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version 1.12, 2002/08/05 20:41:02

version 1.30, 2003/03/25 15:33:48

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<?xml version="1.0"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info> <author>Casati, Paolo</author> <title>Terra machinis mota</title> <date>1658</date>

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

<author>Casati, Paolo</author>

<title>Terra machinis mota</title>

<cvs_file>casat_terra_01_la_1658</cvs_file>

<cvs_version/>

</info> <text> <front> </front> <body> <chap> <pb/>

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

<s><emph type="center"/>GEOMETRICAE, MECHANICAE <lb/>PHYSICAE, HYDROSTATICAE<emph.end type="center"/></s>

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<s><emph type="center"/><emph type="italics"/>Machinarum Coniugatarum vires inter &longs;e comparantur: <lb/>Multiplici Noua Methodo Terræ magnitudo & <lb/>Grauitas inue&longs;tigatur: ARCHIMEDES <lb/>terræ motionem &longs;pondens ab arrogantiæ <lb/>&longs;u&longs;picione vindicatur.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/>AVTHORE <lb/>PAVLO CASATO <lb/>E SOCIETATE IESV <lb/><figure id="fig1"></figure><lb/>ROMÆ.<emph.end type="center"/></s>

<s><emph type="center"/>AVTHORE <lb/>PAVLO CASATO <lb/>E SOCIETATE IESV <lb/><figure id="fig1"/><lb/>ROMÆ.<emph.end type="center"/></s>

<s><emph type="center"/>Ex Typographia Ignatij de Lazaris. </s>

<s>M.DC.LVIII. <lb/><emph type="italics"/>SVPERIORVM PERMISSV.<emph.end type="italics"/><emph.end type="center"/></s><pb/><figure></figure>

<s>M.DC.LVIII. <lb/><emph type="italics"/>SVPERIORVM PERMISSV.<emph.end type="italics"/><emph.end type="center"/></s><pb/><pb/><figure/>

<s><emph type="center"/>ILLVSTRISS. AC REVERENDISS. DOMINO <lb/>D. IOANNI GEORGIO <lb/>PATRITIO VENETO<emph.end type="center"/></s>

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<s>Tuæ <lb/>erit magnanimitatis exilem hanc ob&longs;equij mei te&longs;&longs;eram non <lb/>contemnere. </s>

<s><emph type="center"/>Amice Lector.<emph.end type="center"/></s>

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<s>Sed quia in motu ip&longs;o aqua in partem &longs;ecederet, <lb/>motumque faciliorem efficeret; examinandum fuit, <pb/>qu antum illa afferre po&longs;&longs;et momenti; id quod &longs;ieri non <lb/>potuit &longs;inè Hydro&longs;taticâ exercitatione, qua ignis terræ <lb/>vi&longs;ceribu, inclu&longs;i, aëris, & aquæ grauitates inuice&mtail; <lb/>conferrentur. </s>

<s>Duas in di&longs;&longs;ertationes tribueram hoc opu&longs;culum, <lb/>cum primùm problema hoc in Collegio Romano <lb/>&longs;ub au&longs;picijs Eminenti&longs;&longs;imi Principis Cardinalis Ha&longs;<lb/>&longs;iæ Lantgrauij explicatum e&longs;t ab Illu&longs;tri&longs;&longs;imo Co<lb/>mite Antonio de Mont&longs;ort. </s>

<s>Sed quoniam di&longs;&longs;ertatio<lb/>nes illæ longiores erant, quàm vt facilè hominem ad <lb/>legendum allicerent, & per tempus non licuerat ad <lb/>marginem notas, qua&longs;i eorum, quæ dicuntur, indices, <lb/>apponere, placuit rem totam in quinque di&longs;&longs;ertationes <lb/>di&longs;pertiri, vt legentium commodo &longs;eruirem, additis ad <lb/>marginem notis. </s>

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<s>Nec te pluribus volo. </s>

<s><emph type="center"/>SYNOPSIS TOTIVS OPERIS: <lb/><emph type="italics"/>DISSERT ATIO PRIMA <lb/>Machinarum vires inter &longs;e comparat. </s>

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<s><lb/>In Prouincia Romana.<emph.end type="center"/></s>

<s>O<emph type="italics"/>Pu&longs;culum, cui titulus e&longs;t Terra Machinis mota à <lb/>P. </s>

<s>O<emph type="italics"/>Pu&longs;culum, cui titulus e&longs;t Terra Machinis mota à <lb/>P. Paulo Ca&longs;ato Societ. </s>

<s>Paulo Ca&longs;ato Societ. </s>

<s>No&longs;træ compo&longs;itum, tres viri <lb/>graues, ac docti Eiu&longs;dem No&longs;træ Societ. </s>

<s>perlegerunt, & <lb/>in lucem edi po&longs;&longs;e iudicarunt: quarè facultate mihi conce&longs;&longs;a <lb/>ab Adm. Reu. Padre No&longs;tro Go&longs;vvino Ni<emph.end type="italics"/>K<emph type="italics"/>el Præpo&longs;ito Ge<lb/>nerali, pote&longs;tatem facio vt imprimatur, &longs;i alijs, ad quos <lb/>&longs;pectat, ità vi&longs;um fuerit. </s>

<s>No&longs;træ compo&longs;itum, tres viri <lb/>graues, ac docti Eiu&longs;dem No&longs;træ Societ. </s>

<s>perlegerunt, & <lb/>in lucem edi po&longs;&longs;e iudicarunt: quarè facultate mihi conce&longs;&longs;a <lb/>ab Adm. </s>

<s>Padre No&longs;tro Go&longs;vvino Ni<emph.end type="italics"/>K<emph type="italics"/>el Præpo&longs;ito Ge<lb/>nerali, pote&longs;tatem facio vt imprimatur, &longs;i alijs, ad quos <lb/>&longs;pectat, ità vi&longs;um fuerit. </s>

<s><emph type="italics"/>Ioannes Rhò<emph.end type="italics"/></s><figure></figure>

<s><emph type="italics"/>Ioannes Rhò<emph.end type="italics"/></s><figure/>

<s><emph type="italics"/>Imprimatur, <lb/>Si videbitur Reuerendi&longs;s. Patri Sa<gap/>ri Palatij Apoct. Mag. <lb/>M. </s>

<s>Oddus Vice&longs;g.<emph.end type="italics"/></s><figure/>

<s><emph type="italics"/>Imprimatur, <lb/>Si videbitur Reuerendi&longs;s. </s>

<s><emph type="italics"/>Imprimatur <lb/>Fr. Vinoentius Maria Guini&longs;ius Magi&longs;ter, & Reuerendi&longs;simi <lb/>P. Fr. Raymundi Capi&longs;u<gap/>bi Sac. Ap<gap/>&longs;t. Pal. Magistri Socius Ord. <lb/>Præd.<emph.end type="italics"/></s>

<s>Patri Sa<gap/>ri Palatij Apoct. </s>

<s>Oddus Vice&longs;g.<emph.end type="italics"/></s><figure></figure>

<s><emph type="italics"/>Imprimatur <lb/>Fr. </s>

<s>Vinoentius Maria Guini&longs;ius Magi&longs;ter, & Reuerendi&longs;simi <lb/>P. Fr. </s>

<s>Raymundi Capi&longs;u<gap/>bi Sac. </s>

<s>Ap<gap/>&longs;t. </s>

<s>Magistri Socius Ord. </s>

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

<s><emph type="center"/>Machinarum vires inter &longs;e <lb/>comparat.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

<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"/></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"/>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"/></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><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"/></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"/>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"/></s><s> 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"/></s><s> 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"/></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"/>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"/></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><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"/></s><s> 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>

<s><margin.target id="note1"></margin.target><emph type="italics"/><lb/>I <lb/>Glo&longs;&longs;ocomi <lb/>&longs;eu Pan<gap/>ra <lb/>tij constru<lb/>ctio. <lb/><emph.end type="italics"/></s>

<s><margin.target id="note1"/><emph type="italics"/><lb/>I <lb/>Glo&longs;&longs;ocomi <lb/>&longs;eu Pan<gap/>ra <lb/>tij constru<lb/>ctio. <lb/><emph.end type="italics"/></s>

<s>Sint tympana dentata quinque maior&atail; <lb/>A, B, C, D, E, totidemque minora F, G, H, <lb/>I, K; maximum A circa eundem axem cum <lb/>cylindro S, cui ductarius &longs;unis circumducitur, <lb/>con uertatur: quatuor minor a F, G, H, I, com<lb/>munem cum maioribus B, C, D, E, quibus <lb/>&longs;ingula in axe eodem cohærent, habeant con<lb/>uer&longs;ionem: minimum verò K, addito manu<lb/>brio LM, circùm &longs;e torqueatur, & ex illo <lb/>totius machinæ motus initium &longs;umat. </s>

<s>Ma<lb/>nubrii autem flexus LM, ad tympani K &longs;emi<lb/>diametrum Rationem habeat quintupla&mtail;; <lb/>&longs;ibique pariter reliqua tympana, maiora vi<lb/>delicet cum minoribus &longs;ibi cohærentibus <lb/>comparata, pro portione re&longs;pondeant: nec <lb/>maximi tympani A Radius, atque cylindri <lb/>S illi infixi &longs;emidiameter, à Ratione hac quin<lb/>tuplâ di&longs;sideant. </s>

<s><margin.target id="note2"></margin.target><emph type="italics"/><lb/>II <lb/>Glo&longs;&longs;ocomi <lb/>vires e<gap/>pli<lb/><gap/>tur. <lb/><emph.end type="italics"/></s>

<s><margin.target id="note2"/><emph type="italics"/><lb/>II <lb/>Glo&longs;&longs;ocomi <lb/>vires e<gap/>pli<lb/><gap/>tur. <lb/><emph.end type="italics"/></s>

<s>His ita con&longs;titutis &longs;atis liquet potentiam <lb/>in M applicatam quintuplo velociorem e&longs;&longs;e <lb/>peripheriâ E, quæ ex mutuâ &longs;uorum denti<lb/>culorum ac tympani K collabellatione con<lb/>uertitur. </s>

<s>At peripheria E quintuplo pariter <pb/><figure id="fig2"></figure><pb pagenum="6"/>velociùs mouetur quàm D, & D quàm C, & C <lb/>quàm B, & B quàm A, & A quàm S, hoc e&longs;t <lb/>pondus P illi adne xum. </s>

<s>At peripheria E quintuplo pariter <pb/><figure id="fig2"/><pb pagenum="6"/>velociùs mouetur quàm D, & D quàm C, & C <lb/>quàm B, & B quàm A, & A quàm S, hoc e&longs;t <lb/>pondus P illi adne xum. </s>

<s>Igitur motus poten<lb/>tiæ in M (liceat in pagellâ rem ad calculos <lb/>reuocare) ad <expan abbr="mot&utilde;">motum</expan> ponderis P e&longs;t vt 15625 <lb/>ad 1. &longs;unt nimirum &longs;ex Rationes quintuplæ, <lb/>ex quibus Ratio motûs potentiæ ad motum <lb/>ponderis componitur. </s>

<s>Quare potentia, quæ <lb/>ab&longs;que machinæ &longs;ub&longs;idio centum pondo mo <lb/>uere valeret, hac adhibitâ machinâ pondus <lb/>P librarum 1562500. attollet. </s>

<s><margin.target id="note3"></margin.target><emph type="italics"/><lb/>III <lb/>Cochleæ in<lb/>finitæ Com<lb/>po&longs;itæ uires <lb/>cum Glo&longs;&longs;o<lb/>como com<lb/>parantur. <lb/><emph.end type="italics"/></s>

<s><margin.target id="note3"/><emph type="italics"/><lb/>III <lb/>Cochleæ in<lb/>finitæ Com<lb/>po&longs;itæ uires <lb/>cum Glo&longs;&longs;o<lb/>como com<lb/>parantur. <lb/><emph.end type="italics"/></s>

<s>Iam verò in minorum tympanorum FG <lb/>HIK locum reponantur helices maioru&mtail; <lb/>tympanorum ABCDE denticulis (quos 25 in <lb/>toto ambitu fui&longs;&longs;e exempli gratia &longs;tatuamus) <lb/>congruentes: ip&longs;aque tympana cum &longs;uis <lb/>axibus in &longs;piram deformatis in quadrato lo<lb/>culamento, vt helicis in&longs;initæ natura fert, <lb/>aptè di&longs;ponantur. </s>

<s>Con&longs;tat tympani A pe<lb/>ripheriam quintuplo tantùm velociorem e&longs;&longs;e <lb/>pondere P; at peripheriam B vigequintuplo <lb/>velociorem quàm A: vnicus enim tympani A <lb/>denticulus promouetur ab integrâ ip&longs;ius B <lb/>conuer&longs;ione; ideoque vt &longs;emel A gyrum ab<lb/>&longs;oluat, vicies & quinquies tympanum B con<lb/>uertatur oportet. </s>

<s>Eademque ratione tympani <lb/>C motus cum tympani B motu comparatur, <lb/>cuiuse&longs;t vigequintuplus: quemadmodum & <pb pagenum="7"/>Dip&longs;ius C, & E ip&longs;ius D, & M ip&longs;ius E. </s>

<s>Quare <lb/>Ratio motûs potentiæ M ad motum ponderis <lb/>P, ex vnicâ Ratione quintuplâ, & quinque <lb/>vigequintuplis componitur: E&longs;t igitur motus <lb/>potentiæ ad motum ponderis vt 48828125 <lb/>ad 1: & potentia, quæ pondo centum valeat <lb/>attollere, pondus librarum 4882812500 <lb/>mouebit. </s>

<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"/></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><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>

<s><arrow.to.target n="note4"></arrow.to.target><lb/>Atqui tympanorum ambitum in denticulos <lb/><figure id="fig3"></figure><lb/>æquales di&longs;tribue<lb/>re, eosque &longs;atis &longs;it<lb/>mos, ne facilè vi <lb/>ponderis commi<lb/>nuantur, & i&ntail; <lb/>cylindro ver&longs;atili <lb/>helicem tympani <lb/>denticulis ritè <expan abbr="cõ-gruentem">con<lb/>gruentem</expan> incide<lb/>re, haud &longs;anè o<lb/>&longs;citantem exigunt <lb/>arti&longs;icem. </s>

<s><arrow.to.target n="note4"/><lb/>Atqui tympanorum ambitum in denticulos <lb/><figure id="fig3"/><lb/>æquales di&longs;tribue<lb/>re, eosque &longs;atis &longs;it<lb/>mos, ne facilè vi <lb/>ponderis commi<lb/>nuantur, & i&ntail; <lb/>cylindro ver&longs;atili <lb/>helicem tympani <lb/>denticulis ritè <expan abbr="cõ-gruentem">con<lb/>gruentem</expan> incide<lb/>re, haud &longs;anè o<lb/>&longs;citantem exigunt <lb/>arti&longs;icem. </s>

<s>Porrò <lb/>a&longs;&longs;iduus ille toe <lb/>partium &longs;e inui<lb/>cem atterentium <lb/>affrictus mora&mtail; <lb/>infert non leuem. </s>

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<s>&longs;ici po&longs;&longs;e multiplici axe in peritrochio, qui <lb/>& leui negotio paratur, & moram recipit nul<lb/>lam ex mutuâ membrorum affrictione. </s><pb pagenum="9"/>

<s><margin.target id="note4"></margin.target><emph type="italics"/><lb/>IV <lb/>Difficulta<lb/>tes in heli<lb/>cis constru<lb/>ctione & <lb/><gap/>&longs;<gap/>. <lb/><emph.end type="italics"/></s>

<s><margin.target id="note4"/><emph type="italics"/><lb/>IV <lb/>Difficulta<lb/>tes in heli<lb/>cis constru<lb/>ctione & <lb/><gap/>&longs;<gap/>. <lb/><emph.end type="italics"/></s>

<s>A&longs;&longs;umantur quinque cylindri ABCDE <lb/><arrow.to.target n="note5"></arrow.to.target><lb/>cra&longs;&longs;itudine inæquali (quo enim magis à <lb/>pondere di&longs;tant, graciliores e&longs;&longs;e po&longs;&longs;unt) <lb/>&longs;ingulisque rota canaliculum in ambitu ex<lb/>cauatum habens adijciatur, cuius d<emph type="italics"/>i<emph.end type="italics"/>ameter <lb/>diametri cylindri &longs;ibi cohærentis quintupla <lb/>&longs;it. </s>

<s>A&longs;&longs;umantur quinque cylindri ABCDE <lb/><arrow.to.target n="note5"/><lb/>cra&longs;&longs;itudine inæquali (quo enim magis à <lb/>pondere di&longs;tant, graciliores e&longs;&longs;e po&longs;&longs;unt) <lb/>&longs;ingulisque rota canaliculum in ambitu ex<lb/>cauatum habens adijciatur, cuius d<emph type="italics"/>i<emph.end type="italics"/>ameter <lb/>diametri cylindri &longs;ibi cohærentis quintupla <lb/>&longs;it. </s>

<s>Demùm cylindro F addatur manubrium <lb/>OP eandem Rationem quintuplam habens <lb/>ad illius &longs;emidiametrum. </s>

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<s>Maiore tame&ntail; <lb/>forta&longs;sè compendio, quod hìc rotæ cylindros <lb/>non atterant, nec vllum immineat pericu<lb/>lum, ne ex mutuâ illâ collabellatione den<lb/>tes aliquando excutiantur: quàm ægrè au<lb/>tem excu&longs;&longs;i dentis detrimento occurras, pa<lb/>làm e&longs;t; cum tamen di&longs;ruptum &longs;unem ite<lb/>rum facilè connectas. </s>

<s><margin.target id="note5"></margin.target><emph type="italics"/><lb/>V <lb/>Axes in Pe<lb/>ritrochio <expan abbr="Cõ">Com</expan> <lb/>po&longs;iti faci<lb/>liùs con&longs;tru <lb/>untur, & <lb/>idem præ&longs;ta <lb/>re po&longs;sunt. <lb/><emph.end type="italics"/></s>

<s><margin.target id="note5"/><emph type="italics"/><lb/>V <lb/>Axes in Pe<lb/>ritrochio <expan abbr="Cõ">Com</expan> <lb/>po&longs;iti faci<lb/>liùs con&longs;tru <lb/>untur, & <lb/>idem præ&longs;ta <lb/>re po&longs;sunt. <lb/><emph.end type="italics"/></s>

<s>Vbi licet obiter animum aduertere ad <pb pagenum="10"/><arrow.to.target n="note6"></arrow.to.target><lb/>multorum artificum imperitiam, qui ex ma<lb/>chinarum tantùm augmento vires ad mo<lb/>uenda pondera augeri autumantes, multo la<lb/>bore, nec modicâ argenti iacturâ immanes <lb/>aliquando machinas con&longs;truunt, quæ vel mo<lb/>le &longs;uâ prægrauatæ fati&longs;cunt, vel motam mo<lb/>tui inferunt non mediocrem, adeò vt &longs;olius <lb/>machinæ motio, etiam &longs;eclu<gap/>o pondere, cui <lb/>mouendo de&longs;tinatur machina, validioris po<lb/>tentiæ vires ab&longs;umat: cum tamen rem to<lb/>tam minore negotio, nec &longs;pernendo pecu<lb/>niæ atquè laboris compendio, perficere po&longs;<lb/>&longs;ent, &longs;i rectè intelligerent, quantum machi<lb/>narum compo&longs;itio præ&longs;tet earum augmento. </s>

<s>Vbi licet obiter animum aduertere ad <pb pagenum="10"/><arrow.to.target n="note6"/><lb/>multorum artificum imperitiam, qui ex ma<lb/>chinarum tantùm augmento vires ad mo<lb/>uenda pondera augeri autumantes, multo la<lb/>bore, nec modicâ argenti iacturâ immanes <lb/>aliquando machinas con&longs;truunt, quæ vel mo<lb/>le &longs;uâ prægrauatæ fati&longs;cunt, vel motam mo<lb/>tui inferunt non mediocrem, adeò vt &longs;olius <lb/>machinæ motio, etiam &longs;eclu<gap/>o pondere, cui <lb/>mouendo de&longs;tinatur machina, validioris po<lb/>tentiæ vires ab&longs;umat: cum tamen rem to<lb/>tam minore negotio, nec &longs;pernendo pecu<lb/>niæ atquè laboris compendio, perficere po&longs;<lb/>&longs;ent, &longs;i rectè intelligerent, quantum machi<lb/>narum compo&longs;itio præ&longs;tet earum augmento. </s>

<s><lb/>Id quod ex quinque his axibus in Peritrochio <lb/>inter &longs;e compo&longs;itis luculenti&longs;&longs;imè demon<lb/>&longs;tratur; &longs;i enim axi, cuius diameter palma<lb/>ris, rotam velis infigere, qua po&longs;&longs;is ide&mtail; <lb/>mouere pondus, quod tribus tantùm ex pro<lb/>po&longs;itis rotis A, B, C, mouetur, quàm imma<lb/>nis illa erit? </s>

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<s>Adde quòd illam ex alio in a<lb/>lium locum transferendi pro multiplici ne<lb/>ce&longs;&longs;itate, vix &longs;pes aliqua &longs;upere&longs;&longs;et. </s>

<s><margin.target id="note6"></margin.target><emph type="italics"/>VI <lb/>Machina<lb/>rum Com<lb/>po&longs;itio me<lb/>lior e&longs;t, <expan abbr="quã">quam</expan> <lb/>earum Aug<lb/>mentum, &longs;e<lb/>cundùm ma <lb/>gnitudinem<emph.end type="italics"/></s>

<s><margin.target id="note6"/><emph type="italics"/>VI <lb/>Machina<lb/>rum Com<lb/>po&longs;itio me<lb/>lior e&longs;t, <expan abbr="quã">quam</expan> <lb/>earum Aug<lb/>mentum, &longs;e<lb/>cundùm ma <lb/>gnitudinem<emph.end type="italics"/></s>

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

<s>Primùm enim funis, cui pon<lb/>dus adnecteretur, decem pedes in longitudi<lb/>ne haberet; igitur qui rotam primam A am<lb/>biret, e&longs;&longs;et vt minimùm pedum 50. At rotæ <lb/>&longs;ecundæ motus e&longs;&longs;et prioris quintuplus, igi-<pb 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>Nam &longs;i mul<lb/>tiplici &longs;pirarum &longs;erie ita duceretur funis, vt <lb/>ip&longs;e &longs;e circumplecteretur, motuum Ratio<lb/>nes, &, quod inde con&longs;equitur, potentiæ mo<lb/>menta, ip â euolutione mutarentur, auctis <lb/>&longs;cilicet aut diminutis ex &longs;ubiectâ &longs;pirarum &longs;e<lb/>rie rotarum ac cylindorum diametris. </s>

<s><margin.target id="note7"></margin.target><emph type="italics"/>VII <lb/>Difficultasi <lb/>ex funis lox <lb/>gitudine.<emph.end type="italics"/></s>

<s><margin.target id="note7"/><emph type="italics"/>VII <lb/>Difficultasi <lb/>ex funis lox <lb/>gitudine.<emph.end type="italics"/></s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Hæc eadem, quæ nunc obijcis, mi<lb/><arrow.to.target n="note8"></arrow.to.target><lb/>hi pariter aliquandò nonnihil fecere negotij. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Hæc eadem, quæ nunc obijcis, mi<lb/><arrow.to.target n="note8"/><lb/>hi pariter aliquandò nonnihil fecere negotij. </s>

<s><lb/>Et primùm quidem earum rotularum, qua<lb/>rum velocior e&longs;t motus, funes quoquè gra<lb/>ciliores e&longs;&longs;e debere ob&longs;eruabam, quippe qui<lb/>bus ponderis grauitas minùs reluctetur. </s>

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<s>Deinde quamuis non adeò lon<lb/>gus &longs;uppeteret funiculus, operæ pretium vi<lb/>debatur futurum, &longs;i illo euoluto rotas &longs;i-<pb pagenum="13"/>&longs;teremus (annulum videlicet auer&longs;æ rotæ A <lb/>infixum arctè cum &longs;uperiore cylindro n&etail; <lb/>pondus relaberetur, connectentes) explica<lb/>tum que funiculum, qui in conuer&longs;ione fui&longs;<lb/>&longs;et cylindrum &longs;uperiorem circumplexus, ite<lb/>rum rotæ ap&longs;idi circumduceremus. </s>

<s><margin.target id="note8"></margin.target><emph type="italics"/>Occurritur.<emph.end type="italics"/></s>

<s><margin.target id="note8"/><emph type="italics"/>Occurritur.<emph.end type="italics"/></s>

<s>Verùm cum vrbem obambulans oculos <lb/>fortè in officinam quandam conijcerem, vbi <lb/>obtu&longs;arum nouacularum acies re&longs;tituuntur, <lb/>En, inquam, funiculus in&longs;e&longs;e rediens maio<lb/>ri ac minori rotulæ ità circumplicatus, vt al<lb/>tera ex alterius conuer&longs;ione rotetur, nullos <lb/>motui terminos præ&longs;cribit: quidni igitur con<lb/>&longs;imili ratione funiculus vnâ aut alterâ &longs;pirâ <lb/>cylindrum &longs;uperiorem complectens &longs;ubie<lb/>ctum peritrochium ita apprehendere valeat, <lb/>vt pariter moueantur, nec conuer&longs;ionis &longs;i<lb/>nem inueniant, cum tantundem &longs;uccedere <lb/>po&longs;&longs;it funiculi, quantum dece&longs;&longs;erit? </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"/></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><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"/></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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Quæ fuerit Archimedi mens, planè <lb/><arrow.to.target n="note9"/><lb/>ignoro: potui&longs;&longs;e tamen fieri, vt ille propo&longs;i<lb/>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>Id quod vt minimè dubia de<lb/>mon&longs;tratione conficiam; illud primum, in <lb/>trochleatum v&longs;u extra controuer&longs;iam po&longs;i<lb/>tum accipio, quod, funis extremo trochleæ, <pb pagenum="15"/>cui pondus adnectitur, alligato, potentia re<lb/>liquum extremum arreptum trahens plus <lb/>obtinet ad mouendum momenti, quàm &longs;i <lb/>funis alteri trochleæ à pondere remotæ ad<lb/>necteretur; in primo enim ca&longs;u motus po<lb/>tentiæ ad motum ponderis maiorem habet <lb/>Rationem, quàm in &longs;ecundo. </s>

<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><margin.target id="note9"/><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"/></s><s> 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>

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

<s>Iam <lb/>verò plurimum intere&longs;t, vtri <lb/>trochlearum pondus adiunxe<lb/>ris: &longs;i enim pondus in R ad<lb/>nectatur, potentia K tamdiu <lb/>mouetur, ac ab <emph type="italics"/>S<emph.end type="italics"/> recedit, do<lb/>nec funistotus explicetur: per<lb/>currit igitur &longs;patium funis <lb/>longitudini æquale, videlicet <lb/>quadruplum interualli inter <lb/>R & S. </s>

<s>At verò &longs;i pondus in <lb/>S alligetur, eadem potenti&atail; <pb pagenum="16"/>K ad trochleam R fixam accedit, illamqu&etail; <lb/>tanto &longs;patio tran&longs;greditur, quanta e&longs;t funis <lb/>longitudo: igitur in toto motu percurrit &longs;pa<lb/>tium quintuplum eius, quod à pondere ver<lb/>sùs trochleam R moto perficitur. </s>

<s>Quoniam <lb/>autem quò tardior e&longs;t ponderis motus cum <lb/>motu potentiæ comparatus, eò minùs pon<lb/>deris grauitas virtuti potentiæ trahentis ob<lb/>&longs;i&longs;tit; apertum e&longs;t ac manife&longs;tum faciliùs <lb/>trahi pondus, &longs;i trochleæ S (cui funis in A <lb/>adnectitur) quàm &longs;i trochleæ R alligetur: in <lb/>S nimirum motum obtinet motûs potentiæ <lb/>&longs;ubquintuplum, in R autem &longs;ubquadru<lb/>plum. </s>

<s><margin.target id="note10"></margin.target><emph type="italics"/>IX <lb/>Non æqua<lb/>li facilitate <lb/>moueri pon<lb/>dus. </s>

<s><margin.target id="note10"/><emph type="italics"/>IX <lb/>Non æqua<lb/>li facilitate <lb/>moueri pon<lb/>dus. </s>

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

<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><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"/><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>

<s><margin.target id="note11"></margin.target><emph type="italics"/>X <lb/>Maiorest <lb/>Ratio ad ter <lb/>minu&mtail; <lb/>Misltipli<lb/>cem, quàm <lb/>ad termi<lb/>num Ratio<lb/>nis &longs;imiliter <lb/>Multiplica<lb/>tæ.<emph.end type="italics"/></s>

<s><margin.target id="note11"/><emph type="italics"/>X <lb/>Maiorest <lb/>Ratio ad ter <lb/>minu&mtail; <lb/>Misltipli<lb/>cem, quàm <lb/>ad termi<lb/>num Ratio<lb/>nis &longs;imiliter <lb/>Multiplica<lb/>tæ.<emph.end type="italics"/></s>

<s>Hinc infero maximum e&longs;&longs;e di&longs;crimen i&ntail; <lb/>augendo potentiæ momento, vtrùm trochleæ <lb/>augeantur orbiculis, an verò trochleæ mul<lb/>tiplices exii&longs;dem orbiculis con&longs;tituantur. </s>

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<s>Sint duæ trochleæ binos orbiculos haben<lb/>tes A & B: huic autem tum pondus P, <gap/>m <lb/>funis extremum adnectatur. </s>

<s>Vtique poten-<pb pagenum="18"/><arrow.to.target n="note12"></arrow.to.target><lb/><figure id="fig5"></figure><lb/>tia in F motum ha<lb/>beret quintuplò velo<lb/>ciorem motu ponde<lb/>ris P. </s>

<s>Vtique poten-<pb pagenum="18"/><arrow.to.target n="note12"/><lb/><figure id="fig5"/><lb/>tia in F motum ha<lb/>beret quintuplò velo<lb/>ciorem motu ponde<lb/>ris P. </s>

<s>Ex quatuor a<lb/>lijs orbiculis duæ pa<lb/>riter trochleæ D & C <lb/>con&longs;tituantur: & tro<lb/>chleæ C adnectatur <lb/>prioris funis <expan abbr="extrem&utilde;">extremum</expan>. </s>

<s><lb/>Potentia E quintuplò <lb/>&longs;anè velociùs moue<lb/>tur quàm F, at F quin<lb/>tuplò velociùs quàm <lb/>P; igitur motus po<lb/>tentiæ E ad motum <lb/>ponderis P e&longs;t vt 25 <lb/>ad 1. Quare potentia <lb/>vires habens decem <lb/>pondo trahendi &longs;inè <lb/>machinâ, in F trahe<lb/>ret libras 50, at in E <lb/>libras 250. Quod &longs;i <lb/>tam A quàm B qua<lb/>ternos haberent or<lb/>biculos, potentia i&ntail; <lb/>F tantum 90 libras <lb/>mouere po&longs;&longs;et. </s>

<s><margin.target id="note12"></margin.target><emph type="italics"/>XI <lb/>Trochlea<lb/>rum coniu<lb/>gataru&mtail; <lb/>Compo&longs;itio, <lb/>quàm ma<lb/>gnas vires. </s>

<s><margin.target id="note12"/><emph type="italics"/>XI <lb/>Trochlea<lb/>rum coniu<lb/>gataru&mtail; <lb/>Compo&longs;itio, <lb/>quàm ma<lb/>gnas vires. </s>

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

<s>Con&longs;tat itaque du-<pb pagenum="19"/>plicatis trochleis æquali orbiculorum nume<lb/>ro in&longs;tructis, motum potentiæ in E haber&etail; <lb/>Rationem duplicatam Rationis, quam habet <lb/>motus potentiæ in F ad motum ponderis in <lb/>P: multiplicatis autem pari numero in ea<lb/>dem trochleâ orbiculis, ne duplicari quidem <lb/>motum ip&longs;ius potentiæ F. </s>

<s>Quod &longs;i in E pa<lb/>riter duæ aliæ trochleæ &longs;imiles adiicerentur, <lb/>iam triplicaretur Ratio motûs in F ad mo<lb/>tum in P, & &longs;ic deinceps. </s>

<s>Vno verbo di<lb/>cam: quot &longs;unt paria &longs;imilium trochlearum, <lb/>progre&longs;&longs;io fit tot Rationum &longs;imilium Ratio<lb/>ni, quam habet motus ponderis ad motum <lb/>potentiæ primis trochleis applicatæ. </s>

<s>Sic &longs;i <lb/>e&longs;&longs;ent talium, quales exhibui, trochlearu&mtail; <lb/>paria decem, a&longs;&longs;umendæ e&longs;&longs;ent decem Ra<lb/>tiones quintuplæ; & motus potentiæ ad mo<lb/>tum ponderis Rationem haberet ex his com<lb/>po&longs;itam, quam &longs;cilicet habet vndecimus ter<lb/>minus in progre&longs;sione Rationis quintuplæ <lb/>ad vnitatem, hoc e&longs;t 9765625 ad 1. </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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Si igitur trochleæ omnes ABCD <lb/><arrow.to.target n="note13"/><lb/>tri&longs;pa&longs;ti e&longs;&longs;ent, vnicus equus in E idem pon<lb/>dus trahere po&longs;&longs;et, quod equi 49; cum ta<lb/>men in F, &longs;i A & B tripa&longs;ti fuerint, idem <lb/>valeat trahere quod equi &longs;eptem: &longs;i vero A <lb/>& B &longs;enis in&longs;truerentur orbiculis, æquiuale<lb/>ret equis tredecim. </s>

