texts/archimedes/xml/casat_terra_01_la_1658.xml - Colored diff

Main History Search Repository tree

Return to casat_terra_01_la_1658.xml CVS log

Up to [CVSROOT] / texts / archimedes / xml

Colored diff for /texts/archimedes/xml/Attic/casat_terra_01_la_1658.xml between version 1.26 and 1.27

version 1.26, 2002/08/22 15:44:05

version 1.27, 2002/09/09 22:04:05

Line 74

<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>

Line 114

<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. </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>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/>

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

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

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

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

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

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

Line 182

<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>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>

Line 220

<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>

Line 270

<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"/><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>

Line 320

<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>

Line 344

<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"/><lb/><figure id="fig5"/><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>

Line 354

<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"/><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>

Line 372

<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>

Line 396

<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"/><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>

Line 412

<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>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/>

<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>

Line 450

<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>

Line 474

<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>

Line 482

<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/>

Line 490

<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>

Line 516

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

<s>25920. Quarè etiam gradibus &longs;in<lb/>gulis milliaria Rom. </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>antiqua plura quàm 72 <lb/>re&longs;pondent. </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><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Quæ&longs;iui primùm quoties Solis &longs;e<lb/>midiameter ST contineretur à lineâ SO: dato <lb/>autem SOT gr.o.m.15. reliquus e&longs;t TSO gr. </s>

<s><lb/>89.m.45.cuius Secans SO <expan abbr="parti&utilde;">partium</expan> 22918384. <lb/>52745, quarum Radius ST e&longs;t 100000. <lb/>00000. Deinde po&longs;itâ terræ &longs;emidiametro <lb/>CO Algebricè 1 &rx;, e&longs;t tota CS 1 &rx; &dagger; 22918384 <lb/>52745, cui ex Tychone æquantur &longs;emidia<lb/>metriterre&longs;tres, 1182, hoc e&longs;t 1182 &rx;. </s>

<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>

Line 600

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

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

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

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

Line 638

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

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

<s>45. &longs;ec.42. Ter. </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>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>15. &longs;ec. </s>

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

Line 792

<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"/><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"/><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.

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

Line 816

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> Ita planè, &longs;i mera e&longs;&longs;et argilla: &longs;ed <lb/>tot marmora ac lapides, ingentesque metal-<pb pagenum="47"/>lorum fodinæ, quæ argillæ grauitatem lon<lb/>go &longs;uperant interuallo, non eam vim ad<lb/>dunt ponderis, quæ non facilè æ&longs;timari <lb/>queat? </s>

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

Line 852

<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"/><lb/>4 ad 3. </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>

Line 864

<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>

Line 914

<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>

Line 940

<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"/><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"/><lb/>gnaret. </s>

Line 948

<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. </s>

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><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>

Line 982

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

Line 1016

<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"/><lb/>&longs;copulo palmorum Genuen&longs;ium 440, hoc <lb/>e&longs;t pedum Rom. </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"/><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"/><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"/><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"/><emph type="italics"/>XXXII <lb/>Idem aliter, <lb/>& breuiùs.<emph.end type="italics"/></s>

Line 1074

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

Line 1102

<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><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/>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/>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"/><lb/>tur, vnde demum <lb/>aliqua oritur dif<lb/>ferentia. </s>

Line 1138

<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>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"/><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"/><lb/>inue&longs;tigatione anguli, quem cum perpendi<lb/>culo facit opticus radius &longs;phæricam terræ &longs;u<lb/>perficiem tangens, angulum illum libens <lb/>prætermitterem: vix enim &longs;cio, quàm exa<lb/>ctè deprehendi queat, quamuis organis di<lb/>ligenti&longs;&longs;imè elaboratis non caream. </s>

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

Line 1162

<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>

Line 1174

<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"/>Gal.<emph.end type="italics"/></s><s> An non operæ pretium facturus e&longs;<lb/>&longs;et, qui illud demum in praxim deduceret, <lb/>quod ego olim aliud ne&longs;cio quid meditans <lb/>perficiendum iu&longs;si, &longs;ed aliis curis di&longs;tractus <lb/>ad exitum non perduxi? </s>

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

<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>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>

Line 1202

<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>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>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>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>

Line 1234

<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>

Line 1284

<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"/><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"/><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>

Line 1310

<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.

Line 1318

<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>

Line 1328

<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>

Line 1364

<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>

Line 1380

<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.

<s>lib.

7. <lb/>cap.

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

<s><lb/>Ergo in omni horizontis orbe ip&longs;e qui intuetur, <lb/>centron e&longs;t. </s>

Line 1402

<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. </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>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>

Line 1418

<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"/><lb/><emph type="italics"/>denti&longs;&longs;imis<emph.end type="italics"/> enim, vt Macrobius loquitur lib. </s>

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

<s>cap.

<s>Scip. cap.

<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>

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>

Line 1450

<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>

Line 1464

<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>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>

Line 1484

<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>

Line 1504

<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>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>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>21600 ab aliis po&longs;ito, & à &longs;e ad<lb/>mi&longs;&longs;o. </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>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. Por<lb/>ta lib.17. Mag. nat.in proëm. </s>

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

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

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

Line 1544

<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>lib.

<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"/><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 1572

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

<s>5775. pa&longs;&longs;. </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>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>31 & pa&longs;&longs;. </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>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 1602

<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>

Line 1626

<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>

Line 1634

<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"/><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"/><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 1648

<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>

Line 1662

<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>

Line 1670

<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>

Line 1718

<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>

Line 1736

<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>

Line 1754

<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>

Line 1762

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

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

Line 1790

<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>

Line 1818

2. de C&oelig;lo, vbi Thaletis Mile&longs;ii d&etail; <lb/>causâ terræ quie&longs;centis &longs;ententiam exponit, <pb pagenum="117"/><emph type="italics"/>anquam ex eo, quia innatans &longs;it, tellus ma<lb/>neat, quemadmodum lignum vel aliquid tale <lb/>aliud; etenim horum &longs;uper aerem quidem ni<lb/>hil natura aptum e&longs;t manere, &longs;ed &longs;uper aquam.<emph.end type="italics"/><lb/>Id quod mihi in mentem reuocauit eadem <lb/>pror&longs;usapud Senecam à me iam pridem le<lb/>cta lib.

6. Nat. </s>

6. Nat. quæ&longs;t. </s>

<s>quæ&longs;t. </s>

<s>cap.

