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version 1.9, 2002/07/24 13:04:27

version 1.23, 2002/08/18 16:29:49

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<?xml version="1.0"?>

<!DOCTYPE archimedes [

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info>

<author>Casati, Paolo</author>

<!-- footnotes and margnotes get yanked out of their

<title>Terra machinis mota</title>

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<cvs_file>casat_terra_01_la_1658</cvs_file>

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]><archimedes> <info> <author>Casati, Paolo</author> <title>Terra machinis mota</title> <date>1658</date>

<s><emph type="center"/>TERRA <lb/>MACHINIS MOTA <lb/>DISSERTATIONES<emph.end type="center"/></s>

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<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>

<s><emph type="italics"/>Mer.<emph.end type="italics"/> 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><pb pagenum="2"/>

<s><emph type="italics"/>Mer.<emph.end type="italics"/></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><pb pagenum="2"/>

<s><emph type="italics"/>Gul.<emph.end type="italics"/> 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 &longs;i&longs;tulæ epi&longs;tomio aquam in libertatem <lb/>vindicat. </s>

<s><emph type="italics"/>Gul.<emph.end type="italics"/></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 &longs;i&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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Itane Verò, Galilæe? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> No&longs;tri &longs;ub&longs;ellij erat, quam detule<gap/><lb/>runt litem dirimendam. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> No&longs;tri &longs;ub&longs;ellij erat, quam detule<gap/><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;ilocus, vbi po&longs;&longs;et <expan abbr="cõ&longs;i&longs;tere">con&longs;i&longs;tere</expan>, <lb/>defui&longs;&longs;et. </s>

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<s>Nec planè nullius operæ fuit homi<lb/>nes Mathematicis leui&longs;simè a&longs;pe r&longs;os ad con<lb/>cordiam reuocare; cum alter <expan abbr="diuer&longs;ar&utilde;">diuer&longs;arum</expan> facul-<pb pagenum="3"/>tatum compo&longs;itioni plus ine&longs;&longs;e ad mouen<lb/>dum momenti &longs;atis frigidè cen&longs;eret, alter At<lb/>chimedem in multiplici tympanorum denta<lb/>torum acce&longs;sione facilitatis compendia quæ<lb/>&longs;i&longs;&longs;e affirmaret<gap/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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 in&longs;initâ mechanicu&mtail; <lb/>hoc miraculum fui&longs;&longs;et patraturus. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 in&longs;initâ mechanicu&mtail; <lb/>hoc miraculum fui&longs;&longs;et patraturus. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ita lanè: modò inter nos conue<lb/>niat &longs;ieri 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><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita lanè: modò inter nos conue<lb/>niat &longs;ieri 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 in&longs;initâ idem a&longs;&longs;equi <lb/>potuerit, quod per&longs;icere meditabatur. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Athelicis vires inuentorem &longs;uum <pb pagenum="4"/>atque architectum latuerint? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Athelicis vires inuentorem &longs;uum <pb 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>

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<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Nec ego in&longs;icior, nec diffitetur Gul<lb/>dinus helicis in&longs;initæ 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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Nec ego in&longs;icior, nec diffitetur Gul<lb/>dinus helicis in&longs;initæ 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 pagenum="8"/>hoc potiùs, quod minore operâ parari queat? </s>

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<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 &longs;i<lb/>guram exqui&longs;itè rotundam &longs;i de&longs;ideret, &longs;u<lb/>petuacuo &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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Sed quanto impendio &longs;taret tan<lb/><arrow.to.target n="note7"></arrow.to.target><lb/>tam funium vim comparare, quæ &longs;atis e&longs;&longs;et; <lb/>vt pondus ad vnius decempedæ altitudinem <lb/>&longs;ubleuaretur? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Sed quanto impendio &longs;taret tan<lb/><arrow.to.target n="note7"></arrow.to.target><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 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>

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<s>Vti<lb/>nam & in trochleis &longs;imile funis compen<lb/>dium liceret inuenire. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> An & trochleis tellurem ab Archi<lb/>mede fui&longs;&longs;e loco dimouendam exi&longs;timas? <pb 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><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> An & trochleis tellurem ab Archi<lb/>mede fui&longs;&longs;e loco dimouendam exi&longs;timas? <pb 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>

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<s>Nam &longs;i duas huiu&longs;modi tro<lb/>chleas ità componeres, vt altera ponderiad<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Quæ fuerit Archimedi mens, planè <lb/><arrow.to.target n="note9"></arrow.to.target><lb/>ignoro: potui&longs;&longs;e tamen fieri, vt ille propo&longs;i<lb/>rum trochleis adhibitis a&longs;&longs;equeretur, con<lb/>&longs;tanter a&longs;&longs;ero. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quæ fuerit Archimedi mens, planè <lb/><arrow.to.target n="note9"></arrow.to.target><lb/>ignoro: potui&longs;&longs;e tamen fieri, vt ille propo&longs;i<lb/>rum 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>

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<s><margin.target id="note9"></margin.target><emph type="italics"/>VIII <lb/>Orbiculi <lb/>pauci in plu <lb/>res minores <lb/>tro<gap/>bleas di, <lb/>stributiplus <lb/>po&longs;&longs;unt, <lb/>quàm duæ <lb/>tro<gap/>bleæ ex <lb/>multis mil<lb/>libus orbi<lb/>culorum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Id ego tibi lubens permitto. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Id ego tibi lubens permitto. </s>

<s>Nam <lb/><figure id="fig4"></figure><lb/>&longs;i trochleas duas R & <emph type="italics"/>S<emph.end type="italics"/> pona<lb/><arrow.to.target n="note10"></arrow.to.target><lb/>mus binis orbiculis inftructas, <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>

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<s>vtrili<lb/>bet trochleæ <lb/>adnexu&mtail;, <lb/>demonstra<lb/>tur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Quod præterea Ratione aliquâ mi<gap/><lb/>noris Inæqualitatis propo&longs;itâ, Antecedens <lb/><arrow.to.target n="note11"></arrow.to.target><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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quod præterea Ratione aliquâ mi<gap/><lb/>noris Inæqualitatis propo&longs;itâ, Antecedens <lb/><arrow.to.target n="note11"></arrow.to.target><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, & &longs;iat 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 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>

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<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. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Si igitur trochleæ omnes ABCD <lb/><arrow.to.target n="note13"></arrow.to.target><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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si igitur trochleæ omnes ABCD <lb/><arrow.to.target n="note13"></arrow.to.target><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 pagenum="20"/>cantherius, qui nequear &longs;olus trochlearum <lb/>mulriplicium ope, maius tormentum belli<lb/>cum trahere? </s>

<s><margin.target id="note13"></margin.target><emph type="italics"/>XII <lb/>Vnicus e<lb/>quus f<gap/>cilè <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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Ita planè: &longs;ed ob&longs;eruandum in fu<lb/>nibus. <lb/><arrow.to.target n="note14"></arrow.to.target></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Ita planè: &longs;ed ob&longs;eruandum in fu<lb/>nibus. <lb/><arrow.to.target n="note14"></arrow.to.target></s>

<s><margin.target id="note14"></margin.target><emph type="italics"/>XIII <lb/><gap/>to antum <lb/>funium in <lb/>hac machi<lb/>natione re<lb/>quiratr.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Ne plura: &longs;atis animum ad hoc <lb/>aduerti. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

