="echoid-s12966" xml:space="preserve">3. </s> <s xml:id="echoid-s12967" xml:space="preserve">Si dentur duo parallelopipeda horizontalia F E <lb/>A C, F E A D, ejusdem materiæ & </s> <s xml:id="echoid-s12968" xml:space="preserve">craſſitiei, ſed diverſæ longitu-<lb/>dinis A C, A D, quorum extremitatibus C & </s> <s xml:id="echoid-s12969" xml:space="preserve">D applicentur Po-<lb/>tentiæ rumpentes, harumque directiones ſint perpendiculares in A C <lb/>& </s> <s xml:id="echoid-s12970" xml:space="preserve">A D, ſepoſitâ corporum gravitate requirentur potentiæ ad C <lb/>& </s> <s xml:id="echoid-s12971" xml:space="preserve">D in ratione reciprocâ longitudinum A C, A D.</s> <s xml:id="echoid-s12972" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12973" xml:space="preserve">Quando franguntur hæc parallelopipeda in EAF primo ſolvun-<lb/>tur partes ſuperiores E, tum quæ propiores ſunt ad A, fitque ro-<lb/>tatio circa infimum punctum A, adeoque E A C, E A D poſſunt <lb/>conſiderari ut duo vectes incurvi, quorum centrum motus eſt in A, <lb/>& </s> <s xml:id="echoid-s12974" xml:space="preserve">qui brachia habent EA, AC, tum EA, AD: </s> <s xml:id="echoid-s12975" xml:space="preserve">Eſt autem Cohæ-<lb/>rentia baſium EAF eadem, quia ſunt baſes eædem, adeoque earum <lb/>reſiſtentia eſt eadem; </s> <s xml:id="echoid-s12976" xml:space="preserve">ſed reſiſtentia totius lateris A E poteſt conſi-<lb/>derari inſtar ponderis vel potentiæ applicatæ puncto E vectis E A: <lb/></s> <s xml:id="echoid-s12977" xml:space="preserve">Eſt igitur potentia requiſita in C ad pondus vel potentiam in E, uti <lb/>E A ad A C: </s> <s xml:id="echoid-s12978" xml:space="preserve">& </s> <s xml:id="echoid-s12979" xml:space="preserve">potentia in D, ad idem pondus vel potentiam E, <lb/>uti EA ad AD. </s> <s xml:id="echoid-s12980" xml:space="preserve">quia EA eſt eadem quantitas poteſt poni = 1. </s> <s xml:id="echoid-s12981" xml:space="preserve">hinc <lb/>ſtabit C. </s> <s xml:id="echoid-s12982" xml:space="preserve">E:</s> <s xml:id="echoid-s12983" xml:space="preserve">: 1. </s> <s xml:id="echoid-s12984" xml:space="preserve">AC. </s> <s xml:id="echoid-s12985" xml:space="preserve">ſive {C/E}:</s> <s xml:id="echoid-s12986" xml:space="preserve">: {1.</s> <s xml:id="echoid-s12987" xml:space="preserve">/AC} tum D.</s> <s xml:id="echoid-s12988" xml:space="preserve">E:</s> <s xml:id="echoid-s12989" xml:space="preserve">: 1. </s> <s xml:id="echoid-s12990" xml:space="preserve">AD. </s> <s xml:id="echoid-s12991" xml:space="preserve">ſive {D/E}:</s> <s xml:id="echoid-s12992" xml:space="preserve">: <lb/>{1.</s> <s xml:id="echoid-s12993" xml:space="preserve">/AD} ſed eſt {C/E} ad {D/E}:</s> <s xml:id="echoid-s12994" xml:space="preserve">: C.</s> <s xml:id="echoid-s12995" xml:space="preserve">D. </s> <s xml:id="echoid-s12996" xml:space="preserve">quare C.</s> <s xml:id="echoid-s12997" xml:space="preserve">D:</s> <s xml:id="echoid-s12998" xml:space="preserve">: {1.</s> <s xml:id="echoid-s12999" xml:space="preserve">/AC} {1.</s> <s xml:id="echoid-s13000" xml:space="preserve">/AD}:</s> <s xml:id="echoid-s13001" xml:space="preserve">: AD. </s> <s xml:id="echoid-s13002" xml:space="preserve">AC <lb/>hoc eſt, erit C ad D in ratione reciproca longitudinum AC ad AD.</s> <s xml:id="echoid-s13003" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13004" xml:space="preserve">Hac propoſitione uſus fui in Experimentis præcedentibus, cum <pb o="550" file="0566" n="567" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pondus frangens applicabatur extremitati D ligni AD, cujus mo-<lb/>mentum comparatum fuit cum vi, quæ deſiderata fuiſſet in AD ad <lb/>diſtantiam ab A, æqualem altitudini A E.</s> <s xml:id="echoid-s13005" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div497" type="section" level="1" n="497"> <head xml:id="echoid-head609" xml:space="preserve">PROPOSITIO XXI.</head> <p style="it"> <s xml:id="echoid-s13006" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13007" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13008" xml:space="preserve">fig. </s> <s xml:id="echoid-s13009" xml:space="preserve">2. </s> <s xml:id="echoid-s13010" xml:space="preserve">Si dentur duo parallelopipeda horizontaliter <lb/>parieti infixa, MEACD, FEACK, æque longa, uti A C; </s> <s xml:id="echoid-s13011" xml:space="preserve">æque <lb/>alta, uti E A, ſed variæ latitudinis EM, EF, ex eâdem materiâ, <lb/>tum, ſepoſita corporum gravitate, erit potentia ſeparans applica-<lb/>ta tenuiori ex CD, ad potentiam applicatam latiori parallelopipe-<lb/>do ex CK, uti eſt latitudo EM ad EF, vel uti eſt baſis EM <lb/>ad EF.</s> <s xml:id="echoid-s13012" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13013" xml:space="preserve">Concipiatur parallelopipedum MC diviſum in partes aliquot æ-<lb/>quales ope ſectionum parallelarum ad EAC: </s> <s xml:id="echoid-s13014" xml:space="preserve">atque ita concipiatur <lb/>etiam diviſum parallelopipedum FC in partes prioribus æquales; <lb/></s> <s xml:id="echoid-s13015" xml:space="preserve">erit Cohærentia cujuslibet ſectionis æqualis alteri, adeoque Cohæ-<lb/>rentia Sectionum in parallelopipedo MC, erit uti numerus Sectio-<lb/>num in illo, hoc eſt uti EM. </s> <s xml:id="echoid-s13016" xml:space="preserve">& </s> <s xml:id="echoid-s13017" xml:space="preserve">Cohærentia Sectionum omnium <lb/>in FC, uti numerus earum, hoc eſt uti FE; </s> <s xml:id="echoid-s13018" xml:space="preserve">quare erit Cohæren-<lb/>tia parallelopipedi MC, ad FC, uti eſt EM ad EF.</s> <s xml:id="echoid-s13019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13020" xml:space="preserve">Corol. </s> <s xml:id="echoid-s13021" xml:space="preserve">Eadem demonſtratio locum habet poſitis corporibus MC, <lb/>FC gravibus: </s> <s xml:id="echoid-s13022" xml:space="preserve">dividatur enim AC bifariam in G, per quod conci-<lb/>piatur tranſire planum perpendiculare GOL parallelum baſi AEMF, <lb/>tranſibit hoc per centra gravitatis amborum parallelopipedorum, <lb/>eritque gravitatis directio in hoc plano, ideoque poteſt poni gra-<lb/>vitas totius parallelopipedi MC in plano OG, & </s> <s xml:id="echoid-s13023" xml:space="preserve">alterius paral-<lb/>lelopipedi FC in plano GL. </s> <s xml:id="echoid-s13024" xml:space="preserve">eſt vero pondus corporis MC ad illud <lb/>in FC, uti magnitudo MC ad FC, hoc eſt uti EM ad EF: </s> <s xml:id="echoid-s13025" xml:space="preserve">quare <lb/>pondus agens in plano OG, eſt ad pondus in plano LG, uti EM <lb/>ad EF. </s> <s xml:id="echoid-s13026" xml:space="preserve">Si igitur potentiæ appoſitæ in CD, CK ſecundum Pro-<lb/>poſ. </s> <s xml:id="echoid-s13027" xml:space="preserve">XXI, ſint uti EM ad EF, quæ imminuantur partibus propor-<lb/>tionalibus: </s> <s xml:id="echoid-s13028" xml:space="preserve">uti EM ad EF, ob gravitatem ſuſpenſam in GO, GL, <lb/>manebunt in eadem proportione uti EM ad EF, quare potentiæ in <lb/>CD, CK erunt in eadem proportione.</s> <s xml:id="echoid-s13029" xml:space="preserve"/> </p> <pb o="551" file="0567" n="568" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div498" type="section" level="1" n="498"> <head xml:id="echoid-head610" xml:space="preserve">EXPERIMENTUM CLXXXIV.</head> <p> <s xml:id="echoid-s13030" xml:space="preserve">Hanc Propoſitionem comprobat Experientia; </s> <s xml:id="echoid-s13031" xml:space="preserve">nam parallelopi-<lb/>pedum Quercicum 0, 33 pollic. </s> <s xml:id="echoid-s13032" xml:space="preserve">altum 0, 26 pollic. </s> <s xml:id="echoid-s13033" xml:space="preserve">latum, geſtavit <lb/>ex longitudine 9 pollic. </s> <s xml:id="echoid-s13034" xml:space="preserve">libras 5. </s> <s xml:id="echoid-s13035" xml:space="preserve">verum aliud parallelopipedum 0, 33 <lb/>poll. </s> <s xml:id="echoid-s13036" xml:space="preserve">altum, 0, 52 poll. </s> <s xml:id="echoid-s13037" xml:space="preserve">latum, geſtavit ex longitudine 9 pollic. <lb/></s> <s xml:id="echoid-s13038" xml:space="preserve">libras 10, a quibus tamen rumpebatur.</s> <s xml:id="echoid-s13039" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div499" type="section" level="1" n="499"> <head xml:id="echoid-head611" xml:space="preserve">PROPOSITIO XXII.</head> <p style="it"> <s xml:id="echoid-s13040" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13041" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13042" xml:space="preserve">Fig. </s> <s xml:id="echoid-s13043" xml:space="preserve">1. </s> <s xml:id="echoid-s13044" xml:space="preserve">Si ſint duo parallelopipeda B A C, E A C ho-<lb/>rizontaliter parieti infixa, ex materia perfecte dura, ſintque ejus-<lb/>dem latitudinis E D, & </s> <s xml:id="echoid-s13045" xml:space="preserve">ejusdem longitudinis A C, ſed diverſæ alti-<lb/>tudinis B A, E A, erunt potentiæ rumpentes applicatæ ad extre-<lb/>mum C, in ratione duplicatâ altitudinis A B ad A E.</s> <s xml:id="echoid-s13046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13047" xml:space="preserve">Quia hæc parallelopipeda frangentur in orâ foraminum B A, E A <lb/>per potentiam in C, fit motus circa A, adeoque poſſunt B A, A C, <lb/>tum E A, A C conſiderari ut duo vectes incurvi, qoorum hypomo-<lb/>chlion eſt in A. </s> <s xml:id="echoid-s13048" xml:space="preserve">eſt igitur ex natura vectis reſiſtentia in B contra <lb/>potentiam C, ad reſiſtentiam in E contra eandem potentiam C, <lb/>uti B A ad E A: </s> <s xml:id="echoid-s13049" xml:space="preserve">ſumendo autem alia puncta in A B & </s> <s xml:id="echoid-s13050" xml:space="preserve">A E, quæ <lb/>diſtant ab A, uti A B, ad A E, iis omnibus conveniet eadem demon-<lb/>ſtratio, quare vis omnium punctorum in A B, erit ad eam puncto-<lb/>rum in A E, uti eſt tota A B ad totam A E.</s> <s xml:id="echoid-s13051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13052" xml:space="preserve">Sed quantitas partium ſolvendarum in A B eſt uti A B, quarum <lb/>reſiſtentia eſt ut earum numerus, hoc eſt, uti A B: </s> <s xml:id="echoid-s13053" xml:space="preserve">Sic quantitas par-<lb/>tium ſolvendarum in A E, eſt uti A E, quarum reſiſtentia eſt uti <lb/>A E numerus partium: </s> <s xml:id="echoid-s13054" xml:space="preserve">quamobrem tota reſiſtentia in A B eſt ad <lb/>totam reſiſtentiam in A E, in ratione compoſita ex A B ad A E, <lb/>conſiderando naturam vectis; </s> <s xml:id="echoid-s13055" xml:space="preserve">& </s> <s xml:id="echoid-s13056" xml:space="preserve">ex A B ad A E, conſiderando <lb/>quantitatem partium ſolvendarum; </s> <s xml:id="echoid-s13057" xml:space="preserve">hoc eſt uti <emph style="ol">AB</emph><emph style="super">q</emph> ad <emph style="ol">AE</emph><emph style="super">q</emph>. <lb/></s> <s xml:id="echoid-s13058" xml:space="preserve">quare potentiæ frangentes in C, requiruntur, uti <emph style="ol">AB</emph><emph style="super">q</emph> ad <lb/><emph style="ol">AE</emph><emph style="super">q</emph></s> </p> <pb o="552" file="0568" n="569" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div500" type="section" level="1" n="500"> <head xml:id="echoid-head612" xml:space="preserve">Pro Corporibus Flexibilibus.</head> <p> <s xml:id="echoid-s13059" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13060" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13061" xml:space="preserve">fig. </s> <s xml:id="echoid-s13062" xml:space="preserve">5. </s> <s xml:id="echoid-s13063" xml:space="preserve">Parallelopipedum A B compoſitum ex ſibris fle-<lb/>xibilibus, antequam frangatur, patiatur fibram ſuperiorem B ex-<lb/>tendi in longitudinem B G, ducatur ex centro motus A recta A G, <lb/>in qua terminentur fibræ aliæ totius lateris A B tenſæ, ſi tum vis <lb/>reſiſtentiæ fibrarum ſit in ratione elongationum ſuarum, erit hæc <lb/>vis uti Triangulum A B G: </s> <s xml:id="echoid-s13064" xml:space="preserve">Sit parallelopipedum altitudinis A E <lb/>ejusdem materiæ, quod antequam frangetur, patiatur etiam fibram <lb/>ſuperiorem E extendi uſque in F, ita ut E F ſit = B G, ducatur <lb/>A F, in hac terminabuntur omnes tenſæ fibræ totius lateris A E, po-<lb/>ſitaque fibrarum, reſiſtentia in ratione tenſionum, erit reſiſtentia <lb/>omnium fibrarum, uti eſt Triangulum A E F; </s> <s xml:id="echoid-s13065" xml:space="preserve">quare erit reſiſtentia <lb/>fibrarum in A B, ad reſiſtentiam fibrarum in A E, uti Triangulum <lb/>A B G, ad Triangulum A E F, & </s> <s xml:id="echoid-s13066" xml:space="preserve">quia hæc ſunt æque alta, uti ba-<lb/>ſis A B ad A E. </s> <s xml:id="echoid-s13067" xml:space="preserve">Sed ſunt B A C, E A C vectes incurvi, quare erit reſi-<lb/>ſtentia in B ad eam in E contra potentiam C, uti eſt A B ad A E, idque <lb/>obtinet in omnibus punctis in A B & </s> <s xml:id="echoid-s13068" xml:space="preserve">in A E proportionalem diſtan <lb/>tiam ab A ſervantibus, quare ex natura vectis erit reſiſtentia totius <lb/>lateris A B, ad eam lateris A E, uti A B ad A E: </s> <s xml:id="echoid-s13069" xml:space="preserve">undetota reſiſtentia <lb/>in A B eſt ad eam in A E in ratione compoſita ex A B ad A E, & </s> <s xml:id="echoid-s13070" xml:space="preserve"><lb/>ex A B ad A E, hoc eſt in ratione duplicata A B ad A E, quare po-<lb/>tentiæ applicatæ in C requiruntur uti <emph style="ol">AB</emph><emph style="super">q</emph> ad <emph style="ol">AE</emph><emph style="super">q</emph>.</s> <s xml:id="echoid-s13071" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13072" xml:space="preserve">Valet hæc demonſtratio tantum ſi fibræ corporum elongentur in <lb/>ratione tenſionum, & </s> <s xml:id="echoid-s13073" xml:space="preserve">ita etiam reſiſtant; </s> <s xml:id="echoid-s13074" xml:space="preserve">cum vero id forſitanmo-<lb/>do in pauciſſimis obtinet corporibus, nequaquam demonſtratio uni-<lb/>verſalis eſt; </s> <s xml:id="echoid-s13075" xml:space="preserve">ſed dubito an quidem Lex ipſa obtineat in quibuslibet <lb/>corporibus flexibilibus, unde etiam Geometrice non poterit univer-<lb/>ſaliter probari, agam tamen in ſequentibus de iistantum corporibus, <lb/>quæ huic regulæ ſubjiciuntur.</s> <s xml:id="echoid-s13076" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div501" type="section" level="1" n="501"> <head xml:id="echoid-head613" xml:space="preserve">PROPOSITIO XXIII.</head> <p style="it"> <s xml:id="echoid-s13077" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13078" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13079" xml:space="preserve">fig 3. </s> <s xml:id="echoid-s13080" xml:space="preserve">Si dentur duo horizontalia parallelopipeda <lb/>FEAD, oeak ejusdem materiæ, ſed diverſarum craſſitierum &</s> <s xml:id="echoid-s13081" xml:space="preserve"> <pb o="553" file="0569" n="570" rhead="CORPORUM FIRMORUM."/> longitudinum, ſepoſitâ eorum gravitate, erunt vires frangentes <lb/>in D & </s> <s xml:id="echoid-s13082" xml:space="preserve">k, agentes perpendiculariter in A D & </s> <s xml:id="echoid-s13083" xml:space="preserve">a k, in ratione <lb/>compoſitâ, ex duplicatâ altitudinum A E ad a e, ſimplici latitudi-<lb/>num E F adeo, & </s> <s xml:id="echoid-s13084" xml:space="preserve">inverſa longitudinum A D ad a k.</s> <s xml:id="echoid-s13085" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13086" xml:space="preserve">Nam corpora E A C, e a k æque longa, ſed variæ altitudinis E A, <lb/>e a, habent Cohærentiam in ratione duplicata E A ad, e a, per Prop. <lb/></s> <s xml:id="echoid-s13087" xml:space="preserve">XXII. </s> <s xml:id="echoid-s13088" xml:space="preserve">Corpora variæ latitudinis, habent Cohærentiam in ratione <lb/>latitudinis, per Propoſ. </s> <s xml:id="echoid-s13089" xml:space="preserve">XXI. </s> <s xml:id="echoid-s13090" xml:space="preserve">& </s> <s xml:id="echoid-s13091" xml:space="preserve">corpora diverſæ longitudinis co-<lb/>hærent in ratione inverſa longitudinis, per Propoſ. </s> <s xml:id="echoid-s13092" xml:space="preserve">XX. </s> <s xml:id="echoid-s13093" xml:space="preserve">Quamobrem <lb/>corpora diverſæ longitudinis, latitudinis, & </s> <s xml:id="echoid-s13094" xml:space="preserve">altitudinis cohærent in <lb/>ratione compoſita, ex duplicata altitudinis E A ad, e a, ex directa la-<lb/>titudinis E F ad, e o, & </s> <s xml:id="echoid-s13095" xml:space="preserve">ex inverſa longitudinis A D ad, a k, adeoque <lb/>vires frangentes applicatæ in D & </s> <s xml:id="echoid-s13096" xml:space="preserve">k erunt in hac ratione.</s> <s xml:id="echoid-s13097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13098" xml:space="preserve">Corol. </s> <s xml:id="echoid-s13099" xml:space="preserve">Si ergo duo parallelopipeda a e o k, mnlp, fuerint æque <lb/>longa, habuerintque baſin æqualem, ſed altitudinem, a e, minorem, <lb/>quam mn, erunt Cohærentiæ, uti ſunt altitudines, a e, mn, & </s> <s xml:id="echoid-s13100" xml:space="preserve">ita <lb/>potentiæ frangentes.</s> <s xml:id="echoid-s13101" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13102" xml:space="preserve">Nam vires frangentes parallelopipedum, o k, ſunt ad eas, quæ rupturæ <lb/>ſunt lp, uti <emph style="ol">ae</emph> X eo X ak ad <emph style="ol">mn</emph><emph style="super">q</emph> X ml X np. </s> <s xml:id="echoid-s13103" xml:space="preserve">ſed eſt, ae = ml. <lb/></s> <s xml:id="echoid-s13104" xml:space="preserve">e o, = mn. </s> <s xml:id="echoid-s13105" xml:space="preserve">a k = np. </s> <s xml:id="echoid-s13106" xml:space="preserve">quare ambabus quantitatibus diviſis per a e X <lb/>, e o, X a k, reſtant, a e & </s> <s xml:id="echoid-s13107" xml:space="preserve">mn. </s> <s xml:id="echoid-s13108" xml:space="preserve">quæ ſunt uti vires frangentes in, k, <lb/>& </s> <s xml:id="echoid-s13109" xml:space="preserve">p. </s> <s xml:id="echoid-s13110" xml:space="preserve">atque ita ſunt Cohærentiæ.</s> <s xml:id="echoid-s13111" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div502" type="section" level="1" n="502"> <head xml:id="echoid-head614" xml:space="preserve">PROPOSITIO XXIV.</head> <p style="it"> <s xml:id="echoid-s13112" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13113" xml:space="preserve">XIX fig. </s> <s xml:id="echoid-s13114" xml:space="preserve">3. </s> <s xml:id="echoid-s13115" xml:space="preserve">Si ambo parallelopipeda A E F D, a e o k fue-<lb/>rint ſimilia & </s> <s xml:id="echoid-s13116" xml:space="preserve">horizontalia, baſibus A E F, a e o parietibus in-<lb/>fixis, erunt potentiæ frangentes in D & </s> <s xml:id="echoid-s13117" xml:space="preserve">k in ratione duplicata al-<lb/>titudinum A E, a e. </s> <s xml:id="echoid-s13118" xml:space="preserve">vel A D, a k, vel E F, e o, ſepoſita corporum <lb/>gravitate.</s> <s xml:id="echoid-s13119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13120" xml:space="preserve">Nam eſt Cohærentia baſeos A E F ad eam baſeos, a e o, uti <lb/><emph style="ol">AE</emph><emph style="super">q</emph> X E F ad <emph style="ol">ae</emph><emph style="super">q</emph> X eo per Propoſ. </s> <s xml:id="echoid-s13121" xml:space="preserve">XXI, XXII. </s> <s xml:id="echoid-s13122" xml:space="preserve">Sed eſt potentia <lb/>frangens in D applicata ipſi A D, ad eam in, k, applicatam ad, a k, uti, a k, <lb/>ad A D; </s> <s xml:id="echoid-s13123" xml:space="preserve">quare potentia frangens in D erit ad eam in, k, uti <emph style="ol">AE</emph><emph style="super">q</emph> X <lb/>E F X a k, ad <emph style="ol">ae</emph><emph style="super">q</emph> X eo X A D. </s> <s xml:id="echoid-s13124" xml:space="preserve">Sed eſt E F ad, eo, uti A D ad, ak, quia <pb o="554" file="0570" n="571" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſunt parallelopipeda ſimilia, adeoque loco E F, eo poni poſſunt <lb/>A D, ak; </s> <s xml:id="echoid-s13125" xml:space="preserve">n que erunt potentiæ frangentes uti <emph style="ol">AE</emph><emph style="super">q</emph> X A D X <lb/>ak. </s> <s xml:id="echoid-s13126" xml:space="preserve">& </s> <s xml:id="echoid-s13127" xml:space="preserve"><emph style="ol">ae</emph><emph style="super">q</emph> X ak X A D. </s> <s xml:id="echoid-s13128" xml:space="preserve">quæ ambabus diviſis per A D X ak, dant <lb/><emph style="ol">AE</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13129" xml:space="preserve">& </s> <s xml:id="echoid-s13130" xml:space="preserve"><emph style="ol">ae</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13131" xml:space="preserve">quæ exprimunt magnitudines potentiarum frangen-<lb/>tium: </s> <s xml:id="echoid-s13132" xml:space="preserve">& </s> <s xml:id="echoid-s13133" xml:space="preserve">quia A E, a e:</s> <s xml:id="echoid-s13134" xml:space="preserve">: A D. </s> <s xml:id="echoid-s13135" xml:space="preserve">a k:</s> <s xml:id="echoid-s13136" xml:space="preserve">: E F, e o. </s> <s xml:id="echoid-s13137" xml:space="preserve">erunt quoque ha-<lb/>rum quadrata proportionalia.</s> <s xml:id="echoid-s13138" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div503" type="section" level="1" n="503"> <head xml:id="echoid-head615" xml:space="preserve">PROPOSITIO XXV.</head> <p style="it"> <s xml:id="echoid-s13139" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13140" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13141" xml:space="preserve">fig. </s> <s xml:id="echoid-s13142" xml:space="preserve">3. </s> <s xml:id="echoid-s13143" xml:space="preserve">Si fuerint duo parallelopipeda F C, F D gra-<lb/>via, ejusdem materiei, altitudinis & </s> <s xml:id="echoid-s13144" xml:space="preserve">latitudinis, ſed diverſæ <lb/>longitudinis, habebunt momenta, propter gravitates, in ratione <lb/>duplicata longitudinum A C, A D</s> </p> <p> <s xml:id="echoid-s13145" xml:space="preserve">Centrum gravitatis parallelopipedi F C eſt in medio ſectionis ad <lb/>baſin parallelæ inter A & </s> <s xml:id="echoid-s13146" xml:space="preserve">C, & </s> <s xml:id="echoid-s13147" xml:space="preserve">centrum gravitatis parallelopipedi <lb/>F D eſt in medio ſectionis inter A & </s> <s xml:id="echoid-s13148" xml:space="preserve">D, quoniam in centris gravi-<lb/>tatum concipiendum eſt corporum pondus, pondus parallelopipedi <lb/>F C hærebit in medio A C, & </s> <s xml:id="echoid-s13149" xml:space="preserve">pondus parallelopipedi F D in medio <lb/>A D. </s> <s xml:id="echoid-s13150" xml:space="preserve">ſunt vero A C, A D vectes, quorum centrum motus in A, & </s> <s xml:id="echoid-s13151" xml:space="preserve"><lb/>ex quorum dimidiis diſtantiis pendent pondera: </s> <s xml:id="echoid-s13152" xml:space="preserve">eſt pondus paralle-<lb/>lopipedi F C, ad pondus parallelopipedi F D, uti magnitudo F C ad <lb/>F D. </s> <s xml:id="echoid-s13153" xml:space="preserve">hoceſt uti A C ad A D, ſive {1/2} A C ad {1/2} A D: </s> <s xml:id="echoid-s13154" xml:space="preserve">hæc pendentia ex <lb/>vecte {1/2} A C & </s> <s xml:id="echoid-s13155" xml:space="preserve">{1/2} A D. </s> <s xml:id="echoid-s13156" xml:space="preserve">habebunt momenta uti {1/2} A C X {1/2} A C. </s> <s xml:id="echoid-s13157" xml:space="preserve">& </s> <s xml:id="echoid-s13158" xml:space="preserve">{1/2} <lb/>A D X {1/2} A D, quæ ſunt uti <emph style="ol">AC</emph><emph style="super">q</emph> ad <emph style="ol">AD</emph><emph style="super">q</emph>.</s> <s xml:id="echoid-s13159" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div504" type="section" level="1" n="504"> <head xml:id="echoid-head616" xml:space="preserve">PROPOSITIO XXVI.</head> <p style="it"> <s xml:id="echoid-s13160" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13161" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13162" xml:space="preserve">fig. </s> <s xml:id="echoid-s13163" xml:space="preserve">3. </s> <s xml:id="echoid-s13164" xml:space="preserve">Datis duobus parallelopipedis F C, F D. </s> <s xml:id="echoid-s13165" xml:space="preserve">ejus-<lb/>dem altitudinis A E, & </s> <s xml:id="echoid-s13166" xml:space="preserve">latitudinis E F, gravibus, dataque po-<lb/>tentia frangente applicata ad C, invenire magnitudinem potentiæ <lb/>frangentis appenſæ in D, poſitis directionibus perpendicularibus ad <lb/>A C & </s> <s xml:id="echoid-s13167" xml:space="preserve">A D.</s> <s xml:id="echoid-s13168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13169" xml:space="preserve">Quia baſes parallelopipedorum ſunt eædem, erunt earum Cohæ-<lb/>rentiæ eædem, adeoque momenta potentiarum frangentium, pen-<lb/>dentium ex C & </s> <s xml:id="echoid-s13170" xml:space="preserve">D debent eſſe æqualia: </s> <s xml:id="echoid-s13171" xml:space="preserve">Ponatur magnitudo po- <pb o="555" file="0571" n="572" rhead="CORPORUM FIRMORUM."/> tentiæ pendentis in C = P. </s> <s xml:id="echoid-s13172" xml:space="preserve">& </s> <s xml:id="echoid-s13173" xml:space="preserve">quæ pendere debet ex D vocetur Q. <lb/></s> <s xml:id="echoid-s13174" xml:space="preserve">eſt momentum potentiæ C = P X A C, longitudo vectis, plus mo-<lb/>mento oriundo ex gravitate parallelopipedi F C, quod per Propoſ. </s> <s xml:id="echoid-s13175" xml:space="preserve"><lb/>XXV. </s> <s xml:id="echoid-s13176" xml:space="preserve">eſt uti <emph style="ol">AC</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13177" xml:space="preserve">unde momentum totum eſt = P X A C + <lb/><emph style="ol">AC</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13178" xml:space="preserve">momentum Potentiæ Q eſt = Q X A D longitudo vectis, <lb/>plus momento oriundo ex gravitate parallelopipedi F D. </s> <s xml:id="echoid-s13179" xml:space="preserve">quod per <lb/>Prop. </s> <s xml:id="echoid-s13180" xml:space="preserve">XXV. </s> <s xml:id="echoid-s13181" xml:space="preserve">eſt uti AD<emph style="super">q</emph>. </s> <s xml:id="echoid-s13182" xml:space="preserve">unde totum momentum in hoc paral-<lb/>lelopipedo eſt Q X AD + <emph style="ol">AD</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13183" xml:space="preserve">ambo hæc momenta debent <lb/>eſſe æqualia: </s> <s xml:id="echoid-s13184" xml:space="preserve">adeoque Q X AD + <emph style="ol">AD</emph><emph style="super">q</emph> = P X A C + <emph style="ol">AC</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13185" xml:space="preserve"><lb/>Subtrahendo utrimque <emph style="ol">AD</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13186" xml:space="preserve">& </s> <s xml:id="echoid-s13187" xml:space="preserve">dividendo utramque quantitatem <lb/>per A D manet Q = {P X A C + <emph style="ol">AC</emph><emph style="super">q</emph> - <emph style="ol">AD</emph><emph style="super">q</emph>/AD}. </s> <s xml:id="echoid-s13188" xml:space="preserve">quæ eſt æqualis <lb/>potentiæ applicandæ extremo D.</s> <s xml:id="echoid-s13189" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13190" xml:space="preserve">Corol. </s> <s xml:id="echoid-s13191" xml:space="preserve">1. </s> <s xml:id="echoid-s13192" xml:space="preserve">Si data fuiſſet potentia Q, applicata extremo D, & </s> <s xml:id="echoid-s13193" xml:space="preserve"><lb/>quæreretur potentia P pendenda ex C, inveniretur eodem modo <lb/>potentia P = {Q X A D + <emph style="ol">AD</emph><emph style="super">q</emph> - <emph style="ol">AC</emph><emph style="super">q</emph>/AC}.</s> <s xml:id="echoid-s13194" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div505" type="section" level="1" n="505"> <head xml:id="echoid-head617" xml:space="preserve">PROPOSITIO XXVII.</head> <p style="it"> <s xml:id="echoid-s13195" xml:space="preserve">Data Trabe parallelopipedo gravi, horizontaliter parieti in-<lb/>fixa, determinare pondus, quod alteri extremitati appendi <lb/>poteſt.</s> <s xml:id="echoid-s13196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13197" xml:space="preserve">Quæratur inter Experimenta hujus Capitis Lignum ejusdem ſpe-<lb/>ciei, ac Trabs propoſita; </s> <s xml:id="echoid-s13198" xml:space="preserve">vocetur altitudo ligni in Experimento a. <lb/></s> <s xml:id="echoid-s13199" xml:space="preserve">latitudo b. </s> <s xml:id="echoid-s13200" xml:space="preserve">longitudo l. </s> <s xml:id="echoid-s13201" xml:space="preserve">pondus proximum frangenti, ſed mi-<lb/>nus ſit = p. </s> <s xml:id="echoid-s13202" xml:space="preserve">longitudo datæ trabis ſit = L. </s> <s xml:id="echoid-s13203" xml:space="preserve">altitudo ejus = A. </s> <s xml:id="echoid-s13204" xml:space="preserve"><lb/>latitudo = B. </s> <s xml:id="echoid-s13205" xml:space="preserve">pondus ab extremo geſtandum & </s> <s xml:id="echoid-s13206" xml:space="preserve">incognitum ſit <lb/>= x. </s> <s xml:id="echoid-s13207" xml:space="preserve">gravitas totius Trabis = G.</s> <s xml:id="echoid-s13208" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13209" xml:space="preserve">Quæratur pondus, quod ligneo parallelopipedo appendi poſſet, ſi <lb/>haberet longitudinem datæ Trabis, altitudinem vero & </s> <s xml:id="echoid-s13210" xml:space="preserve">latitudi-<lb/>nem eandem ac lignum in Experimento examinatum, eritque per <lb/>Prop. </s> <s xml:id="echoid-s13211" xml:space="preserve">XX, L, l:</s> <s xml:id="echoid-s13212" xml:space="preserve">: p. </s> <s xml:id="echoid-s13213" xml:space="preserve">{lp/L}. </s> <s xml:id="echoid-s13214" xml:space="preserve">adeoque foret hoc pondus = {lp/L}. </s> <s xml:id="echoid-s13215" xml:space="preserve">Com- <pb o="556" file="0572" n="573" rhead="INTRODUCTIO AD COHÆRENTIAM"/> paretur nunc Cohærentia hujus parallelopipedi, cum ea datæ Tra-<lb/>bis, quæ erit in ratione compoſita ex duplicata altitudinis & </s> <s xml:id="echoid-s13216" xml:space="preserve">ſim-<lb/>plici latitudinis, adeoque uti a a b ad A A B. </s> <s xml:id="echoid-s13217" xml:space="preserve">per Prop. </s> <s xml:id="echoid-s13218" xml:space="preserve">X X I & </s> <s xml:id="echoid-s13219" xml:space="preserve"><lb/>XXII. </s> <s xml:id="echoid-s13220" xml:space="preserve">pondera igitur parallelopipedo & </s> <s xml:id="echoid-s13221" xml:space="preserve">Trabi appendenda erunt <lb/>ut hæ Cohærentiæ, adeoque a a b. </s> <s xml:id="echoid-s13222" xml:space="preserve">A A B:</s> <s xml:id="echoid-s13223" xml:space="preserve">: {l p/L} x. </s> <s xml:id="echoid-s13224" xml:space="preserve">quare erit <lb/>x = {A A B l p.</s> <s xml:id="echoid-s13225" xml:space="preserve">/a a b L} Hoc pondus extremitati Trabis appendi poſſet, ſi <lb/>ipſa nullam gravitatem haberet; </s> <s xml:id="echoid-s13226" xml:space="preserve">nam non conſideravimus gravita-<lb/>tem parallelopipedi ejusdem cum Trabe longitudinis: </s> <s xml:id="echoid-s13227" xml:space="preserve">ſed trabs <lb/>habet gravitatem = G, ejusque centrum gravitatis eſt in dimidiâ <lb/>longitudine, ſive ad {1/2} L. </s> <s xml:id="echoid-s13228" xml:space="preserve">adeoque momentum illius erit {1/2} L G. <lb/></s> <s xml:id="echoid-s13229" xml:space="preserve">quod idem manebit poſito dimidio ponderis ad duplo majorem di-<lb/>ſtantiam, ergo hac quantitate pondus appenſum imminendum eſt, <lb/>quod manebit = {A A B l p-{1/2}/a a b L} G.</s> <s xml:id="echoid-s13230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13231" xml:space="preserve">Quia hoc Problema eſt maximæ utilitatis, Exemplo ulterius il-<lb/>luſtrabo: </s> <s xml:id="echoid-s13232" xml:space="preserve">Sit Trabs Quercica, unum pedem alta & </s> <s xml:id="echoid-s13233" xml:space="preserve">lata, 10 pedes <lb/>longa, altero extremo parieti horizontaliter infixa, quæritur quan-<lb/>tum ponderis ab altero extremo ferre poſſit?</s> <s xml:id="echoid-s13234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13235" xml:space="preserve">Experimentum CVIII. </s> <s xml:id="echoid-s13236" xml:space="preserve">hujus Capitis exhibet parallelopipedum <lb/>Quercicum latitudinis & </s> <s xml:id="echoid-s13237" xml:space="preserve">altitudinis o, 25 poll. </s> <s xml:id="echoid-s13238" xml:space="preserve">quod ad diſtantiam <lb/>8 {1/2} pollicum ſuſtinuit fere uncias 48, ab his enim ruprum fuit: <lb/></s> <s xml:id="echoid-s13239" xml:space="preserve">adeoque hoc idem longitudinis 10 pedum ferre tantum ab extremo <lb/>potuiſſet uncias 3 {2/5}, non conſiderando ejus gravitatem: </s> <s xml:id="echoid-s13240" xml:space="preserve">ſunt Co-<lb/>hærentiæ hujus ligni & </s> <s xml:id="echoid-s13241" xml:space="preserve">propoſitæ Trabis, uti quadrata altitudinum <lb/>ductain latitudines ad ſe mutuo ſunt, quæ inter ſe uti 5 ad 47616. </s> <s xml:id="echoid-s13242" xml:space="preserve"><lb/>adeoque uncias feret Trabs 34385 {17/29}, ſive libras 2149. </s> <s xml:id="echoid-s13243" xml:space="preserve">abextremo, <lb/>ſi careret gravitate: </s> <s xml:id="echoid-s13244" xml:space="preserve">quam cum habet, ejus ratio tenenda eſt: </s> <s xml:id="echoid-s13245" xml:space="preserve">pes <lb/>Cubicus Ligni Quercici modo cæſi eſt plerumque librarum 59 {1/2}, pon-<lb/>dus diſcrepat paululum pro variâ ſiccitate: </s> <s xml:id="echoid-s13246" xml:space="preserve">unde gravitas Trabis eſt <lb/>librar. </s> <s xml:id="echoid-s13247" xml:space="preserve">595. </s> <s xml:id="echoid-s13248" xml:space="preserve">quæ ſuſpenſa concipiatur ex dimidia longitudine tra-<lb/>bis, agit enim hæc gravitas ex centro in dimidia longitudine hæ-<lb/>rente; </s> <s xml:id="echoid-s13249" xml:space="preserve">verum habet pondus dimidium ex duplo majori intervallo <lb/>momentum idem, quare ad extremitatem Trabis appenſæ libræ <pb o="557" file="0573" n="574" rhead="CORPORUM FIRMORUM."/> 297 {1/2} idem faciunt; </s> <s xml:id="echoid-s13250" xml:space="preserve">quia autem Cohærentia tota Trabis modo tanta <lb/>eſt, ut ſuſtineat libras 2149. </s> <s xml:id="echoid-s13251" xml:space="preserve">ab his ſubtrahendæ ſunt libræ 297 {1/2}. </s> <s xml:id="echoid-s13252" xml:space="preserve">& </s> <s xml:id="echoid-s13253" xml:space="preserve"><lb/>relinquetur pondus ab extremo ſuſpendendum = libr. </s> <s xml:id="echoid-s13254" xml:space="preserve">1851 {1/2}.</s> <s xml:id="echoid-s13255" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div506" type="section" level="1" n="506"> <head xml:id="echoid-head618" xml:space="preserve">PROPOSITIO XXVIII.</head> <p style="it"> <s xml:id="echoid-s13256" xml:space="preserve">Invenire longitudinem Trabis parallelopipedi datæ craſſitiei & </s> <s xml:id="echoid-s13257" xml:space="preserve"><lb/>materiæ, quæ extremo ſuo borizontaliter parieti infixa, â pro-<lb/>priâ gravitate frangetur.</s> <s xml:id="echoid-s13258" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13259" xml:space="preserve">Oporter ut inter Experimenta hujus Capitis illud quæratur, quod <lb/>cum eodem ligno, ac in hoc Problemate proponitur, captum eſt, <lb/>tum per Propoſ. </s> <s xml:id="echoid-s13260" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s13261" xml:space="preserve">inveſtigetur Cohærentia ligni ſub data <lb/>craſſitie in aſſumta aliqua longitudine, quæ cognoſcitur ex ponde-<lb/>re appenſo extremo in aliqua diſtantia a pariete; </s> <s xml:id="echoid-s13262" xml:space="preserve">id pondus vocetur <lb/>p. </s> <s xml:id="echoid-s13263" xml:space="preserve">& </s> <s xml:id="echoid-s13264" xml:space="preserve">diſtantia l. </s> <s xml:id="echoid-s13265" xml:space="preserve">erit p l momentum illius ponderis, æquale Cohæ-<lb/>rentiæ Trabis Tum capiatur diſtantia minor a pariete, quæ po-<lb/>natur = c. </s> <s xml:id="echoid-s13266" xml:space="preserve">quoniam per Prop. </s> <s xml:id="echoid-s13267" xml:space="preserve">X X V. </s> <s xml:id="echoid-s13268" xml:space="preserve">parallelopipeda gravia ejus-<lb/>dem materiæ, æque craſſa, ſed diverſæ longitudinis, habent mo-<lb/>menta in ratione duplicata longitudinis; </s> <s xml:id="echoid-s13269" xml:space="preserve">ſi longitudo incognita voce-<lb/>tur x, erunt quadrata ambarum longitudinum c c & </s> <s xml:id="echoid-s13270" xml:space="preserve">x x. </s> <s xml:id="echoid-s13271" xml:space="preserve">Momen-<lb/>tum vero parallelopipedi gravis, & </s> <s xml:id="echoid-s13272" xml:space="preserve">longitudinis c, habetur, ducta <lb/>ejus gravitate, quæ ſit = g, in {1/2} c, quod dat {1/2} c g. </s> <s xml:id="echoid-s13273" xml:space="preserve">adeoque erit c c. </s> <s xml:id="echoid-s13274" xml:space="preserve">x x <lb/>:</s> <s xml:id="echoid-s13275" xml:space="preserve">: {1/2}c g.</s> <s xml:id="echoid-s13276" xml:space="preserve">{1/2} {g x x.</s> <s xml:id="echoid-s13277" xml:space="preserve">/c} quod eſt momentum trabis ſub longitudine quæſita x. <lb/></s> <s xml:id="echoid-s13278" xml:space="preserve">debet vero hoc momentum eſſeæquale momento p l, exprimente Co-<lb/>hærentiam; </s> <s xml:id="echoid-s13279" xml:space="preserve">ergo {1/2} {g x x/c} = p l & </s> <s xml:id="echoid-s13280" xml:space="preserve">x x = {2 c p l,/g}, adeoque extrahendo <lb/>radicem quadratam, habebitur x = {2 c p l.</s> <s xml:id="echoid-s13281" xml:space="preserve">/g} eſtque hæc longitu-<lb/>do quæſita Trabis â proprio frangendæ pondere.</s> <s xml:id="echoid-s13282" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div507" type="section" level="1" n="507"> <head xml:id="echoid-head619" xml:space="preserve">PROPOSITIO XXIX.</head> <p style="it"> <s xml:id="echoid-s13283" xml:space="preserve">Tab XIX. </s> <s xml:id="echoid-s13284" xml:space="preserve">fig. </s> <s xml:id="echoid-s13285" xml:space="preserve">3. </s> <s xml:id="echoid-s13286" xml:space="preserve">Si detur parallolepipedum a e o k borizontale, <lb/>ſua baſi a e o parieti infixum, ejus longitudinis, ut ſua gravita-<lb/>te mox frangeretur, non poteſt dari aliud parallelopipedum ipſi <pb o="558" file="0574" n="575" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſimile & </s> <s xml:id="echoid-s13287" xml:space="preserve">majus, quin baſis ſuſtinendo impar ſit futura: </s> <s xml:id="echoid-s13288" xml:space="preserve">minus & </s> <s xml:id="echoid-s13289" xml:space="preserve"><lb/>ſimile ſua baſi plus cohæſura ſit.</s> <s xml:id="echoid-s13290" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13291" xml:space="preserve">Sit parallelopipedum A E F D ſimile dato a e c k, ſed majus; </s> <s xml:id="echoid-s13292" xml:space="preserve">erit <lb/>Cohærentia baſeos, a e o, ad eam baſeos A E F, uti <emph style="ol">a e</emph><emph style="super">q</emph> X eo ad <emph style="ol">A E</emph><emph style="super">q</emph> <lb/>X E F. </s> <s xml:id="echoid-s13293" xml:space="preserve">ſed quia, a e, ad A E uti, e o, ad E F; </s> <s xml:id="echoid-s13294" xml:space="preserve">erit <emph style="ol">a e</emph><emph style="super">q</emph> X e o ad <emph style="ol">A E</emph><emph style="super">q</emph> X <lb/>E F:</s> <s xml:id="echoid-s13295" xml:space="preserve">: <emph style="ol">a e</emph><emph style="super">q</emph> X a e, <emph style="ol">A E</emph><emph style="super">q</emph> X A E:</s> <s xml:id="echoid-s13296" xml:space="preserve">: <emph style="ol">a e</emph><emph style="super">c</emph>, <emph style="ol">A E</emph><emph style="super">c</emph>:</s> <s xml:id="echoid-s13297" xml:space="preserve">: <emph style="ol">a k</emph><emph style="super">c</emph>, <emph style="ol">A D</emph><emph style="super">c</emph> & </s> <s xml:id="echoid-s13298" xml:space="preserve">quia <lb/>parallelopipeda ſimilia ſunt, eſt <emph style="ol">a k</emph><emph style="super">c</emph> ad <emph style="ol">A D</emph><emph style="super">c</emph>, uti parallelopipe-<lb/>dum, a e o k, ad parallelopipedum A E F D, in qua ratione igitur <lb/>ſunt baſium Cohærentiæ.</s> <s xml:id="echoid-s13299" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13300" xml:space="preserve">Momentum vero ex gravitate parallelopipedi, a e o k, eſt ad mo-<lb/>mentum ex gravitate parallelopipedi A E F D, uti ipſum parallelo-<lb/>pipedum, a e o k, ductum in, {1/2} a k, ad parallelopipedum A E F D du-<lb/>ctum in {1/2} A D. </s> <s xml:id="echoid-s13301" xml:space="preserve">hoc eſt <emph style="ol">a k</emph><emph style="super">c</emph> X {1/2}ak ad A D<emph style="super">c</emph> X {1/2} A D.</s> <s xml:id="echoid-s13302" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13303" xml:space="preserve">Sed eſt Cohærentia baſeos, a e o, ad momentum ex gravitate pa-<lb/>rallelopipedi ſui in majori ratione, quam Cohærentia baſeos A E F <lb/>ad momentum ex gravitate ſui parallelopipedi; </s> <s xml:id="echoid-s13304" xml:space="preserve">ſi enim ordinemus <lb/>ſecundum proportionem quantitates, erit productum extremorum <lb/>majus producto mediorum. </s> <s xml:id="echoid-s13305" xml:space="preserve"><emph style="ol">a k</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s13306" xml:space="preserve"><emph style="ol">a k</emph><emph style="super">c</emph> X {1/2} a k:</s> <s xml:id="echoid-s13307" xml:space="preserve">: <emph style="ol">A D</emph><emph style="super">c</emph>, <emph style="ol">A D</emph><emph style="super">c</emph> X {1/2} A D. <lb/></s> <s xml:id="echoid-s13308" xml:space="preserve">productum extremorum eſt <emph style="ol">a k</emph><emph style="super">c</emph> X <emph style="ol">A D</emph><emph style="super">c</emph> X {1/2} A D. </s> <s xml:id="echoid-s13309" xml:space="preserve">& </s> <s xml:id="echoid-s13310" xml:space="preserve">mediorum eſt <lb/><emph style="ol">a k</emph><emph style="super">c</emph> X {1/2} a k X A D<emph style="super">c</emph>. </s> <s xml:id="echoid-s13311" xml:space="preserve">quibus diviſis per <emph style="ol">a k</emph><emph style="super">c</emph> X A D<emph style="super">c</emph>. </s> <s xml:id="echoid-s13312" xml:space="preserve">manent {1/2} A D. </s> <s xml:id="echoid-s13313" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s13314" xml:space="preserve">{1/2} a k. </s> <s xml:id="echoid-s13315" xml:space="preserve">ſed eſt {1/2} A D majus {1/2} a k, adeoque eſt, a k<emph style="super">c</emph> ad <emph style="ol">a k</emph><emph style="super">c</emph> X {1/2} a k <lb/>in majori ratione, quam A<emph style="ol">D</emph><emph style="super">c</emph> ad <emph style="ol">A</emph>D<emph style="super">c</emph> X {1/2} A D, ergo baſis A E F <lb/>non erit par ferendo parallelopipedi A E F D gravitatem.</s> <s xml:id="echoid-s13316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13317" xml:space="preserve">2°. </s> <s xml:id="echoid-s13318" xml:space="preserve">Sit parallelopipedum A E F D tam longum, ut vix vix ſeſe ferat <lb/>integrum, ſit aliud ſimile ſed minus a e ok; </s> <s xml:id="echoid-s13319" xml:space="preserve">erit Cohærentia baſeos A E F <lb/>ad eam baſeos, a e o:</s> <s xml:id="echoid-s13320" xml:space="preserve">: <emph style="ol">A D</emph><emph style="super">c</emph> ad <emph style="ol">a k</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s13321" xml:space="preserve">& </s> <s xml:id="echoid-s13322" xml:space="preserve">momentum ex gravitate in <lb/>parallelopipedo F D, ad illud in parallelopipedo, o k:</s> <s xml:id="echoid-s13323" xml:space="preserve">: <emph style="ol">A D</emph><emph style="super">c</emph> X {1/2} A D <lb/>ad <emph style="ol">a k</emph><emph style="super">c</emph> X {1/2} a k. </s> <s xml:id="echoid-s13324" xml:space="preserve">ſed eſt Cohærentia baſeos, a e o, ad momentum gra-<lb/>vitatis ſui parallelopipedi in majori ratione quam Cohærentia ba-<lb/>ſeos A E F ad momentum gravitatis ſui parallelopipedi, cum ante <lb/>demonſtraverim <emph style="ol">a k</emph><emph style="super">c</emph>, a k<emph style="super">c</emph> X {1/2} a k eſſe in majori ratione, quam <lb/><emph style="ol">A D</emph><emph style="super">c</emph> ad <emph style="ol">A D</emph><emph style="super">c</emph> X {1/2} A D adeoque poterit a parallelopipedo, a e o k, præ-<lb/>ter propriam gravitatem adhuc geſtari pondus aliud.</s> <s xml:id="echoid-s13325" xml:space="preserve"/> </p> <pb o="559" file="0575" n="576" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div508" type="section" level="1" n="508"> <head xml:id="echoid-head620" xml:space="preserve">PROPOSITIO XXX.</head> <p style="it"> <s xml:id="echoid-s13326" xml:space="preserve">Data longitudine Trabis parallelopipedæ, quæ borizontaliter <lb/>infixa parieti, a propria gravitate fere rumpatur, invenire <lb/>pondus, quod ejus extremo appendi poteſt, ubi datam minorem <lb/>longitudinem acceperit.</s> <s xml:id="echoid-s13327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13328" xml:space="preserve">Sit longitudo datæ Trabis = l, ejus pondus totum = p, erit mo-<lb/>mentum ex pondere = {1/2} p l, quia hoc pondus geſtari concipitur <lb/>ex {1/2} l. </s> <s xml:id="echoid-s13329" xml:space="preserve">Sit longitudo data minor quam l, ſive {l/d}. </s> <s xml:id="echoid-s13330" xml:space="preserve">invenietur pon-<lb/>dus hujus partis hoc medo: </s> <s xml:id="echoid-s13331" xml:space="preserve">ut longitudo prior ad ſuum pondus, <lb/>ita longitudo minor eſt ad ſuum pondus, ſive l, p:</s> <s xml:id="echoid-s13332" xml:space="preserve">: {l, p.</s> <s xml:id="echoid-s13333" xml:space="preserve">/d d} pon-<lb/>dus igitur minoris longitudinis erit = {p.</s> <s xml:id="echoid-s13334" xml:space="preserve">/d} cujus momentum erit = <lb/>{1/2} {p l.</s> <s xml:id="echoid-s13335" xml:space="preserve">/d d} quod ſubtrahatur ex momento priori {1/2} p l, reſtabit momen-<lb/>tum ponderis appendendi, adeoque {1/2} {p l - p l/2 d d} = {p l d d - p l.</s> <s xml:id="echoid-s13336" xml:space="preserve">/2 d d} <lb/>hoc dividatur per longitudinem {l/d} ut pondus habeatur, eritque <lb/>{p l d<emph style="super">3</emph> - p l d/2 d d l} = {p d d - p.</s> <s xml:id="echoid-s13337" xml:space="preserve">/2 d} adeoque præter gravitatem pro-<lb/>priam poterit ex Trabe ſuſpendi pondus = {p d d - p.</s> <s xml:id="echoid-s13338" xml:space="preserve">/2 d}</s> </p> </div> <div xml:id="echoid-div509" type="section" level="1" n="509"> <head xml:id="echoid-head621" xml:space="preserve">PROPOSITIO XXXI.</head> <p style="it"> <s xml:id="echoid-s13339" xml:space="preserve">Dato parallelopipedo maximæ longitudinis fracturæ proximo <lb/>propter propriam gravitatem, & </s> <s xml:id="echoid-s13340" xml:space="preserve">data aliqua longitudine majori, <lb/>invenire craſſitiem alterius parallelopipedi ejusdem materiæ, quod <lb/>ſub data longitudine etiam proprio ponderi vix reſiſtat.</s> <s xml:id="echoid-s13341" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13342" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13343" xml:space="preserve">X I X. </s> <s xml:id="echoid-s13344" xml:space="preserve">fig. </s> <s xml:id="echoid-s13345" xml:space="preserve">3. </s> <s xml:id="echoid-s13346" xml:space="preserve">Sit datum parallelopipedum a e o k maximæ <lb/>longitudinis, ut & </s> <s xml:id="echoid-s13347" xml:space="preserve">data longitudo A D, ſuper qua fieri debeat pa- <pb o="560" file="0576" n="577" rhead="INTRODUCTIO AD COHÆRENTIAM"/> rallelopipedum A E F D, quod vix vix reſiſtat ſuo ponderi.</s> <s xml:id="echoid-s13348" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13349" xml:space="preserve">Sit a e = e o, & </s> <s xml:id="echoid-s13350" xml:space="preserve">vocetur a. </s> <s xml:id="echoid-s13351" xml:space="preserve">a k = b. </s> <s xml:id="echoid-s13352" xml:space="preserve">A D = d. </s> <s xml:id="echoid-s13353" xml:space="preserve">A E quaeſita ſit = x.</s> <s xml:id="echoid-s13354" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13355" xml:space="preserve">Erit parallelopipedum a e o k = a a b. </s> <s xml:id="echoid-s13356" xml:space="preserve">ejuſque momentum ex gra-<lb/>vitate = {1/2} a a b b. </s> <s xml:id="echoid-s13357" xml:space="preserve">Cohærentia baſeos = a<emph style="super">3</emph> parallelopipedum quæſitum <lb/>F D eſt = d x x. </s> <s xml:id="echoid-s13358" xml:space="preserve">ejuſque momentum ex gravitate = {1/2} d d x x. </s> <s xml:id="echoid-s13359" xml:space="preserve">Cohæ-<lb/>rentia baſeos = x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13360" xml:space="preserve">debet eſſe momentum ex gravitate utriuſque pa-<lb/>rallelopipedi ad Cohærentiam ſuam in eâdem proportione, adeo-<lb/>que {1/2} a a b b, a<emph style="super">3</emph>:</s> <s xml:id="echoid-s13361" xml:space="preserve">: {1/2} d d x x. </s> <s xml:id="echoid-s13362" xml:space="preserve">x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13363" xml:space="preserve">multiplicatis extremis & </s> <s xml:id="echoid-s13364" xml:space="preserve">mediis <lb/>per ſe, ſit {1/2} a a b b x<emph style="super">3</emph> = {1/2} a<emph style="super">3</emph> d d x x. </s> <s xml:id="echoid-s13365" xml:space="preserve">diviſo utroque termino per {1/2} <lb/>a a x x, fit b b x = a d d. </s> <s xml:id="echoid-s13366" xml:space="preserve">ergo x = {a d d:</s> <s xml:id="echoid-s13367" xml:space="preserve">/b b} ſive b b. </s> <s xml:id="echoid-s13368" xml:space="preserve">d d:</s> <s xml:id="echoid-s13369" xml:space="preserve">: a. </s> <s xml:id="echoid-s13370" xml:space="preserve">x.</s> <s xml:id="echoid-s13371" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13372" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s13373" xml:space="preserve">Hoc modo breviſſime Problema ſolvitur, quod Ga-<lb/>lilæus ſubtile & </s> <s xml:id="echoid-s13374" xml:space="preserve">operoſum vocat, cujus inventioni haud exiguum <lb/>tempus ſe impendiſſe fatetur; </s> <s xml:id="echoid-s13375" xml:space="preserve">pulcerrimas inde interea elegit ſeque-<lb/>las: </s> <s xml:id="echoid-s13376" xml:space="preserve">nempe fieri non poſſe per artem, nec per Naturam, ut ma-<lb/>chinæ augeantur ad immenſam vaſtitatem, vel ut navigia, pala-<lb/>tia, templa exſtruantur vaſtiſſima, quorum remi, antennæ, tra-<lb/>beationes, catenæ ferreæ, reliquæve conſiſtant partes: </s> <s xml:id="echoid-s13377" xml:space="preserve">imo nec <lb/>Naturam arbores immenſæ magnitudinis producere poſſe, cum ipſa-<lb/>rum rami proprio pondere tandem inflecterentur & </s> <s xml:id="echoid-s13378" xml:space="preserve">frange-<lb/>rentur: </s> <s xml:id="echoid-s13379" xml:space="preserve">ſicut ipſi etiam foret impoſſibile hominibus, equis, aut a-<lb/>liis animalibus oſſa concedere ita conſtructa, ut ſubſiſtere, & </s> <s xml:id="echoid-s13380" xml:space="preserve">ha-<lb/>bita proportione, munia ſua obire queant, cum talia animalia in <lb/>immenſam augenda forent altitudinem, niſi materia adhibeatur, <lb/>quæ ultra vulgarem & </s> <s xml:id="echoid-s13381" xml:space="preserve">dura ſit & </s> <s xml:id="echoid-s13382" xml:space="preserve">reſiſtens, aut talia oſſa ad eam <lb/>deducanter craſſitiem, quæ omnis proportionis expers monſtro-<lb/>ſum reddat animal: </s> <s xml:id="echoid-s13383" xml:space="preserve">Ut hoc aliquo confirmetur exemplo, os femo-<lb/>ris humanum ſumatur, cujus craſſities quidem inæqualis eſt, ſed po-<lb/>natur diameter unius pollicis, & </s> <s xml:id="echoid-s13384" xml:space="preserve">longitudo ſesquipedis, quæro quan-<lb/>ta deſideretur alterius triplo longioris oſſis diameter, ut Cohæren-<lb/>tia hujus ſit æqualis priori? </s> <s xml:id="echoid-s13385" xml:space="preserve">Ex hac Propoſitione diameter poſtula-<lb/>tur 9 pollicum, ergo ut Gigas formaretur 18 altus pedes, quam <lb/>informe monſtrum fieri deberet, cujus os femoris diametrum 9 <lb/>pollicum habeat: </s> <s xml:id="echoid-s13386" xml:space="preserve">cogita qualis craſſities reliquorum oſſium manum <lb/>pedemque conſtituentium erit? </s> <s xml:id="echoid-s13387" xml:space="preserve">ut hoc clarius intelligeretur, Ga-<lb/>lilæus ejuſmodi duo oſſa, quorum unum eſt femur vulgaris homi- <pb o="561" file="0577" n="578" rhead="CORPORUM FIRMORUM."/> nis, alterum Gigantis triplo majoris, exhibuit, quæ quoque in <lb/>noſtra Tab. </s> <s xml:id="echoid-s13388" xml:space="preserve">XXV. </s> <s xml:id="echoid-s13389" xml:space="preserve">fig. </s> <s xml:id="echoid-s13390" xml:space="preserve">3. </s> <s xml:id="echoid-s13391" xml:space="preserve">conſpiciuntur: </s> <s xml:id="echoid-s13392" xml:space="preserve">Si autem Gigantes tam <lb/>craſſa non habuerint oſſa, tum ex materia multo duriore magisque <lb/>reſiſtente quam noſtra ſunt, formata fuerunt. </s> <s xml:id="echoid-s13393" xml:space="preserve">Natura tamen ani-<lb/>malia maxima genuit longiſſimis inſtructa oſſibus, uti Balænas, <lb/>piſceſque alios, verum his conceſſit aquam, non Aërem, pro me-<lb/>dio, in quo ſeſe moveant; </s> <s xml:id="echoid-s13394" xml:space="preserve">quia aquæ gravitas ſpecifica eſt ad Aë-<lb/>rem circiter uti 800 ad 1, hinc animalis & </s> <s xml:id="echoid-s13395" xml:space="preserve">oſſium gravitas in Aqua <lb/>tantundem decreſcit, unde graciliora oſſa, quam quæ ope hujus <lb/>Propoſitionis determinarentur, ſufficiunt.</s> <s xml:id="echoid-s13396" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div510" type="section" level="1" n="510"> <head xml:id="echoid-head622" xml:space="preserve">PROPOSITIO XXXII.</head> <p style="it"> <s xml:id="echoid-s13397" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13398" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13399" xml:space="preserve">fig. </s> <s xml:id="echoid-s13400" xml:space="preserve">3. </s> <s xml:id="echoid-s13401" xml:space="preserve">Dato parallelopipedo E A F D, in quo momen-<lb/>tum gravitatis ad Cohærentiam ſit in quacunque ratione, con-<lb/>ſtruere aliud parallelopipedum o e a k, baſeos proportionalis ad E A F, <lb/>in quo momentum gravitatis ad Cohærentiam ſuam ſit in eadem <lb/>ratione.</s> <s xml:id="echoid-s13402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13403" xml:space="preserve">Vocetur A E a. </s> <s xml:id="echoid-s13404" xml:space="preserve">E F b. </s> <s xml:id="echoid-s13405" xml:space="preserve">A D, c. </s> <s xml:id="echoid-s13406" xml:space="preserve">erit parallelopipedum A E F D <lb/>= a b c. </s> <s xml:id="echoid-s13407" xml:space="preserve">momentum ex gravitate = {1/2} a b c c. </s> <s xml:id="echoid-s13408" xml:space="preserve">& </s> <s xml:id="echoid-s13409" xml:space="preserve">Cohærentia = a a b. </s> <s xml:id="echoid-s13410" xml:space="preserve">quia <lb/>baſes amborum parallelopipedorum ponuntur proportionales, erit E F, <lb/>E A:</s> <s xml:id="echoid-s13411" xml:space="preserve">: oe, ea. </s> <s xml:id="echoid-s13412" xml:space="preserve">ſi o e, = f. </s> <s xml:id="echoid-s13413" xml:space="preserve">& </s> <s xml:id="echoid-s13414" xml:space="preserve">ea = x. </s> <s xml:id="echoid-s13415" xml:space="preserve">erit b. </s> <s xml:id="echoid-s13416" xml:space="preserve">a:</s> <s xml:id="echoid-s13417" xml:space="preserve">; f. </s> <s xml:id="echoid-s13418" xml:space="preserve">x. </s> <s xml:id="echoid-s13419" xml:space="preserve">unde x = {a f.</s> <s xml:id="echoid-s13420" xml:space="preserve">/b} <lb/>ſit, a k = z. </s> <s xml:id="echoid-s13421" xml:space="preserve">erit parallelopipedum, o e a k = {a f f z:</s> <s xml:id="echoid-s13422" xml:space="preserve">/b} ejuſque momen-<lb/>tum ex gravitate = {1/2} {a f f z z.</s> <s xml:id="echoid-s13423" xml:space="preserve">/b} atque Cohærentia = {a a f<emph style="super">3</emph>.</s> <s xml:id="echoid-s13424" xml:space="preserve">/b b} quia <lb/>amborum momenta ex gravitate ad ſuas Cohærentias ſupponuntur <lb/>in eadem ratione, erit {{1/2} a f f z z.</s> <s xml:id="echoid-s13425" xml:space="preserve">/b} {a a f<emph style="super">3</emph>/b b}:</s> <s xml:id="echoid-s13426" xml:space="preserve">: {1/2} a b c c. </s> <s xml:id="echoid-s13427" xml:space="preserve">a a b. </s> <s xml:id="echoid-s13428" xml:space="preserve">unde eli-<lb/>citur z = {c c f.</s> <s xml:id="echoid-s13429" xml:space="preserve">/b}</s> </p> <pb o="562" file="0578" n="579" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div511" type="section" level="1" n="511"> <head xml:id="echoid-head623" xml:space="preserve">PROPOSITIO XXXIII.</head> <p style="it"> <s xml:id="echoid-s13430" xml:space="preserve">Tab XXV. </s> <s xml:id="echoid-s13431" xml:space="preserve">fig 1. </s> <s xml:id="echoid-s13432" xml:space="preserve">Datis duobus parallelopipedis A B C D, <lb/>E G H K, datæ longitudini I L aliud parallelopipedum ejusdem ma-<lb/>teriæ applicare I M N L, quod ad E G H K habeat rationem datam, <lb/>& </s> <s xml:id="echoid-s13433" xml:space="preserve">in quo gravitatis momentum ad ſuam Cohærentiam ſit in eadem <lb/>proportione, in quâ momentum gravitatis A B C D eſt ad ſuam Co-<lb/>hærentiam.</s> <s xml:id="echoid-s13434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13435" xml:space="preserve">Ponatur A B = a. </s> <s xml:id="echoid-s13436" xml:space="preserve">B C = b. </s> <s xml:id="echoid-s13437" xml:space="preserve">A D = d. </s> <s xml:id="echoid-s13438" xml:space="preserve">& </s> <s xml:id="echoid-s13439" xml:space="preserve">in altero ſolido ſit E G = e, <lb/>G H = f. </s> <s xml:id="echoid-s13440" xml:space="preserve">E K = g data ratio ſit uti k ad l. </s> <s xml:id="echoid-s13441" xml:space="preserve">tum præterea I L = p. <lb/></s> <s xml:id="echoid-s13442" xml:space="preserve">I M = x. </s> <s xml:id="echoid-s13443" xml:space="preserve">M N = z.</s> <s xml:id="echoid-s13444" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13445" xml:space="preserve">Erit momentum parallelopipedi A B C D = {1/2} a b d d. <lb/></s> <s xml:id="echoid-s13446" xml:space="preserve">Cohærentia = a a b.</s> <s xml:id="echoid-s13447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13448" xml:space="preserve">Parallelopipedi momentum I M N L = {1/2} p p x z. <lb/></s> <s xml:id="echoid-s13449" xml:space="preserve">Cohærentia = x x z.</s> <s xml:id="echoid-s13450" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13451" xml:space="preserve">Ponitur momentum A B C D ad ſuam Cohærentiam, uti I M N L <lb/>momentum ad ſuam; </s> <s xml:id="echoid-s13452" xml:space="preserve">hoc eſt {1/2} a b d d. </s> <s xml:id="echoid-s13453" xml:space="preserve">a a b:</s> <s xml:id="echoid-s13454" xml:space="preserve">: {1/2} p p x z. </s> <s xml:id="echoid-s13455" xml:space="preserve">x x z. </s> <s xml:id="echoid-s13456" xml:space="preserve">unde <lb/>fit x = {a p p.</s> <s xml:id="echoid-s13457" xml:space="preserve">/d d} præterea ponitur parallelopipedum E G H K ad I M N L <lb/>in ratione k ad l. </s> <s xml:id="echoid-s13458" xml:space="preserve">hoc eſt e f g, p x z:</s> <s xml:id="echoid-s13459" xml:space="preserve">: k. </s> <s xml:id="echoid-s13460" xml:space="preserve">l. </s> <s xml:id="echoid-s13461" xml:space="preserve">adeoque e f g l <lb/>= k p z x & </s> <s xml:id="echoid-s13462" xml:space="preserve">loco x ponendo æquale {a p p.</s> <s xml:id="echoid-s13463" xml:space="preserve">/d d} erit {e f g l = a k p<emph style="super">3</emph> z.</s> <s xml:id="echoid-s13464" xml:space="preserve">/d d} hinc <lb/>z = {d d e f g l.</s> <s xml:id="echoid-s13465" xml:space="preserve">/a k p<emph style="super">3</emph>}</s> </p> </div> <div xml:id="echoid-div512" type="section" level="1" n="512"> <head xml:id="echoid-head624" xml:space="preserve">PROPOSITIO XXXIV.</head> <p style="it"> <s xml:id="echoid-s13466" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13467" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13468" xml:space="preserve">fig. </s> <s xml:id="echoid-s13469" xml:space="preserve">3. </s> <s xml:id="echoid-s13470" xml:space="preserve">Dato parallelopipedo A E F D, una cum pon-<lb/>dere quodam O annexo D. </s> <s xml:id="echoid-s13471" xml:space="preserve">datæ longitudini a k & </s> <s xml:id="echoid-s13472" xml:space="preserve">latitudini e o <lb/>applicare aliud parallelopipedum, cujus momentum ex gravitate, <lb/>ſimul cum pondere P pendente ex k, habeat ad ſuam Cohærentiam <lb/>rationem eandem, quam A E F D cum pondere O ad ſuam Cohæ-<lb/>rentiam.</s> <s xml:id="echoid-s13473" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13474" xml:space="preserve">Vocetur A E a. </s> <s xml:id="echoid-s13475" xml:space="preserve">E F b. </s> <s xml:id="echoid-s13476" xml:space="preserve">A D d. </s> <s xml:id="echoid-s13477" xml:space="preserve">pondus O ſit = o tum longitu- <pb o="563" file="0579" n="580" rhead="CORPORUM FIRMORUM."/> tudo data a k = e, latitudo e o = f. </s> <s xml:id="echoid-s13478" xml:space="preserve">altitudo a e = x pondus p <lb/>= p.</s> <s xml:id="echoid-s13479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13480" xml:space="preserve">Tum erit momentum parallelopipedi A E F D ex gravitate, = <lb/>{1/2} a b d d, & </s> <s xml:id="echoid-s13481" xml:space="preserve">momentum ponderis ſibiannexi = o d: </s> <s xml:id="echoid-s13482" xml:space="preserve">Cohærentia vero <lb/>= a a b. </s> <s xml:id="echoid-s13483" xml:space="preserve">præterea erit momentum ex gravitate parallelopipedi, a e o k, <lb/>= {1/2} e e f x. </s> <s xml:id="echoid-s13484" xml:space="preserve">& </s> <s xml:id="echoid-s13485" xml:space="preserve">momentum ponderis P appenſi = e p. </s> <s xml:id="echoid-s13486" xml:space="preserve">Cohærentia <lb/>= x x f. </s> <s xml:id="echoid-s13487" xml:space="preserve">proponitur vero {1/2} a b d d + d o, a a b:</s> <s xml:id="echoid-s13488" xml:space="preserve">: {1/2} e e f x + e p. </s> <s xml:id="echoid-s13489" xml:space="preserve">x x f <lb/>idcirco {1/2} a b d d f x x + d f o x x = {1/2} a a b e e f x + a a b e p tranſpoſito-<lb/>que {1/2} a a b e e f x. </s> <s xml:id="echoid-s13490" xml:space="preserve">fit {1/2} a b d d f x x + d f o x x - {1/2} a a b e e f x = a a b e p. <lb/></s> <s xml:id="echoid-s13491" xml:space="preserve">factaque diviſione per {1/2} a b d d f + d f o <lb/>fit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} = {a a b e p/{1/2} a b d d f + d f o} <lb/>additiſque {{1/16} a<emph style="super">4</emph> b b e<emph style="super">4</emph> f f/{1/16} a a b b d<emph style="super">4</emph> f f+{1/4} a b d<emph style="super">3</emph> f o + {1/4} d d o o f f}. </s> <s xml:id="echoid-s13492" xml:space="preserve"><lb/>erit x x - {{1/2} a a b e e f x/{1/2} a b d d f + d f o} + {{1/16} a<emph style="super">4</emph> b b e<emph style="super">4</emph> f f/{1/16} a a b b d<emph style="super">4</emph> f f + {1/4} a b d<emph style="super">3</emph> f o + {1/4} d d o o f f} <lb/>= {a a b e p/{1/2} a b d d f + d f o.</s> <s xml:id="echoid-s13493" xml:space="preserve">} + {{1/16} a<emph style="super">4</emph> b b e<emph style="super">4</emph> f f/{1/16} a a b b d<emph style="super">4</emph> f f + {1/4} a b d<emph style="super">3</emph> f o + {1/4} d d f f o} <lb/>atque utrimque extrahendo radicem <lb/>x - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} = {a a b e p/{1/2} a b d d f + d f o.</s> <s xml:id="echoid-s13494" xml:space="preserve">} + {{1/16} a<emph style="super">4</emph> b b e<emph style="super">4</emph> f f/{1/16} a a b b d<emph style="super">4</emph> f f + {1/4} a b d<emph style="super">3</emph> f o + {1/4} d d f f o o} <lb/>tranſpoſitisque - {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} habetur ſola quantitas <lb/>x = {{1/4} a a b e e f/{1/4} a b d d f + {1/2} d f o} + {a a b e p/{1/2} a b d d f + {1/2} d f o}. </s> <s xml:id="echoid-s13495" xml:space="preserve">+ {{1/16} a<emph style="super">4</emph> b b e<emph style="super">4</emph> f f/{1/16} a a b b d<emph style="super">4</emph> f f + {1/4} a b d<emph style="super">3</emph> f o + {1/4} d d f f o o.</s> <s xml:id="echoid-s13496" xml:space="preserve">}.</s> <s xml:id="echoid-s13497" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div513" type="section" level="1" n="513"> <head xml:id="echoid-head625" xml:space="preserve">PROPOSITIO XXXV.</head> <p style="it"> <s xml:id="echoid-s13498" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13499" xml:space="preserve">XXV. </s> <s xml:id="echoid-s13500" xml:space="preserve">fig. </s> <s xml:id="echoid-s13501" xml:space="preserve">2. </s> <s xml:id="echoid-s13502" xml:space="preserve">Dato parallelopipedo A B C D, in quo gravita-<lb/>tis momentum, una cum momento ponderis dati H pendentis ex D, <lb/>ad Cohærentiam ſuam habeat quamlibet rationem; </s> <s xml:id="echoid-s13503" xml:space="preserve">ad rectam da-<lb/>tam I K, applicare aliud parallelopipedum, æquale A B C D, in <pb o="564" file="0580" n="581" rhead="INTRODUCTIO AD COHÆRENTIAM"/> quo gravitatis momentum, una cum momento ponderis ejusdem H <lb/>ſit ad ſuam Cohærentiam in eadem ratione.</s> <s xml:id="echoid-s13504" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13505" xml:space="preserve">Vocetur A B a. </s> <s xml:id="echoid-s13506" xml:space="preserve">B C b. </s> <s xml:id="echoid-s13507" xml:space="preserve">A D c. </s> <s xml:id="echoid-s13508" xml:space="preserve">pondus H. </s> <s xml:id="echoid-s13509" xml:space="preserve">h. </s> <s xml:id="echoid-s13510" xml:space="preserve">I K d. </s> <s xml:id="echoid-s13511" xml:space="preserve">I L x. <lb/></s> <s xml:id="echoid-s13512" xml:space="preserve">L M z.</s> <s xml:id="echoid-s13513" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13514" xml:space="preserve">Erit ſolidum A B C D = a b c. </s> <s xml:id="echoid-s13515" xml:space="preserve">& </s> <s xml:id="echoid-s13516" xml:space="preserve">ſolidum I L M K = d x z. </s> <s xml:id="echoid-s13517" xml:space="preserve">poni-<lb/>tur vero a b c = d x z. </s> <s xml:id="echoid-s13518" xml:space="preserve">adeoque {a b c/d x} = z. </s> <s xml:id="echoid-s13519" xml:space="preserve">momentum ex gravitate <lb/>parallelopipedi A B C D erit = {1/2} a b c c. </s> <s xml:id="echoid-s13520" xml:space="preserve">Cohærentia = a a b. </s> <s xml:id="echoid-s13521" xml:space="preserve">momen-<lb/>tum vero ponderis = h c. </s> <s xml:id="echoid-s13522" xml:space="preserve">ita momentum parallelopipedi I L M K <lb/>ex gravitate = {1/2} d d x z. </s> <s xml:id="echoid-s13523" xml:space="preserve">Cohærentia = x x z. </s> <s xml:id="echoid-s13524" xml:space="preserve">momentum ponde-<lb/>ris H = h d. </s> <s xml:id="echoid-s13525" xml:space="preserve">ponitur {1/2} a b c c + h c. </s> <s xml:id="echoid-s13526" xml:space="preserve">a a b:</s> <s xml:id="echoid-s13527" xml:space="preserve">: {1/2} d d x z + h d, x x z.</s> <s xml:id="echoid-s13528" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13529" xml:space="preserve">Quia vero z = {a b c.</s> <s xml:id="echoid-s13530" xml:space="preserve">/d x} ſubſtituendo hanc quantitatem pro z. </s> <s xml:id="echoid-s13531" xml:space="preserve">habe-<lb/>bebitur <lb/>{1/2} a b c c + h c. </s> <s xml:id="echoid-s13532" xml:space="preserve">a a b:</s> <s xml:id="echoid-s13533" xml:space="preserve">: {1/2} a b c d + h d, {a b c x/d} <lb/>Unde x = {{1/2} a a b c d d + a d d h.</s> <s xml:id="echoid-s13534" xml:space="preserve">/{1/2} a b c<emph style="super">3</emph> + c c h}</s> </p> </div> <div xml:id="echoid-div514" type="section" level="1" n="514"> <head xml:id="echoid-head626" xml:space="preserve">PROPOSITIO XXXVI.</head> <p style="it"> <s xml:id="echoid-s13535" xml:space="preserve">Cohærentiæ reſpectivæ Cylindrorum ejusdem materiæ ſunt ut <lb/>cubi ex baſium diametris.</s> <s xml:id="echoid-s13536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13537" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13538" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13539" xml:space="preserve">fig. </s> <s xml:id="echoid-s13540" xml:space="preserve">4. </s> <s xml:id="echoid-s13541" xml:space="preserve">Sint duo Cylindri A B C D, E F G H ejusdem <lb/>materiæ, qualem conſideravimus huc uſque in Propoſitionibus a <lb/>XIX ad XXXVI. </s> <s xml:id="echoid-s13542" xml:space="preserve">nec ratio habeatur longitudinis vel gravita-<lb/>tis, ſed tantum Cohærentiæ utriuſque baſis, quæ infixa eſt parie-<lb/>ti, e quo cylindri horizontaliter prominent: </s> <s xml:id="echoid-s13543" xml:space="preserve">ducantur diametri <lb/>perpendiculares ad horizontem A B, E F, & </s> <s xml:id="echoid-s13544" xml:space="preserve">chordæ innumeræ his <lb/>parallelæ, in utraque baſi numero æquales arcubus ſubtenſæ ſimi-<lb/>libus; </s> <s xml:id="echoid-s13545" xml:space="preserve">poterunt A B, E F conſiderari ut brachia vectium, quo-<lb/>rum centra motus ſunt in A & </s> <s xml:id="echoid-s13546" xml:space="preserve">E, ſintque alia brachia A D, E H <lb/>æqualia, erit potentia D frangens ad potentiam H, in ratione du-<lb/>plicata A B ad E F per Propoſ: </s> <s xml:id="echoid-s13547" xml:space="preserve">XXII. </s> <s xml:id="echoid-s13548" xml:space="preserve">Sumatur chorda proxima in <lb/>baſi A K B L, uti & </s> <s xml:id="echoid-s13549" xml:space="preserve">in baſi E M F O, cujus centrum motus eſt in aliquo <pb o="565" file="0581" n="582" rhead="CORPORUM FIRMORUM."