<s>Quis ergo adeò debilis <pb 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><margin.target id="note13"/><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"/></s><s> 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"/></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><margin.target id="note14"/><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"/></s><s> 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"/></s><s> 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>

<s>Exhibeantur enim, exempli gratiâ, orbi<lb/>culi 60, ex quibus &longs;i fiant 20 trochleæ trium <lb/>orbiculorum, iam &longs;unt decem trochlearum <lb/>paria, ac proinde decem Rationes vt &longs;um<lb/>mum &longs;eptuplæ; igitur momenrum potentiæ, <lb/>hoc e&longs;t vndecimus ab vnitate terminus, e&longs;t <lb/>vt 282475249. Si verò fiant binos haben<lb/>tes orbiculos, erunt 15 trochlearum pari&atail; <gap/><lb/>ideoq quindecim Rationes quintuplæ, ex qui<lb/>bus Ratio motûs potentiæ ad motum ponde<lb/>ris componitur; erit igitur vt 30517578125 <lb/>ad 1. Con&longs;tat autem ne additis quidem ad<lb/>huc duobus tri&longs;pa&longs;torum paribus, vt &longs;int in <lb/>vniuer&longs;um orbiculi 72, po&longs;&longs;e adeò augeri po<lb/>tentiæ momentum: po&longs;itis &longs;iquidem 12 tri<lb/>&longs;pa&longs;torum paribus momentum potentiæ e&longs;t <lb/>&longs;olùm vt 13841287201. Hinc colligitur <lb/>plus ad mouendum momenti obtinere pau<lb/>ciores orbiculos in &longs;implicioribus trochleis, <lb/>quàm in trochleis maioribus plures orbicu<lb/>los: id quod alicui forta&longs;sè paradoxum ac<lb/>cidat. </s>

<s><margin.target id="note15"></margin.target><emph type="italics"/>XIV <lb/>Pauciores <lb/>orbiculos in <lb/>&longs;implicibus <lb/>trochleis <lb/>plus po&longs;&longs;&etail;, <lb/>quàm plu<lb/>res in mai&atail; <lb/>ribus o&longs;ten<lb/>ditur.<emph.end type="italics"/></s>

<s><margin.target id="note15"/><emph type="italics"/>XIV <lb/>Pauciores <lb/>orbiculos in <lb/>&longs;implicibus <lb/>trochleis <lb/>plus po&longs;&longs;&etail;, <lb/>quàm plu<lb/>res in mai&atail; <lb/>ribus o&longs;ten<lb/>ditur.<emph.end type="italics"/></s>

<s>Nunc igitur &longs;i mihi orbiculos centum ex<lb/>hibeas, &longs;implices trochleas ex &longs;ingulis orbi<lb/>culis &longs;tatuo, fiuntquè 50 trochlearum &longs;im<lb/>plicium paria: adnexo autem pondere eidem <lb/>trochleæ, cui funis extremum alligatur, mo-<pb pagenum="22"/>mentum potentiæ erit triplum: &longs;unt igitur <lb/>50 Rationes triplæ, ex quibus componitur <lb/>Ratio motûs potentiæ ad motum ponderis. </s>

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<s>Ratio autem tripla quintuplicata e&longs;t 243 <lb/>ad 1. Ducatur 243 per &longs;e ip&longs;um, & e&longs;t Ra<lb/>tio decuplicata 59049 ad 1. Hic iterum ter<lb/>minus 59049 per &longs;e ip&longs;um ducatur, & Ratio <lb/>3486.784401 ad 1 e&longs;t ex viginti Rationi<lb/>bus triplis compo&longs;ita. </s>

<s>Ducatur pariter 3486. <lb/>784401 per &longs;e ip&longs;um, & e&longs;t Ratio ex qua<lb/>draginta Rationibus triplis compo&longs;ita 12. <lb/>157665.459056.928801. ad 1. Hæc de<lb/>mùm Ratio ducatur per Rationem triplam <lb/>decuplicatam nimirum per 59049, & pro<lb/>ducitur Ratio, quæ ex 50 Rationibus tri<lb/>plis componitur 717897.987691.852588. <lb/>770249. ad 1. </s>

<s>Quod &longs;i placeat duas adhuc trochleas ter<lb/>nis orbiculis in&longs;tructas adijcere ip&longs;ique pon<lb/>deri immediatè adnectere, vt funium &longs;eptu<lb/>plici ductu faciliùs &longs;u&longs;tineri valeat, adhuc <lb/>Ratio &longs;eptupla addenda, vt ex hac & 50 tri<lb/>plis tota Ratio componatur: & quinquage&longs;i<lb/>mus primus terminus progre&longs;sionis Rationis <lb/>triplæ ducendus e&longs;t per 7, vt habeatur totum <pb pagenum="23"/><arrow.to.target n="note16"></arrow.to.target><lb/>potentiæ momentum 5025285.913842. <lb/>968121.391743. Quarè adhibito conatu, <lb/>quo libras decem ab&longs;què machinâ traheres, <lb/>mouere po&longs;&longs;es libras 50.252859.138429. <lb/>681213.917430. Quod pondus totius ter<lb/>reni globi grauitatem &longs;uperat. </s>

<s>Quod &longs;i placeat duas adhuc trochleas ter<lb/>nis orbiculis in&longs;tructas adijcere ip&longs;ique pon<lb/>deri immediatè adnectere, vt funium &longs;eptu<lb/>plici ductu faciliùs &longs;u&longs;tineri valeat, adhuc <lb/>Ratio &longs;eptupla addenda, vt ex hac & 50 tri<lb/>plis tota Ratio componatur: & quinquage&longs;i<lb/>mus primus terminus progre&longs;sionis Rationis <lb/>triplæ ducendus e&longs;t per 7, vt habeatur totum <pb pagenum="23"/><arrow.to.target n="note16"/><lb/>potentiæ momentum 5025285.913842. <lb/>968121.391743. Quarè adhibito conatu, <lb/>quo libras decem ab&longs;què machinâ traheres, <lb/>mouere po&longs;&longs;es libras 50.252859.138429. <lb/>681213.917430. Quod pondus totius ter<lb/>reni globi grauitatem &longs;uperat. </s>

<s>Orbiculis ita<lb/>que &longs;ex &longs;upra centum Archimedæum pro<gap/><lb/>blema de terræ motione ab&longs;olui po&longs;&longs;e o&longs;ten<lb/>di. </s>

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

<s>Erige enim ad perpendiculum trabes <gap/>uas <lb/>æquali interuallo à &longs;e inuicem di&longs;tinctas: A&longs;<lb/>&longs;umaturque vectis AB, cuius pars decim&atail; <pb pagenum="25"/>&longs;it AC, (quanquam id &longs;culptor non expre&longs;<lb/><arrow.to.target n="note17"></arrow.to.target><lb/>&longs;it) & extremum A &longs;it circa axem trabi AO <lb/>infixum ver&longs;atile, extremum verò B ita à <lb/>trabe ER di&longs;ter, vt a&longs;&longs;umpto &longs;imili vect&etail; <lb/>DE circùm E ver&longs;atili, & vtroque DE, AB <lb/>parallelo horizonti, perpendicularis BF &longs;e<lb/>cet pariter FE partem decimam totius DE. </s>

<s>Erige enim ad perpendiculum trabes <gap/>uas <lb/>æquali interuallo à &longs;e inuicem di&longs;tinctas: A&longs;<lb/>&longs;umaturque vectis AB, cuius pars decim&atail; <pb pagenum="25"/>&longs;it AC, (quanquam id &longs;culptor non expre&longs;<lb/><arrow.to.target n="note17"/><lb/>&longs;it) & extremum A &longs;it circa axem trabi AO <lb/>infixum ver&longs;atile, extremum verò B ita à <lb/>trabe ER di&longs;ter, vt a&longs;&longs;umpto &longs;imili vect&etail; <lb/>DE circùm E ver&longs;atili, & vtroque DE, AB <lb/>parallelo horizonti, perpendicularis BF &longs;e<lb/>cet pariter FE partem decimam totius DE. </s>

<s><lb/>Idquè in con&longs;equentibus vectibus factum in<lb/>telligatur. </s>

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<s>moueri po&longs;&longs;int; ac po&longs;tremus vectis <lb/>MR habeat propè V lingulam &longs;eu momen<lb/>tum, vt quandò trabi ER congruit, &longs;ignifi<lb/>cet vectes omnes con&longs;titutos e&longs;&longs;e horizonti <lb/>parallelos. </s>

<s><margin.target id="note17"></margin.target><emph type="italics"/>XVI <lb/>Statera <expan abbr="cõ-muni">con<lb/>muni</expan> pote&longs;t <lb/>ingens pon<lb/>dus exami<lb/>nari.<emph.end type="italics"/></s>

<s><margin.target id="note17"/><emph type="italics"/>XVI <lb/>Statera <expan abbr="cõ-muni">con<lb/>muni</expan> pote&longs;t <lb/>ingens pon<lb/>dus exami<lb/>nari.<emph.end type="italics"/></s>

<s>Tum applicatâ in M &longs;taterâ examinetur <lb/>omnium vectium &longs;imul momentum graui<lb/>tatis. </s>

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<s>Tum &longs;acoma <lb/>in &longs;tateræ iugo ab aginâ remoueatur adeò, <lb/>vt vectis MR (atque adeò reliqui omnes) <lb/>horizonti parallelus con&longs;tituatur, & &longs;tatera <lb/>indicet æquilibrium ex. </s>

<s>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> 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"/></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><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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Line 475

<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"/></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"/>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"/></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"/>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"/></s><s> 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"/></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"/>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"/></s><s> 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/>

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

<s><emph type="center"/>Terræ grauitatem inue<lb/>&longs;tigat.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Galilæus, Mer&longs;ennus, Guldinus.<emph.end type="italics"/><emph.end type="center"/></s>

<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"/></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><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>

<s>Perpendens itaque corporum vmbras ideo <lb/>&longs;emper in oppo&longs;itam Soli plagam proijci, <pb pagenum="32"/><arrow.to.target n="note18"></arrow.to.target><lb/>quia nulla Solis particula ad perpendiculum <lb/>imminet corpori, quod luce afficitur, i&ntail; <lb/>&longs;pem erigebar aliquid deprehendendi ex &longs;pa<lb/>tio circa Syenen ab antiquis apud Cleome<lb/>dem ob&longs;eruato, in quo gnomones nullam <lb/>proijciun<gap/> vmbram meridianam Sole Tro<lb/>picum Cancri percurrente. </s>

<s>Perpendens itaque corporum vmbras ideo <lb/>&longs;emper in oppo&longs;itam Soli plagam proijci, <pb pagenum="32"/><arrow.to.target n="note18"/><lb/>quia nulla Solis particula ad perpendiculum <lb/>imminet corpori, quod luce afficitur, i&ntail; <lb/>&longs;pem erigebar aliquid deprehendendi ex &longs;pa<lb/>tio circa Syenen ab antiquis apud Cleome<lb/>dem ob&longs;eruato, in quo gnomones nullam <lb/>proijciun<gap/> vmbram meridianam Sole Tro<lb/>picum Cancri percurrente. </s>

<s>Si enim in pla<lb/>no AB erigatur &longs;tylus TI perpendicularis, <lb/>cui immineat Solis extremus limbus O, nul<lb/>la fit vmbra, quia quamuis ab alio extremo S <lb/>veniat radius SN vltimus, & intrà &longs;patium <lb/><figure id="fig6"></figure><lb/>TN nullus alius ve<lb/>niat radius ab eodem <lb/>puncto S radios in or<lb/>bem diffundente, in<lb/>trà illud tamen &longs;pa<lb/>tium TN veniunt <lb/>radij à cæteris om<lb/>nibus punctis inter <lb/>S & O intermediis: <lb/>quare nec vmbra vl<lb/>la aut penumbra ob&longs;eruari pote&longs;t. </s>

<s>Si enim in pla<lb/>no AB erigatur &longs;tylus TI perpendicularis, <lb/>cui immineat Solis extremus limbus O, nul<lb/>la fit vmbra, quia quamuis ab alio extremo S <lb/>veniat radius SN vltimus, & intrà &longs;patium <lb/><figure id="fig6"/><lb/>TN nullus alius ve<lb/>niat radius ab eodem <lb/>puncto S radios in or<lb/>bem diffundente, in<lb/>trà illud tamen &longs;pa<lb/>tium TN veniunt <lb/>radij à cæteris om<lb/>nibus punctis inter <lb/>S & O intermediis: <lb/>quare nec vmbra vl<lb/>la aut penumbra ob&longs;eruari pote&longs;t. </s>

<s>At &longs;i &longs;ty<lb/>lus in LM fuerit, proiicit vmbram LP, in<lb/>trà quod &longs;patium nullus cadit radius dire<lb/>ctus á punctis O & S aut intermediis; penum<lb/>bta verò ex P ad B procedit, donec in B me<lb/>ra lux incipiat. </s>

<s>Cum itaque &longs;patio 300 &longs;ta<lb/>diorum gnomones vmbram non proiicerent, <pb pagenum="33"/>totum hoc &longs;pa<lb/><figure id="fig7"></figure><lb/>tium illud e&longs;t, <lb/>cui Sol ad per<lb/>pendiculum im<lb/>minet. </s>

<s>Cum itaque &longs;patio 300 &longs;ta<lb/>diorum gnomones vmbram non proiicerent, <pb pagenum="33"/>totum hoc &longs;pa<lb/><figure id="fig7"/><lb/>tium illud e&longs;t, <lb/>cui Sol ad per<lb/>pendiculum im<lb/>minet. </s>

<s><margin.target id="note18"></margin.target><emph type="italics"/>XVII <lb/>Terræ ma<lb/>gnitudinem <lb/>eiu&longs;que ad <lb/>Solem pro<lb/>portione&mtail; <lb/>inue&longs;tigare <lb/>ex &longs;patio, <lb/>quod ombris <lb/>earet.<emph.end type="italics"/></s>

<s><margin.target id="note18"/><emph type="italics"/>XVII <lb/>Terræ ma<lb/>gnitudinem <lb/>eiu&longs;que ad <lb/>Solem pro<lb/>portione&mtail; <lb/>inue&longs;tigare <lb/>ex &longs;patio, <lb/>quod ombris <lb/>earet.<emph.end type="italics"/></s>

<s>Sed <expan abbr="quærend&utilde;">quærendum</expan> <lb/>&longs;upererat, quo<lb/>ta totius circuli <lb/>maximi pars e&longs;<lb/>&longs;ent &longs;tadia 300. <lb/>Con&longs;tituto ita<lb/>que terræ centro <lb/>in C, & oculo <lb/>ob&longs;eruatoris i&ntail; <lb/>O, ductum <expan abbr="in-telligebã">in<lb/>telligebam</expan> ex cen<lb/>tro S radium S <lb/>OC, qui cu&mtail; <lb/>radio OT Solem <lb/>contingente da<lb/>bat angulum S <lb/>OT &longs;emidiametrum apparentem Solis Apo<lb/>gæi gr.o.m.15., vt placet Tychoni, Longo<lb/>montano, Magino, Keplero. </s>

<s>Item ex C du<lb/>ctus intelligatur radius Solem tangens, qui <lb/>terræ circulum maximum &longs;ecat in K; & e&longs;t <lb/>OK &longs;emi&longs;sis &longs;patij, quod caret vmbris meri<lb/>dianis die &longs;ol&longs;titij æ&longs;tiui; continet autem &longs;ta-<pb pagenum="34"/>dia 150. Certum e&longs;t angulum OCK mino<lb/>rem e&longs;&longs;e angulo <emph type="italics"/>S<emph.end type="italics"/>OT: &longs;i enim linea CK pro<lb/>ducta terminaretur in T, tunc angulus SOT <lb/>externus maior e&longs;&longs;et interno oppo&longs;ito OCT: <lb/>quia verò, quod veritati magis e&longs;t con&longs;enta<lb/>neum, radius ex C Solem tangens e&longs;t CI vl<lb/>tra T, angulus ISC maior e&longs;t angulo T<emph type="italics"/>S<emph.end type="italics"/>O; <lb/>ac proinde, cum anguli ad T & I &longs;int recti, <lb/>reliquus SCI e&longs;t reliquo SOT minor. </s>

<s>E&longs;t igi<lb/>tur &longs;patium OK minus quàm min.15. Qua<lb/>re vnus gradus complectitur plura quàm <lb/>600 &longs;tadia, ideoquè totus telluris ambitus <lb/>maior e&longs;t &longs;tadijs 216000. <lb/><arrow.to.target n="note19"></arrow.to.target></s>

<s><margin.target id="note19"></margin.target><emph type="italics"/>XVIII <lb/>Stadij Græ<lb/>si quanti<lb/>tas.<emph.end type="italics"/></s>

<s><margin.target id="note19"/><emph type="italics"/>XVIII <lb/>Stadij Græ<lb/>si quanti<lb/>tas.<emph.end type="italics"/></s>

<s>Hìc. autem hærebam in &longs;tadio, ne cum <lb/>Suida errarem; hic enim primùm Milio &longs;ta<lb/>dia 7 1/2 tribuit; &longs;ed po&longs;tmodum Milijs de<lb/>cem, æqualia facit &longs;tadia 80: Cùm verò &longs;ta<lb/>dium pedibus 600 definierit, Milium dein<lb/>de in pedes 4200 di&longs;tribuit: Vnde conficitur <lb/>Milium & 7, & 7 1/2, & 8 &longs;tadia comprehen<lb/>dere. </s>

<s>autem hærebam in &longs;tadio, ne cum <lb/>Suida errarem; hic enim primùm Milio &longs;ta<lb/>dia 7 1/2 tribuit; &longs;ed po&longs;tmodum Milijs de<lb/>cem, æqualia facit &longs;tadia 80: Cùm verò &longs;ta<lb/>dium pedibus 600 definierit, Milium dein<lb/>de in pedes 4200 di&longs;tribuit: Vnde conficitur <lb/>Milium & 7, & 7 1/2, & 8 &longs;tadia comprehen<lb/>dere. </s>

<s>Quarè acquie&longs;cendum potius duxian<lb/>tiquo Scholia&longs;ti Græco in propo&longs;. </s>

<s>5. lib d&etail; <lb/>Gæod. </s>

<s>5. lib d&etail; <lb/>Gæod. Heronis Mechanici, qui &longs;tadium fui&longs;<lb/>&longs;e pa&longs;&longs;uum 100, pa&longs;&longs;um cubitorum 4, cu<lb/>bitum verò digitorum 24 &longs;cribit. </s>

<s>Cum ita<lb/>que pa&longs;&longs;us Romanus pedibus quinque con<lb/>&longs;taret, &longs;inguli verò pedes palmis 4, hoc e&longs;t <lb/>digitis 16, pa&longs;&longs;us <emph type="italics"/>R<emph.end type="italics"/>omanus digitos 80 com-<pb pagenum="35"/>plectebatur, quorum pa&longs;&longs;us Græcus habebat <lb/>96, &longs;c.4.cubitos, &longs;eu, quod idem e&longs;t, pedes <lb/>&longs;ex Romanos. </s>

<s>Stadia igitur &longs;ingula pedes <lb/>Rom. antiquos 600 continebant, hoc e&longs;t pa&longs;<lb/>&longs;us 120. Hinc fit<gap/> terræ ambitum maiorem <lb/>&longs;tadijs 216000, maiorem quoquè e&longs;&longs;e pa&longs;si<lb/>bus <emph type="italics"/>R<emph.end type="italics"/>om. <expan abbr="antiq.">antique</expan> 25920000, hoc e&longs;t mill. <lb/>Rom. 25920. Quarè etiam gradibus &longs;in<lb/>gulis milliaria Rom. antiqua plura quàm 72 <lb/>re&longs;pondent. </s>

<s>Heronis Mechanici, qui &longs;tadium fui&longs;<lb/>&longs;e pa&longs;&longs;uum 100, pa&longs;&longs;um cubitorum 4, cu<lb/>bitum verò digitorum 24 &longs;cribit. </s>

<s>Stadia igitur &longs;ingula pedes <lb/>Rom. </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. 15? </s>

<s>antiquos 600 continebant, hoc e&longs;t pa&longs;<lb/>&longs;us 120. Hinc fit<gap/> terræ ambitum maiorem <lb/>&longs;tadijs 216000, maiorem quoquè e&longs;&longs;e pa&longs;si<lb/>bus <emph type="italics"/>R<emph.end type="italics"/>om. </s>

<s><expan abbr="antiq.">antique</expan> 25920000, hoc e&longs;t mill. </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. <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>

<s>25920. Quarè etiam gradibus &longs;in<lb/>gulis milliaria Rom. </s>

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

<s>Qua<lb/>re <expan abbr="vtrinq;">vtrinque</expan> &longs;ublatâ 1 &rx;, manet æquatio 1181 &rx; <lb/>& 22918384.52745: & in&longs;titutâ diui&longs;ion&etail; <lb/>prouenit pretium vnius Radic<gap/>s 19405. <lb/>91407. &longs;emidiameter terræ CO, quarum So<lb/>lis &longs;emidiameter e&longs;t 100000.00000. E&longs;t igi<lb/>tur tota SC, &longs;i CO inuenta addatur ip&longs;i SO, <pb pagenum="36"/>partium 22937790.44152, quæ e&longs;t Secans <lb/>gr.89.m.45.&longs;ec.o.Ter.43. Quar. 53. &c. </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"/></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/>hoc e&longs;t anguli ISC: atque adeò eius comple<lb/>mentum SCI erit gr.o.m.14.&longs;ec.59. Ter. <lb/>16. Quar. 7. quem metitur arcus OK &longs;tad. </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>

<s><lb/>hoc e&longs;t anguli ISC: atque adeò eius comple<lb/>mentum SCI erit gr.o.m.14.&longs;ec.59. Ter. </s>

<s><lb/>150. Fiat demùm vt arcus OK inuentus <lb/>&longs;crupulorum Quart. 3237367 ad &longs;tadia 150, <lb/>ita totius circuli ambitus &longs;crupulorum Quart. <lb/>4665600000. ad &longs;tadia 216175 (67/100), hoc e&longs;t, <lb/>neglectâ fractione, milliaria Rom. antiqu&atail; <lb/>25941. Quapropter &longs;ingulis gradibus mill. <lb/>Rom. 72. pa&longs;&longs;.58 re&longs;pondent. </s>

<s>7. quem metitur arcus OK &longs;tad. </s>

<s><lb/>150. Fiat demùm vt arcus OK inuentus <lb/>&longs;crupulorum Quart. </s>

<s>3237367 ad &longs;tadia 150, <lb/>ita totius circuli ambitus &longs;crupulorum Quart. </s>

<s><lb/>4665600000. ad &longs;tadia 216175 (67/100), hoc e&longs;t, <lb/>neglectâ fractione, milliaria Rom. </s>

<s>antiqu&atail; <lb/>25941. Quapropter &longs;ingulis gradibus mill. </s>

<s>72. pa&longs;&longs;.58 re&longs;pondent. </s>

<s>Porrò inuentâ peripheriâ, &longs;i fiat vt 22 ad 7 </s>

<s><arrow.to.target n="note20"/><lb/>ita mill. 25941. ad mill. 8253 (21/22), habetur <lb/>diameter proximè minor verâ; & &longs;i fiat vt <lb/>223 ad 71 ita mill. 25941. ad mill. 8259 (54/223), <lb/>diametrum verâ proximè maiorem reperi<lb/>mus: & electo medio Arithmetico rectè &longs;ta<lb/>tuitur terræ diameter mill. Rom. ant. </s>

<s>8253 (21/22), habetur <lb/>diameter proximè minor verâ; & &longs;i fiat vt <lb/>223 ad 71 ita mill. </s>

<s>8259 (54/223), <lb/>diametrum verâ proximè maiorem reperi<lb/>mus: & electo medio Arithmetico rectè &longs;ta<lb/>tuitur terræ diameter mill. </s>

<s>8255. <lb/>pa&longs;&longs; 644, ideòque &longs;emidiameter mill. </s>

<s>4127. <lb/>pa&longs;&longs;. </s>

<s>8255. <lb/>pa&longs;&longs; 644, ideòque &longs;emidiameter mill. 4127. <lb/>pa&longs;&longs;. </s>

<s>822. Quod &longs;i libeat exactiùs operari, <lb/>quoniam circuli diametro po&longs;itâ 1, perime<lb/>ter polygoni laterum 2560 circulo circum<lb/>&longs;cripti minor e&longs;t quàm 3 (14160/100000), perimeter ve<lb/>rò in&longs;eripti maior e&longs;t quàm 3 (14159/100000); fiat pri<lb/>mò vt 3. 14160. ad 1, ita mill. 25941 ad <lb/>mill.8257.pa&longs;&longs;.257, quæ e&longs;t diameter mi-<pb pagenum="38"/>tur, &longs;iue ex lucidâ &longs;pecie (quam ab omni pe<lb/>numbrâ ægrè &longs;ecernas) &longs;iuè ex eclip&longs;ibus in<lb/>ferantur. </s>

<s>25941 ad <lb/>mill.8257.pa&longs;&longs;.257, quæ e&longs;t diameter mi-<pb pagenum="38"/>tur, &longs;iue ex lucidâ &longs;pecie (quam ab omni pe<lb/>numbrâ ægrè &longs;ecernas) &longs;iuè ex eclip&longs;ibus in<lb/>ferantur. </s>

<s>Quod &longs;i a&longs;&longs;umpta Lunæ parallaxis <lb/>à vero aliquantulum ab&longs;it, vel quia à radio<lb/>rum refractione turbetur, vel quia motuum <lb/>periodi non &longs;atis accuratè ad calculos reuo<lb/>centur, interuallorum pariter, quæ inde col<lb/>liguntur, veritas nutat. </s>

<s>Ad hæc fides adhi<lb/>benda e&longs;t antiquis &longs;patium, quod meridianis <lb/>vmbris caret, dimetientibus, atque &longs;tadijs <lb/>300 definientibus; quæ tamen ad notas no<lb/>bis men&longs;uras vt reuocemus, certioribus ad<lb/>huc argumentis indigemus. </s>

<s>Illud tame&ntail; <lb/>hìc minimè di&longs;simulandum videtur, quod <lb/>eruditis non paucis placere video: non eam <lb/>&longs;cilicet &longs;tadij men&longs;uram, quam ex 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>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"/><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. 21600. lgitur &longs;i fiat vt arcus OK <lb/>à te nuper inuentus &longs;crupulorum Quart. <lb/>3237367 ad pa&longs;&longs;. </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>

<s>21600. lgitur &longs;i fiat vt arcus OK <lb/>à te nuper inuentus &longs;crupulorum Quart. </s>

<s><lb/>3237367 ad pa&longs;&longs;. </s>

<s>Rom. 21600, ita tota pe<lb/>ripheria &longs;crup. </s>

<s>21600, ita tota pe<lb/>ripheria &longs;crup. </s>

<s>Quart. </s>

<s>4665600000. ad pa&longs;&longs;. </s>

<s>Quart. 4665600000. ad pa&longs;&longs;. </s>

<s>31.129297, erit multo maior terræ <lb/>ambitus, quàm à te fuerit deprehen&longs;us. </s>

<s><margin.target id="note20"></margin.target><emph type="italics"/>XIX <lb/>Terræ am<lb/>bitus, & dia<lb/>meter.<emph.end type="italics"/></s>

<s><lb/>Rom. 31.129297, erit multo maior terræ <lb/>ambitus, quàm à te fuerit deprehen&longs;us. </s>

<s><margin.target id="note21"></margin.target><emph type="italics"/>XXI <lb/>Stadium A<lb/>lexandri<lb/>num.<emph.end type="italics"/></s>

<s><margin.target id="note20"/><emph type="italics"/>XIX <lb/>Terræ am<lb/>bitus, & dia<lb/>meter.<emph.end type="italics"/></s>

<s><margin.target id="note21"/><emph type="italics"/>XXI <lb/>Stadium A<lb/>lexandri<lb/>num.<emph.end type="italics"/></s>

<s>Sed & con&longs;titutam à Tychone Solis di<lb/>&longs;tantiam, nimis breuibus terminis de&longs;ini<lb/>tam exi&longs;timant Recentiores A&longs;tronomi, So<lb/>lemque altiùs promouendum cen&longs;ent, vt &longs;i<lb/>bi inuicem ph&oelig;nomena omnia ritè re&longs;pon<lb/>deant. </s>

<s>Certè P. Io. </s>

<s>Certè P. Io. Bapti&longs;ta Ricciolius no<lb/>&longs;træ Societatis, qui iam annos plures in A<lb/>&longs;tronomiæ in &longs;tauratione feliciter de&longs;udat, <lb/>Solem Apogæum à telluris centro remouet <lb/>&longs;emidiam. </s>

<s>Bapti&longs;ta Ricciolius no<lb/>&longs;træ Societatis, qui iam annos plures in A<lb/>&longs;tronomiæ in &longs;tauratione feliciter de&longs;udat, <lb/>Solem Apogæum à telluris centro remouet <lb/>&longs;emidiam. </s>

<s>7580., & Solis Apogæi dia<lb/>metrum apparentem &longs;tatuit Tychonicâ ma<lb/><arrow.to.target n="note22"></arrow.to.target><lb/>iorem, nimirùm gr.o.m.30.&longs;ec.30. Qua<lb/>rè &longs;i angulus SOT &longs;it gr.o.m.15.&longs;ec.15., <lb/>complementum TSO e&longs;t gr.89.min.44. <lb/>&longs;ec.45., cuius Secans, SO 22551105.10158, <lb/>quarum partium Radius ST e&longs;t 100000. <pb pagenum="40"/>00000. Sit iam SC &longs;emid. </s>

<s>7580., & Solis Apogæi dia<lb/>metrum apparentem &longs;tatuit Tychonicâ ma<lb/><arrow.to.target n="note22"/><lb/>iorem, nimirùm gr.o.m.30.&longs;ec.30. Qua<lb/>rè &longs;i angulus SOT &longs;it gr.o.m.15.&longs;ec.15., <lb/>complementum TSO e&longs;t gr.89.min.44. <lb/>&longs;ec.45., cuius Secans, SO 22551105.10158, <lb/>quarum partium Radius ST e&longs;t 100000. <pb pagenum="40"/>00000. Sit iam SC &longs;emid. </s>

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

Line 630

Line 639

<s>7579: & Secans SO diuida<lb/>tur per 7579, vt Quotiens 2975.47237, <lb/>prodat quantitatem &longs;emidiametri OC i&ntail; <lb/>partibus Radij ST. </s>

<s>Additâ igitur CO ip&longs;i <lb/>OS, erit tota SC 22554080.57395, quæ <lb/>e&longs;t Secans anguli ISC gr.89.m.44.&longs;ec.45. <lb/>Ter. </s>

<s>Additâ igitur CO ip&longs;i <lb/>OS, erit tota SC 22554080.57395, quæ <lb/>e&longs;t Secans anguli ISC gr.89.m.44.&longs;ec.45. <lb/>Ter. 7. Quar. 17. Quint. 28 1/2, atquè adeo <lb/>complementum SCI gr.o.m.15.&longs;ec.14. <lb/>Ter. 52. Quar. 42. Quint. 31 1/2. Duplicetur <lb/>itaque angulus SCI, & in Scrupula Quinta <lb/>reducatur, & &longs;crupula Quinta 395227503 <lb/>re&longs;pondent &longs;tadijs Alexandrinis 300, hoc e&longs;t <lb/>pa&longs;sibus Rom. 43200. Si igitur arcus OK <lb/>duplicatus e&longs;t pa&longs;&longs;. </s>

<s>17. Quint. </s>

<s>28 1/2, atquè adeo <lb/>complementum SCI gr.o.m.15.&longs;ec.14. <lb/>Ter. </s>

<s>42. Quint. </s>

<s>31 1/2. Duplicetur <lb/>itaque angulus SCI, & in Scrupula Quinta <lb/>reducatur, & &longs;crupula Quinta 395227503 <lb/>re&longs;pondent &longs;tadijs Alexandrinis 300, hoc e&longs;t <lb/>pa&longs;sibus Rom. </s>

<s>43200. Si igitur arcus OK <lb/>duplicatus e&longs;t pa&longs;&longs;. </s>

<s>43200, totus circuli am<lb/>bitus &longs;crup. </s>

<s>Quint. </s>

<s>Quint. 279936.000000.erit pa&longs;&longs;. <lb/><arrow.to.target n="note23"/><lb/>Rom. 30598162. </s>

<s>279936.000000.erit pa&longs;&longs;. <lb/><arrow.to.target n="note23"></arrow.to.target><lb/>Rom. </s>

