Mercurial > hg > mpdl-xml-content
view texts/archimedesOldCVSRepository/archimedes/xml/baldi_mecha_007_la_1621.xml @ 12:f9a6b8344c3a
DESpecs 2.0 Autumn 2009
author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
---|---|
date | Thu, 02 May 2013 11:14:40 +0200 |
parents | 22d6a63640c6 |
children |
line wrap: on
line source
<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink"> <info> <author>Baldi, Bernardino</author> <title>In mechanica Aristotelis problemata exercitationes</title> <date>1621</date> <place>Mainz</place> <translator/> <lang>la</lang> <cvs_file>baldi_mecha_007_la_1621.xml</cvs_file> <cvs_version/> <locator>007.xml</locator> </info> <text> <front> <section> <pb xlink:href="007/01/001.jpg"/> <p type="head"> <s id="s.000001">BERNARDINI<!-- REMOVE S--> BALDI VRBINATIS <lb/>GVASTALLÆ AB­<lb/>BATIS <lb/><emph type="italics"/>IN<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000002">MECHANICA ARISTOTE­<lb/>LIS PROBLEMATA <lb/>EXERCITATIONES:<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000003"><emph type="italics"/>ADIECTA SVCCINCTA NAR­<lb/>ratione de autoris vita & &longs;criptis.<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.000004"><emph type="italics"/>MOGVNTIAE.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="head"> <s id="s.000005">Typis & Sumptibus Viduæ Ioannis Albini.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000006"><lb/>M. D C. XXI.</s> </p> <pb xlink:href="007/01/002.jpg"/> </section> <section> <pb xlink:href="007/01/003.jpg"/> <p type="head"> <s id="s.000007"><emph type="italics"/>NOBILISSIMO AC GENE­<lb/>ROSO DOMINO<emph.end type="italics"/> D. ADAMO PHILIP­<lb/>PO BARONI A CRON­<lb/>BERG, EQVITI, SACRÆ CÆSA­<lb/>REÆ MAIESTATIS, ET SERENISSIMI Principis Archiducis Alberti Camerario intimo & c. <lb/><!-- KEEP S--></s> <s id="s.000008">Domino meo gratio&longs;i&longs;&longs;imo.</s> </p> <p type="main"> <s id="s.000009">Opportune &longs;ub hoc ip&longs;um tem­<lb/>pus, quo in Belgium ad Sere­<lb/>ni&longs;&longs;imos Principes iter ador­<lb/>nat.</s> <s id="s.000010"> Nobili&longs;&longs;ima & Genero&longs;a <lb/>Dom. <!-- REMOVE S-->V.^{ra}, prodit no&longs;tris for­<lb/>mis in publicum editus Com­<lb/>mentarius Bernardini Baldi Vrbinatis Gua­<lb/>&longs;tallæ Abbatis in Ari&longs;totelis Mechanica. <!-- KEEP S--></s> <s id="s.000011">Is <lb/>vir in omni &longs;cientiæ genere, at maxime in Ma­<lb/>thematicis di&longs;ciplinis fuit ver&longs;ati&longs;&longs;imus, quod <lb/>multa ab eo præclare &longs;cripta te&longs;tantur opera, <lb/>ex quibus paucula edita, reliqua vero &longs;pera­<pb xlink:href="007/01/004.jpg"/>mus &longs;uo tempore in publicam lucem produ­<lb/>cenda. </s> <s id="s.000012"> Cum vero nemini &longs;it ob&longs;curum Nobi­<lb/>li&longs;&longs;imæ ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} id &longs;emper <lb/>extiti&longs;&longs;e familiari&longs;&longs;imum, vt tum dome&longs;ticum <lb/>otium, tum maxime peregrinationes, quibus <lb/>totam pæne Europam &longs;umma cum laude <lb/>circum&longs;crip&longs;it, tum variarum linguarum per­<lb/>fecto v&longs;u, tum Mathematicarum di&longs;ciplina­<lb/>rum notitia & exercitio redderet <expan abbr="iucũdiores">iucundiores</expan>, <lb/>nulla me tenet dubitatio quin & Baldum Vr­<lb/>binatem no&longs;tris typis loquentem in hoc iti­<lb/>nere, quod à Deo felici&longs;&longs;imum Nobili&longs;&longs;imæ <lb/>ac Genero&longs;æ Dom. <!-- REMOVE S-->V.^{ræ} precor, in &longs;uum comi­<lb/>tatum ac tutelam beneuolo animo &longs;it admi&longs;­<lb/>&longs;ura.</s> <s id="s.000013"> Id rogo humillime &longs;imulque precor, vt. <lb/></s> <s id="s.000014">hanc meam typographiam plurimis iam re­<lb/>tro annis de inclytæ familiæ Cronbergicæ tu­<lb/>tela gloriantem, &longs;uo fauore pro&longs;equatur, vi­<lb/>duæque afflictæ fortunis beneuole ad&longs;piret.</s> <s id="s.000015"> <lb/>Sic Deus Nobili&longs;&longs;. <!-- REMOVE S-->& Genero&longs;am Dom. <!-- REMOVE S-->V.^{ram} <lb/>illu&longs;tret omnibus bonis, eamque R.^{mo} & Ill.^{mo} <lb/>Principi ac Domino meo Clementi&longs;&longs;imo, D. <lb/><!-- REMOVE S-->Ioanni Suicardo Archiepi&longs;copo Mogunti­<lb/>no Principi Electori ac per <emph type="italics"/>G<emph.end type="italics"/>ermaniam Ar-<pb xlink:href="007/01/005.jpg"/>chicancellario &c. </s> <s id="s.000016">patruo &longs;uo optati&longs;&longs;imo <lb/>&longs;aluo florentique redhibeat &longs;aluum &longs;imili­<lb/>ter florentem ac incolumem.</s> <s id="s.000017"> Moguntiæ è <lb/>typographeio Viduæ Albinianæ, honori No­<lb/>bili&longs;&longs;imæ ac <emph type="italics"/>G<emph.end type="italics"/>enero&longs;æ Dom. <!-- REMOVE S-->Ve&longs;træ perpe­<lb/>tuum dicato. </s> <s id="s.000018">Anno 1621.26.Martij. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/006.jpg"/> </section> <section> <p type="head"> <s id="s.000019">PRAEFATIO.</s> </p> <p type="main"> <s id="s.000020"><emph type="italics"/>Diligenter legenti mihi quæ&longs;tiones il­<lb/>las, in quibus ea quæ ad Mecha­<lb/>nicam facultatem pertinent, expli­<lb/>cantur, multa in mentem venie­<lb/>bant; & primum quidem eorum, quæ ibi dispu­<lb/>tantur, vtilitatem, &longs;ubtilitatem, copiam admi­<lb/>rabar: Tum ex animo dolebam, aureum hunc li­<lb/>bellum propè negligi, & ab iis qui pulcherrimis <lb/>hi&longs;ce &longs;tudiis dant operam, assiduè præ manibus <lb/>non haberi: Multas autem Auctori ip&longs;i haben­<lb/>das referendasque e&longs;&longs;e gratias, qui tam egregiam, <lb/>vtilem & probè in&longs;tructam &longs;upellectilem Archi­<lb/>tectis, Mechanicis, & omnibus ferè Artificibus <lb/>&longs;uppeditauerit. </s> <s id="s.000021">Ari&longs;totelis nomini a&longs;cribitur <lb/>Commentarius, licet nonnulli, &longs;itne Philo&longs;ophi <lb/>illius præclarissimi & acutissimi labor, an non, <lb/>adfirmare &longs;ubdubitauerint. </s> <s id="s.000022">Ari&longs;totelis tamen <lb/>e&longs;&longs;e omnes ferè meliores con&longs;entiunt: Idque tum <lb/>ex phra&longs;i, & explicatione, quæ Ari&longs;totelem &longs;a­<lb/>piunt, tum iudicio &longs;ubtilitatis & rationum, qui-<pb xlink:href="007/01/007.jpg"/>bus quæ&longs;tiones ip&longs;æ ingenio&longs;issimè diluuntur. </s> <s id="s.000023">Vi­<lb/>detur autem mihi, rem accuratius exploranti, &longs;a­<lb/>tis veri&longs;imile (nullum enim habeo opinionis hu­<lb/>ius a&longs;&longs;ertorem,) &longs;ectionem e&longs;&longs;e hanc, & partem <lb/>quandam eius operis nobilissimi, quod idem au­<lb/>ctor De Problematibus edidit, & hanc, ne&longs;cio <lb/>quam ob cau&longs;am; ni&longs;i fortè quod tractatio merè <lb/>Phy&longs;ica non &longs;it, à reliquo corpore di&longs;tractam at­<lb/>que reuul&longs;am. </s> <s id="s.000024">Id certè quod ad rem facit, probè <lb/>nouimus, Diogenem Laërtium inter cætera Ari­<lb/>&longs;totelici ingenij monumenta Mechanica quoque <lb/>adnumera&longs;&longs;e. </s> <s id="s.000025">Quibus con&longs;ideratis magnopere <lb/>&longs;ubit mirari, cur ij qui po&longs;t Ari&longs;totelem floruêre <lb/>atque vixere, Mechanici, Archimedes, Athenæus, <lb/>Heron, Pappus, & cæteri, nullam huius libelli fe­<lb/>cerint commemorationem: & &longs;anè debuerunt; <lb/>neque enim à vero est dissimile, ip&longs;os per hunc ali­<lb/>quatenus profeci&longs;&longs;e. </s> <s id="s.000026">Verum enim uero cum inge­<lb/>nui illi fuerint homines, & nullatenus obtrecta­<lb/>tores, credendum potius est, Comment ariolum i­<lb/>&longs;tud, eorum æuo, paucis cognitum, alicubi in Bi­<lb/>bliothecis latui&longs;&longs;e: etenim cætera quoque Ari&longs;tote­<lb/>lis &longs;cripta, po&longs;t vetu&longs;ta illa tempora, ante Ale­<lb/>xandrum Aphrodi&longs;ien&longs;em, à multis fui&longs;&longs;e igno-<pb xlink:href="007/01/008.jpg"/>rata non dubitamus. </s> <s id="s.000027">Habemus &longs;iquidem, Stra­<lb/>bone te&longs;te, lib. 13. Ari&longs;totelis, & Theophra&longs;ti bi­<lb/>bliothecam, po&longs;t ip&longs;ius Theophra&longs;ti dece&longs;&longs;um, ad <lb/>Neleum quendam Scep&longs;ium, Cori&longs;ci filium, qui <lb/>eius fuerat auditor, perueni&longs;&longs;e; po&longs;t hæc libros, <lb/>blattis olim, & humore corruptos, Apelliconi Te­<lb/>io venditos, & ab eo Athenas translatos, tum <lb/>Athenis captis in Syllæ pote&longs;tatem deueni&longs;&longs;e, eo&longs;­<lb/>que tandem à Sylla acceptos, Tyrannionem <lb/>Grammaticum, vt potuit meliùs emendatos, <lb/>promulga&longs;&longs;e. </s> <s id="s.000028">Ex quibus colligimus, mirum non <lb/>e&longs;&longs;e, Archimedi, Heroni, & alijs qui ante Syllam <lb/>vixêre, fui&longs;&longs;e incognitos. </s> <s id="s.000029">quicquid &longs;it, illud cer­<lb/>tum est, Ari&longs;totelem eorum omnium quidem Me­<lb/>chanicis commentaria edidere, e&longs;&longs;e longè vetu­<lb/>&longs;tissimum. </s> <s id="s.000030">Pappus enim Herone iunior, Athe­<lb/>næus Archimedi æqualis, vterque enim &longs;ub Mar­<lb/>cello, cui Athenæus &longs;uum de bellicis Machinis <lb/><expan abbr="libellū">libellum</expan> dedicauit. </s> <s id="s.000031">Archimedes verò circa CXL. <lb/><!-- KEEP S--></s> <s id="s.000032">Olympiadem floruit, quamobrem po&longs;t Ari&longs;tote­<lb/>lem Olympiadas XL. hoc est, annos ferè CLX. <lb/><!-- KEEP S--></s> <s id="s.000033">I&longs;thæc autem con&longs;iderantibus, facile e&longs;t cogno&longs;ce­<lb/>re facultatis huius nobilitatem, atque dignitatem; <lb/>quippe quod &longs;ummus Philo&longs;ophus non modo eam <pb xlink:href="007/01/009.jpg"/>probauerit, &longs;ed etiam &longs;uis acutissimis lucubra­<lb/>tionibus illu&longs;trauerit. </s> <s id="s.000034">Hanc porro tractationem <lb/>&longs;ubiecto quidem Phy&longs;icam e&longs;&longs;e, demon&longs;tratio­<lb/>nibus verò Geometricam, ip&longs;emet nos docuit <lb/>Ari&longs;toteles, cuius etiam naturæ &longs;unt Per&longs;pecti­<lb/>ua, Specularia, Mu&longs;ica, & cæteræ eiu&longs;dem <lb/>modi facultates, quas quidem &longs;ubalternas Peri­<lb/>patetici appellant. </s> <s id="s.000035">Vitruuius Architecturæ <lb/>membrum, vt ita dicam, & portionem quan­<lb/>dam facit, ait enim Architecturæ partes e&longs;&longs;e tres, <lb/>Ædificationem, Gnomonicam, Machinatio­<lb/>nem. </s> <s id="s.000036">Est autem Architecturâ quidem inferior, <lb/>paret enim Architecto Mechanicus; attamen &longs;i <lb/>cæteras artes &longs;pectes, Architectonica; hæc enim <lb/>omnes ferè &longs;edentariæ, &longs;ellulariæue, quas banau­<lb/>&longs;as Græci appellant, ordine &longs;ubijciuntur, & &longs;a­<lb/>nè latissimos i&longs;thæc habet fines; præcipuè autem <lb/>circa eam ver&longs;atur cognitionem, eamque inter <lb/>cæteras ferè principem, quam dixere Centrobari­<lb/>cam, quæ quidem ad Centri grauitatem, eiu&longs;que <lb/>&longs;peculationem pertinet: quà in &longs;pecie inter vete­<lb/>res primum &longs;ibi vindicauit locum Archimedes, <lb/>mox Heron, deinde Pappus; inter neotericos au-<emph.end type="italics"/><pb xlink:href="007/01/010.jpg"/><emph type="italics"/>tem Commandinus, qui librum de Centro gra­<lb/>uitatis &longs;olidorum &longs;crip&longs;it, & po&longs;t eum G. <!-- REMOVE S-->Vbal­<lb/>dus è Marchion. <!-- REMOVE S-->Montis, qui non modò ab­<lb/>&longs;olutissimum Mechanicorum librum cum maxi­<lb/>ma ingenij &longs;ui laude con&longs;crip&longs;it, &longs;ed & Paraphra­<lb/>&longs;in in librum Æqueponderantium Archimedis <lb/>egregiè concinnauit Centrobaricam hanc, igno­<lb/>tam fui&longs;&longs;e Ari&longs;toteli, &longs;ætis patet. </s> <s id="s.000037">nunquam enim <lb/>in Mechanicis demon&longs;trationibus, quod tamen <lb/>est potissimum, grauitatis centrum nominat, e­<lb/>iu&longs;ue naturam atque vim &longs;peculatur. </s> <s id="s.000038">Diuidi­<lb/>tur autem Mechanice tota, te&longs;te Herone apud <lb/>Pappum libro octauo, in Rationalem, hoc est, <lb/>Theoricam & Chirurgicam, id est, manu ope­<lb/>ratricem, quam Praxim aptè dicere valemus. <lb/></s> <s id="s.000039">Rationalis, &longs;peculationi & <expan abbr="demō&longs;trationibus">demon&longs;trationibus</expan>, ex <lb/>Geometricis, Arithmeticis & Phy&longs;icis rationi­<lb/>bus, dat operam; Chirurgica vero materiam <lb/>tractat, & &longs;e&longs;e in varias artes diffundit, Æra­<lb/>riam, Lignariam, Sculptoriam, Pictoriam, Æ­<lb/>dificatoriam, Machinariam & Thaumaturgi­<lb/>cam, cæterasque eiu&longs;modi. </s> <s id="s.000040">Machinatoriæ au­<lb/>tem &longs;unt partes Manganaria, qua ingentia <emph.end type="italics"/><pb xlink:href="007/01/011.jpg"/><emph type="italics"/>transferuntur pondera, tum ip&longs;a Poliorcetica, <lb/>quæ bellicas Machinas ad vrbium expugnatio­<lb/>nes, quod vel ip&longs;o nomine profitetur, ædificat. </s> <s id="s.000041">At­<lb/>qui hac dere plura &longs;cribere &longs;uper&longs;edemus, ne a­<lb/>ctum agamus: quis quis enim minutè magis hæc <lb/>cogno&longs;cere de&longs;iderat, is Pappum adeat libro cita­<lb/>to, & Guidum Vbaldum in Præfatione quam <lb/>&longs;uo Mechanicorum Operi præpo&longs;uit. </s> <s id="s.000042">Vt autem <lb/>ad Ari&longs;totelis, de quo egimus, libellum reuerta­<lb/>mur, pauci &longs;unt qui ei ante nos &longs;tilum & operam <lb/>commodauerint: Leonicenus Latinum fecit & <lb/>figuris tum breuissimis, & parui &longs;ane ponderis, <lb/>marginalibus adnotatiunculis, in&longs;truxit. </s> <s id="s.000043">Po&longs;t <lb/>hunc Alexander Picolomineus luculentissima <lb/>Paræphra&longs;i illu&longs;trauit. </s> <s id="s.000044">Modo, vt audio, Simon <lb/>Sticinus Hollanden&longs;is quædam edidit, quæ ad <lb/>nos minime peruenêre. </s> <s id="s.000045">Nos demum, omnium, <lb/>tum &longs;cientia, & ingenio, tum ætate, po&longs;tremi huic <lb/>operi manum admouimus; Con&longs;iderantes enim <lb/>Ari&longs;totelem aliis fecerint Mechanici, demon&longs;tra&longs;&longs;e, <lb/>morem huiu&longs;ce facultatis &longs;tudio&longs;is ge&longs;turos nos <lb/>fore arbitrati &longs;umus, &longs;i ea&longs;dem illas quæ&longs;tiones <emph.end type="italics"/><pb xlink:href="007/01/012.jpg"/><emph type="italics"/>Mechanicis, hoc est, Archimedeis probationi­<lb/>bus confirmaremus; dum per latissimos faculta­<lb/>tis huius campos vagantes, alias quoque i&longs;tis af­<lb/>fines dubitationes introducentes &longs;olueremus. <lb/></s> <s id="s.000046"><expan abbr="quicquidautē&longs;ecerimus">quicquid autem fecerimus</expan> profecerimu&longs;ue, Lector <lb/>optime, boni con&longs;ule, & quia fax per manus tra­<lb/>ditur, tu interim de me accipe, vt alijs tradas.<emph.end type="italics"/></s> </p> <pb xlink:href="007/01/013.jpg"/> </section> <section> <p type="head"> <s id="s.000047">DE VITA ET SCRI­<lb/>PTIS BERNARDINI <lb/>BALDI VRBINATIS</s> </p> <p type="head"> <s id="s.000048"><emph type="italics"/>EX LITERIS FABRITII SCHAR­<lb/>loncini ad Illu&longs;trissimum & Reuerendissimum <lb/>Dominum Lælium Ruinum Epi&longs;copum Bal­<lb/>neoregien&longs;em ex-Nuntium Apo&longs;tolicum <lb/>ad Poloniæ Regem & c.<emph.end type="italics"/><!-- KEEP S--></s> </p> <p type="main"> <s id="s.000049">Natus e&longs;t Bern. <!-- REMOVE S-->Baldus Vrbini nobilibus <expan abbr="pa-rētibus">pa­<lb/>rentibus</expan> po&longs;tridie Non. <!-- KEEP S--></s> <s id="s.000050">Iunij anno MDLIII. <lb/></s> <s id="s.000051">Genus traxit, quod me &longs;æpè ab eo memini <lb/>audire, à familia Cantagallina, quæ inter <lb/>Peru&longs;inas illu&longs;tris: hoc autem cognomen, <lb/>Baldi accepto, vt in varietate temporum fit, <lb/>Abauus reliquit, à teneris vnguiculis <expan abbr="pietatē">pietatem</expan> erga Deum <lb/>præ&longs;etulit; nam vt mater eius narrabat, &longs;anctorum imagi­<lb/>nes & Altariola non cum lætitia &longs;olum, &longs;ed cum venera­<lb/>tione anniculus intuebatur. </s> <s id="s.000052">Præceptoribus in adole&longs;cen­<lb/>tia v&longs;us fuit laudati&longs;&longs;imis Io. <!-- REMOVE S-->And. <!-- REMOVE S-->Palatio, & Io. <!-- REMOVE S-->Antonio <lb/>Turoneo, qui altero doctior, & Paulo Manutio maxime <lb/>carus ob latinæ & græcæ linguæ peritiam propè &longs;ingula­<lb/>rem: ad illorum autem &longs;edulitatem tantum animi ardo­<lb/>rem attulit, tantam ingenij ac iudicij vim, vt non tantum <lb/>æqualis &longs;ed omnium vicerit expectationem. </s> <s id="s.000053">Puer adhuc <lb/>Arati apparitiones Italico carmme reddidit. </s> <s id="s.000054">Parens hac <lb/>filij laude & gloria motus anno 1573. eum ad maiorem in­<lb/>genij cultum cape&longs;&longs;endum Patauium mi&longs;it. </s> <s id="s.000055">Hîc in Ema­<lb/>nuelis Margunij familiaritatem &longs;tatim venit, cui porro <pb xlink:href="007/01/014.jpg"/>fuit in amoribus. </s> <s id="s.000056">Homeri Iliad. <!-- REMOVE S-->illo Doctore & interpre­<lb/>te diligentius quam feci&longs;&longs;et antea, euoluit. </s> <s id="s.000057">priuato autem <lb/>&longs;tudio Anacreonti, Pindaro, Æ&longs;chyli, Euripidi, Sophocli <lb/>operam dedit, &longs;ed præ cæteris Theocriti Bucolica triuit, <lb/>ad quod &longs;criptionis genus natura magis ferri videbatur: <lb/>centenos græci alicuius poëtæ ver&longs;us memoriter tenebat, <lb/>&longs;æpeque habebat in ore, in oratoribus græcis ver&longs;andis <lb/>laborem &longs;e aliquem &longs;entire, in poëtis nullum. </s> <s id="s.000058">Scrip&longs;it Pa­<lb/>tauij libellum de Tormentis Bellicis, & eorum inuentori­<lb/>bus, & cum in Tran&longs;alpinorum amicitias incidi&longs;&longs;et, &longs;ibi <lb/>ducebat dedecori ip&longs;os &longs;ua lingua loquentes non intelli­<lb/>gere. </s> <s id="s.000059">quare incredibili celeritate Gallicam & Germani­<lb/>cam didicit. </s> <s id="s.000060">Pe&longs;tilentia ex eo Gymna&longs;io exactus in Pa­<lb/>triam redijt, vbi quinquennium integrum Federico <expan abbr="Cō-mandino">Com­<lb/>mandino</expan> affixus omnes Mathe&longs;eos partes perdidicit, cui <lb/>viro in delineandis figuris ad Euclidis, Pappi, & Heronis <lb/>monumenta manum commodauit: ex eiu&longs;dem obitu do­<lb/>lorem vix con&longs;olabilem &longs;u&longs;tinuit, &longs;u&longs;ceptoque eius vitam <lb/>&longs;cribendi con&longs;ilio, &longs;ubinde ad omnium Mathematicorum <lb/>vitas con&longs;cribendas animum adplicuit, quod & duode­<lb/>cim annorum &longs;patio præ&longs;titit felici&longs;&longs;imè. </s> <s id="s.000061">cum vero Ma­<lb/>thematicarum di&longs;ciplinarum amore torqueretur, ami&longs;&longs;o <lb/>Commandino Præceptore, amicum nactus fuit præ&longs;tan­<lb/>ti&longs;&longs;imum & &longs;ymmy&longs;tam Guidum Vbaldum è Marchioni­<lb/>bus Montis, in cuius &longs;e con&longs;uetudinem daret: quantum <lb/>profeci&longs;&longs;et, o&longs;tendunt ij commentarij quos anno 1582. in <lb/>Ari&longs;t. Mechanica &longs;crip&longs;it. </s> <s id="s.000062">Vt po&longs;tea à grauioribus &longs;tudijs <lb/>ad amœniora animum abduceret, de re nautica poëma I­<lb/>talicè confecit. </s> <s id="s.000063">quo ab&longs;oluto Paradoxa multa Mathema­<lb/>tica explicauit. </s> <s id="s.000064">Fama de Baldi virtutibus di&longs;&longs;ipata Ferran­<lb/>dus Gonzaga Molfetræ Princeps & Gua&longs;tallæ Dominus <lb/>cœpit de illo in &longs;uam familiam a&longs;ci&longs;cendo cogitare, vt qui <lb/>ij&longs;dem caperetur artibus, quibus excellere Baldus inci-<pb xlink:href="007/01/015.jpg"/>piebat: Itaque opera Curtij Arditij honorifice fuit in au­<lb/>lam euocatus, dum vitam non aulicam viueret totus in <lb/>litteras abditus precibus Ve&longs;pa&longs;iani Gonzagæ Sablonetæ <lb/>Ducis ad explanandos Vitruuij libros adactus fuit. </s> <s id="s.000065">quare <lb/><expan abbr="tūc">tunc</expan> natus de <expan abbr="Verborū">Verborum</expan> Vitruuianorum &longs;ignificatione com­<lb/>mentarius; in quo minime mirandum &longs;i minuta quædam <lb/>pro&longs;equutus fuit, quæ viro magno minus e&longs;&longs;e digna vi­<lb/>deantur:illi enim Principi morem ge&longs;&longs;it. </s> <s id="s.000066">&longs;cio dixi&longs;&longs;e ali­<lb/>quando Adrianum Romanum è Polonia reuer&longs;um, vbi <lb/>Vitruuium Palatino cuidam explicauerat, &longs;i commen­<lb/>tarium Baldi in Polonia adhibere potui&longs;&longs;em, aurum quod <lb/>mecum attuli emunxi&longs;&longs;em, quia &longs;atis feci&longs;&longs;em muneri la­<lb/>bore nullo. </s> <s id="s.000067">Cum Ferrando hero &longs;uo obueni&longs;&longs;et nece&longs;&longs;i­<lb/>tas Hi&longs;panias adeundi, illud iter &longs;ine Baldo facere &longs;e po&longs;­<lb/>&longs;e non putabat, non tam vt haberet, qui erudito eloquio <lb/>viæ tæ dium leuaret, quam cui po&longs;&longs;et arcana committere, <lb/>atque adeo à quo iuuaretur con&longs;ilio. </s> <s id="s.000068">Vix viæ &longs;e dederant <lb/>cum Baldus grauem in morbum delap&longs;us itinere cogitur <lb/>de&longs;i&longs;tere: Mediolanum proinde diuertit, vbi à S. <!-- REMOVE S-->Carolo <lb/>Borromæo & benignè exceptus, & tamdiu detentus do­<lb/>nec valetudinem recuperaret. </s> <s id="s.000069">Gua&longs;tallam po&longs;tea &longs;e re­<lb/>cepit, vbi cum ab&longs;ente Domino liberiori otio frueretur, <lb/>libros &longs;ex de Aula eruditi&longs;&longs;imos methodo analytica con­<lb/>&longs;crip&longs;it. </s> <s id="s.000070">alios non commemoro, quod cum otium erit, o­<lb/>mnium &longs;yllabum dabo. </s> <s id="s.000071">Anno 1586. ip&longs;o nihil po&longs;tulante <lb/>eligitur Gua&longs;tallæ Abbas, à quo tempore Iuri Can. <!-- KEEP S--></s> <s id="s.000072">Con­<lb/>cilijs, & SS.Patribus totum &longs;e dedit. </s> <s id="s.000073">Hebreæ & Chaldææ <lb/>linguarum di&longs;cendarum triennium po&longs;uit. </s> <s id="s.000074">Anno 1593. no­<lb/>uæ Gnomonices libros quinque compo&longs;uit. </s> <s id="s.000075">in&longs;equenti <lb/>Chaldæam Onkeli paraphra&longs;in in Pentateuchum vertit <lb/>& commentarios adiunxit; quo exant lato labore in Iob <lb/>ex Heb. <!-- REMOVE S-->fonte paraphra&longs;in texuit, quam & &longs;cholijs illu­<lb/>&longs;trauit. </s> <s id="s.000076">Tabulam Etru&longs;cam Eugubinam interptetatus <pb xlink:href="007/01/016.jpg"/>fuit:in ea autem diuinatione, vt aiebat, &longs;ubci&longs;iuas vnius <lb/>men&longs;is horas con&longs;ump&longs;it. </s> <s id="s.000077">De Firmamento & aquis egre­<lb/>gie &longs;crip&longs;it. </s> <s id="s.000078">Oeconomiam Tropologicam in S.Matthæum <lb/>Card. <!-- REMOVE S-->Baronius, qui non alia Baldi vidit, vehementer pro­<lb/>babat. </s> <s id="s.000079">Romæ dum viueret, fere ne&longs;ciuit quid gereretur <lb/>in Aulis: Arabicæ enim linguæ cum Io. <!-- REMOVE S-->Bapti&longs;ta Raimon­<lb/>do diligenti&longs;&longs;ime &longs;tuduit, & arcana indu&longs;tria Slauonicæ, <lb/>quam perfecte callebat. </s> <s id="s.000080">Ex Arabico vertit Hortum Geo­<lb/>graphicum Anonymi, quem ante &longs;excentos annos flo­<lb/>rui&longs;&longs;e arbitrabatur. </s> <s id="s.000081">Hunc vero extru&longs;i&longs;&longs;et, vt alios Baldi <lb/>libros, Marcus Vel&longs;erus IIvir Aug. <!-- REMOVE S-->&longs;i eo paulo longior <lb/>huius lucis v&longs;ura contigi&longs;&longs;et. </s> <s id="s.000082">Compo&longs;uit & Dictionarium <lb/>Arabicum. <!-- KEEP S--></s> <s id="s.000083">atque cum beati&longs;&longs;imam illam vbertatem in­<lb/>genij a&longs;&longs;idue diffundi nece&longs;&longs;e e&longs;&longs;et, anno 1603. orbem vni­<lb/>uer&longs;um de&longs;cribere aggre&longs;&longs;us fuit; atque ita quidem, vt <lb/>tam quæ ad Hi&longs;toriam, quam quæ ad Geographiam per­<lb/>tinerent complecteretur: Neque illu&longs;trare &longs;olum voluit <lb/>quæ nouerunt antiqui, quemadmodum vi&longs;um Ortelio, <lb/>&longs;ed vel oppidula omnia & pagos, de quibus aliqua in po­<lb/>&longs;tremis &longs;criptoribus mentio. </s> <s id="s.000084">& profecto totum opus ad <lb/>vmbilicum perduxit: non dige&longs;&longs;it tamen vniuer&longs;um. </s> <s id="s.000085">qua­<lb/>tuor aut ni fallor quinque tantum Tomi fuerunt ordine <lb/>Alphabetico di&longs;po&longs;iti:&longs;upere&longs;&longs;ent &longs;eptem aut octo di&longs;po­<lb/>nendi, quantum ex chartarum & fa&longs;ciculorum mole con­<lb/>ijcere licet. </s> <s id="s.000086">Anno 1617. quarto Idus Octob. <!-- KEEP S--></s> <s id="s.000087">po&longs;tea quam <lb/>dies 40. vehementi de&longs;tillatione vexatus fui&longs;&longs;et, &longs;piritum <lb/>Deo reddidit Sacramentis Eccle&longs;iæ omnibus rite muni­<lb/>tus. </s> <s id="s.000088">Statura procerus fuit, facie oblonga & acribus oculis, <lb/>colore &longs;ubfu&longs;co. </s> <s id="s.000089">Membrorum ei fuit decens habitudo, & <lb/>compactum corpus. </s> <s id="s.000090">Diebus fe&longs;tis omnibus &longs;acrum facie­<lb/>bat, ieiunabat bis in hebdomada, eleemo&longs;yni&longs;que paupe­<lb/>res &longs;ubleuabat. </s> <s id="s.000091">In &longs;tudijs &longs;ic a&longs;&longs;iduus fuit, vt &longs;æpe & legeret <lb/>& comederet. </s> <s id="s.000092">S.Augu&longs;tini libros de Ciuitate Dei ter in-<pb xlink:href="007/01/017.jpg"/>ter prandium euoluit. </s> <s id="s.000093">Statim à noctis meridie dum ei vi­<lb/>res firmiores e&longs;&longs;ent ad lucubrandum &longs;urgebat. </s> <s id="s.000094">à prandio <lb/>Euclidem Arabice editum, vel libellum aliquem germa­<lb/>nicum aut gallicum in manus &longs;umebat. </s> <s id="s.000095">Suauitate morum <lb/>& mode&longs;tia, etiam &longs;i ceteræ dotes abfui&longs;&longs;ent, quemlibet <lb/>ad amorem &longs;ui allicere potui&longs;&longs;et. </s> <s id="s.000096">Sermo modicus ei fuit, <lb/>itemque cultus. </s> <s id="s.000097">Nullos vnquam honores petijt, qui à <lb/>Clem. 8. ampli&longs;&longs;imi promi&longs;&longs;i fuerant; nullum emolumen­<lb/>tum quæ&longs;iuit &longs;uo cen&longs;u contentus. </s> <s id="s.000098">facile parcendum e&longs;&longs;e <lb/>dicebat, ijs maxime qui in re leui impegi&longs;&longs;ent, quoniam &longs;i <lb/>quos cen&longs;emus optimos, nudos con&longs;piceremus, nullum <lb/>eorum non iudicaremus multis dignum verberibus. </s> <s id="s.000099">Bi­<lb/>bliothecam habuit non locupletem, &longs;ed &longs;electis <expan abbr="in&longs;tructã">in&longs;tructam</expan> <lb/>codicibus. </s> <s id="s.000100">Verum ire per &longs;ingula longum e&longs;&longs;et. </s> <s id="s.000101">Satis mihi <lb/>de incomparabili Baldi doctrina, & &longs;umma innocentia, ô <lb/>rarum connubium, pauca dixi&longs;&longs;e, quæ for&longs;itan ad imitan­<lb/>dum nimis multa. </s> </p> </section> <section> <p type="head"> <s id="s.000102">SYLLABVS LIBRORVM</s> </p> <p type="head"> <s id="s.000103">omnium B.Abb.Baldi.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.000104">Arati apparitiones è gr.in Ital. <!-- KEEP S--><!-- REMOVE S-->vertit. </s> </p> <p type="main"> <s id="s.000105">De Tormentis Bellicis & eorum Inuentoribus lib. <!-- REMOVE S-->Heronis automata vertit. </s> </p> <p type="main"> <s id="s.000106">Vitas omnium Mathematicorum &longs;crip&longs;it, & trib. </s> <s id="s.000107">in Tom. <lb/><!-- REMOVE S-->2.1.P^{s}.à Thalete ad Chri&longs;tum.2.à Chri&longs;to ad &longs;ua tem­<lb/>pora. </s> </p> <p type="main"> <s id="s.000108">Earumdem vitarum Epitomen Chronologicum confecit. </s> </p> <p type="main"> <s id="s.000109">In Ari&longs;tot. Mechan. Commentar. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000110">De Re nautica Poëmation. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000111">Paradoxorum Mathematicorum liber. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000112">De&longs;criptio Palatij Ducum Vrbinarum quod e&longs;t Vrbini. </s> </p> <p type="main"> <s id="s.000113">Poema cui titulus, Lamus. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/018.jpg"/> <p type="main"> <s id="s.000114">Carmina pia, quæ in&longs;cribuntur, Anni Corona. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000115">De Verborum Vitruuianorum &longs;ignificatione. </s> </p> <p type="main"> <s id="s.000116">Carmina varia & eclogæ mixtæ. </s> </p> <p type="main"> <s id="s.000117">Apologi centum, quos &longs;crip&longs;it æmulatus Leonem Bapt. <lb/><!-- REMOVE S-->Albertum. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000118">De Humanitate Dialogus qui in&longs;cribitur Go&longs;elinus. </s> </p> <p type="main"> <s id="s.000119">Comparatio Vitæ Mona&longs;ticæ cum &longs;eculari. </s> </p> <p type="main"> <s id="s.000120">De Aula libri &longs;ex. </s> </p> <p type="main"> <s id="s.000121">De felicitate Principis Dialogus. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000122">De Dignitate Dial. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000123">Carmina Romana. </s> </p> <p type="main"> <s id="s.000124">Mo&longs;æi fabulam vertit. </s> </p> <p type="main"> <s id="s.000125">De Italici carminis natura Dial. <!-- REMOVE S-->qui in&longs;cribitur Ta&longs;&longs;us. </s> </p> <p type="main"> <s id="s.000126">De vniuer&longs;ali Diluuio poemation. </s> </p> <p type="main"> <s id="s.000127">Nouæ Gnomonices lib. quin que. </s> </p> <p type="main"> <s id="s.000128">Hieremiæ Threnos vertit, & ex Heb. <!-- REMOVE S-->fonte annotat. </s> <s id="s.000129">ad­<lb/>iecit. </s> </p> <p type="main"> <s id="s.000130">Poemation in&longs;criptum, Deiphobe, quod &longs;crip&longs;it æmula­<lb/>tus Lycophonem in Ca&longs;&longs;andra. </s> </p> <p type="main"> <s id="s.000131">Scala cœle&longs;tis.1.Sermones pij & carmina. </s> </p> <p type="main"> <s id="s.000132">Onkeli paraphra&longs;in Chaldæam in Pentateuchum ver­<lb/>tit & vberes commentarios adiecit. </s> </p> <p type="main"> <s id="s.000133">In Iob Paraphra&longs;is latina ex fonte Heb. <!-- REMOVE S-->additis Scholijs. </s> </p> <p type="main"> <s id="s.000134">De &longs;camillis imparibus Vitruuij. </s> </p> <p type="main"> <s id="s.000135">De firmamento & aquis. </s> </p> <p type="main"> <s id="s.000136">Quincti Calabri Paralipomena vertit. </s> </p> <p type="main"> <s id="s.000137">Tabulæ Etru&longs;cæ Eugubinæ Interpretatio. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000138">Oeconomía Tropologicain S.Matthæum. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000139">Vrbini encomium. </s> </p> <p type="main"> <s id="s.000140">Horti geographici ex Arab. <!-- REMOVE S-->ver&longs;io. </s> </p> <p type="main"> <s id="s.000141">Aduer&longs;us Aulam Carmina. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000142">Luciani de mi&longs;erijs.Aulicorum ver&longs;io. </s> </p> <p type="main"> <s id="s.000143">Oratio ad Romæ con&longs;eruatores pro antiquitatum eius <lb/>Vrbis cu&longs;todia. </s> </p> <pb xlink:href="007/01/019.jpg"/> <p type="main"> <s id="s.000144">Vniuer&longs;i orbis geographica & Hi&longs;torica de&longs;criptio con­<lb/>texta ex &longs;eptingentis & eo amplius &longs;criptoribus. </s> </p> <p type="main"> <s id="s.000145">Federici Vrbini Ducis Vita. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000146">Guidi Vbaldi Vrbini Ducis Vita. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000147">Epigrammaton & Odarum libri tres. </s> </p> <p type="main"> <s id="s.000148">Aliorum Carminum liber. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000149">Sententiarum moralium liber. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000150">Dictionarium Arabicum. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000151">Pro Procopio contra Flauium Blondum. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000152">Horographium vniuer&longs;ale. </s> </p> <p type="main"> <s id="s.000153">Epigrammata alia. </s> </p> <p type="main"> <s id="s.000154">Heronis lib. de Balli&longs;tis conuer&longs;io. </s> </p> <p type="main"> <s id="s.000155">Exercitationes in Ari&longs;totelis Mechan. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000156">Templi Ezechielis noua de&longs;criptio. </s> </p> <p type="main"> <s id="s.000157">Antiquitatum Gua&longs;tallen&longs;ium liber. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000158">Hi&longs;toriæ &longs;cribendæ leges. </s> </p> <p type="main"> <s id="s.000159">Et alia quædam. </s> </p> <pb xlink:href="007/01/020.jpg"/> <pb xlink:href="007/01/021.jpg"/> </section> </front> <body> <chap> <p type="head"> <s id="s.000160">IN MECHANICA ARISTOTE­<lb/>LIS PROBLEMATA<!-- REMOVE S--> EXERCITATIONES.<!-- KEEP S--></s> </p> <subchap1> <p type="head"> <s id="s.000161"><emph type="italics"/>Mechanices de&longs;criptio, natura, finis.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000162">MECHANICE, facultas quædam e&longs;t, quæ <lb/>naturali materiâ, Geometricisque; demon­<lb/>&longs;trationibus v&longs;a, ex centrobaricâ, & <expan abbr="eorū">eorum</expan> <lb/>quæ ad vectem & libram rediguntur, &longs;pe­<lb/>culatione; humanæ con&longs;ulens nece&longs;&longs;itati, <lb/>commoditatiqueue, &longs;uapte vi, Naturam i­<lb/>p&longs;am vel &longs;ecundans, vel &longs;uperans, varia, eaque mirabilia <lb/>operatur. </s> <s id="s.000163">Hac diffinitione de&longs;criptionéue breuiter ea fe­<lb/>rè omnia complexi &longs;umus, quæ fu&longs;i&longs;&longs;imè ab Ari&longs;totele, <lb/>Pappo, Guido Vbaldo, & alijs hac de re tradita fuêre. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000164"><emph type="italics"/>Mechanices Obiectum.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000165">Con&longs;iderat autem Mechanicus Graue & Leue. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000166">Graue duplex, Naturâ, Violentiâ. </s> </p> <p type="main"> <s id="s.000167">Graue Naturâ dicitur, quod in&longs;ita propen&longs;ione in <lb/>centrum mundi fertur. </s> <s id="s.000168">Graue autem Violentiâ, quod im­<lb/>pre&longs;&longs;o extrin&longs;ecus pondere ab impellente pellitur. </s> </p> <p type="main"> <s id="s.000169">Leue contrà, quòd Naturâ à centro fertur. </s> </p> <p type="main"> <s id="s.000170">Cæterùm quicquid graue e&longs;t, &longs;ecundum punctum <lb/>e&longs;t, quod Grauitatis centrum dicitur, & hoc duplex, vt <lb/>duplex e&longs;t grauitas, Naturæ, Violentiæ. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/022.jpg"/> <p type="main"> <s id="s.000171">Grauitatis centrum in triplici magnitudine con&longs;i­<lb/>derari pote&longs;t, lineari, planà, &longs;olidâ. </s> </p> <p type="main"> <s id="s.000172">De centro grauitatis linearum nemo &longs;crip&longs;it, &longs;impli­<lb/>ci&longs;&longs;imi enim illud e&longs;t contemplationis. </s> </p> <p type="main"> <s id="s.000173">De centro grauitatis linearum egregiè tractauit Ar­<lb/>chimedes in libro Æqueponderantium, & de quadratu­<lb/>ra Parabole, tum in eo quem de his quæ vehuntur in­<lb/>&longs;crip&longs;it. </s> </p> <p type="main"> <s id="s.000174">De centro grauitatis &longs;olidorum ip&longs;emet olim &longs;cri­<lb/>p&longs;erat Archimedes, &longs;ed ea quæ protulit, temporis iniuriâ <lb/>deperdita, &longs;uâ diligentiâ re&longs;tituit Federicus Commandi­<lb/>nus. </s> </p> <p type="main"> <s id="s.000175">E&longs;&longs;e autem & Leuitatis centrum in rerum natura, <lb/>palam e&longs;t. </s> <s id="s.000176">Punctum enim illud e&longs;t, &longs;ecundum quod leuia <lb/>rectà à centro &longs;ur&longs;um feruntur. </s> <s id="s.000177">Huius autem non memi­<lb/>nêre Mechanici, propterea quod aut nihil, aut parum ad <lb/>eorum rem faciat. </s> </p> <p type="main"> <s id="s.000178">Porro Grauitatis centrum ita definit Heron, & qui <lb/>ab Herone Pappus 1.8. Collectionum Mathematicarum. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000179">Centrum grauitatis <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> corporis e&longs;t pun­<lb/>ctum quoddam intra po&longs;itum, à quo &longs;i graue, mente ap­<lb/>pen&longs;um concipiatur, dum fertur, quie&longs;cit, & &longs;eruat eam <lb/>quam in principio habuit po&longs;itionem; neque in ip&longs;a latio­<lb/>ne circumuertitur. </s> <s id="s.000180">Commandinus verò in lib. de centro <lb/>grauitatis &longs;olidorum hoc pacto: Centrum grauitatis v­<lb/>niu&longs;cuiu&longs;que &longs;olidæ figuræ, e&longs;t punctum illud intra po&longs;i­<lb/>tum, circa quod vndique partes æqualium momentorum <lb/>ad&longs;i&longs;tunt. </s> <s id="s.000181">Si enim per tale centrum ducatur planum, fi­<lb/>guram quomodolibet &longs;ecans, in partes æquè ponderantes <lb/>eam diuidit. </s> <s id="s.000182">Nos verò quàm breui&longs;&longs;imè dicimus: <expan abbr="Centrū">Centrum</expan> <lb/>grauitatis, <expan abbr="vniu&longs;cuiu&longs;q;">vniu&longs;cuiu&longs;que</expan> magnitudinis punctum e&longs;&longs;e intra <lb/>extraue magnitudinem po&longs;itum, per quod &longs;i plano linea <lb/>punctoue diuidatur, in partes &longs;ecatur æqueponderantes. </s> </p> <pb xlink:href="007/01/023.jpg"/> <figure id="id.007.01.023.1.jpg" xlink:href="007/01/023/1.jpg"/> <p type="main"> <s id="s.000183">Diximus, Magnitudinis vt lineæ, plani &longs;olidique; cen­<lb/>trum complecteremur. </s> <s id="s.000184">Erit igitur, vt in præ&longs;enti figura, li­<lb/>neæ quidem centrum A, plani B, &longs;olidi verò C. quod &longs;i ob­<lb/>ijciat qui&longs;piam, lineam & &longs;uperficiem nullam habere gra­<lb/>uitatem; is &longs;ciat, <expan abbr="neq;">neque</expan> corpora Mathematica grauitatem <lb/>habere, Mechanicum verò funes, ha&longs;tas, vectes pro lineis <lb/>&longs;umere; tabulas verò, & eiu&longs;modi plana ad &longs;uperficierum <lb/>naturam referre. </s> </p> <p type="main"> <s id="s.000185">Diximus in&longs;uper, intra extraue. </s> <s id="s.000186">Aliquando enim <lb/>grauitatis centrum extra molem corporis cuius corporis <lb/>centrum e&longs;t, cadit, vt in &longs;equenti figura. </s> </p> <figure id="id.007.01.023.2.jpg" xlink:href="007/01/023/2.jpg"/> <p type="main"> <s id="s.000187">E&longs;to corpus aliquod <lb/>&longs;uperficiesue ABCDE, <lb/>ducatur linea CF, <expan abbr="diuidēs">diuidens</expan> <lb/>figuras in partes hinc inde <lb/>æqueponderantes ABC, <lb/>EDC. <!-- KEEP S--></s> <s id="s.000188">Ducatur & GH. <lb/>diuídens item in partes æ­<lb/>queponderantes GCH, & GAB, EDH. &longs;ecent autem <lb/>&longs;eip&longs;as in I. erit igitur centrum I extra figuræ terminos & <lb/>molem ip&longs;am. </s> <s id="s.000189">Attamen licet hoc verum &longs;it, intra e&longs;&longs;e dici <lb/>pote&longs;t, quippe quod imaginario quodam, & vt ita dicam, <lb/>virtuali ambitu ACDA contineatur. </s> </p> <p type="main"> <s id="s.000190">Dicebamus, duplex e&longs;&longs;e grauitatis centrum, Natu­<pb xlink:href="007/01/024.jpg"/>râ, Violentià: affirmamus modò, hæc re quidem vnum e&longs;­<lb/>&longs;e, & ratione &longs;olum, non autem re ip&longs;a ac &longs;i duo e&longs;&longs;ent con­<lb/>&longs;iderari. </s> </p> <figure id="id.007.01.024.1.jpg" xlink:href="007/01/024/1.jpg"/> <p type="main"> <s id="s.000191">E&longs;to enim grauitatis na­<lb/>turalis centrum B, corporis A, <lb/>&longs;ecundum quod dimi&longs;&longs;um, &longs;ua­<lb/>pte naturâ cadet in C, &longs;i verò <lb/>corpus violenter impellatur in <lb/>D, aliud acquiret centrum gra­<lb/>uitatis ex violentia &longs;ecundum <lb/>quam fertur, motum, in D, <expan abbr="idē">idem</expan> <lb/>autem &longs;unt re, nempe vnum B, <lb/>duo autem &longs;i violentia & natura &longs;eor&longs;um con&longs;ideren­<lb/>tur. </s> </p> <p type="main"> <s id="s.000192">Hæc centra, duo motus &longs;equuntur, rectus vterque, <lb/>Naturalis videlicet, & Violentus. </s> <s id="s.000193">Tertius ex his mixtus, & <lb/>is quidem non rectus, &longs;ed curuus. </s> </p> <figure id="id.007.01.024.2.jpg" xlink:href="007/01/024/2.jpg"/> <p type="main"> <s id="s.000194">Proijciatur enim violen­<lb/>ter corpus graue A &longs;uperante <lb/>igitur violentia, rectà feretur <lb/>in B; ea autem elangue&longs;cente <lb/>paullatim per curuam & mi­<lb/>xtam <expan abbr="lineã">lineam</expan> &longs;ecetur in C, qua­<lb/>tenus enim ad anteriora fer­<lb/>tur, violentia e&longs;t; quatenus ve­<lb/>rò ad inferiores partes, naturæ. </s> <s id="s.000195">Vbi verò peruenit in C, <lb/>violentiâ ce&longs;&longs;ante, naturâ verò manente, rectà deor&longs;um <lb/>fertur DCD. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000196">Cæterùm hæc centra, hiqueue motus, naturalis nem­<lb/>pe, & violentus diuer&longs;imode &longs;e habent adinuicem. </s> <s id="s.000197">Si e­<lb/>nim graue corpus externâ vi adhibita, centrum mundi <lb/>ver&longs;us impellatur, adiuuabunt &longs;e inuicem Natura, Vio­<lb/>lentia, Si autem contra, altera alteri re&longs;i&longs;tet, in motibus <pb xlink:href="007/01/025.jpg"/>autem ad latus, eo magis pugnabunt, quo magis ab infe­<lb/>rioribus ad &longs;uperiora fiet motus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000198"><emph type="italics"/>Mechanices præcipua in&longs;trumenta.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000199">Hic ira con&longs;titutis dicimus, in&longs;trumenta, quibus ad <lb/>varias operationes Mechanici vtuntur, e&longs;&longs;e inter &longs;e qui­<lb/>dem diuer&longs;a, multiplicia, & &longs;i varietatem &longs;pectes, penè in­<lb/>numerabilia; quod quamuis verum &longs;it, ea omnia Ari&longs;tote­<lb/>les ad vectem re ducit, & libram: quod etiam G. <!-- REMOVE S-->Vbaldus <lb/>in libris Mechanicorum fecit. </s> <s id="s.000200">Cæterum qui po&longs;t Ari&longs;to­<lb/>telem floruere Mechanici, omnia ad quinque, quas ap­<lb/>pellant, Potentias, redegêre. </s> <s id="s.000201">Sunt autem ex Herone, Pap­<lb/>po, Guido Vbaldo, qui eos &longs;ecutus e&longs;t, Vectis, Trochlea, <lb/>Axis in Peritrochio, Cuneus, Cochlèa. </s> <s id="s.000202">Videtur autem i­<lb/>p&longs;e G. <!-- REMOVE S-->Vbaldus &longs;extam addere, nempe Libram, de qua & <lb/>primus ip&longs;e Mechanicorum tractatum in&longs;tituit. </s> <s id="s.000203">Verum <lb/>enimuero idem ferè &longs;unt Vectis & Libra, ni&longs;i forte quod <lb/>Libra tunc dicitur, cum brachia &longs;unt æqualia. </s> <s id="s.000204">Vectis vero <lb/>quomodocunque ea &longs;e habeant; quinque harum <expan abbr="Poten-tiarū">Poten­<lb/>tiarum</expan> imagines ita ob oculos ponimus. </s> <s id="s.000205">Vectis A. <!-- KEEP S--></s> <s id="s.000206">Trochlea <lb/>B, Axis in Peritrochio C. <!-- KEEP S--></s> <s id="s.000207">Cuneus D. <!-- KEEP S--></s> <s id="s.000208">Cochlea vero E. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/026.jpg"/> <figure id="id.007.01.026.1.jpg" xlink:href="007/01/026/1.jpg"/> <p type="main"> <s id="s.000209">Porro, Cuneum ad libram reducere conatur Ari­<lb/>&longs;toteles, quod facit & G. Vbaldus, qui eò refert & Co­<lb/>chleam, quippe quod nihil aliud &longs;it Cochlea, quàm Cu­<lb/>neus Cylindro inuolutus. </s> <s id="s.000210">Nos autem duas tantùm Po­<lb/>tentias ad vectem reduci po&longs;&longs;e arbitramur, Trochleam <lb/>nempe, & Axem in Peritrochio. <!-- KEEP S--></s> <s id="s.000211">Nequaquam autem Cu­<lb/>neum & Cochleam. </s> <s id="s.000212">quod latiùs quidem o&longs;tendemus, <lb/>cùm de Cuneo erit nobis &longs;ermo peculiaris. </s> </p> <p type="head"> <s id="s.000213"><emph type="italics"/>De Vecte & Libra &longs;ecundum Ari­<lb/>&longs;totelem.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000214">Ari&longs;toteles in ip&longs;o Mechanicorum ingre&longs;&longs;u ita &longs;cri­<lb/>bit, Mirum videri ab exigua virtute magnum pondus mo-<pb xlink:href="007/01/027.jpg"/>ueri, addito nimirum ponderi pondere, &longs;iquidem & vectis <lb/>e&longs;t pondus. </s> <s id="s.000215">Duplex ergo illi admiratio, &longs;cilicet quòd exi­<lb/>gua potentia moueat ingens pondus, idqueue etiam addito <lb/>vectis ip&longs;ius pondere, fiat. </s> <s id="s.000216">Hoc &longs;ecundum adieci&longs;&longs;e vide­<lb/>tur, amplificationis alicuius gratiâ. </s> <s id="s.000217">Etenim quatenus <lb/>ad rem pertinet, &longs;i mouendis ponderibus vectis ip&longs;ius <lb/>pondus compares, nullius ferè e&longs;&longs;e momenti procul du­<lb/>bio affirmaueris. </s> <s id="s.000218">Sed & illud quoque notandum, aliquan­<lb/>do vectis pondus mouenti auxilium ferre, quod fit vbi <lb/>fulcimento inter potentiam mouentem, & pondus ip&longs;um <lb/>collocato, vectis pars quæ à fulcimento ad potentiam e&longs;t, <lb/>premitur. </s> <s id="s.000219">Tunc enim, vt dicebamus, vectis pondere &longs;uo <lb/>potentiam adiuuat. </s> <s id="s.000220">Contra verò accidit, cum pondus i­<lb/>p&longs;um inter fulcimentum e&longs;t & potentiam vel potentia i­<lb/>p&longs;a inter fulcimentum & pondus. </s> <s id="s.000221">tunc enim vectis vnâ <lb/>cum pondere attollitur. </s> <s id="s.000222">quæ licet vera &longs;int, non tamen in­<lb/>de &longs;equitur, vectis pondus, quicquam quod curandum &longs;it, <lb/>in operatione efficere, aut impedire. </s> </p> <p type="main"> <s id="s.000223">Porrò vectem ita finire po&longs;&longs;umus, longitudinem e&longs;­<lb/>&longs;e quandam inflexibilem, quæ fulcimento dato, datâ po­<lb/>tentiâ datum pondus mouetur. </s> </p> <p type="main"> <s id="s.000224">Ip&longs;a quoque Libra, vt diximus, vectis e&longs;t: eius autem <lb/>naturæ, vt &longs;emper fulcimentum medium obtineat locum <lb/>inter pondus & pondus. </s> <s id="s.000225">Statera autem merus e&longs;t vectis, &longs;i <lb/>&longs;par&longs;um pro fulcimento; appendiculum verò currens pro <lb/>potentia mouente deputaueris. </s> </p> <p type="head"> <s id="s.000226"><emph type="italics"/>De Circulo eiusque natura Ari&longs;totelis doctri­<lb/>na examinata.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000227">Ari&longs;toteles, quicquid mirum in Mechanicis opera­<lb/>tur, id totum admirabili circuli naturæ e&longs;&longs;e tribuendum <lb/>arbitratur. </s> <s id="s.000228">Ait autem, ab&longs;urdum nullatenus e&longs;&longs;e, &longs;i ex re <lb/>mirabili mirandum quippiam oriatur. </s> <s id="s.000229">In circulo autem <pb xlink:href="007/01/028.jpg"/>quatuor inueniri qualitates admiratione dignas. </s> <s id="s.000230"><expan abbr="Primã">Primam</expan>, <lb/>quod ex contrarijs con&longs;tituatur, mouente videlicet & <lb/>moto. </s> <s id="s.000231">Secundam, quòd contraria in eius circumferentia <lb/>inueniantur, quippe quæ cum vnica linea &longs;it, concaua &longs;i­<lb/>mul e&longs;t & conuexa. </s> <s id="s.000232">Tertiam, quod contrarijs feratur mo­<lb/>tionibus, antror&longs;um nimirum, retror&longs;um, &longs;ur&longs;um, atque <lb/>deor&longs;um. </s> <s id="s.000233">Quartam, quod vnicâ exi&longs;tente &longs;emidiametro, <lb/>nullum in ea punctum &longs;umi po&longs;&longs;it, æqualis alteri, in latio­<lb/>ne, velocitatis. </s> <s id="s.000234">Sit enim circulus AB, cuius centrum C, <lb/>&longs;emidiameter AC, &longs;umatur autem in ea punctum D, i­<lb/>tem&qacute;ue punctum E. <!-- KEEP S--></s> <s id="s.000235">Erit itaque in ip&longs;a circulatione D <lb/>tardius E, ip&longs;um verò E tardius A, & ita citius id feretur <lb/>&longs;emper, quod remotius à mouente termino accipitur. </s> </p> <figure id="id.007.01.028.1.jpg" xlink:href="007/01/028/1.jpg"/> <p type="main"> <s id="s.000236">Hæc ex illo, quibus ne vltro a&longs;­<lb/>&longs;en&longs;um præbeamus non vnica de cau­<lb/>&longs;a cohibemur. </s> <s id="s.000237">Dicimus igitur, videri <lb/>nobis, circulum non ex contrarijs <expan abbr="cō-&longs;titui">con­<lb/>&longs;titui</expan>, puta ex manente & moto, &longs;ed ex <lb/>moto &longs;impliciter. </s> <s id="s.000238">Nulla e&longs;t enim &longs;e­<lb/>midiametri pars, quæ non moueatur. <lb/></s> <s id="s.000239">Punctum autem, quod &longs;tat, &longs;emidia­<lb/>metri pars nulla e&longs;t. </s> <s id="s.000240">Et &longs;anè cur moto <lb/><expan abbr="&longs;emidiamētro">&longs;emidiametro</expan> fiat circulus, non ideo accidit, quod <expan abbr="alterū">alterum</expan> <lb/>extremum &longs;tet, alterum verò moueatur:sed ideo quòd &longs;e­<lb/>midiameter perpetuò eandem &longs;eruet longitudinem. </s> <s id="s.000241">Elli­<lb/>p&longs;is &longs;anè centrum habet, &longs;ed ab eo ad circumferentiam <lb/>quatuor tantùm &longs;emidiametri quomodolibet &longs;umpti du­<lb/>cuntur æquales. </s> <s id="s.000242">Si quis igitur &longs;emidiametrum daret pro­<lb/>portione cre&longs;centem & decre&longs;centem, &longs;tante altero ex­<lb/>tremorum Ellip&longs;is de&longs;criberetur. </s> <s id="s.000243">Præterea & &longs;piralis li­<lb/>nea, quæ mixta e&longs;t, altero &longs;emidiametri extremo manen­<lb/>te, altero vero moto producitur. </s> <s id="s.000244">Legem itaque circulo <pb xlink:href="007/01/029.jpg"/>præ&longs;cribit, non quidem quòd hæc extremitas &longs;ter, illa ve­<lb/>rò moueatur, &longs;ed quod &longs;ua circulatione &longs;emper &longs;emidia­<lb/>meter eandem &longs;eruet longitudinem, quod vel ex ip&longs;a cir­<lb/>culi definitione colligitur. </s> </p> <p type="main"> <s id="s.000245">Ad &longs;ecundum miraculum, &longs;cilicet, quòd in circulo <lb/>circum ferentia, quæ vacua linea e&longs;t, concaua &longs;imul &longs;it, & <lb/>conuexa. </s> <s id="s.000246">Diceret qui&longs;piam id, &longs;i modò mirabile e&longs;t non <lb/>circulari tantum, &longs;ed cuilibet curuæ lineæ primo compe­<lb/>tere, etenim & Ellip&longs;is & Hyperbole, & Parabole, & &longs;pi­<lb/>ra, tum Cy&longs;&longs;ois, Conchois, & infinitæ aliæ irregulares <lb/>concauæ &longs;imul &longs;unt & conuexæ. </s> <s id="s.000247">Sed & hæc in &longs;uperficie­<lb/>bus quoque de&longs;iderantur. </s> </p> <p type="main"> <s id="s.000248">Ad tertium, quod contrarijs feratur lationibus, an­<lb/>tror&longs;um, retror&longs;um, &longs;ur&longs;um & deor&longs;um. </s> <s id="s.000249">Dicimus, facilè <lb/>&longs;olui, Nullus enim, re bene per&longs;pectâ, affirmauerit circu­<lb/>lum contrarijs lationibus moueri. </s> </p> <figure id="id.007.01.029.1.jpg" xlink:href="007/01/029/1.jpg"/> <p type="main"> <s id="s.000250">E&longs;to enim circulus ABCD, <lb/>circa centrum E; ponamus ro­<lb/>tari, & A ver&longs;us B, exempli gra­<lb/>tiâ, antror&longs;um, mouebitur <expan abbr="autē">autem</expan> <lb/>& B ver&longs;us C, & C ver&longs;us D, tum <lb/>D ver&longs;us A. <!-- KEEP S--></s> <s id="s.000251">Non puto <expan abbr="quenquã">quenquam</expan> <lb/>dicturum, circulum hunc an­<lb/>tror&longs;um eodem tempore, & re­<lb/>tror&longs;um ferri nec &longs;ur&longs;um aut de­<lb/>or&longs;um, &longs;i enim qui&longs;piam per eius circuli circumferentiam <lb/>ambularet, is certè centrum ip&longs;um &longs;emper ad dexteram <lb/>haberet, vel ad &longs;ini&longs;tram, &longs;i ad dexteram, antror&longs;um ibit, &longs;i <lb/>ad &longs;ini&longs;tram, retror&longs;um. </s> <s id="s.000252">Sed nec &longs;ur&longs;um vel deor&longs;um, e&longs;t <lb/>manife&longs;tum. </s> <s id="s.000253">Nihil autem prohibet eundem motum va­<lb/>rio re&longs;pectu contrarium dici po&longs;&longs;e, id tamen profectò fie­<lb/>ri nequaquam pote&longs;t, nempe A moueri ver&longs;us B, hoc e&longs;t, <pb xlink:href="007/01/030.jpg"/>antror&longs;um, & eandem eodem tempore ver&longs;us B, id e&longs;t, re­<lb/>tror&longs;um; repugnat enim naturæ. </s> </p> <p type="main"> <s id="s.000254">De quarto circuli miraculo, ibi erit nobis &longs;ermo, vbi <lb/>ea perpenderimus primò, quæ Philo&longs;ophus de Circuli <lb/>productione di&longs;&longs;erens in medium profert. </s> <s id="s.000255">Sunt autem e­<lb/>iu&longs;modi: </s> </p> <p type="main"> <s id="s.000256">Circulum quidem duplici notione produci, Natu­<lb/>rali videlicet altera, & altera quæ e&longs;t præter naturam, & <lb/>ideo circularem lineam in ter mixtas computari. </s> </p> <p type="main"> <s id="s.000257">Motus mixtus ait, vel proportione &longs;eruata fit, aut <lb/>non; Si proportione &longs;eruatâ, rectam lineam; ea verò non <lb/>&longs;eruata, circularem lineam produci. </s> </p> <figure id="id.007.01.030.1.jpg" xlink:href="007/01/030/1.jpg"/> <p type="main"> <s id="s.000258">E&longs;to enim rectangu­<lb/>lum ABCD, cuius late­<lb/>ra in datâ &longs;int proportio­<lb/>ne, AD cum AB. <!-- KEEP S--></s> <s id="s.000259">Mo­<lb/>ueatur A, duplici motu, <lb/>Altero quidem tendens <lb/>in B, altero vero ad mo­<lb/>tum lineæ AB, feratur <lb/>ver&longs;us D, &longs;eruata inte­<lb/>rim laterum proportione. </s> <s id="s.000260">Itaque ponatur ex motu ab A <lb/>ver&longs;us B, perueni&longs;&longs;e in E, ex motu autem quo proportio­<lb/>naliter fertur cum linea AB, facta ip&longs;a AB, in FH, perue­<lb/>ni&longs;&longs;e in G, & EG connectatur. </s> <s id="s.000261">Erit igitur Parallelogram­<lb/>mum AEGF, Parallelogrammo ABCD proportiona­<lb/>le &longs;imile, & circa eandem diametrum AGC. <!-- KEEP S--></s> <s id="s.000262">Semper igi­<lb/>tur punctum A &longs;i duabus lationibus feratur, laterum pro­<lb/>portione &longs;eruata, lineam producet rectam, diametrum <lb/>nempe AGC. <!-- KEEP S--></s> <s id="s.000263">Et hoc &longs;anè nullam habet dubitationem, <lb/>ex ijs quæ docet Euclides 1. 6. prop. 24. </s> </p> <p type="main"> <s id="s.000264">His ita demon&longs;tratis hac vti videtur Philo&longs;ophus <pb xlink:href="007/01/031.jpg"/>argumentatione: Si mixtus motus proportione &longs;emotâ, <lb/>rectam producit, &longs;i nunquam &longs;emota, efficiet circulum; &longs;i <lb/>enim modo &longs;eruaretur, modo non, partim recta partim <lb/>non recta produceretur. </s> <s id="s.000265">Ingenio&longs;a quidem argumenta­<lb/>tio, ni vitium contineret. </s> <s id="s.000266">non enim mixtus motus, qui <lb/>nun quam &longs;eruatâ proportione fit, &longs;emper ci, culum pro­<lb/>ducit, &longs;ed & Ellip&longs;im pote&longs;t, & quamlibet aliam lineam, <lb/>cuius nulla pars &longs;it recta. </s> <s id="s.000267">Hanc difficultatem vidit Pico­<lb/>lomineus in &longs;ua Paraphra&longs;i, & eam &longs;oluere conatus e&longs;t, <lb/>&longs;ed quàm bene, aliorum e&longs;to iudicium. </s> <s id="s.000268">Cæterùm fal&longs;um <lb/>e&longs;t, a&longs;&longs;erere circulum ex mixto motu nunquam &longs;eruatâ <lb/>proportione produci. </s> <s id="s.000269">&longs;eruat enim a&longs;&longs;iduè mixtus motus <lb/>quo producitur (&longs;i cum mixto motu producere velimus) <lb/>aliquam proportionem, &longs;ed non eandem. </s> </p> <figure id="id.007.01.031.1.jpg" xlink:href="007/01/031/1.jpg"/> <p type="main"> <s id="s.000270">E&longs;to enim recta AB, cui ad rectos <lb/>angulos AC. <!-- KEEP S--></s> <s id="s.000271">Moueatur autem A, ver­<lb/>&longs;us C per lineam AC, & eodem tempo­<lb/>re linea AC, ver&longs;us B, ita tamen, vt &longs;em­<lb/>per ip&longs;i AB, &longs;it perpendicularis. </s> <s id="s.000272">feratur <lb/>autem eâ lege, vt quam proportionem <lb/>habet motus lineæ AC ver&longs;us B, ad mo­<lb/>tum puncti A ve, &longs;us C, eandem habeat <lb/>ip&longs;e motus ab A ver&longs;us C, ad re&longs;iduum <lb/>lineæ AB, demptâ nempe ea parte quam <lb/>peragrauit linea AC mota ver&longs;us B. <!-- KEEP S--></s> <s id="s.000273">Sit <lb/>autem, cum AC &longs;uo motu peruenerit <lb/>in D, punctum A, &longs;imiliter &longs;uo motu per eam latum perue­<lb/>nitle in E erit ergo ex mixto motu, non quidem in D, nec <lb/>in E, &longs;ed in F, eritque punctum F in circum ferentia circu­<lb/>li, cuius e&longs;t diameter ip&longs;a linea AB, quod quidem demon­<lb/>&longs;tratur ex conuer&longs;a propo&longs;. </s> <s id="s.000274">13. lib. 6. Elem. <!-- KEEP S--></s> <s id="s.000275">E&longs;t enim AE <lb/>hoc e&longs;t DF media proportionalis inter EF, hoc e&longs;t, AD, <lb/>& DB. <!-- KEEP S--></s> <s id="s.000276">Iterum &longs;i fiat motus AC in GH, ad motum H per <pb xlink:href="007/01/032.jpg"/>lineam AC, v&longs;que in C, vt &longs;e habet proportio AG ad <lb/>GH & GH ad GB, erit ex motu mixto A in H, nempe in <lb/>eiu&longs;dem circuli circum ferentia AFHB. ex quibus ha­<lb/>bemus, circulum ex mixto motu fieri po&longs;&longs;e proportioni­<lb/>bus quidem mediarum &longs;eruatis, &longs;ed nunquam ij&longs;dem. </s> </p> <p type="main"> <s id="s.000277">Vera hæc procul dubio &longs;unt; nihilominus, veluti ad <lb/>rectam producendam mixtus motus non e&longs;t nece&longs;&longs;arius, <lb/>licet mixto motu produci po&longs;&longs;it, ita ne que ad circularem, <lb/>& ideo verum non e&longs;&longs;e quod a&longs;&longs;erebat Philo&longs;ophus, cir­<lb/>culum ex mixto motu proportione nunquam &longs;eruatâ ne­<lb/>ce&longs;&longs;ariò produci. </s> </p> <p type="main"> <s id="s.000278">Conatur po&longs;t hæc Ari&longs;toteles rationem afferre, cur <lb/>circuli partes, quò propiores centro fuerint, eo &longs;int tar­<lb/>diores. </s> <s id="s.000279">Ait autem; &longs;i duobus ab eadem potentia latis hoc <lb/>quidem plus repellatur, illud verò minus, æquum e&longs;t tar­<lb/>diùs id moueri quod plus repellitur, eo quod minus. </s> <s id="s.000280">De­<lb/>trahi autem plus lineam, cuius extremum propius e&longs;t cen­<lb/>tro illa quæ &longs;uum habet terminum à centro remotiorem. </s> </p> <figure id="id.007.01.032.1.jpg" xlink:href="007/01/032/1.jpg"/> <p type="main"> <s id="s.000281">E&longs;to, inquit, circulus <lb/>BCDE & alter in eo minor <lb/>MNOP circa idem centrum <lb/>A. Ducanturque; Diametri ma­<lb/>ioris quidem CD, EB, mino­<lb/>ris verò MO, NP. </s> <s id="s.000282">Itaque vbi <lb/>AB circulata eò peruenerit <lb/>vnde e&longs;t gre&longs;&longs;a, ip&longs;a quoque <lb/>AM eo vnde moueri cœpe­<lb/>rat, perueniet. </s> <s id="s.000283">Tardiùs autem <lb/>fertur AM, quam AD, pro­<lb/>pterea quòd AM à centro <lb/>magis retrahatur quàm ip&longs;a AB. <!-- KEEP S--></s> <s id="s.000284">Ducatur igitur ALF & <lb/>à puncto L, ip&longs;i AB perpendicularis L q, cadens in mino-<pb xlink:href="007/01/033.jpg"/>ri circulo, & rur&longs;us ab eodem L ip&longs;i AB, parallela duca­<lb/>tur LS, Ab S verò eidem perpendicularis ST, & ab F i­<lb/>tem FX. </s> <s id="s.000285">Sunt ergo q L, ST, quidem æquales, nempe illæ, <lb/>per quæ, &longs;ecundum naturam, mouentur puncta BM. <!-- KEEP S--></s> <s id="s.000286">Mo­<lb/>tu verò retractionis ad centrum, hoc e&longs;t, præter naturam, <lb/>plus motum e&longs;t M quàm B. <!-- KEEP S--></s> <s id="s.000287">Maior enim e&longs;t M q, ip&longs;a BT, <lb/>quod, ceu notum, &longs;uppo&longs;uit Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000288">nos autem inf. </s> <s id="s.000289">à <lb/>demon&longs;trabimus. </s> <s id="s.000290">Si igitur fiat vt motus præter naturam <lb/>ad motum præter naturam, ita motus <expan abbr="&longs;ecūdum">&longs;ecundum</expan> naturam, <lb/>ad motum &longs;ecundum naturam, punctum B; cum M fuerit <lb/>in L, non erit in S, &longs;ed in F. tunc enim, vt e&longs;t FX motus &longs;e­<lb/>cundùm naturam ad XB, præter naturam, ita e&longs;t q L &longs;e­<lb/>cundum naturam ad q M præter naturam; &longs;ed BF maior <lb/>e&longs;t ML, ergo proportione &longs;eruatâ, velociùs mouetur B <lb/>quàm M circa idem centrum A. <!-- KEEP S--></s> <s id="s.000291">Hæc autem &longs;umma e&longs;t <lb/>eorum quæ præfert Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000292">Cæterùm nos parallelo­<lb/>grammum, quod in figura eius habetur prætermi&longs;imus, <lb/>quippe quod nihil ad eam quæ affertur, demon&longs;tratio­<lb/>nem faciat. </s> </p> <p type="main"> <s id="s.000293">Modò quod pollicebamur, nempe minorem e&longs;&longs;e <lb/>BT, quàm q M, ita demon&longs;tramus. </s> <s id="s.000294"><expan abbr="quoniã">quoniam</expan> ST. ex prop. 13. <lb/>1. 6. media proportionalis e&longs;t inter BT & TE, erit qua­<lb/>dratum TS æquale <expan abbr="parallelogrãmo">parallelogrammo</expan> &longs;eu rectangulo BT, <lb/>TE, item, quoniam q L media proportionalis e&longs;t inter <lb/>M q, & q O. erit quadratum q L æquale rectangulo M q, <lb/>q O, æqualia ergo &longs;unt rectangula BTE, M q O, itaque <lb/>reciproca latera habent proportionalia. </s> <s id="s.000295">quare, vt TE, ad <lb/>q O, ita M q ad TB, &longs;ed TE maior e&longs;t ip&longs;a q O, quippe <lb/>quòd pars &longs;it q O ip&longs;ius TE, maior ergo & M q ip&longs;a TB, <lb/>quod o&longs;tendendum fuerat. </s> </p> <p type="main"> <s id="s.000296">Cæterùm &longs;ubtilia & ingenio&longs;a i&longs;thæc e&longs;&longs;e non nega­<lb/>mus, & longè faciliori & explicatiori modo veritas hæc <lb/>demon&longs;trari pote&longs;t, reiectis nempe illis, &longs;ecundùm, & prae­<pb xlink:href="007/01/034.jpg"/>ter naturam motibus, qui <expan abbr="quidē">quidem</expan> in &longs;implici circulo nece&longs;­<lb/>&longs;ario non cadunt: caderent autem forta&longs;&longs;e, &longs;i de circulo <lb/>res e&longs;&longs;et à <expan abbr="pōderibus">ponderibus</expan> circumlatis ex &longs;tabili centro de&longs;cri­<lb/>pto, qua de re agit G. <!