/> puncto ſemicirculi K A L, vel M E O, eritque iterum potentia fran-<lb/>gens D ad eam in H, in ratione duplicata chordæ in A K B L ad <lb/>eam in E M F O, ſed chordæ arcuum ſimilium ſunt inter ſe ut dia-<lb/>metri circulorum, adeoque erit potentia in D ad eam in H <lb/>in ratione duplicata A B ad E F; </s> <s xml:id="echoid-s13550" xml:space="preserve">quoniam idem obti-<lb/>net in omnibus chordis, erit Cohærentia omnium chor-<lb/>darum in baſi A K B L, ad eam omnium chordarum in baſi <lb/>M E F O, in ratione duplicata diametrorum A B ad E F. </s> <s xml:id="echoid-s13551" xml:space="preserve">Sed <lb/>inter chordas omnes in utraque baſi ſpatium interjacet, quod <lb/>poteſt conſiderari ut latitudo cujuslibet chordæ, quæ major eſt in <lb/>chordis baſeos A K B L, quam in iis baſeos E M F O, eſt vero Co-<lb/>hærentia corporum, etiam in ratione ſuarum latitudinum per Pro-<lb/>poſit. </s> <s xml:id="echoid-s13552" xml:space="preserve">XXI, quare erit potentia frangens D ad eam in H, in ra-<lb/>tione duplicata diametri A B ad diametrum E F, & </s> <s xml:id="echoid-s13553" xml:space="preserve">ſimplici ratione <lb/>latitudinis A B ad E F; </s> <s xml:id="echoid-s13554" xml:space="preserve">quod cum obtineat in omnibus chordis u-<lb/>triuſque baſeos, & </s> <s xml:id="echoid-s13555" xml:space="preserve">ſumma latitudinum in baſi A K B L, ſit ut K L, <lb/>veluti ſumma latitudinum in baſi E M F O eſt ut M O, erit poten-<lb/>tia D frangens baſin A K B L, ad eam in H frangentem baſin E M <lb/>F O, in ratione compoſita ex duplicata altitudinis A B ad E F & </s> <s xml:id="echoid-s13556" xml:space="preserve">ſim-<lb/>plici K L ad M O, hoc eſt uti cubus diametri A B, ad cubum dia-<lb/>metri E F. </s> <s xml:id="echoid-s13557" xml:space="preserve">Sed Cohærentiæ baſium ſunt uti hæ potentiæ D & </s> <s xml:id="echoid-s13558" xml:space="preserve">H <lb/>frangentes, quare Cohærentiæ baſium Cylindrorum reſpectivæ <lb/>ſunt uti Cubi diametrorum ex baſibus.</s> <s xml:id="echoid-s13559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13560" xml:space="preserve">Corol. </s> <s xml:id="echoid-s13561" xml:space="preserve">Creſcit igitur cylindrorum æque longorum Cohærentia <lb/>reſpectiva in majori proportione quam maſſæ: </s> <s xml:id="echoid-s13562" xml:space="preserve">nam creſcit Cohæ-<lb/>rentia in ratione triplicata diametrorum, & </s> <s xml:id="echoid-s13563" xml:space="preserve">maſſæ in ratione du-<lb/>plicata diametrorum; </s> <s xml:id="echoid-s13564" xml:space="preserve">quare unus cylindrus quadruplo craſſior al-<lb/>tero, ſed æque longus plus cohærebit, quam quatuor cylindri te-<lb/>nuiores: </s> <s xml:id="echoid-s13565" xml:space="preserve">Sint ambo Cylindri A B C D, E F G H æque longi, ſed <lb/>diameter baſeos A B dupla ipſius E F, erit Cohærentia baſeos A K <lb/>B L ad eam baſeos E M F O, uti 8 ad 1. </s> <s xml:id="echoid-s13566" xml:space="preserve">maſſa tamen Cylindri A B <lb/>C D eſt ad eam E F G H uti 4 ad 1. </s> <s xml:id="echoid-s13567" xml:space="preserve">quatuor cylindri æquales E F G A <lb/>haberent Cohærentiam & </s> <s xml:id="echoid-s13568" xml:space="preserve">maſſam quadruplo majorem quam E F G H; <lb/></s> <s xml:id="echoid-s13569" xml:space="preserve">ergo firmitas horum omnium ſimul foret minor quam unius, æqua-<lb/>lis maſſæ, A B C D.</s> <s xml:id="echoid-s13570" xml:space="preserve"/> </p> <pb o="566" file="0582" n="583" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div515" type="section" level="1" n="515"> <head xml:id="echoid-head627" xml:space="preserve">PROPOSITIO XXXVII.</head> <p style="it"> <s xml:id="echoid-s13571" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13572" xml:space="preserve">XIX. </s> <s xml:id="echoid-s13573" xml:space="preserve">fig. </s> <s xml:id="echoid-s13574" xml:space="preserve">4. </s> <s xml:id="echoid-s13575" xml:space="preserve">Potentiæ frangentes applicatæ extremitati-<lb/>bus duorum Cylindrorum A B C D, E F P, ejusdem materiæ, ſed <lb/>longitudine & </s> <s xml:id="echoid-s13576" xml:space="preserve">craſſitie diverſorum, ſunt in ratione compoſita ex <lb/>triplicata diametrorum baſium A B, E F. </s> <s xml:id="echoid-s13577" xml:space="preserve">& </s> <s xml:id="echoid-s13578" xml:space="preserve">inverſa longitudi-<lb/>num A D, E P. </s> <s xml:id="echoid-s13579" xml:space="preserve">ſepoſita corporum gravitate.</s> <s xml:id="echoid-s13580" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13581" xml:space="preserve">Eſt Cohærentia baſeos A K B L, ad Cohærentiam baſeos E M F O, <lb/>in ratione triplicata diametri A B ad E F per Propoſ. </s> <s xml:id="echoid-s13582" xml:space="preserve">XXXVI. </s> <s xml:id="echoid-s13583" xml:space="preserve">ad-<lb/>eoque poſitis Cylindris B Q, F P æque longis, erunt potentiæ fran-<lb/>gentes in Q & </s> <s xml:id="echoid-s13584" xml:space="preserve">P, in ratione triplicata diametrorum A B, E F, ſed <lb/>potentia in Q eſt ad eam in D frangentem, uti A D ad A Q per <lb/>Prop. </s> <s xml:id="echoid-s13585" xml:space="preserve">X X. </s> <s xml:id="echoid-s13586" xml:space="preserve">Quare erit potentia frangens in D, ad eam in P Cy-<lb/>lindri F P, in ratione compoſita ex triplicata A B ad E F, & </s> <s xml:id="echoid-s13587" xml:space="preserve">A Q <lb/>= E P ad A D.</s> <s xml:id="echoid-s13588" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div516" type="section" level="1" n="516"> <head xml:id="echoid-head628" xml:space="preserve">PROPOSITIO XXXVIII.</head> <p style="it"> <s xml:id="echoid-s13589" xml:space="preserve">Tab XXIII. </s> <s xml:id="echoid-s13590" xml:space="preserve">fig. </s> <s xml:id="echoid-s13591" xml:space="preserve">37. </s> <s xml:id="echoid-s13592" xml:space="preserve">Duo Cylindri ſimiles A B C D, E F G H <lb/>ejusdem materiæ, horizontaliter parieti infixi, ſuſtinere poſſunt <lb/>ab extremitatibus D & </s> <s xml:id="echoid-s13593" xml:space="preserve">H, pondera I & </s> <s xml:id="echoid-s13594" xml:space="preserve">K quæ ſunt baſibus propor-<lb/>tionalia ſepoſitâ Cylindrorum gravitate.</s> <s xml:id="echoid-s13595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13596" xml:space="preserve">Eſt Cohærentia Cylindri A B C D, ad Cohærentiam Cylindri <lb/>E F G H, uti cubus diametri A B ad cubum diametri E F per Prop. <lb/></s> <s xml:id="echoid-s13597" xml:space="preserve">XXXVI. </s> <s xml:id="echoid-s13598" xml:space="preserve">ſed quia Cylindri ſunt ſimiles, eſt A B, E F:</s> <s xml:id="echoid-s13599" xml:space="preserve">: A D. </s> <s xml:id="echoid-s13600" xml:space="preserve">E H. </s> <s xml:id="echoid-s13601" xml:space="preserve"><lb/>ergo <emph style="ol">AB</emph><emph style="super">c</emph>, <emph style="ol">EF</emph><emph style="super">c</emph>:</s> <s xml:id="echoid-s13602" xml:space="preserve">: <emph style="ol">AD</emph><emph style="super">c</emph>, <emph style="ol">EH</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s13603" xml:space="preserve">unde erunt Cohærentiæ cylindro-<lb/>rum uti <emph style="ol">AD</emph><emph style="super">c</emph>, ad EH<emph style="super">c</emph>. </s> <s xml:id="echoid-s13604" xml:space="preserve">Eſt vero momentum ponderis I = I X <lb/>A D. </s> <s xml:id="echoid-s13605" xml:space="preserve">quod eſt æquale Cohærentiæ baſeos, ſive = <emph style="ol">AD</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s13606" xml:space="preserve">adeoque <lb/>utrimque facta diviſione per A D, erit I = <emph style="ol">AD</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13607" xml:space="preserve">eodem modo pon-<lb/>deris K momentum eſt = K X E H. </s> <s xml:id="echoid-s13608" xml:space="preserve">& </s> <s xml:id="echoid-s13609" xml:space="preserve">Cohærentia, cui æquale <lb/>eſſe debet, eſt = <emph style="ol">EH</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s13610" xml:space="preserve">quareutrimque facta diviſioneper E H, erit <lb/>K = <emph style="ol">EH</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13611" xml:space="preserve">erit igitur pondus I ad pondusK:</s> <s xml:id="echoid-s13612" xml:space="preserve">:<emph style="ol">AD</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13613" xml:space="preserve">E H<emph style="super">q</emph>:</s> <s xml:id="echoid-s13614" xml:space="preserve">: A B<emph style="super">q</emph>. </s> <s xml:id="echoid-s13615" xml:space="preserve"><emph style="ol">EF</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s13616" xml:space="preserve">: <lb/>baſis A B S ad baſin E F R. </s> <s xml:id="echoid-s13617" xml:space="preserve">adeoque pondera ſunt baſibus proportio-<lb/>nalia.</s> <s xml:id="echoid-s13618" xml:space="preserve"/> </p> <pb o="567" file="0583" n="584" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div517" type="section" level="1" n="517"> <head xml:id="echoid-head629" xml:space="preserve">PROPOSITIO XXXIX.</head> <p style="it"> <s xml:id="echoid-s13619" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13620" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13621" xml:space="preserve">fig. </s> <s xml:id="echoid-s13622" xml:space="preserve">37. </s> <s xml:id="echoid-s13623" xml:space="preserve">Sunt momenta gravitatis in Cylindris ejus-<lb/>dem materiæ A B C D, E F G H in ratione compoſitâ ex magnitudi-<lb/>ne Cylindri A B C D, ad E F G H, & </s> <s xml:id="echoid-s13624" xml:space="preserve">ex longitudine A D ad E H.</s> <s xml:id="echoid-s13625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13626" xml:space="preserve">Sunt gravitates horum Cylindrorum, uti ſunt magnitudines: <lb/></s> <s xml:id="echoid-s13627" xml:space="preserve">ſunt centra gravitatis in medio Cylindrorum x & </s> <s xml:id="echoid-s13628" xml:space="preserve">z, quamobrem <lb/>concipiendæ ſunt gravitates ſuſpenſæ ex x & </s> <s xml:id="echoid-s13629" xml:space="preserve">z, quarum momen-<lb/>ta habentur ductis diſtantiis S X, R Z in pondera; </s> <s xml:id="echoid-s13630" xml:space="preserve">ſed eſt S X ad <lb/>R Z:</s> <s xml:id="echoid-s13631" xml:space="preserve">: A D, E H. </s> <s xml:id="echoid-s13632" xml:space="preserve">igitur momenta cylindrorum ſunt in ratione <lb/>compoſita magnitudinum B D ad F H, & </s> <s xml:id="echoid-s13633" xml:space="preserve">longitudinum A D ad E H.</s> <s xml:id="echoid-s13634" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div518" type="section" level="1" n="518"> <head xml:id="echoid-head630" xml:space="preserve">PROPOSITIO XL.</head> <p style="it"> <s xml:id="echoid-s13635" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13636" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13637" xml:space="preserve">fig 37. </s> <s xml:id="echoid-s13638" xml:space="preserve">Dato cylindro A B C D, & </s> <s xml:id="echoid-s13639" xml:space="preserve">pondere I ap-<lb/>penſo extremitati, minimo ſed frangente. </s> <s xml:id="echoid-s13640" xml:space="preserve">invenire longitudinem <lb/>minimam ejusdem cylindri, ut propria gravitate frangatur.</s> <s xml:id="echoid-s13641" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13642" xml:space="preserve">Vocetur longitudo A D dati cylindri l. </s> <s xml:id="echoid-s13643" xml:space="preserve">pondus I datum p. </s> <s xml:id="echoid-s13644" xml:space="preserve">ra-<lb/>dius baſeos A B r. </s> <s xml:id="echoid-s13645" xml:space="preserve">circumferentia c. </s> <s xml:id="echoid-s13646" xml:space="preserve">erit baſis = {1/2} cr. </s> <s xml:id="echoid-s13647" xml:space="preserve">& </s> <s xml:id="echoid-s13648" xml:space="preserve">ſolidi-<lb/>tas cylindri ={1/2} c r l. </s> <s xml:id="echoid-s13649" xml:space="preserve">quia centrum gravitatis eſt in medio cylindri, <lb/>erit momentum gravitatis ={1/2} c r l X {1/2} l. </s> <s xml:id="echoid-s13650" xml:space="preserve">={1/4}c r l l ponderis momen-<lb/>tum erit =p l. </s> <s xml:id="echoid-s13651" xml:space="preserve">longitudo quæſita vocetur x. </s> <s xml:id="echoid-s13652" xml:space="preserve">erit ſoliditas quæſiti <lb/>cylindri ={1/2} c r x. </s> <s xml:id="echoid-s13653" xml:space="preserve">& </s> <s xml:id="echoid-s13654" xml:space="preserve">momentum gravitatis hujus cylindri ={1/4} c r x x. <lb/></s> <s xml:id="echoid-s13655" xml:space="preserve">quod debet eſſe æquale momentoponderis I & </s> <s xml:id="echoid-s13656" xml:space="preserve">momento gravitatis <lb/>in dato cylindro, adeoque {1/4} c r x x =pl + {1/4} c r l l. </s> <s xml:id="echoid-s13657" xml:space="preserve">facta utrim-<lb/>que diviſione per {1/4}cr. </s> <s xml:id="echoid-s13658" xml:space="preserve">fit xx ={pl+{1/4}c r l l/{1/4}cr.</s> <s xml:id="echoid-s13659" xml:space="preserve">}: </s> <s xml:id="echoid-s13660" xml:space="preserve">unde x ={pl+{1/4} crll.</s> <s xml:id="echoid-s13661" xml:space="preserve">/{1/4}cr.</s> <s xml:id="echoid-s13662" xml:space="preserve">}</s> </p> </div> <div xml:id="echoid-div519" type="section" level="1" n="519"> <head xml:id="echoid-head631" xml:space="preserve">PROPOSITIO XLI.</head> <p style="it"> <s xml:id="echoid-s13663" xml:space="preserve">Dato cylindro horizontaliter parieti infigendo, multo longiori <lb/>quam ut ſuum pondus ferat, invenire quænam pars abſcindenda <lb/>ſit, ut absque metu rupturæ parieti immittatur, ſit tamen rupturæ <lb/>proximus.</s> <s xml:id="echoid-s13664" xml:space="preserve"/> </p> <pb o="568" file="0584" n="585" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s13665" xml:space="preserve">Quæratur per Propoſ. </s> <s xml:id="echoid-s13666" xml:space="preserve">XL longitudo minima, quæ propria gra-<lb/>vitate frangitur, hæc parum imminuta applicetur dato cylindro, <lb/>a quo reliqua pars auferatur, ſuperſtes manebit cylindrus quæſitus.</s> <s xml:id="echoid-s13667" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div520" type="section" level="1" n="520"> <head xml:id="echoid-head632" xml:space="preserve">PROPOSITIO XLII.</head> <p style="it"> <s xml:id="echoid-s13668" xml:space="preserve">Dato Cylindro ex cujus extremo pondus appenſum ſit maximum, <lb/>invenire longitudinem alterius cylindri, datæ majoris vel minoris <lb/>craſſitiei, ejusdem materiæ, ex cujus extremo pondus idem ſuſpen-<lb/>ſum ſit maximum, gravitatis cylindrorum non habita ratione.</s> <s xml:id="echoid-s13669" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13670" xml:space="preserve">Sit diameter dati cylindri = a. </s> <s xml:id="echoid-s13671" xml:space="preserve">longitudo = l. </s> <s xml:id="echoid-s13672" xml:space="preserve">pondus adpenſum <lb/>& </s> <s xml:id="echoid-s13673" xml:space="preserve">maximum = p. </s> <s xml:id="echoid-s13674" xml:space="preserve">erit Cohærentia cylindri = a<emph style="super">3</emph>, & </s> <s xml:id="echoid-s13675" xml:space="preserve">momentum <lb/>ponderis = lp. </s> <s xml:id="echoid-s13676" xml:space="preserve">poniturque a<emph style="super">3</emph> = lp. </s> <s xml:id="echoid-s13677" xml:space="preserve">ponatur diameter craſſioris vel <lb/>tenuioris cylindri = a X b. </s> <s xml:id="echoid-s13678" xml:space="preserve">ubi, b, notat numerum integrum majorem <lb/>unitate, vel integrum cum fractione, ſi diameter erit craſſior; </s> <s xml:id="echoid-s13679" xml:space="preserve">ſed <lb/>notat modo fractionem unitate minorem, ſi diameter ſit minor; </s> <s xml:id="echoid-s13680" xml:space="preserve">& </s> <s xml:id="echoid-s13681" xml:space="preserve"><lb/>longitudo quæſita ſit = x. </s> <s xml:id="echoid-s13682" xml:space="preserve">erit momentum ponderis p ex hac longi-<lb/>tudine = p x. </s> <s xml:id="echoid-s13683" xml:space="preserve">eritque a<emph style="super">3</emph>. </s> <s xml:id="echoid-s13684" xml:space="preserve">a<emph style="super">3</emph>b<emph style="super">3</emph>:</s> <s xml:id="echoid-s13685" xml:space="preserve">: lp. </s> <s xml:id="echoid-s13686" xml:space="preserve">px. </s> <s xml:id="echoid-s13687" xml:space="preserve">unde b<emph style="super">3</emph>l = x.</s> <s xml:id="echoid-s13688" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13689" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s13690" xml:space="preserve">Poſſunt dari caſus, in quibus hoc Problema eſt im-<lb/>poſſibile, applicatum ipſi materiæ, quamvis Geometrice videatur <lb/>ſemper ſolvi poſſe: </s> <s xml:id="echoid-s13691" xml:space="preserve">ſi enim cylindrus tenuior breviſſimus eſſe debe-<lb/>ret, ut pondus p graviſſimum ſuſpendat, id nunquam ſuſtinere po-<lb/>terit, pondere p ſuperante Cohærentiam cylindri abſolutam, nam <lb/>nunquam poteſt eſſe Cohærentia major quam abſoluta eſt: </s> <s xml:id="echoid-s13692" xml:space="preserve">licet igitur <lb/>Geometrice ex natura vectis poſſet ex cylindro tenuiſſimo ſuſpen-<lb/>di pondus graviſſimum in diſtantia ad modum parva ab orâ forami-<lb/>nis, id nequaquam obtineret in natura, cum Cohærentia cylindri <lb/>tenuiſſimi admodum parva illico ſolveretur.</s> <s xml:id="echoid-s13693" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div521" type="section" level="1" n="521"> <head xml:id="echoid-head633" xml:space="preserve">PROPOSITIO XLIII.</head> <p style="it"> <s xml:id="echoid-s13694" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13695" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13696" xml:space="preserve">fig. </s> <s xml:id="echoid-s13697" xml:space="preserve">37. </s> <s xml:id="echoid-s13698" xml:space="preserve">Sint duo ſolida ejusdem materiæ A B C D, <lb/>E F G H cylindrica, & </s> <s xml:id="echoid-s13699" xml:space="preserve">ſit quadratum A D ad quadratum E H, ut <lb/>diameter baſeos A B ad diametrum E F, ſint horizontaliter parieti <lb/>infixa, erunt momenta ex eorum gravitateoriunda, etiam eorum Co-<lb/>hærentiæ proportionalia.</s> <s xml:id="echoid-s13700" xml:space="preserve"/> </p> <pb o="569" file="0585" n="586" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s13701" xml:space="preserve">Vocetur A B, a. </s> <s xml:id="echoid-s13702" xml:space="preserve">A D, b. </s> <s xml:id="echoid-s13703" xml:space="preserve">E F c. </s> <s xml:id="echoid-s13704" xml:space="preserve">E H, d. </s> <s xml:id="echoid-s13705" xml:space="preserve">Erit ſoliditas B D ad <lb/>ſoliditatem F H:</s> <s xml:id="echoid-s13706" xml:space="preserve">: a a b. </s> <s xml:id="echoid-s13707" xml:space="preserve">c c d. </s> <s xml:id="echoid-s13708" xml:space="preserve">& </s> <s xml:id="echoid-s13709" xml:space="preserve">momentum e pondere A B C D, <lb/>ad momentum e pondere E F G H:</s> <s xml:id="echoid-s13710" xml:space="preserve">: a a b X {1/2} b. </s> <s xml:id="echoid-s13711" xml:space="preserve">c c d X {1/2} d. <lb/></s> <s xml:id="echoid-s13712" xml:space="preserve">ſed eſt {1/2} b. </s> <s xml:id="echoid-s13713" xml:space="preserve">ad {1/2} d:</s> <s xml:id="echoid-s13714" xml:space="preserve">: b. </s> <s xml:id="echoid-s13715" xml:space="preserve">d. </s> <s xml:id="echoid-s13716" xml:space="preserve">quare momenta oriunda ex ponderibus <lb/>erunt uti a a b b. </s> <s xml:id="echoid-s13717" xml:space="preserve">ad c c d d.</s> <s xml:id="echoid-s13718" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13719" xml:space="preserve">Verum ſupponitur <emph style="ol">AD</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s13720" xml:space="preserve"><emph style="ol">EH</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s13721" xml:space="preserve">: A B, E F. </s> <s xml:id="echoid-s13722" xml:space="preserve">hoc eſt Analytice <lb/>b b. </s> <s xml:id="echoid-s13723" xml:space="preserve">d d:</s> <s xml:id="echoid-s13724" xml:space="preserve">: a. </s> <s xml:id="echoid-s13725" xml:space="preserve">c. </s> <s xml:id="echoid-s13726" xml:space="preserve">adeoque in momentis loco b b, d d. </s> <s xml:id="echoid-s13727" xml:space="preserve">ponendo quan-<lb/>titates proportionales, erunt momenta oriunda ex ponderibus in-<lb/>ter ſe uti a<emph style="super">3</emph>, ad c<emph style="super">3</emph>. </s> <s xml:id="echoid-s13728" xml:space="preserve">Verum Cohærentiæ corporum ſunt inter ſe ut <lb/>Cubi diametrorum per Propoſ. </s> <s xml:id="echoid-s13729" xml:space="preserve">XXXVI. </s> <s xml:id="echoid-s13730" xml:space="preserve">quare Cohærentiæ ho-<lb/>rum cylindrorum erunt inter ſe, uti momenta è ponderibus ſolido-<lb/>rum oriunda.</s> <s xml:id="echoid-s13731" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div522" type="section" level="1" n="522"> <head xml:id="echoid-head634" xml:space="preserve">PROPOSITIO XLIV.</head> <p style="it"> <s xml:id="echoid-s13732" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13733" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13734" xml:space="preserve">fig 37. </s> <s xml:id="echoid-s13735" xml:space="preserve">Dato corpore E F G H, datoque pondere K, <lb/>cujus momentum ſimul cum momento ponderis dati Cylindri ad Co-<lb/>hærentiam ejusdem, habeat quamlibet rationem datam, invenire <lb/>aliud corpus A B C D ſimile priori, cujus momentum gravitatis ad <lb/>Cohærentiam habeat eandem proportionem.</s> <s xml:id="echoid-s13736" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13737" xml:space="preserve">Ponatur {1/2} E F = a. </s> <s xml:id="echoid-s13738" xml:space="preserve">circumferentia baſeos = c. </s> <s xml:id="echoid-s13739" xml:space="preserve">E H = b. </s> <s xml:id="echoid-s13740" xml:space="preserve">pondus <lb/>K = p. </s> <s xml:id="echoid-s13741" xml:space="preserve">{1/2} A B = x. </s> <s xml:id="echoid-s13742" xml:space="preserve">A D = z. </s> <s xml:id="echoid-s13743" xml:space="preserve">ratio detur f ad d.</s> <s xml:id="echoid-s13744" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13745" xml:space="preserve">Eritſoliditas Cylindri = {1/2} a c b. </s> <s xml:id="echoid-s13746" xml:space="preserve">& </s> <s xml:id="echoid-s13747" xml:space="preserve">momentnm ex gravitate oriun-<lb/>dum = {1/4} a c b b. </s> <s xml:id="echoid-s13748" xml:space="preserve">eſt momentum ponderis = p b. </s> <s xml:id="echoid-s13749" xml:space="preserve">Cohærentia baſeos <lb/>= 8a<emph style="super">3</emph>: </s> <s xml:id="echoid-s13750" xml:space="preserve">ſtabunt igitur quantitates ſecundum hanc proportionem <lb/>{1/4} a c b b + p b. </s> <s xml:id="echoid-s13751" xml:space="preserve">a<emph style="super">3</emph>:</s> <s xml:id="echoid-s13752" xml:space="preserve">: f. </s> <s xml:id="echoid-s13753" xml:space="preserve">d.</s> <s xml:id="echoid-s13754" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13755" xml:space="preserve">Quia corpora E F G H, A B C D requiruntur ſimilia, erit a. </s> <s xml:id="echoid-s13756" xml:space="preserve">x:</s> <s xml:id="echoid-s13757" xml:space="preserve">: c. </s> <s xml:id="echoid-s13758" xml:space="preserve">{c x.</s> <s xml:id="echoid-s13759" xml:space="preserve">/a} <lb/>circumferentia baſeos A B. </s> <s xml:id="echoid-s13760" xml:space="preserve">totaque baſis {1/2} {c x x.</s> <s xml:id="echoid-s13761" xml:space="preserve">/a} & </s> <s xml:id="echoid-s13762" xml:space="preserve">ut habeatur <lb/>longitudo A D. </s> <s xml:id="echoid-s13763" xml:space="preserve">fiat {1/2} a c. </s> <s xml:id="echoid-s13764" xml:space="preserve">{1/2} {c x<emph style="super">2</emph>/a}:</s> <s xml:id="echoid-s13765" xml:space="preserve">: b. </s> <s xml:id="echoid-s13766" xml:space="preserve">{b x x/a a} = z. </s> <s xml:id="echoid-s13767" xml:space="preserve">adeoque erit ſo-<lb/>liditas Cylindri A B C D = {1/2} {b c x<emph style="super">4</emph>/a<emph style="super">3</emph>} quæ ducta in dimidiam longitu- <pb o="570" file="0586" n="587" rhead="INTRODUCTIO AD COHÆRENTIAM"/> dinem A D, dabit momentum oriundum ex gravitate = {b b c x<emph style="super">6</emph>.</s> <s xml:id="echoid-s13768" xml:space="preserve">/4 a} <lb/>ſupponatur hic cylindrus ad Cohærentiam ſuam in eadem ratione <lb/>f ad d. </s> <s xml:id="echoid-s13769" xml:space="preserve">erit Cohærentia hujus 8x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13770" xml:space="preserve">unde {b b c x<emph style="super">6</emph>/4 a<emph style="super">5</emph>} 8x<emph style="super">3</emph>:</s> <s xml:id="echoid-s13771" xml:space="preserve">: f. </s> <s xml:id="echoid-s13772" xml:space="preserve">d <lb/>:</s> <s xml:id="echoid-s13773" xml:space="preserve">: {1/4} a c b b + p b a<emph style="super">3</emph>. </s> <s xml:id="echoid-s13774" xml:space="preserve">multiplicatis extremis & </s> <s xml:id="echoid-s13775" xml:space="preserve">mediisperſe, fit {a<emph style="super">3</emph> b b c x<emph style="super">6</emph>/4a<emph style="super">5</emph>} <lb/>= {1/2} a c b b x<emph style="super">3</emph> + 8 p b x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13776" xml:space="preserve">factaque diviſione per {b b c x<emph style="super">3</emph>,/4a a} manet x<emph style="super">3</emph> <lb/>=2a<emph style="super">3</emph> + 3 {2 a a p.</s> <s xml:id="echoid-s13777" xml:space="preserve">/b c} unde x =<emph style="super">3</emph>2 a<emph style="super">3</emph> + 32{a a p.</s> <s xml:id="echoid-s13778" xml:space="preserve">/b c} quo cognito valore <lb/>radii baſeos A B. </s> <s xml:id="echoid-s13779" xml:space="preserve">datur totum corpus A B C D, ejusque longitudo.</s> <s xml:id="echoid-s13780" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div523" type="section" level="1" n="523"> <head xml:id="echoid-head635" xml:space="preserve">PROPOSITIO XLV.</head> <p style="it"> <s xml:id="echoid-s13781" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13782" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13783" xml:space="preserve">fig. </s> <s xml:id="echoid-s13784" xml:space="preserve">37. </s> <s xml:id="echoid-s13785" xml:space="preserve">Dato Cylindro A B C D, cujus momentum <lb/>gravitatis ad Cohærentiam habeat rationem datam f ad, d: </s> <s xml:id="echoid-s13786" xml:space="preserve">ſecto-<lb/>que ab ipſo quolibet fruſto Q D, reperire pondus extremo Q ap-<lb/>pendendum, cujus momentum, unà cum momento ex gravitate re-<lb/>liquæ partis A B Q, ad Cohærentiam ſit in eâdem ratione f ad, d.</s> <s xml:id="echoid-s13787" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13788" xml:space="preserve">Ponatur {1/2} A B = r. </s> <s xml:id="echoid-s13789" xml:space="preserve">circumferentia baſeos = c. </s> <s xml:id="echoid-s13790" xml:space="preserve">longitudo A D = b. <lb/></s> <s xml:id="echoid-s13791" xml:space="preserve">erit baſis = {1/2} c r. </s> <s xml:id="echoid-s13792" xml:space="preserve">& </s> <s xml:id="echoid-s13793" xml:space="preserve">ſoliditas cylindri A B C D = {1/2} b c r. </s> <s xml:id="echoid-s13794" xml:space="preserve">momentum <lb/>oriundum ex gravitate = {1/4} b b c r. </s> <s xml:id="echoid-s13795" xml:space="preserve">Cohærentia vero per Prop. </s> <s xml:id="echoid-s13796" xml:space="preserve">XXXVI. </s> <s xml:id="echoid-s13797" xml:space="preserve"><lb/>eſt uti cubus A B = 8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13798" xml:space="preserve">quare datur {1/4} b b c r. </s> <s xml:id="echoid-s13799" xml:space="preserve">8 r<emph style="super">3</emph>:</s> <s xml:id="echoid-s13800" xml:space="preserve">: f. </s> <s xml:id="echoid-s13801" xml:space="preserve">d.</s> <s xml:id="echoid-s13802" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13803" xml:space="preserve">Abſcindatur a cylindro ſegmentum Q D, ita ut maneat A Q <lb/>= l. </s> <s xml:id="echoid-s13804" xml:space="preserve">erit ſoliditas cylindri A B Q = {1/2} c r l, & </s> <s xml:id="echoid-s13805" xml:space="preserve">momentum ex gra-<lb/>vitate = {1/4} c r l l. </s> <s xml:id="echoid-s13806" xml:space="preserve">pondus inveniendum vocetur = x. </s> <s xml:id="echoid-s13807" xml:space="preserve">quod cum ſu-<lb/>ſpendendum ab extremo Q habebit momentum = l x. </s> <s xml:id="echoid-s13808" xml:space="preserve">quare ſum-<lb/>ma momenti ponderis & </s> <s xml:id="echoid-s13809" xml:space="preserve">Cylindri B Q erit = {1/4} c r l l. </s> <s xml:id="echoid-s13810" xml:space="preserve">+ l x quæ eſt <lb/>ad Cohærentiam baſeos 8r<emph style="super">3</emph>:</s> <s xml:id="echoid-s13811" xml:space="preserve">: f. </s> <s xml:id="echoid-s13812" xml:space="preserve">d. </s> <s xml:id="echoid-s13813" xml:space="preserve">unde {1/4} c r l l + l x = {1/4} b b c r. <lb/></s> <s xml:id="echoid-s13814" xml:space="preserve">hinc erit x = {b b c r - c r l l.</s> <s xml:id="echoid-s13815" xml:space="preserve">/4l}</s> </p> <p> <s xml:id="echoid-s13816" xml:space="preserve">Sed poteſt dari generalior demonſtratio, quæ non modo Cylin-<lb/>dris, ſed Parallelopipedis, Conis, aliisque corporibus regularibus <lb/>applicari poteſt: </s> <s xml:id="echoid-s13817" xml:space="preserve">Sit enim Tab. </s> <s xml:id="echoid-s13818" xml:space="preserve">XXIII, fig. </s> <s xml:id="echoid-s13819" xml:space="preserve">39. </s> <s xml:id="echoid-s13820" xml:space="preserve">Corpus A B C, ab- <pb o="571" file="0587" n="588" rhead="CORPORUM FIRMORUM."/> ſeiſſumque ab eo ſegmentum D E C, quæritur pondus P penden-<lb/>dum ex D, cujus momentum ſimul cum momento partis reliquæ <lb/>A B E D ſit in eadem proportione ad Cohærentiam baſeos A B, quam <lb/>integrum corpus A B C habet ad eandem Cohærentiam. </s> <s xml:id="echoid-s13821" xml:space="preserve">Ducatur <lb/>axis I K C, ſitque centrum gravitatis hujus corporis A B C in G, <lb/>ſegmenti vero abſciſſi D E C in F: </s> <s xml:id="echoid-s13822" xml:space="preserve">tum fiat, uti ſoliditas A B E D, <lb/>ad ſoliditatem D E C, ita F G ad G H. </s> <s xml:id="echoid-s13823" xml:space="preserve">erit punctum H centrum <lb/>gravitatis corporis A B E D: </s> <s xml:id="echoid-s13824" xml:space="preserve">deinde ut I H ad I G, ita pondus inte-<lb/>gri corporis A B C, ad pondus partis A B E D, una cum quodam <lb/>pondere O: </s> <s xml:id="echoid-s13825" xml:space="preserve">tandem ut K I ad H I, ita fiat pondus O ad pondus P, <lb/>erit pondus P ſuſpenſum ex D, pondus quæſitum.</s> <s xml:id="echoid-s13826" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13827" xml:space="preserve">Pendeat pondus O ex puncto H: </s> <s xml:id="echoid-s13828" xml:space="preserve">Quoniam longitudo I H eſt ad <lb/>longitudinem I G, ut pondus corporis A B C ad pondus partis reli-<lb/>quæ A B E D unà cum pondere O, ergo pondus A B C ſuſpenſum <lb/>ex G habet idem momentum, quod pondus A B E D una cum pon-<lb/>dere O ſuſpenſum ex H. </s> <s xml:id="echoid-s13829" xml:space="preserve">Sed quoniam pondus O eſt ad pondus P in <lb/>eadem proportione, in quâ I K eſt ad I H; </s> <s xml:id="echoid-s13830" xml:space="preserve">ergo pondus P pendens <lb/>ex D habebit idem momentum, quod O ex H, additoque com-<lb/>muni momento ponderis A B E D, erit momentum ponderis P, una <lb/>cum momento ponderis A E, æquale momento ejusdem pon-<lb/>deris A B E D, una cum momento ponderis O; </s> <s xml:id="echoid-s13831" xml:space="preserve">proinde etiam <lb/>æquale momento ponderis totius A B C, adeoque momentum pon-<lb/>deris P, una cum momento partis reliquæ A B E D eſt ad Cohæren-<lb/>tiam in eadem proportione, in qua momentum totius corporis <lb/>A B C eſt ad eandem Cohærentiam.</s> <s xml:id="echoid-s13832" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div524" type="section" level="1" n="524"> <head xml:id="echoid-head636" xml:space="preserve">PROPOSITIO XLVI.</head> <p style="it"> <s xml:id="echoid-s13833" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13834" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13835" xml:space="preserve">fig. </s> <s xml:id="echoid-s13836" xml:space="preserve">38. </s> <s xml:id="echoid-s13837" xml:space="preserve">Datis duobus Cylindris E F G H, A B C D, <lb/>æquales baſes E F, A B, ſed diverſas longitudines E H, A D ha-<lb/>bentibus, ex eadem materia confectis, datoque pondere P, cujus <lb/>momentum ſimul cum momento gravitatis E F G H, ſit ad Cohæ-<lb/>rentiam in qualibet ratione, invenire pondus O ex D ſuſpenden-<lb/>dum, cujus momentum ſimul cum ponderis momento in A B C D, ſit <lb/>ad Cohærentiam in eadem ratione.</s> <s xml:id="echoid-s13838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13839" xml:space="preserve">Vocetur radius baſeos E F, a. </s> <s xml:id="echoid-s13840" xml:space="preserve">E H, b. </s> <s xml:id="echoid-s13841" xml:space="preserve">pondus P, p. </s> <s xml:id="echoid-s13842" xml:space="preserve">circumferentia <lb/>baſeos c.</s> <s xml:id="echoid-s13843" xml:space="preserve"/> </p> <pb o="572" file="0588" n="589" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s13844" xml:space="preserve">Erit baſis = {1/2} a c, ſoliditas cylindri = {1/2} a c b. </s> <s xml:id="echoid-s13845" xml:space="preserve">momentum ex <lb/>gravitate = {1/4} a b b c. </s> <s xml:id="echoid-s13846" xml:space="preserve">eſt quoque ponderis momentum = b p. </s> <s xml:id="echoid-s13847" xml:space="preserve">cum <lb/>ſit baſis A B = E F, erit baſis A B = {1/2} a c. </s> <s xml:id="echoid-s13848" xml:space="preserve">ſit longitudo A D = d. <lb/></s> <s xml:id="echoid-s13849" xml:space="preserve">pondus O = x. </s> <s xml:id="echoid-s13850" xml:space="preserve">eritſoliditas Cylindri B D = {1/2} a c d. </s> <s xml:id="echoid-s13851" xml:space="preserve">& </s> <s xml:id="echoid-s13852" xml:space="preserve">momentum <lb/>ex gravitate = {1/4} a c d d. </s> <s xml:id="echoid-s13853" xml:space="preserve">ponderis momentum = d x. </s> <s xml:id="echoid-s13854" xml:space="preserve">ponitur autem <lb/>Cohærentia utriusque Cylindri eadem, quia datur eadem baſis <lb/>ejuſdem materiæ, ad quam cum eadem debeat haberi ratio, ponitur <lb/>{1/4} a b b c + b p = {1/4} a c d d + d x. </s> <s xml:id="echoid-s13855" xml:space="preserve">erit igitur. </s> <s xml:id="echoid-s13856" xml:space="preserve"><lb/>x = {{1/4} a b b c + b p - {1/4} a c d d.</s> <s xml:id="echoid-s13857" xml:space="preserve">/d}</s> </p> </div> <div xml:id="echoid-div525" type="section" level="1" n="525"> <head xml:id="echoid-head637" xml:space="preserve">PROPOSITIO XLVII.</head> <p style="it"> <s xml:id="echoid-s13858" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13859" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13860" xml:space="preserve">fig. </s> <s xml:id="echoid-s13861" xml:space="preserve">38. </s> <s xml:id="echoid-s13862" xml:space="preserve">Datis duobus Cylindris E F G H, A B C D <lb/>ejusdemmateriæ & </s> <s xml:id="echoid-s13863" xml:space="preserve">baſeos, ſed inæqualium longitudinum E H, A D, <lb/>invenire pondus O, quod cum gravitate A B C D eandem habeat <lb/>proportionem ad Cohærentiam, quam E F G H ſolus habet ad ſuam.</s> <s xml:id="echoid-s13864" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13865" xml:space="preserve">Quantitatibus deſignatis iisdem litteris ac in Propoſ. </s> <s xml:id="echoid-s13866" xml:space="preserve">XLVI. </s> <s xml:id="echoid-s13867" xml:space="preserve">erit <lb/>momentum corporis A B C D = {1/4} a c d d, & </s> <s xml:id="echoid-s13868" xml:space="preserve">momentum ponderis <lb/>O = d x. </s> <s xml:id="echoid-s13869" xml:space="preserve">momentum vero E F G H = {1/4} a b b c. </s> <s xml:id="echoid-s13870" xml:space="preserve">Cohærentia utrius-<lb/>que baſeos eſt eadem & </s> <s xml:id="echoid-s13871" xml:space="preserve">= a<emph style="super">3</emph> adeoque. <lb/></s> <s xml:id="echoid-s13872" xml:space="preserve">{1/4} a b b c. </s> <s xml:id="echoid-s13873" xml:space="preserve">a<emph style="super">3</emph>:</s> <s xml:id="echoid-s13874" xml:space="preserve">: {{/1}/4} a c d d + d x. </s> <s xml:id="echoid-s13875" xml:space="preserve">a<emph style="super">3</emph>. </s> <s xml:id="echoid-s13876" xml:space="preserve"><lb/>unde {a b b c - a c d d = x.</s> <s xml:id="echoid-s13877" xml:space="preserve">/4d}</s> </p> </div> <div xml:id="echoid-div526" type="section" level="1" n="526"> <head xml:id="echoid-head638" xml:space="preserve">PROPOSITIO XLVIII.</head> <p style="it"> <s xml:id="echoid-s13878" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13879" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13880" xml:space="preserve">fig. </s> <s xml:id="echoid-s13881" xml:space="preserve">37. </s> <s xml:id="echoid-s13882" xml:space="preserve">Dato Cylindro A B C D & </s> <s xml:id="echoid-s13883" xml:space="preserve">pondere I, cujus <lb/>momentum ſimul cum momento Cylindri A B C D ad ſuam Cohæ-<lb/>rentiam habeat quamlibet proportionem, ſuper datà qualibet baſi <lb/>E F conſtruere alium cylindrum, cujus momentum gravitatis ha-<lb/>beat eandem rationem ad ſuam Cohærentiam.</s> <s xml:id="echoid-s13884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13885" xml:space="preserve">Vocetur radius baſeos A B, r. </s> <s xml:id="echoid-s13886" xml:space="preserve">peripheria c. </s> <s xml:id="echoid-s13887" xml:space="preserve">longitudo A D, b. </s> <s xml:id="echoid-s13888" xml:space="preserve">pon-<lb/>dus I, p. </s> <s xml:id="echoid-s13889" xml:space="preserve">radius baſeos E F, e. </s> <s xml:id="echoid-s13890" xml:space="preserve">longitudo E H, x.</s> <s xml:id="echoid-s13891" xml:space="preserve"/> </p> <pb o="573" file="0589" n="590" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s13892" xml:space="preserve">Erit baſis A B = {1/2} c r. </s> <s xml:id="echoid-s13893" xml:space="preserve">ſoliditas Cylindri B D = {1/2} b c r. </s> <s xml:id="echoid-s13894" xml:space="preserve">momen-<lb/>tum ex gravitate = {1/4} b b c r momentum ponderis I = b p. </s> <s xml:id="echoid-s13895" xml:space="preserve">Cohæ-<lb/>rentia eſt ut 8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13896" xml:space="preserve">ſed Cylindri E H baſis E F eſt = {1/2} {e e c/r} quia r. </s> <s xml:id="echoid-s13897" xml:space="preserve">c:</s> <s xml:id="echoid-s13898" xml:space="preserve">: <lb/>e. </s> <s xml:id="echoid-s13899" xml:space="preserve">{e c.</s> <s xml:id="echoid-s13900" xml:space="preserve">/r} ſoliditas vero = {1/2} {e e c x.</s> <s xml:id="echoid-s13901" xml:space="preserve">/r} & </s> <s xml:id="echoid-s13902" xml:space="preserve">momentum = {1/4} {e e c x x/r}, Cohæ. <lb/></s> <s xml:id="echoid-s13903" xml:space="preserve">rentia eſt 8 e<emph style="super">3</emph>. </s> <s xml:id="echoid-s13904" xml:space="preserve">proponitur vero <lb/>{1/4} b b c r + b p. </s> <s xml:id="echoid-s13905" xml:space="preserve">8 r<emph style="super">3</emph>:</s> <s xml:id="echoid-s13906" xml:space="preserve">: {1/4} {e e c x x.</s> <s xml:id="echoid-s13907" xml:space="preserve">/r} 8 e<emph style="super">3</emph>.</s> <s xml:id="echoid-s13908" xml:space="preserve">. <lb/>unde x = + {b b c e r + 4 b e p.</s> <s xml:id="echoid-s13909" xml:space="preserve">/c r r}</s> </p> </div> <div xml:id="echoid-div527" type="section" level="1" n="527"> <head xml:id="echoid-head639" xml:space="preserve">PROPOSITIO XLIX.</head> <p style="it"> <s xml:id="echoid-s13910" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13911" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13912" xml:space="preserve">fig. </s> <s xml:id="echoid-s13913" xml:space="preserve">37. </s> <s xml:id="echoid-s13914" xml:space="preserve">Dato Cylindro A B C D, cujus momentum <lb/>ex gravitate ſit ad Cohærentiam in quacunque ratione, ſupraquam-<lb/>libet datam baſin E F, ejusdem materiæ alium conſtruere cylin-<lb/>drum, cujus momentum ex gravitate habeat ad ſuam Cohærentiam <lb/>rationem eandem.</s> <s xml:id="echoid-s13915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13916" xml:space="preserve">Quantitatibus deſignatis iiſdem litteris ac in Prop. </s> <s xml:id="echoid-s13917" xml:space="preserve">XLVIII. </s> <s xml:id="echoid-s13918" xml:space="preserve">erit <lb/>momentum cylindri A B C D = {1/4} b b c r, & </s> <s xml:id="echoid-s13919" xml:space="preserve">momentum Cylindri <lb/>E F G H = {1/4} {c e e x x/r}. </s> <s xml:id="echoid-s13920" xml:space="preserve">Cohærentia baſeos A B ad E F, ut 8 r<emph style="super">3</emph> ad 8 e<emph style="super">3</emph>. <lb/></s> <s xml:id="echoid-s13921" xml:space="preserve">quare ordinanda eſt hæc proportio. </s> <s xml:id="echoid-s13922" xml:space="preserve"><lb/>{1/4} {c e e x x.</s> <s xml:id="echoid-s13923" xml:space="preserve">/r} 8 e<emph style="super">3</emph>:</s> <s xml:id="echoid-s13924" xml:space="preserve">: {1/4} b b c r. </s> <s xml:id="echoid-s13925" xml:space="preserve">8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13926" xml:space="preserve"><lb/>unde x = {e b b/r}</s> </p> </div> <div xml:id="echoid-div528" type="section" level="1" n="528"> <head xml:id="echoid-head640" xml:space="preserve">PROPOSITIO L.</head> <p style="it"> <s xml:id="echoid-s13927" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13928" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13929" xml:space="preserve">fig. </s> <s xml:id="echoid-s13930" xml:space="preserve">37. </s> <s xml:id="echoid-s13931" xml:space="preserve">Dato Cylindro A B C D, in quo gravitatis <lb/>momentum ad Cohærentiam habeat quamlibet rationem datam, <lb/>datâque qualibet longitudine E H, alium Cylindrum E F G H ipſi <lb/>applicare, in quo gravitatis momentum ad momentum Cohærentiæ <lb/>ſit in eademratione,</s> </p> <pb o="574" file="0590" n="591" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s13932" xml:space="preserve">Vocetur radius baſeos A B, r, peripheria c. </s> <s xml:id="echoid-s13933" xml:space="preserve">longitudo A D, b. </s> <s xml:id="echoid-s13934" xml:space="preserve">lon-<lb/>gitudo E H, l. </s> <s xml:id="echoid-s13935" xml:space="preserve">radius baſeos E F, x.</s> <s xml:id="echoid-s13936" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13937" xml:space="preserve">Erit cylindrus A B C D = {1/2} b c r. </s> <s xml:id="echoid-s13938" xml:space="preserve">& </s> <s xml:id="echoid-s13939" xml:space="preserve">momentum ejus = {1/4} b b c r. <lb/></s> <s xml:id="echoid-s13940" xml:space="preserve">Cohærentia 8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13941" xml:space="preserve">ut ſoliditas cylindri E F G H habeatur, pone <lb/>r.</s> <s xml:id="echoid-s13942" xml:space="preserve">c:</s> <s xml:id="echoid-s13943" xml:space="preserve">: x. </s> <s xml:id="echoid-s13944" xml:space="preserve">{c x.</s> <s xml:id="echoid-s13945" xml:space="preserve">/r} peripheria baſeos, unde {1/2} {c x x/r} = baſi, ſoliditas = {1/2} {c x x l.</s> <s xml:id="echoid-s13946" xml:space="preserve">/r} <lb/>& </s> <s xml:id="echoid-s13947" xml:space="preserve">momentum ex gravitate = {1/4} {c l l x x.</s> <s xml:id="echoid-s13948" xml:space="preserve">/r} Cohærentia baſeos E F uti <lb/>8 x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13949" xml:space="preserve">quarepoſtulatur proportio 8 x<emph style="super">3</emph>, {1/4} {c l l x x/r}:</s> <s xml:id="echoid-s13950" xml:space="preserve">: 8 r<emph style="super">3</emph>, {1/4} b b c r. </s> <s xml:id="echoid-s13951" xml:space="preserve"><lb/>unde x = {l l r/b b}</s> </p> </div> <div xml:id="echoid-div529" type="section" level="1" n="529"> <head xml:id="echoid-head641" xml:space="preserve">PROPOSITIO LI.</head> <p style="it"> <s xml:id="echoid-s13952" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13953" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s13954" xml:space="preserve">fig. </s> <s xml:id="echoid-s13955" xml:space="preserve">37. </s> <s xml:id="echoid-s13956" xml:space="preserve">Dato Cylindro A B C D & </s> <s xml:id="echoid-s13957" xml:space="preserve">pondere I, quo-<lb/>rum momenta ex gravitate ad Cohærentiam habeant quamcunque <lb/>rationem, invenire alium cylindrum datæ longitudinis, in quo mo-<lb/>mentum gravitatis ad ſuam Cohærentiam habeat eandem rationem.</s> <s xml:id="echoid-s13958" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13959" xml:space="preserve">Vocetur radius baſeos A B, r. </s> <s xml:id="echoid-s13960" xml:space="preserve">peripheria c. </s> <s xml:id="echoid-s13961" xml:space="preserve">longitudo A D, b. </s> <s xml:id="echoid-s13962" xml:space="preserve">pon-<lb/>dus I, p. </s> <s xml:id="echoid-s13963" xml:space="preserve">erit momentum Cylindri ex gravitate, una cum momento <lb/>ponderis I = {1/4} b b c r + p b. </s> <s xml:id="echoid-s13964" xml:space="preserve">Cohærentia ut 8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13965" xml:space="preserve">Vocetur E H, d. <lb/></s> <s xml:id="echoid-s13966" xml:space="preserve">radius baſeos E F, x. </s> <s xml:id="echoid-s13967" xml:space="preserve">erit ejus peripheria = {c x/r}. </s> <s xml:id="echoid-s13968" xml:space="preserve">baſis = {1/2} {c x x.</s> <s xml:id="echoid-s13969" xml:space="preserve">/r} & </s> <s xml:id="echoid-s13970" xml:space="preserve">ſo-<lb/>liditas = {1/2} {c d x x.</s> <s xml:id="echoid-s13971" xml:space="preserve">/r} unde momentum eſt = {1/4} {c d d x x.</s> <s xml:id="echoid-s13972" xml:space="preserve">/r} & </s> <s xml:id="echoid-s13973" xml:space="preserve">Cohæren-<lb/>tia ut 8 x<emph style="super">3</emph>. </s> <s xml:id="echoid-s13974" xml:space="preserve">hinc ſtabunt quantitates ordinatæ in proportionem <lb/>{1/4} {c d d x x,/r} 8 x<emph style="super">3</emph>:</s> <s xml:id="echoid-s13975" xml:space="preserve">: {1/4} b b c r + b p. </s> <s xml:id="echoid-s13976" xml:space="preserve">8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s13977" xml:space="preserve"><lb/>unde x ={{1/4} c d d r r.</s> <s xml:id="echoid-s13978" xml:space="preserve">/{1/4} b b c r + b p}</s> </p> <pb o="575" file="0591" n="592" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div530" type="section" level="1" n="530"> <head xml:id="echoid-head642" xml:space="preserve">PROPOSITIO LII.</head> <p style="it"> <s xml:id="echoid-s13979" xml:space="preserve">Tab. </s> <s xml:id="echoid-s13980" xml:space="preserve">XXV. </s> <s xml:id="echoid-s13981" xml:space="preserve">fig. </s> <s xml:id="echoid-s13982" xml:space="preserve">4. </s> <s xml:id="echoid-s13983" xml:space="preserve">& </s> <s xml:id="echoid-s13984" xml:space="preserve">6. </s> <s xml:id="echoid-s13985" xml:space="preserve">Sit priſma Triangulare A A B C D rectan-<lb/>gulum in B, & </s> <s xml:id="echoid-s13986" xml:space="preserve">horizontale, cujus latus planum A A B inferius & </s> <s xml:id="echoid-s13987" xml:space="preserve"><lb/>horizonti parallelum, angulus ſolidus C C ſuperior, erit Cohæren-<lb/>tia ejus reſpectiva ad eam parallelopipedi baſin A D B C duplo ma-<lb/>jorem habentis, uti ſumma omnium quadratorum linearum f f, <lb/>g g, h h, i i, B C perpendicularium in latus A B, ad ſummam <lb/>omnium quadratorum A D, f F, g G, h H, i i. </s> <s xml:id="echoid-s13988" xml:space="preserve">B C.</s> <s xml:id="echoid-s13989" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13990" xml:space="preserve">Sit latus A B diviſum in partes infinite parvas A f, f g, g h, h i, <lb/>i B: </s> <s xml:id="echoid-s13991" xml:space="preserve">concipiantur ductæ ex his omnibus punctis rectæ f f, g g, h h, <lb/>i i, B C, perpendiculares in A B; </s> <s xml:id="echoid-s13992" xml:space="preserve">completoque quadrato A D C B, <lb/>producantur rectæ uſque in F. </s> <s xml:id="echoid-s13993" xml:space="preserve">G, H, I, C; </s> <s xml:id="echoid-s13994" xml:space="preserve">erit Cohærentia rectæ <lb/>f f in Priſmate, ad Cohærentiam rectæ f F in parallelopipedo, in <lb/>ratione duplicata altitudinis f F ad altitudinem f F per Prop. </s> <s xml:id="echoid-s13995" xml:space="preserve">XXII. <lb/></s> <s xml:id="echoid-s13996" xml:space="preserve">eodem modo erit Cohærentia g g ad g G in ratione duplicata g g ad <lb/>g G, atque ita porro comparata erit Cohærentia aliarum rectarum <lb/>h h, i i, B C in Priſmate, ad Cohærentiam g G, h H, i I, B C in <lb/>parallelopipedo A D B C. </s> <s xml:id="echoid-s13997" xml:space="preserve">Quare uti ſumma quadratorum omnium <lb/>rectarum f f, g g, h h, i i, B C, ad ſummam omnium quadratorum <lb/>A D, f F, G g, H h, I i, C B, ita eſt Cohærentia reſpectiva Priſma-<lb/>tis Trigoni, ad Cohærentiam parallelopipedi, baſin planam A D B C <lb/>habentis duplo majorem.</s> <s xml:id="echoid-s13998" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s13999" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14000" xml:space="preserve">1. </s> <s xml:id="echoid-s14001" xml:space="preserve">Sed omnes rectæ f f, g g, h h, i i, B C infinite parvo in-<lb/>tervallo remotæ complent integrum Triangulum A B C, veluti eæ-<lb/>dem productæ uſque ad D, F, G, H I, C complent Quadratum A D <lb/>C B, quare erit Cohærentia Triangularis baſeos A B C, ad eam Qua-<lb/>dratæ baſeos A D B C, uti quadratum Trianguli A B C, ad quadra-<lb/>tum quadrati A D B C. </s> <s xml:id="echoid-s14002" xml:space="preserve">eſt vero Triangulum A B C dimidium qua-<lb/>drati A D B C, ſive uti 1 ad 2. </s> <s xml:id="echoid-s14003" xml:space="preserve">quorum quadrata ſunt uti 1 ad 4. <lb/></s> <s xml:id="echoid-s14004" xml:space="preserve">quare Cohærentia baſeos triangularis A B C erit ad Cohærentiam <lb/>baſeos A D B C, uti 1 ad 4.</s> <s xml:id="echoid-s14005" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14006" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14007" xml:space="preserve">2. </s> <s xml:id="echoid-s14008" xml:space="preserve">Si in fig. </s> <s xml:id="echoid-s14009" xml:space="preserve">6. </s> <s xml:id="echoid-s14010" xml:space="preserve">Angulus Priſmatis Triangularis D A C in-<lb/>ferne ponatur, & </s> <s xml:id="echoid-s14011" xml:space="preserve">latus planum D C ſuperius, erit Cohærentia re-<lb/>ſpectiva eadem Priſmatis A B C.</s> <s xml:id="echoid-s14012" xml:space="preserve"/> </p> <pb o="576" file="0592" n="593" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s14013" xml:space="preserve">Si enim C D fuerit diviſa quoque in partes infinite parvas C I, <lb/>I H, H G, G F, F D, veluti erat A B; </s> <s xml:id="echoid-s14014" xml:space="preserve">erit dimiſſa recta perpendi-<lb/>cularis Ii = ff. </s> <s xml:id="echoid-s14015" xml:space="preserve">Hh = gg. </s> <s xml:id="echoid-s14016" xml:space="preserve">Gg = Hh. </s> <s xml:id="echoid-s14017" xml:space="preserve">Ff = ii. </s> <s xml:id="echoid-s14018" xml:space="preserve">D A = C B. </s> <s xml:id="echoid-s14019" xml:space="preserve">adeoque <lb/>erunt harum æqualium Cohærentiæ æquales, ergo ſumma Cohæ-<lb/>rentiarum in A D C = ſummæ Cohærentiarum in ABC, ſive priſma <lb/>Trigonum poſitum ut A D E, erit æque cohærens ac priſma Trigo-<lb/>num poſitum ut A B C.</s> <s xml:id="echoid-s14020" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14021" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14022" xml:space="preserve">3. </s> <s xml:id="echoid-s14023" xml:space="preserve">Si ergo parallelopipedum A D B C foret bifariam ſectum <lb/>in duo priſmata Triangularia A D C, A B C, quæ ſeorſim poneren-<lb/>tur, uti in fig. </s> <s xml:id="echoid-s14024" xml:space="preserve">6. </s> <s xml:id="echoid-s14025" xml:space="preserve">jacent, duplo minus cohærerent, quam integrum <lb/>parallelopipedum A D C B.</s> <s xml:id="echoid-s14026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14027" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14028" xml:space="preserve">4. </s> <s xml:id="echoid-s14029" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14030" xml:space="preserve">25. </s> <s xml:id="echoid-s14031" xml:space="preserve">fig. </s> <s xml:id="echoid-s14032" xml:space="preserve">5 Adeoque detur quodlibet aliud priſma Tri-<lb/>gonum K L M, cujus baſis K M jaceat horizontaliter, habebit Cohæ-<lb/>rentiam adeam parallelopipedi ejusdem baſeos & </s> <s xml:id="echoid-s14033" xml:space="preserve">æque alti K S R M, <lb/>uti 1 ad 4. </s> <s xml:id="echoid-s14034" xml:space="preserve">nam ducta perpendiculari L P ſupra K M, tranſeunte per <lb/>angulum K L M, erit K L P trigonum, uti A B C in fig. </s> <s xml:id="echoid-s14035" xml:space="preserve">6. </s> <s xml:id="echoid-s14036" xml:space="preserve">& </s> <s xml:id="echoid-s14037" xml:space="preserve">quadran-<lb/>gulum P K S L eſt veluti in fig. </s> <s xml:id="echoid-s14038" xml:space="preserve">6. </s> <s xml:id="echoid-s14039" xml:space="preserve">A B C D. </s> <s xml:id="echoid-s14040" xml:space="preserve">ita eſt L P M trigonum & </s> <s xml:id="echoid-s14041" xml:space="preserve"><lb/>L P M R quadrangulum: </s> <s xml:id="echoid-s14042" xml:space="preserve">eſt autem Cohærentia Trianguli K L P ad <lb/>eam quadranguli K S L P, uti 1 ad 4. </s> <s xml:id="echoid-s14043" xml:space="preserve">& </s> <s xml:id="echoid-s14044" xml:space="preserve">ita Cohærentia Trigoni L P M, <lb/>ad eam quadranguli P L R M uti 1 ad 4: </s> <s xml:id="echoid-s14045" xml:space="preserve">quare erit Cohærentia prisma-<lb/>tis, cujus baſis eſt Triangulum K L M, ad Cohærentiam parallelo-<lb/>pipedi, cujus baſis eſt quadrangulum K S R M, veluti 1 ad 4.</s> <s xml:id="echoid-s14046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14047" xml:space="preserve">Hanc propoſitionem Experientiæ ſubmittendam eſſe cenſui, ut <lb/>conſtaret, an vera quoque hoc modo foret, an aliquid adhuc la-<lb/>teret, quoniam prima fronte paradoxa apparet.</s> <s xml:id="echoid-s14048" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div531" type="section" level="1" n="531"> <head xml:id="echoid-head643" xml:space="preserve">EXPERIMENTUM CLXXXV.</head> <p> <s xml:id="echoid-s14049" xml:space="preserve">Ex ſpeculo optimi vitri exſciſſa fuit lamella ſesquipedem longa, <lb/>quæ deinde bifariam frangebatur: </s> <s xml:id="echoid-s14050" xml:space="preserve">ex una portione formatum fuit <lb/>priſma Triangulare, veluti eſt KLM in fig. </s> <s xml:id="echoid-s14051" xml:space="preserve">5. </s> <s xml:id="echoid-s14052" xml:space="preserve">cujus quodlibet la-<lb/>tus fuit accuratiſſime, o, 2, pollicis rhenol: </s> <s xml:id="echoid-s14053" xml:space="preserve">ex altera portione præ-<lb/>paratum fuit parallelopipedum rectangulum, veluti eſt K S R M, <lb/>cujus duo latera parallela, K M, S R erant quoque o, 2, pollic. </s> <s xml:id="echoid-s14054" xml:space="preserve">alia <lb/>K S, M R erant perfecte ejusdem altitudinis ac priſma K L M. </s> <s xml:id="echoid-s14055" xml:space="preserve">ut <lb/>partes accuratiſſimæ haberentur, quæ Experimentis inſervirent, <pb o="577" file="0593" n="594" rhead="CORPORUM FIRMORUM."/> amputatæ fuerunt extremitates, manſeruntque longitudines modo, <lb/>7 pollicum. </s> <s xml:id="echoid-s14056" xml:space="preserve">Tum ne â tremoribus ſoli, excitatis ab equis, curru-<lb/>bus, aut hominibus Experimenta turbarentur, in tempus delata ſunt <lb/>nocturnum: </s> <s xml:id="echoid-s14057" xml:space="preserve">Priſma Triangulare immiſſum fuit foramini inſculpto <lb/>Ligno Quercico, cui accuratiſſime congruebat, cujus baſis quo-<lb/>que erat horizontalis; </s> <s xml:id="echoid-s14058" xml:space="preserve">facto Experimento, ponderata fuit pars pris-<lb/>matis, quæ prominebat antea, ponduſque hoc ex centro gravitatis <lb/>ſuſpenſum fuiſſe conſiderabatur, ut momenti haberetur ratio: </s> <s xml:id="echoid-s14059" xml:space="preserve">even-<lb/>tus hi fuerunt in Priſmate Trigono.</s> <s xml:id="echoid-s14060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14061" xml:space="preserve">1°. </s> <s xml:id="echoid-s14062" xml:space="preserve">Ad diſtantiam 3 pollicum Rhenol. </s> <s xml:id="echoid-s14063" xml:space="preserve">â foraminis orâ fractum <lb/>fuit priſma a granis medicis 4219.</s> <s xml:id="echoid-s14064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14065" xml:space="preserve">2°. </s> <s xml:id="echoid-s14066" xml:space="preserve">In alio tentamine ad eandem diſtantiam a foraminis orâ ge-<lb/>ſtare tantum potuit 4204.</s> <s xml:id="echoid-s14067" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14068" xml:space="preserve">3°. </s> <s xml:id="echoid-s14069" xml:space="preserve">In tertio tentamine ad eandem diſtantiam â foraminis ora <lb/>rumpebatur a granis 4200.</s> <s xml:id="echoid-s14070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14071" xml:space="preserve">4°. </s> <s xml:id="echoid-s14072" xml:space="preserve">Ad diſtantiam 4 pollic. </s> <s xml:id="echoid-s14073" xml:space="preserve">Rhenol: </s> <s xml:id="echoid-s14074" xml:space="preserve">a foraminis orâ geſtavit non <lb/>plus, quam 3169 grana.</s> <s xml:id="echoid-s14075" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14076" xml:space="preserve">5°. </s> <s xml:id="echoid-s14077" xml:space="preserve">In repetito tentamine ad eandem diſtantiam 4 pollic. </s> <s xml:id="echoid-s14078" xml:space="preserve">Rhenol: <lb/></s> <s xml:id="echoid-s14079" xml:space="preserve">tulit 3180 grana.</s> <s xml:id="echoid-s14080" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14081" xml:space="preserve">Firmitatis diſcrepantiam candide memorare malui quam ſilere, <lb/>videtur aliquomodo pendere ab arctiori vel laxiori complexu fora-<lb/>minis, cui vitrum immiſſum fuit; </s> <s xml:id="echoid-s14082" xml:space="preserve">forte quoque a profundiori in-<lb/>tromiſſione: </s> <s xml:id="echoid-s14083" xml:space="preserve">forte non eſt æque cohærens in omni parte vitrum: <lb/></s> <s xml:id="echoid-s14084" xml:space="preserve">Tranſeamus ad Experimenta cum parallelopipedo facta, hoc im-<lb/>miſſum fuit foramini quadrangulari in Ligno Quercico, atque ſem-<lb/>per obſervatum fuit; </s> <s xml:id="echoid-s14085" xml:space="preserve">ut latus K M eſſet interius, atque horizonti pa-<lb/>rallelum, tum habita quoque fuit ratio momenti ex gravitate propriâ.</s> <s xml:id="echoid-s14086" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14087" xml:space="preserve">6°. </s> <s xml:id="echoid-s14088" xml:space="preserve">Parallelopipedum ad diſtantiam 4 pollicum a foramine fra-<lb/>ctum fuit a granis 13293.</s> <s xml:id="echoid-s14089" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14090" xml:space="preserve">7°. </s> <s xml:id="echoid-s14091" xml:space="preserve">Tentamen repetitum dedit grana 13279.</s> <s xml:id="echoid-s14092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14093" xml:space="preserve">8°. </s> <s xml:id="echoid-s14094" xml:space="preserve">Ad diſtantiam 3 pollicum a foramine fractum fuit â granis <lb/>17708.</s> <s xml:id="echoid-s14095" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14096" xml:space="preserve">Sunt hæc omnia Experimenta accuratiſſime inſtituta, omnium-<lb/>que circumſtantiarum cura fuit habita, ita ut tuto iis fidere quea-<lb/>mus: </s> <s xml:id="echoid-s14097" xml:space="preserve">comparemus igitur Cohærentiam priſmatis & </s> <s xml:id="echoid-s14098" xml:space="preserve">parallelopipedi: <lb/></s> <s xml:id="echoid-s14099" xml:space="preserve">Priſma in Exp. </s> <s xml:id="echoid-s14100" xml:space="preserve">1°. </s> <s xml:id="echoid-s14101" xml:space="preserve">ad diſtantiam 3 pollic: </s> <s xml:id="echoid-s14102" xml:space="preserve">fractum fuit a granis 4219.</s> <s xml:id="echoid-s14103" xml:space="preserve"> <pb o="578" file="0594" n="595" rhead="INTRODUCTIO AD COHÆRENTIAM"/> parallelopipedum in Exp. </s> <s xml:id="echoid-s14104" xml:space="preserve">VIII. </s> <s xml:id="echoid-s14105" xml:space="preserve">etiam ad diſtantiam 3 pollic: </s> <s xml:id="echoid-s14106" xml:space="preserve">fractum <lb/>fuit a granis 17708. </s> <s xml:id="echoid-s14107" xml:space="preserve">Sunt vero hæ quantitates in hac proportione, <lb/>4219. </s> <s xml:id="echoid-s14108" xml:space="preserve">17708:</s> <s xml:id="echoid-s14109" xml:space="preserve">: 1, 4 {822/4219}.</s> <s xml:id="echoid-s14110" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14111" xml:space="preserve">Priſma in Exp V. </s> <s xml:id="echoid-s14112" xml:space="preserve">fractum fuit ad diſtantiam 4 pollicum a fora-<lb/>mine, pondere 3180 granorum: </s> <s xml:id="echoid-s14113" xml:space="preserve">parallelopipedum ad eandem di-<lb/>ſtantiam fractum fuit in Exp. </s> <s xml:id="echoid-s14114" xml:space="preserve">VII. </s> <s xml:id="echoid-s14115" xml:space="preserve">a granis 13279. </s> <s xml:id="echoid-s14116" xml:space="preserve">ſunt hæ quan-<lb/>titates in hac proportione 3180. </s> <s xml:id="echoid-s14117" xml:space="preserve">13279:</s> <s xml:id="echoid-s14118" xml:space="preserve">: 1, 4 {559/3180}.</s> <s xml:id="echoid-s14119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14120" xml:space="preserve">Ex quibus Experimentis liquet manifeſto, Cohærentiam priſmatis <lb/>K L M, eſſe ad eam parallelopipedi K S R M, uti 1 ad 4. </s> <s xml:id="echoid-s14121" xml:space="preserve">nam fractio-<lb/>nes in hiſce Experimentis ſunt negligendæ, quia a minimis circum-<lb/>ſtantiis oriuntur.</s> <s xml:id="echoid-s14122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14123" xml:space="preserve">Reſpondebant ita calculo Experimenta cum materia rigida in-<lb/>ſtituta, explorandum erat an corpora flexilia eodem modo ſeſe ha-<lb/>berent: </s> <s xml:id="echoid-s14124" xml:space="preserve">adeoque factum eſt ex Ligno Quercico parallelopipedum, <lb/>cujus altitudo K S in Tab. </s> <s xml:id="echoid-s14125" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14126" xml:space="preserve">fig. </s> <s xml:id="echoid-s14127" xml:space="preserve">5. </s> <s xml:id="echoid-s14128" xml:space="preserve">erat 0, 11 pollic: </s> <s xml:id="echoid-s14129" xml:space="preserve">latitudo <lb/>K M 0, 22 pollic. </s> <s xml:id="echoid-s14130" xml:space="preserve">hujus extremo uno immiſſo foramini quadrato, <lb/>alteri prominenti 7 pollicibus appendi potuerunt ponduſcula, quo-<lb/>rum ſumma ſimul cum momento propriæ gravitatis erat 8429 gra-<lb/>norum, tum valde inflexum ruptum fuit,</s> </p> <p> <s xml:id="echoid-s14131" xml:space="preserve">Deinde ex eodem Ligno factum eſt Priſma Trigonum K L M, cu-<lb/>juslatitudo K M erat 0, 22 pollic: </s> <s xml:id="echoid-s14132" xml:space="preserve">altitudo L P 0, 11 pollic: </s> <s xml:id="echoid-s14133" xml:space="preserve">cujus, poſt-<lb/>quam foramini immiſſum erat, extremo eminenti 7 pollicibus appen-<lb/>di potuerunt grana 3109 habita ratione momenti gravitatis, ſed ma-<lb/>gis inflexum fuit, quam parallelopipedum, antequam frangebatur.</s> <s xml:id="echoid-s14134" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14135" xml:space="preserve">Abludit hoc Experimentum a demonſtratione in Propoſitione ex-<lb/>hibita, nam Priſma tantum ferre debuiſſet grana 2107. </s> <s xml:id="echoid-s14136" xml:space="preserve">ſi ejus Co-<lb/>hærentia quadruplo minor illâ Parallelopipedi fuiſſet: </s> <s xml:id="echoid-s14137" xml:space="preserve">Oritur hæc <lb/>aberratio a majori flexilitate Priſmatis, tenuioris ſubſtantiæ quam <lb/>parallelopipedum eſt, hinc antequam frangitur plus inflectitur, <lb/>ſed multo plus ponderis gerit.</s> <s xml:id="echoid-s14138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14139" xml:space="preserve">Confeci aliud parallelopipedum ex Ligno Quercico, cujus latitudo <lb/>K M 0, 20 pollic: </s> <s xml:id="echoid-s14140" xml:space="preserve">altitudo PM o, 10 pollic. </s> <s xml:id="echoid-s14141" xml:space="preserve">quod foramini immiſ-<lb/>ſum quadrato, ab extremitate prominente 5 pollic: </s> <s xml:id="echoid-s14142" xml:space="preserve">geſſit una cum <lb/>ſuo pondere 6929 grana, tum valde inflexum fractum fuit.</s> <s xml:id="echoid-s14143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14144" xml:space="preserve">Ex eodem parallelopipedo fabrefactum eſt Priſma Trigonum <lb/>K L M. </s> <s xml:id="echoid-s14145" xml:space="preserve">quod etiam 5 pollic: </s> <s xml:id="echoid-s14146" xml:space="preserve">extra foramen prominebat, cujus al- <pb o="579" file="0595" n="596" rhead="CORPORUM FIRMORUM."/> teri extremo appendi potuerunt 2405 grana, addito proprio pondere, <lb/>ſed plus inflexum, quam parallelopipedum, ruptum fuit: </s> <s xml:id="echoid-s14147" xml:space="preserve">In quo Ex-<lb/>perimento iterum â demonſtratione datur deviatio, nam ſecundum <lb/>illam modo ferre debuiſſet 1732 grana. </s> <s xml:id="echoid-s14148" xml:space="preserve">Ex hiſce diſcimus quanta <lb/>cum prudentia Geometricæ demonſtrationes ſint applicandæ cor-<lb/>poribus. </s> <s xml:id="echoid-s14149" xml:space="preserve">cum, quæ conveniunt uni corporum generi, in altero ob <lb/>alias conditiones non tam accurate locum habere videantur.</s> <s xml:id="echoid-s14150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14151" xml:space="preserve">Conatus fui priſma Trigonum A B C. </s> <s xml:id="echoid-s14152" xml:space="preserve">fig. </s> <s xml:id="echoid-s14153" xml:space="preserve">6. </s> <s xml:id="echoid-s14154" xml:space="preserve">ex Ligno conficere, <lb/>ejuſque Cohærentiam cum parallelopipedo A B C D duplo craſſiori <lb/>comparare; </s> <s xml:id="echoid-s14155" xml:space="preserve">ſed priſma immiſſum foramini Triangulari ab appenſo <lb/>pondere non modo inflectebatur, ſed quoque invertebatur, ut la-<lb/>tus A C evaſerit ſupremum, angulus ſolidus A B C infimus, quare <lb/>cum ejuſmodi corpore accurata tentamina capi non potuerunt; <lb/></s> <s xml:id="echoid-s14156" xml:space="preserve">atque ejuſmodi inverſio non niſi difficillime præcaveri potuiſſet.</s> <s xml:id="echoid-s14157" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div532" type="section" level="1" n="532"> <head xml:id="echoid-head644" xml:space="preserve">PROPOSITIO LIII.</head> <p style="it"> <s xml:id="echoid-s14158" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14159" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14160" xml:space="preserve">fig. </s> <s xml:id="echoid-s14161" xml:space="preserve">7. </s> <s xml:id="echoid-s14162" xml:space="preserve">Cohærentia reſpectiva parallelopipedi eſt ad <lb/>Cohærentiam Cylindri inſcripti ex eadem materia, uti ſumma qua-<lb/>dratorum factorum â diametro, ad ſummam totidem quadrato-<lb/>rum factorum â Chordis.</s> <s xml:id="echoid-s14163" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14164" xml:space="preserve">Sit circulus diametri C D baſis cylindri muro infixi, concipia-<lb/>tur C D diviſa in partes infinite parvas, per quas traoſeant rectæ, <lb/>quæ ſint chordæ circuli, uti oo, pp. </s> <s xml:id="echoid-s14165" xml:space="preserve">circa circulum deſcribatur <lb/>quadratum A B E F, in cujus lateribus A B, E F terminentur pro-<lb/>ductiones chordarum, erunt totidem rectæ G G, H H, L L, II, <lb/>K K, quot ſunt chordæ: </s> <s xml:id="echoid-s14166" xml:space="preserve">Quando autem rumpitur baſis in fora-<lb/>mine, fit cujuslibet chordæ motus circa punctum aliquod in cir-<lb/>cumferentiâ C L D, adeoque erit Cohærentia reſpectiva chordæ <lb/>O O ad Cohærentiam rectæ G G in quadrato, in ratione dupli-<lb/>cata O O ad G G per Propoſ: </s> <s xml:id="echoid-s14167" xml:space="preserve">XXII. </s> <s xml:id="echoid-s14168" xml:space="preserve">atque ita Cohærentia chor-<lb/>dæ pp erit ad eam rectæ reſpondentis H H in ratione duplicata pp <lb/>ad H H, cumque id obtineat in omnibus aliis chordis earumque <lb/>productionibus, quæ cunctæ ſemper ſunt æquales diametro, erit <lb/>ſumma Cohærentiæ baſeos in cylindro, ad ſummam Cohærentiæ <lb/>quadratæ baſeos ex parallelopipedo, uti ſunt quadrata omnium <pb o="580" file="0596" n="597" rhead="INTRODUCTIO AD COHÆRENTIAM"/> chordarum in circulo, ad quadrata totidem diametrorum.