<s><margin.target id="note22"></margin.target><emph type="italics"/>XXII <lb/>Probabilior<lb/>terræ ma<lb/>gnitudo ex <lb/>eadem me <lb/>tbodo inue<lb/>stigatur.<emph.end type="italics"/></s>

<s><margin.target id="note22"/><emph type="italics"/>XXII <lb/>Probabilior<lb/>terræ ma<lb/>gnitudo ex <lb/>eadem me <lb/>tbodo inue<lb/>stigatur.<emph.end type="italics"/></s>

<s><margin.target id="note23"/><emph type="italics"/>XXIII <lb/>Solis dictan <lb/>ti am à ter<lb/>ra, & pro<lb/>portione&mtail; <lb/><gap/>um ill&atail; <lb/>inue&longs;tiga<lb/>re ex da<lb/>ta terræ ma<lb/>gnitudine, <lb/>Solis Apog. <lb/>diametro ap. </s>

<s><margin.target id="note23"></margin.target><emph type="italics"/>XXIII <lb/>Solis dictan <lb/>ti am à ter<lb/>ra, & pro<lb/>portione&mtail; <lb/><gap/>um ill&atail; <lb/>inue&longs;tiga<lb/>re ex da<lb/>ta terræ ma<lb/>gnitudine, <lb/>Solis Apog. </s>

<s><lb/>diametro ap. </s>

<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"/></s><s> 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;. Domino 10. Bapt. Baliano Pa<lb/>tritio Genuen&longs;i, &longs;i ille no&longs;tro huic colloquio <lb/>intere&longs;&longs;et; ab eo enim accepi &longs;e certi&longs;simo <lb/>experimento didici&longs;&longs;e, telluris ambitum non <lb/>minorem e&longs;&longs;e triginta millibus milliarium. </s>

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

<s>Baliano Pa<lb/>tritio Genuen&longs;i, &longs;i ille no&longs;tro huic colloquio <lb/>intere&longs;&longs;et; ab eo enim accepi &longs;e certi&longs;simo <lb/>experimento didici&longs;&longs;e, telluris ambitum non <lb/>minorem e&longs;&longs;e triginta millibus milliarium. </s>

<s><lb/>Tunc verò non poteram illi acquie&longs;cer&etail;, <lb/>cum viderem indè colligi Solem terræ it&atail; <lb/>vicinum, vt ab illâ non abe&longs;&longs;et &longs;emidiam. </s>

<s><lb/>terr.25; id quod e&longs;t manife&longs;tè fal&longs;um. </s>

<s>Tri<lb/>buebam autem &longs;ingulis &longs;tadiis pa&longs;&longs;us Rom. <pb pagenum="41"/>120, vt 300 &longs;tadia e&longs;&longs;ent totius circuli gr. </s>

<s>Tri<lb/>buebam autem &longs;ingulis &longs;tadiis pa&longs;&longs;us Rom. <pb pagenum="41"/>120, vt 300 &longs;tadia e&longs;&longs;ent totius circuli gr. <lb/>o.m.28.&longs;ec. 35. Ter. 12., dato ambitu <lb/>mill. 30000: & arcus OK cum e&longs;&longs;et gr.o. <lb/>m. </s>

<s><lb/>o.m.28.&longs;ec. </s>

<s>12., dato ambitu <lb/>mill. </s>

<s>30000: & arcus OK cum e&longs;&longs;et gr.o. </s>

<s>14.&longs;ec.17. Ter. </s>

<s>36., angulus ISC gr.89. <lb/>m. </s>

<s>45. &longs;ec.42. Ter. </s>

<s>14.&longs;ec.17. Ter. 36., angulus ISC gr.89. <lb/>m. </s>

<s>24. dabat Secantem SC <lb/>24052069.35. in partibus Radij SI 100000. <lb/>00. Po&longs;itâ verò Tychonicâ &longs;emidiametro <lb/>apparente Solis SOT gr.o.m.15., Secans <lb/>SO erat 22918384. 52. Quare &longs;i per Se<lb/>eantium SO, SC, differentiam OC 1133684. <lb/>83. diuidatur Secans SC, Quotiens 21 dabit <lb/>di&longs;tantiam Solis à terræ centro in &longs;emidia<lb/>metris terre&longs;tribus; id quod aperti&longs;simè fal<lb/>&longs;um e&longs;&longs;e omnibus con&longs;tat. </s>

<s>45. &longs;ec.42. Ter. 24. dabat Secantem SC <lb/>24052069.35. in partibus Radij SI 100000. <lb/>00. Po&longs;itâ verò Tychonicâ &longs;emidiametro <lb/>apparente Solis SOT gr.o.m.15., Secans <lb/>SO erat 22918384. 52. Quare &longs;i per Se<lb/>eantium SO, SC, differentiam OC 1133684. <lb/>83. diuidatur Secans SC, Quotiens 21 dabit <lb/>di&longs;tantiam Solis à terræ centro in &longs;emidia<lb/>metris terre&longs;tribus; id quod aperti&longs;simè fal<lb/>&longs;um e&longs;&longs;e omnibus con&longs;tat. </s>

<s>At quoniam vis, Guldine, &longs;tadia illa 300 <lb/>e&longs;&longs;e pa&longs;&longs;us Romanos 43200, tentemus a&ntail; <lb/>illa terræ magnitudo milliaribns 30000 de<lb/>finita &longs;ub&longs;i&longs;tat. </s>

<s>Si ergo circuli totius peri<lb/>pheria ritè &longs;uas in partes tribuatur, con&longs;tat <lb/>pa&longs;&longs;. </s>

<s>43200 re&longs;pondere gr. </s>

<s>43200 re&longs;pondere gr. o.m. </s>

<s>31. &longs;ec. 6. <lb/>Ter. 14. Quar. 24. præcisè: & angulus SCI <lb/>gr. o. </s>

<s>31. &longs;ec. </s>

<s>24. præcisè: & angulus SCI <lb/>gr. </s>

<s>15.&longs;ec.33. Ter.7. Quar. </s>

<s>15.&longs;ec.33. Ter.7. Quar. 12. habet <lb/><expan abbr="cõplementum">complementum</expan> ISC gr.89.m.44.&longs;ec.26.Ter. <lb/>52. Quar. 48., cuius Secans SC 22110369. <lb/>79050, quarum Radius SI e&longs;t 100000.00000. <lb/>Porrò angu'us SOT &longs;emidiameter apparens <lb/>Solis Apogæi nece&longs;&longs;ariò maior &longs;tatui debet <lb/>angulo SCI con&longs;tituto, cum &longs;ub maiore an-<pb pagenum="42"/>gulo appareat <emph type="italics"/>S<emph.end type="italics"/>ol ex puncto O vicinior&etail;, <lb/>quàm ex puncto C remotiore. </s>

<s>Quare a&longs;&longs;u<lb/>mi non pote&longs;t Solis Apogæi &longs;emidiameter <lb/>apparens, quam ex Ricciolio a&longs;&longs;umebas, gr. <lb/>o m. </s>

<s>15. &longs;ec. 15., neque Tychonica gr.o. <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>12. habet <lb/><expan abbr="cõplementum">complementum</expan> ISC gr.89.m.44.&longs;ec.26.Ter. </s>

<s>48., cuius Secans SC 22110369. <lb/>79050, quarum Radius SI e&longs;t 100000.00000. <lb/>Porrò angu'us SOT &longs;emidiameter apparens <lb/>Solis Apogæi nece&longs;&longs;ariò maior &longs;tatui debet <lb/>angulo SCI con&longs;tituto, cum &longs;ub maiore an-<pb pagenum="42"/>gulo appareat <emph type="italics"/>S<emph.end type="italics"/>ol ex puncto O vicinior&etail;, <lb/>quàm ex puncto C remotiore. </s>

<s>Quare a&longs;&longs;u<lb/>mi non pote&longs;t Solis Apogæi &longs;emidiameter <lb/>apparens, quam ex Ricciolio a&longs;&longs;umebas, gr. </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. 31. <lb/>Fac igitur à Baliano mediam inter hæc ex<lb/>trema Solis Apogæi diametrum apparen<lb/>tem gr.o.m.30.&longs;ec.30. a&longs;&longs;umi, & telluris <lb/>ambitum ita augeri, vt ad illum pa&longs;&longs;us 43200 <lb/>minorem habeant Rationem: & &longs;ibi omnia <lb/>re&longs;pondebunt. </s>

<s>15. &longs;ec. </s>

<s>15., neque Tychonica gr.o. </s>

<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>Statuatur itaque terræ peri<lb/>pheria pa&longs;&longs;.30598162; & pa&longs;&longs;us Rom.43200 <lb/>&longs;unt gr.o.m.30.&longs;ec.29. Ter.45 Quar. 25. <lb/>Quint.4., adeoquè angulus SCI gr.o.min. <lb/>15.&longs;ec. 14. Ter. 52: Quar. 42. Quint. 32. <lb/>cuius Complementi Secans SC 22554080. <lb/>57395 in partibus Radij <emph type="italics"/>S<emph.end type="italics"/>I. </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>31. <lb/>Fac igitur à Baliano mediam inter hæc ex<lb/>trema Solis Apogæi diametrum apparen<lb/>tem gr.o.m.30.&longs;ec.30. a&longs;&longs;umi, & telluris <lb/>ambitum ita augeri, vt ad illum pa&longs;&longs;us 43200 <lb/>minorem habeant Rationem: & &longs;ibi omnia <lb/>re&longs;pondebunt. </s>

<s>Statuatur itaque terræ peri<lb/>pheria pa&longs;&longs;.30598162; & pa&longs;&longs;us Rom.43200 <lb/>&longs;unt gr.o.m.30.&longs;ec.29. Ter.45 Quar. </s>

<s>25. <lb/>Quint.4., adeoquè angulus SCI gr.o.min. </s>

<s><lb/>15.&longs;ec. </s>

<s>42. Quint. </s>

<s>32. <lb/>cuius Complementi Secans SC 22554080. <lb/>57395 in partibus Radij <emph type="italics"/>S<emph.end type="italics"/>I. </s>

<s>Iam anguli SOT <lb/>gr.o.m.15.&longs;ec. </s>

<s>15. Secans Complem. </s>

<s>SO <lb/>22551105.10158. auferatur ex SC; & per <lb/>earum differentiam OC 2975.47237 diui<lb/>sâ totâ SC, prodibit di&longs;tantia SC &longs;emid. </s>

<s>Iam anguli SOT <lb/>gr.o.m.15.&longs;ec. 15. Secans Complem. SO <lb/>22551105.10158. auferatur ex SC; & per <lb/>earum differentiam OC 2975.47237 diui<lb/>sâ totâ SC, prodibit di&longs;tantia SC &longs;emid. </s>

<s><lb/>7580, vt P. Ricciolio placet. </s>

<s>Ricciolio placet. </s>

<s>Quarè exiis, quæ hactenus di&longs;putauimus, <lb/>illud infero, quod auctâ Solis Apogæi diame<lb/>tro apparente, minui debet terræ ambitus, <lb/>vt ad eum pa&longs;&longs;us 43200 maiorem habeant <lb/>Rationem, ne videlicet tam magno inter &longs;e <lb/>di&longs;crimine differant anguli SOT & <emph type="italics"/>S<emph.end type="italics"/>CI, vt <lb/>per Secantium SO & SC, differentiam OC <lb/>diuisâ di&longs;tantiâ SC <emph type="italics"/>S<emph.end type="italics"/>ol terræ vicinior &longs;tatua-<pb pagenum="44"/>tur, quàm par &longs;it ad ph&oelig;nomena omni&atail; <lb/>explicanda. </s>

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<s>Minuenda itaque e&longs;t vel Solis appa<lb/>rens diameter, vel terræ magnitudo; ego ve<lb/>rò illam potiùs paucioribus &longs;crupulis &longs;ecun<lb/>dis definiendam cen&longs;erem, quàm terræ am<lb/>bitum ad pauciora milliaria reuocandum. </s>

<s>S<emph.end type="italics"/>ed quid his longiùs immoramur? </s>

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<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> 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. Rom. 4127 pa&longs;&longs;.822. ad pedes reuoco, <lb/><arrow.to.target n="note24"/><lb/>pedes quinque Romanos antiquos pa&longs;&longs;ibus <lb/>&longs;ingulis tribuens, & &longs;unt pedes 20639110. <lb/>Quia verò &longs;phæræ &longs;unt in triplicatâ Ratione <lb/>&longs;emidiametrorum, comparo terrenam &longs;e<lb/>midiametrum cum &longs;emidiametro pedali al<lb/>terius globi, & <emph type="italics"/>R<emph.end type="italics"/>ationem 1. ad 20.639110 <lb/>v&longs;que, ad quartum terminum continuo, vt <lb/>&longs;it tertius terminus 425.972861.592100. <lb/>quartus autem 8791.700747.414127. <lb/>031000. <emph type="italics"/>S<emph.end type="italics"/>phæra igitur &longs;emidiametri pedalis <lb/>ad terrenam &longs;phæram <emph type="italics"/>R<emph.end type="italics"/>ationem habet ean<lb/>dem, quam vnitas ad quartum hunc termi<lb/>num. </s>

<s>4127 pa&longs;&longs;.822. ad pedes reuoco, <lb/><arrow.to.target n="note24"></arrow.to.target><lb/>pedes quinque Romanos antiquos pa&longs;&longs;ibus <lb/>&longs;ingulis tribuens, & &longs;unt pedes 20639110. <lb/>Quia verò &longs;phæræ &longs;unt in triplicatâ Ratione <lb/>&longs;emidiametrorum, comparo terrenam &longs;e<lb/>midiametrum cum &longs;emidiametro pedali al<lb/>terius globi, & <emph type="italics"/>R<emph.end type="italics"/>ationem 1. ad 20.639110 <lb/>v&longs;que, ad quartum terminum continuo, vt <lb/>&longs;it tertius terminus 425.972861.592100. <lb/>quartus autem 8791.700747.414127. <lb/>031000. <emph type="italics"/>S<emph.end type="italics"/>phæra igitur &longs;emidiametri pedalis <lb/>ad terrenam &longs;phæram <emph type="italics"/>R<emph.end type="italics"/>ationem habet ean<lb/>dem, quam vnitas ad quartum hunc termi<lb/>num. </s>

<s>Vt autem &longs;phæræ argillaceæ, cuius <lb/>&longs;emidiameter pedalis &longs;it, grauitatem per<lb/>&longs;pectam haberem, argillam cum aquâ con<lb/>tuli, & experimento didici argillæ grauita<lb/>tem ad aquæ pondus e&longs;&longs;e vt 27 ad 16. At <lb/>&longs;tanni grauitas ad aquæ grauitatem apud <lb/>Ghetaldum in Archimede Promoto e&longs;t vt <lb/>100 ad (13 19/37), hoc e&longs;t, vt 37 ad 5. <emph type="italics"/>S<emph.end type="italics"/>i igitur <lb/>Ratio &longs;tanni ad aquam, & aquæ ad argillam, <lb/>&longs;cilicet 37 ad 5. & 16 ad 27 in tribus termi<lb/>nis continuetur, ita vt &longs;int 592,80. 135, <lb/>Ratio grauitatis &longs;tanni ad argillæ pondus, da<lb/>tâ molis æqualitate, e&longs;t vt 592 ad 135. </s>

<s><margin.target id="note24"></margin.target><emph type="italics"/>XXIV <lb/>Terreni glo <lb/>bi &longs;oliditas <lb/>inue &longs;tiga<lb/>tur.<emph.end type="italics"/></s>

<s><margin.target id="note24"/><emph type="italics"/>XXIV <lb/>Terreni glo <lb/>bi &longs;oliditas <lb/>inue &longs;tiga<lb/>tur.<emph.end type="italics"/></s>

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

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

<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>

<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>Multiplicetur igitur quar<lb/><arrow.to.target n="note25"/><lb/>tus ille terminus 8791.700747.414127. <lb/>031000. per libras (554 22/37), & prodibit totius <lb/>terræ grauitas, &longs;i ex merâ argillâ con&longs;taret, <lb/>librarum 4.875829.711809.132072. <lb/>(327567 21/37). </s>

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

<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"/><lb/>fateor, ac marmora æqualem argillæ molem <lb/>pondere &longs;uperant: &longs;ed quota demum &longs;phæ<lb/>ræ huius pars illa &longs;unt? </s>

<s>Quod &longs;i quis ill&atail; <lb/>grauiora e&longs;&longs;e inculcet, longè leuiorem a<lb/>quam cogitet, ex qua vici&longs;sim globus hic <lb/>terraqueus con&longs;tat. </s>

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<s>Iam <lb/>verò &longs;i ad aëris vim non modicam terræ ca<lb/>uernis atque cuniculis inclu&longs;am, &longs;eque intrà <lb/>&longs;iccorum corporum particulas non &longs;ibi om<lb/>ninò cohærentes in&longs;inuantem, animum ad<lb/>uertamus, apparebit illicò exuperantiam il<lb/>lam grauitatis hoc defectu vberrimè com<lb/>pen&longs;ari. </s>

<s><margin.target id="note26"></margin.target><emph type="italics"/>XXVI <lb/>Terræ gra<lb/>uitatem pe<lb/>rinde &longs;e ba<lb/>bere proba<lb/>tur, ac &longs;i e&longs;<lb/>&longs;et mera ar<lb/>gilla.<emph.end type="italics"/></s>

<s><margin.target id="note26"/><emph type="italics"/>XXVI <lb/>Terræ gra<lb/>uitatem pe<lb/>rinde &longs;e ba<lb/>bere proba<lb/>tur, ac &longs;i e&longs;<lb/>&longs;et mera ar<lb/>gilla.<emph.end type="italics"/></s>

<s>Sed quoniam motus, cui tellus &longs;uo pon<lb/>dere ob&longs;i&longs;teret, in circum&longs;u&longs;o hoc aëre per-<pb pagenum="48"/>ficiendus e&longs;&longs;et; minuitur adhuc momen<lb/>tum ab halituum aëre leuiorum copiâ penè <lb/>infinitâ, quæ totam hanc molem peruadit. </s>

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<s>Ne<lb/>que indigent metallarii A&longs;trologorum næ<gap/><lb/>nijs, qui imminentem cæli mutationem <pb pagenum="49"/>prædicant; cum ip&longs;i ex immodicâ halituum <lb/>infernè a&longs;cendentium copiâ, quibus vix non <lb/>præfocantur, c&oelig;lum nubibus proximè ob<lb/>ducendum nec dubiè pronuncient. </s>

<s><lb/>quod aqua ip&longs;a (licet aëre grauior, &longs;i &longs;ibi ip&longs;a <lb/>relinquatur) leui&longs;simi vaporis &longs;peciem induit <lb/>calore &longs;ollicitata, quo interior terræ plag&atail; <lb/>abundat: Vbienim octoginta circiter hexa<lb/>podas, quibus extima hæc terræ regio frigi<lb/>di&longs;sima definitur, de&longs;cenderis, tepor primùm <lb/>grati&longs;simus ex frigidâ regione venientem ex<lb/>cipit ac recreat, paulatimque adeò augetur <lb/>calor, vt demùm metalli fo&longs;&longs;ores ve&longs;tem nul<lb/>lam ferant. </s>

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<s>Dabitis, opinor <lb/>vini grauitatem ferè aquæ &longs;ub&longs;e&longs;qui-&longs;exage<lb/>cuplam, vel certè aquæ pondere non maio<lb/>rem; ita vt quodcunque aquæ grauitate præ<lb/>&longs;titerit, haud immeritò vino pariter grauius <lb/>cen&longs;eatur. </s>

<s>Atqui Tartarum ex vino &longs;ub&longs;ide<lb/>re nemo ne&longs;cit; & quod inde elicitur oleum <lb/>Tartari, e&longs;t proximè ad aquam vt 3 ad 2: &longs;pi<lb/>titus autem vini ad aquam communem, Ra<lb/>tionem habet proximè, quam 3 ad 4. Qua<lb/>re &longs;i vinum eiu&longs;dem cum aquâ grauitatis <lb/>con&longs;tituatur, Oleum Tartari ad vinum e&longs;t <lb/>vt 6 ad 4, vinum autem ad &longs;piritum vini vt <lb/><arrow.to.target n="note27"></arrow.to.target><lb/>4 ad 3. </s>

<s>Atqui Tartarum ex vino &longs;ub&longs;ide<lb/>re nemo ne&longs;cit; & quod inde elicitur oleum <lb/>Tartari, e&longs;t proximè ad aquam vt 3 ad 2: &longs;pi<lb/>titus autem vini ad aquam communem, Ra<lb/>tionem habet proximè, quam 3 ad 4. Qua<lb/>re &longs;i vinum eiu&longs;dem cum aquâ grauitatis <lb/>con&longs;tituatur, Oleum Tartari ad vinum e&longs;t <lb/>vt 6 ad 4, vinum autem ad &longs;piritum vini vt <lb/><arrow.to.target n="note27"/><lb/>4 ad 3. </s>

<s><margin.target id="note27"></margin.target><emph type="italics"/>XXVII <lb/>Vini graui<lb/>tas medi&atail; <lb/>Harmonicè <lb/>inter Oleum <lb/>Tartari, & <lb/>Spiritu&mtail; <lb/>vini.<emph.end type="italics"/></s>

<s><margin.target id="note27"/><emph type="italics"/>XXVII <lb/>Vini graui<lb/>tas medi&atail; <lb/>Harmonicè <lb/>inter Oleum <lb/>Tartari, & <lb/>Spiritu&mtail; <lb/>vini.<emph.end type="italics"/></s>

<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"/></s><s> 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"/></s><s> 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>

<s>Nihil e&longs;t, <pb pagenum="52"/><arrow.to.target n="note28"></arrow.to.target><lb/>aiebat ille, quod vim pati perpetuam cen<lb/>&longs;endum &longs;it. </s>

<s>Nihil e&longs;t, <pb pagenum="52"/><arrow.to.target n="note28"/><lb/>aiebat ille, quod vim pati perpetuam cen<lb/>&longs;endum &longs;it. </s>

<s>At &longs;i elementis omnibus terra <lb/>grauitare, ignis leuitate præ&longs;tet; an non. </s>

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<s><lb/>Qui&longs;quis autem ibi ignem à Deo perpetuis <lb/>vinculis eo tantùm con&longs;ilio coerceri exi&longs;ti<lb/>mat, vt &longs;celeratorum carnificinam exerce<gap/>t; <lb/>diligenter per&longs;piciat velim, an non magis <lb/>pro Diuinæ &longs;apientiæ atque omnipotentiæ <lb/>dignitate locuturus ille &longs;it, qui, quemadmo<lb/>dum Iridem licèt naturæ penicillo in nubi<lb/>bus de&longs;criptam, in &longs;empiterni tamen f&oelig;de<lb/>ris te&longs;&longs;eram à Deo a&longs;&longs;umptam nouit, &longs;ic re<lb/>rum naturæ con&longs;entaneum ad&longs;truat hunc or<lb/>dinem, quo vniuer&longs;itatis rerum &longs;ubluna<lb/>rium elementa pro &longs;ui ponderis ratione ita <lb/>di&longs;ponantur, vt centrum omnium graui&longs;si<lb/>mus ignis impiorum carcer atque carnifex <lb/>con&longs;titutus obtineat, illumque minùs gra<lb/>uia elementa terra & aqua deinceps con&longs;e<lb/>quantur, v&longs;que eò dum leui&longs;simus aër cir<lb/>cumfu&longs;us reliqua complectatur. </s>

<s><margin.target id="note28"></margin.target><emph type="italics"/>XXVIII <lb/>Coniecturæ <lb/>pro adstru<lb/>enda ignis <lb/>inferni gra <lb/>uitate.<emph.end type="italics"/></s>

<s><margin.target id="note28"/><emph type="italics"/>XXVIII <lb/>Coniecturæ <lb/>pro adstru<lb/>enda ignis <lb/>inferni gra<lb/>uitate.<emph.end type="italics"/></s>

<s>Fru&longs;tra a&longs;cendentem flammam aperti&longs;si<lb/>mum igneæ leuitatis argumentum obiicie-<pb pagenum="53"/>bant. </s>

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<s>Quare Tarta<lb/>rum ille concipiebat qua&longs;i immen&longs;as Ther<lb/>mas ac balneas efficaci&longs;&longs;imis omnium cau<lb/>&longs;ticorum particulis plenas; quæ proptere&atail; <lb/>lacus & &longs;tagnum ignis, ob quietem &longs;cilicet, <lb/>à Diuinis literis dicuntur. </s>

<s>Cumque plur&atail; <lb/>ijs quidem, quæ à Diuinis literis docemur, <lb/>con&longs;ona, &longs;ed præter eorum, qui aderant, opi<lb/>nionem, de ignis i&longs;tiu&longs;modi naturâ di&longs;pu<lb/>ra&longs;&longs;et; ne quid temerè prolatum videretur, <lb/>&longs;ermonem claudens Lactantij l. </s>

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

<s><lb/>Illud autem e&longs;t, quod quamuis terram decu<lb/>plò grauiorem quis con&longs;titueret, ac ego de<lb/>prehenderim, nihilo tamen minùs tuis illis <lb/>orbiculis moueri facilè po&longs;&longs;et: non tantum <lb/>quia decuplex i&longs;ta grauitas non pertingeret <lb/>ad libras illas 50.000000.000000.000000. <lb/>000000. & eo amplius, verùm etiam qui&atail; <lb/>non totum illud pondus &longs;imul motui repu<lb/><figure id="fig8"></figure><lb/>gnaret. </s>

<s>Sit eni&mtail; <lb/>totus terræ globus <lb/>HIKL, cuius cen<lb/>trum C congruat v<lb/>niuer&longs;i centro, i&ntail; <lb/>quo nullum habet <lb/>momentum ad de<lb/>&longs;cen&longs;um, &longs;ed in eo <lb/>quie&longs;cit. </s>

<s>An non &longs;a<lb/>tis Archimedi fui&longs;<lb/>&longs;et, &longs;iterram vnum <lb/>aut alterum milliare aliò tran&longs;tuli&longs;&longs;et? </s>

<s>Mo<lb/>ueri igitur intelligatur centrum ex C in T, <lb/>& &longs;it terra translata SORV. </s>

<s>Mo<lb/>ueri igitur intelligatur centrum ex C in T, <lb/>& &longs;it terra translata SORV. </s>

<s>Huic motui <lb/>primùm, præter hemi&longs;phærium &longs;uperius <lb/>HLK, non repugnat totum hemi&longs;phærium <lb/>inferius HIK, cuius videlicet partes plurimæ <lb/>&longs;iunt centro C propiores, in quod &longs;uis nuti-<pb pagenum="59"/>bus feruntur. </s>

<s>Ponatur enim CT &longs;emidia<lb/>metri pars mille&longs;ima, hoc e&longs;t mill. </s>

<s>Ponatur enim CT &longs;emidia<lb/>metri pars mille&longs;ima, hoc e&longs;t mill. 4. & eo <lb/>amplius; &longs;egmentorum MON & MVN Ra<lb/>tio inuenietur, ex ijs quæ Archimedes docet <lb/>l. 2. de &longs;ph. </s>

<s>4. & eo <lb/>amplius; &longs;egmentorum MON & MVN Ra<lb/>tio inuenietur, ex ijs quæ Archimedes docet <lb/>l. </s>

<s>2. de &longs;ph. </s>

<s>prop.

2. &longs;unt enim &longs;eg<lb/>menta illa æqualia conis eandem ba&longs;im MN <lb/>habentibus, hi autem ex Eucl. l. 12. prop. </s>

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

<s><lb/>14 inter &longs;e &longs;unt vt altitudines: Quapropter <lb/>inuentis conorum altitudinibus, quas Ar<lb/>chimedes docet, innote&longs;cit Ratio &longs;egmen<lb/>torum &longs;phæricorum conis illis æqualiu&mtail;. </s>

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<s>Præterea &longs;egmentum illud MON <lb/>non eadem obtineret ad de&longs;<gap/>endendum mo<lb/>menta in tantâ centri vicinitate, ac valdè <lb/>procul à centro: neque enim ex hoc, quòd <lb/>experimentis euincere non po&longs;&longs;imus grauia <lb/>centro propiora minùs vrgere deor&longs;u&mtail; <lb/>quàm remotiora (cum illa, quæ in experi<lb/>mentum a&longs;&longs;umuntur, non ea e&longs;&longs;e queant, <lb/>quæ di&longs;crimen inferant &longs;en&longs;u perceptibil&etail;) <lb/>repugnandum e&longs;t rationi mani&longs;e&longs;tæ id &longs;ua<lb/>denti, vbi & ponderis amplitudo & inter<lb/>ualli differentia in&longs;ignis e&longs;t atque con&longs;pi<lb/>cu&atail;. </s>

<s><margin.target id="note29"></margin.target><emph type="italics"/>XXIX <lb/>Telluris <lb/>grauitas <expan abbr="nõ">non</expan> <lb/>tota re &longs;i &longs;te<lb/>ret Archi<lb/>medi traben <lb/><gap/>i.<emph.end type="italics"/></s>

<s><margin.target id="note29"/><emph type="italics"/>XXIX <lb/>Telluris <lb/>grauitas <expan abbr="nõ">non</expan> <lb/>tota re &longs;i &longs;te<lb/>ret Archi<lb/>medi traben <lb/><gap/>i.<emph.end type="italics"/></s>

<s>Hinc fit 24 axibus in peritrochio aut tym<lb/><arrow.to.target n="note30"></arrow.to.target><lb/>panis dentatis, quorum partes e&longs;&longs;ent in Ra<lb/>tione decuplâ, fieri po&longs;&longs;e, vt virtute tres li<lb/>bras mouere valente terra per aliquod &longs;pa<lb/>tium moueretur; illa enim mouere po&longs;&longs;et <lb/>lib 3000000.000000.000000.000000; qui <lb/>numerus excedit &longs;emi&longs;&longs;em ponderis totius <lb/>terræ; ac proinde eou&longs;que moueret, du&mtail; <lb/>&longs;egmentum MON æquale e&longs;&longs;et toti ponderi, <pb pagenum="61"/>quod ab eadem potentiâ po&longs;&longs;et &longs;u&longs;tineri ad<lb/>hibitâ eadem machinâ, habitâ tamen ratio<lb/>ne &longs;egmenti MVN ex parte &longs;u&longs;tentantis &longs;eg<lb/>mentum &longs;uperius, ne tanto impetu deor&longs;um <lb/>vrgeat, quanto vrgeret, &longs;i &longs;egmentum MVN <lb/>non ade&longs;&longs;et. </s>

<s>Hinc fit 24 axibus in peritrochio aut tym<lb/><arrow.to.target n="note30"/><lb/>panis dentatis, quorum partes e&longs;&longs;ent in Ra<lb/>tione decuplâ, fieri po&longs;&longs;e, vt virtute tres li<lb/>bras mouere valente terra per aliquod &longs;pa<lb/>tium moueretur; illa enim mouere po&longs;&longs;et <lb/>lib 3000000.000000.000000.000000; qui <lb/>numerus excedit &longs;emi&longs;&longs;em ponderis totius <lb/>terræ; ac proinde eou&longs;que moueret, du&mtail; <lb/>&longs;egmentum MON æquale e&longs;&longs;et toti ponderi, <pb pagenum="61"/>quod ab eadem potentiâ po&longs;&longs;et &longs;u&longs;tineri ad<lb/>hibitâ eadem machinâ, habitâ tamen ratio<lb/>ne &longs;egmenti MVN ex parte &longs;u&longs;tentantis &longs;eg<lb/>mentum &longs;uperius, ne tanto impetu deor&longs;um <lb/>vrgeat, quanto vrgeret, &longs;i &longs;egmentum MVN <lb/>non ade&longs;&longs;et. </s>

<s>At verò compo&longs;itis tantùm 17 <lb/>helicibus cum tympanis denticulos 25 ha<lb/>bentibus, & vltimo tympano ad axem, cui <lb/>funis ductarius circumuoluitur, Rationem <lb/>quintuplam habente, potentia vnius libræ <lb/>&longs;u&longs;tentatiua applicata manubrio æqualis lon<lb/>gitudinis cum tympanorum &longs;emidiametro, <lb/>po&longs;&longs;et mouere terram ex C in T v&longs;que eò <lb/>dum &longs;egmentum MON e&longs;&longs;et lib 2.910383. <lb/>045673.370361.328125. qui pariter libra<lb/>rum numerus excedit totius terrenæ graui<lb/>tatis &longs;emi&longs;&longs;em: at potentia decem libras lo<lb/>co transferre valens, decuplum pondus mo<lb/>uere po&longs;&longs;et, atque adeò totum globum ele<lb/>uare. </s>

<s>Sed iam Guldinum audiamus, vt cer<lb/>tam telluris magnitudinem &longs;tatuamus. </s>

<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><margin.target id="note30"/><emph type="italics"/>XXX <lb/>Definitur <lb/>machin&atail;, <lb/>qua potui&longs;<lb/>&longs;et tellus mo<lb/>ueri ab Ar<lb/>chimede.<emph.end type="italics"/></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><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"/></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="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"/></s><pb pagenum="63"/><figure/>

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

<s><emph type="center"/>Methodos varias inueniendi <lb/>terræ quantitatem <lb/>proponit.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

