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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>CC-BY-SA</dcterms:rights>
    <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license>
    <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder>
  </metadata>
  <text xml:lang="la" type="free">
<div xml:id="echoid-div1" type="section" level="1" n="1"><pb o="504" file="0504" n="1"/>
</div>
<div xml:id="echoid-div2" type="section" level="1" n="2">
<head xml:id="echoid-head1" xml:space="preserve">ARISTOTELIS</head>
<head xml:id="echoid-head2" xml:space="preserve">STAGIRITAE, <lb/>PERIPATETICORVM</head>
<head xml:id="echoid-head3" xml:space="preserve">PRINCIPIS,</head>
<head xml:id="echoid-head4" xml:space="preserve">Quæſtiones Mechanicæ, <lb/>Nicolao Leonico Thomæo <lb/>interprete.</head>
<head xml:id="echoid-head5" style="it" xml:space="preserve">Quæ ſit artis Mechanicæ facultas.</head>
<p>
  <s xml:id="echoid-s1" xml:space="preserve">MIraculo ſune ea quidem, quæ natura <lb/>contingunt, quorum ignorantur cau <lb/>ſæ: </s>
  <s xml:id="echoid-s2" xml:space="preserve">illa uerò, quæ pręter naturam, <lb/>quæcunque ad hominum vtilitatem <lb/>arte fiunt. </s>
  <s xml:id="echoid-s3" xml:space="preserve">In multis. </s>
  <s xml:id="echoid-s4" xml:space="preserve">n. </s>
  <s xml:id="echoid-s5" xml:space="preserve">natura ei. </s>
  <s xml:id="echoid-s6" xml:space="preserve">qđ <lb/>nobis uſui eſſe poteſt, contrarium facit: </s>
  <s xml:id="echoid-s7" xml:space="preserve">natura <lb/>etenim eundem ſemper habet modum, &amp; </s>
  <s xml:id="echoid-s8" xml:space="preserve">ſimpli <lb/>citer: </s>
  <s xml:id="echoid-s9" xml:space="preserve">vtile autem multifariam <reg norm="commutatur" type="simple">commutat̃</reg>. </s>
  <s xml:id="echoid-s10" xml:space="preserve">Quan <lb/>doigitur quippiam præter naturam oportuerit <lb/>facere, difficultate ſua hæſitationem praſtat, ar-<lb/>teq́ indiget: </s>
  <s xml:id="echoid-s11" xml:space="preserve">quam ob rem eam artis <reg norm="partem" type="context">partẽ</reg>, quæ <lb/>huiuſmodi ſuccurrit difficulcatibus, <reg norm="Mechanicam" type="context">Mechanicã</reg> <lb/>appellamus. </s>
  <s xml:id="echoid-s12" xml:space="preserve">Quemad modum enim Antipho ſcri <lb/>bit poeta, ſic ſe res habet: </s>
  <s xml:id="echoid-s13" xml:space="preserve">arte enim ſuperamus <lb/>da, à quibus natura uincimur. </s>
  <s xml:id="echoid-s14" xml:space="preserve">Huiuſmodi autem <lb/>ſunt, in quibus &amp; </s>
  <s xml:id="echoid-s15" xml:space="preserve">minora ſuperant maiora: </s>
  <s xml:id="echoid-s16" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s17" xml:space="preserve"><lb/><reg norm="quæcunque" type="simple">quæcunq;</reg> </s>
  <s xml:id="echoid-s18" xml:space="preserve">momentum paruum <reg norm="habentia" type="context">habẽtia</reg>, magna
<pb o="505" file="0505" n="2" rhead="Mechanicæ."/>
mouent pondera: </s>
  <s xml:id="echoid-s19" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s20" xml:space="preserve">omnia ferè illa, quæ mecha <lb/>nica nuncupamus, &amp; </s>
  <s xml:id="echoid-s21" xml:space="preserve">problemata. </s>
  <s xml:id="echoid-s22" xml:space="preserve">Sunt autem, <lb/>hæc neque naturalibus omnino quæſtionibus <lb/>eadem, neque ſeiugata valde: </s>
  <s xml:id="echoid-s23" xml:space="preserve">verùm <reg norm="mathema- ticarum" type="context">mathema-<lb/>ticarũ</reg> <reg norm="contemplationum" type="context">contemplationũ</reg> <reg norm="naturaliumque" type="simple">naturaliumq́;</reg> </s>
  <s xml:id="echoid-s24" xml:space="preserve"><reg norm="communia" type="context">cõmunia</reg>.</s>
  <s xml:id="echoid-s25" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div3" type="section" level="1" n="3">
<head xml:id="echoid-head6" style="it" xml:space="preserve">De dignitatiòus, admirandis<reg norm="que" type="simple">̈</reg> Circuli <lb/>proprietatibus.</head>
<p>
  <s xml:id="echoid-s26" xml:space="preserve">DEnumeto autem eorum, quæ hoc in gene-<lb/>re dubitantur, illa eſſe dicuntur, quæ circæ <lb/>vectem fiunt. </s>
  <s xml:id="echoid-s27" xml:space="preserve">Abſurdum enim eſſe videtur, ma-<lb/>gnum moueri pondus ab exigua virtute, <reg norm="cum" type="context">cũ</reg> plu-<lb/>ri præſertim pondere. </s>
  <s xml:id="echoid-s28" xml:space="preserve">quod. </s>
  <s xml:id="echoid-s29" xml:space="preserve">n. </s>
  <s xml:id="echoid-s30" xml:space="preserve">una vecte <reg norm="quiſpiam" type="context">quiſpiã</reg> <lb/>mouere <reg norm="non" type="context">nõ</reg> poteſt, idipſum ponderis citius mo-<lb/>uet, uectis ad illud pondus adiungens. </s>
  <s xml:id="echoid-s31" xml:space="preserve"><reg norm="Oinum" type="context">Oĩum</reg> <reg norm="ant" type="context">ãt</reg> <lb/>huiuſmodi cauſæ <reg norm="principium" type="context">principiũ</reg> habet circulus, Iſtud <lb/>verò ratione contingit; </s>
  <s xml:id="echoid-s32" xml:space="preserve">ex ad mirabili etem̄ mi-<lb/>randum accidere quippiam, non eſt ab ſurdum.</s>
  <s xml:id="echoid-s33" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s34" xml:space="preserve">Maximè autem eſt <reg norm="admirandum" type="context">admirãdum</reg> ſimul contra-<lb/>ria fieri. </s>
  <s xml:id="echoid-s35" xml:space="preserve">Circulus vero ex huiuſmodi eſt conſtitu <lb/>tus: </s>
  <s xml:id="echoid-s36" xml:space="preserve">ſtatim enim ex commoto effectus eſt, &amp; </s>
  <s xml:id="echoid-s37" xml:space="preserve">mæ <lb/>nente, <reg norm="quorum" type="context">quorũ</reg> natura ad ſe inuicem eſt <reg norm="contraria" type="context">cõtraria</reg>. <lb/></s>
  <s xml:id="echoid-s38" xml:space="preserve"><reg norm="quamobrem" type="context">quamobrẽ</reg> iſthæc cernentes minus admirari <reg norm="con- uenit" type="context">cõ-<lb/>uenit</reg> contingentes in illo contrarietas. </s>
  <s xml:id="echoid-s39" 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/>&amp; </s>
  <s xml:id="echoid-s40" xml:space="preserve">curuum. </s>
  <s xml:id="echoid-s41" xml:space="preserve">hæc <reg norm="aunt" type="context">aũt</reg> eo à ſeinuicem diſtant <reg norm="mon" type="context">mõ</reg>, <lb/>quo magnum &amp; </s>
  <s xml:id="echoid-s42" xml:space="preserve">paruum, <reg norm="illorum" type="context">illorũ</reg> etenim medium <lb/>eſt æquale: </s>
  <s xml:id="echoid-s43" xml:space="preserve">horum verò <reg norm="rectum" type="context">rectũ</reg> quapropter cùm, <lb/>ad ſeinuicem <reg norm="commutantur" type="context">cõmutantur</reg>, illa quidem prius æ-<lb/>qualia fieri neceſſe eſt, quàm extremorum vtrũ-<lb/>libet: </s>
  <s xml:id="echoid-s44" xml:space="preserve">lineam verò rectam, <reg norm="quando" type="wordlist">qñ</reg> eſt curua concaua, <lb/>ut ex huiu ſmoà<unsure/>i rurſum curua fit, &amp; </s>
  <s xml:id="echoid-s45" 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:id="echoid-s46" xml:space="preserve">Alterum autem, <reg norm="quod" type="simple">ꝙ</reg> ſimul contrarijs mouetur <lb/>motionibus: </s>
  <s xml:id="echoid-s47" xml:space="preserve">ſimul enim ad anteriorem mouetur <lb/>locum, &amp; </s>
  <s xml:id="echoid-s48" xml:space="preserve">ad poſter<unsure/>iorem. </s>
  <s xml:id="echoid-s49" xml:space="preserve">Et ea, quæ <reg norm="circulum" type="context">circulũ</reg> de-<lb/>ſcribit, linea eodem ſe habet modo: </s>
  <s xml:id="echoid-s50" xml:space="preserve">ex quo. </s>
  <s xml:id="echoid-s51" xml:space="preserve">n. </s>
  <s xml:id="echoid-s52" xml:space="preserve">in <lb/>cipit loco illius extremum, ad eundem rurlus re <lb/>dit:</s>
  <s xml:id="echoid-s53" xml:space="preserve"><unsure/> illa. </s>
  <s xml:id="echoid-s54" xml:space="preserve">n. </s>
  <s xml:id="echoid-s55" xml:space="preserve">continuò commota, extremum rurſus <lb/>efficitur primum. </s>
  <s xml:id="echoid-s56" xml:space="preserve">quamobrem manifeſtum, <reg norm="quod" type="simple">ꝙ</reg> in <lb/>de mutatnm eſt. </s>
  <s xml:id="echoid-s57" xml:space="preserve">quapropter (vt dictum eſt prius) <lb/>non eſt <reg norm="inconueniens" type="context">incõueniens</reg> ipſ<unsure/>u<unsure/>m miracolorum <reg norm="oinum" type="context">oĩum</reg> <lb/>eſſe principlum. </s>
  <s xml:id="echoid-s58" xml:space="preserve">Ea igi ur, quæ circa libram <reg norm="fiunt" type="context">fiũt</reg>, <lb/>ad circulum referuntur: </s>
  <s xml:id="echoid-s59" xml:space="preserve">quæ vero circa vectem, <lb/>ad ipſam <reg norm="libram" type="context">librã</reg>: </s>
  <s xml:id="echoid-s60" xml:space="preserve">alia autem ferè omn<unsure/>ia, quæ circa <lb/>męchanicas ſunt motiones, ad vectern<unsure/>. </s>
  <s xml:id="echoid-s61" xml:space="preserve">Prætereà <lb/><reg norm="etiam" type="context">etiã</reg>, 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:id="echoid-s62" xml:space="preserve">ſed cirius ſemper <lb/>quod à manente termino eſt remo ius, pleraque <lb/>miraculorum <reg norm="accidunt" type="context">accidũt</reg> in circuli motionibus: </s>
  <s xml:id="echoid-s63" xml:space="preserve">de <lb/>quibus in ijs, quæ poſthac addacentur, quęſtioni <lb/>bus erit manifeſtum. </s>
  <s xml:id="echoid-s64" xml:space="preserve">Quoniam autem <reg norm="ſecundum" type="context">ſecundũ</reg> <lb/>contrarias fimul motiones mouetur circulus: </s>
  <s xml:id="echoid-s65" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s66" xml:space="preserve"><lb/><reg norm="alterum" type="context">alterũ</reg> quidem diametri extremum vbi A, in an-<lb/>tè mouetur, alterum verò vbi B. </s>
  <s xml:id="echoid-s67" xml:space="preserve">ad retro; </s>
  <s xml:id="echoid-s68" xml:space="preserve">effi-<lb/>ciunt nonnulli, vt ab vnica motione multi <reg norm="contra" type="context">cõtra</reg> <lb/>rio ſimul moueantur circuli: </s>
  <s xml:id="echoid-s69" xml:space="preserve">quemadmodum, <lb/>ſunt illi, quos in locis <reg norm="proponunt" type="context">proponũt</reg> ſacris, æneos, &amp; </s>
  <s xml:id="echoid-s70" xml:space="preserve"><lb/>ferreos, fabricantes orbiculos. </s>
  <s xml:id="echoid-s71" xml:space="preserve">Si enim A B circu <lb/>lum alter contigerit circulus in quo CD. </s>
  <s xml:id="echoid-s72" 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 <reg norm="idem" type="context">idẽ</reg> <lb/>mota. </s>
  <s xml:id="echoid-s73" xml:space="preserve">In contrarium igitur mouebitur circulus <lb/>vbi CD, ad illum ubi AB. </s>
  <s xml:id="echoid-s74" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s75" xml:space="preserve">rurſus ipſe conti-<lb/>guum ubi EF, in contrarium ſibijpſi mouebitur <lb/>propter eandem cauſam. </s>
  <s xml:id="echoid-s76" xml:space="preserve">Eodem <reg norm="ent" type="context">ẽt</reg> modo ſi plu-
<pb o="507" file="0507" n="4" rhead="Mechanicæ."/>
res fuerint, <reg norm="idem" type="context">idẽ</reg> facient, uno ſolo commoto. </s>
  <s xml:id="echoid-s77" xml:space="preserve">Hane <lb/>igitur in circulo exiſtentem animaduertens na-<lb/>turam architecti, in <reg norm="ſtrumentum" type="context">ſtrumentũ</reg> fabricant, <reg norm="celantes" type="context">celãtes</reg> <lb/>principium, vt machinæ ſolum manifeftum ſit il <lb/>lud, quod <reg norm="admirationem" type="context">admirationẽ</reg> pręſtat, cauſa verò lateat.</s>
  <s xml:id="echoid-s78" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s79" xml:space="preserve">In primis igitur, quæ accidunt circa <reg norm="libram" type="context">librã</reg>, du-<lb/>bitare faciunt, quamnàm ob cauſam exactiores <lb/>minoribus maiores ſunt libræ. </s>
  <s xml:id="echoid-s80" xml:space="preserve">huius autem rei <lb/>principium eſt, quamobrem in ipſo circulo, quæ <lb/>plus à cent<unsure/>ro diſter linea, <reg norm="eadem" type="context">eadẽ</reg> ui <reg norm="commota" type="context">cõmota</reg> cit<unsure/>ius <lb/>fertur, quàm illa, quæ minus diſtar. </s>
  <s xml:id="echoid-s81" xml:space="preserve">Citius enim <lb/>bifariam dicitur: </s>
  <s xml:id="echoid-s82" xml:space="preserve">ſiue enim in minori tempore <lb/>zqualem pertranſi<gap/> <reg norm="locum" type="context">locũ</reg>, citius feciſſe dicimus: <lb/></s>
  <s xml:id="echoid-s83" xml:space="preserve">ſeu in æquali maiorem. </s>
  <s xml:id="echoid-s84" xml:space="preserve">Maior autem in æquali <lb/>tempore maiorem deſcribit circulum: </s>
  <s xml:id="echoid-s85" xml:space="preserve">qui enim <lb/>extra eſt, maior eo qui intus eft. </s>
  <s xml:id="echoid-s86" xml:space="preserve">Horum <reg norm="autem" type="context">autẽ</reg> cau <lb/>fa, qm̄ duas fertur lationesea, quæ circulum de-<lb/>ſcribit, linea. </s>
  <s xml:id="echoid-s87" xml:space="preserve">Quandoquidem igitur in propor-<lb/>tione fertur aliqua id, quod fertur, ſuper rectam <lb/>ferri neceſſe: </s>
  <s xml:id="echoid-s88" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s89" xml:space="preserve">hæc diameter efficitur figuræ, <lb/>quam faciunt illæ, quæ in huiuſmodi proportio <lb/>ne <reg norm="coaptantur" type="simple">coaptant̃</reg>, lineę. </s>
  <s xml:id="echoid-s90" xml:space="preserve">Sit enim proportio <reg norm="ſecundum" type="context">ſecũdum</reg> <lb/>quam latum fertur, quam habet A B ad AC: </s>
  <s xml:id="echoid-s91" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s92" xml:space="preserve">A <lb/>quidem fertur verſus B, A B uerò ſubterferatur <lb/>verſus M C: </s>
  <s xml:id="echoid-s93" xml:space="preserve">latum aut<unsure/>em ſit A quidem ad D. </s>
  <s xml:id="echoid-s94" xml:space="preserve">ubi <lb/>autem eſt A B, uerſus E: </s>
  <s xml:id="echoid-s95" xml:space="preserve"><reg norm="quoniam" type="context">quoniã</reg> igitur la<gap/>ionis <lb/>erat proportio, quam A B habet ad A C, neceſſe <lb/>eſt &amp; </s>
  <s xml:id="echoid-s96" xml:space="preserve">A D ad A E hanc habere proportionem. </s>
  <s xml:id="echoid-s97" xml:space="preserve">Si-<lb/>mile igitur eſt proportione paruum quadrilate-<lb/>rum maiori; </s>
  <s xml:id="echoid-s98" xml:space="preserve"><reg norm="quamobrem" type="context">quamobrẽ</reg> &amp; </s>
  <s xml:id="echoid-s99" xml:space="preserve"><reg norm="eadem" type="context">eadẽ</reg> illorum eſt dia-<lb/>meter: </s>
  <s xml:id="echoid-s100" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s101" xml:space="preserve">A erit ad F. </s>
  <s xml:id="echoid-s102" xml:space="preserve">Eodem etiam <reg norm="oſtendetur" type="simple">oſtendet̃</reg> mo-<lb/>do, vbicu<unsure/><reg norm="nque" type="simple">nq;</reg> </s>
  <s xml:id="echoid-s103" xml:space="preserve">latio deprehendatur; </s>
  <s xml:id="echoid-s104" xml:space="preserve">ſemper enim <lb/>ſupra diametrum erit. </s>
  <s xml:id="echoid-s105" 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:id="echoid-s106" xml:space="preserve">Sienim ſecundum aliam quam-<lb/>piam, <reg norm="non" type="context">nõ</reg> fertur ẜ m dia metrum. </s>
  <s xml:id="echoid-s107" xml:space="preserve">Si autem in nul <lb/>la fertur proportione ſecundum duas lationes <lb/>nullo in tempore, <reg norm="rectam" type="context">rectã</reg> eſſe lationem eſt impoſ-<lb/>ſibile. </s>
  <s xml:id="echoid-s108" xml:space="preserve">Sit enim recta. </s>
  <s xml:id="echoid-s109" xml:space="preserve">Poſita igitur hac pro diame <lb/>tro, &amp; </s>