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<s>Eademque d&etail; <lb/>cæteris, &longs;i plures fuerint trochleæ, ratio e&longs;to. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Non falsâ coniecturâ animum meum <lb/>pro&longs;pexi&longs;ti. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 pagenum="21"/>trochleæ plurium orbiculorum con&longs;tituan</s>

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<s><margin.target id="note16"></margin.target><emph type="italics"/>XV <lb/>Orbiculis <lb/>106 po&longs;&longs;&etail; <lb/>tellure&mtail; <lb/>moueri <expan abbr="de-mõ">de<lb/>mom</expan> &longs;tratur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Quid verò, &longs;i quis maiorem ad<lb/>huc grauitatem telluri tribuat? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Quid verò, &longs;i quis maiorem ad<lb/>huc grauitatem telluri tribuat? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Parum mihi face&longs;&longs;at hic negotij. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 exrra 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> At &longs;taterâ, cuius iugum aliquot <lb/>pa&longs;&longs;uum millia occuparet, &longs;acomatis autem <lb/>munere rupes non exigua &longs;ungeretur. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> At &longs;taterâ, cuius iugum aliquot <lb/>pa&longs;&longs;uum millia occuparet, &longs;acomatis autem <lb/>munere rupes non exigua &longs;ungeretur. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Mittamus i&longs;thæc; quæ à te reru&mtail; <pb pagenum="24"/>huiu&longs;modi apprimè gnaro, animi tantùm <lb/>causâ, in medium proferri &longs;atis video. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Mittamus i&longs;thæc; quæ à te reru&mtail; <pb 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><figure></figure>

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<s>in <emph type="italics"/>S.<emph.end type="italics"/> 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>in <emph type="italics"/>S.<emph.end type="italics"/></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>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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 <gap/>ugenda 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 pagenum="28"/>multiplici componitur. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 <gap/>ugenda 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 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>

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<s>Quantam igitur graui<gap/>tem <lb/>globo huic, qui terras ac maria complecti<lb/>tur, tribuemus? </s><pb pagenum="29"/>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Vereor ne vobis grauis fiam, &longs;i ea <lb/>exponere voluero, quæ aliquando placuit in <lb/>hanc &longs;ententiam commentari. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Vereor ne vobis grauis fiam, &longs;i ea <lb/>exponere voluero, quæ aliquando placuit in <lb/>hanc &longs;ententiam commentari. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Sum planè vacuus: nec facilè patiar <lb/>tam citò abire amicos, quorum eruditâ con<lb/>&longs;uetudine tantoperè recreor. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Si me audieritis, di&longs;putatione&mtail; <lb/>hanc in &longs;equentem diem transferemus; cum <lb/>enim numeris aliquot maioribus<emph type="sup"/>9<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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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"/>9<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Fiat, vt Mer&longs;enno placet. </s><pb pagenum="30"/><figure></figure>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Fiat, vt Mer&longs;enno placet. </s><pb pagenum="30"/><figure></figure>

<s><emph type="center"/>DISSERTATIO <lb/>SECVNDA<emph.end type="center"/></s>

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<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 pagenum="31"/>natione opus habui&longs;&longs;et Archimedes, intelli<lb/>gamus. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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/>c&oelig;pi ad examen reuocare, vt eas, quæ pro<lb/>babili alicui coniecturæ & rationi niterentur, <lb/>à temerè con&longs;titutis, &longs;ecernerem. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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/>c&oelig;pi 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 omuibus <foreign lang="greek">gesmet<gap/>ikk/n a)xri/beian</foreign> de&longs;idera<lb/>rem, & in fingulis 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 cos &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/>e<gap/>im 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>

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<s>antiqua plura quàm 72 <lb/>re&longs;pondent. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> At anguli OCK quantitatem quot <lb/>&longs;crupulis definiebas minorem angulo <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>min. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> At anguli OCK quantitatem quot <lb/>&longs;crupulis definiebas minorem angulo <emph type="italics"/>S<emph.end type="italics"/>OT <lb/>min. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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. </s>

<s><lb/>89.m.45.cuius Secans SO <expan abbr="parti&utilde;">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 &rx;, e&longs;t tota CS 1 &rx; &dagger; 22918384 <lb/>52745, cui ex Tychone æquantur &longs;emidia<lb/>metriterre&longs;tres, 1182, hoc e&longs;t 1182 &rx;. </s>

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<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 Gtæco <lb/>Heronis &longs;cholia&longs;te a&longs;&longs;um p&longs;i&longs;ti, adhibendam <lb/><arrow.to.target n="note21"></arrow.to.target><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"/> Quare Stadium non Romanis pe<lb/>dibus 600 conltat, &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 pagenum="39"/>&longs;ectum à P<gap/>olemæis 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>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 Gtæco <lb/>Heronis &longs;cholia&longs;te a&longs;&longs;um p&longs;i&longs;ti, adhibendam <lb/><arrow.to.target n="note21"></arrow.to.target><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 conltat, &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 pagenum="39"/>&longs;ectum à P<gap/>olemæis 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. </s>

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<s><lb/>parenti, & <lb/>&longs;patio, quod <lb/>vmbris ca<lb/>ret.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Plurimam, opinor, inires gratiam <lb/>ab Eruditi&longs;&longs;. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Plurimam, opinor, inires gratiam <lb/>ab Eruditi&longs;&longs;. </s>

<s>Domino 10. Bapt. </s>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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, & co amplius, ob&longs;eruando venatus <pb 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. </s>

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<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Inuentam terræ &longs;emidiametrum <pb pagenum="45"/>mill. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Inuentam terræ &longs;emidiametrum <pb pagenum="45"/>mill. </s>

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<s>Quoniam verò apud eundem Ghetaldum <lb/>&longs;tanneæ &longs;phæræ, cuius diameter &longs;it vnius pe-<pb pagenum="46"/>dis Rom. </s>

<s>antiqui, grauitas e&longs;t exactè lib. </s>

<s>antiqui, grauitas e&longs;t exactè lib.

<s>304 <lb/>& &longs;phæræ &longs;unt in triplicatâ Ratione diame<lb/>tro rum, &longs;phæra &longs;tannea &longs;emidi ametrum 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>

304 <lb/>& &longs;phæræ &longs;unt in triplicatâ Ratione diame<lb/>tro rum, &longs;phæra &longs;tannea &longs;emidi ametrum 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"></arrow.to.target><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>

<s><margin.target id="note25"></margin.target><emph type="italics"/>XXV <lb/>Terreni glo <lb/>bi grauitas.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ita planè, &longs;i mera e&longs;&longs;et argilla: &longs;ed <lb/>tot marmora ac lapides, ingentesque metal-<pb 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita planè, &longs;i mera e&longs;&longs;et argilla: &longs;ed <lb/>tot marmora ac lapides, ingentesque metal-<pb 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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"></arrow.to.target><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>

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<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 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">aerre</expan>, &longs;ubtili&longs;simisque expirationi<lb/>bus coagmentata mediocrem argillæ graui<lb/>tatem (quantum fas e&longs;t coniectutâ a&longs;&longs;equi) <lb/>obtinere dicatur? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Fallor, &longs;i Tartarus ip&longs;e ad exte<lb/>nuandam terræ grauitatem tibi &longs;uppetias <lb/>non tulerit. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 c&oelig;le&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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Et verò talia afferentem ca&longs;tigare <lb/>quis audeat? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

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<s>in&longs;t. </s>

<s><lb/>cap.