<s>HAVD &longs;atis &longs;cio, an po&longs;<lb/>&longs;im aliquid proferr&etail;, <lb/>quod ve&longs;træ expectatio<lb/>ni faciat &longs;atis in eâ, quam <lb/>nobis hodiè examinan<lb/>dam &longs;tatuimus quæ&longs;tio<lb/>nem de terraquei huius <lb/>globi magnitudine inue&longs;tigandâ: vosidcircò <pb pagenum="64"/>pro ve&longs;trâ humanitate tenuitati meæ ve<lb/>niam dabitis, &longs;i quid afferre contigerit ita <lb/>planum ac facilè, vt ve&longs;trorum ingeniorum <lb/>&longs;ublimitati non re&longs;pondeat. </s>

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<s>His autem duobus cognitis terræ quo-<pb pagenum="65"/>que &longs;emidiametrum latere non po&longs;&longs;e de<lb/>mon&longs;tro. </s>

<s>Sit enim, exempli gratiâ, nota altitudo <lb/>BA Phari Genuen&longs;is (laternam vocant) cum <lb/><arrow.to.target n="note31"></arrow.to.target><lb/>&longs;copulo palmorum Genuen&longs;ium 440, hoc <lb/>e&longs;t pedum Rom. </s>

<s>Sit enim, exempli gratiâ, nota altitudo <lb/>BA Phari Genuen&longs;is (laternam vocant) cum <lb/><arrow.to.target n="note31"/><lb/>&longs;copulo palmorum Genuen&longs;ium 440, hoc <lb/>e&longs;t pedum Rom. ant. </s>

<s>480, ob&longs;eruatusque <lb/>angulus BAD &longs;it gr.89.m.36.&longs;ec.33. Quo<lb/>niam ergo linea AD circulum tangit in D, <lb/>angulus CDA e&longs;t rectus. </s>

<s>Ex B ducta intel<lb/>ligatur BE parallela ip&longs;i CD; e&longs;tque triangu<lb/>lum ABE rectangulum ad E, cuius hypo<lb/>thenu&longs;a AB, & angulus adiacens innotue<lb/>runt. </s>

<s>Quare fiat vt Radius 100000. 00000. <lb/>ad &longs;inum gr.89.m.36.&longs;ec.33.hoc e&longs;t 99997. <lb/>67348, ita AB ped. </s>

<s>Quare fiat vt Radius 100000. 00000. <lb/>ad &longs;inum gr.89.m.36.&longs;ec.33.hoc e&longs;t 99997. <lb/>67348, ita AB ped. 480. ad BE ped. (479 <lb/>98883.27040/100000.00000). Porrò triangula ABE, ACD æqui<lb/>angula &longs;unt propter linearum BE, CD pa<lb/>ralleli&longs;mum, adeoque & &longs;imilia, ac vt AB <lb/>ad BE, ita AC ad CD. </s>

<s>480. ad BE ped. (479 <lb/>98883.27040/100000.00000). Porrò triangula ABE, ACD æqui<lb/>angula &longs;unt propter linearum BE, CD pa<lb/>ralleli&longs;mum, adeoque & &longs;imilia, ac vt AB <lb/>ad BE, ita AC ad CD. </s>

<s>Ponatur autem BC <lb/>vna Radix Algebricè. </s>

<s>Igitur vt AB ped.480 <lb/>ad BE ped. (479 98883.27040/10000000000), ita AC ped. </s>

<s>Igitur vt AB ped.480 <lb/>ad BE ped. (479 98883.27040/10000000000), ita AC ped. 1 &rx; + <lb/>480 ad CD ped (47998883.27040/48000000.00000) &rx; + (479 47463969.79200/48000000.00000). <lb/>E&longs;t autem CD æqualis ip&longs;i CB 1 &rx;. </s>

<s>Quare <lb/>factâ Antithe&longs;i iuxta Algebræ regulas, ma<lb/>net æquatio inter hos terminos (111672960/48000000.00000) &rx; & <lb/>pedes (479 47463969.79200/48000000.00000). In&longs;titutâ denique di<lb/>ui&longs;ione prodir quotiens ped. 20631193., <pb pagenum="66"/>pretium 1 &rx; CB vel <lb/><figure id="fig10"/><lb/>CD. </s>

<s>1 &rx; + <lb/>480 ad CD ped (47998883.27040/48000000.00000) &rx; + (479 47463969.79200/48000000.00000). <lb/>E&longs;t autem CD æqualis ip&longs;i CB 1 &rx;. </s>

<s>E&longs;t ergo inuen<lb/>ta terræ &longs;emidiameter <lb/>mill. Rom. ant. </s>

<s>20631193., <pb pagenum="66"/>pretium 1 &rx; CB vel <lb/><figure id="fig10"></figure><lb/>CD. </s>

<s>E&longs;t ergo inuen<lb/>ta terræ &longs;emidiameter <lb/>mill. </s>

<s>4126, <lb/>pa&longs;&longs;. </s>

<s>238. po&longs;ito angu<lb/>lo ad A gr.89.m.36. <lb/>&longs;ec 33. præcisè. </s>

<s><margin.target id="note31"></margin.target><emph type="italics"/>XXXI <lb/>Prima me<lb/>tbodus in<lb/>ueniendi tel <lb/>luris &longs;emi<lb/>diametrum, <lb/>per Trigo<lb/>nometriam <lb/>& Alge<lb/>bram.<emph.end type="italics"/></s>

<s><margin.target id="note31"/><emph type="italics"/>XXXI <lb/>Prima me<lb/>tbodus in<lb/>ueniendi tel <lb/>luris &longs;emi<lb/>diametrum, <lb/>per Trigo<lb/>nometriam <lb/>& Alge<lb/>bram.<emph.end type="italics"/></s>

<s>Quod &longs;i rem breuiùs <lb/>a&longs;&longs;equi velis, dato an<lb/><arrow.to.target n="note32"></arrow.to.target><lb/>gulo ob&longs;eruato in A gr. </s>

<s>Quod &longs;i rem breuiùs <lb/>a&longs;&longs;equi velis, dato an<lb/><arrow.to.target n="note32"/><lb/>gulo ob&longs;eruato in A gr. <lb/>89.m.36.&longs;ec.33, &longs;umatur AC vt Radius, & <lb/>CD, vt &longs;inus dati anguli. </s>

<s><lb/>89.m.36.&longs;ec.33, &longs;umatur AC vt Radius, & <lb/>CD, vt &longs;inus dati anguli. </s>

<s>Et a&longs;&longs;umptâ BC <lb/>1 &rx; fiat vt Radius 100000.00000. ad dati an<lb/>guli &longs;inum 99997.67348, ita AC ped. </s>

<s>1 &rx; <lb/>+ 480 ad CD ped. (99997.67348&rx;+4799888327040/100000.00000). E&longs;t <lb/>CD ip&longs;i CB 1 &rx; æqualis, atque adeò vtrinque <lb/>demptâ &longs;ractione (99997.67348/100000.00000) &rx;, remanet æqua<lb/>tio inter (232652/100000.00000) &rx; & ped. (4799888327040/100000.00000). Qua<lb/>rè factâ diui&longs;ione habetur pretium 1 &rx; ped. </s>

<s>Et a&longs;&longs;umptâ BC <lb/>1 &rx; fiat vt Radius 100000.00000. ad dati an<lb/>guli &longs;inum 99997.67348, ita AC ped. 1 &rx; <lb/>+ 480 ad CD ped. (99997.67348&rx;+4799888327040/100000.00000). E&longs;t <lb/>CD ip&longs;i CB 1 &rx; æqualis, atque adeò vtrinque <lb/>demptâ &longs;ractione (99997.67348/100000.00000) &rx;, remanet æqua<lb/>tio inter (232652/100000.00000) &rx; & ped. (4799888327040/100000.00000). Qua<lb/>rè factâ diui&longs;ione habetur pretium 1 &rx; ped. <lb/>20631193 vt priùs. </s>

<s><lb/>20631193 vt priùs. </s>

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

<s>Verùm adhuc ab&longs;que Cano<lb/><arrow.to.target n="note33"/><lb/>ne Trigonometrico res tota perfici po&longs;&longs;et, <lb/>&longs;ed non &longs;ine Algebrâ. </s>

<s>Habeatur enim qua<lb/>dratum Geometricum <emph type="italics"/>S<emph.end type="italics"/>H; <lb/>vel etiam &longs;it rectangulum, <lb/><figure id="fig11"></figure><lb/>cuius latus AS maius &longs;it late<lb/>re AH, id quod aliquando <lb/>commodius accidet. </s>

<s>Habeatur enim qua<lb/>dratum Geometricum <emph type="italics"/>S<emph.end type="italics"/>H; <lb/>vel etiam &longs;it rectangulum, <lb/><figure id="fig11"/><lb/>cuius latus AS maius &longs;it late<lb/>re AH, id quod aliquando <lb/>commodius accidet. </s>

<s>Obuer<lb/>tatur latus AH ita, vt con<lb/>gruat radio optico terra&mtail; <lb/>tangenti AD, in &longs;uperior&etail; <lb/>figurâ: eritque triangulum <lb/>ABE &longs;imile triangulo OAS: Nam anguli <lb/>SAH & BEA &longs;unt recti, ac proinde lineæ <lb/>SA, BE parallelæ, intrà quas anguli alterni <lb/>SAO, EBA &longs;unt æquales; &longs;icut & alterni <lb/>EAB, SOA, intra parallelas SO, AE. </s>

<s>Igi<lb/>tur vt OA ad AS, ita AB ad BE: &longs;ed vt AB <lb/>ad BE, ita in &longs;uperiore figurâ AC ad CD; <lb/>ergo vt OA ad AS, ita AC ad CD. </s>

<s>Igi<lb/>tur vt OA ad AS, ita AB ad BE: &longs;ed vt AB <lb/>ad BE, ita in &longs;uperiore figurâ AC ad CD; <lb/>ergo vt OA ad AS, ita AC ad CD. </s>

<s>Quare <lb/>&longs;i latus AS Quadrati vel rectanguli notum &longs;it <lb/>in particulis quibuslibet, facilè innote&longs;cet, <lb/>quot huiu&longs;modi particulas contineat AO. </s>

<s><lb/>Cum verò altitudo AB nota &longs;it ex.gr.ped. <pb pagenum="68"/>480, a&longs;&longs;umatur BC 1 &rx;: tum fiat vt particu<lb/>læ OA ad particulas AS, ita ped. </s>

<s><lb/>Cum verò altitudo AB nota &longs;it ex.gr.ped. <pb pagenum="68"/>480, a&longs;&longs;umatur BC 1 &rx;: tum fiat vt particu<lb/>læ OA ad particulas AS, ita ped. 1 &rx; + 480 <lb/>ad aliud, & proueniet quartus terminus CD <lb/>æqualis ip&longs;i CB 1 &rx;: atque adeò factâ Anti<lb/>the&longs;i, & in&longs;titutâ diui&longs;ione habetur quanti<lb/>tas ip&longs;ius CD. </s>

<s>1 &rx; + 480 <lb/>ad aliud, & proueniet quartus terminus CD <lb/>æqualis ip&longs;i CB 1 &rx;: atque adeò factâ Anti<lb/>the&longs;i, & in&longs;titutâ diui&longs;ione habetur quanti<lb/>tas ip&longs;ius CD. </s>

<s><margin.target id="note33"></margin.target><emph type="italics"/>XXXIII <lb/>Idem aliter <lb/>&longs;ine Trigo<lb/>nometria.<emph.end type="italics"/></s>

<s><margin.target id="note33"/><emph type="italics"/>XXXIII <lb/>Idem aliter <lb/>&longs;ine Trigo<lb/>nometria.<emph.end type="italics"/></s>

<s>quod &longs;inè Algebiâ res tam facilis <lb/><arrow.to.target n="note34"></arrow.to.target><lb/>e&longs;t, vt penè non audeam dicere, ne vulgata <lb/>vile&longs;cat. </s>

<s>quod &longs;inè Algebiâ res tam facilis <lb/><arrow.to.target n="note34"/><lb/>e&longs;t, vt penè non audeam dicere, ne vulgata <lb/>vile&longs;cat. </s>

<s>Fiat vt OI, differentia inter OA & <lb/>AS, ad ip&longs;am AS, ita nota altitudo AB ad <lb/>aliud, & proueniet CD quæ&longs;ita terræ &longs;emi<lb/>diameter. </s>

<s>E&longs;t nimirum AB differentia inter <lb/>AC & CD, & vt tota AC ad totam AO, ita <lb/>ablata CB ad ablatam AI; igitur & reliqua <lb/>AB ad reliquam IO vt tota AC ad totam <lb/>AO: ergo permutando, & diuidendo, vt <lb/>AB ad BC, hoc e&longs;t CD, ita OI ad IA, hoc <lb/>e&longs;t AS. </s>

<s><margin.target id="note34"></margin.target><emph type="italics"/>XXXIV <lb/>Idem &longs;ine <lb/>Trigonome<lb/>tria & &longs;ine <lb/>Algebra.<emph.end type="italics"/></s>

<s><margin.target id="note34"/><emph type="italics"/>XXXIV <lb/>Idem &longs;ine <lb/>Trigonome<lb/>tria & &longs;ine <lb/>Algebra.<emph.end type="italics"/></s>

<s>Et hæc quidem dicta &longs;int, &longs;i fortè angu<lb/><arrow.to.target n="note35"></arrow.to.target><lb/>lum CAD præcogno&longs;cere non libeat. </s>

<s>Et hæc quidem dicta &longs;int, &longs;i fortè angu<lb/><arrow.to.target n="note35"/><lb/>lum CAD præcogno&longs;cere non libeat. </s>

<s>Cæ<lb/>terùm illo cognito rem aggredi licet &longs;ine <lb/>Algebrâ ope &longs;oliûs Trigonometriæ, quæ <lb/>multiplicem &longs;ubmini&longs;trare poterit metho<lb/>dum. </s>

<s>Et primò datâ altitudine AB, & an<lb/>gulo ad A ob&longs;eruato ex. </s>

<s>gr.gr.89.m.36.&longs;ec. </s>

<s>gr.gr.89.m.36.&longs;ec. <lb/>33., notus e&longs;t angulus ad centrum C gr.o. <lb/>m.23.&longs;ec.27, ac proinde eius &longs;ubten&longs;a i&ntail; <lb/>partibus Radij innote&longs;cit. </s>

<s><lb/>33., notus e&longs;t angulus ad centrum C gr.o. </s>

<s><lb/>m.23.&longs;ec.27, ac proinde eius &longs;ubten&longs;a i&ntail; <lb/>partibus Radij innote&longs;cit. </s>

<s>Igitur ductâ BD, <pb pagenum="69"/>duo anguli ad ba&longs;im BD &longs;imul &longs;umpti &longs;unt <lb/>æquales recto CDA vnâ cum angulo ob&longs;er<lb/>uato A. </s>

<s>Igitur ductâ BD, <pb pagenum="69"/>duo anguli ad ba&longs;im BD &longs;imul &longs;umpti &longs;unt <lb/>æquales recto CDA vnâ cum angulo ob&longs;er<lb/>uato A. </s>

<s>Cum verò triangulum CBD &longs;it <gap/>&longs;o<lb/>&longs;celes, vnu&longs;qui&longs;que an<lb/><figure id="fig12"/><lb/>gulorum ad ba&longs;im BD <lb/>e&longs;t æqualis &longs;emirecto & <lb/>&longs;emiangulo ob&longs;eruato. </s>

<s>Cum verò triangulum CBD &longs;it <gap/>&longs;o<lb/>&longs;celes, vnu&longs;qui&longs;que an<lb/><figure id="fig12"></figure><lb/>gulorum ad ba&longs;im BD <lb/>e&longs;t æqualis &longs;emirecto & <lb/>&longs;emiangulo ob&longs;eruato. </s>

<s><lb/>Deme ergo &longs;emiangu<lb/>lum ob&longs;eruatum gr.44. <lb/>48. 16 1/2, ex angulo &longs;e<lb/>mirecto, hoc<gap/> e&longs;t grad. <lb/>45, remanet gr.o.m.11. <lb/>fec. </s>

<s><lb/>Deme ergo &longs;emiangu<lb/>lum ob&longs;eruatum gr.44. <lb/>48. 16 1/2, ex angulo &longs;e<lb/>mirecto, hoc<gap/> e&longs;t grad. </s>

<s><lb/>45, remanet gr.o.m.11. <lb/>fec. </s>

<s>43 1/2 quantitas angu<lb/>li ADB: Hic autem angulus ADB &longs;emper <lb/>e&longs;t femi&longs;fis complementi anguli ad A ob&longs;er<lb/>uati; angulo enim ADB facto ad punctum <lb/>contactûs e&longs;t æqualis angulus in &longs;egmento <lb/>alterno, anguli verò ad peripheriam duplex <lb/>e&longs;t angulus ad centrum C. </s>

<s>In triangulo ita<lb/>que ADB noti &longs;unt duo anguli ad A & ad D; <lb/>& latus BD notum e&longs;t in partibus 682. <lb/>13152.quarum Radius 100000.00000; ideo<lb/>que in ij&longs;dem Radij partibus inuenitur AB <lb/>partium 232657. Iam fiat vt AB partium <lb/>232657 ad Radium 100000.00000, ita AB <lb/>ped. 480 ad aliud, & prodibit quantitas BC <lb/>terrenæ &longs;emidiametri ped. 20631229, hoc <lb/>e&longs;t mill. 4126. pa&longs;&longs;. </s>

<s>480 ad aliud, & prodibit quantitas BC <lb/>terrenæ &longs;emidiametri ped. </s>

<s>20631229, hoc <lb/>e&longs;t mill. </s>

<s>4126. pa&longs;&longs;. </s>

<s>246. Quod verò ali-<pb pagenum="70"/>quod intercedat di&longs;crimen inter hanc & dia<lb/>trum &longs;uperiùs inuentam, nil mirum, qui&atail; <lb/>vbi multiplex diui&longs;io intercedit, fractiones <lb/>aliquæ negligun<lb/><figure id="fig13"></figure><lb/>tur, vnde demum <lb/>aliqua oritur dif<lb/>ferentia. </s>

<s><margin.target id="note35"></margin.target><emph type="italics"/>XXXV <lb/>Idem aliter <lb/>per Trigo<lb/><gap/>ometriam.<emph.end type="italics"/></s>

<s>Sed placeat hìc <lb/><arrow.to.target n="note36"></arrow.to.target><lb/>vnum prætere&atail; <lb/>ob&longs;eruare, quo mi<lb/>rificè &longs;um delecta<lb/>tus, cum primùm <lb/>animaduerti: <expan abbr="Do-ctrinã">Do<lb/>ctrinam</expan> &longs;cilicet Tri<lb/>gonometricam illud idem exhibere po&longs;&longs;&etail;, <lb/>quod ab Algebrâ, in &longs;ecundâ methodo indi<lb/>catâ, po&longs;t omnes æquationes &longs;ubmini&longs;tra<lb/>tur. </s>

<s>246. Quod verò ali-<pb pagenum="70"/>quod intercedat di&longs;crimen inter hanc & dia<lb/>trum &longs;uperiùs inuentam, nil mirum, qui&atail; <lb/>vbi multiplex diui&longs;io intercedit, fractiones <lb/>aliquæ negligun<lb/><figure id="fig13"/><lb/>tur, vnde demum <lb/>aliqua oritur dif<lb/>ferentia. </s>

<s><margin.target id="note35"/><emph type="italics"/>XXXV <lb/>Idem aliter <lb/>per Trigo<lb/><gap/>ometriam.<emph.end type="italics"/></s>

<s>Sed placeat hìc <lb/><arrow.to.target n="note36"/><lb/>vnum prætere&atail; <lb/>ob&longs;eruare, quo mi<lb/>rificè &longs;um delecta<lb/>tus, cum primùm <lb/>animaduerti: <expan abbr="Do-ctrinã">Do<lb/>ctrinam</expan> &longs;cilicet Tri<lb/>gonometricam illud idem exhibere po&longs;&longs;&etail;, <lb/>quod ab Algebrâ, in &longs;ecundâ methodo indi<lb/>catâ, po&longs;t omnes æquationes &longs;ubmini&longs;tra<lb/>tur. </s>

<s>Fiat enim vt Sinus Ver&longs;us comple<lb/>menti anguli ob&longs;eruati, ad eiu&longs;dem anguli <lb/>ob&longs;eruati Sinum Rectum, ita nota altitudo <lb/>ad aliud, & habebitur quæ&longs;ita terræ &longs;emi<lb/>diameter. </s>

Line 1130

Line 1139

<s>Eadem ergo e&longs;t Ratio AB <lb/>ad BC, quæ e&longs;t ED ad DC. </s>

<s>E&longs;t autem AD <pb pagenum="71"/>Sinus anguli ACE, eiusque Sinus Ver&longs;us e&longs;t <lb/>DE. </s>

<s>E&longs;t autem AD <pb pagenum="71"/>Sinus anguli ACE, eiusque Sinus Ver&longs;us e&longs;t <lb/>DE. </s>

<s>At CD e&longs;t æqualis Sinui Recto anguli <lb/>CAD ob&longs;eruati; e&longs;t &longs;iquidem CD æqualis <lb/>&longs;inui complementi anguli C. </s>

<s>At CD e&longs;t æqualis Sinui Recto anguli <lb/>CAD ob&longs;eruati; e&longs;t &longs;iquidem CD æqualis <lb/>&longs;inui complementi anguli C. </s>

<s>Igitur quæ <lb/>Ratio e&longs;t ip&longs;ius DE Sinus Ver&longs;i complemen<lb/>ti anguli ob&longs;eruati, ad DC Sinum anguli A <lb/>ob&longs;eruati, ea e&longs;t ip&longs;ius altitudinis notæ BA, <lb/>ad| quæ&longs;itam terræ &longs;emidiametrum BC. </s>

<s><lb/>Quarè &longs;inum anguli ob&longs;eruati 99997.67348 <lb/>deme ex Radio, & remanet 232652. Sinus <lb/>Ver&longs;us complementi.Iam &longs;i fiat vt 232652. <lb/>ad 99997.67348, ita nota altitudo ped. <lb/>480. ad ped. 20631193, eadem inuenitur <lb/>&longs;emidiameter, quæ &longs;uperiùs per Algebram <lb/>innotuit. </s>

<s>20631193, eadem inuenitur <lb/>&longs;emidiameter, quæ &longs;uperiùs per Algebram <lb/>innotuit. </s>

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

<s><margin.target id="note37"></margin.target><emph type="italics"/>XXXVII <lb/>Quam exa<lb/>ctè ob&longs;erua. </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"/><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"/><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"/></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><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"/></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><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"/></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><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"/></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"/>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"/></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><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. ferè quinquaginta, & in eius ex<lb/>tremo puncto, quod eam cæli plagam re-<pb pagenum="75"/>&longs;piciebat, in qua aliquid occurrebat ob&longs;er<lb/>uandum, axiculum ritè infigi curaui, circa <lb/>quem po&longs;&longs;et dioptra conuerti. </s>

<s>Duxeram in plano <lb/>verticali lineam horizontalem longam pe<lb/>des Rom. </s>

<s>ferè quinquaginta, & in eius ex<lb/>tremo puncto, quod eam cæli plagam re-<pb pagenum="75"/>&longs;piciebat, in qua aliquid occurrebat ob&longs;er<lb/>uandum, axiculum ritè infigi curaui, circa <lb/>quem po&longs;&longs;et dioptra conuerti. </s>

<s>Erat autem <lb/>animus parare regulam longam pedes 42, <lb/>cuius latitudo 4. digitos, cra&longs;&longs;ities aute&mtail; <lb/>duos digitos obtineret; &longs;ic enim fieri po&longs;&longs;e <lb/>&longs;perabam, vt latitudine in altitudinem con<lb/>uersâ, regula non adeò grauis horizontali<lb/>ter con&longs;tituta, & &longs;ecundum alteram extremi<lb/>tatem axiculo in&longs;erta, non &longs;inuaretur, nec <lb/>à &longs;uâ rectitudine deflecteret: cùm maximè <lb/>decreui&longs;&longs;em ita illi aliam regulam breuiorem <lb/>&longs;ubiicere, in modum vectis primi generis, vt <lb/>inferiorem regulam premens eleuarem &longs;u<lb/>periorem, quæ circiter duas tertias &longs;uæ lon<lb/>gitudinis partes (hoc e&longs;t circirer pedem ab <lb/>axiculo, circa quem volueretur, trige&longs;imum) <lb/>&longs;u&longs;tentata à &longs;uppo&longs;ito vecte non e&longs;&longs;et adeò <lb/>obnoxia inflexioni. </s>

<s>Tum regulæ longitudi<lb/>ne in pedes di&longs;tinctâ; accipiendi erant pedes <lb/>41 2/3, vt e&longs;&longs;ent in vniuer&longs;um vnciæ 500; cum <lb/>enim pedis vncia ita &longs;en&longs;ibiliter in laminâ <lb/>metallicâ diuidi queat in particulas 50 vt ha<lb/>beantur vnciæ particulæ cente&longs;imæ, erat Ra<lb/>dius circuli de&longs;cribendi partium 50000, &longs;ub<lb/>duplus numeri, qui habetur in Canone Tri<lb/>gonometrico communi. </s>

<s>Quare &longs;i hoc Ra<lb/>dio in plano verticali de&longs;cribatur arcus, & <pb pagenum="76"/>ad lineam horizontalem excitetur perpendi<lb/>cularis æqualis Tangenti gr. </s>

<s>Quare &longs;i hoc Ra<lb/>dio in plano verticali de&longs;cribatur arcus, & <pb pagenum="76"/>ad lineam horizontalem excitetur perpendi<lb/>cularis æqualis Tangenti gr. 1. (accepto &longs;e. <lb/></s>

<s>1. (accepto &longs;e. <lb/></s>

<s>&longs;emi&longs;&longs;e numeri Canonis in partibus vnciæ <lb/>cente&longs;imis) ab&longs;cindi poterit ex arcu gradus <lb/>vnus, cuius &longs;inus parum di&longs;tabit à palmo <lb/>Romano architectonico. </s>

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Line 1197

<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"/></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><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>

<s>Ne&longs;cio <lb/><arrow.to.target n="note38"/><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>

<s>In triangulum còag-<pb/><figure id="fig14"></figure><pb/><figure id="fig15"></figure><pb/><figure id="fig16"></figure><pb/><figure id="fig17"></figure><pb pagenum="77"/>mentatis tribus tigillis, ducatur recta AB <lb/>vnciarum 10. ex. </s>

<s>In triangulum còag-<pb/><figure id="fig14"/><pb/><figure id="fig15"/><pb/><figure id="fig16"/><pb/><figure id="fig17"/><pb pagenum="77"/>mentatis tribus tigillis, ducatur recta AB <lb/>vnciarum 10. ex. </s>

<s>gr. & &longs;uper eâ fiat triangu<lb/>lum æquilaterum AEB. </s>

<s>& &longs;uper eâ fiat triangu<lb/>lum æquilaterum AEB. </s>

<s>60. <lb/>Relinquitur autem tigillus EF longior, vt in <lb/>FA &longs;ecundùm rectam EA productam in F <lb/>con&longs;tituatur tubulus H infundibuli in mo<lb/>rem excauatus, per quem vi&longs;us rectâ traii<lb/>ciatur in de&longs;tinatum &longs;copum per aciculam <lb/>in E perpendiculariter erectam, ex qua de<lb/>pendet perpendiculum; hoc enim facit cum <lb/>lineâ EA angulum di&longs;tantiæ obiecti à verti<lb/>ce ob&longs;eruatoris. </s>

<s>Quod &longs;i tigilli ni<lb/>mis longi e&longs;&longs;ent, interuallo A<emph type="italics"/>e<emph.end type="italics"/> de&longs;cribantur <lb/>duo arcus &longs;e inuicem &longs;ecantes in <emph type="italics"/>i<emph.end type="italics"/>, & inter<lb/>uallo A<emph type="italics"/>u<emph.end type="italics"/> arcus &longs;e &longs;ecantes in <emph type="italics"/>o<emph.end type="italics"/>: per hæc enim <lb/>puncta ductâ lineâ ex A, accipi poterit AE <lb/>æqualis ip&longs;i AB, & erit angulus BAE gr. 60. <lb/>Relinquitur autem tigillus EF longior, vt in <lb/>FA &longs;ecundùm rectam EA productam in F <lb/>con&longs;tituatur tubulus H infundibuli in mo<lb/>rem excauatus, per quem vi&longs;us rectâ traii<lb/>ciatur in de&longs;tinatum &longs;copum per aciculam <lb/>in E perpendiculariter erectam, ex qua de<lb/>pendet perpendiculum; hoc enim facit cum <lb/>lineâ EA angulum di&longs;tantiæ obiecti à verti<lb/>ce ob&longs;eruatoris. </s>

<s>Quantitas verò huius an<lb/>guli per Trigonometriam reperitur ex datis <lb/>lateribus AE, & A<emph type="italics"/>u<emph.end type="italics"/> & angulo <emph type="italics"/>u<emph.end type="italics"/> AE compre<lb/>hen&longs;o gr. </s>

<s>60. ex con&longs;tructione. </s>

<s>Vel &longs;i fortè <lb/>breuiùs operari placeat, fingatur ex E puncto <lb/>in &longs;emi&longs;&longs;em lateris AB cadere linea perpen<lb/>dicularis, cuius quantitas facilè innote&longs;cit: <lb/>deinde illâ a&longs;&longs;umptâ vt Radio, vt Tangent&etail; <lb/>verò di&longs;tantiâ perpendiculi à medio lineæ <lb/>AB, angulus quæratur, quem facit perpen<lb/>diculum cum fictâ illâ perpendiculari; hic <lb/>enim angulus additus gradibus 30. &longs;i perpen-<pb pagenum="78"/>diculum cadat vltra &longs;emi&longs;&longs;em lineæ AB; <lb/>demptus autem ex gr. </s>

<s>30. &longs;i cadat citrà &longs;e<lb/>mi&longs;&longs;em, dabit angulum di&longs;tantiæ à vertice <lb/>quæ&longs;itum. </s>

<s>Quod &longs;i di&longs;tantia à vertice exce&longs;<lb/>&longs;erit gr. </s>

<s>60 perpendiculum cadet extrà latus <lb/>BE; idcirco &longs;u&longs;pendendum èrit ex I puncto, <lb/>quod bifariam diuidit rectam AE; & &longs;iqui<lb/>dem obiectum in Horizonte fuerit, perpen<lb/>diculum ex I cadet in B, &longs;i verò &longs;upra Hori<lb/>zontem, cadet in latus AB, &longs;i demum infra <lb/>lineam Horizonti parallelam depre&longs;&longs;um fue<lb/>rit, cadet perpendiculum in latus BE: &longs;em<lb/>per autem in note&longs;cet angulus &longs;actus à perpen<lb/>diculo & lineâ FI visûs, dantur enim vel la<lb/>tera IA & AB, vel IE & EB cum angulo <lb/>comprehen&longs;o: vel &longs;altem in vtroque latere <lb/>de&longs;ignari poterit punctum, in quod ad rectos <lb/>angulos cadit linea ex I. </s>

<s><margin.target id="note38"></margin.target><emph type="italics"/>XXXVIII <lb/>V&longs;us Tri<lb/>goni æqui<lb/>lateri ad <lb/>ob&longs;eruandos <lb/>angulos, in <lb/>quo vix er<lb/>rari po&longs;sit à <lb/>Geometra.<emph.end type="italics"/></s>

<s>Quod &longs;i di&longs;tantia à vertice exce&longs;<lb/>&longs;erit gr. 60 perpendiculum cadet extrà latus <lb/>BE; idcirco &longs;u&longs;pendendum èrit ex I puncto, <lb/>quod bifariam diuidit rectam AE; & &longs;iqui<lb/>dem obiectum in Horizonte fuerit, perpen<lb/>diculum ex I cadet in B, &longs;i verò &longs;upra Hori<lb/>zontem, cadet in latus AB, &longs;i demum infra <lb/>lineam Horizonti parallelam depre&longs;&longs;um fue<lb/>rit, cadet perpendiculum in latus BE: &longs;em<lb/>per autem in note&longs;cet angulus &longs;actus à perpen<lb/>diculo & lineâ FI visûs, dantur enim vel la<lb/>tera IA & AB, vel IE & EB cum angulo <lb/>comprehen&longs;o: vel &longs;altem in vtroque latere <lb/>de&longs;ignari poterit punctum, in quod ad rectos <lb/>angulos cadit linea ex I. </s>

<s><margin.target id="note38"/><emph type="italics"/>XXXVIII <lb/>V&longs;us Tri<lb/>goni æqui<lb/>lateri ad <lb/>ob&longs;eruandos <lb/>angulos, in <lb/>quo vix er<lb/>rari po&longs;sit à <lb/>Geometra.<emph.end type="italics"/></s>

<s>Vt verò in quàm minimas particulas di<lb/>ui&longs;am haberet rectam AB, iubebam duci <lb/>AC æqualem vni ex ijs partibus, in quas pri<lb/>mò di&longs;tinctam eam po&longs;uimus, nempe i&ntail; <lb/>vncias pedis, & perfici parallelogrammum <lb/>ABDC. </s>

