Mercurial > hg > mpdl-xml-content
view texts/XML/archimedes/la/casat_terra_018_la_1658.xml @ 10:d7b79f6537bb
Version vom 2009-02-14
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Thu, 02 May 2013 11:08:12 +0200 |
| parents | 22d6a63640c6 |
| children |
line wrap: on
line source
<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Casati, Paolo</author> <title>Terra machinis mota</title> <date>1658</date> <place>Rome</place> <translator></translator> <lang>la</lang> <cvs_file>casat_terra_018_la_1658.xml</cvs_file> <cvs_version></cvs_version> <locator>018.xml</locator> <echodir>/permanent/library/YHAK0YQ4</echodir> </info> <text> <front> </front> <body> <chap> <pb xlink:href="018/01/001.jpg"></pb> <p type="main"> <s><emph type="center"></emph>TERRA <lb></lb>MACHINIS MOTA <lb></lb>DISSERTATIONES<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>GEOMETRICAE, MECHANICAE <lb></lb>PHYSICAE, HYDROSTATICAE<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>In quibus<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Machinarum Coniugatarum vires inter ſe comparantur: <lb></lb>Multiplici Noua Methodo Terræ magnitudo & <lb></lb>Grauitas inueſtigatur: ARCHIMEDES <lb></lb>terræ motionem ſpondens ab arrogantiæ <lb></lb>ſuſpicione vindicatur.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>AVTHORE <lb></lb>PAVLO CASATO <lb></lb>E SOCIETATE IESV <lb></lb><figure id="id.018.01.001.1.jpg" xlink:href="018/01/001/1.jpg"></figure><lb></lb>ROMÆ.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Ex Typographia Ignatij de Lazaris. </s> <s>M.DC.LVIII. <lb></lb><emph type="italics"></emph>SVPERIORVM PERMISSV.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <pb xlink:href="018/01/002.jpg"></pb> <pb xlink:href="018/01/003.jpg"></pb> <figure id="id.018.01.003.1.jpg" xlink:href="018/01/003/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>ILLVSTRISS. AC REVERENDISS. DOMINO <lb></lb>D. IOANNI GEORGIO <lb></lb>PATRITIO VENETO<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><expan abbr="VTRIVSq;">VTRIVSque</expan> SIGNATVRÆ REFERENDARIO <lb></lb><emph type="italics"></emph>PAVLVS CASATVS E SOCIET AT E IESV<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Felicitatem.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>APVD multos arrogantiæ opinione la<lb></lb>borat Archimedes, quòd dato, vbi ip<lb></lb>ſe conſiſteret, loco tellurem ſuis à fun<lb></lb>damentis conuellere ſe poſſe affirma<lb></lb>ret: id ſcilicet per ſummam confiden<lb></lb>tiam dictum putant, quod cum reap<lb></lb>ſe ne tentari quidem, ne dum perfici, <lb></lb>queat, experimento refelli non poteſt. </s> <s>Diſcutienda fuit <lb></lb>conflata in bonum Senem inuidia criminis, quo ſoli erudi<lb></lb>tuli afflantur, qui ſcientijs leuiter aſperſi ſibi ſapientes vi<lb></lb>dentur. </s> <s>Et quanquam me vindice non eget Archimedes, <lb></lb>ſua ſapientia aduersùs calumniantium tela ſatis protectus; <lb></lb>illud fortaſſe non inutile accidat, ſi vel minùs eruditi in<lb></lb>telligant nihil eſſe tam arduum, quod ſuperari non poſſit ſa<lb></lb>pientis induſtria. </s> <s>Tibi certè, Illuſtriſſime Domine, non <lb></lb>iniucundam fore hanc elucubratiunculam præſagit animus <lb></lb>pro ea humanitatis abundantia, qua literarios omnes cona<emph.end type="italics"></emph.end><pb xlink:href="018/01/004.jpg"></pb><emph type="italics"></emph>tus complecti ſoles: Illa enim, vbi in lucem prodire datum <lb></lb>eſt, continuò geſtijt tuum conuolare in ſinum, in quo ſe be<lb></lb>nignè fouendam ſperaret. </s> <s>Alliciebat ingenita clariſſimi <lb></lb>ſanguinis nobilitas auorum nominibus conſpicua, innutrita <lb></lb>virtutibus indoles, morum facilitas ſuauiſſima, grauitas<lb></lb>que comitate condita, ingenij acies perſpicua, eruditio varia <lb></lb>atque præclara. </s> <s>Illud vnum abſterrere poterat properan<lb></lb>tem, quod de mouenda tellure diſputans vix ſe ſuſpicari <lb></lb>debuiſſet aſpiciendam ab homine, qui inter eos delectus, <lb></lb>quos aut ad proponendas dirimendasque partium cauſas, aut <lb></lb>ad Bonum Regimen aduigilare Sapientiſſimus Princeps iuſ<lb></lb>ſit, intentis in Reipublicæ quietem, componendosque ciuium <lb></lb>motus oculis hæret. </s> <s>Sed cum nulla tibi pereant temporis <lb></lb>momenta, qui enim potuiſſes hunc iuuentutis florem matu<lb></lb>ris tot ſcientiarum fructibus coronare, naturæ receſſus phi<lb></lb>loſophando rimari, in infinitas Iuris ambages excurrere, <lb></lb>Theologicæ facultatis adyta penetrare, monumenta Eccle<lb></lb>ſiaſticæ vetuſtatis euoluere, niſi velocis ingenij vigorem aſ<lb></lb>ſiduo ſtudio fouiſſes? </s> <s>Cum, inquam, nulla tibi pereant <lb></lb>temporis momenta, deſperan dum non fuit hiſce Diſſertatio<lb></lb>nibus impetrari poſſe ea horarum reſegmina, quæ aut amæ<lb></lb>nioribus Muſis, aut Mathematicæ contemplationi tribuere <lb></lb>ſoles, vt ſeuerioris negotij laborem literato otio interrum<lb></lb>pas. </s> <s>Nihil hìc tua dignum eruditione, quæ eſt Authoris <lb></lb>tenuitas, inuenies: meæ tamen obſeruantiæ veſtigia non ob<lb></lb>ſcura deprehendas, maximè velim. </s> <s>Multo autem notior <lb></lb>atquè illuſtrior meus erga te animus erit, vbi per tua iuſſa <lb></lb>licuerit mea in re ſtudia officijs vberioribus teſtari. </s> <s>Tuæ <lb></lb>erit magnanimitatis exilem hanc obſequij mei teſſeram non <lb></lb>contemnere. </s> <s>Vale.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="018/01/005.jpg"></pb> <p type="main"> <s><emph type="center"></emph>Amice Lector.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s>MACHINALIS & Hydroſtaticæ Philoſophiæ, <lb></lb>quam premo, ſpecimen aliquod exhibi<lb></lb>turus, ac Prodromum tantiſper emiſſu<lb></lb>rus dum extrema manus operi accedat, <lb></lb>Archimedæum Problema ſelegi, quo tel<lb></lb>lurem moueri poſſe proſitebatur, niſi locus, vbi machi<lb></lb>na conſiſteret, defuiſſet. </s> <s>Qua ille machinatione id per<lb></lb>ficere moliretur, Hiſtoricis diſputandum relinquo. </s> <s>Mul<lb></lb>tiplex ſuppetebat methodus; ſatis ſcio. </s> <s>Placuit tamen <lb></lb>potiſſimùm oſtendere, quantum in hoc negotio machi<lb></lb>narum Compoſitio præſtet earundem Augmento: id<lb></lb>que intrà eiuſdem Facultatis genus; vt vel ſolos Vectes <lb></lb>adhibendo, vel ſolas Trochleas &c. </s> <s>quod verò in vno <lb></lb>genere explicatur, de cæteris dictum facilè intelligitur. </s> <s><lb></lb>Ne quis autem in motu iſto perficiendo aut immenſas, <lb></lb>aut innumeras requiri machinas exiſtimaret, tentaui to<lb></lb>tius globi terraquei grauitatem, quantum coniiciendo <lb></lb>aſſequi fas eſt, explorare: vnde apertâ conſecutione con<lb></lb>ſicitur non adeò multis membris diſtingui oportere ma<lb></lb>chinam hoc in opere neceſſariam: vtinam de materię <lb></lb>ipsâ non ſatis firmâ dubitari non poſſet. </s> <s>Quoniam ve<lb></lb>rò grauitatis notitia pendet ex mole præcognitâ; vt ab<lb></lb>ſolutum eſſet Problema, methodos indicaui, quibus <lb></lb>terræ magnitudinem indagare poſsimus: vt videlicet ex <lb></lb>notâ mole pondus innoteſcat, & hinc definiri poſſit ma<lb></lb>china quæ datæ grauitati mouendæ proportione reſpon<lb></lb>deat. </s> <s>Sed quia in motu ipſo aqua in partem ſecederet, <lb></lb>motumque faciliorem efficeret; examinandum fuit, <pb xlink:href="018/01/006.jpg"></pb>quantum illa afferre poſſet momenti; id quod fieri non <lb></lb>potuit ſinè Hydroſtaticâ exercitatione, qua ignis terræ <lb></lb>viſceribus incluſi, aëris, & aquæ grauitates inuicem̨ <lb></lb>conferrentur. </s> </p> <p type="main"> <s>Duas in diſſertationes tribueram hoc opuſculum, <lb></lb>cum primùm problema hoc in Collegio Romano <lb></lb>ſub auſpicijs Eminentiſſimi Principis Cardinalis Haſ<lb></lb>ſiæ Lantgrauij explicatum eſt ab Illuſtriſſimo Co<lb></lb>mite Antonio de Montſort. </s> <s>Sed quoniam diſſertatio<lb></lb>nes illæ longiores erant, quàm vt facilè hominem ad <lb></lb>legendum allicerent, & per tempus non licuerat ad <lb></lb>marginem notas, quaſi eorum, quæ dicuntur, indices, <lb></lb>apponere, placuit rem totam in quinque diſſertationes <lb></lb>diſpertiri, vt legentium commodo ſeruirem, additis ad <lb></lb>marginem notis. </s> <s>Ne verò pauculis ijs, ad quorum ma<lb></lb>nus olim venit hæc elucubratiuncula, videar malè co<lb></lb>ctam cramben recoxiſſe, non prodeunt ſinè auctario hæ <lb></lb>diſſertationes, quas plurium eruditorum virorum iudi<lb></lb>cia ſubire deſidero, vt doctior fiam. </s> </p> <p type="main"> <s>Fruſtra quæras ex me, vt ea quæ diſſertatione comple<lb></lb>xus ſum, aliorum authoritate firmentur: hæc enim ſi <lb></lb>legiſſem, noluiſſem exſcribere: ideo plura omiſi, quæ <lb></lb>ab alijs dicta deprehendi. </s> <s>Non adeò tamen deſipui, vt <lb></lb>mihi vni Solem illuxiſſe cenſeam: fieri potuit vt hæc ea<lb></lb>dem alijs occurrerent; ſed quæcunque tandem illa ſint, <lb></lb>mihi primùm, nemine prælucente, in mentem vene<lb></lb>runt. </s> <s>Hæc autem eo tantùm conſilio dicta ſunt, nę <lb></lb>plura, quæ in hanc ſententiam afferri potuiſſent, omiſſa <lb></lb>calumnieris: neque enim omnia perſequi otium ſuit. </s> </p> <p type="main"> <s>Quod ſpectat ad ſcriptionis methodum dialogicam; <pb xlink:href="018/01/007.jpg"></pb>illam Platonis exemplum ab omni calumniâ vindicat: <lb></lb>Breuitatem cum perſpicuitate conſectanti methodus hec <lb></lb>magis arridebat. </s> <s>At quid opus erat calculorum progreſ<lb></lb>ſus, quibus numeri illi indagantur, quos in colloquio <lb></lb>diſſertatores afferunt, ad faſtidium inculcare? </s> <s>Id enim <lb></lb>communiter periti Arithmetici non faciunt; ſed calamo <lb></lb>in ſchedulâ taciti inueſtigant: id quod ab huius dialogi <lb></lb>interlocutoribus factum ponimus. </s> <s>Quod ſi quis id mihi <lb></lb>culpæ vertat, ſciat me peccare maluiſſe omittendo, <lb></lb>quam tantâ numerorum vi lectorem onerando. </s> <s>Placuit <lb></lb>verò tres viros de Mathematicis diſciplinis optimè me<lb></lb>ritos (qui diem noſtro æuo obierunt) Galilæum, Mer<lb></lb>ſennum, Guldinum diſſertatores exhibere; vt ex Italicâ <lb></lb>pariter, Gallicâ, atque Germanicâ Matheſi commen<lb></lb>tatiuncula hæc lucem mutuaretur, quam non potuit ab <lb></lb>authore recipere. </s> <s>Nec te pluribus volo. </s> <s>Vale. </s> </p> <p type="main"> <s><emph type="center"></emph>SYNOPSIS TOTIVS OPERIS: <lb></lb><emph type="italics"></emph>DISSERTATIO PRIMA <lb></lb>Machinarum vires inter ſe comparat. </s> <s><lb></lb>DISSERTATIO SECVNDA <lb></lb>Terræ grauitatem inueſtigat. </s> <s><lb></lb>DISSERTATIO TERTIA <lb></lb>Methodos varias inueniendi terræ quantitatem proponit. </s> <s><lb></lb>DISSERTATIO QVARTA <lb></lb>Ex aquæ ſeparatione à terræ motus facilitatem infert. </s> <s><lb></lb>DISSERTATIO QVINTA <lb></lb>Minorem telluris grauitatem in aqua explicat.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <pb xlink:href="018/01/008.jpg"></pb> <p type="main"> <s><emph type="center"></emph>Ioannes Rhò Præpoſitus Prouincialis Societatis Ieſu. </s> <s><lb></lb>In Prouincia Romana.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s>O<emph type="italics"></emph>Puſculum, cui titulus eſt Terra Machinis mota à <lb></lb>P. Paulo Caſato Societ. </s> <s>Noſtræ compoſitum, tres viri <lb></lb>graues, ac docti Eiuſdem Noſtræ Societ. </s> <s>perlegerunt, & <lb></lb>in lucem edi poſſe iudicarunt: quarè facultate mihi conceſſa <lb></lb>ab Adm. Reu. Padre Noſtro Goſvvino Ni<emph.end type="italics"></emph.end>K<emph type="italics"></emph>el Præpoſito Ge<lb></lb>nerali, poteſtatem facio vt imprimatur, ſi alijs, ad quos <lb></lb>ſpectat, ità viſum fuerit. </s> <s>Romæ die 2. Maij 1657.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Ioannes Rhò<emph.end type="italics"></emph.end></s> </p> <figure id="id.018.01.008.1.jpg" xlink:href="018/01/008/1.jpg"></figure> <p type="main"> <s><emph type="italics"></emph>Imprimatur, <lb></lb>Si videbitur Reuerendiſs. Patri Sacri Palatij Apoct. Mag. <lb></lb>M. </s> <s>Oddus Viceſg.<emph.end type="italics"></emph.end></s> </p> <figure id="id.018.01.008.2.jpg" xlink:href="018/01/008/2.jpg"></figure> <p type="main"> <s><emph type="italics"></emph>Imprimatur <lb></lb>Fr. Vinoentius Maria Guiniſius Magiſter, & Reuerendiſsimi <lb></lb>P. Fr. Raymundi Capiſuechi Sac. Apoſt. Pal. Magistri Socius Ord. <lb></lb>Præd.<emph.end type="italics"></emph.end></s> </p> <pb xlink:href="018/01/009.jpg" pagenum="1"></pb> <figure id="id.018.01.009.1.jpg" xlink:href="018/01/009/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>DISSERTATIO <lb></lb>PRIMA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Machinarum vires inter ſe <lb></lb>comparat.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Galilæus, Merſennus, Guldinus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s>NVNQVAM minùs alieno tempo<lb></lb>re acceſſiſtis, Amici, vt me <lb></lb>veſtro aſpectu pariter ac fa<lb></lb>miliariſſimâ collocutione re<lb></lb>crearetis longo ſanè faſtidio <lb></lb>grauem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Mer.<emph.end type="italics"></emph.end></s> <s> Satis in tempore accedo, ſi obſeruan<lb></lb>tiam, qua te plurimos noſtri æui Mathema<lb></lb>ticos ſapientiâ facilè antecedentem colo, <lb></lb>certis documentis liceat declarate. </s> </p> <pb xlink:href="018/01/010.jpg" pagenum="2"></pb> <p type="main"> <s><emph type="italics"></emph>Gul.<emph.end type="italics"></emph.end></s> <s> Id nobis quoquè lucro futurum eſt, <lb></lb>quod dolueris; quos nimirùm ſuauiſſimą <lb></lb>illa tua dicendi facundia poſt moleſtas animi <lb></lb>curas luculentiùs beabit: nemo ſiquidem̨ <lb></lb>pleniùs ex fonte bibit, quàm qui ſubducto <lb></lb>recens fiſtulæ epiſtomio aquam in libertatem <lb></lb>vindicat. </s> <s>Sed quæ demùm nebula ſere nam̨ <lb></lb>tranquillæ mentis diem valuit infuſcare? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Haud procul ab hiſce ædibus obuias <lb></lb>habuiſtis lappas, quæ nec à ſe inuicem, nec à <lb></lb>me, quamuis lite compoſitâ, diuelli poterant. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Itane Verò, Galilæe? </s> <s>auocatum à <lb></lb>mathematicis contemplationibus animum <lb></lb>(quod ſuperi omen obruant) ad fori conten<lb></lb>tiones tranſtuliſti? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Noſtri ſubſellij erat, quam detule<lb></lb>runt litem dirimendam. </s> <s>Hæc autem illos <lb></lb>controuerſia torquebat contentionis fortaſsè <lb></lb>cupidiores quàm veritatis: Qua videlicet <lb></lb>machinatione tellurem loco mouere decreuiſ<lb></lb>ſet Archimedes, niſi locus, vbi poſſet <expan abbr="cõſiſtere">conſiſtere</expan>, <lb></lb>defuiſſet. </s> <s>Hic quidem aptâ quinque <expan abbr="facultatũ">facultatum</expan> <lb></lb>coagmentatione rem totam fuiſſe perficien<lb></lb>dam aſſerebat: Cont<emph type="italics"></emph>r<emph.end type="italics"></emph.end>à verò ille eximias hu<lb></lb>iuſmodi vires vni Gloſſocomo <expan abbr="tribuẽdas">tribuendas</expan> con<lb></lb>tendebat. </s> <s>Nec planè nullius operæ fuit homi<lb></lb>nes Mathematicis leuiſsimè aſperſos ad con<lb></lb>cordiam reuocare; cum alter <expan abbr="diuerſarũ">diuerſarum</expan> facul<pb xlink:href="018/01/011.jpg" pagenum="3"></pb>tatum compoſitioni plus ineſſe ad mouen<lb></lb>dum momenti ſatis frigidè cenſeret, alter Ar<lb></lb>chimedem in multiplici tympanorum denta<lb></lb>torum acceſsione facilitatis compendia quæ<lb></lb>ſiſſe affirmaret.</s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Illud crediderim potiùs vocari <lb></lb>poſſe in controuerſiam, vtrùm ſolâ tympano<lb></lb>rum dentatorum collabellatione, an verò <lb></lb>multiplicatâ helice infinitâ mechanicum̨ <lb></lb>hoc miraculum fuiſſet patraturus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ita lanè: modò inter nos conue<lb></lb>niat fieri poſſe, vt ſtatuamus, quibus mem<lb></lb>bris diſtingueretur celeberrimum illud Ar<lb></lb>chimedis Inuentum Quadrageſimum, quo <lb></lb>datâ potentiâ datum pondus moueri poſſe <lb></lb>iactabat; cui idcircò nonnulli nomen fecere <lb></lb>Pancratio: nullus ſiquidem dubitandi locus <lb></lb>relinquitur, quin hac machinâ telluri motum <lb></lb>conciliare moliretur. </s> <s>Cæterùm cum nihil <lb></lb>nobis niſi coniectura ſuppetat, & quidem̨ <lb></lb>quæ varias duci poteſt in partes, qua nihil <lb></lb>incertius (neque enim me Heronis Alexan<lb></lb>drini in Barulco Gloſſocomum quicquam̨ <lb></lb>moratur) nihil facilè de Archimedis mente <lb></lb>auſim affirmare, cùm dentatis rotis æquè at<lb></lb>que multiplici cochleâ infinitâ idem aſſequi <lb></lb>potuerit, quod perficere meditabatur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Athelicis vires inuentorem ſuum <pb xlink:href="018/01/012.jpg" pagenum="4"></pb>atque architectum latuerint? </s> <s>latuiſſe autem̨ <lb></lb>oporteat, ſi eam Gloſſocomo, quod mera tym<lb></lb>pana dentata conſtituant, poſthabuerit; ne mo <lb></lb>enim ſapiens longioribus ambagibus id perſe<lb></lb>quitur, quod poſſit breuiore <expan abbr="compẽdio">compendio</expan> aſſequi. </s> </p> <p type="main"> <s> <arrow.to.target n="note1"></arrow.to.target> </s> </p> <p type="margin"> <s><margin.target id="note1"></margin.target><emph type="italics"></emph><lb></lb>I <lb></lb>Gloſſocomi <lb></lb>ſeu Pancra<lb></lb>tij constru<lb></lb>ctio. <lb></lb><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sint tympana dentata quinque maiorą <lb></lb>A, B, C, D, E, totidemque minora F, G, H, <lb></lb>I, K; maximum A circa eundem axem cum <lb></lb>cylindro S, cui ductarius funis circumducitur, <lb></lb>con uertatur: quatuor minor a F, G, H, I, com<lb></lb>munem cum maioribus B, C, D, E, quibus <lb></lb>ſingula in axe eodem cohærent, habeant con<lb></lb>uerſionem: minimum verò K, addito manu<lb></lb>brio LM, circùm ſe torqueatur, & ex illo <lb></lb>totius machinæ motus initium ſumat. </s> <s>Ma<lb></lb>nubrii autem flexus LM, ad tympani K ſemi<lb></lb>diametrum Rationem habeat quintuplam̨; <lb></lb>ſibique pariter reliqua tympana, maiora vi<lb></lb>delicet cum minoribus ſibi cohærentibus <lb></lb>comparata, pro portione reſpondeant: nec <lb></lb>maximi tympani A Radius, atque cylindri <lb></lb>S illi infixi ſemidiameter, à Ratione hac quin<lb></lb>tuplâ diſsideant. </s> </p> <p type="main"> <s> <arrow.to.target n="note2"></arrow.to.target> </s> </p> <p type="margin"> <s><margin.target id="note2"></margin.target><emph type="italics"></emph><lb></lb>II <lb></lb>Gloſſocomi <lb></lb>vires expli<lb></lb>cantur. <lb></lb><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>His ita conſtitutis ſatis liquet potentiam <lb></lb>in M applicatam quintuplo velociorem eſſe <lb></lb>peripheriâ E, quæ ex mutuâ ſuorum denti<lb></lb>culorum ac tympani K collabellatione con<lb></lb>uertitur. </s> <s>At peripheria E quintuplo pariter <pb xlink:href="018/01/013.jpg"></pb><figure id="id.018.01.013.1.jpg" xlink:href="018/01/013/1.jpg"></figure><pb xlink:href="018/01/014.jpg" pagenum="6"></pb>velociùs mouetur quàm D, & D quàm C, & C <lb></lb>quàm B, & B quàm A, & A quàm S, hoc eſt <lb></lb>pondus P illi adne xum. </s> <s>Igitur motus poten<lb></lb>tiæ in M (liceat in pagellâ rem ad calculos <lb></lb>reuocare) ad <expan abbr="motũ">motum</expan> ponderis P eſt vt 15625 <lb></lb>ad 1. ſunt nimirum ſex Rationes quintuplæ, <lb></lb>ex quibus Ratio motûs potentiæ ad motum <lb></lb>ponderis componitur. </s> <s>Quare potentia, quæ <lb></lb>abſque machinæ ſubſidio centum pondo mo<lb></lb>uere valeret, hac adhibitâ machinâ pondus <lb></lb>P librarum 1562500. attollet. </s> </p> <p type="main"> <s> <arrow.to.target n="note3"></arrow.to.target> </s> </p> <p type="margin"> <s><margin.target id="note3"></margin.target><emph type="italics"></emph><lb></lb>III <lb></lb>Cochleæ in<lb></lb>finitæ Com<lb></lb>poſitæ uires <lb></lb>cum Gloſſo<lb></lb>como com<lb></lb>parantur. <lb></lb><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Iam verò in minorum tympanorum FG <lb></lb>HIK locum reponantur helices maiorum̨ <lb></lb>tympanorum ABCDE denticulis (quos 25 in <lb></lb>toto ambitu fuiſſe exempli gratia ſtatuamus) <lb></lb>congruentes: ipſaque tympana cum ſuis <lb></lb>axibus in ſpiram deformatis in quadrato lo<lb></lb>culamento, vt helicis inſinitæ natura fert, <lb></lb>aptè diſponantur. </s> <s>Conſtat tympani A pe<lb></lb>ripheriam quintuplo tantùm velociorem eſſe <lb></lb>pondere P; at peripheriam B vigequintuplo <lb></lb>velociorem quàm A: vnicus enim tympani A <lb></lb>denticulus promouetur ab integrâ ipſius B <lb></lb>conuerſione; ideoque vt ſemel A gyrum ab<lb></lb>ſoluat, vicies & quinquies tympanum B con<lb></lb>uertatur oportet. </s> <s>Eademque ratione tympani <lb></lb>C motus cum tympani B motu comparatur, <lb></lb>cuiuseſt vigequintuplus: quemadmodum & <pb xlink:href="018/01/015.jpg" pagenum="7"></pb>D ipſius C, & E ipſius D, & M ipſius E. </s> <s>Quare <lb></lb>Ratio motûs potentiæ M ad motum ponderis <lb></lb>P, ex vnicâ Ratione quintuplâ, & quinque <lb></lb>vigequintuplis componitur: Eſt igitur motus <lb></lb>potentiæ ad motum ponderis vt 48828125 <lb></lb>ad 1: & potentia, quæ pondo centum valeat <lb></lb>attollere, pondus librarum 4882812500 <lb></lb>mouebit. </s> </p> <p type="main"> <s>Cum itaque tam immane pondus moueri <lb></lb>poſſit quinque tantum cochleis inſinitis, <lb></lb>quæ totidem dentatis tympanis congruant; <lb></lb>contra verò, reiectâ helice, decem maiora <lb></lb>totidemque minora tympana componi opus <lb></lb>ſit, vt pondus idem attollatur; liquidò conſtat <lb></lb>longè <expan abbr="faciliorẽ">faciliorem</expan> eſſe multiplicis cochleæ, quàm <lb></lb>Gloſſocomi vſum; ac proinde quadrageſi<lb></lb>mum Archimedis inuentum helicem fuiſſe, <lb></lb>procliuius eſt opinari. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Nec ego inficior, nec diffitetur Gul<lb></lb>dinus helicis infinitæ vires cæteris machi<lb></lb>nationibus longè præſtare: ſed quæ nos cogit <lb></lb>neceſſitas affirmandi Archimedem quadra<lb></lb>geſimo loco in inuentum planè facillimum <lb></lb>incidiſſe? </s> <s>Quis fuerit Archimedææ contem<lb></lb>plationis ſcopus, in quo conquieſceret, me, <lb></lb>fateor, later Quid verò, ſi quis machinæ faci<lb></lb>litatem non in eo ſtatuendam cenſeat, quod <lb></lb>illa paucioribus membris contineatur; ſed in <pb xlink:href="018/01/016.jpg" pagenum="8"></pb>hoc potiùs, quod minore operâ parari queat? </s> </p> <p type="main"> <s><arrow.to.target n="note4"></arrow.to.target><lb></lb>Atqui tympanorum ambitum in denticulos <lb></lb><figure id="id.018.01.016.1.jpg" xlink:href="018/01/016/1.jpg"></figure><lb></lb>æquales diſtribue<lb></lb>re, eosque ſatis ſit<lb></lb>mos, ne facilè vi <lb></lb>ponderis commi<lb></lb>nuantur, & iņ <lb></lb>cylindro verſatili <lb></lb>helicem tympani <lb></lb>denticulis ritè <expan abbr="cõ-gruentem">con<lb></lb>gruentem</expan> incide<lb></lb>re, haud ſanè o<lb></lb>ſcitantem exigunt <lb></lb>artiſicem. </s> <s>Porrò <lb></lb>aſſiduus ille toe <lb></lb>partium ſe inui<lb></lb>cem atterentium <lb></lb>affrictus moram̨ <lb></lb>infert non leuem. </s> <s><lb></lb>Quare nec teme<lb></lb>re dixerit quiſ<lb></lb>piam, denticula<lb></lb>tis tympanis va<lb></lb>lere iuſſis, rem̨ <lb></lb>totam faciliùs per<lb></lb></s> <s>fici poſſe multiplici axe in peritrochio, qui <lb></lb>& leui negotio paratur, & moram recipit nul<lb></lb>lam ex mutuâ membrorum affrictione. </s> </p> <pb xlink:href="018/01/017.jpg" pagenum="9"></pb> <p type="margin"> <s><margin.target id="note4"></margin.target><emph type="italics"></emph><lb></lb>IV <lb></lb>Difficulta<lb></lb>tes in heli<lb></lb>cis constru<lb></lb>ctione & <lb></lb>uſu. <lb></lb><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Aſſumantur quinque cylindri ABCDE <lb></lb><arrow.to.target n="note5"></arrow.to.target><lb></lb>craſſitudine inæquali (quo enim magis à <lb></lb>pondere diſtant, graciliores eſſe poſſunt) <lb></lb>ſingulisque rota canaliculum in ambitu ex<lb></lb>cauatum habens adijciatur, cuius d<emph type="italics"></emph>i<emph.end type="italics"></emph.end>ameter <lb></lb>diametri cylindri ſibi cohærentis quintupla <lb></lb>ſit. </s> <s>Demùm cylindro F addatur manubrium <lb></lb>OP eandem Rationem quintuplam habens <lb></lb>ad illius ſemidiametrum. </s> <s>Hi verò cylindri <lb></lb>paralleli in ſuo conceptaculo facilè verſatiles <lb></lb>ita diſponantur, vt funis ſingulas rotas am<lb></lb>biens ad ſuperiorem cylindrum ductus (ſi <lb></lb>fieri id commode poſſit) congruat lineæ, <lb></lb>quæ horizonti ad perpendiculum inſiſtit. </s> <s><lb></lb>Hìc pariter conſtat Rationem motûs poten<lb></lb>tiæ P ad motum ponderis M ex rationibus <lb></lb>intermedijs, nimirum ſex quintuplis, com<lb></lb>poni. </s> <s>Quarè & hìc motus potentiæ ad pon<lb></lb>deris motum eſt vt 15625 ad 1, vt ſuperiùs, <lb></lb>Merſenne, ratiocinabaris. </s> <s>Maiore tameņ <lb></lb>fortaſsè compendio, quod hìc rotæ cylindros <lb></lb>non atterant, nec vllum immineat pericu<lb></lb>lum, ne ex mutuâ illâ collabellatione den<lb></lb>tes aliquando excutiantur: quàm ægrè au<lb></lb>tem excuſſi dentis detrimento occurras, pa<lb></lb>làm eſt; cum tamen diſruptum funem ite<lb></lb>rum facilè connectas. </s> </p> <p type="margin"> <s><margin.target id="note5"></margin.target><emph type="italics"></emph><lb></lb>V <lb></lb>Axes in Pe<lb></lb>ritrochio <expan abbr="Cõ">Com</expan><lb></lb>poſiti faci<lb></lb>liùs conſtru<lb></lb>untur, & <lb></lb>idem præſta <lb></lb>re poſsunt. <lb></lb><emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Vbi licet obiter animum aduertere ad <pb xlink:href="018/01/018.jpg" pagenum="10"></pb><arrow.to.target n="note6"></arrow.to.target><lb></lb>multorum artificum imperitiam, qui ex ma<lb></lb>chinarum tantùm augmento vires ad mo<lb></lb>uenda pondera augeri autumantes, multo la<lb></lb>bore, nec modicâ argenti iacturâ immanes <lb></lb>aliquando machinas conſtruunt, quæ vel mo<lb></lb>le ſuâ prægrauatæ fatiſcunt, vel motam mo<lb></lb>tui inferunt non mediocrem, adeò vt ſolius <lb></lb>machinæ motio, etiam ſecluſo pondere, cui <lb></lb>mouendo deſtinatur machina, validioris po<lb></lb>tentiæ vires abſumat: cum tamen rem to<lb></lb>tam minore negotio, nec ſpernendo pecu<lb></lb>niæ atquè laboris compendio, perficere poſ<lb></lb>ſent, ſi rectè intelligerent, quantum machi<lb></lb>narum compoſitio præſtet earum augmento. </s> <s><lb></lb>Id quod ex quinque his axibus in Peritrochio <lb></lb>inter ſe compoſitis luculentiſſimè demon<lb></lb>ſtratur; ſi enim axi, cuius diameter palma<lb></lb>ris, rotam velis infigere, qua poſſis idem̨ <lb></lb>mouere pondus, quod tribus tantùm ex pro<lb></lb>poſitis rotis A, B, C, mouetur, quàm imma<lb></lb>nis illa erit? </s> <s>Quippe quæ 125 palmos ſe<lb></lb>cundùm diametrum obtineat: quàm diffi<lb></lb>cilis ad conuerſionem? </s> <s>ob ingentem grauita<lb></lb>tis cardines prementis reſiſtentiam: quàm <lb></lb>multo argento parabilis? </s> <s>cum ea ſola ad tres <lb></lb>A, B, C, ſimul ſumptas eſſet vt minimùm in <lb></lb>Ratione Quadrati ſuæ diametri 125 ad tri<lb></lb>plum Quadratum diametri rotæ A, hoc eſt <pb xlink:href="018/01/019.jpg" pagenum="11"></pb>vt 15625 ad 75; materiem autem tantæ mo<lb></lb>li neceſſariam nec modicâ pecuniâ nec ſinò <lb></lb>multis operis comparari poſſe & elaborari <lb></lb>palàm eſt. </s> <s>Adde quòd illam ex alio in a<lb></lb>lium locum transferendi pro multiplici ne<lb></lb>ceſſitate, vix ſpes aliqua ſupereſſet. </s> </p> <p type="margin"> <s><margin.target id="note6"></margin.target><emph type="italics"></emph>VI <lb></lb>Machina<lb></lb>rum Com<lb></lb>poſitio me<lb></lb>lior eſt, <expan abbr="quã">quam</expan> <lb></lb>earum Aug<lb></lb>mentum, ſe<lb></lb>cundùm ma <lb></lb>gnitudinem<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quamuis verò quinque alios inſuper cy<lb></lb>lindros cum ſuis rotis adijcere opus eſſet, vt <lb></lb>æquale pondus attolleretur, atque tuâ illâ <lb></lb>quinque helicum coagmentatione; in diffi<lb></lb>cultates tamen longè maiores incurrat arti<lb></lb>fex, neceſſe eſt, qui cochleas quinque cum <lb></lb>tympanis examuſſim congruentes formare <lb></lb>iubeatur, ac ille qui decem aut plures axes <lb></lb>in peritrochio effingere velit; in quibus fi<lb></lb>guram exquiſitè rotundam ſi deſideret, ſu<lb></lb>peruacuo ſe labore conficiat: neque enim <lb></lb>anguli, ſi qui ſint, obeſſe quicquam poſſunt, <lb></lb>modò poli, ſeu cardines, circa quos verſan<lb></lb>tur, læues ſint ac politi. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Sed quanto impendio ſtaret tan<lb></lb><arrow.to.target n="note7"></arrow.to.target><lb></lb>tam funium vim comparare, quæ ſatis eſſet; <lb></lb>vt pondus ad vnius decempedæ altitudinem <lb></lb>ſubleuaretur? </s> <s>Primùm enim funis, cui pon<lb></lb>dus adnecteretur, decem pedes in longitudi<lb></lb>ne haberet; igitur qui rotam primam A am<lb></lb>biret, eſſet vt minimùm pedum 50. At rotæ <lb></lb>ſecundæ motus eſſet prioris quintuplus, igi<pb xlink:href="018/01/020.jpg" pagenum="12"></pb>tur rotæ B circumduceretur funis pedum <lb></lb>250, nec diſpari argumentatione conficitur <lb></lb>rotam tertiam C exigere funem pedum <lb></lb>1250, quartam D 6250, quintam demùm <lb></lb>E 31250: ex quibus conflatur ſumma pe<lb></lb>dum 39060, quæ eſſet totius funis longitu<lb></lb>do. </s> <s>Liceat autem hìc diſſimulanter præte<lb></lb>rire immodicam rotarum E, D, & C craſſi<lb></lb>tudinem, vt tàm longus funis earum am<lb></lb>bitûs terminis contineri poſſet. </s> <s>Nam ſi mul<lb></lb>tiplici ſpirarum ſerie ita duceretur funis, vt <lb></lb>ipſe ſe circumplecteretur, motuum Ratio<lb></lb>nes, &, quod inde conſequitur, potentiæ mo<lb></lb>menta, ipsâ euolutione mutarentur, auctis <lb></lb>ſcilicet aut diminutis ex ſubiectâ ſpirarum ſe<lb></lb>rie rotarum ac cylindorum diametris. </s> </p> <p type="margin"> <s><margin.target id="note7"></margin.target><emph type="italics"></emph>VII <lb></lb>Difficultati <lb></lb>ex funis lon<lb></lb>gitudine.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end> Hæc eadem, quæ nunc obijcis, mi<lb></lb><arrow.to.target n="note8"></arrow.to.target><lb></lb>hi pariter aliquandò non nihil fecere negotij. </s> <s><lb></lb>Et primùm quidem earum rotularum, qua<lb></lb>rum velocior eſt motus, funes quoquè gra<lb></lb>ciliores eſſe debere obſeruabam, quippe qui<lb></lb>bus ponderis grauitas minùs reluctetur. </s> <s>Hinc <lb></lb>verò ſatis commodâ conſecutione conficie<lb></lb>bam fieri poſſe, vt exiguis ſpatijs tanta funi<lb></lb>culi longitudo citrà incommodum compre<lb></lb>henderetur. </s> <s>Deinde quamuis non adeò lon<lb></lb>gus ſuppeteret funiculus, operæ pretium vi<lb></lb>debatur futurum, ſi illo euoluto rotas ſi<pb xlink:href="018/01/021.jpg" pagenum="13"></pb>ſteremus (annulum videlicet auerſæ rotæ A <lb></lb>infixum arctè cum ſuperiore cylindro, nę <lb></lb>pondus relaberetur, connectentes) explica<lb></lb>tum que funiculum, qui in conuerſione fuiſ<lb></lb>ſet cylindrum ſuperiorem circumplexus, ite<lb></lb>rum rotæ apſidi circumduceremus. </s> </p> <p type="margin"> <s><margin.target id="note8"></margin.target><emph type="italics"></emph>Occurritur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Verùm cum vrbem obambulans oculos <lb></lb>fortè in officinam quandam conijcerem, vbi <lb></lb>obtuſarum nouacularum acies reſtituuntur, <lb></lb>En, inquam, funiculus in ſeſe rediens maio<lb></lb>ri ac minori rotulæ ità circumplicatus, vt al<lb></lb>tera ex alterius conuerſione rotetur, nullos <lb></lb>motui terminos præſcribit: quidni igitur con<lb></lb>ſimili ratione funiculus vnâ aut alterâ ſpirâ <lb></lb>cylindrum ſuperiorem complectens ſubie<lb></lb>ctum peritrochium ita apprehendere valeat, <lb></lb>vt pariter moueantur, nec conuerſionis fi<lb></lb>nem inueniant, cum tantundem ſuccedere <lb></lb>poſſit funiculi, quantum deceſſerit? </s> <s>Id au<lb></lb>tem ſi fieri poſſe concedas, in ſuperioribus <lb></lb>ſaltem FEDC (nam in inferioribus fortaſsè <lb></lb>ob ponderis nimiam grauitatem ſatius eſſet <lb></lb>funis extremum religare, ne excurreret) <lb></lb>difficultas omnis propoſita euaneſcit. </s> <s>Vti<lb></lb>nam & in trochleis ſimile funis compen<lb></lb>dium liceret inuenire. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> An & trochleis tellurem ab Archi<lb></lb>mede fuiſſe loco dimouendam exiſtimas? <pb xlink:href="018/01/022.jpg" pagenum="14"></pb>Non funium tantùm longitudo aut craſſitu<lb></lb>do, operi non ſatis congrua negotium faceſ<lb></lb>ſeret, ſed & aptæ trochleæ conſtrui omninò <lb></lb>non poſſent. </s> <s>Quis enim Chilioſpaſtum com<lb></lb>ponat? </s> <s>ſed quantulum demùm eſt Chilioſpa<lb></lb>ſti momentum? </s> <s>Neque ſi trochleas decem <lb></lb>orbiculorum millibus inſtrueres, quicquam <lb></lb>poſſes efficere. </s> <s>Nam ſi duas huiuſmodi tro<lb></lb>chleas ità componeres, vt altera ponderi ad<lb></lb>necteretur, altera in ſuperiore loco firmare<lb></lb>tur, eumque adhiberes conatum, quo libras <lb></lb>centum abſque machinâ attolleres, conatu <lb></lb>eodem librarum vicies centena millia moue<lb></lb>re poſſes: ſed quid hoc ad immenſum terre<lb></lb>ni globi pondus? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Quæ fuerit Archimedi mens, planè <lb></lb><arrow.to.target n="note9"></arrow.to.target><lb></lb>ignoro: potuiſſe tamen fieri, vt ille propoſi<lb></lb>tum trochleis adhibitis aſſequeretur, con<lb></lb>ſtanter aſſero. </s> <s>Et quidem, quod ad trochleas <lb></lb>ipſas attinet, ludum puto, modò funes, & <lb></lb>locus vbi conſiſterem, non deeſſent. </s> <s>Cedo <lb></lb>mihi orbiculos quatuor aut ſex ſupra cen<lb></lb>tum; ſatis habeo trochlearum, vt vnicâ ma<lb></lb>nu terram à fundamentis, quibus inſiſtit, <lb></lb>conuellam. </s> <s>Id quod vt minimè dubia de<lb></lb>monſtratione conficiam; illud primum, in <lb></lb>trochleatum vſu extra controuerſiam poſi<lb></lb>tum accipio, quod, funis extremo trochleæ, <pb xlink:href="018/01/023.jpg" pagenum="15"></pb>cui pondus adnectitur, alligato, potentia re<lb></lb>liquum extremum arreptum trahens plus <lb></lb>obtinet ad mouendum momenti, quàm ſi <lb></lb>funis alteri trochleæ à pondere remotæ ad<lb></lb>necteretur; in primo enim caſu motus po<lb></lb>tentiæ ad motum ponderis maiorem habet <lb></lb>Rationem, quàm in ſecundo. </s> </p> <p type="margin"> <s><margin.target id="note9"></margin.target><emph type="italics"></emph>VIII <lb></lb>Orbiculi <lb></lb>pauci in plu<lb></lb>res minores <lb></lb>trochleas di <lb></lb>stributi plus <lb></lb>poſſunt, <lb></lb>quàm duæ <lb></lb>trochleæ ex <lb></lb>multis mil<lb></lb>libus orbi<lb></lb>culorum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Id ego tibi lubens permitto. </s> <s>Nam <lb></lb><figure id="id.018.01.023.1.jpg" xlink:href="018/01/023/1.jpg"></figure><lb></lb>ſi trochleas duas R & <emph type="italics"></emph>S<emph.end type="italics"></emph.end> pona<lb></lb><arrow.to.target n="note10"></arrow.to.target><lb></lb>mus binis orbiculis inſtructas, <lb></lb>funis autem extremum A tro<lb></lb>chleæ S annulo alligetur, & <lb></lb>ducatur funis per ABCDEF <lb></lb>GHIK, conſtat totius funis <lb></lb>longitudinem quadruplam eſ<lb></lb>ſe interualli, quo trochleæ à <lb></lb>ſe inuicem ſeiunguntur. </s> <s>Iam <lb></lb>verò plurimum intereſt, vtri <lb></lb>trochlearum pondus adiunxe<lb></lb>ris: ſi enim pondus in R ad<lb></lb>nectatur, potentia K tamdiu <lb></lb>mouetur, ac ab <emph type="italics"></emph>S<emph.end type="italics"></emph.end> recedit, do<lb></lb>nec funis totus explicetur: per<lb></lb>currit igitur ſpatium funis <lb></lb>longitudini æquale, videlicet <lb></lb>quadruplum interualli inter <lb></lb>R & S. </s> <s>At verò ſi pondus in <lb></lb>S alligetur, eadem potentią <pb xlink:href="018/01/024.jpg" pagenum="16"></pb>K ad trochleam R fixam accedit, illamquę <lb></lb>tanto ſpatio tranſgreditur, quanta eſt funis <lb></lb>longitudo: igitur in toto motu percurrit ſpa<lb></lb>tium quintuplum eius, quod à pondere ver<lb></lb>sùs trochleam R moto perficitur. </s> <s>Quoniam <lb></lb>autem quò tardior eſt ponderis motus cum <lb></lb>motu potentiæ comparatus, eò minùs pon<lb></lb>deris grauitas virtuti potentiæ trahentis ob<lb></lb>ſiſtit; apertum eſt ac manifeſtum faciliùs <lb></lb>trahi pondus, ſi trochleæ S (cui funis in A <lb></lb>adnectitur) quàm ſi trochleæ R alligetur: in <lb></lb>S nimirum motum obtinet motûs potentiæ <lb></lb>ſubquintuplum, in R autem ſubquadru<lb></lb>plum. </s> </p> <p type="margin"> <s><margin.target id="note10"></margin.target><emph type="italics"></emph>IX <lb></lb>Non æqua<lb></lb>li facilitate <lb></lb>moueri pon<lb></lb>dus. </s> <s>vtrili<lb></lb>bet trochleæ <lb></lb>adnexum̨, <lb></lb>demonstra<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Quod præterea Ratione aliquâ min<lb></lb>noris Inæqualitatis propoſitâ, Antecedens <lb></lb><arrow.to.target n="note11"></arrow.to.target><lb></lb>terminus ad Conſequentem duplum maio<lb></lb>rem habeat Rationem, quàm ad alium Con<lb></lb>ſequentem, ad quem habeat Rationem pro<lb></lb>poſitæ rationis duplicatam (ſi tamen ſubdu<lb></lb>plam excipias, cùm eadem ſumma fiat ex <lb></lb>duplicis binarij additione, ac ex mutuâ illo<lb></lb>rum multiplicatione) nihil habet dubitatio<lb></lb>nis. </s> <s>Datâ ſiquidem Ratione ſubtriplâ 3 ad <lb></lb>9, ſi Conſequens 9 geminetur, & fiat 18, <lb></lb>Ratio autem duplicetur inuento tertio con<lb></lb>tinuè proportionali 27, maior eſt Ratio 3 ad <lb></lb>18, quàm 3 ad 27. Similiter maior erit <pb xlink:href="018/01/025.jpg" pagenum="17"></pb>Ratio ad Conſequentem triplum aut qua<lb></lb>druplum, quàm ad alium Conſequentem̨ <lb></lb>terminum Rationis triplicatæ aut quadru<lb></lb>plicatæ, etiam ſi propoſita Ratio ſubduplą <lb></lb>eſſet: ſic ſi fuerit Ratio 2 ad 4, triplus Con<lb></lb>ſequens eſt 12. Conſequens verò Rationis tri<lb></lb>plicatæ eſt 16: eſt autem maior Ratio 2 ad <lb></lb>12, quàm 2 ad 16. </s> </p> <p type="margin"> <s><margin.target id="note11"></margin.target><emph type="italics"></emph>X <lb></lb>Maior est <lb></lb>Ratio ad ter<lb></lb>minum̨ <lb></lb>Multipli<lb></lb>cem, quàm <lb></lb>ad termi<lb></lb>num Ratio<lb></lb>nis ſimiliter <lb></lb>Multiplica<lb></lb>tæ.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Hinc infero maximum eſſe diſcrimen iņ <lb></lb>augendo potentiæ momento, vtrùm trochleæ <lb></lb>augeantur orbiculis, an verò trochleæ mul<lb></lb>tiplices ex iiſdem orbiculis conſtituantur. </s> <s>Si <lb></lb>enim trochleæ duæ S & R, quas nuperrimè <lb></lb>deſcripſiſti, binis prætereà orbiculis augean<lb></lb>tur, ita vt ſingulæ quaternos habeant, mani<lb></lb>feſtum eſt potentiam in K, quæ priùs mo<lb></lb>tum habebat quadruplum motûs ponderis in <lb></lb>R conſtituti, factâ huiuſmodi orbiculorum <lb></lb>acceſsione, motum habere octuplum, vel <lb></lb>quæ priùs quintuplò velocior erat pondere in <lb></lb>S adnexo, factam eſſe noncuplò velociorem. </s> <s><lb></lb>At ſi quatuor hoſce orbiculos non adijcias <lb></lb>prioribus, ſed duas alias trochleas ex illis com<lb></lb>ponas, iam multò maior eſt potentiæ motus <lb></lb>cum ponderis motu comparatus. </s> </p> <p type="main"> <s>Sint duæ trochleæ binos orbiculos haben<lb></lb>tes A & B: huic autem tum pondus P, tum <lb></lb>funis extremum adnectatur. </s> <s>Vtique poten<pb xlink:href="018/01/026.jpg" pagenum="18"></pb><arrow.to.target n="note12"></arrow.to.target><lb></lb><figure id="id.018.01.026.1.jpg" xlink:href="018/01/026/1.jpg"></figure><lb></lb>tia in F motum ha<lb></lb>beret quintuplò velo<lb></lb>ciorem motu ponde<lb></lb>ris P. </s> <s>Ex quatuor a<lb></lb>lijs orbiculis duæ pa<lb></lb>riter trochleæ D & C <lb></lb>conſtituantur: & tro<lb></lb>chleæ C adnectatur <lb></lb>prioris funis <expan abbr="extremũ">extremum</expan>. </s> <s><lb></lb>Potentia E quintuplò <lb></lb>ſanè velociùs moue<lb></lb>tur quàm F, at F quin<lb></lb>tuplò velociùs quàm <lb></lb>P; igitur motus po<lb></lb>tentiæ E ad motum <lb></lb>ponderis P eſt vt 25 <lb></lb>ad 1. Quare potentia <lb></lb>vires habens decem <lb></lb>pondo trahendi ſinè <lb></lb>machinâ, in F trahe<lb></lb>ret libras 50, at in E <lb></lb>libras 250. Quod ſi <lb></lb>tam A quàm B qua<lb></lb>ternos haberent or<lb></lb>biculos, potentia iņ <lb></lb>F tantum 90 libras <lb></lb>mouere poſſet. </s> </p> <p type="margin"> <s><margin.target id="note12"></margin.target><emph type="italics"></emph>XI <lb></lb>Trochlea<lb></lb>rum coniu<lb></lb>gatorum̨ <lb></lb>Compoſitio, <lb></lb>quàm ma<lb></lb>gnas vires. </s> <s><lb></lb>habeat.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Conſtat itaque du<pb xlink:href="018/01/027.jpg" pagenum="19"></pb>plicatis trochleis æquali orbiculorum nume<lb></lb>ro inſtructis, motum potentiæ in E haberę <lb></lb>Rationem duplicatam Rationis, quam habet <lb></lb>motus potentiæ in F ad motum ponderis in <lb></lb>P: multiplicatis autem pari numero in ea<lb></lb>dem trochleâ orbiculis, ne duplicari quidem <lb></lb>motum ipſius potentiæ F. </s> <s>Quod ſi in E pa<lb></lb>riter duæ aliæ trochleæ ſimiles adiicerentur, <lb></lb>iam triplicaretur Ratio motûs in F ad mo<lb></lb>tum in P, & ſic deinceps. </s> <s>Vno verbo di<lb></lb>cam: quot ſunt paria ſimilium trochlearum, <lb></lb>progreſſio fit tot Rationum ſimilium Ratio<lb></lb>ni, quam habet motus ponderis ad motum <lb></lb>potentiæ primis trochleis applicatæ. </s> <s>Sic ſi <lb></lb>eſſent talium, quales exhibui, trochlearum̨ <lb></lb>paria decem, aſſumendæ eſſent decem Ra<lb></lb>tiones quintuplæ; & motus potentiæ ad mo<lb></lb>tum ponderis Rationem haberet ex his com<lb></lb>poſitam, quam ſcilicet habet vndecimus ter<lb></lb>minus in progreſsione Rationis quintuplæ <lb></lb>ad vnitatem, hoc eſt 9765625 ad 1. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Si igitur trochleæ omnes ABCD <lb></lb><arrow.to.target n="note13"></arrow.to.target><lb></lb>triſpaſti eſſent, vnicus equus in E idem pon<lb></lb>dus trahere poſſet, quod equi 49; cum ta<lb></lb>men in F, ſi A & B tripaſti fuerint, idem <lb></lb>valeat trahere quod equi ſeptem: ſi vero A <lb></lb>& B ſenis inſtruerentur orbiculis, æquiuale<lb></lb>ret equis tredecim. </s> <s>Quis ergo adeò debilis <pb xlink:href="018/01/028.jpg" pagenum="20"></pb>cantherius, qui nequear ſolus trochlearum <lb></lb>multiplicium ope, maius tormentum belli<lb></lb>cum trahere? </s> </p> <p type="margin"> <s><margin.target id="note13"></margin.target><emph type="italics"></emph>XII <lb></lb>Vnicus e<lb></lb>quus facilè <lb></lb>poteſt mo<lb></lb>uere ingens <lb></lb><expan abbr="põdus">pondus</expan>, quod <lb></lb>vix poſſent <lb></lb>plures equi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Ita planè: ſed obſeruandum in fu<lb></lb>nibus. <lb></lb><arrow.to.target n="note14"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note14"></margin.target><emph type="italics"></emph>XIII <lb></lb>Quantum <lb></lb>funium in <lb></lb>hac machi<lb></lb>natione re<lb></lb>quiratur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Ne plura: ſatis animum ad hoc <lb></lb>aduerti. </s> <s>Monere volebas tantam requiri <lb></lb>longitudinem funis, qui ſecundas trochleas <lb></lb>D & C circumplectitur, vt vnicus ex D in <lb></lb>C ductus æqualis ſit longitudini ſpatij, quod <lb></lb>potentia in F totum explicans funem, & pon<lb></lb>dus P ad trochleam A vſque deducens, per<lb></lb>curreret. </s> <s>Quarè ſi interuallum trochlearum <lb></lb>AB ſit paſſuum decem, potentia ex F per<lb></lb>curreret paſſus 50: funis itaque trochleas D <lb></lb>& C ambiens longitudinem habeat neceſſę <lb></lb>eſt paſſuum vt minimum 200; trochleą <lb></lb>enim D ibi firmanda eſt, quò funis ABF <lb></lb>explicatus pertingere poſſit. </s> <s>Eademque dę <lb></lb>cæteris, ſi plures fuerint trochleæ, ratio eſto. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Non falsâ coniecturâ animum meum <lb></lb>proſpexiſti. </s> <s>Sed vt ad rem ipſam propiùs <lb></lb>accedamus obſeruandum eſt, propoſito quo<lb></lb>cunque orbiculorum numero, qui tameņ <lb></lb>per 2, vel 4, vel 6, vel alium quemcunque <lb></lb>numerum parem diuidi poſsit, longè maius <lb></lb>eſſe potentiæ momentum, ſi plures trochleæ <lb></lb>pauciorum orbiculorum, quàm ſi pauciores <pb xlink:href="018/01/029.jpg" pagenum="21"></pb>trochleæ plurium orbiculorum conſtituan</s> </p> <p type="main"> <s><arrow.to.target n="note15"></arrow.to.target><lb></lb>tur. </s> <s>Exhibeantur enim, exempli gratiâ, orbi<lb></lb>culi 60, ex quibus ſi fiant 20 trochleæ trium <lb></lb>orbiculorum, iam ſunt decem trochlearum <lb></lb>paria, ac proinde decem Rationes vt ſum<lb></lb>mum ſeptuplæ; igitur momentum potentiæ, <lb></lb>hoc eſt vndecimus ab vnitate terminus, eſt <lb></lb>vt 282475249. Si verò fiant binos haben<lb></lb>tes orbiculos, erunt 15 trochlearum paria, <lb></lb>ideoq quindecim Rationes quintuplæ, ex qui<lb></lb>bus Ratio motûs potentiæ ad motum ponde<lb></lb>ris componitur; erit igitur vt 30517578125 <lb></lb>ad 1. Conſtat autem ne additis quidem ad<lb></lb>huc duobus triſpaſtorum paribus, vt ſint in <lb></lb>vniuerſum orbiculi 72, poſſe adeò augeri po<lb></lb>tentiæ momentum: poſitis ſiquidem 12 tri<lb></lb>ſpaſtorum paribus momentum potentiæ eſt <lb></lb>ſolùm vt 13841287201. Hinc colligitur <lb></lb>plus ad mouendum momenti obtinere pau<lb></lb>ciores orbiculos in ſimplicioribus trochleis, <lb></lb>quàm in trochleis maioribus plures orbicu<lb></lb>los: id quod alicui fortaſsè paradoxum ac<lb></lb>cidat. </s> </p> <p type="margin"> <s><margin.target id="note15"></margin.target><emph type="italics"></emph>XIV <lb></lb>Pauciores <lb></lb>orbiculos in <lb></lb>ſimplicibus <lb></lb>trochleis <lb></lb>plus poſſę, <lb></lb>quàm plu<lb></lb>res in maio<lb></lb>ribus oſten<lb></lb>ditur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Nunc igitur ſi mihi orbiculos centum ex<lb></lb>hibeas, ſimplices trochleas ex ſingulis orbi<lb></lb>culis ſtatuo, fiuntquè 50 trochlearum ſim<lb></lb>plicium paria: adnexo autem pondere eidem <lb></lb>trochleæ, cui funis extremum alligatur, mo<pb xlink:href="018/01/030.jpg" pagenum="22"></pb>mentum potentiæ erit triplum: ſunt igitur <lb></lb>50 Rationes triplæ, ex quibus componitur <lb></lb>Ratio motûs potentiæ ad motum ponderis. </s> <s><lb></lb>Quærendus iraque eſt terminus in progreſ<lb></lb>ſione datæ Rationis triplæ ab vnitate quin<lb></lb>quageſimus primus. </s> </p> <p type="main"> <s>Ratio autem tripla quintuplicata eſt 243 <lb></lb>ad 1. Ducatur 243 per ſe ipſum, & eſt Ra<lb></lb>tio decuplicata 59049 ad 1. Hic iterum ter<lb></lb>minus 59049 per ſe ipſum ducatur, & Ratio <lb></lb>3486.784401 ad 1 eſt ex viginti Rationi<lb></lb>bus triplis compoſita. </s> <s>Ducatur pariter 3486. <lb></lb>784401 per ſe ipſum, & eſt Ratio ex qua<lb></lb>draginta Rationibus triplis compoſita 12. <lb></lb>157665.459056.928801. ad 1. Hæc de<lb></lb>mùm Ratio ducatur per Rationem triplam <lb></lb>decuplicatam nimirum per 59049, & pro<lb></lb>ducitur Ratio, quæ ex 50 Rationibus tri<lb></lb>plis componitur 717897.987691.852588. <lb></lb>770249. ad 1. </s> </p> <p type="main"> <s>Quod ſi placeat duas adhuc trochleas ter<lb></lb>nis orbiculis inſtructas adijcere ipſique pon<lb></lb>deri immediatè adnectere, vt funium ſeptu<lb></lb>plici ductu faciliùs ſuſtineri valeat, adhuc <lb></lb>Ratio ſeptupla addenda, vt ex hac & 50 tri<lb></lb>plis tota Ratio componatur: & quinquageſi<lb></lb>mus primus terminus progreſsionis Rationis <lb></lb>triplæ ducendus eſt per 7, vt habeatur totum <pb xlink:href="018/01/031.jpg" pagenum="23"></pb><arrow.to.target n="note16"></arrow.to.target><lb></lb>potentiæ momentum 5025285.913842. <lb></lb>968121.391743. Quarè adhibito conatu, <lb></lb>quo libras decem abſquè machinâ traheres, <lb></lb>mouere poſſes libras 50.252859.138429. <lb></lb>681213.917430. Quod pondus totius ter<lb></lb>reni globi grauitatem ſuperat. </s> <s>Orbiculis ita<lb></lb>que ſex ſupra centum Archimedæum pro<lb></lb>blema de terræ motione abſolui poſſe oſten<lb></lb>di. </s> </p> <p type="margin"> <s><margin.target id="note16"></margin.target><emph type="italics"></emph>XV <lb></lb>Orbiculis <lb></lb>106 poſſę <lb></lb>tellurem̨ <lb></lb>moueri <expan abbr="de-mõ">de<lb></lb>mon</expan>ſtratur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Quid verò, ſi quis maiorem ad<lb></lb>huc grauitatem telluri tribuat? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Parum mihi faceſſat hic negotij. </s> <s><lb></lb>Addat duas præterea trochleas aut quatuor, <lb></lb>aut plures; & fortè non adeò multas adijcere <lb></lb>oportebit: Mihi ſatis eſt chiliadas illas orbi<lb></lb>culorum atque myriadas, quas multi ad<lb></lb>ſtruunt, tanquam minimè neceſſarias refu<lb></lb>taſſe. </s> <s>Nunc quidem ſolâ coniecturâ terreni <lb></lb>globi grauitatem venari poſſumus: dato au<lb></lb>tem extra terram loco, in quo conſiſteremus, <lb></lb>facile eſſet trochlearum numerum definire: <lb></lb>examinato nimirum ſtaterâ telluris pondere; <lb></lb>quo demum cognito trochlearum, quibus <lb></lb>opus eſſet, numerus innoteſceret. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> At ſtaterâ, cuius iugum aliquot <lb></lb>paſſuum millia occuparet, ſacomatis autem <lb></lb>munere rupes non exigua fungeretur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Mittamus iſthæc; quæ à te rerum̨ <pb xlink:href="018/01/032.jpg" pagenum="24"></pb>huiuſmodi apprimè gnaro, animi tantùm <lb></lb>causâ, in medium proferri ſatis video. </s> <s>La<lb></lb>nius vel cætarius opportunam ſtateram ſup<lb></lb>peditare poſſet; modò ſingulæ libræ in ſuas <lb></lb>vncias ritè diſtributæ iugum diſtinguerent. </s> </p> <figure id="id.018.01.032.1.jpg" xlink:href="018/01/032/1.jpg"></figure> <p type="main"> <s>Erige enim ad perpendiculum trabes duas <lb></lb>æquali interuallo à ſe inuicem diſtinctas: Aſ<lb></lb>ſumaturque vectis AB, cuius pars decimą <pb xlink:href="018/01/033.jpg" pagenum="25"></pb>ſit AC, (quanquam id ſculptor non expreſ<lb></lb><arrow.to.target n="note17"></arrow.to.target><lb></lb>ſit) & extremum A ſit circa axem trabi AO <lb></lb>infixum verſatile, extremum verò B ita à <lb></lb>trabe ER diſter, vt aſſumpto ſimili vectę <lb></lb>DE circùm E verſatili, & vtroque DE, AB <lb></lb>parallelo horizonti, perpendicularis BF ſe<lb></lb>cet pariter FE partem decimam totius DE. </s> <s><lb></lb>Idquè in conſequentibus vectibus factum in<lb></lb>telligatur. </s> <s>Porrò BF, DI &c. </s> <s>ſint ex ma<lb></lb>teriâ ſolidâ, & circa clauiculos extrema B, F, <lb></lb>D &c. </s> <s>moueri poſſint; ac poſtremus vectis <lb></lb>MR habeat propè V lingulam ſeu momen<lb></lb>tum, vt quandò trabi ER congruit, ſignifi<lb></lb>cet vectes omnes conſtitutos eſſe horizonti <lb></lb>parallelos. </s> </p> <p type="margin"> <s><margin.target id="note17"></margin.target><emph type="italics"></emph>XVI <lb></lb>Statera <expan abbr="cõ-muni">con<lb></lb>muni</expan> poteſt <lb></lb>ingens pon<lb></lb>dus exami<lb></lb>nari.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Tum applicatâ in M ſtaterâ examinetur <lb></lb>omnium vectium ſimul momentum graui<lb></lb>tatis. </s> <s>Non grauitatem dico, ſed momen<lb></lb>tum grauitatis; quia vectis AB in F ſuſpen<lb></lb>ſus non ſecundùm totam ſuam grauitatem̨ <lb></lb>deorſum nititur, quia & in A ſuſtinetur, ſed <lb></lb>tantùm ſemiſſem totius ſuæ grauitatis exer<lb></lb>cet. </s> <s>Quia verò DE eſt longitudo decupla <lb></lb>ipſius FE, ideò grauitas totius AB non per<lb></lb>cipitur in D niſi ſecundùm partem ſui vige<lb></lb>ſimam, in H verò ſecundùm partem ducen<lb></lb>teſimam, & ſic deinceps; ita vt ſi fuerint in <lb></lb>vniuerſum octo vectes, percipiatur in M ſo<pb xlink:href="018/01/034.jpg" pagenum="26"></pb>lùm pars vicies millies milleſima grauitatis <lb></lb>totius AB. <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ecundi autem vectis DF gra<lb></lb>uitas percipitur in M ſecundùm partem ſui <lb></lb>bis millies milleſimam. </s> <s>Tertius ſecundùm <lb></lb>partem ducenties milleſimam; & ſic dein<lb></lb>ceps, donec vltimus MR grauitet in M ſe<lb></lb>cundùm ſuæ grauitatis ſemiſſem. </s> <s>Hinc eſt <lb></lb>quod quamuis primus vectis AB valdè craſ<lb></lb>ſus eſſe deberet, atque adeò grauis, vt pon<lb></lb>dus valeret ſuſtinere, conſequentes tameņ <lb></lb>vectes minores, ac minores, quod ad craſſi<lb></lb>tudinem ſpectat, requirerentur: ac proinde <lb></lb>eorum momenta in M ſimul ſumpta noņ <lb></lb>eſſent adeò multa. </s> <s>Ponamus itaque facoma<lb></lb>te in N exiſtente fieri æquilibrium cum ve<lb></lb>ctibus horizonti parallelis. </s> </p> <p type="main"> <s>His ita conſtitutis dimittantur vectes, vt <lb></lb>ferè quantùm poſſunt deſcendant: & in Gad<lb></lb>nectatur pondus. </s> <s>Vel fortaſſe opportunius <lb></lb>erit, ſi BF habeat in B annulum, cui inſeri <lb></lb>poſsit extremum vectis AB; vectis enim ex <lb></lb>annulo extractus ſolus deprimitur, quantum <lb></lb>poteſt, & pondere in C adnexo, aliâ machi<lb></lb>nâ tractoriâ tantiſper eleuatur, dum poſsit <lb></lb>iterum annulo B inſeri. </s> <s>Niſi fortè commo<lb></lb>dius alicui accidat ita machinam conſtruere, <lb></lb>vt iacens pondus illi adnectatur, deinde ma<lb></lb>china ipſa æqualiter eleuetur, vnde fiat vt <pb xlink:href="018/01/035.jpg" pagenum="27"></pb>vectium capita deprimantur. </s> <s>Tum ſacoma <lb></lb>in ſtateræ iugo ab aginâ remoueatur adeò, <lb></lb>vt vectis MR (atque adeò reliqui omnes) <lb></lb>horizonti parallelus conſtituatur, & ſtatera <lb></lb>indicet æquilibrium ex. </s> <s>gr. in <emph type="italics"></emph>S.<emph.end type="italics"></emph.end></s> <s> Sumatur <lb></lb>igitur differentia SN, quot nimirum libras <lb></lb>aut vncias contineat: hæc autem multipli<lb></lb>cetur per momentum, quod habet potentia <lb></lb>in M applicata; id quod fit tot additis ci<lb></lb>phris, quot ſunt vectes, quos ſtatuamus eſſe <lb></lb>octo, SN verò indicare libras 3 vnc. </s> <s>6. Sa<lb></lb>coma igitur in S oſtendit pondus P eſſe libr. </s> <s><lb></lb>300.000000. vnc. 600.000000, hoc eſt in <lb></lb>vniuerſum libr.350.000000. Quare conſtat <lb></lb>diſpoſitis hac ratione 25. vectibus, poſſę <lb></lb>vulgari ſtaterâ examinari pondus libr. </s> <s>250. <lb></lb>000000.000000.000000.000000. Vectium <lb></lb>autem huiuſmodi apta diſpoſitio non ijs ſca<lb></lb>teret difficultatibus, quæ ſuperari non poſ<lb></lb>ſent. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Mihi quidem ſatis perſuaſum eſt, <lb></lb>cas, de quibus hactenus diſſeruimus, machi<lb></lb>nationes ad tellurem loco dimouendam̨, <lb></lb>eiusque pondus examinandum aptas eſſę, <lb></lb>atquè ad potentiæ momenta ferè in immen<lb></lb>ſum augenda longè præſtare machinæ eiuſ<lb></lb>dem multiplicis quàm maioris vſum; in ma<lb></lb>iori etenim augetur ſolùm Ratio, quæ iņ <pb xlink:href="018/01/036.jpg" pagenum="28"></pb>multiplici componitur. </s> <s>Sic peritrochium̨ <lb></lb>diametrum habens decuplam ſui axis facit <lb></lb>potentiæ momentum decuplum: at duo pe<lb></lb>ritrochia Rationem quintuplam ad ſuos axes <lb></lb>habentia ſi componantur ſimul, potentiæ <lb></lb>momentum conſtituunt vigequintuplum̨. </s> <s><lb></lb>Id quod & in cochlearum compoſitione ma<lb></lb>nifeſtum eſt, cum ſatius ſit duas cochleas cum <lb></lb>duobus tympanis componere, quam heli<lb></lb>cem vnam ſtrictiorem vni tympano maiori <lb></lb>congruentem adhibere. </s> <s>Hoc in vectibus, <lb></lb>hoc in trochleis abundè eſt demonſtratum. </s> </p> <p type="main"> <s>Sed adhuc rudioribus quibuſdam eximen<lb></lb>da eſt dubitatio, quæ ancipitem animum̨ <lb></lb>torquet, an videlicet ea ſit totius globi huius, <lb></lb>quem terram dicimus, grauitas, quæ ad <lb></lb>librarum numerum reuocata paucioribus <lb></lb>quàm triginta ciphris explicari queat. </s> <s>Quam<lb></lb>uis enim illam certis finibus circumſcri<lb></lb>ptam, ac numero definitam exiſtiment, ſibi <lb></lb>tamen facilè perſuadent <foreign lang="grc">μηδίfα ταλιχοῡτον χατω<lb></lb>νομασμένον ύπάρχειν</foreign>, vt quidam apud Archi<lb></lb>medem arenæ multitudinem conſiderantes <lb></lb>opinabantur: quaſi Arithmeticæ facultatis <lb></lb>labor vltimus omnem poſt ſe relinqueret no<lb></lb>menclaturam. </s> <s>Quantam igitur grauitatem <lb></lb>globo huic, qui terras ac maria complecti<lb></lb>tur, tribuemus? </s> </p> <pb xlink:href="018/01/037.jpg" pagenum="29"></pb> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Vereor ne vobis grauis fiam, ſi ea <lb></lb>exponere voluero, quæ aliquando placuit in <lb></lb>hanc ſententiam commentari. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Immò verò aures meæ ad iucun<lb></lb>dam hanc diſputationem patent: niſi fortè <lb></lb>negotia habeas, Galilæe, quibus te nunc o<lb></lb>porteat intereſſe. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Sum planè vacuus: nec facilè patiar <lb></lb>tam citò abire amicos, quorum eruditâ con<lb></lb>ſuetudine tantoperè recreor. </s> <s>An aſymbo<lb></lb>lum te receſſurum putas, Guldine; Vnum <lb></lb>habeo, de quo te pariter interrogem, qui a<lb></lb>lios ad dicendum excitas: vbi tamen Mer<lb></lb>ſennus ſuas de terræ grauitate commentatio<lb></lb>nes in medium protulerit. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Si me audieritis, diſputationem̨ <lb></lb>hanc in ſequentem diem transferemus; cum <lb></lb>enim numeris aliquot maioribus<emph type="sup"></emph><emph.end type="sup"></emph.end> opus ha<lb></lb>beam, longè commodius accidet eos in ſche<lb></lb>dulâ domi priuatim adnotatos in promptu <lb></lb>habere, quàm illos inter colloquendum in<lb></lb>ueſtigare non ſine moleſtâ ſermonis interru<lb></lb>ptione, temporis iacturâ, & capitis defati<lb></lb>gatione: nam ſatis nos hodiè torſimus tot <lb></lb>Rationum compoſitarum inuentione. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Fiat, vt Merſenno placet. </s> </p> <pb xlink:href="018/01/038.jpg" pagenum="30"></pb> <figure id="id.018.01.038.1.jpg" xlink:href="018/01/038/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>DISSERTATIO <lb></lb>SECVNDA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Terræ grauitatem inue<lb></lb>ſtigat.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Galilæus, Merſennus, Guldinus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s>CVM ad ingentia onera loco <lb></lb>mouenda machinam mem<lb></lb>bris non adeò multis diſtin<lb></lb>ctam, neque paratu valdè <lb></lb>difficilem conſtrui poſſe, ſatis <lb></lb>heſternâ diſſertatione oſtenderimus; illud <lb></lb>nunc ex te, Merſenne, audire expectamus, <lb></lb>quanta ſit terreni orbis grauitas, vt quàm̨ <lb></lb>magnâ pariter ad eam ſuperandam machi<pb xlink:href="018/01/039.jpg" pagenum="31"></pb>natione opus habuiſſet Archimedes, intelli<lb></lb>gamus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Principio, quoniam id ex me pla<lb></lb>cet audire, grauitatem ex mole inueſtigan<lb></lb>dam intelligens, quotquot apud authores <lb></lb>extabant de terræ magnitudine opiniones, <lb></lb>cœpi ad examen reuocare, vt eas, quæ pro<lb></lb>babili alicui coniecturæ & rationi niterentur, <lb></lb>à temerè conſtitutis, ſecernerem. </s> <s>Cum ve<lb></lb>rò in omnibus <foreign lang="grc">γεομετρικ́ν ἀχρίβειαν</foreign> deſidera<lb></lb>rem, & in ſingulis labem aliquam mihi vi<lb></lb>derer deprehendere, vulgatiſſimæ demùm̨ <lb></lb>opinioni acquieſcendum cenſui, quæ 60 mil<lb></lb>liaria Italica mediocria ſingulis gradibus tri<lb></lb>buit; vt à veritate minimùm recederem, vel <lb></lb>ſaltem eos ſolùm haberem aduerſarios, qui <lb></lb>nimio in antiquitatem ſtudio feruntur. <emph type="italics"></emph>S<emph.end type="italics"></emph.end>cru<lb></lb>pulus tamen, fateor, animum quantumuis <lb></lb>diſſimulantem ſtimulabat, quoties milliaria <lb></lb>huiuſmodi minoribus menſuris diſtinguere <lb></lb>atque ad pedes reuocare opus erat; quem̨ <lb></lb>enim potiſsimùm pedem vſurparem, incer<lb></lb>tus hærebam; cùm pro diuerſa aſſumpti pe<lb></lb>dis longitudine moles tota terreni globi alia <lb></lb>atquè alia deprehenderetur, diſcrimine non <lb></lb>contemnendo. </s> </p> <p type="main"> <s>Perpendens itaque corporum vmbras ideo <lb></lb>ſemper in oppoſitam Soli plagam proijci, <pb xlink:href="018/01/040.jpg" pagenum="32"></pb><arrow.to.target n="note18"></arrow.to.target><lb></lb>quia nulla Solis particula ad perpendiculum <lb></lb>imminet corpori, quod luce afficitur, iņ <lb></lb>ſpem erigebar aliquid deprehendendi ex ſpa<lb></lb>tio circa Syenen ab antiquis apud Cleome<lb></lb>dem obſeruato, in quo gnomones nullam <lb></lb>proijciunt vmbram meridianam Sole Tro<lb></lb>picum Cancri percurrente. </s> <s>Si enim in pla<lb></lb>no AB erigatur ſtylus TI perpendicularis, <lb></lb>cui immineat Solis extremus limbus O, nul<lb></lb>la fit vmbra, quia quamuis ab alio extremo S <lb></lb>veniat radius SN vltimus, & intrà ſpatium <lb></lb><figure id="id.018.01.040.1.jpg" xlink:href="018/01/040/1.jpg"></figure><lb></lb>TN nullus alius ve<lb></lb>niat radius ab eodem <lb></lb>puncto S radios in or<lb></lb>bem diffundente, in<lb></lb>trà illud tamen ſpa<lb></lb>tium TN veniunt <lb></lb>radij à cæteris om<lb></lb>nibus punctis inter <lb></lb>S & O intermediis: <lb></lb>quare nec vmbra vl<lb></lb>la aut penumbra obſeruari poteſt. </s> <s>At ſi ſty<lb></lb>lus in LM fuerit, proiicit vmbram LP, in<lb></lb>trà quod ſpatium nullus cadit radius dire<lb></lb>ctus á punctis O & S aut intermediis; penum<lb></lb>bra verò ex P ad B procedit, donec in B me<lb></lb>ra lux incipiat. </s> <s>Cum itaque ſpatio 300 ſta<lb></lb>diorum gnomones vmbram non proiicerent, <pb xlink:href="018/01/041.jpg" pagenum="33"></pb>totum hoc ſpa<lb></lb><figure id="id.018.01.041.1.jpg" xlink:href="018/01/041/1.jpg"></figure><lb></lb>tium illud eſt, <lb></lb>cui Sol ad per<lb></lb>pendiculum im<lb></lb>minet. </s> </p> <p type="margin"> <s><margin.target id="note18"></margin.target><emph type="italics"></emph>XVII <lb></lb>Terræ ma<lb></lb>gnitudinem <lb></lb>eiuſque ad <lb></lb>Solem pro<lb></lb>portionem̨ <lb></lb>inueſtigare <lb></lb>ex ſpatio, <lb></lb>quod umbris <lb></lb>caret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed <expan abbr="quærendũ">quærendum</expan> <lb></lb>ſupererat, quo<lb></lb>ta totius circuli <lb></lb>maximi pars eſ<lb></lb>ſent ſtadia 300. <lb></lb>Conſtituto ita<lb></lb>que terræ centro <lb></lb>in C, & oculo <lb></lb>obſeruatoris iņ <lb></lb>O, ductum <expan abbr="in-telligebã">in<lb></lb>telligebam</expan> ex cen<lb></lb>tro S radium S <lb></lb>OC, qui cum̨ <lb></lb>radio OT Solem <lb></lb>contingente da<lb></lb>bat angulum S <lb></lb>OT ſemidiametrum apparentem Solis Apo<lb></lb>gæi gr.o.m.15., vt placet Tychoni, Longo<lb></lb>montano, Magino, Keplero. </s> <s>Item ex C du<lb></lb>ctus intelligatur radius Solem tangens, qui <lb></lb>terræ circulum maximum ſecat in K; & eſt <lb></lb>OK ſemiſsis ſpatij, quod caret vmbris meri<lb></lb>dianis die ſolſtitij æſtiui; continet autem ſta<pb xlink:href="018/01/042.jpg" pagenum="34"></pb>dia 150. Certum eſt angulum OCK mino<lb></lb>rem eſſe angulo <emph type="italics"></emph>S<emph.end type="italics"></emph.end>OT: ſi enim linea CK pro<lb></lb>ducta terminaretur in T, tunc angulus SOT <lb></lb>externus maior eſſet interno oppoſito OCT: <lb></lb>quia verò, quod veritati magis eſt conſenta<lb></lb>neum, radius ex C Solem tangens eſt CI vl<lb></lb>tra T, angulus ISC maior eſt angulo T<emph type="italics"></emph>S<emph.end type="italics"></emph.end>O; <lb></lb>ac proinde, cum anguli ad T & I ſint recti, <lb></lb>reliquus SCI eſt reliquo SOT minor. </s> <s>Eſt igi<lb></lb>tur ſpatium OK minus quàm min.15. Qua<lb></lb>re vnus gradus complectitur plura quàm <lb></lb>600 ſtadia, ideoquè totus telluris ambitus <lb></lb>maior eſt ſtadijs 216000. <lb></lb><arrow.to.target n="note19"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note19"></margin.target><emph type="italics"></emph>XVIII <lb></lb>Stadij Græ<lb></lb>si quanti<lb></lb>tas.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Hìc. autem hærebam in ſtadio, ne cum <lb></lb>Suida errarem; hic enim primùm Milio ſta<lb></lb>dia 7 1/2 tribuit; ſed poſtmodum Milijs de<lb></lb>cem, æqualia facit ſtadia 80: Cùm verò ſta<lb></lb>dium pedibus 600 definierit, Milium dein<lb></lb>de in pedes 4200 diſtribuit: Vnde conficitur <lb></lb>Milium & 7, & 7 1/2, & 8 ſtadia comprehen<lb></lb>dere. </s> <s>Quarè acquieſcendum potius duxian<lb></lb>tiquo Scholiaſti Græco in propoſ. </s> <s>5. lib dę <lb></lb>Gæod. Heronis Mechanici, qui ſtadium fuiſ<lb></lb>ſe paſſuum 100, paſſum cubitorum 4, cu<lb></lb>bitum verò digitorum 24 ſcribit. </s> <s>Cum ita<lb></lb>que paſſus Romanus pedibus quinque con<lb></lb>ſtaret, ſinguli verò pedes palmis 4, hoc eſt <lb></lb>digitis 16, paſſus <emph type="italics"></emph>R<emph.end type="italics"></emph.end>omanus digitos 80 com<pb xlink:href="018/01/043.jpg" pagenum="35"></pb>plectebatur, quorum paſſus Græcus habebat <lb></lb>96, ſc.4.cubitos, ſeu, quod idem eſt, pedes <lb></lb>ſex Romanos. </s> <s>Stadia igitur ſingula pedes <lb></lb>Rom. antiquos 600 continebant, hoc eſt paſ<lb></lb>ſus 120. Hinc fit terræ ambitum maiorem <lb></lb>ſtadijs 216000, maiorem quoquè eſſe paſsi<lb></lb>bus <emph type="italics"></emph>R<emph.end type="italics"></emph.end>om. <expan abbr="antiq.">antique</expan> 25920000, hoc eſt mill. <lb></lb>Rom. 25920. Quarè etiam gradibus ſin<lb></lb>gulis milliaria Rom. antiqua plura quàm 72 <lb></lb>reſpondent. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> At anguli OCK quantitatem quot <lb></lb>ſcrupulis definiebas minorem angulo <emph type="italics"></emph>S<emph.end type="italics"></emph.end>OT <lb></lb>min. 15? </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Quæſiui primùm quoties Solis ſe<lb></lb>midiameter ST contineretur à lineâ SO: dato <lb></lb>autem SOT gr.o.m.15. reliquus eſt TSO gr. <lb></lb>89.m.45.cuius Secans SO <expan abbr="partiũ">partium</expan> 22918384. <lb></lb>52745, quarum Radius ST eſt 100000. <lb></lb>00000. Deinde poſitâ terræ ſemidiametro <lb></lb>CO Algebricè 1 ℞, eſt tota CS 1 ℞ † 22918384 <lb></lb>52745, cui ex Tychone æquantur ſemidia<lb></lb>metri terreſtres, 1182, hoc eſt 1182 ℞. </s> <s>Qua<lb></lb>re <expan abbr="vtrinq;">vtrinque</expan> ſublatâ 1 ℞, manet æquatio 1181 ℞ <lb></lb>& 22918384.52745: & inſtitutâ diuiſionę <lb></lb>prouenit pretium vnius Radicis 19405. <lb></lb>91407. ſemidiameter terræ CO, quarum So<lb></lb>lis ſemidiameter eſt 100000.00000. Eſt igi<lb></lb>tur tota SC, ſi CO inuenta addatur ipſi SO, <pb xlink:href="018/01/044.jpg" pagenum="36"></pb>partium 22937790.44152, quæ eſt Secans <lb></lb>gr.89.m.45.ſec.o.Ter.43. Quar. 53. &c. </s> <s><lb></lb>hoc eſt anguli ISC: atque adeò eius comple<lb></lb>mentum SCI erit gr.o.m.14.ſec.59. Ter. <lb></lb>16. Quar. 7. quem metitur arcus OK ſtad. </s> <s><lb></lb>150. Fiat demùm vt arcus OK inuentus <lb></lb>ſcrupulorum Quart. 3237367 ad ſtadia 150, <lb></lb>ita totius circuli ambitus ſcrupulorum Quart. <lb></lb>4665600000. ad ſtadia 216175 (67/100), hoc eſt, <lb></lb>neglectâ fractione, milliaria Rom. antiquą <lb></lb>25941. Quapropter ſingulis gradibus mill. <lb></lb>Rom. 72. paſſ.58 reſpondent. </s> </p> <p type="main"> <s>Porrò inuentâ peripheriâ, ſi fiat vt 22 ad 7 </s> </p> <p type="main"> <s><arrow.to.target n="note20"></arrow.to.target><lb></lb>ita mill. 25941. ad mill. 8253 (21/22), habetur <lb></lb>diameter proximè minor verâ; & ſi fiat vt <lb></lb>223 ad 71 ita mill. 25941. ad mill. 8259 (54/223), <lb></lb>diametrum verâ proximè maiorem reperi<lb></lb>mus: & electo medio Arithmetico rectè ſta<lb></lb>tuitur terræ diameter mill. Rom. ant. </s> <s>8255. <lb></lb>paſſ 644, ideòque ſemidiameter mill. 4127. <lb></lb>paſſ. </s> <s>822. Quod ſi libeat exactiùs operari, <lb></lb>quoniam circuli diametro poſitâ 1, perime<lb></lb>ter polygoni laterum 2560 circulo circum<lb></lb>ſcripti minor eſt quàm 3 (14160/100000), perimeter ve<lb></lb>rò inſcripti maior eſt quàm 3 (14159/100000); fiat pri<lb></lb>mò vt 3. 14160. ad 1, ita mill. 25941 ad <lb></lb>mill.8257.paſſ.257, quæ eſt diameter mi- <pb xlink:href="018/01/045.jpg" pagenum="37"></pb> nor verâ deinde vt 3.14159 ad 1, ita mill. <lb></lb> 25941 ad mill. 8257 paſſ. 283 diametrum<lb></lb> maiorem verâ. </s> <s>Quare cum differentia ſit <lb></lb> paſſ 26, electo medio Arithmetico po<lb></lb> terit aſſumi pro terræ diametro <expan abbr="quãtitas">quantitas</expan> mill. <lb></lb> Rom. antiq. 8257 pasſſ. 270. Sed certas <lb></lb> ob causas placuit aſſumere ambitum mill. <lb></lb> 25941, atque ſemidiametrum mill. 4127. <lb></lb> paſſ 822.</s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end></emph.end> Methodum hanc, qua & Solaris ſe<lb></lb>midiametri cum terrenâ comparatæ Ratio<lb></lb> nem venatus es, & telluris ipſius magnitu<lb></lb> dinem indagaſti, omnino improbare non <lb></lb> auſim; quippe qui apparentem Solis ſemi<lb></lb>diametrum obſeruari poſſe ſatis ſcio, & Solis <lb></lb> à terrâ diſtantiam potiſſimùm ex lunari di<lb></lb> chotomiâ haberi ex Ariſtarcho didici: quan<lb></lb> tum verò interuallum à nobis Lunam ſeiun<lb></lb>gat, eiuſdem parallaxes palà faciunt. </s> <s> Quæ <lb></lb> omnia ſi retè fuerint conſtituta, non infir<lb></lb>mis nititur fundamentis inuenta terræ ma<lb></lb> gnitudo: Sed, vt vera fatear, quamuis Sol <lb></lb> quotidie terrma circumiens luſtret, illum <lb></lb> tamen de terrâ, terræ incola inuitus interro<lb></lb>go; quotus enim quiſque eſt, qui ignoret, <lb></lb> quàm oculatum exigat Astronomum appa<lb></lb>rentium Solis ac Lunæ ſemidiametrorum <lb></lb> conſtitutio? ſivè illæ organis deprehendantur, <lb></lb> <pb xlink:href="018/01/046.jpg" pagenum="38"></pb>tur, ſiue ex lucidâ ſpecie (quam ab omni pe<lb></lb>numbrâ ægrè ſecernas) ſiuè ex eclipſibus in<lb></lb>ferantur. </s> <s>Quod ſi aſſumpta Lunæ parallaxis <lb></lb>à vero aliquantulum abſit, vel quia à radio<lb></lb>rum refractione turbetur, vel quia motuum <lb></lb>periodi non ſatis accuratè ad calculos reuo<lb></lb>centur, interuallorum pariter, quæ inde col<lb></lb>liguntur, veritas nutat. </s> <s>Ad hæc fides adhi<lb></lb>benda eſt antiquis ſpatium, quod meridianis <lb></lb>vmbris caret, dimetientibus, atque ſtadijs <lb></lb>300 definientibus; quæ tamen ad notas no<lb></lb>bis menſuras vt reuocemus, certioribus ad<lb></lb>huc argumentis indigemus. </s> <s>Illud tameņ <lb></lb>hìc minimè diſsimulandum videtur, quod <lb></lb>eruditis non paucis placere video: non eam <lb></lb>ſcilicet ſtadij menſuram, quam ex Græco <lb></lb>Heronis ſcholiaſte aſſumpſiſti, adhibendam <lb></lb><arrow.to.target n="note21"></arrow.to.target><lb></lb>eſſe, ſed eam potiùs, quæ ex ipſius Heronis <lb></lb>Mechanici Iſagoge colligitur dicentis, <emph type="italics"></emph>Diau<emph.end type="italics"></emph.end><lb></lb>l<emph type="italics"></emph>on habet Stadia duo, Plethra duodecim, Ace<lb></lb>nas centum viginti, Cubitos octingentos, Pe<lb></lb>des Alexandrinos Philetæreos mille ducentos, <lb></lb>Italicos autem pedes mille quadringentos qua<lb></lb>draginta.<emph.end type="italics"></emph.end></s> <s> Quare Stadium non Romanis pe<lb></lb>dibus 600 conſtat, ſed Alexandrinis 600, hoc <lb></lb>eſt Italicis, pedibus 720, ſeu paſſibus 144. <lb></lb>Neque enim coniecturâ ſatis probabili caret <lb></lb>Eratoſthenem Alexandrinæ Bibliothecæ præ<pb xlink:href="018/01/047.jpg" pagenum="39"></pb>ſectum à Ptolemæis Euergete, Philopatore, <lb></lb>& Epiphane, vſum fuiſſe menſurâ Ægyptijs <lb></lb>tunc familiari, pede nimirum Alexandrino, <lb></lb>atquè adeò etiam ſtadio, quod ille metieba<lb></lb>tur. </s> <s>Hinc fit ſtadia illa 300 reſpondere paſ<lb></lb>ſibus Romanis 43200: arcum verò OK eſſe <lb></lb>paſſ Rom. 21600. Igitur ſi fiat vt arcus OK <lb></lb>à te nuper inuentus ſcrupulorum Quart. <lb></lb>3237367 ad paſſ. </s> <s>Rom. 21600, ita tota pe<lb></lb>ripheria ſcrup. </s> <s>Quart. 4665600000. ad paſſ. </s> <s><lb></lb>Rom. 31.129297, erit multo maior terræ <lb></lb>ambitus, quàm à te fuerit deprehenſus. </s> </p> <p type="margin"> <s><margin.target id="note20"></margin.target><emph type="italics"></emph>XIX <lb></lb>Terræ am<lb></lb>bitus, & dia<lb></lb>meter.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note21"></margin.target><emph type="italics"></emph>XXI <lb></lb>Stadium A<lb></lb>lexandri<lb></lb>num.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed & conſtitutam à Tychone Solis di<lb></lb>ſtantiam, nimis breuibus terminis defini<lb></lb>tam exiſtimant Recentiores Aſtronomi, So<lb></lb>lemque altiùs promouendum cenſent, vt ſi<lb></lb>bi inuicem phœnomena omnia ritè reſpon<lb></lb>deant. </s> <s>Certè P. Io. Baptiſta Ricciolius no<lb></lb>ſtræ Societatis, qui iam annos plures in A<lb></lb>ſtronomiæ inſtauratione feliciter deſudat, <lb></lb>Solem Apogæum à telluris centro remouet <lb></lb>ſemidiam. </s> <s>terr. </s> <s>7580., & Solis Apogæi dia<lb></lb>metrum apparentem ſtatuit Tychonicâ ma<lb></lb><arrow.to.target n="note22"></arrow.to.target><lb></lb>iorem, nimirùm gr.o.m.30.ſec.30. Qua<lb></lb>rè ſi angulus SOT ſit gr.o.m.15.ſec.15., <lb></lb>complementum TSO eſt gr.89.min.44. <lb></lb>ſec.45., cuius Secans, SO 22551105.10158, <lb></lb>quarum partium Radius ST eſt 100000. <pb xlink:href="018/01/048.jpg" pagenum="40"></pb>00000. Sit iam SC ſemid. </s> <s>terreſt. </s> <s>7580, & <lb></lb>SO ſemid.terr. </s> <s>7579: & Secans SO diuida<lb></lb>tur per 7579, vt Quotiens 2975.47237, <lb></lb>prodat quantitatem ſemidiametri OC iņ <lb></lb>partibus Radij ST. </s> <s>Additâ igitur CO ipſi <lb></lb>OS, erit tota SC 22554080.57395, quæ <lb></lb>eſt Secans anguli ISC gr.89.m.44.ſec.45. <lb></lb>Ter. 7. Quar. 17. Quint. 28 1/2, atquè adeo <lb></lb>complementum SCI gr.o.m.15.ſec.14. <lb></lb>Ter. 52. Quar. 42. Quint. 31 1/2. Duplicetur <lb></lb>itaque angulus SCI, & in Scrupula Quinta <lb></lb>reducatur, & ſcrupula Quinta 395227503 <lb></lb>reſpondent ſtadijs Alexandrinis 300, hoc eſt <lb></lb>paſsibus Rom. 43200. Si igitur arcus OK <lb></lb>duplicatus eſt paſſ. </s> <s>43200, totus circuli am<lb></lb>bitus ſcrup. </s> <s>Quint. 279936.000000.erit paſſ. <lb></lb><arrow.to.target n="note23"></arrow.to.target><lb></lb>Rom. 30598162. </s> </p> <p type="margin"> <s><margin.target id="note22"></margin.target><emph type="italics"></emph>XXII <lb></lb>Probabilior <lb></lb>terræ ma<lb></lb>gnitudo ex <lb></lb>eadem me <lb></lb>tbodo inue<lb></lb>stigatur.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note23"></margin.target><emph type="italics"></emph>XXIII <lb></lb>Solis distan <lb></lb>tiam à ter<lb></lb>ra, & pro<lb></lb>portionem̨ <lb></lb>cum illą <lb></lb>inueſtiga<lb></lb>re ex da<lb></lb>ta terræ ma<lb></lb>gnitudine, <lb></lb>Solis Apog. <lb></lb>diametro ap. </s> <s><lb></lb>parenti, & <lb></lb>ſpatio, quod <lb></lb>vmbris ca<lb></lb>ret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Plurimam, opinor, inires gratiam <lb></lb>ab Eruditiſſ. Domino 10. Bapt. Baliano Pa<lb></lb>tritio Genuenſi, ſi ille noſtro huic colloquio <lb></lb>intereſſet; ab eo enim accepi ſe certiſsimo <lb></lb>experimento didiciſſe, telluris ambitum non <lb></lb>minorem eſſe triginta millibus milliarium. </s> <s><lb></lb>Tunc verò non poteram illi acquieſcerę, <lb></lb>cum viderem indè colligi Solem terræ itą <lb></lb>vicinum, vt ab illâ non abeſſet ſemidiam. </s> <s><lb></lb>terr.25; id quod eſt manifeſtè falſum. </s> <s>Tri<lb></lb>buebam autem ſingulis ſtadiis paſſus Rom. <pb xlink:href="018/01/049.jpg" pagenum="41"></pb>120, vt 300 ſtadia eſſent totius circuli gr. <lb></lb>o.m.28.ſec. 35. Ter. 12., dato ambitu <lb></lb>mill. 30000: & arcus OK cum eſſet gr.o. <lb></lb>m. </s> <s>14.ſec.17. Ter. 36., angulus ISC gr.89. <lb></lb>m. </s> <s>45. ſec. 42. Ter. 24. dabat Secantem SC <lb></lb>24052069.35. in partibus Radij SI 100000. <lb></lb>00. Poſitâ verò Tychonicâ ſemidiametro <lb></lb>apparente Solis SOT gr.o.m.15., Secans <lb></lb>SO erat 22918384. 52. Quare ſi per Se<lb></lb>cantium SO, SC, differentiam OC 1133684. <lb></lb>83. diuidatur Secans SC, Quotiens 21 dabit <lb></lb>diſtantiam Solis à terræ centro in ſemidia<lb></lb>metris terreſtribus; id quod apertiſsimè fal<lb></lb>ſum eſſe omnibus conſtat. </s> </p> <p type="main"> <s>At quoniam vis, Guldine, ſtadia illa 300 <lb></lb>eſſe paſſus Romanos 43200, tentemus aņ <lb></lb>illa terræ magnitudo milliaribus 30000 de<lb></lb>finita ſubſiſtat. </s> <s>Si ergo circuli totius peri<lb></lb>pheria ritè ſuas in partes tribuatur, conſtat <lb></lb>paſſ. </s> <s>43200 reſpondere gr. o.m. </s> <s>31. ſec. 6. <lb></lb>Ter. 14. Quar. 24. præcisè: & angulus SCI <lb></lb>gr. o. </s> <s>m. </s> <s>15. ſec. 33. Ter.7. Quar. 12. habet <lb></lb><expan abbr="cõplementum">complementum</expan> ISC gr. 89. m. 44. ſec. 26. Ter. <lb></lb>52. Quar. 48., cuius Secans SC 22110369. <lb></lb>79050, quarum Radius SI eſt 100000.00000. <lb></lb>Porrò angu'us SOT ſemidiameter apparens <lb></lb>Solis Apogæi neceſſariò maior ſtatui debet <lb></lb>angulo SCI conſtituto, cum ſub maiore an-<pb xlink:href="018/01/050.jpg" pagenum="42"></pb>gulo appareat <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ol ex puncto O viciniorę, <lb></lb>quàm ex puncto C remotiore. </s> <s>Quare aſſu<lb></lb>mi non poteſt Solis Apogæi ſemidiameter <lb></lb>apparens, quam ex Ricciolio aſſumebas, gr. <lb></lb>o m. </s> <s>15. ſec. 15., neque Tychonica gr.o. <lb></lb>m.15. multò minùs Vendelinica gr.o.m.14. <lb></lb>ſec.45: Eam igitur ex noſtro Bullialdo de<lb></lb>ſumamus gr.o.m.16.ſec.9., & complemen<lb></lb>ti Secans SO eſt 21288752.30947. Ablata <lb></lb>itaque SO ex SC relinquit terræ ſemidiame<lb></lb>trum OC 821617.48103. in partibus Radij <lb></lb>SI 100000.00000: id quod fieri omnino non <lb></lb>poteſt, niſi tellus multò maior ſit Sole, & hic <lb></lb>ab illâ remoueatur tantùm ſemidiametros <lb></lb>terreſtres ferè 27: quæ omnia à vero longiſ<lb></lb>ſimè abſunt. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> At fortè Balianus non ita telluris <lb></lb>ambitum tricies millenis milliaribus circum<lb></lb>ſcribit, vt nihil inſuper additum velit, ne<lb></lb>què facilè cum Bullialdo tam magnam ſta<lb></lb>tuet apparentem ſolis Apogæi ſemidiame<lb></lb>trum, hæc enim ſibi inuicem cohærere non <lb></lb>poſſunt. </s> <s>Et (quoniam hìc ex amicorum̨ <lb></lb>placitis aliquid vterque depromimus) quod <lb></lb>ſpectat ad apparentem Solis Apogæi diame<lb></lb>trum P. Ricciolius, qui eam labore improbo <lb></lb>pluſquam trig inta diuerſis methodis quadrin<lb></lb>genties, & eo amplius, obſeruando venatus <pb xlink:href="018/01/051.jpg" pagenum="43"></pb>eſt, certiſsimè ſe demum deprehendiſſe mi<lb></lb>hi aliquando affirmabat, illam nec mino<lb></lb>rem minutis 30. nec maiorem min. 31. <lb></lb>Fac igitur à Baliano mediam inter hæc ex<lb></lb>trema Solis Apogæi diametrum apparen<lb></lb>tem gr. o. m. 30. ſec. 30. aſſumi, & telluris <lb></lb>ambitum ita augeri, vt ad illum paſſus 43200 <lb></lb>minorem habeant Rationem: & ſibi omnia <lb></lb>reſpondebunt. </s> <s>Statuatur itaque terræ peri<lb></lb>pheria paſſ. 30598162; & paſſus Rom. 43200 <lb></lb>ſunt gr. o. m. 30. ſec. 29. Ter.45 Quar. 25. <lb></lb>Quint.4., adeoquè angulus SCI gr.o.min. <lb></lb>15.ſec. 14. Ter. 52: Quar. 42. Quint. 32. <lb></lb>cuius Complementi Secans SC 22554080. <lb></lb>57395 in partibus Radij <emph type="italics"></emph>S<emph.end type="italics"></emph.end>I. </s> <s>Iam anguli SOT <lb></lb>gr. o. m. 15. ſec. 15. Secans Complem. SO <lb></lb>22551105.10158. auferatur ex SC; & per <lb></lb>earum differentiam OC 2975.47237 diui<lb></lb>sâ totâ SC, prodibit diſtantia SC ſemid. </s> <s>terr. </s> <s><lb></lb>7580, vt P. Ricciolio placet. </s> </p> <p type="main"> <s>Quarè ex iis, quæ hactenus diſputauimus, <lb></lb>illud infero, quod auctâ Solis Apogæi diame<lb></lb>tro apparente, minui debet terræ ambitus, <lb></lb>vt ad eum paſſus 43200 maiorem habeant <lb></lb>Rationem, ne videlicet tam magno inter ſe <lb></lb>diſcrimine differant anguli S O T & <emph type="italics"></emph>S<emph.end type="italics"></emph.end>CI, vt <lb></lb>per Secantium SO & SC, differentiam OC <lb></lb>diuisâ diſtantiâ SC <emph type="italics"></emph>S<emph.end type="italics"></emph.end>ol terræ vicinior ſtatua<pb xlink:href="018/01/052.jpg" pagenum="44"></pb>tur, quàm par ſit ad phœnomena omnią <lb></lb>explicanda. </s> <s>Hinc fit retentâ eadem terræ <lb></lb>magnitudine non ita augeri ſemidiametrum <lb></lb>apparentem <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olis Apogæi, vt angulus <emph type="italics"></emph>S<emph.end type="italics"></emph.end>OT <lb></lb>ſit gr. o. m. 15. ſec. 25.; Secans enim <emph type="italics"></emph>S<emph.end type="italics"></emph.end>O eſſet <lb></lb>22306254.81750; quæ ablata ex inuentâ <lb></lb>ſuperiùs <emph type="italics"></emph>S<emph.end type="italics"></emph.end>C 22554080.57395. relinqueret <lb></lb>differentiam OC 247825.75645.atque adeò <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>ol Apogæus ſemid. </s> <s>terr. </s> <s>91. à terrâ remoue<lb></lb>retur. </s> <s>Minuenda itaque eſt vel Solis appa<lb></lb>rens diameter, vel terræ magnitudo; ego ve<lb></lb>rò illam potiùs paucioribus ſcrupulis ſecun<lb></lb>dis definiendam cenſerem, quàm terræ am<lb></lb>bitum ad pauciora milliaria reuocandum. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal. </s> <s>S<emph.end type="italics"></emph.end>ed quid his longiùs immoramur? </s> <s><lb></lb>quorum ſubtilior inueſtigatio à noſtro in<lb></lb>ſtituto aliena deprehenditur. </s> <s>Nemo tę, <lb></lb>Merſenne, reprehendat cæleſtes hypotheſes <lb></lb>ex magno illo Atlante Tychone aſſumen<lb></lb>tem; & quamuis ego pariter in eâ ſim ſen<lb></lb>tentiâ, vt exiſtimem ab Erathoſtene homi<lb></lb>ne Cyrenenſi adhibitum ſtadium Alexandri<lb></lb>num, non autem Græcum, quod aſſumebas, <lb></lb>hanc tamen litem hìc agitare non eſt operæ <lb></lb>pretium. </s> <s>Quapropter perge, ſi placet, qua <lb></lb>cæpiſti viâ, terreni globi grauitatem explorare. </s> <s><lb></lb>rare. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Inuentam terræ ſemidiametrum <pb xlink:href="018/01/053.jpg" pagenum="45"></pb>mill. Rom. 4127 paſſ.822. ad pedes reuoco, <lb></lb><arrow.to.target n="note24"></arrow.to.target><lb></lb>pedes quinque Romanos antiquos paſſibus <lb></lb>ſingulis tribuens, & ſunt pedes 20639110. <lb></lb>Quia verò ſphæræ ſunt in triplicatâ Ratione <lb></lb>ſemidiametrorum, comparo terrenam ſe<lb></lb>midiametrum cum ſemidiametro pedali al<lb></lb>terius globi, & <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ationem 1. ad 20.639110 <lb></lb>vſque, ad quartum terminum continuo, vt <lb></lb>ſit tertius terminus 425.972861.592100. <lb></lb>quartus autem 8791.700747.414127. <lb></lb>031000. <emph type="italics"></emph>S<emph.end type="italics"></emph.end>phæra igitur ſemidiametri pedalis <lb></lb>ad terrenam ſphæram <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ationem habet ean<lb></lb>dem, quam vnitas ad quartum hunc termi<lb></lb>num. </s> <s>Vt autem ſphæræ argillaceæ, cuius <lb></lb>ſemidiameter pedalis ſit, grauitatem per<lb></lb>ſpectam haberem, argillam cum aquâ con<lb></lb>tuli, & experimento didici argillæ grauita<lb></lb>tem ad aquæ pondus eſſe vt 27 ad 16. At <lb></lb>ſtanni grauitas ad aquæ grauitatem apud <lb></lb>Ghetaldum in Archimede Promoto eſt vt <lb></lb>100 ad (13 19/37), hoc eſt, vt 37 ad 5. <emph type="italics"></emph>S<emph.end type="italics"></emph.end>i igitur <lb></lb>Ratio ſtanni ad aquam, & aquæ ad argillam, <lb></lb>ſcilicet 37 ad 5. & 16 ad 27 in tribus termi<lb></lb>nis continuetur, ita vt ſint 592,80. 135, <lb></lb>Ratio grauitatis ſtanni ad argillæ pondus, da<lb></lb>tâ molis æqualitate, eſt vt 592 ad 135. </s> </p> <p type="margin"> <s><margin.target id="note24"></margin.target><emph type="italics"></emph>XXIV <lb></lb>Terreni glo<lb></lb>bi ſoliditas <lb></lb>inueſtiga<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quoniam verò apud eundem Ghetaldum <lb></lb>ſtanneæ ſphæræ, cuius diameter ſit vnius pe<pb xlink:href="018/01/054.jpg" pagenum="46"></pb>dis Rom. antiqui, grauitas eſt exactè lib. 304 <lb></lb>& ſphæræ ſunt in triplicatâ Ratione diame<lb></lb>trorum, ſphæra ſtannea ſemidiametrum ha<lb></lb>bens pedalem, ac proinde diametrum bipe<lb></lb>dalem, eſt octuplo grauior illâ, atque adeò <lb></lb>lib, 2432. Atqui ſtannum ad argillam, eſt <lb></lb>vt 592 2d 135, igitur & eandem Rationem <lb></lb>habent æquales ſphæræ; ideoque ſi ſtannea <lb></lb>ſphæra ſemidiametrum pedalem habens nu<lb></lb>merat in grauitate libras 2432, argillaceą <lb></lb>æqualis erit lib. (554 22/37). Hæc autem ad terræ <lb></lb>globum eſt vt vnitas ad quartum illum ter<lb></lb>minum continuè proportionalem in Ratione <lb></lb>ſemidiametrorum. </s> <s>Multiplicetur igitur quar<lb></lb><arrow.to.target n="note25"></arrow.to.target><lb></lb>tus ille terminus 8791.700747.414127. <lb></lb>031000. per libras (554 22/37), & prodibit totius <lb></lb>terræ grauitas, ſi ex merâ argillâ conſtaret, <lb></lb>librarum 4.875829.711809.132072. <lb></lb>(327567 21/37). </s> </p> <p type="margin"> <s><margin.target id="note25"></margin.target><emph type="italics"></emph>XXV <lb></lb>Terreni glo <lb></lb>bi grauitas.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Immenſum places, Merſenne: lu<lb></lb>culentiſsimè enim demonſtraſti quatuor illis <lb></lb>aut ſex ſupra centum orbiculis, de quibus <lb></lb>heri nobis ſermo erat, tellurem totam facil<lb></lb>limè moueri poſſe, etiam ſi eius grauitati <lb></lb>quingenties millies millena librarum mil<lb></lb>lia adiiceres. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ita planè, ſi mera eſſet argilla: ſed <lb></lb>tot marmora ac lapides, ingentesque metal<pb xlink:href="018/01/055.jpg" pagenum="47"></pb>lorum fodinæ, quæ argillæ grauitatem lon<lb></lb>go ſuperant interuallo, non eam vim ad<lb></lb>dunt ponderis, quæ non facilè æſtimari <lb></lb>queat? </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Immò verò, niſi hæc pariter ad<lb></lb>miſcerentur, vererer plurimùm, ne mihi <lb></lb>tanquam prodigo ſuccenſeretis, qui tantam <lb></lb>telluri grauitatem concederem. </s> <s>Metallą, <lb></lb><arrow.to.target n="note26"></arrow.to.target><lb></lb>fateor, ac marmora æqualem argillæ molem <lb></lb>pondere ſuperant: ſed quota demum ſphæ<lb></lb>ræ huius pars illa ſunt? </s> <s>Quod ſi quis illą <lb></lb>grauiora eſſe inculcet, longè leuiorem a<lb></lb>quam cogitet, ex qua viciſsim globus hic <lb></lb>terraqueus conſtat. </s> <s>Quiſquis enim ſe æquum <lb></lb>rerum æſtimatorem præbuerit, non plus re<lb></lb>periri <expan abbr="metallorũ">metallorum</expan> quàm aquæ autumet: quiņ<lb></lb>immo illorum grauitatem ab huius leuitate <lb></lb>ſi non æquari, aut ſuperari, magnâ ſaltem <lb></lb>ex parte compenſari facilè concedat. </s> <s>Iam <lb></lb>verò ſi ad aëris vim non modicam terræ ca<lb></lb>uernis atque cuniculis incluſam, ſeque intrà <lb></lb>ſiccorum corporum particulas non ſibi om<lb></lb>ninò cohærentes inſinuantem, animum ad<lb></lb>uertamus, apparebit illicò exuperantiam il<lb></lb>lam grauitatis hoc defectu vberrimè com<lb></lb>penſari. </s> </p> <p type="margin"> <s><margin.target id="note26"></margin.target><emph type="italics"></emph>XXVI <lb></lb>Terræ gra<lb></lb>uitatem pe<lb></lb>rinde ſe ba<lb></lb>bere proba<lb></lb>tur, ac ſi eſ<lb></lb>ſet mera ar<lb></lb>gilla.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed quoniam motus, cui tellus ſuo pon<lb></lb>dere obſiſteret, in circumfuſo hoc aëre per<pb xlink:href="018/01/056.jpg" pagenum="48"></pb>ficiendus eſſet; minuitur adhuc momen<lb></lb>tum ab halituum aëre leuiorum copiâ penè <lb></lb>infinitâ, quæ totam hanc molem peruadit. </s> <s><lb></lb>Quemadmodum enim nauis aërem aquâ <lb></lb>leuiorem includens in aquâ non mergitur, ſi <lb></lb>tota moles compoſita æqualis aquæ grauita<lb></lb>tem non vincat; vel ſaltem minore mo<lb></lb>mento deſcendit pro incluſi aëris portione; <lb></lb>haud abſimili ratione fieri poteſt, vt grauiori <lb></lb>corpori tot ſpiritus aëre leuiores permiſcean<lb></lb>tur, vt totius compoſitæ molis grauitas non <lb></lb>mediocriter minuatur. </s> <s>Quantum verò hu<lb></lb>iuſmodi halituum metallicis lapidibus im<lb></lb>miſceatur, ſatis ſciunt, quotquot ſodinarum <lb></lb>latebras penetrârunt. </s> <s>Et vt cæteras miſſas <lb></lb>faciam, Hungaricæ aurifodinæ, mihi ma<lb></lb>gis notæ, omnem præcidunt dubitandi an<lb></lb>ſam. </s> <s>Cum enim duæ pateant ad deſcen<lb></lb>dendum viæ, altera breuiſsima, vtpote re<lb></lb>cta, putei in modum (caminum rectiùs <lb></lb>fortaſſe dixeris) cuius latera muniunt arctè <lb></lb>compacti arborum trunci: altera obliquą, <lb></lb>& longior per cuniculos: per hanc perpetuò <lb></lb>ſe frigidus aër magno impetu in ima fodinæ <lb></lb>viſcera inſinuat, dum ex illâ calida pariter <lb></lb>atque graueolens expiratio erumpit. </s> <s>Ne<lb></lb>que indigent metallarii Aſtrologorum næ<lb></lb>nijs, qui imminentem cæli mutationem <pb xlink:href="018/01/057.jpg" pagenum="49"></pb>prædicant; cum ipſi ex immodicâ halituum <lb></lb>infernè aſcendentium copiâ, quibus vix non <lb></lb>præfocantur, cœlum nubibus proximè ob<lb></lb>ducendum nec dubiè pronuncient. </s> <s>Quid? </s> <s><lb></lb>quod aqua ipſa (licet aëre grauior, ſi ſibi ipſa <lb></lb>relinquatur) leuiſsimi vaporis ſpeciem induit <lb></lb>calore ſollicitata, quo interior terræ plagą <lb></lb>abundat: Vbi enim octoginta circiter hexa<lb></lb>podas, quibus extima hæc terræ regio frigi<lb></lb>diſsima definitur, deſcenderis, tepor primùm <lb></lb>gratiſsimus ex frigidâ regione venientem ex<lb></lb>cipit ac recreat, paulatimque adeò augetur <lb></lb>calor, vt demùm metalli foſſores veſtem nul<lb></lb>lam ferant. </s> </p> <p type="main"> <s>Quantum autem momenti ad pondus mi<lb></lb>nuendum obtineat grauium hæc atque le<lb></lb>uium miſcella, ille facilè intelliget, qui ob<lb></lb>ſeruauerit aliquando ſtibium ad vſus medi<lb></lb>cos excoctum æquè graue reperiri, ac de<lb></lb>prehenſum fuiſſet, antequam igni commit<lb></lb>teretur; quamuis inde vi flammæ ingens va<lb></lb>porum ac fumi copia eruperit; ſpiritus enim, <lb></lb>qui auolârunt, cum aërem leuitate vince<lb></lb>rent, cæteris partibus admiſti molem con<lb></lb>ſtituebant maiorem quidem, ſed non grauio<lb></lb>rem, ac ſit deinde reliqua moles minor, fa<lb></lb>ctâ hac halituum ſeceſsione. </s> <s>Perinde atque <lb></lb>ſi vas æreum aquâ iuxta ac aëre plenum in<pb xlink:href="018/01/058.jpg" pagenum="50"></pb>trà aquam ponderetur, deinde ita eius late<lb></lb>ra comprimantur, vt aquam omnem ac <expan abbr="aẽ-rem">ae<lb></lb>rem</expan> excludant, etiam ſi modicum aliquid æ<lb></lb>ris deteratur, adhuc æqualibus momentis in <lb></lb>aquâ grauitare deprehenditur, ſi ad libræ <lb></lb>examen reuocetur; aeris nimirùm leuitas <lb></lb>æris momenta minuebat. </s> </p> <p type="main"> <s>Ne quis verò ductam ex vaſe ſimilitudi<lb></lb>nem calumnietur; Liberum patrem coga<lb></lb>mus pauliſper philoſophari. </s> <s>Dabitis, opinor <lb></lb>vini grauitatem ferè aquæ ſubſeſqui-ſexage<lb></lb>cuplam, vel certè aquæ pondere non maio<lb></lb>rem; ita vt quodcunque aquæ grauitate præ<lb></lb>ſtiterit, haud immeritò vino pariter grauius <lb></lb>cenſeatur. </s> <s>Atqui Tartarum ex vino ſubſide<lb></lb>re nemo neſcit; & quod inde elicitur oleum <lb></lb>Tartari, eſt proximè ad aquam vt 3 ad 2: ſpi<lb></lb>ritus autem vini ad aquam communem, Ra<lb></lb>tionem habet proximè, quam 3 ad 4. Qua<lb></lb>re ſi vinum eiuſdem cum aquâ grauitatis <lb></lb>conſtituatur, Oleum Tartari ad vinum eſt <lb></lb>vt 6 ad 4, vinum autem ad ſpiritum vini vt <lb></lb><arrow.to.target n="note27"></arrow.to.target><lb></lb>4 ad 3. </s> </p> <p type="margin"> <s><margin.target id="note27"></margin.target><emph type="italics"></emph>XXVII <lb></lb>Vini graui<lb></lb>tas medią <lb></lb>Harmonicè <lb></lb>inter Oleum <lb></lb>Tartari, & <lb></lb>Spiritum̨ <lb></lb>vini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quod ſi vini Tartarum ſimul ac ſpiritum <lb></lb>complectentis grauitas medio loco ſe habet <lb></lb>(& quidem medietate Harmonicâ) inter id <lb></lb>quod grauius, & id quod leuius eſt, quamuis <lb></lb>extrema illa non ita multo diſcriminentur in<pb xlink:href="018/01/059.jpg" pagenum="51"></pb>teruallo: quidni terrena hæc moles ex gra<lb></lb>uiſsimis quidem metallis atque lapidibus, <lb></lb>ſed & ex corporibus alijs argillâ leuioribus, <lb></lb>ex aquâ, <expan abbr="aẽre">aere</expan>, ſubtiliſsimisque expirationi<lb></lb>bus coagmentata mediocrem argillæ graui<lb></lb>tatem (quantum fas eſt coniecturâ aſſequi) <lb></lb>obtinere dicatur? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Fallor, ſi Tartarus ipſe ad exte<lb></lb>nuandam terræ grauitatem tibi ſuppetias <lb></lb>non tulerit. </s> <s>Ob oculos pones immenſa ſpe<lb></lb>læa æternis flammarum globis redundantia, <lb></lb>& exaggeratâ longè latèque patentis impio<lb></lb>rum carceris magnitudine (quam penetra<lb></lb>bilis ignis implet, non modò nihil habens <lb></lb>proni, ſed & ſurſum rectis lineis in cœleſtem <lb></lb>locum ſubuolare contendens) tantum ex tel<lb></lb>lure detrahes ponderis, quantum metallą <lb></lb>omnia atque marmora reſtituere non va<lb></lb>leant. </s> <s>Nec deerit doctiſsimorum virorum <lb></lb>ſuffragium, qui cauernam hanc totius ter<lb></lb>reni globi partem quartam præciſiſſimè ſta<lb></lb>tuunt, cum qua pariter admirabilem illam <lb></lb>Lunaris motûs librationem conſentire inge<lb></lb>niosè opinantur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Et verò talia afferentem caſtigare <lb></lb>quis audeat? </s> <s>Abſtineo tamen, ne fortè ex <lb></lb>vobis audire cogerer iterum, quæ haud ita <lb></lb>pridem neſcio quis diſſerebat. </s> <s>Nihil eſt, <pb xlink:href="018/01/060.jpg" pagenum="52"></pb><arrow.to.target n="note28"></arrow.to.target><lb></lb>aiebat ille, quod vim pati perpetuam cen<lb></lb>ſendum ſit. </s> <s>At ſi elementis omnibus terra <lb></lb>grauitare, ignis leuitate præſtet; an non. </s> <s>æ<lb></lb>ternum aberunt loco, quem ſingulis naturâ <lb></lb>tributum eſt vt velint conſequi? </s> <s>Terra ete<lb></lb>nim, niſi columnis baſim in centro haben<lb></lb>tibus nixa fingatur, tota procul à centro con<lb></lb>quieſcit; ignis verò infimum locum tenet. </s> <s><lb></lb>Quiſquis autem ibi ignem à Deo perpetuis <lb></lb>vinculis eo tantùm conſilio coerceri exiſti<lb></lb>mat, vt ſceleratorum carnificinam exerceat; <lb></lb>diligenter perſpiciat velim, an non magis <lb></lb>pro Diuinæ ſapientiæ atque omnipotentiæ <lb></lb>dignitate locuturus ille ſit, qui, quemadmo<lb></lb>dum Iridem licèt naturæ penicillo in nubi<lb></lb>bus deſcriptam, in ſempiterni tamen fœde<lb></lb>ris teſſeram à Deo aſſumptam nouit, ſic re<lb></lb>rum naturæ conſentaneum adſtruat hunc or<lb></lb>dinem, quo vniuerſitatis rerum ſubluna<lb></lb>rium elementa pro ſui ponderis ratione ita <lb></lb>diſponantur, vt centrum omnium grauiſsi<lb></lb>mus ignis impiorum carcer atque carnifex <lb></lb>conſtitutus obtineat, illumque minùs gra<lb></lb>uia elementa terra & aqua deinceps conſe<lb></lb>quantur, vſque eò dum leuiſsimus aër cir<lb></lb>cumfuſus reliqua complectatur. </s> </p> <p type="margin"> <s><margin.target id="note28"></margin.target><emph type="italics"></emph>XXVIII <lb></lb>Coniecturæ <lb></lb>pro adstru<lb></lb>enda ignis <lb></lb>inferni gra<lb></lb>uitate.