-- REMOVE S-->Vbaldus in Mechanicis tractatu de <lb/>libra. </s> <s id="s.000297">tunc enim dici pote&longs;t, pondus quod aliâs rectà ad <lb/>mundi centrum tenderet, à circuli centro in circulatio­<lb/>ne retrahi, &longs;ed hæc ad circuli naturam, quatenus circulus <lb/>e&longs;t, nequaquam &longs;pectant. </s> </p> <figure id="id.007.01.034.1.jpg" xlink:href="007/01/034/1.jpg"/> <p type="main"> <s id="s.000298">E&longs;to igitur circumferentia <lb/>AFBH, cuius centrum C, dia­<lb/>meter ACB, &longs;emidiameter AC. <lb/>&longs;umatur in AC punctum quod­<lb/>libet, D, & centro C, &longs;patio CD, <lb/>circumferentia de&longs;cribatur <lb/>DGEI. <!-- KEEP S--></s> <s id="s.000299">Dico punctum A velo­<lb/>cius moueri puncto D eâdem <lb/>circulatione rotato. </s> <s id="s.000300">etenim vt <lb/>diameter ad diametrum, & &longs;emidiameter ad &longs;emidiame­<lb/>trum, ita circumferentia ad circumferentiam: igitur vt <lb/>AC ad CD, ita circumferentia AFHB ad circumferen­<lb/>tiam DGEI. <!-- KEEP S--></s> <s id="s.000301">At mota linea CA circa centrum C mo­<lb/>uetur &longs;imul & CD, eodem igitur tempore rotationem <lb/>complent puncta AD, maius ergo &longs;patium eodem tem­<lb/>pore metitur A, ip&longs;a D, quare velocior. </s> <s id="s.000302">Ita igitur &longs;e ha­<lb/>bet velocitas ad velocitatem, vt circumferentia ad cir­<lb/>cumferentiam, & diameter ad diametrum, quare id quod <lb/>mouetur in puncto à centro remotiori, velocius illo mo­<lb/>uetur quod ab eo di&longs;tat minus, quod fuerat <lb/>demon&longs;trandum. </s> </p> <pb xlink:href="007/01/035.jpg"/> </subchap1> </chap> <chap> <p type="head"> <s id="s.000303">QVÆSTIONES <lb/>MECHANICÆ.</s> </p> <subchap1> <p type="head"> <s id="s.000304">QVÆSTIO I.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000305"><emph type="italics"/>Cur maiores libræ exactiores &longs;int mi­<lb/>noribus?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000306">Prioríbus, ceu fundamentis quibu&longs;dam iactis, oppor­<lb/>tunè ad quæ&longs;tiones proponendas, eas queue diluendas &longs;e <lb/>confert Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000307">Porro in propo&longs;ita quæ&longs;tione vide­<lb/>tur prima fronte cau&longs;&longs;am quæri de re quæ non e&longs;t: etenim <lb/>quis affirmauerit vnquam, lances quibus Apothecarij & <lb/>Macellarij vtuntur, magnas eas quidem, illis exactiores <lb/>e&longs;&longs;e quibus Gemmatij, atque Argentarij &longs;iliquis, & &longs;cru­<lb/>pulis minuti&longs;&longs;ima appendunt, quæ tamen perexiguæ &longs;unt, <lb/>& &longs;i illis comparentur minimæ? </s> <s id="s.000308">Veruntamen, ita pror&longs;us <lb/>res habet, vt a&longs;&longs;erit Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000309">Non enim propterea <lb/>quòd illæ magnæ &longs;int, hæ verò exiguæ, hæ &longs;unt illis exa­<lb/>ctiores; &longs;ed quoniam magnæ, rudes &longs;unt, minores verò ex­<lb/>qui&longs;ita diligentia elaboratæ, & à materiæ pertinacia libe­<lb/>riores. </s> <s id="s.000310">Cæteris ergo paribus, exactiores e&longs;&longs;e maiores, ex <lb/>Philo&longs;ophi mente, ita docebimus. </s> </p> <figure id="id.007.01.035.1.jpg" xlink:href="007/01/035/1.jpg"/> <p type="main"> <s id="s.000311">E&longs;to libra maior AB, <lb/>cuius fulcimentum C. <lb/><!-- KEEP S--></s> <s id="s.000312">Minor verò libra DE, <lb/>circa idem <expan abbr="fulcimētum">fulcimentum</expan> <lb/>C, vnà cum maiori, ima­<lb/>ginatione, conuer&longs;a. </s> <s id="s.000313">Ap­<lb/>ponatur quoduis pon­<lb/>dus maiori libræ in A, <lb/>declinetque; exempli gratiâ in F, erit queue minor libra in G, <lb/>in eadem enim linea &longs;unt CGF. <expan abbr="Vnaq;">Vnaque</expan> igitur ex eodem <pb xlink:href="007/01/036.jpg"/>centro C portionem circuli de&longs;cribet GD, AF, eritqueue <lb/>ACF &longs;ector circuli, cuius diameter AB, &longs;ed DCG &longs;e­<lb/>ctor circuli, cuius diameter DE. <!-- KEEP S--></s> <s id="s.000314">Itaque vt diameter ad <lb/>diametrum, ita portio ad portionem: maior autem dia­<lb/>meter AB diametro DE: maior ergo portio AF, portio­<lb/>ne DG. quod autem maius e&longs;t, minus obtutum fallit, ex­<lb/>qui&longs;itius itaque tractum ex maiori AB quàm ex ip&longs;a mi­<lb/>nori DE cogno&longs;cemus, quod fuerat o&longs;tendendum. </s> </p> <p type="main"> <s id="s.000315">Cæterùm hac eadem de cau&longs;&longs;a, A&longs;tronomica in­<lb/>&longs;trumenta, puta A&longs;trolabia, Armillæ, & alia eiu&longs;modi, <lb/>quo ampliora eò exqui&longs;itiora, & certiora probantur. </s> </p> <figure id="id.007.01.036.1.jpg" xlink:href="007/01/036/1.jpg"/> <p type="main"> <s id="s.000316">E&longs;to enim A­<lb/>&longs;trolabium magnum, <lb/>cuius diameter AB, <lb/>paruum autem CD, <lb/>circa idem centrum <lb/>E. <!-- KEEP S--></s> <s id="s.000317">Ducatur à centro <lb/>recta EF tangens ma­<lb/>iorem circulum in F, <lb/><expan abbr="minorē">minorem</expan> verò <expan abbr="&longs;ecãs">&longs;ecans</expan> in <lb/>G, vt igitur GD ad to­<lb/>tum circulum GCD, <lb/>ita FB. ad totum cir­<lb/>culum FAB, vt ergò <lb/>GD ad FB, ita gradus <lb/>&longs;ignati in GD, ad eos qui &longs;ignantur in BF, maiores ergo <lb/>&longs;unt qui in FB, & minutarum partium capaciores. </s> <s id="s.000318">Hinc <lb/>itaque apparet, <expan abbr="in&longs;trumēta">in&longs;trumenta</expan> quælibet quò maiora fuerint, <lb/>eò e&longs;&longs;e & exqui&longs;itiora, quod propo&longs;uerat Ari&longs;toteles, in <lb/>hac quæ&longs;tione de Libra. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000319">Quod autem addit de fraudibus Purpurariorum, <lb/>inquiens; quamobrem machinántur ij qui purpuram ven­<lb/>dunt, vt <expan abbr="pēdendo">pendendo</expan> defraudent, dum ad medium, &longs;partum, <pb xlink:href="007/01/037.jpg"/>non ponentes; tum plumbum in alterutram libræ partem <lb/>infundentes; aut ligni quod ad radicem vergebat, in eam <lb/>quam deferri volunt partem con&longs;tituentes, aut &longs;i nodum <lb/>habuerit, ligni enim grauior ea e&longs;t pars, in qua e&longs;t radix, <lb/>nodus verò radix quæ dam e&longs;t. </s> <s id="s.000320">Hinc quæri po&longs;&longs;et: </s> </p> <p type="head"> <s id="s.000321"><emph type="italics"/>Vtrum libræ quæ ponderibus vacuæ æquilibrant, <lb/>omni pror&longs;us careant fraude?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000322">Videri cuipiam po&longs;&longs;et, libras, quæ ponderibus va­<lb/>cuæ, æquilibrant, omni pror&longs;us fraude carere, verunta­<lb/>men ita non e&longs;t, quod diligentiùs (res enim magni mo­<lb/>menti e&longs;t) di&longs;quiremus. </s> </p> <figure id="id.007.01.037.1.jpg" xlink:href="007/01/037/1.jpg"/> <p type="main"> <s id="s.000323">E&longs;to enim libra AB, ita diui&longs;a <lb/>in C, vt AC &longs;it partium IS, CB ve­<lb/>rò earundem &longs;it 10. apponatur parti <lb/>A lanx ponderans 10, parti vero B <lb/>lanx ponderans 15. ex permutata i­<lb/>gitur proportione libra &longs;u&longs;pen&longs;a in <lb/>C, aequè ponderabit; &longs;i autem appo­<lb/>natur lanci B &longs;acoma vnciarum 6, & in lance A con&longs;titua­<lb/>tur purpura, quæ ita &longs;e habeat ad vncias 6, vt 10 ad 15, ite­<lb/>rum æqueponderabit, &longs;ed vt 10 ad 15, ita 4 ad 6. Purpura­<lb/>rius ergo fraudulentus, ponens in lance A vncias purpuræ <lb/>4, facto æquilibrio petet pretium vnciarum 6, & ita em­<lb/>ptorem decipiet, quod &longs;anè innuerat, non autem demon­<lb/>&longs;trauerat Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000324">Hæc autem faciliora fient ex ijs, <lb/>quæ in &longs;equentibus quæ&longs;tionibus, vbi de vecte agetur, ex­<lb/>plicabuntur. </s> </p> <p type="main"> <s id="s.000325">Detegitur autem fraus, &longs;i alternatim &longs;acoma in pon­<lb/>derando, modo huic, modò illi lanci apponatur. </s> <s id="s.000326">Si enim <lb/>in lance A con&longs;tituatur &longs;acoma, in B verò purpura non fit <lb/>æquilibrium. </s> </p> <pb xlink:href="007/01/038.jpg"/> </subchap1> <subchap1> <p type="head"> <s id="s.000327">QVÆSTIO II.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000328"><emph type="italics"/>Cur, &longs;i &longs;ur&longs;um libræ fulcimentum &longs;it, appo&longs;ito ad alteram partem <lb/>pondere, de&longs;cendat libra, & eo amoto, iterum a&longs;cendat, & ad æqui­<lb/>librium reuertatur. </s> <s id="s.000329">Si verò deor&longs;um fulcimentum fuerit, de­<lb/>pre&longs;&longs;a ad æquilibrium non reuertatur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000330">Bimembrem proponit Philo&longs;ophus quæ&longs;tionem, quam <lb/>trimembrem debuit, triplici &longs;i quidem loco fulcimen­<lb/>tum aptari pote&longs;t, &longs;uperiori, medio, inferiori. </s> <s id="s.000331">Nos de o­<lb/>mnibus verba faciemus. </s> </p> <p type="head"> <s id="s.000332">Prima Quæ&longs;tionis pars.</s> </p> <p type="head"> <s id="s.000333"><emph type="italics"/>De Libra &longs;ur&longs;um fulcimentum habente.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000334">Ari&longs;toteles primam quæ&longs;tionis partem ita &longs;oluit: An <lb/>quia &longs;ur&longs;um parte quidem exi&longs;tente, plus libræ extra per­<lb/>pendiculum &longs;it? </s> <s id="s.000335">Spartum enim perpendiculum e&longs;t: quare <lb/>nece&longs;&longs;e e&longs;t deor&longs;um ferri id quod plus e&longs;t, donec a&longs;cendat <lb/>qua bifariam libram diuidit ad ip&longs;um perpendiculum, <lb/>cum onus incumbat ad libræ partem &longs;ur&longs;us raptam. </s> </p> <figure id="id.007.01.038.1.jpg" xlink:href="007/01/038/1.jpg"/> <p type="main"> <s id="s.000336">Sit libra recta (hoc e&longs;t, in æquilibrio con&longs;tituta) BC, <lb/>&longs;partum autem AD, <lb/>fulcimentum autem <lb/>D, de&longs;uper: &longs;parto au­<lb/>tem deor&longs;um proie­<lb/>cto ad M perpendicu­<lb/>laris erit vbi ADM. <lb/></s> <s id="s.000337">Si igitur in ip&longs;o B po­<lb/>natur onus, erit B qui­<lb/>dem vbi E, C autem <lb/>vbi H, quamobrem <lb/>ea quæ bifariam <expan abbr="librã">libram</expan> <lb/>&longs;ecat, primo quidem erit DM, ip&longs;ius perpendiculi; in<expan abbr="cū-bente">cum­<lb/>bente</expan> <expan abbr="autē">autem</expan> onere, erit DG. quare libræ ip&longs;ius EH, quod <pb xlink:href="007/01/039.jpg"/>extra perpendiculum, e&longs;t AM, vbi e&longs;t q P maius e&longs;t dimi­<lb/>dio. </s> <s id="s.000338">Si igitur amoueatur onus ab E, nece&longs;&longs;e e&longs;t deor&longs;um <lb/>ferri H, minus e&longs;t enim E: &longs;iquidem igitur habuerit &longs;par­<lb/>tum &longs;ur&longs;um, propter hoc a&longs;cendit libra. </s> </p> <p type="main"> <s id="s.000339">Pe&longs;&longs;imè omnes &longs;chema hoc lineârunt, ita vt difficil­<lb/>limum &longs;it auctoris inde &longs;en&longs;um a&longs;&longs;equi. </s> <s id="s.000340">Nos autem cla­<lb/>rius rem ob oculos ponimus. </s> <s id="s.000341">Id ergo &longs;ibi vult Ari&longs;toteles, <lb/>propterea quòd pars iugi HDG maior e&longs;t parte ED q, <lb/>eam eleuatam nece&longs;&longs;e e&longs;t de&longs;cendere, & iterum à perpen­<lb/>diculari ADM bifariam diui&longs;am ad æquilibrium reuer­<lb/>ti, Po&longs;&longs;umus nos idem &longs;impliciori figura demon&longs;trare. </s> </p> <figure id="id.007.01.039.1.jpg" xlink:href="007/01/039/1.jpg"/> <p type="main"> <s id="s.000342">E&longs;to libra AB, bi­<lb/>fariam, diui&longs;a in G, <lb/><expan abbr="fulcimentū">fulcimentum</expan> verò &longs;ur­<lb/>&longs;um vbi D, produca­<lb/>tur perpendicularis <lb/>DC in E. <!-- KEEP S--></s> <s id="s.000343">Stante igi­<lb/>tur libra AB, in æqui­<lb/>librio æqualis e&longs;t pars <lb/>CH, ip&longs;i parti CB <lb/>apponatur pondus in <lb/>B. <!-- KEEP S--></s> <s id="s.000344">Declinabit igitur <lb/>libra mota circa centrum D, fiat autem in FG, &longs;ecetqueue <lb/>perpendicularem in I. <!-- KEEP S--></s> <s id="s.000345">Punctum vero C eodem motu cir­<lb/>ca idem centrum D erit in H. amoueatur pondus appo&longs;i­<lb/>tum: Dico libram à &longs;itu FG declinaturam & iterum re­<lb/>uer&longs;uram in &longs;itum pri&longs;tinum ACB. quoniam enim parti <lb/>GH, quæ æqualis e&longs;t parti HF, additur pars IH, quæ à <lb/>perpendiculari e&longs;t v&longs;que ad H, ip&longs;i verò HF eadem pars <lb/>detrahitur, erit IF minor GI. </s> <s id="s.000346">Superabitur ita que IF à <lb/>GI, de&longs;cendetque FI, a&longs;cendet verò IF, donec iterum li­<pb xlink:href="007/01/040.jpg"/>bra ín partes æquales, vt antea, diuidatur in C, &longs;iat que æ­<lb/>quilibrium. </s> </p> <p type="main"> <s id="s.000347">Hæc Philo&longs;ophi demon&longs;tratio e&longs;t vera illa quidem, <lb/>&longs;ed non ex Mechanicis principijs, hoc e&longs;t, ex centri graui­<lb/>tatis &longs;peculatione; nos igitur clariùs rem exponemus, his <lb/>quæ &longs;equuntur con&longs;ideratis. </s> </p> <p type="main"> <s id="s.000348">Si pondus circa &longs;tabile centrum conuertatur, dimi&longs;­<lb/>&longs;um non &longs;tabit, ni&longs;i &longs;ecundum grauitatis centrum fuerit <lb/>in perpendiculari, quæ per centrum, circa quod conuer­<lb/>titur, ad mundi centrum cadit. </s> <s id="s.000349">Stabit autem in ea per­<lb/>pendiculari in duobus punctis, altero à centro mundi <lb/>remoti&longs;&longs;imo; altero verò eidem quantum licuerit pro­<lb/>ximo. </s> </p> <figure id="id.007.01.040.1.jpg" xlink:href="007/01/040/1.jpg"/> <p type="main"> <s id="s.000350">E&longs;to corpus A, cuius graui­<lb/>tatis centrum B, nixum lineae in­<lb/>flexibili BC, cum qua liberè <lb/>conuertatur circa centrum C. <lb/><!-- KEEP S--></s> <s id="s.000351">Ducatur autem per mundi cen­<lb/>trum perpendicularis BCD. <lb/><!-- KEEP S--></s> <s id="s.000352">Sit igitur primò pondus A <expan abbr="&longs;ecū-dum">&longs;ecun­<lb/>dum</expan> gracilis B centrum, in per­<lb/>pendiculari ip&longs;a &longs;upra centrum <lb/>C, puta in B. <!-- KEEP S--></s> <s id="s.000353">Moueatur & <expan abbr="de&longs;cē-dat">de&longs;cen­<lb/>dat</expan> in E. <!-- KEEP S--></s> <s id="s.000354">Po&longs;t hæc verò in F, hoc <lb/>e&longs;t iterum in ip&longs;a perpendiculari <lb/>infra centrum C. <!-- KEEP S--></s> <s id="s.000355">De&longs;cribet er­<lb/>go circulum ex centro C, nem­<lb/>pe BEF &longs;ecantem perpendicu­<lb/>larem in duobus punctis oppo­<lb/>&longs;itis BF, dico, pondus libe è di-<pb xlink:href="007/01/041.jpg"/>mi&longs;&longs;um in duobus tantum punctis &longs;uapte naturâ perman­<lb/>&longs;urum, BF, in B, primò, quoniam cum corpus ip&longs;um A à <lb/>perpendiculari, quæ &longs;uperficiei loco intelligitur ABCD <lb/>per centrum grauitatis diuidatur, in partes diuiditur æ­<lb/>queponderantes, quare in neutram partem inclinabit. <lb/></s> <s id="s.000356">Stabit igitur erectum, lineæ ip&longs;i fultum, inflexibili BC, <lb/>quæ nititur puncto C. <!-- KEEP S--></s> <s id="s.000357">In E verò non &longs;tabit, quippe quod <lb/>eo &longs;itu centrum ip&longs;um grauitatis &longs;it extra perpendicula­<lb/>rem, & ideo extra fulcimentum &longs;tabile C. <!-- KEEP S--></s> <s id="s.000358">In F verò ite­<lb/>rum &longs;tabit, pendens à centro C, propterea quòd & ibi ab <lb/>eadem perpendiculari diuidatur per grauitatis centrum <lb/>in partes æqueponderantes. </s> <s id="s.000359">E&longs;t igitur re&longs;pectu B, ip&longs;um <lb/>punctum C, fulcimentum deor&longs;um, re&longs;pectu verò F, ful­<lb/>cimentum &longs;ur&longs;um. </s> <s id="s.000360">At quia linea DFCB, à centro mundi, <lb/>quod e&longs;t extra circulum, BEF, circulum ip&longs;um per cen­<lb/>trum C &longs;ecat, erit pars eius DF quidem breui&longs;&longs;ima, ip&longs;a <lb/>verò DB longi&longs;&longs;ima, ex propo&longs;. 8. lib. 3. Elem. <!-- KEEP S--></s> <s id="s.000361">Pondus igi­<lb/>tur A conuer&longs;um &longs;eu liberè motum circa centrum C, in <lb/>duobus tantum locis perpendicularis lineæ &longs;tabit remo­<lb/>ti&longs;&longs;imo altero, vt e&longs;t B, altero verò eidem quam proximo, <lb/>vt e&longs;t F. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000362">Hoc idem egregiè demon&longs;trauit G. Vbald. <!-- REMOVE S-->in &longs;uis <lb/>Mechanicis, Tractatu de Libra prop.1.</s> </p> <p type="main"> <s id="s.000363">Ad hæc autem dubitare quis po&longs;&longs;et, cur experientiâ <lb/>docente, pondera quæ infra fulcimentum habent, vt lan­<lb/>cea &longs;ari&longs;&longs;aue ad planum horizontis perpendiculariter e­<lb/>recta, licet eo ca&longs;u grauitatis centrum in ip&longs;a perpendicu­<lb/>lari con&longs;tituatur, non &longs;tet quidem, &longs;ed altrin&longs;ecus ca­<lb/>dat? </s> </p> <pb xlink:href="007/01/042.jpg"/> <figure id="id.007.01.042.1.jpg" xlink:href="007/01/042/1.jpg"/> <p type="main"> <s id="s.000364">Sit enim horizontis <lb/>planum AB, cui in puncto <lb/>C perpendiculariter ere­<lb/>cta &longs;tatuatur &longs;ari&longs;&longs;a DC, <lb/>cuius grauitatis centrum <lb/>E, in ip&longs;a perpendiculari. <lb/></s> <s id="s.000365">Stabit ergo, ex præmi&longs;&longs;is, <lb/>& certè &longs;tare debuit, &longs;ta­<lb/>retqueue, ni vitium ob&longs;taret <lb/>materiæ; non &longs;tat autem, <lb/>quia difficillimum e&longs;t gra­<lb/>uitatis centrum, &longs;uapte naturâ indiui&longs;ibile, ita ad amu&longs;&longs;im <lb/>&longs;i&longs;tere, vt in neutram partem à perpendiculari declinet. <lb/></s> <s id="s.000366">Hæc igitur ex ijs &longs;peculationibus e&longs;t, quæ ad praxim, ma­<lb/>teriæ vitio impediente, aut vix aut nunquam rediguntur. </s> </p> <p type="main"> <s id="s.000367">Hinc autem ea quæ&longs;tio &longs;oluitur, Cur ij qui &longs;ari&longs;&longs;am <lb/>erectam digito &longs;ummo &longs;u&longs;tinere conantur, non &longs;tent qui­<lb/>dem, &longs;ed digiti motu, &longs;ari&longs;&longs;æ motum &longs;equantur. </s> </p> <p type="main"> <s id="s.000368">Id certè agit, qui nutantis &longs;ari&longs;&longs;æ, digito, motum &longs;e­<lb/>quitur; vt in ip&longs;o motu digitum a&longs;&longs;iduè centro grauitatis <lb/>&longs;ari&longs;&longs;æ &longs;upponat, vnde &longs;it vt nunquam extra fulcimentum <lb/>permanens, nunquam cadat. </s> </p> <p type="main"> <s id="s.000369">Similis huic alia quoque dubitatio &longs;oluitur: Nempe, <lb/>Cur turbines, quibus pueri ludunt, dum quidem rotan­<lb/>tur, &longs;tent erecti, rotatione vero ce&longs;&longs;ante, cadant. </s> </p> <figure id="id.007.01.042.2.jpg" xlink:href="007/01/042/2.jpg"/> <p type="main"> <s id="s.000370">E&longs;to enim Turbo AB, cu­<lb/>ius grauitatis centrum C, planum <lb/>horizontis DE, linea Horizonti <lb/>perpendicularis ABC, tran&longs;iens <lb/>per centrum grauitatis C, &longs;it au­<lb/>tem fulcimentum in B. <expan abbr="Itaq;">Itaque</expan> cum <lb/>centrum grauitatis C &longs;it in ip&longs;a <lb/>perpendiculari, &longs;tabit ex demon-<pb xlink:href="007/01/043.jpg"/>&longs;tratis, at ex vitio materiæ non &longs;tabit. </s> <s id="s.000371">Modò, vt a&longs;&longs;olet, ra­<lb/>pido motu rotetur. </s> <s id="s.000372">Dico, Turbinem, motu &longs;eu rotatione <lb/>durante &longs;tare. </s> <s id="s.000373">ea autem paullatim elangue&longs;cente ín ca­<lb/>&longs;um vergere; ce&longs;&longs;ante verò penitus cadere. </s> <s id="s.000374">fit enim ex in­<lb/>æqualitate materiæ, vel operis ruditate, vel aliâ quauis <lb/>ex cau&longs;&longs;a, grauitatis centrum non e&longs;&longs;e in C, &longs;ed exempli <lb/>gratiâ vbi F, notentur autem hinc inde Turbinis latera <lb/>notis GH. <!-- KEEP S--></s> <s id="s.000375">Vtique cum F extra perpendicularem fuerit, <lb/>cadet Turbo ad partem G; at id ne &longs;iat, efficitur velocita­<lb/>te motus, quo centrum F transfertur in contrariam par­<lb/>tem, vbi I. non autem cadit ver&longs;us H, quoniam eadem ve­<lb/>locitate iterum transfertur in F, quamobrem cum huius­<lb/>cemodi centri a&longs;&longs;idua circa perpendicularem fiat trans­<lb/>latio, ad nullam partem Turbo cadere pote&longs;t; elangue­<lb/>&longs;cente verò motu rotans, paullatim incipit inclinari, do­<lb/>nec eo penitus ce&longs;&longs;ante, ad eam partem cadit, ad quam à <lb/>perpendiculari grauitatis centrum vergit. </s> <s id="s.000376">De&longs;cribit au­<lb/>tem in rotatione grauitatis centrum, quod in medio non <lb/>e&longs;t paruum circulum, per cuius centrum ip&longs;a perpendi­<lb/>cularis pertingit. </s> </p> <p type="main"> <s id="s.000377">Modò redeuntes ad libram, cuius fulcimentum e&longs;t <lb/>&longs;ur&longs;um, alio principio, nempe Mechanico, cur depre&longs;&longs;a <lb/>ad æqualitatem reuertatur, demon&longs;trabimus. </s> </p> <pb xlink:href="007/01/044.jpg"/> <figure id="id.007.01.044.1.jpg" xlink:href="007/01/044/1.jpg"/> <p type="main"> <s id="s.000378">Sit igitur, vt &longs;u­<lb/>periùs, libra AB, cu­<lb/>ius centrum grauita­<lb/>tis C, fulcimentum, <lb/>verò &longs;ur&longs;um, in D li­<lb/>bræ quidem in C per­<lb/>pendiculariter con­<lb/>iunctum. </s> <s id="s.000379">Perpendi­<lb/>cularis verò quæ per <lb/>fulcimentum, & gra­<lb/>uitatis <expan abbr="cētrum">centrum</expan> tran&longs;­<lb/>iens ad mundi cen­<lb/>trum tendit DLE. &longs;tante igitur librâ in &longs;ua æqualitate, e­<lb/>rit centrum grauitatis C in ip&longs;a perpendiculari infra qui­<lb/>dem fulcimentum D. <!-- KEEP S--></s> <s id="s.000380">Loco verò, mundi centro quàm <lb/>proximo. </s> <s id="s.000381">Pondus po&longs;t hæc apponatur in B, Declinabit au­<lb/>tem pars CB, in HF, eleuatâ interim parte AC, in GH. <lb/><!-- KEEP S--></s> <s id="s.000382">Mota igitur libra tota, circa fulcimentum D mouebitur <lb/>circa idem centrum, & grauitatis centrum C, de&longs;cribens <lb/>portionem circuli CH, fi etque; C in H, & quoniam H, hoc <lb/>e&longs;t C, extra perpendicularem fit, amoto pondere, ex lan­<lb/>ce B, cuius pre&longs;&longs;ione libra declinauerat, centrum grauita­<lb/>tis per eandem circulì portionem HC, ad perpendicula­<lb/>rem de&longs;cendet, donec iterum in ea quie&longs;cat, quo ca&longs;u li­<lb/>bra AB ad æquilibrium reuertetur: quod fuerat demon­<lb/>&longs;trandum. </s> </p> <p type="main"> <s id="s.000383">His ita declaratis, o&longs;tendemus, (quod nullus ante <lb/>nos animaduertit) harum librarum, quæ fulcimentum <lb/>habent &longs;ur&longs;um, eam e&longs;&longs;e naturam, vt non à quouis ponde­<lb/>re appo&longs;ito moueantur, vel penitus declinent. </s> </p> <p type="main"> <s id="s.000384">Ij&longs;dem enim &longs;tantibus, addatur quoduis pondus lan­<lb/>ci B; Itaque &longs;i tale fuerit quod &longs;uperet re&longs;i&longs;tentiam, quam <pb xlink:href="007/01/045.jpg"/>illi facit centrum grauitatis contra naturam elatum in H <lb/>mouebitur quædam libra. </s> <s id="s.000385">Sin autem tam parui momenti <lb/>&longs;it, vt eam re&longs;i&longs;tentiam non vincat, &longs;tante circa locum in­<lb/>fimum centro C, non mouebitur aut &longs;altem parum, ip&longs;a <lb/>libra. </s> </p> <p type="main"> <s id="s.000386">Hinc colligimus fieri po&longs;&longs;e, libras illas, quæ non "<lb/>quouis, quantumuis paruo pondere declinant, eas fulci- "<lb/>mentum habere &longs;ur&longs;um. </s> </p> <p type="main"> <s id="s.000387">His addimus, cæteris paribus, re&longs;i&longs;tentiam eò e&longs;&longs;e <lb/>maiorem, quo minus grauitatis centrum di&longs;tat à fulci­<lb/>mento &longs;ur&longs;um, circa quod ip&longs;a libra aduertitur. </s> </p> <figure id="id.007.01.045.1.jpg" xlink:href="007/01/045/1.jpg"/> <p type="main"> <s id="s.000388">E&longs;to libra AB, cuius gra­<lb/>uitatis centrum C, & primò <lb/>quidem eius fulcimentum <lb/>&longs;ur&longs;um &longs;it vbi D, itaque &longs;i ap­<lb/>po&longs;ito pondere declinauerit <lb/>libra ad partes B, punctum <lb/>C, dum a&longs;cendet de&longs;cribet <lb/>portionem circuli CE. fulciatur iterum &longs;ur&longs;um puncto F, <lb/>& iterum declinet ad partes B, & iterum punctum C, dum <lb/>a&longs;cendet, circuli portionem de&longs;cribet CG. <!-- KEEP S--></s> <s id="s.000389">E&longs;t autem <lb/>minor angulus contactus ACE, angulo ACG, magis er­<lb/>go &longs;ur&longs;um, hoc e&longs;t, ad naturam &longs;ui feretur C, per CG, ex <lb/>centro F, quàm per CE, ex centro D, quod fuerat de­<lb/>mon&longs;trandum. </s> </p> <p type="main"> <s id="s.000390">Hæc autem re&longs;i&longs;tentia ex eodem fulcimento & eo­<lb/>dem pondere eo faciliùs &longs;uperabitur, quo longius bra­<lb/>chium libræ fuerit. </s> </p> <p type="main"> <s id="s.000391">E&longs;to enim iterum libra AB, cuius fulcimentum D, <lb/>centrum grauitatis C, &longs;it & alia libra, cuius brachia bre­<lb/>uiora EF, idem habens centrum C, & eidem puncto &longs;u­<lb/>&longs;pen&longs;a D. <!-- KEEP S--></s> <s id="s.000392">Dico igitur, eodem pondere appo&longs;ito, faciliùs <pb xlink:href="007/01/046.jpg"/><figure id="id.007.01.046.1.jpg" xlink:href="007/01/046/1.jpg"/><lb/>declinaturam libram ad <lb/>partes B, quàm &longs;i idem ap­<lb/>poneretur in F. <!-- KEEP S--></s> <s id="s.000393">Demit­<lb/>tatur enim, à puncto B <lb/>horizonti perpendicula­<lb/>ris BG, & ab F item per­<lb/>pendicularis FH, Tum <lb/>iuncta DB, centro D, eo­<lb/>dem vero &longs;patio DB, circuli portio de&longs;cribatur BI, item <lb/>iuncta DF eodem centro D, &longs;patio DF, portio circuli de­<lb/>&longs;cribatu: FK. e&longs;t autem maior DB ip&longs;a DF ex propo&longs;. <lb/></s> <s id="s.000394">21. lib. 1. Elem. quare maioris circuli portio e&longs;t BI quàm <lb/>FK. <!-- KEEP S--></s> <s id="s.000395">Obliquior autem, hoc e&longs;t, à perpendiculari remotior <lb/>e&longs;t motus per FK quàm per BI. maior &longs;i quidem e&longs;t angu­<lb/>lus KFH angulo IBG. quod nos ita probamus. </s> <s id="s.000396">Ducatur <lb/>perpendicularis ip&longs;i DF linea LF contingens circulum <lb/>FK in F, item ip&longs;i DB, perpendicularis MB, contingens <lb/>circulum BI in B, & quia angulus contingentiæ maioris <lb/>circuli minor e&longs;t angulo contingentiæ minoris, erit KFL <lb/>maior IBM, Recti autem &longs;unt DFL, DBM, minor ergo <lb/>DFK re&longs;idua ip&longs;o DBI re&longs;iduo. </s> <s id="s.000397">Maior autem DFC ex <lb/>iam citata propo&longs;. </s> <s id="s.000398"><expan abbr="quã">quam</expan> DBC, erit igitur re&longs;iduum CFK, <lb/>multo minus re&longs;iduo FBI, &longs;ed recti &longs;unt CFH, FBG, ex <lb/>quibus &longs;i detrahantur CFK, FBI, erit re&longs;iduum KFH, <lb/>maius re&longs;iduo IBG, plus ergo retrahitur à perpendicula­<lb/>ri pondus de&longs;cendens per FK quàm per BI, minus igitur <lb/>præualebit re&longs;i&longs;tentiæ in C pondus appen&longs;um in F, quàm <lb/>&longs;i appendatur in B. quod fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.000399">Po&longs;&longs;umus & idem quoque aliter o&longs;tendere. </s> </p> <p type="main"> <s id="s.000400">Sint enim &longs;eor&longs;um duæ libræ, maior AB, mïnor EF, <lb/>quàm commune grauitatis centrum C, fulcimentum ve­<lb/>rò &longs;ur&longs;um D. <!-- KEEP S--></s> <s id="s.000401">Producatur perpendicularis DC, in G & fiat <lb/>CG æqualis CB, CH verò æqualis CF. <!-- KEEP S--></s> <s id="s.000402">Sunt igitur duo <pb xlink:href="007/01/047.jpg"/><figure id="id.007.01.047.1.jpg" xlink:href="007/01/047/1.jpg"/><lb/>vectes DG, DH, quo­<lb/>rum quidem commu­<lb/>ne fulcimentum D, <lb/>pondus verò C, poten­<lb/>tiæ vbi HG. <!-- KEEP S--></s> <s id="s.000403">Sunt au­<lb/>tem hi vectes eius na­<lb/>turæ, in quibus <expan abbr="pōdus">pondus</expan> <lb/>e&longs;t inter fulcimentum <lb/>& potentiam, itaque <lb/>vt &longs;e habet DC, ad <lb/>DG, ita potentia in G <lb/>ad pondus in C, item vt DC ad DH ita potentia in H ad <lb/>idem pondus C, &longs;ed minor e&longs;t propo&longs;itio DC, ad DG <lb/>quàm DC ad DH. minor ergo potentia requiritur in G, <lb/>hoc e&longs;t, in B, quàm in H, hoc e&longs;t in F. <!-- KEEP S--></s> <s id="s.000404">Data igitur ponderis <lb/>æqualitate faciliùs &longs;uperabitur re&longs;i&longs;tentia C in B, quàm <lb/>in F: quod o&longs;tendendum fuerat. </s> </p> <p type="main"> <s id="s.000405">Ad huius libræ naturam illæ quoque rediguntur, <lb/>quarum iugum non rectum quidem, &longs;ed curuum, vel ex <lb/>rectis &longs;ur&longs;um in angulum ad fulcimentum detinentibus, <lb/>nec refert vtrum curuitas &longs;it circuli portio quælibet, aut <lb/>ellip&longs;is &longs;ecundum alterum diametrorum; quod ita de­<lb/>mon&longs;tramus. </s> </p> <figure id="id.007.01.047.2.jpg" xlink:href="007/01/047/2.jpg"/> <p type="main"> <s id="s.000406">E&longs;to libra, cuius iugum <lb/>curuum <expan abbr="angulatūue">angulatumue</expan> ABC, <lb/>cuius fulcimentum B, æqua­<lb/>lia autem brachia AB, BC, <lb/>& pondera item <expan abbr="vtrinq;">vtrinque</expan> ap­<lb/>pen&longs;a æqualia. </s> <s id="s.000407">Demittatur <lb/>ex puncto B ad mundi cen­<lb/>trum perpendicularis BD. <lb/><!-- KEEP S--></s> <s id="s.000408">Stante igitur libra ABC in <lb/>æquilibrio, erit eius graui­<pb xlink:href="007/01/048.jpg"/>tatis centrum in ip&longs;a perpendiculari BD, puta in E. <!-- KEEP S--></s> <s id="s.000409">Ap­<lb/>ponatur pondus in C, declinabit autem libra, &longs;it autem <lb/>iuxta po&longs;itionem FBG. <!-- KEEP S--></s> <s id="s.000410">Centrum igitur grauitatis E per <lb/>portionem EH, erit in H. <!-- KEEP S--></s> <s id="s.000411">A&longs;cendit ergo centrum graui­<lb/>tatis in H, hoc e&longs;t, &longs;ur&longs;um, id e&longs;t, contra eius naturam; a­<lb/>moto igitur pondere ex C, grauitatis centrum extra per­<lb/>pendicularem con&longs;titutum rur&longs;us de&longs;cendet, & iterum <lb/>libra ABC ad æquilibrium reuertetur. </s> <s id="s.000412">Hoc idem egre­<lb/>giè o&longs;tendit G. Vbald. <!-- REMOVE S-->in tractatu de libra, propo&longs;. 4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000413">Hinc ratio pendet earum imaguncularum, quas ex <lb/>contu&longs;a papyro ligneaue leui materia compingunt, per­<lb/>queue manus earum ambas, ferreum filum trajicientes, v­<lb/>trinque plumbea appendunt pondera æqualia, ea <expan abbr="quidē">quidem</expan> <lb/>lege, vt centrum grauitatis infra pedes imaguncula &longs;ta­<lb/>tuatur. </s> <s id="s.000414">Tunc enim exten&longs;o filo imponentes ceu funam­<lb/>bulos per illud, vltrò citroque; decurrere faciunt, imagun­<lb/>cula interim erecta & in neutram partem cadente, quod <lb/>vt figurâ clarius fiat; </s> </p> <figure id="id.007.01.048.1.jpg" xlink:href="007/01/048/1.jpg"/> <p type="main"> <s id="s.000415">E&longs;to imaguncu­<lb/>la AB, per cuius ma­<lb/>nus traijciatur filum <lb/>ferreum curuum <expan abbr="cū">cum</expan> <lb/>æ qualibus ponderi­<lb/>bus hinc inde <expan abbr="appē-&longs;is">appen­<lb/>&longs;is</expan> CD. <!-- KEEP S--></s> <s id="s.000416">Nitatur au­<lb/>tem pedibus filo HI <lb/>in <emph type="italics"/>B<emph.end type="italics"/>, &longs;itque; totìus ma­<lb/>chinæ grauitatis <expan abbr="cē-trum">cen­<lb/>trum</expan> E, &longs;itque <expan abbr="per-pēdicularis">per­<lb/>pendicularis</expan> per gra­<lb/>uitatis <expan abbr="centrū">centrum</expan> tran&longs;i­<lb/>ens A<emph type="italics"/>B<emph.end type="italics"/> E. <!-- KEEP S--></s> <s id="s.000417">Itaque in­<lb/>clinata imaguncula, & conuer&longs;a circa punctum <emph type="italics"/>B<emph.end type="italics"/>, &longs;i de-<pb xlink:href="007/01/049.jpg"/>clinet ad partes I, centrum grauitatis eleuabitur in F. <!-- KEEP S--></s> <s id="s.000418">Si <lb/>verò ad partes H eleuabitur in G. quare cum FG loca <lb/>&longs;int remotiora à mundi centro, quàm &longs;it E, non &longs;tabit gra­<lb/>uitatis centrum in punctis FG, &longs;ed ad infimum locum re­<lb/>uertetur, hoc e&longs;t, in ip&longs;a perpendiculari in E, & imagun­<lb/>cula ad perpendiculum ip&longs;i H<emph type="italics"/>B<emph.end type="italics"/>E filo, hoc e&longs;t, ip&longs;i hori­<lb/>zonti reuertetur. </s> </p> <p type="main"> <s id="s.000419">Hinc etiam Arictum, Te&longs;tudinumqueue demolito­<lb/>riarum Machinarum vis pendet, nempe ex ratione libra­<lb/>rum, quæ fulcimentum habent &longs;ur&longs;um. </s> </p> <figure id="id.007.01.049.1.jpg" xlink:href="007/01/049/1.jpg"/> <p type="main"> <s id="s.000420">E&longs;to enim Aries A<emph type="italics"/>B<emph.end type="italics"/> <lb/>funi appen&longs;us CD, cu­<lb/>ius grauitatis centrum, <lb/>D, perpendicularis verò <lb/>quæ ad mundi centrum <lb/>ip&longs;a CDE. <!-- KEEP S--></s> <s id="s.000421">Stante igitur <lb/>in æquilibrio machina, <lb/>centrum grauitatis erit <lb/>in ip&longs;a perpendiculari. <lb/></s> <s id="s.000422">Applicetur alicubi po­<lb/>tentia retropellens, eleuabitur igitur centrum grauitatis <lb/>per circuli portionem DF, cuius &longs;emidiameter e&longs;t CD, <lb/>&longs;i etqueue iuxta po&longs;itionem CF. <!-- KEEP S--></s> <s id="s.000423">Aries verò in GFH. </s> <s id="s.000424">Di­<lb/>mi&longs;&longs;a itaque Machina centrum F vtpote graue, non &longs;tabit, <lb/>&longs;ed &longs;uapte naturâ reuertetur in D. <!-- KEEP S--></s> <s id="s.000425">Quadruplici autem <lb/>de cau&longs;&longs;a motus Arietis violenti&longs;&longs;imus e&longs;t ex vi naturalis <lb/>ponderis, quo deor&longs;um fertur, tum velocitate naturalis <lb/>motus in de&longs;cendendo auctæ, tum ex vi potentiæ impel­<lb/>lentis, & naturalem motum adiuuantis, tum ex velocita­<lb/>te ex motu violento deor&longs;um & antror&longs;um impellente <lb/>acqui&longs;itâ. </s> <s id="s.000426">Id etiam addimus, eo validiores fore ictus, quò <lb/>grauior fuerit Machina, & maius &longs;patium, quo retrotra­<pb xlink:href="007/01/050.jpg"/>hitur, grauitate ip&longs;a & &longs;patio tum virium vnione opera­<lb/>tionem mirum in modum adiuuantibus. </s> </p> <p type="main"> <s id="s.000427">Hæc nos de Libra &longs;ur&longs;um fulcimentum habente, dí­<lb/>cta voluimus, nunc de ea, cuius fulcimentum deor&longs;um, <lb/>e&longs;t, verba faciemus. </s> </p> <p type="head"> <s id="s.000428">Altera quæ&longs;tionis pars:</s> </p> <p type="head"> <s id="s.000429"><emph type="italics"/>De Libra cuius fulcimentum deor&longs;um e&longs;t.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000430">Si deor&longs;um fuerit, inquit Ari&longs;toteles, id quod &longs;ub­<lb/>&longs;tat, contrarium facit illi quæ &longs;ur&longs;um habet, nempe ad æ­<lb/>quilibrium non reuertitur. </s> <s id="s.000431">Plus enim, ait, dimidio fit li­<lb/>bræ, quæ deor&longs;um e&longs;t pars, quàm quod perpendiculum <lb/>&longs;ecet, quapropter non a&longs;cendit. </s> <s id="s.000432">eleuata enim pars leuior <lb/>e&longs;t. </s> </p> <p type="main"> <s id="s.000433">Hæc ille, qui &longs;chemate quoque rem aperit, at eo a­<lb/>pud interpretes, & Picolomineum Paraphra&longs;tem, ita <expan abbr="mē-dosè">men­<lb/>dosè</expan> lineato, vt inde ob&longs;curitas lucis loco, legentibus of­<lb/>fundatur. </s> <s id="s.000434">Nos, quod & &longs;uprà quoque fecimus, no&longs;tra fi­<lb/>gurâ, &longs;ole ip&longs;o clariorem, ex Ari&longs;to telis ip&longs;ius mente rem <lb/>totam efficiemus. </s> </p> <figure id="id.007.01.050.1.jpg" xlink:href="007/01/050/1.jpg"/> <p type="main"> <s id="s.000435">Sit libra recta, (hoc <lb/>e&longs;t, in æquilibrio con­<lb/>&longs;tituta) vbi NG. </s> <s id="s.000436">Per­<lb/>pendiculum autem (id <lb/>e&longs;t, perpendicularis <lb/>quæ ad mundi <expan abbr="centrū">centrum</expan>) <lb/>KLM. </s> <s id="s.000437">Bifariam igitur <lb/>&longs;ecatur NG. impo&longs;ito <lb/>po&longs;thæc onere in ip&longs;o <lb/>N, erit quidem N, vbi <lb/>O. ip&longs;um autem G vbi <lb/>R. KL autem vbi LP. <pb xlink:href="007/01/051.jpg"/>quare maius e&longs;t KO, quam LR, ip&longs;a parte PKL. </s> <s id="s.000438">Amoto <lb/>igitur onere nece&longs;&longs;e e&longs;t manere. </s> <s id="s.000439">Incumbit enim onus ex­<lb/>ce&longs;&longs;us medietatis eius, vbi e&longs;t F. <!-- KEEP S--></s> <s id="s.000440">Sen&longs;us e&longs;t igitur, idcirco <lb/>partem iugi KLO inclinatam, ad æquilibrium non re­<lb/>uerti, propterea quòd maior &longs;it ip&longs;a KLO pars quæ tra­<lb/>hit, ip&longs;a RKL, quæ trahitur & eleuatur. </s> </p> <figure id="id.007.01.051.1.jpg" xlink:href="007/01/051/1.jpg"/> <p type="main"> <s id="s.000441">Pote&longs;t hoc idem longè <lb/>&longs;impliciori themate demon­<lb/>&longs;trari. </s> <s id="s.000442">E&longs;to enim libra AB, <lb/>cuius centrum C, fulcimen­<lb/>tum vero deor&longs;um D, Per­<lb/>pendicularis per centrum & <lb/>fulcimentum tran&longs;iens EF. <lb/><!-- KEEP S--></s> <s id="s.000443">Apponatur pondus in B, de­<lb/>clinabitque; puta ad GH, cen­<lb/>trum verò C, ex &longs;tabili fulci­<lb/>mento D, circuli portionem de&longs;cribet CI, libra autem <lb/>&longs;ecabit EF perpendicularem in K. Æquales autem &longs;unt <lb/>IG, IH, at ex parte HI de&longs;umpta e&longs;t KI, addita queue ip&longs;i <lb/>IG, maior e&longs;t ergo tota KG, torâ KH. </s> <s id="s.000444">Non igitur KH <lb/>habet KG, &longs;ed libra, ni&longs;i impedita fuerit, cum centro C <lb/>de&longs;cendente per I in M, ad ip&longs;am perpendicularem dela­<lb/>ta, ad in feriorem partem, mutatis vicibus quie&longs;cet, facto <lb/>nempe fulcimento &longs;ur&longs;um, fietque; horizonti æque di&longs;tans <lb/>iuxta po&longs;itionem LMN. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000445">Demon&longs;tratio <expan abbr="quidē">quidem</expan> e&longs;t hæc, &longs;ed non ex proprijs prin­<lb/>cipijs Mechanicis, <expan abbr="nēpe">nempe</expan> ex ratione <expan abbr="cēt">cent</expan>ri grauitatis petitâ. <lb/></s> <s id="s.000446">Ii&longs;dem enim &longs;tantibus, <expan abbr="cū">cum</expan> centrum grauitatis C fiat extra <lb/>perpendicularem, de&longs;cendens ad I, nunquam reuertetur <lb/>in C, a&longs;cenderet enim; &longs;ed &longs;i liberè circa centrum D con­<lb/>uerteretur, de&longs;cendens vt dictum e&longs;t per circulum CIM <lb/>pondus B, fieret in L, A vero in N adepta po&longs;itione <lb/>LMN. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/052.jpg"/> <p type="main"> <s id="s.000447">Cur autem huius libræ, quæ aliàs inutilis e&longs;t, memi­<lb/>nerit Philo&longs;ophus, ea videtur cau&longs;&longs;a, quòd inde vectis vir­<lb/>tutem eliciat, vt &longs;uo loco videbimus. </s> <s id="s.000448">Id autem valde mi­<lb/>rum, hominem acuti&longs;&longs;imum nihil pror&longs;us de ea libra egi&longs;­<lb/>&longs;e, quæ fulcimentum nec &longs;ur&longs;um habet, nec deor&longs;um, &longs;ed <lb/>in ip&longs;o exqui&longs;itè medio, ita vt centrum grauitatis in ip&longs;o­<lb/>met fulcimento con&longs;i&longs;tat. </s> <s id="s.000449">Nos igitur de hac quod operæ <lb/>pretium fuerit, & ad rem, qua de agimus, vtile, in medium <lb/>proferemus. </s> </p> <p type="head"> <s id="s.000450"><emph type="italics"/>De libra cuius fulcimentum est in medio.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000451">Dicimus itaque, libram, cuius fulcimentum nec &longs;ur­<lb/>&longs;um e&longs;t, nec deor&longs;um, &longs;ed pror&longs;us in medio, nempe in ip&longs;o <lb/>grauitatis centro, vbi brachia & pondera vtrinque appo­<lb/>&longs;ita fuerint æqualia, &longs;i ab æquilibrio mouentur, quomo­<lb/>docunque po&longs;ita, &longs;tare nec ab eo, quem adepta e&longs;t, &longs;itu di­<lb/>moueri. </s> </p> <p type="main"> <s id="s.000452">Quæ&longs;tionem hanc perperam tractârunt recentio­<lb/>res quidam, Hieron. <!-- REMOVE S-->Cardanus, Nicolaus Tartalea, & alij <lb/>nonnulli, qui Iordani Nemoracij a&longs;&longs;ertiones &longs;unt &longs;ecuti, <lb/>quorum demon&longs;trationes vel paralogi&longs;mos potiùs egre­<lb/>giè confutauit in libr. </s> <s id="s.000453">Mechanicor. <!-- REMOVE S-->Tractatu de libra pro­<lb/>po&longs;. </s> <s id="s.000454">4. Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->ad cuius probati&longs;&longs;ima &longs;cripta Lecto­<lb/>rem ablegamus. </s> <s id="s.000455">fu&longs;i&longs;&longs;imè enim ibi hac de re & ab&longs;oluti&longs;&longs;i­<lb/>mè agit. </s> <s id="s.000456">Nos autem quidem paucis ea, quæ ad hanc co­<lb/>gnitionem pertinent, explicabimus. </s> </p> <figure id="id.007.01.052.1.jpg" xlink:href="007/01/052/1.jpg"/> <p type="main"> <s id="s.000457">E&longs;to enim libra A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius brachia æqualia, <lb/>& centrum grauitatis <lb/>in C, brachijs verò <lb/>AC, C<emph type="italics"/>B<emph.end type="italics"/> æqualibus, æ­<lb/>qualia pondera hinc <lb/>inde <expan abbr="apponãtur">apponantur</expan>. </s> <s id="s.000458">Tum <pb xlink:href="007/01/053.jpg"/>fulcimento in medio, hoc e&longs;t, vbi grauitatis centrum C <lb/>applicato per centrum ip&longs;um C ducatur perpendicularis, <lb/>quæ ad mundi centrum, DCE, &longs;itque primum libra æ­<lb/>quedi&longs;tans horizonti, con&longs;tituta. </s> <s id="s.000459">Tum ex altera parte <lb/>pre&longs;&longs;a moueatur & fiat iuxta po&longs;itionem FCG. <!-- KEEP S--></s> <s id="s.000460">Dico eam <lb/>dimi&longs;&longs;am permanere, etenim cum grauitatis centrum &longs;it <lb/>in ip&longs;a perpendiculari, in neutram partem verget, &longs;ed nec <lb/>vergere pote&longs;t, quippe quod non circa fulcimentum ceu <lb/>centrum motus, moueatur grauitatis centrum, &longs;ed in ip&longs;o <lb/>&longs;it fulcimento; &longs;itum ergo non mutat. </s> <s id="s.000461">Præterea cum per­<lb/>pendicularis DCE per grauitatis centrum ducatur, cor­<lb/>pus ip&longs;um ex ponderibus & libra con&longs;tans ab ea in partes <lb/>çque ponderantes &longs;ecatur, & ideo ex centri grauitatis dif­<lb/>finitione, quam protulit Pappus, corpus ip&longs;um centro <lb/>grauitatis appen&longs;um, dum fertur quie&longs;cit, & &longs;eruat eam, <lb/>quam à principio habuit po&longs;itione. </s> <s id="s.000462">Et &longs;anè &longs;i partes quo­<lb/>modo libet librâ per grauitatis centrum diuisâ, &longs;unt æ­<lb/>queponderantes nec trahent inuicem, nec trahentur, &longs;ta­<lb/>bit ergo libra, & quam adepta fuerat po&longs;itionem, eam &longs;er­<lb/>uabit. </s> <s id="s.000463">Id tamen non negamus, difficile e&longs;&longs;e libras eiu&longs;ce­<lb/>modi ex materia fabricare, quippe quod non omnia quæ <lb/>vera &longs;unt, & euidenti&longs;&longs;imis demon&longs;trationibus patent, <lb/>commodè ad praxim, ex artis & materiæ imperfectione, <lb/>reducuntur. </s> </p> <p type="main"> <s id="s.000464">Cæterùm harum librarum ea e&longs;t virtus, vt vel mini­<lb/>mo pondere altrin&longs;ecus appo&longs;ito, declinet; quod illis quæ <lb/>centrum &longs;ur&longs;um habent, non euenire, demon&longs;trauimus. </s> </p> <p type="main"> <s id="s.000465">Circa hæc po&longs;&longs;et cuipiam oriri Dubium, num chor­<lb/>dulæ, quibus lances appenduntur, variationem aliquam <lb/>circa ea quæ demon&longs;trata &longs;unt, inducere valeant. </s> </p> <p type="main"> <s id="s.000466">Dicimus nullam inde fieri: E&longs;to enim libra AB, cu­<lb/>ius centrum & fulcimentum C, ab cuius extremitate A <lb/>dependeat, funiculus AD, ab alia verò <emph type="italics"/>B<emph.end type="italics"/>, funiculus <emph type="italics"/>B<emph.end type="italics"/>E, <pb xlink:href="007/01/054.jpg"/><figure id="id.007.01.054.1.jpg" xlink:href="007/01/054/1.jpg"/><lb/>quibus appen&longs;æ &longs;int æ­<lb/>qualis ponderis lances <lb/>DE. <!-- KEEP S--></s> <s id="s.000467">Moueatur libra, <lb/>fiatque in ICH, funi­<lb/>culi verò in lancibus in <lb/>IK, HL. &longs;ecet autem fu­<lb/>niculus IK libram A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>in M, LH verò produ­<lb/>catur & eandem &longs;ecer <lb/>in N. quoniam igitur <lb/>IC, æqualis e&longs;t CH, pa­<lb/>rallelæ autem KI, LN æquales <expan abbr="erūt">erunt</expan> alterni anguli MIC, <lb/>NHC, &longs;ed & anguli ad verticem ICH, BCH æquales <lb/>&longs;unt, quare triangulum IMC, æquale triangulo HNC, <lb/>& latera lateribus, quæ æqualibus angulis &longs;ubtenduntur. <lb/></s> <s id="s.000468">Æqualis e&longs;t igitur linea MC lineæ NC. </s> <s id="s.000469">Itaque &longs;i ponde­<lb/>ra lancesue, KL mente concipiantur appen&longs;æ in punctis <lb/>MN, ex brachiorum & ponderum æqualitate æquepon­<lb/>derabunt. </s> <s id="s.000470">quod fuerat demon&longs;trandum. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000471">QVÆSTIO III.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000472"><emph type="italics"/>Cur exiguæ vires (quod etiam à principio dixerat) vecte magna <lb/>mouent pondera, vectes in&longs;uper onus accipientes, cum facilius <lb/>&longs;it, minorem mouere grauitatem, minor est au­<lb/>tem &longs;ine vecte?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000473">Ari&longs;toteles ita quæ&longs;tionem proponit, vt eam Rheto­<lb/>rico quodam fuco admirabiliorem faciat. </s> <s id="s.000474">Soluit au­<lb/>tem hoc pacto, <expan abbr="inquiēs">inquiens</expan>, fieri po&longs;&longs;e eam e&longs;&longs;e cau&longs;&longs;am, quod <lb/>vectis &longs;it libra, eius nempe generis quod fulcimentum ha­<lb/>bet deor&longs;um, atque id circo in ip&longs;a pre&longs;&longs;ione in partes in­<lb/>æquales vectem diuidi. </s> </p> <pb xlink:href="007/01/055.jpg"/> <figure id="id.007.01.055.1.jpg" xlink:href="007/01/055/1.jpg"/> <p type="main"> <s id="s.000475">Figura quam ex­<lb/>hibet, vix ferè quid &longs;i­<lb/>bi velit explicat. </s> <s id="s.000476">Nos <lb/>ad eius <expan abbr="mētem">mentem</expan> aliam <lb/>proponemus <expan abbr="eamq;">eamque</expan> <lb/>longè clariorem. </s> </p> <p type="main"> <s id="s.000477">E&longs;to vectis A<emph type="italics"/>B<emph.end type="italics"/>, <lb/>cuius fulcimentum, <lb/>deor&longs;um in C, pon­<lb/>dus D, potentia ex vecte, pondus &longs;u&longs;tinens E. <!-- KEEP S--></s> <s id="s.000478">Perpendi­<lb/>cularis per fulcimentum FCG. <!-- KEEP S--></s> <s id="s.000479">Itaque quoniam poten­<lb/>tia in E non &longs;uperat pondus D, nec ab eo &longs;uperatur, &longs;tat <lb/>vectis cum potentia Horizonti æquidi&longs;tans, hoc e&longs;t, in æ­<lb/>quilibrio, vectis autem in puncto C diuiditur in partes æ­<lb/>queponderantes. </s> <s id="s.000480">Modo præualeat potentia ponderi, & <lb/>vectem deprimat, fiat autem in LCH, erit igitur <emph type="italics"/>B<emph.end type="italics"/>, in L, <lb/>A in H, D in K, & CF, quæ vectem in partes æque ponde­<lb/>rantes diuidebat, in CI. <!-- KEEP S--></s> <s id="s.000481">Iam igitur non æqueponderant <lb/>partes, &longs;i quidem pars vectis FCI, aufertur parti HCI, & <lb/>adiungitur parti ICL, quæ ideo &longs;it pondero&longs;ior, vnde & <lb/>potentia ad ponderis eleuationem adiuuatur. </s> <s id="s.000482">Eadem i­<lb/>gitur vtitur hic demon&longs;tratione, quam in explicando ef­<lb/>fectu libræ, cuius fulcimentum deor&longs;um e&longs;t, adhibuerat. <lb/></s> <s id="s.000483">Nec alia de cau&longs;&longs;a, vt &longs;uprà notauimus, videtur eius libræ <lb/>in &longs;uperiori quæ&longs;tione, con&longs;iderationem introduxi&longs;&longs;e. </s> <s id="s.000484">Et <lb/>&longs;anè verum e&longs;t quod concludit, Veruntamen minimi e&longs;t <lb/>momenti ad tantam vim parua illa adiectio, quæ parti ve­<lb/>ctis depre&longs;&longs;æ in ip&longs;a depre&longs;&longs;ione adiungitur. </s> <s id="s.000485">Aliunde igi­<lb/>tur tantæ rei cau&longs;&longs;a e&longs;t petenda, quod & nos deinceps fa­<lb/>ciemus. </s> <s id="s.000486">Videtur autem ip&longs;e quoque Ari&longs;toteles non &longs;ibi <lb/>pror&longs;us in a&longs;&longs;ignata ratione &longs;atis feci&longs;&longs;e, & ideo &longs;ubiungit: <lb/>quoniam ab æquali pondere celerius mouetur maior ca­<lb/>rum quæ à centro &longs;unt duo verò pondera; quod mouet & <pb xlink:href="007/01/056.jpg"/>quod mouetur, quod igitur motum pondus ad mouens <lb/>longitudo patitur ad longitudinem, &longs;emper autem <expan abbr="quã-tum">quan­<lb/>tum</expan> ab hypomochlio (id e&longs;t, fulcimento) di&longs;tabit magis, <lb/>tanto facilius mouebit. </s> <s id="s.000487">Cau&longs;&longs;a autem est, quæ retro com­<lb/>memorata e&longs;t, quoniam quæ plus à centro di&longs;tat <expan abbr="maiorē">maiorem</expan> <lb/>de&longs;cribit circulum. </s> <s id="s.000488">quare ab eadem potentia plus &longs;upera­<lb/>bitur id quod mouetur, quæ plus à fulcimento di&longs;tat. </s> <s id="s.000489">H&ucedil;c <lb/>ille, qui a&longs;&longs;erit duo pondera in vecte con&longs;iderari, Pondus <lb/>nempe motum, & mouentem Potentiam (hanc enim <expan abbr="pō-deris">pon­<lb/>deris</expan> habere vim <expan abbr="atq;">atque</expan> rationem certum e&longs;t) Vires autem <lb/>potentiam acquirere ex brachij longitudine, & ex inde <lb/>con&longs;equenti velocitate, quo enim brachia longiora, eo <lb/>in extremitate velociora, atque idcirco ita &longs;e habere mo­<lb/>tum pondus ad potentiam mouentem, vt brachij longi­<lb/>tudo ad brachij longitudinem: brachia autem vocamus, <lb/>partes illas vectis, quæ à fulcimento ad vtranque vectis <lb/>extremitatem pertingunt, & ideo quantum à fulcimento <lb/>potentia di&longs;tabit magis, eo faciliùs pondus mouebit. </s> </p> <p type="main"> <s id="s.000490">Vera vtique & explorati&longs;&longs;ima hæc a&longs;&longs;ertio e&longs;t. </s> <s id="s.000491">Ve­<lb/>runtamen, cau&longs;&longs;am huiu&longs;ce mirabilis effectus, e&longs;&longs;e velo­<lb/>citatem, quæ brachij longitudinem con&longs;equitur, non af­<lb/>firmamus. </s> <s id="s.000492">quæ enim velocitas in re &longs;tante? </s> <s id="s.000493">Stant autem <lb/>vectis, & libra dum manent in æquilibrio, & nihilo &longs;ecius <lb/>parua potentia ingens &longs;u&longs;tinet pondus. </s> </p> <p type="main"> <s id="s.000494">Dicet ad hæc qui&longs;piam, velocitatem in longiori bra­<lb/>chio &longs;i non actu, &longs;altem potentiâ e&longs;&longs;e maiorem. </s> <s id="s.000495">At quæ&longs;o <lb/>quid in re quæ e&longs;t actu, momenti habet potentia? </s> <s id="s.000496">actu e­<lb/>nim &longs;u&longs;tinet, &longs;u&longs;tinens. </s> <s id="s.000497">Con&longs;equìtur, (id vtique fatemur) <lb/>nece&longs;&longs;ariò velocitas maior motu brachij maioris; non ta­<lb/>men cau&longs;&longs;a e&longs;t cur vis loco vbi velocitas maior &longs;it, appo&longs;i­<lb/>ta magis moueat. </s> <s id="s.000498">Sanè ex velocitate, dum mouentur, <expan abbr="pō-dus">pon­<lb/>dus</expan> acquirere corpora, tum proiecta, tum cadentia cer­<lb/>tum e&longs;t, quod etiam in quæ&longs;tione 19. cum Philo&longs;opho <expan abbr="cō-">con-</expan><pb xlink:href="007/01/057.jpg"/>&longs;iderabimus. </s> <s id="s.000499">Sed hoc ex velocitate & motu &longs;it, quæ &longs;unt <lb/>actu. </s> <s id="s.000500">At brachia in ip&longs;o æquilibrio &longs;u&longs;tinent actu quidem, <lb/>&longs;ed non mouentur. </s> <s id="s.000501">Cæterum videtur Ari&longs;toteles id &longs;ub­<lb/>odora&longs;&longs;e, quod po&longs;tea Archimedes, Mechanicorum prin­<lb/>ceps, in propo&longs;. </s> <s id="s.000502">6. primi Æqueponderantium explicitè <lb/>protulit & probauit: nempe in æquilibrio ita e&longs;&longs;e pondus <lb/>ad pondus, vt brachium ad brachium, ratione permutata. </s> </p> <figure id="id.007.01.057.1.jpg" xlink:href="007/01/057/1.jpg"/> <p type="main"> <s id="s.000503">E&longs;to enim vectis <lb/>AB, quomodolibet <lb/>fulcimento diui&longs;us in <lb/>C. <expan abbr="appēdatur">appendatur</expan> autem <lb/>in A, pondus D, in B <lb/>verò pondus E, ita &longs;e <lb/>habens ad pondus D, vt ip&longs;a AC ad CB. <!-- KEEP S--></s> <s id="s.000504">Stabit igitur ve­<lb/>ctis, & neutram in partem verget, erit enim centrum gra­<lb/>uitatis in C, diui&longs;o nempe ibi vecte in partes æque ponde­<lb/>rantes. </s> <s id="s.000505">Hoc po&longs;t Archimedem, & in&longs;ignes illos veteres <lb/>Mechanicos præclari&longs;&longs;imè demon&longs;trauit G. <!-- REMOVE S-->Vbaldus in <lb/>Mechanicis, Tractatu de Libra propo&longs;. </s> <s id="s.000506">6. nec non de Ve­<lb/>cte propo&longs;. </s> <s id="s.000507">4. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000508">Cæterùm vt aliquid interim, quod no&longs;trum &longs;it, affe­<lb/>ramus, liceat nobis egregios illos viros interrogare, quæ­<lb/>nam mirabilis eius effectionis &longs;it cau&longs;&longs;a? </s> <s id="s.000509">Dicent permu­<lb/>tatam proportionem. </s> <s id="s.000510">Teneo, at nondum acquie&longs;co: pe­<lb/>tam enim, Cur ea rationis permutatio mirabilem illum <lb/>effectum pariat. </s> <s id="s.000511">Hoc quod illi non docent, puto nos, i­<lb/>gnorantiæ &longs;omno &longs;epultos, &longs;omnia&longs;&longs;e. </s> </p> <figure id="id.007.01.057.2.jpg" xlink:href="007/01/057/2.jpg"/> <p type="main"> <s id="s.000512">Æqualitatem &longs;tatus <lb/>e&longs;&longs;e cau&longs;&longs;am, nemo, vt <lb/>puto, inficiabitur. </s> <s id="s.000513">res e&longs;t <lb/>enim per &longs;e clara. </s> <s id="s.000514">E&longs;to &longs;i­<lb/>quidem linea quæpiam AB, applicetur extremitati A po­<pb xlink:href="007/01/058.jpg"/>tentia quædam quæ lineam ad &longs;e trahat ad partes nempe <lb/>A, Tum in B quædam alia potentia ip&longs;i quæ in A potentiae, <lb/>æqualis, quæ lineam trahat &longs;imili modo ad partes B. <!-- KEEP S--></s> <s id="s.000515">Datâ <lb/>igitur harum potentiarum æqualitate, linea AB, nec ad <lb/>partes A, nec ad partes B transferetur, &longs;ed pror&longs;us immo­<lb/>bilis &longs;tabit. </s> </p> <p type="main"> <s id="s.000516">His ita con&longs;titutis, Dico vecte quomodolibet diui&longs;o, <lb/>ponderibu&longs;que vtrinque appo&longs;itis, permutatâ propor­<lb/>tione &longs;ibi inuicem re&longs;pondentibus, rem e&longs;&longs;e redactam ad <lb/>æqualitatem, & inde &longs;tatum fieri, hoc e&longs;t, æquilibrium. </s> </p> <figure id="id.007.01.058.1.jpg" xlink:href="007/01/058/1.jpg"/> <p type="main"> <s id="s.000517">E&longs;to enim vectis AB, quo modo libet diui&longs;us in C, & <lb/>ip&longs;i quidem C fulcimentum &longs;upponatur. </s> <s id="s.000518">Appendantur <lb/>quoque vtrinque pondera ex ratione brachiorum AC, <lb/>CB, &longs;ibi inuicem permutatim re&longs;pondentia, &longs;intque; DE. <lb/><!-- KEEP S--></s> <s id="s.000519">Dico vectem ex æqualitate, in neutram partem <expan abbr="inclina-turū">inclina­<lb/>turum</expan>, &longs;ed perman&longs;urum in æquilibrio. </s> <s id="s.000520">quoniam enim <expan abbr="Pō-dus">Pon­<lb/>dus</expan> D idem pote&longs;t quod brachium CB, addatur in dire­<lb/>ctum ip&longs;i AC, recta AF æqualis ip&longs;i CB, item quoniam <lb/>Pondus E id pote&longs;t quod brachium AC, rectæ CB ad­<lb/>datur in directum BG, ip&longs;i AC æqualis. </s> <s id="s.000521">Igitur cum par­<lb/>tes CA, AF totius FC, æquales &longs;int partibus CB, BG, <lb/>totius CG, erit totum FC, toti CG æquale. </s> <s id="s.000522">Diui&longs;us ita-<pb xlink:href="007/01/059.jpg"/>que erit vectis FG in partes æquales FC, CG in puncto <lb/>fulcimenti C. <!-- KEEP S--></s> <s id="s.000523">Et quoniam æquale in æquale non agit, <lb/>&longs;tabit vectis & in neutram partem inclinabit. </s> <s id="s.000524">Rur&longs;um <lb/>quoniam ad partem FC, duæ &longs;unt brachiorum potentiæ <lb/>FA, HC, appendantur puncto F, duo pondera H, I, ip&longs;is <lb/>DE æqualia, item puncto G, alia duo pondera ij&longs;dem DE <lb/>æqualia KL, iterum æqueponderabit, quippe quod æ­<lb/>qualibus brachijs FCCG æqualia appen&longs;a &longs;int pondera <lb/>HI KL. <!-- KEEP S--></s> <s id="s.000525">Cur igitur &longs;eruata permutatim brachiorum & <lb/>ponderum proportione fiat æquilibrium, ex his quæ de­<lb/>mon&longs;trauimus, clarè patet. </s> </p> <p type="main"> <s id="s.000526">Sed forte dicet qui&longs;piam, &longs;i brachia, pondera &longs;unt, <lb/>vel ponderibus æquipollentia, &longs;u&longs;tinenti duplicabitur <lb/>pondus. </s> </p> <figure id="id.007.01.059.1.jpg" xlink:href="007/01/059/1.jpg"/> <p type="main"> <s id="s.000527">E&longs;to enim vectis AB, <lb/>ita diui&longs;us in C, vt pars <lb/>maior CB minori AC &longs;it <lb/>in proportione quintu­<lb/>pla. </s> <s id="s.000528">Appendatur autem <lb/>in A pondus D, <expan abbr="quintuplū">quintuplum</expan> <lb/>ponderi E appen&longs;o in B. <!-- KEEP S--></s> <s id="s.000529">Si <lb/>igitur brachio AC, quod <lb/>e&longs;t vnum, ad datur pondus <lb/>D, quod e&longs;t quinque, fient &longs;ex, item &longs;i brachio CB, quod <lb/>e&longs;t quinque, addatur pondus E, quod e&longs;t vnum, fient &longs;ex. <lb/></s> <s id="s.000530">Fulcimentum igitur &longs;u&longs;tinebit duodecim, quod e&longs;t ab­<lb/>&longs;urdum ex ijs quæ clarè demon&longs;trauit G. Vbald. <!-- REMOVE S-->in Me­<lb/>chan. <!-- REMOVE S-->tractatu de Libra propo&longs;. </s> <s id="s.000531">5. His re&longs;pondemus, bra­<lb/>chia quidem operari non pondere, &longs;ed potentiâ, quæ vis <lb/>quædam e&longs;t, non autem pondus. </s> <s id="s.000532">Et&longs;i & illud verum &longs;it, da­<lb/>to vecte pondero&longs;o, fulcimentum rum ponderum appen­<lb/>&longs;orum, tum vectis ip&longs;ius pondus &longs;u&longs;tinere. </s> </p> <p type="main"> <s id="s.000533">Iacta huiu&longs;cemodi, quam diximus, æqualitate, &longs;e-<pb xlink:href="007/01/060.jpg"/>quitur nece&longs;&longs;ariò, centrum grauitatis ip&longs;ius vectis cum <lb/>appen&longs;is ponderibus, ac &longs;i vnum idemqueue e&longs;&longs;et corpus <lb/>cadere in perpendiculari quæ per centrum ip&longs;um & ful­<lb/>cimentum tran&longs;iens ad mundi centrum pertingit. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000534">QVÆSTIO IV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000535"><emph type="italics"/>Quærit hic Ari&longs;toteles, cur ij qui in nauis medio &longs;unt remiges ma­<lb/>ximè nauem moueant?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000536">Ait, ideo forta&longs;&longs;e fieri, quòd remus vectis &longs;it, fulcimen­<lb/>tum verò &longs;calmus, &longs;tat enim. </s> <s id="s.000537">Pondus autem mare i­<lb/>p&longs;um, quod à remo propellitur, mouens verò ip&longs;um remi­<lb/>gem, &longs;emper autem plus mouere ponderis qui mouet, <lb/>quo magis di&longs;tatà fulcimento. </s> <s id="s.000538">Ita enim maiorem fieri <lb/>quæ ex centro; Scalmum verò centrum e&longs;&longs;e. </s> <s id="s.000539">Cæterùm in <lb/>medio nauis plurimum remi intus e&longs;&longs;e. </s> <s id="s.000540">Ibi enim nauem <lb/>e&longs;&longs;e lati&longs;&longs;imam. </s> <s id="s.000541">Moueri autem nauim, quoniam <expan abbr="appellē-te">appellen­<lb/>te</expan> mari remo, <expan abbr="extremū">extremum</expan> illius quod intus e&longs;t anterius pro­<lb/>mouetur, cuius motum nauis &longs;equitur, cui &longs;calmus alliga­<lb/>tur. </s> <s id="s.000542">Vbi autem plurimum maris diuidit remus, eo maximè <lb/>nece&longs;&longs;e e&longs;&longs;e propelli. </s> <s id="s.000543">Plurimum autem diuidi vbi plurima <lb/>pars remi à &longs;calmo e&longs;t. </s> <s id="s.000544">Rem facilem, eo quod verbis potu­<lb/>erit, &longs;chemate non declarauit, nos autem apponemus. </s> </p> <figure id="id.007.01.060.1.jpg" xlink:href="007/01/060/1.jpg"/> <p type="main"> <s id="s.000545">E&longs;to enim nauis AB, mare CD, <lb/>remorum alter, qui ad proram EF, cu­<lb/>ius &longs;calmus G, alter verò in medio na­<lb/>uis, HI, circa &longs;calmum K. <!-- KEEP S--></s> <s id="s.000546">Ait igitur, <lb/>remos e&longs;&longs;e vectes, &longs;calmos verò fulci­<lb/>menta, pondus quod remo, ceu vecte, <lb/>mouetur mare ip&longs;um. </s> <s id="s.000547">Itaque quoniam <lb/>nauis lata e&longs;t in medio vbi Scalmus K <lb/>maior pars KH intra nauim e&longs;t, minor <lb/>verò KI, extra. </s> <s id="s.000548">Contra autem remi ad <lb/>proram, nempe EF pars minor EG <pb xlink:href="007/01/061.jpg"/>intra nauim, pars verò maior GF extra nauim e&longs;t. </s> <s id="s.000549">Pondus <lb/>autem eò faciliùs mouetur, quo maior e&longs;t vectis pars, quæ <lb/>à fulcimento e&longs;t ad mouentem potentiam. </s> </p> <p type="main"> <s id="s.000550">Acutè &longs;anè Philo&longs;ophus. <!-- KEEP S--></s> <s id="s.000551">Ego autem &longs;i per mode&longs;tiam <lb/>liceret, dicerem, non quidem e&longs;&longs;e fulcimentum <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>&longs;ed mare ip&longs;um, pondus vero nauim, ad locum &longs;calmi, <expan abbr="nē-pe">nem­<lb/>pe</expan> inter mouentem potentiam, & fulcimentum po&longs;itum, <lb/>etenim & eo pacto po&longs;&longs;umus vti vecte, quod ob&longs;eruat & <lb/>demon&longs;trat G. <!-- REMOVE S-->Vbaldus tractatu de vecte propo&longs;. </s> <s id="s.000552">2. Erunt <lb/>igitur in de&longs;cripta figura puncta FI, quæ in mari &longs;unt, ful­<lb/>cimenta, quibus remorum extrema in ip&longs;a impul&longs;ione ni­<lb/>tuntur, pondera verò &longs;eu pondus pluribus vectibus & po­<lb/>tentijs impul&longs;um nauis ip&longs;a, quæ &longs;calmis e&longs;t annexa. </s> <s id="s.000553">Re&longs;i­<lb/>&longs;tente igitur mari, cedente autem impul&longs;ionibus &longs;calmo, <lb/>nauis eo transfertur, quo &longs;calmi ab ip&longs;a potentia mouen­<lb/>te in anteriorem partem pelluntur. </s> <s id="s.000554">quoniam autem vt <lb/>FG ad FE ita potentia mouens in E ad pondus motum <lb/>in G. item vt IK ad IH ita potentia mouens in H ad pon­<lb/>dus motum in K, maior autem e&longs;t proportio FG ad FE <lb/>quàm proportio IK ad IH. </s> <s id="s.000555">Maiori indiget potentia vt <lb/>pellatur pondus in G quàm pondus in K. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000556">Hæc certè vti diximus ita &longs;e habent. </s> <s id="s.000557">Philo&longs;ophi au­<lb/>tem ratio tunc procederet, &longs;i &longs;tante naui immobili, vt fit <lb/>vbi à Remoræ occulta vi aut ab alio impedimento reti­<lb/>netur, remiges in ip&longs;o remigandi actu mare pul&longs;arent, <lb/>Tunc enim verè &longs;calmus fieret fulcimentum, mare autem <lb/>pondus, remex verò ip&longs;e mouens. </s> </p> <p type="main"> <s id="s.000558">Addimus, fal&longs;um videri quod a&longs;&longs;erit Ari&longs;toteles, <lb/>nempe illos qui in media naui &longs;unt, remiges, maximè na­<lb/>uim mouere; facilius, melius dixi&longs;&longs;et. </s> <s id="s.000559">Si enim maximè, <lb/>quod ait, denotat, maximo &longs;patio, & velocius pror&longs;us fal­<lb/>&longs;um, etenim tardius mouent & minori &longs;patio, quod nos i­<lb/>ta demon&longs;tramus. </s> </p> <pb xlink:href="007/01/062.jpg"/> <figure id="id.007.01.062.1.jpg" xlink:href="007/01/062/1.jpg"/> <p type="main"> <s id="s.000560">E&longs;to enim Remus AB <lb/>qui marí fulcitur in B, Scal­<lb/>mus remi qui ad <expan abbr="prorã">proram</expan> pup­<lb/>pimue C, qui in media naui <lb/>D, maior autem remi pars <lb/>e&longs;t à &longs;calmo Dad A quam i­<lb/>p&longs;ius C 2d A, Pellantur remi & &longs;tante ceu centro BA, in <lb/>E. eodem igitur tempore C eritin F, & D in G, &longs;ed maius <lb/>e&longs;t &longs;patium CF &longs;patio DG, Ergo vnica impul&longs;ione, plus <lb/>mouit &longs;calmum, hoc e&longs;t, nauim, potentia ad puppim pro­<lb/>ramue remigans, quàm ea quæ operatur in media naui vt <lb/>&longs;entire videbatur (&longs;i modo is e&longs;t eius &longs;en&longs;us) Ari&longs;toteles. <lb/><!-- KEEP S--></s> <s id="s.000561">Nece&longs;&longs;arium igitur e&longs;t, quod ait, maximè intelligendum, <lb/>faciliùs, Veritatem hanc cogno&longs;centes Triremium præ­<lb/>fecti robu&longs;tiores quidem remiges ad proram & puppim, <lb/>inualidiores verò circa mediam triremem collocant. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000562">QVÆSTIO V.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000563"><emph type="italics"/>Dubitatur, Cur paruum exi&longs;tens gubernaculum, & in extremo <lb/>nauigio tantas habeat vires, vt ab exiguo temone, & ab hominis <lb/>vnius viribus alioqui modicè vtentis magnæ nauigiorum <lb/>moueantur moles?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000564">AN, inquit, quoniam gubernaculum vectis e&longs;t, onus <lb/>autem mare, Gubernator vero mouens e&longs;t? </s> <s id="s.000565">Non au­<lb/>tem &longs;ecundùm latitudinem veluti remus, mare accipit <lb/>gubernaculum; non enim in ante nauigium mouet, &longs;ed i­<lb/>p&longs;um commotum mare accipiens inclinat obliquè. </s> <s id="s.000566">quo­<lb/>niam enim pondus e&longs;t mare contrario innixum modo na­<lb/>uem inclinat. </s> <s id="s.000567">fulcimentum enim in contrarium ver&longs;atur, <lb/>mare vetò interius, & illud exterius. </s> <s id="s.000568">illud autem &longs;equitur <lb/>nauis quæ illi e&longs;t alligata & remus quidem &longs;ecundum la­<lb/>titudinem onus propellens & ab eodem repul&longs;us in re-<pb xlink:href="007/01/063.jpg"/>ctum propellit, Gubernaculum verò, vt obliquum iacet <lb/>hinc inde in obliquum motionem facit. </s> <s id="s.000569">in extremo <expan abbr="autē">autem</expan>, <lb/>non in medio iacet, quoniam mouenti facillimum e&longs;t mo­<lb/>tum mouere: prima enim pars celerrimè fertur, & quo­<lb/>niam, quemadmodum in ijs quæ feruntur in fine deficit <lb/>latio, &longs;ic ip&longs;ius continui in finem, imbecillima e&longs;t latio. <lb/></s> <s id="s.000570">Imbecillima autem ad expellendum e&longs;t facilis. </s> <s id="s.000571">Propter <lb/>hæc igitur in puppi gubernaculum ponitur, nec minus, <lb/>quoniam parua ibi motione facta, multo maior fit in vlti­<lb/>mo, quia æqualis angulus &longs;emper maiorem ad&longs;pectat, <expan abbr="tã-to">tan­<lb/>to</expan> queue magis, quanto maiores fuerint illæ, quæ continent. <lb/></s> <s id="s.000572">Ex ijs etiam manife&longs;tum e&longs;t, quam ob cau&longs;&longs;am magis in <lb/>contrarium procedit nauigium, quam remi ip&longs;ius palmu­<lb/>la, eadem enim magnitudo ij&longs;dem mota viribus in aëre <lb/>plus quàm in aqua progreditur. </s> <s id="s.000573">Hæc Philo&longs;ophus, qui <lb/>haudquaquam ex more &longs;uo, quod duobus ferè poterat, <lb/>&longs;excentis verbis expo&longs;uit. </s> <s id="s.000574">Licebat enim id tantum dicere, <lb/>Gubernaculum (ita vocat id totum quod gubernaculo & <lb/>temone con&longs;tat) e&longs;&longs;e ceu remum, quo nauis non antror­<lb/>&longs;um, &longs;ed obliquè & ad latus mouetur. </s> <s id="s.000575">quamobrem omnia <lb/>ferè quæ de Temone dicenda fuerant, de remo loquens <lb/>proponit. </s> <s id="s.000576">Ait autem. <!-- KEEP S--></s> </p> <figure id="id.007.01.063.1.jpg" xlink:href="007/01/063/1.jpg"/> <p type="main"> <s id="s.000577">Sit remus AB, <lb/>&longs;calmus vero C, remi <lb/>in nauigio <expan abbr="principiū">principium</expan> <lb/>A, palmula autem, <lb/>quæ in mari B. <!-- KEEP S--></s> <s id="s.000578">Si igi­<lb/>tur A, vbi D transla­<lb/>tum e&longs;t, non erit B v­<lb/>bi E. æqualis enim, <lb/>BE ip&longs;i AD, æquale <lb/>igitur translatum erit, &longs;ed erat minus. </s> <s id="s.000579">erit igitur vbi F, mi­<lb/>nor enim BF, ip&longs;a AD, quare ip&longs;o GF ip&longs;a DG. <!-- KEEP S--></s> <s id="s.000580">Hæc <pb xlink:href="007/01/064.jpg"/>demon&longs;tratio licet vera videatur, rei ta men, de qua e&longs;t <lb/>&longs;ermo, minimè aptatur. </s> <s id="s.000581">Si enim aptaretur in ip&longs;ius remi <lb/>motu, cum palmula e&longs;&longs;et in F, &longs;calmus fieret in G, excur­<lb/>reret ergo vel &longs;calmus per remum, vel remus per <expan abbr="&longs;calmū">&longs;calmum</expan>, <lb/>facta nempe eiu&longs;modi translatione de C in G, & &longs;ic intra <lb/>nauim modo e&longs;&longs;et pars remi DC, modò verò GD, quod <lb/>tamen non fieri ipsâ experientia docemur. </s> <s id="s.000582">Illud quoque <lb/>fal&longs;um e&longs;t, nauim ip&longs;am tantum moueri in aëre, quantum <lb/>e&longs;t &longs;patium AD, hoc e&longs;t, remi extremum quod e&longs;t in naui, <lb/>&longs;iquidem &longs;calmi motu, non autem manubrij remi, nauis <lb/>agatur. </s> <s id="s.000583">Aliter igitur res &longs;e habet, & forte hoc pacto. </s> </p> <figure id="id.007.01.064.1.jpg" xlink:href="007/01/064/1.jpg"/> <p type="main"> <s id="s.000584">Sit remus AB, cuíus <lb/>manubrium A, palmula <lb/>B, &longs;calmus C. <!-- KEEP S--></s> <s id="s.000585">Pellatur an­<lb/>tror&longs;us A, fiatque; in D, tunc <lb/>&longs;i æqualiter mouerentur <lb/>manubrium & palmula, i­<lb/>p&longs;a palmula fieret in G, at <lb/>minus mouetur: fiet ergo <lb/>in E. ip&longs;e verò &longs;calmus C <lb/>translatus erit in F, motaque; erit nauis à C in F, non autem <lb/>ab A in D. <!-- KEEP S--></s> <s id="s.000586">Po&longs;uit autem Ari&longs;toteles &longs;calmum ad medium <lb/>remi, &longs;ed non ad medium collocari &longs;olet, maior enim pars <lb/>in mare propendet puta HB, quo ca&longs;u translationis &longs;pa­<lb/>tium fit maius, nempe ab H in I. fit autem motus &longs;calmi ex <lb/>centris qui &longs;unt in &longs;patio ip&longs;o BE, quatenus autem ad te­<lb/>monem pertinet, quem remum ait, obliquè puppim ip&longs;am <lb/>propellentem, ita &longs;e res habet. </s> </p> <p type="main"> <s id="s.000587">E&longs;to nauis carina AB, prora A, puppis B, Temonis <lb/>ala BC, gubernaculum BD, cardo verò fulcimentumue <lb/>B; facta itaque impul&longs;ione obliquâ gubernaculi à D in E, <lb/>minor fiet motus in mari à C in F, eritqueue temo vbi EGF, <pb xlink:href="007/01/065.jpg"/><figure id="id.007.01.065.1.jpg" xlink:href="007/01/065/1.jpg"/><lb/>cardo verò vbi G, translata igitur e­<lb/>rit eo motu, puppis ip&longs;a à B in G. facta <lb/>itaque paruâ motione puppis ex B in <lb/>G, prora ip&longs;a quæ longè di&longs;tat à pup­<lb/>pi B maiori &longs;patio &longs;uperato translata <lb/>erit in H facta proræ in contrariam <lb/>partem ab ea quæ facta e&longs;t guberna­<lb/>culi motione. </s> <s id="s.000588">Porrò quod & in præ­<lb/>cedente quæ&longs;tione adnotauimus, <expan abbr="lō-gè">lon­<lb/>gè</expan> meliùs procedet demon&longs;tratio &longs;i <lb/><expan abbr="fulcimentū">fulcimentum</expan> mare intelligatur, quàm <lb/>&longs;calmus, neque enim mare ceu pon­<lb/>dus, &longs;ed &longs;calmus ip&longs;e Temonisuecardo, ponderum in&longs;tar <lb/>transferuntur. </s> </p> <p type="main"> <s id="s.000589">Cæterùm in hac &longs;peculatione liceat nobis aliquan­<lb/>tulum à Philo&longs;opho di&longs;&longs;entire. </s> <s id="s.000590">Certè &longs;i breuitas Temo­<lb/>nis, è puppi eminentis, re&longs;pectu longitudinis totius nauis <lb/>con&longs;ideretur, & parua motio, quæ temone guberna culo­<lb/>ue moto fit, nullius ferè momenti erit ad eam quæ in pro. <lb/></s> <s id="s.000591">ra fit translationem. </s> <s id="s.000592">aliter ergo &longs;e rem habere non dubi­<lb/>tamus, & quæ&longs;tionis &longs;olutionem aliunde petendam. </s> <s id="s.000593">Na­<lb/>ui non currente nullum ferè, aut qui vix curandus &longs;it ex <lb/>gubernaculi conuer&longs;ione nauis ad dextram &longs;ini&longs;tramue <lb/>motum fieri. </s> <s id="s.000594">at eâ currente maximum, experientiâ doce­<lb/>mur. </s> <s id="s.000595">Obliqui igitur motus qui validè in puppi &longs;it, cau&longs;&longs;a <lb/>e&longs;t non quidem ex conuer&longs;ione temonis percu&longs;&longs;io maris, <lb/>&longs;ed mare ip&longs;um, cuius fluctus naui currente obliquam te­<lb/>monis alam ad eam partem quæ mari obuertitur, impel­<lb/>lentes temonem cum puppi ad contrariam partem vali­<lb/>di&longs;&longs;imè transferunt. </s> </p> <p type="main"> <s id="s.000596">E&longs;to nauis carina AB, prora B, puppis A, Temo AC, <lb/>gubernaculum AD; Itaque currente naui, Temone in­<lb/>terim & guberna culo in eadem carinæ linea exi&longs;tentibus, <pb xlink:href="007/01/066.jpg"/><figure id="id.007.01.066.1.jpg" xlink:href="007/01/066/1.jpg"/><lb/>Temo quidem mare &longs;ecat, nulla fa­<lb/>ctâ in puppi, nauis ad &longs;ini&longs;tram dex­<lb/>tramue translatione. </s> <s id="s.000597">Si verò mouea­<lb/>tur gubernaculum à D in E, eo moto <lb/>mouebitur aliquantulum & puppis <lb/>ad partes E, quod voluit Ari&longs;toteles. <lb/><!-- KEEP S--></s> <s id="s.000598">Sed minimi, vt diximus, ea res ad tan­<lb/>tum effectum e&longs;t momenti. </s> <s id="s.000599">Temone <lb/>autem in obliquum <expan abbr="cō&longs;tituto">con&longs;tituto</expan> vt AF, <lb/>naui interim, ventorum aut remorum <lb/>vi pul&longs;a proram ver&longs;us currente te­<lb/>monis latus à fluctibus obliquam par­<lb/>tem alamue in ip&longs;o cur&longs;u ferientibus, <lb/>in contrariam partem transfertur, ad <lb/>eam nempe, ad quam ip&longs;um gubernaculum vergit. </s> <s id="s.000600">facta i­<lb/>gitur nauis ceu circa centrum centraue quæ in carina in­<lb/>ter puppim proramue con&longs;iderantur A, fertur in G, prora <lb/>verò in H. ex quibus manife&longs;tè apparet, duo ad nauis ex <lb/>temone in puppi conuer&longs;ione motionem e&longs;&longs;e ne ce&longs;&longs;aria; <lb/>Temonis nempe obliquationem, & nauis cur&longs;um, <expan abbr="quorū">quorum</expan> <lb/>&longs;i alterum &longs;ine altero adhibeatur, nullam fieri quæ alicu­<lb/>ius momenti &longs;it, nauis conuer&longs;ionem. </s> <s id="s.000601">Illud quoque nota­<lb/>mus, carinam in nauis conuer&longs;ione vectis in&longs;tar &longs;e habere, <lb/>cuius pars mota ad puppim, & mouens potentia e&longs;t; fulci­<lb/>mentum verò circa proram, potentia autem mouens ma­<lb/>re ip&longs;um, temonem in nauis cur&longs;u oblique feriens. </s> <s id="s.000602">Vnde <lb/>colligimus naues, quo longiores &longs;unt in mouente ad Te­<lb/>monem adhibita maiori facilitate ad dextram &longs;ini&longs;tram­<lb/>ue propelli: quod &longs;anè ip&longs;emet con&longs;iderauit Ari&longs;toteles, <lb/>quì idcirco inquit, in extremo, non autem in medio temo­<lb/>nem poni eo quod mouenti facilimum &longs;it ab extremo <lb/>motum mouere. </s> </p> <p type="main"> <s id="s.000603">Ex hac no&longs;trâ &longs;peculatione ratio habetur eius ma-<pb xlink:href="007/01/067.jpg"/>chinationis, quâ in magnis fluminibus, ceu Pado, Abdua <lb/>& &longs;imilibus, Portitores, equos, currus, viatore&longs;que; ip&longs;os, è <lb/>ripa in ripam transferunt. </s> <s id="s.000604">Pulcherrima enim res e&longs;t, & <lb/>nobis per&longs;pecti&longs;&longs;ima, qui Gua&longs;tallâ re&longs;identiæ olim no­<lb/>&longs;træ oppido ad Padum, Mantuam pergentes &longs;æpi&longs;&longs;imè ad <lb/>Ca&longs;trum Borgi Iu&longs;is ea qua diximus machinatione lati&longs;­<lb/>&longs;imum eiu&longs;dem Padi aluum tran&longs;iecimus. </s> <s id="s.000605">Habet autem <lb/>&longs;e hoc pacto. </s> </p> <figure id="id.007.01.067.1.jpg" xlink:href="007/01/067/1.jpg"/> <p type="main"> <s id="s.000606">E&longs;to fluminis citerior <lb/>ripa AB, vlterior CD. <!-- KEEP S--></s> <s id="s.000607">Pon­<lb/>tones duo tabulis &longs;trati, & v­<lb/>nà firmiter juncti EF, Temo <lb/>inter eorum puppes extans <lb/>GH, locus in ripa &longs;tabilis A, <lb/>funis, quo pontones, & ma­<lb/>china tota continetur AI. <lb/>fluuij decur&longs;us ver&longs;us BD, <lb/>&longs;tantibus itaque pontonibus <lb/>ad ripam citeriorem AB, Te­<lb/>mone in <expan abbr="neutrã">neutram</expan> partem pul­<lb/>&longs;o, cum aqua decurrens eum <lb/>re&longs;i&longs;tentem non inueniat, <lb/>&longs;cinditur quidem ab eo, &longs;ed <lb/>non propellit, eo autem con­<lb/>uer&longs;o & in GK con&longs;tituto, a­<lb/>la eius GK ab aqua defluente propul&longs;a machinam &longs;ecum <lb/>trahit ver&longs;us ripam CD, factâ motione circa centrum &longs;eu <lb/>&longs;tabilem locum A, otio&longs;is interim portitoribus, donec per <lb/>circuli portionem ML deuenerit ad vlteriorem ripam in <lb/>L. <!-- KEEP S--></s> <s id="s.000608">Vnde iterum temone in contrariam partem conuer&longs;o, <lb/>aquâ &longs;imiliter temonem propellente, per eandem circuli <lb/>portionem ad ripam citeriorem reuertitur, à qua paullo <lb/>antè di&longs;ce&longs;&longs;erat. </s> <s id="s.000609">Ex quibus apparet, motus cau&longs;&longs;am non <pb xlink:href="007/01/068.jpg"/>e&longs;&longs;e &longs;olam cam, quæ ab ala temonis fit, aquæ <expan abbr="percu&longs;&longs;ionē">percu&longs;&longs;ionem</expan>, <lb/>vt &longs;en&longs;erat Ari&longs;toteles, &longs;ed currentis a quæ temonis alam <lb/>ferientis impul&longs;ionem: nihil autem referre, vtrum &longs;tante <lb/>naui a qua currat, vel câ currente a qua &longs;tet, vt in mari fit, <lb/>idem enim vtroque modo temo patitur. </s> <s id="s.000610">Vt autem machi­<lb/>næ huius & totius negotij &longs;pecies facilius animo concipia­<lb/>tur, &longs;chema hoc &longs;tudio&longs;orum oculis &longs;ubijciemus. </s> </p> <figure id="id.007.01.068.1.jpg" xlink:href="007/01/068/1.jpg"/> <p type="main"> <s id="s.000611">Lembi nauiculæue ideo appo&longs;itæ &longs;unt, vt oblongum <lb/>funem &longs;u&longs;tineant; id etenim nî fieret, aquæ immer&longs;us a­<lb/>quam &longs;cindens machinæ motum impediret, ideo etiam <lb/>apponuntur, ne funis madens celeriter maceretur & pu­<lb/>tre&longs;cat. </s> </p> <p type="main"> <s id="s.000612">Huic &longs;peculationi affinis e&longs;t ea, velorum eorum, <lb/>quæ obliquè ventum, excipientia frumentarijs molis <lb/>dant motum, item verticillorum ex papyro, quibus con­<lb/>tra ventum currentes per lu&longs;um pueri vtuntur. </s> <s id="s.000613">vnicum <pb xlink:href="007/01/069.jpg"/>enim horum omnium principium, & eadem, ratio. </s> </p> <p type="main"> <s id="s.000614">Diximus enim, Temonem currente naui, lateraliter <lb/>conuer&longs;um obuios fluctus excipientem puppim ip&longs;am ob­<lb/>liquè in alteram partem transferre. </s> <s id="s.000615">Porrò ea vela, de qui­<lb/>bus loquimur, ventorum flatibus obliquè oppo&longs;ita ean­<lb/>dem ob cau&longs;&longs;am circulariter agitantur, quod vt figurâ eui­<lb/>dentius fiat, </s> </p> <figure id="id.007.01.069.1.jpg" xlink:href="007/01/069/1.jpg"/> <p type="main"> <s id="s.000616">E&longs;to velum AB, brachio <lb/>CE obliquè affixum, ita vt <lb/>angulus ACE maior &longs;it an­<lb/>gulo BCE, ventus obliquè <lb/>velum feriens FG. <expan abbr="Itaq;">Itaque</expan> quo­<lb/>niam ventus in velum obli­<lb/>quum incidit, elabitur velum, <lb/>& circa centrum E vnà cum <lb/>brachio circumuertitur, in <lb/>cuius locum &longs;uccedit velum <lb/>HI, ex qua a&longs;&longs;idua velorum <lb/>&longs;ucce&longs;&longs;ione, brachiorum & a­<lb/>xis cui adhærent, rotatio fit <lb/>perpetua. </s> <s id="s.000617">Sed enim de Te­<lb/>mone agentes non e&longs;t interim cur de caudis auium pi&longs;ci­<lb/>umque taceamus, in&longs;tar enim remonum &longs;unt à Natura i­<lb/>p&longs;a opportunis animalium partibus, po&longs;tremis videlicet, <lb/>appo&longs;iti, quanquam nec &longs;olum Temonis v&longs;um præ&longs;tent, <lb/>vt videbimus. </s> </p> <p type="main"> <s id="s.000618">E&longs;to pi&longs;cis AB, cuius caput A, cauda verò CB. <!-- KEEP S--></s> <s id="s.000619">Hac <lb/>igitur neutram in partem reflexâ, pi&longs;cis pinnarum motu <lb/>rectâ in anteriorem partem progreditur. </s> <s id="s.000620">Si autem nece&longs;­<lb/>&longs;e ei fuerit ad dextram &longs;ini&longs;tramqueue conuerti non pote­<lb/>rit, ni&longs;i cauda ip&longs;a iuuetur. </s> <s id="s.000621">Omnis enim motus progre&longs;&longs;i­<lb/>uus quiete indiget, nec <expan abbr="ab&longs;q;">ab&longs;que</expan> &longs;tabili fulcimento progredi <pb xlink:href="007/01/070.jpg"/><figure id="id.007.01.070.1.jpg" xlink:href="007/01/070/1.jpg"/><lb/>pote&longs;t, quod in libris de ani­<lb/>malium ince&longs;&longs;u docet ip&longs;e­<lb/>met Philo&longs;ophus. <!-- KEEP S--></s> <s id="s.000622">Sit igitur, <lb/>pi&longs;cem conuerti velle, & fie­<lb/>ri capite in D, deflectet illi­<lb/>co caudam in E, caque; aquam <lb/>ceu &longs;tabile quippiam <expan abbr="feriēs">feriens</expan> <lb/>eiqueue quoddammodo fultus, <lb/>reliquum corpus CA refle­<lb/>ctet in D, &longs;i autem conuerti <lb/>velit in F, caudam deflectet in G, & eadem ratione flecte­<lb/>tur in F. <!-- KEEP S--></s> <s id="s.000623">Sed & Temonis quoque v&longs;um præ&longs;tat natatili­<lb/>bus & volatilibus cauda. </s> <s id="s.000624">Sit enim rectus pi&longs;cis, hoc e&longs;t, re­<lb/>ctâ pergens IKL, caudam obliquet in KM itaque ex a­<lb/>quæ in ip&longs;o motu colli&longs;ione, eius po&longs;teriora pellentur vbi <lb/>INO. </s> <s id="s.000625">Hæc itaque nos de Temone, quatenus ad hanc <lb/>quæ&longs;tionem pertinet, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000626">QVÆSTIO VI.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000627"><emph type="italics"/>Dubitatur, Cur quanto Antenna &longs;ublimior fuerit, ÿ&longs;dem velis, & <lb/>vento eodem celeriùs ferantur nauigia?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000628">Soluit Philo&longs;ophus, inquiens: An quia malus quidem <lb/>&longs;it vectis, fulcimentum verò mali &longs;edes, in qua colloca­<lb/>tur, pondus autem quod moueri debet, ip&longs;um nauigium: <lb/>mouens verò is, qui vela tendit &longs;piritus? </s> <s id="s.000629">Si igitur quanto <lb/>remotior fuerit fulcimentum facilius eadem potentia, & <lb/>citiùs idem mouet pondus, altius certè &longs;ublatâ antennâ, <lb/>velum à mali &longs;ede, quae fulcimentum e&longs;t remotius faciens, <lb/>id efficiet. </s> <s id="s.000630">Hæc ille. <!-- KEEP S--></s> <s id="s.000631">quæ &longs;ic figurâ explicamus. </s> </p> <pb xlink:href="007/01/071.jpg"/> <figure id="id.007.01.071.1.jpg" xlink:href="007/01/071/1.jpg"/> <p type="main"> <s id="s.000632">E&longs;to nauis AB, malus CD, <lb/>mali &longs;edes D, locus antennæ <lb/>&longs;ublimior C, depre&longs;&longs;ior E: ita­<lb/>que quoniam CD vectis e&longs;t, <lb/>quo mouens remotior fuerit à <lb/>fulcimento D, eo citiùs & vio­<lb/>lentiùs pellet, velocius ergo <lb/>nauis mouebitur antenna in <lb/>C, quàm in E, con&longs;tituta. </s> </p> <p type="main"> <s id="s.000633">Plau&longs;ibilia &longs;unt hæc, at certè per veritatem ip&longs;am, <lb/>non vera. </s> <s id="s.000634">Rogo, Si fulcimentum dum vectis mouetur, <expan abbr="cē-trum">cen­<lb/>trum</expan> e&longs;t, centrum vtique motus erit D. &longs;pirante igitur va­<lb/>lidè vento inclinabitur malus, fietque; vbi FGD, quæ qui­<lb/>dem inclinatio violentius fiet, vento pellente in F quàm <lb/>in G, vtpote puncto à fulcimento remotiore. </s> <s id="s.000635">Impul&longs;o ma­<lb/>lo, duo nece&longs;&longs;ariò <expan abbr="cō&longs;equentur">con&longs;equentur</expan>, vel enim ad ip&longs;am &longs;edem <lb/>D. frangetur vel puppis ip&longs;a circa D punctum conuer&longs;a, <lb/>vt mali &longs;equatur motum eleuabitur. </s> <s id="s.000636">Prora verò &longs;ubmer­<lb/>getur facta naui in HDI. </s> <s id="s.000637">Quod &longs;i qui&longs;piam funem ad ma­<lb/>li &longs;ummitatem annexam ad ip&longs;am puppim alligauerit in <lb/>B, impedietur &longs;anè mali inclinatio ad partes F, & ideo nul­<lb/>la vis pror&longs;us fiet in D ex vectis ratione. </s> <s id="s.000638">Attamen nihilo <lb/>&longs;ecius, quo &longs;ublimior fuerit antenna, eo faciliùs à &longs;pirante <lb/>vento puppis eleuabitur. </s> <s id="s.000639">quatenus igitur malus vectis <lb/>e&longs;t, hoc tantum quod dicimus operatur. </s> <s id="s.000640">Quod &longs;i contrà <lb/>obiectum fuerit, experientiam docere, quo &longs;ublimior an­<lb/>tenna fuerit, eo citiùs nauigium, &longs;piritu flante moueri. <lb/></s> <s id="s.000641">Re&longs;pon&longs;io facilis, nempe, mirum non e&longs;&longs;e, &longs;i mali pars &longs;ub­<lb/>limior validius à vento feriatur. </s> <s id="s.000642">Videmus enim, & turres <lb/>quo &longs;ublimiores fuerint, eo magis à ventorum impetuo&longs;is <lb/>flatibus infe&longs;tari, quod &longs;anè ad vectis longitudinem refer­<lb/>re, e&longs;&longs;et ridiculum. </s> <s id="s.000643">Cæterùm quod ad puppis faciliorem <lb/>eleuationem ex mali ip&longs;ius altitudine pertinet, ad vectis <pb xlink:href="007/01/072.jpg"/>contemplationem reducimus. </s> <s id="s.000644">e&longs;t enim quæ dam vectium <lb/>&longs;pecies ab alijs non con&longs;iderata, cuius brachia in angu­<lb/>lum de&longs;inunt, vt ip&longs;e angulus in operatione &longs;it fulcimen­<lb/>tum. </s> </p> <figure id="id.007.01.072.1.jpg" xlink:href="007/01/072/1.jpg"/> <p type="main"> <s id="s.000645">E&longs;to enim vectis, de quo agimus, <lb/>ABC, cuius brachia AB, BC. iuncta <lb/>ad angulum B, &longs;itqueue B in operatione <lb/>fulcimentum. </s> <s id="s.000646">Nec quicquam refert <lb/>quatenus ad v&longs;um pertinet, vtrum an­<lb/>gulus ip&longs;e rectus &longs;it, acutus vel obtu­<lb/>&longs;us. </s> <s id="s.000647">&longs;it autem modò rectus. </s> <s id="s.000648">Ponatur i­<lb/>gitur pondus aliquod in C, tum po­<lb/>tentia quædam applicetur in A, quae i­<lb/>p&longs;am vectis extremitatem A propel­<lb/>lat in D. erit igitur AB in DB & an­<lb/>gulo &longs;eruato BC in BE. <!-- KEEP S--></s> <s id="s.000649">Pondus igi­<lb/>tur cum parte vectis BC eleuabitur in E. <!-- KEEP S--></s> <s id="s.000650">In hoc autem <lb/>vectis genere attenditur proportio quam habet AB ad <lb/>BC. <!-- KEEP S--></s> <s id="s.000651">Si enim potentia quæ applicatur in A ita &longs;e habet ad <lb/>pondus in C vt CB, ip&longs;i BA, fiet æquilibrium. </s> <s id="s.000652">Si maior <lb/>autem fuerit proportio potentiæ in A, ad pondus in C, ea <lb/>quam habet AB ad BC, &longs;uperatâ ponderis re&longs;i&longs;tentiâ fiet <lb/>motus. </s> <s id="s.000653">Res autem haud aliter &longs;e habet, ac &longs;i producta in <lb/>F, fieret BF æqualis BC. <!-- KEEP S--></s> <s id="s.000654">Tunc enim vectis ad rectitudi­<lb/>nem, &longs;eruatâ proportione, redigeretur, & ita potentia in <lb/>A, fulcimento B operaretur in F, vt operabatur in C. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000655">Ad huius vectis naturam referuntur fabrorum mal­<lb/>lei, quibus clauos reuellunt, forcipes item quæ tenaci <lb/>mor&longs;u clauorum capita vmbellasue apprendentes, vio­<lb/>lenter è tabulis extrahunt. </s> <s id="s.000656">In malleo itaque &longs;ubtili, vt in <lb/>figura videre e&longs;t, AB vectis e&longs;t pars quæ à fulcimento ad <lb/>potentiam; ac verò quæ à fulcimento ad pondus, ponderi <pb xlink:href="007/01/073.jpg"/><figure id="id.007.01.073.1.jpg" xlink:href="007/01/073/1.jpg"/><lb/>&longs;iquidem æquiparatur re&longs;i­<lb/>&longs;tentia quae fit in C. <!-- KEEP S--></s> <s id="s.000657">I dem ob­<lb/>&longs;eruamus in forcipe, in quo <lb/>duo quidem brachia AD, <lb/>CB, quatenus ad appren&longs;io<lb/>nem pertinet, fulcimentum, <lb/>habent in ip&longs;o <expan abbr="cētro">centro</expan> &longs;eu ver­<lb/>tebra, & ideo quo longiores <lb/>fuerint, eo tenaciùs appre­<lb/>hendunt & retinent. </s> <s id="s.000658">quate­<lb/>nus autem ad extractionem, <lb/>facit, pro vnico forceps totus habetur vecte, cuius <expan abbr="quidē">quidem</expan> <lb/>pars à potentia ad fulcimentum AB. quæ verò à <expan abbr="fulcimē-to">fulcimen­<lb/>to</expan> ad hoc e&longs;t clauum ip&longs;um qui reuellitur AC. <!-- KEEP S--></s> <s id="s.000659">Violenti&longs;­<lb/>&longs;imè autem extrahunt forcipes, propterea quod maxima <lb/>&longs;it proportio longitudinis brachij BA, ad eam quæ e&longs;t ab <lb/>A ad C. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000660">His igitur hoc pacto examinatis, ad nauim & malum <lb/>reuertentes, dicimus, tunc facillimam fieri puppis eleua­<lb/>tionem, proræ verò demer&longs;ionem, cum maxima fuerit <lb/>proportio, quam habet altitudo mali, ad eam nauis <expan abbr="partē">partem</expan> <lb/>quæ à malo ad ip&longs;am puppis extremitatem, pertingit. <lb/></s> <s id="s.000661">Quamobrem prudentes nauium fabri, vt huic difficultati <lb/>occurrant, malum non in medio quidem nauis, &longs;ed in ter­<lb/>tia ferè parte longitudinis quæ à prora e&longs;t, puppim ver&longs;us <lb/>con&longs;tituunt. </s> </p> <figure id="id.007.01.073.2.jpg" xlink:href="007/01/073/2.jpg"/> <p type="main"> <s id="s.000662">E&longs;to enim nauis AB; cuius <lb/>malus CD: prora A: puppis B; <expan abbr="vē-to">ven­<lb/>to</expan> igitur velum impellente, <expan abbr="malū">malum</expan> <lb/>ad partem contrariam vergit, pu­<lb/>ta in FD. </s> <s id="s.000663">At <expan abbr="quoniã">quoniam</expan> catche&longs;ium <lb/>funi ad puppim vnitur in B, nauim, <lb/>hoc e&longs;t, ip&longs;am puppim trahat ne­<pb xlink:href="007/01/074.jpg"/>ce&longs;&longs;e e&longs;t. </s> <s id="s.000664">non pote&longs;t autem; quoniam &longs;uburræ grauitas & <lb/>onera, quæ naui impo&longs;ita inter D. & <emph type="italics"/>B.<emph.end type="italics"/> grauitatis centrum <lb/>circa punctum E con&longs;tituunt, quod quidem vi ventorum <lb/>inclinante malo ab E, in G eleuaretur, quo igitur minor <lb/>fuerit proportio CD ad DE & maius pondus ip&longs;um cu­<lb/>ius grauitatis centrum in E minus præualebit potentia <lb/>pellens in C ad eleuationem partis nauigij, quæ à mali &longs;e­<lb/>de ad puppim intercedit, An igitur malus &longs;it vectis, pes ve­<lb/>rò fulcimentum, pondus autem quod vecte mouetur, <expan abbr="ipsū">ipsum</expan> <lb/>nauigium, vt placuit Ari&longs;toteli, & qua item ratione malus <lb/>in nauim vt vectis operetur, ex ijs quae dicta &longs;unt, facilè pa­<lb/>tet. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000665">QVÆSTIO VII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000666"><emph type="italics"/>Quæritur, Cur quando ex puppi nauigare voluerint, non flante ex <lb/>puppi vento, veli quidem partem, quæ ad gubernatorem vergit, <lb/>con&longs;tringunt; illam verò quæ proram ver&longs;us e&longs;t, pedem <lb/>facientes, relaxant?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000667">Mirabilis huius effectionis cau&longs;&longs;am explicat Ari&longs;tote­<lb/>les. </s> <s id="s.000668">inquit enim, An quia retrahere quidem multo <lb/>exi&longs;tente vento gubernaculum non pote&longs;t, pauco autem <lb/>pote&longs;t, quem con&longs;tringunt? </s> <s id="s.000669">propellit igitur quidem ip&longs;e <lb/>ventus, in puppim verò illum con&longs;tituit gubernaculum, <lb/>retrahens, & mare compellens: &longs;imul & nautæ ip&longs;i cum <lb/>vento contendunt; in contrariam enim &longs;e reclinant par­<lb/>tem. </s> <s id="s.000670">Hæc ille. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000671">Cuius &longs;en&longs;um breuitate &longs;ubob&longs;curum, mirâ facilita­<lb/>te explicat Picolomineus. <!-- KEEP S--></s> <s id="s.000672">Nos autem vt rem lucidiorem <lb/>faciamus, &longs;chema, quod nec ip&longs;e fecit, nec Philo&longs;ophus, <lb/>proponemus. </s> </p> <p type="main"> <s id="s.000673">E&longs;to nauis A <emph type="italics"/>B<emph.end type="italics"/>, cuius prora A, puppis verò D, guber­<lb/>naculum C<emph type="italics"/>B<emph.end type="italics"/>, temonis ala <emph type="italics"/>B<emph.end type="italics"/>D, veli &longs;inus EF, velum vero <lb/>ita con&longs;titutum, vt directè ex puppi flantem ventum exci-<pb xlink:href="007/01/075.jpg"/><figure id="id.007.01.075.1.jpg" xlink:href="007/01/075/1.jpg"/><lb/>piat. </s> <s id="s.000674">Hoc vbi euenerit, naui­<lb/>gium, rectâ è puppi mouetur <lb/>in proram; Si autem ventus la­<lb/>teraliter &longs;pirat, puta à parte <lb/>G ver&longs;us H & nihilo &longs;ecius na­<lb/>uigium, ac &longs;i ventus ex pup­<lb/>pi e&longs;&longs;et antror&longs;um propelle­<lb/>re volunt, velum quidem obli­<lb/>quant partem eius infimam, <lb/>pedem nempe, quæ e&longs;t in F <lb/>contrahentes, Cornu verò <lb/>antennæ vbi E, proram ver&longs;us <lb/>laxantes ventumque; ip&longs;um obliquè excipientes id <expan abbr="efficiūt">efficiunt</expan>, <lb/>vt ventus minus violenter feriat, & minori &longs;ui parte <expan abbr="velū">velum</expan> <lb/>impleat, & quoniam ventus velum pellit in partem con­<lb/>trariam, nempe in H, ip&longs;i vt vento re&longs;i&longs;tant conuer&longs;o gu­<lb/>bernaculo ex C in L, & temone <emph type="italics"/>B<emph.end type="italics"/>D, in <emph type="italics"/>B<emph.end type="italics"/>M compellunt <lb/>proram ad partem à qua ventus ip&longs;e &longs;pirat. </s> <s id="s.000675">Sit igitur inter <lb/>ventum & temonem pugna, illo proram in dextram, hoc <lb/>verò eandem in &longs;ini&longs;tram pellente, <expan abbr="itaq;">itaque</expan> cum neuter præ­<lb/>ualeat, nece&longs;&longs;ario nauis mediam viam, quæ inter <expan abbr="vtramq;">vtramque</expan> <lb/>e&longs;t, &longs;uo cur&longs;u tenet. </s> <s id="s.000676">Nautæ autem ideo in partem nauis <lb/>AE<emph type="italics"/>B<emph.end type="italics"/>, quæ ver&longs;us ventum e&longs;t, &longs;e conferunt, vt vento æqui­<lb/>librium faciant, ne &longs;cilicet naui in <expan abbr="cōtrariam">contrariam</expan> partem pel­<lb/>lente &longs;piritu, eam demergat. </s> <s id="s.000677">Cæterùm quod nec Ari&longs;to­<lb/>teles nec Picolomineus animaduerterunt, velum obli­<lb/>què con&longs;titutum à vento in anteriora impellitur eandem <lb/>ob cau&longs;&longs;am, quam retulimus, vbi de temone & velis, qui­<lb/>bus farinariæ molæ <expan abbr="cōuertuntur">conuertuntur</expan>, verba faceremus. </s> <s id="s.000678">Quod <lb/>autem addit Picolomineus rem ad vectem reduci po&longs;&longs;e, <lb/>non e&longs;t cur &longs;ub &longs;ilentio prætereamus. </s> <s id="s.000679">Ventus, inquit, pon­<lb/>deris gubernaculum mouentis vicem obtinet; centrum <lb/>verò (fulcimentum intelligit) in medio nauis e&longs;t, quod ta-<pb xlink:href="007/01/076.jpg"/>men ad proram vergit, vt faciliùs ip&longs;i vento re&longs;i&longs;tere po&longs;­<lb/>&longs;it. </s> <s id="s.000680">Tunc enim in rectum mouebitur nauis, cum &longs;ibi inui­<lb/>cem æquatæ vires, qua&longs;i libramentum con&longs;tituerint. </s> <s id="s.000681">Hæc <lb/>ille, cuius &longs;en&longs;um figurâ propo&longs;itâ facilè aperiemus. </s> </p> <figure id="id.007.01.076.1.jpg" xlink:href="007/01/076/1.jpg"/> <p type="main"> <s id="s.000682">E&longs;to carina AB, cuius prora <lb/>A, puppis, B temo BC, ventus verò <lb/>obliquè feriens H. <!-- KEEP S--></s> <s id="s.000683">Conuer&longs;us ita­<lb/>que temo vt in BC vndarum vi cur­<lb/>rente naui repul&longs;us &longs;it in EF ten­<lb/>dens ver&longs;us I, quo ca&longs;u prora con­<lb/>uertitur in D, nempe contra <expan abbr="ventū">ventum</expan> <lb/>qui &longs;pirat ex H. fit autem conuer­<lb/>&longs;io circa punctum G, quod fulcimenti locum obtinet. </s> <s id="s.000684"><expan abbr="Vē-tus">Ven­<lb/>tus</expan> verò ad contrariam <expan abbr="partē">partem</expan> proram impellit, repugnans <lb/>Temonis violentiæ contra ip&longs;am proram dirigentis. </s> <s id="s.000685">E&longs;t i­<lb/>gitur AB, &longs;eu DE carina, in&longs;tar vectis, cuius fulcimentum <lb/>G, vis mouens mare quo temo EF repellitur, pondus ve­<lb/>ro, ventus premens in D; quo igitur remotior erit temo à <lb/>fulcimento G, D autem vbi pondus ei vicinius, eo magis <lb/>temo venti vim &longs;uperabit. </s> <s id="s.000686">Hæc Picolominei ratio, quam <lb/>explicauimus, &longs;anè ingenio&longs;a e&longs;t, verum enimuero, quo­<lb/>niam fulcimentum &longs;ui naturâ &longs;tare debet, hic verò <expan abbr="nullã">nullam</expan> <lb/>habeat &longs;tabilitatem, difficultatem patitur. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000687">QVÆSTIO VIII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000688"><emph type="italics"/>Quæritur, Cur ex figuris omnibus rotundæ faciliùs <lb/>moueantur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000689">Trifariam, inquit Ari&longs;toteles, circulum rotari contin­<lb/>git; Aut &longs;ecundum ab&longs;idem <expan abbr="cētro">centro</expan> &longs;imul moto, quem­<lb/>admodum plau&longs;tri vertitur rota; aut circa manens cen­<lb/>trum, veluti trochleæ puteorum, &longs;tante centro: Aut in pa­<lb/>uimento manente centro, &longs;icuti figuli rota conuertitur. <pb xlink:href="007/01/077.jpg"/>Cau&longs;&longs;am verò explicans, ait, celerrima eiu&longs;modi corpora <lb/>e&longs;&longs;e, eo quod paruâ &longs;ui parte planum contingunt, vti cir­<lb/>culus &longs;ecundum punctum, item quoniam non offen&longs;ant: <lb/>Non offen&longs;andi vero e&longs;&longs;e cau&longs;&longs;am, quod &longs;emotum à terra <lb/>habeant angulum. </s> <s id="s.000690">Item propterea quod corpus, cui fiunt <lb/>obuiam, &longs;ecundum pu&longs;illum tangunt. </s> <s id="s.000691">Rectilineo autem <lb/>aliter euenire, quippe quod rectitudine &longs;uâ, multum pla­<lb/>ni contingat. </s> <s id="s.000692">Ad hæc, quo nutat pondus eo mouentem <lb/>mouere. </s> </p> <p type="main"> <s id="s.000693">Hæc ferè Philo&longs;ophus, cuius rationes ad eum &longs;olum­<lb/>modo circularem motum faciunt, qui fit &longs;ecundum ab&longs;i­<lb/>dem, vt in carrorum rotis v&longs;u venit, nec aptantur rotis fi­<lb/>gulorum trochlei&longs;queue, cuiu&longs;modi &longs;unt illæ, quæ &longs;upra <lb/>puteos appenduntur. </s> <s id="s.000694">Nos igitur, ad Ari&longs;totelis mentem, <lb/>primam rotationis &longs;peciem, quæ e&longs;t &longs;ecundum ab&longs;idem, <lb/>examinabimus. </s> </p> <figure id="id.007.01.077.1.jpg" xlink:href="007/01/077/1.jpg"/> <p type="main"> <s id="s.000695">E&longs;to rota &longs;phæ­<lb/>raue AB, cuius cen­<lb/>trum C; Horizontis <lb/>planum DE; conta­<lb/>ctus circuli in plano <lb/>B. <expan abbr="perpēdicularis">perpendicularis</expan> ho­<lb/>rizonti à puncto <expan abbr="cō-tactus">con­<lb/>tactus</expan> B ip&longs;a <emph type="italics"/>B<emph.end type="italics"/>CA, <lb/>tran&longs;iens per <expan abbr="centrū">centrum</expan> <lb/>C, partes rotæ circa <lb/>perpendicularem AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, angulus contactus G<emph type="italics"/>B<emph.end type="italics"/>E. <lb/></s> <s id="s.000696">Primo itaque id con&longs;tat, circulum in puncto planum, &longs;eu <lb/>lineam contingere. </s> <s id="s.000697">At quoniam, vt Mechanici, de circulis <lb/>roti&longs;queue &longs;eu &longs;phæris agimus materialibus, rectè Philo&longs;o­<lb/>phus non in puncto planum præcisè tangere dixit, &longs;ed &longs;e­<lb/>cundum partem &longs;ui minimam. </s> <s id="s.000698">Angulum porro, quem à <lb/>terra &longs;emotum dicit, ip&longs;e angulus e&longs;t contingentiae. </s> <s id="s.000699">eleua­<pb xlink:href="007/01/078.jpg"/>tur enim ex <emph type="italics"/>B<emph.end type="italics"/> in G. <!-- KEEP S--></s> <s id="s.000700">Si autem corpus quodpiam in plano <lb/>fuerit, puta HI in puncto illud tanget ci culus ei occur­<lb/>rens, exempli gratiâ in K. <!-- KEEP S--></s> <s id="s.000701">Hæc igitur accidunt circulari <lb/>figuræ. </s> <s id="s.000702">In lateratis autem &longs;ecus fit, quippe quæ nec in <expan abbr="pū-cto">pun­<lb/>cto</expan> &longs;eu &longs;ecundum paruam &longs;ui partem, planum tangunt, <lb/>nec &longs;emotum vt circulus à plano habent angulum, nec <lb/>impingentes offendiculum in puncto tangunt. </s> <s id="s.000703">Cæterùm <lb/>poti&longs;&longs;imam facilitatis motus in rotatione quæ fit &longs;ecun­<lb/>dum ab&longs;idem, e&longs;&longs;e cau&longs;&longs;am dixit, nempe quò nutat pon­<lb/>dus eò à mouente impelli ac moueri. </s> <s id="s.000704">Primò igitur circu­<lb/>laris &longs;phæricaue figura in æquilibrio &longs;tat; æquales enim <lb/>&longs;unt partes quæ circa perpendicularem: ceu &longs;unt AF<emph type="italics"/>B<emph.end type="italics"/>, <lb/>AG<emph type="italics"/>B.<emph.end type="italics"/> &longs;i enim impul&longs;us fiat ex parte F, pars oppo&longs;ita nuta­<lb/>bit, & propendet in partem G, & &longs;uo nutu motuque; &longs;ecum <lb/>trahet partem AF<emph type="italics"/>B<emph.end type="italics"/>, fietqueue progre&longs;&longs;us. </s> <s id="s.000705">Si enim ducatur <lb/>FCG diameter, ip&longs;i horizonti æ que di&longs;tans, erit veluti li­<lb/>bra, cuius pondera vtrinque AF<emph type="italics"/>B<emph.end type="italics"/>, AG<emph type="italics"/>B<emph.end type="italics"/>, brachia verò <lb/>æqualia CF, CG. <!-- KEEP S--></s> <s id="s.000706">Potentia autem quâ trahitur pellitur­<lb/>ue ad in&longs;tar ponderis &longs;e habet, quo addito partium alteri, <lb/>facto queue rece&longs;&longs;u ab æquilibrio, &longs;equetur motus. </s> <s id="s.000707">Putauêre <lb/>quidam, vt refert Philo&longs;ophus, <expan abbr="circularē">circularem</expan> lineam, ita per­<lb/>peti motu ver&longs;atum iri, vt manentia, propter contrarium <lb/>nixum, manent, neque enim circulus in plano contrarium <lb/>nixum habet, cum &longs;it, veluti dicebamus, in æquilibrio & <lb/>facilis in vtramuis partem moueri. </s> <s id="s.000708">Veruntamen perpe­<lb/>tuum e&longs;&longs;e non po&longs;&longs;e horum corporum motum, ea e&longs;t cau&longs;­<lb/>&longs;a, quod violentum accidat naturæ, & ideo non durabile. <lb/></s> <s id="s.000709">Ad hæc, addit Philo&longs;ophus, Maiores circulos ad minores <lb/>nutum habere <expan abbr="quēdam">quendam</expan>; & nutum maioris ad minoris nu­<lb/>tum, &longs;e habere vt angulos ad angulos, & <expan abbr="diametrū">diametrum</expan> ad dia­<lb/>metrum. </s> <s id="s.000710">Angulos autem hîc &longs;ectores ip&longs;os vocat; oportet <lb/>enim circulos tum maiores tum minores circa idem cen­<lb/>trum e&longs;&longs;e con&longs;titutos. </s> <s id="s.000711">Hæc autem non ab&longs;imili ab eo <lb/>quod &longs;uprà po&longs;uimus &longs;chemate explicantur. </s> </p> <pb xlink:href="007/01/079.jpg"/> <figure id="id.007.01.079.1.jpg" xlink:href="007/01/079/1.jpg"/> <p type="main"> <s id="s.000712">E&longs;to enim circulus <lb/>AB circa centrum, C, <lb/>Horizontis planum DE, <lb/>tangens circulum in B, <lb/>linea verò perpendicu­<lb/>laris per centrum BCA. <lb/><!-- KEEP S--></s> <s id="s.000713">Sit autem circa idem <expan abbr="cē-trum">cen­<lb/>trum</expan> C, minor circulus <lb/>FG, ducatur queue CH &longs;e­<lb/>cus minorem circulum in I, tangens verò maiorem in H, <lb/>con&longs;tituen&longs;queue cum AC linea angulum ACH, duos an­<lb/>gulos, ex Ari&longs;totelis mente comprehendentem, hoc e&longs;t, <lb/>duos &longs;ectores ACH, FCI. quoniam igitur &longs;ector &longs;eu an­<lb/>gulus ACH, &longs;uo &longs;patio &longs;uperat angulum &longs;eu &longs;ectorem <lb/>FGI, facilè ex nutu quem maior &longs;upra minorem habet, <lb/>maior ip&longs;e mìnorem mouet. </s> <s id="s.000714">Videtur autem tacitè Philo­<lb/>&longs;ophus hæc ad vectis naturam referre, cuius altera extre­<lb/>mitatum in centro &longs;it, altera verò in ab &longs;ide, & ita &longs;e habe­<lb/>re nutum maioris &longs;upra minorem, vt vectis ad vectem, hoc <lb/>e&longs;t, &longs;emidiameter ad &longs;emidiametrum, &longs;eu &longs;ector ad &longs;ecto­<lb/>rem, quos quidem &longs;ectores, vt vidimus, angulos appellat. <lb/></s> <s id="s.000715">Hæc autem quæ de nutu refert, licet &longs;ubtilia &longs;int, vera e&longs;­<lb/>&longs;e non videntur. </s> <s id="s.000716">Si enim in figura producatur ad oppo&longs;i­<lb/>tam partem &longs;emidiameter HC in K &longs;ecans minorem cir­<lb/>culum in L, duos alios &longs;ectores angulosue habebimus, <expan abbr="nē-pe">nem­<lb/>pe</expan> KCB, LCG, ip&longs;is ACHFCI æquales. </s> <s id="s.000717"><expan abbr="Itaq;">Itaque</expan> quan­<lb/>tum adiuuat motum anguli ACH maioris nutus, in de­<lb/>&longs;cendendo ad partes B, tantundem retardat anguli item <lb/>maioris KCB, contra nutus (vt ita appellem) in <expan abbr="a&longs;cendē-do">a&longs;cenden­<lb/>do</expan> ad partes A. & &longs;anè quatenus ad rei naturam pertinet <lb/>& ad ip&longs;um æquilibrium, non differunt maiores circuli à <lb/>minoribus, nec &longs;unt maiores minoribus mobiliores, imo <lb/>ex aliqua ratione minores videntur fore ad motum faci­<pb xlink:href="007/01/080.jpg"/>liores, tum quia data materiæ æqualitate &longs;unt leuiores, <lb/>tum etiam quod maior e&longs;t angulus contactus ad planum <lb/>circumferentiae minoris quàm maioris circuli, vt in &longs;ubie­<lb/><figure id="id.007.01.080.1.jpg" xlink:href="007/01/080/1.jpg"/><lb/>cta figura angulus ABC maior <lb/>e&longs;t angulo DBC, in materiali i­<lb/>gitur circulo rotaue maiore &longs;ui <lb/>parte tanget planum DB circu­<lb/>lus, ip&longs;o AB. quicquid tamen fit, <lb/>mobiliores &longs;unt maiores circuli <lb/>non quidem ex natura circuli, <lb/>quæ tam in maioribus quàm in <lb/>ip&longs;is minoribus e&longs;t par, &longs;ed alijs de cau&longs;&longs;is, quas &longs;uo loco <lb/>examinabimus. </s> </p> <p type="main"> <s id="s.000718">Cæterùm vt aliquid de motu qui &longs;ecundum ab&longs;idem <lb/>fit, ex no&longs;tro penu promamus, Dicimus, Circulos, rota&longs;ue, <lb/>quæ hoc pacto mouentur, vel per horizontis planum mo­<lb/>ueri, vel per accliue, aut decliue. </s> <s id="s.000719">Si autem per horizontis <lb/>planum, ideo facilem e&longs;&longs;e motum, quòd nunquam, cæte­<lb/>ris paribus, centrum grauitatis ip&longs;ius corporis à centro <lb/>mundi, in ip&longs;a rotatione, fiat remotius. </s> </p> <figure id="id.007.01.080.2.jpg" xlink:href="007/01/080/2.jpg"/> <p type="main"> <s id="s.000720">E&longs;to enim planum, <lb/>horizontis AB, cui circu­<lb/>lus in&longs;i&longs;tat AD, circa cen­<lb/>trum C, diui&longs;us per <expan abbr="centrū">centrum</expan> <lb/>ip&longs;um à perpendiculari <lb/>ACD; Ducatur autem per <lb/>centrum C recta linea ho­<lb/>rizonti æquidi&longs;tans, ECFG: dum diuidatur circulus vt­<lb/>cunque in partes AH, HF, FI, ID, & CI, CH iungan­<lb/>tur. </s> <s id="s.000721">Po&longs;thæc intelligatur circulum &longs;ecundum ab&longs;idem <lb/>moueri ad partes G, erit igitur aliquando punctum H, <lb/>tangens horizontis planum, tangat autem in K, tum F in <pb xlink:href="007/01/081.jpg"/>L, I in N. <!-- REMOVE S-->D verò in O. <!-- KEEP S--></s> <s id="s.000722">Ducanturqueue KP, LQ, NR, OS <lb/>ip&longs;i AC parallelæ horizonti autem perpendiculares. <lb/></s> <s id="s.000723">Centrum ergo circuli, quod idem & grauitatis e&longs;t <expan abbr="centrū">centrum</expan>, <lb/>feretur per rectam CPQRS, &longs;unt enim KP, LQ, NR, <lb/>OS ip&longs;i AC &longs;emidiametro æquales, <expan abbr="nūquam">nunquam</expan> igitur cen­<lb/>trum ip&longs;um C in circuli rotatione ab horizontis plano e­<lb/>leuabitur, nec à mundi centro fiet remotius. </s> </p> <p type="main"> <s id="s.000724">Hoc autem longè aliter cæteris figuris contingit, <lb/>quarum motus ideo in æqualis, quòd non &longs;emper in rota­<lb/>tione centrum grauitatis eandem &longs;eruet à mundi centro <lb/>di&longs;tantiam. </s> </p> <figure id="id.007.01.081.1.jpg" xlink:href="007/01/081/1.jpg"/> <p type="main"> <s id="s.000725">E&longs;to enim Ellip&longs;is <lb/>ABCD, cuius <expan abbr="cētrum">centrum</expan> <lb/>E, diameter longior <lb/>BED, breuior AEC, <lb/>Horizontis planum, <lb/>FCG. locus contactus <lb/>C perpendicularis à <lb/>contactu per centrum i­<lb/>p&longs;a CEA diuidens El­<lb/>lip&longs;im in partes æquales, & æqueponderantes ABC, <lb/>ADC. <!-- KEEP S--></s> <s id="s.000726">Sumantur in quadrante CD, <expan abbr="pūcta">puncta</expan> HI, tum EH, <lb/>HI iungantur, erit autem EH longior ip&longs;a EC, tum EI, <lb/>ip&longs;a EH & ED, p&longs;a EI. <!-- KEEP S--></s> <s id="s.000727">Rotetur ellip&longs;is &longs;ecun dum ab&longs;i­<lb/>dem, fiet igitur punctum H in K, & à puncto K horizonti <lb/>perpendicularis erigatur KL, quæ fiat æqualis EH. <!-- KEEP S--></s> <s id="s.000728">Po&longs;t <lb/>hæc punctum I erit in M, & ab M perpendicularis, æqua­<lb/>lis EI. rur&longs;us D fiat in O, & ip&longs;i ED, æqualis perpendicu­<lb/>laris OP. <!-- KEEP S--></s> <s id="s.000729">Mota igitur ellip&longs;i à C in K, haud ita difficilis e­<lb/>rit motus, quippe quod haud multum EH &longs;uperet EC, at <lb/>difficilior erit translatio in M, difficillima verò in O. Val<lb/>de enim à &longs;itu E, ibi attollitur grauitatis centrum, a&longs;cen­<lb/>dens nempe vbi P. <!-- KEEP S--></s> <s id="s.000730">Videmus igitur ex his eandem poten­<pb xlink:href="007/01/082.jpg"/>tiam in mouendo ellip&longs;im, haud pariter &longs;e habere, vt in <lb/>mouendo circulum. </s> <s id="s.000731">ibi enim centrum grauitatis fertur <lb/>per æquidi&longs;tantem horizonti, hic verò modò attollitur, <lb/>modò deprimitur, quod &longs;anè mole&longs;tiam & difficultatem <lb/>facit. </s> <s id="s.000732">Sed idem alijs figuris contingere, & maximè latera­<lb/>tis, ita docebimus. </s> </p> <figure id="id.007.01.082.1.jpg" xlink:href="007/01/082/1.jpg"/> <p type="main"> <s id="s.000733">E&longs;to enim triangulum <lb/>æquilaterum ABC, cuius <lb/>grauitatis centrum E hori­<lb/>zontis planum BD. <!-- KEEP S--></s> <s id="s.000734">Demit­<lb/>tatur à vertice A perpendi­<lb/>cularis horizonti AF tran&longs;­<lb/>ibit autem per centrum E, <lb/>& bifariam diuidet ba&longs;im <lb/>BC in F. <!-- KEEP S--></s> <s id="s.000735">Sunt autem trianguli ABF, ACF, æquales & <lb/>æqueponderantes. </s> <s id="s.000736">angulus verò AFC rectus. </s> <s id="s.000737">lungatur <lb/>EC, erit igitur maior EC, ip&longs;a EF. <!-- KEEP S--></s> <s id="s.000738">Rotetur iraque trian­<lb/>gulum circa punctum C, fiatque; EC horizonti perpendi­<lb/>cularis, &longs;itqueue GH, & per E horizonti parallela ducatur <lb/>EK, moto igitur triangulo, centrum grauitatis E transla­<lb/>tum erit in H, &longs;ed KC æqualis e&longs;t EF, minor autem ip&longs;a <lb/>CH, eleuatur ergo centrum grauitatis ab E in H, nempe <lb/>&longs;upra K, totum &longs;patium KH. ex qua eleuatione fit in mo­<lb/>tu difficultas. </s> <s id="s.000739">Idem pror&longs;us eadem demon&longs;tratione o&longs;ten­<lb/>deretur fieri in quadrato & alijs lateratis figuris. </s> <s id="s.000740">Cur igi­<lb/>tur in plano horizontis facillimè circularia, difficile <expan abbr="autē">autem</expan> <lb/>laterata & quæ inæquales habent &longs;emidiametros, mo­<lb/>ueantur, ex dictis clarè patet. </s> </p> <p type="main"> <s id="s.000741">Ad hanc quæ&longs;tionem illud quoque facit, cur per de­<lb/>cliue planum grauiora corpora, & rotunda maximè; ma­<lb/>gno impetu dimi&longs;&longs;a, delabantur. </s> </p> <p type="main"> <s id="s.000742">E&longs;to enim rota &longs;phæraue aut Cylindrus CD, cuius <lb/>centrum E, tangens decliue planum AB in D, quæritur <pb xlink:href="007/01/083.jpg"/>cur dimi&longs;&longs;a hæc magno impetu deferantur ad partes B, <lb/>Ducatur per grauitatis centrum E ad horizontem, BK <lb/>perpendicularis FEL &longs;ecans decliue planum in G, cir­<lb/>cumferentiam verò in H. opponitur autem EG angulo <lb/>recto EDG, maior ergo EG ip&longs;a ED, hoc e&longs;t, EH, inter <lb/><figure id="id.007.01.083.1.jpg" xlink:href="007/01/083/1.jpg"/><lb/>circumferentiam igitur & pla­<lb/>num decliue, &longs;patium interce­<lb/>dit HG. <!-- KEEP S--></s> <s id="s.000743">Ducatur item DI ip&longs;i <lb/>FG æquidi&longs;tans. </s> <s id="s.000744">non tran&longs;ibit <lb/>igitur per centrum E. minor e­<lb/>rit igitur diametro CD, quare <lb/>circulum in partes inæquales <lb/>&longs;ecabit, & non per grauitatis <lb/>centrum, quod idem cum ma­<lb/>gnitudinis &longs;eu figuræ centro &longs;upponitur. </s> <s id="s.000745">Dimi&longs;&longs;a igitur <lb/>rota, contingit quidem planum decliue in puncto D. <!-- KEEP S--></s> <s id="s.000746">At <lb/>centrum grauitatis premit &longs;ecundam per lineam perpen­<lb/>dicularem FG, non &longs;u&longs;tentatur autem in H, quippe quod <lb/>inter planum & circum <expan abbr="ferentiã">ferentiam</expan> intercedat &longs;patium HG, <lb/>nec H locum habeat cui innitatur, corpus autem ita per <lb/>lineam DI e&longs;t diui&longs;um, vt longè maior &longs;it pars IFCHD <lb/>ip&longs;a DI, & centrum in ea parte cadat quæ non fulcitur. </s> <s id="s.000747">i­<lb/>taque &longs;uopte nutu, cum extra fulcimentum &longs;it D & per­<lb/>pendicularem DI ad inferiores partes rapidè rotans de­<lb/>labitur. </s> <s id="s.000748">Ducatur autem perpendicularis GL, parallela <lb/>MN, & quoniam BN breuior e&longs;t BL, erit MN ip&longs;a GL <lb/>breuior. </s> <s id="s.000749">E&longs;t igitur punctum M mundi centro propius <lb/>quàm D & G, quare eò non impedita rota ip&longs;a &longs;uo nutu <lb/>feretur, nec &longs;tabit donec in fimum <expan abbr="locū">locum</expan> vbi quie&longs;cat nan­<lb/>ci&longs;catur. </s> <s id="s.000750">Po&longs;&longs;umus etiam Rota &longs;phæraue in plano decliui <lb/>collocata, datam potentiam inuenire, quæ extremitati <lb/>diametri ad eam partem qua vergit applicata ip&longs;am rotam <lb/>&longs;phæramue impediatne delabatur. </s> </p> <pb xlink:href="007/01/084.jpg"/> <figure id="id.007.01.084.1.jpg" xlink:href="007/01/084/1.jpg"/> <p type="main"> <s id="s.000751">E&longs;to planum in clinatum <lb/>AB, cui Rota &longs;phæraue in&longs;i­<lb/>&longs;tat tangatque; illud in C. <!-- KEEP S--></s> <s id="s.000752">Rota <lb/>verò ip&longs;a &longs;phæraue DC, cu­<lb/>ius centrum E, diameter ve­<lb/>rò DEC ip&longs;i BA ad <expan abbr="punctū">punctum</expan> <lb/>contactus C, perpendicula­<lb/>ris. </s> <s id="s.000753">Ducatur per C ip&longs;i hori­<lb/>zonti perpendiculatis FCG <lb/>circulum <expan abbr="&longs;ecãs">&longs;ecans</expan> in G tum per <lb/>E ip&longs;i CG perpendicularis, ip&longs;i verò BF horizonti æqui­<lb/>di&longs;tans HEI ceu vectis, cuius fulcimentum I re&longs;pondens <lb/>ip&longs;i C, pondus verò in E, vbi grauitatis e&longs;t centrum. </s> <s id="s.000754">Ap­<lb/>plicata igitur potentia in H erit pondus inter fulcimen­<lb/>tum & potentiam, quare vt IE ad IH ita potentia &longs;u&longs;ti­<lb/>nens in H ad pondus in E, quod demon&longs;trandum fuerat. </s> </p> <p type="main"> <s id="s.000755">Quippiam &longs;imile o&longs;tendit Pappus 1. 8. prop. 9. alijs <lb/>tamen &longs;uppo&longs;itis & con&longs;ideratis. </s> <s id="s.000756">Dico præterea, ij&longs;dem <lb/>&longs;tantibus angulum ECI æqualem e&longs;&longs;e angulo inclinatio­<lb/>nis CBF. </s> <s id="s.000757">Producatur HI concurrens cum ip&longs;a AB in K, <lb/>concurret autem propterea, quod CIK rectus &longs;it, ICA <lb/>minor recto, & quoniam HK parallela e&longs;t horizonti BF <lb/>alterni anguli IKC, CBF, æquales erunt. </s> <s id="s.000758">Similes autem <lb/>&longs;unt ECI, ECK, trianguli, e&longs;tqueue ECI angulus æqualis <lb/>angulo EKC, hoc e&longs;t, ip&longs;i CBF. vnde &longs;equitur, quo mi­<lb/>nor fuerit inclinationis angulus, eo facilius rotam &longs;phæ­<lb/>ramue in plano inclinato &longs;u&longs;tineri. </s> <s id="s.000759">quo enim minor fuerit <lb/>angulus ECI, eo minus latus EI & minor proportio EI <lb/>ad IH, & ideo minor potentia &longs;u&longs;tinens requiratur in H. <lb/><!-- KEEP S--></s> <s id="s.000760">Cæterùm accliue & decliue planum nihil differunt ni&longs;i <lb/>re&longs;pectu. </s> </p> <p type="main"> <s id="s.000761">His ita con&longs;ideratis, admonet nos locus, vt pulcher­<lb/>rimam dubitationem diluamus. </s> <s id="s.000762">Quæritur, Cur maiores <pb xlink:href="007/01/085.jpg"/>rotae impingentes, facilius offendicula &longs;uperent quàm mi­<lb/>nores. </s> <s id="s.000763">Neque enim &longs;atisfacere videtur quod ait Ari&longs;tote­<lb/>les, ex contactu in puncto eo anguli à plano eleuatione id <lb/>fieri, alijs ergo principijs dubitatio &longs;oluitur. </s> </p> <figure id="id.007.01.085.1.jpg" xlink:href="007/01/085/1.jpg"/> <p type="main"> <s id="s.000764">E&longs;to rota quidem maior <lb/>AB, circa centrum C minor <lb/>vero DB circa centrum, E, <lb/><expan abbr="tãgentes">tangentes</expan> horizontis planum <lb/>in B. <!-- KEEP S--></s> <s id="s.000765">Diameter maioris AB, <lb/>minoris DB, offendiculum, <lb/>horizonti perpendiculare <lb/>FG. <!-- KEEP S--></s> <s id="s.000766">Ducatur per F horizonti <lb/>parallela FK &longs;ecans minoris <lb/>rotæ peripheriam in H, dia­<lb/>metrum verò AB in K, & à <lb/>puncto H ad <expan abbr="planū">planum</expan> horizon­<lb/>tis perpendicularis demittatur HI: erit autem HI æqua­<lb/>lis ip&longs;i offendiculo FG, & iungantur BH, BF. <expan abbr="Itaq;">Itaque</expan> quo­<lb/>niam BH ab extremo B cadit in triangulum KFB, erit <lb/>KHB angulus maior angulo KFB. </s> <s id="s.000767">Parallelæ autem &longs;unt <lb/><emph type="italics"/>K<emph.end type="italics"/>F, BG, pares ergo anguli <emph type="italics"/>K<emph.end type="italics"/>HB, HBG, pares item <emph type="italics"/>K<emph.end type="italics"/>FB, <lb/>FBG, Maior ergo HBI, ip&longs;o FBC. <!-- KEEP S--></s> <s id="s.000768">At minoris rotæ gra­<lb/>uitatis centrum mouetur &longs;ecundum lineam BH, maius <lb/>verò &longs;ecundum literam BF, difficilius ergo mouebitur, & <lb/>&longs;uperabit offendiculum minor rota, quàm maior: quod <lb/>fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.000769">Po&longs;&longs;umus idem o&longs;tendere magis mechanicè, hoc <lb/>e&longs;t, tem ad vectem reducendo. </s> <s id="s.000770">E&longs;to horizontis planum <lb/>AB, rota maior CD planum tangens in D. rotæ verò ma­<lb/>ioris centrum E. <!-- KEEP S--></s> <s id="s.000771">Rota verò minor FD, tangens itidem <lb/>planum in D. rotæ autem centrum G, offendiculi verò re­<lb/>ctitudo DH. <!-- KEEP S--></s> <s id="s.000772">Ducatur per H ip&longs;i AB horizonti æquidi­<lb/>&longs;tans HI &longs;ecans minorem circulum in K, maiorem verò <pb xlink:href="007/01/086.jpg"/><figure id="id.007.01.086.1.jpg" xlink:href="007/01/086/1.jpg"/><lb/>in I. <!-- KEEP S--></s> <s id="s.000773">Ducantur etiam dia­<lb/>metri maioris quidem <lb/>LEM, minoris NGO, <lb/>Tum à puncto K perpen­<lb/>dicularis ducatur ad <lb/>GO, ip&longs;a KP, item à pun­<lb/>cto I ad EM perpendi­<lb/>cularis <expan abbr="Iq.">Ique</expan> Dico EQ ad <lb/>QL, minorem habere <lb/>proportionem quam GP, <lb/>ad PN. <!-- KEEP S--></s> <s id="s.000774">Connectatur <lb/>GK, & ei per E parallela <lb/>ducatur ER, &longs;ecans maiorem circulum in R, & ab R ip&longs;i <lb/>EM perpendicularis ducatur RS. quoniam igitur ER <lb/>parallela e&longs;t ip&longs;i GK, erit GER angulus HGK angulo <lb/>æqualis. </s> <s id="s.000775">Recti autem &longs;unt HGP, GES reliqui ergo KGP, <lb/>RES ad inuicem &longs;unt æquales. </s> <s id="s.000776">Sed & ESR, GPK recti <lb/>&longs;unt, quare ERSGKP anguli æquales &longs;unt, & trianguli <lb/>GPKESR, per pr. <!-- REMOVE S-->diff. </s> <s id="s.000777">1.6. &longs;imiles. </s> <s id="s.000778">Vt ergo GK hoc e&longs;t <lb/>GN ad GP, ita ER hoc e&longs;t EL ad ES. <!-- KEEP S--></s> <s id="s.000779">Componendo igi­<lb/>tur vt NP ad PG, ita LS ad SE. quamobrem &longs;i fulcimen­<lb/>tum e&longs;&longs;et in S, pondus in E, <expan abbr="potētia">potentia</expan> in L, idem fieret ac fiat <lb/>fulcimento in P, pondere in G, potentia verò in N con&longs;ti­<lb/>tuta. </s> <s id="s.000780">& id quidem &longs;i eiu&longs;dem ponderis vtraque rota &longs;up­<lb/>ponatur. </s> <s id="s.000781">Rur&longs;us quoniam vt DK ad totum circulum DF, <lb/>ita DR ad totum DC. <!-- KEEP S--></s> <s id="s.000782">Minor e&longs;t autem proportio DI ad <lb/>totum circulum DC, ergo minor e&longs;t DI ip&longs;a DR. <!-- KEEP S--></s> <s id="s.000783">Maior <lb/>ergo MI ip&longs;a MR, maior ergo QI ip&longs;a SR, propius ergo <lb/>centro E e&longs;t Q ip&longs;o puncto S, minor e&longs;t igitur proportio <lb/>EG ad LQ quàm ES ad SL. <!-- KEEP S--></s> <s id="s.000784">Minor ergo potentia requi­<lb/>ritur in L ad &longs;u&longs;tinendum pondus E ex fulcimento Q hoc <lb/>e&longs;t I, quàm requiratur in N ad &longs;u&longs;tinendum pondus G ex <lb/>fulcimento P, hoc e&longs;t K. <!-- KEEP S--></s> <s id="s.000785">Minor ergo potentia requiritur <pb xlink:href="007/01/087.jpg"/>ad transferendam maiorem retam CD vltra offendicu­<lb/>lum IV, hoc e&longs;t, DH, quàm requiratur ad trans ferendam <lb/>minorem vltra offendiculum KT, hoc e&longs;t HD, quod fue­<lb/>rat o&longs;tendendum. </s> </p> <p type="main"> <s id="s.000786">Ad hæc, quæri pote&longs;t, quo pacto plau&longs;trorum rotæ <lb/>in ip&longs;a plau&longs;tri conuer&longs;ione &longs;e habeant, nempe quæ &longs;it li­<lb/>nea illa curua, quam in conuer&longs;ione de&longs;cribunt. </s> </p> <figure id="id.007.01.087.1.jpg" xlink:href="007/01/087/1.jpg"/> <p type="main"> <s id="s.000787">E&longs;to rotarum in <lb/>plano orbita, <expan abbr="dū">dum</expan> plau­<lb/>&longs;trum rectâ procedit <lb/>AB, CD, Sunt autem i­<lb/>p&longs;æ lineæ, quod o&longs;ten­<lb/>demus po&longs;tea, æquedi­<lb/>&longs;tantes. </s> <s id="s.000788">Sit itaque pun­<lb/>ctum. </s> <s id="s.000789">B illud in quod <lb/>rota quæ per AB &longs;er­<lb/>tur, eò delata planum <lb/>tangit. </s> <s id="s.000790">D verò alterius rotæ at que plani contactus. </s> <s id="s.000791">Igitur <lb/>dum plau&longs;tri fit conuer&longs;io, punctum D conuer&longs;ionis fit <lb/>centrum. </s> <s id="s.000792">Stat enim interim rota & circa lineam conuer­<lb/>titur, quæ å puncto contactus D per rotæ centrum ducta <lb/>horizontis plano e&longs;t perpendicularis. </s> <s id="s.000793">ea autem &longs;tante, ro­<lb/>ta quæ in B circa centrum D <expan abbr="&longs;emicirculū">&longs;emicirculum</expan> pertran&longs;it DEF, <lb/>vbi autem rota B, peruenerit in F, plau&longs;tro iam in oppo&longs;i­<lb/>tam partem conuer&longs;o, rota quæ e&longs;t in D per lineam DC, <lb/>quæ verò in F per rectam FG mouetur, plau&longs;triqueue fit re­<lb/>gre&longs;&longs;us. </s> <s id="s.000794">Et quoniam vel D in ip&longs;a conuer&longs;ione &longs;tat omnino <lb/>nec quicquam progreditur, vt in prima figura, vel non &longs;tat <lb/>vt in &longs;ecunda, quo ca&longs;u portionem parui circuli de&longs;cribit, <lb/>ip&longs;i maiori circulo & exteriori concentricam. </s> <s id="s.000795">Vnde col­<lb/>ligimus, Plau&longs;trorum conuer&longs;iones flexione&longs;que &longs;emper <lb/>circa centrum, & concentricorum circulorum portiones <lb/>fieri, <emph type="italics"/>H<emph.end type="italics"/>inc etiam di&longs;cimus, cur veteres, vt ex antiquis co­<pb xlink:href="007/01/088.jpg"/>gno&longs;cimus ve&longs;tigijs, circos in quibus cur&longs;us quadrigarum <lb/>fiebant ea forma quæ apparet, efformauerint. </s> <s id="s.000796">Hoc etiam <lb/>theorema probamus. </s> </p> <p type="main"> <s id="s.000797">Cylindros, quorum ba&longs;es axi &longs;unt perpendiculares, <lb/>dum in æquato plano conuoluuntur, rectâ incedere & <lb/>per parallelas, quarum di&longs;tantia axis &longs;eu latoris longitudi­<lb/>ne præfinitur. </s> </p> <figure id="id.007.01.088.1.jpg" xlink:href="007/01/088/1.jpg"/> <p type="main"> <s id="s.000798">E&longs;to enim Cylin­<lb/>drus ABCD, cuius a­<lb/>xis GH, <expan abbr="horizōtis">horizontis</expan> pla­<lb/>no in&longs;i&longs;tens &longs;ecundum <lb/>latus AB, cui latus op­<lb/>po&longs;itum & aequale CD. <lb/><!