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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Thu, 02 May 2013 11:38:23 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <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/> <lang>la</lang> <cvs_file>casat_terra_018_la_1658.xml</cvs_file> <cvs_version/> <locator>018.xml</locator> </info> <text> <front> </front> <body> <chap> <pb xlink:href="018/01/001.jpg"/><p type="main"> <s><emph type="center"/>TERRA <lb/>MACHINIS MOTA <lb/>DISSERTATIONES<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>GEOMETRICAE, MECHANICAE <lb/>PHYSICAE, HYDROSTATICAE<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>In quibus<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Machinarum Coniugatarum vires inter &longs;e comparantur: <lb/>Multiplici Noua Methodo Terræ magnitudo & <lb/>Grauitas inue&longs;tigatur: ARCHIMEDES <lb/>terræ motionem &longs;pondens ab arrogantiæ <lb/>&longs;u&longs;picione vindicatur.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>AVTHORE <lb/>PAVLO CASATO <lb/>E SOCIETATE IESV <lb/><figure id="id.018.01.001.1.jpg" xlink:href="018/01/001/1.jpg"/><lb/>ROMÆ.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Ex Typographia Ignatij de Lazaris. </s> <s>M.DC.LVIII. <lb/><emph type="italics"/>SVPERIORVM PERMISSV.<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="018/01/002.jpg"/> <pb xlink:href="018/01/003.jpg"/><figure id="id.018.01.003.1.jpg" xlink:href="018/01/003/1.jpg"/><p type="main"> <s><emph type="center"/>ILLVSTRISS. AC REVERENDISS. DOMINO <lb/>D. IOANNI GEORGIO <lb/>PATRITIO VENETO<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><expan abbr="VTRIVSq;">VTRIVSque</expan> SIGNATVRÆ REFERENDARIO <lb/><emph type="italics"/>PAVLVS CASATVS E SOCIET AT E IESV<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Felicitatem.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>APVD multos arrogantiæ opinione la­<lb/>borat Archimedes, quòd dato, vbi ip­<lb/>&longs;e con&longs;i&longs;teret, loco tellurem &longs;uis à fun­<lb/>damentis conuellere &longs;e po&longs;&longs;e affirma­<lb/>ret: id &longs;cilicet per &longs;ummam confiden­<lb/>tiam dictum putant, quod cum reap­<lb/>&longs;e ne tentari quidem, ne dum perfici, <lb/>queat, experimento refelli non pote&longs;t. </s> <s>Di&longs;cutienda fuit <lb/>conflata in bonum Senem inuidia criminis, quo &longs;oli erudi­<lb/>tuli afflantur, qui &longs;cientijs leuiter a&longs;per&longs;i &longs;ibi &longs;apientes vi­<lb/>dentur. </s> <s>Et quanquam me vindice non eget Archimedes, <lb/>&longs;ua &longs;apientia aduersùs calumniantium tela &longs;atis protectus; <lb/>illud forta&longs;&longs;e non inutile accidat, &longs;i vel minùs eruditi in­<lb/>telligant nihil e&longs;&longs;e tam arduum, quod &longs;uperari non po&longs;&longs;it &longs;a­<lb/>pientis indu&longs;tria. </s> <s>Tibi certè, Illu&longs;tri&longs;&longs;ime Domine, non <lb/>iniucundam fore hanc elucubratiunculam præ&longs;agit animus <lb/>pro ea humanitatis abundantia, qua literarios omnes cona­<emph.end type="italics"/><pb xlink:href="018/01/004.jpg"/><emph type="italics"/>tus complecti &longs;oles: Illa enim, vbi in lucem prodire datum <lb/>e&longs;t, continuò ge&longs;tijt tuum conuolare in &longs;inum, in quo &longs;e be­<lb/>nignè fouendam &longs;peraret. </s> <s>Alliciebat ingenita clari&longs;&longs;imi <lb/>&longs;anguinis nobilitas auorum nominibus con&longs;picua, innutrita <lb/>virtutibus indoles, morum facilitas &longs;uaui&longs;&longs;ima, grauitas­<lb/>que comitate condita, ingenij acies per&longs;picua, eruditio varia <lb/>atque præclara. </s> <s>Illud vnum ab&longs;terrere poterat properan­<lb/>tem, quod de mouenda tellure di&longs;putans vix &longs;e &longs;u&longs;picari <lb/>debui&longs;&longs;et a&longs;piciendam ab homine, qui inter eos delectus, <lb/>quos aut ad proponendas dirimendasque partium cau&longs;as, aut <lb/>ad Bonum Regimen aduigilare Sapienti&longs;&longs;imus Princeps iu&longs;­<lb/>&longs;it, intentis in Reipublicæ quietem, componendosque ciuium <lb/>motus oculis hæret. </s> <s>Sed cum nulla tibi pereant temporis <lb/>momenta, qui enim potui&longs;&longs;es hunc iuuentutis florem matu­<lb/>ris tot &longs;cientiarum fructibus coronare, naturæ rece&longs;&longs;us phi­<lb/>lo&longs;ophando rimari, in infinitas Iuris ambages excurrere, <lb/>Theologicæ facultatis adyta penetrare, monumenta Eccle­<lb/>&longs;ia&longs;ticæ vetu&longs;tatis euoluere, ni&longs;i velocis ingenij vigorem a&longs;­<lb/>&longs;iduo &longs;tudio foui&longs;&longs;es? </s> <s>Cum, inquam, nulla tibi pereant <lb/>temporis momenta, de&longs;peran dum non fuit hi&longs;ce Di&longs;&longs;ertatio­<lb/>nibus impetrari po&longs;&longs;e ea horarum re&longs;egmina, quæ aut amæ­<lb/>nioribus Mu&longs;is, aut Mathematicæ contemplationi tribuere <lb/>&longs;oles, vt &longs;euerioris negotij laborem literato otio interrum­<lb/>pas. </s> <s>Nihil hìc tua dignum eruditione, quæ e&longs;t Authoris <lb/>tenuitas, inuenies: meæ tamen ob&longs;eruantiæ ve&longs;tigia non ob­<lb/>&longs;cura deprehendas, maximè velim. </s> <s>Multo autem notior <lb/>atquè illu&longs;trior meus erga te animus erit, vbi per tua iu&longs;&longs;a <lb/>licuerit mea in re &longs;tudia officijs vberioribus te&longs;tari. </s> <s>Tuæ <lb/>erit magnanimitatis exilem hanc ob&longs;equij mei te&longs;&longs;eram non <lb/>contemnere. </s> <s>Vale.<emph.end type="italics"/><!-- KEEP S--></s></p><pb xlink:href="018/01/005.jpg"/><p type="main"> <s><emph type="center"/>Amice Lector.<emph.end type="center"/></s></p><p type="main"> <s>MACHINALIS & Hydro&longs;taticæ Philo&longs;ophiæ, <lb/>quam premo, &longs;pecimen aliquod exhibi­<lb/>turus, ac Prodromum tanti&longs;per emi&longs;&longs;u­<lb/>rus dum extrema manus operi accedat, <lb/>Archimedæum Problema &longs;elegi, quo tel­<lb/>lurem moueri po&longs;&longs;e pro&longs;itebatur, ni&longs;i locus, vbi machi­<lb/>na con&longs;i&longs;teret, defui&longs;&longs;et. </s> <s>Qua ille machinatione id per­<lb/>ficere moliretur, Hi&longs;toricis di&longs;putandum relinquo. </s> <s>Mul­<lb/>tiplex &longs;uppetebat methodus; &longs;atis &longs;cio. </s> <s>Placuit tamen <lb/>poti&longs;&longs;imùm o&longs;tendere, quantum in hoc negotio machi­<lb/>narum Compo&longs;itio præ&longs;tet earundem Augmento: id­<lb/>que intrà eiu&longs;dem Facultatis genus; vt vel &longs;olos Vectes <lb/>adhibendo, vel &longs;olas Trochleas &c. </s> <s>quod verò in vno <lb/>genere explicatur, de cæteris dictum facilè intelligitur. </s> <s><lb/>Ne quis autem in motu i&longs;to perficiendo aut immen&longs;as, <lb/>aut innumeras requiri machinas exi&longs;timaret, tentaui to­<lb/>tius globi terraquei grauitatem, quantum coniiciendo <lb/>a&longs;&longs;equi fas e&longs;t, explorare: vnde apertâ con&longs;ecutione con­<lb/>&longs;icitur non adeò multis membris di&longs;tingui oportere ma­<lb/>chinam hoc in opere nece&longs;&longs;ariam: vtinam de materi&etail; <lb/>ipsâ non &longs;atis firmâ dubitari non po&longs;&longs;et. </s> <s>Quoniam ve­<lb/>rò grauitatis notitia pendet ex mole præcognitâ; vt ab­<lb/>&longs;olutum e&longs;&longs;et Problema, methodos indicaui, quibus <lb/>terræ magnitudinem indagare po&longs;simus: vt videlicet ex <lb/>notâ mole pondus innote&longs;cat, & hinc definiri po&longs;&longs;it ma­<lb/>china quæ datæ grauitati mouendæ proportione re&longs;pon­<lb/>deat. </s> <s>Sed quia in motu ip&longs;o aqua in partem &longs;ecederet, <lb/>motumque faciliorem efficeret; examinandum fuit, <pb xlink:href="018/01/006.jpg"/>quantum illa afferre po&longs;&longs;et momenti; id quod fieri non <lb/>potuit &longs;inè Hydro&longs;taticâ exercitatione, qua ignis terræ <lb/>vi&longs;ceribus inclu&longs;i, aëris, & aquæ grauitates inuice&mtail; <lb/>conferrentur. </s></p><p type="main"> <s>Duas in di&longs;&longs;ertationes tribueram hoc opu&longs;culum, <lb/>cum primùm problema hoc in Collegio Romano <lb/>&longs;ub au&longs;picijs Eminenti&longs;&longs;imi Principis Cardinalis Ha&longs;­<lb/>&longs;iæ Lantgrauij explicatum e&longs;t ab Illu&longs;tri&longs;&longs;imo Co­<lb/>mite Antonio de Mont&longs;ort. <!-- KEEP S--></s> <s>Sed quoniam di&longs;&longs;ertatio­<lb/>nes illæ longiores erant, quàm vt facilè hominem ad <lb/>legendum allicerent, & per tempus non licuerat ad <lb/>marginem notas, qua&longs;i eorum, quæ dicuntur, indices, <lb/>apponere, placuit rem totam in quinque di&longs;&longs;ertationes <lb/>di&longs;pertiri, vt legentium commodo &longs;eruirem, additis ad <lb/>marginem notis. </s> <s>Ne verò pauculis ijs, ad quorum ma­<lb/>nus olim venit hæc elucubratiuncula, videar malè co­<lb/>ctam cramben recoxi&longs;&longs;e, non prodeunt &longs;inè auctario hæ <lb/>di&longs;&longs;ertationes, quas plurium eruditorum virorum iudi­<lb/>cia &longs;ubire de&longs;idero, vt doctior fiam. </s></p><p type="main"> <s>Fru&longs;tra quæras ex me, vt ea quæ di&longs;&longs;ertatione comple­<lb/>xus &longs;um, aliorum authoritate firmentur: hæc enim &longs;i <lb/>legi&longs;&longs;em, nolui&longs;&longs;em ex&longs;cribere: ideo plura omi&longs;i, quæ <lb/>ab alijs dicta deprehendi. </s> <s>Non adeò tamen de&longs;ipui, vt <lb/>mihi vni Solem illuxi&longs;&longs;e cen&longs;eam: fieri potuit vt hæc ea­<lb/>dem alijs occurrerent; &longs;ed quæcunque tandem illa &longs;int, <lb/>mihi primùm, nemine prælucente, in mentem vene­<lb/>runt. </s> <s>Hæc autem eo tantùm con&longs;ilio dicta &longs;unt, n&etail; <lb/>plura, quæ in hanc &longs;ententiam afferri potui&longs;&longs;ent, omi&longs;&longs;a <lb/>calumnieris: neque enim omnia per&longs;equi otium &longs;uit. </s></p><p type="main"> <s>Quod &longs;pectat ad &longs;criptionis methodum dialogicam; <pb xlink:href="018/01/007.jpg"/>illam Platonis exemplum ab omni calumniâ vindicat: <lb/>Breuitatem cum per&longs;picuitate con&longs;ectanti methodus hec <lb/>magis arridebat. </s> <s>At quid opus erat calculorum progre&longs;­<lb/>&longs;us, quibus numeri illi indagantur, quos in colloquio <lb/>di&longs;&longs;ertatores afferunt, ad fa&longs;tidium inculcare? </s> <s>Id enim <lb/>communiter periti Arithmetici non faciunt; &longs;ed calamo <lb/>in &longs;chedulâ taciti inue&longs;tigant: id quod ab huius dialogi <lb/>interlocutoribus factum ponimus. </s> <s>Quod &longs;i quis id mihi <lb/>culpæ vertat, &longs;ciat me peccare malui&longs;&longs;e omittendo, <lb/>quam tantâ numerorum vi lectorem onerando. </s> <s>Placuit <lb/>verò tres viros de Mathematicis di&longs;ciplinis optimè me<lb/>ritos (qui diem no&longs;tro æuo obierunt) Galilæum, Mer­<lb/>&longs;ennum, Guldinum di&longs;&longs;ertatores exhibere; vt ex Italicâ <lb/>pariter, Gallicâ, atque Germanicâ Mathe&longs;i commen­<lb/>tatiuncula hæc lucem mutuaretur, quam non potuit ab <lb/>authore recipere. </s> <s>Nec te pluribus volo. </s> <s>Vale. <!-- KEEP S--></s></p><p type="main"> <s><emph type="center"/>SYNOPSIS TOTIVS OPERIS: <lb/><emph type="italics"/>DISSERTATIO PRIMA <lb/>Machinarum vires inter &longs;e comparat. </s> <s><lb/>DISSERTATIO SECVNDA <lb/>Terræ grauitatem inue&longs;tigat. </s> <s><lb/>DISSERTATIO TERTIA <lb/>Methodos varias inueniendi terræ quantitatem proponit. </s> <s><lb/>DISSERTATIO QVARTA <lb/>Ex aquæ &longs;eparatione à terræ motus facilitatem infert. </s> <s><lb/>DISSERTATIO QVINTA <lb/>Minorem telluris grauitatem in aqua explicat.<emph.end type="italics"/><emph.end type="center"/></s></p><pb xlink:href="018/01/008.jpg"/><p type="main"> <s><emph type="center"/>Ioannes Rhò Præpo&longs;itus Prouincialis Societatis Ie&longs;u. </s> <s><lb/>In Prouincia Romana.<emph.end type="center"/></s></p><p type="main"> <s>O<emph type="italics"/>Pu&longs;culum, cui titulus e&longs;t Terra Machinis mota à <lb/>P. <!-- REMOVE S-->Paulo Ca&longs;ato Societ. <!-- KEEP S--></s> <s>No&longs;træ compo&longs;itum, tres viri <lb/>graues, ac docti Eiu&longs;dem No&longs;træ Societ. <!-- KEEP S--></s> <s>perlegerunt, & <lb/>in lucem edi po&longs;&longs;e iudicarunt: quarè facultate mihi conce&longs;&longs;a <lb/>ab Adm. <!-- REMOVE S-->Reu. <!-- REMOVE S-->Padre No&longs;tro Go&longs;vvino Ni<emph.end type="italics"/>K<emph type="italics"/>el Præpo&longs;ito Ge­<lb/>nerali, pote&longs;tatem facio vt imprimatur, &longs;i alijs, ad quos <lb/>&longs;pectat, ità vi&longs;um fuerit. </s> <s>Romæ die 2. Maij 1657.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Ioannes Rhò<emph.end type="italics"/></s></p><figure id="id.018.01.008.1.jpg" xlink:href="018/01/008/1.jpg"/><p type="main"> <s><emph type="italics"/>Imprimatur, <lb/>Si videbitur Reuerendi&longs;s. <!-- REMOVE S-->Patri Sacri Palatij Apoct. <!-- REMOVE S-->Mag. <!-- REMOVE S--><lb/>M. </s> <s>Oddus Vice&longs;g.<emph.end type="italics"/><!-- KEEP S--></s></p><figure id="id.018.01.008.2.jpg" xlink:href="018/01/008/2.jpg"/><p type="main"> <s><emph type="italics"/>Imprimatur <lb/>Fr. <!-- REMOVE S-->Vinoentius Maria Guini&longs;ius Magi&longs;ter, & Reuerendi&longs;simi <lb/>P. Fr. <!-- REMOVE S-->Raymundi Capi&longs;uechi Sac. <!-- REMOVE S-->Apo&longs;t. <!-- REMOVE S-->Pal. <!-- REMOVE S-->Magistri Socius Ord. <!-- REMOVE S--><lb/>Præd.<emph.end type="italics"/><!-- KEEP S--></s> </p><pb xlink:href="018/01/009.jpg" pagenum="1"/><figure id="id.018.01.009.1.jpg" xlink:href="018/01/009/1.jpg"/><p type="main"> <s><emph type="center"/>DISSERTATIO <lb/>PRIMA<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Machinarum vires inter &longs;e <lb/>comparat.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>NVNQVAM minùs alieno tempo­<lb/>re acce&longs;&longs;i&longs;tis, Amici, vt me <lb/>ve&longs;tro a&longs;pectu pariter ac fa­<lb/>miliari&longs;&longs;imâ collocutione re­<lb/>crearetis longo &longs;anè fa&longs;tidio <lb/>grauem. </s></p><p type="main"> <s><emph type="italics"/>Mer.<emph.end type="italics"/><!-- KEEP S--></s><s> Satis in tempore accedo, &longs;i ob&longs;eruan­<lb/>tiam, qua te plurimos no&longs;tri æui Mathema­<lb/>ticos &longs;apientiâ facilè antecedentem colo, <lb/>certis documentis liceat declarate. </s></p><pb xlink:href="018/01/010.jpg" pagenum="2"/><p type="main"> <s><emph type="italics"/>Gul.<emph.end type="italics"/><!-- KEEP S--></s><s> Id nobis quoquè lucro futurum e&longs;t, <lb/>quod dolueris; quos nimirùm &longs;uaui&longs;&longs;im&atail; <lb/>illa tua dicendi facundia po&longs;t mole&longs;tas animi <lb/>curas luculentiùs beabit: nemo &longs;iquide&mtail; <lb/>pleniùs ex fonte bibit, quàm qui &longs;ubducto <lb/>recens fi&longs;tulæ epi&longs;tomio aquam in libertatem <lb/>vindicat. </s> <s>Sed quæ demùm nebula &longs;ere na&mtail; <lb/>tranquillæ mentis diem valuit infu&longs;care? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Haud procul ab hi&longs;ce ædibus obuias <lb/>habui&longs;tis lappas, quæ nec à &longs;e inuicem, nec à <lb/>me, quamuis lite compo&longs;itâ, diuelli poterant. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Itane Verò, Galilæe? </s> <s>auocatum à <lb/>mathematicis contemplationibus animum <lb/>(quod &longs;uperi omen obruant) ad fori conten­<lb/>tiones tran&longs;tuli&longs;ti? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> No&longs;tri &longs;ub&longs;ellij erat, quam detule­<lb/>runt litem dirimendam. </s> <s>Hæc autem illos <lb/>controuer&longs;ia torquebat contentionis forta&longs;sè <lb/>cupidiores quàm veritatis: Qua videlicet <lb/>machinatione tellurem loco mouere decreui&longs;­<lb/>&longs;et Archimedes, ni&longs;i locus, vbi po&longs;&longs;et <expan abbr="cõ&longs;i&longs;tere">con&longs;i&longs;tere</expan>, <lb/>defui&longs;&longs;et. </s> <s>Hic quidem aptâ quinque <expan abbr="facultatũ">facultatum</expan> <lb/>coagmentatione rem totam fui&longs;&longs;e perficien­<lb/>dam a&longs;&longs;erebat: Cont<emph type="italics"/>r<emph.end type="italics"/>à verò ille eximias hu­<lb/>iu&longs;modi vires vni Glo&longs;&longs;ocomo <expan abbr="tribu&etilde;das">tribuendas</expan> con­<lb/>tendebat. </s> <s>Nec planè nullius operæ fuit homi­<lb/>nes Mathematicis leui&longs;simè a&longs;per&longs;os ad con­<lb/>cordiam reuocare; cum alter <expan abbr="diuer&longs;arũ">diuer&longs;arum</expan> facul­<pb xlink:href="018/01/011.jpg" pagenum="3"/>tatum compo&longs;itioni plus ine&longs;&longs;e ad mouen­<lb/>dum momenti &longs;atis frigidè cen&longs;eret, alter Ar­<lb/>chimedem in multiplici tympanorum denta­<lb/>torum acce&longs;sione facilitatis compendia quæ­<lb/>&longs;i&longs;&longs;e affirmaret.</s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Illud crediderim potiùs vocari <lb/>po&longs;&longs;e in controuer&longs;iam, vtrùm &longs;olâ tympano­<lb/>rum dentatorum collabellatione, an verò <lb/>multiplicatâ helice infinitâ mechanicu&mtail; <lb/>hoc miraculum fui&longs;&longs;et patraturus. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ita lanè: modò inter nos conue­<lb/>niat fieri po&longs;&longs;e, vt &longs;tatuamus, quibus mem­<lb/>bris di&longs;tingueretur celeberrimum illud Ar­<lb/>chimedis Inuentum Quadrage&longs;imum, quo <lb/>datâ potentiâ datum pondus moueri po&longs;&longs;e <lb/>iactabat; cui idcircò nonnulli nomen fecere <lb/>Pancratio: nullus &longs;iquidem dubitandi locus <lb/>relinquitur, quin hac machinâ telluri motum <lb/>conciliare moliretur. </s> <s>Cæterùm cum nihil <lb/>nobis ni&longs;i coniectura &longs;uppetat, & quide&mtail; <lb/>quæ varias duci pote&longs;t in partes, qua nihil <lb/>incertius (neque enim me Heronis Alexan­<lb/>drini in Barulco Glo&longs;&longs;ocomum quicqua&mtail; <lb/>moratur) nihil facilè de Archimedis mente <lb/>au&longs;im affirmare, cùm dentatis rotis æquè at­<lb/>que multiplici cochleâ infinitâ idem a&longs;&longs;equi <lb/>potuerit, quod perficere meditabatur. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Athelicis vires inuentorem &longs;uum <pb xlink:href="018/01/012.jpg" pagenum="4"/>atque architectum latuerint? </s> <s>latui&longs;&longs;e aute&mtail; <lb/>oporteat, &longs;i eam Glo&longs;&longs;ocomo, quod mera tym­<lb/>pana dentata con&longs;tituant, po&longs;thabuerit; ne mo <lb/>enim &longs;apiens longioribus ambagibus id per&longs;e­<lb/>quitur, quod po&longs;&longs;it breuiore <expan abbr="comp&etilde;dio">compendio</expan> a&longs;&longs;equi. </s></p><p type="main"> <s><arrow.to.target n="note1"/></s></p><p type="margin"> <s><margin.target id="note1"/><emph type="italics"/><lb/>I <lb/>Glo&longs;&longs;ocomi <lb/>&longs;eu Pancra<lb/>tij constru­<lb/>ctio. <lb/><emph.end type="italics"/></s></p><p type="main"> <s>Sint tympana dentata quinque maior&atail; <lb/>A, B, C, D, E, totidemque minora F, G, H, <lb/>I, K; maximum A circa eundem axem cum <lb/>cylindro S, cui ductarius funis circumducitur, <lb/>con uertatur: quatuor minor a F, G, H, I, com­<lb/>munem cum maioribus B, C, D, E, quibus <lb/>&longs;ingula in axe eodem cohærent, habeant con­<lb/>uer&longs;ionem: minimum verò K, addito manu­<lb/>brio LM, circùm &longs;e torqueatur, & ex illo <lb/>totius machinæ motus initium &longs;umat. </s> <s>Ma­<lb/>nubrii autem flexus LM, ad tympani K &longs;emi­<lb/>diametrum Rationem habeat quintupla&mtail;; <lb/>&longs;ibique pariter reliqua tympana, maiora vi­<lb/>delicet cum minoribus &longs;ibi cohærentibus <lb/>comparata, pro portione re&longs;pondeant: nec <lb/>maximi tympani A Radius, atque cylindri <lb/>S illi infixi &longs;emidiameter, à Ratione hac quin­<lb/>tuplâ di&longs;sideant. </s></p><p type="main"> <s><arrow.to.target n="note2"/></s></p><p type="margin"> <s><margin.target id="note2"/><emph type="italics"/><lb/>II <lb/>Glo&longs;&longs;ocomi <lb/>vires expli­<lb/>cantur. <lb/><emph.end type="italics"/></s></p><p type="main"> <s>His ita con&longs;titutis &longs;atis liquet potentiam <lb/>in M applicatam quintuplo velociorem e&longs;&longs;e <lb/>peripheriâ E, quæ ex mutuâ &longs;uorum denti­<lb/>culorum ac tympani K collabellatione con­<lb/>uertitur. </s> <s>At peripheria E quintuplo pariter <pb xlink:href="018/01/013.jpg"/><figure id="id.018.01.013.1.jpg" xlink:href="018/01/013/1.jpg"/><pb xlink:href="018/01/014.jpg" pagenum="6"/>velociùs mouetur quàm D, & D quàm C, & C <lb/>quàm B, & B quàm A, & A quàm S, hoc e&longs;t <lb/>pondus P illi adne xum. </s> <s>Igitur motus poten­<lb/>tiæ in M (liceat in pagellâ rem ad calculos <lb/>reuocare) ad <expan abbr="motũ">motum</expan> ponderis P e&longs;t vt 15625 <lb/>ad 1. &longs;unt nimirum &longs;ex Rationes quintuplæ, <lb/>ex quibus Ratio motûs potentiæ ad motum <lb/>ponderis componitur. </s> <s>Quare potentia, quæ <lb/>ab&longs;que machinæ &longs;ub&longs;idio centum pondo mo<lb/>uere valeret, hac adhibitâ machinâ pondus <lb/>P librarum 1562500. attollet. </s></p><p type="main"> <s><arrow.to.target n="note3"/></s></p><p type="margin"> <s><margin.target id="note3"/><emph type="italics"/><lb/>III <lb/>Cochleæ in­<lb/>finitæ Com­<lb/>po&longs;itæ uires <lb/>cum Glo&longs;&longs;o­<lb/>como com­<lb/>parantur. <lb/><emph.end type="italics"/></s></p><p type="main"> <s>Iam verò in minorum tympanorum FG <lb/>HIK locum reponantur helices maioru&mtail; <lb/>tympanorum ABCDE denticulis (quos 25 in <lb/>toto ambitu fui&longs;&longs;e exempli gratia &longs;tatuamus) <lb/>congruentes: ip&longs;aque tympana cum &longs;uis <lb/>axibus in &longs;piram deformatis in quadrato lo­<lb/>culamento, vt helicis in&longs;initæ natura fert, <lb/>aptè di&longs;ponantur. </s> <s>Con&longs;tat tympani A pe­<lb/>ripheriam quintuplo tantùm velociorem e&longs;&longs;e <lb/>pondere P; at peripheriam B vigequintuplo <lb/>velociorem quàm A: vnicus enim tympani A <lb/>denticulus promouetur ab integrâ ip&longs;ius B <lb/>conuer&longs;ione; ideoque vt &longs;emel A gyrum ab­<lb/>&longs;oluat, vicies & quinquies tympanum B con­<lb/>uertatur oportet. </s> <s>Eademque ratione tympani <lb/>C motus cum tympani B motu comparatur, <lb/>cuiuse&longs;t vigequintuplus: quemadmodum & <pb xlink:href="018/01/015.jpg" pagenum="7"/>D ip&longs;ius C, & E ip&longs;ius D, & M ip&longs;ius E. <!-- KEEP S--></s> <s>Quare <lb/>Ratio motûs potentiæ M ad motum ponderis <lb/>P, ex vnicâ Ratione quintuplâ, & quinque <lb/>vigequintuplis componitur: E&longs;t igitur motus <lb/>potentiæ ad motum ponderis vt 48828125 <lb/>ad 1: & potentia, quæ pondo centum valeat <lb/>attollere, pondus librarum 4882812500 <lb/>mouebit. </s></p><p type="main"> <s>Cum itaque tam immane pondus moueri <lb/>po&longs;&longs;it quinque tantum cochleis in&longs;initis, <lb/>quæ totidem dentatis tympanis congruant; <lb/>contra verò, reiectâ helice, decem maiora <lb/>totidemque minora tympana componi opus <lb/>&longs;it, vt pondus idem attollatur; liquidò con&longs;tat <lb/>longè <expan abbr="facilior&etilde;">faciliorem</expan> e&longs;&longs;e multiplicis cochleæ, quàm <lb/>Glo&longs;&longs;ocomi v&longs;um; ac proinde quadrage&longs;i­<lb/>mum Archimedis inuentum helicem fui&longs;&longs;e, <lb/>procliuius e&longs;t opinari. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Nec ego inficior, nec diffitetur Gul­<lb/>dinus helicis infinitæ vires cæteris machi­<lb/>nationibus longè præ&longs;tare: &longs;ed quæ nos cogit <lb/>nece&longs;&longs;itas affirmandi Archimedem quadra­<lb/>ge&longs;imo loco in inuentum planè facillimum <lb/>incidi&longs;&longs;e? </s> <s>Quis fuerit Archimedææ contem­<lb/>plationis &longs;copus, in quo conquie&longs;ceret, me, <lb/>fateor, later Quid verò, &longs;i quis machinæ faci­<lb/>litatem non in eo &longs;tatuendam cen&longs;eat, quod <lb/>illa paucioribus membris contineatur; &longs;ed in <pb xlink:href="018/01/016.jpg" pagenum="8"/>hoc potiùs, quod minore operâ parari queat? </s></p><p type="main"> <s><arrow.to.target n="note4"/><lb/>Atqui tympanorum ambitum in denticulos <lb/><figure id="id.018.01.016.1.jpg" xlink:href="018/01/016/1.jpg"/><lb/>æquales di&longs;tribue­<lb/>re, eosque &longs;atis &longs;it­<lb/>mos, ne facilè vi <lb/>ponderis commi­<lb/>nuantur, & i&ntail; <lb/>cylindro ver&longs;atili <lb/>helicem tympani <lb/>denticulis ritè <expan abbr="cõ-gruentem">con­<lb/>gruentem</expan> incide­<lb/>re, haud &longs;anè o­<lb/>&longs;citantem exigunt <lb/>arti&longs;icem. </s> <s>Porrò <lb/>a&longs;&longs;iduus ille toe <lb/>partium &longs;e inui­<lb/>cem atterentium <lb/>affrictus mora&mtail; <lb/>infert non leuem. </s> <s><lb/>Quare nec teme­<lb/>re dixerit qui&longs;­<lb/>piam, denticula­<lb/>tis tympanis va­<lb/>lere iu&longs;&longs;is, re&mtail; <lb/>totam faciliùs per­<lb/></s> <s>fici po&longs;&longs;e multiplici axe in peritrochio, qui <lb/>& leui negotio paratur, & moram recipit nul­<lb/>lam ex mutuâ membrorum affrictione. </s></p><pb xlink:href="018/01/017.jpg" pagenum="9"/><p type="margin"> <s><margin.target id="note4"/><emph type="italics"/><lb/>IV <lb/>Difficulta­<lb/>tes in heli­<lb/>cis constru­<lb/>ctione & <lb/>u&longs;u. <lb/><emph.end type="italics"/></s></p><p type="main"> <s>A&longs;&longs;umantur quinque cylindri ABCDE <lb/><arrow.to.target n="note5"/><lb/>cra&longs;&longs;itudine inæquali (quo enim magis à <lb/>pondere di&longs;tant, graciliores e&longs;&longs;e po&longs;&longs;unt) <lb/>&longs;ingulisque rota canaliculum in ambitu ex­<lb/>cauatum habens adijciatur, cuius d<emph type="italics"/>i<emph.end type="italics"/>ameter <lb/>diametri cylindri &longs;ibi cohærentis quintupla <lb/>&longs;it. </s> <s>Demùm cylindro F addatur manubrium <lb/>OP eandem Rationem quintuplam habens <lb/>ad illius &longs;emidiametrum. </s> <s>Hi verò cylindri <lb/>paralleli in &longs;uo conceptaculo facilè ver&longs;atiles <lb/>ita di&longs;ponantur, vt funis &longs;ingulas rotas am­<lb/>biens ad &longs;uperiorem cylindrum ductus (&longs;i <lb/>fieri id commode po&longs;&longs;it) congruat lineæ, <lb/>quæ horizonti ad perpendiculum in&longs;i&longs;tit. </s> <s><lb/>Hìc pariter con&longs;tat Rationem motûs poten­<lb/>tiæ P ad motum ponderis M ex rationibus <lb/>intermedijs, nimirum &longs;ex quintuplis, com­<lb/>poni. </s> <s>Quarè & hìc motus potentiæ ad pon­<lb/>deris motum e&longs;t vt 15625 ad 1, vt &longs;uperiùs, <lb/>Mer&longs;enne, ratiocinabaris. </s> <s>Maiore tame&ntail; <lb/>forta&longs;sè compendio, quod hìc rotæ cylindros <lb/>non atterant, nec vllum immineat pericu­<lb/>lum, ne ex mutuâ illâ collabellatione den­<lb/>tes aliquando excutiantur: quàm ægrè au­<lb/>tem excu&longs;&longs;i dentis detrimento occurras, pa­<lb/>làm e&longs;t; cum tamen di&longs;ruptum funem ite­<lb/>rum facilè connectas. </s></p><p type="margin"> <s><margin.target id="note5"/><emph type="italics"/><lb/>V <lb/>Axes in Pe­<lb/>ritrochio <expan abbr="Cõ">Com</expan><lb/>po&longs;iti faci­<lb/>liùs con&longs;tru<lb/>untur, & <lb/>idem præ&longs;ta <lb/>re po&longs;sunt. <lb/><emph.end type="italics"/></s></p><p type="main"> <s>Vbi licet obiter animum aduertere ad <pb xlink:href="018/01/018.jpg" pagenum="10"/><arrow.to.target n="note6"/><lb/>multorum artificum imperitiam, qui ex ma­<lb/>chinarum tantùm augmento vires ad mo­<lb/>uenda pondera augeri autumantes, multo la­<lb/>bore, nec modicâ argenti iacturâ immanes <lb/>aliquando machinas con&longs;truunt, quæ vel mo­<lb/>le &longs;uâ prægrauatæ fati&longs;cunt, vel motam mo­<lb/>tui inferunt non mediocrem, adeò vt &longs;olius <lb/>machinæ motio, etiam &longs;eclu&longs;o pondere, cui <lb/>mouendo de&longs;tinatur machina, validioris po­<lb/>tentiæ vires ab&longs;umat: cum tamen rem to­<lb/>tam minore negotio, nec &longs;pernendo pecu­<lb/>niæ atquè laboris compendio, perficere po&longs;­<lb/>&longs;ent, &longs;i rectè intelligerent, quantum machi­<lb/>narum compo&longs;itio præ&longs;tet earum augmento. </s> <s><lb/>Id quod ex quinque his axibus in Peritrochio <lb/>inter &longs;e compo&longs;itis luculenti&longs;&longs;imè demon­<lb/>&longs;tratur; &longs;i enim axi, cuius diameter palma­<lb/>ris, rotam velis infigere, qua po&longs;&longs;is ide&mtail; <lb/>mouere pondus, quod tribus tantùm ex pro­<lb/>po&longs;itis rotis A, B, C, mouetur, quàm imma­<lb/>nis illa erit? </s> <s>Quippe quæ 125 palmos &longs;e­<lb/>cundùm diametrum obtineat: quàm diffi­<lb/>cilis ad conuer&longs;ionem? </s> <s>ob ingentem grauita­<lb/>tis cardines prementis re&longs;i&longs;tentiam: quàm <lb/>multo argento parabilis? </s> <s>cum ea &longs;ola ad tres <lb/>A, B, C, &longs;imul &longs;umptas e&longs;&longs;et vt minimùm in <lb/>Ratione Quadrati &longs;uæ diametri 125 ad tri­<lb/>plum Quadratum diametri rotæ A, hoc e&longs;t <pb xlink:href="018/01/019.jpg" pagenum="11"/>vt 15625 ad 75; materiem autem tantæ mo­<lb/>li nece&longs;&longs;ariam nec modicâ pecuniâ nec &longs;inò <lb/>multis operis comparari po&longs;&longs;e & elaborari <lb/>palàm e&longs;t. </s> <s>Adde quòd illam ex alio in a­<lb/>lium locum transferendi pro multiplici ne­<lb/>ce&longs;&longs;itate, vix &longs;pes aliqua &longs;upere&longs;&longs;et. </s></p><p type="margin"> <s><margin.target id="note6"/><emph type="italics"/>VI <lb/>Machina­<lb/>rum Com­<lb/>po&longs;itio me­<lb/>lior e&longs;t, <expan abbr="quã">quam</expan> <lb/>earum Aug­<lb/>mentum, &longs;e­<lb/>cundùm ma <lb/>gnitudinem<emph.end type="italics"/></s></p><p type="main"> <s>Quamuis verò quinque alios in&longs;uper cy­<lb/>lindros cum &longs;uis rotis adijcere opus e&longs;&longs;et, vt <lb/>æquale pondus attolleretur, atque tuâ illâ <lb/>quinque helicum coagmentatione; in diffi­<lb/>cultates tamen longè maiores incurrat arti­<lb/>fex, nece&longs;&longs;e e&longs;t, qui cochleas quinque cum <lb/>tympanis examu&longs;&longs;im congruentes formare <lb/>iubeatur, ac ille qui decem aut plures axes <lb/>in peritrochio effingere velit; in quibus fi­<lb/>guram exqui&longs;itè rotundam &longs;i de&longs;ideret, &longs;u­<lb/>peruacuo &longs;e labore conficiat: neque enim <lb/>anguli, &longs;i qui &longs;int, obe&longs;&longs;e quicquam po&longs;&longs;unt, <lb/>modò poli, &longs;eu cardines, circa quos ver&longs;an­<lb/>tur, læues &longs;int ac politi. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Sed quanto impendio &longs;taret tan­<lb/><arrow.to.target n="note7"/><lb/>tam funium vim comparare, quæ &longs;atis e&longs;&longs;et; <lb/>vt pondus ad vnius decempedæ altitudinem <lb/>&longs;ubleuaretur? </s> <s>Primùm enim funis, cui pon­<lb/>dus adnecteretur, decem pedes in longitudi­<lb/>ne haberet; igitur qui rotam primam A am­<lb/>biret, e&longs;&longs;et vt minimùm pedum 50. At rotæ <lb/>&longs;ecundæ motus e&longs;&longs;et prioris quintuplus, igi­<pb xlink:href="018/01/020.jpg" pagenum="12"/>tur rotæ B circumduceretur funis pedum <lb/>250, nec di&longs;pari argumentatione conficitur <lb/>rotam tertiam C exigere funem pedum <lb/>1250, quartam D 6250, quintam demùm <lb/>E 31250: ex quibus conflatur &longs;umma pe­<lb/>dum 39060, quæ e&longs;&longs;et totius funis longitu­<lb/>do. </s> <s>Liceat autem hìc di&longs;&longs;imulanter præte­<lb/>rire immodicam rotarum E, D, & C cra&longs;&longs;i­<lb/>tudinem, vt tàm longus funis earum am­<lb/>bitûs terminis contineri po&longs;&longs;et. </s> <s>Nam &longs;i mul­<lb/>tiplici &longs;pirarum &longs;erie ita duceretur funis, vt <lb/>ip&longs;e &longs;e circumplecteretur, motuum Ratio­<lb/>nes, &, quod inde con&longs;equitur, potentiæ mo­<lb/>menta, ipsâ euolutione mutarentur, auctis <lb/>&longs;cilicet aut diminutis ex &longs;ubiectâ &longs;pirarum &longs;e­<lb/>rie rotarum ac cylindorum diametris. </s></p><p type="margin"> <s><margin.target id="note7"/><emph type="italics"/>VII <lb/>Difficultati <lb/>ex funis lon<lb/>gitudine.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/> Hæc eadem, quæ nunc obijcis, mi­<lb/><arrow.to.target n="note8"/><lb/>hi pariter aliquandò non nihil fecere negotij. </s> <s><lb/>Et primùm quidem earum rotularum, qua­<lb/>rum velocior e&longs;t motus, funes quoquè gra­<lb/>ciliores e&longs;&longs;e debere ob&longs;eruabam, quippe qui­<lb/>bus ponderis grauitas minùs reluctetur. </s> <s>Hinc <lb/>verò &longs;atis commodâ con&longs;ecutione conficie­<lb/>bam fieri po&longs;&longs;e, vt exiguis &longs;patijs tanta funi­<lb/>culi longitudo citrà incommodum compre­<lb/>henderetur. </s> <s>Deinde quamuis non adeò lon­<lb/>gus &longs;uppeteret funiculus, operæ pretium vi­<lb/>debatur futurum, &longs;i illo euoluto rotas &longs;i­<pb xlink:href="018/01/021.jpg" pagenum="13"/>&longs;teremus (annulum videlicet auer&longs;æ rotæ A <lb/>infixum arctè cum &longs;uperiore cylindro, n&etail; <lb/>pondus relaberetur, connectentes) explica­<lb/>tum que funiculum, qui in conuer&longs;ione fui&longs;­<lb/>&longs;et cylindrum &longs;uperiorem circumplexus, ite­<lb/>rum rotæ ap&longs;idi circumduceremus. </s></p><p type="margin"> <s><margin.target id="note8"/><emph type="italics"/>Occurritur.<emph.end type="italics"/></s></p><p type="main"> <s>Verùm cum vrbem obambulans oculos <lb/>fortè in officinam quandam conijcerem, vbi <lb/>obtu&longs;arum nouacularum acies re&longs;tituuntur, <lb/>En, inquam, funiculus in &longs;e&longs;e rediens maio­<lb/>ri ac minori rotulæ ità circumplicatus, vt al­<lb/>tera ex alterius conuer&longs;ione rotetur, nullos <lb/>motui terminos præ&longs;cribit: quidni igitur con­<lb/>&longs;imili ratione funiculus vnâ aut alterâ &longs;pirâ <lb/>cylindrum &longs;uperiorem complectens &longs;ubie­<lb/>ctum peritrochium ita apprehendere valeat, <lb/>vt pariter moueantur, nec conuer&longs;ionis fi­<lb/>nem inueniant, cum tantundem &longs;uccedere <lb/>po&longs;&longs;it funiculi, quantum dece&longs;&longs;erit? </s> <s>Id au­<lb/>tem &longs;i fieri po&longs;&longs;e concedas, in &longs;uperioribus <lb/>&longs;altem FEDC (nam in inferioribus forta&longs;sè <lb/>ob ponderis nimiam grauitatem &longs;atius e&longs;&longs;et <lb/>funis extremum religare, ne excurreret) <lb/>difficultas omnis propo&longs;ita euane&longs;cit. </s> <s>Vti­<lb/>nam & in trochleis &longs;imile funis compen­<lb/>dium liceret inuenire. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> An & trochleis tellurem ab Archi­<lb/>mede fui&longs;&longs;e loco dimouendam exi&longs;timas? <pb xlink:href="018/01/022.jpg" pagenum="14"/>Non funium tantùm longitudo aut cra&longs;&longs;itu­<lb/>do, operi non &longs;atis congrua negotium face&longs;­<lb/>&longs;eret, &longs;ed & aptæ trochleæ con&longs;trui omninò <lb/>non po&longs;&longs;ent. </s> <s>Quis enim Chilio&longs;pa&longs;tum com­<lb/>ponat? </s> <s>&longs;ed quantulum demùm e&longs;t Chilio&longs;pa­<lb/>&longs;ti momentum? </s> <s>Neque &longs;i trochleas decem <lb/>orbiculorum millibus in&longs;trueres, quicquam <lb/>po&longs;&longs;es efficere. </s> <s>Nam &longs;i duas huiu&longs;modi tro­<lb/>chleas ità componeres, vt altera ponderi ad­<lb/>necteretur, altera in &longs;uperiore loco firmare­<lb/>tur, eumque adhiberes conatum, quo libras <lb/>centum ab&longs;que machinâ attolleres, conatu <lb/>eodem librarum vicies centena millia moue­<lb/>re po&longs;&longs;es: &longs;ed quid hoc ad immen&longs;um terre­<lb/>ni globi pondus? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Quæ fuerit Archimedi mens, planè <lb/><arrow.to.target n="note9"/><lb/>ignoro: potui&longs;&longs;e tamen fieri, vt ille propo&longs;i­<lb/>tum trochleis adhibitis a&longs;&longs;equeretur, con­<lb/>&longs;tanter a&longs;&longs;ero. </s> <s>Et quidem, quod ad trochleas <lb/>ip&longs;as attinet, ludum puto, modò funes, & <lb/>locus vbi con&longs;i&longs;terem, non dee&longs;&longs;ent. </s> <s>Cedo <lb/>mihi orbiculos quatuor aut &longs;ex &longs;upra cen­<lb/>tum; &longs;atis habeo trochlearum, vt vnicâ ma­<lb/>nu terram à fundamentis, quibus in&longs;i&longs;tit, <lb/>conuellam. </s> <s>Id quod vt minimè dubia de­<lb/>mon&longs;tratione conficiam; illud primum, in <lb/>trochleatum v&longs;u extra controuer&longs;iam po&longs;i­<lb/>tum accipio, quod, funis extremo trochleæ, <pb xlink:href="018/01/023.jpg" pagenum="15"/>cui pondus adnectitur, alligato, potentia re­<lb/>liquum extremum arreptum trahens plus <lb/>obtinet ad mouendum momenti, quàm &longs;i <lb/>funis alteri trochleæ à pondere remotæ ad­<lb/>necteretur; in primo enim ca&longs;u motus po­<lb/>tentiæ ad motum ponderis maiorem habet <lb/>Rationem, quàm in &longs;ecundo. </s></p><p type="margin"> <s><margin.target id="note9"/><emph type="italics"/>VIII <lb/>Orbiculi <lb/>pauci in plu<lb/>res minores <lb/>trochleas di <lb/>stributi plus <lb/>po&longs;&longs;unt, <lb/>quàm duæ <lb/>trochleæ ex <lb/>multis mil­<lb/>libus orbi­<lb/>culorum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Id ego tibi lubens permitto. </s> <s>Nam <lb/><figure id="id.018.01.023.1.jpg" xlink:href="018/01/023/1.jpg"/><lb/>&longs;i trochleas duas R & <emph type="italics"/>S<emph.end type="italics"/> pona­<lb/><arrow.to.target n="note10"/><lb/>mus binis orbiculis in&longs;tructas, <lb/>funis autem extremum A tro­<lb/>chleæ S annulo alligetur, & <lb/>ducatur funis per ABCDEF <lb/>GHIK, con&longs;tat totius funis <lb/>longitudinem quadruplam e&longs;­<lb/>&longs;e interualli, quo trochleæ à <lb/>&longs;e inuicem &longs;eiunguntur. </s> <s>Iam <lb/>verò plurimum intere&longs;t, vtri <lb/>trochlearum pondus adiunxe­<lb/>ris: &longs;i enim pondus in R ad­<lb/>nectatur, potentia K tamdiu <lb/>mouetur, ac ab <emph type="italics"/>S<emph.end type="italics"/> recedit, do­<lb/>nec funis totus explicetur: per­<lb/>currit igitur &longs;patium funis <lb/>longitudini æquale, videlicet <lb/>quadruplum interualli inter <lb/>R & S. <!-- KEEP S--></s> <s>At verò &longs;i pondus in <lb/>S alligetur, eadem potenti&atail; <pb xlink:href="018/01/024.jpg" pagenum="16"/>K ad trochleam R fixam accedit, illamqu&etail; <lb/>tanto &longs;patio tran&longs;greditur, quanta e&longs;t funis <lb/>longitudo: igitur in toto motu percurrit &longs;pa­<lb/>tium quintuplum eius, quod à pondere ver­<lb/>sùs trochleam R moto perficitur. </s> <s>Quoniam <lb/>autem quò tardior e&longs;t ponderis motus cum <lb/>motu potentiæ comparatus, eò minùs pon­<lb/>deris grauitas virtuti potentiæ trahentis ob­<lb/>&longs;i&longs;tit; apertum e&longs;t ac manife&longs;tum faciliùs <lb/>trahi pondus, &longs;i trochleæ S (cui funis in A <lb/>adnectitur) quàm &longs;i trochleæ R alligetur: in <lb/>S nimirum motum obtinet motûs potentiæ <lb/>&longs;ubquintuplum, in R autem &longs;ubquadru­<lb/>plum. </s></p><p type="margin"> <s><margin.target id="note10"/><emph type="italics"/>IX <lb/>Non æqua­<lb/>li facilitate <lb/>moueri pon­<lb/>dus. </s> <s>vtrili­<lb/>bet trochleæ <lb/>adnexu&mtail;, <lb/>demonstra­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Quod præterea Ratione aliquâ min<lb/>noris Inæqualitatis propo&longs;itâ, Antecedens <lb/><arrow.to.target n="note11"/><lb/>terminus ad Con&longs;equentem duplum maio­<lb/>rem habeat Rationem, quàm ad alium Con­<lb/>&longs;equentem, ad quem habeat Rationem pro­<lb/>po&longs;itæ rationis duplicatam (&longs;i tamen &longs;ubdu­<lb/>plam excipias, cùm eadem &longs;umma fiat ex <lb/>duplicis binarij additione, ac ex mutuâ illo­<lb/>rum multiplicatione) nihil habet dubitatio­<lb/>nis. </s> <s>Datâ &longs;iquidem Ratione &longs;ubtriplâ 3 ad <lb/>9, &longs;i Con&longs;equens 9 geminetur, & fiat 18, <lb/>Ratio autem duplicetur inuento tertio con­<lb/>tinuè proportionali 27, maior e&longs;t Ratio 3 ad <lb/>18, quàm 3 ad 27. Similiter maior erit <pb xlink:href="018/01/025.jpg" pagenum="17"/>Ratio ad Con&longs;equentem triplum aut qua­<lb/>druplum, quàm ad alium Con&longs;equente&mtail; <lb/>terminum Rationis triplicatæ aut quadru­<lb/>plicatæ, etiam &longs;i propo&longs;ita Ratio &longs;ubdupl&atail; <lb/>e&longs;&longs;et: &longs;ic &longs;i fuerit Ratio 2 ad 4, triplus Con­<lb/>&longs;equens e&longs;t 12. Con&longs;equens verò Rationis tri­<lb/>plicatæ e&longs;t 16: e&longs;t autem maior Ratio 2 ad <lb/>12, quàm 2 ad 16. </s></p><p type="margin"> <s><margin.target id="note11"/><emph type="italics"/>X <lb/>Maior est <lb/>Ratio ad ter<lb/>minu&mtail; <lb/>Multipli­<lb/>cem, quàm <lb/>ad termi­<lb/>num Ratio­<lb/>nis &longs;imiliter <lb/>Multiplica­<lb/>tæ.<emph.end type="italics"/></s></p><p type="main"> <s>Hinc infero maximum e&longs;&longs;e di&longs;crimen i&ntail; <lb/>augendo potentiæ momento, vtrùm trochleæ <lb/>augeantur orbiculis, an verò trochleæ mul­<lb/>tiplices ex ii&longs;dem orbiculis con&longs;tituantur. </s> <s>Si <lb/>enim trochleæ duæ S & R, quas nuperrimè <lb/>de&longs;crip&longs;i&longs;ti, binis prætereà orbiculis augean­<lb/>tur, ita vt &longs;ingulæ quaternos habeant, mani­<lb/>fe&longs;tum e&longs;t potentiam in K, quæ priùs mo­<lb/>tum habebat quadruplum motûs ponderis in <lb/>R con&longs;tituti, factâ huiu&longs;modi orbiculorum <lb/>acce&longs;sione, motum habere octuplum, vel <lb/>quæ priùs quintuplò velocior erat pondere in <lb/>S adnexo, factam e&longs;&longs;e noncuplò velociorem. </s> <s><lb/>At &longs;i quatuor ho&longs;ce orbiculos non adijcias <lb/>prioribus, &longs;ed duas alias trochleas ex illis com­<lb/>ponas, iam multò maior e&longs;t potentiæ motus <lb/>cum ponderis motu comparatus. </s></p><p type="main"> <s>Sint duæ trochleæ binos orbiculos haben­<lb/>tes A & B: huic autem tum pondus P, tum <lb/>funis extremum adnectatur. </s> <s>Vtique poten­<pb xlink:href="018/01/026.jpg" pagenum="18"/><arrow.to.target n="note12"/><lb/><figure id="id.018.01.026.1.jpg" xlink:href="018/01/026/1.jpg"/><lb/>tia in F motum ha­<lb/>beret quintuplò velo­<lb/>ciorem motu ponde­<lb/>ris P. <!-- KEEP S--></s> <s>Ex quatuor a­<lb/>lijs orbiculis duæ pa­<lb/>riter trochleæ D & C <lb/>con&longs;tituantur: & tro­<lb/>chleæ C adnectatur <lb/>prioris funis <expan abbr="extremũ">extremum</expan>. </s> <s><lb/>Potentia E quintuplò <lb/>&longs;anè velociùs moue­<lb/>tur quàm F, at F quin­<lb/>tuplò velociùs quàm <lb/>P; igitur motus po­<lb/>tentiæ E ad motum <lb/>ponderis P e&longs;t vt 25 <lb/>ad 1. Quare potentia <lb/>vires habens decem <lb/>pondo trahendi &longs;inè <lb/>machinâ, in F trahe­<lb/>ret libras 50, at in E <lb/>libras 250. Quod &longs;i <lb/>tam A quàm B qua­<lb/>ternos haberent or­<lb/>biculos, potentia i&ntail; <lb/>F tantum 90 libras <lb/>mouere po&longs;&longs;et. </s></p><p type="margin"> <s><margin.target id="note12"/><emph type="italics"/>XI <lb/>Trochlea­<lb/>rum coniu­<lb/>gatoru&mtail; <lb/>Compo&longs;itio, <lb/>quàm ma­<lb/>gnas vires. </s> <s><lb/>habeat.<emph.end type="italics"/></s></p><p type="main"> <s>Con&longs;tat itaque du­<pb xlink:href="018/01/027.jpg" pagenum="19"/>plicatis trochleis æquali orbiculorum nume­<lb/>ro in&longs;tructis, motum potentiæ in E haber&etail; <lb/>Rationem duplicatam Rationis, quam habet <lb/>motus potentiæ in F ad motum ponderis in <lb/>P: multiplicatis autem pari numero in ea­<lb/>dem trochleâ orbiculis, ne duplicari quidem <lb/>motum ip&longs;ius potentiæ F. <!-- KEEP S--></s> <s>Quod &longs;i in E pa­<lb/>riter duæ aliæ trochleæ &longs;imiles adiicerentur, <lb/>iam triplicaretur Ratio motûs in F ad mo­<lb/>tum in P, & &longs;ic deinceps. </s> <s>Vno verbo di­<lb/>cam: quot &longs;unt paria &longs;imilium trochlearum, <lb/>progre&longs;&longs;io fit tot Rationum &longs;imilium Ratio­<lb/>ni, quam habet motus ponderis ad motum <lb/>potentiæ primis trochleis applicatæ. </s> <s>Sic &longs;i <lb/>e&longs;&longs;ent talium, quales exhibui, trochlearu&mtail; <lb/>paria decem, a&longs;&longs;umendæ e&longs;&longs;ent decem Ra­<lb/>tiones quintuplæ; & motus potentiæ ad mo­<lb/>tum ponderis Rationem haberet ex his com­<lb/>po&longs;itam, quam &longs;cilicet habet vndecimus ter­<lb/>minus in progre&longs;sione Rationis quintuplæ <lb/>ad vnitatem, hoc e&longs;t 9765625 ad 1. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Si igitur trochleæ omnes ABCD <lb/><arrow.to.target n="note13"/><lb/>tri&longs;pa&longs;ti e&longs;&longs;ent, vnicus equus in E idem pon­<lb/>dus trahere po&longs;&longs;et, quod equi 49; cum ta­<lb/>men in F, &longs;i A & B tripa&longs;ti fuerint, idem <lb/>valeat trahere quod equi &longs;eptem: &longs;i vero A <lb/>& B &longs;enis in&longs;truerentur orbiculis, æquiuale­<lb/>ret equis tredecim. </s> <s>Quis ergo adeò debilis <pb xlink:href="018/01/028.jpg" pagenum="20"/>cantherius, qui nequear &longs;olus trochlearum <lb/>multiplicium ope, maius tormentum belli­<lb/>cum trahere? </s></p><p type="margin"> <s><margin.target id="note13"/><emph type="italics"/>XII <lb/>Vnicus e­<lb/>quus facilè <lb/>pote&longs;t mo­<lb/>uere ingens <lb/><expan abbr="põdus">pondus</expan>, quod <lb/>vix po&longs;&longs;ent <lb/>plures equi.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Ita planè: &longs;ed ob&longs;eruandum in fu­<lb/>nibus. <lb/><arrow.to.target n="note14"/></s></p><p type="margin"> <s><margin.target id="note14"/><emph type="italics"/>XIII <lb/>Quantum <lb/>funium in <lb/>hac machi­<lb/>natione re­<lb/>quiratur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Ne plura: &longs;atis animum ad hoc <lb/>aduerti. </s> <s>Monere volebas tantam requiri <lb/>longitudinem funis, qui &longs;ecundas trochleas <lb/>D & C circumplectitur, vt vnicus ex D in <lb/>C ductus æqualis &longs;it longitudini &longs;patij, quod <lb/>potentia in F totum explicans funem, & pon­<lb/>dus P ad trochleam A v&longs;que deducens, per­<lb/>curreret. </s> <s>Quarè &longs;i interuallum trochlearum <lb/>AB &longs;it pa&longs;&longs;uum decem, potentia ex F per­<lb/>curreret pa&longs;&longs;us 50: funis itaque trochleas D <lb/>& C ambiens longitudinem habeat nece&longs;&longs;&etail; <lb/>e&longs;t pa&longs;&longs;uum vt minimum 200; trochle&atail; <lb/>enim D ibi firmanda e&longs;t, quò funis ABF <lb/>explicatus pertingere po&longs;&longs;it. </s> <s>Eademque d&etail; <lb/>cæteris, &longs;i plures fuerint trochleæ, ratio e&longs;to. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Non falsâ coniecturâ animum meum <lb/>pro&longs;pexi&longs;ti. </s> <s>Sed vt ad rem ip&longs;am propiùs <lb/>accedamus ob&longs;eruandum e&longs;t, propo&longs;ito quo­<lb/>cunque orbiculorum numero, qui tame&ntail; <lb/>per 2, vel 4, vel 6, vel alium quemcunque <lb/>numerum parem diuidi po&longs;sit, longè maius <lb/>e&longs;&longs;e potentiæ momentum, &longs;i plures trochleæ <lb/>pauciorum orbiculorum, quàm &longs;i pauciores <pb xlink:href="018/01/029.jpg" pagenum="21"/>trochleæ plurium orbiculorum con&longs;tituan­</s></p><p type="main"><s><arrow.to.target n="note15"/><lb/>tur. </s> <s>Exhibeantur enim, exempli gratiâ, orbi­<lb/>culi 60, ex quibus &longs;i fiant 20 trochleæ trium <lb/>orbiculorum, iam &longs;unt decem trochlearum <lb/>paria, ac proinde decem Rationes vt &longs;um­<lb/>mum &longs;eptuplæ; igitur momentum potentiæ, <lb/>hoc e&longs;t vndecimus ab vnitate terminus, e&longs;t <lb/>vt 282475249. Si verò fiant binos haben­<lb/>tes orbiculos, erunt 15 trochlearum paria, <lb/>ideoq quindecim Rationes quintuplæ, ex qui­<lb/>bus Ratio motûs potentiæ ad motum ponde­<lb/>ris componitur; erit igitur vt 30517578125 <lb/>ad 1. Con&longs;tat autem ne additis quidem ad­<lb/>huc duobus tri&longs;pa&longs;torum paribus, vt &longs;int in <lb/>vniuer&longs;um orbiculi 72, po&longs;&longs;e adeò augeri po­<lb/>tentiæ momentum: po&longs;itis &longs;iquidem 12 tri­<lb/>&longs;pa&longs;torum paribus momentum potentiæ e&longs;t <lb/>&longs;olùm vt 13841287201. Hinc colligitur <lb/>plus ad mouendum momenti obtinere pau­<lb/>ciores orbiculos in &longs;implicioribus trochleis, <lb/>quàm in trochleis maioribus plures orbicu­<lb/>los: id quod alicui forta&longs;sè paradoxum ac­<lb/>cidat. </s></p><p type="margin"> <s><margin.target id="note15"/><emph type="italics"/>XIV <lb/>Pauciores <lb/>orbiculos in <lb/>&longs;implicibus <lb/>trochleis <lb/>plus po&longs;&longs;&etail;, <lb/>quàm plu­<lb/>res in maio­<lb/>ribus o&longs;ten­<lb/>ditur.<emph.end type="italics"/></s></p><p type="main"> <s>Nunc igitur &longs;i mihi orbiculos centum ex­<lb/>hibeas, &longs;implices trochleas ex &longs;ingulis orbi­<lb/>culis &longs;tatuo, fiuntquè 50 trochlearum &longs;im­<lb/>plicium paria: adnexo autem pondere eidem <lb/>trochleæ, cui funis extremum alligatur, mo­<pb xlink:href="018/01/030.jpg" pagenum="22"/>mentum potentiæ erit triplum: &longs;unt igitur <lb/>50 Rationes triplæ, ex quibus componitur <lb/>Ratio motûs potentiæ ad motum ponderis. </s> <s><lb/>Quærendus iraque e&longs;t terminus in progre&longs;­<lb/>&longs;ione datæ Rationis triplæ ab vnitate quin­<lb/>quage&longs;imus primus. </s></p><p type="main"> <s>Ratio autem tripla quintuplicata e&longs;t 243 <lb/>ad 1. Ducatur 243 per &longs;e ip&longs;um, & e&longs;t Ra­<lb/>tio decuplicata 59049 ad 1. Hic iterum ter­<lb/>minus 59049 per &longs;e ip&longs;um ducatur, & Ratio <lb/>3486.784401 ad 1 e&longs;t ex viginti Rationi­<lb/>bus triplis compo&longs;ita. </s> <s>Ducatur pariter 3486. <lb/>784401 per &longs;e ip&longs;um, & e&longs;t Ratio ex qua­<lb/>draginta Rationibus triplis compo&longs;ita 12. <lb/>157665.459056.928801. ad 1. Hæc de­<lb/>mùm Ratio ducatur per Rationem triplam <lb/>decuplicatam nimirum per 59049, & pro­<lb/>ducitur Ratio, quæ ex 50 Rationibus tri­<lb/>plis componitur 717897.987691.852588. <lb/>770249. ad 1. <!-- KEEP S--></s></p><p type="main"> <s>Quod &longs;i placeat duas adhuc trochleas ter­<lb/>nis orbiculis in&longs;tructas adijcere ip&longs;ique pon­<lb/>deri immediatè adnectere, vt funium &longs;eptu­<lb/>plici ductu faciliùs &longs;u&longs;tineri valeat, adhuc <lb/>Ratio &longs;eptupla addenda, vt ex hac & 50 tri­<lb/>plis tota Ratio componatur: & quinquage&longs;i­<lb/>mus primus terminus progre&longs;sionis Rationis <lb/>triplæ ducendus e&longs;t per 7, vt habeatur totum <pb xlink:href="018/01/031.jpg" pagenum="23"/><arrow.to.target n="note16"/><lb/>potentiæ momentum 5025285.913842. <lb/>968121.391743. Quarè adhibito conatu, <lb/>quo libras decem ab&longs;què machinâ traheres, <lb/>mouere po&longs;&longs;es libras 50.252859.138429. <lb/>681213.917430. Quod pondus totius ter­<lb/>reni globi grauitatem &longs;uperat. </s> <s>Orbiculis ita­<lb/>que &longs;ex &longs;upra centum Archimedæum pro­<lb/>blema de terræ motione ab&longs;olui po&longs;&longs;e o&longs;ten­<lb/>di. </s></p><p type="margin"> <s><margin.target id="note16"/><emph type="italics"/>XV <lb/>Orbiculis <lb/>106 po&longs;&longs;&etail; <lb/>tellure&mtail; <lb/>moueri <expan abbr="de-mõ">de­<lb/>mon</expan>&longs;tratur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Quid verò, &longs;i quis maiorem ad­<lb/>huc grauitatem telluri tribuat? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Parum mihi face&longs;&longs;at hic negotij. </s> <s><lb/>Addat duas præterea trochleas aut quatuor, <lb/>aut plures; & fortè non adeò multas adijcere <lb/>oportebit: Mihi &longs;atis e&longs;t chiliadas illas orbi­<lb/>culorum atque myriadas, quas multi ad­<lb/>&longs;truunt, tanquam minimè nece&longs;&longs;arias refu­<lb/>ta&longs;&longs;e. </s> <s>Nunc quidem &longs;olâ coniecturâ terreni <lb/>globi grauitatem venari po&longs;&longs;umus: dato au­<lb/>tem extra terram loco, in quo con&longs;i&longs;teremus, <lb/>facile e&longs;&longs;et trochlearum numerum definire: <lb/>examinato nimirum &longs;taterâ telluris pondere; <lb/>quo demum cognito trochlearum, quibus <lb/>opus e&longs;&longs;et, numerus innote&longs;ceret. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> At &longs;taterâ, cuius iugum aliquot <lb/>pa&longs;&longs;uum millia occuparet, &longs;acomatis autem <lb/>munere rupes non exigua fungeretur. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Mittamus i&longs;thæc; quæ à te reru&mtail; <pb xlink:href="018/01/032.jpg" pagenum="24"/>huiu&longs;modi apprimè gnaro, animi tantùm <lb/>causâ, in medium proferri &longs;atis video. </s> <s>La­<lb/>nius vel cætarius opportunam &longs;tateram &longs;up­<lb/>peditare po&longs;&longs;et; modò &longs;ingulæ libræ in &longs;uas <lb/>vncias ritè di&longs;tributæ iugum di&longs;tinguerent. </s></p><figure id="id.018.01.032.1.jpg" xlink:href="018/01/032/1.jpg"/><p type="main"> <s>Erige enim ad perpendiculum trabes duas <lb/>æquali interuallo à &longs;e inuicem di&longs;tinctas: A&longs;­<lb/>&longs;umaturque vectis AB, cuius pars decim&atail; <pb xlink:href="018/01/033.jpg" pagenum="25"/>&longs;it AC, (quanquam id &longs;culptor non expre&longs;­<lb/><arrow.to.target n="note17"/><lb/>&longs;it) & extremum A &longs;it circa axem trabi AO <lb/>infixum ver&longs;atile, extremum verò B ita à <lb/>trabe ER di&longs;ter, vt a&longs;&longs;umpto &longs;imili vect&etail; <lb/>DE circùm E ver&longs;atili, & vtroque DE, AB <lb/>parallelo horizonti, perpendicularis BF &longs;e­<lb/>cet pariter FE partem decimam totius DE. <!