Line 1838

<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"/>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>

Line 1920

<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>

Line 1968

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

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

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

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

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

Line 2002

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

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

<s>cubic. </s>

Line 2020

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

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

<s>Iam &longs;i &longs;oliditas mill. 80.325748 <lb/>pa&longs;&longs;. </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"/></s>

Line 2070

<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>

Line 2084

<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"/>

Line 2112

<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 2130

<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. </s>

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>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 2176

<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"/><lb/>tiùs examinanti, vtrùm omni pror&longs;us labe <lb/>careat tua hæc argumentatio. </s>

Line 2220

<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"/><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>

Line 2254

<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"/><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>

Line 2290

<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>

Line 2326

<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>

Line 2352

<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>

Line 2362

<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>

Line 2386

<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"/><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>

Line 2452

<s>Hoc itaque experimento <lb/>non &longs;atis probari no&longs;tri aëris grauitatem ab<lb/>&longs;olutè, mihi certi&longs;simum e&longs;t; &longs;ed illud vnum <lb/>ex inæquali Recipientis pondere antè ac po&longs;t <lb/>aëris extractionem vi antliæ, confici pote&longs;t, <lb/>quod non inficior, &longs;cilicet communem hunc <lb/>no&longs;trum aërem in aëre alio magis raro gra<lb/>uitare po&longs;&longs;e: Id autem nil facit ad quæ&longs;tio<lb/>nem, quam heri examinandam &longs;u&longs;cepimus, <lb/><emph type="italics"/>An tellus machinarum ope translata innataret <lb/>aquis in partem vnam delap&longs;is.<emph.end type="italics"/></s><s> Cum eni&mtail; <lb/>aquæ & cæterorum corporum grauitates <lb/>nobis tantùm innote&longs;cant cum hoc commu<lb/>ni aëre comparatæ, quid confugiendum e&longs;t ad <lb/>aërem ne&longs;cio quem rariorem, quo caremu<gap/>? </s><pb pagenum="172"/>

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

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

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

Line 2480

<s>Sienim datâ Ra<lb/>tione molis corporum totam molem com<lb/>ponentium, & datâ Ratione grauitatis &longs;in<lb/>gulorum aut leuitatis &longs;pecificæ intrà aquam, <lb/>ducatur numerus partium in numerum, quo <lb/>leuitas, aut grauitas de&longs;ignatur, horum &longs;um<lb/>ma &longs;i defectiua &longs;it, molem illam aquâ leuio<lb/>rem indicabit. </s>

<s>Quæramus ex.gr. </s>

<s>Quæramus ex.gr. an dolium <lb/>ferreis circulis firmatum, ac vino plenum, <lb/>&longs;it leuius aquâ, nec ne. </s>

<s>an dolium <lb/>ferreis circulis firmatum, ac vino plenum, <lb/>&longs;it leuius aquâ, nec ne. </s>

<s>Et primùm quarum <lb/>partium ferrum e&longs;t 3, earum &longs;it lignum 400, <lb/>& vinum 100000. Deinde &longs;pecifica in aëre <lb/>grauitas ferri &longs;it 42, ligni 4. vini 5 1/4 ad a<lb/>quam 5 1/3. E&longs;t igitur grauitas &longs;pecifica ferri <lb/>in aquâ + 36 2/3, quæ per 3 numerum partium <lb/>ducta dat totam ferri grauitatem + 110. Gra<lb/>uitas &longs;pecifica ligni in aquâ, &longs;eu potius leui<lb/>tas e&longs;t——1 1/3, quæ per 400 numerum par<lb/>tium ducta dat totam ligni leuitatem—— <lb/>533 1/3. Demum &longs;pecifica leuitas vini in aquâ <pb pagenum="175"/>e&longs;t——(1/12), quæ per numerum partiu&mtail; <lb/>100000 ducta dat totam vini leuitatem—— <lb/>8333 1/3. Si igitur inuentæ &longs;ingularum par<lb/>tium grauitates &longs;eu leuitates in &longs;ummam re<lb/>digantur, erit &longs;umma——8756 2/3 defectiu&atail; <lb/>indicans totius dolii leuitatem in aquâ, &longs;eu <lb/>differentiam, qua aquæ grauitas excedit dolii <lb/>grauitatem in aëre. </s>

Line 2490

<s><margin.target id="note82"/><emph type="italics"/>LXXXII <lb/>Inuenire an <lb/>moles com<lb/>po&longs;ita po&longs;sit <lb/>innatare a<lb/>quæ nec ne, <lb/>ab&longs;que cal<lb/>culo aquæ <lb/>æqualis.<emph.end type="italics"/></s>

<s>TABELLE WAR HIER</s>

<s>TABELLE WAR HIER</s>

<s>Porrò &longs;pecificam dolii grauitatem in aëre <lb/>habemus, &longs;i ab&longs;olutam grauitatem 526726 <lb/>diuidamus per 100403 numerum partium, <lb/>& erit grauitas &longs;pecifica molis compo&longs;itæ <pb pagenum="177"/>(5 246/1000): Vel &longs;i per eundem partium numerum <lb/>diuidatur leuitas ab&longs;oluta——8756 2/3, erit &longs;pe<lb/>cifica molis compo&longs;itæ leuitas in aquâ(27/1000). <lb/>Quarè &longs;i inter nos conueniat, quota portio <lb/>terrenihuius globi inclu&longs;is ignibus tribuen<lb/>da &longs;it, quota aëri cæterisque &longs;ialitibus aquâ le<lb/>uioribus, facilè innote&longs;cet, vtrùm leuitas vin<lb/>cat grauicatem, ducto partium numero per <lb/>leuitatis aut grauitatis denominatorem. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Quod quidem &longs;pectat ad ingen<lb/>tem illam ignium cauernam, qui terræ cen<lb/>trum circumob&longs;ident, memini me ab acu<lb/>ti&longs;simo æquè ac diligenti&longs;simo &longs;ydereorum <lb/>arcanorum &longs;crutatore Gottifredo Wendeli<lb/><arrow.to.target n="note83"/><lb/>no aliquid planè &longs;ingulare accepi&longs;&longs;e, quod <lb/>&longs;um moperè placuit. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Quod quidem &longs;pectat ad ingen<lb/>tem illam ignium cauernam, qui terræ cen<lb/>trum circumob&longs;ident, memini me ab acu<lb/>ti&longs;simo æquè ac diligenti&longs;simo &longs;ydereorum <lb/>arcanorum &longs;crutatore Gottifredo Wendeli<lb/><arrow.to.target n="note83"/><lb/>no aliquid planè &longs;ingulare accepi&longs;&longs;e, quod <lb/>&longs;um moperè placuit. </s>

<s>Hic terræ &longs;emidiame<lb/>trum in partes 100 tribuens, cauernæ æ&longs;tuan<lb/>tis &longs;emidiametro partes 63 concedebat, reli<lb/>quas 37 den&longs;itati cru&longs;tæ huius extimæ; vnde <lb/>fit ignem illum e&longs;&longs;e quartam totius globi <lb/>partem (cubus enim ex 63 e&longs;t &longs;ubquadru<lb/>plus cubi ex 100) cum &longs;it globus ille igneus <lb/>ad totum globum in triplicatâ ratione dia<lb/>metrorum. </s>

Line 2506

<s>Nollem tamen, Guldine, eam tantù&mtail; <lb/>igni leuitatem tribueres, quam aëri ignito <lb/>intrà Æolipilam candentem conuenire ob<lb/>&longs;eruaui: longè enim maiore leuitate prædi<lb/>tam ignis &longs;ub&longs;tantiam &longs;tatuere æquum vide<lb/>tur, quàm &longs;it leuitas aëris per vim à calor&etail; <lb/>extrin&longs;ecùs adueniente rarefacti. </s>