</s> <s xml:id="echoid-s14169" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14170" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14171" xml:space="preserve">1. </s> <s xml:id="echoid-s14172" xml:space="preserve">Poſitis chordis circuli infinite tenuibus, omnes comple-<lb/>bunt circulum C L D L, atque omnes rectæ reſpondentes, uti A E, <lb/>G G, H H &</s> <s xml:id="echoid-s14173" xml:space="preserve">c. </s> <s xml:id="echoid-s14174" xml:space="preserve">complebunt quadratum, quare Cohærentiæ cir-<lb/>cularis baſeos aut quadratæ A E F B, forent inter ſe, uti quadratum <lb/>circuli, ad quadratum quadrati A E F B. </s> <s xml:id="echoid-s14175" xml:space="preserve">Eſt autem circulus ad qua <lb/>dratum circumſcriptum proxime, uti 157 ad 200, quornm quadrata <lb/>ſunt 24649 & </s> <s xml:id="echoid-s14176" xml:space="preserve">40000, ſecundum quam proportionem Cohærentiæ <lb/>cylindrorum parallelopipedis inſcriptorum & </s> <s xml:id="echoid-s14177" xml:space="preserve">æque longorum inve-<lb/>niendæ eſſent: </s> <s xml:id="echoid-s14178" xml:space="preserve">non tamen obſervantur in Experientiis huic propor-<lb/>tioni reſpondere Ligna; </s> <s xml:id="echoid-s14179" xml:space="preserve">an eveniat ob fibrarum flexibilitatem; <lb/></s> <s xml:id="echoid-s14180" xml:space="preserve">velut in Propoſitione præcedenti monui; </s> <s xml:id="echoid-s14181" xml:space="preserve">an ob aliam cauſam? </s> <s xml:id="echoid-s14182" xml:space="preserve"><lb/>nondum mihi conſtat.</s> <s xml:id="echoid-s14183" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14184" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14185" xml:space="preserve">2. </s> <s xml:id="echoid-s14186" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14187" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14188" xml:space="preserve">fig. </s> <s xml:id="echoid-s14189" xml:space="preserve">8. </s> <s xml:id="echoid-s14190" xml:space="preserve">Si fuiſſet corpus ejusdem longitudi-<lb/>nis & </s> <s xml:id="echoid-s14191" xml:space="preserve">materiæ ac Cylindrus, cujus baſis eſſet Ellipſis Z C X D, atque <lb/>axis Ellipſeos minor C D horizontalis, X Z axis major perpendicula-<lb/>ris, productis chordis circuli oo, pp, uſque in Ellipſeos peripheriam r r, <lb/>s s. </s> <s xml:id="echoid-s14192" xml:space="preserve">atque ita porro omnibus; </s> <s xml:id="echoid-s14193" xml:space="preserve">erit Cohærentiarum ſumma in circulo, ad <lb/>eam in Ellipſi, uti quadrata chordarum oo, pp, ad quadrata ordina-<lb/>tarum in Ellipſi rr, ss: </s> <s xml:id="echoid-s14194" xml:space="preserve">ſive ut quadratum areæ circularis, ad qua-<lb/>dratum areæ Ellipticæ: </s> <s xml:id="echoid-s14195" xml:space="preserve">ſed eſt area circularis ad ellipticam, uti dia-<lb/>meter circuli C D, ad axin majorem ellipſeos X Z quare erit Co-<lb/>hærentia circuli ad eam ellipſeos, uti <emph style="ol">C D</emph><emph style="super">q</emph> ad <emph style="ol">X Z</emph><emph style="super">q</emph>.</s> <s xml:id="echoid-s14196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14197" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14198" xml:space="preserve">3. </s> <s xml:id="echoid-s14199" xml:space="preserve">Circumſcripto circa Ellipſin C X D Z rectangulo, quod <lb/>ſit baſis parallelopipedi, erit Cohærentia baſeos Ellipticæ, ad eam <lb/>parallelopipedi, in ratione eadem ac Cohærentia baſeos circularis, <lb/>ad eam quadrati circumſcripti.</s> <s xml:id="echoid-s14200" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14201" xml:space="preserve">Nam eſt parallelogrammum Ellipſi circumſcriptum ad aream El-<lb/>lipſeos, uti quadratum circulo circumſcriptum ad aream circuli: <lb/></s> <s xml:id="echoid-s14202" xml:space="preserve">ſed eſt Cohærentia parallelogrammi circa Ellipſin ad Cohærentiam <lb/>Ellipſeos, uti quadrata productarum ordinatarum in ſua latera, ad <lb/>ordinatarum in Ellipſi quadrata, & </s> <s xml:id="echoid-s14203" xml:space="preserve">quia ordinatæ infinitæ implent <lb/>tandem aream Ellipſeos, uti & </s> <s xml:id="echoid-s14204" xml:space="preserve">productiones earum parallelogram-<lb/>mum, erunt Cohærentiæ uti quadrata arearum; </s> <s xml:id="echoid-s14205" xml:space="preserve">& </s> <s xml:id="echoid-s14206" xml:space="preserve">quia areæ ſunt <lb/>proportionales areis quadrati & </s> <s xml:id="echoid-s14207" xml:space="preserve">circuli huic inſcripti, & </s> <s xml:id="echoid-s14208" xml:space="preserve">harum <lb/>Cohærentiæ uti quadrata arearum, erit Cohærentia parallelogrammi <pb o="581" file="0597" n="598" rhead="CORPORUM FIRMORUM."/> circa Ellipſin, ad Cohærentiam Ellipſeos, in eadem ratione, ac <lb/>Cohærentia quadrati circa circulum, ad Cohærentiam circuli.</s> <s xml:id="echoid-s14209" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div533" type="section" level="1" n="533"> <head xml:id="echoid-head645" xml:space="preserve">PROPOSITIO LIV.</head> <p style="it"> <s xml:id="echoid-s14210" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14211" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14212" xml:space="preserve">fig. </s> <s xml:id="echoid-s14213" xml:space="preserve">9. </s> <s xml:id="echoid-s14214" xml:space="preserve">Sit dimidiati Cylindri ſegmentum A B C D E, <lb/>cujus baſis rectangula A B C applicata parieti perpendiculari ad <lb/>horizontem: </s> <s xml:id="echoid-s14215" xml:space="preserve">ſit parallelopipedum A B C E L M N, cujus baſis pla-<lb/>na A B C rectangula æqualis baſi Cylindrici ſegmenti, latus A B, <lb/>æquale A B, B C æquale B C, A E æquale radio D E in Cylindro, <lb/>erit momentum gravitatis in ſegmento Cylindrico ad momentum gra-<lb/>vitatis in parallelopipedo, uti duo ad tria.</s> <s xml:id="echoid-s14216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14217" xml:space="preserve">Ponatur radius A D = r. </s> <s xml:id="echoid-s14218" xml:space="preserve">peripheria circuli baſeos = p. </s> <s xml:id="echoid-s14219" xml:space="preserve">Iatitudo <lb/>B C = a.</s> <s xml:id="echoid-s14220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14221" xml:space="preserve">Erit area dimidii circuli A D B E A = {1/4} r p, quæ ducta in latitu-<lb/>dinem B C = a, dat ſoliditatem ſegmenti Cylindrici A B C A = {1/4} a p r. <lb/></s> <s xml:id="echoid-s14222" xml:space="preserve">centrum vero gravitatis in ſemicirculo diſtat a centro D circuli quanti-<lb/>tate {8rr/3p}. </s> <s xml:id="echoid-s14223" xml:space="preserve">in quam diſtantiam ducta ſoliditas, dat momentum <lb/>= {2/3} ar<emph style="super">3.</emph></s> </p> <p> <s xml:id="echoid-s14224" xml:space="preserve">Soliditas parallelopipedi A B C E L M N eſt = 2 arr, hujus cen-<lb/>trum gravitatis eſt in medio, cujus directio tranſit per {1/2} A E = {1/2} r. <lb/></s> <s xml:id="echoid-s14225" xml:space="preserve">adeoque erit momentum parallelopipedi = {1/2} r X 2 arr = ar<emph style="super">3</emph>.</s> <s xml:id="echoid-s14226" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14227" xml:space="preserve">Eſt igitur momentum gravitatis in ſegmento cylindrico ad illud <lb/>in parallelopipedo:</s> <s xml:id="echoid-s14228" xml:space="preserve">, {2/3} ar<emph style="super">3</emph>. </s> <s xml:id="echoid-s14229" xml:space="preserve">ar<emph style="super">3</emph>:</s> <s xml:id="echoid-s14230" xml:space="preserve">: 2,3.</s> <s xml:id="echoid-s14231" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14232" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14233" xml:space="preserve">1. </s> <s xml:id="echoid-s14234" xml:space="preserve">Si ergo ex latere B C parallelopipedi abſcindatur {1/3}pars, <lb/>per quam tranſeat ſegmentum parallelum ad ſuperficiem anteriorem <lb/>A B N M, erit momentum ex gravitate in parte reſidua parallelo-<lb/>pipedi æquale momento ſegmenti cylindrici = {2/3} ar<emph style="super">3</emph>.</s> <s xml:id="echoid-s14235" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14236" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14237" xml:space="preserve">2. </s> <s xml:id="echoid-s14238" xml:space="preserve">Ut vero a parallelopipedo A B C L M N abſcindatur <lb/>pars, reliquumque habeat idem momentum gravitatis ac dimidia-<lb/>tus cylindrus, quæratur inter A M = r, ipſiuſque {2/3} partem media <lb/>proportionalis, quæ ſit = A O. </s> <s xml:id="echoid-s14239" xml:space="preserve">tum per O K tranſeat ſegmentum <lb/>parallelum baſi A B C, habebit parallelopipedum A B C O K idem <lb/>gravitatis momentum, quod dimidiatus cylindrus; </s> <s xml:id="echoid-s14240" xml:space="preserve">vocetur enim <lb/>A O, x, erit ſoliditas parallelopipedi A B C K O = 2 arx. </s> <s xml:id="echoid-s14241" xml:space="preserve">ejuſque <pb o="582" file="0598" n="599" rhead="INTRODUCTIO AD COHÆRENTIAM"/> momentum = arxx. </s> <s xml:id="echoid-s14242" xml:space="preserve">quod ponatur æquale momento dimidiati <lb/>cylindri {<emph style="ol">2</emph>/3} ar<emph style="super">3</emph>. </s> <s xml:id="echoid-s14243" xml:space="preserve">utraque quantitate diviſa per ar, remanet {2/3} rr = xx. <lb/></s> <s xml:id="echoid-s14244" xml:space="preserve">unde {2/3} r. </s> <s xml:id="echoid-s14245" xml:space="preserve">x:</s> <s xml:id="echoid-s14246" xml:space="preserve">: x.</s> <s xml:id="echoid-s14247" xml:space="preserve">r. </s> <s xml:id="echoid-s14248" xml:space="preserve">cum igitur A O ſit = x, mediæ proportionali <lb/>inter {2/3} r & </s> <s xml:id="echoid-s14249" xml:space="preserve">r. </s> <s xml:id="echoid-s14250" xml:space="preserve">habebit parallelopipedum A B C K O idem momentum <lb/>gravitatis, quod dimidiatus cylindrus.</s> <s xml:id="echoid-s14251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14252" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14253" xml:space="preserve">3. </s> <s xml:id="echoid-s14254" xml:space="preserve">Si, adb, fuerit chorda circuli, cujus arcus, a E b, vo-<lb/>cetur {p/e}, & </s> <s xml:id="echoid-s14255" xml:space="preserve">chorda, a d b = c. </s> <s xml:id="echoid-s14256" xml:space="preserve">etiam cognoſcetur ſinus verſus <lb/>dE, qui ſit = k. </s> <s xml:id="echoid-s14257" xml:space="preserve">ductis rectis D b, Da, erit Sector circuli D b E a <lb/>= {pr/2e}. </s> <s xml:id="echoid-s14258" xml:space="preserve">ſed Triangulum D b a, eſt {1/2} cr - {1/2} ck, quo ſubducto ex Se-<lb/>ctore {pr/2e}, remanet area, a d b E a = {pr/2e}-{<emph style="ol">1</emph>/2} cr + {1/2} ck, quæ <lb/>multiplicata per B C = a, dabitSolidum a d b fe a = {apr/2e}+{1/2}ack-{1/2}acr. <lb/></s> <s xml:id="echoid-s14259" xml:space="preserve">Centrum vero gravitatis in Segmento b Ead, diſtat a centro D, in recta <lb/>D E = {cek.</s> <s xml:id="echoid-s14260" xml:space="preserve">/3p-3ce} adeoque cum Dd ſit = r-k, diſtabit â d quan-<lb/>titate {cek/3p+3ce}-r+k, quæ diſtantia ducta in magnitudinem ab d E e f, <lb/>dabitmomentum ex gravitate ={apr/2e}+{1/2}ack-{1/2}acrX{cek/3p-3ce} <lb/>{/-r+k.</s> <s xml:id="echoid-s14261" xml:space="preserve">}</s> </p> </div> <div xml:id="echoid-div534" type="section" level="1" n="534"> <head xml:id="echoid-head646" xml:space="preserve">PROPOSITIO LV.</head> <p style="it"> <s xml:id="echoid-s14262" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14263" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14264" xml:space="preserve">fig. </s> <s xml:id="echoid-s14265" xml:space="preserve">10. </s> <s xml:id="echoid-s14266" xml:space="preserve">Sit parallelopipedum, conſideratum abſque <lb/>gravitate, ope diagonalis bifariam ſectum in duo priſmata, quo-<lb/>rum unum ſit C A B M N, cujus latus unum A M horizonti paral-<lb/>lelum ponatur, baſis C A B muro, ad horizontem perpendiculari, <lb/>affixa, pondus, æquabiliter ſupra latus A M diſper ſum, habebit ad <lb/>Cohærentiam baſeos A B C eandem rationem, quam pondus incum-<lb/>bens parti a M, habet ad Cobærentiam ſuæ baſeos, abc, ubicunque <lb/>baſis, abc, ponatur.</s> <s xml:id="echoid-s14267" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14268" xml:space="preserve">Concipiatur fluidum grave æquabiliter impoſitum plano A M ad <pb o="583" file="0599" n="600" rhead="CORPORUM FIRMORUM."/> eandem altitudinem, erit quantitas ejus ſupra A M ad quantitatem ſu-<lb/>pra, a M, uti eſt A M, ad, aM, hoc eſt uti A N, ad, aN. </s> <s xml:id="echoid-s14269" xml:space="preserve">cum vero centrum <lb/>gravitatis fluidi ſupra A M ab A B ſit ad eam ſupra, a M ab ab, uti eſt <lb/>A N ad, a N, erit momentum fluidi ſupra A M ad momentum fluidi <lb/>ſupra, a N, uti eſt A N<emph style="super">q</emph> ad a N. </s> <s xml:id="echoid-s14270" xml:space="preserve">ſed propter Triangula ſimilia C A N, <lb/>ca N, eſt A N ad, a N:</s> <s xml:id="echoid-s14271" xml:space="preserve">: A C, a c. </s> <s xml:id="echoid-s14272" xml:space="preserve">erit A N <emph style="super">q</emph> a N <emph style="super">q</emph>:</s> <s xml:id="echoid-s14273" xml:space="preserve">: A C <emph style="super">q</emph>. </s> <s xml:id="echoid-s14274" xml:space="preserve">a c<emph style="super">q</emph>. <lb/></s> <s xml:id="echoid-s14275" xml:space="preserve">eſt autem Cohærentia baſeos C A B = C A<emph style="super">q</emph> X A B, & </s> <s xml:id="echoid-s14276" xml:space="preserve">Cohærentia <lb/>baſeos c a b = c a<emph style="super">q</emph> X a b. </s> <s xml:id="echoid-s14277" xml:space="preserve">quæ ambæ quantitatesſunt inter ſeuti C A<emph style="super">q</emph> <lb/>ad c a<emph style="super">q</emph>. </s> <s xml:id="echoid-s14278" xml:space="preserve">quare momenta gravitatis fluidi impoſiti plano A M, a M, <lb/>ſunt inter ſe, uti Cohærentiæ baſium C A B, c a b.</s> <s xml:id="echoid-s14279" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div535" type="section" level="1" n="535"> <head xml:id="echoid-head647" xml:space="preserve">PROPOSITIO LVI.</head> <p style="it"> <s xml:id="echoid-s14280" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14281" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14282" xml:space="preserve">fig. </s> <s xml:id="echoid-s14283" xml:space="preserve">10. </s> <s xml:id="echoid-s14284" xml:space="preserve">Si idem priſma A B C M N concipiatur di-<lb/>viſum ſectione, cab, parallela baſi C A B, erit momentum ex gra-<lb/>vitate prismatis C A B M N ad momentum ex gravitate prismatis, <lb/>c a b M N, uti cubus altitudinis A C ad cubum altitudinis, a c, & </s> <s xml:id="echoid-s14285" xml:space="preserve"><lb/>Cohærentia prismatis C A B M N ad eam, cab M N, uti quadratum <lb/>altitudinis A C, ad quadratum altitudinis, ac.</s> <s xml:id="echoid-s14286" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14287" xml:space="preserve">Concipiatur nunc priſma Triangulare C A B M N C habere gra-<lb/>vitatem, adeoque ut ejus momentum ex gravitate oriundum cogno-<lb/>ſcatur, ſit A C = a. </s> <s xml:id="echoid-s14288" xml:space="preserve">A B = b. </s> <s xml:id="echoid-s14289" xml:space="preserve">A N = c. </s> <s xml:id="echoid-s14290" xml:space="preserve">erit Triangulum A C N = {1/2} a c, & </s> <s xml:id="echoid-s14291" xml:space="preserve"><lb/>ſoliditas priſmatis = {1/2} a c b, eſt vero centrum gravitatis priſmatis <lb/>A C N in puncto G, cujus directio tranſit per S, adeo ut C S ſit {2/3} <lb/>totius C N. </s> <s xml:id="echoid-s14292" xml:space="preserve">unde momentum dabitur, ſi ſoliditas priſmatis ducatur <lb/>in {1/3} ipſius A N. </s> <s xml:id="echoid-s14293" xml:space="preserve">erit proinde {1/6} a b c c. </s> <s xml:id="echoid-s14294" xml:space="preserve">Momentum vero Cohærentiæ <lb/>baſeos C A B eſt = a a b. </s> <s xml:id="echoid-s14295" xml:space="preserve">Sit nunc ſectio in a c b. </s> <s xml:id="echoid-s14296" xml:space="preserve">& </s> <s xml:id="echoid-s14297" xml:space="preserve">vocetur ac <lb/>= a. </s> <s xml:id="echoid-s14298" xml:space="preserve">a b ſit = b. </s> <s xml:id="echoid-s14299" xml:space="preserve">a N = {ac/a} eritque hujus priſmatis ac b M N ſoliditas <lb/>= {1/2} {aabc/a} & </s> <s xml:id="echoid-s14300" xml:space="preserve">momentum ex gravitate = {1/6} {a<emph style="super">3</emph> bcc/aa}, Cohærentiæ mo-<lb/>mentum uti aab. </s> <s xml:id="echoid-s14301" xml:space="preserve">Eſt vero {1/6} a b c c. </s> <s xml:id="echoid-s14302" xml:space="preserve">ad {1/6} {a<emph style="super">3</emph> bcc,/aa}. </s> <s xml:id="echoid-s14303" xml:space="preserve">uti a<emph style="super">3</emph> ad a<emph style="super">3</emph>. </s> <s xml:id="echoid-s14304" xml:space="preserve">eſtque <lb/>a a b ad a a b uti a a ad a a. </s> <s xml:id="echoid-s14305" xml:space="preserve">quare ſunt momenta ex gravitate oriun-<lb/>da horum priſmatum inter ſe, uti cubi altitudinum: </s> <s xml:id="echoid-s14306" xml:space="preserve">momenta vero <lb/>Cohærentiæ, uti quadrata earundem altitudinum.</s> <s xml:id="echoid-s14307" xml:space="preserve"/> </p> <pb o="584" file="0600" n="601" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div536" type="section" level="1" n="536"> <head xml:id="echoid-head648" xml:space="preserve">PROPOSITIO LVII.</head> <p style="it"> <s xml:id="echoid-s14308" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14309" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14310" xml:space="preserve">fig. </s> <s xml:id="echoid-s14311" xml:space="preserve">11. </s> <s xml:id="echoid-s14312" xml:space="preserve">Si idem Priſma Triangulare A B C M N po-<lb/>natur horizonti parallelum ita, ut ſuperficies ſuperior ſit Trian-<lb/>gulum, & </s> <s xml:id="echoid-s14313" xml:space="preserve">ſummum, quod geſtari poſſit ab extremo M T; </s> <s xml:id="echoid-s14314" xml:space="preserve">ſit pondus P, <lb/>erit hoc pondus ſemper ſummum, quodgeripoterit ab extremo, quam-<lb/>cunque habuerit hoc prisma longitudinem, ſepoſita ejus gravitate <lb/>propriâ.</s> <s xml:id="echoid-s14315" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14316" xml:space="preserve">Vocetur A B, a. </s> <s xml:id="echoid-s14317" xml:space="preserve">B B, b. </s> <s xml:id="echoid-s14318" xml:space="preserve">D T, c. </s> <s xml:id="echoid-s14319" xml:space="preserve">pondus P. </s> <s xml:id="echoid-s14320" xml:space="preserve">p. </s> <s xml:id="echoid-s14321" xml:space="preserve">ſed d T ſit = d. </s> <s xml:id="echoid-s14322" xml:space="preserve">erit b b <lb/>latus = {b d.</s> <s xml:id="echoid-s14323" xml:space="preserve">/c} Cohærentia baſeos A B B erit = a b b. </s> <s xml:id="echoid-s14324" xml:space="preserve">& </s> <s xml:id="echoid-s14325" xml:space="preserve">Cohærentia <lb/>baſeos a b b erit = {a a b d.</s> <s xml:id="echoid-s14326" xml:space="preserve">/c} Momentum vero ponderis P ſuſpenſi ex <lb/>D T eſt = p c. </s> <s xml:id="echoid-s14327" xml:space="preserve">& </s> <s xml:id="echoid-s14328" xml:space="preserve">momentum ejuſdem ponderis P ſuſpenſi ex dT <lb/>eſt = p d.</s> <s xml:id="echoid-s14329" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14330" xml:space="preserve">Si igitur momentum ponderis P ſuſpenſi ex D T longitudine ha-<lb/>beat ad Cohærentiam baſeos A B B eandem proportionem, quam <lb/>momentum ejuſdem ponderis P ſuſpenſi ex longitudine dT habet <lb/>ad ſuæ baſeos a b b Cohærentiam, tum erit eadem ratio Cohærentiæ <lb/>priſmatis ad momentum ponderis, ſive priſma fuerit longum vel bre-<lb/>ve. </s> <s xml:id="echoid-s14331" xml:space="preserve">ſed p c. </s> <s xml:id="echoid-s14332" xml:space="preserve">eſt ad a a b:</s> <s xml:id="echoid-s14333" xml:space="preserve">: p d. </s> <s xml:id="echoid-s14334" xml:space="preserve">{a a b d.</s> <s xml:id="echoid-s14335" xml:space="preserve">/c} ſupra vero oſtendimus Cohæ-<lb/>rentiam baſeos a b b eſſe = {a a b d.</s> <s xml:id="echoid-s14336" xml:space="preserve">/c} quare datur eadem ratio momen-<lb/>ti ponderis ad Cohærentiam in priſmate integro A B B T M & </s> <s xml:id="echoid-s14337" xml:space="preserve">in <lb/>parte abſciſſa a b b T M.</s> <s xml:id="echoid-s14338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14339" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s14340" xml:space="preserve">Si vero priſmata A B B M T, a b b M T concipiantur <lb/>gravia, ponduſque P ut ante appenſum, non erit eadem ratio mo-<lb/>mentorum ex gravitate propria & </s> <s xml:id="echoid-s14341" xml:space="preserve">pondere P ad Cohærentiam ba-<lb/>ſium in prismatibus longis & </s> <s xml:id="echoid-s14342" xml:space="preserve">brevibus: </s> <s xml:id="echoid-s14343" xml:space="preserve">Nam poſitis omnibus ut ſu-<lb/>pra, erit momentum ex gravitate priſmatis A B B M T oriundum <lb/>= {1/6} abcc. </s> <s xml:id="echoid-s14344" xml:space="preserve">& </s> <s xml:id="echoid-s14345" xml:space="preserve">momentum ex gravitate Priſmatis a b b M T = {1/6} {abdd.</s> <s xml:id="echoid-s14346" xml:space="preserve">/c} <lb/>hiſce addantur momenta ponderis P, quæ ſunt = p c in longiori <lb/>priſmate, & </s> <s xml:id="echoid-s14347" xml:space="preserve">= p d in breviori: </s> <s xml:id="echoid-s14348" xml:space="preserve">adeoque ſtabit hæc proportio {1/6} abcc <pb o="585" file="0601" n="602" rhead="CORPORUM FIRMORUM."/> +pc, aab:</s> <s xml:id="echoid-s14349" xml:space="preserve">: {1/6} {abdd/c + pd}, {aabdd + aabd.</s> <s xml:id="echoid-s14350" xml:space="preserve">}/c<emph style="super">3</emph> + c.</s> <s xml:id="echoid-s14351" xml:space="preserve">} quarc Cohæren-<lb/>tia baſeos a b b c deberet eſſe æqualis {aabdd + aabd.</s> <s xml:id="echoid-s14352" xml:space="preserve">/c<emph style="super">3</emph>+c} ſed eſt mo-<lb/>do æqualis {aabd.</s> <s xml:id="echoid-s14353" xml:space="preserve">/c} adeoque non datur inter ambarum baſium in his <lb/>priſmatibus eadem ratio Cohærentiæ ad momenta ponderis P & </s> <s xml:id="echoid-s14354" xml:space="preserve"><lb/>propriæ gravitatis, uti in priſmatibus gravitate deſtitutis, qua-<lb/>propter ejuſmodi priſma Triangulare, grave poſitum, uti ſemper <lb/>eſt, non eſt corpus ubique ejuſdem reſiſtentiæ.</s> <s xml:id="echoid-s14355" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div537" type="section" level="1" n="537"> <head xml:id="echoid-head649" style="it" xml:space="preserve">De Conis & Pyramidibus.</head> <head xml:id="echoid-head650" xml:space="preserve">PROPOSITIO LVIII.</head> <p style="it"> <s xml:id="echoid-s14356" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14357" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14358" xml:space="preserve">fig. </s> <s xml:id="echoid-s14359" xml:space="preserve">12. </s> <s xml:id="echoid-s14360" xml:space="preserve">Conorum atque Pyramidum, quarum altera <lb/>eſt alterius portio, Cohærentiæ ſunt inter ſe uti cubi baſium, vel <lb/>ſoliditates ipſorum corporum.</s> <s xml:id="echoid-s14361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14362" xml:space="preserve">Sit enim Conus vel pyramis A B G cujus baſis A B. </s> <s xml:id="echoid-s14363" xml:space="preserve">ſecetur pla-<lb/>no C D parallelo ad baſin, erit Cohærentia baſeos A B ad eam in <lb/>C D, in ratione duplicata altitudinis A B ad C D. </s> <s xml:id="echoid-s14364" xml:space="preserve">per Prop. </s> <s xml:id="echoid-s14365" xml:space="preserve">XXII. <lb/></s> <s xml:id="echoid-s14366" xml:space="preserve">& </s> <s xml:id="echoid-s14367" xml:space="preserve">in ratione latitudinis A B ad C D. </s> <s xml:id="echoid-s14368" xml:space="preserve">hoc eſt uti cubus A B ad cubum <lb/>C D; </s> <s xml:id="echoid-s14369" xml:space="preserve">ſed ut cubus A B ad cubum C D, ita conus vel pyramis A B G <lb/>ad conum vel pyramidem C D G, quare erunt Cohærentiæ uti ſunt <lb/>ipſa ſolida.</s> <s xml:id="echoid-s14370" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div538" type="section" level="1" n="538"> <head xml:id="echoid-head651" xml:space="preserve">PROPOSITIO LIX.</head> <p style="it"> <s xml:id="echoid-s14371" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14372" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14373" xml:space="preserve">fig. </s> <s xml:id="echoid-s14374" xml:space="preserve">12. </s> <s xml:id="echoid-s14375" xml:space="preserve">Conorum atque pyramidum, quarum altera <lb/>alterius eſt portio, invenire momenta ex propria gravitate oriunda.</s> <s xml:id="echoid-s14376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14377" xml:space="preserve">Vocetur diameter baſeos A B, a. </s> <s xml:id="echoid-s14378" xml:space="preserve">C D, c. </s> <s xml:id="echoid-s14379" xml:space="preserve">E G longitudo, b. </s> <s xml:id="echoid-s14380" xml:space="preserve">erit f G = {bc.</s> <s xml:id="echoid-s14381" xml:space="preserve">/a} <lb/>& </s> <s xml:id="echoid-s14382" xml:space="preserve">ſoliditas Coni A G B ad ſoliditatem Coni C G D, uti {aab/3} ad {bc<emph style="super">3</emph>.</s> <s xml:id="echoid-s14383" xml:space="preserve">/3a} <pb o="586" file="0602" n="603" rhead="INTRODUCTIO AD COHÆRENTIAM"/> Eſt autem demonſtratum in Prop. </s> <s xml:id="echoid-s14384" xml:space="preserve">XVI, Carrei de Centro <lb/>Gravitatis, in Conis & </s> <s xml:id="echoid-s14385" xml:space="preserve">Pyramidibus centrum gravitatis <lb/>dari in axe G E, ad {1/4} longitudinis G E a puncto baſeos E. </s> <s xml:id="echoid-s14386" xml:space="preserve">Qua <lb/>re momentum Coni aut Pyramidis A G B erit = {aab/3} X {1/4}b. <lb/></s> <s xml:id="echoid-s14387" xml:space="preserve">& </s> <s xml:id="echoid-s14388" xml:space="preserve">momentum Coni aut Pyramidis C G D erit = {bc<emph style="super">3</emph>/3a} X {1/4} {bc/4a}. </s> <s xml:id="echoid-s14389" xml:space="preserve">quæ <lb/>momenta ſunt inter ſe veluti a<emph style="super">4</emph> ad c<emph style="super">4</emph>.</s> <s xml:id="echoid-s14390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14391" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14392" xml:space="preserve">1. </s> <s xml:id="echoid-s14393" xml:space="preserve">Cumbaſes conorum & </s> <s xml:id="echoid-s14394" xml:space="preserve">pyramidum ſunt inter ſe uti a a <lb/>ad c c. </s> <s xml:id="echoid-s14395" xml:space="preserve">erunt momenta ex gravitate in ratione duplicata baſium <lb/>conorum & </s> <s xml:id="echoid-s14396" xml:space="preserve">pyramidum ſimilium.</s> <s xml:id="echoid-s14397" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14398" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14399" xml:space="preserve">2. </s> <s xml:id="echoid-s14400" xml:space="preserve">Et cum Cohærentiæ conorum & </s> <s xml:id="echoid-s14401" xml:space="preserve">pyramidum ſunt inter <lb/>ſe uti a<emph style="super">3</emph> ad c<emph style="super">3</emph>. </s> <s xml:id="echoid-s14402" xml:space="preserve">erunt momenta ex gravitate ad Cohærentiam uti <lb/>Surde ſolida ad Cubos.</s> <s xml:id="echoid-s14403" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div539" type="section" level="1" n="539"> <head xml:id="echoid-head652" xml:space="preserve">PROPOSITIO LX.</head> <p style="it"> <s xml:id="echoid-s14404" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14405" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14406" xml:space="preserve">fig. </s> <s xml:id="echoid-s14407" xml:space="preserve">12. </s> <s xml:id="echoid-s14408" xml:space="preserve">Dato Cono Gravi A B G, maximoque ponde-<lb/>re, quod ab extremo G geſtari poſſit, invenire maximum pondus, <lb/>quod ab extremo C cjusdem Conitruncati C D B A geſtabitur.</s> <s xml:id="echoid-s14409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14410" xml:space="preserve">Quantitatibus deſignatis uti in Propoſitione LIX. </s> <s xml:id="echoid-s14411" xml:space="preserve">quæratur primo <lb/>centrum Gravitatis in cono truncato A B C D, cujus diſtantia a <lb/>puncto E baſeos eſt = {4aab-4bc<emph style="super">3</emph>-9a<emph style="super">3</emph>b/4aa-4c<emph style="super">3</emph>}. </s> <s xml:id="echoid-s14412" xml:space="preserve">eſt autem pondus ipſius <lb/>coni truncati = {aab/3}-{bc<emph style="super">3</emph>/3a}. </s> <s xml:id="echoid-s14413" xml:space="preserve">unde momentum coni truncati erit <lb/>= {4aab-4bc<emph style="super">3</emph>-9a<emph style="super">3</emph>b/4aa-4c<emph style="super">3</emph>} X {aab/3}-{bc<emph style="super">3</emph>/3a} <lb/>Eſt quoque longitudo E f, ex qua pondus ſuſpendetur =b-{bc/a}. <lb/></s> <s xml:id="echoid-s14414" xml:space="preserve">vocatoque pondere incognito & </s> <s xml:id="echoid-s14415" xml:space="preserve">appendendo = x, erit momen-<lb/>tum ejus = bx-{bcx/a}.</s> <s xml:id="echoid-s14416" xml:space="preserve"/> </p> <pb o="587" file="0603" n="604" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s14417" xml:space="preserve">Momentum coni integri B G A eſt = {aabb/12}. </s> <s xml:id="echoid-s14418" xml:space="preserve">& </s> <s xml:id="echoid-s14419" xml:space="preserve">pondere appenſo <lb/>ex G vocato p. </s> <s xml:id="echoid-s14420" xml:space="preserve">cujus momentum eſt = pb. </s> <s xml:id="echoid-s14421" xml:space="preserve">erit momentorum <lb/>horum ſumma = {aabb/12}+pb. </s> <s xml:id="echoid-s14422" xml:space="preserve">quia momenta hæc, tum momenta <lb/>coni truncati ſimul cum pondere incognito ad Cohærentiam baſeos <lb/>ejuſdem A B eandem debent habere rationem, debent momenta <lb/>eſſe æqualia, adeoque {aabb/12}+pb = 4aab-{4bc<emph style="super">3</emph>-9a<emph style="super">3</emph>b/4aa-4c<emph style="super">3</emph>} <lb/>X {aab/3}-{bc<emph style="super">3</emph>/3a + bx - {bcx/a} unde eruitur quantitas incognita <lb/>x = {aabb/12} + pb - {4aab+4bc<emph style="super">3</emph>+9a<emph style="super">3</emph>b/4aa-4c<emph style="super">3</emph>} X {aab/3}-{bc<emph style="super">3</emph>/3a}/b-{bc/a}}.</s> <s xml:id="echoid-s14423" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div540" type="section" level="1" n="540"> <head xml:id="echoid-head653" xml:space="preserve">PROPOSITIO LXI.</head> <p style="it"> <s xml:id="echoid-s14424" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14425" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14426" xml:space="preserve">fig. </s> <s xml:id="echoid-s14427" xml:space="preserve">13. </s> <s xml:id="echoid-s14428" xml:space="preserve">Datis duobus Conis A B G, C D K gravibus, <lb/>ejuſdem materiæ & </s> <s xml:id="echoid-s14429" xml:space="preserve">æqualium baſium, ſed diverſæ longitudinis, <lb/>datoque maximo pondere Q appenſo ex longiſſimo cono A B G, in-<lb/>venire pondus P, appendendum ex vertice K brevioris coni, quod <lb/>etiam ſit maximum.</s> <s xml:id="echoid-s14430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14431" xml:space="preserve">Vocetur A B, 2a. </s> <s xml:id="echoid-s14432" xml:space="preserve">peripheria baſeos, c. </s> <s xml:id="echoid-s14433" xml:space="preserve">M G, b. </s> <s xml:id="echoid-s14434" xml:space="preserve">Q pondus, q. </s> <s xml:id="echoid-s14435" xml:space="preserve">C D <lb/>2a. </s> <s xml:id="echoid-s14436" xml:space="preserve">K L, d. </s> <s xml:id="echoid-s14437" xml:space="preserve">pondus quæſitum P ſit = x.</s> <s xml:id="echoid-s14438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14439" xml:space="preserve">Erit ſoliditas Coni A B G = {acb/6}. </s> <s xml:id="echoid-s14440" xml:space="preserve">ejuſque momentum ex gravitate <lb/>= {acbb/24}. </s> <s xml:id="echoid-s14441" xml:space="preserve">momentum ponderis Q = qb. </s> <s xml:id="echoid-s14442" xml:space="preserve">ſoliditas coni brevioris <lb/>={acd/6} ejus momentum {acdd/24} momentum ponderis P = d x & </s> <s xml:id="echoid-s14443" xml:space="preserve"><lb/>quia baſes conorum ponuntur æquales, erunt Cohærentiæ æquales, <lb/>adeoque cum momentum in uno cono, quod oritur ex propria gra- <pb o="588" file="0604" n="605" rhead="INTRODUCTIO AD COHÆRENTIAM"/> vitate & </s> <s xml:id="echoid-s14444" xml:space="preserve">pondere, ſit ſummum quod ferri poſſit, alterum momen-<lb/>tum in breviori cono quod ſummum erit, debebit eſſe illi æquale <lb/>unde {acbb/24}+qb = {acdd/24}+dx. <lb/></s> <s xml:id="echoid-s14445" xml:space="preserve">ex quibus eruitur x = {acbb/24d} + {qb/d} - {acd/24}.</s> <s xml:id="echoid-s14446" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div541" type="section" level="1" n="541"> <head xml:id="echoid-head654" xml:space="preserve">PROPOSITIO LXII.</head> <p style="it"> <s xml:id="echoid-s14447" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14448" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14449" xml:space="preserve">ſig. </s> <s xml:id="echoid-s14450" xml:space="preserve">14. </s> <s xml:id="echoid-s14451" xml:space="preserve">Datis duobus Conis A B G, C D K gravibus, <lb/>ejusdem materiæ, & </s> <s xml:id="echoid-s14452" xml:space="preserve">æque altis, ſed diverſarum baſium, appenſo-<lb/>que pondere maximo Qex vertice Coni minoris, invenire pondus <lb/>maximum P, quod geſtari poſſit ex vertice G Coni craſſioris.</s> <s xml:id="echoid-s14453" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14454" xml:space="preserve">Vocetur radius baſeos A B, a. </s> <s xml:id="echoid-s14455" xml:space="preserve">peripheria, p. </s> <s xml:id="echoid-s14456" xml:space="preserve">longitudo G M b. <lb/></s> <s xml:id="echoid-s14457" xml:space="preserve">pondus P quæſitum ſit = x. </s> <s xml:id="echoid-s14458" xml:space="preserve">Radius baſeos D C = r. </s> <s xml:id="echoid-s14459" xml:space="preserve">ejus circumferentia <lb/>{pr/a}. </s> <s xml:id="echoid-s14460" xml:space="preserve">longitudo K L = d. </s> <s xml:id="echoid-s14461" xml:space="preserve">pondus Q =q.</s> <s xml:id="echoid-s14462" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14463" xml:space="preserve">Erit ſoliditas coni C D K = {dprr/6a}. </s> <s xml:id="echoid-s14464" xml:space="preserve">ejuſque momentum ex gravi-<lb/>tate = {ddprr/24a}. </s> <s xml:id="echoid-s14465" xml:space="preserve">momentum ponderis Q =dq. </s> <s xml:id="echoid-s14466" xml:space="preserve">ſoliditas vero Coni <lb/>A B G = {abp/6} ejusque momentum ex gravitate = {abbp/24}. </s> <s xml:id="echoid-s14467" xml:space="preserve">momen-<lb/>tum ponderis P = bx. </s> <s xml:id="echoid-s14468" xml:space="preserve">Debent ſummæ momentorum in ſingulo <lb/>Cono ad Cohærentias ſuarum baſium habere eandem rationem, qua-<lb/>re ſtabunt quantitates in hac proportione <lb/>{ddprr/24a} + dq. </s> <s xml:id="echoid-s14469" xml:space="preserve">8r<emph style="super">3</emph>:</s> <s xml:id="echoid-s14470" xml:space="preserve">: {abbp/24} + bx, 8a<emph style="super">3</emph>. <lb/></s> <s xml:id="echoid-s14471" xml:space="preserve">unde eruitur X = {aaddp/24br} + {a<emph style="super">3</emph>dq/br<emph style="super">3</emph>} - {abp/24}.</s> <s xml:id="echoid-s14472" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div542" type="section" level="1" n="542"> <head xml:id="echoid-head655" xml:space="preserve">PROPOSITIO LXIII.</head> <p style="it"> <s xml:id="echoid-s14473" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14474" xml:space="preserve">XXV. </s> <s xml:id="echoid-s14475" xml:space="preserve">ſig. </s> <s xml:id="echoid-s14476" xml:space="preserve">15. </s> <s xml:id="echoid-s14477" xml:space="preserve">Datis duobus Conis A B C, D E F gravi-<lb/>bus, diverſæ longitudinis & </s> <s xml:id="echoid-s14478" xml:space="preserve">non ſimilibus, quorum brevior A B C <pb o="589" file="0605" n="606" rhead="CORPORUM FIRMORUM."/> babeat angulum ſolidum C minorem, quam eſt longioris E D F an-<lb/>gulus F, ſitque ex C pondus P maximum ſuſpenſum, invenire <lb/>pondus Q maximum applicandum angulo ſolido F.</s> <s xml:id="echoid-s14479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14480" xml:space="preserve">Ponatur radius G A baſeos = a. </s> <s xml:id="echoid-s14481" xml:space="preserve">peripheria = c. </s> <s xml:id="echoid-s14482" xml:space="preserve">longitudo G C <lb/>= b. </s> <s xml:id="echoid-s14483" xml:space="preserve">pondus P = p, Radius baſeos H D = r, ejus circumferentia <lb/>= {cr/a}. </s> <s xml:id="echoid-s14484" xml:space="preserve">longitudo H F = l. </s> <s xml:id="echoid-s14485" xml:space="preserve">pondus Q quæſitum = x.</s> <s xml:id="echoid-s14486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14487" xml:space="preserve">Erit ſoliditas Coni A B C = {abc/6}. </s> <s xml:id="echoid-s14488" xml:space="preserve">ejus momentum ex gravitate <lb/>= {abbc/24}. </s> <s xml:id="echoid-s14489" xml:space="preserve">momentum ponderis ipſi appenſi = bp. </s> <s xml:id="echoid-s14490" xml:space="preserve">ſoliditas vero <lb/>Coni E D F = {crrl/6a} ejuſque momentum ex gravitate = {cllrr/24a}. </s> <s xml:id="echoid-s14491" xml:space="preserve">mo-<lb/>mentum ponderis appendendi = lx. </s> <s xml:id="echoid-s14492" xml:space="preserve">Cohærentia baſeos A B eſt ad <lb/>eam baſeos E D, uti 8a<emph style="super">3</emph>, ad 8r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14494" xml:space="preserve">Quia momenta gravitatum tam Conorum, quam ponderum ap-<lb/>penſorum debent ad Cohærentias eandem habere rationem, nam <lb/>uti pondus P eſt maximum, ita Q debet eſſe maximum, ordine-<lb/>tur hæc proportio. <lb/></s> <s xml:id="echoid-s14495" xml:space="preserve">{abbc/24} + bp. </s> <s xml:id="echoid-s14496" xml:space="preserve">8a<emph style="super">3</emph>:</s> <s xml:id="echoid-s14497" xml:space="preserve">: {cllrr/24a} + lx, 8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14498" xml:space="preserve"><lb/>unde erit x = {bbcr<emph style="super">3</emph>/24aal} + {bpr/a<emph style="super">3</emph>l} - {clrr/24a}.</s> <s xml:id="echoid-s14499" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div543" type="section" level="1" n="543"> <head xml:id="echoid-head656" style="it" xml:space="preserve">De Conidibus Parabolicis.</head> <head xml:id="echoid-head657" xml:space="preserve">PROPOSITIO LXIV.</head> <p style="it"> <s xml:id="echoid-s14500" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14501" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14502" xml:space="preserve">fig. </s> <s xml:id="echoid-s14503" xml:space="preserve">1. </s> <s xml:id="echoid-s14504" xml:space="preserve">Sit Conois Parabolica A B C, & </s> <s xml:id="echoid-s14505" xml:space="preserve">portio ex ea <lb/>abſciſſa D B E, quarum axes ſint B F, B G, erit momentum ponderis <lb/>A B C ad momentum ponderis D B E uti Cubus ex F B, ad Cubum <lb/>ex G B.</s> <s xml:id="echoid-s14506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14507" xml:space="preserve">Vocetur C F, r. </s> <s xml:id="echoid-s14508" xml:space="preserve">peripheria ejus circuli c. </s> <s xml:id="echoid-s14509" xml:space="preserve">F B, a. </s> <s xml:id="echoid-s14510" xml:space="preserve">tum radius al-<lb/>terius circuli G E, b. </s> <s xml:id="echoid-s14511" xml:space="preserve">erit axis G B = {abb/rr}. </s> <s xml:id="echoid-s14512" xml:space="preserve">ex natura Parabolæ, &</s> <s xml:id="echoid-s14513" xml:space="preserve"> <pb o="590" file="0606" n="607" rhead="INTRODUCTIO AD COHÆRENTIAM"/> peripheria circuli D G E = {bc/r}. </s> <s xml:id="echoid-s14514" xml:space="preserve">Eſt vero Conoidis parabolicæ A B C <lb/>ſoliditas = {acr/4} per Prop. </s> <s xml:id="echoid-s14515" xml:space="preserve">XIII. </s> <s xml:id="echoid-s14516" xml:space="preserve">Carrei de Dimenſione Solidorum. <lb/></s> <s xml:id="echoid-s14517" xml:space="preserve">& </s> <s xml:id="echoid-s14518" xml:space="preserve">quia centrum gravitatis eſt ad {1/3} F B a puncto F, in axe F B, per <lb/>Prop. </s> <s xml:id="echoid-s14519" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s14520" xml:space="preserve">Carrei de Centro Gravitatis, erit momentum Conoi-<lb/>dis parabolicæ A B C = {aacr/12}. </s> <s xml:id="echoid-s14521" xml:space="preserve">ſed ſolidum D B E eſt = {ab<emph style="super">4</emph>c/4r<emph style="super">3</emph>} cujus <lb/>momentum ex gravitate eſt = {aab<emph style="super">6</emph>c/12r<emph style="super">5</emph>}. </s> <s xml:id="echoid-s14522" xml:space="preserve">datur in Propoſitione. </s> <s xml:id="echoid-s14523" xml:space="preserve"><lb/>{aab<emph style="super">6</emph>c/12r<emph style="super">5</emph>}. </s> <s xml:id="echoid-s14524" xml:space="preserve">{aacr/12}:</s> <s xml:id="echoid-s14525" xml:space="preserve">: {a<emph style="super">3</emph>b<emph style="super">6</emph>/r<emph style="super">6</emph>}a<emph style="super">3</emph>.</s> <s xml:id="echoid-s14526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14527" xml:space="preserve">Quod patet multiplicando hujus Proportionis terminos medios & </s> <s xml:id="echoid-s14528" xml:space="preserve"><lb/>extremos per ſe, proveniuntque producta æqualia, nempe {a<emph style="super">5</emph>b<emph style="super">6</emph>c.</s> <s xml:id="echoid-s14529" xml:space="preserve">/12r<emph style="super">5</emph>}.</s> <s xml:id="echoid-s14530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14531" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s14532" xml:space="preserve">Sunt quadrata momentorum Cohærentiæ harum Conoi-<lb/>dum Parabolicarum inter ſe, uti momenta gravitatis ipſarum Co-<lb/>noidum. </s> <s xml:id="echoid-s14533" xml:space="preserve">Nam ſunt Cohærentiæ inter ſe uti r<emph style="super">3</emph> ad b<emph style="super">3</emph>, quarum qua-<lb/>drata ſunt r<emph style="super">6</emph>, b<emph style="super">6</emph>. </s> <s xml:id="echoid-s14534" xml:space="preserve">eſt vero {aab<emph style="super">6</emph>c/12r<emph style="super">5</emph>} {aacr/12}:</s> <s xml:id="echoid-s14535" xml:space="preserve">: b<emph style="super">6</emph>, r<emph style="super">6</emph>. </s> <s xml:id="echoid-s14536" xml:space="preserve">nam multipli-<lb/>catis extremis mediisque terminis per ſe, habentur producta utrim-<lb/>que æqualia, nempe{aab<emph style="super">6</emph>cr/12}</s> </p> </div> <div xml:id="echoid-div544" type="section" level="1" n="544"> <head xml:id="echoid-head658" xml:space="preserve">PROPOSITIO LXV.</head> <p style="it"> <s xml:id="echoid-s14537" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14538" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14539" xml:space="preserve">fig. </s> <s xml:id="echoid-s14540" xml:space="preserve">2. </s> <s xml:id="echoid-s14541" xml:space="preserve">Datis duabus Conoidibus Parabolicis gravi-<lb/>bus D E F, A B C, ejusdem altitudinis ſed diverſarum baſium, at-<lb/>que pondere dato Q appenſo ex vertice F Conoidis gracilioris, <lb/>invenire pondus P appendendum ex vertice C Conoidis craſſioris, <lb/>ita ut momenta propriarum gravitatum inconoidibus, & </s> <s xml:id="echoid-s14542" xml:space="preserve">ponde-<lb/>rum appenſorum earum verticibus, ſint ad cohærentias baſium in <lb/>eadem proportione.</s> <s xml:id="echoid-s14543" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14544" xml:space="preserve">Vocetur A F, r. </s> <s xml:id="echoid-s14545" xml:space="preserve">C F, b. </s> <s xml:id="echoid-s14546" xml:space="preserve">peripheria baſeos, c, pondus P quæſitum <pb o="591" file="0607" n="608" rhead="CORPORUM FIRMORUM"/> ſit = x. </s> <s xml:id="echoid-s14547" xml:space="preserve">deinde G D = d. </s> <s xml:id="echoid-s14548" xml:space="preserve">F G = b. </s> <s xml:id="echoid-s14549" xml:space="preserve">peripheria baſeos {cd/r}. </s> <s xml:id="echoid-s14550" xml:space="preserve">pondus Q = q.</s> <s xml:id="echoid-s14551" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14552" xml:space="preserve">Erit ſoliditas Parabolicæ Conoidis A B C = {bcr/4} & </s> <s xml:id="echoid-s14553" xml:space="preserve">momentum <lb/>ex gravitate = {bbcr/12}. </s> <s xml:id="echoid-s14554" xml:space="preserve">& </s> <s xml:id="echoid-s14555" xml:space="preserve">momentum ponderis P appenſi = b x. </s> <s xml:id="echoid-s14556" xml:space="preserve">ita <lb/>quoque erit ſoliditas Conoidis D E F = {bcdd/4r}. </s> <s xml:id="echoid-s14557" xml:space="preserve">& </s> <s xml:id="echoid-s14558" xml:space="preserve">momentum ex <lb/>Gravitate = {bbcdd/12r}. </s> <s xml:id="echoid-s14559" xml:space="preserve">atque momentum ponderis Q appenſi = bq. <lb/></s> <s xml:id="echoid-s14560" xml:space="preserve">Cohærentia vero baſeos A B eſt = 8r<emph style="super">3</emph>, & </s> <s xml:id="echoid-s14561" xml:space="preserve">baſeos D E = 8d<emph style="super">3</emph>: </s> <s xml:id="echoid-s14562" xml:space="preserve">ſuppo-<lb/>nitur in Propoſitione {bbcdd/12r} + bq. </s> <s xml:id="echoid-s14563" xml:space="preserve">8d<emph style="super">3</emph>:</s> <s xml:id="echoid-s14564" xml:space="preserve">: {bbcr/12} + bx. </s> <s xml:id="echoid-s14565" xml:space="preserve">8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14566" xml:space="preserve"><lb/>multiplicatis extremis & </s> <s xml:id="echoid-s14567" xml:space="preserve">mediis per ſe, fit {8bbcddr<emph style="super">3</emph>/12r} + 8bqr<emph style="super">3</emph> <lb/>= {8bbcd<emph style="super">3</emph>r/12} + 8bd<emph style="super">3</emph>x. </s> <s xml:id="echoid-s14568" xml:space="preserve">& </s> <s xml:id="echoid-s14569" xml:space="preserve">tranſponendo ac dividendo fit <lb/>{8bbcddr<emph style="super">3</emph>/12r} + 8bqr<emph style="super">3</emph> - {8bbcd<emph style="super">3</emph>r/12}/8bd<emph style="super">3</emph>} = x. </s> <s xml:id="echoid-s14570" xml:space="preserve"><lb/>ſive {bcrr/12d} + {qr<emph style="super">3</emph>/d<emph style="super">3</emph>} - {bcr/12}. </s> <s xml:id="echoid-s14571" xml:space="preserve">= x.</s> <s xml:id="echoid-s14572" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div545" type="section" level="1" n="545"> <head xml:id="echoid-head659" xml:space="preserve">PROPOSITIO LXVI.</head> <p style="it"> <s xml:id="echoid-s14573" xml:space="preserve">Tab XXVI fig. </s> <s xml:id="echoid-s14574" xml:space="preserve">2. </s> <s xml:id="echoid-s14575" xml:space="preserve">Data Conoide Parabolica A B C, datoque <lb/>pondere P, cujus momentum ſimul cum momento ponderis dati ſolidi <lb/>ad Cobærentiam ejuſdem ſolidi, quamlibet babeat proportionem, <lb/>ſuper data baſi aliam Conoidem Parabolicam conſtruere, cujus <lb/>ponderis momentum ad ſuam Cobærentiam ſit in eadem propor-<lb/>tione.</s> <s xml:id="echoid-s14576" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14577" xml:space="preserve">Ponatur F B = r. </s> <s xml:id="echoid-s14578" xml:space="preserve">peripheria = c. </s> <s xml:id="echoid-s14579" xml:space="preserve">F C = a. </s> <s xml:id="echoid-s14580" xml:space="preserve">pondus appenſum = p. <lb/></s> <s xml:id="echoid-s14581" xml:space="preserve">baſeos datæ radius = b. </s> <s xml:id="echoid-s14582" xml:space="preserve">peripheria baſeos datæ = {bc/r}. </s> <s xml:id="echoid-s14583" xml:space="preserve">longitudo <lb/>quæſita = x.</s> <s xml:id="echoid-s14584" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14585" xml:space="preserve">Erit ſolidum A B C = {acr/4}. </s> <s xml:id="echoid-s14586" xml:space="preserve">ejuſque momentum oriundum ex gra- <pb o="592" file="0608" n="609" rhead="INTRODUCTIO AD COHÆRENTIAM"/> vitate = {aacr/12}. </s> <s xml:id="echoid-s14587" xml:space="preserve">momentum ponderis = ap. </s> <s xml:id="echoid-s14588" xml:space="preserve">Cohærentia = 8r<emph style="super">3</emph>. <lb/></s> <s xml:id="echoid-s14589" xml:space="preserve">ſed Conoidis quæſitæ ſoliditas erit = {bbcx/4r}. </s> <s xml:id="echoid-s14590" xml:space="preserve">ejuſque momentum <lb/>= {bbcxx/12r}. </s> <s xml:id="echoid-s14591" xml:space="preserve">& </s> <s xml:id="echoid-s14592" xml:space="preserve">Cohærentia = 8b<emph style="super">3</emph>. </s> <s xml:id="echoid-s14593" xml:space="preserve">ponitur in Propoſitione <lb/>{aacr/12} + ap, 8r<emph style="super">3</emph>:</s> <s xml:id="echoid-s14594" xml:space="preserve">: {bbcxx/12r}. </s> <s xml:id="echoid-s14595" xml:space="preserve">8b<emph style="super">3</emph> <lb/>unde eruitur x = 8aab<emph style="super">3</emph>cr + 96b<emph style="super">3</emph>ap - 8bbcrr.</s> <s xml:id="echoid-s14596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14597" xml:space="preserve">Cognita longitudine parabolæ x, dataque ejus ordinata = b. </s> <s xml:id="echoid-s14598" xml:space="preserve">fa-<lb/>cile invenitur parameter = {bb/x}. </s> <s xml:id="echoid-s14599" xml:space="preserve">quâ erutâ deſcribetur parabola per <lb/>Prop. </s> <s xml:id="echoid-s14600" xml:space="preserve">VII. </s> <s xml:id="echoid-s14601" xml:space="preserve">vel VIII. </s> <s xml:id="echoid-s14602" xml:space="preserve">Hoſpitalii Lib. </s> <s xml:id="echoid-s14603" xml:space="preserve">I. </s> <s xml:id="echoid-s14604" xml:space="preserve">Sect. </s> <s xml:id="echoid-s14605" xml:space="preserve">Coniq. </s> <s xml:id="echoid-s14606" xml:space="preserve">deſcriptâ Para-<lb/>bolâ circa axin circumvolutâ, generabitur Conois parabolica quæ-<lb/>ſita.</s> <s xml:id="echoid-s14607" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div546" type="section" level="1" n="546"> <head xml:id="echoid-head660" xml:space="preserve">PROPOSITIO LXVII.</head> <p style="it"> <s xml:id="echoid-s14608" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14609" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14610" xml:space="preserve">fig. </s> <s xml:id="echoid-s14611" xml:space="preserve">2. </s> <s xml:id="echoid-s14612" xml:space="preserve">Data Conoide parabolica gravi A B C dato-<lb/>que pondere P, cujus momentum ſimul cum momento ponderis dati <lb/>ſolidi ſit in quacunque ratione data, invenire aliam Conoidem pa-<lb/>rabolicam, quæ datam quamlibet babeat longitudinem, & </s> <s xml:id="echoid-s14613" xml:space="preserve">cujus <lb/>momentum ex gravitate ad Cohærentiam ſuam ſit in eadem ratione.</s> <s xml:id="echoid-s14614" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14615" xml:space="preserve">Quantitatibus Conoidis A B C vocatis ut in præcedenti Propoſi-<lb/>tione, erit Conoidis momentum = {aacr/12}. </s> <s xml:id="echoid-s14616" xml:space="preserve">momentum ponderis <lb/>= ap. </s> <s xml:id="echoid-s14617" xml:space="preserve">Cohærentia = 8r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14619" xml:space="preserve">Sit longitudo Conoidis quæſitæ data G F = d. </s> <s xml:id="echoid-s14620" xml:space="preserve">radius baſeos quæ-<lb/>ſitus G D = x. </s> <s xml:id="echoid-s14621" xml:space="preserve">erit ejus peri pheria = {cx/r}, ſolidum = {cdxx/4r}. </s> <s xml:id="echoid-s14622" xml:space="preserve">cujus mo-<lb/>mentum = {cddxx/12r}. </s> <s xml:id="echoid-s14623" xml:space="preserve">Cohærentia = 8x<emph style="super">3</emph>. </s> <s xml:id="echoid-s14624" xml:space="preserve">quare ordinanda hæcpro-<lb/>portio, cum momenta gravitatis ad Cohærentias ſuas debent habe-<lb/>re eandem rationem, {cddxx/12r}. </s> <s xml:id="echoid-s14625" xml:space="preserve">8x<emph style="super">3</emph>:</s> <s xml:id="echoid-s14626" xml:space="preserve">: {aacr/12} + ap. </s> <s xml:id="echoid-s14627" xml:space="preserve">8r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14628" xml:space="preserve"> <pb o="593" file="0609" n="610" rhead="CORPORUM FIRMORUM."/> unde eruitur x = {cddrr/aacr + 12ap}</s> </p> </div> <div xml:id="echoid-div547" type="section" level="1" n="547"> <head xml:id="echoid-head661" xml:space="preserve">PROPOSITIO LXVIII.</head> <p style="it"> <s xml:id="echoid-s14629" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14630" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14631" xml:space="preserve">fig I. </s> <s xml:id="echoid-s14632" xml:space="preserve">Data Conoide Parabolica D B E, datoque <lb/>pondere appenſo P, cujus momentum ſimul cum momento Conoidis <lb/>ex gravitate, ad momentum Cobærentiæ ejuſdem ſolidi quamlibet <lb/>babeat rationem; </s> <s xml:id="echoid-s14633" xml:space="preserve">Conoidem datam ita producere in F, ut ejus pon-<lb/>deris momentum ad ſuam Cobærentiam ſit in eadem ratione.</s> <s xml:id="echoid-s14634" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14635" xml:space="preserve">Ponatur G D radius = r. </s> <s xml:id="echoid-s14636" xml:space="preserve">peripheria circuli baſeos = c. </s> <s xml:id="echoid-s14637" xml:space="preserve">G B = a. <lb/></s> <s xml:id="echoid-s14638" xml:space="preserve">pondus P = p. </s> <s xml:id="echoid-s14639" xml:space="preserve">B F quæſita = x. </s> <s xml:id="echoid-s14640" xml:space="preserve">erit C F radius baſeos = {rrx/a}. </s> <s xml:id="echoid-s14641" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s14642" xml:space="preserve">peripheria circuli baſeos = c {x/a}.</s> <s xml:id="echoid-s14643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14644" xml:space="preserve">Eſt ſolidum DBE = {acr/4}. </s> <s xml:id="echoid-s14645" xml:space="preserve">ejus momentum ex gravitate = {aacr/12}. <lb/></s> <s xml:id="echoid-s14646" xml:space="preserve">& </s> <s xml:id="echoid-s14647" xml:space="preserve">momentum ponderis P = ap. </s> <s xml:id="echoid-s14648" xml:space="preserve">Cohærentia = 8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14649" xml:space="preserve">Eſt autem <lb/>ſolidum A B C = {1/4} crx{x/a}, ejusque momentum {crxx/12}{x/a}. </s> <s xml:id="echoid-s14650" xml:space="preserve">& </s> <s xml:id="echoid-s14651" xml:space="preserve">Cohæ-<lb/>rentia = 8 {r<emph style="super">6</emph>x<emph style="super">3</emph>/a<emph style="super">3</emph>}. </s> <s xml:id="echoid-s14652" xml:space="preserve">Quia igitur ambo momenta Conoidum ad ſuas <lb/>Cohærentias ſupponuntur eſſe in eadem ratione, erit {aacr/12} + ap. </s> <s xml:id="echoid-s14653" xml:space="preserve"><lb/>8r<emph style="super">3</emph>:</s> <s xml:id="echoid-s14654" xml:space="preserve">: {crxx/12} {x.</s> <s xml:id="echoid-s14655" xml:space="preserve">/a}. </s> <s xml:id="echoid-s14656" xml:space="preserve">{8r<emph style="super">3</emph>x/a} {x/a}.</s> <s xml:id="echoid-s14657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14658" xml:space="preserve">Quorum extremis mediisque terminis per ſe multiplicatis, at-<lb/>que diviſione facta per 8 {x/a}. </s> <s xml:id="echoid-s14659" xml:space="preserve">fit {cr<emph style="super">4</emph>xx/12} = {aacr<emph style="super">4</emph>x/12a} + {apr<emph style="super">3</emph>x/a}. <lb/></s> <s xml:id="echoid-s14660" xml:space="preserve">& </s> <s xml:id="echoid-s14661" xml:space="preserve">inſtituta diviſione per {cr<emph style="super">4</emph>/12}. </s> <s xml:id="echoid-s14662" xml:space="preserve">fit <lb/>x x = ax + 12{px/cr}. </s> <s xml:id="echoid-s14663" xml:space="preserve">unde per tranſpoſitionem.</s> <s xml:id="echoid-s14664" xml:space="preserve"> <pb o="594" file="0610" n="611" rhead="INTRODUCTIO AD COHÆRENTIAM"/> xx - ax = 0 hinc additis utrimque, ut radix extrahi <lb/>- {12px/cr} poſſit, {1/4} aa + {6ap/cr} + {36pp/ccrr}. <lb/></s> <s xml:id="echoid-s14665" xml:space="preserve">fit xx - ax + {1/4} aa = {1/4} aa. </s> <s xml:id="echoid-s14666" xml:space="preserve">Radice ex his extracta. </s> <s xml:id="echoid-s14667" xml:space="preserve"><lb/>- {12px/cr} + {6ap/cr} + {6ap/cr} <lb/>+ {36pp/ccrr} + {36pp/ccrr} <lb/>fit x = {1/2}a + {6p/cr} + {aa/4} + {6ap/cr} + {36pp/ccrr}.</s> <s xml:id="echoid-s14668" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div548" type="section" level="1" n="548"> <head xml:id="echoid-head662" xml:space="preserve">PROPOSITIO LXIX.</head> <p style="it"> <s xml:id="echoid-s14669" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14670" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14671" xml:space="preserve">fig. </s> <s xml:id="echoid-s14672" xml:space="preserve">I. </s> <s xml:id="echoid-s14673" xml:space="preserve">In Parabolâ Cubica A B C, & </s> <s xml:id="echoid-s14674" xml:space="preserve">cjus ſeg-<lb/>mento D B E, momenta ex gravitate propria oriunda ſunt inter <lb/>ſe, uti radii A F, D G, elevati ad octavam potentiam.</s> <s xml:id="echoid-s14675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14676" xml:space="preserve">Vocetur radius C F, r. </s> <s xml:id="echoid-s14677" xml:space="preserve">circumferentia circuli baſeos, c. </s> <s xml:id="echoid-s14678" xml:space="preserve">longi-<lb/>tudo B F, a. </s> <s xml:id="echoid-s14679" xml:space="preserve">radius ſegmenti E G, d. </s> <s xml:id="echoid-s14680" xml:space="preserve">erit hujus baſeos circumferen-<lb/>tia = {dc/r}. </s> <s xml:id="echoid-s14681" xml:space="preserve">& </s> <s xml:id="echoid-s14682" xml:space="preserve">longitudo B G = {ad<emph style="super">3</emph>/r<emph style="super">3</emph>}. </s> <s xml:id="echoid-s14683" xml:space="preserve">Soliditas autem Parabolæ Cu-<lb/>bicæ eſt = {3/10} acr, diſtatque ejus centrum gravitatis a puncto F, {3/8}a. <lb/></s> <s xml:id="echoid-s14684" xml:space="preserve">unde momentum hujus erit = {9/86} aacr. </s> <s xml:id="echoid-s14685" xml:space="preserve">Eſt ſoliditas ſegmenti <lb/>D B E = {3acd<emph style="super">5</emph>/10r<emph style="super">4</emph>}. </s> <s xml:id="echoid-s14686" xml:space="preserve">ejuſque momentum {9a acd<emph style="super">8</emph>/80r<emph style="super">7</emph>}. </s> <s xml:id="echoid-s14687" xml:space="preserve">ſed eſt {9/80} aacr, ad <lb/>{9aacd<emph style="super">8</emph>/80r<emph style="super">7</emph>}:</s> <s xml:id="echoid-s14688" xml:space="preserve">: r<emph style="super">8</emph>, ad d<emph style="super">8</emph>. </s> <s xml:id="echoid-s14689" xml:space="preserve">quare momenta integræ Parabolæ Cubicæ <lb/>& </s> <s xml:id="echoid-s14690" xml:space="preserve">ſegmenti ſunt inter ſe, uti radii baſium elevati ad octavam po-<lb/>tentiam.</s> <s xml:id="echoid-s14691" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div549" type="section" level="1" n="549"> <head xml:id="echoid-head663" xml:space="preserve">PROPOSITIO LXX.</head> <p style="it"> <s xml:id="echoid-s14692" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14693" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14694" xml:space="preserve">fig. </s> <s xml:id="echoid-s14695" xml:space="preserve">I. </s> <s xml:id="echoid-s14696" xml:space="preserve">Si conſideretur Parabola Cubica A B C, abs-<lb/>que graritate, at que e vertice B pendeat pondus P, id babebit ad <lb/>Cobærentiam baſeos eandem proportionem, quamcunque longitudi. <lb/></s> <s xml:id="echoid-s14697" xml:space="preserve">nem babuerit Parabola.</s> <s xml:id="echoid-s14698" xml:space="preserve"/> </p> <pb o="595" file="0611" n="612" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s14699" xml:space="preserve">Nam in Parabola Cubica eſt B G. </s> <s xml:id="echoid-s14700" xml:space="preserve">B F:</s> <s xml:id="echoid-s14701" xml:space="preserve">: D E<emph style="super">3</emph>, <emph style="ol">AC</emph><emph style="super">3</emph>. </s> <s xml:id="echoid-s14702" xml:space="preserve">ſed ut <lb/><emph style="ol">DE</emph><emph style="super">3</emph> ad <emph style="ol">AC</emph><emph style="super">3</emph>, ita Cohærentia baſeos D G E ad Cohærentiam ba-<lb/>ſeos A F C. </s> <s xml:id="echoid-s14703" xml:space="preserve">adeoque ſunt hæ Cohærentiæ uti B G ad B F; </s> <s xml:id="echoid-s14704" xml:space="preserve">eſt au-<lb/>tem momentum ponderis P pendentis ex longitudine B G, ad mo-<lb/>mentum ponderis P pendentis ex longitudine B F, uti B G ad B F, <lb/>quare Cohærentiæ baſium, ſunt inter ſe uti momenta ponderis P, <lb/>adeoque erit hoc ſolidum Parabolicum ubivis æqualis Cohærentiæ.</s> <s xml:id="echoid-s14705" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14706" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14707" xml:space="preserve">Idem verum erit de dimidio ſolido parabolico Cubico <lb/>C F B E: </s> <s xml:id="echoid-s14708" xml:space="preserve">ſi ideo in ſuperficie ſuperiori F G B oneretur æquabiliter <lb/>pondere, erit id pondus ſupra F B ad pondus ſupra G B, uti eſt F B <lb/>ad G B, hoc eſt uti Cohærentia baſeos C F ad eam baſeos G E.</s> <s xml:id="echoid-s14709" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div550" type="section" level="1" n="550"> <head xml:id="echoid-head664" xml:space="preserve">PROPOSITIO LXXI.</head> <p style="it"> <s xml:id="echoid-s14710" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14711" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14712" xml:space="preserve">fig. </s> <s xml:id="echoid-s14713" xml:space="preserve">I. </s> <s xml:id="echoid-s14714" xml:space="preserve">Data Conoide Cubica parabolica A B C, <lb/>ejuſque dato ſegmento D B E, una cum appenſo pondere P maximo, <lb/>quod geri poteſt ex D B E, invenire pondus ex vertice E Conoidis <lb/>A B C ſuſpendendum, quod ad ſuam Cobærentiam eandem bæbeat <lb/>rationem ac pondus P cum gravitate D B E ad ſuam.</s> <s xml:id="echoid-s14715" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14716" xml:space="preserve">Quantitatibus deſignatis ut in Propoſitione LXIX, erit momen-<lb/>tum ex gravitate Parabolæ D B E una cum momento ponderis P <lb/>= {9aacd<emph style="super">8</emph>/80r<emph style="super">7</emph>} + {ad<emph style="super">3</emph>p/r<emph style="super">3</emph>}. </s> <s xml:id="echoid-s14717" xml:space="preserve">Cohærentia vero = d<emph style="super">3</emph>. </s> <s xml:id="echoid-s14718" xml:space="preserve">& </s> <s xml:id="echoid-s14719" xml:space="preserve">momentum ex <lb/>gravitate parabolæ A B C = {9/80} aacr & </s> <s xml:id="echoid-s14720" xml:space="preserve">momentum ponderis quæ-<lb/>ſiti = a x. </s> <s xml:id="echoid-s14721" xml:space="preserve">Cohærentia = r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14722" xml:space="preserve">adeoque ordinanda erit hæc propor-<lb/>tio, {9aacd<emph style="super">8</emph>/80r<emph style="super">7</emph>} + {ad<emph style="super">3</emph>p/r<emph style="super">3</emph>}, d<emph style="super">3</emph>:</s> <s xml:id="echoid-s14723" xml:space="preserve">: {9/80} aacr + ax, r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14724" xml:space="preserve">ex quibus eruitur <lb/>pondus quæſitum x = {9/80} {acd<emph style="super">7</emph>/r<emph style="super">4</emph>} + P - {9/80} acr.</s> <s xml:id="echoid-s14725" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div551" type="section" level="1" n="551"> <head xml:id="echoid-head665" xml:space="preserve">PROPOSITIO LXXII.</head> <p style="it"> <s xml:id="echoid-s14726" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14727" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14728" xml:space="preserve">fig. </s> <s xml:id="echoid-s14729" xml:space="preserve">I. </s> <s xml:id="echoid-s14730" xml:space="preserve">Data Conoide Parabolica Cubica D B E una <lb/>cum pondere P appenſo, ſummo quod geſtari poteſt, producere Co-<lb/>noidem, ita ut producta A B C momento ſuæ gravitatis babeat ad <pb o="596" file="0612" n="613" rhead="INTRODUCTIO AD COHÆRENTIAM"/> Cohærentiam ſuam eandem rationem, quam D B E m?</s> <s xml:id="echoid-s14731" xml:space="preserve">mentum cum <lb/>ſuo pondere habet ſuam Cohærentiam.</s> <s xml:id="echoid-s14732" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14733" xml:space="preserve">Quantitatibus vocatis ut ante in Prop. </s> <s xml:id="echoid-s14734" xml:space="preserve">LXIX. </s> <s xml:id="echoid-s14735" xml:space="preserve">erit momentum <lb/>ex gravitate ſolidi D B E = {9/80} a a c r. </s> <s xml:id="echoid-s14736" xml:space="preserve">& </s> <s xml:id="echoid-s14737" xml:space="preserve">momentum ponderis = a p, <lb/>ratio Cohærentiæ = r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14738" xml:space="preserve">Ponatur ordinata quæſita in ſegmento <lb/>= y. </s> <s xml:id="echoid-s14739" xml:space="preserve">ea enim datâ invenitur abſciſia facile, quia ut <emph style="ol">C F</emph><emph style="super">3</emph> ad <emph style="ol">G E</emph><emph style="super">3</emph> <lb/>:</s> <s xml:id="echoid-s14740" xml:space="preserve">: F B, ad G B. </s> <s xml:id="echoid-s14741" xml:space="preserve">hinc etiam r<emph style="super">3</emph>, y<emph style="super">3</emph>:</s> <s xml:id="echoid-s14742" xml:space="preserve">: {a. </s> <s xml:id="echoid-s14743" xml:space="preserve">ay<emph style="super">3</emph>/r<emph style="super">3</emph>} = F B. </s> <s xml:id="echoid-s14744" xml:space="preserve">unde ſoliditas <lb/>A B C quæſitæ paraboloidis erit = {3 a c y<emph style="super">5</emph>/10 r<emph style="super">4</emph>.</s> <s xml:id="echoid-s14745" xml:space="preserve">} & </s> <s xml:id="echoid-s14746" xml:space="preserve">momentum = {9/80} <lb/>{a a c y<emph style="super">8</emph>/r<emph style="super">7</emph>.</s> <s xml:id="echoid-s14747" xml:space="preserve">} ordinentur nunc momenta & </s> <s xml:id="echoid-s14748" xml:space="preserve">Cohærentiæ in proportio-<lb/>nem, erit <lb/>{9/80} a a c r + a p. </s> <s xml:id="echoid-s14749" xml:space="preserve">r<emph style="super">3</emph>:</s> <s xml:id="echoid-s14750" xml:space="preserve">: {9 a a c y<emph style="super">8</emph>. </s> <s xml:id="echoid-s14751" xml:space="preserve">y<emph style="super">3</emph>.</s> <s xml:id="echoid-s14752" xml:space="preserve">/80 r<emph style="super">7</emph>} <lb/>Ex quibus eruitur y = {5r<emph style="super">5</emph>+p r<emph style="super">4</emph>/a c.</s> <s xml:id="echoid-s14753" xml:space="preserve">}</s> </p> </div> <div xml:id="echoid-div552" type="section" level="1" n="552"> <head xml:id="echoid-head666" xml:space="preserve">PROPOSITIO LXXIII.</head> <p style="it"> <s xml:id="echoid-s14754" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14755" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14756" xml:space="preserve">fig. </s> <s xml:id="echoid-s14757" xml:space="preserve">1. </s> <s xml:id="echoid-s14758" xml:space="preserve">In Conoide Parabolica quarti ordinis <lb/>A B C, ejusque ſegmento D B E, exponere quænam ſit Proportio <lb/>momentorum ex propria gravitate ad Cobærentias.</s> <s xml:id="echoid-s14759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14760" xml:space="preserve">Vocetur C F, r. </s> <s xml:id="echoid-s14761" xml:space="preserve">F B, a. </s> <s xml:id="echoid-s14762" xml:space="preserve">Peripheria circuli baſeos = c. </s> <s xml:id="echoid-s14763" xml:space="preserve">& </s> <s xml:id="echoid-s14764" xml:space="preserve">ſit pa-<lb/>rabolæ natura 1 x<unsure/> = y<emph style="super">4</emph>. </s> <s xml:id="echoid-s14765" xml:space="preserve">ſit G E = b. </s> <s xml:id="echoid-s14766" xml:space="preserve">peripheria = {b c/r}. </s> <s xml:id="echoid-s14767" xml:space="preserve">G B <lb/>abſciſſa = {a b<emph style="super">4</emph>/r<emph style="super">4</emph>}</s> </p> <p> <s xml:id="echoid-s14768" xml:space="preserve">Erit ſoliditas Parabolæ A B C = {1/3}a c r. </s> <s xml:id="echoid-s14769" xml:space="preserve">quia in omni Parabola, <lb/>poſito y<emph style="super">m</emph> = x. </s> <s xml:id="echoid-s14770" xml:space="preserve">ſoliditas eſt = {m/2m+4} a c r. </s> <s xml:id="echoid-s14771" xml:space="preserve">Centrum gravitatis <lb/>deinde inveſtigetur, diſtat hoc etiam in omni Parabola a vertice B, <lb/>quantitate {m+2/2m+2} a. </s> <s xml:id="echoid-s14772" xml:space="preserve">adeoque in caſu propoſito diſtabit centrum <lb/>gravitatis a puncto G quantitate {2/8} a. </s> <s xml:id="echoid-s14773" xml:space="preserve">per quam multiplicata ſolidi- <pb o="597" file="0613" n="614" rhead="CORPORUM FIRMORUM."