-- KEEP S--></s> <s><lb/>Idquè in con&longs;equentibus vectibus factum in­<lb/>telligatur. </s> <s>Porrò BF, DI &c. </s> <s>&longs;int ex ma­<lb/>teriâ &longs;olidâ, & circa clauiculos extrema B, F, <lb/>D &c. </s> <s>moueri po&longs;&longs;int; ac po&longs;tremus vectis <lb/>MR habeat propè V lingulam &longs;eu momen­<lb/>tum, vt quandò trabi ER congruit, &longs;ignifi­<lb/>cet vectes omnes con&longs;titutos e&longs;&longs;e horizonti <lb/>parallelos. </s></p><p type="margin"> <s><margin.target id="note17"/><emph type="italics"/>XVI <lb/>Statera <expan abbr="cõ-muni">con­<lb/>muni</expan> pote&longs;t <lb/>ingens pon­<lb/>dus exami­<lb/>nari.<emph.end type="italics"/></s></p><p type="main"> <s>Tum applicatâ in M &longs;taterâ examinetur <lb/>omnium vectium &longs;imul momentum graui­<lb/>tatis. </s> <s>Non grauitatem dico, &longs;ed momen­<lb/>tum grauitatis; quia vectis AB in F &longs;u&longs;pen­<lb/>&longs;us non &longs;ecundùm totam &longs;uam grauitate&mtail; <lb/>deor&longs;um nititur, quia & in A &longs;u&longs;tinetur, &longs;ed <lb/>tantùm &longs;emi&longs;&longs;em totius &longs;uæ grauitatis exer­<lb/>cet. </s> <s>Quia verò DE e&longs;t longitudo decupla <lb/>ip&longs;ius FE, ideò grauitas totius AB non per­<lb/>cipitur in D ni&longs;i &longs;ecundùm partem &longs;ui vige­<lb/>&longs;imam, in H verò &longs;ecundùm partem ducen­<lb/>te&longs;imam, & &longs;ic deinceps; ita vt &longs;i fuerint in <lb/>vniuer&longs;um octo vectes, percipiatur in M &longs;o­<pb xlink:href="018/01/034.jpg" pagenum="26"/>lùm pars vicies millies mille&longs;ima grauitatis <lb/>totius AB. <emph type="italics"/>S<emph.end type="italics"/>ecundi autem vectis DF gra­<lb/>uitas percipitur in M &longs;ecundùm partem &longs;ui <lb/>bis millies mille&longs;imam. </s> <s>Tertius &longs;ecundùm <lb/>partem ducenties mille&longs;imam; & &longs;ic dein­<lb/>ceps, donec vltimus MR grauitet in M &longs;e­<lb/>cundùm &longs;uæ grauitatis &longs;emi&longs;&longs;em. </s> <s>Hinc e&longs;t <lb/>quod quamuis primus vectis AB valdè cra&longs;­<lb/>&longs;us e&longs;&longs;e deberet, atque adeò grauis, vt pon­<lb/>dus valeret &longs;u&longs;tinere, con&longs;equentes tame&ntail; <lb/>vectes minores, ac minores, quod ad cra&longs;&longs;i­<lb/>tudinem &longs;pectat, requirerentur: ac proinde <lb/>eorum momenta in M &longs;imul &longs;umpta no&ntail; <lb/>e&longs;&longs;ent adeò multa. </s> <s>Ponamus itaque facoma­<lb/>te in N exi&longs;tente fieri æquilibrium cum ve­<lb/>ctibus horizonti parallelis. </s></p><p type="main"> <s>His ita con&longs;titutis dimittantur vectes, vt <lb/>ferè quantùm po&longs;&longs;unt de&longs;cendant: & in Gad­<lb/>nectatur pondus. </s> <s>Vel forta&longs;&longs;e opportunius <lb/>erit, &longs;i BF habeat in B annulum, cui in&longs;eri <lb/>po&longs;sit extremum vectis AB; vectis enim ex <lb/>annulo extractus &longs;olus deprimitur, quantum <lb/>pote&longs;t, & pondere in C adnexo, aliâ machi­<lb/>nâ tractoriâ tanti&longs;per eleuatur, dum po&longs;sit <lb/>iterum annulo B in&longs;eri. </s> <s>Ni&longs;i fortè commo­<lb/>dius alicui accidat ita machinam con&longs;truere, <lb/>vt iacens pondus illi adnectatur, deinde ma­<lb/>china ip&longs;a æqualiter eleuetur, vnde fiat vt <pb xlink:href="018/01/035.jpg" pagenum="27"/>vectium capita deprimantur. </s> <s>Tum &longs;acoma <lb/>in &longs;tateræ iugo ab aginâ remoueatur adeò, <lb/>vt vectis MR (atque adeò reliqui omnes) <lb/>horizonti parallelus con&longs;tituatur, & &longs;tatera <lb/>indicet æquilibrium ex. </s> <s>gr. <!-- REMOVE S-->in <emph type="italics"/>S.<emph.end type="italics"/><!-- KEEP S--></s> <s> Sumatur <lb/>igitur differentia SN, quot nimirum libras <lb/>aut vncias contineat: hæc autem multipli­<lb/>cetur per momentum, quod habet potentia <lb/>in M applicata; id quod fit tot additis ci­<lb/>phris, quot &longs;unt vectes, quos &longs;tatuamus e&longs;&longs;e <lb/>octo, SN verò indicare libras 3 vnc. </s> <s>6. Sa­<lb/>coma igitur in S o&longs;tendit pondus P e&longs;&longs;e libr. </s> <s><lb/>300.000000. vnc. 600.000000, hoc e&longs;t in <lb/>vniuer&longs;um libr.350.000000. Quare con&longs;tat <lb/>di&longs;po&longs;itis hac ratione 25. vectibus, po&longs;&longs;&etail; <lb/>vulgari &longs;taterâ examinari pondus libr. </s> <s>250. <lb/>000000.000000.000000.000000. Vectium <lb/>autem huiu&longs;modi apta di&longs;po&longs;itio non ijs &longs;ca­<lb/>teret difficultatibus, quæ &longs;uperari non po&longs;­<lb/>&longs;ent. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Mihi quidem &longs;atis per&longs;ua&longs;um e&longs;t, <lb/>cas, de quibus hactenus di&longs;&longs;eruimus, machi­<lb/>nationes ad tellurem loco dimouenda&mtail;, <lb/>eiusque pondus examinandum aptas e&longs;&longs;&etail;, <lb/>atquè ad potentiæ momenta ferè in immen­<lb/>&longs;um augenda longè præ&longs;tare machinæ eiu&longs;­<lb/>dem multiplicis quàm maioris v&longs;um; in ma­<lb/>iori etenim augetur &longs;olùm Ratio, quæ i&ntail; <pb xlink:href="018/01/036.jpg" pagenum="28"/>multiplici componitur. </s> <s>Sic peritrochiu&mtail; <lb/>diametrum habens decuplam &longs;ui axis facit <lb/>potentiæ momentum decuplum: at duo pe­<lb/>ritrochia Rationem quintuplam ad &longs;uos axes <lb/>habentia &longs;i componantur &longs;imul, potentiæ <lb/>momentum con&longs;tituunt vigequintuplu&mtail;. </s> <s><lb/>Id quod & in cochlearum compo&longs;itione ma­<lb/>nife&longs;tum e&longs;t, cum &longs;atius &longs;it duas cochleas cum <lb/>duobus tympanis componere, quam heli­<lb/>cem vnam &longs;trictiorem vni tympano maiori <lb/>congruentem adhibere. </s> <s>Hoc in vectibus, <lb/>hoc in trochleis abundè e&longs;t demon&longs;tratum. </s></p><p type="main"> <s>Sed adhuc rudioribus quibu&longs;dam eximen­<lb/>da e&longs;t dubitatio, quæ ancipitem animu&mtail; <lb/>torquet, an videlicet ea &longs;it totius globi huius, <lb/>quem terram dicimus, grauitas, quæ ad <lb/>librarum numerum reuocata paucioribus <lb/>quàm triginta ciphris explicari queat. </s> <s>Quam­<lb/>uis enim illam certis finibus circum&longs;cri­<lb/>ptam, ac numero definitam exi&longs;timent, &longs;ibi <lb/>tamen facilè per&longs;uadent <foreign lang="greek">mhdi/va talixou_ton xatw­<lb/>nomasme/non u/pa/rxein</foreign>, vt quidam apud Archi­<lb/>medem arenæ multitudinem con&longs;iderantes <lb/>opinabantur: qua&longs;i Arithmeticæ facultatis <lb/>labor vltimus omnem po&longs;t &longs;e relinqueret no­<lb/>menclaturam. </s> <s>Quantam igitur grauitatem <lb/>globo huic, qui terras ac maria complecti­<lb/>tur, tribuemus? </s></p><pb xlink:href="018/01/037.jpg" pagenum="29"/><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Vereor ne vobis grauis fiam, &longs;i ea <lb/>exponere voluero, quæ aliquando placuit in <lb/>hanc &longs;ententiam commentari. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Immò verò aures meæ ad iucun­<lb/>dam hanc di&longs;putationem patent: ni&longs;i fortè <lb/>negotia habeas, Galilæe, quibus te nunc o­<lb/>porteat intere&longs;&longs;e. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Sum planè vacuus: nec facilè patiar <lb/>tam citò abire amicos, quorum eruditâ con­<lb/>&longs;uetudine tantoperè recreor. </s> <s>An a&longs;ymbo­<lb/>lum te rece&longs;&longs;urum putas, Guldine; Vnum <lb/>habeo, de quo te pariter interrogem, qui a­<lb/>lios ad dicendum excitas: vbi tamen Mer­<lb/>&longs;ennus &longs;uas de terræ grauitate commentatio­<lb/>nes in medium protulerit. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Si me audieritis, di&longs;putatione&mtail; <lb/>hanc in &longs;equentem diem transferemus; cum <lb/>enim numeris aliquot maioribus<emph type="sup"/><emph.end type="sup"/> opus ha­<lb/>beam, longè commodius accidet eos in &longs;che­<lb/>dulâ domi priuatim adnotatos in promptu <lb/>habere, quàm illos inter colloquendum in­<lb/>ue&longs;tigare non &longs;ine mole&longs;tâ &longs;ermonis interru­<lb/>ptione, temporis iacturâ, & capitis defati­<lb/>gatione: nam &longs;atis nos hodiè tor&longs;imus tot <lb/>Rationum compo&longs;itarum inuentione. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Fiat, vt Mer&longs;enno placet. </s></p><pb xlink:href="018/01/038.jpg" pagenum="30"/><figure id="id.018.01.038.1.jpg" xlink:href="018/01/038/1.jpg"/><p type="main"> <s><emph type="center"/>DISSERTATIO <lb/>SECVNDA<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Terræ grauitatem inue­<lb/>&longs;tigat.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>CVM ad ingentia onera loco <lb/>mouenda machinam mem­<lb/>bris non adeò multis di&longs;tin­<lb/>ctam, neque paratu valdè <lb/>difficilem con&longs;trui po&longs;&longs;e, &longs;atis <lb/>he&longs;ternâ di&longs;&longs;ertatione o&longs;tenderimus; illud <lb/>nunc ex te, Mer&longs;enne, audire expectamus, <lb/>quanta &longs;it terreni orbis grauitas, vt quà&mtail; <lb/>magnâ pariter ad eam &longs;uperandam machi­<pb xlink:href="018/01/039.jpg" pagenum="31"/>natione opus habui&longs;&longs;et Archimedes, intelli­<lb/>gamus. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Principio, quoniam id ex me pla­<lb/>cet audire, grauitatem ex mole inue&longs;tigan­<lb/>dam intelligens, quotquot apud authores <lb/>extabant de terræ magnitudine opiniones, <lb/>cœpi ad examen reuocare, vt eas, quæ pro­<lb/>babili alicui coniecturæ & rationi niterentur, <lb/>à temerè con&longs;titutis, &longs;ecernerem. </s> <s>Cum ve­<lb/>rò in omnibus <foreign lang="greek">geometrik/n a)xri/beian</foreign> de&longs;idera­<lb/>rem, & in &longs;ingulis labem aliquam mihi vi­<lb/>derer deprehendere, vulgati&longs;&longs;imæ demù&mtail; <lb/>opinioni acquie&longs;cendum cen&longs;ui, quæ 60 mil­<lb/>liaria Italica mediocria &longs;ingulis gradibus tri­<lb/>buit; vt à veritate minimùm recederem, vel <lb/>&longs;altem eos &longs;olùm haberem aduer&longs;arios, qui <lb/>nimio in antiquitatem &longs;tudio feruntur. <emph type="italics"/>S<emph.end type="italics"/>cru­<lb/>pulus tamen, fateor, animum quantumuis <lb/>di&longs;&longs;imulantem &longs;timulabat, quoties milliaria <lb/>huiu&longs;modi minoribus men&longs;uris di&longs;tinguere <lb/>atque ad pedes reuocare opus erat; que&mtail; <lb/>enim poti&longs;simùm pedem v&longs;urparem, incer­<lb/>tus hærebam; cùm pro diuer&longs;a a&longs;&longs;umpti pe­<lb/>dis longitudine moles tota terreni globi alia <lb/>atquè alia deprehenderetur, di&longs;crimine non <lb/>contemnendo. </s></p><p type="main"> <s>Perpendens itaque corporum vmbras ideo <lb/>&longs;emper in oppo&longs;itam Soli plagam proijci, <pb xlink:href="018/01/040.jpg" pagenum="32"/><arrow.to.target n="note18"/><lb/>quia nulla Solis particula ad perpendiculum <lb/>imminet corpori, quod luce afficitur, i&ntail; <lb/>&longs;pem erigebar aliquid deprehendendi ex &longs;pa­<lb/>tio circa Syenen ab antiquis apud Cleome­<lb/>dem ob&longs;eruato, in quo gnomones nullam <lb/>proijciunt vmbram meridianam Sole Tro­<lb/>picum Cancri percurrente. </s> <s>Si enim in pla­<lb/>no AB erigatur &longs;tylus TI perpendicularis, <lb/>cui immineat Solis extremus limbus O, nul­<lb/>la fit vmbra, quia quamuis ab alio extremo S <lb/>veniat radius SN vltimus, & intrà &longs;patium <lb/><figure id="id.018.01.040.1.jpg" xlink:href="018/01/040/1.jpg"/><lb/>TN nullus alius ve­<lb/>niat radius ab eodem <lb/>puncto S radios in or­<lb/>bem diffundente, in­<lb/>trà illud tamen &longs;pa­<lb/>tium TN veniunt <lb/>radij à cæteris om­<lb/>nibus punctis inter <lb/>S & O intermediis: <lb/>quare nec vmbra vl­<lb/>la aut penumbra ob&longs;eruari pote&longs;t. </s> <s>At &longs;i &longs;ty­<lb/>lus in LM fuerit, proiicit vmbram LP, in­<lb/>trà quod &longs;patium nullus cadit radius dire­<lb/>ctus á punctis O & S aut intermediis; penum­<lb/>bra verò ex P ad B procedit, donec in B me­<lb/>ra lux incipiat. </s> <s>Cum itaque &longs;patio 300 &longs;ta­<lb/>diorum gnomones vmbram non proiicerent, <pb xlink:href="018/01/041.jpg" pagenum="33"/>totum hoc &longs;pa­<lb/><figure id="id.018.01.041.1.jpg" xlink:href="018/01/041/1.jpg"/><lb/>tium illud e&longs;t, <lb/>cui Sol ad per­<lb/>pendiculum im­<lb/>minet. </s></p><p type="margin"> <s><margin.target id="note18"/><emph type="italics"/>XVII <lb/>Terræ ma­<lb/>gnitudinem <lb/>eiu&longs;que ad <lb/>Solem pro­<lb/>portione&mtail; <lb/>inue&longs;tigare <lb/>ex &longs;patio, <lb/>quod umbris <lb/>caret.<emph.end type="italics"/></s></p><p type="main"> <s>Sed <expan abbr="quærendũ">quærendum</expan> <lb/>&longs;upererat, quo­<lb/>ta totius circuli <lb/>maximi pars e&longs;­<lb/>&longs;ent &longs;tadia 300. <lb/>Con&longs;tituto ita­<lb/>que terræ centro <lb/>in C, & oculo <lb/>ob&longs;eruatoris i&ntail; <lb/>O, ductum <expan abbr="in-telligebã">in­<lb/>telligebam</expan> ex cen­<lb/>tro S radium S <lb/>OC, qui cu&mtail; <lb/>radio OT Solem <lb/>contingente da­<lb/>bat angulum S <lb/>OT &longs;emidiametrum apparentem Solis Apo­<lb/>gæi gr.o.m.15., vt placet Tychoni, Longo­<lb/>montano, Magino, Keplero. </s> <s>Item ex C du­<lb/>ctus intelligatur radius Solem tangens, qui <lb/>terræ circulum maximum &longs;ecat in K; & e&longs;t <lb/>OK &longs;emi&longs;sis &longs;patij, quod caret vmbris meri­<lb/>dianis die &longs;ol&longs;titij æ&longs;tiui; continet autem &longs;ta­<pb xlink:href="018/01/042.jpg" pagenum="34"/>dia 150. Certum e&longs;t angulum OCK mino­<lb/>rem e&longs;&longs;e angulo <emph type="italics"/>S<emph.end type="italics"/>OT: &longs;i enim linea CK pro­<lb/>ducta terminaretur in T, tunc angulus SOT <lb/>externus maior e&longs;&longs;et interno oppo&longs;ito OCT: <lb/>quia verò, quod veritati magis e&longs;t con&longs;enta­<lb/>neum, radius ex C Solem tangens e&longs;t CI vl­<lb/>tra T, angulus ISC maior e&longs;t angulo T<emph type="italics"/>S<emph.end type="italics"/>O; <lb/>ac proinde, cum anguli ad T & I &longs;int recti, <lb/>reliquus SCI e&longs;t reliquo SOT minor. </s> <s>E&longs;t igi­<lb/>tur &longs;patium OK minus quàm min.15. Qua­<lb/>re vnus gradus complectitur plura quàm <lb/>600 &longs;tadia, ideoquè totus telluris ambitus <lb/>maior e&longs;t &longs;tadijs 216000. <lb/><arrow.to.target n="note19"/></s></p><p type="margin"> <s><margin.target id="note19"/><emph type="italics"/>XVIII <lb/>Stadij Græ­<lb/>si quanti­<lb/>tas.<emph.end type="italics"/></s></p><p type="main"> <s>Hìc. <!-- REMOVE S-->autem hærebam in &longs;tadio, ne cum <lb/>Suida errarem; hic enim primùm Milio &longs;ta­<lb/>dia 7 1/2 tribuit; &longs;ed po&longs;tmodum Milijs de­<lb/>cem, æqualia facit &longs;tadia 80: Cùm verò &longs;ta­<lb/>dium pedibus 600 definierit, Milium dein­<lb/>de in pedes 4200 di&longs;tribuit: Vnde conficitur <lb/>Milium & 7, & 7 1/2, & 8 &longs;tadia comprehen­<lb/>dere. </s> <s>Quarè acquie&longs;cendum potius duxian­<lb/>tiquo Scholia&longs;ti Græco in propo&longs;. </s> <s>5. lib d&etail; <lb/>Gæod. <!-- REMOVE S-->Heronis Mechanici, qui &longs;tadium fui&longs;­<lb/>&longs;e pa&longs;&longs;uum 100, pa&longs;&longs;um cubitorum 4, cu­<lb/>bitum verò digitorum 24 &longs;cribit. </s> <s>Cum ita­<lb/>que pa&longs;&longs;us Romanus pedibus quinque con­<lb/>&longs;taret, &longs;inguli verò pedes palmis 4, hoc e&longs;t <lb/>digitis 16, pa&longs;&longs;us <emph type="italics"/>R<emph.end type="italics"/>omanus digitos 80 com­<pb xlink:href="018/01/043.jpg" pagenum="35"/>plectebatur, quorum pa&longs;&longs;us Græcus habebat <lb/>96, &longs;c.4.cubitos, &longs;eu, quod idem e&longs;t, pedes <lb/>&longs;ex Romanos. <!-- KEEP S--></s> <s>Stadia igitur &longs;ingula pedes <lb/>Rom. antiquos 600 continebant, hoc e&longs;t pa&longs;­<lb/>&longs;us 120. Hinc fit terræ ambitum maiorem <lb/>&longs;tadijs 216000, maiorem quoquè e&longs;&longs;e pa&longs;si­<lb/>bus <emph type="italics"/>R<emph.end type="italics"/>om. <expan abbr="antiq.">antique</expan> 25920000, hoc e&longs;t mill. <lb/>Rom. 25920. Quarè etiam gradibus &longs;in­<lb/>gulis milliaria Rom. antiqua plura quàm 72 <lb/>re&longs;pondent. </s> </p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> At anguli OCK quantitatem quot <lb/>&longs;crupulis definiebas minorem angulo <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>min. <!-- REMOVE S-->15? </s> </p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Quæ&longs;iui primùm quoties Solis &longs;e­<lb/>midiameter ST contineretur à lineâ SO: dato <lb/>autem SOT gr.o.m.15. reliquus e&longs;t TSO gr. <!-- REMOVE S--><lb/>89.m.45.cuius Secans SO <expan abbr="partiũ">partium</expan> 22918384. <lb/>52745, quarum Radius ST e&longs;t 100000. <lb/>00000. Deinde po&longs;itâ terræ &longs;emidiametro <lb/>CO Algebricè 1 ℞, e&longs;t tota CS 1 ℞ † 22918384 <lb/>52745, cui ex Tychone æquantur &longs;emidia­<lb/>metri terre&longs;tres, 1182, hoc e&longs;t 1182 ℞. </s> <s>Qua­<lb/>re <expan abbr="vtrinq;">vtrinque</expan> &longs;ublatâ 1 ℞, manet æquatio 1181 ℞ <lb/>& 22918384.52745: & in&longs;titutâ diui&longs;ion&etail; <lb/>prouenit pretium vnius Radicis 19405. <lb/>91407. &longs;emidiameter terræ CO, quarum So­<lb/>lis &longs;emidiameter e&longs;t 100000.00000. E&longs;t igi­<lb/>tur tota SC, &longs;i CO inuenta addatur ip&longs;i SO, <pb xlink:href="018/01/044.jpg" pagenum="36"/>partium 22937790.44152, quæ e&longs;t Secans <lb/>gr.89.m.45.&longs;ec.o.Ter.43. Quar. <!-- REMOVE S-->53. &c. </s> <s><lb/>hoc e&longs;t anguli ISC: atque adeò eius comple­<lb/>mentum SCI erit gr.o.m.14.&longs;ec.59. Ter. <!-- REMOVE S--><lb/>16. Quar. <!-- REMOVE S-->7. quem metitur arcus OK &longs;tad. </s> <s><lb/>150. Fiat demùm vt arcus OK inuentus <lb/>&longs;crupulorum Quart. <!-- REMOVE S-->3237367 ad &longs;tadia 150, <lb/>ita totius circuli ambitus &longs;crupulorum Quart. <!-- REMOVE S--><lb/>4665600000. ad &longs;tadia 216175 (67/100), hoc e&longs;t, <lb/>neglectâ fractione, milliaria Rom. <!-- REMOVE S-->antiqu&atail; <lb/>25941. Quapropter &longs;ingulis gradibus mill. <!-- REMOVE S--><lb/>Rom. <!-- REMOVE S-->72. pa&longs;&longs;.58 re&longs;pondent. </s> </p><p type="main"> <s>Porrò inuentâ peripheriâ, &longs;i fiat vt 22 ad 7 </s></p><p type="main"> <s><arrow.to.target n="note20"/><lb/>ita mill. <!-- REMOVE S-->25941. ad mill. <!-- REMOVE S-->8253 (21/22), habetur <lb/>diameter proximè minor verâ; & &longs;i fiat vt <lb/>223 ad 71 ita mill. <!-- REMOVE S-->25941. ad mill. <!-- REMOVE S-->8259 (54/223), <lb/>diametrum verâ proximè maiorem reperi­<lb/>mus: & electo medio Arithmetico rectè &longs;ta­<lb/>tuitur terræ diameter mill. <!-- REMOVE S-->Rom. <!-- REMOVE S-->ant. </s> <s>8255. <lb/>pa&longs;&longs; 644, ideòque &longs;emidiameter mill. <!-- REMOVE S-->4127. <lb/>pa&longs;&longs;. </s> <s>822. Quod &longs;i libeat exactiùs operari, <lb/>quoniam circuli diametro po&longs;itâ 1, perime­<lb/>ter polygoni laterum 2560 circulo circum­<lb/>&longs;cripti minor e&longs;t quàm 3 (14160/100000), perimeter ve­<lb/>rò in&longs;cripti maior e&longs;t quàm 3 (14159/100000); fiat pri­<lb/>mò vt 3. 14160. ad 1, ita mill. <!-- REMOVE S-->25941 ad <lb/>mill.8257.pa&longs;&longs;.257, quæ e&longs;t diameter mi- <!-- page 37 missing in transcription : added by bcfuchs--> <pb xlink:href="018/01/045.jpg" pagenum="37"/> nor verâ deinde vt 3.14159 ad 1, ita mill. <lb/> 25941 ad mill. 8257 pa&longs;&longs;. 283 diametrum<lb/> maiorem verâ. </s><s>Quare cum differentia &longs;it <lb/> pa&longs;&longs; 26, electo medio Arithmetico po­<lb/> terit a&longs;&longs;umi pro terræ diametro <expan abbr="quãtitas">quantitas</expan> mill. <lb/> Rom. antiq. 8257 pas&longs;&longs;. 270. Sed certas <lb/> ob causas placuit a&longs;&longs;umere ambitum mill. <lb/> 25941, atque &longs;emidiametrum mill. 4127. <lb/> pa&longs;&longs; 822.</s></p> <p type="main"><s><emph type="italics"/>Guld.<emph.end/> Methodum hanc, qua & Solaris &longs;e<lb/>midiametri cum terrenâ comparatæ Ratio­<lb/> nem venatus es, & telluris ip&longs;ius magnitu­<lb/> dinem indaga&longs;ti, omnino improbare non <lb/> au&longs;im; quippe qui apparentem Solis &longs;emi­<lb/>diametrum ob&longs;eruari po&longs;&longs;e &longs;atis &longs;cio, & Solis <lb/> à terrâ di&longs;tantiam poti&longs;&longs;imùm ex lunari di­<lb/> chotomiâ haberi ex Ari&longs;tarcho didici: quan­<lb/> tum verò interuallum à nobis Lunam &longs;eiun­<lb/>gat, eiu&longs;dem parallaxes palà faciunt. </s><s> Quæ <lb/> omnia &longs;i retè fuerint con&longs;tituta, non infir­<lb/>mis nititur fundamentis inuenta terræ ma­<lb/> gnitudo: Sed, vt vera fatear, quamuis Sol <lb/> quotidie terrma circumiens lu&longs;tret, illum <lb/> tamen de terrâ, terræ incola inuitus interro­<lb/>go; quotus enim qui&longs;que e&longs;t, qui ignoret, <lb/> quàm oculatum exigat Astronomum appa­<lb/>rentium Solis ac Lunæ &longs;emidiametrorum <lb/> con&longs;titutio? &longs;ivè illæ organis deprehendantur, <lb/> <!-- end missing page --> <pb xlink:href="018/01/046.jpg" pagenum="38"/>tur, &longs;iue ex lucidâ &longs;pecie (quam ab omni pe­<lb/>numbrâ ægrè &longs;ecernas) &longs;iuè ex eclip&longs;ibus in­<lb/>ferantur. </s> <s>Quod &longs;i a&longs;&longs;umpta Lunæ parallaxis <lb/>à vero aliquantulum ab&longs;it, vel quia à radio­<lb/>rum refractione turbetur, vel quia motuum <lb/>periodi non &longs;atis accuratè ad calculos reuo­<lb/>centur, interuallorum pariter, quæ inde col­<lb/>liguntur, veritas nutat. </s> <s>Ad hæc fides adhi­<lb/>benda e&longs;t antiquis &longs;patium, quod meridianis <lb/>vmbris caret, dimetientibus, atque &longs;tadijs <lb/>300 definientibus; quæ tamen ad notas no­<lb/>bis men&longs;uras vt reuocemus, certioribus ad­<lb/>huc argumentis indigemus. </s> <s>Illud tame&ntail; <lb/>hìc minimè di&longs;simulandum videtur, quod <lb/>eruditis non paucis placere video: non eam <lb/>&longs;cilicet &longs;tadij men&longs;uram, quam ex Græco <lb/>Heronis &longs;cholia&longs;te a&longs;&longs;ump&longs;i&longs;ti, adhibendam <lb/><arrow.to.target n="note21"/><lb/>e&longs;&longs;e, &longs;ed eam potiùs, quæ ex ip&longs;ius Heronis <lb/>Mechanici I&longs;agoge colligitur dicentis, <emph type="italics"/>Diau­<emph.end type="italics"/><lb/>l<emph type="italics"/>on habet Stadia duo, Plethra duodecim, Ace­<lb/>nas centum viginti, Cubitos octingentos, Pe­<lb/>des Alexandrinos Philetæreos mille ducentos, <lb/>Italicos autem pedes mille quadringentos qua­<lb/>draginta.<emph.end type="italics"/></s><s> Quare Stadium non Romanis pe­<lb/>dibus 600 con&longs;tat, &longs;ed Alexandrinis 600, hoc <lb/>e&longs;t Italicis, pedibus 720, &longs;eu pa&longs;&longs;ibus 144. <lb/>Neque enim coniecturâ &longs;atis probabili caret <lb/>Erato&longs;thenem Alexandrinæ Bibliothecæ præ­<pb xlink:href="018/01/047.jpg" pagenum="39"/>&longs;ectum à Ptolemæis Euergete, Philopatore, <lb/>& Epiphane, v&longs;um fui&longs;&longs;e men&longs;urâ Ægyptijs <lb/>tunc familiari, pede nimirum Alexandrino, <lb/>atquè adeò etiam &longs;tadio, quod ille metieba­<lb/>tur. </s> <s>Hinc fit &longs;tadia illa 300 re&longs;pondere pa&longs;­<lb/>&longs;ibus Romanis 43200: arcum verò OK e&longs;&longs;e <lb/>pa&longs;&longs; Rom. <!-- REMOVE S-->21600. Igitur &longs;i fiat vt arcus OK <lb/>à te nuper inuentus &longs;crupulorum Quart. <!-- REMOVE S--><lb/>3237367 ad pa&longs;&longs;. </s> <s>Rom. <!-- REMOVE S-->21600, ita tota pe­<lb/>ripheria &longs;crup. </s> <s>Quart. <!-- REMOVE S-->4665600000. ad pa&longs;&longs;. </s> <s><lb/>Rom. <!-- REMOVE S-->31.129297, erit multo maior terræ <lb/>ambitus, quàm à te fuerit deprehen&longs;us. </s> </p><p type="margin"> <s><margin.target id="note20"/><emph type="italics"/>XIX <lb/>Terræ am­<lb/>bitus, & dia­<lb/>meter.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note21"/><emph type="italics"/>XXI <lb/>Stadium A­<lb/>lexandri­<lb/>num.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s>Sed & con&longs;titutam à Tychone Solis di­<lb/>&longs;tantiam, nimis breuibus terminis defini­<lb/>tam exi&longs;timant Recentiores A&longs;tronomi, So­<lb/>lemque altiùs promouendum cen&longs;ent, vt &longs;i­<lb/>bi inuicem phœnomena omnia ritè re&longs;pon­<lb/>deant. </s> <s>Certè P. Io. <!-- REMOVE S-->Bapti&longs;ta Ricciolius no­<lb/>&longs;træ Societatis, qui iam annos plures in A­<lb/>&longs;tronomiæ in&longs;tauratione feliciter de&longs;udat, <lb/>Solem Apogæum à telluris centro remouet <lb/>&longs;emidiam. </s> <s>terr. </s> <s>7580., & Solis Apogæi dia­<lb/>metrum apparentem &longs;tatuit Tychonicâ ma­<lb/><arrow.to.target n="note22"/><lb/>iorem, nimirùm gr.o.m.30.&longs;ec.30. Qua­<lb/>rè &longs;i angulus SOT &longs;it gr.o.m.15.&longs;ec.15., <lb/>complementum TSO e&longs;t gr.89.min.44. <lb/>&longs;ec.45., cuius Secans, SO 22551105.10158, <lb/>quarum partium Radius ST e&longs;t 100000. <pb xlink:href="018/01/048.jpg" pagenum="40"/>00000. Sit iam SC &longs;emid. </s> <s>terre&longs;t. </s> <s>7580, & <lb/>SO &longs;emid.terr. </s> <s>7579: & Secans SO diuida­<lb/>tur per 7579, vt Quotiens 2975.47237, <lb/>prodat quantitatem &longs;emidiametri OC i&ntail; <lb/>partibus Radij ST. </s> <s>Additâ igitur CO ip&longs;i <lb/>OS, erit tota SC 22554080.57395, quæ <lb/>e&longs;t Secans anguli ISC gr.89.m.44.&longs;ec.45. <lb/>Ter. <!-- REMOVE S-->7. Quar. <!-- REMOVE S-->17. Quint. <!-- REMOVE S-->28 1/2, atquè adeo <lb/>complementum SCI gr.o.m.15.&longs;ec.14. <lb/>Ter. <!-- REMOVE S-->52. Quar. <!-- REMOVE S-->42. Quint. <!-- REMOVE S-->31 1/2. Duplicetur <lb/>itaque angulus SCI, & in Scrupula Quinta <lb/>reducatur, & &longs;crupula Quinta 395227503 <lb/>re&longs;pondent &longs;tadijs Alexandrinis 300, hoc e&longs;t <lb/>pa&longs;sibus Rom. <!-- REMOVE S-->43200. Si igitur arcus OK <lb/>duplicatus e&longs;t pa&longs;&longs;. </s> <s>43200, totus circuli am­<lb/>bitus &longs;crup. </s> <s>Quint. <!-- REMOVE S-->279936.000000.erit pa&longs;&longs;. <lb/><arrow.to.target n="note23"/><lb/>Rom. <!-- REMOVE S-->30598162. </s> </p><p type="margin"> <s><margin.target id="note22"/><emph type="italics"/>XXII <lb/>Probabilior <lb/>terræ ma­<lb/>gnitudo ex <lb/>eadem me ­<lb/>tbodo inue­<lb/>stigatur.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note23"/><emph type="italics"/>XXIII <lb/>Solis distan <lb/>tiam à ter­<lb/>ra, & pro­<lb/>portione&mtail; <lb/>cum ill&atail; <lb/>inue&longs;tiga­<lb/>re ex da­<lb/>ta terræ ma­<lb/>gnitudine, <lb/>Solis Apog. <!-- REMOVE S--><lb/>diametro ap. </s> <s><lb/>parenti, & <lb/>&longs;patio, quod <lb/>vmbris ca­<lb/>ret.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Plurimam, opinor, inires gratiam <lb/>ab Eruditi&longs;&longs;. <!-- REMOVE S-->Domino 10. Bapt. <!-- REMOVE S-->Baliano Pa­<lb/>tritio Genuen&longs;i, &longs;i ille no&longs;tro huic colloquio <lb/>intere&longs;&longs;et; ab eo enim accepi &longs;e certi&longs;simo <lb/>experimento didici&longs;&longs;e, telluris ambitum non <lb/>minorem e&longs;&longs;e triginta millibus milliarium. </s> <s><lb/>Tunc verò non poteram illi acquie&longs;cer&etail;, <lb/>cum viderem indè colligi Solem terræ it&atail; <lb/>vicinum, vt ab illâ non abe&longs;&longs;et &longs;emidiam. </s> <s><lb/>terr.25; id quod e&longs;t manife&longs;tè fal&longs;um. </s> <s>Tri­<lb/>buebam autem &longs;ingulis &longs;tadiis pa&longs;&longs;us Rom. <pb xlink:href="018/01/049.jpg" pagenum="41"/>120, vt 300 &longs;tadia e&longs;&longs;ent totius circuli gr. <!-- REMOVE S--><lb/>o.m.28.&longs;ec. <!-- REMOVE S-->35. Ter. <!-- REMOVE S-->12., dato ambitu <lb/>mill. <!-- REMOVE S-->30000: & arcus OK cum e&longs;&longs;et gr.o. <!-- REMOVE S--><lb/>m. </s> <s>14.&longs;ec.17. Ter. <!-- REMOVE S-->36., angulus ISC gr.89. <lb/>m. </s> <s>45. &longs;ec. 42. Ter. <!-- REMOVE S-->24. dabat Secantem SC <lb/>24052069.35. in partibus Radij SI 100000. <lb/>00. Po&longs;itâ verò Tychonicâ &longs;emidiametro <lb/>apparente Solis SOT gr.o.m.15., Secans <lb/>SO erat 22918384. 52. Quare &longs;i per Se­<lb/>cantium SO, SC, differentiam OC 1133684. <lb/>83. diuidatur Secans SC, Quotiens 21 dabit <lb/>di&longs;tantiam Solis à terræ centro in &longs;emidia­<lb/>metris terre&longs;tribus; id quod aperti&longs;simè fal­<lb/>&longs;um e&longs;&longs;e omnibus con&longs;tat. </s> </p><p type="main"> <s>At quoniam vis, Guldine, &longs;tadia illa 300 <lb/>e&longs;&longs;e pa&longs;&longs;us Romanos 43200, tentemus a&ntail; <lb/>illa terræ magnitudo milliaribus 30000 de­<lb/>finita &longs;ub&longs;i&longs;tat. </s> <s>Si ergo circuli totius peri­<lb/>pheria ritè &longs;uas in partes tribuatur, con&longs;tat <lb/>pa&longs;&longs;. </s> <s>43200 re&longs;pondere gr. <!-- REMOVE S-->o.m. </s> <s>31. &longs;ec. <!-- REMOVE S-->6. <lb/>Ter. <!-- REMOVE S-->14. Quar. <!-- REMOVE S-->24. præcisè: & angulus SCI <lb/>gr. <!-- REMOVE S-->o. </s> <s>m. </s> <s>15. &longs;ec. 33. Ter.7. Quar. <!-- REMOVE S-->12. habet <lb/><expan abbr="cõplementum">complementum</expan> ISC gr. 89. m. 44. &longs;ec. 26. Ter. <!-- REMOVE S--><lb/>52. Quar. <!-- REMOVE S-->48., cuius Secans SC 22110369. <lb/>79050, quarum Radius SI e&longs;t 100000.00000. <lb/>Porrò angu'us SOT &longs;emidiameter apparens <lb/>Solis Apogæi nece&longs;&longs;ariò maior &longs;tatui debet <lb/>angulo SCI con&longs;tituto, cum &longs;ub maiore an-<pb xlink:href="018/01/050.jpg" pagenum="42"/>gulo appareat <emph type="italics"/>S<emph.end type="italics"/>ol ex puncto O vicinior&etail;, <lb/>quàm ex puncto C remotiore. </s> <s>Quare a&longs;&longs;u­<lb/>mi non pote&longs;t Solis Apogæi &longs;emidiameter <lb/>apparens, quam ex Ricciolio a&longs;&longs;umebas, gr. <!-- REMOVE S--><lb/>o m. </s> <s>15. &longs;ec. <!-- REMOVE S-->15., neque Tychonica gr.o. <!-- REMOVE S--><lb/>m.15. multò minùs Vendelinica gr.o.m.14. <lb/>&longs;ec.45: Eam igitur ex no&longs;tro Bullialdo de­<lb/>&longs;umamus gr.o.m.16.&longs;ec.9., & complemen­<lb/>ti Secans SO e&longs;t 21288752.30947. Ablata <lb/>itaque SO ex SC relinquit terræ &longs;emidiame­<lb/>trum OC 821617.48103. in partibus Radij <lb/>SI 100000.00000: id quod fieri omnino non <lb/>pote&longs;t, ni&longs;i tellus multò maior &longs;it Sole, & hic <lb/>ab illâ remoueatur tantùm &longs;emidiametros <lb/>terre&longs;tres ferè 27: quæ omnia à vero longi&longs;­<lb/>&longs;imè ab&longs;unt. </s> </p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> At fortè Balianus non ita telluris <lb/>ambitum tricies millenis milliaribus circum­<lb/>&longs;cribit, vt nihil in&longs;uper additum velit, ne­<lb/>què facilè cum Bullialdo tam magnam &longs;ta­<lb/>tuet apparentem &longs;olis Apogæi &longs;emidiame­<lb/>trum, hæc enim &longs;ibi inuicem cohærere non <lb/>po&longs;&longs;unt. </s> <s>Et (quoniam hìc ex amicoru&mtail; <lb/>placitis aliquid vterque depromimus) quod <lb/>&longs;pectat ad apparentem Solis Apogæi diame­<lb/>trum P. Ricciolius, qui eam labore improbo <lb/>plu&longs;quam trig inta diuer&longs;is methodis quadrin­<lb/>genties, & eo amplius, ob&longs;eruando venatus <pb xlink:href="018/01/051.jpg" pagenum="43"/>e&longs;t, certi&longs;simè &longs;e demum deprehendi&longs;&longs;e mi­<lb/>hi aliquando affirmabat, illam nec mino­<lb/>rem minutis 30. nec maiorem min. <!-- REMOVE S-->31. <lb/>Fac igitur à Baliano mediam inter hæc ex­<lb/>trema Solis Apogæi diametrum apparen­<lb/>tem gr. o. m. 30. &longs;ec. 30. a&longs;&longs;umi, & telluris <lb/>ambitum ita augeri, vt ad illum pa&longs;&longs;us 43200 <lb/>minorem habeant Rationem: & &longs;ibi omnia <lb/>re&longs;pondebunt. </s> <s>Statuatur itaque terræ peri­<lb/>pheria pa&longs;&longs;. 30598162; & pa&longs;&longs;us Rom. 43200 <lb/>&longs;unt gr. o. m. 30. &longs;ec. 29. Ter.45 Quar. <!-- REMOVE S-->25. <lb/>Quint.4., adeoquè angulus SCI gr.o.min. <!-- REMOVE S--><lb/>15.&longs;ec. <!-- REMOVE S-->14. Ter. <!-- REMOVE S-->52: Quar. <!-- REMOVE S-->42. Quint. <!-- REMOVE S-->32. <lb/>cuius Complementi Secans SC 22554080. <lb/>57395 in partibus Radij <emph type="italics"/>S<emph.end type="italics"/>I. </s> <s>Iam anguli SOT <lb/>gr. o. m. 15. &longs;ec. <!-- REMOVE S-->15. Secans Complem. <!-- REMOVE S-->SO <lb/>22551105.10158. auferatur ex SC; & per <lb/>earum differentiam OC 2975.47237 diui­<lb/>sâ totâ SC, prodibit di&longs;tantia SC &longs;emid. </s> <s>terr. </s> <s><lb/>7580, vt P. <!-- REMOVE S-->Ricciolio placet. </s> </p><p type="main"> <s>Quarè ex iis, quæ hactenus di&longs;putauimus, <lb/>illud infero, quod auctâ Solis Apogæi diame­<lb/>tro apparente, minui debet terræ ambitus, <lb/>vt ad eum pa&longs;&longs;us 43200 maiorem habeant <lb/>Rationem, ne videlicet tam magno inter &longs;e <lb/>di&longs;crimine differant anguli S O T & <emph type="italics"/>S<emph.end type="italics"/>CI, vt <lb/>per Secantium SO & SC, differentiam OC <lb/>diuisâ di&longs;tantiâ SC <emph type="italics"/>S<emph.end type="italics"/>ol terræ vicinior &longs;tatua­<pb xlink:href="018/01/052.jpg" pagenum="44"/>tur, quàm par &longs;it ad phœnomena omni&atail; <lb/>explicanda. </s> <s>Hinc fit retentâ eadem terræ <lb/>magnitudine non ita augeri &longs;emidiametrum <lb/>apparentem <emph type="italics"/>S<emph.end type="italics"/>olis Apogæi, vt angulus <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>&longs;it gr. o. m. 15. &longs;ec. 25.; Secans enim <emph type="italics"/>S<emph.end type="italics"/>O e&longs;&longs;et <lb/>22306254.81750; quæ ablata ex inuentâ <lb/>&longs;uperiùs <emph type="italics"/>S<emph.end type="italics"/>C 22554080.57395. relinqueret <lb/>differentiam OC 247825.75645.atque adeò <lb/><emph type="italics"/>S<emph.end type="italics"/>ol Apogæus &longs;emid. </s> <s>terr. </s> <s>91. à terrâ remoue­<lb/>retur. </s> <s>Minuenda itaque e&longs;t vel Solis appa­<lb/>rens diameter, vel terræ magnitudo; ego ve­<lb/>rò illam potiùs paucioribus &longs;crupulis &longs;ecun­<lb/>dis definiendam cen&longs;erem, quàm terræ am­<lb/>bitum ad pauciora milliaria reuocandum. </s></p><p type="main"> <s><emph type="italics"/>Gal. <!-- KEEP S--></s> <s>S<emph.end type="italics"/>ed quid his longiùs immoramur? </s> <s><lb/>quorum &longs;ubtilior inue&longs;tigatio à no&longs;tro in­<lb/>&longs;tituto aliena deprehenditur. </s> <s>Nemo t&etail;, <lb/>Mer&longs;enne, reprehendat cæle&longs;tes hypothe&longs;es <lb/>ex magno illo Atlante Tychone a&longs;&longs;umen­<lb/>tem; & quamuis ego pariter in eâ &longs;im &longs;en­<lb/>tentiâ, vt exi&longs;timem ab Eratho&longs;tene homi­<lb/>ne Cyrenen&longs;i adhibitum &longs;tadium Alexandri­<lb/>num, non autem Græcum, quod a&longs;&longs;umebas, <lb/>hanc tamen litem hìc agitare non e&longs;t operæ <lb/>pretium. </s> <s>Quapropter perge, &longs;i placet, qua <lb/>cæpi&longs;ti viâ, terreni globi grauitatem explorare. </s> <s><lb/>rare. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Inuentam terræ &longs;emidiametrum <pb xlink:href="018/01/053.jpg" pagenum="45"/>mill. <!-- REMOVE S-->Rom. <!-- REMOVE S-->4127 pa&longs;&longs;.822. ad pedes reuoco, <lb/><arrow.to.target n="note24"/><lb/>pedes quinque Romanos antiquos pa&longs;&longs;ibus <lb/>&longs;ingulis tribuens, & &longs;unt pedes 20639110. <lb/>Quia verò &longs;phæræ &longs;unt in triplicatâ Ratione <lb/>&longs;emidiametrorum, comparo terrenam &longs;e­<lb/>midiametrum cum &longs;emidiametro pedali al­<lb/>terius globi, & <emph type="italics"/>R<emph.end type="italics"/>ationem 1. ad 20.639110 <lb/>v&longs;que, ad quartum terminum continuo, vt <lb/>&longs;it tertius terminus 425.972861.592100. <lb/>quartus autem 8791.700747.414127. <lb/>031000. <emph type="italics"/>S<emph.end type="italics"/>phæra igitur &longs;emidiametri pedalis <lb/>ad terrenam &longs;phæram <emph type="italics"/>R<emph.end type="italics"/>ationem habet ean­<lb/>dem, quam vnitas ad quartum hunc termi­<lb/>num. </s> <s>Vt autem &longs;phæræ argillaceæ, cuius <lb/>&longs;emidiameter pedalis &longs;it, grauitatem per­<lb/>&longs;pectam haberem, argillam cum aquâ con­<lb/>tuli, & experimento didici argillæ grauita­<lb/>tem ad aquæ pondus e&longs;&longs;e vt 27 ad 16. At <lb/>&longs;tanni grauitas ad aquæ grauitatem apud <lb/>Ghetaldum in Archimede Promoto e&longs;t vt <lb/>100 ad (13 19/37), hoc e&longs;t, vt 37 ad 5. <emph type="italics"/>S<emph.end type="italics"/>i igitur <lb/>Ratio &longs;tanni ad aquam, & aquæ ad argillam, <lb/>&longs;cilicet 37 ad 5. & 16 ad 27 in tribus termi­<lb/>nis continuetur, ita vt &longs;int 592,80. 135, <lb/>Ratio grauitatis &longs;tanni ad argillæ pondus, da­<lb/>tâ molis æqualitate, e&longs;t vt 592 ad 135. </s></p><p type="margin"> <s><margin.target id="note24"/><emph type="italics"/>XXIV <lb/>Terreni glo<lb/>bi &longs;oliditas <lb/>inue&longs;tiga­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s>Quoniam verò apud eundem Ghetaldum <lb/>&longs;tanneæ &longs;phæræ, cuius diameter &longs;it vnius pe­<pb xlink:href="018/01/054.jpg" pagenum="46"/>dis Rom. <!-- REMOVE S-->antiqui, grauitas e&longs;t exactè lib. 304 <lb/>& &longs;phæræ &longs;unt in triplicatâ Ratione diame­<lb/>trorum, &longs;phæra &longs;tannea &longs;emidiametrum ha­<lb/>bens pedalem, ac proinde diametrum bipe­<lb/>dalem, e&longs;t octuplo grauior illâ, atque adeò <lb/>lib, 2432. Atqui &longs;tannum ad argillam, e&longs;t <lb/>vt 592 2d 135, igitur & eandem Rationem <lb/>habent æquales &longs;phæræ; ideoque &longs;i &longs;tannea <lb/>&longs;phæra &longs;emidiametrum pedalem habens nu­<lb/>merat in grauitate libras 2432, argillace&atail; <lb/>æqualis erit lib. (554 22/37). Hæc autem ad terræ <lb/>globum e&longs;t vt vnitas ad quartum illum ter­<lb/>minum continuè proportionalem in Ratione <lb/>&longs;emidiametrorum. </s> <s>Multiplicetur igitur quar­<lb/><arrow.to.target n="note25"/><lb/>tus ille terminus 8791.700747.414127. <lb/>031000. per libras (554 22/37), & prodibit totius <lb/>terræ grauitas, &longs;i ex merâ argillâ con&longs;taret, <lb/>librarum 4.875829.711809.132072. <lb/>(327567 21/37). </s></p><p type="margin"> <s><margin.target id="note25"/><emph type="italics"/>XXV <lb/>Terreni glo <lb/>bi grauitas.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Immen&longs;um places, Mer&longs;enne: lu­<lb/>culenti&longs;simè enim demon&longs;tra&longs;ti quatuor illis <lb/>aut &longs;ex &longs;upra centum orbiculis, de quibus <lb/>heri nobis &longs;ermo erat, tellurem totam facil­<lb/>limè moueri po&longs;&longs;e, etiam &longs;i eius grauitati <lb/>quingenties millies millena librarum mil­<lb/>lia adiiceres. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ita planè, &longs;i mera e&longs;&longs;et argilla: &longs;ed <lb/>tot marmora ac lapides, ingentesque metal­<pb xlink:href="018/01/055.jpg" pagenum="47"/>lorum fodinæ, quæ argillæ grauitatem lon­<lb/>go &longs;uperant interuallo, non eam vim ad­<lb/>dunt ponderis, quæ non facilè æ&longs;timari <lb/>queat? </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Immò verò, ni&longs;i hæc pariter ad­<lb/>mi&longs;cerentur, vererer plurimùm, ne mihi <lb/>tanquam prodigo &longs;uccen&longs;eretis, qui tantam <lb/>telluri grauitatem concederem. </s> <s>Metall&atail;, <lb/><arrow.to.target n="note26"/><lb/>fateor, ac marmora æqualem argillæ molem <lb/>pondere &longs;uperant: &longs;ed quota demum &longs;phæ­<lb/>ræ huius pars illa &longs;unt? </s> <s>Quod &longs;i quis ill&atail; <lb/>grauiora e&longs;&longs;e inculcet, longè leuiorem a­<lb/>quam cogitet, ex qua vici&longs;sim globus hic <lb/>terraqueus con&longs;tat. </s> <s>Qui&longs;quis enim &longs;e æquum <lb/>rerum æ&longs;timatorem præbuerit, non plus re­<lb/>periri <expan abbr="metallorũ">metallorum</expan> quàm aquæ autumet: qui&ntail;<lb/>immo illorum grauitatem ab huius leuitate <lb/>&longs;i non æquari, aut &longs;uperari, magnâ &longs;altem <lb/>ex parte compen&longs;ari facilè concedat. </s> <s>Iam <lb/>verò &longs;i ad aëris vim non modicam terræ ca­<lb/>uernis atque cuniculis inclu&longs;am, &longs;eque intrà <lb/>&longs;iccorum corporum particulas non &longs;ibi om­<lb/>ninò cohærentes in&longs;inuantem, animum ad­<lb/>uertamus, apparebit illicò exuperantiam il­<lb/>lam grauitatis hoc defectu vberrimè com­<lb/>pen&longs;ari. </s></p><p type="margin"> <s><margin.target id="note26"/><emph type="italics"/>XXVI <lb/>Terræ gra­<lb/>uitatem pe­<lb/>rinde &longs;e ba­<lb/>bere proba­<lb/>tur, ac &longs;i e&longs;­<lb/>&longs;et mera ar­<lb/>gilla.<emph.end type="italics"/></s></p><p type="main"> <s>Sed quoniam motus, cui tellus &longs;uo pon­<lb/>dere ob&longs;i&longs;teret, in circumfu&longs;o hoc aëre per­<pb xlink:href="018/01/056.jpg" pagenum="48"/>ficiendus e&longs;&longs;et; minuitur adhuc momen­<lb/>tum ab halituum aëre leuiorum copiâ penè <lb/>infinitâ, quæ totam hanc molem peruadit. </s> <s><lb/>Quemadmodum enim nauis aërem aquâ <lb/>leuiorem includens in aquâ non mergitur, &longs;i <lb/>tota moles compo&longs;ita æqualis aquæ grauita­<lb/>tem non vincat; vel &longs;altem minore mo­<lb/>mento de&longs;cendit pro inclu&longs;i aëris portione; <lb/>haud ab&longs;imili ratione fieri pote&longs;t, vt grauiori <lb/>corpori tot &longs;piritus aëre leuiores permi&longs;cean­<lb/>tur, vt totius compo&longs;itæ molis grauitas non <lb/>mediocriter minuatur. </s> <s>Quantum verò hu­<lb/>iu&longs;modi halituum metallicis lapidibus im­<lb/>mi&longs;ceatur, &longs;atis &longs;ciunt, quotquot &longs;odinarum <lb/>latebras penetrârunt. </s> <s>Et vt cæteras mi&longs;&longs;as <lb/>faciam, Hungaricæ aurifodinæ, mihi ma­<lb/>gis notæ, omnem præcidunt dubitandi an­<lb/>&longs;am. </s> <s>Cum enim duæ pateant ad de&longs;cen­<lb/>dendum viæ, altera breui&longs;sima, vtpote re­<lb/>cta, putei in modum (caminum rectiùs <lb/>forta&longs;&longs;e dixeris) cuius latera muniunt arctè <lb/>compacti arborum trunci: altera obliqu&atail;, <lb/>& longior per cuniculos: per hanc perpetuò <lb/>&longs;e frigidus aër magno impetu in ima fodinæ <lb/>vi&longs;cera in&longs;inuat, dum ex illâ calida pariter <lb/>atque graueolens expiratio erumpit. </s> <s>Ne­<lb/>que indigent metallarii A&longs;trologorum næ<lb/>nijs, qui imminentem cæli mutationem <pb xlink:href="018/01/057.jpg" pagenum="49"/>prædicant; cum ip&longs;i ex immodicâ halituum <lb/>infernè a&longs;cendentium copiâ, quibus vix non <lb/>præfocantur, cœlum nubibus proximè ob­<lb/>ducendum nec dubiè pronuncient. </s> <s>Quid? <!-- KEEP S--></s> <s><lb/>quod aqua ip&longs;a (licet aëre grauior, &longs;i &longs;ibi ip&longs;a <lb/>relinquatur) leui&longs;simi vaporis &longs;peciem induit <lb/>calore &longs;ollicitata, quo interior terræ plag&atail; <lb/>abundat: Vbi enim octoginta circiter hexa­<lb/>podas, quibus extima hæc terræ regio frigi­<lb/>di&longs;sima definitur, de&longs;cenderis, tepor primùm <lb/>grati&longs;simus ex frigidâ regione venientem ex­<lb/>cipit ac recreat, paulatimque adeò augetur <lb/>calor, vt demùm metalli fo&longs;&longs;ores ve&longs;tem nul­<lb/>lam ferant. </s></p><p type="main"> <s>Quantum autem momenti ad pondus mi­<lb/>nuendum obtineat grauium hæc atque le­<lb/>uium mi&longs;cella, ille facilè intelliget, qui ob­<lb/>&longs;eruauerit aliquando &longs;tibium ad v&longs;us medi­<lb/>cos excoctum æquè graue reperiri, ac de­<lb/>prehen&longs;um fui&longs;&longs;et, antequam igni commit­<lb/>teretur; quamuis inde vi flammæ ingens va­<lb/>porum ac fumi copia eruperit; &longs;piritus enim, <lb/>qui auolârunt, cum aërem leuitate vince­<lb/>rent, cæteris partibus admi&longs;ti molem con­<lb/>&longs;tituebant maiorem quidem, &longs;ed non grauio­<lb/>rem, ac &longs;it deinde reliqua moles minor, fa­<lb/>ctâ hac halituum &longs;ece&longs;sione. </s> <s>Perinde atque <lb/>&longs;i vas æreum aquâ iuxta ac aëre plenum in­<pb xlink:href="018/01/058.jpg" pagenum="50"/>trà aquam ponderetur, deinde ita eius late­<lb/>ra comprimantur, vt aquam omnem ac <expan abbr="a&etilde;-rem">ae­<lb/>rem</expan> excludant, etiam &longs;i modicum aliquid æ­<lb/>ris deteratur, adhuc æqualibus momentis in <lb/>aquâ grauitare deprehenditur, &longs;i ad libræ <lb/>examen reuocetur; aeris nimirùm leuitas <lb/>æris momenta minuebat. </s></p><p type="main"> <s>Ne quis verò ductam ex va&longs;e &longs;imilitudi­<lb/>nem calumnietur; Liberum patrem coga­<lb/>mus pauli&longs;per philo&longs;ophari. </s> <s>Dabitis, opinor <lb/>vini grauitatem ferè aquæ &longs;ub&longs;e&longs;qui-&longs;exage­<lb/>cuplam, vel certè aquæ pondere non maio­<lb/>rem; ita vt quodcunque aquæ grauitate præ­<lb/>&longs;titerit, haud immeritò vino pariter grauius <lb/>cen&longs;eatur. </s> <s>Atqui Tartarum ex vino &longs;ub&longs;ide­<lb/>re nemo ne&longs;cit; & quod inde elicitur oleum <lb/>Tartari, e&longs;t proximè ad aquam vt 3 ad 2: &longs;pi­<lb/>ritus autem vini ad aquam communem, Ra­<lb/>tionem habet proximè, quam 3 ad 4. Qua­<lb/>re &longs;i vinum eiu&longs;dem cum aquâ grauitatis <lb/>con&longs;tituatur, Oleum Tartari ad vinum e&longs;t <lb/>vt 6 ad 4, vinum autem ad &longs;piritum vini vt <lb/><arrow.to.target n="note27"/><lb/>4 ad 3. <!-- KEEP S--></s></p><p type="margin"> <s><margin.target id="note27"/><emph type="italics"/>XXVII <lb/>Vini graui­<lb/>tas medi&atail; <lb/>Harmonicè <lb/>inter Oleum <lb/>Tartari, & <lb/>Spiritu&mtail; <lb/>vini.<emph.end type="italics"/></s></p><p type="main"> <s>Quod &longs;i vini Tartarum &longs;imul ac &longs;piritum <lb/>complectentis grauitas medio loco &longs;e habet <lb/>(& quidem medietate Harmonicâ) inter id <lb/>quod grauius, & id quod leuius e&longs;t, quamuis <lb/>extrema illa non ita multo di&longs;criminentur in­<pb xlink:href="018/01/059.jpg" pagenum="51"/>teruallo: quidni terrena hæc moles ex gra­<lb/>ui&longs;simis quidem metallis atque lapidibus, <lb/>&longs;ed & ex corporibus alijs argillâ leuioribus, <lb/>ex aquâ, <expan abbr="a&etilde;re">aere</expan>, &longs;ubtili&longs;simisque expirationi­<lb/>bus coagmentata mediocrem argillæ graui­<lb/>tatem (quantum fas e&longs;t coniecturâ a&longs;&longs;equi) <lb/>obtinere dicatur? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Fallor, &longs;i Tartarus ip&longs;e ad exte­<lb/>nuandam terræ grauitatem tibi &longs;uppetias <lb/>non tulerit. </s> <s>Ob oculos pones immen&longs;a &longs;pe­<lb/>læa æternis flammarum globis redundantia, <lb/>& exaggeratâ longè latèque patentis impio­<lb/>rum carceris magnitudine (quam penetra­<lb/>bilis ignis implet, non modò nihil habens <lb/>proni, &longs;ed & &longs;ur&longs;um rectis lineis in cœle&longs;tem <lb/>locum &longs;ubuolare contendens) tantum ex tel­<lb/>lure detrahes ponderis, quantum metall&atail; <lb/>omnia atque marmora re&longs;tituere non va­<lb/>leant. </s> <s>Nec deerit docti&longs;simorum virorum <lb/>&longs;uffragium, qui cauernam hanc totius ter­<lb/>reni globi partem quartam præci&longs;i&longs;&longs;imè &longs;ta­<lb/>tuunt, cum qua pariter admirabilem illam <lb/>Lunaris motûs librationem con&longs;entire inge­<lb/>niosè opinantur. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Et verò talia afferentem ca&longs;tigare <lb/>quis audeat? </s> <s>Ab&longs;tineo tamen, ne fortè ex <lb/>vobis audire cogerer iterum, quæ haud ita <lb/>pridem ne&longs;cio quis di&longs;&longs;erebat. </s> <s>Nihil e&longs;t, <pb xlink:href="018/01/060.jpg" pagenum="52"/><arrow.to.target n="note28"/><lb/>aiebat ille, quod vim pati perpetuam cen­<lb/>&longs;endum &longs;it. </s> <s>At &longs;i elementis omnibus terra <lb/>grauitare, ignis leuitate præ&longs;tet; an non. </s> <s>æ­<lb/>ternum aberunt loco, quem &longs;ingulis naturâ <lb/>tributum e&longs;t vt velint con&longs;equi? </s> <s>Terra ete­<lb/>nim, ni&longs;i columnis ba&longs;im in centro haben­<lb/>tibus nixa fingatur, tota procul à centro con­<lb/>quie&longs;cit; ignis verò infimum locum tenet. </s> <s><lb/>Qui&longs;quis autem ibi ignem à Deo perpetuis <lb/>vinculis eo tantùm con&longs;ilio coerceri exi&longs;ti­<lb/>mat, vt &longs;celeratorum carnificinam exerceat; <lb/>diligenter per&longs;piciat velim, an non magis <lb/>pro Diuinæ &longs;apientiæ atque omnipotentiæ <lb/>dignitate locuturus ille &longs;it, qui, quemadmo­<lb/>dum Iridem licèt naturæ penicillo in nubi­<lb/>bus de&longs;criptam, in &longs;empiterni tamen fœde­<lb/>ris te&longs;&longs;eram à Deo a&longs;&longs;umptam nouit, &longs;ic re­<lb/>rum naturæ con&longs;entaneum ad&longs;truat hunc or­<lb/>dinem, quo vniuer&longs;itatis rerum &longs;ubluna­<lb/>rium elementa pro &longs;ui ponderis ratione ita <lb/>di&longs;ponantur, vt centrum omnium graui&longs;si­<lb/>mus ignis impiorum carcer atque carnifex <lb/>con&longs;titutus obtineat, illumque minùs gra­<lb/>uia elementa terra & aqua deinceps con&longs;e­<lb/>quantur, v&longs;que eò dum leui&longs;simus aër cir­<lb/>cumfu&longs;us reliqua complectatur. </s></p><p type="margin"> <s><margin.target id="note28"/><emph type="italics"/>XXVIII <lb/>Coniecturæ <lb/>pro adstru­<lb/>enda ignis <lb/>inferni gra<lb/>uitate.<emph.end type="italics"/></s></p><p type="main"> <s>Fru&longs;tra a&longs;cendentem flammam aperti&longs;si­<lb/>mum igneæ leuitatis argumentum obiicie­<pb xlink:href="018/01/061.jpg" pagenum="53"/>bant. </s> <s>Nàm ille &longs;upremo ætheri terrenis ex­<lb/>pirationibus immuni, ac lunari orbitæ fini­<lb/>timo, quem Ari&longs;totele te&longs;te propter con&longs;ue­<lb/>tudinem ignem dicimus, vix aliquid ignis <lb/>præter &longs;plendidum nomen reliquum facie­<lb/>bat. </s> <s>A&longs;cendit in flammâ (&longs;ic ille) humido <lb/>vapori, quem calor eximius rarum fecit, <lb/>permi&longs;ta fuligo, aére &longs;anè non leuior: quidni <lb/>pariter à flammâ in cœlum &longs;ubuolante par­<lb/>ticulæ igneæ abripiantur? </s> <s>quibus vel pru­<lb/>narum vel candentis ferri incolis, nullum e&longs;t <lb/>cum æthereâ regione commercium. </s> <s>A&ntail; <lb/>fumeus vapor igniculorum coloniam in cœ­<lb/>lum deduxi&longs;&longs;e cen&longs;endus e&longs;t, quia illi nobis <lb/>non videntibus in terram relabuntur? </s> <s>Sed <lb/>quis neget, incendio &longs;yluam depopulante, <lb/>immodicam fuliginum copiam in &longs;uperiora <lb/>rapi? </s> <s>quibus tamen ætheream &longs;edem ineptè <lb/>ad&longs;criberemus, quia illas iterum de&longs;cenden­<lb/>tes ob&longs;eruando notare non po&longs;&longs;umus. </s> <s>Quod <lb/>&longs;i ignibus &longs;ub dio &longs;emper excitatis, fuligo <lb/>nulla camino vnquam adhæ&longs;i&longs;&longs;et; nonnè &longs;a­<lb/>tis habui&longs;&longs;emus argumenti, ex quo illius gra­<lb/>uitas innotui&longs;&longs;et, &longs;i quando ingentem fuligi­<lb/>nis ma&longs;&longs;am ex aëre decidentem licui&longs;&longs;et in­<lb/>tueri? </s> <s>Neque enim ideò grauitate &longs;poliamus <lb/>terre&longs;tres pului&longs;culi atomos, quia in aëre va­<lb/>gantes ita &longs;en&longs;um di&longs;sipatæ fugiunt, vt eas <pb xlink:href="018/01/062.jpg" pagenum="54"/>de&longs;cendentes animaduertere nequeamus: &longs;ed <lb/>ad earum grauitatem ad&longs;truendam &longs;atis e&longs;&longs;e <lb/>putamus, quod particulæ illæ vinculum na­<lb/>ctæ, quo lapidem con&longs;tituant, de&longs;cendentes <lb/>&longs;ub a&longs;pectum cadant. </s> <s>Cur igitur tanta&mtail; <lb/>ignium vim in fulmine delap&longs;am, &longs;eque in <lb/>ima terræ vi&longs;cera in&longs;inuantem cernentes, <lb/>perinde atque &longs;axum in aquam decidens <lb/>mergitur, igneæ grauitatis &longs;u&longs;picioni locum <lb/>non damus? </s> <s>Nemo &longs;iquidem facilè credat <lb/>accen&longs;um fulmen á &longs;uperioribus nubis parti­<lb/>bus, quæ inferioribus tenuiores &longs;unt ac leuio­<lb/>res, minùsque ad aqueam naturam vergen­<lb/>tes, deor&longs;um reflecti: cùm nec ignis ex Auro, <lb/>quod ob impetûs ac efficaciæ &longs;imilitudinem <lb/>nomen à fulmine obtinuit, à quoquam re­<lb/>flectatur, &longs;ed in&longs;itâ naturæ vi præceps deor­<lb/>&longs;um feratur: </s></p><p type="main"> <s>Ad hæc ignis genus vniuer&longs;um in &longs;pecies <lb/>certas, quibus iterum partes aliæ atquè aliæ <lb/>&longs;ube&longs;&longs;ent, partiebatur & di&longs;tinguebat: Alti <lb/>enim reperiuntur Ignes luce iuxta atque ca­<lb/>lore con&longs;picui, quorum frequenti&longs;simus e&longs;t <lb/>& communis v&longs;us, atque vulgati&longs;sima noti­<lb/>tia: Alii &longs;unt, qui, quoniam plus fulgoris <lb/>habentes, quàm caloris, oculis tantùm blan­<lb/>diuntur, cum Fatuis Ignibus numerantur: <lb/>Alios demùm qua&longs;i latentes &longs;inu natura fo­<pb xlink:href="018/01/063.jpg" pagenum="55"/>uet, quos luce carentes quamuis Mortuos <lb/>vulgus appellet, nimis tamen viuaci virtute <lb/>præditos vis cau&longs;tica &longs;atis prodit. </s> <s>Ad ter­<lb/>tium hoc ignium genus, qui calidi cum &longs;int, <lb/>non tamen &longs;unt lucidi, reuocabat igniculos, <lb/>qui aquis acribus (Aquas Fortes vulgus ap­<lb/>pellat) permi&longs;ti ac oleo Tartari &longs;eu Vitrioli <lb/>metalla &longs;oluunt, & in Chymicam calce&mtail; <lb/>redigunt breui temporis morâ, cum tamen <lb/>plurium dierum interuallo indigeat, qui&longs;­<lb/>quis ea voluerit ardenti&longs;simæ fornacis igne in <lb/>calcem excoquere. </s> <s>Porrò aquas huiu&longs;modi <lb/>acres ex &longs;alibus extillari, &longs;ales autem graui­<lb/>tate præditos non mediocri ob&longs;eruans illud <lb/>demum inferebat, quod ignes omnium ve­<lb/>hementi&longs;simi, quantum quidem experimen­<lb/>to a&longs;&longs;equi po&longs;&longs;umus, cum grauitate &longs;unt con­<lb/>iuncti, vt in Aquis Fortibus, Oleo Tartari, <lb/>&. </s> <s>Vitrioli, in Auro pulueris pyrii &longs;peciem <lb/>nacto, & in Fulmine licet pa&longs;sim experiri. </s></p><p type="main"> <s>Hæc ferè &longs;unt, &longs;ed paulò pre&longs;siùs atqu&etail; <lb/>&longs;ummatim expo&longs;ita, ex quibus ille conficie­<lb/>bat ignium generi lati&longs;simè patenti &longs;ube&longs;&longs;&etail; <lb/>&longs;pecies qua&longs;dam graui&longs;simorum corporum <lb/>eximiâ vrendi facultate præditorum, quæ <lb/>mundanæ &longs;phæræ centrum meritò teneant, <lb/>ibique perpetuam efficiant noctem, ni&longs;i for­<lb/>tè &longs;ublu&longs;trem, quantum &longs;atis &longs;it ad impia­<pb xlink:href="018/01/064.jpg" pagenum="56"/>rum cruciatus &longs;uarum alienarumque cala­<lb/>mitatum a&longs;pectu augendos. </s> <s>Quare Tarta­<lb/>rum ille concipiebat qua&longs;i immen&longs;as Ther­<lb/>mas ac balneas efficaci&longs;&longs;imis omnium cau­<lb/>&longs;ticorum particulis plenas; quæ proptere&atail; <lb/>lacus & &longs;tagnum ignis, ob quietem &longs;cilicet, <lb/>à Diuinis literis dicuntur. </s> <s>Cumque plur&atail; <lb/>ijs quidem, quæ à Diuinis literis docemur, <lb/>con&longs;ona, &longs;ed præter eorum, qui aderant, opi­<lb/>nionem, de ignis i&longs;tiu&longs;modi naturâ di&longs;pu­<lb/>ta&longs;&longs;et; ne quid temerè prolatum videretur, <lb/>&longs;ermonem claudens Lactantij l. <!