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Fruſtra aſcendentem flammam apertiſsi<lb></lb>mum igneæ leuitatis argumentum obiicie<pb xlink:href="018/01/061.jpg" pagenum="53"></pb>bant. </s> <s>Nàm ille ſupremo ætheri terrenis ex<lb></lb>pirationibus immuni, ac lunari orbitæ fini<lb></lb>timo, quem Ariſtotele teſte propter conſue<lb></lb>tudinem ignem dicimus, vix aliquid ignis <lb></lb>præter ſplendidum nomen reliquum facie<lb></lb>bat. </s> <s>Aſcendit in flammâ (ſic ille) humido <lb></lb>vapori, quem calor eximius rarum fecit, <lb></lb>permiſta fuligo, aére ſanè non leuior: quidni <lb></lb>pariter à flammâ in cœlum ſubuolante par<lb></lb>ticulæ igneæ abripiantur? </s> <s>quibus vel pru<lb></lb>narum vel candentis ferri incolis, nullum eſt <lb></lb>cum æthereâ regione commercium. </s> <s>Aņ <lb></lb>fumeus vapor igniculorum coloniam in cœ<lb></lb>lum deduxiſſe cenſendus eſt, quia illi nobis <lb></lb>non videntibus in terram relabuntur? </s> <s>Sed <lb></lb>quis neget, incendio ſyluam depopulante, <lb></lb>immodicam fuliginum copiam in ſuperiora <lb></lb>rapi? </s> <s>quibus tamen ætheream ſedem ineptè <lb></lb>adſcriberemus, quia illas iterum deſcenden<lb></lb>tes obſeruando notare non poſſumus. </s> <s>Quod <lb></lb>ſi ignibus ſub dio ſemper excitatis, fuligo <lb></lb>nulla camino vnquam adhæſiſſet; nonnè ſa<lb></lb>tis habuiſſemus argumenti, ex quo illius gra<lb></lb>uitas innotuiſſet, ſi quando ingentem fuligi<lb></lb>nis maſſam ex aëre decidentem licuiſſet in<lb></lb>tueri? </s> <s>Neque enim ideò grauitate ſpoliamus <lb></lb>terreſtres puluiſculi atomos, quia in aëre va<lb></lb>gantes ita ſenſum diſsipatæ fugiunt, vt eas <pb xlink:href="018/01/062.jpg" pagenum="54"></pb>deſcendentes animaduertere nequeamus: ſed <lb></lb>ad earum grauitatem adſtruendam ſatis eſſe <lb></lb>putamus, quod particulæ illæ vinculum na<lb></lb>ctæ, quo lapidem conſtituant, deſcendentes <lb></lb>ſub aſpectum cadant. </s> <s>Cur igitur tantam̨ <lb></lb>ignium vim in fulmine delapſam, ſeque in <lb></lb>ima terræ viſcera inſinuantem cernentes, <lb></lb>perinde atque ſaxum in aquam decidens <lb></lb>mergitur, igneæ grauitatis ſuſpicioni locum <lb></lb>non damus? </s> <s>Nemo ſiquidem facilè credat <lb></lb>accenſum fulmen á ſuperioribus nubis parti<lb></lb>bus, quæ inferioribus tenuiores ſunt ac leuio<lb></lb>res, minùsque ad aqueam naturam vergen<lb></lb>tes, deorſum reflecti: cùm nec ignis ex Auro, <lb></lb>quod ob impetûs ac efficaciæ ſimilitudinem <lb></lb>nomen à fulmine obtinuit, à quoquam re<lb></lb>flectatur, ſed inſitâ naturæ vi præceps deor<lb></lb>ſum feratur: </s> </p> <p type="main"> <s>Ad hæc ignis genus vniuerſum in ſpecies <lb></lb>certas, quibus iterum partes aliæ atquè aliæ <lb></lb>ſubeſſent, partiebatur & diſtinguebat: Alti <lb></lb>enim reperiuntur Ignes luce iuxta atque ca<lb></lb>lore conſpicui, quorum frequentiſsimus eſt <lb></lb>& communis vſus, atque vulgatiſsima noti<lb></lb>tia: Alii ſunt, qui, quoniam plus fulgoris <lb></lb>habentes, quàm caloris, oculis tantùm blan<lb></lb>diuntur, cum Fatuis Ignibus numerantur: <lb></lb>Alios demùm quaſi latentes ſinu natura fo<pb xlink:href="018/01/063.jpg" pagenum="55"></pb>uet, quos luce carentes quamuis Mortuos <lb></lb>vulgus appellet, nimis tamen viuaci virtute <lb></lb>præditos vis cauſtica ſatis prodit. </s> <s>Ad ter<lb></lb>tium hoc ignium genus, qui calidi cum ſint, <lb></lb>non tamen ſunt lucidi, reuocabat igniculos, <lb></lb>qui aquis acribus (Aquas Fortes vulgus ap<lb></lb>pellat) permiſti ac oleo Tartari ſeu Vitrioli <lb></lb>metalla ſoluunt, & in Chymicam calcem̨ <lb></lb>redigunt breui temporis morâ, cum tamen <lb></lb>plurium dierum interuallo indigeat, quiſ<lb></lb>quis ea voluerit ardentiſsimæ fornacis igne in <lb></lb>calcem excoquere. </s> <s>Porrò aquas huiuſmodi <lb></lb>acres ex ſalibus extillari, ſales autem graui<lb></lb>tate præditos non mediocri obſeruans illud <lb></lb>demum inferebat, quod ignes omnium ve<lb></lb>hementiſsimi, quantum quidem experimen<lb></lb>to aſſequi poſſumus, cum grauitate ſunt con<lb></lb>iuncti, vt in Aquis Fortibus, Oleo Tartari, <lb></lb>&. </s> <s>Vitrioli, in Auro pulueris pyrii ſpeciem <lb></lb>nacto, & in Fulmine licet paſsim experiri. </s> </p> <p type="main"> <s>Hæc ferè ſunt, ſed paulò preſsiùs atquę <lb></lb>ſummatim expoſita, ex quibus ille conficie<lb></lb>bat ignium generi latiſsimè patenti ſubeſſę <lb></lb>ſpecies quaſdam grauiſsimorum corporum <lb></lb>eximiâ vrendi facultate præditorum, quæ <lb></lb>mundanæ ſphæræ centrum meritò teneant, <lb></lb>ibique perpetuam efficiant noctem, niſi for<lb></lb>tè ſubluſtrem, quantum ſatis ſit ad impia<pb xlink:href="018/01/064.jpg" pagenum="56"></pb>rum cruciatus ſuarum alienarumque cala<lb></lb>mitatum aſpectu augendos. </s> <s>Quare Tarta<lb></lb>rum ille concipiebat quaſi immenſas Ther<lb></lb>mas ac balneas efficaciſſimis omnium cau<lb></lb>ſticorum particulis plenas; quæ proptereą <lb></lb>lacus & ſtagnum ignis, ob quietem ſcilicet, <lb></lb>à Diuinis literis dicuntur. </s> <s>Cumque plurą <lb></lb>ijs quidem, quæ à Diuinis literis docemur, <lb></lb>conſona, ſed præter eorum, qui aderant, opi<lb></lb>nionem, de ignis iſtiuſmodi naturâ diſpu<lb></lb>taſſet; ne quid temerè prolatum videretur, <lb></lb>ſermonem claudens Lactantij l. 7. diu. </s> <s>inſt. </s> <s><lb></lb>cap. 21. authoritate firmauit, vbi de igne <lb></lb>illo ſempiterno impiorum corpora crucian<lb></lb>te loquitur, <emph type="italics"></emph>Cuius natura,<emph.end type="italics"></emph.end> inquit, <emph type="italics"></emph>diuerſa <lb></lb>eſt ab hoc noſtro, quo ad vitæ neceſſaria vti<lb></lb>mur, qui niſi alicuius materiæ fomite alatur, <lb></lb>extinguitur. </s> <s>At ille Diuinus per ſe ipſum <lb></lb>ſemper viuit ac viget ſine vllis alimentis, nec <lb></lb>admiſtum habet fumum, ſed eſt purus ac li<lb></lb>quidus, & in aquæ modum fluidus: non enim <lb></lb>vi aliqua ſurſum verſus vrgetur, ſicut noſter, <lb></lb>quem labes terreni corporis, quo tenetur, & fu<lb></lb>mus intermiſtus exilire cogit &c.<emph.end type="italics"></emph.end></s> <s> Cum ita<lb></lb>que ſuſpicarer, ne quis veſtrum hæc eadem <lb></lb>obiiceret, ſi fortè ad extenuandum telluris <lb></lb>pondus ex inferorum ignibus argumentą <lb></lb>deſumpſiſſem, ſatius duxi abſtinere, ne co<pb xlink:href="018/01/065.jpg" pagenum="57"></pb>gerer hanc inire diſputationem̨. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Haud ego ſanè ineptam dixerim̨ <lb></lb>philoſophiam illam, quæ rerum naturam <lb></lb>per experimenta veſtigat: ſed nec aliquid te<lb></lb>merè pronunciandum, quo vetus opinio <lb></lb>tot ſapientum authoritate firmata de poſſeſ<lb></lb>ſione deiiciatur. </s> <s>Quamuis autem ſententia <lb></lb>hæc videatur adhuc enucleariùs explicanda, <lb></lb>vt igni ſummam grauitatem adſtruat; non <lb></lb>is tamen ego ſum, cui ſtomachum moueant <lb></lb>quæcunque præter opinionem audire con<lb></lb>tigerit. </s> <s>Nec dubito quin, ſi rem penitiùs <lb></lb>introſpicere vellemus, plura occurrerent à <lb></lb>noſtræ diſputationis inſtituto non alieną. </s> <s><lb></lb>Sed quoniam non placet his diutiùs immo<lb></lb>rari, ea commodiorem in locum reiiciamus. </s> <s><lb></lb>Tibi interim datur, Merſenne, terreni glo<lb></lb>bi grauitatem, perpenſis omnibus, haud <lb></lb>multum abeſſe ab eâ grauitate, quam æqua<lb></lb>lis moles argillacea obtineret. </s> <s>Cum verò <lb></lb>res tota ex telluris magnitudine pendere vi<lb></lb>deatur, ne quis ſupereſſet dubitandi locus, <lb></lb>opus eſſet Geometricè perſpectam haberę <lb></lb>telluris magnitudinem. </s> <s>Quare ſi quid ha<lb></lb>bes, Guldine, quo nos poſsis, methodo non <lb></lb>adeò operosâ, in huius problematis cogni<lb></lb>tionem deducere, in medium proferre nę <lb></lb>graueris. </s> </p> <pb xlink:href="018/01/066.jpg" pagenum="58"></pb> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Vnum præterea, quod non parùm <lb></lb><arrow.to.target n="note29"></arrow.to.target><lb></lb>in rem tuam facit, Galilæe, audire placeat. </s> <s><lb></lb>Illud autem eſt, quod quamuis terram decu<lb></lb>plò grauiorem quis conſtitueret, ac ego de<lb></lb>prehenderim, nihilo tamen minùs tuis illis <lb></lb>orbiculis moueri facilè poſſet: non tantum <lb></lb>quia decuplex iſta grauitas non pertingeret <lb></lb>ad libras illas 50.000000.000000.000000. <lb></lb>000000. & eo amplius, verùm etiam quią <lb></lb>non totum illud pondus ſimul motui repu<lb></lb><figure id="id.018.01.066.1.jpg" xlink:href="018/01/066/1.jpg"></figure><lb></lb>gnaret. </s> <s>Sit enim̨ <lb></lb>totus terræ globus <lb></lb>HIKL, cuius cen<lb></lb>trum C congruat v<lb></lb>niuerſi centro, iņ <lb></lb>quo nullum habet <lb></lb>momentum ad de<lb></lb>ſcenſum, ſed in eo <lb></lb>quieſcit. </s> <s>An non ſa<lb></lb>tis Archimedi fuiſ<lb></lb>ſet, ſi terram vnum <lb></lb>aut alterum milliare aliò tranſtuliſſet? </s> <s>Mo<lb></lb>ueri igitur intelligatur centrum ex C in T, <lb></lb>& ſit terra translata SORV. </s> <s>Huic motui <lb></lb>primùm, præter hemiſphærium ſuperius <lb></lb>HLK, non repugnat totum hemiſphærium <lb></lb>inferius HIK, cuius videlicet partes plurimæ <lb></lb>fiunt centro C propiores, in quod ſuis nuti<pb xlink:href="018/01/067.jpg" pagenum="59"></pb>bus feruntur. </s> <s>Ponatur enim CT ſemidia<lb></lb>metri pars milleſima, hoc eſt mill. 4. & eo <lb></lb>amplius; ſegmentorum MON & MVN Ra<lb></lb>tio inuenietur, ex ijs quæ Archimedes docet <lb></lb>l. 2. de ſph. </s> <s>& eyl. </s> <s>prop. 2. ſunt enim ſeg<lb></lb>menta illa æqualia conis eandem baſim MN <lb></lb>habentibus, hi autem ex Eucl. l. 12. prop. </s> <s><lb></lb>14 inter ſe ſunt vt altitudines: Quapropter <lb></lb>inuentis conorum altitudinibus, quas Ar<lb></lb>chimedes docet, innoteſcit Ratio ſegmen<lb></lb>torum ſphæricorum conis illis æqualium̨. </s> <s><lb></lb>Cum itaque CT ſit Radij (1/1000), ſegmenti <lb></lb>MVN altitudo eſt 999, ſegmenti verò <lb></lb>MON altitudo eſt 1001. Fiat igitur vt alti<lb></lb>tudo ſegmenti maioris 1001 ad ſummam <lb></lb>ex eadem altitudine & Radio 2001, ita al<lb></lb>titudo ſegmenti ſphærici minoris 999, ad <lb></lb>coni æqualis altitudinem 1997. Similiter vt <lb></lb>altitudo minoris ſegmenti 999 ad ſummam <lb></lb>ex eadem & Radio 1999, ita altitudo ſeg<lb></lb>menti ſphærici maioris 1001 ad coni æqua<lb></lb>lis altitudinem 2003. Eſt igitur MON ad <lb></lb>MVN vt 2003 ad 1997: atque adeò ſeg<lb></lb>mentum maius addit vltra hemiſphærium <lb></lb>ſolùm totius globi (6/4000). Quare vt tellus ve<lb></lb>niret in T, ſolum ſegmentum ſphæricum̨ <lb></lb>MSORN vt ſummum deorſum versùs C <lb></lb>vrgeret; cui tamen, ne poſtea deſcendet, <pb xlink:href="018/01/068.jpg" pagenum="60"></pb>reliquum ſegmentum MVN obſiſteret, cum <lb></lb>deberet à centro remoueri illo deſcendente: <lb></lb>ac proinde quamuis in motu ſemper auge<lb></lb>retur difficultas mouendi, nunquam tamen <lb></lb>tota grauitas, perciperetur, niſi quando I ve<lb></lb>niſſet in C; tunc enim tota ſphæra deorſum <lb></lb>niteretur. </s> <s>Præterea ſegmentum illud MON <lb></lb>non eadem obtineret ad deſcendendum mo<lb></lb>menta in tantâ centri vicinitate, ac valdè <lb></lb>procul à centro: neque enim ex hoc, quòd <lb></lb>experimentis euincere non poſſimus grauia <lb></lb>centro propiora minùs vrgere deorſum̨ <lb></lb>quàm remotiora (cum illa, quæ in experi<lb></lb>mentum aſſumuntur, non ea eſſe queant, <lb></lb>quæ diſcrimen inferant ſenſu perceptibilę) <lb></lb>repugnandum eſt rationi manifeſtæ id ſua<lb></lb>denti, vbi & ponderis amplitudo & inter<lb></lb>ualli differentia inſignis eſt atque conſpi<lb></lb>cuą. </s> </p> <p type="margin"> <s><margin.target id="note29"></margin.target><emph type="italics"></emph>XXIX <lb></lb>Telluris <lb></lb>grauitas <expan abbr="nõ">non</expan> <lb></lb>tota reſiſte<lb></lb>ret Archi<lb></lb>medi traben<lb></lb>ti.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Hinc fit 24 axibus in peritrochio aut tym<lb></lb><arrow.to.target n="note30"></arrow.to.target><lb></lb>panis dentatis, quorum partes eſſent in Ra<lb></lb>tione decuplâ, fieri poſſe, vt virtute tres li<lb></lb>bras mouere valente terra per aliquod ſpa<lb></lb>tium moueretur; illa enim mouere poſſet <lb></lb>lib 3000000.000000.000000.000000; qui <lb></lb>numerus excedit ſemiſſem ponderis totius <lb></lb>terræ; ac proinde eouſque moueret, dum̨ <lb></lb>ſegmentum MON æquale eſſet toti ponderi, <pb xlink:href="018/01/069.jpg" pagenum="61"></pb>quod ab eadem potentiâ poſſet ſuſtineri ad<lb></lb>hibitâ eadem machinâ, habitâ tamen ratio<lb></lb>ne ſegmenti MVN ex parte ſuſtentantis ſeg<lb></lb>mentum ſuperius, ne tanto impetu deorſum <lb></lb>vrgeat, quanto vrgeret, ſi ſegmentum MVN <lb></lb>non adeſſet. </s> <s>At verò compoſitis tantùm 17 <lb></lb>helicibus cum tympanis denticulos 25 ha<lb></lb>bentibus, & vltimo tympano ad axem, cui <lb></lb>funis ductarius circumuoluitur, Rationem <lb></lb>quintuplam habente, potentia vnius libræ <lb></lb>ſuſtentatiua applicata manubrio æqualis lon<lb></lb>gitudinis cum tympanorum ſemidiametro, <lb></lb>poſſet mouere terram ex C in T vſque eò <lb></lb>dum ſegmentum MON eſſet lib 2.910383. <lb></lb>045673.370361.328125. qui pariter libra<lb></lb>rum numerus excedit totius terrenæ graui<lb></lb>tatis ſemiſſem: at potentia decem libras lo<lb></lb>co transferre valens, decuplum pondus mo<lb></lb>uere poſſet, atque adeò totum globum ele<lb></lb>uare. </s> <s>Sed iam Guldinum audiamus, vt cer<lb></lb>tam telluris magnitudinem ſtatuamus. </s> </p> <p type="margin"> <s><margin.target id="note30"></margin.target><emph type="italics"></emph>XXX <lb></lb>Definitur <lb></lb>machiną, <lb></lb>qua potuiſ<lb></lb>ſet tellus mo<lb></lb>ueri ab Ar<lb></lb>chimede.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Fieri non poteſt, vt paucis me ex<lb></lb>pediam, quia non vna tantùm, aut alterą <lb></lb>ſuppetit methodus, ſed plures aliquando ex<lb></lb>cogitaui, cum hac ſuper re animum diligen<lb></lb>tiùs aduerterem vehementer admirans ab <lb></lb>antiquis nihil ad nos veniſſe, in quo animus <lb></lb>Gemetricus poſſet conquieſcere. </s> <s>Neque fa<pb xlink:href="018/01/070.jpg" pagenum="62"></pb>cilè dixerim, quænam præ cæteris metho<lb></lb>dus arrideat, cum pro diuersâ locorum op<lb></lb>portunitate aliâ atque aliâ methodo vti opor<lb></lb>teat. </s> <s>Quarè conſultius fortaſſe fuerit, vel <lb></lb>omnes pariter ſilentio obuoluere, vel in aliam <lb></lb>diſſertationem reijcere. </s> <s>Quod ſi, quam he<lb></lb>ri Merſennus temporis dilationem ad am<lb></lb>pliores numeros in pagellâ priuatim deſcri<lb></lb>bendos impetrauit, mihi non denegetis, tæ<lb></lb>dio veſtro parcetur, & meo labori. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Rationi conſentanea ſunt, quæ po<lb></lb>ſtulas; neque æquum eſt præproperæ curio<lb></lb>ſitati obſecundantes multiplicis methodi co<lb></lb>gnitione fraudari. <lb></lb><figure id="id.018.01.070.1.jpg" xlink:href="018/01/070/1.jpg"></figure></s> </p> <pb xlink:href="018/01/071.jpg" pagenum="63"></pb> <figure id="id.018.01.071.1.jpg" xlink:href="018/01/071/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>DISSERTATIO <lb></lb>TERTIA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Methodos varias inueniendi <lb></lb>terræ quantitatem <lb></lb>proponit.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Guldinus, Galilæus, Merſennus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s>HAVD ſatis ſcio, an poſ<lb></lb>ſim aliquid proferrę, <lb></lb>quod veſtræ exspectatio<lb></lb>ni faciat ſatis in eâ, quam <lb></lb>nobis hodiè examinan<lb></lb>dam ſtatuimus quæſtio<lb></lb>nem de terraquei huius <lb></lb>globi magnitudine inueſtigandâ: vos idcircò <pb xlink:href="018/01/072.jpg" pagenum="64"></pb>pro veſtrâ humanitate tenuitati meæ ve<lb></lb>niam dabitis, ſi quid afferre contigerit ita <lb></lb>planum ac facilè, vt veſtrorum ingeniorum <lb></lb>ſublimitati non reſpondeat. </s> <s>Nihil habeo <lb></lb>certi quod ſtatuam de terræ quantitate, ne<lb></lb>que enim hactenus otium fuit, quæ conce<lb></lb>peram, in praxim deducere. </s> <s>Fieri autem <lb></lb>poſſe exiſtimo, vt operâ non longâ propo<lb></lb>ſitum ſcopum aſſequamur: duo nimirum̨ <lb></lb>præcognoſci oportet, quibus notis ac certis <lb></lb>terrenam diametrum poſſumus inueſtigarę. </s> <s><lb></lb>Primum eſt altitudo oculi ſupra maris iņ <lb></lb>immenſum patentis ſuperficiem, quæ non <lb></lb>æquabili planitie explicatur, ſed ſphæram̨ <lb></lb>æmulatur: hanc verò altitudinem certiſſi<lb></lb>mè nobis innoteſcere poſſe quis neget? </s> <s>cum <lb></lb>eam funiculo vel phyſicâ aliâ menſurâ ſæ<lb></lb>piùs dimetiri liceat. </s> <s>Alterum, quod in hoc <lb></lb>negotio requiritur, eſt angulus, quem cum <lb></lb>lineâ perpendiculi ad terræ centrum ductâ <lb></lb>conſtituit opticus radius extremum hori<lb></lb>zontem allambens: hunc ſi organo ad id <lb></lb>affabrè elaborato obſeruaueris, ſereno cœlo, <lb></lb>tranquillo mari, cum minima refractionis <lb></lb>ſuſpicio ſubeſſe poteſt, quid certius requi<lb></lb>ras? </s> <s>cum organo eidem in dimetiendis ſy<lb></lb>derum altitudinibus aut diſtantijs acquie<lb></lb>ſcas. </s> <s>His autem duobus cognitis terræ quo<pb xlink:href="018/01/073.jpg" pagenum="65"></pb>que ſemidiametrum latere non poſſe de<lb></lb>monſtro. </s> </p> <p type="main"> <s>Sit enim, exempli gratiâ, nota altitudo <lb></lb>BA Phari Genuenſis (laternam vocant) cum <lb></lb><arrow.to.target n="note31"></arrow.to.target><lb></lb>ſcopulo palmorum Genuenſium 440, hoc <lb></lb>eſt pedum Rom. ant. </s> <s>480, obſeruatusque <lb></lb>angulus BAD ſit gr. 89. m. 36. ſec. 33. Quo<lb></lb>niam ergo linea AD circulum tangit in D, <lb></lb>angulus CDA eſt rectus. </s> <s>Ex B ducta intel<lb></lb>ligatur BE parallela ipſi CD; eſtque triangu<lb></lb>lum ABE rectangulum ad E, cuius hypo<lb></lb>thenuſa AB, & angulus adiacens innotue<lb></lb>runt. </s> <s>Quare fiat vt Radius 100000. 00000. <lb></lb>ad ſinum gr. 89. m. 36. ſec. 33. hoc eſt 99997. <lb></lb>67348, ita AB ped. 480. ad BE ped. (479 <lb></lb>98883.27040/100000.00000). Porrò triangula ABE, ACD æqui<lb></lb>angula ſunt propter linearum BE, CD pa<lb></lb>ralleliſmum, adeoque & ſimilia, ac vt AB <lb></lb>ad BE, ita AC ad CD. </s> <s>Ponatur autem BC <lb></lb>vna Radix Algebricè. </s> <s>Igitur vt AB ped. 480 <lb></lb>ad BE ped. (479 98883.27040/10000000000), ita AC ped. 1 ℞ + <lb></lb>480 ad CD ped. (47998883.27040/48000000.00000) ℞ + (479 47463969.79200/48000000.00000). <lb></lb>Eſt autem CD æqualis ipſi CB 1 ℞. </s> <s>Quare <lb></lb>factâ Antitheſi iuxta Algebræ regulas, ma<lb></lb>net æquatio inter hos terminos (111672960/48000000.00000) ℞ & <lb></lb>pedes (479 47463969.79200/48000000.00000). Inſtitutâ denique di<lb></lb>uiſione prodit quotiens ped. 20631193., <pb xlink:href="018/01/074.jpg" pagenum="66"></pb>pretium 1 ℞ CB vel <lb></lb><figure id="id.018.01.074.1.jpg" xlink:href="018/01/074/1.jpg"></figure><lb></lb>CD. </s> <s>Eſt ergo inuen<lb></lb>ta terræ ſemidiameter <lb></lb>mill. Rom. ant. </s> <s>4126, <lb></lb>paſſ. </s> <s>238. poſito angu<lb></lb>lo ad A gr.89.m.36. <lb></lb>ſec 33. præcisè. </s> </p> <p type="margin"> <s><margin.target id="note31"></margin.target><emph type="italics"></emph>XXXI <lb></lb>Prima me<lb></lb>thodus in<lb></lb>ueniendi tel<lb></lb>luris ſemi<lb></lb>diametrum, <lb></lb>per Trigo<lb></lb>nometriam <lb></lb>& Alge<lb></lb>bram.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quod ſi rem breuiùs <lb></lb>aſſequi velis, dato an<lb></lb><arrow.to.target n="note32"></arrow.to.target><lb></lb>gulo obſeruato in A gr. <lb></lb>89. m. 36. ſec. 33, ſumatur AC vt Radius, & <lb></lb>CD, vt ſinus dati anguli. </s> <s>Et aſſumptâ BC <lb></lb>1 ℞ fiat vt Radius 100000.00000. ad dati an<lb></lb>guli ſinum 99997.67348, ita AC ped. 1 ℞ <lb></lb>+ 480 ad CD ped. (99997.67348℞+4799888327040/100000.00000). Eſt <lb></lb>CD ipſi CB 1 ℞ æqualis, atque adeò vtrinque <lb></lb>demptâ fractione (99997.67348/100000.00000) ℞, remanet æqua<lb></lb>tio inter (232652/100000.00000) ℞ & ped. (4799888327040/100000.00000). Qua<lb></lb>rè factâ diuiſione habetur pretium 1 ℞ ped. <lb></lb>20631193 vt priùs. </s> </p> <p type="margin"> <s><margin.target id="note32"></margin.target><emph type="italics"></emph>XXXII <lb></lb>Idem aliter, <lb></lb>& breuiùs.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Methodus hæc plana eſt atque fa<lb></lb>cilis cuiuis vel leuiter Analyticâ ſcientiâ aſ<lb></lb>perſo: ſed aliquos fortaſſe deterreret, qui vel <lb></lb>ipſum. </s> <s>Algebræ nomen horrent, quamuis <lb></lb>Mathematici audire velint. </s> <s>Alios angulo<lb></lb>rum obſeruatio, & linearum circulo adſcri<lb></lb>ptarum vel inſcriptarum inueſtigatio ex Ca<pb xlink:href="018/01/075.jpg" pagenum="67"></pb>noné defatigat, ſi maximè res ad minimas <lb></lb>Aſtronomicas fractiones deducta exigat par<lb></lb>tis proportionalis inquiſitionem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Satis eſt, ſi peritis Geometris hac <lb></lb>in re fiat ſatis. </s> <s>Verùm adhuc abſque Cano<lb></lb><arrow.to.target n="note33"></arrow.to.target><lb></lb>ne Trigonometrico res tota perfici poſſet, <lb></lb>ſed non ſine Algebrâ. </s> <s>Habeatur enim qua<lb></lb>dratum Geometricum <emph type="italics"></emph>S<emph.end type="italics"></emph.end>H; <lb></lb>vel etiam ſit rectangulum, <lb></lb><figure id="id.018.01.075.1.jpg" xlink:href="018/01/075/1.jpg"></figure><lb></lb>cuius latus AS maius ſit late<lb></lb>re AH, id quod aliquando <lb></lb>commodius accidet. </s> <s>Obuer<lb></lb>tatur latus AH ita, vt con<lb></lb>gruat radio optico terram̨ <lb></lb>tangenti AD, in ſuperiorę <lb></lb>figurâ: eritque triangulum <lb></lb>ABE ſimile triangulo OAS: Nam anguli <lb></lb>SAH & BEA ſunt recti, ac proinde lineæ <lb></lb>SA, BE parallelæ, intrà quas anguli alterni <lb></lb>SAO, EBA ſunt æquales; ſicut & alterni <lb></lb>EAB, SOA, intra parallelas SO, AE. </s> <s>Igi<lb></lb>tur vt OA ad AS, ita AB ad BE: ſed vt AB <lb></lb>ad BE, ita in ſuperiore figurâ AC ad CD; <lb></lb>ergo vt OA ad AS, ita AC ad CD. </s> <s>Quare <lb></lb>ſi latus AS Quadrati vel rectanguli notum ſit <lb></lb>in particulis quibuslibet, facilè innoteſcet, <lb></lb>quot huiuſmodi particulas contineat AO. </s> <s><lb></lb>Cum verò altitudo AB nota ſit ex. gr. ped. <pb xlink:href="018/01/076.jpg" pagenum="68"></pb>480, aſſumatur BC 1 ℞: tum fiat vt particu<lb></lb>læ OA ad particulas AS, ita ped. 1 ℞ + 480 <lb></lb>ad aliud, & proueniet quartus terminus CD <lb></lb>æqualis ipſi CB 1 ℞: atque adeò factâ Anti<lb></lb>theſi, & inſtitutâ diuiſione habetur quanti<lb></lb>tas ipſius CD. </s> </p> <p type="margin"> <s><margin.target id="note33"></margin.target><emph type="italics"></emph>XXXIII <lb></lb>Idem aliter <lb></lb>ſine Trigo<lb></lb>nometria.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quid? </s> <s>quod ſinè Algebrâ res tam facilis <lb></lb><arrow.to.target n="note34"></arrow.to.target><lb></lb>eſt, vt penè non audeam dicere, ne vulgata <lb></lb>vilecat. </s> <s>Fiat vt OI, differentia inter OA & <lb></lb>AS, ad ipſam AS, ita nota altitudo AB ad <lb></lb>aliud, & proueniet CD quæſita terræ ſemi<lb></lb>diameter. </s> <s>Eſt nimirum AB differentia inter <lb></lb>AC & CD, & vt tota AC ad totam AO, ita <lb></lb>ablata CB ad ablatam AI; igitur & reliqua <lb></lb>AB ad reliquam IO vt tota AC ad totam <lb></lb>AO: ergo permutando, & diuidendo, vt <lb></lb>AB ad BC, hoc eſt CD, ita OI ad IA, hoc <lb></lb>eſt AS. </s> </p> <p type="margin"> <s><margin.target id="note34"></margin.target><emph type="italics"></emph>XXXIV <lb></lb>Idem ſine <lb></lb>Trigonome<lb></lb>tria & ſine <lb></lb>Algebra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Et hæc quidem dicta ſint, ſi fortè angu<lb></lb><arrow.to.target n="note35"></arrow.to.target><lb></lb>lum CAD præcognoſcere non libeat. </s> <s>Cæ<lb></lb>terùm illo cognito rem aggredi licet ſine <lb></lb>Algebrâ ope ſoliûs Trigonometriæ, quæ <lb></lb>multiplicem ſubminiſtrare poterit metho<lb></lb>dum. </s> <s>Et primò datâ altitudine AB, & an<lb></lb>gulo ad A obſeruato ex. </s> <s>gr.gr.89.m.36.ſec. <lb></lb>33., notus eſt angulus ad centrum C gr.o. <lb></lb>m. 23. ſec. 27, ac proinde eius ſubtenſa iņ <lb></lb>partibus Radij innoteſcit. </s> <s>Igitur ductâ BD, <pb xlink:href="018/01/077.jpg" pagenum="69"></pb>duo anguli ad baſim BD ſimul ſumpti ſunt <lb></lb>æquales recto CDA vnâ cum angulo obſer<lb></lb>uato A. </s> <s>Cum verò triangulum CBD ſit <gap></gap>ſo<lb></lb>ſceles, vnuſquiſque an<lb></lb><figure id="id.018.01.077.1.jpg" xlink:href="018/01/077/1.jpg"></figure><lb></lb>gulorum ad baſim BD <lb></lb>eſt æqualis ſemirecto & <lb></lb>ſemiangulo obſeruato. </s> <s><lb></lb>Deme ergo ſemiangu<lb></lb>lum obſeruatum gr.44. <lb></lb>48. 16 1/2, ex angulo ſe<lb></lb>mirecto, hoc eſt grad. <lb></lb>45, remanet gr. o. m. 11. <lb></lb>fec. </s> <s>43 1/2 quantitas angu<lb></lb>li ADB: Hic autem angulus ADB ſemper <lb></lb>eſt ſemiſſis complementi anguli ad A obſer<lb></lb>uati; angulo enim ADB facto ad punctum <lb></lb>contactûs eſt æqualis angulus in ſegmento <lb></lb>alterno, anguli verò ad peripheriam duplex <lb></lb>eſt angulus ad centrum C. </s> <s>In triangulo ita<lb></lb>que ADB noti ſunt duo anguli ad A & ad D; <lb></lb>& latus BD notum eſt in partibus 682. <lb></lb>13152.quarum Radius 100000.00000; ideo<lb></lb>que in ijſdem Radij partibus inuenitur AB <lb></lb>partium 232657. Iam fiat vt AB partium <lb></lb>232657 ad Radium 100000.00000, ita AB <lb></lb>ped. 480 ad aliud, & prodibit quantitas BC <lb></lb>terrenæ ſemidiametri ped. 20631229, hoc <lb></lb>eſt mill. 4126. paſſ. </s> <s>246. Quod verò ali<pb xlink:href="018/01/078.jpg" pagenum="70"></pb>quod intercedat diſcrimen inter hanc & dia<lb></lb>trum ſuperiùs inuentam, nil mirum, quią <lb></lb>vbi multiplex diuiſio intercedit, fractiones <lb></lb>aliquæ neglegun<lb></lb><figure id="id.018.01.078.1.jpg" xlink:href="018/01/078/1.jpg"></figure><lb></lb>tur, vnde demum <lb></lb>aliqua oritur dif<lb></lb>ferentia. </s> </p> <p type="margin"> <s><margin.target id="note35"></margin.target><emph type="italics"></emph>XXXV <lb></lb>Idem aliter <lb></lb>per Trigo<lb></lb>nometriam.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed placeat hìc <lb></lb><arrow.to.target n="note36"></arrow.to.target><lb></lb>vnum prætereą <lb></lb>obſeruare, quo mi<lb></lb>rificè ſum delecta<lb></lb>tus, cum primùm <lb></lb>animaduerti: <expan abbr="Do-ctrinã">Do<lb></lb>ctrinam</expan> ſcilicet Tri<lb></lb>gonometricam illud idem exhibere poſſę, <lb></lb>quod ab Algebrâ, in ſecundâ methodo indi<lb></lb>catâ, poſt omnes æquationes ſubminiſtra<lb></lb>tur. </s> <s>Fiat enim vt Sinus Verſus comple<lb></lb>menti anguli obſeruati, ad eiuſdem anguli <lb></lb>obſeruati Sinum Rectum, ita nota altitudo <lb></lb>ad aliud, & habebitur quæſita terræ ſemi<lb></lb>diameter. </s> <s>Sit enim CB terræ ſemidiame<lb></lb>ter, BA nota altitudo, AD linea optica tan<lb></lb>gens in D, per quod ex centro C ducatur re<lb></lb>cta CD, quæ producta in E occurrat peri<lb></lb>pheriæ circuli, interuallo CA, ex eodem <lb></lb>centro deſcripti. </s> <s>Eadem ergo eſt Ratio AB <lb></lb>ad BC, quæ eſt ED ad DC. </s> <s>Eſt autem AD <pb xlink:href="018/01/079.jpg" pagenum="71"></pb>Sinus anguli ACE, eiusque Sinus Verſus eſt <lb></lb>DE. </s> <s>At CD eſt æqualis Sinui Recto anguli <lb></lb>CAD obſeruati; eſt ſiquidem CD æqualis <lb></lb>ſinui complementi anguli C. </s> <s>Igitur quæ <lb></lb>Ratio eſt ipſius DE Sinus Verſi complemen<lb></lb>ti anguli obſeruati, ad DC Sinum anguli A <lb></lb>obſeruati, ea eſt ipſius altitudinis notæ BA, <lb></lb>ad| quæſitam terræ ſemidiametrum BC. </s> <s><lb></lb>Quarè ſinum anguli obſeruati 99997.67348 <lb></lb>deme ex Radio, & remanet 232652. Sinus <lb></lb>Verſus complementi.Iam ſi fiat vt 232652. <lb></lb>ad 99997.67348, ita nota altitudo ped. <lb></lb>480. ad ped. 20631193, eadem inuenitur <lb></lb>ſemidiameter, quæ ſuperiùs per Algebram <lb></lb>innotuit. </s> </p> <p type="margin"> <s><margin.target id="note36"></margin.target><emph type="italics"></emph>XXXVI <lb></lb>Idem aliter <lb></lb>et breuiſſi<lb></lb>mè.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Si perfici res commodè poſſit ſinè <lb></lb><arrow.to.target n="note37"></arrow.to.target><lb></lb>inueſtigatione anguli, quem cum perpendi<lb></lb>culo facit opticus radius ſphæricam terræ ſu<lb></lb>perficiem tangens, angulum illum libens <lb></lb>prætermitterem: vix enim ſcio, quàm exa<lb></lb>ctè deprehendi queat, quamuis organis di<lb></lb>ligentiſſimè elaboratis non caream. </s> </p> <p type="margin"> <s><margin.target id="note37"></margin.target><emph type="italics"></emph>XXXVII <lb></lb>Quam exa<lb></lb>ctè obſerua. </s> <s><lb></lb>ri poſsint <lb></lb>anguli.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Omnem mihi eximo ſcrupulum, <lb></lb>ſi quando contingat in Quadrante lineas, in <lb></lb>quibus minuta diſtinguuntur, ita obliquè ſe<lb></lb>cari â perpendiculo, vt anceps hæream, in <lb></lb>quam minuti partem cadat, cum tameņ <lb></lb>etiam ipſas minutorum minutias perſequi <pb xlink:href="018/01/080.jpg" pagenum="72"></pb>operæ pretium ſit. </s> <s>Latus vnum Quadran<lb></lb>tis ita duplico, vt iam perpendiculum non <lb></lb>ex circuli centro, ſed ab extremâ diametro <lb></lb>pendeat, & obſeruationem inſtituo: hinc <lb></lb>enim ſæpiùs fit, vt ſilum ſericum crudum, <lb></lb>ex quo pilula plumbea ſuſpenditur, minùs <lb></lb>obliquè lineam minutorum ſecet, quàm ſi <lb></lb>ex centro penderet: Et quoniam angulus ad <lb></lb>peripheriam ſubduplus eſt anguli ad cen<lb></lb>trum, notæ verò graduum & minutorum̨ <lb></lb>Quadrantis limbo appoſitæ indicant angulos <lb></lb>ad centrum, angulus à perpendiculo nota<lb></lb>tus, ex. gr. 1. 45 1/2, bifariam diuiditur, & <lb></lb>quæſitus angulus eſt, gr. o. m. 52. ſec. 45. <lb></lb>Quare ſi qua labes obſeruationi adhæreat, <lb></lb>pauculis ſcrupulis ſecundis definitur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Dari id quidem facilè poteſt ſy<lb></lb>derum obſeruatori; in tantâ nimirum diſtan<lb></lb>tiâ ipſius organi magnitudo, quantacunque <lb></lb>demùm illa ſit, planè euaneſcit; ac proinde <lb></lb>iſta, vt ita dicam, virtualis duplicatio Qua<lb></lb>drantis nihil officit. </s> <s>At verò telluris ma<lb></lb>gnitudinem indaganti ex radio optico, res <lb></lb>non ita in plano eſt: ſi enim oculum centro <lb></lb>Quadrantis admoueas ita, vt latus alterum <lb></lb>inſtrumenti congruat lineæ visûs, reliquum <lb></lb>verò latus fuerit, vt dicebas, duplicatum; <lb></lb>angulus à perpendiculo & lineâ visûs ex cen<pb xlink:href="018/01/081.jpg" pagenum="73"></pb>tro, non eſt æqualis angulo à perpendiculo, <lb></lb>& lineâ visûs ex extremâ diametro, quia pa<lb></lb>rallelæ eſſe non poſſunt duæ lineæ eundem̨ <lb></lb>circuli quadrantem tangentes. </s> <s>Oculus au<lb></lb>tem in extremâ diametro poſitus, vtpotè <lb></lb>magis à tellure remotus, plus terræ videt ſub <lb></lb>minore angulo: neque omninò contemnen<lb></lb>da eſt altitudinum differentia, ſi Quadrantis <lb></lb>Radius pedes quinque ſecundùm longitudi<lb></lb>nem habere ponatur; cum circuli in terrâ <lb></lb>maximi quantitas, quæ patet oculo decem <lb></lb>pedes alto, ſit ferè ſeſquialtera eius, quæ pro<lb></lb>ſpicitur ab oculo quinque tantùm pedes à <lb></lb>terrâ remoto. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Non eadem eſt ratio; ſi in arenâ <lb></lb>litoreâ, ac in editâ turri, aut in colle obſer<lb></lb>uationem, vt hìc ſupponimus, inſtituas; cum <lb></lb>enim terræ ſemidiameter aucta oculi altitu<lb></lb>dine ſit Secans Complementi anguli obſer<lb></lb>uati, ſecantes autem angulorum æqualiter <lb></lb>creſcentium addant ſemper maiorem, & <lb></lb>maiorem differentiam, patet quàm modi<lb></lb>cum anguli diſcrimen intercederet, ſi non <lb></lb>ad centrum Quadrantis, ſed ad extremam <lb></lb>circuli diametrum applicaretur oculus iņ <lb></lb>vltimum Horizontem directus ſecundùm <lb></lb>regulam lateri Quadrantis parallelam. </s> <s>Sed <lb></lb>quicquid de hoc eſſe contingat, certum eſt <pb xlink:href="018/01/082.jpg" pagenum="74"></pb>oculo ad centrum applicato perpendiculum <lb></lb>indè ſuſpenſum cadere parallelum perpendi<lb></lb>culo, quod ex extremâ diametro pendet, & <lb></lb>conſtituere angulum cum diametro æqua<lb></lb>lem illi, quem cum eâdem diametro facit <lb></lb>perpendiculum ex eius extremitate ſuſpen<lb></lb>ſum. </s> <s>Quare ſola centri altitudo ſupra terræ <lb></lb>ſuperficiem, aſſumenda eſt tanquam oculi <lb></lb>obſeruatoris altitudo. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Vel ſi minùs placeat perpendiculo <lb></lb>vti, Quadrantis latus horizontaliter iacens <lb></lb>duplicetur, & in extremâ diametro fiat cen<lb></lb>trum, circa quod conuerſa dioptra tantiſper <lb></lb>eleuetur, dum linea fiduciæ congruat radio <lb></lb>optico terram tangenti; nam ſemiſsis anguli <lb></lb>ad centrum facti cum latere horizontaliter <lb></lb>iacente inſiſtentis eidem arcui, eſt angulus <lb></lb>depreſsionis infra horizontem, æqualis an<lb></lb>gulo ACD facto in centro terræ; cuius com<lb></lb>plementum eſt quæſitus angulus CAD. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> An non operæ pretium facturus eſ<lb></lb>ſet, qui illud demum in praxim deduceret, <lb></lb>quod ego olim aliud neſcio quid meditans <lb></lb>perficiendum iuſsi, ſed aliis curis diſtractus <lb></lb>ad exitum non perduxi? </s> <s>Duxeram in plano <lb></lb>verticali lineam horizontalem longam pe<lb></lb>des Rom. ferè quinquaginta, & in eius ex<lb></lb>tremo puncto, quod eam cæli plagam re-<pb xlink:href="018/01/083.jpg" pagenum="75"></pb>ſpeciebat, in qua aliquid occurrebat obſer<lb></lb>uandum, axiculum ritè infigi curaui, circa <lb></lb>quem poſſet dioptra conuerti. </s> <s>Erat autem <lb></lb>animus parare regulam longam pedes 42, <lb></lb>cuius latitudo 4. digitos, craſſities autem̨ <lb></lb>duos digitos obtineret; ſic enim fieri poſſe <lb></lb>ſperabam, vt latitudine in altitudinem con<lb></lb>uersâ, regula non adeò grauis horizontali<lb></lb>ter conſtituta, & ſecundum alteram extremi<lb></lb>tatem axiculo inſerta, non ſinuaretur, nec <lb></lb>à ſuâ rectitudine deflecteret: cùm maximè <lb></lb>decreuiſſem ita illi aliam regulam breuiorem <lb></lb>ſubiicere, in modum vectis primi generis, vt <lb></lb>inferiorem regulam premens eleuarem ſu<lb></lb>periorem, quæ circiter duas tertias ſuæ lon<lb></lb>gitudinis partes (hoc eſt circiter pedem ab <lb></lb>axiculo, circa quem volueretur, trigeſimum) <lb></lb>ſuſtentata à ſuppoſito vecte non eſſet adeò <lb></lb>obnoxia inflexioni. </s> <s>Tum regulæ longitudi<lb></lb>ne in pedes diſtinctâ; accipiendi erant pedes <lb></lb>41 2/3, vt eſſent in vniuerſum vnciæ 500; cum <lb></lb>enim pedis vncia ita ſenſibiliter in laminâ <lb></lb>metallicâ diuidi queat in particulas 50 vt ha<lb></lb>beantur vnciæ particulæ centeſimæ, erat Ra<lb></lb>dius circuli deſcribendi partium 50000, ſub<lb></lb>duplus numeri, qui habetur in Canone Tri<lb></lb>gonometrico communi. </s> <s>Quare ſi hoc Ra<lb></lb>dio in plano verticali deſcribatur arcus, & <pb xlink:href="018/01/084.jpg" pagenum="76"></pb>ad lineam horizontalem excitetur perpendi<lb></lb>cularis æqualis Tangenti gr. 1. (accepto ſe. <lb></lb></s> <s>ſemiſſe numeri Canonis in partibus vnciæ <lb></lb>centeſimis) abſcindi poterit ex arcu gradus <lb></lb>vnus, cuius ſinus parum diſtabit à palmo <lb></lb>Romano architectonico. </s> <s>Quare facilè pote<lb></lb>rit arcus in 60 minuta diuidi, & ex eodem <lb></lb>centro interuallo maiore deſcripto alio arcu, <lb></lb>poterunt duci lineæ tranſuerſæ, in quibus <lb></lb>minutorum partes ſexageſimæ diſtingui po<lb></lb>terunt, prout moris eſt. </s> <s>Hoc inſtrumento pa<lb></lb>rato angulum depreſsionis inſra horizontem, <lb></lb>ſeu potiùs infra lineam horizonti parallelam, <lb></lb>tam clarè poſſumus deprehendere, vt nihil <lb></lb>reliquum <gap></gap>quod deſideremus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Nec omnibus nec vbique locorum <lb></lb>commodum erit tuum hoc inſtrumentum <lb></lb>fabricari, quod vel vni loco affixum ſit opor<lb></lb>tet, vel ægerrimè transferri poſſit. </s> <s>Neſcio <lb></lb><arrow.to.target n="note38"></arrow.to.target><lb></lb>quo fato adhuc penès me in ſemilacerâfffff pa<lb></lb>gellâ durat ſchediaſma hoc, quo ante men<lb></lb>ſes aliquot cuidam, qui ſe in Geometriæ pra<lb></lb>xi exercens dolebat nullum hactenus à ſe ad<lb></lb>hibitum inſtrumentum, cui citrà inſignis <lb></lb>erroris ſuſpicionem poſſet fidere, organum <lb></lb>propoſui, quod & facilè conſtruitur, & vix <lb></lb>vllum relinquit errandi periculum, prout ipſa <lb></lb>docuit experientia. </s> <s>In triangulum còag<pb xlink:href="018/01/090.jpg" pagenum="77"></pb>mentatis tribus tigillis, ducatur recta AB <lb></lb>vnciarum 10. ex. </s> <s>gr. & ſuper eâ fiat triangu<lb></lb>lum æquilaterum AEB. </s> <s>Quod ſi tigilli ni<lb></lb>mis longi eſſent, interuallo A<emph type="italics"></emph>e<emph.end type="italics"></emph.end> deſcribantur <lb></lb>duo arcus ſe inuicem ſecantes in <emph type="italics"></emph>i<emph.end type="italics"></emph.end>, & inter<lb></lb>uallo A<emph type="italics"></emph>u<emph.end type="italics"></emph.end> arcus ſe ſecantes in <emph type="italics"></emph>o<emph.end type="italics"></emph.end>: per hæc enim <lb></lb>puncta ductâ lineâ ex A, accipi poterit AE <lb></lb>æqualis ipſi AB, & erit angulus BAE gr. 60. <lb></lb>Relinquitur autem tigillus EF longior, vt in <lb></lb>FA ſecundùm rectam EA productam in F <lb></lb>conſtituatur tubulus H infundibuli in mo<lb></lb>rem excauatus, per quem viſus rectâ traii<lb></lb>ciatur in deſtinatum ſcopum per aciculam <lb></lb>in E perpendiculariter erectam, ex qua de<lb></lb>pendet perpendiculum; hoc enim facit cum <lb></lb>lineâ EA angulum diſtantiæ obiecti à verti<lb></lb>ce obſeruatoris. </s> <s>Quantitas verò huius an<lb></lb>guli per Trigonometriam reperitur ex datis <lb></lb>lateribus AE, & A<emph type="italics"></emph>u<emph.end type="italics"></emph.end> & angulo <emph type="italics"></emph>u<emph.end type="italics"></emph.end> AE compre<lb></lb>henſo gr. 60. ex conſtructione. </s> <s>Vel ſi fortè <lb></lb>breuiùs operari placeat, fingatur ex E puncto <lb></lb>in ſemiſſem lateris AB cadere linea perpen<lb></lb>dicularis, cuius quantitas facilè innoteſcit: <lb></lb>deinde illâ aſſumptâ vt Radio, vt Tangentę <lb></lb>verò diſtantiâ perpendiculi à medio lineæ <lb></lb>AB, angulus quæratur, quem facit perpen<lb></lb>diculum cum fictâ illâ perpendiculari; hic <lb></lb>enim angulus additus gradibus 30. ſi perpen<pb xlink:href="018/01/091.jpg"></pb><figure id="id.018.01.091.1.jpg" xlink:href="018/01/091/1.jpg"></figure><pb xlink:href="018/01/092.jpg" pagenum="78"></pb>diculum cadat vltra ſemiſſem lineæ AB; <lb></lb>demptus autem ex gr. 30. ſi cadat citrà ſe<lb></lb>miſſem, dabit angulum diſtantiæ à vertice <lb></lb>quæſitum. </s> <s>Quod ſi diſtantia à vertice exceſ<lb></lb>ſerit gr. 60 perpendiculum cadet extrà latus <lb></lb>BE; idcirco ſuſpendendum èrit ex I puncto, <lb></lb>quod bifariam diuidit rectam AE; & ſiqui<lb></lb>dem obiectum in Horizonte fuerit, perpen<lb></lb>diculum ex I cadet in B, ſi verò ſupra Hori<lb></lb>zontem, cadet in latus AB, ſi demum infra <lb></lb>lineam Horizonti parallelam depreſſum fue<lb></lb>rit, cadet perpendiculum in latus BE: ſem<lb></lb>per autem in noteſcet angulus factus à perpen<lb></lb>diculo & lineâ FI visûs, dantur enim vel la<lb></lb>tera IA & AB, vel IE & EB cum angulo <lb></lb>comprehenſo: vel ſaltem in vtroque latere <lb></lb>deſignari poterit punctum, in quod ad rectos <lb></lb>angulos cadit linea ex I. </s> </p> <p type="margin"> <s><margin.target id="note38"></margin.target><emph type="italics"></emph>XXXVIII <lb></lb>Vſus Tri<lb></lb>goni æqui<lb></lb>lateri ad <lb></lb>obſeruandos <lb></lb>angulos, in <lb></lb>quo vix er<lb></lb>rari poſsit à <lb></lb>Geometra.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Vt verò in quàm minimas particulas di<lb></lb>uiſam haberet rectam AB, iubebam duci <lb></lb>AC æqualem vni ex ijs partibus, in quas pri<lb></lb>mò diſtinctam eam poſuimus, nempe iņ <lb></lb>vncias pedis, & perfici parallelogrammum <lb></lb>ABDC. </s> <s>Tum diuisâ AC, & BD in quinque <lb></lb>æquales partes, & ductis parallelis ipſi AB, <lb></lb>inter poſtremas <emph type="italics"></emph>a d<emph.end type="italics"></emph.end> & CD ducatur diagona<lb></lb>li; C <emph type="italics"></emph>d<emph.end type="italics"></emph.end>; & diuiſis pariter ſingulis vncijs iņ <lb></lb>quinque partes, vt factum hìc eſt in vnciâ <pb xlink:href="018/01/093.jpg" pagenum="79"></pb>quintâ, ducantur lineolæ parallelæ ipſi CA, <lb></lb>donec diagonalem attingant: & his paratis <lb></lb>habetur vncia AC diuiſa in partes 500, vel <lb></lb>ſaltem in 250, ſi differentia inter duas pro<lb></lb>ximas lineolas ſenſibilis non ſit. </s> </p> <p type="main"> <s>Quamuis autem tam exiguum triangu<lb></lb>lum AEB non ſit aptum ad acutiores angu<lb></lb>los inueniendos, conſtat tamen poſſe illud <lb></lb>ſinè magno incommodo conſtrui ita, vt pe<lb></lb>des aliquot ſingula latera obtineant; & tunc <lb></lb>etiam minores angulorum particulæ innote<lb></lb>ſcent. </s> <s>Quod ſi quando res ſit quàm exa<lb></lb>ctiſsimè perficienda, poterit lateri FE addi <lb></lb>regula, ex cuius extremo ſecundùm rectam <lb></lb>AE productam ſuſpendatur perpendiculum, <lb></lb>perinde enim erit ac ſi totum triangulum <lb></lb>augeretur. </s> <s>At ſi ex editiore loco deorſum <lb></lb>ſpectandum ſit, & perpendiculum ex I ſu<lb></lb>ſpenſum cadat in latus EB tam propè ipſum <lb></lb>B, vt non facilè poſsint particulæ numera<lb></lb>ri, erigatur ad latus AE regula perpendicu<lb></lb>laris, in qua recta ex B per I ducta faciat an<lb></lb>gulum EIG rectum, & ſumatur IG æqualis <lb></lb>ipſi IE, & ex G ſuſpendatur perpendiculum, <lb></lb>quod intelligatur cadere ex. </s> <s>gr. in R. </s> <s>Si <lb></lb>enim concipiatur ex I aliud perpendiculum <lb></lb>IS, vtique linea IG incidens in duas paralle<lb></lb>las IS, & GR facit angulum SIB externum <pb xlink:href="018/01/094.jpg" pagenum="80"></pb>æqualem interno RGI: inuento igitur RGI, <lb></lb>innoteſcit angulus, quem cum perpendicu<lb></lb>lo facit linea viſualis AE. </s> <s>Cum itaque IE & <lb></lb>IG æquales ſint & ad angulum rectum, con<lb></lb>ceptâ rectâ EG angulus EGI eſt gr. 45, cui <lb></lb>æqualis reliquus GEI additus angulo BEA gr. <lb></lb>60. fit totus angulus GER gr. 105; latus au<lb></lb>tem EG ſubtendens angulum rectum, no<lb></lb>tum eſt, cum nota ſint latera IG, & IE; de<lb></lb>mum notum eſt latus ER. </s> <s>Quare ex notis <lb></lb>lateribus EG & ER vnâ cum angulo com<lb></lb>prehenſo inuenitur angulus EGR, qui dem<lb></lb>ptus ex EGI gr. 45. relinquit notum RGI <lb></lb>æqualem angulo SIB; & ſic innoteſcit angu<lb></lb>lus SIE æqualis angulo, quem facit linea vi<lb></lb>ſualis EA <expan abbr="cũ">cum</expan> lineâ AT iungente oculum ob<lb></lb>ſeruatoris cum centro terræ. </s> <s>Cum igitur ſatis <lb></lb>amplum huiuſmodi triangulum facilè poſsi<lb></lb>mus conſtruere, etiam additâ regulâ IG, & <lb></lb>alibi diuiſam vnciam habere poſsimus iņ <lb></lb>partes ſaltem centeſimas eâ methodo, quam <lb></lb>indicat Adrianus Metius in ſuâ Geometriâ, <lb></lb>patet fieri poſſe, vt quàm euidentiſsimè in<lb></lb>noteſcat angulus ille, quem obſeruatum ſup<lb></lb>ponebam ad inueſtigandam terræ magnitu<lb></lb>dinem. </s> <s>Sed miſsis organis ad inſtitutum <lb></lb>redeamus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Audiui haud ita pridem hominem, <pb xlink:href="018/01/095.jpg" pagenum="81"></pb>qui ex maximâ visûs diſtantiâ, ſeu Hori<lb></lb><arrow.to.target n="note39"></arrow.to.target><lb></lb>zontis Phyſici ſemidiametro, totius telluris <lb></lb>ſemidiametrum colligere ſe poſſe cenſeban. </s> <s><lb></lb>Primùm verò ſtatuebat, quod certum eſt, ab <lb></lb>iis qui de maximâ visûs diſtantiâ diſputant, <lb></lb>non eam inquiri, quæ vel ab oculis variè af<lb></lb>fectis, vel à diuersâ corporum videndorum <lb></lb>magnitudine, vel ab inæquali ſpecierum, <lb></lb>quas vocant, intentionalium, quibus obie<lb></lb>ctum repræſentandi vis ineſt, diffuſione ea<lb></lb>rumue intenſione petenda eſt. </s> <s>Nemo enim <lb></lb>ignorat, ſi iſta ſpectentur, fieri non poſſę, <lb></lb>vt certa visûs diſtantia vniuerſim præſcriba<lb></lb>tur. </s> <s>Acribus ſiquidem & acutis oculis longè <lb></lb>remotiora patere conſtat, quàm hebetiori<lb></lb>bus, quos languidiores radii procul immiſsi <lb></lb>ad viſum non excitant. </s> <s>Vbi verò obiectum <lb></lb>corpus non oculorum vitio latet, ſæpè ſuâ <lb></lb>ſe paruitate ita protegit, vt admiſsi à pupillâ <lb></lb>radii in tenuiſsimum angulum coaleſcentes <lb></lb>eam demùm afficiant Retinæ particulam, <lb></lb>quæ eum ſenſum omnem effugiat, ſentiendi <lb></lb>quoquè munere ſolitaria fungi non poteſt: <lb></lb>vt proinde Dioptrica ſubſidiarias lentes vi<lb></lb>treas in tuboſpicillo ritè diſpoſitas mortali<lb></lb>bus tranſmiſerit, quarum ope inflexi Radii <lb></lb>ampliorem angulum conſtituant, ideòquę <lb></lb>maiorem Retinæ particulam ad videndum <pb xlink:href="018/01/096.jpg" pagenum="82"></pb>proritent. </s> <s>Sed & illud maximè ambiguam <lb></lb>facit visûs diſtantiam, quod pro diſpari luce, <lb></lb>qua corpora imbuuntur, diſpar quoque exi<lb></lb>gunt interuallum, vt ſub aſpectum cadant: <lb></lb>ſic aliquando Perigæam Lunam, quæ antę <lb></lb>pauculas horas ferè pleno orbe immenſą <lb></lb>collucebat, ſereno cœlo amiſſam quærimus, <lb></lb>ſi fortè eius centrum in terreſtris vmbræ a<lb></lb>xem inciderit; cum tamen eadem tenebra<lb></lb>rum immunis, quamuis Apogæa Soli pa<lb></lb>riter Apogæo oppoſita, ſponte in oculos <lb></lb>incurrat. </s> <s>Ea nimirum quamuis remotiorą <lb></lb>conſpiciuntur, quæ vberiori lumine ſiuè in<lb></lb>nato, & inſito, ſiuè extrinſecùs mutuato per<lb></lb>funduntur. </s> </p> <p type="margin"> <s><margin.target id="note39"></margin.target><emph type="italics"></emph>XXXIX <lb></lb>Maxima vi<lb></lb>ſus diſtan<lb></lb>tia ex qui<lb></lb>bus debeat <lb></lb>definiri.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Semotis igitur omnibus hiſce impedi<lb></lb>mentis, per quæ fieret, quominùs certi ali<lb></lb>quid de visûs diſtantiâ ſtatui poſſet; phyſici <lb></lb>horizontis ſemidiameter ex ipsâ terreni glo<lb></lb>bi configuratione petenda eſt. </s> <s>Cum enim <lb></lb>vetus ille error opinantium terræ faciem æ<lb></lb>quabili planitie diffuſam iam dudum exta<lb></lb>buerit, & nemo ſit, qui pilæ in ſpeciem ter<lb></lb>ras ac maria vndique in ſeſe nutibus ſuis con<lb></lb>globata non intelligat; nemo pariter ambi<lb></lb>gat, quin ob conuexam huiuſce globi ſuper<lb></lb>ficiem, inclinatis nimirùm partibus, ſeque <lb></lb>oculo ſubducentibus, aſpectus omnis quan<pb xlink:href="018/01/097.jpg" pagenum="83"></pb>tumuis acerrimus certis terminis circum<lb></lb>ſcribatur. </s> <s>Hinc circulus partem hanc aſpe<lb></lb>ctabilem à latente diſpeſcens, Horizontis <lb></lb>Phyſici nomine donatus eſt, vt ab eo ſecer<lb></lb>natur Horizonte, qui tellurem in duo hemi<lb></lb>ſphæria ſegregans, quia non oculo, ſed <expan abbr="ſolã">ſolam</expan> <lb></lb>ratione comprehendi poteſt, Rationalis di<lb></lb>citur. </s> </p> <p type="main"> <s>Quamuis autem Phyſici Horizontis dia<lb></lb>meter tota intrà terræ craſsitudinem deliteat, <lb></lb>quippe quæ recta eſt linea arcui illi ſubtenſa, <lb></lb>qui extremis terminis oculi Ortum Occa<lb></lb>ſumque circumſpicientis intercluditur: quia <lb></lb>tamen arcus huiuſmodi exiguo diſcriminę <lb></lb>quod vix ſub ſenſum ca<lb></lb><figure id="id.018.01.097.1.jpg" xlink:href="018/01/097/1.jpg"></figure><lb></lb>dat, ſubtenſæ rectæ li<lb></lb>neæ longitudinem ſupe<lb></lb>rat; ideò non abs re ar<lb></lb>cus ipſe pro phyſici hori<lb></lb>zontis ſemidiametro in<lb></lb>diſcriminatim vſurpatur; <lb></lb>huiuſce ſemiſsis maxi<lb></lb>mam obiecti aſpectabilis <lb></lb>diſtantiam metitur. </s> </p> <p type="main"> <s>Ex his ſic ille argumentabatur. </s> <s>Sit arcus <lb></lb><arrow.to.target n="note40"></arrow.to.target><lb></lb>AB menſura diſtantiæ viſus, qui non à rectâ <lb></lb>lineâ ſenſibiliter deflectat<gap></gap>eſt igitur AB recta <lb></lb>perpendiculariter inſiſtens rectæ DC: radius <pb xlink:href="018/01/098.jpg" pagenum="84"></pb>autem opticus DB terram tangens facit cum <lb></lb>ſemidiametro angulum DBC rectum. </s> <s>Igi<lb></lb>tur recta AB ab angulo recto ad B cadens iņ <lb></lb>baſim perpendicularis, eſt medio loco pro<lb></lb>portionalis inter ſegmenta DA & AC. </s> <s>Qua<lb></lb>rè diuiſo quadrato maximæ visûs diſtantiæ <lb></lb>AB per altitudinem AD, prouenit quæſitą <lb></lb>terræ ſemidiameter AC. </s> <s>Verùm arcum <lb></lb>pro rectâ lineâ aſſumere parùm Geometri<lb></lb>cum eſt. </s> </p> <p type="margin"> <s><margin.target id="note40"></margin.target><emph type="italics"></emph>XXXX <lb></lb>Abuſus li<lb></lb>neæ curuæ <lb></lb>pro rectą, <lb></lb>inutilis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Ideò paruipendendendam cenſui <lb></lb>methodum, quæ mihi aliquando occurrit <lb></lb><arrow.to.target n="note41"></arrow.to.target><lb></lb>per circulos Azimuthales; ſi nimirùm duo<lb></lb>rum locorum, quorum alteruter ex alterius <lb></lb>editâ turri conſpici queat, nota fuerit diſtan<lb></lb>tia, & poli altitudo. </s> <s>In ſummâ enim turri <lb></lb>planum horizontale conſtituatur, in eoque <lb></lb>meridiana linea deſcribatur: tum obſeruetur <lb></lb>ſub quo Azimutho locus alter conſpicuus <lb></lb>appareat: & ex his datis quæſita eruantur. </s> <s><lb></lb>Sit PAC loci Meridianus, vbi obſeruatio in<lb></lb>ſtituitur<gap></gap>; Verticalis per vtrumque locum <lb></lb>tranſiens AB, cum Meridiano faciat angu<lb></lb>lum CAB obſeruatum; P verò ſit Polus, & <lb></lb>AP, BP ſint complementa nota datarum <lb></lb>poli eleuationum. </s> <s>Cum itaque in triangu<lb></lb>lo ſphærico BAP nota ſint duo latera AP, <lb></lb>BP, & angulus BAP complementum angu<pb xlink:href="018/01/099.jpg" pagenum="85"></pb>li obſeruati CAB ad duos rectos, inueniatur <lb></lb>AB in gradibus ſeu <lb></lb>graduum particulis. <lb></lb><figure id="id.018.01.099.1.jpg" xlink:href="018/01/099/1.jpg"></figure><lb></lb>Tum fiat vt AB pars, <lb></lb>inuenta ad totum cir<lb></lb>culum, hoc eſt gr. <lb></lb>360, ita data duorum <lb></lb>locorum diſtantia ad <lb></lb>aliud, & prodibunt <lb></lb>milliaria toti circulo <lb></lb>in terrâ maximo reſpondentia. </s> <s>Notâ autem <lb></lb>circularis peripheriæ quantitate neminem <lb></lb>Geometram diameter quæſita latere poterit. </s> <s><lb></lb>Sed quoniam diſtantia illa non adeò exigua <lb></lb>eſſe poteſt, quæ careat omni ſuſpicione abu<lb></lb>sûs rectæ lineæ pro curuâ, ideò methodum <lb></lb>hanc inter quiſquilias, à quibus parùm di<lb></lb>ſtat, reieci. </s> </p> <p type="margin"> <s><margin.target id="note41"></margin.target><emph type="italics"></emph>XXXXI <lb></lb>Secunda me <lb></lb>thodus in<lb></lb>uestigandi <lb></lb>telluris am<lb></lb>bitum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Id tamen per ſummam iniuriam <lb></lb><arrow.to.target n="note42"></arrow.to.target><lb></lb>factum: neque enim magnum intercedere <lb></lb>poteſt diſcrimen, quod propoſito officiat: eſt <lb></lb>ſcilicet diſcrimen minus datâ altitudine. </s> <s>Ex <lb></lb>altitudine enim BA proſpiciénti pateat ar<lb></lb>cus BD, quem ſubtendit recta BD, Tan<lb></lb>gens autem eſt AD. </s> <s>Conſtat ex Archimede <lb></lb>lib. 1. de ſphær. & cyl. </s> <s>Tangentem AD ma<lb></lb>iorem eſſe arcu BD, arcum autem BD maio<lb></lb>rem rectâ BD ſubtensâ: At duæ rectæ BD, <pb xlink:href="018/01/100.jpg" pagenum="86"></pb>BA ſimul ſumptæ maiores ſunt quàm AD, <lb></lb>igitur exceſſus ipſius <lb></lb><figure id="id.018.01.100.1.jpg" xlink:href="018/01/100/1.jpg"></figure><lb></lb>AD ſupra rectam BD <lb></lb>minor eſt, quàm ſit <lb></lb>data altitudo BA; er<lb></lb>go multò minor eſt <lb></lb>exceſſus rectæ AD <lb></lb>tangentis ſupra ar<lb></lb>cum BD, vel arcûs <lb></lb>BD ſupra rectam BD <lb></lb>ſubtenſam. </s> <s>Ne verò <lb></lb>poſitâ altitudine BA notabili, cenſeret quis <lb></lb>inſignem quoque eſſe differentiam inter cur<lb></lb>uam & rectam lineam, quæ locorum inter<lb></lb>ualla metiatur, animaduertere oportet ar<lb></lb>cum BD maiorem eſſe latere BD polygoni <lb></lb>inſcripti, minorem autem latere EF polygo<lb></lb>ni circumſcripti: at exceſſus lateris EF ad la<lb></lb>tus BD habet Rationem, quam EB ad BC. </s> <s><lb></lb>Vnde liquet manifeſtè, quàm modico di<lb></lb>ſcrimine differat arcus à rectâ vel ſubtensâ <lb></lb>BD, vel tangente EF. </s> </p> <p type="margin"> <s><margin.target id="note42"></margin.target><emph type="italics"></emph>XXXXII. </s> <s><lb></lb>Differentia <lb></lb>longitudinis <lb></lb>inter arcum <lb></lb>et eius Tan<lb></lb>gentem vel <lb></lb>ſubtenſam.