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<s>At &longs;i ex editiore loco deor&longs;um <lb/>&longs;pectandum &longs;it, & perpendiculum ex I &longs;u<lb/>&longs;pen&longs;um cadat in latus EB tam propè ip&longs;um <lb/>B, vt non facilè po&longs;sint particulæ numera<lb/>ri, erigatur ad latus AE regula perpendicu<lb/>laris, in qua recta ex B per I ducta faciat an<lb/>gulum EIG rectum, & &longs;umatur IG æqualis <lb/>ip&longs;i IE, & ex G &longs;u&longs;pendatur perpendiculum, <lb/>quod intelligatur cadere ex. </s>

<s>Si <lb/>enim concipiatur ex I aliud perpendiculum <lb/>IS, vtique linea IG incidens in duas paralle<lb/>las IS, & GR facit angulum SIB externum <pb pagenum="80"/>æqualem interno RGI: inuento igitur RGI, <lb/>innote&longs;cit angulus, quem cum perpendicu<lb/>lo facit linea vi&longs;ualis AE. </s>

<s>Cum itaque IE & <lb/>IG æquales &longs;int & ad angulum rectum, con<lb/>ceptâ rectâ EG angulus EGI e&longs;t gr. 45, cui <lb/>æqualis reliquus GEI additus angulo BEA gr. <lb/>60. fit totus angulus GER gr. 105; latus au<lb/>tem EG &longs;ubtendens angulum rectum, no<lb/>tum e&longs;t, cum nota &longs;int latera IG, & IE; de<lb/>mum notum e&longs;t latus ER. </s>

<s>Cum itaque IE & <lb/>IG æquales &longs;int & ad angulum rectum, con<lb/>ceptâ rectâ EG angulus EGI e&longs;t gr. </s>

<s>45, cui <lb/>æqualis reliquus GEI additus angulo BEA gr. </s>

<s><lb/>60. fit totus angulus GER gr. </s>

<s>105; latus au<lb/>tem EG &longs;ubtendens angulum rectum, no<lb/>tum e&longs;t, cum nota &longs;int latera IG, & IE; de<lb/>mum notum e&longs;t latus ER. </s>

<s>Quare ex notis <lb/>lateribus EG & ER vnâ cum angulo com<lb/>prehen&longs;o inuenitur angulus EGR, qui dem<lb/>ptus ex EGI gr. </s>

<s>45. relinquit notum RGI <lb/>æqualem angulo SIB; & &longs;ic innote&longs;cit angu<lb/>lus SIE æqualis angulo, quem facit linea vi<lb/>&longs;ualis EA <expan abbr="c&utilde;">cum</expan> lineâ AT iungente oculum ob<lb/>&longs;eruatoris cum centro terræ. </s>

<s>Quare ex notis <lb/>lateribus EG & ER vnâ cum angulo com<lb/>prehen&longs;o inuenitur angulus EGR, qui dem<lb/>ptus ex EGI gr. 45. relinquit notum RGI <lb/>æqualem angulo SIB; & &longs;ic innote&longs;cit angu<lb/>lus SIE æqualis angulo, quem facit linea vi<lb/>&longs;ualis EA <expan abbr="c&utilde;">cum</expan> lineâ AT iungente oculum ob<lb/>&longs;eruatoris cum centro terræ. </s>

<s>Cum igitur &longs;atis <lb/>amplum huiu&longs;modi triangulum facilè po&longs;si<lb/>mus con&longs;truere, etiam additâ regulâ IG, & <lb/>alibi diui&longs;am vnciam habere po&longs;simus i&ntail; <lb/>partes &longs;altem cente&longs;imas eâ methodo, quam <lb/>indicat Adrianus Metius in &longs;uâ Geometriâ, <lb/>patet fieri po&longs;&longs;e, vt quàm euidenti&longs;simè in<lb/>notefcat angulus ille, quem ob&longs;eruatum &longs;up<lb/>ponebam ad inue&longs;tigandam terræ magnitu<lb/>dinem. </s>

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

<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><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"/><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>Ea nimirum quamuis remotior&atail; <lb/>con&longs;piciuntur, quæ vberiori lumine &longs;iuè in<lb/>nato, & in&longs;ito, &longs;iuè extrin&longs;ecùs mutuato per<lb/>funduntur. </s>

<s><margin.target id="note39"></margin.target><emph type="italics"/>XXXIX <lb/>Maxima vi<lb/>&longs;us dictan<lb/>tia ex qui<lb/>bus debeai <lb/>definiri.<emph.end type="italics"/></s>

<s><margin.target id="note39"/><emph type="italics"/>XXXIX <lb/>Maxima vi<lb/>&longs;us dictan<lb/>tia ex qui<lb/>bus debeai <lb/>definiri.<emph.end type="italics"/></s>

<s>Semotis igitur omnibus hi&longs;ce impedi<lb/>mentis, per quæ fieret, quominùs certi ali<lb/>quid de visûs di&longs;tantiâ &longs;tatui po&longs;&longs;et; phy&longs;ici <lb/>horizontis &longs;emidiameter ex ipsâ terreni glo<lb/>bi configuratione petenda e&longs;t. </s>

Line 1270

Line 1279

<s>Hinc circulus partem hanc a&longs;pe<lb/>ctabilem à latente di&longs;pe&longs;cens, Horizontis <lb/>Phy&longs;ici nomine donatus e&longs;t, vt ab eo &longs;ecer<lb/>natur Horizonte, qui tellurem in duo hemi<lb/>&longs;phæria &longs;egregans, quia non oculo, &longs;ed <expan abbr="&longs;olã">&longs;olam</expan> <lb/>ratione comprehendi pote&longs;t, Rationalis di<lb/>citur. </s>

<s>Quamuis autem Phy&longs;ici Horizontis dia<lb/>meter tota intrà terræ cra&longs;situdinem deliteat, <lb/>quippe quæ recta e&longs;t linea arcui illi &longs;ubten&longs;a, <lb/>qui extremis terminis oculi Ortum Occa<lb/>&longs;umque circum&longs;picientis intercluditur: quia <lb/>tamen arcus huiu&longs;modi exiguo di&longs;crimin&etail; <lb/>quod vix &longs;ub &longs;en&longs;um ca<lb/><figure id="fig18"></figure><lb/>dat, &longs;ubten&longs;æ rectæ li<lb/>neæ longitudinem &longs;upe<lb/>rat; ideò non abs re ar<lb/>cus ip&longs;e pro phy&longs;ici hori<lb/>zontis &longs;emidiametro in<lb/>di&longs;criminatim v&longs;urpatur; <lb/>huiu&longs;ce &longs;emi&longs;sis maxi<lb/>mam obiecti a&longs;pectabilis <lb/>di&longs;tantiam metitur. </s>

<s>Quamuis autem Phy&longs;ici Horizontis dia<lb/>meter tota intrà terræ cra&longs;situdinem deliteat, <lb/>quippe quæ recta e&longs;t linea arcui illi &longs;ubten&longs;a, <lb/>qui extremis terminis oculi Ortum Occa<lb/>&longs;umque circum&longs;picientis intercluditur: quia <lb/>tamen arcus huiu&longs;modi exiguo di&longs;crimin&etail; <lb/>quod vix &longs;ub &longs;en&longs;um ca<lb/><figure id="fig18"/><lb/>dat, &longs;ubten&longs;æ rectæ li<lb/>neæ longitudinem &longs;upe<lb/>rat; ideò non abs re ar<lb/>cus ip&longs;e pro phy&longs;ici hori<lb/>zontis &longs;emidiametro in<lb/>di&longs;criminatim v&longs;urpatur; <lb/>huiu&longs;ce &longs;emi&longs;sis maxi<lb/>mam obiecti a&longs;pectabilis <lb/>di&longs;tantiam metitur. </s>

<s>Ex his &longs;ic ille argumentabatur. </s>

<s>Sit arcus <lb/><arrow.to.target n="note40"></arrow.to.target><lb/>AB men&longs;ura di&longs;tantiæ vi&longs;us, qui non à rectâ <lb/>lineâ &longs;en&longs;ibiliter deflectat<gap/>e&longs;t igitur AB recta <lb/>perpendiculariter in&longs;i&longs;tens rectæ DC: radius <pb pagenum="84"/>autem opticus DB terram tangens facit cum <lb/>&longs;emidiametro angulum DBC rectum. </s>

<s>Sit arcus <lb/><arrow.to.target n="note40"/><lb/>AB men&longs;ura di&longs;tantiæ vi&longs;us, qui non à rectâ <lb/>lineâ &longs;en&longs;ibiliter deflectat<gap/>e&longs;t igitur AB recta <lb/>perpendiculariter in&longs;i&longs;tens rectæ DC: radius <pb pagenum="84"/>autem opticus DB terram tangens facit cum <lb/>&longs;emidiametro angulum DBC rectum. </s>

<s>Igi<lb/>tur recta AB ab angulo recto ad B cadens i&ntail; <lb/>ba&longs;im perpendicularis, e&longs;t medio loco pro<lb/>portionalis inter &longs;egmenta DA & AC. </s>

<s>Igi<lb/>tur recta AB ab angulo recto ad B cadens i&ntail; <lb/>ba&longs;im perpendicularis, e&longs;t medio loco pro<lb/>portionalis inter &longs;egmenta DA & AC. </s>

<s>Qua<lb/>rè diui&longs;o quadrato maximæ visûs di&longs;tantiæ <lb/>AB per altitudinem AD, prouenit quæ&longs;it&atail; <lb/>terræ &longs;emidiameter AC. </s>

<s>Qua<lb/>rè diui&longs;o quadrato maximæ visûs di&longs;tantiæ <lb/>AB per altitudinem AD, prouenit quæ&longs;it&atail; <lb/>terræ &longs;emidiameter AC. </s>

<s>Verùm arcum <lb/>pro rectâ lineâ a&longs;&longs;umere parùm Geometri<lb/>cum e&longs;t. </s>

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

<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><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"/><lb/>per circulos Azimuthales; &longs;i nimirùm duo<lb/>rum locorum, quorum alteruter ex alterius <lb/>editâ turri con&longs;pici queat, nota fuerit di&longs;tan<lb/>tia, & poli altitudo. </s>

<s>In &longs;ummâ enim turri <lb/>planum horizontale con&longs;tituatur, in eoque <lb/>meridiana linea de&longs;cribatur: tum ob&longs;eruetur <lb/>&longs;ub quo Azimutho locus alter con&longs;picuus <lb/>appareat: & ex his datis quæ&longs;ita eruantur. </s>

<s><lb/>Sit PAC loci Meridianus, vbi ob&longs;eruatio in<lb/>&longs;tituitur<gap/>; Verticalis per vtrumque locum <lb/>tran&longs;iens AB, cum Meridiano faciat angu<lb/>lum CAB ob&longs;eruatum; P verò &longs;it Polus, & <lb/>AP, BP &longs;int complementa nota datarum <lb/>poli eleuationum. </s>

<s>Cum itaque in triangu<lb/>lo &longs;phærico BAP nota &longs;int duo latera AP, <lb/>BP, & angulus BAP complementum angu-<pb pagenum="85"/>li ob&longs;eruati CAB ad duos rectos, inueniatur <lb/>AB in gradibus &longs;eu <lb/>graduum particulis. <lb/><figure id="fig19"/><lb/>Tum fiat vt AB pars, <lb/>inuenta ad totum cir<lb/>culum, hoc e&longs;t gr. <lb/>360, ita data duorum <lb/>locorum di&longs;tantia ad <lb/>aliud, & prodibunt <lb/>milliaria toti circulo <lb/>in terrâ maximo re&longs;pondentia. </s>

<s><lb/>360, ita data duorum <lb/>locorum di&longs;tantia ad <lb/>aliud, & prodibunt <lb/>milliaria toti circulo <lb/>in terrâ maximo re&longs;pondentia. </s>

<s>Notâ autem <lb/>circularis peripheriæ quantitate neminem <lb/>Geometram diameter quæ&longs;ita latere poterit. </s>

<s><lb/>Sed quoniam di&longs;tantia illa non adeò exigua <lb/>e&longs;&longs;e pote&longs;t, quæ careat omni &longs;u&longs;picione abu<lb/>sûs rectæ lineæ pro curuâ, ideò methodum <lb/>hanc inter qui&longs;quilias, à quibus parùm di<lb/>&longs;tat, reieci. </s>

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

<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><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Id tamen per &longs;ummam iniuriam <lb/><arrow.to.target n="note42"/><lb/>factum: neque enim magnum intercedere <lb/>pote&longs;t di&longs;crimen, quod propo&longs;ito officiat: e&longs;t <lb/>&longs;cilicet di&longs;crimen minus datâ altitudine. </s>

<s>Ex <lb/>altitudine enim BA pro&longs;piciénti pateat ar<lb/>cus BD, quem &longs;ubtendit recta BD, Tan<lb/>gens autem e&longs;t AD. </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>

<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"/><lb/>AD &longs;upra rectam BD <lb/>minor e&longs;t, quàm &longs;it <lb/>data altitudo BA; er<lb/>go multò minor e&longs;t <lb/>exce&longs;&longs;us rectæ AD <lb/>tangentis &longs;upra ar<lb/>cum BD, vel arcûs <lb/>BD &longs;upra rectam BD <lb/>&longs;ubten&longs;am. </s>

<s>Ne verò <lb/>po&longs;itâ altitudine BA notabili, cen&longs;eret quis <lb/>in&longs;ignem quoque e&longs;&longs;e differentiam inter cur<lb/>uam & rectam lineam, quæ locorum inter<lb/>ualla metiatur, animaduertere oportet ar<lb/>cum BD maiorem e&longs;&longs;e latere BD polygoni <lb/>in&longs;cripti, minorem autem latere EF polygo<lb/>ni circum&longs;cripti: at exce&longs;&longs;us lateris EF ad la<lb/>tus BD habet Rationem, quam EB ad BC. </s>

<s><lb/>Vnde liquet manife&longs;tè, quàm modico di<lb/>&longs;crimine differat arcus à rectâ vel &longs;ubtensâ <lb/>BD, vel tangente EF. </s>

<s><margin.target id="note42"></margin.target><emph type="italics"/>XXXXII. </s>

<s><margin.target id="note42"/><emph type="italics"/>XXXXII. </s>

<s><lb/>Differentia <lb/>longitudinis <lb/>inter arcum <lb/>et eius Tan<lb/>gentem vel <lb/>&longs;ubten&longs;am.<emph.end type="italics"/></s>

<s>Memini me aliquando calculos &longs;ubducen<lb/>tem, quàm longè pateat vi&longs;us Romæ è &longs;um<lb/>mo crucis apice, quæ ædis Apo&longs;tolorum <lb/>Principi &longs;acræ tholo incumbit. </s>

<s>deprehendi&longs;<lb/>&longs;e arcum DB gr. </s>

<s>deprehendi&longs;<lb/>&longs;e arcum DB gr. o. </s>

<s>23. &longs;tatuebam autem <lb/>in &longs;ingulos gradus milliaria Italica 60, vt <pb pagenum="87"/>nunc vulgaris fert opinio, crucis verò altitu<lb/>dinem &longs;upra maris Mediterranci &longs;uperfi<lb/>ciem ponebam palmorum, quorum v&longs;us ho<lb/>diè e&longs;t apud Romanos architectos, circiter <lb/>700. Quare arcus BD erat mill. 23. & Tan<lb/>gens AD mill. (23 441/100000), di&longs;crimine vix pa&longs;<lb/>&longs;uum 4 1/2. Quid igitur officiat, &longs;i quis pro <lb/>arcu BD a&longs;&longs;umat, aut &longs;ubten&longs;am BD, aut <lb/>tangentem EF, aut aliquam ex intermediis? </s>

<s>23. & Tan<lb/>gens AD mill. (23 441/100000), di&longs;crimine vix pa&longs;<lb/>&longs;uum 4 1/2. Quid igitur officiat, &longs;i quis pro <lb/>arcu BD a&longs;&longs;umat, aut &longs;ubten&longs;am BD, aut <lb/>tangentem EF, aut aliquam ex intermediis? </s>

<s><lb/>nullus &longs;iquidem oriri pote&longs;t error, qui &longs;ub <lb/>&longs;en&longs;um cadat. </s>

<s>Quod &longs;i, vt &longs;æpè fieri pote&longs;t, <lb/>di&longs;tantiam BD decempedâ dimetiamur, ni<lb/>hil erit quod de tuâ illâ methodo dubites, <lb/>Mer&longs;enne, non enim arcu pro rectâ abu<lb/>teris. </s>

<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><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>

<s>Simile quid in <lb/>hoc eodem Problemate mihi contigit expe<lb/>riri. </s>

Line 1344

Line 1353

<s>Hæc ta<lb/>men methodus po&longs;t dies aliquos di&longs;plicuit, <lb/>cum animaduerterem ingenio&longs;um A&longs;trono<lb/>mum eâdem viâ ince&longs;si&longs;&longs;e, & quidem fe<lb/>liciùs non Solem &longs;ed &longs;ydera fixa vertici pro<lb/>xima ob&longs;eruando, quæ nec parallaxi nec re, <lb/>fractioni &longs;unt obnoxia. </s>

<s><margin.target id="note43"></margin.target><emph type="italics"/>XXXXIII. </s>

<s><margin.target id="note43"/><emph type="italics"/>XXXXIII. </s>

<s><lb/>Tertia me<lb/>thodus in<lb/>uestigandi <lb/>ambitu&mtail; <lb/>terræ.<emph.end type="italics"/></s>

<s>Cæterùm ne ab in&longs;titutâ quæ&longs;tione de<lb/>flectamus, illud e&longs;t ob&longs;eruandum, quod &longs;i <lb/>cognitâ altitudine BA, & dato angulo ad A, <pb pagenum="89"/>vellet a&longs;&longs;umere triangulum rectangulum ad <lb/>B, vt notam faceret <lb/><figure id="fig21"></figure><lb/>di&longs;tantiam inter B & <lb/>D, &longs;ibique per&longs;uaderet <lb/>aut à ba&longs;i aut ab hy<lb/>pothenusâ illius <expan abbr="triã-guli">trian<lb/>guli</expan> exhiberi di&longs;tan<lb/>tiam BD, longè di<lb/>&longs;taret à veritate. </s>

<s>Cæterùm ne ab in&longs;titutâ quæ&longs;tione de<lb/>flectamus, illud e&longs;t ob&longs;eruandum, quod &longs;i <lb/>cognitâ altitudine BA, & dato angulo ad A, <pb pagenum="89"/>vellet a&longs;&longs;umere triangulum rectangulum ad <lb/>B, vt notam faceret <lb/><figure id="fig21"/><lb/>di&longs;tantiam inter B & <lb/>D, &longs;ibique per&longs;uaderet <lb/>aut à ba&longs;i aut ab hy<lb/>pothenusâ illius <expan abbr="triã-guli">trian<lb/>guli</expan> exhiberi di&longs;tan<lb/>tiam BD, longè di<lb/>&longs;taret à veritate. </s>

<s>Du<lb/>cta &longs;iquidem perpen<lb/>dicularis BH longè <lb/>minor e&longs;t arcu BD, cum &longs;it Tangens &longs;e<lb/>mi&longs;sis illius arcûs: hypothenu&longs;a verò AH <lb/>minor e&longs;t quàm tota Tangens AD, de<lb/>fectu æquali ip &longs;i ba&longs;i BH; &longs;unt enim HB, <lb/>HD æquales, cùm vtraque &longs;it circulum <lb/>tangens ab eodem puncto H ducta. </s>

<s>Qua<lb/>propter deberet aggregatum ex ba&longs;i BH <lb/>& hypothenusâ AH accipere, vt totam <lb/>AD haberet, quæ non multùm differt ab ar<lb/>cu BD, ni&longs;i altitudo BA fuerit mons aut &longs;co<lb/>pulus. </s>

<s>Quod &longs;i tuus ille terrenæ magnicudinis <lb/><arrow.to.target n="note44"></arrow.to.target><lb/>inue&longs;tigator lineam BD pro maximâ vi<lb/>sûs di&longs;tantiâ a&longs;&longs;ump&longs;i&longs;&longs;et, illa vtique media <lb/>e&longs;t proportionalis, ex cuius quadrato per no<lb/>ram altitudinem DA diui&longs;o prouenit tertius <pb pagenum="90"/>terminus, vnde terrena <lb/><figure id="fig22"></figure><lb/>&longs;emidiameter cogno&longs;ci<lb/>tur, non tamen ip&longs;a &longs;e<lb/>midiameter AG e&longs;t ter<lb/>tius analogiæ terminus, <lb/>&longs;ed potius conflatum ex <lb/>DC, CB: latus enim v<lb/>num trianguli rectan<lb/>guli e&longs;t medium propor<lb/>tionale inter differentiam <lb/>hypothenu&longs;æ ac reliqui lateris, & eorum ag<lb/>gregatum: ac proinde vt AD ad DB, it&atail; <lb/>DB ad DCB. </s>

<s>Quod &longs;i tuus ille terrenæ magnicudinis <lb/><arrow.to.target n="note44"/><lb/>inue&longs;tigator lineam BD pro maximâ vi<lb/>sûs di&longs;tantiâ a&longs;&longs;ump&longs;i&longs;&longs;et, illa vtique media <lb/>e&longs;t proportionalis, ex cuius quadrato per no<lb/>ram altitudinem DA diui&longs;o prouenit tertius <pb pagenum="90"/>terminus, vnde terrena <lb/><figure id="fig22"/><lb/>&longs;emidiameter cogno&longs;ci<lb/>tur, non tamen ip&longs;a &longs;e<lb/>midiameter AG e&longs;t ter<lb/>tius analogiæ terminus, <lb/>&longs;ed potius conflatum ex <lb/>DC, CB: latus enim v<lb/>num trianguli rectan<lb/>guli e&longs;t medium propor<lb/>tionale inter differentiam <lb/>hypothenu&longs;æ ac reliqui lateris, & eorum ag<lb/>gregatum: ac proinde vt AD ad DB, it&atail; <lb/>DB ad DCB. </s>

<s>Quare ex inuento tertio ter<lb/>mino debui&longs;&longs;et datam altitudinem DA de<lb/>mere, & re&longs;iduum bifariam diui&longs;um dedi&longs;<lb/>&longs;et quæ&longs;itam &longs;emidiametrum AC. </s>

<s>Hinc <lb/>rectè dicebas arcum illum pro rectâ lineâ <lb/>parùm Geometricè a&longs;&longs;umptum. </s>

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

<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><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>Nec ambigi vllo <lb/>pacto pote&longs;t, an Veteres horizontis phy&longs;ici <lb/>amplitudinem indagantes, altitudinem vl<lb/>lam humanâ maiorem a&longs;&longs;ump&longs;erint; eam <lb/>&longs;iquidem horizonti tribuendam cen&longs;uer&etail; <lb/>magnitudinem, quæ cum &longs;phæricæ &longs;uperfi<lb/>ciei pars &longs;it, à planâ tamen minimùm differ<lb/>re po&longs;&longs;it. </s>

<s>Hinc Macrobius Saturnal. </s>

<s>Hinc Macrobius Saturnal. lib.

7. <lb/>cap.

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>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>Et quia diximus quantum à cen-<emph.end type="italics"/><pb pagenum="92"/><emph type="italics"/>tro acies v&longs;que ad partem orbis extenditur, &longs;i<lb/>nè dubio in horizonte diametros orbis CCCLX <lb/>&longs;tadiorum e&longs;t: & &longs;i vlt eriùs qui intuetur ac<lb/>ce&longs;&longs;erit, &longs;eu retror&longs;um rece&longs;&longs;erit, &longs;imilem cir<lb/>ca &longs;e orbem videbit.<emph.end type="italics"/></s>

<s>Rogaui deinde vtrùm Macrobio potiùs <lb/><arrow.to.target n="note45"></arrow.to.target><lb/>&longs;tadijs 180 Phy&longs;ici Horizontis &longs;emidiame<lb/>trum de&longs;inienti acquie&longs;ceret, an verò &longs;ibi <lb/>cum Recentioribus quibu&longs;dam conueniret, <lb/>qui cum Clauio (cui facilè adh æ&longs;it Blanca<lb/>nus) in cap.2. &longs;phær. </s>

<s>Rogaui deinde vtrùm Macrobio potiùs <lb/><arrow.to.target n="note45"/><lb/>&longs;tadijs 180 Phy&longs;ici Horizontis &longs;emidiame<lb/>trum de&longs;inienti acquie&longs;ceret, an verò &longs;ibi <lb/>cum Recentioribus quibu&longs;dam conueniret, <lb/>qui cum Clauio (cui facilè adh æ&longs;it Blanca<lb/>nus) in cap.2. &longs;phær. </s>

<s>tanquam veritati ma<lb/>ximè con&longs;entaneam ad mittunt eorum &longs;en<lb/>tentiam, qui a&longs;pectum ad milliaria 62 1/2 pro<lb/>trahi opinantur. </s>

<s>Neque enim illum aut cum <lb/>Alberto Magno aut cum Proclo &longs;entire cen<lb/>&longs;ebam, quorum prior &longs;tadia mille, po&longs;te<lb/>rior bis mille horizontis phy&longs;ici &longs;emidiame<lb/>tro dedit. </s>

<s><margin.target id="note45"></margin.target><emph type="italics"/>XXXXV <lb/>Ostenditur <lb/>error ex ab<lb/><gap/>&longs;u lineæ <lb/>curuæ pro <lb/>rect a.<emph.end type="italics"/></s>

<s><margin.target id="note45"/><emph type="italics"/>XXXXV <lb/>Ostenditur <lb/>error ex ab<lb/><gap/>&longs;u lineæ <lb/>curuæ pro <lb/>rect a.<emph.end type="italics"/></s>

<s>Ille quidem con&longs;e&longs;tim Neotericorum<gap/><lb/>&longs;ententiam arripuit: &longs;ed vbi iu&longs;&longs;us e&longs;t AB <lb/>mill. 62 1/2 ad pedes 312500 reuocare, & <lb/>huius numeri quadratum 97656.250000. <lb/>diuidere per DA ped. 6, quanta e&longs;t hominis <lb/>mediocris altitudo, videns AC prouenir&etail; <lb/>maiorem milliarijs 3.000000, ad Macro<lb/>bium con&longs;ugit, & longitudinem AB &longs;tadiis <lb/>180 circum&longs;crip&longs;it: nec &longs;tadia Romana ped. <pb pagenum="93"/>625, &longs;ed Græca ped. 600 fui&longs;&longs;e contende<lb/>bat, cum ex Erato&longs;thene men&longs;ura illa de<lb/>&longs;umpta fui&longs;&longs;et. </s>

<s>Ille quidem con&longs;e&longs;tim Neotericorum<gap/><lb/>&longs;ententiam arripuit: &longs;ed vbi iu&longs;&longs;us e&longs;t AB <lb/>mill. </s>

<s>62 1/2 ad pedes 312500 reuocare, & <lb/>huius numeri quadratum 97656.250000. <lb/>diuidere per DA ped. </s>

<s>6, quanta e&longs;t hominis <lb/>mediocris altitudo, videns AC prouenir&etail; <lb/>maiorem milliarijs 3.000000, ad Macro<lb/>bium con&longs;ugit, & longitudinem AB &longs;tadiis <lb/>180 circum&longs;crip&longs;it: nec &longs;tadia Romana ped. <pb pagenum="93"/>625, &longs;ed Græca ped. </s>

<s>600 fui&longs;&longs;e contende<lb/>bat, cum ex Erato&longs;thene men&longs;ura illa de<lb/>&longs;umpta fui&longs;&longs;et. </s>

<s>Sed hìc pariter Syrtes inue<lb/>nit, cum reuocato &longs;tadiorum 180 numero <lb/>ad pedes 108000, eius quadratum 11664. <lb/>000000. diuidere tentans per pedes 6, quo<lb/>tientem pariter ampli&longs;&longs;imum deprehendit. </s>

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<s>Sed <lb/>placuit miti&longs;&longs;imè agere. </s>

<s>Quapropter eum <lb/>rogaui, vt &longs;altem AB milliarium trium, hoc <lb/>e&longs;t ped. </s>

<s>Quapropter eum <lb/>rogaui, vt &longs;altem AB milliarium trium, hoc <lb/>e&longs;t ped. 15000 con&longs;tituens tentaret, an ex <lb/>a&longs;&longs;umptâ priùs iu&longs;to maiore &longs;emidiametro <lb/>horizontis phy&longs;ici, an verò etiam ex metho<lb/>di ageometriâ enormi<gap/> illa magnitudo ori<lb/>retur: Quadratum itaque ped. 225.000000 <lb/>diuidens per DA ped.6, inueniebat AC ped. <lb/>37.500000, hoc e&longs;t mill. 7500; vnde oritur <lb/>terræ ambitus mill. 47 142 6/7 duplo maior, <lb/>quàm communiter concedatur. </s>

<s>15000 con&longs;tituens tentaret, an ex <lb/>a&longs;&longs;umptâ priùs iu&longs;to maiore &longs;emidiametro <lb/>horizontis phy&longs;ici, an verò etiam ex metho<lb/>di ageometriâ enormi<gap/> illa magnitudo ori<lb/>retur: Quadratum itaque ped. </s>

<s>225.000000 <lb/>diuidens per DA ped.6, inueniebat AC ped. </s>

<s><lb/>37.500000, hoc e&longs;t mill. </s>

<s>7500; vnde oritur <lb/>terræ ambitus mill. </s>

<s>47 142 6/7 duplo maior, <lb/>quàm communiter concedatur. </s>

<s>Mirabatur ille vehementer, quòd præter <lb/>&longs;pem tam procul à vero rece&longs;&longs;i&longs;&longs;et: &longs;ed nec <lb/>conceptam de maiore, iuxta communem <lb/>errorem, horizontis phy&longs;ici &longs;emidiametro <lb/>opinionem deponere audebat: hærebant &longs;ci<lb/>licet animo altè impre&longs;&longs;a plurium authorum <pb pagenum="94"/>effata, quibus 30 milliaria Italica videntur <lb/>mediocris visûs di&longs;tantia: quare multò pro<lb/>babilior ei apparebat Macrobrii atque Era<lb/>to&longs;thenis &longs;ententia di&longs;tantiam huiu&longs;modi &longs;ta, <lb/>&longs;tijs 180 de&longs;inientium. </s>

<s>Nos igitur ad exa<lb/>minandum contulimus telluris ambitum ab <lb/>Erato&longs;thene con&longs;titutum, an cum illa &longs;emi<lb/>diametto &longs;tadiorum 180 cohæreret: <emph type="italics"/>Eui-<emph.end type="italics"/><lb/><arrow.to.target n="note46"></arrow.to.target><lb/><emph type="italics"/>denti&longs;&longs;imis<emph.end type="italics"/> enim, vt Macrobius loquitur lib. </s>

<s>Nos igitur ad exa<lb/>minandum contulimus telluris ambitum ab <lb/>Erato&longs;thene con&longs;titutum, an cum illa &longs;emi<lb/>diametto &longs;tadiorum 180 cohæreret: <emph type="italics"/>Eui-<emph.end type="italics"/><lb/><arrow.to.target n="note46"/><lb/><emph type="italics"/>denti&longs;&longs;imis<emph.end type="italics"/> enim, vt Macrobius loquitur lib. <lb/>1. in &longs;omn. </s>

<s><lb/>1. in &longs;omn. </s>

<s>Scip. cap.