  <s xml:id="echoid-s110" 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:id="echoid-s111" xml:space="preserve">hoc enim demonſtratum eſt prius. </s>
  <s xml:id="echoid-s112" xml:space="preserve">non <lb/>igitur rectam efficiet id, quod ſecundùm nullam <lb/>proportionem in nullo fertur tempore. </s>
  <s xml:id="echoid-s113" xml:space="preserve"><reg norm="Siautem" type="context">Siautẽ</reg> <lb/>ẜm quam piam feratur proportionem, &amp; </s>
  <s xml:id="echoid-s114" 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:id="echoid-s115" xml:space="preserve">Quam-<lb/>obrem circulare eſtid, quod <reg norm="ſecundum" type="context">ſecundũ</reg> 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 <reg norm="per" type="simple">ꝑ</reg>. <lb/></s>
  <s xml:id="echoid-s116" xml:space="preserve">pendiculum peruenit, vt ſit rurſus ipſa à centro <lb/>perpendiculum. </s>
  <s xml:id="echoid-s117" xml:space="preserve">Sit circulas A B C D: </s>
  <s xml:id="echoid-s118" xml:space="preserve">extremum <lb/>autem vbi eſt B, feratur ad ipſum D: </s>
  <s xml:id="echoid-s119" xml:space="preserve">peruenit ſa <lb/>hè aliquando ad ipſum C. </s>
  <s xml:id="echoid-s120" xml:space="preserve">Si <reg norm="quidem" type="context">quidẽ</reg> igit<unsure/>ur in pro <lb/>portione feratur, quam haber BE, EC fertur vti <lb/>que ſecundùm diametrum vbi BC. </s>
  <s xml:id="echoid-s121" xml:space="preserve">nunc autem <lb/>quoniam in nulla propor:</s>
  <s xml:id="echoid-s122" xml:space="preserve"><unsure/> ione, in circunferen-<lb/>tia certè fertur vbi B E C. </s>
  <s xml:id="echoid-s123" 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:id="echoid-s124" xml:space="preserve">quod videtur accidere maiori <lb/>&amp; </s>
  <s xml:id="echoid-s125" xml:space="preserve">minori illarum, q́uæ ex centro circulos deſcri <lb/>bunt. </s>
  <s xml:id="echoid-s126" 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 <reg norm="contrarium" type="context">contrariũ</reg> ad medium, <lb/>ardius fertur minoris <reg norm="extremum" type="context">extremũ</reg>. </s>
  <s xml:id="echoid-s127" xml:space="preserve">Omni quidem
<pb o="509" file="0509" n="6" rhead="Mechanicæ."/>
igitur circulum deſcribenti iſtuc accidit: </s>
  <s xml:id="echoid-s128" xml:space="preserve"><reg norm="fertur- que" type="simple">fertur-<lb/>q́ue</reg> eam quæ ẜm naturam eſt lationem, ſecun-<lb/>dum circunferentiam: </s>
  <s xml:id="echoid-s129" xml:space="preserve">illam verò quę pręter na <lb/>turam, in tranſuerſum, &amp; </s>
  <s xml:id="echoid-s130" xml:space="preserve">ſecundùm centrum. <lb/></s>
  <s xml:id="echoid-s131" xml:space="preserve">maiorem aut<unsure/><reg norm="em" type="context">ẽ</reg> ſemper eam, quæ præter <reg norm="naturam" type="context">naturã</reg> <lb/>eſt, ipſa minor fertur: </s>
  <s xml:id="echoid-s132" xml:space="preserve">quia enim centro eſt vici-<lb/>nior, quod trahit, vincitur magis<unsure/>: </s>
  <s xml:id="echoid-s133" xml:space="preserve">Quòd autem-<unsure/> <lb/>magis quod præter natui<unsure/><reg norm="am" type="context">ã</reg> eſt mouetur ipſa mi-<lb/>nor, quàm maior <reg norm="illarum" type="context">illarũ</reg>, quæ ex centro circulos <lb/><reg norm="deſcribunt" type="context">deſcribũt</reg> ex ijs eſt manifeſtum. </s>
  <s xml:id="echoid-s134" xml:space="preserve">Sit circulus vbi <lb/>B C D E &amp; </s>
  <s xml:id="echoid-s135" xml:space="preserve">alter in hoc minorvbi M N O P, circa <lb/>idem centrum A &amp; </s>
  <s xml:id="echoid-s136" 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:id="echoid-s137" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s138" xml:space="preserve">altera parie longius quadra <lb/>tum ſuppleatur DKRC: </s>
  <s xml:id="echoid-s139" xml:space="preserve">ſi quidem AB circu-<lb/>lum <reg norm="deſcribens" type="context">deſcribẽs</reg> ad id perueniet, vnde eſt egreſſa; </s>
  <s xml:id="echoid-s140" xml:space="preserve"><lb/>manifeſtum eſt quod ad ipſam fertur A B. </s>
  <s xml:id="echoid-s141" xml:space="preserve">Simi <lb/>literetiam A M ad ipſam A M perueniet. </s>
  <s xml:id="echoid-s142" xml:space="preserve">Tar-<lb/>dius autem fertur A M, quàru A B quemadmo-<lb/>dum dictum eſt: </s>
  <s xml:id="echoid-s143" xml:space="preserve">quia maior fit repulſio &amp; </s>
  <s xml:id="echoid-s144" xml:space="preserve">magis <lb/>rerrahitur A M. </s>
  <s xml:id="echoid-s145" xml:space="preserve">Ducatur igitur ipſa A L F, &amp; </s>
  <s xml:id="echoid-s146" xml:space="preserve">ab <lb/>ipſo L perpendiculum ad ip ſam A B, ipſa L Q in <lb/>minore circulo: </s>
  <s xml:id="echoid-s147" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s148" xml:space="preserve">rurſum ab L ducatur iuxta A <lb/>B L S, &amp; </s>
  <s xml:id="echoid-s149" xml:space="preserve">S T ad ipſam A B perpendiculum, &amp; </s>
  <s xml:id="echoid-s150" xml:space="preserve">ip. </s>
  <s xml:id="echoid-s151" xml:space="preserve"><lb/>fa F X: </s>
  <s xml:id="echoid-s152" xml:space="preserve">ipſæ igitur ubi ſunt S T, &amp; </s>
  <s xml:id="echoid-s153" xml:space="preserve">L Q, æquales: </s>
  <s xml:id="echoid-s154" xml:space="preserve"><lb/>ipſa ergo B T minor eſt, quàm M Q. </s>
  <s xml:id="echoid-s155" xml:space="preserve">æquales <lb/>enim rectæ lineæ in æqualibus coniectæ circulis <lb/><reg norm="perpendiculares" type="context">perpẽdiculares</reg> a diametro, <reg norm="minorem" type="context">minorẽ</reg> diametri re-<lb/>fecant <reg norm="ſectionem" type="context">ſectionẽ</reg> in maioribus circulis, eſt autem <lb/>ipſa S T æqualis ipſi L Q. </s>
  <s xml:id="echoid-s156" xml:space="preserve">In quanto autem tema <lb/>pore ipſa A L ipſam M L lata eſt, in tanto tem<gap/> <lb/>poris ſpatio in maiori circulo maiorem, quàm <lb/>fit B S, latum erit extremum ipſius B A. </s>
  <s xml:id="echoid-s157" xml:space="preserve">Latio <lb/>quidem igitur ſecundùm naturam æqualis: </s>
  <s xml:id="echoid-s158" 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:id="echoid-s159" xml:space="preserve">Oportet autem proportionabi-<lb/>liter eſſe, ſicut quod eſt <reg norm="ſecundum" type="context">ſecundũ</reg> <reg norm="naturam" type="context">naturã</reg>, ita quod <lb/>eſt pręter naturam, ad id quod eſt pręter <reg norm="naturam" type="context">naturã</reg>; <lb/></s>
  <s xml:id="echoid-s160" xml:space="preserve">maiorem igituĩ circunferentiam pertranſiuit, <reg norm="quam" type="simple">ꝗ̃</reg> <lb/>ſit ipſa S B. </s>
  <s xml:id="echoid-s161" xml:space="preserve">Neceſſe autem eſt ipſam F B in hoc <lb/><reg norm="rempore" type="context">rẽpore</reg> pertran ſiſſe: </s>
  <s xml:id="echoid-s162" xml:space="preserve">hic. </s>
  <s xml:id="echoid-s163" xml:space="preserve">n. </s>
  <s xml:id="echoid-s164" xml:space="preserve">erit, quando proportio <lb/>nabiliter <reg norm="vtrinque" type="simple">vtrinq;</reg> </s>
  <s xml:id="echoid-s165" xml:space="preserve">accidit, quod eſt præter <reg norm="naturam" type="context">naturã</reg>, <lb/>ad id quod eſt ſecundùm naturam. </s>
  <s xml:id="echoid-s166" xml:space="preserve">Si igitur ma-<lb/>ius eſt, quod ſecundum naturam in maiori, &amp; </s>
  <s xml:id="echoid-s167" xml:space="preserve"><lb/>quod eſt præter naturam. </s>
  <s xml:id="echoid-s168" xml:space="preserve">magis vtique hic coin <lb/>cidit vno modo: </s>
  <s xml:id="echoid-s169" 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:id="echoid-s170" xml:space="preserve">hic enim ſecundùm naturam <reg norm="quidem" type="context">quidẽ</reg> <lb/>figno B fit X F: </s>
  <s xml:id="echoid-s171" xml:space="preserve">eſt enim ab ipſo F <reg norm="perpendiculum" type="context">perpendiculũ</reg>: </s>
  <s xml:id="echoid-s172" xml:space="preserve"><lb/>præter naturam verò ad ipſam X B. </s>
  <s xml:id="echoid-s173" xml:space="preserve">Eſt autem <lb/>quemadmodum F X ad X B, ſic L Q. </s>
  <s xml:id="echoid-s174" xml:space="preserve">ad M Q. </s>
  <s xml:id="echoid-s175" xml:space="preserve">ma <lb/>nifeſtum autem, ſi coniunguntur abipſa B M, <lb/>ad F L. </s>
  <s xml:id="echoid-s176" 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 <reg norm="ſecundum" type="context">ſecundũ</reg> <lb/>naturam, ad id quod eſt præter naturam. </s>
  <s xml:id="echoid-s177" xml:space="preserve">Quam <lb/>igicur ob cauſam ab eadem potentia celerius fe<gap/> <lb/>tur id quod plus à centro diſtat punctum, ex ijs, <lb/>quæ dicta ſunt, eſt manifeſtum.</s>
  <s xml:id="echoid-s178" xml:space="preserve"/>
</p>
</div>
<div xml:id="echoid-div4" type="section" level="1" n="4">
<head xml:id="echoid-head7" style="it" xml:space="preserve">Quæſtiones.</head>
<p>
  <s xml:id="echoid-s179" xml:space="preserve">C V R <reg norm="aunt" type="context">aũt</reg> 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:id="echoid-s180" xml:space="preserve"><reg norm="palam" type="context">palã</reg> eſt ex ijs. </s>
  <s xml:id="echoid-s181" xml:space="preserve">Spar <lb/>tum. </s>
  <s xml:id="echoid-s182" xml:space="preserve">n fit <reg norm="centrum" type="context">centrũ</reg>: </s>
  <s xml:id="echoid-s183" xml:space="preserve">id pã<reg norm="que" type="simple">q;</reg> </s>
  <s xml:id="echoid-s184" xml:space="preserve">manet. <lb/></s>
  <s xml:id="echoid-s185" xml:space="preserve">quod <reg norm="aunt" type="context">aũt</reg> libræ <reg norm="vtrinque" type="simple">vtrinq;</reg> </s>
  <s xml:id="echoid-s186" xml:space="preserve">eſt, exeun <lb/>tes à centro. </s>
  <s xml:id="echoid-s187" xml:space="preserve">Ab <reg norm="eodem" type="context">eodẽ</reg> <reg norm="igitur" type="simple">igit̃</reg> <reg norm="pondere" type="context">põdere</reg> <lb/>citius moueri neceſſe eſt <reg norm="extre- mum" type="context">extre-<lb/>mũ</reg> libræ, quo plus à ſparto diſceſſerit. </s>
  <s xml:id="echoid-s188" xml:space="preserve">Et <reg norm="nonnul" type="context">nõnul</reg> <lb/>la <reg norm="quidem" type="context">quidẽ</reg> in paruis libris impoſita <reg norm="non" type="context">nõ</reg> manifeſta
<pb o="511" file="0511" n="8" rhead="Mechanicæ."/>
fenſui ſunt pondera: </s>
  <s xml:id="echoid-s189" xml:space="preserve">in magis <reg norm="aunt" type="context">aũt</reg> maniſeſta: </s>
  <s xml:id="echoid-s190" xml:space="preserve">ni <lb/>hil enim prohibet minorem moueri magnitudi <lb/>nem, <reg norm="quam" type="simple">ꝗ̃</reg> vt viſioni ſit maniſeſta. </s>
  <s xml:id="echoid-s191" xml:space="preserve">In magna <reg norm="aunt" type="context">aũt</reg> li-<lb/>bra idem pondus viſibile efficit magnitudo. </s>
  <s xml:id="echoid-s192" xml:space="preserve">Quę <lb/>dam verò manifeſta quidem ſunt in <reg norm="vtriſque" type="simple">vtriſq;</reg></s>
  <s xml:id="echoid-s193" xml:space="preserve">, ſed <lb/>multo magis in maioribus, qm̄ multo maior in <lb/>clinationis fit magnitudo ab eodem <reg norm="perondere" type="simple">ꝑondere</reg> <lb/>in maioribus. </s>
  <s xml:id="echoid-s194" xml:space="preserve">Quamobrem machinanturij, qui <lb/>purpuram vendunt, vt pendendo defraudent, <reg norm="tum" type="context">tũ</reg> <lb/>ad medium ſpartum non ponentes: </s>
  <s xml:id="echoid-s195" xml:space="preserve">tum plum-<lb/>bum in alteraruram libræ partem infundentes: <lb/></s>
  <s xml:id="echoid-s196" xml:space="preserve">aut ligni gđ ad <reg norm="radicem" type="context">radicẽ</reg> vergebat, in eam quam de <lb/>ferri vola<unsure/>nt, partem conſtituentes; </s>
  <s xml:id="echoid-s197" xml:space="preserve">aut ſi nodum <lb/>habuerit: </s>
  <s xml:id="echoid-s198" xml:space="preserve">ligni enim grauior illa eſt pars, in qua <lb/>eſt radix, nodus vero radix quædam eſt.</s>
  <s xml:id="echoid-s199" xml:space="preserve"/>
</p>
<div xml:id="echoid-div4" 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:id="echoid-s200" xml:space="preserve">Cut <reg norm="ſiquidem" type="context">ſiquidẽ</reg> ſurſum ſuerit <reg norm="ſpartum" type="context">ſpartũ</reg>, <reg norm="quando" type="wordlist">qñ</reg> <reg norm="deorsum" type="context">deorsũ</reg> lato <lb/>
<anchor type="note" xlink:label="note-0511-01a" xlink:href="note-0511-01"/>
p<reg norm="on" type="context">õ</reg>dere, <reg norm="quiſpiam" type="context">quiſpiã</reg> id admouet, rurſum aſcendit li-<lb/>bra: </s>
  <s xml:id="echoid-s201" xml:space="preserve">ſi autem deorſum conſtitutum ſuerit, non <lb/>aſcendit, ſed manet? </s>
  <s xml:id="echoid-s202" xml:space="preserve">An quia ſurſum <reg norm="quidem" type="context">quidẽ</reg> ſpar <lb/>to exiſtente, plus libræ extra perpendiculum fit: <lb/></s>
  <s xml:id="echoid-s203" xml:space="preserve">ſpartum enim eſt perpendiculum: </s>
  <s xml:id="echoid-s204" xml:space="preserve">quare neceſſe <lb/>eſt deorſum ferri id quod plus eſt, donec aſcen-<lb/>dat quæ bifariam libram diuidit, ad ipſum <reg norm="per- pendiculum" type="context">per-<lb/>pendiculũ</reg>, cùm onus incumbat ad libræ partem <lb/>furſum raptam. </s>
  <s xml:id="echoid-s205" xml:space="preserve">Sit libra recta vbi B C, ſpartum <lb/>autem A D. </s>
  <s xml:id="echoid-s206" xml:space="preserve">hoc igitur deorſum proiecto perpen <lb/>diculum erit vbi A D M. </s>
  <s xml:id="echoid-s207" xml:space="preserve">Si igitur in ipſo B pona <lb/>tur onus, B quidem erit vbi E, C, autem vbi H. </s>
  <s xml:id="echoid-s208" xml:space="preserve"><lb/>quamobrem ea quæ bifariam libram ſecat, pri-<lb/>mo quidem erit D M ipſius perpendiculi: </s>
  <s xml:id="echoid-s209" xml:space="preserve">incum <lb/>bente <reg norm="autem" type="context">autẽ</reg> onere erit D G. </s>
  <s xml:id="echoid-s210" 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:id="echoid-s211" xml:space="preserve">Si igitur amoueatur <lb/>onus abipſo E, neceſſe eſt deorſum ferri H, mi-<lb/><gap/><gap/>s enim eſt ipſum E. </s>
  <s xml:id="echoid-s212" 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:id="echoid-s213" xml:space="preserve">Si <reg norm="autem" type="context">autẽ</reg> deorſum fuerit, id, quod ſubſtat, <reg norm="con" type="context">cõ</reg> <lb/>trarium facit: </s>
  <s xml:id="echoid-s214" xml:space="preserve">plus enim dimidio fit libræ, quæ <lb/>deorſum eſt pars, quàm quod perpendiculum ſe <lb/>cet, quapropter <reg norm="non" type="context">nõ</reg> <reg norm="aſcendit" type="context">aſcẽdit</reg>: </s>
  <s xml:id="echoid-s215" xml:space="preserve">eleuata enim pars le <lb/>uior eſt. </s>
  <s xml:id="echoid-s216" xml:space="preserve">Sit libra recta vbi N O, perpendiculum <lb/>autem K L M <reg norm="bifariam" type="context">bifariã</reg> igitur ſecatu<gap/> K G. </s>
  <s xml:id="echoid-s217" xml:space="preserve">Impo-<lb/>ſito autem onere in ipſo N, erit <reg norm="quidem" type="context">quidẽ</reg> N vbi O, <lb/>ipſum autem G vbi R, K L autem vbi L P. </s>
  <s xml:id="echoid-s218" xml:space="preserve">quare <lb/>maius eſt K O, quàm L R, ipſo P K L. </s>
  <s xml:id="echoid-s219" xml:space="preserve">Et ablato <lb/>igitur onere, neceſſe eſt manere: </s>
  <s xml:id="echoid-s220" xml:space="preserve">in cumbit enim <lb/>ceu onus exceſſus medietatis eius vbi eſt F.</s>
  <s xml:id="echoid-s221" xml:space="preserve"/>
</p>