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Memini me aliquando calculos ſubducen<lb></lb>tem, quàm longè pateat viſus Romæ è ſum<lb></lb>mo crucis apice, quæ ædis Apoſtolorum <lb></lb>Principi ſacræ tholo incumbit. </s> <s>deprehendiſ<lb></lb>ſe arcum DB gr. o. </s> <s>m. </s> <s>23. ſtatuebam autem <lb></lb>in ſingulos gradus milliaria Italica 60, vt <pb xlink:href="018/01/101.jpg" pagenum="87"></pb>nunc vulgaris fert opinio, crucis verò altitu<lb></lb>dinem ſupra maris Mediterranci ſuperfi<lb></lb>ciem ponebam palmorum, quorum vſus ho<lb></lb>diè eſt apud Romanos architectos, circiter <lb></lb>700. Quare arcus BD erat mill. 23. & Tan<lb></lb>gens AD mill. (23 441/100000), diſcrimine vix paſ<lb></lb>ſuum 4 1/2. Quid igitur officiat, ſi quis pro <lb></lb>arcu BD aſſumat, aut ſubtenſam BD, aut <lb></lb>tangentem EF, aut aliquam ex intermediis? </s> <s><lb></lb>nullus ſiquidem oriri poteſt error, qui ſub <lb></lb>ſenſum cadat. </s> <s>Quod ſi, vt ſæpè fieri poteſt, <lb></lb>diſtantiam BD decempedâ dimetiamur, ni<lb></lb>hil erit quod de tuâ illâ methodo dubites, <lb></lb>Merſenne, non enim arcu pro rectâ abu<lb></lb>teris. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Suſpicor Merſenne (detur hoc Ger<lb></lb>mano candori) non tibi rectam pro arcûs <lb></lb>menſurâ aſſumptam diſplicuiſſe; ſed metho<lb></lb>dum illam, quæ tibi nihil de Ptolemæo co<lb></lb>gitanti occurrerat, demùm diſplicuiſſe faci<lb></lb>lè crediderim, vbi eam veteribus quoquè <lb></lb>innotuiſſe deprehendiſti: ideo illam inter <lb></lb>ſcruta reieciſti. </s> <s>Ego quoque, vt vera nar<lb></lb>rem, ſæpiùs doleo, quod veritatem tan<lb></lb>quam peregrinam exceperim, quaſi ad mę <lb></lb>primum diuertiſſet; quam poſtea alienum <lb></lb>limen triuiſſe comperio: nec ſanè me pro<lb></lb>broſis ſuis ſtimulis vrget inuidentia, qua cæ<pb xlink:href="018/01/102.jpg" pagenum="88"></pb>teris veritatis lumen inuideam; ſed terret <lb></lb>calumnia, qua ſæpè apud iniquos iudices fur<lb></lb>ti reus laboras, niſi id aliundè acceptum <lb></lb>ſponte profitens mentiaris: perinde atque ſi <lb></lb>nemo ſolem poſſet intueri, qui alios de eius <lb></lb><arrow.to.target n="note43"></arrow.to.target><lb></lb>luce narrantes non audierit. </s> <s>Simile quid in <lb></lb>hoc eodem Problemate mihi contigit expe<lb></lb>riri. </s> <s>Cum enim locorum duorum AB di<lb></lb>ſtantiam notam ponerem, ac complemen<lb></lb>ta eleuationum poli; obſeruabam Solis di<lb></lb>ſtantiam à vertice SA, quam per Tabulas <lb></lb>Anaclaſticas, & Parallacticas corrigebam; <lb></lb>Tum ex complemento declinationis Solis <lb></lb>SP, complemento altitudinis Poli AP: & di<lb></lb>ſtantia Solis à vertice SA, inquirebam angu<lb></lb>lum ASP; ex quo inuento, vnâ cum latere <lb></lb>SP, & complemento altitudinis poli BP, <lb></lb>inueniebam SB, quod demptum ex SA re<lb></lb>linquebat arcum BA quæſitum. </s> <s>Hæc ta<lb></lb>men methodus poſt dies aliquos diſplicuit, <lb></lb>cum animaduerterem ingenioſum Aſtrono<lb></lb>mum eâdem viâ inceſsiſſe, & quidem fe<lb></lb>liciùs non Solem ſed ſydera fixa vertici pro<lb></lb>xima obſeruando, quæ nec parallaxi nec re, <lb></lb>fractioni ſunt obnoxia. </s> </p> <p type="margin"> <s><margin.target id="note43"></margin.target><emph type="italics"></emph>XXXXIII. </s> <s><lb></lb>Tertia me<lb></lb>thodus in<lb></lb>uestigandi <lb></lb>ambitum̨ <lb></lb>terræ.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Cæterùm ne ab inſtitutâ quæſtione de<lb></lb>flectamus, illud eſt obſeruandum, quod ſi <lb></lb>cognitâ altitudine BA, & dato angulo ad A, <pb xlink:href="018/01/103.jpg" pagenum="89"></pb>vellet aſſumere triangulum rectangulum ad <lb></lb>B, vt notam faceret <lb></lb><figure id="id.018.01.103.1.jpg" xlink:href="018/01/103/1.jpg"></figure><lb></lb>diſtantiam inter B & <lb></lb>D, ſibique perſuaderet <lb></lb>aut à baſi aut ab hy<lb></lb>pothenusâ illius <expan abbr="triã-guli">trian<lb></lb>guli</expan> exhiberi diſtan<lb></lb>tiam BD, longè di<lb></lb>ſtaret à veritate. </s> <s>Du<lb></lb>cta ſiquidem perpen<lb></lb>dicularis BH longè <lb></lb>minor eſt arcu BD, cum ſit Tangens ſe<lb></lb>miſsis illius arcûs: hypothenuſa verò AH <lb></lb>minor eſt quàm tota Tangens AD, de<lb></lb>fectu æquali ipſi baſi BH; ſunt enim HB, <lb></lb>HD æquales, cùm vtraque ſit circulum <lb></lb>tangens ab eodem puncto H ducta. </s> <s>Qua<lb></lb>propter deberet aggregatum ex baſi BH <lb></lb>& hypothenusâ AH accipere, vt totam <lb></lb>AD haberet, quæ non multùm differt ab ar<lb></lb>cu BD, niſi altitudo BA fuerit mons aut ſco<lb></lb>pulus. </s> </p> <p type="main"> <s>Quod ſi tuus ille terrenæ magnitudinis <lb></lb><arrow.to.target n="note44"></arrow.to.target><lb></lb>inueſtigator lineam BD pro maximâ vi<lb></lb>sûs diſtantiâ aſſumpſiſſet, illa vtique media <lb></lb>eſt proportionalis, ex cuius quadrato per no<lb></lb>tam altitudinem DA diuiſo prouenit tertius <pb xlink:href="018/01/104.jpg" pagenum="90"></pb>terminus, vnde terrena <lb></lb><figure id="id.018.01.104.1.jpg" xlink:href="018/01/104/1.jpg"></figure><lb></lb>ſemidiameter cognoſci<lb></lb>tur, non tamen ipſa ſe<lb></lb>midiameter AG eſt ter<lb></lb>tius analogiæ terminus, <lb></lb>ſed potius conflatum ex <lb></lb>DC, CB: latus enim v<lb></lb>num trianguli rectan<lb></lb>guli eſt medium propor<lb></lb>tionale inter differentiam <lb></lb>hypothenuſæ ac reliqui lateris, & eorum ag<lb></lb>gregatum: ac proinde vt AD ad DB, itą <lb></lb>DB ad DCB. </s> <s>Quare ex inuento tertio ter<lb></lb>mino debuiſſet datam altitudinem DA de<lb></lb>mere, & reſiduum bifariam diuiſum dediſ<lb></lb>ſet quæſitam ſemidiametrum AC. </s> <s>Hinc <lb></lb>rectè dicebas arcum illum pro rectâ lineâ <lb></lb>parùm Geometricè aſſumptum. </s> </p> <p type="margin"> <s><margin.target id="note44"></margin.target><emph type="italics"></emph>XXXXIV <lb></lb>Quarta me<lb></lb>thodus in<lb></lb>neniendi ter<lb></lb>ra ſemidia<lb></lb>metrum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Nunquam hominem potui à con<lb></lb>ceptâ ſententiâ reuocare, niſi vbi eum iuſſi <lb></lb>rem rotam in praxim deducere. </s> <s>Statuimus <lb></lb>primùm extra omnem controuerſiam poſi<lb></lb>tum videri, in decernendâ Phyſici horizon<lb></lb>tis amplitudine non incertam ædium aut <lb></lb>montium altitudinem eſſe ſpectandam, ſed <lb></lb>eam ex communi vulgarique hominum ma<lb></lb>gnitudine definiendam. </s> <s>Quandoquidem <pb xlink:href="018/01/105.jpg" pagenum="91"></pb>cum ex ſublimiori loco longiùs viſus eat, ex <lb></lb>humiliori autem breuioribus terminis coer<lb></lb>ceatur, quis non videt certam ſtatui non poſ<lb></lb>ſe visûs diſtantiam, quin certa pariter alti<lb></lb>tudo, ex qua oculus circumſpicere valeat, <lb></lb>conſtituta intelligatur? </s> <s>præter eam verò, <lb></lb>quam humano corpori natura plerunquę <lb></lb>conceſſit, cur hanc præ aliâ eligas altitudi<lb></lb>nem, nulla ſuppetit ratio. </s> <s>Nec ambigi vllo <lb></lb>pacto poteſt, an Veteres horizontis phyſici <lb></lb>amplitudinem indagantes, altitudinem vl<lb></lb>lam humanâ maiorem aſſumpſerint; eam <lb></lb>ſiquidem horizonti tribuendam cenſuerę <lb></lb>magnitudinem, quæ cum ſphæricæ ſuperfi<lb></lb>ciei pars ſit, à planâ tamen minimùm differ<lb></lb>re poſſit. </s> <s>Hinc Macrobius Saturnal. lib. 7. <lb></lb>cap. 14. <emph type="italics"></emph>Vbicunque terrarum ſteteris<emph.end type="italics"></emph.end>, inquit, <lb></lb><emph type="italics"></emph>videris tibi quandam cœli concluſionem vide<lb></lb>re; & hoc eſt quod Horizontem veteres voca<lb></lb>uerunt: quorum indago fideliter deprehendit, <lb></lb>directam ab oculis aciem per planum contrà <lb></lb>aſpicientibus non pergere vltra CLXXX ſta<lb></lb>dia, & inde in orbem iam recuruari. </s> <s>Per pla<lb></lb>num, ideò adieci, quia altitudines longiſſimè <lb></lb>aſpicimus; quippe qui & cælum videmus. </s> <s><lb></lb>Ergo in omni horizontis orbe ipſe qui intuetur, <lb></lb>centron eſt. </s> <s>Et quia diximus quantum à cen<emph.end type="italics"></emph.end><pb xlink:href="018/01/106.jpg" pagenum="92"></pb><emph type="italics"></emph>tro acies vſque ad partem orbis extenditur, ſi<lb></lb>nè dubio in horizonte diametros orbis CCCLX <lb></lb>ſtadiorum eſt: & ſi vlteriùs qui intuetur ac<lb></lb>ceſſerit, ſeu retrorſum receſſerit, ſimilem cir<lb></lb>ca ſe orbem videbit.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Rogaui deinde vtrùm Macrobio potiùs <lb></lb><arrow.to.target n="note45"></arrow.to.target><lb></lb>ſtadijs 180 Phyſici Horizontis ſemidiame<lb></lb>trum definienti acquieſceret, an verò ſibi <lb></lb>cum Recentioribus quibuſdam conueniret, <lb></lb>qui cum Clauio (cui facilè adhæſit Blanca<lb></lb>nus) in cap.2. ſphær. </s> <s>tanquam veritati ma<lb></lb>ximè conſentaneam ad mittunt eorum ſen<lb></lb>tentiam, qui aſpectum ad milliaria 62 1/2 pro<lb></lb>trahi opinantur. </s> <s>Neque enim illum aut cum <lb></lb>Alberto Magno aut cum Proclo ſentire cen<lb></lb>ſebam, quorum prior ſtadia mille, poſte<lb></lb>rior bis mille horizontis phyſici ſemidiame<lb></lb>tro dedit. </s> </p> <p type="margin"> <s><margin.target id="note45"></margin.target><emph type="italics"></emph>XXXXV <lb></lb>Ostenditur <lb></lb>error ex ab<lb></lb>uſu lineæ <lb></lb>curuæ pro <lb></lb>recta.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Ille quidem confeſtim Neotericorum̨<lb></lb>ſententiam arripuit: ſed vbi iuſſus eſt AB <lb></lb>mill. 62 1/2 ad pedes 312500 reuocare, & <lb></lb>huius numeri quadratum 97656.250000. <lb></lb>diuidere per DA ped. 6, quanta eſt hominis <lb></lb>mediocris altitudo, videns AC prouenirę <lb></lb>maiorem milliarijs 3.000000, ad Macro<lb></lb>bium conſugit, & longitudinem AB ſtadiis <lb></lb>180 circumſcripſit: nec ſtadia Romana ped. <pb xlink:href="018/01/107.jpg" pagenum="93"></pb>625, ſed Græca ped. 600 fuiſſe contende<lb></lb>bat, cum ex Eratoſthene menſura illa de<lb></lb>ſumpta fuiſſet. </s> <s>Sed hìc pariter Syrtes inue<lb></lb>nit, cum reuocato ſtadiorum 180 numero <lb></lb>ad pedes 108000, eius quadratum 11664. <lb></lb>000000. diuidere tentans per pedes 6, quo<lb></lb>tientem pariter ampliſſimum deprehendit. </s> <s><lb></lb>Quid ſi voluiſſem contentioſiùs agene, affir<lb></lb>mando Eratoſthenem nec Romanis, nec <lb></lb>Græcis, ſed Alexandrinis ſtadijs longioribus <lb></lb>vſum fuiſſe? </s> <s>Quantò longiùs aberrâſſet? </s> <s>Sed <lb></lb>placuit mitiſſimè agere. </s> <s>Quapropter eum <lb></lb>rogaui, vt ſaltem AB milliarium trium, hoc <lb></lb>eſt ped. 15000 conſtituens tentaret, an ex <lb></lb>aſſumptâ priùs iuſto maiore ſemidiametro <lb></lb>horizontis phyſici, an verò etiam ex metho<lb></lb>di ageometriâ enormis illa magnitudo ori<lb></lb>retur: Quadratum itaque ped. 225.000000 <lb></lb>diuidens per DA ped.6, inueniebat AC ped. <lb></lb>37.500000, hoc eſt mill. 7500; vnde oritur <lb></lb>terræ ambitus mill. 47 142 6/7 duplo maior, <lb></lb>quàm communiter concedatur. </s> </p> <p type="main"> <s>Mirabatur ille vehementer, quòd præter <lb></lb>ſpem tam procul à vero receſſiſſet: ſed nec <lb></lb>conceptam de maiore, iuxta communem <lb></lb>errorem, horizontis phyſici ſemidiametro <lb></lb>opinionem deponere audebat: hærebant ſci<lb></lb>licet animo altè impreſſa plurium authorum <pb xlink:href="018/01/108.jpg" pagenum="94"></pb>effata, quibus 30 milliaria Italica videntur <lb></lb>mediocris visûs diſtantia: quare multò pro<lb></lb>babilior ei apparebat Macrobrii atque Era<lb></lb>toſthenis ſententia diſtantiam huiuſmodi ſta, <lb></lb>ſtijs 180 definientium. </s> <s>Nos igitur ad exa<lb></lb>minandum contulimus telluris ambitum ab <lb></lb>Eratoſthene conſtitutum, an cum illa ſemi<lb></lb>diametto ſtadiorum 180 cohæreret: <emph type="italics"></emph>Eui<emph.end type="italics"></emph.end><lb></lb><arrow.to.target n="note46"></arrow.to.target><lb></lb><emph type="italics"></emph>dentiſſimis<emph.end type="italics"></emph.end> enim, vt Macrobius loquitur lib. <lb></lb>1. in ſomn. </s> <s>Scip. cap. 20. <emph type="italics"></emph>& indubitabilibus <lb></lb>dimenſionibus conſtat vniuerſæ terræ ambitum, <lb></lb>quæ vbicunque vel incolitur, vel inhabitabilis <lb></lb>iacet, habere ſtadiorum millia ducenta quin<lb></lb>quaginta duo.<emph.end type="italics"></emph.end></s> <s> Cum verò huius peripheriæ <lb></lb>pars milleſima quadringenteſima ſint ſtadia <lb></lb>180, per quæ directa ab oculis acies pergit, <lb></lb>arcus BA gr.o.m.15.ſec.25. Ter. 42. &c. </s> <s><lb></lb>metitur angulum BCD in centro factum. </s> <s><lb></lb>At quoniam peripheria ponitur ſtad 252000 <lb></lb>eſt diameter minor verâ ſtad. (80181 9/11), maior <lb></lb>autem verâ (80233 41/223): quarè ſumpto medio <lb></lb>Arithmetico e<gap></gap> diameter AC ſtad. </s> <s>80207 1/2, <lb></lb>& ſemidiameter CA ſtad. </s> <s>40103 3/4. Fiat igitur <lb></lb>vt CB 99998.99293. ſinus complementi <lb></lb>gr.o.m.15.ſec. 25. Ter.42. ad CD Radium <lb></lb>100000.00000, ita CB ſtad.40103 3/4 ad CD <lb></lb>ſtad, 40104, & ped.92. Demptâ autem CA <pb xlink:href="018/01/109.jpg" pagenum="95"></pb>ſemidiametro, remanet AD ped. 242, alti<lb></lb>tudo, ex qua proſpici poteſt in B ita, vt aſpe<lb></lb>ctui pateant ſtadia 180. Quî autem fieri poſ<lb></lb>ſit ab intuente ſimilem ſemper orbem vide<lb></lb>ri, ſiuè vlteriùs acceſſerit, ſiue retrorſum re<lb></lb>ceſſerit, Macrobius ipſe viderit: an ſemper <lb></lb>eam inueniat altitudinem, cui inſiſtat, vt <lb></lb>oculus ab extimâ telluris facie pedibus 242 <lb></lb>ſemoueatur? </s> <s>Horizontis igitur ſemidiame<lb></lb>trum aut ſtadijs 180 minorem eſſe, aut non <lb></lb>ex humani corporis altitudine definiri ne<lb></lb>ceſſe eſt. </s> </p> <p type="margin"> <s><margin.target id="note46"></margin.target><emph type="italics"></emph>XXXXVI <lb></lb>Authorum <lb></lb>aliquorum <lb></lb>lapſus iņ <lb></lb>statuendą <lb></lb>nimia viſus <lb></lb>distantia.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Cum verò ille labantem Macrobij ſen<lb></lb>tentiam ſuffulcire aliquatenus ſe poſſe con<lb></lb>ſideret, ſtadia 180 tribuendo non arcui AB, <lb></lb>ſed rectæ DB terram tangenti, quæ & radij <lb></lb>optici ex oculo D prodeuntis menſura eſt, & <lb></lb>arcu AB longior; operam demum ſe ludere <lb></lb>ſenſit, cum re ad Geometricam normam <lb></lb>reuocatâ tantam opticæ lineæ longitudinem <lb></lb>terrenæ magnitudini minimè congruere ma<lb></lb>nifeſtè deprehendit, etiam ſi oculus à terrâ <lb></lb>pedum 50. interuallo AD ſeiunctus intelliga<lb></lb>tur. </s> <s>Quoniam enim quadratum Tangentis <lb></lb>BD, quæ ſtad. </s> <s>180 ponitur, æquale eſt re<lb></lb>ctangulo ADE, diuidatur quadratum ped. <lb></lb>11664.000000 per 50, & erit DE ped. 233 <lb></lb>280000, hoc eſt ſtadiorum Græcorum (quæ <pb xlink:href="018/01/110.jpg" pagenum="96"></pb>hìc vſurpantur) 388800. Quare diameter <lb></lb>AE, demptis pedibus 50, erit ſtad. </s> <s>388799 <lb></lb>ped. 550. Ex qua diametro colligitur am<lb></lb>bitus longè maior eo, quem Macrobius cum <lb></lb>Eratoſthene conſtituit. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Sed lapſis in ageometriam Erato<lb></lb>ſthene ac Macrobio, quod ſtadia 180 tribue<lb></lb>rint horizontis phyſici ſemidiametro, cum <lb></lb>totum telluris ambitum ſtadijs 252000 de<lb></lb>ſinierint; quid de ijs dicendum, qui terram <lb></lb>paucioribus ſtadijs circumſcribentes (mil<lb></lb>liarijs nimirum 21600, quæ ad ſtadia Græca <lb></lb>180000 reuocantur, quot Ptolemæus toti <lb></lb>terrenæ peripheriæ conceſsit) oculum tamen <lb></lb>ad maiora ſpatia longo limite ducunt? </s> <s>Hi <lb></lb>ſanè longiſsimè abſunt à veritate, cum lineæ <lb></lb>opticæ tribuunt longitudinem ſtadiorum <lb></lb>vt minimum 500. Nam quadratum lineæ <lb></lb>opticæ eſt æquale rectangulo ſub altitudinę <lb></lb>oculi, & terræ diametro auctâ eâdem altitu<lb></lb>dine. </s> <s>Sit ergo D linea optica, & B ſit terræ <lb></lb>diameter, & A ſit altitudo: igitur DQ æqua<lb></lb>tur AQ+A in B. </s> <s>Quare ad inueniendam A <lb></lb>fiat expurgatio per vncias conditionarias qua<lb></lb>drati, ſc. </s> <s>per ſemiſſem coëfficientis B. </s> <s>Sit er<lb></lb>go E æqualis A+B 1/2: igitur E——B 1/2 eſt æqua<lb></lb>lis ipſi A. </s> <s>Factâ itaque prioris æquationis in<lb></lb>terpretatione erit æquatio inter EQ——BQ 1/4 <pb xlink:href="018/01/111.jpg" pagenum="97"></pb>& DQ: & per Antitheſim EQ æquatur <lb></lb>DQ+BQ 1/4 </s> </p> <p type="main"> <s>Cum igitur data ſit peripheria ſtad. </s> <s>180000, <lb></lb>erit diameter B ſtad. </s> <s>57291 2/3 proximè: atquè <lb></lb>adeò BQ 1/4 eſt 820583766 2/3; ipſius verò D <lb></lb>ſtad. </s> <s>500, quadratum 250000. ex quotum <lb></lb>ſummâ 820833766 2/3, quæ æqualis eſt EQ, <lb></lb>ſi eruatur radix, erit E, hoc eſt A+B 1/2 ſtad. <lb></lb>(28650 196/1000), ablatâ autem B 1/2, quæ eſt ſtad. </s> <s><lb></lb>28645 5/6, remanet A ſtad. (<gap></gap>4 36/100) proximè alti<lb></lb>tudo oculi: ex qua altitudine conſtat noņ <lb></lb>eſſe definiendam horizontis phyſici amplitu<lb></lb>dinem. </s> <s>Quod ſ<gap></gap> altitudinem oculi ſtatuere<lb></lb>mus vnius ſtadij, retentâ eâdem opticæ li<lb></lb>neæ longitudine, proueniret terræ diameter <lb></lb>ſtad. </s> <s>249999, quæ maior eſt totâ periphe<lb></lb>riâ ab ipſis conſtitutâ. </s> </p> <p type="main"> <s>Hinc pariter Blancano fucum factum̨ <lb></lb>comperiemus (nam & quandoque bonus <lb></lb>dormitat Homerus) qui maximam mon<lb></lb>tium altitudinem ſeſquimilliari aut duobus <lb></lb>vt ſummum milliaribus definiens, Ætnæ in <lb></lb>Siciliâ duo tantùm milliaria conceſsit, ad<lb></lb>miſit tamen ex Maurolyco dial. </s> <s>3. Coſmogr. <lb></lb>pag. 75.indè proſpici in mare vltra ducenta <lb></lb>paſſuum millia. </s> <s>Namque aſſumptâ lineæ <lb></lb>opticæ terrenum globum tangentis longitu<pb xlink:href="018/01/112.jpg" pagenum="98"></pb>dine mill. 200, huiusque quadrato 40000 <lb></lb>per Ætnæ altitudinem conſtitutam mill. 2 <lb></lb>diuiſo, & ex Quotiente 20000 demptâ mon<lb></lb>tis altitudine, neſcio qua ratione reſiduum <lb></lb>mill. 19998 terrenæ diametro tribuendum, <lb></lb>idem Blancanus Sphæræ part. </s> <s>3.c.5.pag.93. <lb></lb>ſibi gratulatur proximè conuenire cum am<lb></lb>bitu mill. 21600 ab aliis poſito, & à ſe ad<lb></lb>miſſo. </s> <s>Cum tamen hinc debuiſſet potiùs <lb></lb>ſuſpicari montium altitudinem à ſe breuiori<lb></lb>bus, quàm par ſit, terminis definitam, ex <lb></lb>qua tanta ferè colligitur diameter, quantą <lb></lb>eſſe deberet peripheria. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> An igitur eos quoque mendacii <lb></lb>manifeſtos redarguas, qui Alexandrinam̨ <lb></lb>ſpeculam ab inſulâ, in qua extructa fuit, Pha<lb></lb>ron dictam ad eam prouehunt altitudinem, <lb></lb>vt indè naues ſexcentorum milliarium in<lb></lb>teruallo diſsitas videri potuiſſe per ſummam <lb></lb>conſidentiam âffirment? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Vnde fabulam iſtam Io.Bapt. Por<lb></lb>ta lib.17. Mag. nat.in proëm. </s> <s>hauſerit, pror<lb></lb><arrow.to.target n="note47"></arrow.to.target><lb></lb>ſus ignoro. </s> <s>Neque enim Diodorus Siculus, <lb></lb>aut Strabo, aut Cæſar, aut A. Hirtius, aut <lb></lb>Plinius, aut Lucianus, aut Solinus, aut Am<lb></lb>mianus Marcellinus, aut alius ex ijs, quos le<lb></lb>gerim, cum turris illius Alexandrinæ me<lb></lb>minerint, adeò inſanam altitudinem nobis <pb xlink:href="018/01/113.jpg" pagenum="99"></pb>obtrudunt. </s> <s>Quod autem Porta aſſerit in eâ <lb></lb>turri à Ptolemæo conſtitutum ſpeculum̨, <lb></lb>quod deinde cap. 11. ipſe ſpecillum potiùs <lb></lb>quàm ſpeculum vocat, vt ad 600 paſſuum <lb></lb>millia hoſtium naues, quæ eius regiones in<lb></lb>uaderent, conſpiceret, occaſio fuit aliquan<lb></lb>do non nemini opinandi ad ea vſque tempo<lb></lb>ra referendum vſum Tubi optici. </s> <s>Huiuſce <lb></lb>tamen ſpeculi, ſiue ſpecilli, veſtigium nul<lb></lb>lum apud antiquos ſcriptores deprehenderę <lb></lb>potui; quamuis eorum libros multâ diligen<lb></lb>tiâ perſcrutatus. </s> <s>Quapropter ea mihi mens <lb></lb>incidit, vt exiſtimarem Portæ, viro cætero<lb></lb>qui erudito, fucum factum ab inepto quo<lb></lb>piam Typographo, vel ignaro ſcriptore, qui <lb></lb>pro ſpeculâ in Pharo (inſulâ) extructâ, ſpe<lb></lb>culum in Pharo (turri) conſtitutum ſuppo<lb></lb>ſuerit. </s> </p> <p type="margin"> <s><margin.target id="note47"></margin.target><emph type="italics"></emph>XLVII <lb></lb>Fabula de <lb></lb>altitudinę <lb></lb>Phari Ale<lb></lb>xandrinæ <lb></lb>reijcitur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Cæterùm cum tubus opticus vitreis lenti<lb></lb>bus ritè inſtructus ea ſolum corpora diſtinctè <lb></lb>articulatimque videnda proponar, ad quæ <lb></lb>recta oculorum acies pergit, tota hæc fabu<lb></lb>la euaneſcet, vbi tantam altitudinem, quæ <lb></lb>viſum ad milliaria 600 producat, probabili<lb></lb>tate omni carere conſtiterit. </s> <s>Neque opus <lb></lb>erat altitudine illâ immani, cum ideò turris <lb></lb>illa à Ptolemæo Philadelpho (quamuis Amm. <lb></lb>Marcell. lib. 22. à Cleopatrâ, quæ ſoror, & <pb xlink:href="018/01/114.jpg" pagenum="100"></pb>vxor fuit vltimi Ptolemæi cognomento Dio<lb></lb>nyſij turrim illam excelſam excogitatam ſcri<lb></lb>bat) Soſtrati Cnidij architecti operâ extructa <lb></lb>ſuerit, vt noctu accenſæ faces indè præluce<lb></lb>rent nauigantibus, quò breuia & ſyrtes de<lb></lb>clinarent, quibus ora illa fallacibus & inſi<lb></lb>dioſis acceſsibus importuoſa ſcatebat, & di<lb></lb>ſcriminibus plurimis incautos nautas affli<lb></lb>gebat. </s> </p> <p type="main"> <s>Sed iam examinemus quantâ altitudine è <lb></lb>mari eminuerit Pharos illa Alexandrina, ſi <lb></lb>inde ad milliaria 600 viſus excurrere potuit. </s> <s><lb></lb>Poſito terræ ambitu mill. 21600, arcus BA, <lb></lb>in ſuperiori figurâ mill.600 complectitur gra<lb></lb>dus 10. Fiat igitur vt CB Radius 100000. <lb></lb>00000. ad CD 101542.66119 ſecantem̨ <lb></lb>grad. 10, ita ſemidia<lb></lb><figure id="id.018.01.114.1.jpg" xlink:href="018/01/114/1.jpg"></figure><lb></lb>metet CB mill. 3437 1/2 <lb></lb>proximè ad CD mill. <lb></lb>3490 1/2. Ablatâ autem <lb></lb>femidiametro CA, re<lb></lb>manet AD mill. 53. al<lb></lb>titudo turris Alexandri<lb></lb>næ: quanta videlicet <lb></lb>communiter tribui ſolet <lb></lb>halitibus illis, quibus <lb></lb>tum prima illuceſcentis diei, tum poſtrema <lb></lb>aduentantis noctis crepuſcula debemus. </s> <s>Id <pb xlink:href="018/01/115.jpg" pagenum="101"></pb>verò quàm longè à veritate recedat, quid <lb></lb>pluribus opus eſt explicare? </s> <s>quotus enim <lb></lb>quiſque eſt, qui turri octingentis talentis ex<lb></lb>citatæ duûm triumue milliarium altitudi<lb></lb>nem concedat? </s> <s>Pharos igitur Inſula imma<lb></lb>nis ſcopulus fuit 50 ſerè milliaria iuxta per<lb></lb>pendiculum numerans; qua de re mirum <lb></lb>apud ſcriptores omnes ſilentium: ac proin<lb></lb>de tantæ altitudini parùm vtilis accidiſſet ſpe<lb></lb>culæ acceſsio. </s> <s>At ſtatuamus cum Eratoſthe<lb></lb>ne telluris ambitum ſtadiorum 252000, & <lb></lb>ſtadia ſingula ſint Alexandrina |ped. Rom. <lb></lb>720., totus ambitus eſſet mill.Rom. 36288; <lb></lb>igitur milliaria 600 eſſent gr. 5. m. </s> <s>57. Qua<lb></lb>re vt Radius 100000.00000. ad 100541. <lb></lb>64449. ſecantem gr.5.m. 57., ita ſemidia<lb></lb>meter CB mill. 5775. paſſ. </s> <s>419. ad CD <lb></lb>mill. 5806. paſſ. </s> <s>701: ex qua ſi auferatur ſe<lb></lb>midiameter CA, remaneret altitudo AD <lb></lb>mill. 31 & paſſ. </s> <s>282; quæ altitudo adhuc eſt <lb></lb>immanis: & maior hac eſſet, ſi ſtadia illą <lb></lb>252000. non. </s> <s>Alexandrina ſed Græca aſſum<lb></lb>pta fuiſſent; eſſet enim CD ſecans anguli <lb></lb>DCB gr.7.m.8.ſec.38. Non itaque fieri po<lb></lb>tuit, vt ex Alexandrinâ turri ad ſexcenta paſ<lb></lb>ſuum millia proſpectus pateret. </s> </p> <p type="main"> <s>Longè minor eſt Phyſici Horizontis ſe<lb></lb>midiameter, quàm vulgus cenſeat, ſi res Geo<pb xlink:href="018/01/116.jpg" pagenum="102"></pb>metricè perpendatur: creſcit autem eius am<lb></lb>plitudo pro maiori ſpectatoris altitudinę. </s> <s><lb></lb>Hinc quamuis nauclerorum plurimos Geo. <lb></lb>metriâ non ſatis inſtructos ſæpè fugiat ratio, <lb></lb>eorum tamen varia in determinandâ visûs <lb></lb>diſtantiâ ſententias facilè poſſumus concilia<lb></lb>re; alijs ſiquidem ex altiori, alijs ex humilio<lb></lb>ri ſpeculâ proſ picientibus obiectum idem, <lb></lb>illis quidem longiùs, his verò propiùs ſe ob<lb></lb>tulit contemplandum. </s> <s>Quocirca ex huiuſ<lb></lb>modi hominum effatis nihil timendum, <lb></lb>quod datâ telluris magnitudine conſtitutam <lb></lb>Geometricisque rationibus ſolidatam de vi<lb></lb>sûs diſtantiâ ſententiam labefactare poſsit: <lb></lb>duo enim hæc inuicem perpetuo vinculo <lb></lb>colligantur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> At quiſquis ex eorum numero ſue<lb></lb>rit, quos pudet aliquando ſapere, & antiquos <lb></lb>errores dediſcere, vbi visûs diſtantiam eius <lb></lb>opinione minorem demonſtraueris, illicò <lb></lb>terræ magnitudinem non ritè conſtitutam <lb></lb>calumniabitur, & ad Ariſtotelem prouoca<lb></lb>bit, qui lib. 2. de Cœlo text. </s> <s>vlt. </s> <s>ſcribit terræ <lb></lb>circuitum patere quadraginta ſtadiorum̨ <lb></lb>myriadibus, hoc eſt ſtadiis 400000. aut ad <lb></lb>Archimedem, qui in Arenario telluris am<lb></lb>bitum ter mille ſtadiorum millia & eo am<lb></lb>pliùs complecti conſtituit. </s> </p> <pb xlink:href="018/01/117.jpg" pagenum="103"></pb> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Prouocet: per me licet. </s> <s>Eum ta<lb></lb>men monitum velim parum ex Archimede <lb></lb>ſperandum, cum eam <lb></lb>ille magnitudinem da<lb></lb><figure id="id.018.01.117.1.jpg" xlink:href="018/01/117/1.jpg"></figure><lb></lb>tâ operâ ponere volue<lb></lb>rit, quam nemo eo<lb></lb>rum, quibuſcum di<lb></lb>ſputabat, iuſto mino<lb></lb>rem calumniari poſſet. </s> <s><lb></lb>Quodverò ad Ariſtote<lb></lb>lem ſpectat, non mul<lb></lb>tum habet momen<lb></lb>ti Peripatetica autho<lb></lb>ritas, cui apodictica ratio aduerſatur. </s> <s>Porrò <lb></lb>longè melius eſt opticæ lineæ longitudinem <lb></lb>præcognoſcere, & ex illâ terræ magnitudi<lb></lb><arrow.to.target n="note48"></arrow.to.target><lb></lb>nem inueſtigare, quàm incertis coniecturis <lb></lb>telluris ambitum ſtatuere; & infirmo huic <lb></lb>fundamento æquè nutantem de aſpectûs lon<lb></lb>gitudine ſententiam ſuperſtruere. </s> <s>Sit enim <lb></lb>nota altitudo BA, & obſeruatus fuerit angu<lb></lb>lus BAD; notus eſt angulus complementi, <lb></lb>qui eſt ad C: ducta autem recta BD facit <lb></lb>angulum BDA, qui eſt ſemiſſis noti anguli <lb></lb>ad C, vt paulò antè dicebam. </s> <s>Cum itaque <lb></lb>in triangulo BAD datum ſit latus AB, & duo <lb></lb>anguli ad A & ad D innotuerint, inueniri <lb></lb>poterit quantitas lineæ opticæ AD. </s> <s>Tum <pb xlink:href="018/01/118.jpg" pagenum="104"></pb>ex B intelligatur educta perpendiculatis BE, <lb></lb>& in triangulo rectangulo ABE, datis angu<lb></lb>lo A & latere AB, inueniatur latus BE. </s> <s>De<lb></lb>mum quia triangula ABE, ADC rectangula <lb></lb>habentia communem angulum ad A ſunt ſi<gap></gap><lb></lb>milia, fiat vt AB data ad BE inuentam, ita <lb></lb>AD lineæ opticæ longitudo inuenta ad DC <lb></lb>quæſitam terræ ſemidiametrum. </s> </p> <p type="margin"> <s><margin.target id="note48"></margin.target><emph type="italics"></emph>XLVIII <lb></lb>Inuenirę <lb></lb><expan abbr="longitudinẽ">longitudinem</expan> <lb></lb>viſus: & ex <lb></lb>ea Quintą <lb></lb>methodus <lb></lb>vestigandi <lb></lb>terræ ſemi<lb></lb>diametrum,<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> In ijs, quæ hactenus attuliſti ad <lb></lb>terræ ſemidiametrum inueniendam, illud <lb></lb>accidit incommodum, quod totam altitu<lb></lb>dinem ſupra maris ſuperficiem innoteſcere <lb></lb>oportet: id quod haberi non poteſt, niſi aut <lb></lb>prærupta rupes mari immineat, aut turris in <lb></lb>litore ſit conſtituta. </s> <s>Quin methodum ali<lb></lb>quam excogitas, qua etiam ex turri procul ab <lb></lb>æquore in colle poſitâ explorare poſſimus, <lb></lb>quanta ſit terræ magnitudo? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Tentemus pariter, quid poſſimus: <lb></lb>tertius adeſt Galilæus; niſi aliquid inueneri<lb></lb><arrow.to.target n="note49"></arrow.to.target><lb></lb>mus, dicam nos iratis Muſis conueniſſe. </s> <s>Sit <lb></lb>igitur in perpendiculari AC, nota inſignis <lb></lb>aliqua altitudo BA, at non talis, vt eius hu<lb></lb>millimum punctum B ſphæricæ ſuperficiei <lb></lb>adhæreat, cum potiùs ex illâ emineat iņ <lb></lb>colle DB, cuius altitudo ignota eſt: fieri au<lb></lb>tem poſſit, vt liber proſpectus in Horizon<lb></lb>tem pateat, ſiue in ſummo A, ſiue in imo B <pb xlink:href="018/01/119.jpg" pagenum="105"></pb>conſiſtas angulos CAE, CBF obſeruaturus. <lb></lb><figure id="id.018.01.119.1.jpg" xlink:href="018/01/119/1.jpg"></figure><lb></lb>Quibus angulis obſer<lb></lb>uatis intellige rectam <lb></lb>BF occurrere Tangen<lb></lb>ti AE in G. </s> <s>In triangu<lb></lb>lo itaque ABG angu<lb></lb>lus AGB eſt notus, vt<lb></lb>pote differentia duo<lb></lb>rum obſeruatorum C <lb></lb>BG, CAG: angulus A <lb></lb>eſt obſeruatus, & data <lb></lb>eſt altitudo BA: ergo <lb></lb>inueniri poteſt quantitas rectæ BG. </s> <s>Iam du<lb></lb>cantur rectæ CF, CE, & ſunt duo triangula <lb></lb>AEC, BFC rectangula, in quibus duo an<lb></lb>guli EAC, ECA ſimul ſunt æquales duo<lb></lb>bus FBC, FCB: Atqui angulus ECA eſt æ<lb></lb>qualis duobus ECF, FCB; ergo tres ECF, <lb></lb>FCB, CAE ſunt æquales duobus FBC, FCB; <lb></lb>& dempto communi FCB, remanet FBC <lb></lb>æqualis duobus ECF, EAC. </s> <s>Eſt igitur ECF <lb></lb>differentia nota duorum obſeruatorum CAE, <lb></lb>CBF. </s> <s>Ducatur demùm recta CG. </s> <s>Et quo<lb></lb>niam GF, GE ſunt tangentes circulum ab <lb></lb>eodem puncto exeuntes, inter ſe æquales <lb></lb>ſunt, ſicut & CF, CE ex centro ductæ; CG <lb></lb>verò eſt vtrique triangulo FCG, ECG com<lb></lb>munis; ergo angulus ECF notus diuiditur à <pb xlink:href="018/01/120.jpg" pagenum="106"></pb>rectâ CG bifariam. </s> <s>Quare ſi angulorum ob<lb></lb>ſeruatorum ſemidifferentiam GCF addas an<lb></lb>gulo FCB complemento noto anguli obſer<lb></lb>uati in B, notus eſt etiam angulus BCG; ex <lb></lb>quo, vnâ cum angulo CBG obſeruato, & la<lb></lb>tere BG inuento, inuenitur latus CB: Cui ſi <lb></lb>addatur data altitudo BA, notum erit latus <lb></lb>CA vnâ cum angulo ad A obſeruato in trian<lb></lb>gulo AEC rectangulo: quare & inuenitur CE <lb></lb>ſemidiameter quæſita, quæ eſt ipſi CD æqua<lb></lb>lis, vnde innoteſcit altitudo collis BD, & <lb></lb>lineæ opticæ AE longitudo cognoſci poteſt. </s> </p> <p type="margin"> <s><margin.target id="note49"></margin.target><emph type="italics"></emph>XLIX <lb></lb>Sexta me<lb></lb>thodus ter<lb></lb>ræ ſemidia<lb></lb>metrum in<lb></lb>quirendi, & <lb></lb>montis alti<lb></lb>tudinem co<lb></lb>gnoſcendi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>At contingat ex edito quidem monte pro<lb></lb>ſpici poſſe in <expan abbr="extremũ">extremum</expan> <lb></lb><arrow.to.target n="note50"></arrow.to.target><lb></lb><figure id="id.018.01.120.1.jpg" xlink:href="018/01/120/1.jpg"></figure><lb></lb>horizontem, ſed planè <lb></lb>ignotam eſſe montis al<lb></lb>titudinem. </s> <s>Eligatur lo<lb></lb>cus aliquis conſpicuus, <lb></lb>qui ita diſtare cenſea<lb></lb>tur, vt perpendicula<lb></lb>res ex vtroque loco ad <lb></lb>centrum ductæ à pa<lb></lb>ralleliſmo deflectentes <lb></lb>ſenſu dignoſci queant. </s> <s><lb></lb>Hinc enim terræ ſemidiametrum eruerę <lb></lb>poſſumus. </s> <s>Ex A igitur ſit linea AD terram <lb></lb>tangens: obſeruetur angulus CAD. </s> <s>Tum <lb></lb>ad eaſdem vel alias partes eligatur locus B <pb xlink:href="018/01/121.jpg" pagenum="107"></pb>valde diſtans, & obſeruetur pariter angulus <lb></lb>CAB. </s> <s>Diſtantia autem BA vel ſit præcogni<lb></lb>ta, vel ex tertio loco obſeruetur, vt fieri com<lb></lb>muniter ſolet. </s> <s>Demum ex B obſeruetur an<lb></lb>gulus ABC; cognitâ ſcilicet diſtantiâ ipſius <lb></lb>A puncti à vertice obſeruatoris in B, com<lb></lb>plementum ad duos rectos dat angulum <lb></lb>ABC: erit autem indicium diſtantiæ AB <lb></lb>ſufficientis, ſi anguli CAB, CBA ſimul ſum<lb></lb>pti minores fuerint duobus rectis. </s> <s>Quare in <lb></lb>triangulo ABC dato latere BA & angulis <lb></lb>adiacentibus inuenitur latus AC. </s> <s>Inuento <lb></lb>autem latere AC & obſeruato angulo CAD <lb></lb>in triangulo CDA rectangulo, inuenitur CD <lb></lb>quæſita terræ ſemidiameter, nec latebit <lb></lb>montis altitudo. </s> </p> <p type="margin"> <s><margin.target id="note50"></margin.target><emph type="italics"></emph>L. </s> <s><lb></lb>Septima me<lb></lb>thodus in<lb></lb>uestigandi <lb></lb>ſemidiame<lb></lb>trum terræ, <lb></lb>& montis <lb></lb>altitudine.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quod ſi locorum opportunitas ferat, vt <lb></lb>detur altitudo FE nota, ex qua obſeruari <lb></lb><arrow.to.target n="note51"></arrow.to.target><lb></lb>queat angulus CED, & in monte procul poſi<lb></lb>to liber ſit aſcenſus, donec ex A puncto per <lb></lb>E in extremum horizontem D productus ra<lb></lb>dius efficiat angulum CAD, qui obſeruatio<lb></lb>ne cognoſcatur; ea habemus, quæ ad inue<lb></lb>niendam terræ ſemidiametrum, vel ad exa<lb></lb>minandamiam inuentam ſufficiant. </s> <s>Intel<lb></lb>ligatur enim ex F exire recta FG parallela ipſi <lb></lb>CA (perpendiculares ſiquidem EC, AG á <lb></lb>paralleliſmo deflectere ponimus) efformatur <pb xlink:href="018/01/122.jpg" pagenum="108"></pb>triangulum FEG, cuius latus FE datur, an<lb></lb>gulus EGF æqualis angulo EAC obſeruato <lb></lb>innoteſcit propter linearum CA, FG paral<lb></lb>leliſmum, & GEF eſt complementum ad <lb></lb>duos rectos anguli FED obſeruati. </s> <s>Inuenia<lb></lb>tur itaque latus EG; quod ablatum ex EA <lb></lb>diſtantiâ iam notâ duorum locorum, iņ <lb></lb>quibus inſtitutæ ſunt obſeruationes, relin<lb></lb>quit GA. </s> <s>At in triangulo EAC, lateri AC <lb></lb>parallela eſt GF, ergo vt EG ad GA, ita EF <lb></lb>data altitudo ad FC quæſitam ſemidiame<lb></lb>trum. </s> <s>Vel etiam ijſdem poſitis, & obſerua<lb></lb>tis angulis CED, GAE, atque diſtantiâ AE, <lb></lb><arrow.to.target n="note52"></arrow.to.target><lb></lb>in triangulo CAE noti ſunt duo anguli, (an<lb></lb>gulus ſiquidem CEA eſt complementum ad <lb></lb>duos rectos anguli CED obſeruati) & latus <lb></lb>adiacens AE: inueniatur igitur latus EC, ex <lb></lb>quo dempta nota altitudo FE relinquit quæ<lb></lb>ſitam terræ ſemidiametrum. </s> <s>Erit autem <lb></lb>indicium ſufficientis diſtantiæ inter A & E, ſi <lb></lb>angulus CED obſeruatus fuerit maior angu<lb></lb>lo CAE. </s> </p> <p type="margin"> <s><margin.target id="note51"></margin.target><emph type="italics"></emph>LI. </s> <s><lb></lb>Octaua me<lb></lb>thodus in<lb></lb>ueniendi ter<lb></lb>ræ ſemidia<lb></lb>metrum.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note52"></margin.target><emph type="italics"></emph>LII. </s> <s><lb></lb>Idem aliter.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Ea profectò ſunt, quæ hactenus di<lb></lb>ſputata ſunt, vt vix cenſeam fieri poſſe, vt <lb></lb>alicui nulla ex his methodis arrideat. </s> <s>Ve<lb></lb>rùm ſcrupulus eſt, quem fortaſſe ex multo<lb></lb>rum animis non facilè eximas: exiſtima<lb></lb>bunt ſiquidem angulum, quem cum per<pb xlink:href="018/01/123.jpg" pagenum="109"></pb>pendiculo opticus radius conſtituit, nun<lb></lb>quam minimè dubiâ obſeruatione inueſtiga<lb></lb>ri poſſe. </s> <s>Nam vltimum visûs terminum ſi <lb></lb>in terrâ ſpectes, quamuis planiſſima facies <lb></lb>videatur, quî fiat, vt nullus pateat dubita<lb></lb>tioni locus, an molli inclinatione indè per <lb></lb>longa terrarum ſpatia in mare deſcendatur? </s> <s><lb></lb>ac proinde linea illa ab oculo exiens non cir<lb></lb>culum in ſphæricâ ſuperficie contingeret, vt <lb></lb>exigitur. </s> <s>Si verò in immenſum æquor vi<lb></lb>ſus excurrat, etſi ſopitis fructibus otia agat, <lb></lb>nulloque æſtu intumeſcat, quis neſciat At<lb></lb>moſphæram vaporibus non adeò paucis te<lb></lb>nuibuſue ſcatere, vt nulla refractionis, qua <lb></lb>Oceani partes infra horizontem depreſſæ <lb></lb><expan abbr="ẽmergant">emmergant</expan>, ſuſpicio ſuboriri poſſit? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end> Hæc quidem non ea eſſe videntur, <lb></lb>quæ telluris ſemidiametro his methodis in<lb></lb>uentæ officere poſſint: Si enim aliâ atque <lb></lb>aliâ methodo inueſtigetur, nec valdè inſi<lb></lb>gni diſcrimine differant, quæ inueniuntur, <lb></lb>medium Arithmeticum inter extrema in<lb></lb>uenta dabit quantitatem quæſitam ſemidia<lb></lb>metro terræ tribuendam. </s> <s>Tellus quippę <lb></lb>toreuma non eſt vndequaque expolitum; ſed <lb></lb>cum eius partes à centro diſparibus interual<lb></lb>lis abſint, ita tamen vt proximè ſphæram̨ <lb></lb>æmuletur, facis eſt ſi mediocris à centro di-<pb xlink:href="018/01/124.jpg" pagenum="110"></pb>ſtantia innoteſcat. </s> <s>Nihilominus tamen aliam <lb></lb>placet tentare viam nullâ habitâ ratione radii <lb></lb>optici terram tangentis, modò ea ſit duo<lb></lb>rum locorum diſtantia, vt perpendiculares <lb></lb>ad centrum notabiliter deflectant à paralle<lb></lb>liſmo. <lb></lb><arrow.to.target n="note53"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note53"></margin.target><emph type="italics"></emph>LIII: <lb></lb>Nona me<lb></lb>thodus tel<lb></lb>luris ſemi<lb></lb>diametrum <lb></lb>inquirendi.<emph.end type="italics"></emph.end></s> </p> <figure id="id.018.01.124.1.jpg" xlink:href="018/01/124/1.jpg"></figure> <p type="main"> <s>Eligatur itaque alti<lb></lb>tudo quæpiam inſignis <lb></lb>& nota AB, ex cuius <lb></lb>vtroque extremo vi<lb></lb>deatur in monte ad <lb></lb>plura milliaria procul <lb></lb>poſito locus D: loca ve<lb></lb>rò huiuſmodi diſtantia <lb></lb>poſſunt obſeruari potiſ<lb></lb>ſimùm noctu accenſo <lb></lb>ibi igné ab amico, niſi <lb></lb>adſit nota aliqua peculiaris, vt ædificium, <lb></lb>turris &c. </s> <s>Tum ex A obſeruetur angulus <lb></lb>BAD, & ex B angulus ABD, notus enim fiet <lb></lb>reliquus angulus BDA. </s> <s>Ex puncto autem <lb></lb>D obſeruetur angulus BDC, vnde ablato an<lb></lb>gulo BDA noto, reliquus ADC innoteſcit. </s> <s><lb></lb>His paratis in triangulo ABD dantur duo an<lb></lb>guli A & B cum latere adiacente BA, inue<lb></lb>niatur igitur latus AD. </s> <s>Ex hoc autem late<lb></lb>re AD inuento vnâ cum angulo ADC, qu <lb></lb>ex obſeruatione innotuit, & angulo DAC <pb xlink:href="018/01/125.jpg" pagenum="111"></pb>qui eſt complementum anguli obſeruati <lb></lb>DAB ad duos rectos, inueniri poteſt latus <lb></lb>AC quæſita terræ ſemidiameter. </s> </p> <p type="main"> <s>At non vacat montem conſcendere? </s> <s>alia <lb></lb><arrow.to.target n="note54"></arrow.to.target><lb></lb>ſuppetit via, qua leuiori labore propoſitum <lb></lb>aſſequamur. </s> <s>Sit nota altitudo IG, vnde vi<lb></lb>deatur locus aliquis in ſuperficie terræ F: ob<lb></lb>ſerueturque angulus IGF. </s> <s>Quod ſi diſtantia <lb></lb><figure id="id.018.01.125.1.jpg" xlink:href="018/01/125/1.jpg"></figure><lb></lb>GF iam nota non <lb></lb>fuerit, ex tertio <lb></lb>quopiam loco eą <lb></lb>obſeruetur, <expan abbr="inue-niaturq.">inue<lb></lb>niaturque</expan> iuxta Tri<lb></lb>gonometriæ præ<lb></lb>cepta. </s> <s>His com<lb></lb>paratis producatur <lb></lb>GI per terræ cen<lb></lb>trum T vſquę <lb></lb>in O, vt IO ſit <lb></lb>terræ diameter: ex <lb></lb>F cadat in dia<lb></lb>metrum perpendicularis FC. </s> <s>Quoniam̨ <lb></lb>igitur in triangulo GCF rectangulo datur hy<lb></lb>pothenuſa GF, & angulus CGF, inueniantur <lb></lb>reliqua latera FC, CG. </s> <s>Auferatur autem <lb></lb>IG data altitudo ex GC, & remanet IC. </s> <s><lb></lb>Quia verò FC à puncto peripheriæ F cadit <lb></lb>perpendicularis in diametrum IO, eſt me<pb xlink:href="018/01/126.jpg" pagenum="112"></pb>dio loco proportionalis inter diametri ſeg<lb></lb>menta IC, CO; ac proinde quadratum me<lb></lb>diæ CF æquale eſt rectangulo ſub extremis. </s> <s><lb></lb>Itaque quadrato ipſius CF diuiſo per IC ſeg<lb></lb>mentum notum, Quotiens dabit CO, cui <lb></lb>addatur CI, & habetur tota diameter IO <lb></lb><arrow.to.target n="note55"></arrow.to.target><lb></lb>quæſita. </s> </p> <p type="margin"> <s><margin.target id="note54"></margin.target><emph type="italics"></emph>LIV. </s> <s><lb></lb>Decima me<lb></lb>thodus, qua <lb></lb>terræ dia<lb></lb>meter inue<lb></lb>nitur.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note55"></margin.target><emph type="italics"></emph>LV. </s> <s><lb></lb>Idem aliter.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Hæc mihi methodus magis arridet vtpo<lb></lb>te breuior, qua quadratum CF diuido per <lb></lb>IC: cæterùm ſi rem merè Trigonome<lb></lb>tricè perficere quis malit, inuentis CF <lb></lb>& IC, quærat angulum IFC; quem du<lb></lb>plicet, & dupli ſinum ex Tabulis inue<lb></lb>niat: tum fiat vt ſinus inuentus ad Ra<lb></lb>dium ita inuenta CF ad quæſitam ſemidia<lb></lb>metrum FT. </s> <s>Huius operationis ratio pa<lb></lb>tet, quia cum angulus IFO in ſemicircu<lb></lb>lo ſit rectus, triângulum ICF eſt ſimile trian<lb></lb>gulo IFO, igitur angulus inuentus IFC æqua<lb></lb>lis eſt angulo FOC; huius autem duplex eſt <lb></lb>angulus ITF ad centrum, qui proinde inno<lb></lb>teſcit, vnâ cum ſinu FC in partibus Radii <lb></lb>hæc verò linea cum nota ſit etiam in men<lb></lb>ſurâ homogeneâ altitudini datæ IG, manife<lb></lb>ſtabit pariter in eâdem menſurâ Radium TF. </s> </p> <p type="main"> <s>Placetne aliam adhuc inire viam? </s> <s>nec <lb></lb>Dionyſiodori Geometræ protritam veſtigiis; <lb></lb>cuius in ſepulchro inuenta eſt epiſtola ad <pb xlink:href="018/01/127.jpg" pagenum="113"></pb>ſuperos miſſa, qua ſe à ſepulchro ad intimam <lb></lb>terram deſcendiſſe ſignificabat, illudque ſpa<lb></lb>tium ſtadia 42000. complecti. </s> <s>Sint datæ al<lb></lb>titudo eadem IG, ac diſtantia GF, & angu<lb></lb>lus IGF obſeruetur. </s> <s>Ducatur ex I tangens <lb></lb><arrow.to.target n="note56"></arrow.to.target><lb></lb>IH; quæ ſecet GF in H. </s> <s>Quæratur ergo iņ <lb></lb>triangulo GIH rectangulo, ex dato latere GI <lb></lb>& angulo G, latus GH, quod ex GF ablatum <lb></lb>relinquit HF, & quæratur latus IH. </s> <s>Deinde du<lb></lb>ctâ rectâ IF, in triangulo IHF nota ſunt la<lb></lb>tera IH & HF, angulus autem compræhen<lb></lb>ſus IHF æqualis eſt duobus internis notis, ſci<lb></lb>licet recto GIH, & IGH obſeruato: quarę <lb></lb>inueniri poteſt tum latus IF, tum angulus <lb></lb>HIF: cui æqualis eſt angulus IOF in alterno <lb></lb>ſegmento: huius autem duplus eſt angulus <lb></lb>ITF ad centrum. </s> <s>Fiat igitur vt ſinus ſemian<lb></lb>guli inuenti ITF, hoc eſt ſinus anguli HIF, <lb></lb>ad Radium, ita ſemiſsis inuenti lateris IF <lb></lb>ad quæſitam ſemidiametrum TF. </s> </p> <p type="margin"> <s><margin.target id="note56"></margin.target><emph type="italics"></emph>LVI. </s> <s><lb></lb>Vndecimą <lb></lb>methodus <lb></lb>inueniendi <lb></lb>terræ ſemi<lb></lb>diametrum:<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Compendioſiùs fortaſſe operabimur, ſi da<lb></lb>tis IG & GF cum angulo G compræhenſo, <lb></lb><arrow.to.target n="note57"></arrow.to.target><lb></lb>inueniatur baſis IF & angulus GIF, qui eſt <lb></lb>neceſſariò obtuſus. </s> <s>Fiat ergo vt ſinus exceſ<lb></lb>sûs anguli GIF ſupra rectum ad Radium, <lb></lb>ita ſemiſsis inuentæ baſis IF ad quæſitam <lb></lb>terræ ſemidiametrum. </s> </p> <p type="margin"> <s><margin.target id="note57"></margin.target><emph type="italics"></emph>LVII. <lb></lb>Id<gap></gap> breuiùs.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Verùm omiſſo tot linearum apparatu res <pb xlink:href="018/01/128.jpg" pagenum="114"></pb><arrow.to.target n="note58"></arrow.to.target><lb></lb><figure id="id.018.01.128.1.jpg" xlink:href="018/01/128/1.jpg"></figure><lb></lb>facillimè conficitur, e<lb></lb>tiamſi nulla ſit data al<lb></lb>titudo nota. </s> <s>Obſerue<lb></lb>tur diſtantia AD: tum <lb></lb>in A accipiatur angulus <lb></lb>CAD, & in D obſerue<lb></lb>tur angulus, quem cum <lb></lb>verticali lineâ ex D ad <lb></lb>Zenith productâ facit <lb></lb>radius opticus DA; hu<lb></lb>ius enim complementum ad duos rectos <lb></lb>eſt angulus ADC: dato autem latere AD <lb></lb>cum angulis adiacentibus, latere non poſ<lb></lb>ſunt reliqua latera CD quæſita terræ ſemidia<lb></lb>meter, & CA ſemidiameter aucta montis <lb></lb>AB altitudine. </s> </p> <p type="margin"> <s><margin.target id="note58"></margin.target><emph type="italics"></emph>LVIII. </s> <s><lb></lb>Duodecima <lb></lb>methodus <lb></lb>ſemidiame<lb></lb>trum terræ <lb></lb>inuestigan<lb></lb>di, & montis <lb></lb>altitudini.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed iam, Merſenne, cadunt altis dę <lb></lb>montibus vmbræ; nec Galilæum diutur<lb></lb>niore colloquio diſtinere fas eſt. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Rectè mones: præceps in noctem <lb></lb>ruit dies: ſed huiuſmodi colloquia cum in<lb></lb>ſtituuntur, omnis hora momentum eſt. </s> <s>Va<lb></lb>le Galilæe. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Valete amici; & quas debeo gratias <lb></lb>pro humaniſsimâ conſuetudine, nunc planè <lb></lb>non reddo, ſed apud me ſeruo, vt iterum <lb></lb>redire cogamini depoſitum repetituri. </s> </p> <pb xlink:href="018/01/129.jpg" pagenum="115"></pb> <figure id="id.018.01.129.1.jpg" xlink:href="018/01/129/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>DISSERTATIO <lb></lb>QVARTA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Ex aquæ ſeparatione à ter<lb></lb>ra, motus facilitatem <lb></lb>infert.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Guldinus, Galilæus, Merſennus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s>PVRGARE ne tibi mę <lb></lb>debeo, Galilæe, quòd con<lb></lb>dictam Merſenno horam te <lb></lb>adeundi importunus præ<lb></lb>uenerim? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Si putas Batauis in nouâ Zem<lb></lb>blâ poſt longas dierum 84 tenebras lu<pb xlink:href="018/01/130.jpg" pagenum="116"></pb>cem præſto lancibus, Solem dies 14 antici<lb></lb>pantem accidiſſe importunum, ac purgatio<lb></lb>ne opus habuiſſe, quòd legitimum exoriendi <lb></lb>tempus anteuerterit; præſtò ſum, vt intelli<lb></lb>gam, qua te demum excuſatione ab imma<lb></lb>ni hac culpâ eximas. </s> <s>Sed cum expectatus <lb></lb>adueneris, quam tuorum in me meritorum <lb></lb>partem referendâ gratiâ conſequi potero? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Culpam hanc omnem, quantæ<lb></lb>cunque eſt, in te transfero: id ſcilicet profu<lb></lb>sâ tuæ humanitatis ſignificatione effeciſti, vt <lb></lb>mihi liceat eſſe temerario; nec abſurdum̨ <lb></lb>duxerim ſtatim, ac me tui deſiderium ce<lb></lb>pit, aduolare, & immaturum fœtum, ve<lb></lb>riùs dixerim víx dum conceptum, ante tę <lb></lb>ponere, vt vitæ igniculos illi tuâ luce imper<lb></lb>tias. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Siccine iuuat feſtiuis inanium offi<lb></lb>ciorum argutijs iocari? </s> <s>Mittamus iſthæc: & <lb></lb>quam primum ediſſere, quæ te benigna ege<lb></lb>rit Minerua, vt frigidos noſtros cineres fodi<lb></lb>catum venires, ignem ætheriâ vtique domo <lb></lb>ſubductum depoſiturus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld:<emph.end type="italics"></emph.end> Ariſtotelem fortè præ manibus ha<lb></lb>bebam; cumque aliud meditans pagellas te<lb></lb>merè oculo percurrerem, incidi in textum <lb></lb>78. lib. 2. de Cœlo, vbi Thaletis Mileſii dę <lb></lb>causâ terræ quieſcentis ſententiam exponit, <pb xlink:href="018/01/131.jpg" pagenum="117"></pb><emph type="italics"></emph>an quam ex eo, quia innatans ſit, tellus ma<lb></lb>neat, quemadmodum lignum vel aliquid tale <lb></lb>aliud; etenim horum ſuper aerem quidem ni<lb></lb>hil natura aptum eſt manere, ſed ſuper aquam.