-- KEEP S--></s> <s id="s.000799">Moueatur Cylindrus <lb/>rotans, donec latus <lb/>CD, in plano &longs;it vbi EF. <!-- KEEP S--></s> <s id="s.000800">De&longs;cribat autem circuli CB <expan abbr="lineã">lineam</expan> <lb/>BF. <!-- KEEP S--></s> <s id="s.000801">Circulo verò AD lineam AE. <!-- KEEP S--></s> <s id="s.000802">Dico eas rectas e&longs;&longs;e, & <lb/>parallelas. </s> <s id="s.000803">Si enim &longs;uperficies ba&longs;ium DA, CB, extendan­<lb/>tur ita vt horizontis planum &longs;ecent, illud &longs;ecabunt iuxta <lb/>lineas AE BF, recta ergo e&longs;t vtraque. </s> <s id="s.000804">Sed & parallelas e&longs;&longs;e <lb/>ad inuicem ita o&longs;tendimus. </s> <s id="s.000805">quoniam &longs;emicirculus AD, <lb/>æqualis e&longs;t &longs;emicirculo BC, erit linea AE, æqualis lineæ <lb/>BF, &longs;ed & AB, æqualis e&longs;t ip&longs;i DC, quare & ip&longs;i EF. <!-- KEEP S--></s> <s id="s.000806">Oppo­<lb/>&longs;ita igitur quadrilateri figura ABFE latera æqualia &longs;unt, <lb/>quare EF æquedi&longs;tat ip&longs;i AB, tum AE ip&longs;i BF, quod fue­<lb/>rat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.000807">Probabimus etiam &longs;i cylindri ba&longs;es axi perpendicu­<lb/>lares non fuerint, & ideo ellip&longs;es in ip&longs;a rotatione perpla­<lb/>num, parallelas quidem de&longs;cribere, &longs;ed non rectas. </s> </p> <p type="main"> <s id="s.000808">E&longs;to enim Cylindrus ABCD, cuius ba&longs;es ellip&longs;es <expan abbr="inuicē">inuicem</expan> <lb/><expan abbr="æquedi&longs;tãtes">æquedi&longs;tantes</expan>, quarum axes longiores AB, CD, Commu­<lb/>nis autem &longs;ectio cylindri & plani ad axem & horizontem <lb/>planum perpendicularis EHF. <!-- KEEP S--></s> <s id="s.000809">Diuidatur autem &longs;emicir-<pb xlink:href="007/01/089.jpg"/>culus EHF in partes æquales quatuor FI, IH, HG, GE. <lb/><figure id="id.007.01.089.1.jpg" xlink:href="007/01/089/1.jpg"/><lb/>Tum per diui&longs;ionum puncta lateri parallelae, rectæ ducan­<lb/>tur KGL, M<emph type="italics"/>H<emph.end type="italics"/>N, OIP, quæ quidem <expan abbr="cū">cum</expan> ba&longs;es AMB, DNC <lb/>parallelæ &longs;int, erunt inuicem æquales, cumqueue circum­<lb/>ferentia E<emph type="italics"/>H<emph.end type="italics"/>F æquales, eosqueue rectos angulos <expan abbr="cō&longs;tituent">con&longs;tituent</expan>. <lb/></s> <s id="s.000810">Ducatur po&longs;t hæc &longs;eor&longs;um recta QR, & eidem perpendi­<lb/>cularis ST eam &longs;ecans in V. applicetur autem rectæ ST <lb/>æqualis Cylindri lateri BC, ip&longs;a <foreign lang="greek">hz. </foreign></s> <s id="s.000811">ita tamen vt punctum <lb/>E congruat puncto V, &longs;itqueue V<foreign lang="greek">h</foreign> æqualis EB, V<foreign lang="greek">z</foreign> verò æ­<lb/>qualis EC. <!-- KEEP S--></s> <s id="s.000812">Tum fiant VX, XY, YZ, Z<foreign lang="greek">a</foreign> æquales ip&longs;is EG, <lb/>G<emph type="italics"/>H<emph.end type="italics"/>, <emph type="italics"/>H<emph.end type="italics"/>I, IF, & per puncta X, Y, Z, <foreign lang="greek">a</foreign> & paralleli ip&longs;i ST du­<lb/>cantur <foreign lang="greek">o a p, n *z c, l g m, k x q</foreign>, tum & his ex altera parte re­<lb/>&longs;pondentes parallelæ per puncta <foreign lang="greek">b, g, d, e. </foreign></s> <s id="s.000813">Sit autem <foreign lang="greek">o a</foreign> æ­<lb/>qualis AF, <foreign lang="greek">a</foreign> <11> æqualis FD, item <foreign lang="greek">e</foreign> <10>, æqualis EC, <foreign lang="greek">e s</foreign> æqualis <lb/>EB, &longs;ed & <foreign lang="greek">n *z</foreign> aequalis OI, <foreign lang="greek">*z c</foreign> ip&longs;i P, <foreign lang="greek">l</foreign>y ip&longs;i MH, y <foreign lang="greek">m</foreign> verò ip&longs;i <lb/>HN, <expan abbr="tū">tum</expan> <foreign lang="greek">k x</foreign> ip&longs;i KG. & <foreign lang="greek">x q</foreign>, ip&longs;i GL & ip&longs;is æquales & aequa­<lb/>liter po&longs;itæ ad partes R, aliæ parallelæ <expan abbr="aptētur">aptentur</expan> per <foreign lang="greek">b, g, d, c</foreign>, <pb xlink:href="007/01/090.jpg"/>quibus ita di&longs;po&longs;itis per puncta <foreign lang="greek">o, n, l, k, h</foreign>, item per <foreign lang="greek">p, c, m, q, z</foreign>. <lb/></s> <s id="s.000814">ducantur lineæ <foreign lang="greek">oh, pz</foreign>, curuæ quidem & eodem pacto a­<lb/>liæ curuæ illis re&longs;pondentes <foreign lang="greek">h <10>, zs</foreign>, Erunt igitur <foreign lang="greek">o, h, <10>, <lb/>p, z, s</foreign>, parallelæ quidem eo quod lineae quæ inter ip&longs;as du­<lb/>cuntur, parallelæ &longs;int & æquales, non tamen rectæ illæ, <lb/>&longs;ed curuæ. </s> <s id="s.000815">Moto igitur Cylindro circulus EHF rectam <lb/>de&longs;cribet<foreign lang="greek">ae</foreign>, ellip&longs;is verò AMB, curuam <foreign lang="greek">o h r</foreign>, ellip&longs;is au­<lb/>rem DNC, ip&longs;am curuam <foreign lang="greek">pzs. </foreign></s> <s id="s.000816">In hoc <expan abbr="autē">autem</expan> Cylindri mo­<lb/>tu illud mirabile, velociores nempe, in ip&longs;a rotatione e&longs;&longs;e <lb/>ellip&longs;es ip&longs;o circulo EHF. <!-- KEEP S--></s> <s id="s.000817">Ducatur enim recta<foreign lang="greek">o<10></foreign> quæ oc­<lb/>currat ip&longs;i VS in S, & <foreign lang="greek">oh</foreign> iungatur, fietqueue triangulum <lb/><foreign lang="greek">oh</foreign>S. e&longs;t autem, angulus <foreign lang="greek">o</foreign> S <foreign lang="greek">h</foreign> rectus, maior erg. <foreign lang="greek">oh</foreign> i­<lb/>p&longs;a <foreign lang="greek">o</foreign> S, &longs;ed recta <foreign lang="greek">o</foreign> S æqualis e&longs;t ip&longs;i<foreign lang="greek">an</foreign>, hoc e&longs;t, &longs;emicircu­<lb/>lo FHE. multo maior e&longs;t autem curua, <foreign lang="greek">o, n, l, k, h</foreign>, ip&longs;a recta <lb/><foreign lang="greek">oh</foreign>, &longs;ed eodem tempore quo &longs;emicirculus EHF conficit <lb/>in rotatione <expan abbr="&longs;patiū">&longs;patium</expan> <foreign lang="greek">a</foreign> V, eodem dimidia ellip&longs;is BMA me­<lb/>titur curuam <foreign lang="greek">onlkh. </foreign></s> <s id="s.000818">velocior igitur e&longs;t ellip&longs;is ip&longs;o cir­<lb/>culo. </s> </p> <p type="main"> <s id="s.000819">Hæc quoque &longs;peculatio ad motum qui &longs;ecundum <lb/>ab&longs;idem fit, manife&longs;tè pertinet. </s> <s id="s.000820">Coni, quorum ba&longs;es cir­<lb/>culi &longs;unt, &longs;i in plano &longs;ecundum latus rotentur, ba&longs;i circu­<lb/>lum de&longs;cribunt, cuius centrum immobile coni ip&longs;ius e&longs;t <lb/>vertex, &longs;emidiameter verò ip&longs;um latus. </s> </p> <figure id="id.007.01.090.1.jpg" xlink:href="007/01/090/1.jpg"/> <p type="main"> <s id="s.000821">E&longs;to conus ABC cu­<lb/>ius vertex C ba&longs;is AB, axis <lb/>DC, ba&longs;is verò centrum, <lb/>D, latus quo planum tan­<lb/>git BC, &longs;ecatur itaque Co­<lb/>nus per latus BC & axem <lb/>DE à plano horizonti per­<lb/>pendiculari, cuius & coni <lb/>communis &longs;ectio e&longs;t ABC <lb/>triangulum, & quoniam coni grauitatis centrum e&longs;t in <pb xlink:href="007/01/091.jpg"/>axe ip&longs;o, conus in partes æque <expan abbr="pōderantes">ponderantes</expan> &longs;ecatur AEBC, <lb/>AFBC, &longs;tat ergo conus &longs;ibimet æquilibris. </s> <s id="s.000822">Si autem à po­<lb/>tentia quadam moueatur, puta ab A ver&longs;us F, trahitur &longs;e­<lb/>micirculus BEA, à &longs;emicirculo AFB, & ita fit rotatio. </s> <s id="s.000823">Ita­<lb/>que &longs;i imaginemur, in finitos v&longs;que ad verticem parallelos <lb/>ba&longs;i circulos, eorum &longs;emicirculi in ip&longs;o motu & trahent & <lb/>trahentur; at cum ad verticem circuli de&longs;inant, nec ibi &longs;e­<lb/>micirculi &longs;int qui trahant & trahantur, motus rotationis <lb/>pror&longs;us ce&longs;&longs;at & vertex ip&longs;e immobilis fit rotationis cen­<lb/>trum. </s> <s id="s.000824">Quoniam igitur lateris BC, punctum C &longs;tat, B verò <lb/>circa ip&longs;um mouetur, in ip&longs;o motu circulus de&longs;cribitur <lb/>BHIK, cuius &longs;emidiameter BC, & eodem pacto alij cir­<lb/>culi in cono, qui ba&longs;i HEBF &longs;unt æquedi&longs;tantes, circulos <lb/>in plano circa idem centrum de&longs;cribent, vt facile videre <lb/>e&longs;t in obiecto &longs;chemate. </s> <s id="s.000825">Huic &longs;imilem demon&longs;trationem <lb/>affert Heron in libello Automatum, quem nos Tyrones <lb/>adhuc vernacule è Græco translatum, Venetijs prælo <lb/>&longs;ubiecimus. </s> </p> <p type="main"> <s id="s.000826">Porrò &longs;i conus rotundus pro ba&longs;i ellip&longs;im habeat, <lb/>&longs;ectionem videlicet per planum axi non perpendiculare, <lb/>in ip&longs;a rotatione, &longs;tante vertice, ellip&longs;is ba&longs;is, ellip&longs;im de­<lb/>&longs;cribit in plano, cuius maior diameter à puncto quod co­<lb/>ni vertex e&longs;t, ita diuiditur, vt diametri pars maior æqualis <lb/>&longs;it lateri maximo; minor verò æqualis lateri minimo. </s> <s id="s.000827">Sed <lb/>hæc ad aliam pertinent &longs;peculationem. </s> </p> <p type="main"> <s id="s.000828">His itaque de motu rotundorum, qui circa ab&longs;idem <lb/>fit, con&longs;ideratis, reliquum e&longs;&longs;et de motu trochlearum, qui <lb/>circa centrum &longs;it, opportunè agere, &longs;ed cùm in &longs;equenti <lb/>quæ&longs;tione de hoc &longs;ermonem faciat Philo&longs;ophus, ad ea <lb/>quæ ibi di&longs;putabuntur, lectorem ablegamus. </s> </p> <p type="main"> <s id="s.000829">Modò de tertia motus &longs;pecie nobis erit &longs;ermo; in <lb/>qua quidem &longs;pecie nonnulla perpendemus, quæ omi&longs;it A­<lb/>ri&longs;toteles. <!-- KEEP S--></s> <s id="s.000830">Agitur autem hîc de rotundorum corporum <pb xlink:href="007/01/092.jpg"/>motu, qui fit çirca axem horizonti perpendicularem, axis <lb/>altera extremitate in eodem horizontis plano manente, <lb/>vti videre e&longs;t in ip&longs;is figulorum rotis. </s> </p> <p type="main"> <s id="s.000831">Hanc motus &longs;peciem in extrema quæ&longs;tionis parte <lb/>cum duabus alijs &longs;peciebus comparans ait, eam quæ in <lb/>obliquo fit motionem (ita enim hanc, de qua agimus, ap­<lb/>pellat) ip&longs;am impellere mouentem, hoc e&longs;t, nullum ex &longs;e <lb/>ad motum propen&longs;ionem habere, nutumue, & omnia illi <lb/>e&longs;&longs;e à motore, &longs;ecundum verò eam motionem, quæ &longs;upra <lb/>diametrum e&longs;t, &longs;e ip&longs;um mouere circulum. </s> <s id="s.000832">Dixerat enim, <lb/>ea referens quæ &longs;uperiùs circa principium de circulo ver­<lb/>ba faciens, examinauerat, circulum ex duabus fieri latio­<lb/>nibus, altera præter, altera verò &longs;ecundum naturam, & <lb/>ideo hanc &longs;emper nutum habere, & ceu continuo motam <lb/>ab eo moueri qui mouet. </s> <s id="s.000833">Videtur autem clarè profiteri, <lb/>ideo difficiliorem e&longs;&longs;e huius terræ &longs;peciei motum, eo <lb/>quòd nutu careat proprio & tantum ab alieno, vt ita di­<lb/>cam, motore, moueatur. </s> </p> <p type="main"> <s id="s.000834">Veruntamen motum hunc facilitate alijs illis duo­<lb/>bus nequaquam cedere, facilè ex &longs;equentibus o&longs;tende­<lb/>mus. </s> </p> <p type="main"> <s id="s.000835">Primo, quia pondus totum rotati corporis, ex graui­<lb/>tatis centro quod in ip&longs;o axe e&longs;t à plano cui nititur, &longs;u&longs;ti­<lb/>netur: minima quidem &longs;ui parte axe ip&longs;o tangente <expan abbr="planū">planum</expan> <lb/>vnde fit, nullam ferè dum rotatur corpus, circa centrum <lb/>vbi nititur, frictionem partium fieri. </s> <s id="s.000836">Præterea grauitatis <lb/>centrum &longs;emper &longs;tat, nec minimum quidem in ip&longs;a rota­<lb/>tione attollitur, quod &longs;anè cum naturæ &longs;it repugnans, dif­<lb/>ficultatem facit. </s> <s id="s.000837">Ad hæc circa axem ita libratur rota, vt <lb/>quantumuis exigua potentia alteri parti applicetur, alte­<lb/>ra illico &longs;uperata moueatur. </s> <s id="s.000838">Licet enim propriè ea <expan abbr="tantū">tantum</expan> <lb/>corpora æquilibrare dicantur, quæ ob ponderis hinc in de <pb xlink:href="007/01/093.jpg"/>æqualitatem horizonti fiunt æquidi&longs;tantes, nihilominus <lb/>& hic aliquam e&longs;&longs;e æquilibrij &longs;imilitudinem patebit. </s> </p> <figure id="id.007.01.093.1.jpg" xlink:href="007/01/093/1.jpg"/> <p type="main"> <s id="s.000839">E&longs;to enim rota ABCD, <lb/>cuius axis horizonti perpendi­<lb/>cularis FEG tran&longs;iens per cen­<lb/>trum E, tangens autem planum <lb/>in puncto G. <!-- KEEP S--></s> <s id="s.000840">Ducatur diame­<lb/>ter BED, Itaque &longs;i per diame­<lb/>trum BED, & axem FEG cor­<lb/>pus diuidatur, eo quòd <expan abbr="centrū">centrum</expan> <lb/>grauitatis in axe inueniatur, <lb/>corpus ip&longs;um in duas partes <expan abbr="tū">tum</expan> <lb/>mole tum <expan abbr="pōdere">pondere</expan> æquales &longs;ecabitur, nempe BAD, BCD. <lb/><!-- KEEP S--></s> <s id="s.000841">Nulla igitur adhibita vi extranea &longs;tabit corpus in <expan abbr="quodã">quodam</expan>, <lb/>vt diximus, æquilibrio. </s> <s id="s.000842">At alteri partium potentiâ quauis <lb/>licet exigua appo&longs;itâ, puta in C, præualebit pars BCD, & <lb/>partem BAD vel impellet vel rapiet, alterâ interim eius <lb/>motui ob&longs;equente. </s> <s id="s.000843">Potentia igitur quæ in C, nullam rem <lb/>quæ impediat inueniens, veloci&longs;&longs;imè rotam mouet, quod <lb/>eo faciliùs velocius queue fit, quo magis rota e&longs;t in motu, e­<lb/>ius verò diameter maior & potentia mouens à centro re­<lb/>motior, & &longs;anè motus <expan abbr="facilitatē">facilitatem</expan> inde cogno&longs;cimus, quòd <lb/>ip&longs;o impul&longs;ore ab impul&longs;u ce&longs;&longs;ante, diuti&longs;&longs;imè rota im­<lb/>pre&longs;&longs;um motum &longs;eruet, nec ni&longs;i po&longs;t longam rotationem <lb/>omnino quie&longs;cat. </s> </p> <p type="main"> <s id="s.000844">Cæterùm quia &longs;icco, vt aiunt, pede Ari&longs;toteles quæ <lb/>ad hunc motum <expan abbr="pertinēt">pertinent</expan> pertran&longs;ijt, nos quædam quæ ad <lb/>hanc rem faciunt, diligentiùs expendemus. </s> </p> <p type="main"> <s id="s.000845">Quærimus igitur primò; Cur ea quæ hoc pacto <expan abbr="ro-tãtur">ro­<lb/>tantur</expan>, in ip&longs;a rotatione locum non mutent, ni&longs;i extrin&longs;eca <lb/>aliqua id fiat ex cau&longs;&longs;a. </s> </p> <p type="main"> <s id="s.000846">E&longs;to enim rota aut aliud quippiam rotundum ceu <lb/>Turbines &longs;unt, quibus pueri ludunt, quod circa axem ho­<pb xlink:href="007/01/094.jpg"/><figure id="id.007.01.094.1.jpg" xlink:href="007/01/094/1.jpg"/><lb/>rizonti perpendicularem mo­<lb/>ueatur, ABCD, cuius centrum <lb/>E, Diameter AEC. <!-- KEEP S--></s> <s id="s.000847">Modò circa <lb/>centrum E in finiti imaginentur <lb/>circuli, alij alijs minores v&longs;que <lb/>ad <expan abbr="centrū">centrum</expan> ip&longs;um, vti &longs;unt FGH; <lb/>ibi enim circuli e&longs;&longs;e de&longs;inunt, <lb/>vbi nullum amplius e&longs;t &longs;patium. <lb/></s> <s id="s.000848">Applicetur itaque potentia in <lb/>B, quæ rotam v. <!-- REMOVE S-->geat ver&longs;us A. <lb/>eodem igitur tempore & in&longs;imul A ver&longs;us D, D ver&longs;us C, <lb/>& C ver&longs;us B mouebitur. </s> <s id="s.000849">quantum enim &longs;emicirculorum <lb/>à parte CBA tran&longs;it vltra diametrum AEC, tantundem <lb/>&longs;emicirculorum, qui &longs;unt ad partem ADC, tran&longs;ibit ad <lb/>partes CBA. <!-- KEEP S--></s> <s id="s.000850">At vbi de&longs;ierit motus, ibi de&longs;init rotatio; vbi <lb/>autem de&longs;init &longs;patium, de&longs;init motus, &longs;ed vbi de&longs;inunt cir­<lb/>culi, de&longs;init &longs;patium, quare in centro cum non &longs;int circuli, <lb/>nec &longs;patium ibi de&longs;init motus. </s> <s id="s.000851">nulla enim ade&longs;t ratio, cur <lb/>ip&longs;um corpus alio à loco in quo e&longs;t, ex rotatione transfe­<lb/>ratur. </s> <s id="s.000852">Stat ergo rotans, quod fuerat demon&longs;trandum. </s> <s id="s.000853">E&longs;t <lb/>autem hæc demon&longs;tratio ei &longs;imilis, quam &longs;uprà retuli­<lb/>mus de coni in plano circa verticem rotatione, quam ab <lb/>Herone in Automatis excogitatam diximus. </s> </p> <p type="main"> <s id="s.000854">Addimus in hoc rotationis genere corpus in ip&longs;o ­<lb/>motu fieri leuius, idqueue eo magis, quo rotatio velocior. <lb/></s> <s id="s.000855">Cau&longs;&longs;a e&longs;t, quod lateralis motus eum motum aliqualiter <lb/>impedit, qui ex naturali grauitate fit ad centrum, idcirco <lb/>experientiâ docemur, leui&longs;&longs;imos e&longs;&longs;e turbines, quibus pu­<lb/>eri ludunt, &longs;i manus teneantur palmâ, dum citi&longs;&longs;ima rota­<lb/>tione mouentur. </s> </p> <p type="main"> <s id="s.000856">Ad hæc alia proponitur, & &longs;oluitur quæ&longs;tio, Cur ro­<lb/>tunda corpora huic motionis generi &longs;int aptiora. </s> </p> <p type="main"> <s id="s.000857">Explorati&longs;&longs;imum e&longs;t, corporum, quæ ita mouentur, <pb xlink:href="007/01/095.jpg"/>partes eo e&longs;&longs;e velociores, quo magis à centro, circa quod <lb/>mouentur, fuerint remotiores. </s> <s id="s.000858">maius enim eodem tem­<lb/>pore &longs;patium pertran&longs;eunt. </s> <s id="s.000859">quo igitur figura ijs partibus, <lb/>quæ longius à centro ab&longs;unt, abundauerit magis, eo faci­<lb/>lius, & velocius in circulum rotata mouebitur. </s> <s id="s.000860">Modò o­<lb/>&longs;tendemus, circularem cæteras omnes ea qua diximus <lb/>partium à centro remoti&longs;&longs;imarum copiâ abundare. </s> </p> <figure id="id.007.01.095.1.jpg" xlink:href="007/01/095/1.jpg"/> <p type="main"> <s id="s.000861">E&longs;to triangulum puta æqui­<lb/>laterum, ABC circa centrum D. <lb/><!-- KEEP S--></s> <s id="s.000862">Ducantur Catheti per centrum ab <lb/>oppo&longs;itis angulis ad oppo&longs;ita late­<lb/>ra ADG, BDF, CDE, erunt autem <lb/>lateribus perpendiculares. </s> <s id="s.000863"><expan abbr="quoniã">quoniam</expan> <lb/>igitur latera AD, DB, DC, rectis <lb/>angulis &longs;ubtenduntur, maiora <expan abbr="erūt">erunt</expan> <lb/>lateribus DE, DF, DG. tres igitur <lb/>lineæ in hoc triangulo &longs;unt longi&longs;&longs;imæ DA; DB, DC. tres <lb/>verò breui&longs;&longs;imæ DE, DG, DF, quamobrem rotato &longs;uper <lb/>centrum D triangulo, tres tantum partes eius ABC velo­<lb/>ci&longs;&longs;imæ erunt, tres verò tardi&longs;&longs;imæ E, G, F. <!-- KEEP S--></s> <s id="s.000864">Minus igitur a­<lb/>pta e&longs;t motui huic triangularis figura, quam quadrata, in <lb/>qua partes à centro remoti&longs;&longs;imè, & ideo veloci&longs;&longs;imè &longs;unt <lb/>quatuor. </s> <s id="s.000865"><expan abbr="Itaq;">Itaque</expan> quo magis laterata figura angulis abunda­<lb/>bit, eo magis erit ad hunc, & cæteros omnes circulares <lb/>motus aptior. </s> <s id="s.000866">At circulus infinitas, vt ita dicam, partes à <lb/>centro remoti&longs;&longs;imas habet, itaque nulla figura e&longs;t circu­<lb/>lari, in ip&longs;a rotatione, commodior atque velocior. </s> <s id="s.000867">Alia <lb/>quoque de cau&longs;&longs;a id fit, quod dum circularis figura mo­<lb/>uetur, nullis eminentibus angulis aërem verberet <expan abbr="circū-&longs;tãtem">circum­<lb/>&longs;tantem</expan>, ex qua verberatione motus impeditus &longs;it tardior. <lb/></s> <s id="s.000868">Quæri etiam pote&longs;t, Num axe in clinato, rotæ motus ali­<lb/>qualiter impediatur? </s> <s id="s.000869">Nos negatiuam partem amplecti­<lb/>mur. </s> </p> <pb xlink:href="007/01/096.jpg"/> <figure id="id.007.01.096.1.jpg" xlink:href="007/01/096/1.jpg"/> <p type="main"> <s id="s.000870">E&longs;to enim tota ABCD, cuius cen­<lb/>trum E axis inclinatus, circa quem <lb/>conuertitur EGF. <!-- KEEP S--></s> <s id="s.000871">Duobus aute pun­<lb/>ctis fulcitur GF. </s> <s id="s.000872">Sit autem tum gra­<lb/>uius tum figuræ centrum E, Perpen­<lb/>dicularis vero per inferius fulcimen­<lb/>tum tran&longs;iens HFI. </s> <s id="s.000873">Conuer&longs;a igitur <lb/>rota, grauitatis centrum &longs;tabit nec à <lb/>&longs;uo &longs;itu &longs;ur&longs;um deor&longs;umue mouebi­<lb/>tur. </s> <s id="s.000874">E&longs;t autem axis FEG, ceu vectis in <lb/>quo pondus in E, potentiæ &longs;u&longs;tinentes GF; non enim hic <lb/>vt in axe perpendiculari pondus totum ab inferiori fulci­<lb/>mento &longs;u&longs;tinetur. </s> <s id="s.000875">quo igitur minor erit proportio FE ad <lb/>FG, eo minori indigebit potentiâ is qui pondus &longs;u&longs;tinet in <lb/>G. <!-- KEEP S--></s> <s id="s.000876">Et hæc &longs;anè ita &longs;e habent, grauitatis çentro in axe ip&longs;o <lb/>con&longs;tituto, &longs;i enim extra fuerit motus impeditur & moto­<lb/>re ce&longs;&longs;ante citò quie&longs;cit. </s> <s id="s.000877">E&longs;to enim grauitatis centrum in <lb/>K. <!-- KEEP S--></s> <s id="s.000878">Dum igitur circa axem fit motus, centrum circulatum <lb/>aliquando erit in L; Secet autem rotæ diameter AC per­<lb/>pendicularem Hl in M. <!-- KEEP S--></s> <s id="s.000879">Porrò à punctis LK ad ip&longs;am <expan abbr="per-pēdicularem">per­<lb/>pendicularem</expan> ducantur ad rectos angulos lineæ LN, KO. <lb/></s> <s id="s.000880">Maior e&longs;t autem MK ip&longs;a ML, maior ergo MO, ip&longs;a MN. <lb/>magis igitur à mundi centro di&longs;tat punctum N puncto O. <lb/><!-- KEEP S--></s> <s id="s.000881">Centrum ergo grauitatis K &longs;i liberè dimittatur, requie&longs;cet <lb/>in K & contranaturam transferetur in L. <!-- KEEP S--></s> <s id="s.000882">Ce&longs;&longs;ante igitur <lb/>violentiâ & præualente naturâ citò rota &longs;uâ &longs;ponte quie­<lb/>&longs;cet, quod fuerat o&longs;tendendum. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000883">QVÆSTIO IX.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000884"><emph type="italics"/>Quæritur, Cur ea quæ per maiores circulos tolluntur, & trahuntur <lb/>faciliùs, & celeriùs moueri contingat, veluti maioribus tro­<lb/>chleis, & &longs;cytalis &longs;imiliter?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000885">Re&longs;pondet ad hæc Philo&longs;ophus, forte id euenire, quo-<pb xlink:href="007/01/097.jpg"/>niam quanto maior fuerit illa quæ à centro e&longs;t, in æquali <lb/>tempore maius mouetur &longs;patium. </s> <s id="s.000886">quamobrem æquali <lb/>exi&longs;tente onere idem faciet. </s> <s id="s.000887">Ita enim dixerat de <expan abbr="librarū">librarum</expan> <lb/>natura, & differentijs agens, maiores minoribus exactio­<lb/>res e&longs;&longs;e. </s> <s id="s.000888">Circulos verò libras, in quibus centrum &longs;partum, <lb/>&longs;emidiametri hinc in de æqualia brachia. </s> </p> <p type="main"> <s id="s.000889">Quod vltimo loco affirmauit, trochleas e&longs;&longs;e in&longs;tar <lb/>librarum, verum e&longs;t. </s> <s id="s.000890">Quod autem dixit, faciliùs & cele­<lb/>rius mouere maiores libras ijs quæ minores &longs;unt, &longs;i &longs;impli­<lb/>citer intelligatur, fal&longs;um, quippe quod facilitas motus, in <lb/>tractorijs machinis velocitati &longs;it contraria, quod demon­<lb/>&longs;trauit Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->in tractatu de Trochlea in 2. Corol­<lb/>lario propo&longs;itione vltima. </s> </p> <p type="main"> <s id="s.000891">Ad id autem quod dixit, quo <expan abbr="maiorēs">maiores</expan> fuerint tro­<lb/>chleæ, eo faciliùs mouere, non e&longs;t, vt dicebamus, &longs;impli­<lb/>citer verum, quod facilè o&longs;tendemus. </s> </p> <figure id="id.007.01.097.1.jpg" xlink:href="007/01/097/1.jpg"/> <p type="main"> <s id="s.000892">E&longs;to enim trochlea AB circa centrum C, appen&longs;a in <lb/>puncto D, perpendicularis quæ ad mundi centrum DCE, <lb/>pondera æqualia vtrinque appen&longs;a FG. <!-- KEEP S--></s> <s id="s.000893">E&longs;to item alia <lb/>Trochlea, eaque; maior HI, circa centrum K appen&longs;a in L, <lb/>perpendicularis, quæ ad mundi centrum LKM, æqualia <pb xlink:href="007/01/098.jpg"/>pondera vtrinque appen&longs;a N, O. <!-- KEEP S--></s> <s id="s.000894">Dico maiorem Hl ip&longs;a <lb/>minori DE facilius pondera non mouere, eo quòd &longs;it ma­<lb/>ior, illa verò difficiliùs, propterea quòd &longs;it minor. </s> <s id="s.000895">Et enim, <lb/>quoniam vtraque trochlea per centrum grauitatis à per­<lb/>pendiculari diuiditur, erunt partes DAE, DBE, æque <expan abbr="pō-derantes">pon­<lb/>derantes</expan>. </s> <s id="s.000896">Eadem ratione ip&longs;æ quoque LHM, LIM æquè <lb/>ponderabunt. </s> <s id="s.000897">Itaque &longs;i quantumuis pu&longs;illa pondera ad­<lb/>das, <expan abbr="vtriq;">vtrique</expan> earum ad alteram partem tolletur <expan abbr="æquilibriū">æquilibrium</expan>, <lb/>nec minus requiritur pondus vt recedat ab æquilibrio <lb/>Trochlea minor, quàm maior. </s> <s id="s.000898">Vnico autem verbo con­<lb/>cludi pote&longs;t di&longs;putatio, <expan abbr="tã">tam</expan> in minori quàm in maiori, bra­<lb/>chia &longs;iqui dem bifariam diuiduntur, ergo in <expan abbr="vtri&longs;q;">vtri&longs;que</expan> eadem <lb/>brachiorum proportio, & eadem ponderum ratio. </s> </p> <p type="main"> <s id="s.000899">Explorati&longs;&longs;ima &longs;unt hæc. </s> <s id="s.000900">Veruntamen cùm res ip&longs;a <lb/>doceat, verum e&longs;&longs;e quod &longs;cribit Ari&longs;toteles, huius effe­<lb/>ctus cau&longs;&longs;a aliunde à nobis, nempe à mechanicis princi­<lb/>pijs, e&longs;t mutuanda. </s> <s id="s.000901">Dico igitur, Axium, circa quos tro­<lb/>chleæ rotæue conuertuntur ad rotas ip&longs;as, varias habere <lb/>proportiones. </s> <s id="s.000902">O&longs;tendemus autem <expan abbr="rotã">rotam</expan> illam, trochleam­<lb/>ue faciliùs moueri, & mouere pondera, quo rotæ diame­<lb/>ter ad axis diametrum maiorem habuerit proportionem, <lb/>& ideo fieri po&longs;&longs;e rotam maiorem ad &longs;uum axem <expan abbr="minorē">minorem</expan> <lb/>habere proportionem quam rotam minorem ad &longs;uum. </s> </p> <figure id="id.007.01.098.1.jpg" xlink:href="007/01/098/1.jpg"/> <p type="main"> <s id="s.000903">E&longs;to enim <lb/>trochlea AB cir­<lb/>ca centrum C, <lb/>cuius diameter <lb/>DCE &longs;it in ip&longs;a <lb/>quæ ad mundi <lb/>centrum <expan abbr="perpē-diculari">perpen­<lb/>diculari</expan>: &longs;it au­<lb/>tem appen&longs;a in D. <!-- KEEP S--></s> <s id="s.000904">Alia &longs;imiliter ei æqualis &longs;it trochlea F <lb/>G circa centrum H, cuius diameter IHK, conueniens <pb xlink:href="007/01/099.jpg"/>cum perpendiculari quæ ad mundi centrum. </s> <s id="s.000905">appendatur <lb/>autem in I. <!-- KEEP S--></s> <s id="s.000906">Habeant autem & axes, circa quos conuertan­<lb/>tur. </s> <s id="s.000907">Hi &longs;i æquales fuerint, proportione non mutatâ idem <lb/>operabuntur. </s> <s id="s.000908">Modò ponantur inæquales, &longs;itqueue axis ro­<lb/>tæ AB, cra&longs;&longs;ior axe rotæ FG, &longs;itqueue cra&longs;&longs;ioris quidem &longs;emi­<lb/>diameter CL, &longs;ubtilioris autem HM. </s> <s id="s.000909">Dico per trochleam <lb/>FG facilius attolli pondera æqualia quàm per AB, licet <lb/>altera trochlearum alteri &longs;it æqualis. </s> <s id="s.000910">Quoniam enim me­<lb/>chanica corpora &longs;ine materia & pondere non &longs;unt, onera <lb/><expan abbr="appē&longs;a">appen&longs;a</expan> & trochlearum ip&longs;arum grauitas ex &longs;uperiori par­<lb/>te prement axes, vbi puncta L, M, quæres, &longs;ecutâ in uicem <lb/>corporum &longs;olidorum fricatione, motum ip&longs;um trochlea­<lb/>rum difficiliorem & a&longs;periorem facit. </s> <s id="s.000911">Succedit igitur im­<lb/>pedimentum loco ponderis. </s> <s id="s.000912">Duos igitur habemus vectes <lb/>DC, IH, quorum fulcimenta contra ip&longs;a C, H. <!-- KEEP S--></s> <s id="s.000913">Pondera <lb/>verò inter fulcimenta & potentias in L, M. <!-- KEEP S--></s> <s id="s.000914">Intelligantur <lb/>autem potentiæ applicatæ punctis DI. <!-- KEEP S--></s> <s id="s.000915">Igitur ex natura e­<lb/>iu&longs;modi vectis, in quo pondus inter fulcimentum e&longs;t & <lb/>potentiam erit vt CL, ad CD, ita potentia in D ad <expan abbr="pōdus">pondus</expan>, <lb/>hoc e&longs;t, re&longs;i&longs;tentiam fricationis, quæ fit in L. <!-- KEEP S--></s> <s id="s.000916">Sed maior <lb/>e&longs;t proportio CL ad CD quàm HM ad HI. <!-- KEEP S--></s> <s id="s.000917">Maior igitur <lb/>ad &longs;uperandum idem &longs;eu æquale impedimentum poten­<lb/>tia requiritur in D, quam in I. <!-- KEEP S--></s> <s id="s.000918">Itaque cum vis tota in rota­<lb/>rum & axium, diametrorum proportione con&longs;i&longs;tat, fieri <lb/>pote&longs;t, quod dicebamus, minorem trochleam dari, quæ <lb/>maiorem habeat proportionem ad &longs;uum axem, quàm, <lb/>maior ad &longs;uum, quo ca&longs;u minor rota facilius impedimen­<lb/>tum, quod diximus, ip&longs;a maiori rota &longs;eu trochlea &longs;upera­<lb/>bit. </s> <s id="s.000919">Veruntamen quoniam ex materia fiunt tum axes tum <lb/>rotæ, nec rei natura patitur axes &longs;ubtiles, & imbecilles <lb/>magna <expan abbr="pōdera">pondera</expan> &longs;u&longs;tinere po&longs;&longs;e, idcirco cra&longs;&longs;iores fiunt, qu&etail; <lb/>cra&longs;&longs;itudo cum proportione magis à magnarum rotarum <lb/>diametris &longs;uperetur; fit hinc maiores rotas datâ axium pa-<pb xlink:href="007/01/100.jpg"/>ritate facilius impedimentum &longs;uperare quàm minores, & <lb/>hoc videtur &longs;en&longs;i&longs;&longs;e Philo&longs;ophus in ip&longs;a quæ&longs;tionis huius <lb/>propo&longs;itione, Hinc aurigæ vulgo axungiâ (quæ inde no­<lb/>men trahit) axium a&longs;peritates mitigant, vt minor in rotan­<lb/>do, ex fricatione fiat re&longs;i&longs;tentia. </s> <s id="s.000920">Concludimus igitur, fa­<lb/>cillimè trochleam illam pondus trahere, quæ cum maxi­<lb/>ma &longs;it, axem habet minimum, cumqueue axungiâ aliaue vn­<lb/>ctuo&longs;a materia perfu&longs;um. </s> <s id="s.000921">De manubrijs, quæ rotarum a­<lb/>xibus aptantur, nemo ferè verba fecit; nos igitur de his a­<lb/>liquid; &longs;iquidem res ad &longs;peculationem, qua de agimus, <expan abbr="nē-pe">nem­<lb/>pe</expan> Mechanicam pertinet. </s> </p> <p type="main"> <s id="s.000922">Manubria vectes &longs;unt, & ad vectium naturam redu­<lb/>cuntur, eorum &longs;cilicet, in quibus fulcimentum e&longs;t inter <lb/>pondus & potentiam. </s> <s id="s.000923">In his autem attenditur proportio, <lb/>quam habet manubrij longitudo ad ip&longs;um axis &longs;emidia­<lb/>metrum, eo enim faciliùs mouent, quo eorum longitudo <lb/>ad axium &longs;emidiametros proportionem, habuerit ma­<lb/>iorem. </s> <s id="s.000924">Duabus autem partibus con&longs;tant, alterâ, quæ ab <lb/>axe ad angulum; quæ verè vectis e&longs;t; alterâ, cui manus i­<lb/>p&longs;a admouetur, ex qua res tota manubrium dicitur. </s> <s id="s.000925">Fiunt <lb/>autem manubria hæc vt plurimum amouibilia, &longs;unt <expan abbr="tamē">tamen</expan> <lb/>ceu rotarum ip&longs;arum partes, & rotis ip&longs;is commodè affi­<lb/>gerentur, ni&longs;i in rotatione à tran&longs;uer&longs;arijs, quibus rotæ &longs;u­<lb/>&longs;tinentur, impedimentum fieret. </s> </p> <figure id="id.007.01.100.1.jpg" xlink:href="007/01/100/1.jpg"/> <p type="main"> <s id="s.000926">E&longs;to enim rota AB, cu­<lb/>ius axis E, terebretur autem <lb/>in F, ibiqueue paxillus affigatur <lb/>FK. <!-- KEEP S--></s> <s id="s.000927">Sit & alia rota CD, cu­<lb/>ius axis G, manubrium axi <lb/>appo&longs;itum GHI. <!-- KEEP S--></s> <s id="s.000928">Sint autem <lb/>rotæ æquales & axes æqua­<lb/>les. </s> <s id="s.000929">Sint etiam æqualia ip&longs;a <lb/>&longs;patia EF, GH, hoc e&longs;t, ma-<pb xlink:href="007/01/101.jpg"/>nubrij GHI longitudo. </s> <s id="s.000930">Dico, eâdem facilitate moueri AB <lb/>rotam à potentia in FK, quâ mouetur CB, à potentia po­<lb/>&longs;ita in HI, datis ip&longs;i nempe potentijs æqualibus. </s> <s id="s.000931">Produca­<lb/>tur enim IH, v&longs;que ad rotæ CD latus in L, & LG ducatur, <lb/>& FE in rota AB iungatur. </s> <s id="s.000932">Erunt igitur FE LG inter &longs;e æ­<lb/>quales. </s> <s id="s.000933">Sunt autem eorum circulorum &longs;emidiametri, qui <lb/>à punctis FL, in ip&longs;a rotatione de&longs;cribuntur. </s> <s id="s.000934">Ita igitur &longs;e <lb/>habebit potentia applicata in L ad diametrum &longs;emidia­<lb/>metrumue axis rotæ CD, vt &longs;e habet potentia applicata <lb/>in F, ad diametrum &longs;emidiametrumue axis E rotæ AB, &longs;ed <lb/>&longs;patia &longs;unt æqualia & potentiæ æquales, quare nihil re­<lb/>fert, vtrum manubrium lateri affigatur, vel axi à latere ro­<lb/>tæ &longs;eparatum applicetur. </s> </p> <figure id="id.007.01.101.1.jpg" xlink:href="007/01/101/1.jpg"/> <p type="main"> <s id="s.000935">Duplex autem e&longs;t ma­<lb/>nubriorum forma; altera e­<lb/>nim rectis partibus con&longs;tat, <lb/>altera verò curua e&longs;t tota, <lb/>&longs;ed rectis vtimur vt mani­<lb/>bus apprendamus, curuis <lb/>verò vt locum illis appona­<lb/>mus, & pedis pre&longs;&longs;ione ceu <lb/>in molis lapideis, quibus <lb/>gladij acuuntur, fieri a&longs;&longs;olet, conuertantur. </s> <s id="s.000936">Cur autem <lb/>manubria hæc curua fiant, ea videtur ratio, ne videlicet <lb/>manubrij capite &longs;upra centrum in linea quæ per centrum <lb/>tran&longs;it, <expan abbr="cō&longs;tituto">con&longs;tituto</expan>, factâ interim pre&longs;&longs;ione motus à centro, <lb/>ad quod directè fieret pre&longs;&longs;io, impediretur. </s> <s id="s.000937">Curuitas <expan abbr="autē">autem</expan> <lb/>facilitatem quandam habet, ex qua factâ modicâ flexione <lb/>axis caput, dum premitur ab ip&longs;a perpendiculari linea le­<lb/>niter abducitur. </s> <s id="s.000938">quæ cum ce&longs;&longs;ent in manubrijs quæ manu <lb/>aguntur, ideo alia forma, nempe ex rectis partibus pa&longs;&longs;im <lb/>fiunt. </s> <s id="s.000939">E&longs;to igitur illud quod ex rectis partibus AB, curuum <lb/>verò CD, linea verò, &longs;ecundum quam pede fit pre&longs;&longs;io <pb xlink:href="007/01/102.jpg"/>CDE. <!-- KEEP S--></s> <s id="s.000940">Hæc itaque de manubrijs &longs;eu vectibus nos con&longs;i­<lb/>dera&longs;&longs;e &longs;it &longs;atis. </s> </p> <p type="main"> <s id="s.000941">Quæri interim po&longs;&longs;et, Cur duabus datis rotis æqua­<lb/>lis magnitudinis in æqualis ponderis, circa æquales axes <lb/>con&longs;titutis leuior faciliùs moueatur & citiùs quie&longs;cat; <lb/>grauior verò difficilius moueatur & tardiùs ce&longs;&longs;et à mo­<lb/>tu, ea videtur ratio, quod grauior re&longs;i&longs;tens magis cum &longs;u­<lb/>peratur impre&longs;&longs;am vim &longs;u&longs;cipit, & diutiùs retinet, quod <lb/>ce&longs;&longs;at in leuiore. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000942">QVÆSTIO X.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000943"><emph type="italics"/>Dubitat Ari&longs;toteles, Cur faciliùs, quando &longs;ine pondere est, mouea­<lb/>tur libra, quàm cum pondus habet. </s> <s id="s.000944">Simili modo rota, & eiu&longs;modi <lb/>quidpiam, quod grauius quidem est, item quod maius & <lb/>grauius minori, & leuiori?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000945">Breuiter autem &longs;oluit, ait enim, An quia non &longs;olum in <lb/>contrarium quod graue e&longs;t, &longs;ed in obliquam etiam dif­<lb/>ficulter mouetur? </s> <s id="s.000946">In contrarium enim ei ad quod vergit <lb/>onus mouere difficile e&longs;t, quo autem vergit, e&longs;t facile. </s> <s id="s.000947">In <lb/>obliquum autem haudquaquam vergit. </s> <s id="s.000948">Nos quod ip&longs;e <lb/>non fecit figurâ ip&longs;a appo&longs;itâ rem clariorem faciemus. </s> </p> <figure id="id.007.01.102.1.jpg" xlink:href="007/01/102/1.jpg"/> <p type="main"> <s id="s.000949">E&longs;to libra AB, cuius ful­<lb/>cimentum C, pondera vtrin­<lb/>que appen&longs;a AB, quorum v­<lb/>trumque ponderet 10. Item <lb/>libra DE, cuius fulcimentum <lb/>F pondere vero appen&longs;a D, E, <lb/>ip&longs;is A, B, dimidio leuiora, <expan abbr="nē-pe">nem­<lb/>pe</expan> S. <!-- KEEP S--></s> <s id="s.000950">Addatur ponderi B pon­<lb/>dus G, & ponderi E pondus <lb/>H, quorum &longs;imiliter <expan abbr="vtrumq;">vtrumque</expan> <lb/>ponderet S, nutabunt igitur <lb/>libræ ponderibus appo&longs;itis, & <pb xlink:href="007/01/103.jpg"/>BG &longs;ecetur in K, EH verò in N, grauius e&longs;t autem GB, e&longs;t <lb/>enim IS, ip&longs;o EH, quod e&longs;t 10. Difficiliùs autem de&longs;cen­<lb/>det BG, quàm EH. hoc autem ex doctrina Ari&longs;totelis, <lb/>quia non &longs;olum in contrarium quod graue e&longs;t, &longs;ed in obli­<lb/>quum etiam difficulter mouetur, in contrarium enim ei <lb/>ad quod vergit onus mouere difficile e&longs;t, quò autem ver­<lb/>git facilè in obliquum autem puta per lineas BK, EN non <lb/>vergit onus. </s> <s id="s.000951">Difficiliùs ergo in obliquum mouebitur pon­<lb/>dus BG ip&longs;o pondere EH. vtrumque autem in de&longs;cen&longs;u <lb/>retrahitur nempe à perpendicularibus BI, EM & retra­<lb/>ctionis quidem anguli &longs;unt æquales & æquales ip&longs;æ retra­<lb/>ctiones. </s> <s id="s.000952">Sed grauius e&longs;t pondus GB. quod autem grauius <lb/>e&longs;t, violentius <expan abbr="de&longs;cēdit">de&longs;cendit</expan> eo quod e&longs;t leuius. </s> <s id="s.000953">maiori igitur ni­<lb/>&longs;u atque impetu cum cætera paria &longs;int, de&longs;cendet pondus <lb/>BG, ip&longs;o EH, quod è diametro Ari&longs;totelis a&longs;&longs;ertioni e&longs;t <lb/>contrarium. </s> <s id="s.000954">ex alijs igitur principijs veritas ip&longs;a e&longs;t eruen­<lb/>da. </s> <s id="s.000955">Dicimus autem id ex proportionum fieri inæqualita­<lb/>te; quia enim is ad 10. proportionem habet &longs;e&longs;quialteram, <lb/>10. verò ad 5. duplam, maiorem proportionem habet EH <lb/>ad oppo&longs;itum pondus D, quàm BG ad pondus A, facilius <lb/>ergo trahet libra DE leuior pondus D, quàm ip&longs;a AB, gra­<lb/>uior pondus A, quod vtique fuerat o&longs;tendendum. </s> <s id="s.000956">Alia <lb/>quoque cau&longs;&longs;a & hæc accidentalis ad hunc effectum pa­<lb/>riendum concurrit, axium nempe ad fulcimenta, in qui­<lb/>bus rotantur, fricatio. </s> <s id="s.000957">quo enim maius e&longs;t pondus cæteris <lb/>paribus, quod nos in præ cedente quæ&longs;tione demon&longs;tra­<lb/>uimus, eò maiìor fit ip&longs;a colli&longs;io. </s> </p> <p type="main"> <s id="s.000958">Porrò huius <expan abbr="quoq;">quoque</expan> &longs;peculationis e&longs;t, Cur æqualia & <lb/>&longs;imilia corpora in æqualibus &longs;imilibu&longs;queue ba&longs;ibus con&longs;ti­<lb/>tuta eodem &longs;imiliqueue plano fulta, ponderibus tamen in­<lb/>æqualia, non eâdem facilitate euertantur, &longs;ed horum gra­<lb/>uiora difficilius. </s> </p> <pb xlink:href="007/01/104.jpg"/> <figure id="id.007.01.104.1.jpg" xlink:href="007/01/104/1.jpg"/> <p type="main"> <s id="s.000959">Sit enim Pri&longs;ma &longs;eu <lb/>Cylindrus ABCD, cuius <lb/>grauitatis centrum E in <lb/>plano Cl, ba&longs;i fultus CD. <lb/><!-- KEEP S--></s> <s id="s.000960">Sit & alter Cylindrus <lb/>FGHI, cuius grauitatis <lb/>centrum K fultus ba&longs;i HI <lb/>æqualis quidem & &longs;imilis <lb/>ip&longs;i AD. <!-- KEEP S--></s> <s id="s.000961">Sit autem grauior FGHI, ip&longs;o ABCD. Dico, pari <lb/>potentiâ vtrumque impellente, facilius euer&longs;um iri Cy­<lb/>lindrum AD, ip&longs;o Fl. </s> <s id="s.000962">Ducantur EC, KH, & æquales po­<lb/>tentiæ applicentur punctis BG, pellentes Cylindros ad <lb/>partes AF. <!-- KEEP S--></s> <s id="s.000963">Euer&longs;io autem non fiet donec facta corporis <lb/>conuer&longs;ione circa puncta CH, grauitatis centra E, K <expan abbr="trãs-ferunturin">trans­<lb/>feruntur in</expan> L, M, in ip&longs;is &longs;cilicet <expan abbr="perpēdicularibus">perpendicularibus</expan> ACFH. <lb/><!-- KEEP S--></s> <s id="s.000964">Demittantur EN, KO, perpendiculares ip&longs;is CD, HF. </s> <s id="s.000965">Et <lb/>quoniam CNE, HOK anguli recti &longs;unt, erunt EC KH i­<lb/>p&longs;is EN, KO, maiores, quare & LC, MH ip&longs;is EN KO, ma­<lb/>iores attolluntur ergo in ip&longs;a euer&longs;ione, grauitatum cen­<lb/>tra E in L, K in M. <!-- KEEP S--></s> <s id="s.000966">At quod grauius e&longs;t, difficilius contra <lb/>&longs;ui naturam mouetur, ideo difficilius euertetur corpus <lb/>FI, ip&longs;o AD, quod fuerat demon&longs;trandum. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.000967">QVÆSTIO XI.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.000968"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;uper &longs;cytalas facilius portentur onera <lb/>quàm &longs;uper currus, cum tamen ij magnas habeant rotas, <lb/>illæ verò pu&longs;illas?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.000969">Optimè re&longs;pondet dubitationi. </s> <s id="s.000970">An, inquiens, quoniam <lb/>in &longs;cytalis nulla e&longs;t offen&longs;atio; in curribus verò axis <lb/>e&longs;t, ad quem offen&longs;ant. </s> <s id="s.000971">De&longs;uper enim illum premunt, & <lb/>à lateribus. </s> <s id="s.000972">quod autem e&longs;t in &longs;cytalis ad i&longs;thæc duo mo­<lb/>uetur & inferiori &longs;ub&longs;trato &longs;patio, & onere &longs;uperimpo&longs;i-<pb xlink:href="007/01/105.jpg"/>to, in vtri&longs;que enim ijs reuoluitur locis circulus, & motus <lb/>impellitur. </s> <s id="s.000973">Tam appo&longs;itè paucis verbis veritatem expli­<lb/>cauit, vt ferè quicquid in&longs;uper ad datur, &longs;uperuacaneum <lb/>videri po&longs;&longs;it. </s> <s id="s.000974">quicquid tamen &longs;it, ad maiorem claritatem <lb/>aliquantulum in hac ip&longs;a quæ&longs;tione immorabimur. </s> </p> <p type="main"> <s id="s.000975">Rotatas &longs;cytalas proponit hîc Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.000976">Coniun­<lb/>ctas autem e&longs;&longs;e rotas ip&longs;is &longs;cytalis e&longs;t intelligendum, nem­<lb/>pe, vt &longs;imul rotæ cum &longs;cytalis conuertantur. </s> <s id="s.000977">Secus enim <lb/>axium & Rotarum fieret offen&longs;atio, cuius offen&longs;ationis <lb/>vim & effectum cum nouerit Ari&longs;toteles, vel hoc ip&longs;o lo­<lb/>co te&longs;te, mirum e&longs;t, nihil de ea egi&longs;&longs;e quæ&longs;tione 9. vbi nos <lb/>hac de re fu&longs;i&longs;&longs;imè tractauimus. </s> </p> <p type="main"> <s id="s.000978">Cæterùm quod de rotatis &longs;cytalis &longs;cribit Philo&longs;o­<lb/>phus, notandum, à Pappo quidem lib. 8. & à no&longs;tris Me­<lb/>chanicis pa&longs;&longs;im ab&longs;que rotis Cylindrica &longs;implici videli­<lb/>cet, & tereti formâ ad v&longs;um adhiberi. </s> <s id="s.000979">E&longs;to igitur Ari­<lb/><figure id="id.007.01.105.1.jpg" xlink:href="007/01/105/1.jpg"/><lb/>&longs;totelis quidem &longs;cytala <lb/>AB, Pappi verò &longs;eu vul­<lb/>garis, & communis CD. <lb/><!-- KEEP S--></s> <s id="s.000980">His non modò lapicidæ <lb/>pa&longs;&longs;im, &longs;ed & nautæ na­<lb/>uiumqueue fabri &longs;ubdu­<lb/>cendis & mari inducen­<lb/>dis nauibus vtuntur, quod varare dicunt vernaculè, Hi­<lb/>&longs;panico, vt arbitror, vocabulo. </s> <s id="s.000981">ca enim natio teres lignum <lb/>baculumue appellat Varam. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.000982">Quæri autem po&longs;&longs;et, vtra harum formatum &longs;it vti­<lb/>lior atque commodior? </s> <s id="s.000983">Nos rotatas laudamus magis in <lb/>plano duroqueue &longs;olo, minus enim tangunt & minus offen­<lb/>&longs;ant; in molliori autem & minus duro proponimus non <lb/>rotatas, &longs;iquidem rotæ &longs;ui naturâ pondere pre&longs;&longs;æ &longs;olum, <lb/>facillimè &longs;cindunt & ab&longs;orbentur. </s> </p> <p type="main"> <s id="s.000984">Quatenus autem ad v&longs;um pertinet. </s> <s id="s.000985">E&longs;to horizontis <pb xlink:href="007/01/106.jpg"/><figure id="id.007.01.106.1.jpg" xlink:href="007/01/106/1.jpg"/><lb/>planum AB, &longs;cytalae duae <lb/>CD, EF, Pondus verò <lb/>eis impo&longs;itum G, tan­<lb/>gens ip&longs;as in <expan abbr="pūctis">punctis</expan> CE, <lb/>&longs;cytalæ autem planum <lb/>in punctis D, F, Pellatur <lb/>à potentia quapiam <expan abbr="pō-dus">pon­<lb/>dus</expan> G ad anteriora, <expan abbr="nē-pe">nen­<lb/>pe</expan> ad partes E. rotabuntur igitur &longs;cytalæ & pars quædam <lb/>&longs;cytalæ D, in qua &longs;it contactus a&longs;cendet in I, C verò de­<lb/>&longs;cendet in H, nulla re motum impediente, quippe quòd <lb/>nulla ponderis &longs;cytalarum, & plani ad inuicem fiat offen­<lb/>&longs;atio. </s> <s id="s.000986">Præterea cum &longs;cytalarum centra ab horizontis pla­<lb/>no æqualiter di&longs;tent, pondus quidem horizonti æquidi­<lb/>&longs;tanter mouetur, & ideo eius centrum grauitatis nequa­<lb/>quam, in motu qui &longs;it, eleuatur. </s> </p> <p type="main"> <s id="s.000987">Cæterùm materiæ imperfectione remota nihil re­<lb/>fert ad facilitatem, vtrum maioris minorisue diametri <lb/>&longs;int &longs;cytalæ, vt ea po&longs;ita eo quod maiores circuli faciliùs <lb/>offendicula &longs;uperent, quod demon&longs;tratum e&longs;t in quæ&longs;tio­<lb/>ne 8. eo vtiliores &longs;unt &longs;cytalæ, quo cra&longs;&longs;iores. </s> <s id="s.000988">Quatenus <lb/>autem ad plau&longs;tri naturam &longs;pectat, cuius ad &longs;cytalas Phi­<lb/>lo&longs;ophus fecit comparationem, vt o&longs;ten damus difficilius <lb/>ex eo moueri pondera. </s> </p> <figure id="id.007.01.106.2.jpg" xlink:href="007/01/106/2.jpg"/> <p type="main"> <s id="s.000989">E&longs;to plau&longs;tri rota <lb/>KL, cuius centrum M, a­<lb/>xis verò NO circa quem <lb/>rota ip&longs;a conuertitur KL. <lb/><!-- KEEP S--></s> <s id="s.000990">Funis quo rota ex axis <lb/>centro M trahitur MP, <lb/>pondus vero QR. </s> <s id="s.000991">Quo­<lb/>niam igitur pondus axem <lb/>premit in N, axis autem rotæ modiolum in O, & eodem, <pb xlink:href="007/01/107.jpg"/>tempore potentia quæ trahit in P, axem admouet modio­<lb/>lo in parte V. duplex itaque fit ex fricatione &longs;eu offen&longs;a­<lb/>tione impedimentum, infra nempe, vbi O, & ad latus vbi <lb/>V. quæ quidem offen&longs;iones currus motum reddunt diffi­<lb/>ciliorem, quæ quidem difficultas eo maior erit, quo ma­<lb/>ior fuerit pondus axem premens, & minor proportio &longs;e­<lb/>midiametri rotæ KM, ad axis &longs;emidiametrum MO. </s> <s id="s.000992">Cur <lb/>igitur &longs;cytalis facilius pondera transferantur quam plau­<lb/>&longs;tris, apertè ex dictis ad Ari&longs;to telis mentem demon&longs;tra­<lb/>uimus. </s> </p> <p type="main"> <s id="s.000993">Cæterùm quod ip&longs;e reticuit, nos dicemus, nempe <lb/>validi&longs;&longs;imè enormia pondera per &longs;cytalas moueri, &longs;i &longs;cy­<lb/>talis ip&longs;is vectes adiungantur. </s> <s id="s.000994">Et &longs;anè motus erit tardi&longs;&longs;i­<lb/>mus, veruntamen tarditas ip&longs;a facilitate, quæ in de fit, v­<lb/>berrimè compen&longs;atur. </s> </p> <figure id="id.007.01.107.1.jpg" xlink:href="007/01/107/1.jpg"/> <p type="main"> <s id="s.000995">E&longs;to igitur horizontis planum AB, &longs;cytalæ CD, fo­<lb/>ramina in &longs;cytalis EFGH, vectes foraminibus in&longs;erti IE, <lb/>KF, LG, MH. </s> <s id="s.000996">Pondus vero &longs;cytalis impo&longs;itum N. <!-- KEEP S--></s> <s id="s.000997">Appli­<lb/>catis igìtur quatuor potentijs extremitatibus vectium I, <lb/><emph type="italics"/>K<emph.end type="italics"/>, L, M, ij&longs;que in anteriora propul&longs;is, fiet &longs;cytalarum rota-<pb xlink:href="007/01/108.jpg"/>tio, & ponderis N translatio ad anteriores partes B. <!-- KEEP S--></s> <s id="s.000998">E&longs;to <lb/>item &longs;eor&longs;um &longs;cytala PR, cuius centrum Q, vectis eidem <lb/>per centrum in&longs;ertus O, P, Q, R. facto igitur vectis motu <lb/>O P Q R fiet ex O; centro <expan abbr="autē">autem</expan> Q circuli quadrans O T. <lb/>exi&longs;tente igitur O in T erit P in S. facta quartæ partis ip&longs;ius <lb/>&longs;cytalæ rotatione. </s> <s id="s.000999">Et quoniam ex eodem centro &longs;unt qua­<lb/>drantes PSOT. erit vt OQ ad QP. ita quadrans OT, ad <lb/>quadrantem PS. <!-- KEEP S--></s> <s id="s.001000">Maxima autem e&longs;t proportio OQ, ad <lb/>QP. </s> <s id="s.001001">Maxima igitur proportio OT ad PS. <!-- KEEP S--></s> <s id="s.001002">Ex magno igitur <lb/>motu O ad T, paruus &longs;it &longs;cytalæ motus à P in S. tardius i­<lb/>gitur progreditur &longs;cytala, quæ longioribus vectibus rota­<lb/>tur, vis tamen maxima, quippe quod vt &longs;e habet QP, hoc <lb/>e&longs;t, QR ad QO, ita potentia in O ad pondus quod premit <lb/>in P vel in V. <!-- KEEP S--></s> <s id="s.001003">Facillimè itaque pondera vectibus & &longs;cyta­<lb/>lis per horizontis planum transferri, exi&longs;tis patet. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001004">QVAESTIO XII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001005"><emph type="italics"/>Quæritur, Cur Mi&longs;&longs;ilia longius funda mittantur quam manu, <lb/>præ&longs;ertim cum proijcienti fundæ pondus addatur lapidis &longs;eu mi&longs;&longs;i­<lb/>lis ponderi: & minus mi&longs;&longs;ili, manu proiecto, com­<lb/>prehendatur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001006">Soluit Philo&longs;ophus, inquiens, fortè ita fieri, quòd fun­<lb/>ditor mi&longs;&longs;ile proijciat iam ex funda commotum, &longs;iqui­<lb/>dem fundam circulo &longs;ubinde rotans, iaculatur, ex manu <lb/>autem à quiete e&longs;t initium. </s> <s id="s.001007">Omnia autem cum in motu <lb/>&longs;unt, quàm cum quie&longs;cunt, facilius mouentur. </s> <s id="s.001008">Addit præ­<lb/>terea, An & ob eam cau&longs;&longs;am e&longs;t, &longs;ed nec minus etiam, quia <lb/>infunde v&longs;u manus quidem fit centrum, funda verò quod <lb/>à centro exit? </s> <s id="s.001009">quantò igitur productius fuerit quod à cen­<lb/>tro e&longs;t, tanto citiùs mouetur; iactus autem, qui manu fit, <lb/>fundæ re&longs;pectu breuior e&longs;t. </s> </p> <p type="main"> <s id="s.001010">Hæc Philo&longs;ophus. <!-- KEEP S--></s> <s id="s.001011">Et &longs;anè perquàm appo&longs;itè, <expan abbr="itaq;">itaque</expan> <pb xlink:href="007/01/109.jpg"/>illi pror&longs;us a&longs;&longs;entirer, ni&longs;i pro comperto haberem, in iactu <lb/>qui fundâ fit, non e&longs;&longs;e manum ip&longs;am motus centium, &longs;ed <lb/>potius partem illam brachij, quæ humero iungitur, & id­<lb/>eo motum eo fieri velociorem, quo longior e&longs;t linea quæ <lb/>ab humero ad &longs;ummitatem fundæ e&longs;t, ea quæ ab humero <lb/>ad manum ip&longs;am. </s> <s id="s.001012">Illud quoque mirabile e&longs;t, quod non <lb/>ob&longs;eruat Ari&longs;toteles, nempe à funditoribus in ip&longs;o eiacu­<lb/>landi actu, tardam fieri circa caput fundæ rotationem. <lb/></s> <s id="s.001013">Quamobrem con&longs;iderandum e&longs;t, quo pacto fiat à tardi­<lb/>tate velocitas. </s> <s id="s.001014">Re&longs;pondemus, velocitatem acquiri non ex <lb/>&longs;implici, quæ circa funditoris caput &longs;it, rotatione, &longs;ed ex <lb/>eo impetu qui fit in ip&longs;a lapidis emi&longs;&longs;ione, qui quidem im­<lb/>petus &longs;i ante vel po&longs;t illud tempus fiat, quod à funditore <lb/>captatur, ca&longs;&longs;a pror&longs;us & inualida fit ip&longs;a iaculatio. </s> </p> <figure id="id.007.01.109.1.jpg" xlink:href="007/01/109/1.jpg"/> <p type="main"> <s id="s.001015">E&longs;to funda AB, manus <lb/>B, brachium BC. <!-- KEEP S--></s> <s id="s.001016">Vt igitur &longs;e <lb/>habet CH, ad CB, ita veloci­<lb/>tas AD ad velocitatem, BE; <lb/>Vidimus nos pueros, arundi­<lb/>ni ad caput &longs;ci&longs;&longs;æ, paruos la­<lb/>pides in&longs;erentes, arundinem­<lb/>queue manu rotantes longi&longs;&longs;i­<lb/>mè lapides ip&longs;os proijcere; A­<lb/>rundo FG, lapis F, manus G, <lb/>brachium GH. <!-- KEEP S--></s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001017">QVÆSTIO XIII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001018"><emph type="italics"/>Quæritur, Cur circa idem iugum, maiores collopes (vectes &longs;unt, <lb/>quos alij &longs;cytalas appellant, vt Pappus & Heron) faciliùs quàm mi­<lb/>nores mouentur: & item &longs;uculæ, quæ graciliores &longs;unt eadem <lb/>vi quam cra&longs;&longs;iores?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001019">Ideo hoc fieri po&longs;&longs;e docet Philo&longs;ophus, quòd <expan abbr="tamiugū">tam iugum</expan> <lb/>quam &longs;ucula <expan abbr="cētrum">centrum</expan> &longs;it, prominentes autem collopum <pb xlink:href="007/01/110.jpg"/>longitudines eæ lineæ quæ &longs;unt à centro. </s> <s id="s.001020">Celeriùs autem <lb/>moueri & plus ab eadem vi quæ maiorum &longs;unt <expan abbr="circulorū">circulorum</expan> <lb/>quàm quæ minorum. </s> <s id="s.001021">quippe quod ab ea dem vi plus <expan abbr="trã&longs;-feratur">tran&longs;­<lb/>feratur</expan> illud extremum quod longius à centro di&longs;tat. </s> <s id="s.001022">In <lb/>gracilioribus verò &longs;uculis datâ collopum paritate plus e&longs;­<lb/>&longs;e id quod à ligno di&longs;tat. </s> </p> <figure id="id.007.01.110.1.jpg" xlink:href="007/01/110/1.jpg"/> <p type="main"> <s id="s.001023">E&longs;to iugum &longs;ucu­<lb/>laue maior, AB circa <lb/>centrum C, minor verò <lb/>circa idem <expan abbr="centrū">centrum</expan> DE. <lb/><!-- KEEP S--></s> <s id="s.001024">Collops <expan abbr="autē">autem</expan> AF, pon­<lb/>dus quod per iugum at­<lb/>tollitur G. <!-- KEEP S--></s> <s id="s.001025">A it igitur A­<lb/>ri&longs;toteles, &longs;uculas, iu­<lb/>gaue AB, DE ceu cen­<lb/>tra e&longs;&longs;e, à quibus extat colops AB, ex maiori quidem, totâ <lb/>&longs;ui parte BF, ex minori autem EF. quo igitur, ait, longior <lb/>fuerit collops extans, eo maior, & deo velocior ad <expan abbr="partē">partem</expan> <lb/>F per maiorem circulum FH, fiet collopis motus & pon­<lb/>deris eleuatio, at maior e&longs;t collops EF ip&longs;o BF, facil. </s> <s id="s.001026">us er­<lb/>go mouebitur pondus per &longs;uculam DE, ex collope EF, ab <lb/>eadem vi, quam per &longs;uculam AB, & collopem BF. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001027">Hæc &longs;en&longs;i&longs;&longs;e videtur Ari&longs;to teles, qui cra&longs;&longs;a, vt aiunt, <lb/>Minerua rem pulchram & &longs;ubtilem e&longs;t pro&longs;equutus. </s> <s id="s.001028">Di­<lb/>cimus igitur primò, in&longs;trumentum illud quod Latini &longs;u­<lb/>culam, id e&longs;t, &longs;ero&longs;ulam, à &longs;tridore arbitror qui in conuer­<lb/>&longs;ione fit, appellauere, Græci verò <foreign lang="greek">o)/non</foreign>, id e&longs;t, A &longs;inum, quip­<lb/>pe quod ceu A &longs;inus pondera &longs;u&longs;tineat portetque. </s> <s id="s.001029">Hanc <lb/>eandem Machinam veteres Mechanici vocauere Axem <lb/>in Peritrochio, cuius nos imaginem, è Pàppo in 8. Col­<lb/>lect. <!-- REMOVE S-->Mathematicarum de&longs;umptam in ip&longs;o huius no&longs;tri o­<lb/>peris initio, inter quinque Potentias propo&longs;uimus. </s> <s id="s.001030">Huius <lb/>vim inter antiquos diligenti&longs;&longs;ime examinauêre Heron, & <pb xlink:href="007/01/111.jpg"/>ip&longs;emet Pappus, inter iuniores verò Guilibaldus eo Tra­<lb/>ctatu quem hac de Potentia Mechanicis &longs;uis in&longs;eruit. <lb/></s> <s id="s.001031">Summa e&longs;t, hanc Machinam ad vectem reduci. </s> <s id="s.001032">Nec ve­<lb/>rum e&longs;t quod &longs;cribit Ari&longs;to teles, iugum &longs;uculamue cen­<lb/>tra e&longs;&longs;e, hæc enim centrum habent, quod in figura &longs;upe­<lb/>rius po&longs;ita notatur &longs;igno C. igitur vt &longs;e habet FC, ad CA, <lb/>ita pondus G ad potentiam in F; e&longs;t autem maior propor­<lb/>tio FC ad CD, quàm FC, ad CA. faciliùs ergo mouebit <lb/>potentia quæ in F, pondus in D, quàm eadem potentia F, <lb/>pondus in A, hoc e&longs;t, G. <!-- KEEP S--></s> <s id="s.001033">Huius naturæ &longs;unt quo que Erga­<lb/>tæ, quas machinas no&longs;tri, Græco luxato vocabulo Arga­<lb/>nos appellant. </s> <s id="s.001034">Suculæ enim reuera &longs;unt, po&longs;itione <expan abbr="tantū">tantum</expan> <lb/>ab eis differentes, non enim plano horizontis ergatæ æ­<lb/>quidi&longs;tant, ceu &longs;uculæ & Axis in Peritrochio, &longs;ed eidem <lb/>fiunt perpendiculares. </s> <s id="s.001035">Cæterùm facilitatem à velocitate <lb/>non oriri &longs;uperius demon&longs;trauimus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001036">QVAESTIO XIV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001037"><emph type="italics"/>Proponitur dubitatio, Cur eiu&longs;dem magnitudinis lignum facilius <lb/>genu frangatur &longs;i qui&longs;piam æque diductis manibus extrema com­<lb/>prehendens fregerit, quàm &longs;i iuxta genu. </s> <s id="s.001038">Et &longs;i terræ applicans pede <lb/>&longs;uperpo&longs;ito manu hinc inde diducta confregerit <lb/>quàm propè.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001039">Soluitur à Philo&longs;opho paucis verbis, An quia ibi genu <lb/>centrum e&longs;t, hic verò ip&longs;e pes? </s> <s id="s.001040">quanto autem remotius <lb/>à centro fuerit, facilius mouetur quodcunque: Moueri <lb/>autem quod frangitur nece&longs;&longs;e e&longs;t. </s> </p> <p type="main"> <s id="s.001041">E&longs;to lignum quod frangi debet AB, genu vel pedis <lb/>locus C, manuum latè diductarum &longs;itus DE, minus didu­<lb/>ctarum FG; ltaque quoniam DE magis à centro C di&longs;tant <lb/>quàm FG, velocius mouebuntur puncta DE ip&longs;is FG, er­<lb/>go inde facilius fiet fractio quam ex FG. <!-- KEEP S--></s> <s id="s.001042">Hæc ille ex &longs;uis <pb xlink:href="007/01/112.jpg"/><figure id="id.007.01.112.1.jpg" xlink:href="007/01/112/1.jpg"/><lb/>principijs. </s> <s id="s.001043">Nos dili­<lb/>gentius, &longs;i fieri poterit, <lb/>effectus huius cau&longs;&longs;am <lb/>per&longs;crutemur. </s> <s id="s.001044">E&longs;to igi­<lb/>tur in &longs;ecunda figura <lb/>lignum oblongum AB, <lb/>cuius medium C, linea <lb/>ducatur CD perpen­<lb/>dicularis ip&longs;i AB. <!-- KEEP S--></s> <s id="s.001045">Ad­<lb/>moueatur genu <expan abbr="pūcto">puncto</expan> <lb/>C, manus verò diuari­<lb/>centur in AB, facta i­<lb/>gitur vtrinque impre&longs;­<lb/>&longs;ione, lignum non <expan abbr="frã-getur">fran­<lb/>getur</expan>, ni&longs;i partium in CD coniunctarum &longs;eparatio fiat, <lb/>&longs;itqueue altera in E, altera verò in F, fractum ergo erit <expan abbr="lignū">lignum</expan>, <lb/>& centro C immobili permanente, partes facto angulo <lb/>GCH erunt in GC, HC: Modò lignum &longs;uæ integritati re­<lb/>&longs;tituetur, & denuò admoto genu puncto C, manus didu­<lb/>cantur in I, K, quæ loca viciniora &longs;int ip&longs;i C, quam AB, Di­<lb/>co hinc difficilius fractionem fieri quam ex AB. <!