<s>Nam cum <lb/>aquæ intrà Æolipilam ex&longs;uctæ pondus fue<lb/>rit granorum 5425, facilè reperiemus illius <lb/>&longs;oliditatem; in pede &longs;iquidem cubico &longs;unt <lb/>digiti &longs;olidi 4096: Et quia pes cubicus aquæ <lb/>habet in pondere lib. </s>

<s>80, quarum &longs;in<lb/>gulæ &longs;unt vnc. </s>

<s>12, hoc e&longs;t gran. 6912, to<lb/>tius pedis cubici aquæ pondus e&longs;t gran. <lb/>552960. Si igitur grana 552960 dant digi<lb/>tos &longs;olidos 4096, grana 5425 dabunt di<lb/>gitos &longs;olidos (40 5/27). Quis autem &longs;ub&longs;tantiæ <lb/>ignis habenti in mole 40 & eo amplius digi<lb/>tos &longs;olidos, non facilè tribuat longi&longs;simè <pb pagenum="179"/>maiorem leuitatem in aëre communi quàm <lb/>vt ob&longs;i&longs;tat quatuor granorum grauitati? </s>

<s>12, hoc e&longs;t gran. </s>

<s>6912, to<lb/>tius pedis cubici aquæ pondus e&longs;t gran. </s>

<s><lb/>552960. Si igitur grana 552960 dant digi<lb/>tos &longs;olidos 4096, grana 5425 dabunt di<lb/>gitos &longs;olidos (40 5/27). Quis autem &longs;ub&longs;tantiæ <lb/>ignis habenti in mole 40 & eo amplius digi<lb/>tos &longs;olidos, non facilè tribuat longi&longs;simè <pb pagenum="179"/>maiorem leuitatem in aëre communi quàm <lb/>vt ob&longs;i&longs;tat quatuor granorum grauitati? </s>

<s>Ignis <lb/>enim naturam in motum maximè pronam <lb/>&longs;i attentiùs con&longs;ideremus, nihilquè igne le<lb/>uius nobis innotui&longs;&longs;e anim aduertamus, cum <lb/>in tertiâ poti&longs;simum & &longs;upremâ aëris regio<lb/>ne ignitæ impre&longs;siones Meteorologicæ ac<lb/>cendantur, nemo facilè negauerit ignis leui<lb/>tatem &longs;altem tantam e&longs;&longs;e, quæ vincat me<lb/>dullæ &longs;ambuceæ grauitatem, datâ molis æ<lb/>qualitate; nihil quippe medullâ &longs;ambuceâ <lb/>leuius, hoc e&longs;t minùs graue, potui adhuc <lb/>deprehendere. </s>

<s>Medullam enim &longs;ambuci <lb/>vtcunque viridis cylindricam expendi, cuius <lb/>altitudo erat digitorum 2 2/3 & ba&longs;is diameter <lb/>digiti 1/4, fuitque pondus gran. </s>

<s>Medullam enim &longs;ambuci <lb/>vtcunque viridis cylindricam expendi, cuius <lb/>altitudo erat digitorum 2 2/3 & ba&longs;is diameter <lb/>digiti 1/4, fuitque pondus gran. 3: æqualis au<lb/>tem cylindri cerei pondus fuit gran. 72. At<lb/>qui &longs;i ignis tanta &longs;it leuitas &longs;ur&longs;um, quant&atail; <lb/>e&longs;t medullæ &longs;ambuceæ grauitas deor&longs;u&mtail;, <lb/>multò maior e&longs;t ignis leuitas quàm aeris igni<lb/>ti in Æolipilâ. </s>

<s>3: æqualis au<lb/>tem cylindri cerei pondus fuit gran. </s>

<s>72. At<lb/>qui &longs;i ignis tanta &longs;it leuitas &longs;ur&longs;um, quant&atail; <lb/>e&longs;t medullæ &longs;ambuceæ grauitas deor&longs;u&mtail;, <lb/>multò maior e&longs;t ignis leuitas quàm aeris igni<lb/>ti in Æolipilâ. </s>

<s>Nam quia ba&longs;is diameter <lb/>e&longs;t digiti 1/4, & altitudo dig. </s>

<s>2 2/3, &longs;i diametri <lb/>quadratum 1/16 ducatur in altitudinem <gap/>/3, na<lb/>betur parallelepipedum digiti &longs;olidi 1/6: hoc <lb/>autem parallelepipedum e&longs;t ad cyliudrum <lb/>in Ratione ba&longs;ium, quadratum autem dia<lb/>metri ad circulum habet maiorem rationem <pb pagenum="180"/>quàm 14 ad 11, minorem verò quàm 284 <lb/>ad 223: igitur vt 14 ad 11 ita 1/6 ad (11/14) maio<lb/>rem vero; & vt 284 ad 223, ita 1/6 ad (223/1704) mi<lb/>norem vero. </s>

<s>Inuentæ quantitates (11/14) & (223/1704) re<lb/>ducantur ad eandem denominationem, & <lb/>&longs;unt (78744.18732/143136), differentia autem e&longs;t 12 parti<lb/>cularum; & &longs;umpto medio Arithmetico &longs;o<lb/>liditas cylindruli dati e&longs;t (18738/143136), hoc e&longs;t (3123/23856). Si <lb/>igitur medulla &longs;ambucea, cuius &longs;oliditas e&longs;t <lb/>dig. (3123/<gap/>3856) habet pondus gran. 3, medull&atail;, <lb/>cuius &longs;oliditas e&longs;&longs;et dig. (40 5/27), haberet pondus <lb/>gran. 920. Ignis itaque leuitas in aëre &longs;i tan<lb/>ta fuerit, quanta e&longs;t medullæ &longs;ambuceæ gra<lb/>uitas, erit gran.——920, quorum 5425 e&longs;t <lb/>grauitas aquæ &longs;ecundum molem æqualis. </s>

<s>3, medull&atail;, <lb/>cuius &longs;oliditas e&longs;&longs;et dig. (40 5/27), haberet pondus <lb/>gran. </s>

<s>920. Ignis itaque leuitas in aëre &longs;i tan<lb/>ta fuerit, quanta e&longs;t medullæ &longs;ambuceæ gra<lb/>uitas, erit gran.——920, quorum 5425 e&longs;t <lb/>grauitas aquæ &longs;ecundum molem æqualis. </s>

<s><lb/>Ergo &longs;i aquæ grauitas in aëre 5425 dat ignis <lb/>in aëre leuitatem——920, aquæ grauitas 5 1/3 <lb/>dat ignis leuitatem——(4906/5425); quæ &longs;i addatur <lb/>leuitati aëris in aqua——5 1/<gap/>, erit leuitas ignis <lb/>in aquâ &longs;altem——(6 25<gap/>/1<gap/>). Et id quidem, Gul<lb/>dine, tuà methodo: quanquam ægetrimè <lb/>mihi per&longs;uadeo tantulam leuitatem e&longs;&longs;e igni <lb/>tribuendam. </s>

Line 2570

<s>Sic &longs;i ferri leuitatem in mercurio ex. </s>

<s>gr. <lb/>deprehendebam æqualem drachmis 29 1/2 e<lb/>iu&longs;dem autem ferri grauitas in aquâ erat dra<lb/>chm. </s>