<emph.end type="italics"></emph.end><lb></lb>Id quod mihi in mentem reuocauit eadem <lb></lb>prorſus apud Senecam à me iam pridem le<lb></lb>cta lib. 6. Nat. quæſt. </s> <s>cap. 6. terram videli<lb></lb>cet totam, Thaletis opinione, ſubiecto hu<lb></lb>more portari, & innatare, ita vt vndâ ſuſti<lb></lb>neatur orbis velut aliquod grande nauigium. </s> <s><lb></lb>Ex quo ille ab eodem Senecâ lib. 3. cap. 13. <lb></lb>reiectus non ſatis aptè terræ motuum cauſam <lb></lb>inferebat, perindè atque ſi nauigium hoc in<lb></lb>natans concuteretur. </s> <s>Tum, quæ eſt phan<lb></lb>taſmatum atque formarum menti inhæren<lb></lb>tium mira connexio, vix cæperam tacitus <lb></lb>ridere commenticium ingentis huius nauigii <lb></lb>nullos in ſcopulos impacti tremorem, cum <lb></lb>in eius grauitatis conſiderationem delapſus <lb></lb>ſum: tenuique hac vellicatione excitatæ he<lb></lb>ſterni noſtri congreſſus reliquiæ animo inſi<lb></lb>dentes me protinus abripuerunt, & ſenſim <lb></lb>nec aduertentem deduxerunt ad eam cogi<lb></lb>tationem, vt ſuſpicarer ex aquarum naturâ, <lb></lb>ad tellurem Archimedæis machinationibus <lb></lb>mouendam, ſubſidium aliquod comparari <lb></lb>poſſe. </s> <s>Plura illicò huic cogitato affinia iņ <lb></lb>mentem confusè & permixtè irruperunt, <pb xlink:href="018/01/132.jpg" pagenum="118"></pb>quæ ſubitam approbationem temerè extor<lb></lb>quere viderentur; ſed quoniam, vbi multa <lb></lb>ſunt, quæ ſibi aptis nexibus cohærere de<lb></lb>beant, ne veritatis compages luxata pereat, <lb></lb>periculoſum & lubricum eſt facilè aſſentiri, <lb></lb>nolui me in præcipitem locum committere; <lb></lb>ſuſtinendam potiùs tantiſper omnem aſſen<lb></lb>ſionem duxi, dum rem totam diſcretè & <lb></lb>electè ſuas in partes, te pro tuâ ſapientiâ <lb></lb>opem ferente, digererem. </s> <s>En habes, qui<lb></lb>bus ſtimulis actus mihi imperare non potue<lb></lb>rim, vt à te diutiùs abeſſem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Gratias tibi habeo, mi Guldine, im<lb></lb>mortales; quod ſpem iniicias audiendi ex te <lb></lb>hodie, quid de iis ſentias, quæ iam tum ab <lb></lb>anno huius ſæculi duodecimo conſcripſi de <lb></lb>Innatantibus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Librum legi tuo dignum ingenio; <lb></lb>nec potuit feliciùs enodari, quam conſtitue<lb></lb>ras examinandam quæſtionem de ſolidis in<lb></lb>natantibus, quamuis humido ſecundùm ſpe<lb></lb>ciem grauioribus, ſi quidem ſolitaria ſuman<lb></lb>tur, componentibus tamen vnâ cum aërę <lb></lb>ſibi adhæreſcente molem aquâ non grauio<lb></lb>rem. </s> <s>Illud maximè dolui, quod nactus ſim <lb></lb>exemplar ſiue Bibliopolæ ſine Bibliopegi in<lb></lb>curiâ mutilarum integro folio, & quidem il<lb></lb>lo ipſo, in quo totius futuræ diſputationis <pb xlink:href="018/01/133.jpg" pagenum="119"></pb>fundamenta ſternis: ac, quæ mihi aduerſą <lb></lb>eſt fortuna, nuſquam licuit integrum librum <lb></lb>reperire, ex quo noſtri exemplaris hiatum <lb></lb>ſupplerem, Id quod te præmonuiſſe oppor<lb></lb>tunum fuit, ne, ſi fortè nobis non conuene<lb></lb>rit, me contradicendi ſtudio actum putes: <lb></lb>niſi me tamen mea fallit opinio, in minimis <lb></lb>diſſentiemus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Libens audio, qui contra ſenſerint. </s> <s><lb></lb>Sed ne te longiùs ab inſtituto tuo, veriùs di<lb></lb>cam, noſtro, abducam; quidnam ex aquâ <lb></lb>emolumenti ſperas ad facilem terræ motio<lb></lb>nem, de qua nobis fuit diſputatio? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Futurum puto, vt plurimum pon<lb></lb>deris de terreno hoc orbe, qui aquam pariter <lb></lb>ac terram complectitur, deduceretur. </s> <s>Illud <lb></lb>enim extra omnem controuerſiam poſitum <lb></lb><arrow.to.target n="note59"></arrow.to.target><lb></lb>accipio, quod aqua aëre grauior eſt; & fluida <lb></lb>cùm ſit, ſemper ad inferiora delabitur, vt <lb></lb>infra aërem vniuerſi centro vicinior conſiſtat. </s> <s><lb></lb>Ex quo fit, vt nuſquam quieſcat, niſi vbi <lb></lb>nullus patet locus, in quem deſcendat. </s> <s>Qua<lb></lb>rè cum ſola ſuperficies ſphærica paribus ra<lb></lb>diis à centro remoueatur, aquæ quieſcentis <lb></lb>ſuperficiem ſphæricam eſſe neceſſe eſt: quan<lb></lb>doquidem ſiquæ ſuperficiei partes à centro <lb></lb>longiùs abeſſent, vtpote altiores ad motum <lb></lb>procliues non ſubſiſterent, ſed humiliorem <pb xlink:href="018/01/134.jpg" pagenum="120"></pb>in locum defluerent: neque enim ex eo a<lb></lb>quam ſponte aſcendere dixerim, quòd ea in <lb></lb>vitreis fiſtulis immerſis aliquantulum aſcen<lb></lb>dat. </s> </p> <p type="margin"> <s><margin.target id="note59"></margin.target><emph type="italics"></emph>LIX <lb></lb>Aquæ ſu<lb></lb>perficies est <lb></lb>ſphærica.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Nemo id facilè inficietur: immo, ſi <lb></lb>id quidem in rem tuam faciat, vltro dabo <lb></lb>maria omnia, quæ aquarum communionę <lb></lb>iunguntur (ſi æſtum omnem ſublatum, ven<lb></lb>tosque ſilentes animo fingamus) non eſſę <lb></lb>alia alijs ſecundùm ſuperficiem altiora: qui<lb></lb>bus enim frænis cohiberentur Sinûs Arabici <lb></lb>aquæ, ſi altiores eſſent, ne in Erytræum ma<lb></lb>re influerent? </s> <s>aut quibus aggeribus obſtrue<lb></lb>retur fretum Herculeum, ne Oceanus Atlan<lb></lb>ticus ac Mediterraneum mare in vnâ ſu<lb></lb>perficie aquarum libramentum ſuſciperent? </s> </p> <p type="main"> <s>Quod verò de aquâ in immerſis fiſtulis <lb></lb>vtrinque hiantibus aſcendente addis, nihil <lb></lb>planè officit naturæ aquarum ſe in ſphæram <lb></lb>circa terræ centrum conglobantium; neque <lb></lb>illicò poſſe aquam ad digiti altitudinem̨ <lb></lb>ſponte aſcendere affirmandum eſt, quòd il<lb></lb>lam in tenuiſſimis fiſtulis eò pertingere ali<lb></lb>quando videamus; quò enim ampliores ſunt <lb></lb>fiſtulæ, eò minùs in iis aquam aſſurgerę <lb></lb>conſtat, nec fortè ſine ſuſpicione minoris, <lb></lb>quàm appareat, altitudinis, propter ſpecie<lb></lb>rum viſibilium ex vitro refractionem, iņ <pb xlink:href="018/01/135.jpg" pagenum="121"></pb>ampliſsimis igitur lacuum marium que alueis <lb></lb>quantùm illa aſcendat, quod ſphæricam ſu<lb></lb>perficiem corrumpat? </s> <s>Sed nec aquam om<lb></lb>ninò ſponte dixerim in fiſtulâ aſcenderę <lb></lb>Quando enim fiſtula deprimitur, vt aquæ <lb></lb>immergatur, vtique ſubiectus aër premitur, <lb></lb><arrow.to.target n="note60"></arrow.to.target><lb></lb>& locum ſubeunti fiſtulæ concedens, quâ <lb></lb>patet via, recedit, vt locum ſuppleat à fiſtu<lb></lb>lâ deorſum motâ relictum. </s> <s>Sicut autem <lb></lb>aër, cui corpus in motu occurrit, comprimi<lb></lb>tur, ita is, qui ponè eſt, paululum diſtrahi<lb></lb>tur ac rareſcit; hic verò ad ingenium rediens <lb></lb>proximum aërem attrahit ad ſupplendum <lb></lb>locum à fiſtulâ relictum; cumque nullus <lb></lb>ſubiectus aër tam in promptu ſit, quàm is <lb></lb>qui fiſtulæ cauitatem implet, hic exfugitur; <lb></lb>atque adeò cum aér fiſtulæ ſurſum mouea<lb></lb>tur, ſubiectus aër compreſſus in fiſtulæ caui<lb></lb>tatem ſuccedit, per quam faciliùs elabitur, <lb></lb>ac per impulſionem, aut compreſſionem <lb></lb>contigui aëris, qui lateribus adiacet. </s> <s>Por<lb></lb>rò ea eſt fluidorum corporum natura, vt <lb></lb>conceptum ex motu impetum, etiam intrà <lb></lb>homogeneum corpus, non ita facilè remit<lb></lb>tant; quemadmodum in aquâ colore aliquo <lb></lb>infectâ intrà aliam aquam leuiſſimè effusâ <lb></lb>videre eſt. </s> <s>Hinc eſt aërem ſurſum in fiſtulâ <lb></lb>incitatum ex concepto impetu tantiſper per<pb xlink:href="018/01/136.jpg" pagenum="122"></pb>gere in motu, & ita pellere ſuperiorem aë<lb></lb>rem, vt hic eum qui fiſtulæ latera extrinſe<lb></lb>cùs obſidet, propellat, fiatque per inferius <lb></lb>hiantis fiſtulæ oſculum illa circumpulſio, de <lb></lb>qua Pla<emph type="italics"></emph>t<emph.end type="italics"></emph.end>o in Timæo, vel ſaltem, vt cum ve<lb></lb><gap></gap>tris Philoſophis loquar, ab aſcendente aëre <lb></lb>per fiſtulam liberrimè abſque vllo alterius <lb></lb>aëris intercurrentis obice, attrahitur aër in<lb></lb>ferior. </s> </p> <p type="margin"> <s><margin.target id="note60"></margin.target><emph type="italics"></emph>LX. </s> <s><lb></lb>Cur aquą <lb></lb>in tubo v<lb></lb>trinque bi<lb></lb>ante aſeen<lb></lb>dat aliquan <lb></lb>tulum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Veriùs fortaſſe dixeris & attrahi <lb></lb>pariter & circumpelli: </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Vbi igitur inferioris oſ oſculi labra ſu<lb></lb>biectam aquam ita attigerint, vt aer ſucce<lb></lb>dere nequeat, illud neceſſariò fit, vt aſcen<lb></lb>dentem aerem aqua ſubiecta conſequatur <lb></lb>ſiue attracta, ſiue ex circumpulſione propul<lb></lb>ſa. </s> <s>Cum autem hoc à naturâ liquoribus <lb></lb>comparatum ſit, quod ſolidis corporibus ad<lb></lb>hæreſcant; vbi aliquid aquæ ſurſum ab aere <lb></lb>aſcendente eleuatæ, internis fiſtulæ lateribus <lb></lb>adhæſerit, iam non deorſum vrget contrą <lb></lb>vim aéris aſcendentis, qui propterea in reli<lb></lb>quam aquam non adhæreſcentem vires ſuas <lb></lb>omnes exercet. </s> <s>At quia in tenuiſsimâ fiſtu<lb></lb>lâ cylindrulus aquæ primùm eleuatus ita ferè <lb></lb>totu<gap></gap> adhæret fiſtulæ, vt vix in medio relin<lb></lb>quat capillarem medullam ab aëre ſuſtenta<lb></lb>tam, multò faciliùs pergit in aſcenſu, & alias <pb xlink:href="018/01/137.jpg" pagenum="123"></pb>aquæ particulas ſecum rapit ſurſum; donec <lb></lb>demum præter aquam ſponte adhærentem <lb></lb>lateribus, tantum aquæ ab aere ſuſtineatur, <lb></lb>vt eam dimittere non poſſit, quin ipſe magis <lb></lb>diſtrahatur & rareſcat: id quod natura potiùs <lb></lb>refugit, quàm permittere tantillæ aquæ <lb></lb>ſuſpenſionem. </s> <s>Niſi fortè malles dicere, a<lb></lb>quam illam medullarem conſtitutam intrà <lb></lb>aquam lateribus adhærentem iam non conari <lb></lb>deorſum. </s> <s>Quando verò amplior eſt fiſtulæ <lb></lb>capacitas, conſtat <expan abbr="aẽrem">aerrem</expan> non tantâ velocita<lb></lb>te per eam ferri ſurſum cæteris paribus, ac per <lb></lb>fiſtulam tenuiorem, & præterea cylindrulus <lb></lb>aquæ ſurſum attractus ampliorem habet ba<lb></lb>ſim, & in minori altitudine habetur tota ea <lb></lb>quantitas aquæ, quæ valet ab aere ſuſtentari: <lb></lb>hinc fit eò minùs aquam attolli, quò am<lb></lb>plior eſt fiſtula. </s> <s>Mitto hìc diſputare an in<lb></lb>ſenſibilis aquæ expiratio adhærens fiſtulæ, <lb></lb>vel in eam incurrens, excitet electricam <lb></lb>vitri expirationem; an verò ea fiſtulam le<lb></lb>uiſſimè humectans, dum attactu illo ſtatim <lb></lb>concreſcit, ſtatim ſubiectam aquam attrahat <lb></lb>vt ſibi veniat, quemadmodum in calamo <lb></lb>ſcriptorio ſæpe obſeruare eſt, quando atra<lb></lb>mento valdè diluto vtimur; vix enim hu<lb></lb>mens calamus ſubiectum atramentum con<lb></lb>tingit, cum eo confeſtim imbuitur. </s> <s>Hæc <pb xlink:href="018/01/138.jpg" pagenum="124"></pb>ſcilicet nos longiùs, quàm par ſit, abdu<lb></lb>cerent. </s> <s>Illud certum eſt, quod aqua ſponte <lb></lb>fluens ita ſemper ad humiliora loca delabi<lb></lb>tur, vt à ſphæricâ ſuperficie non recedat, ſi <lb></lb>res Phyſicè ſaltem conſideretur. </s> <s>Atque adeò <lb></lb>id tibi vltrò concedens audire expecto, quid <lb></lb>indè conficias. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Non eandem eſſe ſemper aquæ ſu<lb></lb>perficiem; quò enim maioribus à centro in<lb></lb>teruallis ſemouetur, eò propiùs æquatam̨ <lb></lb>planitiem æmulatur; at centro vicinior ma<lb></lb>iori conuexitate inflectitur; hìc ſcilicet mi<lb></lb>noris, ibi maioris ſphæræ portio eſt. </s> <s>Iam <lb></lb>verò vt pla<lb></lb>niùs & aper<lb></lb>tiùs verbis <lb></lb><figure id="id.018.01.138.1.jpg" xlink:href="018/01/138/1.jpg"></figure><lb></lb><arrow.to.target n="note61"></arrow.to.target><lb></lb>complectar, <lb></lb>quod volo, <lb></lb>ex Graphi<lb></lb>de <expan abbr="ſubſidiũ">ſubſidium</expan> <lb></lb><expan abbr="petã">petam</expan>. </s> <s>Sit pro <lb></lb>globo terra<lb></lb>queo circu<lb></lb>lus ABCD, <lb></lb>cuius cen<lb></lb>trum T <expan abbr="cõ-gruat">con<lb></lb>gruat</expan> vniuerſi centro, & BAE mare Hyper<lb></lb><gap></gap>oreum, FCD Oceanus Indicus aut Æthio<pb xlink:href="018/01/139.jpg" pagenum="125"></pb>picus, vel alius, quamcunque demum ſor<lb></lb>tiatur appellationem. </s> <s>Ambigi non poteſt, <lb></lb>quin maria hæc in eadem ſphæricâ ſuperficie <lb></lb>exiſtant, quandoquidem ab vniuerſi centro <lb></lb>T paribus interuallis diſiunguntur. </s> <s>At ſi <lb></lb>tellurem ab vniuerſi centro (quod, ne iņ <lb></lb>vocabulis laboremus, centrum grauium̨ <lb></lb>liceat appellare, cum eius rationem habue<lb></lb>rit natura ſuum cuique corpori locum tri<lb></lb>buens) remotam intelligamus, ita vt illius <lb></lb>quidem centrum ſit T, centrum verò gra<lb></lb>uium ſit V; non eadem manere poteſt v<lb></lb>triuſque maris ſuperficies; ſed Hyperboreum <lb></lb>ſubſidere magis & explicari debet, Indicum <lb></lb>verò aſſurgere, Cum enim aqua A remo<lb></lb>tior ſit quàm B & E à centro V, poteſt de<lb></lb>ſcendere, nec conſiſtet, niſi vbi fuerit ſu<lb></lb>perficies BIE. </s> <s>Contra autem aqua F & D <lb></lb>remotior eſt quàm C à centro V; poteſt <lb></lb>igitur verſus C deſcendere; & relicto loco <lb></lb>ad F & ad D, aſſurget<gap></gap> in H, & erit ſuper<lb></lb>ficies FHD maiorem habens conuexita<lb></lb>tem̨. </s> </p> <p type="margin"> <s><margin.target id="note61"></margin.target><emph type="italics"></emph>LXI <lb></lb>Si tellus a<lb></lb>liò trahere<lb></lb>tur, aquą <lb></lb>mutaret fi<lb></lb>guram.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quod ſi ad latus iaceat aqua, vt MNO, <lb></lb>factâ translatione centri ex Vin T, vtique <lb></lb>ex M versùs O deſcendet; ſed ſi mons OS <lb></lb>prohibeat, demùm conſiſtet aqua circa vni<lb></lb>uerſi centrum V in ſuperficie ſphæricâ RNS. <pb xlink:href="018/01/140.jpg" pagenum="126"></pb>Idemque dę <lb></lb><figure id="id.018.01.140.1.jpg" xlink:href="018/01/140/1.jpg"></figure><lb></lb>cæteris eſto iu<lb></lb>dicium; nulla <lb></lb>ſiquidem repe<lb></lb>riri poſſet a<lb></lb>quarum con<lb></lb>gregatio, quæ <lb></lb>tellure transla<lb></lb>tâ, ſe aliam in <lb></lb><expan abbr="ſuperficiẽ">ſuperficiem</expan> non <lb></lb>conglobaret, <lb></lb>altioribus par<lb></lb>tibus in inferiorem locum delapſis. <lb></lb><arrow.to.target n="note62"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note62"></margin.target><emph type="italics"></emph>LXII <lb></lb>Noua hypo<lb></lb>theſis mari<lb></lb>ni æstus in<lb></lb>dicatur, ſed <lb></lb>non proba<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Ignoſce, quæſo, interpellanti. </s> <s>Ne<lb></lb>ſcio quam mihi inijcis ſuſpicionem nouæ <lb></lb>hypotheſis, qua citra omnem telluris verti<lb></lb>ginem ſiuè in orbe annuo, ſiuè circa ſuum <lb></lb>axem, marinus æſtus explicari poſſet: ſi ni<lb></lb>mirum terræ centrum lento ac tenui motu <lb></lb>vltro citroque commeans centro grauium<lb></lb>congrueret ſolùm in medio fluxu aut reflu<lb></lb>xu. </s> <s>Si enim T accedat ad V, aqua incipit <lb></lb>ex S refluere verſus M, vbi aqua ſemper au<lb></lb>getur, quò magis centrum T recedit ab V <lb></lb>in X: iterumque fluit ex M in O, cum cen<lb></lb>trum ab X recedens in V & in T ſua per <lb></lb>veſtigia eò remeat, vnde diſceſſit, ſeruatâ<lb></lb>que in motu reciprocando conſtantiâ, al<pb xlink:href="018/01/141.jpg" pagenum="127"></pb>ternas fluxûs, & refluxûs vices efficit in ad<lb></lb>uerſis litoribus. </s> <s>Quod ſi in oppoſitis eiuſ<lb></lb>dem aluei ripis eodem tempore fluxus con<lb></lb>tingat aut refluxus, vt in B & E, aut in F & <lb></lb>D; tunc opinari quis poſſet mare illud eam <lb></lb>habere poſitionem, vt in illud incidat linea <lb></lb>motûs, quæ ex centro grauium per terræ <lb></lb>centrum ducitur: dum enim aqua deprimitur <lb></lb>ex A in I, augetur in B & E, ſi litus fluxui <lb></lb>obſtet, aut vlteriora ſpatia occupat in P & K: <lb></lb>dum verò aſſurgit ex C in H, minuitur in F & <lb></lb>D. </s> <s>Porrò alternâ hac nutantis terræ mo<lb></lb>tione non magis eius ſtabilitas vacillaret, <lb></lb>quàm illiùs firmitati obſit trepidationis mo<lb></lb>tus à pleriſque admiſſus ob variam centri <lb></lb>grauitatis poſitionem: ſtare ſiquidem terra <lb></lb>dicitur, quæ ſuo ex loco non decedit, quam<lb></lb>quam in eo ſuæ diametri particulam (1/4000000) <lb></lb>percurrat. </s> <s>Finge enim motûs extremos <lb></lb>terminos T & X non ampliùs paſſum vnum <lb></lb>diſtare à grauium centro V: tanta eſt aqua<lb></lb>rum in immenſum patentium copia, vt èxi<lb></lb>guâ inclinatione, quam motu illo acquire<lb></lb>rent, dilabentes æſtum non exiguum effi<lb></lb>cerent: qui tamen in lacubus, anguſtiori<lb></lb>busque alueis ob minorem aquarum copiam <lb></lb>non perciperetur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Blandiuntur iſthæc facilè mentis <pb xlink:href="018/01/142.jpg" pagenum="128"></pb>oculis: ſed ſi rem penitiùs introſpicere per <lb></lb>otium liceret, haud ſatis ſcio, quàm aptè <lb></lb>commentum hoc cum marini æſtûs phæno<lb></lb>menis cohæreret. </s> <s>Nec pauca in hanc ſen<lb></lb>tentiam afferri poſſent: ſed non vacat his im<lb></lb>morari, ne longiùs ab inſtituto digrediar, <lb></lb>aut ſortè, quæ eſt fugacis memoriæ incon<lb></lb>ſtantia, excidant, quæ nunc animo obuer<lb></lb>ſantur. </s> <s>De mari certè, quod Kiùn, in In<lb></lb>ſulâ Hainan, alluit, illud notatu dignum <lb></lb>ſcribunt Sinæ Geographi, quod maris æſtum <lb></lb>Diurnum non ſentiat, ſed per dimidiam <lb></lb>menſis partem versùs Ortum, per reliquam <lb></lb>dimidiam versùs Occaſum fluat. </s> <s>Quid? </s> <s><lb></lb>Quod in vertice montis Hucùng in Fokien <lb></lb>Prouinciâ puteus eſt (Hiai nomen eſt) cuius <lb></lb>aqua æſtum marinum ſuo acceſſu & receſſu <lb></lb>refert. </s> <s>Adde huic fontem prope Nuikiang <lb></lb>in Suchuen Prouinciâ, quem modò aſcen<lb></lb>dentem modò deſcendentem æſtûs marini <lb></lb>horas adeò procul à mari ſequi obſeruatum <lb></lb>eſt. </s> <s>Hos autem æſtus ex motu illo orbis, <lb></lb>quem innuebas, non oriri palàm eſt. </s> <s>Quòd <lb></lb>ſi ex tam remotâ Sinatum regione petitum <lb></lb>argumentum reijcis, mihi ſanè conſtat non <lb></lb>hanc eſſe æſtûs effectricem cauſam; nam <lb></lb>ipſa quoque flumina, terræ centro accedente <lb></lb>ad centrum grauitatis aut recedente, diebus <pb xlink:href="018/01/143.jpg" pagenum="129"></pb>ſingulis cursûs velocitatem incitarent re<lb></lb>mitterentque, aut etiam ſuum in caput re<lb></lb>laberentur; id quod nondum licuit obſerua<lb></lb>re. </s> <s>Præterquam quod vix dixeris, quo mo<lb></lb>uente tellus viciſſim commearet, citrà fabu<lb></lb>larum figmenta. </s> </p> <p type="main"> <s>At ſi contingere poſſet, vt machinarum </s> </p> <p type="main"> <s><arrow.to.target n="note63"></arrow.to.target><lb></lb>ope telluris centrum ex V in T transferretur, <lb></lb>fluminis GL aqua ex G reflueret in L, & in <lb></lb>eundem alueum ſe inſinuaret mare vſquę <lb></lb>dum tota aquæ ſuperficies continua in ſphæ<lb></lb>ram inflexa conſiſteret, cum non haberet, <lb></lb>quò deſcenderet. </s> <s>Hinc illud fit, quod cum <lb></lb>maria omnia (niſi fortè Caſpium velis exci<lb></lb>pere, cui tamen per ſubterraneos cuniculos <lb></lb>cum Ponto Euxino communio eſt) ſibi in<lb></lb>uicem continuata iunctaque ſint, terrâ in <lb></lb>partem vnam translatâ, aquæ ferè omnes in <lb></lb>oppoſitam recederent, vel per patentem al<lb></lb>ueum dilabentes, vel etiam exundantes: <lb></lb>idem quippe tunc aquarum conceptaculis <lb></lb>contingeret, ac ſi nunc vas liquore quaſi <lb></lb>plenum magis & magis inclinaretur, totus <lb></lb>enim demùm liquor effunderetur. </s> <s>Quarè <lb></lb>vniuerſa ferè aqua ſuperiorem locum relin<lb></lb>quens in H conflueret eò velociùs, quò lon<lb></lb>giùs telluris centrum T recederet ab V cen<lb></lb>tro grauium ſeu vniuerſi. </s> </p> <pb xlink:href="018/01/144.jpg" pagenum="130"></pb> <p type="margin"> <s><margin.target id="note63"></margin.target><emph type="italics"></emph>LXIII <lb></lb>Tellurę <lb></lb>translata fe<lb></lb>rè tota aqua <lb></lb>ab ea ſeiun<lb></lb>geretur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> In eo igitur, ſi quid video, machi<lb></lb>nalis motionis, qua terra transferretur, faci<lb></lb>litatem conſtituis, quod eo ipſo tempore, <lb></lb>quo terra ſupra FVD planum (quod ho<lb></lb>rizontale vocetur) attolleretur, aqua de<lb></lb>ſcenderet; ac proinde ſuperioris partis pon<lb></lb>dus minueretur, donec demum terra pro<lb></lb>cul à centro translata totius ferè aquæ ponde<lb></lb>re leuaretur, quæ circa vniuerſi centrum V <lb></lb>aqueum in globum ſuis ſe nutibus confor<lb></lb>maret. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ita planè: nec illud quidem con<lb></lb>temnendum eſſet compendium, ſi ponderis <lb></lb>aquæ rationes ineamus. </s> <s>Quotam enim ter<lb></lb>raquei huius globi partem conſtituendam <lb></lb>eſſe aquam cenſes? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Res eſt, in qua Geometriæ apices <lb></lb>perſequi non poſſumus, cum exactâ ma<lb></lb>rium omnium notitiâ careamus, & planè <lb></lb>varia ſit aquarum profunditas: qua propter <lb></lb>coniecturis contentos nos eſſe oportet. </s> <s>Et <lb></lb>quidem quod ad aquarum ſuperficiem per<lb></lb>tinet, eas arbitror æquis cum terrâ portioni<lb></lb>bus globi conuexitatem diſpertire: altitudi<lb></lb>nem verò adeò inconſtantem reperio, vt ſi <lb></lb>profunditates maiores cum minoribus com<lb></lb>penſemus, vix vltra milliaris dodrantem aut <lb></lb>integrum milliare altitudini in vniuerſum <pb xlink:href="018/01/145.jpg" pagenum="131"></pb>tribuendum exiſtimem̨. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end> Qúæ ſentis, approbo; immenſæ <lb></lb><arrow.to.target n="note64"></arrow.to.target><lb></lb>ſiquidem illæ altitudines & abyſſi aquarum <lb></lb>rariſſimæ ſunt, quæ bolide nullâ explorari <lb></lb>poſſint. </s> <s>Idcircò libentiùs vniuersè altitu<lb></lb>dinem ſolùm dodrantalem aquis tribuo, mil<lb></lb>liari aſſumpto pro aſſe. </s> <s>Iam, ſi placet, <lb></lb>aquæ grauitatem ad calculos reuocemus, & <lb></lb>globi perimetrum accipiamus, quam olim <lb></lb>Merſennus, nobis non repugnantibus, con<lb></lb>ſtituebat mill. Rom. ant. </s> <s>25941. Perime<lb></lb>tro conſtitutâ, diametrum ſic inquiro ex ra<lb></lb>tionibus Vietæ: Vt 31415.926536 ad <lb></lb>10000.000000, ita maximi circuli periphe<lb></lb>ria mill. 25941 ad diametrum mill. 8257<lb></lb>paſſ. </s> <s>276. Igitur ſi diameter in peripheriam <lb></lb>ducatur, producetur ſphærica ſuperficies <lb></lb>mill. quadrat. </s> <s>214.201996. paſſ. </s> <s>quad. </s> <s><lb></lb>716000: Huius autem ſemiſsis mill. 107. <lb></lb>100998. paſſ. </s> <s>358000. erit ſuperficies a<lb></lb>quæ. </s> </p> <p type="margin"> <s><margin.target id="note64"></margin.target><emph type="italics"></emph>LXIV <lb></lb>Totius a<lb></lb>quæ quanti<lb></lb>tas, & gra<lb></lb>uitas inqui<lb></lb>ritur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Et vt breuitati ſeruiam, duco inuentam <lb></lb>aquæ ſuperficiem in altitudinem conſtitutam <lb></lb>mill.3/4: ne ſcilicet longioribus ambagibus in <lb></lb>quiram totius globi ſoliditatem. </s> <s>Deinde in<lb></lb>ſtitutâ analogiâ, <emph type="italics"></emph>vt cubus diametri inuentæ <lb></lb>ad cubum eiuſdem diametri mulctatæ dodran<lb></lb>te milliaris, ita ſoliditas ſphæræ ex inuenta dia<emph.end type="italics"></emph.end><pb xlink:href="018/01/146.jpg" pagenum="132"></pb><emph type="italics"></emph>metro ad ſoliditatem alterius ſphæræ,<emph.end type="italics"></emph.end> inue<lb></lb>niam harum ſphærarum differentiam, cuius <lb></lb>differentiæ ſemiſſis aquarum ſoliditati tri<lb></lb>buatur. </s> <s>Neque enim eſt operæ pretium <lb></lb>nos ipſos hoc labore conficere; quandoqui<lb></lb>dem vix diſcreparet inuentus numerus ab eo, <lb></lb>qui ex ductu ſuperficiei in altitudinem pro<lb></lb>dibit. </s> <s>Duco igitur aquæ ſuperficiem mill. <lb></lb>107.100998 paſſ. </s> <s>358000 in altitudinem <lb></lb>mill. 3/4, & prodit ſoliditas milliarium cubi<lb></lb>corum 80.325748, & paſſ. </s> <s>cubic. </s> <s>768. <lb></lb>500000. </s> </p> <p type="main"> <s>Inuentâ ſoliditate grauitatem inueſtigo: <lb></lb>& quamuis ſciam marinam aquam ob ad<lb></lb>mixtam ſalis copiam grauiorem eſſe aquâ <lb></lb>communi; vt tamen compenſetur, ſi quid <lb></lb>plus æquo tributum eſt ſuperficiei, aut pro<lb></lb>funditati, communem aquæ grauitatem ac<lb></lb>cipio; Et quoniam milliaribus Romanis an<lb></lb>tiquis vtimur, pondus pedis cubici antiqui, <lb></lb>hoc eſt amphoræ aquâ plenæ, eſt lib. 80. <lb></lb>Igitur quia milliare cubicum conſtat pedi<lb></lb>bus ſolidis 125000.000000, hic numerus per <lb></lb>lib. 80 ductus dabit libras 10.000000.000000 <lb></lb>grauitatem ſingularium milliarium cubico<lb></lb>rum aquæ. </s> <s>Iam ſi ſoliditas mill. 80.325748 <lb></lb>paſſ. </s> <s>768.500000. ducatur per libras 10. <lb></lb>000000.000000. erit totius aquæ pondus lib. <pb xlink:href="018/01/147.jpg" pagenum="133"></pb>803.257487.685000.000000. <lb></lb><arrow.to.target n="note65"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note65"></margin.target><emph type="italics"></emph>LXV <lb></lb>Pondus ter<lb></lb>reni globi <lb></lb>quàm nota<lb></lb>biliter mi<lb></lb>nueretur ex <lb></lb>aquæ ſeceſ<lb></lb>ſione.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Hoc autem pondus ex totius globi graui<lb></lb>tate demptum faciliorem efficeret terræ <lb></lb>motionem, vbi iam tota terra aliquo uſque <lb></lb>ab vniuerſi centro receſſiſſet, ibique aquam <lb></lb>ferè totam, quæ nunc in globi ſuperficię <lb></lb>fluit, reliquiſſet. </s> <s>Sed quid ſi in maris fundo <lb></lb>amplæ pateant voragines, per quas in tellu<lb></lb>ris cuniculos aqua ſe inſinuer, ingentesque <lb></lb>abyſſos creet? </s> <s>An non per hiatus eoſdem <lb></lb>aqua ſe exoneraret tellure in altum ſublatâ ? <lb></lb>Ex quo & illud conſequeretur, quod in im<lb></lb>menſa illa hydrophylacia aër tenuisque va<lb></lb>por defluenti aquæ ſuccederet, fieretque to<lb></lb>tius compoſitæ molis grauitas ſecundùm <lb></lb>ſpeciem minor. </s> <s>Verùm terræ viſcera nę <lb></lb>ſcrutemur; aquasque illas hypogæas ſuis in <lb></lb>conceptaculis ſtagnantes relinquamus. </s> <s>A<lb></lb>qua certè, quæ terræ faciem nunc alluit, <lb></lb>tanta eſt, vt ſi eam diſceſſiſſe in locum alium <lb></lb>à tellure animo concipiamus, continuo non <lb></lb>exigua ſanè momenta ex globo terraqueo <lb></lb>dempta intelligamus. </s> <s>Et ſi ad manum eſſet <lb></lb>ſchedula, in qua Merſennus rationes digeſſit, <lb></lb>quibus telluris grauitatem nudius tertius in<lb></lb>ueſtigabat, numerum hunc librarum ex illo <lb></lb>ſubducentibus conſtaret non planè contem<lb></lb>nendum eſſe hoc laboris compendium. </s> </p> <pb xlink:href="018/01/148.jpg" pagenum="134"></pb> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Secum illam tulit Merſennus: ſed <lb></lb>non eſt opus grauitatem hanc aquæ cum to<lb></lb>tius globi pondere comparare, ſatis enim per <lb></lb>ſe patet, quàm inſignis foret iſta ponderis <lb></lb>deceſſio. </s> <s>Vnum autem hìc obſeruo, quod </s> </p> <p type="main"> <s><arrow.to.target n="note66"></arrow.to.target><lb></lb>nimirum, quamuis ingens hæc ponderis di<lb></lb>minutio tunc ſolùm contingeret, quando <lb></lb>terra eſſet ab aquis diuulſa, & ab vniuerſi <lb></lb>centro V tota abeſſet, emolumentum tamen <lb></lb>non paruum faceret in motione aſſiduus a<lb></lb>quarum fluxus in partem oppoſitam. </s> <s>Si enim <lb></lb>globus plano FD ſectus eò transferatur, vt <lb></lb>vniuerſi <expan abbr="cẽ-trum">cen<lb></lb>trum</expan> V iņ <lb></lb><figure id="id.018.01.148.1.jpg" xlink:href="018/01/148/1.jpg"></figure><lb></lb><expan abbr="eodẽ">eodem</expan> ſit pla<lb></lb>no, non ſo<lb></lb>lùm <expan abbr="nõ">non</expan> per<lb></lb>cipitur toti<lb></lb>us globi, ſed <lb></lb>ne totius qui<lb></lb>dem <expan abbr="fegmẽ-ti">fegmen<lb></lb>ti</expan> FAD gra<lb></lb>uitas: <expan abbr="quan-doquidẽ">quan<lb></lb>doquidem</expan> ſeg<lb></lb>mentum FA <lb></lb>D de orſum non conatur contra vim ſurſum <lb></lb>mouentem aut ſuſtinentem, niſi iuxta mo<lb></lb>menta ponderis, quibus ſuperat momentą <pb xlink:href="018/01/149.jpg" pagenum="135"></pb>ſegmenti FCD oppoſito conatu in idem cen<lb></lb>trum V nitentis, ne indè remoueatur. </s> <s>At<lb></lb>qui aquæ pars aliqua ſupra planum FD exi<lb></lb>ſtens infra illud deſcendit; igitur in ſegmen<lb></lb>to FAE minuitur pondus, & fit ponderis ac<lb></lb>ceſſio ſegmento FCD; quarè multò minor <lb></lb>eſt differentia grauitatum inter ſegmenta, ac <lb></lb>proinde minor in mouendo labor, aut in ſu<lb></lb>ſtinendo. </s> <s>Quemad modum enim ſi in libræ <lb></lb>lancibus poſita fuerint pondera inæqualia, & <lb></lb>exlance grauiore pars ponderis transferatur <lb></lb>in alteram lancem, propiùs accedunt ad <lb></lb>æquilibrium, & faciliùs ſuſtinetur lanx gra<lb></lb>uior; Sic etiam pondus aliquod aquæ ex <lb></lb>ſegmento maiore FAD tranſlatum in ſeg<lb></lb>mentum minus FCD, efficit minorem <lb></lb>ponderum inæqualitatem, ac proinde minor <lb></lb>grauitas percipitur à mouente globum, vel <lb></lb>ſuſtinente. </s> </p> <p type="margin"> <s><margin.target id="note66"></margin.target><emph type="italics"></emph>LXVI <lb></lb>Facilitas <lb></lb>mouendi ter<lb></lb>ram ex de<lb></lb>fluxu aqua<lb></lb>rum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Opportunè ſuggeſſiſti, quæ mę <lb></lb>aliò abſtractum prorſus effugerant. </s> <s>Thales <lb></lb>Mileſius ſuo illo ingenti nauigio me longiùs <lb></lb>abduxerat. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Quid illud eſt? </s> <s>an putas terram̨ <lb></lb>aquis innatare, aut poſſe pari facilitate atque <lb></lb>nauigium trahi ſeu impelli? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Minimè omnium: ſed neſcio quæ <lb></lb>mens mihi incidit, vt inciperem ſuſpicari, <pb xlink:href="018/01/150.jpg" pagenum="136"></pb>an telluris centro ex V<gap></gap>in T machinationi<lb></lb>bus translato, & aquâ in oppoſitam partem <lb></lb>confluente, fieri poſſet, vt aquæ terra inna<lb></lb>taret, aut ſaltem aliquid de grauitare remit<lb></lb>teret. </s> <s>Id quod opportuniore ſchemate ex<lb></lb>hibeo. </s> <s>Sit idem terræ globus ABCE, cu<lb></lb>ius centrum T non congruat ampliùs cum <lb></lb>centro V. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> At ecce Merſennum in ipſo tem<lb></lb>pore. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> In facinore manifeſto deprehenſi <lb></lb>pœnas dabitis, boni viri. </s> <s>Nullus eſt infi<lb></lb>ciandi locus. </s> <s>Graphium adhuc tenet Gul<lb></lb>dinus; Galilæus cubito incumbens attentus <lb></lb>operam dabat. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Salue amicum caput. </s> <s>Quicquid in <lb></lb>nobis eſt criminis, animaduertatur; ſed te <lb></lb>iudice. </s> <s>Dabimus, quas volueris pœnas. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Vtique leues, ſi fuerint peccato <lb></lb>pares. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Vos nunquam ſatis de hoc apud <lb></lb>me purgabitis, quod ante condictam mihi <lb></lb>horam conueneritis, amæna ſcientiarum <lb></lb>ſpatia, me prætermiſſo, percurrentes. </s> <s>Ve<lb></lb>niam non impetrabitis, niſi me illicò in ſua<lb></lb>uiſſimi doctiſſimique veſtri ſermonis con<lb></lb>ſortium admittentes probaueritis vos mihi <lb></lb>veſtra cogitata non inuidiſſe, </s> </p> <pb xlink:href="018/01/151.jpg" pagenum="137"></pb> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Præclarè nobiſcum agitur, te iudicè. </s> <s><lb></lb>Culpâ vacamus: nam præmium nobis, non <lb></lb>pœna decernitur. </s> <s>Quarè rumpe moras, Gul<lb></lb>dine, & quæ nobis eſſet diſputatio, ediſ<lb></lb>ſere. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ex ingenitâ aquarum propenſio<lb></lb>ne, qua ſemper ad ima delabuntur, animad<lb></lb>uertebamus oriri poſſe, vt ſi telluris globus <lb></lb>Archimedæis machinationibus extra vniuerſi <lb></lb>centrum transferretur, aquæ in oppoſitam <lb></lb>motui partem delabentes, vt fierent centro <lb></lb>viciniores, minùs grauem relinquerent ſu<lb></lb>periorem terræ portionem. </s> <s>Si enim eſſet <lb></lb>ABCE terræ globus, cuius centrum T non <lb></lb>congrueret centro V, quod vniuerſi, aut ſal<lb></lb><figure id="id.018.01.151.1.jpg" xlink:href="018/01/151/1.jpg"></figure><lb></lb>tem <expan abbr="grauiũ">grauium</expan> <lb></lb><expan abbr="elementariũ">elementarium</expan> <lb></lb>centrum ſta</s> <s><lb></lb>tuitur, aquæ <lb></lb>omnes, qui<lb></lb>bus liberą <lb></lb>pateret ad <lb></lb><expan abbr="fluendũ">fluendum</expan> via, <lb></lb><expan abbr="deſcenderẽt">deſcenderent</expan> <lb></lb>verſus C, vt <lb></lb>ad centrum <lb></lb>V propiùs <lb></lb>accederent, <pb xlink:href="018/01/152.jpg" pagenum="138"></pb>& in ſphæricâ demum ſuperficie FHD pari<lb></lb>bus radijs à centro V remota conſiſterent. </s> <s><lb></lb>Cum itaque ſuperiori ſegmento fieret pon<lb></lb>deris aquæ deceſſio, inferiori autem acceſ<lb></lb>ſio, aliquod haberetur in perficiendâ mo<lb></lb>tione compendium: Hæc verò diſſerenti<lb></lb>bus nobis incidit ſuſpicio, an fortè continge<lb></lb>re poſſet, aquis in partem vnam delapſis <lb></lb>terram innatare. </s> </p> <p type="main"> <s>Sit enim globus terraqueus ABCE, cu<lb></lb>ius centrum T ad illud interuallum à centro <lb></lb>V venerit machinarum vi, vt aqua deorſum <lb></lb><arrow.to.target n="note67"></arrow.to.target><lb></lb><figure id="id.018.01.152.1.jpg" xlink:href="018/01/152/1.jpg"></figure><lb></lb>delapſa ſit B <lb></lb>HECB, & <lb></lb>portionem B <lb></lb>CE circum<lb></lb>plectatur. </s> <s><expan abbr="Iã">Iam</expan> <lb></lb>verò dimit<lb></lb>tatur tellus à <lb></lb>ſuſpendente: <lb></lb><expan abbr="nõ">non</expan> facilè de. </s> <s><lb></lb>finirem, v<lb></lb>trùm terrą <lb></lb>conſiſteret, <lb></lb>an potius de<lb></lb>ſcenderet ex T in V, an verò etiam ſponte <lb></lb>aſcenderet longiùs recedens ab V. </s> <s>Verùm <lb></lb>ſi ſponte ſuâ aliquo uſque aſcenderet, iam̨ <pb xlink:href="018/01/153.jpg" pagenum="139"></pb>nihil ſupereſſet laboris Archimedi, vt eò il<lb></lb>lam deduceret: ſi conſiſteret, iam innataret <lb></lb>aquis, ac proinde non multo labore fuiſſet <lb></lb>opus, vt ex V in T transferretur: ſi demùm <lb></lb>deſcenderet, illud ſaltem haberetur emolu<lb></lb>menti, quod intrà aquam exiſtenti multum <lb></lb>ponderis decederet, & motio faciliùs perfi<lb></lb>ceretur. </s> </p> <p type="margin"> <s><margin.target id="note67"></margin.target><emph type="italics"></emph>LXVII <lb></lb>Facilitas <lb></lb>motus terræ, <lb></lb>antequam̨ <lb></lb>ab aqua ſe<lb></lb>iungeretur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Lepidum ſanè inuentum ad vin<lb></lb>dicandum à calumniâ Archimedem, ſi cui <lb></lb>fortè audaciùs locutus videatur: neque enim <lb></lb>ex machinis ſolùm, de quibus abundè Gali<lb></lb>læus diſputabat, verùm etiam ex ipsâ aquâ <lb></lb>ſubſidium non leue peti poſſet ad tellurem̨ <lb></lb>loco dimouendam. </s> <s>Sed quid potiùs dicen<lb></lb>dum exiſtimas? </s> <s>innataret-ne? </s> <s>an verò de<lb></lb>ſcenderet? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ex his fluctibus enauigare ſolus <lb></lb>non poſſum: vobis pariter adremigandum <lb></lb>eſt. </s> <s>Illud primum ſtatuere oportet, vtrùm <lb></lb>terrenus globus ſit aquâ leuior ſecundùm <lb></lb>ſpeciem; deinde quota pars ex aquis ſponte <lb></lb>emergeret: vt hinc innoteſcat, quantum̨ <lb></lb>fuiſſet Archimedi laborandum. </s> <s>Et quod <lb></lb>ad primum ſpectat, certum eſt aërem vni<lb></lb>uerſum in terræ cauernis deliteſcentem̨, <lb></lb>omnesque halitus, & corpora aquis leuiora <lb></lb>plurimum poſſe demere de grauitate: aër <pb xlink:href="018/01/154.jpg" pagenum="140"></pb>enim, dum corpus in aëre ſuſpenditur, nec <lb></lb>grauitatem addit, nec leuitatem: at ſi cor<lb></lb>pus aquæ inſiſtat, ex aëre recipit leuita<lb></lb>tem. <lb></lb><arrow.to.target n="note68"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note68"></margin.target><emph type="italics"></emph>LXVIII <lb></lb>Pondus tel<lb></lb>luris in a<lb></lb>qua minue<lb></lb>retur, ob in<lb></lb>cluſos bali<lb></lb>tus.<emph.end type="italics"></emph.end></s> </p> <figure id="id.018.01.154.1.jpg" xlink:href="018/01/154/1.jpg"></figure> <p type="main"> <s>Sit enim vas AR æreum <lb></lb>parallelepipedum <expan abbr="vacuũ">vacuum</expan>, <lb></lb>cuius moles ſolida, hoc eſt <lb></lb>vnâ cum aëre incluſo, ſit <lb></lb>pedalis: expendatur iņ <lb></lb>aëre, & ſit lib. 12. Vtique <lb></lb>ſi aquæ imponatur, nata<lb></lb>bit, cum pes cubicus a<lb></lb>quæ ſit lib. Rom. 80; eſt <lb></lb>enim grauitas molis compoſitæ ex vaſis ma<lb></lb>tèriâ & aëre ad grauitatem aquæ, vt;. </s> <s>3. ad 20. <lb></lb>At ſi ſeruata eadem materia, & æris denſi<lb></lb>tate eâdem manente, confletur in maſſam, <lb></lb>aut ex eâ fiat vas minoris capacitatis, erit <lb></lb>quidem in aëre idem pondus, at non item <lb></lb>in aquâ. </s> <s>Haud diſpari ratione aër terræ vi<lb></lb>ſceribus incluſus, qui ad extenuandum orbis <lb></lb>pondus in aëre nihil iuuat, niſi quatenus lo<lb></lb>cum occupat cæteroqui grauioribus corpo<lb></lb>ribus replendum, intrà aquam conferret in<lb></lb>ſuper leuitatem, & de grauiorum corporum <lb></lb>pondere aliquid demeret. </s> <s>Quod ſi ignem <lb></lb>aëre multò leuiorem addamus, qui plurima <lb></lb>globi huius ſpatia implet, incrementum ac<pb xlink:href="018/01/155.jpg" pagenum="141"></pb>cipiet leuitas non contemnendum; cum po<lb></lb>tiſſimùm ex globi totius grauitate demen<lb></lb>dum ſit huius aquæ terram circumplectentis <lb></lb>pondus: iam enim non pars eſſet oneris mo<lb></lb>uendi, ſed eſſet medium, in quo motus per<lb></lb>ficeretur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end> Aëris, & ignis copiam in terrâ de<lb></lb><arrow.to.target n="note69"></arrow.to.target><lb></lb>liteſcentem certis menſuris definire non poſ<lb></lb>ſumus, ſed coniecturas tantùm perſequi ne<lb></lb>ceſſe eſt: illud potius à Philoſopho exigi poſ<lb></lb>ſe videtur, vt aëris grauitatem cum aquâ <lb></lb>comparatam determinet. </s> <s>Quamuis autem <lb></lb>conſtipato intrà vas aëre aliquando depre<lb></lb>henderim aërem quadringenties aquâ leuio<lb></lb>rem, mihi tamen omninò non ſatis facio: ex <lb></lb>illo enim experimento hoc certè euincitur, <lb></lb>quod aër conſtipatus in aere communi non <lb></lb>conſtipato grauitat: ſed cum varia ſit aëris <lb></lb>conſtipatio, inconſtans pariter eſt grauitatis <lb></lb>menſura, quæ ex illâ colligitur. </s> <s>Quare aëris <lb></lb>grauitatem explorare oporteret in medio le<lb></lb>uiore, quemadmodum aqua non intrà aquam <lb></lb>ſed in aëre expenditur. </s> <s>Et quidem ſubiit ani<lb></lb>mum aliquando hæc cogitatio, vt ſubiectis <lb></lb>pruni aërem vehementer calefacerem, in <lb></lb>quo aërem <expan abbr="cõmunem">communem</expan> phialæ incluſum ex<lb></lb>penderem; vt exploratâ deinde eiuſdem <pb xlink:href="018/01/156.jpg" pagenum="142"></pb>phialæ grauitate in aëre communi minùs ta<lb></lb>ro, innoteſceret aëris pondus: ſed cum per<lb></lb>ſpectum haberem ex prunis vaporem cali<lb></lb>dum aſcendere, timui, ne motus aſcenden<lb></lb>tis vaporis ac medii commoti mihi fucum <lb></lb>faceret, vt detractum de grauitate cenſerem, <lb></lb>quicquid virium ad deſcendendum occur<lb></lb>rentis vaporis motus impediret. </s> <s>Præter<lb></lb>quam quod ex variâ aeris calefacti raritatę, <lb></lb>varia pariter deprehenderetur aëris commu<lb></lb>nis grauitas. </s> </p> <p type="margin"> <s><margin.target id="note69"></margin.target><emph type="italics"></emph>LXIX <lb></lb>Aquæ & aë<lb></lb>ris grauita<lb></lb>tes compa<lb></lb>rantur, & <lb></lb>inquirun<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> De aëris conſtipati grauitate nullus <lb></lb>dubito, nequè de eiuſdem dilatati leuitate; Id <lb></lb>quod ex hac potiſſimùm occaſione depre<lb></lb>hendi. </s> <s>Mirabar maris æſtum Lunæ moti<lb></lb>bus adeò conſtanter obſequentem, cauſam<lb></lb>que curioſiùs inueſtigans animus nunquam <lb></lb>quieuit, niſi vbi ſuſpicari cœpit latere in ma<lb></lb>ris fundo corpora, quæ aſcendente ad Me<lb></lb>ridianum Lunâ intumeſcerent, aquasque <lb></lb>attollerent, Lunâ verò ad Occaſum deſcen<lb></lb>dente ſubſiderent cum aquis. </s> <s>Hinc pro <lb></lb>maiore huiuſmodi corporum copiâ, aut mi<lb></lb>nore, aut pro inæquali eorum contumaciâ, <lb></lb>aut facilitate ad intumeſcendum, æſtuum <lb></lb>inæqualitas ſatis explicata videbatur. </s> <s>Vt au<lb></lb>tem aliquod marini æſtûs, ex corpore ad Lu<pb xlink:href="018/01/157.jpg" pagenum="143"></pb>næ nutum intumeſcente, veſtigium obſer<lb></lb>uarem, Biſemuti glebam nullum ignem paſ<lb></lb>ſam mihi comparaui (Biſemutum noſtri ho<lb></lb>mines vocant plumbum cinereum, quod in<lb></lb>ter plumbi albi & nigri ſpeciem medium <lb></lb>eſt) congruæ retortæ impoſui, ignem ſe<lb></lb>cundùm gradus adminiſtraui horas duode<lb></lb>cim, & qui extillauit humor candidus ac dul<lb></lb>cis, amplo capacique Recipiente excepi: <lb></lb>hunc iterum ac tertiò, vt artifices loquuntur, <lb></lb>rectificaui, vt purior euaderet ac dulcior. </s> <s><lb></lb>Huius liquoris libram vnam conieci in vi<lb></lb>treum vaſculum tantæ capacitatis, vt liquor <lb></lb>phialæ beſſem impleret, reliquum trientem <lb></lb>aër occuparet. </s> <s>Vitrum optimè clauſum, ne <lb></lb>quid expirare poſſet, in loco, vbi quieſceret, <lb></lb>ſtatui; nec ſinè animi voluptate licebat in <lb></lb>Plenilunijs manifeſta incluſi liquoris incre<lb></lb>menta obſeruare, in Nouilunijs verò decre<lb></lb>menta, neque ea tantùm, quæ prioribus in<lb></lb>crementis reſponderent, ſed vt aliquid de<lb></lb>ceſſiſſe videretur ex eâ liquoris quantitate, <lb></lb>quam primùm infuderam. </s> <s>Contigit au<lb></lb>tem, vt, curioſitate animum vellicantę, <lb></lb>phialam tùm in Pleniluniis, tum in Noui<lb></lb>luniis expenderem, ſemperque paria depre<lb></lb>hendi grauitatis momenta, perinde atque ſi <lb></lb>tunc primùm in phialam liquorem inieciſſ<pb xlink:href="018/01/158.jpg" pagenum="144"></pb>ſem. </s> <s>Ex quibus intellexi, quantum grauita<lb></lb>tis ſecundùm ſpeciem decederet liquori in<lb></lb>tumeſcenti, tantum accedere aëri intrà phia<lb></lb>lam apprimè occluſam conſtipato: contrà <lb></lb>verò liquore ad minora ſpatia coanguſtato <lb></lb>aërem quidem incluſum dilatari<gap></gap>ſed huius <lb></lb>rareſcentis leuitate auctâ, maiorem illius <lb></lb>condenſati grauitatem compenſari. </s> </p> <p type="main"> <s>Nec diſsimilem grauitatis conſtantiam <lb></lb>obſeruabimus, ſi vitreum globum, cui lon<lb></lb>giuſculum collum & gracile adhæreat, vini <lb></lb>ſpiritu ex multiplici diſtillatione tenuiſſimo <lb></lb>repleamus, aëre collum occupante; oſcu<lb></lb>lum autem Hermetis ſigillo claudatur. </s> <s>Ex <lb></lb>calore enim rareſcet vini ſpiritus, aëremque <lb></lb>conſtipabit, & frigore ſubſequente ſubſidet, <lb></lb>aëri locum relinquens: neque tamen Ther<lb></lb>moſcopii huius grauitas variabitur, cum̨ <lb></lb>vnius corporis conſtipati grauitas alterius rari <lb></lb>leuitate compenſetur. </s> <s>Hinc tamen certą <lb></lb>definiri non poſſe momenta, quibus aër <lb></lb>compreſſus deorſum nitatur, palam eſt. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Rem ego quantâ potui diligentiâ <lb></lb>aliter inueſtigaui, & aërem non quadrin<lb></lb>genties tantùm, ſed etiam adhuc triplo le<lb></lb>uiorem inueni, ita vt grauitas aquæ ad gra<lb></lb>uitatem aëris non ſit in minori Ratione quàm <lb></lb>1200 ad 1, ſed potiùs in maiori Rationę. <pb xlink:href="018/01/159.jpg" pagenum="145"></pb>Ita verò ſe habuit obſeruatio. </s> <s>Æream Æo<lb></lb>lipilam propemodùm candentem omnique <lb></lb>humore deſtitutam expendi primùm bilan<lb></lb>ce iuſtiſsimâ; deinde eiuſdem refrigeratæ & <lb></lb>ad naturalem temperiem reſtitutæ pondus <lb></lb>examinaui, & animaduerti illam factam̨ <lb></lb>fuiſſe quatuor vt minimum grauis grauio<lb></lb>rem: Hinc intuli aërem, qui rarefactionę <lb></lb>exierat, & naturali condenſatione fuerat ite<lb></lb>rùm in Æolipilam admiſſus, habere in gra<lb></lb>uitate quatuor grana. </s> <s>Iterum Æolipilam, <lb></lb>vt priùs, calefeci, quæ eiuſdem quoquè pon<lb></lb>deris, vt priùs, inuenta eſt: & illicò eius ro<lb></lb>ſtrum in aquam immerſi, vt aquam ſugeret: <lb></lb>ſuxit autem aquæ vncias 9, drachmas 3, gra<lb></lb>na 25; quæ ſunt in vniuerſum (ſi ſingulis <lb></lb>drachmis grana 72 tribuantur, & vnciis gra<lb></lb>na 576) grana 5425; quod eſt pondus aquæ <lb></lb>occupantis idem ſpatium, quod occupabat <lb></lb>aër vi rarefactionis excluſus. </s> <s>Eſt igitur gra<lb></lb>uitas aquæ granorum 5425 ad grauitatem̨ <lb></lb>aëris ſecundùm molem æqualis gran 4, hoc <lb></lb>eſt vt 1356 ad 1. Quarè ſatis liberaliter age<lb></lb>re mihi videor, ſi dixero aërem ad aquam in <lb></lb>leuitate eſſe vt 1200 ad 1. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Quàm vellem hæc omninò veri<lb></lb>tati congruere! Sed veniam dabis non qui<lb></lb>dem improbanti conatum, ſed penſicula<pb xlink:href="018/01/160.jpg" pagenum="146"></pb><arrow.to.target n="note70"></arrow.to.target><lb></lb>tiùs examinanti, vtrùm omni prorſus labe <lb></lb>careat tua hæc argumentatio. </s> <s>Sit vas cu<lb></lb>preum AR molis vnâ cum incluſo aëre pe<lb></lb>dalis, & vaſis pondus lib. 80, quod eſt pon<lb></lb>dus pedis cubici aquæ. </s> <s>Eſt igitur vas eiuſ<lb></lb>dem ſpecificæ grauitatis cum aquâ; atque <lb></lb>adeò cum grauitas cupri ad grauitatem aquæ <lb></lb>ſit vt 71. ad 8, moles cupri ad molem aëris <lb></lb>incluſi eſt vt 8 ad 63. Quarè vas aëre plenum <lb></lb>nihil in aquâ grauitat, aut leuitat; ſed ſi mer<lb></lb>gatur intrà aquam, quæ aëre excluſo impleat <lb></lb>vaſis capacitatem, iam vas intrà aquam pon<lb></lb>dus habebit lib. 80. minùs pondere, quod <lb></lb>habet aqua ſecundùm molem cupro æqualis. </s> <s><lb></lb>Quia igitur moles cupri eſt (8/71) pedis cubici, <lb></lb>fiat vt 71 ad 8, ita lib. 80 pondus pedis cu<lb></lb>bici aquæ, ad lib. 9. (1/71) pondus aquæ æqualis <lb></lb>cupro vaſis. </s> <s>Erit itaque vaſis pleni aquâ in<lb></lb>trà aquam grauitas lib. (70 70/71): quod quidem <lb></lb>pondus tribuendum eſt cupro, non autem <lb></lb>aquæ vas implenti, quæ intrà aquam non <lb></lb>grauitat: cum maximè idem eſſet in aquâ <lb></lb>eiuſdem cupri pondus, etiamſi in maſſam <lb></lb>conflatum nihil aquæ contineret. </s> <s>Quan<lb></lb>quam non nego grauitatem illam cupri iņ <lb></lb>aquâ eſſe æqualem grauitati molis aqueæ vas <lb></lb>implentis, ſi illa extra aquam in aere<gap></gap><lb></lb>transferatur; eſt enim moles aquæ vas im<pb xlink:href="018/01/161.jpg" pagenum="147"></pb>plentis (63/71) pedis cubici. </s> </p> <p type="margin"> <s><margin.target id="note70"></margin.target><emph type="italics"></emph>LXX <lb></lb>Si vas in li<lb></lb>quore <expan abbr="põde-retur">ponde<lb></lb>retur</expan> nunc <lb></lb>plenum aë<lb></lb>re, nunc ple<lb></lb>num liquo<lb></lb>re illo, diffe<lb></lb>rentia pon<lb></lb>derum est <lb></lb>pondus li<lb></lb>quoris im<lb></lb>plentis capa<lb></lb>citatem va<lb></lb>ſis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>At manente eâdem vaſis mole intelliga<lb></lb>tur aucta materia; & diminuta capacitas, ita <lb></lb>vt ſit vaſis pondus in aëre lib. 100 ſeſqui<lb></lb>quartum prioris: erit moles cupri (10/71) pedis <lb></lb>cubici, & capacitas (61/71). Quarè aqua æqualis <lb></lb>cupro habet pondus lib. (11 19/71): igitur vas intrà <lb></lb>aquam plenum aquâ habet pondus lib. (88 52/71) <lb></lb>at plenum aëre intrà aquam amittet pondus <lb></lb>integri pedis cubici, & ſolùm erit lib. 20. <lb></lb>Horum igitur ponderum differentia (68 52/71) æ<lb></lb>qualis eſt ponderi aquæ implentis capacita<lb></lb>tem vaſis, quæ ex conſtitutâ hypotheſi eſt (61/71) <lb></lb>pedis cubici. </s> </p> <p type="main"> <s>Similiter ſi intrà idem vas admittantur <lb></lb>aquæ (10/71), reliquam capacitatem (51/71) impleat <lb></lb>aër: moles cupri & aëris occupat in aquâ (61/71) <lb></lb>pedis cubici: igitur ex lib. 100 auferuntur <lb></lb>lib. (68 52/71), & pondus vaſis in aquâ eſt lib. (31 19/71). <lb></lb>At quando totum replebatur aquâ, pondus <lb></lb>erat lib. (88 52/71), igitur differentia lib. (57 33/71) eſt <lb></lb>grauitas æqualis grauitati (51/71) pedis cubici aquæ, <lb></lb>quæ impleret vaſis ſpatium ab aëre occupa<lb></lb>tum, ſi aqua illa in aëre extra aquam ex<lb></lb>penderetur. </s> </p> <p type="main"> <s>Quemadmodum igitur ex eiuſdem vaſis <pb xlink:href="018/01/162.jpg" pagenum="148"></pb><arrow.to.target n="note71"></arrow.to.target><lb></lb>ponderibus intrà <expan abbr="aquã">aquam</expan>, <expan abbr="quãdo">quando</expan> eſt <expan abbr="plenũ">plenum</expan> aquâ, <lb></lb>ac quando eſt plenum aëre, rectè infertur ho. <lb></lb></s> <s><expan abbr="rũ">rum</expan> ponderum <expan abbr="differentiã">differentiam</expan> eſſe æqualem pon<lb></lb>deri aquæ implentis locum <expan abbr="aẽris">aeris</expan>, ſi illa pon<lb></lb>deretur in aëre: ſic ex differentiâ ponderum <lb></lb>Æolipilæ intrà aërem communem conſtitu<lb></lb>tæ, quando plena eſt aëre communi, ac <lb></lb>quando plena eſt aëre ignito, ex hac, inquam, <lb></lb>differentiâ rectè illata videtur grauitas aëris <lb></lb>communis Æolipilam implentis, ſi aër iſte <lb></lb>ponderaretur in aëre ignito tanquam in me<gap></gap><lb></lb>dio. </s> <s>Cum autem differentia huiuſmodi ſit <lb></lb>granorum quatuor, pondus aëris communis <lb></lb>æolipilam implentis eſt gran. 4. non quidem <lb></lb>abſolutè, ſed tantùm in medio leuitatis eiuſ<lb></lb>dem ac raritatis, quam habebat aër Æolipi<lb></lb><emph type="italics"></emph>l<emph.end type="italics"></emph.end>æ candentis: ſicuti etiam aqua vas A R im<lb></lb>plens, de quo dicebam, non habet graui<lb></lb>tatem lib. (68 52/71) in quocunque medio, ſed tan<lb></lb>tùm in aëre leuitatis ac raritatis eiuſdem cum <lb></lb>aëre, qui vaſis capacitatem implebat. </s> <s>Qua<lb></lb>re non ego facilè dixerim quatuor illa grana <lb></lb>fuiſſe pondus aëris primùm eiecti, qui iterùm <lb></lb>receptus fuit; ille enim aër nullum habebat <lb></lb>pondus in aëre communi; & ſi pondus ha<lb></lb>beat in aëre ignito, tota illa grauitas non <lb></lb>pertinet ad ſolum aërem, qui recipitur, ſed <lb></lb>ad illum, qui totam Æolipilam implet. </s> <s>Si<pb xlink:href="018/01/163.jpg" pagenum="149"></pb>cut ſi aqua implens vas A R attenuaretur ſe<lb></lb>cundùm aliquam partem in aërem, & reli<lb></lb>qua eiiceretur, iterum autem ad naturalem <lb></lb>denſitatem rediens eiectam aquam exſuge<lb></lb>ret, differentia ponderis vaſis non ſoli aquæ <lb></lb>eiectæ tribuenda eſſet, ſed toti aquæ vas im<lb></lb>plenti. </s> <s>Hinc eſt quod, cum aqua in Æoli<lb></lb>pilam admiſſa non ſit ſecundùm molem̨ <lb></lb>æqualis toti aëri, qui eam implebat, ac pro<lb></lb>inde non ſit æqualis moli, quæ habet pon<lb></lb>dus gran. 4, non habetur præcisè Ratio gra<lb></lb>uitatum ſecundùm ſpeciem. </s> </p> <p type="margin"> <s><margin.target id="note71"></margin.target><emph type="italics"></emph>LXXI <lb></lb>Experimen<lb></lb>tum Aeoli<lb></lb>pilæ ad ſum<lb></lb>mum osten<lb></lb>dit grauita<lb></lb>tem aëris <expan abbr="cõ-munis">con<lb></lb>munis</expan> iņ <lb></lb>aëre ignito, <lb></lb>non autem <lb></lb>abſolutè: nec <lb></lb>ex eo habe<lb></lb>tur quæſita <lb></lb>proportio <lb></lb>grauitatum <lb></lb>aquæ & aë<lb></lb>ris.