<s>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 vii<lb/>mur, qui ni&longs;i alicuius materiæ fomite alatur, <lb/>extinguitur. </s>

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 vii<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 exibire cogit &c.<emph.end type="italics"/> 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 du xi ab&longs;tinere, ne co-<pb pagenum="57"/>gerer hanc inire di&longs;putatione&mtail;. </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 exibire 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 du xi ab&longs;tinere, ne co-<pb pagenum="57"/>gerer hanc inire di&longs;putatione&mtail;. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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 enucleatiùs 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>

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<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/>grau<gap/>ris. </s><pb pagenum="58"/>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Vnum præterea, quod non parùm <lb/><arrow.to.target n="note29"></arrow.to.target><lb/>in rem tuam facit, Galilæe, audire placeat. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Vnum præterea, quod non parùm <lb/><arrow.to.target n="note29"></arrow.to.target><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="fig8"></figure><lb/>gnaret. </s>

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<s>prop.

<s>2. &longs;unt enim &longs;eg<lb/>menta illa æqualia conis eandem ba&longs;im MN <lb/>habentibus, hi autem ex Eucl. </s>

2. &longs;unt enim &longs;eg<lb/>menta illa æqualia conis eandem ba&longs;im MN <lb/>habentibus, hi autem ex Eucl. </s>

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<s><margin.target id="note30"></margin.target><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"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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 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>

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<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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="fig9"></figure></s><pb pagenum="63"/><figure></figure>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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="fig9"></figure></s><pb pagenum="63"/><figure></figure>

<s><emph type="center"/>DISSERTATIO <lb/>TERTIA<emph.end type="center"/></s>

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<s><margin.target id="note32"></margin.target><emph type="italics"/>XXXII <lb/>Idem aliter, <lb/>& breuiùs.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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;eriptarum inue&longs;tigatio ex Ca-<pb pagenum="67"/>noné de&longs;atigat, &longs;i maximè res ad minimas <lb/>A&longs;t ronomicas fractiones deducta exigat par<lb/>tis proportionalis inqui&longs;itionem. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Satis e&longs;t, &longs;i peritis Geometris hac <lb/>in re fiat &longs;atis. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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"></arrow.to.target><lb/>ne Trigonometrico res tota perfici po&longs;&longs;et, <lb/>&longs;ed non &longs;ine Algebrâ. </s>

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<s><margin.target id="note36"></margin.target><emph type="italics"/>XXXVI <lb/>Idem aliter <lb/>et breui&longs;&longs;i<lb/>mè.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Si perficires commodè po&longs;&longs;it &longs;inè <lb/><arrow.to.target n="note37"></arrow.to.target><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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si perficires commodè po&longs;&longs;it &longs;inè <lb/><arrow.to.target n="note37"></arrow.to.target><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>

<s><margin.target id="note37"></margin.target><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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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;equ<gap/><pb pagenum="72"/>operæ pretium &longs;it. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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;equ<gap/><pb 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 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;itferè &longs;e&longs;quialtera eius, quæ pro<lb/>&longs;picitur ab oculo quinque tantùm pedes à <lb/>terrâ remoto. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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. </s>

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<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/>reliqunm <gap/>quod de&longs;ideremus. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Nec omnibus nec vbique locorum <lb/>commodum erit tuum hoc in&longs;trum<gap/>ntum <lb/>fabricari, quod vel vni loco affixum &longs;it opor<lb/>tet<gap/>vel ægerrimè transferri po&longs;&longs;it. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Nec omnibus nec vbique locorum <lb/>commodum erit tuum hoc in&longs;trum<gap/>ntum <lb/>fabricari, quod vel vni loco affixum &longs;it opor<lb/>tet<gap/>vel ægerrimè transferri po&longs;&longs;it. </s>

<s>Ne&longs;cio <lb/><arrow.to.target n="note38"></arrow.to.target><lb/>quo fato adhu<gap/>penès me in femilacerâ pa<lb/>gellâ dura<gap/>&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>

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<s>Sed mi&longs;sis organis ad in&longs;titutum <lb/>redeamus. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Audiui haud ita pridem hominem, <pb pagenum="81"/>quiex maximâ visûs di&longs;tantiâ, &longs;eu Hori<lb/><arrow.to.target n="note39"></arrow.to.target><lb/>zontis Phy&longs;ici &longs;emidiametro, totius telluris <lb/>&longs;emidiametrum colligere &longs;e po&longs;&longs;e cen&longs;eban. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Audiui haud ita pridem hominem, <pb pagenum="81"/>quiex maximâ visûs di&longs;tantiâ, &longs;eu Hori<lb/><arrow.to.target n="note39"></arrow.to.target><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>

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<s><margin.target id="note40"></margin.target><emph type="italics"/>XXXX <lb/>Abu&longs;us li<lb/>neæ curuæ <lb/>pro rect&atail;, <lb/>inutilis.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Ideò paruiperrdendendam cen&longs;ui <lb/>methodum, quæ mihi aliquando occurrit <lb/><arrow.to.target n="note41"></arrow.to.target><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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Ideò paruiperrdendendam cen&longs;ui <lb/>methodum, quæ mihi aliquando occurrit <lb/><arrow.to.target n="note41"></arrow.to.target><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>

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<s><margin.target id="note41"></margin.target><emph type="italics"/>XXXXI <lb/>Secunda me <lb/>thodus in<lb/>uestigandi <lb/>telluris am<lb/>bitum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Id tamen per &longs;ummam iniuriam <lb/><arrow.to.target n="note42"></arrow.to.target><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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Id tamen per &longs;ummam iniuriam <lb/><arrow.to.target n="note42"></arrow.to.target><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. </s>

<s>Con&longs;tat ex Archimede <lb/>lib. </s>

<s>Con&longs;tat ex Archimede <lb/>lib.

<s>1. de &longs;phær & cyl. </s>

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 pagenum="86"/>BA &longs;imul &longs;umptæ maiores &longs;unt quàm AD, <lb/>igitur exce&longs;&longs;us ip&longs;ius <lb/><figure id="fig20"></figure><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>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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;plicuiffe; &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><emph type="italics"/>Guld.<emph.end type="italics"/></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;plicuiffe; &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 nat<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/>limentriui&longs;&longs;e comperio: nec &longs;anè me pro<lb/>bro&longs;is &longs;uis &longs;timulis vrget inuidentia, qua cæ-<pb 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"></arrow.to.target><lb/>luce narrantes non audierit. </s>

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<s><margin.target id="note44"></margin.target><emph type="italics"/>XXXXIV <lb/>Quarta me<lb/>thodus in<lb/>neniendi ter<lb/>ra &longs;emidia<lb/>metrum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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>

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<s>Hinc Macrobius Saturnal. </s>

<s>lib.

7. <lb/>cap.

<s>14. <emph type="italics"/>Vbicunque terrarum &longs;teteris<emph.end type="italics"/>, inquit, <lb/><emph type="italics"/>videris tibi quandam c&oelig;li 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>

14. <emph type="italics"/>Vbicunque terrarum &longs;teteris<emph.end type="italics"/>, inquit, <lb/><emph type="italics"/>videris tibi quandam c&oelig;li 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>

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<s>cap.