20. <emph type="italics"/>& indubitabilibus <lb/>dimen&longs;ionibus con&longs;tat vniuer&longs;æ terræ ambitum, <lb/>quæ vbicunque vel incolitur, vel inhabitabilis <lb/>iacet, habere &longs;tadiorum millia ducenta quin<lb/>quaginta duo.<emph.end type="italics"/></s>

<s> Cum verò huius peripheriæ <lb/>pars mille&longs;ima quadringente&longs;ima &longs;int &longs;tadia <lb/>180, per quæ directa ab oculis acies pergit, <lb/>arcus BA gr.o.m.15.&longs;ec.25. Ter. 42. &c. </s>

<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>

<s><lb/>metitur angulum BCD in centro factum. </s>

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<s>80207 1/2, <lb/>& &longs;emidiameter CA &longs;tad. </s>

<s>40103 3/4. Fiat igitur <lb/>vt CB 99998.99293. &longs;inus complementi <lb/>gr.o.m.15.&longs;ec. </s>

<s>40103 3/4. Fiat igitur <lb/>vt CB 99998.99293. &longs;inus complementi <lb/>gr.o.m.15.&longs;ec. 25. Ter.42. ad CD Radium <lb/>100000.00000, ita CB &longs;tad.40103 3/4 ad CD <lb/>&longs;tad, 40104, & ped.92. Demptâ autem CA <pb pagenum="95"/>&longs;emidiametro, remanet AD ped. 242, alti<lb/>tudo, ex qua pro&longs;pici pote&longs;t in B ita, vt a&longs;pe<lb/>ctui pateant &longs;tadia 180. Quî autem &longs;ieri po&longs;<lb/>&longs;it ab intuente &longs;imilem &longs;emper orbem vide<lb/>ri, &longs;iuè vlteriùs acce&longs;&longs;erit, &longs;iue retror&longs;um re<lb/>ce&longs;&longs;erit, Macrobius ip&longs;e viderit: an &longs;emper <lb/>eam inueniat altinudinem, cui in&longs;i&longs;tat, vt <lb/>oculus ab extimâ telluris facie pedibus 242 <lb/>&longs;emoueatur? </s>

<s>25. Ter.42. ad CD Radium <lb/>100000.00000, ita CB &longs;tad.40103 3/4 ad CD <lb/>&longs;tad, 40104, & ped.92. Demptâ autem CA <pb pagenum="95"/>&longs;emidiametro, remanet AD ped. </s>

<s>242, alti<lb/>tudo, ex qua pro&longs;pici pote&longs;t in B ita, vt a&longs;pe<lb/>ctui pateant &longs;tadia 180. Quî autem &longs;ieri po&longs;<lb/>&longs;it ab intuente &longs;imilem &longs;emper orbem vide<lb/>ri, &longs;iuè vlteriùs acce&longs;&longs;erit, &longs;iue retror&longs;um re<lb/>ce&longs;&longs;erit, Macrobius ip&longs;e viderit: an &longs;emper <lb/>eam inueniat altinudinem, cui in&longs;i&longs;tat, vt <lb/>oculus ab extimâ telluris facie pedibus 242 <lb/>&longs;emoueatur? </s>

<s>Horizontis igitur &longs;emidiame<lb/>trum aut &longs;tadijs 180 minorem e&longs;&longs;e, aut non <lb/>ex humani corporis altitudine de&longs;iniri ne<lb/>ce&longs;&longs;e e&longs;t. </s>

<s><margin.target id="note46"></margin.target><emph type="italics"/>XXXXVI <lb/>Authorum <lb/>aliquorum <lb/>lap&longs;us i&ntail; <lb/>statuend&atail; <lb/>nimia vi&longs;us <lb/>distantia.<emph.end type="italics"/></s>

<s><margin.target id="note46"/><emph type="italics"/>XXXXVI <lb/>Authorum <lb/>aliquorum <lb/>lap&longs;us i&ntail; <lb/>statuend&atail; <lb/>nimia vi&longs;us <lb/>distantia.<emph.end type="italics"/></s>

<s>Cum verò ille labantem Macrobij &longs;en<lb/>tentiam &longs;uffulcire aliquatenus &longs;e po&longs;&longs;e con<lb/>&longs;ideret, &longs;tadia 180 tribuendo non arcui AB, <lb/>&longs;ed rectæ DB terram tangenti, quæ & radij <lb/>optici ex oculo D prodeuntis men&longs;ura e&longs;t, & <lb/>arcu AB longior; operam demum &longs;e ludere <lb/>&longs;en&longs;it, cum re ad Geometricam normam <lb/>reuocatâ tantam opticæ lineæ longitudinem <lb/>terrenæ magnitudini minimè congruere ma<lb/>ni&longs;e&longs;tè deprehendit, etiam &longs;i oculus à terrâ <lb/>pedum 50. interuallo AD &longs;eiunctus intelliga<lb/>tur. </s>

<s>Quoniam enim quadratum Tangentis <lb/>BD, quæ &longs;tad. </s>

<s>180 ponitur, æquale e&longs;t re<lb/>ctangulo ADE, diuidatur quadratum ped. </s>

<s>180 ponitur, æquale e&longs;t re<lb/>ctangulo ADE, diuidatur quadratum ped. <lb/>11664.000000 per 50, & erit DE ped. 233 <lb/>280000, hoce&longs;t &longs;tadiorum Græcorum (quæ <pb pagenum="96"/>hìc v&longs;urpantur) 388800. Quare diameter <lb/>AE, demptis pedibus 50, erit &longs;tad. </s>

<s>233 <lb/>280000, hoce&longs;t &longs;tadiorum Græcorum (quæ <pb pagenum="96"/>hìc v&longs;urpantur) 388800. Quare diameter <lb/>AE, demptis pedibus 50, erit &longs;tad. </s>

<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"/></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>388799 <lb/>ped. 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"/></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>per &longs;emi&longs;&longs;em coëfficientis B. </s>

<s>Sit er<lb/>go E æqualis A+B 1/2: igitur E——B 1/2 e&longs;t æqua<lb/>lis ip&longs;i A. </s>

<s>Sit er<lb/>go E æqualis A+B 1/2: igitur E——B 1/2 e&longs;t æqua<lb/>lis ip&longs;i A. </s>

<s>Factâ itaque prioris æquationis in<lb/>terpretatione erit æquatio inter EQ——BQ 1/4 <pb pagenum="97"/>& DQ: & per Antithe&longs;im EQ æquatur <lb/>DQ+BQ 1/4 </s>

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<s>Hinc pariter Blancano fucum factu&mtail; <lb/>comperiemus (nam & quandoque bonus <lb/>dormitat Homerus) qui maximam mon<lb/>tium altitudinem &longs;e&longs;quimilliari aut duobus <lb/>vt &longs;ummum milliaribus de&longs;iniens, Ætnæ in <lb/>Siciliâ duo tantùm milliaria conce&longs;sit, ad<lb/>mi&longs;ittamen ex Maurolyco dial. </s>

<s>3. Co&longs;mogr<gap/><lb/>pag. </s>

<s>3. Co&longs;mogr<gap/><lb/>pag. 75.indè pro&longs;pici in mare vltra ducenta <lb/>pa&longs;&longs;uum millia. </s>

<s>Namque a&longs;&longs;umptâ lineæ <lb/>opticæ terrenum globum tangenti<gap/> longitu-<pb pagenum="98"/>dine mill. 200, huiusque quadrato 40000 <lb/>per Ætnæ altitudinem con&longs;titutam mill. 2 <lb/>diui&longs;o, & ex Quotiente 20000 demptâ mon<lb/>tis altitudine, ne&longs;cio qua ratione re&longs;iduum <lb/>mill. 19998 terrenæ diametro tribuendum, <lb/>idem Blancanus Sphæræ part. </s>

<s>75.indè pro&longs;pici in mare vltra ducenta <lb/>pa&longs;&longs;uum millia. </s>

<s>Namque a&longs;&longs;umptâ lineæ <lb/>opticæ terrenum globum tangenti<gap/> longitu-<pb pagenum="98"/>dine mill. </s>

<s>200, huiusque quadrato 40000 <lb/>per Ætnæ altitudinem con&longs;titutam mill. </s>

<s>2 <lb/>diui&longs;o, & ex Quotiente 20000 demptâ mon<lb/>tis altitudine, ne&longs;cio qua ratione re&longs;iduum <lb/>mill. </s>

<s>19998 terrenæ diametro tribuendum, <lb/>idem Blancanus Sphæræ part. </s>

<s>3.c.5.pag.93. <lb/>&longs;ibi gratulatur proximè conuenire cum am<lb/>bitu mill. </s>

<s>3.c.5.pag.93. <lb/>&longs;ibi gratulatur proximè conuenire cum am<lb/>bitu mill. 21600 ab aliis po&longs;ito, & à &longs;e ad<lb/>mi&longs;&longs;o. </s>

<s>21600 ab aliis po&longs;ito, & à &longs;e ad<lb/>mi&longs;&longs;o. </s>

<s>Cum tamen hinc debui&longs;&longs;et potiùs <lb/>&longs;u&longs;picari montium altitudinem à &longs;e breuiori<lb/>bus, quàm par &longs;it, terminis 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"/></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"/>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"/></s><s> 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. Por<lb/>ta lib.17. Mag. nat.in proëm. </s>

<s>nat.in proëm. </s>

<s>hau&longs;erit, pror<lb/><arrow.to.target n="note47"></arrow.to.target><lb/>&longs;us ignoro. </s>

<s>hau&longs;erit, pror<lb/><arrow.to.target n="note47"/><lb/>&longs;us ignoro. </s>

<s>Neque enim Diodorus Siculus, <lb/>aut Strabo, aut Cæ&longs;ar, aut A. Hirtius, aut <lb/>Plinius, aut Lucianus, aut Solinus, aut Am<lb/>mianus Marcellinus, aut alius ex ijs, quos le<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>

<s>Quapropter ea mihi mens <lb/>incidit, vt exi&longs;timarem Portæ, viro cætero<lb/>qui erudito, fucum factum ab inepto quo<lb/>piam Typographo, vel ignaro &longs;criptore, qui <lb/>pro &longs;peculâ in Pharo (in&longs;ulâ) extructâ, &longs;pe<lb/>culum in Pharo (turri) con&longs;titutum &longs;uppo<lb/>&longs;uerit. </s>

<s><margin.target id="note47"></margin.target><emph type="italics"/>XLVII <lb/>Fabula de <lb/>altitudin&etail; <lb/>Phari Ale<lb/>xandrinæ <lb/>reijcitur.<emph.end type="italics"/></s>

<s><margin.target id="note47"/><emph type="italics"/>XLVII <lb/>Fabula de <lb/>altitudin&etail; <lb/>Phari Ale<lb/>xandrinæ <lb/>reijcitur.<emph.end type="italics"/></s>

<s>Cæterùm cum tubus opticus vitreis lenti<lb/>bus ritè in&longs;tructus ea &longs;olum corpora di&longs;tinctè <lb/>articulatimque videnda proponar, ad quæ <lb/>recta oculorum acies pergit, tota hæc fabu<gap/><lb/>la euane&longs;cet, vbi tantam altitudinem, quæ <lb/>vi&longs;um ad milliaria 600 producat, probab<gap/><lb/>tate omni carere con&longs;titerit. </s>

<s>Neque opus <lb/>erat altitudine illâ imman<gap/>, cum ideò turris <lb/>illa à Ptolemæo Philadelpho (quamuis Amm. </s>

<s>Neque opus <lb/>erat altitudine illâ imman<gap/>, cum ideò turris <lb/>illa à Ptolemæo Philadelpho (quamuis Amm. <lb/>Marcell. lib.

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><lb/>Marcell. </s>

<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>

<s><lb/>Po&longs;ito terræ ambitu mill. </s>

<s><lb/>Po&longs;ito terræ ambitu mill. 21600, arcus BA, <lb/>in &longs;uperiori &longs;igurâ mill.600 complectitur gra<lb/>dus 10. Fiat igitur vt CB Radius 100000. <lb/>00000. ad CD 101542.66119 &longs;ecante&mtail; <lb/>grad. 10, ita &longs;emidia<lb/><figure id="fig23"/><lb/>metet CB mill. 3437 1/2 <lb/>proximè ad CD mill. <lb/>3490 1/2. Ablatâ autem <lb/>femidiametro CA, re<lb/>manet AD mill. 53. al<lb/>titudo turris Alexandri<lb/>næ: quanta videlicet <lb/>communiter tribui &longs;olet <lb/>halitibus illis, quibus <lb/>tum prima illuce&longs;centis diei, tum po&longs;trema <lb/>aduentantis noctis crepu&longs;cula deb<gap/>mus. </s>

<s>21600, arcus BA, <lb/>in &longs;uperiori &longs;igurâ mill.600 complectitur gra<lb/>dus 10. Fiat igitur vt CB Radius 100000. <lb/>00000. ad CD 101542.66119 &longs;ecante&mtail; <lb/>grad. </s>

<s>10, ita &longs;emidia<lb/><figure id="fig23"></figure><lb/>metet CB mill. </s>

<s>3437 1/2 <lb/>proximè ad CD mill. </s>

<s><lb/>3490 1/2. Ablatâ autem <lb/>femidiametro CA, re<lb/>manet AD mill. </s>

<s>53. al<lb/>titudo turris Alexandri<lb/>næ: quanta videlicet <lb/>communiter tribui &longs;olet <lb/>halitibus illis, quibus <lb/>tum prima illuce&longs;centis diei, tum po&longs;trema <lb/>aduentantis noctis crepu&longs;cula deb<gap/>mus. </s>

<s>Id <pb pagenum="101"/>verò quàm longè à veritate recedat, quid <lb/>pluribus opus e&longs;t explicare? </s>

Line 1566

Line 1573

<s>Pharos igitur In&longs;ula imma<lb/>nis &longs;copulus fuit 50 &longs;erè milliaria iuxta per<lb/>pendiculum numerans; qua de re mirum <lb/>apud &longs;criptores omnes &longs;ilentium: ac proin<lb/>de tantæ altitudini parùm vtilis accidi&longs;&longs;et &longs;pe<lb/>culæ acce&longs;sio. </s>

<s>At &longs;tatuamus cum Erato&longs;the<lb/>ne telluris ambitum &longs;tadiorum 252000, & <lb/>&longs;tadia &longs;ingula &longs;int Alexandrina |ped. </s>

<s>At &longs;tatuamus cum Erato&longs;the<lb/>ne telluris ambitum &longs;tadiorum 252000, & <lb/>&longs;tadia &longs;ingula &longs;int Alexandrina |ped. Rom. <lb/>720., totus ambitus e&longs;&longs;et mill.Rom. 36288; <lb/>igitur milliaria 600 e&longs;&longs;ent gr. 5. m. </s>

<s><lb/>720., totus ambitus e&longs;&longs;et mill.Rom. </s>

<s>36288; <lb/>igitur milliaria 600 e&longs;&longs;ent gr. </s>

<s>57. Qua<lb/>re vt Radius 100000.00000. ad 100541. <lb/>64449. &longs;ecantem gr.5.m. </s>

<s>57. Qua<lb/>re vt Radius 100000.00000. ad 100541. <lb/>64449. &longs;ecantem gr.5.m. 57., ita &longs;emidia<lb/>meter CB mill. 5775. pa&longs;&longs;. </s>

<s>57., ita &longs;emidia<lb/>meter CB mill. </s>

<s>5775. pa&longs;&longs;. </s>

<s>5806. pa&longs;&longs;. </s>

<s>701: ex qua &longs;i au&longs;eratur &longs;e<lb/>midiameter CA, remaneret altitudo AD <lb/>mill. </s>

<s>419. ad CD <lb/>mill. 5806. pa&longs;&longs;. </s>

<s>701: ex qua &longs;i au&longs;eratur &longs;e<lb/>midiameter CA, remaneret altitudo AD <lb/>mill. 31 & pa&longs;&longs;. </s>

<s>31 & pa&longs;&longs;. </s>

<s>282; quæ altitudo adhuc e&longs;t <lb/>immanis: & maior hac e&longs;&longs;et, &longs;i &longs;tadia ill&atail; <lb/>252000. non. </s>

Line 1596

Line 1603

<s>Longè minor e&longs;t Phy&longs;ici Horizontis &longs;e<lb/>midiameter, quàm vulgus cen&longs;eat, &longs;i res Geo-<pb pagenum="102"/>metricè perpendatur: cre&longs;cit autem eius am<lb/>plitudo pro ma<gap/>ori &longs;pectatoris altitudin&etail;. </s>

<s><lb/>Hinc quamuis nauclerorum plurimos Geo. </s>

<s><lb/>Hinc quamuis nauclerorum plurimos Geo. <lb/>metriâ non &longs;atis in&longs;tructos &longs;æpè fugiat ratio, <lb/>eorum tamen varia in determinandâ visûs <lb/>di&longs;tantiâ &longs;ententias facilè po&longs;&longs;umus concilia<lb/>re; alijs &longs;iquidem ex altiori, alijs ex humilio<lb/>ri &longs;peculâ pro&longs; picientibus obiectum idem, <lb/>illis quidem longiùs, his verò propiùs &longs;e ob<lb/>tulit contemplandum. </s>

<s><lb/>metriâ non &longs;atis in&longs;tructos &longs;æpè fugiat ratio, <lb/>eorum tamen varia in determinandâ visûs <lb/>di&longs;tantiâ &longs;ententias facilè po&longs;&longs;umus concilia<lb/>re; alijs &longs;iquidem ex altiori, alijs ex humilio<lb/>ri &longs;peculâ pro&longs; picientibus obiectum idem, <lb/>illis quidem longiùs, his verò propiùs &longs;e ob<lb/>tulit contemplandum. </s>

<s>Quocirca ex huiu&longs;<lb/>modi hominum effatis nihil timendum, <lb/>quod datâ telluris magnitudine con&longs;titutam <lb/>Geometricisque rationibus &longs;olidatam de vi<lb/>sûs di&longs;tantiâ &longs;ententiam labefactare po&longs;sit: <lb/>duo enim hæc inuicem perpetuo vinculo <lb/>colligantur. </s>

<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>

<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"/></s><s> 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>

<s>Eum ta<lb/>men monitum velim parum ex Archimede <lb/>&longs;perandum, cum eam <lb/>iHe magnitudinem da<lb/><figure id="fig24"/><lb/>tâ operâ ponere volue<lb/>rit, quam nemo eo<lb/>rum, quibu&longs;cum di<lb/>&longs;putabat, iu&longs;to mino<lb/>rem calumniari po&longs;&longs;et. </s>

<s><lb/>Quodverò ad Ari&longs;tote<lb/>lem &longs;pectat, non mul<lb/>tum habet momen<lb/>ti Peripatetica autho<lb/>ritas, cui apodictica ratio aduer&longs;atur. </s>

<s>Porrò <lb/>longè melius e&longs;t opticæ lineæ longitudinem <lb/>præcogno&longs;cere, & ex illâ terræ magnitudi<lb/><arrow.to.target n="note48"></arrow.to.target><lb/>nem inue&longs;tigare, quàm incertis coniecturis <lb/>telluris ambitum &longs;tatuere; & infirmo huic <lb/>&longs;undamento æquè nutantem de a&longs;pectûs lon<lb/>gitudine &longs;ententiam &longs;uper&longs;<gap/>ruere. </s>

<s>Porrò <lb/>longè melius e&longs;t opticæ lineæ longitudinem <lb/>præcogno&longs;cere, & ex illâ terræ magnitudi<lb/><arrow.to.target n="note48"/><lb/>nem inue&longs;tigare, quàm incertis coniecturis <lb/>telluris ambitum &longs;tatuere; & infirmo huic <lb/>&longs;undamento æquè nutantem de a&longs;pectûs lon<lb/>gitudine &longs;ententiam &longs;uper&longs;<gap/>ruere. </s>

<s>Sit enim <lb/>nota altitudo BA, & ob&longs;eruatus fuerit angu<lb/>lus BAD; notus e&longs;t angulus complementi, <lb/>qui e&longs;t ad C: ducta autem recta BD facit <lb/>angulum BDA, qui e&longs;t &longs;emi&longs;&longs;is noti anguli <lb/>ad C, vt paulò antè dicebam. </s>

<s>Cum itaque <lb/>in triangulo BAD datum &longs;it latus AB, & duo <lb/>anguli ad A & ad D innotuerint, inueniri <lb/>poterit quantitas lineæ opticæ AD. </s>

<s>Cum itaque <lb/>in triangulo BAD datum &longs;it latus AB, & duo <lb/>anguli ad A & ad D innotuerint, inueniri <lb/>poterit quantitas lineæ opticæ AD. </s>

<s>Tum <pb pagenum="104"/>ex B intelligatur educta perpendiculatis BE, <lb/>& in triangulo rectangulo ABE, datis angu<lb/>lo A & latere AB, inueniatur latus BE. </s>

<s>De<lb/>mum quia triangula ABE, ADC rectangula <lb/>habentia communem angulum ad A &longs;unt &longs;i<gap/><lb/>milia, fiat vt AB data ad BE inuentam, ita <lb/>AD lineæ opticæ longitudo inuenta ad DC <lb/>quæ&longs;itam terræ &longs;emidiametrum. </s>

<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><margin.target id="note48"/><emph type="italics"/>XLVIII <lb/>Inuenir&etail; <lb/><expan abbr="longitudin&etilde;">longitudinem</expan> <lb/>vi&longs;us: & ex <lb/>ea Quint&atail; <lb/>methodus <lb/>vestigandi <lb/>terræ &longs;emi<lb/>diametrum,<emph.end type="italics"/></s>

<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><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"/></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><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"/><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>

<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"/><lb/>Quibus angulis ob&longs;er<lb/>uatis intellige rectam <lb/>BF occurrere Tangen<lb/>ti AE in G. </s>

<s>In triangu<lb/>lo itaque ABG angu<lb/>lus AGB e&longs;t notus, vt<lb/>pote differentia duo<lb/>rum ob&longs;eruatorum C <lb/>BG, CAG: angulus A <lb/>e&longs;t ob&longs;eruatus, & data <lb/>e&longs;t altitudo BA: ergo <lb/>inueniri pote&longs;t quantitas rectæ BG. </s>

Line 1642

Line 1649

<s>E&longs;t igitur ECF <lb/>differentia nota duorum ob&longs;eruatorum CAE, <lb/>CBF. </s>

<s>Ducatur demùm recta CG. </s>

<s>Ducatur demùm recta CG. </s>

<s>Et quo<lb/>niam GF, GE &longs;unt tangentes circulum ab <lb/>eodem puncto exeuntes, inter &longs;e æquales <lb/>&longs;unt, &longs;icut & CF, CE ex centro ductæ; CG <lb/>verò e&longs;t vtrique triangulo FCG, ECG com<lb/>munis; ergo angulus ECF notus diuiditur à <pb pagenum="106"/>rectâ CG bi&longs;ariam. </s>

<s>Quare &longs;i angulorum ob<lb/>&longs;eruatorum &longs;emidi&longs;&longs;erentiam GCF addas an<lb/>gulo FCB complemento noto anguli ob&longs;er<lb/>uati in B, notus e&longs;t etiam angulus BCG; ex <lb/>quo, vnâ cum angulo CBG ob&longs;eruato, & la<lb/>tere BG inuento, inuenitur latus CB: Cui &longs;i <lb/>addatur data altitudo BA, notum erit latus <lb/>CA vnâ cum angulo ad A ob&longs;eruato in trian<lb/>gulo AEC rectangulo: quare & inuenitur CE <lb/>&longs;emidiameter quæ&longs;ita, quæ e&longs;t ip&longs;i CD æqua<lb/>lis, vnde innote&longs;cit altitudo collis BD, & <lb/>lineæ opticæ AE longitudo cogno&longs;ci pote&longs;t. </s>

<s><margin.target id="note49"></margin.target><emph type="italics"/>XLIX <lb/>Sexta me<lb/>tbodus ter<lb/>ræ &longs;emidia<lb/>metrum in<lb/>quirendi, & <lb/>montis alti<lb/>tudinem co<lb/>gno&longs;cendi.<emph.end type="italics"/></s>

<s><margin.target id="note49"/><emph type="italics"/>XLIX <lb/>Sexta me<lb/>tbodus ter<lb/>ræ &longs;emidia<lb/>metrum in<lb/>quirendi, & <lb/>montis alti<lb/>tudinem co<lb/>gno&longs;cendi.<emph.end type="italics"/></s>

<s>At contingat ex edito quidem monte pro<lb/>&longs;pici po&longs;&longs;e in <expan abbr="extrem&utilde;">extremum</expan> <lb/><arrow.to.target n="note50"></arrow.to.target><lb/><figure id="fig26"></figure><lb/>horizontem, &longs;ed planè <lb/>ignotam e&longs;&longs;e montis al<lb/>titudnem. </s>

<s>At contingat ex edito quidem monte pro<lb/>&longs;pici po&longs;&longs;e in <expan abbr="extrem&utilde;">extremum</expan> <lb/><arrow.to.target n="note50"/><lb/><figure id="fig26"/><lb/>horizontem, &longs;ed planè <lb/>ignotam e&longs;&longs;e montis al<lb/>titudnem. </s>

<s>Eligatur lo<lb/>cus aliquis con&longs;picuus, <lb/>qui ita di&longs;tare cen&longs;ea<lb/>tur, vt perpendicula<lb/>res ex vtroque loco ad <lb/>centrum ductæ à pa<lb/>ralleli&longs;mo deffectentes <lb/>&longs;en&longs;u digno&longs;ci queant. </s>

<s><lb/>Hinc enim terræ &longs;emidiametrum eruer&etail; <lb/>po&longs;&longs;umus. </s>

<s>Ex A igitur &longs;it linea AD terram <lb/>tangens: ob&longs;eruetur angulus CAD. </s>

<s>Ex A igitur &longs;it linea AD terram <lb/>tangens: ob&longs;eruetur angulus CAD. </s>

<s>Tum <lb/>ad ea&longs;dem vel alias partes eligatur locus B <pb pagenum="107"/>valde di&longs;tans, & ob&longs;eruetur pariter angulus <lb/>CAB. </s>

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<s>Demum ex B ob&longs;eruetur an<lb/>gulus ABC; cognitâ &longs;cilicet di&longs;tantiâ ip&longs;ius <lb/>A puncti à vertice ob&longs;eruatoris in B, com<lb/>plementum ad duos rectos dat angulum <lb/>ABC: erit autem indicium di&longs;tantiæ AB <lb/>&longs;ufficientis, &longs;i anguli CAB, CBA &longs;imul &longs;um<lb/>pti minores fuerint duobus rectis. </s>

<s>Quare in <lb/>triangulo ABC dato latere BA & angulis <lb/>adiacentibus inuenitur latus AC. </s>

<s>Quare in <lb/>triangulo ABC dato latere BA & angulis <lb/>adiacentibus inuenitur latus AC. </s>

<s>Inuento <lb/>autem latere AC & ob&longs;eruato angulo CAD <lb/>in triangulo CDA rectangulo, inuenitur CD <lb/>quæ&longs;ita terræ &longs;emidiameter, nec latebit <lb/>montis altitudo. </s>

<s><lb/>Septima me<lb/>thodus in<lb/>uestigandi <lb/>&longs;emidiame<lb/>trum terræ, <lb/>& montis <lb/>altitudin<gap/>.<emph.end type="italics"/></s>

<s>Quod &longs;i locorum opportunitas ferat, vt <lb/>detur altitudo FE nota, ex qua ob&longs;eruari <lb/><arrow.to.target n="note51"></arrow.to.target><lb/>queat angulus CED, & in monte procul po&longs;i<lb/>to liber &longs;it a&longs;cen&longs;us, donec ex A puncto per <lb/>E in extremum horizontem D productus ra<lb/>dius efficiat angulum CAD, qui ob&longs;eruatio<lb/>ne cogno&longs;catur; ea habemus, quæ ad inue<lb/>niendam terræ &longs;emidiametrum, vel ad exa<lb/>minandamiam inuentam &longs;ufficiant. </s>

<s>Quod &longs;i locorum opportunitas ferat, vt <lb/>detur altitudo FE nota, ex qua ob&longs;eruari <lb/><arrow.to.target n="note51"/><lb/>queat angulus CED, & in monte procul po&longs;i<lb/>to liber &longs;it a&longs;cen&longs;us, donec ex A puncto per <lb/>E in extremum horizontem D productus ra<lb/>dius efficiat angulum CAD, qui ob&longs;eruatio<lb/>ne cogno&longs;catur; ea habemus, quæ ad inue<lb/>niendam terræ &longs;emidiametrum, vel ad exa<lb/>minandamiam inuentam &longs;ufficiant. </s>

<s>Intel<lb/>ligatur enim ex F exire recta FG parallela ip&longs;i <lb/>CA (perpendiculares &longs;iquidem EC, AG á <lb/>paralleli&longs;mo deflectere ponimus) e&longs;&longs;ormatur <pb pagenum="108"/>triangulum FEG, cuius latus FE datur, an<lb/>gulus EGF æqualis angulo EAC ob&longs;eruato <lb/>innote&longs;cit propter linearum CA, FG paral<lb/>leli&longs;mum, & GEF e&longs;t complementum ad <lb/>duos rectos anguli FED ob&longs;eruati. </s>

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<s>At in triangulo EAC, lateri AC <lb/>parallela e&longs;t GF, ergo vt EG ad GA, ita EF <lb/>data altitudo ad FC quæ&longs;itam &longs;emidiame<lb/>trum. </s>

<s>Vel etiam ij&longs;dem po&longs;itis, & ob&longs;erua<lb/>tis angulis CED, GAE, atque di&longs;tantiâ AE, <lb/><arrow.to.target n="note52"></arrow.to.target><lb/>in triangulo CAE noti &longs;unt duo anguli, (an<lb/>gulus &longs;iquidem CEA e&longs;t complementum ad <lb/>duos rectos anguli CED ob&longs;eruati) & latus <lb/>adiacens AE: inueniatur igitur latus EC, ex <lb/>quo dempta nota altitudo FE relinquit quæ<lb/>&longs;itam terræ &longs;emidiametrum. </s>

<s>Vel etiam ij&longs;dem po&longs;itis, & ob&longs;erua<lb/>tis angulis CED, GAE, atque di&longs;tantiâ AE, <lb/><arrow.to.target n="note52"/><lb/>in triangulo CAE noti &longs;unt duo anguli, (an<lb/>gulus &longs;iquidem CEA e&longs;t complementum ad <lb/>duos rectos anguli CED ob&longs;eruati) & latus <lb/>adiacens AE: inueniatur igitur latus EC, ex <lb/>quo dempta nota altitudo FE relinquit quæ<lb/>&longs;itam terræ &longs;emidiametrum. </s>

<s>Erit autem <lb/>indicium &longs;ufficientis di&longs;tantiæ inter A & E, &longs;i <lb/>angulus CED ob&longs;eruatus fuerit maior angu<lb/>lo CAE. </s>

<s><lb/>Octau a me<lb/>thodus in<lb/>ueniendi ter <lb/>ræ &longs;emidia<lb/>metrum.<emph.end type="italics"/></s>

<s><lb/>Idem aliter.<emph.end type="italics"/></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><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>Tellus quipp&etail; <lb/>toreuma non e&longs;t vndequaque expolitum; &longs;ed <lb/>cum eius partes à centro di&longs;paribus interual<lb/>lis ab&longs;int, ita tamen vt proximè &longs;phæra&mtail; <lb/>æmuletus, facis e&longs;t &longs;i mediocris à centro di-<pb pagenum="110"/>&longs;tantia innote&longs;cat. </s>

<s>Nihilominus tamen aliam <lb/>placet tentare viam nullâ habitâ ratione radii <lb/>optici terram tangentis, modò ea &longs;it duo<lb/>rum locorum di&longs;tantia, vt perpendiculares <lb/>ad centrum notabiliter deflectant à paralle<lb/>li&longs;mo. <lb/><arrow.to.target n="note53"></arrow.to.target></s>

<s><margin.target id="note53"></margin.target><emph type="italics"/>LIII: <lb/>Nona me<lb/>thodus tel<lb/>luris &longs;emi<lb/>diametrum <lb/>inquir ndi.<emph.end type="italics"/></s><figure></figure>

<s><margin.target id="note53"/><emph type="italics"/>LIII: <lb/>Nona me<lb/>thodus tel<lb/>luris &longs;emi<lb/>diametrum <lb/>inquir ndi.<emph.end type="italics"/></s><figure/>

<s>Eligatur itaque alti<lb/>tudo quæpiam in&longs;ignis <lb/>& nota AB, ex cuius <lb/>vtroque extremo vi<lb/>deatur in monte ad <lb/>plura milliaria procul <lb/>po&longs;ito locus D: loca ve<lb/>rò huiu&longs;modi di&longs;tantia <lb/>po&longs;&longs;unt ob&longs;eruari poti&longs;<lb/>&longs;imùm noctu accen&longs;o <lb/>ibi igné ab amico, ni&longs;i <lb/>ad&longs;it nota aliqua peculiaris, vt ædi&longs;icium, <lb/>turris &c. </s>

<s>Tum ex A ob&longs;eruetur angulus <lb/>BAD, & ex B angulus ABD, notus enim fiet <lb/>reliquus angulus BDA. </s>

<s>Tum ex A ob&longs;eruetur angulus <lb/>BAD, & ex B angulus ABD, notus enim fiet <lb/>reliquus angulus BDA. </s>

<s>Ex puncto autem <lb/>D ob&longs;eruetur angulus BDC, vnde ablato an<lb/>gulo BDA noto, reliquus ADC innote&longs;cit. </s>

<s><lb/>His paratis in triangulo ABD dantur duo an<lb/>guli A & B cum latere adiacente BA, inue<lb/>niatur igitur latus AD. </s>

<s><lb/>His paratis in triangulo ABD dantur duo an<lb/>guli A & B cum latere adiacente BA, inue<lb/>niatur igitur latus AD. </s>

<s>Ex hoc autem late<lb/>re AD inuento vnâ cum angulo ADC, qu <lb/>ex ob&longs;eruatione innotuit, & angulo DAC <pb pagenum="111"/>qui e&longs;t complementum anguli ob&longs;eruati <lb/>DAB ad duos rectos, inueniri pote&longs;t latus <lb/>AC quæ&longs;ita terræ &longs;emidiameter. </s>

<s>At non vacat montem con&longs;cendere? </s>

<s>alia <lb/><arrow.to.target n="note54"></arrow.to.target><lb/>&longs;uppetit via, qua leuiori labore propo&longs;itum <lb/>a&longs;&longs;equamur. </s>

<s>alia <lb/><arrow.to.target n="note54"/><lb/>&longs;uppetit via, qua leuiori labore propo&longs;itum <lb/>a&longs;&longs;equamur. </s>