-- REMOVE S-->7. diu. </s> <s>in&longs;t. </s> <s><lb/>cap. 21. authoritate firmauit, vbi de igne <lb/>illo &longs;empiterno impiorum corpora crucian­<lb/>te loquitur, <emph type="italics"/>Cuius natura,<emph.end type="italics"/> inquit, <emph type="italics"/>diuer&longs;a <lb/>e&longs;t ab hoc no&longs;tro, quo ad vitæ nece&longs;&longs;aria vti­<lb/>mur, qui ni&longs;i alicuius materiæ fomite alatur, <lb/>extinguitur. </s> <s>At ille Diuinus per &longs;e ip&longs;um <lb/>&longs;emper viuit ac viget &longs;ine vllis alimentis, nec <lb/>admi&longs;tum habet fumum, &longs;ed e&longs;t purus ac li­<lb/>quidus, & in aquæ modum fluidus: non enim <lb/>vi aliqua &longs;ur&longs;um ver&longs;us vrgetur, &longs;icut no&longs;ter, <lb/>quem labes terreni corporis, quo tenetur, & fu­<lb/>mus intermi&longs;tus exilire cogit &c.<emph.end type="italics"/></s><s> Cum ita­<lb/>que &longs;u&longs;picarer, ne quis ve&longs;trum hæc eadem <lb/>obiiceret, &longs;i fortè ad extenuandum telluris <lb/>pondus ex inferorum ignibus argument&atail; <lb/>de&longs;ump&longs;i&longs;&longs;em, &longs;atius duxi ab&longs;tinere, ne co­<pb xlink:href="018/01/065.jpg" pagenum="57"/>gerer hanc inire di&longs;putatione&mtail;. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Haud ego &longs;anè ineptam dixeri&mtail; <lb/>philo&longs;ophiam illam, quæ rerum naturam <lb/>per experimenta ve&longs;tigat: &longs;ed nec aliquid te­<lb/>merè pronunciandum, quo vetus opinio <lb/>tot &longs;apientum authoritate firmata de po&longs;&longs;e&longs;­<lb/>&longs;ione deiiciatur. </s> <s>Quamuis autem &longs;ententia <lb/>hæc videatur adhuc enucleariùs explicanda, <lb/>vt igni &longs;ummam grauitatem ad&longs;truat; non <lb/>is tamen ego &longs;um, cui &longs;tomachum moueant <lb/>quæcunque præter opinionem audire con­<lb/>tigerit. </s> <s>Nec dubito quin, &longs;i rem penitiùs <lb/>intro&longs;picere vellemus, plura occurrerent à <lb/>no&longs;træ di&longs;putationis in&longs;tituto non alien&atail;. </s> <s><lb/>Sed quoniam non placet his diutiùs immo­<lb/>rari, ea commodiorem in locum reiiciamus. </s> <s><lb/>Tibi interim datur, Mer&longs;enne, terreni glo­<lb/>bi grauitatem, perpen&longs;is omnibus, haud <lb/>multum abe&longs;&longs;e ab eâ grauitate, quam æqua­<lb/>lis moles argillacea obtineret. </s> <s>Cum verò <lb/>res tota ex telluris magnitudine pendere vi­<lb/>deatur, ne quis &longs;upere&longs;&longs;et dubitandi locus, <lb/>opus e&longs;&longs;et Geometricè per&longs;pectam haber&etail; <lb/>telluris magnitudinem. </s> <s>Quare &longs;i quid ha­<lb/>bes, Guldine, quo nos po&longs;sis, methodo non <lb/>adeò operosâ, in huius problematis cogni­<lb/>tionem deducere, in medium proferre n&etail; <lb/>graueris. </s></p><pb xlink:href="018/01/066.jpg" pagenum="58"/><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Vnum præterea, quod non parùm <lb/><arrow.to.target n="note29"/><lb/>in rem tuam facit, Galilæe, audire placeat. </s> <s><lb/>Illud autem e&longs;t, quod quamuis terram decu­<lb/>plò grauiorem quis con&longs;titueret, ac ego de­<lb/>prehenderim, nihilo tamen minùs tuis illis <lb/>orbiculis moueri facilè po&longs;&longs;et: non tantum <lb/>quia decuplex i&longs;ta grauitas non pertingeret <lb/>ad libras illas 50.000000.000000.000000. <lb/>000000. & eo amplius, verùm etiam qui&atail; <lb/>non totum illud pondus &longs;imul motui repu­<lb/><figure id="id.018.01.066.1.jpg" xlink:href="018/01/066/1.jpg"/><lb/>gnaret. </s> <s>Sit eni&mtail; <lb/>totus terræ globus <lb/>HIKL, cuius cen­<lb/>trum C congruat v­<lb/>niuer&longs;i centro, i&ntail; <lb/>quo nullum habet <lb/>momentum ad de­<lb/>&longs;cen&longs;um, &longs;ed in eo <lb/>quie&longs;cit. </s> <s>An non &longs;a­<lb/>tis Archimedi fui&longs;­<lb/>&longs;et, &longs;i terram vnum <lb/>aut alterum milliare aliò tran&longs;tuli&longs;&longs;et? </s> <s>Mo­<lb/>ueri igitur intelligatur centrum ex C in T, <lb/>& &longs;it terra translata SORV. <!-- KEEP S--></s> <s>Huic motui <lb/>primùm, præter hemi&longs;phærium &longs;uperius <lb/>HLK, non repugnat totum hemi&longs;phærium <lb/>inferius HIK, cuius videlicet partes plurimæ <lb/>fiunt centro C propiores, in quod &longs;uis nuti­<pb xlink:href="018/01/067.jpg" pagenum="59"/>bus feruntur. </s> <s>Ponatur enim CT &longs;emidia­<lb/>metri pars mille&longs;ima, hoc e&longs;t mill. <!-- REMOVE S-->4. & eo <lb/>amplius; &longs;egmentorum MON & MVN Ra­<lb/>tio inuenietur, ex ijs quæ Archimedes docet <lb/>l. <!-- REMOVE S-->2. de &longs;ph. </s> <s>& eyl. </s> <s>prop. 2. &longs;unt enim &longs;eg­<lb/>menta illa æqualia conis eandem ba&longs;im MN <lb/>habentibus, hi autem ex Eucl. <!-- REMOVE S-->l. <!-- REMOVE S-->12. prop. </s> <s><lb/>14 inter &longs;e &longs;unt vt altitudines: Quapropter <lb/>inuentis conorum altitudinibus, quas Ar­<lb/>chimedes docet, innote&longs;cit Ratio &longs;egmen­<lb/>torum &longs;phæricorum conis illis æqualiu&mtail;. </s> <s><lb/>Cum itaque CT &longs;it Radij (1/1000), &longs;egmenti <lb/>MVN altitudo e&longs;t 999, &longs;egmenti verò <lb/>MON altitudo e&longs;t 1001. <!--neuer Satz-->Fiat igitur vt alti­<lb/>tudo &longs;egmenti maioris 1001 ad &longs;ummam <lb/>ex eadem altitudine & Radio 2001, ita al­<lb/>titudo &longs;egmenti &longs;phærici minoris 999, ad <lb/>coni æqualis altitudinem 1997. <!--neuer Satz-->Similiter vt <lb/>altitudo minoris &longs;egmenti 999 ad &longs;ummam <lb/>ex eadem & Radio 1999, ita altitudo &longs;eg­<lb/>menti &longs;phærici maioris 1001 ad coni æqua­<lb/>lis altitudinem 2003. <!--neuer Satz-->E&longs;t igitur MON ad <lb/>MVN vt 2003 ad 1997: atque adeò &longs;eg­<lb/>mentum maius addit vltra hemi&longs;phærium <lb/>&longs;olùm totius globi (6/4000). <!--neuer Satz-->Quare vt tellus ve­<lb/>niret in T, &longs;olum &longs;egmentum &longs;phæricu&mtail; <lb/>MSORN vt &longs;ummum deor&longs;um versùs C <lb/>vrgeret; cui tamen, ne po&longs;tea de&longs;cendet, <pb xlink:href="018/01/068.jpg" pagenum="60"/>reliquum &longs;egmentum MVN ob&longs;i&longs;teret, cum <lb/>deberet à centro remoueri illo de&longs;cendente: <lb/>ac proinde quamuis in motu &longs;emper auge­<lb/>retur difficultas mouendi, nunquam tamen <lb/>tota grauitas, perciperetur, ni&longs;i quando I ve­<lb/>ni&longs;&longs;et in C; tunc enim tota &longs;phæra deor&longs;um <lb/>niteretur. </s> <s>Præterea &longs;egmentum illud MON <lb/>non eadem obtineret ad de&longs;cendendum mo­<lb/>menta in tantâ centri vicinitate, ac valdè <lb/>procul à centro: neque enim ex hoc, quòd <lb/>experimentis euincere non po&longs;&longs;imus grauia <lb/>centro propiora minùs vrgere deor&longs;u&mtail; <lb/>quàm remotiora (cum illa, quæ in experi­<lb/>mentum a&longs;&longs;umuntur, non ea e&longs;&longs;e queant, <lb/>quæ di&longs;crimen inferant &longs;en&longs;u perceptibil&etail;) <lb/>repugnandum e&longs;t rationi manife&longs;tæ id &longs;ua­<lb/>denti, vbi & ponderis amplitudo & inter­<lb/>ualli differentia in&longs;ignis e&longs;t atque con&longs;pi­<lb/>cu&atail;. </s></p><p type="margin"> <s><margin.target id="note29"/><emph type="italics"/>XXIX <lb/>Telluris <lb/>grauitas <expan abbr="nõ">non</expan> <lb/>tota re&longs;i&longs;te­<lb/>ret Archi­<lb/>medi traben<lb/>ti.<emph.end type="italics"/></s></p><p type="main"> <s>Hinc fit 24 axibus in peritrochio aut tym­<lb/><arrow.to.target n="note30"/><lb/>panis dentatis, quorum partes e&longs;&longs;ent in Ra­<lb/>tione decuplâ, fieri po&longs;&longs;e, vt virtute tres li­<lb/>bras mouere valente terra per aliquod &longs;pa­<lb/>tium moueretur; illa enim mouere po&longs;&longs;et <lb/>lib 3000000.000000.000000.000000; qui <lb/>numerus excedit &longs;emi&longs;&longs;em ponderis totius <lb/>terræ; ac proinde eou&longs;que moueret, du&mtail; <lb/>&longs;egmentum MON æquale e&longs;&longs;et toti ponderi, <pb xlink:href="018/01/069.jpg" pagenum="61"/>quod ab eadem potentiâ po&longs;&longs;et &longs;u&longs;tineri ad­<lb/>hibitâ eadem machinâ, habitâ tamen ratio­<lb/>ne &longs;egmenti MVN ex parte &longs;u&longs;tentantis &longs;eg­<lb/>mentum &longs;uperius, ne tanto impetu deor&longs;um <lb/>vrgeat, quanto vrgeret, &longs;i &longs;egmentum MVN <lb/>non ade&longs;&longs;et. </s> <s>At verò compo&longs;itis tantùm 17 <lb/>helicibus cum tympanis denticulos 25 ha­<lb/>bentibus, & vltimo tympano ad axem, cui <lb/>funis ductarius circumuoluitur, Rationem <lb/>quintuplam habente, potentia vnius libræ <lb/>&longs;u&longs;tentatiua applicata manubrio æqualis lon­<lb/>gitudinis cum tympanorum &longs;emidiametro, <lb/>po&longs;&longs;et mouere terram ex C in T v&longs;que eò <lb/>dum &longs;egmentum MON e&longs;&longs;et lib 2.910383. <lb/>045673.370361.328125. qui pariter libra­<lb/>rum numerus excedit totius terrenæ graui­<lb/>tatis &longs;emi&longs;&longs;em: at potentia decem libras lo­<lb/>co transferre valens, decuplum pondus mo­<lb/>uere po&longs;&longs;et, atque adeò totum globum ele­<lb/>uare. </s> <s>Sed iam Guldinum audiamus, vt cer­<lb/>tam telluris magnitudinem &longs;tatuamus. </s></p><p type="margin"> <s><margin.target id="note30"/><emph type="italics"/>XXX <lb/>Definitur <lb/>machin&atail;, <lb/>qua potui&longs;­<lb/>&longs;et tellus mo<lb/>ueri ab Ar­<lb/>chimede.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Fieri non pote&longs;t, vt paucis me ex­<lb/>pediam, quia non vna tantùm, aut alter&atail; <lb/>&longs;uppetit methodus, &longs;ed plures aliquando ex­<lb/>cogitaui, cum hac &longs;uper re animum diligen­<lb/>tiùs aduerterem vehementer admirans ab <lb/>antiquis nihil ad nos veni&longs;&longs;e, in quo animus <lb/>Gemetricus po&longs;&longs;et conquie&longs;cere. </s> <s>Neque fa­<pb xlink:href="018/01/070.jpg" pagenum="62"/>cilè dixerim, quænam præ cæteris metho­<lb/>dus arrideat, cum pro diuersâ locorum op­<lb/>portunitate aliâ atque aliâ methodo vti opor­<lb/>teat. </s> <s>Quarè con&longs;ultius forta&longs;&longs;e fuerit, vel <lb/>omnes pariter &longs;ilentio obuoluere, vel in aliam <lb/>di&longs;&longs;ertationem reijcere. </s> <s>Quod &longs;i, quam he­<lb/>ri Mer&longs;ennus temporis dilationem ad am­<lb/>pliores numeros in pagellâ priuatim de&longs;cri­<lb/>bendos impetrauit, mihi non denegetis, tæ­<lb/>dio ve&longs;tro parcetur, & meo labori. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Rationi con&longs;entanea &longs;unt, quæ po­<lb/>&longs;tulas; neque æquum e&longs;t præproperæ curio­<lb/>&longs;itati ob&longs;ecundantes multiplicis methodi co­<lb/>gnitione fraudari. <lb/><figure id="id.018.01.070.1.jpg" xlink:href="018/01/070/1.jpg"/></s></p><pb xlink:href="018/01/071.jpg" pagenum="63"/><figure id="id.018.01.071.1.jpg" xlink:href="018/01/071/1.jpg"/><p type="main"> <s><emph type="center"/>DISSERTATIO <lb/>TERTIA<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Methodos varias inueniendi <lb/>terræ quantitatem <lb/>proponit.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>HAVD &longs;atis &longs;cio, an po&longs;­<lb/>&longs;im aliquid proferr&etail;, <lb/>quod ve&longs;træ exspectatio­<lb/>ni faciat &longs;atis in eâ, quam <lb/>nobis hodiè examinan­<lb/>dam &longs;tatuimus quæ&longs;tio­<lb/>nem de terraquei huius <lb/>globi magnitudine inue&longs;tigandâ: vos idcircò <pb xlink:href="018/01/072.jpg" pagenum="64"/>pro ve&longs;trâ humanitate tenuitati meæ ve­<lb/>niam dabitis, &longs;i quid afferre contigerit ita <lb/>planum ac facilè, vt ve&longs;trorum ingeniorum <lb/>&longs;ublimitati non re&longs;pondeat. </s> <s>Nihil habeo <lb/>certi quod &longs;tatuam de terræ quantitate, ne­<lb/>que enim hactenus otium fuit, quæ conce­<lb/>peram, in praxim deducere. </s> <s>Fieri autem <lb/>po&longs;&longs;e exi&longs;timo, vt operâ non longâ propo­<lb/>&longs;itum &longs;copum a&longs;&longs;equamur: duo nimiru&mtail; <lb/>præcogno&longs;ci oportet, quibus notis ac certis <lb/>terrenam diametrum po&longs;&longs;umus inue&longs;tigar&etail;. </s> <s><lb/>Primum e&longs;t altitudo oculi &longs;upra maris i&ntail; <lb/>immen&longs;um patentis &longs;uperficiem, quæ non <lb/>æquabili planitie explicatur, &longs;ed &longs;phæra&mtail; <lb/>æmulatur: hanc verò altitudinem certi&longs;&longs;i­<lb/>mè nobis innote&longs;cere po&longs;&longs;e quis neget? </s> <s>cum <lb/>eam funiculo vel phy&longs;icâ aliâ men&longs;urâ &longs;æ­<lb/>piùs dimetiri liceat. </s> <s>Alterum, quod in hoc <lb/>negotio requiritur, e&longs;t angulus, quem cum <lb/>lineâ perpendiculi ad terræ centrum ductâ <lb/>con&longs;tituit opticus radius extremum hori­<lb/>zontem allambens: hunc &longs;i organo ad id <lb/>affabrè elaborato ob&longs;eruaueris, &longs;ereno cœlo, <lb/>tranquillo mari, cum minima refractionis <lb/>&longs;u&longs;picio &longs;ube&longs;&longs;e pote&longs;t, quid certius requi­<lb/>ras? </s> <s>cum organo eidem in dimetiendis &longs;y­<lb/>derum altitudinibus aut di&longs;tantijs acquie­<lb/>&longs;cas. </s> <s>His autem duobus cognitis terræ quo­<pb xlink:href="018/01/073.jpg" pagenum="65"/>que &longs;emidiametrum latere non po&longs;&longs;e de­<lb/>mon&longs;tro. </s></p><p type="main"> <s>Sit enim, exempli gratiâ, nota altitudo <lb/>BA Phari Genuen&longs;is (laternam vocant) cum <lb/><arrow.to.target n="note31"/><lb/>&longs;copulo palmorum Genuen&longs;ium 440, hoc <lb/>e&longs;t pedum Rom. <!-- REMOVE S-->ant. </s> <s>480, ob&longs;eruatusque <lb/>angulus BAD &longs;it gr. 89. m. 36. &longs;ec. 33. Quo­<lb/>niam ergo linea AD circulum tangit in D, <lb/>angulus CDA e&longs;t rectus. </s> <s>Ex B ducta intel­<lb/>ligatur BE parallela ip&longs;i CD; e&longs;tque triangu­<lb/>lum ABE rectangulum ad E, cuius hypo­<lb/>thenu&longs;a AB, & angulus adiacens innotue­<lb/>runt. </s> <s>Quare fiat vt Radius 100000. 00000. <lb/>ad &longs;inum gr. 89. m. 36. &longs;ec. 33. hoc e&longs;t 99997. <lb/>67348, ita AB ped. <!-- REMOVE S-->480. ad BE ped. (479 <lb/>98883.27040/100000.00000). Porrò triangula ABE, ACD æqui­<lb/>angula &longs;unt propter linearum BE, CD pa­<lb/>ralleli&longs;mum, adeoque & &longs;imilia, ac vt AB <lb/>ad BE, ita AC ad CD. <!-- KEEP S--></s> <s>Ponatur autem BC <lb/>vna Radix Algebricè. </s> <s>Igitur vt AB ped. 480 <lb/>ad BE ped. (479 98883.27040/10000000000), ita AC ped. <!-- REMOVE S-->1 ℞ + <lb/>480 ad CD ped. (47998883.27040/48000000.00000) ℞ + (479 47463969.79200/48000000.00000). <lb/>E&longs;t autem CD æqualis ip&longs;i CB 1 ℞. </s> <s>Quare <lb/>factâ Antithe&longs;i iuxta Algebræ regulas, ma­<lb/>net æquatio inter hos terminos (111672960/48000000.00000) ℞ & <lb/>pedes (479 47463969.79200/48000000.00000). In&longs;titutâ denique di­<lb/>ui&longs;ione prodit quotiens ped. <!-- REMOVE S-->20631193., <pb xlink:href="018/01/074.jpg" pagenum="66"/>pretium 1 ℞ CB vel <lb/><figure id="id.018.01.074.1.jpg" xlink:href="018/01/074/1.jpg"/><lb/>CD. <!-- KEEP S--></s> <s>E&longs;t ergo inuen­<lb/>ta terræ &longs;emidiameter <lb/>mill. <!-- REMOVE S-->Rom. <!-- REMOVE S-->ant. </s> <s>4126, <lb/>pa&longs;&longs;. </s> <s>238. po&longs;ito angu­<lb/>lo ad A gr.89.m.36. <lb/>&longs;ec 33. præcisè. </s></p><p type="margin"> <s><margin.target id="note31"/><emph type="italics"/>XXXI <lb/>Prima me­<lb/>thodus in­<lb/>ueniendi tel<lb/>luris &longs;emi­<lb/>diametrum, <lb/>per Trigo­<lb/>nometriam <lb/>& Alge­<lb/>bram.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s>Quod &longs;i rem breuiùs <lb/>a&longs;&longs;equi velis, dato an­<lb/><arrow.to.target n="note32"/><lb/>gulo ob&longs;eruato in A gr. <!-- REMOVE S--><lb/>89. m. 36. &longs;ec. 33, &longs;umatur AC vt Radius, & <lb/>CD, vt &longs;inus dati anguli. </s> <s>Et a&longs;&longs;umptâ BC <lb/>1 ℞ fiat vt Radius 100000.00000. ad dati an­<lb/>guli &longs;inum 99997.67348, ita AC ped. <!-- REMOVE S-->1 ℞ <lb/>+ 480 ad CD ped. (99997.67348℞+4799888327040/100000.00000). E&longs;t <lb/>CD ip&longs;i CB 1 ℞ æqualis, atque adeò vtrinque <lb/>demptâ fractione (99997.67348/100000.00000) ℞, remanet æqua­<lb/>tio inter (232652/100000.00000) ℞ & ped. (4799888327040/100000.00000). Qua­<lb/>rè factâ diui&longs;ione habetur pretium 1 ℞ ped. <!-- REMOVE S--><lb/>20631193 vt priùs. </s> </p><p type="margin"> <s><margin.target id="note32"/><emph type="italics"/>XXXII <lb/>Idem aliter, <lb/>& breuiùs.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Methodus hæc plana e&longs;t atque fa­<lb/>cilis cuiuis vel leuiter Analyticâ &longs;cientiâ a&longs;­<lb/>per&longs;o: &longs;ed aliquos forta&longs;&longs;e deterreret, qui vel <lb/>ip&longs;um. </s> <s>Algebræ nomen horrent, quamuis <lb/>Mathematici audire velint. </s> <s>Alios angulo­<lb/>rum ob&longs;eruatio, & linearum circulo ad&longs;cri­<lb/>ptarum vel in&longs;criptarum inue&longs;tigatio ex Ca­<pb xlink:href="018/01/075.jpg" pagenum="67"/>noné defatigat, &longs;i maximè res ad minimas <lb/>A&longs;tronomicas fractiones deducta exigat par­<lb/>tis proportionalis inqui&longs;itionem. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Satis e&longs;t, &longs;i peritis Geometris hac <lb/>in re fiat &longs;atis. </s> <s>Verùm adhuc ab&longs;que Cano­<lb/><arrow.to.target n="note33"/><lb/>ne Trigonometrico res tota perfici po&longs;&longs;et, <lb/>&longs;ed non &longs;ine Algebrâ. </s> <s>Habeatur enim qua­<lb/>dratum Geometricum <emph type="italics"/>S<emph.end type="italics"/>H; <lb/>vel etiam &longs;it rectangulum, <lb/><figure id="id.018.01.075.1.jpg" xlink:href="018/01/075/1.jpg"/><lb/>cuius latus AS maius &longs;it late­<lb/>re AH, id quod aliquando <lb/>commodius accidet. </s> <s>Obuer­<lb/>tatur latus AH ita, vt con­<lb/>gruat radio optico terra&mtail; <lb/>tangenti AD, in &longs;uperior&etail; <lb/>figurâ: eritque triangulum <lb/>ABE &longs;imile triangulo OAS: Nam anguli <lb/>SAH & BEA &longs;unt recti, ac proinde lineæ <lb/>SA, BE parallelæ, intrà quas anguli alterni <lb/>SAO, EBA &longs;unt æquales; &longs;icut & alterni <lb/>EAB, SOA, intra parallelas SO, AE. <!-- KEEP S--></s> <s>Igi­<lb/>tur vt OA ad AS, ita AB ad BE: &longs;ed vt AB <lb/>ad BE, ita in &longs;uperiore figurâ AC ad CD; <lb/>ergo vt OA ad AS, ita AC ad CD. <!-- KEEP S--></s> <s>Quare <lb/>&longs;i latus AS Quadrati vel rectanguli notum &longs;it <lb/>in particulis quibuslibet, facilè innote&longs;cet, <lb/>quot huiu&longs;modi particulas contineat AO. </s> <s><lb/>Cum verò altitudo AB nota &longs;it ex. gr. ped. <pb xlink:href="018/01/076.jpg" pagenum="68"/>480, a&longs;&longs;umatur BC 1 ℞: tum fiat vt particu­<lb/>læ OA ad particulas AS, ita ped. <!-- REMOVE S-->1 ℞ + 480 <lb/>ad aliud, & proueniet quartus terminus CD <lb/>æqualis ip&longs;i CB 1 ℞: atque adeò factâ Anti­<lb/>the&longs;i, & in&longs;titutâ diui&longs;ione habetur quanti­<lb/>tas ip&longs;ius CD. <!-- KEEP S--></s> </p><p type="margin"> <s><margin.target id="note33"/><emph type="italics"/>XXXIII <lb/>Idem aliter <lb/>&longs;ine Trigo­<lb/>nometria.<emph.end type="italics"/></s></p><p type="main"> <s>Quid? <!-- KEEP S--></s> <s>quod &longs;inè Algebrâ res tam facilis <lb/><arrow.to.target n="note34"/><lb/>e&longs;t, vt penè non audeam dicere, ne vulgata <lb/>vilecat. </s> <s>Fiat vt OI, differentia inter OA & <lb/>AS, ad ip&longs;am AS, ita nota altitudo AB ad <lb/>aliud, & proueniet CD quæ&longs;ita terræ &longs;emi­<lb/>diameter. </s> <s>E&longs;t nimirum AB differentia inter <lb/>AC & CD, & vt tota AC ad totam AO, ita <lb/>ablata CB ad ablatam AI; igitur & reliqua <lb/>AB ad reliquam IO vt tota AC ad totam <lb/>AO: ergo permutando, & diuidendo, vt <lb/>AB ad BC, hoc e&longs;t CD, ita OI ad IA, hoc <lb/>e&longs;t AS. </s></p><p type="margin"> <s><margin.target id="note34"/><emph type="italics"/>XXXIV <lb/>Idem &longs;ine <lb/>Trigonome­<lb/>tria & &longs;ine <lb/>Algebra.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s>Et hæc quidem dicta &longs;int, &longs;i fortè angu­<lb/><arrow.to.target n="note35"/><lb/>lum CAD præcogno&longs;cere non libeat. </s> <s>Cæ­<lb/>terùm illo cognito rem aggredi licet &longs;ine <lb/>Algebrâ ope &longs;oliûs Trigonometriæ, quæ <lb/>multiplicem &longs;ubmini&longs;trare poterit metho­<lb/>dum. </s> <s>Et primò datâ altitudine AB, & an­<lb/>gulo ad A ob&longs;eruato ex. </s> <s>gr.gr.89.m.36.&longs;ec. <!-- REMOVE S--><lb/>33., notus e&longs;t angulus ad centrum C gr.o. <!-- REMOVE S--><lb/>m. 23. &longs;ec. 27, ac proinde eius &longs;ubten&longs;a i&ntail; <lb/>partibus Radij innote&longs;cit. </s> <s>Igitur ductâ BD, <pb xlink:href="018/01/077.jpg" pagenum="69"/>duo anguli ad ba&longs;im BD &longs;imul &longs;umpti &longs;unt <lb/>æquales recto CDA vnâ cum angulo ob&longs;er­<lb/>uato A. <!-- KEEP S--></s> <s>Cum verò triangulum CBD &longs;it <gap/>&longs;o­<lb/>&longs;celes, vnu&longs;qui&longs;que an­<lb/><figure id="id.018.01.077.1.jpg" xlink:href="018/01/077/1.jpg"/><lb/>gulorum ad ba&longs;im BD <lb/>e&longs;t æqualis &longs;emirecto & <lb/>&longs;emiangulo ob&longs;eruato. </s> <s><lb/>Deme ergo &longs;emiangu­<lb/>lum ob&longs;eruatum gr.44. <lb/>48. 16 1/2, ex angulo &longs;e­<lb/>mirecto, hoc e&longs;t grad. <!-- REMOVE S--><lb/>45, remanet gr. o. m. 11. <lb/>fec. </s> <s>43 1/2 quantitas angu­<lb/>li ADB: Hic autem angulus ADB &longs;emper <lb/>e&longs;t &longs;emi&longs;&longs;is complementi anguli ad A ob&longs;er­<lb/>uati; angulo enim ADB facto ad punctum <lb/>contactûs e&longs;t æqualis angulus in &longs;egmento <lb/>alterno, anguli verò ad peripheriam duplex <lb/>e&longs;t angulus ad centrum C. <!-- KEEP S--></s> <s>In triangulo ita­<lb/>que ADB noti &longs;unt duo anguli ad A & ad D; <lb/>& latus BD notum e&longs;t in partibus 682. <lb/>13152.quarum Radius 100000.00000; ideo­<lb/>que in ij&longs;dem Radij partibus inuenitur AB <lb/>partium 232657. Iam fiat vt AB partium <lb/>232657 ad Radium 100000.00000, ita AB <lb/>ped. <!-- REMOVE S-->480 ad aliud, & prodibit quantitas BC <lb/>terrenæ &longs;emidiametri ped. <!-- REMOVE S-->20631229, hoc <lb/>e&longs;t mill. <!-- REMOVE S-->4126. pa&longs;&longs;. </s> <s>246. Quod verò ali­<pb xlink:href="018/01/078.jpg" pagenum="70"/>quod intercedat di&longs;crimen inter hanc & dia­<lb/>trum &longs;uperiùs inuentam, nil mirum, qui&atail; <lb/>vbi multiplex diui&longs;io intercedit, fractiones <lb/>aliquæ neglegun­<lb/><figure id="id.018.01.078.1.jpg" xlink:href="018/01/078/1.jpg"/><lb/>tur, vnde demum <lb/>aliqua oritur dif­<lb/>ferentia. </s></p><p type="margin"> <s><margin.target id="note35"/><emph type="italics"/>XXXV <lb/>Idem aliter <lb/>per Trigo­<lb/>nometriam.<emph.end type="italics"/></s></p><p type="main"> <s>Sed placeat hìc <lb/><arrow.to.target n="note36"/><lb/>vnum prætere&atail; <lb/>ob&longs;eruare, quo mi­<lb/>rificè &longs;um delecta­<lb/>tus, cum primùm <lb/>animaduerti: <expan abbr="Do-ctrinã">Do­<lb/>ctrinam</expan> &longs;cilicet Tri­<lb/>gonometricam illud idem exhibere po&longs;&longs;&etail;, <lb/>quod ab Algebrâ, in &longs;ecundâ methodo indi­<lb/>catâ, po&longs;t omnes æquationes &longs;ubmini&longs;tra­<lb/>tur. </s> <s>Fiat enim vt Sinus Ver&longs;us comple­<lb/>menti anguli ob&longs;eruati, ad eiu&longs;dem anguli <lb/>ob&longs;eruati Sinum Rectum, ita nota altitudo <lb/>ad aliud, & habebitur quæ&longs;ita terræ &longs;emi­<lb/>diameter. </s> <s>Sit enim CB terræ &longs;emidiame­<lb/>ter, BA nota altitudo, AD linea optica tan­<lb/>gens in D, per quod ex centro C ducatur re­<lb/>cta CD, quæ producta in E occurrat peri­<lb/>pheriæ circuli, interuallo CA, ex eodem <lb/>centro de&longs;cripti. </s> <s>Eadem ergo e&longs;t Ratio AB <lb/>ad BC, quæ e&longs;t ED ad DC. </s> <s>E&longs;t autem AD <pb xlink:href="018/01/079.jpg" pagenum="71"/>Sinus anguli ACE, eiusque Sinus Ver&longs;us e&longs;t <lb/>DE. <!-- KEEP S--></s> <s>At CD e&longs;t æqualis Sinui Recto anguli <lb/>CAD ob&longs;eruati; e&longs;t &longs;iquidem CD æqualis <lb/>&longs;inui complementi anguli C. <!-- KEEP S--></s> <s>Igitur quæ <lb/>Ratio e&longs;t ip&longs;ius DE Sinus Ver&longs;i complemen­<lb/>ti anguli ob&longs;eruati, ad DC Sinum anguli A <lb/>ob&longs;eruati, ea e&longs;t ip&longs;ius altitudinis notæ BA, <lb/>ad| quæ&longs;itam terræ &longs;emidiametrum BC. <!-- KEEP S--></s> <s><lb/>Quarè &longs;inum anguli ob&longs;eruati 99997.67348 <lb/>deme ex Radio, & remanet 232652. Sinus <lb/>Ver&longs;us complementi.Iam &longs;i fiat vt 232652. <lb/>ad 99997.67348, ita nota altitudo ped. <!-- REMOVE S--><lb/>480. ad ped. <!-- REMOVE S-->20631193, eadem inuenitur <lb/>&longs;emidiameter, quæ &longs;uperiùs per Algebram <lb/>innotuit. </s> </p><p type="margin"> <s><margin.target id="note36"/><emph type="italics"/>XXXVI <lb/>Idem aliter <lb/>et breui&longs;&longs;i­<lb/>mè.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Si perfici res commodè po&longs;&longs;it &longs;inè <lb/><arrow.to.target n="note37"/><lb/>inue&longs;tigatione anguli, quem cum perpendi­<lb/>culo facit opticus radius &longs;phæricam terræ &longs;u­<lb/>perficiem tangens, angulum illum libens <lb/>prætermitterem: vix enim &longs;cio, quàm exa­<lb/>ctè deprehendi queat, quamuis organis di­<lb/>ligenti&longs;&longs;imè elaboratis non caream. </s></p><p type="margin"> <s><margin.target id="note37"/><emph type="italics"/>XXXVII <lb/>Quam exa­<lb/>ctè ob&longs;erua. </s> <s><lb/>ri po&longs;sint <lb/>anguli.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Omnem mihi eximo &longs;crupulum, <lb/>&longs;i quando contingat in Quadrante lineas, in <lb/>quibus minuta di&longs;tinguuntur, ita obliquè &longs;e­<lb/>cari â perpendiculo, vt anceps hæream, in <lb/>quam minuti partem cadat, cum tame&ntail; <lb/>etiam ip&longs;as minutorum minutias per&longs;equi <pb xlink:href="018/01/080.jpg" pagenum="72"/>operæ pretium &longs;it. </s> <s>Latus vnum Quadran­<lb/>tis ita duplico, vt iam perpendiculum non <lb/>ex circuli centro, &longs;ed ab extremâ diametro <lb/>pendeat, & ob&longs;eruationem in&longs;tituo: hinc <lb/>enim &longs;æpiùs fit, vt &longs;ilum &longs;ericum crudum, <lb/>ex quo pilula plumbea &longs;u&longs;penditur, minùs <lb/>obliquè lineam minutorum &longs;ecet, quàm &longs;i <lb/>ex centro penderet: Et quoniam angulus ad <lb/>peripheriam &longs;ubduplus e&longs;t anguli ad cen­<lb/>trum, notæ verò graduum & minutoru&mtail; <lb/>Quadrantis limbo appo&longs;itæ indicant angulos <lb/>ad centrum, angulus à perpendiculo nota­<lb/>tus, ex. gr. 1. 45 1/2, bifariam diuiditur, & <lb/>quæ&longs;itus angulus e&longs;t, gr. o. m. 52. &longs;ec. 45. <lb/>Quare &longs;i qua labes ob&longs;eruationi adhæreat, <lb/>pauculis &longs;crupulis &longs;ecundis definitur. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Dari id quidem facilè pote&longs;t &longs;y­<lb/>derum ob&longs;eruatori; in tantâ nimirum di&longs;tan­<lb/>tiâ ip&longs;ius organi magnitudo, quantacunque <lb/>demùm illa &longs;it, planè euane&longs;cit; ac proinde <lb/>i&longs;ta, vt ita dicam, virtualis duplicatio Qua­<lb/>drantis nihil officit. </s> <s>At verò telluris ma­<lb/>gnitudinem indaganti ex radio optico, res <lb/>non ita in plano e&longs;t: &longs;i enim oculum centro <lb/>Quadrantis admoueas ita, vt latus alterum <lb/>in&longs;trumenti congruat lineæ visûs, reliquum <lb/>verò latus fuerit, vt dicebas, duplicatum; <lb/>angulus à perpendiculo & lineâ visûs ex cen­<pb xlink:href="018/01/081.jpg" pagenum="73"/>tro, non e&longs;t æqualis angulo à perpendiculo, <lb/>& lineâ visûs ex extremâ diametro, quia pa­<lb/>rallelæ e&longs;&longs;e non po&longs;&longs;unt duæ lineæ eunde&mtail; <lb/>circuli quadrantem tangentes. </s> <s>Oculus au­<lb/>tem in extremâ diametro po&longs;itus, vtpotè <lb/>magis à tellure remotus, plus terræ videt &longs;ub <lb/>minore angulo: neque omninò contemnen­<lb/>da e&longs;t altitudinum differentia, &longs;i Quadrantis <lb/>Radius pedes quinque &longs;ecundùm longitudi­<lb/>nem habere ponatur; cum circuli in terrâ <lb/>maximi quantitas, quæ patet oculo decem <lb/>pedes alto, &longs;it ferè &longs;e&longs;quialtera eius, quæ pro­<lb/>&longs;picitur ab oculo quinque tantùm pedes à <lb/>terrâ remoto. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Non eadem e&longs;t ratio; &longs;i in arenâ <lb/>litoreâ, ac in editâ turri, aut in colle ob&longs;er­<lb/>uationem, vt hìc &longs;upponimus, in&longs;tituas; cum <lb/>enim terræ &longs;emidiameter aucta oculi altitu­<lb/>dine &longs;it Secans Complementi anguli ob&longs;er­<lb/>uati, &longs;ecantes autem angulorum æqualiter <lb/>cre&longs;centium addant &longs;emper maiorem, & <lb/>maiorem differentiam, patet quàm modi­<lb/>cum anguli di&longs;crimen intercederet, &longs;i non <lb/>ad centrum Quadrantis, &longs;ed ad extremam <lb/>circuli diametrum applicaretur oculus i&ntail; <lb/>vltimum Horizontem directus &longs;ecundùm <lb/>regulam lateri Quadrantis parallelam. </s> <s>Sed <lb/>quicquid de hoc e&longs;&longs;e contingat, certum e&longs;t <pb xlink:href="018/01/082.jpg" pagenum="74"/>oculo ad centrum applicato perpendiculum <lb/>indè &longs;u&longs;pen&longs;um cadere parallelum perpendi­<lb/>culo, quod ex extremâ diametro pendet, & <lb/>con&longs;tituere angulum cum diametro æqua­<lb/>lem illi, quem cum eâdem diametro facit <lb/>perpendiculum ex eius extremitate &longs;u&longs;pen­<lb/>&longs;um. </s> <s>Quare &longs;ola centri altitudo &longs;upra terræ <lb/>&longs;uperficiem, a&longs;&longs;umenda e&longs;t tanquam oculi <lb/>ob&longs;eruatoris altitudo. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Vel &longs;i minùs placeat perpendiculo <lb/>vti, Quadrantis latus horizontaliter iacens <lb/>duplicetur, & in extremâ diametro fiat cen­<lb/>trum, circa quod conuer&longs;a dioptra tanti&longs;per <lb/>eleuetur, dum linea fiduciæ congruat radio <lb/>optico terram tangenti; nam &longs;emi&longs;sis anguli <lb/>ad centrum facti cum latere horizontaliter <lb/>iacente in&longs;i&longs;tentis eidem arcui, e&longs;t angulus <lb/>depre&longs;sionis infra horizontem, æqualis an­<lb/>gulo ACD facto in centro terræ; cuius com­<lb/>plementum e&longs;t quæ&longs;itus angulus CAD. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> An non operæ pretium facturus e&longs;­<lb/>&longs;et, qui illud demum in praxim deduceret, <lb/>quod ego olim aliud ne&longs;cio quid meditans <lb/>perficiendum iu&longs;si, &longs;ed aliis curis di&longs;tractus <lb/>ad exitum non perduxi? </s> <s>Duxeram in plano <lb/>verticali lineam horizontalem longam pe­<lb/>des Rom. <!-- REMOVE S-->ferè quinquaginta, & in eius ex­<lb/>tremo puncto, quod eam cæli plagam re-<pb xlink:href="018/01/083.jpg" pagenum="75"/>&longs;peciebat, in qua aliquid occurrebat ob&longs;er­<lb/>uandum, axiculum ritè infigi curaui, circa <lb/>quem po&longs;&longs;et dioptra conuerti. </s> <s>Erat autem <lb/>animus parare regulam longam pedes 42, <lb/>cuius latitudo 4. digitos, cra&longs;&longs;ities aute&mtail; <lb/>duos digitos obtineret; &longs;ic enim fieri po&longs;&longs;e <lb/>&longs;perabam, vt latitudine in altitudinem con­<lb/>uersâ, regula non adeò grauis horizontali­<lb/>ter con&longs;tituta, & &longs;ecundum alteram extremi­<lb/>tatem axiculo in&longs;erta, non &longs;inuaretur, nec <lb/>à &longs;uâ rectitudine deflecteret: cùm maximè <lb/>decreui&longs;&longs;em ita illi aliam regulam breuiorem <lb/>&longs;ubiicere, in modum vectis primi generis, vt <lb/>inferiorem regulam premens eleuarem &longs;u­<lb/>periorem, quæ circiter duas tertias &longs;uæ lon­<lb/>gitudinis partes (hoc e&longs;t circiter pedem ab <lb/>axiculo, circa quem volueretur, trige&longs;imum) <lb/>&longs;u&longs;tentata à &longs;uppo&longs;ito vecte non e&longs;&longs;et adeò <lb/>obnoxia inflexioni. </s> <s>Tum regulæ longitudi­<lb/>ne in pedes di&longs;tinctâ; accipiendi erant pedes <lb/>41 2/3, vt e&longs;&longs;ent in vniuer&longs;um vnciæ 500; cum <lb/>enim pedis vncia ita &longs;en&longs;ibiliter in laminâ <lb/>metallicâ diuidi queat in particulas 50 vt ha­<lb/>beantur vnciæ particulæ cente&longs;imæ, erat Ra­<lb/>dius circuli de&longs;cribendi partium 50000, &longs;ub­<lb/>duplus numeri, qui habetur in Canone Tri­<lb/>gonometrico communi. </s> <s>Quare &longs;i hoc Ra­<lb/>dio in plano verticali de&longs;cribatur arcus, & <pb xlink:href="018/01/084.jpg" pagenum="76"/>ad lineam horizontalem excitetur perpendi­<lb/>cularis æqualis Tangenti gr. <!-- REMOVE S-->1. (accepto &longs;e. <lb/></s> <s>&longs;emi&longs;&longs;e numeri Canonis in partibus vnciæ <lb/>cente&longs;imis) ab&longs;cindi poterit ex arcu gradus <lb/>vnus, cuius &longs;inus parum di&longs;tabit à palmo <lb/>Romano architectonico. </s> <s>Quare facilè pote­<lb/>rit arcus in 60 minuta diuidi, & ex eodem <lb/>centro interuallo maiore de&longs;cripto alio arcu, <lb/>poterunt duci lineæ tran&longs;uer&longs;æ, in quibus <lb/>minutorum partes &longs;exage&longs;imæ di&longs;tingui po­<lb/>terunt, prout moris e&longs;t. </s> <s>Hoc in&longs;trumento pa­<lb/>rato angulum depre&longs;sionis in&longs;ra horizontem, <lb/>&longs;eu potiùs infra lineam horizonti parallelam, <lb/>tam clarè po&longs;&longs;umus deprehendere, vt nihil <lb/>reliquum <gap/>quod de&longs;ideremus. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Nec omnibus nec vbique locorum <lb/>commodum erit tuum hoc in&longs;trumentum <lb/>fabricari, quod vel vni loco affixum &longs;it opor­<lb/>tet, vel ægerrimè transferri po&longs;&longs;it. </s> <s>Ne&longs;cio <lb/><arrow.to.target n="note38"/><lb/>quo fato adhuc penès me in &longs;emilacerâfffff pa­<lb/>gellâ durat &longs;chedia&longs;ma hoc, quo ante men­<lb/>&longs;es aliquot cuidam, qui &longs;e in Geometriæ pra­<lb/>xi exercens dolebat nullum hactenus à &longs;e ad­<lb/>hibitum in&longs;trumentum, cui citrà in&longs;ignis <lb/>erroris &longs;u&longs;picionem po&longs;&longs;et fidere, organum <lb/>propo&longs;ui, quod & facilè con&longs;truitur, & vix <lb/>vllum relinquit errandi periculum, prout ip&longs;a <lb/>docuit experientia. </s> <s>In triangulum còag­<!--<pb xlink:href="018/01/085.jpg"/><pb xlink:href="018/01/086.jpg"/> NOTE: fig15 and fig16 extend over 2 pages <figure id="id.018.01.086.1.jpg" xlink:href="018/01/086/1.jpg"/><pb xlink:href="018/01/087.jpg"/><pb xlink:href="018/01/088.jpg"/><figure id="id.018.01.088.1.jpg" xlink:href="018/01/088/1.jpg"/><pb xlink:href="018/01/089.jpg"/><figure id="id.018.01.089.1.jpg" xlink:href="018/01/089/1.jpg"/>--><pb xlink:href="018/01/090.jpg" pagenum="77"/>mentatis tribus tigillis, ducatur recta AB <lb/>vnciarum 10. ex. </s> <s>gr. <!-- REMOVE S-->& &longs;uper eâ fiat triangu­<lb/>lum æquilaterum AEB. </s> <s>Quod &longs;i tigilli ni­<lb/>mis longi e&longs;&longs;ent, interuallo A<emph type="italics"/>e<emph.end type="italics"/> de&longs;cribantur <lb/>duo arcus &longs;e inuicem &longs;ecantes in <emph type="italics"/>i<emph.end type="italics"/>, & inter­<lb/>uallo A<emph type="italics"/>u<emph.end type="italics"/> arcus &longs;e &longs;ecantes in <emph type="italics"/>o<emph.end type="italics"/>: per hæc enim <lb/>puncta ductâ lineâ ex A, accipi poterit AE <lb/>æqualis ip&longs;i AB, & erit angulus BAE gr. <!-- REMOVE S-->60. <lb/>Relinquitur autem tigillus EF longior, vt in <lb/>FA &longs;ecundùm rectam EA productam in F <lb/>con&longs;tituatur tubulus H infundibuli in mo­<lb/>rem excauatus, per quem vi&longs;us rectâ traii­<lb/>ciatur in de&longs;tinatum &longs;copum per aciculam <lb/>in E perpendiculariter erectam, ex qua de­<lb/>pendet perpendiculum; hoc enim facit cum <lb/>lineâ EA angulum di&longs;tantiæ obiecti à verti­<lb/>ce ob&longs;eruatoris. </s> <s>Quantitas verò huius an­<lb/>guli per Trigonometriam reperitur ex datis <lb/>lateribus AE, & A<emph type="italics"/>u<emph.end type="italics"/> & angulo <emph type="italics"/>u<emph.end type="italics"/> AE compre­<lb/>hen&longs;o gr. <!-- REMOVE S-->60. ex con&longs;tructione. </s> <s>Vel &longs;i fortè <lb/>breuiùs operari placeat, fingatur ex E puncto <lb/>in &longs;emi&longs;&longs;em lateris AB cadere linea perpen­<lb/>dicularis, cuius quantitas facilè innote&longs;cit: <lb/>deinde illâ a&longs;&longs;umptâ vt Radio, vt Tangent&etail; <lb/>verò di&longs;tantiâ perpendiculi à medio lineæ <lb/>AB, angulus quæratur, quem facit perpen­<lb/>diculum cum fictâ illâ perpendiculari; hic <lb/>enim angulus additus gradibus 30. &longs;i perpen­<pb xlink:href="018/01/091.jpg"/><figure id="id.018.01.091.1.jpg" xlink:href="018/01/091/1.jpg"/><pb xlink:href="018/01/092.jpg" pagenum="78"/>diculum cadat vltra &longs;emi&longs;&longs;em lineæ AB; <lb/>demptus autem ex gr. <!-- REMOVE S-->30. &longs;i cadat citrà &longs;e­<lb/>mi&longs;&longs;em, dabit angulum di&longs;tantiæ à vertice <lb/>quæ&longs;itum. </s> <s>Quod &longs;i di&longs;tantia à vertice exce&longs;­<lb/>&longs;erit gr. <!-- REMOVE S-->60 perpendiculum cadet extrà latus <lb/>BE; idcirco &longs;u&longs;pendendum èrit ex I puncto, <lb/>quod bifariam diuidit rectam AE; & &longs;iqui­<lb/>dem obiectum in Horizonte fuerit, perpen­<lb/>diculum ex I cadet in B, &longs;i verò &longs;upra Hori­<lb/>zontem, cadet in latus AB, &longs;i demum infra <lb/>lineam Horizonti parallelam depre&longs;&longs;um fue­<lb/>rit, cadet perpendiculum in latus BE: &longs;em­<lb/>per autem in note&longs;cet angulus factus à perpen­<lb/>diculo & lineâ FI visûs, dantur enim vel la­<lb/>tera IA & AB, vel IE & EB cum angulo <lb/>comprehen&longs;o: vel &longs;altem in vtroque latere <lb/>de&longs;ignari poterit punctum, in quod ad rectos <lb/>angulos cadit linea ex I. <!-- KEEP S--></s> </p><p type="margin"> <s><margin.target id="note38"/><emph type="italics"/>XXXVIII <lb/>V&longs;us Tri­<lb/>goni æqui­<lb/>lateri ad <lb/>ob&longs;eruandos <lb/>angulos, in <lb/>quo vix er­<lb/>rari po&longs;sit à <lb/>Geometra.<emph.end type="italics"/><!-- KEEP S--></s></p><p type="main"> <s>Vt verò in quàm minimas particulas di­<lb/>ui&longs;am haberet rectam AB, iubebam duci <lb/>AC æqualem vni ex ijs partibus, in quas pri­<lb/>mò di&longs;tinctam eam po&longs;uimus, nempe i&ntail; <lb/>vncias pedis, & perfici parallelogrammum <lb/>ABDC. </s> <s>Tum diuisâ AC, & BD in quinque <lb/>æquales partes, & ductis parallelis ip&longs;i AB, <lb/>inter po&longs;tremas <emph type="italics"/>a d<emph.end type="italics"/> & CD ducatur diagona­<lb/>li; C <emph type="italics"/>d<emph.end type="italics"/>; & diui&longs;is pariter &longs;ingulis vncijs i&ntail; <lb/>quinque partes, vt factum hìc e&longs;t in vnciâ <pb xlink:href="018/01/093.jpg" pagenum="79"/>quintâ, ducantur lineolæ parallelæ ip&longs;i CA, <lb/>donec diagonalem attingant: & his paratis <lb/>habetur vncia AC diui&longs;a in partes 500, vel <lb/>&longs;altem in 250, &longs;i differentia inter duas pro­<lb/>ximas lineolas &longs;en&longs;ibilis non &longs;it. </s></p><p type="main"> <s>Quamuis autem tam exiguum triangu­<lb/>lum AEB non &longs;it aptum ad acutiores angu­<lb/>los inueniendos, con&longs;tat tamen po&longs;&longs;e illud <lb/>&longs;inè magno incommodo con&longs;trui ita, vt pe­<lb/>des aliquot &longs;ingula latera obtineant; & tunc <lb/>etiam minores angulorum particulæ innote­<lb/>&longs;cent. </s> <s>Quod &longs;i quando res &longs;it quàm exa­<lb/>cti&longs;simè perficienda, poterit lateri FE addi <lb/>regula, ex cuius extremo &longs;ecundùm rectam <lb/>AE productam &longs;u&longs;pendatur perpendiculum, <lb/>perinde enim erit ac &longs;i totum triangulum <lb/>augeretur. </s> <s>At &longs;i ex editiore loco deor&longs;um <lb/>&longs;pectandum &longs;it, & perpendiculum ex I &longs;u­<lb/>&longs;pen&longs;um cadat in latus EB tam propè ip&longs;um <lb/>B, vt non facilè po&longs;sint particulæ numera­<lb/>ri, erigatur ad latus AE regula perpendicu­<lb/>laris, in qua recta ex B per I ducta faciat an­<lb/>gulum EIG rectum, & &longs;umatur IG æqualis <lb/>ip&longs;i IE, & ex G &longs;u&longs;pendatur perpendiculum, <lb/>quod intelligatur cadere ex. </s> <s>gr. <!-- REMOVE S-->in R. <!-- KEEP S--></s> <s>Si <lb/>enim concipiatur ex I aliud perpendiculum <lb/>IS, vtique linea IG incidens in duas paralle­<lb/>las IS, & GR facit angulum SIB externum <pb xlink:href="018/01/094.jpg" pagenum="80"/>æqualem interno RGI: inuento igitur RGI, <lb/>innote&longs;cit angulus, quem cum perpendicu­<lb/>lo facit linea vi&longs;ualis AE. <!-- KEEP S--></s> <s>Cum itaque IE & <lb/>IG æquales &longs;int & ad angulum rectum, con­<lb/>ceptâ rectâ EG angulus EGI e&longs;t gr. <!-- REMOVE S-->45, cui <lb/>æqualis reliquus GEI additus angulo BEA gr. <!-- REMOVE S--><lb/>60. fit totus angulus GER gr. <!-- REMOVE S-->105; latus au­<lb/>tem EG &longs;ubtendens angulum rectum, no­<lb/>tum e&longs;t, cum nota &longs;int latera IG, & IE; de­<lb/>mum notum e&longs;t latus ER. </s> <s>Quare ex notis <lb/>lateribus EG & ER vnâ cum angulo com­<lb/>prehen&longs;o inuenitur angulus EGR, qui dem­<lb/>ptus ex EGI gr. <!-- REMOVE S-->45. relinquit notum RGI <lb/>æqualem angulo SIB; & &longs;ic innote&longs;cit angu­<lb/>lus SIE æqualis angulo, quem facit linea vi­<lb/>&longs;ualis EA <expan abbr="cũ">cum</expan> lineâ AT iungente oculum ob­<lb/>&longs;eruatoris cum centro terræ. </s> <s>Cum igitur &longs;atis <lb/>amplum huiu&longs;modi triangulum facilè po&longs;si­<lb/>mus con&longs;truere, etiam additâ regulâ IG, & <lb/>alibi diui&longs;am vnciam habere po&longs;simus i&ntail; <lb/>partes &longs;altem cente&longs;imas eâ methodo, quam <lb/>indicat Adrianus Metius in &longs;uâ Geometriâ, <lb/>patet fieri po&longs;&longs;e, vt quàm euidenti&longs;simè in­<lb/>note&longs;cat angulus ille, quem ob&longs;eruatum &longs;up­<lb/>ponebam ad inue&longs;tigandam terræ magnitu­<lb/>dinem. </s> <s>Sed mi&longs;sis organis ad in&longs;titutum <lb/>redeamus. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Audiui haud ita pridem hominem, <pb xlink:href="018/01/095.jpg" pagenum="81"/>qui ex maximâ visûs di&longs;tantiâ, &longs;eu Hori­<lb/><arrow.to.target n="note39"/><lb/>zontis Phy&longs;ici &longs;emidiametro, totius telluris <lb/>&longs;emidiametrum colligere &longs;e po&longs;&longs;e cen&longs;eban. </s> <s><lb/>Primùm verò &longs;tatuebat, quod certum e&longs;t, ab <lb/>iis qui de maximâ visûs di&longs;tantiâ di&longs;putant, <lb/>non eam inquiri, quæ vel ab oculis variè af­<lb/>fectis, vel à diuersâ corporum videndorum <lb/>magnitudine, vel ab inæquali &longs;pecierum, <lb/>quas vocant, intentionalium, quibus obie­<lb/>ctum repræ&longs;entandi vis ine&longs;t, diffu&longs;ione ea­<lb/>rumue inten&longs;ione petenda e&longs;t. </s> <s>Nemo enim <lb/>ignorat, &longs;i i&longs;ta &longs;pectentur, fieri non po&longs;&longs;&etail;, <lb/>vt certa visûs di&longs;tantia vniuer&longs;im præ&longs;criba­<lb/>tur. </s> <s>Acribus &longs;iquidem & acutis oculis longè <lb/>remotiora patere con&longs;tat, quàm hebetiori­<lb/>bus, quos languidiores radii procul immi&longs;si <lb/>ad vi&longs;um non excitant. </s> <s>Vbi verò obiectum <lb/>corpus non oculorum vitio latet, &longs;æpè &longs;uâ <lb/>&longs;e paruitate ita protegit, vt admi&longs;si à pupillâ <lb/>radii in tenui&longs;simum angulum coale&longs;centes <lb/>eam demùm afficiant Retinæ particulam, <lb/>quæ eum &longs;en&longs;um omnem effugiat, &longs;entiendi <lb/>quoquè munere &longs;olitaria fungi non pote&longs;t: <lb/>vt proinde Dioptrica &longs;ub&longs;idiarias lentes vi­<lb/>treas in tubo&longs;picillo ritè di&longs;po&longs;itas mortali­<lb/>bus tran&longs;mi&longs;erit, quarum ope inflexi Radii <lb/>ampliorem angulum con&longs;tituant, ideòqu&etail; <lb/>maiorem Retinæ particulam ad videndum <pb xlink:href="018/01/096.jpg" pagenum="82"/>proritent. </s> <s>Sed & illud maximè ambiguam <lb/>facit visûs di&longs;tantiam, quod pro di&longs;pari luce, <lb/>qua corpora imbuuntur, di&longs;par quoque exi­<lb/>gunt interuallum, vt &longs;ub a&longs;pectum cadant: <lb/>&longs;ic aliquando Perigæam Lunam, quæ ant&etail; <lb/>pauculas horas ferè pleno orbe immen&longs;&atail; <lb/>collucebat, &longs;ereno cœlo ami&longs;&longs;am quærimus, <lb/>&longs;i fortè eius centrum in terre&longs;tris vmbræ a­<lb/>xem inciderit; cum tamen eadem tenebra­<lb/>rum immunis, quamuis Apogæa Soli pa­<lb/>riter Apogæo oppo&longs;ita, &longs;ponte in oculos <lb/>incurrat. </s> <s>Ea nimirum quamuis remotior&atail; <lb/>con&longs;piciuntur, quæ vberiori lumine &longs;iuè in­<lb/>nato, & in&longs;ito, &longs;iuè extrin&longs;ecùs mutuato per­<lb/>funduntur. </s></p><p type="margin"> <s><margin.target id="note39"/><emph type="italics"/>XXXIX <lb/>Maxima vi­<lb/>&longs;us di&longs;tan­<lb/>tia ex qui­<lb/>bus debeat <lb/>definiri.<emph.end type="italics"/></s></p><p type="main"> <s>Semotis igitur omnibus hi&longs;ce impedi­<lb/>mentis, per quæ fieret, quominùs certi ali­<lb/>quid de visûs di&longs;tantiâ &longs;tatui po&longs;&longs;et; phy&longs;ici <lb/>horizontis &longs;emidiameter ex ipsâ terreni glo­<lb/>bi configuratione petenda e&longs;t. </s> <s>Cum enim <lb/>vetus ille error opinantium terræ faciem æ­<lb/>quabili planitie diffu&longs;am iam dudum exta­<lb/>buerit, & nemo &longs;it, qui pilæ in &longs;peciem ter­<lb/>ras ac maria vndique in &longs;e&longs;e nutibus &longs;uis con­<lb/>globata non intelligat; nemo pariter ambi­<lb/>gat, quin ob conuexam huiu&longs;ce globi &longs;uper­<lb/>ficiem, inclinatis nimirùm partibus, &longs;eque <lb/>oculo &longs;ubducentibus, a&longs;pectus omnis quan­<pb xlink:href="018/01/097.jpg" pagenum="83"/>tumuis acerrimus certis terminis circum­<lb/>&longs;cribatur. </s> <s>Hinc circulus partem hanc a&longs;pe­<lb/>ctabilem à latente di&longs;pe&longs;cens, Horizontis <lb/>Phy&longs;ici nomine donatus e&longs;t, vt ab eo &longs;ecer­<lb/>natur Horizonte, qui tellurem in duo hemi­<lb/>&longs;phæria &longs;egregans, quia non oculo, &longs;ed <expan abbr="&longs;olã">&longs;olam</expan> <lb/>ratione comprehendi pote&longs;t, Rationalis di­<lb/>citur. </s></p><p type="main"> <s>Quamuis autem Phy&longs;ici Horizontis dia­<lb/>meter tota intrà terræ cra&longs;situdinem deliteat, <lb/>quippe quæ recta e&longs;t linea arcui illi &longs;ubten&longs;a, <lb/>qui extremis terminis oculi Ortum Occa­<lb/>&longs;umque circum&longs;picientis intercluditur: quia <lb/>tamen arcus huiu&longs;modi exiguo di&longs;crimin&etail; <lb/>quod vix &longs;ub &longs;en&longs;um ca­<lb/><figure id="id.018.01.097.1.jpg" xlink:href="018/01/097/1.jpg"/><lb/>dat, &longs;ubten&longs;æ rectæ li­<lb/>neæ longitudinem &longs;upe­<lb/>rat; ideò non abs re ar­<lb/>cus ip&longs;e pro phy&longs;ici hori­<lb/>zontis &longs;emidiametro in­<lb/>di&longs;criminatim v&longs;urpatur; <lb/>huiu&longs;ce &longs;emi&longs;sis maxi­<lb/>mam obiecti a&longs;pectabilis <lb/>di&longs;tantiam metitur. </s></p><p type="main"> <s>Ex his &longs;ic ille argumentabatur. </s> <s>Sit arcus <lb/><arrow.to.target n="note40"/><lb/>AB men&longs;ura di&longs;tantiæ vi&longs;us, qui non à rectâ <lb/>lineâ &longs;en&longs;ibiliter deflectat<gap/>e&longs;t igitur AB recta <lb/>perpendiculariter in&longs;i&longs;tens rectæ DC: radius <pb xlink:href="018/01/098.jpg" pagenum="84"/>autem opticus DB terram tangens facit cum <lb/>&longs;emidiametro angulum DBC rectum. </s> <s>Igi­<lb/>tur recta AB ab angulo recto ad B cadens i&ntail; <lb/>ba&longs;im perpendicularis, e&longs;t medio loco pro­<lb/>portionalis inter &longs;egmenta DA & AC. <!-- KEEP S--></s> <s>Qua­<lb/>rè diui&longs;o quadrato maximæ visûs di&longs;tantiæ <lb/>AB per altitudinem AD, prouenit quæ&longs;it&atail; <lb/>terræ &longs;emidiameter AC. <!-- KEEP S--></s> <s>Verùm arcum <lb/>pro rectâ lineâ a&longs;&longs;umere parùm Geometri­<lb/>cum e&longs;t. </s></p><p type="margin"> <s><margin.target id="note40"/><emph type="italics"/>XXXX <lb/>Abu&longs;us li­<lb/>neæ curuæ <lb/>pro rect&atail;, <lb/>inutilis.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Ideò paruipendendendam cen&longs;ui <lb/>methodum, quæ mihi aliquando occurrit <lb/><arrow.to.target n="note41"/><lb/>per circulos Azimuthales; &longs;i nimirùm duo­<lb/>rum locorum, quorum alteruter ex alterius <lb/>editâ turri con&longs;pici queat, nota fuerit di&longs;tan­<lb/>tia, & poli altitudo. </s> <s>In &longs;ummâ enim turri <lb/>planum horizontale con&longs;tituatur, in eoque <lb/>meridiana linea de&longs;cribatur: tum ob&longs;eruetur <lb/>&longs;ub quo Azimutho locus alter con&longs;picuus <lb/>appareat: & ex his datis quæ&longs;ita eruantur. </s> <s><lb/>Sit PAC loci Meridianus, vbi ob&longs;eruatio in­<lb/>&longs;tituitur<gap/>; Verticalis per vtrumque locum <lb/>tran&longs;iens AB, cum Meridiano faciat angu­<lb/>lum CAB ob&longs;eruatum; P verò &longs;it Polus, & <lb/>AP, BP &longs;int complementa nota datarum <lb/>poli eleuationum. </s> <s>Cum itaque in triangu­<lb/>lo &longs;phærico BAP nota &longs;int duo latera AP, <lb/>BP, & angulus BAP complementum angu­<pb xlink:href="018/01/099.jpg" pagenum="85"/>li ob&longs;eruati CAB ad duos rectos, inueniatur <lb/>AB in gradibus &longs;eu <lb/>graduum particulis. <lb/><figure id="id.018.01.099.1.jpg" xlink:href="018/01/099/1.jpg"/><lb/>Tum fiat vt AB pars, <lb/>inuenta ad totum cir­<lb/>culum, hoc e&longs;t gr. <!-- REMOVE S--><lb/>360, ita data duorum <lb/>locorum di&longs;tantia ad <lb/>aliud, & prodibunt <lb/>milliaria toti circulo <lb/>in terrâ maximo re&longs;pondentia. </s> <s>Notâ autem <lb/>circularis peripheriæ quantitate neminem <lb/>Geometram diameter quæ&longs;ita latere poterit. </s> <s><lb/>Sed quoniam di&longs;tantia illa non adeò exigua <lb/>e&longs;&longs;e pote&longs;t, quæ careat omni &longs;u&longs;picione abu­<lb/>sûs rectæ lineæ pro curuâ, ideò methodum <lb/>hanc inter qui&longs;quilias, à quibus parùm di­<lb/>&longs;tat, reieci. </s></p><p type="margin"> <s><margin.target id="note41"/><emph type="italics"/>XXXXI <lb/>Secunda me <lb/>thodus in­<lb/>uestigandi <lb/>telluris am­<lb/>bitum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Id tamen per &longs;ummam iniuriam <lb/><arrow.to.target n="note42"/><lb/>factum: neque enim magnum intercedere <lb/>pote&longs;t di&longs;crimen, quod propo&longs;ito officiat: e&longs;t <lb/>&longs;cilicet di&longs;crimen minus datâ altitudine. </s> <s>Ex <lb/>altitudine enim BA pro&longs;piciénti pateat ar­<lb/>cus BD, quem &longs;ubtendit recta BD, Tan­<lb/>gens autem e&longs;t AD. <!