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Id meæ ſententiæ vlteriùs fauet: ſi <lb></lb>enim aquæ moles, quam ſuxit Æolipila, <lb></lb>minor eſt mole aëris, qui numerat in pon<lb></lb>dere grana 4, plus aliquid aquæ addendum <lb></lb>erit, vt moles æquales ſint; atque adeò mul<lb></lb>tò maior erit Ratio grauitatis aquæ ad gra<lb></lb>uitatem aëris, quam ſit deprehenſa Ratio <lb></lb>1356 ad 1. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Non hæc eo conſilio afferebam, vt <lb></lb>irem contrà; ſed tantùm vt rem paulò ob<lb></lb>ſcuriorem mihi ipſe enucleatiùs explicarem, <lb></lb>& te audirem, ſi quid ſortè à veritate aut à <lb></lb>tuâ mente alienum intelligerem. </s> <s>Cæterùm <lb></lb>non nego maiorem eſſe Rationem grauitatis <lb></lb>aquæ æolipilam implentis ad grauitatem aë<lb></lb>ris eam pariter implentis, ac ſit Ratio gra<pb xlink:href="018/01/164.jpg" pagenum="150"></pb>uitatis aquæ exſuctæ ad eiuſdem aëris graui<lb></lb>tatem; modò hæc aquæ grauitas intelligatur <lb></lb>non in quocunque medio, ſed in eodem, in <lb></lb>quo aër communis grauis eſt, in aëre vide<lb></lb>licet ignito & rariſſimo. </s> <s>Verùm cum re<lb></lb>rum grauitates definiamus habitâ rationę <lb></lb>medij omnium rariſſimi atque leuiſſimi ex <lb></lb>ijs, quibus communiter vtimur, hoc autem <lb></lb>medium aër ſit, non video, cur aëris & <lb></lb>aquæ grauitates inuicem conferre oporteat <lb></lb>ratione medij, cuius nullus futurus eſt vſus. </s> <s><lb></lb>Quod ſi metalla aquæ immerſa dicuntur in <lb></lb>aquâ minùs grauitare pro ratione diſcrimi<lb></lb>nis, quod interſpecificas grauitates interce<lb></lb>dit; cum aquam inter & aquam, aut aërem <lb></lb>inter & <expan abbr="aẽrem">aerrem</expan> nulla reperiatur communiter <lb></lb>differentia, nulla pariter aquæ in aquâ aut aë<lb></lb>ris in aëre eſt grauitatio: ac proinde cum <lb></lb>aër in aëre conſtituatur, nulla eſt eius graui<lb></lb>tas, quam cum aquâ comparare oporteat. </s> </p> <p type="main"> <s>Sed & vnum præterea addo, ſi placet. </s> <s><lb></lb>Si ferri grauitatem cum aquæ grauitate con<lb></lb>ferre voluero, ferrum primùm in aëre ex<lb></lb>pendo, deinde in aquâ; & quæ fuerit pon<lb></lb>derum differentia, eam tribuo grauitati aquæ <lb></lb>ſecundùm molem æqualis ferro; & vt totum <lb></lb>ferri pondus ad hanc differentiam, ita graui<lb></lb>tatem ferri ad aquæ grauitatem ſecundùm <pb xlink:href="018/01/165.jpg" pagenum="151"></pb>ſpeciem pronuncio, ſi tamen vtraque moles <lb></lb>in aëre fuerit; & ſit vt 42 ad 5 1/3. Nam ſi <lb></lb>tam ferrum quàm aqua intra oleum (cuius <lb></lb>grauitas ſpecifica in aëre eſt 4 3/4) collocentur, <lb></lb>grauitas ferri in oleo erit partium 37 1/4, qua<lb></lb>rum grauitas aquæ erit ſolùm (7/12); quæ <emph type="italics"></emph>R<emph.end type="italics"></emph.end>atio <lb></lb>longè maior eſt eâ Ratione, quam habent <lb></lb>grauitates in aëre. </s> </p> <p type="main"> <s>Diſcriminis huius ratio eſt, quia vt inue<lb></lb><arrow.to.target n="note72"></arrow.to.target><lb></lb>nirem Rationem grauitatum aquæ & ferri in <lb></lb>oleo, ſacoma ſeu æquipondium debuiſſet pa<lb></lb>riter eſſe in oleo; quia autem ſacoma ſemper <lb></lb>fuit in aëre. </s> <s>& examinatum eſt ferri pondus <lb></lb>in aëre, grauitas quoque ferri & aquæ com<lb></lb>paratur ſolum in aëre. </s> <s>Quod ſi in libræ ex<lb></lb>tremitate appenderetur globus ferreus vn<lb></lb>ciarum 42 in aëre, qui in oleo immergere<lb></lb>tur, reſponderet ſacomati ferreo in aëre exi<lb></lb>ſtenti vnciarum 37 1/4: at ſi ſacoma ſit pariter <lb></lb>in oleo, quia ferreum eſt, & æqualiter à cen<lb></lb>tro libræ diſtat, erit æquale ponderi, quod <lb></lb>examinatur, hoc eſt vnc.42. Globus autem <lb></lb>ferreus ſi in aquâ immergeretur, reſpon<lb></lb>deret ſacomati ferreo in aëre exiſtenti vnc. </s> <s><lb></lb>36 2/3: atqui ſi vnciæ 37 1/4 in aëre æquiponde<lb></lb>rant vncijs 42 in oleo, vnciæ 36 1/3 in aërę <lb></lb>æquiponderant vnciis (41 51/149) in oleo; igitur <pb xlink:href="018/01/166.jpg" pagenum="152"></pb>eidem globo ferreo in aquâ poſito æquipon<lb></lb>derat ſacoma ferreum in oleo vnc. (41 51/149). Sa<lb></lb>comatum igitur 42 & (41 51/149) differentia (98/149) da<lb></lb>bit grauitatem aquæ in oleo comparatam̨ <lb></lb>cum grauitate ferri; ita vt ferri grauitas iņ <lb></lb>oleo ad aquæ grauitatem in oleo ſit vt 42 <lb></lb>ad (98/149), quæ eſt planè eadem Ratio ſuperiùs in<lb></lb>dicata 37 1/4 ad (7/12), hoc eſt 63 6/7 ad 1. </s> </p> <p type="margin"> <s><margin.target id="note72"></margin.target><emph type="italics"></emph>LXXII <lb></lb>Ratio duo<lb></lb>rum graui<lb></lb>um in vno <lb></lb>medio, vt ba<lb></lb>beatur, de<lb></lb>bet æquipon<lb></lb>dium eſſe in <lb></lb>eodem me<lb></lb>dio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Ex his, quæ carere videntur omni diffi<lb></lb>cultate, & ſatis manifeſta ſunt, infeto 4 il<lb></lb>la grana, quæ tribuis ponderi aëris commu<lb></lb>nis Æolipilam implentis, nullam aëris gra<lb></lb>uitatem indicare per ſe, & immediatè; non <lb></lb><expan abbr="aẽris">aeris</expan> in aëre communi, quia in eo, Vt dice<lb></lb>bam, non grauitat; non aëris communis in <lb></lb>aëre ignito, vt paulò ante tibi permittebam, <lb></lb>quia ſacoma ſeu æquipondium, quo vſus es <lb></lb>ad grauitatem explorandam, non erat pari<lb></lb>ter in aëre ignito: id quod fieri oportuiſſet. </s> <s><lb></lb>Nam ſi vas aliquod aquâ plenum intrà a<lb></lb>quam ponderes, & ſacoma ſit pariter iņ <lb></lb>aquâ; iterum autem ſacomate intrà aquam <lb></lb>exiſtente idem vas aëre plenum in aquâ ex<lb></lb>pendas, vtique ponderum differentia noņ <lb></lb>dabit aquæ pondus in aëre. </s> <s>Ergo pariter <lb></lb>cum vas aëre communi plenum expenderis <lb></lb>in aëre communi, & iterum in eodem <expan abbr="aẽre">aere</expan> <pb xlink:href="018/01/167.jpg" pagenum="153"></pb>communi ponderaueris idem vas plenum̨ <lb></lb><expan abbr="aẽre">aëre</expan> ignito, ponderum differentia non eſt <lb></lb>pondus aëris communis æolipilam implen<lb></lb>tis. </s> </p> <p type="main"> <s>Exemplo rem declaro: & accipio illud <lb></lb>idem vas cupreum AR, de quo antea dixi<lb></lb>mus, quod cum in aëre ſit lib. 100, intrà <lb></lb>aquam plenum aquâ eſſet lib (88 52/71), ſed intrà <lb></lb>aquam plenum aëre ſolùm eſſet lib. 20; vn<lb></lb>de intulimus aquæ vas implentis pondus iņ <lb></lb>aëre eſſe lib. (68 52/71). Ponamus ſacoma eſſę <lb></lb>ferreum, & illud pariter intrà aquam exiſte<lb></lb>re. </s> <s>Quoniam igitur ferrum 36 2/3 in aërę, <lb></lb>æquiponderat ferro 42 in aquâ, ferrum (88 52/71) <lb></lb>in aëre, æquiponderabit ferro (101 499/781) in aquâ; <lb></lb>& hoc faciet æquilibrium cum vaſe cupreo <lb></lb>pleno aquâ. </s> <s>Item quia ferrum 36 2/3 in aëre <lb></lb>æquiponderat ferro 42 in aquâ, ferrum 20 <lb></lb>in aëre æquiponderabit ferro (22 10/11) in aquâ; & <lb></lb>hoc conſtituet æquilibrium cum vaſe cupreo <lb></lb>pleno aëre intrà aquam. </s> <s>Iam ſumo diffe<lb></lb>rentiam inter duo hæc ſacomata, quæ ſunt <lb></lb>vt (101 499/781) ad (22 10/11), & eſt differentia lib. (78 580/781); <lb></lb>quod ſanè non eſt pondus aquæ vaſis capa<lb></lb>citatem implentis, ſi illa in aëre ponderetur, <lb></lb>ſed eſt multò maius. </s> <s>Pro diuersâ autem̨ <lb></lb>materiâ ſiue plumbeâ, ſiue æreâ, ſiue argen<pb xlink:href="018/01/168.jpg" pagenum="154"></pb>teâ, aut ſtanneâ, ex qua ſacomata conſta<lb></lb>rent, alia atquè alia oriretur differentia, vt <lb></lb>patet. </s> <s>Id quod non in librâ tantùm, ſed in <lb></lb>ſtaterâ quoquè contingeret. <lb></lb><arrow.to.target n="note73"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note73"></margin.target><emph type="italics"></emph>LXXIII <lb></lb>Aëris com<lb></lb>munis & a<lb></lb>quæ graui<lb></lb>tas in aëre <lb></lb>ignito minor <lb></lb>est, quàm̨ <lb></lb>fuerit depre<lb></lb>henſa.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quapropter aërem communem in aërę <lb></lb>ignito conſtitutum leuiorem eſſe 4 granis, <lb></lb>quæ in medio eodem eſſent, apertè con<lb></lb>ſtat; illis ſiquidem æquiponderat in medio <lb></lb>craſſiore: atque adeò aqua deprehenſa gra<lb></lb>norum 5425 in aëre communi, ſi in aërę <lb></lb>ignito conſtitueretur, multò paucioribus <lb></lb>granis æquiponderaret in eodem medio exi<lb></lb>ſtentibus; & quidem pro ratione materiæ <lb></lb>ſacomatis; ſi enim eſſent grana metallica, <lb></lb>multò pauciora requirerentur ad faciendum <lb></lb>æquilibrium cum aquâ, quàm ſi eſſent gra<lb></lb>na hordei. </s> <s>Similiter ſi particulæ ex medul<lb></lb>lâ ſambuci, aut materiâ leuiore quàm aqua, <lb></lb>fungerentur munere ſacomatis, tunc librâ in <lb></lb>aërem ignitum translatâ, minuendum eſſet <lb></lb>ſacomatis pondus; quemadmodum 100 vn<lb></lb>ciæ auri, & vnciæ (108 24/55) ferri in aere noņ <lb></lb>æquiponderant, quæ tamen in aquâ conſti<lb></lb>tuerent æquilibrium, quandoquidem tam <lb></lb>100 vnciæ auri quàm (108 24/55) ferri in aquâ po<lb></lb>ſitæ æquiponderant ſacomari vnc. </s> <s>94 2/3 in aë<lb></lb>re. </s> <s>Quarè nihil hìc certi mihi videor inue<lb></lb>nire, in quo pedem figam. </s> </p> <pb xlink:href="018/01/169.jpg" pagenum="155"></pb> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Si aliquid intelligo, haud procul <lb></lb>abes ab eorum ſententiâ, qui omnem aëri <lb></lb>grauitatem adimunt: idcirco enim rem hanc <lb></lb>ad viuum reſecas, vt illa prorſus euaneſcat. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Quo iure omnium ſententia ferro <lb></lb>& plumbo leuitatem negaret, quia vt pluri<lb></lb>mum grauitant in medijs communibus, <lb></lb>quamuis in hydrargyro aſcendant & inna<lb></lb>tent; ita aërem pariter grauem apud nos eſſe <lb></lb>inſicior, quamuis ſi in purum æthera tranſ<lb></lb>ferretur, ibi grauitaret, quemadmodum & <lb></lb>aër præter naturam condenſatus in vtribus, <lb></lb>in aëre libero grauitat: ibi ſiquidem grauita<lb></lb>re poterit, vbi medium leuius, in quo ſit, <lb></lb>inueniet. </s> <s>Immò memini me olim vento</s> </p> <p type="main"> <s><arrow.to.target n="note74"></arrow.to.target><lb></lb>rum deſcendentium cauſam reieciſſe in aë<lb></lb>ris ſeu halitûs grauitatem; ſicut enim gra<lb></lb>uia deſcendentia, ita & leuia aſcendentią <lb></lb>impetum in motu concipiunt, & augent; ex <lb></lb>quo ſit, vt, quemadmodum lignum in aquam <lb></lb>cadens profundiùs mergitur, quàm par ſit, <lb></lb>vnde poſteà emergit, ita pariter halitus in<lb></lb>ſimo hoc aëre leuiores aſcendentes conci<lb></lb>piant impetum, quo deferantur vltra termi<lb></lb>nos ſuæ quieti debitos in ſupremum aerëm <lb></lb>ipſis halitibus leuiorem; in quo cum iam <lb></lb>graues ſint, deſcendant, & obuios halitus <lb></lb>aſcendentes reflectant. </s> <s>Si igitur aerem hunc <pb xlink:href="018/01/170.jpg" pagenum="156"></pb>infimum lagenæ incluſum transferremus in <lb></lb>puriſſimum æthera, vel ſaltem in altiſſimi <lb></lb>montis, pura Caucaſi, verticem, ibique la<lb></lb>genam expenderemus; deinde eiuſdem aquâ <lb></lb>plenæ pondus inueſtigaremus, tunc innote<lb></lb>ſceret Ratio grauitatum aquæ & aëris in me<lb></lb>dio illo leuiore. </s> <s>Cæterum infimæ huius re<lb></lb>gionis incolæ de aëris grauitate diſputantes, <lb></lb>non video, quid certi definire poſſint, neque <lb></lb>quos ſtatuant Rationum terminos. </s> </p> <p type="margin"> <s><margin.target id="note74"></margin.target><emph type="italics"></emph>LXXIV <lb></lb>Venti de<lb></lb>ſcendentis <lb></lb>cauſa obiter <lb></lb>indicatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Abiret igitur in immenſum hæc di<lb></lb>ſputatio, & certius nihil, vt opinor, depre<lb></lb>henderemus, quod in rem noſtram faceret. </s> <s><lb></lb>Quapropter præſtaret ijs, quæ veritati pro<lb></lb>xima videntur, aſſumptis, progredi in eâ, <lb></lb>quam conſtitueramus, quæſtione. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Rectè mones, Galilæe. </s> <s>Sed præ<lb></lb>ſtabit fortaſsè hæc in aliud colloquium reij<lb></lb>cere; neque enim mihi per tempus licet apud <lb></lb>vos diutiùs eſſe, niſi poſthabito negotiolo, <lb></lb>quod me aliquantulum vrget, nec omnino <lb></lb>perire vellem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Commodis tuis nos ſeruire oportet: <lb></lb>præterquam quod non hodie diem ſine line â <lb></lb>duximus. </s> <s>Quare bonis auibus perge, quò te <lb></lb>negotia vocant. </s> </p> <pb xlink:href="018/01/171.jpg" pagenum="157"></pb> <figure id="id.018.01.171.1.jpg" xlink:href="018/01/171/1.jpg"></figure> <p type="main"> <s><emph type="center"></emph>DISSERTATIO <lb></lb>QVINTA<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Minorem telluris grauita<lb></lb>tem in aqua ex<lb></lb>plicat.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>Guldinus, Merſennus, Galilæus.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s>POSTREMAM heſterni ſer<lb></lb>monis noſtri clauſulam <lb></lb>recolenti in memoriam <lb></lb>venit, neſcio quid dę <lb></lb>aëris grauitate ſcriptum <lb></lb>literis Herbipoli haud <lb></lb>ita pridem datis ad ami<pb xlink:href="018/01/172.jpg" pagenum="158"></pb>cum, quarum exemplar nactus ſepoſueram. </s> <s><lb></lb>Excutiens itaque ſcrinium, quod mihi hoc <lb></lb>epiſtolarum genus ſeruat, demum, quod <lb></lb>quærebam; inueni; immo & mecum attuli, <lb></lb>ne, ſi fortè vobis aliqua ſubleſtæ fidei ſuſpi<lb></lb>cio de me ſuboriretur, tabulæ de eſſent, quas <lb></lb>proferrem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Nemo noſtrûm eſt, qui fidem in<lb></lb>firmare audeat Germano candori. </s> <s>neque ra<lb></lb>bulis eges, neque teſtibus, me quidem iu<lb></lb>dice: ſatis eſt te narraſſe, vt fidem adhi<lb></lb>beam. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> An aliquid, quod vel tuæ, Merſen<lb></lb>ne, vel meæ aduerſetur ſententiæ, prolatu<lb></lb>rus Guldinus, idquè nobis minùs placitu<lb></lb>rum, ſuſpicans, ideo literarum exemplar at<lb></lb>tulit, vt omnem à ſe inuidiam auertens iņ <lb></lb>alium declinet? </s> <s>Quæcunque tandem illą <lb></lb>ſint, in medium fidenti animo profer, Gul<lb></lb>dine. </s> <s>Non hìc partium, ſed vno veritatis <lb></lb>ſtudio tenemur. </s> <s>Nulla ne aëri tribuendą <lb></lb>grauitas? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Immo verò non modica; ſi eum, <lb></lb>à quo datæ ſunt literæ, audiamus; vocat ſi<lb></lb>quidem luculentiſsimum grauitatis aeris ar<lb></lb>gumentum, id, quod ab Eruditiſſimis Vi<lb></lb>ris obſeruatum eſt ex occaſione experimen<lb></lb>ti, quod ad Vacuum inueſtigandum inſti<pb xlink:href="018/01/173.jpg" pagenum="159"></pb>tuebatur. </s> <s>Paratum eſt vas vitreum eximiæ <lb></lb><arrow.to.target n="note75"></arrow.to.target><lb></lb>ſpiſſitudinis, & capacitatis tantæ, vt menſu<lb></lb>ras 32, hoc eſt aquæ vncias, vt minimum, <lb></lb>circiter mille, contineret, in Recipientis <lb></lb>Chymici formam elaboratum. </s> <s>Huius col<lb></lb>lo adglutinatum eſt ſingulari arte ac firmi<lb></lb>tudine epiſtomium ex orichalco tranſuerſam <lb></lb>habens clauem verſatilem aptiſſimè ſuo lo<lb></lb>culamento congruentem, ne quid ex vaſę <lb></lb>poſſit effluere, aut in illud ſe inſiuare niſi eâ <lb></lb>conuersâ. </s> <s>Ex orichalco pariter conſtructus <lb></lb>eſt firmiſſimus tubus hians vtrinque, ſed in <lb></lb>angulum inflexus, vt parti breuiori immitti <lb></lb>poſſit epiſtomium Recipientis (ſic liceat ap<lb></lb>pellare) pars verò longior fungi poſſit mu<lb></lb>nere antliæ duobus aſſariis ritè inſtructæ, vt <lb></lb>per alterum quidem Recipienti proximum <lb></lb>reducto embolo attrahi poſſit corpus, quo <lb></lb>illud impletur, per alterum verò aſſarium <lb></lb>congruo loco in antliæ dorſo conſtitutum <lb></lb>corpus illud atractum exprimi poſſit, cum <lb></lb>impellitur adduciturque truſillum: cuius <lb></lb>capiti tranſuerſum manubrium adnectitur, <lb></lb>vt duo ſimul poſſint antliam agitare: immò <lb></lb>quia, licèt initio facilis ſit antliæ agitatio, <lb></lb>paulatim tamen adeò creſcit difficultas em<lb></lb>bolum reducendi ab aſſario Recipienti proxi<lb></lb>mo, vt demum duo robuſtiſſimi iuuenes ſu<pb xlink:href="018/01/174.jpg" pagenum="160"></pb>dore manantes ac totis viribus adnitentes vix <lb></lb>illum ampliùs extrahere poſſint, aut prohi<lb></lb>bere, ne ſponte relabatur intus, & cum im<lb></lb>petu ac ſonitu illidatur ad partes tubi proxi<lb></lb>mas Recipienti; ideò extremo manubrio fu<lb></lb>niculi duo adnectuntur, vt plures opem fer<lb></lb>re poſſint. </s> <s>Ne verò, dum antlia agitatur, <lb></lb>poſsit aër per tenuiſsimas rimulas (ſi fortè <lb></lb>Recipientis epiſtomium & extremus antliæ <lb></lb>tubus non ſibi exquiſitâ collabellatione con<lb></lb>gruerent) ſe latenter inſinuare; antlia ligneæ <lb></lb>cupæ firmiſsimè affigitur ita, vt immiſſa in <lb></lb>cupam aqua Recipientis epiſtomium, eius<lb></lb>que clauem verſatilem contegat, & ſolum <lb></lb>illud antliæ oſculum ex aquâ emineat, cu<lb></lb>pæ ſcilicet labro incumbens, per quod em<lb></lb>bolus agitatur. </s> </p> <p type="margin"> <s><margin.target id="note75"></margin.target><emph type="italics"></emph>LXXV <lb></lb>Experimen<lb></lb>tum, quo ten<lb></lb>tatum est <lb></lb>Vacuum, & <lb></lb>quæſita aë<lb></lb>ris grauitas.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>His omnibus ritè paratis, ac reuolutâ ver<lb></lb>ſatili claue, vt pateret exitus aëri Recipien<lb></lb>tis (quod antequam imponeretur antliæ, fuit <lb></lb>ſtaterâ examinatum) agitata eſt aliquot ho<lb></lb>ras antlia; ac demum vbi præ nimiâ diffi<lb></lb>cultate extrahendi piſtillum, ceſſatum eſt, <lb></lb>clauſum eſt vas clauis conuolutione, ac refi<lb></lb>xum ab antliâ iterum expenſum eſt, & anti<lb></lb>quo ponderi deerant lotones 2 3/5, hoc eſt vn<lb></lb>cia (1 3/10). </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Et dubitabis adhuc, an aëri vas <pb xlink:href="018/01/175.jpg" pagenum="161"></pb>implenti tribuendum eſſet pondus; quod aë<lb></lb>re extracto defuit? </s> <s>tibi certè non adſtipu<lb></lb>larentur, quicunque liquorem, puta oleum <lb></lb>aut mel, ad libram vendunt; quæ enim in<lb></lb>ter vas plenum ac vacuum differentia pon<lb></lb>derum intercedit, eam liquori tribuendam <lb></lb>nemo negat. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Sed quid, ſi vas in aquâ expende<lb></lb><arrow.to.target n="note76"></arrow.to.target><lb></lb>rent nunc quidem melle, nunc verò aërę <lb></lb>plenum? </s> <s>an grauitatum differentiam itą <lb></lb>melli tribueres, vt velles pro eâ pretium ſol<lb></lb>uere? </s> </p> <p type="margin"> <s><margin.target id="note76"></margin.target><emph type="italics"></emph>LXXVI <lb></lb>Ex differen<lb></lb>tia <expan abbr="põderum">ponderum</expan> <lb></lb>vaſis pleni, <lb></lb>& vacui, <lb></lb><expan abbr="nõ">non</expan> probatur <lb></lb>quæſita aë<lb></lb>ris grauitas<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Minimè omnium: quia præter <lb></lb>mellis pondus ſublatum, etiam de vaſis gra<lb></lb>uitate non parùm demeret incluſi aëris le<lb></lb>uitas. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Quid ni igitur vaſis grauitati de<lb></lb>tractum pariter aſſeras ab incluſo aëre ma<lb></lb>ximè raro, ac proinde longè leuiore, quàm <lb></lb>aër iſte communis? </s> <s>Ex quo illud vnum con<lb></lb>ficitur, quod vltro do, aërem ſcilicet noſtrum <lb></lb>futurum grauem, ſi phialæ incluſus tranſ<lb></lb>ferretur in aërem ratiſsimum Recipientis, & <lb></lb>in eodem medio eſſet æquipondium, quo <lb></lb>aëris communis grauitas exploraretur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Ex Ariſtotelis Vacuum proſcribentis <lb></lb>officinâ iſthæc depromere oportet; & quan<lb></lb>doquidem negari non poteſt aërem vi antliæ <pb xlink:href="018/01/176.jpg" pagenum="162"></pb>extractum ſpatia reliquiſſe, in quæ nullum <lb></lb>corpus extrinſecùs aduocatum ſuccederę <lb></lb>queat, mauultis aliquid aëris contumaciſsi<lb></lb>mi, qui modò minorem modò maiorem oc<lb></lb>cupet locum, violentâ ratiocinatione in va<lb></lb>ſe concludere, quàm Vacuum, quod ſponte <lb></lb>menti occurrit, admittere, vobisque inqui<lb></lb>rendæ veritatis viam obſtruitis. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Non opus eſt corpora amouere, <lb></lb><arrow.to.target n="note77"></arrow.to.target><lb></lb>vt progrediatur Philoſophia in Vacuo. </s> <s>Mi<lb></lb>hi ſanè nullus relinquitur ambigendi locus, <lb></lb>an aere per vim rariſsimo Recipiens implea<lb></lb>tur; aperto enim refixi ab antliâ vaſis epiſto<lb></lb>mio, tantâ vi externus aër irrumpebat iņ <lb></lb>vas, vt illud hominem è regione ſtantem ad <lb></lb>ſe raperet: Vacuo autem, quod, præter cor<lb></lb>pus aptum continere, nil addit niſi corporis <lb></lb>contenti negationem, nullam attrahendi fa<lb></lb>cultatem phyſicam concedo. </s> <s>Sed nequę <lb></lb>aërem externum ſponte irrupiſſe cenſeo, vt <lb></lb>ſuppleret Vacuum; palàm enim aërem at<lb></lb>trahi deprehendit non-nemo, qui apertum <lb></lb>os ſuum ſatis eminus admouit, & confeſtim <lb></lb>deficiente ſpiritu manibus ſignum; vt ſę <lb></lb>amouerent, dedit, ipſe ad diſcedendum <lb></lb>impotens factus. </s> <s>Nec differebitur alius, cui <lb></lb>digitum admouenti cutem cum carne pænè <lb></lb>abſtraxit, non negatio corporis, ſed vis aëris <pb xlink:href="018/01/177.jpg" pagenum="163"></pb>ad ingenitam minoris raritatis menſuram̨ <lb></lb>ſeſe reſtituentis. </s> <s>Ne quod autem ſupereſſe <lb></lb>de veritate dubium poſſit, ipſe ſe aër prodi<lb></lb>dit, vbi refixum ab antliâ vas optimè clau<lb></lb>ſum immerſum fuit collo tenus in aquam <lb></lb>puriſsimam, & conuolutâ denuo claue ver<lb></lb>ſatili reſeratum; magno ſiquidem impetu <lb></lb>atque tumultu, ebullientis aquæ inſtar, vel <lb></lb>potiùs fontis copioſiſſimi, irrumpebat aqua <lb></lb>in vas per collum (non tamen ſinè bullis at<lb></lb>què copiosâ ſpumâ) illudque paulatim ad <lb></lb>ſummum vſque repleuit. </s> <s>Nunquam tamen <lb></lb>id aſſequi potuerunt, vt omnem prorſus aë<lb></lb>rem excluſum viderent; nam cum in expe<lb></lb>rimentum adhibitum primùm fuiſſet vas <lb></lb>27 menſurarum capax, non ſuxit aquæ men<lb></lb>ſuras niſi 26 3/4: cumque iterum minori vaſe <lb></lb>20 circiter menſurarum capace idem tentaſ<lb></lb>ſent, adeò repletum fuit, vt vix ſpatium, <lb></lb>quod auellana nux repleret, remanſerit aquâ <lb></lb>vacuum, quod ſpatium aër replebat in ſphæ<lb></lb>rulam conglobatus, qui & ad aquæ motum <lb></lb>hùc illùc manifeſtè diſcurrebat. </s> <s>Et quamuis <lb></lb>hinc ſpes facta eſſet, adhibito minore Reci<lb></lb>piente, omnem prorsus aërem extrahendi, <lb></lb>rem tamen eò deducere nunquam potue<lb></lb>runt. </s> </p> <p type="margin"> <s><margin.target id="note77"></margin.target><emph type="italics"></emph>LXXVII <lb></lb>Experimen<lb></lb>tum probat <lb></lb>non dari Va <lb></lb>cuum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Nullus dubitabam, quin contin<pb xlink:href="018/01/178.jpg" pagenum="164"></pb><arrow.to.target n="note78"></arrow.to.target><lb></lb>geret in minori Recipiente minus quoque <lb></lb><expan abbr="aẽris">aëris</expan> relinqui; quia, cùm quælibet aëris par<lb></lb>ticula certos habeat raritatis terminos, quos <lb></lb>nequit tranſilire, patet paucioribus particulis <lb></lb>ad eam raritatem adductis impleri ſpatium <lb></lb>minus, pluribus verò ſpatium maius. </s> <s>Hinc <lb></lb>eſt longiori tempore opus eſſe ad extrahen<lb></lb>dum aërem ex maiore vaſe quàm ex minore, <lb></lb>non ſecundùm Rationem capacitatis eorum, <lb></lb>quaſi ſemper æquales particulas antlia extra<lb></lb>heret, ſed ſpectatâ raritate minore, quam, cæ<lb></lb>teris paribus, in vaſe maiore ſuſcipiunt. </s> <s>Po<lb></lb>namus enim, exempli gratiâ, <expan abbr="aērem">aerrem</expan> ex di<lb></lb>ſtractione extendi poſſe ad ſpatium centu<lb></lb>plò maius, ac naturaliter occupet, & antliam <lb></lb>primo ductu extrahere quatuor digitos cu<lb></lb>bicos aëris: hi autem ſint pars milleſima ca<lb></lb>pacitatis vaſis: igitur poſt primum antliæ du<lb></lb>ctum illa pars milleſima ſpatij diſtribuitur <lb></lb>inter reſiduas aëris partes 999: poſt ſecun<lb></lb>dum ductum duæ ſpatij partes milleſimæ <lb></lb>inter seliquas 998 vnâ cum aliquâ aëris ap<lb></lb>pendice; quia ſecundo ductu non extrahitur <lb></lb>vna milleſima integra totius primi aëris, ſed <lb></lb>aliquid minus, ſcilicet (999/1000) vnius milleſimæ; <lb></lb>& ſic deinceps, donec demùm decem partes <lb></lb>aëris ab initio in vaſe exiſtentis, aſſumptâ <lb></lb>centuplâ raritate, impleant totum ſpatium. <pb xlink:href="018/01/179.jpg" pagenum="165"></pb>Quare cum magis ſemper ac magis à natu<lb></lb>rali ſtatu aër recedat, nil mirum ſi ſemper <lb></lb>extrahendi difficultas augeatur; quia æquale <lb></lb>incrementum raritatis ſemper paucioribus <lb></lb>partibus communicatum maiorem ſingulis <lb></lb>infert violentiam. </s> <s>Ex quo patet ad eam ex<lb></lb>trahendi difficultatem citiùs perueniri in va<lb></lb>ſe minori, quia ſingulæ aëris particulæ ſin<lb></lb>gulis antliæ ductibus plus diſtrahuntur, quàm <lb></lb>in vaſe maiori: nam ſi quatuor digiti ſint <lb></lb>ſolùm pars vaſis centeſima, primo ductu <lb></lb>partes 99 aëris debent inter ſe diſtribuerę <lb></lb>quatuor digitos ſpatij, quod ſpatium in vaſe <lb></lb>ampliore diſtribuebatur inter partes 999. <lb></lb>Hæc autem maior violentia, quam patitur <lb></lb>aër maximè rarus, in cauſâ eſt, cur primùm <lb></lb>tanto impetu irrumpat aqua, & poſtmodum <lb></lb>paulatim aſcendat; quò enim magis à natu<lb></lb>rali ſtatu remouetur aër, ſicut vim vlterio<lb></lb>rem inferenti contumaciùs reſiſtit, ita maio<lb></lb>re impetu reſtituit ſeſe, & aquæ reſiſtentiam <lb></lb>faciliùs vincit, cum maximè aqua ad mino<lb></lb>rem altitudinem euehatur; at vbi aqua adhuc <lb></lb>altiùs eleuanda eſt, atque aër à minori rari<lb></lb>tate violentâ recedit, & hic ſegniùs ſeſe con<lb></lb>trahit, & illa validiùs reſiſtit, ac proinde len<lb></lb>tior quoque eſt motus aquæ paulatim aſcen<lb></lb>dentis, & vas replentis. <pb xlink:href="018/01/180.jpg" pagenum="166"></pb><arrow.to.target n="note79"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note78"></margin.target><emph type="italics"></emph>LXXVIII <lb></lb>Indicatur <lb></lb>cauſa eo<lb></lb>rum, quæ in <lb></lb>allato expe<lb></lb>rimento con <lb></lb>tingunt.<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note79"></margin.target><emph type="italics"></emph>LXXIX <lb></lb>Aquæ tu<lb></lb>multuantis <lb></lb>cauſa expli<lb></lb>catur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Sed quid illud eſt, quod tantum <lb></lb>aſcendentis aquæ tumultum, bullas, atque <lb></lb>ſpumam excitat? </s> <s>An quia colli anguſtias <lb></lb>prætergreſſa aqua à plurimis aëris particulis <lb></lb>totius vaſis latitudinem occupantibus quaſi <lb></lb>in fruſta diſcerpitur, dum ſingulæ aliquid <lb></lb>liquoris ad ſe rapere conantur? </s> <s>An verò quia <lb></lb>tanto impetu ſeſe contrahit aër, vt. </s> <s>ſpiritus <lb></lb>aquæ admiſti cogantur ita rareſcere, vt in<lb></lb>termiſti aqueis particulis & bullas & ſpumam <lb></lb>creent? </s> <s>An veròquia aër ipſe non planè ho<lb></lb>mogeneum corpus eſt, ſed alias habet par<lb></lb>tes alijs ad raritatem proniores, atque adeò <lb></lb>inæquali impetu attractæ aqueæ particulæ <lb></lb>diſtrahuntur, atque tumultum excitare vi<lb></lb>dentur? </s> <s>Quàm varias autem corporum om<lb></lb>nium expirationes aër excipiat, atque inui<lb></lb>cem permiſceat, nemo eſt Philoſophus, qui <lb></lb>ignoret; & argumento eſt ipſa naturalis re<lb></lb>ſpirandi facultas, quæ licet aërem promiſcuè <lb></lb>attrahat in pulmones, minùs tamen profi<lb></lb>cuum expiratione reijcit, retentis vtiliori<lb></lb>bus particulis, quas cum ſanguine commi<lb></lb>ſceat, vt per arteriam venoſam in ſiniſtrum <lb></lb>cordis ventriculum deſcendentes elaboren<lb></lb>tur in ſpiritus vitales primùm, ac deinde ani<lb></lb>males. </s> <s>Quod ſi quis in cubiculo eodem diu<lb></lb>tiùs maneat, neque liceat aut libeat apertis <pb xlink:href="018/01/181.jpg" pagenum="167"></pb>feneſtris nouum aërem alijs vtilibus ſpiritibus <lb></lb>imbutum excipere, ſatis experitur, quantum <lb></lb>aërem inter & aërem interſit. </s> <s>Hinc vix poſ<lb></lb>ſum aliquando non ſubridere, cum diuerſa<lb></lb>rum gentium mores aut corporis habitum <lb></lb>viribus è cælo dimiſſis tribui audio ab ali<lb></lb>quibus, qui vbi caloris aut frigoris mentio<lb></lb>nem fecerint, illicò propoſitæ quæſtioni ſe <lb></lb>feciſſe ſatis exiſtimant. </s> <s>Cauſa tamen iņ <lb></lb>promptu eſt, cum ex vitalium atque anima<lb></lb>lium ſpirituum diuerſitate alia atque alia cor<lb></lb>poris habitudo, ingenium, mores profici<lb></lb>ſcantur; ſpiritibus autem fabricandis noņ <lb></lb>vltimo loco inſeruit aër, quem inſpiramus; <lb></lb>hic verò pro regionum varietate alias atque <lb></lb>alias recipit ex tellure expirationes. </s> <s>Quarę <lb></lb>non facilè mihi perſuadere poſſum vas ali<lb></lb>quod omninò homogeneis aëris particulis <lb></lb>impleri; atque adeò, ſi per vim rareſcant, <lb></lb>inæqualiter etiam eas rareſcere, atque inæ<lb></lb>qualem ſubire violentiam oportet: & quod <lb></lb>hinc ſequitur, inæquali impetu ſeſe poſtmo<lb></lb>dum contrahant, neceſſe eſt. </s> </p> <p type="main"> <s> <arrow.to.target n="note80"></arrow.to.target> </s> </p> <p type="margin"> <s><margin.target id="note80"></margin.target><emph type="italics"></emph>LXXX <lb></lb>Eiuſdem̨ <lb></lb>experimenti <lb></lb>extenſio: & <lb></lb>eorum, quæ <lb></lb>accidunt, <lb></lb>cauſæ indi<lb></lb>cantur bre<lb></lb>uiter.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Huic inæquali particularum rari<lb></lb>tati ego pariter plurimum tribuendum cen<lb></lb>ſeo; cum enim vas Recipiens primùm aquâ <lb></lb>repletum fuerit, & antliæ impoſitum, faci<lb></lb>is erat initio antliæ agitatio, ſed demum eò <pb xlink:href="018/01/182.jpg" pagenum="168"></pb> venit difficultas extrahendi embolum, vt <lb></lb>opus fuerit ceſſare, quamuis non omnis a qua <lb></lb>exhauſta fuiſſet; id ſcilicet nunquam potuit <lb></lb>obtineri. </s> <s>Refixo autem ab antliâ vaſe, & re<lb></lb>ſerato epiſtomio in aquâ mundiſſimâ, hæc <lb></lb>vt prius aſcendebat, ſed excitatâ copioſiore <lb></lb>ſpumâ & pluribus bullis, ac quando ſolo aë<lb></lb>re vas fuerat repletum: id quod contigiſſe <lb></lb>exiſtimo, quia maior eſt inæqualitas raritatis <lb></lb>in partibus illis partim aqueis, partim ex aquâ <lb></lb>eductis. </s> <s>Nam cum primùm aqua extrahi<lb></lb>tur, ſeparantur ab illâ ſpiritus aliqui & parti<lb></lb>culæ, quæ facilè expirarent, & ſuprema va<lb></lb>ſis ſpatia occupant; deinde etiam partes <lb></lb>aqueæ minùs contumaces rareſcunt, inter <lb></lb>quas aliqua datur inæqualitas: ſicut enim <lb></lb>aqua igni appoſita non tota ſtatim in vapo<lb></lb>res ſoluitur, ſed aliæ præ alijs particulæ faci<lb></lb>liùs ſoluuntur, ita vbi per diſtractionem ſol<lb></lb>ui debet carum compages, aliæ ſe exhibent <lb></lb>præ alijs contumaces ad rareſcendum. </s> <s>Fieri <lb></lb>autem eam, quam dixi ſpirituum ſepara<lb></lb>tionem ex eo conſtat, quod poſtmodum vas <lb></lb>totum aquâ repleri nequit, partes enim va<lb></lb>ſis ſupremas ſpiritus illi occupant. </s> <s>Immo <lb></lb>cùm per apertum epiſtomium immiſſus <lb></lb>fuiſſet copioſus fumus, hic quidem per a<lb></lb>quam aſcendebat, ſed eius ſuperficiei in<pb xlink:href="018/01/183.jpg" pagenum="169"></pb>cumbens ſuprema vaſis ſpatia non petebat, <lb></lb>niſi cum demum calido linteo obuolutum <lb></lb>fuiſſet vas: tunc enim vi caloris faciliùs rare<lb></lb>ſcebat fumus, quàm ſpiritus illi per vim ad<lb></lb>huc rari; ac proinde cum fumus ampliorą <lb></lb>ſpatia exigens comprimeret vicinum ſpiri<lb></lb>tum, qui propterea à violento ſtatu recede<lb></lb>bat, tunc poterat fumus in ſuperiora ſpatią <lb></lb>leuior factus aſcendere. </s> </p> <p type="main"> <s>Sed & illud hanc ſpirituum ſeu halituum <lb></lb>ſeparationem oſtendit; quod non nemo ex<lb></lb>cogitauit, vt citiùs, quando opus eſſet, ex<lb></lb>perimentum inſtitueret, & vitreum vas Re<lb></lb>cipiens exhauriret. </s> <s>Ingens vas æneum plu<lb></lb>rium vrnarum capax conſtructum fuit opti<lb></lb>mè clauſum, præterquam in imo, vbi epi<lb></lb>ſtomium cum claue verſatili habebat, vt poſ<lb></lb>ſet antliæ imponi, & in ſummo pariter tu<lb></lb>bus extabat claue verſatili tranſuersâ accu<lb></lb>ratiſsimè clauſus, ac ſummo tubo imponi <lb></lb>poterat Recipiens vitreum. </s> <s>Et vt omnis ſu<lb></lb>ſpicio aëris ſe furtim inſinuantis auerteretur, <lb></lb>tubum circumplectebatur vaſculum aquâ <lb></lb>repletum, ne aut per clauis verſatilis rimulas, <lb></lb>aut per tubi oſculum ſe aër inſinuaret. </s> <s>Ænei <lb></lb>vaſis aquâ pleni epiſtomio infimo applicita <lb></lb>eſt antlia, & aliquot horas agitata, ita vt <lb></lb>cenſeretur aquâ pænè vacuum; tum clauſo <pb xlink:href="018/01/184.jpg" pagenum="170"></pb>epiſtomio reſeruatum eſt vas ad tempus ex<lb></lb>perimenti inſtituendi. </s> <s>Vbi igitur rem per<lb></lb>ficere oportuit, impoſitum eſt ſuperiori tubo <lb></lb>vas vitreum Recipiens aquâ plenum, & re<lb></lb>uolutâ claue verſatili, quæ tubum vaſis ænei <lb></lb>claudebat, apertoque Recipientis epiſtomio, <lb></lb>cæpit illicò aqua Recipientis delabi in vas <lb></lb>æneum, & ſimul ex vaſe æneo aſcendebant <lb></lb>bullæ infinitæ ac radii quidam vnionum in<lb></lb>ſtar lucidiſsimi, & frequentiſsimi: nec ceſſa<lb></lb>uit hic aquæ & bullarum radiorumque con<lb></lb>flictus, quamdiu durauit aquæ in ſubiectum <lb></lb>vas æneum vel lapſus, vel attractio. </s> <s>Poſt <lb></lb>horam integram, cum nec dum tota exhau<lb></lb>ſta fuiſſet aqua, remotum fuit vas vitreum <lb></lb>Recipiens, eius epiſtomio priùs clauſo, & <lb></lb>aquæ puriſsimæ, vt aliàs, impoſitum; con<lb></lb>uolutâque denuò claue verſatili irrumpebat, <lb></lb>vt aliàs, aqua cum tumultu, & ſpumâ, non <lb></lb>tamen eâ copiâ, qua cùm per antliam extra<lb></lb>cta fuerat aqua ex Recipiente. </s> <s>Ex quibus <lb></lb>apertè conſtat in vaſe æneo ſpatium fuiſſę <lb></lb>occupatum à ſpiritibus ex aquâ eductis, qui <lb></lb>proinde patente exitu in vas vitreum Reci<lb></lb>piens erumpebant, cùm aqua ex Recipiente <lb></lb>in ſubiectum vas æneum tum attraheretur, <lb></lb>rum etiam fortè dilaberetur: quis enim dicat <lb></lb>id, quod aſcendebat fuiſſe Vacuum, nimi<pb xlink:href="018/01/185.jpg" pagenum="171"></pb>rum negationem? </s> <s>Quoniam verò Reci<lb></lb>pientis ſpatium ab aquâ deſcendente reli<lb></lb>ctum non ſolis ſpiritibus eductis ex aquâ Re<lb></lb>cipientis replebatur, ſed alijs præterea, qui ex <lb></lb>ſubiecto vaſe aſcenderant, quid mirum, ſi <lb></lb>ſinguli minorem violentiam in raritate paſ<lb></lb>ſi, minore quoquè impetu ſe contrahentes <lb></lb>minorem aquæ copiam demùm attrahe<lb></lb>rent? </s> </p> <p type="main"> <s>Quare nihil eſt in toto hoc experimento; <lb></lb>quod vel leuem inferat Vacui ſuſpicionem; <lb></lb>immò in oculos ſemper incurrit corpus, te<lb></lb>nue illud quidem ac rarum, à quo vaſis ſpa<lb></lb>tia occupantur. </s> <s>Hoc itaque experimento <lb></lb>non ſatis probari noſtri aëris grauitatem ab<lb></lb>ſolutè, mihi certiſsimum eſt; ſed illud vnum <lb></lb>ex inæquali Recipientis pondere antè ac poſt <lb></lb>aëris extractionem vi antliæ, confici poteſt, <lb></lb>quod non inficior, ſcilicet communem hunc <lb></lb>noſtrum aërem in aëre alio magis raro gra<lb></lb>uitare poſſe: Id autem nil facit ad quæſtio<lb></lb>nem, quam heri examinandam ſuſcepimus, <lb></lb><emph type="italics"></emph>An tellus machinarum ope translata innataret <lb></lb>aquis in partem vnam delapſis.<emph.end type="italics"></emph.end></s> <s> Cum enim̨ <lb></lb>aquæ & cæterorum corporum grauitates <lb></lb>nobis tantùm innoteſcant cum hoc commu<lb></lb>ni aëre comparatæ, quid confugiendum eſt ad <lb></lb>aërem neſcio quem rariorem, quo caremus? </s> </p> <pb xlink:href="018/01/186.jpg" pagenum="172"></pb> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Quam igitur excogitaſti viam, <lb></lb>qua ad propoſitum quæſtionis terminum <lb></lb>euadamus? </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Ex ijs, quæ minimum habent du<lb></lb>bitationis, ad ignota progrediendum cenſeo. </s> <s><lb></lb>Illud autem carere videtur omni dubitatio<lb></lb>ne, quod ſi aqua in aëre grauis eſt vt 5 1/3, aër </s> </p> <p type="main"> <s><arrow.to.target n="note81"></arrow.to.target><lb></lb>viciſsim in aquâ leuis eſt vt 5 1/3. Nam, vt <lb></lb>herì ratiocinabamur, vas cupreum pedalę <lb></lb>lib. 80. nihil grauitat in aquâ, ſi aëre implea<lb></lb>tur, quia ſcilicet aëris incluſi leuitas elidit <lb></lb>eam cupri grauitatem, quam aqua non tol<lb></lb>lit: Cum enim cuprum amittat ſolùm lib. <lb></lb>(9 1/71) ratione aquæ ſecundùm molem æqualis, <lb></lb>reliquum pondus decedit ratione leuitatis aë<lb></lb>ris: illud autem eſt pondus aquæ ſecundùm <lb></lb>molem aëri æqualis. </s> <s>Quarè ſi æolipila can<lb></lb>dens amiſit 4 grana ponderis, licebit argue<lb></lb>re aërem ignitum in aëre communi leuitare <lb></lb>vt 4. Item quia in eodem aëre communi <lb></lb>aqua æolipilam implens grauior eſt granis <lb></lb>5425, ſacomate ſemper in eodem medio exi<lb></lb>ſtente, colligere poſſumus Rationem ali<lb></lb>quam inter aquam & aërem ignitum, mu<lb></lb>tuantes ab Algebrâ numeros defectiuos. </s> </p> <p type="margin"> <s><margin.target id="note81"></margin.target><emph type="italics"></emph>LXXXI <lb></lb>Quomodo <lb></lb>inueniatur <lb></lb>quanta ſit <lb></lb>aëris igniti <lb></lb>leuitas iņ <lb></lb>aqua.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Eſt ſiquidem in aëre communi æqualium <lb></lb>molium grauitas ſimili granorum menſurâ <lb></lb>deprehenſa, Aquæ quidem ſaltem graną <pb xlink:href="018/01/187.jpg" pagenum="173"></pb>5425, Aëris communis grauitas grana o, <lb></lb>Aëris igniti grauitas grana o——4, quoniam <lb></lb>aër ignitus non grauitat ſed leuitat, & com<lb></lb>munis non grauitat aut leuitat. </s> <s>In noſtro <lb></lb>igitur aëre communi aqua ad aërem ignitum <lb></lb>eſt in pondere vt 5425 ado——4. Et quo<lb></lb>niam aquæ grauitatem in aëre communi po<lb></lb>nimus 5 1/3, fiat vt 5425 ad o——4, ita 5 1/3 ad <lb></lb>o——(64/16275). Eſt ergo aëris igniti grauitas in <lb></lb>aëre communi o——(64/16275). Atqui aëris com<lb></lb>munis grauitas in aquâ eſt o——5 1/3, igitur ſi <lb></lb>iungantur hæ differentiæ grauitatum, erit <lb></lb>o——(5 5489/16275) grauitas aëris igniti in aquâ, hoc <lb></lb>eſt leuitas. </s> </p> <p type="main"> <s>Quod verò hac methodo ritè inueſtigata <lb></lb>ſit leuitas aeris igniti in aquâ, conſtabit hoc <lb></lb>exemplo. </s> <s>Grauitas Mercurii eſt 71 1/2, aquæ <lb></lb>5 1/3, olei 4 3/4: igitur grauitas olei in aquâ eſt <lb></lb>o——(7/12), & grauitas aquæ in Mercurio eſt <lb></lb>o——(66 2/12). & ſi differentiæ iſtæ iungantur, <lb></lb>erit grauitas olei in mercurio o——(66 9/12); quæ <lb></lb>eadem eſt cum illâ, qua immediatè oleum <lb></lb>cum mercurio comparatur, & eſt 4 3/4 —— <lb></lb>71 1/2. Si igitur aeris igniti grauitas in aërę <lb></lb>communi, iungatur aëris communis graui<lb></lb>tati in aquâ, ritè habetur aëris igniti grauitas <pb xlink:href="018/01/188.jpg" pagenum="174"></pb>in aquâ. </s> <s>Hanc autem grauitatem defecti<lb></lb>uam vocemus leuitatem, nec ab hac vocę <lb></lb>abhorreamus. </s> </p> <p type="main"> <s>Et ſanè vſus iſte numerorum defectiuo<lb></lb><arrow.to.target n="note82"></arrow.to.target><lb></lb>rum ad leuitatem exprimendam mihi vide<lb></lb>tur aptiſſimus, ita vt leuiſſimo negotio con<lb></lb>ſtet, vtrùm oblata moles compoſita leuior <lb></lb>ſit, an grauior quàm aqua. </s> <s>Si enim datâ Ra<lb></lb>tione molis corporum totam molem com<lb></lb>ponentium, & datâ Ratione grauitatis ſin<lb></lb>gulorum aut leuitatis ſpecificæ intrà aquam, <lb></lb>ducatur numerus partium in numerum, quo <lb></lb>leuitas, aut grauitas deſignatur, horum ſum<lb></lb>ma ſi defectiua ſit, molem illam aquâ leuio<lb></lb>rem indicabit. </s> <s>Quæramus ex. gr. an dolium <lb></lb>ferreis circulis firmatum, ac vino plenum, <lb></lb>ſit leuius aquâ, nec ne. </s> <s>Et primùm quarum <lb></lb>partium ferrum eſt 3, earum ſit lignum 400, <lb></lb>& vinum 100000. Deinde ſpecifica in aëre <lb></lb>grauitas ferri ſit 42, ligni 4. vini 5 1/4 ad a<lb></lb>quam 5 1/3. Eſt igitur grauitas ſpecifica ferri <lb></lb>in aquâ + 36 2/3, quæ per 3 numerum partium <lb></lb>ducta dat totam ferri grauitatem + 110. Gra<lb></lb>uitas ſpecifica ligni in aquâ, ſeu potius leui<lb></lb>tas eſt——1 1/3, quæ per 400 numerum par<lb></lb>tium ducta dat totam ligni leuitatem—— <lb></lb>533 1/3. Demum ſpecifica leuitas vini in aquâ <pb xlink:href="018/01/189.jpg" pagenum="175"></pb>eſt——(1/12), quæ per numerum partium̨ <lb></lb>100000 ducta dat totam vini leuitatem—— <lb></lb>8333 1/3. Si igitur inuentæ ſingularum par<lb></lb>tium grauitates ſeu leuitates in ſummam re<lb></lb>digantur, erit ſumma——8756 2/3 defectiuą <lb></lb>indicans totius dolii leuitatem in aquâ, ſeu <lb></lb>differentiam, qua aquæ grauitas excedit dolii <lb></lb>grauitatem in aëre. </s> <s>Nam ſi aquæ grauitas <lb></lb>5 1/3 ducatur per 3 fit 16, ducta per 400 dat <lb></lb>2133 1/3, ducta per 100000 dat 533333 1/3; quæ <lb></lb>in ſummam redactæ dant totam aquæ graui<lb></lb>tatem 535482 2/3, à qua deficit dolii grauitas <lb></lb>particulis 8756 2/3. Id quod conſtabit, ſi par<lb></lb>tium dolii grauitatem in aëre examinemus; <lb></lb>ligni enim partes 400 per ſpecificam graui<lb></lb>tatem 4 ductæ dant abſolutam ligni grauita<lb></lb>tem 1600; iterum partes 100000 vini per gra<lb></lb>uitatem ſpecificam 5 1/4 ductæ dant abſolutam <lb></lb>vini grauitatem 525000: demum partes 3 <lb></lb>ferri per 42 ductæ dant totam grauitatem <lb></lb>ferri 126: quæ ſi in ſummam redigantur, erit <lb></lb>tota dolii grauitas in aere 526726. Hæc au<lb></lb>tem grauitas ſubducta ex grauitate aquæ æ<lb></lb>qualis relinquit e<expan abbr="ãdem">andem</expan> <expan abbr="differentiã——8756">differentia ——8756</expan> 2/3</s> </p> <pb xlink:href="018/01/190.jpg" pagenum="176"></pb> <p type="margin"> <s><margin.target id="note82"></margin.target><emph type="italics"></emph>LXXXII <lb></lb>Inuenire an <lb></lb>moles com<lb></lb>poſita poſsit <lb></lb>innatare a<lb></lb>quæ nec ne, <lb></lb>abſque cal<lb></lb>culo aquæ <lb></lb>æqualis.<emph.end type="italics"></emph.end></s> </p> <p type="table"> <s>TABELLE WAR HIER</s> </p> <p type="main"> <s>Porrò ſpecificam dolii grauitatem in aëre <lb></lb>habemus, ſi abſolutam grauitatem 526726 <lb></lb>diuidamus per 100403 numerum partium, <lb></lb>& erit grauitas ſpecifica molis compoſitæ <pb xlink:href="018/01/191.jpg" pagenum="177"></pb>(5 246/1000): Vel ſi per eundem partium numerum <lb></lb>diuidatur leuitas abſoluta——8756 2/3, erit ſpe<lb></lb>cifica molis compoſitæ leuitas in aquâ (27/1000). <lb></lb>Quarè ſi inter nos conueniat, quota portio <lb></lb>terreni huius globi incluſis ignibus tribuen<lb></lb>da ſit, quota aëri cæterisque halitibus aquâ le<lb></lb>uioribus, facilè innoteſcet, vtrùm leuitas vin<lb></lb>cat grauitatem, ducto partium numero per <lb></lb>leuitatis aut grauitatis denominatorem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Quod quidem ſpectat ad ingen<lb></lb>tem illam ignium cauernam, qui terræ cen<lb></lb>trum circumobſident, memini me ab acu<lb></lb>tiſsimo æquè ac diligentiſsimo ſydereorum <lb></lb>arcanorum ſcrutatore Gottifredo Wendeli<lb></lb><arrow.to.target n="note83"></arrow.to.target><lb></lb>no aliquid planè ſingulare accepiſſe, quod <lb></lb>ſummoperè placuit. </s> <s>Hic terræ ſemidiame<lb></lb>trum in partes 100 tribuens, cauernæ æſtuan<lb></lb>tis ſemidiametro partes 63 concedebat, reli<lb></lb>quas 37 denſitati cruſtæ huius extimæ; vnde <lb></lb>fit ignem illum eſſe quartam totius globi <lb></lb>partem (cubus enim ex 63 eſt ſubquadru<lb></lb>plus cubi ex 100) cum ſit globus ille igneus <lb></lb>ad totum globum in triplicatâ ratione dia<lb></lb>metrorum. </s> <s>Ne verò id ab ipſo temerè ex<lb></lb>cogitatum videretur, addebat, præter pro<lb></lb>babiles coniecturas & rationes non paucas, <pb xlink:href="018/01/192.jpg" pagenum="178"></pb>ex aſſiduâ plurimorum annorum obſeruatio<lb></lb>ne id ſibi innotuiſſe, cum videret Lunam <lb></lb>ad intimam, hoc eſt concauam, huius cru<lb></lb>ſtæ ſuperficiem ita motus ſuos temperate, vt <lb></lb>creet admirabilem illam librationem, quæ <lb></lb>torquet Aſtronomico-Phyſicorum ingenia: <lb></lb>cuius motûs hypotheſes nondum, quod <lb></lb>ſciam, publici iuris fecit. <lb></lb><arrow.to.target n="note84"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note83"></margin.target><emph type="italics"></emph>LXXXIII <lb></lb>Ignis ſub<lb></lb>terraneus <lb></lb>est quarta <lb></lb>pars globi <lb></lb>terreni ex <lb></lb>ſententią <lb></lb>VVendeli<lb></lb>ni<emph.end type="italics"></emph.end></s> </p> <p type="margin"> <s><margin.target id="note84"></margin.target><emph type="italics"></emph>LXXXIV <lb></lb>Tenteatur <lb></lb>innestigatio <lb></lb>leuitatis i<lb></lb>gnis.