-- KEEP S--></s> <s id="s.001046">Con&longs;ide­<lb/>ramus enim in integro ligno AB, duos vectes ACD, BCD, <lb/>quorum anguli concurrunt in commune fulcimentum C, <lb/>Sunt autem vectes angulati, & eius naturæ, quam exami­<lb/>nauimus in quæ&longs;tiones. </s> <s id="s.001047">E&longs;t igitur re&longs;i&longs;tentia, qua ligni <lb/>partes vniuntur in D, loco ponderis: &longs;uperanda hæc e&longs;t, vt <lb/>ligni fiat fractio. </s> <s id="s.001048">Dico id facilius ce&longs;&longs;urum, &longs;i fiat ex pun­<lb/>ctis A, B, remotioribus quam ex IK, ip&longs;i puncto C propio<lb/>ribus: etenim vt AC, ad CD, ita re&longs;i&longs;tentia quæ fit in D ad <lb/>potentiam in A, item vt &longs;e habet IC ad CD, ita re&longs;i&longs;tentia <lb/>in Dad potentiam in I, &longs;ed minor e&longs;t proportio IC ad CD, <lb/>quam AC ad CD. ergo facilius potentia quæ e&longs;t in A, re­<lb/>&longs;i&longs;tentiam &longs;uperabit, quæ e&longs;t in D, quam ea quæ e&longs;t in I, <pb xlink:href="007/01/113.jpg"/>quod fuerat demon&longs;trandum. </s> <s id="s.001049">Idem autem <expan abbr="intelligendū">intelligendum</expan> <lb/>e&longs;t de parte CB; eadem enim e&longs;t ratio. </s> <s id="s.001050">Cur igitur longio­<lb/>ra & graciliora ligna facilè frangantur, ex i&longs;tis clare patet: <lb/>nempe quia maxima e&longs;t proportio longitudinis ad cra&longs;&longs;i­<lb/>tudinem, cuius quidem cra&longs;&longs;itudinis &longs;patium loco partis <lb/>illius in vecte &longs;uccedit, quæ pertingit à fulcimento ad <expan abbr="pō-dus">pon­<lb/>dus</expan>, hoc e&longs;t, ad ip&longs;am re&longs;i&longs;tentiam. </s> <s id="s.001051">Sed nos hac eadem de <lb/>re nonnulla in declaranda quæ&longs;tione 16. perpendemus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001052">QVAESTIO XV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001053"><emph type="italics"/>Proponitur inuestigandum, Cur litterales crocæ (glareas dicunt <lb/>Latini, vel calculos, quos vmbilicos appellat Cicero lib. 2. de Orat.) <lb/>rotundâ &longs;int figurâ, cum aliquando ex magnis &longs;int la­<lb/>pidibus te&longs;tisue?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001054">A It Philo&longs;ophus, ideo forta&longs;&longs;e fieri, quòd ca quæ à me­<lb/>dio magis recedunt, in motionibus, celerius feran­<lb/>tur; me dium e&longs;&longs;e centrum, interuallum vero quæ à cen­<lb/>tro, &longs;emper autem maiorem ab æquali motione maiorem <lb/>de&longs;cribere circulum; quod autem maius in æquali tem­<lb/>pore &longs;patium tran&longs;it, celerius ferri; quæ autem celerius ex <lb/>æquali feruntur &longs;patio vehementius impetere, quæ <expan abbr="autē">autem</expan> <lb/>impetunt, impeti magis, & ideo quæ magis à centro di­<lb/>&longs;tant, nece&longs;&longs;e e&longs;&longs;e confringi, quod cum glareæ &longs;eu crocæ <lb/>patiantur, nece&longs;&longs;ariò rotundas fieri. </s> <s id="s.001055">Hactenus ille, & &longs;anè <lb/>probabiliter. </s> <s id="s.001056">Verum enimuerò aliter &longs;eres habere vide­<lb/>tur: &longs;iquidem enim à rotatione ex maiori à centro di&longs;tan­<lb/>tia id fieret, maiores quidem glareæ crocæue e&longs;&longs;ent ro­<lb/>tundiores, at nos non maximas modò, &longs;ed & minimas, <lb/>ea&longs;que magis angulis carere, & ad rotunditatem accede­<lb/>re videmus. </s> <s id="s.001057">Præterea non moueri eas circa centrum pa­<lb/>lam e&longs;t, imò vt varia &longs;unt figura, ita varijs quoque motio­<lb/>nibus, ex agitatione moueri. </s> <s id="s.001058">Id &longs;anè explorati&longs;&longs;imum e&longs;t, <pb xlink:href="007/01/114.jpg"/>angulos omnes, & eminentias quaslibet in corporibus e&longs;­<lb/>&longs;e infirmiores, offen&longs;ionibus enim expo&longs;itæ &longs;unt, nec re&longs;i­<lb/>&longs;tendi habent facultatem. </s> <s id="s.001059">Itaque in attritione quæ fit in <lb/>eorum agitatione perpetua, eminentiæ contunduntur, & <lb/>&longs;uperficies ip&longs;a paullatim leuigatur. </s> </p> <figure id="id.007.01.114.1.jpg" xlink:href="007/01/114/1.jpg"/> <p type="main"> <s id="s.001060">E&longs;to angulatus lapis ABCD. <lb/><!-- KEEP S--></s> <s id="s.001061">Dum igitur perpeti motione <expan abbr="atq;">atque</expan> <lb/>a&longs;&longs;iduâ ver&longs;atione agitatur, fer­<lb/>turqueue, eminentiæ anguliqueue, vt­<lb/>pote debiles & imbecilli, conte­<lb/>runtur, & inde figura fit quædam <lb/>irregularis, ad primam quidem la­<lb/>pidis <expan abbr="formã">formam</expan> accedens, leuis tamen <lb/>& quouis angulo carens, qualis e&longs;t E remotis ABCD, an­<lb/>gularibus eminentijs. </s> </p> <p type="main"> <s id="s.001062">Hanc eandem ob cau&longs;&longs;am, &longs;culptores antequam mar­<lb/>moribus vltimum læuorem inducant, dentato malleo pri­<lb/>mum quidem vtuntur, tum demum eminentiores parti­<lb/>culas radula facilè amouentes &longs;uperficiem ip&longs;am læuem <lb/>& adæquatam reddunt. </s> </p> <p type="main"> <s id="s.001063">Hinc etiam no&longs;trates Architecti, in arcium propu­<lb/>gnaculis efformandis acutos angulos <expan abbr="deuitãt">deuitant</expan>, vtpote de­<lb/>biliores, & magis offen&longs;ionibus obnoxios. </s> <s id="s.001064">quod nec Vi­<lb/>truuium latuit, qui ideo lib. 1. cap. 5. ita &longs;cribit: <emph type="italics"/>Turres itaque <lb/>rotundæ aut polygoniæ &longs;unt faciendæ, quadratas enim machinæ <lb/>celerius di&longs;&longs;ipant; & angulos, Arietes tundendo frangunt, in ro­<lb/>tundationibus autem, vti cuneos ad centrum adigendo lædere non <lb/>po&longs;&longs;unt.<emph.end type="italics"/> Hæc ille. <!-- KEEP S--></s> <s id="s.001065">Cur autem no&longs;tri rotundas figuras alias <lb/>vtiles reijciant, ab ijs petendum qui in ea facultate ver­<lb/>&longs;antur. </s> <s id="s.001066">Porrò quod ad hanc eandem &longs;peculationem facit, <lb/>videmus, antiquas &longs;tatuas, vt &longs;æpius auribus, na&longs;o, digitis, <lb/>manibu&longs;ue atque pedibus carere, quippe quod imbecillæ <lb/>&longs;int partes, & facilè quouis occur&longs;u mutilentur. </s> <s id="s.001067">Quæ o-<pb xlink:href="007/01/115.jpg"/>mnia cùm vera &longs;int, nemo, vt arbitror, dixerit, ab&longs;olutè, <lb/>quod voluit Ari&longs;toteles, id ex rotatione velociori & par­<lb/>tium à centro remotione, fieri. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001068">QVAESTIO XVI.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001069"><emph type="italics"/>Dubitatur, quare, quò longiora &longs;unt ligna, <expan abbr="tãto">tanto</expan> imbecilliora fiant, <lb/>& &longs;i tolluntur, inflectuntur magis: tamet&longs;i quod breue est ceu bi­<lb/>cubitum fuerit, tenue, quod verò cubitorum cen­<lb/>tum cra&longs;&longs;um?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001070">Ex &longs;uis principijs &longs;oluit Ari&longs;toteles. </s> <s id="s.001071">Inquit enim: An <lb/>quia & vectis & onus & hypomochlium, id e&longs;t, fulci­<lb/>mentum in leuando, fit ip&longs;a ligni proceritas? </s> <s id="s.001072">Prior <expan abbr="namq;">namque</expan> <lb/>illius pars ceu hypomochlium fit, quod verò in extremo <lb/>e&longs;t, pondus: quamobrem quanto exten&longs;ius fuerit id quod <lb/>à fulcimento e&longs;t, in flecti nece&longs;&longs;e e&longs;t magis; quo enim plus <lb/>à fulcimento di&longs;tat, eo magis incuruari nece&longs;&longs;e e&longs;t. </s> <s id="s.001073">Ne­<lb/>ce&longs;&longs;ariò igitur extrema vectis eleuantur. </s> <s id="s.001074">Si igitur flexilis <lb/>fuerit vectis, ip&longs;um inflecti magis cum extollitur nece&longs;&longs;e <lb/>e&longs;t, quod longis accidit lignis, in breuibus autem quod vl­<lb/>timum e&longs;t, quie&longs;centi hypomochlio depropè fit. </s> <s id="s.001075">Hæc <lb/>&longs;ubiectâ figurâ ob oculos ponimus. </s> </p> <figure id="id.007.01.115.1.jpg" xlink:href="007/01/115/1.jpg"/> <p type="main"> <s id="s.001076">E&longs;to longum ac fle­<lb/>xile lignum AB, manu ele­<lb/>uetur in A, flectetur <expan abbr="itaq;">itaque</expan> <lb/>in B, & declinabit in C. et­<lb/>enim manus quæ &longs;u&longs;tinet <lb/>in A, fulcimenti loco &longs;uccedit: longitudo vero AB ponde­<lb/>ris vices refert, at que vectis, quare quo longius abfuerit à <lb/>fulcimento, id e&longs;t, manu extremum B, eo magis flectetur; <lb/>&longs;i autem lignum breuius fuerit, nempe terminatum in D, <lb/>nequaquam flectetur, eò quòd eius extremum D minus à <lb/>fulcimento quod e&longs;t in A &longs;it remotum. </s> <s id="s.001077">Hæc igitur e&longs;t <expan abbr="mēs">mens</expan> <pb xlink:href="007/01/116.jpg"/>Ari&longs;totelis, cuius quidem &longs;ententiam non damnamus; <lb/>quippiam tamen addimus. </s> <s id="s.001078">Dicimus autem materiam, <lb/>quatenus ad hanc contemplationem &longs;pectat, in duplici <lb/>e&longs;&longs;e differentia. </s> <s id="s.001079">aut enim rarefactionis & con&longs;tipationis <lb/>e&longs;t incapax, vt in chalybe videmus, nitro, metallo, mar­<lb/>more, aut capax quidem, & hæc duplex: Vel enim natura <lb/>nata e&longs;t ad rectitudinem quandam, vt arborum flagella <lb/>virgæque, aut non item, ceu &longs;tannum, plumbum, & cæte­<lb/>ra eiu&longs;modi. </s> </p> <figure id="id.007.01.116.1.jpg" xlink:href="007/01/116/1.jpg"/> <p type="main"> <s id="s.001080">E&longs;to primò vitreum <lb/>corpus gracile, procerum, <lb/>teres AB, manu capiatur in <lb/>A, <expan abbr="itaq.">itaque</expan> pondere ip&longs;ius cor­<lb/>poris præualente ad partes <lb/>B, quia in C puncto, quod <lb/>circa medium e&longs;t, ex parte <lb/>&longs;uperiori non fit rarefactio, <lb/>nec in in feriori con&longs;tipatio, <lb/>nec interim datur penetra­<lb/>tio corporum, fit fractio à <lb/>&longs;uperiori parte, & pars CB à <lb/>reliqua parte AC, auul&longs;a & <lb/>&longs;eparata cadit in D, &longs;uccedit autem ip&longs;a &longs;eparatio rarefa­<lb/>ctioni. </s> <s id="s.001081">Porrò quod materias ha&longs;ce non flexibiles diximus, <lb/>&longs;ed frangibiles, non ideo negamus vel &longs;en&longs;u docente, ali­<lb/>quam in ijs fieri flexionem. </s> <s id="s.001082">Si autem lignea fuerit mate­<lb/>ria, caque; flexibilis, vt EF, &longs;i manu eleuetur in E, præualen­<lb/>te pondere in F flectetur vbi G. ibi enim à parte &longs;uperiori <lb/>fit rarefactio, ab in feriori verò con&longs;tipatio, & pars GF de­<lb/>clinabit in H, quæ declinatio eò v&longs;que procedet, quo ra­<lb/>refactio & con&longs;tipatio competens naturæ illius materiæ, <lb/>quæ flectitur ad &longs;ummam inten&longs;ionem deuenerint; tunc <lb/>&longs;i vis maior ingruerit, frangetur omnino: &longs;i &longs;ecus facta ibi <pb xlink:href="007/01/117.jpg"/>re&longs;i&longs;tentia, vbi rarefactio fit & con&longs;tipatio per inclina­<lb/>tionem &longs;ur&longs;um feretur pars in clinata & nutans, tum in <lb/>contrariam partem tendens reflectetur, vt videre e&longs;t in <lb/>virga IN. </s> <s id="s.001083">Declinans enim in KL, repellente ea quæ infra <lb/>K fit materiæ conden&longs;atione, impetu ex de&longs;cen&longs;u acqui­<lb/>&longs;ito facta reflexione a&longs;cendit in KM, donec paullatim cir­<lb/>ca pri&longs;tinam rectitudinem reuertatur, & hic quidem mo­<lb/>tus vibratio dicitur, agitatioue. </s> <s id="s.001084">Si autem virga plumbea <lb/>fuerit, naturâ non factâ ad rectitudinem, puta OP, pro­<lb/>prio vincente pondere, ad partes declinabit QS, fietque; in <lb/>QR rarefacta, nempe &longs;uperiori parte ea con&longs;tipata infe­<lb/>riori in Q, nec reflectetur, quippe quòd eius natura con­<lb/>den&longs;ationem & rarefactionem commodè patiatur, nec <lb/>facta &longs;it ad rectitudinem. </s> </p> <p type="main"> <s id="s.001085">Porrò tripliciter fieri pote&longs;t horum oblongorum <lb/>corporum eleuatio, nempe vel extremorum alteio, aut &longs;i <lb/>ambobus, &longs;i vtrinque &longs;u&longs;pendatur, vel alicubi inter extre­<lb/>ma. </s> <s id="s.001086">De priori modo iam egimus. </s> <s id="s.001087">Modò &longs;u&longs;pendatur in <lb/>medio vt AB, in C. eo igitur ca&longs;u cum fulcimentum &longs;it in <lb/>C, <expan abbr="vtrinq;">vtrinque</expan> fit flexio in D, & E, & id quidem &longs;i materia fle­<lb/>xionem patitur: &longs;in minus, fractio fit in C. <!-- KEEP S--></s> <s id="s.001088">Si autem ab ex­<lb/><figure id="id.007.01.117.1.jpg" xlink:href="007/01/117/1.jpg"/><lb/>tremis fiat &longs;u&longs;pen&longs;io, vt in <lb/>AB, tunc ceu duo vectes <lb/>fient, quorum fulcimenta in <lb/>extremis AB. <!-- KEEP S--></s> <s id="s.001089">Pondera au­<lb/>tem communia in medio vbi <lb/>C remoti&longs;&longs;ima enim ea pars e&longs;t ab extremis AB. <!-- KEEP S--></s> <s id="s.001090">Cedente <lb/><figure id="id.007.01.117.2.jpg" xlink:href="007/01/117/2.jpg"/><lb/>igitur materia &longs;uomet pon­<lb/>deri, &longs;iquidem in flexibilis fu­<lb/>erit, frangetur, & fiet <expan abbr="partiū">partium</expan> <lb/>&longs;eparatio in C, duoque in de <lb/>corpora AD, BE. <!-- KEEP S--></s> <s id="s.001091">Si autem fle­<lb/>xionis capax, vt AB in po&longs;tre­<pb xlink:href="007/01/118.jpg"/>ma figura, facta ex contrario, nempe in in feriori parte cir­<lb/>ca C rarefactione, in &longs;uperiori verò conden&longs;atione, pon­<lb/>dere præualente curuabitur, fietque; lignum quidue aliud <lb/>huiu&longs;modi, vt ADB, nec amplius pondere &longs;uapte naturâ <lb/>inferiùs vergente ad rectitudinem reuertetur. </s> </p> <p type="main"> <s id="s.001092">Cæterùm cur oblonga & graciliora corpora facilius <lb/>illis, quæ contrario &longs;e habent modo, frangantur, ex me­<lb/>chanicis principijs in quæ&longs;tione 14. apertè demon&longs;traui­<lb/>mus. </s> <s id="s.001093">Modò vt ex hac contemplatione, quæ aliàs inutilis <lb/>videtur, aliquam vtilitatem capiamus, & ex his quæ con­<lb/>templabimur, Architecti prudentiores fiant, i&longs;thæc ip&longs;a, <lb/>de quibus agimus, ad rem ædificatoriam commodè apta­<lb/>bimus. </s> <s id="s.001094">Transferamus igitur cogitationem ad eam <expan abbr="trabiū">trabium</expan> <lb/>compagem, quæ ad tecta &longs;u&longs;tinenda ex tran&longs;uer&longs;ario ar­<lb/>rectarioque; &longs;it, & duobus cauterijs, quam no&longs;tri à Latinis <lb/>detorto vocabulo Bi&longs;cauterium dicunt. </s> <s id="s.001095">Per&longs;crutabimur <lb/>enim, vnde illi tanta ad &longs;u&longs;tinendum vis, & quæ compa­<lb/>gem hanc con&longs;equantur pa&longs;&longs;iones. </s> <s id="s.001096">quamuis enim fabri <lb/>meræ praxi, quod vtile e&longs;t efficiant, nos meliorum inge­<lb/>niorum gratiâ, rei ip&longs;ius cau&longs;&longs;as diligenter examinatas in <lb/>medium proferemus; nec de hac re tantùm agemus, &longs;ed <lb/>de Cameris quoque, fornicibus eorumqueue vitijs & virtu­<lb/>tibus quatenus ad Mechanicum pertinet, &longs;ermonem ha­<lb/>bebimus. </s> <s id="s.001097">Quærimus primo, cur perpendiculariter erectae <lb/>trabes &longs;uperimpo&longs;ita pondera validi&longs;&longs;ime &longs;u&longs;tineant? </s> <s id="s.001098">Et <lb/>&longs;ane hoc omnes norunt, &longs;ed non per cau&longs;&longs;as. </s> </p> <p type="main"> <s id="s.001099">E&longs;to horizontis planum, illudqueue &longs;olidi&longs;&longs;imum, & <lb/>impenetrabile AB, trabs eidem ad perpendiculum erecta <lb/>CD fulta ba&longs;i vbi C grauitatis centrum F. pondus &longs;uper­<lb/>impo&longs;itum FG, cuius grauitatis centrum H: Sint autem <lb/>H & E in eadem perpendiculari, quæ ad mundi centrum <lb/>HEC. </s> <s id="s.001100">Itaque eo quod tum penderis tum trabis centra <lb/>grauitent in perpendiculari, illa verò fulciatur in C, to-<pb xlink:href="007/01/119.jpg"/><figure id="id.007.01.119.1.jpg" xlink:href="007/01/119/1.jpg"/><lb/>tius ponderis moles recumbet <lb/>in C: non de&longs;cendet autem in I, <lb/>propterea quod &longs;upponatur i­<lb/>p&longs;um planum AB, impenetrabi­<lb/>le. </s> <s id="s.001101">Igitur vt pondus H de&longs;cen­<lb/>dat in C, alterum duorum e&longs;t <lb/>nece&longs;&longs;arium, nempe vel trabem <lb/>&longs;ubiectam comminui, aut eius <lb/>partes &longs;e&longs;e penetrare, & plura <lb/>corpora e&longs;&longs;e in eodem loco, pu­<lb/>ta KC, quorum hoc &longs;ecundum <lb/>naturæ penitus repugnat, illud <lb/>vero primum, penè impo&longs;&longs;ibile. </s> <s id="s.001102">Diuidatur enim trabs in <lb/>partes æquales tres, lineis KL, ip&longs;a igitur KC infima &longs;u&longs;ti­<lb/>net mediam KL, hæc verò &longs;upremam LD, hæc autem <expan abbr="pō-dus">pon­<lb/>dus</expan>, ip&longs;um &longs;uperpo&longs;itum in H. <!-- KEEP S--></s> <s id="s.001103">Seigitur &longs;u&longs;tinent partes. <lb/></s> <s id="s.001104">Sed illud totum partibus con&longs;tat. </s> <s id="s.001105">ergo pondus totum à <lb/>trabe tota, hoc e&longs;t, à &longs;e toto &longs;u&longs;tinetur. </s> </p> <p type="main"> <s id="s.001106">Præterea in præcedenti quæ&longs;tione mon&longs;trauimus <lb/>tunc facilem e&longs;&longs;e gracilis & oblongi ligni fractionem, <expan abbr="cū">cum</expan> <lb/>maxima e&longs;t longitudinis ad cra&longs;&longs;itudinem proportio. </s> <s id="s.001107">Hîc <lb/>verò contrà accidit, etenim MD pars vectis quæ à fulci­<lb/>mento e&longs;t ad potentiam minimam habet proportionem <lb/>ad rectam DC, quæ à fulcimento ad locum fractionis ex­<lb/>tenditur, vbi C, quod vt euidentius pateat, </s> </p> <figure id="id.007.01.119.2.jpg" xlink:href="007/01/119/2.jpg"/> <p type="main"> <s id="s.001108">E&longs;to &longs;eor&longs;um trabs AB, <lb/>cuius medium C. <!-- KEEP S--></s> <s id="s.001109">Sit autem <lb/>pondus D impo&longs;itum pun­<lb/>cto C. facilè igitur frange­<lb/>tur lignum AB, propterea <lb/>quòd maxima &longs;it proportio <lb/>AC ad CE; re&longs;i&longs;tentia verò <lb/>fiat in E, addatur vniaturque; <pb xlink:href="007/01/120.jpg"/>ligno AB lignum FH. <!-- KEEP S--></s> <s id="s.001110">Cra&longs;&longs;ius igitur e&longs;t totum AL, ip&longs;o <lb/>AH, & ideo minor proportio AC ad CG quàm AC, ad <lb/>CE. <!-- KEEP S--></s> <s id="s.001111">Addatur adhuc & IM. </s> <s id="s.001112">Longè itaque difficilius fran­<lb/>getur in K propterea quòd longè minor &longs;it proportio AC <lb/>ad CK quàm eiu&longs;dem ad CE & CG. <!-- KEEP S--></s> <s id="s.001113">His igitur con&longs;ide­<lb/>ratis, & demon&longs;tratis concludimus, impo&longs;&longs;ibile e&longs;&longs;e ere­<lb/>ctam trabem ponderi cedere, & frangi. </s> </p> <p type="main"> <s id="s.001114">Dicet autem qui&longs;piam, haec &longs;i vera &longs;unt, quo gracilius <lb/>fuerit fulcrum, eo validiùs &longs;u&longs;tinebit, & frangetur minus, <lb/>quod oppido fal&longs;um e&longs;t. </s> <s id="s.001115">Re&longs;pondemus, id non ex propor­<lb/>tionum naturâ, &longs;ed ex materiæ ip&longs;ius infirmitate fieri. </s> <s id="s.001116">Ita <lb/>quoque invecte non materiam, quatenus ad vim pertinet, <lb/>&longs;ed proportiones partium con&longs;ideramus. </s> <s id="s.001117">Vtrumque igi­<lb/>tur requiritur ad fulcri validitatem proportio longitudi­<lb/>nis ad cra&longs;&longs;itudinem debita, & materiæ ip&longs;ius robur & <lb/>fortitudo. </s> <s id="s.001118">Præterea, quoniam pondus, cui fulcrum re&longs;i­<lb/>&longs;tit, vel ex natura premit, vel ex violentia, illud quidem <lb/>per lineam perpendicularem, quæ ad mundi <expan abbr="cētrum">centrum</expan>, hoc <lb/>autem lateraliter & diuer&longs;i modè, varia fit fulcrorum di&longs;­<lb/>po&longs;itio. </s> <s id="s.001119">Cuius rei &longs;umma hæc e&longs;t, vt &longs;emper contra impe­<lb/>tum &longs;upponantur. </s> </p> <figure id="id.007.01.120.1.jpg" xlink:href="007/01/120/1.jpg"/> <p type="main"> <s id="s.001120">E&longs;to enim horizontis planum <lb/>AB, <expan abbr="eidē">eidem</expan> perpendiculares CADB, <lb/>ítaque &longs;i naturaliter pondus pre­<lb/>mat ex C, fulcrum &longs;upponetur AE. <lb/><!-- KEEP S--></s> <s id="s.001121">Si autem ex F ip&longs;um GE, &longs;i verò ex <lb/>H, &longs;upponatur iuxta BE. <!-- KEEP S--></s> <s id="s.001122">Si verò &longs;e­<lb/>cundum I ponderi opponatur KE. <lb/></s> <s id="s.001123">Hæc nos de arrectarijs fulcrisue; <lb/>nunc de tran&longs;uer&longs;arijs, & inclinatis agemus, & primum <lb/>de tran&longs;uer&longs;arijs, quatenus ad tectorum trabeationes &longs;pe­<lb/>ctat. </s> </p> <p type="main"> <s id="s.001124">E&longs;to tran&longs;uer&longs;aria trabs AB, muris <expan abbr="vtrinq;">vtrinque</expan> fulta CD, <pb xlink:href="007/01/121.jpg"/><figure id="id.007.01.121.1.jpg" xlink:href="007/01/121/1.jpg"/><lb/>cuius grauitatis centrum <lb/>E, in <expan abbr="perpēdiculari">perpendiculari</expan> FEG, <lb/>quæ quidem ad mundi <lb/>centrum vergit. </s> <s id="s.001125"><expan abbr="Itaq;">Itaque</expan> eo­<lb/>dem tendente grauitatis <lb/>centro, &longs;i pondus quod <lb/>premit in E, non præua­<lb/>leat vnioni <expan abbr="partiū">partium</expan> ip&longs;ius <lb/>materiæ quæ e&longs;t in E, re&longs;i&longs;tet trabs &longs;uomet ponderi, nec <lb/>frangetur. </s> <s id="s.001126">Si autem vel in firmitate materiæ, aut vitio, vel <lb/>maxima existente proportione AF ad FE, fractio fiet in E, <lb/>& &longs;ecutâ partium &longs;eparatione duæ fient vtrin que trabes <lb/>AH, Bl, quorum grauitatis centra KL. <!-- KEEP S--></s> <s id="s.001127">Erunt igitur duo <lb/>vectes AE, BE, quorum fulcimenta MN, quamobrem &longs;i <lb/>proportio EM ad MH ita præualeat, vt pondus quod e &longs;t <lb/>in E, &longs;uperet pondus muri O &longs;uperimpo&longs;iti, & item muri <lb/>P, corruent quidem trabes, & murorum fiet hinc inde di&longs;­<lb/>&longs;ipatio. </s> <s id="s.001128">Si autem non præualuerit ea, quam diximus, pro­<lb/>portio, &longs;u&longs;pen&longs;æ remanebunt vtrinque trabes vt AHBI. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001129">Huic difficultati egregiè occurrunt Architecti, ali­<lb/>quando autem hoc modo: </s> </p> <figure id="id.007.01.121.2.jpg" xlink:href="007/01/121/2.jpg"/> <p type="main"> <s id="s.001130">E&longs;to tran&longs;uer&longs;aria <lb/>trabs &longs;uâ gracilitate, alia­<lb/>ue de cau&longs;&longs;a imbecilla <lb/>AB, muri quibus <expan abbr="vtrinq;">vtrinque</expan> <lb/>&longs;u&longs;tinetur CD, Trabis i­<lb/>p&longs;ius grauitatis centrum <lb/>G. <!-- KEEP S--></s> <s id="s.001131">Itaque adpactis trabi <lb/>lignis EF, capreolos ad­<lb/>dunt muro vtrinque ful­<lb/>tos CE, DF, eorum capita adpactis lignis admouentes EF, <lb/>&longs;ed & tunc validi&longs;&longs;ima fit colligatio, &longs;i inter E & F capreo­<lb/>lorum capita integrum lignum trabi &longs;upponatur EF. <!-- KEEP S--></s> <s id="s.001132">Ra­<pb xlink:href="007/01/122.jpg"/>tio autem validitatis patet; premente enim grauitatis <expan abbr="cē-tro">cen­<lb/>tro</expan> in G, fulcra hinc inde &longs;uccurrunt CE, DF, quæ cum &longs;e­<lb/>ip&longs;is fieri non valeant breuiora, ne corpori detur penetra­<lb/>tio, re&longs;i&longs;tunt & robu&longs;ti&longs;&longs;imè ip&longs;i ponderi &longs;uperimpo&longs;ito <lb/>contra nituntur. </s> <s id="s.001133">Videntur autem in hoc opere duo con­<lb/>&longs;iderari vectes, GH, GB, quorum fulcimenta EF, potentia <lb/>premens vtrinque G. <!-- KEEP S--></s> <s id="s.001134">Pondera autem parietum partes ca­<lb/>pitibus trabis impo&longs;itæ in A & B. <!-- KEEP S--></s> <s id="s.001135">Quoniam igitur parua <lb/>e&longs;t proportio GE ad EH, parua potentia premens in G, <lb/>maximè autem pondus in A, fieri non pote&longs;t trabem fran­<lb/>gi aut muros vtrinque di&longs;&longs;ipare in AB. <!-- KEEP S--></s> <s id="s.001136">Po&longs;&longs;unt etiam to­<lb/>tius trabis tres partes con&longs;iderari AE, EF, FB, quarum ful­<lb/>cimenta quatuor A, E, F, B, Diui&longs;o igitur pondere & mul­<lb/>tiplicatis fulcimentis impo&longs;&longs;ibile e&longs;t trabem conuelli & <lb/>vitium facere. </s> </p> <p type="main"> <s id="s.001137">Sed & tectorum contignationes imbecillaque; tran&longs;­<lb/>uer&longs;aria Mechanici corroborare &longs;olent, additis nempe <lb/>arrectaria trabe atque cauterijs. </s> </p> <figure id="id.007.01.122.1.jpg" xlink:href="007/01/122/1.jpg"/> <p type="main"> <s id="s.001138">E&longs;to enim tran&longs;­<lb/>uer&longs;aria trabs AB <lb/>parietibus vtrinque <lb/>fulta I, K, <expan abbr="arrectariū">arrectarium</expan> <lb/>CD. <!-- KEEP S--></s> <s id="s.001139">Cauterij vtrin­<lb/>que AD, BD, ita <lb/>tran&longs;uer&longs;ariæ trabi <lb/>in AB, & arrectario <lb/>in D in&longs;erti, vt ne­<lb/>quaquam inde ela­<lb/>bi valeant. </s> <s id="s.001140">Tum ferrea fa&longs;cia EF mediam tran&longs;uer&longs;ariam <lb/>trabem AB, à parte inferiori ip&longs;i arrectario connectens, <lb/>Debet autem arrectarij pes vbi C, aliquantulum à tran&longs;­<lb/>uer&longs;aria trabe di&longs;tare, ne deor&longs;um ex pondere vergente <lb/>paululum arrectario ip&longs;am tran&longs;uer&longs;ariam premat. </s> <s id="s.001141">His i-<pb xlink:href="007/01/123.jpg"/>gitur ita con&longs;titutis pondus quidem tran&longs;uer&longs;ariæ trabis, <lb/>quod &longs;uapte naturâ premit in medio vbi C, ferrea fa&longs;cia, <lb/>arrectariæ trabi affixa di&longs;tinetur, Arrectariam cauterij &longs;u­<lb/>&longs;tinent, hos verò tran&longs;uer&longs;ariæ capita AB, quibus indun­<lb/>tur. </s> <s id="s.001142">Tota igitur eiu&longs;cemodi operis vis in eo con&longs;i&longs;tit, vt <lb/>probè cauterij tran&longs;uersariæ & arrectariæ trabi in&longs;eran­<lb/>tur. </s> <s id="s.001143">fixis enim cauteriorum pedibus in AB, non <expan abbr="de&longs;cendēt">de&longs;cendent</expan> <lb/>à partibus &longs;eu capitibus D, ijs verò &longs;tantibus &longs;tabit & arre­<lb/>ctarium, quo inde &longs;u&longs;pen&longs;o tran&longs;uer&longs;aria trabs ei ex ferrea <lb/>fa&longs;cia alligata nequaquam pendebit. </s> <s id="s.001144">Stabit ergo compa­<lb/>ges tota & &longs;uapte vi robu&longs;ti&longs;&longs;imè connexa totius tecti <lb/>pondus &longs;u&longs;tinebit. </s> </p> <p type="main"> <s id="s.001145">Quoniam autem v&longs;u venire &longs;olet, cauterios nimia <lb/>longitudine debiles, aliquando tum proprio tum extra­<lb/>neo cedentes ponderi deor&longs;um vergentes pandare, Ar­<lb/>chitecti capreolis hinc inde &longs;uppo&longs;itis, ceu fulcris, huic <lb/>medentur infirmitati. </s> </p> <figure id="id.007.01.123.1.jpg" xlink:href="007/01/123/1.jpg"/> <p type="main"> <s id="s.001146">Sint enim cauterij <lb/>debiles hinc inde AB, <lb/>AC, media trabs arre­<lb/>ctaria, quam <expan abbr="Monachū">Monachum</expan> <lb/>dicimus AD. <!-- KEEP S--></s> <s id="s.001147">Cauterio­<lb/>rum mediæ partes E, F, <lb/>in punctis igitur EF, vtpote maximè ab extremis di&longs;tanti­<lb/>bus debiles cauterij valde laborant. </s> <s id="s.001148">Itaque &longs;uppo&longs;itis v­<lb/>trinque arrectariolis EH, Fl, eorum capitibus E, F, duos <lb/>cauteriolos &longs;ibi ip&longs;is ad pedem arrectarij in D, re&longs;i&longs;tentes <lb/>apponunt. </s> <s id="s.001149">quibus ita con&longs;titutis nec E, nec F ad partes H, <lb/>I, de&longs;cendere valent. </s> <s id="s.001150">Capiatur enim inter EH, quoduis <lb/>punctum G, & BG, DG, connectantur, erunt autem BG, <lb/>DG ip&longs;is BE ED breuiores ex 21. primi elem. </s> <s id="s.001151">Tunc igitur <lb/>punctum E fiet in G cum BE, ED fient in BG, DG, quod <lb/>non cedentibus B, D, & &longs;ibi ip&longs;is breuioribus factis parti-<pb xlink:href="007/01/124.jpg"/>bus BE, ED, pror&longs;us e&longs;t impo&longs;&longs;ibile. </s> <s id="s.001152">&longs;tabunt igitur in eo­<lb/>rum rectitudine cauterij AB, AC, nec pandabunt, quod <lb/>fieri querebatur. </s> </p> <p type="main"> <s id="s.001153">Hîc autem damnandi veniunt ij, qui tran&longs;uer&longs;ariæ <lb/>quidem trabis capitibus cauteriorum pedes non <expan abbr="in&longs;erūt">in&longs;erunt</expan>, <lb/>&longs;ed ea vice tran&longs;uer&longs;ariolo quodam medios cauterios v­<lb/>trinque connectunt ad in&longs;tar elementi A, quam compa­<lb/>gem, capram, appellant. </s> <s id="s.001154">Sint enim cauterij hinc inde AB, <lb/>AC, quorum medias partes connectit tran&longs;uer&longs;ariolum, <lb/>DE. <!-- KEEP S--></s> <s id="s.001155">Dico igitur colligationem i&longs;tam magnopere impro­<lb/>bandam. </s> <s id="s.001156">Sunt enim AB, AC vectes, quorum commune <lb/>fulcimentum A, potentiæ hinc inde diuaricantes B, C, <lb/>pondera inter fulcimentum & potentias DE. quoniam i­<lb/>gitur vt DH ad AB, ita potentia in B, ad pondus in D, par­<lb/>ua quidem potentia, pondus in D di&longs;trahet & &longs;uperabit: <lb/>facillimaque; in de fiet tran&longs;uer&longs;ariolì à capreolis ip&longs;is vtrin­<lb/>que reuul&longs;io: Et quoniam centrum quidem e&longs;t A, facta in <lb/>D, E, parua diuaricatione, maxima fit in BC, vtpote parti­<lb/>bus ab ip&longs;o centro A quam remotis. </s> <s id="s.001157">Calcitrant igitur li­<lb/>beri prope cauteriorum pedes, & muros ip&longs;os &longs;ummos, <lb/>non &longs;ine magno operis totius vitio, &longs;ua calcitratione pro­<lb/>pellunt. </s> </p> <p type="main"> <s id="s.001158">Hæc nos de trabeationibus, modò ad fornicum ca­<lb/>merarumque; naturam &longs;tilum transferemus; id enim &longs;uadet <lb/>vtilitas, imo & nece&longs;&longs;itas ip&longs;a. </s> <s id="s.001159">Pauci enim ante nos hæc <lb/>tractarunt, & &longs;anè his probè non cognitis aut neglectis, <lb/>Architecti fabriqueue ingentes per&longs;æpe incurrunt, & inex­<lb/>plicabiles difficultates. </s> <s id="s.001160">Dicimus igitur primò, coctiles la­<lb/>teres, & non cuneatos lapides ad rectam lineam di&longs;po&longs;i<lb/>tos, non &longs;tare. </s> </p> <p type="main"> <s id="s.001161">Sint enim muri vtrinque AC, BD. <!-- KEEP S--></s> <s id="s.001162">Ducatur hori­<lb/>zonti æquidi&longs;tans CD, iuxta quam lateres lapide&longs;ue non <lb/>cuneati, &longs;eriatim collocentur EF. <!-- KEEP S--></s> <s id="s.001163">Dicimus amoto arma­<pb xlink:href="007/01/125.jpg"/><figure id="id.007.01.125.1.jpg" xlink:href="007/01/125/1.jpg"/><lb/>mento, hoc e&longs;t, pro­<lb/>hibente ip&longs;o lateres <lb/>ruere. </s> <s id="s.001164">Producantur <lb/>enim AC in G, BD <lb/>verò in H, cum ip&longs;is <lb/>CG, DH, æquales <lb/>fiant CI, DK, & recta <lb/>IK iungatur, erit igi­<lb/>tur GD &longs;patium ip&longs;i <lb/>CK &longs;patio &longs;imile qui­<lb/>dem & æquale, quod <lb/>cùm ita &longs;it, nihil prohibet quin tota laterum GD moles in <lb/>&longs;patium CK transferatur, & corruat. </s> </p> <p type="main"> <s id="s.001165">Si autem cunei ip&longs;i latere&longs;ue, cuneatim di&longs;po&longs;iti, ita <lb/>&longs;int vt ad vnum centrum tendant, licet ad rectam lineam <lb/>collocentur, non delabentur, &longs;ed &longs;tabunt; quod ita o&longs;ten­<lb/>demus. </s> </p> <figure id="id.007.01.125.2.jpg" xlink:href="007/01/125/2.jpg"/> <p type="main"> <s id="s.001166">Sint cunei latere&longs;ue <lb/>cuneatim di&longs;po&longs;iti ABCD, <lb/>tendentes ad centrum, &longs;eu <lb/>commune punctum E, Du­<lb/>cantur CAE, DBE, &longs;intqueue <lb/>muri vtrinque ponderi re&longs;i­<lb/>&longs;tentes CL, DM, Demitta­<lb/>tur perpendicularis, quæ ad <lb/>mundi centrum FGE &longs;ecans AB, in G. <!-- KEEP S--></s> <s id="s.001167">Tum fiat GK aequa­<lb/>lis GF & per K ip&longs;i AGB parallela ducatur, HKI claudens <lb/>&longs;patium AHIB. <!-- KEEP S--></s> <s id="s.001168">Quoniam igitur vt EC, ad EA, ita CD ad <lb/>AB per 4. propo&longs;. lib. 6. maior erit CD ip&longs;a AB, & eâdem <lb/>de cau&longs;&longs;a maior AB, ip&longs;a HI, & idcirco maius ABDC &longs;pa­<lb/>tium, &longs;patio AHIB. <!-- KEEP S--></s> <s id="s.001169">Non igitur pote&longs;t linea CD, fieri in <lb/>AB, neque AB, in HI, neque &longs;patium totum CABD, tran&longs;­<lb/>ferri in &longs;patium AHIB non data (quod naturæ ip&longs;i repu­<pb xlink:href="007/01/126.jpg"/>gnat) corporum penetratione. </s> <s id="s.001170">Stabunt ergo cunei, quod <lb/>fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.001171">Verum enimuero, debilis hæc &longs;tructura e&longs;t, & eo de­<lb/>bilior, quo vani latitudo fuerit maior, cuneorum verò al­<lb/>titudo minor. </s> <s id="s.001172">Idem enim patitur quod epi&longs;tylia in &longs;pecie <lb/>Aræos&longs;tyla, quæ, vt &longs;cribit Vitruuius lib. 3. c. <!-- REMOVE S-->2. propter in­<lb/>teruallorum magnitudinem franguntur. </s> <s id="s.001173">Id quoque ha­<lb/>bet vitij, quod cunei ita di&longs;po&longs;iti &longs;uo pondere incumbas <lb/>vtrinque violenti&longs;&longs;imè pellant. </s> <s id="s.001174">Vtilis tamen e&longs;&longs;e pote&longs;t <lb/>ad portarum & fene&longs;trarum, quæ in medijs muris &longs;unt, & <lb/>mediocri vano aperiuntur, &longs;uperliminaria. </s> </p> <p type="main"> <s id="s.001175">Si verò ad minorem circuli portionem curuetur Ca­<lb/>mera, vtilior quidem erit &longs;tructura ea ip&longs;a, de qua locuti <lb/>&longs;umus; non tamen omninò &longs;ine vitio. </s> </p> <figure id="id.007.01.126.1.jpg" xlink:href="007/01/126/1.jpg"/> <p type="main"> <s id="s.001176">E&longs;to fornix ex minori <lb/>circuli portione AB, cuius in­<lb/>cumbæ AF, BH muris fultæ <lb/>AC, BD. <!-- KEEP S--></s> <s id="s.001177">Con&longs;tet autem vel <lb/>ex lapidibus cuneatis, vel ex <lb/>coctilibus lateribus ad E <expan abbr="cē-trum">cen­<lb/>trum</expan> tendentibus. </s> <s id="s.001178">Sitque; for­<lb/>nicis linea exterior FGH, in­<lb/>terior AIB. <!-- KEEP S--></s> <s id="s.001179">Ducantur EA, <lb/>ED, & producantur in M, N. <lb/><!-- KEEP S--></s> <s id="s.001180">Quoniam igitur vt EM ad EA, ita MGN ad AIB, maior e­<lb/>rit MGN linea ip&longs;a AIB, quamobrem fieri non pote&longs;t vt <lb/>aptetur lineæ AIB, & in eius locum de&longs;cendat. </s> <s id="s.001181">Stabit igi­<lb/>tur, incumbis vtrinque non cedentibus. </s> <s id="s.001182">Validè autem <lb/>&longs;peciem hanc, loca quibus incumbit, propellere, ita o­<lb/>&longs;tendemus. </s> </p> <p type="main"> <s id="s.001183">Producatur in eadem figura CA in K, & DB in L. <lb/><!-- KEEP S--></s> <s id="s.001184">Partes igitur quæ muris ad perpendiculum fulciuntur, <lb/>&longs;unt AKF, BLH, minimæ illæ quidem, maxima verò pars <pb xlink:href="007/01/127.jpg"/>e&longs;t extra fulcimenta, nempe tota AKLB quæ idcircó &longs;uo­<lb/>pte pondere deor&longs;um vergens & in incumbas <expan abbr="vtrinq;">vtrinque</expan> pel­<lb/>lens aperitur, & facillimè vitium facit. </s> <s id="s.001185">Eiu&longs;dem ferè na­<lb/>turæ ea &longs;pecies e&longs;t, quæ vel ex media, vel ex minori ellip&longs;is <lb/>&longs;ecundum maiorem diametrum fit &longs;egmento. </s> <s id="s.001186">Vtilior ta­<lb/>men hæc e&longs;t, præcipuè circa incumbas, propterea quod <lb/>partes habeat erectiores, & circulari illa de qua egimus, <lb/>magis fultas. </s> <s id="s.001187">circa medium autem pote&longs;t videri debilior, <lb/>quippe quod ellip&longs;is ibi circulo curuetur minus. </s> </p> <p type="main"> <s id="s.001188">Ea verò forma, qua mirum in modum delectati &longs;unt <lb/>Barbari, qui declinante imperio Italiam inua&longs;erunt, & <lb/>bonam emendati&longs;&longs;imamqueue antiquorum ædificandi ra­<lb/>tionem deturparunt, ex duobus con&longs;tat circuli portioni­<lb/>bus, quamobrem Albertus lib. 3. ho&longs;ce arcus, compo&longs;itos, <lb/>appellat. </s> <s id="s.001189">Circinantur autem hoc pacto, diui&longs;a nempe <lb/>&longs;ubten&longs;a, in partes tres, ea&longs;que æquales, ponitur circini <lb/>pes in altero diui&longs;ionum puncto & pars circuli de&longs;cribi­<lb/>tur, mox in altero puncto circini pede collocato alia cir­<lb/>culi portio lineatur, quibus arcus ip&longs;e integratur. </s> <s id="s.001190">Appel­<lb/>lant autem tertium acutum, eo quod ex &longs;ubten&longs;a in tres <lb/>partes diui&longs;a, arcus non fiat rotundus, &longs;ed in acutum an­<lb/>gulum ex duabus circuli portionibus de&longs;inens. </s> </p> <figure id="id.007.01.127.1.jpg" xlink:href="007/01/127/1.jpg"/> <p type="main"> <s id="s.001191">Sint igitur muri <lb/>AC, BD, in quibus v­<lb/>trinque incumbæ KA, <lb/>BI. <!-- KEEP S--></s> <s id="s.001192">Ducatur itaque &longs;ub­<lb/>ten&longs;a horizonti æquidi­<lb/>&longs;tans AP, quæ in tres æ­<lb/>quales partes diuidatur <lb/>punctis E, F, tum centris <lb/>EF, circulorum portio­<lb/>nes de&longs;cribantur hinc <lb/>AG, HK, inde verò BG, <pb xlink:href="007/01/128.jpg"/>IH, ex quibus arcus totus integratur. </s> <s id="s.001193">Vtilis hæc quidem <lb/>&longs;pecies e&longs;t, licet inuenu&longs;ta, propterea quod haud violen­<lb/>ter incumbas vtrinque repellat, & in &longs;ummo magnis &longs;u&longs;ti­<lb/>nendis oneribus &longs;it apta. </s> <s id="s.001194">Producantur CH in N, DB verò <lb/>in O, &longs;itqueue centrum grauitatis AG in L, partis vero BG <lb/>in M. <!-- KEEP S--></s> <s id="s.001195">Quoniam igitur centra hæc ob elatam portionum <lb/>con&longs;titutionem quam proxima lineis AN, BO, fulcimen­<lb/>torum fiunt, maximè <expan abbr="&longs;u&longs;tinētur">&longs;u&longs;tinentur</expan>, & deor&longs;um potius quam <lb/>lateraliter incumbas ip&longs;as premunt. </s> <s id="s.001196">Si quid tamen <expan abbr="habēt">habent</expan> <lb/>vitij, illud e&longs;t quod grauitatis centra momentum haben­<lb/>tia ad interiorem partem ver&longs;us PQ vim faciant, & ni&longs;i <lb/>partes magno &longs;uperimpo&longs;ito pondere comprimantur, <lb/>partes quæ &longs;unt circa HG, &longs;ur&longs;um pellentes aliquali &longs;ibi <lb/>rectitudine comparata corruunt, facta nempe circa L, M, <lb/>coniunctarum partium &longs;eparatione. </s> </p> <p type="main"> <s id="s.001197">His hoc pacto explicatis de &longs;emicirculari fornice a­<lb/>gemus, quæ cæteris omnibus vtilior e&longs;t, & longè pulcher­<lb/>rima, quamobrem Antiquis Architectis omnibus inpri­<lb/>mis admodum familiaris: </s> </p> <figure id="id.007.01.128.1.jpg" xlink:href="007/01/128/1.jpg"/> <p type="main"> <s id="s.001198">E&longs;to vanum <lb/>ABCD, muris v­<lb/>trinque clau&longs;um. <lb/></s> <s id="s.001199">Ducatur per <expan abbr="sū-mitates">sum­<lb/>mitates</expan> <expan abbr="murorū">murorum</expan> <lb/>horizonti æqui­<lb/>di&longs;tans recta AD, <lb/>hac bifariam &longs;e­<lb/>cta in E, eodem <lb/>centro E, &longs;patio <lb/>verò EA &longs;emicir­<lb/>culus de&longs;cribatur <lb/>AFD, concaua <lb/>nempe ip&longs;ius for-<pb xlink:href="007/01/129.jpg"/>nicis pars; tum eodem centro, &longs;patio verò EG, circinetur <lb/>GHI eiu&longs;dem fornicis pars conuexa. </s> <s id="s.001200">Po&longs;t hæc productis <lb/>lineis BH, CD, in OP, &longs;ecetur fornix tota in tres æquales <lb/>partes AGKM, MNLK, NDIL, & KME, LNE iungantur, <lb/>&longs;int autem partium ip&longs;arum grauitatis centra QRS. </s> <s id="s.001201">E&longs;t <lb/>autem R in ip&longs;a perpendiculari HE. </s> <s id="s.001202">Quoniam igitur <lb/>partium AGKM, DILN, quæ <expan abbr="vtrinq;">vtrinque</expan> &longs;unt grauitatis cen­<lb/>tra QS, in ip&longs;is &longs;unt fulcimentorum lineis OH PD, &longs;uâ <lb/>&longs;ponte fulcimentis eas &longs;u&longs;tinentibus partes ip&longs;æ &longs;tabunt. <lb/></s> <s id="s.001203">Pars autem media KMNL deor&longs;um vergente per ip&longs;am <lb/>HE lineam grauitatis centro, &longs;i parumper vel incumbæ <lb/>vel partes vtrinque AG<emph type="italics"/>K<emph.end type="italics"/>M, DILN cedant, vtpote quæ à <lb/>fulcimentis e&longs;t remoti&longs;&longs;ima, magno impetu &longs;uopte pon­<lb/>dere deor&longs;um feretur. </s> <s id="s.001204">quæ igitur in his &longs;emicircularibus <lb/>fornicibus partes &longs;tabiliores &longs;int, quæ verò ca&longs;ibus obno­<lb/>xiæ, ex his quæ diximus, clarè patet. </s> </p> <p type="main"> <s id="s.001205">Cæterùm cur incumbis manentibus fornix &longs;tet, ea <lb/>cau&longs;&longs;a e&longs;t, quod partes exteriores G<emph type="italics"/>K<emph.end type="italics"/>, <emph type="italics"/>K<emph.end type="italics"/>L, LI, maiores &longs;int <lb/>in ferioribus & oppo&longs;itis AM, MN, NG; quod &longs;uprà de­<lb/>mon&longs;trauimus. </s> </p> <p type="main"> <s id="s.001206">Si quid autem vitij in hac &longs;pecie e&longs;t, illud quidem <lb/>e&longs;t, quod &longs;umma pars <emph type="italics"/>K<emph.end type="italics"/>MNL deor&longs;um vergens magnâ vi <lb/>partes, quæ vtrinque &longs;unt, repellat, ex qua re &longs;olidarum <lb/>partium fit &longs;olutio, & inde ruina. </s> </p> <p type="main"> <s id="s.001207">Huic difficultati vt occurrerent peritiores Archite­<lb/>cti, plura excogitârunt remedia. </s> <s id="s.001208">Primum enim parietes <lb/>hinc inde ita &longs;olidos, cra&longs;&longs;os & firmos faciunt, vt &longs;uapte vi <lb/>re&longs;i&longs;tentes dimoueri loco nequeant, vel para&longs;tatas <expan abbr="addūt">addunt</expan> <lb/>vt in figura TX, VY. </s> <s id="s.001209">Præterea & ferrea claui ex incumba <lb/>in incumbam ducta & vtrinque firmata contrarias partes <lb/>validi&longs;&longs;imè connectunt, quæ calcitrantes (ita enim lo­<lb/>quuntur no&longs;trates <emph type="italics"/>A<emph.end type="italics"/>rchitecti,) fornicis pedes cohibent, & <lb/>&longs;olidum ne &longs;oluatur impediunt. </s> <s id="s.001210">qua in &longs;pecie dubitan<expan abbr="dū">dum</expan> <pb xlink:href="007/01/130.jpg"/>e&longs;&longs;et, an optimo loco &longs;it a &longs;it clauis, quæ per centrum? </s> <s id="s.001211">Et <lb/>&longs;anè videtur, quippe quod circa incumbas impetus fiat <lb/>maior. </s> <s id="s.001212">Ego autem vtilius ibi poni arbitror, vbi <expan abbr="punctaq.">punctaque</expan> <lb/>5. hoc e&longs;t, in medio tertiarum illarum partium, quæ vtrin­<lb/>que incumbis in&longs;i&longs;tunt, propterea quod primus impul&longs;us <lb/>ex media parte quæ impendet, ibi fiat. </s> <s id="s.001213">Rarò tamen boni <lb/>Architecti eo loco aptare &longs;olent, eo quòd eiu&longs;modi cla­<lb/>ues vel pulcherrimis ædificijs minuant gratiam. </s> <s id="s.001214">Vnde fit <lb/>vt nunquam &longs;atis laudetur Lucianus ille Benuerardus <lb/>Lauranen&longs;is Dalmata, qui nullibi apparentes eas po&longs;uit <lb/>in admirabili illa Vrbini Aula, quam Federico Feltrio, fe­<lb/>lici&longs;&longs;imo æquè & inuicti&longs;&longs;imo Duci, ædificauit. </s> </p> <p type="main"> <s id="s.001215">Tertio denique modo huic infirmitati me dentur, <lb/>vt videre e&longs;t in &longs;equenti figura, in qua vanum ADBC, mu­<lb/>ri vtrinque AF, BH, fornix verò FGH. </s> <s id="s.001216">Itaque dum muros <lb/><figure id="id.007.01.130.1.jpg" xlink:href="007/01/130/1.jpg"/><lb/>ex&longs;truunt, arre­<lb/>ctarias trabes, ro­<lb/>bore aliaue mate­<lb/>ria firmi&longs;&longs;ima, illis <lb/>in&longs;erunt, quales <lb/>&longs;unt IF<emph type="italics"/>K<emph.end type="italics"/> LHM, <lb/>ea proceritate vt <lb/>futuri fornicis &longs;u­<lb/>perent &longs;ummita­<lb/>tem. </s> <s id="s.001217">Con&longs;umma­<lb/>to enim fornice, <lb/>nondum tamen, <lb/>exarmato, tran&longs;­<lb/>uer&longs;ariam <expan abbr="trabē">trabem</expan> à <lb/>&longs;ummo fornicis <lb/>dor&longs;o parumper <lb/>eminentem in punctis I, L, arrectarijs trabibus validi&longs;&longs;i­<lb/>mis clauibus connectunt, tum punctis NP, Oq, capreolos <pb xlink:href="007/01/131.jpg"/>tran&longs;uer&longs;ario, & arrectarijs ferreis, clauis affigunt. </s> <s id="s.001218">Qui­<lb/>bus ita concinnatis, facta fornicis validâ pre&longs;&longs;ione in G, <lb/>incumbi&longs;que F, H, ad exteriora repul&longs;is, AB &longs;patium non <lb/>fit maius. </s> <s id="s.001219">Repul&longs;is enim incumbis & muros propelli ne­<lb/>ce&longs;&longs;e e&longs;t, & cum muris ip&longs;as in&longs;ertas trabes, I<emph type="italics"/>K<emph.end type="italics"/>, LM. </s> <s id="s.001220">At va­<lb/>ricari non po&longs;&longs;unt, nî &longs;ecum trahant puncta PQ, quod fie­<lb/>ri non pote&longs;t, propterea quod in punctis N, O, validè di&longs;­<lb/>tineantur. </s> <s id="s.001221">Itaque &longs;patio AB non dilatato nulla fit ip&longs;ius <lb/>fornicis di&longs;&longs;olutio, quod vtique à principio ceu propo&longs;i­<lb/>tus finis quærebatur. </s> <s id="s.001222">Sed dicet qui&longs;piam, Nonne pende­<lb/>bit tran&longs;uer&longs;aria trabs in ip&longs;a di&longs;tractione arrectariorum, <lb/>pre&longs;&longs;a in punctis N, O? aut parum dicimus, aut nihil. </s> <s id="s.001223">Cum <lb/>enim PQ proxima &longs;int punctis FH, quæ cum arrectarijs à <lb/>muro di&longs;tinentur, magna in ijs fit vtrobique re&longs;i&longs;tentia. </s> </p> <p type="main"> <s id="s.001224">Rebus igitur ita &longs;e habentibus cum ob&longs;erua&longs;&longs;ent Ar­<lb/>chitecti, ob enormitatem ponderis fornices in tertia illa <lb/><figure id="id.007.01.131.1.jpg" xlink:href="007/01/131/1.jpg"/><lb/>parte quæ &longs;umma e&longs;t <lb/>laborare, <expan abbr="quãtum">quantum</expan> ter­<lb/>tijs vtrinque partibus <lb/>&longs;oliditatis addunt, tan­<lb/>tundem ex illa parte <lb/>&longs;uprema demere <expan abbr="&longs;olēt">&longs;olent</expan>, <lb/>vt videre e&longs;t in &longs;ubie­<lb/>cta figura, in qua par­<lb/>tes A, B, &longs;olidæ & cra&longs;­<lb/>&longs;iores, quibus hærent <lb/>partes, quæ CE, DG <lb/>cra&longs;&longs;æ quidem & illæ, <lb/>tum vero &longs;umma EFG, <lb/>alijs &longs;ubtilior. </s> <s id="s.001225">Minus <lb/>igitur grauante ponde­<lb/>re in F, minor fit ad incumbas pre&longs;&longs;io, aut &longs;i qua fit, à <expan abbr="partiū">partium</expan> <lb/>ACE, BDG &longs;oliditate haud inualidè &longs;u&longs;tinetur. </s> </p> <pb xlink:href="007/01/132.jpg"/> <p type="main"> <s id="s.001226">Cæterùm admonet nos locus, vt aliquid de forni­<lb/>cum di&longs;&longs;olutionibus in medium afferamus: cau&longs;&longs;is enim <lb/>morborum cognitis, facilius periti medici adhibere &longs;o­<lb/>lent remedia. </s> </p> <figure id="id.007.01.132.1.jpg" xlink:href="007/01/132/1.jpg"/> <p type="main"> <s id="s.001227">E&longs;to enim &longs;emicircula­<lb/>ris fornix ABC, cuius cen­<lb/>trum E, perpendicularis ve­<lb/>rò quæ per centrum DBE, &longs;e­<lb/>micirculi ABC, diameter <lb/>AEC, incumbæ <expan abbr="vtrinq;">vtrinque</expan> A, C. <lb/><!-- KEEP S--></s> <s id="s.001228">Itaque &longs;i nulla fiat incumba­<lb/>rum repul&longs;io, &longs;tabit fornix; &longs;i verò fiat, ruinam faciet. </s> </p> <p type="main"> <s id="s.001229">Pellantur itaque ad exteriores partes, vt in &longs;ecunda <lb/><figure id="id.007.01.132.2.jpg" xlink:href="007/01/132/2.jpg"/><lb/>figura, H in F, & C in G, <lb/>ex qua pul&longs;ione cum ma­<lb/>ius fiat &longs;patium quod in­<lb/>tegro fornice impleba­<lb/>tur, iam di&longs;tractis <expan abbr="vtrinq;">vtrinque</expan> <lb/>fornicis partibus <expan abbr="nō">non</expan> im­<lb/>pletur, Diuiditur igitur <lb/>locus maior factus in tres partes, quarum hinc inde duas <lb/>replent fornicis partes, tertiam verò quæ media e&longs;t, re­<lb/>plet in&longs;ertus, ne vacuum detur, aër, vt in figura videre e&longs;t, <lb/>in qua &longs;olutæ vtrinque fornicis partes HIKF, PMNG, aër <lb/>autem medius &longs;patium replens IKMN. </s> <s id="s.001230">Diuidantur &longs;in­<lb/>guli quadrantes FK, GN, in partes tres, quarum duæ &longs;int <lb/>hinc inde FQ, GR, & à centris, quæ &longs;eparatis quadranti­<lb/>bus facta &longs;unt in ST, rectæ ducantur SQV. TRX. <!-- KEEP S--></s> <s id="s.001231">Quo­<lb/>niam igitur tertiæ partes vtrinque VIKQ MNRX pro­<lb/>pria grauitate depre&longs;&longs;æ, nullum quo &longs;u&longs;tineantur fulci­<lb/>mentum habent, corruent quidem. </s> <s id="s.001232">Ducantur autem re­<lb/>ctæ QI, RM, con&longs;tituentes cum ip&longs;is QV, RX pares an­<lb/>gulos VQI MRX. </s> <s id="s.001233">Itaque centris QR partes QIRM ad <pb xlink:href="007/01/133.jpg"/>inferiores partes deuoluentur, fientqueue QI, RM, vbi QZ, <lb/>RZ. </s> <s id="s.001234">Si autem QI, RM perpendicularibus quæ à punctis <lb/>QR ad perpendicularem DE ducuntur, fuerint maiores <lb/>conuenient alicubi in ip&longs;a perpendiculari, & altera alte­<lb/>ram &longs;u&longs;tinebit; &longs;i autem æquales tangent &longs;e & nihilomi­<lb/>nus fiet ruina, &longs;i minores nec &longs;e inuicem tangent, & nullà <lb/>re prohibente deor&longs;um corruent. </s> <s id="s.001235">tangant autem &longs;e in <expan abbr="pū-cto">pun­<lb/>cto</expan> Z. quo pacto igitur fornices incumbis cedentibus in <lb/>medio aperti, <expan abbr="di&longs;&longs;oluãtur">di&longs;&longs;oluantur</expan> & ruinam faciant, ex i&longs;tis patet. </s> </p> <p type="main"> <s id="s.001236">Ex demon&longs;tratis qua&longs;i ex con&longs;ectario habemus for­<lb/>nices quo fuerint cra&longs;&longs;iores dato pari incumbarum &longs;ece&longs;­<lb/>&longs;u, ruinæ minus e&longs;&longs;e obnoxios quàm tenuiores, hoc e&longs;t, <lb/>maiori aperitione indigere ad ruinam cra&longs;&longs;iores quam te­<lb/>nuiores, quod licet ex iam dictis re&longs;ultet, nos tamen cla­<lb/>rius ex &longs;ubiecto &longs;chemate demon&longs;trabimus. </s> </p> <figure id="id.007.01.133.1.jpg" xlink:href="007/01/133/1.jpg"/> <p type="main"> <s id="s.001237">E&longs;to enim cra&longs;&longs;ioris <lb/>fornicis pars <expan abbr="quidē">quidem</expan> ABCD, <lb/>tenuioris EFCD circa <expan abbr="idē">idem</expan> <lb/>centrum R. <!-- KEEP S--></s> <s id="s.001238">Ducatur au­<lb/>tem RM, &longs;ecans CD in G. <lb/>EF in H AB, in M. <!-- KEEP S--></s> <s id="s.001239">Centro <lb/>igitur G fiet euer&longs;io portio­<lb/>num fornicum, MD, HD, <lb/>Ducantur GA, GE & producta AD in N ip&longs;i AN perpen­<lb/>dicularis ducatur GN. quoniam igitur GE cadit in trian­<lb/>gulo AGN erit ex 21. propo&longs;. lib. 1. elem. GA, maior GE. <lb/></s> <s id="s.001240">Corruente igitur maioris fornicis portione MD, recta <lb/>GA centro G punctum A de&longs;cribet portionem AI, mino­<lb/>ris interim ex GE, de&longs;cribente EL, at cadenti angulo A <lb/>occurrit in perpendiculari IK in puncto I angulus oppo­<lb/>&longs;itæ portionis, O, ip&longs;i autem E cadenti per EL non occur­<lb/>ret punctum P, cadens per Pq eo quod neutrum eorum <lb/>pertingat ad perpendicularem IK. <!-- REMOVE S-->Tenuioris ergo forni­<pb xlink:href="007/01/134.jpg"/>cis partes è &longs;uis locis auul&longs;æ ex eadem aperitione ruinam <lb/>facient, quod non contingit partibus cra&longs;&longs;ioris. </s> <s id="s.001241">quod &longs;a­<lb/>nè fuerat de clarandum. </s> </p> <p type="main"> <s id="s.001242">Quæritur adhuc, quare grauiores fornices in &longs;um­<lb/>mis ædificijs non &longs;ine vitio fiant? </s> </p> <p type="main"> <s id="s.001243">E&longs;to ædificium ABGH, cuius <expan abbr="vtrinq;">vtrinque</expan> muri ABCD, <lb/>EFGH, maiorum &longs;ummitates AD, EH, mediæ murorum <lb/>partes KL, fornicum &longs;ummus quidem DIE, medius verò <lb/><figure id="id.007.01.134.1.jpg" xlink:href="007/01/134/1.jpg"/><lb/>KML. Dico, magis cedere pul­<lb/>&longs;os muros &longs;ummos circa DE, <lb/>quam in medio circa KL. <!-- KEEP S--></s> <s id="s.001244">Sunt <lb/>enim muri BA, GH ceu vectes <lb/>quidam, <expan abbr="quorū">quorum</expan> extremis par­<lb/>tibus à fulcimentis BG remo­<lb/>ti&longs;&longs;imis potentia admouetur, <lb/>hoc e&longs;t, ip&longs;ius fornicis DIE ad <lb/>DE incumbans repul&longs;io; lon­<lb/>gior e&longs;t autem pars à <expan abbr="fulcimē-to">fulcimen­<lb/>to</expan> ad potentiam AB, ip&longs;a BK. <lb/><!-- KEEP S--></s> <s id="s.001245">Data igitur paritate potentia­<lb/>rum plus operabitur ea quæ in <lb/>D, illa quæ K. facilius ergo re­<lb/>pellentur muri in DE quàm in <lb/>KL. <!-- KEEP S--></s> <s id="s.001246">Alia quoque ratio intercedit, &longs;iquidem pondus muri <lb/>&longs;uperioris ADK, premens inferiorem murum KBC, cum <lb/>&longs;ua grauitate firmiorem, & pul&longs;ionibus minus obnoxium <lb/>reddit. </s> <s id="s.001247">Difficilius enim propellitur id quod graue e&longs;t <expan abbr="quã">quam</expan> <lb/>quod leue, vt nos quæ&longs;tione 10. demon&longs;trauimus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001248">QVÆSTIO XVII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001249"><emph type="italics"/>Quærit Ari&longs;toteles, Cur paruo exi&longs;tente cuneo magna &longs;cindantur <lb/>pondera & corporum moles, validaque, fiat impre&longs;&longs;io?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001250">In parua re magnum negotium. </s> <s id="s.001251">Etenim quæ&longs;tio hæc <pb xlink:href="007/01/135.jpg"/>clari&longs;&longs;imorum virorum ingenia magnopere fatigauit. </s> <s id="s.001252">Ex <lb/>quibus Ari&longs;toteles inter veteres, Guid. <!-- REMOVE S-->Vbald. <!-- REMOVE S-->inter re­<lb/>centiores ad vectis naturam (ne quid in Mechanicis ad <lb/>vectem non reduci putaretur) cuneum ip&longs;um trahere co­<lb/><figure id="id.007.01.135.1.jpg" xlink:href="007/01/135/1.jpg"/><lb/>nati &longs;unt. </s> <s id="s.001253">Nos autem pro <lb/>veritate certantes, &longs;i in <lb/>horum &longs;ententiam vltrò <lb/>non tran&longs;ierimus, multa <lb/>venia digni à non iniquo <lb/>iudice exi&longs;timabimur. </s> <s id="s.001254">A­<lb/>ri&longs;totelis mentem clarè <lb/>& fusè explicat G. V­<lb/>bald. <!-- REMOVE S-->in Mechan. vbi de <lb/>Cuneo peculiariter a­<lb/>git. </s> </p> <p type="main"> <s id="s.001255">E&longs;to igitur &longs;cindendum quippiam ABCD, Cuneus <lb/>EFG, cuius pars HFI &longs;ci&longs;&longs;uræ in&longs;erta HI, facta igitur vali­<lb/>da percu&longs;&longs;ione in EG, fiet vt cum EG fuerit in NO, H &longs;it v­<lb/>bi N, A vbi P, itemque I vbi O, D verò vbi Q & facta erit <lb/>&longs;ci&longs;&longs;io NSO, toti nempe cuneo EFG, æqualis. </s> <s id="s.001256">Vult igitur <lb/>Ari&longs;toteles, duos in cuneo vectes con&longs;iderari EF, GF, quo­<lb/>rum alterius, nempe EF, fulcimentum &longs;it in H, pondus ve­<lb/>ro in F; alterius autem, hoc e&longs;t, GF fulcimentum quidem <lb/>&longs;it in I, pondus verò itidem &longs;it in F. <!-- KEEP S--></s> <s id="s.001257">His nequaquam con­<lb/>&longs;entiens G. Vbald. <!-- REMOVE S-->aliam viam ingreditur. </s> <s id="s.001258">Ait enim EHF <lb/>vectes quidem e&longs;&longs;e, quorum commune fulcimentum F, <lb/>potentias verò mouentes in EG. <!-- KEEP S--></s> <s id="s.001259">Pondera vtrinque inter <lb/>fulcimenta & potentias, vbi HI, idemque; e&longs;&longs;e ac &longs;i EF, GF, <lb/>&longs;eor&longs;um à cuneo con&longs;iderati in puncto F, adinuicem fulti <lb/>atque di&longs;tracti pondera pellerent H in NP, I verò in O, <lb/>Q.</s> <s id="s.001260"> Verum enimuerò quoniam cunei angulus non muta­<lb/>tur, nec vertex ip&longs;e centri vllum pror&longs;us præbet v&longs;um, nec <lb/>eius latera vtrinque di&longs;tracta ad contrarias partes didu­<pb xlink:href="007/01/136.jpg"/>cuntur, vectes in cuneo hoc pacto con&longs;iderare videtur à <lb/>veritate alienum. </s> <s id="s.001261">Ari&longs;totelis autem &longs;olutionem fal&longs;am e&longs;­<lb/>&longs;e, clarè patet. </s> <s id="s.001262">quo pacto enim F pellet ex fulcimento H i­<lb/>p&longs;am ligni partem OS, & idem F ex fulcimento I pellet <lb/>oppo&longs;itam partem NS, &longs;i inuicem contendentes extremæ <lb/>vectium partes in F, altera alteri ne quicquam operentur, <lb/>e&longs;t impedimento? </s> <s id="s.001263">Et &longs;anè opinionis fal&longs;itas inde patet, <lb/>quòd videamus materiæ partes &longs;ci&longs;&longs;as, in ip&longs;o &longs;ci&longs;&longs;ionis a­<lb/>ctu facta di&longs;tractione à cunei vertice nequaquam tangi. <lb/></s> <s id="s.001264">At eiu&longs;modi operationes per contactum fieri nulli e&longs;t i­<lb/>gnotum. </s> <s id="s.001265">Solutio igitur i&longs;ta meo iudicio, tanto Philo&longs;o­<lb/>pho pror&longs;us videtur indigna. </s> </p> <p type="main"> <s id="s.001266">Porrò G. Vbald. <!-- REMOVE S-->ijs quæ de diuaricatis vectibus in <lb/>medium adduxerat non acquie&longs;cens alias quærit cau&longs;&longs;as, <lb/>cur cuneus minoris anguli validiùs &longs;cindat. </s> <s id="s.001267">Idque; ex quo­<lb/>dam lemmate demon&longs;trare conatur, figura autem eius ita <lb/>ferè &longs;e habet. </s> </p> <figure id="id.007.01.136.1.jpg" xlink:href="007/01/136/1.jpg"/> <p type="main"> <s id="s.001268">E&longs;to cuneus ABC, <lb/>item alius DEF. <expan abbr="Demō-&longs;trauit">Demon­<lb/>&longs;trauit</expan> igitur ex a&longs;&longs;um­<lb/>pto, quo acutior fuerit <lb/>angulus BIM, eo facilius <lb/>pondera moueri, & ideo <lb/>facilius ceu vecte AB <lb/>moueri pondus I quàm <lb/>vecte DE pondus Q.</s> <s id="s.001269"> In­<lb/>geniosè quidem. </s> <s id="s.001270">At ma­<lb/>gnam hæc apud me ha­<lb/>bent difficultatem. </s> <s id="s.001271">Si e­<lb/>nim ita &longs;e habet AB, ad BI, vt DE, ad EQ (ip&longs;æ enim DE, <lb/>EQ &longs;upponuntur æquales) ergo eadem æquali&longs;ue poten­<lb/>tia æqualiter mouebit pondera I & Q.</s> <s id="s.001272"> quod ip&longs;i eiu&longs;dem <lb/>demon&longs;trationi pror&longs;us concludit contrarium. </s> <s id="s.001273">Nec meo <pb xlink:href="007/01/137.jpg"/>quidem iudicio id &longs;equi videtur, propterea quod ex Pap­<lb/>po ea quæ in planis inclinatis mouentur, redigantur ad li­<lb/>bram. </s> <s id="s.001274">Ratio enim valde e&longs;t diuer&longs;a, &longs;iquidem pondera <lb/>quæ in planis inclinatis mouentur, certa habent fulci­<lb/>menta & determinatas tum brachiorum tum ponderum <lb/>proportiones, quæ omnia in cuneo, nec quidem mente <lb/>concipi po&longs;&longs;e, clarè patet. </s> </p> <p type="main"> <s id="s.001275">His igitur difficultatibus con&longs;ideratis, Nos cunei <lb/>vim, ad alia e&longs;&longs;e principia referendam pro comperto ha­<lb/>bemus. </s> <s id="s.001276">Ordimur igitur hoc pacto. </s> <s id="s.001277">Cuneo quidem res di­<lb/>uidi certum e&longs;t. </s> <s id="s.001278">Cæterùm quæ natura diuidere apta &longs;unt, <lb/>tria &longs;unt, punctum, linea, &longs;uperficies, Puncto enim linea, <lb/>lineâ &longs;uperficies, &longs;uperficie autem corpus ip&longs;um diuidi­<lb/>tur. </s> <s id="s.001279">quæ omnia à Mathematico ab&longs;que materia con&longs;ide­<lb/>rantur. </s> <s id="s.001280">De diui&longs;ione autem quæ fit ex puncto, nihil agit <lb/>Mechanicus, qui corporibus quidem vtitur, ad cuius na­<lb/>turam non trahitur punctum, cuius partes &longs;unt nullæ. </s> <s id="s.001281">At <lb/>non lineis & &longs;uperficiebus modò corpora diuiduntur, &longs;ed <lb/>etiam corporibus, quod verum e&longs;t, at ea corpora ad linea­<lb/>rum & &longs;uperficierum naturam quodammodo aptari faci­<lb/>lè docebimus. </s> <s id="s.001282">Dicimus igitur, duplicem e&longs;&longs;e Cuneorum <lb/>&longs;peciem, linearem vnam, &longs;uperficialem alteram. </s> <s id="s.001283">linearem <lb/>appello, quæ ad lineæ naturam magnopere accedit. </s> <s id="s.001284">Tales <lb/>&longs;unt orbiculares illæ cu&longs;pides, quibus ad perforandum v­<lb/>timur, & ideo vernaculè Pantirolos vocamus. </s> <s id="s.001285">Acus item <lb/>&longs;utorij, & cætera quæ non &longs;ecus ac linea in punctum de&longs;i­<lb/>nunt, & imaginariam quandam lineam ceu axem in eo <lb/>puncto de&longs;inentem continent. </s> <s id="s.001286">Ad lineam quoque refe­<lb/>runtur lateratæ cu&longs;pides oblongæ, & &longs;ubtiles ceu &longs;ubulæ, <lb/>claui, en&longs;es, pugiones, & his &longs;imilia, quæ cum adacta vali­<lb/>dam faciant partium &longs;eparationem ad cunei naturam <expan abbr="nō">non</expan> <lb/>referre magnæ videretur dementiæ. </s> <s id="s.001287">Et tunc quanto ma­<lb/>gis corpora hæc ad linearem naturam accedunt, eo ma­<pb xlink:href="007/01/138.jpg"/>gis penetrant. </s> <s id="s.001288">Sed & hoc idem in rebus non ab arte, &longs;ed <lb/>ab ip&longs;a natura productis facile e&longs;t cogno&longs;cere. </s> <s id="s.001289">Quis enim <lb/>non experitur, quàm validè culex, infirmi&longs;&longs;imum animal, <lb/>& ea paruitate qua e&longs;t, hominum & cæterorum <expan abbr="animaliū">animalium</expan>, <lb/>cutes aculeata probo&longs;cide penetret? </s> <s id="s.001290">Id vtique non alia de <lb/>cau&longs;&longs;a fit, quod ad imaginariæ lineæ &longs;ubtilitatem quam, <lb/>proximè accedat. </s> <s id="s.001291">Ve&longs;pæ quoque, Apes, Scorpiones a­<lb/>culeis i&longs;tis ceu linearibus cuneis vtuntur. </s> <s id="s.001292">Nec refert, vt <lb/>diximus, vtrum laterati &longs;int, ceu &longs;ubulæ, & claui, vel ro­<lb/>tundi & vtrum plura paucioraue latera habeant, dummo­<lb/>do in punctum & aculeatam aciem de&longs;inant. </s> <s id="s.001293">Altera por­<lb/>ro cuneorum &longs;pecies &longs;uperficiei naturam &longs;apit, acie &longs;iqui­<lb/>dem in lineam de&longs;init, quæ &longs;uperficiei e&longs;t terminus, <expan abbr="quã">quam</expan>obrem huc ea omnia referuntur, quæ acie ipsâ &longs;cindunt, <lb/>ceu &longs;unt cunei propriè dicti, de quibus hoc loco e&longs;t &longs;er­<lb/>mo, cultra, en&longs;es, a&longs;ciæ, &longs;ecures, &longs;calpra lata, & cætera e­<lb/>iu&longs;modi, quibus corpora acie &longs;cinduntur. </s> <s id="s.001294">Quidam his ad­<lb/>dunt &longs;erras, quibus haud pror&longs;us a&longs;&longs;entimur. </s> <s id="s.001295">Etenim alia <lb/>ratione diuidunt, &longs;icut & limæ &longs;olent, deterendo enim, <expan abbr="nō">non</expan> <lb/>&longs;cindendo ferri, ligni, & marmorum duritiem diuidunt & <lb/>domant. </s> <s id="s.001296">His igitur <expan abbr="cō&longs;ideratis">con&longs;ideratis</expan>, &longs;i daretur ex materia qua­<lb/>piam in frangibili cuneus, qui maximè ad &longs;uperficiei natu­<lb/>ram accederet, vel paruo labore tenaci&longs;&longs;ima ligna validi&longs;­<lb/>&longs;imè &longs;cinderet, & ideo optimè res gladijs illis diuiditur, <lb/>qui magis ad &longs;uperficiei naturam accedunt. </s> <s id="s.001297">Ex quibus o­<lb/>mnibus, nî fallimur, clarè patet, cur acutiores angulo cu­<lb/>nei obtu&longs;ioribus facilius &longs;cindant, quæ quidem ratio lon­<lb/>gè ab ea di&longs;tat, ex qua cæteri ferè omnes Cuneum ad ve­<lb/>ctis naturam referre hactenus contenderunt. </s> </p> <p type="main"> <s id="s.001298">Cæterùm vtramque eorum quos diximus, <expan abbr="cuneorū">cuneorum</expan> <lb/>&longs;peciem &longs;olerti&longs;&longs;ima cognouit Natura, & ideo quoniam <lb/>res vel contu&longs;ione vel perforatione, vel &longs;ecatione confi­<lb/>ciuntur, triplicem dentium qualitatem dentatis animali-<pb xlink:href="007/01/139.jpg"/><figure id="id.007.01.139.1.jpg" xlink:href="007/01/139/1.jpg"/><lb/>bus dedit, Molares, <lb/>qui & Maxillares ap­<lb/>pellantur, quibus <lb/>cibus contunditur, <lb/>Canini, quibus fit <lb/>perforatio, Anterio­<lb/>res, quibus cibus <lb/>&longs;cinditur, quos ideo <lb/><foreign lang="greek">temnikou\s</foreign>, id e&longs;t, &longs;ecan­<lb/>tes appellant Graeci. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001299">Molares KK, <lb/>Canini L, L, Temni­<lb/>ci &longs;eu &longs;ecantes M. <!-- KEEP S--></s> <s id="s.001300">Cuneus orbicularis lineari&longs;queue AB, in <lb/>quo axis linea e&longs;t, ad cuius naturam accedit AB cuneus <lb/>&longs;uperficialis CD, accedens ad &longs;uperficiei naturam, quam <lb/>vitro imaginamur EFGD, in aciem cunei de&longs;inentem, <lb/>GD, Lateratus lineari&longs;que cuneus, clauus HI. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001301">Cunei autem omnes dupliciter &longs;unt efficaces, vel e­<lb/>nim malleo, vt in ijs fit, quibus lìgna &longs;cinduntur & &longs;calpris <lb/>fieri &longs;olet, adiguntur, vel impul&longs;u & pre&longs;&longs;ione, vt in gla­<lb/>dijs fit, pugionibus, cælatorum &longs;calpris, &longs;ubulis, & cæteris <lb/>eiu&longs;modi. </s> <s id="s.001302">Quidam etiam &longs;unt, qui licet mallei ictu non <lb/>adigantur, malleum coniunctum habent, ceu &longs;unt &longs;ecu­<lb/>res, ligones, A&longs;ciæ, & his &longs;imilia, quæ ex percu&longs;&longs;ione &longs;e­<lb/>metip&longs;a &longs;cindendis rebus in&longs;erunt & validè penetrant. <lb/></s> <s id="s.001303">De vi autem & efficacia ictus &longs;eu percu&longs;&longs;ionis hic &longs;uper­<lb/>&longs;edemus aliquid, ea de re, in &longs;equenti quæ&longs;tione verba fa­<lb/>cturi. </s> </p> <p type="main"> <s id="s.001304">Multa hîc addere potui&longs;&longs;emus ad Cochleam &longs;pe­<lb/>ctantia, quippe quòd Cochlea cuneus &longs;it Cylindro inuo­<lb/>lutus, qui quidem ad mallei, &longs;ed vectis virtute &longs;ibi adiun­<lb/>ctâ, validi&longs;&longs;imè operatur, & &longs;excentis in&longs;eruit v&longs;ibus. </s> <s id="s.001305">Ve­<lb/>runtamen cùm de hac &longs;pecie egregiè di&longs;&longs;erat G. Vbaldus, <pb xlink:href="007/01/140.jpg"/>con&longs;ultò hanc di&longs;putationem omittimus; idque hac quo­<lb/>que de cau&longs;&longs;a, quod nihil de cochlea, ac &longs;i eam non noui&longs;­<lb/>&longs;et, locutus &longs;it Ari&longs;toteles. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001306">Po&longs;&longs;umus autem in actu &longs;ci&longs;&longs;ionis, quæ cuneo fit, a­<lb/>liâ tamen ratione vectem con&longs;iderare, nempe non in cu­<lb/>neo quidem, &longs;ed in ip&longs;a re quæ &longs;cinditur. </s> </p> <figure id="id.007.01.140.1.jpg" xlink:href="007/01/140/1.jpg"/> <p type="main"> <s id="s.001307">E&longs;to enim quip­<lb/>piam &longs;ci&longs;&longs;ile ABCD, <lb/>cui alteri extremita­<lb/>tum, puta BD, cuneus <lb/>adigatur EFG, <expan abbr="fiatq;">fiatque</expan> <lb/>&longs;ci&longs;&longs;io per longitudi­<lb/>nem &longs;ecundum <expan abbr="lineã">lineam</expan> <lb/>EH. facta igitur ex <lb/>cunei ingre&longs;&longs;u <expan abbr="partiū">partium</expan> &longs;eparatione B, expelletur in I, D ve­<lb/>rò in K. fient igitur materiæ &longs;ci&longs;&longs;æ partes AIBH, CKDH, <lb/>ceu duo vectes, quorum hinc inde in corpore ip&longs;o fulci­<lb/>menta L, M potentiæ vtrinque dilatantes BD, pondus ve­<lb/>rò materiæ re&longs;i&longs;tentia, in &longs;eparationis loco vbi N. <!-- KEEP S--></s> <s id="s.001308">Duca­<lb/>tur NL, quanto itaque BN maiorem habebit proportio­<lb/>nem ad LN, eo faciliùs re&longs;i&longs;tentia quæ in N, &longs;uperabitur. <lb/></s> <s id="s.001309">Mutatur <expan abbr="autē">autem</expan> a&longs;&longs;iduè in ip&longs;a &longs;ci&longs;&longs;ione fulcimentum, & <expan abbr="cū">cum</expan> <lb/>fulcimento ip&longs;a proportio. </s> <s id="s.001310">Pertingente enim &longs;ci&longs;&longs;ione in <lb/>O, <expan abbr="fulcimētum">fulcimentum</expan> fit in P. quo ca&longs;u &longs;ci&longs;&longs;ura e&longs;t facilior, quip­<lb/>pe quod maiorem habeat proportionem BO ad OP, <expan abbr="quã">quam</expan> <lb/>BN ad NL. </s> <s id="s.001311">Hoc autem experiuntur materiarij, qui primis <lb/>ictibus, &longs;ecuriculâ nondum probè adactâ, & nondum fa­<lb/>ctâ notabili &longs;ci&longs;&longs;ione difficultatem &longs;entiunt, mox <expan abbr="factaiã">facta iam</expan> <lb/>&longs;eparatione facillima paullatim fit materiæ totius &longs;epara­<lb/>tio. </s> <s id="s.001312">Hoc idem & nos ab&longs;que cunei v&longs;u experimur, cum ba­<lb/>culum aut quippiam tale manibus diductis &longs;cindimus. </s> <s id="s.001313">à <lb/>principio enim difficultatem &longs;entimus, deinde ex ea <expan abbr="quã">quam</expan> <lb/>diximus proportione &longs;ci&longs;&longs;io ip&longs;a fit apprime facilis. </s> <s id="s.001314">Vti-<pb xlink:href="007/01/141.jpg"/>mur etiam vecte cuneato ad &longs;cindendum & aperiendum: <lb/>adacto enim &longs;ci&longs;&longs;uræ cuneo, idqueue manu malleoue, tum <lb/>ab altera extremitate pre&longs;&longs;o, valida fit ex vectis vi <expan abbr="cōtinui">continui</expan> <lb/><figure id="id.007.01.141.1.jpg" xlink:href="007/01/141/1.jpg"/><lb/>corporis &longs;eparatio. </s> <s id="s.001315">Ma­<lb/>teria &longs;ci&longs;&longs;ilis AB <expan abbr="&longs;calprū">&longs;calprum</expan> <lb/>ceu vectis cuneatus CD, <lb/>cuius fulcimentum, E, <lb/>pondus verò vbi C, po­<lb/>tentia vbi D, quo ca&longs;u <lb/>quo maior e&longs;t proportio <lb/>DE ad EC, eo e&longs;t ip&longs;a &longs;ci&longs;&longs;io leuior & facilior. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001316">QVAESTIO XVIII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001317"><emph type="italics"/>Quærit hic Ari&longs;toteles, Cur per Trochleas ab exigua potentia in­<lb/>gentia moueantur pondera?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001318">De Trochlea Pappus, & veteres: inter recentiores e­<lb/>gregiè admodum, vt omnia examinauit in Mechani­<lb/>cis G. Vbaldus. <!-- KEEP S--></s> <s id="s.001319">Nos tamen interim po&longs;t clari&longs;&longs;imos illos <lb/>viros aliquid quod nouitatem & &longs;ubtilitatem &longs;apiat, de <lb/>no&longs;tro penu promemus. </s> <s id="s.001320">Et &longs;anè inuentis quidem addere <lb/>res e&longs;t facilis, at quod inuentis addas inuenire haud adeo <lb/>facile. </s> <s id="s.001321">Sed nos primum Philo&longs;ophi ip&longs;ius dicta ad <expan abbr="trutinã">trutinam</expan> <lb/>reuocemus. </s> <s id="s.001322">Ita autem quæ&longs;tionem proponit; Cur &longs;i qui&longs;­<lb/>piam Trochleas componens duas, in &longs;ignis duobus, ad &longs;e <lb/>inuicem iunctis contrario ad Trochleas modo circulo fu­<lb/>nem circumduxerit, cuius alterum quidem caput tigno­<lb/>rum appendatur alteri, alterum verò Trochleis &longs;it <expan abbr="innixū">innixum</expan> <lb/>& à funis initio trahere cœperit, magna trahit pondera, li­<lb/>cet imbecillium fuerit virium? </s> </p> <p type="main"> <s id="s.001323">Ob&longs;eueri&longs;&longs;ima expo&longs;itio, & nî res e&longs;&longs;et vulgò per &longs;e <lb/>nota, dequeue ea Vitruuius & Mechanici non egi&longs;&longs;ent, diffi­<lb/>cile vtique e&longs;&longs;et ex eius verbis &longs;en&longs;um a&longs;&longs;equi. </s> </p> <pb xlink:href="007/01/142.jpg"/> <p type="main"> <s id="s.001324">Tigna &longs;anè voca&longs;&longs;e videtur ea ligna, quæ à Vitruuio <lb/>Rechami dicuntur, in quibus nempe ip&longs;i in&longs;eruntur orbi­<lb/>culi. </s> <s id="s.001325">Et&longs;i de tignis eiu&longs;modi aliud quippiam &longs;entire videa­<lb/>tur Picolomineus. <!-- KEEP S--></s> <s id="s.001326">Græca lectio pro tignis habet <foreign lang="greek">cu/la</foreign>, id <lb/>e&longs;t, ligna; item vbi Leoniceni ver&longs;io legit, ad &longs;e inuicem <lb/>iunctis, textus habet <foreign lang="greek">sumbai/nousin e(autoi=s e)nanti/ws</foreign>, hoc e&longs;t, in­<lb/>uicem ex oppo&longs;ito concurrunt. </s> <s id="s.001327">Certè locum totum ita <lb/>redderem: Cur &longs;i quis duas Trochleas fecerit, in duobus <lb/>lignis &longs;ibi ex oppo&longs;ito concurrentibus, ei&longs;queue Trochleis <lb/>circumpo&longs;uerit funem, cuius alterum caput alteri ligno­<lb/>rum &longs;it annexum, alterum verò Trochleis cohæreat, vel <lb/>apponatur. </s> <s id="s.001328">Si quis alterum funis principium trahat, ma­<lb/>gna trahat pondera, et&longs;i trahens potentia &longs;it exigua? </s> <s id="s.001329">Nos <lb/>verbis figuram, & figurâ verba ip&longs;a elucidabimus. </s> </p> <figure id="id.007.01.142.1.jpg" xlink:href="007/01/142/1.jpg"/> <p type="main"> <s id="s.001330">Sint duo ligna ex oppo&longs;ito concurrentia, <lb/>in quibus Trochleæ, hoc e&longs;t, orbiculi AB, fu­<lb/>nis ductarius DABC, cuius alterum caput re­<lb/>ligatum e&longs;t ligno trochleæ A, vbi e&longs;t C. <!-- KEEP S--></s> <s id="s.001331">Tro­<lb/>chlea A loco &longs;tabili commendata, vbi E. <!-- KEEP S--></s> <s id="s.001332">Pon­<lb/>dus alteri ligno Trochleæ appen&longs;um F. <!-- KEEP S--></s> <s id="s.001333">Tra­<lb/>cto itaque fune DABC, eleuatur & trahitur <lb/>pondus F. <!-- KEEP S--></s> <s id="s.001334">Ex quibus clarè patet, <expan abbr="Philo&longs;ophū">Philo&longs;ophum</expan> <lb/>propo&longs;ui&longs;&longs;e Trochleam duobus tantum orbi­<lb/>culis munitam, quod vtique &longs;atis erat ad ex­<lb/>plicationem. </s> <s id="s.001335">Inquit autem, faciliùs vecte <expan abbr="quã">quam</expan> <lb/>manu pondus moueri. </s> <s id="s.001336">Trochleam vero (id <lb/>e&longs;t, orbiculum; ita enim e&longs;t intelligendum) e&longs;­<lb/>&longs;e vectem, aut vectis virtute operari. </s> <s id="s.001337">Ita autem <lb/>videtur argumentari. </s> <s id="s.001338">Si vnicâ Trochleâ plus trahitur <lb/>quàm manu, multo faci ius & velocius id fiet duobus, <lb/>quibus plus, vt ip&longs;e ait, quàm in duplici velocitate pon­<lb/>dus leuabitur. </s> <s id="s.001339">Summa dictorum e&longs;t, ex multiplicatione <lb/>orbiculorum pondus ip&longs;um imminui, & minori difficul-<pb xlink:href="007/01/143.jpg"/>tate leuari, quod &longs;anè verum e&longs;t. </s> <s id="s.001340">Nos tamen nonnulla <expan abbr="cō-&longs;iderabimus">con­<lb/>&longs;iderabimus</expan>. </s> <s id="s.001341">quod ait, vecte facilius moueri pondera <lb/>quam manu, &longs;emper non e&longs;t verum. </s> <s id="s.001342">Si enim vectis pars <lb/>quæ à fulcimento ad manum breuior fuerit illâ, quæ à <lb/>fulcimento ad pondus difficilius vecte pondus mouebi­<lb/>tur quam manu. </s> <s id="s.001343">Idem quoque accidet, &longs;i eo modo vecte <lb/>vtamur, quem ob&longs;eruat Guidus Vbald. <!-- REMOVE S-->Tract. </s> <s id="s.001344">de Vecte <lb/>prop. 3. Po&longs;ita nempe inter fulcimentum & pondus &longs;u&longs;ti­<lb/>nente potentiâ. </s> <s id="s.001345">Præterea quod a&longs;&longs;eruit Ari&longs;toteles, Tro­<lb/>chleas ad vectem reduci, verum quidem e&longs;t, &longs;ed aptius di­<lb/>xi&longs;&longs;et ad libram, etenim vectis vtcunque à fulcimento di­<lb/>uiditur. </s> <s id="s.001346">Libra verò quod & orbiculis ex centro accidit, <lb/>&longs;emper bifariam. </s> <s id="s.001347">Ad hæc videtur ille ad orbiculorum <lb/>multiplicitatem Trochlearum vim referre. </s> <s id="s.001348">Si enim, ait, <lb/>vnicâ Trochleâ pondus facile trahitur, id multo validius <lb/>pluribus fiet. </s> <s id="s.001349">Veruntamen non ab&longs;olutè ex orbiculorum <lb/>multiplicatione id fieri ita o&longs;tendemus. </s> </p> <figure id="id.007.01.143.1.jpg" xlink:href="007/01/143/1.jpg"/> <p type="main"> <s id="s.001350">Sint duæ op­<lb/>po&longs;itæ lineae rectae, <lb/>vtpote trabes AB, <lb/>CD, <expan abbr="inuicē">inuicem</expan> æqui­<lb/>di&longs;tantes & ip&longs;æ <lb/>&longs;tabiles: &longs;uperiori <lb/>tres appendantur <lb/>orbiculi ex <expan abbr="pūctis">punctis</expan> <lb/>E, F, G, <expan abbr="nēpe">nempe</expan> ML, <lb/>PQ, TV. inferiori <lb/><expan abbr="autē">autem</expan> duobus pun­<lb/>ctis IH, nempe <lb/>NO, RS. </s> <s id="s.001351">Erunt i­<lb/>gitur in vniuer&longs;um <lb/>quinque, indatur per eos funis ductarius KLMNOP <lb/>QRSTVX, ex cuius extremitate pendeat pondus X, <pb xlink:href="007/01/144.jpg"/>Trahatur funis in K. <!-- KEEP S--></s> <s id="s.001352">Dico ex multiplicatione <expan abbr="orbiculorū">orbiculorum</expan>, <lb/>trahenti pondus nequaquam minui. </s> <s id="s.001353">Sint autem orbicu­<lb/>lorum diametri, LM, NO, PQ, RS, TV, applicetur poten­<lb/>tîa in S. <!-- KEEP S--></s> <s id="s.001354">Erit igitur ad hoc vt &longs;u&longs;tineat æqualis ponderi X, <lb/>orbiculi enim TV &longs;emidiametri &longs;unt æquales. </s> <s id="s.001355">Transfe­<lb/>ratur <expan abbr="potētia">potentia</expan> in q, & ita deinceps donec perueniatur in K, <lb/>vbi funis ip&longs;ius e&longs;t principium, Idem e&longs;t igitur &longs;eruata &longs;em­<lb/>per &longs;emidiametrorum æqualitate ac &longs;i potentia quæ e&longs;t in <lb/>K, applicata intelligatur in T vel in V. vbicunque enim <lb/>collocetur, ponderi erit æqualis. </s> <s id="s.001356">Nihil igitur rebus ita <lb/>di&longs;po&longs;itis, orbiculorum multiplicatio ad facilitatem ope­<lb/>ratur. </s> <s id="s.001357">Alia itaque ratio quærenda e&longs;t, quam non &longs;atis ex­<lb/>plica&longs;&longs;e videtur Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.001358">Probabimus autem, nullam <lb/>ex &longs;uperioribus orbiculis fieri ponderum imminutionem, <lb/>&longs;ed totam vim in inferioribus con&longs;i&longs;tere. </s> <s id="s.001359">At nos interim <lb/>quippiam quod ad rem faciat, proponamus. </s> </p> <figure id="id.007.01.144.1.jpg" xlink:href="007/01/144/1.jpg"/> <p type="main"> <s id="s.001360">E&longs;to punctum A, cui rectæ ap­<lb/>pendantur lineæ BAC, diui&longs;æ qui­<lb/>dem in A, &longs;it autem lineæ BA caput <lb/>B, ip&longs;ius verò CA caput C. <!-- KEEP S--></s> <s id="s.001361">Modò <lb/>intelligantur vnitæ in A, &longs;itqueue vni­<lb/>ca linea à puncto A ceu funiculus <lb/>dependens BAC; Appendatur capi­<lb/>ti B pondus B. <!-- KEEP S--></s> <s id="s.001362">Capiti vero C, <expan abbr="pōdus">pondus</expan> <lb/>C, inter &longs;e æqualia. </s> <s id="s.001363">Potentia igitur <lb/>in A, duo &longs;u&longs;tinebit pondera BC. <lb/><!-- KEEP S--></s> <s id="s.001364">Pondera verò ex æqualitate æque­<lb/>ponderabunt. </s> <s id="s.001365">Quod &longs;i B potentia <lb/>dicatur &longs;u&longs;tinens pondus C, aut C <lb/>potentia &longs;u&longs;tinens pondus D, vel <lb/>duæ potentiæ inter &longs;e æquales, nihil <lb/>refert. </s> <s id="s.001366">Vtcunque enim id &longs;it, fiet æquilibrium. </s> <s id="s.001367">Habemus <lb/>igitur ex i&longs;tis ad &longs;u&longs;tinendum pondus ex &longs;uperiori parte <pb xlink:href="007/01/145.jpg"/>appen&longs;um potentiam requiri ip&longs;i ponderi æqualem. </s> <s id="s.001368">Ani­<lb/>mo po&longs;thæc concipiatur alia recta linea DEF, cuius inte­<lb/>gra longitudo &longs;i extenderetur, e&longs;&longs;et DE, EF. <!-- KEEP S--></s> <s id="s.001369">Appendatur <lb/>in E pondus E æquale alteri ponderum B vel, C, &longs;int autem <lb/>duæ potentiæ pondus E &longs;u&longs;tinentes D, F. <!-- KEEP S--></s> <s id="s.001370">Vtraque igitur <lb/>dimidium &longs;u&longs;tinebit ponderis E, &longs;ed potentia quæ &longs;u&longs;ti­<lb/>nebat pondus B, in C erat ip&longs;i B æqualis, vbi appen&longs;io pon­<lb/>deris erat in &longs;uperiori parte in A, hîc autem, vbi appen&longs;io <lb/>e&longs;t in parte in feriori, vtraque potentia dimidium &longs;u&longs;tinet <lb/>appen&longs;i ponderis. </s> <s id="s.001371">Videmus igitur illam appen&longs;ionem <lb/>quidem pondus nullatenus imminuere, hanc verò pon­<lb/>dus ip&longs;um, bifariam diui&longs;um, &longs;u&longs;tinentibus potentijs im­<lb/>partiri. </s> <s id="s.001372">Hæc in lineis, Mathematicâ v&longs;i ab&longs;tractione, con­<lb/>&longs;iderauimus, nunc verò eadem mechanicè perpenda­<lb/>mus. </s> </p> <figure id="id.007.01.145.1.jpg" xlink:href="007/01/145/1.jpg"/> <p type="main"> <s id="s.001373">Sit igitur <lb/>punctum A, vt <lb/>in &longs;equenti figu­<lb/>ra clauus paxil­<lb/>lu&longs;ue, cui appen­<lb/>&longs;us funiculus <lb/>BAC, & funicu­<lb/>li capitibus pon­<lb/>dera BC, &longs;it quo­<lb/>que anulus D, <lb/>per quem traìe­<lb/>ctus funiculus <lb/>EDF. <!-- KEEP S--></s> <s id="s.001374">Anulo au­<lb/>tem <expan abbr="cōiunctum">coniunctum</expan> <lb/>pondus G. <!-- KEEP S--></s> <s id="s.001375">His igitur ita con&longs;titutis, eadem demon&longs;tra­<lb/>buntur quæ &longs;uperius, nempe oportere vt fiat æquilibrium <lb/>B, C, e&longs;&longs;e æqualia, tum potentias, quæ &longs;unt in EF pondus <lb/>G inter eas diui&longs;um &longs;u&longs;tinere. </s> <s id="s.001376">Porrò volentes Mechanici <pb xlink:href="007/01/146.jpg"/>funiculos circa paxillum, & anulum ad attollenda & de­<lb/>primenda pondera mouere incommodè illis vtique &longs;uc­<lb/>cedebat, clauo & anulo motum difficilem facientibus. <lb/></s> <s id="s.001377">Quamobrem vt difficultati occurrerent, ad locum claui <lb/>clauo ip&longs;i orbiculum circumpo&longs;uerunt, & anuli itidem <lb/>loco orbiculum aptauerunt. </s> <s id="s.001378">Hæc autem agentes rei i­<lb/>p&longs;ius naturam non mutauerunt, &longs;ed &longs;ibi, vt diximus, ex or­<lb/>biculis maximam commoditatem <expan abbr="atq;">atque</expan> facilitatem com­<lb/>parârunt. </s> </p> <p type="main"> <s id="s.001379">Ex his principîjs tota Trochlearum ratio pendet, <lb/>quæ tamen alia quoque con&longs;ideratione in idem tenden­<lb/>te examinari pote&longs;t, quod quidem fecere veteres, & ip&longs;e, <lb/>qui veteres optimè imitatus e&longs;t, Guid. <!-- KEEP S--></s> <s id="s.001380">Vbaldus. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001381">Vidimus vtique nos, à potentia quæ e&longs;t in B, pondus <lb/>par &longs;u&longs;tineri in C, Potentiam autem quæ e&longs;t in E <expan abbr="dimidiū">dimidium</expan> <lb/>&longs;u&longs;tinere ponderis quod e&longs;t in G. <!-- KEEP S--></s> <s id="s.001382">Nos igitur ij&longs;dem in&longs;i­<lb/>&longs;tentes adiecta libra, vecteue, bifariam diui&longs;o rem ip&longs;am <lb/>ex &longs;ubiecto diagrammate lucidiorem faciemus. </s> </p> <p type="main"> <s id="s.001383">E&longs;to linea quædam &longs;tabilis ceu trabs horizonti æ­<lb/>quedi&longs;tans AB, cui in A funiculus annectatur AC, cuius <lb/>extremum C vecti cuidam alligetur CD, in medio diui&longs;o <lb/>vbi E, tum alteri vectis eiu&longs;dem extremitati D, funiculus <lb/>nectatur DG, & à puncto E pondus appendatur F. puta li­<lb/>brarum mille, Tum puncto G in medio vectis HI, funis re­<lb/>ligetur DG, & ex altero vectis extremo alligato fune HK <lb/>commendetur loco &longs;tabili in K, & ab alio capite vectis vbi <lb/>I ad medium vectis MN, vbi L, funis annectatur lL, tum <lb/>ex vectis capite M, funis commendetur MO, loco &longs;tabili <lb/>in O, & alteri capiti N, funis, NP, qui alligetur medio ve­<lb/>cti QR in P, & ex Q, funis QS. </s> <s id="s.001384">Commendetur loco &longs;tabili <lb/>in S, & alteri vectis extremo R funis alligetur RT, cui <lb/>quidem potentia &longs;u&longs;tinens applicetur in T. <!-- KEEP S--></s> <s id="s.001385">Dico igitur, <pb xlink:href="007/01/147.jpg"/><figure id="id.007.01.147.1.jpg" xlink:href="007/01/147/1.jpg"/><lb/>rebus ita di&longs;po&longs;itis, <lb/>potentiam in T ita <lb/>&longs;e habere ad pondus <lb/>F, vt vnum ad &longs;exde­<lb/>cim, hoc e&longs;t, in pro­<lb/>portione e&longs;&longs;e &longs;ub­<lb/>&longs;exdecupla. </s> <s id="s.001386">Sunt <lb/>autem, hic vectes <lb/>quatuor in feriorum <lb/>cubiculorum, loco, <lb/>CD, HI, MN, QR, <lb/>quorum, centra E, <lb/>G, L, P. quoniam e­<lb/>nim A hoc e&longs;t, C, v­<lb/>nà cum potentia G, <lb/>hoc e&longs;t, D, &longs;u&longs;tinet <lb/>pondus F alterum, <lb/>ponderis dimidium <lb/>&longs;u&longs;tinebit C, <expan abbr="alterū">alterum</expan> <lb/>vero D. erunt igitur <lb/>vtrinque librae quin­<lb/>gentæ. </s> <s id="s.001387">Tum potentia in K, hoc e&longs;t, in H, vna cum poten­<lb/>tia in L, hoc e&longs;t, in I &longs;u&longs;tinebunt quingenta. </s> <s id="s.001388">Quare <expan abbr="vtraq;">vtraque</expan> <lb/>ducenta quinquaginta, &longs;ed hoc totum bifariam diuiditur <lb/>inter potentias, O, id e&longs;t, M, & P, id e&longs;t H. erunt igitur v­<lb/>trinque centum viginti quinque. </s> <s id="s.001389">Ea autem &longs;umma <expan abbr="iterū">iterum</expan> <lb/>bifariam diuìditur, hoc e&longs;t, inter potentias S, id e&longs;t, Q & <lb/>T, id e&longs;t, R, quare vtraque &longs;u&longs;tinet &longs;exaginta duo cum di­<lb/>midio. </s> <s id="s.001390">Sed numerus i&longs;te ad Millenarium ita &longs;e habet vt v­<lb/>num ad &longs;exdecim. </s> <s id="s.001391">Hinc colligimus, pondus totum inter <lb/>loca &longs;tabilia diuidi, nempe A, K, O, S, & ip&longs;am potentiam <lb/>quæ &longs;u&longs;tinet in T, & locis ip&longs;is &longs;tabilibus quindecim par­<lb/>tes integri ponderis, potentia verò T &longs;extam decimam <pb xlink:href="007/01/148.jpg"/>tantùm commendari. </s> <s id="s.001392">Itaque &longs;i ex puncto V appendere­<lb/>tur AB, in X potentia, quæ in X &longs;u&longs;tineret mille, minus <lb/>&longs;exaginta duo cum dimidio, quod quidem à potentia in <lb/>T &longs;u&longs;tinetur; quod &longs;i alius adderetur orbiculus, & fierent <lb/>quinque, potentia in T &longs;u&longs;tineret trige&longs;imam &longs;ecundam <lb/>partem integri ponderis, hoc e&longs;t, dimidium librarum &longs;e­<lb/>xaginta duarum cum dimidio, nempe triginta & vnam <lb/>cum quarta parte, &longs;i item textus adderetur, potentia in T <lb/>&longs;exage&longs;imam partem &longs;u&longs;tineret integri ponderis, hoc e&longs;t, <lb/>libras quindecim & 5/8 libræ vnius. </s> <s id="s.001393">Vnde patet clarè pon­<lb/>deris diminutionem fieri ex orbiculis inferioribus, non <lb/>autem ex &longs;uperioribus, &longs;uperiores autem addi non nece&longs;­<lb/>&longs;itatis quidem, &longs;ed commoditatis gratiâ: neque enim ab&longs;­<lb/>que &longs;uperioribus vnico ductario fune fieri po&longs;&longs;et attractio <lb/>& ponderis ip&longs;ius eleuatio. </s> <s id="s.001394">Hactenus igitur nobis i&longs;thæc <lb/>de Trochleæ natura & vi po&longs;t alios, con&longs;idera&longs;&longs;e &longs;it &longs;atis. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001395">QVÆSTIO XIX.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001396"><emph type="italics"/>Dubitat Philo&longs;ophus, Cur &longs;i quis &longs;uper lignum magnam imponat <lb/>&longs;ecurim, de&longs;uperque magnum adijciat pondus, ligni quippiam quod <lb/>curandum &longs;it, non diuidit; &longs;i verò &longs;ecurim extollens percutiat, illud <lb/>&longs;cindit, cum alioquin multo minus habeat ponderis id quod <lb/>percutit, quam illud quod &longs;uperiacet <lb/>& premit?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001397">Poterat Ari&longs;toteles, nî fallimur, rem breuius & vniuer­<lb/>&longs;alius proponere. </s> <s id="s.001398">Scilicet cur motus ponderi addat <lb/>pondus & efficacius ex motu quam ex immoto pondere <lb/>mota res operetur. </s> <s id="s.001399">Soluit autem. </s> <s id="s.001400">An, inquiens, ideo fit, <lb/>quia omnia cum motu fiunt, & graue ip&longs;um grauitatis ma­<lb/>gis a&longs;&longs;umit motum, dum mouetur quam dum quie&longs;cit? <lb/></s> <s id="s.001401">Incumbens igitur connatam graui motionem non moue­<lb/>tur, motum verò & &longs;ecundum hanc mouetur & &longs;ecun-<pb xlink:href="007/01/149.jpg"/>dum eam quæ e&longs;t <expan abbr="percutiētis">percutientis</expan>? </s> <s id="s.001402">Hæc præclarè quidem, cæ­<lb/>tera autem, quæ de cuneo iterat, nempe ad vectem eius o­<lb/>perationem referri &longs;uperius confutauimus. </s> <s id="s.001403">Porrò effe­<lb/>ctus huius, de quo agitur, di&longs;putatio illuc &longs;pectat, videli­<lb/>cet ad cadentium atque proiectorum naturam. </s> <s id="s.001404">Ad maio­<lb/>rem autem rei euidentiam hæc addimus. </s> </p> <figure id="id.007.01.149.1.jpg" xlink:href="007/01/149/1.jpg"/> <p type="main"> <s id="s.001405">E&longs;to libra AB, cu­<lb/>ius centrum C, libra­<lb/>ta æqualibus ponde­<lb/>ribus DE, apponatur <lb/>ponderi E pondus F, <lb/>item ponderi D pon­<lb/>dus G ip&longs;i ponderi F <lb/>æquale, æquilibrabit <lb/>itidem, Modò non apponatur &longs;impliciter pondus G &longs;ex <lb/>ex H in lancem A dimittatur, tunc &longs;anè non æquilibrabit, <lb/>&longs;ed libram deprimet. </s> <s id="s.001406">Duo enim in pondere dimi&longs;&longs;o con­<lb/>&longs;iderantur pondera; naturale &longs;cilicet, & quod motu ip&longs;i <lb/>moto, ponderi e&longs;t acqui&longs;itum. </s> <s id="s.001407">Itaque quo motus fuerit <lb/>maior, puta &longs;i cadat ex I, grauitas ex maiori motu fiet ma­<lb/>ior. </s> <s id="s.001408">quod vtique efficacius fieret &longs;i pondus G non dimit­<lb/>tetur modo remoto prohibente, &longs;ed proijceretur. </s> <s id="s.001409">Tunc <lb/>enim tria concurrerent, grauitas naturalis, grauitas ac­<lb/>qui&longs;ita ex naturali motu, & ea quæ naturali adijcitur ex <lb/>violentia. </s> <s id="s.001410">Pondus igitur &longs;ecuri impo&longs;itum & &longs;ecuris ip&longs;ius <lb/>naturalis grauitas naturali tantum grauitate operantur, <lb/>& ideo minus efficaciter. </s> <s id="s.001411">Huc autem ea ferè pertinent <lb/>quæ nos à principio de duobus centris retulimus, natura­<lb/>lis nempe grauitatis, & acqui&longs;itæ. </s> </p> <p type="main"> <s id="s.001412">Cæterùm cur mallei & &longs;ecuris ictus &longs;it violenti&longs;&longs;i­<lb/>mus, ideo fit quod non ex vnico neque duplici, &longs;ed ex tri­<lb/>plici grauitate operetur. </s> <s id="s.001413">E&longs;to enim &longs;ecuris A, cuius manu­<lb/>brium AB, brachium vero &longs;ecuri vtentis BC, erit igitur C <pb xlink:href="007/01/150.jpg"/><figure id="id.007.01.150.1.jpg" xlink:href="007/01/150/1.jpg"/><lb/>locus vbi humero <lb/>brachium iungi­<lb/>tur, motus ip&longs;ius <lb/>centrum, attollit <lb/>autem &longs;ecurim is <lb/>qui percutit, & re­<lb/>tro ad &longs;capulas re­<lb/>ducens totis viri­<lb/>bus ex centro C <lb/>&longs;ecurim vibrat, <lb/>portionem circuli <lb/>de&longs;cribens ADE <lb/>ictumqueue faciens <lb/>in E. <!-- KEEP S--></s> <s id="s.001414">Vires igitur acquirit &longs;ecuris, tum ex naturali grauita­<lb/>te, cadens ex D, in E, tum ex proprio pondere, tum etiam <lb/>ex violentia eidem à percutiente impre&longs;&longs;a. </s> <s id="s.001415">Fiunt autem <lb/>motus tam naturalis quàm violentus eo validiores, quo <lb/>maius e&longs;t &longs;patium, quo res mota mouetur, idqueue praecipuè <lb/>cum violentia ip&longs;am &longs;ecundat naturam. </s> <s id="s.001416">Itaque maior fit <lb/>ictus in E quàm in F, & in F maior quàm in D. <!-- KEEP S--></s> <s id="s.001417">Item violen­<lb/>tius feriret percutiens, &longs;i manubrium e&longs;&longs;et longius, puta <lb/>BG. <!-- KEEP S--></s> <s id="s.001418">Tunc enim maior e&longs;&longs;et circulus GH, & motus tum <lb/>prolixior, tum velocior. </s> <s id="s.001419">quo igitur longiora habet bra­<lb/>chia is qui &longs;ecuri malleoue vtitur, data virium paritate, ex <lb/>eadem ratione validius percellit. </s> <s id="s.001420">E&longs;t autem &longs;ecuris, vel <lb/>malleus cuneatus, vel cuneus malleatus manubrio in&longs;er­<lb/>tus. </s> <s id="s.001421">An autem operetur efficacius cuneus malleo percu&longs;­<lb/>&longs;us, aut cum manubrio motus, vt fit in &longs;ecuri, data aciei & <lb/>ponderis æqualitate, difficile e&longs;t determinare. </s> <s id="s.001422">Certè va­<lb/>lidius, & certius fieri &longs;ci&longs;&longs;ionem ex cuneo & malleo, ea ra­<lb/>tio e&longs;t, quod cuneus adactus, nec inde remotus eam inte<lb/>rim &longs;eruat, quam antea fecerat partium &longs;eparationem, <pb xlink:href="007/01/151.jpg"/>quod quidem &longs;ecuri non accidit, quæ adacta ad nouam <lb/>percu&longs;&longs;ionem faciendam extrahitur. </s> </p> <p type="main"> <s id="s.001423">Hoc etiam con&longs;ideramus, &longs;ecuris in circulo motum, <lb/>ex A in D, e&longs;&longs;e videndum, id e&longs;t, non &longs;ecundum naturam, <lb/>&longs;ur&longs;um enim fertur quod e&longs;t graue, ex D verò in F <expan abbr="mixtū">mixtum</expan>: <lb/>magis autem ad naturalem accedere qui fit ex F in E. <!-- KEEP S--></s> <s id="s.001424">Tar­<lb/>dior ergo ex A in D, velocior ex D, in F, veloci&longs;&longs;imus ex F <lb/>in E; quædam quæ ad hanc rem faciunt, egregiè con&longs;ide­<lb/>rat Guid, Vbald. <!-- REMOVE S-->in calce Tractatus, De Cuneo; ip&longs;um <lb/>con&longs;ule. </s> </p> <p type="main"> <s id="s.001425">Ad hæc &longs;uccurrit nobis pulcherrima quæ&longs;tio. </s> <s id="s.001426">Du­<lb/>bitari enim pote&longs;t, vtrum ictus ex en&longs;e efficacior &longs;it à par­<lb/>te quæ e&longs;t circa aciem, aut circa medium en&longs;em, vel pro­<lb/>pe manubrium capulumue; etenim hinc inde &longs;unt ra­<lb/>tiones. </s> </p> <p type="main"> <s id="s.001427">E&longs;to quidem en&longs;is AB, cuius capulus A, &longs;piculum ve <lb/>rò B, centrum grauitatis C, pars capulo proxima D. <!-- KEEP S--></s> <s id="s.001428">Libra­<lb/>to itaque gladio tres fiunt circulorum portiones BE, CF, <lb/>DG, quæritur quo loco ictus &longs;it validior, nempe in E, in F, <lb/>velin G. <!-- KEEP S--></s> <s id="s.001429">Videtur validiorem futurum in E, quippe quod <lb/>ex maiori &longs;emidiametro AB, maioris &longs;it circuli portio BE, <lb/>& ideo velocior motus ex B in E. <!-- KEEP S--></s> <s id="s.001430">Contra efficaciorem <lb/>futurum apparet in F, propterea quod ibi ex centro C to­<lb/>tius fiat grauitatis impre&longs;&longs;io, fieri autem validi&longs;&longs;imum in <lb/>G, licet ibi motus &longs;it tardior inde videtur, quod &longs;i con&longs;ide­<lb/>retur en&longs;is vt vectis, cuius fulcimentum e&longs;t A, potentia <lb/>premens in B, ponderis vero loco re&longs;i&longs;tentia rei quæ per­<lb/>cutitur in D. <!-- KEEP S--></s> <s id="s.001431">Maior e&longs;t autem proportio BA, ad AD, quam <lb/>BA ad AC, & ideo violentior fiet pre&longs;&longs;io ex ictu in D, <expan abbr="quã">quam</expan> <lb/>in C. <!-- KEEP S--></s> <s id="s.001432">Hi&longs;ce hoc pacto con&longs;ideratis, putarem ictum effica­<lb/>ciorem fieri in F ex medio C, quam ex extremis & oppo­<lb/>&longs;itis partibus EG. <!-- KEEP S--></s> <s id="s.001433">Licet enim in B velocitas &longs;it maior, dee&longs;t <lb/>ibi pondus. </s> <s id="s.001434">Si enim en&longs;is iterum vt vectis con&longs;ideretur, e­<pb xlink:href="007/01/152.jpg"/>runt AB. duo fulcimenta &longs;u&longs;tinentía pondus in C, vbi gra­<lb/>uitatis e&longs;t centrum. </s> <s id="s.001435">Si igitur paria fuerint &longs;patia BC, CA, <lb/><figure id="id.007.01.152.1.jpg" xlink:href="007/01/152/1.jpg"/><lb/>in B erit dìmidium <lb/>ponderis C, quantum <lb/>ergo velocitate præ­<lb/>ualet ictus in B, <expan abbr="tantū">tantum</expan> <lb/>ponderis amittit. </s> <s id="s.001436">D <lb/>verò plus quidem de <lb/>pondere participat, <lb/>&longs;ed velocitatis habet <lb/>minimum, in C verò <lb/>velocitas e&longs;t medio­<lb/>cris, tota tamen ip&longs;ius <lb/>ex grauitatis centro <lb/>ponderis fit impre&longs;­<lb/>&longs;io. </s> </p> <p type="main"> <s id="s.001437">Quidam, quod huc pertinet, vt ex acie ip&longs;a quæ lon­<lb/>gius à capulo abe&longs;t, violenti&longs;&longs;imum facerent ictum, Ar­<lb/>gentum viuum, quod &longs;ui naturâ graui&longs;&longs;imum quidem e&longs;t <lb/>& mobili&longs;&longs;imum in canali à manubrio ad verticem exca­<lb/>uato infundunt, quo in gladij de&longs;cen&longs;u ad verticem velo­<lb/>ci&longs;&longs;imè delato illuc transfert grauitatem totam, quare <lb/>tum velocitate tum grauitate concurrentibus ictus fit <lb/>violenti&longs;&longs;imus & longè validi&longs;&longs;imus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001438">QVAESTIO XX.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001439"><emph type="italics"/>Dubitatur, Cur &longs;tatera qua carnes ponderantur, paruo appendicu­<lb/>lo, magna trutinet onera, cum alioqui tota, dimidiata exi&longs;tat <lb/>libra, altera vero parte &longs;ola &longs;it <lb/>&longs;tatera?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001440">Soluit Philo&longs;ophus, inquiens, &longs;tateram &longs;imul, & vectem <lb/>e&longs;&longs;e & libram, ip&longs;ius verò libræ centra &longs;eu fulcimenta <pb xlink:href="007/01/153.jpg"/>e&longs;&longs;e ibi vbi fit &longs;u&longs;pen&longs;io. </s> <s id="s.001441">Pondera verò hinc in de in lance <lb/>& appendiculo, loco &longs;cilicet æquipondij, appendiculo <lb/>&longs;uccedente. </s> <s id="s.001442">Reducit autem demon&longs;trationem ad ea quæ <lb/>&longs;tatuit ip&longs;e Mechanica principia; nempe ad circulum & <lb/>circuli virtutem. </s> <s id="s.001443">Ait igitur, appendiculum licet parui <expan abbr="pō-deris">pon­<lb/>deris</expan> &longs;it, ideo maiori ponderi virtute æquari, quod lon­<lb/>gius à centro, hoc e&longs;t, ab ip&longs;o fulcimento &longs;i&longs;tatur. </s> <s id="s.001444">quic­<lb/>quid tamen &longs;it, &longs;tateram e&longs;&longs;e vectem, res e&longs;t explorati&longs;­<lb/>&longs;ima. </s> </p> <figure id="id.007.01.153.1.jpg" xlink:href="007/01/153/1.jpg"/> <p type="main"> <s id="s.001445">E&longs;to igitur &longs;tatera AB, <lb/>cuius appendiculum cur­<lb/>rens F, fulcimentum cen­<lb/>trumue C, lanx quæ cate­<lb/>na &longs;u&longs;penditur E &longs;patium <lb/>à loco fulcimenti ad ap­<lb/>pendiculum CF. quod ve­<lb/>rò à fulcimento ad cate­<lb/>nam, ex qua lanx appen­<lb/>ditur AC. <!-- KEEP S--></s> <s id="s.001446">Intelligatur autem & aliud fulcimentum D, &longs;it­<lb/>queue maius &longs;patium AD, quam AC. <!-- KEEP S--></s> <s id="s.001447">Porrò ita &longs;e habeat <lb/>pondus in E ad appendiculi F pondus, vt CF &longs;patium, ad <lb/>&longs;patium AC, quo ca&longs;u &longs;eruata, permutatim, ponderum & <lb/>brachiorum proportione, fiet aequilibrium. </s> <s id="s.001448">Si autem pon­<lb/>deribus ita con&longs;titutis iterum &longs;u&longs;pendatur in D, non fiet <lb/>æquilibrium, propterea quod minor &longs;it proportio DF ad <lb/>DA, ea quæ e&longs;t FC ad CA. <!-- KEEP S--></s> <s id="s.001449">Minor ergo e&longs;t proportio FD <lb/>ad DA, quam ponderis E ad pondus F, & idcirco facta <lb/>&longs;u&longs;pen&longs;ione præualebit pondus E ponderi F. <!-- KEEP S--></s> <s id="s.001450">Ita que vt it e­<lb/>rum fiat æquilibrium, nece&longs;&longs;e e&longs;t <expan abbr="iterū">iterum</expan> proportiones bra­<lb/>chiorum &longs;eu &longs;patiorum proportionibus ponderum æqua­<lb/>re. </s> <s id="s.001451">Transferatur igitur (lancis interim immoto pondere) <lb/>ip&longs;um appendiculum in B, fiatque vt FC ad CA, ita BD ad <lb/>DA. <!-- KEEP S--></s> <s id="s.001452">Stabit autem iterum &longs;tatera ad eam redacta quam <pb xlink:href="007/01/154.jpg"/>diximus brachiorum & ponderum permutatam propor­<lb/>tionem. </s> </p> <p type="main"> <s id="s.001453">Nos &longs;tateris vtimur ex duplici fulcimento, altero <lb/>propiori, altero à lance &longs;eu loco, vbi lanx appenditur, re­<lb/>motiori, illa grauiora appendimus pondera, & non per <lb/>vncias & libras, &longs;ed per libras tantum & &longs;elibra ponde­<lb/>ramus; & hoc &longs;tateræ latus eo quod minus minutè &longs;it di­<lb/>ui&longs;um; vulgo no&longs;trates Gro&longs;&longs;um, hoc e&longs;t, rude & cra&longs;&longs;um <lb/>appellant. </s> <s id="s.001454">Aliud verò, cum fulcimentum e&longs;t loco appen­<lb/>&longs;ionis lancis vicinius, & per libras, &longs;elibras & vncias diui­<lb/>ditur, quo quidem minora appendimus pondera, eò quod <lb/><expan abbr="exqui&longs;itiorē">exqui&longs;itiorem</expan> contineat diui&longs;ionem, &longs;ubtile dicunt. </s> <s id="s.001455">Rectè <lb/>igitur dicebat Philo&longs;ophus, in &longs;tatera plures e&longs;&longs;e libras, <lb/>quamquam & ea quoque de cau&longs;&longs;a dici po&longs;&longs;it, quod, quot <lb/>&longs;unt appendiculi, è loco in locum translationes, totidem <lb/>ex proportionum variatione fiant libræ. </s> <s id="s.001456">Et hoc quidem <lb/>&longs;en&longs;i&longs;&longs;e videtur Ari&longs;toteles. <!-- KEEP S--></s> </p> <figure id="id.007.01.154.1.jpg" xlink:href="007/01/154/1.jpg"/> <p type="main"> <s id="s.001457">Po&longs;&longs;emus & alio <lb/>modo &longs;tatera vti, nempe <lb/>&longs;tabili appendiculo, mo­<lb/>bili autem fulcimento. <lb/></s> <s id="s.001458">E&longs;to enim &longs;tatera AB, <lb/>cuius lanx C appen&longs;a in <lb/>A, appendiculum verò <lb/>&longs;tabile D, appen&longs;um in <lb/>B, Apponatur ip&longs;i l&atail;nci <lb/>C, pondus E. <!-- KEEP S--></s> <s id="s.001459">Vnicum ergo fiet corpus CEABD con&longs;tans <lb/>ex lance, libra & ponderibus. </s> <s id="s.001460">Habet ergo hoc totum gra­<lb/>uitatis &longs;uæ centrum, quod quidem vbi &longs;it e&longs;t ignotum. </s> <s id="s.001461">Ex <lb/>illo autem inuento &longs;i corpus totum appendatur, partes æ­<lb/>queponderabunt. </s> <s id="s.001462">Appendatur autem, puta in G, &longs;it <expan abbr="autē">autem</expan> <lb/>grauitatis centrum in H. <!-- KEEP S--></s> <s id="s.001463">Quoniam igitur H e&longs;t extra ful­<lb/>cimentum G, declinabit &longs;tateræ pars GA, centro G per <pb xlink:href="007/01/155.jpg"/>circuli portionem Hl, à centro grauitatis in ip&longs;a de&longs;cen­<lb/>&longs;ione de&longs;criptam. </s> <s id="s.001464">Si autem grauitatis centrum fuerit vbi <lb/>K, eo quod ibi quoque &longs;it extra fulcimentum G, de&longs;cen­<lb/>det pars GB, de&longs;cribente interim grauitatis centro K, cir­<lb/>culi portionem KL. ltaque &longs;i &longs;tateram totam eum ponde­<lb/>ribus trahamus <expan abbr="pellamu&longs;q;">pellamu&longs;que</expan> vltro citroque;, immoto appen­<lb/>diculo erit aliquando fulcimentum in ea linea perpendi­<lb/>culari vel loco ip&longs;o, vbi e&longs;t grauitatis centrum, quo ca&longs;u <lb/>&longs;tatera &longs;tabit, & tunc ita erit diui&longs;a, vt fiat brachiorum & <lb/>ponderum eadem ratio, ordine permutato. </s> <s id="s.001465">Hic autem <lb/>modus ideo non e&longs;t in v&longs;u, quod mole&longs;tum &longs;it libram &longs;eu <lb/>&longs;tateram cum ponderibus vltro citroqueue transferre, quæ <lb/>difficultas commodè appendiculi mobilitate vitatur. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001466">QVAESTIO XXI.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001467"><emph type="italics"/>Quæritur, Cur facilius dentes extrahunt Chirurgi, denti forcipis <lb/>onere adiecto, quam &longs;i &longs;ola manu vtantur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001468">Re&longs;pondet Philo&longs;ophus, An quia ex manu, magis quam <lb/>ex dentiforcipe lubrius elabitur dens? </s> <s id="s.001469">An ferro id po­<lb/>tius accidit quam digitis, quoniam vndique dentem non <lb/>comprehendunt, quod mollis facit digitorum caro; ad­<lb/>hæret enim & complectitur magis. </s> <s id="s.001470">Hæc &longs;ecunda ratio <lb/>videtur primam de&longs;truere, & contrarium pror&longs;us &longs;enten­<lb/>tiæ, quæ in problemate proponitur, a&longs;&longs;erere. </s> <s id="s.001471">Si Græca ad <lb/>verbum reddas ita habent: An magis ip&longs;a manu labile e&longs;t <lb/>ferrum, & ip&longs;um vndique (dentem nempe) non comple­<lb/>ctitur, caro autem digitorum cum mollis &longs;it, adhæret ma­<lb/>gis, & vndique congruit. </s> <s id="s.001472">Certè vt &longs;ententia non &longs;it con­<lb/>traria propo&longs;itioni, Græca ver&longs;io ita videtur concinnan­<lb/>da: Vel magis è manu elabitur, mollis enim e&longs;t digitorum <lb/>caro, ferrum autem circumplectitur, & haeret magis. </s> <s id="s.001473">quic­<lb/>quid &longs;it, Græcam lectionem contrarium ei quod quæri-<pb xlink:href="007/01/156.jpg"/>tur, affirmare certum e&longs;t. </s> <s id="s.001474">Picolomineus, Ideo, inquit, di­<lb/>gitorum caro mollis minus aptè extrahit, quod dentem <lb/>totum comprehendere non pote&longs;t, quod ferrum ob &longs;uam <lb/>durítiem & con&longs;tantiam commodi&longs;&longs;imè facit. </s> <s id="s.001475">Sen&longs;um ex <lb/>mente reddidit, quod ex verbis non poterat. </s> <s id="s.001476">Subiungit <lb/>denique Ari&longs;toteles, An quia dentiforcipes &longs;int duo con­<lb/>trarij vectes vnicum habentes fulcimentum, ip&longs;am &longs;cili­<lb/>cet in &longs;trumenti partium connexionem. </s> <s id="s.001477">Hoc igitur ad ex­<lb/>tractionem vtuntur^{**}, vt facilius moueant. </s> <s id="s.001478">Figuram hoc <lb/>pacto proponit Philo&longs;ophus. <!-- KEEP S--></s> </p> <figure id="id.007.01.156.1.jpg" xlink:href="007/01/156/1.jpg"/> <p type="main"> <s id="s.001479">E&longs;to dentiforcipis alterum <lb/>quidem extremum vbi A, alte­<lb/>rum autem quod extrahit B, ve­<lb/>ctis vbi ADF, alter vectis, vbi <lb/>BCE, fulcimentum verò CGD <lb/>connexio vbi G. <!-- KEEP S--></s> <s id="s.001480">Dens autem pondus: vtroque igitur ve­<lb/>cte B, & F &longs;imul comprehendentes mouent, Hæc ille. <!-- KEEP S--></s> <s id="s.001481">At­<lb/>tamen rem ip&longs;am &longs;ubtilius con&longs;iderantibus aliter videtur <lb/>habere, ac ip&longs;e a&longs;&longs;erat. </s> <s id="s.001482">Et &longs;anè dentisforcipis brachia ve­<lb/>ctes e&longs;&longs;e, quorum commune fulcimentum e&longs;t in ip&longs;o cen­<lb/>tro vbi vertebra, nemo negauerit. </s> <s id="s.001483">Dentem autem e&longs;&longs;e <lb/>pondus, ego quidem ab&longs;olute non dixerim. </s> <s id="s.001484">Pondus <expan abbr="autē">autem</expan> <lb/>hîc proprie e&longs;t ip&longs;a dentis durities, cuius re&longs;i&longs;tentia eo fa­<lb/>cilius &longs;uperatur, quo maior e&longs;t proportio brachiorum à <lb/>manu ad vertebram, ad partem illam quæ à vertebra e&longs;t <lb/>ad dentem. </s> <s id="s.001485">At dentis ex con&longs;trictione fractio nihil facit <lb/>pror&longs;us ad extractionem: id tamen operatur brachio­<lb/>rum longitudine dentiforceps, quod valide ex vectium <lb/>oppo&longs;itorum vi dentes con&longs;tringit & extractioni commo­<lb/>dum reddit & facilem. </s> <s id="s.001486">Neque enim totus Dentiforceps <lb/>hic ceu vectis vnicus operatur, quod fit in forcipibus quas <lb/>Tenaleas vocamus, quibus è tabulis claui reuelluntur, <lb/>qua de re nos quae&longs;tione 6. verba fecimus. </s> <s id="s.001487">Quo pacto <expan abbr="autē">autem</expan> <pb xlink:href="007/01/157.jpg"/>dentis ex Dentiforcipe extractio ad vectem reducatur, <lb/>&longs;ubtilius e&longs;t perpendendum, neque enim res e&longs;t in propa­<lb/>tulo. </s> </p> <p type="main"> <s id="s.001488">Dicimus igitur, tum dentem ip&longs;um, tum dentifor­<lb/>cipem vectes e&longs;&longs;e, varia tamen ratione & &longs;atis &longs;ane diuer­<lb/>&longs;a. </s> <s id="s.001489">Dens enim fit vectis eius nempe naturæ quæ fulcimen­<lb/>tum habet in angulo, quo ca&longs;u ip&longs;ius Dentiforcipis <expan abbr="partiū">partium</expan>, <lb/>quibus Dens apprehenditur, ea quæ longior e&longs;t poten­<lb/>tiæ mouentis loco &longs;uccedit, breuior vero fulcimentum <lb/>facit, Dentis vero re&longs;i&longs;tentia ponderis vices refert. </s> </p> <figure id="id.007.01.157.1.jpg" xlink:href="007/01/157/1.jpg"/> <p type="main"> <s id="s.001490">E&longs;to enim dens qui­<lb/>dem A, cuius diameter <lb/>BC, longitudo v&longs;que ad <lb/>extremas radices CD, <lb/>pars dentiforcipis breui­<lb/>or CG, longior BG. <!-- KEEP S--></s> <s id="s.001491">Fit <lb/>ergo vectis BCD, habens <lb/>fulcimentum in C. <!-- KEEP S--></s> <s id="s.001492">Den­<lb/>te igitur apprehen&longs;o in BC, & manu dentiforcipe ceu ve­<lb/>cte ad inferiora compre&longs;&longs;o C, fit fulcimentum centrum­<lb/>ue. </s> <s id="s.001493">Stante enim puncto C, trahente autem potentia quæ <lb/>e&longs;t in B, fit motus ip&longs;ius B, per circuli portionem BE, radi­<lb/>cis vero D, fit motus per DF, & inde ip&longs;ius dentis extra­<lb/>ctio facilis. </s> <s id="s.001494">Quibus con&longs;ideratis vt rem ad proportiones <lb/>quatenus fieri pote&longs;t reducamus, dicimus, quo maior fu­<lb/>erit proportio BC, ad CD, hoc e&longs;t, partis vectis, quæ à ful­<lb/>cimento ad potentiam ad eam quæ à fulcimento e&longs;t ad <lb/>pondus, eo facilius fieri dentis auul&longs;ionem, quod vtique <lb/>demon&longs;trandum fuerat. </s> </p> <p type="main"> <s id="s.001495">Porro quod in calce quæ&longs;tionis addit Philo&longs;ophus, <lb/>Dentes commotos facilius manu extrahi quam in&longs;tru­<lb/>mento, nulla ratione probat. </s> <s id="s.001496">Ego autem arbitror, huc <lb/>pertinere ea verba, quæ &longs;uperius habentur, videlicet fer­<pb xlink:href="007/01/158.jpg"/>rum quidem non vndique dentem <expan abbr="comprehēdere">comprehendere</expan>, quod <lb/>mollis facit digitorum caro, quæ id circo adhæret & com­<lb/>plectitur magis. </s> <s id="s.001497">An autem ita &longs;it, alij videant, nobis enim <lb/>digito rem o&longs;tendi&longs;&longs;e fuerit &longs;atis. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001498">QVÆSTIO XXII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001499"><emph type="italics"/>Hîc quærit Ari&longs;toteles, Cur nuces ab&longs;que ictu facile confringuntur <lb/>in&longs;trumentis quæ ad eum faciunt v&longs;um, & hoc licet multum aufe­<lb/>ratur virium, ce&longs;&longs;ante motu & violentia, quod accidit dum mal­<lb/>leo confringuntur. </s> <s id="s.001500">Addit præterea, citius fieri confractionem <lb/>graui, & duro in&longs;trumento ferreo vide­<lb/>licet quàm ligneo.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001501">Soluit, inquiens, id fieri quod in&longs;trumentum duobus <lb/>vectibus con&longs;tet, coëuntibus in connexione &longs;eu verte­<lb/>bra, & idcirco eo violentius fieri confractionem, quo mi­<lb/>nus e&longs;t &longs;patium à nuce, quæ frangitur, ad vertebram. </s> <s id="s.001502">ma­<lb/>ius verò quod à vertebra ad extremitates, quæ confrin­<lb/>gentis manu comprimuntur. </s> <s id="s.001503">Ait igitur, & id quam oppo­<lb/>&longs;ite, vim ex vectibus ictus loco &longs;uccedere & idem operari. </s> </p> <figure id="id.007.01.158.1.jpg" xlink:href="007/01/158/1.jpg"/> <p type="main"> <s id="s.001504">E&longs;to igitur in &longs;trumentum, <lb/>de quo agimus CDBF, ex duo­<lb/>bus vectibus con&longs;tans, quorum <lb/>alter CAF, alter vero DAB ver­<lb/>tebra &longs;eu connexio A locus v­<lb/>bi nux frangitur K, manubria <lb/>vero BF. quo igitur prolixiores <lb/>erunt AB, AF, breuiores vero ACAD, violentius fiet <expan abbr="cō-fractio">con­<lb/>fractio</expan>. </s> <s id="s.001505">Erit autem nucis re&longs;i&longs;tentia loco ponderis A, ful­<lb/>cimentum BF loco potentiæ. </s> <s id="s.001506">Itaque nî maior &longs;it propor­<lb/>tio potentiæ ad re&longs;i&longs;tentiam, quam brachij à potentia ad <lb/>fulcimentum ad eam partem quæ à fulcimento e&longs;t ad nu­<lb/>cem, non fiet confractio. </s> <s id="s.001507">eo autem magis &longs;uperabit, quo <pb xlink:href="007/01/159.jpg"/>maior fuerit pars vectis quæ à potentia ad fulcimentum. </s> </p> <p type="main"> <s id="s.001508">Quod autem addit Ari&longs;toteles, eo maiorem fieri <lb/>vectium eleuationem, hoc e&longs;t, in&longs;trumenti aperitionem, <lb/>quo magis nux quæ frangitur, fuerit propior fulcimento, <lb/>hoc e&longs;t, ip&longs;i vertebræ, facile o&longs;tenditur ex conuer&longs;a 21. <lb/>propo&longs;. lib. 1. Elem. </s> <s id="s.001509">&longs;i enim ab extremitatibus vnius lineæ <lb/>ad ea&longs;dem partes con&longs;tituantur duæ lineæ maiores con­<lb/>currentes in angulo, & ab ij&longs;dem extremitatibus duæ a­<lb/>liæ minores, quæ intra triangulum à maioribus con&longs;titu­<lb/>tum cadant, maiorem angulum continebunt. </s> <s id="s.001510">At talis e&longs;t <lb/>angulus qui fit in in &longs;trumento, cum partes vectis à verte­<lb/>bra ad nucem fuerint breuiores. </s> <s id="s.001511">magìs ergo dilatantur <lb/>vectes, & magis dilatati magis comprimuntur, magis au­<lb/>tem compre&longs;&longs;i validius frangunt, quod dixerat Ari&longs;to­<lb/>teles. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001512">Cæterum & illud quod &longs;cribit, ex grauiori & durio­<lb/>ri materia in&longs;trumentum citius fractionem facere, quam <lb/>ex leuiori & minus dura, ex parte quidem materiæ verum <lb/>e&longs;t, nec pertinet ad proportionem, quæ &longs;ane in <expan abbr="huiu&longs;modī">huiu&longs;modi</expan> <lb/>in&longs;trumentis formæ ferè habent rationem. </s> <s id="s.001513">Nos hi&longs;ce in­<lb/>&longs;trumentis non vtimur. </s> <s id="s.001514">Sunt autem &longs;imilia in&longs;trumentis <lb/>illis, quibus figuli cretaceas pilas ad chirobali&longs;tarum v&longs;um <lb/>facere & efformare con&longs;ueuerunt. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001515">QVÆSTIO XXIII.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001516">Pvlcherrimam proponit hoc loco Philo&longs;ophus con­<lb/>templationem, eamque ad mixtos motus <expan abbr="pertinētem">pertinentem</expan>. <lb/></s> <s id="s.001517">Mixtorum autem motuum &longs;peculationem antiquis Me­<lb/>chanicis fui&longs;&longs;e tum vtilem tum etiam familiarem, norunt <lb/>ij qui norunt quæ de lineis &longs;piralibus Helici&longs;ue, cy&longs;&longs;oidi­<lb/>bus, conchoidibus & alijs eiu&longs;cemodi &longs;cripta & contem­<lb/>plata reperiuntur, quibus tum ad duarum mediarum pro­<pb xlink:href="007/01/160.jpg"/>portionalium inuentionem, tum ad circuli quadratio­<lb/>nem vti &longs;olent. </s> <s id="s.001518">Quod autem hîc quærit Ari&longs;toteles, ita &longs;e <lb/>habet. </s> </p> <p type="head"> <s id="s.001519"><emph type="italics"/>Cur &longs;i duo extrema in Rhombo puncta duabus ferantur lationibus, <lb/>haudquaquam æqualem vtrumque eorum pertran&longs;it rectam, &longs;ed <lb/>multo plus alteram? </s> <s id="s.001520">Item cur quod &longs;uper latus fertur, minus per­<lb/>tran&longs;eat quam ip&longs;um latus. </s> <s id="s.001521">Illud enim diametrum pertran&longs;ire <lb/>certum est, hoc vero maius latus, licet hoc vnica, illud au­<lb/>tem duabus feratur lationibus?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001522">Difficile hoc intellectu prima fronte, & &longs;ane admi­<lb/>rabile, itaque in tentam contemplationem requirit. </s> <s id="s.001523">Nos <lb/>primo cum Ari&longs;totele, rem totam explicabimus, tum ali­<lb/>quid forta&longs;&longs;e non pœnitendum no&longs;tro de promptuario <lb/>proferemus. </s> </p> <figure id="id.007.01.160.1.jpg" xlink:href="007/01/160/1.jpg"/> <p type="main"> <s id="s.001524">E&longs;to itaque Rhombus ABCD, <lb/>cuius latera AB, BD, DC, CA, diame­<lb/>trorum maior AD, minor BC, &longs;ecan­<lb/>tes &longs;e inuicem in puncto &longs;eu figuræ <lb/>centro K. <!-- KEEP S--></s> <s id="s.001525">Sunt <expan abbr="autē">autem</expan> ex ip&longs;ius Rhom­<lb/>bi natura latera æqualia & parallela, <lb/>Angulorum vero qui maiori diame­<lb/>tro opponuntur, recto maiores, qui <lb/>vero minori minores. </s> <s id="s.001526">His igitur con­<lb/>&longs;ideratis, intelligatur punctum A mo­<lb/>ueri peculiari & &longs;implici motu, per li­<lb/>neam AB, ab A ver&longs;us B, & eodem <expan abbr="tē-pore">tem­<lb/>pore</expan> moueri totam lineam AB, ver&longs;us lineam DC, hac ta­<lb/>men lege, vt &longs;emper eidem DC feratur parallela, & eius <lb/>alterum extremorum feratur per AC, alterum vero per <lb/>BD, Intelligatur etiam punctum B moueri eodem tem­<lb/>pore proprio motu, eoque &longs;implici, per eandem rectam <lb/>BA, ver&longs;us A, & cum eadem, vt dictum e&longs;t, mota; ferri ver-<pb xlink:href="007/01/161.jpg"/>&longs;us CD. <!-- KEEP S--></s> <s id="s.001527">Erunt autem &longs;emper AB puncta in eadem linea <lb/>quæ mouetur, &longs;ibi inuicem ex contrarijs partibus occur­<lb/>rentia. </s> <s id="s.001528">Itaque cum ex duobus motibus &longs;emper propor­<lb/>tionalibus, hoc e&longs;t, laterum proportione &longs;eruata, recta <lb/>producatur, vt demon&longs;tratum e&longs;t à principio, vbi produ­<lb/>ctio circuli ex Philo&longs;ophi mente e&longs;t declarata, <expan abbr="vtraq;">vtraque</expan> pun­<lb/>cta quæ eandem laterum proportionem &longs;eruantia <expan abbr="mouē-tur">mouen­<lb/>tur</expan>, rectas lineas <expan abbr="producēt">producent</expan> A quidem AD, B autem ip&longs;am <lb/>BC. <!-- KEEP S--></s> <s id="s.001529">Feratur igitur A, tum mixto tum &longs;implici motu per <lb/>diametrum AD. <!-- KEEP S--></s> <s id="s.001530">B vero quoque tum mixto, tum proprio <lb/>per diametrum BC, &longs;upponitur autem motus omnes &longs;im­<lb/>plices, tum punctorum, tum etiam lineae, à qua puncta ip&longs;a <lb/>feruntur, æquali velocitate fieri. </s> <s id="s.001531">Illud igitur mirabile e&longs;t, <lb/>cuius etiam ratio quæritur, quo pacto eodem tempore ea­<lb/>dem que velocitate latum A quidem totam percurrat AD <lb/>maiorem, B vero totam BC, eamque longe minorem? <lb/></s> <s id="s.001532">Porro nece&longs;&longs;e fuit rem in Rhombo &longs;peculari, non autem <lb/>in quadrato & altera parte longiori rectangulo, in quibus <lb/>diametri (quod Rhombo non accidit) &longs;unt æquales. </s> <s id="s.001533">Ima­<lb/>ginemur igitur A, proprio motu percurri&longs;&longs;e &longs;patium AE, <lb/>nempe ip&longs;ius AB lineæ dimidium. </s> <s id="s.001534">Erit igitur in E, item li­<lb/>neam totam AB eodem tempore pertran&longs;i&longs;&longs;e dimidia op­<lb/>po&longs;itarum linearum, ACBD, & e&longs;&longs;e translatam, vbi FKG. <lb/></s> <s id="s.001535">Quoniam igitur æquali celeritate lineæ AB extremitas <lb/>A, translata e&longs;t in F & A, punctum per eam motum in E, e­<lb/>rit &longs;patium AE, æquale &longs;patio AF. <!-- KEEP S--></s> <s id="s.001536">Ductis igitur lineis <lb/>FKG, EKH lateribus AB, AC æquidi&longs;tantibus, erit figura <lb/>AEKF. </s> <s id="s.001537">Rhombus &longs;imilis quidem Rhombo ABCD, recta <lb/>igitur FK æqualis erit oppo&longs;itæ AE. quare A punctum <lb/>translatum erit ex mixto motu in K. <!-- KEEP S--></s> <s id="s.001538">Eodem pacto <expan abbr="quoniã">quoniam</expan> <lb/>punctum B. eadem velocitate mouetur ver&longs;us A, & linea <lb/>AB ver&longs;us CD, cum B fuerit in E extremum lineæ motæ <lb/>BA, <expan abbr="nēpe">nempe</expan> B erit in G. æquales ergo &longs;unt BE, BG & Rhom­<pb xlink:href="007/01/162.jpg"/>bus EBGK, circa diametrum BKC ip&longs;i Rhombo ABCD <lb/>&longs;imilis, & ideo GK æqualis oppo&longs;itæ BE & BG æqualis <lb/>EK. <!-- KEEP S--></s> <s id="s.001539">Cum ergo B confecerit &longs;patium BE, erit ex mixto <lb/>motu in K, &longs;uperato nempe &longs;patio BK, idque eodem tem­<lb/>pore quo A percurrerat totum &longs;patium AK. <!-- KEEP S--></s> <s id="s.001540">Ex æquali i­<lb/>gitur &longs;implicium motuum velocitate, in æqualia &longs;patia <lb/>AB puncta pertran&longs;ierunt, quæ res miraculo, cuius dilu­<lb/>tio quæritur, præbet occa&longs;ionem. </s> </p> <p type="main"> <s id="s.001541">Porro quod de dimidijs diametris demon&longs;tratum <lb/>e&longs;t, po&longs;&longs;umus & de totis eadem ratione concludere, quip­<lb/>pe quod eadem &longs;it proportio partium ad partes, quæ to­<lb/>tius ad totum. </s> <s id="s.001542">Hæc igitur prima e&longs;t pars propo&longs;itæ quæ­<lb/>&longs;tionis. </s> <s id="s.001543">Secunda vero dubitatio ita habet; Nempe mirum <lb/>videri punctum B, cum peruenerit in C, extremum lineæ <lb/>BA, videlicet ip&longs;um B, translatum e&longs;&longs;e in D, licet æquali­<lb/>ter moueantur linea BA, per lineam BD, & punctum B per <lb/>lineam BA. &longs;itque BC ip&longs;a BD maior. </s> <s id="s.001544">Primam dubitatio­<lb/>nem hoc pacto &longs;oluit Philo&longs;ophus; A fertur tum proprio, <lb/>tum alieno motu, hoc e&longs;t, lineæ AB ver&longs;us oppo&longs;itam par­<lb/>tem CD, Itaque cum vterque motus deor&longs;um vergat, mo­<lb/>tus fit velocior. </s> <s id="s.001545">Contra vero B proprio quidem motu fer­<lb/>tur ver&longs;us A, hoc e&longs;t, &longs;ur&longs;um, alieno vero, hoc e&longs;t, lineæ BA <lb/>ver&longs;us D, hoc e&longs;t, deor&longs;um, qui motus cum inuicem aduer­<lb/>&longs;entur, motus ip&longs;e fit tardior, non igitur e&longs;t mirum, A eo­<lb/>dem tempore maius &longs;patium pertran&longs;ire quam B. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001546">Hæc &longs;olutio non modo vera videtur, &longs;ed mirabilis <lb/>& ip&longs;omet Philo&longs;opho digni&longs;&longs;ima, cui quidem <expan abbr="temerariū">temerarium</expan> <lb/>iudicaremus contradicere, nî in genere ver&longs;aremur, in <lb/>quo non probabilia quæruntur, &longs;ed demon&longs;trata, &longs;ed ve­<lb/>ra. </s> <s id="s.001547">Futilem igitur e&longs;&longs;e rationem hanc ip&longs;ius Ari&longs;totelis <lb/>pace, hoc pacto o&longs;tendemus. </s> </p> <p type="main"> <s id="s.001548">E&longs;to quadratum ABCD, cuius diametri ACBD &longs;e­<lb/>cantes &longs;e&longs;e in E, moueatur eodem pacto BA, ver&longs;us CD, <pb xlink:href="007/01/163.jpg"/><figure id="id.007.01.163.1.jpg" xlink:href="007/01/163/1.jpg"/><lb/>item A, ver&longs;us B, & B ver&longs;us A, ita­<lb/>que punctum A tum proprio tum <lb/>alieno, hoc e&longs;t lineæ illud <expan abbr="deferē-tis">deferen­<lb/>tis</expan> motu deor&longs;um trudet, hoc e&longs;t, <lb/>ver&longs;us CD. <!-- KEEP S--></s> <s id="s.001549">Motus ergo velocior <lb/>erit motu puncti B, quod lationi­<lb/>bus fertur ferè contrarijs, hoc e&longs;t, <lb/>ex B ver&longs;us A &longs;ur&longs;um, cum linea <lb/>autem BA ver&longs;us C deor&longs;um. </s> <s id="s.001550">Ve­<lb/>locius tamen non mouetur, quip­<lb/>pe quod æquali tempore æquale <lb/>&longs;patium vtrum que punctum conficiat. </s> <s id="s.001551">Stante igitur cau&longs;­<lb/>&longs;a &longs;equi debui&longs;&longs;et effectus; non &longs;equitur autem, Ari&longs;tote­<lb/>lis igitur cau&longs;&longs;a non e&longs;t cau&longs;&longs;a. </s> <s id="s.001552">Rhombo quoque inuer&longs;o <lb/>idem clarius o&longs;tendemus hoc pacto: Sit Rhombus ABCD, <lb/><figure id="id.007.01.163.2.jpg" xlink:href="007/01/163/2.jpg"/><lb/>cuius diametri AC, BD &longs;ecan­<lb/>tes &longs;e&longs;e in E. <!-- KEEP S--></s> <s id="s.001553">Mota igitur linea <lb/>AB ver&longs;us CD, nempe deor&longs;um <lb/>& A quoque deor&longs;um ver&longs;us B, <lb/>contra vero B quidem &longs;ur­<lb/>&longs;um ver&longs;us A, deor&longs;um vero <lb/>ver&longs;us C, erit B tardior A, &longs;ed <lb/>contrarium fit, quippe quod <lb/>longior &longs;it BD, per quam mouetur B ip&longs;a AC, per quam <lb/>mouetur A. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001554">His igitur non &longs;atisfacientibus veriorem &longs;i per im­<lb/>becillitatem no&longs;tram licuerit, huius effectus cau&longs;&longs;am in­<lb/>ue&longs;tigabimus. </s> <s id="s.001555">Rationibus igitur & veritate contra aucto­<lb/>ritatem & probabilitatem e&longs;t nobis pugnandum: quod & <lb/>intrepide faciemus. </s> </p> <p type="main"> <s id="s.001556">Dicimus igitur, in quouis parallelogrammo &longs;it illud <lb/>quadratum aut altera parte longius, vel idem Rhombus <lb/>Rhomboi&longs;ue &longs;emper mixtos motus proportione &longs;eruata <pb xlink:href="007/01/164.jpg"/>fieri per diametros. </s> <s id="s.001557">Cæterum díametrorum ad latera <lb/>proportiones e&longs;&longs;e varias (quadratis exceptis, in quibus ea­<lb/>dem e&longs;t &longs;emper) explorati&longs;&longs;imum. </s> <s id="s.001558">Illud quoque certum <lb/>e&longs;t, in rectangulis nunquam dari po&longs;&longs;e diametros lateri­<lb/>bus vtcunque captis æquales, &longs;emper enim diametri re­<lb/>ctis angulis &longs;ubtruduntur. </s> <s id="s.001559">In Rhombis vero & Rhombo­<lb/>idibus diametrorum ad latera proportiones variant. </s> <s id="s.001560">Dari <lb/>enim po&longs;&longs;unt diametri lateribus longiores item æquales, <lb/>& lateribus quoque ip&longs;is breuiores. </s> </p> <p type="main"> <s id="s.001561">Itaque diametrorum & laterum varia adinuicem <lb/>ratione &longs;e habentibus, attentis proportionibus, <expan abbr="mixtorū">mixtorum</expan> <lb/>& &longs;implicium motuum diuer&longs;a fiet, & varia comparatio. <lb/></s> <s id="s.001562">in quadratis motus mixtus, qui per diametros &longs;emper ve­<lb/>locior erit &longs;implici qui per latera, Idem quoque in altera <lb/>parte longiori, in quo mixti quidem motus per diametros <lb/>erunt velociores, &longs;implices vero qui per latera, tardiores <lb/><expan abbr="quidē">quidem</expan>, &longs;ed ex illis tardior qui per latus breuius. </s> <s id="s.001563">In Rhom­<lb/>bis autem mixtus motus qui fit per diametros inæqualis. <lb/></s> <s id="s.001564">Velocior enim qui per longiorem diametrum, tardior <lb/>qui per breuiorem. </s> <s id="s.001565">Itaque &longs;implices motus punctorum <lb/>per latera ad eum qui fit per diametros non eodem pacto <lb/>&longs;e habent. </s> <s id="s.001566">Porro cum Rhomboides variæ &longs;int <expan abbr="diametrorū">diametrorum</expan> <lb/>ad latera habitudines, varia quoque dari pote&longs;t propor­<lb/>tio. </s> <s id="s.001567">aliquando enim diametri dari po&longs;&longs;unt lateribus maio­<lb/>res quando que, alter eorum minor. </s> <s id="s.001568">Si autem Rhombus in <lb/>duos &longs;oluatur triangulos, alter diametrorum datur æqua­<lb/>lis æqualibus lateribus æquicrurium triangulorum; <expan abbr="itaq;">itaque</expan> <lb/>in i&longs;tis mixti motus per diametros aequeveloces erunt &longs;im­<lb/>plicibus, qui per latera longiora, velociores autem illis <lb/>qui per latera breuiora. </s> <s id="s.001569">His igitur hoc pacto non perfun­<lb/>ctoriè con&longs;ideratis, facile ex proprijs cau&longs;&longs;is, nî fallimur, <lb/>hocce Ari&longs;totelicum & mirabile Problema &longs;oluitur. </s> </p> <pb xlink:href="007/01/165.jpg"/> <figure id="id.007.01.165.1.jpg" xlink:href="007/01/165/1.jpg"/> <p type="main"> <s id="s.001570">E&longs;to enim Rhombus ABDC, <lb/>cuius diameter longior AD maior &longs;it <lb/>tum lateribus, tum etiam altera dia­<lb/>metro BC. &longs;ecent autem &longs;e inuicem <lb/>diametri in E. <!-- KEEP S--></s> <s id="s.001571">Ducatur queue ip&longs;is AB, <lb/>CD, parallela FG &longs;ecans longiorem <lb/>diametrum AD, in H, breuiorem ve­<lb/>ro BC in I. & per I ip&longs;is BD AC paral­<lb/>lela ducatur KIL, Cum ergo B mixto <lb/>motu per diametrum BC erit in I & <lb/>A per diametrum AD, mixto &longs;imili­<lb/>ter motu erit in H, & quia motus mi­<lb/>xti fiunt per diametros, vt dictum e&longs;t, <lb/>vt &longs;e habet AD ad BC, ita AE ad EB, per 15. propos. 5. elem. <lb/></s> <s id="s.001572">item vt AE ad EB, ita per 4. propo&longs;. 6. AH ad BI. e&longs;t enim <lb/>IH ip&longs;i AB parallela. </s> <s id="s.001573">Longior e&longs;t autem AH ip&longs;a BI, quip­<lb/>pe quod AE longior &longs;it ip&longs;a EB. motus igitur mixtus pun­<lb/>cti A per diametrum AD v&longs;que ad H velocior e&longs;t motu B, <lb/>per diametrum BC v&longs;que ad I. <!-- KEEP S--></s> <s id="s.001574">Mota igitur linea AB mo­<lb/>uebuntur communia eius & diametrorum BC, AD pun­<lb/>cta, quibus &longs;ecantur &longs;emper diametrorum proportione <lb/>&longs;eruata. </s> <s id="s.001575">Quibus ita &longs;e habentibus, nil mirum e&longs;t punctum <lb/>A motum per AD velociorem e&longs;&longs;e mixto motu puncti B, <lb/>quod per minorem diametrum fertur BC. quod fuerat <lb/>demon&longs;trandum. </s> <s id="s.001576">quatenus vero ad &longs;ecundam problema­<lb/>tis partem pertinet, dicimus Propo&longs;itionem non e&longs;&longs;e vni­<lb/>uer&longs;alem. </s> <s id="s.001577">Si enim Rhombus detur, ex duobus æquilateris <lb/>triangulis con&longs;tans, breuior diameter lateribus erit aequa­<lb/>lis, quare non mouebitur citius motu &longs;implici punctum <lb/>per latus ac faciat mixto per minorem diametrum, quod <lb/>vt mirum propo&longs;uerat Ari&longs;toteles. </s> <s id="s.001578">Si autem latus ip&longs;um <lb/>breuiori diametro &longs;it <expan abbr="lōgius">longius</expan>, nec mirum quoque erit &longs;im­<lb/>plici motu moueri velocius quam mixto, quippe quod, vt <pb xlink:href="007/01/166.jpg"/>dictum e&longs;t, motus i&longs;ti à proportionibus linearum, per quas <lb/>mouentur, legem velocitatis atque tarditatis accipiant. <lb/></s> <s id="s.001579">Hæc igitur nos circa hoc mirabile Ari&longs;totelicum proble­<lb/>ma con&longs;iderare &longs;it &longs;atis. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001580">QVÆSTIO XXIV.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.001581">Mirabilem aliam quæ&longs;tionem proponit Ari&longs;toteles, <lb/>quæ itidem ad mixtos motus pertinet. </s> </p> <p type="main"> <s id="s.001582"><emph type="italics"/>Dubitatio est, quam ob cau&longs;&longs;am maior circulus æqualem minori <lb/>circulo circumuoluitur lineam, quando circa idem centrum fue­<lb/>rint po&longs;iti. </s> <s id="s.001583">Seor&longs;um autem reuoluti quemadmodum alterius ma­<lb/>gnitudo ad alterius magnitudinem &longs;e habet, ita & illorum adin­<lb/>uicem fiunt lineæ? </s> <s id="s.001584">Præterea vno etiam & eodem vtri&longs;que exi&longs;ten­<lb/>te centro. </s> <s id="s.001585">Aliquando quidem tanta &longs;it linea, quam conuoluuntur, <lb/>quantum minor per &longs;e conuoluitur circulus, quandoque vero quan­<lb/>tum maior.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001586">Hæc ille, qui vt prober maiorem circulum in &longs;ua ro­<lb/>tatione maiorem lineam pertran&longs;ire, minorem vero mi­<lb/>norem; ait &longs;en&longs;u cogno&longs;ci angulum maioris circuli, id e&longs;t, <lb/>eius qui maiorem habet circumferentiam, e&longs;&longs;e maiorem, <lb/>eius vero qui minorem, minorem. </s> <s id="s.001587">Ita autem &longs;e habere cir­<lb/>cumferentias vt &longs;e habent anguli, & eandem <expan abbr="proportionē">proportionem</expan> <lb/>habere per quas tum maior, tum minor circulus circum­<lb/>uoluuntur. </s> <s id="s.001588">Ad quorum clariorem intelligentiam ea re­<lb/>uocare oportet in memoriam, quæ dixit de maiorum cir­<lb/>culorum ad minores circulos nutu. </s> <s id="s.001589">Hic enim, quod ibi <lb/>quoque fecerat, &longs;ectorem ip&longs;um angulum appellauit, an­<lb/>gulum vero maiorem maioris circuli &longs;ectorem, & mino­<lb/>rem angulum minoris ip&longs;ius circuli &longs;ectorem dixit. </s> <s id="s.001590">Clau­<lb/>dit igitur dicens: quoniam circumferentiæ &longs;e habent vt <lb/>anguli, hoc e&longs;t, vt &longs;ectores, maior erit circumferentia ma­<lb/>ioris circuli, & ex con&longs;equenti maior linea, per quam cir-<pb xlink:href="007/01/167.jpg"/>cumuoluitur, ea per quam minor. </s> <s id="s.001591">Demon&longs;trationem ve­<lb/>ro ex &longs;en&longs;u petijt. </s> <s id="s.001592">Sat autem erat &longs;i dixi&longs;&longs;et, ita &longs;e habere <lb/>circumferentias vt &longs;e habent diametri &longs;eu &longs;emidiametri, <lb/>& ideo lineas in rotatione de&longs;criptas inuicem &longs;e habere vt <lb/>diametros. </s> <s id="s.001593">Ob&longs;curiu&longs;culè, hæc &longs;ua figura o&longs;tendit Ari&longs;to­<lb/>teles. <!-- KEEP S--></s> <s id="s.001594">Nos igitur claritatem amantibus, no&longs;tram aliquan­<lb/>to, nî fallimur, clariorem, proponemus. </s> </p> <figure id="id.007.01.167.1.jpg" xlink:href="007/01/167/1.jpg"/> <p type="main"> <s id="s.001595">E&longs;to circulus <lb/>maior ABCD, mi­<lb/>nor FGHI, circa i­<lb/>dem, & commune <lb/><expan abbr="cētrum">centrum</expan> E. <!-- KEEP S--></s> <s id="s.001596">Circum­<lb/>uoluatur maior ad <lb/>partes D. <!-- KEEP S--></s> <s id="s.001597">Sint <expan abbr="autē">autem</expan> <lb/>diametri, maioris <lb/><expan abbr="quidē">quidem</expan> AEC, BED, <lb/>minoris verò FEH, <lb/>GEI, fitque CD, <lb/>quadrans maioris, <lb/>HI vero minoris circuli. </s> <s id="s.001598">Moto igitur maiori circulo <expan abbr="&longs;ecū-dum">&longs;ecun­<lb/>dum</expan> ab&longs;idem, cum D fuerit in K erit CK ip&longs;i CD æqualis, <lb/>fietque; DE ex puncto K perpendicularis ip&longs;i CK, eritque vbi <lb/>KO, & quia punctum I e&longs;t in linea DE, erit I facta <expan abbr="quadrã-tis">quadran­<lb/>tis</expan> rotatione in linea KO vbi L, centrum vero E in ip&longs;a <lb/>KO, vbi O. <!-- KEEP S--></s> <s id="s.001599">Reuoluto igitur quadrante maioris, & confe­<lb/>cto &longs;patio CK minoris circuli quadrans HI conficiet &longs;pa­<lb/>tium HL, quod ip&longs;i CK &longs;patio e&longs;t æquale. </s> <s id="s.001600">quod autem in <lb/>quadrantibus fit, in totis etiam fit circulis. </s> <s id="s.001601">Motus igitur <lb/>minor circulus circa centrum E, vnica rotatione æquauit <lb/>&longs;patium rotationis maioris circuli. </s> <s id="s.001602">Mirabile itaque e&longs;t mi­<lb/>norem circulum eodem tempore & circa idem centrum <lb/>circumuolutum, lineam pertran&longs;i&longs;&longs;e æqualem circumfe­<lb/>rentiæ maioris circuli. </s> <s id="s.001603">Nec &longs;ecius admirationem facit ro­<pb xlink:href="007/01/168.jpg"/>tato minori circulo, maiorem vna <expan abbr="circumuolutū">circumuolutum</expan> lineam <lb/>metiri circumferentiæ minoris circuli æqualem. </s> <s id="s.001604">Rotetur <lb/>enim minoris circuli quadrans HI per rectam HL. erit i­<lb/>gitur punctum I vbi M, æquali exi&longs;tente recta HM, ip&longs;i <lb/>curuæ HI. <!-- KEEP S--></s> <s id="s.001605">Tunc autem facto motu centrum E erit vbi P, <lb/>exi&longs;tente EP, ip&longs;i HM æquali, demittatur autem ex P per <lb/>M, ip&longs;is HL CK perpendicularis PMN. </s> <s id="s.001606">Et quoniam in <lb/>eadem linea &longs;unt DIE, vbi E fuerit in PI erit in M, & D in <lb/>N. quamobrem rotata quarta minoris circuli parte, ma­<lb/>ioris interim circuli quadrans confecit &longs;patium CN æ­<lb/>quale ip&longs;i HM, hoc minus circuli quadranti HI, quod vti­<lb/>que e&longs;t admirabile. </s> </p> <p type="main"> <s id="s.001607">Porro cau&longs;&longs;am effectus huius mirifici diligenter quæ­<lb/>rit Philo&longs;ophus, & inueneram accurate explicat. </s> <s id="s.001608">Occur­<lb/>rit autem primo ab&longs;urdæ cuidam opinioni. </s> <s id="s.001609">Diceret enim <lb/>qui&longs;piam, ideo tardius moueri maiorem circulum, ad mo­<lb/>tum minoris, quod interim <expan abbr="dū">dum</expan> minor moueretur, aliquas <lb/>inter rotandum moras interponeret, minor vero ad mo­<lb/>tum maioris &longs;patia aliqua tran&longs;iliret, & ita &longs;patiorum fieri <lb/>ad æquationem. </s> <s id="s.001610">Porro demon&longs;trationem aggre&longs;&longs;urus haec <lb/>a&longs;&longs;umit principia. </s> <s id="s.001611">Eandem aequalemue potentiam, <expan abbr="aliquã">aliquam</expan> <lb/>magnitudinem tardius quidem mouere, aliquam vero <lb/>celerius. </s> <s id="s.001612">quod autem natum e&longs;t aptum moueri, tardius <lb/>moueri, &longs;i &longs;imul cum non apto nato moueri, moueatur, <lb/>quam &longs;i &longs;eparatim moueretur, celerius autem &longs;i non &longs;imul <lb/><figure id="id.007.01.168.1.jpg" xlink:href="007/01/168/1.jpg"/><lb/>cum eo moueatur. </s> <s id="s.001613">E&longs;to enim corpus A leue <lb/>quidem & aptum natum moueri &longs;ur&longs;um, cui <lb/>connectatur B, aptum natum moueri deor­<lb/>&longs;um, Si quis igitur mouere conetur corpus A <lb/>&longs;ur&longs;um difficilius mouebit, & tardius <expan abbr="iunctū">iunctum</expan> <lb/>nempe ip&longs;i B, quam &longs;i ab ip&longs;o e&longs;&longs;et <expan abbr="&longs;eiūctum">&longs;eiunctum</expan>. <lb/></s> <s id="s.001614">Praeterea quod non &longs;uo, &longs;ed alieno motu mo­<lb/>uetur, impo&longs;&longs;ibile e&longs;&longs;e plus eo moueri qui <pb xlink:href="007/01/169.jpg"/>mouet, &longs;iquidem non &longs;uo, &longs;ed alieno motu mouetur. </s> <s id="s.001615">Mo­<lb/>to igitur &longs;uo motu maiori circulo, minor non &longs;uo moue­<lb/>tur, &longs;ed motu maioris circuli, & ideo non plus mouetur <lb/>quam ille moueatur, mouetur autem maiori &longs;patio quam <lb/>ex &longs;e moueretur, propterea quod maior &longs;it maioris circu­<lb/>li, à quo &longs;imul defertur, circumferentia. </s> <s id="s.001616">Item &longs;i minor &longs;uo <lb/>motu circumuoluatur, maiorem feret &longs;ecum, & ideo non <lb/>plus in &longs;ua rotatione mouebitur maior, quam ip&longs;e minor <lb/>circulus moueatur. </s> <s id="s.001617">Summa rei haec e&longs;t, alterum ferri ab al­<lb/>tero & latum ad ferentis &longs;patium moueri. </s> <s id="s.001618">Licet enim al­<lb/>tero moto, alter interim moueatur, nihil refert. </s> <s id="s.001619">E&longs;t enim <lb/>ac &longs;i is qui fertur, nullam habeat motionem, aut &longs;i eam ha­<lb/>beat, ip&longs;a nequaquam vtatur. </s> <s id="s.001620">quod non fit &longs;i vterque &longs;e­<lb/>paratim circa proprium centrum moueatur, tunc enim <lb/>magnus magnum, paruus vero paruum &longs;patium conficit. <lb/></s> <s id="s.001621">Hinc decipi ait Ari&longs;toteles illum, qui putat vtrum que cir­<lb/>culum per &longs;e &longs;uper idem centrum in rotatione moueri, li­<lb/>cet enim videatur, re vera non e&longs;t. </s> <s id="s.001622">Id enim vtique certum <lb/>e&longs;t, cum à maiori circulo minor fertur, circa maioris cen­<lb/>trum motum fieri. </s> <s id="s.001623">Si vero maior à minori feratur circa mi­<lb/>noris circuli centrum motum fieri. </s> <s id="s.001624">Hæc ferè Philo&longs;ophi <lb/>e&longs;t mens, cuius &longs;olutionem e&longs;&longs;e certi&longs;&longs;imam, & ex veris <lb/>cau&longs;&longs;is non dubitamus. </s> </p> <p type="main"> <s id="s.001625">Hinc ad aliam eamqueue certam a&longs;&longs;ertionem tran&longs;i­<lb/>mus. </s> <s id="s.001626">Dicimus enim, nullam materialem <expan abbr="rotã">rotam</expan> circa axem <lb/>eidem affixum, dum rotatur, po&longs;&longs;e eundem locum &longs;eruare, <lb/>ni&longs;i cauum fiat, quod axem ip&longs;um recipiat, in tran&longs;uer&longs;a­<lb/>rijs quibus rota &longs;u&longs;tinetur & progre&longs;&longs;iuum axis motum <lb/>impediat. </s> </p> <p type="main"> <s id="s.001627">E&longs;to enim rota ABCD, cuius centrum E, diametri <lb/>AEC, BED, e&longs;to alia minor rota GH, item minor KL, tum <lb/>minor NO, & adhuc minor QR, circa idem centrum E. <lb/><!-- KEEP S--></s> <s id="s.001628">Rotetur itaque &longs;ecundum ab&longs;idem integri quadrantis <pb xlink:href="007/01/170.jpg"/><figure id="id.007.01.170.1.jpg" xlink:href="007/01/170/1.jpg"/><lb/>&longs;patium CD, eritque <lb/>D, in F, item &longs;i ex rota <lb/>GH, ex quadrante <lb/>HT, erit T in I. <!-- KEEP S--></s> <s id="s.001629">Ex a­<lb/>lijs item minoribus in <lb/>M, P, S. erit <expan abbr="itaq;">itaque</expan> <expan abbr="lon-gi&longs;&longs;imū">lon­<lb/>gi&longs;&longs;imum</expan> &longs;patium CF, <lb/><expan abbr="breui&longs;&longs;imū">breui&longs;&longs;imum</expan> vero RS, <lb/>Mota igitur rota cir­<lb/>ca <expan abbr="circulū">circulum</expan> &longs;eu axem, <lb/>QR, maior rota &longs;pa­<lb/>tio mouebitur RS, <lb/>quod &longs;i intra QR, circa centrum E alij infiniti imaginen­<lb/>tur circuli, quo propio es centro fuerint, eo maioris rotæ <lb/>progre&longs;&longs;us erit minor, donec ad centrum deueniatur, vbi <lb/>cum non &longs;it circulus, nullus fiet progre&longs;&longs;iuus motus, &longs;ed <lb/>circa ip&longs;um centrum nulla facta loci mutatione rotabi­<lb/>tur. </s> <s id="s.001630">At cum nulla materialis rota circa lineam punctumue <lb/>imaginarium conuerti po&longs;&longs;it, ideo axi ferreo alteriu&longs;ue <lb/>materiæ circa quem & cum quo circumuoluatur rota, ca­<lb/>uum &longs;emirotundum incidere oportet, in quo in&longs;ertus axis <lb/>dum conuertitur à loco in quo conuertitur, non recedat. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001631">QVÆSTIO XXV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001632"><emph type="italics"/>Quæritur, Cur lectulorum &longs;pondas &longs;ecundum duplam faciant pro­<lb/>portionem, hanc quidem &longs;ex pedum, vel paulo ampliorem, illam <lb/>vero trium. </s> <s id="s.001633">Item cur vectes funesue non &longs;ecundum <lb/>diametrum extendantur?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001634">Primam quæ&longs;tionis partem ita diluit Philo&longs;ophus, for­<lb/>ta&longs;&longs;e tantæ fieri &longs;olitos magnitudinis lectulos vt corpo­<lb/>ribus &longs;int proportionem habentes, & ideo fieri &longs;ecundum <lb/>&longs;pondas dupli longitudine nempe cubitorum quatuor, <lb/>latitudine vero duorum. </s> </p> <pb xlink:href="007/01/171.jpg"/> <p type="main"> <s id="s.001635">No&longs;trates alia vtuntur proportione, &longs;e&longs;quialtera, vi­<lb/>delicet, quam Græci Hemioliam dicunt, communiter e­<lb/>nim pedes quatuor latos faciunt plus minu&longs;ue, longos ve­<lb/>ro circiter &longs;ex. </s> <s id="s.001636">quod ideo fit vt in eis duo corpora commo­<lb/>dius cubare po&longs;&longs;int. </s> <s id="s.001637">Lecturi autem, de quibus loquitur <lb/>Philo&longs;ophus, ad vnum tantummodo &longs;u&longs;tinendum facti <lb/>videntur, quicquid tamen &longs;it, nullam ferè habet res ex <lb/>hac parte dubitationem. </s> </p> <p type="main"> <s id="s.001638">Secunda quæ&longs;tionis &longs;ectio ea erat, Cur non <expan abbr="&longs;ecundū">&longs;ecundum</expan> <lb/>diametros funes extendantur? </s> <s id="s.001639">Re&longs;tium funiumue in le­<lb/>ctulis muniendis v&longs;us non e&longs;t apud nos. </s> <s id="s.001640">etenim feretra <lb/>tantum, &longs;eu &longs;andapilas, quibus defunctorum corpora ef­<lb/>feruntur, funibus ad ea &longs;u&longs;tinenda inteximus. </s> </p> <p type="main"> <s id="s.001641">Cæterum lectos tabulis &longs;eu a&longs;&longs;eribus &longs;ternimus, qui­<lb/>bus &longs;accos paleis plenos imponimus, &longs;accis vero culcitras, <lb/>& tormenta, ne tabularum durities cubantes offendat. <lb/></s> <s id="s.001642">Atqui in re facili multum labora&longs;&longs;e videtur Ari&longs;toteles, <lb/>tum etiam ob&longs;cure & inuolute nimis quæ&longs;tionem tracta&longs;­<lb/>&longs;e. </s> <s id="s.001643">Difficilem enim apud eum habet hæc explicationem, <lb/>tum ea quam diximus de cau&longs;&longs;a, tum etiam quod Græca <lb/>lectio & Latina ver&longs;io corrupta, vt apparet, præ manibus <lb/>habeantur. </s> <s id="s.001644">Sane vt veritatem hoc loco vindicaret in lu­<lb/>cem, egregie laborauit Picolomineus nec parum profe­<lb/>cit. </s> <s id="s.001645">Cæterum currentes non &longs;ecundum diametrum extru­<lb/>dantur, triplicem affert Philo&longs;ophus rationem. </s> <s id="s.001646">Prima e&longs;t <lb/>vt &longs;pondarum ligna, minus di&longs;trahantur. </s> <s id="s.001647">Secunda, vt <expan abbr="pō-dus">pon­<lb/>dus</expan> inde commodius &longs;u&longs;tineatur. </s> <s id="s.001648">Tertia, vt in ip&longs;a textura <lb/>minus re&longs;tium funiumue ab&longs;umatur. </s> </p> <p type="main"> <s id="s.001649">Ad primam, cur exten&longs;is diametraliter funibus <expan abbr="&longs;pō-dæ">&longs;pon­<lb/>dæ</expan> ip&longs;æ di&longs;trahantur di&longs;cindanturue, nec ille nec alij do­<lb/>cent. </s> <s id="s.001650">Ego autem demon&longs;trarem hoc pacto. </s> </p> <p type="main"> <s id="s.001651">E&longs;to &longs;ponda ABCD, cuius longitudo AB, cra&longs;&longs;itudo <lb/>AC, in ea foramen vtrinque pertinens EF, re&longs;tis per fora-<pb xlink:href="007/01/172.jpg"/><figure id="id.007.01.172.1.jpg" xlink:href="007/01/172/1.jpg"/><lb/>men inditus GFE, &longs;itque E pars &longs;eu ca­<lb/>put exterius, quod nodo in E di&longs;tine­<lb/>tur. </s> <s id="s.001652">Sit autem &longs;pondæ lignum iuxta <lb/>longitudinem vt natura a&longs;&longs;olet &longs;ci&longs;&longs;ile. <lb/></s> <s id="s.001653">Vis quædam, fune ita extento applice­<lb/>tur in G, quae funem ip&longs;um ad &longs;e violen­<lb/>ter trahat. </s> <s id="s.001654">non di&longs;cindetur idcirco <lb/>&longs;ponda eo quod non diametraliter fu­<lb/>nis extendatur. </s> <s id="s.001655">Modo facta capitis G <lb/>translatione in H, trahatur valide fu­<lb/>nis, fiet autem pre&longs;&longs;io valida in F. ibi e­<lb/>nìm impedimentum facit angulus, ne funis ip&longs;a dum tra­<lb/>hitur, rectitudinem a&longs;&longs;equatur. </s> <s id="s.001656">Itaque vi præualente, li­<lb/>gno vero &longs;ci&longs;&longs;ili, minus re&longs;i&longs;tente, funis, a&longs;&longs;ecuta rectitudi­<lb/>ne, fiet in HIE &longs;ci&longs;&longs;a &longs;ponda ad <expan abbr="quãtitatem">quantitatem</expan> trianguli FIE, <lb/>quod fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.001657">Cur autem funes ab angulo in angulum exten&longs;æ mi­<lb/>nus commode pondus &longs;u&longs;tineant, &longs;atis patet. </s> <s id="s.001658">quo enim fu­<lb/>nis <expan abbr="lōgior">longior</expan>, eo debilior, & pre&longs;&longs;io quæ in medio fit, ea vide­<lb/>licet parte quæ ab extremis e&longs;t remoti&longs;&longs;ima, magis funem <lb/>fatigat. </s> <s id="s.001659">Longiores autem funes &longs;unt quæ diametraliter <lb/>extenduntur. </s> </p> <figure id="id.007.01.172.2.jpg" xlink:href="007/01/172/2.jpg"/> <p type="main"> <s id="s.001660">Quatenus ad <expan abbr="tertiã">tertiam</expan> <lb/>rationem pertinet, hoc <lb/>pacto funes intexit <lb/>Philo&longs;oph^{9}. E&longs;to lectu­<lb/>lus cum &longs;uis <expan abbr="&longs;pōdis">&longs;pondis</expan> AB <lb/>CD, cuius &longs;ponda AD, <lb/>&longs;it pedum &longs;ex, AB vero <lb/><expan abbr="triū">trium</expan>, Diuidatur AD bi­<lb/>faríam in E & BC in F. item AE in tres AG, GH, HE & in <lb/>totidem ED, nempe EL, LM, MD. </s> <s id="s.001661">Similiter medietas al­<lb/>terius <expan abbr="&longs;pōdæ">&longs;pondæ</expan> BF in tres partes di&longs;tinguatur BN, NO, OF, <pb xlink:href="007/01/173.jpg"/>& FC &longs;imiliter in tres FI, IK, KC, tum altero funis capite <lb/>in ducto per foramen A, ibique probe firmato, indatur per <lb/>F, inde per I, po&longs;tea per GHK CE, & in E probe alligetur: <lb/>Erunt igitur funis quatuor partes æquales AF, IG, HK, <lb/>EC, quibus adijciuntur particulæ cadentes extra, quæ <lb/>&longs;unt FI, GH, KC. </s> <s id="s.001662">Po&longs;t hæc alterius funis principium per <lb/>foramen traijcitur, quod e&longs;t in angulo B. <!-- KEEP S--></s> <s id="s.001663">Deinde per E, in­<lb/>de per L, N, O, M, D, F & in F probe vincitur, & nodo fa­<lb/>cto obfirmatur. </s> <s id="s.001664">Erunt igitur aliæ quatuor alterius funis <lb/>partes, tum inter &longs;e, tum etiam &longs;upra dictis æquales, nem­<lb/>pe BE, NL, OM, FD, quibus illæ pariter adijciuntur par­<lb/>ticulæ, quæ cadat extra, videlicet EL, NO, MD. <expan abbr="quoniã">quoniam</expan> <lb/>igitur quadratis ex BA, AE æquale e&longs;t quadratum BE, erit <lb/>BE quadratum 18. cuius latus radixue 4 1/3 quam proxime. <lb/></s> <s id="s.001665">Sunt autem huius longitudinis funes æquales octo. </s> <s id="s.001666">Ea­<lb/>rum igitur &longs;imul &longs;umptarum longitudo erit pedum 34 2/3 vel <lb/>circiter, quibus &longs;i ad dantur pedes &longs;ex funium qui cadunt <lb/>extra, erit re&longs;tis totius longitudo expan&longs;a pedum 40 2/3 plus <lb/>minu&longs;ue. </s> <s id="s.001667">Picolomineus vero ait 34 2/3, omi&longs;it enim particu­<lb/>las illas &longs;ex, quæ, vt diximus, cadunt extra. </s> <s id="s.001668">Idem rationem <lb/>funium diametraliter exten&longs;arum in idem, ait e&longs;&longs;e longi­<lb/>tudinis pedum 40 1/2. Hic autem eas <expan abbr="quoq;">quoque</expan> particulas præ­<lb/>termittit, quæ extra cadunt. </s> <s id="s.001669">Itaque his additis clare pa­<lb/>tet, plus re&longs;tium in&longs;umi diametraliter ip&longs;is, quam latera­<lb/>liter exten&longs;is. </s> <s id="s.001670">Cæterum ratio, qua Philo&longs;ophus hæc pro­<lb/>bare conatur, adeo e&longs;t mutila, inuoluta, ob&longs;cura, vt Delio <lb/>pror&longs;us, vt aiunt, indigeat natatore. </s> <s id="s.001671">Huius loci in explica­<lb/>bilem difficultatem, vidit Picolomineus, qui idcirco at­<lb/>te&longs;tatus e&longs;t, interpretes in hac exponenda fui&longs;&longs;e halluci­<lb/>natos. </s> <s id="s.001672">Certe Græca lectio ver&longs;ione ip&longs;a Latina non e&longs;t <lb/>clarior. </s> <s id="s.001673">Nos interim ne inutilem ferè &longs;peculationem ni­<lb/>mia diligentia, eaque forta&longs;&longs;e fru&longs;tranea pro&longs;equamur, a­<lb/>lijs difficultatem hanc di&longs;&longs;oluendam aut ceu Gordij no­<pb xlink:href="007/01/174.jpg"/>dum gladio &longs;cindendo relinquemus. </s> <s id="s.001674">Sed interim &longs;ubit <lb/>mirari, cur veteres vtiliori modo prætermi&longs;&longs;o, <expan abbr="inutilioiē">inutiliorem</expan> <lb/>fuerint amplexati. </s> <s id="s.001675">Poterant enim reticulatim hoc per li­<lb/>neas lateribus æquidi&longs;tantes intexere. </s> </p> <figure id="id.007.01.174.1.jpg" xlink:href="007/01/174/1.jpg"/> <p type="main"> <s id="s.001676">E&longs;to enim lectulus <lb/>eiu&longs;dem dimen&longs;ionis <lb/>ABCD, in cuius latere <lb/>AD &longs;int foramina quin­<lb/>que E, F, G, H, I, totidem <lb/>in latere oppo&longs;ito QP, <lb/>ONM. </s> <s id="s.001677">Duo vero in la­<lb/>tere breuiori AB, nempe <lb/>RS, & toti dem in oppo&longs;ito KL incipiatur exten&longs;io à fora­<lb/>mine E, per QP, F, GON, HIM & in M funis obfirmetur, <lb/>tum alterius funis caput in datur &longs;i lib et per K, & inde per <lb/>S, R, L & in L con&longs;tringatur. </s> <s id="s.001678">Sunt autem omnes EQ, FP, <lb/>GO, NN, IM, pedum quindecim, quibus &longs;i addantur KS, <lb/>RL, &longs;inguli pedum &longs;ex erunt pedum xxvii. </s> <s id="s.001679">quibus adiectis <lb/>particulis extra cadentibus QP, FG, ON, HI, & RS, erit <lb/>integra &longs;umma pedum xxxii. </s> <s id="s.001680">Vide igitur quantum hinc <lb/>minus in&longs;umatur re&longs;tium quam eo modo, quem proba­<lb/>uit, & ceu vtiliorem propo&longs;uit Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.001681">Præterea vali­<lb/>di&longs;&longs;imum e&longs;t hoc texturæ opus nec ex eo fit vera &longs;ponda­<lb/>rum di&longs;tractio &longs;ci&longs;&longs;ioue, quibus haud parum obnoxia e&longs;t <lb/>ea ratio, quam præfert ip&longs;e Philo&longs;ophus. <!-- KEEP S--></s> <s id="s.001682">Concludimus i­<lb/>gitur, aut nos eius verba & &longs;en&longs;um non intellexi&longs;&longs;e, aut <lb/>veteres ip&longs;os, quorum v&longs;um ip&longs;e explicat, rei, quam nos <lb/>proponimus, naturam & commoditatem (quod ta­<lb/>men vix credibile e&longs;t) igno­<lb/>rare. </s> </p> <pb xlink:href="007/01/175.jpg"/> </subchap1> <subchap1> <p type="head"> <s id="s.001683">QVÆSTIO XXVI.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001684"><emph type="italics"/>Proponitur à Philo &longs;opho examinandum, Cur difficilius &longs;it, langa <lb/>ligna ab extremo &longs;uper humeros ferre, quam &longs;ecundum me­<lb/>dium, æquali exi&longs;tente pondere?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001685">Dvo hîc con&longs;iderat, vibrationem, & pondus. </s> <s id="s.001686">Ait enim <lb/>primo fieri po&longs;&longs;e, procera ligna vibratione impedien­<lb/>te, difficilius ferri. </s> <s id="s.001687">Quærerer autem qui&longs;piam, (ip&longs;e enim <lb/>id reticet) cur vibratio hæc ferenti &longs;it nocua. </s> <s id="s.001688">Nos itaque <lb/>id expliçare conabimur. </s> </p> <figure id="id.007.01.175.1.jpg" xlink:href="007/01/175/1.jpg"/> <p type="main"> <s id="s.001689">E&longs;to igitur lignum <lb/>oblongum, flexile, & vt <lb/>ita dicam, vibrabile <lb/>AB, imponatur hume­<lb/>ro, eique hæreat in C, <lb/>manu vero &longs;u&longs;tineatur facta compre&longs;&longs;ione in B. <!-- KEEP S--></s> <s id="s.001690">Nutet i­<lb/>gitur & vibretur, in ip&longs;a vibratione, ad partem A. <!-- KEEP S--></s> <s id="s.001691">Sit au­<lb/>tem centrum grauitatis eius D, Lignum igitur in ip&longs;a vi­<lb/>bratione de&longs;cendet &longs;ua pre&longs;&longs;us grauitate in E, tum facta <lb/>ligni con&longs;tipatione in ea parte quæ e&longs;t inferius inter C & <lb/>D, & inde re&longs;i&longs;tentia, eodem fere impetu quo de&longs;cende­<lb/>rat, repul&longs;um per D, nec enim in &longs;ua rectitudine &longs;tabit, a­<lb/>&longs;cendet in F, facta iterum materiæ con&longs;tipatione inter C <lb/>& F. <!-- KEEP S--></s> <s id="s.001692">Mouebitur igitur lignum &longs;ua grauitate, motu fre­<lb/>quenti&longs;&longs;imo, &longs;ur&longs;um deor&longs;um, & is interim qui lignum hu­<lb/>mero fert, procedit antror&longs;um, impedit igitur motus i&longs;te, <lb/>qui fit &longs;ur&longs;um deor&longs;um lationem, quæ fit ad anteriora; La­<lb/>torem ip&longs;um quodammodo retrahens. </s> <s id="s.001693">Si autem medio <lb/>ligno &longs;upponatur humerus, eo quod vibratio &longs;it minor. <lb/></s> <s id="s.001694">breuiores enim partes &longs;unt, quæ à medío ad extrema mi­<lb/>nus à vibratione remorabitur ferens. </s> </p> <p type="main"> <s id="s.001695">Quoniam autem non &longs;ola vibratio in hoc lationis <lb/>modo, nempe ex ligni extremitate difficultatem facit, ait <pb xlink:href="007/01/176.jpg"/>Philo&longs;ophus, forte id fieri, quoniam licet nihil inflecta­<lb/>tur, neque multam habeat longitudinem, difficilius <expan abbr="tamē">tamen</expan> <lb/>&longs;it ad ferendum ab extremo, eo quod facilius eleuetur ex <lb/>medio quam ab extremis, & ideo &longs;ic ferre &longs;it facilius. <lb/></s> <s id="s.001696">Cur autem ex medio facilius eleuetur, cau&longs;&longs;am e&longs;&longs;e ait, <lb/>quod eleuato medio ligno extrema &longs;e&longs;e inuicem &longs;u&longs;pen­<lb/>dant, & altera pars alteram bene &longs;ubleuet. </s> <s id="s.001697">Medium enim <lb/>fieri velut centrum, vbi is &longs;upponit humerum qui eleuat <lb/>aut fert. </s> <s id="s.001698">Extremorum autem interim altero depre&longs;&longs;o al­<lb/>terum &longs;u&longs;tolli. </s> <s id="s.001699">Nos interim Mechanicis principijs, quod <lb/>ip&longs;e non fecit, rem clariorem efficiemus. </s> </p> <p type="main"> <s id="s.001700">E&longs;to enim oblongum lignum AB, cui humerus &longs;up­<lb/>ponatur in B, manus vero premendo &longs;u&longs;tinens in B. &longs;it au­<lb/>tem ligni pars maxima AC, minima CB, inaioris autem ad <lb/>minorem proportio exempli gratia &longs;it &longs;excupla. </s> <s id="s.001701">Ad hoc i­<lb/>gitur vt fiat æquilibrium inter potentiam &longs;u&longs;tinentem in <lb/>B, & pondus comprimens in A, ita &longs;e habere oportet po­<lb/>tentiam in B, ad pondus in A, vt &longs;e habet pars ligni AC ad <lb/><figure id="id.007.01.176.1.jpg" xlink:href="007/01/176/1.jpg"/><lb/>partem CD. <!-- KEEP S--></s> <s id="s.001702">E&longs;to igitur pon­<lb/>dus in A, puta librarum &longs;ex. <lb/></s> <s id="s.001703">Erit igitur potentia quæ in B <lb/>ad hoc vt &longs;u&longs;tineat librarum <lb/>triginta &longs;ex, quas &longs;i addas <expan abbr="pō-deri">pon­<lb/>deri</expan> in A, fiet humerus in C <lb/>&longs;u&longs;tinens pondus librarum quadraginta duo. </s> <s id="s.001704">Si autem <lb/>humerus medio ligno, hoc e&longs;t, in D &longs;upponatur, ad hoc vt <lb/>fiat æquilibrium, nece&longs;&longs;e erit potentiam in B e&longs;&longs;e æqua­<lb/>lem ponderi in A, quod e&longs;t &longs;ex, quare humerus &longs;u&longs;tinebit <lb/>duodecim. </s> <s id="s.001705">Vnde patet, longe difficilius portari lignum <lb/>ex C extremo, quam ex D medio; quod Mechanice fue­<lb/>rat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.001706">Po&longs;&longs;umus & aliter idem o&longs;tendere. </s> <s id="s.001707">Intelligatur e­<lb/>nim ij&longs;dem &longs;uppo&longs;itis, vectem quidem e&longs;&longs;e AB, cuius ful-<pb xlink:href="007/01/177.jpg"/>cimentum quidem B, pondus A, potentia &longs;u&longs;tinens in C, <lb/>nempe inter fulcimentum & pondus. </s> <s id="s.001708">Res igitur ad eum <lb/>vectis v&longs;um reducitur, de quo G. <!-- REMOVE S-->Vbaldus tractatu de Ve­<lb/>cte, propo&longs;. 3.</s> <s id="s.001709">Quare vtile o&longs;tendit, ita &longs;e habere oportet <lb/>potentiam &longs;u&longs;tinentem ad pondus, vt totus vectis ad par­<lb/>tem eius quæ à potentia ad fulcimentum. </s> <s id="s.001710">Ita igitur &longs;e ha­<lb/>bebit pre&longs;&longs;io, quæ fit in C ad pondus in A, vt totus vectis <lb/>AB ad partem eius CB, quæ à potentia ad fulcimentum. <lb/></s> <s id="s.001711">Erit igitur potentia &longs;eptupla ponderi, & ideo &longs;u&longs;tinebit <lb/>pondus librarum quadraginta duarum. </s> <s id="s.001712">quod fuerat o­<lb/>&longs;tendendum. </s> </p> <p type="main"> <s id="s.001713">Hinc alia quæ&longs;tio huic affinis &longs;oluitur, Cur ha&longs;ta &longs;a­<lb/>ri&longs;&longs;aue &longs;olo iacens manu ad alteram extremitatum ap­<lb/>pren&longs;a difficillime extollatur? </s> </p> <figure id="id.007.01.177.1.jpg" xlink:href="007/01/177/1.jpg"/> <p type="main"> <s id="s.001714">E&longs;to igitur &longs;ari&longs;&longs;a ha­<lb/>&longs;taue iacens AB, cuius ex­<lb/>tremitati A manus ad &longs;u­<lb/>&longs;tollendum applicetur, &longs;it <lb/>autem pars quæ digitis capitur AC, quæritur cur pars re­<lb/>liqua CB difficillime &longs;u&longs;tollatur? </s> <s id="s.001715">Facile dubitatio ex præ­<lb/>demon&longs;tratis &longs;oluitur. </s> <s id="s.001716">E&longs;t enim C fulcimentum, &longs;upponi­<lb/>tur enim loco, pugno ad &longs;u&longs;tollendum clau&longs;o, digitus in­<lb/>dex, potentia autem premens in A, vt &longs;uperet grauitatem <lb/>CB, e&longs;t manus ip&longs;ius corpus, hoc e&longs;t illa manus ip&longs;ius pars, <lb/>qua pondus facta &longs;uppre&longs;&longs;ione &longs;u&longs;tollitur. </s> <s id="s.001717">E&longs;t igitur AB <lb/>vectis, cuius fulcimentum C, pondus B, potentia A, <expan abbr="Itaq;">Itaque</expan> <lb/>quoniam maxima e&longs;t proportio BA ad AC, maximam e&longs;­<lb/>&longs;e oportet potentiam pondus &longs;u&longs;tollentem in C. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001718">Huc etiam illud pertinet, Cur ha&longs;ta &longs;olo iacente, &longs;i <lb/>alterum extremorum manu &longs;u&longs;tollatur, alterum vero ve­<lb/>loci&longs;&longs;ime &longs;ur&longs;um vibretur, & eodem tempore manus ha­<lb/>&longs;tæ &longs;ic vibratæ &longs;upponatur, haud magna difficultate ha&longs;tæ <lb/>ad perpendiculum fit erectio. </s> </p> <pb xlink:href="007/01/178.jpg"/> <figure id="id.007.01.178.1.jpg" xlink:href="007/01/178/1.jpg"/> <p type="main"> <s id="s.001719">Sit enim ha&longs;ta AB, quæ <lb/>manu ex B capta eleuetur in <lb/>C, & fiat in AC, tum facta ex <lb/>C partis A veloci vibratione, <lb/>ip&longs;a extremitas A transferatur <lb/>in D, &longs;itque vbi CD, tum velo­<lb/>ci manus depre&longs;&longs;ione extremi­<lb/>tas C transferatur in E, <expan abbr="fiatq;">fiatque</expan> <lb/>EF horizonti perpendicularis; <lb/>quod vbi factum fuerit, erunt <lb/>in eadem linea quæ ad centrum mundi, manus ip&longs;a quæ <lb/>&longs;u&longs;tinet, & grauitatis ip&longs;ius centrum G, quare manus ip&longs;a <lb/>facta vibratione tantum portat, quantum præci&longs;e ip&longs;ius <lb/>e&longs;t ha&longs;tæ pondus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001720">QVAESTIO XXVII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001721"><emph type="italics"/>Dubitatur, Cur &longs;i valde procerum fuerit idem pondus, difficilius <lb/>&longs;uper humeros ge&longs;tatur, etiam&longs;i medium qui&longs;piam illud fe­<lb/>rat quam &longs;i breuius &longs;it?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001722">Qvæ&longs;tio hæc &longs;uperiori e&longs;t affinis. </s> <s id="s.001723">Ait autem Philo&longs;o­<lb/>phus, cau&longs;&longs;am non e&longs;&longs;e id, quod in præcedenti quæ­<lb/>&longs;tione dixerat, &longs;ed vibrationem: quo enim longiora &longs;unt <lb/>ligna, eo magis eorum extrema vibrantur, debiliora enim <lb/>&longs;unt & à medio remotiora, quare &longs;uopte pondere facilius <lb/>nutant. </s> <s id="s.001724">Si autem breuiora &longs;int ea cau&longs;&longs;a ce&longs;&longs;ante minor <lb/>fit aut nulla vibratio, quare breuiora feruntur facilius. <lb/></s> <s id="s.001725">Dupliciter autem vibratione ip&longs;a, portans offenditur, <lb/>tum ex cau&longs;&longs;a quam in &longs;uperiori quæ&longs;tione con&longs;ideraui­<lb/>mus, nempe quod motus &longs;ur&longs;um deor&longs;um a&longs;&longs;iduus, pro­<lb/>gredientis motum impediat, tum etiam quod duplici <lb/>pre&longs;&longs;ione grauetur ferentis humerus, quod Philo&longs;ophus <lb/>non animaduertit. </s> </p> <p type="main"> <s id="s.001726">Sit enim oblongum lignum AB, quod humero me-<pb xlink:href="007/01/179.jpg"/><figure id="id.007.01.179.1.jpg" xlink:href="007/01/179/1.jpg"/><lb/>dio loco &longs;u&longs;tineatur in C. <lb/>nutabunt ergo extrema AB, <lb/>à centro C, valde remota, <lb/>cadent autem &longs;imul A m D, <lb/>& B in E trahere &longs;ecum conantes medium C, quare is qui <lb/>in C &longs;u&longs;tinet, non modo ligni &longs;u&longs;tinet pondus ex grauita­<lb/>tis centro quod e&longs;t in C, &longs;ed impetum quoque in ip&longs;a ex­<lb/>tremorum depre&longs;&longs;ione acqui&longs;itum ex ipsa violentia. </s> <s id="s.001727">Illud <lb/>autem &longs;ubtiliter con&longs;ideramus, portantem ex vibratione <lb/>per inter ualla deprimi & &longs;ubleuari. </s> <s id="s.001728">fiat enim vibratum li­<lb/>gnum ex contrario motu, vbi FCG. alleuiabit igitur eo <lb/>ca&longs;u portantem, &longs;iquidem impetus ex motu ip&longs;o acqui&longs;i­<lb/>tus, medium C trahat ad &longs;uperiora. </s> <s id="s.001729"><expan abbr="Itaq;">Itaque</expan> cum e&longs;t in DCE <lb/>portans plus &longs;u&longs;tinet in ACD, æquale, in FCG minus, <lb/>quod vtique demon&longs;trandum fuerat. </s> <s id="s.001730">E&longs;t autem quæ&longs;tio <lb/>hæc illi familiaris, quam 16. loco explicauimus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001731">QVAESTIO XXVIII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001732"><emph type="italics"/>Quæritur, Cur iuxta puteos celonia faciunt eo quo vi&longs;untur mo­<lb/>do? </s> <s id="s.001733">Ligno enim plumbi adiungunt pondus, cum alioquin vas <lb/>ip&longs;um & plenum & vacuum pon­<lb/>dus habeat.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001734">Re&longs;pondet optime Philo&longs;ophus, hauriendi opus duo­<lb/>bus temporibus diuidi, nempe dum vas ip&longs;um vacuum <lb/>demittitur, dum que extrahitur plenum: Contingere au­<lb/>tem, vacuum facile demitti, plenum autem difficulter ex­<lb/>trahi. </s> <s id="s.001735">Expedire nihilominus tardius, hoc e&longs;t difficilius di­<lb/>mitti vt facilius extrahatur, plumbo nempe coadiuuante, <lb/>& &longs;ane Philo&longs;ophi &longs;olutio e&longs;t lucidi&longs;&longs;ima. </s> <s id="s.001736">Nos autem luci <lb/>ip&longs;i lucem aliquam adhuc afferre conabimur. </s> </p> <p type="main"> <s id="s.001737">E&longs;to Celomum (Latine Tolenonem appellant) ABC, <lb/>cuius arrectarium BD, tran&longs;uer&longs;um lignum AC, quod <pb xlink:href="007/01/180.jpg"/><figure id="id.007.01.180.1.jpg" xlink:href="007/01/180/1.jpg"/><lb/>conuertitur, circa <expan abbr="pūctum">punctum</expan> &longs;eu <lb/>fulcimentum B, pondus, plum­<lb/>bumue, vbi A, &longs;itula E, funi ap­<lb/>pen&longs;a CE. <!-- KEEP S--></s> <s id="s.001738">Dico rebus ita con­<lb/>&longs;titutis difficilem quidem e&longs;&longs;e <lb/>vacuæ &longs;itulæ demi&longs;&longs;ionem, fa­<lb/>cile vero eiu&longs;dem extractio­<lb/>nem. </s> <s id="s.001739">Vectis diui&longs;i, &longs;itulæ, ac <lb/>ponderis, ad hoc vt fiat æquili­<lb/>brium, ca debet e&longs;&longs;e propor­<lb/>tio, vt quemadmodum &longs;e habet AB ad BC, ita &longs;e habeat <lb/>plenæ &longs;itulæ pondus E ad ip&longs;um pondus A, &longs;uperabit ergo <lb/>pondus in A &longs;itulam vacuam in E nec fiet æquilibrium, i­<lb/>taque vt vacua &longs;itula demittatur, tanta vis adhibenda e&longs;t <lb/>quantum e&longs;t ip&longs;ius aquæ, qua &longs;itula impletur pondus, quæ <lb/>vis dum apponitur difficilem, vt dicebamus, efficit &longs;itulæ <lb/>vacuæ demi&longs;&longs;ionem. </s> <s id="s.001740">Plena vero &longs;itula &longs;it æquilibrium, vn­<lb/>de quantumuis pu&longs;illa vi adhibita, &longs;itula extrahitur, qua&longs;i <lb/>ex &longs;emetip&longs;a ponderis appen&longs;i virtute a&longs;cendens. </s> <s id="s.001741">Quan­<lb/>tum igitur pondus dum vacua demittitur impedit, tan­<lb/>tundem plena dum extrahitur, adiuuat. </s> <s id="s.001742">Quae cum ita &longs;int, <lb/>&longs;i paria &longs;unt difficultas in demittendo, & facilitas in ex­<lb/>trahendo, quæ ratio hoc in negotio vtilitatis? </s> <s id="s.001743">Sane &longs;itula <lb/>vacua, manu per funem facile demittitur, plena vero dif­<lb/>ficile extrahitur, v&longs;u autem Celonij res <expan abbr="permutãtur">permutantur</expan>. </s> <s id="s.001744">Cor­<lb/>poris enim proprij pondere, dum premit, adiuuatur de­<lb/>mittens, qui per funem &longs;implicem extrahendo, ab eodem <lb/>proprij corporis pondere impediebatur. </s> <s id="s.001745">quod quidem ex <lb/>corporis pondere, auxilium, ingentem parit in extrahen­<lb/>do commoditatem. </s> </p> <p type="main"> <s id="s.001746">Quippiam &longs;imile accidit, aquas è puteis extrahen­<lb/>tibus v&longs;u trochleæ. </s> <s id="s.001747">Sit enim trochlea puteo imminens <lb/>ABCD, cuius centrum E &longs;u&longs;pen&longs;a quidem in A, funis, cui <pb xlink:href="007/01/181.jpg"/>&longs;itula &longs;u&longs;penditur FCABG, &longs;itula vero G. <!-- KEEP S--></s> <s id="s.001748">E&longs;t igitur dia­<lb/>meter CED, in&longs;tar libræ, quare vt fiat æquilibrium nece&longs;­<lb/>&longs;e e&longs;t capiti funis F, potentiam applicare, quæ &longs;it æqualis <lb/><figure id="id.007.01.181.1.jpg" xlink:href="007/01/181/1.jpg"/><lb/>pondere &longs;itulæ aqua plenæ, itaque extra­<lb/>hens proprijs viribus <expan abbr="corporīs">corporis</expan> pondus ad­<lb/>ijciens facile &longs;itulam aqua plenam extra­<lb/>hit, ex qua re magna extrahentibus fit <lb/>commoditas. </s> <s id="s.001749">Patet autem diuer&longs;o modo <lb/>extrahentes iuuare Celonium. <!-- KEEP S--></s> <s id="s.001750">& Tro­<lb/>chleam, ibi enim corporis mole adiuuatur <lb/>demittens vacuam, hic vero qui extrahit <lb/>plenam aqua &longs;itulam. </s> </p> <p type="main"> <s id="s.001751">Cæterum Celonij partem BC, qui à <lb/>fulcimento ad funem longe maiorem e&longs;­<lb/>&longs;e oportet, ip&longs;a AB, vt &longs;itula in profundum po&longs;&longs;it demitti, <lb/>quamobrem ita &longs;e debet habere pondus in A, ad pondus <lb/>&longs;itulæ plenæ, vt &longs;e habet brachium &longs;eu pars BC, ad par­<lb/>tem BA. <!-- KEEP S--></s> <s id="s.001752">Tunc enim ex permutata proportione efficitur <lb/>æquilibrium. </s> </p> <p type="main"> <s id="s.001753">Illud addimus, nouum non ae&longs;&longs;e Architectis Mecha­<lb/>nici&longs;que, tum hominum tum animalium vt commodius <lb/>machinas moueant, adhibere pondera corporum. </s> <s id="s.001754">Nec e­<lb/>nim alia ratione mouentur Rotæ illæ, quas ob hanc cau&longs;­<lb/>&longs;am ambulatorias vocant; quarum v&longs;us ad Mangana, ad <lb/>extrahendas è puteis aquas, & ad farinarias quoque mo­<lb/>las agitandas adhibetur. </s> </p> <p type="main"> <s id="s.001755">Porro Tollenonem bellicam Machinam à Celonio <lb/>tum forma tum pote&longs;tate nihil differre, videre e&longs;t apud <lb/>veteres Mechanicos, Heronem Byzantium, & alios. </s> <s id="s.001756">apud <lb/>neotericos vero hac de re agunt Daniel Barbarus in Vi­<lb/>truuium, & Iu&longs;tus Lip&longs;ius in librum quem de bellicis <lb/>machinis edidit, eleganti&longs;&longs;i­<lb/>mum. </s> </p> <pb xlink:href="007/01/182.jpg"/> </subchap1> <subchap1> <p type="head"> <s id="s.001757">QVAESTIO XXIX.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001758"><emph type="italics"/>Dubitatur, Cur quando &longs;uper ligno, aut huiu&longs;modi quopiam, duo <lb/>portauerint homines, idem pondus non æqualiter premun­<lb/>tur, &longs;ed ille magis cui vicinius fuerit <lb/>pondus?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001759">Soluit Ari&longs;toteles, inquiens, lignum e&longs;&longs;e vectem, pon­<lb/>dus vero fulcimentum; res quæ mouetur is qui ponde­<lb/>ri e&longs;t proximior: mouens vero qui remotior. </s> <s id="s.001760">Itaque quo <lb/>magis remotus e&longs;t à pondere, hoc e&longs;t, à fulcimento is qui <lb/>mouet, eo violentius is premitur qui altera vectis parte <lb/>eaque breuiori, mouetur. </s> </p> <figure id="id.007.01.182.1.jpg" xlink:href="007/01/182/1.jpg"/> <p type="main"> <s id="s.001761">E&longs;to lignum AB, pondus <lb/>C appen&longs;um in E, vicinius ex­<lb/>tremo B quam ip&longs;i A, &longs;it <expan abbr="autē">autem</expan> <lb/><expan abbr="portãtium">portantium</expan> alter quidem AF, <lb/>alter vero BG, Imaginemur <lb/>itaque locum E à pondere ita <lb/>figi & deprimi, vt &longs;ur&longs;um qui­<lb/>dem ferri nequaquam po&longs;&longs;it, <lb/>circa vero punctum E, ceu <lb/>circa centrum fulcimentum­<lb/>ne ip&longs;um vectem conuerti. </s> <s id="s.001762">Lignum ergo AB vectis: mo­<lb/>uens potentia A, pars vectis à potentia ad fulcimentum <lb/>AE pars eiu&longs;dem quæ à fulcimento ad rem motam EB, & <lb/>quoniam quanto longior e&longs;t pars vectis EA ip&longs;a EB, eo fa­<lb/>cilius potentia quæ e&longs;t in A, operatur in id quod e&longs;t in B, &longs;i <lb/>res ad proportiones redigatur, erit potentia in A, ad id <lb/>quod mouetur &longs;eu premitur in B, vt pars vectis EB ad par­<lb/>tem EA, &longs;ed maior e&longs;t AE ip&longs;a EB, ergo maiorem partem <lb/>&longs;u&longs;tinet ponderis, & plus premitur is qui in E, & qui mo­<lb/>uet in A. <!-- KEEP S--></s> <s id="s.001763">Hæc fere Philo&longs;ophi e&longs;t &longs;ententia: Picolomi­<lb/>neus vero Paraphra&longs;tes appo&longs;ite duos vectes in vnico li-<pb xlink:href="007/01/183.jpg"/>gno con&longs;iderat, alterum AB, alterum BA, in primo A e&longs;t <lb/>mouens B, motum in &longs;ecundo B, mouens A vero motum <lb/>in quibus vectibus &longs;emper idem & commune fulcimen­<lb/>tum E. <!-- KEEP S--></s> <s id="s.001764">Et quoniam in propo&longs;ito diagrammate breuior e&longs;t <lb/>pars vectis EB, quæque à mouente ad fulcimentum, parte <lb/>illa quæ ab eodem fulcìmento ad rem motam, minus o­<lb/>peratur B in A, quam A in B, & ideo qui in B mouetur plus <lb/>premitur, contra vero quia maior e&longs;t pars EA ip&longs;a parte <lb/>EB, magis operatur qui in A in ip&longs;um B, quam econtra. </s> <s id="s.001765">Et <lb/>&longs;ane con&longs;ideratio hæc &longs;ubtilis e&longs;t & ingenio&longs;a, & quæ &longs;i <lb/>recte intelligatur, quatenus ad proportiones & effectum <lb/>ip&longs;um demon&longs;trandum pertinet, à veritate ip&longs;a non ab­<lb/>horret, Quicquid tamen &longs;it, Mechanice magis hoc pacto <lb/>quæ&longs;tio diluetur. </s> <s id="s.001766">Dicimus enim, pondus quidem vere e&longs;­<lb/>&longs;e pondus, non autem fulcimentum, vt &longs;ibi fingebat Ari­<lb/>&longs;toteles: lignum vero vectem, duo autem qui pondus &longs;u­<lb/>&longs;tinent pro duplici fulcimento haberi, vtri&longs;que enim ve­<lb/>ctis cum appen&longs;o pondere innititur. </s> <s id="s.001767">Pote&longs;t etiam alter <lb/>eorum pro potentia mouente, alter vero pro fulcimen­<lb/>to, & &longs;ic vici&longs;&longs;im. </s> <s id="s.001768">E&longs;t autem, quomodocunque res accipia­<lb/>tur, pondus inter fulcimentum. </s> <s id="s.001769">& potentiam. </s> <s id="s.001770">Quare ex <lb/>ijs quæ demon&longs;trauit G. Vbald. <!-- REMOVE S-->de hoc vectis genere lo­<lb/>quens, vt &longs;e habet AE pars ad AB vectem totum, ita po­<lb/>tentia quæ &longs;u&longs;tinet in B, ad pondus appen&longs;um in E, & vt <lb/>BE ad BA ita potentia quæ &longs;u&longs;tinet in A ad pondus quod <lb/>in E. <!-- KEEP S--></s> <s id="s.001771">At minor e&longs;t proportio BE, ad BA, quam AE ad AB, <lb/>quare magis &longs;uperatur pondus in E à potentia quæ in A, <lb/>quam à potentia quæ in B, & ideo plus ponderis &longs;u&longs;tinet <lb/>ferens in B, quam ferens in A, quod fuerat demon&longs;tran­<lb/>dum. </s> </p> <p type="main"> <s id="s.001772">Hinc colligimus, pondere in medio vecte appen&longs;o <lb/>ferentes æqualiter &longs;u&longs;tinere, propterea quod totius vectis <lb/>ad partes ip&longs;as proportio &longs;it eadem, vel æqualis. </s> </p> <pb xlink:href="007/01/184.jpg"/> <p type="main"> <s id="s.001773">Pulchre autem dubitari pote&longs;t, an idem pror&longs;us con­<lb/>tingat, &longs;i alterum eorum qui &longs;u&longs;tinent, &longs;it &longs;tatura quidem <lb/>procerior, alter vero humilior. </s> </p> <figure id="id.007.01.184.1.jpg" xlink:href="007/01/184/1.jpg"/> <p type="main"> <s id="s.001774">Sit enim vectis AB, in cuius <lb/>medio pondus H libere appen­<lb/>&longs;um ex C, alter portantium pro­<lb/>cerior AD, humilior vero BE. &longs;it <lb/>autem horizontis planum DE, <lb/>demittatur à puncto Cad <expan abbr="horizō-tem">horizon­<lb/>tem</expan> perpendicularis, ip&longs;is vero <lb/>AD, BE, æquidi&longs;tans CF. <!-- KEEP S--></s> <s id="s.001775">Tran&longs;i­<lb/>bit autem per ip&longs;ius ponderis, <lb/>grauitatis centrum H. Dico igi­<lb/>tur, nil referre quatenus ad pondus &longs;u&longs;tinendum perti­<lb/>net, vtrum portantes &longs;int &longs;tatura pares velne. </s> <s id="s.001776">Ducatur e­<lb/>nim horizonti æquidi&longs;tans GB, &longs;ecans perpendicularem <lb/>CF in I. <!-- KEEP S--></s> <s id="s.001777">Quoniam igitur AG æquidi&longs;tans e&longs;t ip&longs;i CI erit <lb/>vt AC ad CB per 4. &longs;exti elem, ita GI ad IB. <!-- KEEP S--></s> <s id="s.001778">Sunt ergo GI, <lb/>IB inter &longs;e æquales. </s> <s id="s.001779">Intelligatur itaque pondus H, <expan abbr="&longs;olutū">&longs;olutum</expan> <lb/>à puncto C appen&longs;um e&longs;&longs;e libere ex puncto I, hoc e&longs;t, ex <lb/>medio vectis GB, æqualiter ergo diui&longs;um erit pondus in­<lb/>ter portantes, licet alter procerior, alter vero &longs;tatura pu­<lb/>milior, quod fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.001780">Si autem pondus ita vecti alligatum &longs;it vt libere non <lb/>pendeat, vecte ex vna parte eleuato, ex altera vero de­<lb/>pre&longs;&longs;o, grauitatis centrum ad eam partem verget quæ <lb/>magis ab horizonte attollitur, & ad eam ip&longs;am partem <lb/>vectis à pondere ad &longs;u&longs;tinentem fit breuior. </s> </p> <p type="main"> <s id="s.001781">E&longs;to enim vectis AB, cuius medium C, pondus vecti <lb/>in C alligatum CFG, cuius grauitatis centrum H eorum <lb/>qui portant procerior AB, humilior BE, horizontis <expan abbr="planū">planum</expan> <lb/>DE. <!-- KEEP S--></s> <s id="s.001782">Demittatur per centrum H horizonti perpendicu­<lb/>laris IHK, &longs;ecans vectem quidem in I, horizontis vero pla-<pb xlink:href="007/01/185.jpg"/><figure id="id.007.01.185.1.jpg" xlink:href="007/01/185/1.jpg"/><lb/>num in K. <!-- KEEP S--></s> <s id="s.001783">Po&longs;t hæc intelligatur pon­<lb/>dus &longs;olutum quidem à puncto C, ap­<lb/>pen&longs;um vero ex puncto I. <!-- KEEP S--></s> <s id="s.001784">Stabit igitur <lb/>ex definitione centri grauitatis nec &longs;i­<lb/>tu &longs;uo mouebitur. </s> <s id="s.001785">Dico autem par­<lb/>tem AI ip&longs;a IB e&longs;&longs;e breuiorem, hoc e&longs;t, <lb/>punctum I cadere inter C & A. <!-- KEEP S--></s> <s id="s.001786">Si e­<lb/>nim non cadat, vel cadet in C, aut in­<lb/>ter C & B, cadat autem &longs;i fieri pote&longs;t <lb/>in C. <!-- KEEP S--></s> <s id="s.001787">Erit igitur CHK horizonti perpendicularis, &longs;ed ei­<lb/>dem perpendicularis AD. <!-- KEEP S--></s> <s id="s.001788">Erunt igitur BCK BAD anguli <lb/>inter &longs;e æquales, &longs;ed ip&longs;i BAD angulo æqualis e&longs;t CIH, <lb/>quare & BCH ip&longs;i CIH æqualis erit. </s> <s id="s.001789">Producto igitur la­<lb/>tere IC trianguli ICH erit exterior angulus æqualis inte­<lb/>riori ex oppo&longs;ito, quod e&longs;t ab&longs;urdum. </s> <s id="s.001790">non ergo I cadet in <lb/>C. <!-- KEEP S--></s> <s id="s.001791">Eadem autem ratione mon&longs;trabitur non cadere inter <lb/>CB, cadet ergo inter CA, & ideo minor AI ip&longs;a IB. <!-- KEEP S--></s> <s id="s.001792">Itaque <lb/>vt &longs;e habet BI ad BA, ita potentia in A ad pondus in I, &longs;ed <lb/>maiorem proportionem habet BI ad BA, quam IA ad AB. <lb/><!-- KEEP S--></s> <s id="s.001793">Ergo minor potentia requiretur in B quam in A, & &longs;ane <lb/>pars IB re&longs;pondet potentiæ &longs;u&longs;tinenti in A, at IA potentiæ <lb/>&longs;u&longs;tinenti in B, minor e&longs;t autem AI ip&longs;a IB, ergo maior po­<lb/>tentia requiritur in B, quam in A, quod fuerat demon­<lb/>&longs;trandum. </s> </p> <p type="main"> <s id="s.001794">Hoc item concludetur, &longs;i portantes &longs;tatura quidem <lb/>pares fuerint, &longs;ed per planum ambulent horizonti accliue <lb/>aut decliue. </s> <s id="s.001795">Si enim pondus libere pendeat, vectis <expan abbr="partiū">partium</expan> <lb/>proportio non mutabitur; &longs;r autem libere non pendeat, <lb/>is magis laborabit qui in a&longs;cen&longs;u præibit, minus vero qui <lb/>in de&longs;cen&longs;u. </s> </p> <p type="main"> <s id="s.001796">Hinc quoque Carrucarum ratio pendet, quæ dupli­<lb/>ci manubrio vnica rota vulgo &longs;unt in v&longs;u, pro vecte enim <lb/>habentur, cuius fulcimentum ad contactum plani & ro­<pb xlink:href="007/01/186.jpg"/>tæ; potentiæ vero ad extremitatem duplicis manubrij. <lb/></s> <s id="s.001797">Reducitur enim ad idem genus vectis, in quo pondus in­<lb/>ter fulcimentum e&longs;t & potentiam. </s> <s id="s.001798">quo igitur minor fue­<lb/>rit proportio partis vectis quæ à centro grauitatis ad i­<lb/>p&longs;um fulcimentum, ad totum vectem eo facilius pondus <lb/>eleuabitur. </s> </p> <p type="main"> <s id="s.001799">Cur autem difficilime hæ per accliue horizonti pla­<lb/>num pellantur, duplici fit de cau&longs;&longs;a, tum quia grauitatis <lb/>centrum ad ip&longs;um portantem &longs;eu pellentem vergit, & id­<lb/>eo pars quæ a fulcimento ad centrum grauitatis ponderis <lb/>fit maior, tum etiam quoniam ip&longs;um graue contra &longs;ui na­<lb/>turam &longs;ur&longs;us pellitur ferturque. </s> </p> <p type="main"> <s id="s.001800">Quærere ad hæc qui&longs;piam po&longs;&longs;et, Cur Baiuli ma­<lb/>gna ferentes pondera, curui in cedant? </s> <s id="s.001801">Dixerit autem ali­<lb/>quis, ponderis grauitate eos deprimentis id fieri. </s> <s id="s.001802">Nos au­<lb/>tem duplici item de cau&longs;&longs;a id fieri putamus, tum ea quam <lb/>con&longs;iderauimus, tum etiam alia, nempe vt grauitatis cen­<lb/>trum ip&longs;ius ponderis quod &longs;u&longs;tinent, in perpendiculari <lb/>collocent, ne &longs;i extra ponatur is qui fert à centro extra <lb/>fulcimentum po&longs;ito, ad eam partem ad quam vergit tra­<lb/>hatur, & pondere ip&longs;o opprimatur. </s> </p> <p type="main"> <s id="s.001803">Eadem de cau&longs;&longs;a fit quoque vt ij qui magna ponde­<lb/>ra &longs;ini&longs;tro ferunt humero, in dextram partem inclinentur, <lb/>qui vero dextro, contrario modo &longs;e habeant, æquatur e­<lb/>nim pondus eo pacto, & grauitatis centrum in ip&longs;a per­<lb/>pendiculari collocatur. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001804">QVÆSTIO XXX.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001805"><emph type="italics"/>Cur a&longs;&longs;urgentes omnes fœmori tibiam ad acutum angulum con&longs;ti­<lb/>tuamus & pectori thoraciue &longs;imiliter fœmur, quod nî fiat <lb/>haudquaquam &longs;urgere poterunt?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001806">Ait Philo&longs;ophus, forte id fieri, quod æqualitas &longs;it o­<lb/>mnino quietis cau&longs;&longs;a, rectum vero angulum quietis <pb xlink:href="007/01/187.jpg"/>angulum e&longs;&longs;e, & &longs;tationem facere, nec alia de cau&longs;&longs;a &longs;tan­<lb/>tem ip&longs;i terræ e&longs;&longs;e perpendicularem, & ideo caput & pe­<lb/>des in eadem linea habere, &longs;edentem vero non item. </s> <s id="s.001807"><expan abbr="Tūc">Tunc</expan> <lb/>autem à &longs;e&longs;&longs;ione &longs;urrectionem fieri, cum caput & pedes in <lb/>vna linea collocantur, quod &longs;ane fit cum pectus & crura <lb/>acutum cum ip&longs;o fœmore angulum faciunt. </s> </p> <figure id="id.007.01.187.1.jpg" xlink:href="007/01/187/1.jpg"/> <p type="main"> <s id="s.001808">E&longs;to enim &longs;tans AB hori­<lb/>zonti IBK perpendicularis, cù­<lb/>ius caput A, pedes vero B, &longs;edeat <lb/>modo &longs;itque eius cum capite <lb/>Thorax CD, fœmur DE, crura <lb/>EF, &longs;intque CDE, DEF anguli <lb/>recti, quibus ita con&longs;titutis non <lb/>&longs;unt in eadem linea caput C & <lb/>pedes F. <!-- KEEP S--></s> <s id="s.001809">Surgere itaque non po­<lb/>terit &longs;edens, propterea quod <lb/>partes omnes corporìs non &longs;int <lb/>horizonti perpendiculares. </s> <s id="s.001810">Ad <lb/>hoc autem vt &longs;urrectio fiat, nece&longs;&longs;e e&longs;t vt &longs;edens retrahat <lb/>quidem pedes in H, & pectore in clinato acutum cum fœ­<lb/>more angulum con&longs;tituat GDE, quo ca&longs;u fient in eadem <lb/>recta linea, eaque horizonti perpendiculari caput in G, <lb/>& pedes in H, ex cuius &longs;itus natura commoda fiet ab ip&longs;o <lb/>&longs;edente &longs;urrectio. </s> <s id="s.001811">Hæc fere, licet alijs ab eo verbis expli­<lb/>cata, ip&longs;ius e&longs;t Philo&longs;ophi &longs;ententia; quæ licet vera &longs;it, non <lb/>tamen ex proprijs, hoc e&longs;t, Mechanicis principijs e&longs;t peti­<lb/>ta. </s> <s id="s.001812">quod quidem nos facere conabimur. </s> </p> <p type="main"> <s id="s.001813">Dicimus autem primo, &longs;edentem non ideo quie&longs;ce­<lb/>re, vt &longs;entit Ari&longs;toteles, quod rectus angulus quietis &longs;it <lb/>cau&longs;&longs;a, &longs;ed propterea quod eius thoracis tum etiam fœ­<lb/>morum pondus ab ip&longs;a &longs;ede &longs;u&longs;tineantur; crura vero & <lb/>pedes ideo non laborent, quod partim &longs;u&longs;pen&longs;a &longs;int, par­<lb/>tim &longs;olo ip&longs;i innitantur. </s> <s id="s.001814">Quare cum corpus totum nec &longs;e <pb xlink:href="007/01/188.jpg"/>&longs;u&longs;tineat, nec à pedibus &longs;u&longs;tineatur, fit quies & la&longs;&longs;itudi­<lb/>nis alleuatio. </s> <s id="s.001815">Natura autem ideo commodam hominibus <lb/>&longs;e&longs;&longs;ionem facere volui&longs;&longs;e inde apparet, quod clunes, qui­<lb/>bus tota &longs;uperior pars, & grauior nititur, carno&longs;am fece­<lb/>rit, & ceruicalis cuiu&longs;dam in&longs;tar mollem & facilem. </s> <s id="s.001816">Sed <lb/>nos ad quæ&longs;tionem. </s> </p> <figure id="id.007.01.188.1.jpg" xlink:href="007/01/188/1.jpg"/> <p type="main"> <s id="s.001817">E&longs;to enim &longs;tans AB, cuius caput A, <lb/>Thorax AC, fœmora CD, crura DB, pe­<lb/>des vero B, centrum vero grauitatis in i­<lb/>p&longs;o Thorace E. <!-- KEEP S--></s> <s id="s.001818">Modo &longs;edeat, &longs;itque ca­<lb/>put in F, Thorax FG, fœmora GH, crura <lb/>HI, pedes I, grauitatis vero centrum vbi <lb/>K. <!-- KEEP S--></s> <s id="s.001819">Producatur recta FG in L, &longs;itque FL <lb/>horizonti perpendicularis. </s> <s id="s.001820">Centrum er­<lb/>go grauitatis K fulcitur puncto G, hoc e&longs;t, <lb/>puncto L, in quo po&longs;teriores pedes ip&longs;ius <lb/>&longs;ed is &longs;olo hærent. </s> <s id="s.001821">efficit autem &longs;edens <lb/>duos rectos angulos FGH, GHI. <!-- KEEP S--></s> <s id="s.001822">Rebus <lb/>igitur ita di&longs;po&longs;itis &longs;eruatis rectis angulis, non fiet &longs;urre­<lb/>ctio, & id quidem non ideo quod, vt ait Philo&longs;ophus, æ­<lb/>qualitas & rectitudo angulorum quietis &longs;it cau&longs;&longs;a, &longs;ed <lb/>propterea quod centro grauitatis extra pedum <expan abbr="fulcimē-tum">fulcimen­<lb/>tum</expan> con&longs;tituto, non habet centrum &longs;tabilem locum cui in <lb/>actu &longs;urrectionis hæreat, & fulciatur, vnde fit vt &longs;i &longs;edenti <lb/>&longs;ubtrahatur &longs;edes remoto prohibente, &longs;edens pror&longs;us cor­<lb/>ruat. </s> <s id="s.001823">Modo retrahat qui &longs;edet crura, & pedes ponat in M, <lb/>à puncto autem M, horizonti perpendicularis erigatur <lb/>MN. erit ergo fulcimentum in M, &longs;ed adhuc &longs;urgere non <lb/>poterit, centro grauitatis adhuc extra lineam MN, quæ <lb/>per fulcimentum e&longs;t, con&longs;tituto. </s> <s id="s.001824">Reclinetur autem pe­<lb/>ctus ad anteriora, & cum fœmore acutum angulum faciat <lb/>&longs;itque vbi GO, erit igitur grauitatis centrum vbi P, hoc <lb/>e&longs;t, in ip&longs;a perpendiculari NM, fiet igitur inde commoda <pb xlink:href="007/01/189.jpg"/>&longs;urrectio, propterea quod in eadem linea facta &longs;int, graui­<lb/>tatis centrum P, & fulcimentum ip&longs;um M. <!