-- KEEP S--></s> <s>Con&longs;tat ex Archimede <lb/>lib. 1. de &longs;phær. & cyl. </s> <s>Tangentem AD ma­<lb/>iorem e&longs;&longs;e arcu BD, arcum autem BD maio­<lb/>rem rectâ BD &longs;ubtensâ: At duæ rectæ BD, <pb xlink:href="018/01/100.jpg" pagenum="86"/>BA &longs;imul &longs;umptæ maiores &longs;unt quàm AD, <lb/>igitur exce&longs;&longs;us ip&longs;ius <lb/><figure id="id.018.01.100.1.jpg" xlink:href="018/01/100/1.jpg"/><lb/>AD &longs;upra rectam BD <lb/>minor e&longs;t, quàm &longs;it <lb/>data altitudo BA; er­<lb/>go multò minor e&longs;t <lb/>exce&longs;&longs;us rectæ AD <lb/>tangentis &longs;upra ar­<lb/>cum BD, vel arcûs <lb/>BD &longs;upra rectam BD <lb/>&longs;ubten&longs;am. </s> <s>Ne verò <lb/>po&longs;itâ altitudine BA notabili, cen&longs;eret quis <lb/>in&longs;ignem quoque e&longs;&longs;e differentiam inter cur­<lb/>uam & rectam lineam, quæ locorum inter­<lb/>ualla metiatur, animaduertere oportet ar­<lb/>cum BD maiorem e&longs;&longs;e latere BD polygoni <lb/>in&longs;cripti, minorem autem latere EF polygo­<lb/>ni circum&longs;cripti: at exce&longs;&longs;us lateris EF ad la­<lb/>tus BD habet Rationem, quam EB ad BC. <!-- KEEP S--></s> <s><lb/>Vnde liquet manife&longs;tè, quàm modico di­<lb/>&longs;crimine differat arcus à rectâ vel &longs;ubtensâ <lb/>BD, vel tangente EF. </s></p><p type="margin"> <s><margin.target id="note42"/><emph type="italics"/>XXXXII. </s> <s><lb/>Differentia <lb/>longitudinis <lb/>inter arcum <lb/>et eius Tan­<lb/>gentem vel <lb/>&longs;ubten&longs;am.<emph.end type="italics"/></s></p><p type="main"> <s>Memini me aliquando calculos &longs;ubducen­<lb/>tem, quàm longè pateat vi&longs;us Romæ è &longs;um­<lb/>mo crucis apice, quæ ædis Apo&longs;tolorum <lb/>Principi &longs;acræ tholo incumbit. </s> <s>deprehendi&longs;­<lb/>&longs;e arcum DB gr. <!-- REMOVE S-->o. </s> <s>m. </s> <s>23. &longs;tatuebam autem <lb/>in &longs;ingulos gradus milliaria Italica 60, vt <pb xlink:href="018/01/101.jpg" pagenum="87"/>nunc vulgaris fert opinio, crucis verò altitu­<lb/>dinem &longs;upra maris Mediterranci &longs;uperfi­<lb/>ciem ponebam palmorum, quorum v&longs;us ho­<lb/>diè e&longs;t apud Romanos architectos, circiter <lb/>700. Quare arcus BD erat mill. <!-- REMOVE S-->23. & Tan­<lb/>gens AD mill. (23 441/100000), di&longs;crimine vix pa&longs;­<lb/>&longs;uum 4 1/2. Quid igitur officiat, &longs;i quis pro <lb/>arcu BD a&longs;&longs;umat, aut &longs;ubten&longs;am BD, aut <lb/>tangentem EF, aut aliquam ex intermediis? </s> <s><lb/>nullus &longs;iquidem oriri pote&longs;t error, qui &longs;ub <lb/>&longs;en&longs;um cadat. </s> <s>Quod &longs;i, vt &longs;æpè fieri pote&longs;t, <lb/>di&longs;tantiam BD decempedâ dimetiamur, ni­<lb/>hil erit quod de tuâ illâ methodo dubites, <lb/>Mer&longs;enne, non enim arcu pro rectâ abu­<lb/>teris. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Su&longs;picor Mer&longs;enne (detur hoc Ger­<lb/>mano candori) non tibi rectam pro arcûs <lb/>men&longs;urâ a&longs;&longs;umptam di&longs;plicui&longs;&longs;e; &longs;ed metho­<lb/>dum illam, quæ tibi nihil de Ptolemæo co­<lb/>gitanti occurrerat, demùm di&longs;plicui&longs;&longs;e faci­<lb/>lè crediderim, vbi eam veteribus quoquè <lb/>innotui&longs;&longs;e deprehendi&longs;ti: ideo illam inter <lb/>&longs;cruta reieci&longs;ti. </s> <s>Ego quoque, vt vera nar­<lb/>rem, &longs;æpiùs doleo, quod veritatem tan­<lb/>quam peregrinam exceperim, qua&longs;i ad m&etail; <lb/>primum diuerti&longs;&longs;et; quam po&longs;tea alienum <lb/>limen triui&longs;&longs;e comperio: nec &longs;anè me pro­<lb/>bro&longs;is &longs;uis &longs;timulis vrget inuidentia, qua cæ­<pb xlink:href="018/01/102.jpg" pagenum="88"/>teris veritatis lumen inuideam; &longs;ed terret <lb/>calumnia, qua &longs;æpè apud iniquos iudices fur­<lb/>ti reus laboras, ni&longs;i id aliundè acceptum <lb/>&longs;ponte profitens mentiaris: perinde atque &longs;i <lb/>nemo &longs;olem po&longs;&longs;et intueri, qui alios de eius <lb/><arrow.to.target n="note43"/><lb/>luce narrantes non audierit. </s> <s>Simile quid in <lb/>hoc eodem Problemate mihi contigit expe­<lb/>riri. </s> <s>Cum enim locorum duorum AB di­<lb/>&longs;tantiam notam ponerem, ac complemen­<lb/>ta eleuationum poli; ob&longs;eruabam Solis di­<lb/>&longs;tantiam à vertice SA, quam per Tabulas <lb/>Anacla&longs;ticas, & Parallacticas corrigebam; <lb/>Tum ex complemento declinationis Solis <lb/>SP, complemento altitudinis Poli AP: & di­<lb/>&longs;tantia Solis à vertice SA, inquirebam angu­<lb/>lum ASP; ex quo inuento, vnâ cum latere <lb/>SP, & complemento altitudinis poli BP, <lb/>inueniebam SB, quod demptum ex SA re­<lb/>linquebat arcum BA quæ&longs;itum. </s> <s>Hæc ta­<lb/>men methodus po&longs;t dies aliquos di&longs;plicuit, <lb/>cum animaduerterem ingenio&longs;um A&longs;trono­<lb/>mum eâdem viâ ince&longs;si&longs;&longs;e, & quidem fe­<lb/>liciùs non Solem &longs;ed &longs;ydera fixa vertici pro­<lb/>xima ob&longs;eruando, quæ nec parallaxi nec re, <lb/>fractioni &longs;unt obnoxia. </s></p><p type="margin"> <s><margin.target id="note43"/><emph type="italics"/>XXXXIII. </s> <s><lb/>Tertia me­<lb/>thodus in­<lb/>uestigandi <lb/>ambitu&mtail; <lb/>terræ.<emph.end type="italics"/></s></p><p type="main"> <s>Cæterùm ne ab in&longs;titutâ quæ&longs;tione de­<lb/>flectamus, illud e&longs;t ob&longs;eruandum, quod &longs;i <lb/>cognitâ altitudine BA, & dato angulo ad A, <pb xlink:href="018/01/103.jpg" pagenum="89"/>vellet a&longs;&longs;umere triangulum rectangulum ad <lb/>B, vt notam faceret <lb/><figure id="id.018.01.103.1.jpg" xlink:href="018/01/103/1.jpg"/><lb/>di&longs;tantiam inter B & <lb/>D, &longs;ibique per&longs;uaderet <lb/>aut à ba&longs;i aut ab hy­<lb/>pothenusâ illius <expan abbr="triã-guli">trian­<lb/>guli</expan> exhiberi di&longs;tan­<lb/>tiam BD, longè di­<lb/>&longs;taret à veritate. </s> <s>Du­<lb/>cta &longs;iquidem perpen­<lb/>dicularis BH longè <lb/>minor e&longs;t arcu BD, cum &longs;it Tangens &longs;e­<lb/>mi&longs;sis illius arcûs: hypothenu&longs;a verò AH <lb/>minor e&longs;t quàm tota Tangens AD, de­<lb/>fectu æquali ip&longs;i ba&longs;i BH; &longs;unt enim HB, <lb/>HD æquales, cùm vtraque &longs;it circulum <lb/>tangens ab eodem puncto H ducta. </s> <s>Qua­<lb/>propter deberet aggregatum ex ba&longs;i BH <lb/>& hypothenusâ AH accipere, vt totam <lb/>AD haberet, quæ non multùm differt ab ar­<lb/>cu BD, ni&longs;i altitudo BA fuerit mons aut &longs;co­<lb/>pulus. </s></p><p type="main"> <s>Quod &longs;i tuus ille terrenæ magnitudinis <lb/><arrow.to.target n="note44"/><lb/>inue&longs;tigator lineam BD pro maximâ vi­<lb/>sûs di&longs;tantiâ a&longs;&longs;ump&longs;i&longs;&longs;et, illa vtique media <lb/>e&longs;t proportionalis, ex cuius quadrato per no­<lb/>tam altitudinem DA diui&longs;o prouenit tertius <pb xlink:href="018/01/104.jpg" pagenum="90"/>terminus, vnde terrena <lb/><figure id="id.018.01.104.1.jpg" xlink:href="018/01/104/1.jpg"/><lb/>&longs;emidiameter cogno&longs;ci­<lb/>tur, non tamen ip&longs;a &longs;e­<lb/>midiameter AG e&longs;t ter­<lb/>tius analogiæ terminus, <lb/>&longs;ed potius conflatum ex <lb/>DC, CB: latus enim v­<lb/>num trianguli rectan­<lb/>guli e&longs;t medium propor­<lb/>tionale inter differentiam <lb/>hypothenu&longs;æ ac reliqui lateris, & eorum ag­<lb/>gregatum: ac proinde vt AD ad DB, it&atail; <lb/>DB ad DCB. </s> <s>Quare ex inuento tertio ter­<lb/>mino debui&longs;&longs;et datam altitudinem DA de­<lb/>mere, & re&longs;iduum bifariam diui&longs;um dedi&longs;­<lb/>&longs;et quæ&longs;itam &longs;emidiametrum AC. <!-- KEEP S--></s> <s>Hinc <lb/>rectè dicebas arcum illum pro rectâ lineâ <lb/>parùm Geometricè a&longs;&longs;umptum. </s></p><p type="margin"> <s><margin.target id="note44"/><emph type="italics"/>XXXXIV <lb/>Quarta me­<lb/>thodus in­<lb/>neniendi ter­<lb/>ra &longs;emidia­<lb/>metrum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Nunquam hominem potui à con­<lb/>ceptâ &longs;ententiâ reuocare, ni&longs;i vbi eum iu&longs;&longs;i <lb/>rem rotam in praxim deducere. </s> <s>Statuimus <lb/>primùm extra omnem controuer&longs;iam po&longs;i­<lb/>tum videri, in decernendâ Phy&longs;ici horizon­<lb/>tis amplitudine non incertam ædium aut <lb/>montium altitudinem e&longs;&longs;e &longs;pectandam, &longs;ed <lb/>eam ex communi vulgarique hominum ma­<lb/>gnitudine definiendam. </s> <s>Quandoquidem <pb xlink:href="018/01/105.jpg" pagenum="91"/>cum ex &longs;ublimiori loco longiùs vi&longs;us eat, ex <lb/>humiliori autem breuioribus terminis coer­<lb/>ceatur, quis non videt certam &longs;tatui non po&longs;­<lb/>&longs;e visûs di&longs;tantiam, quin certa pariter alti­<lb/>tudo, ex qua oculus circum&longs;picere valeat, <lb/>con&longs;tituta intelligatur? </s> <s>præter eam verò, <lb/>quam humano corpori natura plerunqu&etail; <lb/>conce&longs;&longs;it, cur hanc præ aliâ eligas altitudi­<lb/>nem, nulla &longs;uppetit ratio. </s> <s>Nec ambigi vllo <lb/>pacto pote&longs;t, an Veteres horizontis phy&longs;ici <lb/>amplitudinem indagantes, altitudinem vl­<lb/>lam humanâ maiorem a&longs;&longs;ump&longs;erint; eam <lb/>&longs;iquidem horizonti tribuendam cen&longs;uer&etail; <lb/>magnitudinem, quæ cum &longs;phæricæ &longs;uperfi­<lb/>ciei pars &longs;it, à planâ tamen minimùm differ­<lb/>re po&longs;&longs;it. </s> <s>Hinc Macrobius Saturnal. <!-- REMOVE S-->lib. 7. <lb/>cap. 14. <emph type="italics"/>Vbicunque terrarum &longs;teteris<emph.end type="italics"/>, inquit, <lb/><emph type="italics"/>videris tibi quandam cœli conclu&longs;ionem vide­<lb/>re; & hoc e&longs;t quod Horizontem veteres voca­<lb/>uerunt: quorum indago fideliter deprehendit, <lb/>directam ab oculis aciem per planum contrà <lb/>a&longs;picientibus non pergere vltra CLXXX &longs;ta­<lb/>dia, & inde in orbem iam recuruari. </s> <s>Per pla­<lb/>num, ideò adieci, quia altitudines longi&longs;&longs;imè <lb/>a&longs;picimus; quippe qui & cælum videmus. </s> <s><lb/>Ergo in omni horizontis orbe ip&longs;e qui intuetur, <lb/>centron e&longs;t. </s> <s>Et quia diximus quantum à cen­<emph.end type="italics"/><pb xlink:href="018/01/106.jpg" pagenum="92"/><emph type="italics"/>tro acies v&longs;que ad partem orbis extenditur, &longs;i­<lb/>nè dubio in horizonte diametros orbis CCCLX <lb/>&longs;tadiorum e&longs;t: & &longs;i vlteriùs qui intuetur ac­<lb/>ce&longs;&longs;erit, &longs;eu retror&longs;um rece&longs;&longs;erit, &longs;imilem cir­<lb/>ca &longs;e orbem videbit.<emph.end type="italics"/></s></p><p type="main"> <s>Rogaui deinde vtrùm Macrobio potiùs <lb/><arrow.to.target n="note45"/><lb/>&longs;tadijs 180 Phy&longs;ici Horizontis &longs;emidiame­<lb/>trum definienti acquie&longs;ceret, an verò &longs;ibi <lb/>cum Recentioribus quibu&longs;dam conueniret, <lb/>qui cum Clauio (cui facilè adhæ&longs;it Blanca­<lb/>nus) in cap.2. &longs;phær. </s> <s>tanquam veritati ma­<lb/>ximè con&longs;entaneam ad mittunt eorum &longs;en­<lb/>tentiam, qui a&longs;pectum ad milliaria 62 1/2 pro­<lb/>trahi opinantur. </s> <s>Neque enim illum aut cum <lb/>Alberto Magno aut cum Proclo &longs;entire cen­<lb/>&longs;ebam, quorum prior &longs;tadia mille, po&longs;te­<lb/>rior bis mille horizontis phy&longs;ici &longs;emidiame­<lb/>tro dedit. </s></p><p type="margin"> <s><margin.target id="note45"/><emph type="italics"/>XXXXV <lb/>Ostenditur <lb/>error ex ab­<lb/>u&longs;u lineæ <lb/>curuæ pro <lb/>recta.<emph.end type="italics"/></s></p><p type="main"> <s>Ille quidem confe&longs;tim Neotericoru&mtail;<lb/>&longs;ententiam arripuit: &longs;ed vbi iu&longs;&longs;us e&longs;t AB <lb/>mill. <!-- REMOVE S-->62 1/2 ad pedes 312500 reuocare, & <lb/>huius numeri quadratum 97656.250000. <lb/>diuidere per DA ped. <!-- REMOVE S-->6, quanta e&longs;t hominis <lb/>mediocris altitudo, videns AC prouenir&etail; <lb/>maiorem milliarijs 3.000000, ad Macro­<lb/>bium con&longs;ugit, & longitudinem AB &longs;tadiis <lb/>180 circum&longs;crip&longs;it: nec &longs;tadia Romana ped. <pb xlink:href="018/01/107.jpg" pagenum="93"/>625, &longs;ed Græca ped. <!-- REMOVE S-->600 fui&longs;&longs;e contende­<lb/>bat, cum ex Erato&longs;thene men&longs;ura illa de­<lb/>&longs;umpta fui&longs;&longs;et. </s> <s>Sed hìc pariter Syrtes inue­<lb/>nit, cum reuocato &longs;tadiorum 180 numero <lb/>ad pedes 108000, eius quadratum 11664. <lb/>000000. diuidere tentans per pedes 6, quo­<lb/>tientem pariter ampli&longs;&longs;imum deprehendit. </s> <s><lb/>Quid &longs;i volui&longs;&longs;em contentio&longs;iùs agene, affir­<lb/>mando Erato&longs;thenem nec Romanis, nec <lb/>Græcis, &longs;ed Alexandrinis &longs;tadijs longioribus <lb/>v&longs;um fui&longs;&longs;e? </s> <s>Quantò longiùs aberrâ&longs;&longs;et? </s> <s>Sed <lb/>placuit miti&longs;&longs;imè agere. </s> <s>Quapropter eum <lb/>rogaui, vt &longs;altem AB milliarium trium, hoc <lb/>e&longs;t ped. <!-- REMOVE S-->15000 con&longs;tituens tentaret, an ex <lb/>a&longs;&longs;umptâ priùs iu&longs;to maiore &longs;emidiametro <lb/>horizontis phy&longs;ici, an verò etiam ex metho­<lb/>di ageometriâ enormis illa magnitudo ori­<lb/>retur: Quadratum itaque ped. <!-- REMOVE S-->225.000000 <lb/>diuidens per DA ped.6, inueniebat AC ped. <!-- REMOVE S--><lb/>37.500000, hoc e&longs;t mill. <!-- REMOVE S-->7500; vnde oritur <lb/>terræ ambitus mill. <!-- REMOVE S-->47 142 6/7 duplo maior, <lb/>quàm communiter concedatur. </s> </p><p type="main"> <s>Mirabatur ille vehementer, quòd præter <lb/>&longs;pem tam procul à vero rece&longs;&longs;i&longs;&longs;et: &longs;ed nec <lb/>conceptam de maiore, iuxta communem <lb/>errorem, horizontis phy&longs;ici &longs;emidiametro <lb/>opinionem deponere audebat: hærebant &longs;ci­<lb/>licet animo altè impre&longs;&longs;a plurium authorum <pb xlink:href="018/01/108.jpg" pagenum="94"/>effata, quibus 30 milliaria Italica videntur <lb/>mediocris visûs di&longs;tantia: quare multò pro­<lb/>babilior ei apparebat Macrobrii atque Era­<lb/>to&longs;thenis &longs;ententia di&longs;tantiam huiu&longs;modi &longs;ta, <lb/>&longs;tijs 180 definientium. </s> <s>Nos igitur ad exa­<lb/>minandum contulimus telluris ambitum ab <lb/>Erato&longs;thene con&longs;titutum, an cum illa &longs;emi­<lb/>diametto &longs;tadiorum 180 cohæreret: <emph type="italics"/>Eui­<emph.end type="italics"/><lb/><arrow.to.target n="note46"/><lb/><emph type="italics"/>denti&longs;&longs;imis<emph.end type="italics"/> enim, vt Macrobius loquitur lib. <!-- REMOVE S--><lb/>1. in &longs;omn. </s> <s>Scip. <!-- REMOVE S-->cap. 20. <emph type="italics"/>& indubitabilibus <lb/>dimen&longs;ionibus con&longs;tat vniuer&longs;æ terræ ambitum, <lb/>quæ vbicunque vel incolitur, vel inhabitabilis <lb/>iacet, habere &longs;tadiorum millia ducenta quin­<lb/>quaginta duo.<emph.end type="italics"/></s> <s> Cum verò huius peripheriæ <lb/>pars mille&longs;ima quadringente&longs;ima &longs;int &longs;tadia <lb/>180, per quæ directa ab oculis acies pergit, <lb/>arcus BA gr.o.m.15.&longs;ec.25. Ter. <!-- REMOVE S-->42. &c. </s> <s><lb/>metitur angulum BCD in centro factum. </s> <s><lb/>At quoniam peripheria ponitur &longs;tad 252000 <lb/>e&longs;t diameter minor verâ &longs;tad. (80181 9/11), maior <lb/>autem verâ (80233 41/223): quarè &longs;umpto medio <lb/>Arithmetico e<gap/> diameter AC &longs;tad. </s> <s>80207 1/2, <lb/>& &longs;emidiameter CA &longs;tad. </s> <s>40103 3/4. Fiat igitur <lb/>vt CB 99998.99293. &longs;inus complementi <lb/>gr.o.m.15.&longs;ec. <!-- REMOVE S-->25. Ter.42. ad CD Radium <lb/>100000.00000, ita CB &longs;tad.40103 3/4 ad CD <lb/>&longs;tad, 40104, & ped.92. Demptâ autem CA <pb xlink:href="018/01/109.jpg" pagenum="95"/>&longs;emidiametro, remanet AD ped. <!-- REMOVE S-->242, alti­<lb/>tudo, ex qua pro&longs;pici pote&longs;t in B ita, vt a&longs;pe­<lb/>ctui pateant &longs;tadia 180. Quî autem fieri po&longs;­<lb/>&longs;it ab intuente &longs;imilem &longs;emper orbem vide­<lb/>ri, &longs;iuè vlteriùs acce&longs;&longs;erit, &longs;iue retror&longs;um re­<lb/>ce&longs;&longs;erit, Macrobius ip&longs;e viderit: an &longs;emper <lb/>eam inueniat altitudinem, cui in&longs;i&longs;tat, vt <lb/>oculus ab extimâ telluris facie pedibus 242 <lb/>&longs;emoueatur? </s> <s>Horizontis igitur &longs;emidiame­<lb/>trum aut &longs;tadijs 180 minorem e&longs;&longs;e, aut non <lb/>ex humani corporis altitudine definiri ne­<lb/>ce&longs;&longs;e e&longs;t. </s></p><p type="margin"> <s><margin.target id="note46"/><emph type="italics"/>XXXXVI <lb/>Authorum <lb/>aliquorum <lb/>lap&longs;us i&ntail; <lb/>statuend&atail; <lb/>nimia vi&longs;us <lb/>distantia.<emph.end type="italics"/></s></p><p type="main"> <s>Cum verò ille labantem Macrobij &longs;en­<lb/>tentiam &longs;uffulcire aliquatenus &longs;e po&longs;&longs;e con­<lb/>&longs;ideret, &longs;tadia 180 tribuendo non arcui AB, <lb/>&longs;ed rectæ DB terram tangenti, quæ & radij <lb/>optici ex oculo D prodeuntis men&longs;ura e&longs;t, & <lb/>arcu AB longior; operam demum &longs;e ludere <lb/>&longs;en&longs;it, cum re ad Geometricam normam <lb/>reuocatâ tantam opticæ lineæ longitudinem <lb/>terrenæ magnitudini minimè congruere ma­<lb/>nife&longs;tè deprehendit, etiam &longs;i oculus à terrâ <lb/>pedum 50. interuallo AD &longs;eiunctus intelliga­<lb/>tur. </s> <s>Quoniam enim quadratum Tangentis <lb/>BD, quæ &longs;tad. </s> <s>180 ponitur, æquale e&longs;t re­<lb/>ctangulo ADE, diuidatur quadratum ped. <!-- REMOVE S--><lb/>11664.000000 per 50, & erit DE ped. <!-- REMOVE S-->233 <lb/>280000, hoc e&longs;t &longs;tadiorum Græcorum (quæ <pb xlink:href="018/01/110.jpg" pagenum="96"/>hìc v&longs;urpantur) 388800. Quare diameter <lb/>AE, demptis pedibus 50, erit &longs;tad. </s> <s>388799 <lb/>ped. <!-- REMOVE S-->550. Ex qua diametro colligitur am­<lb/>bitus longè maior eo, quem Macrobius cum <lb/>Erato&longs;thene con&longs;tituit. </s> </p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Sed lap&longs;is in ageometriam Erato­<lb/>&longs;thene ac Macrobio, quod &longs;tadia 180 tribue­<lb/>rint horizontis phy&longs;ici &longs;emidiametro, cum <lb/>totum telluris ambitum &longs;tadijs 252000 de­<lb/>&longs;inierint; quid de ijs dicendum, qui terram <lb/>paucioribus &longs;tadijs circum&longs;cribentes (mil­<lb/>liarijs nimirum 21600, quæ ad &longs;tadia Græca <lb/>180000 reuocantur, quot Ptolemæus toti <lb/>terrenæ peripheriæ conce&longs;sit) oculum tamen <lb/>ad maiora &longs;patia longo limite ducunt? </s> <s>Hi <lb/>&longs;anè longi&longs;simè ab&longs;unt à veritate, cum lineæ <lb/>opticæ tribuunt longitudinem &longs;tadiorum <lb/>vt minimum 500. Nam quadratum lineæ <lb/>opticæ e&longs;t æquale rectangulo &longs;ub altitudin&etail; <lb/>oculi, & terræ diametro auctâ eâdem altitu­<lb/>dine. </s> <s>Sit ergo D linea optica, & B &longs;it terræ <lb/>diameter, & A &longs;it altitudo: igitur DQ æqua­<lb/>tur AQ+A in B. </s> <s>Quare ad inueniendam A <lb/>fiat expurgatio per vncias conditionarias qua­<lb/>drati, &longs;c. </s> <s>per &longs;emi&longs;&longs;em coëfficientis B. </s> <s>Sit er­<lb/>go E æqualis A+B 1/2: igitur E——B 1/2 e&longs;t æqua­<lb/>lis ip&longs;i A. <!-- KEEP S--></s> <s>Factâ itaque prioris æquationis in­<lb/>terpretatione erit æquatio inter EQ——BQ 1/4 <pb xlink:href="018/01/111.jpg" pagenum="97"/>& DQ: & per Antithe&longs;im EQ æquatur <lb/>DQ+BQ 1/4 </s></p><p type="main"> <s>Cum igitur data &longs;it peripheria &longs;tad. </s> <s>180000, <lb/>erit diameter B &longs;tad. </s> <s>57291 2/3 proximè: atquè <lb/>adeò BQ 1/4 e&longs;t 820583766 2/3; ip&longs;ius verò D <lb/>&longs;tad. </s> <s>500, quadratum 250000. ex quotum <lb/>&longs;ummâ 820833766 2/3, quæ æqualis e&longs;t EQ, <lb/>&longs;i eruatur radix, erit E, hoc e&longs;t A+B 1/2 &longs;tad. <lb/>(28650 196/1000), ablatâ autem B 1/2, quæ e&longs;t &longs;tad. </s> <s><lb/>28645 5/6, remanet A &longs;tad. (<gap/>4 36/100) proximè alti­<lb/>tudo oculi: ex qua altitudine con&longs;tat no&ntail; <lb/>e&longs;&longs;e definiendam horizontis phy&longs;ici amplitu­<lb/>dinem. </s> <s>Quod &longs;<gap/> altitudinem oculi &longs;tatuere­<lb/>mus vnius &longs;tadij, retentâ eâdem opticæ li­<lb/>neæ longitudine, proueniret terræ diameter <lb/>&longs;tad. </s> <s>249999, quæ maior e&longs;t totâ periphe­<lb/>riâ ab ip&longs;is con&longs;titutâ. </s></p><p type="main"> <s>Hinc pariter Blancano fucum factu&mtail; <lb/>comperiemus (nam & quandoque bonus <lb/>dormitat Homerus) qui maximam mon­<lb/>tium altitudinem &longs;e&longs;quimilliari aut duobus <lb/>vt &longs;ummum milliaribus definiens, Ætnæ in <lb/>Siciliâ duo tantùm milliaria conce&longs;sit, ad­<lb/>mi&longs;it tamen ex Maurolyco dial. </s> <s>3. Co&longs;mogr. <lb/>pag. <!-- REMOVE S-->75.indè pro&longs;pici in mare vltra ducenta <lb/>pa&longs;&longs;uum millia. </s> <s>Namque a&longs;&longs;umptâ lineæ <lb/>opticæ terrenum globum tangentis longitu­<pb xlink:href="018/01/112.jpg" pagenum="98"/>dine mill. <!-- REMOVE S-->200, huiusque quadrato 40000 <lb/>per Ætnæ altitudinem con&longs;titutam mill. <!-- REMOVE S-->2 <lb/>diui&longs;o, & ex Quotiente 20000 demptâ mon­<lb/>tis altitudine, ne&longs;cio qua ratione re&longs;iduum <lb/>mill. <!-- REMOVE S-->19998 terrenæ diametro tribuendum, <lb/>idem Blancanus Sphæræ part. </s> <s>3.c.5.pag.93. <lb/>&longs;ibi gratulatur proximè conuenire cum am­<lb/>bitu mill. <!-- REMOVE S-->21600 ab aliis po&longs;ito, & à &longs;e ad­<lb/>mi&longs;&longs;o. </s> <s>Cum tamen hinc debui&longs;&longs;et potiùs <lb/>&longs;u&longs;picari montium altitudinem à &longs;e breuiori­<lb/>bus, quàm par &longs;it, terminis definitam, ex <lb/>qua tanta ferè colligitur diameter, quant&atail; <lb/>e&longs;&longs;e deberet peripheria. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> An igitur eos quoque mendacii <lb/>manife&longs;tos redarguas, qui Alexandrina&mtail; <lb/>&longs;peculam ab in&longs;ulâ, in qua extructa fuit, Pha­<lb/>ron dictam ad eam prouehunt altitudinem, <lb/>vt indè naues &longs;excentorum milliarium in­<lb/>teruallo di&longs;sitas videri potui&longs;&longs;e per &longs;ummam <lb/>con&longs;identiam âffirment? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Vnde fabulam i&longs;tam Io.Bapt. <!-- REMOVE S-->Por­<lb/>ta lib.17. Mag. nat.in proëm. </s> <s>hau&longs;erit, pror­<lb/><arrow.to.target n="note47"/><lb/>&longs;us ignoro. </s> <s>Neque enim Diodorus Siculus, <lb/>aut Strabo, aut Cæ&longs;ar, aut A. Hirtius, aut <lb/>Plinius, aut Lucianus, aut Solinus, aut Am­<lb/>mianus Marcellinus, aut alius ex ijs, quos le­<lb/>gerim, cum turris illius Alexandrinæ me­<lb/>minerint, adeò in&longs;anam altitudinem nobis <pb xlink:href="018/01/113.jpg" pagenum="99"/>obtrudunt. </s> <s>Quod autem Porta a&longs;&longs;erit in eâ <lb/>turri à Ptolemæo con&longs;titutum &longs;peculu&mtail;, <lb/>quod deinde cap. 11. ip&longs;e &longs;pecillum potiùs <lb/>quàm &longs;peculum vocat, vt ad 600 pa&longs;&longs;uum <lb/>millia ho&longs;tium naues, quæ eius regiones in­<lb/>uaderent, con&longs;piceret, occa&longs;io fuit aliquan­<lb/>do non nemini opinandi ad ea v&longs;que tempo­<lb/>ra referendum v&longs;um Tubi optici. </s> <s>Huiu&longs;ce <lb/>tamen &longs;peculi, &longs;iue &longs;pecilli, ve&longs;tigium nul­<lb/>lum apud antiquos &longs;criptores deprehender&etail; <lb/>potui; quamuis eorum libros multâ diligen­<lb/>tiâ per&longs;crutatus. </s> <s>Quapropter ea mihi mens <lb/>incidit, vt exi&longs;timarem Portæ, viro cætero­<lb/>qui erudito, fucum factum ab inepto quo­<lb/>piam Typographo, vel ignaro &longs;criptore, qui <lb/>pro &longs;peculâ in Pharo (in&longs;ulâ) extructâ, &longs;pe­<lb/>culum in Pharo (turri) con&longs;titutum &longs;uppo­<lb/>&longs;uerit. </s></p><p type="margin"> <s><margin.target id="note47"/><emph type="italics"/>XLVII <lb/>Fabula de <lb/>altitudin&etail; <lb/>Phari Ale­<lb/>xandrinæ <lb/>reijcitur.<emph.end type="italics"/></s></p><p type="main"> <s>Cæterùm cum tubus opticus vitreis lenti­<lb/>bus ritè in&longs;tructus ea &longs;olum corpora di&longs;tinctè <lb/>articulatimque videnda proponar, ad quæ <lb/>recta oculorum acies pergit, tota hæc fabu­<lb/>la euane&longs;cet, vbi tantam altitudinem, quæ <lb/>vi&longs;um ad milliaria 600 producat, probabili­<lb/>tate omni carere con&longs;titerit. </s> <s>Neque opus <lb/>erat altitudine illâ immani, cum ideò turris <lb/>illa à Ptolemæo Philadelpho (quamuis Amm. <!-- REMOVE S--><lb/>Marcell. <!-- REMOVE S-->lib. 22. à Cleopatrâ, quæ &longs;oror, & <pb xlink:href="018/01/114.jpg" pagenum="100"/>vxor fuit vltimi Ptolemæi cognomento Dio­<lb/>ny&longs;ij turrim illam excel&longs;am excogitatam &longs;cri­<lb/>bat) So&longs;trati Cnidij architecti operâ extructa <lb/>&longs;uerit, vt noctu accen&longs;æ faces indè præluce­<lb/>rent nauigantibus, quò breuia & &longs;yrtes de­<lb/>clinarent, quibus ora illa fallacibus & in&longs;i­<lb/>dio&longs;is acce&longs;sibus importuo&longs;a &longs;catebat, & di­<lb/>&longs;criminibus plurimis incautos nautas affli­<lb/>gebat. </s> </p><p type="main"> <s>Sed iam examinemus quantâ altitudine è <lb/>mari eminuerit Pharos illa Alexandrina, &longs;i <lb/>inde ad milliaria 600 vi&longs;us excurrere potuit. </s> <s><lb/>Po&longs;ito terræ ambitu mill. <!-- REMOVE S-->21600, arcus BA, <lb/>in &longs;uperiori figurâ mill.600 complectitur gra­<lb/>dus 10. Fiat igitur vt CB Radius 100000. <lb/>00000. ad CD 101542.66119 &longs;ecante&mtail; <lb/>grad. <!-- REMOVE S-->10, ita &longs;emidia­<lb/><figure id="id.018.01.114.1.jpg" xlink:href="018/01/114/1.jpg"/><lb/>metet CB mill. <!-- REMOVE S-->3437 1/2 <lb/>proximè ad CD mill. <!-- REMOVE S--><lb/>3490 1/2. Ablatâ autem <lb/>femidiametro CA, re­<lb/>manet AD mill. <!-- REMOVE S-->53. al­<lb/>titudo turris Alexandri­<lb/>næ: quanta videlicet <lb/>communiter tribui &longs;olet <lb/>halitibus illis, quibus <lb/>tum prima illuce&longs;centis diei, tum po&longs;trema <lb/>aduentantis noctis crepu&longs;cula debemus. </s> <s>Id <pb xlink:href="018/01/115.jpg" pagenum="101"/>verò quàm longè à veritate recedat, quid <lb/>pluribus opus e&longs;t explicare? </s> <s>quotus enim <lb/>qui&longs;que e&longs;t, qui turri octingentis talentis ex­<lb/>citatæ duûm triumue milliarium altitudi­<lb/>nem concedat? </s> <s>Pharos igitur In&longs;ula imma­<lb/>nis &longs;copulus fuit 50 &longs;erè milliaria iuxta per­<lb/>pendiculum numerans; qua de re mirum <lb/>apud &longs;criptores omnes &longs;ilentium: ac proin­<lb/>de tantæ altitudini parùm vtilis accidi&longs;&longs;et &longs;pe­<lb/>culæ acce&longs;sio. </s> <s>At &longs;tatuamus cum Erato&longs;the­<lb/>ne telluris ambitum &longs;tadiorum 252000, & <lb/>&longs;tadia &longs;ingula &longs;int Alexandrina |ped. <!-- REMOVE S-->Rom. <!-- REMOVE S--><lb/>720., totus ambitus e&longs;&longs;et mill.Rom. <!-- REMOVE S-->36288; <lb/>igitur milliaria 600 e&longs;&longs;ent gr. <!-- REMOVE S-->5. m. </s> <s>57. Qua­<lb/>re vt Radius 100000.00000. ad 100541. <lb/>64449. &longs;ecantem gr.5.m. <!-- REMOVE S-->57., ita &longs;emidia­<lb/>meter CB mill. <!-- REMOVE S-->5775. pa&longs;&longs;. </s> <s>419. ad CD <lb/>mill. <!-- REMOVE S-->5806. pa&longs;&longs;. </s> <s>701: ex qua &longs;i auferatur &longs;e­<lb/>midiameter CA, remaneret altitudo AD <lb/>mill. <!-- REMOVE S-->31 & pa&longs;&longs;. </s> <s>282; quæ altitudo adhuc e&longs;t <lb/>immanis: & maior hac e&longs;&longs;et, &longs;i &longs;tadia ill&atail; <lb/>252000. non. </s> <s>Alexandrina &longs;ed Græca a&longs;&longs;um­<lb/>pta fui&longs;&longs;ent; e&longs;&longs;et enim CD &longs;ecans anguli <lb/>DCB gr.7.m.8.&longs;ec.38. Non itaque fieri po­<lb/>tuit, vt ex Alexandrinâ turri ad &longs;excenta pa&longs;­<lb/>&longs;uum millia pro&longs;pectus pateret. </s></p><p type="main"> <s>Longè minor e&longs;t Phy&longs;ici Horizontis &longs;e­<lb/>midiameter, quàm vulgus cen&longs;eat, &longs;i res Geo­<pb xlink:href="018/01/116.jpg" pagenum="102"/>metricè perpendatur: cre&longs;cit autem eius am­<lb/>plitudo pro maiori &longs;pectatoris altitudin&etail;. </s> <s><lb/>Hinc quamuis nauclerorum plurimos Geo. <!-- REMOVE S--><lb/>metriâ non &longs;atis in&longs;tructos &longs;æpè fugiat ratio, <lb/>eorum tamen varia in determinandâ visûs <lb/>di&longs;tantiâ &longs;ententias facilè po&longs;&longs;umus concilia­<lb/>re; alijs &longs;iquidem ex altiori, alijs ex humilio­<lb/>ri &longs;peculâ pro&longs; picientibus obiectum idem, <lb/>illis quidem longiùs, his verò propiùs &longs;e ob­<lb/>tulit contemplandum. </s> <s>Quocirca ex huiu&longs;­<lb/>modi hominum effatis nihil timendum, <lb/>quod datâ telluris magnitudine con&longs;titutam <lb/>Geometricisque rationibus &longs;olidatam de vi­<lb/>sûs di&longs;tantiâ &longs;ententiam labefactare po&longs;sit: <lb/>duo enim hæc inuicem perpetuo vinculo <lb/>colligantur. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> At qui&longs;quis ex eorum numero &longs;ue­<lb/>rit, quos pudet aliquando &longs;apere, & antiquos <lb/>errores dedi&longs;cere, vbi visûs di&longs;tantiam eius <lb/>opinione minorem demon&longs;traueris, illicò <lb/>terræ magnitudinem non ritè con&longs;titutam <lb/>calumniabitur, & ad Ari&longs;totelem prouoca­<lb/>bit, qui lib. 2. de Cœlo text. </s> <s>vlt. </s> <s>&longs;cribit terræ <lb/>circuitum patere quadraginta &longs;tadioru&mtail; <lb/>myriadibus, hoc e&longs;t &longs;tadiis 400000. aut ad <lb/>Archimedem, qui in Arenario telluris am­<lb/>bitum ter mille &longs;tadiorum millia & eo am­<lb/>pliùs complecti con&longs;tituit. </s></p><pb xlink:href="018/01/117.jpg" pagenum="103"/><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Prouocet: per me licet. </s> <s>Eum ta­<lb/>men monitum velim parum ex Archimede <lb/>&longs;perandum, cum eam <lb/>ille magnitudinem da­<lb/><figure id="id.018.01.117.1.jpg" xlink:href="018/01/117/1.jpg"/><lb/>tâ operâ ponere volue­<lb/>rit, quam nemo eo­<lb/>rum, quibu&longs;cum di­<lb/>&longs;putabat, iu&longs;to mino­<lb/>rem calumniari po&longs;&longs;et. </s> <s><lb/>Quodverò ad Ari&longs;tote­<lb/>lem &longs;pectat, non mul­<lb/>tum habet momen­<lb/>ti Peripatetica autho­<lb/>ritas, cui apodictica ratio aduer&longs;atur. </s> <s>Porrò <lb/>longè melius e&longs;t opticæ lineæ longitudinem <lb/>præcogno&longs;cere, & ex illâ terræ magnitudi­<lb/><arrow.to.target n="note48"/><lb/>nem inue&longs;tigare, quàm incertis coniecturis <lb/>telluris ambitum &longs;tatuere; & infirmo huic <lb/>fundamento æquè nutantem de a&longs;pectûs lon­<lb/>gitudine &longs;ententiam &longs;uper&longs;truere. </s> <s>Sit enim <lb/>nota altitudo BA, & ob&longs;eruatus fuerit angu­<lb/>lus BAD; notus e&longs;t angulus complementi, <lb/>qui e&longs;t ad C: ducta autem recta BD facit <lb/>angulum BDA, qui e&longs;t &longs;emi&longs;&longs;is noti anguli <lb/>ad C, vt paulò antè dicebam. </s> <s>Cum itaque <lb/>in triangulo BAD datum &longs;it latus AB, & duo <lb/>anguli ad A & ad D innotuerint, inueniri <lb/>poterit quantitas lineæ opticæ AD. <!-- KEEP S--></s> <s>Tum <pb xlink:href="018/01/118.jpg" pagenum="104"/>ex B intelligatur educta perpendiculatis BE, <lb/>& in triangulo rectangulo ABE, datis angu­<lb/>lo A & latere AB, inueniatur latus BE. </s> <s>De­<lb/>mum quia triangula ABE, ADC rectangula <lb/>habentia communem angulum ad A &longs;unt &longs;i<gap/><lb/>milia, fiat vt AB data ad BE inuentam, ita <lb/>AD lineæ opticæ longitudo inuenta ad DC <lb/>quæ&longs;itam terræ &longs;emidiametrum. </s></p><p type="margin"> <s><margin.target id="note48"/><emph type="italics"/>XLVIII <lb/>Inuenir&etail; <lb/><expan abbr="longitudin&etilde;">longitudinem</expan> <lb/>vi&longs;us: & ex <lb/>ea Quint&atail; <lb/>methodus <lb/>vestigandi <lb/>terræ &longs;emi­<lb/>diametrum,<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> In ijs, quæ hactenus attuli&longs;ti ad <lb/>terræ &longs;emidiametrum inueniendam, illud <lb/>accidit incommodum, quod totam altitu­<lb/>dinem &longs;upra maris &longs;uperficiem innote&longs;cere <lb/>oportet: id quod haberi non pote&longs;t, ni&longs;i aut <lb/>prærupta rupes mari immineat, aut turris in <lb/>litore &longs;it con&longs;tituta. </s> <s>Quin methodum ali­<lb/>quam excogitas, qua etiam ex turri procul ab <lb/>æquore in colle po&longs;itâ explorare po&longs;&longs;imus, <lb/>quanta &longs;it terræ magnitudo? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Tentemus pariter, quid po&longs;&longs;imus: <lb/>tertius ade&longs;t Galilæus; ni&longs;i aliquid inueneri­<lb/><arrow.to.target n="note49"/><lb/>mus, dicam nos iratis Mu&longs;is conueni&longs;&longs;e. </s> <s>Sit <lb/>igitur in perpendiculari AC, nota in&longs;ignis <lb/>aliqua altitudo BA, at non talis, vt eius hu­<lb/>millimum punctum B &longs;phæricæ &longs;uperficiei <lb/>adhæreat, cum potiùs ex illâ emineat i&ntail; <lb/>colle DB, cuius altitudo ignota e&longs;t: fieri au­<lb/>tem po&longs;&longs;it, vt liber pro&longs;pectus in Horizon­<lb/>tem pateat, &longs;iue in &longs;ummo A, &longs;iue in imo B <pb xlink:href="018/01/119.jpg" pagenum="105"/>con&longs;i&longs;tas angulos CAE, CBF ob&longs;eruaturus. <lb/><figure id="id.018.01.119.1.jpg" xlink:href="018/01/119/1.jpg"/><lb/>Quibus angulis ob&longs;er­<lb/>uatis intellige rectam <lb/>BF occurrere Tangen­<lb/>ti AE in G. <!-- KEEP S--></s> <s>In triangu­<lb/>lo itaque ABG angu­<lb/>lus AGB e&longs;t notus, vt­<lb/>pote differentia duo­<lb/>rum ob&longs;eruatorum C <lb/>BG, CAG: angulus A <lb/>e&longs;t ob&longs;eruatus, & data <lb/>e&longs;t altitudo BA: ergo <lb/>inueniri pote&longs;t quantitas rectæ BG. </s> <s>Iam du­<lb/>cantur rectæ CF, CE, & &longs;unt duo triangula <lb/>AEC, BFC rectangula, in quibus duo an­<lb/>guli EAC, ECA &longs;imul &longs;unt æquales duo­<lb/>bus FBC, FCB: Atqui angulus ECA e&longs;t æ­<lb/>qualis duobus ECF, FCB; ergo tres ECF, <lb/>FCB, CAE &longs;unt æquales duobus FBC, FCB; <lb/>& dempto communi FCB, remanet FBC <lb/>æqualis duobus ECF, EAC. </s> <s>E&longs;t igitur ECF <lb/>differentia nota duorum ob&longs;eruatorum CAE, <lb/>CBF. </s> <s>Ducatur demùm recta CG. <!-- KEEP S--></s> <s>Et quo­<lb/>niam GF, GE &longs;unt tangentes circulum ab <lb/>eodem puncto exeuntes, inter &longs;e æquales <lb/>&longs;unt, &longs;icut & CF, CE ex centro ductæ; CG <lb/>verò e&longs;t vtrique triangulo FCG, ECG com­<lb/>munis; ergo angulus ECF notus diuiditur à <pb xlink:href="018/01/120.jpg" pagenum="106"/>rectâ CG bifariam. </s> <s>Quare &longs;i angulorum ob­<lb/>&longs;eruatorum &longs;emidifferentiam GCF addas an­<lb/>gulo FCB complemento noto anguli ob&longs;er­<lb/>uati in B, notus e&longs;t etiam angulus BCG; ex <lb/>quo, vnâ cum angulo CBG ob&longs;eruato, & la­<lb/>tere BG inuento, inuenitur latus CB: Cui &longs;i <lb/>addatur data altitudo BA, notum erit latus <lb/>CA vnâ cum angulo ad A ob&longs;eruato in trian­<lb/>gulo AEC rectangulo: quare & inuenitur CE <lb/>&longs;emidiameter quæ&longs;ita, quæ e&longs;t ip&longs;i CD æqua­<lb/>lis, vnde innote&longs;cit altitudo collis BD, & <lb/>lineæ opticæ AE longitudo cogno&longs;ci pote&longs;t. </s></p><p type="margin"> <s><margin.target id="note49"/><emph type="italics"/>XLIX <lb/>Sexta me­<lb/>thodus ter­<lb/>ræ &longs;emidia­<lb/>metrum in­<lb/>quirendi, & <lb/>montis alti­<lb/>tudinem co­<lb/>gno&longs;cendi.<emph.end type="italics"/></s></p><p type="main"> <s>At contingat ex edito quidem monte pro­<lb/>&longs;pici po&longs;&longs;e in <expan abbr="extremũ">extremum</expan> <lb/><arrow.to.target n="note50"/><lb/><figure id="id.018.01.120.1.jpg" xlink:href="018/01/120/1.jpg"/><lb/>horizontem, &longs;ed planè <lb/>ignotam e&longs;&longs;e montis al­<lb/>titudinem. </s> <s>Eligatur lo­<lb/>cus aliquis con&longs;picuus, <lb/>qui ita di&longs;tare cen&longs;ea­<lb/>tur, vt perpendicula­<lb/>res ex vtroque loco ad <lb/>centrum ductæ à pa­<lb/>ralleli&longs;mo deflectentes <lb/>&longs;en&longs;u digno&longs;ci queant. </s> <s><lb/>Hinc enim terræ &longs;emidiametrum eruer&etail; <lb/>po&longs;&longs;umus. </s> <s>Ex A igitur &longs;it linea AD terram <lb/>tangens: ob&longs;eruetur angulus CAD. <!-- KEEP S--></s> <s>Tum <lb/>ad ea&longs;dem vel alias partes eligatur locus B <pb xlink:href="018/01/121.jpg" pagenum="107"/>valde di&longs;tans, & ob&longs;eruetur pariter angulus <lb/>CAB. </s> <s>Di&longs;tantia autem BA vel &longs;it præcogni­<lb/>ta, vel ex tertio loco ob&longs;eruetur, vt fieri com­<lb/>muniter &longs;olet. </s> <s>Demum ex B ob&longs;eruetur an­<lb/>gulus ABC; cognitâ &longs;cilicet di&longs;tantiâ ip&longs;ius <lb/>A puncti à vertice ob&longs;eruatoris in B, com­<lb/>plementum ad duos rectos dat angulum <lb/>ABC: erit autem indicium di&longs;tantiæ AB <lb/>&longs;ufficientis, &longs;i anguli CAB, CBA &longs;imul &longs;um­<lb/>pti minores fuerint duobus rectis. </s> <s>Quare in <lb/>triangulo ABC dato latere BA & angulis <lb/>adiacentibus inuenitur latus AC. <!-- KEEP S--></s> <s>Inuento <lb/>autem latere AC & ob&longs;eruato angulo CAD <lb/>in triangulo CDA rectangulo, inuenitur CD <lb/>quæ&longs;ita terræ &longs;emidiameter, nec latebit <lb/>montis altitudo. </s></p><p type="margin"> <s><margin.target id="note50"/><emph type="italics"/>L. <!-- KEEP S--></s> <s><lb/>Septima me­<lb/>thodus in­<lb/>uestigandi <lb/>&longs;emidiame­<lb/>trum terræ, <lb/>& montis <lb/>altitudine.<emph.end type="italics"/></s></p><p type="main"> <s>Quod &longs;i locorum opportunitas ferat, vt <lb/>detur altitudo FE nota, ex qua ob&longs;eruari <lb/><arrow.to.target n="note51"/><lb/>queat angulus CED, & in monte procul po&longs;i­<lb/>to liber &longs;it a&longs;cen&longs;us, donec ex A puncto per <lb/>E in extremum horizontem D productus ra­<lb/>dius efficiat angulum CAD, qui ob&longs;eruatio­<lb/>ne cogno&longs;catur; ea habemus, quæ ad inue­<lb/>niendam terræ &longs;emidiametrum, vel ad exa­<lb/>minandamiam inuentam &longs;ufficiant. </s> <s>Intel­<lb/>ligatur enim ex F exire recta FG parallela ip&longs;i <lb/>CA (perpendiculares &longs;iquidem EC, AG á <lb/>paralleli&longs;mo deflectere ponimus) efformatur <pb xlink:href="018/01/122.jpg" pagenum="108"/>triangulum FEG, cuius latus FE datur, an­<lb/>gulus EGF æqualis angulo EAC ob&longs;eruato <lb/>innote&longs;cit propter linearum CA, FG paral­<lb/>leli&longs;mum, & GEF e&longs;t complementum ad <lb/>duos rectos anguli FED ob&longs;eruati. </s> <s>Inuenia­<lb/>tur itaque latus EG; quod ablatum ex EA <lb/>di&longs;tantiâ iam notâ duorum locorum, i&ntail; <lb/>quibus in&longs;titutæ &longs;unt ob&longs;eruationes, relin­<lb/>quit GA. </s> <s>At in triangulo EAC, lateri AC <lb/>parallela e&longs;t GF, ergo vt EG ad GA, ita EF <lb/>data altitudo ad FC quæ&longs;itam &longs;emidiame­<lb/>trum. </s> <s>Vel etiam ij&longs;dem po&longs;itis, & ob&longs;erua­<lb/>tis angulis CED, GAE, atque di&longs;tantiâ AE, <lb/><arrow.to.target n="note52"/><lb/>in triangulo CAE noti &longs;unt duo anguli, (an­<lb/>gulus &longs;iquidem CEA e&longs;t complementum ad <lb/>duos rectos anguli CED ob&longs;eruati) & latus <lb/>adiacens AE: inueniatur igitur latus EC, ex <lb/>quo dempta nota altitudo FE relinquit quæ­<lb/>&longs;itam terræ &longs;emidiametrum. </s> <s>Erit autem <lb/>indicium &longs;ufficientis di&longs;tantiæ inter A & E, &longs;i <lb/>angulus CED ob&longs;eruatus fuerit maior angu­<lb/>lo CAE. </s></p><p type="margin"> <s><margin.target id="note51"/><emph type="italics"/>LI. <!-- KEEP S--></s> <s><lb/>Octaua me­<lb/>thodus in­<lb/>ueniendi ter<lb/>ræ &longs;emidia­<lb/>metrum.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note52"/><emph type="italics"/>LII. <!-- KEEP S--></s> <s><lb/>Idem aliter.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Ea profectò &longs;unt, quæ hactenus di­<lb/>&longs;putata &longs;unt, vt vix cen&longs;eam fieri po&longs;&longs;e, vt <lb/>alicui nulla ex his methodis arrideat. </s> <s>Ve­<lb/>rùm &longs;crupulus e&longs;t, quem forta&longs;&longs;e ex multo­<lb/>rum animis non facilè eximas: exi&longs;tima­<lb/>bunt &longs;iquidem angulum, quem cum per­<pb xlink:href="018/01/123.jpg" pagenum="109"/>pendiculo opticus radius con&longs;tituit, nun­<lb/>quam minimè dubiâ ob&longs;eruatione inue&longs;tiga­<lb/>ri po&longs;&longs;e. </s> <s>Nam vltimum visûs terminum &longs;i <lb/>in terrâ &longs;pectes, quamuis plani&longs;&longs;ima facies <lb/>videatur, quî fiat, vt nullus pateat dubita­<lb/>tioni locus, an molli inclinatione indè per <lb/>longa terrarum &longs;patia in mare de&longs;cendatur? </s> <s><lb/>ac proinde linea illa ab oculo exiens non cir­<lb/>culum in &longs;phæricâ &longs;uperficie contingeret, vt <lb/>exigitur. </s> <s>Si verò in immen&longs;um æquor vi­<lb/>&longs;us excurrat, et&longs;i &longs;opitis fructibus otia agat, <lb/>nulloque æ&longs;tu intume&longs;cat, quis ne&longs;ciat At­<lb/>mo&longs;phæram vaporibus non adeò paucis te­<lb/>nuibu&longs;ue &longs;catere, vt nulla refractionis, qua <lb/>Oceani partes infra horizontem depre&longs;&longs;æ <lb/><expan abbr="&etilde;mergant">emmergant</expan>, &longs;u&longs;picio &longs;uboriri po&longs;&longs;it? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/> Hæc quidem non ea e&longs;&longs;e videntur, <lb/>quæ telluris &longs;emidiametro his methodis in­<lb/>uentæ officere po&longs;&longs;int: Si enim aliâ atque <lb/>aliâ methodo inue&longs;tigetur, nec valdè in&longs;i­<lb/>gni di&longs;crimine differant, quæ inueniuntur, <lb/>medium Arithmeticum inter extrema in­<lb/>uenta dabit quantitatem quæ&longs;itam &longs;emidia­<lb/>metro terræ tribuendam. </s> <s>Tellus quipp&etail; <lb/>toreuma non e&longs;t vndequaque expolitum; &longs;ed <lb/>cum eius partes à centro di&longs;paribus interual­<lb/>lis ab&longs;int, ita tamen vt proximè &longs;phæra&mtail; <lb/>æmuletur, facis e&longs;t &longs;i mediocris à centro di-<pb xlink:href="018/01/124.jpg" pagenum="110"/>&longs;tantia innote&longs;cat. </s> <s>Nihilominus tamen aliam <lb/>placet tentare viam nullâ habitâ ratione radii <lb/>optici terram tangentis, modò ea &longs;it duo­<lb/>rum locorum di&longs;tantia, vt perpendiculares <lb/>ad centrum notabiliter deflectant à paralle­<lb/>li&longs;mo. <lb/><arrow.to.target n="note53"/></s></p><p type="margin"> <s><margin.target id="note53"/><emph type="italics"/>LIII: <lb/>Nona me­<lb/>thodus tel­<lb/>luris &longs;emi­<lb/>diametrum <lb/>inquirendi.<emph.end type="italics"/></s></p><figure id="id.018.01.124.1.jpg" xlink:href="018/01/124/1.jpg"/><p type="main"> <s>Eligatur itaque alti­<lb/>tudo quæpiam in&longs;ignis <lb/>& nota AB, ex cuius <lb/>vtroque extremo vi­<lb/>deatur in monte ad <lb/>plura milliaria procul <lb/>po&longs;ito locus D: loca ve­<lb/>rò huiu&longs;modi di&longs;tantia <lb/>po&longs;&longs;unt ob&longs;eruari poti&longs;­<lb/>&longs;imùm noctu accen&longs;o <lb/>ibi igné ab amico, ni&longs;i <lb/>ad&longs;it nota aliqua peculiaris, vt ædificium, <lb/>turris &c. </s> <s>Tum ex A ob&longs;eruetur angulus <lb/>BAD, & ex B angulus ABD, notus enim fiet <lb/>reliquus angulus BDA. <!-- KEEP S--></s> <s>Ex puncto autem <lb/>D ob&longs;eruetur angulus BDC, vnde ablato an­<lb/>gulo BDA noto, reliquus ADC innote&longs;cit. </s> <s><lb/>His paratis in triangulo ABD dantur duo an­<lb/>guli A & B cum latere adiacente BA, inue­<lb/>niatur igitur latus AD. <!-- KEEP S--></s> <s>Ex hoc autem late­<lb/>re AD inuento vnâ cum angulo ADC, qu <lb/>ex ob&longs;eruatione innotuit, & angulo DAC <pb xlink:href="018/01/125.jpg" pagenum="111"/>qui e&longs;t complementum anguli ob&longs;eruati <lb/>DAB ad duos rectos, inueniri pote&longs;t latus <lb/>AC quæ&longs;ita terræ &longs;emidiameter. </s></p><p type="main"> <s>At non vacat montem con&longs;cendere? </s> <s>alia <lb/><arrow.to.target n="note54"/><lb/>&longs;uppetit via, qua leuiori labore propo&longs;itum <lb/>a&longs;&longs;equamur. </s> <s>Sit nota altitudo IG, vnde vi­<lb/>deatur locus aliquis in &longs;uperficie terræ F: ob­<lb/>&longs;erueturque angulus IGF. </s> <s>Quod &longs;i di&longs;tantia <lb/><figure id="id.018.01.125.1.jpg" xlink:href="018/01/125/1.jpg"/><lb/>GF iam nota non <lb/>fuerit, ex tertio <lb/>quopiam loco e&atail; <lb/>ob&longs;eruetur, <expan abbr="inue-niaturq.">inue­<lb/>niaturque</expan> iuxta Tri­<lb/>gonometriæ præ­<lb/>cepta. </s> <s>His com­<lb/>paratis producatur <lb/>GI per terræ cen­<lb/>trum T v&longs;qu&etail; <lb/>in O, vt IO &longs;it <lb/>terræ diameter: ex <lb/>F cadat in dia­<lb/>metrum perpendicularis FC. </s> <s>Quonia&mtail; <lb/>igitur in triangulo GCF rectangulo datur hy­<lb/>pothenu&longs;a GF, & angulus CGF, inueniantur <lb/>reliqua latera FC, CG. <!-- KEEP S--></s> <s>Auferatur autem <lb/>IG data altitudo ex GC, & remanet IC. </s> <s><lb/>Quia verò FC à puncto peripheriæ F cadit <lb/>perpendicularis in diametrum IO, e&longs;t me­<pb xlink:href="018/01/126.jpg" pagenum="112"/>dio loco proportionalis inter diametri &longs;eg­<lb/>menta IC, CO; ac proinde quadratum me­<lb/>diæ CF æquale e&longs;t rectangulo &longs;ub extremis. </s> <s><lb/>Itaque quadrato ip&longs;ius CF diui&longs;o per IC &longs;eg­<lb/>mentum notum, Quotiens dabit CO, cui <lb/>addatur CI, & habetur tota diameter IO <lb/><arrow.to.target n="note55"/><lb/>quæ&longs;ita. </s></p><p type="margin"> <s><margin.target id="note54"/><emph type="italics"/>LIV. <!-- KEEP S--></s> <s><lb/>Decima me­<lb/>thodus, qua <lb/>terræ dia­<lb/>meter inue­<lb/>nitur.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note55"/><emph type="italics"/>LV. <!-- KEEP S--></s> <s><lb/>Idem aliter.<emph.end type="italics"/></s></p><p type="main"> <s>Hæc mihi methodus magis arridet vtpo­<lb/>te breuior, qua quadratum CF diuido per <lb/>IC: cæterùm &longs;i rem merè Trigonome­<lb/>tricè perficere quis malit, inuentis CF <lb/>& IC, quærat angulum IFC; quem du­<lb/>plicet, & dupli &longs;inum ex Tabulis inue­<lb/>niat: tum fiat vt &longs;inus inuentus ad Ra­<lb/>dium ita inuenta CF ad quæ&longs;itam &longs;emidia­<lb/>metrum FT. </s> <s>Huius operationis ratio pa­<lb/>tet, quia cum angulus IFO in &longs;emicircu­<lb/>lo &longs;it rectus, triângulum ICF e&longs;t &longs;imile trian­<lb/>gulo IFO, igitur angulus inuentus IFC æqua­<lb/>lis e&longs;t angulo FOC; huius autem duplex e&longs;t <lb/>angulus ITF ad centrum, qui proinde inno­<lb/>te&longs;cit, vnâ cum &longs;inu FC in partibus Radii <lb/>hæc verò linea cum nota &longs;it etiam in men­<lb/>&longs;urâ homogeneâ altitudini datæ IG, manife­<lb/>&longs;tabit pariter in eâdem men&longs;urâ Radium TF. <!-- KEEP S--></s></p><p type="main"> <s>Placetne aliam adhuc inire viam? </s> <s>nec <lb/>Diony&longs;iodori Geometræ protritam ve&longs;tigiis; <lb/>cuius in &longs;epulchro inuenta e&longs;t epi&longs;tola ad <pb xlink:href="018/01/127.jpg" pagenum="113"/>&longs;uperos mi&longs;&longs;a, qua &longs;e à &longs;epulchro ad intimam <lb/>terram de&longs;cendi&longs;&longs;e &longs;ignificabat, illudque &longs;pa­<lb/>tium &longs;tadia 42000. complecti. </s> <s>Sint datæ al­<lb/>titudo eadem IG, ac di&longs;tantia GF, & angu­<lb/>lus IGF ob&longs;eruetur. </s> <s>Ducatur ex I tangens <lb/><arrow.to.target n="note56"/><lb/>IH; quæ &longs;ecet GF in H. <!-- KEEP S--></s> <s>Quæratur ergo i&ntail; <lb/>triangulo GIH rectangulo, ex dato latere GI <lb/>& angulo G, latus GH, quod ex GF ablatum <lb/>relinquit HF, & quæratur latus IH. </s> <s>Deinde du­<lb/>ctâ rectâ IF, in triangulo IHF nota &longs;unt la­<lb/>tera IH & HF, angulus autem compræhen­<lb/>&longs;us IHF æqualis e&longs;t duobus internis notis, &longs;ci­<lb/>licet recto GIH, & IGH ob&longs;eruato: quar&etail; <lb/>inueniri pote&longs;t tum latus IF, tum angulus <lb/>HIF: cui æqualis e&longs;t angulus IOF in alterno <lb/>&longs;egmento: huius autem duplus e&longs;t angulus <lb/>ITF ad centrum. </s> <s>Fiat igitur vt &longs;inus &longs;emian­<lb/>guli inuenti ITF, hoc e&longs;t &longs;inus anguli HIF, <lb/>ad Radium, ita &longs;emi&longs;sis inuenti lateris IF <lb/>ad quæ&longs;itam &longs;emidiametrum TF. <!-- KEEP S--></s></p><p type="margin"> <s><margin.target id="note56"/><emph type="italics"/>LVI. <!-- KEEP S--></s> <s><lb/>Vndecim&atail; <lb/>methodus <lb/>inueniendi <lb/>terræ &longs;emi­<lb/>diametrum:<emph.end type="italics"/></s></p><p type="main"> <s>Compendio&longs;iùs forta&longs;&longs;e operabimur, &longs;i da­<lb/>tis IG & GF cum angulo G compræhen&longs;o, <lb/><arrow.to.target n="note57"/><lb/>inueniatur ba&longs;is IF & angulus GIF, qui e&longs;t <lb/>nece&longs;&longs;ariò obtu&longs;us. </s> <s>Fiat ergo vt &longs;inus exce&longs;­<lb/>sûs anguli GIF &longs;upra rectum ad Radium, <lb/>ita &longs;emi&longs;sis inuentæ ba&longs;is IF ad quæ&longs;itam <lb/>terræ &longs;emidiametrum. </s></p><p type="margin"> <s><margin.target id="note57"/><emph type="italics"/>LVII. <lb/>Id<gap/> breuiùs.<emph.end type="italics"/></s></p><p type="main"> <s>Verùm omi&longs;&longs;o tot linearum apparatu res <pb xlink:href="018/01/128.jpg" pagenum="114"/><arrow.to.target n="note58"/><lb/><figure id="id.018.01.128.1.jpg" xlink:href="018/01/128/1.jpg"/><lb/>facillimè conficitur, e­<lb/>tiam&longs;i nulla &longs;it data al­<lb/>titudo nota. </s> <s>Ob&longs;erue­<lb/>tur di&longs;tantia AD: tum <lb/>in A accipiatur angulus <lb/>CAD, & in D ob&longs;erue­<lb/>tur angulus, quem cum <lb/>verticali lineâ ex D ad <lb/>Zenith productâ facit <lb/>radius opticus DA; hu­<lb/>ius enim complementum ad duos rectos <lb/>e&longs;t angulus ADC: dato autem latere AD <lb/>cum angulis adiacentibus, latere non po&longs;­<lb/>&longs;unt reliqua latera CD quæ&longs;ita terræ &longs;emidia­<lb/>meter, & CA &longs;emidiameter aucta montis <lb/>AB altitudine. </s></p><p type="margin"> <s><margin.target id="note58"/><emph type="italics"/>LVIII. <!-- KEEP S--></s> <s><lb/>Duodecima <lb/>methodus <lb/>&longs;emidiame­<lb/>trum terræ <lb/>inuestigan­<lb/>di, & montis <lb/>altitudini.<emph.end type="italics"/></s></p><p type="main"> <s>Sed iam, Mer&longs;enne, cadunt altis d&etail; <lb/>montibus vmbræ; nec Galilæum diutur­<lb/>niore colloquio di&longs;tinere fas e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Rectè mones: præceps in noctem <lb/>ruit dies: &longs;ed huiu&longs;modi colloquia cum in­<lb/>&longs;tituuntur, omnis hora momentum e&longs;t. </s> <s>Va­<lb/>le Galilæe. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Valete amici; & quas debeo gratias <lb/>pro humani&longs;simâ con&longs;uetudine, nunc planè <lb/>non reddo, &longs;ed apud me &longs;eruo, vt iterum <lb/>redire cogamini depo&longs;itum repetituri. </s></p><pb xlink:href="018/01/129.jpg" pagenum="115"/><figure id="id.018.01.129.1.jpg" xlink:href="018/01/129/1.jpg"/><p type="main"> <s><emph type="center"/>DISSERTATIO <lb/>QVARTA<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Ex aquæ &longs;eparatione à ter­<lb/>ra, motus facilitatem <lb/>infert.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s>PVRGARE ne tibi m&etail; <lb/>debeo, Galilæe, quòd con­<lb/>dictam Mer&longs;enno horam te <lb/>adeundi importunus præ­<lb/>uenerim? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Si putas Batauis in nouâ Zem­<lb/>blâ po&longs;t longas dierum 84 tenebras lu­<pb xlink:href="018/01/130.jpg" pagenum="116"/>cem præ&longs;to lancibus, Solem dies 14 antici­<lb/>pantem accidi&longs;&longs;e importunum, ac purgatio­<lb/>ne opus habui&longs;&longs;e, quòd legitimum exoriendi <lb/>tempus anteuerterit; præ&longs;tò &longs;um, vt intelli­<lb/>gam, qua te demum excu&longs;atione ab imma­<lb/>ni hac culpâ eximas. </s> <s>Sed cum expectatus <lb/>adueneris, quam tuorum in me meritorum <lb/>partem referendâ gratiâ con&longs;equi potero? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Culpam hanc omnem, quantæ­<lb/>cunque e&longs;t, in te transfero: id &longs;cilicet profu­<lb/>sâ tuæ humanitatis &longs;ignificatione effeci&longs;ti, vt <lb/>mihi liceat e&longs;&longs;e temerario; nec ab&longs;urdu&mtail; <lb/>duxerim &longs;tatim, ac me tui de&longs;iderium ce­<lb/>pit, aduolare, & immaturum fœtum, ve­<lb/>riùs dixerim víx dum conceptum, ante t&etail; <lb/>ponere, vt vitæ igniculos illi tuâ luce imper­<lb/>tias. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Siccine iuuat fe&longs;tiuis inanium offi­<lb/>ciorum argutijs iocari? </s> <s>Mittamus i&longs;thæc: & <lb/>quam primum edi&longs;&longs;ere, quæ te benigna ege­<lb/>rit Minerua, vt frigidos no&longs;tros cineres fodi­<lb/>catum venires, ignem ætheriâ vtique domo <lb/>&longs;ubductum depo&longs;iturus. </s></p><p type="main"> <s><emph type="italics"/>Guld:<emph.end type="italics"/> Ari&longs;totelem fortè præ manibus ha­<lb/>bebam; cumque aliud meditans pagellas te­<lb/>merè oculo percurrerem, incidi in textum <lb/>78. lib. 2. de Cœlo, vbi Thaletis Mile&longs;ii d&etail; <lb/>causâ terræ quie&longs;centis &longs;ententiam exponit, <pb xlink:href="018/01/131.jpg" pagenum="117"/><emph type="italics"/>an quam ex eo, quia innatans &longs;it, tellus ma­<lb/>neat, quemadmodum lignum vel aliquid tale <lb/>aliud; etenim horum &longs;uper aerem quidem ni­<lb/>hil natura aptum e&longs;t manere, &longs;ed &longs;uper aquam.<emph.end type="italics"/><lb/>Id quod mihi in mentem reuocauit eadem <lb/>pror&longs;us apud Senecam à me iam pridem le­<lb/>cta lib. 6. Nat. <!-- REMOVE S-->quæ&longs;t. </s> <s>cap. 6. terram videli­<lb/>cet totam, Thaletis opinione, &longs;ubiecto hu­<lb/>more portari, & innatare, ita vt vndâ &longs;u&longs;ti­<lb/>neatur orbis velut aliquod grande nauigium. </s> <s><lb/>Ex quo ille ab eodem Senecâ lib. 3. cap. 13. <lb/>reiectus non &longs;atis aptè terræ motuum cau&longs;am <lb/>inferebat, perindè atque &longs;i nauigium hoc in­<lb/>natans concuteretur. </s> <s>Tum, quæ e&longs;t phan­<lb/>ta&longs;matum atque formarum menti inhæren­<lb/>tium mira connexio, vix cæperam tacitus <lb/>ridere commenticium ingentis huius nauigii <lb/>nullos in &longs;copulos impacti tremorem, cum <lb/>in eius grauitatis con&longs;iderationem delap&longs;us <lb/>&longs;um: tenuique hac vellicatione excitatæ he­<lb/>&longs;terni no&longs;tri congre&longs;&longs;us reliquiæ animo in&longs;i­<lb/>dentes me protinus abripuerunt, & &longs;en&longs;im <lb/>nec aduertentem deduxerunt ad eam cogi­<lb/>tationem, vt &longs;u&longs;picarer ex aquarum naturâ, <lb/>ad tellurem Archimedæis machinationibus <lb/>mouendam, &longs;ub&longs;idium aliquod comparari <lb/>po&longs;&longs;e. </s> <s>Plura illicò huic cogitato affinia i&ntail; <lb/>mentem confusè & permixtè irruperunt, <pb xlink:href="018/01/132.jpg" pagenum="118"/>quæ &longs;ubitam approbationem temerè extor­<lb/>quere viderentur; &longs;ed quoniam, vbi multa <lb/>&longs;unt, quæ &longs;ibi aptis nexibus cohærere de­<lb/>beant, ne veritatis compages luxata pereat, <lb/>periculo&longs;um & lubricum e&longs;t facilè a&longs;&longs;entiri, <lb/>nolui me in præcipitem locum committere; <lb/>&longs;u&longs;tinendam potiùs tanti&longs;per omnem a&longs;&longs;en­<lb/>&longs;ionem duxi, dum rem totam di&longs;cretè & <lb/>electè &longs;uas in partes, te pro tuâ &longs;apientiâ <lb/>opem ferente, digererem. </s> <s>En habes, qui­<lb/>bus &longs;timulis actus mihi imperare non potue­<lb/>rim, vt à te diutiùs abe&longs;&longs;em. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Gratias tibi habeo, mi Guldine, im­<lb/>mortales; quod &longs;pem iniicias audiendi ex te <lb/>hodie, quid de iis &longs;entias, quæ iam tum ab <lb/>anno huius &longs;æculi duodecimo con&longs;crip&longs;i de <lb/>Innatantibus. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Librum legi tuo dignum ingenio; <lb/>nec potuit feliciùs enodari, quam con&longs;titue­<lb/>ras examinandam quæ&longs;tionem de &longs;olidis in­<lb/>natantibus, quamuis humido &longs;ecundùm &longs;pe­<lb/>ciem grauioribus, &longs;i quidem &longs;olitaria &longs;uman­<lb/>tur, componentibus tamen vnâ cum aër&etail; <lb/>&longs;ibi adhære&longs;cente molem aquâ non grauio­<lb/>rem. </s> <s>Illud maximè dolui, quod nactus &longs;im <lb/>exemplar &longs;iue Bibliopolæ &longs;ine Bibliopegi in­<lb/>curiâ mutilarum integro folio, & quidem il­<lb/>lo ip&longs;o, in quo totius futuræ di&longs;putationis <pb xlink:href="018/01/133.jpg" pagenum="119"/>fundamenta &longs;ternis: ac, quæ mihi aduer&longs;&atail; <lb/>e&longs;t fortuna, nu&longs;quam licuit integrum librum <lb/>reperire, ex quo no&longs;tri exemplaris hiatum <lb/>&longs;upplerem, Id quod te præmonui&longs;&longs;e oppor­<lb/>tunum fuit, ne, &longs;i fortè nobis non conuene­<lb/>rit, me contradicendi &longs;tudio actum putes: <lb/>ni&longs;i me tamen mea fallit opinio, in minimis <lb/>di&longs;&longs;entiemus. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Libens audio, qui contra &longs;en&longs;erint. </s> <s><lb/>Sed ne te longiùs ab in&longs;tituto tuo, veriùs di­<lb/>cam, no&longs;tro, abducam; quidnam ex aquâ <lb/>emolumenti &longs;peras ad facilem terræ motio­<lb/>nem, de qua nobis fuit di&longs;putatio? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Futurum puto, vt plurimum pon­<lb/>deris de terreno hoc orbe, qui aquam pariter <lb/>ac terram complectitur, deduceretur. </s> <s>Illud <lb/>enim extra omnem controuer&longs;iam po&longs;itum <lb/><arrow.to.target n="note59"/><lb/>accipio, quod aqua aëre grauior e&longs;t; & fluida <lb/>cùm &longs;it, &longs;emper ad inferiora delabitur, vt <lb/>infra aërem vniuer&longs;i centro vicinior con&longs;i&longs;tat. </s> <s><lb/>Ex quo fit, vt nu&longs;quam quie&longs;cat, ni&longs;i vbi <lb/>nullus patet locus, in quem de&longs;cendat. </s> <s>Qua­<lb/>rè cum &longs;ola &longs;uperficies &longs;phærica paribus ra­<lb/>diis à centro remoueatur, aquæ quie&longs;centis <lb/>&longs;uperficiem &longs;phæricam e&longs;&longs;e nece&longs;&longs;e e&longs;t: quan­<lb/>doquidem &longs;iquæ &longs;uperficiei partes à centro <lb/>longiùs abe&longs;&longs;ent, vtpote altiores ad motum <lb/>procliues non &longs;ub&longs;i&longs;terent, &longs;ed humiliorem <pb xlink:href="018/01/134.jpg" pagenum="120"/>in locum defluerent: neque enim ex eo a­<lb/>quam &longs;ponte a&longs;cendere dixerim, quòd ea in <lb/>vitreis fi&longs;tulis immer&longs;is aliquantulum a&longs;cen­<lb/>dat. </s></p><p type="margin"> <s><margin.target id="note59"/><emph type="italics"/>LIX <lb/>Aquæ &longs;u­<lb/>perficies est <lb/>&longs;phærica.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Nemo id facilè inficietur: immo, &longs;i <lb/>id quidem in rem tuam faciat, vltro dabo <lb/>maria omnia, quæ aquarum communion&etail; <lb/>iunguntur (&longs;i æ&longs;tum omnem &longs;ublatum, ven­<lb/>tosque &longs;ilentes animo fingamus) non e&longs;&longs;&etail; <lb/>alia alijs &longs;ecundùm &longs;uperficiem altiora: qui­<lb/>bus enim frænis cohiberentur Sinûs Arabici <lb/>aquæ, &longs;i altiores e&longs;&longs;ent, ne in Erytræum ma­<lb/>re influerent? </s> <s>aut quibus aggeribus ob&longs;true­<lb/>retur fretum Herculeum, ne Oceanus Atlan­<lb/>ticus ac Mediterraneum mare in vnâ &longs;u­<lb/>perficie aquarum libramentum &longs;u&longs;ciperent? </s></p><p type="main"> <s>Quod verò de aquâ in immer&longs;is fi&longs;tulis <lb/>vtrinque hiantibus a&longs;cendente addis, nihil <lb/>planè officit naturæ aquarum &longs;e in &longs;phæram <lb/>circa terræ centrum conglobantium; neque <lb/>illicò po&longs;&longs;e aquam ad digiti altitudine&mtail; <lb/>&longs;ponte a&longs;cendere affirmandum e&longs;t, quòd il­<lb/>lam in tenui&longs;&longs;imis fi&longs;tulis eò pertingere ali­<lb/>quando videamus; quò enim ampliores &longs;unt <lb/>fi&longs;tulæ, eò minùs in iis aquam a&longs;&longs;urger&etail; <lb/>con&longs;tat, nec fortè &longs;ine &longs;u&longs;picione minoris, <lb/>quàm appareat, altitudinis, propter &longs;pecie­<lb/>rum vi&longs;ibilium ex vitro refractionem, i&ntail; <pb xlink:href="018/01/135.jpg" pagenum="121"/>ampli&longs;simis igitur lacuum marium que alueis <lb/>quantùm illa a&longs;cendat, quod &longs;phæricam &longs;u­<lb/>perficiem corrumpat? </s> <s>Sed nec aquam om­<lb/>ninò &longs;ponte dixerim in fi&longs;tulâ a&longs;cender&etail; <lb/>Quando enim fi&longs;tula deprimitur, vt aquæ <lb/>immergatur, vtique &longs;ubiectus aër premitur, <lb/><arrow.to.target n="note60"/><lb/>& locum &longs;ubeunti fi&longs;tulæ concedens, quâ <lb/>patet via, recedit, vt locum &longs;uppleat à fi&longs;tu­<lb/>lâ deor&longs;um motâ relictum. </s> <s>Sicut autem <lb/>aër, cui corpus in motu occurrit, comprimi­<lb/>tur, ita is, qui ponè e&longs;t, paululum di&longs;trahi­<lb/>tur ac rare&longs;cit; hic verò ad ingenium rediens <lb/>proximum aërem attrahit ad &longs;upplendum <lb/>locum à fi&longs;tulâ relictum; cumque nullus <lb/>&longs;ubiectus aër tam in promptu &longs;it, quàm is <lb/>qui fi&longs;tulæ cauitatem implet, hic exfugitur; <lb/>atque adeò cum aér fi&longs;tulæ &longs;ur&longs;um mouea­<lb/>tur, &longs;ubiectus aër compre&longs;&longs;us in fi&longs;tulæ caui­<lb/>tatem &longs;uccedit, per quam faciliùs elabitur, <lb/>ac per impul&longs;ionem, aut compre&longs;&longs;ionem <lb/>contigui aëris, qui lateribus adiacet. </s> <s>Por­<lb/>rò ea e&longs;t fluidorum corporum natura, vt <lb/>conceptum ex motu impetum, etiam intrà <lb/>homogeneum corpus, non ita facilè remit­<lb/>tant; quemadmodum in aquâ colore aliquo <lb/>infectâ intrà aliam aquam leui&longs;&longs;imè effusâ <lb/>videre e&longs;t. </s> <s>Hinc e&longs;t aërem &longs;ur&longs;um in fi&longs;tulâ <lb/>incitatum ex concepto impetu tanti&longs;per per­<pb xlink:href="018/01/136.jpg" pagenum="122"/>gere in motu, & ita pellere &longs;uperiorem aë­<lb/>rem, vt hic eum qui fi&longs;tulæ latera extrin&longs;e­<lb/>cùs ob&longs;idet, propellat, fiatque per inferius <lb/>hiantis fi&longs;tulæ o&longs;culum illa circumpul&longs;io, de <lb/>qua Pla<emph type="italics"/>t<emph.end type="italics"/>o in Timæo, vel &longs;altem, vt cum ve­<lb/><gap/>tris Philo&longs;ophis loquar, ab a&longs;cendente aëre <lb/>per fi&longs;tulam liberrimè ab&longs;que vllo alterius <lb/>aëris intercurrentis obice, attrahitur aër in­<lb/>ferior. </s></p><p type="margin"> <s><margin.target id="note60"/><emph type="italics"/>LX. <!-- KEEP S--></s> <s><lb/>Cur aqu&atail; <lb/>in tubo v­<lb/>trinque bi­<lb/>ante a&longs;een­<lb/>dat aliquan <lb/>tulum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Veriùs forta&longs;&longs;e dixeris & attrahi <lb/>pariter & circumpelli: </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Vbi igitur inferioris o&longs; o&longs;culi labra &longs;u­<lb/>biectam aquam ita attigerint, vt aer &longs;ucce­<lb/>dere nequeat, illud nece&longs;&longs;ariò fit, vt a&longs;cen­<lb/>dentem aerem aqua &longs;ubiecta con&longs;equatur <lb/>&longs;iue attracta, &longs;iue ex circumpul&longs;ione propul­<lb/>&longs;a. </s> <s>Cum autem hoc à naturâ liquoribus <lb/>comparatum &longs;it, quod &longs;olidis corporibus ad­<lb/>hære&longs;cant; vbi aliquid aquæ &longs;ur&longs;um ab aere <lb/>a&longs;cendente eleuatæ, internis fi&longs;tulæ lateribus <lb/>adhæ&longs;erit, iam non deor&longs;um vrget contr&atail; <lb/>vim aéris a&longs;cendentis, qui propterea in reli­<lb/>quam aquam non adhære&longs;centem vires &longs;uas <lb/>omnes exercet. </s> <s>At quia in tenui&longs;simâ fi&longs;tu­<lb/>lâ cylindrulus aquæ primùm eleuatus ita ferè <lb/>totu<gap/> adhæret fi&longs;tulæ, vt vix in medio relin­<lb/>quat capillarem medullam ab aëre &longs;u&longs;tenta­<lb/>tam, multò faciliùs pergit in a&longs;cen&longs;u, & alias <pb xlink:href="018/01/137.jpg" pagenum="123"/>aquæ particulas &longs;ecum rapit &longs;ur&longs;um; donec <lb/>demum præter aquam &longs;ponte adhærentem <lb/>lateribus, tantum aquæ ab aere &longs;u&longs;tineatur, <lb/>vt eam dimittere non po&longs;&longs;it, quin ip&longs;e magis <lb/>di&longs;trahatur & rare&longs;cat: id quod natura potiùs <lb/>refugit, quàm permittere tantillæ aquæ <lb/>&longs;u&longs;pen&longs;ionem. </s> <s>Ni&longs;i fortè malles dicere, a­<lb/>quam illam medullarem con&longs;titutam intrà <lb/>aquam lateribus adhærentem iam non conari <lb/>deor&longs;um. </s> <s>Quando verò amplior e&longs;t fi&longs;tulæ <lb/>capacitas, con&longs;tat <expan abbr="a&etilde;rem">aerrem</expan> non tantâ velocita­<lb/>te per eam ferri &longs;ur&longs;um cæteris paribus, ac per <lb/>fi&longs;tulam tenuiorem, & præterea cylindrulus <lb/>aquæ &longs;ur&longs;um attractus ampliorem habet ba­<lb/>&longs;im, & in minori altitudine habetur tota ea <lb/>quantitas aquæ, quæ valet ab aere &longs;u&longs;tentari: <lb/>hinc fit eò minùs aquam attolli, quò am­<lb/>plior e&longs;t fi&longs;tula. </s> <s>Mitto hìc di&longs;putare an in­<lb/>&longs;en&longs;ibilis aquæ expiratio adhærens fi&longs;tulæ, <lb/>vel in eam incurrens, excitet electricam <lb/>vitri expirationem; an verò ea fi&longs;tulam le­<lb/>ui&longs;&longs;imè humectans, dum attactu illo &longs;tatim <lb/>concre&longs;cit, &longs;tatim &longs;ubiectam aquam attrahat <lb/>vt &longs;ibi veniat, quemadmodum in calamo <lb/>&longs;criptorio &longs;æpe ob&longs;eruare e&longs;t, quando atra­<lb/>mento valdè diluto vtimur; vix enim hu­<lb/>mens calamus &longs;ubiectum atramentum con­<lb/>tingit, cum eo confe&longs;tim imbuitur. </s> <s>Hæc <pb xlink:href="018/01/138.jpg" pagenum="124"/>&longs;cilicet nos longiùs, quàm par &longs;it, abdu­<lb/>cerent. </s> <s>Illud certum e&longs;t, quod aqua &longs;ponte <lb/>fluens ita &longs;emper ad humiliora loca delabi­<lb/>tur, vt à &longs;phæricâ &longs;uperficie non recedat, &longs;i <lb/>res Phy&longs;icè &longs;altem con&longs;ideretur. </s> <s>Atque adeò <lb/>id tibi vltrò concedens audire expecto, quid <lb/>indè conficias. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Non eandem e&longs;&longs;e &longs;emper aquæ &longs;u­<lb/>perficiem; quò enim maioribus à centro in­<lb/>teruallis &longs;emouetur, eò propiùs æquata&mtail; <lb/>planitiem æmulatur; at centro vicinior ma­<lb/>iori conuexitate inflectitur; hìc &longs;cilicet mi­<lb/>noris, ibi maioris &longs;phæræ portio e&longs;t. </s> <s>Iam <lb/>verò vt pla­<lb/>niùs & aper­<lb/>tiùs verbis <lb/><figure id="id.018.01.138.1.jpg" xlink:href="018/01/138/1.jpg"/><lb/><arrow.to.target n="note61"/><lb/>complectar, <lb/>quod volo, <lb/>ex Graphi­<lb/>de <expan abbr="&longs;ub&longs;idiũ">&longs;ub&longs;idium</expan> <lb/><expan abbr="petã">petam</expan>. </s> <s>Sit pro <lb/>globo terra­<lb/>queo circu­<lb/>lus ABCD, <lb/>cuius cen­<lb/>trum T <expan abbr="cõ-gruat">con­<lb/>gruat</expan> vniuer&longs;i centro, & BAE mare Hyper­<lb/><gap/>oreum, FCD Oceanus Indicus aut Æthio­<pb xlink:href="018/01/139.jpg" pagenum="125"/>picus, vel alius, quamcunque demum &longs;or­<lb/>tiatur appellationem. </s> <s>Ambigi non pote&longs;t, <lb/>quin maria hæc in eadem &longs;phæricâ &longs;uperficie <lb/>exi&longs;tant, quandoquidem ab vniuer&longs;i centro <lb/>T paribus interuallis di&longs;iunguntur. </s> <s>At &longs;i <lb/>tellurem ab vniuer&longs;i centro (quod, ne i&ntail; <lb/>vocabulis laboremus, centrum grauiu&mtail; <lb/>liceat appellare, cum eius rationem habue­<lb/>rit natura &longs;uum cuique corpori locum tri­<lb/>buens) remotam intelligamus, ita vt illius <lb/>quidem centrum &longs;it T, centrum verò gra­<lb/>uium &longs;it V; non eadem manere pote&longs;t v­<lb/>triu&longs;que maris &longs;uperficies; &longs;ed Hyperboreum <lb/>&longs;ub&longs;idere magis & explicari debet, Indicum <lb/>verò a&longs;&longs;urgere, Cum enim aqua A remo­<lb/>tior &longs;it quàm B & E à centro V, pote&longs;t de­<lb/>&longs;cendere, nec con&longs;i&longs;tet, ni&longs;i vbi fuerit &longs;u­<lb/>perficies BIE. </s> <s>Contra autem aqua F & D <lb/>remotior e&longs;t quàm C à centro V; pote&longs;t <lb/>igitur ver&longs;us C de&longs;cendere; & relicto loco <lb/>ad F & ad D, a&longs;&longs;urget<gap/> in H, & erit &longs;uper­<lb/>ficies FHD maiorem habens conuexita­<lb/>te&mtail;. </s></p><p type="margin"> <s><margin.target id="note61"/><emph type="italics"/>LXI <lb/>Si tellus a­<lb/>liò trahere­<lb/>tur, aqu&atail; <lb/>mutaret fi­<lb/>guram.<emph.end type="italics"/></s></p><p type="main"> <s>Quod &longs;i ad latus iaceat aqua, vt MNO, <lb/>factâ translatione centri ex Vin T, vtique <lb/>ex M versùs O de&longs;cendet; &longs;ed &longs;i mons OS <lb/>prohibeat, demùm con&longs;i&longs;tet aqua circa vni­<lb/>uer&longs;i centrum V in &longs;uperficie &longs;phæricâ RNS. <pb xlink:href="018/01/140.jpg" pagenum="126"/>Idemque d&etail; <lb/><figure id="id.018.01.140.1.jpg" xlink:href="018/01/140/1.jpg"/><lb/>cæteris e&longs;to iu­<lb/>dicium; nulla <lb/>&longs;iquidem repe­<lb/>riri po&longs;&longs;et a­<lb/>quarum con­<lb/>gregatio, quæ <lb/>tellure transla­<lb/>tâ, &longs;e aliam in <lb/><expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> non <lb/>conglobaret, <lb/>altioribus par­<lb/>tibus in inferiorem locum delap&longs;is. <lb/><arrow.to.target n="note62"/></s></p><p type="margin"> <s><margin.target id="note62"/><emph type="italics"/>LXII <lb/>Noua hypo­<lb/>the&longs;is mari­<lb/>ni æstus in­<lb/>dicatur, &longs;ed <lb/>non proba­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Igno&longs;ce, quæ&longs;o, interpellanti. </s> <s>Ne­<lb/>&longs;cio quam mihi inijcis &longs;u&longs;picionem nouæ <lb/>hypothe&longs;is, qua citra omnem telluris verti­<lb/>ginem &longs;iuè in orbe annuo, &longs;iuè circa &longs;uum <lb/>axem, marinus æ&longs;tus explicari po&longs;&longs;et: &longs;i ni­<lb/>mirum terræ centrum lento ac tenui motu <lb/>vltro citroque commeans centro grauium<lb/>congrueret &longs;olùm in medio fluxu aut reflu­<lb/>xu. </s> <s>Si enim T accedat ad V, aqua incipit <lb/>ex S refluere ver&longs;us M, vbi aqua &longs;emper au­<lb/>getur, quò magis centrum T recedit ab V <lb/>in X: iterumque fluit ex M in O, cum cen­<lb/>trum ab X recedens in V & in T &longs;ua per <lb/>ve&longs;tigia eò remeat, vnde di&longs;ce&longs;&longs;it, &longs;eruatâ­<lb/>que in motu reciprocando con&longs;tantiâ, al­<pb xlink:href="018/01/141.jpg" pagenum="127"/>ternas fluxûs, & refluxûs vices efficit in ad­<lb/>uer&longs;is litoribus. </s> <s>Quod &longs;i in oppo&longs;itis eiu&longs;­<lb/>dem aluei ripis eodem tempore fluxus con­<lb/>tingat aut refluxus, vt in B & E, aut in F & <lb/>D; tunc opinari quis po&longs;&longs;et mare illud eam <lb/>habere po&longs;itionem, vt in illud incidat linea <lb/>motûs, quæ ex centro grauium per terræ <lb/>centrum ducitur: dum enim aqua deprimitur <lb/>ex A in I, augetur in B & E, &longs;i litus fluxui <lb/>ob&longs;tet, aut vlteriora &longs;patia occupat in P & K: <lb/>dum verò a&longs;&longs;urgit ex C in H, minuitur in F & <lb/>D. <!-- KEEP S--></s> <s>Porrò alternâ hac nutantis terræ mo­<lb/>tione non magis eius &longs;tabilitas vacillaret, <lb/>quàm illiùs firmitati ob&longs;it trepidationis mo­<lb/>tus à pleri&longs;que admi&longs;&longs;us ob variam centri <lb/>grauitatis po&longs;itionem: &longs;tare &longs;iquidem terra <lb/>dicitur, quæ &longs;uo ex loco non decedit, quam­<lb/>quam in eo &longs;uæ diametri particulam (1/4000000) <lb/>percurrat. </s> <s>Finge enim motûs extremos <lb/>terminos T & X non ampliùs pa&longs;&longs;um vnum <lb/>di&longs;tare à grauium centro V: tanta e&longs;t aqua­<lb/>rum in immen&longs;um patentium copia, vt èxi­<lb/>guâ inclinatione, quam motu illo acquire­<lb/>rent, dilabentes æ&longs;tum non exiguum effi­<lb/>cerent: qui tamen in lacubus, angu&longs;tiori­<lb/>busque alueis ob minorem aquarum copiam <lb/>non perciperetur. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Blandiuntur i&longs;thæc facilè mentis <pb xlink:href="018/01/142.jpg" pagenum="128"/>oculis: &longs;ed &longs;i rem penitiùs intro&longs;picere per <lb/>otium liceret, haud &longs;atis &longs;cio, quàm aptè <lb/>commentum hoc cum marini æ&longs;tûs phæno­<lb/>menis cohæreret. </s> <s>Nec pauca in hanc &longs;en­<lb/>tentiam afferri po&longs;&longs;ent: &longs;ed non vacat his im­<lb/>morari, ne longiùs ab in&longs;tituto digrediar, <lb/>aut &longs;ortè, quæ e&longs;t fugacis memoriæ incon­<lb/>&longs;tantia, excidant, quæ nunc animo obuer­<lb/>&longs;antur. </s> <s>De mari certè, quod Kiùn, in In­<lb/>&longs;ulâ Hainan, alluit, illud notatu dignum <lb/>&longs;cribunt Sinæ Geographi, quod maris æ&longs;tum <lb/>Diurnum non &longs;entiat, &longs;ed per dimidiam <lb/>men&longs;is partem versùs Ortum, per reliquam <lb/>dimidiam versùs Occa&longs;um fluat. </s> <s>Quid? <!-- KEEP S--></s> <s><lb/>Quod in vertice montis Hucùng in Fokien <lb/>Prouinciâ puteus e&longs;t (Hiai nomen e&longs;t) cuius <lb/>aqua æ&longs;tum marinum &longs;uo acce&longs;&longs;u & rece&longs;&longs;u <lb/>refert. </s> <s>Adde huic fontem prope Nuikiang <lb/>in Suchuen Prouinciâ, quem modò a&longs;cen­<lb/>dentem modò de&longs;cendentem æ&longs;tûs marini <lb/>horas adeò procul à mari &longs;equi ob&longs;eruatum <lb/>e&longs;t. </s> <s>Hos autem æ&longs;tus ex motu illo orbis, <lb/>quem innuebas, non oriri palàm e&longs;t. </s> <s>Quòd <lb/>&longs;i ex tam remotâ Sinatum regione petitum <lb/>argumentum reijcis, mihi &longs;anè con&longs;tat non <lb/>hanc e&longs;&longs;e æ&longs;tûs effectricem cau&longs;am; nam <lb/>ip&longs;a quoque flumina, terræ centro accedente <lb/>ad centrum grauitatis aut recedente, diebus <pb xlink:href="018/01/143.jpg" pagenum="129"/>&longs;ingulis cursûs velocitatem incitarent re­<lb/>mitterentque, aut etiam &longs;uum in caput re­<lb/>laberentur; id quod nondum licuit ob&longs;erua­<lb/>re. </s> <s>Præterquam quod vix dixeris, quo mo­<lb/>uente tellus vici&longs;&longs;im commearet, citrà fabu­<lb/>larum figmenta. </s></p><p type="main"> <s>At &longs;i contingere po&longs;&longs;et, vt machinarum </s></p><p type="main"> <s><arrow.to.target n="note63"/><lb/>ope telluris centrum ex V in T transferretur, <lb/>fluminis GL aqua ex G reflueret in L, & in <lb/>eundem alueum &longs;e in&longs;inuaret mare v&longs;qu&etail; <lb/>dum tota aquæ &longs;uperficies continua in &longs;phæ­<lb/>ram inflexa con&longs;i&longs;teret, cum non haberet, <lb/>quò de&longs;cenderet. </s> <s>Hinc illud fit, quod cum <lb/>maria omnia (ni&longs;i fortè Ca&longs;pium velis exci­<lb/>pere, cui tamen per &longs;ubterraneos cuniculos <lb/>cum Ponto Euxino communio e&longs;t) &longs;ibi in­<lb/>uicem continuata iunctaque &longs;int, terrâ in <lb/>partem vnam translatâ, aquæ ferè omnes in <lb/>oppo&longs;itam recederent, vel per patentem al­<lb/>ueum dilabentes, vel etiam exundantes: <lb/>idem quippe tunc aquarum conceptaculis <lb/>contingeret, ac &longs;i nunc vas liquore qua&longs;i <lb/>plenum magis & magis inclinaretur, totus <lb/>enim demùm liquor effunderetur. </s> <s>Quarè <lb/>vniuer&longs;a ferè aqua &longs;uperiorem locum relin­<lb/>quens in H conflueret eò velociùs, quò lon­<lb/>giùs telluris centrum T recederet ab V cen­<lb/>tro grauium &longs;eu vniuer&longs;i. </s></p><pb xlink:href="018/01/144.jpg" pagenum="130"/><p type="margin"> <s><margin.target id="note63"/><emph type="italics"/>LXIII <lb/>Tellur&etail; <lb/>translata fe­<lb/>rè tota aqua <lb/>ab ea &longs;eiun­<lb/>geretur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> In eo igitur, &longs;i quid video, machi­<lb/>nalis motionis, qua terra transferretur, faci­<lb/>litatem con&longs;tituis, quod eo ip&longs;o tempore, <lb/>quo terra &longs;upra FVD planum (quod ho­<lb/>rizontale vocetur) attolleretur, aqua de­<lb/>&longs;cenderet; ac proinde &longs;uperioris partis pon­<lb/>dus minueretur, donec demum terra pro­<lb/>cul à centro translata totius ferè aquæ ponde­<lb/>re leuaretur, quæ circa vniuer&longs;i centrum V <lb/>aqueum in globum &longs;uis &longs;e nutibus confor­<lb/>maret. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ita planè: nec illud quidem con­<lb/>temnendum e&longs;&longs;et compendium, &longs;i ponderis <lb/>aquæ rationes ineamus. </s> <s>Quotam enim ter­<lb/>raquei huius globi partem con&longs;tituendam <lb/>e&longs;&longs;e aquam cen&longs;es? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Res e&longs;t, in qua Geometriæ apices <lb/>per&longs;equi non po&longs;&longs;umus, cum exactâ ma­<lb/>rium omnium notitiâ careamus, & planè <lb/>varia &longs;it aquarum profunditas: qua propter <lb/>coniecturis contentos nos e&longs;&longs;e oportet. </s> <s>Et <lb/>quidem quod ad aquarum &longs;uperficiem per­<lb/>tinet, eas arbitror æquis cum terrâ portioni­<lb/>bus globi conuexitatem di&longs;pertire: altitudi­<lb/>nem verò adeò incon&longs;tantem reperio, vt &longs;i <lb/>profunditates maiores cum minoribus com­<lb/>pen&longs;emus, vix vltra milliaris dodrantem aut <lb/>integrum milliare altitudini in vniuer&longs;um <pb xlink:href="018/01/145.jpg" pagenum="131"/>tribuendum exi&longs;time&mtail;. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/> Qúæ &longs;entis, approbo; immen&longs;æ <lb/><arrow.to.target n="note64"/><lb/>&longs;iquidem illæ altitudines & aby&longs;&longs;i aquarum <lb/>rari&longs;&longs;imæ &longs;unt, quæ bolide nullâ explorari <lb/>po&longs;&longs;int. </s> <s>Idcircò libentiùs vniuersè altitu­<lb/>dinem &longs;olùm dodrantalem aquis tribuo, mil­<lb/>liari a&longs;&longs;umpto pro a&longs;&longs;e. </s> <s>Iam, &longs;i placet, <lb/>aquæ grauitatem ad calculos reuocemus, & <lb/>globi perimetrum accipiamus, quam olim <lb/>Mer&longs;ennus, nobis non repugnantibus, con­<lb/>&longs;tituebat mill. <!-- REMOVE S-->Rom. <!-- REMOVE S-->ant. </s> <s>25941. Perime­<lb/>tro con&longs;titutâ, diametrum &longs;ic inquiro ex ra­<lb/>tionibus Vietæ: Vt 31415.926536 ad <lb/>10000.000000, ita maximi circuli periphe­<lb/>ria mill. <!-- REMOVE S-->25941 ad diametrum mill. <!-- REMOVE S-->8257­<lb/>pa&longs;&longs;. </s> <s>276. Igitur &longs;i diameter in peripheriam <lb/>ducatur, producetur &longs;phærica &longs;uperficies <lb/>mill. <!-- REMOVE S-->quadrat. </s> <s>214.201996. pa&longs;&longs;. </s> <s>quad. </s> <s><lb/>716000: Huius autem &longs;emi&longs;sis mill. <!-- REMOVE S-->107. <lb/>100998. pa&longs;&longs;. </s> <s>358000. erit &longs;uperficies a­<lb/>quæ. </s></p><p type="margin"> <s><margin.target id="note64"/><emph type="italics"/>LXIV <lb/>Totius a­<lb/>quæ quanti­<lb/>tas, & gra­<lb/>uitas inqui­<lb/>ritur.<emph.end type="italics"/></s></p><p type="main"> <s>Et vt breuitati &longs;eruiam, duco inuentam <lb/>aquæ &longs;uperficiem in altitudinem con&longs;titutam <lb/>mill.3/4: ne &longs;cilicet longioribus ambagibus in <lb/>quiram totius globi &longs;oliditatem. </s> <s>Deinde in­<lb/>&longs;titutâ analogiâ, <emph type="italics"/>vt cubus diametri inuentæ <lb/>ad cubum eiu&longs;dem diametri mulctatæ dodran­<lb/>te milliaris, ita &longs;oliditas &longs;phæræ ex inuenta dia­<emph.end type="italics"/><pb xlink:href="018/01/146.jpg" pagenum="132"/><emph type="italics"/>metro ad &longs;oliditatem alterius &longs;phæræ,<emph.end type="italics"/> inue­<lb/>niam harum &longs;phærarum differentiam, cuius <lb/>differentiæ &longs;emi&longs;&longs;is aquarum &longs;oliditati tri­<lb/>buatur. </s> <s>Neque enim e&longs;t operæ pretium <lb/>nos ip&longs;os hoc labore conficere; quandoqui­<lb/>dem vix di&longs;creparet inuentus numerus ab eo, <lb/>qui ex ductu &longs;uperficiei in altitudinem pro­<lb/>dibit. </s> <s>Duco igitur aquæ &longs;uperficiem mill. <!-- REMOVE S--><lb/>107.100998 pa&longs;&longs;. </s> <s>358000 in altitudinem <lb/>mill. <!-- REMOVE S-->3/4, & prodit &longs;oliditas milliarium cubi­<lb/>corum 80.325748, & pa&longs;&longs;. </s> <s>cubic. </s> <s>768. <lb/>500000. </s></p><p type="main"> <s>Inuentâ &longs;oliditate grauitatem inue&longs;tigo: <lb/>& quamuis &longs;ciam marinam aquam ob ad­<lb/>mixtam &longs;alis copiam grauiorem e&longs;&longs;e aquâ <lb/>communi; vt tamen compen&longs;etur, &longs;i quid <lb/>plus æquo tributum e&longs;t &longs;uperficiei, aut pro­<lb/>funditati, communem aquæ grauitatem ac­<lb/>cipio; Et quoniam milliaribus Romanis an­<lb/>tiquis vtimur, pondus pedis cubici antiqui, <lb/>hoc e&longs;t amphoræ aquâ plenæ, e&longs;t lib. 80. <lb/>Igitur quia milliare cubicum con&longs;tat pedi­<lb/>bus &longs;olidis 125000.000000, hic numerus per <lb/>lib. 80 ductus dabit libras 10.000000.000000 <lb/>grauitatem &longs;ingularium milliarium cubico­<lb/>rum aquæ. </s> <s>Iam &longs;i &longs;oliditas mill. <!-- REMOVE S-->80.325748 <lb/>pa&longs;&longs;. </s> <s>768.500000. ducatur per libras 10. <lb/>000000.000000. erit totius aquæ pondus lib. <pb xlink:href="018/01/147.jpg" pagenum="133"/>803.257487.685000.000000. <lb/><arrow.to.target n="note65"/></s></p><p type="margin"> <s><margin.target id="note65"/><emph type="italics"/>LXV <lb/>Pondus ter­<lb/>reni globi <lb/>quàm nota­<lb/>biliter mi­<lb/>nueretur ex <lb/>aquæ &longs;ece&longs;­<lb/>&longs;ione.<emph.end type="italics"/></s></p><p type="main"> <s>Hoc autem pondus ex totius globi graui­<lb/>tate demptum faciliorem efficeret terræ <lb/>motionem, vbi iam tota terra aliquo u&longs;que <lb/>ab vniuer&longs;i centro rece&longs;&longs;i&longs;&longs;et, ibique aquam <lb/>ferè totam, quæ nunc in globi &longs;uperfici&etail; <lb/>fluit, reliqui&longs;&longs;et. </s> <s>Sed quid &longs;i in maris fundo <lb/>amplæ pateant voragines, per quas in tellu­<lb/>ris cuniculos aqua &longs;e in&longs;inuer, ingentesque <lb/>aby&longs;&longs;os creet? </s> <s>An non per hiatus eo&longs;dem <lb/>aqua &longs;e exoneraret tellure in altum &longs;ublatâ ? <lb/>Ex quo & illud con&longs;equeretur, quod in im­<lb/>men&longs;a illa hydrophylacia aër tenuisque va­<lb/>por defluenti aquæ &longs;uccederet, fieretque to­<lb/>tius compo&longs;itæ molis grauitas &longs;ecundùm <lb/>&longs;peciem minor. </s> <s>Verùm terræ vi&longs;cera n&etail; <lb/>&longs;crutemur; aquasque illas hypogæas &longs;uis in <lb/>conceptaculis &longs;tagnantes relinquamus. </s> <s>A­<lb/>qua certè, quæ terræ faciem nunc alluit, <lb/>tanta e&longs;t, vt &longs;i eam di&longs;ce&longs;&longs;i&longs;&longs;e in locum alium <lb/>à tellure animo concipiamus, continuo non <lb/>exigua &longs;anè momenta ex globo terraqueo <lb/>dempta intelligamus. </s> <s>Et &longs;i ad manum e&longs;&longs;et <lb/>&longs;chedula, in qua Mer&longs;ennus rationes dige&longs;&longs;it, <lb/>quibus telluris grauitatem nudius tertius in­<lb/>ue&longs;tigabat, numerum hunc librarum ex illo <lb/>&longs;ubducentibus con&longs;taret non planè contem­<lb/>nendum e&longs;&longs;e hoc laboris compendium. </s></p><pb xlink:href="018/01/148.jpg" pagenum="134"/><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Secum illam tulit Mer&longs;ennus: &longs;ed <lb/>non e&longs;t opus grauitatem hanc aquæ cum to­<lb/>tius globi pondere comparare, &longs;atis enim per <lb/>&longs;e patet, quàm in&longs;ignis foret i&longs;ta ponderis <lb/>dece&longs;&longs;io. </s> <s>Vnum autem hìc ob&longs;eruo, quod </s></p><p type="main"> <s><arrow.to.target n="note66"/><lb/>nimirum, quamuis ingens hæc ponderis di­<lb/>minutio tunc &longs;olùm contingeret, quando <lb/>terra e&longs;&longs;et ab aquis diuul&longs;a, & ab vniuer&longs;i <lb/>centro V tota abe&longs;&longs;et, emolumentum tamen <lb/>non paruum faceret in motione a&longs;&longs;iduus a­<lb/>quarum fluxus in partem oppo&longs;itam. </s> <s>Si enim <lb/>globus plano FD &longs;ectus eò transferatur, vt <lb/>vniuer&longs;i <expan abbr="c&etilde;-trum">cen­<lb/>trum</expan> V i&ntail; <lb/><figure id="id.018.01.148.1.jpg" xlink:href="018/01/148/1.jpg"/><lb/><expan abbr="eod&etilde;">eodem</expan> &longs;it pla­<lb/>no, non &longs;o­<lb/>lùm <expan abbr="nõ">non</expan> per­<lb/>cipitur toti­<lb/>us globi, &longs;ed <lb/>ne totius qui­<lb/>dem <expan abbr="fegm&etilde;-ti">fegmen­<lb/>ti</expan> FAD gra­<lb/>uitas: <expan abbr="quan-doquid&etilde;">quan­<lb/>doquidem</expan> &longs;eg­<lb/>mentum FA <lb/>D de or&longs;um non conatur contra vim &longs;ur&longs;um <lb/>mouentem aut &longs;u&longs;tinentem, ni&longs;i iuxta mo­<lb/>menta ponderis, quibus &longs;uperat moment&atail; <pb xlink:href="018/01/149.jpg" pagenum="135"/>&longs;egmenti FCD oppo&longs;ito conatu in idem cen­<lb/>trum V nitentis, ne indè remoueatur. </s> <s>At­<lb/>qui aquæ pars aliqua &longs;upra planum FD exi­<lb/>&longs;tens infra illud de&longs;cendit; igitur in &longs;egmen­<lb/>to FAE minuitur pondus, & fit ponderis ac­<lb/>ce&longs;&longs;io &longs;egmento FCD; quarè multò minor <lb/>e&longs;t differentia grauitatum inter &longs;egmenta, ac <lb/>proinde minor in mouendo labor, aut in &longs;u­<lb/>&longs;tinendo. </s> <s>Quemad modum enim &longs;i in libræ <lb/>lancibus po&longs;ita fuerint pondera inæqualia, & <lb/>exlance grauiore pars ponderis transferatur <lb/>in alteram lancem, propiùs accedunt ad <lb/>æquilibrium, & faciliùs &longs;u&longs;tinetur lanx gra­<lb/>uior; Sic etiam pondus aliquod aquæ ex <lb/>&longs;egmento maiore FAD tran&longs;latum in &longs;eg­<lb/>mentum minus FCD, efficit minorem <lb/>ponderum inæqualitatem, ac proinde minor <lb/>grauitas percipitur à mouente globum, vel <lb/>&longs;u&longs;tinente. </s></p><p type="margin"> <s><margin.target id="note66"/><emph type="italics"/>LXVI <lb/>Facilitas <lb/>mouendi ter­<lb/>ram ex de­<lb/>fluxu aqua­<lb/>rum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Opportunè &longs;ugge&longs;&longs;i&longs;ti, quæ m&etail; <lb/>aliò ab&longs;tractum pror&longs;us effugerant. </s> <s>Thales <lb/>Mile&longs;ius &longs;uo illo ingenti nauigio me longiùs <lb/>abduxerat. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Quid illud e&longs;t? </s> <s>an putas terra&mtail; <lb/>aquis innatare, aut po&longs;&longs;e pari facilitate atque <lb/>nauigium trahi &longs;eu impelli? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Minimè omnium: &longs;ed ne&longs;cio quæ <lb/>mens mihi incidit, vt inciperem &longs;u&longs;picari, <pb xlink:href="018/01/150.jpg" pagenum="136"/>an telluris centro ex V<gap/>in T machinationi­<lb/>bus translato, & aquâ in oppo&longs;itam partem <lb/>confluente, fieri po&longs;&longs;et, vt aquæ terra inna­<lb/>taret, aut &longs;altem aliquid de grauitare remit­<lb/>teret. </s> <s>Id quod opportuniore &longs;chemate ex­<lb/>hibeo. </s> <s>Sit idem terræ globus ABCE, cu­<lb/>ius centrum T non congruat ampliùs cum <lb/>centro V. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> At ecce Mer&longs;ennum in ip&longs;o tem­<lb/>pore. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> In facinore manife&longs;to deprehen&longs;i <lb/>pœnas dabitis, boni viri. </s> <s>Nullus e&longs;t infi­<lb/>ciandi locus. </s> <s>Graphium adhuc tenet Gul­<lb/>dinus; Galilæus cubito incumbens attentus <lb/>operam dabat. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Salue amicum caput. </s> <s>Quicquid in <lb/>nobis e&longs;t criminis, animaduertatur; &longs;ed te <lb/>iudice. </s> <s>Dabimus, quas volueris pœnas. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Vtique leues, &longs;i fuerint peccato <lb/>pares. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Vos nunquam &longs;atis de hoc apud <lb/>me purgabitis, quod ante condictam mihi <lb/>horam conueneritis, amæna &longs;cientiarum <lb/>&longs;patia, me prætermi&longs;&longs;o, percurrentes. </s> <s>Ve­<lb/>niam non impetrabitis, ni&longs;i me illicò in &longs;ua­<lb/>ui&longs;&longs;imi docti&longs;&longs;imique ve&longs;tri &longs;ermonis con­<lb/>&longs;ortium admittentes probaueritis vos mihi <lb/>ve&longs;tra cogitata non inuidi&longs;&longs;e, </s></p><pb xlink:href="018/01/151.jpg" pagenum="137"/><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Præclarè nobi&longs;cum agitur, te iudicè. </s> <s><lb/>Culpâ vacamus: nam præmium nobis, non <lb/>pœna decernitur. </s> <s>Quarè rumpe moras, Gul­<lb/>dine, & quæ nobis e&longs;&longs;et di&longs;putatio, edi&longs;­<lb/>&longs;ere. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ex ingenitâ aquarum propen&longs;io­<lb/>ne, qua &longs;emper ad ima delabuntur, animad­<lb/>uertebamus oriri po&longs;&longs;e, vt &longs;i telluris globus <lb/>Archimedæis machinationibus extra vniuer&longs;i <lb/>centrum transferretur, aquæ in oppo&longs;itam <lb/>motui partem delabentes, vt fierent centro <lb/>viciniores, minùs grauem relinquerent &longs;u­<lb/>periorem terræ portionem. </s> <s>Si enim e&longs;&longs;et <lb/>ABCE terræ globus, cuius centrum T non <lb/>congrueret centro V, quod vniuer&longs;i, aut &longs;al­<lb/><figure id="id.018.01.151.1.jpg" xlink:href="018/01/151/1.jpg"/><lb/>tem <expan abbr="grauiũ">grauium</expan> <lb/><expan abbr="elementariũ">elementarium</expan> <lb/>centrum &longs;ta­</s> <s><lb/>tuitur, aquæ <lb/>omnes, qui­<lb/>bus liber&atail; <lb/>pateret ad <lb/><expan abbr="fluendũ">fluendum</expan> via, <lb/><expan abbr="de&longs;cender&etilde;t">de&longs;cenderent</expan> <lb/>ver&longs;us C, vt <lb/>ad centrum <lb/>V propiùs <lb/>accederent, <pb xlink:href="018/01/152.jpg" pagenum="138"/>& in &longs;phæricâ demum &longs;uperficie FHD pari­<lb/>bus radijs à centro V remota con&longs;i&longs;terent. </s> <s><lb/>Cum itaque &longs;uperiori &longs;egmento fieret pon­<lb/>deris aquæ dece&longs;&longs;io, inferiori autem acce&longs;­<lb/>&longs;io, aliquod haberetur in perficiendâ mo­<lb/>tione compendium: Hæc verò di&longs;&longs;erenti­<lb/>bus nobis incidit &longs;u&longs;picio, an fortè continge­<lb/>re po&longs;&longs;et, aquis in partem vnam delap&longs;is <lb/>terram innatare. </s></p><p type="main"> <s>Sit enim globus terraqueus ABCE, cu­<lb/>ius centrum T ad illud interuallum à centro <lb/>V venerit machinarum vi, vt aqua deor&longs;um <lb/><arrow.to.target n="note67"/><lb/><figure id="id.018.01.152.1.jpg" xlink:href="018/01/152/1.jpg"/><lb/>delap&longs;a &longs;it B <lb/>HECB, & <lb/>portionem B <lb/>CE circum­<lb/>plectatur. </s> <s><expan abbr="Iã">Iam</expan> <lb/>verò dimit­<lb/>tatur tellus à <lb/>&longs;u&longs;pendente: <lb/><expan abbr="nõ">non</expan> facilè de. </s> <s><lb/>finirem, v­<lb/>trùm terr&atail; <lb/>con&longs;i&longs;teret, <lb/>an potius de­<lb/>&longs;cenderet ex T in V, an verò etiam &longs;ponte <lb/>a&longs;cenderet longiùs recedens ab V. <!-- KEEP S--></s> <s>Verùm <lb/>&longs;i &longs;ponte &longs;uâ aliquo u&longs;que a&longs;cenderet, ia&mtail; <pb xlink:href="018/01/153.jpg" pagenum="139"/>nihil &longs;upere&longs;&longs;et laboris Archimedi, vt eò il­<lb/>lam deduceret: &longs;i con&longs;i&longs;teret, iam innataret <lb/>aquis, ac proinde non multo labore fui&longs;&longs;et <lb/>opus, vt ex V in T transferretur: &longs;i demùm <lb/>de&longs;cenderet, illud &longs;altem haberetur emolu­<lb/>menti, quod intrà aquam exi&longs;tenti multum <lb/>ponderis decederet, & motio faciliùs perfi­<lb/>ceretur. </s></p><p type="margin"> <s><margin.target id="note67"/><emph type="italics"/>LXVII <lb/>Facilitas <lb/>motus terræ, <lb/>antequa&mtail; <lb/>ab aqua &longs;e­<lb/>iungeretur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Lepidum &longs;anè inuentum ad vin­<lb/>dicandum à calumniâ Archimedem, &longs;i cui <lb/>fortè audaciùs locutus videatur: neque enim <lb/>ex machinis &longs;olùm, de quibus abundè Gali­<lb/>læus di&longs;putabat, verùm etiam ex ipsâ aquâ <lb/>&longs;ub&longs;idium non leue peti po&longs;&longs;et ad tellure&mtail; <lb/>loco dimouendam. </s> <s>Sed quid potiùs dicen­<lb/>dum exi&longs;timas? </s> <s>innataret-ne? </s> <s>an verò de­<lb/>&longs;cenderet? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ex his fluctibus enauigare &longs;olus <lb/>non po&longs;&longs;um: vobis pariter adremigandum <lb/>e&longs;t. </s> <s>Illud primum &longs;tatuere oportet, vtrùm <lb/>terrenus globus &longs;it aquâ leuior &longs;ecundùm <lb/>&longs;peciem; deinde quota pars ex aquis &longs;ponte <lb/>emergeret: vt hinc innote&longs;cat, quantu&mtail; <lb/>fui&longs;&longs;et Archimedi laborandum. </s> <s>Et quod <lb/>ad primum &longs;pectat, certum e&longs;t aërem vni­<lb/>uer&longs;um in terræ cauernis delite&longs;cente&mtail;, <lb/>omnesque halitus, & corpora aquis leuiora <lb/>plurimum po&longs;&longs;e demere de grauitate: aër <pb xlink:href="018/01/154.jpg" pagenum="140"/>enim, dum corpus in aëre &longs;u&longs;penditur, nec <lb/>grauitatem addit, nec leuitatem: at &longs;i cor­<lb/>pus aquæ in&longs;i&longs;tat, ex aëre recipit leuita­<lb/>tem. <lb/><arrow.to.target n="note68"/></s></p><p type="margin"> <s><margin.target id="note68"/><emph type="italics"/>LXVIII <lb/>Pondus tel­<lb/>luris in a­<lb/>qua minue­<lb/>retur, ob in­<lb/>clu&longs;os bali­<lb/>tus.<emph.end type="italics"/></s></p><figure id="id.018.01.154.1.jpg" xlink:href="018/01/154/1.jpg"/><p type="main"> <s>Sit enim vas AR æreum <lb/>parallelepipedum <expan abbr="vacuũ">vacuum</expan>, <lb/>cuius moles &longs;olida, hoc e&longs;t <lb/>vnâ cum aëre inclu&longs;o, &longs;it <lb/>pedalis: expendatur i&ntail; <lb/>aëre, & &longs;it lib. 12. Vtique <lb/>&longs;i aquæ imponatur, nata­<lb/>bit, cum pes cubicus a­<lb/>quæ &longs;it lib. <!-- REMOVE S-->Rom. <!-- REMOVE S-->80; e&longs;t <lb/>enim grauitas molis compo&longs;itæ ex va&longs;is ma­<lb/>tèriâ & aëre ad grauitatem aquæ, vt;. </s> <s>3. ad 20. <lb/>At &longs;i &longs;eruata eadem materia, & æris den&longs;i­<lb/>tate eâdem manente, confletur in ma&longs;&longs;am, <lb/>aut ex eâ fiat vas minoris capacitatis, erit <lb/>quidem in aëre idem pondus, at non item <lb/>in aquâ. </s> <s>Haud di&longs;pari ratione aër terræ vi­<lb/>&longs;ceribus inclu&longs;us, qui ad extenuandum orbis <lb/>pondus in aëre nihil iuuat, ni&longs;i quatenus lo­<lb/>cum occupat cæteroqui grauioribus corpo­<lb/>ribus replendum, intrà aquam conferret in­<lb/>&longs;uper leuitatem, & de grauiorum corporum <lb/>pondere aliquid demeret. </s> <s>Quod &longs;i ignem <lb/>aëre multò leuiorem addamus, qui plurima <lb/>globi huius &longs;patia implet, incrementum ac­<pb xlink:href="018/01/155.jpg" pagenum="141"/>cipiet leuitas non contemnendum; cum po­<lb/>ti&longs;&longs;imùm ex globi totius grauitate demen­<lb/>dum &longs;it huius aquæ terram circumplectentis <lb/>pondus: iam enim non pars e&longs;&longs;et oneris mo­<lb/>uendi, &longs;ed e&longs;&longs;et medium, in quo motus per­<lb/>ficeretur. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/> Aëris, & ignis copiam in terrâ de­<lb/><arrow.to.target n="note69"/><lb/>lite&longs;centem certis men&longs;uris definire non po&longs;­<lb/>&longs;umus, &longs;ed coniecturas tantùm per&longs;equi ne­<lb/>ce&longs;&longs;e e&longs;t: illud potius à Philo&longs;opho exigi po&longs;­<lb/>&longs;e videtur, vt aëris grauitatem cum aquâ <lb/>comparatam determinet. </s> <s>Quamuis autem <lb/>con&longs;tipato intrà vas aëre aliquando depre­<lb/>henderim aërem quadringenties aquâ leuio­<lb/>rem, mihi tamen omninò non &longs;atis facio: ex <lb/>illo enim experimento hoc certè euincitur, <lb/>quod aër con&longs;tipatus in aere communi non <lb/>con&longs;tipato grauitat: &longs;ed cum varia &longs;it aëris <lb/>con&longs;tipatio, incon&longs;tans pariter e&longs;t grauitatis <lb/>men&longs;ura, quæ ex illâ colligitur. </s> <s>Quare aëris <lb/>grauitatem explorare oporteret in medio le­<lb/>uiore, quemadmodum aqua non intrà aquam <lb/>&longs;ed in aëre expenditur. </s> <s>Et quidem &longs;ubiit ani­<lb/>mum aliquando hæc cogitatio, vt &longs;ubiectis <lb/>pruni aërem vehementer calefacerem, in <lb/>quo aërem <expan abbr="cõmunem">communem</expan> phialæ inclu&longs;um ex­<lb/>penderem; vt exploratâ deinde eiu&longs;dem <pb xlink:href="018/01/156.jpg" pagenum="142"/>phialæ grauitate in aëre communi minùs ta­<lb/>ro, innote&longs;ceret aëris pondus: &longs;ed cum per­<lb/>&longs;pectum haberem ex prunis vaporem cali­<lb/>dum a&longs;cendere, timui, ne motus a&longs;cenden­<lb/>tis vaporis ac medii commoti mihi fucum <lb/>faceret, vt detractum de grauitate cen&longs;erem, <lb/>quicquid virium ad de&longs;cendendum occur­<lb/>rentis vaporis motus impediret. </s> <s>Præter­<lb/>quam quod ex variâ aeris calefacti raritat&etail;, <lb/>varia pariter deprehenderetur aëris commu­<lb/>nis grauitas. </s></p><p type="margin"> <s><margin.target id="note69"/><emph type="italics"/>LXIX <lb/>Aquæ & aë­<lb/>ris grauita­<lb/>tes compa­<lb/>rantur, & <lb/>inquirun­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> De aëris con&longs;tipati grauitate nullus <lb/>dubito, nequè de eiu&longs;dem dilatati leuitate; Id <lb/>quod ex hac poti&longs;&longs;imùm occa&longs;ione depre­<lb/>hendi. </s> <s>Mirabar maris æ&longs;tum Lunæ moti­<lb/>bus adeò con&longs;tanter ob&longs;equentem, cau&longs;am­<lb/>que curio&longs;iùs inue&longs;tigans animus nunquam <lb/>quieuit, ni&longs;i vbi &longs;u&longs;picari cœpit latere in ma­<lb/>ris fundo corpora, quæ a&longs;cendente ad Me­<lb/>ridianum Lunâ intume&longs;cerent, aquasque <lb/>attollerent, Lunâ verò ad Occa&longs;um de&longs;cen­<lb/>dente &longs;ub&longs;iderent cum aquis. </s> <s>Hinc pro <lb/>maiore huiu&longs;modi corporum copiâ, aut mi­<lb/>nore, aut pro inæquali eorum contumaciâ, <lb/>aut facilitate ad intume&longs;cendum, æ&longs;tuum <lb/>inæqualitas &longs;atis explicata videbatur. </s> <s>Vt au­<lb/>tem aliquod marini æ&longs;tûs, ex corpore ad Lu­<pb xlink:href="018/01/157.jpg" pagenum="143"/>næ nutum intume&longs;cente, ve&longs;tigium ob&longs;er­<lb/>uarem, Bi&longs;emuti glebam nullum ignem pa&longs;­<lb/>&longs;am mihi comparaui (Bi&longs;emutum no&longs;tri ho­<lb/>mines vocant plumbum cinereum, quod in­<lb/>ter plumbi albi & nigri &longs;peciem medium <lb/>e&longs;t) congruæ retortæ impo&longs;ui, ignem &longs;e­<lb/>cundùm gradus admini&longs;traui horas duode­<lb/>cim, & qui extillauit humor candidus ac dul­<lb/>cis, amplo capacique Recipiente excepi: <lb/>hunc iterum ac tertiò, vt artifices loquuntur, <lb/>rectificaui, vt purior euaderet ac dulcior. </s> <s><lb/>Huius liquoris libram vnam conieci in vi­<lb/>treum va&longs;culum tantæ capacitatis, vt liquor <lb/>phialæ be&longs;&longs;em impleret, reliquum trientem <lb/>aër occuparet. </s> <s>Vitrum optimè clau&longs;um, ne <lb/>quid expirare po&longs;&longs;et, in loco, vbi quie&longs;ceret, <lb/>&longs;tatui; nec &longs;inè animi voluptate licebat in <lb/>Plenilunijs manife&longs;ta inclu&longs;i liquoris incre­<lb/>menta ob&longs;eruare, in Nouilunijs verò decre­<lb/>menta, neque ea tantùm, quæ prioribus in­<lb/>crementis re&longs;ponderent, &longs;ed vt aliquid de­<lb/>ce&longs;&longs;i&longs;&longs;e videretur ex eâ liquoris quantitate, <lb/>quam primùm infuderam. </s> <s>Contigit au­<lb/>tem, vt, curio&longs;itate animum vellicant&etail;, <lb/>phialam tùm in Pleniluniis, tum in Noui­<lb/>luniis expenderem, &longs;emperque paria depre­<lb/>hendi grauitatis momenta, perinde atque &longs;i <lb/>tunc primùm in phialam liquorem inieci&longs;&longs;<pb xlink:href="018/01/158.jpg" pagenum="144"/>&longs;em. </s> <s>Ex quibus intellexi, quantum grauita­<lb/>tis &longs;ecundùm &longs;peciem decederet liquori in­<lb/>tume&longs;centi, tantum accedere aëri intrà phia­<lb/>lam apprimè occlu&longs;am con&longs;tipato: contrà <lb/>verò liquore ad minora &longs;patia coangu&longs;tato <lb/>aërem quidem inclu&longs;um dilatari<gap/>&longs;ed huius <lb/>rare&longs;centis leuitate auctâ, maiorem illius <lb/>conden&longs;ati grauitatem compen&longs;ari. </s></p><p type="main"> <s>Nec di&longs;similem grauitatis con&longs;tantiam <lb/>ob&longs;eruabimus, &longs;i vitreum globum, cui lon­<lb/>giu&longs;culum collum & gracile adhæreat, vini <lb/>&longs;piritu ex multiplici di&longs;tillatione tenui&longs;&longs;imo <lb/>repleamus, aëre collum occupante; o&longs;cu­<lb/>lum autem Hermetis &longs;igillo claudatur. </s> <s>Ex <lb/>calore enim rare&longs;cet vini &longs;piritus, aëremque <lb/>con&longs;tipabit, & frigore &longs;ub&longs;equente &longs;ub&longs;idet, <lb/>aëri locum relinquens: neque tamen Ther­<lb/>mo&longs;copii huius grauitas variabitur, cu&mtail; <lb/>vnius corporis con&longs;tipati grauitas alterius rari <lb/>leuitate compen&longs;etur. </s> <s>Hinc tamen cert&atail; <lb/>definiri non po&longs;&longs;e momenta, quibus aër <lb/>compre&longs;&longs;us deor&longs;um nitatur, palam e&longs;t. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Rem ego quantâ potui diligentiâ <lb/>aliter inue&longs;tigaui, & aërem non quadrin­<lb/>genties tantùm, &longs;ed etiam adhuc triplo le­<lb/>uiorem inueni, ita vt grauitas aquæ ad gra­<lb/>uitatem aëris non &longs;it in minori Ratione quàm <lb/>1200 ad 1, &longs;ed potiùs in maiori Ration&etail;. <pb xlink:href="018/01/159.jpg" pagenum="145"/>Ita verò &longs;e habuit ob&longs;eruatio. </s> <s>Æream Æo­<lb/>lipilam propemodùm candentem omnique <lb/>humore de&longs;titutam expendi primùm bilan­<lb/>ce iu&longs;ti&longs;simâ; deinde eiu&longs;dem refrigeratæ & <lb/>ad naturalem temperiem re&longs;titutæ pondus <lb/>examinaui, & animaduerti illam facta&mtail; <lb/>fui&longs;&longs;e quatuor vt minimum grauis grauio­<lb/>rem: Hinc intuli aërem, qui rarefaction&etail; <lb/>exierat, & naturali conden&longs;atione fuerat ite­<lb/>rùm in Æolipilam admi&longs;&longs;us, habere in gra­<lb/>uitate quatuor grana. </s> <s>Iterum Æolipilam, <lb/>vt priùs, calefeci, quæ eiu&longs;dem quoquè pon­<lb/>deris, vt priùs, inuenta e&longs;t: & illicò eius ro­<lb/>&longs;trum in aquam immer&longs;i, vt aquam &longs;ugeret: <lb/>&longs;uxit autem aquæ vncias 9, drachmas 3, gra­<lb/>na 25; quæ &longs;unt in vniuer&longs;um (&longs;i &longs;ingulis <lb/>drachmis grana 72 tribuantur, & vnciis gra­<lb/>na 576) grana 5425; quod e&longs;t pondus aquæ <lb/>occupantis idem &longs;patium, quod occupabat <lb/>aër vi rarefactionis exclu&longs;us. </s> <s>E&longs;t igitur gra­<lb/>uitas aquæ granorum 5425 ad grauitate&mtail; <lb/>aëris &longs;ecundùm molem æqualis gran 4, hoc <lb/>e&longs;t vt 1356 ad 1. Quarè &longs;atis liberaliter age­<lb/>re mihi videor, &longs;i dixero aërem ad aquam in <lb/>leuitate e&longs;&longs;e vt 1200 ad 1. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Quàm vellem hæc omninò veri­<lb/>tati congruere! Sed veniam dabis non qui­<lb/>dem improbanti conatum, &longs;ed pen&longs;icula­<pb xlink:href="018/01/160.jpg" pagenum="146"/><arrow.to.target n="note70"/><lb/>tiùs examinanti, vtrùm omni pror&longs;us labe <lb/>careat tua hæc argumentatio. </s> <s>Sit vas cu­<lb/>preum AR molis vnâ cum inclu&longs;o aëre pe­<lb/>dalis, & va&longs;is pondus lib. 80, quod e&longs;t pon­<lb/>dus pedis cubici aquæ. </s> <s>E&longs;t igitur vas eiu&longs;­<lb/>dem &longs;pecificæ grauitatis cum aquâ; atque <lb/>adeò cum grauitas cupri ad grauitatem aquæ <lb/>&longs;it vt 71. ad 8, moles cupri ad molem aëris <lb/>inclu&longs;i e&longs;t vt 8 ad 63. Quarè vas aëre plenum <lb/>nihil in aquâ grauitat, aut leuitat; &longs;ed &longs;i mer­<lb/>gatur intrà aquam, quæ aëre exclu&longs;o impleat <lb/>va&longs;is capacitatem, iam vas intrà aquam pon­<lb/>dus habebit lib. 80. minùs pondere, quod <lb/>habet aqua &longs;ecundùm molem cupro æqualis. </s> <s><lb/>Quia igitur moles cupri e&longs;t (8/71) pedis cubici, <lb/>fiat vt 71 ad 8, ita lib. 80 pondus pedis cu­<lb/>bici aquæ, ad lib. 9. (1/71) pondus aquæ æqualis <lb/>cupro va&longs;is. </s> <s>Erit itaque va&longs;is pleni aquâ in­<lb/>trà aquam grauitas lib. (70 70/71): quod quidem <lb/>pondus tribuendum e&longs;t cupro, non autem <lb/>aquæ vas implenti, quæ intrà aquam non <lb/>grauitat: cum maximè idem e&longs;&longs;et in aquâ <lb/>eiu&longs;dem cupri pondus, etiam&longs;i in ma&longs;&longs;am <lb/>conflatum nihil aquæ contineret. </s> <s>Quan­<lb/>quam non nego grauitatem illam cupri i&ntail; <lb/>aquâ e&longs;&longs;e æqualem grauitati molis aqueæ vas <lb/>implentis, &longs;i illa extra aquam in aere<gap/><lb/>transferatur; e&longs;t enim moles aquæ vas im­<pb xlink:href="018/01/161.jpg" pagenum="147"/>plentis (63/71) pedis cubici. </s></p><p type="margin"> <s><margin.target id="note70"/><emph type="italics"/>LXX <lb/>Si vas in li­<lb/>quore <expan abbr="põde-retur">ponde­<lb/>retur</expan> nunc <lb/>plenum aë­<lb/>re, nunc ple­<lb/>num liquo­<lb/>re illo, diffe­<lb/>rentia pon­<lb/>derum est <lb/>pondus li­<lb/>quoris im­<lb/>plentis capa­<lb/>citatem va­<lb/>&longs;is.