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Nollem tamen, Guldine, eam tantùm̨ <lb></lb>igni leuitatem tribueres, quam aëri ignito <lb></lb>intrà Æolipilam candentem conuenire ob<lb></lb>ſeruaui: longè enim maiore leuitate prædi<lb></lb>tam ignis ſubſtantiam ſtatuere æquum vide<lb></lb>tur, quàm ſit leuitas aëris per vim à calorę <lb></lb>extrinſecùs adueniente rarefacti. </s> <s>Nam cum <lb></lb>aquæ intrà Æolipilam exſuctæ pondus fue<lb></lb>rit granorum 5425, facilè reperiemus illius <lb></lb>ſoliditatem; in pede ſiquidem cubico ſunt <lb></lb>digiti ſolidi 4096: Et quia pes cubicus aquæ <lb></lb>habet in pondere lib. Rom. 80, quarum ſin<lb></lb>gulæ ſunt vnc. </s> <s>12, hoc eſt gran. 6912, to<lb></lb>tius pedis cubici aquæ pondus eſt gran. <lb></lb>552960. Si igitur grana 552960 dant digi<lb></lb>tos ſolidos 4096, grana 5425 dabunt di<lb></lb>gitos ſolidos (40 5/27). Quis autem ſubſtantiæ <lb></lb>ignis habenti in mole 40 & eo amplius digi<lb></lb>tos ſolidos, non facilè tribuat longiſsimè <pb xlink:href="018/01/193.jpg" pagenum="179"></pb>maiorem leuitatem in aëre communi quàm <lb></lb>vt obſiſtat quatuor granorum grauitati? </s> <s>Ignis <lb></lb>enim naturam in motum maximè pronam <lb></lb>ſi attentiùs conſideremus, nihilquè igne le<lb></lb>uius nobis innotuiſſe animaduertamus, cum <lb></lb>in tertiâ potiſsimum & ſupremâ aëris regio<lb></lb>ne ignitæ impreſsiones Meteorologicæ ac<lb></lb>cendantur, nemo facilè negauerit ignis leui<lb></lb>tatem ſaltem tantam eſſe, quæ vincat me<lb></lb>dullæ ſambuceæ grauitatem, datâ molis æ<lb></lb>qualitate; nihil quippe medullâ ſambuceâ <lb></lb>leuius, hoc eſt minùs graue, potui adhuc <lb></lb>deprehendere. </s> <s>Medullam enim ſambuci <lb></lb>vtcunque viridis cylindricam expendi, cuius <lb></lb>altitudo erat digitorum 2 2/3 & baſis diameter <lb></lb>digiti 1/4, fuitque pondus gran. 3: æqualis au<lb></lb>tem cylindri cerei pondus fuit gran. 72. At<lb></lb>qui ſi ignis tanta ſit leuitas ſurſum, quantą <lb></lb>eſt medullæ ſambuceæ grauitas deorſum̨, <lb></lb>multò maior eſt ignis leuitas quàm aeris igni<lb></lb>ti in Æolipilâ. </s> <s>Nam quia baſis diameter <lb></lb>eſt digiti 1/4, & altitudo dig. </s> <s>2 2/3, ſi diametri <lb></lb>quadratum 1/16 ducatur in altitudinem <gap></gap>/3, na<lb></lb>betur parallelepipedum digiti ſolidi 1/6: hoc <lb></lb>autem parallelepipedum eſt ad cylindrum <lb></lb>in Ratione baſium, quadratum autem dia<lb></lb>metri ad circulum habet maiorem rationem <pb xlink:href="018/01/194.jpg" pagenum="180"></pb>quàm 14 ad 11, minorem verò quàm 284 <lb></lb>ad 223: igitur vt 14 ad 11 ita 1/6 ad (11/14) maio<lb></lb>rem vero; & vt 284 ad 223, ita 1/6 ad (223/1704) mi<lb></lb>norem vero. </s> <s>Inuentæ quantitates (11/14) & (223/1704) re<lb></lb>ducantur ad eandem denominationem, & <lb></lb>ſunt (78744.18732/143136), differentia autem eſt 12 parti<lb></lb>cularum; & ſumpto medio Arithmetico ſo<lb></lb>liditas cylindruli dati eſt (18738/143136), hoc eſt (3123/23856). Si <lb></lb>igitur medulla ſambucea, cuius ſoliditas eſt <lb></lb>dig. (3123/23856) habet pondus gran. 3, medullą, <lb></lb>cuius ſoliditas eſſet dig. (40 5/27), haberet pondus <lb></lb>gran. 920. Ignis itaque leuitas in aëre ſi tan<lb></lb>ta fuerit, quanta eſt medullæ ſambuceæ gra<lb></lb>uitas, erit gran.——920, quorum 5425 eſt <lb></lb>grauitas aquæ ſecundum molem æqualis. </s> <s><lb></lb>Ergo ſi aquæ grauitas in aëre 5425 dat ignis <lb></lb>in aëre leuitatem——920, aquæ grauitas 5 1/3 <lb></lb>dat ignis leuitatem——(4906/5425); quæ ſi addatur <lb></lb>leuitati aëris in aqua——5 1/3, erit leuitas ignis <lb></lb>in aquâ ſaltem——(6 258/1085). Et id quidem, Gul<lb></lb>dine, tuà methodo: quanquam ægerrimè <lb></lb>mihi perſuadeo tantulam leuitatem eſſe igni <lb></lb>tribuendam. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Vtinam non adeò vorax ignis eſſet, <lb></lb>& pateretur ſe vaſculo concludi: veſtram̨ <lb></lb>hanc litem momento dirimerem librà, quam <lb></lb>aliquando excogitaui ad examinandam cor-</s> </p> <pb xlink:href="018/01/195.jpg" pagenum="181"></pb> <p type="main"> <s><arrow.to.target n="note85"></arrow.to.target><lb></lb>porum leuitatem in mercurio. </s> <s>Tranſuerſa<lb></lb>ria duo EF, CD planè æqualia, bifariam di<lb></lb><figure id="id.018.01.195.1.jpg" xlink:href="018/01/195/1.jpg"></figure><lb></lb>uiſa in A & I, in<lb></lb>ſerui tigillo AB ita, <lb></lb>vt circà axiculos A <lb></lb>& I facilè verſatilia <lb></lb>eſſent, additâ lin<lb></lb>gulà, quæ æquili<lb></lb>brium indicaret. </s> <s><lb></lb>Extremitati C ſty<lb></lb>lum deorſum ver<lb></lb>gentem adieci, qui <lb></lb>ſubiectum corpus tangeret; & ex ſuperioris <lb></lb>iugi EF extremitate E, lanx H pendebat: <lb></lb>reliquæ extremitates FD filo iungebantur æ<lb></lb>quali interuallo AI, ne alterum iugum ſinè <lb></lb>altero moueretur; additumque eſt plumbi <lb></lb>momentum brachijs. </s> <s>AF & ID, vt fieret <lb></lb>æquilibrium cum lance H & ſtylo addito in <lb></lb>C; adeò vt iuga EF, CD ſemper inuicem & <lb></lb>horizonti parallela eſſent, niſi accepto ex<lb></lb>trinſecùs impetu remouerentur à paralle<lb></lb>liſmo. </s> </p> <p type="margin"> <s><margin.target id="note85"></margin.target><emph type="italics"></emph>LXXXV <lb></lb>Instrumen<lb></lb>tum, quo ex<lb></lb>aminari poſ<lb></lb>ſunt leuitaſ <lb></lb>tes. </s> <s>corpora <lb></lb>in medio <lb></lb>grauiore, & <lb></lb>media ipſa <lb></lb>comparari <lb></lb>ſecundùm̨ <lb></lb>grauitatem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Tum vaſculum KL ritè collocatum mer<lb></lb>curio implebam, & ſolidum, cuius exami<lb></lb>nanda erat leuitas, mercurio impoſitum ita <lb></lb>ſubijciebam ſtylo C, vt pondere in lance H <lb></lb>deorſum vrgente attolleretur F & D, ac proſ<pb xlink:href="018/01/196.jpg" pagenum="182"></pb>inde cum extremitate C deprimeretur ſoli<lb></lb>dum O intrà mercurium, cuius partes æqua<lb></lb>les moli immerſæ effluebant: atquè ita pon<lb></lb>dus in H temperabam, vt iuga EF, CD, ho<lb></lb>rizonti parallela conſiſterent, quando ſuper<lb></lb>ficies ſolidi immerſi vnicam cum circumfu<lb></lb>ſo mercurio ſuperficiem conſtituebant. </s> <s>Qua<lb></lb>re pondus in H grauitans æqualiter reſiſte<lb></lb>bat leuitati ſolidi ſursùm conantis in mercu<lb></lb>rio: cumque ex Archimede lib. de inſid. </s> <s><lb></lb>hum. </s> <s>prop. 6. conſtet ſolidum leuius humi<lb></lb>do immerſum tantâ vi ſurſum ferri, quantâ <lb></lb>humidum molem ſolido æqualem habens <lb></lb>grauius eſt ipſo ſolido, colligebam, quantò <lb></lb>grauior ſecundùm ſpeciem eſſet mercurius, <lb></lb>quàm immerſum ſolidum. </s> <s>Deinde idem̨ <lb></lb>ſolidum in aquâ expendebam vel eadem li<lb></lb>brâ, ſi in aquâ pariter leuitabat, vel librâ <lb></lb>communi, ſi grauius erat quàm aquâ. </s> <s>Col<lb></lb>lectis demùm in ſummam huiuſmodi pon<lb></lb>deribus ſeu differentijs grauitatum, ſi iņ <lb></lb>mercurio leuitans ſolidum grauitabat in aquâ, <lb></lb>ſiue ſubtracto minori pondere ex maiore, ſi <lb></lb>in vtroque leuitabat; ſumma vel reſiduum <lb></lb>dabat mihi exceſſum grauitatis mercurij ſu<lb></lb>pra grauitatem aquæ: alterutrius autem̨ <lb></lb>pondere cognito, reliqui pondus innoteſce<lb></lb>bat. </s> </p> <pb xlink:href="018/01/197.jpg" pagenum="183"></pb> <p type="main"> <s>Sic ſi ferri leuitatem in mercurio ex. </s> <s>gr. <lb></lb>deprehendebam æqualem drachmis 29 1/2 e<lb></lb>iuſdem autem ferri grauitas in aquâ erat dra<lb></lb>chm. </s> <s>36 2/3, arguebam ferrum medium eſſe <lb></lb>inter mercurium & aquam; adeòque addi<lb></lb>tis hiſce differentijs, nota erat differentia in<lb></lb>ter mercurium & aquam 66 1/6: quarè ponde<lb></lb>rato ferro in aëre & inuento drachm. </s> <s>42, a<lb></lb>qua reperitur 5 1/3, atque adeò mercurius 71 1/2. <lb></lb>Quod ſi ferri loco ſolidum ligneum vſurpa<lb></lb>bam, cuius leuitas in mercurio eſſet 67 1/2, le<lb></lb>uitas verò in aquâ 1 1/3; quia in vtroque leui<lb></lb>tabat, intelligebam aquæ grauitatem me<lb></lb>diam eſſe inter lignum & mercurium: qua<lb></lb>propter harum leuitatum differentia 66 1/6, vt <lb></lb>priùs, eſt differentia inter aquam & mercu<lb></lb>rium. </s> </p> <p type="main"> <s>Hac, inquam, librâ, quam tunc eum in <lb></lb>vſum excogitaui, ſi vaſculum igne plenum <lb></lb>& clauſum, ne auolet, dederitis, eius leuita<lb></lb>tem intrà aquam in vaſe KL explorabimus, <lb></lb>additâ, pro ut opus fuerit, vel demptâ ipſius <lb></lb>vaſculi intrà aquam grauitate vel leuitate. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Nolo me duriorem præbere iņ <lb></lb>extenuandâ ignis leuitate, quamuis aëris in <lb></lb>æolipilâ candenti leuitatem non adeò mul<lb></lb>tam deprehenderim. </s> <s>Vnam aliquam ſtatue <pb xlink:href="018/01/198.jpg" pagenum="184"></pb>probabilem, Merſenne, quæ tamen longiſ<lb></lb>ſimè abſit à tuâ illâ pluſquam millecuplâ Ra<lb></lb>tione, quam inter aeris & aquæ grauitates in<lb></lb>tercedere opinaris; non enim facilè acquie<lb></lb>ſcerem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Galilæo ſaltem poteris acquieſce<lb></lb>re aërem quadringenties tantùm aquâ leuio<lb></lb>rem ſtatuenti; ignis autem adhuc aëre le<lb></lb>uior eſt. </s> <s>Quid caput abnuentis in morem <lb></lb><arrow.to.target n="note86"></arrow.to.target><lb></lb>nutat? </s> <s>Hoc certè, quod addo, nemo æquus <lb></lb>iudex reijciat; quandoquidem probabiles <lb></lb>coniecturas perſequi neceſſe eſt, vbi ipſam <lb></lb>veritatem certò aſſequi non datur. </s> <s>Inter <lb></lb>grauia nihil adhuc nobis innocuit auro gra<lb></lb>uius, inter leuia nihil igne leuius: aqua & <lb></lb>aër medio loco conſiſtunt. </s> <s>Quamobrem <lb></lb>ſicut grauium grauitates in aere tanquam̨ <lb></lb>communi medio inuicem comparamus, ita <lb></lb>leuium leuitates in aquâ tanquam communi <lb></lb>medio conferri inuicem poſſe videntur. </s> <s>Hinc <lb></lb>ſi ponatur leuiſſimum corpus ita ſe habere <lb></lb>ad medium, vnde leuitas deſumitur, vt cor<lb></lb>pus grauiſſimum ſe habet ad medium, ex <lb></lb>quo grauitas incipit denominari, nihil ab<lb></lb>ſurdum ſtatuitur, & corporum motrices fa<lb></lb>cultates ſibi proportione reſpondent. </s> <s>Sicut <lb></lb>igitur in aere grauitas aquæ eſt partium 5 1/3, <lb></lb>quarum grauitas auri eſt 100, quidni parites <pb xlink:href="018/01/199.jpg" pagenum="185"></pb>quarum partium —— 5 1/3 conſtituiſti leuitatem <lb></lb>aëris in aquâ, earum——100 ſtatuas ignis <lb></lb>leuitatem in aquâ? </s> <s>Vide, quò demum ve<lb></lb>nerim, Guldine, vt tibi morem geram. </s> </p> <p type="margin"> <s><margin.target id="note86"></margin.target><emph type="italics"></emph>LXXXVI <lb></lb>Alia hypo<lb></lb>thesis de i<lb></lb>gnis leuita<lb></lb>te examina<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Iam planè videris paulò mitiùs <lb></lb>atque veriſimiliùs opinari. </s> <s>Et vt meam fa<lb></lb>cilitatem tibi probem, ſiquidem placuit <lb></lb>Wendelini ſententia quartam orbis huius <lb></lb>partem tribuens æſtuanti cauernæ ignium <lb></lb>plenæ, eam vltrò admitto, & ignis leuita<lb></lb>tem ad aquam aſſumo partium——100, qua<lb></lb>rum aëris leuitas eſt——5 1/3. Reliquis verò <lb></lb>tribus orbis huius quadrantibus quam conce<lb></lb>dis grauitatem? </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Si perpendantur omnia, fortaſsè <lb></lb>non deberent cenſeri grauiores argillâ. </s> <s>Pri<lb></lb>mùm quia aqua, quæ terræ faciem alluit <lb></lb>aëri finitima, ſerè tota demenda eſt ex pon<lb></lb>dere, cùm illa, ex hypotheſi initio conſtitutâ, <lb></lb>habeat rationem medij, in quo motus per<lb></lb>ficitur, & ad vnam partem confluxerit. </s> <s>De<lb></lb>inde quia aqua terræ venas permeans benè <lb></lb>multa eſt, & intrà aquam conſtituta nihil <lb></lb>addit ponderis. </s> <s>Præterea reliqua moles, quæ <lb></lb>demptâ aquâ ſupereſt, tam multum habet <lb></lb>aeris halituumque intrà aquam leuitantium, <lb></lb>vt plurimum elidant grauitatis metallorum <pb xlink:href="018/01/200.jpg" pagenum="186"></pb>ac marmorum. </s> <s>Quarè ſi tribus orbis qua<lb></lb>drantibus argillæ grauitas tribuatur, maxi<lb></lb>mè probabili coniecturâ vti videatur, qui ſi<gap></gap><lb></lb>opinetur. <lb></lb><arrow.to.target n="note87"></arrow.to.target></s> </p> <p type="margin"> <s><margin.target id="note87"></margin.target><emph type="italics"></emph>XXCVII <lb></lb>Globus ter<lb></lb>renus in ea <lb></lb>hypotheſi in <lb></lb>nataturus <lb></lb>aquæ vide<lb></lb>tur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Quoniam verò aquæ grauitas ad argillæ <lb></lb>grauitatem in aëre, vt olim me dicere me<lb></lb>mini, eſt vt 16 ad 27, poſitâ aquæ grauita<lb></lb>te 5 1/3, argillæ grauitas in aere eſt 9: igitur <lb></lb>argillæ grauitas in aquâ eſt 3 2/3. Tres itaque <lb></lb>partes orbis ſi per 3 2/3 ducantur, erit grauitas <lb></lb>11, & vna pars ignis eſt leuitatem habens <lb></lb>——100: ſi addantur, erit globi huius con<lb></lb>flati ex hac variâ corporum miſcellâ leuitas <lb></lb>——89 intrà aquam: ac proinde ſi aqua v<lb></lb>nam in partem ſecederet, tellure translatâ, <lb></lb>globus hic innataret, cum leuior ſit aquâ. </s> <s><lb></lb>Nam ſi comparetur grauitas abſoluta aquæ <lb></lb>ſecundùm molem æqualis toti globo, cum <lb></lb>grauitate abſolutâ ipſius globi, reperietur diſ<lb></lb>ferentia 89. Quia enim ignis leuitas ad aquam <lb></lb>eſt——100, aquæ grauitas ad ignem eſt + <lb></lb>100: quia verò argillæ grauitas ad aquam eſt <lb></lb>3 2/3, argillæ grauitas ad ignem eſt 103 2/3 At<lb></lb>qui tres globi partes ex hypotheſi ſunt argil<lb></lb>la, reliqua pars eſt ignis, igitur ſi argillæ gra<lb></lb>uitas 103 2/3 ducatur per 3, erit globi grauitas <lb></lb>311: ſi verò aquæ grauitas ad ignem 100 <pb xlink:href="018/01/201.jpg" pagenum="187"></pb>ducatur per 4, erit grauitas molis aqueæ <lb></lb>æqualis 400. Cum itaque grauitas aquæ ad <lb></lb>grauitatem molis confla<gap></gap> ex 3/4 argillæ & 1/4 <lb></lb>ignis, ſit vt 400 ad 311, conſtat molem̨ <lb></lb>conflatam innataturam. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Quin aquæ grauitatem in <expan abbr="aẽre">aëre</expan> po<lb></lb><arrow.to.target n="note88"></arrow.to.target><lb></lb>tiùs, quàm in igne, conſideras? </s> <s>An timui<lb></lb>ſti, ne globus hic ex aëre communi in purio<lb></lb>rem æthera auolaret? </s> <s>Quando quidem ſi le<lb></lb>uitas aeris ad aquam eſt——5 1/3, & leuitas <lb></lb>ignis ad aquam eſt——100, leuitas ignis ad <lb></lb>aërem eſt——94 2/3: eſt autem argillæ grauitas <lb></lb>in aëre 9. Igitur tres orbis quadrantes ha<lb></lb>berent grauitatem vt 27, & reliquus qua<lb></lb>drans leuitatem vt——94 2/3, atquè adeo totus <lb></lb>orbis leuitatem haberet in aere vt—— 67 2/3; <lb></lb>hoc eſt ſi per 4 numerum partium diuida<lb></lb>tur, leuitas ſpecifica totius globi in aere eſ<lb></lb>ſet——(16 11/12) </s> </p> <p type="margin"> <s><margin.target id="note88"></margin.target><emph type="italics"></emph>XXCVIII <lb></lb>Imò leuior <lb></lb>eſſet ſecun<lb></lb>dùm <expan abbr="ſpeciẽ">ſpeciem</expan> <lb></lb>aëre.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Lynceus es, Galilæe, nihil noņ <lb></lb><arrow.to.target n="note89"></arrow.to.target><lb></lb>vides. </s> <s>Mirabar pariter, cur omiſsâ aquæ & <lb></lb>argillæ grauitate in aëre, confugerit Merſen<lb></lb>nus ad earum grauitatem in igne; cum ta<lb></lb>men ex aquâ emergens globus in aërem ve<lb></lb>niat; qui eſt aquæ circumfuſus, non verò in <lb></lb>ignem. </s> <s>Quemadmodum enim ſi mercurio <pb xlink:href="018/01/202.jpg" pagenum="188"></pb>(cuius grauitas in aere 71 1/2) imponatur ex <lb></lb>aëre ferrum (cuius grauitas 42) innatatio <lb></lb>ferri debet conſiderari iuxta differentiam gra<lb></lb>uitatum in aëre, & leuitatio ferri ex mercurio <lb></lb>in aërem eſt——29 1/2. At ſi mercurio ſuper<lb></lb>fuſa ſit aqua, leuitas ferri deſumenda eſt ex <lb></lb>differentiâ inter grauitatem mercurij & gra<lb></lb>uitatem ferri, quod intrà aquam non am<lb></lb>pliùs graue eſt vt 42, ſed vt 36 2/3: quare leui<lb></lb>tas ferri tunc eſt maior, videlicet vt——34 5/6. <lb></lb>Ita ſimiliter cùm globus terrenus ex aquâ in <lb></lb>aerem, non in ignem veniret, eius grauitas <lb></lb>cum aëre debuit, non cum igne, compa<lb></lb>rari. </s> </p> <p type="margin"> <s><margin.target id="note89"></margin.target><emph type="italics"></emph>XXCIX <lb></lb>Solida plus <lb></lb>leuitant ex <lb></lb>mercurio in <lb></lb>aquam <expan abbr="quã">quam</expan> <lb></lb>in aërem.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Qui aquam mercurio ſuperfudiſti, <lb></lb><arrow.to.target n="note90"></arrow.to.target><lb></lb>cur pariter non circumfudiſti? </s> <s>tunc enim <lb></lb>mercurij in aquâ exiſtentis grauitas non eſ<lb></lb>ſet 71 1/6 ſed 66 1/2, & in illo leuitas ferri (cuius <lb></lb>grauitas in aquâ 36 2/3) eſſet pariter——29 1/2. <lb></lb>Duo ſiquidem æqualia corpora inæqualiter <lb></lb>grauia ſecundùm ſpeciem ſi in eodem me<lb></lb>dio conſtituantur, quodcunque illud ſit, ean<lb></lb>dem ſemper ſeruant differentiam, quia vtri<lb></lb>que æqualis fit grauitatis deceſsio aut acceſsio <lb></lb>pro maiori aut minori grauitate medij. </s> <s>Igi<lb></lb>rur ſi terreni globi grauitas ſpecifica compa<lb></lb>rata cum ſpecificâ grauitate aquæ in vno me<pb xlink:href="018/01/203.jpg" pagenum="189"></pb>dio habet certam differentiam, vt in ignę <lb></lb>dixi exceſſum grauitatis aquæ ſupra grauita<lb></lb>tem globi terreni ex igne & argillâ conflati <lb></lb>eſſe 89; in quocunque medio conſtituantur, <lb></lb>eundem habebit exceſſum. </s> <s>Sic in aëre gra<lb></lb>uitas 3/4 argillæ & 1/4 ignis eſſet defectiua, vt re<lb></lb>ctè Galilæus ratiocinabatur, videlicet—— <lb></lb>67 2/3, & grauitas æqualis molis aquæ in aëre <lb></lb>eſſet poſitiua, nimirùm 21 1/3 (ducto 4 per <lb></lb>5 1/3) differentia autem, qua maior numerus <lb></lb>21 1/3 excedit minorem —— 67 2/3, eſt 89 planè <lb></lb>eadem ac prius. </s> <s>Satis igitur fuit in vno ali<lb></lb>quo medio differentiam reperire, cùm illa <lb></lb>ſemper eadem maneat. </s> <s>Opportunius verò <lb></lb>accidit in medio omnium leuiſsimo, in quo <lb></lb>ignis ipſe globi molem componens nihil <lb></lb>grauitat, examen illud inſtituere, quia om<lb></lb>nes partium grauitates poſitiuæ ſunt, nulla <lb></lb>defectiua. </s> </p> <p type="margin"> <s><margin.target id="note90"></margin.target><emph type="italics"></emph>XC <lb></lb>Ratio <expan abbr="gra-uitatũ">gra<lb></lb>uitatum</expan> duo<lb></lb>rum corpo<lb></lb>rum in vno <lb></lb>medio, est <lb></lb>eadem iņ <lb></lb>omni medio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Cæterùm non timui, ne terrenus globus <lb></lb>auolaret, quemadmodum ouorum putami<lb></lb>na, vt aiunt, matutino rore impleta & meri<lb></lb>diano Soli expoſita. </s> <s>Qui enim tres orbis qua<lb></lb>drantes intrà aquam exiſtimat grauiores non <lb></lb>eſſe, quàm ſi ex merâ argilla conſtarent, <lb></lb>quia aqua illis permiſta nihil grauitat, & aër <lb></lb>valde leuitat, fortaſsè non item aſſerat tres <pb xlink:href="018/01/204.jpg" pagenum="190"></pb>orbis quadrantes in aëre conſtitutos eâdem <lb></lb>ſecundùm ſpeciem grauitate cum argillâ præ<lb></lb>ditos eſſe: quia iam aër in aëre nihil leuitat, <lb></lb>& halitus incluſi minùs leuitant, & aqua ſa<lb></lb>tis grauitat, & cætera omnia corpora tan<lb></lb>tum addunt ponderis, quantum illis detrahe<lb></lb>bat aqua, intrà quam exiſtebant, ſcilicet iux<lb></lb>tà molis æqualitatem. </s> <s>Id quod pariter di<lb></lb>ctum velim, ſi globus iſte intrà leuiſſimum <lb></lb>ignem conſtitutus intelligatur, neque enim <lb></lb>ibi tres orbis quadrantes æqualiter cum ar<lb></lb>gillâ grauitarent, ſed longè validiùs. </s> <s>Quan<lb></lb>do autem paulò antè grauitatum rationes <lb></lb>iniens tres orbis quadrante, quaſi ex merà ar<lb></lb>gillâ in igne conſtitutâ aſſumpſi, id fuit ſo<lb></lb>lùm ad explicandam hypotheſim, qua tri<lb></lb>buebatur grauitas ſpecifica æqualis grauitati <lb></lb>argillaceæ. </s> <s>Quarè ſi orbis in aëre conſtitua<lb></lb>tur, non ea tantùm eſt illius grauitas, quæ <lb></lb>tribus quadrantibus ex argillâ conueniat, ſed <lb></lb>perinde ſe habet, ac ſi totus ex argillâ con<lb></lb>ſtaret, vt olim citra omnem controuerſiam <lb></lb>admittebamus; adeòque nullum ſubeſſet pe<lb></lb>riculum, ne auolaret. </s> <s>Nam ſi poſito ignę <lb></lb>omnium leuiſsimo aëris grauitas eſt † 94 2/3, <lb></lb>argillæ grauitas eſt † 103 2/3, ac proinde cum <lb></lb>orbis totus ex argillâ conſtitutus ponatur. </s> <s><lb></lb>grauior eſt aëre; cum tamen intrà aquam̨ <pb xlink:href="018/01/205.jpg" pagenum="191"></pb>perinde ſe habere poſſe videatur, atque ſi tres <lb></lb>tantùm quadrantes argillacei eſſent, & reli<lb></lb>quus igneus. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Vereor plurimùm, ne iſta, quæ <lb></lb><arrow.to.target n="note91"></arrow.to.target><lb></lb>poſtremo loco attuliſti, plus habeant ſpeciei <lb></lb>quàm veritatis. </s> <s>& facilè ſuſpicor non omni<lb></lb>nò ſeriò à te prolata; ſed quia vidiſti me iņ <lb></lb>tabellam illam oculos curioſiùs coniicien<lb></lb>tem,, voluiſti oſcitantiam tentare, & ad at<lb></lb>tentionem reuocare. </s> <s>Attentiſsimo tamen <lb></lb>animo excepi omnia; ſolùm enim vt phan<lb></lb>taſiæ contentioni parcerem, labrum illud, <lb></lb>in quo moriens Seneca ſanguinem cum vitâ <lb></lb>effundit, reſpiciebam; illudque mihi nunc <lb></lb>aquâ, nunc ſtanno liquente plenum finge<lb></lb>bam perpendens, vtrùm fieri poſsit corpus <lb></lb>aliquod, cui in vno medio conuenit grauitas <lb></lb>ſpecifica argillæ, in alio medio maiorem aut <lb></lb>minorem grauitatem <expan abbr="ſpecificã">ſpecificam</expan> obtinere; nec <lb></lb>ſatis poteram percipere, quî fieri poſſet, vt <lb></lb>totus globus haberet in aëre grauitatem ar<lb></lb>gillæ. </s> <s>non autem ſimilem argillæ grauitatem <lb></lb>obtinere poſſet in aquâ. </s> </p> <p type="margin"> <s><margin.target id="note91"></margin.target><emph type="italics"></emph>XCI <lb></lb>Eadem mo<lb></lb>les compoſi<lb></lb>ta quam ſpe<lb></lb>cificam gra<lb></lb>uitatem ba<lb></lb>bet in vno <lb></lb>medio, habet <lb></lb>in quocun<lb></lb>cunque me<lb></lb>dio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Fingamus enim corpus, cuius duæ partes <lb></lb>ſint ferrum, vna marmor, duæ cera, vna <lb></lb>aër, & vna lapis: eſt autem in aere ſpecifica <lb></lb>grauitas ferri 42, marmoris 21, ceræ 5, aë<lb></lb>ris 0, lapidis 14. igitur ſingularum partium <pb xlink:href="018/01/206.jpg" pagenum="192"></pb>grauitatibus in ſummam collectis erit graui<lb></lb>tas tota in aëre 129; quæ ſi per 7 diuidatur, <lb></lb>quia ſunt ſeptem æquales dati corporis par<lb></lb>tes, erit grauitas ſpecifica huiuſmodi corporis <lb></lb>in aere 18 3/7. Iam corpus hoc, cuius grauitas <lb></lb>ſpecifica 18 3/7, comparemus cum ſtanno </s> </p> <p type="table"> <s>TABELLE WAR HIER</s> </p> <p type="main"> <s>communi, cuius grauitas ſpecifica 39; erit <lb></lb>dati corporis leuitas in ſtanno liquente—— <lb></lb>20 4/7; quæ ſi per 7 numerum partium duca<lb></lb>tur, erit tota leuitas ——144. Eadem autem <lb></lb>leuitas habetur, ſi ſingulæ partes cum ſtan<lb></lb>no conferantur; eſt enim duarum partium <lb></lb>ferri in ſtanno grauitas † 6, vnius partis <lb></lb>marmoris leuitas——18, duarum partium <pb xlink:href="018/01/207.jpg" pagenum="193"></pb>ceræ leuitas ——68, vnius partis aëris leuitas <lb></lb>—— 39, & vnius partis lapidis leuitas——25: <lb></lb>quæ ſi in ſummam referantur, erit corporis <lb></lb>dati leuitas in ſtanno liquente ——144. Qua<lb></lb>propter tam in ſtanno quàm in aëre perinde <lb></lb>ſe habet, ac ſi corpus homogeneum eſſet, <lb></lb>cuius grauitas ſpecifica eſſet 18 3/7. </s> <s>Sed in aquâ etiam non dubito, quin pari<lb></lb>ter ſe habeat vt corpus, cuius grauitas ſit <lb></lb>18 3/7 ad aquam, cuius grauitas 5 1/3: erit enim <lb></lb>corporis huius ſpecifica grauitas in aquâ + <lb></lb>(13 2/21), quæ per 7 ducta dat + abſolutam corpo<lb></lb>ris in aquâ grauitatem † 91 2/3. Hæc verò eſt <lb></lb>planè eadem, ac ſi in ſummam conferantur <lb></lb>grauitas duarum partium ferri + 73 1/3, graui<lb></lb>tas vnius partis marmoris + 15 2/3, leuitas duą <lb></lb>rum partium ceræ——<gap></gap> 2/3, leuitas vnius par<lb></lb>tis aëris —— 5 1/3, & grauitas vnius partis lapi<lb></lb>dis + 8 2/3: ex his enim pariter habetur graui<lb></lb>tas in aquá + 91 2/3. In quocunque igitur me<lb></lb>dio conſtituatur, perinde ſe habet, atque ſi <lb></lb>grauitas ſpecifica in medio leuiſsimo, iņ <lb></lb>quo nulla poſiti corporis pars leuis eſt, hoc <lb></lb>eſt in aëre, eſſet + 18 3/7. </s> </p> <p type="main"> <s>Ex his infero terrenum globum eandem <lb></lb>ſemper habere ſpecificam grauitatem in quo<lb></lb>cunque medio; ac proinde ſi in aquâ habet <pb xlink:href="018/01/208.jpg" pagenum="194"></pb>leuitatem —— 89, quia in quatuor partes di<lb></lb>ſtinctus ponitur (cum corpori leuiſſimo mo<lb></lb>lem componenti 1/4 tribuatur) diuidatur 89 <lb></lb>per 4, & erit leuitas ſpecifica in aquâ—— <lb></lb>22 1/4: Si igitur grauitas aquæ in igne + 100 illi <lb></lb>addatur, erit grauitas ſpecifica terreni globi <lb></lb>in igne + 77 3/4. In quocunque igitur medio <lb></lb>terrenus globus ſemper haberet ſpecificam <lb></lb>grauitatem vt + 77 3/4 in medio leuiſsimo, hoc <lb></lb>eſt in igne, ſi cæterorum corporum grauitas <lb></lb>ad idem medium, hoc eſt ignem, compare<lb></lb>tur. </s> <s>Quia verò aëris communis in igne gra<lb></lb>uitas eſt † 94 2/3, grauitas autem ſpecifica glo<lb></lb>bi terreni eſt † 77 3/4, ſequitur terreni globi ſpe<lb></lb>cificam leuitatem in aëre communi eſſe—— <lb></lb>(16 11/12), quæ ſi per 4 numerum partium duca<lb></lb>tur, dabit abſolutam globi leuitatem in aëre <lb></lb>——67 2/3, vt Galilæus argumentabatur: tellus <lb></lb>igitur aere leuior eſſet. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Qui inter ſalebras ambulat, non <lb></lb>ſemper ad numerum greſſus ponit. </s> <s>Id I mihi <lb></lb><arrow.to.target n="note92"></arrow.to.target><lb></lb>quoquè contigiſſe videtur, qui non ſatis di<lb></lb>lucidè verbis ſum complexus, quod vole<lb></lb>bam. </s> <s>Sed mihi nunc per veſtram humani<lb></lb>tatem licebit meam mentem interpretari. </s> <s><lb></lb>Toti huic globo, quem incolimus, aquam <lb></lb>terramque complectenti, argillæ grauitatem <pb xlink:href="018/01/209.jpg" pagenum="195"></pb>ſpecificam tribuo; ideò intrà aërem conſi<lb></lb>ſtit, nec vllum ſubeſt auolandi in ætherą <lb></lb>periculum. </s> <s>At ſublatis marium atquè flu<lb></lb>minum aquis, quas in latus ſeceſſiſſe poni<lb></lb>mus, reliquæ molis grauitas minor eſt; quia, <lb></lb>ſublatâ marium grauitate, ad ſolius terræ & <lb></lb>metallorum grauitatem leuitas ignis incluſi <lb></lb>& halituum habet maiorem Rationem, quàm <lb></lb>haberet ad grauitatem terræ ſimul & aquæ; ac <lb></lb>proinde cum maneant eadem corpora leuia, <lb></lb>& minuantur grauia, minor quoquè eſſe vi<lb></lb>detur ſpecifica grauitas totius globi. </s> <s>Quem<lb></lb>admodum ſi ex æreo vaſe aëris pleno aufe<lb></lb>ram partem metalli, manente eodem aëre, <lb></lb>fit minor ſpecifica vaſis grauitas. </s> <s>Quamuis <lb></lb>autem ſublato vno globi quadrante, qui igni <lb></lb>tribuitur, & ſublatis marium, lacuumque, <lb></lb>& fluminum aquis, quæ ſupereſt moles ſit <lb></lb>minor tribus totius orbis quadrantibus, ac <lb></lb>proinde minor tribus quadrantibus molis, <lb></lb>quæ reſtat ſublatâ tantùm aquâ, mihi tamen <lb></lb>minutas quæſtiunculas non conſectanti ſatis <lb></lb>videbatur tribus quadrantibus molis reliquæ <lb></lb>argillaceam grauitatem tribuere; vt ſi fortè <lb></lb>grauitas iſta iuſto minor eſſet, compenſaretur <lb></lb>diminutâ ignis mole, quæ ſtatuebatur ſolùm <lb></lb>quadrans reliquæ molis, cum tamen eſſet 1/4 <lb></lb>totius globi. </s> </p> <pb xlink:href="018/01/210.jpg" pagenum="196"></pb> <p type="margin"> <s><margin.target id="note92"></margin.target><emph type="italics"></emph>XCII <lb></lb>Moli <expan abbr="cõ">com</expan>po<lb></lb>ſitæ ſi quid <lb></lb>additur aut <lb></lb>dematur, e<lb></lb>ius grauitas <lb></lb>ſpecifica mu <lb></lb>tatur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sed ſi placeat grauitatem illam augere, <lb></lb>ſtatuamus tres illos quadrantes non argillæ, <lb></lb>ſed Magnetis grauitatem habere; eſt autem <lb></lb>magnetis grauitas 26 ad aquæ grauitatem <lb></lb>5 1/3 in aëre: quare magnetis grauitas in aquâ <lb></lb>eſt 20 2/3, & grauitas in igne 120 2/3; ideòque <lb></lb>grauitas trium quadrantum in aquâ, cum̨ <lb></lb>ex magnete conſtent, eſt 62, & leuitas <lb></lb>conueniens vni quadranti ignis in aquâ eſt <lb></lb>——100: igitur leuitas globi in aquâ eſt <expan abbr="tãtùm">tantùm</expan> <lb></lb>—— 38. Quando verò totus globus ex aquâ <lb></lb>pariter & terrâ conflatus accipitur, iam au<lb></lb>ctâ grauitate, alia eſt ſpecifica totius globi <lb></lb>grauitas, qualis eſſet ex. </s> <s>gr. grauitas mar<lb></lb>moris aut alia, cum non videatur aſſumi <lb></lb>poſſe tanquam mera argilla, ſi tres quadran<lb></lb>tes ex magnete ſtatuantur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> At ſi globo non reſtituatur aqua, <lb></lb>quæ in latus ſeceſſit, augebiturnè grauitas <lb></lb>ſpecifica molis, quæ ex tribus quadrantibus <lb></lb>magnetis, & vno quadrante ignis conflatur? </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Niſi quid addatur aut dematur, <lb></lb>fieri non poteſt vt grauitas ſpecifica variatio<lb></lb>nem ſubeat, </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Nobis igitur conuenit. </s> <s>Quapropter <lb></lb>ſi globi leuitas in aquâ eſt——38, per 4 nu<lb></lb>merum partium diuidatur, & erit leuitas <lb></lb>ſpecifica terreni globi in aquâ——9 1/2; cui ſi <pb xlink:href="018/01/211.jpg" pagenum="197"></pb>addatur grauitas aquæ in aere † 5 1/3, erit ſpe<lb></lb>cifica globi leuitas in aere ——4 1/6. Quàm̨ <lb></lb>bellè itaque res Archimedi ſucceſſiſſet: quan<lb></lb>do quidem vbi eò terram eleuaſſet, vt aqua <lb></lb>in latus ſeceſſiſſet, telluris globus non ſolùm <lb></lb>ex aquâ emergeret, ſed relictâ in vniuerſi <lb></lb>centro aquâ auolaret ſupra aërem, donec of<lb></lb>fenderet medium æqualis leuitatis ſupra aë<lb></lb>rem communem. </s> <s>Quarè machinationibus <lb></lb>opus eſſet non ad mouendam, ſed ad reti<lb></lb>nendam tellurem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Quod tellus, ſublatâ aquâ, leuior <lb></lb>ſit quàm aer iſte communis, quem ſpiritu <lb></lb>ducimus, vix adduci poſſum, vt credam: id <lb></lb>autem cùm ex hypotheſi à vobis conſtitutâ <lb></lb>ſequatur, hypotheſi ipſi probabilitatem de<lb></lb>mit. </s> <s>Quapropter aut nimiam igni leuita<lb></lb>tem, aut nimiam molem tribuiſtis; atquę <lb></lb>adeò vtramque aut alterutram temperarę <lb></lb>oportet. </s> <s>Equidem exiſtimo in leuitate po<lb></lb>tiùs peccatum fuiſſe quàm in mole: mihi ſi<lb></lb>quidem facilè perſuadeo ingentem ignium <lb></lb>vim intimis terræ viſceribus concludi, quo<lb></lb>rum potiſſimùm adminiſtratione naturą <lb></lb>perficit pretioſam illam metallorum ſupel<lb></lb>lectilem, quibus ſodinæ ditantur: certum <lb></lb>eſt autem calore humidum attenuante com<lb></lb>miſceri ſpiritus metallicos partibus fixis, at<pb xlink:href="018/01/212.jpg" pagenum="198"></pb>què vniri; ibi verò res tota perficitur, quò <lb></lb>ſolis calor pertingere nequit: quamobrem <lb></lb>cum in tantá à centro diſtantiâ producantur <lb></lb>metalla, totque milliarium craſſitudinem̨ <lb></lb>permeet calor, haud ægrè venio in doctiſſi<lb></lb>mi Wendelini ſententiam, ſi maximè cum <lb></lb>Lunæ libratione cohæreat. </s> <s>Sed quoniam <lb></lb>ignis ille acerrimus eſt (quò autem tenuior <lb></lb>ignis, eò languidior eſt) non adeò multam <lb></lb>fortaſsè tenuitatem obtinet, vt eius leuitas ad <lb></lb>aquam ſit vt auri grauitas ad aerem, quem<lb></lb>admodum aſſum pſiſtis. </s> <s>Animum autem <lb></lb>aduertite, vtrùm eam potiùs Rationem ha<lb></lb>beat ignis leuitas ad aëris leuitatem in aquâ, <lb></lb>quam habet terræ ſeu argillæ grauitas ad <lb></lb>aquæ grauitatem in aere. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Si me audieritis, nullas hìc conie<lb></lb>cturas conſectabimur, præter eam, quam <lb></lb>olim à nobis conſtitutam nemo facilè infi<lb></lb>cietur, videlicet telluris globum vniuerſum <lb></lb>in aere grauitate argillaceâ præditum eſſę. <lb></lb><arrow.to.target n="note93"></arrow.to.target><lb></lb>Globi ſoliditatem inueſtigemus, eamquę <lb></lb>per ſpecificam argillæ grauitatem ducamus; <lb></lb>ex quo innoteſcet abſoluta grauitas globi: <lb></lb>Hinc demamus abſolutam aquæ grauitatem, <lb></lb>quæ obtinetur ductâ aquæ ſpecificâ grauitate <lb></lb>in eius ſoliditatem. </s> <s>Reſiduum grauitatis ab<lb></lb>ſolutæ globi diuiſum per reſiduum ſoliditatis <pb xlink:href="018/01/213.jpg" pagenum="199"></pb>demptâ ſoliditate aquæ, dabit ſpecificam̨ <lb></lb>grauitatem globi demptâ aquâ. </s> </p> <p type="margin"> <s><margin.target id="note93"></margin.target><emph type="italics"></emph>XCIII <lb></lb>Terreni glo. <lb></lb></s> <s>ſbi grauitas <lb></lb>pecificą <lb></lb>maior est: <lb></lb>grauitatę <lb></lb>argillæ, ſi <lb></lb>aqua dema<lb></lb>tur ex glo<lb></lb>bo.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Primùm globi ſoliditatem habemus, ſi <lb></lb>inuentæ ſub initium noſtri heſterni ſermonis <lb></lb>ſuperficiei ſphæricæ mill. quad. </s> <s>214.201996. <lb></lb>paſſ. </s> <s>716000, accipiamus trientem mill. quad. </s> <s><lb></lb>71.400665. paſſ. </s> <s>572000, & ducamus per <lb></lb>telluris ſemidiametrum mill. 4128. paſſ. </s> <s><lb></lb>638: fiet enim totius globi ſoliditas mill. cu<lb></lb>bicorum 294787.501105. paſſ. </s> <s>850936000. <lb></lb>Ex hac globi ſoliditate ſi inuenta ſuperiùs <lb></lb>aquæ ſoliditas mill. cub. </s> <s>80.325748. paſſ. </s> <s><lb></lb>768500000. auferatur, relinquitur mill. cub <lb></lb>294707.175357. paſſ. </s> <s>82.436000. ſoliditas <lb></lb>reliqui globi demptâ aquâ. </s> <s>s </s> </p> <p type="main"> <s>Deinde globi ſoliditas paſſ cub. </s> <s>294. <lb></lb>787501.105850.936000 ducatur per 9 ſpe<lb></lb>cificam grauitatem argi læ in aere, & eſt ab<lb></lb>ſoluta globi grauitas 2653.087509.952658. <lb></lb>424000. Item aquæ ſoliditas paſſ.cub 80325. <lb></lb>748768.500000. ducatur per 5 1/3 ſpecificam <lb></lb>aquæ grauitatem, & fit abſoluta aquæ graui<lb></lb>tas 428403.993432.000000. Dematur hæc <lb></lb>aquæ grauitas ex terreni globi grauitate, & <lb></lb>remanet 2652.659105.959226.424000. <lb></lb>grauitas reſidui globi demptâ aquâ. </s> </p> <p type="main"> <s>Demùm reſidua hæc grauitas 2652. <lb></lb>659105.959226.424000. diuidatur per re<pb xlink:href="018/01/214.jpg" pagenum="200"></pb>ſiduum ſoliditatis demptâ aquâ, nempè per <lb></lb>numerum paſſ. </s> <s>cub. </s> <s>294.707175.357082. <lb></lb>436000. Et qui prodibit Quotiens (9 9994/10.000000) <lb></lb>proximè dabit reſidui globi ſpecificam gra<lb></lb>uitatem pauló maiorem grauitare argillaceâ. </s> <s><lb></lb>Quia nimirum aquæ demptæ grauitas ſpeci<lb></lb>fica minor eſt grauitate argillæ. </s> <s>Quod ſi <lb></lb>pars dempta fuiſſet argilla, aut argillâ gra<lb></lb>uior, diminuta fuiſſet grauitas ſpecifica; vt <lb></lb>quando ex vaſe metallico aëris pleno pars ali<lb></lb>qua metalli aufertur: Et hoc ſolùm in caſu <lb></lb>admittenda ſunt, quæ paulò antè Merſennus <lb></lb>dicebat; quia tunc reſiduum pondus ad pon<lb></lb>dus ablatum habet minorem Rationem̨, <lb></lb>quàm reſidua moles ad molem ablatam; hìc <lb></lb>autem contrà, quia grauitas aquæ minor eſt <lb></lb>grauitate argillæ, reſiduum pondus ad pon<lb></lb>dus ablatum habet maiorem Rationem, <lb></lb>quàm reſidua moles ad molem aquæ abla<lb></lb>tam. </s> </p> <p type="main"> <s>Quarè ſi totius globi terraquei grauitas <lb></lb><arrow.to.target n="note94"></arrow.to.target><lb></lb>ſpecifica non fuerit in aere minor grauitate <lb></lb>ſpecificâ aquæ, fieri non poteſt, vt aquis in <lb></lb>vnam partem ſecedentibus terra reliqua in<lb></lb>natet, ſemper enim grauitas ſpecifica terræ <lb></lb>maior erit ſpecificâ grauitate aquæ. </s> </p> <p type="margin"> <s><margin.target id="note94"></margin.target><emph type="italics"></emph>XCIV <lb></lb>Si telluri <lb></lb>tribuatur <lb></lb>grauitas ar<lb></lb>gillacea, a<lb></lb>quæ in latus <lb></lb>ſecedenti <expan abbr="nõ">non</expan> <lb></lb>innataret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Si<gap></gap> enim primùm totius globi ſpecific<gap></gap><lb></lb>grauitas ad aquæ grauitatem ſpecificam vt <pb xlink:href="018/01/215.jpg" pagenum="201"></pb>RT ad SV: quia verò abſoluta grauitas globi <lb></lb>rerraquei comparatur cum æquali mole a<lb></lb><figure id="id.018.01.215.1.jpg" xlink:href="018/01/215/1.jpg"></figure><lb></lb>quæ, erit pariter grauitas abſolu<lb></lb>ta globi terraquei ad grauitatem <lb></lb>abſolutam æqualis globi tantum<lb></lb>modò aquei vt RT ad SV. </s> <s>Dein<lb></lb>de ex globo terraqueo auferatur <lb></lb>aqua, cuius grauitas TO; æqua<lb></lb>lis aqua ex globo aqueo demptą <lb></lb>æqualem habet grauitatem VN: <lb></lb>& ſunt reſiduæ grauitates RO & <lb></lb>SN inæquales, quia ex inæqualibus RT, SV, <lb></lb>ablatæ ſunt æquales grauitates OT, VN. </s> <s><lb></lb>Cum itaque maior ſit Ratio RT maioris ad <lb></lb>OT, quàm SV minoris ad VN, erit per <lb></lb>conuerſionem Rationis minor Ratio RT ad <lb></lb>RO, quàm SV ad SN; igitur & viciſſim̨ <lb></lb>minor erit Ratio RT ad SV, quàm RO ad <lb></lb>SN. </s> <s>Igitur reſidua globi terreni grauitas <lb></lb>RO ad reſiduam globi aquei ſecundùm mo<lb></lb>lem æqualis grauitatem SN habet maiorem <lb></lb>Rationem, quàm totius globi terraquei gra<lb></lb>uitas RT ad totius globi aquei æqualis gra<lb></lb>uitatem SV, hoc eſt, quàm argillæ grauitas <lb></lb>ad grauitatem aquæ. </s> <s>Fieri itaque non poteſt, <lb></lb>vt terra aquis innatet. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Valeat igitur Thales Mileſius cum <lb></lb>ſuo illo nauigio. </s> <s>Et ſanè noſtra hac diſputa<pb xlink:href="018/01/216.jpg" pagenum="202"></pb>tione nos operam luſiſſe non puto; facilè <lb></lb>enim in eam ſententiam delabi quis poſſet, <lb></lb>vt ſibi perſuaderet ab incluſis terræ halitibus <lb></lb>atque ignibus tantum demi grauitatis, vt illa <lb></lb>intrà aquam leuior eſſet ſecundùm ſpeciem: <lb></lb>quæ quidem vnica eſt innatationis cauſą. </s> <s><lb></lb>Niſi quis fortè ex eorum numero, qui la<lb></lb>minam metallicam ratione figuræ in mul<lb></lb>tam latitudinem explicatæ, ideòque diffi<lb></lb>ciliùs, (vt ipſi quidem loquuntur) ſubie<lb></lb>ctam aquam diuidentis, innatare cenſent, <lb></lb>ambigeret pariter, an idem terræ quoquę <lb></lb>contingere poſſet. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Errorem hunc iamdudum aureo <lb></lb>illo tuo de Innatantibus libello profligaſti; <lb></lb>Galilæe: vixque puto aliquem ſupereſſe, qui <lb></lb>cramben hanc recoquat, præter eos, quos <lb></lb>iuuat ex antiquioribus tantùm codicibus ru<lb></lb>dioris ſæculi puluerem colligere. </s> <s>Nihil Gul<lb></lb>dino, nihil mihi eſt cum huiuſmodi homi<lb></lb>num genere commercij: quapropter miſſos <lb></lb>illos prorsùs faciamus: quamuis enim motui <lb></lb>tarditatem aliquam inferre poſſit figura, im<lb></lb>pedire tamen omninò non poteſt, ſi illa qui<lb></lb>dem per ſe reſpiciatur; quod ſi ea fuerit cor<lb></lb>poris grauis figura, quæ leuioris aeris partem <lb></lb>ſecum deferat, aeri vtique non figuræ tri<lb></lb>buenda eſt innatatio, quatenus ex aere, & <pb xlink:href="018/01/217.jpg" pagenum="203"></pb>metallo laminæ componitur moles, cuius <lb></lb>pondus minus eſt pondere æqualis molis <lb></lb>aquæ. </s> <s>Cum autem nihil ſimile in terrâ con<lb></lb>tingere poſſit, quandoquidem aër ille, qui <lb></lb>valles ex aquâ extantes impleret, nihil con<lb></lb>ferret leuitatis (quemadmodum & in naui, <lb></lb>qui ſupra aquæ ſuperficiem aer, nauis pon<lb></lb>dus non minuit, nam intrà aerem non leui<lb></lb>tat) nulla ſpes nobis reliqua eſt innatationis <lb></lb>terræ: ſed quicquid in tellure machinationi<lb></lb>bus mouendâ compendij haberet Archime<lb></lb>des ex aquis, totum illud eſſet ex eâ ponde<lb></lb>ris diminutione, quam ſubeunt ſolida gra<lb></lb>uiora aquis immerſa. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gul.<emph.end type="italics"></emph.end></s> <s> Ita planè, ſi terræ tantùm ratio ha<lb></lb><arrow.to.target n="note95"></arrow.to.target><lb></lb>beatur: nam compendium aliud, nec illud <lb></lb>contemnendum, antequam heri aduenires <lb></lb>Merſenne, obſeruabamus ex ipſius aquæ ſe<lb></lb>iunctione, cuius grauitatem ad calculos re<lb></lb>uocantes deprehendebamus non minorem <lb></lb>libris Rom. 803.257487.685000.000000. <lb></lb>Quæ ſi ex totius globi grauitate argilla<lb></lb>ceâ dematur, relinquet reliquæ terræ pon<lb></lb>dus. </s> </p> <p type="margin"> <s><margin.target id="note95"></margin.target><emph type="italics"></emph>XCV <lb></lb>Terra intra <lb></lb>aquam mi<lb></lb>nùs ponde<lb></lb>raret.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Vt autem totius globi grauitatem ad li<lb></lb>bras reuocem, accipio vnius milliaris cubici <lb></lb>ex argillâ grauitatem: cum verò aquæ gra<lb></lb>uitas ad argillæ grauitatem ſit vt 5 1/2 ad 9, <pb xlink:href="018/01/218.jpg" pagenum="204"></pb>milliaris autem cubici ex aquâ pondus iam <lb></lb>inuenerim lib. 10.000000.000000. erit quar<lb></lb>tus analogiæ terminus lib. 16.875000.000000 <lb></lb>pondus vnius milliaris cubici ex argillâ. </s> <s>Per <lb></lb>hanc igitur grauitatem duco inuentam paulò <lb></lb>antè globi ſoliditatem mill. 294787.501105. <lb></lb>paſſ. </s> <s>850936000, & prouenit demùm to<lb></lb>tius globi terraquei grauitas, ſi mera argilla <lb></lb>effet, lib. 4.974539.081161.234545. <lb></lb>000000. quæ fortaſsè paulò maior erit eâ gra<lb></lb><arrow.to.target n="note96"></arrow.to.target><lb></lb>uitate, quam Merſenne, ſtatuebas, quia in <lb></lb>terræ diametro inueniendâ minùs accuratis <lb></lb>rationibus vtebaris, ſi ſatis memini. </s> <s>Ex in<lb></lb>uentâ itaque globi grauitate ſi dematur con<lb></lb>ſtituta aquarum grauitas, remanet ſolius ter<lb></lb>ræ pondus lib. 4.973735.823673.549545. <lb></lb>000000. </s> </p> <p type="margin"> <s><margin.target id="note96"></margin.target><emph type="italics"></emph>XCVI <lb></lb>Terræ gra<lb></lb>uitas libra<lb></lb>rum nume<lb></lb>ro<gap></gap> probabili <lb></lb>explicata.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Cum verò grauitas hæc intrà aquam non <lb></lb>tota percipiatur, ſed ſolùm iuxta exceſſum <lb></lb>grauitatis ſpecificæ argillæ ſupra grauitatem <lb></lb>aquæ ſpecificam, ſatis conſtat, quantùm <lb></lb>minueretur terræ pondus, & quantò faciliùs <lb></lb>moueretur. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Eam tamen hic intelligis, puto, ad<lb></lb>hibendam circumſcriptionem, vt non toti <lb></lb>globo, ſed illi tantùm parti, quæ aquis cir<lb></lb>cumfunderetur, grauitatem adimerent aquæ, <lb></lb>parem ponderi molis aqueæ æqualis; neque <pb xlink:href="018/01/219.jpg" pagenum="205"></pb>enim terra vniuerſa intrà aquam demerſą <lb></lb>deliteſceret. </s> <s>Prætereà quamuis totius terreæ <lb></lb>portionis in aquâ exiſtentis grauitas minuere<lb></lb>tur, ſegmenti tamen vltra Vniuerſi cen<lb></lb>trum poſiti grauitas imminuta vel auctą <lb></lb>nihil iuuaret, cùm motui illa non repugnet, <lb></lb>dum deſcendit: ideò ſolùm ſegmenti ſupe<lb></lb>rioris pars aquis immerſa attendenda eſſet: <lb></lb>atque adeò quò magis terræ centrum ab vni<lb></lb>uerſi centro remoueretur, eò augeretur ma<lb></lb>gis pondus, quia plus terrenæ molis ex aquis <lb></lb>extaret. </s> <s>Neque enim aliud terræ conringe<lb></lb>ret, quâm ſolido cuilibet corpori, quod ex <lb></lb>humore in vaſe extrahitur, cuius maior mo<lb></lb>les emergit ex aquâ, quàm ſit moles aquæ <lb></lb><arrow.to.target n="note97"></arrow.to.target><lb></lb>accurrentis ad replendum ſpatium à corpo<lb></lb>re ſolido relictum. </s> <s>Quia ſcilicet ſi aqua ma<lb></lb>neret in eâdem ſuperficie, nec deprimere<lb></lb>tur, ſolidi tanta moles emergeret, quanta eſt <lb></lb>moles, quæ relinquit ſpatium intra aquam: <lb></lb>ſed quoniam aqua infra illam ſuperficiem̨ <lb></lb>deprimitur, quam priùs conſtituebat, & re<lb></lb>linquit aliam prætereà ſolidi partem ab aquâ <lb></lb>immunem, ideò moles, quæ ex aquâ emer<lb></lb>git, maior eſt mole aquæ accurrentis ad re<lb></lb>plendum ſpatium relictum à corpore eleua<lb></lb>to. </s> <s>Sic in vaſe HX, corpus AB totum in<lb></lb>trà aquam, cuius ſuperficies ſit CD, ſi ex-<pb xlink:href="018/01/220.jpg" pagenum="206"></pb><figure id="id.018.01.220.1.jpg" xlink:href="018/01/220/1.jpg"></figure><lb></lb>trahatur ex A in H, pars CH, quæ ſuprą <lb></lb>ſuperficiem aquæ CD eleuatur, æqualis eſt <lb></lb>parti, quæ replebat ſpatium GB: hoc autem <lb></lb>ſpatium relictum implet aqua deſcendens ex <lb></lb>C in E, ac proinde totum corpus HE extrą <lb></lb>aquam manet; quæ moles maior eſt molę <lb></lb>HC, hoc eſt mole aquæ deſcendentis DE ad <lb></lb>replendum ſpatium ſibi æquale GB. </s> <s>Idem <lb></lb>igitur terræ contingeret, quæ & eleuaretur <lb></lb>ſupra locum, vbi erat ſuperficies aquæ, & <lb></lb>infra illum locum ſuperficies aquæ deprime. </s> <s><lb></lb>retur; ex quo fieret maiorem terræ partem <lb></lb>ex aquis emergere. </s> </p> <p type="margin"> <s><margin.target id="note97"></margin.target><emph type="italics"></emph>XCVII <lb></lb>Solidi moles <lb></lb>ex humido <lb></lb>emergĕs, ma<lb></lb>ior est mole <lb></lb>humidi ac<lb></lb>currentis a<gap></gap><lb></lb>replendum <lb></lb>ſpatium.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> At aquæ illæ nullo vaſe contine<lb></lb>rentur, aut alueo. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Perinde eſt ſi aqua vaſis lateribus <lb></lb>circumſcripta certam figuram induat, ac ſi <lb></lb>ſuis ſe nutibus ipſa in ſphæram diſponat. </s> <s>Il<lb></lb>lud quidem contingeret, quod cùm aqua ex <lb></lb>maiori eleuatione terræ in minorem ſemper <pb xlink:href="018/01/221.jpg" pagenum="207"></pb>ac minorem ſphæram ſe conformaret, ra<lb></lb>tionem haberet vaſis minoris & minoris; <lb></lb>atque adeò aqua magis & magis deprimere<lb></lb>tur, etiam datâ æquali terræ eleuationę. </s> <s><lb></lb>Sint enim duo vaſa ſimilia ſed inæqualia, in <lb></lb>quibus ſint duo corpora ſimilia & æqualią <lb></lb><arrow.to.target n="note98"></arrow.to.target><lb></lb>AB in minori, & KL in maiori ſimiliter po<lb></lb>ſita: & ſit continua ſolidorum immerſorum <lb></lb>& aquæ circumfuſæ ſuperficies. </s> <s>Extrahatur <lb></lb>ex aquâ vtrumque ſolidum pari velocitatę; <lb></lb>vtique citiùs emerget omninò illud, quod <lb></lb>eſt in minori vaſe, quàm quod eſt in maiori; <lb></lb>& multò plus aquæ deſcendere debet in ma<lb></lb>iori quàm in minori, ac proinde plus eleuari <lb></lb>debet ſolidum in maiori vaſe, quàm in mi<lb></lb>nori, vt æqualis moles emineat ſupra aquæ <lb></lb>deſcendentis ſuperficiem. </s> </p> <p type="margin"> <s><margin.target id="note98"></margin.target><emph type="italics"></emph>XCVIII <lb></lb>Idem <expan abbr="ſolidũ">ſolidum</expan> <lb></lb>vt extraba<lb></lb>tur ex hu<lb></lb>mido, plus <lb></lb>debet eleua<lb></lb>ri in vaſę <lb></lb>maiori <expan abbr="quã">quam</expan> <lb></lb>in minori, <lb></lb>& plus a<lb></lb>quæ deſcen<lb></lb>dit in vaſe <lb></lb>maiori, <expan abbr="quã">quam</expan> <lb></lb>in minori. </s> <s><lb></lb>Hæc veritas <lb></lb>infertur ex <lb></lb>contradicto<lb></lb>ria hypothe<lb></lb>ſi.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Sit enim primò aquæ in vaſe minori ſu<lb></lb>perficies CD, in vaſe autem maiori OM: <lb></lb>deinde ita extrahatur vtrumque ſolidum, vt <lb></lb>æquales partes HE & VS emineant ſupra ſu<lb></lb>perficiem, quam denuò acquiſiuit aqua de<lb></lb>ſcendens in locum à ſolido eleuato relictum. </s> <s><lb></lb>Dico maiorem eſſe eleuationem VK ſuprą <lb></lb>primam ſuperficiem OM, in vaſe maiori, <lb></lb>quàm ſit eleuatio AH ſupra primam ſuper<lb></lb>ficiem CD in vaſe minori; ac proinde ſpa<lb></lb>tium relictum NL maius eſſe ſpatio relicto <pb xlink:href="018/01/222.jpg" pagenum="208"></pb>GB, & aquam OMRS deſcendentem eſſę <lb></lb>maiorem aquâ CDFE deſcendente. </s> </p> <p type="main"> <s>Nam ſi KV non eſt maior quàm AH, <lb></lb>ergo aut æqualis, aut minor. </s> <s>Sit æqualis: er<lb></lb>go quia HG & VN æquales ſunt ex hypothe<lb></lb>ſi, & VK ipſi HA æqualis dicitur, etiam <lb></lb>reliquæ KN & AG, hoc eſt OS & CE, æqua<lb></lb>les ſunt: ergo aquæ OMRS & CDFE æqua<lb></lb>lem habentes altitudinem ſunt inter ſe vt <lb></lb>baſes, hoc eſt vt ſuperficies OM & CD. </s> <s>At<lb></lb>qui ſuperficies OM maior eſt ſuperficie CD, <lb></lb>ergo aqua OMRS maior eſt quàm aquą <lb></lb>CDFE: ſed aqua deſcendens eſt æqualis mo<lb></lb>li corporis NL, quæ replebat ſpatium reli<lb></lb>ctum; igitur maior eſt moles NL quàm GB: <lb></lb>eſt autem NL æqualis parti eleuatæ VO, & <lb></lb>GB æqualis eſt parti eleuatæ HC, ergo VO <lb></lb>maior eſt moles <expan abbr="quãm">quàm</expan> HC: hæ verò moles <lb></lb>VO & HC ſunt vt altitudines, quia ex hypo<lb></lb>theſi data ſolida ſunt æqualia, ſimilia, & ſi<lb></lb>militer poſita; ergo maior eſt altitudo KV <lb></lb>quam altitudo AH. </s> </p> <p type="main"> <s>Quod ſi KV dicatur minor quàm AH <lb></lb>ergo ex æqualibus VN, HG, demptis inæ<lb></lb>qualibus, remanet KN maior quam AG, <lb></lb>hoc eſt OS maior quam CE: aqua igitur <lb></lb>OMRS maiorem habens baſim ac maiorem <lb></lb>altitudinem, quam aqua CDFE, maior quo<pb xlink:href="018/01/223.jpg" pagenum="209"></pb><figure id="id.018.01.223.1.jpg" xlink:href="018/01/223/1.jpg"></figure><lb></lb>què erit; ac proinde & moles NL, hoc eſt VO, <lb></lb>maior mole GB, hoc eſt HC; & vt priùs ele<lb></lb>uatio KV maior eleuatione AH. </s> <s>Quare vide<lb></lb>tis hoc adeò certum eſſe, vt<gap></gap> ex ipſo negante <lb></lb>eleuationem in maiori vaſe maiorem eſſę <lb></lb>eleuatione in minori vaſe, veritatis huius con<lb></lb>feſſio extorqueatur, ijs admiſſis, quæ con<lb></lb>tradicens ponit. </s> </p> <p type="main"> <s><emph type="italics"></emph>Metſ.