<s>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"/> 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. </s>

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. </s>

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<s>550. Ex qua diametro colligitur am<lb/>bitus longè maior eo, quem Macrobius cum <lb/>Erato&longs;thene con&longs;tituit. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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;eribentes (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><emph type="italics"/>Guld.<emph.end type="italics"/></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;eribentes (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>

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<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 de&longs;initam, ex <lb/>qua tanta ferè colligitur diameter, quant&atail; <lb/>e&longs;&longs;e deberet peripheria. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> An igitur cos 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 â ffirment? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> An igitur cos 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 â ffirment? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Vnde fabulam i&longs;tam Io.Bapt. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vnde fabulam i&longs;tam Io.Bapt. </s>

<s>nat.in proëm. </s>

<s>Por<lb/>ta lib.17. Mag. nat.in proëm. </s>

<s>hau&longs;erit, pror<lb/><arrow.to.target n="note47"></arrow.to.target><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<gap/><lb/>gerim, cum turris illius Alexandrinæ me<lb/>minerint, adeò in&longs;anam altitudinem nobis <pb 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. </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.

<s>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 nonnemini opinandi ad ea v&longs;que tempo<lb/>ra referendum v&longs;um Tubi optici. </s>

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 nonnemini 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>

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<s><lb/>Marcell. </s>

<s>lib.

<s>22. à Cleopatrâ, quæ &longs;oror, & <pb 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>

22. à Cleopatrâ, quæ &longs;oror, & <pb 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>

<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>

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<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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, illi<gap/>ò <lb/>terræ magnitudinem non ritè con&longs;titutam <lb/>calumniabitur, & ad Ari&longs;totelem prouoca<lb/>bit, qui lib. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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, illi<gap/>ò <lb/>terræ magnitudinem non ritè con&longs;titutam <lb/>calumniabitur, & ad Ari&longs;totelem prouoca<lb/>bit, qui lib.

<s>2. de C&oelig;lo text. </s>

2. de C&oelig;lo text. </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/>pliù<gap/> complecti con&longs;tituit. </s><pb pagenum="103"/>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Prouocet: per me licet. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Prouocet: per me licet. </s>

<s>Eum ta<lb/>men monitum velim parum ex Archimede <lb/>&longs;perandum, cum eam <lb/>iHe magnitudinem da<lb/><figure id="fig24"></figure><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>

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<s><margin.target id="note48"></margin.target><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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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;uper&longs;iciem 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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;uper&longs;iciem 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Tentemus pariter, quid po&longs;&longs;imus: <lb/>tertius ade&longs;t Galilæus; ni&longs;i aliquid inueneri<lb/><arrow.to.target n="note49"></arrow.to.target><lb/>mus, dicam nos iratis Mu&longs;is conueni&longs;&longs;e. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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"></arrow.to.target><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;uper&longs;iciei <lb/>adhæreat, cum potiùs ex illâ emineat i&ntail; <lb/>colle DB, cuius altitudo ignota e&longs;t: &longs;ieri 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 pagenum="105"/>con&longs;i&longs;tas angulos CAE, CBF ob&longs;eruaturus. <lb/><figure id="fig25"></figure><lb/>Quibus angulis ob&longs;er<lb/>uatis intellige rectam <lb/>BF occurrere Tangen<lb/>ti AE in G. </s>

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<s><lb/>Idem aliter.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Ea profectò funt, quæ hactenus di<lb/>&longs;putata &longs;nnt, vt vix cen&longs;eam fieri po&longs;&longs;e, vt <lb/>alicui nulla ex his methodis arrideat. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Ea profectò funt, quæ hactenus di<lb/>&longs;putata &longs;nnt, 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 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>

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<s>Sed iam, Mer&longs;enne, cadunt altis d&etail; <lb/>montibus vmbræ; nec Galilæum diutur<lb/>niore colloquio di&longs;tinere &longs;as e&longs;t. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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 ccgamini depo&longs;itum repetituri. </s><pb pagenum="115"/><figure></figure>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 ccgamini depo&longs;itum repetituri. </s><pb pagenum="115"/><figure></figure>

<s><emph type="center"/>DISSERTATIO <lb/>QVARTA<emph.end type="center"/></s>

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<s>PVRGARE ne tibi m&etail; <lb/>debeo, Galilæe, quòd con<lb/>dictam Mer&longs;enno horam te <lb/>adeundi importunus præ<lb/>uenetim? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Si putas Batauis in nouâ Zem<lb/>blâ po&longs;t longas dierum 84 tenebras lu-<pb pagenum="116"/>cem præltolantibus, Solem dies 14 antici<lb/>pantem accidi&longs;&longs;e importunum, ac purgatio<lb/>ne opus habui&longs;&longs;e, quòd legitimum exoriendi <lb/>tem pus 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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Si putas Batauis in nouâ Zem<lb/>blâ po&longs;t longas dierum 84 tenebras lu-<pb pagenum="116"/>cem præltolantibus, Solem dies 14 antici<lb/>pantem accidi&longs;&longs;e importunum, ac purgatio<lb/>ne opus habui&longs;&longs;e, quòd legitimum exoriendi <lb/>tem pus 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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 f&oelig;tum, ve<lb/>riùs dixerim víx dum conceptum, ante t&etail; <lb/>ponere, vt vitæ igniculos illi tuâ luce imper<lb/>tias. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 f&oelig;tum, ve<lb/>riùs dixerim víx dum conceptum, ante t&etail; <lb/>ponere, vt vitæ igniculos illi tuâ luce imper<lb/>tias. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Siccine iuuat fe&longs;tiuis inanium offi<lb/>ciorum argutijs iocari? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld:<emph.end type="italics"/> Ari&longs;totelem fortè præmanibus ha<lb/>bebam; cumque aliud meditans pagellas te<lb/>merè oculo percurrerem, incidi in textum <lb/>78. lib. </s>

<s>2. de C&oelig;lo, vbi Thaletis Mile&longs;ii d&etail; <lb/>causâ terræ quie&longs;centis &longs;ententiam exponit, <pb pagenum="117"/><emph type="italics"/>anquam 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;usapud Senecam à me iam pridem le<lb/>cta lib. </s>

2. de C&oelig;lo, vbi Thaletis Mile&longs;ii d&etail; <lb/>causâ terræ quie&longs;centis &longs;ententiam exponit, <pb pagenum="117"/><emph type="italics"/>anquam 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;usapud Senecam à me iam pridem le<lb/>cta lib.

6. Nat. </s>

<s>quæ&longs;t. </s>

<s>cap.

<s>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>

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. </s>

<s><lb/>Ex quo ille ab eodem Senecâ lib.

3. cap.

