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| author | Josef Willenborg <jwillenborg@mpiwg-berlin.mpg.de> |
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| date | Wed, 09 Nov 2011 15:27:46 +0100 |
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<?xml version="1.0" encoding="UTF-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> <metadata> <dcterms:identifier>ECHO:XSY685ZD.xml</dcterms:identifier> <dcterms:creator identifier="GND:118650130">Aristoteles</dcterms:creator> <dcterms:contributor identifier="GND:102377138">Leonicus Thomaeus, Nicolaus</dcterms:contributor> <dcterms:title xml:lang="la">Quaestiones Mechanicae</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1585</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">lat</dcterms:language> <dcterms:rights>open access</dcterms:rights> <dcterms:license>http://echo.mpiwg-berlin.mpg.de/policy/oa_basics/declaration</dcterms:license> <dcterms:accessRights>free</dcterms:accessRights> </metadata> <text xml:lang="la" type="free"> <div type="section" level="1" n="1"><pb o="504" file="0504" n="1"/> </div> <div type="section" level="1" n="2"> <head xml:space="preserve">ARISTOTELIS</head> <head xml:space="preserve">STAGIRITAE, <lb/>PERIPATETICORVM</head> <head xml:space="preserve">PRINCIPIS,</head> <head xml:space="preserve">Quæſtiones Mechanicæ, <lb/>Nicolao Leonico Thomæo <lb/>interprete.</head> <head style="it" xml:space="preserve">Quæ ſit artis Mechanicæ facultas.</head> <p> <s xml:space="preserve">MIraculo ſune ea quidem, quæ natura <lb/>contingunt, quorum ignorantur cau <lb/>ſæ: </s> <s xml:space="preserve">illa uerò, quæ pręter naturam, <lb/>quæcunque ad hominum vtilitatem <lb/>arte fiunt. </s> <s xml:space="preserve">In multis. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">natura ei. </s> <s xml:space="preserve">qđ <lb/>nobis uſui eſſe poteſt, contrarium facit: </s> <s xml:space="preserve">natura <lb/>etenim eundem ſemper habet modum, & </s> <s xml:space="preserve">ſimpli <lb/>citer: </s> <s xml:space="preserve">vtile autem multifariam commutat̃. </s> <s xml:space="preserve">Quan <lb/>doigitur quippiam præter naturam oportuerit <lb/>facere, difficultate ſua hæſitationem praſtat, ar-<lb/>teq́ indiget: </s> <s xml:space="preserve">quam ob rem eam artis partẽ, quæ <lb/>huiuſmodi ſuccurrit difficulcatibus, Mechanicã <lb/>appellamus. </s> <s xml:space="preserve">Quemad modum enim Antipho ſcri <lb/>bit poeta, ſic ſe res habet: </s> <s xml:space="preserve">arte enim ſuperamus <lb/>da, à quibus natura uincimur. </s> <s xml:space="preserve">Huiuſmodi autem <lb/>ſunt, in quibus & </s> <s xml:space="preserve">minora ſuperant maiora: </s> <s xml:space="preserve">& </s> <s xml:space="preserve"><lb/>quæcunq; </s> <s xml:space="preserve">momentum paruum habẽtia, magna <pb o="505" file="0505" n="2" rhead="Mechanicæ."/> mouent pondera: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">omnia ferè illa, quæ mecha <lb/>nica nuncupamus, & </s> <s xml:space="preserve">problemata. </s> <s xml:space="preserve">Sunt autem, <lb/>hæc neque naturalibus omnino quæſtionibus <lb/>eadem, neque ſeiugata valde: </s> <s xml:space="preserve">verùm mathema-<lb/>ticarũ contemplationũ naturaliumq́; </s> <s xml:space="preserve">cõmunia.</s> <s xml:space="preserve"/> </p> </div> <div type="section" level="1" n="3"> <head style="it" xml:space="preserve">De dignitatiòus, admirandis̈ Circuli <lb/>proprietatibus.</head> <p> <s xml:space="preserve">DEnumeto autem eorum, quæ hoc in gene-<lb/>re dubitantur, illa eſſe dicuntur, quæ circæ <lb/>vectem fiunt. </s> <s xml:space="preserve">Abſurdum enim eſſe videtur, ma-<lb/>gnum moueri pondus ab exigua virtute, cũ plu-<lb/>ri præſertim pondere. </s> <s xml:space="preserve">quod. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">una vecte quiſpiã <lb/>mouere nõ poteſt, idipſum ponderis citius mo-<lb/>uet, uectis ad illud pondus adiungens. </s> <s xml:space="preserve">Oĩum ãt <lb/>huiuſmodi cauſæ principiũ habet circulus, Iſtud <lb/>verò ratione contingit; </s> <s xml:space="preserve">ex ad mirabili etem̄ mi-<lb/>randum accidere quippiam, non eſt ab ſurdum.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Maximè autem eſt admirãdum ſimul contra-<lb/>ria fieri. </s> <s xml:space="preserve">Circulus vero ex huiuſmodi eſt conſtitu <lb/>tus: </s> <s xml:space="preserve">ſtatim enim ex commoto effectus eſt, & </s> <s xml:space="preserve">mæ <lb/>nente, quorũ natura ad ſe inuicem eſt cõtraria. <lb/></s> <s xml:space="preserve">quamobrẽ iſthæc cernentes minus admirari cõ-<lb/>uenit contingentes in illo contrarietas. </s> <s xml:space="preserve">In pri-<lb/>mis enim lineæ illi, quæ circuli orbem amplecti <lb/>tur, nullam habenti latitudinem, contraria quo-<lb/>dammodo ineſſe apparent, concauum ſcilicet, <lb/>& </s> <s xml:space="preserve">curuum. </s> <s xml:space="preserve">hæc aũt eo à ſeinuicem diſtant mõ, <lb/>quo magnum & </s> <s xml:space="preserve">paruum, illorũ etenim medium <lb/>eſt æquale: </s> <s xml:space="preserve">horum verò rectũ quapropter cùm, <lb/>ad ſeinuicem cõmutantur, illa quidem prius æ-<lb/>qualia fieri neceſſe eſt, quàm extremorum vtrũ-<lb/>libet: </s> <s xml:space="preserve">lineam verò rectam, qñ eſt curua concaua, <lb/>ut ex huiu ſmoà<unsure/>i rurſum curua fit, & </s> <s xml:space="preserve">circularis <pb o="506" file="0506" n="3" rhead="Ariſt. Quæſtiones"/> Vnum quidem igitur iſtuc abſurdum ineſt circti<unsure/> <lb/>lo. </s> <s xml:space="preserve">Alterum autem, ꝙ ſimul contrarijs mouetur <lb/>motionibus: </s> <s xml:space="preserve">ſimul enim ad anteriorem mouetur <lb/>locum, & </s> <s xml:space="preserve">ad poſter<unsure/>iorem. </s> <s xml:space="preserve">Et ea, quæ circulũ de-<lb/>ſcribit, linea eodem ſe habet modo: </s> <s xml:space="preserve">ex quo. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">in <lb/>cipit loco illius extremum, ad eundem rurlus re <lb/>dit:</s> <s xml:space="preserve"><unsure/> illa. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">continuò commota, extremum rurſus <lb/>efficitur primum. </s> <s xml:space="preserve">quamobrem manifeſtum, ꝙ in <lb/>de mutatnm eſt. </s> <s xml:space="preserve">quapropter (vt dictum eſt prius) <lb/>non eſt incõueniens ipſ<unsure/>u<unsure/>m miracolorum oĩum <lb/>eſſe principlum. </s> <s xml:space="preserve">Ea igi ur, quæ circa libram fiũt, <lb/>ad circulum referuntur: </s> <s xml:space="preserve">quæ vero circa vectem, <lb/>ad ipſam librã: </s> <s xml:space="preserve">alia autem ferè omn<unsure/>ia, quæ circa <lb/>męchanicas ſunt motiones, ad vectern<unsure/>. </s> <s xml:space="preserve">Prætereà <lb/>etiã, quoniam vnica exiſtente, quæ ex cehtro eſt, <lb/>linea, nullum aliud alij, quæ in illa ſunt puncto-<lb/>rum æqua velocitate feratur; </s> <s xml:space="preserve">ſed cirius ſemper <lb/>quod à manente termino eſt remo ius, pleraque <lb/>miraculorum accidũt in circuli motionibus: </s> <s xml:space="preserve">de <lb/>quibus in ijs, quæ poſthac addacentur, quęſtioni <lb/>bus erit manifeſtum. </s> <s xml:space="preserve">Quoniam autem ſecundũ <lb/>contrarias fimul motiones mouetur circulus: </s> <s xml:space="preserve">& </s> <s xml:space="preserve"><lb/>alterũ quidem diametri extremum vbi A, in an-<lb/>tè mouetur, alterum verò vbi B. </s> <s xml:space="preserve">ad retro; </s> <s xml:space="preserve">effi-<lb/>ciunt nonnulli, vt ab vnica motione multi cõtra <lb/>rio ſimul moueantur circuli: </s> <s xml:space="preserve">quemadmodum, <lb/>ſunt illi, quos in locis proponũt ſacris, æneos, & </s> <s xml:space="preserve"><lb/>ferreos, fabricantes orbiculos. </s> <s xml:space="preserve">Si enim A B circu <lb/>lum alter contigerit circulus in quo CD. </s> <s xml:space="preserve">mota <lb/>circuli in quo A B, diametro in antè, mouebitur <lb/>C D ad retro, diametro circuli vbi eſt A, circa idẽ <lb/>mota. </s> <s xml:space="preserve">In contrarium igitur mouebitur circulus <lb/>vbi CD, ad illum ubi AB. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">rurſus ipſe conti-<lb/>guum ubi EF, in contrarium ſibijpſi mouebitur <lb/>propter eandem cauſam. </s> <s xml:space="preserve">Eodem ẽt modo ſi plu- <pb o="507" file="0507" n="4" rhead="Mechanicæ."/> res fuerint, idẽ facient, uno ſolo commoto. </s> <s xml:space="preserve">Hane <lb/>igitur in circulo exiſtentem animaduertens na-<lb/>turam architecti, in ſtrumentũ fabricant, celãtes <lb/>principium, vt machinæ ſolum manifeftum ſit il <lb/>lud, quod admirationẽ pręſtat, cauſa verò lateat.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">In primis igitur, quæ accidunt circa librã, du-<lb/>bitare faciunt, quamnàm ob cauſam exactiores <lb/>minoribus maiores ſunt libræ. </s> <s xml:space="preserve">huius autem rei <lb/>principium eſt, quamobrem in ipſo circulo, quæ <lb/>plus à cent<unsure/>ro diſter linea, eadẽ ui cõmota cit<unsure/>ius <lb/>fertur, quàm illa, quæ minus diſtar. </s> <s xml:space="preserve">Citius enim <lb/>bifariam dicitur: </s> <s xml:space="preserve">ſiue enim in minori tempore <lb/>zqualem pertranſi@ locũ, citius feciſſe dicimus: <lb/></s> <s xml:space="preserve">ſeu in æquali maiorem. </s> <s xml:space="preserve">Maior autem in æquali <lb/>tempore maiorem deſcribit circulum: </s> <s xml:space="preserve">qui enim <lb/>extra eſt, maior eo qui intus eft. </s> <s xml:space="preserve">Horum autẽ cau <lb/>fa, qm̄ duas fertur lationesea, quæ circulum de-<lb/>ſcribit, linea. </s> <s xml:space="preserve">Quandoquidem igitur in propor-<lb/>tione fertur aliqua id, quod fertur, ſuper rectam <lb/>ferri neceſſe: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">hæc diameter efficitur figuræ, <lb/>quam faciunt illæ, quæ in huiuſmodi proportio <lb/>ne coaptant̃, lineę. </s> <s xml:space="preserve">Sit enim proportio ſecũdum <lb/>quam latum fertur, quam habet A B ad AC: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">A <lb/>quidem fertur verſus B, A B uerò ſubterferatur <lb/>verſus M C: </s> <s xml:space="preserve">latum aut<unsure/>em ſit A quidem ad D. </s> <s xml:space="preserve">ubi <lb/>autem eſt A B, uerſus E: </s> <s xml:space="preserve">quoniã igitur la@ionis <lb/>erat proportio, quam A B habet ad A C, neceſſe <lb/>eſt & </s> <s xml:space="preserve">A D ad A E hanc habere proportionem. </s> <s xml:space="preserve">Si-<lb/>mile igitur eſt proportione paruum quadrilate-<lb/>rum maiori; </s> <s xml:space="preserve">quamobrẽ & </s> <s xml:space="preserve">eadẽ illorum eſt dia-<lb/>meter: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">A erit ad F. </s> <s xml:space="preserve">Eodem etiam oſtendet̃ mo-<lb/>do, vbicu<unsure/>nq; </s> <s xml:space="preserve">latio deprehendatur; </s> <s xml:space="preserve">ſemper enim <lb/>ſupra diametrum erit. </s> <s xml:space="preserve">Manifeſtum igitur, quòd <lb/>id, quod ſecundum diametrum duabus fertur la <lb/>tionibus, neceſſariò ſecundum laterum propor- <pb o="508" file="0508" n="5" rhead="Ariſt. Quæſtiones."