<div xml:id="echoid-div5" 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:id="echoid-s222" 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:id="echoid-s223" xml:space="preserve">cùm ſacilius ſit mino-<lb/>grem mouere grauitatem: </s>
  <s xml:id="echoid-s224" xml:space="preserve">minor <reg norm="autem" type="context">autẽ</reg> eſt ſine ve-<lb/>cte. </s>
  <s xml:id="echoid-s225" xml:space="preserve">An <reg norm="quoniam" type="context">quoniã</reg> ipſe vectis eſt in cauſa hbra exi-<lb/>ſtens, <reg norm="ſpartum" type="context">ſpartũ</reg> infernè habens, in inæqualia diui-<lb/>ſa. </s>
  <s xml:id="echoid-s226" xml:space="preserve">hypomochlion enim eſt ſpartum. </s>
  <s xml:id="echoid-s227" xml:space="preserve">a mbo nan <lb/>que ſtamt, vt centrum. </s>
  <s xml:id="echoid-s228" xml:space="preserve">quoniam autem ab ęqua-<lb/>ſi pondere celerius mouetur maior earum, q̃ à <lb/>centro ſunt: </s>
  <s xml:id="echoid-s229" xml:space="preserve">duo verò pondera, quod mouet, &amp; </s>
  <s xml:id="echoid-s230" xml:space="preserve"><lb/>quod mouetur: </s>
  <s xml:id="echoid-s231" xml:space="preserve">quod igitur motum pondus ad-<lb/>mouens, longitudo patitur ad <reg norm="longitudinem" type="context">longitudinẽ</reg>. </s>
  <s xml:id="echoid-s232" xml:space="preserve">ſem <lb/>per autem quanto ab hy pomochlio diſtabit ma <lb/>gis, tanto facilius mo<unsure/>uebit. </s>
  <s xml:id="echoid-s233" xml:space="preserve">Cauſa autem eſt, quę <lb/>retro <reg norm="commemorata" type="context">cõmemorata</reg> eſt: </s>
  <s xml:id="echoid-s234" xml:space="preserve">quoniam quę plus à cen-<lb/><gap/>ro diſtat, maiorem deſcribit circuium: </s>
  <s xml:id="echoid-s235" xml:space="preserve">quare ab <lb/>eadem potentia plus ſeparabitur mouens illud, <lb/>quod plus ab hypomochlio diſtabit. </s>
  <s xml:id="echoid-s236" xml:space="preserve">Sit uectis <lb/>vbi A B, pondus vbi C, quod mouet <reg norm="autenvbi" type="context">autẽvbi</reg> D, <lb/>hy pomochlion vbi E. </s>
  <s xml:id="echoid-s237" xml:space="preserve">quod autem vbi eſt D mo <lb/>u<unsure/>ens, vbi F. </s>
  <s xml:id="echoid-s238" xml:space="preserve">motum autem vbi C. </s>
  <s xml:id="echoid-s239" xml:space="preserve">pondus, vbi G.</s>
  <s xml:id="echoid-s240" xml:space="preserve"/>
</p>
<div xml:id="echoid-div6" 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:id="echoid-s241" 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:id="echoid-s242" xml:space="preserve">An quia remus vectis eſt: </s>
  <s xml:id="echoid-s243" 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:id="echoid-s244" xml:space="preserve">ve-<lb/>ctem autem mouens ipſe eſt remex. </s>
  <s xml:id="echoid-s245" xml:space="preserve">Semper <reg norm="aunt" type="context">aũt</reg> <lb/>plus mouet ponderis, quanto magis ab hypomo <lb/>chlio diſtabit, quicunque id mouet. </s>
  <s xml:id="echoid-s246" xml:space="preserve">maior enim <lb/>ita fit, quæ ex centro. </s>
  <s xml:id="echoid-s247" xml:space="preserve">ſcalmus autem hypomo-<lb/>chlion exiſtens, centrum eſt. </s>
  <s xml:id="echoid-s248" xml:space="preserve">In medio autem na <lb/>uis plurimum remi intus eſt: </s>
  <s xml:id="echoid-s249" xml:space="preserve">ilia enim parte la-<lb/>tiſſima eſt nauis: </s>
  <s xml:id="echoid-s250" xml:space="preserve">quare maior <reg norm="vtrinque" type="simple">vtrinq;</reg> </s>
  <s xml:id="echoid-s251" xml:space="preserve">remi pars <lb/><reg norm="vtrorunque" type="simple">vtrorunq;</reg> </s>
  <s xml:id="echoid-s252" xml:space="preserve">nauis parietum intrin ſecus eſt. </s>
  <s xml:id="echoid-s253" 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:id="echoid-s254" xml:space="preserve">nauem verò ſcalmo alligatam ſi-<lb/>mul promoueri contingit, quo remi extremum. <lb/></s>
  <s xml:id="echoid-s255" xml:space="preserve">vbi enim plurimum maris diuidit remus, eò ma-<lb/>ximè propelli neceſſe eſt. </s>
  <s xml:id="echoid-s256" xml:space="preserve">plurimum autem di<gap/>i <lb/>dit, vbi pars plurima remia ſcalmo eſt. </s>
  <s xml:id="echoid-s257" xml:space="preserve">Et eam <lb/>cauſam remiges, qui in media ſunt naui, mouent <lb/>illam maximè. </s>
  <s xml:id="echoid-s258" xml:space="preserve">maxima enim remi pars à ſcalmo <lb/>in nauis medio intus eſt.</s>
  <s xml:id="echoid-s259" xml:space="preserve"/>
</p>
<div xml:id="echoid-div7" 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:id="echoid-s260" xml:space="preserve">Cur paruum exiſtens gubernaculum, &amp; </s>
  <s xml:id="echoid-s261" 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, &amp; </s>
  <s xml:id="echoid-s262" xml:space="preserve">ab hominis vnius viribus alioqùin <lb/>modicè vtentis, magnę nauigiorum moueantur <lb/>moles? </s>
  <s xml:id="echoid-s263" xml:space="preserve">An quoniam gubernaculum vectis eſt: </s>
  <s xml:id="echoid-s264" xml:space="preserve">o-<lb/><gap/>us autem mare: </s>
  <s xml:id="echoid-s265" xml:space="preserve">gubernator verò mouens eſt. <lb/></s>
  <s xml:id="echoid-s266" xml:space="preserve">Non autem ſecundum <reg norm="latitudinem" type="context">latitudinẽ</reg>, veluti remus, <lb/>mare accipit gubernaculum: </s>
  <s xml:id="echoid-s267" xml:space="preserve">non enim in antè <lb/>nauigium mouet, ſed ipſum commotum mare <lb/>accipiens inclinat obliquè: </s>
  <s xml:id="echoid-s268" xml:space="preserve">quoniam enim pon-<lb/>dus eſt mare, contrario innixum modo nauem <lb/>inclinat. </s>
  <s xml:id="echoid-s269" xml:space="preserve">hypomochlion enim in contrarium <lb/>verſatur: </s>
  <s xml:id="echoid-s270" xml:space="preserve">mare vero interius, ſi illud exterius. </s>
  <s xml:id="echoid-s271" xml:space="preserve"><lb/>illud autem ſequitur nauis, quoniam illi eſt ai<unsure/>li-<lb/><gap/>ata. </s>
  <s xml:id="echoid-s272" xml:space="preserve">Et remus quidem ſecundùm latitudinem
<pb o="514" file="0514" n="11" rhead="Ariſt. Quæſtiones."/>
onus propellens, &amp; </s>
  <s xml:id="echoid-s273" xml:space="preserve">ab eodem repulſus, in <reg norm="rectum" type="context">rectũ</reg> <lb/>propellit: </s>
  <s xml:id="echoid-s274" xml:space="preserve">gubernaculum autem, ut obliquum ia <lb/>cet, hinc inde in obliquum <reg norm="motionem" type="context">motionē</reg> facit. </s>
  <s xml:id="echoid-s275" xml:space="preserve">In ex <lb/>tremo <reg norm="autem" type="context">autē</reg>, &amp; </s>
  <s xml:id="echoid-s276" xml:space="preserve">non in medio iacet, quoniam mo <lb/>uenti <reg norm="facilimum" type="context">facilimū</reg> eſt ab extremo motum mouere. <lb/></s>
  <s xml:id="echoid-s277" xml:space="preserve">Prim a enim pars celerimè fertur; </s>
  <s xml:id="echoid-s278" xml:space="preserve"><reg norm="quoniam" type="context">quoniã</reg> quem <lb/>adm odum in ijs quæ feruntur, in fine deficit la-<lb/>tio, ſic ipſius <reg norm="continui" type="context">cōtinui</reg> in fine imbeciliſſima eſt la-<lb/>tio. </s>
  <s xml:id="echoid-s279" xml:space="preserve">imbeciliſſima autem ad expellendum eſt fa <lb/>cilis. </s>
  <s xml:id="echoid-s280" xml:space="preserve">Propter hæcigitur in puppi gubernaculum <lb/>ponitur. </s>
  <s xml:id="echoid-s281" xml:space="preserve">Nec minus, <reg norm="quoniam" type="context">quoniā</reg> parua ibi motione <lb/>ſacta, multò maius interuallum fit in ultimo: </s>
  <s xml:id="echoid-s282" xml:space="preserve"><reg norm="quia" type="simple">ꝗa</reg> <lb/>æqualis angulus ſemper maiorem ſpectat: </s>
  <s xml:id="echoid-s283" xml:space="preserve"><reg norm="tan- toque" type="simple">tan-<lb/>toq́ue</reg> magis. </s>
  <s xml:id="echoid-s284" xml:space="preserve">quanto maiores fuerint illæ, quæ <lb/>con<gap/>in<reg norm="en" type="context">ẽ</reg>t. </s>
  <s xml:id="echoid-s285" xml:space="preserve">Ex ijs etiam manifeſtum eſt, quam ob <lb/>cauſſam magis in contrarium procedit <reg norm="nauigium" type="context">nauigiũ</reg>, <lb/>quàm remi ipſius palmula. </s>
  <s xml:id="echoid-s286" xml:space="preserve">eadem enim magni <lb/>tudoijſdem mota uiribus, in aete plus, quàm in <lb/>aqua progreditur. </s>
  <s xml:id="echoid-s287" xml:space="preserve">Si enim A B remus, Guerò <lb/>ſcalmus: </s>
  <s xml:id="echoid-s288" xml:space="preserve">A autem in nauigio ſit remi <reg norm="principium" type="context">principiũ</reg>, <lb/>B uerò in mari palmula. </s>
  <s xml:id="echoid-s289" xml:space="preserve">Si igitur A ubi D tranſ. </s>
  <s xml:id="echoid-s290" xml:space="preserve"><lb/>latum eſt, non erit B ubi E: </s>
  <s xml:id="echoid-s291" xml:space="preserve">æqualis enim B E ipſi <lb/>A C. </s>
  <s xml:id="echoid-s292" xml:space="preserve">æquale igitur <reg norm="tranſlatum" type="context">tranſlatū</reg> erit, ſed minus. </s>
  <s xml:id="echoid-s293" xml:space="preserve">erit <lb/>igitur ubi eſt F. </s>
  <s xml:id="echoid-s294" xml:space="preserve">minor enim C F, ipſa A D. </s>
  <s xml:id="echoid-s295" xml:space="preserve">quare <lb/>ipſa G F, ipſa D F. </s>
  <s xml:id="echoid-s296" xml:space="preserve">ſimiles enim ſunt trianguli. </s>
  <s xml:id="echoid-s297" xml:space="preserve"><lb/>Stans autem erit medium, ubi eſt C. </s>
  <s xml:id="echoid-s298" xml:space="preserve">in <reg norm="contrarium" type="context">contrariũ</reg> <lb/>enim ipſi, quod in mari eſt, extremo uidelicet B <lb/>procedit, ubi extremum in nauigio eſt A. </s>
  <s xml:id="echoid-s299" xml:space="preserve">Non <lb/>procedere <reg norm="autenubi" type="context">autēubi</reg> eſt D. </s>
  <s xml:id="echoid-s300" xml:space="preserve">niſi commouere<gap/>ur na <lb/>uigium, &amp; </s>
  <s xml:id="echoid-s301" xml:space="preserve">eo transferretur, ubi remi eſt princi-<lb/>plum Idipſnm etiam facit gubernaculam, niſi <reg norm="quod" type="simple">ꝙ</reg> <lb/>(ut dictum eſt terro) nihil nauigio ad id, quod-<lb/>antè eſt, confert, ſed ſolùm puppim in <reg norm="obliquum" type="context">obliquũ</reg> <lb/>pell<gap/>t, <reg norm="ubicunque" type="simple">ubicunq;</reg> </s>
  <s xml:id="echoid-s302" xml:space="preserve">fuerit in con<gap/>rari<reg norm="um" type="context">ū</reg> enim eo mo <lb/>do uergit prora. </s>
  <s xml:id="echoid-s303" 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:id="echoid-s304" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s305" xml:space="preserve"><reg norm="quemadmodum" type="context">quemadmodũ</reg> ſcalmus <lb/>remo. </s>
  <s xml:id="echoid-s306" xml:space="preserve">Medium autem procedit ſecundùm quod <lb/>gubernaculum <reg norm="transfertur" type="context">trãsfertur</reg>. </s>
  <s xml:id="echoid-s307" xml:space="preserve">ſi <reg norm="quidem" type="context">quidē</reg> introrſus agit, <lb/>&amp; </s>
  <s xml:id="echoid-s308" xml:space="preserve">puppis eo transfertur. </s>
  <s xml:id="echoid-s309" xml:space="preserve">prora verò ad contra-<lb/>rium vergit. </s>
  <s xml:id="echoid-s310" xml:space="preserve">in eodem enim exiſtente prora, to-<lb/>tum transfertur nauigium.</s>
  <s xml:id="echoid-s311" xml:space="preserve"/>
</p>
<div xml:id="echoid-div8" 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:id="echoid-s312" xml:space="preserve">Cur quando antenna ſublimior fuerit, ijſdem <lb/>
<anchor type="note" xlink:label="note-0515-01a" xlink:href="note-0515-01"/>
uelis, &amp; </s>
  <s xml:id="echoid-s313" xml:space="preserve">uento <reg norm="eodem" type="context">eodẽ</reg> celerius <reg norm="feruntur" type="context">ferũtur</reg> nauigia? </s>
  <s xml:id="echoid-s314" xml:space="preserve">An <lb/>quia malus quidem fit uectis: </s>
  <s xml:id="echoid-s315" xml:space="preserve">hypomochlion ue <lb/>rò mali ſedes, in qua collocatur: </s>
  <s xml:id="echoid-s316" xml:space="preserve">pondus autem, <lb/>quod moueri debet, ipſum nauigium: </s>
  <s xml:id="echoid-s317" xml:space="preserve">mou<gap/>s ve <lb/>ro is, qui vela tendit, ſpiri<gap/>us. </s>
  <s xml:id="echoid-s318" xml:space="preserve">Si igitur quanto re <lb/>motius fuerit hypomochion, facilius eadem po-<lb/>tentia, &amp; </s>
  <s xml:id="echoid-s319" xml:space="preserve">citius idem mouet pondus, altius cer-<lb/>tè ſublata antenna, velum à mali ſede, quæ hypo <lb/>mochlion eſt, remo<gap/>ius faciens, id efficie<gap/>.</s>
  <s xml:id="echoid-s320" xml:space="preserve"/>
</p>
<div xml:id="echoid-div9" 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:id="echoid-s321" 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:id="echoid-s322" xml:space="preserve">illam ve-<lb/>rò quæ proram verſus eſt, pedem facientes rela <lb/>xant? </s>
  <s xml:id="echoid-s323" xml:space="preserve">An quia retrahere quidem multo exiſten <lb/>tevento gubernaculum non poteſt: </s>
  <s xml:id="echoid-s324" xml:space="preserve">pauco <reg norm="autem" type="context">autẽ</reg> <lb/>poteſt, quem conſtringunt. </s>
  <s xml:id="echoid-s325" xml:space="preserve">Propellit quidem igi <lb/>tur ipſe ventus: </s>
  <s xml:id="echoid-s326" xml:space="preserve">in puppim vero illum <reg norm="conſtituit" type="context">cōſtituit</reg>, <lb/>gubernaculum retrahens, &amp; </s>
  <s xml:id="echoid-s327" xml:space="preserve">mare <reg norm="compellens" type="context">compellẽs</reg>: </s>
  <s xml:id="echoid-s328" xml:space="preserve">ſi-<lb/>mul &amp; </s>
  <s xml:id="echoid-s329" xml:space="preserve">nautæ ipſi cum vento contendunt: </s>
  <s xml:id="echoid-s330" xml:space="preserve">in <reg norm="con- trariam" type="context">cõ-<lb/>trariam</reg> enim ſe reclinant partem.</s>
  <s xml:id="echoid-s331" xml:space="preserve"/>
</p>
<div xml:id="echoid-div10" 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:id="echoid-s332" xml:space="preserve">Cur ex figurarum genere, q̃cun<reg norm="que" type="simple">q;</reg> </s>
  <s xml:id="echoid-s333" xml:space="preserve">rot<reg norm="un" type="context">ũ</reg>dę ſunt <lb/>
<anchor type="note" xlink:label="note-0515-03a" xlink:href="note-0515-03"/>
&amp; </s>
  <s xml:id="echoid-s334" xml:space="preserve">circinatæ, facilius mouentur? </s>
  <s xml:id="echoid-s335" xml:space="preserve">Trifariam <reg norm="autem" type="context">autẽ</reg> <lb/>circulum rotari contingit. </s>
  <s xml:id="echoid-s336" xml:space="preserve">aut enim <gap/>m abſidem <lb/>centro ſimul moto, quemadmodum paluſtriver <lb/>titur rota: </s>
  <s xml:id="echoid-s337" xml:space="preserve">aut circa manens <reg norm="centrum" type="context">centrū</reg>, veluti tro-<lb/>chleæ ſtante centro: </s>
  <s xml:id="echoid-s338" xml:space="preserve">autin pauimento manente <lb/><gap/><reg norm="en" type="context">ẽ</reg>tro, ſicut figuli rota conuertitur. </s>
  <s xml:id="echoid-s339" xml:space="preserve">An celer<gap/>ima
<pb o="516" file="0516" n="13" rhead="Ariſt. Quæſtiones"/>
quidem huiuſmodi ſunt, quoniam parua ſuipa<gap/> <lb/>te planum contingunt, veluti circulas <reg norm="ſecundum" type="context">ſecūdum</reg> <lb/>punctum: </s>
  <s xml:id="echoid-s340" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s341" xml:space="preserve">quoniam non offenſant: </s>
  <s xml:id="echoid-s342" xml:space="preserve">à terra em̄ <lb/>ſemotus eſt angulus. </s>
  <s xml:id="echoid-s343" xml:space="preserve">Pręterea etiam cui obuiam <lb/>fiunt corpori, id rurſum ſecundùm puſillam tan <lb/>gunt. </s>