<s><lb/>deprehendebam æqualem drachmis 29 1/2 e<lb/>iu&longs;dem autem ferri grauitas in aquâ erat dra<lb/>chm. </s>

<s>36 2/3, arguebam ferrum medium e&longs;&longs;e <lb/>inter mercurium & aquam; adeòque addi<lb/>tis hi&longs;ce differentijs, nota erat differentia in<lb/>ter mercurium & aquam 66 1/6: quarè ponde<lb/>rato ferro in aëre & inuento drachm. </s>

Line 2584

<s>Vnam aliquam &longs;tatue <pb pagenum="184"/>probabilem, Mer&longs;enne, quæ tamen longi&longs;<lb/>&longs;imè ab&longs;it à tuâ illâ plu&longs;quam millecuplâ Ra<lb/>tione, quam inter aeris & aquæ grauitates in<lb/>tercedere opinaris; non enim facilè acquie<lb/>&longs;cerem. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Galilæo &longs;altem poteris acquie&longs;ce<lb/>re aërem quadringenties tantùm aquâ leuio<lb/>rem &longs;tatuenti; ignis autem adhuc aëre le<lb/>uior e&longs;t. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Galilæo &longs;altem poteris acquie&longs;ce<lb/>re aërem quadringenties tantùm aquâ leuio<lb/>rem &longs;tatuenti; ignis autem adhuc aëre le<lb/>uior e&longs;t. </s>

<s>Quid caput abnuentis in morem <lb/><arrow.to.target n="note86"/><lb/>nutat? </s>

Line 2606

<s>Et vt meam fa<lb/>cilitatem tibi probem, &longs;iquidem placuit <lb/>VVendelini &longs;ententia quartam orbis huius <lb/>partem tribuens æ&longs;tuanti cauernæ ignium <lb/>plenæ, eam vltrò admitto, & ignis leuita<lb/>tem ad aquam a&longs;&longs;umo partium——100, qua<lb/>rum aëris leuitas e&longs;t——5 1/3. Reliquis verò <lb/>tribus orbis huius quadrantibus quam conce<lb/>dis grauitatem? </s>

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

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

<s>Pri<lb/>mùm quia aqua, quæ terræ faciem alluic <lb/>aëri finitima, &longs;erè tota demenda e&longs;t ex pon<lb/>dere, cùm illa, ex hypothe&longs;i initio con&longs;titutâ, <lb/>habeat rationem medij, in quo motus per<lb/>ficitur, & ad vnam partem confluxerit. </s>

Line 2638

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

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

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

<s>tunc enim <lb/>mercurij in aquâ exi&longs;tentis grauitas non e&longs;<lb/>&longs;et 71 1/6 &longs;ed 66 1/2, & in illo leuitas ferri (cuius <lb/>grauitas in aquâ 36 2/3) e&longs;&longs;et pariter——29 1/2. <lb/>Duo &longs;iquidem æqualia corpora inæqualiter <lb/>grauia &longs;ecundùm &longs;peciem &longs;i in eodem me<lb/>dio con&longs;tituantur, quodcunque illud &longs;it, ean<lb/>dem &longs;emper &longs;eruant differentiam, quia vtri<lb/>que æqualis fit grauitatis dece&longs;sio aut acce&longs;sio <lb/>pro maiori aut minori grauitate medij. </s>

Line 2688

<s>Quia verò aëris communis in igne gra<lb/>uitas e&longs;t + 94 2/3, grauitas autem &longs;pecifica glo<lb/>bi terreni e&longs;t + 77 3/4, &longs;equitur terreni globi &longs;pe<lb/>cificam leuitatem in aëre communi e&longs;&longs;e—— <lb/>(16 11/12), quæ &longs;i per 4 numerum partium duca<lb/>tur, dabit ab&longs;olutam globi leuitatem in aëre <lb/>——67 2/3, vt Galilæus argumentabatur: tellus <lb/>igitur aere leuior e&longs;&longs;et. </s>

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

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

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

Line 2706

<s>Sed &longs;i placeat grauitatem illam augere, <lb/>&longs;tatuamus tres illos quadrantes non argillæ, <lb/>&longs;ed Magnetis grauitatem habere; e&longs;t autem <lb/>magnetis grauitas 26 ad aquæ grauitatem <lb/>5 1/3 in aëre: quare magnetis grauitas in aquâ <lb/>e&longs;t 20 2/3, & grauitas in igne 120 2/3; ideòque <lb/>grauitas trium quadrantum in aquâ, cu&mtail; <lb/>ex magnete con&longs;tent, e&longs;t 62, & leuitas <lb/>conueniens vni quadranti ignis in aquâ e&longs;t <lb/>——100: igitur leuitas globi in aquâ e&longs;t <expan abbr="tãtùm">tantùm</expan> <lb/>—— 38. Quando verò totus globus ex aquâ <lb/>pariter & terrâ conflatus accipitur, iam au<lb/>ctâ grauitate, alia e&longs;t &longs;pecifica totius globi <lb/>grauitas, qualis e&longs;&longs;et ex. </s>

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

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

<s><emph type="italics"/>Guld.<emph.end type="italics"/></s><s> At &longs;i globo non re&longs;tituatur aqua, <lb/>quæ in latus &longs;ece&longs;&longs;it, augebiturnè grauitas <lb/>&longs;pecifica molis, quæ ex tribus quadrantibus <lb/>magnetis, & vno quadrante ignis conflatur? </s>

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

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

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

Line 2738

<s>&longs;bi grauitas <lb/>peci fic&atail; <lb/>maior est<gap/><lb/>grauitat&etail; <lb/>argillæ, &longs;i <lb/>aqua dema<lb/>tur ex gio<lb/>bo.<emph.end type="italics"/></s>

<s>Primùm globi &longs;oliditatem habemus, &longs;i <lb/>inuentæ &longs;ub initium no&longs;tri he&longs;terni &longs;ermonis <lb/>&longs;uperficiei &longs;phæricæ mill. </s>

<s>Primùm globi &longs;oliditatem habemus, &longs;i <lb/>inuentæ &longs;ub initium no&longs;tri he&longs;terni &longs;ermonis <lb/>&longs;uperficiei &longs;phæricæ mill. quad. </s>

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

<s>716000, accipiamus trientem mill. </s>

<s>716000, accipiamus trientem mill. quad. </s>

<s><lb/>71.400665. pa&longs;&longs;. </s>

<s>572000, & ducamus per <lb/>telluris &longs;emidiametrum mill. </s>

<s>572000, & ducamus per <lb/>telluris &longs;emidiametrum mill. 4128. pa&longs;&longs;. </s>

<s>4128. pa&longs;&longs;. </s>

<s><lb/>638: fiet enim totius globi &longs;oliditas mill. </s>

<s>cu<lb/>bicorum 294787.501105. pa&longs;&longs;. </s>

<s><lb/>638: fiet enim totius globi &longs;oliditas mill. cu<lb/>bicorum 294787.501105. pa&longs;&longs;. </s>