/> tionem fertur. </s> <s xml:space="preserve">Sienim ſecundum aliam quam-<lb/>piam, nõ fertur ẜ m dia metrum. </s> <s xml:space="preserve">Si autem in nul <lb/>la fertur proportione ſecundum duas lationes <lb/>nullo in tempore, rectã eſſe lationem eſt impoſ-<lb/>ſibile. </s> <s xml:space="preserve">Sit enim recta. </s> <s xml:space="preserve">Poſita igitur hac pro diame <lb/>tro, & </s> <s xml:space="preserve">circum reple is lateribus, illud quod fer-<lb/>tur, ſecundum laterum pro portionem ferri n<unsure/>e-<lb/>ceſſe eſt: </s> <s xml:space="preserve">hoc enim demonſtratum eſt prius. </s> <s xml:space="preserve">non <lb/>igitur rectam efficiet id, quod ſecundùm nullam <lb/>proportionem in nullo fertur tempore. </s> <s xml:space="preserve">Siautẽ <lb/>ẜm quam piam feratur proportionem, & </s> <s xml:space="preserve">in tem <lb/>pore quopiam hoc neceſſe eſt tem pus rectam eſ <lb/>ſe lationem, per ea, quæ retro ſunt dicta. </s> <s xml:space="preserve">Quam-<lb/>obrem circulare eſtid, quod ſecundũ nullam, <lb/>proportionem nullo in tempore duas fertur la-<lb/>tiones Quòd quidem igitur ea, quæ circulum do<unsure/> <lb/>ſcribir, duas ſimul feratur lationes, manifeſtum <lb/>eſt cùm ex iſtis, tum quia ẜ m rectum lata, aſt ꝑ. <lb/></s> <s xml:space="preserve">pendiculum peruenit, vt ſit rurſus ipſa à centro <lb/>perpendiculum. </s> <s xml:space="preserve">Sit circulas A B C D: </s> <s xml:space="preserve">extremum <lb/>autem vbi eſt B, feratur ad ipſum D: </s> <s xml:space="preserve">peruenit ſa <lb/>hè aliquando ad ipſum C. </s> <s xml:space="preserve">Si quidẽ igit<unsure/>ur in pro <lb/>portione feratur, quam haber BE, EC fertur vti <lb/>que ſecundùm diametrum vbi BC. </s> <s xml:space="preserve">nunc autem <lb/>quoniam in nulla propor:</s> <s xml:space="preserve"><unsure/> ione, in circunferen-<lb/>tia certè fertur vbi B E C. </s> <s xml:space="preserve">Si autem duobus ab <lb/>eadem potemtia latis, hoc quidem plus ræpella-<lb/>tur, illud verò minus, rationi conſentaneum eſt <lb/>tardius moueri id, quod plus repellitur, eo qùod <lb/>repellitur minus: </s> <s xml:space="preserve">quod videtur accidere maiori <lb/>& </s> <s xml:space="preserve">minori illarum, q́uæ ex centro circulos deſcri <lb/>bunt. </s> <s xml:space="preserve">quoniam enim proprius eſt manenti, eius <lb/>quæ minor eſt, extrem um, quàm id quod eſt ma <lb/>oris, veluti retractum in contrariũ ad medium, <lb/>ardius fertur minoris extremũ. </s> <s xml:space="preserve">Omni quidem <pb o="509" file="0509" n="6" rhead="Mechanicæ."/> igitur circulum deſcribenti iſtuc accidit: </s> <s xml:space="preserve">fertur-<lb/>q́ue eam quæ ẜm naturam eſt lationem, ſecun-<lb/>dum circunferentiam: </s> <s xml:space="preserve">illam verò quę pręter na <lb/>turam, in tranſuerſum, & </s> <s xml:space="preserve">ſecundùm centrum. <lb/></s> <s xml:space="preserve">maiorem aut<unsure/>ẽ ſemper eam, quæ præter naturã <lb/>eſt, ipſa minor fertur: </s> <s xml:space="preserve">quia enim centro eſt vici-<lb/>nior, quod trahit, vincitur magis<unsure/>: </s> <s xml:space="preserve">Quòd autem-<unsure/> <lb/>magis quod præter natui<unsure/>ã eſt mouetur ipſa mi-<lb/>nor, quàm maior illarũ, quæ ex centro circulos <lb/>deſcribũt ex ijs eſt manifeſtum. </s> <s xml:space="preserve">Sit circulus vbi <lb/>B C D E & </s> <s xml:space="preserve">alter in hoc minorvbi M N O P, circa <lb/>idem centrum A & </s> <s xml:space="preserve">proijciantur diametri in ma <lb/>gno quidem, in quibus CD, BE, in minori ve-<lb/>10 ipſæ MO, N P: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">altera parie longius quadra <lb/>tum ſuppleatur DKRC: </s> <s xml:space="preserve">ſi quidem AB circu-<lb/>lum deſcribẽs ad id perueniet, vnde eſt egreſſa; </s> <s xml:space="preserve"><lb/>manifeſtum eſt quod ad ipſam fertur A B. </s> <s xml:space="preserve">Simi <lb/>literetiam A M ad ipſam A M perueniet. </s> <s xml:space="preserve">Tar-<lb/>dius autem fertur A M, quàru A B quemadmo-<lb/>dum dictum eſt: </s> <s xml:space="preserve">quia maior fit repulſio & </s> <s xml:space="preserve">magis <lb/>rerrahitur A M. </s> <s xml:space="preserve">Ducatur igitur ipſa A L F, & </s> <s xml:space="preserve">ab <lb/>ipſo L perpendiculum ad ip ſam A B, ipſa L Q in <lb/>minore circulo: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">rurſum ab L ducatur iuxta A <lb/>B L S, & </s> <s xml:space="preserve">S T ad ipſam A B perpendiculum, & </s> <s xml:space="preserve">ip. </s> <s xml:space="preserve"><lb/>fa F X: </s> <s xml:space="preserve">ipſæ igitur ubi ſunt S T, & </s> <s xml:space="preserve">L Q, æquales: </s> <s xml:space="preserve"><lb/>ipſa ergo B T minor eſt, quàm M Q. </s> <s xml:space="preserve">æquales <lb/>enim rectæ lineæ in æqualibus coniectæ circulis <lb/>perpẽdiculares a diametro, minorẽ diametri re-<lb/>fecant ſectionẽ in maioribus circulis, eſt autem <lb/>ipſa S T æqualis ipſi L Q. </s> <s xml:space="preserve">In quanto autem tema <lb/>pore ipſa A L ipſam M L lata eſt, in tanto tem@ <lb/>poris ſpatio in maiori circulo maiorem, quàm <lb/>fit B S, latum erit extremum ipſius B A. </s> <s xml:space="preserve">Latio <lb/>quidem igitur ſecundùm naturam æqualis: </s> <s xml:space="preserve">ea <lb/>a<unsure/>utem quæ præter naturam eſt minor, videlices <pb o="510" file="0510" n="7" rhead="Ariſt. Quæſtiones."/> B T, quàm M Q. </s> <s xml:space="preserve">Oportet autem proportionabi-<lb/>liter eſſe, ſicut quod eſt ſecundũ naturã, ita quod <lb/>eſt pręter naturam, ad id quod eſt pręter naturã; <lb/></s> <s xml:space="preserve">maiorem igituĩ circunferentiam pertranſiuit, ꝗ̃ <lb/>ſit ipſa S B. </s> <s xml:space="preserve">Neceſſe autem eſt ipſam F B in hoc <lb/>rẽpore pertran ſiſſe: </s> <s xml:space="preserve">hic. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">erit, quando proportio <lb/>nabiliter vtrinq; </s> <s xml:space="preserve">accidit, quod eſt præter naturã, <lb/>ad id quod eſt ſecundùm naturam. </s> <s xml:space="preserve">Si igitur ma-<lb/>ius eſt, quod ſecundum naturam in maiori, & </s> <s xml:space="preserve"><lb/>quod eſt præter naturam. </s> <s xml:space="preserve">magis vtique hic coin <lb/>cidit vno modo: </s> <s xml:space="preserve">ita quod B ſit latum per ipſam <lb/>B F in tanto tempore, in quo M punctum per <lb/>ipſam M L. </s> <s xml:space="preserve">hic enim ſecundùm naturam quidẽ <lb/>figno B fit X F: </s> <s xml:space="preserve">eſt enim ab ipſo F perpendiculũ: </s> <s xml:space="preserve"><lb/>præter naturam verò ad ipſam X B. </s> <s xml:space="preserve">Eſt autem <lb/>quemadmodum F X ad X B, ſic L Q. </s> <s xml:space="preserve">ad M Q. </s> <s xml:space="preserve">ma <lb/>nifeſtum autem, ſi coniunguntur abipſa B M, <lb/>ad F L. </s> <s xml:space="preserve">Si autem minor, aut maior quàm ſit F B, <lb/>erit illa quam latum eſt B, non ſimiliter erit, ne-<lb/>que proportionale in vtriſque quod eſt ſecundũ <lb/>naturam, ad id quod eſt præter naturam. </s> <s xml:space="preserve">Quam <lb/>igicur ob cauſam ab eadem potentia celerius fe@ <lb/>tur id quod plus à centro diſtat punctum, ex ijs, <lb/>quæ dicta ſunt, eſt manifeſtum.</s> <s xml:space="preserve"/> </p> </div> <div type="section" level="1" n="4"> <head style="it" xml:space="preserve">Quæſtiones.</head> <p> <s xml:space="preserve">C V R aũt maiores libræ exactiores <lb/> <anchor type="note" xlink:label="note-0510-01a" xlink:href="note-0510-01"/> ſunt minotib<emph style="sub">9</emph>. </s> <s xml:space="preserve">palã eſt ex ijs. </s> <s xml:space="preserve">Spar <lb/>tum. </s> <s xml:space="preserve">n fit centrũ: </s> <s xml:space="preserve">id pãq; </s> <s xml:space="preserve">manet. <lb/></s> <s xml:space="preserve">quod aũt libræ vtrinq; </s> <s xml:space="preserve">eſt, exeun <lb/>tes à centro. </s> <s xml:space="preserve">Ab eodẽ igit̃ põdere <lb/>citius moueri neceſſe eſt extre-<lb/>mũ libræ, quo plus à ſparto diſceſſerit. </s> <s xml:space="preserve">Et nõnul <lb/>la quidẽ in paruis libris impoſita nõ manifeſta <pb o="511" file="0511" n="8" rhead="Mechanicæ."/> fenſui ſunt pondera: </s> <s xml:space="preserve">in magis aũt maniſeſta: </s> <s xml:space="preserve">ni <lb/>hil enim prohibet minorem moueri magnitudi <lb/>nem, ꝗ̃ vt viſioni ſit maniſeſta. </s> <s xml:space="preserve">In magna aũt li-<lb/>bra idem pondus viſibile efficit magnitudo. </s> <s xml:space="preserve">Quę <lb/>dam verò manifeſta quidem ſunt in vtriſq;</s> <s xml:space="preserve">, ſed <lb/>multo magis in maioribus, qm̄ multo maior in <lb/>clinationis fit magnitudo ab eodem ꝑondere <lb/>in maioribus. </s> <s xml:space="preserve">Quamobrem machinanturij, qui <lb/>purpuram vendunt, vt pendendo defraudent, tũ <lb/>ad medium ſpartum non ponentes: </s> <s xml:space="preserve">tum plum-<lb/>bum in alteraruram libræ partem infundentes: <lb/></s> <s xml:space="preserve">aut ligni gđ ad radicẽ vergebat, in eam quam de <lb/>ferri vola<unsure/>nt, partem conſtituentes; </s> <s xml:space="preserve">aut ſi nodum <lb/>habuerit: </s> <s xml:space="preserve">ligni enim grauior illa eſt pars, in qua <lb/>eſt radix, nodus vero radix quædam eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="1"> <note position="left" xlink:label="note-0510-01" xlink:href="note-0510-01a" xml:space="preserve">1</note> </div> <p> <s xml:space="preserve">Cut ſiquidẽ ſurſum ſuerit ſpartũ, qñ deorsũ lato <lb/> <anchor type="note" xlink:label="note-0511-01a" xlink:href="note-0511-01"/> põdere, quiſpiã id admouet, rurſum aſcendit li-<lb/>bra: </s> <s xml:space="preserve">ſi autem deorſum conſtitutum ſuerit, non <lb/>aſcendit, ſed manet? </s> <s xml:space="preserve">An quia ſurſum quidẽ ſpar <lb/>to exiſtente, plus libræ extra perpendiculum fit: <lb/></s> <s xml:space="preserve">ſpartum enim eſt perpendiculum: </s> <s xml:space="preserve">quare neceſſe <lb/>eſt deorſum ferri id quod plus eſt, donec aſcen-<lb/>dat quæ bifariam libram diuidit, ad ipſum per-<lb/>pendiculũ, cùm onus incumbat ad libræ partem <lb/>furſum raptam. </s> <s xml:space="preserve">Sit libra recta vbi B C, ſpartum <lb/>autem A D. </s> <s xml:space="preserve">hoc igitur deorſum proiecto perpen <lb/>diculum erit vbi A D M. </s> <s xml:space="preserve">Si igitur in ipſo B pona <lb/>tur onus, B quidem erit vbi E, C, autem vbi H. </s> <s xml:space="preserve"><lb/>quamobrem ea quæ bifariam libram ſecat, pri-<lb/>mo quidem erit D M ipſius perpendiculi: </s> <s xml:space="preserve">incum <lb/>bente autẽ onere erit D G. </s> <s xml:space="preserve">quare libra ipſius vbi <lb/>E H, quod extra perpendiculum eſt A M, vbi eſt <lb/>P Q, maius eſt dimidio. </s> <s xml:space="preserve">Si igitur amoueatur <lb/>onus abipſo E, neceſſe eſt deorſum ferri H, mi-<lb/>@@s enim eſt ipſum E. </s> <s xml:space="preserve">Si quidem igitur ſurſum <pb o="512" file="0512" n="9" rhead="Ariſt. Quæſtiones"/> habuerit ſpartum, rurſum propter hoc aſcendit<unsure/> <lb/>libta. </s> <s xml:space="preserve">Si autẽ deorſum fuerit, id, quod ſubſtat, cõ <lb/>trarium facit: </s> <s xml:space="preserve">plus enim dimidio fit libræ, quæ <lb/>deorſum eſt pars, quàm quod perpendiculum ſe <lb/>cet, quapropter nõ aſcẽdit: </s> <s xml:space="preserve">eleuata enim pars le <lb/>uior eſt. </s> <s xml:space="preserve">Sit libra recta vbi N O, perpendiculum <lb/>autem K L M bifariã igitur ſecatu@ K G. </s> <s xml:space="preserve">Impo-<lb/>ſito autem onere in ipſo N, erit quidẽ N vbi O, <lb/>ipſum autem G vbi R, K L autem vbi L P. </s> <s xml:space="preserve">quare <lb/>maius eſt K O, quàm L R, ipſo P K L. </s> <s xml:space="preserve">Et ablato <lb/>igitur onere, neceſſe eſt manere: </s> <s xml:space="preserve">in cumbit enim <lb/>ceu onus exceſſus medietatis eius vbi eſt F.