<emph.end type="italics"></emph.end></s> <s> Priuſquàm vlteriùs progrediatis, <lb></lb>vnum vellem ex te quærere; an ſcilicet aliqua <lb></lb>ſit inter eleuationes ſolidorum & depreſſio<lb></lb>nes aquatum in vaſis inæqualibus analogią <lb></lb>ſaltem reciproca, ita vt quæ Ratio eſt eleua<lb></lb>tionis KV in vaſe maiori ad eleuationem AH <lb></lb>in minori, eadem Ratio ſit depreſſionis aquæ <lb></lb>CE, hoc eſt AG, in minori ad depreſſionem <lb></lb>aquæ OS, hoc eſt KN in maiori. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Nulla eſt ſiue directa, ſiue recipro<pb xlink:href="018/01/224.jpg" pagenum="210"></pb>ca inter eleuationes ſolidi ac depreſſiones a<lb></lb><arrow.to.target n="note99"></arrow.to.target><lb></lb>quæ analogia, præterquàm in vno caſu. </s> <s>Non <lb></lb>quidem directa, quia, vt dicebam, KV ma<lb></lb>ior eſt quàm AH, ergo maior eſt Ratio KV <lb></lb>ad AG, quàm HA ad AG; atqui AG maior <lb></lb>eſt quàm KN, ergo maior eſt Ratio KV ad <lb></lb>KN quàm KV ad AG; ergò multò maior eſt <lb></lb>Ratio KV ad KN quàm HA ad AG. </s> <s>Noņ <lb></lb>eſſe autem reciprocam analogiam ſic oſtendo. </s> </p> <p type="margin"> <s><margin.target id="note99"></margin.target><emph type="italics"></emph>XCIX <lb></lb>Eleuationes <lb></lb>ſolidi, & <lb></lb>depreſſiones <lb></lb>humidi iņ <lb></lb>vaſis inæ<lb></lb>qualibus <expan abbr="nõ">non</expan> <lb></lb>ſunt propor<lb></lb>tionales, ni ſi <lb></lb>in vno caſu.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Aqua OMRS circumfuſa eſt æqualis moli <lb></lb>NL, hoc eſt VO; addatur vtrique commu<lb></lb>nis moles NO, erit tota moles duobus pla<lb></lb>nis KOM & NSR parallelis contenta æqualis <lb></lb>moli corporis KL ſeu VS. </s> <s>Item aqua CDFE <lb></lb>circumfuſa æqualis eſt moli GB, hoc eſt HC; <lb></lb>& additâ communi mole AE, erit tota mo<lb></lb>les planis ACD & GEF parallelis contentą <lb></lb>æqualis moli corporis AB ſeu HE. </s> <s>Atqui HE <lb></lb>& VS æquales ſunt moles ex hypotheſi; igi<lb></lb>tur & moles GD æqualis eſt moli NM: ergo <lb></lb>per 34. lib. 11. baſes cum altitudinibus re<lb></lb>ciprocantur, & vt AG ad KN, ita ſuperficies <lb></lb>vaſis maioris ad ſuperficiem vaſis minoris. </s> </p> <p type="main"> <s>Prætereà aqua circumfuſa OMRS æqua<lb></lb>lis eſt moli VO, ergo ad molem KS habet <lb></lb>eandem Rationem quam VO ad KS, hoc eſt <lb></lb>quam altitudines KV ad KN. </s> <s>At aqua cir<lb></lb>cumfuſa ad molem KS, quia in eâdem ſunt <pb xlink:href="018/01/225.jpg" pagenum="211"></pb>altitudine OS, eſt vt ſuperficies vaſis minus <lb></lb>ſuperficie ſolidi VY ad ipſam ſuperficiem ſo<lb></lb>lidi; igitur VK eleuatio ſolidi ad KN depreſ<lb></lb>ſionem aquæ eſt vt ſuperficies vaſis maioris <lb></lb>minùs ſuperficie ſolidi ad ipſam ſuperficiem <lb></lb>ſolidi VY: & componendo vt VN corporis <lb></lb>emerſio ad KN aquæ depreſſionem, ita ſu<lb></lb>perficies vaſis maioris ad ſuperficiem ſolidi <lb></lb>VY. </s> <s>Eâdem methodo oſtenditur HA eleua<lb></lb>tionem ſolidi ad AG depreſſionem aquæ eſſe, <lb></lb>vt eſt ſuperficies vaſis minoris minùs ſuper<lb></lb>ficie ſolidi HT ad ipſam ſuperficiem ſolidi: & <lb></lb>componendo vt HG ad GA, ita ſuperficies <lb></lb>vaſis minoris ad ſuperficiem ſolidi HT. </s> </p> <figure id="id.018.01.225.1.jpg" xlink:href="018/01/225/1.jpg"></figure> <p type="main"> <s>Quoniam igitur vt ſuperficies vaſis maio<lb></lb>ris ad ſuperficiem minoris, ita GA ad NK; <lb></lb>ſi eſſet VK ad HA vt GA ad NK, iam eſſet vt <lb></lb>VK ad HA ita ſuperficies vaſis maioris ad ſu<pb xlink:href="018/01/226.jpg" pagenum="212"></pb>perficiem minoris: ſed vt VK ad HA, itą <lb></lb>moles VO ad molem HC, hoc eſt aquą <lb></lb>OMRS ad aquam CDFE; ergo vt ſuperficies <lb></lb>vaſis maioris ad ſuperficiem minoris, hoc eſt <lb></lb>vt GA ad NK, ita aqua OMRS ad aquam̨ <lb></lb>CDFE. </s> <s>Atqui aquæ iſtæ circumfuſæ habent <lb></lb>Rationem compoſitam ex Rationibus altitu<lb></lb>dinum & baſium; ergo Ratio GA ad NK <lb></lb>æqualis eſt <emph type="italics"></emph>R<emph.end type="italics"></emph.end>ationi compoſitæ <emph type="italics"></emph>ex Rationi<emph.end type="italics"></emph.end><lb></lb>bus altitudinum GA ad N<emph type="italics"></emph>K,<emph.end type="italics"></emph.end> & baſium CD <lb></lb>ad OM. </s> <s>Cum verò fieri non poſſit vt (quan<lb></lb>do Ratio non componitur ex duabus Ratio<lb></lb>nibus, quarum altera ſit alterius ſubduplica<lb></lb>ta, vt Ratio compoſita ex Rationibus 4 ad 2 <lb></lb>& 2 ad 8, eſt eadem cum Ratione 2 ad 4 <lb></lb>conuerſa prions Rationis 4 ad 2, quemad<lb></lb>modum hic non contingere ſuppono) Ratio <lb></lb>aliqua compoſita eadem ſit directè cum vnâ <lb></lb>ex Rationibus componentibus, niſi alterą <lb></lb>Ratio componens ſit Ratio æqualitatis (ſic <lb></lb>Ratio compoſita ex Rationibus 4 ad 4 & 4 ad <lb></lb>3 eſt 16 ad 12 eadem cum Ratione 4 ad 3, <lb></lb>quia Ratio æqualitatis aliam Rationem mul<lb></lb>tiplicans eam non mutat) conſtet autem ex <lb></lb>demonſtratis AG maiorem eſſe quàm KN, <lb></lb>ſequitur baſes aquarum CD & OM haberę <lb></lb>Rationem æqualitatis. </s> <s>At baſes iſtæ ſunt ſu<lb></lb>perficies vaſorum minùs ſuperficie ſolidi im<pb xlink:href="018/01/227.jpg" pagenum="213"></pb>miſſi; igitur ſi baſibus æqualibus addantur <lb></lb>ipſæ æquales ſuperficies ſolidi, erunt ſuperfi<lb></lb>cies vaſorum æquales: id quod eſt contra hy<lb></lb>potheſim. </s> <s>Non igitur eſt vt VK ad HA ita <lb></lb>AG ad KN. </s> </p> <p type="main"> <s><emph type="italics"></emph>S<emph.end type="italics"></emph.end>it enim iterum, ſi fieri poteſt, VK ad <lb></lb>HA, vt AG ad KN: VK prima vel eſt maior <lb></lb>quàm AG tertia, vel minor, vel æqualis. </s> <s>Si <lb></lb>maior, ergo per 14. 5. etiam HA ſecundą <lb></lb>maior eſt quàm KN quarta; eſt autem VK <lb></lb>ex dictis etiam maior quàm HA; igitur VK <lb></lb>eſt maxima & KN minima; igitur per 25. 5. <lb></lb>VK ſimul cum KN maior eſt quàm HA & <lb></lb>AG ſimul, quod eſt contra hypotheſim, iux<lb></lb>ta quam VN & HG æquales ſunt. </s> <s>Si VK mi<lb></lb>nor eſt quàm AG, etiam HA minor eſt quàm <lb></lb>KN; ſed HA minor eſt quàm VK ex dictis; <lb></lb>ergo HA eſt omnium minima & AG <expan abbr="omniũ">omnium</expan><lb></lb>maxima; ergo per 25.5. HG maior eſt quàm <lb></lb>VN, contra hypotheſim. </s> </p> <p type="main"> <s>At verò ſi demùm VK prima æqualis ſit <lb></lb>AG tertiæ, etiam HA ſecunda æqualis eſt <lb></lb>KN quartæ: ergo per 7.5. vt VK ad KN ita <lb></lb>GA ad AH. </s> <s>At ex demonſtratis vt VK ad KN, <lb></lb>ita ſuperficies vaſis maioris minùs ſuperficie <lb></lb>ſolidi ad ſuperficiem ſolidi VY, & vt GA ad <lb></lb>AH, ita ſuperficies ſolidi HT, hoc eſt VY, <lb></lb>ad ſuperficiem vaſis minoris minùs ſuperfi<pb xlink:href="018/01/228.jpg" pagenum="214"></pb>cie ſolidi. </s> <s>Igitur ſuperficies ſolidi eſt medio <lb></lb>loco proportionalis inter differentias, quibus <lb></lb>ſuperficies ſolidi exceditur à ſuperficiebus va<lb></lb>ſorum: ergo componendo & permutando vt <lb></lb>ſuperficies vaſis maioris ad ſuperficiem mi<lb></lb>noris, ita ſuperficies ſolidi HT ad ſuperficiem <lb></lb>vaſis minoris minùs ſuperficie ſolidi, hoc eſt <lb></lb>ſuperficiem aquæ CD. </s> <s>Sed vt ſuperficies ſo<lb></lb>lidi HT ad ſuperficiem CD, ita moles AE <lb></lb>ad aquam CDFE eiuſdem altitudinis: & quia <lb></lb>AG ex hypotheſi eſt æqualis ipſi VK, moles <lb></lb>AE eſt æqualis ipſi moli VO, hoc eſt aquæ <lb></lb>OMRS. ergo vt ſuperficies HT ad ſuperfi<lb></lb>ciem CD, ita aqua OMRS ad aquam CDFE; <lb></lb>ergo per 11. 5. vt ſuperficies vaſis maioris ad <lb></lb>ſuperficiem minoris, hoc eſt vt aquarum al<lb></lb>titudines AG ad KN, ita aqua OMRS ad a<lb></lb>quam CDFE. </s> <s>Sunt igitur aquæ inter ſe re<lb></lb>ciprocè vt earum altitudines: Ratio autem̨ <lb></lb>molium ex Rationibus altitudinum & <expan abbr="baſiũ">baſium</expan> <lb></lb>componitur, baſes verò non habent rationem <lb></lb>æqualitatis; ergo aquarum ſuperficies OM <lb></lb>ad CD ſunt in duplicatâ Ratione altitudinum <lb></lb>reciprocè ſumptarum, hoc eſt vt quadratum̨ <lb></lb>GA ad quadratum KN. </s> <s>Id quod ſic breui<lb></lb>ter demonſtro Algebricis notis. </s> </p> <p type="main"> <s>Sit GA altitudo R, & KN altitudo ſit S: <lb></lb>ſuperficies CD ſit D planum, & ſuperficies <pb xlink:href="018/01/229.jpg" pagenum="215"></pb>OM ſit Z planum. </s> <s>lgitur aqua CDEF eſt <lb></lb>D plan. in R; & aqua OMRS eſt Z plan; iņ <lb></lb>S. </s> <s>Quare cum ſit Z plan. in S ad D plan. in R, <lb></lb>vt R ad S. erit per 16. 6. vel 19. 7. Z pl. </s> <s>in S. <lb></lb>quadr. </s> <s>æquale D plano in R quadratum: ‘er<lb></lb>go Z planum ad D planum, hoc eſt ſuperfi<lb></lb>cies OM ad ſuperficiem CD, eſt vt R qua<lb></lb>dratum ad S quadratum: ſunt igitur ſuperfi<lb></lb>cies aquarum in duplicatâ Ratione altitudi<lb></lb>num AG ad KN. </s> <s>At in Ratione AG ad KN <lb></lb>eſt ſuperficies vaſis maioris ad ſuperficiem̨ <lb></lb>minoris, ergo ſuperficies OM ad ſuperficiem <lb></lb>CD eſt in duplicatâ Ratione ſuperficiei vaſis <lb></lb>maioris ad ſuperficiem minoris. </s> </p> <p type="main"> <s>Datis itaque vaſis ſimilibus inæqualibus, <lb></lb>& datâ Ratione ſuperficierum huiuſmodi va<lb></lb>ſorum, poterimus reperire ſuperficiem ſoli<lb></lb>di VY aut HT; quæ ex vaſorum ſuperficie<lb></lb><arrow.to.target n="note100"></arrow.to.target><lb></lb>bus dempta reliquam aquæ ſuperficiem relin<lb></lb>quat in duplicatâ Ratione ſuperficierum va<lb></lb>ſorum. </s> <s>Cum enim ſolidorum ſuperficies HT, <lb></lb>VY habeant Rationem æqualitatis, maior eſt <lb></lb>Ratio totius ſuperficiei vaſis maioris ad totam <lb></lb>ſuperficiem minoris, quàm ablatæ VY ad <lb></lb>ablatam HT, ergo per 33 5. apud Clau. ma<lb></lb>ior eſt Ratio reliquæ OM ad reliquam CD, <lb></lb>quàm totius ad totam: quare poteſt etiam̨ <lb></lb>haberi Ratio duplicata Rationis totius ad to<pb xlink:href="018/01/230.jpg" pagenum="216"></pb>tam. </s> <s>Sic autem inueſtigo ſuperficiem VY, <lb></lb>quæ ſit media proportionalis inter differen<lb></lb>tias illius & ſuperficiei vaſorum, hoc eſt in<lb></lb>ter OM & CD. </s> </p> <p type="margin"> <s><margin.target id="note100"></margin.target><emph type="italics"></emph>C <lb></lb>Ex datis <lb></lb>duabus ſu<lb></lb>perficiebus <lb></lb>auferre ean<lb></lb>dem ſuperfi<lb></lb>ciem, quæ re <lb></lb>linquat re<lb></lb>sidua in Ra<lb></lb>tione dupli<lb></lb>cata data<lb></lb>rum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Ratio ſuperficierum vaſorum ſit data 8 <lb></lb>ad 4; Ratio duplicata eſt 8. ad 2. Pono ſu<lb></lb>perficiem ſolidi VY Algebricè 1℞. </s> <s>Quare ſu<lb></lb>perficies aquæ OM eſt 8——1℞, & ſuperfi<lb></lb>cies CD eſt 4——1℞: quæ ſunt inter ſe in du<lb></lb>plicatâ Ratione ſuperficiei vaſorum: igitur <lb></lb>8——1℞ ad 4——1℞. </s> <s>eſt vt 8 ad 2 ergo per <lb></lb>19. 7. 16——2℞ æquatur 32——8℞. </s> <s>Et fa<lb></lb>ctâ Antitheſi æquatio demum eſt inter 16 & <lb></lb>6℞. </s> <s>In ſtitutâ it aque diuiſione 1℞ eſt 2 2/3 ſuper<lb></lb>ficies VY; quæ ablata ex 8 ſuperficie vaſis <lb></lb>maioris relinquit ſuperficiem OM 5 1/3, & <lb></lb>ablata ex ſuperficie vaſis minoris, hoc eſt ex <lb></lb>4, relinquit ſuperficiem CD 1 1/3: eſt autem <lb></lb>2 2/3 medio loco proportionalis inter 5 1/3 & 1 1/3, <lb></lb>quæ præterea ſuperficies 5 1/3, & 1/3 ſunt in Ra<lb></lb>tione duplicatâ Rationis 8 ad 4, hoc eſt in <lb></lb>Ratione 8 ad 2. Iam verò ſi baſes aquarum <lb></lb>OM ad CD ſint vt 8 ad 2, altitudines ve<lb></lb>rò KN & GA reciprocè vt ſuperficies va<lb></lb>ſorum, hoc eſt KN 4, & GA 8, erit aquą <lb></lb>OMRS 32, & aqua CDFE 16, planè iņ <lb></lb>Ratione, quam habent ſuperficies vaſorum, <lb></lb>in quibus ipſæ aquæ exiſtunt. </s> </p> <pb xlink:href="018/01/231.jpg" pagenum="217"></pb> <p type="main"> <s>Quare hoc vno in caſu quando ſuperficies <lb></lb>ſolidi immiſſi eſt media proportionalis inter <lb></lb>exceſſus, quos relinquit in ſuperficiebus va<lb></lb>ſorum, poteſt contingere eleuationes ſolidi <lb></lb>reciprocari cum depreſſionibus aquæ; quan<lb></lb>do ſcilicet eleuatio ſolidi in maiori vaſe eſt <lb></lb>æqualis depreſſioni aquæ in minori, & con<lb></lb>trà eleuatio ſolidi in minori æqualis eſt de<lb></lb>preſſioni aquæ in maiori: </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Operæ profectò pretium fuit hac <lb></lb>ſuper re te interrogare, de qua neminem di<lb></lb>ſputantem audiſſe me memini aut legiſſe. </s> <s><lb></lb>Sed vt ad terram aquis delapſis circumfuſam <lb></lb>reuertamur, eadem-nè erit depreſſionis aquæ <lb></lb>Ratio, quæ in vaſis, de quibus hactenus fuit <lb></lb>ſermo? </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Eadem eſſe ratio omnino non po<lb></lb>teſt; quia aquæ deſcenſus non ex ſolo ſpatio, <lb></lb>quod ab eleuatâ terrâ relinqueretur, pende<lb></lb>ret, quemadmodum ſi globus ex aquâ iņ <lb></lb>vaſe eximeretur, ſed etiam ex diuersâ ipſius <lb></lb>aquæ in ſphæram conformatione. </s> <s>Cum <lb></lb>verò aliam ſemper & aliam diuerſarum̨ <lb></lb>ſphærarum portionem conſtitueret, ſeu po<lb></lb>tius Meniſcorum ſolidorum, donec demùm <lb></lb>in ſphæram integram aqueam diſponeretur, <lb></lb>nulla certa & conſtans Ratio afferri poteſt; <lb></lb>ſed dato certo ſpatio, quod à centro terræ <pb xlink:href="018/01/232.jpg" pagenum="218"></pb>translato perficeretur in certâ ab vniuerſi <lb></lb>centro diſtantiâ, inueſtigare oporteret, cuius <lb></lb>in ſphæræ ſuperficiem ſe data aquæ moles <lb></lb>diſponeret in vtroque motûs termino, vt in<lb></lb>de colligeretur, quantum terræ ex aquis iņ <lb></lb>motu illo emerſiſſet. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Abſtineamus nunc, ſi placet, ab <lb></lb>hoc labore: quamuis datâ ſectione lunulari, <lb></lb>& inuentis dimidiæ ſectionis centro grauita<lb></lb>tis, ac viâ rotationis, poſſemus ſoliditatem <lb></lb>Meniſcoidis ſphærici inuenire; ſatis nunc <lb></lb>nobis eſſe puto inquirere; quantam in alti<lb></lb>tudinem ſuſtolli terram oporteret, vt nul<lb></lb>lum amplius ſubſidium afferret aqua circum<lb></lb>fuſa minuens terræ grauitatem. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Res eſt non adeò difficilis aut ope<lb></lb><arrow.to.target n="note101"></arrow.to.target><lb></lb>roſa. </s> <s>Inuenire ſcilicet oportet ſemidiame<lb></lb><gap></gap>rum ſphæræ, quam ſola aqua conſtitueret; <lb></lb>& huic addere ſemidiametrum terræ; hæc <lb></lb>enim eſſet ea centri terræ atque centri vni<lb></lb>uerſi diſtantia, in qua nihil terræ intrà aquam <lb></lb>eſſet. </s> <s>Vt autem ſphæræ, quam aqua effi<lb></lb>ceret, ſemidiametrum habeamus; cum data <lb></lb>ſit aquæ ſoliditas, quam ſuperius poſuimus, <lb></lb>fiat vt 11 ad 21, ita data ſphæræ aqueæ ſo<lb></lb>liditas paſſ. </s> <s>cub. </s> <s>80325. 748768. 500000, <lb></lb>ad aliud, & prouenit 153349. 156739. <lb></lb>863636. cubus diametri minoris verâ. </s> <s>Item <pb xlink:href="018/01/233.jpg" pagenum="219"></pb>fiat vt 223 ad 426, ita data ſphæræ ſolidi<lb></lb>tas 80325. 748768. 500000. ad 153447. <lb></lb>394508. 434977. cubum diametri maioris <lb></lb>verâ. </s> <s>Si igitur horum numerorum radix cu<lb></lb>bica extrahatur, habebimus ſphæræ diame<lb></lb>trum tùm minorem, tùm maiorem verâ. </s> </p> <p type="margin"> <s><margin.target id="note101"></margin.target><emph type="italics"></emph>CI <lb></lb>Quantum̨ <lb></lb>elenanda eſ <lb></lb>ſet tellus, vt <lb></lb>omnino ab <lb></lb>aqua ſeiun<lb></lb>geretur.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end> Hùc nos deueniſſe gaudeo, noņ <lb></lb>tantùm vt propoſitæ quæſtionis metam ali<lb></lb>quam attingamus, ſed etiam vt methodum <lb></lb>obſeruem, qua cubicam radicem eruere ſo<lb></lb>les; alijs enim alia eſt methodus, & nimis <lb></lb>attentum animum exigunt, dum ſeorſim in<lb></lb>ſtituendæ ſunt multiplicationes, quæ ſub da<lb></lb>tum numerum transferantur: & periculum̨ <lb></lb>ſæpius ſubeſt, ne per imprudentiam alium̨ <lb></lb>pro alio numerum ſupponas. </s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Vtrum ea, quæ mihi familiaris eſt <lb></lb>methodus, omnium facillima ſit, ignoro: <lb></lb>mihi tamen arridet magis, cum in poteſtate <lb></lb>meâ ſemper ſit operationem totam ex ordi<lb></lb>ne recognoſcere. </s> <s>Cæterùm fieri non poteſt, <lb></lb>quin plures requirantur operationes, cum̨ <lb></lb>præter cubum primi lateris oporteat inueni<lb></lb>re ſolidum ex triplo quadrato primi lateris in <lb></lb>latus ſecundum, & ſolidum ex triplo laterę <lb></lb>primo in quadratum lateris ſecundi, & de<lb></lb>mum ipſius lateris ſecundi cubum. </s> <s>Quarę <lb></lb>hic in ſchedula, quoniam ſic placet, dato<pb xlink:href="018/01/234.jpg" pagenum="220"></pb>rum cuborum radicem extraham in vſum̨ <lb></lb>noſtræ quæſtionis. </s> <s>Hæc autem mihi eſt re<lb></lb>gulą. </s> </p> <p type="main"> <s>Poſt quartam quamque figuram, vt mo<lb></lb><arrow.to.target n="note102"></arrow.to.target><lb></lb>ris eſt, puncto notatam, primi puncti latus <lb></lb>deſcribo & eius cubum extraho, id quod om<lb></lb>nibus methodis commune eſt: deinde late<lb></lb>ris primi inuenti triplum ſcribo ſub penulti<lb></lb>má figurâ ſecundi puncti, ipſum verò latus <lb></lb>primum ſub antepenultimâ figurâ: & hos <lb></lb>duos numeros inuicem duco, ſcilicet triplum <lb></lb>lateris primi in ipſum: & qui producitur nu<lb></lb>merus (ſub antepenultimâ pariter figurâ col<lb></lb>locatus) eſt Diuiſor; Quotiens verò eſt latus <lb></lb>ſecundum. </s> </p> <p type="margin"> <s><margin.target id="note102"></margin.target><emph type="italics"></emph>CII <lb></lb>Radicis cu<lb></lb>bicæ facilis <lb></lb>extractio.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s>Tum latus ſecundum duco in triplum la<lb></lb>teris primi, & productum ſcribo ſub penul<lb></lb>timâ figurâ; atquè hunc addo priori produ<lb></lb>cto. </s> <s>Summam multiplico per latus ſecun<lb></lb>dum, & producto addo Cubum ſecundi la<lb></lb>teris collocatum ſub figurâ puncto notatâ. </s> <s><lb></lb>Summam demùm ex propoſito numero ſub<lb></lb>duco, & ſic deinceps. </s> </p> <p type="main"> <s>Quoniam it aque numeri hìc propoſiti ſunt <lb></lb>18 ciphrarum, & ſunt ſex puncta, vt tempo<lb></lb>ri parcam & labori, prima quatuor punctą <lb></lb>accipio pro primo puncto; & ex Tabulà, in <lb></lb>qua habeo myriadem cuborum, inuenio ma<pb xlink:href="018/01/235.jpg" pagenum="221"></pb>ximum cubum C, cuius latus eſt A: ſubtra<lb></lb>ho C ex D, & remanet E, cui addo tres fi<lb></lb>guras ad ſequens punctum pertinentes. </s> <s>De<lb></lb>inde triplico A, & eſt F, quem ſub penulti<lb></lb>mâ figurâ colloco, cui ſubſcribo A ſub figu<lb></lb>râ antepenultimâ. </s> <s>Duco A in F, & produ<lb></lb>citur G: & aſſumpto G tanquam diuiſore nu<lb></lb>meri E, habeo Quotientem B, ſcilicet latus <lb></lb>ſecundum: Tum B in F duco, & produci<lb></lb>tur H ſub penultimâ figurâ. </s> <s>Additis G & H, <lb></lb>fit ſumma I: quæ per latus ſecundum ductą <lb></lb>producit K; cui ſub puncto dati numeri ſub<lb></lb>ſcribitur lateris ſecundi B cubus L; atque ex <lb></lb>K & L fit ſumma M auferenda ex E: & qui re<lb></lb>linquitur numerus N, pertinet ad ſequens <lb></lb>punctum. </s> </p> <p type="main"> <s>Quod ſpectat ad numerorum collocatio<lb></lb>nem ſub penultimâ vel antepenultimá figu<lb></lb><arrow.to.target n="note103"></arrow.to.target><lb></lb>râ, ſatis videtis id factum eſſe propter com<lb></lb>pendium, quo omittuntur ciphræ nullita<lb></lb>tis, vltimo loco addendæ; eſt ſiquidem la<lb></lb>teris primi numerus decadicus, ſi cum late<lb></lb>re ſecundo comparetur: quare dum triplica<lb></lb>tur, & fit F, vna ciphra nullitatis eſſet ſub <lb></lb>puncto: & dum hoc triplum per ipſum la<lb></lb>tus ducitur, in producto eſſent vltimo loco <lb></lb>duæ ciphræ ideò ſub antepenultimâ figurâ <lb></lb>collocatur numerus productus, vt relinqua</s> </p> <pb xlink:href="018/01/236.jpg"></pb> <p type="margin"> <s><margin.target id="note103"></margin.target><emph type="italics"></emph>CIII <lb></lb>Huius me<lb></lb>thodi ratio <lb></lb>ostenditur.<emph.end type="italics"></emph.end></s> </p> <p type="table"> <s>TABELLE WAR HIER</s> </p> <p type="main"> <pb xlink:href="018/01/237.jpg" pagenum="223"></pb> <s>tur locus ciphrarum: id quod vt certiùs fiat, <lb></lb>colloco A ſub F ita, vt A ſit ſub antepenulti<lb></lb>mâ figurâ. </s> <s>Quia verò quando B in F duci<lb></lb>tur, vnica tantùm eſſet ciphra nullitatis ad <lb></lb>ipſum F pertinens, ideò productus H ſcribi<lb></lb>tur ſub penultimâ figurâ. </s> <s>Cubus demùm L <lb></lb>ſub puncto collocatur, quia nullam habet <lb></lb>ciphram nullitatis, quæ omittatur. </s> <lb></lb> <s>Quod autem pertinet ad ipſam metho<lb></lb>dum, res clara eſt. </s> <s>Dum enim triplum la<lb></lb>teris primi ducitur in latus ipſum, hoc eſt F <lb></lb>in A, producitur G, quod eſt triplum qua<lb></lb>drati ipſius A. </s> <s>Dum verò B in F ducitur, & <lb></lb>fit H, planum, quod fit, eſt ex latere ſecun<lb></lb>do in triplum lateris primi. </s> <s>Additis G & H <lb></lb>fit ſumma I, hoc eſt 3 A Quad. + 3 A in B. </s> <s><lb></lb>Hæc ſumma multiplicatur per B, & fit K, <lb></lb>hoc eſt 3 A Quadr. in B + 3 A in B Quadr. </s> <s><lb></lb>Additur demum L cubus ipſius B, vt ipſius <lb></lb>lateris A + B cubus ſit A cub. + 3 A Quadr. <lb></lb>in B + 3 A in B Quadr. + B cub. </s> </p> <p type="main"> <s><emph type="italics"></emph>Merſ.<emph.end type="italics"></emph.end></s> <s> Præſagiebat animus me aliquid ex <lb></lb>te auditurum, quod operationem hanc fa<lb></lb>cilem redderet atque expeditam, vixque pu<lb></lb>to aliquid addi poſſe facilitatis atque perſpi<lb></lb>cuitatis; cum nullâ hìc opus ſit numerorum <lb></lb>translatione, & triplicatio lateris primi A, <lb></lb>aut multiplicatio lateris ſecundi B in F tri<pb xlink:href="018/01/238.jpg" pagenum="224"></pb>plum lateris primi facillimè perficiuntur abſ<lb></lb>que eo, quod opus ſit multiplicatorem ſub <lb></lb>multiplicando deſcribere. </s> <s>Eſt itaque ſphæ<lb></lb>ræ aqueæ diameter minor verâ paſſ. </s> <s>535254. <lb></lb>maior autem verâ paſſ. </s> <s>535368. Quare ſta<lb></lb>tui poteſt diameter vera paſſ. </s> <s>535300 rotun<lb></lb>dè, & ſemidiameter mill. 267. paſſ: 650: <lb></lb>quæ ſi addatur terreni globi ſemidiametro à <lb></lb>nobis ſuperiùs aſſumptæ mill. 4128 paſſ 638, <lb></lb><arrow.to.target n="note104"></arrow.to.target><lb></lb>dabit mill. 4356 paſſ. </s> <s>288. diſtantiam cen<lb></lb>triterræ ab vniuerſi centro, quando iam aqua <lb></lb>in ſphæram conglobata nihil iuuaret terræ <lb></lb>motionem. </s> <s>Nunquam autem, puto, ab Ar<lb></lb>chimede aliquis exigat machinationum ſpe<lb></lb>cimen exhiberi tanto motu. </s> <s>Ex quo fit nun<lb></lb>quam totius telluris pondus debuiſſe ab Ar<lb></lb>chimede ſuſtineri, atque adeò faciliùs perfi<lb></lb>ci potuiſſe illam motionem, ac vulgus exi<lb></lb>ſtimet, modò locus ſuppeteret, in quo ma<lb></lb>chinæ firmarentur. </s> <s>Aqua enim dum deor<lb></lb>ſum niteretur, quamuis ob minorem in ſpe<lb></lb>cie grauitatem non poſſet terram ſuſtinerę, <lb></lb>aliquantulum tamen repugnaret deſcenden<lb></lb>ti, minueretque ſuſtinentis laborem. </s> </p> <p type="margin"> <s><margin.target id="note104"></margin.target><emph type="italics"></emph>CIV <lb></lb>Archimedi <lb></lb>tellurem mo<lb></lb>uenti per ali<lb></lb>quot millia<lb></lb>ria, noņ <lb></lb>fuiſſet opus <lb></lb>totum pon<lb></lb>dus ſustine<lb></lb>re.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Rectè intuliſti, quod volebam̨; <lb></lb>aquâ videlicet infimam terræ portionem̨ <lb></lb>ſubeunte ita futurum vt minueretur terræ <lb></lb>pondus, vt hinc aliqua mouendi aut ſuſtinen<pb xlink:href="018/01/239.jpg" pagenum="225"></pb>di facilitas oriretur. </s> <s>Quamuis verò facilè per<lb></lb>mittam aquam repugnare terræ deſcenden<lb></lb>ti, hæc enim intrà aquam deſcendere noņ <lb></lb>poteſt, quin aquæ ſuperficies in maiorem <lb></lb>ſphæram conglobata magis ab vniuerſi cen<lb></lb>tro recedat; quia tamen dubitare quis poſ<lb></lb>ſet, an corpora grauia motui ſurſum relu<lb></lb>ctentur, quando ita mouerentur, vt nihil <lb></lb>leuius infrà ſe, ac centro vicinius haberent; <lb></lb>aqua autem tunc ita moueretur, & in orbem <lb></lb>diſponeretur, vt nihil eſſet centro vicinius, <lb></lb>infra quod conſiſtere expeteret, nihil enim <lb></lb>circumflui aëris propiùs abeſſet à centro; <lb></lb>ideò ex ipsâ minori terræ grauitatione potiùs <lb></lb>quàm ex aquæ deorſum nitentis reſiſtentiâ <lb></lb>rem explicandam cenſerem. </s> <s>Grauitas ſi<lb></lb>quidem eſt vis diſponendi ſe in vniuerſo iņ <lb></lb>loco ſibi debito infra alia corpora: quò au<lb></lb>rem magis diſſimilia ſunt corpora ſecundùm <lb></lb>locum, quem exigunt, & quò plures corpo<lb></lb>rum ſpecies inter illa deberent intercipi, ſi <lb></lb>iuxta naturæ propenſionem ſingulæ diſpo<lb></lb>nerentur, eò etiam grauiora ſecundum ſpe<lb></lb>ciem ſunt ea, quæ centro viciniora eſſe exi<lb></lb>gunt. </s> <s>Quarè tota grauitationis ratio & niſus, <lb></lb>quo vnum corpus infra aliud deſcendere co<lb></lb>natur, in quo exiſtit tanquam in medio, ori<lb></lb>tur ex diſſimilitudine ſecundùm grauitatem. <pb xlink:href="018/01/240.jpg" pagenum="226"></pb>Quò igitur maior eſt grauitatis diſſimilitudo, <lb></lb>eò pariter maior eſt grauitatio, & conatus <lb></lb>deorſum validior. </s> <s>Atqui quodcunque pon<lb></lb>dus grauius eſt aquâ, eſt multo grauius aëre; <lb></lb>igitur magis ab aëre differt quàm ab aquâ, <lb></lb>magiſquè in aëre grauitat quàm in aquá: cum <lb></lb>autem grauitet propter diſſimilitudinem, to<lb></lb>ta grauitatio petenda eſt iuxta exceſſum, quo <lb></lb>ſuperat aquæ grauitatem. </s> </p> <p type="main"> <s>Eâdem ratione ea quæ leuiora ſunt aquâ, <lb></lb><arrow.to.target n="note105"></arrow.to.target><lb></lb>intrà aquam leuitatem habent iuxta differen<lb></lb>tiam, qua vincuntur à grauitate aquæ. </s> <s>At<lb></lb>que hinc facilè definitur cuiuſcunque ſolidi <lb></lb>innatantis quota portio emergat ex aquâ aut <lb></lb>alio humido: ibi enim ſolidum intrans hu<lb></lb>morem conſiſtit, vbi grauitas partis in aëre <lb></lb>extantis æqualis eſt leuitati portionis in hu<lb></lb>mido immerſæ: id autem fit, quando pars <lb></lb>demerſa ad extantem eſt vt grauitas ſpecifi<lb></lb>ca ſolidi innatantis ad differentiam grauita<lb></lb>tum ſolidi & humidi. </s> <s>Si enim quæratur <lb></lb>quota portio plumbi extaret ex mercurio (eſt <lb></lb>autem plumbum ad mercurium vt 11 ad <lb></lb>13) ſtatim dicetur molis plumbeæ (2/13) extare, <lb></lb>& (11/13) immergi; quia nimirum ſingulæ partes <lb></lb>immerſæ in mercurio leuitant vt 2, ſingulæ <lb></lb>autem in aëre extantes grauitant vt 11. Si <lb></lb>igitur vt grauitas in aëre ad leuitatem in mer<pb xlink:href="018/01/241.jpg" pagenum="227"></pb>curio, ita moles immerſa ad molem extan<lb></lb>tem, paria ſunt grauitatis & leuitatis mo<lb></lb>menta: nam partes 11 leuitantes vt 2 ha<lb></lb>bent momentum leuitatis 22; & duæ partes <lb></lb>in aëre grauitantes vt 11 habent momentum <lb></lb>grauitatis vt 22; igitur ſequitur conſiſtentia. </s> <s><lb></lb>Quod ſi vlteriùs deprimatur plumbum in<lb></lb>trà mercurium, augentur leuitatis momen<lb></lb>ta, & minuitur grauitas, ideò ſibi relictum <lb></lb>aſcendit; & ſi plures plumbi partes quàm <lb></lb>(2/13) extrahantur ex mercurio, deſcendet, quia <lb></lb>grauitatis momenta augentur ſupra momen<lb></lb>ta leuitatis; & ibi demum quieſcet, vbi fit <lb></lb>momentorum æqualitas. </s> </p> <p type="margin"> <s><margin.target id="note105"></margin.target><emph type="italics"></emph>CV <lb></lb>Quota pars <lb></lb>ſolidi inna<lb></lb>tantis emer<lb></lb>gat ex hu<lb></lb>mido.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>Gal.<emph.end type="italics"></emph.end></s> <s> Habetis ſuper quo ad rauim vſque <lb></lb>diſputetis, ſi hanc perſequi quæſtionem vo<lb></lb>lueritis; & illud fortaſſe demum conficietis, <lb></lb>incertum eſſe, vtrùm grauia in aquâ minùs <lb></lb>conentur deorſum <expan abbr="quã">quam</expan> in aere, an verò quam<lb></lb>uis æquè conentur, minùs tamen proficiant <lb></lb>propter aquæ in oppoſitum conantis reſiſten <lb></lb>tiam: cum vtroque ſcilicet experimenta co<lb></lb>hærent. </s> </p> <p type="main"> <s><emph type="italics"></emph>Guld.<emph.end type="italics"></emph.end></s> <s> Haud tanti eſt: ſed iſtis dimiſſis, <lb></lb>ad alia, ſi lubet, tranſeamus: ſatis enim pro <lb></lb>Archimede diſſeruimus. </s> </p> <p type="main"> <s><emph type="center"></emph>LAVS DEO.<emph.end type="center"></emph.end></s> </p> <pb xlink:href="018/01/242.jpg"></pb> <p type="main"> <s><emph type="center"></emph>INDEX<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>RERVM NOTABILIVM<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="center"></emph>Prior numerus notam marginalem, poſterior <lb></lb>paginam indicat.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>ARchimedis inuentum helicem fuiſſe, procliuius eſt opi<lb></lb>nari, num.<emph.end type="italics"></emph.end>3 7 </s> </p> <p type="main"> <s><emph type="italics"></emph>Axe multiplici in peritrochio faciliùe quàm denticulatis <lb></lb>tympanis res perficitur, n.<emph.end type="italics"></emph.end>4 8 </s> </p> <p type="main"> <s><emph type="italics"></emph>Axis in Peritrochio compoſitio, n.<emph.end type="italics"></emph.end>5 9 </s> </p> <p type="main"> <s><emph type="italics"></emph>Archimedes an trochleis tellurem loco dimouendam existi<lb></lb>marit, n.<emph.end type="italics"></emph.end>7 13 </s> </p> <p type="main"> <s><emph type="italics"></emph>Angulo obſeruationis quid obsit, & quàm exactè haberi poſ<lb></lb>ſit, num.<emph.end type="italics"></emph.end>37 72 </s> </p> <p type="main"> <s><emph type="italics"></emph>Angulus depreſſionis nouo instrumento deprehendi poteſt <lb></lb>num.<emph.end type="italics"></emph.end>37 74 </s> </p> <p type="main"> <s><emph type="italics"></emph>Authorum aliquorum lapſus in ſtatuenda nimia viſus di<lb></lb>stantia, n.<emph.end type="italics"></emph.end>46 94 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aquæ ſuperficies est ſphærica, n.<emph.end type="italics"></emph.end>59 119 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aqua cur in tubo vtrinque hiante aſcendat aliquantulum, <lb></lb>num.<emph.end type="italics"></emph.end>60 121 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aqua mutaret figuram, ſi tellus aliò traheretur, n.<emph.end type="italics"></emph.end>61 124 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aqua tota ab ea ſeiungeretur Tellure translata, n<emph.end type="italics"></emph.end>63 129 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aquæ totius quantitas, & grauitas inquiritur, n.<emph.end type="italics"></emph.end>64 131 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aquæ & aëris grauitates comparantur, & inquiruntur, <lb></lb>num.<emph.end type="italics"></emph.end>69 141 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem alio modo, n.<emph.end type="italics"></emph.end>69 144 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aeolipilæ experimentum quantum ostendat, n.<emph.end type="italics"></emph.end>71 148 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aëris communis & aquæ grauitas in aëre ignito minor est, <lb></lb>quàm fuerit deprehenſa, n.<emph.end type="italics"></emph.end>73 154 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aëris grauitas non probatur ex differentia ponderum vaſis <lb></lb>pleni et vacui, n.<emph.end type="italics"></emph.end>76 161 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aquæ tumuluantis cauſa explicatur, n.<emph.end type="italics"></emph.end>79 166 </s> </p> <p type="main"> <s><emph type="italics"></emph>Eiuſdem experimenti extenſio, & eorum, quæ acci<emph.end type="italics"></emph.end><pb xlink:href="018/01/243.jpg"></pb><emph type="italics"></emph>dunt, cauſæ indicantur, n.<emph.end type="italics"></emph.end>80 167 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aëris igniti leuitas quanta ſit in aqua, n.<emph.end type="italics"></emph.end>81 172 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aquæ an moles compoſita poſſit innatare nec ne, absque cal<lb></lb>culo aquæ æqualis, n.<emph.end type="italics"></emph.end>82 174 </s> </p> <p type="main"> <s><emph type="italics"></emph>Archimedi tellurem mouenti per aliquot milliaria, non fuiſ<lb></lb>ſet opus totum pondus ſuſtinere, n.<emph.end type="italics"></emph.end>104 224 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>C<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>COchleæ infinitæ compoſitæ vires cum Gloſſocomo com<lb></lb>parantur, n.<emph.end type="italics"></emph.end>3 6 </s> </p> <p type="main"> <s><emph type="italics"></emph>Cochleæ multiplicis vſus facilior quam Gloſſocomi, n.<emph.end type="italics"></emph.end>3 7 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>F<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>FVnis longitudini occurritur, n.<emph.end type="italics"></emph.end>7 11 </s> </p> <p type="main"> <s><emph type="italics"></emph>Funis conditio & qualitas ibidem, <lb></lb>Fabula de altitudine Phari Alexandrinæ reijcitur, n.<emph.end type="italics"></emph.end>47 98 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>G<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>GLoſſocomi, ſeu Pancratij conſtructio, n.<emph.end type="italics"></emph.end>1 4 </s> </p> <p type="main"> <s><emph type="italics"></emph>Gloſſocomi vires explicantur, n.<emph.end type="italics"></emph.end>2 4 </s> </p> <p type="main"> <s><emph type="italics"></emph>Globus terrenus in certa hypotheſi innataturus aquæ vide<lb></lb>tur, n.<emph.end type="italics"></emph.end>87 186 </s> </p> <p type="main"> <s><emph type="italics"></emph><gap></gap>Imo leuior eſſet ſecun dum ſpeciem aëre, n.<emph.end type="italics"></emph.end>88 187 </s> </p> <p type="main"> <s><emph type="italics"></emph>Grauitatum ratio duorum corporum in vno medio est ea<lb></lb>dem in omni medio, n.<emph.end type="italics"></emph.end>90 188 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>H<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>HElicis conſtructionis difficultas & vſus n.<emph.end type="italics"></emph.end>4 8 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>I<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>INfernus quantam terræ partem occupet, n.<emph.end type="italics"></emph.end>27 51 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ignis inferni grauitas quanta ſit ex coniectura, n.<emph.end type="italics"></emph.end>28 52 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ignis variæ ſpecies, & qualitas, n.<emph.end type="italics"></emph.end>28 54 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ignis ſubterraneus eſt quarta pars globi terreni ex ſenten<lb></lb>tia Wendelini, n.<emph.end type="italics"></emph.end>83 177 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ignis leuitatis inueſtigatio tentatur, n.<emph.end type="italics"></emph.end>84 178 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ignis leuitas alia hypotheſi examinatur, n.<emph.end type="italics"></emph.end>86 184 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>L<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>LIneæ curuæ pro recta abuſus inutilis, n.<emph.end type="italics"></emph.end>40 83 </s> </p> <p type="main"> <s><emph type="italics"></emph>Longitudinis differentia inter arcum & eius tangentem <lb></lb>vel ſubtenſam, n.<emph.end type="italics"></emph.end>42 85 </s> </p> <p type="main"> <s><emph type="italics"></emph>Lineæ curuæ pro recta abuſus cui errori expoſitus, n.<emph.end type="italics"></emph.end>45 92 </s> </p> <p type="main"> <s><emph type="italics"></emph>Longitudinem viſus inuenire, n.<emph.end type="italics"></emph.end>48 103 </s> </p> <p type="main"> <s><emph type="italics"></emph>Leuitas corporum in medio grauiore examinatur inſtru<lb></lb>mento, n.<emph.end type="italics"></emph.end>85 181 </s> </p> <pb xlink:href="018/01/244.jpg"></pb> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>M<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>MAchina quæ intellecta ab Archimede pro motu terra, <lb></lb>num.<emph.end type="italics"></emph.end>0 3 </s> </p> <p type="main"> <s><emph type="italics"></emph>Machinarum compoſitio melior eſt quàm earum <expan abbr="augmẽtum">augmentum</expan>, <lb></lb>ſecundum magnitudinem, n.<emph.end type="italics"></emph.end>6 10 </s> </p> <p type="main"> <s><emph type="italics"></emph>Moles minor <expan abbr="eiuſdẽ">eiuſdem</expan> rei aliquando grauior maiori, n<emph.end type="italics"></emph.end>26 49 </s> </p> <p type="main"> <s><emph type="italics"></emph>Machina definitur, qua potuiſſet tellus moueri ab Archi<lb></lb>mede, n.<emph.end type="italics"></emph.end>30 60 </s> </p> <p type="main"> <s><emph type="italics"></emph>Marini æſtus noua hypotheſis in dicatur, ſed non probatur, <lb></lb>num.<emph.end type="italics"></emph.end>62 126 </s> </p> <p type="main"> <s><emph type="italics"></emph>Moles compoſita eadem quam ſpecificam grauitatem habet <lb></lb>in vno medio habet in quocunque medio n.<emph.end type="italics"></emph.end>91 191 </s> </p> <p type="main"> <s><emph type="italics"></emph>Moli compoſitæ ſiquid addatur aut dematur eius grauitas <lb></lb>ſpecifica mutatur, n.<emph.end type="italics"></emph.end>92 194 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>O<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>OR<gap></gap>culi pauci in plures minores trochleas diſtributi <lb></lb>plus poſſunt, quam duæ trochleæ ex multis millibus <lb></lb>orbiculorum, n.<emph.end type="italics"></emph.end>8 14 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>P<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>POndus terreni globi quam notabiliter minueretur iņ <lb></lb>aquæ ſeceſſione, n.<emph.end type="italics"></emph.end>65 133 </s> </p> <p type="main"> <s><emph type="italics"></emph>Pondus Telluris in aqua minueretur obincluſos halitus. </s> <s><lb></lb>num.<emph.end type="italics"></emph.end>68 140 </s> </p> <p type="main"> <s><emph type="italics"></emph>POnderis quæ differentia, ſi vas nunc plenum, nunc <expan abbr="vacuũ">vacuum</expan> <lb></lb>in liquore ponderetur.<emph.end type="italics"></emph.end>70 146 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>R<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>RAtio maior est, ad terminum multiplicem, quàm ad <lb></lb>terminum rationis ſim<gap></gap>liter multiplicatæ, n.<emph.end type="italics"></emph.end>10 16 </s> </p> <p type="main"> <s><emph type="italics"></emph>Ratio duorum grauium in vno medio, vt habeatur, debet <lb></lb>æquipondium eſſe in eodem medio, n.<emph.end type="italics"></emph.end>72 151 </s> </p> <p type="main"> <s><emph type="italics"></emph>Radicis cubicæ facilis extractio, n.<emph.end type="italics"></emph.end>102 220 </s> </p> <p type="main"> <s><emph type="italics"></emph>Huius methodi ratio oſtenditur, n.<emph.end type="italics"></emph.end>103 221 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>S<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>STatera communi potest ingens pondus moueri, n.<emph.end type="italics"></emph.end>16 25 </s> </p> <p type="main"> <s><emph type="italics"></emph>Eius constructio, ibid. </s> <s><lb></lb>Stadij Græci quantitas, n.<emph.end type="italics"></emph.end>18 34 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solis obſeruatio difficultatem patitur, n.<emph.end type="italics"></emph.end>20 37 </s> </p> <p type="main"> <s><emph type="italics"></emph>Stadium Alexandrinum, n.<emph.end type="italics"></emph.end>21 38 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solis diſtantiam a terra, & proportionem cum illa inueſti<lb></lb>gare inuentis aliquibus, n.<emph.end type="italics"></emph.end>23. 40 </s> </p> <pb xlink:href="018/01/245.jpg"></pb> <p type="main"> <s><emph type="italics"></emph>Solida plus leuitant ex mercurio in aquam quàm in aerem, <lb></lb>num.<emph.end type="italics"></emph.end>89 187 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solidi moles ex humido emergens, maior est mole humidi <lb></lb>accurrentis ad replendum ſpatium, n.<emph.end type="italics"></emph.end>97 205 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solidum idem vt extrabatur ex humido, plus debet eleuari <lb></lb>in vaſe maiori quàm in minori, & plus aquæ deſcendit <lb></lb>in vaſe maiori quàm in minori, n.<emph.end type="italics"></emph.end>98 207 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solidi eleuationes, & depreſſiones humidi in vaſis in æqua<lb></lb>libus, non ſunt proportionales, ni ſi in vno caſu, n.<emph.end type="italics"></emph.end>99 210 </s> </p> <p type="main"> <s><emph type="italics"></emph>Superficiem eundem auferre ex datis duabus ſuperficiebus <lb></lb>quæ relinquat reſidua in ratione duplicata datarum̨, <lb></lb>num.<emph.end type="italics"></emph.end>100 215 </s> </p> <p type="main"> <s><emph type="italics"></emph>Solidi in natantis quota pars emergat ex humido, n.<emph.end type="italics"></emph.end>105 226 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>T<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>TRochleæ vtrilibet adnexum pondus non æquali facili<lb></lb>tate mouetur, n.<emph.end type="italics"></emph.end>9 15 </s> </p> <p type="main"> <s><emph type="italics"></emph>Trochlearum coniugatarum compoſitio, quàm magnas vi<lb></lb>res habeat, n.<emph.end type="italics"></emph.end>11 18 </s> </p> <p type="main"> <s><emph type="italics"></emph>Quantum funium in hac machinatione requiratur, nume<lb></lb>ro<emph.end type="italics"></emph.end>13 20 </s> </p> <p type="main"> <s>P<emph type="italics"></emph>auciores orbiculi in ſimplicibus trochleis plus poſſunt, <lb></lb>quam plures in maioribus, n.<emph.end type="italics"></emph.end>14 21 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terra quot orbiculis moueri poſſit, n.<emph.end type="italics"></emph.end>15 22 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ pondus an paucioribus quàm 30, ciphris explicari <lb></lb>queat, n.<emph.end type="italics"></emph.end>16 28 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ magnitudo ex communi ſententia, n.<emph.end type="italics"></emph.end>16 31 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ ad ſolem proportionem ex ſpatio quod vmbris caret <lb></lb>inuestigare, n.<emph.end type="italics"></emph.end>17 32 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ ambitus & diameter, n.<emph.end type="italics"></emph.end>19 36 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ magnitudo probabilior, n.<emph.end type="italics"></emph.end>22 39 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ ſoliditas inueſtigatur, n.<emph.end type="italics"></emph.end>24 45 </s> </p> <p type="main"> <s><emph type="italics"></emph>Eiuſdem grauitas, n<emph.end type="italics"></emph.end>25 46 </s> </p> <p type="main"> <s><emph type="italics"></emph>Hæc ſe habet ac ſi eſſet mera argilla, n.<emph.end type="italics"></emph.end>26 47 </s> </p> <p type="main"> <s><emph type="italics"></emph>Telluris grauitas non tota reſiſteret Archimedi trahenti, <lb></lb>num.<emph.end type="italics"></emph.end>29 58 </s> </p> <p type="main"> <s><emph type="italics"></emph>Huius ſemidiametrum per primam methodum inuestigare <lb></lb>cum Trigonometria, & Algebra, n.<emph.end type="italics"></emph.end>31 65 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aliter & breuius, n.<emph.end type="italics"></emph.end>32 66 </s> </p> <p type="main"> <s><emph type="italics"></emph>Aliter ſine Trigonometria, n.<emph.end type="italics"></emph.end>33 67 </s> </p> <p type="main"> <s><emph type="italics"></emph>Item ſine Trigonometria, & ſine Algebra, n.<emph.end type="italics"></emph.end>34 68 </s> </p> <pb xlink:href="018/01/246.jpg"></pb> <p type="main"> <s><emph type="italics"></emph>Item aliter per Trigonometriam, n.<emph.end type="italics"></emph.end>35 68 </s> </p> <p type="main"> <s><emph type="italics"></emph>Item aliter, & breuiſſimè, n.<emph.end type="italics"></emph.end>36 70 </s> </p> <p type="main"> <s><emph type="italics"></emph>Trigoni æquilateri vſus ad obſeruandos angulos in quo <lb></lb>vix errari poſſit à Geometra, n.<emph.end type="italics"></emph.end>38 76 </s> </p> <p type="main"> <s><emph type="italics"></emph>Telluris ambitus ſecunda methodo inueſtigatur, n.<emph.end type="italics"></emph.end>41 84 </s> </p> <p type="main"> <s><emph type="italics"></emph>Tertia methodus inuestigandi ambitum terræ, n.<emph.end type="italics"></emph.end>43 88 </s> </p> <p type="main"> <s><emph type="italics"></emph>Quarta methodus inueniendi terræ ſemidiametrum, n.<emph.end type="italics"></emph.end>44 89 </s> </p> <p type="main"> <s><emph type="italics"></emph>Quinta methodus terræ ſemidiametrum inuestigandi, nu<lb></lb>mero<emph.end type="italics"></emph.end>48 103 </s> </p> <p type="main"> <s><emph type="italics"></emph>Eiuſdem ſexe a methodus, n.<emph.end type="italics"></emph.end>45 104 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem ſeptima methodo inuestigandi, n.<emph.end type="italics"></emph.end>50 106 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem octaua methodo inuestigandi, n.<emph.end type="italics"></emph.end>51 107 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem aliter, n.<emph.end type="italics"></emph.end>52 108 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem nona methodo inquirendi, n.<emph.end type="italics"></emph.end>53 110 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem decima methodo inquirendi, n.<emph.end type="italics"></emph.end>54 111 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem aliter, n.<emph.end type="italics"></emph.end>55 112 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem vndecima methodo inueniendum, n.<emph.end type="italics"></emph.end>56 113 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem breuius, n.<emph.end type="italics"></emph.end>57 113 </s> </p> <p type="main"> <s><emph type="italics"></emph>Idem duodecima methodo inuestigandi, n.<emph.end type="italics"></emph.end>58 114 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terram mouendi facilitas ex defluxu aquarum, n.<emph.end type="italics"></emph.end>66 135 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ motus facilitas antequam ab aqua ſeiungeretur, <lb></lb>num.<emph.end type="italics"></emph.end>67 139 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terreni globi grauitas ſpecifica maior eſt grauitate argil<lb></lb>læ, ſi aqua dematur ex globo, n.<emph.end type="italics"></emph.end>93 198 </s> </p> <p type="main"> <s><emph type="italics"></emph>Telluri ſi tribuatur grauitas argillacea, aquæ in latus ſe<lb></lb>cedenti non innataret, n.<emph.end type="italics"></emph.end>94 200 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terra intrà aquam minùs ponderaret, n.<emph.end type="italics"></emph.end>94 203 </s> </p> <p type="main"> <s><emph type="italics"></emph>Terræ grauitas librarum numero probabili explicata, nu<lb></lb>mero<emph.end type="italics"></emph.end>96 204 </s> </p> <p type="main"> <s><emph type="italics"></emph>Tellus quantum eleuanda eſſet, vt omnino ab aqua ſeiun<lb></lb>geretur, n.<emph.end type="italics"></emph.end>101 218 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>V<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s><emph type="italics"></emph>HVngaricæ aurifodinæ deſcriptio, n.<emph.end type="italics"></emph.end>26 48 </s> </p> <p type="main"> <s><emph type="italics"></emph>Vini grauitas est media harmonicè inter oleum tarta<lb></lb>ri, & ſpiritum vini, n.<emph.end type="italics"></emph.end>27 50 </s> </p> <p type="main"> <s><emph type="italics"></emph>Viſus distanti a maxima ex quibæs debeat definiri, n.<emph.end type="italics"></emph.end>39 81 </s> </p> <p type="main"> <s><emph type="italics"></emph>Venti deſcendentis cauſa obiter indicatur, n.<emph.end type="italics"></emph.end>74 155 </s> </p> <p type="main"> <s><emph type="italics"></emph>Vacuum tentatum experimento aliquo, & quæ ſita aeris gra<lb></lb>uitas, n.<emph.end type="italics"></emph.end>75 159 </s> </p> <p type="main"> <s><emph type="italics"></emph>Vacuum non dari experimento probatur, n.<emph.end type="italics"></emph.end>77 162 </s> </p> <p type="main"> <s><emph type="center"></emph><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> </chap> </body> <back></back> </text> </archimedes>