  <s xml:id="echoid-s344" xml:space="preserve">ſi autem rectilineum eſſet, rectitudine ſua <lb/>multum plani contingeret. </s>
  <s xml:id="echoid-s345" xml:space="preserve">Ad hæc quò mutat <lb/>pondus, eo motor mouet. </s>
  <s xml:id="echoid-s346" xml:space="preserve">cùm igitur ad rectum <lb/>ſuper plano circuli fuerit diameter, <reg norm="planum" type="context">planū</reg> ſecun <lb/>dùm punctum, <reg norm="contingente" type="context">contingēte</reg> circulo æquale vtriu-<lb/>que pondus difterminat diameter. </s>
  <s xml:id="echoid-s347" xml:space="preserve">cùm <reg norm="autem" type="context">autē</reg> mo <lb/>uetur, plus illico, ad quòd mouetur, ceui<gap/>de nu <lb/>tans. </s>
  <s xml:id="echoid-s348" xml:space="preserve">ab impellẽre facilius in ante mouetur: </s>
  <s xml:id="echoid-s349" xml:space="preserve">quò <lb/>enim vnumquodque vergit, mouetur ex facili: <lb/></s>
  <s xml:id="echoid-s350" xml:space="preserve">ſi quidem difficulter ad <reg norm="contrarium" type="context">cōtrarium</reg> nutus ſui mo <lb/>uetur modum. </s>
  <s xml:id="echoid-s351" xml:space="preserve">Præterea nonnulli autumn<gap/>nt <reg norm="quod" type="simple">ꝙ</reg> <lb/>circuli linea in perpeti verſatur motu, quemad-<lb/>modum manentia propter contrarium <reg norm="nixum" type="context">nixũ</reg> ma <lb/>nent: </s>
  <s xml:id="echoid-s352" xml:space="preserve">ſicur maioribus contingit circulis ad mino <lb/>res. </s>
  <s xml:id="echoid-s353" xml:space="preserve">Celerius enim ab æquali mouentur potentia <lb/>maiores circuli, <reg norm="mouentque" type="simple">mouentq́ue</reg> onera, quoniam cir <lb/>culi maioris angulus ad minoris angulum cir-<lb/>culi nutum habet quendam: </s>
  <s xml:id="echoid-s354" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s355" xml:space="preserve">ſicut diameter ad <lb/>diametrum, ita maior circulus ad minorem. </s>
  <s xml:id="echoid-s356" xml:space="preserve">it fi <lb/>niti autem ſunt minores. </s>
  <s xml:id="echoid-s357" xml:space="preserve">Si autem ad alte<gap/>um <lb/>nutum habet circulus, ſimiliter eſt bene mobi-<lb/>lis. </s>
  <s xml:id="echoid-s358" xml:space="preserve">Et aliam ſanè habet inclinationem circulus, <lb/>&amp; </s>
  <s xml:id="echoid-s359" xml:space="preserve">ea quæ à circulo mouentur, licèt <reg norm="planitiem" type="context">planitiẽ</reg> abſi-<lb/>de non contingat, ſed aut iuxta <reg norm="planitiem" type="context">planitiẽ</reg>, aut velu <lb/>tì trocleæ. </s>
  <s xml:id="echoid-s360" xml:space="preserve">etenim hoc ſe habentes modo facilli-<lb/>me mouentur, &amp; </s>
  <s xml:id="echoid-s361" xml:space="preserve">onera commouent. </s>
  <s xml:id="echoid-s362" xml:space="preserve">An <reg norm="non" type="context">nõ</reg> quia <lb/>parua ſui portione cùm tangit, tum offenſat cir-<lb/>culus, ſed aliam ob cauſam. </s>
  <s xml:id="echoid-s363" 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:id="echoid-s364" xml:space="preserve">quam ob rem illarum alte-
<pb o="517" file="0517" n="14" rhead="Mechanicæ."/>
ram pro nutu ſemper habet, &amp; </s>
  <s xml:id="echoid-s365" xml:space="preserve">veluti continuo <lb/>motum illum mòuent, <reg norm="quicunque" type="simple">quicunq;</reg> </s>
  <s xml:id="echoid-s366" xml:space="preserve">mouent, quan-<lb/>do ſecundùm circun ferentiam illum mouerint: <lb/></s>
  <s xml:id="echoid-s367" xml:space="preserve">latam enim ipſam mouent. </s>
  <s xml:id="echoid-s368" xml:space="preserve">Eam quidem igitur, <lb/>quæ in obliquum eſt, motionem ipſum impellit <lb/>mouens: </s>
  <s xml:id="echoid-s369" xml:space="preserve">ſecundum vero illam, quæ ſuper diame <lb/>trum eſt, ſeipſum mouet circulus.</s>
  <s xml:id="echoid-s370" xml:space="preserve"/>
</p>
<div xml:id="echoid-div11" 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:id="echoid-s371" xml:space="preserve">Cur ea, quæ per maiores circulos tolluntur &amp; </s>
  <s xml:id="echoid-s372" xml:space="preserve"><lb/>
<anchor type="note" xlink:label="note-0517-01a" xlink:href="note-0517-01"/>
trahuntur, facilius &amp; </s>
  <s xml:id="echoid-s373" xml:space="preserve">ci<gap/>ius moueri contingit, ve <lb/>lu<gap/>i maioribus trochleis quàm minoribus, &amp; </s>
  <s xml:id="echoid-s374" xml:space="preserve"><lb/>fcytalis ſimiliter? </s>
  <s xml:id="echoid-s375" xml:space="preserve">An <reg norm="quoniam" type="context">quoniã</reg>, qnanto maior fue-<lb/>ri<gap/><gap/>illa quæ à centro eſt, in ęquali tempore maius <lb/>mouetur ſpatium. </s>
  <s xml:id="echoid-s376" xml:space="preserve">Quam ob rem æquali <reg norm="inexiſtem" type="context">inexiſtẽ</reg> <lb/>te onere, idem faciet: </s>
  <s xml:id="echoid-s377" xml:space="preserve">quemadmodum diximus, <lb/>&amp; </s>
  <s xml:id="echoid-s378" xml:space="preserve">maiores libras minoribus exactiores eſſe. </s>
  <s xml:id="echoid-s379" xml:space="preserve">ſpar <lb/>tum enim in illis centrum eſt: </s>
  <s xml:id="echoid-s380" xml:space="preserve">libræ autem vtrin <lb/>que partes, quæ ex centro ſunt, exiſtunt.</s>
  <s xml:id="echoid-s381" xml:space="preserve"/>
</p>
<div xml:id="echoid-div12" 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:id="echoid-s382" 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:id="echoid-s383" xml:space="preserve">Similiq́ mo <lb/>do rota, &amp; </s>
  <s xml:id="echoid-s384" xml:space="preserve">huiuſmodi quippiam, quod grauius <lb/>quidem eſt, maius autem minore &amp; </s>
  <s xml:id="echoid-s385" xml:space="preserve">leuiore? </s>
  <s xml:id="echoid-s386" xml:space="preserve">An <lb/>quia non ſolùm in contrarium quod graue eſt, <lb/>ſed in obliquum etiam difficulter mouetur. </s>
  <s xml:id="echoid-s387" xml:space="preserve">In <lb/>contrarium enim ei, ad quod vergit onus, moue-<lb/>re difficile eſt: </s>
  <s xml:id="echoid-s388" xml:space="preserve">quò autem vergit, eſt facilè. </s>
  <s xml:id="echoid-s389" xml:space="preserve">in obli <lb/>quum autem haudquaquam vergit.</s>
  <s xml:id="echoid-s390" xml:space="preserve"/>
</p>
<div xml:id="echoid-div13" 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:id="echoid-s391" xml:space="preserve">Cur ſuper ſcytalas facilius portantur onera, <lb/>
<anchor type="note" xlink:label="note-0517-03a" xlink:href="note-0517-03"/>
qu<reg norm="am" type="context">ã</reg> ſ<gap/>per currus, cùm <reg norm="tamen" type="wordlist">tamẽ</reg> ij magnas habeant <lb/>rotas, illæ verò puſillas? </s>
  <s xml:id="echoid-s392" xml:space="preserve">An qui in ſcytalis nulla <lb/>eſt offen ſatio, in curribus autem axis eſt, ad <reg norm="quem" type="context">quẽ</reg> <lb/>offenſant. </s>
  <s xml:id="echoid-s393" xml:space="preserve">deſuper enim illum premunt, &amp; </s>
  <s xml:id="echoid-s394" xml:space="preserve">late-<lb/>ribus. </s>
  <s xml:id="echoid-s395" xml:space="preserve">quod autem eſt in ſcycalis, ad iſthæc duo <lb/>mouetur, &amp; </s>
  <s xml:id="echoid-s396" xml:space="preserve">inſernè ſubſtrato ſpatio, &amp; </s>
  <s xml:id="echoid-s397" xml:space="preserve">onere ſu <lb/>per impoſito. </s>
  <s xml:id="echoid-s398" xml:space="preserve">in vtriſque enim ijs reuoluitur lo-<lb/>cis circulus, &amp; </s>
  <s xml:id="echoid-s399" xml:space="preserve">motus impellitur.</s>
  <s xml:id="echoid-s400" xml:space="preserve"/>
</p>
<div xml:id="echoid-div14" 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:id="echoid-s401" 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:id="echoid-s402" xml:space="preserve">Præterea ſic quidem duo mouet pondera, <lb/>fundæ videlicet, &amp; </s>
  <s xml:id="echoid-s403" xml:space="preserve">miſſilis: </s>
  <s xml:id="echoid-s404" xml:space="preserve">illo <reg norm="aunt" type="context">aũt</reg> modo ſolum <lb/>miſſile. </s>
  <s xml:id="echoid-s405" xml:space="preserve">An quia in funda quidem commotum <lb/>miſſile funditur, proijcit: </s>
  <s xml:id="echoid-s406" xml:space="preserve">fundam enim circulo <lb/>ſubinde rotans, id iaculatur: </s>
  <s xml:id="echoid-s407" xml:space="preserve">ex manu autem à <lb/>quiete eſt initium: </s>
  <s xml:id="echoid-s408" xml:space="preserve">omnia autem cùm in motu <lb/>ſunt, quàm cùm quieſcunt, facilius <reg norm="mouentur" type="context">mouẽtur</reg>. </s>
  <s xml:id="echoid-s409" xml:space="preserve">An <lb/>&amp; </s>
  <s xml:id="echoid-s410" xml:space="preserve">eam ob cauſam e<gap/>t, ſed nec minus etiam, quia <lb/>in fundæ vſu manus quidem fit centrum: </s>
  <s xml:id="echoid-s411" xml:space="preserve">ſunda <lb/>vero, quod à centro exit. </s>
  <s xml:id="echoid-s412" xml:space="preserve">quanto <reg norm="aunt" type="context">aũt</reg> productius <lb/>ſueritid, quod à <reg norm="centro" type="context">cētro</reg> eſt, tanto citius mouetur. <lb/></s>
  <s xml:id="echoid-s413" xml:space="preserve">iactus <reg norm="aunt" type="context">aūt</reg> qui <reg norm="manu" type="context">māu</reg> fit, fundę reſpectu breuis eſt.</s>
  <s xml:id="echoid-s414" xml:space="preserve"/>
</p>
<div xml:id="echoid-div15" 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:id="echoid-s415" 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:id="echoid-s416" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s417" xml:space="preserve">item ſuculæ, <lb/>quæ graciliores ſunt, ab <reg norm="eadem" type="context">eadẽ</reg> <reg norm="viquam" type="simple">viꝗ̃</reg> craſſiores? </s>
  <s xml:id="echoid-s418" xml:space="preserve">An <lb/>quía ſecula quidem, &amp; </s>
  <s xml:id="echoid-s419" xml:space="preserve">iugum <reg norm="centrum" type="context">cētrum</reg> eſt: </s>
  <s xml:id="echoid-s420" xml:space="preserve">pro-<lb/>minentes autem longitudines eæ, quæ ſunt à <reg norm="cen- tro" type="context">cē-<lb/>tro</reg>. </s>
  <s xml:id="echoid-s421" xml:space="preserve">Celerius autem &amp; </s>
  <s xml:id="echoid-s422" xml:space="preserve">plus mouentur quæ maio <lb/>rum ſunt circulorum ab eadem vi, quàm quę mi <lb/>norum. </s>
  <s xml:id="echoid-s423" xml:space="preserve">ab eadem enim vi plus transfertur id <lb/>extremum, quod longius à centro diſtat. </s>
  <s xml:id="echoid-s424" xml:space="preserve">Quam <lb/>ob rem ad iugum quidem inſtrumenta faciunt <lb/>collopas, quibus facilius verſant: </s>
  <s xml:id="echoid-s425" xml:space="preserve">in gracilibus <lb/>autem ſuculis plus fit id, quod extra lignum e<gap/><gap/>. <lb/></s>
  <s xml:id="echoid-s426" xml:space="preserve">hoc autem id efficitur, quod à centro exit.</s>
  <s xml:id="echoid-s427" xml:space="preserve"/>
</p>
<div xml:id="echoid-div16" 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:id="echoid-s428" 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:id="echoid-s429" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s430" xml:space="preserve">ſi terræ illud applicans pede ſu-<lb/>perimpoſito manu longè diducta confregerit, <reg norm="quam" type="simple">ꝗ̃</reg> <lb/>prope? </s>
  <s xml:id="echoid-s431" xml:space="preserve">An quiaibi quidem genu <reg norm="centrum" type="context">centrũ</reg> eſt, hic <lb/>vero ipſe pes. </s>
  <s xml:id="echoid-s432" xml:space="preserve">quanto autem remotius à centro
<pb o="519" file="0519" n="16" rhead="Mechanicæ."/>
ſuerit, faciliùs mouetur <reg norm="quodcunque" type="simple">quodcunq;</reg></s>
  <s xml:id="echoid-s433" xml:space="preserve">. moueriau-<lb/>tem quod frangitur, neceſſe eſt.</s>
  <s xml:id="echoid-s434" xml:space="preserve"/>
</p>
<div xml:id="echoid-div17" 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:id="echoid-s435" 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:id="echoid-s436" xml:space="preserve">An quia ea, q̃ <lb/>plus recedunt à medio in motionibus, feruntur <lb/>celeriùs. </s>
  <s xml:id="echoid-s437" xml:space="preserve">medium enim fit centrum: </s>
  <s xml:id="echoid-s438" xml:space="preserve"><reg norm="intcruallum" type="context">intcruallũ</reg> <lb/>verò ea, quæ à centro. </s>
  <s xml:id="echoid-s439" xml:space="preserve">Sem per autem maior ab <lb/>æquali motione maiorem deſcribit circulum. <lb/></s>
  <s xml:id="echoid-s440" xml:space="preserve">quod autem maius in æquali pertranſit <reg norm="tempore" type="context">tẽpore</reg>, <lb/>celerius fertur: </s>
  <s xml:id="echoid-s441" xml:space="preserve">quæ autem celeriùs ex ę quali fe <lb/>runtur ſpatio, uehementiùs im petunt: </s>
  <s xml:id="echoid-s442" xml:space="preserve">quę <reg norm="autem" type="context">autẽ</reg> <lb/>magis impetunt impetuntur &amp; </s>
  <s xml:id="echoid-s443" xml:space="preserve">magis. </s>
  <s xml:id="echoid-s444" xml:space="preserve">quam ob <lb/>rem ea quæ plus à medio diſtant, <reg norm="confringi" type="context">cōfringi</reg> neceſ <lb/>ſe eſt, id autem cùm patiantur, rotunda fieri eſt <lb/>neceſſarium. </s>
  <s xml:id="echoid-s445" xml:space="preserve">Crocis autem propter maris mo-<lb/>tum, quoniam ſimul cum illo agitantur, in perpe <lb/>tua eſſe accidit motione, <reg norm="eoque" type="simple">eoq́;</reg> </s>
  <s xml:id="echoid-s446" xml:space="preserve">verſatas <reg norm="mon" type="context">mō</reg> ſem <lb/>per offenſare. </s>
  <s xml:id="echoid-s447" xml:space="preserve">id autem ipſis maximè extremis <lb/>contingere partibus eſt neceſſe.</s>
  <s xml:id="echoid-s448" xml:space="preserve"/>
</p>
<div xml:id="echoid-div18" 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:id="echoid-s449" 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:id="echoid-s450" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s451" xml:space="preserve">ſi tollantur, in flectuntur magis: <lb/></s>
  <s xml:id="echoid-s452" xml:space="preserve">tametſi quod breue quidem eſt, ceu bicubitum, <lb/>fuerit tenue: </s>
  <s xml:id="echoid-s453" xml:space="preserve">quod verò cubitorum centum, craſ <lb/>ſum? </s>
  <s xml:id="echoid-s454" xml:space="preserve">An <reg norm="quia" type="simple">ꝗa</reg> &amp; </s>
  <s xml:id="echoid-s455" xml:space="preserve">vectis, &amp; </s>
  <s xml:id="echoid-s456" xml:space="preserve">onus, &amp; </s>
  <s xml:id="echoid-s457" xml:space="preserve">hypomochlion <lb/>in leuando ipſa fit ligni proceritas: </s>
  <s xml:id="echoid-s458" xml:space="preserve">prior <reg norm="nanque" type="simple">nanq;</reg> </s>
  <s xml:id="echoid-s459" xml:space="preserve"><lb/>illius pars ceu hypomochlion fit, quod verò in <lb/>extremo eſt, <reg norm="pondus" type="context">pōdus</reg>. </s>
  <s xml:id="echoid-s460" xml:space="preserve">quam ob rem quanto exten. </s>
  <s xml:id="echoid-s461" xml:space="preserve"><lb/>ſius fuerit id, quod ab hypocomochlio eſt, tanto <lb/>inflecti neceſſe <reg norm="em" type="context">ẽ</reg> magis. </s>
  <s xml:id="echoid-s462" xml:space="preserve">quo enim plus ab hypo-<lb/>mochlio diſtat, eo magis incuruari neceſſe eſt. </s>
  <s xml:id="echoid-s463" xml:space="preserve"><lb/>neceſſario igitur extrema vectis eleuantur. </s>
  <s xml:id="echoid-s464" xml:space="preserve">Siigi <lb/>tur flexilis fuerit vectis, ipſum inflecti magis <lb/>cùm extollitur neceſſe eſt: </s>
  <s xml:id="echoid-s465" xml:space="preserve">quod <reg norm="longis" type="context">lõgis</reg> accidit li <lb/>gnis. </s>
  <s xml:id="echoid-s466" xml:space="preserve">in breuibus autem quod <reg norm="vltimum" type="context">vltimũ</reg> eſt, quie-