-- KEEP S--></s> <s id="s.001825">Acutum vero <lb/>angulum in &longs;urrectione nece&longs;&longs;arium e&longs;&longs;e clare patet, non <lb/>autem effectus ip&longs;ius e&longs;&longs;e cau&longs;&longs;am, vt videtur &longs;en&longs;i&longs;&longs;e Ari­<lb/>&longs;toteles; nisi dicamus, cau&longs;&longs;am e&longs;&longs;e cau&longs;&longs;æ, &longs;iquidem acuti <lb/>qui fiunt anguli centrum & pedes in eadem linea collo­<lb/>cant, quicquid tamen &longs;it, nos ideo &longs;urrectionem fieri dici­<lb/>mus, quod immutatis angulis centrum grauitatis &longs;upra <lb/>fulcimentum, fulcimento vero &longs;ub ip&longs;o grauitatis centro <lb/>collocetur, & hæc e&longs;t cau&longs;&longs;a proxima. </s> <s id="s.001826">Hæc nos ad Ari&longs;to­<lb/>telem. </s> <s id="s.001827">Modo qua&longs;dam alias quæ&longs;tiones, nec inutiles &longs;ed <lb/>& eas non iniucundas quoque proponemus. </s> </p> <p type="main"> <s id="s.001828">Primum igitur quærimus, Cur hominum & cætero­<lb/>rum animalium, quæ aliquando erecto corpore incedunt, <lb/>pedes non quidem breues &longs;int & rotundi, &longs;ed longiores <lb/>potius, & in inferiorem partem porrecti? </s> <s id="s.001829">Item cur magis <lb/>ad digitos quam ad calcaneum porrigantur? </s> </p> <figure id="id.007.01.189.1.jpg" xlink:href="007/01/189/1.jpg"/> <p type="main"> <s id="s.001830">E&longs;to homo animalue quodpiam &longs;tans <lb/>AB, cuius pes CD, pedis pars quæ ad digitos <lb/>BC. quae vero ad calcaneum BD fœmoris ver­<lb/>tebra E, centrum vero grauitatis ip&longs;ius cor­<lb/>poris F. <!-- KEEP S--></s> <s id="s.001831">Primum igitur &longs;tatuendum e&longs;t, ho­<lb/>minem & cætera fere animalia à Natura fa­<lb/>cta e&longs;&longs;e vt ad anteriora moueantur, & ideo o­<lb/>mnes fere quod in &longs;enioribus manife&longs;te ap­<lb/>paret, ad anteriora ex ip&longs;a corporis di&longs;po&longs;i­<lb/>tione vergant. </s> <s id="s.001832">Itaque dum qui &longs;tat horizon­<lb/>ti pror&longs;us e&longs;t perpendicularis, grauitatis centrum F in ip&longs;a <lb/>perpendiculari con&longs;tituitur quæ ad mundi centrum AB, <lb/>& ideo corporis moles pondu&longs;que fulcitur puncto B. <!-- KEEP S--></s> <s id="s.001833">Mo­<lb/>do fiat ex vertebra E thoracis AE, inclinatio in anteriora, <lb/>in GE & grauitatis centrum D diluetur in H, & per H per­<lb/>pendicularis demittatur HI, non erit ** extra pedis ful­<pb xlink:href="007/01/190.jpg"/>cimentum BC. <!-- KEEP S--></s> <s id="s.001834">Stabit ergo qui ita inclinatur, nec corruet: <lb/>&longs;i autem adhuc propendeat magis, fiatque in KE, centro <lb/>grauitatis con&longs;tituto in M, ducatur per M perpendicula­<lb/>ris ML, quare quoniam linea ML extra pedis fulcimen­<lb/>tum cadit, corruet qui eo pacto inclinatur nec &longs;u&longs;tinebi­<lb/>tur. </s> <s id="s.001835">Cur igitur natura animalibus quae erecto corpore am­<lb/>balant, pedes in anteriora porrectos fecerit, hinc clare <lb/>patet. </s> </p> <p type="main"> <s id="s.001836">Hinc etiam ceu con&longs;ectarium habemus, cur homi­<lb/>nes &longs;i impellantur, magis ad ca&longs;um in po&longs;teriora quam in <lb/>anteriora &longs;int proni. </s> <s id="s.001837">Nec non etiam cur &longs;imiæ, vr&longs;i, & &longs;i <lb/>quæ cætera eiu&longs;modi animalia diutius erecto corpore <lb/>ambulare nequeant, nempe ideo quod eorum corporum <lb/>moles valde in anteriora propendeat, nec ita commodo, <lb/>vt humanis euenit corporibus, pedum ip&longs;orum ba&longs;ibus <lb/>fulciantur. </s> </p> <p type="main"> <s id="s.001838">Quærere item haud importune po&longs;&longs;umus, Cur gral­<lb/>latores non &longs;tent erecti, ni&longs;i a&longs;&longs;idue moueantur? </s> <s id="s.001839">Solutio <lb/>facilis. </s> <s id="s.001840">grallæ etenim duobus tantum punctis &longs;olum tan­<lb/>gunt, nec porrecti beneficio, quod ambulantibus accidit, <lb/>vti po&longs;&longs;unt. </s> <s id="s.001841">quamobrem grauitatis centrum fit extra ful­<lb/>cimentum, & ideo coguntur grallatores a&longs;&longs;iduo motu <lb/>grauitatis centro fulcimentum &longs;upponere, quod dum fit, <lb/>à ca&longs;u prohibentur. </s> </p> <p type="main"> <s id="s.001842">Pote&longs;t autem id quod fulcitur, tripliciter fulciri, <expan abbr="nē-peaut">nem­<lb/>pe aut</expan> puncto, aut linea, aut &longs;uperficie. </s> </p> <p type="main"> <s id="s.001843">Quod puncto fulcitur, nulla reimpediente ad quam­<lb/>uis partem cadere pote&longs;t, centrum &longs;iquidem, motus, pun­<lb/>ctum e&longs;t. </s> </p> <p type="main"> <s id="s.001844">Quod linea fulcitur ad duas tantum partes, ea&longs;que <lb/>oppo&longs;itas, habet ca&longs;um. </s> <s id="s.001845">&longs;it illud &longs;uperficies, corpu&longs;ue in <lb/>latus con&longs;titutum. </s> </p> <pb xlink:href="007/01/191.jpg"/> <figure id="id.007.01.191.1.jpg" xlink:href="007/01/191/1.jpg"/> <p type="main"> <s id="s.001846">E&longs;to horizontis pla­<lb/>num ABCD, cui ad re­<lb/>ctos angulos in&longs;i&longs;tat &longs;u­<lb/>perficies EFGH, &longs;ecun­<lb/>dum latus FG. <!-- KEEP S--></s> <s id="s.001847">Sit autem <lb/>ip&longs;ius &longs;uperficiei grauita­<lb/>tis centrum I. à quo ad <lb/>horizontis planum per­<lb/>pendicularis demittatur IK. <!-- REMOVE S-->Cadet autem in lineam FG. <lb/>per propo&longs;. </s> <s id="s.001848">38. vndecimi elem. </s> <s id="s.001849">& anguli IKG IKF recti e­<lb/>runt. </s> <s id="s.001850">Itaque &longs;uperficie EFGH circa lineam FKG ceu cir­<lb/>ca axem mota punctum I peripheriam de&longs;cribet LIM, & <lb/>&longs;iquidem cadat ad partes CD, grauitatis centrum erit vbi <lb/>M. <!-- KEEP S--></s> <s id="s.001851">Si vero ad partes AB, fiet vbi L. <!-- KEEP S--></s> <s id="s.001852">Sunt autem LKM <expan abbr="pū-cta">pun­<lb/>cta</expan> in recta LKM, quæ quidem communis &longs;ectio e&longs;t plani <lb/>horizontis, & plani per IKLM, tran&longs;euntis. </s> </p> <figure id="id.007.01.191.2.jpg" xlink:href="007/01/191/2.jpg"/> <p type="main"> <s id="s.001853">Idem quoque de cor­<lb/>pore dicimus in latus col­<lb/>locato. </s> <s id="s.001854">E&longs;to enim cubus <lb/>LO, cuius grauitatis cen­<lb/>trum R, latus vero quo ful­<lb/>citur, NO, Si enim ita col­<lb/>locetur, vt interna &longs;uperfi­<lb/>cies LNOQ ad rectos an­<lb/>gulos horizonti &longs;it con&longs;ti­<lb/>tuta, demi&longs;&longs;a perpendicu­<lb/>laris à puncto R, ea det in S, in ip&longs;a linea NSO. <!-- KEEP S--></s> <s id="s.001855">Cadente i­<lb/>gitur corpore fiet motus circa lineam NO, centro graui­<lb/>tatis interim peripheriam TRV. de&longs;cribente. </s> </p> <p type="main"> <s id="s.001856">Hinc animaduertere licet, Cur prouidi&longs;&longs;ima Natu­<lb/>ra nulli animantium vnicum dederit pedem, &longs;ed aut qua­<lb/>ternos, aut &longs;altem binos, & binos quidem ip&longs;os virtute <lb/>quaternos, &longs;iquidem in quolibet animantium bipedum <pb xlink:href="007/01/192.jpg"/>pede duo &longs;altem puncta con&longs;iderantur, quibus ip&longs;um ani-<lb/>mal fulcitur. </s> </p> <figure id="id.007.01.192.1.jpg" xlink:href="007/01/192/1.jpg"/> <p type="main"> <s id="s.001857">Sint enim humani pedis ve­<lb/>&longs;tigia A, B, C, D, in vtroque igitur <lb/>duo puncta con&longs;iderantur, A, B, <lb/>C, D, illa quidem ad digitos, hæc <lb/>autem ad calcaneum. </s> <s id="s.001858">Idem quo­<lb/>que in auium pedibus ob&longs;erua­<lb/>tur, ex quibus concludimus, bi­<lb/>pedum omnium fulcimentum e&longs;­<lb/>&longs;e quadruplex. </s> <s id="s.001859">Porro quadrupe­<lb/>dia eo quod tota corporis mole <lb/>ad in feriora vergant, quatuor ful­<lb/>cimenta, eaque di&longs;tincta, & commode ab inuicem remo­<lb/>ta eademmet Natura præparauit. </s> </p> <p type="main"> <s id="s.001860">Eadem quoque in artificialibus con&longs;ideramus. </s> <s id="s.001861">Sit <lb/>enim vas quodpiam ABC, cuius pes vnicus, i&longs;que rotun­<lb/>dus BC, grauitatis vero centrum D. <!-- KEEP S--></s> <s id="s.001862">Quoniam igitur in <lb/>pedis ip&longs;ius peripheria, infinita puncta intelligantur, dici <lb/>quodammodo pote&longs;t vas ip&longs;um infinitis fere punctis, licet <lb/><figure id="id.007.01.192.2.jpg" xlink:href="007/01/192/2.jpg"/><lb/>pes vnicus &longs;it, &longs;u&longs;tineri. </s> <s id="s.001863">Non­<lb/>nulla autem corpora artifi­<lb/>cialia. </s> <s id="s.001864">quatuor pedibus &longs;u­<lb/>&longs;tinentur, vt men&longs;æ <expan abbr="quædã">quædam</expan>, <lb/>nonnulla etiam tribus, vt <lb/>tripodes, qui nomen ab ip&longs;o <lb/>pedum numero &longs;ortiuntur. <lb/></s> <s id="s.001865">Sit enim triangulum EFG, <lb/>cuius centrum grauitatis H, <lb/>nitatur autem tribus pun­<lb/>ctis I, K, L, &longs;tabit igitur. </s> <s id="s.001866">Si <lb/>autem duobus tantum; non &longs;tabit. </s> <s id="s.001867">ducta enim IK &longs;i pun­<lb/>ctis tantum IK innitatur, con&longs;tituto grauitatis centro <pb xlink:href="007/01/193.jpg"/>extra fulcimentum IK, verget cedens ver&longs;is partes, L, Si <lb/>autem innitatur punctis IL, cadet ad partes K. <!-- KEEP S--></s> <s id="s.001868">Sivero ip&longs;is <lb/>KL, cadet ad partes I.Ex quibus apparet, inanimata cor­<lb/>pora aut vnico pede plurium virtutem habente, aut &longs;al­<lb/>tem tribus actu, vt &longs;u&longs;tineantur, indigere. </s> </p> <p type="main"> <s id="s.001869">Hinc etiam patet, cur &longs;enes, imbecilles, curui, & pe­<lb/>dibus capti, baculi baculorumue fulcimento egeant, ete­<lb/>nim cum hi debiles &longs;int, & in anteriorem partem magno­<lb/>pere propendeant, ne grauitatis centrum extra fulcimen­<lb/>tum fiat, baculo vel baculis indigent, quibus centrum i­<lb/>p&longs;um fulciatur. </s> </p> <p type="main"> <s id="s.001870">Cæterum cur duplici genu ingeniculati difficile in <lb/>eo &longs;itu permaneant, ea cau&longs;&longs;a e&longs;t, quod grauitatis centrum <lb/>in thorace con&longs;titutum, duobus genibus fulciatur, eo&longs;­<lb/>que premat. </s> <s id="s.001871">quæ quidem genua eo quod natura apta na­<lb/>ta non &longs;int, veluti pedes, ad &longs;u&longs;tinendam corporis molem <lb/>laborant, idque eo magis, quod cum o&longs;&longs;ea &longs;int, cutem in­<lb/>ter o&longs;&longs;ium & plani duritiem con&longs;titutam, accidit arctari, <lb/>& ideo dolorem & mole&longs;tiam ingeniculatis facere. </s> </p> <p type="main"> <s id="s.001872">Si autem vnico tantum genu qui&longs;piam nitatur, dif­<lb/>ficultatem &longs;entiet longe minorem. </s> <s id="s.001873">Triplici enim fulci­<lb/><figure id="id.007.01.193.1.jpg" xlink:href="007/01/193/1.jpg"/><lb/>mento eo ca&longs;u ingeniculatus <lb/>fulcitur. </s> <s id="s.001874">Sit enim ingenicula­<lb/>tus ABCDE, cuius grauitatis <lb/>centrum F. dextrum vero ge­<lb/>nu, cui nititur D, &longs;ini&longs;trum ve­<lb/>ro, quod eleuatur B. <!-- KEEP S--></s> <s id="s.001875">Tribus ergo fulcimentis ingenicula­<lb/>tus vt diximus, &longs;u&longs;tinetur, CDE. <!-- KEEP S--></s> <s id="s.001876">Diuiditur itaque pondus <lb/>in tres partes, & ideo &longs;ingulæ minus fatigantur. </s> <s id="s.001877">Magis ta­<lb/>men laborat punctum D, vtpote illud, cui ad perpendicu­<lb/>lum F grauitatis centrum innititur. </s> </p> <p type="main"> <s id="s.001878">Vtique illud quoque mirabile e&longs;t, Aues dormientes <lb/>vnico tantum pede fulciri, & quod magis mirum e&longs;t, dor­<pb xlink:href="007/01/194.jpg"/>mientes po&longs;&longs;e, quod vel ip&longs;is vigilantibus e&longs;t difficile. </s> <s id="s.001879">Cur <lb/>id Natura docente faciant, eam puto e&longs;&longs;e cau&longs;&longs;am, quod <lb/>dum dormiunt, caput &longs;ini&longs;træ alæ, vt naturali calore iu­<lb/>uentur, &longs;upponunt, quapropter ad eam partem declinan­<lb/>tes, vt interim æquilibrium faciant, pedem &longs;ubleuant, & <lb/>eo ca&longs;u ceu inutilem retrahunt atque &longs;u&longs;pendunt: addita <lb/>item alia cau&longs;&longs;a, nempe vt pedem ip&longs;um dormientes nati­<lb/>uo calore confoueant. </s> </p> <p type="main"> <s id="s.001880">Quæritur etiam, Cur ij qui inclinantur, vt <expan abbr="rē">rem</expan> quam­<lb/>piam à &longs;olo &longs;u&longs;tollant, alterum crurium ad anteriora, <expan abbr="nē-pever&longs;us">nem­<lb/>pe ver&longs;us</expan> manum ip&longs;am, quam porrigunt, extendant? </s> </p> <figure id="id.007.01.194.1.jpg" xlink:href="007/01/194/1.jpg"/> <p type="main"> <s id="s.001881">E&longs;to enim qui&longs;piam ABCD, <lb/>cuius crura BC, BD, grauitatis <lb/>centrum E, velit autem quippiam <lb/>à &longs;olo tollere quod &longs;it in F. &longs;it per­<lb/>pendicularis, quæ per grauitatis <lb/>centrum GEH. </s> <s id="s.001882">Dum igitur ad <lb/>anteriora ínclinatur, centrum a­<lb/>mouet à perpendiculari, quam­<lb/>obrem docente Natura, crus BC <lb/>ad centrum ip&longs;um fulciendum. <lb/></s> <s id="s.001883">ad anteriora, hoc e&longs;t, ver&longs;us rem <lb/>&longs;u&longs;tollendam porrigitur. </s> </p> <p type="main"> <s id="s.001884">Huius quoque &longs;peculationis e&longs;t inue&longs;tigare, Cur <lb/>quadrupedia dum gradiuntur, pedes diametraliter mo­<lb/>ueant. </s> <s id="s.001885">Cuius rei verba fecit ip&longs;e quoque Philo&longs;ophus lib. <lb/> de animalium ince&longs;&longs;u cap. 12. </s> <s id="s.001886">Nos autem ad maiorem de­<lb/>clarationem, quod ip&longs;e Phy&longs;icis principijs fecit, mecha­<lb/>nicis demon&longs;trabimus. </s> </p> <p type="main"> <s id="s.001887">Sint duæ in plano parallelæ AB, CD, in quibus qua­<lb/>drupedis pedes E, F, B, D, quorum EF, anteriores, BD vero <lb/>po&longs;teriores. </s> <s id="s.001888">iungantur BDEF, eritque EBDF parallelo­<lb/>grammum altera parte longius, cuius diametri ducantur <pb xlink:href="007/01/195.jpg"/><figure id="id.007.01.195.1.jpg" xlink:href="007/01/195/1.jpg"/><lb/>ED, BF, &longs;ecantes &longs;e&longs;e in G, vbi & grauitatis <lb/>centrum. </s> <s id="s.001889">Moto igitur po&longs;teriori &longs;ini&longs;tro pe­<lb/>de B in K, &longs;i anteriorem E, eodem tempore <lb/>moueret in I, &longs;tantibus interim DF, ceu ful­<lb/>cimentis, centrum G extra fulcimenta fieret <lb/>ad partes BE. <!-- KEEP S--></s> <s id="s.001890">Caderet igitur ad partes BE. <!-- KEEP S--></s> <s id="s.001891">Si <lb/>autem eodem tempore moueret dextros eo­<lb/>dem pacto centrum extra fulcimenta po&longs;i­<lb/>tum caderet ad partes ip&longs;as DF. <!-- KEEP S--></s> <s id="s.001892">Si autem <lb/>moto pede B in K, & eodem tempore F in L, <lb/>& D in H, E, in I, centrum erit in diametris HI, KL, hoc <lb/>e&longs;t, vbi M, fultum quidem ab ip&longs;is pedibus K, L, H, I. <!-- KEEP S--></s> <s id="s.001893">Hoc <lb/>igitur pacto transfertur vici&longs;&longs;im cum grauitatis centro &longs;i­<lb/>mul translatis fulcimentis &longs;e&longs;e diametraliter re&longs;ponden­<lb/>tibus; quod vtique demon&longs;trandum fuerat. </s> </p> <p type="main"> <s id="s.001894">Sane & bipedia quoque alternatim gradiendo gra­<lb/>uitatis centrum transferunt. </s> <s id="s.001895">Dum enim dextrum crus e­<lb/>leuatur, centrum &longs;ini&longs;tro fulcitur, & econtra. </s> </p> <p type="main"> <s id="s.001896">Naturalia i&longs;thæc &longs;unt; in artificialibus autem quæri <lb/>po&longs;&longs;et, Cur Architecti, Arcium muros non ad perpendi­<lb/>culum erectos, &longs;ed intror&longs;um inclinatos con&longs;tituant? </s> </p> <figure id="id.007.01.195.2.jpg" xlink:href="007/01/195/2.jpg"/> <p type="main"> <s id="s.001897">Vtique hoc faciunt, vt minus <lb/>&longs;int ad ruinam proni. </s> <s id="s.001898">E&longs;to enim <lb/>murus ad interiorem partem ver­<lb/>gens ABCD, Cuius grauitatis cen­<lb/>trum E ba&longs;is BC erigatur à puncto <lb/>B horizonti perpendicularis BF, & <lb/>ad eundem à centro grauitatis E <lb/>demittatur EM, tum BE iungatur. <lb/></s> <s id="s.001899">Po&longs;t hæc à puncto BG angulum. <lb/></s> <s id="s.001900">cum linea horizontis BK faciens recto maiorem. </s> <s id="s.001901">Ita que <lb/>murus hoc pacto con&longs;titutus ad interiorem partem &longs;uo <lb/>pondere vergit, cadere autem non pote&longs;t, vel quod viuæ <pb xlink:href="007/01/196.jpg"/>rupi, cui forte hæret, fulciatur, vel anti&longs;tatis, quos no­<lb/>&longs;trates &longs;perones & contra fortes appellant, innitatur. </s> <s id="s.001902">Sed <lb/>nec in anteriora corruet, quandoquidem ruinam factu­<lb/>ras, nece&longs;&longs;e e&longs;t vt grauitatis centrum &longs;ecum trahat in per­<lb/>pendiculari BF, & demum in eam quæ vltra perpendicu­<lb/>larem e&longs;t BG, facta nempe circa B, ceu circa centrum, <expan abbr="cō-uer&longs;ione">con­<lb/>uer&longs;ione</expan>. </s> <s id="s.001903">Moueatur autem & ex &longs;emidiametro BE cen­<lb/>tro B portio circuli de&longs;cribatur EH, quæ &longs;ecet BG in H, <lb/>& BF in I; Et quia EM &longs;emidiametro BK perpendicularis <lb/>per B, centrum non tran&longs;it, erit EM ip&longs;a BK, hoc e&longs;t, BI <lb/>brevior. </s> <s id="s.001904">Ab&longs;cindatur ex BI, ip&longs;i EM æqualis LB. </s> <s id="s.001905">Erit igi­<lb/>tur punctum L infra punctum I, hoc e&longs;t, ip&longs;o I, mundi cen­<lb/>tro propius. </s> <s id="s.001906">Nece&longs;&longs;e igitur erit ad hoc vt murus corruat, <lb/>centrum grauitatis E facta circa B, conuer&longs;ione aliquan­<lb/>do fieri in I, vt demum transferri po&longs;&longs;it in H, &longs;ed I remo­<lb/>tius e&longs;t à mundi centro ip&longs;is E, L, a&longs;cendet igitur graue <lb/>contra &longs;ui naturam ex E in I, at hoc e&longs;t impo&longs;&longs;ibile; quod <lb/>fuerat demon&longs;trandum. </s> </p> <p type="main"> <s id="s.001907">Ex his ij&longs;dem principijs alia &longs;oluitur quæ&longs;tio, Cur <lb/>&longs;cilicet Campanaria turris quæ Pi&longs;is vi&longs;itur, nec non alia <lb/>Bononiæ in foro prope A&longs;ellorum turrim, quam à nobili <lb/>olim Cari&longs;endorum familia ex&longs;tructam, Cari&longs;endam vo­<lb/>cant, cuius meminit & Dantes Poeta &longs;ummus in &longs;ua Co­<lb/>mœdia. </s> <s id="s.001908">Propendet autem hæc in latus, & ita propendet <lb/>vt perpendicularis, quæ à &longs;ummo inclinatæ partis in &longs;o­<lb/>lum demittitur, longe cadat ab ip&longs;a, cui nititur, ba&longs;i, quod <lb/>&longs;ane mirabile videtur, muros nempe, in ruinam pronos, <lb/>ruinam non facere. </s> </p> <p type="main"> <s id="s.001909">E&longs;to enim turris ABCD, ba&longs;i fulta BC, horizontis <lb/>planum BCF latera AB, DC, centrum vero grauitatis to­<lb/>tius molis E. <!-- KEEP S--></s> <s id="s.001910">Propendeat autem ad partes DC ex angulo <lb/>DCF. <!-- KEEP S--></s> <s id="s.001911">Ita autem con&longs;tituta intelligatur vt perpendicula­<lb/>ris ab A, in planum horizontis demi&longs;&longs;a per grauitatis cen-<pb xlink:href="007/01/197.jpg"/><figure id="id.007.01.197.1.jpg" xlink:href="007/01/197/1.jpg"/><lb/>trum E extra ba&longs;im BC, non cadat, <lb/>cadat autem in C. <!-- KEEP S--></s> <s id="s.001912">Quoniam igitur <lb/>ABCD moles per E grauitatis cen­<lb/>trum diuiditur, in partes &longs;ecatur æ­<lb/>queponderantes, &longs;ed & centrum. <lb/></s> <s id="s.001913">grauitatis extra fulcimentum non <lb/>cadit, quare nec pars ACD, trahet <lb/>partem ABC, nec centrum extra <lb/>fulcimentum po&longs;itum locum petet <lb/>centro mundi viciniorem. </s> <s id="s.001914">Cur igitur Cari&longs;enda &longs;tet, & e­<lb/>gregia illa turris campanaria quæ Pi&longs;is prope &longs;ummum <lb/>Templum marmoribus præclare ex&longs;tructa videtur, licet <lb/>ruinam minentur, &longs;tent æternum, nec cadant, ex his quæ <lb/>con&longs;iderauimus, liquido patet. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001915">QVAESTIO XXXI<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001916"><emph type="italics"/>Cur facilius moueatur commotum quam manens, veluti currus <lb/>commotos citius agitant, quam moueri incipientes?<emph.end type="italics"/></s> </p> <p type="head"> <s id="s.001917"><emph type="italics"/>Hoc quæritur.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001918">Problema hoc e&longs;t mere Phy&longs;icum; verumtamen quo­<lb/>niam ad localem motum pertinet, de quo ip&longs;e quoque <lb/>Mechanicus agit, Hi&longs;ce quæ&longs;tionibus contemplatio hæc <lb/>inter&longs;eritur. </s> <s id="s.001919">Soluit autem Ari&longs;toteles inquiens, id forta&longs;­<lb/>&longs;e ea de cau&longs;&longs;a fieri, quod difficillimum &longs;it pondus moue­<lb/>re, quod in contrarium mouetur. </s> <s id="s.001920">Demit enim quippiam <lb/>de motoris potentia re&longs;i&longs;tens, licet mouens ip&longs;o moto &longs;it <lb/>longe potentius atque velocius. </s> <s id="s.001921">nece&longs;&longs;e enim e&longs;&longs;e id tar­<lb/>dius moueri quod repellitur. </s> <s id="s.001922">Hæc verba licet de ea po­<lb/>tentia dicta videantur, quæ rem motam in contrariam. <lb/></s> <s id="s.001923">partem repellit, nihilominus illi quoque aptantur quæ <lb/>rem immobilem à principio mouere conatur. </s> <s id="s.001924">e&longs;t enim re­<lb/>&longs;i&longs;tentia rei quæ à &longs;tatu ad motum transfertur ceu <expan abbr="quidã">quidam</expan> <pb xlink:href="007/01/198.jpg"/>contrarius motus. </s> <s id="s.001925">Contra autem accidit illi qui rem mo­<lb/>tam mouet in ip&longs;o motu: eo enim ca&longs;u mouens ab ip&longs;o rei <lb/>motu magnopere iuuatur, cooperatur enim motus moto­<lb/>ri, in ip&longs;am rem motam operanti. </s> <s id="s.001926">Auget autem res mota <lb/>quodammodo mouentis potentiam. </s> <s id="s.001927">quod enim à mouen­<lb/>te pateretur, ex &longs;e ip&longs;a agit res quæ mouetur. </s> </p> <figure id="id.007.01.198.1.jpg" xlink:href="007/01/198/1.jpg"/> <p type="main"> <s id="s.001928">E&longs;to horizontis pla­<lb/>num AB, cui moles quæ­<lb/>dam in&longs;i&longs;tat, CD. <!-- KEEP S--></s> <s id="s.001929">Modo <lb/>potentia quædam appli­<lb/>cetur vbi E, quæ molem in <lb/>anteriora propellat, id <lb/>e&longs;t, ver&longs;us B. Primum igitur, quoniam à quiete ad motum <lb/>fit tran&longs;itus, re&longs;i&longs;tit &longs;ua quiere corpus graue, potentiæ im­<lb/>pellenti, &longs;uperata demum re&longs;i&longs;tentia moles quæ moueri <lb/>cœpit, fertur in F & mouetur, quare potentia quæ à prin­<lb/>cipio re&longs;i&longs;tentiam rei non motæ &longs;uperauerat, pellendo <lb/>rem motam pergens facilius pellit: Duo enim &longs;unt quo­<lb/>dammodo motores, mouens videlicet ip&longs;e, & motus quo <lb/>res mota mouetur. </s> <s id="s.001930">facilius ergo pelletur ex F in G, quam <lb/>ex D in F, & ex G in B, quam ex F in G, & eo motus fiet in <lb/>progre&longs;&longs;u facilior atque in ip&longs;a velocitate velocior, quo <lb/>magis in ip&longs;a motione mouetur. </s> </p> <p type="main"> <s id="s.001931">Hinc &longs;oluitur ea quæ&longs;tio apud Phy&longs;icos difficillima, <lb/>Cur nempe in motu naturali velocitas v&longs;que augeatur; <lb/>etenim ibi Natura mouens e&longs;t, atque eadem in&longs;eparabilis <lb/>à remota, vrget igitur a&longs;&longs;idue, à principio quidem tar dius, <lb/>po&longs;t hæc autem ea quam diximus, de cau&longs;&longs;a v&longs;que & v&longs;que <lb/>velocius. </s> <s id="s.001932">Motus ergo fit in motu, qui motus cum &longs;emper à <lb/>motore, & motu ip&longs;o augeatur, cre&longs;cit ex progre&longs;&longs;u in im­<lb/>men&longs;um. </s> <s id="s.001933">Certe cau&longs;&longs;am velocitatis auctæ eam e&longs;&longs;e, quod <lb/>potentia mouens rem motam in motu ip&longs;o moueat, nemo <lb/>vt arbitror, inficias ibit, acquirit enim corpus motum <expan abbr="pō-dero&longs;itatem">pon-<pb xlink:href="007/01/199.jpg"/>dero&longs;itatem</expan> quandam accidentalem, quæ cum ex motu <lb/>perinde augeatur, ip&longs;um motum faciliorem, eoque velo­<lb/>ciorem facit. </s> <s id="s.001934">Di&longs;putat hæc & Simplicius lib. 7. Phy&longs;ic. <!-- REMOVE S-->c. <lb/><!-- REMOVE S-->11. Ari&longs;totelis de Natura libros exponens. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001935">QVAESTIO XXXII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001936"><emph type="italics"/>Quæritur hic, Cur ea quæ proijciuntur, ce&longs;&longs;ent <lb/>à latione?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001937">Hoc itidem problema e&longs;t mere Phy&longs;icum. <!-- KEEP S--></s> <s id="s.001938">Ad quod ea <lb/>pertinent quæ à Philo&longs;opho tractantur libro Natu­<lb/>ralium 8. & lib. 1. de Cœlo. <!-- KEEP S--></s> <s id="s.001939">Tres autem affert &longs;ubdubitan­<lb/>do rationes, An quia impellens de&longs;init potentia, vel pro­<lb/>pter retractionem, vel propter rei proiectæ in<expan abbr="clinationē">clinationem</expan>, <lb/>quando ea valentior fuerit quam proijcientis vires? </s> </p> <p type="main"> <s id="s.001940">Quicquid dicat Philo&longs;ophus, id vtique explorati&longs;­<lb/>&longs;imum e&longs;t. </s> <s id="s.001941">Proiecta ideo à motu ce&longs;&longs;are, propterea quod <lb/>impre&longs;&longs;io, cuius impetu & virtute feruntur, non &longs;it proie­<lb/>ctus quidem naturalis, &longs;ed mere accidentalis & violenta, <lb/>at nullum accidentale & violentum quodque, non natu­<lb/>rale e&longs;t, perpetuum e&longs;t. </s> <s id="s.001942">Ce&longs;&longs;at ergo accidentalis illa im­<lb/>pre&longs;&longs;io, eaque paullatim ce&longs;&longs;ante proiecti motus elan­<lb/>gue&longs;cit, donec quietem pror&longs;us adipi&longs;catur. </s> <s id="s.001943">Illud quoque <lb/>notamus, quod à multis vidimus non ob&longs;eruatum, nempe <lb/>violentum motum violentia præualente non differre à <lb/>naturali, & ideo tardiorem e&longs;&longs;e à principio po&longs;t hæc, in i­<lb/>p&longs;o motu fieri velociorem, remittente demum paullatim <lb/>impre&longs;&longs;a violentia, tardiorem, donec impetus, & cum im­<lb/>petu motus euane&longs;cat, & res ip&longs;a mota quietem adipi&longs;ca­<lb/>tur. </s> <s id="s.001944">Vnde etiam experientia docemur, ictum ex proiectis <lb/>violentius fieri, &longs;i fiat paullo remotior à principio, & tunc <lb/>demum e&longs;&longs;e innocenti&longs;&longs;imum, cum ibi fit, vbi proiectum <lb/>ex motu plene acqui&longs;ito, &longs;ummam adeptum e&longs;t velocita­<pb xlink:href="007/01/200.jpg"/>tem. </s> <s id="s.001945">Hinc videmus, vel pueros ip&longs;os, docente Natura <expan abbr="cū">cum</expan> <lb/>nuces, vel aliud quippiam, parieti alli&longs;um frangere <expan abbr="conã-tur">conan­<lb/>tur</expan>, à pariete moderato aliquo &longs;patio recedere. </s> <s id="s.001946">Si autem <lb/>eos interroges, cur id faciant, re&longs;pondebunt, vt inde ictus <lb/>valentius fiat atque efficacius. </s> <s id="s.001947">Eleganter ex Simplicij & <lb/>Alexandri Aphrodi&longs;ien&longs;is doctrina, quæ lucidi&longs;&longs;ima e&longs;t, <lb/>quæ&longs;tionem hanc in &longs;ua Paraphra&longs;i explicat Picolomi­<lb/>neus. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.001948">QVAESTIO XXXIII.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001949"><emph type="italics"/>Dubitatur, Cur proiecta moueantur, licet impellens à proiectis &longs;e­<lb/>paretur; vel vt verbis Philo&longs;ophi vtar, Cur quippiam non pecu­<lb/>liarem &longs;ibi fertur lationem impul&longs;ore alioquin <lb/>non con&longs;equente?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001950">Soluit, inquiens, an videlicet, quoniam primum, id e&longs;t, <lb/>impellens ip&longs;e, id efficit vt alterum, nempe proiectum <lb/>ip&longs;um impellat, illud vero (hoc e&longs;t proiectum) alterum <lb/>impellat, hoc e&longs;t, aërem ip&longs;um mediumue, quod à proie­<lb/>cto repelletur. </s> <s id="s.001951">Ce&longs;&longs;are autem motum, cum res eo deue­<lb/>nit, vt motus eidem à proijciente impre&longs;&longs;us, non po&longs;&longs;it <lb/>amplius rem proiectam mouere, & itidem rem ip&longs;am, aë­<lb/>rem videlicet non po&longs;&longs;it amplius repellere. </s> <s id="s.001952">Vel etiam <lb/>quando ip&longs;ius lati grauitas nutu &longs;uo declinat magis quam <lb/>impellentis in ante &longs;it potentia. </s> <s id="s.001953">Vtique res per &longs;e &longs;atis cla­<lb/>ra. </s> <s id="s.001954">etenim motus impre&longs;&longs;us accidentalis e&longs;t, quod vero la­<lb/>tioni violentæ re&longs;i&longs;tit principium, naturale, & ab ip&longs;o mo­<lb/>to in&longs;eparabile, vincente igitur quod natura e&longs;t, paulla­<lb/>tim remittitur quod ex accidenti e&longs;t, & inde proiecti fit <lb/>quies. </s> <s id="s.001955">E&longs;t autem & hoc quoque Problema pure phy&longs;icum, <lb/>& &longs;uperiori, de quo immediate egimus, perquam familia­<lb/>re, quamobrem ex ij&longs;dem pror&longs;us &longs;oluitur <lb/>principijs. </s> </p> <pb xlink:href="007/01/201.jpg"/> </subchap1> <subchap1> <p type="head"> <s id="s.001956">QVÆSTIO XXXIV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.001957"><emph type="italics"/>Cur neque parua multum, neque magna nimis longe proijci queunt, <lb/>&longs;ed proportionem quandam habere oportet proiecta ip&longs;a ad <lb/>eius vires qui proijcit?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.001958">Pvlchre dubitationem diluit, inquiens, An quia nece&longs;­<lb/>&longs;e e&longs;t quod proijcitur, & impellitur contraniti ei vnde <lb/>impellitur. </s> <s id="s.001959">Quod autem magnitudine &longs;ua nihil cedit, aut <lb/>imbecillitate nihil contra nititur, non efficit <expan abbr="proiectionē">proiectionem</expan> <lb/>neque impul&longs;ionem. </s> <s id="s.001960">quod enim multo impellentis exce­<lb/>dit vires, haud quaquam cedit. </s> <s id="s.001961">Quod vero e&longs;t multo im­<lb/>becillius, nihil contranititur, & impre&longs;&longs;ionem non &longs;u&longs;ci­<lb/>pit. </s> <s id="s.001962">Aliam quoque adiungit rationem, videlicet, Tantum <lb/>ferri id quod fertur quantum aëris mouerit ad <expan abbr="profundū">profundum</expan> <lb/>(hoc e&longs;t, ad eam partem aëris remotiorem, ad quam fer­<lb/>tur) etenim proiectum à principio dum fertur aërem pel­<lb/>lit, non pellit autem &longs;i nihil mouetur. </s> <s id="s.001963">Accidit igitur vt <lb/>concludit Philo&longs;ophus, proiecta i&longs;thæc contrarijs ex cau­<lb/>&longs;is minus moueri. </s> <s id="s.001964">quod enim valde paruum e&longs;t nihil mo­<lb/>uet imbecillitate &longs;ua impediente. </s> <s id="s.001965">quod vero valde ma­<lb/>gnum e&longs;t, ex contraria cau&longs;&longs;a nihil mouet, nempe quod <lb/>ob magnitudinem &longs;uam nihil moueatur. </s> <s id="s.001966">Vnde fit pro­<lb/>portionem inter proiectum & proijcientem e&longs;&longs;e inprimis <lb/>ad motum, nece&longs;&longs;ariam. </s> <s id="s.001967">Hæc eadem præclare in &longs;ua Pa­<lb/>raphra&longs;i explicat Picolomineus. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.001968">Huic nos, de proiectis quæ&longs;tioni, hæc addimus. </s> </p> <p type="main"> <s id="s.001969">Cur proiecta corpora non &longs;ibimet ip&longs;is &longs;ecundum, <lb/>partes æquegrauia, &longs;i fuerint irregularis figuræ in ip&longs;o mo­<lb/>tu, &longs;ecundum grauiorem partem antror&longs;us inuiolento, & <lb/>deor&longs;um in naturali ferantur, & dum in latione conuer­<lb/>tuntur, &longs;onitum edant. </s> </p> <p type="main"> <s id="s.001970">E&longs;to pila ABCD, cuius centrum E concinnata ex <lb/>di&longs;pari materia leui, nempe BCD, & graui ABD. non ergo <pb xlink:href="007/01/202.jpg"/><figure id="id.007.01.202.1.jpg" xlink:href="007/01/202/1.jpg"/><lb/>erit <expan abbr="centrū">centrum</expan> grauitatis & cen­<lb/>trum molis, &longs;it autem grauita­<lb/>tis centrum F. <!-- KEEP S--></s> <s id="s.001971">De&longs;cendat cor­<lb/>pus prohibente remoto per <lb/>rectam AG. <!-- KEEP S--></s> <s id="s.001972">Et quoniam gra­<lb/>uiora deor&longs;um tendunt ma­<lb/>gis, &longs;i à principio motus gra­<lb/>uior pars fuerit &longs;upra in ip&longs;o <lb/>de&longs;cen&longs;u conuertet ir pila, & <lb/>&longs;itum non &longs;eruabit donec &longs;u­<lb/>perior pars ea quæ grauior, <lb/>deor&longs;um fiat, vt videre e&longs;t in <lb/>pila HIK, cuius centrum e&longs;t G. pars grauior HIK. </s> <s id="s.001973">Si au­<lb/>tem eadem pila, laterali motu violenter feratur ver&longs;us <lb/>N, ad eam quoque partem conuertetur pars grauior. </s> <s id="s.001974">fa­<lb/>cto enim molis &longs;eu magnitudinis centro vbi L, grauior <lb/>pars fiet in MNO; quæcunque igitur &longs;unt corpora ita <expan abbr="cō-&longs;tituta">con­<lb/>&longs;tituta</expan>, vt in illis non &longs;it idem molis & grauitatis centrum <lb/>in ip&longs;a latione conuertentur, & eorum pars grauior an­<lb/>tror&longs;us fiet. </s> <s id="s.001975">Sonitus porro in ip&longs;o motu editi ea e&longs;t cau&longs;&longs;a, <lb/>quod irregulare corpus à principio incipit conuerti, & in <lb/>ip&longs;a conuer&longs;ione dum fertur aërem verberat, & ab eodem <lb/>vici&longs;&longs;im reuerberatur, ex qua reuerberatione fit corporis <lb/>rotatio dum fertur, & ip&longs;e &longs;onitus, quem Græci <foreign lang="greek">roi/zon</foreign><lb/>Rhœzum appellant. </s> </p> <p type="main"> <s id="s.001976">Ad hanc quoque &longs;peculationem pertinet, Cur lapi­<lb/>des ad &longs;uperficiem aquæ proiecti non &longs;tatim demergan­<lb/>tur, &longs;ed aliquot vicibus a quæ &longs;uperficiem radentes, abea, <lb/>dem re&longs;iliant. </s> </p> <p type="main"> <s id="s.001977">E&longs;to aquæ &longs;uperficies AB, lapis proiectus C, tangens <lb/>aquæ &longs;uperficiem in D, & inde re&longs;iliens in E, mox iterum <lb/>eandem tangens in F, & re&longs;iliens in G, donec <expan abbr="violēto">violento</expan> mo­<lb/>tu ce&longs;&longs;ante demergatur. </s> <s id="s.001978">Vtique lapis C, proiectus in D, <pb xlink:href="007/01/203.jpg"/><figure id="id.007.01.203.1.jpg" xlink:href="007/01/203/1.jpg"/><lb/>ni&longs;i medio den&longs;iori, aqua vi­<lb/>delicet, repelleretur, pene­<lb/>traret per D, in H. <!-- KEEP S--></s> <s id="s.001979">At eo re&longs;i­<lb/>&longs;tente, & adhuc vigente im­<lb/>petu, fertur in E ad angulos <lb/>fere pares. </s> <s id="s.001980">Dico autem fere, <lb/>&longs;iquidem maior e&longs;t ADC ip&longs;o EDF, propterea quod vis <lb/>non &longs;it eadem, &longs;ed minor ea quæ ex D pellit in E. <!-- KEEP S--></s> <s id="s.001981">Durante <lb/>igitur impetu quo pellitur antror&longs;um, fiunt ip&longs;æ re&longs;ilitio­<lb/>nes, & eo ce&longs;&longs;ante, re&longs;ilitiones ce&longs;&longs;ant, & lapis &longs;uapte gra­<lb/>uitate demergitur. </s> </p> <p type="main"> <s id="s.001982">Huc quoque &longs;pectat, Cur pila lu&longs;oria in horizontis <lb/>planum proiecta ad pares re&longs;iliat, angulos nempe rectos? </s> </p> <figure id="id.007.01.203.2.jpg" xlink:href="007/01/203/2.jpg"/> <p type="main"> <s id="s.001983">E&longs;to horizontis planum <lb/>AB, in quod à puncto C per <lb/>lineam perpendicularem CE <lb/>cadat proijciaturue pila DE, <lb/>cuius grauitatis centrum F. <lb/><!-- KEEP S--></s> <s id="s.001984">Tangit autem planum in <expan abbr="pū-cto">pun­<lb/>cto</expan> E. <!-- KEEP S--></s> <s id="s.001985">Perpendicularis ergo <lb/>EC, circulum DE per <expan abbr="centrū">centrum</expan> <lb/>&longs;ecat, hoc e&longs;t, in partes æ qua­<lb/>les & æqueponderantes, &longs;ed <lb/>dum pila cadit proijciturue, <lb/>agit in planum horizontis, vbi E, & in eodem puncto re. <lb/></s> <s id="s.001986">petitur, quare cum cadens & agens diuidatur in partes æ­<lb/>quales & æqueponderantes & item repatiens & re&longs;iliens <lb/>diuidatur item in partes æquales & æqueponderantes, ita <lb/>re&longs;ilit repatiendo, vti egerat in cadendo, hoc e&longs;t; ad angu­<lb/>los pares; quod fuerat demon&longs;trandum. </s> <s id="s.001987">Modo &longs;it <expan abbr="planū">planum</expan> <lb/>aliquod ita ad horizontem inclinatum, vt GH, & in illud <lb/>cadat proijciaturue eadem pila. </s> <s id="s.001988">Dico eam ab eodem in­<lb/>clinato plano ad pares angulos re&longs;ilire non tamen rectos. <pb xlink:href="007/01/204.jpg"/>Vtique pila cadens, planum non tanget in E. e&longs;&longs;et enim <lb/>GH, vbi AB, Tangat autem in I, & à centro F ad contin­<lb/>gentiæ punctum I, recta ducatur FI. </s> <s id="s.001989">Erit igitur FI (prop. <lb/>18. lib. 3. elem.) ip&longs;i GH plano perpendicularis. </s> <s id="s.001990">Ducatur <lb/>item peri, ip&longs;i EC, parallela IK, &longs;ecans pilæ circumferen­<lb/>tiam in K. <!-- KEEP S--></s> <s id="s.001991">Agit ergo & repatitur pila in puncto Inon æ. <lb/></s> <s id="s.001992">qualiter inæquales. </s> <s id="s.001993">etenim &longs;unt partes KDLEI, & IK, eo <lb/>quod IK &longs;ecet circulum non per centrum. </s> <s id="s.001994">repellitur ergo <lb/>in repatiendo non æqualiter, &longs;ed iuxta inæqualitatem ea­<lb/>rundem partium. </s> <s id="s.001995">Ducatur autem recta in circulo LI æ­<lb/>qualis ip&longs;i IK. <!-- REMOVE S-->Erit igitur LEI, æqualis IK, & tota KDLI æ­<lb/>qualis toti IKDL. </s> <s id="s.001996">Vt igitur actio e&longs;t per de&longs;cen&longs;um iuxta <lb/>rectam KI, ita e&longs;t repa&longs;&longs;io per a&longs;cen&longs;um ex IL. </s> <s id="s.001997">Dico autem <lb/>angulos KIH, LIG e&longs;&longs;e æquales & &longs;ingulos recto minores. <lb/></s> <s id="s.001998">Connectantur FL, FK. <!-- KEEP S--></s> <s id="s.001999">Quoniam igitur IK portio æqualis <lb/>e&longs;t portioni IEL, & recta LI æqualis rectæ IK, & LF æqua­<lb/>lis ip&longs;i FK, & FI communis, triangulum LFI, æquale e&longs;t <lb/>triangulo IFK. </s> <s id="s.002000">Quare & angulus FIL aequalis angulo FIK, <lb/>&longs;ed GIF, HIF recti &longs;unt, ergo re&longs;idui LIG, KIH æquales <lb/>&longs;unt inter &longs;e comparati, & recto minores; quod fuerat o­<lb/>&longs;tendendum. </s> </p> <p type="main"> <s id="s.002001">Hinc colligimus, quo magis planum ab æquidi&longs;tan­<lb/>tia horizontis rece&longs;&longs;erit, eo pilam in eo proiectam in par­<lb/>tes in æqualiores diuidi & ad minores ip&longs;i plano angulos <lb/>re&longs;ilire. </s> <s id="s.002002">Nihil autem refert, vtrum planum, in quod pila <lb/>cadit, ad horizontem &longs;it inclinatum, vel eodem horizonti <lb/>æquedi&longs;tante pila non ad perpendiculas, &longs;ed iuxta <expan abbr="aliquē">aliquem</expan> <lb/>angulum in illud proijciatur. </s> <s id="s.002003">Hæc &longs;ane ita ex demon&longs;tra­<lb/>tione fieri o&longs;tenduntur. </s> <s id="s.002004">Veruntamen quoniam proiecta <lb/>pila materialis e&longs;t, & ideo nec æqualis, nec æqueponde­<lb/>rans & &longs;ua grauitate re&longs;i&longs;tens, non ad pares ex amu&longs;&longs;i re&longs;i­<lb/>lit angulos, &longs;ed minores aliquantulum in re&longs;ilitione, re. <lb/></s> <s id="s.002005">mittente nimirum vi in ip&longs;a reactione. </s> <s id="s.002006">Et &longs;ane fieri non <pb xlink:href="007/01/205.jpg"/>pote&longs;t, pilam à plano re&longs;ilientem eo peruenire vnde à <lb/>principio di&longs;ce&longs;&longs;erat; Id enim &longs;i daretur, æterna quoque <lb/>pilæ ip&longs;ius daretur re&longs;ilitio, & paullatim vi & impetu re­<lb/>mittente per parua interualla motus e&longs;&longs;et, donec res quæ <lb/>mouebatur, omnino quie&longs;cat. </s> </p> </subchap1> <subchap1> <p type="head"> <s id="s.002007">QVÆSTIO XXXV.<!-- KEEP S--></s> </p> <p type="head"> <s id="s.002008"><emph type="italics"/>Quærit hoc vltimo Problemate Ari&longs;toteles, Cur ea quæ in vorti­<lb/>co&longs;is feruntur aquis, ad medium tandem agan­<lb/>tur omnia?<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002009">Tribus rationibus &longs;oluit; quarum prima e&longs;t: Quicquid <lb/>fertur, magnitudinem habet, cuius extrema in duo­<lb/>bus &longs;unt circulis, hoc in minori, illud in maiori. </s> <s id="s.002010">Et quo­<lb/>niam maior velocior e&longs;t, magnitudo media, non æquali­<lb/>ter fertur, &longs;ed à maiori quidem pellitur, à minori vero re­<lb/>trahitur, vnde transuer&longs;us fit magnitudinis motus, & ip&longs;a <lb/>magnitudo ad interiorem propellitur circulum, itaque <lb/>eodem pacto, è maiori in minorem propul&longs;a in centrum. <lb/></s> <s id="s.002011">tantum fertur, & ibi quie&longs;cit. </s> </p> <figure id="id.007.01.205.1.jpg" xlink:href="007/01/205/1.jpg"/> <p type="main"> <s id="s.002012">E&longs;to vortex AB, cuius cen­<lb/>trum C, magnitudo quæ fer­<lb/>tur AD, maior circulus AFB, <lb/>minor DHEG. <!-- KEEP S--></s> <s id="s.002013">Velocitas igi­<lb/>tur in A maior e&longs;t velocitate <lb/>quæ in D, magnitudinis ergo <lb/>extremum A, velocius rapitur <lb/>in A quam eiu&longs;dem extremum <lb/>inferius D, in D. <!-- KEEP S--></s> <s id="s.002014">Velocitas igi­<lb/>tur maioris circuli pellit Aver­<lb/>&longs;us F. tarditas vero minoris cir­<lb/>culi D retrahit ad partes G. conuertitur itaque magnitu­<lb/>do inter pellentem & retrahentem circulum, donec ex­<pb xlink:href="007/01/206.jpg"/>tremitas A in circulo minori fuerit vbi H, D vero vbi I, & <lb/>ita deinceps eadem ratione vbi KL, donec paullatim fe­<lb/>ratur in centrum C, facto nempe à maiori in minorem cir­<lb/>culum tran&longs;itu. </s> </p> <p type="main"> <s id="s.002015">Secunda ratio ita habet, quia quod fertur, &longs;imili &longs;e <lb/>habet modo ad omnes circulos propter centrum, hoc e&longs;t, <lb/>in quouis circulo, qui circa idem centrum fertur. </s> <s id="s.002016">Omnes <lb/>autem circuli mouentur, centrum vero &longs;tat, nece&longs;&longs;e e&longs;t à <lb/>motu tandem id quod mouetur ad quietis locum, hoc e&longs;t, <lb/>in centrum ip&longs;um peruenire. </s> </p> <p type="main"> <s id="s.002017">Tertia, quoniam circulorum, qui in vorticibus fiunt, <lb/>velocitas, & ideo impetus non e&longs;t æqualis, &longs;ed &longs;emper ex­<lb/>terior e&longs;t interiore velocior & violentior, Æqualis autem <lb/>&longs;emper in mota magnitudine, grauitas, diuer&longs;i mode &longs;e <lb/>habet ad circulos, à quibus mouetur, & ideo modo vin­<lb/>citur, modo vincit: vincitur autem à velocioribus circulis, <lb/>vincit autem tardiores. </s> <s id="s.002018">Ita que quoniam &longs;ua grauitate re­<lb/>&longs;i&longs;tens, maioris circuli motum pror&longs;us non &longs;equitur, ad <lb/>tardiorem reijcitur, hoc e&longs;t, interiorem, & &longs;ic deinceps, <lb/>donec tandem centrum ip&longs;um nanci&longs;catur, in quo nec &longs;u­<lb/>perans, nec &longs;uperata quie&longs;cit. </s> </p> <p type="main"> <s id="s.002019">Hæ &longs;unt rationes, licet ob&longs;curi&longs;&longs;ime propo&longs;itæ, qui­<lb/>bus, vt diximus, vtitur Ari&longs;toteles. <!-- KEEP S--></s> <s id="s.002020">acutæ &longs;ane illæ <expan abbr="quidē">quidem</expan>, <lb/>attamen haudquaquam vltro admittendæ. </s> </p> <p type="main"> <s id="s.002021">Primo enim fal&longs;um videtur, quod a&longs;&longs;erit, vortices <lb/>circulos e&longs;&longs;e, & circa idem centrum fieri atque rotari. </s> <s id="s.002022">Spi­<lb/>ræ enim potius &longs;unt, quæ ab exteriori parte <expan abbr="remotioreq;">remotioreque</expan> <lb/>incipientes &longs;piraliter circumuolutæ, ad intimam tandem <lb/>partem, quæ media e&longs;t & centri vices gerit, deueniunt. <lb/></s> <s id="s.002023">qua veritate cognita, omnis pror&longs;us difficultas tollitur, <lb/>Cum enim ea quæ feruntur, ab aqua ferantur, aqua vero <lb/>feratur &longs;piraliter, ea quoque &longs;piraliter ferri, e&longs;t nece&longs;&longs;a-<pb xlink:href="007/01/207.jpg"/>rium. </s> <s id="s.002024">Hæc autem clariora erunt &longs;i quo pacto vortices <lb/>fiant, qui&longs;piam con&longs;iderauerit. </s> </p> <figure id="id.007.01.207.1.jpg" xlink:href="007/01/207/1.jpg"/> <p type="main"> <s id="s.002025">E&longs;to fluminis cuiu&longs;piam curua <lb/>eademque profunda ripa ABCD. <lb/><!-- KEEP S--></s> <s id="s.002026">Aquæ vero moles rapida EFDC, <lb/>quæ quidem eo quod magno impe­<lb/>tu deferatur in C, ripæ ip&longs;ius <expan abbr="naturã">naturam</expan> <lb/>&longs;equens turbinatim circum uoluitur, <lb/>egre&longs;&longs;a autem extra locum &longs;eu ripam <lb/>B rotationis principium &longs;ecundans, <lb/>in &longs;eip&longs;am &longs;piraliter contorquetur, <lb/>& vorticem efficit GHFIK, cuius <lb/>quidem centrum e&longs;t vbi K. <!-- KEEP S--></s> </p> <p type="main"> <s id="s.002027">Alia quoque de cau&longs;&longs;a, ex quie&longs;cente nimirum, & <lb/>mota aqua fiunt &longs;piræ vorticesue. </s> <s id="s.002028">E&longs;to enim fluminis ripa <lb/><figure id="id.007.01.207.2.jpg" xlink:href="007/01/207/2.jpg"/><lb/>ABC, &longs;inum efficiens, qui a quam ex <lb/>ripæ ip&longs;ius obiectu contineat quie­<lb/>&longs;centem, Cur&longs;us vero fluminis liber & <lb/>rectus, &longs;it inter lineas AC, DE. <!-- KEEP S--></s> <s id="s.002029">Itaque <lb/>dum aqua AC rapide fertur ad partes <lb/>A, quie&longs;centem ABC iuxta lineam. <lb/></s> <s id="s.002030">CA lateraliter propellit, & eius qui­<lb/>dem partem quam tangit, &longs;ecum ra­<lb/>pit, puta ex F in G. <!-- KEEP S--></s> <s id="s.002031">Delata igitur aqua <lb/>& currente ex F ver&longs;us G quie&longs;cens <lb/>lateraliter eidem &longs;e&longs;e aliqualiter op­<lb/>ponit, & currentem repellit ex G in H. <!-- KEEP S--></s> <s id="s.002032">Cœpto <expan abbr="itaq;">itaque</expan> &longs;pirali <lb/>motu aqua circumuoluitur &longs;ecundum lineam GHK, do­<lb/>nec perueniat ad centrum I, vbi circumuolutæ aquæ par­<lb/>tes &longs;e&longs;e inuicem tangunt. </s> <s id="s.002033">Porro vortices i&longs;ti &longs;piræue, quod <lb/>nos per Padum, Abduam, & magna flumina nauigantes <lb/>ob&longs;eruauimus, non eodem permanent loco, &longs;ed rapientis <lb/>aquæ motum &longs;ecundantes, paullatim in currentem <expan abbr="aquã">aquam</expan> <pb xlink:href="007/01/208.jpg"/>delati euane&longs;cunt, fiunt etiam eiu&longs;cemodi vortices nau­<lb/>tis quidem valde formidabiles etiam in mari, de quibus <lb/>Poëta libro Æneidos primo. </s> </p> <p type="main"> <s id="s.002034">— <emph type="italics"/>a&longs;t illam ter fluctus ibidem <lb/>Torquet agens circum, & rapidus vorat æquore vortex.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002035">Sed & idem quoque de vorticibus, qui in fluminibus <lb/>fiunt libro 7. </s> </p> <p type="main"> <s id="s.002036">— <emph type="italics"/>hunc inter fluuio Tiberinus amœno <lb/>Vorticibus rapidis, & multa flauus arena <lb/>In mare prorumpit.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002037">Fiunt autem in mari partim occultis de cau&longs;&longs;is, partim <lb/>etiam ex violentia aquarum &longs;ibi inuicem obuiantium a­<lb/>gitatione. </s> <s id="s.002038">Sed nos hi&longs;ce explicatis commode ad ea quæ <lb/>dixerat Ari&longs;toteles, reuertemur. </s> </p> <p type="main"> <s id="s.002039">Dicimus igitur, primam eius rationem haud magni <lb/>videri ponderis, &longs;iquidem non per circulos actu di&longs;tinctos <lb/>aqua circumfertur, &longs;ed ip&longs;amet &longs;ua mole tota &longs;imul. </s> </p> <figure id="id.007.01.208.1.jpg" xlink:href="007/01/208/1.jpg"/> <p type="main"> <s id="s.002040">E&longs;to enim vortex AB, cu­<lb/>ius centrum C, &longs;emidiameter <lb/>CA, fiat autem rotatio totius a­<lb/>quæ CA ad partes D, in linea <lb/>autem AC, &longs;it corpus aliquod a­<lb/>quæ rotatione <expan abbr="circumlatū">circumlatum</expan> AE, <lb/>inter circulos maiorem ADB, <lb/>minorem EFG. velocius autem <lb/>mouetur ADB, ip&longs;o EFG, citius <lb/>ergo fertur pars &longs;uperior ip&longs;ius <lb/>corporis vbi A, quam inferior <lb/>vbi E. <!-- KEEP S--></s> <s id="s.002041">At id nec A repellit, nec E retrahit, &longs;iquidem eodem <lb/>tempore quo A permeauit <expan abbr="circulū">circulum</expan> ADB, eodem & E per­<lb/>currit circulum EFG. <expan abbr="Itaq;">Itaque</expan> A reuer&longs;o in A & E, punctum <lb/>reuer&longs;um erit in E, nulla facta corporis E quoad &longs;itum, <lb/>muratione quod voluit Ari&longs;toteles. <!-- KEEP S--></s> </p> <pb xlink:href="007/01/209.jpg"/> <p type="main"> <s id="s.002042">Ad &longs;ecundam vero dicimus, non ideo quod omnes <lb/>circuli æqualiter circa centrum &longs;erantur, ni&longs;i alia <expan abbr="quæpiã">quæpiam</expan> <lb/>extranea vis interce&longs;&longs;erit, quæ ea ab exterioribus circulis <lb/>pellens agat in medium. </s> </p> <figure id="id.007.01.209.1.jpg" xlink:href="007/01/209/1.jpg"/> <p type="main"> <s id="s.002043">Tertia quoque ratio la­<lb/>borare videtur. </s> </p> <p type="main"> <s id="s.002044">E&longs;to enim vortex AB, <lb/>cuius centrum C, &longs;it autem <lb/>corpus aliquod E, cuius na­<lb/>tura apta &longs;it rotationi aliqua­<lb/>tenus re&longs;i&longs;tere. </s> <s id="s.002045">Quoniam i­<lb/>gitur eius re&longs;i&longs;tentia <expan abbr="aliquã-tulum">aliquan­<lb/>tulum</expan> ab aqua rapiente &longs;u­<lb/>peratur in ip&longs;a rotatione, par­<lb/>tim aquae impetum &longs;equetur, <lb/>partim &longs;uapte natura retardabitur. </s> <s id="s.002046">Quamobrem aqua <lb/>quæ e&longs;t in A, translata in H, corpus ip&longs;um non erit in H, <lb/>&longs;ed in G. <!-- KEEP S--></s> <s id="s.002047">Tardius igitur corpus quam aqua ip&longs;a, rotatio­<lb/>nem complebit, non tamen propterea, ni&longs;i alia quæ piam <lb/>ad&longs;it cau&longs;&longs;a, feretur in medium. </s> </p> <p type="main"> <s id="s.002048">Cæterum horum vorticum effectum & cau&longs;&longs;am ob­<lb/>&longs;eruare licet, &longs;i va&longs;e quopiam aqua pleno aquam ip&longs;am <lb/>baculo manuue circulariter agitauerimus, fiet enim vor­<lb/>tex, & &longs;i quippiam quod leue &longs;it, in aquam motam proie­<lb/>cerimus, ea quam diximus de cau&longs;&longs;a in motum ip&longs;um, hoc <lb/>e&longs;t, vorticis &longs;piræue, centrum feretur. </s> </p> <p type="main"> <s id="s.002049">Hæc nos, vt vera proponimus, & forta&longs;&longs;e decipimur. <lb/></s> <s id="s.002050">Certe Philo&longs;opho tantæ auctoritatis contradicere, ma­<lb/>gnæ videtur audaciæ, aut potius in&longs;aniæ. </s> <s id="s.002051">Quicquid ta­<lb/>men &longs;it, pro pulcherrima veritate labora&longs;&longs;e, à parte <lb/>aliqua laudis non fuerit pror&longs;us, vt <lb/>arbitror, alienum. </s> </p> <pb xlink:href="007/01/210.jpg"/> </subchap1> </chap> <chap> <p type="head"> <s id="s.002052">APPENDIX.<!-- KEEP S--></s> </p> <p type="main"> <s id="s.002053">Modum inueniendarum duarum mediarum propor­<lb/>tionalium non tantum vtilem e&longs;&longs;e, &longs;ed pror&longs;us nece&longs;­<lb/>&longs;arium, illi norunt, qui in Mechanicis di&longs;ciplinis vel <expan abbr="parū">parum</expan> <lb/>fuerint ver&longs;ati. </s> <s id="s.002054">Nulla enim alia ratio e&longs;t, qua corporeae ma­<lb/>gnitudines &longs;eruata figura & &longs;imilitudine augeri propor­<lb/>tionaliter imminuiue po&longs;&longs;int. </s> <s id="s.002055">Quamobrem factum e&longs;t vt <lb/>in his inueniendis tum vetu&longs;ti&longs;&longs;imo tum etiam in feriori æ­<lb/>uo, clari&longs;&longs;imi Viri magnopere laborauerint. </s> <s id="s.002056">Plato etenim, <lb/>Eudoxus (cuius modum repudiauit Eutocius) Heron A­<lb/>lexandrinus, Philon Byzantius, Apollonius, clari&longs;&longs;imi <lb/>Geometræ, Diocles, Pappus, Sporus, Menæchmus, Ar­<lb/>chytas Tarentinus, Platoni æqualis: Erato&longs;thenes, & Ni­<lb/>comedes ad has inueniendas varias rationes <expan abbr="excogitarūt">excogitarunt</expan>, <lb/>quorum omnium modos, & in&longs;trumenta, <expan abbr="demon&longs;tratio-ne&longs;q;">demon&longs;tratio­<lb/>ne&longs;que</expan> diligenti&longs;&longs;ime collegit, & in illos <expan abbr="Cōmentarios">Commentarios</expan> con­<lb/>iecit idemmet Eutocius, quos eleganti&longs;&longs;imos in Archime­<lb/>dis libros de Sphæra & Cylindro &longs;crip&longs;it. </s> <s id="s.002057">Nos autem ijs o­<lb/>mnibus accurate per&longs;pectis, & diligenti&longs;&longs;ime ponderatis, <lb/>inuenimus eos fere omnes tentando negotium ab&longs;olue­<lb/>re, quod &longs;ane laborio&longs;um valde e&longs;t & operantibus permo­<lb/>le&longs;tum. </s> <s id="s.002058">Itaque cum modum praximue inueni&longs;&longs;emus, ex <lb/>qua is qui operatur tuti&longs;&longs;ime & facillime ad quæ &longs;itas ip&longs;as <lb/>medias manu ducitur, hunc pulcherrimæ huius facultatis <lb/>&longs;tudio &longs;is inuidere nefarium iudicauimus. </s> <s id="s.002059">Quod &longs;i <expan abbr="qui&longs;piã">qui&longs;piam</expan> <lb/>dixerit, Balli&longs;tarum, Catapultarum, Scorpionum, & cæ­<lb/>terarum eiu&longs;cemodi Machinarum v&longs;um, olim apud nos <lb/>de&longs;ij&longs;&longs;e, & ideo Problema hoc videri &longs;uperuacaneum, Re­<lb/>&longs;pondemus, nulla alia ratione æneorum tormentorum pi­<lb/>las augeri imminuiue &longs;eruata ponderis ratione po&longs;&longs;e, in­<lb/>numeraque e&longs;&longs;e, quæ vt rite perficiantur, hæc penitus in­<lb/>digent &longs;peculatione. </s> <s id="s.002060">Nos rem Mechanicis vtilem, Me. <pb xlink:href="007/01/211.jpg"/>chanicis no&longs;tris Exercitationibus annectere, haud im­<lb/>portunum iudicauimus. </s> <s id="s.002061">Sed tempus e&longs;t, vt his breuiter <lb/>præfatis, ad rem ip&longs;am <expan abbr="explicandã">explicandam</expan> commode accedamus. </s> </p> <p type="head"> <s id="s.002062"><emph type="italics"/>Datis duabus proportionalibus prima, & quarta duas inter eas <lb/>medias in continua proportione inuenire.<emph.end type="italics"/></s> </p> <p type="main"> <s id="s.002063">Esto prima datarum AB, quarta BC, inter quas <expan abbr="&longs;ecundã">&longs;ecundam</expan> <lb/>& tertiam oportet inuenire. </s> <s id="s.002064">Ducatur recta DE, cui à <lb/>puncto F, vtcunque &longs;umpto, perpendicularis demittatur <lb/>FG, Tum ab F ver&longs;us D duplicetur quarta BC, &longs;itque FH, <lb/>deinde ab H ip&longs;i FG parallela demittatur HI, & ab HF <lb/>ab&longs;cindatur HK, ip&longs;ius BC quartæ medietati æqualis. <lb/></s> <s id="s.002065">Po&longs;thæc puncto K &longs;patio autem medietati, primæ data­<lb/>rum æquali, in linea HI notetur punctum L, & ip&longs;i HL <lb/>fiat æqualis FM, & KM iungatur. </s> <s id="s.002066">His ita con&longs;titutis pare­<lb/>tur &longs;eor&longs;um &longs;cheda regulaue quæpiam NO, in cuius late­<lb/>re accipiatur OP, æqualis medietati primæ datarum &longs;eu <lb/>ip&longs;i KL. <!-- KEEP S--></s> <s id="s.002067">Tum regulæ latus aptetur puncto L, extremum <lb/>vero O, feratur a&longs;&longs;idue per rectam EK, ver&longs;us K, nunquam <lb/><figure id="id.007.01.211.1.jpg" xlink:href="007/01/211/1.jpg"/><pb xlink:href="007/01/212.jpg"/>interim regulæ latere ON amoto à puncto L, idque do­<lb/>nec punctum P, obuians incidat in lineam KM, puta vbi <lb/>Q extremum vero O inueniatur in R, notato igitur in li­<lb/>nea EK puncto R habebitur, quod quærebatur. </s> <s id="s.002068">Erunt i­<lb/>gitur AB prima, RK &longs;ecunda, QL tertia, BC quarta. </s> </p> <p type="main"> <s id="s.002069">Hæc praxis ij&longs;dem principijs demon&longs;tratur, quibus <lb/>&longs;uam ex Conchoide o&longs;tendit Nicomedes. </s> <s id="s.002070">Conficit ille <lb/>in&longs;trumentum, ex quo de&longs;cribit <expan abbr="Conchoidē">Conchoidem</expan>, ex qua po&longs;t­<lb/>ea duas medias venatur. </s> <s id="s.002071">Nos autem nec in&longs;trumentum <lb/>con&longs;truimus nec Conchoidem de&longs;cribimus, & duabus fe­<lb/>re lineis rem ab&longs;oluimus, vt nemo fere non dixerit, hoci­<lb/>&longs;tud quod docemus, à Nicomedea praxi e&longs;&longs;e pror&longs;us a­<lb/>lienum. </s> </p> <p type="main"> <s id="s.002072">Sed nos, vt eius, quam o&longs;tendimus, operationis de­<lb/>mon&longs;tratio habeatur; ip&longs;ius Nicomedis ex Pappi libro 3. <lb/>propo&longs;. </s> <s id="s.002073">5. de&longs;umptam in medio afferemus, quippe quod <lb/>i&longs;thæc ea quam in &longs;uis in Archimedem commentarijs re­<lb/>fert Eutocius, &longs;it lucidior. </s> </p> <p type="main"> <s id="s.002074">Datis duabus rectis lineis CD, DA; duæ mediæ in <lb/>continua proportione hoc modo a&longs;&longs;umuntur. </s> </p> <p type="main"> <s id="s.002075">Compleatur ABCD parallelogrammum, & <expan abbr="vtraq;">vtraque</expan> <lb/>ip&longs;arum AB, BC, bifariam &longs;ecetur in punctis L, E, iuncta­<lb/>que LD producatur; & occurrat productæ CB, in G, ip&longs;i <lb/>vero BC ad rectos angulos ducatur EF, & CF iungatur, <lb/>quæ &longs;it æqualis AL. <!-- KEEP S--></s> <s id="s.002076">Iungatur præterea FG & ip&longs;i paralle­<lb/>la &longs;it CH, eritque angulus KCH, æqualis angulo CGF. <lb/></s> <s id="s.002077">Tum à dato puncto F ducatur FHK, quae faciat KH æqua­<lb/>lem ip&longs;i AL vel CF. <!-- KEEP S--></s> <s id="s.002078">Hoc enim per lineam Conchoidem <lb/>fieri po&longs;&longs;e o&longs;tendit Nicomedes, & iuncta KD producatur, <lb/>occurratque ip&longs;i BA, productæ in puncto M. <!-- KEEP S--></s> <s id="s.002079">Dico vt DC <lb/>ad CK ita CK ad MA & MA ad AD. <!-- KEEP S--></s> <s id="s.002080">Quoniam enim BC <lb/>bifariam &longs;ecta e&longs;t in E, & ip&longs;i adijcitur CK. <!-- KEEP S--></s> <s id="s.002081">Rectangulum <lb/>BKC per 6. &longs;ecundi: vna cum quadrato ex CE, æquale e&longs;t <pb xlink:href="007/01/213.jpg"/><figure id="id.007.01.213.1.jpg" xlink:href="007/01/213/1.jpg"/><lb/>quadrato ex EK. commune apponatur ex EF quadratum, <lb/>ergo rectangulum BKC vna cum quadrato CF æquale <lb/>e&longs;t quadratis ex KE, EF, hoc e&longs;t, quadrato ex FK. <!-- KEEP S--></s> <s id="s.002082">Et quo­<lb/>niam vt MA ad AB, ita e&longs;t MD ad DK, vt autem MD ad <lb/>DK per 2. &longs;exti, ita BC ad C<emph type="italics"/>K<emph.end type="italics"/> erit vt MA ad AB, ita BC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s> <s id="s.002083">Atque e&longs;t ip&longs;ius AB dimidia AL, & ip&longs;ius BC, du­<lb/>pla CG, e&longs;t igitur vt MA ad AL, ita GC ad C<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s> <s id="s.002084">Sed vt GC <lb/>ad C<emph type="italics"/>K<emph.end type="italics"/>, ita FH ad H<emph type="italics"/>K<emph.end type="italics"/> propter lineas parallelas GF, CH. <lb/>quare & componendo vt ML, ad LA, ita F<emph type="italics"/>K<emph.end type="italics"/> ad <emph type="italics"/>K<emph.end type="italics"/>H, &longs;ed <lb/>AL ponitur æqualis H<emph type="italics"/>K<emph.end type="italics"/>, quoniam & ip&longs;i CF, ergo & ML <lb/>per 9. lib. 5. æqualis erit F<emph type="italics"/>K<emph.end type="italics"/>, & quadratum ex ML, æquale <lb/>quadrato ex F<emph type="italics"/>K<emph.end type="italics"/>. <!-- KEEP S--></s> <s id="s.002085">e&longs;t autem quadrato ex ML, æquale re­<lb/>ctangulum BMA vna cum quadrato ex AL & quadrato <lb/>ex Fk æquale o&longs;ten&longs;um e&longs;t rectangulum BkC vna cum. <pb xlink:href="007/01/214.jpg"/>quadrato ex CF, quorum quidem quadratum ex AL æ­<lb/>quale e&longs;t quadrato ex CF, ponitur enim AL, ip&longs;i CF æ­<lb/>qualis, ergo reliquum BMA rectangulum æquale e&longs;t reli­<lb/>quo BkC. <!-- KEEP S--></s> <s id="s.002086">Vt igitur MB ad Bk, ita Ck ad MA. <!-- KEEP S--></s> <s id="s.002087">Sed vt MD <lb/>ad Bk, ita DC ad Ck. <!-- KEEP S--></s> <s id="s.002088">quare vt DC ad Ck, ita e&longs;t Ck ad <lb/>MA. vt autem MD ad Bk, ita MA, ad AD. <!-- KEEP S--></s> <s id="s.002089">Ergo vt DC, <lb/>prima, ad Ck &longs;ecundam, ita Ck &longs;ecunda ad MA tertiam, <lb/>& MA tertia ad AD quartam, quod fuerat demon&longs;tran­<lb/>dum. </s> <s id="s.002090">Hæc Pappus. <!-- KEEP S--></s> <s id="s.002091">Quod autem in no&longs;tra Praxi diximus, <lb/>QL e&longs;&longs;e tertiam, ea ratio e&longs;t, quod LR vt in prima figura <lb/>e&longs;t, &longs;it æqualis ip&longs;i LM &longs;ecundæ figuræ, in demon&longs;tratio­<lb/>ne Pappi, ex quibus demptis QR & LA, quæ &longs;unt æqua­<lb/>les, reliqua QL primæ figuræ æqualis e&longs;t AM &longs;ecundæ fi­<lb/>guræ, hoc e&longs;t, ip&longs;i tertiæ proportionali: E&longs;t igitur, vt in pri­<lb/>ma figura dicebamus, AB prima, kR &longs;ecunda, QL tertia, <lb/>BC quarta. </s> </p> <p type="main"> <s id="s.002092">Vides igitur tu qui legis, nos ex Nicomedis demon­<lb/>&longs;tratione (quatenus ad praxin pertinet) &longs;uperflua re&longs;eca&longs;­<lb/>&longs;e, & ab&longs;que Conchoidis in&longs;trumento lineaue rem ip&longs;am <lb/>confeci&longs;&longs;e, idque non tentantes, vt alij, &longs;ed progre­<lb/>dientes, & qua&longs;i manuductos quæ&longs;i­<lb/>tum inue&longs;tiga&longs;&longs;e. </s> </p> <p type="head"> <s id="s.002093">FINIS.<lb/> <!-- KEEP S--></s> </p> </chap> </body> <back/> </text> </archimedes>