/> tas parabolæ, dabit {2/15} a a c r. </s> <s xml:id="echoid-s14774" xml:space="preserve">eodem modo reperitur momentum <lb/>ſegmenti D B E = {2a a c b<emph style="super">10</emph>/15 r<emph style="super">9</emph>}. </s> <s xml:id="echoid-s14775" xml:space="preserve">Eſt autem Cohærentia baſeos Parabo-<lb/>læ A B C = 8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14776" xml:space="preserve">& </s> <s xml:id="echoid-s14777" xml:space="preserve">Cohærentia baſeos D G E = 8b3. </s> <s xml:id="echoid-s14778" xml:space="preserve">quare momen-<lb/>tum Parabolæ A B C, ad ſuam Cohærentiam eſt, ut {2/15} a a c r ad 8r3. <lb/></s> <s xml:id="echoid-s14779" xml:space="preserve">& </s> <s xml:id="echoid-s14780" xml:space="preserve">momentum ſegmenti D B E ad ſuam Cohærentiam, uti {2a a c b<emph style="super">10</emph>/15 r<emph style="super">9</emph>.</s> <s xml:id="echoid-s14781" xml:space="preserve">} <lb/>ad 8b<emph style="super">3</emph>.</s> <s xml:id="echoid-s14782" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14783" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14784" xml:space="preserve">1. </s> <s xml:id="echoid-s14785" xml:space="preserve">Ergo ſolidi Parabolici A B C, Cohærentia ad ſuum momen-<lb/>tum ex gravitate eſt in minori ratione, quam Cohærentia ſegmenti <lb/>D B E ad ſuum momentum. </s> <s xml:id="echoid-s14786" xml:space="preserve">Nam Cohærentia A B C ad ſuum mo-<lb/>mentum eſt ut r<emph style="super">3</emph> ad {2/15} a a c r. </s> <s xml:id="echoid-s14787" xml:space="preserve">ſive ut r<emph style="super">9</emph> ad {2/15} a a c r<emph style="super">7</emph>. </s> <s xml:id="echoid-s14788" xml:space="preserve">eſt Cohæren-<lb/>tia ſegmenti D B E ad ſuum momentum uti b3 ad {2 a a c b<emph style="super">10</emph>/15 r<emph style="super">9</emph>.</s> <s xml:id="echoid-s14789" xml:space="preserve">} ſive uti <lb/>r9 ad {2/15} a a c b<emph style="super">7</emph>. </s> <s xml:id="echoid-s14790" xml:space="preserve">quia autem r eſt major quam b. </s> <s xml:id="echoid-s14791" xml:space="preserve">erit ratio r<emph style="super">9</emph> ad {2/15} <lb/>a a c r<emph style="super">7</emph> minor quam r<emph style="super">9</emph>, ad {2/15} a a c b7.</s> <s xml:id="echoid-s14792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14793" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14794" xml:space="preserve">2. </s> <s xml:id="echoid-s14795" xml:space="preserve">Ergo majus pondus poterit vertici B ſegmenti D B E <lb/>appendi, quam paraboloidis A B C.</s> <s xml:id="echoid-s14796" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div553" type="section" level="1" n="553"> <head xml:id="echoid-head667" xml:space="preserve">PROPOSITIO LXXIV.</head> <p style="it"> <s xml:id="echoid-s14797" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14798" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14799" xml:space="preserve">fig. </s> <s xml:id="echoid-s14800" xml:space="preserve">1. </s> <s xml:id="echoid-s14801" xml:space="preserve">Dato ſegmento præcedentis Paraboloidis <lb/>D B E gravi, atque pondere P maximo, quod geſtari poſſit, inve-<lb/>nire pondus ex vertice B Parabolæ A B C geſtandum.</s> <s xml:id="echoid-s14802" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14803" xml:space="preserve">Quantitatibus deſignatis ut ante, & </s> <s xml:id="echoid-s14804" xml:space="preserve">pondere P vocato = p. </s> <s xml:id="echoid-s14805" xml:space="preserve">quæ-<lb/>ſito = x. </s> <s xml:id="echoid-s14806" xml:space="preserve">ordinanda erit hæc proportio {2 a a c b<emph style="super">10</emph>/15 r<emph style="super">9</emph>} + {a b<emph style="super">4</emph> p. </s> <s xml:id="echoid-s14807" xml:space="preserve">8 b<emph style="super">3</emph>:</s> <s xml:id="echoid-s14808" xml:space="preserve">:/r<emph style="super">4</emph>} <lb/>{2/15} a a c r + a x. </s> <s xml:id="echoid-s14809" xml:space="preserve">8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14810" xml:space="preserve">ex quibus eruitur x = {2 a c b 7/15 r<emph style="super">6</emph>} + {b p/r}-{2/15<unsure/>} a c r.</s> <s xml:id="echoid-s14811" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div554" type="section" level="1" n="554"> <head xml:id="echoid-head668" xml:space="preserve">PROPOSITIO LXXV.</head> <p style="it"> <s xml:id="echoid-s14812" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14813" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14814" xml:space="preserve">Fig. </s> <s xml:id="echoid-s14815" xml:space="preserve">3. </s> <s xml:id="echoid-s14816" xml:space="preserve">Sit Parabola Apolloniana A D B, cujus <lb/>Tangens ſit T A, ducta ſit T B parallela ad A D, circa A T veluti <lb/>axin & </s> <s xml:id="echoid-s14817" xml:space="preserve">radio T B circumagatur Parabola, deſcribetur corpus pa-<lb/>raboliforme A C B A fig. </s> <s xml:id="echoid-s14818" xml:space="preserve">4. </s> <s xml:id="echoid-s14819" xml:space="preserve">cujus baſis eſt C T B, dico hoc corpus <pb o="598" file="0614" n="615" rhead="INTRODUCTIO AD COHÆRENTIAM"/> baſi C B parieti infixum, ita ut axis A T ſit horizontalis, ſua gra-<lb/>vitate eſſe in omni ſectione æqualis Cohærentiæ.</s> <s xml:id="echoid-s14820" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14821" xml:space="preserve">Propoſuit hoc Cl. </s> <s xml:id="echoid-s14822" xml:space="preserve">Leibnitſius in Actis Lipſ. </s> <s xml:id="echoid-s14823" xml:space="preserve">A°. </s> <s xml:id="echoid-s14824" xml:space="preserve">1684 inſtar ad-<lb/>ditamenti, quod abſque demonſtratione reliquit, quam hic adde-<lb/>mus: </s> <s xml:id="echoid-s14825" xml:space="preserve">Vocetur A T, a. </s> <s xml:id="echoid-s14826" xml:space="preserve">T B, r. </s> <s xml:id="echoid-s14827" xml:space="preserve">circumferentia circuli, cujus T B <lb/>eſt radius, ſit = c. </s> <s xml:id="echoid-s14828" xml:space="preserve">Erit ſoliditas corporis A C B = {1/10} a c r. </s> <s xml:id="echoid-s14829" xml:space="preserve">Cen-<lb/>trum vero gravitatis eſt in axe A T, diſſitum a puncto T = {1/6} a, un-<lb/>de momentum gravitatis in hoc corpore A C B eſt = {1/60} a a c r. </s> <s xml:id="echoid-s14830" xml:space="preserve">Co-<lb/>hærentia autem eſt ut Cubus baſeos C B = 8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14831" xml:space="preserve">fiat ſectio in O, pla-<lb/>no F O E parallelo baſi C T B. </s> <s xml:id="echoid-s14832" xml:space="preserve">voceturque A O = d. </s> <s xml:id="echoid-s14833" xml:space="preserve">erit O E = {d d r/a a}. <lb/></s> <s xml:id="echoid-s14834" xml:space="preserve">quia T B. </s> <s xml:id="echoid-s14835" xml:space="preserve">O E:</s> <s xml:id="echoid-s14836" xml:space="preserve">: peripheria circuli â B deſcripti, ad peripheriam ab E. </s> <s xml:id="echoid-s14837" xml:space="preserve"><lb/>erit hæc peripheria = {c d d/a a}. </s> <s xml:id="echoid-s14838" xml:space="preserve">quare ſoliditas corporis A F O E <lb/>= {c d<emph style="super">5</emph> r.</s> <s xml:id="echoid-s14839" xml:space="preserve">/10a<emph style="super">4</emph>} Centrum gravitatis in A F E diſtat ab O = {1/6} d. </s> <s xml:id="echoid-s14840" xml:space="preserve">adeoque <lb/>erit momentum hujus corporis ex gravitate = {c d<emph style="super">6</emph> r.</s> <s xml:id="echoid-s14841" xml:space="preserve">/60 a<emph style="super">4</emph>} Cohærentia <lb/>baſeos E O F eſt uti Cubus ex E F = {8d<emph style="super">6</emph> r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14842" xml:space="preserve">/a<emph style="super">6</emph>} Si igitur momenta <lb/>gravitatis in corpore A C B & </s> <s xml:id="echoid-s14843" xml:space="preserve">A F E ſint ad Cohærentias ſuarum <lb/>baſium in eadem ratione, erunt quantitates proportionales, ordi-<lb/>nentur igitur in proportionem <lb/>{1/60} a a c r. </s> <s xml:id="echoid-s14844" xml:space="preserve">8r<emph style="super">3</emph>:</s> <s xml:id="echoid-s14845" xml:space="preserve">: {1 c d<emph style="super">6</emph>r/60 a<emph style="super">4</emph>}, {8d<emph style="super">6</emph>r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14846" xml:space="preserve">/a<emph style="super">6</emph>}</s> </p> <p> <s xml:id="echoid-s14847" xml:space="preserve">Multiplicatis extremis mediisque terminis, habetur <lb/>{1/60} a a c r X {8 d<emph style="super">6</emph> r<emph style="super">3</emph>.</s> <s xml:id="echoid-s14848" xml:space="preserve">/a<emph style="super">6</emph>} & </s> <s xml:id="echoid-s14849" xml:space="preserve">{1 c d<emph style="super">6</emph> r/60 a<emph style="super">4</emph>} X 8 r<emph style="super">3</emph>. <lb/></s> <s xml:id="echoid-s14850" xml:space="preserve">quæ quantitates ſunt inter ſe æquales, adeoque priores erant pro-<lb/>portionales, unde momenta cujuslibet ſectionis in hoc corpore <lb/>paraboliformi ſunt ſemper ad ſuas Cohærentias in eadem propor-<lb/>tione, hoc eſt, erit corpus grave ubivis æquabilis reſiſtentiæ. </s> <s xml:id="echoid-s14851" xml:space="preserve"><lb/>Q. </s> <s xml:id="echoid-s14852" xml:space="preserve">E. </s> <s xml:id="echoid-s14853" xml:space="preserve">D.</s> <s xml:id="echoid-s14854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14855" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14856" xml:space="preserve">Si corpus paraboliforme A B C ſecetur bifariam plano ho-<lb/>rizontali tranſeunte per axem A T, erit corpus A T B E A in qua-<lb/>libet Sectione O E æquabilis Cohærentiæ.</s> <s xml:id="echoid-s14857" xml:space="preserve"/> </p> <pb o="599" file="0615" n="616" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div555" type="section" level="1" n="555"> <head xml:id="echoid-head669" xml:space="preserve">PROPOSITIO LXXVI.</head> <p style="it"> <s xml:id="echoid-s14858" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14859" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14860" xml:space="preserve">fig. </s> <s xml:id="echoid-s14861" xml:space="preserve">4. </s> <s xml:id="echoid-s14862" xml:space="preserve">Dato ſegmento gravi E A F corporis ejusdem <lb/>par aboliformis A B C & </s> <s xml:id="echoid-s14863" xml:space="preserve">pondere P maximo appenſo vertici A; </s> <s xml:id="echoid-s14864" xml:space="preserve">in-<lb/>venire pondus maximum, quod ex vertice eodem A ſolidi gravis <lb/>B A C ſuſpendi poterit.</s> <s xml:id="echoid-s14865" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14866" xml:space="preserve">Quantitibus vocatis ut ante, erit momentum ſegmenti E A F <lb/>ex gravitate = {1 d<emph style="super">6</emph>c r/60a<emph style="super">4</emph>}. </s> <s xml:id="echoid-s14867" xml:space="preserve">pondus P vocetur = p. </s> <s xml:id="echoid-s14868" xml:space="preserve">erit hujus momen-<lb/>tum = p d. </s> <s xml:id="echoid-s14869" xml:space="preserve">pondus quæſitum vocetur = x, erit momentum = a x. </s> <s xml:id="echoid-s14870" xml:space="preserve">qua-<lb/>re ſegmenti momentum E A F una cum ſuo pondere P debet ha-<lb/>bere eandem rationem ad ſuam Cohærentiam, uti momentum A B C <lb/>cum ſuo pondere x ad ſuam, unde ordinanda erit hæc proportio <lb/>{1 d<emph style="super">6</emph> c r/60 a<emph style="super">4</emph>} + d p. </s> <s xml:id="echoid-s14871" xml:space="preserve">{8 d<emph style="super">6</emph> r<emph style="super">3</emph>/a<emph style="super">6</emph>}:</s> <s xml:id="echoid-s14872" xml:space="preserve">: {1/66<unsure/>} a a c r. </s> <s xml:id="echoid-s14873" xml:space="preserve">+ a x. </s> <s xml:id="echoid-s14874" xml:space="preserve">8 r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14875" xml:space="preserve">unde erit <lb/>x = {a<emph style="super">5</emph> p/d<emph style="super">5</emph>}.</s> <s xml:id="echoid-s14876" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div556" type="section" level="1" n="556"> <head xml:id="echoid-head670" xml:space="preserve">PROPOSITIO LXXVII.</head> <p style="it"> <s xml:id="echoid-s14877" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14878" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14879" xml:space="preserve">fig. </s> <s xml:id="echoid-s14880" xml:space="preserve">5. </s> <s xml:id="echoid-s14881" xml:space="preserve">Sit Parabola D A B, in qua D B or dinata <lb/>habeatur pro axe, circa quem parabola circum volvatur, genera-<lb/>bitur corpus paraboliforme, cujus momentum ex gravitate & </s> <s xml:id="echoid-s14882" xml:space="preserve">Cohæ-<lb/>rentia reſpectiva poſtulentur determinanda, ut & </s> <s xml:id="echoid-s14883" xml:space="preserve">ſegmenti F K B F.</s> <s xml:id="echoid-s14884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14885" xml:space="preserve">Vocetur A D, r. </s> <s xml:id="echoid-s14886" xml:space="preserve">D B, a. </s> <s xml:id="echoid-s14887" xml:space="preserve">peripheria circuli a puncto A deſcri-<lb/>bendi ſit = c. </s> <s xml:id="echoid-s14888" xml:space="preserve">erit ſoliditas corporis paraboliformis = {4/45} a c r: </s> <s xml:id="echoid-s14889" xml:space="preserve">diſtat <lb/>autem centrum gravitatis in axe D B a puncto D, quantitate {5/16} a. <lb/></s> <s xml:id="echoid-s14890" xml:space="preserve">adeoque erit momentum ex gravitate hujus ſolidi = {1/12} a a c r. </s> <s xml:id="echoid-s14891" xml:space="preserve">Co-<lb/>hærentia vero reſpectiva erit = 8r<emph style="super">3</emph>. </s> <s xml:id="echoid-s14892" xml:space="preserve">ut autem momentum ſeg-<lb/>menti F K B C determinemus, vocetur A E, x. </s> <s xml:id="echoid-s14893" xml:space="preserve">erit E D = r - x. </s> <s xml:id="echoid-s14894" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s14895" xml:space="preserve">C B = a-a{x.</s> <s xml:id="echoid-s14896" xml:space="preserve">/r} peripheria a puncto F circuli deſcribenda erit <lb/>= {c r- c x.</s> <s xml:id="echoid-s14897" xml:space="preserve">/r} quare ſoliditas hujus ſegmenti erit <pb o="600" file="0616" n="617" rhead="INTRODUCTIO AD COHÆRENTIAM"/> {4 a c r r- 8 a c r x+4 a c x x-4 a c r r {x/r}-8 a c r {x/r}-4 a c x x {x/r}/15 r}. <lb/></s> <s xml:id="echoid-s14898" xml:space="preserve">quæ quantitas multiplicata per {5/16} a-{5/16}a {x/r}. </s> <s xml:id="echoid-s14899" xml:space="preserve">dat momentum <lb/>ſegmenti F K B F. </s> <s xml:id="echoid-s14900" xml:space="preserve">eſt autem Cohærentia baſeos F C K = 8 r<emph style="super">3</emph>-16 r r x <lb/>+ 16 r x x-8 x 3. </s> <s xml:id="echoid-s14901" xml:space="preserve">quare determinata ſunt momenta ſolidi A B O, <lb/>F B K. </s> <s xml:id="echoid-s14902" xml:space="preserve">& </s> <s xml:id="echoid-s14903" xml:space="preserve">Cohærentiæ ipſorum.</s> <s xml:id="echoid-s14904" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div557" type="section" level="1" n="557"> <head xml:id="echoid-head671" xml:space="preserve">PROPOSITIO LXXVIII.</head> <p style="it"> <s xml:id="echoid-s14905" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14906" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14907" xml:space="preserve">fig. </s> <s xml:id="echoid-s14908" xml:space="preserve">6. </s> <s xml:id="echoid-s14909" xml:space="preserve">Solidi parabolici utrimque plani A M O F E, <lb/>cujus vertex eſt E, tum abſciſſæ portionis D G P E H, Cohæren-<lb/>tiæ baſium A M O F, D G P H, parieti ad horizontem perpendicu-<lb/>lari affix arum ſunt inter ſe ut longitudines axium E B. </s> <s xml:id="echoid-s14910" xml:space="preserve">E C. </s> <s xml:id="echoid-s14911" xml:space="preserve">poſi-<lb/>tis ſuperficiebus A E F, M E O ad horizontem perpendicularibus.</s> <s xml:id="echoid-s14912" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14913" xml:space="preserve">Nam eſt Cohærentia baſeos A F O M, ad D G P H in ratione du-<lb/>plicata altitudinis A F, ad D G. </s> <s xml:id="echoid-s14914" xml:space="preserve">& </s> <s xml:id="echoid-s14915" xml:space="preserve">ſimplici latitudinis F O, ad <lb/>G P. </s> <s xml:id="echoid-s14916" xml:space="preserve">ſed eſt G P = F O. </s> <s xml:id="echoid-s14917" xml:space="preserve">quare erunt ambarum baſium Cohærentiæ, <lb/>uti quadrata altitudinum A F, D G. </s> <s xml:id="echoid-s14918" xml:space="preserve">ſed ex natura Parabolæ eſt E B, <lb/>E C:</s> <s xml:id="echoid-s14919" xml:space="preserve">: <emph style="ol">A F<emph style="super">q</emph></emph>. </s> <s xml:id="echoid-s14920" xml:space="preserve"><emph style="ol">D G<emph style="super">q</emph></emph>. </s> <s xml:id="echoid-s14921" xml:space="preserve">quare ſunt Cohærentiæ baſium uti longitudines <lb/>axium E B, E C.</s> <s xml:id="echoid-s14922" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14923" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14924" xml:space="preserve">1. </s> <s xml:id="echoid-s14925" xml:space="preserve">Si ſolidi Parabolici dimidium E B F O E conſideretur, <lb/>& </s> <s xml:id="echoid-s14926" xml:space="preserve">abſciſſa portio E C G P E, vel alterum dimidium E B A M E, & </s> <s xml:id="echoid-s14927" xml:space="preserve"><lb/>abſciſſa portio E C D H E, eadem demonſtratio locum habebit, <lb/>eritque Cohærentia baſeos B F O, ad C G P, aut B A M ad D C H, <lb/>uti longitudo E B ad E C</s> </p> <p> <s xml:id="echoid-s14928" xml:space="preserve">Corol 2. </s> <s xml:id="echoid-s14929" xml:space="preserve">Si ex vertice integri vel dimidii ſolidi hujus Parabolici <lb/>pendeat pondus P, hujus momentum ad Cohærentiam baſium <lb/>A M O F, D G P H eandem habebit rationem, adeoque erunt <lb/>ejuſmodi ſolida æqualis ubivis Cohærentiæ, non conſiderata eorum <lb/>gravitate.</s> <s xml:id="echoid-s14930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14931" xml:space="preserve">Nam momentum ponderis P pendentis ex vecte E B, eſt ad mo-<lb/>mentum ejuſdem ponderis P, pendentis ex vecte E C, veluti eſt <lb/>E B ad E C: </s> <s xml:id="echoid-s14932" xml:space="preserve">ſed Cohærentiæ horum ſolidorum ſunt uti E B ad E C, <pb o="601" file="0617" n="618" rhead="CORPORUM FIRMORUM."/> quare momentum ponderis P habet ad utriuſque ſolidi Cohæren-<lb/>tiam eandem rationem.</s> <s xml:id="echoid-s14933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14934" xml:space="preserve">Corol. </s> <s xml:id="echoid-s14935" xml:space="preserve">3. </s> <s xml:id="echoid-s14936" xml:space="preserve">Si dimidii ſolidi parabolici E B A M E ſuperficiei ſupe-<lb/>riori E B E imponatur aliquod parallelopipedum grave, aut pon-<lb/>dus æquabiliter ſuper eam diſperſum, erit uti quantitas ponderis <lb/>ſupra B E, ad eam ſupra portionem C E E, ita Cohærentia ſolidi <lb/>E A B E ad Cohærentiam ſolidi E D C E: </s> <s xml:id="echoid-s14937" xml:space="preserve">quamobrem erit Cohæren-<lb/>tia proportionalis ponderi impoſito, & </s> <s xml:id="echoid-s14938" xml:space="preserve">ſolidum æquabilis Cohæren-<lb/>tiæ per totam longitudinem.</s> <s xml:id="echoid-s14939" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div558" type="section" level="1" n="558"> <head xml:id="echoid-head672" xml:space="preserve">PROPOSITIO LXXIX.</head> <p> <s xml:id="echoid-s14940" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14941" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14942" xml:space="preserve">fig. </s> <s xml:id="echoid-s14943" xml:space="preserve">6. </s> <s xml:id="echoid-s14944" xml:space="preserve">Solidi Parabolici F O E M A E momentum <lb/>ex gravitate ad Cohærentiam baſeos A F O M majorem rationem <lb/>habet, quam portionis D G P E H momentum ex gravitate ad Co-<lb/>hærentiam baſeos D G P H.</s> <s xml:id="echoid-s14945" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14946" xml:space="preserve">Vocetur F A, a. </s> <s xml:id="echoid-s14947" xml:space="preserve">E B, b. </s> <s xml:id="echoid-s14948" xml:space="preserve">D G, c. </s> <s xml:id="echoid-s14949" xml:space="preserve">erit C E = {bcc.</s> <s xml:id="echoid-s14950" xml:space="preserve">/aa} Sit F O = d. <lb/></s> <s xml:id="echoid-s14951" xml:space="preserve">erit ſoliditas corporis A F E = {2/3} a b d. </s> <s xml:id="echoid-s14952" xml:space="preserve">& </s> <s xml:id="echoid-s14953" xml:space="preserve">ſoliditas corporis D G P E <lb/>= 2{b c<emph style="super">3</emph> d.</s> <s xml:id="echoid-s14954" xml:space="preserve">/3 aa} diſtat autem centrum gravitatis in plano parabolico <lb/>A F E {2/5} b, a puncto B in axe B E, adeoque diſtabit tantundem in <lb/>ſegmenti E E B medio a baſi A M F O. </s> <s xml:id="echoid-s14955" xml:space="preserve">hinc erit momentum <lb/>ſolidi Parabolici A F O E M = {4/15} a b b d. </s> <s xml:id="echoid-s14956" xml:space="preserve">& </s> <s xml:id="echoid-s14957" xml:space="preserve">momentum ſolidi <lb/>D G P E = {4 b b c<emph style="super">5</emph> d.</s> <s xml:id="echoid-s14958" xml:space="preserve">/15 a<emph style="super">4</emph>} Cohærentia baſeos ſolidi A F O E M eſt = a a d. </s> <s xml:id="echoid-s14959" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s14960" xml:space="preserve">Cohærentia ſolidi D G P E H = c c d. </s> <s xml:id="echoid-s14961" xml:space="preserve">quare erit momen-<lb/>tum ſolidi A F O E M ad ſuam Cohærentiam, uti {4/15} a b b d. </s> <s xml:id="echoid-s14962" xml:space="preserve"><lb/>ad a a d. </s> <s xml:id="echoid-s14963" xml:space="preserve">= {4/15} b b, ad a. </s> <s xml:id="echoid-s14964" xml:space="preserve">Et Momentum ſolidi D G P E H ad <lb/>ſuam Cohærentiam uti 4{b b c<emph style="super">5</emph>d/15 a<emph style="super">4</emph>} ad c c d. </s> <s xml:id="echoid-s14965" xml:space="preserve">= {4/15} b b c<emph style="super">3</emph>, ad a<emph style="super">4</emph>. </s> <s xml:id="echoid-s14966" xml:space="preserve">Sed <lb/>eſt b b ad a in majori ratione, quam b b c<emph style="super">3</emph> ad a<emph style="super">4</emph>. </s> <s xml:id="echoid-s14967" xml:space="preserve">quia a eſt major <lb/>quam c. </s> <s xml:id="echoid-s14968" xml:space="preserve">Ergo eſt momentum ex gravitate in ſolido A F E O M ad <lb/>ſuam Cohærentiam in majori ratione, quam eſt momentum gra-<lb/>vitatis in ſolido D G P H ad ſuam.</s> <s xml:id="echoid-s14969" xml:space="preserve"/> </p> <pb o="602" file="0618" n="619" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div559" type="section" level="1" n="559"> <head xml:id="echoid-head673" xml:space="preserve">PROPOSITIO LXXX.</head> <p> <s xml:id="echoid-s14970" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14971" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s14972" xml:space="preserve">fig. </s> <s xml:id="echoid-s14973" xml:space="preserve">6. </s> <s xml:id="echoid-s14974" xml:space="preserve">Dato momento ſolidi parabolici A F O E M, <lb/>& </s> <s xml:id="echoid-s14975" xml:space="preserve">ponderis P ex vertice pendentis, datoque momento ſolidi abſciſſi <lb/>D G P E H, invenire pondus ex vertice E ſuſpendendum, ita ut <lb/>momentum ſolidi A F O E M cum ſuo pondere, ſit ad momentum ſo-<lb/>lidi D G P E cum ſuo in eadem proportione ad Cohærentias.</s> <s xml:id="echoid-s14976" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14977" xml:space="preserve">Quantitatibus deſignatis ut in præcedenti Propoſitione, & </s> <s xml:id="echoid-s14978" xml:space="preserve">pon-<lb/>dere appenſo ex E B = p. </s> <s xml:id="echoid-s14979" xml:space="preserve">pondere ex E C poſito = x, ordi-<lb/>nabitur hæc proportio.</s> <s xml:id="echoid-s14980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14981" xml:space="preserve">{4/15}a b b d + b p. </s> <s xml:id="echoid-s14982" xml:space="preserve">a a d:</s> <s xml:id="echoid-s14983" xml:space="preserve">: {4/15} {b b c<emph style="super">5</emph> d/a<emph style="super">4</emph>} + {b c c x.</s> <s xml:id="echoid-s14984" xml:space="preserve">/a a} c c d. <lb/></s> <s xml:id="echoid-s14985" xml:space="preserve">unde eruitur x = {4/15} a b d + p --<unsure/> {4/15} {b c<emph style="super">3</emph> d.</s> <s xml:id="echoid-s14986" xml:space="preserve">/a a}</s> </p> </div> <div xml:id="echoid-div560" type="section" level="1" n="560"> <head xml:id="echoid-head674" xml:space="preserve">PROPOSITIO LXXXI.</head> <p> <s xml:id="echoid-s14987" xml:space="preserve">Tab. </s> <s xml:id="echoid-s14988" xml:space="preserve">26. </s> <s xml:id="echoid-s14989" xml:space="preserve">fig. </s> <s xml:id="echoid-s14990" xml:space="preserve">6. </s> <s xml:id="echoid-s14991" xml:space="preserve">Si momentum Gravitatis in ſolido parabolico <lb/>A F O E M, & </s> <s xml:id="echoid-s14992" xml:space="preserve">momentum ponderis P ex vertice E pendentis, ha-<lb/>beat ad Cohærentiam baſeos A F O M eandem rationem, erit <lb/>magnitudo ſolidi Parabolici ſexies ſumta æqualis ponderi P decies <lb/>quinquies aucto.</s> <s xml:id="echoid-s14993" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s14994" xml:space="preserve">Nam quantitatibus deſignatis ut ante, erit momentum gravitatis in <lb/>ſolido parabolico = {4/15} a b b d. </s> <s xml:id="echoid-s14995" xml:space="preserve">momentum ponderis P = b p. </s> <s xml:id="echoid-s14996" xml:space="preserve">Cohæ-<lb/>rentia baſeos = a a d; </s> <s xml:id="echoid-s14997" xml:space="preserve">ad quam cum utrumque momentum habet <lb/>eandem rationem, erit {4/15} a b b d = b p. </s> <s xml:id="echoid-s14998" xml:space="preserve">ſive {4/15} a b d = p. </s> <s xml:id="echoid-s14999" xml:space="preserve">unde 4 a b d <lb/>= 15 p. </s> <s xml:id="echoid-s15000" xml:space="preserve">Sed {2/3} a b d. </s> <s xml:id="echoid-s15001" xml:space="preserve">conſtituunt magnitudinem ſolidi parabolici, ea <lb/>vero ſexies ſumta eſt = 4 a b d. </s> <s xml:id="echoid-s15002" xml:space="preserve">quare ſexies magnitudo ſolidi eſt <lb/>= ponderi P decies quinquies aucto.</s> <s xml:id="echoid-s15003" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div561" type="section" level="1" n="561"> <head xml:id="echoid-head675" xml:space="preserve">PROPOSITIO LXXXII.</head> <p> <s xml:id="echoid-s15004" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15005" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15006" xml:space="preserve">fig. </s> <s xml:id="echoid-s15007" xml:space="preserve">7. </s> <s xml:id="echoid-s15008" xml:space="preserve">Sit ſolidum Paraboliforme A T C K B, ita <lb/>ut C ſit vertex Parabolæ, C T Tangens, in quam perpendicula-<lb/>ris ſit T A ſecans parabolam in A, ſit baſis T C K affixa parieti <pb o="603" file="0619" n="620" rhead="CORPORUM FIRMORUM."/> ad horizontem perpendiculari, erit momentum gravitatis in ſolido <lb/>A T C K B, ad momentum gravitatis in ſegmento A O F M B, poſi-<lb/>tâ ſectione O F M parallela ad T C K, uti Cohærentia baſeos <lb/>T C K ad Cohærentiam baſeos O F M.</s> <s xml:id="echoid-s15009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15010" xml:space="preserve">Vocetur C T, r. </s> <s xml:id="echoid-s15011" xml:space="preserve">A T, a. </s> <s xml:id="echoid-s15012" xml:space="preserve">O A, b. </s> <s xml:id="echoid-s15013" xml:space="preserve">O F, {b br.</s> <s xml:id="echoid-s15014" xml:space="preserve">/a a} C K, c. </s> <s xml:id="echoid-s15015" xml:space="preserve">Eſt ſpatium <lb/>O F A = {1/3} O F X O A = {1/3} {b<emph style="super">3</emph> r,/a a} & </s> <s xml:id="echoid-s15016" xml:space="preserve">ſpatium T C A = {1/3} a r: </s> <s xml:id="echoid-s15017" xml:space="preserve">adeo-<lb/>que ſoliditas O F M A B eſt = {b<emph style="super">3</emph> c r.</s> <s xml:id="echoid-s15018" xml:space="preserve">/3 a a} & </s> <s xml:id="echoid-s15019" xml:space="preserve">ſoliditas T C K A B = {1/3} a r c. <lb/></s> <s xml:id="echoid-s15020" xml:space="preserve">diſtantia autem centri gravitatis ab O F in plano O F A eſt = {3/10} A O. </s> <s xml:id="echoid-s15021" xml:space="preserve"><lb/>adeoque erit in corpore O F A M. </s> <s xml:id="echoid-s15022" xml:space="preserve">a ſectione O F M remotum {3/10} A O. </s> <s xml:id="echoid-s15023" xml:space="preserve"><lb/>hinc momentum ſolidi O A B M F, erit = {b<emph style="super">4</emph> c r.</s> <s xml:id="echoid-s15024" xml:space="preserve">/10 a a} & </s> <s xml:id="echoid-s15025" xml:space="preserve">momentum ſo-<lb/>lidi T C K A B ex gravitate erit = {a a r c.</s> <s xml:id="echoid-s15026" xml:space="preserve">/10} Eſt autem Cohærentia <lb/>baſeos O F M = {b<emph style="super">4</emph> r r c.</s> <s xml:id="echoid-s15027" xml:space="preserve">/a<emph style="super">4</emph>} & </s> <s xml:id="echoid-s15028" xml:space="preserve">Cohærentia baſeos T C K = r r c: </s> <s xml:id="echoid-s15029" xml:space="preserve">ordi-<lb/>nentur momenta gravitatis & </s> <s xml:id="echoid-s15030" xml:space="preserve">Cohærentiæ in proportionem, erit <lb/>{b<emph style="super">4</emph> c r.</s> <s xml:id="echoid-s15031" xml:space="preserve">/10 a a} {b<emph style="super">4</emph> r r c/a<emph style="super">4</emph>}:</s> <s xml:id="echoid-s15032" xml:space="preserve">: {a a r c.</s> <s xml:id="echoid-s15033" xml:space="preserve">/10} r r c. </s> <s xml:id="echoid-s15034" xml:space="preserve"><lb/>multiplicando enim extrema & </s> <s xml:id="echoid-s15035" xml:space="preserve">media per ſe habentur producta <lb/>utrimque æqualia. </s> <s xml:id="echoid-s15036" xml:space="preserve">{b<emph style="super">4</emph> c c r<emph style="super">3</emph>/10 a a} = {a a b<emph style="super">4</emph> c c r<emph style="super">3</emph>.</s> <s xml:id="echoid-s15037" xml:space="preserve">/10 a<emph style="super">4</emph>} adeoque quantitates an-<lb/>tea fuerunt proportionales, unde momenta gravium ſunt inter <lb/>ſe veluti Cohærentiæ: </s> <s xml:id="echoid-s15038" xml:space="preserve">hoc etiam alio modo demonſtravit Cl. </s> <s xml:id="echoid-s15039" xml:space="preserve"><lb/>Leibnitſius.</s> <s xml:id="echoid-s15040" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div562" type="section" level="1" n="562"> <head xml:id="echoid-head676" xml:space="preserve">PROPOSITIO LXXXIII.</head> <p> <s xml:id="echoid-s15041" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15042" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15043" xml:space="preserve">fig. </s> <s xml:id="echoid-s15044" xml:space="preserve">8. </s> <s xml:id="echoid-s15045" xml:space="preserve">Sit ſolidum B R S A a D C parallelopipedum <lb/>rectangulum, cujus latus B D C E ad horizontem perpendiculare: <lb/></s> <s xml:id="echoid-s15046" xml:space="preserve">ſit ſolidum parabolicum A a B E R S ex priori abſciſſum, atque ver-<lb/>tex parabolæ in a & </s> <s xml:id="echoid-s15047" xml:space="preserve">A, axes in a R, A S. </s> <s xml:id="echoid-s15048" xml:space="preserve">ordinatæ B R, E S: </s> <s xml:id="echoid-s15049" xml:space="preserve">tum <lb/>ſolidum reliquum B D C E a A baſi B D C E applicatum parieti per- <pb o="604" file="0620" n="621" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pendiculari, habebit momentum gravitatis, ad momentum ſegmen-<lb/>ti a A F G H, cujus baſis F G H eſt parallela ad B D C E, uti Cohæ-<lb/>rentia B D C E, eſt ad Cohærentiam F G H.</s> <s xml:id="echoid-s15050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15051" xml:space="preserve">Vocetur A D, a. </s> <s xml:id="echoid-s15052" xml:space="preserve">D B, b. </s> <s xml:id="echoid-s15053" xml:space="preserve">D C, c. </s> <s xml:id="echoid-s15054" xml:space="preserve">a G, x. </s> <s xml:id="echoid-s15055" xml:space="preserve">erit G F = {b x x.</s> <s xml:id="echoid-s15056" xml:space="preserve">/a a} Eſt <lb/>vero planum a G F = {1/3} a G X G F = {1b x<emph style="super">3</emph>/3a a} & </s> <s xml:id="echoid-s15057" xml:space="preserve">ſoliditas corporis <lb/>A a H G F = {b c x<emph style="super">3</emph>.</s> <s xml:id="echoid-s15058" xml:space="preserve">/3 a a} Cohærentia baſeos F G H ={b b x<emph style="super">4</emph> c.</s> <s xml:id="echoid-s15059" xml:space="preserve">/a<emph style="super">4</emph>} momen-<lb/>tum vero = {b c x<emph style="super">4</emph>/12 a a}. </s> <s xml:id="echoid-s15060" xml:space="preserve">quia centrum gravitatis in plano a D B, diſtat ab <lb/>F G = {1/4} a G. </s> <s xml:id="echoid-s15061" xml:space="preserve">ſoliditas corporis a A D B C eſt {1/3} a b c. </s> <s xml:id="echoid-s15062" xml:space="preserve">momentum <lb/>= {a ab c.</s> <s xml:id="echoid-s15063" xml:space="preserve">/12} & </s> <s xml:id="echoid-s15064" xml:space="preserve">Cohærentia baſeos D B C = b b c. </s> <s xml:id="echoid-s15065" xml:space="preserve">Eſt vero <lb/>{a a b c.</s> <s xml:id="echoid-s15066" xml:space="preserve">/12} b b c:</s> <s xml:id="echoid-s15067" xml:space="preserve">: {b c x<emph style="super">4</emph>.</s> <s xml:id="echoid-s15068" xml:space="preserve">/12 a a} {b b c x<emph style="super">4</emph>.</s> <s xml:id="echoid-s15069" xml:space="preserve">/a<emph style="super">4</emph>}</s> </p> <p> <s xml:id="echoid-s15070" xml:space="preserve">Quare hoc ſolidum ſe<unsure/>iſſum in quocunque loco ſectione parallelâ <lb/>ad baſin B D C, ſemper habebit momenta ſuæ gravitatis in ratione <lb/>Cohærentiæ baſium.</s> <s xml:id="echoid-s15071" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div563" type="section" level="1" n="563"> <head xml:id="echoid-head677" xml:space="preserve">PROPOSITIO LXXXIV.</head> <p> <s xml:id="echoid-s15072" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15073" xml:space="preserve">XXVI fig. </s> <s xml:id="echoid-s15074" xml:space="preserve">9. </s> <s xml:id="echoid-s15075" xml:space="preserve">Dato Cuneo paraboliformi D C O B F cujus <lb/>baſis D C O B parieti perpendiculari ad horizontem ſit infixa, axis <lb/>parabolæ A F, invenire momentum gravitatis, Cohærentiam ba-<lb/>ſeos, at que eadem in ſegmento K E G F, cujus baſis K E G ſit pa-<lb/>rallela ad C D B O.</s> <s xml:id="echoid-s15076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15077" xml:space="preserve">Vocetur C O, a. </s> <s xml:id="echoid-s15078" xml:space="preserve">O B, b. </s> <s xml:id="echoid-s15079" xml:space="preserve">A F, d. </s> <s xml:id="echoid-s15080" xml:space="preserve">invenietur ſoliditas Cunei pa-<lb/>rabolici D C O B F = {2/3} a b d. </s> <s xml:id="echoid-s15081" xml:space="preserve">diſtantia Centri gravitatis a baſi D C O B <lb/>in ſegmento horizontali A F, eſt = {2/7} A F = {2/7} d. </s> <s xml:id="echoid-s15082" xml:space="preserve">adeoque erit momen-<lb/>tum Cunei ex gravitate = {4/35} a b d d. </s> <s xml:id="echoid-s15083" xml:space="preserve">eſt vero Cohærentia baſeos = a a b. <lb/></s> <s xml:id="echoid-s15084" xml:space="preserve">adeoque erit momentum ex gravitate ad Cohærentiam uti {4/35} d d <lb/>ad a. </s> <s xml:id="echoid-s15085" xml:space="preserve">Vocetur H F x. </s> <s xml:id="echoid-s15086" xml:space="preserve">erit Cohærentia baſeos. </s> <s xml:id="echoid-s15087" xml:space="preserve">K E G = {a a b x<emph style="super">2</emph>.</s> <s xml:id="echoid-s15088" xml:space="preserve">/d d} <lb/>& </s> <s xml:id="echoid-s15089" xml:space="preserve">momentum ex gravitate = {4 a b x{7/2}.</s> <s xml:id="echoid-s15090" xml:space="preserve">/35 d{3/2}}</s> </p> <pb o="605" file="0621" n="622" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div564" type="section" level="1" n="564"> <head xml:id="echoid-head678" style="it" xml:space="preserve">De Corporibus Hyperbolicis.</head> <head xml:id="echoid-head679" xml:space="preserve">PROPOSITIO LXXXV.</head> <p> <s xml:id="echoid-s15091" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15092" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15093" xml:space="preserve">fig. </s> <s xml:id="echoid-s15094" xml:space="preserve">10. </s> <s xml:id="echoid-s15095" xml:space="preserve">Corporis Hyperbolici generati ex circum-<lb/>gyrata Hyperbola A B D circa axin A D, cujus baſis E D B eſt pa-<lb/>rieti perpendiculari ad horizontem affixa, determinare momentum <lb/>ex gravitate, & </s> <s xml:id="echoid-s15096" xml:space="preserve">Cohærentiam baſeos B D E reſpectivam.</s> <s xml:id="echoid-s15097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15098" xml:space="preserve">Vocetur A D, a. </s> <s xml:id="echoid-s15099" xml:space="preserve">& </s> <s xml:id="echoid-s15100" xml:space="preserve">axis Hyperbolæ primus A L, 2 b. </s> <s xml:id="echoid-s15101" xml:space="preserve">B D radius <lb/>baſeos, r. </s> <s xml:id="echoid-s15102" xml:space="preserve">circumferentia circuli a puncto B deſ<unsure/>cripti, c. </s> <s xml:id="echoid-s15103" xml:space="preserve">tum erue-<lb/>tur ſoliditas corporis Hyperbolici = {a a c r + 3 a b c r.</s> <s xml:id="echoid-s15104" xml:space="preserve">/6 a + 12 b} Centri <lb/>gravitatis in axe A D diſtantia â puncto D eſt = {a a + 4 a b.</s> <s xml:id="echoid-s15105" xml:space="preserve">/4 a + 12 b} <lb/>Soliditate igitur per hanc diſtantiam â D multiplicata, habebitur <lb/>momentum corporis Hyperbolici <lb/>{a<emph style="super">4</emph> c r + 7 a<emph style="super">3</emph> b c r + 12 a a b b c r.</s> <s xml:id="echoid-s15106" xml:space="preserve">/24 a a + 120 a b + 144 b b} <lb/>Cohærentia autem baſeos eſt = 8 r<emph style="super">3</emph>.</s> <s xml:id="echoid-s15107" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div565" type="section" level="1" n="565"> <head xml:id="echoid-head680" xml:space="preserve">PROPOSITIO LXXXVI.</head> <p> <s xml:id="echoid-s15108" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15109" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15110" xml:space="preserve">fig. </s> <s xml:id="echoid-s15111" xml:space="preserve">10. </s> <s xml:id="echoid-s15112" xml:space="preserve">Corporis Hyperbolici A B E Cohærentia, eſt <lb/>ad Cohærentiam ſegmenti F A G, in ratione compoſita ex D A X <lb/>D L X B E. </s> <s xml:id="echoid-s15113" xml:space="preserve">ad H A X H L X G F.</s> <s xml:id="echoid-s15114" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15115" xml:space="preserve">A L ſupponitur axis Hyperbolæ primus, ponatur pondus I pen-<lb/>dens ex vertice Hyperbolæ A B E eſſe ſummum, quod appendi poſ-<lb/>ſit, adeoque æquale Cohærentiæ baſeos B D E. </s> <s xml:id="echoid-s15116" xml:space="preserve">& </s> <s xml:id="echoid-s15117" xml:space="preserve">pondus K pen-<lb/>dens ex vertice ſegmenti F A G etiam ſummum, ſeu æquale Co-<lb/>hærentiæ baſeos F G, tum pondus I eſt ad pondus K in ratione <lb/>Cubi B E ad Cubum F G, ſive <emph style="ol">B E<emph style="super">q</emph></emph> X B E ad <emph style="ol">F G</emph> X F G. </s> <s xml:id="echoid-s15118" xml:space="preserve">ſed eſt <lb/>B E ad <emph style="ol">F G<emph style="super">q</emph></emph> ex natura Hyperbolæ, uti D A X D L ad H A <lb/>X H L. </s> <s xml:id="echoid-s15119" xml:space="preserve">adeoque his loco quadratorum poſitis, erit pondus I ad pon-<lb/>dus K, uti D A X D L X B E, ad H A X H L X F G.</s> <s xml:id="echoid-s15120" xml:space="preserve"/> </p> <pb o="606" file="0622" n="623" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div566" type="section" level="1" n="566"> <head xml:id="echoid-head681" xml:space="preserve">PROPOSITIO LXXXVII.</head> <p> <s xml:id="echoid-s15121" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15122" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15123" xml:space="preserve">fig. </s> <s xml:id="echoid-s15124" xml:space="preserve">10. </s> <s xml:id="echoid-s15125" xml:space="preserve">Determinare momentum ex gravitate corpo-<lb/>ris Hyperbolici A B E, ejusque ſegmenti F A G. </s> <s xml:id="echoid-s15126" xml:space="preserve">cujus baſis F G pa-<lb/>rallela eſt ad B E.</s> <s xml:id="echoid-s15127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15128" xml:space="preserve">Momentum integri corporis Hyperbolici determinavimus in <lb/>Propoſitione LXXXV. </s> <s xml:id="echoid-s15129" xml:space="preserve">={a<emph style="super">4</emph>cr+7a<emph style="super">3</emph>bcr+12aabbcr.</s> <s xml:id="echoid-s15130" xml:space="preserve">/24aa+120ab+144bb} Verum <lb/>nunc ſegmenti F A G momentum determinandum quoque erit: <lb/></s> <s xml:id="echoid-s15131" xml:space="preserve">Vocetur A H, x, tum ex natura Hyperbolæ eſt D A X D L, ad <lb/>H A X H L:</s> <s xml:id="echoid-s15132" xml:space="preserve">: B D<emph style="super">q</emph>, H F<emph style="super">q</emph>, ſive eſt aa+2ab, xx+2bx:</s> <s xml:id="echoid-s15133" xml:space="preserve">: rr, <lb/>{rrxx+2bxrr:</s> <s xml:id="echoid-s15134" xml:space="preserve">/aa+2ab} ut nunc peripheria deſcribenda a puncto F radii <lb/>H F habeatur, fiat r. </s> <s xml:id="echoid-s15135" xml:space="preserve">c:</s> <s xml:id="echoid-s15136" xml:space="preserve">: r {xx+2bx.</s> <s xml:id="echoid-s15137" xml:space="preserve">/aa+2ab} c{xx+2bx.</s> <s xml:id="echoid-s15138" xml:space="preserve">/aa+2ab} <lb/>ut ſoliditas obtineatur, multiplicanda hæc peripheria per radium, <lb/>& </s> <s xml:id="echoid-s15139" xml:space="preserve">per{xx+3xb.</s> <s xml:id="echoid-s15140" xml:space="preserve">/6x+12b} quod dat productum <lb/>{crx<emph style="super">4</emph>+5bcrx<emph style="super">3</emph>+6bbcx<emph style="super">3</emph>/6aax+12abx+12aab+144abb} = ſoliditati ſegmenti F A G. </s> <s xml:id="echoid-s15141" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15142" xml:space="preserve">quoniam centrum gravitatis in axe H A diſtat a G F, quantitate <lb/>{xx+4xb.</s> <s xml:id="echoid-s15143" xml:space="preserve">/4x+12b} per hanc quantitatem multiplicata ſoliditas dabit <lb/>productum{crx<emph style="super">6</emph>+9bcrx<emph style="super">5</emph>+26bbcrx<emph style="super">4</emph>+24b<emph style="super">3</emph>crx<emph style="super">3</emph>/24aaxx+48abxx+120aabx+720abbx+144aabb+1728ab<emph style="super">3</emph>.</s> <s xml:id="echoid-s15144" xml:space="preserve">} <lb/>quod eſt æquale momento ſegmenti F A G.</s> <s xml:id="echoid-s15145" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div567" type="section" level="1" n="567"> <head xml:id="echoid-head682" xml:space="preserve">PROPOSITIO LXXXVIII.</head> <p style="it"> <s xml:id="echoid-s15146" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15147" xml:space="preserve">XXVI fig. </s> <s xml:id="echoid-s15148" xml:space="preserve">11. </s> <s xml:id="echoid-s15149" xml:space="preserve">Sit Hyperbola AMB, & </s> <s xml:id="echoid-s15150" xml:space="preserve">dimidium primi axis <lb/>A C, & </s> <s xml:id="echoid-s15151" xml:space="preserve">dimidium axis conjugati C D, circa C D concipiatur circum-<lb/>volvi figura B A C D, quæritur ut determinetur momentum ſolidi <lb/>generati, & </s> <s xml:id="echoid-s15152" xml:space="preserve">Cohærentia baſeos B D, affixæ parieti perpendiculari ad <lb/>borizontem.</s> <s xml:id="echoid-s15153" xml:space="preserve"/> </p> <pb o="607" file="0623" n="624" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15154" xml:space="preserve">Vocetur C A, a. </s> <s xml:id="echoid-s15155" xml:space="preserve">CD, b. </s> <s xml:id="echoid-s15156" xml:space="preserve">circumferentia deſcripta a puncto B <lb/>ſit c. </s> <s xml:id="echoid-s15157" xml:space="preserve">invenietur ſoliditas corporis generati = {bcr/3}. </s> <s xml:id="echoid-s15158" xml:space="preserve">centrum gravi-<lb/>tatis in axe CD diſtat a puncto D = {7/16} D C = {7/16}b. </s> <s xml:id="echoid-s15159" xml:space="preserve">quare momen-<lb/>tum ex gravitate erit {7bbcr/48}. </s> <s xml:id="echoid-s15160" xml:space="preserve">quia autem D B eſt = 2a<emph style="super">a</emph> <lb/>erit Cohærentia = 8 a<emph style="super">3</emph>2.</s> <s xml:id="echoid-s15161" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div568" type="section" level="1" n="568"> <head xml:id="echoid-head683" xml:space="preserve">PROPOSITIO LXXXIX.</head> <p> <s xml:id="echoid-s15162" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15163" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15164" xml:space="preserve">fig. </s> <s xml:id="echoid-s15165" xml:space="preserve">12. </s> <s xml:id="echoid-s15166" xml:space="preserve">Sit ſolidum Hyperbolicum ABCE, in quo <lb/>ſegmentum LIKM baſi parallelum, erit Cohærentia ſolidi ABC <lb/>ad eam ſegmenti LIKMC, utirectangulumex GC, GH ad rectan-<lb/>gulum ex NC, NH.</s> <s xml:id="echoid-s15167" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15168" xml:space="preserve">Sit C H axis Hyperbolæ primus, quo ducto erit Cohærentia <lb/>baſeos A B F E ad Cohærentiam baſeos LIKM, in ratione dupli-<lb/>cata E A ad LI. </s> <s xml:id="echoid-s15169" xml:space="preserve">ſed eſt quadratum E A ad quadratum LI, uti re-<lb/>ctangulum ex abſciſſa G C X per G H, ad rectangulum ex abſciſſa-<lb/>N C in N H. </s> <s xml:id="echoid-s15170" xml:space="preserve">quare patet propoſitum.</s> <s xml:id="echoid-s15171" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div569" type="section" level="1" n="569"> <head xml:id="echoid-head684" xml:space="preserve">De Hemisphæriis.</head> <head xml:id="echoid-head685" xml:space="preserve">PROPOSITIO XC.</head> <p> <s xml:id="echoid-s15172" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15173" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15174" xml:space="preserve">fig. </s> <s xml:id="echoid-s15175" xml:space="preserve">13. </s> <s xml:id="echoid-s15176" xml:space="preserve">Momentum Hemisphærii inſcripti cylindro, <lb/>baſi affixa parieti, eſt dimidium momenti ipſius Cylindri habentis <lb/>eandem baſin & </s> <s xml:id="echoid-s15177" xml:space="preserve">altitudinem.</s> <s xml:id="echoid-s15178" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15179" xml:space="preserve">Vocetur enim radius A D baſeos, r. </s> <s xml:id="echoid-s15180" xml:space="preserve">& </s> <s xml:id="echoid-s15181" xml:space="preserve">peripheria circuli, c. </s> <s xml:id="echoid-s15182" xml:space="preserve">erit <lb/>ipſa baſis = {cr/2} hæc multiplicata per A E = r. </s> <s xml:id="echoid-s15183" xml:space="preserve">dat ſoliditatem Cylin-<lb/>dri circumſcripti C A E = {crr/2}, cujus centrum gravitatis eſt in me-<lb/>dio ſive in {1/2} r. </s> <s xml:id="echoid-s15184" xml:space="preserve">adeoque erit momentum cylindri ={cr<emph style="super">3</emph>/4}. </s> <s xml:id="echoid-s15185" xml:space="preserve">Eſt au-<lb/>tem ſoliditas Cylindri ad eam hemisphærii, uti 3 ad 2, adeoque <pb o="608" file="0624" n="625" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ſoliditas hemisphærii A B C erit = {crr:</s> <s xml:id="echoid-s15186" xml:space="preserve">/3}. </s> <s xml:id="echoid-s15187" xml:space="preserve">abeſt quoque in hemisphæ-<lb/>rio centrum gravitatis {3/8} r ab A C. </s> <s xml:id="echoid-s15188" xml:space="preserve">adeoque erit hemisphærii <lb/>momentum = {cr<emph style="super">3</emph>/8}. </s> <s xml:id="echoid-s15189" xml:space="preserve">quod eſt duplo minus quam momentum Cy-<lb/>lindri.</s> <s xml:id="echoid-s15190" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div570" type="section" level="1" n="570"> <head xml:id="echoid-head686" xml:space="preserve">PROPOSITIO XCI.</head> <p style="it"> <s xml:id="echoid-s15191" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15192" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15193" xml:space="preserve">fig. </s> <s xml:id="echoid-s15194" xml:space="preserve">14. </s> <s xml:id="echoid-s15195" xml:space="preserve">Determinare Cohærentiam hemisphærii <lb/>A B C & </s> <s xml:id="echoid-s15196" xml:space="preserve">ſegmenti ejus F B E, cujus baſis parallela baſi A D C. </s> <s xml:id="echoid-s15197" xml:space="preserve">po-<lb/>ſitis his baſibus parieti affixis.</s> <s xml:id="echoid-s15198" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15199" xml:space="preserve">Sunt hæ Cohærentiæ inter ſe, uti Cubi diametrorum in baſibus <lb/>A C, F E. </s> <s xml:id="echoid-s15200" xml:space="preserve">ut autem magnitudines horum cuborum noſcantur, vo-<lb/>cetur A D aut D B, r. </s> <s xml:id="echoid-s15201" xml:space="preserve">B G ſit = x. </s> <s xml:id="echoid-s15202" xml:space="preserve">eritque F G<emph style="super">q</emph> = 2rx-xx, unde <lb/>Cubus F G = 2rx-xx X 2rx - xx. </s> <s xml:id="echoid-s15203" xml:space="preserve">& </s> <s xml:id="echoid-s15204" xml:space="preserve">Cubus A D = r<emph style="super">3</emph>. </s> <s xml:id="echoid-s15205" xml:space="preserve">qua-<lb/>re Cohærentia baſeos A D C eſt ad eam baſeos F G E uti r<emph style="super">3</emph> ad <lb/>2rx - xx X 2rx - xx.</s> <s xml:id="echoid-s15206" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div571" type="section" level="1" n="571"> <head xml:id="echoid-head687" xml:space="preserve">PROPOSITIO XCII.</head> <p style="it"> <s xml:id="echoid-s15207" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15208" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15209" xml:space="preserve">fig. </s> <s xml:id="echoid-s15210" xml:space="preserve">14. </s> <s xml:id="echoid-s15211" xml:space="preserve">Dati Hemispbærii ABC, & </s> <s xml:id="echoid-s15212" xml:space="preserve">ſegmenti <lb/>FBE invenire momenta ex gravitate oriunda, poſitis baſibus <lb/>A C, F E parieti ad horizontem perpendiculari affixis.</s> <s xml:id="echoid-s15213" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15214" xml:space="preserve">Vocetur radius circuli A D, r. </s> <s xml:id="echoid-s15215" xml:space="preserve">circumferentia circuli c. </s> <s xml:id="echoid-s15216" xml:space="preserve">erit mo. <lb/></s> <s xml:id="echoid-s15217" xml:space="preserve">mentum Hemisphærii = {cr<emph style="super">3</emph>/8} per Propoſitionem XC: </s> <s xml:id="echoid-s15218" xml:space="preserve">Ponatur <lb/>B G = x. </s> <s xml:id="echoid-s15219" xml:space="preserve">& </s> <s xml:id="echoid-s15220" xml:space="preserve">G F = y. </s> <s xml:id="echoid-s15221" xml:space="preserve">ſumatur Gg pars infinite parva, erit <lb/>hæc = dx, ut proinde habeatur peripheria circuli deſcripti â <lb/>puncto F. </s> <s xml:id="echoid-s15222" xml:space="preserve">fiat ut r, c:</s> <s xml:id="echoid-s15223" xml:space="preserve">: y. </s> <s xml:id="echoid-s15224" xml:space="preserve">{cy/r} = peripheriæ, quæ ductain {1/2}y, dabit <lb/>{cyy/2r} = circulo; </s> <s xml:id="echoid-s15225" xml:space="preserve">hic multiplicatus per d x, dabit {cyvdx/2r} differentiale <lb/>ſolidum; </s> <s xml:id="echoid-s15226" xml:space="preserve">verum ex natura ſphæræ eſt yy = 2rx - xx unde pro yy <lb/>ſubſtituendo hunc valorem, fit{cyydx/2r} = cxdx - {cxxdx/2r}, cujusin- <pb o="609" file="0625" n="626" rhead="CORPORUM FIRMORUM."/> tegralis erit {cxx/2}-{cx<emph style="super">3</emph>/6r}, quæ eſt quantitas æqualis ſegmento ſphæ-<lb/>rico F B E. </s> <s xml:id="echoid-s15227" xml:space="preserve">centrum autem gravitatis abeſt ab F E = {3/8} x, adeoque <lb/>momentum erit = {3/16}cx<emph style="super">3</emph>-{3cx<emph style="super">4</emph>/48r}.</s> <s xml:id="echoid-s15228" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15229" xml:space="preserve">Poſſet hæc doctrina admodum amplificari conſiderationibus plu-<lb/>rimorum Solidorum, quæ ex convolutis curvis diverſiſſimorum ge-<lb/>nerum vario modo naſcuntur, aut quæ compoſita ſunt ex curvis <lb/>ſuperficiebus varii generis; </s> <s xml:id="echoid-s15230" xml:space="preserve">quorum momenta gravitatis; </s> <s xml:id="echoid-s15231" xml:space="preserve">centra <lb/>gravitatis; </s> <s xml:id="echoid-s15232" xml:space="preserve">Cohærentiæ baſium, & </s> <s xml:id="echoid-s15233" xml:space="preserve">aliorum ſegmentorum baſibus <lb/>parallelorum; </s> <s xml:id="echoid-s15234" xml:space="preserve">pondera appenſa conſtantia, variabilia, mererentur <lb/>inquiri & </s> <s xml:id="echoid-s15235" xml:space="preserve">demonſtrari. </s> <s xml:id="echoid-s15236" xml:space="preserve">Verum ita hæc Diſſertatio in magnum vo-<lb/>lumen Geometricum increviſſet: </s> <s xml:id="echoid-s15237" xml:space="preserve">Qui tamen plura ſubtilia circa <lb/>Cohærentiam ſolidorum, infinitaque corpora æquabilis reſiſtentiæ <lb/>per totam longitudinem cognoſcere deſiderat, adeat, quæ Cl. </s> <s xml:id="echoid-s15238" xml:space="preserve">Paren-<lb/>tius eleganter demonſtravit in L’ Hiſt. </s> <s xml:id="echoid-s15239" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s15240" xml:space="preserve">Roy. </s> <s xml:id="echoid-s15241" xml:space="preserve">A°. </s> <s xml:id="echoid-s15242" xml:space="preserve">1710. <lb/></s> <s xml:id="echoid-s15243" xml:space="preserve">Puteus profecto inexhauſtus reſtat; </s> <s xml:id="echoid-s15244" xml:space="preserve">ſed qui exercitatum poſtulat <lb/>Geometram, ne ſub ipſis pereat Aquis: </s> <s xml:id="echoid-s15245" xml:space="preserve">interea ſolent profundiſſi-<lb/>mæ conſiderationes plus acuminis & </s> <s xml:id="echoid-s15246" xml:space="preserve">doctrinæ oſtentare, quam uti-<lb/>litatis afferre, quare claudam hoc Caput generali Propoſitione â Cl. </s> <s xml:id="echoid-s15247" xml:space="preserve"><lb/>Grando inventa.</s> <s xml:id="echoid-s15248" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div572" type="section" level="1" n="572"> <head xml:id="echoid-head688" xml:space="preserve">PROPOSITIO XCIII.</head> <p style="it"> <s xml:id="echoid-s15249" xml:space="preserve">Infinita ſolida reperire, quæ cum uno ſui extremo fuerint pa-<lb/>rieti infixa horizontaliter, reſpectu proprii ponderis æqualis ſint <lb/>Cohærentiæ.</s> <s xml:id="echoid-s15250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15251" xml:space="preserve">Sumatur pro curva verticali complementum ordinariæ Parabolæ, <lb/>cujus ordinatæ ad Tangentem verticis applicantur; </s> <s xml:id="echoid-s15252" xml:space="preserve">pro figura vero <lb/>horizontali aſſumatur, aut rectangulum, aut Triangulum, aut quæ-<lb/>libet ex infinitis Parabolis eundem verticem reſpicientibus, cujus <lb/>ordinatæ fint, ut abſciſſarum axis poteſtates a quolibet exponen-<lb/>te m indicatæ. </s> <s xml:id="echoid-s15253" xml:space="preserve">Dico ſolidum ex utraque figura reſultans tale eſſe, <lb/>ut vi proprii ponderis ubique æqualiter cohæreat, ita ut ſi totum <lb/>nequeat frangi juxta ſectionem muro inhærentem, nec ulla ejus <lb/>portio perſectionem alteram, eidem muro parallelam, poſſit avel- <pb o="610" file="0626" n="627" rhead="INTRODUCTIO AD COHÆRENTIAM"/> li. </s> <s xml:id="echoid-s15254" xml:space="preserve">Nam ejuſmodi ſolida erunt ſemper ad ſolidum priſmaticum cir-<lb/>cumſcriptum in eadem ratione (quæcunque portio eorum aſſumta <lb/>fuerit) in eà videlicet, quæ eſt 1 ad m+3 (præterquam ubirectan-<lb/>gulum pro figura horizontali aſſumetur, quia ob ordinatas conſtan-<lb/>tes evaneſcit index m, & </s> <s xml:id="echoid-s15255" xml:space="preserve">remanet ſola ratio ſubtripla, quia index <lb/>unitatis conſtantis eſt nullus, unde m = 0) & </s> <s xml:id="echoid-s15256" xml:space="preserve">diſtantia centri gra-<lb/>vitatis, cujuslibet portionis horum ſolidorum â ſuâ baſi ſemper erit <lb/>proportionalis abſciſſæ, nimirum ad ipſam, ut m + 2 ad m + 5 <lb/>(& </s> <s xml:id="echoid-s15257" xml:space="preserve">in primo caſu rectanguli horizontalis, evaneſcente m, ut 2 ad 5 <lb/>duntaxat.) </s> <s xml:id="echoid-s15258" xml:space="preserve">Quare momentum cujusvis portionis ſolidi erit, ut <lb/>productum y z x x, y exprimente altitudinem verticalem ſectionis, <lb/>z ejus baſin, x abſciſſam axeos? </s> <s xml:id="echoid-s15259" xml:space="preserve">nam pondus ſolidi proportionale <lb/>eſt circumſcripto priſmati y z x, & </s> <s xml:id="echoid-s15260" xml:space="preserve">diſtantia centri gravitatis, rur-<lb/>ſus eidem x proportionalis eſt, Cohærentiæ vero in dicta ſectione <lb/>momentum proportionale eſt producto ex baſi in quadratum altitu-<lb/>dinis ſectionis, videlicet ipſi yyz, atque ob aſſumtam verticalem <lb/>figuram in complemento parabolæ, cujus applicata y eſt ut x x, <lb/>evadit momentum Cohærentiæ ut y z x x: </s> <s xml:id="echoid-s15261" xml:space="preserve">ergo momentum pon-<lb/>deris cujusvis portionis ſolidi, ultra ſuam baſin protenſi, eſt pro-<lb/>portionale momento Cohærentiæ in ſua baſi, unde quodlibet ejuſ-<lb/>modi ſolidum eſt ubivis æqualis Cohærentiæ.</s> <s xml:id="echoid-s15262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15263" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15264" xml:space="preserve">Loco infinitarum Parabolarum infinitæ Hyperbolæ eidem <lb/>propoſito conducere poſſunt, comparando ſolida hinc prodeuntia <lb/>ad ſolida inſcripta, pro circumſcriptis, eſt enim ſimilis ratio,</s> </p> </div> <div xml:id="echoid-div573" type="section" level="1" n="573"> <head xml:id="echoid-head689" xml:space="preserve">CAPUT SEXTUM.</head> <head xml:id="echoid-head690" style="it" xml:space="preserve">De Cohærentia Corporum quibus fulcrum ſupponitur.</head> <head xml:id="echoid-head691" xml:space="preserve">PROPOSITIO XCIV.</head> <p style="it"> <s xml:id="echoid-s15265" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15266" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s15267" xml:space="preserve">fig. </s> <s xml:id="echoid-s15268" xml:space="preserve">1. </s> <s xml:id="echoid-s15269" xml:space="preserve">Si detur ſolidum A B C, quod in medio B <lb/>ſuffulciatur fulcro D, potentiæ ſingulæ extremitatibus A & </s> <s xml:id="echoid-s15270" xml:space="preserve">C <lb/>applicatæ & </s> <s xml:id="echoid-s15271" xml:space="preserve">frangentes ſolidum requiruntur inter ſe æquales, tum <lb/>illi potentiæ, quæ ſolidum dimidiæ longitudinis, uti A B, parie-<lb/>ti infixum frangebat.</s> <s xml:id="echoid-s15272" xml:space="preserve"/> </p> <pb o="611" file="0627" n="628" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15273" xml:space="preserve">Conſideretur ſolidi longitudo ABC inſtar vectis æqualium cru-<lb/>rum, cujus medio D ſupponitur fulcrum, utrique extremitati au-<lb/>tem A & </s> <s xml:id="echoid-s15274" xml:space="preserve">C applicatur potentia, quæ utrimque æqualis erit, ſi æ-<lb/>quilibrium ab utraque parte dabitur, atque inſlexiones ſecundum <lb/>BE, BF æquales. </s> <s xml:id="echoid-s15275" xml:space="preserve">Potentia autem applicata extremitati C & </s> <s xml:id="echoid-s15276" xml:space="preserve">de-<lb/>primens, nihil aliud agit, quam reſiſtentiam exercere contra po-<lb/>tentiam A deprimentem partem AB. </s> <s xml:id="echoid-s15277" xml:space="preserve">adeoque idem agit potentia <lb/>C ſupra fulcrum D, ac paries, in quo foramen erat DBC, cujus <lb/>inferior extrema ora D erat fulcrum, ſuperior ora B reſiſtebat di-<lb/>rectione deorſum, quare potentia A, quæ frangebat ſolidum parieti <lb/>infixum in BD, idem nunc franget ſupra fulcrum D.</s> <s xml:id="echoid-s15278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15279" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15280" xml:space="preserve">Veluti igitur ſolidum A B parieti infixum, tantæ longitu-<lb/>dinis fieri potuit, ut â momento propriæ gravitatis frangatur, ita <lb/>quoque ſolidum A B C duplo longius factum, ejusdemque craſſitiei, <lb/>ſuo medio impoſitum fulcro D frangetur â momento ſuæ gravi-<lb/>tatis.</s> <s xml:id="echoid-s15281" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15282" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s15283" xml:space="preserve">Hanc Propoſitionem in dubium vocavit Honor. </s> <s xml:id="echoid-s15284" xml:space="preserve">Fabry <lb/>in ſua Prop. </s> <s xml:id="echoid-s15285" xml:space="preserve">LXI. </s> <s xml:id="echoid-s15286" xml:space="preserve">de reſiſtentia ſolidorum, opinatus momenta pon-<lb/>derum frangentium applicatorum extremitati alterutri A, vel C <lb/>parallelopipedi A B C, cujus fulcrum eſt in medio B, eſſe modo di-<lb/>midium ponderis frangentis appenſi in C ex parallelopipedo B C <lb/>infixo parieti uſque ad B. </s> <s xml:id="echoid-s15287" xml:space="preserve">quia ambo momenta ponderum A & </s> <s xml:id="echoid-s15288" xml:space="preserve">C <lb/>ſimul eandem ſummam habent, quam C ſolum ex vecte CB, & </s> <s xml:id="echoid-s15289" xml:space="preserve">cum <lb/>eadem Cohærentia ſit ſuperanda in D B, pondera A & </s> <s xml:id="echoid-s15290" xml:space="preserve">C modo re-<lb/>quiri dimidia ponderis C appenſi vecti C B. </s> <s xml:id="echoid-s15291" xml:space="preserve">Quod profecto erro-<lb/>neum eſt, cum enim pondus applicabitur ad C vectis B quod Co-<lb/>hærentiam D B ſolvet, ponamus ſuperficiem vectis D B eſſe appli-<lb/>catam ſuperficiei D B parietis: </s> <s xml:id="echoid-s15292" xml:space="preserve">ergo oportet, ut ſuperficies D B pa-<lb/>rietis exerceat reſiſtentiam, quando D B ſuperficies vectis ſeparabi-<lb/>tur, adeoque debebit D B ſuperficies parietis tantopere retine-<lb/>ri, quanta eſt vis vectim avellens: </s> <s xml:id="echoid-s15293" xml:space="preserve">ſive hoc retinere exerceatur <lb/>a gravitate parietis, ſive a potentia A applicata vecti A B, idem eſt, <lb/>eadem vis deſideratur; </s> <s xml:id="echoid-s15294" xml:space="preserve">quare momentum ponderis vel potentiæ in <lb/>A ex vecte A B = BC, ſi fuerit æquale momento C in CB, reſi-<lb/>ſtentiam exercet æqualem viribus agentibusin CB, unde quodlibet <lb/>pondus applicatum in A & </s> <s xml:id="echoid-s15295" xml:space="preserve">C parallelopipedo A B C, debet eſſe <pb o="612" file="0628" n="629" rhead="INTRODUCTIO AD COHÆRENTIAM"/> æquale ponderi C, applicato ejus dimidiæ longitudini C B ad ean-<lb/>dem Cohærentiam D B ſuperandam.</s> <s xml:id="echoid-s15296" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15297" xml:space="preserve">Ne aliquis ſuperſtes maneret ſcrupulus Experimento rem ulterius <lb/>confirmandam judicavi.</s> <s xml:id="echoid-s15298" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div574" type="section" level="1" n="574"> <head xml:id="echoid-head692" xml:space="preserve">EXPERIMENTUM CLXXXVI.</head> <p> <s xml:id="echoid-s15299" xml:space="preserve">Sumtum fuit parallelopipedum Quercicum ABC, cujus quodli-<lb/>bet latus erat 0, 11 pollic. </s> <s xml:id="echoid-s15300" xml:space="preserve">Rhenol:</s> <s xml:id="echoid-s15301" xml:space="preserve">, in quo aliqua intermedia lon-<lb/>gitudo ABC ſumebatur 16 pollicum: </s> <s xml:id="echoid-s15302" xml:space="preserve">prominente utrimque æquali <lb/>portione pro Experimento ſequenti, impoſitum fuit hypomochlio <lb/>priſmatico D in medio, fractumque fuit in D B ab appenſis utrim-<lb/>quein A & </s> <s xml:id="echoid-s15303" xml:space="preserve">C ponderibus librarum 2. </s> <s xml:id="echoid-s15304" xml:space="preserve">Unciarum 15, drachmæ unius: <lb/></s> <s xml:id="echoid-s15305" xml:space="preserve">Deinde ejuſdem ligni portionem B C immiſi foramini quadrato ma-<lb/>chinæ divulſoriæ, ita ut emineret 8 pollic: </s> <s xml:id="echoid-s15306" xml:space="preserve">parsubipondus applicaba-<lb/>tur, fractumque fuit ad oram foraminis a libris 3, uncia 1, drach-<lb/>mis 2. </s> <s xml:id="echoid-s15307" xml:space="preserve">Quod pondus quidem eſt paulo majus quam dimidium <lb/>præcedentis ſummæ, ſed hoc fit, quia foramini aliquouſque im-<lb/>mittendum fuit B C, ſoletque a partibus immiſſis reſiſtentia quoque <lb/>exerceri uti pluribus Experimentis poſtea liquebit in Cap. </s> <s xml:id="echoid-s15308" xml:space="preserve">VII: </s> <s xml:id="echoid-s15309" xml:space="preserve">& </s> <s xml:id="echoid-s15310" xml:space="preserve"><lb/>VIII. </s> <s xml:id="echoid-s15311" xml:space="preserve">memorandis: </s> <s xml:id="echoid-s15312" xml:space="preserve">ſecundum Fabry demonſtrationem debuiſſet <lb/>pondus applicatum ad C, quo flecteretur uſque in DF, eſſe libra, <lb/>rum 5. </s> <s xml:id="echoid-s15313" xml:space="preserve">unciarum 14. </s> <s xml:id="echoid-s15314" xml:space="preserve">drachmarum 2. </s> <s xml:id="echoid-s15315" xml:space="preserve">a quo pondus in Experimento <lb/>procul abfuit.</s> <s xml:id="echoid-s15316" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div575" type="section" level="1" n="575"> <head xml:id="echoid-head693" xml:space="preserve">PROPOSITIO XCV.</head> <p style="it"> <s xml:id="echoid-s15317" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15318" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s15319" xml:space="preserve">fig. </s> <s xml:id="echoid-s15320" xml:space="preserve">2. </s> <s xml:id="echoid-s15321" xml:space="preserve">Si Solidum ABbC non fulciatur in medio <lb/>d, ſed in alio loco quocunque D propioriextremo A, & </s> <s xml:id="echoid-s15322" xml:space="preserve">potentia appli-<lb/>cata in C æquilibrium modo agat cum potentia A, erit potentia <lb/>in A frangens ſolidum ſupra fulcrum poſitum in D, ad eam, quæ <lb/>frangebat idem ſolidum ſupra fulcrum d, uti A d ad A D.</s> <s xml:id="echoid-s15323" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15324" xml:space="preserve">Quoniam potentia C ſupponitur ſemper tanta, ut deprimendo <lb/>partem b C vel B C æquilibrium agat cum potentia applicata in A, <lb/>idem agit ac paries firmus, in cujus foramine poſitum ſolidum reti-<lb/>nebatur, adeoque poſito ſolido A B in foramine, ex quo emineat <pb o="613" file="0629" n="630" rhead="CORPORUM FIRMORUM."/> quantitate A B: </s> <s xml:id="echoid-s15325" xml:space="preserve">aut Ab in foramine ex quo emineat quantitate <lb/>A b, erit ex natura vectis momentum potentiæ A, in diſtantia A B, <lb/>ad momentum potentiæ A, in diſtantia A b. </s> <s xml:id="echoid-s15326" xml:space="preserve">uti A b, ad AB. </s> <s xml:id="echoid-s15327" xml:space="preserve">ſed Co-<lb/>hærentia ſolidi eſt eadem, cum altitudo D B = bd. </s> <s xml:id="echoid-s15328" xml:space="preserve">ponitur, adeo-<lb/>que potentia frangens in diſtantia AB, erit ad eam in diſtantia Ab, <lb/>uti Ab, ad AB.</s> <s xml:id="echoid-s15329" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15330" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15331" xml:space="preserve">1. </s> <s xml:id="echoid-s15332" xml:space="preserve">Adeoque accedente fulcro D propius ad A, fieri poteſt, ut <lb/>requiratur potentia admodum magna, quæ frangat ſolidum ſupra <lb/>fulcrum D. </s> <s xml:id="echoid-s15333" xml:space="preserve">Verum potentia applicata extremo A, ſi fuerit æqualis <lb/>Cohærentiæ ſolidi abſolutæ, franget partes ſolidi, quibus adhæ-<lb/>ret, & </s> <s xml:id="echoid-s15334" xml:space="preserve">cum Cohærentia abſoluta corporum determinatæ magnitu-<lb/>dinis exiſtit, ſolidum non frangetur in B D ſupra ſulcrum, quia ad <lb/>eam rupturam vis major, quam quæ Cohærentiæ abſolutæ æqualis <lb/>eſt, requifitur.</s> <s xml:id="echoid-s15335" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15336" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15337" xml:space="preserve">2. </s> <s xml:id="echoid-s15338" xml:space="preserve">Potentia autem C applicata alteri extremo, poſita lon-<lb/>gitudine priori C b, aut poſteriori C B, eſt uti C B ad C b. </s> <s xml:id="echoid-s15339" xml:space="preserve">quia au-<lb/>tem C B nunquam fieri poteſt duplo major Cb, nunquam potentia <lb/>C fiet duplo minor.</s> <s xml:id="echoid-s15340" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15341" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15342" xml:space="preserve">3. </s> <s xml:id="echoid-s15343" xml:space="preserve">Cum vero potentia A, frangens ſolidum in B D, increſce-<lb/>re poſſit in inſignem uſque magnitudinem, patet ſummam ambarum <lb/>potentiarum frangentium corpus ſupra D non manere eandem, ſed <lb/>increſcere eo plus, quo fulcrum D ponitur propius A: </s> <s xml:id="echoid-s15344" xml:space="preserve">adeoque <lb/>nunquam ſumma potentiarum frangentium A & </s> <s xml:id="echoid-s15345" xml:space="preserve">C eſt minor, quam <lb/>cum fulcrum ponitur ſub medio in d,</s> </p> <p> <s xml:id="echoid-s15346" xml:space="preserve">Hæc optime animadvertit olim Galilæus in Mechanicæ Dialogo <lb/>2. </s> <s xml:id="echoid-s15347" xml:space="preserve">pag. </s> <s xml:id="echoid-s15348" xml:space="preserve">121. </s> <s xml:id="echoid-s15349" xml:space="preserve">Edit. </s> <s xml:id="echoid-s15350" xml:space="preserve">Holl.