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="2"> <note position="right" xlink:label="note-0511-01" xlink:href="note-0511-01a" xml:space="preserve">2</note> </div> <p> <s xml:space="preserve">Cur exiguę vires (quem admodum à principio <lb/> <anchor type="note" xlink:label="note-0512-01a" xlink:href="note-0512-01"/> dictum eſt) vecte magna mouent pondera, vecis <lb/>inſuper onus accipien tis? </s> <s xml:space="preserve">cùm ſacilius ſit mino-<lb/>grem mouere grauitatem: </s> <s xml:space="preserve">minor autẽ eſt ſine ve-<lb/>cte. </s> <s xml:space="preserve">An quoniã ipſe vectis eſt in cauſa hbra exi-<lb/>ſtens, ſpartũ infernè habens, in inæqualia diui-<lb/>ſa. </s> <s xml:space="preserve">hypomochlion enim eſt ſpartum. </s> <s xml:space="preserve">a mbo nan <lb/>que ſtamt, vt centrum. </s> <s xml:space="preserve">quoniam autem ab ęqua-<lb/>ſi pondere celerius mouetur maior earum, q̃ à <lb/>centro ſunt: </s> <s xml:space="preserve">duo verò pondera, quod mouet, & </s> <s xml:space="preserve"><lb/>quod mouetur: </s> <s xml:space="preserve">quod igitur motum pondus ad-<lb/>mouens, longitudo patitur ad longitudinẽ. </s> <s xml:space="preserve">ſem <lb/>per autem quanto ab hy pomochlio diſtabit ma <lb/>gis, tanto facilius mo<unsure/>uebit. </s> <s xml:space="preserve">Cauſa autem eſt, quę <lb/>retro cõmemorata eſt: </s> <s xml:space="preserve">quoniam quę plus à cen-<lb/>@ro diſtat, maiorem deſcribit circuium: </s> <s xml:space="preserve">quare ab <lb/>eadem potentia plus ſeparabitur mouens illud, <lb/>quod plus ab hypomochlio diſtabit. </s> <s xml:space="preserve">Sit uectis <lb/>vbi A B, pondus vbi C, quod mouet autẽvbi D, <lb/>hy pomochlion vbi E. </s> <s xml:space="preserve">quod autem vbi eſt D mo <lb/>u<unsure/>ens, vbi F. </s> <s xml:space="preserve">motum autem vbi C. </s> <s xml:space="preserve">pondus, vbi G.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="3"> <note position="left" xlink:label="note-0512-01" xlink:href="note-0512-01a" xml:space="preserve">3</note> </div> <p> <s xml:space="preserve">Cur ij, qui in nauis medio ſunt remiges, maxi <lb/> <anchor type="note" xlink:label="note-0512-02a" xlink:href="note-0512-02"/> me nauem mouent? </s> <s xml:space="preserve">An quia remus vectis eſt: </s> <s xml:space="preserve">hy <pb o="513" file="0513" n="10" rhead="Mechanicæ."/> pomochlion auteni fit ſcalmus, ſtat enim ille ẜ <lb/>pondus verò mare eſt, quod propellit remus: </s> <s xml:space="preserve">ve-<lb/>ctem autem mouens ipſe eſt remex. </s> <s xml:space="preserve">Semper aũt <lb/>plus mouet ponderis, quanto magis ab hypomo <lb/>chlio diſtabit, quicunque id mouet. </s> <s xml:space="preserve">maior enim <lb/>ita fit, quæ ex centro. </s> <s xml:space="preserve">ſcalmus autem hypomo-<lb/>chlion exiſtens, centrum eſt. </s> <s xml:space="preserve">In medio autem na <lb/>uis plurimum remi intus eſt: </s> <s xml:space="preserve">ilia enim parte la-<lb/>tiſſima eſt nauis: </s> <s xml:space="preserve">quare maior vtrinq; </s> <s xml:space="preserve">remi pars <lb/>vtrorunq; </s> <s xml:space="preserve">nauis parietum intrin ſecus eſt. </s> <s xml:space="preserve">Moue-<lb/>tur autem nauis, quoniam appellente ad mare <lb/>remo, extremum illius quod intus eſt, in ante <lb/>prom ouctur. </s> <s xml:space="preserve">nauem verò ſcalmo alligatam ſi-<lb/>mul promoueri contingit, quo remi extremum. <lb/></s> <s xml:space="preserve">vbi enim plurimum maris diuidit remus, eò ma-<lb/>ximè propelli neceſſe eſt. </s> <s xml:space="preserve">plurimum autem di@i <lb/>dit, vbi pars plurima remia ſcalmo eſt. </s> <s xml:space="preserve">Et eam <lb/>cauſam remiges, qui in media ſunt naui, mouent <lb/>illam maximè. </s> <s xml:space="preserve">maxima enim remi pars à ſcalmo <lb/>in nauis medio intus eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="4"> <note position="left" xlink:label="note-0512-02" xlink:href="note-0512-02a" xml:space="preserve">4</note> </div> <p> <s xml:space="preserve">Cur paruum exiſtens gubernaculum, & </s> <s xml:space="preserve">in ex-<lb/> <anchor type="note" xlink:label="note-0513-01a" xlink:href="note-0513-01"/> tremo nauigio tantas habet vires, vt ab exiguo <lb/>temone, & </s> <s xml:space="preserve">ab hominis vnius viribus alioqùin <lb/>modicè vtentis, magnę nauigiorum moueantur <lb/>moles? </s> <s xml:space="preserve">An quoniam gubernaculum vectis eſt: </s> <s xml:space="preserve">o-<lb/>@us autem mare: </s> <s xml:space="preserve">gubernator verò mouens eſt. <lb/></s> <s xml:space="preserve">Non autem ſecundum latitudinẽ, veluti remus, <lb/>mare accipit gubernaculum: </s> <s xml:space="preserve">non enim in antè <lb/>nauigium mouet, ſed ipſum commotum mare <lb/>accipiens inclinat obliquè: </s> <s xml:space="preserve">quoniam enim pon-<lb/>dus eſt mare, contrario innixum modo nauem <lb/>inclinat. </s> <s xml:space="preserve">hypomochlion enim in contrarium <lb/>verſatur: </s> <s xml:space="preserve">mare vero interius, ſi illud exterius. </s> <s xml:space="preserve"><lb/>illud autem ſequitur nauis, quoniam illi eſt ai<unsure/>li-<lb/>@ata. </s> <s xml:space="preserve">Et remus quidem ſecundùm latitudinem <pb o="514" file="0514" n="11" rhead="Ariſt. Quæſtiones."/> onus propellens, & </s> <s xml:space="preserve">ab eodem repulſus, in rectũ <lb/>propellit: </s> <s xml:space="preserve">gubernaculum autem, ut obliquum ia <lb/>cet, hinc inde in obliquum motionē facit. </s> <s xml:space="preserve">In ex <lb/>tremo autē, & </s> <s xml:space="preserve">non in medio iacet, quoniam mo <lb/>uenti facilimū eſt ab extremo motum mouere. <lb/></s> <s xml:space="preserve">Prim a enim pars celerimè fertur; </s> <s xml:space="preserve">quoniã quem <lb/>adm odum in ijs quæ feruntur, in fine deficit la-<lb/>tio, ſic ipſius cōtinui in fine imbeciliſſima eſt la-<lb/>tio. </s> <s xml:space="preserve">imbeciliſſima autem ad expellendum eſt fa <lb/>cilis. </s> <s xml:space="preserve">Propter hæcigitur in puppi gubernaculum <lb/>ponitur. </s> <s xml:space="preserve">Nec minus, quoniā parua ibi motione <lb/>ſacta, multò maius interuallum fit in ultimo: </s> <s xml:space="preserve">ꝗa <lb/>æqualis angulus ſemper maiorem ſpectat: </s> <s xml:space="preserve">tan-<lb/>toq́ue magis. </s> <s xml:space="preserve">quanto maiores fuerint illæ, quæ <lb/>con@inẽt. </s> <s xml:space="preserve">Ex ijs etiam manifeſtum eſt, quam ob <lb/>cauſſam magis in contrarium procedit nauigiũ, <lb/>quàm remi ipſius palmula. </s> <s xml:space="preserve">eadem enim magni <lb/>tudoijſdem mota uiribus, in aete plus, quàm in <lb/>aqua progreditur. </s> <s xml:space="preserve">Si enim A B remus, Guerò <lb/>ſcalmus: </s> <s xml:space="preserve">A autem in nauigio ſit remi principiũ, <lb/>B uerò in mari palmula. </s> <s xml:space="preserve">Si igitur A ubi D tranſ. </s> <s xml:space="preserve"><lb/>latum eſt, non erit B ubi E: </s> <s xml:space="preserve">æqualis enim B E ipſi <lb/>A C. </s> <s xml:space="preserve">æquale igitur tranſlatū erit, ſed minus. </s> <s xml:space="preserve">erit <lb/>igitur ubi eſt F. </s> <s xml:space="preserve">minor enim C F, ipſa A D. </s> <s xml:space="preserve">quare <lb/>ipſa G F, ipſa D F. </s> <s xml:space="preserve">ſimiles enim ſunt trianguli. </s> <s xml:space="preserve"><lb/>Stans autem erit medium, ubi eſt C. </s> <s xml:space="preserve">in contrariũ <lb/>enim ipſi, quod in mari eſt, extremo uidelicet B <lb/>procedit, ubi extremum in nauigio eſt A. </s> <s xml:space="preserve">Non <lb/>procedere autēubi eſt D. </s> <s xml:space="preserve">niſi commouere@ur na <lb/>uigium, & </s> <s xml:space="preserve">eo transferretur, ubi remi eſt princi-<lb/>plum Idipſnm etiam facit gubernaculam, niſi ꝙ <lb/>(ut dictum eſt terro) nihil nauigio ad id, quod-<lb/>antè eſt, confert, ſed ſolùm puppim in obliquũ <lb/>pell@t, ubicunq; </s> <s xml:space="preserve">fuerit in con@rariū enim eo mo <lb/>do uergit prora. </s> <s xml:space="preserve">Vbi igitur applicatum eſt gu- <pb o="515" file="0515" n="12" rhead="Mechanicæ."/> bernaculum, id oporter rei motæ, ceu quoddam <lb/>intelligere medium: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">quemadmodũ ſcalmus <lb/>remo. </s> <s xml:space="preserve">Medium autem procedit ſecundùm quod <lb/>gubernaculum trãsfertur. </s> <s xml:space="preserve">ſi quidē introrſus agit, <lb/>& </s> <s xml:space="preserve">puppis eo transfertur. </s> <s xml:space="preserve">prora verò ad contra-<lb/>rium vergit. </s> <s xml:space="preserve">in eodem enim exiſtente prora, to-<lb/>tum transfertur nauigium.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="5"> <note position="right" xlink:label="note-0513-01" xlink:href="note-0513-01a" xml:space="preserve">5</note> </div> <p> <s xml:space="preserve">Cur quando antenna ſublimior fuerit, ijſdem <lb/> <anchor type="note" xlink:label="note-0515-01a" xlink:href="note-0515-01"/> uelis, & </s> <s xml:space="preserve">uento eodẽ celerius ferũtur nauigia? </s> <s xml:space="preserve">An <lb/>quia malus quidem fit uectis: </s> <s xml:space="preserve">hypomochlion ue <lb/>rò mali ſedes, in qua collocatur: </s> <s xml:space="preserve">pondus autem, <lb/>quod moueri debet, ipſum nauigium: </s> <s xml:space="preserve">mou@s ve <lb/>ro is, qui vela tendit, ſpiri@us. </s> <s xml:space="preserve">Si igitur quanto re <lb/>motius fuerit hypomochion, facilius eadem po-<lb/>tentia, & </s> <s xml:space="preserve">citius idem mouet pondus, altius cer-<lb/>tè ſublata antenna, velum à mali ſede, quæ hypo <lb/>mochlion eſt, remo@ius faciens, id efficie@.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="6"> <note position="right" xlink:label="note-0515-01" xlink:href="note-0515-01a" xml:space="preserve">6</note> </div> <p> <s xml:space="preserve">Cur quando ex puppi nauigare voluerint, non <lb/> <anchor type="note" xlink:label="note-0515-02a" xlink:href="note-0515-02"/> flante ex puppi vento, veli quidem partem, quæ <lb/>ad gubernatorem vergit, conſtringunt: </s> <s xml:space="preserve">illam ve-<lb/>rò quæ proram verſus eſt, pedem facientes rela <lb/>xant? </s> <s xml:space="preserve">An quia retrahere quidem multo exiſten <lb/>tevento gubernaculum non poteſt: </s> <s xml:space="preserve">pauco autẽ <lb/>poteſt, quem conſtringunt. </s> <s xml:space="preserve">Propellit quidem igi <lb/>tur ipſe ventus: </s> <s xml:space="preserve">in puppim vero illum cōſtituit, <lb/>gubernaculum retrahens, & </s> <s xml:space="preserve">mare compellẽs: </s> <s xml:space="preserve">ſi-<lb/>mul & </s> <s xml:space="preserve">nautæ ipſi cum vento contendunt: </s> <s xml:space="preserve">in cõ-<lb/>trariam enim ſe reclinant partem.