<s>13. <lb/>reiectus non &longs;atis aptèterræ motuum cau&longs;am <lb/>inferebat, perindè atque &longs;i nauigium hoc in<lb/>natans concuteretur. </s>

13. <lb/>reiectus non &longs;atis aptèterræ 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 commentitium 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 companari <lb/>po&longs;&longs;e. </s>

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<s>En habes, qui<lb/>bus &longs;timulis actus mihi imperare non potue<lb/>rim, vt à te diutiùs abe&longs;&longs;em. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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 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 præmonni&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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Libens audio, qui contra &longs;en&longs;erint. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Futurum puto, vt plurimum pon<lb/>deris de terreno hoc orbe, qui aquam pariter <lb/>ac terram complectitur, deduceretur. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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"></arrow.to.target><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;icentro vicinior con&longs;i&longs;tat. </s>

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<s><margin.target id="note59"></margin.target><emph type="italics"/>LIX <lb/>Aquæ &longs;u<lb/>perficies est <lb/>&longs;phærica.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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 in&longs;luerent? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 in&longs;luerent? </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>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Veriùs &longs;orta&longs;&longs;e dixeris & attrahi <lb/>pariter & circumpelli: </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Veriùs &longs;orta&longs;&longs;e dixeris & attrahi <lb/>pariter & circumpelli: </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Vbi igitur inferioris o&longs;<gap/> labra &longs;u<lb/>biectam aquam ita attigerint, vt aer &longs;uece<lb/>dere nequeat, illud nece&longs;&longs;ariò fit, vt a&longs;cen<lb/>dentem aetem aqua &longs;ubiecta con&longs;equatur <lb/>&longs;iue attracta, &longs;iue ex circumpul&longs;ione propul<lb/>&longs;a. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Vbi igitur inferioris o&longs;<gap/> labra &longs;u<lb/>biectam aquam ita attigerint, vt aer &longs;uece<lb/>dere nequeat, illud nece&longs;&longs;ariò fit, vt a&longs;cen<lb/>dentem aetem 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;eri<gap/>, 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>

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<s>Atque adeò <lb/>id tibi vltrò concedens audire expecto, quid <lb/>indè conficias. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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="fig29"></figure><lb/><arrow.to.target n="note61"></arrow.to.target><lb/>complectar, <lb/>quod volo, <lb/>ex Graphi<lb/>de <expan abbr="&longs;ub&longs;idi&utilde;">&longs;ub&longs;idium</expan> <lb/><expan abbr="petã">petam</expan>. </s>

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<s><margin.target id="note62"></margin.target><emph type="italics"/>LXII <lb/>Noua bypo<lb/>the&longs;is mari<lb/>ni æstus in<lb/>di<gap/>atur, &longs;ed <lb/>non proba<lb/>tur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Igno&longs;ce, quæ&longs;o, interpellanti. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Igno&longs;ce, quæ&longs;o, interpellanti. </s>

<s>Ne<lb/>&longs;cio quam mihi inijcis &longs;u&longs;picionem no <gap/>æ <lb/>hypothe&longs;is, qua citra omnem <gap/>elluris 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 grauiun<gap/><lb/>congrueret &longs;olùm in medio fluxu aut reflu<lb/>xu. </s>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Blandiuntur i&longs;thæc facilè mentis <pb 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><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Blandiuntur i&longs;thæc facilè mentis <pb 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>

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<s><margin.target id="note63"></margin.target><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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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, donee demum terra pro<lb/>cul à centro translata totius ferè aquæ ponde<lb/>re leuaretur, quæ cirea vniuer&longs;i centrum V <lb/>aqueum in globum &longs;uis &longs;e nutibus confor<lb/>maret. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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, donee demum terra pro<lb/>cul à centro translata totius ferè aquæ ponde<lb/>re leuaretur, quæ cirea vniuer&longs;i centrum V <lb/>aqueum in globum &longs;uis &longs;e nutibus confor<lb/>maret. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ita planè: nec illud quidem con<lb/>temnendum e&longs;&longs;et compendium, &longs;i ponderis <lb/>aquæ rationes ineamus. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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 oporter. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 oporter. </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 pagenum="131"/>tribuendum exi&longs;time&mtail;. </s>

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<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. </s>

<s>80. <lb/>Igitur quia milliare cubicum con&longs;tat pedi<lb/>bus &longs;olidis 125000.000000, hic numerus per <lb/>lib. </s>

80. <lb/>Igitur quia milliare cubicum con&longs;tat pedi<lb/>bus &longs;olidis 125000.000000, hic numerus per <lb/>lib.

<s>80 ductus dabit libras 10.000000.000000 <lb/>grauitatem &longs;ingularium milliarium cubico<lb/>rum aquæ. </s>

80 ductus dabit libras 10.000000.000000 <lb/>grauitatem &longs;ingularium milliarium cubico<lb/>rum aquæ. </s>

<s>Iam &longs;i &longs;oliditas mill. </s>

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<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><pb pagenum="134"/>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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 pet <lb/>&longs;e patet, quàm in&longs;ignis foret i&longs;ta ponderis <lb/>dece&longs;&longs;io. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 pet <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>

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<s><margin.target id="note66"></margin.target><emph type="italics"/>LXVI <lb/>Facilitas <lb/>mouendi ter<lb/>ram ex de<lb/>fluxu aqua<lb/>rum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Opportunè &longs;ugge&longs;&longs;i&longs;ti, quæ m&etail; <lb/>aliò ab&longs;tractum pror&longs;us effugerant. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 longtùs <lb/>abduxerat. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Quid illud e&longs;t? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Minimè omnium: &longs;ed ne&longs;cio quæ <lb/>mens mihi incidit, vt inciperem &longs;u&longs;picari, <pb 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><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Minimè omnium: &longs;ed ne&longs;cio quæ <lb/>mens mihi incidit, vt inciperem &longs;u&longs;picari, <pb 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. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> At ecce Mer&longs;ennum in ip&longs;o tem<lb/>pore. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> At ecce Mer&longs;ennum in ip&longs;o tem<lb/>pore. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> In &longs;acinore manife&longs;to deprehen&longs;i <lb/>p&oelig;nas dabitis, boni viri. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> In &longs;acinore manife&longs;to deprehen&longs;i <lb/>p&oelig;nas 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Salue amicum caput. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 p&oelig;nas. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Vtique leues, &longs;i fuerint peccato <lb/>pares. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vtique leues, &longs;i fuerint peccato <lb/>pares. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 veftri &longs;ermonis con<lb/>&longs;ortium admittentes probaueritis vo<gap/>ihi <lb/>ve&longs;tra cogitata non<gap/>inuidi&longs;&longs;e,<gap/></s><pb pagenum="137"/>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Præclarè nobi&longs;cum agitur, te iudicè. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Præclarè nobi&longs;cum agitur, te iudicè. </s>

<s><lb/>Culpâ vacamus: nam præmium nobis, non <lb/>p&oelig;na decernitur. </s>

<s>Quarè rumpe moras, Gul<lb/>dine, & quæ nobis e&longs;&longs;et di&longs;putatio, edi&longs;<lb/>&longs;ere. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ex ingenitâ aquarum propen&longs;io<lb/>ne, qua &longs;emper ad ima delabuntur, ani mad<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><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ex ingenitâ aquarum propen&longs;io<lb/>ne, qua &longs;emper ad ima delabuntur, ani mad<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="fig32"></figure><lb/>tem <expan abbr="graui&utilde;">grauium</expan> <lb/><expan abbr="elementari&utilde;">elementarium</expan> <lb/>centrum &longs;ta. </s>

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<s><margin.target id="note67"></margin.target><emph type="italics"/>LXVII <lb/>Facilitas <lb/>motus terræ, <lb/>antequa&mtail; <lb/>ab aqua &longs;e<lb/>iungeretur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