</s> <s xml:id="echoid-s15351" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div576" type="section" level="1" n="576"> <head xml:id="echoid-head694" xml:space="preserve">PROPOSITIO CXVI.</head> <p style="it"> <s xml:id="echoid-s15352" xml:space="preserve">Tab XXVII. </s> <s xml:id="echoid-s15353" xml:space="preserve">fig. </s> <s xml:id="echoid-s15354" xml:space="preserve">2. </s> <s xml:id="echoid-s15355" xml:space="preserve">Productum duarum potentiarum applicatarum <lb/>in A & </s> <s xml:id="echoid-s15356" xml:space="preserve">C ſolido A b C, impoſito fulcro d, idque frangentium, eſt ad <lb/>productum aliarum duarum potentiarum poſitarum in A & </s> <s xml:id="echoid-s15357" xml:space="preserve">C & </s> <s xml:id="echoid-s15358" xml:space="preserve">ſoli-<lb/>dum idem frangentium, ſed impoſitum fulcro D, uti rectangulum <lb/>A B C ad rectangulum A b C.</s> <s xml:id="echoid-s15359" xml:space="preserve"/> </p> <pb o="614" file="0630" n="631" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s15360" xml:space="preserve">Eſt momentum potentiæ A applicatæ vecti A b = A X A b. </s> <s xml:id="echoid-s15361" xml:space="preserve">Eſt <lb/>momentum alterius potentiæ A, quam diſtinctionis ergo vocabo <lb/>= a appenſæ vecti AB. </s> <s xml:id="echoid-s15362" xml:space="preserve">= a X AB ambarum potentiarum momenta <lb/>producere coſdem effectus ſupponitur, hoc eſt frangere ſolidum, <lb/>adeoque ſunt æqualia: </s> <s xml:id="echoid-s15363" xml:space="preserve">unde A X A b = a X A B. </s> <s xml:id="echoid-s15364" xml:space="preserve">Eodem modo <lb/>potentia C applicata vecti C b habet momentum = c X C b. </s> <s xml:id="echoid-s15365" xml:space="preserve">alia <lb/>potentia applicata eidem extremo C, vocetur D, hæc agens in <lb/>longitudinem CB. </s> <s xml:id="echoid-s15366" xml:space="preserve">habet momentum = D X CB. </s> <s xml:id="echoid-s15367" xml:space="preserve">quæ ambo mo-<lb/>menta potentiarum eoſdem effectus edentium, nempe fracturam <lb/>ſolidi, ſunt æqualia.</s> <s xml:id="echoid-s15368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15369" xml:space="preserve">adeoque A X Ab = a X A B. <lb/></s> <s xml:id="echoid-s15370" xml:space="preserve">& </s> <s xml:id="echoid-s15371" xml:space="preserve">C X Cb = D X C B. </s> <s xml:id="echoid-s15372" xml:space="preserve"><lb/>ducendo has quantitates æquales in ſe <lb/>fit A C X Ab X Cb = aD X AB X CB. </s> <s xml:id="echoid-s15373" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15374" xml:space="preserve">ponendo in proportione <lb/>erit AC, aD:</s> <s xml:id="echoid-s15375" xml:space="preserve">: AB X CB, Ab X Cb.</s> <s xml:id="echoid-s15376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15377" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15378" xml:space="preserve">Ergo productum potentiarum ſolidum frangentium & </s> <s xml:id="echoid-s15379" xml:space="preserve">ex-<lb/>tremis A & </s> <s xml:id="echoid-s15380" xml:space="preserve">C appenſarum, ſemper erit eo majus, quo fulcrum D <lb/>propius extremitati alterutri A aut C ponitur: </s> <s xml:id="echoid-s15381" xml:space="preserve">minimum vero eſt, <lb/>poſito in medio d.</s> <s xml:id="echoid-s15382" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div577" type="section" level="1" n="577"> <head xml:id="echoid-head695" xml:space="preserve">CAPUT SEPTIMUM.</head> <head xml:id="echoid-head696" style="it" xml:space="preserve">De Cohærentia reſpectiva ſolidorum duobus fulcris <lb/>impoſitorum.</head> <p> <s xml:id="echoid-s15383" xml:space="preserve">Eſt examen de Cohærentia reſpectiva firmorum corporum, quæ <lb/>utraque extremitate fulcro imponuntur, non exiguæ utilita-<lb/>tis, quoniam ex trabibus utrimque ſuffultis pondera graviſſima ſæpe <lb/>ſuſpenduntur, aut onera medio earum imponuntur; </s> <s xml:id="echoid-s15384" xml:space="preserve">adeoque Co-<lb/>hærentia maxima deſideratur determinanda, ut trabs tenuis ferat <lb/>tuto pondus maximum; </s> <s xml:id="echoid-s15385" xml:space="preserve">tum ut ex arbore trabes illius generis ſece-<lb/>mus, quæ minima Ligni quantitate conſtant, & </s> <s xml:id="echoid-s15386" xml:space="preserve">tamen ſint for- <pb o="615" file="0631" n="632" rhead="CORPORUM FIRMORUM."/> tiſſimæ: </s> <s xml:id="echoid-s15387" xml:space="preserve">diſcrepat præterea hoc examen multum ab eo Capitis V, <lb/>in quo corpora uno extremo foramini immiſſa arcte comprehende-<lb/>bantur, hic vero extrema libera manent ſurſumque adſcendunt <lb/>medio impoſitis ponderibus; </s> <s xml:id="echoid-s15388" xml:space="preserve">quod efficit, ut minus nunc reſiſtant ea, <lb/>quæ ex fibris longioribus concreverunt, quam quando foramini <lb/>aliquouſque inſeruntur: </s> <s xml:id="echoid-s15389" xml:space="preserve">Galilæus hanc doctrinæ partem non qui-<lb/>dem intactam reliquit, ſed tantum unâ alterave Propoſitione in-<lb/>choavit, quam longe pluribus amplificarunt deinde Marchettus, <lb/>Varignonus, Parentius, Grandi; </s> <s xml:id="echoid-s15390" xml:space="preserve">eſt vero multo ſubtilior inveſti-<lb/>gatu reliquis, quia hic Natura vectium longitudines, momentaque <lb/>ponderum occultaſſe præcipue videtur: </s> <s xml:id="echoid-s15391" xml:space="preserve">ab Experimentis autem <lb/>primo incipiam, quia hæ baſes ſequentium omnium eſſe debent, <lb/>quæ ſunt capta Machinæ ope repræſentatæ in Tab. </s> <s xml:id="echoid-s15392" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s15393" xml:space="preserve">fig. </s> <s xml:id="echoid-s15394" xml:space="preserve">36.</s> <s xml:id="echoid-s15395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15396" xml:space="preserve">Sunt AA, AA duo aſſeres ſuis pedibus BB inſiſtentes, qui ſe-<lb/>cum invicem junguntur ope 4 lignorum transverſorum EE, EE, <lb/>EE, EE, ne a ſe vel tantillum recedant; </s> <s xml:id="echoid-s15397" xml:space="preserve">diſtant aſſeres AA a ſe <lb/>mutuo 18 pollic: </s> <s xml:id="echoid-s15398" xml:space="preserve">Rhenol: </s> <s xml:id="echoid-s15399" xml:space="preserve">uterque rimam C, C capit ejus latitudi-<lb/>nis, ut corpora examinata accurate comprehendat: </s> <s xml:id="echoid-s15400" xml:space="preserve">Machina im-<lb/>ponitur Tabulæ T T, perforatæ in K, per quam tranſit Funis FF, <lb/>annexus Lanci G, cui pondera P frangentia corporis D D Cohæ-<lb/>rentiam imponuntur. </s> <s xml:id="echoid-s15401" xml:space="preserve">In rimâ C C poteſt utraque extremitas cor-<lb/>poris D D inter tentandum libere aſſurgere, ſuntque earum infima, <lb/>vera fulcra; </s> <s xml:id="echoid-s15402" xml:space="preserve">rimas ejuſmodi inſculpere tenebar, quoniam exami-<lb/>nans corpora diverſæ altitudinis deprehendebam, ea fulcris tan-<lb/>tummodo impoſita, aliquando intorqueriita, ut latiorpars niteretur <lb/>fieri horizontalis, quæ accuratiſſime perpendicularis manere de-<lb/>bebat; </s> <s xml:id="echoid-s15403" xml:space="preserve">rimæ C C hoc incommodum præcavent: </s> <s xml:id="echoid-s15404" xml:space="preserve">Tum ex uno & </s> <s xml:id="echoid-s15405" xml:space="preserve"><lb/>eodem aſſere Ligni Quercici mediocris duritiei præparata ſunt va-<lb/>ria parallelopipeda, ſecundum longitudinem ex Ligno fiſſa, ne <lb/>corpora ex fibris flexuoſis incurvatiſque conſtarent; </s> <s xml:id="echoid-s15406" xml:space="preserve">omnia ejuſ-<lb/>dem longitudinis ſumebantur, & </s> <s xml:id="echoid-s15407" xml:space="preserve">æque lata, nempe 0, 26 pollic: <lb/></s> <s xml:id="echoid-s15408" xml:space="preserve">ſed diverſæ altitudinis, quam in Experimentis indicabo.</s> <s xml:id="echoid-s15409" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div578" type="section" level="1" n="578"> <head xml:id="echoid-head697" xml:space="preserve">EXPERIMENTUM CLXXXVII.</head> <p> <s xml:id="echoid-s15410" xml:space="preserve">Altitudo primi Ligni fuit 0, 33. </s> <s xml:id="echoid-s15411" xml:space="preserve">pollic: </s> <s xml:id="echoid-s15412" xml:space="preserve">hoc medio F ab appenſis <pb o="616" file="0632" n="633" rhead="INTRODUCTIO AD COHÆRENTIAM"/> libris 13 {1/2}, pedetentim impoſitis, valde inflectebatur introrſum, & </s> <s xml:id="echoid-s15413" xml:space="preserve"><lb/>frangebatur, quia autem diſtantia binorum aſſerum A A, A A ſemper <lb/>manebat eadem, diſtantia ponderis ab utroque fulcro ſemper fuit <lb/>quoque eadem, ſive 9 pollicum, ut & </s> <s xml:id="echoid-s15414" xml:space="preserve">in omnibus Experimentis.</s> <s xml:id="echoid-s15415" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div579" type="section" level="1" n="579"> <head xml:id="echoid-head698" xml:space="preserve">EXPERIMENTUM CLXXXVIII.</head> <p> <s xml:id="echoid-s15416" xml:space="preserve">Secundum parallelopipedum Quercicum fuit altum 0, 40. </s> <s xml:id="echoid-s15417" xml:space="preserve">pollic: <lb/></s> <s xml:id="echoid-s15418" xml:space="preserve">quod in medio fractum ab appenſis libris 23 {1/2}.</s> <s xml:id="echoid-s15419" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div580" type="section" level="1" n="580"> <head xml:id="echoid-head699" xml:space="preserve">EXPERIMENTUM CLXXXIX.</head> <p> <s xml:id="echoid-s15420" xml:space="preserve">Tertium parallelopipedum Quercicum fuit altum 0, 52 pollic: <lb/></s> <s xml:id="echoid-s15421" xml:space="preserve">quod in medio fractum fuit ab appenſis libris 31 {1/2}.</s> <s xml:id="echoid-s15422" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div581" type="section" level="1" n="581"> <head xml:id="echoid-head700" xml:space="preserve">EXPERIMENTUM CXC.</head> <p> <s xml:id="echoid-s15423" xml:space="preserve">Quartum parallelopipedum Quercicum fuit altum 0, 58. </s> <s xml:id="echoid-s15424" xml:space="preserve">pollic: <lb/></s> <s xml:id="echoid-s15425" xml:space="preserve">& </s> <s xml:id="echoid-s15426" xml:space="preserve">in medio ſolvebatur a libris 32 {1/2}.</s> <s xml:id="echoid-s15427" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div582" type="section" level="1" n="582"> <head xml:id="echoid-head701" xml:space="preserve">EXPERIMENTUM CXCI.</head> <p> <s xml:id="echoid-s15428" xml:space="preserve">Quintum erat 0, 68 pollic: </s> <s xml:id="echoid-s15429" xml:space="preserve">altum, quod ante fracturam ſuſtinuit <lb/>libras 50 {1/2}.</s> <s xml:id="echoid-s15430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15431" xml:space="preserve">Capta fuerunt hæc Experimenta cum parallelopipedis diverſæ al-<lb/>titudinis, ut conſtaret, an hoc modo examinatum Lignum cohæ-<lb/>reret in ratione duplicata altitudinis, calculo ſubducto hæc inven-<lb/>ta fuerunt.</s> <s xml:id="echoid-s15432" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 33. # 40. # 52. # 58. # 68. <lb/>Altitudinum Quadrata # 1089. # 1600. # 2704. # 3364. # 4624. <lb/>Pondera in Experimentis # 13 {1/2}. # 23 {1/2}. # 31 {1/2}. # 32 {1/2}. # 50 {1/2}. <lb/>Pondera ex Calculo # 13 {1/2}. # 19 {101/121}. # 33 {63/121}. # 41 {55/121}. # 57 {39/121}. <lb/></note> <p> <s xml:id="echoid-s15433" xml:space="preserve">Ad Calculum Experimenta propinque accedunt, ab eo tamen <lb/>aberrant, quod vel ab inæquali Ligni Cohærentia per totam ſub-<lb/>ſtantiam, vel â flexilitate fibrarum variâ pendere poteſt, quibus <lb/>obſervatis ad aliorum Lignorum examen properandum eſſe judicavi, <pb o="617" file="0633" n="634" rhead="CORPORUM FIRMORUM."/> ut clarius conſtaret an regula locum habere debeat, an vero ſæpius <lb/>ab eadem aberratio daretur: </s> <s xml:id="echoid-s15434" xml:space="preserve">Cæteroquin Cl. </s> <s xml:id="echoid-s15435" xml:space="preserve">Parentius cum pa-<lb/>rallelopipedis Ligni Quercici plurima inſtituit tentamina, deſcripta <lb/>in L’ Hiſt. </s> <s xml:id="echoid-s15436" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s15437" xml:space="preserve">Roy. </s> <s xml:id="echoid-s15438" xml:space="preserve">A°. </s> <s xml:id="echoid-s15439" xml:space="preserve">1707. </s> <s xml:id="echoid-s15440" xml:space="preserve">quæ addi merentur, quamvis <lb/>non deſcripta inveniam cum omni curâ, quæ in accurato Experimen-<lb/>to deſideratur; </s> <s xml:id="echoid-s15441" xml:space="preserve">cum inflexionem lignorum uno extremo retento-<lb/>rum non notat Autor, ſumens præterea Ligna diverſarum arbo-<lb/>rum, aut ramorum, quorum unum mollius, alterum durius <lb/>erat; </s> <s xml:id="echoid-s15442" xml:space="preserve">ex quibus quidem diſcimus, Cohærentiam Ligni ejuſdem no-<lb/>minis admodum diſcrepare, non tamen licet ſequelas deducere ſpe-<lb/>ctantes Legem Cohærentiæ in diverſa corporum altitudine.</s> <s xml:id="echoid-s15443" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15444" xml:space="preserve">1°. </s> <s xml:id="echoid-s15445" xml:space="preserve">Sumſit parallelopipedum Ligni Quercici teneri, 5 lineas la-<lb/>tum, 6 altum, 11 pollices longum, quod duobus fulcris impoſi-<lb/>tum ex medio ſuſtinuit libras 34 {1/2} antequam rumpebatur: </s> <s xml:id="echoid-s15446" xml:space="preserve">vox <lb/>altitudo indicat ſatis hoc latus ad horizontem perpendiculare <lb/>fuiſſe.</s> <s xml:id="echoid-s15447" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15448" xml:space="preserve">2°. </s> <s xml:id="echoid-s15449" xml:space="preserve">Aliud inſtituit Experimentum cum parallelopipedo Querci-<lb/>co, priori ſimili & </s> <s xml:id="echoid-s15450" xml:space="preserve">æquali, ſed erat Lignum durius, hoc ex me-<lb/>dio ſui ſuſtinuit libras 92. </s> <s xml:id="echoid-s15451" xml:space="preserve">antequam rumpebatur, poſitum eodem <lb/>modo.</s> <s xml:id="echoid-s15452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15453" xml:space="preserve">3° Elegit ex Ligno Quercico tenero parallelopipedum 4 {1/3} lineas <lb/>altum, 5 {2/3} lin. </s> <s xml:id="echoid-s15454" xml:space="preserve">latum, 10 pollic: </s> <s xml:id="echoid-s15455" xml:space="preserve">longum, quod ex medio ſuſtinuit, <lb/>antequam frangebatur, libras 25.</s> <s xml:id="echoid-s15456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15457" xml:space="preserve">4°. </s> <s xml:id="echoid-s15458" xml:space="preserve">Ex eodem Ligno Quercico factum fuit parallelopipedum 4 {2/3} <lb/>lineas altum, 5 {2/3} lineas latum, 14 pollices longum, quod ſuſtinuit <lb/>ex medio ſuſpenſas libras 28 {1/2}.</s> <s xml:id="echoid-s15459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15460" xml:space="preserve">Utinam Autor notaſſet diſtantiam fulcrorum a ſe invicem, ne <lb/>enim quis opinetur, poſito parallelopipedo 10 pollicum, talem <lb/>quoque fuiſſe diſtantiam, quippe introrſum flectuntur Ligna pluri-<lb/>mum, atque ad minimum deſiderantur 14 pollices longa, ut ful-<lb/>crorum diſtantia ſit 10 pollicum; </s> <s xml:id="echoid-s15461" xml:space="preserve">ſi vero poſuerimus diſtantias ful-<lb/>crorum in binis Experimentis III, IV. </s> <s xml:id="echoid-s15462" xml:space="preserve">fuiſſe 10 & </s> <s xml:id="echoid-s15463" xml:space="preserve">14 pollicum, tum <lb/>ab Ligno Experimenti IV. </s> <s xml:id="echoid-s15464" xml:space="preserve">tantum geſtandæ fuiſſent libræ 18 {5024/11967}. <lb/></s> <s xml:id="echoid-s15465" xml:space="preserve">non vero 28 {1/2}. </s> <s xml:id="echoid-s15466" xml:space="preserve">Quia igitur non accuratius Experimenta Parentii <lb/>deſcripta ſunt, plura non addam, potius tranſiuns ad noſtra Ten-<lb/>tamina cum parallelopipedis Ligni Ulmi capta.</s> <s xml:id="echoid-s15467" xml:space="preserve"/> </p> <pb o="618" file="0634" n="635" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s15468" xml:space="preserve">Hæc omnia ex eodem aſſere confecta ſunt, ſingulorum longitudi-<lb/>nes fuerunt æquales, nempe 24 pollicum, quamvis diſtantia fulcrorum <lb/>ſemper tantum fuerit 18 pollicum & </s> <s xml:id="echoid-s15469" xml:space="preserve">immutabilis, erat omnium la-<lb/>titudo eadem, nempe 0, 26 pollic: </s> <s xml:id="echoid-s15470" xml:space="preserve">altitudo varia, quæ notatur, at-<lb/>que accuratiſſime ex medio ſemper ſuſpenſa fuerunt pondera.</s> <s xml:id="echoid-s15471" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div583" type="section" level="1" n="583"> <head xml:id="echoid-head702" xml:space="preserve">EXPERIMENTUM CXCII.</head> <p> <s xml:id="echoid-s15472" xml:space="preserve">Parallelopipedum Ulmi 0, 25 poll: </s> <s xml:id="echoid-s15473" xml:space="preserve">altum, in medio fractum <lb/>fuit ab appenſis libris 3.</s> <s xml:id="echoid-s15474" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div584" type="section" level="1" n="584"> <head xml:id="echoid-head703" xml:space="preserve">EXPERIMENTUM CXCIII.</head> <p> <s xml:id="echoid-s15475" xml:space="preserve">Parallelopipedum Ulmi 0, 35 pollic. </s> <s xml:id="echoid-s15476" xml:space="preserve">altum, in medio fractum <lb/>fuit a libris 7.</s> <s xml:id="echoid-s15477" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div585" type="section" level="1" n="585"> <head xml:id="echoid-head704" xml:space="preserve">EXPERIMENTUM CXCIV.</head> <p> <s xml:id="echoid-s15478" xml:space="preserve">Parallelopipedum Ulmi 0, 43 pollic: </s> <s xml:id="echoid-s15479" xml:space="preserve">altum, in medio fractum fuit <lb/>a libris 8 {1/2}.</s> <s xml:id="echoid-s15480" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div586" type="section" level="1" n="586"> <head xml:id="echoid-head705" xml:space="preserve">EXPERIMENTUM CXCV.</head> <p> <s xml:id="echoid-s15481" xml:space="preserve">Parallelopipedum Ulmi 0, 52. </s> <s xml:id="echoid-s15482" xml:space="preserve">pollic: </s> <s xml:id="echoid-s15483" xml:space="preserve">altum, ſolutum in medio <lb/>fuit a libris 19.</s> <s xml:id="echoid-s15484" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15485" xml:space="preserve">Iterum videamus, quænam aberratio Cohærentiæ corporum ſit <lb/>a regula, qua affirmabatur corporum diverſæ altitudinis Cohæren-<lb/>tiam eſſe in ratione duplicata altitudinis, ut unico ictu cuncta vi-<lb/>deantur, in tabellam conjeci Experimenta & </s> <s xml:id="echoid-s15486" xml:space="preserve">calculum.</s> <s xml:id="echoid-s15487" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 25. # 35. # 43. # 52. <lb/>Altitudinum Quadrata # 625. # 1225. # 1849. # 2704. <lb/>Cohærentiæ in Experimentis # 3. # 7. # 8 {1/2}. # 19. <lb/>Cohærentiæ ex Calculo. # 3. # 5 {550/625}. # 8 {547/625}. # 12 {612/625}. <lb/></note> <pb o="619" file="0635" n="636" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15488" xml:space="preserve">Ex quibus videmus Experimentum CXCII & </s> <s xml:id="echoid-s15489" xml:space="preserve">CXCIV congrue-<lb/>re cum regula, ſed Exp. </s> <s xml:id="echoid-s15490" xml:space="preserve">CXCIII. </s> <s xml:id="echoid-s15491" xml:space="preserve">& </s> <s xml:id="echoid-s15492" xml:space="preserve">CXCV. </s> <s xml:id="echoid-s15493" xml:space="preserve">aberrare; </s> <s xml:id="echoid-s15494" xml:space="preserve">imo ſi pona-<lb/>mus Experimentum CXCIII. </s> <s xml:id="echoid-s15495" xml:space="preserve">eſſe fundamentale, aberrabit Exp. <lb/></s> <s xml:id="echoid-s15496" xml:space="preserve">CXCV. </s> <s xml:id="echoid-s15497" xml:space="preserve">nam 1225. </s> <s xml:id="echoid-s15498" xml:space="preserve">7:</s> <s xml:id="echoid-s15499" xml:space="preserve">: 2704. </s> <s xml:id="echoid-s15500" xml:space="preserve">15 {553/1225}. </s> <s xml:id="echoid-s15501" xml:space="preserve">et ſi Exp. </s> <s xml:id="echoid-s15502" xml:space="preserve">CXCV. </s> <s xml:id="echoid-s15503" xml:space="preserve">ſumatur <lb/>pro fundamentali primo, quocum reliqua comparantur, major ab-<lb/>erratio a regula obſervabitur: </s> <s xml:id="echoid-s15504" xml:space="preserve">nam Cohærentia Experim. </s> <s xml:id="echoid-s15505" xml:space="preserve">CXCII. </s> <s xml:id="echoid-s15506" xml:space="preserve"><lb/>debuiſſet deprehendi librar: </s> <s xml:id="echoid-s15507" xml:space="preserve">4 {105/2704}. </s> <s xml:id="echoid-s15508" xml:space="preserve">ea Experimenti CXCIII. </s> <s xml:id="echoid-s15509" xml:space="preserve">æqualis <lb/>libris 8 {1643/2704}. </s> <s xml:id="echoid-s15510" xml:space="preserve">ea Experimenti CXCIV æqualis libris 12 {1683/2704}.</s> <s xml:id="echoid-s15511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15512" xml:space="preserve">Hiſce aberrationibus obſervatis ad examen alterius Ligni me <lb/>accinxi, ut conſtaret an in alio regula Univerſalis daretur, an ite-<lb/>rum deviatio; </s> <s xml:id="echoid-s15513" xml:space="preserve">adeoque Fraxinum elegi, atque ex eodem aſſere <lb/>confecta fuerunt parallelopipeda accuratiſſime ejusdem longitudi-<lb/>nis, latitudinis atque altitudinis ac priora, ex quibus pondera ſu-<lb/>ſpenſa in medio, & </s> <s xml:id="echoid-s15514" xml:space="preserve">frangentia Cohærentiam expreſſerunt: </s> <s xml:id="echoid-s15515" xml:space="preserve">eventus <lb/>fuerunt ſequentes.</s> <s xml:id="echoid-s15516" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div587" type="section" level="1" n="587"> <head xml:id="echoid-head706" xml:space="preserve">EXPERIMENTUM CXCVI.</head> <p> <s xml:id="echoid-s15517" xml:space="preserve">Parallelopipedum Fraxini 0, 23 pollic: </s> <s xml:id="echoid-s15518" xml:space="preserve">altum, â pondere pendente <lb/>ex medio adeo inflexum fuit, ut rumpi non potuerit.</s> <s xml:id="echoid-s15519" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div588" type="section" level="1" n="588"> <head xml:id="echoid-head707" xml:space="preserve">EXPERIMENTUM CXCVII.</head> <p> <s xml:id="echoid-s15520" xml:space="preserve">Parallelopipedum Fraxini 0, 33 pollic: </s> <s xml:id="echoid-s15521" xml:space="preserve">altum, in medio fractum <lb/>fuit ab appenſis libris 19 {1/2}. </s> <s xml:id="echoid-s15522" xml:space="preserve">â quibus valde inflexum fuit.</s> <s xml:id="echoid-s15523" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div589" type="section" level="1" n="589"> <head xml:id="echoid-head708" xml:space="preserve">EXPERIMENTUM CXCVIII.</head> <p> <s xml:id="echoid-s15524" xml:space="preserve">Parallelopipedum Fraxini 0, 42 pollic: </s> <s xml:id="echoid-s15525" xml:space="preserve">altum, in medio fractum <lb/>fuit ab appenſis libris 24 {1/2}.</s> <s xml:id="echoid-s15526" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div590" type="section" level="1" n="590"> <head xml:id="echoid-head709" xml:space="preserve">EXPERIMENTUM CXCIX.</head> <p> <s xml:id="echoid-s15527" xml:space="preserve">Parallelopipedum Fraxini 0, 51 pollic: </s> <s xml:id="echoid-s15528" xml:space="preserve">altum frangebatur in <lb/>medio ab appenſis libris 32 {1/2}.</s> <s xml:id="echoid-s15529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15530" xml:space="preserve">Examini ſubjiciantur hæc Experimenta, tumque conſtabit <pb o="620" file="0636" n="637" rhead="INTRODUCTIO AD COHÆRENTIAM"/> maximam aberrationem ab univerſali regula hic dari, uti tabula <lb/>oſtendit.</s> <s xml:id="echoid-s15531" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 33. # 42. # 51. <lb/>Altitudinum Quadrata # 1089. # 1764. # 2601. <lb/>Cohærentiæ in Experimentis, # 19 {1/2}. # 24 {1/2}. # 32 {1/2}. <lb/>Cohærentiæ ex Calculo. # 19 {1/2}. # 31 {213/363}. # 46 {417/726}. <lb/></note> <p> <s xml:id="echoid-s15532" xml:space="preserve">Calculus igitur alias omnino quantitates indicat, quam quæ in <lb/>Experimentis deprehenduntur; </s> <s xml:id="echoid-s15533" xml:space="preserve">cum Cohærentiæ longe minores exi-<lb/>ſtant.</s> <s xml:id="echoid-s15534" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15535" xml:space="preserve">Quoniam tamen adeo recepta fuit opinio, regulam Univerſalem <lb/>dari, qua corporum Cohærentia in ratione duplicata altitudinis <lb/>ponitur, iterum cum alio Ligno Experimenta eſſe capienda putavi: <lb/></s> <s xml:id="echoid-s15536" xml:space="preserve">Confecta igitur ex Ligno Piceæ fuerunt parallelopipeda, & </s> <s xml:id="echoid-s15537" xml:space="preserve">qui-<lb/>dem ex eodem aſſere omnia, ex ligno ſibi proximo, quæ accura-<lb/>te æque longa lataque ac priora fuerunt, altitudine tantum inter <lb/>ſe diverſa, eventus hi notati fuerunt.</s> <s xml:id="echoid-s15538" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div591" type="section" level="1" n="591"> <head xml:id="echoid-head710" xml:space="preserve">EXPERIMENTUM CC.</head> <p> <s xml:id="echoid-s15539" xml:space="preserve">Parallelopipedum Piceæ altum 0, 25. </s> <s xml:id="echoid-s15540" xml:space="preserve">pollic: </s> <s xml:id="echoid-s15541" xml:space="preserve">diffractum fuit a li-<lb/>bris 5 {1/2}. </s> <s xml:id="echoid-s15542" xml:space="preserve">ex medio appenſis.</s> <s xml:id="echoid-s15543" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div592" type="section" level="1" n="592"> <head xml:id="echoid-head711" xml:space="preserve">EXPERIMENTUM CCI.</head> <p> <s xml:id="echoid-s15544" xml:space="preserve">Parallelopipedum Piceæ altum 0, 35 pollic, ſolvebatur ab appen-<lb/>ſis in medio libris 11 {1/2}.</s> <s xml:id="echoid-s15545" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div593" type="section" level="1" n="593"> <head xml:id="echoid-head712" xml:space="preserve">EXPERIMENTUM CCII.</head> <p> <s xml:id="echoid-s15546" xml:space="preserve">Parallelopipedum Piceæ altum 0, 41 pollic. </s> <s xml:id="echoid-s15547" xml:space="preserve">diffractum fuit in <lb/>medio ab appenſis libris 14.</s> <s xml:id="echoid-s15548" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div594" type="section" level="1" n="594"> <head xml:id="echoid-head713" xml:space="preserve">EXPERIMENTUM CCIII.</head> <p> <s xml:id="echoid-s15549" xml:space="preserve">Parallelopipedum Piceæ altum 0, 52 pollic. </s> <s xml:id="echoid-s15550" xml:space="preserve">fractum fuit a libris <lb/>22. </s> <s xml:id="echoid-s15551" xml:space="preserve">ex medio applicatis.</s> <s xml:id="echoid-s15552" xml:space="preserve"/> </p> <pb o="621" file="0637" n="638" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15553" xml:space="preserve">Quæ Experimenta multo accuratius cum regula univerſali con-<lb/>veniunt, uti ex inſpecta Tabula liquet</s> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 25. # 35. # 41. # 52. <lb/>Quadrata Altitudinum # 625. # 1225. # 1681. # 2704. <lb/>Cohærentiæ in Experim. # 5 {1/2}. # 11 {1/2}. # 14. # 22. <lb/>Cohærentiæ ex Calculo # 5 {1/2}. # 10 {39/50}. # 14 {472/625}. # 23 {3/4}. <lb/></note> <p> <s xml:id="echoid-s15554" xml:space="preserve">Tandem curavi parallelopipeda æque longa & </s> <s xml:id="echoid-s15555" xml:space="preserve">craſſa ac priora ex <lb/>Ligno Tiliæ, & </s> <s xml:id="echoid-s15556" xml:space="preserve">quidem ex eodem aſſere, cum quibus capta ten-<lb/>tamina ſequentes effectus dederunt.</s> <s xml:id="echoid-s15557" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div595" type="section" level="1" n="595"> <head xml:id="echoid-head714" xml:space="preserve">EXPERIMENTUM CCIV.</head> <p> <s xml:id="echoid-s15558" xml:space="preserve">Parallelopipedum Tiliæ 0, 24 pollic. </s> <s xml:id="echoid-s15559" xml:space="preserve">altum, fractum fuit in me-<lb/>dio ab libris 5, & </s> <s xml:id="echoid-s15560" xml:space="preserve">unciis 10.</s> <s xml:id="echoid-s15561" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div596" type="section" level="1" n="596"> <head xml:id="echoid-head715" xml:space="preserve">EXPERIMENTUM CCV.</head> <p> <s xml:id="echoid-s15562" xml:space="preserve">Parallelopipedum Tiliæ 0, 34 poll: </s> <s xml:id="echoid-s15563" xml:space="preserve">altum in medio fractum fuit <lb/>a libris 12.</s> <s xml:id="echoid-s15564" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div597" type="section" level="1" n="597"> <head xml:id="echoid-head716" xml:space="preserve">EXPERIMENTUM CCVI.</head> <p> <s xml:id="echoid-s15565" xml:space="preserve">Parallelopipedum Tiliæ 0, 43. </s> <s xml:id="echoid-s15566" xml:space="preserve">poll. </s> <s xml:id="echoid-s15567" xml:space="preserve">altum in medio fractum fuit <lb/>a libris 14.</s> <s xml:id="echoid-s15568" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div598" type="section" level="1" n="598"> <head xml:id="echoid-head717" xml:space="preserve">EXPERIMENTUM CCVII.</head> <p> <s xml:id="echoid-s15569" xml:space="preserve">Parallelopipedum Tiliæ 0, 50 poll. </s> <s xml:id="echoid-s15570" xml:space="preserve">altum in medio fractum fuit <lb/>a libris 19.</s> <s xml:id="echoid-s15571" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15572" xml:space="preserve">Quæ iterum in ordinatam Tabulam reducta, ſic ſtant</s> </p> <note position="right" xml:space="preserve"> <lb/>Altitudines Lignorum # 24. # 34. # 43. # 50. <lb/>Altitudinum Quadrata # 576. # 1156. # 1849. # 2500. <lb/>Cohærentiæ in Experim. # 5 {10/16}. # 12. # 14. # 19. <lb/>Cohærentiæ ex Calculo. # 5 {10/16}. # 11 {333/1152}. # 18 {61/4608}. # 24 {1908/4608}. <lb/></note> <p> <s xml:id="echoid-s15573" xml:space="preserve">In quibus Experimentis proinde aberratio a regula etiam obſer-<lb/>vatur: </s> <s xml:id="echoid-s15574" xml:space="preserve">Quid igitur concludemus ex his omnibus ſecum invicem <lb/>comparatis? </s> <s xml:id="echoid-s15575" xml:space="preserve">1°. </s> <s xml:id="echoid-s15576" xml:space="preserve">Dari corpora, quorum Cohærentia eſt in ratione <pb o="622" file="0638" n="639" rhead="INTRODUCTIO AD COHÆRENTIAM"/> duplicata altitudinis, veluti vitrum eſt, ſecundum Experimenta <lb/>ab CLXXVIII. </s> <s xml:id="echoid-s15577" xml:space="preserve">ad CLXXXIV. </s> <s xml:id="echoid-s15578" xml:space="preserve">2°. </s> <s xml:id="echoid-s15579" xml:space="preserve">Tum dari alia, quorum Cohæ-<lb/>rentia accedit appropinquando ad eam proportionem, veluti eſt <lb/>Lignum Quercicum, ſecundum Experimenta ab CLXII ad CLXVII. <lb/></s> <s xml:id="echoid-s15580" xml:space="preserve">& </s> <s xml:id="echoid-s15581" xml:space="preserve">ab CLXXXVII. </s> <s xml:id="echoid-s15582" xml:space="preserve">ad CXCII. </s> <s xml:id="echoid-s15583" xml:space="preserve">ut & </s> <s xml:id="echoid-s15584" xml:space="preserve">Lignum Piceæ, ſecundum <lb/>Experimenta ab CLXXIV. </s> <s xml:id="echoid-s15585" xml:space="preserve">CLXXVII. </s> <s xml:id="echoid-s15586" xml:space="preserve">& </s> <s xml:id="echoid-s15587" xml:space="preserve">a CC ad CCIV. </s> <s xml:id="echoid-s15588" xml:space="preserve"><lb/>3°. </s> <s xml:id="echoid-s15589" xml:space="preserve">Deinde dari alia, quæ ab hac proportione magis abludunt, <lb/>quemadmodum Lignum Fraxini & </s> <s xml:id="echoid-s15590" xml:space="preserve">Lignum Tiliæ, ſecundum Ex-<lb/>perimenta ab CXCVI ad CC, & </s> <s xml:id="echoid-s15591" xml:space="preserve">ab CCIV ad CCVIII.</s> <s xml:id="echoid-s15592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15593" xml:space="preserve">Valde flexilium Cohærentia non in tam alta ratione aſſurgit <lb/>quam quidem corporum duriorum, quia fibræ, quæ prius fran-<lb/>guntur, valde quam extenduntur: </s> <s xml:id="echoid-s15594" xml:space="preserve">quæ poſtremo rumpuntur, po-<lb/>tius in initio comprimuntur, quod potiſſimum obtinet in corporibus <lb/>altioribus, quorum Cohærentia ſemper obſervatur plus quoque re-<lb/>cedere â vulgari regula.</s> <s xml:id="echoid-s15595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15596" xml:space="preserve">Non dubito, quin ſi plura Lignorum genera examinaviſſem, de-<lb/>prehendiſſem nonnunquam majores, nonnunquam minores aber-<lb/>rationes: </s> <s xml:id="echoid-s15597" xml:space="preserve">forte quoque pro diverſâ corporum ſiccitate, humidita-<lb/>te, ætate qua concreverunt, tempore quo ſciſſa ſunt, regione in <lb/>qua creverunt, proportiones diſcrepabunt, idcirco non video Na-<lb/>turam regulis adeo univerſalibus gaudere ubivis, ac vulgo quæ-<lb/>runtur: </s> <s xml:id="echoid-s15598" xml:space="preserve">alia competit in hac doctrina corporibus valde duris, alia <lb/>minus duris, alia flexibilibus. </s> <s xml:id="echoid-s15599" xml:space="preserve">alia flexibilioribus, alia flexibiliſſimis; <lb/></s> <s xml:id="echoid-s15600" xml:space="preserve">& </s> <s xml:id="echoid-s15601" xml:space="preserve">quia corpora ſæpe gradus ſuos flexibilitatis immutant, veluti Ligna <lb/>faciunt ætate increſcendo, & </s> <s xml:id="echoid-s15602" xml:space="preserve">tempore poſtquam cæſa ſunt, variis <lb/>regulis ſubjicientur, quæ determinatu ſemper erunt difficillimæ; </s> <s xml:id="echoid-s15603" xml:space="preserve"><lb/>quemadmodum etiam in quanam data conditione præſenti ſint cor-<lb/>pora, ut iis aut hæc, aut alia applicari regula queat: </s> <s xml:id="echoid-s15604" xml:space="preserve">Idcirco ſagacita-<lb/>tem Mathematicorum ſemper aliquomodo eludet doctrina Firmita-<lb/>tis, nec opinor aliquem datum iri, qui a priori affirmare ſemper <lb/>poterit; </s> <s xml:id="echoid-s15605" xml:space="preserve">datam Trabem, ex dato Ligno confectam, ad medium <lb/>ſui poſſe ſuſpendere pondus determinandum ope calculi, quod <lb/>maximum ſit. </s> <s xml:id="echoid-s15606" xml:space="preserve">Appropinquare licebit ad veritatem, & </s> <s xml:id="echoid-s15607" xml:space="preserve">compara-<lb/>re noſtra Experimenta cum data Trabe, indeque ope calculi quæ-<lb/>dam determinare, ſed quæ abludere notabiliter poterunt â verâ Co-<lb/>hærentiâ: </s> <s xml:id="echoid-s15608" xml:space="preserve">Quatenus enim Cohærentia non eſt in ratione duplicata <pb o="623" file="0639" n="640" rhead="CORPORUM FIRMORUM."/> altitudinis, & </s> <s xml:id="echoid-s15609" xml:space="preserve">plus minuſve ab ea proportione diſcedit, fiet prima <lb/>aberratio: </s> <s xml:id="echoid-s15610" xml:space="preserve">2°. </s> <s xml:id="echoid-s15611" xml:space="preserve">In Experimentis noſtris adhibuimus lignum opti-<lb/>mæ notæ, non nodoſum, non intortis fibris, ſed mere rectis con-<lb/>ſtans; </s> <s xml:id="echoid-s15612" xml:space="preserve">cum Trabs inſignis longitudinis & </s> <s xml:id="echoid-s15613" xml:space="preserve">craſſitiei ſemper ſit no-<lb/>doſa, & </s> <s xml:id="echoid-s15614" xml:space="preserve">partim fibris rectis, partim flexuoſis conſtet; </s> <s xml:id="echoid-s15615" xml:space="preserve">adeoque <lb/>iterum Cohærentia Ligni in Experimento examinati & </s> <s xml:id="echoid-s15616" xml:space="preserve">propoſitæ <lb/>trabis non accurate reſpondebit proportionibus craſſitiei, altitudi-<lb/>nis, & </s> <s xml:id="echoid-s15617" xml:space="preserve">longitudinis: </s> <s xml:id="echoid-s15618" xml:space="preserve">3°. </s> <s xml:id="echoid-s15619" xml:space="preserve">prout Trabs fuerit humidior ſicciorve, in <lb/>calidiori vel frigidiori excreverit regione, annoſior aut tenerior fue-<lb/>rit, magis minuſve firma erit: </s> <s xml:id="echoid-s15620" xml:space="preserve">Progreſſum itaque ope Experimen-<lb/>torum noſtrorum aliquem utcunque exiguum, me in Phyſica feciſſe, <lb/>& </s> <s xml:id="echoid-s15621" xml:space="preserve">præſtitiſſe opinor ea, quæ fundamenta manere poterunt hujus do-<lb/>ctrinæ, nequaquam Firmitatis doctrinam penitus abſolviſſe.</s> <s xml:id="echoid-s15622" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15623" xml:space="preserve">Poterunt autem ex noſtris Experimentis firmitates Lignorum <lb/>diverſorum cognoſci, comparando pondera Cohærentiam expri-<lb/>mentia, quæ appenſa fuerunt parallelopipedis æque altis, latis, <lb/>longiſque, atque deprehendentur ſecundum hanc proportionem Fir-<lb/>mitates eorum reſpectivæ.</s> <s xml:id="echoid-s15624" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Quercus. # Ulmus. # Fraxinus. # Picea. # Tilia. <lb/>15 {405/2178}. # 7. # 19 {19/135}. # 11 {1/2}. # 12 {207/289}. <lb/></note> <p> <s xml:id="echoid-s15625" xml:space="preserve">Quia tamen plurimorum corporum firmitates appropinquant ad <lb/>proportionem, duplicatæ altitudinis, eam aſſumere poterimus, ut <lb/>ſupra, tumque plurima pulcherrimaque exhiberi poterunt Theo-<lb/>remata, quæ nunc aggredior.</s> <s xml:id="echoid-s15626" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div599" type="section" level="1" n="599"> <head xml:id="echoid-head718" xml:space="preserve">PROPOSITIO XCVII.</head> <p style="it"> <s xml:id="echoid-s15627" xml:space="preserve">Tab XXIV. </s> <s xml:id="echoid-s15628" xml:space="preserve">fig. </s> <s xml:id="echoid-s15629" xml:space="preserve">7. </s> <s xml:id="echoid-s15630" xml:space="preserve">Si detur aſſer aut parallelopipedum D A B <lb/>C E F, impoſitum duobus fulcris A & </s> <s xml:id="echoid-s15631" xml:space="preserve">B, ex cujus medio K agat <lb/>pondus P, erit hujus Cohærentia, ad eam quam haberet, impoſito <lb/>latere A F C B fulcris, uti eſt B C ad E C:</s> <s xml:id="echoid-s15632" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15633" xml:space="preserve">Nam eſt Cohærentia parallelopipedi ita impoſiti ſuis fulcris A & </s> <s xml:id="echoid-s15634" xml:space="preserve">B <lb/>ac hic repræſentatur, in ratione compoſita ex E C latitudine & </s> <s xml:id="echoid-s15635" xml:space="preserve">du-<lb/>plicata altitudinis C B. </s> <s xml:id="echoid-s15636" xml:space="preserve">ſive uti E C X <emph style="ol">CB</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15637" xml:space="preserve">Atque eſt Cohæren-<lb/>tia ejuſdem parallelopipedi impoſiti lateri A F C B, in ratione com- <pb o="624" file="0640" n="641" rhead="INTRODUCTIO AD COHÆRENTIAM"/> compoſita latitudinis C B, & </s> <s xml:id="echoid-s15638" xml:space="preserve">altitudinis E C duplicatâ, ſive B C <lb/>X <emph style="ol">E C</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15639" xml:space="preserve">ſed eſt E C X <emph style="ol">CB</emph><emph style="super">q</emph> ad B C X <emph style="ol">E C</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s15640" xml:space="preserve">: CB, EC, quare <lb/>erit Cohærentia hujus parallelopipedi, ad eam, cujus latus inferius <lb/>eſt A F C B, uti C B ad E C.</s> <s xml:id="echoid-s15641" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15642" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15643" xml:space="preserve">1. </s> <s xml:id="echoid-s15644" xml:space="preserve">Ergo aſſeris Lignei vel parallelopipedi firmitas poteſt <lb/>eſſe admodum variâ, pro diverſo ſitu, quem ſupra fulcra accepit: </s> <s xml:id="echoid-s15645" xml:space="preserve">ſi <lb/>enim E C ſit major C B, erit firmitas aſſeris in ſitu ſecundo major <lb/>quam in primo.</s> <s xml:id="echoid-s15646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15647" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15648" xml:space="preserve">2. </s> <s xml:id="echoid-s15649" xml:space="preserve">Et datis duobus aſſeribus æque longis, æque firmis, <lb/>diverſarum baſium & </s> <s xml:id="echoid-s15650" xml:space="preserve">utrimque fulcro impoſitis, erunt eorum lati-<lb/>tudines reciproce uti ſunt quadrata altitudinum.</s> <s xml:id="echoid-s15651" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15652" xml:space="preserve">Ponatur enim altitudo B C = A latitudo E C = B. </s> <s xml:id="echoid-s15653" xml:space="preserve">erit Cohærentia <lb/>= A A X B. </s> <s xml:id="echoid-s15654" xml:space="preserve">vocetur alterius altitudo a. </s> <s xml:id="echoid-s15655" xml:space="preserve">latitudo b. </s> <s xml:id="echoid-s15656" xml:space="preserve">erit hujus Co-<lb/>hærentia = aa X b. </s> <s xml:id="echoid-s15657" xml:space="preserve">ponuntur firmitates æquales, adeoque</s> </p> <p> <s xml:id="echoid-s15658" xml:space="preserve">A A X B = aa X b. </s> <s xml:id="echoid-s15659" xml:space="preserve">unde B. </s> <s xml:id="echoid-s15660" xml:space="preserve">b:</s> <s xml:id="echoid-s15661" xml:space="preserve">: aa. </s> <s xml:id="echoid-s15662" xml:space="preserve">A A.</s> <s xml:id="echoid-s15663" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15664" xml:space="preserve">Corol 3. </s> <s xml:id="echoid-s15665" xml:space="preserve">Quare datâ altitudine duorum præcedentium aſſerum <lb/>& </s> <s xml:id="echoid-s15666" xml:space="preserve">unius latitudine, invenitur latitudo alterius: </s> <s xml:id="echoid-s15667" xml:space="preserve">nam erit B = {aab.</s> <s xml:id="echoid-s15668" xml:space="preserve">/AA} <lb/>& </s> <s xml:id="echoid-s15669" xml:space="preserve">data latitudine amborum aſſerum & </s> <s xml:id="echoid-s15670" xml:space="preserve">altitudine unius, invenitur <lb/>altitudo alterius, cum {aab/B} = A.</s> <s xml:id="echoid-s15671" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15672" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15673" xml:space="preserve">4. </s> <s xml:id="echoid-s15674" xml:space="preserve">Si igitur aſſer fuerit longus, & </s> <s xml:id="echoid-s15675" xml:space="preserve">erigatur ſecundum <lb/>ſuam longitudinem, ut fiat, a b c d, in Tab. </s> <s xml:id="echoid-s15676" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s15677" xml:space="preserve">fig. </s> <s xml:id="echoid-s15678" xml:space="preserve">VII. </s> <s xml:id="echoid-s15679" xml:space="preserve">at-<lb/>que utrimque imponatur fulcro, b c & </s> <s xml:id="echoid-s15680" xml:space="preserve">e. </s> <s xml:id="echoid-s15681" xml:space="preserve">firmiſſimus erit, pote-<lb/>ritque ex ſui medio pondus maximum appenſum gerere.</s> <s xml:id="echoid-s15682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15683" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15684" xml:space="preserve">5. </s> <s xml:id="echoid-s15685" xml:space="preserve">Ex his diſcimus Trabium oneribus ſuſtinendis deſtina-<lb/>tarum firmitates poſſe augeri, non augendo earum pretium, nec <lb/>quantitatem Ligni, nec pondus proprium.</s> <s xml:id="echoid-s15686" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15687" xml:space="preserve">Sit enim Trabs alta & </s> <s xml:id="echoid-s15688" xml:space="preserve">lata 12 pollices, adeoque cujus ſectio eſt <lb/>144 pollic. </s> <s xml:id="echoid-s15689" xml:space="preserve">quadratorum: </s> <s xml:id="echoid-s15690" xml:space="preserve">detur alia trabs altitudinis 14 pollic. </s> <s xml:id="echoid-s15691" xml:space="preserve">la-<lb/>titudinis 10 poll: </s> <s xml:id="echoid-s15692" xml:space="preserve">erit hujus ſectio 140 pollic. </s> <s xml:id="echoid-s15693" xml:space="preserve">quadratorum, adeo-<lb/>que erit ſoliditas prioris Trabis ad eam poſterioris uti 144 ad 140. <lb/></s> <s xml:id="echoid-s15694" xml:space="preserve">ſed firmitas primæ eſt ut 144 X 12. </s> <s xml:id="echoid-s15695" xml:space="preserve">& </s> <s xml:id="echoid-s15696" xml:space="preserve">ſecundæ uti 196 X 10, quæ <lb/>ſunt inter ſe uti 1728 ad 1960. </s> <s xml:id="echoid-s15697" xml:space="preserve">quare poſterior Trabs erit fortior <lb/>& </s> <s xml:id="echoid-s15698" xml:space="preserve">minoris pretii, cum minus ligni in ſe contineat.</s> <s xml:id="echoid-s15699" xml:space="preserve"/> </p> <pb o="625" file="0641" n="642" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15700" xml:space="preserve">Ut manifeſto appareret, quomodo diminuendo quantitatem Ligni, <lb/>& </s> <s xml:id="echoid-s15701" xml:space="preserve">Trabibus variam dando altitudinem, augeretur earum robur, Pa-<lb/>rentius ſequentem tabulam dedit in L’Hiſt. </s> <s xml:id="echoid-s15702" xml:space="preserve">de L’Acad. </s> <s xml:id="echoid-s15703" xml:space="preserve">Roy. </s> <s xml:id="echoid-s15704" xml:space="preserve">1708.</s> <s xml:id="echoid-s15705" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Latitudo. # Altitudo. # Firmltas. # Soliditas. <lb/>12 # 12 # 1728 # 144. <lb/>11 # 13 # 1859 # 143. <lb/>10 # 14 # 1960 # 140. <lb/>9 # 15 # 2025 # 135. <lb/>8 # 16 # 2048 # 128. <lb/>7 # 17 # 2023 # 119. <lb/>6 # 18 # 1944 # 108. <lb/></note> <p> <s xml:id="echoid-s15706" xml:space="preserve">Non tamen licet latitudinem imminuere ad lubitum, quippe tum <lb/>a vi minima laterali facillime rumperetur, quamobrem certa requiri-<lb/>tur latitudo reſpectu altitudinis, quam in ſequenti Propoſitione <lb/>determinabimus.</s> <s xml:id="echoid-s15707" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div600" type="section" level="1" n="600"> <head xml:id="echoid-head719" xml:space="preserve">PROPOSITIO XCVIII.</head> <p style="it"> <s xml:id="echoid-s15708" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15709" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s15710" xml:space="preserve">fig. </s> <s xml:id="echoid-s15711" xml:space="preserve">8. </s> <s xml:id="echoid-s15712" xml:space="preserve">Dato Cylindro R A S V B T, ex eo fabre-<lb/>facere parallelopipedum R S V T maximæ Cohærentiæ.</s> <s xml:id="echoid-s15713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15714" xml:space="preserve">Sit baſis Cylindri circulus R A S V B T, cui ſit inſcripta baſis pa-<lb/>rallelopipedi rectangula R S V T maximæ reſiftentiæ, & </s> <s xml:id="echoid-s15715" xml:space="preserve">maxi-<lb/>mum, quod huic circulo inſcribi poſſit: </s> <s xml:id="echoid-s15716" xml:space="preserve">Sit R S ipſius latitudo, <lb/>quæ ſecet A B in Q, ſit S V ipſius altitudo: </s> <s xml:id="echoid-s15717" xml:space="preserve">poterit C Q conſide-<lb/>rari ut abſciſſa, quam voco x. </s> <s xml:id="echoid-s15718" xml:space="preserve">radius C S vocetur = r. </s> <s xml:id="echoid-s15719" xml:space="preserve">erit ob <lb/>Triangulum rectangulum C Q S: </s> <s xml:id="echoid-s15720" xml:space="preserve">recta Q S = rr - xx.</s> <s xml:id="echoid-s15721" xml:space="preserve"> unde <lb/>R S dupla ipſius Q S, erit = 2 rr - xx.</s> <s xml:id="echoid-s15722" xml:space="preserve"> quare multiplicando qua-<lb/>dratum S V per R S, ut habeatur omnis firmitas, dabitur 4 xx X 2 <lb/>rr - xx ſive 8 xx rr - xx.</s> <s xml:id="echoid-s15723" xml:space="preserve"> hujus valoris ſumendo maximum, <lb/>habebitur {8dx X 2rrx - 3x<emph style="super">3</emph>/rr - xx} = 0. </s> <s xml:id="echoid-s15724" xml:space="preserve">unde deducitur 2rr = 3xx. <lb/></s> <s xml:id="echoid-s15725" xml:space="preserve">atque dividendo utrumque membrum per 3, erit {2/3} rr = xx. </s> <s xml:id="echoid-s15726" xml:space="preserve">hinc <lb/>quadratum Q S eſt = {1/3} rr. </s> <s xml:id="echoid-s15727" xml:space="preserve">quamobrem erit <emph style="ol">C Q</emph><emph style="super">q</emph>.</s> <s xml:id="echoid-s15728" xml:space="preserve"><emph style="ol">QS</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s15729" xml:space="preserve">: {2/3}, {1/3}:</s> <s xml:id="echoid-s15730" xml:space="preserve">: 2, 1. </s> <s xml:id="echoid-s15731" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15732" xml:space="preserve">C Q, QS:</s> <s xml:id="echoid-s15733" xml:space="preserve">: SV. </s> <s xml:id="echoid-s15734" xml:space="preserve">RS:</s> <s xml:id="echoid-s15735" xml:space="preserve">: 2, 1:</s> <s xml:id="echoid-s15736" xml:space="preserve">: 7. </s> <s xml:id="echoid-s15737" xml:space="preserve">5. </s> <s xml:id="echoid-s15738" xml:space="preserve">proxime. </s> <s xml:id="echoid-s15739" xml:space="preserve">Ut in dato <pb o="626" file="0642" n="643" rhead="INTRODUCTIO AD COHÆRENTIAM"/> circulo R A S B inſcribantur lineæ R S, S V, ſumantur duæ lineæ <lb/>ad libitum, quarum X Z ſit 5, Z Y 7 partium, quæ jungantur ad <lb/>angulum rectum X Z Y: </s> <s xml:id="echoid-s15740" xml:space="preserve">per tria puncta X, Z, Y. </s> <s xml:id="echoid-s15741" xml:space="preserve">deſcribatur cir-<lb/>culus, fiat hic, vel alius ipſi æqualis, concentricus dato R A S B, <lb/>atque ex punctis X, Z, Y, ducantur ad centrum C rectæ, ſecabi-<lb/>tur peripheria in punctis R, S, V. </s> <s xml:id="echoid-s15742" xml:space="preserve">quæ ſi jungantur rectis R S, S V. <lb/></s> <s xml:id="echoid-s15743" xml:space="preserve">ſatisfactum erit quæſito.</s> <s xml:id="echoid-s15744" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div601" type="section" level="1" n="601"> <head xml:id="echoid-head720" xml:space="preserve">PROPOSITIO XCIX.</head> <p style="it"> <s xml:id="echoid-s15745" xml:space="preserve">Tab XXIV fig. </s> <s xml:id="echoid-s15746" xml:space="preserve">9. </s> <s xml:id="echoid-s15747" xml:space="preserve">Si parallelopipedum vel cylindrus A O, in <lb/>medio B ſuffultus, propria gravitate utriuſque extremi B A, B O <lb/>fuerit fractur æ proximus, hic utroque extremo A & </s> <s xml:id="echoid-s15748" xml:space="preserve">O fulcro im-<lb/>poſitus, propriâ gravitate in medio B fractur æ quoque proximus <lb/>erit.</s> <s xml:id="echoid-s15749" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15750" xml:space="preserve">Concipiatur primo fulcrum in medio B, & </s> <s xml:id="echoid-s15751" xml:space="preserve">loco gravitatis utri-<lb/>uſque extremi A B, B O, pondera R & </s> <s xml:id="echoid-s15752" xml:space="preserve">Q extremis appenſa eun-<lb/>dem præſtare effectum, quibus ſcilicet ſolidum in B redditur fra-<lb/>cturæ proximum, tum Fulcrum B tantopere premit ſurſum hoc ſo-<lb/>lidum, quantum ambo pondera R + Q agunt deorſum: </s> <s xml:id="echoid-s15753" xml:space="preserve">Quam <lb/>obrem concipiatur ſolidum A B O converti, atque extrema A & </s> <s xml:id="echoid-s15754" xml:space="preserve">O <lb/>imponi fulcris, quæ reſiſtant tantopere ac pondera R + Q egerunt, <lb/>atque ex medio B appendi pondus, quod deorſum agat, quantum <lb/>fulcrum B antea egit ſurſum, manifeſtum eſt Cylindrum in codem <lb/>ſtatu ac ante poni, hoc eſt fieri rupturæ proximum: </s> <s xml:id="echoid-s15755" xml:space="preserve">ſed pondera <lb/>R + Q agere ſuppoſita ſunt, quantum gravitas totius ſolidi A B O, <lb/>adeoque fulcrum B egit ſurſum, quantum gravitabat ſolidum, hinc <lb/>pondus in medio B, æquale actioni fulcri, erit etiam æquale gra-<lb/>vitati ſolidi, quare gravitas ſolidi A B O ponit id ipſum duobus <lb/>fulcris impoſitum, etiam fracturæ proximum.</s> <s xml:id="echoid-s15756" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15757" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15758" xml:space="preserve">Ergo parallelopipedum vel Cylindrus, qui propriâ gra-<lb/>vitate frangeretur duobus impoſitus fulcris, poteſt eſſe duplo lon-<lb/>gior. </s> <s xml:id="echoid-s15759" xml:space="preserve">quam parallelopipedum vel Cylindrus uno ſui extremo pa-<lb/>rieti infixus.</s> <s xml:id="echoid-s15760" xml:space="preserve"/> </p> <pb o="627" file="0643" n="644" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div602" type="section" level="1" n="602"> <head xml:id="echoid-head721" xml:space="preserve">PROPOSITIO C.</head> <p style="it"> <s xml:id="echoid-s15761" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15762" xml:space="preserve">XXVI. </s> <s xml:id="echoid-s15763" xml:space="preserve">fig. </s> <s xml:id="echoid-s15764" xml:space="preserve">9. </s> <s xml:id="echoid-s15765" xml:space="preserve">Si dentur duo Cylindri ejuſdem diametri <lb/>vel parallelopipeda æque alta & </s> <s xml:id="echoid-s15766" xml:space="preserve">lata, ſed diverſæ longitudinis <lb/>D O, K L, quorum mediis B, M appenſa ſint pondera P, T, æ-<lb/>qualia, erunt borum momenta, uti longitudines D O, K L.</s> <s xml:id="echoid-s15767" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15768" xml:space="preserve">Nam agit pondus P tanquam ex vecte A B, & </s> <s xml:id="echoid-s15769" xml:space="preserve">pondus T ex vecte <lb/>M K, adeoque erit momentum ponderis P, ad momentum ponde-<lb/>ris T ſibi æqualis, uti B A ad M K, vel ut dupla B A ad duplam <lb/>M K, hoc eſt ut D O ad K L.</s> <s xml:id="echoid-s15770" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div603" type="section" level="1" n="603"> <head xml:id="echoid-head722" xml:space="preserve">PROPOSITIO CI.</head> <p style="it"> <s xml:id="echoid-s15771" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15772" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s15773" xml:space="preserve">fig 9 & </s> <s xml:id="echoid-s15774" xml:space="preserve">14. </s> <s xml:id="echoid-s15775" xml:space="preserve">Data trabe ex dato ligno, impoſitaque <lb/>libere duobus fulcris, invenire quantum firmitatis in ſui medio <lb/>babeat.</s> <s xml:id="echoid-s15776" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15777" xml:space="preserve">Solvi poterit hoc Problema comparando firmitatem parallelopi-<lb/>pedi alicujus examinati ex eodem ligno cum data Trabe, ſequenti <lb/>modo: </s> <s xml:id="echoid-s15778" xml:space="preserve">Sit fig. </s> <s xml:id="echoid-s15779" xml:space="preserve">9. </s> <s xml:id="echoid-s15780" xml:space="preserve">aliquod parallelopipedum antea examinatum A B O, <lb/>ex cujus medio B pondus appenſum diffringens P, exprimens fir-<lb/>mitatem, fit cognitum, quod ponatur = p. </s> <s xml:id="echoid-s15781" xml:space="preserve">longitudo A B = a. <lb/></s> <s xml:id="echoid-s15782" xml:space="preserve">altitudo A C = b. </s> <s xml:id="echoid-s15783" xml:space="preserve">latitudo C D = d. </s> <s xml:id="echoid-s15784" xml:space="preserve">Sit data Trabs fig. </s> <s xml:id="echoid-s15785" xml:space="preserve">14. </s> <s xml:id="echoid-s15786" xml:space="preserve">E S. </s> <s xml:id="echoid-s15787" xml:space="preserve"><lb/>cujus dimidia longitudo E X ſit = e. </s> <s xml:id="echoid-s15788" xml:space="preserve">altitudo E F = f. </s> <s xml:id="echoid-s15789" xml:space="preserve">latitudo F G <lb/>= g. </s> <s xml:id="echoid-s15790" xml:space="preserve">& </s> <s xml:id="echoid-s15791" xml:space="preserve">pondus in medio appendendum = z. </s> <s xml:id="echoid-s15792" xml:space="preserve">Erit ex natura vectis <lb/>potentia in B, ad eam in X pro eodem momento, uti E X ad A B <lb/>:</s> <s xml:id="echoid-s15793" xml:space="preserve">: ë, a. </s> <s xml:id="echoid-s15794" xml:space="preserve">unde erit firmitas in B ad eam in X, in ratione compoſita <lb/>ex quadrato A C ad quadratum E F, ex C D ad F G, & </s> <s xml:id="echoid-s15795" xml:space="preserve">ex E X ad <lb/>A B: </s> <s xml:id="echoid-s15796" xml:space="preserve">quæ expreſſa Algebrice ſtabunt e X bb X d. </s> <s xml:id="echoid-s15797" xml:space="preserve">a X ff X g. </s> <s xml:id="echoid-s15798" xml:space="preserve"><lb/>:</s> <s xml:id="echoid-s15799" xml:space="preserve">: p. </s> <s xml:id="echoid-s15800" xml:space="preserve">z adeoque erit pondus z. </s> <s xml:id="echoid-s15801" xml:space="preserve">ſive firmitas quæſita ={p X a X ff X g.</s> <s xml:id="echoid-s15802" xml:space="preserve">/e X bb X d} <lb/>Oportet ut moniti præcedentis memores ſimus, nempe hoc eſſe <lb/>omne quod a Geometria præſtari poſſit, ſed Phyſice Trabem non <lb/>ſemper hanc firmitatem habituram.</s> <s xml:id="echoid-s15803" xml:space="preserve"/> </p> <pb o="628" file="0644" n="645" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div604" type="section" level="1" n="604"> <head xml:id="echoid-head723" xml:space="preserve">PROPOSITIO CII.</head> <p style="it"> <s xml:id="echoid-s15804" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15805" xml:space="preserve">XXIV. </s> <s xml:id="echoid-s15806" xml:space="preserve">fig. </s> <s xml:id="echoid-s15807" xml:space="preserve">14. </s> <s xml:id="echoid-s15808" xml:space="preserve">Si detur Cylindrus, priſma, vel paralle-<lb/>lopipedum E F G S, quod uno extremo E F G parieti infixum, ab <lb/>altero extremo S ferre poteſt pondus ‘P, quod eſt maximum; </s> <s xml:id="echoid-s15809" xml:space="preserve">im-<lb/>poſitum idem ſolidum duobus fulcris N. </s> <s xml:id="echoid-s15810" xml:space="preserve">V. </s> <s xml:id="echoid-s15811" xml:space="preserve">poterit ex medio X ge-<lb/>ſtare pondus P quadruplo majus quam ante, non conſiderata ſolidi <lb/>gravitate.</s> <s xml:id="echoid-s15812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15813" xml:space="preserve">Nam ſi pondus P poſſit ferri ab extremo S ſolidi F S uno ſui ex-<lb/>tremo parieti infixi, poterit pondus duplo majus quam P geſtari <lb/>ex X dimidio ipſius G S. </s> <s xml:id="echoid-s15814" xml:space="preserve">poſito proinde ſolido ſuper duobus fulcris <lb/>N, V. </s> <s xml:id="echoid-s15815" xml:space="preserve">& </s> <s xml:id="echoid-s15816" xml:space="preserve">pondere P in medio X, idem eſt ac ſi duorum vectium <lb/>E X, V X extremis appenderetur, adeoque cum duplum pondus <lb/>P ex vecte E X ferri poſſit, itidem duplum pondus ex vecte V X ge-<lb/>retur, quamobrem quadruplum pondus P ab utroque ſimul ferri <lb/>poterit ex medio X.</s> <s xml:id="echoid-s15817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15818" xml:space="preserve">Quoniam hæc Propoſitio parum paradoxa videri poſſet, eam <lb/>lubuit confirmare ſequenti Experimento.</s> <s xml:id="echoid-s15819" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div605" type="section" level="1" n="605"> <head xml:id="echoid-head724" xml:space="preserve">EXPERIMENTUM CCVIII.</head> <p> <s xml:id="echoid-s15820" xml:space="preserve">Sumtum fuit parallelopipedum Quercicum rectangulum, cujus <lb/>quodlibet latus erat, o, 21 pollic. </s> <s xml:id="echoid-s15821" xml:space="preserve">tum bina fulcra 9 pollicibus a ſe <lb/>removebantur, in medio appenſum fuit pondus, qûod pedetentim <lb/>auctum ad libras 6 + unc. </s> <s xml:id="echoid-s15822" xml:space="preserve">1. </s> <s xml:id="echoid-s15823" xml:space="preserve">+ drachm. </s> <s xml:id="echoid-s15824" xml:space="preserve">5 {1/2} valde inflectebat & </s> <s xml:id="echoid-s15825" xml:space="preserve"><lb/>frangebat parallelopipedum: </s> <s xml:id="echoid-s15826" xml:space="preserve">deinde partem ejuſdem parallelopipe-<lb/>di immiſi foramini machinæ divulſoriæ, ut horizontaliter pone-<lb/>retur, ejus extremo appendi pondus, quod valde quam inflecte-<lb/>bat, unde removendum fuit continuo, ut ejus directionis linea a <lb/>foramine ſemper diſtaret 9 pollicibus, ad id requirebatur longitu-<lb/>do 14 pollieum, cujus extremo pondus 199 drachmarum appen-<lb/>ſum, parallelopipedum inflexit, ut modo diſtiterit 9 pollicibus a <lb/>foramine, tumque ſimul diffregit: </s> <s xml:id="echoid-s15827" xml:space="preserve">ſed ſunt 195 {3/8} drachmæ pondus <lb/>ſubquadruplum prioris, quod cenſeri poteſt idem ac 199 drachmæ <lb/>in Experimento, adeoque penitus confirmatur Propoſitio.</s> <s xml:id="echoid-s15828" xml:space="preserve"/> </p> <pb o="629" file="0645" n="646" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s15829" xml:space="preserve">Unde error Pardieſii liquet, qui Prop. </s> <s xml:id="echoid-s15830" xml:space="preserve">VIII. </s> <s xml:id="echoid-s15831" xml:space="preserve">de viribus moven-<lb/>tibus dixerat, corpora ſuffulta in duobus extremis duplo majo-<lb/>rem vim habere, ac iſta, quæ affiguntur uno ſolum termino, li-<lb/>cet alias æque craſſa & </s> <s xml:id="echoid-s15832" xml:space="preserve">æque longa ſint.</s> <s xml:id="echoid-s15833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15834" xml:space="preserve">Corol 1. </s> <s xml:id="echoid-s15835" xml:space="preserve">Si ergo pondus P fuerit maximum, quod applicari poſ-<lb/>ſit ſolido F S una ſui extremitate parieti infixo, erit idem pon-<lb/>dus P maximum, ex medio X ſolidi pendendum producti ad qua-<lb/>druplo majorem longitudinem, & </s> <s xml:id="echoid-s15836" xml:space="preserve">utrimque fulcro impoſiti.</s> <s xml:id="echoid-s15837" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15838" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15839" xml:space="preserve">2. </s> <s xml:id="echoid-s15840" xml:space="preserve">Vel ſi ſolidum F S utrimque innixnm fulcro, accepe-<lb/>rit latitudinem quadruplo minorem F G, retenta eadem longitudi-<lb/>ne G S: </s> <s xml:id="echoid-s15841" xml:space="preserve">aut ſi acceperit altitudinem duplo minorem, retenta ca-<lb/>dem latitudine & </s> <s xml:id="echoid-s15842" xml:space="preserve">longitudine, poterit ex medio X geſtare idem <lb/>pondus P, quod quoque maximum erit.</s> <s xml:id="echoid-s15843" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div606" type="section" level="1" n="606"> <head xml:id="echoid-head725" xml:space="preserve">PROPOSITIO CIII.</head> <p style="it"> <s xml:id="echoid-s15844" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15845" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s15846" xml:space="preserve">fig. </s> <s xml:id="echoid-s15847" xml:space="preserve">40. </s> <s xml:id="echoid-s15848" xml:space="preserve">Si parallelopipedum, priſma, vel Cylindrus <lb/>fuerit impoſitus duobus fulcris A & </s> <s xml:id="echoid-s15849" xml:space="preserve">B, & </s> <s xml:id="echoid-s15850" xml:space="preserve">pondus P ex medio C <lb/>ſuſpenſum ſit maximum, id ex alio loco E, propiori alterutri ex-<lb/>tremo ſuſpenſum, non erit maximum, poteritque ex E pondusma-<lb/>jus ſuſpendi, quod erit ad pondus ex C geſtatum, uti quadratum <lb/>A C ad rectangulum A E B.</s> <s xml:id="echoid-s15851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15852" xml:space="preserve">Nam Cohærentia ſolidi æque craſſi eſt in puncto E eadem quæ <lb/>in puncto C, adeoque momentum fulcri A ſuſtinentis pondus ex <lb/>medio C, eſt ut A X A C. </s> <s xml:id="echoid-s15853" xml:space="preserve">& </s> <s xml:id="echoid-s15854" xml:space="preserve">momentum fulcri B uti B X B C. <lb/></s> <s xml:id="echoid-s15855" xml:space="preserve">Sed momentum fulcri A ſuſtinentis pondus ex longitudine A E eſt <lb/>uti a X A E. </s> <s xml:id="echoid-s15856" xml:space="preserve">a diſtinctionis ergo ponitur, & </s> <s xml:id="echoid-s15857" xml:space="preserve">momentum fulcri B <lb/>ſuſtinentis pondus ex B E eſt ut b X B E. </s> <s xml:id="echoid-s15858" xml:space="preserve">b etiam diſtinctionis er-<lb/>go ponitur: </s> <s xml:id="echoid-s15859" xml:space="preserve">hinc erit A X A C = a X A E. </s> <s xml:id="echoid-s15860" xml:space="preserve">& </s> <s xml:id="echoid-s15861" xml:space="preserve">B X B C = b X B E. </s> <s xml:id="echoid-s15862" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s15863" xml:space="preserve">multiplicatis quantitatibus æqualibus per ſe erit A B X A C X B C <lb/>= a b X A E X B E. </s> <s xml:id="echoid-s15864" xml:space="preserve">unde A B ad a b:</s> <s xml:id="echoid-s15865" xml:space="preserve">: A E X B E: </s> <s xml:id="echoid-s15866" xml:space="preserve">A C X B C. </s> <s xml:id="echoid-s15867" xml:space="preserve">ve-<lb/>rum uti ſunt inter ſeproducta actionum vel reſiſtentiarum fulcrorum, <lb/>ita ſunt Cohærentiæ locorum intermediorum in E & </s> <s xml:id="echoid-s15868" xml:space="preserve">C, & </s> <s xml:id="echoid-s15869" xml:space="preserve">ita quoque <lb/>ſunt pondera ab iisdem locis geſtanda, quare pondus inC, erit ad pon-<lb/>dus geſtandum in E, uti A E X E B. </s> <s xml:id="echoid-s15870" xml:space="preserve">ad A <emph style="ol">C</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15871" xml:space="preserve">adeoque pondus P, <lb/>quod ex C ſuſpenſum erat maximum, ex E ſuſpenſum non erit <pb o="630" file="0646" n="647" rhead="INTRODUCTIO AD COHÆRENTIAM"/> maximum: </s> <s xml:id="echoid-s15872" xml:space="preserve">& </s> <s xml:id="echoid-s15873" xml:space="preserve">quia A C<emph style="super">q</emph> eſt majus rectangulo A E B, poterit ex E <lb/>ſuſpendi pondus multo majus: </s> <s xml:id="echoid-s15874" xml:space="preserve">imo quia A E B poteſt fieri infinite <lb/>parvum rectangulum, ſi A E fiat infinite parva, poterit ex E ſu-<lb/>ſpendi pondus inſinite magnum reſpectu ponderis ex C ſuſpen-<lb/>dendi.</s> <s xml:id="echoid-s15875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15876" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15877" xml:space="preserve">Quia pondus P ex medio C ipſius A B ſuſpenſum poteſt <lb/>eſſe quadruplo majus pondere ab extremo ſuſpenſo, ſi ſolidum A B <lb/>ab altero extremo parieti fuerit infixum, erit pondus P ex medio ſolidi <lb/>A B duobus fulcris impoſiti, ad pondus ex extremo ſolidi A B pa-<lb/>rieti infixi, uti <emph style="ol">AB</emph><emph style="super">q</emph> ad <emph style="ol">AC</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15878" xml:space="preserve">vel uti 4 <emph style="ol">AC</emph><emph style="super">q</emph> ad <emph style="ol">AC</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15879" xml:space="preserve">adeoque erit <lb/>pondus ex E ſuſpenſum, poſito ſolido ſuper duobus fulcris, ad pon-<lb/>dus ab extremo ſolidi parieti infixi annexum & </s> <s xml:id="echoid-s15880" xml:space="preserve">maximum, uti 4 A C <lb/>X C B ad A E X E B.</s> <s xml:id="echoid-s15881" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div607" type="section" level="1" n="607"> <head xml:id="echoid-head726" xml:space="preserve">PROPOSITIO CIV.</head> <p style="it"> <s xml:id="echoid-s15882" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15883" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s15884" xml:space="preserve">fig. </s> <s xml:id="echoid-s15885" xml:space="preserve">40. </s> <s xml:id="echoid-s15886" xml:space="preserve">Dato pondere maximo P, quod ex medio <lb/>parallelopipedi, priſmatis vel Cylindri ferri poteft, datoque alio <lb/>majori, invenire locum in ſolido ex quo ſuſpendi poterit, & </s> <s xml:id="echoid-s15887" xml:space="preserve">in quo <lb/>maximum erit.</s> <s xml:id="echoid-s15888" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15889" xml:space="preserve">Sit pondus P = p. </s> <s xml:id="echoid-s15890" xml:space="preserve">pondus majus ſit = d p. </s> <s xml:id="echoid-s15891" xml:space="preserve">ubi d notat <lb/>numerum vel integrum, vel integrum cum fractione quacunque. <lb/></s> <s xml:id="echoid-s15892" xml:space="preserve">vocetur C A, a. </s> <s xml:id="echoid-s15893" xml:space="preserve">C E, x. </s> <s xml:id="echoid-s15894" xml:space="preserve">erit A E = a-x. </s> <s xml:id="echoid-s15895" xml:space="preserve">& </s> <s xml:id="echoid-s15896" xml:space="preserve">E B = a + x. </s> <s xml:id="echoid-s15897" xml:space="preserve">& </s> <s xml:id="echoid-s15898" xml:space="preserve">re-<lb/>ctangulum A E B = aa-xx.</s> <s xml:id="echoid-s15899" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15900" xml:space="preserve">Quia demonſtratum eſt pondus P ſuſpenſum ex medio C eſſe ad <lb/>pondus d p ſuſpendendum ex E, uti rectangulum A E B ad qua-<lb/>dratum A C erit a a-xx, a a:</s> <s xml:id="echoid-s15901" xml:space="preserve">: p. </s> <s xml:id="echoid-s15902" xml:space="preserve">d p. </s> <s xml:id="echoid-s15903" xml:space="preserve">adeoque x x = {a a -a a p.</s> <s xml:id="echoid-s15904" xml:space="preserve">/d p} <lb/>& </s> <s xml:id="echoid-s15905" xml:space="preserve">extracta radice erit x =aa-{aa/d} Ut ergo conſtructio fiat, ſupra <lb/>A C dimidiam ſolidi longitudinem deſcribatur ſemicirculus: </s> <s xml:id="echoid-s15906" xml:space="preserve">fiat <lb/>hæc proportio d. </s> <s xml:id="echoid-s15907" xml:space="preserve">a:</s> <s xml:id="echoid-s15908" xml:space="preserve">: a, {aa/d}. </s> <s xml:id="echoid-s15909" xml:space="preserve">quæ ſit = A F: </s> <s xml:id="echoid-s15910" xml:space="preserve">hæc accommodetur ſe-<lb/>micirculo, ut una extremitate jaceat in A, tum ducatur F C, ca-<lb/>piatur C E = C F, eritque punctum E quæſitum, ex quo pondus d p <lb/>ſuſpendi poterit & </s> <s xml:id="echoid-s15911" xml:space="preserve">maximum erit.</s> <s xml:id="echoid-s15912" xml:space="preserve"/> </p> <pb o="631" file="0647" n="648" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div608" type="section" level="1" n="608"> <head xml:id="echoid-head727" xml:space="preserve">PROPOSITIO CV.