<pb o="520" file="0520" n="17" rhead="Ariſt. Quæſtiones"/>
ſcenti hy pomochlio deprope ſit.</s>
  <s xml:id="echoid-s467" xml:space="preserve"/>
</p>
<div xml:id="echoid-div19" 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:id="echoid-s468" xml:space="preserve">Cur a paruo exift<gap/>nte cuneo magna ſcindun-<lb/>tur pondera, &amp; </s>
  <s xml:id="echoid-s469" xml:space="preserve">corporum moles, validaque fit <lb/>impreſſio? </s>
  <s xml:id="echoid-s470" xml:space="preserve">An quia cuneus duo ſunt vectes ſibi <lb/>inuicem contrarij: </s>
  <s xml:id="echoid-s471" xml:space="preserve">vterque autem &amp; </s>
  <s xml:id="echoid-s472" xml:space="preserve">pondus ha <lb/>b<gap/>t, &amp; </s>
  <s xml:id="echoid-s473" xml:space="preserve">hypomochlion, quod diuellit, &amp; </s>
  <s xml:id="echoid-s474" xml:space="preserve">compri-<lb/>mit. </s>
  <s xml:id="echoid-s475" xml:space="preserve">Plagæ quinetiam ipſius latio pondus, quod <lb/>percutit &amp; </s>
  <s xml:id="echoid-s476" xml:space="preserve">mouet, magnum facit: </s>
  <s xml:id="echoid-s477" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s478" xml:space="preserve"><reg norm="quoniam" type="context">quoniā</reg> mo <lb/>tum mouet, pſa celeritate valentius fit. </s>
  <s xml:id="echoid-s479" xml:space="preserve">paruo au <lb/>tem exiſtente vecte, magnæ illum conſequuntur <lb/>vires: </s>
  <s xml:id="echoid-s480" xml:space="preserve">quam ob rem vltra magnitndinis <reg norm="decentiam" type="context">decentiã</reg> <lb/>later mouens, Sit cuneus vbi A B C, quod verò <lb/>cuneo ſcinditur, D E F G. </s>
  <s xml:id="echoid-s481" 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:id="echoid-s482" xml:space="preserve">percuſſa igitur A C, vtroque illorum vtitur <lb/>vecte: </s>
  <s xml:id="echoid-s483" xml:space="preserve">ſcindit enim ipſum B.</s>
  <s xml:id="echoid-s484" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s485" 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 <reg norm="contrario" type="context">cõtrario</reg> ad <lb/>trochleas modo circulo funem circunduxerit, <lb/>cuius alterum quidem caput tigonrum appenda <lb/>tur alteri, alterum varò troclheis ſit innixum, &amp; </s>
  <s xml:id="echoid-s486" xml:space="preserve"><lb/>à funis initio trahere coeperit, magna trahit pon <lb/>dera, licet imbecillium fuerit virium? </s>
  <s xml:id="echoid-s487" xml:space="preserve">An quia <lb/>idem <reg norm="pondus" type="context">põdus</reg> à minori potentia ſi mouetur, vecte <lb/>medio <reg norm="transfertur" type="context">trãsfertur</reg> magis, quàm à manu: </s>
  <s xml:id="echoid-s488" xml:space="preserve">trochlea <lb/>autem idem vecti facit. </s>
  <s xml:id="echoid-s489" xml:space="preserve">quam ob rem ſi vna faci-<lb/>lius traher, &amp; </s>
  <s xml:id="echoid-s490" 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:id="echoid-s491" 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:id="echoid-s492" xml:space="preserve">illa nanque minus etiam pondus effe-<lb/>cit. </s>
  <s xml:id="echoid-s493" xml:space="preserve"><reg norm="Parique" type="simple">Pariq́;</reg> </s>
  <s xml:id="echoid-s494" xml:space="preserve">modo ſi ad plures iniectus fuerit funis <lb/>in paucis trochleis, multa ſit differentia. </s>
  <s xml:id="echoid-s495" xml:space="preserve"><reg norm="quam" type="context">quã</reg> ob
<pb o="521" file="0521" n="18" rhead="Mechanicæ"/>
rem à prima pondere quat<gap/>or minas trahente, <lb/>ab vl im a trahi multò minus. </s>
  <s xml:id="echoid-s496" xml:space="preserve">Et in re ædifica-<lb/>toria faciliter magn<gap/> a mouen<gap/> pondera, <reg norm="traducunt" type="context">traducũt</reg> <lb/>enim ab una trochlea ad aliam, &amp; </s>
  <s xml:id="echoid-s497" xml:space="preserve">rurſus ab illa <lb/>ad ſuculas, &amp; </s>
  <s xml:id="echoid-s498" xml:space="preserve">vectes. </s>
  <s xml:id="echoid-s499" xml:space="preserve">hoc autem idem eſt, ac ſi <lb/>multas facerent trochleas.</s>
  <s xml:id="echoid-s500" xml:space="preserve"/>
</p>
<div xml:id="echoid-div20" 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:id="echoid-s501" xml:space="preserve">Cur ſi quis ſuper lignum <reg norm="magnam" type="context">magnã</reg> imponat ſe-<lb/>
<anchor type="note" xlink:label="note-0521-01a" xlink:href="note-0521-01"/>
carim, <reg norm="deſuperque" type="simple">deſuperq;</reg> </s>
  <s xml:id="echoid-s502" xml:space="preserve">illi magnum adijciat pondus, <lb/>ligni quippiam quod curandum ſit, non diuidit: <lb/></s>
  <s xml:id="echoid-s503" xml:space="preserve">ſiverò ſecurim extoll<gap/>s percutiat, illud ſcindit, <lb/>cùm alioquin multò minus habeat ponderis id <lb/>quod percutit, quàm id quod ſuperiacet, &amp; </s>
  <s xml:id="echoid-s504" xml:space="preserve">pre-<lb/>mit? </s>
  <s xml:id="echoid-s505" xml:space="preserve">An quia omnia cum motu fiunt: </s>
  <s xml:id="echoid-s506" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s507" xml:space="preserve">graue <lb/>ipſum grauitatis magis aſſumit motum <reg norm="dum" type="context">dũ</reg> mo-<lb/>uetur, <reg norm="quam" type="simple">ꝗ̃</reg> dum quieſcit Incumbensigitur conua-<lb/>tum graui motionem non mouetur, motum ve-<lb/>rò &amp; </s>
  <s xml:id="echoid-s508" xml:space="preserve">ſecundum hanc mouetur, &amp; </s>
  <s xml:id="echoid-s509" xml:space="preserve">ſecundùm <reg norm="eam" type="context">eã</reg> <lb/>quæ eſt percutientis. </s>
  <s xml:id="echoid-s510" xml:space="preserve">Pręterea ſecuris ipſa effici-<lb/>tur cuneus: </s>
  <s xml:id="echoid-s511" xml:space="preserve">paruus <reg norm="autem" type="context">autẽ</reg> exiſtens cuneus magna <lb/>diuidit cum ex duobus ſit vectibus contrario ad <lb/>ſeſe inuicem modo conſtitutis</s>
</p>
<div xml:id="echoid-div21" 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:id="echoid-s512" xml:space="preserve">Cur ſtatera, qua carnes <reg norm="ponderantur" type="context">ponderãtur</reg>, 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:id="echoid-s513" xml:space="preserve">vbi enim onus impo-<lb/>nitur, ſolùm ſuſpenditur lanx: </s>
  <s xml:id="echoid-s514" xml:space="preserve">in altera verò par <lb/>te, ſola eſt ſtatera. </s>
  <s xml:id="echoid-s515" xml:space="preserve">An quia ſimul libram &amp; </s>
  <s xml:id="echoid-s516" xml:space="preserve"><reg norm="vectem" type="context">vectẽ</reg> <lb/>ipſam contingit eſſe ſtateram. </s>
  <s xml:id="echoid-s517" xml:space="preserve">libram quidem, <lb/>vbi ſpartorum quodcunque ſtateræ fit centrum: <lb/></s>
  <s xml:id="echoid-s518" xml:space="preserve">in altera enim parte lancem, in altera autem pro <lb/>lance æquipondij appendiculum habet. </s>
  <s xml:id="echoid-s519" xml:space="preserve">quod li-<lb/>bre incumbit, ceu ſi quis alterain apponeret lan-<lb/>cem, &amp; </s>
  <s xml:id="echoid-s520" xml:space="preserve">ilii pondus imponeret. </s>
  <s xml:id="echoid-s521" xml:space="preserve"><reg norm="manifeſtum" type="context">manifeſtũ</reg> enim, <lb/>quòd tantundem tradit ponderis ei quod in alte <lb/>raiacet lance. </s>
  <s xml:id="echoid-s522" xml:space="preserve">Quemadmodum autem ſi vna li-<lb/>bra multæ ſint libræ, ſic talia inſunt ſparta mul.</s>
  <s xml:id="echoid-s523" xml:space="preserve">
<pb o="522" file="0522" n="19" rhead="Ariſt. Quæſtiones"/>
tain eiuſmodi libra: </s>
  <s xml:id="echoid-s524" xml:space="preserve">quorum <reg norm="vniuſcuiuſque" type="simple">vniuſcuiuſq;</reg> </s>
  <s xml:id="echoid-s525" xml:space="preserve">quod <lb/>intrinſecus eſt ad <reg norm="appendiculum" type="context">appẽdiculum</reg>, ſtateræ eſt dimi-<lb/>dium. </s>
  <s xml:id="echoid-s526" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s527" xml:space="preserve">omnino iſtud libra eſt, vnam <reg norm="quidem" type="context">quidẽ</reg> ha-<lb/>benslancem, in qua pondus <reg norm="appenditur" type="context">appẽditur</reg>: </s>
  <s xml:id="echoid-s528" xml:space="preserve">alteram <lb/>verò, vbi in ſtatera æquipondium. </s>
  <s xml:id="echoid-s529" xml:space="preserve">Quam ob rem <lb/>appendiculum ad alteram ſui partem eſt ſtatera. <lb/></s>
  <s xml:id="echoid-s530" xml:space="preserve">huiuſmodi autem <reg norm="exiſtens" type="context">exiſtēs</reg> multæ ſunt libræ, <reg norm="totque" type="simple">totq́;</reg> </s>
  <s xml:id="echoid-s531" xml:space="preserve"><lb/>quot fuerint ſparta. </s>
  <s xml:id="echoid-s532" xml:space="preserve">Semper autem quod lanci <lb/>propinquius eſt ſpartum, <reg norm="appenſoque" type="simple">appenſoq́ue</reg> oneri, ma-<lb/>ius trahit <reg norm="pondus" type="context">pōdus</reg>: </s>
  <s xml:id="echoid-s533" xml:space="preserve">quoniam fit quidem omnis ſta-<lb/>tera inuerſus vectis: </s>
  <s xml:id="echoid-s534" xml:space="preserve">hypomochlion nã<reg norm="que" type="simple">q;</reg> </s>
  <s xml:id="echoid-s535" xml:space="preserve">vnum-<lb/>quodque ſpartum ſuperne exiſtens: </s>
  <s xml:id="echoid-s536" xml:space="preserve">pondus <reg norm="verum" type="context">verũ</reg> <lb/>id quod lanci ineſt. </s>
  <s xml:id="echoid-s537" xml:space="preserve">Quanto autem productior ve <lb/>ctis ſuerit longitudo ab ipfo hypomochlio, <reg norm="tanto" type="context">tãto</reg> <lb/>ibi quidem faciliùs mouet: </s>
  <s xml:id="echoid-s538" xml:space="preserve">hic autem æquilibri-<lb/>brium facit, <reg norm="pondusque" type="simple">pondusq́ue</reg> ſtateræ trutinat, quod <lb/>ad æquipondij vergit appendiculum.</s>
  <s xml:id="echoid-s539" xml:space="preserve"/>
</p>
<div xml:id="echoid-div22" 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:id="echoid-s540" xml:space="preserve">Cur medici ſacilius dentes <reg norm="extrahunt" type="context">extrahūt</reg> dentifor-<lb/>cipis onere adiecto, quàm ſi ſola vtantur manu? <lb/></s>
  <s xml:id="echoid-s541" xml:space="preserve">An quia ex manu magis quàm ex dentiforcipe <lb/>lubricus elabitur <reg norm="dens" type="context">dẽs</reg>? </s>
  <s xml:id="echoid-s542" xml:space="preserve">An ferro id potius accidit <lb/>quàm digitis, quoniam vndique dentem non <reg norm="com- prehendunt" type="context">cō-<lb/>prehendunt</reg>: </s>
  <s xml:id="echoid-s543" xml:space="preserve">quod mollis digitorum facit caro: </s>
  <s xml:id="echoid-s544" xml:space="preserve"><lb/>adhæret enim, &amp; </s>
  <s xml:id="echoid-s545" xml:space="preserve"><reg norm="complectitur" type="context">cõplectitur</reg> magis. </s>
  <s xml:id="echoid-s546" xml:space="preserve">An quia den <lb/><gap/>iſorceps duo contrarij vectes, vnicum habentes <lb/>hypom ochlion, eius ſcilicet inſtrumenti conne-<lb/>xionem. </s>
  <s xml:id="echoid-s547" xml:space="preserve">Hoc igitur ad extractionem vtuntur or-<lb/>gano, vt facilius moueant. </s>
  <s xml:id="echoid-s548" xml:space="preserve">Sic dentiforcipis alte-<lb/>rum quidem exrremum vbi eſt A: </s>
  <s xml:id="echoid-s549" xml:space="preserve">alterum <reg norm="autem" type="context">autẽ</reg> <lb/>quod extrahit B. </s>
  <s xml:id="echoid-s550" xml:space="preserve">vectis autem vbi A D F: </s>
  <s xml:id="echoid-s551" xml:space="preserve">alterve <lb/>rò vectis vbi B C E. </s>
  <s xml:id="echoid-s552" xml:space="preserve">hypomochlion <reg norm="autem" type="context">autẽ</reg> C G D: </s>
  <s xml:id="echoid-s553" xml:space="preserve"><lb/>connexio verò vbi G: </s>
  <s xml:id="echoid-s554" xml:space="preserve"><reg norm="dens" type="context">dẽs</reg> autem pondus. </s>
  <s xml:id="echoid-s555" xml:space="preserve"><reg norm="Vtroque" type="simple">Vtroq;</reg> </s>
  <s xml:id="echoid-s556" xml:space="preserve"><lb/>igitur B &amp; </s>
  <s xml:id="echoid-s557" xml:space="preserve">F ſimul comprehendentes mouent. </s>
  <s xml:id="echoid-s558" xml:space="preserve"><lb/>quando autem commotus fuerit, faciliùs manu <lb/>trahitur, quàm inſtrumento.</s>
  <s xml:id="echoid-s559" xml:space="preserve"/>
</p>
<pb o="523" file="0523" n="20" rhead="Mechanicæ"/>
<p>
  <s xml:id="echoid-s560" xml:space="preserve">Cur nuces abſque ictu facilè <reg norm="confrigun" type="context">cõfrigun</reg> <reg norm="tinſtru- mentis" type="context">tinſtru-<lb/>mẽtis</reg>, quæ ad eum fiunt vſum? </s>
  <s xml:id="echoid-s561" xml:space="preserve">multumeinim au <lb/>fertur virium, motionis ſcilicet, &amp; </s>
  <s xml:id="echoid-s562" xml:space="preserve">violẽ<gap/>iæ. </s>
  <s xml:id="echoid-s563" xml:space="preserve">Prę-<lb/>terea duro &amp; </s>
  <s xml:id="echoid-s564" xml:space="preserve">graui comprimens inſtrumento ci <lb/>tiùs conſringet, quàm ligneo &amp; </s>
  <s xml:id="echoid-s565" xml:space="preserve">leui. </s>
  <s xml:id="echoid-s566" xml:space="preserve">An quia ſic <lb/>vtrinqne à duobus comprimitur vectibus ipſa <lb/>nux: </s>
  <s xml:id="echoid-s567" xml:space="preserve">a vecte autem facile diuelluntur onera. </s>
  <s xml:id="echoid-s568" xml:space="preserve">id <lb/>enim <reg norm="inſtrumentum" type="context">inſtrumẽtum</reg> ex duobus componitur vecti <lb/>bus idem habentibus hypomochlion, connexio-<lb/>nem videlicet <gap/>pſam vbi eſt A. </s>
  <s xml:id="echoid-s569" xml:space="preserve">Quemadmodum <lb/>igitur fuere diductę <reg norm="ſecundum" type="context">ſecundũ</reg> extrema motis C D <lb/>ipſæ F E, ſic à parua faciliter potentia conducun <lb/>tur. </s>
  <s xml:id="echoid-s570" xml:space="preserve">Quod igitur cum percuſſione ſeciſſet <reg norm="pondus" type="context">põdus</reg>, <lb/>id valentiores illa E C, &amp; </s>
  <s xml:id="echoid-s571" xml:space="preserve">F D vectes efficiunt. </s>
  <s xml:id="echoid-s572" xml:space="preserve">ele <lb/>uatione enim in contrarium ela<gap/>i &amp; </s>
  <s xml:id="echoid-s573" xml:space="preserve"><reg norm="comprimen- tes" type="context">comprimẽ-<lb/>tes</reg>, frangunt vbi eſt K. </s>
  <s xml:id="echoid-s574" xml:space="preserve">Hanc etiam ob cauſam <lb/>quanto vicinius fuerit K ipſum A, confringitur <lb/>celerius. </s>
  <s xml:id="echoid-s575" xml:space="preserve">quanto enim ab hypomochlio plus di-<lb/>ſtat vectis, facilius &amp; </s>
  <s xml:id="echoid-s576" xml:space="preserve">plus mouet ab <reg norm="eadem" type="context">eadẽ</reg> poten-<lb/>tia. </s>
  <s xml:id="echoid-s577" xml:space="preserve">Eſt igitur A quidem hypomochlion: </s>
  <s xml:id="echoid-s578" xml:space="preserve">ipſa au-<lb/>tem D A F vectis: </s>
  <s xml:id="echoid-s579" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s580" xml:space="preserve">item ipia C A E. </s>
  <s xml:id="echoid-s581" xml:space="preserve">Quanto igi-<lb/>tur ipſum K vicinius ſuerit angulo ipſius A, <reg norm="tanto" type="context">tãto</reg> <lb/>vicinius fit connexioni vbi eſt A. </s>
  <s xml:id="echoid-s582" xml:space="preserve">hoc autem eſt <lb/>hypomochlion. </s>
  <s xml:id="echoid-s583" xml:space="preserve">Ab eadem igitur potentia appli-<lb/>cante F E plus extolli neceſſe eſt. </s>
  <s xml:id="echoid-s584" xml:space="preserve">Quam ob rem <lb/><reg norm="quoniam" type="context">quoniã</reg> ex contrario eſt eleuatio, neceſſe eſt ma-<lb/>gis com primi. </s>
  <s xml:id="echoid-s585" xml:space="preserve">quod autem comprimitur magis, <lb/>ci<gap/>ius frangitur.</s>