<s>850936000. <lb/>Ex hac globi &longs;oliditate &longs;i inuenta &longs;uperiùs <lb/>aquæ &longs;oliditas mill. cub. </s>

<s>850936000. <lb/>Ex hac globi &longs;oliditate &longs;i inuenta &longs;uperiùs <lb/>aquæ &longs;oliditas mill. </s>

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

<s><lb/>768500000. auferatur, relinquitur mill. </s>

<s><lb/>768500000. auferatur, relinquitur mill. cub <lb/>294707.175357. pa&longs;&longs;. </s>

<s>cub <lb/>294707.175357. pa&longs;&longs;. </s>

<s>82.436000. &longs;olidita <lb/>reliqui globi demptâ aquâ. </s>

Line 2806

<s><lb/>Ni&longs;i quis fortè ex eorum numero, qui la<lb/>minam metallicam ratione figuræ in mul<lb/>tam latitudinem explicatæ, ideòque diffi<lb/>ciliùs, (vt ip&longs;i quidem loquuntur) &longs;ubie<lb/>ctam aquam diuidentis, innatare cen&longs;ent, <lb/>ambigeret pariter, an idem terræ quoqu&etail; <lb/>contingere po&longs;&longs;et. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Errorem hunc iamdudum aureo <lb/>illo tuo de Innatantibus libello profliga&longs;ti; <lb/>Galilæe: vixque puto aliquem &longs;upere&longs;&longs;e, qui <lb/>cramben hanc recoquat, præter eos, quos <lb/>iuuat ex antiquioribus tantùm codicibus ru<lb/>dioris &longs;æculi puluerem colligere. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Errorem hunc iamdudum aureo <lb/>illo tuo de Innatantibus libello profliga&longs;ti; <lb/>Galilæe: vixque puto aliquem &longs;upere&longs;&longs;e, qui <lb/>cramben hanc recoquat, præter eos, quos <lb/>iuuat ex antiquioribus tantùm codicibus ru<lb/>dioris &longs;æculi puluerem colligere. </s>

<s>Nihil Gul<lb/>dino, nihil mihi e&longs;t cum huiu&longs;modi homi<lb/>num genere commercij: quapropter mi&longs;&longs;os <lb/>illos prorsùs faciamus: quamuis enim motui <lb/>tarditatem aliquam inferre po&longs;&longs;it figura, im<lb/>pedire tamen omninò non pote&longs;t, &longs;i illa qui<lb/>dem per &longs;e re&longs;piciatur; quod &longs;i ea fuerit cor<lb/>poris grauis figura, quæ leuioris aeris partem <lb/><gap/> deferat, aeri vtique non &longs;iguræ <gap/><lb/>buenda e&longs;t innatatio, quatenus ex aere, & <pb pagenum="203"/>metallo laminæ componitur moles, cuius <lb/>pondus minus e&longs;t pondere æqualis molis <lb/>aquæ. </s>

<s>Cum autem nihil &longs;imile in terrâ con<lb/>tingere po&longs;&longs;it, quandoquidem aër ille, qui <lb/>valles ex aquâ extantes impleret, nihil con<lb/>ferret leuitatis (quemadmodum & in naui, <lb/>qui &longs;upra aquæ &longs;uperficiem aer, nauis pon<lb/>dus non minuit, nam intrà aerem non leui<lb/>tat) nulla &longs;pes nobis reliqua e&longs;t innatationis <lb/>terræ: &longs;ed quicquid in tellure machinationi<lb/>bus mouendâ compendij haberet Archime<lb/>des ex aquis, totum illud e&longs;&longs;et ex eâ ponde<lb/>ris diminutione, quam &longs;ubeunt &longs;olida gra<lb/>uiora aquis immer&longs;a. </s>

<s><emph type="italics"/>Gul.<emph.end type="italics"/></s><s> Ita planè, &longs;i terræ tantùm ratio ha<lb/><arrow.to.target n="note95"/><lb/>beatur: nam compendium aliud, nec illud <lb/>contemnendum, antequam heri aduenires <lb/>Mer&longs;enne, ob&longs;eruabamus ex ip&longs;ius aquæ &longs;e<lb/>iunctione, cuius grauitatem ad calculos re<lb/>uocantes deprehendebamus non minorem <lb/>libris Rom. </s>

<s><emph type="italics"/>Gul.<emph.end type="italics"/></s><s> Ita planè, &longs;i terræ tantùm ratio ha<lb/><arrow.to.target n="note95"/><lb/>beatur: nam compendium aliud, nec illud <lb/>contemnendum, antequam heri aduenires <lb/>Mer&longs;enne, ob&longs;eruabamus ex ip&longs;ius aquæ &longs;e<lb/>iunctione, cuius grauitatem ad calculos re<lb/>uocantes deprehendebamus non minorem <lb/>libris Rom. 803.257487.685000.000000. <lb/>Quæ &longs;i ex totius globi grauitate argilla<lb/>ceâ dematur, relinquet reliquæ terræ pon<lb/>dus. </s>

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

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

Line 2824

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

<s>Per <lb/>hanc igitur grauitatem duco inuentam paulò <lb/>antè globi &longs;oliditatem mill. </s>

<s>Per <lb/>hanc igitur grauitatem duco inuentam paulò <lb/>antè globi &longs;oliditatem mill. 294787.501105. <lb/>pa&longs;&longs;. </s>

<s>294787.501105. <lb/>pa&longs;&longs;. </s>

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

Line 2856

<s><margin.target id="note97"/><emph type="italics"/>XCVII <lb/>Solidi moles <lb/>ex bumido <lb/>emerg&ebreve;s, ma<lb/>ior est mole <lb/>humidi ac<lb/>currentis a<gap/><lb/>replendum <lb/>&longs;patium.<emph.end type="italics"/></s>

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

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

<s><emph type="italics"/>Gal.<emph.end type="italics"/></s><s> Perinde e&longs;t &longs;i aqua va&longs;is lateribus <lb/>circum&longs;cripta certam figuram induat, ac &longs;i <lb/>&longs;uis &longs;e nutibus ip&longs;a in &longs;phæram di&longs;ponat. </s>

Line 2876

<s>Nam &longs;i KV non e&longs;t maior quàm AH, <lb/>ergo aut æqualis, aut minor. </s>

<s>Sit æqualis: er<lb/>go quia HG & VN æquales &longs;unt ex hypothe<lb/>&longs;i, & VK ip&longs;i HA æqualis dicitur, etiam <lb/>reliquæ KN & AG, hoc e&longs;t OS & CE, æqua<lb/>les &longs;unt: ergo aquæ OMRS & CDFE æqua<lb/>lem habentes altitudinem &longs;unt inter &longs;e vt <lb/>ba&longs;es, hoc e&longs;t vt &longs;uperficies OM & CD. </s>