</head> <p style="it"> <s xml:id="echoid-s15913" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15914" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s15915" xml:space="preserve">fig. </s> <s xml:id="echoid-s15916" xml:space="preserve">3. </s> <s xml:id="echoid-s15917" xml:space="preserve">Dato ſolido A B, utrimque fulcro innixo, <lb/>ac datæ altitudinis & </s> <s xml:id="echoid-s15918" xml:space="preserve">latitudinis, atque dato pondere maximo ſu-<lb/>ſpenſo ex E loco non medio, invenire latitudinem alterius ſolidi <lb/>D F æque longi, duobus fulcris impoſiti, quod in ſui medio G idem pon-<lb/>dus geſtare poſſit.</s> <s xml:id="echoid-s15919" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15920" xml:space="preserve">Quia pondera ex locis E & </s> <s xml:id="echoid-s15921" xml:space="preserve">C ſuſpenſa ponuntur maxima, quæ <lb/>geſtari â ſolidis poſſunt, erunt æqualia Cohærentiis eorum loco-<lb/>rum: </s> <s xml:id="echoid-s15922" xml:space="preserve">Eſt autem Cohærentia in loco E ad eam in loco medio C, uti <lb/><emph style="ol">D C</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15923" xml:space="preserve">ad rectangulum ex A E X E B. </s> <s xml:id="echoid-s15924" xml:space="preserve">fiat nunc latitudo ſolidi A B, <lb/>ad D F uti eſt rectangulum A E X E B ad D C<emph style="super">q</emph>. </s> <s xml:id="echoid-s15925" xml:space="preserve">eritque Cohærentia <lb/>in puncto medio C, ſolidi D F æqualis Cohærentiæ in puncto E ſo-<lb/>lidi A B. </s> <s xml:id="echoid-s15926" xml:space="preserve">Vocetur proinde latitudo ſolidi A B = l. </s> <s xml:id="echoid-s15927" xml:space="preserve">& </s> <s xml:id="echoid-s15928" xml:space="preserve">ſolidi D F <lb/>= x. </s> <s xml:id="echoid-s15929" xml:space="preserve">erit x = {lX A C<emph style="super">q</emph>/A E X E B}.</s> <s xml:id="echoid-s15930" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div609" type="section" level="1" n="609"> <head xml:id="echoid-head728" xml:space="preserve">PROPOSITIO CVI.</head> <p style="it"> <s xml:id="echoid-s15931" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15932" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s15933" xml:space="preserve">fig. </s> <s xml:id="echoid-s15934" xml:space="preserve">4. </s> <s xml:id="echoid-s15935" xml:space="preserve">Dato ſoldio A B longiſſimo & </s> <s xml:id="echoid-s15936" xml:space="preserve">craſſiſſimo, <lb/>impoſitoque duobus fulcris, ex cujus medio C pendeat pondus maxi-<lb/>mum, invenire longitudinem ſolidi ſimilis D E imponendi ſuis ful-<lb/>cris, multo minoris craſſitiei, quod gerat idem pondus ex ſui me-<lb/>dio.</s> <s xml:id="echoid-s15937" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15938" xml:space="preserve">Vocetur longitudo dimidia A C ſolidi longioris & </s> <s xml:id="echoid-s15939" xml:space="preserve">craſſioris A B <lb/>l. </s> <s xml:id="echoid-s15940" xml:space="preserve">altitudo a. </s> <s xml:id="echoid-s15941" xml:space="preserve">latitudo b. </s> <s xml:id="echoid-s15942" xml:space="preserve">Tum longitudo dimidia ſo-<lb/>lidi tenuioris D E, ſit D G & </s> <s xml:id="echoid-s15943" xml:space="preserve">vocetur x. </s> <s xml:id="echoid-s15944" xml:space="preserve">cujus altitudo c. </s> <s xml:id="echoid-s15945" xml:space="preserve">latitu-<lb/>do d. </s> <s xml:id="echoid-s15946" xml:space="preserve">Eſt Cohærentia ſolidi A C B ad eam ſolidi D G E. </s> <s xml:id="echoid-s15947" xml:space="preserve">æque <lb/>longi ſuppoſiti, in ratione duplicata altitudinis a a ad eam altitu-<lb/>dinis c c & </s> <s xml:id="echoid-s15948" xml:space="preserve">latitudinis b ad d. </s> <s xml:id="echoid-s15949" xml:space="preserve">poſitis his ſolidis non æque longis, erit <lb/>momentum ponderis pendentis ex C ad illud ex G, in ratione D G <lb/>ad A C. </s> <s xml:id="echoid-s15950" xml:space="preserve">quamobrem in requiſitis Cohærentiis æqualibus utriuſque <lb/>ſolidi A C B, D G E, erit a a b x = c c d l. </s> <s xml:id="echoid-s15951" xml:space="preserve">unde x = {c c d l.</s> <s xml:id="echoid-s15952" xml:space="preserve">/a a b} Si <pb o="632" file="0648" n="649" rhead="INTRODUCTIO AD COHÆRENTIAM"/> igitur a a b. </s> <s xml:id="echoid-s15953" xml:space="preserve">ſit major quam c c d l erit Problema impoſſibile.</s> <s xml:id="echoid-s15954" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div610" type="section" level="1" n="610"> <head xml:id="echoid-head729" xml:space="preserve">PROPOSITIO CVII.</head> <p style="it"> <s xml:id="echoid-s15955" xml:space="preserve">Tab. </s> <s xml:id="echoid-s15956" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s15957" xml:space="preserve">fig. </s> <s xml:id="echoid-s15958" xml:space="preserve">10. </s> <s xml:id="echoid-s15959" xml:space="preserve">Ad datam longitudinem A L infinita ſolida <lb/>priſmatica aut Cylindrica applicare, quæ utrimque in A & </s> <s xml:id="echoid-s15960" xml:space="preserve">L ſuf-<lb/>fulta in medio gerant pondus, babeantque Cohærentiam æqualem <lb/>Cohærentiæ dati priſmatis vel Cylindri, cujus longitudo eſt A E, <lb/>altitudo A F, latitudo F G.</s> <s xml:id="echoid-s15961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15962" xml:space="preserve">Fiat ut A E ad A L, ita F G ad F D, & </s> <s xml:id="echoid-s15963" xml:space="preserve">per D, inter aſympto-<lb/>tos E A, A F deſcripta intelligatur Hyperbola C D C quadratica, <lb/>cujus ordinatæ F D, B C ſint reciproce ut abſciſſarum B A, A F <lb/>quadrata; </s> <s xml:id="echoid-s15964" xml:space="preserve">ita ut productum ex quadrato B A in B C ſemper ſit æqua-<lb/>le producto quadrati A F in F D. </s> <s xml:id="echoid-s15965" xml:space="preserve">Quodlibet priſma arbitrariæ al-<lb/>titudinis A B, latitudinis correſpondentis ordinatæ B C, & </s> <s xml:id="echoid-s15966" xml:space="preserve">datæ <lb/>longitudinis A L ſatisfaciet quæſito. </s> <s xml:id="echoid-s15967" xml:space="preserve">Nam poſitis priſmatibus æque <lb/>longis, ut A L, erit Cohærentia eorum in ratione duplicata altitu-<lb/>dinis A B, A F, & </s> <s xml:id="echoid-s15968" xml:space="preserve">ſimplici latitudinis B C, F D. </s> <s xml:id="echoid-s15969" xml:space="preserve">ſive <emph style="ol">A B</emph><emph style="super">q</emph> X B C & </s> <s xml:id="echoid-s15970" xml:space="preserve"><lb/><emph style="ol">A F</emph><emph style="super">q</emph> X F D. </s> <s xml:id="echoid-s15971" xml:space="preserve">ſed ex natura Hyperbolæ eſt <emph style="ol">A B</emph><emph style="super">q</emph> X B C = <emph style="ol">A F</emph><emph style="super">q</emph> <lb/>XX F D. </s> <s xml:id="echoid-s15972" xml:space="preserve">quare hæc priſmata, aut cylindri æqualem Cohæren-<lb/>tiam habent; </s> <s xml:id="echoid-s15973" xml:space="preserve">quæ nunc demonſtranda eſt æqualis illi priſmatis dati <lb/>A F G E. </s> <s xml:id="echoid-s15974" xml:space="preserve">Eſt momentum pondéris ſuſpenſi ex medio A L. </s> <s xml:id="echoid-s15975" xml:space="preserve">ad mo-<lb/>mentum ponderis ſuſpenſi ex medio A E, uti A L ad A E: </s> <s xml:id="echoid-s15976" xml:space="preserve">quare ſi <lb/>Cohærentiæ priſmatum ſint inter ſe uti hæc momenta, erunt priſ-<lb/>mata æqualis Cohærentiæ: </s> <s xml:id="echoid-s15977" xml:space="preserve">Cohærentia dati priſmatis eſt = <emph style="ol">A F</emph><emph style="super">q</emph> <lb/>X F G. </s> <s xml:id="echoid-s15978" xml:space="preserve">Cohærentia alterius eſt <emph style="ol">A B</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15979" xml:space="preserve">X B C. </s> <s xml:id="echoid-s15980" xml:space="preserve">adeoque debent eſſe <lb/><emph style="ol">A F</emph><emph style="super">q</emph> X F G. </s> <s xml:id="echoid-s15981" xml:space="preserve">A E:</s> <s xml:id="echoid-s15982" xml:space="preserve">:<emph style="ol">A B</emph> X B C, A L. </s> <s xml:id="echoid-s15983" xml:space="preserve">eſt <emph style="ol">A B</emph><emph style="super">q</emph> X B C. </s> <s xml:id="echoid-s15984" xml:space="preserve">= <emph style="ol">A F</emph><emph style="super">q</emph> <lb/>X F D. </s> <s xml:id="echoid-s15985" xml:space="preserve">adeoque hac quantitate loco prioris poſita, erit <emph style="ol">A F</emph><emph style="super">q</emph> X F G: <lb/></s> <s xml:id="echoid-s15986" xml:space="preserve">A E:</s> <s xml:id="echoid-s15987" xml:space="preserve">: <emph style="ol">A F</emph><emph style="super">q</emph> X F D, A L. </s> <s xml:id="echoid-s15988" xml:space="preserve">antecedentibus terminis proportionis di-<lb/>viſis per <emph style="ol">A F</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s15989" xml:space="preserve">erit F G. </s> <s xml:id="echoid-s15990" xml:space="preserve">A E:</s> <s xml:id="echoid-s15991" xml:space="preserve">: F D: </s> <s xml:id="echoid-s15992" xml:space="preserve">A L. </s> <s xml:id="echoid-s15993" xml:space="preserve">quæ quantitates ſunt <lb/>proportionales per conſtructionem, adeoque erunt Cohærentiæ <lb/>quemadmodum momenta ponderum. </s> <s xml:id="echoid-s15994" xml:space="preserve">Q. </s> <s xml:id="echoid-s15995" xml:space="preserve">E. </s> <s xml:id="echoid-s15996" xml:space="preserve">D.</s> <s xml:id="echoid-s15997" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s15998" xml:space="preserve">Corol. </s> <s xml:id="echoid-s15999" xml:space="preserve">Extendi poteſt hæc Propoſitio etiam ad Priſmata, Paralle-<lb/>lopipeda, & </s> <s xml:id="echoid-s16000" xml:space="preserve">Cylindros, quæ uno extremo ſui parietibus inſiguntur, <lb/>ex altero extremo pondus gerunt.</s> <s xml:id="echoid-s16001" xml:space="preserve"/> </p> <pb o="633" file="0649" n="650" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div611" type="section" level="1" n="611"> <head xml:id="echoid-head730" xml:space="preserve">PROPOSITIO CVIII.</head> <p style="it"> <s xml:id="echoid-s16002" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16003" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16004" xml:space="preserve">fig. </s> <s xml:id="echoid-s16005" xml:space="preserve">11. </s> <s xml:id="echoid-s16006" xml:space="preserve">Infinita ſolida priſmatica datæ latitudinis <lb/>invenire, quæ utrimque fulta, æqualis ſint Cohærentiæ reſpectu <lb/>propriæ gravitatis.</s> <s xml:id="echoid-s16007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16008" xml:space="preserve">Sit parabola A I H I. </s> <s xml:id="echoid-s16009" xml:space="preserve">ejus axis A B, ordinatæ B I, F H, B I. </s> <s xml:id="echoid-s16010" xml:space="preserve">di-<lb/>co quodlibet priſma longitudinis ejuſdem ac eſt ordinata quælibet <lb/>B I aut F H, & </s> <s xml:id="echoid-s16011" xml:space="preserve">altitudinis B A vel F A, atque datæ conſtantis la-<lb/>titudinis ſatisfacere propoſito: </s> <s xml:id="echoid-s16012" xml:space="preserve">nam ob naturam parabolæ eſt A B, <lb/>A F:</s> <s xml:id="echoid-s16013" xml:space="preserve">: <emph style="ol">I B</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16014" xml:space="preserve"><emph style="ol">H F</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16015" xml:space="preserve">eſtque ſoliditas priſmatis ex longitudine I B, & </s> <s xml:id="echoid-s16016" xml:space="preserve"><lb/>altitudine A B, uti I B X A B. </s> <s xml:id="echoid-s16017" xml:space="preserve">& </s> <s xml:id="echoid-s16018" xml:space="preserve">ſoliditas alterius priſmatis = A F <lb/>X F H. </s> <s xml:id="echoid-s16019" xml:space="preserve">ſed I B X A B. </s> <s xml:id="echoid-s16020" xml:space="preserve">A F X H F:</s> <s xml:id="echoid-s16021" xml:space="preserve">: <emph style="ol">I B</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s16022" xml:space="preserve"><emph style="ol">H F</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s16023" xml:space="preserve">momenta gravita-<lb/>tis horum priſmatum ſunt <emph style="ol">I B</emph><emph style="super">c</emph> X I B. </s> <s xml:id="echoid-s16024" xml:space="preserve"><emph style="ol">H F</emph><emph style="super">c</emph> X H F. </s> <s xml:id="echoid-s16025" xml:space="preserve">verum Cohæren-<lb/>tiæ eorundem ſunt <emph style="ol">A B</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16026" xml:space="preserve"><emph style="ol">A F</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16027" xml:space="preserve">quæ ſunt <emph style="ol">I B</emph><emph style="super">qq</emph>. </s> <s xml:id="echoid-s16028" xml:space="preserve"><emph style="ol">H F</emph><emph style="super">qq</emph>. </s> <s xml:id="echoid-s16029" xml:space="preserve">quæ ſunt uti <lb/>momenta gravitatis, adeoque demonſtrato Cohærentias eſſe uti ſunt <lb/>gravitates, erunt hæc ſolida æqualis Cohærentiæ.</s> <s xml:id="echoid-s16030" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16031" xml:space="preserve">Coroll. </s> <s xml:id="echoid-s16032" xml:space="preserve">Hinc ungula ſolida parabolica erecta ex Cylindro ſuper <lb/>parabola A I B, eademve ad alteram diametri partem duplicata, <lb/>erecto, per planum baſi, utcunque inclinatum, & </s> <s xml:id="echoid-s16033" xml:space="preserve">per verticem A <lb/>tranſiens, foret ſolidum reſpectu ſui ponderis in qualibet ſui parte <lb/>æqualiter reſiſtens: </s> <s xml:id="echoid-s16034" xml:space="preserve">ſive ſuſtineretur in linea A B, ſive fulcris ſub <lb/>ejus perimetro circumpoſitis fulciretur: </s> <s xml:id="echoid-s16035" xml:space="preserve">nam diametro A B diviſa <lb/>in quotlibet æquales partes, erectiſque planis per omnia diviſionum <lb/>puncta, & </s> <s xml:id="echoid-s16036" xml:space="preserve">correſpondentes ordinatas parabolæ, haberentur toti-<lb/>dem priſmata, huic ungulæ inſcripta, quæ ſui ponderis reſpectu, <lb/>juxta hanc Propoſitionem, æqualis eſſent Cohærentiæ, & </s> <s xml:id="echoid-s16037" xml:space="preserve">quæ <lb/>ungulæ ipſius ſoliditatem, aucto omnium numero, & </s> <s xml:id="echoid-s16038" xml:space="preserve">diminuta <lb/>ſingulorum latitudine, facile exhaurirent: </s> <s xml:id="echoid-s16039" xml:space="preserve">quemadmodum deduxit <lb/>Cl. </s> <s xml:id="echoid-s16040" xml:space="preserve">Grandi.</s> <s xml:id="echoid-s16041" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div612" type="section" level="1" n="612"> <head xml:id="echoid-head731" xml:space="preserve">PROPOSITIO CIX.</head> <p style="it"> <s xml:id="echoid-s16042" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16043" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16044" xml:space="preserve">fig. </s> <s xml:id="echoid-s16045" xml:space="preserve">12. </s> <s xml:id="echoid-s16046" xml:space="preserve">Dato cuneo A B P C D, & </s> <s xml:id="echoid-s16047" xml:space="preserve">pondere maxi-<lb/>mo, quod extremo C D appendi poſſit, cum Cunei baſis A B P pa- <pb o="634" file="0650" n="651" rhead="INTRODUCTIO AD COHÆRENTIAM"/> rieti ſit affixa, invenire Cobærentiam cujuslibet ſegmenti F E K ad <lb/>baſin A B P paralleli, poſito Cuneo ſuper duobus fulcris A & </s> <s xml:id="echoid-s16048" xml:space="preserve">C D. <lb/></s> <s xml:id="echoid-s16049" xml:space="preserve">& </s> <s xml:id="echoid-s16050" xml:space="preserve">latere A C borizontali.</s> <s xml:id="echoid-s16051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16052" xml:space="preserve">Sit pondus applicatum extremo C D vocatum P, erit ejus mo-<lb/>mentum = P X A C, quod eſt æquale Cohærentiæ baſeos cunei, <lb/>quia ponitur pondus P eſſe maximum: </s> <s xml:id="echoid-s16053" xml:space="preserve">ſi nunc cuneus foret priſma <lb/>ubivis æque latum, impoſitumque duobus fulcris A & </s> <s xml:id="echoid-s16054" xml:space="preserve">C D, me-<lb/>diumque punctum ſit H, poterit per Propoſ. </s> <s xml:id="echoid-s16055" xml:space="preserve">CII. </s> <s xml:id="echoid-s16056" xml:space="preserve">ex H ſuſpendi pon-<lb/>dus quadruplo majus, quam ante ex C D, cum cuneus parieti erat <lb/>affixus; </s> <s xml:id="echoid-s16057" xml:space="preserve">adeoque pondus 4 P ſuſpenſum ex H, agit ex vecte H C, <lb/>unde ejus momentum eſt = 4 P X H C. </s> <s xml:id="echoid-s16058" xml:space="preserve">ſed Cohærentia priſmatis <lb/>cujus altitudo foret A B, eſt ad Cohærentiam ſolidi, cujus altitudo <lb/>eſt H G, uti <emph style="ol">A B</emph><emph style="super">q</emph> ad <emph style="ol">H G</emph><emph style="super">q</emph>: </s> <s xml:id="echoid-s16059" xml:space="preserve">quare pondus, quod applicatum cunei <lb/>medio altitudinis H G, ſuo momento Cohærentiam exprimet <lb/>ſegmenti H G L, erit = {4 P X H C X <emph style="ol">H G</emph><emph style="super">q</emph>/<emph style="ol">A B</emph><emph style="super">q</emph>}. </s> <s xml:id="echoid-s16060" xml:space="preserve">Sed eſt Cohæren-<lb/>tia ſegmenti F E K ad Cohærentiam ſegmenti H G L. </s> <s xml:id="echoid-s16061" xml:space="preserve">in ratione com-<lb/>poſita ex <emph style="ol">H C</emph><emph style="super">q</emph> X <emph style="ol">F E</emph><emph style="super">q</emph> ad A F X F C X <emph style="ol">H G</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16062" xml:space="preserve">adeoque Cohæren-<lb/>tia ſegmenti F E K erit = {4 P X <emph style="ol">H C</emph><emph style="super">c</emph> X <emph style="ol">F E</emph><emph style="super">q</emph>/<emph style="ol">A B</emph><emph style="super">q</emph> X A F X F C}.</s> <s xml:id="echoid-s16063" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div613" type="section" level="1" n="613"> <head xml:id="echoid-head732" xml:space="preserve">PROPOSITIO CX.</head> <p style="it"> <s xml:id="echoid-s16064" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16065" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16066" xml:space="preserve">fig. </s> <s xml:id="echoid-s16067" xml:space="preserve">13. </s> <s xml:id="echoid-s16068" xml:space="preserve">Data pyramide A B D E C cujus baſis qua-<lb/>drangula, rectangula, & </s> <s xml:id="echoid-s16069" xml:space="preserve">ſimul ſit A D C angulus rectus, datoque <lb/>pondere maximo appenſo extremitati C pyramidis affix æ parieti, <lb/>invenire Cohærentiam cujuslibet ſegmenti G I K L paralleli ad ba-<lb/>ſin A B D E poſita pyramide ſuper duobus fulcris in D & </s> <s xml:id="echoid-s16070" xml:space="preserve">C, & </s> <s xml:id="echoid-s16071" xml:space="preserve">la-<lb/>tere D E C horizontali.</s> <s xml:id="echoid-s16072" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16073" xml:space="preserve">Ponatur pondus, quod extremitati C appenſum fuit maximum, <lb/>cum baſis A B D E pyramidis applicabatur parieti = P. </s> <s xml:id="echoid-s16074" xml:space="preserve">fuit ejus <lb/>momentum = P X D C, quod eſt æquale Cohærentiæ ad baſin pyra-<lb/>midis, impoſita pyramide duobus fulcris in D & </s> <s xml:id="echoid-s16075" xml:space="preserve">C. </s> <s xml:id="echoid-s16076" xml:space="preserve">ſit punctum G <lb/>dimidium ipſius F C, adeoque pondus appenſum ad G foret 4 P, ſi <lb/>ſolidum fuiſſet priſma ubivis æque altum & </s> <s xml:id="echoid-s16077" xml:space="preserve">latum, & </s> <s xml:id="echoid-s16078" xml:space="preserve">ejus momen- <pb o="635" file="0651" n="652" rhead="CORPORUM FIRMORUM."/> tum foret = 4 P X G C. </s> <s xml:id="echoid-s16079" xml:space="preserve">quod exprimeret Cohærentiam ſegmenti <lb/>tranſeuntis per punctum G, & </s> <s xml:id="echoid-s16080" xml:space="preserve">paralleli ad baſin A B E D. </s> <s xml:id="echoid-s16081" xml:space="preserve">ſed eſt <lb/>ſegmentum G I K L in pyramide, ejuſque Cohærentia ad Cohæren-<lb/>tiam ſegmenti in priſmate, (quod foret æquale baſi A B E D) in ra <lb/>tione duplicata G I ad A D, & </s> <s xml:id="echoid-s16082" xml:space="preserve">ſimplici I K ad A B: </s> <s xml:id="echoid-s16083" xml:space="preserve">adeoque erit <lb/><emph style="ol">D A</emph><emph style="super">q</emph> X A B, 4 P X F C:</s> <s xml:id="echoid-s16084" xml:space="preserve">: <emph style="ol">G I</emph><emph style="super">q</emph> X I K. </s> <s xml:id="echoid-s16085" xml:space="preserve">{<emph style="ol">G I</emph><emph style="super">q</emph> X I K X 4 P X F C/D A<emph style="super">q</emph> X A B}. <lb/></s> <s xml:id="echoid-s16086" xml:space="preserve">quod exprimet Cohærentiam ſegmenti G I K L, quæ reſpectu Cohæ-<lb/>rentiæ pyramidis baſi affixæ parieti eſt, uti {<emph style="ol">G I</emph><emph style="super">q</emph> X I K X 4 P X F C/<emph style="ol">D A</emph><emph style="super">q</emph> X A B} <lb/>ad D C X P. </s> <s xml:id="echoid-s16087" xml:space="preserve">Eodem modo facile eruetur Cohærentia ſegmenti <lb/>M O S. </s> <s xml:id="echoid-s16088" xml:space="preserve">eſt enim Cohærentia hujus, ad Cohærentiam ſegmenti <lb/>G I K L in ratione compoſita ex <emph style="ol">D G</emph><emph style="super">q</emph> ad D M X M C, & </s> <s xml:id="echoid-s16089" xml:space="preserve"><emph style="ol">O M</emph><emph style="super">q</emph> X O S <lb/>ad <emph style="ol">G I</emph><emph style="super">q</emph> X I K. </s> <s xml:id="echoid-s16090" xml:space="preserve">quare erit Cohærentia ſegmenti M O S <lb/>={<emph style="ol">D G</emph><emph style="super">q</emph> X <emph style="ol">O M</emph><emph style="super">q</emph> X O S X 4 P X F C/M C X <emph style="ol">D A</emph><emph style="super">q</emph> X A B}.</s> <s xml:id="echoid-s16091" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16092" xml:space="preserve">Corol. </s> <s xml:id="echoid-s16093" xml:space="preserve">Eodem modo Cohærentia ſegmenti cujuslibet baſi paral-<lb/>leli in Cono erui poterit, modo habeamus rationem axeos loco la-<lb/>teris D C in hac pyramide conceptæ: </s> <s xml:id="echoid-s16094" xml:space="preserve">aut in quacunque pyramide <lb/>ratio axeos etiam habeatur, tumque facile cujuslibet ſegmenti Co-<lb/>hærentia determinabitur.</s> <s xml:id="echoid-s16095" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div614" type="section" level="1" n="614"> <head xml:id="echoid-head733" xml:space="preserve">PROPOSITIO CXI.</head> <p style="it"> <s xml:id="echoid-s16096" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16097" xml:space="preserve">XXVIII. </s> <s xml:id="echoid-s16098" xml:space="preserve">fig. </s> <s xml:id="echoid-s16099" xml:space="preserve">1. </s> <s xml:id="echoid-s16100" xml:space="preserve">Si fuerit ſolidum A B C D compoſitum ex duo-<lb/>bus Conis æque altis, & </s> <s xml:id="echoid-s16101" xml:space="preserve">ejusdem baſeos B G D ſibi in vicem impoſi-<lb/>tis, quod utrimque fulciatur in A & </s> <s xml:id="echoid-s16102" xml:space="preserve">C. </s> <s xml:id="echoid-s16103" xml:space="preserve">erit Cobærentia ſegmenti <lb/>B G D, ad Cobærentiam ſegmenti H E I perpendicularis ad bori-<lb/>zontem, in ratione compoſita ex A E X E C X <emph style="ol">B D</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s16104" xml:space="preserve">ad <emph style="ol">A G</emph><emph style="super">q</emph> <lb/>X <emph style="ol">I H</emph><emph style="super">c</emph>.</s> <s xml:id="echoid-s16105" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16106" xml:space="preserve">Si foret A B C D Priſma vel Cylindrus ubivis æque latus, eſſet <lb/>Cohærentia in I H ad eam in B D, ut A G<emph style="super">q</emph> ad A E X E C. </s> <s xml:id="echoid-s16107" xml:space="preserve">cum ve-<lb/>ro ſegmenta H I, B D ſint inæqualia in Cono duplici, & </s> <s xml:id="echoid-s16108" xml:space="preserve">ſint cir-<lb/>cularia, quorum Cohærentia eſt in ratione Cubica diametrorum, <pb o="636" file="0652" n="653" rhead="INTRODUCTIO AD COHÆRENTIAM"/> erit Cohærentia ſegmenti I H ad Cohærentiam ſegmenti B D, in <lb/>ratione compoſita ex <emph style="ol">A G</emph><emph style="super">q</emph> ad A E X E C & </s> <s xml:id="echoid-s16109" xml:space="preserve">ex ratione <emph style="ol">I H</emph><emph style="super">c</emph> ad <lb/><emph style="ol">B D</emph><emph style="super">c.</emph></s> <s xml:id="echoid-s16110" xml:space="preserve">adeoque erunt Cohærentiæ ſegmentorum I H, B D:</s> <s xml:id="echoid-s16111" xml:space="preserve">: <emph style="ol">A G</emph><emph style="super">q</emph> <lb/>X <emph style="ol">I H</emph><emph style="super">c</emph> ad A E X E C X <emph style="ol">B D</emph><emph style="super">c</emph>.</s> <s xml:id="echoid-s16112" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div615" type="section" level="1" n="615"> <head xml:id="echoid-head734" xml:space="preserve">PROPOSITIO CXII.</head> <p style="it"> <s xml:id="echoid-s16113" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16114" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16115" xml:space="preserve">fig. </s> <s xml:id="echoid-s16116" xml:space="preserve">14. </s> <s xml:id="echoid-s16117" xml:space="preserve">Sit parabolois A C E utrimque fulta in <lb/>A & </s> <s xml:id="echoid-s16118" xml:space="preserve">E, cujus axis borizontalis ſecetur ſegmentis L K, F H per-<lb/>pendicularibus ad axin A B. </s> <s xml:id="echoid-s16119" xml:space="preserve">erit Cohærentia ſegmenti L K ad Co-<lb/>bærentiam ſegmenti F H, in ratione compoſita ex A G X I L, ad <lb/>I B X F G.</s> <s xml:id="echoid-s16120" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16121" xml:space="preserve">Nam eſt Cohærentia ſegmenti L K ad eam ſegmenti F H, uti <lb/><emph style="ol">A G</emph><emph style="super">q</emph> X <emph style="ol">I L</emph><emph style="super">c</emph>, ad A I X I B X <emph style="ol">F G</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s16122" xml:space="preserve">ſed eſt Cubus I L = <emph style="ol">I L</emph><emph style="super">q</emph> X I L. </s> <s xml:id="echoid-s16123" xml:space="preserve">ita <lb/><emph style="ol">F G</emph><emph style="super">c</emph> = F G<emph style="super">q</emph> X F G. </s> <s xml:id="echoid-s16124" xml:space="preserve">eſt vero I L<emph style="super">q</emph>, <emph style="ol">F G</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s16125" xml:space="preserve">: A I, A G adeoque A I X I L, <lb/>A G X F G:</s> <s xml:id="echoid-s16126" xml:space="preserve">: <emph style="ol">I L</emph><emph style="super">c</emph>, <emph style="ol">F G</emph><emph style="super">c</emph>. </s> <s xml:id="echoid-s16127" xml:space="preserve">hinc erit Cohærentia ſegmenti L K, ad <lb/>eam ſegmenti F H:</s> <s xml:id="echoid-s16128" xml:space="preserve">: A G<emph style="super">q</emph> X A I X I L, A I, X I B X A G X F G. <lb/></s> <s xml:id="echoid-s16129" xml:space="preserve">factaque utriuſque quantitatis diviſione per A G X A I, erit Cohæ-<lb/>rentia L K ad eam in F H:</s> <s xml:id="echoid-s16130" xml:space="preserve">: A G X I L ad I B X F G.</s> <s xml:id="echoid-s16131" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div616" type="section" level="1" n="616"> <head xml:id="echoid-head735" xml:space="preserve">PROPOSITIO CXIII.</head> <p style="it"> <s xml:id="echoid-s16132" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16133" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16134" xml:space="preserve">fig. </s> <s xml:id="echoid-s16135" xml:space="preserve">5. </s> <s xml:id="echoid-s16136" xml:space="preserve">Solidum ſemicirculare A C E B F D, utrim-<lb/>que in A & </s> <s xml:id="echoid-s16137" xml:space="preserve">B ſuffultum, eſt ubivis æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16139" xml:space="preserve">Ducatur enim quælibet D C, E F perpendicularis in diametrum <lb/>A B, eritque Cohærentia C D ad E F in ratione duplicata altitudi-<lb/>nis D C ad E F, quatenus altitudinem ſolidi ſpectamus: </s> <s xml:id="echoid-s16140" xml:space="preserve">verum <lb/>eſt momentum ponderis maximi ſuſpenſi ex D, ad momentum <lb/>ſuſpenſi ex F, uti rectangulum A D X D B, ad rectangulum A F X F B. <lb/></s> <s xml:id="echoid-s16141" xml:space="preserve">verum ex natura circuli, uti A D X D B ad A F X F B:</s> <s xml:id="echoid-s16142" xml:space="preserve">: <emph style="ol">D C</emph><emph style="super">q</emph>, ad <lb/><emph style="ol">F E</emph><emph style="super">q</emph>:</s> <s xml:id="echoid-s16143" xml:space="preserve">: Cohærentia in D C ad Cohærentiam in F E. </s> <s xml:id="echoid-s16144" xml:space="preserve">adeoque erit <lb/>momentum ponderis maximi idem in E F ac in C D, erit igitur hoc <lb/>ſolidum ubivis æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16146" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16147" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16148" xml:space="preserve">fig. </s> <s xml:id="echoid-s16149" xml:space="preserve">6. </s> <s xml:id="echoid-s16150" xml:space="preserve">Corol. </s> <s xml:id="echoid-s16151" xml:space="preserve">1. </s> <s xml:id="echoid-s16152" xml:space="preserve">Si A C E B D F ſit circulus, & </s> <s xml:id="echoid-s16153" xml:space="preserve">proinde <lb/>ſolidum fuerit diſcus circularis, qui utrimque ad extremum dia- <pb o="637" file="0653" n="654" rhead="CORPORUM FIRMORUM."/> metri A B fulcris ſuſtineatur, erit adhuc ſolidum æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16155" xml:space="preserve">Corol. </s> <s xml:id="echoid-s16156" xml:space="preserve">2. </s> <s xml:id="echoid-s16157" xml:space="preserve">Si A C E B ſit ſemiellipſis, erit ſolidum ſemiellipticum <lb/>adhuc æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16158" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16159" xml:space="preserve">Corol. </s> <s xml:id="echoid-s16160" xml:space="preserve">3. </s> <s xml:id="echoid-s16161" xml:space="preserve">Et ſi A C E B F D ſit integra Ellipſis, erit ſolidum hoc <lb/>etiam æqualis reſiſtentiæ per totam ſuam longitudinem.</s> <s xml:id="echoid-s16162" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div617" type="section" level="1" n="617"> <head xml:id="echoid-head736" xml:space="preserve">PROPOSITIO CXIV.</head> <p style="it"> <s xml:id="echoid-s16163" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16164" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16165" xml:space="preserve">fig. </s> <s xml:id="echoid-s16166" xml:space="preserve">7. </s> <s xml:id="echoid-s16167" xml:space="preserve">Si detur corpus Ellipticum Z dD M B b, <lb/>utrimque ſuffultum in Z & </s> <s xml:id="echoid-s16168" xml:space="preserve">M, atque Ellipſeos ea fuerit natura, ut <lb/>ordinatarum S <emph style="ol">D</emph><emph style="super">3</emph>, ad <emph style="ol">s d</emph><emph style="super">3</emph>:</s> <s xml:id="echoid-s16169" xml:space="preserve">: M S X S Z ad M s X s Z erit hoc cor-<lb/>pus, ſepoſita gravitate, ubivis æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16171" xml:space="preserve">Nam eſt Cohærentia corporis hujus in ſegmento S D ad eam in <lb/>ſegmento s d, uti Cubus S D ad Cubum s d. </s> <s xml:id="echoid-s16172" xml:space="preserve">hoc eſt uti M S X S Z ad <lb/>M s X s Z. </s> <s xml:id="echoid-s16173" xml:space="preserve">ſed eſt momentum ponderis appenſi ex S, ad momentum <lb/>ponderis appenſi ex s. </s> <s xml:id="echoid-s16174" xml:space="preserve">uti M S X S D, ad M s X s Z. </s> <s xml:id="echoid-s16175" xml:space="preserve">quare erit mo-<lb/>mentum ponderis ejuſdem ubivis applicati uti Cohærentia illius <lb/>loci, adeoque eſt hoc corpus ubivis æqualis reſiſtentiæ.</s> <s xml:id="echoid-s16176" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div618" type="section" level="1" n="618"> <head xml:id="echoid-head737" xml:space="preserve">PROPOSITIO CXV.</head> <p style="it"> <s xml:id="echoid-s16177" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16178" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16179" xml:space="preserve">fig. </s> <s xml:id="echoid-s16180" xml:space="preserve">8. </s> <s xml:id="echoid-s16181" xml:space="preserve">Si ex priori Spbæroide fiat ſegmentum <lb/>tranſiens per diametrum, quale eſt Z a A M B b. </s> <s xml:id="echoid-s16182" xml:space="preserve">idque utrimque <lb/>fulciatur ad extremum diametri in Z & </s> <s xml:id="echoid-s16183" xml:space="preserve">M, erit boc corpus ubivis <lb/>æqualis Cohærentiæ.</s> <s xml:id="echoid-s16184" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16185" xml:space="preserve">Fiant ſectiones b c a, B C A perpendiculares in diametrum Z b <lb/>B M, & </s> <s xml:id="echoid-s16186" xml:space="preserve">formabuntur Triangula a b c, A B C, ſimilia; </s> <s xml:id="echoid-s16187" xml:space="preserve">adeoque uti <lb/>b c, B C:</s> <s xml:id="echoid-s16188" xml:space="preserve">: c a, C A. </s> <s xml:id="echoid-s16189" xml:space="preserve">Sed eſt Cohærentia Trianguli a b c, ad eam <lb/>Trianguli A B C in ratione duplicata c b ad C B, tum c a ad C A, <lb/>hoceſt, c b ad C B. </s> <s xml:id="echoid-s16190" xml:space="preserve">adeoque ſunt Cohærentiæ uti <emph style="ol">c b</emph><emph style="super">3</emph> ad <emph style="ol">C B</emph><emph style="super">3</emph>: </s> <s xml:id="echoid-s16191" xml:space="preserve">ſed <lb/>eſt momentum ponderis in b, ad illud in B, uti Z b X b M, ad <lb/>Z B X B M. </s> <s xml:id="echoid-s16192" xml:space="preserve">ſed eſt Z b X b M ad Z B X B M ex natura hujus ſphæ-<lb/>roidis:</s> <s xml:id="echoid-s16193" xml:space="preserve">: <emph style="ol">c b</emph><emph style="super">3</emph> ad <emph style="ol">C B</emph><emph style="super">3</emph>. </s> <s xml:id="echoid-s16194" xml:space="preserve">quæ ſunt uti Cohærentiæ, adeoque erit hoc <lb/>corpus ubivis æqualis Cohærentiæ.</s> <s xml:id="echoid-s16195" xml:space="preserve"/> </p> <pb o="638" file="0654" n="655" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div619" type="section" level="1" n="619"> <head xml:id="echoid-head738" xml:space="preserve">PROPOSITIO CXVI.</head> <p style="it"> <s xml:id="echoid-s16196" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16197" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16198" xml:space="preserve">fig. </s> <s xml:id="echoid-s16199" xml:space="preserve">9. </s> <s xml:id="echoid-s16200" xml:space="preserve">Si detur corpus Z B M A N, cujus baſis <lb/>borizontalis Z B M B ſit duplex parabola, cujus vertex B, axis <lb/>B B, erit boc corpus utrimque in Z & </s> <s xml:id="echoid-s16201" xml:space="preserve">M ſuffultum ubivis æqua-<lb/>lis Cohærentiæ.</s> <s xml:id="echoid-s16202" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16203" xml:space="preserve">Quia altitudo hujus corporis eſt = B C & </s> <s xml:id="echoid-s16204" xml:space="preserve">in omni puncto eadem, <lb/>erit Cohærentia uti eſt latitudo B B, b b. </s> <s xml:id="echoid-s16205" xml:space="preserve">ſed eſt ex natura parabo-<lb/>læ, uti B B ad b b, ita B<emph style="ol">M</emph><emph style="super">q</emph>. </s> <s xml:id="echoid-s16206" xml:space="preserve">ad Z b X b M. </s> <s xml:id="echoid-s16207" xml:space="preserve">eſt autem momentum <lb/>ponderis in B ad illud in b. </s> <s xml:id="echoid-s16208" xml:space="preserve">uti <emph style="ol">B M</emph><emph style="super">q</emph> ad Z b X b M adeoque uti Co-<lb/>hærentia: </s> <s xml:id="echoid-s16209" xml:space="preserve">erit ergo hoc ſolidum ubivis æqualis Cohærentiæ.</s> <s xml:id="echoid-s16210" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div620" type="section" level="1" n="620"> <head xml:id="echoid-head739" xml:space="preserve">PROPOSITIO CXVII.</head> <p style="it"> <s xml:id="echoid-s16211" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16212" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16213" xml:space="preserve">fig. </s> <s xml:id="echoid-s16214" xml:space="preserve">15. </s> <s xml:id="echoid-s16215" xml:space="preserve">Sit B A F triangulum, baſis ſolidi, atque <lb/>A C C F parabola, cujus axis A B, vertex A, erit boc ſolidum <lb/>ubivis æqualis Cohærentiæ, modo fulciatur utrimque in A F <lb/>& </s> <s xml:id="echoid-s16216" xml:space="preserve">B.</s> <s xml:id="echoid-s16217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16218" xml:space="preserve">Fiant enim ſectiones G D, K L perpendiculares in baſin A F B. <lb/></s> <s xml:id="echoid-s16219" xml:space="preserve">erit Cohærentia in D G ad K L, in ratione compoſita ex duplicata <lb/>D G ad K L, & </s> <s xml:id="echoid-s16220" xml:space="preserve">D E ad P L: </s> <s xml:id="echoid-s16221" xml:space="preserve">eſt vero D E ad P L:</s> <s xml:id="echoid-s16222" xml:space="preserve">: B D, B L. </s> <s xml:id="echoid-s16223" xml:space="preserve">& </s> <s xml:id="echoid-s16224" xml:space="preserve"><lb/><emph style="ol">D G</emph><emph style="super">q</emph> ad <emph style="ol">K</emph>L<emph style="super">q</emph>:</s> <s xml:id="echoid-s16225" xml:space="preserve">: F D, F L. </s> <s xml:id="echoid-s16226" xml:space="preserve">quare rationes Cohærentiarum in ſectio-<lb/>nibus D G, K L reducuntur ad rationes F D, ad F L, & </s> <s xml:id="echoid-s16227" xml:space="preserve">D B ad <lb/>L B. </s> <s xml:id="echoid-s16228" xml:space="preserve">hoc eſt F D X D B & </s> <s xml:id="echoid-s16229" xml:space="preserve">F L X L B. </s> <s xml:id="echoid-s16230" xml:space="preserve">ſed momentum ponderis ap-<lb/>plicati in D G, eſt ad momentum ejuſdem applicati in ſectione K L, <lb/>uti F D X D B, ad F L X L B. </s> <s xml:id="echoid-s16231" xml:space="preserve">quare momentum ponderis eſt in <lb/>qualibet ſectione ad Cohærentiam in eadem ratione, hoc eſt ſoli-<lb/>dum ejuſdem ubivis reſiſtentiæ.</s> <s xml:id="echoid-s16232" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16233" xml:space="preserve">Appendicis inſtar huic Capiti adnectam quædam Experimenta ab <lb/>aliis inſtituta, ut corporum firmitas cognoſcatur: </s> <s xml:id="echoid-s16234" xml:space="preserve">Sumſit Mariot-<lb/>tus virgam vitream cylindricam, diametri 1 {3/4} lineæ, longitudinis <lb/>11 pollic; </s> <s xml:id="echoid-s16235" xml:space="preserve">quam impoſuit duobus fulcris, 9 pollices a ſe remotis, <lb/>ex medio pondus libræ 1 {3/4} ſuſpenſum, cylindrum fregit.</s> <s xml:id="echoid-s16236" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16237" xml:space="preserve">Sumtum fuit parallelopipedum Glaciei, longum 15 pollices, la-<lb/>tum 4, altum 3 {1/3} pollic. </s> <s xml:id="echoid-s16238" xml:space="preserve">hoc horizontaliter impoſitum binis fulcris <pb o="639" file="0655" n="656" rhead="CORPORUM FIRMORUM."/> 12 pollices a ſe remotis, ex medio ſuſpenſum tenuit pondus librar. <lb/></s> <s xml:id="echoid-s16239" xml:space="preserve">350, tumque diffractum, veluti notavit Hookius: </s> <s xml:id="echoid-s16240" xml:space="preserve">vide Hookiana <lb/>a Derbamo edita pag. </s> <s xml:id="echoid-s16241" xml:space="preserve">130. </s> <s xml:id="echoid-s16242" xml:space="preserve">Eadem examinandi methodo uſus fuit <lb/>Cl. </s> <s xml:id="echoid-s16243" xml:space="preserve">Mairan in Tractatu de Glacie; </s> <s xml:id="echoid-s16244" xml:space="preserve">qui Tubum vitreum diametri 4 <lb/>linearum implevit aqua, quam ſivit congelari, tum undique latera <lb/>tubi paulum calefecit, ut cylindrum glacialem internum, jam ſo-<lb/>lutum a lateribus eximere poſſet, & </s> <s xml:id="echoid-s16245" xml:space="preserve">cum eo Experimentum cape-<lb/>re: </s> <s xml:id="echoid-s16246" xml:space="preserve">Cylindrum impoſuit duobus fulcris 6 pollices â ſe diſtantibus, <lb/>ex medio pendebat funis cum pondere, quod = unciis 17 + drach-<lb/>mis 2 fregit glaciem, repetiit hoc Experimentum aliquoties, ſed cum <lb/>diverſo ſucceſſu, prout glacies pluribus vel paucioribus bullis aëreis <lb/>ſcatebat, aut tempeſtatis calor friguſve variabant.</s> <s xml:id="echoid-s16247" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div621" type="section" level="1" n="621"> <head xml:id="echoid-head740" xml:space="preserve">CAPUT OCTAVUM.</head> <head xml:id="echoid-head741" style="it" xml:space="preserve">De Cohærentia ſolidorum utrimque a foramine arcto <lb/>exceptorum.</head> <p> <s xml:id="echoid-s16248" xml:space="preserve">Examinanda reſtat Cohærentia corporum, quæ utrimque ful. <lb/></s> <s xml:id="echoid-s16249" xml:space="preserve">ciuntur, ſed quorum extrema immiſſa ſunt foraminibus, ar-<lb/>cte hæc ipſa comprehendentibus, adeo ut differat hoc examen ab <lb/>eo in Capite VII inſtituto, quod ibi extrema corporum libere inni-<lb/>tebantur fulcris, hic nunc concludantur in foraminibus; </s> <s xml:id="echoid-s16250" xml:space="preserve">ſi Geo-<lb/>metrice de Cohærentia modo ratiocinaremur, nulla differentia vi-<lb/>deretur dari, ſive corpora libere fulcris impoſita fuerint, ſive in <lb/>foraminibus comprehendantur, ſed valde differt corporum in utro-<lb/>que caſu firmitas, quemadmodum Mariottus & </s> <s xml:id="echoid-s16251" xml:space="preserve">Parentius invene-<lb/>runt. </s> <s xml:id="echoid-s16252" xml:space="preserve">Meretur corporum Cohærentia hæc explorari, quia Trabes, <lb/>quæ ædium tabulationibus, pavimentisque inſerviunt, utroque ſui <lb/>extremo parietibus infiguntur, iiſque tanquam foraminibus inclu-<lb/>duntur, impedientibus quominus partes extremæ adſcendant, ſi <lb/>locis intermediis onus grave imponeretur; </s> <s xml:id="echoid-s16253" xml:space="preserve">ut tranſeam plures ca-<lb/>ſus, in quibus corporum extrema concluſa retinentur, intermediâ <lb/>interim maſſâ reſiſtentiam contra quamlibet vim exercente.</s> <s xml:id="echoid-s16254" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16255" xml:space="preserve">Hiſce tentaminibus inſerviit quoque machina in Tab. </s> <s xml:id="echoid-s16256" xml:space="preserve">XXIII. </s> <s xml:id="echoid-s16257" xml:space="preserve">fig.</s> <s xml:id="echoid-s16258" xml:space="preserve"> <pb o="640" file="0656" n="657" rhead="INTRODUCTIO AD COHÆRENTIAM"/> 36. </s> <s xml:id="echoid-s16259" xml:space="preserve">depicta, in cujus aſſeribus lateralibus A A inſculpta ſunt fora-<lb/>mina diverſæ amplitudinis, quibus parallelopipeda examinanda im-<lb/>miſſa fuerunt.</s> <s xml:id="echoid-s16260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16261" xml:space="preserve">Omnia parallelopipeda, quæ his Experimentis inſervierunt, <lb/>erant ex bono ligno abſque nodis, fibriſve flexuoſis electa, ex eo-<lb/>dem diſſecta aſſere, quæ ejuſdem Ligni fuerunt, imo ex eodem <lb/>aſſere, qui parallelopipeda, in priori Capite examinata, præbue-<lb/>rat, ut melius comparari poſſet Cohærentia illius modi cum hocce: <lb/></s> <s xml:id="echoid-s16262" xml:space="preserve">Memoravi ſupra, diſtantiam amborum aſſerum A A, in machina <lb/>deſcripta eſſe 18 pollic. </s> <s xml:id="echoid-s16263" xml:space="preserve">Rhenol. </s> <s xml:id="echoid-s16264" xml:space="preserve">adeoque conſtans erit fulcrorum <lb/>diſtantia in Experimentis deſcribendis: </s> <s xml:id="echoid-s16265" xml:space="preserve">Omnia parallelopipeda <lb/>longitudinis 2 pedum facta ſunt, ut utrimque paulum ex forami-<lb/>nibus eminerent, horumque medio appenſus funis cum annexis <lb/>ponderibus, quæ perpetuo ſed pedetentim aucta fuerunt, donec <lb/>lignum fregerint.</s> <s xml:id="echoid-s16266" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div622" type="section" level="1" n="622"> <head xml:id="echoid-head742" xml:space="preserve">EXPERIMENTUM CCIX.</head> <p> <s xml:id="echoid-s16267" xml:space="preserve">Sumtum fuit parallelopipedum Piceæ, altum 0, 40 pollic. </s> <s xml:id="echoid-s16268" xml:space="preserve">latum <lb/>0, 44 pollices, quod foraminibus immiſſum ex medio ſuſtinuit li-<lb/>bras 49 {1/2}. </s> <s xml:id="echoid-s16269" xml:space="preserve">tumque frangebatur; </s> <s xml:id="echoid-s16270" xml:space="preserve">antea tamen inſigniter in medio de-<lb/>primebatur, non autem tantopere ac cum libere binis impoſitum <lb/>erat fulcris; </s> <s xml:id="echoid-s16271" xml:space="preserve">extrema, quæ binis foraminibus inſederant ſigna im-<lb/>preſſionis receperant ab oris foraminum, quia enim ora interior & </s> <s xml:id="echoid-s16272" xml:space="preserve"><lb/>inferior foraminis fulcrum fuit, impreſſa erat parallelopipedo, ſed <lb/>aſſurgenti ejus extremo obſtiterat ora foraminis ſuperior & </s> <s xml:id="echoid-s16273" xml:space="preserve">exte-<lb/>rior, quæ hinc etiam notam impreſſionis cum parallelopipedo com-<lb/>municaverat; </s> <s xml:id="echoid-s16274" xml:space="preserve">hoc obſervatum fuit in omnibus Experimentis ſequen-<lb/>tibus, ſemel id indicaſſe ſufficiat.</s> <s xml:id="echoid-s16275" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div623" type="section" level="1" n="623"> <head xml:id="echoid-head743" xml:space="preserve">EXPERIMENTUM CCX.</head> <p> <s xml:id="echoid-s16276" xml:space="preserve">Parallelopipedum ejuſdem Piceæ altum 0, 50 pollic. </s> <s xml:id="echoid-s16277" xml:space="preserve">latum quo-<lb/>que 0, 50 pollic. </s> <s xml:id="echoid-s16278" xml:space="preserve">eodem modo examinatum, ſuſtinuit ex ſui medio <lb/>libras 62, a quibus elapſo minuto, fractum fuit.</s> <s xml:id="echoid-s16279" xml:space="preserve"/> </p> <pb o="641" file="0657" n="658" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s16280" xml:space="preserve">Primo obſervamus in comparatis his binis Experimentis Cohæ-<lb/>rentiam non eſſe in ratione compoſita ex duplicata altitudinis & </s> <s xml:id="echoid-s16281" xml:space="preserve"><lb/>ſimplici latitudinis, quippe tum parallelopipedum 0, 50 poll. </s> <s xml:id="echoid-s16282" xml:space="preserve">altum <lb/>latumque debuiſſet ſuſtinere libras 87 {1354/1408}, cum ruptum fuerit a <lb/>libris 62. </s> <s xml:id="echoid-s16283" xml:space="preserve">adeoque aberratio a regula ſuperius aſſumta hic datur ingens.</s> <s xml:id="echoid-s16284" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16285" xml:space="preserve">Secundo ſi comparemus Experimentum CCII. </s> <s xml:id="echoid-s16286" xml:space="preserve">cum Exp, CCIX. <lb/></s> <s xml:id="echoid-s16287" xml:space="preserve">ingentem diſcrepantiam, inter utramque Cohærentiam corporis <lb/>libere fulcris impoſiti, & </s> <s xml:id="echoid-s16288" xml:space="preserve">utrimque foraminibus incluſi, notamus, <lb/>nam parallelopipedum Exp. </s> <s xml:id="echoid-s16289" xml:space="preserve">CCIX, ſi utrimque fulcro libere fuiſſet <lb/>impoſitum, ex medio ſui tantum geſtaſſet pondus libr. </s> <s xml:id="echoid-s16290" xml:space="preserve">22 {12034/21853}. </s> <s xml:id="echoid-s16291" xml:space="preserve">ſed <lb/>tulit libras 49. </s> <s xml:id="echoid-s16292" xml:space="preserve">plus; </s> <s xml:id="echoid-s16293" xml:space="preserve">adeoque ultra duplo majorem gravitatem. </s> <s xml:id="echoid-s16294" xml:space="preserve">Et <lb/>ſi comparemus Experimentum CCIII. </s> <s xml:id="echoid-s16295" xml:space="preserve">cum Exp. </s> <s xml:id="echoid-s16296" xml:space="preserve">CCX. </s> <s xml:id="echoid-s16297" xml:space="preserve">notamus, ſi <lb/>hoc parallelopipedum libere utrimque fulcris fuiſſet impoſitum, tan-<lb/>tum id geſtare potuiſſe libr. </s> <s xml:id="echoid-s16298" xml:space="preserve">39, {713/1033}. </s> <s xml:id="echoid-s16299" xml:space="preserve">cum tamen a foraminibus ex-<lb/>ceptum tulerit libr. </s> <s xml:id="echoid-s16300" xml:space="preserve">62. </s> <s xml:id="echoid-s16301" xml:space="preserve">quod pondus non eſt duplum prioris, <lb/>quamobrem inter hæc Experimenta magna regnat anomalia, veluti <lb/>in omnibus deſcribendis infra quoque deprehendi.</s> <s xml:id="echoid-s16302" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div624" type="section" level="1" n="624"> <head xml:id="echoid-head744" xml:space="preserve">EXPERIMENTUM CCXI.</head> <p> <s xml:id="echoid-s16303" xml:space="preserve">Parallelopipedum Ulmi, cujus quodlibet latus erat 0, 35 pollic. <lb/></s> <s xml:id="echoid-s16304" xml:space="preserve">fractum fuit a libris 34 ex ſui medio pendentibus.</s> <s xml:id="echoid-s16305" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div625" type="section" level="1" n="625"> <head xml:id="echoid-head745" xml:space="preserve">EXPERIMENTUM CCXII.</head> <p> <s xml:id="echoid-s16306" xml:space="preserve">Parallelopipedum Ulmi, cujus quodlibet latus fuit 0, 42 pollic. <lb/></s> <s xml:id="echoid-s16307" xml:space="preserve">fractum fuit a libris 68 ex medio applicatis.</s> <s xml:id="echoid-s16308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16309" xml:space="preserve">Comparando iterum hæc Experimenta inter ſe notamus, Cohæ-<lb/>rentiam non dari in ratione compoſita ex ſimplici latitudinis & </s> <s xml:id="echoid-s16310" xml:space="preserve">dupli-<lb/>cata altitudinis, quoniam tum Cohærentia Exper. </s> <s xml:id="echoid-s16311" xml:space="preserve">CCXII. </s> <s xml:id="echoid-s16312" xml:space="preserve">obſervan-<lb/>da fuiſſet libr. </s> <s xml:id="echoid-s16313" xml:space="preserve">58 {32042/42875}, quæ fuit libr. </s> <s xml:id="echoid-s16314" xml:space="preserve">68. </s> <s xml:id="echoid-s16315" xml:space="preserve">adeoque major.</s> <s xml:id="echoid-s16316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16317" xml:space="preserve">Et comparando Experimentum CXCIII. </s> <s xml:id="echoid-s16318" xml:space="preserve">cum CCXI. </s> <s xml:id="echoid-s16319" xml:space="preserve">apparet pa-<lb/>rallelopipedum Exp. </s> <s xml:id="echoid-s16320" xml:space="preserve">CCXI. </s> <s xml:id="echoid-s16321" xml:space="preserve">fulcris libere impoſitum ex ſui medio pon-<lb/>dus laturum librarum 9 {13475/31850}. </s> <s xml:id="echoid-s16322" xml:space="preserve">quod exceptum utrimque a foramini-<lb/>bus ex medio tulit libras 34. </s> <s xml:id="echoid-s16323" xml:space="preserve">adeoque ultra triplo plus.</s> <s xml:id="echoid-s16324" xml:space="preserve"/> </p> <pb o="642" file="0658" n="659" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s16325" xml:space="preserve">Et comparando Experimentum CXCIV cum CCXII. </s> <s xml:id="echoid-s16326" xml:space="preserve">apparet <lb/>parallelopipedum CCXII fulcris libere impoſitum ex medio geſta-<lb/>turum pondus libr. </s> <s xml:id="echoid-s16327" xml:space="preserve">13 {8580/96148}. </s> <s xml:id="echoid-s16328" xml:space="preserve">nunc autem foraminibus exceptum ge-<lb/>ſtavit libras 68, adeoque fere quintuplo plus.</s> <s xml:id="echoid-s16329" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div626" type="section" level="1" n="626"> <head xml:id="echoid-head746" xml:space="preserve">EXPERIMENTUM CCXIII.</head> <p> <s xml:id="echoid-s16330" xml:space="preserve">Parallelopipedum Tiliæ, cujus quodlibet latus fuit 0, 34 pollic, <lb/>ſuſtinuit ex medio appenſas libras 40, a quibus elapſo tempore <lb/>frangebatur.</s> <s xml:id="echoid-s16331" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div627" type="section" level="1" n="627"> <head xml:id="echoid-head747" xml:space="preserve">EXPERIMENTUM CCXIV.</head> <p> <s xml:id="echoid-s16332" xml:space="preserve">Parallelopipedum Tiliæ, cujus quodlibet latus erat 0, 40 pollic. <lb/></s> <s xml:id="echoid-s16333" xml:space="preserve">fractum fuit a libris 62 ex medio appenſis.</s> <s xml:id="echoid-s16334" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div628" type="section" level="1" n="628"> <head xml:id="echoid-head748" xml:space="preserve">EXPERIMENTUM CCXV.</head> <p> <s xml:id="echoid-s16335" xml:space="preserve">Parallelopipedum Tiliæ, cujus quodlibet latus 0, 50 pollic. </s> <s xml:id="echoid-s16336" xml:space="preserve">te-<lb/>nuit ex medio appenſas libras 75, a quibus tamen frangebatur tem-<lb/>pore elapſo.</s> <s xml:id="echoid-s16337" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16338" xml:space="preserve">Comparando Experimentum CCXIII cum CCXIV, videtur <lb/>Cohærentia utriuſque parallelopipedi minor quam in ratione com-<lb/>poſita ex ſimplici latitudinis & </s> <s xml:id="echoid-s16339" xml:space="preserve">duplicata altitudinis, quippe Co-<lb/>hærentia Experimenti CCXIV. </s> <s xml:id="echoid-s16340" xml:space="preserve">tum obſervanda fuiſſet libr. </s> <s xml:id="echoid-s16341" xml:space="preserve">65 {5240/39304} <lb/>quæ tamen modo fuit libr. </s> <s xml:id="echoid-s16342" xml:space="preserve">62. </s> <s xml:id="echoid-s16343" xml:space="preserve">& </s> <s xml:id="echoid-s16344" xml:space="preserve">comparando Experimentum <lb/>CCXIII. </s> <s xml:id="echoid-s16345" xml:space="preserve">cum CCXV, iterum regnat minor in Cohærentia ratio, <lb/>quam quæ conſtat ex ſimplici latitudinis per duplicatam altitudi-<lb/>nis, quippe tum parallelopipedum Experimenti CCXV ſecun-<lb/>dum proportionem ferre debuiſſet libras 127 {8302/39304}. </s> <s xml:id="echoid-s16346" xml:space="preserve">cum modo geſta-<lb/>vit libras 75.</s> <s xml:id="echoid-s16347" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16348" xml:space="preserve">Et comparando Experimentum CCV cum CCXIII. </s> <s xml:id="echoid-s16349" xml:space="preserve">ſuſtinuiſſet <lb/>parallelopipedum Exper. </s> <s xml:id="echoid-s16350" xml:space="preserve">CCXIII libere fulcris impoſitum ex ſui <lb/>medio pondus libr. </s> <s xml:id="echoid-s16351" xml:space="preserve">15 {5292/7514}. </s> <s xml:id="echoid-s16352" xml:space="preserve">nunc foraminibus utrimque exceptum <lb/>fere triplo plus ex medio geſtavit, tulit enim libras 40.</s> <s xml:id="echoid-s16353" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16354" xml:space="preserve">Et conferendo Experimentum CCVI. </s> <s xml:id="echoid-s16355" xml:space="preserve">cum Exper. </s> <s xml:id="echoid-s16356" xml:space="preserve">CCXIV. </s> <s xml:id="echoid-s16357" xml:space="preserve">tu- <pb o="643" file="0659" n="660" rhead="CORPORUM FIRMORUM."/> liſſet hoc parallelopipedum libere fulcris impoſitum pondus libr. <lb/></s> <s xml:id="echoid-s16358" xml:space="preserve">18 {14334/24037}. </s> <s xml:id="echoid-s16359" xml:space="preserve">nunc utrimque foraminibus incluſum geſtavit libras 62. </s> <s xml:id="echoid-s16360" xml:space="preserve"><lb/>adeoque ultra triplo plus, quam ſi fulcris inniteretur.</s> <s xml:id="echoid-s16361" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div629" type="section" level="1" n="629"> <head xml:id="echoid-head749" xml:space="preserve">EXPERIMENTUM CCXVI.</head> <p> <s xml:id="echoid-s16362" xml:space="preserve">Parallelopipedum Fraxini, cujus quodlibet latus erat 0, 33 pol-<lb/>lic. </s> <s xml:id="echoid-s16363" xml:space="preserve">infixum utrimque foramini ſuſtinuit aliquamdiu ex medio ſu-<lb/>ſpenſas libras 57. </s> <s xml:id="echoid-s16364" xml:space="preserve">tandem tamen ruptum fuit.</s> <s xml:id="echoid-s16365" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div630" type="section" level="1" n="630"> <head xml:id="echoid-head750" xml:space="preserve">EXPERIMENTUM CCXVII.</head> <p> <s xml:id="echoid-s16366" xml:space="preserve">Parallelopipedum Fraxini, cujus quodlibet latus fuit 0, 42 pol-<lb/>lic.</s> <s xml:id="echoid-s16367" xml:space="preserve">, ex medio geſtavit libras 115, tumque frangebatur.</s> <s xml:id="echoid-s16368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16369" xml:space="preserve">Comparando hæc bina Experimenta inter ſe, videtur Cohæren-<lb/>tia in ratione compoſita ex ſimplici latitudinis & </s> <s xml:id="echoid-s16370" xml:space="preserve">duplicata altitu-<lb/>dinis ſatis accurate dari, nam ſecundum hanc proportionem paral-<lb/>lelopipedum Experimenti CCXVII deberet gerere pondus librarum <lb/>117 {18387/35937}. </s> <s xml:id="echoid-s16371" xml:space="preserve">cum geſtavit libras 115, quod pondus ſatis appropinquat.</s> <s xml:id="echoid-s16372" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16373" xml:space="preserve">Præterea ſecundum Experimentum CXCVII, parallelopipedum <lb/>Experimenti CCXVI libere utrimque fulcris impoſitum ex medio <lb/>geſtaſſet pondus librar: </s> <s xml:id="echoid-s16374" xml:space="preserve">24 {52471/56628}. </s> <s xml:id="echoid-s16375" xml:space="preserve">foraminibus immiſſum tenuit libras <lb/>57, adeoque fere triplo plus. </s> <s xml:id="echoid-s16376" xml:space="preserve">Et ſecundum Experimentum CXCVIII, <lb/>parallelopipedum Experimenti CCXVII libere fulcris impoſitum <lb/>ſuſtinuiſſet in medio libras 39 {12691/22932}. </s> <s xml:id="echoid-s16377" xml:space="preserve">fractum fuit utrimque in fora-<lb/>mine retentum a libris 115, adeoque fere triplo majus pondus ge-<lb/>ſtavit,</s> </p> </div> <div xml:id="echoid-div631" type="section" level="1" n="631"> <head xml:id="echoid-head751" xml:space="preserve">EXPERIMENTUM CCXVIII.</head> <p> <s xml:id="echoid-s16378" xml:space="preserve">Parallelopipedum Quercicum, cujus quodlibet latus fuit 0, 35 <lb/>pollic in medio ſuſtinuit libras 57 aliquamdiu, a quibus tamen <lb/>ruptum fuit.</s> <s xml:id="echoid-s16379" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div632" type="section" level="1" n="632"> <head xml:id="echoid-head752" xml:space="preserve">EXPERIMENTUM CCXIX.</head> <p> <s xml:id="echoid-s16380" xml:space="preserve">Parallelopipedum Quercicum, cujus quodlibet latus erat 0, 40 <pb o="644" file="0660" n="661" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pollic. </s> <s xml:id="echoid-s16381" xml:space="preserve">utrimque foramini immiſſum fractum eſt a libris 80 ex me-<lb/>dio pendentibus.</s> <s xml:id="echoid-s16382" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div633" type="section" level="1" n="633"> <head xml:id="echoid-head753" xml:space="preserve">EXPERIMENTUM CCXX.</head> <p> <s xml:id="echoid-s16383" xml:space="preserve">Parallelopipedum Quercicum, 0, 40 poll. </s> <s xml:id="echoid-s16384" xml:space="preserve">latum, 0, 50 altum, <lb/>utrimque foramini incluſum, æque longum ex medio geſtaverat <lb/>libras 31 {3/18}, ſed erat lignum tenerum; </s> <s xml:id="echoid-s16385" xml:space="preserve">quod eſt Experimentum Pa-<lb/>rentii.</s> <s xml:id="echoid-s16386" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16387" xml:space="preserve">Conferendo bina Experimenta CCXVIII & </s> <s xml:id="echoid-s16388" xml:space="preserve">CCXIX ſecum in-<lb/>vicem videtur proportio compoſita ex ſimplici latitudinis & </s> <s xml:id="echoid-s16389" xml:space="preserve">dupli-<lb/>cata altitudinis in utraque Cohærentia ſatis accurate dari, nam ſe-<lb/>cundum hanc proportionem, Cohærentia parallelopipedi in Expe-<lb/>rimento CCXIX deberet eſſe 85 {7625/42875}, quæ fuit 80 librarum.</s> <s xml:id="echoid-s16390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16391" xml:space="preserve">Et Comparando Experimentum CLXXXVIII. </s> <s xml:id="echoid-s16392" xml:space="preserve">cum Exp CCXIX, <lb/>liquet parallelopipedum Experimenti CCXIX. </s> <s xml:id="echoid-s16393" xml:space="preserve">libere duobus ful-<lb/>cris impoſitum potuiſſe modo geſtare libras 36 {16/104}; </s> <s xml:id="echoid-s16394" xml:space="preserve">foraminibus ex-<lb/>ceptum tulit libras 80, adeoque ultra duplo plus.</s> <s xml:id="echoid-s16395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16396" xml:space="preserve">Si vero intueamur Experimentum CCXX, quod eſt a Cl. </s> <s xml:id="echoid-s16397" xml:space="preserve">Pa-<lb/>rentio factum, apparet ingentem eſſe in Cohærentia ejuſdem ligni <lb/>diſcrepantiam, nam parallelopipedum noſtri Experimenti CCXIX <lb/>geſtavit libras 80, cum id Parentii tantum tulit libras 31 {1/6}. </s> <s xml:id="echoid-s16398" xml:space="preserve">ſi vero <lb/>ex eodem Ligno, ac ex quo noſtra ſunt compoſita ſolida, fuiſſet <lb/>fabrefactum, tuliſſet libras 125. </s> <s xml:id="echoid-s16399" xml:space="preserve">forſitan Cl. </s> <s xml:id="echoid-s16400" xml:space="preserve">Parentius non ſatis <lb/>accuratum tentamen inſtituit, Lignumque lateraliter inverſum fuit <lb/>ob altitudinem multum excedentem latitudinem, quemadmodum fa-<lb/>cile evenit, (imo in initio mihi contigit, cui tamen incommodo <lb/>obviam ivi) tumque multo minor Cohærentia obſervari debuit.</s> <s xml:id="echoid-s16401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16402" xml:space="preserve">Verum regnant in omnibus Experimentis hujus Capitis magnæ <lb/>anomaliæ, receſſuſque a proportionibus in ſuperioribus Experimentis <lb/>repertis, quos obſervaſſent Philoſophi, ſi operæ manum quoque <lb/>admoviſſent; </s> <s xml:id="echoid-s16403" xml:space="preserve">ſed quantum ſuperat Cohærentia ſolidorum foraminibus <lb/>utrimque exceptorum eam, quæ in ipſis datur, libere fulcris ex-<lb/>ceptis? </s> <s xml:id="echoid-s16404" xml:space="preserve">aliquando bis, aliquando ter, imo & </s> <s xml:id="echoid-s16405" xml:space="preserve">ultra: </s> <s xml:id="echoid-s16406" xml:space="preserve">Mariottus ex <lb/>Experimento a ſe inſtituto collegerat, Cohærentiam corporum, <lb/>utrimque foramini infixorum, eſſe duplo majorem illâ, quæ in <pb o="645" file="0661" n="662" rhead="CORPORUM FIRMORUM."/> iisdem obſervatur corporibus utrimque a fulcro exceptis, idque <lb/>collegit, quia in duobus locis ſimul franguntur prope foramina, <lb/>cum ea, quæ libere a fulcris ſuſtinentur, modo frangantur in me-<lb/>dio: </s> <s xml:id="echoid-s16407" xml:space="preserve">Sumſit virgam vitream diametri {3/4} lineæ, quam utrimque fo-<lb/>raminibus 9 pollices a ſe diſtantibus infixit, pondus libr. </s> <s xml:id="echoid-s16408" xml:space="preserve">3. </s> <s xml:id="echoid-s16409" xml:space="preserve">& </s> <s xml:id="echoid-s16410" xml:space="preserve">un-<lb/>ciæ 1 ex medio ſuſpenſum hanc in duobus locis fregit; </s> <s xml:id="echoid-s16411" xml:space="preserve">cum ejuſ-<lb/>modi virga vitrea libere impoſita fulcris, 9 pollices â ſe remotis, <lb/>in medio rupta fuit a libris 1 {3/4}, quod pondus eſt fere dimidium prio-<lb/>ris: </s> <s xml:id="echoid-s16412" xml:space="preserve">non dubito de hoc Experimento, verum ex uno non licet Uni-<lb/>verſalem regulam deducere; </s> <s xml:id="echoid-s16413" xml:space="preserve">ſi Mariottus plura tentamina feciſſet, <lb/>nobiſcum anomalias magnas Cohærentiæ, tum aliquando eam tri-<lb/>plo majorem in corporibus infixis utrimque foramini obſervaſſet, <lb/>quam in iis, quæ fulcris libere imponuntur: </s> <s xml:id="echoid-s16414" xml:space="preserve">Si Parentiana conſu-<lb/>lamus Experimenta, tum corpora, foraminibus excepta, non du-<lb/>plo plus cohærerent, quam quæ fulcris innituntur, nam Lignum <lb/>Quercicum libere fulcris impoſitum, ruptum fuit in medio a libris 34 {1/2}. <lb/></s> <s xml:id="echoid-s16415" xml:space="preserve">ſed parallelopipedum alterum priori æquale & </s> <s xml:id="echoid-s16416" xml:space="preserve">ſimile, utrimque fora-<lb/>minibus infixum, geſſit modo libras 51, quod procul abeſt a li-<lb/>bris 65, quas-ſecundum regulam Mariotti geſtare debuiſſet; </s> <s xml:id="echoid-s16417" xml:space="preserve">ſed <lb/>univerſalis regula tradi hic nequit, uti Experimenta noſtra evice-<lb/>runt, cum aliquando duplo, triplove major Cohærentia regnet in <lb/>corporibus a foraminibus exceptis, imo proportiones intermediæ <lb/>etiam dentur variæ.</s> <s xml:id="echoid-s16418" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16419" xml:space="preserve">Quare autem Cohærentia corporum in hoc Capite tanto major eſt, <lb/>quam quæ libere fulcris imponebantur? </s> <s xml:id="echoid-s16420" xml:space="preserve">mihi hæc ratio eſſe videtur: <lb/></s> <s xml:id="echoid-s16421" xml:space="preserve">Quando Lignum libere imponitur fulcris, ipſiuſque medio pondera ap-<lb/>penduntur, deorſum in flectitur quam plurimum, quod multo minus <lb/>fit corpore foraminibus immiſſo: </s> <s xml:id="echoid-s16422" xml:space="preserve">poſito ligno ſuper duobus fulcris & </s> <s xml:id="echoid-s16423" xml:space="preserve"><lb/>magnâ ſimul inflexione, partes inferiores ligni plurimum incurvatæ, <lb/>â ſe mutuo divelluntur, & </s> <s xml:id="echoid-s16424" xml:space="preserve">quaſi ex ſeſe extrahuntur, plus autem ex-<lb/>trahuntur exteriores quam interiores fibræ, unde harum reſiſtentia eſt <lb/>minor, fractiſque exterioribus, ſequuntur facile aliæ: </s> <s xml:id="echoid-s16425" xml:space="preserve">Verum, ligno <lb/>immiſſo duobus foraminibus, flexio non magna fit, ideo partes ex <lb/>ſe mutuo non extrahuntur, ſed omnes, quæ digitatim ſibi impli-<lb/>citæ erant, ſimul ſolvi debent, & </s> <s xml:id="echoid-s16426" xml:space="preserve">quaſi abradi, antequam ab ap-<lb/>penſo pondere lignum rumpatur, unde longe plus virium requiri- <pb o="646" file="0662" n="663" rhead="INTRODUCTIO AD COHÆRENTIAM"/> tur, ut ſolvatur lignum foraminibus exceptum: </s> <s xml:id="echoid-s16427" xml:space="preserve">Quo igitur Lig-<lb/>num plus tenderetur in lineam rectam, & </s> <s xml:id="echoid-s16428" xml:space="preserve">minus inflecteretur, eo <lb/>plus ponderis ſolventis in medio poſtularet, non enim rumpi poſ-<lb/>ſet, niſi abraſis fere omnibus aſperitatibus, quibuſcum partes con-<lb/>creverunt: </s> <s xml:id="echoid-s16429" xml:space="preserve">ſi autem minus arcte lignum in foraminibus hæſerit, <lb/>ita ut plus inflecti introrſum a pondere appenſo poſſit, tum quoque <lb/>â minori pondere rumpetur: </s> <s xml:id="echoid-s16430" xml:space="preserve">Unde in hiſce Experimentis valde er-<lb/>rare poterimus, & </s> <s xml:id="echoid-s16431" xml:space="preserve">vix aliquid certi concludere, niſi ſummâ cum <lb/>curâ capiantur; </s> <s xml:id="echoid-s16432" xml:space="preserve">atque hoc in principio obſervavi, quotieſcunque <lb/>enim Lignum foraminibus immiſeram, quodnon arctiſſime compre-<lb/>hendebatur, cedebat introrſum a pondere appenſo valdequam, & </s> <s xml:id="echoid-s16433" xml:space="preserve"><lb/>facilius frangebatur; </s> <s xml:id="echoid-s16434" xml:space="preserve">unde poſtea adeo arcta reddidi foramina, ut <lb/>non niſi vi magna intrudi potuerint parallelopipeda, quod cum non <lb/>obſervaverit Mariottus, inde etiam in ipſius Experimentum error <lb/>irrepere potuit.</s> <s xml:id="echoid-s16435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16436" xml:space="preserve">Quoniam in Architectura eſt ſummæ utilitatis cognoſcere firmi-<lb/>tatem trabium, quæ deſtinatæ ſunt gerendis oneribus in repoſito-<lb/>riis & </s> <s xml:id="echoid-s16437" xml:space="preserve">Granariis, eum in finem aliquot Tabulas ſupputavi fundatas <lb/>in Experimentis noſtris, in quibus uno oculi ictu videri poteſt, <lb/>quantæ firmitatis Trabs datæ longitudinis & </s> <s xml:id="echoid-s16438" xml:space="preserve">craſſitiei, quæ parie-<lb/>ti infigitur ſit futura; </s> <s xml:id="echoid-s16439" xml:space="preserve">innituntur autem illi hypotheſi, Corporum <lb/>firmitatem eſſe in ratione latitudinis, inverſa longitudinis, & </s> <s xml:id="echoid-s16440" xml:space="preserve">du-<lb/>plicata altitudinis; </s> <s xml:id="echoid-s16441" xml:space="preserve">ſimiles olim Tabulas exhibuit Parentius in <lb/>L’ Hiſt. </s> <s xml:id="echoid-s16442" xml:space="preserve">de L’ Acad. </s> <s xml:id="echoid-s16443" xml:space="preserve">Roy. </s> <s xml:id="echoid-s16444" xml:space="preserve">A°. </s> <s xml:id="echoid-s16445" xml:space="preserve">1708, ſed ſuis innixas Experimentis, <lb/>quæ plurimum a noſtris differunt, unde alias de novo ſupputare <lb/>tenebar, quæ ſpeciminis ergo tantum exhibentur.</s> <s xml:id="echoid-s16446" xml:space="preserve"/> </p> <pb o="647" file="0663" n="664" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div634" type="section" level="1" n="634"> <head xml:id="echoid-head754" xml:space="preserve">TABULA</head> <p> <s xml:id="echoid-s16447" xml:space="preserve">Continens pondera, quæ medio Trabium Quercicarum, utro-<lb/>que extremo parietibus infixarum, poſſent imponi, ita tamen ut <lb/>ſint maxima, fundata in Experimento CCXIX.