<emph.end type="italics"/></s></p><p type="main"> <s>At manente eâdem va&longs;is mole intelliga­<lb/>tur aucta materia; & diminuta capacitas, ita <lb/>vt &longs;it va&longs;is pondus in aëre lib. 100 &longs;e&longs;qui­<lb/>quartum prioris: erit moles cupri (10/71) pedis <lb/>cubici, & capacitas (61/71). Quarè aqua æqualis <lb/>cupro habet pondus lib. (11 19/71): igitur vas intrà <lb/>aquam plenum aquâ habet pondus lib. (88 52/71) <lb/>at plenum aëre intrà aquam amittet pondus <lb/>integri pedis cubici, & &longs;olùm erit lib. 20. <lb/>Horum igitur ponderum differentia (68 52/71) æ­<lb/>qualis e&longs;t ponderi aquæ implentis capacita­<lb/>tem va&longs;is, quæ ex con&longs;titutâ hypothe&longs;i e&longs;t (61/71) <lb/>pedis cubici. </s></p><p type="main"> <s>Similiter &longs;i intrà idem vas admittantur <lb/>aquæ (10/71), reliquam capacitatem (51/71) impleat <lb/>aër: moles cupri & aëris occupat in aquâ (61/71) <lb/>pedis cubici: igitur ex lib. 100 auferuntur <lb/>lib. (68 52/71), & pondus va&longs;is in aquâ e&longs;t lib. (31 19/71). <lb/>At quando totum replebatur aquâ, pondus <lb/>erat lib. (88 52/71), igitur differentia lib. (57 33/71) e&longs;t <lb/>grauitas æqualis grauitati (51/71) pedis cubici aquæ, <lb/>quæ impleret va&longs;is &longs;patium ab aëre occupa­<lb/>tum, &longs;i aqua illa in aëre extra aquam ex­<lb/>penderetur. </s></p><p type="main"> <s>Quemadmodum igitur ex eiu&longs;dem va&longs;is <pb xlink:href="018/01/162.jpg" pagenum="148"/><arrow.to.target n="note71"/><lb/>ponderibus intrà <expan abbr="aquã">aquam</expan>, <expan abbr="quãdo">quando</expan> e&longs;t <expan abbr="plenũ">plenum</expan> aquâ, <lb/>ac quando e&longs;t plenum aëre, rectè infertur ho. <lb/></s> <s><expan abbr="rũ">rum</expan> ponderum <expan abbr="differentiã">differentiam</expan> e&longs;&longs;e æqualem pon­<lb/>deri aquæ implentis locum <expan abbr="a&etilde;ris">aeris</expan>, &longs;i illa pon­<lb/>deretur in aëre: &longs;ic ex differentiâ ponderum <lb/>Æolipilæ intrà aërem communem con&longs;titu­<lb/>tæ, quando plena e&longs;t aëre communi, ac <lb/>quando plena e&longs;t aëre ignito, ex hac, inquam, <lb/>differentiâ rectè illata videtur grauitas aëris <lb/>communis Æolipilam implentis, &longs;i aër i&longs;te <lb/>ponderaretur in aëre ignito tanquam in me<gap/><lb/>dio. </s> <s>Cum autem differentia huiu&longs;modi &longs;it <lb/>granorum quatuor, pondus aëris communis <lb/>æolipilam implentis e&longs;t gran. <!-- REMOVE S-->4. non quidem <lb/>ab&longs;olutè, &longs;ed tantùm in medio leuitatis eiu&longs;­<lb/>dem ac raritatis, quam habebat aër Æolipi­<lb/><emph type="italics"/>l<emph.end type="italics"/>æ candentis: &longs;icuti etiam aqua vas A R im­<lb/>plens, de quo dicebam, non habet graui­<lb/>tatem lib. (68 52/71) in quocunque medio, &longs;ed tan­<lb/>tùm in aëre leuitatis ac raritatis eiu&longs;dem cum <lb/>aëre, qui va&longs;is capacitatem implebat. </s> <s>Qua­<lb/>re non ego facilè dixerim quatuor illa grana <lb/>fui&longs;&longs;e pondus aëris primùm eiecti, qui iterùm <lb/>receptus fuit; ille enim aër nullum habebat <lb/>pondus in aëre communi; & &longs;i pondus ha­<lb/>beat in aëre ignito, tota illa grauitas non <lb/>pertinet ad &longs;olum aërem, qui recipitur, &longs;ed <lb/>ad illum, qui totam Æolipilam implet. </s> <s>Si­<pb xlink:href="018/01/163.jpg" pagenum="149"/>cut &longs;i aqua implens vas A R attenuaretur &longs;e­<lb/>cundùm aliquam partem in aërem, & reli­<lb/>qua eiiceretur, iterum autem ad naturalem <lb/>den&longs;itatem rediens eiectam aquam ex&longs;uge­<lb/>ret, differentia ponderis va&longs;is non &longs;oli aquæ <lb/>eiectæ tribuenda e&longs;&longs;et, &longs;ed toti aquæ vas im­<lb/>plenti. </s> <s>Hinc e&longs;t quod, cum aqua in Æoli­<lb/>pilam admi&longs;&longs;a non &longs;it &longs;ecundùm mole&mtail; <lb/>æqualis toti aëri, qui eam implebat, ac pro­<lb/>inde non &longs;it æqualis moli, quæ habet pon­<lb/>dus gran. <!-- REMOVE S-->4, non habetur præcisè Ratio gra­<lb/>uitatum &longs;ecundùm &longs;peciem. </s> </p><p type="margin"> <s><margin.target id="note71"/><emph type="italics"/>LXXI <lb/>Experimen­<lb/>tum Aeoli­<lb/>pilæ ad &longs;um­<lb/>mum osten­<lb/>dit grauita­<lb/>tem aëris <expan abbr="cõ-munis">con­<lb/>munis</expan> i&ntail; <lb/>aëre ignito, <lb/>non autem <lb/>ab&longs;olutè: nec <lb/>ex eo habe­<lb/>tur quæ&longs;ita <lb/>proportio <lb/>grauitatum <lb/>aquæ & aë­<lb/>ris.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Id meæ &longs;ententiæ vlteriùs fauet: &longs;i <lb/>enim aquæ moles, quam &longs;uxit Æolipila, <lb/>minor e&longs;t mole aëris, qui numerat in pon­<lb/>dere grana 4, plus aliquid aquæ addendum <lb/>erit, vt moles æquales &longs;int; atque adeò mul­<lb/>tò maior erit Ratio grauitatis aquæ ad gra­<lb/>uitatem aëris, quam &longs;it deprehen&longs;a Ratio <lb/>1356 ad 1. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Non hæc eo con&longs;ilio afferebam, vt <lb/>irem contrà; &longs;ed tantùm vt rem paulò ob­<lb/>&longs;curiorem mihi ip&longs;e enucleatiùs explicarem, <lb/>& te audirem, &longs;i quid &longs;ortè à veritate aut à <lb/>tuâ mente alienum intelligerem. </s> <s>Cæterùm <lb/>non nego maiorem e&longs;&longs;e Rationem grauitatis <lb/>aquæ æolipilam implentis ad grauitatem aë­<lb/>ris eam pariter implentis, ac &longs;it Ratio gra­<pb xlink:href="018/01/164.jpg" pagenum="150"/>uitatis aquæ ex&longs;uctæ ad eiu&longs;dem aëris graui­<lb/>tatem; modò hæc aquæ grauitas intelligatur <lb/>non in quocunque medio, &longs;ed in eodem, in <lb/>quo aër communis grauis e&longs;t, in aëre vide­<lb/>licet ignito & rari&longs;&longs;imo. </s> <s>Verùm cum re­<lb/>rum grauitates definiamus habitâ ration&etail; <lb/>medij omnium rari&longs;&longs;imi atque leui&longs;&longs;imi ex <lb/>ijs, quibus communiter vtimur, hoc autem <lb/>medium aër &longs;it, non video, cur aëris & <lb/>aquæ grauitates inuicem conferre oporteat <lb/>ratione medij, cuius nullus futurus e&longs;t v&longs;us. </s> <s><lb/>Quod &longs;i metalla aquæ immer&longs;a dicuntur in <lb/>aquâ minùs grauitare pro ratione di&longs;crimi­<lb/>nis, quod inter&longs;pecificas grauitates interce­<lb/>dit; cum aquam inter & aquam, aut aërem <lb/>inter & <expan abbr="a&etilde;rem">aerrem</expan> nulla reperiatur communiter <lb/>differentia, nulla pariter aquæ in aquâ aut aë­<lb/>ris in aëre e&longs;t grauitatio: ac proinde cum <lb/>aër in aëre con&longs;tituatur, nulla e&longs;t eius graui­<lb/>tas, quam cum aquâ comparare oporteat. </s></p><p type="main"> <s>Sed & vnum præterea addo, &longs;i placet. </s> <s><lb/>Si ferri grauitatem cum aquæ grauitate con­<lb/>ferre voluero, ferrum primùm in aëre ex­<lb/>pendo, deinde in aquâ; & quæ fuerit pon­<lb/>derum differentia, eam tribuo grauitati aquæ <lb/>&longs;ecundùm molem æqualis ferro; & vt totum <lb/>ferri pondus ad hanc differentiam, ita graui­<lb/>tatem ferri ad aquæ grauitatem &longs;ecundùm <pb xlink:href="018/01/165.jpg" pagenum="151"/>&longs;peciem pronuncio, &longs;i tamen vtraque moles <lb/>in aëre fuerit; & &longs;it vt 42 ad 5 1/3. Nam &longs;i <lb/>tam ferrum quàm aqua intra oleum (cuius <lb/>grauitas &longs;pecifica in aëre e&longs;t 4 3/4) collocentur, <lb/>grauitas ferri in oleo erit partium 37 1/4, qua­<lb/>rum grauitas aquæ erit &longs;olùm (7/12); quæ <emph type="italics"/>R<emph.end type="italics"/>atio <lb/>longè maior e&longs;t eâ Ratione, quam habent <lb/>grauitates in aëre. </s></p><p type="main"> <s>Di&longs;criminis huius ratio e&longs;t, quia vt inue­<lb/><arrow.to.target n="note72"/><lb/>nirem Rationem grauitatum aquæ & ferri in <lb/>oleo, &longs;acoma &longs;eu æquipondium debui&longs;&longs;et pa­<lb/>riter e&longs;&longs;e in oleo; quia autem &longs;acoma &longs;emper <lb/>fuit in aëre. </s> <s>& examinatum e&longs;t ferri pondus <lb/>in aëre, grauitas quoque ferri & aquæ com­<lb/>paratur &longs;olum in aëre. </s> <s>Quod &longs;i in libræ ex­<lb/>tremitate appenderetur globus ferreus vn­<lb/>ciarum 42 in aëre, qui in oleo immergere­<lb/>tur, re&longs;ponderet &longs;acomati ferreo in aëre exi­<lb/>&longs;tenti vnciarum 37 1/4: at &longs;i &longs;acoma &longs;it pariter <lb/>in oleo, quia ferreum e&longs;t, & æqualiter à cen­<lb/>tro libræ di&longs;tat, erit æquale ponderi, quod <lb/>examinatur, hoc e&longs;t vnc.42. Globus autem <lb/>ferreus &longs;i in aquâ immergeretur, re&longs;pon­<lb/>deret &longs;acomati ferreo in aëre exi&longs;tenti vnc. </s> <s><lb/>36 2/3: atqui &longs;i vnciæ 37 1/4 in aëre æquiponde­<lb/>rant vncijs 42 in oleo, vnciæ 36 1/3 in aër&etail; <lb/>æquiponderant vnciis (41 51/149) in oleo; igitur <pb xlink:href="018/01/166.jpg" pagenum="152"/>eidem globo ferreo in aquâ po&longs;ito æquipon­<lb/>derat &longs;acoma ferreum in oleo vnc. (41 51/149). Sa­<lb/>comatum igitur 42 & (41 51/149) differentia (98/149) da­<lb/>bit grauitatem aquæ in oleo comparata&mtail; <lb/>cum grauitate ferri; ita vt ferri grauitas i&ntail; <lb/>oleo ad aquæ grauitatem in oleo &longs;it vt 42 <lb/>ad (98/149), quæ e&longs;t planè eadem Ratio &longs;uperiùs in­<lb/>dicata 37 1/4 ad (7/12), hoc e&longs;t 63 6/7 ad 1. <!-- KEEP S--></s></p><p type="margin"> <s><margin.target id="note72"/><emph type="italics"/>LXXII <lb/>Ratio duo­<lb/>rum graui­<lb/>um in vno <lb/>medio, vt ba­<lb/>beatur, de­<lb/>bet æquipon­<lb/>dium e&longs;&longs;e in <lb/>eodem me­<lb/>dio.<emph.end type="italics"/></s></p><p type="main"> <s>Ex his, quæ carere videntur omni diffi­<lb/>cultate, & &longs;atis manife&longs;ta &longs;unt, infeto 4 il­<lb/>la grana, quæ tribuis ponderi aëris commu­<lb/>nis Æolipilam implentis, nullam aëris gra­<lb/>uitatem indicare per &longs;e, & immediatè; non <lb/><expan abbr="a&etilde;ris">aeris</expan> in aëre communi, quia in eo, Vt dice­<lb/>bam, non grauitat; non aëris communis in <lb/>aëre ignito, vt paulò ante tibi permittebam, <lb/>quia &longs;acoma &longs;eu æquipondium, quo v&longs;us es <lb/>ad grauitatem explorandam, non erat pari­<lb/>ter in aëre ignito: id quod fieri oportui&longs;&longs;et. </s> <s><lb/>Nam &longs;i vas aliquod aquâ plenum intrà a­<lb/>quam ponderes, & &longs;acoma &longs;it pariter i&ntail; <lb/>aquâ; iterum autem &longs;acomate intrà aquam <lb/>exi&longs;tente idem vas aëre plenum in aquâ ex­<lb/>pendas, vtique ponderum differentia no&ntail; <lb/>dabit aquæ pondus in aëre. </s> <s>Ergo pariter <lb/>cum vas aëre communi plenum expenderis <lb/>in aëre communi, & iterum in eodem <expan abbr="a&etilde;re">aere</expan> <pb xlink:href="018/01/167.jpg" pagenum="153"/>communi ponderaueris idem vas plenu&mtail; <lb/><expan abbr="a&etilde;re">aëre</expan> ignito, ponderum differentia non e&longs;t <lb/>pondus aëris communis æolipilam implen­<lb/>tis. </s></p><p type="main"> <s>Exemplo rem declaro: & accipio illud <lb/>idem vas cupreum AR, de quo antea dixi­<lb/>mus, quod cum in aëre &longs;it lib. 100, intrà <lb/>aquam plenum aquâ e&longs;&longs;et lib (88 52/71), &longs;ed intrà <lb/>aquam plenum aëre &longs;olùm e&longs;&longs;et lib. 20; vn­<lb/>de intulimus aquæ vas implentis pondus i&ntail; <lb/>aëre e&longs;&longs;e lib. (68 52/71). Ponamus &longs;acoma e&longs;&longs;&etail; <lb/>ferreum, & illud pariter intrà aquam exi&longs;te­<lb/>re. </s> <s>Quoniam igitur ferrum 36 2/3 in aër&etail;, <lb/>æquiponderat ferro 42 in aquâ, ferrum (88 52/71) <lb/>in aëre, æquiponderabit ferro (101 499/781) in aquâ; <lb/>& hoc faciet æquilibrium cum va&longs;e cupreo <lb/>pleno aquâ. </s> <s>Item quia ferrum 36 2/3 in aëre <lb/>æquiponderat ferro 42 in aquâ, ferrum 20 <lb/>in aëre æquiponderabit ferro (22 10/11) in aquâ; & <lb/>hoc con&longs;tituet æquilibrium cum va&longs;e cupreo <lb/>pleno aëre intrà aquam. </s> <s>Iam &longs;umo diffe­<lb/>rentiam inter duo hæc &longs;acomata, quæ &longs;unt <lb/>vt (101 499/781) ad (22 10/11), & e&longs;t differentia lib. (78 580/781); <lb/>quod &longs;anè non e&longs;t pondus aquæ va&longs;is capa­<lb/>citatem implentis, &longs;i illa in aëre ponderetur, <lb/>&longs;ed e&longs;t multò maius. </s> <s>Pro diuersâ aute&mtail; <lb/>materiâ &longs;iue plumbeâ, &longs;iue æreâ, &longs;iue argen­<pb xlink:href="018/01/168.jpg" pagenum="154"/>teâ, aut &longs;tanneâ, ex qua &longs;acomata con&longs;ta­<lb/>rent, alia atquè alia oriretur differentia, vt <lb/>patet. </s> <s>Id quod non in librâ tantùm, &longs;ed in <lb/>&longs;taterâ quoquè contingeret. <lb/><arrow.to.target n="note73"/></s></p><p type="margin"> <s><margin.target id="note73"/><emph type="italics"/>LXXIII <lb/>Aëris com­<lb/>munis & a­<lb/>quæ graui­<lb/>tas in aëre <lb/>ignito minor <lb/>est, quà&mtail; <lb/>fuerit depre­<lb/>hen&longs;a.<emph.end type="italics"/></s></p><p type="main"> <s>Quapropter aërem communem in aër&etail; <lb/>ignito con&longs;titutum leuiorem e&longs;&longs;e 4 granis, <lb/>quæ in medio eodem e&longs;&longs;ent, apertè con­<lb/>&longs;tat; illis &longs;iquidem æquiponderat in medio <lb/>cra&longs;&longs;iore: atque adeò aqua deprehen&longs;a gra­<lb/>norum 5425 in aëre communi, &longs;i in aër&etail; <lb/>ignito con&longs;titueretur, multò paucioribus <lb/>granis æquiponderaret in eodem medio exi­<lb/>&longs;tentibus; & quidem pro ratione materiæ <lb/>&longs;acomatis; &longs;i enim e&longs;&longs;ent grana metallica, <lb/>multò pauciora requirerentur ad faciendum <lb/>æquilibrium cum aquâ, quàm &longs;i e&longs;&longs;ent gra­<lb/>na hordei. </s> <s>Similiter &longs;i particulæ ex medul­<lb/>lâ &longs;ambuci, aut materiâ leuiore quàm aqua, <lb/>fungerentur munere &longs;acomatis, tunc librâ in <lb/>aërem ignitum translatâ, minuendum e&longs;&longs;et <lb/>&longs;acomatis pondus; quemadmodum 100 vn­<lb/>ciæ auri, & vnciæ (108 24/55) ferri in aere no&ntail; <lb/>æquiponderant, quæ tamen in aquâ con&longs;ti­<lb/>tuerent æquilibrium, quandoquidem tam <lb/>100 vnciæ auri quàm (108 24/55) ferri in aquâ po­<lb/>&longs;itæ æquiponderant &longs;acomari vnc. </s> <s>94 2/3 in aë­<lb/>re. </s> <s>Quarè nihil hìc certi mihi videor inue­<lb/>nire, in quo pedem figam. </s></p><pb xlink:href="018/01/169.jpg" pagenum="155"/><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Si aliquid intelligo, haud procul <lb/>abes ab eorum &longs;ententiâ, qui omnem aëri <lb/>grauitatem adimunt: idcirco enim rem hanc <lb/>ad viuum re&longs;ecas, vt illa pror&longs;us euane&longs;cat. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Quo iure omnium &longs;ententia ferro <lb/>& plumbo leuitatem negaret, quia vt pluri­<lb/>mum grauitant in medijs communibus, <lb/>quamuis in hydrargyro a&longs;cendant & inna­<lb/>tent; ita aërem pariter grauem apud nos e&longs;&longs;e <lb/>in&longs;icior, quamuis &longs;i in purum æthera tran&longs;­<lb/>ferretur, ibi grauitaret, quemadmodum & <lb/>aër præter naturam conden&longs;atus in vtribus, <lb/>in aëre libero grauitat: ibi &longs;iquidem grauita­<lb/>re poterit, vbi medium leuius, in quo &longs;it, <lb/>inueniet. </s> <s>Immò memini me olim vento­</s></p><p type="main"> <s><arrow.to.target n="note74"/><lb/>rum de&longs;cendentium cau&longs;am reieci&longs;&longs;e in aë­<lb/>ris &longs;eu halitûs grauitatem; &longs;icut enim gra­<lb/>uia de&longs;cendentia, ita & leuia a&longs;cendenti&atail; <lb/>impetum in motu concipiunt, & augent; ex <lb/>quo &longs;it, vt, quemadmodum lignum in aquam <lb/>cadens profundiùs mergitur, quàm par &longs;it, <lb/>vnde po&longs;teà emergit, ita pariter halitus in­<lb/>&longs;imo hoc aëre leuiores a&longs;cendentes conci­<lb/>piant impetum, quo deferantur vltra termi­<lb/>nos &longs;uæ quieti debitos in &longs;upremum aerëm <lb/>ip&longs;is halitibus leuiorem; in quo cum iam <lb/>graues &longs;int, de&longs;cendant, & obuios halitus <lb/>a&longs;cendentes reflectant. </s> <s>Si igitur aerem hunc <pb xlink:href="018/01/170.jpg" pagenum="156"/>infimum lagenæ inclu&longs;um transferremus in <lb/>puri&longs;&longs;imum æthera, vel &longs;altem in alti&longs;&longs;imi <lb/>montis, pura Cauca&longs;i, verticem, ibique la­<lb/>genam expenderemus; deinde eiu&longs;dem aquâ <lb/>plenæ pondus inue&longs;tigaremus, tunc innote­<lb/>&longs;ceret Ratio grauitatum aquæ & aëris in me­<lb/>dio illo leuiore. </s> <s>Cæterum infimæ huius re­<lb/>gionis incolæ de aëris grauitate di&longs;putantes, <lb/>non video, quid certi definire po&longs;&longs;int, neque <lb/>quos &longs;tatuant Rationum terminos. </s></p><p type="margin"> <s><margin.target id="note74"/><emph type="italics"/>LXXIV <lb/>Venti de­<lb/>&longs;cendentis <lb/>cau&longs;a obiter <lb/>indicatur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Abiret igitur in immen&longs;um hæc di­<lb/>&longs;putatio, & certius nihil, vt opinor, depre­<lb/>henderemus, quod in rem no&longs;tram faceret. </s> <s><lb/>Quapropter præ&longs;taret ijs, quæ veritati pro­<lb/>xima videntur, a&longs;&longs;umptis, progredi in eâ, <lb/>quam con&longs;titueramus, quæ&longs;tione. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Rectè mones, Galilæe. <!-- KEEP S--></s> <s>Sed præ­<lb/>&longs;tabit forta&longs;sè hæc in aliud colloquium reij­<lb/>cere; neque enim mihi per tempus licet apud <lb/>vos diutiùs e&longs;&longs;e, ni&longs;i po&longs;thabito negotiolo, <lb/>quod me aliquantulum vrget, nec omnino <lb/>perire vellem. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Commodis tuis nos &longs;eruire oportet: <lb/>præterquam quod non hodie diem &longs;ine line â <lb/>duximus. </s> <s>Quare bonis auibus perge, quò te <lb/>negotia vocant. </s></p><pb xlink:href="018/01/171.jpg" pagenum="157"/><figure id="id.018.01.171.1.jpg" xlink:href="018/01/171/1.jpg"/><p type="main"> <s><emph type="center"/>DISSERTATIO <lb/>QVINTA<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Minorem telluris grauita­<lb/>tem in aqua ex­<lb/>plicat.<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>Guldinus, Mer&longs;ennus, Galilæus.<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s>POSTREMAM he&longs;terni &longs;er­<lb/>monis no&longs;tri clau&longs;ulam <lb/>recolenti in memoriam <lb/>venit, ne&longs;cio quid d&etail; <lb/>aëris grauitate &longs;criptum <lb/>literis Herbipoli haud <lb/>ita pridem datis ad ami­<pb xlink:href="018/01/172.jpg" pagenum="158"/>cum, quarum exemplar nactus &longs;epo&longs;ueram. </s> <s><lb/>Excutiens itaque &longs;crinium, quod mihi hoc <lb/>epi&longs;tolarum genus &longs;eruat, demum, quod <lb/>quærebam; inueni; immo & mecum attuli, <lb/>ne, &longs;i fortè vobis aliqua &longs;uble&longs;tæ fidei &longs;u&longs;pi­<lb/>cio de me &longs;uboriretur, tabulæ de e&longs;&longs;ent, quas <lb/>proferrem. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Nemo no&longs;trûm e&longs;t, qui fidem in­<lb/>firmare audeat Germano candori. </s> <s>neque ra­<lb/>bulis eges, neque te&longs;tibus, me quidem iu­<lb/>dice: &longs;atis e&longs;t te narra&longs;&longs;e, vt fidem adhi­<lb/>beam. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> An aliquid, quod vel tuæ, Mer&longs;en­<lb/>ne, vel meæ aduer&longs;etur &longs;ententiæ, prolatu­<lb/>rus Guldinus, idquè nobis minùs placitu­<lb/>rum, &longs;u&longs;picans, ideo literarum exemplar at­<lb/>tulit, vt omnem à &longs;e inuidiam auertens i&ntail; <lb/>alium declinet? </s> <s>Quæcunque tandem ill&atail; <lb/>&longs;int, in medium fidenti animo profer, Gul­<lb/>dine. </s> <s>Non hìc partium, &longs;ed vno veritatis <lb/>&longs;tudio tenemur. </s> <s>Nulla ne aëri tribuend&atail; <lb/>grauitas? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Immo verò non modica; &longs;i eum, <lb/>à quo datæ &longs;unt literæ, audiamus; vocat &longs;i­<lb/>quidem luculenti&longs;simum grauitatis aeris ar­<lb/>gumentum, id, quod ab Eruditi&longs;&longs;imis Vi­<lb/>ris ob&longs;eruatum e&longs;t ex occa&longs;ione experimen­<lb/>ti, quod ad Vacuum inue&longs;tigandum in&longs;ti­<pb xlink:href="018/01/173.jpg" pagenum="159"/>tuebatur. </s> <s>Paratum e&longs;t vas vitreum eximiæ <lb/><arrow.to.target n="note75"/><lb/>&longs;pi&longs;&longs;itudinis, & capacitatis tantæ, vt men&longs;u­<lb/>ras 32, hoc e&longs;t aquæ vncias, vt minimum, <lb/>circiter mille, contineret, in Recipientis <lb/>Chymici formam elaboratum. </s> <s>Huius col­<lb/>lo adglutinatum e&longs;t &longs;ingulari arte ac firmi­<lb/>tudine epi&longs;tomium ex orichalco tran&longs;uer&longs;am <lb/>habens clauem ver&longs;atilem apti&longs;&longs;imè &longs;uo lo­<lb/>culamento congruentem, ne quid ex va&longs;&etail; <lb/>po&longs;&longs;it effluere, aut in illud &longs;e in&longs;iuare ni&longs;i eâ <lb/>conuersâ. </s> <s>Ex orichalco pariter con&longs;tructus <lb/>e&longs;t firmi&longs;&longs;imus tubus hians vtrinque, &longs;ed in <lb/>angulum inflexus, vt parti breuiori immitti <lb/>po&longs;&longs;it epi&longs;tomium Recipientis (&longs;ic liceat ap­<lb/>pellare) pars verò longior fungi po&longs;&longs;it mu­<lb/>nere antliæ duobus a&longs;&longs;ariis ritè in&longs;tructæ, vt <lb/>per alterum quidem Recipienti proximum <lb/>reducto embolo attrahi po&longs;&longs;it corpus, quo <lb/>illud impletur, per alterum verò a&longs;&longs;arium <lb/>congruo loco in antliæ dor&longs;o con&longs;titutum <lb/>corpus illud atractum exprimi po&longs;&longs;it, cum <lb/>impellitur adduciturque tru&longs;illum: cuius <lb/>capiti tran&longs;uer&longs;um manubrium adnectitur, <lb/>vt duo &longs;imul po&longs;&longs;int antliam agitare: immò <lb/>quia, licèt initio facilis &longs;it antliæ agitatio, <lb/>paulatim tamen adeò cre&longs;cit difficultas em­<lb/>bolum reducendi ab a&longs;&longs;ario Recipienti proxi­<lb/>mo, vt demum duo robu&longs;ti&longs;&longs;imi iuuenes &longs;u­<pb xlink:href="018/01/174.jpg" pagenum="160"/>dore manantes ac totis viribus adnitentes vix <lb/>illum ampliùs extrahere po&longs;&longs;int, aut prohi­<lb/>bere, ne &longs;ponte relabatur intus, & cum im­<lb/>petu ac &longs;onitu illidatur ad partes tubi proxi­<lb/>mas Recipienti; ideò extremo manubrio fu­<lb/>niculi duo adnectuntur, vt plures opem fer­<lb/>re po&longs;&longs;int. </s> <s>Ne verò, dum antlia agitatur, <lb/>po&longs;sit aër per tenui&longs;simas rimulas (&longs;i fortè <lb/>Recipientis epi&longs;tomium & extremus antliæ <lb/>tubus non &longs;ibi exqui&longs;itâ collabellatione con­<lb/>gruerent) &longs;e latenter in&longs;inuare; antlia ligneæ <lb/>cupæ firmi&longs;simè affigitur ita, vt immi&longs;&longs;a in <lb/>cupam aqua Recipientis epi&longs;tomium, eius­<lb/>que clauem ver&longs;atilem contegat, & &longs;olum <lb/>illud antliæ o&longs;culum ex aquâ emineat, cu­<lb/>pæ &longs;cilicet labro incumbens, per quod em­<lb/>bolus agitatur. </s></p><p type="margin"> <s><margin.target id="note75"/><emph type="italics"/>LXXV <lb/>Experimen­<lb/>tum, quo ten<lb/>tatum est <lb/>Vacuum, & <lb/>quæ&longs;ita aë­<lb/>ris grauitas.<emph.end type="italics"/></s></p><p type="main"> <s>His omnibus ritè paratis, ac reuolutâ ver­<lb/>&longs;atili claue, vt pateret exitus aëri Recipien­<lb/>tis (quod antequam imponeretur antliæ, fuit <lb/>&longs;taterâ examinatum) agitata e&longs;t aliquot ho­<lb/>ras antlia; ac demum vbi præ nimiâ diffi­<lb/>cultate extrahendi pi&longs;tillum, ce&longs;&longs;atum e&longs;t, <lb/>clau&longs;um e&longs;t vas clauis conuolutione, ac refi­<lb/>xum ab antliâ iterum expen&longs;um e&longs;t, & anti­<lb/>quo ponderi deerant lotones 2 3/5, hoc e&longs;t vn­<lb/>cia (1 3/10). </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Et dubitabis adhuc, an aëri vas <pb xlink:href="018/01/175.jpg" pagenum="161"/>implenti tribuendum e&longs;&longs;et pondus; quod aë­<lb/>re extracto defuit? </s> <s>tibi certè non ad&longs;tipu­<lb/>larentur, quicunque liquorem, puta oleum <lb/>aut mel, ad libram vendunt; quæ enim in­<lb/>ter vas plenum ac vacuum differentia pon­<lb/>derum intercedit, eam liquori tribuendam <lb/>nemo negat. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Sed quid, &longs;i vas in aquâ expende­<lb/><arrow.to.target n="note76"/><lb/>rent nunc quidem melle, nunc verò aër&etail; <lb/>plenum? </s> <s>an grauitatum differentiam it&atail; <lb/>melli tribueres, vt velles pro eâ pretium &longs;ol­<lb/>uere? </s></p><p type="margin"> <s><margin.target id="note76"/><emph type="italics"/>LXXVI <lb/>Ex differen­<lb/>tia <expan abbr="põderum">ponderum</expan> <lb/>va&longs;is pleni, <lb/>& vacui, <lb/><expan abbr="nõ">non</expan> probatur <lb/>quæ&longs;ita aë­<lb/>ris grauitas<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Minimè omnium: quia præter <lb/>mellis pondus &longs;ublatum, etiam de va&longs;is gra­<lb/>uitate non parùm demeret inclu&longs;i aëris le­<lb/>uitas. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Quid ni igitur va&longs;is grauitati de­<lb/>tractum pariter a&longs;&longs;eras ab inclu&longs;o aëre ma­<lb/>ximè raro, ac proinde longè leuiore, quàm <lb/>aër i&longs;te communis? </s> <s>Ex quo illud vnum con­<lb/>ficitur, quod vltro do, aërem &longs;cilicet no&longs;trum <lb/>futurum grauem, &longs;i phialæ inclu&longs;us tran&longs;­<lb/>ferretur in aërem rati&longs;simum Recipientis, & <lb/>in eodem medio e&longs;&longs;et æquipondium, quo <lb/>aëris communis grauitas exploraretur. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Ex Ari&longs;totelis Vacuum pro&longs;cribentis <lb/>officinâ i&longs;thæc depromere oportet; & quan­<lb/>doquidem negari non pote&longs;t aërem vi antliæ <pb xlink:href="018/01/176.jpg" pagenum="162"/>extractum &longs;patia reliqui&longs;&longs;e, in quæ nullum <lb/>corpus extrin&longs;ecùs aduocatum &longs;ucceder&etail; <lb/>queat, mauultis aliquid aëris contumaci&longs;si­<lb/>mi, qui modò minorem modò maiorem oc­<lb/>cupet locum, violentâ ratiocinatione in va­<lb/>&longs;e concludere, quàm Vacuum, quod &longs;ponte <lb/>menti occurrit, admittere, vobisque inqui­<lb/>rendæ veritatis viam ob&longs;truitis. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Non opus e&longs;t corpora amouere, <lb/><arrow.to.target n="note77"/><lb/>vt progrediatur Philo&longs;ophia in Vacuo. </s> <s>Mi­<lb/>hi &longs;anè nullus relinquitur ambigendi locus, <lb/>an aere per vim rari&longs;simo Recipiens implea­<lb/>tur; aperto enim refixi ab antliâ va&longs;is epi&longs;to­<lb/>mio, tantâ vi externus aër irrumpebat i&ntail; <lb/>vas, vt illud hominem è regione &longs;tantem ad <lb/>&longs;e raperet: Vacuo autem, quod, præter cor­<lb/>pus aptum continere, nil addit ni&longs;i corporis <lb/>contenti negationem, nullam attrahendi fa­<lb/>cultatem phy&longs;icam concedo. </s> <s>Sed nequ&etail; <lb/>aërem externum &longs;ponte irrupi&longs;&longs;e cen&longs;eo, vt <lb/>&longs;uppleret Vacuum; palàm enim aërem at­<lb/>trahi deprehendit non-nemo, qui apertum <lb/>os &longs;uum &longs;atis eminus admouit, & confe&longs;tim <lb/>deficiente &longs;piritu manibus &longs;ignum; vt &longs;&etail; <lb/>amouerent, dedit, ip&longs;e ad di&longs;cedendum <lb/>impotens factus. </s> <s>Nec differebitur alius, cui <lb/>digitum admouenti cutem cum carne pænè <lb/>ab&longs;traxit, non negatio corporis, &longs;ed vis aëris <pb xlink:href="018/01/177.jpg" pagenum="163"/>ad ingenitam minoris raritatis men&longs;ura&mtail; <lb/>&longs;e&longs;e re&longs;tituentis. </s> <s>Ne quod autem &longs;upere&longs;&longs;e <lb/>de veritate dubium po&longs;&longs;it, ip&longs;e &longs;e aër prodi­<lb/>dit, vbi refixum ab antliâ vas optimè clau­<lb/>&longs;um immer&longs;um fuit collo tenus in aquam <lb/>puri&longs;simam, & conuolutâ denuo claue ver­<lb/>&longs;atili re&longs;eratum; magno &longs;iquidem impetu <lb/>atque tumultu, ebullientis aquæ in&longs;tar, vel <lb/>potiùs fontis copio&longs;i&longs;&longs;imi, irrumpebat aqua <lb/>in vas per collum (non tamen &longs;inè bullis at­<lb/>què copiosâ &longs;pumâ) illudque paulatim ad <lb/>&longs;ummum v&longs;que repleuit. </s> <s>Nunquam tamen <lb/>id a&longs;&longs;equi potuerunt, vt omnem pror&longs;us aë­<lb/>rem exclu&longs;um viderent; nam cum in expe­<lb/>rimentum adhibitum primùm fui&longs;&longs;et vas <lb/>27 men&longs;urarum capax, non &longs;uxit aquæ men­<lb/>&longs;uras ni&longs;i 26 3/4: cumque iterum minori va&longs;e <lb/>20 circiter men&longs;urarum capace idem tenta&longs;­<lb/>&longs;ent, adeò repletum fuit, vt vix &longs;patium, <lb/>quod auellana nux repleret, reman&longs;erit aquâ <lb/>vacuum, quod &longs;patium aër replebat in &longs;phæ­<lb/>rulam conglobatus, qui & ad aquæ motum <lb/>hùc illùc manife&longs;tè di&longs;currebat. </s> <s>Et quamuis <lb/>hinc &longs;pes facta e&longs;&longs;et, adhibito minore Reci­<lb/>piente, omnem prorsus aërem extrahendi, <lb/>rem tamen eò deducere nunquam potue­<lb/>runt. </s></p><p type="margin"> <s><margin.target id="note77"/><emph type="italics"/>LXXVII <lb/>Experimen­<lb/>tum probat <lb/>non dari Va <lb/>cuum.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Nullus dubitabam, quin contin­<pb xlink:href="018/01/178.jpg" pagenum="164"/><arrow.to.target n="note78"/><lb/>geret in minori Recipiente minus quoque <lb/><expan abbr="a&etilde;ris">aëris</expan> relinqui; quia, cùm quælibet aëris par­<lb/>ticula certos habeat raritatis terminos, quos <lb/>nequit tran&longs;ilire, patet paucioribus particulis <lb/>ad eam raritatem adductis impleri &longs;patium <lb/>minus, pluribus verò &longs;patium maius. </s> <s>Hinc <lb/>e&longs;t longiori tempore opus e&longs;&longs;e ad extrahen­<lb/>dum aërem ex maiore va&longs;e quàm ex minore, <lb/>non &longs;ecundùm Rationem capacitatis eorum, <lb/>qua&longs;i &longs;emper æquales particulas antlia extra­<lb/>heret, &longs;ed &longs;pectatâ raritate minore, quam, cæ­<lb/>teris paribus, in va&longs;e maiore &longs;u&longs;cipiunt. </s> <s>Po­<lb/>namus enim, exempli gratiâ, <expan abbr="aērem">aerrem</expan> ex di­<lb/>&longs;tractione extendi po&longs;&longs;e ad &longs;patium centu­<lb/>plò maius, ac naturaliter occupet, & antliam <lb/>primo ductu extrahere quatuor digitos cu­<lb/>bicos aëris: hi autem &longs;int pars mille&longs;ima ca­<lb/>pacitatis va&longs;is: igitur po&longs;t primum antliæ du­<lb/>ctum illa pars mille&longs;ima &longs;patij di&longs;tribuitur <lb/>inter re&longs;iduas aëris partes 999: po&longs;t &longs;ecun­<lb/>dum ductum duæ &longs;patij partes mille&longs;imæ <lb/>inter seliquas 998 vnâ cum aliquâ aëris ap­<lb/>pendice; quia &longs;ecundo ductu non extrahitur <lb/>vna mille&longs;ima integra totius primi aëris, &longs;ed <lb/>aliquid minus, &longs;cilicet (999/1000) vnius mille&longs;imæ; <lb/>& &longs;ic deinceps, donec demùm decem partes <lb/>aëris ab initio in va&longs;e exi&longs;tentis, a&longs;&longs;umptâ <lb/>centuplâ raritate, impleant totum &longs;patium. <pb xlink:href="018/01/179.jpg" pagenum="165"/>Quare cum magis &longs;emper ac magis à natu­<lb/>rali &longs;tatu aër recedat, nil mirum &longs;i &longs;emper <lb/>extrahendi difficultas augeatur; quia æquale <lb/>incrementum raritatis &longs;emper paucioribus <lb/>partibus communicatum maiorem &longs;ingulis <lb/>infert violentiam. </s> <s>Ex quo patet ad eam ex­<lb/>trahendi difficultatem citiùs perueniri in va­<lb/>&longs;e minori, quia &longs;ingulæ aëris particulæ &longs;in­<lb/>gulis antliæ ductibus plus di&longs;trahuntur, quàm <lb/>in va&longs;e maiori: nam &longs;i quatuor digiti &longs;int <lb/>&longs;olùm pars va&longs;is cente&longs;ima, primo ductu <lb/>partes 99 aëris debent inter &longs;e di&longs;tribuer&etail; <lb/>quatuor digitos &longs;patij, quod &longs;patium in va&longs;e <lb/>ampliore di&longs;tribuebatur inter partes 999. <lb/>Hæc autem maior violentia, quam patitur <lb/>aër maximè rarus, in cau&longs;â e&longs;t, cur primùm <lb/>tanto impetu irrumpat aqua, & po&longs;tmodum <lb/>paulatim a&longs;cendat; quò enim magis à natu­<lb/>rali &longs;tatu remouetur aër, &longs;icut vim vlterio­<lb/>rem inferenti contumaciùs re&longs;i&longs;tit, ita maio­<lb/>re impetu re&longs;tituit &longs;e&longs;e, & aquæ re&longs;i&longs;tentiam <lb/>faciliùs vincit, cum maximè aqua ad mino­<lb/>rem altitudinem euehatur; at vbi aqua adhuc <lb/>altiùs eleuanda e&longs;t, atque aër à minori rari­<lb/>tate violentâ recedit, & hic &longs;egniùs &longs;e&longs;e con­<lb/>trahit, & illa validiùs re&longs;i&longs;tit, ac proinde len­<lb/>tior quoque e&longs;t motus aquæ paulatim a&longs;cen­<lb/>dentis, & vas replentis. <pb xlink:href="018/01/180.jpg" pagenum="166"/><arrow.to.target n="note79"/></s></p><p type="margin"> <s><margin.target id="note78"/><emph type="italics"/>LXXVIII <lb/>Indicatur <lb/>cau&longs;a eo­<lb/>rum, quæ in <lb/>allato expe­<lb/>rimento con <lb/>tingunt.<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note79"/><emph type="italics"/>LXXIX <lb/>Aquæ tu­<lb/>multuantis <lb/>cau&longs;a expli­<lb/>catur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Sed quid illud e&longs;t, quod tantum <lb/>a&longs;cendentis aquæ tumultum, bullas, atque <lb/>&longs;pumam excitat? </s> <s>An quia colli angu&longs;tias <lb/>prætergre&longs;&longs;a aqua à plurimis aëris particulis <lb/>totius va&longs;is latitudinem occupantibus qua&longs;i <lb/>in fru&longs;ta di&longs;cerpitur, dum &longs;ingulæ aliquid <lb/>liquoris ad &longs;e rapere conantur? </s> <s>An verò quia <lb/>tanto impetu &longs;e&longs;e contrahit aër, vt. </s> <s>&longs;piritus <lb/>aquæ admi&longs;ti cogantur ita rare&longs;cere, vt in­<lb/>termi&longs;ti aqueis particulis & bullas & &longs;pumam <lb/>creent? </s> <s>An veròquia aër ip&longs;e non planè ho­<lb/>mogeneum corpus e&longs;t, &longs;ed alias habet par­<lb/>tes alijs ad raritatem proniores, atque adeò <lb/>inæquali impetu attractæ aqueæ particulæ <lb/>di&longs;trahuntur, atque tumultum excitare vi­<lb/>dentur? </s> <s>Quàm varias autem corporum om­<lb/>nium expirationes aër excipiat, atque inui­<lb/>cem permi&longs;ceat, nemo e&longs;t Philo&longs;ophus, qui <lb/>ignoret; & argumento e&longs;t ip&longs;a naturalis re­<lb/>&longs;pirandi facultas, quæ licet aërem promi&longs;cuè <lb/>attrahat in pulmones, minùs tamen profi­<lb/>cuum expiratione reijcit, retentis vtiliori­<lb/>bus particulis, quas cum &longs;anguine commi­<lb/>&longs;ceat, vt per arteriam veno&longs;am in &longs;ini&longs;trum <lb/>cordis ventriculum de&longs;cendentes elaboren­<lb/>tur in &longs;piritus vitales primùm, ac deinde ani­<lb/>males. </s> <s>Quod &longs;i quis in cubiculo eodem diu­<lb/>tiùs maneat, neque liceat aut libeat apertis <pb xlink:href="018/01/181.jpg" pagenum="167"/>fene&longs;tris nouum aërem alijs vtilibus &longs;piritibus <lb/>imbutum excipere, &longs;atis experitur, quantum <lb/>aërem inter & aërem inter&longs;it. </s> <s>Hinc vix po&longs;­<lb/>&longs;um aliquando non &longs;ubridere, cum diuer&longs;a­<lb/>rum gentium mores aut corporis habitum <lb/>viribus è cælo dimi&longs;&longs;is tribui audio ab ali­<lb/>quibus, qui vbi caloris aut frigoris mentio­<lb/>nem fecerint, illicò propo&longs;itæ quæ&longs;tioni &longs;e <lb/>feci&longs;&longs;e &longs;atis exi&longs;timant. </s> <s>Cau&longs;a tamen i&ntail; <lb/>promptu e&longs;t, cum ex vitalium atque anima­<lb/>lium &longs;pirituum diuer&longs;itate alia atque alia cor­<lb/>poris habitudo, ingenium, mores profici­<lb/>&longs;cantur; &longs;piritibus autem fabricandis no&ntail; <lb/>vltimo loco in&longs;eruit aër, quem in&longs;piramus; <lb/>hic verò pro regionum varietate alias atque <lb/>alias recipit ex tellure expirationes. </s> <s>Quar&etail; <lb/>non facilè mihi per&longs;uadere po&longs;&longs;um vas ali­<lb/>quod omninò homogeneis aëris particulis <lb/>impleri; atque adeò, &longs;i per vim rare&longs;cant, <lb/>inæqualiter etiam eas rare&longs;cere, atque inæ­<lb/>qualem &longs;ubire violentiam oportet: & quod <lb/>hinc &longs;equitur, inæquali impetu &longs;e&longs;e po&longs;tmo­<lb/>dum contrahant, nece&longs;&longs;e e&longs;t. </s></p><p type="main"> <s><arrow.to.target n="note80"/></s></p><p type="margin"> <s><margin.target id="note80"/><emph type="italics"/>LXXX <lb/>Eiu&longs;de&mtail; <lb/>experimenti <lb/>exten&longs;io: & <lb/>eorum, quæ <lb/>accidunt, <lb/>cau&longs;æ indi­<lb/>cantur bre­<lb/>uiter.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Huic inæquali particularum rari­<lb/>tati ego pariter plurimum tribuendum cen­<lb/>&longs;eo; cum enim vas Recipiens primùm aquâ <lb/>repletum fuerit, & antliæ impo&longs;itum, faci­<lb/>is erat initio antliæ agitatio, &longs;ed demum eò <pb xlink:href="018/01/182.jpg" pagenum="168"/> venit difficultas extrahendi embolum, vt <lb/>opus fuerit ce&longs;&longs;are, quamuis non omnis a qua <lb/>exhau&longs;ta fui&longs;&longs;et; id &longs;cilicet nunquam potuit <lb/>obtineri. </s> <s>Refixo autem ab antliâ va&longs;e, & re­<lb/>&longs;erato epi&longs;tomio in aquâ mundi&longs;&longs;imâ, hæc <lb/>vt prius a&longs;cendebat, &longs;ed excitatâ copio&longs;iore <lb/>&longs;pumâ & pluribus bullis, ac quando &longs;olo aë­<lb/>re vas fuerat repletum: id quod contigi&longs;&longs;e <lb/>exi&longs;timo, quia maior e&longs;t inæqualitas raritatis <lb/>in partibus illis partim aqueis, partim ex aquâ <lb/>eductis. </s> <s>Nam cum primùm aqua extrahi­<lb/>tur, &longs;eparantur ab illâ &longs;piritus aliqui & parti­<lb/>culæ, quæ facilè expirarent, & &longs;uprema va­<lb/>&longs;is &longs;patia occupant; deinde etiam partes <lb/>aqueæ minùs contumaces rare&longs;cunt, inter <lb/>quas aliqua datur inæqualitas: &longs;icut enim <lb/>aqua igni appo&longs;ita non tota &longs;tatim in vapo­<lb/>res &longs;oluitur, &longs;ed aliæ præ alijs particulæ faci­<lb/>liùs &longs;oluuntur, ita vbi per di&longs;tractionem &longs;ol­<lb/>ui debet carum compages, aliæ &longs;e exhibent <lb/>præ alijs contumaces ad rare&longs;cendum. </s> <s>Fieri <lb/>autem eam, quam dixi &longs;pirituum &longs;epara­<lb/>tionem ex eo con&longs;tat, quod po&longs;tmodum vas <lb/>totum aquâ repleri nequit, partes enim va­<lb/>&longs;is &longs;upremas &longs;piritus illi occupant. </s> <s>Immo <lb/>cùm per apertum epi&longs;tomium immi&longs;&longs;us <lb/>fui&longs;&longs;et copio&longs;us fumus, hic quidem per a­<lb/>quam a&longs;cendebat, &longs;ed eius &longs;uperficiei in­<pb xlink:href="018/01/183.jpg" pagenum="169"/>cumbens &longs;uprema va&longs;is &longs;patia non petebat, <lb/>ni&longs;i cum demum calido linteo obuolutum <lb/>fui&longs;&longs;et vas: tunc enim vi caloris faciliùs rare­<lb/>&longs;cebat fumus, quàm &longs;piritus illi per vim ad­<lb/>huc rari; ac proinde cum fumus amplior&atail; <lb/>&longs;patia exigens comprimeret vicinum &longs;piri­<lb/>tum, qui propterea à violento &longs;tatu recede­<lb/>bat, tunc poterat fumus in &longs;uperiora &longs;pati&atail; <lb/>leuior factus a&longs;cendere. </s></p><p type="main"> <s>Sed & illud hanc &longs;pirituum &longs;eu halituum <lb/>&longs;eparationem o&longs;tendit; quod non nemo ex­<lb/>cogitauit, vt citiùs, quando opus e&longs;&longs;et, ex­<lb/>perimentum in&longs;titueret, & vitreum vas Re­<lb/>cipiens exhauriret. </s> <s>Ingens vas æneum plu­<lb/>rium vrnarum capax con&longs;tructum fuit opti­<lb/>mè clau&longs;um, præterquam in imo, vbi epi­<lb/>&longs;tomium cum claue ver&longs;atili habebat, vt po&longs;­<lb/>&longs;et antliæ imponi, & in &longs;ummo pariter tu­<lb/>bus extabat claue ver&longs;atili tran&longs;uersâ accu­<lb/>rati&longs;simè clau&longs;us, ac &longs;ummo tubo imponi <lb/>poterat Recipiens vitreum. </s> <s>Et vt omnis &longs;u­<lb/>&longs;picio aëris &longs;e furtim in&longs;inuantis auerteretur, <lb/>tubum circumplectebatur va&longs;culum aquâ <lb/>repletum, ne aut per clauis ver&longs;atilis rimulas, <lb/>aut per tubi o&longs;culum &longs;e aër in&longs;inuaret. </s> <s>Ænei <lb/>va&longs;is aquâ pleni epi&longs;tomio infimo applicita <lb/>e&longs;t antlia, & aliquot horas agitata, ita vt <lb/>cen&longs;eretur aquâ pænè vacuum; tum clau&longs;o <pb xlink:href="018/01/184.jpg" pagenum="170"/>epi&longs;tomio re&longs;eruatum e&longs;t vas ad tempus ex­<lb/>perimenti in&longs;tituendi. </s> <s>Vbi igitur rem per­<lb/>ficere oportuit, impo&longs;itum e&longs;t &longs;uperiori tubo <lb/>vas vitreum Recipiens aquâ plenum, & re­<lb/>uolutâ claue ver&longs;atili, quæ tubum va&longs;is ænei <lb/>claudebat, apertoque Recipientis epi&longs;tomio, <lb/>cæpit illicò aqua Recipientis delabi in vas <lb/>æneum, & &longs;imul ex va&longs;e æneo a&longs;cendebant <lb/>bullæ infinitæ ac radii quidam vnionum in­<lb/>&longs;tar lucidi&longs;simi, & frequenti&longs;simi: nec ce&longs;&longs;a­<lb/>uit hic aquæ & bullarum radiorumque con­<lb/>flictus, quamdiu durauit aquæ in &longs;ubiectum <lb/>vas æneum vel lap&longs;us, vel attractio. </s> <s>Po&longs;t <lb/>horam integram, cum nec dum tota exhau­<lb/>&longs;ta fui&longs;&longs;et aqua, remotum fuit vas vitreum <lb/>Recipiens, eius epi&longs;tomio priùs clau&longs;o, & <lb/>aquæ puri&longs;simæ, vt aliàs, impo&longs;itum; con­<lb/>uolutâque denuò claue ver&longs;atili irrumpebat, <lb/>vt aliàs, aqua cum tumultu, & &longs;pumâ, non <lb/>tamen eâ copiâ, qua cùm per antliam extra­<lb/>cta fuerat aqua ex Recipiente. </s> <s>Ex quibus <lb/>apertè con&longs;tat in va&longs;e æneo &longs;patium fui&longs;&longs;&etail; <lb/>occupatum à &longs;piritibus ex aquâ eductis, qui <lb/>proinde patente exitu in vas vitreum Reci­<lb/>piens erumpebant, cùm aqua ex Recipiente <lb/>in &longs;ubiectum vas æneum tum attraheretur, <lb/>rum etiam fortè dilaberetur: quis enim dicat <lb/>id, quod a&longs;cendebat fui&longs;&longs;e Vacuum, nimi­<pb xlink:href="018/01/185.jpg" pagenum="171"/>rum negationem? </s> <s>Quoniam verò Reci­<lb/>pientis &longs;patium ab aquâ de&longs;cendente reli­<lb/>ctum non &longs;olis &longs;piritibus eductis ex aquâ Re­<lb/>cipientis replebatur, &longs;ed alijs præterea, qui ex <lb/>&longs;ubiecto va&longs;e a&longs;cenderant, quid mirum, &longs;i <lb/>&longs;inguli minorem violentiam in raritate pa&longs;­<lb/>&longs;i, minore quoquè impetu &longs;e contrahentes <lb/>minorem aquæ copiam demùm attrahe­<lb/>rent? </s></p><p type="main"> <s>Quare nihil e&longs;t in toto hoc experimento; <lb/>quod vel leuem inferat Vacui &longs;u&longs;picionem; <lb/>immò in oculos &longs;emper incurrit corpus, te­<lb/>nue illud quidem ac rarum, à quo va&longs;is &longs;pa­<lb/>tia occupantur. </s> <s>Hoc itaque experimento <lb/>non &longs;atis probari no&longs;tri aëris grauitatem ab­<lb/>&longs;olutè, mihi certi&longs;simum e&longs;t; &longs;ed illud vnum <lb/>ex inæquali Recipientis pondere antè ac po&longs;t <lb/>aëris extractionem vi antliæ, confici pote&longs;t, <lb/>quod non inficior, &longs;cilicet communem hunc <lb/>no&longs;trum aërem in aëre alio magis raro gra­<lb/>uitare po&longs;&longs;e: Id autem nil facit ad quæ&longs;tio­<lb/>nem, quam heri examinandam &longs;u&longs;cepimus, <lb/><emph type="italics"/>An tellus machinarum ope translata innataret <lb/>aquis in partem vnam delap&longs;is.<emph.end type="italics"/></s><s> Cum eni&mtail; <lb/>aquæ & cæterorum corporum grauitates <lb/>nobis tantùm innote&longs;cant cum hoc commu­<lb/>ni aëre comparatæ, quid confugiendum e&longs;t ad <lb/>aërem ne&longs;cio quem rariorem, quo caremus? </s></p><pb xlink:href="018/01/186.jpg" pagenum="172"/><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Quam igitur excogita&longs;ti viam, <lb/>qua ad propo&longs;itum quæ&longs;tionis terminum <lb/>euadamus? </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ex ijs, quæ minimum habent du­<lb/>bitationis, ad ignota progrediendum cen&longs;eo. </s> <s><lb/>Illud autem carere videtur omni dubitatio­<lb/>ne, quod &longs;i aqua in aëre grauis e&longs;t vt 5 1/3, aër </s></p><p type="main"> <s><arrow.to.target n="note81"/><lb/>vici&longs;sim in aquâ leuis e&longs;t vt 5 1/3. Nam, vt <lb/>herì ratiocinabamur, vas cupreum pedal&etail; <lb/>lib. 80. nihil grauitat in aquâ, &longs;i aëre implea­<lb/>tur, quia &longs;cilicet aëris inclu&longs;i leuitas elidit <lb/>eam cupri grauitatem, quam aqua non tol­<lb/>lit: Cum enim cuprum amittat &longs;olùm lib. <lb/>(9 1/71) ratione aquæ &longs;ecundùm molem æqualis, <lb/>reliquum pondus decedit ratione leuitatis aë­<lb/>ris: illud autem e&longs;t pondus aquæ &longs;ecundùm <lb/>molem aëri æqualis. </s> <s>Quarè &longs;i æolipila can­<lb/>dens ami&longs;it 4 grana ponderis, licebit argue­<lb/>re aërem ignitum in aëre communi leuitare <lb/>vt 4. Item quia in eodem aëre communi <lb/>aqua æolipilam implens grauior e&longs;t granis <lb/>5425, &longs;acomate &longs;emper in eodem medio exi­<lb/>&longs;tente, colligere po&longs;&longs;umus Rationem ali­<lb/>quam inter aquam & aërem ignitum, mu­<lb/>tuantes ab Algebrâ numeros defectiuos. </s></p><p type="margin"> <s><margin.target id="note81"/><emph type="italics"/>LXXXI <lb/>Quomodo <lb/>inueniatur <lb/>quanta &longs;it <lb/>aëris igniti <lb/>leuitas i&ntail; <lb/>aqua.<emph.end type="italics"/></s></p><p type="main"> <s>E&longs;t &longs;iquidem in aëre communi æqualium <lb/>molium grauitas &longs;imili granorum men&longs;urâ <lb/>deprehen&longs;a, Aquæ quidem &longs;altem gran&atail; <pb xlink:href="018/01/187.jpg" pagenum="173"/>5425, Aëris communis grauitas grana o, <lb/>Aëris igniti grauitas grana o——4, quoniam <lb/>aër ignitus non grauitat &longs;ed leuitat, & com­<lb/>munis non grauitat aut leuitat. </s> <s>In no&longs;tro <lb/>igitur aëre communi aqua ad aërem ignitum <lb/>e&longs;t in pondere vt 5425 ado——4. Et quo­<lb/>niam aquæ grauitatem in aëre communi po­<lb/>nimus 5 1/3, fiat vt 5425 ad o——4, ita 5 1/3 ad <lb/>o——(64/16275). E&longs;t ergo aëris igniti grauitas in <lb/>aëre communi o——(64/16275). Atqui aëris com­<lb/>munis grauitas in aquâ e&longs;t o——5 1/3, igitur &longs;i <lb/>iungantur hæ differentiæ grauitatum, erit <lb/>o——(5 5489/16275) grauitas aëris igniti in aquâ, hoc <lb/>e&longs;t leuitas. </s></p><p type="main"> <s>Quod verò hac methodo ritè inue&longs;tigata <lb/>&longs;it leuitas aeris igniti in aquâ, con&longs;tabit hoc <lb/>exemplo. </s> <s>Grauitas Mercurii e&longs;t 71 1/2, aquæ <lb/>5 1/3, olei 4 3/4: igitur grauitas olei in aquâ e&longs;t <lb/>o——(7/12), & grauitas aquæ in Mercurio e&longs;t <lb/>o——(66 2/12). & &longs;i differentiæ i&longs;tæ iungantur, <lb/>erit grauitas olei in mercurio o——(66 9/12); quæ <lb/>eadem e&longs;t cum illâ, qua immediatè oleum <lb/>cum mercurio comparatur, & e&longs;t 4 3/4 —— <lb/>71 1/2. Si igitur aeris igniti grauitas in aër&etail; <lb/>communi, iungatur aëris communis graui­<lb/>tati in aquâ, ritè habetur aëris igniti grauitas <pb xlink:href="018/01/188.jpg" pagenum="174"/>in aquâ. </s> <s>Hanc autem grauitatem defecti­<lb/>uam vocemus leuitatem, nec ab hac voc&etail; <lb/>abhorreamus. </s></p><p type="main"> <s>Et &longs;anè v&longs;us i&longs;te numerorum defectiuo­<lb/><arrow.to.target n="note82"/><lb/>rum ad leuitatem exprimendam mihi vide­<lb/>tur apti&longs;&longs;imus, ita vt leui&longs;&longs;imo negotio con­<lb/>&longs;tet, vtrùm oblata moles compo&longs;ita leuior <lb/>&longs;it, an grauior quàm aqua. </s> <s>Si enim datâ Ra­<lb/>tione molis corporum totam molem com­<lb/>ponentium, & datâ Ratione grauitatis &longs;in­<lb/>gulorum aut leuitatis &longs;pecificæ intrà aquam, <lb/>ducatur numerus partium in numerum, quo <lb/>leuitas, aut grauitas de&longs;ignatur, horum &longs;um­<lb/>ma &longs;i defectiua &longs;it, molem illam aquâ leuio­<lb/>rem indicabit. </s> <s>Quæramus ex. gr. <!-- REMOVE S-->an dolium <lb/>ferreis circulis firmatum, ac vino plenum, <lb/>&longs;it leuius aquâ, nec ne. </s> <s>Et primùm quarum <lb/>partium ferrum e&longs;t 3, earum &longs;it lignum 400, <lb/>& vinum 100000. Deinde &longs;pecifica in aëre <lb/>grauitas ferri &longs;it 42, ligni 4. vini 5 1/4 ad a­<lb/>quam 5 1/3. E&longs;t igitur grauitas &longs;pecifica ferri <lb/>in aquâ + 36 2/3, quæ per 3 numerum partium <lb/>ducta dat totam ferri grauitatem + 110. Gra­<lb/>uitas &longs;pecifica ligni in aquâ, &longs;eu potius leui­<lb/>tas e&longs;t——1 1/3, quæ per 400 numerum par­<lb/>tium ducta dat totam ligni leuitatem—— <lb/>533 1/3. Demum &longs;pecifica leuitas vini in aquâ <pb xlink:href="018/01/189.jpg" pagenum="175"/>e&longs;t——(1/12), quæ per numerum partiu&mtail; <lb/>100000 ducta dat totam vini leuitatem—— <lb/>8333 1/3. Si igitur inuentæ &longs;ingularum par­<lb/>tium grauitates &longs;eu leuitates in &longs;ummam re­<lb/>digantur, erit &longs;umma——8756 2/3 defectiu&atail; <lb/>indicans totius dolii leuitatem in aquâ, &longs;eu <lb/>differentiam, qua aquæ grauitas excedit dolii <lb/>grauitatem in aëre. </s> <s>Nam &longs;i aquæ grauitas <lb/>5 1/3 ducatur per 3 fit 16, ducta per 400 dat <lb/>2133 1/3, ducta per 100000 dat 533333 1/3; quæ <lb/>in &longs;ummam redactæ dant totam aquæ graui­<lb/>tatem 535482 2/3, à qua deficit dolii grauitas <lb/>particulis 8756 2/3. Id quod con&longs;tabit, &longs;i par­<lb/>tium dolii grauitatem in aëre examinemus; <lb/>ligni enim partes 400 per &longs;pecificam graui­<lb/>tatem 4 ductæ dant ab&longs;olutam ligni grauita­<lb/>tem 1600; iterum partes 100000 vini per gra­<lb/>uitatem &longs;pecificam 5 1/4 ductæ dant ab&longs;olutam <lb/>vini grauitatem 525000: demum partes 3 <lb/>ferri per 42 ductæ dant totam grauitatem <lb/>ferri 126: quæ &longs;i in &longs;ummam redigantur, erit <lb/>tota dolii grauitas in aere 526726. Hæc au­<lb/>tem grauitas &longs;ubducta ex grauitate aquæ æ­<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"/><p type="margin"> <s><margin.target id="note82"/><emph type="italics"/>LXXXII <lb/>Inuenire an <lb/>moles com­<lb/>po&longs;ita po&longs;sit <lb/>innatare a­<lb/>quæ nec ne, <lb/>ab&longs;que cal­<lb/>culo aquæ <lb/>æqualis.<emph.end type="italics"/></s></p><p type="table"> <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"> <s>Porrò &longs;pecificam dolii grauitatem in aëre <lb/>habemus, &longs;i ab&longs;olutam grauitatem 526726 <lb/>diuidamus per 100403 numerum partium, <lb/>& erit grauitas &longs;pecifica molis compo&longs;itæ <pb xlink:href="018/01/191.jpg" pagenum="177"/>(5 246/1000): Vel &longs;i per eundem partium numerum <lb/>diuidatur leuitas ab&longs;oluta——8756 2/3, erit &longs;pe­<lb/>cifica molis compo&longs;itæ leuitas in aquâ (27/1000). <lb/>Quarè &longs;i inter nos conueniat, quota portio <lb/>terreni huius globi inclu&longs;is ignibus tribuen­<lb/>da &longs;it, quota aëri cæterisque halitibus aquâ le­<lb/>uioribus, facilè innote&longs;cet, vtrùm leuitas vin­<lb/>cat grauitatem, ducto partium numero per <lb/>leuitatis aut grauitatis denominatorem. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Quod quidem &longs;pectat ad ingen­<lb/>tem illam ignium cauernam, qui terræ cen­<lb/>trum circumob&longs;ident, memini me ab acu­<lb/>ti&longs;simo æquè ac diligenti&longs;simo &longs;ydereorum <lb/>arcanorum &longs;crutatore Gottifredo Wendeli­<lb/><arrow.to.target n="note83"/><lb/>no aliquid planè &longs;ingulare accepi&longs;&longs;e, quod <lb/>&longs;ummoperè placuit. </s> <s>Hic terræ &longs;emidiame­<lb/>trum in partes 100 tribuens, cauernæ æ&longs;tuan­<lb/>tis &longs;emidiametro partes 63 concedebat, reli­<lb/>quas 37 den&longs;itati cru&longs;tæ huius extimæ; vnde <lb/>fit ignem illum e&longs;&longs;e quartam totius globi <lb/>partem (cubus enim ex 63 e&longs;t &longs;ubquadru­<lb/>plus cubi ex 100) cum &longs;it globus ille igneus <lb/>ad totum globum in triplicatâ ratione dia­<lb/>metrorum. </s> <s>Ne verò id ab ip&longs;o temerè ex­<lb/>cogitatum videretur, addebat, præter pro­<lb/>babiles coniecturas & rationes non paucas, <pb xlink:href="018/01/192.jpg" pagenum="178"/>ex a&longs;&longs;iduâ plurimorum annorum ob&longs;eruatio­<lb/>ne id &longs;ibi innotui&longs;&longs;e, cum videret Lunam <lb/>ad intimam, hoc e&longs;t concauam, huius cru­<lb/>&longs;tæ &longs;uperficiem ita motus &longs;uos temperate, vt <lb/>creet admirabilem illam librationem, quæ <lb/>torquet A&longs;tronomico-Phy&longs;icorum ingenia: <lb/>cuius motûs hypothe&longs;es nondum, quod <lb/>&longs;ciam, publici iuris fecit. <lb/><arrow.to.target n="note84"/></s></p><p type="margin"> <s><margin.target id="note83"/><emph type="italics"/>LXXXIII <lb/>Ignis &longs;ub­<lb/>terraneus <lb/>est quarta <lb/>pars globi <lb/>terreni ex <lb/>&longs;ententi&atail; <lb/>VVendeli­<lb/>ni<emph.end type="italics"/></s></p><p type="margin"> <s><margin.target id="note84"/><emph type="italics"/>LXXXIV <lb/>Tenteatur <lb/>innestigatio <lb/>leuitatis i­<lb/>gnis.