<s>At<lb/>qui &longs;uperficies OM maior e&longs;t &longs;uperficie CD, <lb/>ergo aqua OMRS maior e&longs;t quàm aqu&atail; <lb/>CDFE: &longs;ed aqua de&longs;cendens e&longs;t æqualis mo<lb/>li corporis NL, quæ replebat &longs;patium reli<lb/>ctum; igitur maior e&longs;t moles NL quàm GB: <lb/>e&longs;t autem NL æqualis parti eleuatæ VO, & <lb/>GB æqualis e&longs;t parti eleuatæ HC, ergo VO <lb/>maior e&longs;t moles <expan abbr="quãm">quamm</expan> HC: hæ verò moles <lb/>VO & HC &longs;unt vt altitudines, quia ex hypo<lb/>the&longs;i data &longs;olida &longs;unt æqualia, &longs;imilia, & &longs;i<lb/>militer po&longs;ita; ergo maior e&longs;t altitudo KV <lb/>quam altitudo AH. </s>

<s>Quod &longs;i KV dicatur minor quàm AH <lb/>ergo ex æqualibus VN, HG, demptis inæ<lb/>qualibus, remanet KN maior quam AG, <lb/>hoc e&longs;t OS maior quam CE: aqua igitur <lb/>OMRS maiorem habens ba&longs;im ac maiorem <lb/>altitudinem, quam aqua CDFE, maior quo-<pb pagenum="209"/><figure id="fig37"/><lb/>què erit; ac proinde & moles NL, hoc e&longs;t VO, <lb/>maior mole GB, hoc e&longs;t HC; & vt priùs ele<lb/>uatio KV maior eleuatione AH. </s>

<s>Quare vide<lb/>tis hoc adeò certum e&longs;&longs;e, vt<gap/> ex ip&longs;o negante <lb/>eleuationem in maiori va&longs;e maiorem e&longs;&longs;&etail; <lb/>eleuatione in minori va&longs;e, veritatis huius con<lb/>fe&longs;&longs;io extorqueatur, ijs admi&longs;&longs;is, quæ con<lb/>tradicens ponit. </s>

<s><emph type="italics"/>Met&longs;.<emph.end type="italics"/></s><s> Priu&longs;quàm vlteriùs progrediatis, <lb/>vnum vellem ex te quærere; an &longs;cilicet aliqua <lb/>&longs;it inter eleuationes &longs;olidorum & depre&longs;&longs;io<lb/>nes aquatum in va&longs;is inæqualibus analogi&atail; <lb/>&longs;altem reciproca, ita vt quæ Ratio e&longs;t eleua<lb/>tionis KV in va&longs;e maiori ad eleuationem AH <lb/>in minori, eadem Ratio &longs;it depre&longs;&longs;ionis aquæ <lb/>CE, hoc e&longs;t AG, in minori ad depre&longs;&longs;ionem <lb/>aquæ OS, hoc e&longs;t KN in maiori. </s>

<s><emph type="italics"/>Met&longs;.<emph.end type="italics"/></s><s> Priu&longs;quàm vlteriùs progrediatis, <lb/>vnum vellem ex te quærere; an &longs;cilicet aliqua <lb/>&longs;it inter eleuationes &longs;olidorum & depre&longs;&longs;io<lb/>nes aquatum in va&longs;is inæqualibus analogi&atail; <lb/>&longs;altem reciproca, ita vt quæ Ratio e&longs;t eleua<lb/>tionis KV in va&longs;e maiori ad eleuationem AH <lb/>in minori, eadem Ratio &longs;it depre&longs;&longs;ionis aquæ <lb/>CE, hoc e&longs;t AG, in minori ad depre&longs;&longs;ionem <lb/>aquæ OS, hoc e&longs;t KN in maiori. </s>

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

Line 2902

11. ba&longs;es cum altitudinibus re<lb/>ciprocantur, & vt AG ad KN, ita &longs;uperficies <lb/>va&longs;is maioris ad &longs;uperficiem va&longs;is minoris. </s>

<s>Prætereà aqua circumfu&longs;a OMRS æqua<lb/>lis e&longs;t moli VO, ergo ad molem KS habet <lb/>eandem Rationem quam VO ad KS, hoc e&longs;t <lb/>quam altitudines KV ad KN. </s>

<s>Prætereà aqua circumfu&longs;a OMRS æqua<lb/>lis e&longs;t moli VO, ergo ad molem KS habet <lb/>eandem Rationem quam VO ad KS, hoc e&longs;t <lb/>quam altitudines KV ad KN. </s>

<s>At aqua cir<lb/>cum&longs;u&longs;a ad mo'em KS, quia in eâdem &longs;unt <pb pagenum="211"/>altitudine OS, e&longs;t vt &longs;uperficies va&longs;is minus <lb/>&longs;uperficie &longs;olidi VY ad ip&longs;am &longs;uperficiem &longs;o<lb/>lidi; igitur VK eleuatio &longs;olidi ad KN depre&longs;<lb/>&longs;ionem aquæ e&longs;t vt &longs;uperficies va&longs;is maioris <lb/>minùs &longs;uperficie &longs;olidi ad ip&longs;am &longs;uperficiem <lb/>&longs;olidi VY: & componendo vt VN corporis <lb/>emer&longs;io ad KN aquæ depre&longs;&longs;ionem, ita &longs;u<lb/>perficies va&longs;is maioris ad &longs;uperficiem &longs;olidi <lb/>VY. </s>

Line 2910

<s>Quoniam igitur vt &longs;uperficies va&longs;is maio. </s>

<s><lb/>ris ad &longs;uperficiem minoris, ita GA ad NK; <lb/>&longs;i e&longs;&longs;et VK ad HA vt GA ad NK, iam e&longs;&longs;et vt <lb/>VK ad HA ita &longs;uperficies va&longs;is maioris ad &longs;u-<pb pagenum="212"/>perficiem minoris: &longs;ed vt VK ad HA, it&atail; <lb/>moles VO ad molem HC, hoc e&longs;t aqu&atail; <lb/>OMRS ad aquam CDFE; ergo vt &longs;uperficies <lb/>va&longs;is maioris ad &longs;uperficiem minoris, hoc e&longs;t <lb/>vt GA ad NK, ita aqua OMRS ad aqua&mtail; <lb/>CDFE. </s>

<s>Atquiaquæ i&longs;tæ circumfu&longs;æ habent <lb/>Rationem compo&longs;itam ex Rationibus altitu<lb/>dinum & ba&longs;ium; ergo Ratio GA ad NK <lb/>æqualis e&longs;t <emph type="italics"/>R<emph.end type="italics"/>ationi compo&longs;itæ <emph type="italics"/>ex Rationi-<emph.end type="italics"/><lb/>bus altitudinum GA ad N<emph type="italics"/>K,<emph.end type="italics"/> & ba&longs;ium CD <lb/>ad OM. </s>

Line 2918

<s>At ba&longs;es i&longs;tæ &longs;unt &longs;u<lb/>perficies va&longs;orum minùs &longs;uperficie &longs;olidi im-<pb pagenum="213"/>mi&longs;&longs;i; igitur &longs;i ba&longs;ibus æqualibus addantur <lb/>ip&longs;æ æquales &longs;uperficies &longs;olidi, erunt &longs;uperfi<lb/>cies va&longs;orum æquales: id quod e&longs;t contra hy<lb/>pothe&longs;im. </s>