</s> <s xml:id="echoid-s16448" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Longitudo \\ pedum # # # # # # Latitudo baſeos ſupponitur 10 pollicum, \\ Altitudo ponitur horum pollicum <lb/># 10 # 11 # 12 # 13 # 14 <lb/>6 # 312500 # 378125 # 450000 # 529125 # 612500 <lb/>8 # 234312 # 283593 # 337500 # 409596 # 459375 <lb/>10 # 187500 # 226875 # 270000 # 317475 # 367500 <lb/>12 # 156250 # 189062 # 225000 # 264562 # 306250 <lb/>14 # 133928 # 162053 # 192857 # 256768 # 262500 <lb/>16 # 117187 # 141796 # 168750 # 204798 # 229687 <lb/>18 # 104166 # 122986 # 150000 # 176375 # 204166 <lb/>20 # 93700 # 113437 # 135000 # 158737 # 183750 <lb/>22 # 85227 # 103125 # 122717 # 143313 # 167045 <lb/>24 # 78125 # 94531 # 112500 # 132281 # 153125 <lb/>26 # 72115 # 87259 # 103846 # 132013 # 141346 <lb/>28 # 66964 # 81026 # 96428 # 128384 # 131250 <lb/>30 # 62500 # 75625 # 90000 # 105725 # 122500 <lb/>32 # 58593 # 70898 # 84375 # 104899 # 114843 <lb/>34 # 55147 # 66728 # 79401 # 93375 # 108088 <lb/>36 # 52083 # 61493 # 75000 # 88187 # 102083 <lb/>38 # 49342 # 59703 # 71052 # 83546 # 96710 <lb/>40 # 46850 # 56718 # 67500 # 79368 # 91875 <lb/>42 # 44642 # 54017 # 65783 # 77350 # 87500 <lb/>44 # 42613 # 51562 # 61363 # 72153 # 83522 <lb/></note> <pb o="648" file="0664" n="665" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s16449" xml:space="preserve">In hac Tabula ſupponitur latitudo baſeos Trabis Quercicæ <lb/>conſtans, nempe 11 pollicum</s> </p> <note position="right" xml:space="preserve"> <lb/>Longitudines \\ in pedibus # # # # # # Altitudines vero horum pollicum <lb/># 11 # 12 # 13 # 14 # 15 <lb/>6 # 415937 # 495000 # 580937 # 673750 # 773437 <lb/>8 # 311953 # 371250 # 435703 # 505312 # 580078 <lb/>10 # 249562 # 297000 # 348562 # 404250 # 464062 <lb/>12 # 202968 # 247500 # 290468 # 336875 # 386718 <lb/>14 # 178258 # 212142 # 248973 # 288750 # 331473 <lb/>16 # 155976 # 185625 # 217851 # 252656 # 290039 <lb/>18 # 138645 # 165000 # 193645 # 224583 # 257812 <lb/>20 # 124681 # 148500 # 174281 # 202125 # 232031 <lb/>22 # 113437 # 135000 # 158437 # 183750 # 210937 <lb/>24 # 101484 # 123750 # 145234 # 168437 # 193359 <lb/>26 # 95985 # 114230 # 134062 # 155480 # 178485 <lb/>28 # 89129 # 106021 # 124486 # 144375 # 165736 <lb/>30 # 83187 # 99000 # 116187 # 134750 # 154687 <lb/>32 # 77988 # 92812 # 108925 # 126328 # 145019 <lb/>34 # 73400 # 87350 # 102518 # 118897 # 136488 <lb/>36 # 69322 # 82500 # 96822 # 112291 # 128906 <lb/>38 # 65674 # 78150 # 91727 # 106381 # 122121 <lb/>40 # 62345 # 74250 # 87140 # 101062 # 116015 <lb/></note> <pb o="649" file="0665" n="666" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s16450" xml:space="preserve">Quoniam in Hollandia ſolemus Trabibus Piceæ uti ad laquearia <lb/>conſtruenda, propter pretium Ligni Quercici nimium, volui etiam <lb/>has adnectere Tabulas, quæ robur Trabium Picearum parietibus <lb/>utrimque exceptarum in medio ſui exhibent; </s> <s xml:id="echoid-s16451" xml:space="preserve">innituntur hæ Tabulæ <lb/>Experimento CCX.</s> <s xml:id="echoid-s16452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16453" xml:space="preserve">In hac Tabula ſupponitur latitudo baſeos 10 pollic.</s> <s xml:id="echoid-s16454" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Longitudines \\ in pedibus # # # # # # Altitudines vero horum pollicum. <lb/># 10 # 11 # 12 # 13 # 14 <lb/>6 # 124000 # 150015 # 178560 # 209560 # 243040 <lb/>8 # 93000 # 112511 # 133920 # 157170 # 182280 <lb/>10 # 74400 # 90009 # 107136 # 125736 # 145824 <lb/>12 # 61000 # 75007 # 89280 # 104784 # 121520 <lb/>14 # 53142 # 65006 # 76525 # 89811 # 104160 <lb/>16 # 46500 # 56255 # 66960 # 78585 # 91140 <lb/>18 # 41333 # 50005 # 59520 # 69853 # 81013 <lb/>20 # 37200 # 45004 # 53568 # 62868 # 72912 <lb/>22 # 33863 # 40913 # 48698 # 57152 # 66282 <lb/>24 # 31000 # 37503 # 44640 # 52392 # 60760 <lb/>26 # 28623 # 34619 # 41206 # 48360 # 56093 <lb/>28 # 26571 # 32503 # 38262 # 44905 # 52080 <lb/>30 # 24800 # 30003 # 35712 # 41912 # 48608 <lb/>32 # 23250 # 28127 # 33480 # 39792 # 45570 <lb/>34 # 21882 # 26473 # 31510 # 36981 # 42890 <lb/>36 # 20666 # 25002 # 29710 # 34926 # 40506 <lb/>38 # 19581 # 23686 # 28194 # 33088 # 38374 <lb/>40 # 18600 # 22502 # 26784 # 31434 # 36456 <lb/></note> <pb o="650" file="0666" n="667" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <p> <s xml:id="echoid-s16455" xml:space="preserve">In hac Tabula ſupponitur latitudo baſeos Trabis Piceæ con-<lb/>ſtans, nempe 11 pollicum</s> </p> <note position="right" xml:space="preserve"> <lb/>Longitudines \\ in pedibus # # # # # # Altitudines vero horum pollicum <lb/># 11 # 12 # 13 # 14 # 15 <lb/>6 # 167544 # 196416 # 230516 # 252537 # 306900 <lb/>8 # 125658 # 147312 # 172887 # 189403 # 230175 <lb/>10 # 100526 # 117849 # 138309 # 151522 # 184140 <lb/>12 # 83772 # 98208 # 115258 # 126268 # 153450 <lb/>14 # 71804 # 84178 # 98792 # 108230 # 131528 <lb/>16 # 62829 # 73656 # 86443 # 94701 # 115087 <lb/>18 # 55848 # 65472 # 76838 # 84179 # 102300 <lb/>20 # 50263 # 58924 # 69154 # 75761 # 92070 <lb/>22 # 45693 # 53568 # 62868 # 68873 # 83700 <lb/>24 # 41881 # 49104 # 57129 # 63134 # 76725 <lb/>26 # 38664 # 45326 # 53196 # 58277 # 70823 <lb/>28 # 35902 # 42089 # 49396 # 54115 # 65764 <lb/>30 # 33508 # 39283 # 46103 # 50507 # 61380 <lb/>32 # 31414 # 36828 # 43221 # 47350 # 57543 <lb/>34 # 29566 # 34661 # 40679 # 44565 # 54158 <lb/>36 # 27924 # 32736 # 38419 # 42089 # 51150 <lb/>38 # 26454 # 31013 # 36397 # 39874 # 48458 <lb/>40 # 25131 # 29462 # 34577 # 37880 # 46035 <lb/></note> <pb o="651" file="0667" n="668" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div635" type="section" level="1" n="635"> <head xml:id="echoid-head755" xml:space="preserve">EXPERIMENTUM CCXXI.</head> <p> <s xml:id="echoid-s16456" xml:space="preserve">Coronæ loco meretur addi Paradoxon, quod firmitatem qua-<lb/>dratorum vitreorum, quæ feneſtris imponuntur, ſpectat: </s> <s xml:id="echoid-s16457" xml:space="preserve">nempe <lb/>omne quadratum vitreum, ſive magnum, ſive parvum, conſtans <lb/>ex lamellis vitreis æque craſſis, & </s> <s xml:id="echoid-s16458" xml:space="preserve">ejuſdem indolis, infixum un-<lb/>diquaque ſpondæ, ejuſdem eſt firmitatis.</s> <s xml:id="echoid-s16459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16460" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16461" xml:space="preserve">XXVIII. </s> <s xml:id="echoid-s16462" xml:space="preserve">fig. </s> <s xml:id="echoid-s16463" xml:space="preserve">2 & </s> <s xml:id="echoid-s16464" xml:space="preserve">4. </s> <s xml:id="echoid-s16465" xml:space="preserve">Sint duo quadrata vitrea A B C D, & </s> <s xml:id="echoid-s16466" xml:space="preserve">F E. <lb/></s> <s xml:id="echoid-s16467" xml:space="preserve">concipiantur diviſa in rectangula ſimilia M S, Q H. </s> <s xml:id="echoid-s16468" xml:space="preserve">erit ejuſmodi re-<lb/>ctangulum inſtar parallelopipedi utrimque infixi foramini, quod ſupra <lb/>conſideravimus, in medio ipſius MS, & </s> <s xml:id="echoid-s16469" xml:space="preserve">Q H ponatur pondus frangens, <lb/>erit ejus diſtantia a fulcro I&</s> <s xml:id="echoid-s16470" xml:space="preserve">Q æqualis dimidio M N & </s> <s xml:id="echoid-s16471" xml:space="preserve">Q H. </s> <s xml:id="echoid-s16472" xml:space="preserve">quare erit <lb/>momentum ponderis in utroque caſu ratione vectis, reciproce uti <lb/>diſtantia a fulcris I & </s> <s xml:id="echoid-s16473" xml:space="preserve">Q. </s> <s xml:id="echoid-s16474" xml:space="preserve">ſed eſt latitudo rectanguli M S ad eam <lb/>Q H. </s> <s xml:id="echoid-s16475" xml:space="preserve">ut M N ad Q H. </s> <s xml:id="echoid-s16476" xml:space="preserve">adeoque per Prop. </s> <s xml:id="echoid-s16477" xml:space="preserve">XXI. </s> <s xml:id="echoid-s16478" xml:space="preserve">Cap. </s> <s xml:id="echoid-s16479" xml:space="preserve">V. </s> <s xml:id="echoid-s16480" xml:space="preserve">erit ejus <lb/>Cohærentia ad eam in Q H, uti M E ad Q P. </s> <s xml:id="echoid-s16481" xml:space="preserve">quoniam vero ante de-<lb/>monſtrabam ratione vectis Cohærentiam eſſe ut Q H ad M N, quæ <lb/>ſunt ut Q P ad M E, erit Cohærentia ipſius M S ad eam Q H, uti <lb/>M E X Q P. </s> <s xml:id="echoid-s16482" xml:space="preserve">ad Q P X M E, hoc eſt erunt Cohærentiæ inter ſe æqua-<lb/>les: </s> <s xml:id="echoid-s16483" xml:space="preserve">eadem demonſtratio convenit omnibus aliis rectangulis in <lb/>utroque quadrato, quamobrem cum rectangula ſunt numero æqua-<lb/>lia & </s> <s xml:id="echoid-s16484" xml:space="preserve">ſimilia in utroque, erit etiam ſumma Cohærentiæ æqualis in <lb/>utroque quadrato, hoc eſt erit æque firmum omne quadratum. </s> <s xml:id="echoid-s16485" xml:space="preserve"><lb/>Convenit hæc demonſtratio cum ipſa Experientia, quemadmodum <lb/>aliquoties expertus fui cum quadratis ex vitreis lamellis vulgaribus <lb/>factis: </s> <s xml:id="echoid-s16486" xml:space="preserve">hæ autem ſuſtinent abſque fractura facile libras 60. </s> <s xml:id="echoid-s16487" xml:space="preserve">in me-<lb/>dio ſibi impoſitas; </s> <s xml:id="echoid-s16488" xml:space="preserve">unde patet, quod vim venti facile eludant, ſi <lb/>non fuerint nimis magnæ: </s> <s xml:id="echoid-s16489" xml:space="preserve">Facilius enim majores lamellæ a vento <lb/>franguntur, quam minores, quia ventus majori quantitate agit in <lb/>majorem ſuperficiem, quam in minorem, & </s> <s xml:id="echoid-s16490" xml:space="preserve">idcirco facilius ma-<lb/>jora vitra diffringit.</s> <s xml:id="echoid-s16491" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16492" xml:space="preserve">Mariottus inſtituit quoque nonnulla Experimenta circa firmita-<lb/>tem chartæ & </s> <s xml:id="echoid-s16493" xml:space="preserve">ferri ſtanno obducti, verum quia non memorat ho-<lb/>rum corporum craſſitiem, licet latitudinem & </s> <s xml:id="echoid-s16494" xml:space="preserve">longitudinem an-<lb/>notaverit, non multum lucis ex iis Experimentis fœnerari poſſu- <pb o="652" file="0668" n="669" rhead="INTRODUCTIO AD COHÆRENTIAM"/> mus, non enim omne ferrum album eſt æque craſſum, quo id eſt <lb/>craſſius, eo eſt fortius: </s> <s xml:id="echoid-s16495" xml:space="preserve">in charta major adhuc obtinet varietas, <lb/>pro craſſitie non tantum, ſed majori minorive glutinis admixti co-<lb/>pia, quamobrem, qui hoc Thema perpolire vellet, majori cum <lb/>cura attendere ad omnia deberet.</s> <s xml:id="echoid-s16496" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div636" type="section" level="1" n="636"> <head xml:id="echoid-head756" xml:space="preserve">CAPUT NONUM.</head> <head xml:id="echoid-head757" xml:space="preserve">De Cohærentia corporum compreſſorum.</head> <p> <s xml:id="echoid-s16497" xml:space="preserve">Summæ utilitatis eſt cognoviſſe quantæ firmitatis ſint corpora <lb/>oblonga, quæ horizonti perpendiculariter impoſita, ponderi-<lb/>bus ſuſtinendis deſtinantur; </s> <s xml:id="echoid-s16498" xml:space="preserve">trabibus enim ſecundum longitudinem <lb/>erectis graviſſimas ſuperſtruimus domos, moles ponderoſiſſimas im-<lb/>ponimus; </s> <s xml:id="echoid-s16499" xml:space="preserve">imo illis fulcimus altos parietes, amplas ædes, excel-<lb/>ſiſſimas turres, maximas naves bellicas.</s> <s xml:id="echoid-s16500" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16501" xml:space="preserve">Trabs cujuslibet craſſitiei moli utcunque gravi ſuſtinendæ par non <lb/>eſt; </s> <s xml:id="echoid-s16502" xml:space="preserve">a nimiâ enim ſibi incumbente flectitur, incurvatur, tandem <lb/>frangitur; </s> <s xml:id="echoid-s16503" xml:space="preserve">neceſſarium igitur eſt, ut exploremus & </s> <s xml:id="echoid-s16504" xml:space="preserve">demonſtremus, <lb/>quænam ſit datæ Trabis firmitas, & </s> <s xml:id="echoid-s16505" xml:space="preserve">quodnam pondus ſibi impo-<lb/>ſitum ferre poſſit, quodnam recuſet.</s> <s xml:id="echoid-s16506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16507" xml:space="preserve">Poſtulare autem poſſum tanquam demonſtratum, corpuſcula ul-<lb/>tima, ſubtiliſſima, perfecte ſolida, non amplius diffringi a viribus <lb/>comprimentibus, quas Ars vel Natura adhiberet.</s> <s xml:id="echoid-s16508" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16509" xml:space="preserve">Si fuerint corpuſcula ultima Cubi, Parallelopipeda rectangula, <lb/>aut Hexangula ordinata, quæ maſſam majorem compoſitura ordina-<lb/>tim ſint ſibi impoſita, ut nullum relinquant porum, & </s> <s xml:id="echoid-s16510" xml:space="preserve">forment <lb/>corpus oblongum, rectum, poterit hæc maſſa ſuſtinere onus quod-<lb/>cunque, premens ſecundum axin maſſæ, abſque ulla ſolutione <lb/>ejuſve metu.</s> <s xml:id="echoid-s16511" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16512" xml:space="preserve">Concipiatur enim maſſa conſtare ex tribus cubis ita accumulatis, <lb/>ut parallelopipedum conſtituant, cui incumbat onus premens per-<lb/>pendiculariter latus, quod attingit; </s> <s xml:id="echoid-s16513" xml:space="preserve">tum infimus cubus ab inter-<lb/>medio preſſus, nequicquam cedit, quia eſt perfecte durus; </s> <s xml:id="echoid-s16514" xml:space="preserve">inter-<lb/>medius preſſus a ſupremo ob eandem rationem non cedit; </s> <s xml:id="echoid-s16515" xml:space="preserve">uti nec <lb/>ſupremus cedit oneri prementi; </s> <s xml:id="echoid-s16516" xml:space="preserve">& </s> <s xml:id="echoid-s16517" xml:space="preserve">quia directio oneris eſt perpen- <pb o="653" file="0669" n="670" rhead="CORPORUM FIRMORUM."/> dicularis in quodlibet latus trium cuborum, ubiſe contingunt, nullus <lb/>lateraliter cedet, adeoque ejuſmodi maſſa feret onus utcunque gra-<lb/>ve: </s> <s xml:id="echoid-s16518" xml:space="preserve">ſi igitur ex pluribus ſeriebus cuborum, aut parallelopipedorum, <lb/>eodem ordinato modo ſibi impoſitorum maſia magna componatur, <lb/>hæc poterit, ut ante, onus utcunque grave ſuſtinere abſque ſolu-<lb/>tione, ejuſve metu.</s> <s xml:id="echoid-s16519" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16520" xml:space="preserve">Si vero maſſa conſtet ex corpuſculis poros inter ſe relinquenti-<lb/>bus, tum, quæ non lata ſe premunt ſuperficie, quæque preſſa de-<lb/>terminant lateraliter alia, quibus incumbunt, hæc maſſa non <lb/>poterit ſuſtinere pondus quodcunque, ſed in partes ſolvi po-<lb/>terit.</s> <s xml:id="echoid-s16521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16522" xml:space="preserve">Cohærent partes majoris maſſæ vi finita inter ſe, adeoque dari <lb/>poteſt preſſio major quam eſt Cohærentia, atque oppoſitæ dire-<lb/>ctionis, quæ partes ſolvat: </s> <s xml:id="echoid-s16523" xml:space="preserve">quamobrem ſi partes ſuperiores ita in-<lb/>cumbant inferioribus, ut has directe deorſum non premant, ſed <lb/>oblique, tum preſſione ſuperante Cohærentiam cedent partes in-<lb/>trorſum, quia ibi dantur pori, quo cedere poſſunt; </s> <s xml:id="echoid-s16524" xml:space="preserve">vel cedent extror-<lb/>ſum, ubi nihil eſt quod reſiſtat.</s> <s xml:id="echoid-s16525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16526" xml:space="preserve">Quoniam omnia corpora majora ope Microſcopiorum obſervan-<lb/>tur componi ex ſolidis plurimos poros inter ſe conſtituentibus, & </s> <s xml:id="echoid-s16527" xml:space="preserve"><lb/>inordinato ſitu locatis, patet hæc compreſſa non eſſe immutabilis <lb/>figuræ, ſed introrſum poſſe cedere & </s> <s xml:id="echoid-s16528" xml:space="preserve">extrorſum; </s> <s xml:id="echoid-s16529" xml:space="preserve">adeoque preſſio-<lb/>ne valde auctâ poſſe diffringi aut diſſolvi, partibus ſcilicet lateraliter <lb/>extrorſum cedentibus â cauſa premente.</s> <s xml:id="echoid-s16530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16531" xml:space="preserve">Non tamen introceſius partium, erit in ratione ponderum pre-<lb/>mentium: </s> <s xml:id="echoid-s16532" xml:space="preserve">Vid. </s> <s xml:id="echoid-s16533" xml:space="preserve">Tab. </s> <s xml:id="echoid-s16534" xml:space="preserve">XVIII. </s> <s xml:id="echoid-s16535" xml:space="preserve">fig. </s> <s xml:id="echoid-s16536" xml:space="preserve">5. </s> <s xml:id="echoid-s16537" xml:space="preserve">ſit enim corpus, ab C, quod <lb/>preſſum ab impoſito pondere P deorſum cedit ab a uſque ad b: </s> <s xml:id="echoid-s16538" xml:space="preserve">ſi <lb/>nunc introceſſus corporis ab C forent proportionales ponderibus <lb/>comprimentibus, ſequitur ab impoſito alio pondere, vocando R, <lb/>quod foret ad pondus P in majori ratione, quam a C eſt ad a b, <lb/>corpus plus compreſſum iri, quam eſt ipſa longitudo a C, quod <lb/>eſt abſurdum; </s> <s xml:id="echoid-s16539" xml:space="preserve">adeoque neceſſarium eſt, ut introceſius corporis a <lb/>pondere R ſint in minori ratione, quam a pondere P.</s> <s xml:id="echoid-s16540" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16541" xml:space="preserve">Præterea, quo maſſa magna conſtet ex partibus figura magis re-<lb/>gulari donatis, & </s> <s xml:id="echoid-s16542" xml:space="preserve">latioribus ſuperficiebus ſe contingentibus, per <lb/>quas preſſionum directiones tranſeunt perpendiculariter, eo cæte- <pb o="654" file="0670" n="671" rhead="INTRODUCTIO AD COHÆRENTIAM"/> ris paribus poterit maſia plus ponderis prementis ſuſtinere, minusque <lb/>introrſum & </s> <s xml:id="echoid-s16543" xml:space="preserve">extrorſum cedet, quam ſi fuerit conflata ex partibus <lb/>admodum irregularis figuræ, & </s> <s xml:id="echoid-s16544" xml:space="preserve">valde quam inordinato modo ſibi <lb/>accumulatis.</s> <s xml:id="echoid-s16545" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16546" xml:space="preserve">Hinc reſiſtentia vel firmitas corporum compreſſorum non pen-<lb/>debit tantum â denſitate ſive inde orta gravitate corporum, ſed <lb/>etiam a partium eorum magis minuſve ordinata figura, & </s> <s xml:id="echoid-s16547" xml:space="preserve">accumu-<lb/>latione.</s> <s xml:id="echoid-s16548" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16549" xml:space="preserve">Si proinde corpus conſtet ex partibus inordinatæ figuræ, inor-<lb/>dinato ſitu congeſtis, tum compreſſione magna cedent introrſum <lb/>& </s> <s xml:id="echoid-s16550" xml:space="preserve">extrorſum, incurvabuntur, inflectentur, auctâque compreſſio-<lb/>ne rumpentur in medio, ubi maxime inflectuntur, vel in loco mi-<lb/>nime omnium Cohærenti.</s> <s xml:id="echoid-s16551" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16552" xml:space="preserve">Antequam ad Experimenta accedam, primo machinam deſcri-<lb/>bam, cujus ope peracta ſunt: </s> <s xml:id="echoid-s16553" xml:space="preserve">proſtat depicta in Tab. </s> <s xml:id="echoid-s16554" xml:space="preserve">XXVII. </s> <s xml:id="echoid-s16555" xml:space="preserve">fig. <lb/></s> <s xml:id="echoid-s16556" xml:space="preserve">16. </s> <s xml:id="echoid-s16557" xml:space="preserve">Compoſita fuit ex duobus aſſeribus A A, B B, ligni Quercici, <lb/>quadratis, quorum ſingula latera ſunt 17 pollicum Rhenol, infimo <lb/>aſſeri B B infixa ſunt accurate perpendiculariter quatuor ſtyli C, C, <lb/>C, C, viginti pollices longi, juxta quos aſſer ſuperior A A libere <lb/>ſurſum deorſumque adſcendit, cui eum in finem 4 foramina in-<lb/>ſculpta fuerunt, ut aſſer A A ſemper perpendiculariter ad horizontem <lb/>poni poſſet, quatuor ſtylis C C C C inſculptæ ſunt diviſiones, ean-<lb/>dem diſtantiam ab aſſere infimo B B iudicantes: </s> <s xml:id="echoid-s16558" xml:space="preserve">In medio aſſeris <lb/>A A ſed in ſuperficie inferiori, quoque in media ſuperficie ſuperiori <lb/>aſſeris B B ad D foveola erat, partim ut medium cognoſceretur <lb/>ſemper, partim ut ligna examinanda melius in medio poni ſerva-<lb/>rique poſſent: </s> <s xml:id="echoid-s16559" xml:space="preserve">ſuperficiei ſuperiori aſſeris A A inſcripti fuerunt ali-<lb/>quot circuli concentrici, quorum commune centrum erat medium <lb/>aſſeris, reſpondens quoque medio foveolæ deſcriptæ; </s> <s xml:id="echoid-s16560" xml:space="preserve">hi duceban-<lb/>tur circuli, ut pondera æqualia in eadem diſtantia a centro poni <lb/>poſſent; </s> <s xml:id="echoid-s16561" xml:space="preserve">cumque præterea diametri aliquot circulos ſecabant, bi-<lb/>narum diametrorum extremitatibus impoſitis ponderibus æquali-<lb/>bus, ſemper premebatur aſſer A A æquabiliter deorſum, & </s> <s xml:id="echoid-s16562" xml:space="preserve">facili <lb/>artificio horizontaliter ſervari poterat: </s> <s xml:id="echoid-s16563" xml:space="preserve">Ligna, examinata intra <lb/>utrumque aſſerem A A, B B, poſita fuerunt perpendiculariter ad ho-<lb/>rizontem, pondera P, P, impoſita fuerunt ſemper ita, ut aſſer <pb o="655" file="0671" n="672" rhead="CORPORUM FIRMORUM."/> A A horizontalis manſerit, aut dirigi potuerit manus leviſſimo ope-<lb/>re, non turbante Experimentum, auctaque fuerunt pondera, donec <lb/>Ligna interpoſita frangebantur: </s> <s xml:id="echoid-s16564" xml:space="preserve">Omnia erant parallelopipeda, quæ <lb/>in medio ſemper maxime inflexa rupta fuerunt; </s> <s xml:id="echoid-s16565" xml:space="preserve">eventus obſervati <lb/>ſunt ſequentes.</s> <s xml:id="echoid-s16566" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div637" type="section" level="1" n="637"> <head xml:id="echoid-head758" xml:space="preserve">EXPERIMENTUM CCXXII.</head> <p> <s xml:id="echoid-s16567" xml:space="preserve">Parallelopipedum Quercicum 18 pollices longum, cujus ſingula <lb/>latera fuerunt 0, 23, pollic: </s> <s xml:id="echoid-s16568" xml:space="preserve">fractum fuit in medio a libris 23 aſſeri <lb/>ſuperiori A A impoſitis.</s> <s xml:id="echoid-s16569" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div638" type="section" level="1" n="638"> <head xml:id="echoid-head759" xml:space="preserve">EXPERIMENTUM CCXXIII.</head> <p> <s xml:id="echoid-s16570" xml:space="preserve">Idem Parallelopipedum 9 pollices longum fractum fuit a libris <lb/>92. </s> <s xml:id="echoid-s16571" xml:space="preserve">impoſitis.</s> <s xml:id="echoid-s16572" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div639" type="section" level="1" n="639"> <head xml:id="echoid-head760" xml:space="preserve">EXPERIMENTUM CCXXIV.</head> <p> <s xml:id="echoid-s16573" xml:space="preserve">Idem parallelopipedum 8 pollices longum fractum fuit a libris <lb/>118 perpendiculariter prementibus.</s> <s xml:id="echoid-s16574" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div640" type="section" level="1" n="640"> <head xml:id="echoid-head761" xml:space="preserve">EXPERIMENTUM CCXXV.</head> <p> <s xml:id="echoid-s16575" xml:space="preserve">Aliud parallelopipedum Quercicum, 12 pollices longum, cujus <lb/>reliqua latera erant 0, 35 pollic. </s> <s xml:id="echoid-s16576" xml:space="preserve">fractum fuit in medio a libris 185. <lb/></s> <s xml:id="echoid-s16577" xml:space="preserve">impoſitis.</s> <s xml:id="echoid-s16578" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div641" type="section" level="1" n="641"> <head xml:id="echoid-head762" xml:space="preserve">EXPERIMENTUM CCXXVI.</head> <p> <s xml:id="echoid-s16579" xml:space="preserve">Parallelopipedum Fraxini 18 pollices longum, cujus unum la-<lb/>tus erat 0, 25 poll. </s> <s xml:id="echoid-s16580" xml:space="preserve">alterum 0, 24 pollic. </s> <s xml:id="echoid-s16581" xml:space="preserve">fractum fuit a libris 15 <lb/>impoſitis.</s> <s xml:id="echoid-s16582" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div642" type="section" level="1" n="642"> <head xml:id="echoid-head763" xml:space="preserve">EXPERIMENTUM CCXXVII.</head> <p> <s xml:id="echoid-s16583" xml:space="preserve">Idem parallelopipedum 6 pollices longum, fractum fuit in medio-<lb/>a libris 132 impoſitis.</s> <s xml:id="echoid-s16584" xml:space="preserve"/> </p> <pb o="656" file="0672" n="673" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div643" type="section" level="1" n="643"> <head xml:id="echoid-head764" xml:space="preserve">EXPERIMENTUM CCXXVIII.</head> <p> <s xml:id="echoid-s16585" xml:space="preserve">Aliud parallelopipedum Fraxini 12 pollices longum cujus unum <lb/>latus erat 0, 34 poll. </s> <s xml:id="echoid-s16586" xml:space="preserve">alterum 0, 24 poll. </s> <s xml:id="echoid-s16587" xml:space="preserve">fractum fuit a libris 55 <lb/>ſuperpoſitis aſſeri.</s> <s xml:id="echoid-s16588" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div644" type="section" level="1" n="644"> <head xml:id="echoid-head765" xml:space="preserve">EXPERIMENTUM CCXXIX.</head> <p> <s xml:id="echoid-s16589" xml:space="preserve">Idem parallelopipedum 9 pollices longum fractum fuit a libris <lb/>100.</s> <s xml:id="echoid-s16590" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div645" type="section" level="1" n="645"> <head xml:id="echoid-head766" xml:space="preserve">EXPERIMENTUM CCXXX.</head> <p> <s xml:id="echoid-s16591" xml:space="preserve">Aliud parallelopipedum Fraxini 18 pollices longum, cujus late-<lb/>ra erant 0, 42 pollic. </s> <s xml:id="echoid-s16592" xml:space="preserve">& </s> <s xml:id="echoid-s16593" xml:space="preserve">0, 24 pollic fractum fuit a libris 30.</s> <s xml:id="echoid-s16594" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div646" type="section" level="1" n="646"> <head xml:id="echoid-head767" xml:space="preserve">EXPERIMENTUM CCXXXI.</head> <p> <s xml:id="echoid-s16595" xml:space="preserve">Idem parallelopipedum 11 {1/2} pollic. </s> <s xml:id="echoid-s16596" xml:space="preserve">longum frangebatur a libris <lb/>74 impoſitis.</s> <s xml:id="echoid-s16597" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div647" type="section" level="1" n="647"> <head xml:id="echoid-head768" xml:space="preserve">EXPERIMENTUM CCXXXII.</head> <p> <s xml:id="echoid-s16598" xml:space="preserve">Aliud parallelopipedum Fraxini 11 {1/2} pollic longum, cujus latera <lb/>erant 0, 22 pollic. </s> <s xml:id="echoid-s16599" xml:space="preserve">& </s> <s xml:id="echoid-s16600" xml:space="preserve">0, 52 pollic. </s> <s xml:id="echoid-s16601" xml:space="preserve">fractum fuit a libris 80.</s> <s xml:id="echoid-s16602" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div648" type="section" level="1" n="648"> <head xml:id="echoid-head769" xml:space="preserve">EXPERIMENTUM CCXXXIII.</head> <p> <s xml:id="echoid-s16603" xml:space="preserve">Parallelopipedum Tiliæ 12 pollices longum, cujus latera erant <lb/>0, 35 pollic. </s> <s xml:id="echoid-s16604" xml:space="preserve">& </s> <s xml:id="echoid-s16605" xml:space="preserve">0, 25 pollic. </s> <s xml:id="echoid-s16606" xml:space="preserve">fractum fuit a libris 45.</s> <s xml:id="echoid-s16607" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div649" type="section" level="1" n="649"> <head xml:id="echoid-head770" xml:space="preserve">EXPERIMENTUM CCXXXIV.</head> <p> <s xml:id="echoid-s16608" xml:space="preserve">Idem parallelopipedum 11 pollices longum, fractum fuit a libris <lb/>54. </s> <s xml:id="echoid-s16609" xml:space="preserve">impoſitis.</s> <s xml:id="echoid-s16610" xml:space="preserve"/> </p> <pb o="657" file="0673" n="674" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div650" type="section" level="1" n="650"> <head xml:id="echoid-head771" xml:space="preserve">EXPERIMENTUM CCXXXV.</head> <p> <s xml:id="echoid-s16611" xml:space="preserve">Aliud parallelopipedum Tiliæ 12 longum pollices, cujus latera <lb/>erant 0, 44 pollic. </s> <s xml:id="echoid-s16612" xml:space="preserve">& </s> <s xml:id="echoid-s16613" xml:space="preserve">0, 25 pollic. </s> <s xml:id="echoid-s16614" xml:space="preserve">fractum fuit a libris 48.</s> <s xml:id="echoid-s16615" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div651" type="section" level="1" n="651"> <head xml:id="echoid-head772" xml:space="preserve">EXPERIMENTUM CCXXXVI.</head> <p> <s xml:id="echoid-s16616" xml:space="preserve">Idem longum 11 pollices fractum fuit a libris 48.</s> <s xml:id="echoid-s16617" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div652" type="section" level="1" n="652"> <head xml:id="echoid-head773" xml:space="preserve">EXPERIMENTUM CCXXXVII.</head> <p> <s xml:id="echoid-s16618" xml:space="preserve">Aliud parallelopipedum Tiliæ longum 12 pollices, cujus latera <lb/>erant 0, 25 pollic. </s> <s xml:id="echoid-s16619" xml:space="preserve">& </s> <s xml:id="echoid-s16620" xml:space="preserve">0, 50 pollic. </s> <s xml:id="echoid-s16621" xml:space="preserve">fractum fuit a libris 68.</s> <s xml:id="echoid-s16622" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div653" type="section" level="1" n="653"> <head xml:id="echoid-head774" xml:space="preserve">EXPERIMENTUM CCXXXVIII.</head> <p> <s xml:id="echoid-s16623" xml:space="preserve">Idem parallelopipedum 11 pollices longum, rumpebatur a li-<lb/>bris 80.</s> <s xml:id="echoid-s16624" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div654" type="section" level="1" n="654"> <head xml:id="echoid-head775" xml:space="preserve">EXPERIMENTUM CCXXXIX.</head> <p> <s xml:id="echoid-s16625" xml:space="preserve">Parallelopipedum Piceæ longum 12 pollices, cujus latera erant <lb/>0, 25 pollic. </s> <s xml:id="echoid-s16626" xml:space="preserve">& </s> <s xml:id="echoid-s16627" xml:space="preserve">0, 42 pollic. </s> <s xml:id="echoid-s16628" xml:space="preserve">fractum fuit a libris 79.</s> <s xml:id="echoid-s16629" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div655" type="section" level="1" n="655"> <head xml:id="echoid-head776" xml:space="preserve">EXPERIMENTUM CCXL.</head> <p> <s xml:id="echoid-s16630" xml:space="preserve">Idem longum 10 pollices frangebatur a libris 83.</s> <s xml:id="echoid-s16631" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div656" type="section" level="1" n="656"> <head xml:id="echoid-head777" xml:space="preserve">EXPERIMENTUM CCXLI.</head> <p> <s xml:id="echoid-s16632" xml:space="preserve">Aliud parallelopidedum Piceæ longum 12 pollices, cujus latera <lb/>erant 0, 34 poll. </s> <s xml:id="echoid-s16633" xml:space="preserve">fractum fuit a libris 136.</s> <s xml:id="echoid-s16634" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div657" type="section" level="1" n="657"> <head xml:id="echoid-head778" xml:space="preserve">EXPERIMENTUM CCXLII.</head> <p> <s xml:id="echoid-s16635" xml:space="preserve">Patallelopipedum Ulmi longum 11 pollices, cujus latera erant <pb o="658" file="0674" n="675" rhead="INTRODUCTIO AD COHÆRENTIAM"/> 0, 25 pollic. </s> <s xml:id="echoid-s16636" xml:space="preserve">& </s> <s xml:id="echoid-s16637" xml:space="preserve">0, 35 pollic. </s> <s xml:id="echoid-s16638" xml:space="preserve">fractum fuit a libris 20.</s> <s xml:id="echoid-s16639" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div658" type="section" level="1" n="658"> <head xml:id="echoid-head779" xml:space="preserve">EXPERIMENTUM CCXLIII.</head> <p> <s xml:id="echoid-s16640" xml:space="preserve">Parallelopipedum Tiliæ 12 pollic. </s> <s xml:id="echoid-s16641" xml:space="preserve">longum, cujus latera erant <lb/>0, 34 poll fractum fuit a libris 81.</s> <s xml:id="echoid-s16642" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16643" xml:space="preserve">Hæc ſunt prima Experimenta in hac doctrina firmitatis corpo-<lb/>rum compreſſorum, quæ utinam â poſteris promoveatur examinan-<lb/>do Lapidum, laterum, metallorum, oſſium, aliorumque corpo-<lb/>rum Cohærentiam! nam utilitatem generi humano afferet inſignem; <lb/></s> <s xml:id="echoid-s16644" xml:space="preserve">nec univerſales dari Regulæ, nec demonſtrari poterunt univerſales <lb/>eſſe, prius quam innumera Experimenta inſtituta ſint: </s> <s xml:id="echoid-s16645" xml:space="preserve">Ex noſtris <lb/>nonnullas ſequelas deducemus, quæ in iis Lignis veræ ſunt, an <lb/>quoque in aliis, ignoro?</s> <s xml:id="echoid-s16646" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16647" xml:space="preserve">1°. </s> <s xml:id="echoid-s16648" xml:space="preserve">Sequitur ex omnibus Experimentis hujus Capitis, Lignum per-<lb/>pendiculariter ad horizontem erectum eo minus ſibi impoſiti pon-<lb/>deris geſtare poſſe, quo longius exiſtit: </s> <s xml:id="echoid-s16649" xml:space="preserve">unde in omni ſimili caſu, <lb/>in quo premitur ſecundum longitudinem a cauſâ quâcunque ſem-<lb/>per eo minus reſiſtet viribus prementibus, quo longius erit.</s> <s xml:id="echoid-s16650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16651" xml:space="preserve">2°. </s> <s xml:id="echoid-s16652" xml:space="preserve">Neque eſt Lignum immenſi roboris ad onera ſuſtinenda. </s> <s xml:id="echoid-s16653" xml:space="preserve">quam-<lb/>vis ſit rectiſſimum, atque deorſum perpendiculariter prematur ſe-<lb/>cundum fibrarum ſuarum decurſum, cum omnia parallelopipeda <lb/>examinata vi minori, quam libris 200 diffracta fuerunt.</s> <s xml:id="echoid-s16654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16655" xml:space="preserve">Sed paulo propius Cohærentia horum corporum examinari ad-<lb/>huc poterit, & </s> <s xml:id="echoid-s16656" xml:space="preserve">explorari quænam ſit proportio reſiſtentiæ poſito <lb/>eodem Ligno diverſæ longitudinis, ſed ejuſdem craſſitiei: </s> <s xml:id="echoid-s16657" xml:space="preserve">tum quæ-<lb/>nam detur poſitis craſſitiebus & </s> <s xml:id="echoid-s16658" xml:space="preserve">longitudinibus diverſis.</s> <s xml:id="echoid-s16659" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div659" type="section" level="1" n="659"> <head xml:id="echoid-head780" xml:space="preserve">PROPOSITIO CXVIII.</head> <p style="it"> <s xml:id="echoid-s16660" xml:space="preserve">Vires reſiſtentiæ Lignorum ejuſdem craſſitiei, ſed diverſæ lon-<lb/>gitudinis, perpendiculariter ad horizontem erectorum & </s> <s xml:id="echoid-s16661" xml:space="preserve">a ponde-<lb/>ribus directe impoſitis æquabiliter deorſum preſſorum, ſunt proxi-<lb/>me in ratione duplicatâ inverſa longitudinum.</s> <s xml:id="echoid-s16662" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16663" xml:space="preserve">Nam parallelopipedum Quercicum Experimenti CCXXII.</s> <s xml:id="echoid-s16664" xml:space="preserve">, 18 <lb/>pollices longum fractum fuit a libris 23. </s> <s xml:id="echoid-s16665" xml:space="preserve">idem parallelopipedum <pb o="659" file="0675" n="676" rhead="CORPORUM FIRMORUM."/> Experimenti CCXXIII, longum 9 pollices fractum fuit a libris 92. <lb/></s> <s xml:id="echoid-s16666" xml:space="preserve">quadratum longitudinis 18 eſt 324. </s> <s xml:id="echoid-s16667" xml:space="preserve">& </s> <s xml:id="echoid-s16668" xml:space="preserve">longitudinis 9, eſt 81. </s> <s xml:id="echoid-s16669" xml:space="preserve">ſunt <lb/>vero 23, 92:</s> <s xml:id="echoid-s16670" xml:space="preserve">: 81, 324. </s> <s xml:id="echoid-s16671" xml:space="preserve">ſed pondera frangentia ſunt æqualia reſi-<lb/>ſtentiis lignorum, adeoque ſunt reſiſtentiæ in ratione duplicata in-<lb/>verſa longitudinum; </s> <s xml:id="echoid-s16672" xml:space="preserve">quæ proportio tamen in aliis Experimentis <lb/>etiam demonſtranda erit: </s> <s xml:id="echoid-s16673" xml:space="preserve">In Experimento CCXXIV. </s> <s xml:id="echoid-s16674" xml:space="preserve">idem paral-<lb/>lelopipedum 8 longum pollices fractum fuit a libris 118, in hoc ta-<lb/>men Cohærentia paulo major, quam in memorata proportione, <lb/>obſervatur; </s> <s xml:id="echoid-s16675" xml:space="preserve">quod fieri facile poteſt ab inæquali firmitate Ligni, <lb/>quæ ſemper laxitatem quandam Phyſicam, non rigorem Mathema-<lb/>ticum poſtulat: </s> <s xml:id="echoid-s16676" xml:space="preserve">nam comparando Cohærentiam in longitudine 18 <lb/>pollic. </s> <s xml:id="echoid-s16677" xml:space="preserve">cum ea ſub longitudine 8 pollic. </s> <s xml:id="echoid-s16678" xml:space="preserve">datur proportio uti 7452 ad <lb/>7552. </s> <s xml:id="echoid-s16679" xml:space="preserve">ordinando enim quantitates ſecundum proportionem inver-<lb/>ſam quadratorum & </s> <s xml:id="echoid-s16680" xml:space="preserve">multiplicando extremos medioſque terminos <lb/>per ſe, memorata prodeunt producta. </s> <s xml:id="echoid-s16681" xml:space="preserve">23. </s> <s xml:id="echoid-s16682" xml:space="preserve">118:</s> <s xml:id="echoid-s16683" xml:space="preserve">: 64. </s> <s xml:id="echoid-s16684" xml:space="preserve">324 nam eſt <lb/>23 X 324 = 7452 & </s> <s xml:id="echoid-s16685" xml:space="preserve">118 X 64 = 7552. </s> <s xml:id="echoid-s16686" xml:space="preserve">Alia tamen Experimen-<lb/>ta cum proportione aſſignata melius conveniunt: </s> <s xml:id="echoid-s16687" xml:space="preserve">nam parallelopi-<lb/>pedum Fraxini in Experimento CCXXVI. </s> <s xml:id="echoid-s16688" xml:space="preserve">longum 18 pollices fra-<lb/>ctum fuit a libris 15. </s> <s xml:id="echoid-s16689" xml:space="preserve">idem parallelopipedum 6 pollices longum in <lb/>Experimento CCXXVII. </s> <s xml:id="echoid-s16690" xml:space="preserve">fractum fuit a libris 132. </s> <s xml:id="echoid-s16691" xml:space="preserve">ſi capiantur <lb/>longitudinum 18 & </s> <s xml:id="echoid-s16692" xml:space="preserve">6, quadrata, hæc ſunt 324 & </s> <s xml:id="echoid-s16693" xml:space="preserve">36, in quæ ducta <lb/>ambo pondera frangentia dant 324 X 15 = 4860. </s> <s xml:id="echoid-s16694" xml:space="preserve">& </s> <s xml:id="echoid-s16695" xml:space="preserve">132 X 36 <lb/>= 4752. </s> <s xml:id="echoid-s16696" xml:space="preserve">quæ appropinquant ſatis ad ſe invicem. </s> <s xml:id="echoid-s16697" xml:space="preserve">Ita in Experi-<lb/>mento CCXXVIII, parallelopipedum Fraxini 12 pollices longum <lb/>fractum fuit a libris 55, quadratum longitudinis 12 eſt 144 quod <lb/>ductum in 55 eſt = 7920. </s> <s xml:id="echoid-s16698" xml:space="preserve">& </s> <s xml:id="echoid-s16699" xml:space="preserve">in Experimento CCXXIX idem pa-<lb/>rallelopipedum 9 pollices longum, fractum fuit a libris 100. </s> <s xml:id="echoid-s16700" xml:space="preserve">ducen-<lb/>do quadratum longitudinis 9 pollicum in 100, habetur 8100 quod <lb/>productum iterum appropinquat ad præcedentem numerum 7920.</s> <s xml:id="echoid-s16701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16702" xml:space="preserve">In Experimento CCXXX. </s> <s xml:id="echoid-s16703" xml:space="preserve">parallelopipedum 18 pollices longum <lb/>fractum fuit a libris 30: </s> <s xml:id="echoid-s16704" xml:space="preserve">quadratum longitudinis ductum in 30 dat <lb/>9720: </s> <s xml:id="echoid-s16705" xml:space="preserve">ſed idem parallelopipedum in Experimento CCXXXI, lon-<lb/>gum 11 {1/2} pollic. </s> <s xml:id="echoid-s16706" xml:space="preserve">fractum eſt a libris 74, quadratum longitudinis <lb/>ductum in 74 dat 9768, quod iterum eſt proximum.</s> <s xml:id="echoid-s16707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16708" xml:space="preserve">Lignum Tiliæ deinde conſideremus in Experimento CCXXXIII. <lb/></s> <s xml:id="echoid-s16709" xml:space="preserve">parallelopipedum 12 pollices longum fractum fuit a libris 45. </s> <s xml:id="echoid-s16710" xml:space="preserve">quod <pb o="660" file="0676" n="677" rhead="INTRODUCTIO AD COHÆRENTIAM"/> pondus ductum in 144. </s> <s xml:id="echoid-s16711" xml:space="preserve">quod eſt quadratum longitudinis, dat 6480, <lb/>ſed in Experimento CCXXXIV. </s> <s xml:id="echoid-s16712" xml:space="preserve">idem parallelopipedum longum <lb/>11 pollices fractum fuit a libris 54: </s> <s xml:id="echoid-s16713" xml:space="preserve">quæ ductæ in quadratum lon-<lb/>gitudinis = 121, dant 6534. </s> <s xml:id="echoid-s16714" xml:space="preserve">quod iterum appropinquat ad propor. <lb/></s> <s xml:id="echoid-s16715" xml:space="preserve">tionem: </s> <s xml:id="echoid-s16716" xml:space="preserve">in Experimento CCXXXVII. </s> <s xml:id="echoid-s16717" xml:space="preserve">productum quadrati lon-<lb/>gitudinis per vim reſiſtentiæ 68 dat 9792. </s> <s xml:id="echoid-s16718" xml:space="preserve">& </s> <s xml:id="echoid-s16719" xml:space="preserve">in Experimento <lb/>CCXXXVIII productum quadrati longitudinis per libras 80 dat <lb/>9680, qui numeri iterum ſunt ſibi propinqui: </s> <s xml:id="echoid-s16720" xml:space="preserve">in Experimento <lb/>CCXXXIX parallelopipedum Piceæ 12 pollic. </s> <s xml:id="echoid-s16721" xml:space="preserve">longum fractum <lb/>fuit a libris 79. </s> <s xml:id="echoid-s16722" xml:space="preserve">quadratum longitudinis in reſiſtentiam ductum dat <lb/>11376. </s> <s xml:id="echoid-s16723" xml:space="preserve">idem modo 10 pollices longum fractumque a libris 83, dat <lb/>pro producto ex quadrato longitudinis per reſiſtentiam 8300, ubi <lb/>aberratio eſt notabilis, an hæc in Picea ſemper erit, an vero alii <lb/>proportioni auſcultabit, nondum mihi conſtat, id ex pluribus Ex-<lb/>perimentis deducendum foret. </s> <s xml:id="echoid-s16724" xml:space="preserve">Reſat ut daretur demonſtratio, <lb/>quare hæc ligna reſiſtant in ratione inverſa duplicata longitudinum, <lb/>quam nondum eruere potui.</s> <s xml:id="echoid-s16725" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div660" type="section" level="1" n="660"> <head xml:id="echoid-head781" xml:space="preserve">PROPOSITIO CXIX.</head> <p style="it"> <s xml:id="echoid-s16726" xml:space="preserve">Parallelopipeda ejusdem Ligni, quoad longitudinem & </s> <s xml:id="echoid-s16727" xml:space="preserve">craſſitiem <lb/>diverſa, preſſa ſecundum longitudinem, exercent vires reſiſtentiæ, <lb/>quæ ſuni in ratione inverſa duplicata longitudinum, in ratione <lb/>ſimplici craſſitiei lateris, quod non inflectitur, & </s> <s xml:id="echoid-s16728" xml:space="preserve">in ratione du-<lb/>plicata craſſitiei lateris, quod inflectitur.</s> <s xml:id="echoid-s16729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16730" xml:space="preserve">Patebit hoc ex comparatis inter ſe Experimentis CCXXII & </s> <s xml:id="echoid-s16731" xml:space="preserve"><lb/>CCXXV: </s> <s xml:id="echoid-s16732" xml:space="preserve">nam in Exper. </s> <s xml:id="echoid-s16733" xml:space="preserve">CCXXII parallelopipedum Quercicum <lb/>18 pollices longum, cujus ſingula latera erant 0, 23 pollic. </s> <s xml:id="echoid-s16734" xml:space="preserve">ſuſtinuit <lb/>libras 23. </s> <s xml:id="echoid-s16735" xml:space="preserve">in Exper. </s> <s xml:id="echoid-s16736" xml:space="preserve">CCXXV. </s> <s xml:id="echoid-s16737" xml:space="preserve">parallelopipedum 12 pollices lon-<lb/>gum, cujus ſingula latera ſunt 0, 35 pollic. </s> <s xml:id="echoid-s16738" xml:space="preserve">ſuſtinuit libras 185. </s> <s xml:id="echoid-s16739" xml:space="preserve">ut <lb/>igitur pateat Propoſitio, primum quæramus quantum reſiſtentiæ <lb/>habuiſſet parallelopipedum Experimenti CCXXII, ſi non fuiſſet <lb/>18 pollic. </s> <s xml:id="echoid-s16740" xml:space="preserve">ſed tantum 12 pollicum, quæ eſt longitudo Ligni ex <lb/>Experimento CCXXV. </s> <s xml:id="echoid-s16741" xml:space="preserve">quia ſecundum Propoſitionem præceden-<lb/>tem reſiſtentia ejuſdem parallelopipedi eſt in ratione duplicata in-<lb/>verſa longitudinis, erit 144, quadratum longitudinis 12 pollic.</s> <s xml:id="echoid-s16742" xml:space="preserve">, ad <pb o="661" file="0677" n="678" rhead="CORPORUM FIRMORUM."/> 324, quadratum longitudinis 18 pollic.</s> <s xml:id="echoid-s16743" xml:space="preserve">, ita reſiſtentia 23 ad 51 {1/4} libr. <lb/></s> <s xml:id="echoid-s16744" xml:space="preserve">adeoque parallelopipedum Experimenti CCXXII modo 12 longum <lb/>pollices geſtare poſſet 51 {3/4} libr.</s> <s xml:id="echoid-s16745" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16746" xml:space="preserve">Deinde quæratur quantum foret parallelopipedi, cujus unum <lb/>latus eſt o, 35 pollic. </s> <s xml:id="echoid-s16747" xml:space="preserve">cum alterum, cujus latus eſt o, 23 pollic. </s> <s xml:id="echoid-s16748" xml:space="preserve">& </s> <s xml:id="echoid-s16749" xml:space="preserve"><lb/>æque longum, ſuſtineat libras 51 {3/4}. </s> <s xml:id="echoid-s16750" xml:space="preserve">& </s> <s xml:id="echoid-s16751" xml:space="preserve">ſit hoc latus, quod non infle-<lb/>ctitur, etiamſi moveatur in eodem plano, in quo ante extitit; </s> <s xml:id="echoid-s16752" xml:space="preserve">quia <lb/>alterum latus incurvatur, debet reſiſtentia hæc neceſſario eſſe in <lb/>ratione magnitudinis lateris, hoc eſt uti 23 ad 35. </s> <s xml:id="echoid-s16753" xml:space="preserve">adeoque 23, <lb/>35:</s> <s xml:id="echoid-s16754" xml:space="preserve">: 51 {3/4}. </s> <s xml:id="echoid-s16755" xml:space="preserve">78 {2/3} proxime, idcirco parallelopipedum 12 longum pol-<lb/>lices, cujus unum latus o, 23 pollic. </s> <s xml:id="echoid-s16756" xml:space="preserve">alterum o, 35 pollic. </s> <s xml:id="echoid-s16757" xml:space="preserve">poſſet ge-<lb/>ſtare libras 78 {2/3}.</s> <s xml:id="echoid-s16758" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16759" xml:space="preserve">Sed nunc pervenimus ad latera parallelopipedorum, quæ incur-<lb/>vantur; </s> <s xml:id="echoid-s16760" xml:space="preserve">hæc inflexa reſiſtunt eodem modo ac ſolida inſlexa, quæ <lb/>examina vimus in Cap. </s> <s xml:id="echoid-s16761" xml:space="preserve">V, VI, VII. </s> <s xml:id="echoid-s16762" xml:space="preserve">quorum reſiſtentia demonſtrata <lb/>fuit in ratione duplicata craſſitiei, quæ inſlectitur. </s> <s xml:id="echoid-s16763" xml:space="preserve">Latera pa-<lb/>rallelopipedorum ſunt, o, 23 & </s> <s xml:id="echoid-s16764" xml:space="preserve">o, 35 poll. </s> <s xml:id="echoid-s16765" xml:space="preserve">quorum quadrata ſunt <lb/>529 & </s> <s xml:id="echoid-s16766" xml:space="preserve">1225, quæratur ergo robur proportionale ultimo quadrato: <lb/></s> <s xml:id="echoid-s16767" xml:space="preserve">529. </s> <s xml:id="echoid-s16768" xml:space="preserve">1225:</s> <s xml:id="echoid-s16769" xml:space="preserve">: 78 {2/3}. </s> <s xml:id="echoid-s16770" xml:space="preserve">182 cum fractione: </s> <s xml:id="echoid-s16771" xml:space="preserve">debuiſſet igitur parallelopipe-<lb/>dum Experimenti CCXXV ferre pondus librar. </s> <s xml:id="echoid-s16772" xml:space="preserve">182. </s> <s xml:id="echoid-s16773" xml:space="preserve">ipſum vero <lb/>Experimentum dedit libras 185. </s> <s xml:id="echoid-s16774" xml:space="preserve">quod pondus cum calculo accura-<lb/>te ſatis congruit.</s> <s xml:id="echoid-s16775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16776" xml:space="preserve">Ut magis confirmemur hanc Propoſitionem eſſe veram, exami-<lb/>nemus reſiſtentias, quas parallelopipeda Tiliæ in Experimentis <lb/>CCXXXIII & </s> <s xml:id="echoid-s16777" xml:space="preserve">CCXLIII exhibuerunt. </s> <s xml:id="echoid-s16778" xml:space="preserve">quæ ambo æque longa fue-<lb/>runt, ſed primum habuit laterum craſſities o, 25: </s> <s xml:id="echoid-s16779" xml:space="preserve">o, 35 poll. </s> <s xml:id="echoid-s16780" xml:space="preserve">alte-<lb/>rum habuit latera o, 34 pollic. </s> <s xml:id="echoid-s16781" xml:space="preserve">Comparemus nunc inter ſe latera, <lb/>quæ non inflectuntur, quorum reſiſtentia eſt in ratione ſimplici <lb/>craſitiei, hæc latera ſunt 35, 34. </s> <s xml:id="echoid-s16782" xml:space="preserve">adeoque ponantur in proportio-<lb/>35, 34:</s> <s xml:id="echoid-s16783" xml:space="preserve">: libr. </s> <s xml:id="echoid-s16784" xml:space="preserve">45, libr. </s> <s xml:id="echoid-s16785" xml:space="preserve">43 {5/7}. </s> <s xml:id="echoid-s16786" xml:space="preserve">deinde comparentur inter ſe reſiſten-<lb/>tiæ laterum, quæ inflectuntur, quæ ſunt in ratione duplicata craſ-<lb/>ſitierum; </s> <s xml:id="echoid-s16787" xml:space="preserve">latera quæ inflectuntur ſemper ſunt tenuiſſima; </s> <s xml:id="echoid-s16788" xml:space="preserve">adeoque <lb/>25 & </s> <s xml:id="echoid-s16789" xml:space="preserve">34. </s> <s xml:id="echoid-s16790" xml:space="preserve">quorum quadrata ſunt 625 & </s> <s xml:id="echoid-s16791" xml:space="preserve">1156. </s> <s xml:id="echoid-s16792" xml:space="preserve">ordinando igitur <lb/>proportionem 625, 1156:</s> <s xml:id="echoid-s16793" xml:space="preserve">: libr. </s> <s xml:id="echoid-s16794" xml:space="preserve">43 {5/7}. </s> <s xml:id="echoid-s16795" xml:space="preserve">libr. </s> <s xml:id="echoid-s16796" xml:space="preserve">80. </s> <s xml:id="echoid-s16797" xml:space="preserve">Calculus igitur <lb/>ſuppeditat libras 80 geſtandas a parallelopipedo Experimenti <lb/>CCXLIII. </s> <s xml:id="echoid-s16798" xml:space="preserve">eventus docuit libras 81 fuiſſe ſuſtentatas, qui proinde <pb o="662" file="0678" n="679" rhead="INTRODUCTIO AD COHÆRENTIAM"/> accuratiſſime convenit cum calculo.</s> <s xml:id="echoid-s16799" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16800" xml:space="preserve">Scholion. </s> <s xml:id="echoid-s16801" xml:space="preserve">Ex his binis Propoſitionibus, tum ex Experimentis <lb/>facile a priori ſupputari poteſt, quantum oneris data Trabs dati <lb/>Ligni, perpendiculariter ſibi impoſiti geret: </s> <s xml:id="echoid-s16802" xml:space="preserve">non injucun dum erit id <lb/>aliquo exemplo illuſtraviſſe: </s> <s xml:id="echoid-s16803" xml:space="preserve">Sit igitur Trabs 30 pedes longa, ex <lb/>ligno Quercico, quadrata, nempe cujus quodlibet latus eſt 12 pol-<lb/>lic. </s> <s xml:id="echoid-s16804" xml:space="preserve">quæritur quantum ponderis ſibi impoſiti ſuſtinere poterit abſ-<lb/>que ruptura.</s> <s xml:id="echoid-s16805" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16806" xml:space="preserve">Eligatur Experimentum CCXXV pro fundamento, in quo pa-<lb/>rallelopipedum Quercicum 12 longum pollices, & </s> <s xml:id="echoid-s16807" xml:space="preserve">cujus reli-<lb/>qua latera ſunt 0, 35 pollic. </s> <s xml:id="echoid-s16808" xml:space="preserve">ſuſtinuit libras 185: </s> <s xml:id="echoid-s16809" xml:space="preserve">Suppo-<lb/>natur primum Trabs ejuſdem craſſitiei ac parallelopipedum: <lb/></s> <s xml:id="echoid-s16810" xml:space="preserve">tum foret per Propoſ. </s> <s xml:id="echoid-s16811" xml:space="preserve">CXVIII. </s> <s xml:id="echoid-s16812" xml:space="preserve">reſiſtentia contra pondus impoſitum <lb/>in ratione inverſa duplicata longitudinis; </s> <s xml:id="echoid-s16813" xml:space="preserve">longitudines ſunt inter <lb/>ſe uti 30 ad 1, horum quadrata uti 900 ad 1. </s> <s xml:id="echoid-s16814" xml:space="preserve">adeoque 900. </s> <s xml:id="echoid-s16815" xml:space="preserve">1:</s> <s xml:id="echoid-s16816" xml:space="preserve">: li-<lb/>br. </s> <s xml:id="echoid-s16817" xml:space="preserve">185. </s> <s xml:id="echoid-s16818" xml:space="preserve">libr. </s> <s xml:id="echoid-s16819" xml:space="preserve">{37/180}. </s> <s xml:id="echoid-s16820" xml:space="preserve">pondus idcirco ab hac Trabe 30 alta pedes, & </s> <s xml:id="echoid-s16821" xml:space="preserve"><lb/>craſſitiei 0, 35 pollic, geſtari tantum poſſet = {37/184} libr.</s> <s xml:id="echoid-s16822" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16823" xml:space="preserve">Comparemus nunc craſſities laterum parallelopipedi & </s> <s xml:id="echoid-s16824" xml:space="preserve">Trabis, <lb/>quæ ſint latera non inſlectenda, quorum reſiſtentia igitur eſt in ra-<lb/>tione craſſitierum: </s> <s xml:id="echoid-s16825" xml:space="preserve">craſſities ſunt 0, 35 pollic. </s> <s xml:id="echoid-s16826" xml:space="preserve">& </s> <s xml:id="echoid-s16827" xml:space="preserve">12 pollic. </s> <s xml:id="echoid-s16828" xml:space="preserve">quæ <lb/>ſunt inter ſe uti 35 ad 1200, ſive 7 ad 240. </s> <s xml:id="echoid-s16829" xml:space="preserve">atque ordinando pro-<lb/>portionem hanc 7. </s> <s xml:id="echoid-s16830" xml:space="preserve">240:</s> <s xml:id="echoid-s16831" xml:space="preserve">: libr. </s> <s xml:id="echoid-s16832" xml:space="preserve">{37/129}. </s> <s xml:id="echoid-s16833" xml:space="preserve">libr. </s> <s xml:id="echoid-s16834" xml:space="preserve">7 {1/21}, adeoque aſſer Querci-<lb/>cus 30 pedes longus, cujus unum latus foret 12 pollic. </s> <s xml:id="echoid-s16835" xml:space="preserve">alterum la-<lb/>tus o, 35 pollic. </s> <s xml:id="echoid-s16836" xml:space="preserve">tautum ferre poſſet pondus ſibi impoſitum 7 {1/21} libr.</s> <s xml:id="echoid-s16837" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16838" xml:space="preserve">Tandem comparemus craſſities laterum, quæ inflectuntur, <lb/>quorum reſiſtentia eſt in ratione duplicata craſſitierum, craſſities <lb/>ſunt inter ſe uti 7 ad 240. </s> <s xml:id="echoid-s16839" xml:space="preserve">quorum quadrata ſunt 49 & </s> <s xml:id="echoid-s16840" xml:space="preserve">57600: </s> <s xml:id="echoid-s16841" xml:space="preserve">po-<lb/>natur 49. </s> <s xml:id="echoid-s16842" xml:space="preserve">57600:</s> <s xml:id="echoid-s16843" xml:space="preserve">: libr. </s> <s xml:id="echoid-s16844" xml:space="preserve">7 {1/21}. </s> <s xml:id="echoid-s16845" xml:space="preserve">libr. </s> <s xml:id="echoid-s16846" xml:space="preserve">8284 {504/1029}. </s> <s xml:id="echoid-s16847" xml:space="preserve">adeoque omne pondus <lb/>ferendum ab hac Trabe foret 8284 librarum; </s> <s xml:id="echoid-s16848" xml:space="preserve">ut igitur maneat in-<lb/>tegra, minus oneranda foret.</s> <s xml:id="echoid-s16849" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16850" xml:space="preserve">Si eadem Trabs longitudinem 15 pedum modo habuiſſet, qua-<lb/>druplo plus ponderis geſtare poſſet, adeoque libras 33136. </s> <s xml:id="echoid-s16851" xml:space="preserve">& </s> <s xml:id="echoid-s16852" xml:space="preserve">in <lb/>longitudine 7 {1/2} pedum iterum quadruplo plus ſive 1325 44 libras. <lb/></s> <s xml:id="echoid-s16853" xml:space="preserve">Conficiuntur ſæpe poſtæ januarum ex ejuſmodi Trabe 7 {1/2} pedum <lb/>longa, pedem quadratum craſſa, quibus anterior domûs facies, <lb/>aut angulus innititur, videmus ex hoc calculo Trabem tam bre- <pb o="663" file="0679" n="680" rhead="CORPORUM FIRMORUM."/> vem memoratæque craſſitiei facile gravitatem ſibi impoſitam ferre <lb/>poſſe, cum tamen ſimul patet non eſſe Trabem erectam infiniti <lb/>roboris vel reſiſtentiæ.</s> <s xml:id="echoid-s16854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16855" xml:space="preserve">Exigeret ordo, ut nunc agerem de Cohærentia corporum cavo-<lb/>rum. </s> <s xml:id="echoid-s16856" xml:space="preserve">quæ poteſt dupliciter conſiderari, 1°. </s> <s xml:id="echoid-s16857" xml:space="preserve">quatenus corporibus <lb/>cavis vis externa applicatur. </s> <s xml:id="echoid-s16858" xml:space="preserve">2°. </s> <s xml:id="echoid-s16859" xml:space="preserve">quatenus vis interna diſtendens agit, <lb/>cui laterum Cohærentia reſiſtit: </s> <s xml:id="echoid-s16860" xml:space="preserve">Primum caſum incepit conſiderare <lb/>Galilæus, quem ſecutus fuit Parentius, hujus errores annotans; <lb/></s> <s xml:id="echoid-s16861" xml:space="preserve">in hoc negotio mihi penitus ſatisfacere nondum potui, maluique <lb/>id differre in aliud tempus, luci publicæ expoſiturus tum Experi-<lb/>menta & </s> <s xml:id="echoid-s16862" xml:space="preserve">demonſtrationes, quæ Caput ſibi poſtulant novum, cum <lb/>clariſſime omnia intellexerim. </s> <s xml:id="echoid-s16863" xml:space="preserve">Alter caſus ſpectat tuborum firmi-<lb/>tates, qui fluidis impleti, ab eorum preſſionibus extrorſum ur-<lb/>gentur: </s> <s xml:id="echoid-s16864" xml:space="preserve">de his incepit agere Mariottus in Tractat de Mouvem: </s> <s xml:id="echoid-s16865" xml:space="preserve">des <lb/>Eaux part. </s> <s xml:id="echoid-s16866" xml:space="preserve">5. </s> <s xml:id="echoid-s16867" xml:space="preserve">diſcour. </s> <s xml:id="echoid-s16868" xml:space="preserve">2. </s> <s xml:id="echoid-s16869" xml:space="preserve">tum Romerus in Diverſ Ouvrag. </s> <s xml:id="echoid-s16870" xml:space="preserve">des <lb/>Meſſieurs de L’Acad. </s> <s xml:id="echoid-s16871" xml:space="preserve">Roy. </s> <s xml:id="echoid-s16872" xml:space="preserve">pag. </s> <s xml:id="echoid-s16873" xml:space="preserve">516. </s> <s xml:id="echoid-s16874" xml:space="preserve">quorum Experimenta cum <lb/>ſufficiant, hic tantum ſequi potero, atque uno alterove confir-<lb/>mare obſervato.</s> <s xml:id="echoid-s16875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16876" xml:space="preserve">Compoſuit Mariottus Tympanum cylindricum A B X Z Tab. <lb/></s> <s xml:id="echoid-s16877" xml:space="preserve">XXVIII. </s> <s xml:id="echoid-s16878" xml:space="preserve">fig. </s> <s xml:id="echoid-s16879" xml:space="preserve">5. </s> <s xml:id="echoid-s16880" xml:space="preserve">cujus diameter baſeos & </s> <s xml:id="echoid-s16881" xml:space="preserve">altitudo erat 1 pedis, am-<lb/>bæ baſes A B, X Z erant lamellæ cupreæ, quarum craſſities fuit <lb/>{1/12} pollicis; </s> <s xml:id="echoid-s16882" xml:space="preserve">ſuperficies autem cylindrica conſtabat ex lamina ferrea, <lb/>ſtanno obducta, quæ convoluta inſe, ſtanno etiam ſibi afferruminata <lb/>fuit, ut & </s> <s xml:id="echoid-s16883" xml:space="preserve">baſi ſuperiori A B, quam X Z inferiori, atque ut melius â <lb/>ferrumine teneretur, filum ferreum annuli inſtar convolutum, <lb/>tympani ſu eriorem partem in CD ambibat: </s> <s xml:id="echoid-s16884" xml:space="preserve">medio ſuperioris ba-<lb/>ſeos A B inſertus erat tubus G F ferreus ſtanno obductus, 50 pedes <lb/>altus, atque baſi A B afferruminatus: </s> <s xml:id="echoid-s16885" xml:space="preserve">impoſita baſi X Z tribus ful-<lb/>cris, impletum fuit tympanum & </s> <s xml:id="echoid-s16886" xml:space="preserve">tubus aquâ uſque ad ſummum, <lb/>a cujus preſſione baſes A B, X Z reddebantur convexæ; </s> <s xml:id="echoid-s16887" xml:space="preserve">præterea <lb/>ferrumen ſolvebatur prope G, ad longitudinem 4 pollicum, ef-<lb/>fluente aqua per hanc rimam: </s> <s xml:id="echoid-s16888" xml:space="preserve">refecto tubo, atque iterum impleto <lb/>aquâ, baſeos inferioris XZ ferrumen ruptum fuit. </s> <s xml:id="echoid-s16889" xml:space="preserve">Deinde aliud <lb/>Tympanum fabrefieri fecit, cujus extrema concludebantur a baſibus <lb/>AB, XZ, aliquouſque ad rectum angulum circumflexis, ita ut tym-<lb/>panum ab iis caperetur, quemadmodum capſulæ ab operculo ligneo, <pb o="664" file="0680" n="681" rhead="INTRODUCTIO AD COHÆRENTIAM"/> & </s> <s xml:id="echoid-s16890" xml:space="preserve">ſimul Tubus F G productus fuit ad longitudinem 100 pedum: </s> <s xml:id="echoid-s16891" xml:space="preserve">In <lb/>quo apparatu aquâ penitus repleto, tandem a parte inferiori fiſ-<lb/>ſura oriebatur ab S verſus R, quæ tranſverſe deinde ſerpebat ab R <lb/>verſus T, ferrumine interim partes bene tenente; </s> <s xml:id="echoid-s16892" xml:space="preserve">manſerat vero <lb/>apparatus integer tubo tantum ad 80 & </s> <s xml:id="echoid-s16893" xml:space="preserve">90 pedes uſque aquâ re-<lb/>pleto.</s> <s xml:id="echoid-s16894" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16895" xml:space="preserve">Ita quidem firmitatem ferri demonſtravit Mariottus, utinam ad-<lb/>didiſſet cujuſnam craſſitiei fuiſſet, nam omne ferrum ſtanno obdu-<lb/>ctum non eſt æque craſſum: </s> <s xml:id="echoid-s16896" xml:space="preserve">quia autem aquæ ductibus potius in-<lb/>ſerviunt tubi plumbei, Experimenta cum hiſce capta erunt majoris <lb/>utilitatis.</s> <s xml:id="echoid-s16897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16898" xml:space="preserve">Confectum fuit Tympanum plumbeum, cujus diameter in me-<lb/>dio erat 1 pedis, altitudo 18 pollic. </s> <s xml:id="echoid-s16899" xml:space="preserve">ambo extrema ad ſe appropin-<lb/>quabant, ut modo diametrum 8 pollicum habuerint, quæ inſiſtebant <lb/>laminæ plumbeæ planæ: </s> <s xml:id="echoid-s16900" xml:space="preserve">ex medio ſuperioris exſurgebat tubus <lb/>plumbeus 100 pedes altus, omnis hic apparatus ferrumine conjun-<lb/>gebatur ſecum invicem, ferrumen latitudinem unius pollicis occu-<lb/>pabat, & </s> <s xml:id="echoid-s16901" xml:space="preserve">altitudinem 8 linearum: </s> <s xml:id="echoid-s16902" xml:space="preserve">craſſities plumbi componentis <lb/>Tympanum ejuſque baſis erat 2 {1/2} linearum: </s> <s xml:id="echoid-s16903" xml:space="preserve">apparatus hic impletus <lb/>aqua uſque ad 100 pedes manſit integer, baſi tamen ſuperiori & </s> <s xml:id="echoid-s16904" xml:space="preserve"><lb/>inferiori ſe incurvante ad altitudinem {1/2} pollicis; </s> <s xml:id="echoid-s16905" xml:space="preserve">tum medium <lb/>Tympani lima abraſum fuit ad altitudinem circiter 6 pollicum & </s> <s xml:id="echoid-s16906" xml:space="preserve"><lb/>ad latitudinem 4 pollicum, craſſitie plumbi reducta ad 1 lineam, <lb/>vel paulo minus, oriebatur inflatio, findebatur plumbum ad lon-<lb/>gitudinem 3 pollicum, omni effluente per fiſſuram aqua: </s> <s xml:id="echoid-s16907" xml:space="preserve">adeoque <lb/>plumbum craſſitiei 2 {1/2} linearum firmitate ſuâ pluſquam ſufficit ad <lb/>preſſionem aquæ 100 pedes altæ perferendam in tubo diametri 1 <lb/>pedis, hinc tuto ponitur craſſities {2/10} pollicis ſufficientis firmitatis. <lb/></s> <s xml:id="echoid-s16908" xml:space="preserve">Romerus memorat in Experimento Verſalleano Tubum plumbeum <lb/>diametri 16 pollicum, craſſitiei 6 {1/3} linearum, altitudinis 50 pedum <lb/>ſufficientem firmitatem habuiſſe ad aquæ preſſioni reſiſtendum, <lb/>quod mirum non eſt, nam ſecundum Experimentum Mariotti mo-<lb/>do allatum, craſſities 3 {1/3} linearum ſufficeret, imo minor adhuc: </s> <s xml:id="echoid-s16909" xml:space="preserve"><lb/>Ex his Experimentis poterimus craſſities tuborum plumbeorum <lb/>facile determinare, ut habeant datam firmitatem, reſiſtantque <lb/>preſſionibus aquæ in data altitudine, nam demonſtratum eſt in Hy- <pb o="665" file="0681" n="682" rhead="CORPORUM FIRMORUM."/> droſtatica, 1° preſſionem aquæ lateralem eſſe perpendiculari æqualem. <lb/></s> <s xml:id="echoid-s16910" xml:space="preserve">2°. </s> <s xml:id="echoid-s16911" xml:space="preserve">aquam premere in ratione altitudinis. </s> <s xml:id="echoid-s16912" xml:space="preserve">3°. </s> <s xml:id="echoid-s16913" xml:space="preserve">aquæ preſſionem in <lb/>tubos æque longos, ſed diverſarum diametrorum, eſſe uti periphe-<lb/>rias, hoc eſt, uti diametros tuborum. </s> <s xml:id="echoid-s16914" xml:space="preserve">Quibus ſi 4°. </s> <s xml:id="echoid-s16915" xml:space="preserve">addamus, reſi-<lb/>ſtentiam metallorum eſſe in ratione duplicata craſſitierum ſuarum, <lb/>totum negotium facile deduci poteſt: </s> <s xml:id="echoid-s16916" xml:space="preserve">hoc autem ultimum an <lb/>plumbo conveniat explorare volui, cum Mariottus videatur in re-<lb/>gula prima, quam dedit, de eo dubitaſſe, etiamſi eam proportio-<lb/>nem admiſerit in materiis fragilibus, uti in ferro fuſo, aliiſque; </s> <s xml:id="echoid-s16917" xml:space="preserve">quam-<lb/>obrem cepi laminam plumbeam {9/200} poll. </s> <s xml:id="echoid-s16918" xml:space="preserve">craſſam {7/36} poll. </s> <s xml:id="echoid-s16919" xml:space="preserve">latam, cu-<lb/>jus extremitates utrimque figebantur, ſupraſcandendo duo bacula, <lb/>a ſe 7 pollicibus remora, medio imponebatur cylindrus diametri {3/4} <lb/>pollicis, cui annectebatur Lanx cum ponderibus, quorum omnium <lb/>ſumma cum evaſerat = libris 10, + unc. </s> <s xml:id="echoid-s16920" xml:space="preserve">6. </s> <s xml:id="echoid-s16921" xml:space="preserve">+ drachm. </s> <s xml:id="echoid-s16922" xml:space="preserve">2. </s> <s xml:id="echoid-s16923" xml:space="preserve">in <lb/>medio rumpebatur lamella: </s> <s xml:id="echoid-s16924" xml:space="preserve">Deinde ſumta fuit alia lamella plum-<lb/>bea, æque lata ac prior, eodem modo tenſa etiam, ſed cujus <lb/>craſſities erat {9/100} poll. </s> <s xml:id="echoid-s16925" xml:space="preserve">adeoque duplo craſſior priori erat, hæc ex <lb/>medio ſui ſuſtinuit pondus librar. </s> <s xml:id="echoid-s16926" xml:space="preserve">45. </s> <s xml:id="echoid-s16927" xml:space="preserve">adeoque fuit firmitas hujus <lb/>laminæ in ratione duplicata craſſitiei, quam proportionem Ro-<lb/>merus etiam aſſumſit, atque ex his omnibus ſequentes exſurgunt <lb/>Regulæ.</s> <s xml:id="echoid-s16928" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div661" type="section" level="1" n="661"> <head xml:id="echoid-head782" style="it" xml:space="preserve">Regula prima.</head> <p> <s xml:id="echoid-s16929" xml:space="preserve">Si manente altitudine aquæ eadem mutanda eſt tuborum diame-<lb/>ter, ut firmitas maneat, ſumenda eſt craſſities metalli in ratione <lb/>ſubduplicata diametri.</s> <s xml:id="echoid-s16930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16931" xml:space="preserve">Nam preſſio aquæ in latera tuborum æque altorum, ſed di-<lb/>verſæ diametri, eſt in diametrorum ratione, & </s> <s xml:id="echoid-s16932" xml:space="preserve">quia firmitates <lb/>metallorum ſunt in ratione duplicata craſſitierum, ſi fiant craſſi-<lb/>ties metallicæ in ratione ſubduplicata diametrorum, erunt firmita-<lb/>tes proportionales preſſionibus.</s> <s xml:id="echoid-s16933" xml:space="preserve"/> </p> <pb o="666" file="0682" n="683" rhead="INTRODUCTIO AD COHÆRENTIAM"/> </div> <div xml:id="echoid-div662" type="section" level="1" n="662"> <head xml:id="echoid-head783" style="it" xml:space="preserve">Regula Secunda.</head> <p> <s xml:id="echoid-s16934" xml:space="preserve">Si immutetur Tuborum altitudo, manente diametro, etiam <lb/>metallica craſſities requiritur in ratione ſubduplicata altitudinum, <lb/>ut maneat proportionalis firmitas.</s> <s xml:id="echoid-s16935" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div663" type="section" level="1" n="663"> <head xml:id="echoid-head784" style="it" xml:space="preserve">Regula Tertia.</head> <p> <s xml:id="echoid-s16936" xml:space="preserve">Hinc mutata Tuborum altitudine & </s> <s xml:id="echoid-s16937" xml:space="preserve">diametro, requiritur metal-<lb/>lica craſſities in ratione compoſita, ex ſubduplicatâ diametrorum <lb/>& </s> <s xml:id="echoid-s16938" xml:space="preserve">ſubduplicatâ altitudinum ratione.</s> <s xml:id="echoid-s16939" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16940" xml:space="preserve">Si igitur craſſities maxima ponatur = C. </s> <s xml:id="echoid-s16941" xml:space="preserve">minor = c. </s> <s xml:id="echoid-s16942" xml:space="preserve">altitudo <lb/>maxim<emph style="super">a</emph> = A, minor = a. </s> <s xml:id="echoid-s16943" xml:space="preserve">diameter maxima = D minor = d. </s> <s xml:id="echoid-s16944" xml:space="preserve">erit <lb/>C. </s> <s xml:id="echoid-s16945" xml:space="preserve">c:</s> <s xml:id="echoid-s16946" xml:space="preserve">: D. </s> <s xml:id="echoid-s16947" xml:space="preserve">d. <lb/></s> <s xml:id="echoid-s16948" xml:space="preserve">& </s> <s xml:id="echoid-s16949" xml:space="preserve">C. </s> <s xml:id="echoid-s16950" xml:space="preserve">c:</s> <s xml:id="echoid-s16951" xml:space="preserve">: A. </s> <s xml:id="echoid-s16952" xml:space="preserve">a. </s> <s xml:id="echoid-s16953" xml:space="preserve"><lb/>atque multiplicando antecedentes per ſe, & </s> <s xml:id="echoid-s16954" xml:space="preserve">conſequentes fit CC, <lb/>c c:</s> <s xml:id="echoid-s16955" xml:space="preserve">: AD, a d. </s> <s xml:id="echoid-s16956" xml:space="preserve">adeoque datis A, a, D, d & </s> <s xml:id="echoid-s16957" xml:space="preserve">C. </s> <s xml:id="echoid-s16958" xml:space="preserve">cognoſcitur <lb/>quoque c. </s> <s xml:id="echoid-s16959" xml:space="preserve">craſſities invenienda:</s> <s xml:id="echoid-s16960" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16961" xml:space="preserve">Innixus Experimento Mariotti cum plumbeo Tympano facto, in <lb/>quo craſſities 0, 2 pollic. </s> <s xml:id="echoid-s16962" xml:space="preserve">retinebat aquam in tubo 100 pedes alto, <lb/>diametri 1 pedis, tum huic regulæ Tertiæ conſtruxi ſequentem Tabu-<lb/>lam, in qua poſitis Tubis diverſarum altitudinum & </s> <s xml:id="echoid-s16963" xml:space="preserve">amplitudinum <lb/>craſſities plumbi determinatur, quæ ſufficientis firmitatis erit.