<s>Sit nota altitudo IG, vnde vi<lb/>deatur locus aliquis in &longs;uperficie terræ F: ob<lb/>&longs;erueturque angulus IGF. </s>

<s>Quod &longs;i di&longs;tantia <lb/><figure id="fig27"></figure><lb/>GF iam nota non <lb/>fuerit, ex tertio <lb/>quopiam loco e&atail; <lb/>ob&longs;eruetur, <expan abbr="inue-niaturq.">inue<lb/>niaturque</expan> iuxta Tri<lb/>gonometriæ præ<lb/>cepta. </s>

<s>Quod &longs;i di&longs;tantia <lb/><figure id="fig27"/><lb/>GF iam nota non <lb/>fuerit, ex tertio <lb/>quopiam loco e&atail; <lb/>ob&longs;eruetur, <expan abbr="inue-niaturq.">inue<lb/>niaturque</expan> iuxta Tri<lb/>gonometriæ præ<lb/>cepta. </s>

<s>His com<lb/>paratis producatur <lb/>GI per terræ cen<lb/>trum T v&longs;qu&etail; <lb/>in O, vt IO &longs;it <lb/>terræ diameter: ex <lb/>F cadat in dia<lb/>metrum perpendicularis FC. </s>

<s>Quonia&mtail; <lb/>igitur in triangulo GCF rectangulo datur hy<lb/>pothenu&longs;a GF, & angulus CGF, inueniantur <lb/>reliqua latera FC, CG. </s>

<s>Quonia&mtail; <lb/>igitur in triangulo GCF rectangulo datur hy<lb/>pothenu&longs;a GF, & angulus CGF, inueniantur <lb/>reliqua latera FC, CG. </s>

<s>Auferatur autem <lb/>IG data altitudo ex GC, & remanet IC. </s>

<s><lb/>Quia verò FC à puncto peripheriæ F cadit <lb/>perpendicularis in diametrum IO, e&longs;t me-<pb pagenum="112"/>dio loco proportio nalis inter diametri &longs;eg<lb/>menta IC, CO; ac proinde quadratum me<lb/>diæ CF æquale e&longs;t rectangu lo &longs;ub extremis. </s>

<s><lb/>Itaque quadrato ip&longs;ius CF diui&longs;o per IC &longs;eg<lb/>mentum notum, Quotiens dabit CO, cui <lb/>addatur CI, & habetur tota diameter IO <lb/><arrow.to.target n="note55"></arrow.to.target><lb/>quæ&longs;ita. </s>

<s><lb/>Decima me<lb/>thodus, qua <lb/>terræ dia<lb/>meter inue<lb/>nitur.<emph.end type="italics"/></s>

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

<s>Hæc mihi methodus magis arridet vtpo<lb/>te breuior, qua quadratum CF diuido per <lb/>IC: cæterùm &longs;i rem merè Trigonome<lb/>tricè perficere quis malit, inuentis CF <lb/>& IC, quærat angulum IFC; quem du<lb/>plicet, & dupli &longs;inum ex Tabulis inue<lb/>niat: tum fiat vt &longs;inus inuentus ad Ra<lb/>dium ita inuenta CF ad quæ&longs;itam &longs;emidia<lb/>metrum FT. </s>

<s>Huius operationis ratio pa<lb/>tet, quia cum angulus IFO in &longs;emicircu<lb/>lo &longs;it rectus, triângulum ICF e&longs;t &longs;imile trian<lb/>gulo IFO, igitur angulus inuentus IFC æqua<lb/>lis e&longs;t angulo FOC; huius autem duplex e&longs;t <lb/>angulus ITF ad centrum, qui proinde inno<lb/>te&longs;cit, vnâ cum &longs;inu FC in partibus Radii <lb/>hæc verò linea cum nota &longs;it etiam in men<lb/>&longs;urâ homogeneâ altitudini datæ IG, manife<lb/>&longs;tabit pariter in eâdem men&longs;urâ Radium TF. </s>

<s>Placetne aliam adhuc inire viam? </s>

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<s>Sint datæ al<lb/>titudo eadem IG, ac di&longs;tantia GF, & angu<lb/>lus IGF ob&longs;eruetur. </s>

<s>Ducatur ex I tangens <lb/><arrow.to.target n="note56"></arrow.to.target><lb/>IH; quæ &longs;ecet GF in H. </s>

<s>Ducatur ex I tangens <lb/><arrow.to.target n="note56"/><lb/>IH; quæ &longs;ecet GF in H. </s>

<s>Quæratur ergo i&ntail; <lb/>triangulo GIH rectangulo, ex dato latere GI <lb/>& angulo G, latus GH, quod ex GF ablatum <lb/>relinquit HF, & quæratur latus IH. </s>

<s>Deinde du<lb/>ctâ rectâ IF, in triangulo IHF nota &longs;unt la<lb/>tera IH & HF, angulus autem compræhen<lb/>&longs;us IHF æqualis e&longs;t duobus internis notis, &longs;ci<lb/>licet recto GIH, & IGH ob&longs;eruato: quar&etail; <lb/>inueniri pote&longs;t tum latus IF, tum angulus <lb/>HIF: cui æqualis e&longs;t angulus IOF in alterno <lb/>&longs;egmento: huius autem duplus e&longs;t angulus <lb/>ITF ad centrum. </s>

<s>Fiat igitur vt &longs;inus &longs;emian<lb/>guli inuenti ITF, hoc e&longs;t&longs;inus angult HIF, <lb/>ad Radium, ita &longs;emi&longs;sis inuenti lateris IF <lb/>ad quæ&longs;itam &longs;emidiametrum TF. </s>

<s><lb/>Vndecim&atail; <lb/>methodus <lb/>inueniendi <lb/>terræ &longs;emi<lb/>diametrum<gap/><emph.end type="italics"/></s>

<s>Compendio&longs;iùs forta&longs;&longs;e operabimur, &longs;i da<lb/>tis IG & GF cum angulo G compræhen&longs;o, <lb/><arrow.to.target n="note57"></arrow.to.target><lb/>inueniatur ba&longs;is IF & angulus GIF, qui e&longs;t <lb/>nece&longs;&longs;ariò obtu&longs;us. </s>

<s>Compendio&longs;iùs forta&longs;&longs;e operabimur, &longs;i da<lb/>tis IG & GF cum angulo G compræhen&longs;o, <lb/><arrow.to.target n="note57"/><lb/>inueniatur ba&longs;is IF & angulus GIF, qui e&longs;t <lb/>nece&longs;&longs;ariò obtu&longs;us. </s>

<s>Fiat ergo vt &longs;inus exce&longs;<lb/>sûs anguli GIF &longs;upra rectum ad Radium, <lb/>ita &longs;emi&longs;sis inuentæ ba&longs;is IF ad quæ&longs;itam <lb/>terræ &longs;emidiametrum. </s>

<s><margin.target id="note57"></margin.target><emph type="italics"/>LVII. <lb/>Id<gap/> breuiùs.<emph.end type="italics"/></s>

<s><margin.target id="note57"/><emph type="italics"/>LVII. <lb/>Id<gap/> breuiùs.<emph.end type="italics"/></s>

<s>Verùm omi&longs;&longs;o tot linearum apparatu res <pb pagenum="114"/><arrow.to.target n="note58"></arrow.to.target><lb/><figure id="fig28"></figure><lb/>facillimè conficitur, e<lb/>tiam&longs;i nulla &longs;it data al<lb/>titudo nota. </s>

<s>Verùm omi&longs;&longs;o tot linearum apparatu res <pb pagenum="114"/><arrow.to.target n="note58"/><lb/><figure id="fig28"/><lb/>facillimè conficitur, e<lb/>tiam&longs;i nulla &longs;it data al<lb/>titudo nota. </s>

<s>Ob&longs;erue<lb/>tur di&longs;tantia AD: tum <lb/>in A accipiatur angulus <lb/>CAD, & in D ob&longs;erue<lb/>tur angulus, quem cum <lb/>verticali lineâ ex D ad <lb/>Zenith productâ facit <lb/>radius opticus DA; hu<lb/>ius enim complementum ad duos rectos <lb/>e&longs;t angulus ADC: dato autem latere AD <lb/>cum angulis adiacentibus, latere non po&longs;<lb/>&longs;unt reliqua latera CD quæ&longs;ita terræ &longs;emidia<lb/>meter, & CA &longs;emidiameter aucta montis <lb/>AB altitudine. </s>

<s><margin.target id="note58"></margin.target><emph type="italics"/>LVIII. </s>

<s><margin.target id="note58"/><emph type="italics"/>LVIII. </s>

<s><lb/>Duodecima <lb/>methodus <lb/>&longs;emidiame<lb/>trum terræ <lb/>inuestigan<lb/>di, & montis <lb/>altitudini.<emph.end type="italics"/></s>

<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"/></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><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>Va<lb/>le Galilæe. </s>

<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="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/>

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

<s><emph type="center"/>Ex aquæ &longs;eparatione à ter<lb/>ra, motus facilitatem <lb/>infert.<emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

<s><emph type="center"/><emph type="italics"/>Guldinus, Galilæus, Mer&longs;ennus.<emph.end type="italics"/><emph.end type="center"/></s>

<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"/></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><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"/></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"/>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"/></s><s> 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>

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. </s>

6. Nat. quæ&longs;t. </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>

Line 1832

Line 1839

<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"/></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"/>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"/></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><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"/></s><s> 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"/></s><s> 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>

<s>Illud <lb/>enim extra omnem controuer&longs;iam po&longs;itum <lb/><arrow.to.target n="note59"/><lb/>accipio, quod aqua aëre grauior e&longs;t; & fluida <lb/>cùm &longs;it, &longs;emper ad inferiora delabitur, vt <lb/>infra aërem vniuer&longs;icentro vicinior con&longs;i&longs;tat. </s>

<s><lb/>Ex quo fit, vt nu&longs;quam quie&longs;cat, ni&longs;i vbi <lb/>nullus patet locus, in quem de&longs;cendat. </s>

<s>Qua<lb/>rè cum &longs;ola &longs;uperficies &longs;phærica paribus ra<lb/>diis à centro remoueatur, aquæ quie&longs;centis <lb/>&longs;uperficiem &longs;phæricam e&longs;&longs;e nece&longs;&longs;e e&longs;t: quan<lb/>doquidem &longs;iquæ &longs;uperficiei partes à centro <lb/>longiùs abe&longs;&longs;ent, vtpote altiores ad motum <lb/>procliues non &longs;ub&longs;i&longs;terent, &longs;ed humiliorem <pb pagenum="120"/>in locum defluerent: neque enim ex eo a<lb/>quam &longs;ponte a&longs;cendere dixerim, quòd ea in <lb/>vitreis fi&longs;tulis immer&longs;is aliquantulum a&longs;cen<lb/>dat. </s>

<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><margin.target id="note59"/><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"/></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><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>

<s>Quod verò de aquâ in immer&longs;is fi&longs;tulis <lb/>vtrinque hiantibus a&longs;cendente addis, nihil <lb/>planè officit naturæ aquarum &longs;e in &longs;phæram <lb/>circa terræ centrum conglobantium; neque <lb/>illicò po&longs;&longs;e aquam ad digitivaltitudine&mtail; <lb/>&longs;ponte a&longs;cendere affirmandum e&longs;t, quòd il<lb/>lam in tenui&longs;&longs;imis fi&longs;tulis eò pertingere ali<lb/>quando videamus; quò enim ampliores &longs;unt <lb/>fi&longs;tulæ, eò minùs in iis aquam af&longs;urger&etail; <lb/>con&longs;tat, nec fortè &longs;ine &longs;u&longs;picione minoris, <lb/>quàm appareat, altitudinis, propter &longs;pecie<lb/>rum vi&longs;ibilium ex vitro refractionem, i&ntail; <pb pagenum="121"/>ampli&longs;simis igitur lacuum marium que alueis <lb/>quantùm illa a&longs;cendat, quod &longs;phæricam &longs;u<lb/>perficiem corrumpat? </s>

<s>Sed nec aquam om<lb/>ninò &longs;ponte dixerim in fi&longs;tulâ a&longs;cender&etail; <lb/>Quando enim fi&longs;tula deprimitur, vt aquæ <lb/>immergatur, vtique &longs;ubiectus aër premitur, <lb/><arrow.to.target n="note60"></arrow.to.target><lb/>& locum &longs;ubeunti fi&longs;tulæ concedens, quâ <lb/>patet via, recedit, vt locum &longs;uppleat à fi&longs;tu<lb/>lâ deor&longs;um motâ relictum. </s>

<s>Sed nec aquam om<lb/>ninò &longs;ponte dixerim in fi&longs;tulâ a&longs;cender&etail; <lb/>Quando enim fi&longs;tula deprimitur, vt aquæ <lb/>immergatur, vtique &longs;ubiectus aër premitur, <lb/><arrow.to.target n="note60"/><lb/>& locum &longs;ubeunti fi&longs;tulæ concedens, quâ <lb/>patet via, recedit, vt locum &longs;uppleat à fi&longs;tu<lb/>lâ deor&longs;um motâ relictum. </s>

<s>Sicut autem <lb/>aër, cui corpus in motu occutrit, comprimi<lb/>tur, ita is, qui ponè e&longs;t, paululum di&longs;trahi<lb/>tur ac rare&longs;cit; hic verò ad ingenium rediens <lb/>proximum aërem attrahit ad &longs;upplendum <lb/>locum à fi&longs;tulâ relictum; cumque nullus <lb/>&longs;ubiectus aër tam in promptu &longs;it, quàm is <lb/>qui fi&longs;tulæ cauitatem implet, hic ex&longs;ugitur; <lb/>atque adeò cum aér fi&longs;tulæ &longs;ur&longs;um mouea<lb/>tur, &longs;ubiectus aër compre&longs;&longs;us in fi&longs;tulæ caui<lb/>tatem &longs;uccedit, per quam faciliùs elabitur, <lb/>ac per impul&longs;ionem, aut compre&longs;&longs;ionem <lb/>contigui aëris, qui lateribus adiacet. </s>

Line 1866

Line 1873

<s>Hinc e&longs;t aërem &longs;ur&longs;um in &longs;i&longs;tulâ <lb/>incitatum ex concepto impetu tanti&longs;per per-<pb pagenum="122"/>gere in motu, & ita pellere &longs;uperiorem aë<lb/>rem, vt hic eum qui fi&longs;tulæ latera extrin&longs;e<lb/>cùs ob&longs;idet, propellat, fiatque per inferius <lb/>hiantis fi&longs;tulæ o&longs;culum illa circumpul&longs;io, de <lb/>qua Pla<emph type="italics"/>t<emph.end type="italics"/>o in Timæo, vel &longs;altem, vt cum ve<lb/><gap/>tris Philo&longs;ophis loquar, ab a&longs;cendente aëre <lb/>per fi&longs;tulam liberrimè ab&longs;que vllo alterius <lb/>aëris intercurrentis obice, attrahitur aër in<lb/>ferior. </s>

<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"/></s><s> 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"/></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><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>

Line 1890

Line 1897

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

<s>Iam <lb/>verò vt pla<lb/>niùs & aper<lb/>tiùs verbis <lb/><figure id="fig29"/><lb/><arrow.to.target n="note61"/><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>

<s>Sit pro <lb/>globo terra<lb/>queo circu<lb/>lus ABCD, <lb/>cuius cen<lb/>trum T <expan abbr="cõ-gruat">con<lb/>gruat</expan> vniuer&longs;i centro, & BAE mare Hyper<lb/><gap/>oreum, FCD Oceanus Indicus aut Æthio-<pb pagenum="125"/>picus, vel alius, quamcunque demum &longs;or<lb/>tiatur appellationem. </s>

Line 1902

Line 1909

<s>Contra autem aqua F & D <lb/>remotior e&longs;t quàm C à centro V; pote&longs;t <lb/>igitur ver&longs;us C de&longs;cendere; & relicto loco <lb/>ad F & ad D, a&longs;&longs;urget<gap/> in H, & erit &longs;uper<lb/>ficies FHD maiorem habens conuexita<lb/>te&mtail;. </s>

<s><margin.target id="note61"></margin.target><emph type="italics"/>LXI <lb/>Si tellus a<lb/>liò trabere<lb/>tur, aqu&atail; <lb/>mutaret fi<lb/>guram.<emph.end type="italics"/></s>

<s><margin.target id="note61"/><emph type="italics"/>LXI <lb/>Si tellus a<lb/>liò trabere<lb/>tur, aqu&atail; <lb/>mutaret fi<lb/>guram.<emph.end type="italics"/></s>

<s>Quod &longs;i ad latus iaceat aqua, vt MNO, <lb/>factâ translatione centri ex Vin T, vtique <lb/>ex M versùs O de&longs;cendet; &longs;ed &longs;i mons OS <lb/>prohibeat, demùm con&longs;i&longs;tet aqua circa vni<lb/>uer&longs;i centrum V in &longs;uper&longs;icie &longs;phæricâ RNS. <pb pagenum="126"/>Idemque d&etail; <lb/><figure id="fig30"></figure><lb/>cæteris e&longs;to iu<lb/>dicium; nulla <lb/>&longs;iquidem repe<lb/>riri po&longs;&longs;et a<lb/>quarum con<lb/>gregatio, quæ <lb/>tellure transla<lb/>tâ, &longs;e aliam in <lb/><expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> non <lb/>conglobaret, <lb/>altioribus par<lb/>tibus in inferiorem locum delap&longs;is. <lb/><arrow.to.target n="note62"></arrow.to.target></s>

<s>Quod &longs;i ad latus iaceat aqua, vt MNO, <lb/>factâ translatione centri ex Vin T, vtique <lb/>ex M versùs O de&longs;cendet; &longs;ed &longs;i mons OS <lb/>prohibeat, demùm con&longs;i&longs;tet aqua circa vni<lb/>uer&longs;i centrum V in &longs;uper&longs;icie &longs;phæricâ RNS. <pb pagenum="126"/>Idemque d&etail; <lb/><figure id="fig30"/><lb/>cæteris e&longs;to iu<lb/>dicium; nulla <lb/>&longs;iquidem repe<lb/>riri po&longs;&longs;et a<lb/>quarum con<lb/>gregatio, quæ <lb/>tellure transla<lb/>tâ, &longs;e aliam in <lb/><expan abbr="&longs;uperfici&etilde;">&longs;uperficiem</expan> non <lb/>conglobaret, <lb/>altioribus par<lb/>tibus in inferiorem locum delap&longs;is. <lb/><arrow.to.target n="note62"/></s>

<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><margin.target id="note62"/><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"/></s><s> 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>

<s>Si enim T accedat ad V, aqua incipit <lb/>ex S refluere ver&longs;us M, vbi aqua &longs;emper au<lb/>getur, quò magis centrum T recedit ab V <lb/>in X: iterumque fluit ex M in O, cum cen<lb/>trum ab X recedens in V & in T &longs;ua per <lb/>ve&longs;tigia eò remeat, vnde di&longs;ce&longs;&longs;it, &longs;eruatâ<lb/>que in motu reciprocando con&longs;tantiâ, al-<pb pagenum="127"/>ternas fluxûs, & refluxûs vices efficit in ad<lb/>uer&longs;is litoribus. </s>

<s>Quod &longs;i in oppo&longs;itis eiu&longs;<lb/>dem aluei ripis eodem tempore fluxus con<lb/>tingat aut refluxus, vt in B & E, aut in F & <lb/>D; tunc opinari quis po&longs;&longs;et mare illud eam <lb/>habere po&longs;itionem, vt in illud incidat linea <lb/>motûs, quæ ex centro grauium per terræ <lb/>centrum ducitur: dum enim aqua deprimitur <lb/>ex A in I, augetur in B & E, &longs;i litus fluxui <lb/>ob&longs;tet, aut vlteriora &longs;patia occupat in P & K: <lb/>dum verò a&longs;&longs;urgit ex C in H, minuitur in F & <lb/>D. </s>

<s>Porrò alternâ hac nutantis terræ mo<lb/>tione non magis eius &longs;tabilitas vacillaret, <lb/>quàm illiùs firmitati ob&longs;it trepidationis mo<lb/>tus à pleri&longs;que admi&longs;&longs;us ob variam centri <lb/>grauitatis po&longs;itionem: &longs;tare &longs;iquidem terra <lb/>dicitur, quæ &longs;uo ex loco non decedit, quam<lb/>quam in eo &longs;uæ diametri particulam (1/4000000) <lb/>percurrat. </s>

<s>Finge enim motûs extremos <lb/>terminos T & X non ampliùs pa&longs;&longs;um vnum <lb/>di&longs;tare à grauium centro V: tanta e&longs;t aqua<lb/>rum in immen&longs;um patentium copia, vt èxi<lb/>guâ inclinatione, quam motu illo acquire<lb/>rent, dilabentes æ&longs;tum non exiguum effi<lb/>cerent: qui tamen in lacubus, angu&longs;tiori<lb/>busque alueis ob minorem aquarum copiam <lb/>non perciperetur. </s>

<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><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>

<s>De mari certè, quod Kiùn, in In<lb/>&longs;ulâ Hainan, alluit, illud notatu dignum <lb/>&longs;cribunt Sinæ Geographi, quod maris æ&longs;tum <lb/>Diurnum non &longs;entiat, &longs;ed per dimidiam <lb/>men&longs;is partem versùs Ortum, per reliquam <lb/>dimidiam versùs Occa&longs;um fluat. </s>

<s><lb/>Quod in vertice montis Hucùng in Fokien <lb/>Prouinciâ puteus e&longs;t (Hiai nomen e&longs;t) cuius <lb/>aqua æ&longs;tum marinum &longs;uo acce&longs;&longs;u & rece&longs;&longs;u <lb/>refert. </s>

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<s>At &longs;i contingere po&longs;&longs;et, vt machinarum </s>

<s><arrow.to.target n="note63"></arrow.to.target><lb/>ope telluris centrum ex V in T transferretur, <lb/>fluminis GL aqua ex G reflueret in L, & in <lb/>eundem alueum &longs;e in&longs;inuaret mare v&longs;qu&etail; <lb/>dum tota aquæ &longs;uperficies continua in &longs;phæ<lb/>ram inflexa con&longs;i&longs;teret, cum non haberet, <lb/>quò de&longs;cenderet. </s>

<s><arrow.to.target n="note63"/><lb/>ope telluris centrum ex V in T transferretur, <lb/>fluminis GL aqua ex G reflueret in L, & in <lb/>eundem alueum &longs;e in&longs;inuaret mare v&longs;qu&etail; <lb/>dum tota aquæ &longs;uperficies continua in &longs;phæ<lb/>ram inflexa con&longs;i&longs;teret, cum non haberet, <lb/>quò de&longs;cenderet. </s>

<s>Hinc illud fit, quod cum <lb/>maria omnia (ni&longs;i fortè Ca&longs;pium velis exci<lb/>pere, cui tamen per &longs;ubterraneos cuniculos <lb/>cum Ponto Euxino communio e&longs;t) &longs;ibi in<lb/>uicem continuata iunctaque &longs;int, terrâ in <lb/>partem vnam translatâ, aquæ ferè omnes in <lb/>oppo&longs;itam recederent, vel per patentem al<lb/>ueum dilabentes, vel etiam exundantes: <lb/>idem quippe tunc aquarum conceptaculis <lb/>contingeret, ac &longs;i nunc vas liquore qua&longs;i <lb/>plenum magis & magis inclinaretur, totus <lb/>enim demùm liquor effunderetur. </s>

<s>Quarè <lb/>vniuer&longs;a ferè aqua &longs;uperiorem locum relin<lb/>quens in H conflueret eò velociùs, quò lon<lb/>giùs telluris centrum T recederet ab V cen<lb/>tro grauium &longs;eu vniuer&longs;i. </s><pb pagenum="130"/>

<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><margin.target id="note63"/><emph type="italics"/>LXIII <lb/>Tellur&etail; <lb/>translata fe<lb/>rè tota aqua <lb/>ab ea &longs;eiun<lb/>geretur.<emph.end type="italics"/></s>

<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"/>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"/></s><s> 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"/></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><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>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Qúæ &longs;entis, approbo; immen&longs;æ <lb/><arrow.to.target n="note64"></arrow.to.target><lb/>&longs;iquidem illæ altitudines & aby&longs;&longs;i aquarum <lb/>rari&longs;&longs;imæ &longs;unt, quæ bolide nullâ explorari <lb/>po&longs;&longs;int. </s>

<s><emph type="italics"/>Guld.<emph.end type="italics"/> Qúæ &longs;entis, approbo; immen&longs;æ <lb/><arrow.to.target n="note64"/><lb/>&longs;iquidem illæ altitudines & aby&longs;&longs;i aquarum <lb/>rari&longs;&longs;imæ &longs;unt, quæ bolide nullâ explorari <lb/>po&longs;&longs;int. </s>

<s>Idcircò libentiùs vuiuersè altitu<lb/>dinem &longs;olùm dodrantalem aquis tribuo, mil<lb/>liari a&longs;&longs;umpto pro a&longs;&longs;e. </s>

<s>Iam, &longs;i placet, <lb/>aquæ grauitatem ad calculos reuocemus, & <lb/>globi perimetrum accipiamus, quam olim <lb/>Mer&longs;ennus, nobis non repugnantibus, con<lb/>&longs;tituebat mill. </s>

<s>Iam, &longs;i placet, <lb/>aquæ grauitatem ad calculos reuocemus, & <lb/>globi perimetrum accipiamus, quam olim <lb/>Mer&longs;ennus, nobis non repugnantibus, con<lb/>&longs;tituebat mill. Rom. ant. </s>

<s>25941. Perime<lb/>tro con&longs;titutâ, diametrum &longs;ic inquiro ex ra<lb/>tionibus Vietæ: Vt 31415.926536 ad <lb/>10000.000000, ita maximi circuli periphe<lb/>ria mill. </s>

<s>25941 ad diametrum mill. </s>

<s>8257<lb/>pa&longs;&longs;. </s>

<s>25941. Perime<lb/>tro con&longs;titutâ, diametrum &longs;ic inquiro ex ra<lb/>tionibus Vietæ: Vt 31415.926536 ad <lb/>10000.000000, ita maximi circuli periphe<lb/>ria mill. 25941 ad diametrum mill. 8257<lb/>pa&longs;&longs;. </s>

<s>276. Igitur &longs;idiameter in peripheriam <lb/>ducatur, producetur &longs;phærica &longs;uperficies <lb/>mill. quadrat. </s>

<s>276. Igitur &longs;idiameter in peripheriam <lb/>ducatur, producetur &longs;phærica &longs;uperficies <lb/>mill. </s>

<s>quadrat. </s>

<s>214.201996. pa&longs;&longs;. </s>

<s><lb/>716000: Huius autem &longs;emi&longs;sis mill. </s>

<s><lb/>716000: Huius autem &longs;emi&longs;sis mill. 107. <lb/>100998. pa&longs;&longs;. </s>

<s>107. <lb/>100998. pa&longs;&longs;. </s>

<s>358000. erit &longs;uper&longs;icies a<lb/>quæ. </s>

<s><margin.target id="note64"></margin.target><emph type="italics"/>LXIV <lb/>Totius a<lb/>quæ quanti<lb/>tas, & gra<lb/>uitas in qui<lb/>ritur.<emph.end type="italics"/></s>

<s><margin.target id="note64"/><emph type="italics"/>LXIV <lb/>Totius a<lb/>quæ quanti<lb/>tas, & gra<lb/>uitas in qui<lb/>ritur.<emph.end type="italics"/></s>

<s>Et vt breuitati &longs;eruiam, duco inuentam <lb/>aquæ &longs;uperficiem in altitudinem con&longs;titutam <lb/>mill.3/4: ne &longs;cilicet longioribus ambagibus in <lb/>quiram totius globi &longs;oliditatem. </s>

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<s>Neque enim e&longs;t operæ pretium <lb/>nos ip&longs;os hoc labore conficere; quandoqui<lb/>dem vix di&longs;creparet inuentus numerus ab eo, <lb/>qui ex ductu &longs;uperficiei in altitudinem pro<lb/>dibit. </s>

<s>Duco igitur aquæ &longs;uperficiem mill. </s>

<s>Duco igitur aquæ &longs;uperficiem mill. <lb/>107.100998 pa&longs;&longs;. </s>

<s><lb/>107.100998 pa&longs;&longs;. </s>

<s>358000 in altitudinem <lb/>mill. </s>

<s>3/4, & prodit &longs;oliditas milliarium cubi<lb/>corum 80.325748, & pa&longs;&longs;. </s>

<s>358000 in altitudinem <lb/>mill. 3/4, & prodit &longs;oliditas milliarium cubi<lb/>corum 80.325748, & pa&longs;&longs;. </s>

<s>cubic. </s>

<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>

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>

<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. 80.325748 <lb/>pa&longs;&longs;. </s>

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

<s>80.325748 <lb/>pa&longs;&longs;. </s>

<s>768.500000. ducatur per libras 10. <lb/>000000.000000. erit totius aquæ pondus lib. <pb pagenum="133"/>803.257487.685000.000000. <lb/><arrow.to.target n="note65"></arrow.to.target></s>

<s>768.500000. ducatur per libras 10. <lb/>000000.000000. erit totius aquæ pondus lib. <pb pagenum="133"/>803.257487.685000.000000. <lb/><arrow.to.target n="note65"/></s>

<s><margin.target id="note65"></margin.target><emph type="italics"/>LXV <lb/>Pondus ter<lb/>reni globi <lb/>quàm nota<lb/>biliter mi<lb/>nueretur ex <lb/>aquæ &longs;ece&longs;<lb/>&longs;iane.<emph.end type="italics"/></s>

<s><margin.target id="note65"/><emph type="italics"/>LXV <lb/>Pondus ter<lb/>reni globi <lb/>quàm nota<lb/>biliter mi<lb/>nueretur ex <lb/>aquæ &longs;ece&longs;<lb/>&longs;iane.<emph.end type="italics"/></s>

<s>Hoc autem pondus ex totius globi graui<lb/>tate demptum faciliorem efficeret terræ <lb/>motionem, vbi iam tota terra aliquou&longs;que <lb/>ab vniuer&longs;i centro rece&longs;&longs;i&longs;&longs;et, ibique aquam <lb/>ferè totam, quæ nunc in globi &longs;uperfici&etail; <lb/>fluit, reliqui&longs;&longs;et. </s>

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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"/></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><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>

<s><arrow.to.target n="note66"></arrow.to.target><lb/>nimirum, quamuis ingens hæc ponderis di<lb/>minutio tunc &longs;olùm contingeret, quando <lb/>terra e&longs;&longs;et ab aquis diuul&longs;a, & ab vniuer&longs;i <lb/>centro V tota abe&longs;&longs;et, emolumentum tamen <lb/>non paruum faceret in motione a&longs;&longs;iduus a<lb/>quarum fluxus in partem oppo&longs;itam. </s>

<s><arrow.to.target n="note66"/><lb/>nimirum, quamuis ingens hæc ponderis di<lb/>minutio tunc &longs;olùm contingeret, quando <lb/>terra e&longs;&longs;et ab aquis diuul&longs;a, & ab vniuer&longs;i <lb/>centro V tota abe&longs;&longs;et, emolumentum tamen <lb/>non paruum faceret in motione a&longs;&longs;iduus a<lb/>quarum fluxus in partem oppo&longs;itam. </s>

<s>Si enim <lb/>globus plano FD &longs;ectus eò transferatur, vt <lb/>vniuer&longs;i <expan abbr="c&etilde;-trum">cen<lb/>trum</expan> V i&ntail; <lb/><figure id="fig31"></figure><lb/><expan abbr="eod&etilde;">eodem</expan> &longs;it pla<lb/>no, non &longs;o<lb/>lùm <expan abbr="nõ">non</expan> per<lb/>cipitur toti<lb/>us globi, &longs;ed <lb/>netotius qui<lb/>dem <expan abbr="fegm&etilde;-ti">fegmen<lb/>ti</expan> FAD gra<lb/>uitas: <expan abbr="quan-doquid&etilde;">quan<lb/>doquidem</expan> &longs;eg<lb/>mentum FA <lb/>D de or&longs;um non conatur contra vim &longs;ur&longs;um <lb/>mouentem aut &longs;u&longs;tinentem, ni&longs;i iuxta mo<lb/>menta ponderis, quibus &longs;uperat moment&atail; <pb pagenum="135"/>&longs;egmenti FCD oppo&longs;ito conatu in idem cen<lb/>trum V nitentis, ne indè remoueatur. </s>

<s>Si enim <lb/>globus plano FD &longs;ectus eò transferatur, vt <lb/>vniuer&longs;i <expan abbr="c&etilde;-trum">cen<lb/>trum</expan> V i&ntail; <lb/><figure id="fig31"/><lb/><expan abbr="eod&etilde;">eodem</expan> &longs;it pla<lb/>no, non &longs;o<lb/>lùm <expan abbr="nõ">non</expan> per<lb/>cipitur toti<lb/>us globi, &longs;ed <lb/>netotius qui<lb/>dem <expan abbr="fegm&etilde;-ti">fegmen<lb/>ti</expan> FAD gra<lb/>uitas: <expan abbr="quan-doquid&etilde;">quan<lb/>doquidem</expan> &longs;eg<lb/>mentum FA <lb/>D de or&longs;um non conatur contra vim &longs;ur&longs;um <lb/>mouentem aut &longs;u&longs;tinentem, ni&longs;i iuxta mo<lb/>menta ponderis, quibus &longs;uperat moment&atail; <pb pagenum="135"/>&longs;egmenti FCD oppo&longs;ito conatu in idem cen<lb/>trum V nitentis, ne indè remoueatur. </s>