  <s xml:id="echoid-s586" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s587" xml:space="preserve">Cur ſi duo extrema in rhombo puncta dua-<lb/>bus ferantur lationibus, haudquaquam æquale <lb/>vtrunque <reg norm="eorum" type="context">eorũ</reg> pertianſit rectam, ſed multò plus <lb/>alterum ?</s>
  <s xml:id="echoid-s588" xml:space="preserve">idem autem eſt ſermo, cur quod ſuper <lb/>latus fertur, minus pertranſit, quàm ipſum latus. <lb/></s>
  <s xml:id="echoid-s589" xml:space="preserve">illud enim diametrum <reg norm="minorem" type="context">minorẽ</reg>, hoc verò maius <lb/>latus. </s>
  <s xml:id="echoid-s590" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s591" 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:id="echoid-s592" 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:id="echoid-s593" xml:space="preserve">feratur <reg norm="aurem" type="context">aurẽ</reg> &amp; </s>
  <s xml:id="echoid-s594" xml:space="preserve">ipſa A B in ipſa A C iuxta <lb/>C D eadem celeritate cum illis. </s>
  <s xml:id="echoid-s595" 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:id="echoid-s596" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s597" xml:space="preserve"><reg norm="vtranque" type="simple">vtranq;</reg> </s>
  <s xml:id="echoid-s598" xml:space="preserve">ſimul pertranſiſſe, &amp; </s>
  <s xml:id="echoid-s599" xml:space="preserve">ipſa<gap/><gap/> <lb/>A B ipſum la<unsure/>tus A C. </s>
  <s xml:id="echoid-s600" xml:space="preserve">latum enim ſit ipſum A ip <lb/>ſam A E, A B autem ipſam A E, &amp; </s>
  <s xml:id="echoid-s601" xml:space="preserve">proiecta ſit <lb/>F G iuxta ipſum A B, &amp; </s>
  <s xml:id="echoid-s602" xml:space="preserve">ab ipſo E ſimiliter replea <lb/>tur. </s>
  <s xml:id="echoid-s603" xml:space="preserve">Simile igitur fit, quod repletum eſt ipſi toti. <lb/></s>
  <s xml:id="echoid-s604" xml:space="preserve">æqualis igirur A F ipſi A E ipſa autem A B ipſam <lb/>A F lata erit. </s>
  <s xml:id="echoid-s605" xml:space="preserve">in diametro igitur erit <reg norm="ſecundum" type="context context">ſecūdū</reg> K. </s>
  <s xml:id="echoid-s606" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s607" xml:space="preserve"><lb/>fem per neceſſe eſt ipſum ferri ſecundùm diame <lb/>trum. </s>
  <s xml:id="echoid-s608" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s609" xml:space="preserve">ſimul A B latus pertranfit latus A C, &amp; </s>
  <s xml:id="echoid-s610" xml:space="preserve"><lb/>ipſum A diametrum pertranſit A D. </s>
  <s xml:id="echoid-s611" xml:space="preserve">Similiter <reg norm="ent" type="context">ẽt</reg> <lb/>demon ſtrabitur &amp; </s>
  <s xml:id="echoid-s612" xml:space="preserve">ipſum B in ipſa B C diametro <lb/>latum. </s>
  <s xml:id="echoid-s613" xml:space="preserve">æqualis enim eſt ipſa B E ipſi B G Reple. </s>
  <s xml:id="echoid-s614" xml:space="preserve"><lb/>to igitur ab ipſo G. </s>
  <s xml:id="echoid-s615" xml:space="preserve">quod intus eſt, toti eſt ſimi-<lb/>le: </s>
  <s xml:id="echoid-s616" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s617" xml:space="preserve">ipſum B in ipſa diame<gap/>ro erit ſecundùm la <lb/>terum connexionem. </s>
  <s xml:id="echoid-s618" xml:space="preserve">Et ſimul latus pertranſit <lb/>latus, &amp; </s>
  <s xml:id="echoid-s619" xml:space="preserve">B ipſum B C diametrum. </s>
  <s xml:id="echoid-s620" xml:space="preserve">Simuligitur A <lb/>multo plus ipſa A B <reg norm="pertranſit" type="context">pertrāſit</reg>: </s>
  <s xml:id="echoid-s621" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s622" xml:space="preserve">ipſum latus, mi-<lb/>nus latus eadem lata celeritate: </s>
  <s xml:id="echoid-s623" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s624" xml:space="preserve">ipſum latus <lb/>maiorem, quàm B, pertranſiuit vna latum latio-<lb/>ne. </s>
  <s xml:id="echoid-s625" xml:space="preserve">Quanto enim acutior fuerit rhombus, diame <lb/>ter quidem minor ſit. </s>
  <s xml:id="echoid-s626" xml:space="preserve">A C <reg norm="autem" type="context">autẽ</reg> maior: </s>
  <s xml:id="echoid-s627" xml:space="preserve">latus ve-<lb/>ro ipſius B C minus. </s>
  <s xml:id="echoid-s628" xml:space="preserve"><reg norm="Abſurdum" type="context">Abſurdū</reg> eſt enim (vt <reg norm="dictum" type="context">dictũ</reg>) <lb/>id quod duabus fertur lationibus, <reg norm="aliquando" type="context">aliquãdo</reg> ferri <lb/>tardius illo. </s>
  <s xml:id="echoid-s629" xml:space="preserve">quod fertur vnica: </s>
  <s xml:id="echoid-s630" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s631" xml:space="preserve"><reg norm="vtriſque" type="simple">vtriſq;</reg> </s>
  <s xml:id="echoid-s632" xml:space="preserve">poſitis <lb/>æquali velocitate punctis, <reg norm="alterum" type="context">alterū</reg> pertranſire ma <lb/>iorem. </s>
  <s xml:id="echoid-s633" xml:space="preserve">Cauſa autem eſt, <reg norm="quoniam" type="context">quoniã</reg> ei quod ab obt<gap/> <lb/>ſo ſertur angulo ambæ ferè <reg norm="contrariæ" type="context">cōtrariæ</reg> fiunt latio-<lb/>n<unsure/>es, &amp; </s>
  <s xml:id="echoid-s634" xml:space="preserve">illa <reg norm="ſecundum" type="context context">ſecūdū</reg> <reg norm="quam" type="context">quā</reg> ipſum fertur, &amp; </s>
  <s xml:id="echoid-s635" xml:space="preserve">illa ſecun <lb/><reg norm="dum" type="context">dũ</reg> <reg norm="quam" type="context">quã</reg> ipſum à latere defertur. </s>
  <s xml:id="echoid-s636" xml:space="preserve">Ei <reg norm="autem" type="context">autẽ</reg> quod ab <lb/><gap/>cuto fertur, accidit vt ad <reg norm="idem" type="context">idē</reg> feratur, coadiuuat
<pb o="525" file="0525" n="22" rhead="Mechanicæ."/>
<gap/>nim quæ ipſius eſt lateris, <reg norm="illam" type="context">illã</reg> quæ eſt ſuper dia-<lb/>metrum. </s>
  <s xml:id="echoid-s637" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s638" xml:space="preserve">quanto hunc quidem acutiorem fe-<lb/>ceris, illum verò obtuſum magis: </s>
  <s xml:id="echoid-s639" xml:space="preserve">hæc <reg norm="quidem" type="context">quidē</reg> tar-<lb/>dior erit, illa verò celerior. </s>
  <s xml:id="echoid-s640" xml:space="preserve">Hæ <reg norm="quidem" type="context">quidẽ</reg> igitur ma-<lb/>gis contrariæ fiunt, qm̄ obtuſior fit angulus: </s>
  <s xml:id="echoid-s641" xml:space="preserve">illæ <lb/>verò ad <reg norm="idem" type="context">idẽ</reg> magis, qm̄ lineæ coarctantur: </s>
  <s xml:id="echoid-s642" xml:space="preserve">ipſum <lb/>enim A ferè ad idem fertur ſecundum ambas la <lb/>tiones. </s>
  <s xml:id="echoid-s643" xml:space="preserve">Coadiuuatur igitur altera: </s>
  <s xml:id="echoid-s644" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s645" xml:space="preserve">quanto ſanè <lb/>acutior fuerit angulus, tanto magis ipſum A ad <lb/>contrarium: </s>
  <s xml:id="echoid-s646" xml:space="preserve">ipſum. </s>
  <s xml:id="echoid-s647" xml:space="preserve">n. </s>
  <s xml:id="echoid-s648" xml:space="preserve">ad B fertur: </s>
  <s xml:id="echoid-s649" xml:space="preserve">latus <reg norm="autem" type="context">autẽ</reg> de-<lb/>fertipſum ad D. </s>
  <s xml:id="echoid-s650" xml:space="preserve">Et quanto ſanè obtuſior fuerit <lb/>angulus, magis contrariæ fiunt lationes: </s>
  <s xml:id="echoid-s651" xml:space="preserve">rectior <lb/>enim efficitur linea. </s>
  <s xml:id="echoid-s652" xml:space="preserve">ſi <reg norm="autem" type="context">autẽ</reg> omnino recta fieret, <lb/>penitus vtique eſſent contrariæ latus verò ſecun <lb/>dùm vnicam latuum lationem à nullo præpedi-<lb/>tur: </s>
  <s xml:id="echoid-s653" xml:space="preserve">rationabiliter igitur maiorem pertranſit.</s>
  <s xml:id="echoid-s654" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s655" xml:space="preserve">Dubitatur quam ob cauſam maior circulus ę-<lb/>qualem minori circulo conuoluit<unsure/>ur lineam, <reg norm="qum" type="context">qū</reg><unsure/> <lb/>circa idem centrum fuerint poſiti: </s>
  <s xml:id="echoid-s656" xml:space="preserve">ſeorſum <reg norm="autem" type="context">autẽ</reg> <lb/>reuoluti, quemadmodum alterius magnitudo ad <lb/>magnitudiuem ſe habet alterius, fic &amp; </s>
  <s xml:id="echoid-s657" xml:space="preserve"><reg norm="illorum" type="context">illorũ</reg> ad <lb/>ſeinuicem fiunt lineæ. </s>
  <s xml:id="echoid-s658" xml:space="preserve">Præterea vno et<gap/><reg norm="am" type="context">ã</reg> &amp; </s>
  <s xml:id="echoid-s659" xml:space="preserve"><reg norm="eodem" type="context">eodē</reg> <lb/>v<unsure/>triſque exiſtente centro, aliquando quidem tan <lb/>ta ſit linea, quam conuoluuntur, quantam minor <lb/>per ſe conuoluitur circulus, <reg norm="quandoque" type="simple">quandoq;</reg> </s>
  <s xml:id="echoid-s660" xml:space="preserve">verò <reg norm="quan- tam" type="context">quã-<lb/>tam</reg> maior. </s>
  <s xml:id="echoid-s661" xml:space="preserve">Quòd quidem igitur maiorem con <lb/>uoluitur maior, manifeſtum eſt. </s>
  <s xml:id="echoid-s662" 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:id="echoid-s663" xml:space="preserve">quam ob rem eandem habebunt propor-<lb/>tionem ſecundùm ſenſum ad ſe lineæ. </s>
  <s xml:id="echoid-s664" xml:space="preserve">ſecun-<lb/>dùm quas fuerint conuoluti. </s>
  <s xml:id="echoid-s665" xml:space="preserve">verùm enimuerò <lb/>quòd etiam æqualem conuoluuntur, quando cir<unsure/> <lb/>t<unsure/>a idem fuerint poſiti centrum, <reg norm="manifeſtum" type="context">manifeſtũ</reg> eſt: </s>
  <s xml:id="echoid-s666" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s667" xml:space="preserve"><lb/>ſic fiunt aliquando <reg norm="quidem" type="context">quidē</reg> 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:id="echoid-s668" xml:space="preserve">minor verò vbi <lb/>E C B: </s>
  <s xml:id="echoid-s669" xml:space="preserve"><reg norm="vtriſque" type="simple">vtriſq́;</reg> </s>
  <s xml:id="echoid-s670" xml:space="preserve">autem centrum A. </s>
  <s xml:id="echoid-s671" xml:space="preserve">Et quam qui-<lb/>dem per ſe magnus conuoluitur, ſit vbi F I: </s>
  <s xml:id="echoid-s672" xml:space="preserve"><reg norm="quam" type="context">quã</reg> <lb/>vero per ſe minor vbi GK, æqualis A. </s>
  <s xml:id="echoid-s673" xml:space="preserve">Si igitur mi <lb/>norem mouero, idem mouens <reg norm="centum" type="context">centū</reg> vbi A, ma-<lb/>ior autem ſit annexus. </s>
  <s xml:id="echoid-s674" xml:space="preserve"><reg norm="quando" type="wordlist">qñ</reg> igitur A B fuerit recta <lb/>ad ipſam G K, ſimul &amp; </s>
  <s xml:id="echoid-s675" xml:space="preserve">A C fit recta ad ipſam F I. <lb/></s>
  <s xml:id="echoid-s676" xml:space="preserve">quam ob rem ęqualem ſemper tranſlata erit ip-<lb/>ſam quidem G K, vbi eſt G B circunferentia: </s>
  <s xml:id="echoid-s677" xml:space="preserve">ip-<lb/>ſam verò FL, quæ eſt vbi F C. </s>
  <s xml:id="echoid-s678" xml:space="preserve">Si <reg norm="aunt" type="context">aũt</reg> quarta pars <lb/>æqualem conuoluitur, manifeſtum eſt, <reg norm="quod" type="simple">ꝙ</reg> totus <lb/>circulus toti circulo æqualem conuoluetur. </s>
  <s xml:id="echoid-s679" xml:space="preserve">qua <lb/>re <reg norm="quando" type="wordlist">qñ</reg> B C, linea ad ipſum peruenerit K, &amp; </s>
  <s xml:id="echoid-s680" xml:space="preserve">ipſa <lb/>F C circunferentia erit in ipſa C L: </s>
  <s xml:id="echoid-s681" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s682" xml:space="preserve">vniuerſus <lb/>crit conuolutus circulus. </s>
  <s xml:id="echoid-s683" xml:space="preserve"><reg norm="Similique" type="simple">Similiq́;</reg> </s>
  <s xml:id="echoid-s684" xml:space="preserve">modo ſi ma-<lb/>gnum mouero, illi <reg norm="paruuum" type="context">paruuū</reg> annectens, eodem exi <lb/>ftente <reg norm="centro" type="context">cẽtro</reg>, ſimul cum A C ipſi A B perpendicu <lb/>lum &amp; </s>
  <s xml:id="echoid-s685" xml:space="preserve">recta eri<gap/>: </s>
  <s xml:id="echoid-s686" xml:space="preserve">hæc quidem ad ipſam F I, illa <lb/>verò ad G M. </s>
  <s xml:id="echoid-s687" xml:space="preserve">Quam ob rem quando hæc <reg norm="quidem" type="context">quidẽ</reg> <lb/>æqualem ipſi G M pert<unsure/><reg norm="ranſiuerit" type="context">rãſiuerit</reg>, illa verò ipſi F I, <lb/>&amp; </s>
  <s xml:id="echoid-s688" xml:space="preserve">rurſum facta fuerit recta ipſa F A ad ipſam <lb/>F L. </s>
  <s xml:id="echoid-s689" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s690" xml:space="preserve">ipſa A C rurſum recta, velut à principio <lb/>erant in ipſis M I. </s>
  <s xml:id="echoid-s691" xml:space="preserve">Hoc autem neque aliqua in-<lb/>tercedente mora maioris ad minorem, vt. </s>
  <s xml:id="echoid-s692" xml:space="preserve">ſ. </s>
  <s xml:id="echoid-s693" xml:space="preserve">per <lb/>aliquod temporis ſpatium ſtaret in eodem pun-<lb/>cto: </s>
  <s xml:id="echoid-s694" xml:space="preserve">neque tranſiliente minore aliquod <reg norm="punctum" type="context">punctū</reg>, <lb/>maiorem quidem æqualem minori pertranſire, <lb/>hunc a<gap/>tem maiori, abſurdum eſt. </s>
  <s xml:id="echoid-s695" xml:space="preserve">Præterea vni-<lb/>ea etiam ſemper exiſtente motione, <reg norm="centrum" type="context">centrū</reg> mo-<lb/>rum interdum quidem magnam, nonnunquàm <lb/>verò minorem conuerti, admirandum eſt. </s>
  <s xml:id="echoid-s696" xml:space="preserve">Idem <lb/>enim celeritate eadem latus <reg norm="æqualem" type="context">æqualẽ</reg> natum hoc <lb/>eft pertranſire: </s>
  <s xml:id="echoid-s697" xml:space="preserve">eadem autem celeritate vtroque
<pb o="527" file="0527" n="24" rhead="Mechanicæ."/>
modo æqualem licet mouere. </s>
  <s xml:id="echoid-s698" xml:space="preserve">Principium autem <lb/>ſumendum eſt circa iſtorum cauſam, <reg norm="quod" type="simple">ꝙ</reg> eadem <lb/>potentia &amp; </s>
  <s xml:id="echoid-s699" xml:space="preserve">æqualis hanc quidem tardiùs mouet <lb/>magnitudinem, illam verò celeriùs. </s>
  <s xml:id="echoid-s700" xml:space="preserve">Si enim fue-<lb/>rit quippiam, quod à ſeipſo moueri <reg norm="natum" type="context">natũ</reg> non ſit, <lb/>ſi ſimul &amp; </s>
  <s xml:id="echoid-s701" xml:space="preserve">illud mouerit, quod <reg norm="natum" type="context">natũ</reg> eſt moueri. <lb/></s>
  <s xml:id="echoid-s702" xml:space="preserve">tardius mouebitur, quàm ſi ipſum per ſe moue-<lb/>retur. </s>
  <s xml:id="echoid-s703" xml:space="preserve">Et ſi quidem natum fuerit moueri, non ſi-<lb/>mul <reg norm="aunt" type="context">aũt</reg> moueatur, ſimiliter ſe habebit. </s>
  <s xml:id="echoid-s704" xml:space="preserve">Et im<unsure/>poſ <lb/>ſibile certè eſt plus moueri, quàm mouens: </s>
  <s xml:id="echoid-s705" xml:space="preserve">non <lb/>enim ſuam ipſius mouetur motionem. </s>
  <s xml:id="echoid-s706" 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, <reg norm="quod" type="simple">ꝙ</reg> tantum ipſius rectæ maior <reg norm="pertram" type="context">pertrã</reg> <lb/>ſit, quantum eſt impulſus: </s>
  <s xml:id="echoid-s707" xml:space="preserve">tantum <reg norm="aunt" type="context">aũt</reg> eſt impul-<lb/>ſus, quantum paruus eſt motus: </s>
  <s xml:id="echoid-s708" xml:space="preserve">æqualem igitur <lb/>ipſius rectæ pertranſiuerunt. </s>