</s> <s xml:id="echoid-s16964" xml:space="preserve"/> </p> <pb o="667" file="0683" n="684" rhead="CORPORUM FIRMORUM."/> </div> <div xml:id="echoid-div664" type="section" level="1" n="664"> <head xml:id="echoid-head785" xml:space="preserve">TABULA</head> <p> <s xml:id="echoid-s16965" xml:space="preserve">Continens craſſities laterum Tuborum plumbeorum fon tibu <lb/>inſervientium in lineis, quæſunt {1/10} pollicis earumque decimal ibus <lb/>determinatas, ponitur tamen pollex {1/12} pedis.</s> <s xml:id="echoid-s16966" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/># # Alt. Tubor. \\ in pedib. # # # # # # # # # Diametri tuborum in pollicibus ab 1 ad 9 <lb/># 1 # 2 # 3 # 4 # 5 # 6 # 7 # 8 # 9 <lb/>10 # 0,5905 # 0,7186 # 0,7952 # 0,8304 # 0,9036 # 0,9457 # 0,9829 # 1,0163 # 1,0466 <lb/>15 # 0,6687 # 0,7953 # 0,8361 # 0,9457 # 0,9858 # 1,0466 # 1,0877 # 1,1247 # 1,1582 <lb/>20 # 0,7186 # 0,8545 # 0,9457 # 1,0163 # 1,0745 # 1,1287 # 1,1688 # 1,2084 # 1,2446 <lb/>25 # 0,7598 # 0,9036 # 1,0000 # 1,0745 # 1,1362 # 1,1891 # 1,2359 # 1,2777 # 1,3161 <lb/>30 # 0,7953 # 0,9457 # 1,0467 # 1,1247 # 1,1892 # 1,2449 # 1,2934 # 1,3373 # 1,3774 <lb/>35 # 0,8060 # 0,9829 # 1,0877 # 1,1688 # 1,2359 # 1,2935 # 1,3444 # 1,3900 # 1,4315 <lb/>40 # 0,8545 # 1,0163 # 1,1247 # 1,2085 # 1,2778 # 1,3374 # 1,3900 # 1,4372 # 1,4802 <lb/>45 # 0,8801 # 1,0467 # 1,1582 # 1,2163 # 1,3160 # 1,3773 # 1,4315 # 1,4853 # 1,5204 <lb/>50 # 0,9036 # 1,0745 # 1,1892 # 1,2778 # 1,3514 # 1,4142 # 1,4698 # 1,5195 # 1,5650 <lb/>55 # 0,9253 # 1,1004 # 1,2178 # 1,3087 # 1,3837 # 1,4483 # 1,5052 # 1,5560 # 1,6028 <lb/>60 # 0,9457 # 1,1246 # 1,2446 # 1,3374 # 1,4142 # 1,4801 # 1,5383 # 1,5919 # 1,6380 <lb/>65 # 0,9648 # 1,1474 # 1,2831 # 1,3645 # 1,4437 # 1,5101 # 1,5693 # 1,6226 # 1,6712 <lb/>70 # 0,9829 # 1,1688 # 1,2935 # 1,3900 # 1,4690 # 1,5383 # 1,5987 # 1,6530 # 1,7024 <lb/>75 # 1,0000 # 1,1892 # 1,3160 # 1,4142 # 1,4953 # 1,5650 # 1,6265 # 1,6818 # 1,7320 <lb/>80 # 1,0163 # 1,2085 # 1,3374 # 1,4372 # 1,5196 # 1,5904 # 1,6530 # 1,7091 # 1,7600 <lb/>85 # 1,0315 # 1,2270 # 1,3582 # 1,4659 # 1,5428 # 1,6150 # 1,6783 # 1,7312 # 1,7871 <lb/>90 # 1,0467 # 1,2446 # 1,3774 # 1,4802 # 1,5650 # 1,6380 # 1,7022 # 1,7602 # 1,8128 <lb/>95 # 1,0633 # 1,2615 # 1,3961 # 1,5003 # 1,5863 # 1,6603 # 1,7215 # 1,7841 # 1,8417 <lb/>100 # 1,0745 # 1,2799 # 1,4142 # 1,5196 # 1,6068 # 16817 # 1,7478 # 1,8080 # 1,8612 <lb/></note> <p> <s xml:id="echoid-s16967" xml:space="preserve">Interim notatum velim plumbum fuſum nec tuſum malleo, eſſe <lb/>aliquando admodum poroſum, unde ſi canales è plumbo fuſo ca-<lb/>perentur, craſſiores eſſe deberent, quam Tabula indicat, ſed <lb/>facillime tubi conſtruuntur ex plumbo plano, vi mallei circumpli-<lb/>cato, tumque pori ſimul occluduntur:</s> <s xml:id="echoid-s16968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16969" xml:space="preserve">Quoniam in Cap. </s> <s xml:id="echoid-s16970" xml:space="preserve">III. </s> <s xml:id="echoid-s16971" xml:space="preserve">examinavimus cohærentias metallorum, <pb o="668" file="0684" n="685" rhead="INTRODUCTIO AD COHÆRENTIAM"/> facile determinari poterit, quanta requiratur craſſities tubi con-<lb/>ſtruendi ex ferro aut cupro, quæ datæ diametri & </s> <s xml:id="echoid-s16972" xml:space="preserve">longitudinis ſuf-<lb/>ficit reſiſtendæ preſſioni aquæ.</s> <s xml:id="echoid-s16973" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div665" type="section" level="1" n="665"> <head xml:id="echoid-head786" xml:space="preserve">CAPUT DECIMUM.</head> <head xml:id="echoid-head787" style="it" xml:space="preserve">Tentamen de corporum Duritie.</head> <p> <s xml:id="echoid-s16974" xml:space="preserve">Si doctrina Cohærentiæ firmorum parum huc uſque cognita ſit, <lb/>eſt profecto Durities multo minus adhuc a mortalibus explo-<lb/>rata; </s> <s xml:id="echoid-s16975" xml:space="preserve">quod prima fronte magis mirandum, quam hoc Thema cum <lb/>curâ excutienti, apparebit, graviſſimis & </s> <s xml:id="echoid-s16976" xml:space="preserve">inſolubilibus difficulta-<lb/>tibus ſeſe perpetuo offerentibus: </s> <s xml:id="echoid-s16977" xml:space="preserve">quamobrem nonnulla, Duritiem <lb/>ſpectantia annotans, nequaquam ab imis fundamentis eam aggreſ-<lb/>ſus, appellavi modo hoc caput Tentamen de corporum duritie.</s> <s xml:id="echoid-s16978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s16979" xml:space="preserve">Dura vocamus, quorum partes adeo firme ſecum cohærent, ut <lb/>non niſi vi, quæ magna nobis videtur, a ſe mutuo avelli queant: <lb/></s> <s xml:id="echoid-s16980" xml:space="preserve">Mollium partes viribus minoribus cedunt ſeparanturque: </s> <s xml:id="echoid-s16981" xml:space="preserve">Inter duriſ-<lb/>ſima ponuntur adamas, gemmæ pretioſæ pellucidæque, ſilices: </s> <s xml:id="echoid-s16982" xml:space="preserve"><lb/>minus dura ſunt vitrum, plurimi lapides, chalybs, metallaque non-<lb/>nulla: </s> <s xml:id="echoid-s16983" xml:space="preserve">Mollia ſunt ſericum, partes membranaceæ animalium, <lb/>cannabini funes, & </s> <s xml:id="echoid-s16984" xml:space="preserve">innumera alia: </s> <s xml:id="echoid-s16985" xml:space="preserve">Quoniam igitur durorum par-<lb/>tes fortius quam corporum mollium cohærent, nonne videtur, <lb/>maſſam æque gravem, aut æque craſſam corporis duri firmiorem <lb/>fore quam mollioris maſſa eſt, eodem explorata modo? </s> <s xml:id="echoid-s16986" xml:space="preserve">ita ratioci-<lb/>nium ſuaderet, verum id non perpetuo obtinere experientia ſug-<lb/>gerit, paradoxo hic latente: </s> <s xml:id="echoid-s16987" xml:space="preserve">Vitrum exemplo inſerviat, quod du-<lb/>ritie inſigni donatum, & </s> <s xml:id="echoid-s16988" xml:space="preserve">cujus partes ſecum valde cohærentes, etiam <lb/>ſe fortiter attrahunt, maſſamque cohærentem componere debe-<lb/>bunt: </s> <s xml:id="echoid-s16989" xml:space="preserve">Sericum, Chordæ ex animalium inteſtinis factæ, funis can-<lb/>nabinus mollia ſunt corpora vitri reſpectu; </s> <s xml:id="echoid-s16990" xml:space="preserve">ſi igitur ex vitro at-<lb/>que ex Serico, chordis, cannabe. </s> <s xml:id="echoid-s16991" xml:space="preserve">cylindri æque craſſi formen-<lb/>tur, qui ſecundum longitudinem tracti rumpantur; </s> <s xml:id="echoid-s16992" xml:space="preserve">quis horum <lb/>maxime quis minime, cohærebit? </s> <s xml:id="echoid-s16993" xml:space="preserve">fortiſſimum videtur fore vitrum, <lb/>duris compoſitum ex partibus; </s> <s xml:id="echoid-s16994" xml:space="preserve">at viribus longe minoribus frangitur, <lb/>quam cannabis, chorda aut Sericum: </s> <s xml:id="echoid-s16995" xml:space="preserve">intueamur enim Experi- <pb o="669" file="0685" n="686" rhead="CORPORUM FIRMORUM."/> mentum LXXXI. </s> <s xml:id="echoid-s16996" xml:space="preserve">ex quo patet Cylindrum vitreum, diametri 0, <lb/>23 poll. </s> <s xml:id="echoid-s16997" xml:space="preserve">fractum a libris 118, aliudque diametri 0, 25 pollic ru-<lb/>ptum a libris 150: </s> <s xml:id="echoid-s16998" xml:space="preserve">ſed in Experimento LXXXVI. </s> <s xml:id="echoid-s16999" xml:space="preserve">funis cannabi-<lb/>nus circumferentiæ 0, 6 pollicum ferre potuit libris 210. </s> <s xml:id="echoid-s17000" xml:space="preserve">hujus craſ-<lb/>ſities nondum vitrum adæquabat: </s> <s xml:id="echoid-s17001" xml:space="preserve">in Experimento C chorda inte-<lb/>ſtinalis diametri 0, 0 3 pollicis tenuit libras 27. </s> <s xml:id="echoid-s17002" xml:space="preserve">ſi igitur hæc dia-<lb/>metrum 0, 23 pollicis habuiſſet, uti vitri cylindrus, fuiſſet plus-<lb/>quam ſepties major, quam proinde 50 ejuſinodi chordæ circiter <lb/>conſtituiſſent, quæ tenuiſſent pondus librarum 1350. </s> <s xml:id="echoid-s17003" xml:space="preserve">Serici Co-<lb/>hærentia non minor fuiſſet: </s> <s xml:id="echoid-s17004" xml:space="preserve">quamobrem evidentiſſimum eſt Cohæ-<lb/>rentiam maſſæ totius corpus durum componentis non ſemper ſu-<lb/>perare eam, quam mollia habent.</s> <s xml:id="echoid-s17005" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17006" xml:space="preserve">Ex hoc exemplo ſequitur, Cohærentiam lateralem partium cor-<lb/>poris duri eſſe majorem quam in molli, ſed longitudinalem ſirmi-<lb/>tatem ſuperari in duro ab ea, quam mollia nonnulla habent.</s> <s xml:id="echoid-s17007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17008" xml:space="preserve">Si Microſcopiorum ope corporum horum partes, fabricam, <lb/>ſitum, nexumque intueri liceret, ratio dari poſſet, quare hæc ita <lb/>ſe habeant, verum viſu nos hic deſtituente, non nifi conjecturis <lb/>relinqueretur locus, â quibus merito abſtinemus.</s> <s xml:id="echoid-s17009" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17010" xml:space="preserve">Cum igitur corporum durities ſit etiam Cohærentia partium, <lb/>ſed magis lateralis, quam ſecundum fibrarum longitudinem, ani <lb/>mo volutare coepi, an quantitas Duritiei non poſſet ad examen vo-<lb/>cari, talia meditanti nihil diſſicilius viſum fuit; </s> <s xml:id="echoid-s17011" xml:space="preserve">diverſiſſimis igi-<lb/>tur methodis propoſitis, rejectiſque iterum, tandem incidi in <lb/>ſequentem, quæ licet omnium viſa fuerit optima, nihilominus <lb/>plurimis obnoxia eſt difficultatibus, admodum compoſita, nec adeo <lb/>accurata ac ipſe deſideraviſſem: </s> <s xml:id="echoid-s17012" xml:space="preserve">ſi proinde Eruditis non penitus <lb/>ſatisfaciat, hi ſciant, nec eam mihi ſatisfeciſſe; </s> <s xml:id="echoid-s17013" xml:space="preserve">id tantum ex-<lb/>optans, ut melior inveniatur, atque hactenus adeo incognita du-<lb/>rities corporum in veſtigetur majori curâ.</s> <s xml:id="echoid-s17014" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17015" xml:space="preserve">Ex diverſis lignorum generibus præparata ſunt exigua parallelo-<lb/>pipeda quadrangula, æque craſſa, quorum quodlibet latus fuit 0, <lb/>15 pollicis, qualia quoque ex metallis ſunt confecta, cum duri-<lb/>ties transverſe ſuam Cohærentiam oſtendat, hæc tranſverſe eodem <lb/>cuneo diſſecanda eſſe ratus fui; </s> <s xml:id="echoid-s17016" xml:space="preserve">ictus vero mallei incidentis in cu-<lb/>neum frequentiores deſiderari, ut corpus durum ſecetur, quam <pb o="670" file="0686" n="687" rhead="INTRODUCTIO AD COHÆRENTIAM"/> molle, ictuumque numerum duritiem exhibiturum.</s> <s xml:id="echoid-s17017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17018" xml:space="preserve">Verum plurima corpora diverſa gravitate ſpecifica donantur, <lb/>nec ſub eodem volumine eandem quantitatem corpoream compre-<lb/>hendunt, adeoque cum parallelopipeda æque magna diſſecan-<lb/>tur, non eadem quantitas corporea dividitur, ſed graviorum <lb/>major, leviorum minor, unde ictuum in cuneum illapſorum quan-<lb/>titas duritiem exhibere non poterit corporum. </s> <s xml:id="echoid-s17019" xml:space="preserve">niſi dividantur per <lb/>gravitatem corporum, quotientes tum exhibebunt durities quæſi-<lb/>tas: </s> <s xml:id="echoid-s17020" xml:space="preserve">Ut ictus corporis percutientis cuneum ſemper foret æqualis, <lb/>adhibita fuit Machina percuſſoria, quam exhibet Tab. </s> <s xml:id="echoid-s17021" xml:space="preserve">XXVIII. <lb/></s> <s xml:id="echoid-s17022" xml:space="preserve">fig. </s> <s xml:id="echoid-s17023" xml:space="preserve">3, ex filo H K A ſuſpenſus fuit globus eburneus A, qui elevatus <lb/>continuo uſque ad normam exſtantem B, indeque dimiſſus, ſemper <lb/>cadebat cum eadem velocitate, iiſdemque viribus in cuneum C D. </s> <s xml:id="echoid-s17024" xml:space="preserve"><lb/>ſollicite cautum fuit, ut hujus globi centrum oſcillationis directe <lb/>ſemper percuſſerit cuneum C D; </s> <s xml:id="echoid-s17025" xml:space="preserve">erat G parallelopipedum plum-<lb/>beum 100 librarum, ut foret immobile, & </s> <s xml:id="echoid-s17026" xml:space="preserve">orbatum elaſticitate ex <lb/>ictu oriunda: </s> <s xml:id="echoid-s17027" xml:space="preserve">E F exhibet parallelopipedum tranſverſe ſecandum: </s> <s xml:id="echoid-s17028" xml:space="preserve"><lb/>C D eſt ferreus cuneus, cujus acies primo reddita fuit politiſſima, <lb/>atque inclinata planities lævigatiſſima & </s> <s xml:id="echoid-s17029" xml:space="preserve">plana: </s> <s xml:id="echoid-s17030" xml:space="preserve">manu detinui cu-<lb/>neum C D, ut eadem vi applicaretur corpori E F, nec reſiliri poſ-<lb/>ſet facto ictu, ſuftinebatur tamen inferius a plano, ut accuratiſſi-<lb/>me ab A feriretur: </s> <s xml:id="echoid-s17031" xml:space="preserve">certo ictuum numero abſoluto deprehendebam <lb/>ultimum non requiri tantum, ac priores fuerant, ad corporis in-<lb/>tegram diſciſſionem, tum globus ex minori altitudine elevatus fuit, <lb/>indeque fractiones ſurrexerunt, quæ ſimul cum numero ictuum <lb/>deprehenduntur in ſequenti Tabula: </s> <s xml:id="echoid-s17032" xml:space="preserve">bis modo contigit cunei aciem <lb/>fuiſſe acuendam, quod fieri adeo ſollicite non potuit, quin quædam <lb/>immutatio fuerit inducta ſuperficiei, impediens quominus tentamina <lb/>poſteriora cum prioribus accuratiſſime conveniant; </s> <s xml:id="echoid-s17033" xml:space="preserve">ne decipiam, <lb/>malui defectus annotare, præſtare hoc opinor, quam inani jactan-<lb/>tia ignaros fallere: </s> <s xml:id="echoid-s17034" xml:space="preserve">ecce Experimentorum eventum.</s> <s xml:id="echoid-s17035" xml:space="preserve"/> </p> <pb o="671" file="0687" n="688" rhead="CORPORUM FIRMORUM."/> <p> <s xml:id="echoid-s17036" xml:space="preserve">Tabula exhibens numerum ictuum, quibus corpora diſciſſa fue-<lb/>runt, tum gravitates Specificas & </s> <s xml:id="echoid-s17037" xml:space="preserve">durities</s> </p> <note position="right" xml:space="preserve"> <lb/># Numerus ictuum. # Gravitates ſpecificæ. # Durities. <lb/>LignumAbietis # 10,625 # 0,550 # 21,145 <lb/>Alni # 10,121 # 0,588 # 17,212 <lb/>Buxi # 42. # 1,031 # 40,737 <lb/>Ceraſi # 9,876 # 0,623 # 15,852 <lb/>Ceraſi nigri # 10,548 # 0,653 # 16,153 <lb/>Ebenum # 15,612 # 1,177 # 13,264 <lb/>Fagi # 13,596 # 0,854 # 15,920 <lb/>Fraxini # 18,750 # 0,840 # 22,321 <lb/>Granadille # 30,224 # 1,313 # 23,019 <lb/>Guajaci # 64,843 # 1,333 # 48,644 <lb/>Nucis # 20 # 0,631 # 31,695 <lb/>Oleæ # 52 # 1,482 # 35,080 <lb/>Piceæ # 10,234 # 0,525 # 19,493 <lb/>Piceæ, Gryne # 11,882 # 0,536 # 22,167 <lb/>Piri # 11 # 0,746 # 15,745 <lb/>Pomi # 11,55 # 0,781 # 14,788 <lb/>Pruni # 18,529 # 0,663 # 27,947 <lb/>Oxyacanthæ # 17. # 0,765 # 23,533 <lb/>Paarde vlys # 92. # 2,695 # 34,13 <lb/>Quercicum # 25,323 # 0,929 # 27,258 <lb/>Sakkerdane # 19. # 0,867 # 21,914 <lb/>Santali rubri # 17,289 # 1,128 # 15,327 <lb/>Suykerkiſte # 35,769 # 1,051 # 29,401 <lb/>Tiliæ # 7,065 # 0,639 # 11,057 <lb/>Ulmi # 17,293 # 0,600 # 28,821 <lb/></note> <pb o="672" file="0688" n="689" rhead="INTRODUCTIO AD COHÆRENTIAM"/> <note position="right" xml:space="preserve"> <lb/># Numerus ictuum. # Gravitates ſpecificæ. # Durities. <lb/>Metallum. Plumbum # 27 # 11,325 # 2,304 <lb/>Stannum # 35 # 7,471 # 4,550 <lb/>Argentum minoris valoris \\ Hollandici # 171 # 10,340 # 16,536 <lb/>Aurum ducator. # 240 # 18,261 # 13,142 <lb/>Cuprum rubrum # 99 # 8,784 # 11,278 <lb/>Orichalcum # 312 # 8,000 # 39, <lb/>Ferrum Suecicum # 616 # 7,645 # 80,575 <lb/>Aqua vulgaris # # 1,000 # <lb/></note> <p> <s xml:id="echoid-s17038" xml:space="preserve">Si corpora duriora Chalybe, aut æque dura exploranda forent, <lb/>prius cuneus multo durior ex aliâ materiâ conficiendus erit: </s> <s xml:id="echoid-s17039" xml:space="preserve">atta-<lb/>men dubito an corpora valde fragilia, uti vitrum & </s> <s xml:id="echoid-s17040" xml:space="preserve">ſimilia, hac <lb/>methodo exmianari poſſent, cum ſimulac aliqua vi cuneus in ipſa adi-<lb/>gatur, ſtatim in plurima diſſilient fragmenta: </s> <s xml:id="echoid-s17041" xml:space="preserve">ſed præſtantior & </s> <s xml:id="echoid-s17042" xml:space="preserve"><lb/>univerſalior methodus a poſteris quidem invenietur, monere tan-<lb/>tum voluimus, quid incognitum in doctrina Cohærentiæ corpo-<lb/>rum firmorum & </s> <s xml:id="echoid-s17043" xml:space="preserve">accuratius indagandum reſtabat.</s> <s xml:id="echoid-s17044" xml:space="preserve"/> </p> <pb o="673" file="0689" n="690"/> </div> <div xml:id="echoid-div666" type="section" level="1" n="666"> <head xml:id="echoid-head788" xml:space="preserve">EPHEMERIDES <lb/>METEOROLOGICÆ <lb/>ULTRAJECTINÆ <lb/>ANNI MDCCXXVIII.</head> <p> <s xml:id="echoid-s17045" xml:space="preserve">HIppocrates morbos Epidemicos, in Thaſo ſævientes per-<lb/>pendens, eorum origiuem a Ventis, ab Aëris varia <lb/>conſtitutione, annique tempeſtate derivavit: </s> <s xml:id="echoid-s17046" xml:space="preserve">ideo mor-<lb/>bos deſcripturus, brevem hiſtoriam præmittit Vento-<lb/>rum, qui plerumque quatuor anni tempeſtatibus ſpira-<lb/>verant; </s> <s xml:id="echoid-s17047" xml:space="preserve">tum pluviarum, earumque copiæ, ſiccitatum æſtivarum, & </s> <s xml:id="echoid-s17048" xml:space="preserve"><lb/>ardoris, tandemque Hyemalis frigoris; </s> <s xml:id="echoid-s17049" xml:space="preserve">in quibus tantam indu-<lb/>ſtriam collocavit, ut accuratius morbi intelligi poſſent, & </s> <s xml:id="echoid-s17050" xml:space="preserve">ſequen-<lb/>tibus temporibus, in ſimili Aëris temperiei præviſi evitarentur.</s> <s xml:id="echoid-s17051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17052" xml:space="preserve">Eſt profecto admodum veroſimile Epidemicorum morborum ſe-<lb/>mina in Aëre hærere, quoniam plures eodem morbo afflicti ſimul <lb/>decumbunt, eandem inſpirantes Auram, qua excluſa vel igne <lb/>aliiſve modis mutata morbus avertitur; </s> <s xml:id="echoid-s17053" xml:space="preserve">ut & </s> <s xml:id="echoid-s17054" xml:space="preserve">ab iis evitatur, qui <lb/>affectum relinquentes locum, in aliam regionem proficiſcuntur; <lb/></s> <s xml:id="echoid-s17055" xml:space="preserve">fruſtra eos in vitio ſex rerum nonnaturalium quæſiveris, cum do-<lb/>minari obſerventur morbi Epidemici in eos, qui diverſiſſimam vi-<lb/>vendi rationem ſecuti ſunt.</s> <s xml:id="echoid-s17056" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17057" xml:space="preserve">Ut igitur hoc morborum genus cognoſcatur, diligentiſſime At-<lb/>moſphæra aërea perveſtiganda eſt; </s> <s xml:id="echoid-s17058" xml:space="preserve">quam ſi exploratam habere-<lb/>mus, non diu indoles morborum ab ea pendentium lateret; </s> <s xml:id="echoid-s17059" xml:space="preserve">verum <lb/>ſperari id vix poteft, cum maſſa ſit innumera exhalationum va-<lb/>rietate imprægnata, tam earum, quæ ex corporibus in Terræ ſu-<lb/>perficie poſitis effluunt, quam quæ ex imis ejus viſceribus per per-<lb/>ſpiracula in altum elevantur, quarum miſturæ vaſorum cutaneo- <pb o="674" file="0690" n="691" rhead="EPHEMERIDES METEOROLOGICÆ"/> rum abſorbentium ope, aut ſimul cum ſaliva deglutitæ, aut in pul-<lb/>mones inſpiratæ, ſanguinem ingreſſæ miro modo mutant, ſolvunt, <lb/>aut denſiorem reddunt, vaſa ſtimulant, eaſque mutationes indu-<lb/>cunt, quæ ſanitati noxiæ, vitæ periculum ſæpe inferunt.</s> <s xml:id="echoid-s17060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17061" xml:space="preserve">Anno 1727 per omnem fere Hollandiam febris Epidemica graſ-<lb/>ſata fuit, ſæviter in plurimos debacchata cives, multosque interi-<lb/>mens; </s> <s xml:id="echoid-s17062" xml:space="preserve">quo tempore Trajectina civitas plane immunis ab eodem <lb/>manſit morbo, neque ejus loco cum aliis præter conſuetudinem <lb/>conflictavit, neque plures amiſſos luxit cives: </s> <s xml:id="echoid-s17063" xml:space="preserve">Hæc incolumitas <lb/>partim altiori urbis ſitui, ſoloque ſanitati non noxias exhalationes <lb/>emittenti, partim ſapientibus & </s> <s xml:id="echoid-s17064" xml:space="preserve">prudentiſſimis conſiliis Ampliſ-<lb/>ſimi Magiſtratus debetur, qui, ut per foſſas tam intra urbem, quam <lb/>quæ mænia ambiunt, puriſſima fluviatilis Aqua perpetuo decurre-<lb/>ret, aut bis quotidie renovaretur, ſollicite curarunt; </s> <s xml:id="echoid-s17065" xml:space="preserve">quo novus <lb/>purusque Aër ſimul in urbem invehebatur, illeque, qui ſtagnantis <lb/>aquæ ſordibus inquinaretur, unà cum Aquâ effluebat. </s> <s xml:id="echoid-s17066" xml:space="preserve">Aliquando <lb/>tamen Ægritudines præcaveri non poſſunt, ſed unà cum ventis <lb/>provectæ late per regionem ſparguntur: </s> <s xml:id="echoid-s17067" xml:space="preserve">& </s> <s xml:id="echoid-s17068" xml:space="preserve">quia in vicinia urbis <lb/>eadem febris ac in Hollandia ſævire inceperat, verebar ne quan-<lb/>doque urbem in vaderet: </s> <s xml:id="echoid-s17069" xml:space="preserve">quamobrem ſollicite operam dedi, ut <lb/>Atmoſphæræ conſtitutionem obſervarem, ventos, pluvias, exha-<lb/>latæ aquæ copiam, calorem, ejuſque cum frigore viciſſitudines <lb/>annotarem, Hippocratem tantum inæqualibus paſſibus & </s> <s xml:id="echoid-s17070" xml:space="preserve">è longin-<lb/>quo imitaturus. </s> <s xml:id="echoid-s17071" xml:space="preserve">Eſt hæc origo & </s> <s xml:id="echoid-s17072" xml:space="preserve">ſcopus noſtrarum Ephemeridum <lb/>Anno 1728 conſcriptarum; </s> <s xml:id="echoid-s17073" xml:space="preserve">interim nullus Epidemius invaſit ur-<lb/>bem, imo morbi toto anni decurſu ſolito pauciores fuerunt, nec de <lb/>tropæis frequentibus ſibi gloriam comparavit Libitina: </s> <s xml:id="echoid-s17074" xml:space="preserve">quicunque <lb/>tamen ſimul majori numero affuerunt, notavi, ut & </s> <s xml:id="echoid-s17075" xml:space="preserve">tempus invaſio-<lb/>nis, & </s> <s xml:id="echoid-s17076" xml:space="preserve">quo ceſſaverunt; </s> <s xml:id="echoid-s17077" xml:space="preserve">unde forſitan aliqua, minor ta-<lb/>men quam eſſe potuiſſet, fluet utilitas: </s> <s xml:id="echoid-s17078" xml:space="preserve">verum Phyſica tanto plus <lb/>ſibi vindicabit. </s> <s xml:id="echoid-s17079" xml:space="preserve">Quod ſi Medici exemplar hoc, ſeu potius Hippocra-<lb/>ticum, ſecuti, ejuſmodi Ephemeridibus operam in diverſis regio-<lb/>nibus navarent, Atmoſphæræ indolem citius intelligeremus, <lb/>multaque innoteſcerent melius Meteora, quorum alta huc uſque <lb/>ignorantia: </s> <s xml:id="echoid-s17080" xml:space="preserve">inſuper morborum plurium ſemina præviderentur: </s> <s xml:id="echoid-s17081" xml:space="preserve">ne-<lb/>que res magni eſt laboris, cum obſervationes ter ſingulo captæ die, <pb o="675" file="0691" n="692" rhead="ULTRAJECTINÆ ANN. MDCCXXVIII."/> intra minuti ſpatium conſcribi queant; </s> <s xml:id="echoid-s17082" xml:space="preserve">ſed operæ pretium erit <lb/>Ephemeridum Tabulam paulum clarius explicuiſſe.</s> <s xml:id="echoid-s17083" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17084" xml:space="preserve">Eſt Tabula in duodecim diviſa partes, quot menſibus conſtat <lb/>annus, horum nomina lateraliter ad ſiniſtram appoſita ſunt: </s> <s xml:id="echoid-s17085" xml:space="preserve">de-<lb/>currit ſpatium, cuilibet menſi dicatum, horizontaliter a dextra ad <lb/>ſiniſtram, diviſum in dies, qui menſem conſtituunt: </s> <s xml:id="echoid-s17086" xml:space="preserve">ſinguli a ſe <lb/>diſtinguuntur lineæ craſſioris ope perpendiculariter deorſum ductæ; <lb/></s> <s xml:id="echoid-s17087" xml:space="preserve">intra binas craſſiores duæ continentur ſubtiliores illis parallelæ, <lb/>diem dividentes trifariam; </s> <s xml:id="echoid-s17088" xml:space="preserve">quarum prima diviſio, ſcilicet quæ ma-<lb/>xime ſiniſtra deſtinatur obſervationibus, quæ ab hora 12 nocturna <lb/>uſque ad octavam antimeridianam evenerunt, conſcribendis; </s> <s xml:id="echoid-s17089" xml:space="preserve">me-<lb/>dia continet quæ ab hoc tempore uſque ad quartam poſtmeridiem <lb/>contigerunt, pars dextra & </s> <s xml:id="echoid-s17090" xml:space="preserve">tertia recipit, quæ ab hac hora uſque <lb/>ad mediam noctem obſervata ſunt; </s> <s xml:id="echoid-s17091" xml:space="preserve">ita accuratiſſime tempus cujus-<lb/>vis phænomeni Aërei ſcribi noſcique poteſt.</s> <s xml:id="echoid-s17092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17093" xml:space="preserve">Anterius ad lævam conſpiciuntur numeri deorſum currentes, <lb/>30, 10, 8, 6, 4, 2, 29. </s> <s xml:id="echoid-s17094" xml:space="preserve">10, 8, 6, 4, 2, 28. </s> <s xml:id="echoid-s17095" xml:space="preserve">deſignantes pollices 30, aut 29, <lb/>aut 28, ſimul cum lineolis intermediis, quæ ſunt {1/12} pollicis; </s> <s xml:id="echoid-s17096" xml:space="preserve">his <lb/>numeris altitudo Barometri definitur, puncto deſignanda reſpon-<lb/>dente numero; </s> <s xml:id="echoid-s17097" xml:space="preserve">punctorum acervum ſi conſideras, lineam miris <lb/>flexibus decurrentem per totam menſis longitudinem habes, in <lb/>qua quænam altitudo Mercurii in tubo ter quolibet die fuerit, il-<lb/>lico ſpectatur: </s> <s xml:id="echoid-s17098" xml:space="preserve">quælibet tamen diviſio complectitur motum Mer-<lb/>curii {1/12} pollicis æqualem.</s> <s xml:id="echoid-s17099" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17100" xml:space="preserve">Menſes â ſe invicem diſtinguuntur latiori quodam ſpatio, deſti-<lb/>nato excipiendis ſignis ſuo præfixis diei, & </s> <s xml:id="echoid-s17101" xml:space="preserve">cæli ſtatum indicanti-<lb/>bus: </s> <s xml:id="echoid-s17102" xml:space="preserve">Lineolæ breves interruptæ, horizontaliter exporrectæ cælum <lb/>nubibus obductum ſignificant: </s> <s xml:id="echoid-s17103" xml:space="preserve">Lineolæ ſurſum deorſumque cur-<lb/>rentes, pluviam: </s> <s xml:id="echoid-s17104" xml:space="preserve">quinque puncta, quorum unum eſt in medio, ne-<lb/>bulam. </s> <s xml:id="echoid-s17105" xml:space="preserve">Sex puncta quæ ordine paria deorſum ducuntur, Grandi-<lb/>nem, parvæ cruces, Nivem: </s> <s xml:id="echoid-s17106" xml:space="preserve">omnibus abſentibus ſignis cælum ſe-<lb/>renum notatur.</s> <s xml:id="echoid-s17107" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17108" xml:space="preserve">Quadrata ſpatia, ſupremam cujusvis menſis ſeriem componentia, <lb/>numeros continent, qui altitudinem Thermoſcopii Fahrenheytii <lb/>exprimunt: </s> <s xml:id="echoid-s17109" xml:space="preserve">hi obſervati ſunt hora 7 matutina: </s> <s xml:id="echoid-s17110" xml:space="preserve">12 meridiana: </s> <s xml:id="echoid-s17111" xml:space="preserve">& </s> <s xml:id="echoid-s17112" xml:space="preserve">11 <lb/>veſpertina.</s> <s xml:id="echoid-s17113" xml:space="preserve"/> </p> <pb o="676" file="0692" n="693" rhead="EPHEMERIDES METEOROLOGICÆ"/> <p> <s xml:id="echoid-s17114" xml:space="preserve">Quæ ſequitur ſeries, ſigna complectitur formata ex lineola cum <lb/>corpore annexo, plagas ventorum indicantia, quas cuſpis reſpicit <lb/>ventorum impetum numeri juxta poſiti notant.</s> <s xml:id="echoid-s17115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17116" xml:space="preserve">Tertia ſpatiorum ſeries habet numeros pluviæ delapſæ quantita-<lb/>tem exprimentes.</s> <s xml:id="echoid-s17117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17118" xml:space="preserve">Quarta ſeries numeris ſuis denotat quantitatem Aquæ, quæ ex <lb/>vaſe parallelopipedo, Aëri aperto commiſſo, in Auras exhalavit.</s> <s xml:id="echoid-s17119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17120" xml:space="preserve">Tonitrua depinguntur ope flexuoſi teli cuſpide acuta rotundaque <lb/>cauda terminati.</s> <s xml:id="echoid-s17121" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17122" xml:space="preserve">Auroram tandem Boream, ſeu Lumen Septentrionale infimo <lb/>ponitur ordine literiſque A, B junctis deſcribitur: </s> <s xml:id="echoid-s17123" xml:space="preserve">ob oculos ſi <lb/>Tabulam poſueris, clare hæc intelliges, & </s> <s xml:id="echoid-s17124" xml:space="preserve">una methodum, quæ <lb/>brevis, compendioſa, facilis; </s> <s xml:id="echoid-s17125" xml:space="preserve">ſed noſtra non eſt, imitatus modo <lb/>fui eam, quæ in Philoſ. </s> <s xml:id="echoid-s17126" xml:space="preserve">Tranſ reperitur.</s> <s xml:id="echoid-s17127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17128" xml:space="preserve">Altitudo maxima Barometri hoc anno fuit paulum ſupra 29 pol-<lb/>lices, 6 lineas, primo Octobris die, ad eam tamen fere adſcende-<lb/>rat duodecimo Decembris, quo die omnium intenſiſſime gelavit: <lb/></s> <s xml:id="echoid-s17129" xml:space="preserve">Altitudo minima contigit vigeſimo Octobris, quo deſcenderat <lb/>uſque ad 28 pollices: </s> <s xml:id="echoid-s17130" xml:space="preserve">quare omnis mutatio Altitudinis Mercurii <lb/>intra altitudinem 1 {1/2} pollicis ſubſtitit hoc anno.</s> <s xml:id="echoid-s17131" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17132" xml:space="preserve">Frigus toto anno mite fuit, cum Thermoſcopium ſummum indicans <lb/>frigus, noctu undecimi vel duodecimi Decembris tantum ad notam <lb/>vigeſimam deſcendit: </s> <s xml:id="echoid-s17133" xml:space="preserve">eſt autem noſtrum Thermoſcopium in Aëre <lb/>aperto poſitum, orientalem ſpectans plagam, nunquam a Sole illuſtra-<lb/>tum, ad 20 pedes ſupra ſolum elevatum, ita ut Atmoſphæræ calorem <lb/>accurate indicet: </s> <s xml:id="echoid-s17134" xml:space="preserve">Id ſingulare fuit, quod novem prioribus diebus <lb/>menſis Decembris Mercurius in tubo Torricelliano admodum humilis <lb/>exſtiterit, regnante tamen gelu, ſpirantibuſque ventis ab omni <lb/>plaga, ſi Boream exceperis; </s> <s xml:id="echoid-s17135" xml:space="preserve">ita a vigeſimo ſeptimo Decembris de-<lb/>ſcendere perrexit uſque ad ultimum anni diem continuato tamen <lb/>gelu. </s> <s xml:id="echoid-s17136" xml:space="preserve">Obſervamus quoque, gelu, quod ſub aliqua Lunæ quadra-<lb/>tura, aut eam uno alterove die prævertit, non perduraſſe ad aliam <lb/>Quadraturam abſque remiſſione; </s> <s xml:id="echoid-s17137" xml:space="preserve">ita menſis Februarii die ſeptimo <lb/>gelare incepit, regelavit die decimo ſeptimo; </s> <s xml:id="echoid-s17138" xml:space="preserve">novilunium hoc men-<lb/>ſe contigit die 9, hora 14 & </s> <s xml:id="echoid-s17139" xml:space="preserve">23, & </s> <s xml:id="echoid-s17140" xml:space="preserve">Quadratura prima die decimo-<lb/>ſeptimo horâ 19 & </s> <s xml:id="echoid-s17141" xml:space="preserve">19: </s> <s xml:id="echoid-s17142" xml:space="preserve">ita primo Novembris gelavit per ſex ſuc- <pb o="677" file="0693" n="694" rhead="ULTRAJECTINÆ ANN. MDCCXXVIII."/> ceſſivos dies, Novilunium etiam contigit ipſo die Novembris pri-<lb/>mo, ceſſavit gelu cum Quadratura.</s> <s xml:id="echoid-s17143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17144" xml:space="preserve">Gelu quoque incepit poſt quartum diem Decembris, regelavit <lb/>decimo ſexto, verum quadratura prima Lunæ Septimo Decembris <lb/>dabatur, plenilunium die decimoſexto horâ 2, 7. </s> <s xml:id="echoid-s17145" xml:space="preserve">Quadratura ul-<lb/>tima Lunæ contigit Decembris vigeſimo tertio horâ, 10, 58, & </s> <s xml:id="echoid-s17146" xml:space="preserve"><lb/>gelare quoque iterum cœpit veſpera diei vigeſimi quarti Decembris: <lb/></s> <s xml:id="echoid-s17147" xml:space="preserve">Ejuſmodi viciſſitudines congelationis & </s> <s xml:id="echoid-s17148" xml:space="preserve">regelationis ſolent fere ſem-<lb/>per in hac Terræ plaga obſervari ſimul cum Lunæ phaſibus incedere: </s> <s xml:id="echoid-s17149" xml:space="preserve"><lb/>ſunt hæ actiones Lunæ in Atmoſphæram inſignes Hyeme: </s> <s xml:id="echoid-s17150" xml:space="preserve">an æſtate <lb/>igitur etiam non aliquid præſtabunt, etiamſi multo minus? </s> <s xml:id="echoid-s17151" xml:space="preserve">vide-<lb/>tur, quamvis nondum id fuerit obſervatum accurate; </s> <s xml:id="echoid-s17152" xml:space="preserve">hæc etiam <lb/>ratio eſt quare ſemper crediderim ad Lunæ Phaſes atten-<lb/>dendum eſſe, quoties nonnulla capientur Experimenta, præcipue <lb/>quæ ab Aëris variâ conditione & </s> <s xml:id="echoid-s17153" xml:space="preserve">temperie multum pendent, fa-<lb/>teor in plurimis Lunam nihil operari poſſe; </s> <s xml:id="echoid-s17154" xml:space="preserve">ſed cum in quædam <lb/>actionem exerceat, hæc nunquam intelligentur, niſi vis aliquid <lb/>in illis peragens annotetur.</s> <s xml:id="echoid-s17155" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17156" xml:space="preserve">Maximus calor uſſit vigeſimo nono Junii, nam tempore meri-<lb/>diano Thermoſcopium elevatum fuit ad octuageſimum ſextum, cum <lb/>reliquis calidioribus Menſis Julii diebus tantum ad gradum octua-<lb/>geſimum quartum adſcenderit liquor.</s> <s xml:id="echoid-s17157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17158" xml:space="preserve">Quantitas pluviæ toto delapſa anno altitudinem perpendicula-<lb/>rem habuit 30 pollicum Rhenol. </s> <s xml:id="echoid-s17159" xml:space="preserve">2 {17/60} linear. </s> <s xml:id="echoid-s17160" xml:space="preserve">quæ ſolito multo <lb/>major annum humidum conſtituit, nihilominus modice fer-<lb/>tilem. </s> <s xml:id="echoid-s17161" xml:space="preserve">Januarius omnium maxime pluvioſus fuit: </s> <s xml:id="echoid-s17162" xml:space="preserve">quo ceciderunt <lb/>4 pollices cum 1 linea pluviæ; </s> <s xml:id="echoid-s17163" xml:space="preserve">ſicciſſimus fuit Februarius, tantum <lb/>5 lineas Aquæ colligens.</s> <s xml:id="echoid-s17164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17165" xml:space="preserve">Pluviam colligo in vaſe quadrati pedis ſuperficiem habente, aquam <lb/>per epiſtomium in recipiens vitreum quadrangulum demittente; <lb/></s> <s xml:id="echoid-s17166" xml:space="preserve">quod prius dimenſum, dein in lineas diviſum eſt, accuratiſſime <lb/>Aquæ ſingulis diebus delapſæ quantitatem indicans, dimittens in <lb/>auras nihil, attamen notandum hoc modo me æque rorem, ac <lb/>aquam, nivem, grandinem, & </s> <s xml:id="echoid-s17167" xml:space="preserve">quicquid ex Aëre deciduum eſt, re-<lb/>cepiſſe.</s> <s xml:id="echoid-s17168" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17169" xml:space="preserve">Aëri aperto commiſſum quoque fuit vas plumbeum, unum altum <pb o="678" file="0694" n="695" rhead="EPHEMERIDES METEOROLOGICÆ"/> pedem, ſed parallelopipedum quadrangulum, cujus quodlibet la-<lb/>tus 6 pollicum: </s> <s xml:id="echoid-s17170" xml:space="preserve">hoc ſingulo menſe Aqua fuit recenti impletum, <lb/>ut tamen Aquæ ad pollicis diſtantiam infra oram fuerit, ne illapſa <lb/>pluvia transflueret. </s> <s xml:id="echoid-s17171" xml:space="preserve">Ex hoc vaſe Aqua in vapores abiit, quorum <lb/>quantitas aliquando quotidie, interdum ſingula ſeptimana menſu-<lb/>rata fuit, habita ſimul ratione pluviæ illapſæ: </s> <s xml:id="echoid-s17172" xml:space="preserve">In vapores toto <lb/>anno abiverunt 462 {1/2} lineæ Aquæ, quæ ſunt 38 {1/2} pollices, adeoque <lb/>major quantitas in vapores abiit, quam ex cælorediit. </s> <s xml:id="echoid-s17173" xml:space="preserve">Anterioribus <lb/>menſis Decembris diebus glacies nihil exhalavit, potius augmen-<lb/>tum ponderis accepit, quia Aër admodum humidus fuit, flante <lb/>ſæpius Zephyro, Noto, & </s> <s xml:id="echoid-s17174" xml:space="preserve">Libanoto, qui etiamſi gelu attulerint, <lb/>non expertes humido tamen fuerunt.</s> <s xml:id="echoid-s17175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17176" xml:space="preserve">Grando inſignis magnitudinis & </s> <s xml:id="echoid-s17177" xml:space="preserve">copiæ cecidit Junii vigeſimo <lb/>quarto, ab hora duodecima meridiana uſque ad primam, terribili-<lb/>bus rutilantibus fulminibus, mugientibuſque tonitribus; </s> <s xml:id="echoid-s17178" xml:space="preserve">grandinis <lb/>ſoluta quantitas dedit altitudinem 14 Linearum; </s> <s xml:id="echoid-s17179" xml:space="preserve">dies moderate ca-<lb/>lidi præceſſerant, neque ante meridianum tempus calorem ultra <lb/>ſolitum patiebatur, cum Thermoſcopium ad gradus 63, 70, 52 tri-<lb/>bus obſervationis temporibus deprehenſum fuerit: </s> <s xml:id="echoid-s17180" xml:space="preserve">cæteroquin rara <lb/>tonitrua niſi menſe Majo audita fuerunt.</s> <s xml:id="echoid-s17181" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17182" xml:space="preserve">Sed fertiliſſimus annus Aurorarum Borealium fuit, meteori admo-<lb/>dum incogniti antiquis temporibus, nunc frequentiſſimi, nam octo-<lb/>decim hoc anno hac in urbe apparuerunt: </s> <s xml:id="echoid-s17183" xml:space="preserve">Illa vigeſimi Martii appa-<lb/>rebat inter Septentrionem & </s> <s xml:id="echoid-s17184" xml:space="preserve">Ortum, totam hanc occupans cæli <lb/>plagam, flante vento leniſſimo occidentali, pauciſque & </s> <s xml:id="echoid-s17185" xml:space="preserve">tenuibus <lb/>cælo obducto nubibus: </s> <s xml:id="echoid-s17186" xml:space="preserve">Oriebatur ex alba nubecula, 17 gradibus <lb/>ſupra horizontem elevata, ex qua integræ lucentes nubes interdum, <lb/>ſed vicibus admodum interruptis, emittebantur: </s> <s xml:id="echoid-s17187" xml:space="preserve">Lux exſurgens <lb/>nubecula erat rapidiſſimo delata motu Zenith verſus, illudque trans-<lb/>iens, nec memini me unquam nubes majori pernicitate agitatas <lb/>ſpectaſſe: </s> <s xml:id="echoid-s17188" xml:space="preserve">aliquando ceſſabat 5, 6, 7 minutorum ſpatio, mox ful-<lb/>gentius rediens. </s> <s xml:id="echoid-s17189" xml:space="preserve">Obſervavi hanc Lucem ab hora 7 ad 8 {1/2} veſperti-<lb/>nam, ultra quam nihil amplius apparuit; </s> <s xml:id="echoid-s17190" xml:space="preserve">eodem tempore interim <lb/>fulgebat annulus albus Lunam ambiens diametri 47 graduum.</s> <s xml:id="echoid-s17191" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17192" xml:space="preserve">Secundo Octobris ingens erat lumen Boreale, quod conſpexi <lb/>ab hora 10 ad 11 veſpertinam, hujus color erat rubicundior, quam <pb o="679" file="0695" n="696" rhead="ULTRAJECTINÆ ANN. MDCCXXVIII."/> unquam conſpexi, radii lucidi & </s> <s xml:id="echoid-s17193" xml:space="preserve">valde micantes ex horizonte egredi <lb/>videbantur, qui tamen nunquam aſſurrexerunt ultra 45 gradus, cito <lb/>evanidi, nec ultra minutum perdurantes: </s> <s xml:id="echoid-s17194" xml:space="preserve">erat hoc lumen adeo <lb/>tenue, ut Lucem ſtellarum fixarum tertiæ magnitudinis tranſmit-<lb/>tens non confuderit: </s> <s xml:id="echoid-s17195" xml:space="preserve">cælum undique erat ſerenum, plagâ Boreâ <lb/>excepta: </s> <s xml:id="echoid-s17196" xml:space="preserve">omnia objecta in Terræ ſuperficie fere æque clare con-<lb/>ſpiciebantur, ac in Lunæ Quadratura fieri ſolet.</s> <s xml:id="echoid-s17197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17198" xml:space="preserve">Duodecimo Octobris Aurora Borealis oborta fuit, quo tempo-<lb/>re Conſtellationibus Boreis in ſpecula demonſtrandis occupa-<lb/>bar: </s> <s xml:id="echoid-s17199" xml:space="preserve">oriebatur horâ 10, 35. </s> <s xml:id="echoid-s17200" xml:space="preserve">ceſſavit penitus hora 10 minu-<lb/>tis 50: </s> <s xml:id="echoid-s17201" xml:space="preserve">erat in plagâ Cæli Boreâ nubium atrarum congeries, <lb/>non tamen ultra 10 gradibus ſupra horizontem elevatarum; </s> <s xml:id="echoid-s17202" xml:space="preserve">ex <lb/>harum ſuperficie ſuperiori emittebantur radii luminoſi Zenith ver-<lb/>ſus recta adſcendentes, arctiſſimi, quâ parte nubi adhærebant, ſed <lb/>latius explicati Zenith verſus eundo, in ipſo ortu ex nube fulgen-<lb/>tiſſimi, ſed in progreſſu rariores minufque lucidi, non autem ad-<lb/>ſcenderunt ultra 25 gradus ſupra horizontem; </s> <s xml:id="echoid-s17203" xml:space="preserve">radii ultra minutum <lb/>non perſtabant; </s> <s xml:id="echoid-s17204" xml:space="preserve">aliquando etiam latius explicabantur in ipſa nube, <lb/>tum tamen non adeo fulgebant, ac qui emittebantur: </s> <s xml:id="echoid-s17205" xml:space="preserve">nubes hæc lu-<lb/>minoſa a ſeptentrione ortum & </s> <s xml:id="echoid-s17206" xml:space="preserve">occaſum verſus 8 gradibus circiter <lb/>ſe explicabat; </s> <s xml:id="echoid-s17207" xml:space="preserve">ventusqne ſpirabat placidus Euro-Boreus.</s> <s xml:id="echoid-s17208" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17209" xml:space="preserve">Novembris ſecundo, ut & </s> <s xml:id="echoid-s17210" xml:space="preserve">vigeſimo tertio in plaga cæli Borea <lb/>nubes luminoſa erat, donata lumine æquabili, & </s> <s xml:id="echoid-s17211" xml:space="preserve">parum fulgente, <lb/>ex nube non emittebantur radii, quemadmodum in aliis Auroris Bo-<lb/>realibus fieri conſuevit, perdurabant aliquot horis, verum nec finem, <lb/>nec initium phænomeni obſervavi.</s> <s xml:id="echoid-s17212" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17213" xml:space="preserve">Reliquæ Auroræ Boreales nihil ſingulare, quam quod ſæpius ab <lb/>aliis notatum fuit, conſpiciendum præbuerunt.</s> <s xml:id="echoid-s17214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17215" xml:space="preserve">Sunt hæc præcipua meteora Anno 1728 obſervata, plura ex ipſis <lb/>Ephemeridibus colligi poſſunt.</s> <s xml:id="echoid-s17216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17217" xml:space="preserve">Admodum neceſſe eſt, ut quædam de Thermoſcopio, quo uſusfui, <lb/>addam: </s> <s xml:id="echoid-s17218" xml:space="preserve">bulbus conoideus, gracili adhærens tubo, impletus eſt liquore <lb/>cæruleo, veluti Florentinum impleri rubro ſpiritu ſolebat: </s> <s xml:id="echoid-s17219" xml:space="preserve">Scala divi-<lb/>ſionishæc eſt: </s> <s xml:id="echoid-s17220" xml:space="preserve">Thermoſcopium immiſſum calido & </s> <s xml:id="echoid-s17221" xml:space="preserve">erumpentiè vivo <lb/>animali ſanguini, liquorem gerit certo modo rarefactum, ubi ponitur <lb/>nota 96, ſed idemliquor deſcendit ad aliam notam, 32, ſimulac bulbus <pb o="680" file="0696" n="697" rhead="EPHEMERIDES METEOROLOGICÆ"/> Aquæ immittitur incipienti in glaciem abire; </s> <s xml:id="echoid-s17222" xml:space="preserve">totum igitur ſpatium <lb/>intermedium diviſum eſt in 64 æquales partes: </s> <s xml:id="echoid-s17223" xml:space="preserve">Nix permixta cum <lb/>Sale Ammoniaco, tempore hyberno atque ſummo regnante gelu <lb/>circa bulbum copioſe circumpoſita liquorem condenſat, ût deſcen-<lb/>dat ad notam 10, ita ut inter principium glaciei & </s> <s xml:id="echoid-s17224" xml:space="preserve">ſummum frigus <lb/>artificiale intercedant notæ æquales prioribus 22. </s> <s xml:id="echoid-s17225" xml:space="preserve">â 10 ad 0 conti-<lb/>nuatur Scala deorſum, ut frigus, forte artificiali adhuc majus, <lb/>obſervari etiam poſſet; </s> <s xml:id="echoid-s17226" xml:space="preserve">ita quoque ſupra notam 96 ſcala aliquouſ-<lb/>que ſurſum producitur, ut major calor indicaretur.</s> <s xml:id="echoid-s17227" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17228" xml:space="preserve">Convenit hæc ſcala cum eâ Ingenioſiſſimi D°. </s> <s xml:id="echoid-s17229" xml:space="preserve">Fahrenheytii, cujus <lb/>Mercurio impleta Thermoſcopia ita reſpondent, ut ad gradum 32 <lb/>ponatur indicium Aquæ mox in glaciem abituræ: </s> <s xml:id="echoid-s17230" xml:space="preserve">ad 96 calor ſangui-<lb/>nis humani; </s> <s xml:id="echoid-s17231" xml:space="preserve">intermediique gradus ab utroque Thermoſcopio eidem <lb/>calori expoſito indicantur: </s> <s xml:id="echoid-s17232" xml:space="preserve">Verum differt ſcala infra 32 gradum; <lb/></s> <s xml:id="echoid-s17233" xml:space="preserve">nam Thermoſcopia Mercurio impleta, deſcendunt ad gradum 0, im-<lb/>miſſa nivi cum ſale Ammoniaco permixtæ, cum noſtrum tantum ad <lb/>gradum 10 deſcendat.</s> <s xml:id="echoid-s17234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17235" xml:space="preserve">Ex his certiſſimis terminis quilibet noſtras obſervationes cum iis, <lb/>quæ ope aliorum Thermoſcopiorum peractæ ſunt, comparare fa-<lb/>cile poterit: </s> <s xml:id="echoid-s17236" xml:space="preserve">fatendum tamen eſt Thermoſcopicas obſervationes <lb/>raro capi ſolere ſatis cauté, eaſque plurimum differre prout huic <lb/>alterive plagæ expoſita fuerint inſtrumenta; </s> <s xml:id="echoid-s17237" xml:space="preserve">ideo cum duobus in <lb/>diverſis locis poſitis noſtras obſervationes condidimus.</s> <s xml:id="echoid-s17238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17239" xml:space="preserve">Barometro uſus fui accurato, cujus mox dabo fabricam, etiamſi <lb/>enim vulgatiſſima ſit machina, perraro rite conſtructa habetur, <lb/>relicto utplurimum aëre in ſuperiori tubi parte, atque inter Mer-<lb/>curii interſtitia; </s> <s xml:id="echoid-s17240" xml:space="preserve">ſolent enim argentum vivum tubo infundere, bul-<lb/>lamque aëream per ipſum tranſmittere, aliquoties tubum inclinan-<lb/>do, quo magna quidem pars Aëris intercepti hinc inde e Mercu-<lb/>rio educitur, non tamen omnis: </s> <s xml:id="echoid-s17241" xml:space="preserve">methodus ita implendi tubos ru-<lb/>ſticis imperitiſque ſufficiat: </s> <s xml:id="echoid-s17242" xml:space="preserve">ſed ecquis â cachinno ſe temperet, eam <lb/>a Philoſophis probatam deprehendens? </s> <s xml:id="echoid-s17243" xml:space="preserve">aſt ex hoc ungue Leonem. <lb/></s> <s xml:id="echoid-s17244" xml:space="preserve">Accuratiſſima methodus, operoſa quidem verum Dii nil niſi laboribus <lb/>vendunt, & </s> <s xml:id="echoid-s17245" xml:space="preserve">quidem hæc eſt: </s> <s xml:id="echoid-s17246" xml:space="preserve">Mercurius puriſſimus in ampla calefactus <lb/>probe phiala includatur recipienti Boyleano, ex quo ſollicite edu-<lb/>catur omnis aër, interim Mercurium agitando leniter; </s> <s xml:id="echoid-s17247" xml:space="preserve">qui bullas <pb o="681" file="0697" n="698" rhead="ULTRAJECTINÆ ANN MDCCXXVIII."/> ex interſtitiis ſuis aëreas dimittet, quibus orbatus erit elapſo diei <lb/>intervallo: </s> <s xml:id="echoid-s17248" xml:space="preserve">tum tubum cape novum, alterutra extremitate clauſum, <lb/>interne bene mundum, ſiccunique, quem filo chalybeo, cujus <lb/>extremitati aliquantum ſiccæ puræque alutæ alligaveris, puriorem <lb/>reddes, aëremque a parietibus averruncabis. </s> <s xml:id="echoid-s17249" xml:space="preserve">Deinde Tubum æqua-<lb/>biliter calefac largum latumque ante focum, ne diſſiliat, ita aër <lb/>facilius a parietibus vitri, â quibus attractus non facile recedit, <lb/>avelletur: </s> <s xml:id="echoid-s17250" xml:space="preserve">tum Mercurium prudenter abſque concuſſione ex reci-<lb/>piente ſublatum eidem calori ſubmitte: </s> <s xml:id="echoid-s17251" xml:space="preserve">Dein tubus gracilis, priori <lb/>longior, & </s> <s xml:id="echoid-s17252" xml:space="preserve">qui cavitati illius immitti poſſit, ad fundum uſque in am-<lb/>pliorem inſeratur; </s> <s xml:id="echoid-s17253" xml:space="preserve">ejus utraque extremitas ſit aperta, alterutra au-<lb/>tem latior & </s> <s xml:id="echoid-s17254" xml:space="preserve">infundibuli inſtar, cui Mercurius facile infundi poſ-<lb/>ſit: </s> <s xml:id="echoid-s17255" xml:space="preserve">quo apparatu præmiſſo, calidus infundibulo capilliformi infun-<lb/>datur Mercurius, qui ita lente illapſus in fundum amplioris tubi <lb/>ſurſum adſcendet, aëremque expellet omnem: </s> <s xml:id="echoid-s17256" xml:space="preserve">tubo penitus im-<lb/>pleto, prudenter & </s> <s xml:id="echoid-s17257" xml:space="preserve">lente capilliformis extrahatur, curando ut am-<lb/>plior impletus maneat, ita nullam aëream bullam, utcunque aciem <lb/>intenderis, in tubo obſervabis: </s> <s xml:id="echoid-s17258" xml:space="preserve">inverſus hic tubus, vaſculo alium <lb/>adhuc continenti immiſſus, primum impletus uſque ad ſummitatem <lb/>manebit, etiamſi longitudinem 40 pollicum & </s> <s xml:id="echoid-s17259" xml:space="preserve">ultra habuerit, ſed <lb/>concuſſione cum tubo communicata, ſubſidebit Mercurius, & </s> <s xml:id="echoid-s17260" xml:space="preserve">ad <lb/>29 pollices, plus minusve hærebit, accuratiſſimum cum Atmoſphæræ <lb/>pondere æquilibrium ſervaturus; </s> <s xml:id="echoid-s17261" xml:space="preserve">Barometrum hoc modo confe-<lb/>ctum ſolet paulo altius ſuſpendere Mercurium, quam vulgaria: </s> <s xml:id="echoid-s17262" xml:space="preserve">ita <lb/>noſtrum, quocum obſervationes cepimus, confectum fuit; </s> <s xml:id="echoid-s17263" xml:space="preserve">inſi-<lb/>ſtens vaſculo diametri 4 pollicum, unde ſubſidente Mercurio ex <lb/>tubo ad 28 pollices, vel adſcendente ad 30 pollices, ne quidem <lb/>{1/1600} pollicis differentia in altitudine Mercurii in vaſculo ſtagnantis <lb/>datur; </s> <s xml:id="echoid-s17264" xml:space="preserve">hic apparatus æneæ impoſitus laminæ, quæ humido aëris <lb/>expandenti non ſubjicitur, veram altitudinem Mercurii repræſen-<lb/>tat: </s> <s xml:id="echoid-s17265" xml:space="preserve">Inveni aliam quoque methodum accurate Tubum implendi, <lb/>nec magis operoſam priori; </s> <s xml:id="echoid-s17266" xml:space="preserve">ſit Tubus ultra 40 longus pollices, <lb/>partem, uno pollice ab extremo diſtantem, in Lampadis flamma can-<lb/>defac, atque in tubum gracilem extrahe, interim extremo antliam <lb/>affige cæmenti ope, tubumque alliga aſſerculo, ne inter tractan-<lb/>dum frangatur; </s> <s xml:id="echoid-s17267" xml:space="preserve">poſtquam probe mundificatus eſt, calefiat æquabi- <pb o="682" file="0698" n="699" rhead="EPHEMERIDES METEOROLOGICÆ"/> liter ad ignem, extremumque alterum Mercurio omni Aëre orba-<lb/>to, ſecundum deſcriptam methodum, & </s> <s xml:id="echoid-s17268" xml:space="preserve">calido, immitte; </s> <s xml:id="echoid-s17269" xml:space="preserve">incline-<lb/>tur tubus, ita ut perpendicularis altitudo 29 pollicum ſit in aliqua <lb/>parte capillari tubi, tum educatur Aër ex tubo antliæ ope, ita ut <lb/>Mercurius aſſurgat in tubum & </s> <s xml:id="echoid-s17270" xml:space="preserve">quidem uſque in capillarem angu-<lb/>ſtiam; </s> <s xml:id="echoid-s17271" xml:space="preserve">tum digito chirotheca munito claudatur inferius tubi extre-<lb/>mum, & </s> <s xml:id="echoid-s17272" xml:space="preserve">flamma Lampadis tubi ope directa in capillarem angu-<lb/>ſtiam liquefaciat claudatque vitrum ita, ut immediate fere clauſura <lb/>Mercurium tangat, tum hoc calore rarefactus Aër, ſi quis adhuc <lb/>hæreret, excludetur ex anguſtia; </s> <s xml:id="echoid-s17273" xml:space="preserve">ſublato dein digito, erigatur <lb/>Tubus, in quo Mercurius ſubſidebit donec cum Atmoſphæræ pon-<lb/>dere æquilibrium egerit: </s> <s xml:id="echoid-s17274" xml:space="preserve">nullibi in tubo ita impleto vel minimum <lb/>Aëris indicium obſervabis, atque ad eandem altitudinem ac in priori <lb/>Tubo animadvertes Mercurium ſuſpendi.</s> <s xml:id="echoid-s17275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17276" xml:space="preserve">Verum ad morbos pergamus, qui potiſſimum hoc Anno regna-<lb/>runt; </s> <s xml:id="echoid-s17277" xml:space="preserve">hi Epidemicorum nomen non merentur, quum contagio hu-<lb/>mano non proſerpſerunt: </s> <s xml:id="echoid-s17278" xml:space="preserve">Febres Vernales Tertianæ ultra medium <lb/>menſis Aprilis occeperunt, neque plusquam menſis ſpatio regna-<lb/>verunt; </s> <s xml:id="echoid-s17279" xml:space="preserve">mites fuerunt omnes, ſolitis tantum ſtipatæ ſymptomati-<lb/>bus, nam invadebant cum horrore, frigore, laſſitudine, capitis do-<lb/>lore, vix alia diſtingui potuerunt ſymptomata, quod, quam lene <lb/>febrium genus fuerit, indicat: </s> <s xml:id="echoid-s17280" xml:space="preserve">calor deinde cum ſudoribus ſeque-<lb/>batur, elapſisque duodecim aut tredecim horis æger prorſus li-<lb/>ber, ſed debilitatus relinquebatur uſque ad ſequentem parc-<lb/>xyſmum, qui raro plus octo vicibus redibat. </s> <s xml:id="echoid-s17281" xml:space="preserve">Id omnibus commu-<lb/>ne fuit, ut, licet urina rubra ſedimenti copiam demiſerit, tamen <lb/>deſierint in Coryzam, febrili materiâ in Schneideri membranam de-<lb/>lata: </s> <s xml:id="echoid-s17282" xml:space="preserve">hæc frequentes ſternutationes & </s> <s xml:id="echoid-s17283" xml:space="preserve">Lymphæ deſtillationes ex-<lb/>citabat, tandem deſcendens Pulmonem verſus,, membranas prio-<lb/>ri continuas, Tracheamque inveſtientes, occupabat, hinc tuſſi-<lb/>cula, & </s> <s xml:id="echoid-s17284" xml:space="preserve">anxietas, intra duos tamen profligata dies: </s> <s xml:id="echoid-s17285" xml:space="preserve">Curabantur <lb/>ſponte, aut adhibitis amaris antifebrilibus, ſudoriferiſve, quibus <lb/>tamen Coryza præverti non potuit: </s> <s xml:id="echoid-s17286" xml:space="preserve">Rediit febris vehementior & </s> <s xml:id="echoid-s17287" xml:space="preserve"><lb/>pertinacior iis hominibus, qui elapſo anno inter peregrinandum <lb/>per Hollandiæ urbes febre ſæviſſimâ Epidemicâ correpti fuerant; <lb/></s> <s xml:id="echoid-s17288" xml:space="preserve">in his enim morbi materia, Hepar occupans, non plane extincta, <pb o="683" file="0699" n="700" rhead="ULTRAJECTINÆ ANN. MDCCXXVIII."/> & </s> <s xml:id="echoid-s17289" xml:space="preserve">â calore Vernali ſoluta, priſtinam totum corpus percurrendo <lb/>videbatur luſura Tragœdiam, ſed aliquot datis vomitoriis, poſtea <lb/>Cortice feliciter profligabatur, necrediit. </s> <s xml:id="echoid-s17290" xml:space="preserve">Febres hæ viſæ fuerunt ex-<lb/>citari â ſubitaneo frigore calorem notabilem præcedentium dierum <lb/>ſequente, nam ab 18 Aprilis initium modo ſumſerunt, quo die Gran-<lb/>do & </s> <s xml:id="echoid-s17291" xml:space="preserve">Nix in aliquâ ceciderunt copiâ, flante Borea tum hoc, tum <lb/>præcedenti die, quorum frigus corpora ſubito conſtringebat, â ca-<lb/>lore præteritorum dierum jam aperta.</s> <s xml:id="echoid-s17292" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17293" xml:space="preserve">Sub finem Julii invaſerunt febres continuæ putridæ, quæ vehe-<lb/>mentes fuerunt, æroſque valde labefactando in præſens conjicie-<lb/>bant periculum, plures tamen evaſerunt, quam mortui ſunt: </s> <s xml:id="echoid-s17294" xml:space="preserve">Inva-<lb/>debant pulſu citato & </s> <s xml:id="echoid-s17295" xml:space="preserve">inæquali, cum frigore dorſi & </s> <s xml:id="echoid-s17296" xml:space="preserve">lumborum, <lb/>magno capitis dolore, anxietate inſigni, quæ toto decurſu morbi <lb/>perduravit, mox ſubſequebatur calor & </s> <s xml:id="echoid-s17297" xml:space="preserve">ſitis: </s> <s xml:id="echoid-s17298" xml:space="preserve">jam tertio die lin-<lb/>gua erat arida, nigroque obducta muco: </s> <s xml:id="echoid-s17299" xml:space="preserve">urina primis 10 diebus ru-<lb/>bra, aliquando flammea, nonnunquam turbida: </s> <s xml:id="echoid-s17300" xml:space="preserve">illico ægri debiles <lb/>& </s> <s xml:id="echoid-s17301" xml:space="preserve">laſſi, atque potiſſimum in dorſum decumbebant; </s> <s xml:id="echoid-s17302" xml:space="preserve">ſomnus me-<lb/>diocris, ſed parum reficiens, abſente tamen delirio; </s> <s xml:id="echoid-s17303" xml:space="preserve">ſanguis Ve-<lb/>næ ſectione eductus inflammatorii inſtar pelliculam corneam con-<lb/>trahebat: </s> <s xml:id="echoid-s17304" xml:space="preserve">ita eodem ſtatu decem primis diebus permanſit morbus, <lb/>fuitque febris perfecte homotonos; </s> <s xml:id="echoid-s17305" xml:space="preserve">elapſo plerumque die decimo <lb/>vel undecimo in urina incepit apparere nubecula, imminuebatur <lb/>febris, & </s> <s xml:id="echoid-s17306" xml:space="preserve">ſenſim decreſcens, penitus elapſis quatuordecim diebus <lb/>ceſſabat, interim Criſi larga per urinam ſe manifeſtante. </s> <s xml:id="echoid-s17307" xml:space="preserve">Qui mo-<lb/>riebantur, raro decimum quintum diem attigerunt, ſed his elapſo <lb/>decimo die exacerbata fuit febris, quæ vires omnes poſternens, <lb/>rationem perturbans, anxietatem augens, tandem ad orcum ægro-<lb/>tos demiſit: </s> <s xml:id="echoid-s17308" xml:space="preserve">Corripuit hæc Synochus homines adultæ ætatis, ve-<lb/>getos, ſucco & </s> <s xml:id="echoid-s17309" xml:space="preserve">ſanguine plenos, manentibus infantibus & </s> <s xml:id="echoid-s17310" xml:space="preserve">Seni-<lb/>bus ab eo immunibus: </s> <s xml:id="echoid-s17311" xml:space="preserve">Non regnaverunt hæ febres ultra Auguſti <lb/>medium.</s> <s xml:id="echoid-s17312" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17313" xml:space="preserve">Menſe Septembri aliquouſque elapſo ſeſe manifeſtaverunt Fe-<lb/>bres Tertianæ duplices, alternâ die mitiores, alternâ acriores, <lb/>mitiſſimæ autem fuerunt, & </s> <s xml:id="echoid-s17314" xml:space="preserve">non uti autumnales ſolent, quarum <lb/>pertinacia non niſi potentioribus auxiliis domari ſolet; </s> <s xml:id="echoid-s17315" xml:space="preserve">ſed hæ æque <lb/>facile curabantur, ac Vernales, non ultra 14 excurrentes dies, <pb o="684" file="0700" n="701" rhead="EPHEMERIDES METEOROLOGICÆ"/> nec ullo ſtipatæ ſymptomate, quod has comitari non ſolet.</s> <s xml:id="echoid-s17316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17317" xml:space="preserve">In principio Octobris Coryza plurimos corripuit, cum viciſſitu-<lb/>dines caloris diurni & </s> <s xml:id="echoid-s17318" xml:space="preserve">frigoris nocturni magnæ erant: </s> <s xml:id="echoid-s17319" xml:space="preserve">noctu enim <lb/>gelabat, interdiu Thermoſcopium adſcenderat ad gradus 56, 54, <lb/>58, 70, 64, ſpirante Subſolano & </s> <s xml:id="echoid-s17320" xml:space="preserve">Notapeliote hinc corpora in-<lb/>terdiu denudata ad calorem evitandum, veſperi & </s> <s xml:id="echoid-s17321" xml:space="preserve">noctu a frigore <lb/>eo facilius corripiebantur, atque frigidus Aër perpetuo ad nares <lb/>allapſus inflammationem membranæ Schneiderianæ induxit.</s> <s xml:id="echoid-s17322" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17323" xml:space="preserve">Menſe Novembri quædam obſervatæ fuerunt Tertianæ & </s> <s xml:id="echoid-s17324" xml:space="preserve">Quar-<lb/>tanæ, ſed paucæ, & </s> <s xml:id="echoid-s17325" xml:space="preserve">illico Corticis Peruviani ope feliciter profli-<lb/>gatæ.</s> <s xml:id="echoid-s17326" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s17327" xml:space="preserve">Frigido tandem menſe Decembris iterum aliquæ obſervatae ſunt <lb/>continuæ & </s> <s xml:id="echoid-s17328" xml:space="preserve">putridæ, non tamen copioſæ; </s> <s xml:id="echoid-s17329" xml:space="preserve">incipiebant cum hor-<lb/>ripulationibus, frigore totius corpus, rigore, pulſu citato inæquali, <lb/>exiguo capitis dolore; </s> <s xml:id="echoid-s17330" xml:space="preserve">mox calor digitos pungens oriebatur, pro-<lb/>hibito tamen ſudore; </s> <s xml:id="echoid-s17331" xml:space="preserve">urinæ rubræ pellucidæque parva ſitis aderat, <lb/>lingua arida, in medio parum fuſca, aſt aridiora labia & </s> <s xml:id="echoid-s17332" xml:space="preserve">tumida: <lb/></s> <s xml:id="echoid-s17333" xml:space="preserve">poſt quintum diem ſomnolenti fiebant ægri, aliquando per triduum <lb/>dormientes, vix excitandi, a ſomno tamen ſemper refecti, in-<lb/>terim vultus triſtis, oculi luctuoſi, involuntariis madentes lachry-<lb/>mis, ſummaque acceſſit debilitas; </s> <s xml:id="echoid-s17334" xml:space="preserve">Urina elapſo die decimo criti-<lb/>ca, & </s> <s xml:id="echoid-s17335" xml:space="preserve">ita uſque ad morbi finem continuata, ſed tanta cum difficul-<lb/>tate reddebatur ut ſemel modo horarum 24 ſpatio prodierit, & </s> <s xml:id="echoid-s17336" xml:space="preserve"><lb/>non niſi cum dolore; </s> <s xml:id="echoid-s17337" xml:space="preserve">ſanguis in principio Venæ Sectione eductus, <lb/>admodum inflammatus, illico cruſta coriacea obductus; </s> <s xml:id="echoid-s17338" xml:space="preserve">alvus in <lb/>quibuſdam pertinaciter conſtipata, continuis emollienda erat Clyſ-<lb/>matibus humectantibus & </s> <s xml:id="echoid-s17339" xml:space="preserve">lubricantibus, fæces tamen naturalibus <lb/>prodierunt ſimillimæ in nonnullis diarrhæa obſervabatur, hi tamen <lb/>in majus diſcrimen conjecti perpetuo deliraverunt: </s> <s xml:id="echoid-s17340" xml:space="preserve">hæ febres ho-<lb/>motonæ fuerunt 14 aut 15 diebus, deinde miteſcere cæperunt, <lb/>prorſus deſinentes vigeſimo die, ſed ægros relinquentes debiliſſi-<lb/>mos; </s> <s xml:id="echoid-s17341" xml:space="preserve">neminem ex his mortuum deprehendi, ſervati omnes hac <lb/>methodo tractati; </s> <s xml:id="echoid-s17342" xml:space="preserve">venam ſecando, potum emollientem, hume-<lb/>ctantem, acidiuſculum, nitroſum ſubminiſtrando, alvum emollien-<lb/>do lenibus ſolventibus humectantibuſque enematibus: </s> <s xml:id="echoid-s17343" xml:space="preserve">cibos ſuppe-<lb/>ditando leves, imprimis Lac ebutyratum, in quod natura verge- <pb file="0701" n="702"/> <pb file="0701a" n="703"/> <anchor type="figure" xlink:label="fig-0701a-01a" xlink:href="fig-0701a-01"/> <pb file="0702" n="704"/> <pb o="685" file="0703" n="705" rhead="ULTRAJECTINÆ ANN. MDCCXXVIII."/> bat, ægris illud impenſe flagitantibus, & </s> <s xml:id="echoid-s17344" xml:space="preserve">eventu ſucceſſus com-<lb/>probante felices.</s> <s xml:id="echoid-s17345" xml:space="preserve"/> </p> <div xml:id="echoid-div666" type="float" level="2" n="1"> <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> </div> <p> <s xml:id="echoid-s17346" xml:space="preserve">Eccebrevem morborum hiſtoriam, quos hoc Anno in urbe obſer-<lb/>vavi: </s> <s xml:id="echoid-s17347" xml:space="preserve">Sunt hæ Ephemerides noſtræ primæ, hinc non adeo perfectæ <lb/>ac deſiderari poſſent, ſed fabricando fabri fimus; </s> <s xml:id="echoid-s17348" xml:space="preserve">plura, nunc omiſ-<lb/>ſa, in ſequentibus addentur; </s> <s xml:id="echoid-s17349" xml:space="preserve">has plus laboris quam acuminis con-<lb/>tinere, inficias non eo; </s> <s xml:id="echoid-s17350" xml:space="preserve">ſed data continent, ex quibus poſtea ratio-<lb/>cinii ope plurima & </s> <s xml:id="echoid-s17351" xml:space="preserve">ſubtiliſſima deduci poterunt, modo multorum <lb/>annorum ſeries prius colligamus, tum eas ſecum invicem compare-<lb/>mus: </s> <s xml:id="echoid-s17352" xml:space="preserve">Eſt enim Phyſica laboris plena, lento gradu promovenda, <lb/>obſervationibus & </s> <s xml:id="echoid-s17353" xml:space="preserve">Experimentis amplificanda, ut tandem aliquid <lb/>certi in ea ſtabiliamus.</s> <s xml:id="echoid-s17354" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div668" type="section" level="1" n="667"> <head xml:id="echoid-head789" xml:space="preserve">FINIS.</head> <figure> <image file="0703-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0703-01"/> </figure> <pb file="0704" n="706"/> <pb file="0705" n="707"/> <pb file="0705a" n="708"/> <figure> <image file="0705a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0705a-01"/> </figure> <pb file="0706" n="709"/> <pb file="0707" n="710"/> <pb file="0707a" n="711"/> <figure> <image file="0707a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0707a-01"/> </figure> <pb file="0708" n="712"/> <pb file="0709" n="713"/> <pb file="0709a" n="714"/> <figure> <image file="0709a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0709a-01"/> </figure> <pb file="0710" n="715"/> <pb file="0711" n="716"/> <pb file="0711a" n="717"/> <figure> <image file="0711a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0711a-01"/> </figure> <pb file="0712" n="718"/> <pb file="0713" n="719"/> <pb file="0713a" n="720"/> <figure> <image file="0713a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0713a-01"/> </figure> <pb file="0714" n="721"/> <pb file="0715" n="722"/> <pb file="0715a" n="723"/> <figure> <image file="0715a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0715a-01"/> </figure> <pb file="0716" n="724"/> <pb file="0717" n="725"/> <pb file="0717a" n="726"/> <figure> <image file="0717a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0717a-01"/> </figure> <pb file="0718" n="727"/> <pb file="0719" n="728"/> <pb file="0719a" n="729"/> <figure> <image file="0719a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0719a-01"/> </figure> <pb file="0720" n="730"/> <pb file="0721" n="731"/> <pb file="0721a" n="732"/> <figure> <image file="0721a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0721a-01"/> </figure> <pb file="0722" n="733"/> <pb file="0723" n="734"/> <pb file="0723a" n="735"/> <figure> <image file="0723a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0723a-01"/> </figure> <pb file="0724" n="736"/> <pb file="0725" n="737"/> <pb file="0725a" n="738"/> <figure> <image file="0725a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0725a-01"/> </figure> <pb file="0726" n="739"/> <pb file="0727" n="740"/> <pb file="0727a" n="741"/> <figure> <image file="0727a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0727a-01"/> </figure> <pb file="0728" n="742"/> <pb file="0729" n="743"/> <pb file="0729a" n="744"/> <figure> <image file="0729a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0729a-01"/> </figure> <pb file="0730" n="745"/> <pb file="0731" n="746"/> <pb file="0731a" n="747"/> <figure> <image file="0731a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0731a-01"/> </figure> <pb file="0732" n="748"/> <pb file="0733" n="749"/> <pb file="0733a" n="750"/> <figure> <image file="0733a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0733a-01"/> </figure> <pb file="0734" n="751"/> <pb file="0735" n="752"/> <pb file="0735a" n="753"/> <figure> <image file="0735a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0735a-01"/> </figure> <pb file="0736" n="754"/> <pb file="0737" n="755"/> <pb file="0737a" n="756"/> <figure> <image file="0737a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0737a-01"/> </figure> <pb file="0738" n="757"/> <pb file="0739" n="758"/> <pb file="0739a" n="759"/> <figure> <image file="0739a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0739a-01"/> </figure> <pb file="0740" n="760"/> <pb file="0741" n="761"/> <pb file="0741a" n="762"/> <figure> <image file="0741a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0741a-01"/> </figure> <pb file="0742" n="763"/> <pb file="0743" n="764"/> <pb file="0743a" n="765"/> <figure> <image file="0743a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0743a-01"/> </figure> <pb file="0744" n="766"/> <pb file="0745" n="767"/> <pb file="0745a" n="768"/> <figure> <image file="0745a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0745a-01"/> </figure> <pb file="0746" n="769"/> <pb file="0747" n="770"/> <pb file="0747a" n="771"/> <figure> <image file="0747a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0747a-01"/> </figure> <pb file="0748" n="772"/> <pb file="0749" n="773"/> <pb file="0749a" n="774"/> <figure> <image file="0749a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0749a-01"/> </figure> <pb file="0750" n="775"/> <pb file="0751" n="776"/> <pb file="0751a" n="777"/> <figure> <image file="0751a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0751a-01"/> </figure> <pb file="0752" n="778"/> <pb file="0753" n="779"/> <pb file="0753a" n="780"/> <figure> <image file="0753a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0753a-01"/> </figure> <pb file="0754" n="781"/> <pb file="0755" n="782"/> <pb file="0755a" n="783"/> <figure> <image file="0755a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0755a-01"/> </figure> <pb file="0756" n="784"/> <pb file="0757" n="785"/> <pb file="0757a" n="786"/> <figure> <image file="0757a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0757a-01"/> </figure> <pb file="0758" n="787"/> <pb file="0759" n="788"/> <pb file="0759a" n="789"/> <figure> <image file="0759a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0759a-01"/> </figure> <pb file="0760" n="790"/> <pb file="0761" n="791"/> <pb file="0762" n="792"/> <pb file="0763" n="793"/> <pb file="0764" n="794"/> </div></text> </echo>