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<s>an verò de<lb/>&longs;cenderet? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ex his fluctibus enauigare &longs;olus <lb/>non po&longs;&longs;um: vobis pariter adremigandum <lb/>e&longs;t. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

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<s><margin.target id="note68"></margin.target><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><figure></figure>

<s>Sit enim vas AR æreum <lb/>parallelepipedum <expan abbr="vacu&utilde;">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. </s>

<s>12. Vtique <lb/>&longs;i aquæ imponatur, nata<lb/>bit, cum pes cubicus a<lb/>quæ &longs;it lib. </s>

12. Vtique <lb/>&longs;i aquæ imponatur, nata<lb/>bit, cum pes cubicus a<lb/>quæ &longs;it lib. </s>

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<s><margin.target id="note69"></margin.target><emph type="italics"/>LXIX <lb/>Aquæ & aë<lb/>ris grauita<lb/>tes compa<lb/>rantur, & <lb/>inquirun<lb/>tur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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 c&oelig;pit 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>

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<s>Hinc tamen cert&atail; <lb/>definiri non po&longs;&longs;e momenta, quibus aër <lb/>compre&longs;&longs;us deor&longs;um nitarur, palam e&longs;t. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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 pagenum="145"/>Ita verò &longs;e habuit ob&longs;eruatio. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 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>

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<s>E&longs;tigitur 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. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Quàm vellem hæc omninò veri<lb/>tati congruere! Sed veniam dabis non qui<lb/>dem improbanti conatum, &longs;ed pen&longs;icula-<pb pagenum="146"/><arrow.to.target n="note70"></arrow.to.target><lb/>tiùs examinanti, vtrùm omni pror&longs;us labe <lb/>careat tua hæc argumentatio. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 pagenum="146"/><arrow.to.target n="note70"></arrow.to.target><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. </s>

<s>Sit vas cu<lb/>preum AR molis vnâ cum inclu&longs;o aëre pe<lb/>dalis, & va&longs;is pondus lib.

<s>80, quod e&longs;t pon<lb/>dus pedis cubiciaquæ. </s>

80, quod e&longs;t pon<lb/>dus pedis cubiciaquæ. </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. </s>

<s>80. minùs pondere, quod <lb/>habet aqua &longs;ecundùm molem cupro æqualis. </s>

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. </s>

<s><lb/>Quia igitur moles cupri e&longs;t (8/71) pedis cubici, <lb/>fiat vt 71 ad 8, ita lib.

<s>80 pondus pedis cu<lb/>bici aquæ, ad lib. </s>

80 pondus pedis cu<lb/>bici aquæ, ad lib.

<s>9. (1/71) pondus aquæ æqualis <lb/>cupro va&longs;is. </s>

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>

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<s><margin.target id="note70"></margin.target><emph type="italics"/>LXX <lb/>Sivas 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>

<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. </s>

<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.

<s>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. </s>

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.

<s>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>

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>

<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. </s>

<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.

<s>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 cubiciaquæ, <lb/>quæ impleret va&longs;is &longs;patium ab aëre occupa<lb/>tum, &longs;i aqua illa in aëre extra aquam ex<lb/>penderetut. </s>

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 cubiciaquæ, <lb/>quæ impleret va&longs;is &longs;patium ab aëre occupa<lb/>tum, &longs;i aqua illa in aëre extra aquam ex<lb/>penderetut. </s>

<s>Quemadmodum igitur ex eiu&longs;dem va&longs;is <pb pagenum="148"/><arrow.to.target n="note71"></arrow.to.target><lb/>ponderibus intrà <expan abbr="aquã">aquam</expan>, <expan abbr="quãdo">quando</expan> e&longs;t <expan abbr="plen&utilde;">plenum</expan> aquâ, <lb/>ac quando e&longs;t plenum aëre, rectè infertur ho. <lb/></s>

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<s><margin.target id="note71"></margin.target><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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Non hæc eo con&longs;ilio af&longs;erebam, 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 verita<gap/>e aut à <lb/>tuâ mente alienum intelligerem. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Non hæc eo con&longs;ilio af&longs;erebam, 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 verita<gap/>e 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 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>

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<s>Ergo pariter <lb/>cum vas aëre communi plenum expenderis <lb/>in aëre communi, & iterum in eodem <expan abbr="a&etilde;re">aerre</expan> <pb pagenum="153"/>communi ponderaueris idem vas plenu&mtail; <lb/><expan abbr="a&etilde;re">aerre</expan> ignito, ponderum differentia non e&longs;t <lb/>pondus aëris communis æolipilam implen<lb/>tis. </s>

<s>Exemplo rem declaro: & accipio illud <lb/>idem vas cupreum AR, de quo antea dixi<lb/>mus, quod cum in aëre &longs;it lib. </s>

<s>Exemplo rem declaro: & accipio illud <lb/>idem vas cupreum AR, de quo antea dixi<lb/>mus, quod cum in aëre &longs;it lib.

<s>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. </s>

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.

<s>20; vn<lb/>de jntulimus 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>

20; vn<lb/>de jntulimus 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>

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<s>Quarè nihil hìc certi mihi videor inue<lb/>nire, in quo pedem &longs;igam. </s><pb pagenum="155"/>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Si aliquid intelligo, haud procul <lb/>abes ab eorum &longs;ententiâ, qui omn em aëri <lb/>grauitatem adimunt: idcirco enim rem hanc <lb/>ad viuum re&longs;ecas, vt illa pror&longs;us euane&longs;cat. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si aliquid intelligo, haud procul <lb/>abes ab eorum &longs;ententiâ, qui omn em aëri <lb/>grauitatem adimunt: idcirco enim rem hanc <lb/>ad viuum re&longs;ecas, vt illa pror&longs;us euane&longs;cat. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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>

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<s><margin.target id="note74"></margin.target><emph type="italics"/>LXXIV <lb/>Venti de<lb/>&longs;cendentis <lb/>cau&longs;a obiter <lb/>indicatur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Rectè mones, Galilæe. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Rectè mones, Galilæe. </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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Commodis tuis nos &longs;eruire oportot: <lb/>præterquam quod non hodie diem &longs;ine line â <lb/>duximus. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Commodis tuis nos &longs;eruire oportot: <lb/>præterquam quod non hodie diem &longs;ine line â <lb/>duximus. </s>

<s>Quare bonis auibus perge, quò te <lb/>negotia vocant. </s><pb pagenum="157"/><figure></figure>

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<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 &longs;idei &longs;u&longs;pi<lb/>cio de me &longs;uboriretur, tabulæ de e&longs;&longs;ent, quas <lb/>proferrem. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Nemo no&longs;trûm e&longs;t, qui fidem in<lb/>&longs;irmare audeat Germano candori. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Nemo no&longs;trûm e&longs;t, qui fidem in<lb/>&longs;irmare 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 &longs;idem adhi<lb/>beam. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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>

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<s>Nulla ne aëri tribuend&atail; <lb/>grauitas? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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 pagenum="159"/>tuebatur. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 pagenum="159"/>tuebatur. </s>

<s>Paratum e&longs;t vas vitreum eximiæ <lb/><arrow.to.target n="note75"></arrow.to.target><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>