  <s xml:id="echoid-s709" xml:space="preserve">Neceſſe igitur eſt <lb/>ſi reuolutus minor maiorem impellet, reuol<gap/>i ſi<unsure/> <lb/>mul cum impulſione: </s>
  <s xml:id="echoid-s710" xml:space="preserve">tantum <reg norm="aunt" type="context">aūt</reg> quantum mi-<lb/>nor reuolutus eſt, ſi nihil ipſe ſub ipſius motio-<lb/>ne mouetur. </s>
  <s xml:id="echoid-s711" xml:space="preserve">Qūo enim, &amp; </s>
  <s xml:id="echoid-s712" xml:space="preserve">quantum mouit, tan-<lb/>tum <reg norm="motum" type="context">motũ</reg> eſſe neceſſe eſt, quod mouetur ab ill<gap/> <lb/>ſed profectò paruus circulus <reg norm="tantum" type="context">tãtum</reg> ſeipſum cir-<lb/>culariter mouit, quantum eſt pedalis quantitas: </s>
  <s xml:id="echoid-s713" xml:space="preserve"><lb/>(tantum enim ſit id quod motus eſt) &amp; </s>
  <s xml:id="echoid-s714" xml:space="preserve">magnus <lb/>igitur tantum motus erit. </s>
  <s xml:id="echoid-s715" xml:space="preserve"><reg norm="Similique" type="simple">Similiq́;</reg> </s>
  <s xml:id="echoid-s716" xml:space="preserve">modo ſi ma-<lb/>gnus <reg norm="paruum" type="context">paruū</reg> mouebit, motus erit paruus, quēad-<lb/>modum maior. </s>
  <s xml:id="echoid-s717" xml:space="preserve">Per ſe <reg norm="aunt" type="context">aūt</reg> motus illorum vtrum-<lb/>libet ſiue celeriter, ſeu tardè eadem velocitate, <lb/>ſtatim quantum maior natus eſt circunſerri li-<lb/>neam: </s>
  <s xml:id="echoid-s718" xml:space="preserve">quod <reg norm="difficultatem" type="context">difficultatē</reg> facit, quod non ſimiliter <lb/>ſaciunt, quando fuerint connexi. </s>
  <s xml:id="echoid-s719" xml:space="preserve">hoc autem eſt, <lb/>ſi alteri ab altero moueatur, non <reg norm="quam" type="context">quã</reg> natus eſt, <lb/><gap/>eque peculiarem motionem. </s>
  <s xml:id="echoid-s720" xml:space="preserve">Nihil enim referr <lb/><reg norm="citcumponere" type="context">citcũponere</reg>, &amp; </s>
  <s xml:id="echoid-s721" xml:space="preserve">annectere, aut <reg norm="coniungere" type="context">cōiungere</reg> vtrum-
<pb o="528" file="0528" n="25" rhead="Ariſt Queſtiones"/>
liber alteri. </s>
  <s xml:id="echoid-s722" xml:space="preserve">ſimiliter enim quando hic quidem <lb/>mouer, ille vero mouetur ab iſto; </s>
  <s xml:id="echoid-s723" xml:space="preserve">quantum <reg norm="vtique" type="simple">vtiq;</reg> <lb/></s>
  <s xml:id="echoid-s724" xml:space="preserve">mouerit alter, tantum alter mouebitur. </s>
  <s xml:id="echoid-s725" xml:space="preserve">Quando <lb/>quidem igitur adiacens mouerit, aut propenſus, <lb/>non ſemper conueluitur: </s>
  <s xml:id="echoid-s726" xml:space="preserve"><reg norm="quando" type="context">quādo</reg> verò circa idem <lb/>poſi<gap/>i fuerint <reg norm="centrum" type="context">cẽtrum</reg>, alterum ab altero ſemper <lb/>conuolui neceſſe eſt. </s>
  <s xml:id="echoid-s727" xml:space="preserve">Sed nihilominus non ſuam <lb/>ipſius motionem mouetur alter, ſed veluti <reg norm="nullam" type="context">nullã</reg> <lb/>haberet motionem: </s>
  <s xml:id="echoid-s728" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s729" xml:space="preserve">ſi habuerit, illa autem <reg norm="non" type="context">nõ</reg> <lb/>vtatur, tan<gap/>undem accidit. </s>
  <s xml:id="echoid-s730" xml:space="preserve">Quandoquidem igi-<lb/>tur màgnus moueri ſibi alligatum paruum, par-<lb/>uus mouetur <reg norm="quantum" type="context">quãtum</reg> ille: </s>
  <s xml:id="echoid-s731" xml:space="preserve"><reg norm="quando" type="context">quādo</reg> autem paruus, <lb/>rurſus magnus quantum iſte: </s>
  <s xml:id="echoid-s732" xml:space="preserve">ſeparatus <reg norm="aunt" type="context">aũt</reg> vter-<lb/>que ſeipſum mouet. </s>
  <s xml:id="echoid-s733" xml:space="preserve">Quod autem eodem exiſten <lb/>te centro, &amp; </s>
  <s xml:id="echoid-s734" xml:space="preserve">mouente eadem velocitate, accidit <lb/>inæqualem illos <reg norm="pertranſire" type="context">pertrāſire</reg> lineam, paralogiſmo <lb/>fophiſticę vtitur is, qui dubitat. </s>
  <s xml:id="echoid-s735" xml:space="preserve">idem enim am-<lb/>bobus eſt <reg norm="centrum" type="context">centrũ</reg>, verùm per accidens, velúti mu <lb/>ſicum &amp; </s>
  <s xml:id="echoid-s736" xml:space="preserve">album. </s>
  <s xml:id="echoid-s737" xml:space="preserve">eſſe enim vtriuſque circuli cen-<lb/>tro <reg norm="non" type="context">nō</reg> eodem vtitur. </s>
  <s xml:id="echoid-s738" xml:space="preserve">Quandoquidem igitur mo-<lb/>uens fuerit paruus, vt illius centrum &amp; </s>
  <s xml:id="echoid-s739" xml:space="preserve">princi-<lb/>pium: </s>
  <s xml:id="echoid-s740" xml:space="preserve">quando verò magnus, vt illius. </s>
  <s xml:id="echoid-s741" xml:space="preserve">non igitur <lb/>idem ſim pliciter mouet, ſed eſt quomodo.</s>
  <s xml:id="echoid-s742" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s743" xml:space="preserve">Cur lect<gap/>lorum ſpondas <reg norm="ſecundum" type="context">ſecūdum</reg> duplam fa-<lb/>
<anchor type="note" xlink:label="note-0528-01a" xlink:href="note-0528-01"/>
ciunt proportionem, hanc quidem ſex <reg norm="pedum" type="context">pedū</reg> vel <lb/>paulo am pliorem, illam vero trium: </s>
  <s xml:id="echoid-s744" xml:space="preserve">curve non <lb/>ſecundùm diametrum illos reſtibus extendunt? <lb/></s>
  <s xml:id="echoid-s745" xml:space="preserve">An tantos quidem magnitudine faciunt, vt cor-<lb/>poribus ſint proportionem <reg norm="habentes" type="context">habẽtes</reg>: </s>
  <s xml:id="echoid-s746" xml:space="preserve">fiunt enim <lb/>ſic ſecundum ſpondas dupli, longitudine <reg norm="quidem" type="context">quidẽ</reg> <lb/>cubitorum quatuor, latitudine vero <reg norm="duorum" type="context">duorũ</reg>. </s>
  <s xml:id="echoid-s747" xml:space="preserve">Ex-<lb/>tendunt autem illos <reg norm="non" type="context">nō</reg> ſecundùm diametrum, <lb/>ſed ex oppoſito, vt &amp; </s>
  <s xml:id="echoid-s748" xml:space="preserve">ligna minus diſtra hantur. </s>
  <s xml:id="echoid-s749" xml:space="preserve"><lb/>celertrimè enim <reg norm="ſcinduntur" type="context">ſcindũtur</reg> ſecundum naturam <lb/>diuiſa, &amp; </s>
  <s xml:id="echoid-s750" xml:space="preserve">eodem modo diſtenta laborant ma-
<pb o="529" file="0529" n="26" rhead="Mechanicæ."/>
<gap/>imè. </s>
  <s xml:id="echoid-s751" 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:id="echoid-s752" xml:space="preserve">Præterea hoc etiam modo minus <lb/>abſumitur reſtium. </s>
  <s xml:id="echoid-s753" xml:space="preserve">Sit enim lectulus A F G K, &amp; </s>
  <s xml:id="echoid-s754" xml:space="preserve"><lb/>bifariam diuidatur ipſa F G ſecundùm B, æqua-<lb/>lia certè foramina ſunt in ipſa F B, &amp; </s>
  <s xml:id="echoid-s755" xml:space="preserve">in ipſa F A. <lb/></s>
  <s xml:id="echoid-s756" xml:space="preserve">latera enim ſunt æqualia. </s>
  <s xml:id="echoid-s757" xml:space="preserve">nam totum F G <reg norm="duplum" type="context">duplũ</reg> <lb/>eſt. </s>
  <s xml:id="echoid-s758" 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:id="echoid-s759" xml:space="preserve">ita vbi H, <lb/>poſtea vbi E, &amp; </s>
  <s xml:id="echoid-s760" xml:space="preserve">eodem ſemper modo, donec ad <lb/>angulum peruenerint alium. </s>
  <s xml:id="echoid-s761" xml:space="preserve">Duo enim anguli <lb/>reſtis habent capi a. </s>
  <s xml:id="echoid-s762" xml:space="preserve">æquales autem ſunt reſtes <lb/>ſecundum curuaturas, videlicet A B; </s>
  <s xml:id="echoid-s763" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s764" xml:space="preserve">B C ipſis <lb/>C D, &amp; </s>
  <s xml:id="echoid-s765" xml:space="preserve">D H. </s>
  <s xml:id="echoid-s766" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s767" xml:space="preserve">aliæ ſimili ſe habet modo, quo-<lb/>niam eadem demonſtratio. </s>
  <s xml:id="echoid-s768" xml:space="preserve">ipſa enim AB æqua-<lb/>lis eſt ipſi H E: </s>
  <s xml:id="echoid-s769" xml:space="preserve">æqualia enim ſunt latera ſpatij <lb/>B G, M A, &amp; </s>
  <s xml:id="echoid-s770" xml:space="preserve">foramina æquè diſtant, ipſa autem <lb/>B G æquelis eſt ipſi M A: </s>
  <s xml:id="echoid-s771" xml:space="preserve">angulus enim B æqua-<lb/>lis eſt angulo G: </s>
  <s xml:id="echoid-s772" xml:space="preserve">in æqualibus enim hic quidem <lb/>intus, ille vero extra. </s>
  <s xml:id="echoid-s773" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s774" xml:space="preserve">B quidem eſt ſemirectus: </s>
  <s xml:id="echoid-s775" xml:space="preserve"><lb/>eſt enim F B æqualis ipſi F A: </s>
  <s xml:id="echoid-s776" xml:space="preserve">&amp; </s>
  <s xml:id="echoid-s777" xml:space="preserve">angulus vbi F, re <lb/>ctus eſt. </s>
  <s xml:id="echoid-s778" xml:space="preserve">B <reg norm="autem" type="context">autẽ</reg> angulus æqualis ei vbi eſt G, quo-<lb/>niam quadratum altera parte longius <reg norm="duplum" type="context">duplũ</reg> eſt: </s>
  <s xml:id="echoid-s779" xml:space="preserve"><lb/>&amp; </s>
  <s xml:id="echoid-s780" xml:space="preserve">ad medium eſt curuatura. </s>
  <s xml:id="echoid-s781" xml:space="preserve"><reg norm="quamobrem" type="context">quamobrẽ</reg> A D ip-<lb/>ſi E G eſt æqualis: </s>
  <s xml:id="echoid-s782" xml:space="preserve">huic verò ipſa H M. </s>
  <s xml:id="echoid-s783" xml:space="preserve"><reg norm="Similique" type="simple">Similiq́ue</reg> <lb/>modo demonſtrantur aliæ, <reg norm="quoniam" type="context">quoniã</reg> æquales ſunt <lb/>duæ, quæ ſec<reg norm="un" type="context">ũ</reg>dùm curuataras ſunt, duabus. </s>
  <s xml:id="echoid-s784" xml:space="preserve">Qua <lb/>re manifeſtum eſt, <reg norm="quod" type="simple">ꝙ</reg> tot ſunt reſtes in lectulo, <lb/>quot ſunt quatuor, ſicut A B. </s>
  <s xml:id="echoid-s785" xml:space="preserve">Quanta autem fora <lb/><reg norm="minum" type="context">minũ</reg> eſt multirudo in ipſo F G latere, &amp; </s>
  <s xml:id="echoid-s786" xml:space="preserve">in eius <lb/>dimidio F B eſt medietas. </s>
  <s xml:id="echoid-s787" xml:space="preserve">Quamobrem in dimi-<lb/>diato lectulo tantæ reſtium magnitudines <reg norm="erunt" type="context">erũt</reg>, <lb/>quantum eſt A B: </s>
  <s xml:id="echoid-s788" xml:space="preserve">multitudine verò tot, quot in <lb/>B G ſunt foramina. </s>
  <s xml:id="echoid-s789" 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 &amp; </s>
  <s xml:id="echoid-s790" xml:space="preserve">B F ſimul <lb/>ſumpris. </s>
  <s xml:id="echoid-s791" 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:id="echoid-s792" xml:space="preserve">æqualia autem, quot in ip <lb/>fis F B, F A, ſunt foramina: </s>
  <s xml:id="echoid-s793" xml:space="preserve">maiores autem ſunt</s>
</p>
<div xml:id="echoid-div23" 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:id="echoid-s794" xml:space="preserve">ipſæ A F, B F, quæ exiſtentes, quàm A B, <lb/>quare reſtis in tantum maior, quantum ambola <lb/><gap/>era diame<gap/>ro ſunt maiora.</s>
  <s xml:id="echoid-s795" xml:space="preserve"/>
</p>
<p>
  <s xml:id="echoid-s796" 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:id="echoid-s797" xml:space="preserve">An quia vibrato ligno <lb/>ipſum extremum prohibet ferre vibratione ma-<lb/>gis retrahens lationem? </s>
  <s xml:id="echoid-s798" xml:space="preserve">An quoniam licèt nihil <lb/>inflectatur, neque multam habeat <reg norm="longitudinem" type="context">longitudinẽ</reg>, <lb/>difficilius tamen ad ferendum eſt ab extremo, <lb/>quoniam faciliùs ex medio eleuatur, quàm ab <lb/>extremo, &amp; </s>
  <s xml:id="echoid-s799" xml:space="preserve">ideo ſic ferre eſt facilius: </s>
  <s xml:id="echoid-s800" xml:space="preserve">Cauſa <reg norm="aunt" type="context">aũt</reg>, <lb/>qm̄ ſecundùm medium quidem eleuato ligno, <lb/>ſemper ſeſe inuicem ſuſpendunt extrema, &amp; </s>
  <s xml:id="echoid-s801" 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:id="echoid-s802" xml:space="preserve"><reg norm="Extremorum" type="context">Extremorũ</reg> igitur v<gap/><gap/>rũ<reg norm="que" type="simple">q;</reg> </s>
  <s xml:id="echoid-s803" xml:space="preserve">deorſum vergens, <lb/>ſurſum ſuſpenditur. </s>
  <s xml:id="echoid-s804" xml:space="preserve"><reg norm="quod" type="simple">ꝙ</reg> ſi ab extremo eleuetur, <lb/>aut feratur, non ſanè facit: </s>
  <s xml:id="echoid-s805" xml:space="preserve">ſed vniuerſum pon-<lb/>dus ad vnum vergit medium, quò eleuatur, aut <lb/>fertur. </s>
  <s xml:id="echoid-s806" xml:space="preserve">Sit medium vbi A, extrema B C. </s>
  <s xml:id="echoid-s807" xml:space="preserve">Eleuatio <lb/>igitur aut portato ſecundùm A, ipſum q́uidem B <lb/>deorſum <gap/>utans, ſurſum eleuat C: </s>
  <s xml:id="echoid-s808" xml:space="preserve">ipſum autem <lb/>C deorſum nutans, B ſurſum eleuat: </s>
  <s xml:id="echoid-s809" xml:space="preserve">ambo au-<lb/>tem ſurſum eleuata hoc fac<gap/>unt.</s>
  <s xml:id="echoid-s810" xml:space="preserve"/>
</p>
<div xml:id="echoid-div24" 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:id="echoid-s811" xml:space="preserve">Cur ſi valde procerum fuerit <reg norm="idem" type="context">idẽ</reg> 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:id="echoid-s812" xml:space="preserve">Quod <lb/><gap/>nim dudum dictum eſt, cauſa <reg norm="non" type="context">nõ</reg> eſt: </s>
  <s xml:id="echoid-s813" xml:space="preserve">ſed vibra-
<pb o="531" file="0531" n="28" rhead="Mechanicę."/>
tio nunc eſt cauſa. </s>
  <s xml:id="echoid-s814" xml:space="preserve"><reg norm="quando" type="wordlist">qñ</reg>. </s>
  <s xml:id="echoid-s815" xml:space="preserve">n. </s>
  <s xml:id="echoid-s816" xml:space="preserve">productius fuerit, vibran <lb/>tur extrema: </s>
  <s xml:id="echoid-s817" xml:space="preserve">quamobrem contingit portantem <lb/>difficilius geſtare. </s>
  <s xml:id="echoid-s818" xml:space="preserve">Vibrationis <reg norm="aunt" type="context">aũt</reg> <reg norm="cam" type="context">cã</reg> eſt, <reg norm="quoniam" type="context">quoniã</reg> <lb/>ab <reg norm="eadem" type="context">eadẽ</reg> motione magis transferuntur extrema, <lb/>quanto procerius fuerit <reg norm="lignum" type="context">lignũ</reg>. </s>
  <s xml:id="echoid-s819" xml:space="preserve">Humerus <reg norm="quidem" type="context">quidẽ</reg> <lb/>fit <reg norm="centrum" type="context">centrũ</reg> vbi A: </s>
  <s xml:id="echoid-s820" xml:space="preserve">manet. </s>
  <s xml:id="echoid-s821" xml:space="preserve">n. </s>
  <s xml:id="echoid-s822" xml:space="preserve">is. </s>
  <s xml:id="echoid-s823" xml:space="preserve">ipſæ <reg norm="aunt" type="context">aũt</reg> AB, AC, quę <lb/>ſunt ex centro. </s>
  <s xml:id="echoid-s824" xml:space="preserve">quanto <reg norm="aunt" type="context">aũt</reg> maius fuerit id quod <lb/>ex centro eſt, ſiue A B, ſeu A C, plus transfertur <lb/>ſpatij. </s>
  <s xml:id="echoid-s825" xml:space="preserve">Demonſtratum autem eſt hoc prius.</s>
  <s xml:id="echoid-s826" xml:space="preserve"/>
</p>
<div xml:id="echoid-div25" 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:id="echoid-s827" 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:id="echoid-s828" xml:space="preserve">ligno. </s>