<s>Non igitur e&longs;t vt VK ad HA ita <lb/>AG ad KN. </s>

<s>Non igitur e&longs;t vt VK ad HA ita <lb/>AG ad KN. </s>

<s><emph type="italics"/>S<emph.end type="italics"/>it enim iterum, &longs;i fieri pote&longs;t, VK ad <lb/>HA, vt AG ad KN: VK prima vel e&longs;t maior <lb/>quàm AG tertia, vel minor, vel æqualis. </s>

Line 2926

<s>Si VK mi<lb/>nor e&longs;t quàm AG, etiam HA minor e&longs;t quàm <lb/>KN; &longs;ed HA minor e&longs;t quàm VK ex dictis; <lb/>ergo HA e&longs;t omnium minima & AG omniu <lb/>maxima; ergo per 25.5. HG maior e&longs;t quàm <lb/>VN, contra hypothe&longs;im. </s>

<s>At verò &longs;i demùm VK prima æqualis &longs;it <lb/>AG tertiæ, etiam HA &longs;ecunda æqualis e&longs;t <lb/>KN quartæ: ergo per 7.5. vt VK ad KN ita <lb/>GA ad AH. </s>

<s>At verò &longs;i demùm VK prima æqualis &longs;it <lb/>AG tertiæ, etiam HA &longs;ecunda æqualis e&longs;t <lb/>KN quartæ: ergo per 7.5. vt VK ad KN ita <lb/>GA ad AH. </s>

<s>At ex demon&longs;tratis vt VK ad KN, <lb/>ita &longs;uperficies va&longs;is maioris minùs &longs;uperficie <lb/>&longs;olidi ad &longs;uperficiem &longs;olidi VY, & vt GA ad <lb/>AH, ita &longs;uperficies &longs;olidi HT, hoc e&longs;t VY, <lb/>ad &longs;uperficiem va&longs;is minoris minùs &longs;uperfi-<pb pagenum="214"/>cie &longs;olidi. </s>

<s>Igitur &longs;uperficies &longs;olidi e&longs;t medio <lb/>loco proportionalis inter differentias, quibus <lb/>&longs;uperficies &longs;olidi exceditur à &longs;uperficiebus va<lb/>&longs;orum: ergo componendo & permutando vt <lb/>&longs;uperficies va&longs;is maioris ad &longs;uperficiem mi<lb/>noris, ita &longs;uperficies &longs;olidi HT ad &longs;uperficiem <lb/>va&longs;is minoris minùs &longs;uperficie &longs;olidi, hoc e&longs;t <lb/>&longs;uperficiem aquæ CD. </s>

<s>Sed vt &longs;uperficies &longs;o<lb/>lidi HT ad &longs;uperficiem CD, ita moles AE <lb/>ad aquam CDFE eiu&longs;dem altitudinis: & quia <lb/>AG ex hypothe&longs;i e&longs;t æqualis ip&longs;i VK, moles <lb/>AE e&longs;t æqualis ip&longs;i moli VO, hoc e&longs;t aquæ <lb/>OMRS. ergo vt &longs;uperficies HT ad &longs;uperfi<lb/>ciem CD, ita aqua OMRS ad aquam CDFE; <lb/>ergo per 11. 5. vt &longs;uperficies va&longs;is maioris ad <lb/>&longs;uperficiem minoris, hoc e&longs;t vt aquarum al<lb/>titudines AG ad KN, ita aqua OMRS ad a<lb/>quam CDFE. </s>

<s>Sunt igitur aquæ inter &longs;e re<lb/>ciprocè vt earum altitudines: Ratio aute&mtail; <lb/>molium ex Rationibus altitudinum & <expan abbr="ba&longs;i&utilde;">ba&longs;ium</expan> <lb/>componitur, ba&longs;es verò non habent rationem <lb/>æqualitatis; ergo aquarum &longs;uperficies OM <lb/>ad CD &longs;unt in duplicatâ Ratione altitudinum <lb/>reciprocè &longs;umptarum, hoc e&longs;t vt quadratu&mtail; <lb/>GA ad quadratum KN. </s>

<s>Id quod &longs;ic breui<lb/>ter demon&longs;tro Algebricis notis. </s>

<s>Sit GA altitudo R, & KN altitudo &longs;it S: <lb/>&longs;uperficies CD &longs;it D planum, & &longs;uperficies <pb pagenum="215"/>OM &longs;it Z planum. </s>

<s>lgitur aqua CDEF e&longs;t <lb/>D plan. </s>

<s>lgitur aqua CDEF e&longs;t <lb/>D plan. in R; & aqua OMRS e&longs;t Z plan; i&ntail; <lb/>S. </s>

<s>Quare cum &longs;it Z plan. in S ad D plan. in R, <lb/>vt R ad S. erit per 16. 6. vel 19. 7. Z pl. </s>

<s>in R; & aqua OMRS e&longs;t Z plan; i&ntail; <lb/>S. </s>

<s>Quare cum &longs;it Z plan. </s>

<s>in S. <lb/>quadr. </s>

<s>æquale D plano in R quadratum: ‘er<lb/>go Z planum ad D planum, hoc e&longs;t &longs;uperfi<lb/>cies OM ad &longs;uperficiem CD, e&longs;t vt R qua<lb/>dratum ad Squadratum: &longs;unt igitur &longs;uperfi<lb/>cies aquarum in duplicatâ Ratione altitudi<lb/>num AG ad KN. </s>

<s>At in Ratione AG ad KN <lb/>e&longs;t &longs;uperficies va&longs;is maioris ad &longs;uperfieie&mtail; <lb/>minoris, ergo &longs;uperficies OM ad &longs;uperficiem <lb/>CD e&longs;t in duplicatâ Ratione &longs;uperficiei va&longs;is <lb/>maioris ad &longs;uperficiem minoris. </s>

<s>Datis itaque va&longs;is &longs;imilibus inæqualibus, <lb/>& datâ Ratione &longs;uperficierum huiu&longs;modi va<lb/>&longs;orum, poterimus reperire &longs;uperficiem &longs;oli<lb/>di VY aut HT; quæ ex va&longs;orum &longs;uperficie<lb/><arrow.to.target n="note100"/><lb/>bus dempta reliquam aquæ &longs;uperficiem relin<lb/>quat in duplicatâ Ratione &longs;uperficierum va<lb/>&longs;orum. </s>

<s>Cum enim &longs;olidorum &longs;uperficies HT, <lb/>VY habeant Rationem æqualitatis, maior e&longs;t <lb/>Ratio totius &longs;uperficiei va&longs;is maioris ad totam <lb/>&longs;uperficiem minoris, quàm ablatæ VY ad <lb/>ablatam HT, ergo per 33 5. apud Clau. ma<lb/>ior e&longs;t Ratio reliquæ OM ad reliquam CD, <lb/>quàm <gap/>o<gap/> ad totam: quare pote&longs;t eria&mtail; <lb/>haberi Ratio duplicata Rationis totius ad to-<pb pagenum="216"/>tam. </s>

<s>ma<lb/>ior e&longs;t Ratio reliquæ OM ad reliquam CD, <lb/>quàm <gap/>o<gap/> ad totam: quare pote&longs;t eria&mtail; <lb/>haberi Ratio duplicata Rationis totius ad to-<pb pagenum="216"/>tam. </s>