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<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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Et dubitabis adhuc, an aëri vas <pb pagenum="161"/>implenti tribuendum e&longs;&longs;et pondus; quod aë<lb/>re extracto defuit? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Et dubitabis adhuc, an aëri vas <pb 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Sed quid, &longs;i vas in aquâ expende<lb/><arrow.to.target n="note76"></arrow.to.target><lb/>rent nunc quidem melle, nunc verò aër&etail; <lb/>plenum? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Sed quid, &longs;i vas in aquâ expende<lb/><arrow.to.target n="note76"></arrow.to.target><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>

<s><margin.target id="note76"></margin.target><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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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><emph type="italics"/>Guld.<emph.end type="italics"/></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/>&longs;icitur, 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Non opus e&longs;t corpora amouere, <lb/><arrow.to.target n="note77"></arrow.to.target><lb/>vt progrediatur Philo&longs;ophia in Vacuo. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Non opus e&longs;t corpora amouere, <lb/><arrow.to.target n="note77"></arrow.to.target><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 re&longs;ixi 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>

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<s><margin.target id="note77"></margin.target><emph type="italics"/>LXXVII <lb/>Experimen<lb/>tum probat <lb/>non dari Va <lb/>cuum.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Nullus dubitabam, quin contin-<pb pagenum="164"/><arrow.to.target n="note78"></arrow.to.target><lb/>geret in minori Recipiente minus quoque <lb/><expan abbr="a&etilde;ris">aerris</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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Nullus dubitabam, quin contin-<pb pagenum="164"/><arrow.to.target n="note78"></arrow.to.target><lb/>geret in minori Recipiente minus quoque <lb/><expan abbr="a&etilde;ris">aerris</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>

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<s><margin.target id="note79"></margin.target><emph type="italics"/>LXXIX <lb/>Aquæ tu<lb/>multuantis <lb/>cau&longs;a expli<lb/>catur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Sed quid illud e&longs;t, quod tantum <lb/>a&longs;cendentis aquæ tumultum, bullas, atque <lb/>&longs;pumam excitat? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

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<s><margin.target id="note80"></margin.target><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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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/><gap/>is erat initio antliæ agitatio, &longs;ed demum cò <pb 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><emph type="italics"/>Guld.<emph.end type="italics"/></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/><gap/>is erat initio antliæ agitatio, &longs;ed demum cò <pb 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>

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<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"/> 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 caremu<gap/>? </s><pb pagenum="172"/>

<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 caremu<gap/>? </s><pb pagenum="172"/>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Quam igitur excogita&longs;ti viam, <lb/>qua ad propo&longs;itum quæ&longs;tionis terminum <lb/>euadamus? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Quam igitur excogita&longs;ti viam, <lb/>qua ad propo&longs;itum quæ&longs;tionis terminum <lb/>euadamus? </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Ex ijs, quæ minimum habent du<lb/>bitationis, ad ignota progrediendum cen&longs;eo. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><arrow.to.target n="note81"></arrow.to.target><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. </s>

<s><arrow.to.target n="note81"></arrow.to.target><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.

<s>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>

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>

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<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 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/>terrenihuius globi inclu&longs;is ignibus tribuen<lb/>da &longs;it, quota aëri cæterisque &longs;ialitibus aquâ le<lb/>uioribus, facilè innote&longs;cet, vtrùm leuitas vin<lb/>cat grauicatem, ducto partium numero per <lb/>leuitatis aut grauitatis denominatorem. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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"></arrow.to.target><lb/>no aliquid planè &longs;ingulare accepi&longs;&longs;e, quod <lb/>&longs;um moperè placuit. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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"></arrow.to.target><lb/>no aliquid planè &longs;ingulare accepi&longs;&longs;e, quod <lb/>&longs;um moperè 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>

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<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/<gap/>, erit leuitas ignis <lb/>in aquâ &longs;altem——(6 25<gap/>/1<gap/>). Et id quidem, Gul<lb/>dine, tuà methodo: quanquam ægetrimè <lb/>mihi per&longs;uadeo tantulam leuitatem e&longs;&longs;e igni <lb/>tribuendam. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Vtinam non adeò vorax ignis e&longs;&longs;et, <lb/>& pateretur &longs;e va&longs;culo concludi: ve&longs;tra&mtail; <lb/>ha<gap/> litem momento dirimerem librà, quam <lb/>aliquando excogitaui ad examinandam cor-</s><pb pagenum="181"/>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Vtinam non adeò vorax ignis e&longs;&longs;et, <lb/>& pateretur &longs;e va&longs;culo concludi: ve&longs;tra&mtail; <lb/>ha<gap/> litem momento dirimerem librà, quam <lb/>aliquando excogitaui ad examinandam cor-</s><pb pagenum="181"/>

<s><arrow.to.target n="note85"></arrow.to.target><lb/>porum leuitatem in mercurio. </s>

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<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-<pb 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/>&longs;icies &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. </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.

<s>de in&longs;id. </s>

de in&longs;id. </s>

<s>prop.

<s>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>

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>

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<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, prout opus fuerit, vel demptâ ip&longs;ius <lb/>va&longs;culi intrà aquam grauitate vel leuitate. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Nolo me duriorem præbere i&ntail; <lb/>extenuandâ ignis leuitate, quamuis aëris in <lb/>æolipilâ candenti leuitatem non adeò mul<lb/><gap/>am deprehenderim. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Nolo me duriorem præbere i&ntail; <lb/>extenuandâ ignis leuitate, quamuis aëris in <lb/>æolipilâ candenti leuitatem non adeò mul<lb/><gap/>am deprehenderim. </s>

<s>Vnam aliquam &longs;tatue <pb 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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"></arrow.to.target><lb/>nutat? </s>

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<s><margin.target id="note86"></margin.target><emph type="italics"/>LXXXVI <lb/>Alia bypo<lb/>th<gap/>is de i<lb/>gnis leuit<gap/><lb/><gap/> examina<lb/><gap/>ur.<emph.end type="italics"/></s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Iam planè videris paulò mitiùs <lb/>atque veri&longs;imiliùs opinari. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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/>VVendelini &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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Si perpendantur omnia, forta&longs;sè <lb/>non deberent cen&longs;eri grauiores argillâ. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 alluic <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>

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<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 <gap/>/<gap/> 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 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Quin aquæ grauitatem in <expan abbr="a&etilde;re">aerre</expan> po<lb/><arrow.to.target n="note88"></arrow.to.target><lb/>tiùs, quàm in igne, con&longs;ideras? </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quin aquæ grauitatem in <expan abbr="a&etilde;re">aerre</expan> po<lb/><arrow.to.target n="note88"></arrow.to.target><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>

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<s><margin.target id="note88"></margin.target><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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Lynceus es, Galilæe, nihil no&ntail; <lb/><arrow.to.target n="note89"></arrow.to.target><lb/>vides. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Lynceus es, Galilæe, nihil no&ntail; <lb/><arrow.to.target n="note89"></arrow.to.target><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 circum&longs;u&longs;us, non verò in <lb/>ignem. </s>

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<s><margin.target id="note89"></margin.target><emph type="italics"/>XXCIX <lb/>Solida plus <lb/>leuitant e<gap/><lb/>mercurio in <lb/>aquam <expan abbr="quã">quam</expan> <lb/>in aërem.<emph.end type="italics"/></s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Qui aquam mercurio &longs;uper&longs;udi&longs;ti, <lb/><arrow.to.target n="note90"></arrow.to.target><lb/>cur pariter non circumfudi&longs;ti? </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Qui aquam mercurio &longs;uper&longs;udi&longs;ti, <lb/><arrow.to.target n="note90"></arrow.to.target><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>