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="7"> <note position="right" xlink:label="note-0515-02" xlink:href="note-0515-02a" xml:space="preserve">7</note> </div> <p> <s xml:space="preserve">Cur ex figurarum genere, q̃cunq; </s> <s xml:space="preserve">rotũdę ſunt <lb/> <anchor type="note" xlink:label="note-0515-03a" xlink:href="note-0515-03"/> & </s> <s xml:space="preserve">circinatæ, facilius mouentur? </s> <s xml:space="preserve">Trifariam autẽ <lb/>circulum rotari contingit. </s> <s xml:space="preserve">aut enim @m abſidem <lb/>centro ſimul moto, quemadmodum paluſtriver <lb/>titur rota: </s> <s xml:space="preserve">aut circa manens centrū, veluti tro-<lb/>chleæ ſtante centro: </s> <s xml:space="preserve">autin pauimento manente <lb/>@ẽtro, ſicut figuli rota conuertitur. </s> <s xml:space="preserve">An celer@ima <pb o="516" file="0516" n="13" rhead="Ariſt. Quæſtiones"/> quidem huiuſmodi ſunt, quoniam parua ſuipa@ <lb/>te planum contingunt, veluti circulas ſecūdum <lb/>punctum: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">quoniam non offenſant: </s> <s xml:space="preserve">à terra em̄ <lb/>ſemotus eſt angulus. </s> <s xml:space="preserve">Pręterea etiam cui obuiam <lb/>fiunt corpori, id rurſum ſecundùm puſillam tan <lb/>gunt. </s> <s xml:space="preserve">ſi autem rectilineum eſſet, rectitudine ſua <lb/>multum plani contingeret. </s> <s xml:space="preserve">Ad hæc quò mutat <lb/>pondus, eo motor mouet. </s> <s xml:space="preserve">cùm igitur ad rectum <lb/>ſuper plano circuli fuerit diameter, planū ſecun <lb/>dùm punctum, contingēte circulo æquale vtriu-<lb/>que pondus difterminat diameter. </s> <s xml:space="preserve">cùm autē mo <lb/>uetur, plus illico, ad quòd mouetur, ceui@de nu <lb/>tans. </s> <s xml:space="preserve">ab impellẽre facilius in ante mouetur: </s> <s xml:space="preserve">quò <lb/>enim vnumquodque vergit, mouetur ex facili: <lb/></s> <s xml:space="preserve">ſi quidem difficulter ad cōtrarium nutus ſui mo <lb/>uetur modum. </s> <s xml:space="preserve">Præterea nonnulli autumn@nt ꝙ <lb/>circuli linea in perpeti verſatur motu, quemad-<lb/>modum manentia propter contrarium nixũ ma <lb/>nent: </s> <s xml:space="preserve">ſicur maioribus contingit circulis ad mino <lb/>res. </s> <s xml:space="preserve">Celerius enim ab æquali mouentur potentia <lb/>maiores circuli, mouentq́ue onera, quoniam cir <lb/>culi maioris angulus ad minoris angulum cir-<lb/>culi nutum habet quendam: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ſicut diameter ad <lb/>diametrum, ita maior circulus ad minorem. </s> <s xml:space="preserve">it fi <lb/>niti autem ſunt minores. </s> <s xml:space="preserve">Si autem ad alte@um <lb/>nutum habet circulus, ſimiliter eſt bene mobi-<lb/>lis. </s> <s xml:space="preserve">Et aliam ſanè habet inclinationem circulus, <lb/>& </s> <s xml:space="preserve">ea quæ à circulo mouentur, licèt planitiẽ abſi-<lb/>de non contingat, ſed aut iuxta planitiẽ, aut velu <lb/>tì trocleæ. </s> <s xml:space="preserve">etenim hoc ſe habentes modo facilli-<lb/>me mouentur, & </s> <s xml:space="preserve">onera commouent. </s> <s xml:space="preserve">An nõ quia <lb/>parua ſui portione cùm tangit, tum offenſat cir-<lb/>culus, ſed aliam ob cauſam. </s> <s xml:space="preserve">ea autem eſt, quæ di <lb/>cta eſt prius, quod circulus ſcilicet ex duabus ef-<lb/>fectus eſt lationibus: </s> <s xml:space="preserve">quam ob rem illarum alte- <pb o="517" file="0517" n="14" rhead="Mechanicæ."/> ram pro nutu ſemper habet, & </s> <s xml:space="preserve">veluti continuo <lb/>motum illum mòuent, quicunq; </s> <s xml:space="preserve">mouent, quan-<lb/>do ſecundùm circun ferentiam illum mouerint: <lb/></s> <s xml:space="preserve">latam enim ipſam mouent. </s> <s xml:space="preserve">Eam quidem igitur, <lb/>quæ in obliquum eſt, motionem ipſum impellit <lb/>mouens: </s> <s xml:space="preserve">ſecundum vero illam, quæ ſuper diame <lb/>trum eſt, ſeipſum mouet circulus.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="8"> <note position="right" xlink:label="note-0515-03" xlink:href="note-0515-03a" xml:space="preserve">8</note> </div> <p> <s xml:space="preserve">Cur ea, quæ per maiores circulos tolluntur & </s> <s xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-0517-01a" xlink:href="note-0517-01"/> trahuntur, facilius & </s> <s xml:space="preserve">ci@ius moueri contingit, ve <lb/>lu@i maioribus trochleis quàm minoribus, & </s> <s xml:space="preserve"><lb/>fcytalis ſimiliter? </s> <s xml:space="preserve">An quoniã, qnanto maior fue-<lb/>ri@@illa quæ à centro eſt, in ęquali tempore maius <lb/>mouetur ſpatium. </s> <s xml:space="preserve">Quam ob rem æquali inexiſtẽ <lb/>te onere, idem faciet: </s> <s xml:space="preserve">quemadmodum diximus, <lb/>& </s> <s xml:space="preserve">maiores libras minoribus exactiores eſſe. </s> <s xml:space="preserve">ſpar <lb/>tum enim in illis centrum eſt: </s> <s xml:space="preserve">libræ autem vtrin <lb/>que partes, quæ ex centro ſunt, exiſtunt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="9"> <note position="right" xlink:label="note-0517-01" xlink:href="note-0517-01a" xml:space="preserve">9</note> </div> <p> <s xml:space="preserve">Cur facilius quando ſine pondere eſt, moue-<lb/> <anchor type="note" xlink:label="note-0517-02a" xlink:href="note-0517-02"/> tur libra, quàm cum pondus habet? </s> <s xml:space="preserve">Similiq́ mo <lb/>do rota, & </s> <s xml:space="preserve">huiuſmodi quippiam, quod grauius <lb/>quidem eſt, maius autem minore & </s> <s xml:space="preserve">leuiore? </s> <s xml:space="preserve">An <lb/>quia non ſolùm in contrarium quod graue eſt, <lb/>ſed in obliquum etiam difficulter mouetur. </s> <s xml:space="preserve">In <lb/>contrarium enim ei, ad quod vergit onus, moue-<lb/>re difficile eſt: </s> <s xml:space="preserve">quò autem vergit, eſt facilè. </s> <s xml:space="preserve">in obli <lb/>quum autem haudquaquam vergit.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="10"> <note position="right" xlink:label="note-0517-02" xlink:href="note-0517-02a" xml:space="preserve">10</note> </div> <p> <s xml:space="preserve">Cur ſuper ſcytalas facilius portantur onera, <lb/> <anchor type="note" xlink:label="note-0517-03a" xlink:href="note-0517-03"/> quã ſ@per currus, cùm tamẽ ij magnas habeant <lb/>rotas, illæ verò puſillas? </s> <s xml:space="preserve">An qui in ſcytalis nulla <lb/>eſt offen ſatio, in curribus autem axis eſt, ad quẽ <lb/>offenſant. </s> <s xml:space="preserve">deſuper enim illum premunt, & </s> <s xml:space="preserve">late-<lb/>ribus. </s> <s xml:space="preserve">quod autem eſt in ſcycalis, ad iſthæc duo <lb/>mouetur, & </s> <s xml:space="preserve">inſernè ſubſtrato ſpatio, & </s> <s xml:space="preserve">onere ſu <lb/>per impoſito. </s> <s xml:space="preserve">in vtriſque enim ijs reuoluitur lo-<lb/>cis circulus, & </s> <s xml:space="preserve">motus impellitur.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="11"> <note position="right" xlink:label="note-0517-03" xlink:href="note-0517-03a" xml:space="preserve">11</note> </div> <pb o="518" file="0518" n="15" rhead="Ariſt. Quæſtiones"/> <p> <s xml:space="preserve">Curlongius feruntur miſſilia funda, quàm ma <lb/> <anchor type="note" xlink:label="note-0518-01a" xlink:href="note-0518-01"/> numiſſa, cùm alioquin proiector mann magis <lb/>pondus comprehendat, quàm cùmillud ſuſpen-<lb/>dit? </s> <s xml:space="preserve">Præterea ſic quidem duo mouet pondera, <lb/>fundæ videlicet, & </s> <s xml:space="preserve">miſſilis: </s> <s xml:space="preserve">illo aũt modo ſolum <lb/>miſſile. </s> <s xml:space="preserve">An quia in funda quidem commotum <lb/>miſſile funditur, proijcit: </s> <s xml:space="preserve">fundam enim circulo <lb/>ſubinde rotans, id iaculatur: </s> <s xml:space="preserve">ex manu autem à <lb/>quiete eſt initium: </s> <s xml:space="preserve">omnia autem cùm in motu <lb/>ſunt, quàm cùm quieſcunt, facilius mouẽtur. </s> <s xml:space="preserve">An <lb/>& </s> <s xml:space="preserve">eam ob cauſam e@t, ſed nec minus etiam, quia <lb/>in fundæ vſu manus quidem fit centrum: </s> <s xml:space="preserve">ſunda <lb/>vero, quod à centro exit. </s> <s xml:space="preserve">quanto aũt productius <lb/>ſueritid, quod à cētro eſt, tanto citius mouetur. <lb/></s> <s xml:space="preserve">iactus aūt qui māu fit, fundę reſpectu breuis eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="12"> <note position="left" xlink:label="note-0518-01" xlink:href="note-0518-01a" xml:space="preserve">12</note> </div> <p> <s xml:space="preserve">Cur circa idem iugum maiores collopes faci-<lb/> <anchor type="note" xlink:label="note-0518-02a" xlink:href="note-0518-02"/> lius, quàm minores mouentur? </s> <s xml:space="preserve">& </s> <s xml:space="preserve">item ſuculæ, <lb/>quæ graciliores ſunt, ab eadẽ viꝗ̃ craſſiores? </s> <s xml:space="preserve">An <lb/>quía ſecula quidem, & </s> <s xml:space="preserve">iugum cētrum eſt: </s> <s xml:space="preserve">pro-<lb/>minentes autem longitudines eæ, quæ ſunt à cē-<lb/>tro. </s> <s xml:space="preserve">Celerius autem & </s> <s xml:space="preserve">plus mouentur quæ maio <lb/>rum ſunt circulorum ab eadem vi, quàm quę mi <lb/>norum. </s> <s xml:space="preserve">ab eadem enim vi plus transfertur id <lb/>extremum, quod longius à centro diſtat. </s> <s xml:space="preserve">Quam <lb/>ob rem ad iugum quidem inſtrumenta faciunt <lb/>collopas, quibus facilius verſant: </s> <s xml:space="preserve">in gracilibus <lb/>autem ſuculis plus fit id, quod extra lignum e@@. <lb/></s> <s xml:space="preserve">hoc autem id efficitur, quod à centro exit.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="13"> <note position="left" xlink:label="note-0518-02" xlink:href="note-0518-02a" xml:space="preserve">13</note> </div> <p> <s xml:space="preserve">Cur eiuſdem magnitudinis lignum facilius <lb/> <anchor type="note" xlink:label="note-0518-03a" xlink:href="note-0518-03"/> genus frangitur, ſi quiſpiam æquì diductis mani <lb/>bus extrema comprehendens fregerit, quàm ſi <lb/>iuxta genu: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ſi terræ illud applicans pede ſu-<lb/>perimpoſito manu longè diducta confregerit, ꝗ̃ <lb/>prope? </s> <s xml:space="preserve">An quiaibi quidem genu centrũ eſt, hic <lb/>vero ipſe pes. </s> <s xml:space="preserve">quanto autem remotius à centro <pb o="519" file="0519" n="16" rhead="Mechanicæ."/> ſuerit, faciliùs mouetur quodcunq;</s> <s xml:space="preserve">. moueriau-<lb/>tem quod frangitur, neceſſe eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="14"> <note position="left" xlink:label="note-0518-03" xlink:href="note-0518-03a" xml:space="preserve">14</note> </div> <p> <s xml:space="preserve">Cur eæ quæ circa littora appellantur Crocæ, <lb/> <anchor type="note" xlink:label="note-0519-01a" xlink:href="note-0519-01"/> rotunda ſunt figura, cùm alioquin à principio ex <lb/>magnis ſint lapidibus, oſtreiſve? </s> <s xml:space="preserve">An quia ea, q̃ <lb/>plus recedunt à medio in motionibus, feruntur <lb/>celeriùs. </s> <s xml:space="preserve">medium enim fit centrum: </s> <s xml:space="preserve">intcruallũ <lb/>verò ea, quæ à centro. </s> <s xml:space="preserve">Sem per autem maior ab <lb/>æquali motione maiorem deſcribit circulum. <lb/></s> <s xml:space="preserve">quod autem maius in æquali pertranſit tẽpore, <lb/>celerius fertur: </s> <s xml:space="preserve">quæ autem celeriùs ex ę quali fe <lb/>runtur ſpatio, uehementiùs im petunt: </s> <s xml:space="preserve">quę autẽ <lb/>magis impetunt impetuntur & </s> <s xml:space="preserve">magis. </s> <s xml:space="preserve">quam ob <lb/>rem ea quæ plus à medio diſtant, cōfringi neceſ <lb/>ſe eſt, id autem cùm patiantur, rotunda fieri eſt <lb/>neceſſarium. </s> <s xml:space="preserve">Crocis autem propter maris mo-<lb/>tum, quoniam ſimul cum illo agitantur, in perpe <lb/>tua eſſe accidit motione, eoq́; </s> <s xml:space="preserve">verſatas mō ſem <lb/>per offenſare. </s> <s xml:space="preserve">id autem ipſis maximè extremis <lb/>contingere partibus eſt neceſſe.