<emph.end type="italics"/></s></p><p type="main"> <s>Nollem tamen, Guldine, eam tantù&mtail; <lb/>igni leuitatem tribueres, quam aëri ignito <lb/>intrà Æolipilam candentem conuenire ob­<lb/>&longs;eruaui: longè enim maiore leuitate prædi­<lb/>tam ignis &longs;ub&longs;tantiam &longs;tatuere æquum vide­<lb/>tur, quàm &longs;it leuitas aëris per vim à calor&etail; <lb/>extrin&longs;ecùs adueniente rarefacti. </s> <s>Nam cum <lb/>aquæ intrà Æolipilam ex&longs;uctæ pondus fue­<lb/>rit granorum 5425, facilè reperiemus illius <lb/>&longs;oliditatem; in pede &longs;iquidem cubico &longs;unt <lb/>digiti &longs;olidi 4096: Et quia pes cubicus aquæ <lb/>habet in pondere lib. <!-- REMOVE S-->Rom. <!-- REMOVE S-->80, quarum &longs;in­<lb/>gulæ &longs;unt vnc. </s> <s>12, hoc e&longs;t gran. <!-- REMOVE S-->6912, to­<lb/>tius pedis cubici aquæ pondus e&longs;t gran. <!-- REMOVE S--><lb/>552960. Si igitur grana 552960 dant digi­<lb/>tos &longs;olidos 4096, grana 5425 dabunt di­<lb/>gitos &longs;olidos (40 5/27). Quis autem &longs;ub&longs;tantiæ <lb/>ignis habenti in mole 40 & eo amplius digi­<lb/>tos &longs;olidos, non facilè tribuat longi&longs;simè <pb xlink:href="018/01/193.jpg" pagenum="179"/>maiorem leuitatem in aëre communi quàm <lb/>vt ob&longs;i&longs;tat quatuor granorum grauitati? </s> <s>Ignis <lb/>enim naturam in motum maximè pronam <lb/>&longs;i attentiùs con&longs;ideremus, nihilquè igne le­<lb/>uius nobis innotui&longs;&longs;e animaduertamus, cum <lb/>in tertiâ poti&longs;simum & &longs;upremâ aëris regio­<lb/>ne ignitæ impre&longs;siones Meteorologicæ ac­<lb/>cendantur, nemo facilè negauerit ignis leui­<lb/>tatem &longs;altem tantam e&longs;&longs;e, quæ vincat me­<lb/>dullæ &longs;ambuceæ grauitatem, datâ molis æ­<lb/>qualitate; nihil quippe medullâ &longs;ambuceâ <lb/>leuius, hoc e&longs;t minùs graue, potui adhuc <lb/>deprehendere. </s> <s>Medullam enim &longs;ambuci <lb/>vtcunque viridis cylindricam expendi, cuius <lb/>altitudo erat digitorum 2 2/3 & ba&longs;is diameter <lb/>digiti 1/4, fuitque pondus gran. <!-- REMOVE S-->3: æqualis au­<lb/>tem cylindri cerei pondus fuit gran. <!-- REMOVE S-->72. At­<lb/>qui &longs;i ignis tanta &longs;it leuitas &longs;ur&longs;um, quant&atail; <lb/>e&longs;t medullæ &longs;ambuceæ grauitas deor&longs;u&mtail;, <lb/>multò maior e&longs;t ignis leuitas quàm aeris igni­<lb/>ti in Æolipilâ. </s> <s>Nam quia ba&longs;is diameter <lb/>e&longs;t digiti 1/4, & altitudo dig. </s> <s>2 2/3, &longs;i diametri <lb/>quadratum 1/16 ducatur in altitudinem <gap/>/3, na­<lb/>betur parallelepipedum digiti &longs;olidi 1/6: hoc <lb/>autem parallelepipedum e&longs;t ad cylindrum <lb/>in Ratione ba&longs;ium, quadratum autem dia­<lb/>metri ad circulum habet maiorem rationem <pb xlink:href="018/01/194.jpg" pagenum="180"/>quàm 14 ad 11, minorem verò quàm 284 <lb/>ad 223: igitur vt 14 ad 11 ita 1/6 ad (11/14) maio­<lb/>rem vero; & vt 284 ad 223, ita 1/6 ad (223/1704) mi­<lb/>norem vero. </s> <s>Inuentæ quantitates (11/14) & (223/1704) re­<lb/>ducantur ad eandem denominationem, & <lb/>&longs;unt (78744.18732/143136), differentia autem e&longs;t 12 parti­<lb/>cularum; & &longs;umpto medio Arithmetico &longs;o­<lb/>liditas cylindruli dati e&longs;t (18738/143136), hoc e&longs;t (3123/23856). Si <lb/>igitur medulla &longs;ambucea, cuius &longs;oliditas e&longs;t <lb/>dig. (3123/23856) habet pondus gran. <!-- REMOVE S-->3, medull&atail;, <lb/>cuius &longs;oliditas e&longs;&longs;et dig. (40 5/27), haberet pondus <lb/>gran. <!-- REMOVE S-->920. Ignis itaque leuitas in aëre &longs;i tan­<lb/>ta fuerit, quanta e&longs;t medullæ &longs;ambuceæ gra­<lb/>uitas, erit gran.——920, quorum 5425 e&longs;t <lb/>grauitas aquæ &longs;ecundum molem æqualis. </s> <s><lb/>Ergo &longs;i aquæ grauitas in aëre 5425 dat ignis <lb/>in aëre leuitatem——920, aquæ grauitas 5 1/3 <lb/>dat ignis leuitatem——(4906/5425); quæ &longs;i addatur <lb/>leuitati aëris in aqua——5 1/3, erit leuitas ignis <lb/>in aquâ &longs;altem——(6 258/1085). Et id quidem, Gul­<lb/>dine, tuà methodo: quanquam ægerrimè <lb/>mihi per&longs;uadeo tantulam leuitatem e&longs;&longs;e igni <lb/>tribuendam. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Vtinam non adeò vorax ignis e&longs;&longs;et, <lb/>& pateretur &longs;e va&longs;culo concludi: ve&longs;tra&mtail; <lb/>hanc litem momento dirimerem librà, quam <lb/>aliquando excogitaui ad examinandam cor-</s></p><pb xlink:href="018/01/195.jpg" pagenum="181"/><p type="main"> <s><arrow.to.target n="note85"/><lb/>porum leuitatem in mercurio. </s> <s>Tran&longs;uer&longs;a­<lb/>ria duo EF, CD planè æqualia, bifariam di­<lb/><figure id="id.018.01.195.1.jpg" xlink:href="018/01/195/1.jpg"/><lb/>ui&longs;a in A & I, in­<lb/>&longs;erui tigillo AB ita, <lb/>vt circà axiculos A <lb/>& I facilè ver&longs;atilia <lb/>e&longs;&longs;ent, additâ lin­<lb/>gulà, quæ æquili­<lb/>brium indicaret. </s> <s><lb/>Extremitati C &longs;ty­<lb/>lum deor&longs;um ver­<lb/>gentem adieci, qui <lb/>&longs;ubiectum corpus tangeret; & ex &longs;uperioris <lb/>iugi EF extremitate E, lanx H pendebat: <lb/>reliquæ extremitates FD filo iungebantur æ­<lb/>quali interuallo AI, ne alterum iugum &longs;inè <lb/>altero moueretur; additumque e&longs;t plumbi <lb/>momentum brachijs. </s> <s>AF & ID, vt fieret <lb/>æquilibrium cum lance H & &longs;tylo addito in <lb/>C; adeò vt iuga EF, CD &longs;emper inuicem & <lb/>horizonti parallela e&longs;&longs;ent, ni&longs;i accepto ex­<lb/>trin&longs;ecùs impetu remouerentur à paralle­<lb/>li&longs;mo. </s></p><p type="margin"> <s><margin.target id="note85"/><emph type="italics"/>LXXXV <lb/>Instrumen­<lb/>tum, quo ex­<lb/>aminari po&longs;­<lb/>&longs;unt leuita&longs; <lb/>tes. </s> <s>corpora <lb/>in medio <lb/>grauiore, & <lb/>media ip&longs;a <lb/>comparari <lb/>&longs;ecundù&mtail; <lb/>grauitatem.<emph.end type="italics"/></s></p><p type="main"> <s>Tum va&longs;culum KL ritè collocatum mer­<lb/>curio implebam, & &longs;olidum, cuius exami­<lb/>nanda erat leuitas, mercurio impo&longs;itum ita <lb/>&longs;ubijciebam &longs;tylo C, vt pondere in lance H <lb/>deor&longs;um vrgente attolleretur F & D, ac pro&longs;<pb xlink:href="018/01/196.jpg" pagenum="182"/>inde cum extremitate C deprimeretur &longs;oli­<lb/>dum O intrà mercurium, cuius partes æqua­<lb/>les moli immer&longs;æ effluebant: atquè ita pon­<lb/>dus in H temperabam, vt iuga EF, CD, ho­<lb/>rizonti parallela con&longs;i&longs;terent, quando &longs;uper­<lb/>ficies &longs;olidi immer&longs;i vnicam cum circumfu­<lb/>&longs;o mercurio &longs;uperficiem con&longs;tituebant. </s> <s>Qua­<lb/>re pondus in H grauitans æqualiter re&longs;i&longs;te­<lb/>bat leuitati &longs;olidi &longs;ursùm conantis in mercu­<lb/>rio: cumque ex Archimede lib. de in&longs;id. </s> <s><lb/>hum. </s> <s>prop. 6. con&longs;tet &longs;olidum leuius humi­<lb/>do immer&longs;um tantâ vi &longs;ur&longs;um ferri, quantâ <lb/>humidum molem &longs;olido æqualem habens <lb/>grauius e&longs;t ip&longs;o &longs;olido, colligebam, quantò <lb/>grauior &longs;ecundùm &longs;peciem e&longs;&longs;et mercurius, <lb/>quàm immer&longs;um &longs;olidum. </s> <s>Deinde ide&mtail; <lb/>&longs;olidum in aquâ expendebam vel eadem li­<lb/>brâ, &longs;i in aquâ pariter leuitabat, vel librâ <lb/>communi, &longs;i grauius erat quàm aquâ. </s> <s>Col­<lb/>lectis demùm in &longs;ummam huiu&longs;modi pon­<lb/>deribus &longs;eu differentijs grauitatum, &longs;i i&ntail; <lb/>mercurio leuitans &longs;olidum grauitabat in aquâ, <lb/>&longs;iue &longs;ubtracto minori pondere ex maiore, &longs;i <lb/>in vtroque leuitabat; &longs;umma vel re&longs;iduum <lb/>dabat mihi exce&longs;&longs;um grauitatis mercurij &longs;u­<lb/>pra grauitatem aquæ: alterutrius aute&mtail; <lb/>pondere cognito, reliqui pondus innote&longs;ce­<lb/>bat. </s></p><pb xlink:href="018/01/197.jpg" pagenum="183"/><p type="main"> <s>Sic &longs;i ferri leuitatem in mercurio ex. </s> <s>gr. <!-- REMOVE S--><lb/>deprehendebam æqualem drachmis 29 1/2 e­<lb/>iu&longs;dem autem ferri grauitas in aquâ erat dra­<lb/>chm. </s> <s>36 2/3, arguebam ferrum medium e&longs;&longs;e <lb/>inter mercurium & aquam; adeòque addi­<lb/>tis hi&longs;ce differentijs, nota erat differentia in­<lb/>ter mercurium & aquam 66 1/6: quarè ponde­<lb/>rato ferro in aëre & inuento drachm. </s> <s>42, a­<lb/>qua reperitur 5 1/3, atque adeò mercurius 71 1/2. <lb/>Quod &longs;i ferri loco &longs;olidum ligneum v&longs;urpa­<lb/>bam, cuius leuitas in mercurio e&longs;&longs;et 67 1/2, le­<lb/>uitas verò in aquâ 1 1/3; quia in vtroque leui­<lb/>tabat, intelligebam aquæ grauitatem me­<lb/>diam e&longs;&longs;e inter lignum & mercurium: qua­<lb/>propter harum leuitatum differentia 66 1/6, vt <lb/>priùs, e&longs;t differentia inter aquam & mercu­<lb/>rium. </s></p><p type="main"> <s>Hac, inquam, librâ, quam tunc eum in <lb/>v&longs;um excogitaui, &longs;i va&longs;culum igne plenum <lb/>& clau&longs;um, ne auolet, dederitis, eius leuita­<lb/>tem intrà aquam in va&longs;e KL explorabimus, <lb/>additâ, pro ut opus fuerit, vel demptâ ip&longs;ius <lb/>va&longs;culi intrà aquam grauitate vel leuitate. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Nolo me duriorem præbere i&ntail; <lb/>extenuandâ ignis leuitate, quamuis aëris in <lb/>æolipilâ candenti leuitatem non adeò mul­<lb/>tam deprehenderim. </s> <s>Vnam aliquam &longs;tatue <pb xlink:href="018/01/198.jpg" pagenum="184"/>probabilem, Mer&longs;enne, quæ tamen longi&longs;­<lb/>&longs;imè ab&longs;it à tuâ illâ plu&longs;quam millecuplâ Ra­<lb/>tione, quam inter aeris & aquæ grauitates in­<lb/>tercedere opinaris; non enim facilè acquie­<lb/>&longs;cerem. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Galilæo &longs;altem poteris acquie&longs;ce­<lb/>re aërem quadringenties tantùm aquâ leuio­<lb/>rem &longs;tatuenti; ignis autem adhuc aëre le­<lb/>uior e&longs;t. </s> <s>Quid caput abnuentis in morem <lb/><arrow.to.target n="note86"/><lb/>nutat? </s> <s>Hoc certè, quod addo, nemo æquus <lb/>iudex reijciat; quandoquidem probabiles <lb/>coniecturas per&longs;equi nece&longs;&longs;e e&longs;t, vbi ip&longs;am <lb/>veritatem certò a&longs;&longs;equi non datur. </s> <s>Inter <lb/>grauia nihil adhuc nobis innocuit auro gra­<lb/>uius, inter leuia nihil igne leuius: aqua & <lb/>aër medio loco con&longs;i&longs;tunt. </s> <s>Quamobrem <lb/>&longs;icut grauium grauitates in aere tanqua&mtail; <lb/>communi medio inuicem comparamus, ita <lb/>leuium leuitates in aquâ tanquam communi <lb/>medio conferri inuicem po&longs;&longs;e videntur. </s> <s>Hinc <lb/>&longs;i ponatur leui&longs;&longs;imum corpus ita &longs;e habere <lb/>ad medium, vnde leuitas de&longs;umitur, vt cor­<lb/>pus graui&longs;&longs;imum &longs;e habet ad medium, ex <lb/>quo grauitas incipit denominari, nihil ab­<lb/>&longs;urdum &longs;tatuitur, & corporum motrices fa­<lb/>cultates &longs;ibi proportione re&longs;pondent. </s> <s>Sicut <lb/>igitur in aere grauitas aquæ e&longs;t partium 5 1/3, <lb/>quarum grauitas auri e&longs;t 100, quidni parites <pb xlink:href="018/01/199.jpg" pagenum="185"/>quarum partium —— 5 1/3 con&longs;titui&longs;ti leuitatem <lb/>aëris in aquâ, earum——100 &longs;tatuas ignis <lb/>leuitatem in aquâ? </s> <s>Vide, quò demum ve­<lb/>nerim, Guldine, vt tibi morem geram. </s></p><p type="margin"> <s><margin.target id="note86"/><emph type="italics"/>LXXXVI <lb/>Alia hypo­<lb/>thesis de i­<lb/>gnis leuita­<lb/>te examina­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Iam planè videris paulò mitiùs <lb/>atque veri&longs;imiliùs opinari. </s> <s>Et vt meam fa­<lb/>cilitatem tibi probem, &longs;iquidem placuit <lb/>Wendelini &longs;ententia quartam orbis huius <lb/>partem tribuens æ&longs;tuanti cauernæ ignium <lb/>plenæ, eam vltrò admitto, & ignis leuita­<lb/>tem ad aquam a&longs;&longs;umo partium——100, qua­<lb/>rum aëris leuitas e&longs;t——5 1/3. Reliquis verò <lb/>tribus orbis huius quadrantibus quam conce­<lb/>dis grauitatem? </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Si perpendantur omnia, forta&longs;sè <lb/>non deberent cen&longs;eri grauiores argillâ. </s> <s>Pri­<lb/>mùm quia aqua, quæ terræ faciem alluit <lb/>aëri finitima, &longs;erè tota demenda e&longs;t ex pon­<lb/>dere, cùm illa, ex hypothe&longs;i initio con&longs;titutâ, <lb/>habeat rationem medij, in quo motus per­<lb/>ficitur, & ad vnam partem confluxerit. </s> <s>De­<lb/>inde quia aqua terræ venas permeans benè <lb/>multa e&longs;t, & intrà aquam con&longs;tituta nihil <lb/>addit ponderis. </s> <s>Præterea reliqua moles, quæ <lb/>demptâ aquâ &longs;upere&longs;t, tam multum habet <lb/>aeris halituumque intrà aquam leuitantium, <lb/>vt plurimum elidant grauitatis metallorum <pb xlink:href="018/01/200.jpg" pagenum="186"/>ac marmorum. </s> <s>Quarè &longs;i tribus orbis qua­<lb/>drantibus argillæ grauitas tribuatur, maxi­<lb/>mè probabili coniecturâ vti videatur, qui &longs;i<gap/><lb/>opinetur. <lb/><arrow.to.target n="note87"/></s></p><p type="margin"> <s><margin.target id="note87"/><emph type="italics"/>XXCVII <lb/>Globus ter­<lb/>renus in ea <lb/>hypothe&longs;i in <lb/>nataturus <lb/>aquæ vide­<lb/>tur.<emph.end type="italics"/></s></p><p type="main"> <s>Quoniam verò aquæ grauitas ad argillæ <lb/>grauitatem in aëre, vt olim me dicere me­<lb/>mini, e&longs;t vt 16 ad 27, po&longs;itâ aquæ grauita­<lb/>te 5 1/3, argillæ grauitas in aere e&longs;t 9: igitur <lb/>argillæ grauitas in aquâ e&longs;t 3 2/3. Tres itaque <lb/>partes orbis &longs;i per 3 2/3 ducantur, erit grauitas <lb/>11, & vna pars ignis e&longs;t leuitatem habens <lb/>——100: &longs;i addantur, erit globi huius con­<lb/>flati ex hac variâ corporum mi&longs;cellâ leuitas <lb/>——89 intrà aquam: ac proinde &longs;i aqua v­<lb/>nam in partem &longs;ecederet, tellure translatâ, <lb/>globus hic innataret, cum leuior &longs;it aquâ. </s> <s><lb/>Nam &longs;i comparetur grauitas ab&longs;oluta aquæ <lb/>&longs;ecundùm molem æqualis toti globo, cum <lb/>grauitate ab&longs;olutâ ip&longs;ius globi, reperietur di&longs;­<lb/>ferentia 89. Quia enim ignis leuitas ad aquam <lb/>e&longs;t——100, aquæ grauitas ad ignem e&longs;t + <lb/>100: quia verò argillæ grauitas ad aquam e&longs;t <lb/>3 2/3, argillæ grauitas ad ignem e&longs;t 103 2/3 At­<lb/>qui tres globi partes ex hypothe&longs;i &longs;unt argil­<lb/>la, reliqua pars e&longs;t ignis, igitur &longs;i argillæ gra­<lb/>uitas 103 2/3 ducatur per 3, erit globi grauitas <lb/>311: &longs;i verò aquæ grauitas ad ignem 100 <pb xlink:href="018/01/201.jpg" pagenum="187"/>ducatur per 4, erit grauitas molis aqueæ <lb/>æqualis 400. Cum itaque grauitas aquæ ad <lb/>grauitatem molis confla<gap/> ex 3/4 argillæ & 1/4 <lb/>ignis, &longs;it vt 400 ad 311, con&longs;tat mole&mtail; <lb/>conflatam innataturam. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Quin aquæ grauitatem in <expan abbr="a&etilde;re">aëre</expan> po­<lb/><arrow.to.target n="note88"/><lb/>tiùs, quàm in igne, con&longs;ideras? </s> <s>An timui­<lb/>&longs;ti, ne globus hic ex aëre communi in purio­<lb/>rem æthera auolaret? </s> <s>Quando quidem &longs;i le­<lb/>uitas aeris ad aquam e&longs;t——5 1/3, & leuitas <lb/>ignis ad aquam e&longs;t——100, leuitas ignis ad <lb/>aërem e&longs;t——94 2/3: e&longs;t autem argillæ grauitas <lb/>in aëre 9. Igitur tres orbis quadrantes ha­<lb/>berent grauitatem vt 27, & reliquus qua­<lb/>drans leuitatem vt——94 2/3, atquè adeo totus <lb/>orbis leuitatem haberet in aere vt—— 67 2/3; <lb/>hoc e&longs;t &longs;i per 4 numerum partium diuida­<lb/>tur, leuitas &longs;pecifica totius globi in aere e&longs;­<lb/>&longs;et——(16 11/12) </s></p><p type="margin"> <s><margin.target id="note88"/><emph type="italics"/>XXCVIII <lb/>Imò leuior <lb/>e&longs;&longs;et &longs;ecun­<lb/>dùm <expan abbr="&longs;peci&etilde;">&longs;peciem</expan> <lb/>aëre.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Lynceus es, Galilæe, nihil no&ntail; <lb/><arrow.to.target n="note89"/><lb/>vides. </s> <s>Mirabar pariter, cur omi&longs;sâ aquæ & <lb/>argillæ grauitate in aëre, confugerit Mer&longs;en­<lb/>nus ad earum grauitatem in igne; cum ta­<lb/>men ex aquâ emergens globus in aërem ve­<lb/>niat; qui e&longs;t aquæ circumfu&longs;us, non verò in <lb/>ignem. </s> <s>Quemadmodum enim &longs;i mercurio <pb xlink:href="018/01/202.jpg" pagenum="188"/>(cuius grauitas in aere 71 1/2) imponatur ex <lb/>aëre ferrum (cuius grauitas 42) innatatio <lb/>ferri debet con&longs;iderari iuxta differentiam gra­<lb/>uitatum in aëre, & leuitatio ferri ex mercurio <lb/>in aërem e&longs;t——29 1/2. At &longs;i mercurio &longs;uper­<lb/>fu&longs;a &longs;it aqua, leuitas ferri de&longs;umenda e&longs;t ex <lb/>differentiâ inter grauitatem mercurij & gra­<lb/>uitatem ferri, quod intrà aquam non am­<lb/>pliùs graue e&longs;t vt 42, &longs;ed vt 36 2/3: quare leui­<lb/>tas ferri tunc e&longs;t maior, videlicet vt——34 5/6. <lb/>Ita &longs;imiliter cùm globus terrenus ex aquâ in <lb/>aerem, non in ignem veniret, eius grauitas <lb/>cum aëre debuit, non cum igne, compa­<lb/>rari. </s></p><p type="margin"> <s><margin.target id="note89"/><emph type="italics"/>XXCIX <lb/>Solida plus <lb/>leuitant ex <lb/>mercurio in <lb/>aquam <expan abbr="quã">quam</expan> <lb/>in aërem.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Qui aquam mercurio &longs;uperfudi&longs;ti, <lb/><arrow.to.target n="note90"/><lb/>cur pariter non circumfudi&longs;ti? </s> <s>tunc enim <lb/>mercurij in aquâ exi&longs;tentis grauitas non e&longs;­<lb/>&longs;et 71 1/6 &longs;ed 66 1/2, & in illo leuitas ferri (cuius <lb/>grauitas in aquâ 36 2/3) e&longs;&longs;et pariter——29 1/2. <lb/>Duo &longs;iquidem æqualia corpora inæqualiter <lb/>grauia &longs;ecundùm &longs;peciem &longs;i in eodem me­<lb/>dio con&longs;tituantur, quodcunque illud &longs;it, ean­<lb/>dem &longs;emper &longs;eruant differentiam, quia vtri­<lb/>que æqualis fit grauitatis dece&longs;sio aut acce&longs;sio <lb/>pro maiori aut minori grauitate medij. </s> <s>Igi­<lb/>rur &longs;i terreni globi grauitas &longs;pecifica compa­<lb/>rata cum &longs;pecificâ grauitate aquæ in vno me­<pb xlink:href="018/01/203.jpg" pagenum="189"/>dio habet certam differentiam, vt in ign&etail; <lb/>dixi exce&longs;&longs;um grauitatis aquæ &longs;upra grauita­<lb/>tem globi terreni ex igne & argillâ conflati <lb/>e&longs;&longs;e 89; in quocunque medio con&longs;tituantur, <lb/>eundem habebit exce&longs;&longs;um. </s> <s>Sic in aëre gra­<lb/>uitas 3/4 argillæ & 1/4 ignis e&longs;&longs;et defectiua, vt re­<lb/>ctè Galilæus ratiocinabatur, videlicet—— <lb/>67 2/3, & grauitas æqualis molis aquæ in aëre <lb/>e&longs;&longs;et po&longs;itiua, nimirùm 21 1/3 (ducto 4 per <lb/>5 1/3) differentia autem, qua maior numerus <lb/>21 1/3 excedit minorem —— 67 2/3, e&longs;t 89 planè <lb/>eadem ac prius. </s> <s>Satis igitur fuit in vno ali­<lb/>quo medio differentiam reperire, cùm illa <lb/>&longs;emper eadem maneat. </s> <s>Opportunius verò <lb/>accidit in medio omnium leui&longs;simo, in quo <lb/>ignis ip&longs;e globi molem componens nihil <lb/>grauitat, examen illud in&longs;tituere, quia om­<lb/>nes partium grauitates po&longs;itiuæ &longs;unt, nulla <lb/>defectiua. </s></p><p type="margin"> <s><margin.target id="note90"/><emph type="italics"/>XC <lb/>Ratio <expan abbr="gra-uitatũ">gra­<lb/>uitatum</expan> duo­<lb/>rum corpo­<lb/>rum in vno <lb/>medio, est <lb/>eadem i&ntail; <lb/>omni medio.<emph.end type="italics"/></s></p><p type="main"> <s>Cæterùm non timui, ne terrenus globus <lb/>auolaret, quemadmodum ouorum putami­<lb/>na, vt aiunt, matutino rore impleta & meri­<lb/>diano Soli expo&longs;ita. </s> <s>Qui enim tres orbis qua­<lb/>drantes intrà aquam exi&longs;timat grauiores non <lb/>e&longs;&longs;e, quàm &longs;i ex merâ argilla con&longs;tarent, <lb/>quia aqua illis permi&longs;ta nihil grauitat, & aër <lb/>valde leuitat, forta&longs;sè non item a&longs;&longs;erat tres <pb xlink:href="018/01/204.jpg" pagenum="190"/>orbis quadrantes in aëre con&longs;titutos eâdem <lb/>&longs;ecundùm &longs;peciem grauitate cum argillâ præ­<lb/>ditos e&longs;&longs;e: quia iam aër in aëre nihil leuitat, <lb/>& halitus inclu&longs;i minùs leuitant, & aqua &longs;a­<lb/>tis grauitat, & cætera omnia corpora tan­<lb/>tum addunt ponderis, quantum illis detrahe­<lb/>bat aqua, intrà quam exi&longs;tebant, &longs;cilicet iux­<lb/>tà molis æqualitatem. </s> <s>Id quod pariter di­<lb/>ctum velim, &longs;i globus i&longs;te intrà leui&longs;&longs;imum <lb/>ignem con&longs;titutus intelligatur, neque enim <lb/>ibi tres orbis quadrantes æqualiter cum ar­<lb/>gillâ grauitarent, &longs;ed longè validiùs. </s> <s>Quan­<lb/>do autem paulò antè grauitatum rationes <lb/>iniens tres orbis quadrante, qua&longs;i ex merà ar­<lb/>gillâ in igne con&longs;titutâ a&longs;&longs;ump&longs;i, id fuit &longs;o­<lb/>lùm ad explicandam hypothe&longs;im, qua tri­<lb/>buebatur grauitas &longs;pecifica æqualis grauitati <lb/>argillaceæ. </s> <s>Quarè &longs;i orbis in aëre con&longs;titua­<lb/>tur, non ea tantùm e&longs;t illius grauitas, quæ <lb/>tribus quadrantibus ex argillâ conueniat, &longs;ed <lb/>perinde &longs;e habet, ac &longs;i totus ex argillâ con­<lb/>&longs;taret, vt olim citra omnem controuer&longs;iam <lb/>admittebamus; adeòque nullum &longs;ube&longs;&longs;et pe­<lb/>riculum, ne auolaret. </s> <s>Nam &longs;i po&longs;ito ign&etail; <lb/>omnium leui&longs;simo aëris grauitas e&longs;t † 94 2/3, <lb/>argillæ grauitas e&longs;t † 103 2/3, ac proinde cum <lb/>orbis totus ex argillâ con&longs;titutus ponatur. </s> <s><lb/>grauior e&longs;t aëre; cum tamen intrà aqua&mtail; <pb xlink:href="018/01/205.jpg" pagenum="191"/>perinde &longs;e habere po&longs;&longs;e videatur, atque &longs;i tres <lb/>tantùm quadrantes argillacei e&longs;&longs;ent, & reli­<lb/>quus igneus. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Vereor plurimùm, ne i&longs;ta, quæ <lb/><arrow.to.target n="note91"/><lb/>po&longs;tremo loco attuli&longs;ti, plus habeant &longs;peciei <lb/>quàm veritatis. </s> <s>& facilè &longs;u&longs;picor non omni­<lb/>nò &longs;eriò à te prolata; &longs;ed quia vidi&longs;ti me i&ntail; <lb/>tabellam illam oculos curio&longs;iùs coniicien­<lb/>tem,, volui&longs;ti o&longs;citantiam tentare, & ad at­<lb/>tentionem reuocare. </s> <s>Attenti&longs;simo tamen <lb/>animo excepi omnia; &longs;olùm enim vt phan­<lb/>ta&longs;iæ contentioni parcerem, labrum illud, <lb/>in quo moriens Seneca &longs;anguinem cum vitâ <lb/>effundit, re&longs;piciebam; illudque mihi nunc <lb/>aquâ, nunc &longs;tanno liquente plenum finge­<lb/>bam perpendens, vtrùm fieri po&longs;sit corpus <lb/>aliquod, cui in vno medio conuenit grauitas <lb/>&longs;pecifica argillæ, in alio medio maiorem aut <lb/>minorem grauitatem <expan abbr="&longs;pecificã">&longs;pecificam</expan> obtinere; nec <lb/>&longs;atis poteram percipere, quî fieri po&longs;&longs;et, vt <lb/>totus globus haberet in aëre grauitatem ar­<lb/>gillæ. </s> <s>non autem &longs;imilem argillæ grauitatem <lb/>obtinere po&longs;&longs;et in aquâ. </s></p><p type="margin"> <s><margin.target id="note91"/><emph type="italics"/>XCI <lb/>Eadem mo­<lb/>les compo&longs;i­<lb/>ta quam &longs;pe<lb/>cificam gra­<lb/>uitatem ba­<lb/>bet in vno <lb/>medio, habet <lb/>in quocun­<lb/>cunque me­<lb/>dio.<emph.end type="italics"/></s></p><p type="main"> <s>Fingamus enim corpus, cuius duæ partes <lb/>&longs;int ferrum, vna marmor, duæ cera, vna <lb/>aër, & vna lapis: e&longs;t autem in aere &longs;pecifica <lb/>grauitas ferri 42, marmoris 21, ceræ 5, aë­<lb/>ris 0, lapidis 14. igitur &longs;ingularum partium <pb xlink:href="018/01/206.jpg" pagenum="192"/>grauitatibus in &longs;ummam collectis erit graui­<lb/>tas tota in aëre 129; quæ &longs;i per 7 diuidatur, <lb/>quia &longs;unt &longs;eptem æquales dati corporis par­<lb/>tes, erit grauitas &longs;pecifica huiu&longs;modi corporis <lb/>in aere 18 3/7. Iam corpus hoc, cuius grauitas <lb/>&longs;pecifica 18 3/7, comparemus cum &longs;tanno </s></p><p type="table"> <s>TABELLE WAR HIER<!--Keep S--></s></p><p type="main"><s>communi, cuius grauitas &longs;pecifica 39; erit <lb/>dati corporis leuitas in &longs;tanno liquente—— <lb/>20 4/7; quæ &longs;i per 7 numerum partium duca­<lb/>tur, erit tota leuitas ——144. Eadem autem <lb/>leuitas habetur, &longs;i &longs;ingulæ partes cum &longs;tan­<lb/>no conferantur; e&longs;t enim duarum partium <lb/>ferri in &longs;tanno grauitas † 6, vnius partis <lb/>marmoris leuitas——18, duarum partium <pb xlink:href="018/01/207.jpg" pagenum="193"/>ceræ leuitas ——68, vnius partis aëris leuitas <lb/>—— 39, & vnius partis lapidis leuitas——25: <lb/>quæ &longs;i in &longs;ummam referantur, erit corporis <lb/>dati leuitas in &longs;tanno liquente ——144. Qua­<lb/>propter tam in &longs;tanno quàm in aëre perinde <lb/>&longs;e habet, ac &longs;i corpus homogeneum e&longs;&longs;et, <lb/>cuius grauitas &longs;pecifica e&longs;&longs;et 18 3/7. </s> <s>Sed in aquâ etiam non dubito, quin pari­<lb/>ter &longs;e habeat vt corpus, cuius grauitas &longs;it <lb/>18 3/7 ad aquam, cuius grauitas 5 1/3: erit enim <lb/>corporis huius &longs;pecifica grauitas in aquâ + <lb/>(13 2/21), quæ per 7 ducta dat + ab&longs;olutam corpo­<lb/>ris in aquâ grauitatem † 91 2/3. Hæc verò e&longs;t <lb/>planè eadem, ac &longs;i in &longs;ummam conferantur <lb/>grauitas duarum partium ferri + 73 1/3, graui­<lb/>tas vnius partis marmoris + 15 2/3, leuitas du&atail; <lb/>rum partium ceræ——<gap/> 2/3, leuitas vnius par­<lb/>tis aëris —— 5 1/3, & grauitas vnius partis lapi­<lb/>dis + 8 2/3: ex his enim pariter habetur graui­<lb/>tas in aquá + 91 2/3. In quocunque igitur me­<lb/>dio con&longs;tituatur, perinde &longs;e habet, atque &longs;i <lb/>grauitas &longs;pecifica in medio leui&longs;simo, i&ntail; <lb/>quo nulla po&longs;iti corporis pars leuis e&longs;t, hoc <lb/>e&longs;t in aëre, e&longs;&longs;et + 18 3/7. </s></p><p type="main"> <s>Ex his infero terrenum globum eandem <lb/>&longs;emper habere &longs;pecificam grauitatem in quo­<lb/>cunque medio; ac proinde &longs;i in aquâ habet <pb xlink:href="018/01/208.jpg" pagenum="194"/>leuitatem —— 89, quia in quatuor partes di­<lb/>&longs;tinctus ponitur (cum corpori leui&longs;&longs;imo mo­<lb/>lem componenti 1/4 tribuatur) diuidatur 89 <lb/>per 4, & erit leuitas &longs;pecifica in aquâ—— <lb/>22 1/4: Si igitur grauitas aquæ in igne + 100 illi <lb/>addatur, erit grauitas &longs;pecifica terreni globi <lb/>in igne + 77 3/4. In quocunque igitur medio <lb/>terrenus globus &longs;emper haberet &longs;pecificam <lb/>grauitatem vt + 77 3/4 in medio leui&longs;simo, hoc <lb/>e&longs;t in igne, &longs;i cæterorum corporum grauitas <lb/>ad idem medium, hoc e&longs;t ignem, compare­<lb/>tur. </s> <s>Quia verò aëris communis in igne gra­<lb/>uitas e&longs;t † 94 2/3, grauitas autem &longs;pecifica glo­<lb/>bi terreni e&longs;t † 77 3/4, &longs;equitur terreni globi &longs;pe­<lb/>cificam leuitatem in aëre communi e&longs;&longs;e—— <lb/>(16 11/12), quæ &longs;i per 4 numerum partium duca­<lb/>tur, dabit ab&longs;olutam globi leuitatem in aëre <lb/>——67 2/3, vt Galilæus argumentabatur: tellus <lb/>igitur aere leuior e&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Qui inter &longs;alebras ambulat, non <lb/>&longs;emper ad numerum gre&longs;&longs;us ponit. </s> <s>Id I mihi <lb/><arrow.to.target n="note92"/><lb/>quoquè contigi&longs;&longs;e videtur, qui non &longs;atis di­<lb/>lucidè verbis &longs;um complexus, quod vole­<lb/>bam. </s> <s>Sed mihi nunc per ve&longs;tram humani­<lb/>tatem licebit meam mentem interpretari. </s> <s><lb/>Toti huic globo, quem incolimus, aquam <lb/>terramque complectenti, argillæ grauitatem <pb xlink:href="018/01/209.jpg" pagenum="195"/>&longs;pecificam tribuo; ideò intrà aërem con&longs;i­<lb/>&longs;tit, nec vllum &longs;ube&longs;t auolandi in æther&atail; <lb/>periculum. </s> <s>At &longs;ublatis marium atquè flu­<lb/>minum aquis, quas in latus &longs;ece&longs;&longs;i&longs;&longs;e poni­<lb/>mus, reliquæ molis grauitas minor e&longs;t; quia, <lb/>&longs;ublatâ marium grauitate, ad &longs;olius terræ & <lb/>metallorum grauitatem leuitas ignis inclu&longs;i <lb/>& halituum habet maiorem Rationem, quàm <lb/>haberet ad grauitatem terræ &longs;imul & aquæ; ac <lb/>proinde cum maneant eadem corpora leuia, <lb/>& minuantur grauia, minor quoquè e&longs;&longs;e vi­<lb/>detur &longs;pecifica grauitas totius globi. </s> <s>Quem­<lb/>admodum &longs;i ex æreo va&longs;e aëris pleno aufe­<lb/>ram partem metalli, manente eodem aëre, <lb/>fit minor &longs;pecifica va&longs;is grauitas. </s> <s>Quamuis <lb/>autem &longs;ublato vno globi quadrante, qui igni <lb/>tribuitur, & &longs;ublatis marium, lacuumque, <lb/>& fluminum aquis, quæ &longs;upere&longs;t moles &longs;it <lb/>minor tribus totius orbis quadrantibus, ac <lb/>proinde minor tribus quadrantibus molis, <lb/>quæ re&longs;tat &longs;ublatâ tantùm aquâ, mihi tamen <lb/>minutas quæ&longs;tiunculas non con&longs;ectanti &longs;atis <lb/>videbatur tribus quadrantibus molis reliquæ <lb/>argillaceam grauitatem tribuere; vt &longs;i fortè <lb/>grauitas i&longs;ta iu&longs;to minor e&longs;&longs;et, compen&longs;aretur <lb/>diminutâ ignis mole, quæ &longs;tatuebatur &longs;olùm <lb/>quadrans reliquæ molis, cum tamen e&longs;&longs;et 1/4 <lb/>totius globi. </s></p><pb xlink:href="018/01/210.jpg" pagenum="196"/><p type="margin"> <s><margin.target id="note92"/><emph type="italics"/>XCII <lb/>Moli <expan abbr="cõ">com</expan>po­<lb/>&longs;itæ &longs;i quid <lb/>additur aut <lb/>dematur, e­<lb/>ius grauitas <lb/>&longs;pecifica mu <lb/>tatur.<emph.end type="italics"/></s></p><p type="main"> <s>Sed &longs;i placeat grauitatem illam augere, <lb/>&longs;tatuamus tres illos quadrantes non argillæ, <lb/>&longs;ed Magnetis grauitatem habere; e&longs;t autem <lb/>magnetis grauitas 26 ad aquæ grauitatem <lb/>5 1/3 in aëre: quare magnetis grauitas in aquâ <lb/>e&longs;t 20 2/3, & grauitas in igne 120 2/3; ideòque <lb/>grauitas trium quadrantum in aquâ, cu&mtail; <lb/>ex magnete con&longs;tent, e&longs;t 62, & leuitas <lb/>conueniens vni quadranti ignis in aquâ e&longs;t <lb/>——100: igitur leuitas globi in aquâ e&longs;t <expan abbr="tãtùm">tantùm</expan> <lb/>—— 38. Quando verò totus globus ex aquâ <lb/>pariter & terrâ conflatus accipitur, iam au­<lb/>ctâ grauitate, alia e&longs;t &longs;pecifica totius globi <lb/>grauitas, qualis e&longs;&longs;et ex. </s> <s>gr. <!-- REMOVE S-->grauitas mar­<lb/>moris aut alia, cum non videatur a&longs;&longs;umi <lb/>po&longs;&longs;e tanquam mera argilla, &longs;i tres quadran­<lb/>tes ex magnete &longs;tatuantur. </s> </p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> At &longs;i globo non re&longs;tituatur aqua, <lb/>quæ in latus &longs;ece&longs;&longs;it, augebiturnè grauitas <lb/>&longs;pecifica molis, quæ ex tribus quadrantibus <lb/>magnetis, & vno quadrante ignis conflatur? </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Ni&longs;i quid addatur aut dematur, <lb/>fieri non pote&longs;t vt grauitas &longs;pecifica variatio­<lb/>nem &longs;ubeat, </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Nobis igitur conuenit. </s> <s>Quapropter <lb/>&longs;i globi leuitas in aquâ e&longs;t——38, per 4 nu­<lb/>merum partium diuidatur, & erit leuitas <lb/>&longs;pecifica terreni globi in aquâ——9 1/2; cui &longs;i <pb xlink:href="018/01/211.jpg" pagenum="197"/>addatur grauitas aquæ in aere † 5 1/3, erit &longs;pe­<lb/>cifica globi leuitas in aere ——4 1/6. Quà&mtail; <lb/>bellè itaque res Archimedi &longs;ucce&longs;&longs;i&longs;&longs;et: quan­<lb/>do quidem vbi eò terram eleua&longs;&longs;et, vt aqua <lb/>in latus &longs;ece&longs;&longs;i&longs;&longs;et, telluris globus non &longs;olùm <lb/>ex aquâ emergeret, &longs;ed relictâ in vniuer&longs;i <lb/>centro aquâ auolaret &longs;upra aërem, donec of­<lb/>fenderet medium æqualis leuitatis &longs;upra aë­<lb/>rem communem. </s> <s>Quarè machinationibus <lb/>opus e&longs;&longs;et non ad mouendam, &longs;ed ad reti­<lb/>nendam tellurem. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Quod tellus, &longs;ublatâ aquâ, leuior <lb/>&longs;it quàm aer i&longs;te communis, quem &longs;piritu <lb/>ducimus, vix adduci po&longs;&longs;um, vt credam: id <lb/>autem cùm ex hypothe&longs;i à vobis con&longs;titutâ <lb/>&longs;equatur, hypothe&longs;i ip&longs;i probabilitatem de­<lb/>mit. </s> <s>Quapropter aut nimiam igni leuita­<lb/>tem, aut nimiam molem tribui&longs;tis; atqu&etail; <lb/>adeò vtramque aut alterutram temperar&etail; <lb/>oportet. </s> <s>Equidem exi&longs;timo in leuitate po­<lb/>tiùs peccatum fui&longs;&longs;e quàm in mole: mihi &longs;i­<lb/>quidem facilè per&longs;uadeo ingentem ignium <lb/>vim intimis terræ vi&longs;ceribus concludi, quo­<lb/>rum poti&longs;&longs;imùm admini&longs;tratione natur&atail; <lb/>perficit pretio&longs;am illam metallorum &longs;upel­<lb/>lectilem, quibus &longs;odinæ ditantur: certum <lb/>e&longs;t autem calore humidum attenuante com­<lb/>mi&longs;ceri &longs;piritus metallicos partibus fixis, at­<pb xlink:href="018/01/212.jpg" pagenum="198"/>què vniri; ibi verò res tota perficitur, quò <lb/>&longs;olis calor pertingere nequit: quamobrem <lb/>cum in tantá à centro di&longs;tantiâ producantur <lb/>metalla, totque milliarium cra&longs;&longs;itudine&mtail; <lb/>permeet calor, haud ægrè venio in docti&longs;&longs;i­<lb/>mi Wendelini &longs;ententiam, &longs;i maximè cum <lb/>Lunæ libratione cohæreat. </s> <s>Sed quoniam <lb/>ignis ille acerrimus e&longs;t (quò autem tenuior <lb/>ignis, eò languidior e&longs;t) non adeò multam <lb/>forta&longs;sè tenuitatem obtinet, vt eius leuitas ad <lb/>aquam &longs;it vt auri grauitas ad aerem, quem­<lb/>admodum a&longs;&longs;um p&longs;i&longs;tis. </s> <s>Animum autem <lb/>aduertite, vtrùm eam potiùs Rationem ha­<lb/>beat ignis leuitas ad aëris leuitatem in aquâ, <lb/>quam habet terræ &longs;eu argillæ grauitas ad <lb/>aquæ grauitatem in aere. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Si me audieritis, nullas hìc conie­<lb/>cturas con&longs;ectabimur, præter eam, quam <lb/>olim à nobis con&longs;titutam nemo facilè infi­<lb/>cietur, videlicet telluris globum vniuer&longs;um <lb/>in aere grauitate argillaceâ præditum e&longs;&longs;&etail;. <lb/><arrow.to.target n="note93"/><lb/>Globi &longs;oliditatem inue&longs;tigemus, eamqu&etail; <lb/>per &longs;pecificam argillæ grauitatem ducamus; <lb/>ex quo innote&longs;cet ab&longs;oluta grauitas globi: <lb/>Hinc demamus ab&longs;olutam aquæ grauitatem, <lb/>quæ obtinetur ductâ aquæ &longs;pecificâ grauitate <lb/>in eius &longs;oliditatem. </s> <s>Re&longs;iduum grauitatis ab­<lb/>&longs;olutæ globi diui&longs;um per re&longs;iduum &longs;oliditatis <pb xlink:href="018/01/213.jpg" pagenum="199"/>demptâ &longs;oliditate aquæ, dabit &longs;pecifica&mtail; <lb/>grauitatem globi demptâ aquâ. </s></p><p type="margin"> <s><margin.target id="note93"/><emph type="italics"/>XCIII <lb/>Terreni glo. <lb/></s> <s>&longs;bi grauitas <lb/>pecific&atail; <lb/>maior est: <lb/>grauitat&etail; <lb/>argillæ, &longs;i <lb/>aqua dema­<lb/>tur ex glo­<lb/>bo.<emph.end type="italics"/></s></p><p type="main"> <s>Primùm globi &longs;oliditatem habemus, &longs;i <lb/>inuentæ &longs;ub initium no&longs;tri he&longs;terni &longs;ermonis <lb/>&longs;uperficiei &longs;phæricæ mill. <!-- REMOVE S-->quad. </s> <s>214.201996. <lb/>pa&longs;&longs;. </s> <s>716000, accipiamus trientem mill. <!-- REMOVE S-->quad. </s> <s><lb/>71.400665. pa&longs;&longs;. </s> <s>572000, & ducamus per <lb/>telluris &longs;emidiametrum mill. <!-- REMOVE S-->4128. pa&longs;&longs;. </s> <s><lb/>638: fiet enim totius globi &longs;oliditas mill. <!-- REMOVE S-->cu­<lb/>bicorum 294787.501105. pa&longs;&longs;. </s> <s>850936000. <lb/>Ex hac globi &longs;oliditate &longs;i inuenta &longs;uperiùs <lb/>aquæ &longs;oliditas mill. <!-- REMOVE S-->cub. </s> <s>80.325748. pa&longs;&longs;. </s> <s><lb/>768500000. auferatur, relinquitur mill. <!-- REMOVE S-->cub <lb/>294707.175357. pa&longs;&longs;. </s> <s>82.436000. &longs;oliditas <lb/>reliqui globi demptâ aquâ. </s> <s>s </s></p><p type="main"> <s>Deinde globi &longs;oliditas pa&longs;&longs; cub. </s> <s>294. <lb/>787501.105850.936000 ducatur per 9 &longs;pe­<lb/>cificam grauitatem argi læ in aere, & e&longs;t ab­<lb/>&longs;oluta globi grauitas 2653.087509.952658. <lb/>424000. Item aquæ &longs;oliditas pa&longs;&longs;.cub 80325. <lb/>748768.500000. ducatur per 5 1/3 &longs;pecificam <lb/>aquæ grauitatem, & fit ab&longs;oluta aquæ graui­<lb/>tas 428403.993432.000000. Dematur hæc <lb/>aquæ grauitas ex terreni globi grauitate, & <lb/>remanet 2652.659105.959226.424000. <lb/>grauitas re&longs;idui globi demptâ aquâ. </s></p><p type="main"> <s>Demùm re&longs;idua hæc grauitas 2652. <lb/>659105.959226.424000. diuidatur per re­<pb xlink:href="018/01/214.jpg" pagenum="200"/>&longs;iduum &longs;oliditatis demptâ aquâ, nempè per <lb/>numerum pa&longs;&longs;. </s> <s>cub. </s> <s>294.707175.357082. <lb/>436000. Et qui prodibit Quotiens (9 9994/10.000000) <lb/>proximè dabit re&longs;idui globi &longs;pecificam gra­<lb/>uitatem pauló maiorem grauitare argillaceâ. </s> <s><lb/>Quia nimirum aquæ demptæ grauitas &longs;peci­<lb/>fica minor e&longs;t grauitate argillæ. </s> <s>Quod &longs;i <lb/>pars dempta fui&longs;&longs;et argilla, aut argillâ gra­<lb/>uior, diminuta fui&longs;&longs;et grauitas &longs;pecifica; vt <lb/>quando ex va&longs;e metallico aëris pleno pars ali­<lb/>qua metalli aufertur: Et hoc &longs;olùm in ca&longs;u <lb/>admittenda &longs;unt, quæ paulò antè Mer&longs;ennus <lb/>dicebat; quia tunc re&longs;iduum pondus ad pon­<lb/>dus ablatum habet minorem Ratione&mtail;, <lb/>quàm re&longs;idua moles ad molem ablatam; hìc <lb/>autem contrà, quia grauitas aquæ minor e&longs;t <lb/>grauitate argillæ, re&longs;iduum pondus ad pon­<lb/>dus ablatum habet maiorem Rationem, <lb/>quàm re&longs;idua moles ad molem aquæ abla­<lb/>tam. </s></p><p type="main"> <s>Quarè &longs;i totius globi terraquei grauitas <lb/><arrow.to.target n="note94"/><lb/>&longs;pecifica non fuerit in aere minor grauitate <lb/>&longs;pecificâ aquæ, fieri non pote&longs;t, vt aquis in <lb/>vnam partem &longs;ecedentibus terra reliqua in­<lb/>natet, &longs;emper enim grauitas &longs;pecifica terræ <lb/>maior erit &longs;pecificâ grauitate aquæ. </s></p><p type="margin"> <s><margin.target id="note94"/><emph type="italics"/>XCIV <lb/>Si telluri <lb/>tribuatur <lb/>grauitas ar­<lb/>gillacea, a­<lb/>quæ in latus <lb/>&longs;ecedenti <expan abbr="nõ">non</expan> <lb/>innataret.<emph.end type="italics"/></s></p><p type="main"> <s>Si<gap/> enim primùm totius globi &longs;pecific<gap/><lb/>grauitas ad aquæ grauitatem &longs;pecificam vt <pb xlink:href="018/01/215.jpg" pagenum="201"/>RT ad SV: quia verò ab&longs;oluta grauitas globi <lb/>rerraquei comparatur cum æquali mole a­<lb/><figure id="id.018.01.215.1.jpg" xlink:href="018/01/215/1.jpg"/><lb/>quæ, erit pariter grauitas ab&longs;olu­<lb/>ta globi terraquei ad grauitatem <lb/>ab&longs;olutam æqualis globi tantum­<lb/>modò aquei vt RT ad SV. </s> <s>Dein­<lb/>de ex globo terraqueo auferatur <lb/>aqua, cuius grauitas TO; æqua­<lb/>lis aqua ex globo aqueo dempt&atail; <lb/>æqualem habet grauitatem VN: <lb/>& &longs;unt re&longs;iduæ grauitates RO & <lb/>SN inæquales, quia ex inæqualibus RT, SV, <lb/>ablatæ &longs;unt æquales grauitates OT, VN. </s> <s><lb/>Cum itaque maior &longs;it Ratio RT maioris ad <lb/>OT, quàm SV minoris ad VN, erit per <lb/>conuer&longs;ionem Rationis minor Ratio RT ad <lb/>RO, quàm SV ad SN; igitur & vici&longs;&longs;i&mtail; <lb/>minor erit Ratio RT ad SV, quàm RO ad <lb/>SN. </s> <s>Igitur re&longs;idua globi terreni grauitas <lb/>RO ad re&longs;iduam globi aquei &longs;ecundùm mo­<lb/>lem æqualis grauitatem SN habet maiorem <lb/>Rationem, quàm totius globi terraquei gra­<lb/>uitas RT ad totius globi aquei æqualis gra­<lb/>uitatem SV, hoc e&longs;t, quàm argillæ grauitas <lb/>ad grauitatem aquæ. </s> <s>Fieri itaque non pote&longs;t, <lb/>vt terra aquis innatet. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Valeat igitur Thales Mile&longs;ius cum <lb/>&longs;uo illo nauigio. </s> <s>Et &longs;anè no&longs;tra hac di&longs;puta­<pb xlink:href="018/01/216.jpg" pagenum="202"/>tione nos operam lu&longs;i&longs;&longs;e non puto; facilè <lb/>enim in eam &longs;ententiam delabi quis po&longs;&longs;et, <lb/>vt &longs;ibi per&longs;uaderet ab inclu&longs;is terræ halitibus <lb/>atque ignibus tantum demi grauitatis, vt illa <lb/>intrà aquam leuior e&longs;&longs;et &longs;ecundùm &longs;peciem: <lb/>quæ quidem vnica e&longs;t innatationis cau&longs;&atail;. </s> <s><lb/>Ni&longs;i quis fortè ex eorum numero, qui la­<lb/>minam metallicam ratione figuræ in mul­<lb/>tam latitudinem explicatæ, ideòque diffi­<lb/>ciliùs, (vt ip&longs;i quidem loquuntur) &longs;ubie­<lb/>ctam aquam diuidentis, innatare cen&longs;ent, <lb/>ambigeret pariter, an idem terræ quoqu&etail; <lb/>contingere po&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Errorem hunc iamdudum aureo <lb/>illo tuo de Innatantibus libello profliga&longs;ti; <lb/>Galilæe: vixque puto aliquem &longs;upere&longs;&longs;e, qui <lb/>cramben hanc recoquat, præter eos, quos <lb/>iuuat ex antiquioribus tantùm codicibus ru­<lb/>dioris &longs;æculi puluerem colligere. </s> <s>Nihil Gul­<lb/>dino, nihil mihi e&longs;t cum huiu&longs;modi homi­<lb/>num genere commercij: quapropter mi&longs;&longs;os <lb/>illos prorsùs faciamus: quamuis enim motui <lb/>tarditatem aliquam inferre po&longs;&longs;it figura, im­<lb/>pedire tamen omninò non pote&longs;t, &longs;i illa qui­<lb/>dem per &longs;e re&longs;piciatur; quod &longs;i ea fuerit cor­<lb/>poris grauis figura, quæ leuioris aeris partem <lb/>&longs;ecum deferat, aeri vtique non figuræ tri­<lb/>buenda e&longs;t innatatio, quatenus ex aere, & <pb xlink:href="018/01/217.jpg" pagenum="203"/>metallo laminæ componitur moles, cuius <lb/>pondus minus e&longs;t pondere æqualis molis <lb/>aquæ. </s> <s>Cum autem nihil &longs;imile in terrâ con­<lb/>tingere po&longs;&longs;it, quandoquidem aër ille, qui <lb/>valles ex aquâ extantes impleret, nihil con­<lb/>ferret leuitatis (quemadmodum & in naui, <lb/>qui &longs;upra aquæ &longs;uperficiem aer, nauis pon­<lb/>dus non minuit, nam intrà aerem non leui­<lb/>tat) nulla &longs;pes nobis reliqua e&longs;t innatationis <lb/>terræ: &longs;ed quicquid in tellure machinationi­<lb/>bus mouendâ compendij haberet Archime­<lb/>des ex aquis, totum illud e&longs;&longs;et ex eâ ponde­<lb/>ris diminutione, quam &longs;ubeunt &longs;olida gra­<lb/>uiora aquis immer&longs;a. </s></p><p type="main"> <s><emph type="italics"/>Gul.<emph.end type="italics"/><!-- KEEP S--></s><s> Ita planè, &longs;i terræ tantùm ratio ha­<lb/><arrow.to.target n="note95"/><lb/>beatur: nam compendium aliud, nec illud <lb/>contemnendum, antequam heri aduenires <lb/>Mer&longs;enne, ob&longs;eruabamus ex ip&longs;ius aquæ &longs;e­<lb/>iunctione, cuius grauitatem ad calculos re­<lb/>uocantes deprehendebamus non minorem <lb/>libris Rom. <!-- REMOVE S-->803.257487.685000.000000. <lb/>Quæ &longs;i ex totius globi grauitate argilla­<lb/>ceâ dematur, relinquet reliquæ terræ pon­<lb/>dus. </s> </p><p type="margin"> <s><margin.target id="note95"/><emph type="italics"/>XCV <lb/>Terra intra <lb/>aquam mi­<lb/>nùs ponde­<lb/>raret.<emph.end type="italics"/></s></p><p type="main"> <s>Vt autem totius globi grauitatem ad li­<lb/>bras reuocem, accipio vnius milliaris cubici <lb/>ex argillâ grauitatem: cum verò aquæ gra­<lb/>uitas ad argillæ grauitatem &longs;it vt 5 1/2 ad 9, <pb xlink:href="018/01/218.jpg" pagenum="204"/>milliaris autem cubici ex aquâ pondus iam <lb/>inuenerim lib. 10.000000.000000. erit quar­<lb/>tus analogiæ terminus lib. 16.875000.000000 <lb/>pondus vnius milliaris cubici ex argillâ. </s> <s>Per <lb/>hanc igitur grauitatem duco inuentam paulò <lb/>antè globi &longs;oliditatem mill. <!-- REMOVE S-->294787.501105. <lb/>pa&longs;&longs;. </s> <s>850936000, & prouenit demùm to­<lb/>tius globi terraquei grauitas, &longs;i mera argilla <lb/>effet, lib. 4.974539.081161.234545. <lb/>000000. quæ forta&longs;sè paulò maior erit eâ gra­<lb/><arrow.to.target n="note96"/><lb/>uitate, quam Mer&longs;enne, &longs;tatuebas, quia in <lb/>terræ diametro inueniendâ minùs accuratis <lb/>rationibus vtebaris, &longs;i &longs;atis memini. </s> <s>Ex in­<lb/>uentâ itaque globi grauitate &longs;i dematur con­<lb/>&longs;tituta aquarum grauitas, remanet &longs;olius ter­<lb/>ræ pondus lib. 4.973735.823673.549545. <lb/>000000. </s></p><p type="margin"> <s><margin.target id="note96"/><emph type="italics"/>XCVI <lb/>Terræ gra­<lb/>uitas libra­<lb/>rum nume­<lb/>ro<gap/> probabili <lb/>explicata.<emph.end type="italics"/></s></p><p type="main"> <s>Cum verò grauitas hæc intrà aquam non <lb/>tota percipiatur, &longs;ed &longs;olùm iuxta exce&longs;&longs;um <lb/>grauitatis &longs;pecificæ argillæ &longs;upra grauitatem <lb/>aquæ &longs;pecificam, &longs;atis con&longs;tat, quantùm <lb/>minueretur terræ pondus, & quantò faciliùs <lb/>moueretur. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Eam tamen hic intelligis, puto, ad­<lb/>hibendam circum&longs;criptionem, vt non toti <lb/>globo, &longs;ed illi tantùm parti, quæ aquis cir­<lb/>cumfunderetur, grauitatem adimerent aquæ, <lb/>parem ponderi molis aqueæ æqualis; neque <pb xlink:href="018/01/219.jpg" pagenum="205"/>enim terra vniuer&longs;a intrà aquam demer&longs;&atail; <lb/>delite&longs;ceret. </s> <s>Prætereà quamuis totius terreæ <lb/>portionis in aquâ exi&longs;tentis grauitas minuere­<lb/>tur, &longs;egmenti tamen vltra Vniuer&longs;i cen­<lb/>trum po&longs;iti grauitas imminuta vel auct&atail; <lb/>nihil iuuaret, cùm motui illa non repugnet, <lb/>dum de&longs;cendit: ideò &longs;olùm &longs;egmenti &longs;upe­<lb/>rioris pars aquis immer&longs;a attendenda e&longs;&longs;et: <lb/>atque adeò quò magis terræ centrum ab vni­<lb/>uer&longs;i centro remoueretur, eò augeretur ma­<lb/>gis pondus, quia plus terrenæ molis ex aquis <lb/>extaret. </s> <s>Neque enim aliud terræ conringe­<lb/>ret, quâm &longs;olido cuilibet corpori, quod ex <lb/>humore in va&longs;e extrahitur, cuius maior mo­<lb/>les emergit ex aquâ, quàm &longs;it moles aquæ <lb/><arrow.to.target n="note97"/><lb/>accurrentis ad replendum &longs;patium à corpo­<lb/>re &longs;olido relictum. </s> <s>Quia &longs;cilicet &longs;i aqua ma­<lb/>neret in eâdem &longs;uperficie, nec deprimere­<lb/>tur, &longs;olidi tanta moles emergeret, quanta e&longs;t <lb/>moles, quæ relinquit &longs;patium intra aquam: <lb/>&longs;ed quoniam aqua infra illam &longs;uperficie&mtail; <lb/>deprimitur, quam priùs con&longs;tituebat, & re­<lb/>linquit aliam prætereà &longs;olidi partem ab aquâ <lb/>immunem, ideò moles, quæ ex aquâ emer­<lb/>git, maior e&longs;t mole aquæ accurrentis ad re­<lb/>plendum &longs;patium relictum à corpore eleua­<lb/>to. </s> <s>Sic in va&longs;e HX, corpus AB totum in­<lb/>trà aquam, cuius &longs;uperficies &longs;it CD, &longs;i ex-<pb xlink:href="018/01/220.jpg" pagenum="206"/><figure id="id.018.01.220.1.jpg" xlink:href="018/01/220/1.jpg"/><lb/>trahatur ex A in H, pars CH, quæ &longs;upr&atail; <lb/>&longs;uperficiem aquæ CD eleuatur, æqualis e&longs;t <lb/>parti, quæ replebat &longs;patium GB: hoc autem <lb/>&longs;patium relictum implet aqua de&longs;cendens ex <lb/>C in E, ac proinde totum corpus HE extr&atail; <lb/>aquam manet; quæ moles maior e&longs;t mol&etail; <lb/>HC, hoc e&longs;t mole aquæ de&longs;cendentis DE ad <lb/>replendum &longs;patium &longs;ibi æquale GB. </s> <s>Idem <lb/>igitur terræ contingeret, quæ & eleuaretur <lb/>&longs;upra locum, vbi erat &longs;uperficies aquæ, & <lb/>infra illum locum &longs;uperficies aquæ deprime. </s> <s><lb/>retur; ex quo fieret maiorem terræ partem <lb/>ex aquis emergere. </s></p><p type="margin"> <s><margin.target id="note97"/><emph type="italics"/>XCVII <lb/>Solidi moles <lb/>ex humido <lb/>emerg&ebreve;s, ma­<lb/>ior est mole <lb/>humidi ac­<lb/>currentis a<gap/><lb/>replendum <lb/>&longs;patium.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> At aquæ illæ nullo va&longs;e contine­<lb/>rentur, aut alueo. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Perinde e&longs;t &longs;i aqua va&longs;is lateribus <lb/>circum&longs;cripta certam figuram induat, ac &longs;i <lb/>&longs;uis &longs;e nutibus ip&longs;a in &longs;phæram di&longs;ponat. </s> <s>Il­<lb/>lud quidem contingeret, quod cùm aqua ex <lb/>maiori eleuatione terræ in minorem &longs;emper <pb xlink:href="018/01/221.jpg" pagenum="207"/>ac minorem &longs;phæram &longs;e conformaret, ra­<lb/>tionem haberet va&longs;is minoris & minoris; <lb/>atque adeò aqua magis & magis deprimere­<lb/>tur, etiam datâ æquali terræ eleuation&etail;. </s> <s><lb/>Sint enim duo va&longs;a &longs;imilia &longs;ed inæqualia, in <lb/>quibus &longs;int duo corpora &longs;imilia & æquali&atail; <lb/><arrow.to.target n="note98"/><lb/>AB in minori, & KL in maiori &longs;imiliter po­<lb/>&longs;ita: & &longs;it continua &longs;olidorum immer&longs;orum <lb/>& aquæ circumfu&longs;æ &longs;uperficies. </s> <s>Extrahatur <lb/>ex aquâ vtrumque &longs;olidum pari velocitat&etail;; <lb/>vtique citiùs emerget omninò illud, quod <lb/>e&longs;t in minori va&longs;e, quàm quod e&longs;t in maiori; <lb/>& multò plus aquæ de&longs;cendere debet in ma­<lb/>iori quàm in minori, ac proinde plus eleuari <lb/>debet &longs;olidum in maiori va&longs;e, quàm in mi­<lb/>nori, vt æqualis moles emineat &longs;upra aquæ <lb/>de&longs;cendentis &longs;uperficiem. </s></p><p type="margin"> <s><margin.target id="note98"/><emph type="italics"/>XCVIII <lb/>Idem <expan abbr="&longs;olidũ">&longs;olidum</expan> <lb/>vt extraba­<lb/>tur ex hu­<lb/>mido, plus <lb/>debet eleua­<lb/>ri in va&longs;&etail; <lb/>maiori <expan abbr="quã">quam</expan> <lb/>in minori, <lb/>& plus a­<lb/>quæ de&longs;cen­<lb/>dit in va&longs;e <lb/>maiori, <expan abbr="quã">quam</expan> <lb/>in minori. </s> <s><lb/>Hæc veritas <lb/>infertur ex <lb/>contradicto­<lb/>ria hypothe­<lb/>&longs;i.<emph.end type="italics"/></s></p><p type="main"> <s>Sit enim primò aquæ in va&longs;e minori &longs;u­<lb/>perficies CD, in va&longs;e autem maiori OM: <lb/>deinde ita extrahatur vtrumque &longs;olidum, vt <lb/>æquales partes HE & VS emineant &longs;upra &longs;u­<lb/>perficiem, quam denuò acqui&longs;iuit aqua de­<lb/>&longs;cendens in locum à &longs;olido eleuato relictum. </s> <s><lb/>Dico maiorem e&longs;&longs;e eleuationem VK &longs;upr&atail; <lb/>primam &longs;uperficiem OM, in va&longs;e maiori, <lb/>quàm &longs;it eleuatio AH &longs;upra primam &longs;uper­<lb/>ficiem CD in va&longs;e minori; ac proinde &longs;pa­<lb/>tium relictum NL maius e&longs;&longs;e &longs;patio relicto <pb xlink:href="018/01/222.jpg" pagenum="208"/>GB, & aquam OMRS de&longs;cendentem e&longs;&longs;&etail; <lb/>maiorem aquâ CDFE de&longs;cendente. </s></p><p type="main"> <s>Nam &longs;i KV non e&longs;t maior quàm AH, <lb/>ergo aut æqualis, aut minor. </s> <s>Sit æqualis: er­<lb/>go quia HG & VN æquales &longs;unt ex hypothe­<lb/>&longs;i, & VK ip&longs;i HA æqualis dicitur, etiam <lb/>reliquæ KN & AG, hoc e&longs;t OS & CE, æqua­<lb/>les &longs;unt: ergo aquæ OMRS & CDFE æqua­<lb/>lem habentes altitudinem &longs;unt inter &longs;e vt <lb/>ba&longs;es, hoc e&longs;t vt &longs;uperficies OM & CD. <!