<s>At<lb/>qui aquæ pars aliqua &longs;upra planum FD exi<lb/>&longs;tens infra illud de&longs;cendit; igitur in &longs;egmen<lb/>to FAE minuitur pondus, & fit ponderis ac<lb/>ce&longs;&longs;io &longs;egmento FCD; quarè multò minor <lb/>e&longs;t differentia grauitatum inter &longs;egmenta, ac <lb/>proinde minor in mouendo labor, aut in &longs;u<lb/>&longs;tinendo. </s>

<s>Quemad modum enim &longs;i in libræ <lb/>lancibus po&longs;ita fuerint pondera inæqualia, & <lb/>exlance grauiore pars ponderis transferatur <lb/>in alteram lancem, propiùs accedunt ad <lb/>æquilibrium, & faciliùs &longs;u&longs;tinetur lanx gra<lb/>uior; Sic etiam pondus aliquod aquæ ex <lb/>&longs;egmento maiore FAD tran&longs;latum in &longs;eg<lb/>mentum minus FCD, efficit minorem <lb/>ponderum inæqualitatem, ac proinde minor <lb/>grauitas percipitur à mouente globum, vel <lb/>&longs;u&longs;tinente. </s>

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

<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><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"/></s><s> 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"/></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><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>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"/></s><s> 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"/></s><s> 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"/></s><s> 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"/></s><s> 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"/></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><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"/></s><s> 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"/></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><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>

<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"/><lb/>tem <expan abbr="graui&utilde;">grauium</expan> <lb/><expan abbr="elementari&utilde;">elementarium</expan> <lb/>centrum &longs;ta. </s>

<s><lb/>tuitur, aquæ <lb/>omnes, qui<lb/>bus liber&atail; <lb/>pateret ad <lb/><expan abbr="fluend&utilde;">fluendum</expan> via, <lb/><expan abbr="de&longs;cender&etilde;t">de&longs;cenderent</expan> <lb/>ver&longs;us C, vt <lb/>ad centrum <lb/>V propiùs <lb/>accederent, <pb pagenum="138"/>& in &longs;phæricâ demum &longs;uperficie FHD pari<lb/>bus radijs à centro V remota con&longs;i&longs;terent. </s>

<s><lb/>Cum itaque &longs;uperiori &longs;egmento &longs;ieret pon<lb/>deris aquæ dece&longs;&longs;io, inferiori autem acce&longs;<lb/>&longs;io, aliquod haberetur in perficiendâ mo<lb/>tione compendium: Hæc verò di&longs;&longs;erenti<lb/>bus nobis incidit &longs;u&longs;picio, an fortè continge<lb/>re po&longs;&longs;et, aquis in partem vnam delap&longs;is <lb/>terram innatare. </s>

<s>Sit enim globus terraqueus ABCE, cu<lb/>ius centrum T ad illud interuallum à centro <lb/>V venerit machinarum vi, vt aqua deor&longs;um <lb/><arrow.to.target n="note67"></arrow.to.target><lb/><figure id="fig33"></figure><lb/>delap&longs;a &longs;it B <lb/>HECB, & <lb/>portionem B <lb/>CE circum<lb/>plectatur. </s>

<s>Sit enim globus terraqueus ABCE, cu<lb/>ius centrum T ad illud interuallum à centro <lb/>V venerit machinarum vi, vt aqua deor&longs;um <lb/><arrow.to.target n="note67"/><lb/><figure id="fig33"/><lb/>delap&longs;a &longs;it B <lb/>HECB, & <lb/>portionem B <lb/>CE circum<lb/>plectatur. </s>

<s><expan abbr="Iã">Iam</expan> <lb/>verò dimit<lb/>tatur tellus à <lb/>&longs;u&longs;pendente: <lb/><expan abbr="nõ">non</expan> facilè de. </s>

<s><lb/>finirem, v<lb/>trùm terr&atail; <lb/>con&longs;i&longs;teret, <lb/>an potius de<lb/>&longs;cenderet ex T in V, an verò etiam &longs;ponte <lb/>a&longs;cenderet longiùs recedens ab V. </s>

<s><lb/>finirem, v<lb/>trùm terr&atail; <lb/>con&longs;i&longs;teret, <lb/>an potius de<lb/>&longs;cenderet ex T in V, an verò etiam &longs;ponte <lb/>a&longs;cenderet longiùs recedens ab V. </s>

<s>Verùm <lb/>&longs;i &longs;ponte &longs;uâ aliquou&longs;que a&longs;cenderet, ia&mtail; <pb pagenum="139"/>nihil &longs;upere&longs;&longs;et laboris Archimedi, vt eò il<lb/>lam deduceret: &longs;i con&longs;i&longs;teret, iam innataret <lb/>aquis, ac proinde non multo labore fui&longs;&longs;et <lb/>opus, vt ex V in T transferretur: &longs;i demùm <lb/>de&longs;cenderet, illud &longs;altem haberetur emolu<lb/>menti, quod intrà aquam exi&longs;tenti multum <lb/>ponderis decederet, & motio faciliùs perfi<lb/>ceretur. </s>

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

<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><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>

Line 2114

Line 2121

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

<s>Et quod <lb/>ad primum &longs;pectat, certum e&longs;t aërem vni<lb/>uer&longs;um in terræ cauernis delite&longs;cente&mtail;, <lb/>omnesque halitus, & corpora aquis leuiora <lb/>plurimum po&longs;&longs;e demere de grauitate: aër <pb pagenum="140"/>enim, dum corpus in aëre &longs;u&longs;penditur, nec <lb/>grauitatem addit, nec leuitatem: at &longs;i cor<lb/>pus aquæ in&longs;i&longs;tat, ex aëre recipit leuita<lb/>tem. <lb/><arrow.to.target n="note68"></arrow.to.target></s>

<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><margin.target id="note68"/><emph type="italics"/>LXVIII <lb/>Pondus tel<lb/>luris in a<lb/>qua minue<lb/>retur, ob in<lb/>clu&longs;os bali<lb/>tus.<emph.end type="italics"/></s><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.

12. Vtique <lb/>&longs;i aquæ imponatur, nata<lb/>bit, cum pes cubicus a<lb/>quæ &longs;it lib. Rom. 80; e&longs;t <lb/>enim grauitas molis compo&longs;itæ ex va&longs;is ma<lb/>tèriâ & aëre ad grauitatem aquæ, vt;. </s>

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

<s>80; e&longs;t <lb/>enim grauitas molis compo&longs;itæ ex va&longs;is ma<lb/>tèriâ & aëre ad grauitatem aquæ, vt;. </s>

<s>3. ad 20. <lb/>At &longs;i &longs;eruata eadem materia, & æris den&longs;i<lb/>tate eâdem manente, confletur in ma&longs;&longs;am, <lb/>aut ex eâ fiat vas minoris capacitatis, erit <lb/>quidem in aëre idem pondus, at non item <lb/>in aquâ. </s>

Line 2136

Line 2143

<s>Quod &longs;i ignem <lb/>aëre multò leuiorem addamus, qui plurima <lb/>globi huius &longs;patia implet, incrementum ac-<pb pagenum="141"/>cipiet leuitas non contemnendum; cum po<lb/>ti&longs;&longs;imùm ex globi totius grauitate demen<lb/>dum &longs;it huius aquæ terram circumplectentis <lb/>pondus: iam enim non pars e&longs;&longs;et oneris mo<lb/>uendi, &longs;ed e&longs;&longs;et medium, in quo motus per<lb/>&longs;iceretur. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Aëris, & ignis copiam in terrâ de<lb/><arrow.to.target n="note69"></arrow.to.target><lb/>lite&longs;centem certis men&longs;uris definire non po&longs;<lb/>&longs;umus, &longs;ed coniecturas tantùm per&longs;equi ne<lb/>ce&longs;&longs;e e&longs;t: illud potius à Philo&longs;opho exigi po&longs;<lb/>&longs;e videtur, vt aëris grauitatem cum aquâ <lb/>comparatam determinet. </s>

<s><emph type="italics"/>Gal.<emph.end type="italics"/> Aëris, & ignis copiam in terrâ de<lb/><arrow.to.target n="note69"/><lb/>lite&longs;centem certis men&longs;uris definire non po&longs;<lb/>&longs;umus, &longs;ed coniecturas tantùm per&longs;equi ne<lb/>ce&longs;&longs;e e&longs;t: illud potius à Philo&longs;opho exigi po&longs;<lb/>&longs;e videtur, vt aëris grauitatem cum aquâ <lb/>comparatam determinet. </s>

<s>Quamuis autem <lb/>con&longs;tipato intrà vas aëre aliquando depre<lb/>henderim aërem quadringenties aquâ leuio<lb/>rem, mihi tamen omninò non &longs;atis facio: ex <lb/>illo enim experimento hoc certè euincitur, <lb/>quod aër con&longs;tipatus in aere communi non <lb/>con&longs;tipato grauitat: &longs;ed cum varia &longs;it aëris <lb/>con&longs;tipatio, incon&longs;tans pariter e&longs;t grauitatis <lb/>men&longs;ura, quæ ex illâ colligitur. </s>

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<s>Præter<lb/>quamquod ex variâ aeris calefacti raritat&etail;, <lb/>varia pariter deprehenderetur aëris commu<lb/>nis grauitas. </s>

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

<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><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>

Line 2170

Line 2177

<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"/></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><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>

<s>Iterum Æolipilam, <lb/>vt priùs, calefeci, quæ eiu&longs;dem quoquè pon<lb/>deris, vt priùs, inuenta e&longs;t: & illicò eius ro<lb/>&longs;trum in aquam immer&longs;i, vt aquam &longs;ugeret: <lb/>&longs;uxit autem aquæ vncias 9, drachmas 3, gra<lb/>na 25; quæ &longs;unt in vniuer&longs;um (&longs;i fingulis <lb/>drachmis grana 72 tribuantur, & vnciis gra<lb/>na 576) grana 5425; quod e&longs;t pondus aquæ <lb/>occupantis idem &longs;patium, quod occupabat <lb/>aër vi rarefactionis exclu&longs;us. </s>

<s>E&longs;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"/></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><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"/><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>

<s>Quan<lb/>quam non nego grauitatem illam cupri i&ntail; <lb/>aquâ e&longs;&longs;e æqualem grauitati molis aqueæ vas <lb/>implentis, &longs;i illa extra aquam in aere<gap/><lb/>transferatur; e&longs;t enim moles aquæ vas im-<pb pagenum="147"/>plentis (63/71) pedis cubici. </s>

<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><margin.target id="note70"/><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>

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

<s><expan abbr="r&utilde;">rum</expan> ponderum <expan abbr="differentiã">differentiam</expan> e&longs;&longs;e æqualem pon<lb/>deri aquæ implentis locum <expan abbr="a&etilde;ris">aerris</expan>, &longs;i illa pon<lb/>deretur in aëre: &longs;ic ex differentiâ ponderum <lb/>Æolipilæ intrà aërem communem con&longs;titu<lb/>tæ, quando plena e&longs;t aëre communi, ac <lb/>quando plena e&longs;t aëre ignito, ex hac, inquam, <lb/>differentiâ rectè illata videtur grauitas aëris <lb/>communis Æolipilam implentis, &longs;i aër i&longs;te <lb/>ponderaretur in aëre ignito tanquam in me<gap/><lb/>dio. </s>

<s>Cum autem differentia huiu&longs;modi &longs;it <lb/>granorum quatuor, pondus aëris communis <lb/>æolipilam implentis e&longs;t gran. </s>

<s>Cum autem differentia huiu&longs;modi &longs;it <lb/>granorum quatuor, pondus aëris communis <lb/>æolipilam implentis e&longs;t gran. 4. non quidem <lb/>ab&longs;olutè, &longs;ed tantùm in medio leuitatis eiu&longs;<lb/>dem ac raritatis, quam habebat aër Æolipi<lb/><emph type="italics"/>l<emph.end type="italics"/>æ candentis: &longs;icuti etiam aqua vas A R im<lb/>plens, de quo dicebam, non habet graui<lb/>tatem lib. (68 52/71) in quocunque medio, &longs;ed tan<lb/>tùm in aëre leuitatis ac raritatis eiu&longs;dem cum <lb/>aëre, qui va&longs;is capacitatem implebat. </s>

<s>4. non quidem <lb/>ab&longs;olutè, &longs;ed tantùm in medio leuitatis eiu&longs;<lb/>dem ac raritatis, quam habebat aër Æolipi<lb/><emph type="italics"/>l<emph.end type="italics"/>æ candentis: &longs;icuti etiam aqua vas A R im<lb/>plens, de quo dicebam, non habet graui<lb/>tatem lib. (68 52/71) in quocunque medio, &longs;ed tan<lb/>tùm in aëre leuitatis ac raritatis eiu&longs;dem cum <lb/>aëre, qui va&longs;is capacitatem implebat. </s>

<s>Qua<lb/>re non ego facilè dixerim quatuor illa grana <lb/>fu i&longs;&longs;e pondus aëris primùm eiecti, qu, iterùm <lb/>receptus fuit; ille enim aër nullum habebat <lb/>pondus in aëre communi; & &longs;i pondus ha<lb/>beat in aëre ignito, tota illa grauitas non <lb/>pertinet ad &longs;olum aërem, qui recipitur, &longs;ed <lb/>ad illum, qui totam Æolipilam implet. </s>

<s>Si-<pb pagenum="149"/>cut &longs;i aqua implens vas A R attenuaretur &longs;e<lb/>cundùm aliquam partem in aërem, & reli<lb/>qua eiiceretur, iterum autem ad naturalem <lb/>den&longs;itatem rediens eiectam aquam ex&longs;uge<lb/>ret, differentia ponderis va&longs;is non &longs;oli aquæ <lb/>eiectæ tribuenda e&longs;&longs;et, &longs;ed toti aquæ vas im<lb/>plenti. </s>

<s>Hinc e&longs;t quod, cum aqua in Æoli<lb/>pilam admi&longs;&longs;a non &longs;it &longs;ecundùm mole&mtail; <lb/>æqualis toti aëri, qui eam implebat, ac pro<lb/>inde non &longs;it æqualis moli, quæ habet pon<lb/>dus gran. </s>

<s>4, non habetur præcisè Ratio gra<lb/>uitatum &longs;ecundùm &longs;peciem. </s>

<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><margin.target id="note71"/><emph type="italics"/>LXXI <lb/>Experimen<lb/>tum Aeoli<lb/>pilæ ad &longs;um<lb/>mum osten<lb/>dit grauita<lb/>tem aëris <expan abbr="cõ-munis">con<lb/>munis</expan> i&ntail; <lb/>aëre ignito, <lb/>non autem <lb/>ab&longs;olutè: nec <lb/>ex eo habe<lb/>tur quæ&longs;ita <lb/>proportio <lb/>grauitatum <lb/>aquæ & aë<lb/>ris.<emph.end type="italics"/></s>

<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"/>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"/></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><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>

Line 2242

Line 2249

<s><lb/>Si ferri grauitatem cum aquæ grauitate con<lb/>ferre voluero, ferrum primùm in aëre ex<lb/>pendo, deinde in aquâ; & quæ fuerit pon<lb/>derum differentia, eam tribuo grauitati aquæ <lb/>&longs;ecundùm molem æqualis ferro; & vt totum <lb/>ferri pondus ad hanc differentiam, ita graui<lb/>tatem ferri ad aquæ grauitatem &longs;ecundùm <pb pagenum="151"/>&longs;peciem pronuncio, &longs;i tamen vtraque moles <lb/>in aëre fuerit; & &longs;it vt 42 ad 5 1/3. Nam &longs;i <lb/>tam ferrum quàm aqua intra oleum (cuius <lb/>grauitas &longs;pecifica in aëre e&longs;t 4 3/4) collocentur, <lb/>grauitas ferri in oleo erit partium 37 1/4, qua<lb/>rum grauitas aquæ erit &longs;olùm (7/12); quæ <emph type="italics"/>R<emph.end type="italics"/>atio <lb/>longè maior e&longs;t eâ Ratione, quam habent <lb/>grauitates in aëre. </s>

<s>Di&longs;criminis huius ratio e&longs;t, quia vt inue<lb/><arrow.to.target n="note72"></arrow.to.target><lb/>nirem Rationem grauitatum aquæ & ferri in <lb/>oleo, &longs;acoma &longs;eu æquipondium debui&longs;&longs;et pa<lb/>riter e&longs;&longs;e in oleo; quia autem &longs;acoma &longs;emper <lb/>fuit in aëre. </s>

<s>Di&longs;criminis huius ratio e&longs;t, quia vt inue<lb/><arrow.to.target n="note72"/><lb/>nirem Rationem grauitatum aquæ & ferri in <lb/>oleo, &longs;acoma &longs;eu æquipondium debui&longs;&longs;et pa<lb/>riter e&longs;&longs;e in oleo; quia autem &longs;acoma &longs;emper <lb/>fuit in aëre. </s>

<s>& examinatum e&longs;t ferri pondus <lb/>in aëre, grauitas quoque ferri & aquæ com<lb/>paratur &longs;olum in aëre. </s>

<s>Quod &longs;i in libræ ex<lb/>tremitate appenderetur globus ferreus vn<lb/>ciarum 42 in aëre, qui in oleo immergere<lb/>tur, re&longs;ponderet &longs;acomatiferreo in aëre exi<lb/>&longs;tenti vnciarum 37 1/4: at &longs;i &longs;acoma &longs;it pariter <lb/>in oleo, quia ferreum e&longs;t, & æqualiter à cen<lb/>tro libræ di&longs;tat, erit æquale ponderi, quod <lb/>examinatur, hoc e&longs;t vnc.42. Globus autem <lb/>ferreus &longs;i in aquâ immergeretur, re&longs;pon<lb/>deret &longs;acomati ferreo in aëre exi&longs;tenti vnc. </s>

<s><lb/>36 2/3: atqui &longs;i vnciæ 37 1/4 in aëre æquiponde<lb/>rant vncijs 42 in oleo, vnciæ 36 1/3 in aër&etail; <lb/>æquiponderant vnciis (41 51/149) in oleo; igitur <pb pagenum="152"/>eidem globo ferreo in aquâ po&longs;ito æquipon<lb/>derat &longs;acoma ferreum in oleo vnc. (41 51/149). Sa<lb/>comatum igitur 42 & (41 51/149) differentia (98/149) da<lb/>bit grauitatem aquæ in oleo comparata&mtail; <lb/>cum grauitate ferri; ita vt ferri grauitas i&ntail; <lb/>oleo ad aquæ grauitatem in oleo &longs;it vt 42 <lb/>ad (98/149), quæ e&longs;t planè eadem Ratio &longs;uperiùs in<lb/>dicata 37 1/4 ad (7/12), hoc e&longs;t 63 6/7 ad 1. </s>

<s><margin.target id="note72"></margin.target><emph type="italics"/>LXXII <lb/>Ratio duo<lb/>rum graui<lb/>um in vno <lb/>medio, vt ba<lb/>beatur, de<lb/>bet æquipon<lb/>dium e&longs;&longs;e in <lb/>eodem me<lb/>dio.<emph.end type="italics"/></s>

<s><margin.target id="note72"/><emph type="italics"/>LXXII <lb/>Ratio duo<lb/>rum graui<lb/>um in vno <lb/>medio, vt ba<lb/>beatur, de<lb/>bet æquipon<lb/>dium e&longs;&longs;e in <lb/>eodem me<lb/>dio.<emph.end type="italics"/></s>

<s>Ex his, quæ carere videntur omni diffi<lb/>cultate, & &longs;atis manife&longs;ta &longs;unt, infeto 4 il<lb/>la grana, quæ tribuis ponderi aëris commu<lb/>nis Æolipilam implentis, nullam aëris gra<lb/>uitatem indicare per &longs;e, & immediatè; non <lb/><expan abbr="a&etilde;ris">aerris</expan> in aëre communi, quia in eo, Vt dice<lb/>bam, non grauitat; non aëris communis in <lb/>aëre ignito, vt paulò ante tibi permittebam, <lb/>quia &longs;acoma &longs;eu æquipondium, quo v&longs;us es <lb/>ad grauitatem explorandam, non erat pari<lb/>ter in aëre ignito: id quod fieri oportui&longs;&longs;et. </s>

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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>Pro diuersâ aute&mtail; <lb/>materiâ &longs;iue plumbeâ, &longs;iue æreâ, &longs;iue argen-<pb pagenum="154"/>teâ, aut &longs;tanneâ, ex qua &longs;acomata con&longs;ta<lb/>rent, alia atquè alia oriretur differentia, vt <lb/>patet. </s>

<s>Id quod non in librâ tantùm, &longs;ed in <lb/>&longs;taterâ quoquè contingeret. <lb/><arrow.to.target n="note73"></arrow.to.target></s>

<s>Id quod non in librâ tantùm, &longs;ed in <lb/>&longs;taterâ quoquè contingeret. <lb/><arrow.to.target n="note73"/></s>

<s><margin.target id="note73"></margin.target><emph type="italics"/>LXXIII <lb/>Aëris com<lb/>munis & a<lb/>quæ graui<lb/>tas in aëre <lb/>ignito minor <lb/>est, quà&mtail; <lb/>fuerit depre<lb/>ben&longs;a.<emph.end type="italics"/></s>

<s><margin.target id="note73"/><emph type="italics"/>LXXIII <lb/>Aëris com<lb/>munis & a<lb/>quæ graui<lb/>tas in aëre <lb/>ignito minor <lb/>est, quà&mtail; <lb/>fuerit depre<lb/>ben&longs;a.<emph.end type="italics"/></s>

<s>Quapropter aërem communem in aër&etail; <lb/>ignito con&longs;titutum leuiorem e&longs;&longs;e 4 granis, <lb/>quæ in medio eodem e&longs;&longs;ent, apertè con<lb/>&longs;tat; illis &longs;iquidem æquiponderat in medio <lb/>cra&longs;&longs;iore: atque adeò aqua deprehen&longs;a gra<lb/>norum 5425 in aëre communi, &longs;i in aër&etail; <lb/>ignito con&longs;titueretur, multò paucioribus <lb/>granis æquiponderaret in eodem medio exi<lb/>&longs;tentibus; & quidem pro ratione materiæ <lb/>&longs;acomatis; &longs;i enim e&longs;&longs;ent grana metallica, <lb/>multò pauciora requirerentur ad faciendum <lb/>æquilibrium cum aquâ, quàm &longs;i e&longs;&longs;ent gra<lb/>na hordei. </s>

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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"/></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"/>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"/></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><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>

<s><arrow.to.target n="note74"></arrow.to.target><lb/>rum de&longs;cendentium cau&longs;am reieci&longs;&longs;e in aë<lb/>ris &longs;eu halitûs grauitatem; &longs;icut enim gra<lb/>uia de&longs;cendentia, ita & leuia a&longs;cendenti&atail; <lb/>impetum in motu concipiunt, & augent; ex <lb/>quo &longs;it, vt, quemadmodum lignum in aquam <lb/>cadens pro&longs;undiùs mergitur, quàm par &longs;it, <lb/>vnde po&longs;teà emergit, ita pariter halitus in<lb/>&longs;imo hoc aëre leuiores a&longs;cendentes conci<lb/>piant impetum, quo deferantur vltra termi<lb/>nos &longs;uæ quieti debitos in &longs;upremum aerëm <lb/>ip&longs;is halitibus leuiorem; in quo cum iam <lb/>graues &longs;int, de&longs;cendant, & obuios halitus <lb/>a&longs;cendentes reflectant. </s>

<s><arrow.to.target n="note74"/><lb/>rum de&longs;cendentium cau&longs;am reieci&longs;&longs;e in aë<lb/>ris &longs;eu halitûs grauitatem; &longs;icut enim gra<lb/>uia de&longs;cendentia, ita & leuia a&longs;cendenti&atail; <lb/>impetum in motu concipiunt, & augent; ex <lb/>quo &longs;it, vt, quemadmodum lignum in aquam <lb/>cadens pro&longs;undiùs mergitur, quàm par &longs;it, <lb/>vnde po&longs;teà emergit, ita pariter halitus in<lb/>&longs;imo hoc aëre leuiores a&longs;cendentes conci<lb/>piant impetum, quo deferantur vltra termi<lb/>nos &longs;uæ quieti debitos in &longs;upremum aerëm <lb/>ip&longs;is halitibus leuiorem; in quo cum iam <lb/>graues &longs;int, de&longs;cendant, & obuios halitus <lb/>a&longs;cendentes reflectant. </s>

<s>Si igitur aerem hunc <pb pagenum="156"/>infimum lagenæ inclu&longs;um transferremus in <lb/>puri&longs;&longs;imum æthera, vel &longs;altem in alti&longs;&longs;imi <lb/>montis, puta Cauca&longs;i, verticem, ibique la<gap/><lb/>genam expenderemus; deinde eiu&longs;dem aquâ <lb/>plenæ pondus inue&longs;tigaremus, tunc innote<lb/>&longs;ceret Ratio grauitatum aquæ & aëris in me<lb/>dio illo leuiore. </s>

<s>Cæterum in&longs;imæ huius re<lb/>gionis incolæ de aëris grauitate di&longs;putantes, <lb/>non video, quid certi de&longs;inire po&longs;&longs;int, neque <lb/>quos &longs;tatuant Rationum terminos. </s>

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

<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><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"/></s><s> 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"/></s><s> 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>

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

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

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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"/></s><s> 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"/></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><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"/></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><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>

<s>Paratum e&longs;t vas vitreum eximiæ <lb/><arrow.to.target n="note75"/><lb/>&longs;pi&longs;&longs;itudinis, & capacitatis tantæ, vt men&longs;u<lb/>ras 32, hoc e&longs;t aquæ vncias, vt minimum, <lb/>circiter mille, contineret, in Recipientis <lb/>Chymici formam elaboratum. </s>

<s>Huius col<lb/>lo adglutinatum e&longs;t &longs;ingulari arte ac firmi<lb/>tudine epi&longs;tomium ex orichalco tran&longs;uer&longs;am <lb/>habens clauem ver&longs;atilem apti&longs;&longs;imè &longs;uo lo<lb/>culamento congruentem, ne quid ex va&longs;&etail; <lb/>po&longs;&longs;it effluere, aut in illud &longs;e in&longs;iuare ni&longs;i eâ <lb/>conuersâ. </s>

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<s>Ne verò, dum antlia agitatur, <lb/>po&longs;sit aër per tenui&longs;simas rimulas (&longs;i fortè <lb/>Recipientis epi&longs;tomium & extremus antliæ <lb/>tubus non &longs;ibi exqui&longs;itâ collabellatione con<lb/>gruerent) &longs;e latenter in&longs;inuare; antlia ligneæ <lb/>cupæ firmi&longs;simè affigiturita, vt immi&longs;&longs;a in <lb/>cupam aqua Recipientis epi&longs;tomium, eius<lb/>que clauem ver&longs;atilem contegat, & &longs;olum <lb/>illud antliæ o&longs;culum ex aquâ emineat, cu<lb/>pæ &longs;cilicet labro incumbens, per quod em<lb/>bolus agitatur. </s>

<s><margin.target id="note75"></margin.target><emph type="italics"/>LXXV <lb/>Experimen<lb/>tum, quo ten <lb/>tatum est <lb/>Vacuum, & <lb/>quæ&longs;ita aë<lb/>ris grauitas.<emph.end type="italics"/></s>

<s><margin.target id="note75"/><emph type="italics"/>LXXV <lb/>Experimen<lb/>tum, quo ten <lb/>tatum est <lb/>Vacuum, & <lb/>quæ&longs;ita aë<lb/>ris grauitas.<emph.end type="italics"/></s>

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

<s>an grauitatum differentiam it&atail; <lb/>melli tribueres, vt velles pro eâ pretium &longs;ol<lb/>uere? </s>

<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><margin.target id="note76"/><emph type="italics"/>LXXVI <lb/>Ex differen<lb/>tia <expan abbr="põderum">ponderum</expan> <lb/>va&longs;is pleni, <lb/>& vacui, <lb/><expan abbr="nõ">non</expan> probatur <lb/>quæ&longs;ita aë<lb/>ris grauitas<emph.end type="italics"/></s>

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

<s>Mi<lb/>hi &longs;anè nullus relinquitur ambigendi locus, <lb/>an aere per vim rari&longs;simo Recipiens implea<lb/>tur; aperto enim 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>

Line 2378

Line 2385

<s>Et quamuis <lb/>hinc &longs;pes &longs;acta e&longs;&longs;et, adhibito minore Reci<lb/>piente, omnem prorsus aërem extrahendi, <lb/>rem tamen eò deducere nunquam potue<lb/>runt. </s>

<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><margin.target id="note77"/><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"/></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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Nullus dubitabam, quin contin-<pb pagenum="164"/><arrow.to.target n="note78"/><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>

<s>Po<lb/>namus enim, exempli gratiâ, <expan abbr="a&emacr;rem">aerrem</expan> ex di<lb/>&longs;tractione extendi po&longs;&longs;e ad &longs;patium centu<lb/>plò maius, ac naturaliter occupet, & antliam <lb/>primo ductu extrahere quatuor digitos cu<lb/>bicos aëris: hi autem &longs;int pars mille&longs;ima ca<lb/>pacitatis va&longs;is: igitur po&longs;t primum antliæ du<lb/>ctum illa pars mille&longs;ima &longs;patij di&longs;tribuitur <lb/>inter re&longs;iduas aëris partes 999: po&longs;t &longs;ecun<lb/>dum ductum duæ &longs;patij partes mille&longs;imæ <lb/>inter seliquas 998 vnâ cum aliquâ aëris ap<lb/>pendice; quia &longs;ecundo ductu non extrahitur <lb/>vna mille&longs;ima integra totius primi aëris, &longs;ed <lb/>aliquid minus, &longs;cilicet (999/1000) vnius mille&longs;imæ; <lb/>& &longs;ic deinceps, donec demùm decem partes <lb/>aëris ab initio in va&longs;e exi&longs;tentis, a&longs;&longs;umptâ <lb/>centuplâ raritate, impleant totum &longs;patium. <pb pagenum="165"/>Quare cum magis &longs;emper ac magis à natu<lb/>rali&longs;tatu aër recedat, nil mirum &longs;i &longs;emper <lb/>extrahendi difficultas augeatur; quia æquale <lb/>incrementum raritatis &longs;emper paucioribus <lb/>partibus communicatum maiorem &longs;ingulis <lb/>infert violentiam. </s>

<s>Ex quo patet ad eam ex<lb/>trahendi difficultatem citiùs perueniri in va<lb/>&longs;e minori, quia &longs;ingulæ aëris particulæ &longs;in<lb/>gulis antliæ ductibus plus di&longs;trahuntur, quàm <lb/>in va&longs;e maiori: nam &longs;i quatuor digiti &longs;int <lb/>&longs;olùm pars va&longs;is cente&longs;ima, primo ductu <lb/>partes 99 aëris debent inter &longs;e di&longs;tribuer&etail; <lb/>quatuor digitos &longs;patij, quod &longs;patium in va&longs;e <lb/>ampliore di&longs;tribuebatur inter partes 999. <lb/>Hæc autem maior violentia, quam patitut <lb/>aër maximè rarus, in cau&longs;â e&longs;t, cur primùm <lb/>tanto impetu irrumpat aqua, & po&longs;tmodum <lb/>paulatim a&longs;cendat; quò enim magis à natu<lb/>rali &longs;tatu remouetur aër, &longs;icut vim vlterio<lb/>rem inferenti contumaciùs re&longs;i&longs;tit, ita maio<lb/>re impetu re&longs;tituit &longs;e&longs;e, & aquæ re&longs;i&longs;tentiam <lb/>faciliùs vincit, cum maximè aqua ad mino<lb/>rem altitudinem euehatur; at vbi aqua adhuc <lb/>altiùs eleuanda e&longs;t, atque aër à minori rari<lb/>tate violentâ recedit, & hic &longs;egniùs &longs;e&longs;e con<lb/>trahit, & illa validiùs re&longs;i&longs;tit, ac proinde len<lb/>tior quoque e&longs;t motus aquæ paulatim a&longs;cen<lb/>dentis, & vas replentis. <pb pagenum="166"/><arrow.to.target n="note79"></arrow.to.target></s>

<s><margin.target id="note78"></margin.target><emph type="italics"/>LXXVIII <lb/>Indicatur <lb/>cau&longs;a eo<lb/>rum, quæ in <lb/>allato expe<lb/>rimento con <lb/>tingunt.<emph.end type="italics"/></s>

<s><margin.target id="note78"/><emph type="italics"/>LXXVIII <lb/>Indicatur <lb/>cau&longs;a eo<lb/>rum, quæ in <lb/>allato expe<lb/>rimento con <lb/>tingunt.<emph.end type="italics"/></s>

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