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="15"> <note position="right" xlink:label="note-0519-01" xlink:href="note-0519-01a" xml:space="preserve">15</note> </div> <p> <s xml:space="preserve">Cur quanto longiora ſuntligna, tanto imbe-<lb/> <anchor type="note" xlink:label="note-0519-02a" xlink:href="note-0519-02"/> cilliora fiunt: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ſi tollantur, in flectuntur magis: <lb/></s> <s xml:space="preserve">tametſi quod breue quidem eſt, ceu bicubitum, <lb/>fuerit tenue: </s> <s xml:space="preserve">quod verò cubitorum centum, craſ <lb/>ſum? </s> <s xml:space="preserve">An ꝗa & </s> <s xml:space="preserve">vectis, & </s> <s xml:space="preserve">onus, & </s> <s xml:space="preserve">hypomochlion <lb/>in leuando ipſa fit ligni proceritas: </s> <s xml:space="preserve">prior nanq; </s> <s xml:space="preserve"><lb/>illius pars ceu hypomochlion fit, quod verò in <lb/>extremo eſt, pōdus. </s> <s xml:space="preserve">quam ob rem quanto exten. </s> <s xml:space="preserve"><lb/>ſius fuerit id, quod ab hypocomochlio eſt, tanto <lb/>inflecti neceſſe ẽ magis. </s> <s xml:space="preserve">quo enim plus ab hypo-<lb/>mochlio diſtat, eo magis incuruari neceſſe eſt. </s> <s xml:space="preserve"><lb/>neceſſario igitur extrema vectis eleuantur. </s> <s xml:space="preserve">Siigi <lb/>tur flexilis fuerit vectis, ipſum inflecti magis <lb/>cùm extollitur neceſſe eſt: </s> <s xml:space="preserve">quod lõgis accidit li <lb/>gnis. </s> <s xml:space="preserve">in breuibus autem quod vltimũ eſt, quie- <pb o="520" file="0520" n="17" rhead="Ariſt. Quæſtiones"/> ſcenti hy pomochlio deprope ſit.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="16"> <note position="right" xlink:label="note-0519-02" xlink:href="note-0519-02a" xml:space="preserve">16</note> </div> <p> <s xml:space="preserve">Cur a paruo exift@nte cuneo magna ſcindun-<lb/>tur pondera, & </s> <s xml:space="preserve">corporum moles, validaque fit <lb/>impreſſio? </s> <s xml:space="preserve">An quia cuneus duo ſunt vectes ſibi <lb/>inuicem contrarij: </s> <s xml:space="preserve">vterque autem & </s> <s xml:space="preserve">pondus ha <lb/>b@t, & </s> <s xml:space="preserve">hypomochlion, quod diuellit, & </s> <s xml:space="preserve">compri-<lb/>mit. </s> <s xml:space="preserve">Plagæ quinetiam ipſius latio pondus, quod <lb/>percutit & </s> <s xml:space="preserve">mouet, magnum facit: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">quoniā mo <lb/>tum mouet, pſa celeritate valentius fit. </s> <s xml:space="preserve">paruo au <lb/>tem exiſtente vecte, magnæ illum conſequuntur <lb/>vires: </s> <s xml:space="preserve">quam ob rem vltra magnitndinis decentiã <lb/>later mouens, Sit cuneus vbi A B C, quod verò <lb/>cuneo ſcinditur, D E F G. </s> <s xml:space="preserve">vectis igitur ſit ipſa <lb/>A B, pondus verò ipſius B inferior pars, hypomo <lb/>chlion autem D G, huic autem contrarius vect is <lb/>B C. </s> <s xml:space="preserve">percuſſa igitur A C, vtroque illorum vtitur <lb/>vecte: </s> <s xml:space="preserve">ſcindit enim ipſum B.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Cur ſi quiſpiam trochleas componens duas in <lb/> <anchor type="note" xlink:label="note-0520-01a" xlink:href="note-0520-01"/> tignis duobus ad ſe inuicem inuctis cõtrario ad <lb/>trochleas modo circulo funem circunduxerit, <lb/>cuius alterum quidem caput tigonrum appenda <lb/>tur alteri, alterum varò troclheis ſit innixum, & </s> <s xml:space="preserve"><lb/>à funis initio trahere coeperit, magna trahit pon <lb/>dera, licet imbecillium fuerit virium? </s> <s xml:space="preserve">An quia <lb/>idem põdus à minori potentia ſi mouetur, vecte <lb/>medio trãsfertur magis, quàm à manu: </s> <s xml:space="preserve">trochlea <lb/>autem idem vecti facit. </s> <s xml:space="preserve">quam ob rem ſi vna faci-<lb/>lius traher, & </s> <s xml:space="preserve">ab vnico tractu multò grauius tra-<lb/>het, quàm facere poſſit manus, idip ſum duæ tro-<lb/>chleæ plus quàm in dupla velocitate leuabunt. <lb/></s> <s xml:space="preserve">Minus enim altera trahit, quàm ſi ip ſa per ſeip-<lb/>ſam traheret, quando circa alteram iniectus ſue <lb/>rit funis: </s> <s xml:space="preserve">illa nanque minus etiam pondus effe-<lb/>cit. </s> <s xml:space="preserve">Pariq́; </s> <s xml:space="preserve">modo ſi ad plures iniectus fuerit funis <lb/>in paucis trochleis, multa ſit differentia. </s> <s xml:space="preserve">quã ob <pb o="521" file="0521" n="18" rhead="Mechanicæ"/> rem à prima pondere quat@or minas trahente, <lb/>ab vl im a trahi multò minus. </s> <s xml:space="preserve">Et in re ædifica-<lb/>toria faciliter magn@ a mouen@ pondera, traducũt <lb/>enim ab una trochlea ad aliam, & </s> <s xml:space="preserve">rurſus ab illa <lb/>ad ſuculas, & </s> <s xml:space="preserve">vectes. </s> <s xml:space="preserve">hoc autem idem eſt, ac ſi <lb/>multas facerent trochleas.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="17"> <note position="left" xlink:label="note-0520-01" xlink:href="note-0520-01a" xml:space="preserve">18</note> </div> <p> <s xml:space="preserve">Cur ſi quis ſuper lignum magnã imponat ſe-<lb/> <anchor type="note" xlink:label="note-0521-01a" xlink:href="note-0521-01"/> carim, deſuperq; </s> <s xml:space="preserve">illi magnum adijciat pondus, <lb/>ligni quippiam quod curandum ſit, non diuidit: <lb/></s> <s xml:space="preserve">ſiverò ſecurim extoll@s percutiat, illud ſcindit, <lb/>cùm alioquin multò minus habeat ponderis id <lb/>quod percutit, quàm id quod ſuperiacet, & </s> <s xml:space="preserve">pre-<lb/>mit? </s> <s xml:space="preserve">An quia omnia cum motu fiunt: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">graue <lb/>ipſum grauitatis magis aſſumit motum dũ mo-<lb/>uetur, ꝗ̃ dum quieſcit Incumbensigitur conua-<lb/>tum graui motionem non mouetur, motum ve-<lb/>rò & </s> <s xml:space="preserve">ſecundum hanc mouetur, & </s> <s xml:space="preserve">ſecundùm eã <lb/>quæ eſt percutientis. </s> <s xml:space="preserve">Pręterea ſecuris ipſa effici-<lb/>tur cuneus: </s> <s xml:space="preserve">paruus autẽ exiſtens cuneus magna <lb/>diuidit cum ex duobus ſit vectibus contrario ad <lb/>ſeſe inuicem modo conſtitutis</s> </p> <div type="float" level="2" n="18"> <note position="right" xlink:label="note-0521-01" xlink:href="note-0521-01a" xml:space="preserve">19</note> </div> <p> <s xml:space="preserve">Cur ſtatera, qua carnes ponderãtur, paruo ap-<lb/> <anchor type="note" xlink:label="note-0521-02a" xlink:href="note-0521-02"/> pendiculo magna trutinat onera, cùm alioquin <lb/>tota dimidiata exiftar libra? </s> <s xml:space="preserve">vbi enim onus impo-<lb/>nitur, ſolùm ſuſpenditur lanx: </s> <s xml:space="preserve">in altera verò par <lb/>te, ſola eſt ſtatera. </s> <s xml:space="preserve">An quia ſimul libram & </s> <s xml:space="preserve">vectẽ <lb/>ipſam contingit eſſe ſtateram. </s> <s xml:space="preserve">libram quidem, <lb/>vbi ſpartorum quodcunque ſtateræ fit centrum: <lb/></s> <s xml:space="preserve">in altera enim parte lancem, in altera autem pro <lb/>lance æquipondij appendiculum habet. </s> <s xml:space="preserve">quod li-<lb/>bre incumbit, ceu ſi quis alterain apponeret lan-<lb/>cem, & </s> <s xml:space="preserve">ilii pondus imponeret. </s> <s xml:space="preserve">manifeſtũ enim, <lb/>quòd tantundem tradit ponderis ei quod in alte <lb/>raiacet lance. </s> <s xml:space="preserve">Quemadmodum autem ſi vna li-<lb/>bra multæ ſint libræ, ſic talia inſunt ſparta mul.</s> <s xml:space="preserve"> <pb o="522" file="0522" n="19" rhead="Ariſt. Quæſtiones"/> tain eiuſmodi libra: </s> <s xml:space="preserve">quorum vniuſcuiuſq; </s> <s xml:space="preserve">quod <lb/>intrinſecus eſt ad appẽdiculum, ſtateræ eſt dimi-<lb/>dium. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">omnino iſtud libra eſt, vnam quidẽ ha-<lb/>benslancem, in qua pondus appẽditur: </s> <s xml:space="preserve">alteram <lb/>verò, vbi in ſtatera æquipondium. </s> <s xml:space="preserve">Quam ob rem <lb/>appendiculum ad alteram ſui partem eſt ſtatera. <lb/></s> <s xml:space="preserve">huiuſmodi autem exiſtēs multæ ſunt libræ, totq́; </s> <s xml:space="preserve"><lb/>quot fuerint ſparta. </s> <s xml:space="preserve">Semper autem quod lanci <lb/>propinquius eſt ſpartum, appenſoq́ue oneri, ma-<lb/>ius trahit pōdus: </s> <s xml:space="preserve">quoniam fit quidem omnis ſta-<lb/>tera inuerſus vectis: </s> <s xml:space="preserve">hypomochlion nãq; </s> <s xml:space="preserve">vnum-<lb/>quodque ſpartum ſuperne exiſtens: </s> <s xml:space="preserve">pondus verũ <lb/>id quod lanci ineſt. </s> <s xml:space="preserve">Quanto autem productior ve <lb/>ctis ſuerit longitudo ab ipfo hypomochlio, tãto <lb/>ibi quidem faciliùs mouet: </s> <s xml:space="preserve">hic autem æquilibri-<lb/>brium facit, pondusq́ue ſtateræ trutinat, quod <lb/>ad æquipondij vergit appendiculum.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="19"> <note position="right" xlink:label="note-0521-02" xlink:href="note-0521-02a" xml:space="preserve">20</note> </div> <p> <s xml:space="preserve">Cur medici ſacilius dentes extrahūt dentifor-<lb/>cipis onere adiecto, quàm ſi ſola vtantur manu? <lb/></s> <s xml:space="preserve">An quia ex manu magis quàm ex dentiforcipe <lb/>lubricus elabitur dẽs? </s> <s xml:space="preserve">An ferro id potius accidit <lb/>quàm digitis, quoniam vndique dentem non cō-<lb/>prehendunt: </s> <s xml:space="preserve">quod mollis digitorum facit caro: </s> <s xml:space="preserve"><lb/>adhæret enim, & </s> <s xml:space="preserve">cõplectitur magis. </s> <s xml:space="preserve">An quia den <lb/>@iſorceps duo contrarij vectes, vnicum habentes <lb/>hypom ochlion, eius ſcilicet inſtrumenti conne-<lb/>xionem. </s> <s xml:space="preserve">Hoc igitur ad extractionem vtuntur or-<lb/>gano, vt facilius moueant. </s> <s xml:space="preserve">Sic dentiforcipis alte-<lb/>rum quidem exrremum vbi eſt A: </s> <s xml:space="preserve">alterum autẽ <lb/>quod extrahit B. </s> <s xml:space="preserve">vectis autem vbi A D F: </s> <s xml:space="preserve">alterve <lb/>rò vectis vbi B C E. </s> <s xml:space="preserve">hypomochlion autẽ C G D: </s> <s xml:space="preserve"><lb/>connexio verò vbi G: </s> <s xml:space="preserve">dẽs autem pondus. </s> <s xml:space="preserve">Vtroq; </s> <s xml:space="preserve"><lb/>igitur B & </s> <s xml:space="preserve">F ſimul comprehendentes mouent. </s> <s xml:space="preserve"><lb/>quando autem commotus fuerit, faciliùs manu <lb/>trahitur, quàm inſtrumento.</s> <s xml:space="preserve"/> </p> <pb o="523" file="0523" n="20" rhead="Mechanicæ"/> <p> <s xml:space="preserve">Cur nuces abſque ictu facilè cõfrigun tinſtru-<lb/>mẽtis, quæ ad eum fiunt vſum? </s> <s xml:space="preserve">multumeinim au <lb/>fertur virium, motionis ſcilicet, & </s> <s xml:space="preserve">violẽ@iæ. </s> <s xml:space="preserve">Prę-<lb/>terea duro & </s> <s xml:space="preserve">graui comprimens inſtrumento ci <lb/>tiùs conſringet, quàm ligneo & </s> <s xml:space="preserve">leui. </s> <s xml:space="preserve">An quia ſic <lb/>vtrinqne à duobus comprimitur vectibus ipſa <lb/>nux: </s> <s xml:space="preserve">a vecte autem facile diuelluntur onera. </s> <s xml:space="preserve">id <lb/>enim inſtrumẽtum ex duobus componitur vecti <lb/>bus idem habentibus hypomochlion, connexio-<lb/>nem videlicet @pſam vbi eſt A. </s> <s xml:space="preserve">Quemadmodum <lb/>igitur fuere diductę ſecundũ extrema motis C D <lb/>ipſæ F E, ſic à parua faciliter potentia conducun <lb/>tur. </s> <s xml:space="preserve">Quod igitur cum percuſſione ſeciſſet põdus, <lb/>id valentiores illa E C, & </s> <s xml:space="preserve">F D vectes efficiunt. </s> <s xml:space="preserve">ele <lb/>uatione enim in contrarium ela@i & </s> <s xml:space="preserve">comprimẽ-<lb/>tes, frangunt vbi eſt K. </s> <s xml:space="preserve">Hanc etiam ob cauſam <lb/>quanto vicinius fuerit K ipſum A, confringitur <lb/>celerius. </s> <s xml:space="preserve">quanto enim ab hypomochlio plus di-<lb/>ſtat vectis, facilius & </s> <s xml:space="preserve">plus mouet ab eadẽ poten-<lb/>tia. </s> <s xml:space="preserve">Eſt igitur A quidem hypomochlion: </s> <s xml:space="preserve">ipſa au-<lb/>tem D A F vectis: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">item ipia C A E. </s> <s xml:space="preserve">Quanto igi-<lb/>tur ipſum K vicinius ſuerit angulo ipſius A, tãto <lb/>vicinius fit connexioni vbi eſt A. </s> <s xml:space="preserve">hoc autem eſt <lb/>hypomochlion. </s> <s xml:space="preserve">Ab eadem igitur potentia appli-<lb/>cante F E plus extolli neceſſe eſt. </s> <s xml:space="preserve">Quam ob rem <lb/>quoniã ex contrario eſt eleuatio, neceſſe eſt ma-<lb/>gis com primi. </s> <s xml:space="preserve">quod autem comprimitur magis, <lb/>ci@ius frangitur.