<s>Sic autem inue&longs;ligo &longs;uperficiem VY, <lb/>quæ &longs;it media proportionalis inter differen<lb/>tias illius & &longs;uperficiei va&longs;orum, hoc e&longs;t in<lb/>ter OM & CD. </s>

Line 2978

<s>Quare hoc vno in ca&longs;u quando &longs;uperficies <lb/>&longs;olidi immi&longs;&longs;i e&longs;t media proportionalis inter <lb/>exce&longs;&longs;us, quos relinquit in &longs;uperficiebus va<lb/>&longs;orum, pote&longs;t contingere eleuationes &longs;olidi <lb/>reciprocari cum depre&longs;&longs;ionibus aquæ; quan<lb/>do &longs;cilicet eleuatio &longs;olidi in maiori va&longs;e e&longs;t <lb/>æqualis depre&longs;&longs;ioni aquæ in minori, & con<lb/>trà eleuatio &longs;olidi in minori æqualis e&longs;t de<lb/>pre&longs;&longs;ioni aquæ in maiori: </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Operæ profectò pretium fuit hac <lb/>&longs;uper re te interrogare, de qua neminem di<lb/>&longs;putantem audi&longs;&longs;e me memini aut legi&longs;&longs;e. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Operæ profectò pretium fuit hac <lb/>&longs;uper re te interrogare, de qua neminem di<lb/>&longs;putantem audi&longs;&longs;e me memini aut legi&longs;&longs;e. </s>

<s><lb/>Sed vt ad terram aquis delap&longs;is circumfu&longs;am <lb/>reuertamur, eadem-nè erit depre&longs;&longs;ionis aquæ <lb/>Ratio, quæ in va&longs;is, de quibus hactenus fuit <lb/>&longs;ermo? </s>

Line 3044

<s>Quod autem pertinet ad ip&longs;am metho<lb/>dum, res clara e&longs;t. </s>

<s>Dum enim triplum la<lb/>teris primi ducitur in latus ip&longs;um, hoc e&longs;t F <lb/>in A, producitur G, quod e&longs;t triplum qua<lb/>drati ip&longs;ius A. </s>

<s>Dum enim triplum la<lb/>teris primi ducitur in latus ip&longs;um, hoc e&longs;t F <lb/>in A, producitur G, quod e&longs;t triplum qua<lb/>drati ip&longs;ius A. </s>

<s>Dum verò B in F ducitur, & <lb/>fit H, planum, quod fit, e&longs;t ex latere &longs;ecun<lb/>do in triplum lateris primi. </s>

<s>Additis G & H <lb/>fit &longs;umma I, hoc e&longs;t 3 A Quad. + 3 A in B. </s>

<s><lb/>Hæc &longs;umma multiplicatur per B, & fit K, <lb/>hoc e&longs;t 3 A Quadr. </s>

<s><lb/>Hæc &longs;umma multiplicatur per B, & fit K, <lb/>hoc e&longs;t 3 A Quadr. in B + 3 A in B Quadr. </s>

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

<s><lb/>Additur demum L cubus ip&longs;ius B, vt ip&longs;ius <lb/>lateris A + B cubus &longs;it A cub. + 3 A Quadr. </s>

<s><lb/>Additur demum L cubus ip&longs;ius B, vt ip&longs;ius <lb/>lateris A + B cubus &longs;it A cub. + 3 A Quadr. <lb/>in B + 3 A in B Quadr. + B cub. </s>

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

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Præ&longs;agiebat animus me aliquid ex <lb/>te auditurum, quod operationem hanc fa<lb/>cilem redderet atque expeditam, vixque pu<lb/>to aliquid addi po&longs;&longs;e facilitatis atque per&longs;pi<lb/>cuitatis; cum nullâ hìc opus &longs;it numerorum <lb/>translatione, & triplicatio lateris primi A, <lb/>aut multiplicatio lateris &longs;ecundi B in F tri-<pb pagenum="224"/>plum lateris primi facillimè perficiuntur ab&longs;<lb/>que eo, quod opus &longs;it multiplicatorem &longs;ub <lb/>multiplicando de&longs;cribere. </s>

<s><emph type="italics"/>Mer&longs;.<emph.end type="italics"/></s><s> Præ&longs;agiebat animus me aliquid ex <lb/>te auditurum, quod operationem hanc fa<lb/>cilem redderet atque expeditam, vixque pu<lb/>to aliquid addi po&longs;&longs;e facilitatis atque per&longs;pi<lb/>cuitatis; cum nullâ hìc opus &longs;it numerorum <lb/>translatione, & triplicatio lateris primi A, <lb/>aut multiplicatio lateris &longs;ecundi B in F tri-<pb pagenum="224"/>plum lateris primi facillimè perficiuntur ab&longs;<lb/>que eo, quod opus &longs;it multiplicatorem &longs;ub <lb/>multiplicando de&longs;cribere. </s>

<s>E&longs;t itaque &longs;phæ<lb/>ræ aqueæ diameter minor verâ pa&longs;&longs;. </s>

Line 3066

<s>535368. Quare &longs;ta<lb/>tui pote&longs;t diameter vera pa&longs;&longs;. </s>

<s>535300 rotun<lb/>dè, & &longs;emidiameter mill. </s>

<s>535300 rotun<lb/>dè, & &longs;emidiameter mill. 267. pa&longs;&longs;: 650: <lb/>quæ &longs;i addatur terreni globi &longs;emidiametro à <lb/>nobis &longs;uperiùs a&longs;&longs;umptæ mill. 4128 pa&longs;&longs; 638, <lb/><arrow.to.target n="note104"/><lb/>dabit mill. 4356 pa&longs;&longs;. </s>

<s>267. pa&longs;&longs;: 650: <lb/>quæ &longs;i addatur terreni globi &longs;emidiametro à <lb/>nobis &longs;uperiùs a&longs;&longs;umptæ mill. </s>

<s>4128 pa&longs;&longs; 638, <lb/><arrow.to.target n="note104"/><lb/>dabit mill. </s>

<s>4356 pa&longs;&longs;. </s>

<s>288. di&longs;tantiam cen<lb/>triterræ ab vniuer&longs;i centro, quando iam aqua <lb/>in &longs;phæram conglobata nihil iuuaret terræ <lb/>motionem. </s>

Line 3134

<s><emph type="italics"/>Aqua cur in tubo vtrinque hiante a&longs;cendat aliquantulum, <lb/>num.<emph.end type="italics"/>60 121 </s>

<s><emph type="italics"/>Aqua mutaret figuram, &longs;i tellus aliò traheretur, n.<emph.end type="italics"/>61 124 </s>

<s><emph type="italics"/>Aqua mutaret figuram, &longs;i tellus aliò traheretur, n.<emph.end type="italics"/>61 124 </s>

<s><emph type="italics"/>Aqua tota ab ea &longs;eiungeretur Tellure translata, n<emph.end type="italics"/>63 129 </s>

Legend:

Removed from v.1.26
changed lines
	Added in v.1.27