  <s xml:id="echoid-s829" xml:space="preserve">n. </s>
  <s xml:id="echoid-s830" xml:space="preserve">plumbi <reg norm="adiungunt" type="context">adiũgunt</reg> pondus: </s>
  <s xml:id="echoid-s831" xml:space="preserve"><reg norm="cum" type="context">cũ</reg> <lb/>alioquin vas ipſum &amp; </s>
  <s xml:id="echoid-s832" xml:space="preserve">plenum, &amp; </s>
  <s xml:id="echoid-s833" xml:space="preserve">vacuum pon-<lb/>dus habeat? </s>
  <s xml:id="echoid-s834" xml:space="preserve">An qm̄ duobus tem poribus hau<gap/>ien <lb/>di, diuiſo opere, (intingere. </s>
  <s xml:id="echoid-s835" xml:space="preserve">n. </s>
  <s xml:id="echoid-s836" xml:space="preserve">oportet, &amp; </s>
  <s xml:id="echoid-s837" xml:space="preserve">id ſur-<lb/>ſum trahere) continget demittere <reg norm="quidem" type="context">quidẽ</reg> vacuum <lb/>faciliter, trahere vero plenum difficulter. </s>
  <s xml:id="echoid-s838" xml:space="preserve"><reg norm="Commo- dum" type="context">Cōmo-<lb/>dum</reg> igitur eſt paulò tardius illud demittere, <reg norm="cum" type="context">cū</reg> <lb/>multò leuius effectum ſuſtolatur pondus. </s>
  <s xml:id="echoid-s839" xml:space="preserve">id <reg norm="autem" type="context">autẽ</reg> <lb/>facit in extremo celonio adiunctum plumbum, <lb/>aut lapis. </s>
  <s xml:id="echoid-s840" xml:space="preserve">demittenti quidem maius ſit pondus, <reg norm="qui" type="simple">ꝗ</reg> <lb/>fi ſolummodo vacuum oportet demittere: </s>
  <s xml:id="echoid-s841" xml:space="preserve">cum <lb/>verò plenum fuerit, ſurſum id rapit plumbum, <lb/>aut quicquid ponderis inerit. </s>
  <s xml:id="echoid-s842" xml:space="preserve">Quam ob rem faci <lb/>liora hoc modo ambo ſunt, quàm illo.</s>
  <s xml:id="echoid-s843" xml:space="preserve"/>
</p>
<div xml:id="echoid-div26" 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:id="echoid-s844" xml:space="preserve">Cur <reg norm="quando" type="wordlist">qñ</reg> ſuper ligno, aut <reg norm="hmoni" type="context">hmõi</reg> 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 <reg norm="geſtantibus" type="context">geſtãtibus</reg>? </s>
  <s xml:id="echoid-s845" xml:space="preserve">An <lb/>quoniam vectis quidem lignum efficitur, <reg norm="pondus" type="context">põdus</reg> <lb/>verò hypomochlion: </s>
  <s xml:id="echoid-s846" xml:space="preserve">qui autem propior eſt pon-<lb/>deri ex ijs, qui illud geſtant, id quod mouetur: </s>
  <s xml:id="echoid-s847" xml:space="preserve">al <lb/>ter verò <reg norm="portantium" type="context">portantiũ</reg>, quod mouet. </s>
  <s xml:id="echoid-s848" xml:space="preserve">Quanto igitur <lb/>plus diſtat à pondere, tanto facilius mouet, &amp; </s>
  <s xml:id="echoid-s849" xml:space="preserve"><lb/>alerum premit magis inferius, veluti contrani-<lb/><gap/>te pondere impoſito, quod hypomochlion
<pb o="532" file="0532" n="29" rhead="Ariſt. Quæſtiones."/>
factum Eſt. </s>
  <s xml:id="echoid-s850" xml:space="preserve">Si autem in medio inerit pondus, ni-<lb/>hilo magis alter alteri fit pondus, aut mouet: </s>
  <s xml:id="echoid-s851" xml:space="preserve">ſed <lb/>eodem modo alteri alt<unsure/>er fit pondus.</s>
  <s xml:id="echoid-s852" xml:space="preserve"/>
</p>
<div xml:id="echoid-div27" 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:id="echoid-s853" xml:space="preserve">Cur ſurgentes omnes, femori crus ad acutum <lb/>
<anchor type="note" xlink:label="note-0532-01a" xlink:href="note-0532-01"/>
c<reg norm="on" type="context">õ</reg>ſtituentes <reg norm="angulum" type="context">angulũ</reg>, &amp; </s>
  <s xml:id="echoid-s854" xml:space="preserve">thoraci ſimiliter femur, <lb/>ſurgunt? </s>
  <s xml:id="echoid-s855" xml:space="preserve">quod ſi non, haudquaquam ſurgere po-<lb/>terunt. </s>
  <s xml:id="echoid-s856" xml:space="preserve">An quia id quod æquale eſt, quietis <reg norm="vbique" type="simple">vbiq;</reg> <lb/></s>
  <s xml:id="echoid-s857" xml:space="preserve">eſt cauſa: </s>
  <s xml:id="echoid-s858" xml:space="preserve">rectus <reg norm="autem" type="context">autẽ</reg> angulus æqualitatis eſt, <reg norm="ſta- tionemque" type="simple">ſta-<lb/>tionemq́;</reg> </s>
  <s xml:id="echoid-s859" xml:space="preserve">facit: </s>
  <s xml:id="echoid-s860" xml:space="preserve"><reg norm="quamobrem" type="context">quamobrẽ</reg> ad ſimiles fertur an-<lb/>gulos ipſi terræ circumferentiæ: </s>
  <s xml:id="echoid-s861" xml:space="preserve">non enim quod <lb/>ad rectum eſt ipſi pauimento. </s>
  <s xml:id="echoid-s862" xml:space="preserve">An q̇m̄ ſurgens fit <lb/>rectus, <reg norm="ſtantem" type="context">ſtantẽ</reg> vero neceſſe eſt <reg norm="perpendiculum" type="context">perpẽdiculum</reg> eſſe <lb/>ad terram. </s>
  <s xml:id="echoid-s863" xml:space="preserve"><reg norm="ſiquidem" type="context">ſiquidẽ</reg> igitur ad <reg norm="rectum" type="context">rectũ</reg> debet eſſe, hoc <lb/><reg norm="aunt" type="context">aũt</reg> eſt caput <reg norm="ſecundum" type="context">ſecundũ</reg> pedes habere, &amp; </s>
  <s xml:id="echoid-s864" xml:space="preserve">fieri opor <lb/>tet, cùm ſurgit. </s>
  <s xml:id="echoid-s865" xml:space="preserve">Quandoquidem igitur fuerit <gap/>e <lb/>dens, ſecundum parallelum pedes habet, &amp; </s>
  <s xml:id="echoid-s866" xml:space="preserve">ca-<lb/>put, &amp; </s>
  <s xml:id="echoid-s867" xml:space="preserve">non in æquali. </s>
  <s xml:id="echoid-s868" xml:space="preserve">Caput ſit A, thorax A B, fe-<lb/>mur B C, crura C D. </s>
  <s xml:id="echoid-s869" xml:space="preserve">ad rectum autem ſit &amp; </s>
  <s xml:id="echoid-s870" xml:space="preserve">tho-<lb/>rãx vbi A B, ipſi femori, &amp; </s>
  <s xml:id="echoid-s871" xml:space="preserve">cruri ſemur ſic feden-<lb/>te. </s>
  <s xml:id="echoid-s872" xml:space="preserve">quamobrem eo ſe <reg norm="habentem" type="context">habẽtem</reg> modo ſurgere eſt <lb/>impoſſibile. </s>
  <s xml:id="echoid-s873" xml:space="preserve">neceſſe autem eſt crus reclinare, pe-<lb/>desque conſtituere ſub capite. </s>
  <s xml:id="echoid-s874" xml:space="preserve">hoc autem erit, ſi <lb/>C D fiet, vbi C F, &amp; </s>
  <s xml:id="echoid-s875" xml:space="preserve">fimul ſurgere continget, &amp; </s>
  <s xml:id="echoid-s876" xml:space="preserve">in <lb/>eadem ęquali habere caput &amp; </s>
  <s xml:id="echoid-s877" xml:space="preserve">pedes. </s>
  <s xml:id="echoid-s878" xml:space="preserve">ipſa autem <lb/>C F a cutum facit angulum ad ipſam B C.</s>
  <s xml:id="echoid-s879" xml:space="preserve"/>
</p>
<div xml:id="echoid-div28" 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:id="echoid-s880" xml:space="preserve">Cur facilius mouetur <reg norm="commotu" type="context">cõmotu</reg>, quàm manens? <lb/></s>
  <s xml:id="echoid-s881" xml:space="preserve">
<anchor type="note" xlink:label="note-0532-02a" xlink:href="note-0532-02"/>
veluti currus citiùs <reg norm="commotus" type="context">cõmotus</reg> agitant, quàm mo-<lb/>ueri in cipientes. </s>
  <s xml:id="echoid-s882" xml:space="preserve">An quia <reg norm="difficillimum" type="context">difficillimũ</reg> eſt pondus <lb/>mouere, quod in <reg norm="contrarium" type="context context">cõtrariũ</reg> mouetur. </s>
  <s xml:id="echoid-s883" xml:space="preserve">aufert enim <lb/>quiddam ex motoris potentia, licèt multo fit ve-<lb/>locior: </s>
  <s xml:id="echoid-s884" xml:space="preserve">neceſſe nanque eſt <reg norm="tardiorem" type="context">tardiorẽ</reg> eſſe impulſio <lb/>nem illius quod repellitur. </s>
  <s xml:id="echoid-s885" xml:space="preserve">Secundo autẽloco ſi <lb/>quieuerit: </s>
  <s xml:id="echoid-s886" xml:space="preserve">reſiſtit enim ipſum <reg norm="quieſcens" type="context">quieſcẽs</reg>. </s>
  <s xml:id="echoid-s887" xml:space="preserve">Quod <reg norm="aunt" type="context">aũt</reg> <lb/>mouetur ad id ipſum ad quod impellitur, impel-<lb/>lenti ſimile facit, ceu ſi quiſpiam <reg norm="mouentis" type="context">mouẽtis</reg> poten
<pb o="533" file="0533" n="30" rhead="De Mundo."/>
tiam, &amp; </s>
  <s xml:id="echoid-s888" xml:space="preserve">celeritatem augeret. </s>
  <s xml:id="echoid-s889" xml:space="preserve">quod enim<unsure/> ab illo <lb/>pateretur, vtique ipſum tacit ex ſe commotum.</s>
  <s xml:id="echoid-s890" xml:space="preserve"/>
</p>
<div xml:id="echoid-div29" 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:id="echoid-s891" xml:space="preserve">Cur ea, quæ proijci<gap/><gap/>ntur, ceſſant à latione? </s>
  <s xml:id="echoid-s892" xml:space="preserve">An <lb/>
<anchor type="note" xlink:label="note-0533-01a" xlink:href="note-0533-01"/>
quia impellens deſinit potentia, v<gap/>l propter retra <lb/>ctionem, vel propter rei proiectę inclinationem, <lb/>quando ea valentior fuerit, quam proijcientis vi <lb/>res. </s>
  <s xml:id="echoid-s893" xml:space="preserve">Aut iſthæc ambigere, principium relinquen-<lb/>tes, abſurdum eſt.</s>
  <s xml:id="echoid-s894" xml:space="preserve"/>
</p>
<div xml:id="echoid-div30" 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:id="echoid-s895" 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:id="echoid-s896" xml:space="preserve">An <lb/>videlicet quoniam primum id efficit, <gap/><gap/>al<gap/>erum <lb/>impellat: </s>
  <s xml:id="echoid-s897" xml:space="preserve">illudque rurſum, v<gap/> alterum? </s>
  <s xml:id="echoid-s898" xml:space="preserve">Ceſſat au-<lb/>tem quando non poteſt amplius facere primum <lb/>impellens id quod fertur, vt impellat, &amp; </s>
  <s xml:id="echoid-s899" xml:space="preserve"><reg norm="quando" type="wordlist">qñ</reg> ip-<lb/>ſius lati grauitas nut<gap/> ſuo declinat magis, quàm <lb/>impellentis in antè ſit potentia,</s>
</p>
<div xml:id="echoid-div31" 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:id="echoid-s900" 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 <reg norm="commenſurationem" type="context">commẽſurationem</reg> <reg norm="quandam" type="context">quandã</reg> <lb/>illa habere oportet ad id quod proijcit? </s>
  <s xml:id="echoid-s901" xml:space="preserve">An quia <lb/>neceſſe eſt quod proijcitur, &amp; </s>
  <s xml:id="echoid-s902" xml:space="preserve">impelli<gap/><gap/>r, <reg norm="contra- ni" type="context">cõtra-<lb/>ni</reg> i ei vnde impellitur? </s>
  <s xml:id="echoid-s903" 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:id="echoid-s904" xml:space="preserve">Quod enim multo impellentis excedit vi-<lb/>res, haud <reg norm="quaquam" type="context">quaquã</reg> cedit: </s>
  <s xml:id="echoid-s905" xml:space="preserve">quod verò multo eſt im-<lb/>berillius. </s>
  <s xml:id="echoid-s906" xml:space="preserve">nihil contranititur. </s>
  <s xml:id="echoid-s907" xml:space="preserve">An quia <reg norm="tantum" type="context">tãtum</reg> fer-<lb/>tur id quod fertur, <reg norm="quantum" type="context">quantũ</reg> aeris mouerit ad pro-<lb/>fundum: </s>
  <s xml:id="echoid-s908" xml:space="preserve">quod autem non mouetur, <reg norm="neque" type="simple">neq;</reg> </s>
  <s xml:id="echoid-s909" xml:space="preserve">moue <lb/>bit quippiam accidit autem illis ambo iſthæc ha <lb/>bere. </s>
  <s xml:id="echoid-s910" xml:space="preserve">Valde enim magnum, &amp; </s>
  <s xml:id="echoid-s911" xml:space="preserve">valde paruum, ceù <lb/>non mota exiſtunt: </s>
  <s xml:id="echoid-s912" xml:space="preserve">alterum nanque nihil mouet <lb/>alterum verò nihil mouetur.</s>
  <s xml:id="echoid-s913" xml:space="preserve"/>
</p>
<div xml:id="echoid-div32" 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:id="echoid-s914" 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:id="echoid-s915" xml:space="preserve">An quia ma-<lb/>gnitudinem habet quocunque ferrur: </s>
  <s xml:id="echoid-s916" 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:id="echoid-s917" xml:space="preserve">quare ma-<lb/>ior diſtrahit: </s>
  <s xml:id="echoid-s918" xml:space="preserve"><reg norm="quoniam" type="context">quoniã</reg> celerius fertur, &amp; </s>
  <s xml:id="echoid-s919" xml:space="preserve">tranſuer-<lb/>ſum impellit illud ad minorem: </s>
  <s xml:id="echoid-s920" xml:space="preserve">quoniam autem <lb/>id quod ſertur, latitudinem habet, &amp; </s>
  <s xml:id="echoid-s921" xml:space="preserve">iſte rurſus <lb/>idem eff<gap/>cit &amp; </s>
  <s xml:id="echoid-s922" xml:space="preserve">ad interiorem propellit, donec ad <lb/>medium perueniat. </s>
  <s xml:id="echoid-s923" xml:space="preserve">An quia quod fertur, ſimili <lb/>ſe habet modo ad omnes circulos propter me-<lb/>dium. </s>
  <s xml:id="echoid-s924" xml:space="preserve">medium enim in vnoquoque circulo ęqua <lb/>liter diſtat. </s>
  <s xml:id="echoid-s925" xml:space="preserve">An quia quorum quidem circũauctæ <lb/>quæ latio non ſuperior propter magnitudinem, <lb/>ſed grauitate ſua circuli <reg norm="celeritatem" type="context">celeritatẽ</reg> excellunt, ea <lb/>neceſſe eſt relinqui, &amp; </s>
  <s xml:id="echoid-s926" xml:space="preserve">tardiùs ferri, tardius <reg norm="aunt" type="context">aũt</reg> <lb/>minor circulus fertur. </s>
  <s xml:id="echoid-s927" xml:space="preserve">non idem enim in tempo-<lb/>re æquali magnus <reg norm="cum" type="context">cũ</reg> paruo reuoluitur circulus, <lb/>quando circa idem ſuerint medium. </s>
  <s xml:id="echoid-s928" xml:space="preserve"><reg norm="quamobrem" type="context">quamobrẽ</reg> <lb/>in minori circulo relinqui eſt neceſſe, donec ad <lb/>medium perueniant. </s>
  <s xml:id="echoid-s929" xml:space="preserve">Quorum cunque autem ſu-<lb/>perior à principio fuerit latio, ea finiensidem eſ <lb/>ficiet. </s>
  <s xml:id="echoid-s930" xml:space="preserve">oportet enim <gap/><reg norm="an" type="context">ã</reg>c quidem ſtatim, alterum <lb/>verò celeritate ſuperare grauitatem, quam <reg norm="obrem" type="context">obrẽ</reg> <lb/>ad <reg norm="interiorem" type="context">interiorẽ</reg> ſemper circulum relinquetur quod-<lb/>cunque. </s>
  <s xml:id="echoid-s931" xml:space="preserve">Neceſſe enim eſt, quod non ſuperatur, <lb/>aut in exteriori, aut in interiori moueri: </s>
  <s xml:id="echoid-s932" 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:id="echoid-s933" xml:space="preserve">cele-<lb/>rior enim exterioris circuli eſt latio: </s>
  <s xml:id="echoid-s934" xml:space="preserve">reſtat igitur, <lb/>vtid, quod non ſuperatur, ad interiorem tranſ-<lb/>feratur. </s>
  <s xml:id="echoid-s935" xml:space="preserve">ſemper autem vnumquodque proficit, vt <lb/>non ſuperetur. </s>
  <s xml:id="echoid-s936" xml:space="preserve">Quoniam verò peruenire ad me-<lb/>dium, finem quidem efficit, vt quippiam <reg norm="non" type="context">nõ</reg> mo-<lb/>ueatur, ſtat autem ſolummodo ipſum centrum: <lb/></s>
  <s xml:id="echoid-s937" xml:space="preserve">ad hoc ſanè omnia congregari neceſſe eſt.</s>
  <s xml:id="echoid-s938" xml:space="preserve"/>
</p>
<div xml:id="echoid-div33" 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 xml:id="echoid-div35" type="section" level="1" n="5">
<head xml:id="echoid-head8" style="it" xml:space="preserve">Mechanicarum quæſtionum finis.</head>
  </div></text>
</echo>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Fri, 02 Dec 2016 14:37:22 +0100
parents	22d6a63640c6
children