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Cur ſi duo extrema in rhombo puncta dua-<lb/>bus ferantur lationibus, haudquaquam æquale <lb/>vtrunque eorũ pertianſit rectam, ſed multò plus <lb/>alterum ?</s> <s xml:space="preserve">idem autem eſt ſermo, cur quod ſuper <lb/>latus fertur, minus pertranſit, quàm ipſum latus. <lb/></s> <s xml:space="preserve">illud enim diametrum minorẽ, hoc verò maius <lb/>latus. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">hoc quidem vnica, illud verò duabus ſer <pb o="524" file="0524" n="21" rhead="Ariſt Quæſtiones."/> t<unsure/>ur lationibus. </s> <s xml:space="preserve">Feratur enim ex ipſa A B, A qui-<lb/>dem ad ipſum B, B vero ad ipſum D eadem cele <lb/>ritate. </s> <s xml:space="preserve">feratur aurẽ & </s> <s xml:space="preserve">ipſa A B in ipſa A C iuxta <lb/>C D eadem celeritate cum illis. </s> <s xml:space="preserve">neceſſe igitur eſt <lb/>A quidem in ipſa A D diametro ferri, B verò in <lb/>ipſa B C. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">vtranq; </s> <s xml:space="preserve">ſimul pertranſiſſe, & </s> <s xml:space="preserve">ipſa@@ <lb/>A B ipſum la<unsure/>tus A C. </s> <s xml:space="preserve">latum enim ſit ipſum A ip <lb/>ſam A E, A B autem ipſam A E, & </s> <s xml:space="preserve">proiecta ſit <lb/>F G iuxta ipſum A B, & </s> <s xml:space="preserve">ab ipſo E ſimiliter replea <lb/>tur. </s> <s xml:space="preserve">Simile igitur fit, quod repletum eſt ipſi toti. <lb/></s> <s xml:space="preserve">æqualis igirur A F ipſi A E ipſa autem A B ipſam <lb/>A F lata erit. </s> <s xml:space="preserve">in diametro igitur erit ſecūdū K. </s> <s xml:space="preserve">& </s> <s xml:space="preserve"><lb/>fem per neceſſe eſt ipſum ferri ſecundùm diame <lb/>trum. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ſimul A B latus pertranfit latus A C, & </s> <s xml:space="preserve"><lb/>ipſum A diametrum pertranſit A D. </s> <s xml:space="preserve">Similiter ẽt <lb/>demon ſtrabitur & </s> <s xml:space="preserve">ipſum B in ipſa B C diametro <lb/>latum. </s> <s xml:space="preserve">æqualis enim eſt ipſa B E ipſi B G Reple. </s> <s xml:space="preserve"><lb/>to igitur ab ipſo G. </s> <s xml:space="preserve">quod intus eſt, toti eſt ſimi-<lb/>le: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ipſum B in ipſa diame@ro erit ſecundùm la <lb/>terum connexionem. </s> <s xml:space="preserve">Et ſimul latus pertranſit <lb/>latus, & </s> <s xml:space="preserve">B ipſum B C diametrum. </s> <s xml:space="preserve">Simuligitur A <lb/>multo plus ipſa A B pertrāſit: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ipſum latus, mi-<lb/>nus latus eadem lata celeritate: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ipſum latus <lb/>maiorem, quàm B, pertranſiuit vna latum latio-<lb/>ne. </s> <s xml:space="preserve">Quanto enim acutior fuerit rhombus, diame <lb/>ter quidem minor ſit. </s> <s xml:space="preserve">A C autẽ maior: </s> <s xml:space="preserve">latus ve-<lb/>ro ipſius B C minus. </s> <s xml:space="preserve">Abſurdū eſt enim (vt dictũ) <lb/>id quod duabus fertur lationibus, aliquãdo ferri <lb/>tardius illo. </s> <s xml:space="preserve">quod fertur vnica: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">vtriſq; </s> <s xml:space="preserve">poſitis <lb/>æquali velocitate punctis, alterū pertranſire ma <lb/>iorem. </s> <s xml:space="preserve">Cauſa autem eſt, quoniã ei quod ab obt@ <lb/>ſo ſertur angulo ambæ ferè cōtrariæ fiunt latio-<lb/>n<unsure/>es, & </s> <s xml:space="preserve">illa ſecūdū quā ipſum fertur, & </s> <s xml:space="preserve">illa ſecun <lb/>dũ quã ipſum à latere defertur. </s> <s xml:space="preserve">Ei autẽ quod ab <lb/>@cuto fertur, accidit vt ad idē feratur, coadiuuat <pb o="525" file="0525" n="22" rhead="Mechanicæ."/> @nim quæ ipſius eſt lateris, illã quæ eſt ſuper dia-<lb/>metrum. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">quanto hunc quidem acutiorem fe-<lb/>ceris, illum verò obtuſum magis: </s> <s xml:space="preserve">hæc quidē tar-<lb/>dior erit, illa verò celerior. </s> <s xml:space="preserve">Hæ quidẽ igitur ma-<lb/>gis contrariæ fiunt, qm̄ obtuſior fit angulus: </s> <s xml:space="preserve">illæ <lb/>verò ad idẽ magis, qm̄ lineæ coarctantur: </s> <s xml:space="preserve">ipſum <lb/>enim A ferè ad idem fertur ſecundum ambas la <lb/>tiones. </s> <s xml:space="preserve">Coadiuuatur igitur altera: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">quanto ſanè <lb/>acutior fuerit angulus, tanto magis ipſum A ad <lb/>contrarium: </s> <s xml:space="preserve">ipſum. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">ad B fertur: </s> <s xml:space="preserve">latus autẽ de-<lb/>fertipſum ad D. </s> <s xml:space="preserve">Et quanto ſanè obtuſior fuerit <lb/>angulus, magis contrariæ fiunt lationes: </s> <s xml:space="preserve">rectior <lb/>enim efficitur linea. </s> <s xml:space="preserve">ſi autẽ omnino recta fieret, <lb/>penitus vtique eſſent contrariæ latus verò ſecun <lb/>dùm vnicam latuum lationem à nullo præpedi-<lb/>tur: </s> <s xml:space="preserve">rationabiliter igitur maiorem pertranſit.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Dubitatur quam ob cauſam maior circulus ę-<lb/>qualem minori circulo conuoluit<unsure/>ur lineam, qū<unsure/> <lb/>circa idem centrum fuerint poſiti: </s> <s xml:space="preserve">ſeorſum autẽ <lb/>reuoluti, quemadmodum alterius magnitudo ad <lb/>magnitudiuem ſe habet alterius, fic & </s> <s xml:space="preserve">illorũ ad <lb/>ſeinuicem fiunt lineæ. </s> <s xml:space="preserve">Præterea vno et@ã & </s> <s xml:space="preserve">eodē <lb/>v<unsure/>triſque exiſtente centro, aliquando quidem tan <lb/>ta ſit linea, quam conuoluuntur, quantam minor <lb/>per ſe conuoluitur circulus, quandoq; </s> <s xml:space="preserve">verò quã-<lb/>tam maior. </s> <s xml:space="preserve">Quòd quidem igitur maiorem con <lb/>uoluitur maior, manifeſtum eſt. </s> <s xml:space="preserve">angulus enim <lb/>ſen ſu videtur eſſe cuiuſque circunferentia pro-<lb/>priæ diametri maioris circuli maior, minoris mi <lb/>nor. </s> <s xml:space="preserve">quam ob rem eandem habebunt propor-<lb/>tionem ſecundùm ſenſum ad ſe lineæ. </s> <s xml:space="preserve">ſecun-<lb/>dùm quas fuerint conuoluti. </s> <s xml:space="preserve">verùm enimuerò <lb/>quòd etiam æqualem conuoluuntur, quando cir<unsure/> <lb/>t<unsure/>a idem fuerint poſiti centrum, manifeſtũ eſt: </s> <s xml:space="preserve">& </s> <s xml:space="preserve"><lb/>ſic fiunt aliquando quidē æquales lineæ, ſecun- <pb o="526" file="0526" n="23" rhead="Ariſt Quæſtiones"/> dum quam maior conuoluitur circulus, aliquan <lb/>do verò ſecundùm quam minor Sit enim circu-<lb/>lus maior quidem vbi D F C. </s> <s xml:space="preserve">minor verò vbi <lb/>E C B: </s> <s xml:space="preserve">vtriſq́; </s> <s xml:space="preserve">autem centrum A. </s> <s xml:space="preserve">Et quam qui-<lb/>dem per ſe magnus conuoluitur, ſit vbi F I: </s> <s xml:space="preserve">quã <lb/>vero per ſe minor vbi GK, æqualis A. </s> <s xml:space="preserve">Si igitur mi <lb/>norem mouero, idem mouens centū vbi A, ma-<lb/>ior autem ſit annexus. </s> <s xml:space="preserve">qñ igitur A B fuerit recta <lb/>ad ipſam G K, ſimul & </s> <s xml:space="preserve">A C fit recta ad ipſam F I. <lb/></s> <s xml:space="preserve">quam ob rem ęqualem ſemper tranſlata erit ip-<lb/>ſam quidem G K, vbi eſt G B circunferentia: </s> <s xml:space="preserve">ip-<lb/>ſam verò FL, quæ eſt vbi F C. </s> <s xml:space="preserve">Si aũt quarta pars <lb/>æqualem conuoluitur, manifeſtum eſt, ꝙ totus <lb/>circulus toti circulo æqualem conuoluetur. </s> <s xml:space="preserve">qua <lb/>re qñ B C, linea ad ipſum peruenerit K, & </s> <s xml:space="preserve">ipſa <lb/>F C circunferentia erit in ipſa C L: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">vniuerſus <lb/>crit conuolutus circulus. </s> <s xml:space="preserve">Similiq́; </s> <s xml:space="preserve">modo ſi ma-<lb/>gnum mouero, illi paruuū annectens, eodem exi <lb/>ftente cẽtro, ſimul cum A C ipſi A B perpendicu <lb/>lum & </s> <s xml:space="preserve">recta eri@: </s> <s xml:space="preserve">hæc quidem ad ipſam F I, illa <lb/>verò ad G M. </s> <s xml:space="preserve">Quam ob rem quando hæc quidẽ <lb/>æqualem ipſi G M pert<unsure/>rãſiuerit, illa verò ipſi F I, <lb/>& </s> <s xml:space="preserve">rurſum facta fuerit recta ipſa F A ad ipſam <lb/>F L. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ipſa A C rurſum recta, velut à principio <lb/>erant in ipſis M I. </s> <s xml:space="preserve">Hoc autem neque aliqua in-<lb/>tercedente mora maioris ad minorem, vt. </s> <s xml:space="preserve">ſ. </s> <s xml:space="preserve">per <lb/>aliquod temporis ſpatium ſtaret in eodem pun-<lb/>cto: </s> <s xml:space="preserve">neque tranſiliente minore aliquod punctū, <lb/>maiorem quidem æqualem minori pertranſire, <lb/>hunc a@tem maiori, abſurdum eſt. </s> <s xml:space="preserve">Præterea vni-<lb/>ea etiam ſemper exiſtente motione, centrū mo-<lb/>rum interdum quidem magnam, nonnunquàm <lb/>verò minorem conuerti, admirandum eſt. </s> <s xml:space="preserve">Idem <lb/>enim celeritate eadem latus æqualẽ natum hoc <lb/>eft pertranſire: </s> <s xml:space="preserve">eadem autem celeritate vtroque <pb o="527" file="0527" n="24" rhead="Mechanicæ."