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<s><lb/>grauior e&longs;t aëre; cum tamen intrà aqua&mtail; <pb 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Vereor plurimùm, ne i&longs;ta, quæ <lb/><arrow.to.target n="note91"></arrow.to.target><lb/>po&longs;tremo loco attuli&longs;ti, plus habeant &longs;peciei <lb/>quàm veritatis. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Vereor plurimùm, ne i&longs;ta, quæ <lb/><arrow.to.target n="note91"></arrow.to.target><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>

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<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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Qui inter &longs;alebras ambulat, non <lb/>&longs;emper ad numerum gre&longs;&longs;us ponit. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Qui inter &longs;alebras ambulat, non <lb/>&longs;emper ad numerum gre&longs;&longs;us ponit. </s>

<s>Id<gap/> mihi <lb/><arrow.to.target n="note92"></arrow.to.target><lb/>quoquè contigi&longs;&longs;e videtur, qui non &longs;atis di<lb/>lucidè verbis &longs;um complexus, quod vole<lb/>bam. </s>

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<s>grauitas mar<lb/>moris aut alia, cum non videatur a&longs;&longs;umi <lb/>po&longs;&longs;e <gap/>anquam mera argilla, &longs;i tres quadran<lb/>tes ex magnete &longs;tatuantur. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> Ni&longs;i quid addatur aut dematur, <lb/>fieri non pote&longs;t vt grauitas &longs;pecifica variatio<lb/>nem &longs;ubeat, </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Nobis igitur conuenit. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 pagenum="197"/>addatur grauitas aquæ in aere &dagger; 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<gap/>quan<lb/>doquidem vbi cò 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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>

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<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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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"></arrow.to.target><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><emph type="italics"/>Guld.<emph.end type="italics"/></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"></arrow.to.target><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 pagenum="199"/>demptâ &longs;oliditate aquæ, dabit &longs;pecifica&mtail; <lb/>grauitatem globi demptâ aquâ. </s>

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<s>Fieri itaque non pote&longs;t, <lb/>vt terra aquis innatet. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Valeat igitur Thales Mile&longs;ius cum <lb/>&longs;uo illo nauigio. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Valeat igitur Thales Mile&longs;ius cum <lb/>&longs;uo illo nauigio. </s>

<s>F<gap/>&longs;anè <gap/>&longs;tra hac di&longs;puta-<pb 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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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/><gap/> deferat, aeri vtique non &longs;iguræ <gap/><lb/>buenda e&longs;t innatatio, quatenus ex aere, & <pb 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>

<s><emph type="italics"/>Gul.<emph.end type="italics"/> Ita planè, &longs;i terræ tantùm ratio ha<lb/><arrow.to.target n="note95"></arrow.to.target><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. </s>

<s><emph type="italics"/>Gul.<emph.end type="italics"/></s><s> Ita planè, &longs;i terræ tantùm ratio ha<lb/><arrow.to.target n="note95"></arrow.to.target><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. </s>

<s>803.257487.685000.000000. <lb/>Quæ &longs;i ex totius globi grauitate argilla<lb/>ceâ dematur, relinquet reliquæ terræ pon<lb/>dus. </s>

<s><margin.target id="note95"></margin.target><emph type="italics"/>XCV <lb/>Terraintra <lb/>aguam mi<lb/>nùs ponde<lb/>raret.<emph.end type="italics"/></s>

<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 <gap/> ad 9, <pb pagenum="204"/>milliatis autem cubici ex aquâ pondus iam <lb/>inuenerim lib. </s>

<s>10.000000.000000. erit quar<lb/>tus analogiæ terminus lib. </s>

10.000000.000000. erit quar<lb/>tus analogiæ terminus lib.

<s>16.875000.000000 <lb/>pondus vnius milliaris cubici ex argillâ. </s>

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. </s>

<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. </s>

<s>850936000, & prouenit demùm to<lb/>tius globi terraquei grauitas, &longs;i mera argilla <lb/>effet, lib.

<s>4.974539.081161.234545. <lb/>000000. quæ forta&longs;sè paulò maior erit eâ gra<lb/><arrow.to.target n="note96"></arrow.to.target><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>

4.974539.081161.234545. <lb/>000000. quæ forta&longs;sè paulò maior erit eâ gra<lb/><arrow.to.target n="note96"></arrow.to.target><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. </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>

<s><margin.target id="note96"></margin.target><emph type="italics"/>XCVI <lb/>Terræ gra<lb/>uitas libra<lb/>rum nume<lb/>ro<gap/> probabili <lb/>explicata.<emph.end type="italics"/></s>

<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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/>cum&longs;underetur, grauitatem adimerent aquæ, <lb/>parem ponderi molis aqueæ æqualis; neque <pb pagenum="205"/>enim terra vniuer&longs;a intrà aquam demer&longs;&atail; <lb/>delite&longs;ceret. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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/>cum&longs;underetur, grauitatem adimerent aquæ, <lb/>parem ponderi molis aqueæ æqualis; neque <pb 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>

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<s><margin.target id="note97"></margin.target><emph type="italics"/>XCVII <lb/>Solidi moles <lb/>ex bumido <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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> At aquæ illæ nullo va&longs;e contine<lb/>rentur, aut alueo. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> At aquæ illæ nullo va&longs;e contine<lb/>rentur, aut alueo. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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 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>

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<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>

<s><emph type="italics"/>Met&longs;.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Met&longs;.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Nulla e&longs;t &longs;iue directa, &longs;iue recipro-<pb pagenum="210"/>ca inter eleuationes &longs;olidi ac depre&longs;&longs;iones a<lb/><arrow.to.target n="note99"></arrow.to.target><lb/>quæ analogia, præterquàm in vno ca&longs;u. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Nulla e&longs;t &longs;iue directa, &longs;iue recipro-<pb pagenum="210"/>ca inter eleuationes &longs;olidi ac depre&longs;&longs;iones a<lb/><arrow.to.target n="note99"></arrow.to.target><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>

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<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. </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.

<s>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>

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>

<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. </s>

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<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>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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 diuei&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 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Res e&longs;t non adeò difficilis aut ope<lb/><arrow.to.target n="note101"></arrow.to.target><lb/>ro&longs;a. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Res e&longs;t non adeò difficilis aut ope<lb/><arrow.to.target n="note101"></arrow.to.target><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>

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<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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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><emph type="italics"/>Gal.<emph.end type="italics"/></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>

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<s><lb/>in B + 3 A in B Quadr. + B cub. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/> 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 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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></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 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>

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<s><margin.target id="note104"></margin.target><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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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 pagenum="225"/>di facilitas oriretur. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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 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/>circumfiui aëris propiùs abe&longs;&longs;et à centro; <lb/>ideò exipsâ minori terræ grauitatione potiùs <lb/>quàm ex aquæ deor&longs;um nitentis re&longs;i&longs;tentiâ <lb/>rem explicandam cen&longs;erem. </s>

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<s><margin.target id="note105"></margin.target><emph type="italics"/>CV <lb/>Quota pars <lb/>&longs;olidi inna<lb/>tantis emer<lb/>gat ex hu<lb/><gap/>ido.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Gal.<emph.end type="italics"/></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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> 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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/></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>

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