-- KEEP S--></s> <s>At­<lb/>qui &longs;uperficies OM maior e&longs;t &longs;uperficie CD, <lb/>ergo aqua OMRS maior e&longs;t quàm aqu&atail; <lb/>CDFE: &longs;ed aqua de&longs;cendens e&longs;t æqualis mo­<lb/>li corporis NL, quæ replebat &longs;patium reli­<lb/>ctum; igitur maior e&longs;t moles NL quàm GB: <lb/>e&longs;t autem NL æqualis parti eleuatæ VO, & <lb/>GB æqualis e&longs;t parti eleuatæ HC, ergo VO <lb/>maior e&longs;t moles <expan abbr="quãm">quàm</expan> HC: hæ verò moles <lb/>VO & HC &longs;unt vt altitudines, quia ex hypo­<lb/>the&longs;i data &longs;olida &longs;unt æqualia, &longs;imilia, & &longs;i­<lb/>militer po&longs;ita; ergo maior e&longs;t altitudo KV <lb/>quam altitudo AH. <!-- KEEP S--></s></p><p type="main"> <s>Quod &longs;i KV dicatur minor quàm AH <lb/>ergo ex æqualibus VN, HG, demptis inæ­<lb/>qualibus, remanet KN maior quam AG, <lb/>hoc e&longs;t OS maior quam CE: aqua igitur <lb/>OMRS maiorem habens ba&longs;im ac maiorem <lb/>altitudinem, quam aqua CDFE, maior quo­<pb xlink:href="018/01/223.jpg" pagenum="209"/><figure id="id.018.01.223.1.jpg" xlink:href="018/01/223/1.jpg"/><lb/>què erit; ac proinde & moles NL, hoc e&longs;t VO, <lb/>maior mole GB, hoc e&longs;t HC; & vt priùs ele­<lb/>uatio KV maior eleuatione AH. <!-- KEEP S--></s> <s>Quare vide­<lb/>tis hoc adeò certum e&longs;&longs;e, vt<gap/> ex ip&longs;o negante <lb/>eleuationem in maiori va&longs;e maiorem e&longs;&longs;&etail; <lb/>eleuatione in minori va&longs;e, veritatis huius con­<lb/>fe&longs;&longs;io extorqueatur, ijs admi&longs;&longs;is, quæ con­<lb/>tradicens ponit. </s></p><p type="main"> <s><emph type="italics"/>Met&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Priu&longs;quàm vlteriùs progrediatis, <lb/>vnum vellem ex te quærere; an &longs;cilicet aliqua <lb/>&longs;it inter eleuationes &longs;olidorum & depre&longs;&longs;io­<lb/>nes aquatum in va&longs;is inæqualibus analogi&atail; <lb/>&longs;altem reciproca, ita vt quæ Ratio e&longs;t eleua­<lb/>tionis KV in va&longs;e maiori ad eleuationem AH <lb/>in minori, eadem Ratio &longs;it depre&longs;&longs;ionis aquæ <lb/>CE, hoc e&longs;t AG, in minori ad depre&longs;&longs;ionem <lb/>aquæ OS, hoc e&longs;t KN in maiori. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Nulla e&longs;t &longs;iue directa, &longs;iue recipro­<pb xlink:href="018/01/224.jpg" pagenum="210"/>ca inter eleuationes &longs;olidi ac depre&longs;&longs;iones a­<lb/><arrow.to.target n="note99"/><lb/>quæ analogia, præterquàm in vno ca&longs;u. </s> <s>Non <lb/>quidem directa, quia, vt dicebam, KV ma­<lb/>ior e&longs;t quàm AH, ergo maior e&longs;t Ratio KV <lb/>ad AG, quàm HA ad AG; atqui AG maior <lb/>e&longs;t quàm KN, ergo maior e&longs;t Ratio KV ad <lb/>KN quàm KV ad AG; ergò multò maior e&longs;t <lb/>Ratio KV ad KN quàm HA ad AG. </s> <s>No&ntail; <lb/>e&longs;&longs;e autem reciprocam analogiam &longs;ic o&longs;tendo. </s></p><p type="margin"> <s><margin.target id="note99"/><emph type="italics"/>XCIX <lb/>Eleuationes <lb/>&longs;olidi, & <lb/>depre&longs;&longs;iones <lb/>humidi i&ntail; <lb/>va&longs;is inæ­<lb/>qualibus <expan abbr="nõ">non</expan> <lb/>&longs;unt propor<lb/>tionales, ni &longs;i <lb/>in vno ca&longs;u.<emph.end type="italics"/></s></p><p type="main"> <s>Aqua OMRS circumfu&longs;a e&longs;t æqualis moli <lb/>NL, hoc e&longs;t VO; addatur vtrique commu­<lb/>nis moles NO, erit tota moles duobus pla­<lb/>nis KOM & NSR parallelis contenta æqualis <lb/>moli corporis KL &longs;eu VS. </s> <s>Item aqua CDFE <lb/>circumfu&longs;a æqualis e&longs;t moli GB, hoc e&longs;t HC; <lb/>& additâ communi mole AE, erit tota mo­<lb/>les planis ACD & GEF parallelis content&atail; <lb/>æqualis moli corporis AB &longs;eu HE. </s> <s>Atqui HE <lb/>& VS æquales &longs;unt moles ex hypothe&longs;i; igi­<lb/>tur & moles GD æqualis e&longs;t moli NM: ergo <lb/>per 34. lib. 11. ba&longs;es cum altitudinibus re­<lb/>ciprocantur, & vt AG ad KN, ita &longs;uperficies <lb/>va&longs;is maioris ad &longs;uperficiem va&longs;is minoris. </s></p><p type="main"> <s>Prætereà aqua circumfu&longs;a OMRS æqua­<lb/>lis e&longs;t moli VO, ergo ad molem KS habet <lb/>eandem Rationem quam VO ad KS, hoc e&longs;t <lb/>quam altitudines KV ad KN. <!-- KEEP S--></s> <s>At aqua cir­<lb/>cumfu&longs;a ad molem KS, quia in eâdem &longs;unt <pb xlink:href="018/01/225.jpg" pagenum="211"/>altitudine OS, e&longs;t vt &longs;uperficies va&longs;is minus <lb/>&longs;uperficie &longs;olidi VY ad ip&longs;am &longs;uperficiem &longs;o­<lb/>lidi; igitur VK eleuatio &longs;olidi ad KN depre&longs;­<lb/>&longs;ionem aquæ e&longs;t vt &longs;uperficies va&longs;is maioris <lb/>minùs &longs;uperficie &longs;olidi ad ip&longs;am &longs;uperficiem <lb/>&longs;olidi VY: & componendo vt VN corporis <lb/>emer&longs;io ad KN aquæ depre&longs;&longs;ionem, ita &longs;u­<lb/>perficies va&longs;is maioris ad &longs;uperficiem &longs;olidi <lb/>VY. </s> <s>Eâdem methodo o&longs;tenditur HA eleua­<lb/>tionem &longs;olidi ad AG depre&longs;&longs;ionem aquæ e&longs;&longs;e, <lb/>vt e&longs;t &longs;uperficies va&longs;is minoris minùs &longs;uper­<lb/>ficie &longs;olidi HT ad ip&longs;am &longs;uperficiem &longs;olidi: & <lb/>componendo vt HG ad GA, ita &longs;uperficies <lb/>va&longs;is minoris ad &longs;uperficiem &longs;olidi HT. </s></p><figure id="id.018.01.225.1.jpg" xlink:href="018/01/225/1.jpg"/><p type="main"> <s>Quoniam igitur vt &longs;uperficies va&longs;is maio­<lb/>ris ad &longs;uperficiem minoris, ita GA ad NK; <lb/>&longs;i e&longs;&longs;et VK ad HA vt GA ad NK, iam e&longs;&longs;et vt <lb/>VK ad HA ita &longs;uperficies va&longs;is maioris ad &longs;u­<pb xlink:href="018/01/226.jpg" pagenum="212"/>perficiem minoris: &longs;ed vt VK ad HA, it&atail; <lb/>moles VO ad molem HC, hoc e&longs;t aqu&atail; <lb/>OMRS ad aquam CDFE; ergo vt &longs;uperficies <lb/>va&longs;is maioris ad &longs;uperficiem minoris, hoc e&longs;t <lb/>vt GA ad NK, ita aqua OMRS ad aqua&mtail; <lb/>CDFE. <!-- KEEP S--></s> <s>Atqui aquæ i&longs;tæ circumfu&longs;æ habent <lb/>Rationem compo&longs;itam ex Rationibus altitu­<lb/>dinum & ba&longs;ium; ergo Ratio GA ad NK <lb/>æqualis e&longs;t <emph type="italics"/>R<emph.end type="italics"/>ationi compo&longs;itæ <emph type="italics"/>ex Rationi­<emph.end type="italics"/><lb/>bus altitudinum GA ad N<emph type="italics"/>K,<emph.end type="italics"/> & ba&longs;ium CD <lb/>ad OM. </s> <s>Cum verò fieri non po&longs;&longs;it vt (quan­<lb/>do Ratio non componitur ex duabus Ratio­<lb/>nibus, quarum altera &longs;it alterius &longs;ubduplica­<lb/>ta, vt Ratio compo&longs;ita ex Rationibus 4 ad 2 <lb/>& 2 ad 8, e&longs;t eadem cum Ratione 2 ad 4 <lb/>conuer&longs;a prions Rationis 4 ad 2, quemad­<lb/>modum hic non contingere &longs;uppono) Ratio <lb/>aliqua compo&longs;ita eadem &longs;it directè cum vnâ <lb/>ex Rationibus componentibus, ni&longs;i alter&atail; <lb/>Ratio componens &longs;it Ratio æqualitatis (&longs;ic <lb/>Ratio compo&longs;ita ex Rationibus 4 ad 4 & 4 ad <lb/>3 e&longs;t 16 ad 12 eadem cum Ratione 4 ad 3, <lb/>quia Ratio æqualitatis aliam Rationem mul­<lb/>tiplicans eam non mutat) con&longs;tet autem ex <lb/>demon&longs;tratis AG maiorem e&longs;&longs;e quàm KN, <lb/>&longs;equitur ba&longs;es aquarum CD & OM haber&etail; <lb/>Rationem æqualitatis. </s> <s>At ba&longs;es i&longs;tæ &longs;unt &longs;u­<lb/>perficies va&longs;orum minùs &longs;uperficie &longs;olidi im­<pb xlink:href="018/01/227.jpg" pagenum="213"/>mi&longs;&longs;i; igitur &longs;i ba&longs;ibus æqualibus addantur <lb/>ip&longs;æ æquales &longs;uperficies &longs;olidi, erunt &longs;uperfi­<lb/>cies va&longs;orum æquales: id quod e&longs;t contra hy­<lb/>pothe&longs;im. </s> <s>Non igitur e&longs;t vt VK ad HA ita <lb/>AG ad KN. <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>S<emph.end type="italics"/>it enim iterum, &longs;i fieri pote&longs;t, VK ad <lb/>HA, vt AG ad KN: VK prima vel e&longs;t maior <lb/>quàm AG tertia, vel minor, vel æqualis. </s> <s>Si <lb/>maior, ergo per 14. 5. etiam HA &longs;ecund&atail; <lb/>maior e&longs;t quàm KN quarta; e&longs;t autem VK <lb/>ex dictis etiam maior quàm HA; igitur VK <lb/>e&longs;t maxima & KN minima; igitur per 25. 5. <lb/>VK &longs;imul cum KN maior e&longs;t quàm HA & <lb/>AG &longs;imul, quod e&longs;t contra hypothe&longs;im, iux­<lb/>ta quam VN & HG æquales &longs;unt. </s> <s>Si VK mi­<lb/>nor e&longs;t quàm AG, etiam HA minor e&longs;t quàm <lb/>KN; &longs;ed HA minor e&longs;t quàm VK ex dictis; <lb/>ergo HA e&longs;t omnium minima & AG <expan abbr="omniũ">omnium</expan><lb/>maxima; ergo per 25.5. HG maior e&longs;t quàm <lb/>VN, contra hypothe&longs;im. </s></p><p type="main"> <s>At verò &longs;i demùm VK prima æqualis &longs;it <lb/>AG tertiæ, etiam HA &longs;ecunda æqualis e&longs;t <lb/>KN quartæ: ergo per 7.5. vt VK ad KN ita <lb/>GA ad AH. <!-- KEEP S--></s> <s>At ex demon&longs;tratis vt VK ad KN, <lb/>ita &longs;uperficies va&longs;is maioris minùs &longs;uperficie <lb/>&longs;olidi ad &longs;uperficiem &longs;olidi VY, & vt GA ad <lb/>AH, ita &longs;uperficies &longs;olidi HT, hoc e&longs;t VY, <lb/>ad &longs;uperficiem va&longs;is minoris minùs &longs;uperfi­<pb xlink:href="018/01/228.jpg" pagenum="214"/>cie &longs;olidi. </s> <s>Igitur &longs;uperficies &longs;olidi e&longs;t medio <lb/>loco proportionalis inter differentias, quibus <lb/>&longs;uperficies &longs;olidi exceditur à &longs;uperficiebus va­<lb/>&longs;orum: ergo componendo & permutando vt <lb/>&longs;uperficies va&longs;is maioris ad &longs;uperficiem mi­<lb/>noris, ita &longs;uperficies &longs;olidi HT ad &longs;uperficiem <lb/>va&longs;is minoris minùs &longs;uperficie &longs;olidi, hoc e&longs;t <lb/>&longs;uperficiem aquæ CD. <!-- KEEP S--></s> <s>Sed vt &longs;uperficies &longs;o­<lb/>lidi HT ad &longs;uperficiem CD, ita moles AE <lb/>ad aquam CDFE eiu&longs;dem altitudinis: & quia <lb/>AG ex hypothe&longs;i e&longs;t æqualis ip&longs;i VK, moles <lb/>AE e&longs;t æqualis ip&longs;i moli VO, hoc e&longs;t aquæ <lb/>OMRS. ergo vt &longs;uperficies HT ad &longs;uperfi­<lb/>ciem CD, ita aqua OMRS ad aquam CDFE; <lb/>ergo per 11. 5. vt &longs;uperficies va&longs;is maioris ad <lb/>&longs;uperficiem minoris, hoc e&longs;t vt aquarum al­<lb/>titudines AG ad KN, ita aqua OMRS ad a­<lb/>quam CDFE. <!-- KEEP S--></s> <s>Sunt igitur aquæ inter &longs;e re­<lb/>ciprocè vt earum altitudines: Ratio aute&mtail; <lb/>molium ex Rationibus altitudinum & <expan abbr="ba&longs;iũ">ba&longs;ium</expan> <lb/>componitur, ba&longs;es verò non habent rationem <lb/>æqualitatis; ergo aquarum &longs;uperficies OM <lb/>ad CD &longs;unt in duplicatâ Ratione altitudinum <lb/>reciprocè &longs;umptarum, hoc e&longs;t vt quadratu&mtail; <lb/>GA ad quadratum KN. <!-- KEEP S--></s> <s>Id quod &longs;ic breui­<lb/>ter demon&longs;tro Algebricis notis. </s></p><p type="main"> <s>Sit GA altitudo R, & KN altitudo &longs;it S: <lb/>&longs;uperficies CD &longs;it D planum, & &longs;uperficies <pb xlink:href="018/01/229.jpg" pagenum="215"/>OM &longs;it Z planum. </s> <s>lgitur aqua CDEF e&longs;t <lb/>D plan. <!-- REMOVE S-->in R; & aqua OMRS e&longs;t Z plan; i&ntail; <lb/>S. <!-- KEEP S--></s> <s>Quare cum &longs;it Z plan. <!-- REMOVE S-->in S ad D plan. <!-- REMOVE S-->in R, <lb/>vt R ad S. erit per 16. 6. vel 19. 7. Z pl. </s> <s>in S. <lb/>quadr. </s> <s>æquale D plano in R quadratum: ‘er­<lb/>go Z planum ad D planum, hoc e&longs;t &longs;uperfi­<lb/>cies OM ad &longs;uperficiem CD, e&longs;t vt R qua­<lb/>dratum ad S quadratum: &longs;unt igitur &longs;uperfi­<lb/>cies aquarum in duplicatâ Ratione altitudi­<lb/>num AG ad KN. <!-- KEEP S--></s> <s>At in Ratione AG ad KN <lb/>e&longs;t &longs;uperficies va&longs;is maioris ad &longs;uperficie&mtail; <lb/>minoris, ergo &longs;uperficies OM ad &longs;uperficiem <lb/>CD e&longs;t in duplicatâ Ratione &longs;uperficiei va&longs;is <lb/>maioris ad &longs;uperficiem minoris. </s></p><p type="main"> <s>Datis itaque va&longs;is &longs;imilibus inæqualibus, <lb/>& datâ Ratione &longs;uperficierum huiu&longs;modi va­<lb/>&longs;orum, poterimus reperire &longs;uperficiem &longs;oli­<lb/>di VY aut HT; quæ ex va&longs;orum &longs;uperficie­<lb/><arrow.to.target n="note100"/><lb/>bus dempta reliquam aquæ &longs;uperficiem relin­<lb/>quat in duplicatâ Ratione &longs;uperficierum va­<lb/>&longs;orum. </s> <s>Cum enim &longs;olidorum &longs;uperficies HT, <lb/>VY habeant Rationem æqualitatis, maior e&longs;t <lb/>Ratio totius &longs;uperficiei va&longs;is maioris ad totam <lb/>&longs;uperficiem minoris, quàm ablatæ VY ad <lb/>ablatam HT, ergo per 33 5. apud Clau. <!-- REMOVE S-->ma­<lb/>ior e&longs;t Ratio reliquæ OM ad reliquam CD, <lb/>quàm totius ad totam: quare pote&longs;t etia&mtail; <lb/>haberi Ratio duplicata Rationis totius ad to­<pb xlink:href="018/01/230.jpg" pagenum="216"/>tam. </s> <s>Sic autem inue&longs;tigo &longs;uperficiem VY, <lb/>quæ &longs;it media proportionalis inter differen­<lb/>tias illius & &longs;uperficiei va&longs;orum, hoc e&longs;t in­<lb/>ter OM & CD. </s></p><p type="margin"> <s><margin.target id="note100"/><emph type="italics"/>C <lb/>Ex datis <lb/>duabus &longs;u­<lb/>perficiebus <lb/>auferre ean­<lb/>dem &longs;uperfi­<lb/>ciem, quæ re <lb/>linquat re­<lb/>sidua in Ra­<lb/>tione dupli­<lb/>cata data­<lb/>rum.<emph.end type="italics"/></s></p><p type="main"> <s>Ratio &longs;uperficierum va&longs;orum &longs;it data 8 <lb/>ad 4; Ratio duplicata e&longs;t 8. ad 2. Pono &longs;u­<lb/>perficiem &longs;olidi VY Algebricè 1℞. </s> <s>Quare &longs;u­<lb/>perficies aquæ OM e&longs;t 8——1℞, & &longs;uperfi­<lb/>cies CD e&longs;t 4——1℞: quæ &longs;unt inter &longs;e in du­<lb/>plicatâ Ratione &longs;uperficiei va&longs;orum: igitur <lb/>8——1℞ ad 4——1℞. </s> <s>e&longs;t vt 8 ad 2 ergo per <lb/>19. 7. 16——2℞ æquatur 32——8℞. </s> <s>Et fa­<lb/>ctâ Antithe&longs;i æquatio demum e&longs;t inter 16 & <lb/>6℞. </s> <s>In &longs;titutâ it aque diui&longs;ione 1℞ e&longs;t 2 2/3 &longs;uper­<lb/>ficies VY; quæ ablata ex 8 &longs;uperficie va&longs;is <lb/>maioris relinquit &longs;uperficiem OM 5 1/3, & <lb/>ablata ex &longs;uperficie va&longs;is minoris, hoc e&longs;t ex <lb/>4, relinquit &longs;uperficiem CD 1 1/3: e&longs;t autem <lb/>2 2/3 medio loco proportionalis inter 5 1/3 & 1 1/3, <lb/>quæ præterea &longs;uperficies 5 1/3, & 1/3 &longs;unt in Ra­<lb/>tione duplicatâ Rationis 8 ad 4, hoc e&longs;t in <lb/>Ratione 8 ad 2. Iam verò &longs;i ba&longs;es aquarum <lb/>OM ad CD &longs;int vt 8 ad 2, altitudines ve­<lb/>rò KN & GA reciprocè vt &longs;uperficies va­<lb/>&longs;orum, hoc e&longs;t KN 4, & GA 8, erit aqu&atail; <lb/>OMRS 32, & aqua CDFE 16, planè i&ntail; <lb/>Ratione, quam habent &longs;uperficies va&longs;orum, <lb/>in quibus ip&longs;æ aquæ exi&longs;tunt. </s></p><pb xlink:href="018/01/231.jpg" pagenum="217"/><p type="main"> <s>Quare hoc vno in ca&longs;u quando &longs;uperficies <lb/>&longs;olidi immi&longs;&longs;i e&longs;t media proportionalis inter <lb/>exce&longs;&longs;us, quos relinquit in &longs;uperficiebus va­<lb/>&longs;orum, pote&longs;t contingere eleuationes &longs;olidi <lb/>reciprocari cum depre&longs;&longs;ionibus aquæ; quan­<lb/>do &longs;cilicet eleuatio &longs;olidi in maiori va&longs;e e&longs;t <lb/>æqualis depre&longs;&longs;ioni aquæ in minori, & con­<lb/>trà eleuatio &longs;olidi in minori æqualis e&longs;t de­<lb/>pre&longs;&longs;ioni aquæ in maiori: </s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Operæ profectò pretium fuit hac <lb/>&longs;uper re te interrogare, de qua neminem di­<lb/>&longs;putantem audi&longs;&longs;e me memini aut legi&longs;&longs;e. </s> <s><lb/>Sed vt ad terram aquis delap&longs;is circumfu&longs;am <lb/>reuertamur, eadem-nè erit depre&longs;&longs;ionis aquæ <lb/>Ratio, quæ in va&longs;is, de quibus hactenus fuit <lb/>&longs;ermo? </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Eadem e&longs;&longs;e ratio omnino non po­<lb/>te&longs;t; quia aquæ de&longs;cen&longs;us non ex &longs;olo &longs;patio, <lb/>quod ab eleuatâ terrâ relinqueretur, pende­<lb/>ret, quemadmodum &longs;i globus ex aquâ i&ntail; <lb/>va&longs;e eximeretur, &longs;ed etiam ex diuersâ ip&longs;ius <lb/>aquæ in &longs;phæram conformatione. </s> <s>Cum <lb/>verò aliam &longs;emper & aliam diuer&longs;aru&mtail; <lb/>&longs;phærarum portionem con&longs;titueret, &longs;eu po­<lb/>tius Meni&longs;corum &longs;olidorum, donec demùm <lb/>in &longs;phæram integram aqueam di&longs;poneretur, <lb/>nulla certa & con&longs;tans Ratio afferri pote&longs;t; <lb/>&longs;ed dato certo &longs;patio, quod à centro terræ <pb xlink:href="018/01/232.jpg" pagenum="218"/>translato perficeretur in certâ ab vniuer&longs;i <lb/>centro di&longs;tantiâ, inue&longs;tigare oporteret, cuius <lb/>in &longs;phæræ &longs;uperficiem &longs;e data aquæ moles <lb/>di&longs;poneret in vtroque motûs termino, vt in­<lb/>de colligeretur, quantum terræ ex aquis i&ntail; <lb/>motu illo emer&longs;i&longs;&longs;et. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Ab&longs;tineamus nunc, &longs;i placet, ab <lb/>hoc labore: quamuis datâ &longs;ectione lunulari, <lb/>& inuentis dimidiæ &longs;ectionis centro grauita­<lb/>tis, ac viâ rotationis, po&longs;&longs;emus &longs;oliditatem <lb/>Meni&longs;coidis &longs;phærici inuenire; &longs;atis nunc <lb/>nobis e&longs;&longs;e puto inquirere; quantam in alti­<lb/>tudinem &longs;u&longs;tolli terram oporteret, vt nul­<lb/>lum amplius &longs;ub&longs;idium afferret aqua circum­<lb/>fu&longs;a minuens terræ grauitatem. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Res e&longs;t non adeò difficilis aut ope­<lb/><arrow.to.target n="note101"/><lb/>ro&longs;a. </s> <s>Inuenire &longs;cilicet oportet &longs;emidiame­<lb/><gap/>rum &longs;phæræ, quam &longs;ola aqua con&longs;titueret; <lb/>& huic addere &longs;emidiametrum terræ; hæc <lb/>enim e&longs;&longs;et ea centri terræ atque centri vni­<lb/>uer&longs;i di&longs;tantia, in qua nihil terræ intrà aquam <lb/>e&longs;&longs;et. </s> <s>Vt autem &longs;phæræ, quam aqua effi­<lb/>ceret, &longs;emidiametrum habeamus; cum data <lb/>&longs;it aquæ &longs;oliditas, quam &longs;uperius po&longs;uimus, <lb/>fiat vt 11 ad 21, ita data &longs;phæræ aqueæ &longs;o­<lb/>liditas pa&longs;&longs;. </s> <s>cub. </s> <s>80325. 748768. 500000, <lb/>ad aliud, & prouenit 153349. 156739. <lb/>863636. cubus diametri minoris verâ. </s> <s>Item <pb xlink:href="018/01/233.jpg" pagenum="219"/>fiat vt 223 ad 426, ita data &longs;phæræ &longs;olidi­<lb/>tas 80325. 748768. 500000. ad 153447. <lb/>394508. 434977. cubum diametri maioris <lb/>verâ. </s> <s>Si igitur horum numerorum radix cu­<lb/>bica extrahatur, habebimus &longs;phæræ diame­<lb/>trum tùm minorem, tùm maiorem verâ. </s></p><p type="margin"> <s><margin.target id="note101"/><emph type="italics"/>CI <lb/>Quantu&mtail; <lb/>elenanda e&longs; <lb/>&longs;et tellus, vt <lb/>omnino ab <lb/>aqua &longs;eiun­<lb/>geretur.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Hùc nos deueni&longs;&longs;e gaudeo, no&ntail; <lb/>tantùm vt propo&longs;itæ quæ&longs;tionis metam ali­<lb/>quam attingamus, &longs;ed etiam vt methodum <lb/>ob&longs;eruem, qua cubicam radicem eruere &longs;o­<lb/>les; alijs enim alia e&longs;t methodus, & nimis <lb/>attentum animum exigunt, dum &longs;eor&longs;im in­<lb/>&longs;tituendæ &longs;unt multiplicationes, quæ &longs;ub da­<lb/>tum numerum transferantur: & periculu&mtail; <lb/>&longs;æpius &longs;ube&longs;t, ne per imprudentiam aliu&mtail; <lb/>pro alio numerum &longs;upponas. </s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Vtrum ea, quæ mihi familiaris e&longs;t <lb/>methodus, omnium facillima &longs;it, ignoro: <lb/>mihi tamen arridet magis, cum in pote&longs;tate <lb/>meâ &longs;emper &longs;it operationem totam ex ordi­<lb/>ne recogno&longs;cere. </s> <s>Cæterùm fieri non pote&longs;t, <lb/>quin plures requirantur operationes, cu&mtail; <lb/>præter cubum primi lateris oporteat inueni­<lb/>re &longs;olidum ex triplo quadrato primi lateris in <lb/>latus &longs;ecundum, & &longs;olidum ex triplo later&etail; <lb/>primo in quadratum lateris &longs;ecundi, & de­<lb/>mum ip&longs;ius lateris &longs;ecundi cubum. </s> <s>Quar&etail; <lb/>hic in &longs;chedula, quoniam &longs;ic placet, dato­<pb xlink:href="018/01/234.jpg" pagenum="220"/>rum cuborum radicem extraham in v&longs;u&mtail; <lb/>no&longs;træ quæ&longs;tionis. </s> <s>Hæc autem mihi e&longs;t re­<lb/>gul&atail;. </s></p><p type="main"> <s>Po&longs;t quartam quamque figuram, vt mo­<lb/><arrow.to.target n="note102"/><lb/>ris e&longs;t, puncto notatam, primi puncti latus <lb/>de&longs;cribo & eius cubum extraho, id quod om­<lb/>nibus methodis commune e&longs;t: deinde late­<lb/>ris primi inuenti triplum &longs;cribo &longs;ub penulti­<lb/>má figurâ &longs;ecundi puncti, ip&longs;um verò latus <lb/>primum &longs;ub antepenultimâ figurâ: & hos <lb/>duos numeros inuicem duco, &longs;cilicet triplum <lb/>lateris primi in ip&longs;um: & qui producitur nu­<lb/>merus (&longs;ub antepenultimâ pariter figurâ col­<lb/>locatus) e&longs;t Diui&longs;or; Quotiens verò e&longs;t latus <lb/>&longs;ecundum. </s></p><p type="margin"> <s><margin.target id="note102"/><emph type="italics"/>CII <lb/>Radicis cu­<lb/>bicæ facilis <lb/>extractio.<emph.end type="italics"/></s></p><p type="main"> <s>Tum latus &longs;ecundum duco in triplum la­<lb/>teris primi, & productum &longs;cribo &longs;ub penul­<lb/>timâ figurâ; atquè hunc addo priori produ­<lb/>cto. </s> <s>Summam multiplico per latus &longs;ecun­<lb/>dum, & producto addo Cubum &longs;ecundi la­<lb/>teris collocatum &longs;ub figurâ puncto notatâ. </s> <s><lb/>Summam demùm ex propo&longs;ito numero &longs;ub­<lb/>duco, & &longs;ic deinceps. </s></p><p type="main"> <s>Quoniam it aque numeri hìc propo&longs;iti &longs;unt <lb/>18 ciphrarum, & &longs;unt &longs;ex puncta, vt tempo­<lb/>ri parcam & labori, prima quatuor punct&atail; <lb/>accipio pro primo puncto; & ex Tabulà, in <lb/>qua habeo myriadem cuborum, inuenio ma­<pb xlink:href="018/01/235.jpg" pagenum="221"/>ximum cubum C, cuius latus e&longs;t A: &longs;ubtra­<lb/>ho C ex D, & remanet E, cui addo tres fi­<lb/>guras ad &longs;equens punctum pertinentes. </s> <s>De­<lb/>inde triplico A, & e&longs;t F, quem &longs;ub penulti­<lb/>mâ figurâ colloco, cui &longs;ub&longs;cribo A &longs;ub figu­<lb/>râ antepenultimâ. </s> <s>Duco A in F, & produ­<lb/>citur G: & a&longs;&longs;umpto G tanquam diui&longs;ore nu­<lb/>meri E, habeo Quotientem B, &longs;cilicet latus <lb/>&longs;ecundum: Tum B in F duco, & produci­<lb/>tur H &longs;ub penultimâ figurâ. </s> <s>Additis G & H, <lb/>fit &longs;umma I: quæ per latus &longs;ecundum duct&atail; <lb/>producit K; cui &longs;ub puncto dati numeri &longs;ub­<lb/>&longs;cribitur lateris &longs;ecundi B cubus L; atque ex <lb/>K & L fit &longs;umma M auferenda ex E: & qui re­<lb/>linquitur numerus N, pertinet ad &longs;equens <lb/>punctum. </s></p><p type="main"> <s>Quod &longs;pectat ad numerorum collocatio­<lb/>nem &longs;ub penultimâ vel antepenultimá figu­<lb/><arrow.to.target n="note103"/><lb/>râ, &longs;atis videtis id factum e&longs;&longs;e propter com­<lb/>pendium, quo omittuntur ciphræ nullita­<lb/>tis, vltimo loco addendæ; e&longs;t &longs;iquidem la­<lb/>teris primi numerus decadicus, &longs;i cum late­<lb/>re &longs;ecundo comparetur: quare dum triplica­<lb/>tur, & fit F, vna ciphra nullitatis e&longs;&longs;et &longs;ub <lb/>puncto: & dum hoc triplum per ip&longs;um la­<lb/>tus ducitur, in producto e&longs;&longs;ent vltimo loco <lb/>duæ ciphræ ideò &longs;ub antepenultimâ figurâ <lb/>collocatur numerus productus, vt relinqua­</s></p><pb xlink:href="018/01/236.jpg"/><p type="margin"> <s><margin.target id="note103"/><emph type="italics"/>CIII <lb/>Huius me­<lb/>thodi ratio <lb/>ostenditur.<emph.end type="italics"/></s></p><p type="table"> <s>TABELLE WAR HIER<!-- KEEP S--></s></p><p type="main"><pb xlink:href="018/01/237.jpg" pagenum="223"/> <s>tur locus ciphrarum: id quod vt certiùs fiat, <lb/>colloco A &longs;ub F ita, vt A &longs;it &longs;ub antepenulti­<lb/>mâ figurâ. </s> <s>Quia verò quando B in F duci­<lb/>tur, vnica tantùm e&longs;&longs;et ciphra nullitatis ad <lb/>ip&longs;um F pertinens, ideò productus H &longs;cribi­<lb/>tur &longs;ub penultimâ figurâ. </s> <s>Cubus demùm L <lb/>&longs;ub puncto collocatur, quia nullam habet <lb/>ciphram nullitatis, quæ omittatur. </s><lb/> <s>Quod autem pertinet ad ip&longs;am metho­<lb/>dum, res clara e&longs;t. </s> <s>Dum enim triplum la­<lb/>teris primi ducitur in latus ip&longs;um, hoc e&longs;t F <lb/>in A, producitur G, quod e&longs;t triplum qua­<lb/>drati ip&longs;ius A. <!-- KEEP S--></s> <s>Dum verò B in F ducitur, & <lb/>fit H, planum, quod fit, e&longs;t ex latere &longs;ecun­<lb/>do in triplum lateris primi. </s> <s>Additis G & H <lb/>fit &longs;umma I, hoc e&longs;t 3 A Quad. + 3 A in B. </s> <s><lb/>Hæc &longs;umma multiplicatur per B, & fit K, <lb/>hoc e&longs;t 3 A Quadr. <!-- REMOVE S-->in B + 3 A in B Quadr. <!-- KEEP S--></s> <s><lb/>Additur demum L cubus ip&longs;ius B, vt ip&longs;ius <lb/>lateris A + B cubus &longs;it A cub. + 3 A Quadr. <!-- REMOVE S--><lb/>in B + 3 A in B Quadr. + B cub. </s> </p><p type="main"> <s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/><!-- KEEP S--></s><s> Præ&longs;agiebat animus me aliquid ex <lb/>te auditurum, quod operationem hanc fa­<lb/>cilem redderet atque expeditam, vixque pu­<lb/>to aliquid addi po&longs;&longs;e facilitatis atque per&longs;pi­<lb/>cuitatis; cum nullâ hìc opus &longs;it numerorum <lb/>translatione, & triplicatio lateris primi A, <lb/>aut multiplicatio lateris &longs;ecundi B in F tri­<pb xlink:href="018/01/238.jpg" pagenum="224"/>plum lateris primi facillimè perficiuntur ab&longs;­<lb/>que eo, quod opus &longs;it multiplicatorem &longs;ub <lb/>multiplicando de&longs;cribere. </s> <s>E&longs;t itaque &longs;phæ­<lb/>ræ aqueæ diameter minor verâ pa&longs;&longs;. </s> <s>535254. <lb/>maior autem verâ pa&longs;&longs;. </s> <s>535368. Quare &longs;ta­<lb/>tui pote&longs;t diameter vera pa&longs;&longs;. </s> <s>535300 rotun­<lb/>dè, & &longs;emidiameter mill. <!-- REMOVE S-->267. pa&longs;&longs;: 650: <lb/>quæ &longs;i addatur terreni globi &longs;emidiametro à <lb/>nobis &longs;uperiùs a&longs;&longs;umptæ mill. <!-- REMOVE S-->4128 pa&longs;&longs; 638, <lb/><arrow.to.target n="note104"/><lb/>dabit mill. <!-- REMOVE S-->4356 pa&longs;&longs;. </s> <s>288. di&longs;tantiam cen­<lb/>triterræ ab vniuer&longs;i centro, quando iam aqua <lb/>in &longs;phæram conglobata nihil iuuaret terræ <lb/>motionem. </s> <s>Nunquam autem, puto, ab Ar­<lb/>chimede aliquis exigat machinationum &longs;pe­<lb/>cimen exhiberi tanto motu. </s> <s>Ex quo fit nun­<lb/>quam totius telluris pondus debui&longs;&longs;e ab Ar­<lb/>chimede &longs;u&longs;tineri, atque adeò faciliùs perfi­<lb/>ci potui&longs;&longs;e illam motionem, ac vulgus exi­<lb/>&longs;timet, modò locus &longs;uppeteret, in quo ma­<lb/>chinæ firmarentur. </s> <s>Aqua enim dum deor­<lb/>&longs;um niteretur, quamuis ob minorem in &longs;pe­<lb/>cie grauitatem non po&longs;&longs;et terram &longs;u&longs;tiner&etail;, <lb/>aliquantulum tamen repugnaret de&longs;cenden­<lb/>ti, minueretque &longs;u&longs;tinentis laborem. </s></p><p type="margin"> <s><margin.target id="note104"/><emph type="italics"/>CIV <lb/>Archimedi <lb/>tellurem mo<lb/>uenti per ali­<lb/>quot millia­<lb/>ria, no&ntail; <lb/>fui&longs;&longs;et opus <lb/>totum pon­<lb/>dus &longs;ustine­<lb/>re.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Rectè intuli&longs;ti, quod voleba&mtail;; <lb/>aquâ videlicet infimam terræ portione&mtail; <lb/>&longs;ubeunte ita futurum vt minueretur terræ <lb/>pondus, vt hinc aliqua mouendi aut &longs;u&longs;tinen­<pb xlink:href="018/01/239.jpg" pagenum="225"/>di facilitas oriretur. </s> <s>Quamuis verò facilè per­<lb/>mittam aquam repugnare terræ de&longs;cenden­<lb/>ti, hæc enim intrà aquam de&longs;cendere no&ntail; <lb/>pote&longs;t, quin aquæ &longs;uperficies in maiorem <lb/>&longs;phæram conglobata magis ab vniuer&longs;i cen­<lb/>tro recedat; quia tamen dubitare quis po&longs;­<lb/>&longs;et, an corpora grauia motui &longs;ur&longs;um relu­<lb/>ctentur, quando ita mouerentur, vt nihil <lb/>leuius infrà &longs;e, ac centro vicinius haberent; <lb/>aqua autem tunc ita moueretur, & in orbem <lb/>di&longs;poneretur, vt nihil e&longs;&longs;et centro vicinius, <lb/>infra quod con&longs;i&longs;tere expeteret, nihil enim <lb/>circumflui aëris propiùs abe&longs;&longs;et à centro; <lb/>ideò ex ipsâ minori terræ grauitatione potiùs <lb/>quàm ex aquæ deor&longs;um nitentis re&longs;i&longs;tentiâ <lb/>rem explicandam cen&longs;erem. </s> <s>Grauitas &longs;i­<lb/>quidem e&longs;t vis di&longs;ponendi &longs;e in vniuer&longs;o i&ntail; <lb/>loco &longs;ibi debito infra alia corpora: quò au­<lb/>rem magis di&longs;&longs;imilia &longs;unt corpora &longs;ecundùm <lb/>locum, quem exigunt, & quò plures corpo­<lb/>rum &longs;pecies inter illa deberent intercipi, &longs;i <lb/>iuxta naturæ propen&longs;ionem &longs;ingulæ di&longs;po­<lb/>nerentur, eò etiam grauiora &longs;ecundum &longs;pe­<lb/>ciem &longs;unt ea, quæ centro viciniora e&longs;&longs;e exi­<lb/>gunt. </s> <s>Quarè tota grauitationis ratio & ni&longs;us, <lb/>quo vnum corpus infra aliud de&longs;cendere co­<lb/>natur, in quo exi&longs;tit tanquam in medio, ori­<lb/>tur ex di&longs;&longs;imilitudine &longs;ecundùm grauitatem. <pb xlink:href="018/01/240.jpg" pagenum="226"/>Quò igitur maior e&longs;t grauitatis di&longs;&longs;imilitudo, <lb/>eò pariter maior e&longs;t grauitatio, & conatus <lb/>deor&longs;um validior. </s> <s>Atqui quodcunque pon­<lb/>dus grauius e&longs;t aquâ, e&longs;t multo grauius aëre; <lb/>igitur magis ab aëre differt quàm ab aquâ, <lb/>magi&longs;què in aëre grauitat quàm in aquá: cum <lb/>autem grauitet propter di&longs;&longs;imilitudinem, to­<lb/>ta grauitatio petenda e&longs;t iuxta exce&longs;&longs;um, quo <lb/>&longs;uperat aquæ grauitatem. </s></p><p type="main"> <s>Eâdem ratione ea quæ leuiora &longs;unt aquâ, <lb/><arrow.to.target n="note105"/><lb/>intrà aquam leuitatem habent iuxta differen­<lb/>tiam, qua vincuntur à grauitate aquæ. </s> <s>At­<lb/>que hinc facilè definitur cuiu&longs;cunque &longs;olidi <lb/>innatantis quota portio emergat ex aquâ aut <lb/>alio humido: ibi enim &longs;olidum intrans hu­<lb/>morem con&longs;i&longs;tit, vbi grauitas partis in aëre <lb/>extantis æqualis e&longs;t leuitati portionis in hu­<lb/>mido immer&longs;æ: id autem fit, quando pars <lb/>demer&longs;a ad extantem e&longs;t vt grauitas &longs;pecifi­<lb/>ca &longs;olidi innatantis ad differentiam grauita­<lb/>tum &longs;olidi & humidi. </s> <s>Si enim quæratur <lb/>quota portio plumbi extaret ex mercurio (e&longs;t <lb/>autem plumbum ad mercurium vt 11 ad <lb/>13) &longs;tatim dicetur molis plumbeæ (2/13) extare, <lb/>& (11/13) immergi; quia nimirum &longs;ingulæ partes <lb/>immer&longs;æ in mercurio leuitant vt 2, &longs;ingulæ <lb/>autem in aëre extantes grauitant vt 11. Si <lb/>igitur vt grauitas in aëre ad leuitatem in mer­<pb xlink:href="018/01/241.jpg" pagenum="227"/>curio, ita moles immer&longs;a ad molem extan­<lb/>tem, paria &longs;unt grauitatis & leuitatis mo­<lb/>menta: nam partes 11 leuitantes vt 2 ha­<lb/>bent momentum leuitatis 22; & duæ partes <lb/>in aëre grauitantes vt 11 habent momentum <lb/>grauitatis vt 22; igitur &longs;equitur con&longs;i&longs;tentia. </s> <s><lb/>Quod &longs;i vlteriùs deprimatur plumbum in­<lb/>trà mercurium, augentur leuitatis momen­<lb/>ta, & minuitur grauitas, ideò &longs;ibi relictum <lb/>a&longs;cendit; & &longs;i plures plumbi partes quàm <lb/>(2/13) extrahantur ex mercurio, de&longs;cendet, quia <lb/>grauitatis momenta augentur &longs;upra momen­<lb/>ta leuitatis; & ibi demum quie&longs;cet, vbi fit <lb/>momentorum æqualitas. </s></p><p type="margin"> <s><margin.target id="note105"/><emph type="italics"/>CV <lb/>Quota pars <lb/>&longs;olidi inna­<lb/>tantis emer­<lb/>gat ex hu­<lb/>mido.<emph.end type="italics"/></s></p><p type="main"> <s><emph type="italics"/>Gal.<emph.end type="italics"/><!-- KEEP S--></s><s> Habetis &longs;uper quo ad rauim v&longs;que <lb/>di&longs;putetis, &longs;i hanc per&longs;equi quæ&longs;tionem vo­<lb/>lueritis; & illud forta&longs;&longs;e demum conficietis, <lb/>incertum e&longs;&longs;e, vtrùm grauia in aquâ minùs <lb/>conentur deor&longs;um <expan abbr="quã">quam</expan> in aere, an verò quam­<lb/>uis æquè conentur, minùs tamen proficiant <lb/>propter aquæ in oppo&longs;itum conantis re&longs;i&longs;ten <lb/>tiam: cum vtroque &longs;cilicet experimenta co­<lb/>hærent. </s></p><p type="main"> <s><emph type="italics"/>Guld.<emph.end type="italics"/><!-- KEEP S--></s><s> Haud tanti e&longs;t: &longs;ed i&longs;tis dimi&longs;&longs;is, <lb/>ad alia, &longs;i lubet, tran&longs;eamus: &longs;atis enim pro <lb/>Archimede di&longs;&longs;eruimus. </s></p><p type="main"> <s><emph type="center"/>LAVS DEO.<emph.end type="center"/></s></p><pb xlink:href="018/01/242.jpg"/><p type="main"> <s><emph type="center"/>INDEX<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>RERVM NOTABILIVM<emph.end type="center"/></s></p><p type="main"> <s><emph type="center"/>Prior numerus notam marginalem, po&longs;terior <lb/>paginam indicat.<emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>ARchimedis inuentum helicem fui&longs;&longs;e, procliuius e&longs;t opi­<lb/>nari, num.<emph.end type="italics"/>3 7 </s></p><p type="main"> <s><emph type="italics"/>Axe multiplici in peritrochio faciliùe quàm denticulatis <lb/>tympanis res perficitur, n.<emph.end type="italics"/>4 8 </s></p><p type="main"> <s><emph type="italics"/>Axis in Peritrochio compo&longs;itio, n.<emph.end type="italics"/>5 9 </s></p><p type="main"> <s><emph type="italics"/>Archimedes an trochleis tellurem loco dimouendam existi­<lb/>marit, n.<emph.end type="italics"/>7 13 </s></p><p type="main"> <s><emph type="italics"/>Angulo ob&longs;eruationis quid obsit, & quàm exactè haberi po&longs;­<lb/>&longs;it, num.<emph.end type="italics"/>37 72 </s></p><p type="main"> <s><emph type="italics"/>Angulus depre&longs;&longs;ionis nouo instrumento deprehendi pote&longs;t <lb/>num.<emph.end type="italics"/>37 74 </s></p><p type="main"> <s><emph type="italics"/>Authorum aliquorum lap&longs;us in &longs;tatuenda nimia vi&longs;us di­<lb/>stantia, n.<emph.end type="italics"/>46 94 </s></p><p type="main"> <s><emph type="italics"/>Aquæ &longs;uperficies est &longs;phærica, n.<emph.end type="italics"/>59 119 </s></p><p type="main"> <s><emph type="italics"/>Aqua cur in tubo vtrinque hiante a&longs;cendat aliquantulum, <lb/>num.<emph.end type="italics"/>60 121 </s></p><p type="main"> <s><emph type="italics"/>Aqua mutaret figuram, &longs;i tellus aliò traheretur, n.<emph.end type="italics"/>61 124 <!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>Aqua tota ab ea &longs;eiungeretur Tellure translata, n<emph.end type="italics"/>63 129 </s></p><p type="main"> <s><emph type="italics"/>Aquæ totius quantitas, & grauitas inquiritur, n.<emph.end type="italics"/>64 131 </s></p><p type="main"> <s><emph type="italics"/>Aquæ & aëris grauitates comparantur, & inquiruntur, <lb/>num.<emph.end type="italics"/>69 141 </s></p><p type="main"> <s><emph type="italics"/>Idem alio modo, n.<emph.end type="italics"/>69 144 </s></p><p type="main"> <s><emph type="italics"/>Aeolipilæ experimentum quantum ostendat, n.<emph.end type="italics"/>71 148 </s></p><p type="main"> <s><emph type="italics"/>Aëris communis & aquæ grauitas in aëre ignito minor est, <lb/>quàm fuerit deprehen&longs;a, n.<emph.end type="italics"/>73 154 </s></p><p type="main"> <s><emph type="italics"/>Aëris grauitas non probatur ex differentia ponderum va&longs;is <lb/>pleni et vacui, n.<emph.end type="italics"/>76 161 </s></p><p type="main"> <s><emph type="italics"/>Aquæ tumuluantis cau&longs;a explicatur, n.<emph.end type="italics"/>79 166 </s></p><p type="main"> <s><emph type="italics"/>Eiu&longs;dem experimenti exten&longs;io, & eorum, quæ acci­<emph.end type="italics"/><pb xlink:href="018/01/243.jpg"/><emph type="italics"/>dunt, cau&longs;æ indicantur, n.<emph.end type="italics"/>80 167 </s></p><p type="main"> <s><emph type="italics"/>Aëris igniti leuitas quanta &longs;it in aqua, n.<emph.end type="italics"/>81 172 </s></p><p type="main"> <s><emph type="italics"/>Aquæ an moles compo&longs;ita po&longs;&longs;it innatare nec ne, absque cal­<lb/>culo aquæ æqualis, n.<emph.end type="italics"/>82 174 </s></p><p type="main"> <s><emph type="italics"/>Archimedi tellurem mouenti per aliquot milliaria, non fui&longs;­<lb/>&longs;et opus totum pondus &longs;u&longs;tinere, n.<emph.end type="italics"/>104 224 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>C<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>COchleæ infinitæ compo&longs;itæ vires cum Glo&longs;&longs;ocomo com­<lb/>parantur, n.<emph.end type="italics"/>3 6 </s></p><p type="main"> <s><emph type="italics"/>Cochleæ multiplicis v&longs;us facilior quam Glo&longs;&longs;ocomi, n.<emph.end type="italics"/>3 7 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>F<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>FVnis longitudini occurritur, n.<emph.end type="italics"/>7 11 </s></p><p type="main"> <s><emph type="italics"/>Funis conditio & qualitas ibidem, <lb/>Fabula de altitudine Phari Alexandrinæ reijcitur, n.<emph.end type="italics"/>47 98 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>G<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>GLo&longs;&longs;ocomi, &longs;eu Pancratij con&longs;tructio, n.<emph.end type="italics"/>1 4 </s></p><p type="main"> <s><emph type="italics"/>Glo&longs;&longs;ocomi vires explicantur, n.<emph.end type="italics"/>2 4 </s></p><p type="main"> <s><emph type="italics"/>Globus terrenus in certa hypothe&longs;i innataturus aquæ vide­<lb/>tur, n.<emph.end type="italics"/>87 186 </s></p><p type="main"> <s><emph type="italics"/><gap/>Imo leuior e&longs;&longs;et &longs;ecun dum &longs;peciem aëre, n.<emph.end type="italics"/>88 187 </s></p><p type="main"> <s><emph type="italics"/>Grauitatum ratio duorum corporum in vno medio est ea­<lb/>dem in omni medio, n.<emph.end type="italics"/>90 188 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>H<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>HElicis con&longs;tructionis difficultas & v&longs;us n.<emph.end type="italics"/>4 8 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>I<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>INfernus quantam terræ partem occupet, n.<emph.end type="italics"/>27 51 </s></p><p type="main"> <s><emph type="italics"/>Ignis inferni grauitas quanta &longs;it ex coniectura, n.<emph.end type="italics"/>28 52 </s></p><p type="main"> <s><emph type="italics"/>Ignis variæ &longs;pecies, & qualitas, n.<emph.end type="italics"/>28 54 </s></p><p type="main"> <s><emph type="italics"/>Ignis &longs;ubterraneus e&longs;t quarta pars globi terreni ex &longs;enten­<lb/>tia Wendelini, n.<emph.end type="italics"/>83 177 </s></p><p type="main"> <s><emph type="italics"/>Ignis leuitatis inue&longs;tigatio tentatur, n.<emph.end type="italics"/>84 178 </s></p><p type="main"> <s><emph type="italics"/>Ignis leuitas alia hypothe&longs;i examinatur, n.<emph.end type="italics"/>86 184 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>L<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>LIneæ curuæ pro recta abu&longs;us inutilis, n.<emph.end type="italics"/>40 83 </s></p><p type="main"> <s><emph type="italics"/>Longitudinis differentia inter arcum & eius tangentem <lb/>vel &longs;ubten&longs;am, n.<emph.end type="italics"/>42 85 </s></p><p type="main"> <s><emph type="italics"/>Lineæ curuæ pro recta abu&longs;us cui errori expo&longs;itus, n.<emph.end type="italics"/>45 92 </s></p><p type="main"> <s><emph type="italics"/>Longitudinem vi&longs;us inuenire, n.<emph.end type="italics"/>48 103 </s></p><p type="main"> <s><emph type="italics"/>Leuitas corporum in medio grauiore examinatur in&longs;tru­<lb/>mento, n.<emph.end type="italics"/>85 181 </s></p><pb xlink:href="018/01/244.jpg"/><p type="main"> <s><emph type="center"/><emph type="italics"/>M<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>MAchina quæ intellecta ab Archimede pro motu terra, <lb/>num.<emph.end type="italics"/>0 3 </s></p><p type="main"> <s><emph type="italics"/>Machinarum compo&longs;itio melior e&longs;t quàm earum <expan abbr="augm&etilde;tum">augmentum</expan>, <lb/>&longs;ecundum magnitudinem, n.<emph.end type="italics"/>6 10 </s></p><p type="main"> <s><emph type="italics"/>Moles minor <expan abbr="eiu&longs;d&etilde;">eiu&longs;dem</expan> rei aliquando grauior maiori, n<emph.end type="italics"/>26 49 </s></p><p type="main"> <s><emph type="italics"/>Machina definitur, qua potui&longs;&longs;et tellus moueri ab Archi­<lb/>mede, n.<emph.end type="italics"/>30 60 </s></p><p type="main"> <s><emph type="italics"/>Marini æ&longs;tus noua hypothe&longs;is in dicatur, &longs;ed non probatur, <lb/>num.<emph.end type="italics"/>62 126 </s></p><p type="main"> <s><emph type="italics"/>Moles compo&longs;ita eadem quam &longs;pecificam grauitatem habet <lb/>in vno medio habet in quocunque medio n.<emph.end type="italics"/>91 191 </s></p><p type="main"> <s><emph type="italics"/>Moli compo&longs;itæ &longs;iquid addatur aut dematur eius grauitas <lb/>&longs;pecifica mutatur, n.<emph.end type="italics"/>92 194 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>O<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>OR<gap/>culi pauci in plures minores trochleas di&longs;tributi <lb/>plus po&longs;&longs;unt, quam duæ trochleæ ex multis millibus <lb/>orbiculorum, n.<emph.end type="italics"/>8 14 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>P<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>POndus terreni globi quam notabiliter minueretur i&ntail; <lb/>aquæ &longs;ece&longs;&longs;ione, n.<emph.end type="italics"/>65 133 </s></p><p type="main"> <s><emph type="italics"/>Pondus Telluris in aqua minueretur obinclu&longs;os halitus. </s> <s><lb/>num.<emph.end type="italics"/>68 140 </s></p><p type="main"> <s><emph type="italics"/>POnderis quæ differentia, &longs;i vas nunc plenum, nunc <expan abbr="vacuũ">vacuum</expan> <lb/>in liquore ponderetur.<emph.end type="italics"/>70 146 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>R<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>RAtio maior est, ad terminum multiplicem, quàm ad <lb/>terminum rationis &longs;im<gap/>liter multiplicatæ, n.<emph.end type="italics"/>10 16 </s></p><p type="main"> <s><emph type="italics"/>Ratio duorum grauium in vno medio, vt habeatur, debet <lb/>æquipondium e&longs;&longs;e in eodem medio, n.<emph.end type="italics"/>72 151 </s></p><p type="main"> <s><emph type="italics"/>Radicis cubicæ facilis extractio, n.<emph.end type="italics"/>102 220 </s></p><p type="main"> <s><emph type="italics"/>Huius methodi ratio o&longs;tenditur, n.<emph.end type="italics"/>103 221 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>S<emph.end type="italics"/><emph.end type="center"/></s></p><p type="main"> <s><emph type="italics"/>STatera communi potest ingens pondus moueri, n.<emph.end type="italics"/>16 25 </s></p><p type="main"> <s><emph type="italics"/>Eius constructio, ibid. </s> <s><lb/>Stadij Græci quantitas, n.<emph.end type="italics"/>18 34 </s></p><p type="main"> <s><emph type="italics"/>Solis ob&longs;eruatio difficultatem patitur, n.<emph.end type="italics"/>20 37 </s></p><p type="main"> <s><emph type="italics"/>Stadium Alexandrinum, n.<emph.end type="italics"/>21 38 </s></p><p type="main"> <s><emph type="italics"/>Solis di&longs;tantiam a terra, & proportionem cum illa inue&longs;ti­<lb/>gare inuentis aliquibus, n.<emph.end type="italics"/>23. 40 </s></p><pb xlink:href="018/01/245.jpg"/><p type="main"> <s><emph type="italics"/>Solida plus leuitant ex mercurio in aquam quàm in aerem, <lb/>num.<emph.end type="italics"/>89 187 </s></p><p type="main"> <s><emph type="italics"/>Solidi moles ex humido emergens, maior est mole humidi <lb/>accurrentis ad replendum &longs;patium, n.<emph.end type="italics"/>97 205 </s></p><p type="main"> <s><emph type="italics"/>Solidum idem vt extrabatur ex humido, plus debet eleuari <lb/>in va&longs;e maiori quàm in minori, & plus aquæ de&longs;cendit <lb/>in va&longs;e maiori quàm in minori, n.<emph.end type="italics"/>98 207 </s></p><p type="main"> <s><emph type="italics"/>Solidi eleuationes, & depre&longs;&longs;iones humidi in va&longs;is in æqua­<lb/>libus, non &longs;unt proportionales, ni &longs;i in vno ca&longs;u, n.<emph.end type="italics"/>99 210 </s></p><p type="main"> <s><emph type="italics"/>Superficiem eundem auferre ex datis duabus &longs;uperficiebus <lb/>quæ relinquat re&longs;idua in ratione duplicata dataru&mtail;, <lb/>num.<emph.end type="italics"/>100 215 </s></p><p type="main"> <s><emph type="italics"/>Solidi in natantis quota pars emergat ex humido, n.<emph.end type="italics"/>105 226 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>T<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>TRochleæ vtrilibet adnexum pondus non æquali facili­<lb/>tate mouetur, n.<emph.end type="italics"/>9 15 </s></p><p type="main"> <s><emph type="italics"/>Trochlearum coniugatarum compo&longs;itio, quàm magnas vi­<lb/>res habeat, n.<emph.end type="italics"/>11 18 </s></p><p type="main"> <s><emph type="italics"/>Quantum funium in hac machinatione requiratur, nume­<lb/>ro<emph.end type="italics"/>13 20 </s></p><p type="main"> <s>P<emph type="italics"/>auciores orbiculi in &longs;implicibus trochleis plus po&longs;&longs;unt, <lb/>quam plures in maioribus, n.<emph.end type="italics"/>14 21 </s></p><p type="main"> <s><emph type="italics"/>Terra quot orbiculis moueri po&longs;&longs;it, n.<emph.end type="italics"/>15 22 </s></p><p type="main"> <s><emph type="italics"/>Terræ pondus an paucioribus quàm 30, ciphris explicari <lb/>queat, n.<emph.end type="italics"/>16 28 </s></p><p type="main"> <s><emph type="italics"/>Terræ magnitudo ex communi &longs;ententia, n.<emph.end type="italics"/>16 31 </s></p><p type="main"> <s><emph type="italics"/>Terræ ad &longs;olem proportionem ex &longs;patio quod vmbris caret <lb/>inuestigare, n.<emph.end type="italics"/>17 32 </s></p><p type="main"> <s><emph type="italics"/>Terræ ambitus & diameter, n.<emph.end type="italics"/>19 36 </s></p><p type="main"> <s><emph type="italics"/>Terræ magnitudo probabilior, n.<emph.end type="italics"/>22 39 </s></p><p type="main"> <s><emph type="italics"/>Terræ &longs;oliditas inue&longs;tigatur, n.<emph.end type="italics"/>24 45 </s></p><p type="main"> <s><emph type="italics"/>Eiu&longs;dem grauitas, n<emph.end type="italics"/>25 46 </s></p><p type="main"> <s><emph type="italics"/>Hæc &longs;e habet ac &longs;i e&longs;&longs;et mera argilla, n.<emph.end type="italics"/>26 47 </s></p><p type="main"> <s><emph type="italics"/>Telluris grauitas non tota re&longs;i&longs;teret Archimedi trahenti, <lb/>num.<emph.end type="italics"/>29 58 </s></p><p type="main"> <s><emph type="italics"/>Huius &longs;emidiametrum per primam methodum inuestigare <lb/>cum Trigonometria, & Algebra, n.<emph.end type="italics"/>31 65 </s></p><p type="main"> <s><emph type="italics"/>Aliter & breuius, n.<emph.end type="italics"/>32 66 </s></p><p type="main"> <s><emph type="italics"/>Aliter &longs;ine Trigonometria, n.<emph.end type="italics"/>33 67 </s></p><p type="main"> <s><emph type="italics"/>Item &longs;ine Trigonometria, & &longs;ine Algebra, n.<emph.end type="italics"/>34 68 </s></p><pb xlink:href="018/01/246.jpg"/><p type="main"> <s><emph type="italics"/>Item aliter per Trigonometriam, n.<emph.end type="italics"/>35 68 </s></p><p type="main"> <s><emph type="italics"/>Item aliter, & breui&longs;&longs;imè, n.<emph.end type="italics"/>36 70 </s></p><p type="main"> <s><emph type="italics"/>Trigoni æquilateri v&longs;us ad ob&longs;eruandos angulos in quo <lb/>vix errari po&longs;&longs;it à Geometra, n.<emph.end type="italics"/>38 76 </s></p><p type="main"> <s><emph type="italics"/>Telluris ambitus &longs;ecunda methodo inue&longs;tigatur, n.<emph.end type="italics"/>41 84 </s></p><p type="main"> <s><emph type="italics"/>Tertia methodus inuestigandi ambitum terræ, n.<emph.end type="italics"/>43 88 </s></p><p type="main"> <s><emph type="italics"/>Quarta methodus inueniendi terræ &longs;emidiametrum, n.<emph.end type="italics"/>44 89 </s></p><p type="main"> <s><emph type="italics"/>Quinta methodus terræ &longs;emidiametrum inuestigandi, nu­<lb/>mero<emph.end type="italics"/>48 103 </s></p><p type="main"> <s><emph type="italics"/>Eiu&longs;dem &longs;exe a methodus, n.<emph.end type="italics"/>45 104 </s></p><p type="main"> <s><emph type="italics"/>Idem &longs;eptima methodo inuestigandi, n.<emph.end type="italics"/>50 106 </s></p><p type="main"> <s><emph type="italics"/>Idem octaua methodo inuestigandi, n.<emph.end type="italics"/>51 107 </s></p><p type="main"> <s><emph type="italics"/>Idem aliter, n.<emph.end type="italics"/>52 108 </s></p><p type="main"> <s><emph type="italics"/>Idem nona methodo inquirendi, n.<emph.end type="italics"/>53 110 </s></p><p type="main"> <s><emph type="italics"/>Idem decima methodo inquirendi, n.<emph.end type="italics"/>54 111 </s></p><p type="main"> <s><emph type="italics"/>Idem aliter, n.<emph.end type="italics"/>55 112 </s></p><p type="main"> <s><emph type="italics"/>Idem vndecima methodo inueniendum, n.<emph.end type="italics"/>56 113 </s></p><p type="main"> <s><emph type="italics"/>Idem breuius, n.<emph.end type="italics"/>57 113 </s></p><p type="main"> <s><emph type="italics"/>Idem duodecima methodo inuestigandi, n.<emph.end type="italics"/>58 114 </s></p><p type="main"> <s><emph type="italics"/>Terram mouendi facilitas ex defluxu aquarum, n.<emph.end type="italics"/>66 135 </s></p><p type="main"> <s><emph type="italics"/>Terræ motus facilitas antequam ab aqua &longs;eiungeretur, <lb/>num.<emph.end type="italics"/>67 139 </s></p><p type="main"> <s><emph type="italics"/>Terreni globi grauitas &longs;pecifica maior e&longs;t grauitate argil­<lb/>læ, &longs;i aqua dematur ex globo, n.<emph.end type="italics"/>93 198 </s></p><p type="main"> <s><emph type="italics"/>Telluri &longs;i tribuatur grauitas argillacea, aquæ in latus &longs;e­<lb/>cedenti non innataret, n.<emph.end type="italics"/>94 200 </s></p><p type="main"> <s><emph type="italics"/>Terra intrà aquam minùs ponderaret, n.<emph.end type="italics"/>94 203 </s></p><p type="main"> <s><emph type="italics"/>Terræ grauitas librarum numero probabili explicata, nu­<lb/>mero<emph.end type="italics"/>96 204 </s></p><p type="main"> <s><emph type="italics"/>Tellus quantum eleuanda e&longs;&longs;et, vt omnino ab aqua &longs;eiun­<lb/>geretur, n.<emph.end type="italics"/>101 218 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>V<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p><p type="main"> <s><emph type="italics"/>HVngaricæ aurifodinæ de&longs;criptio, n.<emph.end type="italics"/>26 48 </s></p><p type="main"> <s><emph type="italics"/>Vini grauitas est media harmonicè inter oleum tarta­<lb/>ri, & &longs;piritum vini, n.<emph.end type="italics"/>27 50 </s></p><p type="main"> <s><emph type="italics"/>Vi&longs;us distanti a maxima ex quibæs debeat definiri, n.<emph.end type="italics"/>39 81 </s></p><p type="main"> <s><emph type="italics"/>Venti de&longs;cendentis cau&longs;a obiter indicatur, n.<emph.end type="italics"/>74 155 </s></p><p type="main"> <s><emph type="italics"/>Vacuum tentatum experimento aliquo, & quæ &longs;ita aeris gra­<lb/>uitas, n.<emph.end type="italics"/>75 159 </s></p><p type="main"> <s><emph type="italics"/>Vacuum non dari experimento probatur, n.<emph.end type="italics"/>77 162 </s></p><p type="main"> <s><emph type="center"/><emph type="italics"/>FINIS.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s></p> </chap> </body> <back/> </text></archimedes>