/> modo æqualem licet mouere. </s> <s xml:space="preserve">Principium autem <lb/>ſumendum eſt circa iſtorum cauſam, ꝙ eadem <lb/>potentia & </s> <s xml:space="preserve">æqualis hanc quidem tardiùs mouet <lb/>magnitudinem, illam verò celeriùs. </s> <s xml:space="preserve">Si enim fue-<lb/>rit quippiam, quod à ſeipſo moueri natũ non ſit, <lb/>ſi ſimul & </s> <s xml:space="preserve">illud mouerit, quod natũ eſt moueri. <lb/></s> <s xml:space="preserve">tardius mouebitur, quàm ſi ipſum per ſe moue-<lb/>retur. </s> <s xml:space="preserve">Et ſi quidem natum fuerit moueri, non ſi-<lb/>mul aũt moueatur, ſimiliter ſe habebit. </s> <s xml:space="preserve">Et im<unsure/>poſ <lb/>ſibile certè eſt plus moueri, quàm mouens: </s> <s xml:space="preserve">non <lb/>enim ſuam ipſius mouetur motionem. </s> <s xml:space="preserve">Si igitur<unsure/> <lb/>circulus maior vbi A, minor autem vbi B, ſi mi-<lb/>nor maiorem impellet non reuolutum ex ſe, ma<unsure/> <lb/>nifeſtum eſt, ꝙ tantum ipſius rectæ maior pertrã <lb/>ſit, quantum eſt impulſus: </s> <s xml:space="preserve">tantum aũt eſt impul-<lb/>ſus, quantum paruus eſt motus: </s> <s xml:space="preserve">æqualem igitur <lb/>ipſius rectæ pertranſiuerunt. </s> <s xml:space="preserve">Neceſſe igitur eſt <lb/>ſi reuolutus minor maiorem impellet, reuol@i ſi<unsure/> <lb/>mul cum impulſione: </s> <s xml:space="preserve">tantum aūt quantum mi-<lb/>nor reuolutus eſt, ſi nihil ipſe ſub ipſius motio-<lb/>ne mouetur. </s> <s xml:space="preserve">Qūo enim, & </s> <s xml:space="preserve">quantum mouit, tan-<lb/>tum motũ eſſe neceſſe eſt, quod mouetur ab ill@ <lb/>ſed profectò paruus circulus tãtum ſeipſum cir-<lb/>culariter mouit, quantum eſt pedalis quantitas: </s> <s xml:space="preserve"><lb/>(tantum enim ſit id quod motus eſt) & </s> <s xml:space="preserve">magnus <lb/>igitur tantum motus erit. </s> <s xml:space="preserve">Similiq́; </s> <s xml:space="preserve">modo ſi ma-<lb/>gnus paruū mouebit, motus erit paruus, quēad-<lb/>modum maior. </s> <s xml:space="preserve">Per ſe aūt motus illorum vtrum-<lb/>libet ſiue celeriter, ſeu tardè eadem velocitate, <lb/>ſtatim quantum maior natus eſt circunſerri li-<lb/>neam: </s> <s xml:space="preserve">quod difficultatē facit, quod non ſimiliter <lb/>ſaciunt, quando fuerint connexi. </s> <s xml:space="preserve">hoc autem eſt, <lb/>ſi alteri ab altero moueatur, non quã natus eſt, <lb/>@eque peculiarem motionem. </s> <s xml:space="preserve">Nihil enim referr <lb/>citcũponere, & </s> <s xml:space="preserve">annectere, aut cōiungere vtrum- <pb o="528" file="0528" n="25" rhead="Ariſt Queſtiones"/> liber alteri. </s> <s xml:space="preserve">ſimiliter enim quando hic quidem <lb/>mouer, ille vero mouetur ab iſto; </s> <s xml:space="preserve">quantum vtiq; <lb/></s> <s xml:space="preserve">mouerit alter, tantum alter mouebitur. </s> <s xml:space="preserve">Quando <lb/>quidem igitur adiacens mouerit, aut propenſus, <lb/>non ſemper conueluitur: </s> <s xml:space="preserve">quādo verò circa idem <lb/>poſi@i fuerint cẽtrum, alterum ab altero ſemper <lb/>conuolui neceſſe eſt. </s> <s xml:space="preserve">Sed nihilominus non ſuam <lb/>ipſius motionem mouetur alter, ſed veluti nullã <lb/>haberet motionem: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">ſi habuerit, illa autem nõ <lb/>vtatur, tan@undem accidit. </s> <s xml:space="preserve">Quandoquidem igi-<lb/>tur màgnus moueri ſibi alligatum paruum, par-<lb/>uus mouetur quãtum ille: </s> <s xml:space="preserve">quādo autem paruus, <lb/>rurſus magnus quantum iſte: </s> <s xml:space="preserve">ſeparatus aũt vter-<lb/>que ſeipſum mouet. </s> <s xml:space="preserve">Quod autem eodem exiſten <lb/>te centro, & </s> <s xml:space="preserve">mouente eadem velocitate, accidit <lb/>inæqualem illos pertrāſire lineam, paralogiſmo <lb/>fophiſticę vtitur is, qui dubitat. </s> <s xml:space="preserve">idem enim am-<lb/>bobus eſt centrũ, verùm per accidens, velúti mu <lb/>ſicum & </s> <s xml:space="preserve">album. </s> <s xml:space="preserve">eſſe enim vtriuſque circuli cen-<lb/>tro nō eodem vtitur. </s> <s xml:space="preserve">Quandoquidem igitur mo-<lb/>uens fuerit paruus, vt illius centrum & </s> <s xml:space="preserve">princi-<lb/>pium: </s> <s xml:space="preserve">quando verò magnus, vt illius. </s> <s xml:space="preserve">non igitur <lb/>idem ſim pliciter mouet, ſed eſt quomodo.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Cur lect@lorum ſpondas ſecūdum duplam fa-<lb/> <anchor type="note" xlink:label="note-0528-01a" xlink:href="note-0528-01"/> ciunt proportionem, hanc quidem ſex pedū vel <lb/>paulo am pliorem, illam vero trium: </s> <s xml:space="preserve">curve non <lb/>ſecundùm diametrum illos reſtibus extendunt? <lb/></s> <s xml:space="preserve">An tantos quidem magnitudine faciunt, vt cor-<lb/>poribus ſint proportionem habẽtes: </s> <s xml:space="preserve">fiunt enim <lb/>ſic ſecundum ſpondas dupli, longitudine quidẽ <lb/>cubitorum quatuor, latitudine vero duorũ. </s> <s xml:space="preserve">Ex-<lb/>tendunt autem illos nō ſecundùm diametrum, <lb/>ſed ex oppoſito, vt & </s> <s xml:space="preserve">ligna minus diſtra hantur. </s> <s xml:space="preserve"><lb/>celertrimè enim ſcindũtur ſecundum naturam <lb/>diuiſa, & </s> <s xml:space="preserve">eodem modo diſtenta laborant ma- <pb o="529" file="0529" n="26" rhead="Mechanicæ."/> @imè. </s> <s xml:space="preserve">Amplius, quoniam opus eſt, vt reſtes pon-<lb/>dus ferre poſſint, ſic certè pondere impoſito mi-<lb/>nus laborabunt, ſi tranſuerſim, quàm ſi obliquè <lb/>extendantur. </s> <s xml:space="preserve">Præterea hoc etiam modo minus <lb/>abſumitur reſtium. </s> <s xml:space="preserve">Sit enim lectulus A F G K, & </s> <s xml:space="preserve"><lb/>bifariam diuidatur ipſa F G ſecundùm B, æqua-<lb/>lia certè foramina ſunt in ipſa F B, & </s> <s xml:space="preserve">in ipſa F A. <lb/></s> <s xml:space="preserve">latera enim ſunt æqualia. </s> <s xml:space="preserve">nam totum F G duplũ <lb/>eſt. </s> <s xml:space="preserve">Extendunt autem, vt deſcriptum eſt, ab ipſo <lb/>A ad ipſum B ita vbi eſt C, ita vbi D: </s> <s xml:space="preserve">ita vbi H, <lb/>poſtea vbi E, & </s> <s xml:space="preserve">eodem ſemper modo, donec ad <lb/>angulum peruenerint alium. </s> <s xml:space="preserve">Duo enim anguli <lb/>reſtis habent capi a. </s> <s xml:space="preserve">æquales autem ſunt reſtes <lb/>ſecundum curuaturas, videlicet A B; </s> <s xml:space="preserve">& </s> <s xml:space="preserve">B C ipſis <lb/>C D, & </s> <s xml:space="preserve">D H. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">aliæ ſimili ſe habet modo, quo-<lb/>niam eadem demonſtratio. </s> <s xml:space="preserve">ipſa enim AB æqua-<lb/>lis eſt ipſi H E: </s> <s xml:space="preserve">æqualia enim ſunt latera ſpatij <lb/>B G, M A, & </s> <s xml:space="preserve">foramina æquè diſtant, ipſa autem <lb/>B G æquelis eſt ipſi M A: </s> <s xml:space="preserve">angulus enim B æqua-<lb/>lis eſt angulo G: </s> <s xml:space="preserve">in æqualibus enim hic quidem <lb/>intus, ille vero extra. </s> <s xml:space="preserve">& </s> <s xml:space="preserve">B quidem eſt ſemirectus: </s> <s xml:space="preserve"><lb/>eſt enim F B æqualis ipſi F A: </s> <s xml:space="preserve">& </s> <s xml:space="preserve">angulus vbi F, re <lb/>ctus eſt. </s> <s xml:space="preserve">B autẽ angulus æqualis ei vbi eſt G, quo-<lb/>niam quadratum altera parte longius duplũ eſt: </s> <s xml:space="preserve"><lb/>& </s> <s xml:space="preserve">ad medium eſt curuatura. </s> <s xml:space="preserve">quamobrẽ A D ip-<lb/>ſi E G eſt æqualis: </s> <s xml:space="preserve">huic verò ipſa H M. </s> <s xml:space="preserve">Similiq́ue <lb/>modo demonſtrantur aliæ, quoniã æquales ſunt <lb/>duæ, quæ ſecũdùm curuataras ſunt, duabus. </s> <s xml:space="preserve">Qua <lb/>re manifeſtum eſt, ꝙ tot ſunt reſtes in lectulo, <lb/>quot ſunt quatuor, ſicut A B. </s> <s xml:space="preserve">Quanta autem fora <lb/>minũ eſt multirudo in ipſo F G latere, & </s> <s xml:space="preserve">in eius <lb/>dimidio F B eſt medietas. </s> <s xml:space="preserve">Quamobrem in dimi-<lb/>diato lectulo tantæ reſtium magnitudines erũt, <lb/>quantum eſt A B: </s> <s xml:space="preserve">multitudine verò tot, quot in <lb/>B G ſunt foramina. </s> <s xml:space="preserve">Hoc autem nihil refert dice <pb o="530" file="0530" n="27" rhead="Ariſt. Quæſtiones"/> re, quàm quot ſunt in ipſis A F & </s> <s xml:space="preserve">B F ſimul <lb/>ſumpris. </s> <s xml:space="preserve">Si autem ſecundum diametrum exten-<lb/>dantur reſtes, quemad modum ſe habet in lectu-<lb/>lo A B C D, dimidia non tot ſunt, quot ambo-<lb/>rum latera F A F G. </s> <s xml:space="preserve">æqualia autem, quot in ip <lb/>fis F B, F A, ſunt foramina: </s> <s xml:space="preserve">maiores autem ſunt</s> </p> <div type="float" level="2" n="20"> <note position="left" xlink:label="note-0528-01" xlink:href="note-0528-01a" xml:space="preserve">25</note> </div> <p> <s xml:space="preserve">ipſæ A F, B F, quæ exiſtentes, quàm A B, <lb/>quare reſtis in tantum maior, quantum ambola <lb/>@era diame@ro ſunt maiora.</s> <s xml:space="preserve"/> </p> <p> <s xml:space="preserve">Cur difficilius eſt longa ligna ab extremo ſu-<lb/> <anchor type="note" xlink:label="note-0530-01a" xlink:href="note-0530-01"/> per humeros ferre, quàm ſecundum medium, æ-<lb/>quali exiſtente pondere? </s> <s xml:space="preserve">An quia vibrato ligno <lb/>ipſum extremum prohibet ferre vibratione ma-<lb/>gis retrahens lationem? </s> <s xml:space="preserve">An quoniam licèt nihil <lb/>inflectatur, neque multam habeat longitudinẽ, <lb/>difficilius tamen ad ferendum eſt ab extremo, <lb/>quoniam faciliùs ex medio eleuatur, quàm ab <lb/>extremo, & </s> <s xml:space="preserve">ideo ſic ferre eſt facilius: </s> <s xml:space="preserve">Cauſa aũt, <lb/>qm̄ ſecundùm medium quidem eleuato ligno, <lb/>ſemper ſeſe inuicem ſuſpendunt extrema, & </s> <s xml:space="preserve">al-<lb/>tera pars alteram bene ſubleuat medium enim <lb/>veluti centrum fit, vbi habet is, qui eleuat, aut <lb/>ſert. </s> <s xml:space="preserve">Extremorũ igitur v@@rũq; </s> <s xml:space="preserve">deorſum vergens, <lb/>ſurſum ſuſpenditur. </s> <s xml:space="preserve">ꝙ ſi ab extremo eleuetur, <lb/>aut feratur, non ſanè facit: </s> <s xml:space="preserve">ſed vniuerſum pon-<lb/>dus ad vnum vergit medium, quò eleuatur, aut <lb/>fertur. </s> <s xml:space="preserve">Sit medium vbi A, extrema B C. </s> <s xml:space="preserve">Eleuatio <lb/>igitur aut portato ſecundùm A, ipſum q́uidem B <lb/>deorſum @utans, ſurſum eleuat C: </s> <s xml:space="preserve">ipſum autem <lb/>C deorſum nutans, B ſurſum eleuat: </s> <s xml:space="preserve">ambo au-<lb/>tem ſurſum eleuata hoc fac@unt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="21"> <note position="left" xlink:label="note-0530-01" xlink:href="note-0530-01a" xml:space="preserve">26</note> </div> <p> <s xml:space="preserve">Cur ſi valde procerum fuerit idẽ pondus diffi-<lb/> <anchor type="note" xlink:label="note-0530-02a" xlink:href="note-0530-02"/> cilius ſuper humeros geſtatur, etiam ſi medium <lb/>quiſpiam illud ferat, quàm ſi breuius ſit? </s> <s xml:space="preserve">Quod <lb/>@nim dudum dictum eſt, cauſa nõ eſt: </s> <s xml:space="preserve">ſed vibra- <pb o="531" file="0531" n="28" rhead="Mechanicę."/> tio nunc eſt cauſa. </s> <s xml:space="preserve">qñ. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">productius fuerit, vibran <lb/>tur extrema: </s> <s xml:space="preserve">quamobrem contingit portantem <lb/>difficilius geſtare. </s> <s xml:space="preserve">Vibrationis aũt cã eſt, quoniã <lb/>ab eadẽ motione magis transferuntur extrema, <lb/>quanto procerius fuerit lignũ. </s> <s xml:space="preserve">Humerus quidẽ <lb/>fit centrũ vbi A: </s> <s xml:space="preserve">manet. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">is. </s> <s xml:space="preserve">ipſæ aũt AB, AC, quę <lb/>ſunt ex centro. </s> <s xml:space="preserve">quanto aũt maius fuerit id quod <lb/>ex centro eſt, ſiue A B, ſeu A C, plus transfertur <lb/>ſpatij. </s> <s xml:space="preserve">Demonſtratum autem eſt hoc prius.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="22"> <note position="left" xlink:label="note-0530-02" xlink:href="note-0530-02a" xml:space="preserve">27</note> </div> <p> <s xml:space="preserve">Cur iuxta puteos celonia faciunt eo qui viſun <lb/> <anchor type="note" xlink:label="note-0531-01a" xlink:href="note-0531-01"/> tur modo: </s> <s xml:space="preserve">ligno. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">plumbi adiũgunt pondus: </s> <s xml:space="preserve">cũ <lb/>alioquin vas ipſum & </s> <s xml:space="preserve">plenum, & </s> <s xml:space="preserve">vacuum pon-<lb/>dus habeat? </s> <s xml:space="preserve">An qm̄ duobus tem poribus hau@ien <lb/>di, diuiſo opere, (intingere. </s> <s xml:space="preserve">n. </s> <s xml:space="preserve">oportet, & </s> <s xml:space="preserve">id ſur-<lb/>ſum trahere) continget demittere quidẽ vacuum <lb/>faciliter, trahere vero plenum difficulter. </s> <s xml:space="preserve">Cōmo-<lb/>dum igitur eſt paulò tardius illud demittere, cū <lb/>multò leuius effectum ſuſtolatur pondus. </s> <s xml:space="preserve">id autẽ <lb/>facit in extremo celonio adiunctum plumbum, <lb/>aut lapis. </s> <s xml:space="preserve">demittenti quidem maius ſit pondus, ꝗ <lb/>fi ſolummodo vacuum oportet demittere: </s> <s xml:space="preserve">cum <lb/>verò plenum fuerit, ſurſum id rapit plumbum, <lb/>aut quicquid ponderis inerit. </s> <s xml:space="preserve">Quam ob rem faci <lb/>liora hoc modo ambo ſunt, quàm illo.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="23"> <note position="right" xlink:label="note-0531-01" xlink:href="note-0531-01a" xml:space="preserve">28</note> </div> <p> <s xml:space="preserve">Cur qñ ſuper ligno, aut hmõi quopiam duo <lb/> <anchor type="note" xlink:label="note-0531-02a" xlink:href="note-0531-02"/> portauerint homines æquale pondus, non ſimili <lb/>ter premuntur, ſi ad vnum non declinet pondus, <lb/>ſeu magis, quanto vicinius fuerit geſtãtibus? </s> <s xml:space="preserve">An <lb/>quoniam vectis quidem lignum efficitur, põdus <lb/>verò hypomochlion: </s> <s xml:space="preserve">qui autem propior eſt pon-<lb/>deri ex ijs, qui illud geſtant, id quod mouetur: </s> <s xml:space="preserve">al <lb/>ter verò portantiũ, quod mouet. </s> <s xml:space="preserve">Quanto igitur <lb/>plus diſtat à pondere, tanto facilius mouet, & </s> <s xml:space="preserve"><lb/>alerum premit magis inferius, veluti contrani-<lb/>@te pondere impoſito, quod hypomochlion <pb o="532" file="0532" n="29" rhead="Ariſt. Quæſtiones."/> factum Eſt. </s> <s xml:space="preserve">Si autem in medio inerit pondus, ni-<lb/>hilo magis alter alteri fit pondus, aut mouet: </s> <s xml:space="preserve">ſed <lb/>eodem modo alteri alt<unsure/>er fit pondus.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="24"> <note position="right" xlink:label="note-0531-02" xlink:href="note-0531-02a" xml:space="preserve">29</note> </div> <p> <s xml:space="preserve">Cur ſurgentes omnes, femori crus ad acutum <lb/> <anchor type="note" xlink:label="note-0532-01a" xlink:href="note-0532-01"/> cõſtituentes angulũ, & </s> <s xml:space="preserve">thoraci ſimiliter femur, <lb/>ſurgunt? </s> <s xml:space="preserve">quod ſi non, haudquaquam ſurgere po-<lb/>terunt. </s> <s xml:space="preserve">An quia id quod æquale eſt, quietis vbiq; <lb/></s> <s xml:space="preserve">eſt cauſa: </s> <s xml:space="preserve">rectus autẽ angulus æqualitatis eſt, ſta-<lb/>tionemq́; </s> <s xml:space="preserve">facit: </s> <s xml:space="preserve">quamobrẽ ad ſimiles fertur an-<lb/>gulos ipſi terræ circumferentiæ: </s> <s xml:space="preserve">non enim quod <lb/>ad rectum eſt ipſi pauimento. </s> <s xml:space="preserve">An q̇m̄ ſurgens fit <lb/>rectus, ſtantẽ vero neceſſe eſt perpẽdiculum eſſe <lb/>ad terram. </s> <s xml:space="preserve">ſiquidẽ igitur ad rectũ debet eſſe, hoc <lb/>aũt eſt caput ſecundũ pedes habere, & </s> <s xml:space="preserve">fieri opor <lb/>tet, cùm ſurgit. </s> <s xml:space="preserve">Quandoquidem igitur fuerit @e <lb/>dens, ſecundum parallelum pedes habet, & </s> <s xml:space="preserve">ca-<lb/>put, & </s> <s xml:space="preserve">non in æquali. </s> <s xml:space="preserve">Caput ſit A, thorax A B, fe-<lb/>mur B C, crura C D. </s> <s xml:space="preserve">ad rectum autem ſit & </s> <s xml:space="preserve">tho-<lb/>rãx vbi A B, ipſi femori, & </s> <s xml:space="preserve">cruri ſemur ſic feden-<lb/>te. </s> <s xml:space="preserve">quamobrem eo ſe habẽtem modo ſurgere eſt <lb/>impoſſibile. </s> <s xml:space="preserve">neceſſe autem eſt crus reclinare, pe-<lb/>desque conſtituere ſub capite. </s> <s xml:space="preserve">hoc autem erit, ſi <lb/>C D fiet, vbi C F, & </s> <s xml:space="preserve">fimul ſurgere continget, & </s> <s xml:space="preserve">in <lb/>eadem ęquali habere caput & </s> <s xml:space="preserve">pedes. </s> <s xml:space="preserve">ipſa autem <lb/>C F a cutum facit angulum ad ipſam B C.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="25"> <note position="left" xlink:label="note-0532-01" xlink:href="note-0532-01a" xml:space="preserve">30</note> </div> <p> <s xml:space="preserve">Cur facilius mouetur cõmotu, quàm manens? <lb/></s> <s xml:space="preserve"> <anchor type="note" xlink:label="note-0532-02a" xlink:href="note-0532-02"/> veluti currus citiùs cõmotus agitant, quàm mo-<lb/>ueri in cipientes. </s> <s xml:space="preserve">An quia difficillimũ eſt pondus <lb/>mouere, quod in cõtrariũ mouetur. </s> <s xml:space="preserve">aufert enim <lb/>quiddam ex motoris potentia, licèt multo fit ve-<lb/>locior: </s> <s xml:space="preserve">neceſſe nanque eſt tardiorẽ eſſe impulſio <lb/>nem illius quod repellitur. </s> <s xml:space="preserve">Secundo autẽloco ſi <lb/>quieuerit: </s> <s xml:space="preserve">reſiſtit enim ipſum quieſcẽs. </s> <s xml:space="preserve">Quod aũt <lb/>mouetur ad id ipſum ad quod impellitur, impel-<lb/>lenti ſimile facit, ceu ſi quiſpiam mouẽtis poten <pb o="533" file="0533" n="30" rhead="De Mundo."/> tiam, & </s> <s xml:space="preserve">celeritatem augeret. </s> <s xml:space="preserve">quod enim<unsure/> ab illo <lb/>pateretur, vtique ipſum tacit ex ſe commotum.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="26"> <note position="left" xlink:label="note-0532-02" xlink:href="note-0532-02a" xml:space="preserve">31</note> </div> <p> <s xml:space="preserve">Cur ea, quæ proijci@@ntur, ceſſant à latione? </s> <s xml:space="preserve">An <lb/> <anchor type="note" xlink:label="note-0533-01a" xlink:href="note-0533-01"/> quia impellens deſinit potentia, v@l propter retra <lb/>ctionem, vel propter rei proiectę inclinationem, <lb/>quando ea valentior fuerit, quam proijcientis vi <lb/>res. </s> <s xml:space="preserve">Aut iſthæc ambigere, principium relinquen-<lb/>tes, abſurdum eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="27"> <note position="right" xlink:label="note-0533-01" xlink:href="note-0533-01a" xml:space="preserve">32</note> </div> <p> <s xml:space="preserve">Cur quippiam non pecularem ſibi fertur latio <lb/> <anchor type="note" xlink:label="note-0533-02a" xlink:href="note-0533-02"/> nem, impulfore alioquin non conſequente? </s> <s xml:space="preserve">An <lb/>videlicet quoniam primum id efficit, @@al@erum <lb/>impellat: </s> <s xml:space="preserve">illudque rurſum, v@ alterum? </s> <s xml:space="preserve">Ceſſat au-<lb/>tem quando non poteſt amplius facere primum <lb/>impellens id quod fertur, vt impellat, & </s> <s xml:space="preserve">qñ ip-<lb/>ſius lati grauitas nut@ ſuo declinat magis, quàm <lb/>impellentis in antè ſit potentia,</s> </p> <div type="float" level="2" n="28"> <note position="right" xlink:label="note-0533-02" xlink:href="note-0533-02a" xml:space="preserve">33</note> </div> <p> <s xml:space="preserve">Cur neque parua valde, neque magna longè <lb/> <anchor type="note" xlink:label="note-0533-03a" xlink:href="note-0533-03"/> proijci queunt, ſed commẽſurationem quandã <lb/>illa habere oportet ad id quod proijcit? </s> <s xml:space="preserve">An quia <lb/>neceſſe eſt quod proijcitur, & </s> <s xml:space="preserve">impelli@@r, cõtra-<lb/>ni i ei vnde impellitur? </s> <s xml:space="preserve">quod autem magnitudi-<lb/>ne ſua nihil cedit, aut imbellicitate nihil contra-<lb/>nititur non efficit proiectionem, neque impulſio <lb/>nem. </s> <s xml:space="preserve">Quod enim multo impellentis excedit vi-<lb/>res, haud quaquã cedit: </s> <s xml:space="preserve">quod verò multo eſt im-<lb/>berillius. </s> <s xml:space="preserve">nihil contranititur. </s> <s xml:space="preserve">An quia tãtum fer-<lb/>tur id quod fertur, quantũ aeris mouerit ad pro-<lb/>fundum: </s> <s xml:space="preserve">quod autem non mouetur, neq; </s> <s xml:space="preserve">moue <lb/>bit quippiam accidit autem illis ambo iſthæc ha <lb/>bere. </s> <s xml:space="preserve">Valde enim magnum, & </s> <s xml:space="preserve">valde paruum, ceù <lb/>non mota exiſtunt: </s> <s xml:space="preserve">alterum nanque nihil mouet <lb/>alterum verò nihil mouetur.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="29"> <note position="right" xlink:label="note-0533-03" xlink:href="note-0533-03a" xml:space="preserve">34</note> </div> <p> <s xml:space="preserve">Cur ea quæ in vorticoſis feruntur aquis, ad <lb/> <anchor type="note" xlink:label="note-0533-04a" xlink:href="note-0533-04"/> medium tandem aguntur omnia? </s> <s xml:space="preserve">An quia ma-<lb/>gnitudinem habet quocunque ferrur: </s> <s xml:space="preserve">quam <pb o="534" file="0534" n="31" rhead="Ariſt. Quæſtiones Mech."/> ob rem illius extrema in duobus ſunt circulis, <lb/>hoc quidem minori illo verò maiori: </s> <s xml:space="preserve">quare ma-<lb/>ior diſtrahit: </s> <s xml:space="preserve">quoniã celerius fertur, & </s> <s xml:space="preserve">tranſuer-<lb/>ſum impellit illud ad minorem: </s> <s xml:space="preserve">quoniam autem <lb/>id quod ſertur, latitudinem habet, & </s> <s xml:space="preserve">iſte rurſus <lb/>idem eff@cit & </s> <s xml:space="preserve">ad interiorem propellit, donec ad <lb/>medium perueniat. </s> <s xml:space="preserve">An quia quod fertur, ſimili <lb/>ſe habet modo ad omnes circulos propter me-<lb/>dium. </s> <s xml:space="preserve">medium enim in vnoquoque circulo ęqua <lb/>liter diſtat. </s> <s xml:space="preserve">An quia quorum quidem circũauctæ <lb/>quæ latio non ſuperior propter magnitudinem, <lb/>ſed grauitate ſua circuli celeritatẽ excellunt, ea <lb/>neceſſe eſt relinqui, & </s> <s xml:space="preserve">tardiùs ferri, tardius aũt <lb/>minor circulus fertur. </s> <s xml:space="preserve">non idem enim in tempo-<lb/>re æquali magnus cũ paruo reuoluitur circulus, <lb/>quando circa idem ſuerint medium. </s> <s xml:space="preserve">quamobrẽ <lb/>in minori circulo relinqui eſt neceſſe, donec ad <lb/>medium perueniant. </s> <s xml:space="preserve">Quorum cunque autem ſu-<lb/>perior à principio fuerit latio, ea finiensidem eſ <lb/>ficiet. </s> <s xml:space="preserve">oportet enim @ãc quidem ſtatim, alterum <lb/>verò celeritate ſuperare grauitatem, quam obrẽ <lb/>ad interiorẽ ſemper circulum relinquetur quod-<lb/>cunque. </s> <s xml:space="preserve">Neceſſe enim eſt, quod non ſuperatur, <lb/>aut in exteriori, aut in interiori moueri: </s> <s xml:space="preserve">in illo <lb/>autem in quo eſt, impoſſibile eſt ferri, quod non <lb/>ſuperatur adhuc vero minus in exteriori: </s> <s xml:space="preserve">cele-<lb/>rior enim exterioris circuli eſt latio: </s> <s xml:space="preserve">reſtat igitur, <lb/>vtid, quod non ſuperatur, ad interiorem tranſ-<lb/>feratur. </s> <s xml:space="preserve">ſemper autem vnumquodque proficit, vt <lb/>non ſuperetur. </s> <s xml:space="preserve">Quoniam verò peruenire ad me-<lb/>dium, finem quidem efficit, vt quippiam nõ mo-<lb/>ueatur, ſtat autem ſolummodo ipſum centrum: <lb/></s> <s xml:space="preserve">ad hoc ſanè omnia congregari neceſſe eſt.</s> <s xml:space="preserve"/> </p> <div type="float" level="2" n="30"> <note position="right" xlink:label="note-0533-04" xlink:href="note-0533-04a" xml:space="preserve">35</note> </div> </div> <div type="section" level="1" n="5"> <head style="it" xml:space="preserve">Mechanicarum quæſtionum finis.</head> </div></text> </echo>